LMFDB - Embedded newform 525.2.bf.d.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.d.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(-0.599900 + 1.62484i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.28024 - 1.94949i) q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} +(-0.599900 + 1.62484i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.28024 - 1.94949i) q^{9} +(3.67423 + 2.12132i) q^{11} +(-3.53553 - 3.53553i) q^{13} +(-0.707107 - 3.67423i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(1.36603 - 0.366025i) q^{17} +(3.49768 - 2.40130i) q^{18} +(-6.06218 + 3.50000i) q^{19} +(-0.449490 - 4.56048i) q^{21} +(-4.24264 + 4.24264i) q^{22} +(4.09808 + 1.09808i) q^{23} +(-2.04989 - 4.44949i) q^{24} +(6.12372 - 3.53553i) q^{26} +(4.53553 - 2.53553i) q^{27} -7.07107 q^{29} +(0.500000 - 0.866025i) q^{31} +(-5.65099 + 4.69748i) q^{33} +2.00000i q^{34} +(0.965926 + 0.258819i) q^{37} +(-2.56218 - 9.56218i) q^{38} +(7.86566 - 3.62372i) q^{39} +7.07107i q^{41} +(6.39425 + 1.05524i) q^{42} +(3.53553 + 3.53553i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(1.46410 - 5.46410i) q^{47} +(6.82843 - 1.17157i) q^{48} +(4.33013 - 5.50000i) q^{49} +(-0.224745 + 2.43916i) q^{51} +(0.732051 + 2.73205i) q^{53} +(1.80348 + 7.12372i) q^{54} +(2.44949 - 7.07107i) q^{56} +(-2.05025 - 11.9497i) q^{57} +(2.58819 - 9.65926i) q^{58} +(-0.707107 + 1.22474i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(1.00000 + 1.00000i) q^{62} +(7.67972 + 2.00548i) q^{63} -8.00000i q^{64} +(-4.34847 - 9.43879i) q^{66} +(0.258819 + 0.965926i) q^{67} +(-4.24264 + 6.00000i) q^{69} +7.07107i q^{71} +(8.45946 - 0.661498i) q^{72} +(-6.76148 + 1.81173i) q^{73} +(-0.707107 + 1.22474i) q^{74} +(-11.1962 - 0.803848i) q^{77} +(2.07107 + 12.0711i) q^{78} +(-6.06218 + 3.50000i) q^{79} +(1.39898 + 8.89060i) q^{81} +(-9.65926 - 2.58819i) q^{82} +(1.00000 - 1.00000i) q^{83} +(-6.12372 + 3.53553i) q^{86} +(4.24194 - 11.4894i) q^{87} +(-11.5911 + 3.10583i) q^{88} +(7.77817 + 13.4722i) q^{89} +(12.5000 + 4.33013i) q^{91} +(1.10721 + 1.33195i) q^{93} +(6.92820 + 4.00000i) q^{94} +(-7.07107 + 7.07107i) q^{97} +(5.92820 + 7.92820i) q^{98} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.250000\pi$
$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	−0.599900	+	1.62484i	−0.346353	+	0.938104i
$3$	−0.599900	+	1.62484i	−0.346353	+	0.938104i
$4$		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
$9$	−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	$-0.493877\pi$
$13$	−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	−0.0893296	−	0.996002i	$-0.528472\pi$
$17$	1.36603	−	0.366025i	0.331310	−	0.0887742i	0.420639	+	0.907228i	$0.361806\pi$
$18$	3.49768	−	2.40130i	0.824411	−	0.565992i
$19$	−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
$21$	−0.449490	−	4.56048i	−0.0980867	−	0.995178i
$22$	−4.24264	+	4.24264i	−0.904534	+	0.904534i
$23$	4.09808	+	1.09808i	0.854508	+	0.228965i	0.659377	−	0.751812i	$-0.270820\pi$
$23$	4.09808	+	1.09808i	0.854508	+	0.228965i	0.195131	+	0.980777i	$0.437487\pi$
$24$	−2.04989	−	4.44949i	−0.418432	−	0.908248i
$25$		0			0
$26$	6.12372	−	3.53553i	1.20096	−	0.693375i
$27$	4.53553	−	2.53553i	0.872864	−	0.487964i
$28$		0			0
$29$	−7.07107			−1.31306			−0.656532	−	0.754298i	$-0.727977\pi$
$29$	−7.07107			−1.31306			−0.656532	+	0.754298i	$0.727977\pi$
$30$		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
$33$	−5.65099	+	4.69748i	−0.983711	+	0.817726i
$34$			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
$39$	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	$0.813805\pi$
$42$	6.39425	+	1.05524i	0.986655	+	0.162827i
$43$	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	$-0.781298\pi$
$47$	1.46410	−	5.46410i	0.213561	−	0.797021i	0.986668	−	0.162745i	$-0.0520349\pi$
$48$	6.82843	−	1.17157i	0.985599	−	0.169102i
$49$	4.33013	−	5.50000i	0.618590	−	0.785714i
$50$		0			0
$51$	−0.224745	+	2.43916i	−0.0314706	+	0.341550i
$52$		0			0
$53$	0.732051	+	2.73205i	0.100555	+	0.375276i	0.997803	−	0.0662507i	$-0.0211037\pi$
$53$	0.732051	+	2.73205i	0.100555	+	0.375276i	−0.897248	+	0.441527i	$0.854437\pi$
$54$	1.80348	+	7.12372i	0.245423	+	0.969416i
$55$		0			0
$56$	2.44949	−	7.07107i	0.327327	−	0.944911i
$57$	−2.05025	−	11.9497i	−0.271563	−	1.58278i
$58$	2.58819	−	9.65926i	0.339846	−	1.26832i
