LMFDB - Embedded newform 450.2.p.d.293.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (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:	$3.59326809096$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.293
Dual form			450.2.p.d.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.67303 - 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.67303 - 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +(3.00000 - 1.73205i) q^{11} +(-1.67303 - 0.448288i) q^{12} +(3.34607 - 0.896575i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.24264 - 4.24264i) q^{17} +(-0.776457 - 2.89778i) q^{18} -2.00000i q^{19} -3.00000 q^{21} +(-0.896575 - 3.34607i) q^{22} +(-0.776457 - 2.89778i) q^{23} +(-0.866025 + 1.50000i) q^{24} -3.46410i q^{26} +(3.67423 - 3.67423i) q^{27} +(1.22474 + 1.22474i) q^{28} +(4.33013 + 7.50000i) q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.965926 - 0.258819i) q^{32} +(4.24264 - 4.24264i) q^{33} +(-5.19615 + 3.00000i) q^{34} -3.00000 q^{36} +(-2.44949 + 2.44949i) q^{37} +(-1.93185 - 0.517638i) q^{38} +(5.19615 - 3.00000i) q^{39} +(7.50000 + 4.33013i) q^{41} +(-0.776457 + 2.89778i) q^{42} +(-2.68973 + 10.0382i) q^{43} -3.46410 q^{44} -3.00000 q^{46} +(0.776457 - 2.89778i) q^{47} +(1.22474 + 1.22474i) q^{48} +(-3.46410 - 2.00000i) q^{49} +(-9.00000 - 5.19615i) q^{51} +(-3.34607 - 0.896575i) q^{52} +(-2.59808 - 4.50000i) q^{54} +(1.50000 - 0.866025i) q^{56} +(-0.896575 - 3.34607i) q^{57} +(8.36516 - 2.24144i) q^{58} +(3.46410 - 6.00000i) q^{59} +(6.50000 + 11.2583i) q^{61} +(7.07107 + 7.07107i) q^{62} +(-5.01910 + 1.34486i) q^{63} -1.00000i q^{64} +(-3.00000 - 5.19615i) q^{66} +(3.13801 + 11.7112i) q^{67} +(1.55291 + 5.79555i) q^{68} +(-2.59808 - 4.50000i) q^{69} -3.46410i q^{71} +(-0.776457 + 2.89778i) q^{72} +(-9.79796 - 9.79796i) q^{73} +(1.73205 + 3.00000i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-5.79555 + 1.55291i) q^{77} +(-1.55291 - 5.79555i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(6.12372 - 6.12372i) q^{82} +(-2.89778 - 0.776457i) q^{83} +(2.59808 + 1.50000i) q^{84} +(9.00000 + 5.19615i) q^{86} +(10.6066 + 10.6066i) q^{87} +(-0.896575 + 3.34607i) q^{88} -1.73205 q^{89} -6.00000 q^{91} +(-0.776457 + 2.89778i) q^{92} +(-4.48288 + 16.7303i) q^{93} +(-2.59808 - 1.50000i) q^{94} +(1.50000 - 0.866025i) q^{96} +(6.69213 + 1.79315i) q^{97} +(-2.82843 + 2.82843i) q^{98} +(5.19615 - 9.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 24 q^{11} + 4 q^{16} - 24 q^{21} - 40 q^{31} - 24 q^{36} + 60 q^{41} - 24 q^{46} - 72 q^{51} + 12 q^{56} + 52 q^{61} - 24 q^{66} - 8 q^{76} + 36 q^{81} + 72 q^{86} - 48 q^{91} + 12 q^{96}+O(q^{100}) $ 8 * q + 24 * q^11 + 4 * q^16 - 24 * q^21 - 40 * q^31 - 24 * q^36 + 60 * q^41 - 24 * q^46 - 72 * q^51 + 12 * q^56 + 52 * q^61 - 24 * q^66 - 8 * q^76 + 36 * q^81 + 72 * q^86 - 48 * q^91 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.67303	−	0.448288i	0.965926	−	0.258819i
$3$	1.67303	−	0.448288i	0.965926	−	0.258819i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$	−1.67303	−	0.448288i	−0.632347	−	0.169437i	−0.0716124	−	0.997433i	$-0.522814\pi$
$7$	−1.67303	−	0.448288i	−0.632347	−	0.169437i	−0.560734	+	0.827996i	$0.689481\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.59808	−	1.50000i	0.866025	−	0.500000i
$10$		0			0
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$	−1.67303	−	0.448288i	−0.482963	−	0.129410i
$13$	3.34607	−	0.896575i	0.928032	−	0.248665i	0.237016	−	0.971506i	$-0.423830\pi$
$13$	3.34607	−	0.896575i	0.928032	−	0.248665i	0.691015	+	0.722840i	$0.257164\pi$
$14$	−0.866025	+	1.50000i	−0.231455	+	0.400892i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.999567	−	0.0294245i	$-0.990633\pi$
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.0294245	−	0.999567i	$-0.509367\pi$
$18$	−0.776457	−	2.89778i	−0.183013	−	0.683013i
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$	−3.00000			−0.654654
$22$	−0.896575	−	3.34607i	−0.191151	−	0.713384i
$23$	−0.776457	−	2.89778i	−0.161903	−	0.604228i	−0.998415	−	0.0562805i	$-0.982076\pi$
$23$	−0.776457	−	2.89778i	−0.161903	−	0.604228i	0.836512	−	0.547948i	$-0.184591\pi$
$24$	−0.866025	+	1.50000i	−0.176777	+	0.306186i
$25$		0			0
$26$		−	3.46410i		−	0.679366i
$27$	3.67423	−	3.67423i	0.707107	−	0.707107i
$28$	1.22474	+	1.22474i	0.231455	+	0.231455i
$29$	4.33013	+	7.50000i	0.804084	+	1.39272i	0.916907	+	0.399100i	$0.130677\pi$
$29$	4.33013	+	7.50000i	0.804084	+	1.39272i	−0.112823	+	0.993615i	$0.535989\pi$
$30$		0			0
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	4.24264	−	4.24264i	0.738549	−	0.738549i
$34$	−5.19615	+	3.00000i	−0.891133	+	0.514496i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−2.44949	+	2.44949i	−0.402694	+	0.402694i	−0.879181	−	0.476488i	$-0.841910\pi$
$37$	−2.44949	+	2.44949i	−0.402694	+	0.402694i	0.476488	+	0.879181i	$0.341910\pi$
$38$	−1.93185	−	0.517638i	−0.313388	−	0.0839720i
$39$	5.19615	−	3.00000i	0.832050	−	0.480384i
$40$		0			0
$41$	7.50000	+	4.33013i	1.17130	+	0.676252i	0.953987	−	0.299849i	$-0.0969363\pi$
$41$	7.50000	+	4.33013i	1.17130	+	0.676252i	0.217317	+	0.976101i	$0.430270\pi$
$42$	−0.776457	+	2.89778i	−0.119810	+	0.447137i
$43$	−2.68973	+	10.0382i	−0.410179	+	1.53081i	0.384120	+	0.923283i	$0.374505\pi$
$43$	−2.68973	+	10.0382i	−0.410179	+	1.53081i	−0.794299	+	0.607527i	$0.792162\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	−3.00000			−0.442326
$47$	0.776457	−	2.89778i	0.113258	−	0.422684i	−0.885893	−	0.463890i	$-0.846453\pi$
$47$	0.776457	−	2.89778i	0.113258	−	0.422684i	0.999151	+	0.0412058i	$0.0131199\pi$
$48$	1.22474	+	1.22474i	0.176777	+	0.176777i
$49$	−3.46410	−	2.00000i	−0.494872	−	0.285714i
$50$		0			0
$51$	−9.00000	−	5.19615i	−1.26025	−	0.727607i
$52$	−3.34607	−	0.896575i	−0.464016	−	0.124333i
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$	−2.59808	−	4.50000i	−0.353553	−	0.612372i
$55$		0			0
$56$	1.50000	−	0.866025i	0.200446	−	0.115728i
$57$	−0.896575	−	3.34607i	−0.118754	−	0.443197i
$58$	8.36516	−	2.24144i	1.09840	−	0.294315i
$59$	3.46410	−	6.00000i	0.450988	−	0.781133i	−0.547460	−	0.836832i	$-0.684405\pi$
$59$	3.46410	−	6.00000i	0.450988	−	0.781133i	0.998448	+	0.0556984i	$0.0177385\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	7.07107	+	7.07107i	0.898027	+	0.898027i
$63$	−5.01910	+	1.34486i	−0.632347	+	0.169437i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$	3.13801	+	11.7112i	0.383369	+	1.43075i	0.840721	+	0.541468i	$0.182131\pi$
$67$	3.13801	+	11.7112i	0.383369	+	1.43075i	−0.457352	+	0.889286i	$0.651202\pi$
$68$	1.55291	+	5.79555i	0.188319	+	0.702814i
$69$	−2.59808	−	4.50000i	−0.312772	−	0.541736i
$70$		0			0
$71$		−	3.46410i		−	0.411113i	−0.978645	−	0.205557i	$-0.934100\pi$
$71$		−	3.46410i		−	0.411113i	0.978645	−	0.205557i	$-0.0659005\pi$
$72$	−0.776457	+	2.89778i	−0.0915064	+	0.341506i
$73$	−9.79796	−	9.79796i	−1.14676	−	1.14676i	−0.987185	−	0.159579i	$-0.948986\pi$
$73$	−9.79796	−	9.79796i	−1.14676	−	1.14676i	−0.159579	−	0.987185i	$-0.551014\pi$
$74$	1.73205	+	3.00000i	0.201347	+	0.348743i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−5.79555	+	1.55291i	−0.660465	+	0.176971i
$78$	−1.55291	−	5.79555i	−0.175833	−	0.656217i
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	0.292306	+	0.956325i	$0.405577\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	6.12372	−	6.12372i	0.676252	−	0.676252i
$83$	−2.89778	−	0.776457i	−0.318072	−	0.0852272i	0.0962507	−	0.995357i	$-0.469315\pi$
$83$	−2.89778	−	0.776457i	−0.318072	−	0.0852272i	−0.414323	+	0.910130i	$0.635982\pi$
$84$	2.59808	+	1.50000i	0.283473	+	0.163663i
