LMFDB - Embedded newform 450.2.p.f.443.2

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			443.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	450.443
Dual form			450.2.p.f.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-0.896575 - 3.34607i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-0.896575 - 3.34607i) 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} +(-0.896575 + 3.34607i) 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} +(-1.67303 - 0.448288i) q^{22} +(5.79555 + 1.55291i) 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} +(0.258819 - 0.965926i) q^{32} +(-2.89778 - 0.776457i) q^{33} +(-2.59808 - 1.50000i) q^{34} +(1.50000 - 2.59808i) q^{36} +(4.89898 - 4.89898i) q^{37} +(1.81173 + 6.76148i) q^{38} +6.00000i q^{39} +(-10.5000 + 6.06218i) q^{41} +(-4.24264 - 4.24264i) q^{42} +(5.01910 - 1.34486i) q^{43} -1.73205 q^{44} +6.00000 q^{46} +(-5.79555 + 1.55291i) q^{47} +(0.448288 - 1.67303i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(-4.50000 - 2.59808i) q^{51} +(0.896575 + 3.34607i) q^{52} +(2.59808 - 4.50000i) q^{54} +(-3.00000 - 1.73205i) q^{56} +(3.13801 + 11.7112i) q^{57} +(-0.896575 + 3.34607i) 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} +(-1.67303 - 0.448288i) q^{67} +(-2.89778 - 0.776457i) q^{68} +10.3923 q^{69} +13.8564i q^{71} +(0.776457 - 2.89778i) q^{72} +(-6.12372 - 6.12372i) q^{73} +(3.46410 - 6.00000i) q^{74} +(3.50000 + 6.06218i) q^{76} +(-1.55291 + 5.79555i) q^{77} +(1.55291 + 5.79555i) q^{78} +(3.46410 + 2.00000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(-8.57321 + 8.57321i) q^{82} +(-3.10583 - 11.5911i) q^{83} +(-5.19615 - 3.00000i) q^{84} +(4.50000 - 2.59808i) q^{86} +(-1.55291 + 5.79555i) q^{87} +(-1.67303 + 0.448288i) q^{88} +6.92820 q^{89} +12.0000 q^{91} +(5.79555 - 1.55291i) q^{92} +(9.79796 + 9.79796i) q^{93} +(-5.19615 + 3.00000i) q^{94} -1.73205i q^{96} +(2.24144 + 8.36516i) 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.67303	−	0.448288i	0.965926	−	0.258819i
$3$	1.67303	−	0.448288i	0.965926	−	0.258819i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$	−0.896575	−	3.34607i	−0.338874	−	1.26469i	−0.899608	−	0.436698i	$-0.856148\pi$
$7$	−0.896575	−	3.34607i	−0.338874	−	1.26469i	0.560734	−	0.827996i	$-0.310519\pi$
$8$	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	0.256520	−	0.966539i	$-0.417424\pi$
$11$	−1.50000	−	0.866025i	−0.452267	−	0.261116i	−0.708787	+	0.705422i	$0.750757\pi$
$12$	1.22474	−	1.22474i	0.353553	−	0.353553i
$13$	−0.896575	+	3.34607i	−0.248665	+	0.928032i	0.722840	+	0.691015i	$0.242836\pi$
$13$	−0.896575	+	3.34607i	−0.248665	+	0.928032i	−0.971506	+	0.237016i	$0.923830\pi$
$14$	−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	0.401405	−	0.915901i	$-0.368522\pi$
$17$	−2.12132	−	2.12132i	−0.514496	−	0.514496i	−0.915901	+	0.401405i	$0.868522\pi$
$18$	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
$22$	−1.67303	−	0.448288i	−0.356692	−	0.0955753i
$23$	5.79555	+	1.55291i	1.20846	+	0.323805i	0.806156	−	0.591703i	$-0.201544\pi$
$23$	5.79555	+	1.55291i	1.20846	+	0.323805i	0.402300	+	0.915508i	$0.368211\pi$
$24$	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	$-0.937565\pi$
$29$	−1.73205	+	3.00000i	−0.321634	+	0.557086i	0.659192	+	0.751975i	$0.270899\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−2.89778	−	0.776457i	−0.504438	−	0.135164i
$34$	−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	$0.0571389\pi$
$38$	1.81173	+	6.76148i	0.293902	+	1.09686i
$39$			6.00000i			0.960769i
$40$		0			0
$41$	−10.5000	+	6.06218i	−1.63982	+	0.946753i	−0.658932	+	0.752202i	$0.728992\pi$
$41$	−10.5000	+	6.06218i	−1.63982	+	0.946753i	−0.980892	+	0.194551i	$0.937675\pi$
$42$	−4.24264	−	4.24264i	−0.654654	−	0.654654i
$43$	5.01910	−	1.34486i	0.765405	−	0.205090i	0.145065	−	0.989422i	$-0.453661\pi$
$43$	5.01910	−	1.34486i	0.765405	−	0.205090i	0.620341	+	0.784332i	$0.286994\pi$
$44$	−1.73205			−0.261116
$45$		0			0
$46$	6.00000			0.884652
$47$	−5.79555	+	1.55291i	−0.845369	+	0.226516i	−0.655407	−	0.755276i	$-0.727503\pi$
$47$	−5.79555	+	1.55291i	−0.845369	+	0.226516i	−0.189961	+	0.981792i	$0.560836\pi$
$48$	0.448288	−	1.67303i	0.0647048	−	0.241481i
$49$	−4.33013	+	2.50000i	−0.618590	+	0.357143i
$50$		0			0
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	0.896575	+	3.34607i	0.124333	+	0.464016i
$53$		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
$57$	3.13801	+	11.7112i	0.415640	+	1.55119i
$58$	−0.896575	+	3.34607i	−0.117726	+	0.439360i
$59$	−6.06218	−	10.5000i	−0.789228	−	1.36698i	−0.926440	−	0.376442i	$-0.877147\pi$
$59$	−6.06218	−	10.5000i	−0.789228	−	1.36698i	0.137212	−	0.990542i	$-0.456186\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	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
$67$	−1.67303	−	0.448288i	−0.204393	−	0.0547671i	0.155170	−	0.987888i	$-0.450408\pi$
$67$	−1.67303	−	0.448288i	−0.204393	−	0.0547671i	−0.359563	+	0.933121i	$0.617074\pi$
$68$	−2.89778	−	0.776457i	−0.351407	−	0.0941593i
$69$	10.3923			1.25109
$70$		0			0
$71$			13.8564i			1.64445i	0.569160	+	0.822226i	$0.307268\pi$
$71$			13.8564i			1.64445i	−0.569160	+	0.822226i	$0.692732\pi$
$72$	0.776457	−	2.89778i	0.0915064	−	0.341506i
$73$	−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
$77$	−1.55291	+	5.79555i	−0.176971	+	0.660465i
$78$	1.55291	+	5.79555i	0.175833	+	0.656217i
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	0.682048	−	0.731307i	$-0.261089\pi$
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	−0.292306	+	0.956325i	$0.594423\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	−8.57321	+	8.57321i	−0.946753	+	0.946753i
$83$	−3.10583	−	11.5911i	−0.340909	−	1.27229i	−0.897319	−	0.441382i	$-0.854488\pi$
