LMFDB - Embedded newform 450.2.p.f.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.f.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.448288 + 1.67303i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(3.34607 + 0.896575i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.448288 + 1.67303i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(3.34607 + 0.896575i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-1.50000 + 0.866025i) q^{11} +(1.22474 - 1.22474i) q^{12} +(3.34607 - 0.896575i) q^{13} +(1.73205 - 3.00000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.12132 + 2.12132i) q^{17} +(-2.12132 + 2.12132i) q^{18} +7.00000i q^{19} +(-3.00000 + 5.19615i) q^{21} +(0.448288 + 1.67303i) q^{22} +(1.55291 + 5.79555i) q^{23} +(-0.866025 - 1.50000i) q^{24} -3.46410i q^{26} +(3.67423 - 3.67423i) q^{27} +(-2.44949 - 2.44949i) q^{28} +(1.73205 + 3.00000i) q^{29} +(4.00000 - 6.92820i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.776457 - 2.89778i) q^{33} +(2.59808 - 1.50000i) q^{34} +(1.50000 + 2.59808i) q^{36} +(4.89898 - 4.89898i) q^{37} +(6.76148 + 1.81173i) q^{38} +6.00000i q^{39} +(-10.5000 - 6.06218i) q^{41} +(4.24264 + 4.24264i) q^{42} +(-1.34486 + 5.01910i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(-1.55291 + 5.79555i) q^{47} +(-1.67303 + 0.448288i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(-3.34607 - 0.896575i) q^{52} +(-2.59808 - 4.50000i) q^{54} +(-3.00000 + 1.73205i) q^{56} +(-11.7112 - 3.13801i) q^{57} +(3.34607 - 0.896575i) q^{58} +(6.06218 - 10.5000i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-5.65685 - 5.65685i) q^{62} +(-7.34847 - 7.34847i) q^{63} -1.00000i q^{64} -3.00000 q^{66} +(0.448288 + 1.67303i) q^{67} +(-0.776457 - 2.89778i) q^{68} -10.3923 q^{69} -13.8564i q^{71} +(2.89778 - 0.776457i) q^{72} +(-6.12372 - 6.12372i) q^{73} +(-3.46410 - 6.00000i) q^{74} +(3.50000 - 6.06218i) q^{76} +(-5.79555 + 1.55291i) q^{77} +(5.79555 + 1.55291i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(4.50000 + 7.79423i) q^{81} +(-8.57321 + 8.57321i) q^{82} +(-11.5911 - 3.10583i) q^{83} +(5.19615 - 3.00000i) q^{84} +(4.50000 + 2.59808i) q^{86} +(-5.79555 + 1.55291i) q^{87} +(0.448288 - 1.67303i) q^{88} -6.92820 q^{89} +12.0000 q^{91} +(1.55291 - 5.79555i) q^{92} +(9.79796 + 9.79796i) q^{93} +(5.19615 + 3.00000i) q^{94} +1.73205i q^{96} +(-8.36516 - 2.24144i) q^{97} +(3.53553 - 3.53553i) q^{98} +5.19615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{6}+O(q^{10}) $ 8 * q + 12 * q^6	$ 8 q + 12 q^{6} - 12 q^{11} + 4 q^{16} - 24 q^{21} + 32 q^{31} + 12 q^{36} - 84 q^{41} + 48 q^{46} - 36 q^{51} - 24 q^{56} + 16 q^{61} - 24 q^{66} + 28 q^{76} + 36 q^{81} + 36 q^{86} + 96 q^{91}+O(q^{100}) $ 8 * q + 12 * q^6 - 12 * q^11 + 4 * q^16 - 24 * q^21 + 32 * q^31 + 12 * q^36 - 84 * q^41 + 48 * q^46 - 36 * q^51 - 24 * q^56 + 16 * q^61 - 24 * q^66 + 28 * q^76 + 36 * q^81 + 36 * q^86 + 96 * q^91

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
$3$	−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
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	3.34607	+	0.896575i	1.26469	+	0.338874i	0.827996	−	0.560734i	$-0.189481\pi$
$7$	3.34607	+	0.896575i	1.26469	+	0.338874i	0.436698	+	0.899608i	$0.356148\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$		0			0
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	0.256520	+	0.966539i	$0.417424\pi$
$12$	1.22474	−	1.22474i	0.353553	−	0.353553i
$13$	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	$0.257164\pi$
$14$	1.73205	−	3.00000i	0.462910	−	0.801784i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.12132	+	2.12132i	0.514496	+	0.514496i	0.915901	−	0.401405i	$-0.131478\pi$
$17$	2.12132	+	2.12132i	0.514496	+	0.514496i	−0.401405	+	0.915901i	$0.631478\pi$
$18$	−2.12132	+	2.12132i	−0.500000	+	0.500000i
$19$			7.00000i			1.60591i	0.596040	+	0.802955i	$0.296740\pi$
$19$			7.00000i			1.60591i	−0.596040	+	0.802955i	$0.703260\pi$
$20$		0			0
$21$	−3.00000	+	5.19615i	−0.654654	+	1.13389i
$22$	0.448288	+	1.67303i	0.0955753	+	0.356692i
$23$	1.55291	+	5.79555i	0.323805	+	1.20846i	0.915508	+	0.402300i	$0.131789\pi$
$23$	1.55291	+	5.79555i	0.323805	+	1.20846i	−0.591703	+	0.806156i	$0.701544\pi$
$24$	−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
$28$	−2.44949	−	2.44949i	−0.462910	−	0.462910i
$29$	1.73205	+	3.00000i	0.321634	+	0.557086i	0.980825	−	0.194889i	$-0.0624347\pi$
$29$	1.73205	+	3.00000i	0.321634	+	0.557086i	−0.659192	+	0.751975i	$0.729101\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.776457	−	2.89778i	−0.135164	−	0.504438i
$34$	2.59808	−	1.50000i	0.445566	−	0.257248i
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	4.89898	−	4.89898i	0.805387	−	0.805387i	−0.178545	−	0.983932i	$-0.557139\pi$
$37$	4.89898	−	4.89898i	0.805387	−	0.805387i	0.983932	+	0.178545i	$0.0571389\pi$
$38$	6.76148	+	1.81173i	1.09686	+	0.293902i
$39$			6.00000i			0.960769i
$40$		0			0
$41$	−10.5000	−	6.06218i	−1.63982	−	0.946753i	−0.980892	−	0.194551i	$-0.937675\pi$
$41$	−10.5000	−	6.06218i	−1.63982	−	0.946753i	−0.658932	−	0.752202i	$-0.728992\pi$
$42$	4.24264	+	4.24264i	0.654654	+	0.654654i
$43$	−1.34486	+	5.01910i	−0.205090	+	0.765405i	0.784332	+	0.620341i	$0.213006\pi$
$43$	−1.34486	+	5.01910i	−0.205090	+	0.765405i	−0.989422	+	0.145065i	$0.953661\pi$
$44$	1.73205			0.261116
$45$		0			0
$46$	6.00000			0.884652
$47$	−1.55291	+	5.79555i	−0.226516	+	0.845369i	0.755276	+	0.655407i	$0.227503\pi$
$47$	−1.55291	+	5.79555i	−0.226516	+	0.845369i	−0.981792	+	0.189961i	$0.939164\pi$
$48$	−1.67303	+	0.448288i	−0.241481	+	0.0647048i
$49$	4.33013	+	2.50000i	0.618590	+	0.357143i
$50$		0			0
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	−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
$56$	−3.00000	+	1.73205i	−0.400892	+	0.231455i
$57$	−11.7112	−	3.13801i	−1.55119	−	0.415640i
$58$	3.34607	−	0.896575i	0.439360	−	0.117726i
$59$	6.06218	−	10.5000i	0.789228	−	1.36698i	−0.137212	−	0.990542i	$-0.543814\pi$
$59$	6.06218	−	10.5000i	0.789228	−	1.36698i	0.926440	−	0.376442i	$-0.122853\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−5.65685	−	5.65685i	−0.718421	−	0.718421i
$63$	−7.34847	−	7.34847i	−0.925820	−	0.925820i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−3.00000			−0.369274
$67$	0.448288	+	1.67303i	0.0547671	+	0.204393i	0.987888	−	0.155170i	$-0.0495924\pi$
$67$	0.448288	+	1.67303i	0.0547671	+	0.204393i	−0.933121	+	0.359563i	$0.882926\pi$
$68$	−0.776457	−	2.89778i	−0.0941593	−	0.351407i
$69$	−10.3923			−1.25109
$70$		0			0
$71$		−	13.8564i		−	1.64445i	−0.569160	−	0.822226i	$-0.692732\pi$
$71$		−	13.8564i		−	1.64445i	0.569160	−	0.822226i	$-0.307268\pi$
$72$	2.89778	−	0.776457i	0.341506	−	0.0915064i
$73$	−6.12372	−	6.12372i	−0.716728	−	0.716728i	0.251206	−	0.967934i	$-0.419173\pi$
$73$	−6.12372	−	6.12372i	−0.716728	−	0.716728i	−0.967934	+	0.251206i	$0.919173\pi$
$74$	−3.46410	−	6.00000i	−0.402694	−	0.697486i
$75$		0			0
$76$	3.50000	−	6.06218i	0.401478	−	0.695379i
$77$	−5.79555	+	1.55291i	−0.660465	+	0.176971i
$78$	5.79555	+	1.55291i	0.656217	+	0.175833i
$79$	−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
$82$	−8.57321	+	8.57321i	−0.946753	+	0.946753i
$83$	−11.5911	−	3.10583i	−1.27229	−	0.340909i	−0.441382	−	0.897319i	$-0.645512\pi$
$83$	−11.5911	−	3.10583i	−1.27229	−	0.340909i	−0.830908	+	0.556410i	$0.812178\pi$