$85$		0			0
$86$	9.00000	+	5.19615i	0.970495	+	0.560316i
$87$	10.6066	+	10.6066i	1.13715	+	1.13715i
$88$	−0.896575	+	3.34607i	−0.0955753	+	0.356692i
$89$	−1.73205			−0.183597			−0.0917985	−	0.995778i	$-0.529262\pi$
$89$	−1.73205			−0.183597			−0.0917985	+	0.995778i	$0.529262\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$	−0.776457	+	2.89778i	−0.0809513	+	0.302114i
$93$	−4.48288	+	16.7303i	−0.464853	+	1.73485i
$94$	−2.59808	−	1.50000i	−0.267971	−	0.154713i
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	6.69213	+	1.79315i	0.679483	+	0.182067i	0.582023	−	0.813173i	$-0.302261\pi$
$97$	6.69213	+	1.79315i	0.679483	+	0.182067i	0.0974602	+	0.995239i	$0.468928\pi$
$98$	−2.82843	+	2.82843i	−0.285714	+	0.285714i
$99$	5.19615	−	9.00000i	0.522233	−	0.904534i
$100$		0			0
$101$	12.0000	−	6.92820i	1.19404	−	0.689382i	0.234823	−	0.972038i	$-0.424549\pi$
$101$	12.0000	−	6.92820i	1.19404	−	0.689382i	0.959221	+	0.282656i	$0.0912155\pi$
$102$	−7.34847	+	7.34847i	−0.727607	+	0.727607i
$103$	−3.34607	+	0.896575i	−0.329698	+	0.0883422i	−0.419871	−	0.907584i	$-0.637925\pi$
$103$	−3.34607	+	0.896575i	−0.329698	+	0.0883422i	0.0901732	+	0.995926i	$0.471258\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$		0			0
$107$	2.12132	+	2.12132i	0.205076	+	0.205076i	0.802171	−	0.597095i	$-0.203678\pi$
$107$	2.12132	+	2.12132i	0.205076	+	0.205076i	−0.597095	+	0.802171i	$0.703678\pi$
$108$	−5.01910	+	1.34486i	−0.482963	+	0.129410i
$109$			5.00000i			0.478913i	0.970907	+	0.239457i	$0.0769693\pi$
$109$			5.00000i			0.478913i	−0.970907	+	0.239457i	$0.923031\pi$
$110$		0			0
$111$	−3.00000	+	5.19615i	−0.284747	+	0.493197i
$112$	−0.448288	−	1.67303i	−0.0423592	−	0.158087i
$113$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$113$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$114$	−3.46410			−0.324443
$115$		0			0
$116$		−	8.66025i		−	0.804084i
$117$	7.34847	−	7.34847i	0.679366	−	0.679366i
$118$	−4.89898	−	4.89898i	−0.450988	−	0.450988i
$119$	5.19615	+	9.00000i	0.476331	+	0.825029i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	12.5570	−	3.36465i	1.13686	−	0.304621i
$123$	14.4889	+	3.88229i	1.30642	+	0.350054i
$124$	8.66025	−	5.00000i	0.777714	−	0.449013i
$125$		0			0
$126$			5.19615i			0.462910i
$127$	3.67423	−	3.67423i	0.326036	−	0.326036i	−0.525041	−	0.851077i	$-0.675950\pi$
$127$	3.67423	−	3.67423i	0.326036	−	0.326036i	0.851077	+	0.525041i	$0.175950\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$			18.0000i			1.58481i
$130$		0			0
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	0.214438	−	0.976738i	$-0.431208\pi$
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	−0.738661	+	0.674078i	$0.764541\pi$
$132$	−5.79555	+	1.55291i	−0.504438	+	0.135164i
$133$	−0.896575	+	3.34607i	−0.0777430	+	0.290141i
$134$	12.1244			1.04738
$135$		0			0
$136$	6.00000			0.514496
$137$	−3.10583	+	11.5911i	−0.265349	+	0.990295i	0.696688	+	0.717375i	$0.254656\pi$
$137$	−3.10583	+	11.5911i	−0.265349	+	0.990295i	−0.962037	+	0.272921i	$0.912010\pi$
$138$	−5.01910	+	1.34486i	−0.427254	+	0.114482i
$139$	−3.46410	−	2.00000i	−0.293821	−	0.169638i	0.345843	−	0.938293i	$-0.387593\pi$
$139$	−3.46410	−	2.00000i	−0.293821	−	0.169638i	−0.639664	+	0.768655i	$0.720926\pi$
$140$		0			0
$141$		−	5.19615i		−	0.437595i
$142$	−3.34607	−	0.896575i	−0.280796	−	0.0752389i
$143$	8.48528	−	8.48528i	0.709575	−	0.709575i
$144$	2.59808	+	1.50000i	0.216506	+	0.125000i
$145$		0			0
$146$	−12.0000	+	6.92820i	−0.993127	+	0.573382i
$147$	−6.69213	−	1.79315i	−0.551958	−	0.147897i
$148$	3.34607	−	0.896575i	0.275045	−	0.0736980i
$149$	−2.59808	+	4.50000i	−0.212843	+	0.368654i	−0.952603	−	0.304216i	$-0.901606\pi$
$149$	−2.59808	+	4.50000i	−0.212843	+	0.368654i	0.739760	+	0.672870i	$0.234939\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	1.41421	+	1.41421i	0.114708	+	0.114708i
$153$	−17.3867	−	4.65874i	−1.40563	−	0.376637i
$154$			6.00000i			0.483494i
$155$		0			0
$156$	−6.00000			−0.480384
$157$	5.37945	+	20.0764i	0.429327	+	1.60227i	0.754288	+	0.656543i	$0.227982\pi$
$157$	5.37945	+	20.0764i	0.429327	+	1.60227i	−0.324961	+	0.945727i	$0.605351\pi$
$158$	1.03528	+	3.86370i	0.0823622	+	0.307380i
$159$		0			0
$160$		0			0
$161$			5.19615i			0.409514i
$162$	−6.36396	−	6.36396i	−0.500000	−	0.500000i
$163$	−12.2474	−	12.2474i	−0.959294	−	0.959294i	0.0399091	−	0.999203i	$-0.487293\pi$
$163$	−12.2474	−	12.2474i	−0.959294	−	0.959294i	−0.999203	+	0.0399091i	$0.987293\pi$
$164$	−4.33013	−	7.50000i	−0.338126	−	0.585652i
$165$		0			0
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	−8.69333	+	2.32937i	−0.672710	+	0.180252i	−0.578975	−	0.815345i	$-0.696547\pi$
$167$	−8.69333	+	2.32937i	−0.672710	+	0.180252i	−0.0937349	+	0.995597i	$0.529881\pi$
$168$	2.12132	−	2.12132i	0.163663	−	0.163663i
$169$	−0.866025	+	0.500000i	−0.0666173	+	0.0384615i
$170$		0			0
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	7.34847	−	7.34847i	0.560316	−	0.560316i
$173$	23.1822	+	6.21166i	1.76251	+	0.472264i	0.987223	−	0.159344i	$-0.0509379\pi$
$173$	23.1822	+	6.21166i	1.76251	+	0.472264i	0.775288	+	0.631607i	$0.217605\pi$
$174$	12.9904	−	7.50000i	0.984798	−	0.568574i
$175$		0			0
$176$	3.00000	+	1.73205i	0.226134	+	0.130558i
$177$	3.10583	−	11.5911i	0.233448	−	0.871241i
$178$	−0.448288	+	1.67303i	−0.0336006	+	0.125399i
$179$	−24.2487			−1.81243			−0.906217	−	0.422813i	$-0.861043\pi$
$179$	−24.2487			−1.81243			−0.906217	+	0.422813i	$0.861043\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	−1.55291	+	5.79555i	−0.115110	+	0.429595i
$183$	15.9217	+	15.9217i	1.17696	+	1.17696i
$184$	2.59808	+	1.50000i	0.191533	+	0.110581i
$185$		0			0
$186$	15.0000	+	8.66025i	1.09985	+	0.635001i
$187$	−20.0764	−	5.37945i	−1.46813	−	0.393385i
$188$	−2.12132	+	2.12132i	−0.154713	+	0.154713i
$189$	−7.79423	+	4.50000i	−0.566947	+	0.327327i
$190$		0			0
$191$	−15.0000	+	8.66025i	−1.08536	+	0.626634i	−0.932338	−	0.361588i	$-0.882235\pi$
$191$	−15.0000	+	8.66025i	−1.08536	+	0.626634i	−0.153024	+	0.988222i	$0.548901\pi$
$192$	−0.448288	−	1.67303i	−0.0323524	−	0.120741i
$193$	16.7303	−	4.48288i	1.20428	−	0.322685i	0.399762	−	0.916619i	$-0.369093\pi$
$193$	16.7303	−	4.48288i	1.20428	−	0.322685i	0.804513	+	0.593934i	$0.202426\pi$
$194$	3.46410	−	6.00000i	0.248708	−	0.430775i
$195$		0			0
$196$	2.00000	+	3.46410i	0.142857	+	0.247436i
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	0.336966	−	0.941517i	$-0.390599\pi$
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	−0.941517	+	0.336966i	$0.890599\pi$
$198$	−7.34847	−	7.34847i	−0.522233	−	0.522233i
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$		0			0
$201$	10.5000	+	18.1865i	0.740613	+	1.28278i
$202$	−3.58630	−	13.3843i	−0.252331	−	0.941713i
$203$	−3.88229	−	14.4889i	−0.272483	−	1.01692i
$204$	5.19615	+	9.00000i	0.363803	+	0.630126i
$205$		0			0
$206$			3.46410i			0.241355i
$207$	−6.36396	−	6.36396i	−0.442326	−	0.442326i
$208$	2.44949	+	2.44949i	0.169842	+	0.169842i
$209$	−3.46410	−	6.00000i	−0.239617	−	0.415029i
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$		0			0
$213$	−1.55291	−	5.79555i	−0.106404	−	0.397105i
$214$	2.59808	−	1.50000i	0.177601	−	0.102538i
$215$		0			0
$216$			5.19615i			0.353553i
$217$	12.2474	−	12.2474i	0.831411	−	0.831411i
$218$	4.82963	+	1.29410i	0.327104	+	0.0876472i
$219$	−20.7846	−	12.0000i	−1.40449	−	0.810885i
$220$		0			0
$221$	−18.0000	−	10.3923i	−1.21081	−	0.699062i
$222$	4.24264	+	4.24264i	0.284747	+	0.284747i
$223$	−4.03459	+	15.0573i	−0.270176	+	1.00831i	0.688829	+	0.724923i	$0.258125\pi$
$223$	−4.03459	+	15.0573i	−0.270176	+	1.00831i	−0.959005	+	0.283387i	$0.908542\pi$