$83$	−3.10583	−	11.5911i	−0.340909	−	1.27229i	0.556410	−	0.830908i	$-0.312178\pi$
$84$	−5.19615	−	3.00000i	−0.566947	−	0.327327i
$85$		0			0
$86$	4.50000	−	2.59808i	0.485247	−	0.280158i
$87$	−1.55291	+	5.79555i	−0.166490	+	0.621349i
$88$	−1.67303	+	0.448288i	−0.178346	+	0.0477876i
$89$	6.92820			0.734388			0.367194	−	0.930144i	$-0.380318\pi$
$89$	6.92820			0.734388			0.367194	+	0.930144i	$0.380318\pi$
$90$		0			0
$91$	12.0000			1.25794
$92$	5.79555	−	1.55291i	0.604228	−	0.161903i
$93$	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
$97$	2.24144	+	8.36516i	0.227584	+	0.849354i	0.981353	+	0.192215i	$0.0615669\pi$
$97$	2.24144	+	8.36516i	0.227584	+	0.849354i	−0.753769	+	0.657139i	$0.771766\pi$
$98$	−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	0.170847	−	0.985298i	$-0.445350\pi$
$101$	−6.00000	−	3.46410i	−0.597022	−	0.344691i	−0.767869	+	0.640607i	$0.778683\pi$
$102$	−5.01910	−	1.34486i	−0.496965	−	0.133161i
$103$	−4.48288	+	16.7303i	−0.441711	+	1.64849i	0.282766	+	0.959189i	$0.408748\pi$
$103$	−4.48288	+	16.7303i	−0.441711	+	1.64849i	−0.724477	+	0.689299i	$0.757919\pi$
$104$	1.73205	+	3.00000i	0.169842	+	0.294174i
$105$		0			0
$106$		0			0
$107$	−2.12132	−	2.12132i	−0.205076	−	0.205076i	0.597095	−	0.802171i	$-0.296322\pi$
$107$	−2.12132	−	2.12132i	−0.205076	−	0.205076i	−0.802171	+	0.597095i	$0.796322\pi$
$108$	1.34486	−	5.01910i	0.129410	−	0.482963i
$109$		−	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
$112$	−3.34607	−	0.896575i	−0.316173	−	0.0847184i
$113$	−17.3867	−	4.65874i	−1.63560	−	0.438258i	−0.680069	−	0.733148i	$-0.738050\pi$
$113$	−17.3867	−	4.65874i	−1.63560	−	0.438258i	−0.955531	+	0.294891i	$0.904717\pi$
$114$	6.06218	+	10.5000i	0.567775	+	0.983415i
$115$		0			0
$116$			3.46410i			0.321634i
$117$	2.68973	+	10.0382i	0.248665	+	0.928032i
$118$	−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
$122$	1.03528	−	3.86370i	0.0937295	−	0.349803i
$123$	−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	$0.0974607\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	7.79423	−	4.50000i	0.686244	−	0.396203i
$130$		0			0
$131$	3.00000	−	1.73205i	0.262111	−	0.151330i	−0.363186	−	0.931717i	$-0.618311\pi$
$131$	3.00000	−	1.73205i	0.262111	−	0.151330i	0.625297	+	0.780387i	$0.284978\pi$
$132$	−2.89778	+	0.776457i	−0.252219	+	0.0675819i
$133$	23.4225	−	6.27603i	2.03098	−	0.544201i
$134$	−1.73205			−0.149626
$135$		0			0
$136$	−3.00000			−0.257248
$137$	−2.89778	+	0.776457i	−0.247574	+	0.0663372i	−0.380472	−	0.924793i	$-0.624238\pi$
$137$	−2.89778	+	0.776457i	−0.247574	+	0.0663372i	0.132898	+	0.991130i	$0.457572\pi$
$138$	10.0382	−	2.68973i	0.854508	−	0.228965i
$139$	−4.33013	+	2.50000i	−0.367277	+	0.212047i	−0.672268	−	0.740308i	$-0.734680\pi$
$139$	−4.33013	+	2.50000i	−0.367277	+	0.212047i	0.304991	+	0.952355i	$0.401346\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$	3.58630	+	13.3843i	0.300956	+	1.12318i
$143$	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
$148$	1.79315	−	6.69213i	0.147396	−	0.550090i
$149$	−5.19615	−	9.00000i	−0.425685	−	0.737309i	0.570799	−	0.821090i	$-0.306634\pi$
$149$	−5.19615	−	9.00000i	−0.425685	−	0.737309i	−0.996484	+	0.0837813i	$0.973300\pi$
$150$		0			0
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	4.94975	+	4.94975i	0.401478	+	0.401478i
$153$	−8.69333	−	2.32937i	−0.702814	−	0.188319i
$154$			6.00000i			0.483494i
$155$		0			0
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$157$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$158$	3.86370	+	1.03528i	0.307380	+	0.0823622i
$159$		0			0
$160$		0			0
$161$		−	20.7846i		−	1.63806i
$162$	2.32937	−	8.69333i	0.183013	−	0.683013i
$163$	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		−0.965926	−	0.258819i	$-0.916667\pi$
$167$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$168$	−5.79555	−	1.55291i	−0.447137	−	0.119810i
$169$	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
$173$	1.55291	+	5.79555i	0.118066	+	0.440628i	0.999498	−	0.0316829i	$-0.0100867\pi$
$173$	1.55291	+	5.79555i	0.118066	+	0.440628i	−0.881432	+	0.472311i	$0.843420\pi$
$174$			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
$178$	6.69213	−	1.79315i	0.501596	−	0.134402i
$179$	3.46410			0.258919			0.129460	−	0.991585i	$-0.458676\pi$
$179$	3.46410			0.258919			0.129460	+	0.991585i	$0.458676\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	11.5911	−	3.10583i	0.859190	−	0.230219i
$183$	1.79315	−	6.69213i	0.132554	−	0.494697i
$184$	5.19615	−	3.00000i	0.383065	−	0.221163i
$185$		0			0
$186$	12.0000	+	6.92820i	0.879883	+	0.508001i
$187$	1.34486	+	5.01910i	0.0983461	+	0.367033i
$188$	−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	0.999736	+	0.0229818i	$0.00731599\pi$
$191$	21.0000	+	12.1244i	1.51951	+	0.877288i	0.519771	+	0.854306i	$0.326017\pi$
$192$	−0.448288	−	1.67303i	−0.0323524	−	0.120741i
$193$	2.24144	−	8.36516i	0.161342	−	0.602138i	−0.837136	−	0.546995i	$-0.815772\pi$
$193$	2.24144	−	8.36516i	0.161342	−	0.602138i	0.998478	−	0.0551431i	$-0.0175615\pi$
$194$	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	$-0.923579\pi$
$197$	−16.9706	−	16.9706i	−1.20910	−	1.20910i	−0.237785	−	0.971318i	$-0.576421\pi$
$198$	−5.01910	+	1.34486i	−0.356692	+	0.0955753i
$199$		−	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
$202$	−6.69213	−	1.79315i	−0.470857	−	0.126166i
$203$	11.5911	+	3.10583i	0.813536	+	0.217986i
$204$	−5.19615			−0.363803
$205$		0			0
$206$			17.3205i			1.20678i
$207$	17.3867	−	4.65874i	1.20846	−	0.323805i
$208$	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	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$		0			0
$213$	6.21166	+	23.1822i	0.425616	+	1.58842i
$214$	−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