$59$	−0.707107	+	1.22474i	−0.0920575	+	0.159448i	−0.908377	−	0.418153i	$-0.862678\pi$
$59$	−0.707107	+	1.22474i	−0.0920575	+	0.159448i	0.816319	+	0.577601i	$0.196011\pi$
$60$		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
$63$	7.67972	+	2.00548i	0.967553	+	0.252667i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−4.34847	−	9.43879i	−0.535260	−	1.16184i
$67$	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	$0.137826\pi$
$71$			7.07107i			0.839181i	−0.907713	+	0.419591i	$0.862174\pi$
$72$	8.45946	−	0.661498i	0.996957	−	0.0779583i
$73$	−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
$78$	2.07107	+	12.0711i	0.234502	+	1.36678i
$79$	−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
$81$	1.39898	+	8.89060i	0.155442	+	0.987845i
$82$	−9.65926	−	2.58819i	−1.06669	−	0.285818i
$83$	1.00000	−	1.00000i	0.109764	−	0.109764i	−0.650092	−	0.759856i	$-0.725269\pi$
$83$	1.00000	−	1.00000i	0.109764	−	0.109764i	0.759856	+	0.650092i	$0.225269\pi$
$84$		0			0
$85$		0			0
$86$	−6.12372	+	3.53553i	−0.660338	+	0.381246i
$87$	4.24194	−	11.4894i	0.454783	−	1.23179i
$88$	−11.5911	+	3.10583i	−1.23562	+	0.331082i
$89$	7.77817	+	13.4722i	0.824485	+	1.42805i	0.902312	+	0.431083i	$0.141868\pi$
$89$	7.77817	+	13.4722i	0.824485	+	1.42805i	−0.0778275	+	0.996967i	$0.524798\pi$
$90$		0			0
$91$	12.5000	+	4.33013i	1.31036	+	0.453921i
$92$		0			0
$93$	1.10721	+	1.33195i	0.114812	+	0.138117i
$94$	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	0.00861771	−	0.999963i	$-0.497257\pi$
$101$	−8.57321	−	4.94975i	−0.853067	−	0.492518i	−0.861684	+	0.507445i	$0.830590\pi$
$102$	−3.24969	−	1.19980i	−0.321767	−	0.118798i
$103$	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	$0.354217\pi$
$107$	−4.02628	+	15.0263i	−0.389235	+	1.45265i	−0.831381	+	0.555702i	$0.812449\pi$
$108$		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	$0.631295\pi$
$113$	−14.0000	+	14.0000i	−1.31701	+	1.31701i	−0.916132	+	0.400878i	$0.868705\pi$
$114$	17.0741	+	1.57321i	1.59914	+	0.147345i
$115$		0			0
$116$		0			0
$117$	1.16938	+	14.9543i	0.108109	+	1.38253i
$118$	−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
$123$	−11.4894	−	4.24194i	−1.03596	−	0.382483i
$124$		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	$-0.981789\pi$
$127$	−10.6066	+	10.6066i	−0.941184	+	0.941184i	0.0571802	+	0.998364i	$0.481789\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$	−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
$133$	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	0.448486	−	0.893790i	$-0.351963\pi$
$137$	15.0263	−	4.02628i	1.28378	−	0.343988i	0.835295	+	0.549801i	$0.185297\pi$
$138$	−6.64324	−	7.99171i	−0.565510	−	0.680299i
$139$		−	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
$144$	−2.19275	+	11.7980i	−0.182729	+	0.983163i
$145$		0			0
$146$		−	9.89949i		−	0.819288i
$147$	6.33900	+	10.3352i	0.522832	+	0.852436i
$148$		0			0
$149$	4.24264	+	7.34847i	0.347571	+	0.602010i	0.985817	−	0.167822i	$-0.0536733\pi$
$149$	4.24264	+	7.34847i	0.347571	+	0.602010i	−0.638247	+	0.769832i	$0.720340\pi$
$150$		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
$153$	−3.82843	−	1.82843i	−0.309510	−	0.147820i
$154$	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
$159$	−4.87832	−	0.449490i	−0.386876	−	0.0356469i
$160$		0			0
$161$	−11.0227	+	2.12132i	−0.868711	+	0.167183i
$162$	−12.6569	−	1.34315i	−0.994416	−	0.105527i
$163$	−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	0.924020	−	0.382344i	$-0.124883\pi$
$167$	7.00000	+	7.00000i	0.541676	+	0.541676i	−0.382344	+	0.924020i	$0.624883\pi$
$168$	10.0199	+	8.22198i	0.773055	+	0.634339i
$169$			12.0000i			0.923077i
$170$		0			0
$171$	20.6464	+	3.83732i	1.57887	+	0.293447i
$172$		0			0
$173$	−2.73205	−	0.732051i	−0.207714	−	0.0556568i	0.153462	−	0.988155i	$-0.450958\pi$
$173$	−2.73205	−	0.732051i	−0.207714	−	0.0556568i	−0.361176	+	0.932498i	$0.617625\pi$
$174$	14.1421	+	10.0000i	1.07211	+	0.758098i
$175$		0			0
$176$		−	16.9706i		−	1.27920i
$177$	−1.56583	−	1.88366i	−0.117695	−	0.141585i
$178$	−21.2504	+	5.69402i	−1.59278	+	0.426785i
$179$	9.89949	−	17.1464i	0.739923	−	1.28158i	−0.212607	−	0.977138i	$-0.568195\pi$
$179$	9.89949	−	17.1464i	0.739923	−	1.28158i	0.952529	−	0.304446i	$-0.0984714\pi$
$180$		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
$183$	6.82843	−	1.17157i	0.504772	−	0.0866052i