$224$	−1.73205			−0.115728
$225$		0			0
$226$		0			0
$227$	6.21166	−	23.1822i	0.412282	−	1.53866i	−0.377936	−	0.925832i	$-0.623366\pi$
$227$	6.21166	−	23.1822i	0.412282	−	1.53866i	0.790218	−	0.612826i	$-0.209967\pi$
$228$	−0.896575	+	3.34607i	−0.0593772	+	0.221599i
$229$	4.33013	+	2.50000i	0.286143	+	0.165205i	0.636201	−	0.771523i	$-0.280505\pi$
$229$	4.33013	+	2.50000i	0.286143	+	0.165205i	−0.350058	+	0.936728i	$0.613838\pi$
$230$		0			0
$231$	−9.00000	+	5.19615i	−0.592157	+	0.341882i
$232$	−8.36516	−	2.24144i	−0.549200	−	0.147158i
$233$	4.24264	−	4.24264i	0.277945	−	0.277945i	−0.554343	−	0.832288i	$-0.687031\pi$
$233$	4.24264	−	4.24264i	0.277945	−	0.277945i	0.832288	+	0.554343i	$0.187031\pi$
$234$	−5.19615	−	9.00000i	−0.339683	−	0.588348i
$235$		0			0
$236$	−6.00000	+	3.46410i	−0.390567	+	0.225494i
$237$	−4.89898	+	4.89898i	−0.318223	+	0.318223i
$238$	10.0382	−	2.68973i	0.650680	−	0.174349i
$239$	10.3923	−	18.0000i	0.672222	−	1.16432i	−0.305050	−	0.952336i	$-0.598673\pi$
$239$	10.3923	−	18.0000i	0.672222	−	1.16432i	0.977273	−	0.211987i	$-0.0679934\pi$
$240$		0			0
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$	−0.707107	−	0.707107i	−0.0454545	−	0.0454545i
$243$	4.03459	−	15.0573i	0.258819	−	0.965926i
$244$		−	13.0000i		−	0.832240i
$245$		0			0
$246$	7.50000	−	12.9904i	0.478183	−	0.828236i
$247$	−1.79315	−	6.69213i	−0.114095	−	0.425810i
$248$	−2.58819	−	9.65926i	−0.164350	−	0.613364i
$249$	−5.19615			−0.329293
$250$		0			0
$251$			10.3923i			0.655956i	0.944685	+	0.327978i	$0.106367\pi$
$251$			10.3923i			0.655956i	−0.944685	+	0.327978i	$0.893633\pi$
$252$	5.01910	+	1.34486i	0.316173	+	0.0847184i
$253$	−7.34847	−	7.34847i	−0.461994	−	0.461994i
$254$	−2.59808	−	4.50000i	−0.163018	−	0.282355i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$257$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$258$	17.3867	+	4.65874i	1.08245	+	0.290041i
$259$	5.19615	−	3.00000i	0.322873	−	0.186411i
$260$		0			0
$261$	22.5000	+	12.9904i	1.39272	+	0.804084i
$262$	−4.89898	+	4.89898i	−0.302660	+	0.302660i
$263$	−23.1822	−	6.21166i	−1.42948	−	0.383027i	−0.540641	−	0.841253i	$-0.681818\pi$
$263$	−23.1822	−	6.21166i	−1.42948	−	0.383027i	−0.888836	+	0.458226i	$0.848485\pi$
$264$			6.00000i			0.369274i
$265$		0			0
$266$	3.00000	+	1.73205i	0.183942	+	0.106199i
$267$	−2.89778	+	0.776457i	−0.177341	+	0.0475184i
$268$	3.13801	−	11.7112i	0.191685	−	0.715377i
$269$	−1.73205			−0.105605			−0.0528025	−	0.998605i	$-0.516815\pi$
$269$	−1.73205			−0.105605			−0.0528025	+	0.998605i	$0.516815\pi$
$270$		0			0
$271$	−10.0000			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$272$	1.55291	−	5.79555i	0.0941593	−	0.351407i
$273$	−10.0382	+	2.68973i	−0.607539	+	0.162790i
$274$	10.3923	+	6.00000i	0.627822	+	0.362473i
$275$		0			0
$276$			5.19615i			0.312772i
$277$	−10.0382	−	2.68973i	−0.603137	−	0.161610i	−0.0556866	−	0.998448i	$-0.517735\pi$
$277$	−10.0382	−	2.68973i	−0.603137	−	0.161610i	−0.547450	+	0.836838i	$0.684401\pi$
$278$	−2.82843	+	2.82843i	−0.169638	+	0.169638i
$279$			30.0000i			1.79605i
$280$		0			0
$281$	4.50000	−	2.59808i	0.268447	−	0.154988i	−0.359734	−	0.933055i	$-0.617133\pi$
$281$	4.50000	−	2.59808i	0.268447	−	0.154988i	0.628182	+	0.778067i	$0.283799\pi$
$282$	−5.01910	−	1.34486i	−0.298883	−	0.0800854i
$283$	5.01910	−	1.34486i	0.298354	−	0.0799438i	−0.106537	−	0.994309i	$-0.533976\pi$
$283$	5.01910	−	1.34486i	0.298354	−	0.0799438i	0.404891	+	0.914365i	$0.367309\pi$
$284$	−1.73205	+	3.00000i	−0.102778	+	0.178017i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$	−10.6066	−	10.6066i	−0.626088	−	0.626088i
$288$	2.12132	−	2.12132i	0.125000	−	0.125000i
$289$			19.0000i			1.11765i
$290$		0			0
$291$	12.0000			0.703452
$292$	3.58630	+	13.3843i	0.209872	+	0.783255i
$293$	7.76457	+	28.9778i	0.453611	+	1.69290i	0.692139	+	0.721764i	$0.256668\pi$
$293$	7.76457	+	28.9778i	0.453611	+	1.69290i	−0.238528	+	0.971136i	$0.576665\pi$
$294$	−3.46410	+	6.00000i	−0.202031	+	0.349927i
$295$		0			0
$296$		−	3.46410i		−	0.201347i
$297$	4.65874	−	17.3867i	0.270328	−	1.00888i
$298$	3.67423	+	3.67423i	0.212843	+	0.212843i
$299$	−5.19615	−	9.00000i	−0.300501	−	0.520483i
$300$		0			0
$301$	9.00000	−	15.5885i	0.518751	−	0.898504i
$302$	−9.65926	+	2.58819i	−0.555828	+	0.148934i
$303$	16.9706	−	16.9706i	0.974933	−	0.974933i
$304$	1.73205	−	1.00000i	0.0993399	−	0.0573539i
$305$		0			0
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	−3.67423	+	3.67423i	−0.209700	+	0.209700i	−0.804140	−	0.594440i	$-0.797374\pi$
$307$	−3.67423	+	3.67423i	−0.209700	+	0.209700i	0.594440	+	0.804140i	$0.297374\pi$
$308$	5.79555	+	1.55291i	0.330232	+	0.0884855i
$309$	−5.19615	+	3.00000i	−0.295599	+	0.170664i
$310$		0			0
$311$	−21.0000	−	12.1244i	−1.19080	−	0.687509i	−0.232313	−	0.972641i	$-0.574629\pi$
$311$	−21.0000	−	12.1244i	−1.19080	−	0.687509i	−0.958488	+	0.285132i	$0.907963\pi$
$312$	−1.55291	+	5.79555i	−0.0879165	+	0.328109i
$313$	0.896575	−	3.34607i	0.0506774	−	0.189131i	−0.935947	−	0.352141i	$-0.885454\pi$
$313$	0.896575	−	3.34607i	0.0506774	−	0.189131i	0.986624	+	0.163010i	$0.0521204\pi$
$314$	20.7846			1.17294
$315$		0			0
$316$	4.00000			0.225018
$317$	−1.55291	+	5.79555i	−0.0872204	+	0.325511i	−0.995725	−	0.0923631i	$-0.970558\pi$
$317$	−1.55291	+	5.79555i	−0.0872204	+	0.325511i	0.908505	+	0.417874i	$0.137225\pi$
$318$		0			0
$319$	25.9808	+	15.0000i	1.45464	+	0.839839i
$320$		0			0
$321$	4.50000	+	2.59808i	0.251166	+	0.145010i
$322$	5.01910	+	1.34486i	0.279703	+	0.0749463i
$323$	−8.48528	+	8.48528i	−0.472134	+	0.472134i
$324$	−7.79423	+	4.50000i	−0.433013	+	0.250000i
$325$		0			0
$326$	−15.0000	+	8.66025i	−0.830773	+	0.479647i
$327$	2.24144	+	8.36516i	0.123952	+	0.462595i
$328$	−8.36516	+	2.24144i	−0.461889	+	0.123763i
$329$	−2.59808	+	4.50000i	−0.143237	+	0.248093i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	2.12132	+	2.12132i	0.116423	+	0.116423i
$333$	−2.68973	+	10.0382i	−0.147396	+	0.550090i
$334$			9.00000i			0.492458i
$335$		0			0
$336$	−1.50000	−	2.59808i	−0.0818317	−	0.141737i
$337$	3.58630	+	13.3843i	0.195358	+	0.729087i	0.992174	+	0.124864i	$0.0398496\pi$
$337$	3.58630	+	13.3843i	0.195358	+	0.729087i	−0.796815	+	0.604223i	$0.793484\pi$
$338$	0.258819	+	0.965926i	0.0140779	+	0.0525394i
$339$		0			0
$340$		0			0
$341$			34.6410i			1.87592i
$342$	−5.79555	+	1.55291i	−0.313388	+	0.0839720i
$343$	13.4722	+	13.4722i	0.727430	+	0.727430i
$344$	−5.19615	−	9.00000i	−0.280158	−	0.485247i
$345$		0			0
$346$	12.0000	−	20.7846i	0.645124	−	1.11739i
$347$	11.5911	−	3.10583i	0.622243	−	0.166730i	0.0660960	−	0.997813i	$-0.478946\pi$
$347$	11.5911	−	3.10583i	0.622243	−	0.166730i	0.556147	+	0.831084i	$0.312279\pi$
$348$	−3.88229	−	14.4889i	−0.208112	−	0.776686i
$349$	0.866025	−	0.500000i	0.0463573	−	0.0267644i	−0.476642	−	0.879097i	$-0.658146\pi$
$349$	0.866025	−	0.500000i	0.0463573	−	0.0267644i	0.523000	+	0.852333i	$0.324813\pi$
$350$		0			0
$351$	9.00000	−	15.5885i	0.480384	−	0.832050i
$352$	2.44949	−	2.44949i	0.130558	−	0.130558i
$353$	−23.1822	−	6.21166i	−1.23387	−	0.330613i	−0.417782	−	0.908547i	$-0.637192\pi$
$353$	−23.1822	−	6.21166i	−1.23387	−	0.330613i	−0.816083	+	0.577934i	$0.803859\pi$
$354$	−10.3923	−	6.00000i	−0.552345	−	0.318896i
$355$		0			0
$356$	1.50000	+	0.866025i	0.0794998	+	0.0458993i
$357$	12.7279	+	12.7279i	0.673633	+	0.673633i
$358$	−6.27603	+	23.4225i	−0.331698	+	1.23792i
$359$	17.3205			0.914141			0.457071	−	0.889430i	$-0.348899\pi$
$359$	17.3205			0.914141			0.457071	+	0.889430i	$0.348899\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	1.81173	−	6.76148i	0.0952226	−	0.355376i