$218$	−1.03528	−	3.86370i	−0.0701178	−	0.261683i
$219$	−12.9904	−	7.50000i	−0.877809	−	0.506803i
$220$		0			0
$221$	9.00000	−	5.19615i	0.605406	−	0.349531i
$222$	3.10583	−	11.5911i	0.208450	−	0.777944i
$223$	10.0382	−	2.68973i	0.672207	−	0.180117i	0.0934584	−	0.995623i	$-0.470208\pi$
$223$	10.0382	−	2.68973i	0.672207	−	0.180117i	0.578749	+	0.815506i	$0.303541\pi$
$224$	−3.46410			−0.231455
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−2.89778	+	0.776457i	−0.192332	+	0.0515353i	−0.353699	−	0.935359i	$-0.615076\pi$
$227$	−2.89778	+	0.776457i	−0.192332	+	0.0515353i	0.161367	+	0.986894i	$0.448410\pi$
$228$	8.57321	+	8.57321i	0.567775	+	0.567775i
$229$	19.0526	−	11.0000i	1.25903	−	0.726900i	0.286143	−	0.958187i	$-0.407627\pi$
$229$	19.0526	−	11.0000i	1.25903	−	0.726900i	0.972886	+	0.231287i	$0.0742935\pi$
$230$		0			0
$231$			10.3923i			0.683763i
$232$	0.896575	+	3.34607i	0.0588631	+	0.219680i
$233$	2.12132	−	2.12132i	0.138972	−	0.138972i	−0.634198	−	0.773171i	$-0.718670\pi$
$233$	2.12132	−	2.12132i	0.138972	−	0.138972i	0.773171	+	0.634198i	$0.218670\pi$
$234$	5.19615	+	9.00000i	0.339683	+	0.588348i
$235$		0			0
$236$	−10.5000	−	6.06218i	−0.683492	−	0.394614i
$237$	6.69213	+	1.79315i	0.434701	+	0.116478i
$238$	−2.68973	+	10.0382i	−0.174349	+	0.650680i
$239$	5.19615	+	9.00000i	0.336111	+	0.582162i	0.983698	−	0.179830i	$-0.0575549\pi$
$239$	5.19615	+	9.00000i	0.336111	+	0.582162i	−0.647586	+	0.761992i	$0.724222\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	−5.65685	−	5.65685i	−0.363636	−	0.363636i
$243$	4.03459	−	15.0573i	0.258819	−	0.965926i
$244$		−	4.00000i		−	0.256074i
$245$		0			0
$246$	−10.5000	+	18.1865i	−0.669456	+	1.15953i
$247$	−23.4225	−	6.27603i	−1.49034	−	0.399334i
$248$	7.72741	+	2.07055i	0.490691	+	0.131480i
$249$	−10.3923	−	18.0000i	−0.658586	−	1.14070i
$250$		0			0
$251$		−	25.9808i		−	1.63989i	−0.572441	−	0.819946i	$-0.694004\pi$
$251$		−	25.9808i		−	1.63989i	0.572441	−	0.819946i	$-0.305996\pi$
$252$	−10.0382	−	2.68973i	−0.632347	−	0.169437i
$253$	−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
$257$	6.98811	−	26.0800i	0.435907	−	1.62683i	−0.302981	−	0.952997i	$-0.597982\pi$
$257$	6.98811	−	26.0800i	0.435907	−	1.62683i	0.738887	−	0.673829i	$-0.235352\pi$
$258$	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
$263$	−1.55291	−	5.79555i	−0.0957568	−	0.357369i	0.901376	−	0.433037i	$-0.142558\pi$
$263$	−1.55291	−	5.79555i	−0.0957568	−	0.357369i	−0.997133	+	0.0756674i	$0.975891\pi$
$264$	−2.59808	+	1.50000i	−0.159901	+	0.0923186i
$265$		0			0
$266$	21.0000	−	12.1244i	1.28759	−	0.743392i
$267$	11.5911	−	3.10583i	0.709364	−	0.190074i
$268$	−1.67303	+	0.448288i	−0.102197	+	0.0273835i
$269$	6.92820			0.422420			0.211210	−	0.977441i	$-0.432260\pi$
$269$	6.92820			0.422420			0.211210	+	0.977441i	$0.432260\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	−2.89778	+	0.776457i	−0.175704	+	0.0470796i
$273$	20.0764	−	5.37945i	1.21508	−	0.325579i
$274$	−2.59808	+	1.50000i	−0.156956	+	0.0906183i
$275$		0			0
$276$	9.00000	−	5.19615i	0.541736	−	0.312772i
$277$	−2.68973	−	10.0382i	−0.161610	−	0.603137i	−0.998448	−	0.0556866i	$-0.982265\pi$
$277$	−2.68973	−	10.0382i	−0.161610	−	0.603137i	0.836838	−	0.547450i	$-0.184401\pi$
$278$	−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	0.929214	−	0.369541i	$-0.120485\pi$
$281$	18.0000	+	10.3923i	1.07379	+	0.619953i	0.144575	+	0.989494i	$0.453818\pi$
$282$	−7.34847	+	7.34847i	−0.437595	+	0.437595i
$283$	−8.06918	+	30.1146i	−0.479663	+	1.79013i	0.123314	+	0.992368i	$0.460648\pi$
$283$	−8.06918	+	30.1146i	−0.479663	+	1.79013i	−0.602977	+	0.797759i	$0.706019\pi$
$284$	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
$288$	−0.776457	−	2.89778i	−0.0457532	−	0.170753i
$289$		−	8.00000i		−	0.470588i
$290$		0			0
$291$	7.50000	+	12.9904i	0.439658	+	0.761510i
$292$	−8.36516	−	2.24144i	−0.489534	−	0.131170i
$293$	−5.79555	−	1.55291i	−0.338580	−	0.0907222i	0.0855230	−	0.996336i	$-0.472744\pi$
$293$	−5.79555	−	1.55291i	−0.338580	−	0.0907222i	−0.424103	+	0.905614i	$0.639411\pi$
$294$	−4.33013	+	7.50000i	−0.252538	+	0.437409i
$295$		0			0
$296$		−	6.92820i		−	0.402694i
$297$	−8.69333	+	2.32937i	−0.504438	+	0.135164i
$298$	−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
$302$	−2.58819	+	9.65926i	−0.148934	+	0.555828i
$303$	−11.5911	−	3.10583i	−0.665892	−	0.178425i
$304$	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	$0.297374\pi$
$308$	1.55291	+	5.79555i	0.0884855	+	0.330232i
$309$			30.0000i			1.70664i
$310$		0			0
$311$	−3.00000	+	1.73205i	−0.170114	+	0.0982156i	−0.582640	−	0.812731i	$-0.697980\pi$
$311$	−3.00000	+	1.73205i	−0.170114	+	0.0982156i	0.412525	+	0.910946i	$0.364647\pi$
$312$	4.24264	+	4.24264i	0.240192	+	0.240192i
$313$	−8.36516	+	2.24144i	−0.472827	+	0.126694i	−0.487361	−	0.873201i	$-0.662040\pi$
$313$	−8.36516	+	2.24144i	−0.472827	+	0.126694i	0.0145337	+	0.999894i	$0.495374\pi$
$314$		0			0
$315$		0			0
$316$	4.00000			0.225018
$317$	−5.79555	+	1.55291i	−0.325511	+	0.0872204i	−0.417874	−	0.908505i	$-0.637225\pi$
$317$	−5.79555	+	1.55291i	−0.325511	+	0.0872204i	0.0923631	+	0.995725i	$0.470558\pi$
$318$		0			0
$319$	5.19615	−	3.00000i	0.290929	−	0.167968i
$320$		0			0
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$	−5.37945	−	20.0764i	−0.299785	−	1.11881i
$323$	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
$327$	−1.79315	−	6.69213i	−0.0991615	−	0.370076i
$328$	−3.13801	+	11.7112i	−0.173268	+	0.646644i
$329$	10.3923	+	18.0000i	0.572946	+	0.992372i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−8.48528	−	8.48528i	−0.465690	−	0.465690i
$333$	5.37945	−	20.0764i	0.294792	−	1.10018i
$334$		0			0
$335$		0			0
$336$	−6.00000			−0.327327