$184$	−10.3923	+	6.00000i	−0.766131	+	0.442326i
$185$		0			0
$186$	−2.22474	+	1.02494i	−0.163126	+	0.0751525i
$187$	5.79555	+	1.55291i	0.423813	+	0.113560i
$188$		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	$0.199101\pi$
$192$	12.9988	+	4.79920i	0.938104	+	0.346353i
$193$	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	0.592113	−	0.805855i	$-0.298294\pi$
$197$	−3.00000	−	3.00000i	−0.213741	−	0.213741i	−0.805855	+	0.592113i	$0.798294\pi$
$198$	17.9452	−	1.40325i	1.27531	−	0.0997246i
$199$	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
$201$	−1.72474	−	0.158919i	−0.121654	−	0.0112093i
$202$	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
$207$	−7.20390	−	10.4930i	−0.500706	−	0.729316i
$208$	−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
$213$	−11.4894	−	4.24194i	−0.787240	−	0.290653i
$214$	−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
$219$	1.11243	−	12.0732i	0.0751711	−	0.815832i
$220$		0			0
$221$	−6.12372	−	3.53553i	−0.411926	−	0.237826i
$222$	−1.56583	−	1.88366i	−0.105091	−	0.126423i
$223$	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	−0.642595	−	0.766206i	$-0.722142\pi$
$227$	−12.2942	+	3.29423i	−0.815997	+	0.218646i	−0.173401	+	0.984851i	$0.555476\pi$
$228$		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
$231$	8.02270	−	17.7098i	0.527855	−	1.16522i
$232$	14.1421	−	14.1421i	0.928477	−	0.928477i
$233$	−2.73205	−	0.732051i	−0.178983	−	0.0479582i	0.168215	−	0.985750i	$-0.446200\pi$
$233$	−2.73205	−	0.732051i	−0.178983	−	0.0479582i	−0.347197	+	0.937792i	$0.612867\pi$
$234$	−20.8560	−	3.87628i	−1.36340	−	0.253400i
$235$		0			0
$236$		0			0
$237$	−2.05025	−	11.9497i	−0.133178	−	0.776220i
$238$	−2.31079	−	4.76028i	−0.149786	−	0.308563i
$239$	28.2843			1.82956			0.914779	−	0.403955i	$-0.132365\pi$
$239$	28.2843			1.82956			0.914779	+	0.403955i	$0.132365\pi$
$240$		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
$243$	−15.2851	−	3.06035i	−0.980540	−	0.196322i
$244$		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
$249$	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
$257$	3.29423	−	12.2942i	0.205488	−	0.766893i	−0.783812	−	0.620998i	$-0.786727\pi$
$257$	3.29423	−	12.2942i	0.205488	−	0.766893i	0.989300	−	0.145894i	$-0.0466060\pi$
$258$	−2.07107	−	12.0711i	−0.128939	−	0.751512i
$259$	−2.59808	+	0.500000i	−0.161437	+	0.0310685i
$260$		0			0
$261$	16.1237	+	13.7850i	0.998033	+	0.853268i
$262$	−6.21166	−	23.1822i	−0.383757	−	1.43220i
$263$	4.39230	+	16.3923i	0.270841	+	1.01079i	0.958577	+	0.284832i	$0.0919379\pi$
$263$	4.39230	+	16.3923i	0.270841	+	1.01079i	−0.687736	+	0.725961i	$0.741395\pi$
$264$	1.90702	−	20.6969i	0.117369	−	1.27381i
$265$		0			0
$266$	17.1464	+	19.7990i	1.05131	+	1.21395i
$267$	−26.5563	+	4.55635i	−1.62522	+	0.278844i
$268$		0			0
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	−0.766824	−	0.641857i	$-0.778164\pi$
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	0.939277	+	0.343161i	$0.111498\pi$
$270$		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
$273$	−14.5345	+	17.7129i	−0.879670	+	1.07203i
$274$			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	$-0.861390\pi$
$281$		−	14.1421i		−	0.843649i	0.906677	−	0.421825i	$-0.138610\pi$
$282$	−10.6556	+	8.85765i	−0.634532	+	0.527465i
$283$	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
$291$	−7.24745	−	15.7313i	−0.424853	−	0.922186i
$292$		0			0
$293$	16.0000	−	16.0000i	0.934730	−	0.934730i	−0.0632667	−	0.997997i	$-0.520152\pi$
$293$	16.0000	−	16.0000i	0.934730	−	0.934730i	0.997997	+	0.0632667i	$0.0201519\pi$
$294$	−16.4384	+	4.87628i	−0.958709	+	0.284390i
$295$		0			0
$296$	−2.44949	+	1.41421i	−0.142374	+	0.0821995i
$297$	22.0433	+	0.305174i	1.27908	+	0.0177080i
$298$	−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
$303$	13.1856	−	10.9608i	0.757495	−	0.629681i
$304$	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	$-0.609202\pi$
$307$	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	$0.0402901\pi$
$311$	28.1691	+	16.2635i	1.59732	+	0.922216i	0.605325	+	0.795979i	$0.293043\pi$
$312$	−8.48387	+	22.9788i	−0.480305	+	1.30092i
$313$	−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	−0.975443	−	0.220253i	$-0.929312\pi$
$317$	−0.366025	+	1.36603i	−0.0205580	+	0.0767236i	0.954885	+	0.296977i	$0.0959784\pi$
$318$	2.39960	−	6.49938i	0.134563	−	0.364467i
