LMFDB - Embedded newform 450.2.p.d.257.2

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			257.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	450.257
Dual form			450.2.p.d.443.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(0.448288 - 1.67303i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(0.448288 - 1.67303i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(3.00000 - 1.73205i) q^{11} +(0.448288 - 1.67303i) q^{12} +(-0.896575 - 3.34607i) q^{13} +(0.866025 - 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.24264 - 4.24264i) q^{17} +(-2.89778 + 0.776457i) q^{18} +2.00000i q^{19} -3.00000 q^{21} +(3.34607 - 0.896575i) q^{22} +(-2.89778 + 0.776457i) 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} +(0.258819 + 0.965926i) q^{32} +(-4.24264 - 4.24264i) q^{33} +(5.19615 - 3.00000i) q^{34} -3.00000 q^{36} +(-2.44949 - 2.44949i) q^{37} +(-0.517638 + 1.93185i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(7.50000 + 4.33013i) q^{41} +(-2.89778 - 0.776457i) q^{42} +(10.0382 + 2.68973i) q^{43} +3.46410 q^{44} -3.00000 q^{46} +(2.89778 + 0.776457i) q^{47} +(1.22474 - 1.22474i) q^{48} +(3.46410 + 2.00000i) q^{49} +(-9.00000 - 5.19615i) q^{51} +(0.896575 - 3.34607i) q^{52} +(2.59808 + 4.50000i) q^{54} +(1.50000 - 0.866025i) q^{56} +(3.34607 - 0.896575i) q^{57} +(-2.24144 - 8.36516i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(6.50000 + 11.2583i) q^{61} +(-7.07107 + 7.07107i) q^{62} +(1.34486 + 5.01910i) q^{63} +1.00000i q^{64} +(-3.00000 - 5.19615i) q^{66} +(-11.7112 + 3.13801i) q^{67} +(5.79555 - 1.55291i) q^{68} +(2.59808 + 4.50000i) q^{69} -3.46410i q^{71} +(-2.89778 - 0.776457i) q^{72} +(-9.79796 + 9.79796i) q^{73} +(-1.73205 - 3.00000i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-1.55291 - 5.79555i) q^{77} +(-5.79555 + 1.55291i) q^{78} +(3.46410 - 2.00000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(6.12372 + 6.12372i) q^{82} +(-0.776457 + 2.89778i) q^{83} +(-2.59808 - 1.50000i) q^{84} +(9.00000 + 5.19615i) q^{86} +(-10.6066 + 10.6066i) q^{87} +(3.34607 + 0.896575i) q^{88} +1.73205 q^{89} -6.00000 q^{91} +(-2.89778 - 0.776457i) q^{92} +(16.7303 + 4.48288i) q^{93} +(2.59808 + 1.50000i) q^{94} +(1.50000 - 0.866025i) q^{96} +(-1.79315 + 6.69213i) 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.448288	−	1.67303i	−0.258819	−	0.965926i
$3$	−0.448288	−	1.67303i	−0.258819	−	0.965926i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$	0.448288	−	1.67303i	0.169437	−	0.632347i	−0.827996	−	0.560734i	$-0.810519\pi$
$7$	0.448288	−	1.67303i	0.169437	−	0.632347i	0.997433	−	0.0716124i	$-0.0228145\pi$
$8$	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	$0.158432\pi$
$12$	0.448288	−	1.67303i	0.129410	−	0.482963i
$13$	−0.896575	−	3.34607i	−0.248665	−	0.928032i	−0.971506	−	0.237016i	$-0.923830\pi$
$13$	−0.896575	−	3.34607i	−0.248665	−	0.928032i	0.722840	−	0.691015i	$-0.242836\pi$
$14$	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	0.0294245	−	0.999567i	$-0.490633\pi$
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.999567	−	0.0294245i	$-0.00936746\pi$
$18$	−2.89778	+	0.776457i	−0.683013	+	0.183013i
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$		0			0
$21$	−3.00000			−0.654654
$22$	3.34607	−	0.896575i	0.713384	−	0.191151i
$23$	−2.89778	+	0.776457i	−0.604228	+	0.161903i	−0.547948	−	0.836512i	$-0.684591\pi$
$23$	−2.89778	+	0.776457i	−0.604228	+	0.161903i	−0.0562805	+	0.998415i	$0.517924\pi$
$24$	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	$-0.869323\pi$
$29$	−4.33013	−	7.50000i	−0.804084	−	1.39272i	0.112823	−	0.993615i	$-0.464011\pi$
$30$		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	$0.811667\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−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	0.476488	−	0.879181i	$-0.341910\pi$
$37$	−2.44949	−	2.44949i	−0.402694	−	0.402694i	−0.879181	+	0.476488i	$0.841910\pi$
$38$	−0.517638	+	1.93185i	−0.0839720	+	0.313388i
$39$	−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	$0.430270\pi$
$42$	−2.89778	−	0.776457i	−0.447137	−	0.119810i
$43$	10.0382	+	2.68973i	1.53081	+	0.410179i	0.923283	−	0.384120i	$-0.125495\pi$
$43$	10.0382	+	2.68973i	1.53081	+	0.410179i	0.607527	+	0.794299i	$0.292162\pi$
$44$	3.46410			0.522233
$45$		0			0
$46$	−3.00000			−0.442326
$47$	2.89778	+	0.776457i	0.422684	+	0.113258i	0.463890	−	0.885893i	$-0.346453\pi$
$47$	2.89778	+	0.776457i	0.422684	+	0.113258i	−0.0412058	+	0.999151i	$0.513120\pi$
$48$	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
$52$	0.896575	−	3.34607i	0.124333	−	0.464016i
$53$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$53$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$54$	2.59808	+	4.50000i	0.353553	+	0.612372i
$55$		0			0
$56$	1.50000	−	0.866025i	0.200446	−	0.115728i
$57$	3.34607	−	0.896575i	0.443197	−	0.118754i
$58$	−2.24144	−	8.36516i	−0.294315	−	1.09840i
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	−0.998448	−	0.0556984i	$-0.982261\pi$
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	0.547460	+	0.836832i	$0.315595\pi$
$60$		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
$63$	1.34486	+	5.01910i	0.169437	+	0.632347i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$	−11.7112	+	3.13801i	−1.43075	+	0.383369i	−0.889286	−	0.457352i	$-0.848798\pi$
$67$	−11.7112	+	3.13801i	−1.43075	+	0.383369i	−0.541468	+	0.840721i	$0.682131\pi$
$68$	5.79555	−	1.55291i	0.702814	−	0.188319i
$69$	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	$-0.0659005\pi$
$72$	−2.89778	−	0.776457i	−0.341506	−	0.0915064i
$73$	−9.79796	+	9.79796i	−1.14676	+	1.14676i	−0.159579	+	0.987185i	$0.551014\pi$