$337$	11.7112	+	3.13801i	0.637951	+	0.170939i	0.563275	−	0.826269i	$-0.309541\pi$
$337$	11.7112	+	3.13801i	0.637951	+	0.170939i	0.0746760	+	0.997208i	$0.476208\pi$
$338$	0.965926	+	0.258819i	0.0525394	+	0.0140779i
$339$	−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
$347$	−3.88229	+	14.4889i	−0.208412	+	0.777804i	0.779970	+	0.625816i	$0.215234\pi$
$347$	−3.88229	+	14.4889i	−0.208412	+	0.777804i	−0.988382	+	0.151988i	$0.951433\pi$
$348$	1.55291	+	5.79555i	0.0832449	+	0.310674i
$349$	6.92820	+	4.00000i	0.370858	+	0.214115i	0.673833	−	0.738883i	$-0.264647\pi$
$349$	6.92820	+	4.00000i	0.370858	+	0.214115i	−0.302975	+	0.952998i	$0.597980\pi$
$350$		0			0
$351$	9.00000	+	15.5885i	0.480384	+	0.832050i
$352$	−1.22474	+	1.22474i	−0.0652791	+	0.0652791i
$353$	5.43520	+	20.2844i	0.289287	+	1.07963i	0.945650	+	0.325187i	$0.105427\pi$
$353$	5.43520	+	20.2844i	0.289287	+	1.07963i	−0.656363	+	0.754445i	$0.727906\pi$
$354$	−18.1865	−	10.5000i	−0.966603	−	0.558069i
$355$		0			0
$356$	6.00000	−	3.46410i	0.317999	−	0.183597i
$357$	−4.65874	+	17.3867i	−0.246567	+	0.920200i
$358$	3.34607	−	0.896575i	0.176845	−	0.0473855i
$359$	24.2487			1.27980			0.639899	−	0.768459i	$-0.278976\pi$
$359$	24.2487			1.27980			0.639899	+	0.768459i	$0.278976\pi$
$360$		0			0
$361$	−30.0000			−1.57895
$362$	−1.93185	+	0.517638i	−0.101536	+	0.0272065i
$363$	−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
$367$	3.58630	+	13.3843i	0.187203	+	0.698653i	0.994148	+	0.108026i	$0.0344529\pi$
$367$	3.58630	+	13.3843i	0.187203	+	0.698653i	−0.806945	+	0.590627i	$0.798880\pi$
$368$	4.24264	−	4.24264i	0.221163	−	0.221163i
$369$	−18.1865	+	31.5000i	−0.946753	+	1.63982i
$370$		0			0
$371$		0			0
$372$	13.3843	+	3.58630i	0.693942	+	0.185941i
$373$	4.48288	−	16.7303i	0.232115	−	0.866263i	−0.747314	−	0.664471i	$-0.768657\pi$
$373$	4.48288	−	16.7303i	0.232115	−	0.866263i	0.979428	−	0.201792i	$-0.0646765\pi$
$374$	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
$378$	−17.3867	−	4.65874i	−0.894274	−	0.239620i
$379$			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
$382$	23.4225	+	6.27603i	1.19840	+	0.321110i
$383$	11.5911	+	3.10583i	0.592278	+	0.158700i	0.542494	−	0.840060i	$-0.317480\pi$
$383$	11.5911	+	3.10583i	0.592278	+	0.158700i	0.0497839	+	0.998760i	$0.484147\pi$
$384$	−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	$-0.748471\pi$
$389$	5.19615	−	9.00000i	0.263455	−	0.456318i	0.967158	+	0.254177i	$0.0818045\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	−1.29410	+	4.82963i	−0.0653617	+	0.243933i
$393$	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	$0.424655\pi$
$398$	−2.58819	−	9.65926i	−0.129734	−	0.484175i
$399$	36.3731	−	21.0000i	1.82093	−	1.05131i
$400$		0			0
$401$	−4.50000	+	2.59808i	−0.224719	+	0.129742i	−0.608134	−	0.793835i	$-0.708081\pi$
$401$	−4.50000	+	2.59808i	−0.224719	+	0.129742i	0.383414	+	0.923576i	$0.374748\pi$
$402$	−2.89778	+	0.776457i	−0.144528	+	0.0387262i
$403$	−26.7685	+	7.17260i	−1.33344	+	0.357293i
$404$	−6.92820			−0.344691
$405$		0			0
$406$	12.0000			0.595550
$407$	−11.5911	+	3.10583i	−0.574550	+	0.153950i
$408$	−5.01910	+	1.34486i	−0.248482	+	0.0665807i
$409$	6.06218	−	3.50000i	0.299755	−	0.173064i	−0.342578	−	0.939490i	$-0.611300\pi$
$409$	6.06218	−	3.50000i	0.299755	−	0.173064i	0.642333	+	0.766426i	$0.277967\pi$
$410$		0			0
$411$	−4.50000	+	2.59808i	−0.221969	+	0.128154i
$412$	4.48288	+	16.7303i	0.220856	+	0.824244i
$413$	−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
$418$	3.13801	−	11.7112i	0.153485	−	0.572815i
$419$	−5.19615	−	9.00000i	−0.253849	−	0.439679i	0.710734	−	0.703461i	$-0.248363\pi$
$419$	−5.19615	−	9.00000i	−0.253849	−	0.439679i	−0.964582	+	0.263783i	$0.915030\pi$
$420$		0			0
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	0.291953	+	0.956433i	$0.405695\pi$
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	−0.974272	+	0.225377i	$0.927639\pi$
$422$	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
$427$	−13.3843	−	3.58630i	−0.647710	−	0.173553i
$428$	−2.89778	−	0.776457i	−0.140069	−	0.0375315i
$429$	5.19615	−	9.00000i	0.250873	−	0.434524i
$430$		0			0
$431$			3.46410i			0.166860i	0.996514	+	0.0834300i	$0.0265875\pi$
$431$			3.46410i			0.166860i	−0.996514	+	0.0834300i	$0.973413\pi$
$432$	−1.34486	−	5.01910i	−0.0647048	−	0.241481i
$433$	−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
$437$	−10.8704	+	40.5689i	−0.520002	+	1.94067i
$438$	−14.4889	−	3.88229i	−0.692306	−	0.185503i
$439$	13.8564	+	8.00000i	0.661330	+	0.381819i	0.792784	−	0.609503i	$-0.208631\pi$
$439$	13.8564	+	8.00000i	0.661330	+	0.381819i	−0.131453	+	0.991322i	$0.541964\pi$
$440$		0			0
$441$	−7.50000	+	12.9904i	−0.357143	+	0.618590i
$442$	7.34847	−	7.34847i	0.349531	−	0.349531i
$443$	6.98811	+	26.0800i	0.332015	+	1.23910i	0.907069	+	0.420982i	$0.138315\pi$
$443$	6.98811	+	26.0800i	0.332015	+	1.23910i	−0.575054	+	0.818116i	$0.695019\pi$
$444$		−	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
$448$	−3.34607	+	0.896575i	−0.158087	+	0.0423592i
$449$	−39.8372			−1.88003			−0.940016	−	0.341130i	$-0.889190\pi$
$449$	−39.8372			−1.88003			−0.940016	+	0.341130i	$0.889190\pi$
$450$		0			0
$451$	21.0000			0.988851
$452$	−17.3867	+	4.65874i	−0.817800	+	0.219129i
$453$	−4.48288	+	16.7303i	−0.210624	+	0.786059i
$454$	−2.59808	+	1.50000i	−0.121934	+	0.0703985i
$455$		0			0
$456$	10.5000	+	6.06218i	0.491708	+	0.283887i
$457$	6.72432	+	25.0955i	0.314550	+	1.17392i	0.924408	+	0.381406i	$0.124560\pi$
$457$	6.72432	+	25.0955i	0.314550	+	1.17392i	−0.609857	+	0.792511i	$0.708773\pi$
$458$	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	0.806833	−	0.590779i	$-0.201180\pi$
$461$	15.0000	+	8.66025i	0.698620	+	0.403348i	−0.108213	+	0.994128i	$0.534513\pi$