$84$	5.19615	−	3.00000i	0.566947	−	0.327327i
$85$		0			0
$86$	4.50000	+	2.59808i	0.485247	+	0.280158i
$87$	−5.79555	+	1.55291i	−0.621349	+	0.166490i
$88$	0.448288	−	1.67303i	0.0477876	−	0.178346i
$89$	−6.92820			−0.734388			−0.367194	−	0.930144i	$-0.619682\pi$
$89$	−6.92820			−0.734388			−0.367194	+	0.930144i	$0.619682\pi$
$90$		0			0
$91$	12.0000			1.25794
$92$	1.55291	−	5.79555i	0.161903	−	0.604228i
$93$	9.79796	+	9.79796i	1.01600	+	1.01600i
$94$	5.19615	+	3.00000i	0.535942	+	0.309426i
$95$		0			0
$96$			1.73205i			0.176777i
$97$	−8.36516	−	2.24144i	−0.849354	−	0.227584i	−0.192215	−	0.981353i	$-0.561567\pi$
$97$	−8.36516	−	2.24144i	−0.849354	−	0.227584i	−0.657139	+	0.753769i	$0.728234\pi$
$98$	3.53553	−	3.53553i	0.357143	−	0.357143i
$99$	5.19615			0.522233
$100$		0			0
$101$	−6.00000	+	3.46410i	−0.597022	+	0.344691i	−0.767869	−	0.640607i	$-0.778683\pi$
$101$	−6.00000	+	3.46410i	−0.597022	+	0.344691i	0.170847	+	0.985298i	$0.445350\pi$
$102$	1.34486	+	5.01910i	0.133161	+	0.496965i
$103$	16.7303	−	4.48288i	1.64849	−	0.441711i	0.689299	−	0.724477i	$-0.257919\pi$
$103$	16.7303	−	4.48288i	1.64849	−	0.441711i	0.959189	+	0.282766i	$0.0912520\pi$
$104$	−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
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$	6.00000	+	10.3923i	0.569495	+	0.986394i
$112$	0.896575	+	3.34607i	0.0847184	+	0.316173i
$113$	−4.65874	−	17.3867i	−0.438258	−	1.63560i	−0.733148	−	0.680069i	$-0.761950\pi$
$113$	−4.65874	−	17.3867i	−0.438258	−	1.63560i	0.294891	−	0.955531i	$-0.404717\pi$
$114$	−6.06218	+	10.5000i	−0.567775	+	0.983415i
$115$		0			0
$116$		−	3.46410i		−	0.321634i
$117$	−10.0382	−	2.68973i	−0.928032	−	0.248665i
$118$	−8.57321	−	8.57321i	−0.789228	−	0.789228i
$119$	5.19615	+	9.00000i	0.476331	+	0.825029i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	3.86370	−	1.03528i	0.349803	−	0.0937295i
$123$	14.8492	−	14.8492i	1.33891	−	1.33891i
$124$	−6.92820	+	4.00000i	−0.622171	+	0.359211i
$125$		0			0
$126$	−9.00000	+	5.19615i	−0.801784	+	0.462910i
$127$	7.34847	−	7.34847i	0.652071	−	0.652071i	−0.301420	−	0.953491i	$-0.597461\pi$
$127$	7.34847	−	7.34847i	0.652071	−	0.652071i	0.953491	+	0.301420i	$0.0974607\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−7.79423	−	4.50000i	−0.686244	−	0.396203i
$130$		0			0
$131$	3.00000	+	1.73205i	0.262111	+	0.151330i	0.625297	−	0.780387i	$-0.284978\pi$
$131$	3.00000	+	1.73205i	0.262111	+	0.151330i	−0.363186	+	0.931717i	$0.618311\pi$
$132$	−0.776457	+	2.89778i	−0.0675819	+	0.252219i
$133$	−6.27603	+	23.4225i	−0.544201	+	2.03098i
$134$	1.73205			0.149626
$135$		0			0
$136$	−3.00000			−0.257248
$137$	−0.776457	+	2.89778i	−0.0663372	+	0.247574i	−0.991130	−	0.132898i	$-0.957572\pi$
$137$	−0.776457	+	2.89778i	−0.0663372	+	0.247574i	0.924793	+	0.380472i	$0.124238\pi$
$138$	−2.68973	+	10.0382i	−0.228965	+	0.854508i
$139$	4.33013	+	2.50000i	0.367277	+	0.212047i	0.672268	−	0.740308i	$-0.265320\pi$
$139$	4.33013	+	2.50000i	0.367277	+	0.212047i	−0.304991	+	0.952355i	$0.598654\pi$
$140$		0			0
$141$	−9.00000	−	5.19615i	−0.757937	−	0.437595i
$142$	−13.3843	−	3.58630i	−1.12318	−	0.300956i
$143$	−4.24264	+	4.24264i	−0.354787	+	0.354787i
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	−7.50000	+	4.33013i	−0.620704	+	0.358364i
$147$	−6.12372	+	6.12372i	−0.505076	+	0.505076i
$148$	−6.69213	+	1.79315i	−0.550090	+	0.147396i
$149$	5.19615	−	9.00000i	0.425685	−	0.737309i	−0.570799	−	0.821090i	$-0.693366\pi$
$149$	5.19615	−	9.00000i	0.425685	−	0.737309i	0.996484	+	0.0837813i	$0.0266997\pi$
$150$		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	$0.966722\pi$
$152$	−4.94975	−	4.94975i	−0.401478	−	0.401478i
$153$	−2.32937	−	8.69333i	−0.188319	−	0.702814i
$154$			6.00000i			0.483494i
$155$		0			0
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$157$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$158$	1.03528	+	3.86370i	0.0823622	+	0.307380i
$159$		0			0
$160$		0			0
$161$			20.7846i			1.63806i
$162$	8.69333	−	2.32937i	0.683013	−	0.183013i
$163$	2.44949	+	2.44949i	0.191859	+	0.191859i	0.796499	−	0.604640i	$-0.206683\pi$
$163$	2.44949	+	2.44949i	0.191859	+	0.191859i	−0.604640	+	0.796499i	$0.706683\pi$
$164$	6.06218	+	10.5000i	0.473377	+	0.819912i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$167$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$168$	−1.55291	−	5.79555i	−0.119810	−	0.447137i
$169$	−0.866025	+	0.500000i	−0.0666173	+	0.0384615i
$170$		0			0
$171$	10.5000	−	18.1865i	0.802955	−	1.39076i
$172$	3.67423	−	3.67423i	0.280158	−	0.280158i
$173$	5.79555	+	1.55291i	0.440628	+	0.118066i	0.472311	−	0.881432i	$-0.343420\pi$
$173$	5.79555	+	1.55291i	0.440628	+	0.118066i	−0.0316829	+	0.999498i	$0.510087\pi$
$174$			6.00000i			0.454859i
$175$		0			0
$176$	−1.50000	−	0.866025i	−0.113067	−	0.0652791i
$177$	14.8492	+	14.8492i	1.11614	+	1.11614i
$178$	−1.79315	+	6.69213i	−0.134402	+	0.501596i
$179$	−3.46410			−0.258919			−0.129460	−	0.991585i	$-0.541324\pi$
$179$	−3.46410			−0.258919			−0.129460	+	0.991585i	$0.541324\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	3.10583	−	11.5911i	0.230219	−	0.859190i
$183$	−6.69213	+	1.79315i	−0.494697	+	0.132554i
$184$	−5.19615	−	3.00000i	−0.383065	−	0.221163i
$185$		0			0
$186$	12.0000	−	6.92820i	0.879883	−	0.508001i
$187$	−5.01910	−	1.34486i	−0.367033	−	0.0983461i
$188$	4.24264	−	4.24264i	0.309426	−	0.309426i
$189$	15.5885	−	9.00000i	1.13389	−	0.654654i
$190$		0			0
$191$	21.0000	−	12.1244i	1.51951	−	0.877288i	0.519771	−	0.854306i	$-0.326017\pi$
$191$	21.0000	−	12.1244i	1.51951	−	0.877288i	0.999736	−	0.0229818i	$-0.00731599\pi$
$192$	1.67303	+	0.448288i	0.120741	+	0.0323524i
$193$	−8.36516	+	2.24144i	−0.602138	+	0.161342i	−0.546995	−	0.837136i	$-0.684228\pi$
$193$	−8.36516	+	2.24144i	−0.602138	+	0.161342i	−0.0551431	+	0.998478i	$0.517561\pi$
$194$	−4.33013	+	7.50000i	−0.310885	+	0.538469i
$195$		0			0
$196$	−2.50000	−	4.33013i	−0.178571	−	0.309295i
$197$	16.9706	+	16.9706i	1.20910	+	1.20910i	0.971318	+	0.237785i	$0.0764212\pi$
$197$	16.9706	+	16.9706i	1.20910	+	1.20910i	0.237785	+	0.971318i	$0.423579\pi$
$198$	1.34486	−	5.01910i	0.0955753	−	0.356692i
$199$		−	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
$201$	−3.00000			−0.211604
$202$	1.79315	+	6.69213i	0.126166	+	0.470857i
$203$	3.10583	+	11.5911i	0.217986	+	0.813536i
$204$	5.19615			0.363803
$205$		0			0
$206$		−	17.3205i		−	1.20678i
$207$	4.65874	−	17.3867i	0.323805	−	1.20846i
$208$	2.44949	+	2.44949i	0.169842	+	0.169842i
$209$	−6.06218	−	10.5000i	−0.419330	−	0.726300i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$		0			0
$213$	23.1822	+	6.21166i	1.58842	+	0.425616i
$214$	2.59808	−	1.50000i	0.177601	−	0.102538i
$215$		0			0
$216$			5.19615i			0.353553i
$217$	19.5959	−	19.5959i	1.33026	−	1.33026i
$218$	−3.86370	−	1.03528i	−0.261683	−	0.0701178i
$219$	12.9904	−	7.50000i	0.877809	−	0.506803i
$220$		0			0
$221$	9.00000	+	5.19615i	0.605406	+	0.349531i
$222$	11.5911	−	3.10583i	0.777944	−	0.208450i
$223$	−2.68973	+	10.0382i	−0.180117	+	0.672207i	0.815506	+	0.578749i	$0.196459\pi$
$223$	−2.68973	+	10.0382i	−0.180117	+	0.672207i	−0.995623	+	0.0934584i	$0.970208\pi$
$224$	3.46410			0.231455
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−0.776457	+	2.89778i	−0.0515353	+	0.192332i	−0.986894	−	0.161367i	$-0.948410\pi$