$73$	−9.79796	+	9.79796i	−1.14676	+	1.14676i	−0.987185	+	0.159579i	$0.948986\pi$
$74$	−1.73205	−	3.00000i	−0.201347	−	0.348743i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−1.55291	−	5.79555i	−0.176971	−	0.660465i
$78$	−5.79555	+	1.55291i	−0.656217	+	0.175833i
$79$	3.46410	−	2.00000i	0.389742	−	0.225018i	−0.292306	−	0.956325i	$-0.594423\pi$
$79$	3.46410	−	2.00000i	0.389742	−	0.225018i	0.682048	+	0.731307i	$0.261089\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	6.12372	+	6.12372i	0.676252	+	0.676252i
$83$	−0.776457	+	2.89778i	−0.0852272	+	0.318072i	−0.995357	−	0.0962507i	$-0.969315\pi$
$83$	−0.776457	+	2.89778i	−0.0852272	+	0.318072i	0.910130	+	0.414323i	$0.135982\pi$
$84$	−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
$88$	3.34607	+	0.896575i	0.356692	+	0.0955753i
$89$	1.73205			0.183597			0.0917985	−	0.995778i	$-0.470738\pi$
$89$	1.73205			0.183597			0.0917985	+	0.995778i	$0.470738\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$	−2.89778	−	0.776457i	−0.302114	−	0.0809513i
$93$	16.7303	+	4.48288i	1.73485	+	0.464853i
$94$	2.59808	+	1.50000i	0.267971	+	0.154713i
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−1.79315	+	6.69213i	−0.182067	+	0.679483i	0.813173	+	0.582023i	$0.197739\pi$
$97$	−1.79315	+	6.69213i	−0.182067	+	0.679483i	−0.995239	+	0.0974602i	$0.968928\pi$
$98$	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
$103$	0.896575	+	3.34607i	0.0883422	+	0.329698i	0.995926	−	0.0901732i	$-0.0287421\pi$
$103$	0.896575	+	3.34607i	0.0883422	+	0.329698i	−0.907584	+	0.419871i	$0.862075\pi$
$104$	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	$-0.796322\pi$
$107$	−2.12132	+	2.12132i	−0.205076	+	0.205076i	0.597095	+	0.802171i	$0.296322\pi$
$108$	1.34486	+	5.01910i	0.129410	+	0.482963i
$109$		−	5.00000i		−	0.478913i	−0.970907	−	0.239457i	$-0.923031\pi$
$109$		−	5.00000i		−	0.478913i	0.970907	−	0.239457i	$-0.0769693\pi$
$110$		0			0
$111$	−3.00000	+	5.19615i	−0.284747	+	0.493197i
$112$	1.67303	−	0.448288i	0.158087	−	0.0423592i
$113$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$113$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$114$	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
$122$	3.36465	+	12.5570i	0.304621	+	1.13686i
$123$	3.88229	−	14.4889i	0.350054	−	1.30642i
$124$	−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	0.851077	−	0.525041i	$-0.175950\pi$
$127$	3.67423	+	3.67423i	0.326036	+	0.326036i	−0.525041	+	0.851077i	$0.675950\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		−	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	$0.764541\pi$
$132$	−1.55291	−	5.79555i	−0.135164	−	0.504438i
$133$	3.34607	+	0.896575i	0.290141	+	0.0777430i
$134$	−12.1244			−1.04738
$135$		0			0
$136$	6.00000			0.514496
$137$	−11.5911	−	3.10583i	−0.990295	−	0.265349i	−0.272921	−	0.962037i	$-0.587990\pi$
$137$	−11.5911	−	3.10583i	−0.990295	−	0.265349i	−0.717375	+	0.696688i	$0.754656\pi$
$138$	1.34486	+	5.01910i	0.114482	+	0.427254i
$139$	3.46410	+	2.00000i	0.293821	+	0.169638i	0.639664	−	0.768655i	$-0.279074\pi$
$139$	3.46410	+	2.00000i	0.293821	+	0.169638i	−0.345843	+	0.938293i	$0.612407\pi$
$140$		0			0
$141$		−	5.19615i		−	0.437595i
$142$	0.896575	−	3.34607i	0.0752389	−	0.280796i
$143$	−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
$147$	1.79315	−	6.69213i	0.147897	−	0.551958i
$148$	−0.896575	−	3.34607i	−0.0736980	−	0.275045i
$149$	2.59808	−	4.50000i	0.212843	−	0.368654i	−0.739760	−	0.672870i	$-0.765061\pi$
$149$	2.59808	−	4.50000i	0.212843	−	0.368654i	0.952603	+	0.304216i	$0.0983945\pi$
$150$		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
$153$	−4.65874	+	17.3867i	−0.376637	+	1.40563i
$154$		−	6.00000i		−	0.483494i
$155$		0			0
$156$	−6.00000			−0.480384
$157$	−20.0764	+	5.37945i	−1.60227	+	0.429327i	−0.945727	−	0.324961i	$-0.894649\pi$
$157$	−20.0764	+	5.37945i	−1.60227	+	0.429327i	−0.656543	+	0.754288i	$0.727982\pi$
$158$	3.86370	−	1.03528i	0.307380	−	0.0823622i
$159$		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	−0.999203	−	0.0399091i	$-0.987293\pi$
$163$	−12.2474	+	12.2474i	−0.959294	+	0.959294i	0.0399091	+	0.999203i	$0.487293\pi$
$164$	4.33013	+	7.50000i	0.338126	+	0.585652i
$165$		0			0
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	−2.32937	−	8.69333i	−0.180252	−	0.672710i	−0.995597	−	0.0937349i	$-0.970119\pi$
$167$	−2.32937	−	8.69333i	−0.180252	−	0.672710i	0.815345	−	0.578975i	$-0.196547\pi$
$168$	−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
$173$	6.21166	−	23.1822i	0.472264	−	1.76251i	−0.159344	−	0.987223i	$-0.550938\pi$
$173$	6.21166	−	23.1822i	0.472264	−	1.76251i	0.631607	−	0.775288i	$-0.282395\pi$
$174$	−12.9904	+	7.50000i	−0.984798	+	0.568574i
$175$		0			0
$176$	3.00000	+	1.73205i	0.226134	+	0.130558i
$177$	11.5911	+	3.10583i	0.871241	+	0.233448i
$178$	1.67303	+	0.448288i	0.125399	+	0.0336006i
$179$	24.2487			1.81243			0.906217	−	0.422813i	$-0.138957\pi$
$179$	24.2487			1.81243			0.906217	+	0.422813i	$0.138957\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	−5.79555	−	1.55291i	−0.429595	−	0.115110i
$183$	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
$187$	5.37945	−	20.0764i	0.393385	−	1.46813i
$188$	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	$0.548901\pi$
$192$	1.67303	−	0.448288i	0.120741	−	0.0323524i
$193$	−4.48288	−	16.7303i	−0.322685	−	1.20428i	−0.916619	−	0.399762i	$-0.869093\pi$
$193$	−4.48288	−	16.7303i	−0.322685	−	1.20428i	0.593934	−	0.804513i	$-0.297574\pi$
$194$	−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	$-0.609401\pi$
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	0.941517	+	0.336966i	$0.109401\pi$
$198$	−7.34847	+	7.34847i	−0.522233	+	0.522233i