$462$	2.68973	+	10.0382i	0.125137	+	0.467019i
$463$	−3.58630	+	13.3843i	−0.166670	+	0.622019i	0.831152	+	0.556046i	$0.187682\pi$
$463$	−3.58630	+	13.3843i	−0.166670	+	0.622019i	−0.997821	+	0.0659737i	$0.978985\pi$
$464$	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	0.838851	−	0.544362i	$-0.183228\pi$
$467$	6.36396	+	6.36396i	0.294489	+	0.294489i	−0.544362	+	0.838851i	$0.683228\pi$
$468$	7.34847	+	7.34847i	0.339683	+	0.339683i
$469$			6.00000i			0.277054i
$470$		0			0
$471$		0			0
$472$	−11.7112	−	3.13801i	−0.539053	−	0.144439i
$473$	−8.69333	−	2.32937i	−0.399720	−	0.107105i
$474$	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	$-0.962830\pi$
$479$	−8.66025	+	15.0000i	−0.395697	+	0.685367i	0.597493	+	0.801874i	$0.296164\pi$
$480$		0			0
$481$	12.0000	+	20.7846i	0.547153	+	0.947697i
$482$	0.258819	−	0.965926i	0.0117889	−	0.0439967i
$483$	−9.31749	−	34.7733i	−0.423960	−	1.58224i
$484$	−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	$0.435146\pi$
$488$	−1.03528	−	3.86370i	−0.0468648	−	0.174902i
$489$	5.19615	+	3.00000i	0.234978	+	0.135665i
$490$		0			0
$491$	−19.5000	+	11.2583i	−0.880023	+	0.508081i	−0.870666	−	0.491875i	$-0.836312\pi$
$491$	−19.5000	+	11.2583i	−0.880023	+	0.508081i	−0.00935679	+	0.999956i	$0.502978\pi$
$492$	−5.43520	+	20.2844i	−0.245038	+	0.914493i
$493$	10.0382	−	2.68973i	0.452098	−	0.121139i
$494$	−24.2487			−1.09100
$495$		0			0
$496$	8.00000			0.359211
$497$	46.3644	−	12.4233i	2.07973	−	0.557262i
$498$	−14.6969	−	14.6969i	−0.658586	−	0.658586i
$499$	−16.4545	+	9.50000i	−0.736604	+	0.425278i	−0.820833	−	0.571168i	$-0.806490\pi$
$499$	−16.4545	+	9.50000i	−0.736604	+	0.425278i	0.0842294	+	0.996446i	$0.473157\pi$
$500$		0			0
$501$		0			0
$502$	−6.72432	−	25.0955i	−0.300121	−	1.12007i
$503$		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
$507$	1.67303	+	0.448288i	0.0743020	+	0.0199092i
$508$	2.68973	−	10.0382i	0.119337	−	0.445373i
$509$	10.3923	+	18.0000i	0.460631	+	0.797836i	0.998992	−	0.0448779i	$-0.0142899\pi$
$509$	10.3923	+	18.0000i	0.460631	+	0.797836i	−0.538362	+	0.842714i	$0.680957\pi$
$510$		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
$517$	10.0382	+	2.68973i	0.441479	+	0.118294i
$518$	−23.1822	−	6.21166i	−1.01857	−	0.272925i
$519$	5.19615	+	9.00000i	0.228086	+	0.395056i
$520$		0			0
$521$		−	5.19615i		−	0.227648i	−0.993501	−	0.113824i	$-0.963690\pi$
$521$		−	5.19615i		−	0.227648i	0.993501	−	0.113824i	$-0.0363099\pi$
$522$	2.68973	+	10.0382i	0.117726	+	0.439360i
$523$	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
$527$	6.21166	−	23.1822i	0.270584	−	1.00983i
$528$	−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
$533$	−10.8704	−	40.5689i	−0.470849	−	1.75723i
$534$	10.3923	−	6.00000i	0.449719	−	0.259645i
$535$		0			0
$536$	−1.50000	+	0.866025i	−0.0647901	+	0.0374066i
$537$	5.79555	−	1.55291i	0.250097	−	0.0670132i
$538$	6.69213	−	1.79315i	0.288518	−	0.0773082i
$539$	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	$0.358537\pi$
$542$	−27.0459	+	7.24693i	−1.16172	+	0.311282i
$543$	−3.34607	+	0.896575i	−0.143593	+	0.0384757i
$544$	−2.59808	+	1.50000i	−0.111392	+	0.0643120i
$545$		0			0
$546$	18.0000	−	10.3923i	0.770329	−	0.444750i
$547$	−5.82774	−	21.7494i	−0.249176	−	0.929938i	−0.971238	−	0.238110i	$-0.923472\pi$
$547$	−5.82774	−	21.7494i	−0.249176	−	0.929938i	0.722062	−	0.691828i	$-0.243195\pi$
$548$	−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
$553$	3.58630	−	13.3843i	0.152505	−	0.569157i
$554$	−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	0.923323	−	0.384024i	$-0.125462\pi$
$557$	12.7279	+	12.7279i	0.539299	+	0.539299i	−0.384024	+	0.923323i	$0.625462\pi$
$558$	23.1822	+	6.21166i	0.981382	+	0.262960i
$559$			18.0000i			0.761319i
$560$		0			0
$561$	4.50000	+	7.79423i	0.189990	+	0.329073i
$562$	20.0764	+	5.37945i	0.846871	+	0.226919i
$563$	14.4889	+	3.88229i	0.610634	+	0.163619i	0.550866	−	0.834593i	$-0.314297\pi$
$563$	14.4889	+	3.88229i	0.610634	+	0.163619i	0.0597675	+	0.998212i	$0.480964\pi$
$564$	−5.19615	+	9.00000i	−0.218797	+	0.378968i
$565$		0			0
$566$			31.1769i			1.31046i
$567$	−30.1146	−	8.06918i	−1.26469	−	0.338874i
$568$	9.79796	+	9.79796i	0.411113	+	0.411113i
$569$	9.52628	−	16.5000i	0.399362	−	0.691716i	−0.594285	−	0.804255i	$-0.702565\pi$
$569$	9.52628	−	16.5000i	0.399362	−	0.691716i	0.993647	+	0.112539i	$0.0358982\pi$
$570$		0			0
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$	1.55291	−	5.79555i	0.0649306	−	0.242324i
$573$	40.5689	+	10.8704i	1.69479	+	0.454117i
$574$	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	$0.490202\pi$
$578$	−2.07055	−	7.72741i	−0.0861236	−	0.321418i
$579$		−	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
$587$	31.8756	−	8.54103i	1.31564	−	0.352526i	0.468300	−	0.883569i	$-0.344867\pi$
$587$	31.8756	−	8.54103i	1.31564	−	0.352526i	0.847345	+	0.531043i	$0.178200\pi$
$588$	−2.24144	+	8.36516i	−0.0924354	+	0.344974i
$589$	−48.4974	+	28.0000i	−1.99830	+	1.15372i
$590$		0			0
$591$	−36.0000	−	20.7846i	−1.48084	−	0.854965i
$592$	−1.79315	−	6.69213i	−0.0736980	−	0.275045i
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	−0.918378	−	0.395705i	$-0.870500\pi$
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	0.395705	+	0.918378i	$0.370500\pi$
$594$	−7.79423	+	4.50000i	−0.319801	+	0.184637i
$595$		0			0
$596$	−9.00000	−	5.19615i	−0.368654	−	0.212843i
$597$	−4.48288	−	16.7303i	−0.183472	−	0.684727i
$598$	−5.37945	+	20.0764i	−0.219982	+	0.820985i
$599$	−6.92820	−	12.0000i	−0.283079	−	0.490307i	0.689063	−	0.724702i	$-0.258022\pi$
$599$	−6.92820	−	12.0000i	−0.283079	−	0.490307i	−0.972141	+	0.234395i	$0.924689\pi$
$600$		0			0
$601$	14.5000	−	25.1147i	0.591467	−	1.02445i	−0.402568	−	0.915390i	$-0.631882\pi$