$227$	−0.776457	+	2.89778i	−0.0515353	+	0.192332i	0.935359	+	0.353699i	$0.115076\pi$
$228$	8.57321	+	8.57321i	0.567775	+	0.567775i
$229$	−19.0526	−	11.0000i	−1.25903	−	0.726900i	−0.286143	−	0.958187i	$-0.592373\pi$
$229$	−19.0526	−	11.0000i	−1.25903	−	0.726900i	−0.972886	+	0.231287i	$0.925707\pi$
$230$		0			0
$231$		−	10.3923i		−	0.683763i
$232$	−3.34607	−	0.896575i	−0.219680	−	0.0588631i
$233$	−2.12132	+	2.12132i	−0.138972	+	0.138972i	−0.773171	−	0.634198i	$-0.781330\pi$
$233$	−2.12132	+	2.12132i	−0.138972	+	0.138972i	0.634198	+	0.773171i	$0.281330\pi$
$234$	−5.19615	+	9.00000i	−0.339683	+	0.588348i
$235$		0			0
$236$	−10.5000	+	6.06218i	−0.683492	+	0.394614i
$237$	−1.79315	−	6.69213i	−0.116478	−	0.434701i
$238$	10.0382	−	2.68973i	0.650680	−	0.174349i
$239$	−5.19615	+	9.00000i	−0.336111	+	0.582162i	−0.983698	−	0.179830i	$-0.942445\pi$
$239$	−5.19615	+	9.00000i	−0.336111	+	0.582162i	0.647586	+	0.761992i	$0.275778\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$	5.65685	+	5.65685i	0.363636	+	0.363636i
$243$	−15.0573	+	4.03459i	−0.965926	+	0.258819i
$244$		−	4.00000i		−	0.256074i
$245$		0			0
$246$	−10.5000	−	18.1865i	−0.669456	−	1.15953i
$247$	6.27603	+	23.4225i	0.399334	+	1.49034i
$248$	2.07055	+	7.72741i	0.131480	+	0.490691i
$249$	10.3923	−	18.0000i	0.658586	−	1.14070i
$250$		0			0
$251$			25.9808i			1.63989i	0.572441	+	0.819946i	$0.305996\pi$
$251$			25.9808i			1.63989i	−0.572441	+	0.819946i	$0.694004\pi$
$252$	2.68973	+	10.0382i	0.169437	+	0.632347i
$253$	−7.34847	−	7.34847i	−0.461994	−	0.461994i
$254$	−5.19615	−	9.00000i	−0.326036	−	0.564710i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	26.0800	−	6.98811i	1.62683	−	0.435907i	0.673829	−	0.738887i	$-0.264648\pi$
$257$	26.0800	−	6.98811i	1.62683	−	0.435907i	0.952997	+	0.302981i	$0.0979818\pi$
$258$	−6.36396	+	6.36396i	−0.396203	+	0.396203i
$259$	20.7846	−	12.0000i	1.29149	−	0.745644i
$260$		0			0
$261$		−	10.3923i		−	0.643268i
$262$	2.44949	−	2.44949i	0.151330	−	0.151330i
$263$	−5.79555	−	1.55291i	−0.357369	−	0.0957568i	0.0756674	−	0.997133i	$-0.475891\pi$
$263$	−5.79555	−	1.55291i	−0.357369	−	0.0957568i	−0.433037	+	0.901376i	$0.642558\pi$
$264$	2.59808	+	1.50000i	0.159901	+	0.0923186i
$265$		0			0
$266$	21.0000	+	12.1244i	1.28759	+	0.743392i
$267$	3.10583	−	11.5911i	0.190074	−	0.709364i
$268$	0.448288	−	1.67303i	0.0273835	−	0.102197i
$269$	−6.92820			−0.422420			−0.211210	−	0.977441i	$-0.567740\pi$
$269$	−6.92820			−0.422420			−0.211210	+	0.977441i	$0.567740\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	−0.776457	+	2.89778i	−0.0470796	+	0.175704i
$273$	−5.37945	+	20.0764i	−0.325579	+	1.21508i
$274$	2.59808	+	1.50000i	0.156956	+	0.0906183i
$275$		0			0
$276$	9.00000	+	5.19615i	0.541736	+	0.312772i
$277$	10.0382	+	2.68973i	0.603137	+	0.161610i	0.547450	−	0.836838i	$-0.315599\pi$
$277$	10.0382	+	2.68973i	0.603137	+	0.161610i	0.0556866	+	0.998448i	$0.482265\pi$
$278$	3.53553	−	3.53553i	0.212047	−	0.212047i
$279$	−20.7846	+	12.0000i	−1.24434	+	0.718421i
$280$		0			0
$281$	18.0000	−	10.3923i	1.07379	−	0.619953i	0.144575	−	0.989494i	$-0.453818\pi$
$281$	18.0000	−	10.3923i	1.07379	−	0.619953i	0.929214	+	0.369541i	$0.120485\pi$
$282$	−7.34847	+	7.34847i	−0.437595	+	0.437595i
$283$	30.1146	−	8.06918i	1.79013	−	0.479663i	0.797759	−	0.602977i	$-0.206019\pi$
$283$	30.1146	−	8.06918i	1.79013	−	0.479663i	0.992368	+	0.123314i	$0.0393522\pi$
$284$	−6.92820	+	12.0000i	−0.411113	+	0.712069i
$285$		0			0
$286$	3.00000	+	5.19615i	0.177394	+	0.307255i
$287$	−29.6985	−	29.6985i	−1.75305	−	1.75305i
$288$	−2.89778	−	0.776457i	−0.170753	−	0.0457532i
$289$		−	8.00000i		−	0.470588i
$290$		0			0
$291$	7.50000	−	12.9904i	0.439658	−	0.761510i
$292$	2.24144	+	8.36516i	0.131170	+	0.489534i
$293$	−1.55291	−	5.79555i	−0.0907222	−	0.338580i	0.905614	−	0.424103i	$-0.139411\pi$
$293$	−1.55291	−	5.79555i	−0.0907222	−	0.338580i	−0.996336	+	0.0855230i	$0.972744\pi$
$294$	4.33013	+	7.50000i	0.252538	+	0.437409i
$295$		0			0
$296$			6.92820i			0.402694i
$297$	−2.32937	+	8.69333i	−0.135164	+	0.504438i
$298$	−7.34847	−	7.34847i	−0.425685	−	0.425685i
$299$	10.3923	+	18.0000i	0.601003	+	1.04097i
$300$		0			0
$301$	−9.00000	+	15.5885i	−0.518751	+	0.898504i
$302$	−9.65926	+	2.58819i	−0.555828	+	0.148934i
$303$	−3.10583	−	11.5911i	−0.178425	−	0.665892i
$304$	−6.06218	+	3.50000i	−0.347690	+	0.200739i
$305$		0			0
$306$	−9.00000			−0.514496
$307$	−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
$309$			30.0000i			1.70664i
$310$		0			0
$311$	−3.00000	−	1.73205i	−0.170114	−	0.0982156i	0.412525	−	0.910946i	$-0.364647\pi$
$311$	−3.00000	−	1.73205i	−0.170114	−	0.0982156i	−0.582640	+	0.812731i	$0.697980\pi$
$312$	−4.24264	−	4.24264i	−0.240192	−	0.240192i
$313$	2.24144	−	8.36516i	0.126694	−	0.472827i	−0.873201	−	0.487361i	$-0.837960\pi$
$313$	2.24144	−	8.36516i	0.126694	−	0.472827i	0.999894	+	0.0145337i	$0.00462638\pi$
$314$		0			0
$315$		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
$319$	−5.19615	−	3.00000i	−0.290929	−	0.167968i
$320$		0			0
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$	20.0764	+	5.37945i	1.11881	+	0.299785i
$323$	−14.8492	+	14.8492i	−0.826234	+	0.826234i
$324$		−	9.00000i		−	0.500000i
$325$		0			0
$326$	3.00000	−	1.73205i	0.166155	−	0.0959294i
$327$	6.69213	+	1.79315i	0.370076	+	0.0991615i
$328$	11.7112	−	3.13801i	0.646644	−	0.173268i
$329$	−10.3923	+	18.0000i	−0.572946	+	0.992372i
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	8.48528	+	8.48528i	0.465690	+	0.465690i
$333$	−20.0764	+	5.37945i	−1.10018	+	0.294792i
$334$		0			0
$335$		0			0
$336$	−6.00000			−0.327327
$337$	−3.13801	−	11.7112i	−0.170939	−	0.637951i	−0.997208	−	0.0746760i	$-0.976208\pi$
$337$	−3.13801	−	11.7112i	−0.170939	−	0.637951i	0.826269	−	0.563275i	$-0.190459\pi$
$338$	0.258819	+	0.965926i	0.0140779	+	0.0525394i
$339$	31.1769			1.69330
$340$		0			0
$341$			13.8564i			0.750366i
$342$	−14.8492	−	14.8492i	−0.802955	−	0.802955i
$343$	−4.89898	−	4.89898i	−0.264520	−	0.264520i
$344$	−2.59808	−	4.50000i	−0.140079	−	0.242624i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−14.4889	+	3.88229i	−0.777804	+	0.208412i	−0.625816	−	0.779970i	$-0.715234\pi$
$347$	−14.4889	+	3.88229i	−0.777804	+	0.208412i	−0.151988	+	0.988382i	$0.548567\pi$
$348$	5.79555	+	1.55291i	0.310674	+	0.0832449i
$349$	−6.92820	+	4.00000i	−0.370858	+	0.214115i	−0.673833	−	0.738883i	$-0.735353\pi$
$349$	−6.92820	+	4.00000i	−0.370858	+	0.214115i	0.302975	+	0.952998i	$0.402020\pi$
$350$		0			0
$351$	9.00000	−	15.5885i	0.480384	−	0.832050i
$352$	−1.22474	+	1.22474i	−0.0652791	+	0.0652791i
$353$	20.2844	+	5.43520i	1.07963	+	0.289287i	0.754445	−	0.656363i	$-0.227906\pi$
$353$	20.2844	+	5.43520i	1.07963	+	0.289287i	0.325187	+	0.945650i	$0.394573\pi$
$354$	18.1865	−	10.5000i	0.966603	−	0.558069i
$355$		0			0
$356$	6.00000	+	3.46410i	0.317999	+	0.183597i
$357$	−17.3867	+	4.65874i	−0.920200	+	0.246567i
$358$	−0.896575	+	3.34607i	−0.0473855	+	0.176845i
$359$	−24.2487			−1.27980			−0.639899	−	0.768459i	$-0.721024\pi$
$359$	−24.2487			−1.27980			−0.639899	+	0.768459i	$0.721024\pi$
$360$		0			0
$361$	−30.0000			−1.57895
$362$	−0.517638	+	1.93185i	−0.0272065	+	0.101536i
$363$	−9.79796	−	9.79796i	−0.514259	−	0.514259i
$364$	−10.3923	−	6.00000i	−0.544705	−	0.314485i
$365$		0			0
$366$			6.92820i			0.362143i