$363$	0.448288	−	1.67303i	0.0235290	−	0.0878114i
$364$	5.19615	+	3.00000i	0.272352	+	0.157243i
$365$		0			0
$366$	19.5000	−	11.2583i	1.01928	−	0.588482i
$367$	−3.34607	−	0.896575i	−0.174663	−	0.0468009i	0.170427	−	0.985370i	$-0.445485\pi$
$367$	−3.34607	−	0.896575i	−0.174663	−	0.0468009i	−0.345091	+	0.938569i	$0.612152\pi$
$368$	2.12132	−	2.12132i	0.110581	−	0.110581i
$369$	25.9808			1.35250
$370$		0			0
$371$		0			0
$372$	12.2474	−	12.2474i	0.635001	−	0.635001i
$373$	13.3843	−	3.58630i	0.693011	−	0.185692i	0.104913	−	0.994481i	$-0.466544\pi$
$373$	13.3843	−	3.58630i	0.693011	−	0.185692i	0.588098	+	0.808790i	$0.299877\pi$
$374$	−10.3923	+	18.0000i	−0.537373	+	0.930758i
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$	21.2132	+	21.2132i	1.09254	+	1.09254i
$378$	2.32937	+	8.69333i	0.119810	+	0.447137i
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$	4.50000	−	7.79423i	0.230542	−	0.399310i
$382$	4.48288	+	16.7303i	0.229364	+	0.855998i
$383$	−6.21166	−	23.1822i	−0.317401	−	1.18456i	−0.921733	−	0.387824i	$-0.873227\pi$
$383$	−6.21166	−	23.1822i	−0.317401	−	1.18456i	0.604333	−	0.796732i	$-0.293440\pi$
$384$	−1.73205			−0.0883883
$385$		0			0
$386$		−	17.3205i		−	0.881591i
$387$	8.06918	+	30.1146i	0.410179	+	1.53081i
$388$	−4.89898	−	4.89898i	−0.248708	−	0.248708i
$389$	−12.9904	−	22.5000i	−0.658638	−	1.14080i	−0.980968	−	0.194168i	$-0.937799\pi$
$389$	−12.9904	−	22.5000i	−0.658638	−	1.14080i	0.322330	−	0.946627i	$-0.395534\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	3.86370	−	1.03528i	0.195146	−	0.0522893i
$393$	−11.5911	−	3.10583i	−0.584694	−	0.156668i
$394$	−10.3923	+	6.00000i	−0.523557	+	0.302276i
$395$		0			0
$396$	−9.00000	+	5.19615i	−0.452267	+	0.261116i
$397$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$397$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$398$	−9.65926	−	2.58819i	−0.484175	−	0.129734i
$399$			6.00000i			0.300376i
$400$		0			0
$401$	−18.0000	−	10.3923i	−0.898877	−	0.518967i	−0.0220414	−	0.999757i	$-0.507017\pi$
$401$	−18.0000	−	10.3923i	−0.898877	−	0.518967i	−0.876836	+	0.480790i	$0.840350\pi$
$402$	20.2844	−	5.43520i	1.01170	−	0.271083i
$403$	−8.96575	+	33.4607i	−0.446616	+	1.66679i
$404$	−13.8564			−0.689382
$405$		0			0
$406$	−15.0000			−0.744438
$407$	−3.10583	+	11.5911i	−0.153950	+	0.574550i
$408$	10.0382	−	2.68973i	0.496965	−	0.133161i
$409$	1.73205	+	1.00000i	0.0856444	+	0.0494468i	0.542211	−	0.840243i	$-0.317588\pi$
$409$	1.73205	+	1.00000i	0.0856444	+	0.0494468i	−0.456566	+	0.889689i	$0.650921\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$	3.34607	+	0.896575i	0.164849	+	0.0441711i
$413$	−8.48528	+	8.48528i	−0.417533	+	0.417533i
$414$	−7.79423	+	4.50000i	−0.383065	+	0.221163i
$415$		0			0
$416$	3.00000	−	1.73205i	0.147087	−	0.0849208i
$417$	−6.69213	−	1.79315i	−0.327715	−	0.0878110i
$418$	−6.69213	+	1.79315i	−0.327323	+	0.0877059i
$419$	5.19615	−	9.00000i	0.253849	−	0.439679i	−0.710734	−	0.703461i	$-0.751637\pi$
$419$	5.19615	−	9.00000i	0.253849	−	0.439679i	0.964582	+	0.263783i	$0.0849701\pi$
$420$		0			0
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	0.718076	−	0.695965i	$-0.245023\pi$
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	−0.961761	+	0.273890i	$0.911690\pi$
$422$	−15.5563	−	15.5563i	−0.757271	−	0.757271i
$423$	−2.32937	−	8.69333i	−0.113258	−	0.422684i
$424$		0			0
$425$		0			0
$426$	−6.00000			−0.290701
$427$	−5.82774	−	21.7494i	−0.282024	−	1.05253i
$428$	−0.776457	−	2.89778i	−0.0375315	−	0.140069i
$429$	10.3923	−	18.0000i	0.501745	−	0.869048i
$430$		0			0
$431$			6.92820i			0.333720i	0.985981	+	0.166860i	$0.0533628\pi$
$431$			6.92820i			0.333720i	−0.985981	+	0.166860i	$0.946637\pi$
$432$	5.01910	+	1.34486i	0.241481	+	0.0647048i
$433$	7.34847	+	7.34847i	0.353145	+	0.353145i	0.861278	−	0.508133i	$-0.169664\pi$
$433$	7.34847	+	7.34847i	0.353145	+	0.353145i	−0.508133	+	0.861278i	$0.669664\pi$
$434$	−8.66025	−	15.0000i	−0.415705	−	0.720023i
$435$		0			0
$436$	2.50000	−	4.33013i	0.119728	−	0.207375i
$437$	−5.79555	+	1.55291i	−0.277239	+	0.0742860i
$438$	−16.9706	+	16.9706i	−0.810885	+	0.810885i
$439$	17.3205	−	10.0000i	0.826663	−	0.477274i	−0.0260459	−	0.999661i	$-0.508292\pi$
$439$	17.3205	−	10.0000i	0.826663	−	0.477274i	0.852709	+	0.522387i	$0.174958\pi$
$440$		0			0
$441$	−12.0000			−0.571429
$442$	−14.6969	+	14.6969i	−0.699062	+	0.699062i
$443$	8.69333	+	2.32937i	0.413033	+	0.110672i	0.459351	−	0.888255i	$-0.348082\pi$
$443$	8.69333	+	2.32937i	0.413033	+	0.110672i	−0.0463181	+	0.998927i	$0.514749\pi$
$444$	5.19615	−	3.00000i	0.246598	−	0.142374i
$445$		0			0
$446$	13.5000	+	7.79423i	0.639244	+	0.369067i
$447$	−2.32937	+	8.69333i	−0.110175	+	0.411181i
$448$	−0.448288	+	1.67303i	−0.0211796	+	0.0790434i
$449$	13.8564			0.653924			0.326962	−	0.945037i	$-0.393975\pi$
$449$	13.8564			0.653924			0.326962	+	0.945037i	$0.393975\pi$
$450$		0			0
$451$	30.0000			1.41264
$452$		0			0
$453$	−12.2474	−	12.2474i	−0.575435	−	0.575435i
$454$	−20.7846	−	12.0000i	−0.975470	−	0.563188i
$455$		0			0
$456$	3.00000	+	1.73205i	0.140488	+	0.0811107i
$457$	30.1146	+	8.06918i	1.40870	+	0.377460i	0.881461	−	0.472256i	$-0.156560\pi$
$457$	30.1146	+	8.06918i	1.40870	+	0.377460i	0.527240	+	0.849717i	$0.323227\pi$
$458$	3.53553	−	3.53553i	0.165205	−	0.165205i
$459$	−31.1769			−1.45521
$460$		0			0
$461$	10.5000	−	6.06218i	0.489034	−	0.282344i	−0.235140	−	0.971962i	$-0.575555\pi$
$461$	10.5000	−	6.06218i	0.489034	−	0.282344i	0.724174	+	0.689618i	$0.242221\pi$
$462$	2.68973	+	10.0382i	0.125137	+	0.467019i
$463$	−16.7303	+	4.48288i	−0.777524	+	0.208337i	−0.625693	−	0.780069i	$-0.715184\pi$
$463$	−16.7303	+	4.48288i	−0.777524	+	0.208337i	−0.151831	+	0.988406i	$0.548517\pi$
$464$	−4.33013	+	7.50000i	−0.201021	+	0.348179i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.980264	+	0.197692i	$0.0633445\pi$
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.197692	+	0.980264i	$0.436655\pi$
$468$	−10.0382	+	2.68973i	−0.464016	+	0.124333i
$469$		−	21.0000i		−	0.969690i
$470$		0			0
$471$	18.0000	+	31.1769i	0.829396	+	1.43656i
$472$	1.79315	+	6.69213i	0.0825365	+	0.308030i
$473$	9.31749	+	34.7733i	0.428418	+	1.59888i
$474$	3.46410	+	6.00000i	0.159111	+	0.275589i
$475$		0			0
$476$		−	10.3923i		−	0.476331i
$477$		0			0
$478$	−14.6969	−	14.6969i	−0.672222	−	0.672222i
$479$	13.8564	+	24.0000i	0.633115	+	1.09659i	0.986911	+	0.161265i	$0.0515575\pi$
$479$	13.8564	+	24.0000i	0.633115	+	1.09659i	−0.353796	+	0.935323i	$0.615109\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	−16.4207	+	4.39992i	−0.747944	+	0.200411i
$483$	2.32937	+	8.69333i	0.105990	+	0.395560i
$484$	−0.866025	+	0.500000i	−0.0393648	+	0.0227273i
$485$		0			0
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−17.1464	+	17.1464i	−0.776979	+	0.776979i	−0.979316	−	0.202337i	$-0.935146\pi$
$487$	−17.1464	+	17.1464i	−0.776979	+	0.776979i	0.202337	+	0.979316i	$0.435146\pi$
$488$	−12.5570	−	3.36465i	−0.568430	−	0.152310i
$489$	−25.9808	−	15.0000i	−1.17489	−	0.678323i
$490$		0			0
$491$	12.0000	+	6.92820i	0.541552	+	0.312665i	0.745708	−	0.666273i	$-0.232111\pi$
$491$	12.0000	+	6.92820i	0.541552	+	0.312665i	−0.204155	+	0.978938i	$0.565445\pi$
$492$	−10.6066	−	10.6066i	−0.478183	−	0.478183i
$493$	13.4486	−	50.1910i	0.605696	−	2.26049i
$494$	−6.92820			−0.311715
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−1.55291	+	5.79555i	−0.0696577	+	0.259966i
$498$	−1.34486	+	5.01910i	−0.0602648	+	0.224911i
$499$	−38.1051	−	22.0000i	−1.70582	−	0.984855i	−0.939599	−	0.342277i	$-0.888802\pi$