$319$	−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
$327$	−22.6432	+	18.8225i	−1.25217	+	1.04089i
$328$	−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
$333$	−1.69798	−	2.47323i	−0.0930485	−	0.135532i
$334$	−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	$-0.793484\pi$
$337$	−3.53553	+	3.53553i	−0.192593	+	0.192593i	0.604223	+	0.796815i	$0.293484\pi$
$338$	−16.3923	−	4.39230i	−0.891624	−	0.238910i
$339$	−14.3492	−	31.1464i	−0.779342	−	1.69164i
$340$		0			0
$341$	3.67423	−	2.12132i	0.198971	−	0.114876i
$342$	−12.7990	+	26.7990i	−0.692090	+	1.44912i
$343$	−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	0.381042	−	0.924558i	$-0.375565\pi$
$347$	21.8564	−	5.85641i	1.17331	−	0.314388i	0.792271	+	0.610169i	$0.208899\pi$
$348$		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	0.930527	−	0.366223i	$-0.119349\pi$
$353$	−1.09808	−	4.09808i	−0.0584447	−	0.218119i	−0.988972	+	0.148105i	$0.952683\pi$
$354$	3.14626	−	1.44949i	0.167222	−	0.0770395i
$355$		0			0
$356$		0			0
$357$	−2.28327	−	6.06520i	−0.120843	−	0.321005i
$358$	19.7990	+	19.7990i	1.04641	+	1.04641i
$359$	0.707107	+	1.22474i	0.0373197	+	0.0646396i	0.884082	−	0.467332i	$-0.154785\pi$
$359$	0.707107	+	1.22474i	0.0373197	+	0.0646396i	−0.846762	+	0.531971i	$0.821451\pi$
$360$		0			0
$361$	15.0000	−	25.9808i	0.789474	−	1.36741i
$362$	1.09808	−	4.09808i	0.0577136	−	0.215390i
$363$	−11.9497	+	2.05025i	−0.627199	+	0.107610i
$364$		0			0
$365$		0			0
$366$	−0.898979	+	9.75663i	−0.0469904	+	0.509987i
$367$	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
$369$	13.7850	−	16.1237i	0.717617	−	0.839368i
$370$		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
$378$	−12.5233	−	14.8717i	−0.644127	−	0.764919i
$379$			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
$381$	−10.8712	−	23.5970i	−0.556947	−	1.20891i
$382$	4.14110	+	15.4548i	0.211877	+	0.790737i
$383$	−16.3923	−	4.39230i	−0.837608	−	0.224436i	−0.185578	−	0.982630i	$-0.559416\pi$
$383$	−16.3923	−	4.39230i	−0.837608	−	0.224436i	−0.652030	+	0.758193i	$0.726082\pi$
$384$	−11.3137	+	16.0000i	−0.577350	+	0.816497i
$385$		0			0
$386$			32.5269i			1.65558i
$387$	−1.16938	−	14.9543i	−0.0594427	−	0.760172i
$388$		0			0
$389$	−14.8492	+	25.7196i	−0.752886	+	1.30404i	0.193532	+	0.981094i	$0.438006\pi$
$389$	−14.8492	+	25.7196i	−0.752886	+	1.30404i	−0.946418	+	0.322944i	$0.895328\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	2.33975	+	19.6603i	0.118175	+	0.992993i
$393$	−4.97056	−	28.9706i	−0.250732	−	1.46137i
$394$	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
$399$	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	$0.114085\pi$
$402$	0.848387	−	2.29788i	0.0423137	−	0.114608i
$403$	−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
$408$	−4.42883	−	5.32780i	−0.219260	−	0.263766i
$409$	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
$411$	−2.47219	+	26.8307i	−0.121944	+	1.32346i
$412$		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
$417$	17.8733	+	6.59890i	0.875259	+	0.323150i
$418$	10.8704	−	40.5689i	0.531689	−	1.98429i
$419$	14.1421			0.690889			0.345444	−	0.938439i	$-0.387728\pi$
$419$	14.1421			0.690889			0.345444	+	0.938439i	$0.387728\pi$
$420$		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
$423$	−13.9907	+	9.60521i	−0.680252	+	0.467021i
$424$	−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
$429$	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	$0.688367\pi$
$432$	−17.8544	−	10.6405i	−0.859021	−	0.511940i
$433$	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
$438$	16.0851	+	5.93871i	0.768578	+	0.283763i
$439$	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
$441$	−20.5959	+	4.09978i	−0.980758	+	0.195227i
$442$	7.07107	−	7.07107i	0.336336	−	0.336336i
$443$	10.9282	+	2.92820i	0.519215	+	0.139123i	0.508903	−	0.860824i	$-0.330051\pi$
$443$	10.9282	+	2.92820i	0.519215	+	0.139123i	0.0103113	+	0.999947i	$0.496718\pi$
$444$		0			0
$445$		0			0
$446$	−12.2474	+	7.07107i	−0.579934	+	0.334825i
$447$	−14.4853	+	2.48528i	−0.685130	+	0.117550i
$448$	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
$453$	6.64324	+	7.99171i	0.312127	+	0.375483i
$454$		−	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
$459$	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	$0.947345\pi$
$462$	21.2555	+	17.4414i	0.988895	+	0.811449i