$367$	−13.3843	−	3.58630i	−0.698653	−	0.187203i	−0.108026	−	0.994148i	$-0.534453\pi$
$367$	−13.3843	−	3.58630i	−0.698653	−	0.187203i	−0.590627	+	0.806945i	$0.701120\pi$
$368$	−4.24264	+	4.24264i	−0.221163	+	0.221163i
$369$	18.1865	+	31.5000i	0.946753	+	1.63982i
$370$		0			0
$371$		0			0
$372$	−3.58630	−	13.3843i	−0.185941	−	0.693942i
$373$	−16.7303	+	4.48288i	−0.866263	+	0.232115i	−0.664471	−	0.747314i	$-0.731343\pi$
$373$	−16.7303	+	4.48288i	−0.866263	+	0.232115i	−0.201792	+	0.979428i	$0.564677\pi$
$374$	−2.59808	+	4.50000i	−0.134343	+	0.232689i
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	8.48528	+	8.48528i	0.437014	+	0.437014i
$378$	−4.65874	−	17.3867i	−0.239620	−	0.894274i
$379$			1.00000i			0.0513665i	0.999670	+	0.0256833i	$0.00817614\pi$
$379$			1.00000i			0.0513665i	−0.999670	+	0.0256833i	$0.991824\pi$
$380$		0			0
$381$	9.00000	+	15.5885i	0.461084	+	0.798621i
$382$	−6.27603	−	23.4225i	−0.321110	−	1.19840i
$383$	3.10583	+	11.5911i	0.158700	+	0.592278i	0.998760	+	0.0497839i	$0.0158533\pi$
$383$	3.10583	+	11.5911i	0.158700	+	0.592278i	−0.840060	+	0.542494i	$0.817480\pi$
$384$	0.866025	−	1.50000i	0.0441942	−	0.0765466i
$385$		0			0
$386$			8.66025i			0.440795i
$387$	11.0227	−	11.0227i	0.560316	−	0.560316i
$388$	6.12372	+	6.12372i	0.310885	+	0.310885i
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	0.703702	−	0.710495i	$-0.251529\pi$
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	−0.967158	+	0.254177i	$0.918196\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	−4.82963	+	1.29410i	−0.243933	+	0.0653617i
$393$	−4.24264	+	4.24264i	−0.214013	+	0.214013i
$394$	20.7846	−	12.0000i	1.04711	−	0.604551i
$395$		0			0
$396$	−4.50000	−	2.59808i	−0.226134	−	0.130558i
$397$	−14.6969	+	14.6969i	−0.737618	+	0.737618i	−0.972117	−	0.234498i	$-0.924655\pi$
$397$	−14.6969	+	14.6969i	−0.737618	+	0.737618i	0.234498	+	0.972117i	$0.424655\pi$
$398$	−9.65926	−	2.58819i	−0.484175	−	0.129734i
$399$	−36.3731	−	21.0000i	−1.82093	−	1.05131i
$400$		0			0
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	0.383414	−	0.923576i	$-0.374748\pi$
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	−0.608134	+	0.793835i	$0.708081\pi$
$402$	−0.776457	+	2.89778i	−0.0387262	+	0.144528i
$403$	7.17260	−	26.7685i	0.357293	−	1.33344i
$404$	6.92820			0.344691
$405$		0			0
$406$	12.0000			0.595550
$407$	−3.10583	+	11.5911i	−0.153950	+	0.574550i
$408$	1.34486	−	5.01910i	0.0665807	−	0.248482i
$409$	−6.06218	−	3.50000i	−0.299755	−	0.173064i	0.342578	−	0.939490i	$-0.388700\pi$
$409$	−6.06218	−	3.50000i	−0.299755	−	0.173064i	−0.642333	+	0.766426i	$0.722033\pi$
$410$		0			0
$411$	−4.50000	−	2.59808i	−0.221969	−	0.128154i
$412$	−16.7303	−	4.48288i	−0.824244	−	0.220856i
$413$	29.6985	−	29.6985i	1.46137	−	1.46137i
$414$	−15.5885	−	9.00000i	−0.766131	−	0.442326i
$415$		0			0
$416$	3.00000	−	1.73205i	0.147087	−	0.0849208i
$417$	−6.12372	+	6.12372i	−0.299880	+	0.299880i
$418$	−11.7112	+	3.13801i	−0.572815	+	0.153485i
$419$	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
$421$	−14.0000	−	24.2487i	−0.682318	−	1.18181i	−0.974272	−	0.225377i	$-0.927639\pi$
$421$	−14.0000	−	24.2487i	−0.682318	−	1.18181i	0.291953	−	0.956433i	$-0.405695\pi$
$422$	−2.82843	−	2.82843i	−0.137686	−	0.137686i
$423$	12.7279	−	12.7279i	0.618853	−	0.618853i
$424$		0			0
$425$		0			0
$426$	12.0000	−	20.7846i	0.581402	−	1.00702i
$427$	3.58630	+	13.3843i	0.173553	+	0.647710i
$428$	−0.776457	−	2.89778i	−0.0375315	−	0.140069i
$429$	−5.19615	−	9.00000i	−0.250873	−	0.434524i
$430$		0			0
$431$		−	3.46410i		−	0.166860i	−0.996514	−	0.0834300i	$-0.973413\pi$
$431$		−	3.46410i		−	0.166860i	0.996514	−	0.0834300i	$-0.0265875\pi$
$432$	5.01910	+	1.34486i	0.241481	+	0.0647048i
$433$	−18.3712	−	18.3712i	−0.882862	−	0.882862i	0.110962	−	0.993825i	$-0.464607\pi$
$433$	−18.3712	−	18.3712i	−0.882862	−	0.882862i	−0.993825	+	0.110962i	$0.964607\pi$
$434$	−13.8564	−	24.0000i	−0.665129	−	1.15204i
$435$		0			0
$436$	−2.00000	+	3.46410i	−0.0957826	+	0.165900i
$437$	−40.5689	+	10.8704i	−1.94067	+	0.520002i
$438$	−3.88229	−	14.4889i	−0.185503	−	0.692306i
$439$	−13.8564	+	8.00000i	−0.661330	+	0.381819i	−0.792784	−	0.609503i	$-0.791369\pi$
$439$	−13.8564	+	8.00000i	−0.661330	+	0.381819i	0.131453	+	0.991322i	$0.458036\pi$
$440$		0			0
$441$	−7.50000	−	12.9904i	−0.357143	−	0.618590i
$442$	7.34847	−	7.34847i	0.349531	−	0.349531i
$443$	26.0800	+	6.98811i	1.23910	+	0.332015i	0.818116	−	0.575054i	$-0.195019\pi$
$443$	26.0800	+	6.98811i	1.23910	+	0.332015i	0.420982	+	0.907069i	$0.361685\pi$
$444$		−	12.0000i		−	0.569495i
$445$		0			0
$446$	9.00000	+	5.19615i	0.426162	+	0.246045i
$447$	12.7279	+	12.7279i	0.602010	+	0.602010i
$448$	0.896575	−	3.34607i	0.0423592	−	0.158087i
$449$	39.8372			1.88003			0.940016	−	0.341130i	$-0.110810\pi$
$449$	39.8372			1.88003			0.940016	+	0.341130i	$0.110810\pi$
$450$		0			0
$451$	21.0000			0.988851
$452$	−4.65874	+	17.3867i	−0.219129	+	0.817800i
$453$	16.7303	−	4.48288i	0.786059	−	0.210624i
$454$	2.59808	+	1.50000i	0.121934	+	0.0703985i
$455$		0			0
$456$	10.5000	−	6.06218i	0.491708	−	0.283887i
$457$	−25.0955	−	6.72432i	−1.17392	−	0.314550i	−0.381406	−	0.924408i	$-0.624560\pi$
$457$	−25.0955	−	6.72432i	−1.17392	−	0.314550i	−0.792511	+	0.609857i	$0.791227\pi$
$458$	−15.5563	+	15.5563i	−0.726900	+	0.726900i
$459$	15.5885			0.727607
$460$		0			0
$461$	15.0000	−	8.66025i	0.698620	−	0.403348i	−0.108213	−	0.994128i	$-0.534513\pi$
$461$	15.0000	−	8.66025i	0.698620	−	0.403348i	0.806833	+	0.590779i	$0.201180\pi$
$462$	−10.0382	−	2.68973i	−0.467019	−	0.125137i
$463$	13.3843	−	3.58630i	0.622019	−	0.166670i	0.0659737	−	0.997821i	$-0.478985\pi$
$463$	13.3843	−	3.58630i	0.622019	−	0.166670i	0.556046	+	0.831152i	$0.312318\pi$
$464$	−1.73205	+	3.00000i	−0.0804084	+	0.139272i
$465$		0			0
$466$	1.50000	+	2.59808i	0.0694862	+	0.120354i
$467$	−6.36396	−	6.36396i	−0.294489	−	0.294489i	0.544362	−	0.838851i	$-0.316772\pi$
$467$	−6.36396	−	6.36396i	−0.294489	−	0.294489i	−0.838851	+	0.544362i	$0.816772\pi$
$468$	7.34847	+	7.34847i	0.339683	+	0.339683i
$469$			6.00000i			0.277054i
$470$		0			0
$471$		0			0
$472$	3.13801	+	11.7112i	0.144439	+	0.539053i
$473$	−2.32937	−	8.69333i	−0.107105	−	0.399720i
$474$	−6.92820			−0.318223
$475$		0			0
$476$		−	10.3923i		−	0.476331i
$477$		0			0
$478$	7.34847	+	7.34847i	0.336111	+	0.336111i
$479$	8.66025	+	15.0000i	0.395697	+	0.685367i	0.993190	−	0.116507i	$-0.0371697\pi$
$479$	8.66025	+	15.0000i	0.395697	+	0.685367i	−0.597493	+	0.801874i	$0.703836\pi$
$480$		0			0
$481$	12.0000	−	20.7846i	0.547153	−	0.947697i
$482$	0.965926	−	0.258819i	0.0439967	−	0.0117889i
$483$	−34.7733	−	9.31749i	−1.58224	−	0.423960i
$484$	6.92820	−	4.00000i	0.314918	−	0.181818i
$485$		0			0
$486$			15.5885i			0.707107i
$487$	−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	$0.435146\pi$
$488$	−3.86370	−	1.03528i	−0.174902	−	0.0468648i
$489$	−5.19615	+	3.00000i	−0.234978	+	0.135665i
$490$		0			0
$491$	−19.5000	−	11.2583i	−0.880023	−	0.508081i	−0.00935679	−	0.999956i	$-0.502978\pi$
$491$	−19.5000	−	11.2583i	−0.880023	−	0.508081i	−0.870666	+	0.491875i	$0.836312\pi$
$492$	−20.2844	+	5.43520i	−0.914493	+	0.245038i
$493$	−2.68973	+	10.0382i	−0.121139	+	0.452098i
$494$	24.2487			1.09100
$495$		0			0
$496$	8.00000			0.359211
$497$	12.4233	−	46.3644i	0.557262	−	2.07973i