$499$	−38.1051	−	22.0000i	−1.70582	−	0.984855i	−0.766220	−	0.642578i	$-0.777865\pi$
$500$		0			0
$501$	−13.5000	+	7.79423i	−0.603136	+	0.348220i
$502$	10.0382	+	2.68973i	0.448027	+	0.120048i
$503$	−6.36396	+	6.36396i	−0.283755	+	0.283755i	−0.834605	−	0.550850i	$-0.814304\pi$
$503$	−6.36396	+	6.36396i	−0.283755	+	0.283755i	0.550850	+	0.834605i	$0.314304\pi$
$504$	2.59808	−	4.50000i	0.115728	−	0.200446i
$505$		0			0
$506$	−9.00000	+	5.19615i	−0.400099	+	0.230997i
$507$	−1.22474	+	1.22474i	−0.0543928	+	0.0543928i
$508$	−5.01910	+	1.34486i	−0.222686	+	0.0596687i
$509$	−2.59808	+	4.50000i	−0.115158	+	0.199459i	−0.917843	−	0.396944i	$-0.870071\pi$
$509$	−2.59808	+	4.50000i	−0.115158	+	0.199459i	0.802685	+	0.596403i	$0.203404\pi$
$510$		0			0
$511$	12.0000	+	20.7846i	0.530849	+	0.919457i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−7.34847	−	7.34847i	−0.324443	−	0.324443i
$514$		0			0
$515$		0			0
$516$	9.00000	−	15.5885i	0.396203	−	0.686244i
$517$	−2.68973	−	10.0382i	−0.118294	−	0.441479i
$518$	−1.55291	−	5.79555i	−0.0682311	−	0.254642i
$519$	41.5692			1.82469
$520$		0			0
$521$			5.19615i			0.227648i	0.993501	+	0.113824i	$0.0363099\pi$
$521$			5.19615i			0.227648i	−0.993501	+	0.113824i	$0.963690\pi$
$522$	18.3712	−	18.3712i	0.804084	−	0.804084i
$523$	8.57321	+	8.57321i	0.374880	+	0.374880i	0.869251	−	0.494371i	$-0.164601\pi$
$523$	8.57321	+	8.57321i	0.374880	+	0.374880i	−0.494371	+	0.869251i	$0.664601\pi$
$524$	3.46410	+	6.00000i	0.151330	+	0.262111i
$525$		0			0
$526$	−12.0000	+	20.7846i	−0.523225	+	0.906252i
$527$	57.9555	−	15.5291i	2.52458	−	0.676460i
$528$	5.79555	+	1.55291i	0.252219	+	0.0675819i
$529$	12.1244	−	7.00000i	0.527146	−	0.304348i
$530$		0			0
$531$		−	20.7846i		−	0.901975i
$532$	2.44949	−	2.44949i	0.106199	−	0.106199i
$533$	28.9778	+	7.76457i	1.25517	+	0.336321i
$534$			3.00000i			0.129823i
$535$		0			0
$536$	−10.5000	−	6.06218i	−0.453531	−	0.261846i
$537$	−40.5689	+	10.8704i	−1.75068	+	0.469092i
$538$	−0.448288	+	1.67303i	−0.0193271	+	0.0721296i
$539$	−13.8564			−0.596838
$540$		0			0
$541$	−43.0000			−1.84871			−0.924357	−	0.381528i	$-0.875398\pi$
$541$	−43.0000			−1.84871			−0.924357	+	0.381528i	$0.875398\pi$
$542$	−2.58819	+	9.65926i	−0.111172	+	0.414901i
$543$	11.7112	−	3.13801i	0.502577	−	0.134665i
$544$	−5.19615	−	3.00000i	−0.222783	−	0.128624i
$545$		0			0
$546$			10.3923i			0.444750i
$547$	1.67303	+	0.448288i	0.0715337	+	0.0191674i	0.294408	−	0.955680i	$-0.404877\pi$
$547$	1.67303	+	0.448288i	0.0715337	+	0.0191674i	−0.222875	+	0.974847i	$0.571544\pi$
$548$	8.48528	−	8.48528i	0.362473	−	0.362473i
$549$	33.7750	+	19.5000i	1.44148	+	0.832240i
$550$		0			0
$551$	15.0000	−	8.66025i	0.639021	−	0.368939i
$552$	5.01910	+	1.34486i	0.213627	+	0.0572412i
$553$	6.69213	−	1.79315i	0.284578	−	0.0762525i
$554$	−5.19615	+	9.00000i	−0.220763	+	0.382373i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−25.4558	−	25.4558i	−1.07860	−	1.07860i	−0.996635	−	0.0819634i	$-0.973881\pi$
$557$	−25.4558	−	25.4558i	−1.07860	−	1.07860i	−0.0819634	−	0.996635i	$-0.526119\pi$
$558$	28.9778	+	7.76457i	1.22673	+	0.328701i
$559$			36.0000i			1.52264i
$560$		0			0
$561$	−36.0000			−1.51992
$562$	−1.34486	−	5.01910i	−0.0567296	−	0.211718i
$563$	−5.43520	−	20.2844i	−0.229066	−	0.854887i	−0.980734	−	0.195346i	$-0.937417\pi$
$563$	−5.43520	−	20.2844i	−0.229066	−	0.854887i	0.751668	−	0.659542i	$-0.229250\pi$
$564$	−2.59808	+	4.50000i	−0.109399	+	0.189484i
$565$		0			0
$566$		−	5.19615i		−	0.218411i
$567$	−11.0227	+	11.0227i	−0.462910	+	0.462910i
$568$	2.44949	+	2.44949i	0.102778	+	0.102778i
$569$	3.46410	+	6.00000i	0.145223	+	0.251533i	0.929456	−	0.368933i	$-0.120277\pi$
$569$	3.46410	+	6.00000i	0.145223	+	0.251533i	−0.784233	+	0.620466i	$0.786943\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	−11.5911	+	3.10583i	−0.484649	+	0.129861i
$573$	−21.2132	+	21.2132i	−0.886194	+	0.886194i
$574$	−12.9904	+	7.50000i	−0.542208	+	0.313044i
$575$		0			0
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	24.4949	−	24.4949i	1.01974	−	1.01974i	0.0199346	−	0.999801i	$-0.493654\pi$
$577$	24.4949	−	24.4949i	1.01974	−	1.01974i	0.999801	−	0.0199346i	$-0.00634581\pi$
$578$	18.3526	+	4.91756i	0.763367	+	0.204544i
$579$	25.9808	−	15.0000i	1.07972	−	0.623379i
$580$		0			0
$581$	4.50000	+	2.59808i	0.186691	+	0.107786i
$582$	3.10583	−	11.5911i	0.128741	−	0.480467i
$583$		0			0
$584$	13.8564			0.573382
$585$		0			0
$586$	30.0000			1.23929
$587$	−0.776457	+	2.89778i	−0.0320478	+	0.119604i	−0.980097	−	0.198520i	$-0.936386\pi$
$587$	−0.776457	+	2.89778i	−0.0320478	+	0.119604i	0.948049	+	0.318125i	$0.103053\pi$
$588$	4.89898	+	4.89898i	0.202031	+	0.202031i
$589$	17.3205	+	10.0000i	0.713679	+	0.412043i
$590$		0			0
$591$	−18.0000	−	10.3923i	−0.740421	−	0.427482i
$592$	−3.34607	−	0.896575i	−0.137522	−	0.0368490i
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	−0.918378	−	0.395705i	$-0.870500\pi$
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	0.395705	+	0.918378i	$0.370500\pi$
$594$	−15.5885	−	9.00000i	−0.639602	−	0.369274i
$595$		0			0
$596$	4.50000	−	2.59808i	0.184327	−	0.106421i
$597$	−4.48288	−	16.7303i	−0.183472	−	0.684727i
$598$	−10.0382	+	2.68973i	−0.410492	+	0.109991i
$599$	−13.8564	+	24.0000i	−0.566157	+	0.980613i	0.430784	+	0.902455i	$0.358237\pi$
$599$	−13.8564	+	24.0000i	−0.566157	+	0.980613i	−0.996941	+	0.0781581i	$0.975096\pi$
$600$		0			0
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	0.934780	+	0.355228i	$0.115597\pi$
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	−0.159754	+	0.987157i	$0.551070\pi$
$602$	−12.7279	−	12.7279i	−0.518751	−	0.518751i
$603$	25.7196	+	25.7196i	1.04738	+	1.04738i
$604$			10.0000i			0.406894i
$605$		0			0
$606$	−12.0000	−	20.7846i	−0.487467	−	0.844317i
$607$	−10.3106	−	38.4797i	−0.418495	−	1.56184i	−0.777730	−	0.628598i	$-0.783629\pi$
$607$	−10.3106	−	38.4797i	−0.418495	−	1.56184i	0.359235	−	0.933247i	$-0.383038\pi$
$608$	−0.517638	−	1.93185i	−0.0209930	−	0.0783469i
$609$	−12.9904	−	22.5000i	−0.526397	−	0.911746i
$610$		0			0
$611$		−	10.3923i		−	0.420428i
$612$	12.7279	+	12.7279i	0.514496	+	0.514496i
$613$	−12.2474	−	12.2474i	−0.494670	−	0.494670i	0.415104	−	0.909774i	$-0.363745\pi$
$613$	−12.2474	−	12.2474i	−0.494670	−	0.494670i	−0.909774	+	0.415104i	$0.863745\pi$
$614$	2.59808	+	4.50000i	0.104850	+	0.181605i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	−34.7733	+	9.31749i	−1.39992	+	0.375108i	−0.878317	−	0.478079i	$-0.841333\pi$
$617$	−34.7733	+	9.31749i	−1.39992	+	0.375108i	−0.521605	+	0.853187i	$0.674666\pi$
$618$	1.55291	+	5.79555i	0.0624674	+	0.233131i
$619$	−19.0526	+	11.0000i	−0.765787	+	0.442127i	−0.831370	−	0.555720i	$-0.812443\pi$
$619$	−19.0526	+	11.0000i	−0.765787	+	0.442127i	0.0655827	+	0.997847i	$0.479109\pi$
$620$		0			0
$621$	−13.5000	−	7.79423i	−0.541736	−	0.312772i
$622$	−17.1464	+	17.1464i	−0.687509	+	0.687509i
$623$	2.89778	+	0.776457i	0.116097	+	0.0311081i
$624$	5.19615	+	3.00000i	0.208013	+	0.120096i
$625$		0			0
$626$	−3.00000	−	1.73205i	−0.119904	−	0.0692267i
$627$	−8.48528	−	8.48528i	−0.338869	−	0.338869i
$628$	5.37945	−	20.0764i	0.214664	−	0.801135i
$629$	20.7846			0.828737
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	1.03528	−	3.86370i	0.0411811	−	0.153690i
$633$	9.86233	−	36.8067i	0.391992	−	1.46294i
$634$	5.19615	+	3.00000i	0.206366	+	0.119145i
$635$		0			0
$636$		0			0
$637$	−13.3843	−	3.58630i	−0.530304	−	0.142094i
$638$	21.2132	−	21.2132i	0.839839	−	0.839839i
$639$	−5.19615	−	9.00000i	−0.205557	−	0.356034i
$640$		0			0
$641$	28.5000	−	16.4545i	1.12568	−	0.649913i	0.182837	−	0.983143i	$-0.441472\pi$