$463$	−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	−0.923741	−	0.383017i	$-0.874885\pi$
$467$	1.46410	−	5.46410i	0.0677505	−	0.252848i	0.991492	+	0.130168i	$0.0415518\pi$
$468$		0			0
$469$	−1.73205	−	2.00000i	−0.0799787	−	0.0923514i
$470$		0			0
$471$	6.89898	+	0.635674i	0.317888	+	0.0292903i
$472$	−1.03528	−	3.86370i	−0.0476524	−	0.177841i
$473$	5.49038	+	20.4904i	0.252448	+	0.942149i
$474$	17.0741	+	1.57321i	0.784240	+	0.0722601i
$475$		0			0
$476$		0			0
$477$	3.65685	−	7.65685i	0.167436	−	0.350583i
$478$	−10.3528	+	38.6370i	−0.473524	+	1.76722i
$479$	−4.24264	+	7.34847i	−0.193851	+	0.335760i	−0.946523	−	0.322635i	$-0.895431\pi$
$479$	−4.24264	+	7.34847i	−0.193851	+	0.335760i	0.752672	+	0.658396i	$0.228765\pi$
$480$		0			0
$481$	−2.50000	−	4.33013i	−0.113990	−	0.197437i
$482$	−24.0000	−	24.0000i	−1.09317	−	1.09317i
$483$	3.16571	−	19.1828i	0.144045	−	0.872846i
$484$		0			0
$485$		0			0
$486$	9.77526	−	19.7597i	0.443415	−	0.896317i
$487$	−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	$0.103385\pi$
$491$			14.1421i			0.638226i	−0.947717	+	0.319113i	$0.896615\pi$
$492$		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
$498$	−3.41421	+	0.585786i	−0.152995	+	0.0262497i
$499$	−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
$501$	−15.5732	+	7.17461i	−0.695760	+	0.320538i
$502$	9.65926	+	2.58819i	0.431114	+	0.115517i
$503$	−24.0000	+	24.0000i	−1.07011	+	1.07011i	−0.0727574	+	0.997350i	$0.523180\pi$
$503$	−24.0000	+	24.0000i	−1.07011	+	1.07011i	−0.997350	+	0.0727574i	$0.976820\pi$
$504$	−19.3704	+	11.3485i	−0.862826	+	0.505501i
$505$		0			0
$506$	−22.0454	+	12.7279i	−0.980038	+	0.565825i
$507$	−19.4981	−	7.19881i	−0.865943	−	0.319710i
$508$		0			0
$509$	4.24264	+	7.34847i	0.188052	+	0.325715i	0.944601	−	0.328222i	$-0.106449\pi$
$509$	4.24264	+	7.34847i	0.188052	+	0.325715i	−0.756549	+	0.653937i	$0.773116\pi$
$510$		0			0
$511$	14.0000	−	12.1244i	0.619324	−	0.536350i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−18.6208	+	31.2452i	−0.822130	+	1.37951i
$514$	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	−0.224335	−	0.974512i	$-0.572021\pi$
$521$	−26.9444	−	15.5563i	−1.18046	−	0.681536i	−0.956120	+	0.292976i	$0.905354\pi$
$522$	−24.7323	+	16.9798i	−1.08250	+	0.743184i
$523$	−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
$528$	27.5745	+	10.1806i	1.20003	+	0.443056i
$529$	−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
$537$	21.9216	+	26.3713i	0.945985	+	1.13801i
$538$	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
$543$	1.79970	−	4.87453i	0.0772326	−	0.209186i
$544$		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	$-0.681421\pi$
$547$	7.07107	−	7.07107i	0.302337	−	0.302337i	0.841928	+	0.539591i	$0.181421\pi$
$548$		0			0
$549$	−2.19275	+	11.7980i	−0.0935844	+	0.503525i
$550$		0			0
$551$	42.8661	−	24.7487i	1.82616	−	1.05433i
$552$	−3.51472	−	20.4853i	−0.149596	−	0.871911i
$553$	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	−0.640112	−	0.768281i	$-0.721112\pi$
$557$	−19.1244	+	5.12436i	−0.810325	+	0.217126i	−0.170213	+	0.985407i	$0.554445\pi$
$558$	−0.330749	−	4.22973i	−0.0140017	−	0.179059i
$559$		−	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	$0.144260\pi$
$563$	8.05256	+	30.0526i	0.339375	+	1.26656i	−0.559673	+	0.828714i	$0.689073\pi$
$564$		0			0
$565$		0			0
$566$			32.5269i			1.36721i
$567$	−13.6019	−	19.5445i	−0.571227	−	0.820792i
$568$	−14.1421	−	14.1421i	−0.593391	−	0.593391i
$569$	0.707107	+	1.22474i	0.0296435	+	0.0513440i	0.880467	−	0.474108i	$-0.157229\pi$
$569$	0.707107	+	1.22474i	0.0296435	+	0.0513440i	−0.850823	+	0.525452i	$0.823896\pi$
$570$		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
$573$	3.31371	+	19.3137i	0.138432	+	0.806842i
$574$	25.9808	−	5.00000i	1.08442	−	0.208696i
$575$		0			0
$576$	−15.5959	+	18.2419i	−0.649830	+	0.760080i
$577$	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
$579$	−3.65513	+	39.6691i	−0.151902	+	1.64859i
$580$		0			0
$581$	−1.22474	+	3.53553i	−0.0508110	+	0.146679i
$582$	24.1421	−	4.14214i	1.00072	−	0.171697i
$583$	−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	0.385952	−	0.922519i	$-0.373873\pi$
$587$	−13.0000	−	13.0000i	−0.536567	−	0.536567i	−0.922519	+	0.385952i	$0.873873\pi$
$588$		0			0
$589$			7.00000i			0.288430i
$590$		0			0