$498$	−14.6969	−	14.6969i	−0.658586	−	0.658586i
$499$	16.4545	+	9.50000i	0.736604	+	0.425278i	0.820833	−	0.571168i	$-0.193510\pi$
$499$	16.4545	+	9.50000i	0.736604	+	0.425278i	−0.0842294	+	0.996446i	$0.526843\pi$
$500$		0			0
$501$		0			0
$502$	25.0955	+	6.72432i	1.12007	+	0.300121i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$	10.3923			0.462910
$505$		0			0
$506$	−9.00000	+	5.19615i	−0.400099	+	0.230997i
$507$	−0.448288	−	1.67303i	−0.0199092	−	0.0743020i
$508$	−10.0382	+	2.68973i	−0.445373	+	0.119337i
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	−0.998992	−	0.0448779i	$-0.985710\pi$
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	0.538362	+	0.842714i	$0.319043\pi$
$510$		0			0
$511$	−15.0000	−	25.9808i	−0.663561	−	1.14932i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	25.7196	+	25.7196i	1.13555	+	1.13555i
$514$		−	27.0000i		−	1.19092i
$515$		0			0
$516$	4.50000	+	7.79423i	0.198101	+	0.343122i
$517$	−2.68973	−	10.0382i	−0.118294	−	0.441479i
$518$	−6.21166	−	23.1822i	−0.272925	−	1.01857i
$519$	−5.19615	+	9.00000i	−0.228086	+	0.395056i
$520$		0			0
$521$			5.19615i			0.227648i	0.993501	+	0.113824i	$0.0363099\pi$
$521$			5.19615i			0.227648i	−0.993501	+	0.113824i	$0.963690\pi$
$522$	−10.0382	−	2.68973i	−0.439360	−	0.117726i
$523$	12.2474	+	12.2474i	0.535544	+	0.535544i	0.922217	−	0.386673i	$-0.126376\pi$
$523$	12.2474	+	12.2474i	0.535544	+	0.535544i	−0.386673	+	0.922217i	$0.626376\pi$
$524$	−1.73205	−	3.00000i	−0.0756650	−	0.131056i
$525$		0			0
$526$	−3.00000	+	5.19615i	−0.130806	+	0.226563i
$527$	23.1822	−	6.21166i	1.00983	−	0.270584i
$528$	2.12132	−	2.12132i	0.0923186	−	0.0923186i
$529$	−11.2583	+	6.50000i	−0.489493	+	0.282609i
$530$		0			0
$531$	−31.5000	+	18.1865i	−1.36698	+	0.789228i
$532$	17.1464	−	17.1464i	0.743392	−	0.743392i
$533$	−40.5689	−	10.8704i	−1.75723	−	0.470849i
$534$	−10.3923	−	6.00000i	−0.449719	−	0.259645i
$535$		0			0
$536$	−1.50000	−	0.866025i	−0.0647901	−	0.0374066i
$537$	1.55291	−	5.79555i	0.0670132	−	0.250097i
$538$	−1.79315	+	6.69213i	−0.0773082	+	0.288518i
$539$	−8.66025			−0.373024
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	−7.24693	+	27.0459i	−0.311282	+	1.16172i
$543$	0.896575	−	3.34607i	0.0384757	−	0.143593i
$544$	2.59808	+	1.50000i	0.111392	+	0.0643120i
$545$		0			0
$546$	18.0000	+	10.3923i	0.770329	+	0.444750i
$547$	21.7494	+	5.82774i	0.929938	+	0.249176i	0.691828	−	0.722062i	$-0.256805\pi$
$547$	21.7494	+	5.82774i	0.929938	+	0.249176i	0.238110	+	0.971238i	$0.423472\pi$
$548$	2.12132	−	2.12132i	0.0906183	−	0.0906183i
$549$		−	12.0000i		−	0.512148i
$550$		0			0
$551$	−21.0000	+	12.1244i	−0.894630	+	0.516515i
$552$	7.34847	−	7.34847i	0.312772	−	0.312772i
$553$	−13.3843	+	3.58630i	−0.569157	+	0.152505i
$554$	5.19615	−	9.00000i	0.220763	−	0.382373i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	−12.7279	−	12.7279i	−0.539299	−	0.539299i	0.384024	−	0.923323i	$-0.374538\pi$
$557$	−12.7279	−	12.7279i	−0.539299	−	0.539299i	−0.923323	+	0.384024i	$0.874538\pi$
$558$	6.21166	+	23.1822i	0.262960	+	0.981382i
$559$			18.0000i			0.761319i
$560$		0			0
$561$	4.50000	−	7.79423i	0.189990	−	0.329073i
$562$	−5.37945	−	20.0764i	−0.226919	−	0.846871i
$563$	3.88229	+	14.4889i	0.163619	+	0.610634i	0.998212	+	0.0597675i	$0.0190359\pi$
$563$	3.88229	+	14.4889i	0.163619	+	0.610634i	−0.834593	+	0.550866i	$0.814297\pi$
$564$	5.19615	+	9.00000i	0.218797	+	0.378968i
$565$		0			0
$566$		−	31.1769i		−	1.31046i
$567$	8.06918	+	30.1146i	0.338874	+	1.26469i
$568$	9.79796	+	9.79796i	0.411113	+	0.411113i
$569$	−9.52628	−	16.5000i	−0.399362	−	0.691716i	0.594285	−	0.804255i	$-0.297435\pi$
$569$	−9.52628	−	16.5000i	−0.399362	−	0.691716i	−0.993647	+	0.112539i	$0.964102\pi$
$570$		0			0
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	−0.913584	−	0.406651i	$-0.866697\pi$
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	0.808962	+	0.587861i	$0.200030\pi$
$572$	5.79555	−	1.55291i	0.242324	−	0.0649306i
$573$	10.8704	+	40.5689i	0.454117	+	1.69479i
$574$	−36.3731	+	21.0000i	−1.51818	+	0.876523i
$575$		0			0
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$	−23.2702	+	23.2702i	−0.968749	+	0.968749i	−0.999526	−	0.0307771i	$-0.990202\pi$
$577$	−23.2702	+	23.2702i	−0.968749	+	0.968749i	0.0307771	+	0.999526i	$0.490202\pi$
$578$	−7.72741	−	2.07055i	−0.321418	−	0.0861236i
$579$		−	15.0000i		−	0.623379i
$580$		0			0
$581$	−36.0000	−	20.7846i	−1.49353	−	0.862291i
$582$	−10.6066	−	10.6066i	−0.439658	−	0.439658i
$583$		0			0
$584$	8.66025			0.358364
$585$		0			0
$586$	−6.00000			−0.247858
$587$	8.54103	−	31.8756i	0.352526	−	1.31564i	−0.531043	−	0.847345i	$-0.678200\pi$
$587$	8.54103	−	31.8756i	0.352526	−	1.31564i	0.883569	−	0.468300i	$-0.155133\pi$
$588$	8.36516	−	2.24144i	0.344974	−	0.0924354i
$589$	48.4974	+	28.0000i	1.99830	+	1.15372i
$590$		0			0
$591$	−36.0000	+	20.7846i	−1.48084	+	0.854965i
$592$	6.69213	+	1.79315i	0.275045	+	0.0736980i
$593$	12.7279	−	12.7279i	0.522673	−	0.522673i	−0.395705	−	0.918378i	$-0.629500\pi$
$593$	12.7279	−	12.7279i	0.522673	−	0.522673i	0.918378	+	0.395705i	$0.129500\pi$
$594$	7.79423	+	4.50000i	0.319801	+	0.184637i
$595$		0			0
$596$	−9.00000	+	5.19615i	−0.368654	+	0.212843i
$597$	16.7303	+	4.48288i	0.684727	+	0.183472i
$598$	20.0764	−	5.37945i	0.820985	−	0.219982i
$599$	6.92820	−	12.0000i	0.283079	−	0.490307i	−0.689063	−	0.724702i	$-0.741978\pi$
$599$	6.92820	−	12.0000i	0.283079	−	0.490307i	0.972141	+	0.234395i	$0.0753109\pi$
$600$		0			0
$601$	14.5000	+	25.1147i	0.591467	+	1.02445i	0.994035	+	0.109061i	$0.0347845\pi$
$601$	14.5000	+	25.1147i	0.591467	+	1.02445i	−0.402568	+	0.915390i	$0.631882\pi$
$602$	12.7279	+	12.7279i	0.518751	+	0.518751i
$603$	1.34486	−	5.01910i	0.0547671	−	0.204393i
$604$			10.0000i			0.406894i
$605$		0			0
$606$	−12.0000			−0.487467
$607$	−3.58630	−	13.3843i	−0.145564	−	0.543250i	−0.999730	−	0.0232502i	$-0.992599\pi$
$607$	−3.58630	−	13.3843i	−0.145564	−	0.543250i	0.854166	−	0.520000i	$-0.174068\pi$
$608$	1.81173	+	6.76148i	0.0734755	+	0.274214i
$609$	−20.7846			−0.842235
$610$		0			0
$611$			20.7846i			0.840855i
$612$	−2.32937	+	8.69333i	−0.0941593	+	0.351407i
$613$	−4.89898	−	4.89898i	−0.197868	−	0.197868i	0.601218	−	0.799085i	$-0.294683\pi$
$613$	−4.89898	−	4.89898i	−0.197868	−	0.197868i	−0.799085	+	0.601218i	$0.794683\pi$
$614$	2.59808	+	4.50000i	0.104850	+	0.181605i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	43.4667	−	11.6469i	1.74990	−	0.468885i	0.765297	−	0.643678i	$-0.222592\pi$
$617$	43.4667	−	11.6469i	1.74990	−	0.468885i	0.984605	+	0.174793i	$0.0559256\pi$
$618$	28.9778	+	7.76457i	1.16566	+	0.312337i
$619$	−11.2583	+	6.50000i	−0.452510	+	0.261257i	−0.708890	−	0.705319i	$-0.750804\pi$
$619$	−11.2583	+	6.50000i	−0.452510	+	0.261257i	0.256379	+	0.966576i	$0.417470\pi$
$620$		0			0
$621$	27.0000	+	15.5885i	1.08347	+	0.625543i
$622$	−2.44949	+	2.44949i	−0.0982156	+	0.0982156i
$623$	−23.1822	−	6.21166i	−0.928776	−	0.248865i
$624$	−5.19615	+	3.00000i	−0.208013	+	0.120096i
$625$		0			0
$626$	−7.50000	−	4.33013i	−0.299760	−	0.173067i
$627$	20.2844	−	5.43520i	0.810083	−	0.217061i
$628$		0			0
$629$	20.7846			0.828737
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	1.03528	−	3.86370i	0.0411811	−	0.153690i
$633$	4.89898	+	4.89898i	0.194717	+	0.194717i
$634$	5.19615	+	3.00000i	0.206366	+	0.119145i