$641$	28.5000	−	16.4545i	1.12568	−	0.649913i	0.942845	+	0.333230i	$0.108139\pi$
$642$	3.67423	−	3.67423i	0.145010	−	0.145010i
$643$	−5.01910	+	1.34486i	−0.197934	+	0.0530362i	−0.356424	−	0.934324i	$-0.616004\pi$
$643$	−5.01910	+	1.34486i	−0.197934	+	0.0530362i	0.158490	+	0.987361i	$0.449337\pi$
$644$	2.59808	−	4.50000i	0.102379	−	0.177325i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	14.8492	+	14.8492i	0.583784	+	0.583784i	0.935941	−	0.352157i	$-0.114552\pi$
$647$	14.8492	+	14.8492i	0.583784	+	0.583784i	−0.352157	+	0.935941i	$0.614552\pi$
$648$	2.32937	+	8.69333i	0.0915064	+	0.341506i
$649$		−	24.0000i		−	0.942082i
$650$		0			0
$651$	15.0000	−	25.9808i	0.587896	−	1.01827i
$652$	4.48288	+	16.7303i	0.175563	+	0.655210i
$653$	−4.65874	−	17.3867i	−0.182311	−	0.680393i	−0.995190	−	0.0979610i	$-0.968768\pi$
$653$	−4.65874	−	17.3867i	−0.182311	−	0.680393i	0.812880	−	0.582432i	$-0.197899\pi$
$654$	8.66025			0.338643
$655$		0			0
$656$			8.66025i			0.338126i
$657$	−40.1528	−	10.7589i	−1.56651	−	0.419745i
$658$	3.67423	+	3.67423i	0.143237	+	0.143237i
$659$	10.3923	+	18.0000i	0.404827	+	0.701180i	0.994301	−	0.106606i	$-0.0339985\pi$
$659$	10.3923	+	18.0000i	0.404827	+	0.701180i	−0.589475	+	0.807787i	$0.700665\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−7.72741	+	2.07055i	−0.300334	+	0.0804743i
$663$	−34.7733	−	9.31749i	−1.35048	−	0.361861i
$664$	2.59808	−	1.50000i	0.100825	−	0.0582113i
$665$		0			0
$666$	9.00000	+	5.19615i	0.348743	+	0.201347i
$667$	18.3712	−	18.3712i	0.711335	−	0.711335i
$668$	8.69333	+	2.32937i	0.336355	+	0.0901261i
$669$			27.0000i			1.04388i
$670$		0			0
$671$	39.0000	+	22.5167i	1.50558	+	0.869246i
$672$	−2.89778	+	0.776457i	−0.111784	+	0.0299525i
$673$	9.86233	−	36.8067i	0.380165	−	1.41879i	−0.465485	−	0.885056i	$-0.654120\pi$
$673$	9.86233	−	36.8067i	0.380165	−	1.41879i	0.845649	−	0.533739i	$-0.179213\pi$
$674$	13.8564			0.533729
$675$		0			0
$676$	1.00000			0.0384615
$677$	1.55291	−	5.79555i	0.0596833	−	0.222741i	−0.929642	−	0.368464i	$-0.879884\pi$
$677$	1.55291	−	5.79555i	0.0596833	−	0.222741i	0.989326	+	0.145722i	$0.0465506\pi$
$678$		0			0
$679$	−10.3923	−	6.00000i	−0.398820	−	0.230259i
$680$		0			0
$681$		−	41.5692i		−	1.59294i
$682$	33.4607	+	8.96575i	1.28127	+	0.343316i
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	−0.525879	−	0.850559i	$-0.676264\pi$
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	0.850559	+	0.525879i	$0.176264\pi$
$684$			6.00000i			0.229416i
$685$		0			0
$686$	16.5000	−	9.52628i	0.629973	−	0.363715i
$687$	8.36516	+	2.24144i	0.319151	+	0.0855162i
$688$	−10.0382	+	2.68973i	−0.382703	+	0.102545i
$689$		0			0
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$	−16.9706	−	16.9706i	−0.645124	−	0.645124i
$693$	−12.7279	+	12.7279i	−0.483494	+	0.483494i
$694$		−	12.0000i		−	0.455514i
$695$		0			0
$696$	−15.0000			−0.568574
$697$	−13.4486	−	50.1910i	−0.509403	−	1.90112i
$698$	−0.258819	−	0.965926i	−0.00979645	−	0.0365608i
$699$	5.19615	−	9.00000i	0.196537	−	0.340411i
$700$		0			0
$701$		−	12.1244i		−	0.457931i	−0.973435	−	0.228965i	$-0.926466\pi$
$701$		−	12.1244i		−	0.457931i	0.973435	−	0.228965i	$-0.0735342\pi$
$702$	−12.7279	−	12.7279i	−0.480384	−	0.480384i
$703$	4.89898	+	4.89898i	0.184769	+	0.184769i
$704$	−1.73205	−	3.00000i	−0.0652791	−	0.113067i
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	−23.1822	+	6.21166i	−0.871857	+	0.233613i
$708$	−8.48528	+	8.48528i	−0.318896	+	0.318896i
$709$	−35.5070	+	20.5000i	−1.33349	+	0.769894i	−0.985834	−	0.167727i	$-0.946357\pi$
$709$	−35.5070	+	20.5000i	−1.33349	+	0.769894i	−0.347661	+	0.937620i	$0.613024\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	1.22474	−	1.22474i	0.0458993	−	0.0458993i
$713$	28.9778	+	7.76457i	1.08523	+	0.290785i
$714$	15.5885	−	9.00000i	0.583383	−	0.336817i
$715$		0			0
$716$	21.0000	+	12.1244i	0.784807	+	0.453108i
$717$	9.31749	−	34.7733i	0.347968	−	1.29863i
$718$	4.48288	−	16.7303i	0.167299	−	0.624370i
$719$	−6.92820			−0.258378			−0.129189	−	0.991620i	$-0.541237\pi$
$719$	−6.92820			−0.258378			−0.129189	+	0.991620i	$0.541237\pi$
$720$		0			0
$721$	6.00000			0.223452
$722$	3.88229	−	14.4889i	0.144484	−	0.539221i
$723$	−20.8207	−	20.8207i	−0.774329	−	0.774329i
$724$	−6.06218	−	3.50000i	−0.225299	−	0.130076i
$725$		0			0
$726$	−1.50000	−	0.866025i	−0.0556702	−	0.0321412i
$727$	−5.01910	−	1.34486i	−0.186148	−	0.0498782i	0.164541	−	0.986370i	$-0.447386\pi$
$727$	−5.01910	−	1.34486i	−0.186148	−	0.0498782i	−0.350689	+	0.936492i	$0.614052\pi$
$728$	4.24264	−	4.24264i	0.157243	−	0.157243i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	54.0000	−	31.1769i	1.99726	−	1.15312i
$732$	−5.82774	−	21.7494i	−0.215399	−	0.803882i
$733$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$733$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$734$	−1.73205	+	3.00000i	−0.0639312	+	0.110732i
$735$		0			0
$736$	−1.50000	−	2.59808i	−0.0552907	−	0.0957664i
$737$	29.6985	+	29.6985i	1.09396	+	1.09396i
$738$	6.72432	−	25.0955i	0.247525	−	0.923778i
$739$			4.00000i			0.147142i	0.997290	+	0.0735712i	$0.0234396\pi$
$739$			4.00000i			0.147142i	−0.997290	+	0.0735712i	$0.976560\pi$
$740$		0			0
$741$	−6.00000	−	10.3923i	−0.220416	−	0.381771i
$742$		0			0
$743$	6.98811	+	26.0800i	0.256369	+	0.956782i	0.967324	+	0.253544i	$0.0815964\pi$
$743$	6.98811	+	26.0800i	0.256369	+	0.956782i	−0.710955	+	0.703238i	$0.751737\pi$
$744$	−8.66025	−	15.0000i	−0.317500	−	0.549927i
$745$		0			0
$746$		−	13.8564i		−	0.507319i
$747$	−8.69333	+	2.32937i	−0.318072	+	0.0852272i
$748$	14.6969	+	14.6969i	0.537373	+	0.537373i
$749$	−2.59808	−	4.50000i	−0.0949316	−	0.164426i
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$	2.89778	−	0.776457i	0.105671	−	0.0283145i
$753$	4.65874	+	17.3867i	0.169774	+	0.633605i
$754$	25.9808	−	15.0000i	0.946164	−	0.546268i
$755$		0			0
$756$	9.00000			0.327327
$757$	−31.8434	+	31.8434i	−1.15737	+	1.15737i	−0.172327	+	0.985040i	$0.555129\pi$
$757$	−31.8434	+	31.8434i	−1.15737	+	1.15737i	−0.985040	+	0.172327i	$0.944871\pi$
$758$	−7.72741	−	2.07055i	−0.280672	−	0.0752058i
$759$	−15.5885	−	9.00000i	−0.565825	−	0.326679i
$760$		0			0
$761$	−34.5000	−	19.9186i	−1.25062	−	0.722048i	−0.279391	−	0.960178i	$-0.590132\pi$
$761$	−34.5000	−	19.9186i	−1.25062	−	0.722048i	−0.971233	+	0.238129i	$0.923466\pi$
$762$	−6.36396	−	6.36396i	−0.230542	−	0.230542i
$763$	2.24144	−	8.36516i	0.0811455	−	0.302839i
$764$	17.3205			0.626634
$765$		0			0
$766$	−24.0000			−0.867155
$767$	6.21166	−	23.1822i	0.224290	−	0.837061i
$768$	−0.448288	+	1.67303i	−0.0161762	+	0.0603704i
$769$	−19.9186	−	11.5000i	−0.718283	−	0.414701i	0.0958377	−	0.995397i	$-0.469447\pi$
$769$	−19.9186	−	11.5000i	−0.718283	−	0.414701i	−0.814120	+	0.580696i	$0.802780\pi$
$770$		0			0
$771$		0			0
$772$	−16.7303	−	4.48288i	−0.602138	−	0.161342i
$773$	25.4558	−	25.4558i	0.915583	−	0.915583i	−0.0811212	−	0.996704i	$-0.525850\pi$
$773$	25.4558	−	25.4558i	0.915583	−	0.915583i	0.996704	+	0.0811212i	$0.0258501\pi$
$774$	31.1769			1.12063
$775$		0			0
$776$	−6.00000	+	3.46410i	−0.215387	+	0.124354i
$777$	7.34847	−	7.34847i	0.263625	−	0.263625i
$778$	−25.0955	+	6.72432i	−0.899717	+	0.241078i
$779$	8.66025	−	15.0000i	0.310286	−	0.537431i
$780$		0			0
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$	12.7279	+	12.7279i	0.455150	+	0.455150i
$783$	43.4667	+	11.6469i	1.55337	+	0.416225i
$784$		−	4.00000i		−	0.142857i
$785$		0			0
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$	−0.896575	−	3.34607i	−0.0319595	−	0.119274i	0.948103	−	0.317962i	$-0.102999\pi$