$591$	6.67423	−	3.07483i	0.274541	−	0.126482i
$592$	−1.03528	−	3.86370i	−0.0425496	−	0.158797i
$593$	17.7583	+	4.75833i	0.729247	+	0.195401i	0.604294	−	0.796761i	$-0.293455\pi$
$593$	17.7583	+	4.75833i	0.729247	+	0.195401i	0.124953	+	0.992163i	$0.460122\pi$
$594$	−8.48528	+	30.0000i	−0.348155	+	1.23091i
$595$		0			0
$596$		0			0
$597$	−2.66390	+	2.21441i	−0.109026	+	0.0906299i
$598$	28.9778	−	7.76457i	1.18499	−	0.317517i
$599$	9.89949	−	17.1464i	0.404482	−	0.700584i	−0.589779	−	0.807565i	$-0.700785\pi$
$599$	9.89949	−	17.1464i	0.404482	−	0.700584i	0.994261	+	0.106981i	$0.0341184\pi$
$600$		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
$603$	1.29289	−	2.70711i	0.0526507	−	0.110242i
$604$		0			0
$605$		0			0
$606$	10.1464	+	22.0239i	0.412170	+	0.894658i
$607$	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
$609$	3.17837	+	32.2474i	0.128794	+	1.30673i
$610$		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	0.527492	−	0.849560i	$-0.323132\pi$
$617$	−8.00000	−	8.00000i	−0.322068	−	0.322068i	−0.849560	+	0.527492i	$0.823132\pi$
$618$	−5.65099	+	4.69748i	−0.227316	+	0.188960i
$619$	−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
$621$	21.3712	−	5.41045i	0.857596	−	0.217114i
$622$	−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
$627$	17.8161	−	48.2554i	0.711508	−	1.92714i
$628$		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
$633$	−1.19980	+	3.24969i	−0.0476878	+	0.129164i
$634$	−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
$639$	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	$0.729301\pi$
$642$	29.3029	−	24.3585i	1.15649	−	0.961355i
$643$	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	−0.231867	−	0.972747i	$-0.574483\pi$
$647$	1.36603	−	0.366025i	0.0537040	−	0.0143899i	0.285571	+	0.958358i	$0.407817\pi$
$648$	−20.5792	−	14.9833i	−0.808426	−	0.588598i
$649$	−5.19615	+	3.00000i	−0.203967	+	0.117760i
$650$		0			0
$651$	−4.17423	−	1.89097i	−0.163601	−	0.0741129i
$652$		0			0
$653$	−36.8827	−	9.88269i	−1.44333	−	0.386739i	−0.549632	−	0.835407i	$-0.685232\pi$
$653$	−36.8827	−	9.88269i	−1.44333	−	0.386739i	−0.893699	+	0.448667i	$0.851899\pi$
$654$	−17.4240	−	37.8207i	−0.681334	−	1.47890i
$655$		0			0
$656$	24.4949	−	14.1421i	0.956365	−	0.552158i
$657$	18.9497	+	9.05025i	0.739300	+	0.353084i
$658$	−21.1117	−	1.51575i	−0.823018	−	0.0590901i
$659$	−28.2843			−1.10180			−0.550899	−	0.834572i	$-0.685715\pi$
$659$	−28.2843			−1.10180			−0.550899	+	0.834572i	$0.685715\pi$
$660$		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
$663$	9.41832	−	7.82913i	0.365777	−	0.304058i
$664$			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
$669$	−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	$-0.410031\pi$
$673$	−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	$0.402230\pi$
$677$	−11.3468	+	42.3468i	−0.436092	+	1.62752i	−0.738438	+	0.674321i	$0.764436\pi$
$678$	47.7990	−	8.20101i	1.83571	−	0.314958i
$679$	8.66025	−	25.0000i	0.332350	−	0.959412i
$680$		0			0
$681$	2.02270	−	21.9524i	0.0775102	−	0.841218i
$682$	1.55291	+	5.79555i	0.0594642	+	0.221923i
$683$	6.22243	+	23.2224i	0.238095	+	0.888582i	0.976729	+	0.214476i	$0.0688043\pi$
$683$	6.22243	+	23.2224i	0.238095	+	0.888582i	−0.738635	+	0.674106i	$0.764529\pi$
$684$		0			0
$685$		0			0
$686$	−23.2702	−	12.0208i	−0.888459	−	0.458957i
$687$	0.878680	+	5.12132i	0.0335237	+	0.195391i
$688$	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
$693$	23.9628	+	23.6597i	0.910272	+	0.898760i
$694$			32.0000i			1.21470i
$695$		0			0
$696$	14.4949	+	31.4626i	0.549428	+	1.19259i
$697$	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	$-0.868800\pi$
$701$		−	21.2132i		−	0.801212i	0.916250	−	0.400606i	$-0.131200\pi$
$702$	18.8099	−	31.5624i	0.709934	−	1.19125i
$703$	−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
$711$	20.6464	+	3.83732i	0.774302	+	0.143911i
$712$	−42.5007	−	11.3880i	−1.59278	−	0.426785i
$713$	3.00000	−	3.00000i	0.112351	−	0.112351i
$714$	9.12096	−	0.898979i	0.341343	−	0.0336435i
$715$		0			0
$716$		0			0
$717$	−16.9677	+	45.9575i	−0.633672	+	1.71632i
$718$	−1.93185	+	0.517638i	−0.0720961	+	0.0193181i
$719$	−9.89949	−	17.1464i	−0.369189	−	0.639454i	0.620250	−	0.784404i	$-0.287031\pi$
$719$	−9.89949	−	17.1464i	−0.369189	−	0.639454i	−0.989439	+	0.144950i	$0.953698\pi$
$720$		0			0
$721$	1.50000	+	7.79423i	0.0558629	+	0.290272i