$635$		0			0
$636$		0			0
$637$	16.7303	+	4.48288i	0.662880	+	0.177618i
$638$	−4.24264	+	4.24264i	−0.167968	+	0.167968i
$639$	−20.7846	+	36.0000i	−0.822226	+	1.42414i
$640$		0			0
$641$	19.5000	−	11.2583i	0.770204	−	0.444677i	−0.0627436	−	0.998030i	$-0.519985\pi$
$641$	19.5000	−	11.2583i	0.770204	−	0.444677i	0.832947	+	0.553352i	$0.186652\pi$
$642$	1.34486	+	5.01910i	0.0530775	+	0.198088i
$643$	−35.1337	+	9.41404i	−1.38554	+	0.371254i	−0.873129	−	0.487489i	$-0.837913\pi$
$643$	−35.1337	+	9.41404i	−1.38554	+	0.371254i	−0.512408	+	0.858742i	$0.671246\pi$
$644$	10.3923	−	18.0000i	0.409514	−	0.709299i
$645$		0			0
$646$	10.5000	+	18.1865i	0.413117	+	0.715540i
$647$	21.2132	+	21.2132i	0.833977	+	0.833977i	0.988058	−	0.154081i	$-0.0492417\pi$
$647$	21.2132	+	21.2132i	0.833977	+	0.833977i	−0.154081	+	0.988058i	$0.549242\pi$
$648$	−8.69333	−	2.32937i	−0.341506	−	0.0915064i
$649$			21.0000i			0.824322i
$650$		0			0
$651$	24.0000	+	41.5692i	0.940634	+	1.62923i
$652$	−0.896575	−	3.34607i	−0.0351126	−	0.131042i
$653$	−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	$-0.197899\pi$
$654$	3.46410	−	6.00000i	0.135457	−	0.234619i
$655$		0			0
$656$		−	12.1244i		−	0.473377i
$657$	6.72432	+	25.0955i	0.262341	+	0.979068i
$658$	14.6969	+	14.6969i	0.572946	+	0.572946i
$659$	−5.19615	−	9.00000i	−0.202413	−	0.350590i	0.746892	−	0.664945i	$-0.231545\pi$
$659$	−5.19615	−	9.00000i	−0.202413	−	0.350590i	−0.949306	+	0.314355i	$0.898212\pi$
$660$		0			0
$661$	16.0000	−	27.7128i	0.622328	−	1.07790i	−0.366723	−	0.930330i	$-0.619520\pi$
$661$	16.0000	−	27.7128i	0.622328	−	1.07790i	0.989051	−	0.147573i	$-0.0471463\pi$
$662$	27.0459	−	7.24693i	1.05117	−	0.281660i
$663$	−12.7279	+	12.7279i	−0.494312	+	0.494312i
$664$	10.3923	−	6.00000i	0.403300	−	0.232845i
$665$		0			0
$666$			20.7846i			0.805387i
$667$	−14.6969	+	14.6969i	−0.569068	+	0.569068i
$668$		0			0
$669$	−15.5885	−	9.00000i	−0.602685	−	0.347960i
$670$		0			0
$671$	−6.00000	−	3.46410i	−0.231627	−	0.133730i
$672$	−1.55291	+	5.79555i	−0.0599050	+	0.223568i
$673$	1.79315	−	6.69213i	0.0691209	−	0.257963i	−0.922715	−	0.385483i	$-0.874035\pi$
$673$	1.79315	−	6.69213i	0.0691209	−	0.257963i	0.991836	+	0.127520i	$0.0407017\pi$
$674$	−12.1244			−0.467013
$675$		0			0
$676$	1.00000			0.0384615
$677$	−3.10583	+	11.5911i	−0.119367	+	0.445483i	−0.999576	−	0.0291023i	$-0.990735\pi$
$677$	−3.10583	+	11.5911i	−0.119367	+	0.445483i	0.880210	+	0.474585i	$0.157402\pi$
$678$	8.06918	−	30.1146i	0.309895	−	1.15654i
$679$	−25.9808	−	15.0000i	−0.997050	−	0.575647i
$680$		0			0
$681$	−4.50000	−	2.59808i	−0.172440	−	0.0995585i
$682$	13.3843	+	3.58630i	0.512510	+	0.137327i
$683$	−23.3345	+	23.3345i	−0.892871	+	0.892871i	−0.994792	−	0.101922i	$-0.967501\pi$
$683$	−23.3345	+	23.3345i	−0.892871	+	0.892871i	0.101922	+	0.994792i	$0.467501\pi$
$684$	−18.1865	+	10.5000i	−0.695379	+	0.401478i
$685$		0			0
$686$	−6.00000	+	3.46410i	−0.229081	+	0.132260i
$687$	26.9444	−	26.9444i	1.02799	−	1.02799i
$688$	−5.01910	+	1.34486i	−0.191351	+	0.0512724i
$689$		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	$0.784708\pi$
$692$	−4.24264	−	4.24264i	−0.161281	−	0.161281i
$693$	17.3867	+	4.65874i	0.660465	+	0.176971i
$694$			15.0000i			0.569392i
$695$		0			0
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$	−9.41404	−	35.1337i	−0.356582	−	1.33078i
$698$	2.07055	+	7.72741i	0.0783716	+	0.292487i
$699$	−2.59808	−	4.50000i	−0.0982683	−	0.170206i
$700$		0			0
$701$		−	17.3205i		−	0.654187i	−0.944992	−	0.327093i	$-0.893931\pi$
$701$		−	17.3205i		−	0.654187i	0.944992	−	0.327093i	$-0.106069\pi$
$702$	−12.7279	−	12.7279i	−0.480384	−	0.480384i
$703$	34.2929	+	34.2929i	1.29338	+	1.29338i
$704$	0.866025	+	1.50000i	0.0326396	+	0.0565334i
$705$		0			0
$706$	10.5000	−	18.1865i	0.395173	−	0.684459i
$707$	−23.1822	+	6.21166i	−0.871857	+	0.233613i
$708$	−5.43520	−	20.2844i	−0.204267	−	0.762336i
$709$	34.6410	−	20.0000i	1.30097	−	0.751116i	0.320400	−	0.947282i	$-0.396183\pi$
$709$	34.6410	−	20.0000i	1.30097	−	0.751116i	0.980571	+	0.196167i	$0.0628493\pi$
$710$		0			0
$711$	12.0000			0.450035
$712$	4.89898	−	4.89898i	0.183597	−	0.183597i
$713$	46.3644	+	12.4233i	1.73636	+	0.465257i
$714$			18.0000i			0.673633i
$715$		0			0
$716$	3.00000	+	1.73205i	0.112115	+	0.0647298i
$717$	−12.7279	−	12.7279i	−0.475333	−	0.475333i
$718$	−6.27603	+	23.4225i	−0.234219	+	0.874118i
$719$	−27.7128			−1.03351			−0.516757	−	0.856132i	$-0.672861\pi$
$719$	−27.7128			−1.03351			−0.516757	+	0.856132i	$0.672861\pi$
$720$		0			0
$721$	60.0000			2.23452
$722$	−7.76457	+	28.9778i	−0.288967	+	1.07844i
$723$	−1.67303	+	0.448288i	−0.0622208	+	0.0166720i
$724$	1.73205	+	1.00000i	0.0643712	+	0.0371647i
$725$		0			0
$726$	−12.0000	+	6.92820i	−0.445362	+	0.257130i
$727$	10.0382	+	2.68973i	0.372296	+	0.0997564i	0.440115	−	0.897941i	$-0.354938\pi$
$727$	10.0382	+	2.68973i	0.372296	+	0.0997564i	−0.0678194	+	0.997698i	$0.521604\pi$
$728$	−8.48528	+	8.48528i	−0.314485	+	0.314485i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	−13.5000	+	7.79423i	−0.499316	+	0.288280i
$732$	6.69213	+	1.79315i	0.247348	+	0.0662768i
$733$	−50.1910	+	13.4486i	−1.85385	+	0.496737i	−0.999728	−	0.0233418i	$-0.992569\pi$
$733$	−50.1910	+	13.4486i	−1.85385	+	0.496737i	−0.854119	+	0.520078i	$0.825903\pi$
$734$	−6.92820	+	12.0000i	−0.255725	+	0.442928i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	−2.12132	−	2.12132i	−0.0781398	−	0.0781398i
$738$	35.1337	−	9.41404i	1.29329	−	0.346536i
$739$		−	41.0000i		−	1.50821i	−0.656754	−	0.754105i	$-0.728071\pi$
$739$		−	41.0000i		−	1.50821i	0.656754	−	0.754105i	$-0.271929\pi$
$740$		0			0
$741$	−42.0000			−1.54291
$742$		0			0
$743$	4.65874	+	17.3867i	0.170913	+	0.637855i	0.997212	+	0.0746233i	$0.0237754\pi$
$743$	4.65874	+	17.3867i	0.170913	+	0.637855i	−0.826299	+	0.563232i	$0.809558\pi$
$744$	−13.8564			−0.508001
$745$		0			0
$746$			17.3205i			0.634149i
$747$	25.4558	+	25.4558i	0.931381	+	0.931381i
$748$	3.67423	+	3.67423i	0.134343	+	0.134343i
$749$	5.19615	+	9.00000i	0.189863	+	0.328853i
$750$		0			0
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$	−5.79555	+	1.55291i	−0.211342	+	0.0566290i
$753$	−43.4667	−	11.6469i	−1.58401	−	0.424435i
$754$	10.3923	−	6.00000i	0.378465	−	0.218507i
$755$		0			0
$756$	−18.0000			−0.654654
$757$	26.9444	−	26.9444i	0.979310	−	0.979310i	−0.0204799	−	0.999790i	$-0.506519\pi$
$757$	26.9444	−	26.9444i	0.979310	−	0.979310i	0.999790	+	0.0204799i	$0.00651940\pi$
$758$	0.965926	+	0.258819i	0.0350840	+	0.00940073i
$759$	15.5885	−	9.00000i	0.565825	−	0.326679i
$760$		0			0
$761$	−30.0000	−	17.3205i	−1.08750	−	0.627868i	−0.154590	−	0.987979i	$-0.549406\pi$
$761$	−30.0000	−	17.3205i	−1.08750	−	0.627868i	−0.932910	+	0.360111i	$0.882739\pi$
$762$	17.3867	−	4.65874i	0.629852	−	0.168768i
$763$	3.58630	−	13.3843i	0.129833	−	0.484543i
$764$	−24.2487			−0.877288
$765$		0			0
$766$	12.0000			0.433578
$767$	10.8704	−	40.5689i	0.392507	−	1.46486i
$768$	−1.22474	−	1.22474i	−0.0441942	−	0.0441942i
$769$	−12.1244	−	7.00000i	−0.437215	−	0.252426i	0.265200	−	0.964193i	$-0.414562\pi$
$769$	−12.1244	−	7.00000i	−0.437215	−	0.252426i	−0.702416	+	0.711767i	$0.747895\pi$
$770$		0			0
$771$			46.7654i			1.68421i
$772$	8.36516	+	2.24144i	0.301069	+	0.0806711i
$773$	38.1838	−	38.1838i	1.37337	−	1.37337i	0.517985	−	0.855390i	$-0.326682\pi$