$787$	−0.896575	−	3.34607i	−0.0319595	−	0.119274i	−0.980063	+	0.198688i	$0.936332\pi$
$788$	3.10583	+	11.5911i	0.110641	+	0.412916i
$789$	−41.5692			−1.47990
$790$		0			0
$791$		0			0
$792$	2.68973	+	10.0382i	0.0955753	+	0.356692i
$793$	31.8434	+	31.8434i	1.13079	+	1.13079i
$794$		0			0
$795$		0			0
$796$	−5.00000	+	8.66025i	−0.177220	+	0.306955i
$797$	40.5689	−	10.8704i	1.43702	−	0.385049i	0.545533	−	0.838089i	$-0.316327\pi$
$797$	40.5689	−	10.8704i	1.43702	−	0.385049i	0.891490	+	0.453040i	$0.149660\pi$
$798$	5.79555	+	1.55291i	0.205160	+	0.0549726i
$799$	−15.5885	+	9.00000i	−0.551480	+	0.318397i
$800$		0			0
$801$	−4.50000	+	2.59808i	−0.159000	+	0.0917985i
$802$	−14.6969	+	14.6969i	−0.518967	+	0.518967i
$803$	−46.3644	−	12.4233i	−1.63617	−	0.438409i
$804$		−	21.0000i		−	0.740613i
$805$		0			0
$806$	30.0000	+	17.3205i	1.05670	+	0.610089i
$807$	−2.89778	+	0.776457i	−0.102007	+	0.0273326i
$808$	−3.58630	+	13.3843i	−0.126166	+	0.470857i
$809$	6.92820			0.243583			0.121791	−	0.992556i	$-0.461136\pi$
$809$	6.92820			0.243583			0.121791	+	0.992556i	$0.461136\pi$
$810$		0			0
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$	−3.88229	+	14.4889i	−0.136242	+	0.508460i
$813$	−16.7303	+	4.48288i	−0.586758	+	0.157221i
$814$	10.3923	+	6.00000i	0.364250	+	0.210300i
$815$		0			0
$816$		−	10.3923i		−	0.363803i
$817$	20.0764	+	5.37945i	0.702384	+	0.188203i
$818$	1.41421	−	1.41421i	0.0494468	−	0.0494468i
$819$	−15.5885	+	9.00000i	−0.544705	+	0.314485i
$820$		0			0
$821$	−16.5000	+	9.52628i	−0.575854	+	0.332469i	−0.759484	−	0.650526i	$-0.774548\pi$
$821$	−16.5000	+	9.52628i	−0.575854	+	0.332469i	0.183630	+	0.982995i	$0.441215\pi$
$822$	20.0764	+	5.37945i	0.700245	+	0.187630i
$823$	−28.4416	+	7.62089i	−0.991410	+	0.265648i	−0.717843	−	0.696205i	$-0.754870\pi$
$823$	−28.4416	+	7.62089i	−0.991410	+	0.265648i	−0.273567	+	0.961853i	$0.588204\pi$
$824$	1.73205	−	3.00000i	0.0603388	−	0.104510i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	−31.8198	−	31.8198i	−1.10648	−	1.10648i	−0.993609	−	0.112874i	$-0.963994\pi$
$827$	−31.8198	−	31.8198i	−1.10648	−	1.10648i	−0.112874	−	0.993609i	$-0.536006\pi$
$828$	2.32937	+	8.69333i	0.0809513	+	0.302114i
$829$		−	29.0000i		−	1.00721i	−0.863934	−	0.503606i	$-0.832006\pi$
$829$		−	29.0000i		−	1.00721i	0.863934	−	0.503606i	$-0.167994\pi$
$830$		0			0
$831$	−18.0000			−0.624413
$832$	−0.896575	−	3.34607i	−0.0310832	−	0.116004i
$833$	6.21166	+	23.1822i	0.215221	+	0.803216i
$834$	−3.46410	+	6.00000i	−0.119952	+	0.207763i
$835$		0			0
$836$			6.92820i			0.239617i
$837$	13.4486	+	50.1910i	0.464853	+	1.73485i
$838$	−7.34847	−	7.34847i	−0.253849	−	0.253849i
$839$	19.0526	+	33.0000i	0.657767	+	1.13929i	0.981192	+	0.193033i	$0.0618323\pi$
$839$	19.0526	+	33.0000i	0.657767	+	1.13929i	−0.323425	+	0.946254i	$0.604834\pi$
$840$		0			0
$841$	−23.0000	+	39.8372i	−0.793103	+	1.37370i
$842$	−9.65926	+	2.58819i	−0.332880	+	0.0891949i
$843$	6.36396	−	6.36396i	0.219186	−	0.219186i
$844$	−19.0526	+	11.0000i	−0.655816	+	0.378636i
$845$		0			0
$846$	−9.00000			−0.309426
$847$	−1.22474	+	1.22474i	−0.0420827	+	0.0420827i
$848$		0			0
$849$	7.79423	−	4.50000i	0.267497	−	0.154440i
$850$		0			0
$851$	9.00000	+	5.19615i	0.308516	+	0.178122i
$852$	−1.55291	+	5.79555i	−0.0532020	+	0.198552i
$853$	4.48288	−	16.7303i	0.153491	−	0.572835i	−0.845739	−	0.533597i	$-0.820840\pi$
$853$	4.48288	−	16.7303i	0.153491	−	0.572835i	0.999230	−	0.0392388i	$-0.0124933\pi$
$854$	−22.5167			−0.770504
$855$		0			0
$856$	−3.00000			−0.102538
$857$	−10.8704	+	40.5689i	−0.371326	+	1.38581i	0.487314	+	0.873227i	$0.337977\pi$
$857$	−10.8704	+	40.5689i	−0.371326	+	1.38581i	−0.858640	+	0.512580i	$0.828690\pi$
$858$	−14.6969	−	14.6969i	−0.501745	−	0.501745i
$859$	19.0526	+	11.0000i	0.650065	+	0.375315i	0.788481	−	0.615059i	$-0.210868\pi$
$859$	19.0526	+	11.0000i	0.650065	+	0.375315i	−0.138416	+	0.990374i	$0.544201\pi$
$860$		0			0
$861$	−22.5000	−	12.9904i	−0.766798	−	0.442711i
$862$	6.69213	+	1.79315i	0.227935	+	0.0610750i
$863$	−10.6066	+	10.6066i	−0.361053	+	0.361053i	−0.864201	−	0.503148i	$-0.832175\pi$
$863$	−10.6066	+	10.6066i	−0.361053	+	0.361053i	0.503148	+	0.864201i	$0.332175\pi$
$864$	2.59808	−	4.50000i	0.0883883	−	0.153093i
$865$		0			0
$866$	9.00000	−	5.19615i	0.305832	−	0.176572i
$867$	8.51747	+	31.7876i	0.289268	+	1.07956i
$868$	−16.7303	+	4.48288i	−0.567864	+	0.152159i
$869$	−6.92820	+	12.0000i	−0.235023	+	0.407072i
$870$		0			0
$871$	21.0000	+	36.3731i	0.711558	+	1.23245i
$872$	−3.53553	−	3.53553i	−0.119728	−	0.119728i
$873$	20.0764	−	5.37945i	0.679483	−	0.182067i
$874$			6.00000i			0.202953i
$875$		0			0
$876$	12.0000	+	20.7846i	0.405442	+	0.702247i
$877$	4.48288	+	16.7303i	0.151376	+	0.564943i	0.999388	+	0.0349667i	$0.0111325\pi$
$877$	4.48288	+	16.7303i	0.151376	+	0.564943i	−0.848012	+	0.529976i	$0.822201\pi$
$878$	−5.17638	−	19.3185i	−0.174694	−	0.651968i
$879$	25.9808	+	45.0000i	0.876309	+	1.51781i
$880$		0			0
$881$		−	1.73205i		−	0.0583543i	−0.999574	−	0.0291771i	$-0.990711\pi$
$881$		−	1.73205i		−	0.0583543i	0.999574	−	0.0291771i	$-0.00928869\pi$
$882$	−3.10583	+	11.5911i	−0.104579	+	0.390293i
$883$	30.6186	+	30.6186i	1.03040	+	1.03040i	0.999523	+	0.0308754i	$0.00982951\pi$
$883$	30.6186	+	30.6186i	1.03040	+	1.03040i	0.0308754	+	0.999523i	$0.490170\pi$
$884$	10.3923	+	18.0000i	0.349531	+	0.605406i
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	23.1822	−	6.21166i	0.778383	−	0.208567i	0.152311	−	0.988333i	$-0.451328\pi$
$887$	23.1822	−	6.21166i	0.778383	−	0.208567i	0.626072	+	0.779766i	$0.284662\pi$
$888$	−1.55291	−	5.79555i	−0.0521124	−	0.194486i
$889$	−7.79423	+	4.50000i	−0.261410	+	0.150925i
$890$		0			0
$891$		−	31.1769i		−	1.04447i
$892$	11.0227	−	11.0227i	0.369067	−	0.369067i
$893$	−5.79555	−	1.55291i	−0.193941	−	0.0519663i
$894$	7.79423	+	4.50000i	0.260678	+	0.150503i
$895$		0			0
$896$	1.50000	+	0.866025i	0.0501115	+	0.0289319i
$897$	−12.7279	−	12.7279i	−0.424973	−	0.424973i
$898$	3.58630	−	13.3843i	0.119676	−	0.446639i
$899$	−86.6025			−2.88836
$900$		0			0
$901$		0			0
$902$	7.76457	−	28.9778i	0.258532	−	0.964854i
$903$	8.06918	−	30.1146i	0.268525	−	1.00215i
$904$		0			0
$905$		0			0
$906$	−15.0000	+	8.66025i	−0.498342	+	0.287718i
$907$	8.36516	+	2.24144i	0.277761	+	0.0744257i	0.395010	−	0.918677i	$-0.370741\pi$
$907$	8.36516	+	2.24144i	0.277761	+	0.0744257i	−0.117250	+	0.993102i	$0.537408\pi$
$908$	−16.9706	+	16.9706i	−0.563188	+	0.563188i
$909$	20.7846	−	36.0000i	0.689382	−	1.19404i
$910$		0			0
$911$	−48.0000	+	27.7128i	−1.59031	+	0.918166i	−0.597058	+	0.802198i	$0.703664\pi$
$911$	−48.0000	+	27.7128i	−1.59031	+	0.918166i	−0.993253	+	0.115968i	$0.963003\pi$
$912$	2.44949	−	2.44949i	0.0811107	−	0.0811107i
$913$	−10.0382	+	2.68973i	−0.332216	+	0.0890170i
$914$	15.5885	−	27.0000i	0.515620	−	0.893081i
$915$		0			0
$916$	−2.50000	−	4.33013i	−0.0826023	−	0.143071i
$917$	8.48528	+	8.48528i	0.280209	+	0.280209i
$918$	−8.06918	+	30.1146i	−0.266323	+	0.993929i
$919$			40.0000i			1.31948i	0.751495	+	0.659739i	$0.229333\pi$
$919$			40.0000i			1.31948i	−0.751495	+	0.659739i	$0.770667\pi$
$920$		0			0
$921$	−4.50000	+	7.79423i	−0.148280	+	0.256829i
$922$	−3.13801	−	11.7112i	−0.103345	−	0.385689i
$923$	−3.10583	−	11.5911i	−0.102230	−	0.381526i
$924$	10.3923			0.341882
$925$		0			0
$926$			17.3205i			0.569187i
$927$	−7.34847	+	7.34847i	−0.241355	+	0.241355i
$928$	6.12372	+	6.12372i	0.201021	+	0.201021i
$929$	−3.46410	−	6.00000i	−0.113653	−	0.196854i	0.803587	−	0.595187i	$-0.202922\pi$
$929$	−3.46410	−	6.00000i	−0.113653	−	0.196854i	−0.917241	+	0.398333i	$0.869589\pi$