$722$	30.0000	+	30.0000i	1.11648	+	1.11648i
$723$	−26.5730	−	31.9668i	−0.988259	−	1.18886i
$724$		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	$-0.903442\pi$
$727$	−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
$738$	16.9798	+	24.7323i	0.625034	+	0.910409i
$739$	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	−0.475931	−	0.879482i	$-0.657889\pi$
$743$	11.0000	−	11.0000i	0.403551	−	0.403551i	0.879482	+	0.475931i	$0.157889\pi$
$744$	−4.87832	−	0.449490i	−0.178848	−	0.0164791i
$745$		0			0
$746$	28.1691	+	16.2635i	1.03135	+	0.595447i
$747$	−4.22973	+	0.330749i	−0.154758	+	0.0121015i
$748$		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
$753$	11.4894	+	4.24194i	0.418696	+	0.154585i
$754$	−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
$759$	−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	$0.476852\pi$
$762$	36.2132	−	6.21320i	1.31187	−	0.225081i
$763$	−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	$-0.976073\pi$
$773$	−4.75833	−	17.7583i	−0.171145	−	0.638723i	0.826031	−	0.563625i	$-0.190594\pi$
$774$	20.8560	+	3.87628i	0.749655	+	0.139330i
$775$		0			0
$776$		−	28.2843i		−	1.01535i
$777$	0.746165	−	4.52142i	0.0267685	−	0.162205i
$778$	−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
$783$	−32.0711	+	17.9289i	−1.14613	+	0.640728i
$784$	−27.7128	−	4.00000i	−0.989743	−	0.142857i
$785$		0			0
$786$	41.3939	+	3.81405i	1.47647	+	0.136043i
$787$	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
$789$	−29.2699	−	2.69694i	−1.04204	−	0.0960136i
$790$		0			0
$791$	17.1464	−	49.4975i	0.609657	−	1.75993i
$792$	32.4853	+	15.5147i	1.15431	+	0.551292i
$793$	−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	0.940888	−	0.338717i	$-0.109993\pi$
$797$	17.0000	+	17.0000i	0.602171	+	0.602171i	−0.338717	+	0.940888i	$0.609993\pi$
$798$	−42.4564	+	15.9829i	−1.50294	+	0.565787i
$799$		−	8.00000i		−	0.283020i
$800$		0			0
$801$	8.52781	−	45.8833i	0.301315	−	1.62121i
$802$	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
$807$	6.26330	+	7.53465i	0.220479	+	0.265232i
$808$	27.0459	−	7.24693i	0.951472	−	0.254946i
$809$	9.89949	−	17.1464i	0.348048	−	0.602836i	−0.637855	−	0.770157i	$-0.720178\pi$
$809$	9.89949	−	17.1464i	0.348048	−	0.602836i	0.985903	+	0.167320i	$0.0535114\pi$
$810$		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
$813$	23.8995	−	4.10051i	0.838192	−	0.143811i
$814$	−5.19615	+	3.00000i	−0.182125	+	0.105150i
$815$		0			0
$816$	8.89898	−	4.09978i	0.311527	−	0.143521i
$817$	−33.8074	−	9.05867i	−1.18277	−	0.316923i
$818$	−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	$0.229376\pi$
$822$	−35.7466	−	13.1978i	−1.24681	−	0.460326i
$823$	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	0.321118	−	0.947039i	$-0.395941\pi$
$827$	−18.0000	−	18.0000i	−0.625921	−	0.625921i	−0.947039	+	0.321118i	$0.895941\pi$
$828$		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
$831$	15.5227	+	1.43027i	0.538477	+	0.0496154i
$832$	−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
$837$	0.0719302	−	5.19565i	0.00248627	−	0.179588i
$838$	−5.17638	+	19.3185i	−0.178815	+	0.667347i
$839$	35.3553			1.22060			0.610301	−	0.792170i	$-0.291049\pi$
$839$	35.3553			1.22060			0.610301	+	0.792170i	$0.291049\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$	8.41858	−	31.4186i	0.290124	−	1.08276i
$843$	22.9788	+	8.48387i	0.791431	+	0.292200i
$844$		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
$849$	−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	−0.903941	−	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	0.266905	−	0.963723i	$-0.413999\pi$
$857$	28.6865	−	7.68653i	0.979913	−	0.262567i	0.713008	+	0.701156i	$0.247332\pi$
$858$	−17.9970	+	48.7453i	−0.614408	+	1.66414i
$859$	−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
$861$	32.2474	−	3.17837i	1.09899	−	0.108319i
$862$	2.82843	−	2.82843i	0.0963366	−	0.0963366i
$863$	38.2487	+	10.2487i	1.30200	+	0.348870i	0.842207	−	0.539155i	$-0.181256\pi$
$863$	38.2487	+	10.2487i	1.30200	+	0.348870i	0.459795	+	0.888025i	$0.347923\pi$
$864$		0			0
$865$		0			0
$866$	−18.3712	+	10.6066i	−0.624278	+	0.360427i
$867$	−4.39340	−	25.6066i	−0.149208	−	0.869646i
$868$		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
$873$	29.9087	−	2.33875i	1.01226	−	0.0791547i
$874$		−	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