$601$	14.5000	−	25.1147i	0.591467	−	1.02445i	0.994035	−	0.109061i	$-0.0347845\pi$
$602$	−12.7279	−	12.7279i	−0.518751	−	0.518751i
$603$	−5.01910	+	1.34486i	−0.204393	+	0.0547671i
$604$			10.0000i			0.406894i
$605$		0			0
$606$	−12.0000			−0.487467
$607$	13.3843	+	3.58630i	0.543250	+	0.145564i	0.520000	−	0.854166i	$-0.325932\pi$
$607$	13.3843	+	3.58630i	0.543250	+	0.145564i	0.0232502	+	0.999730i	$0.492599\pi$
$608$	6.76148	+	1.81173i	0.274214	+	0.0734755i
$609$	20.7846			0.842235
$610$		0			0
$611$		−	20.7846i		−	0.840855i
$612$	−8.69333	+	2.32937i	−0.351407	+	0.0941593i
$613$	−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
$617$	11.6469	−	43.4667i	0.468885	−	1.74990i	−0.174793	−	0.984605i	$-0.555926\pi$
$617$	11.6469	−	43.4667i	0.468885	−	1.74990i	0.643678	−	0.765297i	$-0.277408\pi$
$618$	7.76457	+	28.9778i	0.312337	+	1.16566i
$619$	11.2583	+	6.50000i	0.452510	+	0.261257i	0.708890	−	0.705319i	$-0.249196\pi$
$619$	11.2583	+	6.50000i	0.452510	+	0.261257i	−0.256379	+	0.966576i	$0.582530\pi$
$620$		0			0
$621$	27.0000	−	15.5885i	1.08347	−	0.625543i
$622$	−2.44949	+	2.44949i	−0.0982156	+	0.0982156i
$623$	−6.21166	−	23.1822i	−0.248865	−	0.928776i
$624$	5.19615	+	3.00000i	0.208013	+	0.120096i
$625$		0			0
$626$	−7.50000	+	4.33013i	−0.299760	+	0.173067i
$627$	5.43520	−	20.2844i	0.217061	−	0.810083i
$628$		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	$0.369672\pi$
$632$	3.86370	−	1.03528i	0.153690	−	0.0411811i
$633$	4.89898	+	4.89898i	0.194717	+	0.194717i
$634$	−5.19615	+	3.00000i	−0.206366	+	0.119145i
$635$		0			0
$636$		0			0
$637$	−4.48288	−	16.7303i	−0.177618	−	0.662880i
$638$	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	0.832947	−	0.553352i	$-0.186652\pi$
$641$	19.5000	+	11.2583i	0.770204	+	0.444677i	−0.0627436	+	0.998030i	$0.519985\pi$
$642$	−5.01910	−	1.34486i	−0.198088	−	0.0530775i
$643$	9.41404	−	35.1337i	0.371254	−	1.38554i	−0.487489	−	0.873129i	$-0.662087\pi$
$643$	9.41404	−	35.1337i	0.371254	−	1.38554i	0.858742	−	0.512408i	$-0.171246\pi$
$644$	−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	0.154081	−	0.988058i	$-0.450758\pi$
$647$	−21.2132	−	21.2132i	−0.833977	−	0.833977i	−0.988058	+	0.154081i	$0.950758\pi$
$648$	−2.32937	−	8.69333i	−0.0915064	−	0.341506i
$649$			21.0000i			0.824322i
$650$		0			0
$651$	24.0000	−	41.5692i	0.940634	−	1.62923i
$652$	3.34607	+	0.896575i	0.131042	+	0.0351126i
$653$	−17.3867	−	4.65874i	−0.680393	−	0.182311i	−0.0979610	−	0.995190i	$-0.531232\pi$
$653$	−17.3867	−	4.65874i	−0.680393	−	0.182311i	−0.582432	+	0.812880i	$0.697899\pi$
$654$	−3.46410	−	6.00000i	−0.135457	−	0.234619i
$655$		0			0
$656$			12.1244i			0.473377i
$657$	−25.0955	−	6.72432i	−0.979068	−	0.262341i
$658$	14.6969	+	14.6969i	0.572946	+	0.572946i
$659$	5.19615	−	9.00000i	0.202413	−	0.350590i	−0.746892	−	0.664945i	$-0.768455\pi$
$659$	5.19615	−	9.00000i	0.202413	−	0.350590i	0.949306	+	0.314355i	$0.101788\pi$
$660$		0			0
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	0.989051	+	0.147573i	$0.0471463\pi$
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	−0.366723	+	0.930330i	$0.619520\pi$
$662$	7.24693	−	27.0459i	0.281660	−	1.05117i
$663$	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
$672$	−5.79555	+	1.55291i	−0.223568	+	0.0599050i
$673$	−6.69213	+	1.79315i	−0.257963	+	0.0691209i	−0.385483	−	0.922715i	$-0.625965\pi$
$673$	−6.69213	+	1.79315i	−0.257963	+	0.0691209i	0.127520	+	0.991836i	$0.459298\pi$
$674$	12.1244			0.467013
$675$		0			0
$676$	1.00000			0.0384615
$677$	−11.5911	+	3.10583i	−0.445483	+	0.119367i	−0.474585	−	0.880210i	$-0.657402\pi$
$677$	−11.5911	+	3.10583i	−0.445483	+	0.119367i	0.0291023	+	0.999576i	$0.490735\pi$
$678$	−30.1146	+	8.06918i	−1.15654	+	0.309895i
$679$	25.9808	−	15.0000i	0.997050	−	0.575647i
$680$		0			0
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$	−3.58630	−	13.3843i	−0.137327	−	0.512510i
$683$	23.3345	−	23.3345i	0.892871	−	0.892871i	−0.101922	−	0.994792i	$-0.532499\pi$
$683$	23.3345	−	23.3345i	0.892871	−	0.892871i	0.994792	+	0.101922i	$0.0324991\pi$
$684$	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
$688$	1.34486	−	5.01910i	0.0512724	−	0.191351i
$689$		0			0
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$	4.24264	+	4.24264i	0.161281	+	0.161281i
$693$	4.65874	+	17.3867i	0.176971	+	0.660465i
$694$			15.0000i			0.569392i
$695$		0			0
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$	35.1337	+	9.41404i	1.33078	+	0.356582i
$698$	7.72741	+	2.07055i	0.292487	+	0.0783716i
$699$	2.59808	−	4.50000i	0.0982683	−	0.170206i
$700$		0			0
$701$			17.3205i			0.654187i	0.944992	+	0.327093i	$0.106069\pi$
$701$			17.3205i			0.654187i	−0.944992	+	0.327093i	$0.893931\pi$
$702$	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
$707$	−6.21166	+	23.1822i	−0.233613	+	0.871857i
$708$	−20.2844	−	5.43520i	−0.762336	−	0.204267i
$709$	−34.6410	−	20.0000i	−1.30097	−	0.751116i	−0.320400	−	0.947282i	$-0.603817\pi$
$709$	−34.6410	−	20.0000i	−1.30097	−	0.751116i	−0.980571	+	0.196167i	$0.937151\pi$
$710$		0			0
$711$	12.0000			0.450035
$712$	4.89898	−	4.89898i	0.183597	−	0.183597i
$713$	12.4233	+	46.3644i	0.465257	+	1.73636i
$714$			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
$718$	23.4225	−	6.27603i	0.874118	−	0.234219i
$719$	27.7128			1.03351			0.516757	−	0.856132i	$-0.327139\pi$
$719$	27.7128			1.03351			0.516757	+	0.856132i	$0.327139\pi$
$720$		0			0
$721$	60.0000			2.23452
$722$	−28.9778	+	7.76457i	−1.07844	+	0.288967i
$723$	0.448288	−	1.67303i	0.0166720	−	0.0622208i
$724$	−1.73205	+	1.00000i	−0.0643712	+	0.0371647i
$725$		0			0
$726$	−12.0000	−	6.92820i	−0.445362	−	0.257130i
$727$	−2.68973	−	10.0382i	−0.0997564	−	0.372296i	0.897941	−	0.440115i	$-0.145062\pi$