$199$			10.0000i			0.708881i	0.935079	+	0.354441i	$0.115329\pi$
$199$			10.0000i			0.708881i	−0.935079	+	0.354441i	$0.884671\pi$
$200$		0			0
$201$	10.5000	+	18.1865i	0.740613	+	1.28278i
$202$	13.3843	−	3.58630i	0.941713	−	0.252331i
$203$	−14.4889	+	3.88229i	−1.01692	+	0.272483i
$204$	−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
$213$	−5.79555	+	1.55291i	−0.397105	+	0.106404i
$214$	−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
$218$	1.29410	−	4.82963i	0.0876472	−	0.327104i
$219$	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
$223$	15.0573	+	4.03459i	1.00831	+	0.270176i	0.724923	−	0.688829i	$-0.241875\pi$
$223$	15.0573	+	4.03459i	1.00831	+	0.270176i	0.283387	+	0.959005i	$0.408542\pi$
$224$	1.73205			0.115728
$225$		0			0
$226$		0			0
$227$	23.1822	+	6.21166i	1.53866	+	0.412282i	0.925832	−	0.377936i	$-0.123366\pi$
$227$	23.1822	+	6.21166i	1.53866	+	0.412282i	0.612826	+	0.790218i	$0.290033\pi$
$228$	3.34607	+	0.896575i	0.221599	+	0.0593772i
$229$	−4.33013	−	2.50000i	−0.286143	−	0.165205i	0.350058	−	0.936728i	$-0.386162\pi$
$229$	−4.33013	−	2.50000i	−0.286143	−	0.165205i	−0.636201	+	0.771523i	$0.719495\pi$
$230$		0			0
$231$	−9.00000	+	5.19615i	−0.592157	+	0.341882i
$232$	2.24144	−	8.36516i	0.147158	−	0.549200i
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	0.554343	−	0.832288i	$-0.312969\pi$
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	−0.832288	+	0.554343i	$0.812969\pi$
$234$	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
$238$	−2.68973	−	10.0382i	−0.174349	−	0.650680i
$239$	−10.3923	+	18.0000i	−0.672222	+	1.16432i	0.305050	+	0.952336i	$0.401327\pi$
$239$	−10.3923	+	18.0000i	−0.672222	+	1.16432i	−0.977273	+	0.211987i	$0.932007\pi$
$240$		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
$243$	−15.0573	−	4.03459i	−0.965926	−	0.258819i
$244$			13.0000i			0.832240i
$245$		0			0
$246$	7.50000	−	12.9904i	0.478183	−	0.828236i
$247$	6.69213	−	1.79315i	0.425810	−	0.114095i
$248$	−9.65926	+	2.58819i	−0.613364	+	0.164350i
$249$	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	$0.893633\pi$
$252$	−1.34486	+	5.01910i	−0.0847184	+	0.316173i
$253$	−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		0.965926	−	0.258819i	$-0.0833333\pi$
$257$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$258$	4.65874	−	17.3867i	0.290041	−	1.08245i
$259$	−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
$263$	−6.21166	+	23.1822i	−0.383027	+	1.42948i	0.458226	+	0.888836i	$0.348485\pi$
$263$	−6.21166	+	23.1822i	−0.383027	+	1.42948i	−0.841253	+	0.540641i	$0.818182\pi$
$264$		−	6.00000i		−	0.369274i
$265$		0			0
$266$	3.00000	+	1.73205i	0.183942	+	0.106199i
$267$	−0.776457	−	2.89778i	−0.0475184	−	0.177341i
$268$	−11.7112	−	3.13801i	−0.715377	−	0.191685i
$269$	1.73205			0.105605			0.0528025	−	0.998605i	$-0.483185\pi$
$269$	1.73205			0.105605			0.0528025	+	0.998605i	$0.483185\pi$
$270$		0			0
$271$	−10.0000			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$272$	5.79555	+	1.55291i	0.351407	+	0.0941593i
$273$	2.68973	+	10.0382i	0.162790	+	0.607539i
$274$	−10.3923	−	6.00000i	−0.627822	−	0.362473i
$275$		0			0
$276$			5.19615i			0.312772i
$277$	2.68973	−	10.0382i	0.161610	−	0.603137i	−0.836838	−	0.547450i	$-0.815599\pi$
$277$	2.68973	−	10.0382i	0.161610	−	0.603137i	0.998448	−	0.0556866i	$-0.0177348\pi$
$278$	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	$0.283799\pi$
$282$	1.34486	−	5.01910i	0.0800854	−	0.298883i
$283$	−1.34486	−	5.01910i	−0.0799438	−	0.298354i	0.914365	−	0.404891i	$-0.132691\pi$
$283$	−1.34486	−	5.01910i	−0.0799438	−	0.298354i	−0.994309	+	0.106537i	$0.966024\pi$
$284$	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
$292$	−13.3843	+	3.58630i	−0.783255	+	0.209872i
$293$	28.9778	−	7.76457i	1.69290	−	0.453611i	0.721764	−	0.692139i	$-0.243332\pi$
$293$	28.9778	−	7.76457i	1.69290	−	0.453611i	0.971136	+	0.238528i	$0.0766649\pi$
$294$	3.46410	−	6.00000i	0.202031	−	0.349927i
$295$		0			0
$296$		−	3.46410i		−	0.201347i
$297$	17.3867	+	4.65874i	1.00888	+	0.270328i
$298$	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
$302$	−2.58819	−	9.65926i	−0.148934	−	0.555828i
$303$	−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	0.594440	−	0.804140i	$-0.297374\pi$
$307$	−3.67423	−	3.67423i	−0.209700	−	0.209700i	−0.804140	+	0.594440i	$0.797374\pi$
$308$	1.55291	−	5.79555i	0.0884855	−	0.330232i
$309$	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	$0.907963\pi$
$312$	−5.79555	−	1.55291i	−0.328109	−	0.0879165i
$313$	−3.34607	−	0.896575i	−0.189131	−	0.0506774i	0.163010	−	0.986624i	$-0.447880\pi$
$313$	−3.34607	−	0.896575i	−0.189131	−	0.0506774i	−0.352141	+	0.935947i	$0.614546\pi$
$314$	−20.7846			−1.17294
$315$		0			0
$316$	4.00000			0.225018
$317$	−5.79555	−	1.55291i	−0.325511	−	0.0872204i	0.0923631	−	0.995725i	$-0.470558\pi$
$317$	−5.79555	−	1.55291i	−0.325511	−	0.0872204i	−0.417874	+	0.908505i	$0.637225\pi$
$318$		0			0
$319$	−25.9808	−	15.0000i	−1.45464	−	0.839839i
$320$		0			0
$321$	4.50000	+	2.59808i	0.251166	+	0.145010i
$322$	−1.34486	+	5.01910i	−0.0749463	+	0.279703i
$323$	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
$327$	−8.36516	+	2.24144i	−0.462595	+	0.123952i
$328$	2.24144	+	8.36516i	0.123763	+	0.461889i
$329$	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
$333$	10.0382	+	2.68973i	0.550090	+	0.147396i
$334$		−	9.00000i		−	0.492458i
$335$		0			0
$336$	−1.50000	−	2.59808i	−0.0818317	−	0.141737i
$337$	−13.3843	+	3.58630i	−0.729087	+	0.195358i	−0.604223	−	0.796815i	$-0.706516\pi$
$337$	−13.3843	+	3.58630i	−0.729087	+	0.195358i	−0.124864	+	0.992174i	$0.539850\pi$
$338$	0.965926	−	0.258819i	0.0525394	−	0.0140779i