$879$	16.3991	+	35.5959i	0.553128	+	1.20062i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	1.93823	−	29.6352i	0.0652636	−	0.997868i
$883$	−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	$0.249482\pi$
$887$	−7.68653	+	28.6865i	−0.258089	+	0.963200i	−0.966346	+	0.257245i	$0.917185\pi$
$888$	−0.828427	−	4.82843i	−0.0278002	−	0.162031i
$889$	12.9904	−	37.5000i	0.435683	−	1.25771i
$890$		0			0
$891$	−13.7196	+	35.6339i	−0.459625	+	1.19378i
$892$		0			0
$893$	10.2487	+	38.2487i	0.342960	+	1.27994i
$894$	1.90702	−	20.6969i	0.0637804	−	0.692209i
$895$		0			0
$896$	−29.3939	+	5.65685i	−0.981981	+	0.188982i
$897$	36.2132	−	6.21320i	1.20912	−	0.207453i
$898$		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
$903$	14.5345	−	17.7129i	0.483679	−	0.589449i
$904$		−	56.0000i		−	1.86253i
$905$		0			0
$906$	−13.3485	+	6.14966i	−0.443473	+	0.204309i
$907$	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	$0.199175\pi$
$911$			35.3553i			1.17137i	−0.810537	+	0.585687i	$0.800825\pi$
$912$	−37.2946	+	31.0018i	−1.23495	+	1.02657i
$913$	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
$918$	5.07107	+	9.07107i	0.167370	+	0.299390i
$919$	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
$921$	10.8712	+	23.5970i	0.358217	+	0.777547i
$922$	−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
$927$	−7.41970	+	5.09393i	−0.243695	+	0.167307i
$928$		0			0
$929$	7.77817	+	13.4722i	0.255194	+	0.442008i	0.964948	−	0.262441i	$-0.0845275\pi$
$929$	7.77817	+	13.4722i	0.255194	+	0.442008i	−0.709754	+	0.704449i	$0.751194\pi$
$930$		0			0
$931$	−7.00000	+	48.4974i	−0.229416	+	1.58944i
$932$		0			0
$933$	−43.3243	+	36.0140i	−1.41837	+	1.17905i
$934$	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	$-0.671207\pi$
$937$	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	0.736539	−	0.676396i	$-0.236459\pi$
$941$	15.9217	+	9.19239i	0.519032	+	0.299663i	−0.217506	+	0.976059i	$0.569792\pi$
$942$	−3.39355	+	9.19151i	−0.110568	+	0.299476i
$943$	−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	−0.999980	−	0.00627092i	$-0.998004\pi$
$947$	−4.02628	+	15.0263i	−0.130837	+	0.488288i	0.869144	+	0.494559i	$0.164671\pi$
$948$		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	$-0.441403\pi$
$953$	36.0000	−	36.0000i	1.16615	−	1.16615i	0.983103	−	0.183051i	$-0.0585973\pi$
$954$	9.12096	+	7.79796i	0.295302	+	0.252468i
$955$		0			0
$956$		0			0
$957$	39.9585	−	33.2162i	1.29168	−	1.07373i
$958$	−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
$963$	38.4745	−	26.4143i	1.23982	−	0.851189i
$964$		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	$-0.559739\pi$
$967$	24.7487	−	24.7487i	0.795866	−	0.795866i	0.982441	+	0.186575i	$0.0597387\pi$
$968$	−19.1244	−	5.12436i	−0.614680	−	0.164703i
$969$	−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
$973$	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	−0.0103108	−	0.999947i	$-0.503282\pi$
$977$	15.0263	−	4.02628i	0.480733	−	0.128812i	0.491044	+	0.871135i	$0.336615\pi$
$978$	3.76733	−	3.13165i	0.120466	−	0.100139i
$979$			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	$0.125070\pi$
$983$	9.88269	+	36.8827i	0.315209	+	1.17637i	−0.608586	+	0.793488i	$0.708263\pi$
$984$	31.4626	−	14.4949i	1.00299	−	0.462080i
$985$		0			0
$986$		−	14.1421i		−	0.450377i
$987$	−25.5770	−	4.22095i	−0.814125	−	0.134354i
$988$		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
$993$	−1.70711	+	0.292893i	−0.0541734	+	0.00929469i
$994$	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
$999$	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.368.1	yes	8
3.2	odd	2		525.2.bf.a.368.1	yes	8
5.2	odd	4		525.2.bf.a.32.2	yes	8
5.3	odd	4	inner	525.2.bf.d.32.1	yes	8
5.4	even	2		525.2.bf.a.368.2	yes	8
7.2	even	3	inner	525.2.bf.d.443.2	yes	8
15.2	even	4	inner	525.2.bf.d.32.2	yes	8
15.8	even	4		525.2.bf.a.32.1	✓	8
15.14	odd	2	inner	525.2.bf.d.368.2	yes	8
21.2	odd	6		525.2.bf.a.443.2	yes	8
35.2	odd	12		525.2.bf.a.107.1	yes	8
35.9	even	6		525.2.bf.a.443.1	yes	8
35.23	odd	12	inner	525.2.bf.d.107.2	yes	8
105.2	even	12	inner	525.2.bf.d.107.1	yes	8
105.23	even	12		525.2.bf.a.107.2	yes	8
105.44	odd	6	inner	525.2.bf.d.443.1	yes	8

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

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

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