$727$	−2.68973	−	10.0382i	−0.0997564	−	0.372296i	−0.997698	+	0.0678194i	$0.978396\pi$
$728$	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
$732$	−1.79315	−	6.69213i	−0.0662768	−	0.247348i
$733$	13.4486	−	50.1910i	0.496737	−	1.85385i	−0.0233418	−	0.999728i	$-0.507431\pi$
$733$	13.4486	−	50.1910i	0.496737	−	1.85385i	0.520078	−	0.854119i	$-0.325903\pi$
$734$	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
$738$	−9.41404	+	35.1337i	−0.346536	+	1.29329i
$739$		−	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
$743$	17.3867	+	4.65874i	0.637855	+	0.170913i	0.563232	−	0.826299i	$-0.309558\pi$
$743$	17.3867	+	4.65874i	0.637855	+	0.170913i	0.0746233	+	0.997212i	$0.476225\pi$
$744$	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	0.988761	−	0.149505i	$-0.0477681\pi$
$751$	10.0000	+	17.3205i	0.364905	+	0.632034i	−0.623856	+	0.781540i	$0.714435\pi$
$752$	−1.55291	+	5.79555i	−0.0566290	+	0.211342i
$753$	−11.6469	−	43.4667i	−0.424435	−	1.58401i
$754$	−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	$0.00651940\pi$
$758$	0.258819	+	0.965926i	0.00940073	+	0.0350840i
$759$	−15.5885	−	9.00000i	−0.565825	−	0.326679i
$760$		0			0
$761$	−30.0000	+	17.3205i	−1.08750	+	0.627868i	−0.932910	−	0.360111i	$-0.882739\pi$
$761$	−30.0000	+	17.3205i	−1.08750	+	0.627868i	−0.154590	+	0.987979i	$0.549406\pi$
$762$	4.65874	−	17.3867i	0.168768	−	0.629852i
$763$	−13.3843	+	3.58630i	−0.484543	+	0.129833i
$764$	24.2487			0.877288
$765$		0			0
$766$	12.0000			0.433578
$767$	40.5689	−	10.8704i	1.46486	−	0.392507i
$768$	−1.22474	−	1.22474i	−0.0441942	−	0.0441942i
$769$	12.1244	−	7.00000i	0.437215	−	0.252426i	−0.265200	−	0.964193i	$-0.585438\pi$
$769$	12.1244	−	7.00000i	0.437215	−	0.252426i	0.702416	+	0.711767i	$0.252105\pi$
$770$		0			0
$771$		−	46.7654i		−	1.68421i
$772$	−2.24144	−	8.36516i	−0.0806711	−	0.301069i
$773$	−38.1838	+	38.1838i	−1.37337	+	1.37337i	−0.517985	+	0.855390i	$0.673318\pi$
$773$	−38.1838	+	38.1838i	−1.37337	+	1.37337i	−0.855390	+	0.517985i	$0.826682\pi$
$774$	7.79423	−	13.5000i	0.280158	−	0.485247i
$775$		0			0
$776$	7.50000	+	4.33013i	0.269234	+	0.155443i
$777$	−40.1528	−	10.7589i	−1.44047	−	0.385974i
$778$	2.68973	−	10.0382i	0.0964314	−	0.359887i
$779$	−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
$783$	4.65874	+	17.3867i	0.166490	+	0.621349i
$784$			5.00000i			0.178571i
$785$		0			0
$786$	3.00000	−	5.19615i	0.107006	−	0.185341i
$787$	−16.7303	−	4.48288i	−0.596372	−	0.159797i	−0.0520081	−	0.998647i	$-0.516562\pi$
$787$	−16.7303	−	4.48288i	−0.596372	−	0.159797i	−0.544364	+	0.838849i	$0.683229\pi$
$788$	−23.1822	−	6.21166i	−0.825832	−	0.221281i
$789$	−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
$797$	6.21166	−	23.1822i	0.220028	−	0.821156i	−0.764308	−	0.644852i	$-0.776919\pi$
$797$	6.21166	−	23.1822i	0.220028	−	0.821156i	0.984336	−	0.176304i	$-0.0564143\pi$
$798$	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
$803$	3.88229	+	14.4889i	0.137003	+	0.511302i
$804$	−2.59808	+	1.50000i	−0.0916271	+	0.0529009i
$805$		0			0
$806$	−24.0000	+	13.8564i	−0.845364	+	0.488071i
$807$	11.5911	−	3.10583i	0.408026	−	0.109330i
$808$	−6.69213	+	1.79315i	−0.235428	+	0.0630828i
$809$	−12.1244			−0.426270			−0.213135	−	0.977023i	$-0.568367\pi$
$809$	−12.1244			−0.426270			−0.213135	+	0.977023i	$0.568367\pi$
$810$		0			0
$811$	−41.0000			−1.43970			−0.719852	−	0.694127i	$-0.755791\pi$
$811$	−41.0000			−1.43970			−0.719852	+	0.694127i	$0.755791\pi$
$812$	11.5911	−	3.10583i	0.406768	−	0.108993i
$813$	−46.8449	+	12.5521i	−1.64292	+	0.440220i
$814$	−10.3923	+	6.00000i	−0.364250	+	0.210300i
$815$		0			0
$816$	−4.50000	+	2.59808i	−0.157532	+	0.0909509i
$817$	9.41404	+	35.1337i	0.329356	+	1.22917i
$818$	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	0.738367	−	0.674399i	$-0.235597\pi$
$821$	15.0000	+	8.66025i	0.523504	+	0.302245i	−0.214863	+	0.976644i	$0.568931\pi$
$822$	−3.67423	+	3.67423i	−0.128154	+	0.128154i
$823$	3.58630	−	13.3843i	0.125011	−	0.466546i	−0.874829	−	0.484431i	$-0.839027\pi$
$823$	3.58630	−	13.3843i	0.125011	−	0.466546i	0.999840	+	0.0178851i	$0.00569330\pi$
$824$	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	0.994056	−	0.108870i	$-0.0347231\pi$
$827$	25.4558	+	25.4558i	0.885186	+	0.885186i	−0.108870	+	0.994056i	$0.534723\pi$
$828$	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
$832$	3.34607	+	0.896575i	0.116004	+	0.0310832i
$833$	14.4889	+	3.88229i	0.502010	+	0.134513i
$834$	−4.33013	+	7.50000i	−0.149940	+	0.259704i
$835$		0			0
$836$		−	12.1244i		−	0.419330i
$837$	40.1528	+	10.7589i	1.38788	+	0.371882i
$838$	−7.34847	−	7.34847i	−0.253849	−	0.253849i
$839$	17.3205	−	30.0000i	0.597970	−	1.03572i	−0.395150	−	0.918617i	$-0.629307\pi$
$839$	17.3205	−	30.0000i	0.597970	−	1.03572i	0.993120	−	0.117098i	$-0.0373593\pi$
$840$		0			0
$841$	8.50000	+	14.7224i	0.293103	+	0.507670i
$842$	−7.24693	+	27.0459i	−0.249746	+	0.932064i
$843$	34.7733	+	9.31749i	1.19766	+	0.320911i
$844$	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
$853$	−36.8067	+	9.86233i	−1.26024	+	0.337680i	−0.826283	−	0.563255i	$-0.809549\pi$
$853$	−36.8067	+	9.86233i	−1.26024	+	0.337680i	−0.433955	+	0.900935i	$0.642882\pi$
$854$	−13.8564			−0.474156
$855$		0			0
$856$	−3.00000			−0.102538
$857$	−40.5689	+	10.8704i	−1.38581	+	0.371326i	−0.873227	−	0.487314i	$-0.837977\pi$
$857$	−40.5689	+	10.8704i	−1.38581	+	0.371326i	−0.512580	+	0.858640i	$0.671310\pi$
$858$	2.68973	−	10.0382i	0.0918257	−	0.342698i
$859$	−11.2583	+	6.50000i	−0.384129	+	0.221777i	−0.679613	−	0.733571i	$-0.737852\pi$
$859$	−11.2583	+	6.50000i	−0.384129	+	0.221777i	0.295484	+	0.955348i	$0.404519\pi$
$860$		0			0
$861$	63.0000	+	36.3731i	2.14703	+	1.23959i
$862$	0.896575	+	3.34607i	0.0305375	+	0.113967i