$339$		0			0
$340$		0			0
$341$			34.6410i			1.87592i
$342$	−1.55291	−	5.79555i	−0.0839720	−	0.313388i
$343$	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
$347$	3.10583	+	11.5911i	0.166730	+	0.622243i	0.997813	+	0.0660960i	$0.0210543\pi$
$347$	3.10583	+	11.5911i	0.166730	+	0.622243i	−0.831084	+	0.556147i	$0.812279\pi$
$348$	−14.4889	+	3.88229i	−0.776686	+	0.208112i
$349$	−0.866025	+	0.500000i	−0.0463573	+	0.0267644i	−0.523000	−	0.852333i	$-0.675187\pi$
$349$	−0.866025	+	0.500000i	−0.0463573	+	0.0267644i	0.476642	+	0.879097i	$0.341854\pi$
$350$		0			0
$351$	9.00000	−	15.5885i	0.480384	−	0.832050i
$352$	2.44949	+	2.44949i	0.130558	+	0.130558i
$353$	−6.21166	+	23.1822i	−0.330613	+	1.23387i	0.577934	+	0.816083i	$0.303859\pi$
$353$	−6.21166	+	23.1822i	−0.330613	+	1.23387i	−0.908547	+	0.417782i	$0.862808\pi$
$354$	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
$358$	23.4225	+	6.27603i	1.23792	+	0.331698i
$359$	−17.3205			−0.914141			−0.457071	−	0.889430i	$-0.651101\pi$
$359$	−17.3205			−0.914141			−0.457071	+	0.889430i	$0.651101\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	6.76148	+	1.81173i	0.355376	+	0.0952226i
$363$	−1.67303	−	0.448288i	−0.0878114	−	0.0235290i
$364$	−5.19615	−	3.00000i	−0.272352	−	0.157243i
$365$		0			0
$366$	19.5000	−	11.2583i	1.01928	−	0.588482i
$367$	0.896575	−	3.34607i	0.0468009	−	0.174663i	−0.938569	−	0.345091i	$-0.887848\pi$
$367$	0.896575	−	3.34607i	0.0468009	−	0.174663i	0.985370	+	0.170427i	$0.0545148\pi$
$368$	−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
$373$	−3.58630	−	13.3843i	−0.185692	−	0.693011i	−0.994481	−	0.104913i	$-0.966544\pi$
$373$	−3.58630	−	13.3843i	−0.185692	−	0.693011i	0.808790	−	0.588098i	$-0.200123\pi$
$374$	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
$378$	8.69333	−	2.32937i	0.447137	−	0.119810i
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$		0			0
$381$	4.50000	−	7.79423i	0.230542	−	0.399310i
$382$	−16.7303	+	4.48288i	−0.855998	+	0.229364i
$383$	−23.1822	+	6.21166i	−1.18456	+	0.317401i	−0.796732	−	0.604333i	$-0.793440\pi$
$383$	−23.1822	+	6.21166i	−1.18456	+	0.317401i	−0.387824	+	0.921733i	$0.626773\pi$
$384$	1.73205			0.0883883
$385$		0			0
$386$		−	17.3205i		−	0.881591i
$387$	−30.1146	+	8.06918i	−1.53081	+	0.410179i
$388$	−4.89898	+	4.89898i	−0.248708	+	0.248708i
$389$	12.9904	+	22.5000i	0.658638	+	1.14080i	0.980968	+	0.194168i	$0.0622006\pi$
$389$	12.9904	+	22.5000i	0.658638	+	1.14080i	−0.322330	+	0.946627i	$0.604466\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	1.03528	+	3.86370i	0.0522893	+	0.195146i
$393$	−3.10583	+	11.5911i	−0.156668	+	0.584694i
$394$	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	$-0.250000\pi$
$397$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$398$	−2.58819	+	9.65926i	−0.129734	+	0.484175i
$399$		−	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	$0.840350\pi$
$402$	5.43520	+	20.2844i	0.271083	+	1.01170i
$403$	33.4607	+	8.96575i	1.66679	+	0.446616i
$404$	13.8564			0.689382
$405$		0			0
$406$	−15.0000			−0.744438
$407$	−11.5911	−	3.10583i	−0.574550	−	0.153950i
$408$	−2.68973	−	10.0382i	−0.133161	−	0.496965i
$409$	−1.73205	−	1.00000i	−0.0856444	−	0.0494468i	0.456566	−	0.889689i	$-0.349079\pi$
$409$	−1.73205	−	1.00000i	−0.0856444	−	0.0494468i	−0.542211	+	0.840243i	$0.682412\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$	−0.896575	+	3.34607i	−0.0441711	+	0.164849i
$413$	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
$417$	1.79315	−	6.69213i	0.0878110	−	0.327715i
$418$	1.79315	+	6.69213i	0.0877059	+	0.327323i
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	−0.964582	−	0.263783i	$-0.915030\pi$
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	0.710734	+	0.703461i	$0.248363\pi$
$420$		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
$423$	−8.69333	+	2.32937i	−0.422684	+	0.113258i
$424$		0			0
$425$		0			0
$426$	−6.00000			−0.290701
$427$	21.7494	−	5.82774i	1.05253	−	0.282024i
$428$	−2.89778	+	0.776457i	−0.140069	+	0.0375315i
$429$	−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	$0.946637\pi$
$432$	−1.34486	+	5.01910i	−0.0647048	+	0.241481i
$433$	7.34847	−	7.34847i	0.353145	−	0.353145i	−0.508133	−	0.861278i	$-0.669664\pi$
$433$	7.34847	−	7.34847i	0.353145	−	0.353145i	0.861278	+	0.508133i	$0.169664\pi$
$434$	8.66025	+	15.0000i	0.415705	+	0.720023i
$435$		0			0
$436$	2.50000	−	4.33013i	0.119728	−	0.207375i
$437$	−1.55291	−	5.79555i	−0.0742860	−	0.277239i
$438$	16.9706	+	16.9706i	0.810885	+	0.810885i
$439$	−17.3205	+	10.0000i	−0.826663	+	0.477274i	−0.852709	−	0.522387i	$-0.825042\pi$
$439$	−17.3205	+	10.0000i	−0.826663	+	0.477274i	0.0260459	+	0.999661i	$0.491708\pi$
$440$		0			0
$441$	−12.0000			−0.571429
$442$	−14.6969	−	14.6969i	−0.699062	−	0.699062i
$443$	2.32937	−	8.69333i	0.110672	−	0.413033i	−0.888255	−	0.459351i	$-0.848082\pi$
$443$	2.32937	−	8.69333i	0.110672	−	0.413033i	0.998927	+	0.0463181i	$0.0147488\pi$
$444$	−5.19615	+	3.00000i	−0.246598	+	0.142374i
$445$		0			0
$446$	13.5000	+	7.79423i	0.639244	+	0.369067i
$447$	−8.69333	−	2.32937i	−0.411181	−	0.110175i
$448$	1.67303	+	0.448288i	0.0790434	+	0.0211796i
$449$	−13.8564			−0.653924			−0.326962	−	0.945037i	$-0.606025\pi$
$449$	−13.8564			−0.653924			−0.326962	+	0.945037i	$0.606025\pi$
$450$		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
$457$	−8.06918	+	30.1146i	−0.377460	+	1.40870i	0.472256	+	0.881461i	$0.343440\pi$
$457$	−8.06918	+	30.1146i	−0.377460	+	1.40870i	−0.849717	+	0.527240i	$0.823227\pi$
$458$	−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	$0.242221\pi$
$462$	−10.0382	+	2.68973i	−0.467019	+	0.125137i