$773$	38.1838	−	38.1838i	1.37337	−	1.37337i	0.855390	−	0.517985i	$-0.173318\pi$
$774$	−7.79423	−	13.5000i	−0.280158	−	0.485247i
$775$		0			0
$776$	7.50000	−	4.33013i	0.269234	−	0.155443i
$777$	10.7589	+	40.1528i	0.385974	+	1.44047i
$778$	−10.0382	+	2.68973i	−0.359887	+	0.0964314i
$779$	42.4352	−	73.5000i	1.52040	−	2.63341i
$780$		0			0
$781$	12.0000	+	20.7846i	0.429394	+	0.743732i
$782$	12.7279	+	12.7279i	0.455150	+	0.455150i
$783$	17.3867	+	4.65874i	0.621349	+	0.166490i
$784$			5.00000i			0.178571i
$785$		0			0
$786$	3.00000	+	5.19615i	0.107006	+	0.185341i
$787$	4.48288	+	16.7303i	0.159797	+	0.596372i	0.998647	+	0.0520081i	$0.0165622\pi$
$787$	4.48288	+	16.7303i	0.159797	+	0.596372i	−0.838849	+	0.544364i	$0.816771\pi$
$788$	−6.21166	−	23.1822i	−0.221281	−	0.825832i
$789$	5.19615	−	9.00000i	0.184988	−	0.320408i
$790$		0			0
$791$		−	62.3538i		−	2.21705i
$792$	−3.67423	+	3.67423i	−0.130558	+	0.130558i
$793$	9.79796	+	9.79796i	0.347936	+	0.347936i
$794$	10.3923	+	18.0000i	0.368809	+	0.638796i
$795$		0			0
$796$	−5.00000	+	8.66025i	−0.177220	+	0.306955i
$797$	23.1822	−	6.21166i	0.821156	−	0.220028i	0.176304	−	0.984336i	$-0.443586\pi$
$797$	23.1822	−	6.21166i	0.821156	−	0.220028i	0.644852	+	0.764308i	$0.276919\pi$
$798$	−29.6985	+	29.6985i	−1.05131	+	1.05131i
$799$	−15.5885	+	9.00000i	−0.551480	+	0.318397i
$800$		0			0
$801$	18.0000	+	10.3923i	0.635999	+	0.367194i
$802$	−3.67423	+	3.67423i	−0.129742	+	0.129742i
$803$	14.4889	+	3.88229i	0.511302	+	0.137003i
$804$	2.59808	+	1.50000i	0.0916271	+	0.0529009i
$805$		0			0
$806$	−24.0000	−	13.8564i	−0.845364	−	0.488071i
$807$	3.10583	−	11.5911i	0.109330	−	0.408026i
$808$	1.79315	−	6.69213i	0.0630828	−	0.235428i
$809$	12.1244			0.426270			0.213135	−	0.977023i	$-0.431633\pi$
$809$	12.1244			0.426270			0.213135	+	0.977023i	$0.431633\pi$
$810$		0			0
$811$	−41.0000			−1.43970			−0.719852	−	0.694127i	$-0.755791\pi$
$811$	−41.0000			−1.43970			−0.719852	+	0.694127i	$0.755791\pi$
$812$	3.10583	−	11.5911i	0.108993	−	0.406768i
$813$	12.5521	−	46.8449i	0.440220	−	1.64292i
$814$	10.3923	+	6.00000i	0.364250	+	0.210300i
$815$		0			0
$816$	−4.50000	−	2.59808i	−0.157532	−	0.0909509i
$817$	−35.1337	−	9.41404i	−1.22917	−	0.329356i
$818$	−4.94975	+	4.94975i	−0.173064	+	0.173064i
$819$	−31.1769	−	18.0000i	−1.08941	−	0.628971i
$820$		0			0
$821$	15.0000	−	8.66025i	0.523504	−	0.302245i	−0.214863	−	0.976644i	$-0.568931\pi$
$821$	15.0000	−	8.66025i	0.523504	−	0.302245i	0.738367	+	0.674399i	$0.235597\pi$
$822$	−3.67423	+	3.67423i	−0.128154	+	0.128154i
$823$	−13.3843	+	3.58630i	−0.466546	+	0.125011i	−0.484431	−	0.874829i	$-0.660973\pi$
$823$	−13.3843	+	3.58630i	−0.466546	+	0.125011i	0.0178851	+	0.999840i	$0.494307\pi$
$824$	−8.66025	+	15.0000i	−0.301694	+	0.522550i
$825$		0			0
$826$	−21.0000	−	36.3731i	−0.730683	−	1.26558i
$827$	−25.4558	−	25.4558i	−0.885186	−	0.885186i	0.108870	−	0.994056i	$-0.465277\pi$
$827$	−25.4558	−	25.4558i	−0.885186	−	0.885186i	−0.994056	+	0.108870i	$0.965277\pi$
$828$	−12.7279	+	12.7279i	−0.442326	+	0.442326i
$829$			34.0000i			1.18087i	0.807086	+	0.590434i	$0.201044\pi$
$829$			34.0000i			1.18087i	−0.807086	+	0.590434i	$0.798956\pi$
$830$		0			0
$831$	−9.00000	+	15.5885i	−0.312207	+	0.540758i
$832$	−0.896575	−	3.34607i	−0.0310832	−	0.116004i
$833$	3.88229	+	14.4889i	0.134513	+	0.502010i
$834$	4.33013	+	7.50000i	0.149940	+	0.259704i
$835$		0			0
$836$			12.1244i			0.419330i
$837$	−10.7589	−	40.1528i	−0.371882	−	1.38788i
$838$	−7.34847	−	7.34847i	−0.253849	−	0.253849i
$839$	−17.3205	−	30.0000i	−0.597970	−	1.03572i	−0.993120	−	0.117098i	$-0.962641\pi$
$839$	−17.3205	−	30.0000i	−0.597970	−	1.03572i	0.395150	−	0.918617i	$-0.370693\pi$
$840$		0			0
$841$	8.50000	−	14.7224i	0.293103	−	0.507670i
$842$	−27.0459	+	7.24693i	−0.932064	+	0.249746i
$843$	9.31749	+	34.7733i	0.320911	+	1.19766i
$844$	−3.46410	+	2.00000i	−0.119239	+	0.0688428i
$845$		0			0
$846$	−9.00000	−	15.5885i	−0.309426	−	0.535942i
$847$	−19.5959	+	19.5959i	−0.673324	+	0.673324i
$848$		0			0
$849$			54.0000i			1.85328i
$850$		0			0
$851$	36.0000	+	20.7846i	1.23406	+	0.712487i
$852$	−16.9706	−	16.9706i	−0.581402	−	0.581402i
$853$	9.86233	−	36.8067i	0.337680	−	1.26024i	−0.563255	−	0.826283i	$-0.690451\pi$
$853$	9.86233	−	36.8067i	0.337680	−	1.26024i	0.900935	−	0.433955i	$-0.142882\pi$
$854$	13.8564			0.474156
$855$		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	$0.828690\pi$
$858$	−10.0382	+	2.68973i	−0.342698	+	0.0918257i
$859$	11.2583	+	6.50000i	0.384129	+	0.221777i	0.679613	−	0.733571i	$-0.262148\pi$
$859$	11.2583	+	6.50000i	0.384129	+	0.221777i	−0.295484	+	0.955348i	$0.595481\pi$
$860$		0			0
$861$	63.0000	−	36.3731i	2.14703	−	1.23959i
$862$	−3.34607	−	0.896575i	−0.113967	−	0.0305375i
$863$	−16.9706	+	16.9706i	−0.577685	+	0.577685i	−0.934265	−	0.356580i	$-0.883943\pi$
$863$	−16.9706	+	16.9706i	−0.577685	+	0.577685i	0.356580	+	0.934265i	$0.383943\pi$
$864$	2.59808	−	4.50000i	0.0883883	−	0.153093i
$865$		0			0
$866$	−22.5000	+	12.9904i	−0.764581	+	0.441431i
$867$	13.3843	+	3.58630i	0.454553	+	0.121797i
$868$	−26.7685	+	7.17260i	−0.908583	+	0.243454i
$869$	3.46410	−	6.00000i	0.117512	−	0.203536i
$870$		0			0
$871$	3.00000	+	5.19615i	0.101651	+	0.176065i
$872$	2.82843	+	2.82843i	0.0957826	+	0.0957826i
$873$	18.3712	+	18.3712i	0.621770	+	0.621770i
$874$			42.0000i			1.42067i
$875$		0			0
$876$	−15.0000			−0.506803
$877$	7.17260	+	26.7685i	0.242202	+	0.903909i	0.974769	+	0.223215i	$0.0716551\pi$
$877$	7.17260	+	26.7685i	0.242202	+	0.903909i	−0.732568	+	0.680694i	$0.761678\pi$
$878$	4.14110	+	15.4548i	0.139756	+	0.521575i
$879$	10.3923			0.350524
$880$		0			0
$881$		−	6.92820i		−	0.233417i	−0.993166	−	0.116709i	$-0.962766\pi$
$881$		−	6.92820i		−	0.233417i	0.993166	−	0.116709i	$-0.0372343\pi$
$882$	−14.4889	+	3.88229i	−0.487866	+	0.130723i
$883$	8.57321	+	8.57321i	0.288512	+	0.288512i	0.836492	−	0.547980i	$-0.184603\pi$
$883$	8.57321	+	8.57321i	0.288512	+	0.288512i	−0.547980	+	0.836492i	$0.684603\pi$
$884$	−5.19615	−	9.00000i	−0.174766	−	0.302703i
$885$		0			0
$886$	13.5000	−	23.3827i	0.453541	−	0.785557i
$887$	−46.3644	+	12.4233i	−1.55677	+	0.417134i	−0.931638	−	0.363388i	$-0.881620\pi$
$887$	−46.3644	+	12.4233i	−1.55677	+	0.417134i	−0.625128	+	0.780522i	$0.714953\pi$
$888$	−11.5911	−	3.10583i	−0.388972	−	0.104225i
$889$	31.1769	−	18.0000i	1.04564	−	0.603701i
$890$		0			0
$891$	−13.5000	−	7.79423i	−0.452267	−	0.261116i
$892$	7.34847	−	7.34847i	0.246045	−	0.246045i
$893$	−40.5689	−	10.8704i	−1.35759	−	0.363764i
$894$	15.5885	−	9.00000i	0.521356	−	0.301005i
$895$		0			0
$896$	−3.00000	−	1.73205i	−0.100223	−	0.0578638i
$897$	−34.7733	+	9.31749i	−1.16105	+	0.311102i
$898$	10.3106	−	38.4797i	0.344070	−	1.28409i
$899$	27.7128			0.924274
$900$		0			0
$901$		0			0
$902$	5.43520	−	20.2844i	0.180972	−	0.675398i
$903$	−22.0454	−	22.0454i	−0.733625	−	0.733625i
$904$	15.5885	+	9.00000i	0.518464	+	0.299336i
$905$		0			0
$906$		−	17.3205i		−	0.575435i
$907$	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	$0.537408\pi$
$908$	2.12132	−	2.12132i	0.0703985	−	0.0703985i
$909$	20.7846			0.689382
$910$		0			0
$911$	−30.0000	+	17.3205i	−0.993944	+	0.573854i	−0.906451	−	0.422311i	$-0.861219\pi$
$911$	−30.0000	+	17.3205i	−0.993944	+	0.573854i	−0.0874934	+	0.996165i	$0.527886\pi$
$912$	−3.13801	−	11.7112i	−0.103910	−	0.387798i