$930$		0			0
$931$	−4.00000	+	6.92820i	−0.131095	+	0.227063i
$932$	−5.79555	+	1.55291i	−0.189840	+	0.0508674i
$933$	−40.5689	−	10.8704i	−1.32817	−	0.355881i
$934$	31.1769	−	18.0000i	1.02014	−	0.588978i
$935$		0			0
$936$			10.3923i			0.339683i
$937$	−9.79796	+	9.79796i	−0.320085	+	0.320085i	−0.848800	−	0.528714i	$-0.822674\pi$
$937$	−9.79796	+	9.79796i	−0.320085	+	0.320085i	0.528714	+	0.848800i	$0.322674\pi$
$938$	−20.2844	−	5.43520i	−0.662311	−	0.177466i
$939$		−	6.00000i		−	0.195803i
$940$		0			0
$941$	−4.50000	−	2.59808i	−0.146696	−	0.0846949i	0.424856	−	0.905261i	$-0.360325\pi$
$941$	−4.50000	−	2.59808i	−0.146696	−	0.0846949i	−0.571551	+	0.820566i	$0.693658\pi$
$942$	34.7733	−	9.31749i	1.13298	−	0.303580i
$943$	6.72432	−	25.0955i	0.218974	−	0.817222i
$944$	6.92820			0.225494
$945$		0			0
$946$	36.0000			1.17046
$947$	−6.98811	+	26.0800i	−0.227083	+	0.847486i	0.754476	+	0.656328i	$0.227891\pi$
$947$	−6.98811	+	26.0800i	−0.227083	+	0.847486i	−0.981559	+	0.191158i	$0.938776\pi$
$948$	6.69213	−	1.79315i	0.217350	−	0.0582388i
$949$	−41.5692	−	24.0000i	−1.34939	−	0.779073i
$950$		0			0
$951$			10.3923i			0.336994i
$952$	−10.0382	−	2.68973i	−0.325340	−	0.0871745i
$953$	−29.6985	+	29.6985i	−0.962028	+	0.962028i	−0.999305	−	0.0372767i	$-0.988132\pi$
$953$	−29.6985	+	29.6985i	−0.962028	+	0.962028i	0.0372767	+	0.999305i	$0.488132\pi$
$954$		0			0
$955$		0			0
$956$	−18.0000	+	10.3923i	−0.582162	+	0.336111i
$957$	50.1910	+	13.4486i	1.62244	+	0.434733i
$958$	26.7685	−	7.17260i	0.864852	−	0.231736i
$959$	10.3923	−	18.0000i	0.335585	−	0.581250i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	8.48528	+	8.48528i	0.273576	+	0.273576i
$963$	8.69333	+	2.32937i	0.280139	+	0.0750629i
$964$			17.0000i			0.547533i
$965$		0			0
$966$	9.00000			0.289570
$967$	13.8969	+	51.8640i	0.446895	+	1.66783i	0.710885	+	0.703309i	$0.248295\pi$
$967$	13.8969	+	51.8640i	0.446895	+	1.66783i	−0.263990	+	0.964525i	$0.585039\pi$
$968$	0.258819	+	0.965926i	0.00831876	+	0.0310460i
$969$	−10.3923	+	18.0000i	−0.333849	+	0.578243i
$970$		0			0
$971$		−	38.1051i		−	1.22285i	−0.791302	−	0.611426i	$-0.790596\pi$
$971$		−	38.1051i		−	1.22285i	0.791302	−	0.611426i	$-0.209404\pi$
$972$	−11.0227	+	11.0227i	−0.353553	+	0.353553i
$973$	4.89898	+	4.89898i	0.157054	+	0.157054i
$974$	12.1244	+	21.0000i	0.388489	+	0.672883i
$975$		0			0
$976$	−6.50000	+	11.2583i	−0.208060	+	0.360370i
$977$	−40.5689	+	10.8704i	−1.29791	+	0.347775i	−0.840661	−	0.541562i	$-0.817833\pi$
$977$	−40.5689	+	10.8704i	−1.29791	+	0.347775i	−0.457253	+	0.889337i	$0.651167\pi$
$978$	−21.2132	+	21.2132i	−0.678323	+	0.678323i
$979$	−5.19615	+	3.00000i	−0.166070	+	0.0958804i
$980$		0			0
$981$	7.50000	+	12.9904i	0.239457	+	0.414751i
$982$	9.79796	−	9.79796i	0.312665	−	0.312665i
$983$	−8.69333	−	2.32937i	−0.277274	−	0.0742954i	0.117502	−	0.993073i	$-0.462511\pi$
$983$	−8.69333	−	2.32937i	−0.277274	−	0.0742954i	−0.394776	+	0.918777i	$0.629178\pi$
$984$	−12.9904	+	7.50000i	−0.414118	+	0.239091i
$985$		0			0
$986$	−45.0000	−	25.9808i	−1.43309	−	0.827396i
$987$	−2.32937	+	8.69333i	−0.0741447	+	0.276712i
$988$	−1.79315	+	6.69213i	−0.0570477	+	0.212905i
$989$	31.1769			0.991368
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−2.58819	+	9.65926i	−0.0821751	+	0.306682i
$993$	−9.79796	−	9.79796i	−0.310929	−	0.310929i
$994$	5.19615	+	3.00000i	0.164812	+	0.0951542i
$995$		0			0
$996$	4.50000	+	2.59808i	0.142588	+	0.0823232i
$997$	40.1528	+	10.7589i	1.27165	+	0.340738i	0.830663	−	0.556775i	$-0.187961\pi$
$997$	40.1528	+	10.7589i	1.27165	+	0.340738i	0.440988	+	0.897513i	$0.354628\pi$
$998$	−31.1127	+	31.1127i	−0.984855	+	0.984855i
$999$			18.0000i			0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.d.293.2	yes	8
3.2	odd	2		1350.2.q.b.1043.1		8
5.2	odd	4	inner	450.2.p.d.257.2	yes	8
5.3	odd	4	inner	450.2.p.d.257.1	✓	8
5.4	even	2	inner	450.2.p.d.293.1	yes	8
9.2	odd	6	inner	450.2.p.d.443.2	yes	8
9.7	even	3		1350.2.q.b.143.1		8
15.2	even	4		1350.2.q.b.557.1		8
15.8	even	4		1350.2.q.b.557.2		8
15.14	odd	2		1350.2.q.b.1043.2		8
45.2	even	12	inner	450.2.p.d.407.2	yes	8
45.7	odd	12		1350.2.q.b.1007.1		8
45.29	odd	6	inner	450.2.p.d.443.1	yes	8
45.34	even	6		1350.2.q.b.143.2		8
45.38	even	12	inner	450.2.p.d.407.1	yes	8
45.43	odd	12		1350.2.q.b.1007.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.d.257.1	✓	8	5.3	odd	4	inner
450.2.p.d.257.2	yes	8	5.2	odd	4	inner
450.2.p.d.293.1	yes	8	5.4	even	2	inner
450.2.p.d.293.2	yes	8	1.1	even	1	trivial
450.2.p.d.407.1	yes	8	45.38	even	12	inner
450.2.p.d.407.2	yes	8	45.2	even	12	inner
450.2.p.d.443.1	yes	8	45.29	odd	6	inner
450.2.p.d.443.2	yes	8	9.2	odd	6	inner
1350.2.q.b.143.1		8	9.7	even	3
1350.2.q.b.143.2		8	45.34	even	6
1350.2.q.b.557.1		8	15.2	even	4
1350.2.q.b.557.2		8	15.8	even	4
1350.2.q.b.1007.1		8	45.7	odd	12
1350.2.q.b.1007.2		8	45.43	odd	12
1350.2.q.b.1043.1		8	3.2	odd	2
1350.2.q.b.1043.2		8	15.14	odd	2

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.67303 - 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.67303 - 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +(3.00000 - 1.73205i) q^{11} +(-1.67303 - 0.448288i) q^{12} +(3.34607 - 0.896575i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.24264 - 4.24264i) q^{17} +(-0.776457 - 2.89778i) q^{18} -2.00000i q^{19} -3.00000 q^{21} +(-0.896575 - 3.34607i) q^{22} +(-0.776457 - 2.89778i) q^{23} +(-0.866025 + 1.50000i) q^{24} -3.46410i q^{26} +(3.67423 - 3.67423i) q^{27} +(1.22474 + 1.22474i) q^{28} +(4.33013 + 7.50000i) q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.965926 - 0.258819i) q^{32} +(4.24264 - 4.24264i) q^{33} +(-5.19615 + 3.00000i) q^{34} -3.00000 q^{36} +(-2.44949 + 2.44949i) q^{37} +(-1.93185 - 0.517638i) q^{38} +(5.19615 - 3.00000i) q^{39} +(7.50000 + 4.33013i) q^{41} +(-0.776457 + 2.89778i) q^{42} +(-2.68973 + 10.0382i) q^{43} -3.46410 q^{44} -3.00000 q^{46} +(0.776457 - 2.89778i) q^{47} +(1.22474 + 1.22474i) q^{48} +(-3.46410 - 2.00000i) q^{49} +(-9.00000 - 5.19615i) q^{51} +(-3.34607 - 0.896575i) q^{52} +(-2.59808 - 4.50000i) q^{54} +(1.50000 - 0.866025i) q^{56} +(-0.896575 - 3.34607i) q^{57} +(8.36516 - 2.24144i) q^{58} +(3.46410 - 6.00000i) q^{59} +(6.50000 + 11.2583i) q^{61} +(7.07107 + 7.07107i) q^{62} +(-5.01910 + 1.34486i) q^{63} -1.00000i q^{64} +(-3.00000 - 5.19615i) q^{66} +(3.13801 + 11.7112i) q^{67} +(1.55291 + 5.79555i) q^{68} +(-2.59808 - 4.50000i) q^{69} -3.46410i q^{71} +(-0.776457 + 2.89778i) q^{72} +(-9.79796 - 9.79796i) q^{73} +(1.73205 + 3.00000i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-5.79555 + 1.55291i) q^{77} +(-1.55291 - 5.79555i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(6.12372 - 6.12372i) q^{82} +(-2.89778 - 0.776457i) q^{83} +(2.59808 + 1.50000i) q^{84} +(9.00000 + 5.19615i) q^{86} +(10.6066 + 10.6066i) q^{87} +(-0.896575 + 3.34607i) q^{88} -1.73205 q^{89} -6.00000 q^{91} +(-0.776457 + 2.89778i) q^{92} +(-4.48288 + 16.7303i) q^{93} +(-2.59808 - 1.50000i) q^{94} +(1.50000 - 0.866025i) q^{96} +(6.69213 + 1.79315i) q^{97} +(-2.82843 + 2.82843i) q^{98} +(5.19615 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 24 q^{11} + 4 q^{16} - 24 q^{21} - 40 q^{31} - 24 q^{36} + 60 q^{41} - 24 q^{46} - 72 q^{51} + 12 q^{56} + 52 q^{61} - 24 q^{66} - 8 q^{76} + 36 q^{81} + 72 q^{86} - 48 q^{91} + 12 q^{96}+O(q^{100}) \) 8 * q + 24 * q^11 + 4 * q^16 - 24 * q^21 - 40 * q^31 - 24 * q^36 + 60 * q^41 - 24 * q^46 - 72 * q^51 + 12 * q^56 + 52 * q^61 - 24 * q^66 - 8 * q^76 + 36 * q^81 + 72 * q^86 - 48 * q^91 + 12 * q^96

Introduction

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