$463$	4.48288	+	16.7303i	0.208337	+	0.777524i	0.988406	+	0.151831i	$0.0485170\pi$
$463$	4.48288	+	16.7303i	0.208337	+	0.777524i	−0.780069	+	0.625693i	$0.784816\pi$
$464$	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	−0.197692	+	0.980264i	$0.563345\pi$
$467$	−25.4558	+	25.4558i	−1.17796	+	1.17796i	−0.980264	+	0.197692i	$0.936655\pi$
$468$	2.68973	+	10.0382i	0.124333	+	0.464016i
$469$			21.0000i			0.969690i
$470$		0			0
$471$	18.0000	+	31.1769i	0.829396	+	1.43656i
$472$	−6.69213	+	1.79315i	−0.308030	+	0.0825365i
$473$	34.7733	−	9.31749i	1.59888	−	0.428418i
$474$	−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	$-0.948443\pi$
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	0.353796	−	0.935323i	$-0.384891\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	−4.39992	−	16.4207i	−0.200411	−	0.747944i
$483$	8.69333	−	2.32937i	0.395560	−	0.105990i
$484$	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	0.202337	−	0.979316i	$-0.435146\pi$
$487$	−17.1464	−	17.1464i	−0.776979	−	0.776979i	−0.979316	+	0.202337i	$0.935146\pi$
$488$	−3.36465	+	12.5570i	−0.152310	+	0.568430i
$489$	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
$493$	−50.1910	−	13.4486i	−2.26049	−	0.605696i
$494$	6.92820			0.311715
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−5.79555	−	1.55291i	−0.259966	−	0.0696577i
$498$	5.01910	+	1.34486i	0.224911	+	0.0602648i
$499$	38.1051	+	22.0000i	1.70582	+	0.984855i	0.939599	+	0.342277i	$0.111198\pi$
$499$	38.1051	+	22.0000i	1.70582	+	0.984855i	0.766220	+	0.642578i	$0.222135\pi$
$500$		0			0
$501$	−13.5000	+	7.79423i	−0.603136	+	0.348220i
$502$	−2.68973	+	10.0382i	−0.120048	+	0.448027i
$503$	6.36396	+	6.36396i	0.283755	+	0.283755i	0.834605	−	0.550850i	$-0.185696\pi$
$503$	6.36396	+	6.36396i	0.283755	+	0.283755i	−0.550850	+	0.834605i	$0.685696\pi$
$504$	−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
$508$	1.34486	+	5.01910i	0.0596687	+	0.222686i
$509$	2.59808	−	4.50000i	0.115158	−	0.199459i	−0.802685	−	0.596403i	$-0.796596\pi$
$509$	2.59808	−	4.50000i	0.115158	−	0.199459i	0.917843	+	0.396944i	$0.129929\pi$
$510$		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
$517$	10.0382	−	2.68973i	0.441479	−	0.118294i
$518$	−5.79555	+	1.55291i	−0.254642	+	0.0682311i
$519$	−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	−0.494371	−	0.869251i	$-0.664601\pi$
$523$	8.57321	−	8.57321i	0.374880	−	0.374880i	0.869251	+	0.494371i	$0.164601\pi$
$524$	−3.46410	−	6.00000i	−0.151330	−	0.262111i
$525$		0			0
$526$	−12.0000	+	20.7846i	−0.523225	+	0.906252i
$527$	15.5291	+	57.9555i	0.676460	+	2.52458i
$528$	1.55291	−	5.79555i	0.0675819	−	0.252219i
$529$	−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
$533$	7.76457	−	28.9778i	0.336321	−	1.25517i
$534$		−	3.00000i		−	0.129823i
$535$		0			0
$536$	−10.5000	−	6.06218i	−0.453531	−	0.261846i
$537$	−10.8704	−	40.5689i	−0.469092	−	1.75068i
$538$	1.67303	+	0.448288i	0.0721296	+	0.0193271i
$539$	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	$0.875398\pi$
$542$	−9.65926	−	2.58819i	−0.414901	−	0.111172i
$543$	−3.13801	−	11.7112i	−0.134665	−	0.502577i
$544$	5.19615	+	3.00000i	0.222783	+	0.128624i
$545$		0			0
$546$			10.3923i			0.444750i
$547$	−0.448288	+	1.67303i	−0.0191674	+	0.0715337i	−0.974847	−	0.222875i	$-0.928456\pi$
$547$	−0.448288	+	1.67303i	−0.0191674	+	0.0715337i	0.955680	+	0.294408i	$0.0951226\pi$
$548$	−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
$552$	−1.34486	+	5.01910i	−0.0572412	+	0.213627i
$553$	−1.79315	−	6.69213i	−0.0762525	−	0.284578i
$554$	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	0.0819634	−	0.996635i	$-0.473881\pi$
$557$	25.4558	−	25.4558i	1.07860	−	1.07860i	0.996635	−	0.0819634i	$-0.0261191\pi$
$558$	7.76457	−	28.9778i	0.328701	−	1.22673i
$559$		−	36.0000i		−	1.52264i
$560$		0			0
$561$	−36.0000			−1.51992
$562$	5.01910	−	1.34486i	0.211718	−	0.0567296i
$563$	−20.2844	+	5.43520i	−0.854887	+	0.229066i	−0.659542	−	0.751668i	$-0.729250\pi$
$563$	−20.2844	+	5.43520i	−0.854887	+	0.229066i	−0.195346	+	0.980734i	$0.562583\pi$
$564$	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	0.784233	−	0.620466i	$-0.213057\pi$
$569$	−3.46410	−	6.00000i	−0.145223	−	0.251533i	−0.929456	+	0.368933i	$0.879723\pi$
$570$		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	$0.139994\pi$
$572$	−3.10583	−	11.5911i	−0.129861	−	0.484649i
$573$	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	0.999801	+	0.0199346i	$0.00634581\pi$
$577$	24.4949	+	24.4949i	1.01974	+	1.01974i	0.0199346	+	0.999801i	$0.493654\pi$
$578$	4.91756	−	18.3526i	0.204544	−	0.763367i
$579$	−25.9808	+	15.0000i	−1.07972	+	0.623379i
$580$		0			0
$581$	4.50000	+	2.59808i	0.186691	+	0.107786i
$582$	11.5911	+	3.10583i	0.480467	+	0.128741i
$583$		0			0
$584$	−13.8564			−0.573382
$585$		0			0
$586$	30.0000			1.23929
$587$	−2.89778	−	0.776457i	−0.119604	−	0.0320478i	0.198520	−	0.980097i	$-0.436386\pi$
$587$	−2.89778	−	0.776457i	−0.119604	−	0.0320478i	−0.318125	+	0.948049i	$0.603053\pi$
$588$	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
$592$	0.896575	−	3.34607i	0.0368490	−	0.137522i
$593$	12.7279	+	12.7279i	0.522673	+	0.522673i	0.918378	−	0.395705i	$-0.129500\pi$
$593$	12.7279	+	12.7279i	0.522673	+	0.522673i	−0.395705	+	0.918378i	$0.629500\pi$
$594$	15.5885	+	9.00000i	0.639602	+	0.369274i
$595$		0			0
$596$	4.50000	−	2.59808i	0.184327	−	0.106421i
$597$	16.7303	−	4.48288i	0.684727	−	0.183472i
$598$	2.68973	+	10.0382i	0.109991	+	0.410492i
$599$	13.8564	−	24.0000i	0.566157	−	0.980613i	−0.430784	−	0.902455i	$-0.641763\pi$
$599$	13.8564	−	24.0000i	0.566157	−	0.980613i	0.996941	−	0.0781581i	$-0.0249039\pi$
$600$		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