$913$	20.0764	−	5.37945i	0.664432	−	0.178034i
$914$	−12.9904	+	22.5000i	−0.429684	+	0.744234i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$	8.48528	+	8.48528i	0.280209	+	0.280209i
$918$	4.03459	−	15.0573i	0.133161	−	0.496965i
$919$			22.0000i			0.725713i	0.931845	+	0.362857i	$0.118198\pi$
$919$			22.0000i			0.725713i	−0.931845	+	0.362857i	$0.881802\pi$
$920$		0			0
$921$	−4.50000	−	7.79423i	−0.148280	−	0.256829i
$922$	−4.48288	−	16.7303i	−0.147636	−	0.550984i
$923$	−12.4233	−	46.3644i	−0.408918	−	1.52610i
$924$	−5.19615	+	9.00000i	−0.170941	+	0.296078i
$925$		0			0
$926$		−	13.8564i		−	0.455350i
$927$	−50.1910	−	13.4486i	−1.64849	−	0.441711i
$928$	2.44949	+	2.44949i	0.0804084	+	0.0804084i
$929$	17.3205	+	30.0000i	0.568267	+	0.984268i	0.996737	+	0.0807121i	$0.0257194\pi$
$929$	17.3205	+	30.0000i	0.568267	+	0.984268i	−0.428470	+	0.903556i	$0.640947\pi$
$930$		0			0
$931$	−17.5000	+	30.3109i	−0.573539	+	0.993399i
$932$	2.89778	−	0.776457i	0.0949199	−	0.0254337i
$933$	4.24264	−	4.24264i	0.138898	−	0.138898i
$934$	−7.79423	+	4.50000i	−0.255035	+	0.147244i
$935$		0			0
$936$	9.00000	−	5.19615i	0.294174	−	0.169842i
$937$	−24.4949	+	24.4949i	−0.800213	+	0.800213i	−0.983129	−	0.182915i	$-0.941447\pi$
$937$	−24.4949	+	24.4949i	−0.800213	+	0.800213i	0.182915	+	0.983129i	$0.441447\pi$
$938$	5.79555	+	1.55291i	0.189232	+	0.0507044i
$939$	12.9904	+	7.50000i	0.423925	+	0.244753i
$940$		0			0
$941$	−18.0000	−	10.3923i	−0.586783	−	0.338779i	0.177041	−	0.984203i	$-0.443347\pi$
$941$	−18.0000	−	10.3923i	−0.586783	−	0.338779i	−0.763825	+	0.645424i	$0.776681\pi$
$942$		0			0
$943$	18.8281	−	70.2674i	0.613127	−	2.28822i
$944$	12.1244			0.394614
$945$		0			0
$946$	−9.00000			−0.292615
$947$	−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	$0.938776\pi$
$948$	−1.79315	+	6.69213i	−0.0582388	+	0.217350i
$949$	−25.9808	−	15.0000i	−0.843371	−	0.486921i
$950$		0			0
$951$	−9.00000	−	5.19615i	−0.291845	−	0.168497i
$952$	−10.0382	−	2.68973i	−0.325340	−	0.0871745i
$953$	−23.3345	+	23.3345i	−0.755879	+	0.755879i	−0.975570	−	0.219690i	$-0.929495\pi$
$953$	−23.3345	+	23.3345i	−0.755879	+	0.755879i	0.219690	+	0.975570i	$0.429495\pi$
$954$		0			0
$955$		0			0
$956$	9.00000	−	5.19615i	0.291081	−	0.168056i
$957$	7.34847	−	7.34847i	0.237542	−	0.237542i
$958$	16.7303	−	4.48288i	0.540532	−	0.144835i
$959$	−5.19615	+	9.00000i	−0.167793	+	0.290625i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−16.9706	−	16.9706i	−0.547153	−	0.547153i
$963$	−2.32937	−	8.69333i	−0.0750629	−	0.280139i
$964$		−	1.00000i		−	0.0322078i
$965$		0			0
$966$	−18.0000	+	31.1769i	−0.579141	+	1.00310i
$967$	−0.896575	−	3.34607i	−0.0288319	−	0.107602i	0.950010	−	0.312218i	$-0.101072\pi$
$967$	−0.896575	−	3.34607i	−0.0288319	−	0.107602i	−0.978842	+	0.204616i	$0.934405\pi$
$968$	−2.07055	−	7.72741i	−0.0665501	−	0.248368i
$969$	−18.1865	−	31.5000i	−0.584236	−	1.01193i
$970$		0			0
$971$			3.46410i			0.111168i	0.998454	+	0.0555842i	$0.0177021\pi$
$971$			3.46410i			0.111168i	−0.998454	+	0.0555842i	$0.982298\pi$
$972$	15.0573	+	4.03459i	0.482963	+	0.129410i
$973$	12.2474	+	12.2474i	0.392635	+	0.392635i
$974$	12.1244	+	21.0000i	0.388489	+	0.672883i
$975$		0			0
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	2.89778	−	0.776457i	0.0927081	−	0.0248411i	−0.212167	−	0.977233i	$-0.568052\pi$
$977$	2.89778	−	0.776457i	0.0927081	−	0.0248411i	0.304875	+	0.952392i	$0.401385\pi$
$978$	1.55291	+	5.79555i	0.0496567	+	0.185321i
$979$	10.3923	−	6.00000i	0.332140	−	0.191761i
$980$		0			0
$981$	−6.00000	+	10.3923i	−0.191565	+	0.331801i
$982$	−15.9217	+	15.9217i	−0.508081	+	0.508081i
$983$	34.7733	+	9.31749i	1.10910	+	0.297182i	0.766464	−	0.642288i	$-0.222015\pi$
$983$	34.7733	+	9.31749i	1.10910	+	0.297182i	0.342633	+	0.939469i	$0.388681\pi$
$984$			21.0000i			0.669456i
$985$		0			0
$986$	9.00000	+	5.19615i	0.286618	+	0.165479i
$987$	−25.4558	−	25.4558i	−0.810268	−	0.810268i
$988$	6.27603	−	23.4225i	0.199667	−	0.745168i
$989$	−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	$0.397103\pi$
$992$	2.07055	−	7.72741i	0.0657401	−	0.245345i
$993$	−46.8449	+	12.5521i	−1.48658	+	0.398327i
$994$	−41.5692	−	24.0000i	−1.31850	−	0.761234i
$995$		0			0
$996$	−18.0000	+	10.3923i	−0.570352	+	0.329293i
$997$	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	$0.354628\pi$
$998$	13.4350	−	13.4350i	0.425278	−	0.425278i
$999$		−	36.0000i		−	1.13899i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.448288 + 1.67303i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(3.34607 + 0.896575i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.448288 + 1.67303i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(3.34607 + 0.896575i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-1.50000 + 0.866025i) q^{11} +(1.22474 - 1.22474i) q^{12} +(3.34607 - 0.896575i) q^{13} +(1.73205 - 3.00000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.12132 + 2.12132i) q^{17} +(-2.12132 + 2.12132i) q^{18} +7.00000i q^{19} +(-3.00000 + 5.19615i) q^{21} +(0.448288 + 1.67303i) q^{22} +(1.55291 + 5.79555i) q^{23} +(-0.866025 - 1.50000i) q^{24} -3.46410i q^{26} +(3.67423 - 3.67423i) q^{27} +(-2.44949 - 2.44949i) q^{28} +(1.73205 + 3.00000i) q^{29} +(4.00000 - 6.92820i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.776457 - 2.89778i) q^{33} +(2.59808 - 1.50000i) q^{34} +(1.50000 + 2.59808i) q^{36} +(4.89898 - 4.89898i) q^{37} +(6.76148 + 1.81173i) q^{38} +6.00000i q^{39} +(-10.5000 - 6.06218i) q^{41} +(4.24264 + 4.24264i) q^{42} +(-1.34486 + 5.01910i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(-1.55291 + 5.79555i) q^{47} +(-1.67303 + 0.448288i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(-3.34607 - 0.896575i) q^{52} +(-2.59808 - 4.50000i) q^{54} +(-3.00000 + 1.73205i) q^{56} +(-11.7112 - 3.13801i) q^{57} +(3.34607 - 0.896575i) q^{58} +(6.06218 - 10.5000i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-5.65685 - 5.65685i) q^{62} +(-7.34847 - 7.34847i) q^{63} -1.00000i q^{64} -3.00000 q^{66} +(0.448288 + 1.67303i) q^{67} +(-0.776457 - 2.89778i) q^{68} -10.3923 q^{69} -13.8564i q^{71} +(2.89778 - 0.776457i) q^{72} +(-6.12372 - 6.12372i) q^{73} +(-3.46410 - 6.00000i) q^{74} +(3.50000 - 6.06218i) q^{76} +(-5.79555 + 1.55291i) q^{77} +(5.79555 + 1.55291i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(4.50000 + 7.79423i) q^{81} +(-8.57321 + 8.57321i) q^{82} +(-11.5911 - 3.10583i) q^{83} +(5.19615 - 3.00000i) q^{84} +(4.50000 + 2.59808i) q^{86} +(-5.79555 + 1.55291i) q^{87} +(0.448288 - 1.67303i) q^{88} -6.92820 q^{89} +12.0000 q^{91} +(1.55291 - 5.79555i) q^{92} +(9.79796 + 9.79796i) q^{93} +(5.19615 + 3.00000i) q^{94} +1.73205i q^{96} +(-8.36516 - 2.24144i) q^{97} +(3.53553 - 3.53553i) q^{98} +5.19615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{6}+O(q^{10}) \) 8 * q + 12 * q^6	\( 8 q + 12 q^{6} - 12 q^{11} + 4 q^{16} - 24 q^{21} + 32 q^{31} + 12 q^{36} - 84 q^{41} + 48 q^{46} - 36 q^{51} - 24 q^{56} + 16 q^{61} - 24 q^{66} + 28 q^{76} + 36 q^{81} + 36 q^{86} + 96 q^{91}+O(q^{100}) \) 8 * q + 12 * q^6 - 12 * q^11 + 4 * q^16 - 24 * q^21 + 32 * q^31 + 12 * q^36 - 84 * q^41 + 48 * q^46 - 36 * q^51 - 24 * q^56 + 16 * q^61 - 24 * q^66 + 28 * q^76 + 36 * q^81 + 36 * q^86 + 96 * q^91

Introduction

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