$607$	38.4797	−	10.3106i	1.56184	−	0.418495i	0.628598	−	0.777730i	$-0.283629\pi$
$607$	38.4797	−	10.3106i	1.56184	−	0.418495i	0.933247	+	0.359235i	$0.116962\pi$
$608$	−1.93185	+	0.517638i	−0.0783469	+	0.0209930i
$609$	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	−0.909774	−	0.415104i	$-0.863745\pi$
$613$	−12.2474	+	12.2474i	−0.494670	+	0.494670i	0.415104	+	0.909774i	$0.363745\pi$
$614$	−2.59808	−	4.50000i	−0.104850	−	0.181605i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	−9.31749	−	34.7733i	−0.375108	−	1.39992i	−0.853187	−	0.521605i	$-0.825334\pi$
$617$	−9.31749	−	34.7733i	−0.375108	−	1.39992i	0.478079	−	0.878317i	$-0.341333\pi$
$618$	5.79555	−	1.55291i	0.233131	−	0.0624674i
$619$	19.0526	−	11.0000i	0.765787	−	0.442127i	−0.0655827	−	0.997847i	$-0.520891\pi$
$619$	19.0526	−	11.0000i	0.765787	−	0.442127i	0.831370	+	0.555720i	$0.187557\pi$
$620$		0			0
$621$	−13.5000	−	7.79423i	−0.541736	−	0.312772i
$622$	−17.1464	−	17.1464i	−0.687509	−	0.687509i
$623$	0.776457	−	2.89778i	0.0311081	−	0.116097i
$624$	−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
$628$	−20.0764	−	5.37945i	−0.801135	−	0.214664i
$629$	−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	$0.603171\pi$
$632$	3.86370	+	1.03528i	0.153690	+	0.0411811i
$633$	−36.8067	−	9.86233i	−1.46294	−	0.391992i
$634$	−5.19615	−	3.00000i	−0.206366	−	0.119145i
$635$		0			0
$636$		0			0
$637$	3.58630	−	13.3843i	0.142094	−	0.530304i
$638$	−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
$643$	1.34486	+	5.01910i	0.0530362	+	0.197934i	0.987361	−	0.158490i	$-0.0506626\pi$
$643$	1.34486	+	5.01910i	0.0530362	+	0.197934i	−0.934324	+	0.356424i	$0.883996\pi$
$644$	−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	$-0.885448\pi$
$647$	−14.8492	+	14.8492i	−0.583784	+	0.583784i	0.352157	+	0.935941i	$0.385448\pi$
$648$	8.69333	−	2.32937i	0.341506	−	0.0915064i
$649$			24.0000i			0.942082i
$650$		0			0
$651$	15.0000	−	25.9808i	0.587896	−	1.01827i
$652$	−16.7303	+	4.48288i	−0.655210	+	0.175563i
$653$	−17.3867	+	4.65874i	−0.680393	+	0.182311i	−0.582432	−	0.812880i	$-0.697899\pi$
$653$	−17.3867	+	4.65874i	−0.680393	+	0.182311i	−0.0979610	+	0.995190i	$0.531232\pi$
$654$	−8.66025			−0.338643
$655$		0			0
$656$			8.66025i			0.338126i
$657$	10.7589	−	40.1528i	0.419745	−	1.56651i
$658$	3.67423	−	3.67423i	0.143237	−	0.143237i
$659$	−10.3923	−	18.0000i	−0.404827	−	0.701180i	0.589475	−	0.807787i	$-0.299335\pi$
$659$	−10.3923	−	18.0000i	−0.404827	−	0.701180i	−0.994301	+	0.106606i	$0.966001\pi$
$660$		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	$0.307396\pi$
$662$	−2.07055	−	7.72741i	−0.0804743	−	0.300334i
$663$	−9.31749	+	34.7733i	−0.361861	+	1.35048i
$664$	−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
$668$	2.32937	−	8.69333i	0.0901261	−	0.336355i
$669$		−	27.0000i		−	1.04388i
$670$		0			0
$671$	39.0000	+	22.5167i	1.50558	+	0.869246i
$672$	−0.776457	−	2.89778i	−0.0299525	−	0.111784i
$673$	−36.8067	−	9.86233i	−1.41879	−	0.380165i	−0.533739	−	0.845649i	$-0.679213\pi$
$673$	−36.8067	−	9.86233i	−1.41879	−	0.380165i	−0.885056	+	0.465485i	$0.845880\pi$
$674$	−13.8564			−0.533729
$675$		0			0
$676$	1.00000			0.0384615
$677$	5.79555	+	1.55291i	0.222741	+	0.0596833i	0.368464	−	0.929642i	$-0.379884\pi$
$677$	5.79555	+	1.55291i	0.222741	+	0.0596833i	−0.145722	+	0.989326i	$0.546551\pi$
$678$		0			0
$679$	10.3923	+	6.00000i	0.398820	+	0.230259i
$680$		0			0
$681$		−	41.5692i		−	1.59294i
$682$	−8.96575	+	33.4607i	−0.343316	+	1.28127i
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$		−	6.00000i		−	0.229416i
$685$		0			0
$686$	16.5000	−	9.52628i	0.629973	−	0.363715i
$687$	−2.24144	+	8.36516i	−0.0855162	+	0.319151i
$688$	2.68973	+	10.0382i	0.102545	+	0.382703i
$689$		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
$697$	50.1910	−	13.4486i	1.90112	−	0.509403i
$698$	−0.965926	+	0.258819i	−0.0365608	+	0.00979645i
$699$	−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
$707$	−6.21166	−	23.1822i	−0.233613	−	0.871857i
$708$	8.48528	+	8.48528i	0.318896	+	0.318896i
$709$	35.5070	−	20.5000i	1.33349	−	0.769894i	0.347661	−	0.937620i	$-0.386976\pi$
$709$	35.5070	−	20.5000i	1.33349	−	0.769894i	0.985834	+	0.167727i	$0.0536426\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	1.22474	+	1.22474i	0.0458993	+	0.0458993i
$713$	7.76457	−	28.9778i	0.290785	−	1.08523i
$714$	−15.5885	+	9.00000i	−0.583383	+	0.336817i
$715$		0			0
$716$	21.0000	+	12.1244i	0.784807	+	0.453108i
$717$	34.7733	+	9.31749i	1.29863	+	0.347968i
$718$	−16.7303	−	4.48288i	−0.624370	−	0.167299i
$719$	6.92820			0.258378			0.129189	−	0.991620i	$-0.458763\pi$
$719$	6.92820			0.258378			0.129189	+	0.991620i	$0.458763\pi$
$720$		0			0
$721$	6.00000			0.223452
$722$	14.4889	+	3.88229i	0.539221	+	0.144484i
$723$	−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
$727$	1.34486	−	5.01910i	0.0498782	−	0.186148i	−0.936492	−	0.350689i	$-0.885948\pi$
$727$	1.34486	−	5.01910i	0.0498782	−	0.186148i	0.986370	+	0.164541i	$0.0526142\pi$
$728$	−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
$732$	21.7494	−	5.82774i	0.803882	−	0.215399i
$733$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$733$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$734$	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
$738$	−25.0955	−	6.72432i	−0.923778	−	0.247525i
$739$		−	4.00000i		−	0.147142i	−0.997290	−	0.0735712i	$-0.976560\pi$
$739$		−	4.00000i		−	0.147142i	0.997290	−	0.0735712i	$-0.0234396\pi$
$740$		0			0
$741$	−6.00000	−	10.3923i	−0.220416	−	0.381771i
$742$		0			0
$743$	26.0800	−	6.98811i	0.956782	−	0.256369i	0.253544	−	0.967324i	$-0.418404\pi$
$743$	26.0800	−	6.98811i	0.956782	−	0.256369i	0.703238	+	0.710955i	$0.251737\pi$
$744$	8.66025	+	15.0000i	0.317500	+	0.549927i
$745$		0			0
$746$		−	13.8564i		−	0.507319i
$747$	−2.32937	−	8.69333i	−0.0852272	−	0.318072i
$748$	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	$0.155049\pi$
$752$	0.776457	+	2.89778i	0.0283145	+	0.105671i
$753$	17.3867	−	4.65874i	0.633605	−	0.169774i
$754$	−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	−0.985040	−	0.172327i	$-0.944871\pi$
$757$	−31.8434	−	31.8434i	−1.15737	−	1.15737i	−0.172327	−	0.985040i	$-0.555129\pi$
$758$	−2.07055	+	7.72741i	−0.0752058	+	0.280672i
$759$	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
$763$	−8.36516	−	2.24144i	−0.302839	−	0.0811455i
$764$	−17.3205			−0.626634
$765$		0			0
$766$	−24.0000			−0.867155
$767$	23.1822	+	6.21166i	0.837061	+	0.224290i
$768$	1.67303	+	0.448288i	0.0603704	+	0.0161762i
$769$	19.9186	+	11.5000i	0.718283	+	0.414701i	0.814120	−	0.580696i	$-0.197220\pi$
$769$	19.9186	+	11.5000i	0.718283	+	0.414701i	−0.0958377	+	0.995397i	$0.530553\pi$
$770$		0			0
$771$		0			0
$772$	4.48288	−	16.7303i	0.161342	−	0.602138i
$773$	−25.4558	−	25.4558i	−0.915583	−	0.915583i	0.0811212	−	0.996704i	$-0.474150\pi$
$773$	−25.4558	−	25.4558i	−0.915583	−	0.915583i	−0.996704	+	0.0811212i	$0.974150\pi$
$774$	−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
$778$	6.72432	+	25.0955i	0.241078	+	0.899717i
$779$	−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
$783$	11.6469	−	43.4667i	0.416225	−	1.55337i
$784$			4.00000i			0.142857i
$785$		0			0
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$	3.34607	−	0.896575i	0.119274	−	0.0319595i	−0.198688	−	0.980063i	$-0.563668\pi$
$787$	3.34607	−	0.896575i	0.119274	−	0.0319595i	0.317962	+	0.948103i	$0.397001\pi$
$788$	11.5911	−	3.10583i	0.412916	−	0.110641i
$789$	41.5692			1.47990
$790$		0			0
$791$		0			0
$792$	−10.0382	+	2.68973i	−0.356692	+	0.0955753i
$793$	31.8434	−	31.8434i	1.13079	−	1.13079i
$794$		0			0
$795$		0			0
$796$	−5.00000	+	8.66025i	−0.177220	+	0.306955i
$797$	10.8704	+	40.5689i	0.385049	+	1.43702i	0.838089	+	0.545533i	$0.183673\pi$
$797$	10.8704	+	40.5689i	0.385049	+	1.43702i	−0.453040	+	0.891490i	$0.649660\pi$
$798$	1.55291	−	5.79555i	0.0549726	−	0.205160i
$799$	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
$803$	−12.4233	+	46.3644i	−0.438409	+	1.63617i
$804$			21.0000i			0.740613i
$805$		0			0
$806$	30.0000	+	17.3205i	1.05670	+	0.610089i
$807$	−0.776457	−	2.89778i	−0.0273326	−	0.102007i
$808$	13.3843	+	3.58630i	0.470857	+	0.126166i
$809$	−6.92820			−0.243583			−0.121791	−	0.992556i	$-0.538864\pi$
$809$	−6.92820			−0.243583			−0.121791	+	0.992556i	$0.538864\pi$
$810$		0			0
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$	−14.4889	−	3.88229i	−0.508460	−	0.136242i
$813$	4.48288	+	16.7303i	0.157221	+	0.586758i
$814$	−10.3923	−	6.00000i	−0.364250	−	0.210300i
$815$		0			0
$816$		−	10.3923i		−	0.363803i
$817$	−5.37945	+	20.0764i	−0.188203	+	0.702384i
$818$	−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	$0.441215\pi$
$822$	−5.37945	+	20.0764i	−0.187630	+	0.700245i
$823$	7.62089	+	28.4416i	0.265648	+	0.991410i	0.961853	+	0.273567i	$0.0882037\pi$
$823$	7.62089	+	28.4416i	0.265648	+	0.991410i	−0.696205	+	0.717843i	$0.745130\pi$
$824$	−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	0.112874	−	0.993609i	$-0.463994\pi$
$827$	31.8198	−	31.8198i	1.10648	−	1.10648i	0.993609	−	0.112874i	$-0.0360055\pi$
$828$	8.69333	−	2.32937i	0.302114	−	0.0809513i
$829$			29.0000i			1.00721i	0.863934	+	0.503606i	$0.167994\pi$
$829$			29.0000i			1.00721i	−0.863934	+	0.503606i	$0.832006\pi$
$830$		0			0
$831$	−18.0000			−0.624413
$832$	3.34607	−	0.896575i	0.116004	−	0.0310832i
$833$	23.1822	−	6.21166i	0.803216	−	0.215221i
$834$	3.46410	−	6.00000i	0.119952	−	0.207763i
$835$		0			0
$836$			6.92820i			0.239617i
$837$	−50.1910	+	13.4486i	−1.73485	+	0.464853i
$838$	−7.34847	+	7.34847i	−0.253849	+	0.253849i
$839$	−19.0526	−	33.0000i	−0.657767	−	1.13929i	−0.981192	−	0.193033i	$-0.938168\pi$
$839$	−19.0526	−	33.0000i	−0.657767	−	1.13929i	0.323425	−	0.946254i	$-0.395166\pi$
$840$		0			0
$841$	−23.0000	+	39.8372i	−0.793103	+	1.37370i
$842$	−2.58819	−	9.65926i	−0.0891949	−	0.332880i
$843$	−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
$852$	−5.79555	−	1.55291i	−0.198552	−	0.0532020i
$853$	−16.7303	−	4.48288i	−0.572835	−	0.153491i	−0.0392388	−	0.999230i	$-0.512493\pi$
$853$	−16.7303	−	4.48288i	−0.572835	−	0.153491i	−0.533597	+	0.845739i	$0.679160\pi$
$854$	22.5167			0.770504
$855$		0			0
$856$	−3.00000			−0.102538
$857$	−40.5689	−	10.8704i	−1.38581	−	0.371326i	−0.512580	−	0.858640i	$-0.671310\pi$
$857$	−40.5689	−	10.8704i	−1.38581	−	0.371326i	−0.873227	+	0.487314i	$0.837977\pi$
$858$	−14.6969	+	14.6969i	−0.501745	+	0.501745i
$859$	−19.0526	−	11.0000i	−0.650065	−	0.375315i	0.138416	−	0.990374i	$-0.455799\pi$
$859$	−19.0526	−	11.0000i	−0.650065	−	0.375315i	−0.788481	+	0.615059i	$0.789132\pi$
$860$		0			0
$861$	−22.5000	−	12.9904i	−0.766798	−	0.442711i
$862$	−1.79315	+	6.69213i	−0.0610750	+	0.227935i
$863$	10.6066	+	10.6066i	0.361053	+	0.361053i	0.864201	−	0.503148i	$-0.167825\pi$
$863$	10.6066	+	10.6066i	0.361053	+	0.361053i	−0.503148	+	0.864201i	$0.667825\pi$
$864$	−2.59808	+	4.50000i	−0.0883883	+	0.153093i
$865$		0			0
$866$	9.00000	−	5.19615i	0.305832	−	0.176572i
$867$	−31.7876	+	8.51747i	−1.07956	+	0.289268i
$868$	4.48288	+	16.7303i	0.152159	+	0.567864i
$869$	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
$873$	−5.37945	−	20.0764i	−0.182067	−	0.679483i
$874$		−	6.00000i		−	0.202953i
$875$		0			0
$876$	12.0000	+	20.7846i	0.405442	+	0.702247i
$877$	−16.7303	+	4.48288i	−0.564943	+	0.151376i	−0.529976	−	0.848012i	$-0.677799\pi$
$877$	−16.7303	+	4.48288i	−0.564943	+	0.151376i	−0.0349667	+	0.999388i	$0.511133\pi$
$878$	−19.3185	+	5.17638i	−0.651968	+	0.174694i
$879$	−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	$-0.00928869\pi$
$882$	−11.5911	−	3.10583i	−0.390293	−	0.104579i
$883$	30.6186	−	30.6186i	1.03040	−	1.03040i	0.0308754	−	0.999523i	$-0.490170\pi$
$883$	30.6186	−	30.6186i	1.03040	−	1.03040i	0.999523	−	0.0308754i	$-0.00982951\pi$
$884$	−10.3923	−	18.0000i	−0.349531	−	0.605406i
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	6.21166	+	23.1822i	0.208567	+	0.778383i	0.988333	+	0.152311i	$0.0486716\pi$
$887$	6.21166	+	23.1822i	0.208567	+	0.778383i	−0.779766	+	0.626072i	$0.784662\pi$
$888$	−5.79555	+	1.55291i	−0.194486	+	0.0521124i
$889$	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
$893$	−1.55291	+	5.79555i	−0.0519663	+	0.193941i
$894$	−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
$898$	−13.3843	−	3.58630i	−0.446639	−	0.119676i
$899$	86.6025			2.88836
$900$		0			0
$901$		0			0
$902$	28.9778	+	7.76457i	0.964854	+	0.258532i
$903$	−30.1146	−	8.06918i	−1.00215	−	0.268525i
$904$		0			0
$905$		0			0
$906$	−15.0000	+	8.66025i	−0.498342	+	0.287718i
$907$	−2.24144	+	8.36516i	−0.0744257	+	0.277761i	−0.993102	−	0.117250i	$-0.962592\pi$
$907$	−2.24144	+	8.36516i	−0.0744257	+	0.277761i	0.918677	+	0.395010i	$0.129259\pi$
$908$	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
$913$	2.68973	+	10.0382i	0.0890170	+	0.332216i
$914$	−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
$918$	30.1146	+	8.06918i	0.993929	+	0.266323i
$919$		−	40.0000i		−	1.31948i	−0.751495	−	0.659739i	$-0.770667\pi$
$919$		−	40.0000i		−	1.31948i	0.751495	−	0.659739i	$-0.229333\pi$
$920$		0			0
$921$	−4.50000	+	7.79423i	−0.148280	+	0.256829i
$922$	11.7112	−	3.13801i	0.385689	−	0.103345i
$923$	−11.5911	+	3.10583i	−0.381526	+	0.102230i
$924$	−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	0.917241	−	0.398333i	$-0.130411\pi$
$929$	3.46410	+	6.00000i	0.113653	+	0.196854i	−0.803587	+	0.595187i	$0.797078\pi$
$930$		0			0
$931$	−4.00000	+	6.92820i	−0.131095	+	0.227063i
$932$	−1.55291	−	5.79555i	−0.0508674	−	0.189840i
$933$	−10.8704	+	40.5689i	−0.355881	+	1.32817i
$934$	−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	0.528714	−	0.848800i	$-0.322674\pi$
$937$	−9.79796	−	9.79796i	−0.320085	−	0.320085i	−0.848800	+	0.528714i	$0.822674\pi$
$938$	−5.43520	+	20.2844i	−0.177466	+	0.662311i
$939$			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	$0.693658\pi$
$942$	9.31749	+	34.7733i	0.303580	+	1.13298i
$943$	−25.0955	−	6.72432i	−0.817222	−	0.218974i
$944$	−6.92820			−0.225494
$945$		0			0
$946$	36.0000			1.17046
$947$	−26.0800	−	6.98811i	−0.847486	−	0.227083i	−0.191158	−	0.981559i	$-0.561224\pi$
$947$	−26.0800	−	6.98811i	−0.847486	−	0.227083i	−0.656328	+	0.754476i	$0.727891\pi$
$948$	−1.79315	−	6.69213i	−0.0582388	−	0.217350i
$949$	41.5692	+	24.0000i	1.34939	+	0.779073i
$950$		0			0
$951$			10.3923i			0.336994i
$952$	2.68973	−	10.0382i	0.0871745	−	0.325340i
$953$	29.6985	+	29.6985i	0.962028	+	0.962028i	0.999305	−	0.0372767i	$-0.0118683\pi$
$953$	29.6985	+	29.6985i	0.962028	+	0.962028i	−0.0372767	+	0.999305i	$0.511868\pi$
$954$		0			0
$955$		0			0
$956$	−18.0000	+	10.3923i	−0.582162	+	0.336111i
$957$	−13.4486	+	50.1910i	−0.434733	+	1.62244i
$958$	−7.17260	−	26.7685i	−0.231736	−	0.864852i
$959$	−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
$963$	2.32937	−	8.69333i	0.0750629	−	0.280139i
$964$		−	17.0000i		−	0.547533i
$965$		0			0
$966$	9.00000			0.289570
$967$	−51.8640	+	13.8969i	−1.66783	+	0.446895i	−0.964525	−	0.263990i	$-0.914961\pi$
$967$	−51.8640	+	13.8969i	−1.66783	+	0.446895i	−0.703309	+	0.710885i	$0.748295\pi$
$968$	0.965926	−	0.258819i	0.0310460	−	0.00831876i
$969$	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
$977$	−10.8704	−	40.5689i	−0.347775	−	1.29791i	−0.889337	−	0.457253i	$-0.848833\pi$
$977$	−10.8704	−	40.5689i	−0.347775	−	1.29791i	0.541562	−	0.840661i	$-0.317833\pi$
$978$	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
$983$	−2.32937	+	8.69333i	−0.0742954	+	0.277274i	−0.993073	−	0.117502i	$-0.962511\pi$
$983$	−2.32937	+	8.69333i	−0.0742954	+	0.277274i	0.918777	+	0.394776i	$0.129178\pi$
$984$	12.9904	−	7.50000i	0.414118	−	0.239091i
$985$		0			0
$986$	−45.0000	−	25.9808i	−1.43309	−	0.827396i
$987$	−8.69333	−	2.32937i	−0.276712	−	0.0741447i
$988$	6.69213	+	1.79315i	0.212905	+	0.0570477i
$989$	−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	$0.397103\pi$
$992$	−9.65926	−	2.58819i	−0.306682	−	0.0821751i
$993$	−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
$997$	−10.7589	+	40.1528i	−0.340738	+	1.27165i	0.556775	+	0.830663i	$0.312039\pi$
$997$	−10.7589	+	40.1528i	−0.340738	+	1.27165i	−0.897513	+	0.440988i	$0.854628\pi$
$998$	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.257.2	yes	8
3.2	odd	2		1350.2.q.b.557.1		8
5.2	odd	4	inner	450.2.p.d.293.1	yes	8
5.3	odd	4	inner	450.2.p.d.293.2	yes	8
5.4	even	2	inner	450.2.p.d.257.1	✓	8
9.2	odd	6	inner	450.2.p.d.407.2	yes	8
9.7	even	3		1350.2.q.b.1007.1		8
15.2	even	4		1350.2.q.b.1043.2		8
15.8	even	4		1350.2.q.b.1043.1		8
15.14	odd	2		1350.2.q.b.557.2		8
45.2	even	12	inner	450.2.p.d.443.1	yes	8
45.7	odd	12		1350.2.q.b.143.2		8
45.29	odd	6	inner	450.2.p.d.407.1	yes	8
45.34	even	6		1350.2.q.b.1007.2		8
45.38	even	12	inner	450.2.p.d.443.2	yes	8
45.43	odd	12		1350.2.q.b.143.1		8

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

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)

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

L-functions

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