$863$	16.9706	−	16.9706i	0.577685	−	0.577685i	−0.356580	−	0.934265i	$-0.616057\pi$
$863$	16.9706	−	16.9706i	0.577685	−	0.577685i	0.934265	+	0.356580i	$0.116057\pi$
$864$	−2.59808	−	4.50000i	−0.0883883	−	0.153093i
$865$		0			0
$866$	−22.5000	−	12.9904i	−0.764581	−	0.441431i
$867$	−3.58630	−	13.3843i	−0.121797	−	0.454553i
$868$	7.17260	−	26.7685i	0.243454	−	0.908583i
$869$	−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
$877$	−26.7685	−	7.17260i	−0.903909	−	0.242202i	−0.223215	−	0.974769i	$-0.571655\pi$
$877$	−26.7685	−	7.17260i	−0.903909	−	0.242202i	−0.680694	+	0.732568i	$0.738322\pi$
$878$	15.4548	+	4.14110i	0.521575	+	0.139756i
$879$	−10.3923			−0.350524
$880$		0			0
$881$			6.92820i			0.233417i	0.993166	+	0.116709i	$0.0372343\pi$
$881$			6.92820i			0.233417i	−0.993166	+	0.116709i	$0.962766\pi$
$882$	−3.88229	+	14.4889i	−0.130723	+	0.487866i
$883$	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
$887$	−12.4233	+	46.3644i	−0.417134	+	1.55677i	0.363388	+	0.931638i	$0.381620\pi$
$887$	−12.4233	+	46.3644i	−0.417134	+	1.55677i	−0.780522	+	0.625128i	$0.785047\pi$
$888$	−3.10583	−	11.5911i	−0.104225	−	0.388972i
$889$	−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
$893$	−10.8704	−	40.5689i	−0.363764	−	1.35759i
$894$	−15.5885	−	9.00000i	−0.521356	−	0.301005i
$895$		0			0
$896$	−3.00000	+	1.73205i	−0.100223	+	0.0578638i
$897$	−9.31749	+	34.7733i	−0.311102	+	1.16105i
$898$	−38.4797	+	10.3106i	−1.28409	+	0.344070i
$899$	−27.7128			−0.924274
$900$		0			0
$901$		0			0
$902$	20.2844	−	5.43520i	0.675398	−	0.180972i
$903$	−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
$907$	−2.24144	−	8.36516i	−0.0744257	−	0.277761i	0.918677	−	0.395010i	$-0.129259\pi$
$907$	−2.24144	−	8.36516i	−0.0744257	−	0.277761i	−0.993102	+	0.117250i	$0.962592\pi$
$908$	−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	−0.0874934	−	0.996165i	$-0.527886\pi$
$911$	−30.0000	−	17.3205i	−0.993944	−	0.573854i	−0.906451	+	0.422311i	$0.861219\pi$
$912$	11.7112	+	3.13801i	0.387798	+	0.103910i
$913$	−5.37945	+	20.0764i	−0.178034	+	0.664432i
$914$	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
$918$	−15.0573	+	4.03459i	−0.496965	+	0.133161i
$919$			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
$922$	16.7303	+	4.48288i	0.550984	+	0.147636i
$923$	−46.3644	−	12.4233i	−1.52610	−	0.408918i
$924$	5.19615	+	9.00000i	0.170941	+	0.296078i
$925$		0			0
$926$			13.8564i			0.455350i
$927$	13.4486	+	50.1910i	0.441711	+	1.64849i
$928$	2.44949	+	2.44949i	0.0804084	+	0.0804084i
$929$	−17.3205	+	30.0000i	−0.568267	+	0.984268i	0.428470	+	0.903556i	$0.359053\pi$
$929$	−17.3205	+	30.0000i	−0.568267	+	0.984268i	−0.996737	+	0.0807121i	$0.974281\pi$
$930$		0			0
$931$	−17.5000	−	30.3109i	−0.573539	−	0.993399i
$932$	0.776457	−	2.89778i	0.0254337	−	0.0949199i
$933$	−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	$0.441447\pi$
$938$	1.55291	+	5.79555i	0.0507044	+	0.189232i
$939$	−12.9904	+	7.50000i	−0.423925	+	0.244753i
$940$		0			0
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	−0.763825	−	0.645424i	$-0.776681\pi$
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	0.177041	+	0.984203i	$0.443347\pi$
$942$		0			0
$943$	−70.2674	+	18.8281i	−2.28822	+	0.613127i
$944$	−12.1244			−0.394614
$945$		0			0
$946$	−9.00000			−0.292615
$947$	−26.0800	+	6.98811i	−0.847486	+	0.227083i	−0.656328	−	0.754476i	$-0.727891\pi$
$947$	−26.0800	+	6.98811i	−0.847486	+	0.227083i	−0.191158	+	0.981559i	$0.561224\pi$
$948$	6.69213	−	1.79315i	0.217350	−	0.0582388i
$949$	25.9808	−	15.0000i	0.843371	−	0.486921i
$950$		0			0
$951$	−9.00000	+	5.19615i	−0.291845	+	0.168497i
$952$	2.68973	+	10.0382i	0.0871745	+	0.325340i
$953$	23.3345	−	23.3345i	0.755879	−	0.755879i	−0.219690	−	0.975570i	$-0.570505\pi$
$953$	23.3345	−	23.3345i	0.755879	−	0.755879i	0.975570	+	0.219690i	$0.0705047\pi$
$954$		0			0
$955$		0			0
$956$	9.00000	+	5.19615i	0.291081	+	0.168056i
$957$	7.34847	−	7.34847i	0.237542	−	0.237542i
$958$	−4.48288	+	16.7303i	−0.144835	+	0.540532i
$959$	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
$963$	−8.69333	−	2.32937i	−0.280139	−	0.0750629i
$964$		−	1.00000i		−	0.0322078i
$965$		0			0
$966$	−18.0000	−	31.1769i	−0.579141	−	1.00310i
$967$	3.34607	+	0.896575i	0.107602	+	0.0288319i	0.312218	−	0.950010i	$-0.398928\pi$
$967$	3.34607	+	0.896575i	0.107602	+	0.0288319i	−0.204616	+	0.978842i	$0.565595\pi$
$968$	−7.72741	−	2.07055i	−0.248368	−	0.0665501i
$969$	18.1865	−	31.5000i	0.584236	−	1.01193i
$970$		0			0
$971$		−	3.46410i		−	0.111168i	−0.998454	−	0.0555842i	$-0.982298\pi$
$971$		−	3.46410i		−	0.111168i	0.998454	−	0.0555842i	$-0.0177021\pi$
$972$	−4.03459	−	15.0573i	−0.129410	−	0.482963i
$973$	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
$977$	0.776457	−	2.89778i	0.0248411	−	0.0927081i	−0.952392	−	0.304875i	$-0.901385\pi$
$977$	0.776457	−	2.89778i	0.0248411	−	0.0927081i	0.977233	+	0.212167i	$0.0680520\pi$
$978$	5.79555	+	1.55291i	0.185321	+	0.0496567i
$979$	−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
$983$	9.31749	+	34.7733i	0.297182	+	1.10910i	0.939469	+	0.342633i	$0.111319\pi$
$983$	9.31749	+	34.7733i	0.297182	+	1.10910i	−0.642288	+	0.766464i	$0.722015\pi$
$984$			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
$988$	−23.4225	+	6.27603i	−0.745168	+	0.199667i
$989$	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	$0.397103\pi$
$992$	7.72741	−	2.07055i	0.245345	−	0.0657401i
$993$	12.5521	−	46.8449i	0.398327	−	1.48658i
$994$	41.5692	−	24.0000i	1.31850	−	0.761234i
$995$		0			0
$996$	−18.0000	−	10.3923i	−0.570352	−	0.329293i
$997$	−10.7589	−	40.1528i	−0.340738	−	1.27165i	−0.897513	−	0.440988i	$-0.854628\pi$
$997$	−10.7589	−	40.1528i	−0.340738	−	1.27165i	0.556775	−	0.830663i	$-0.312039\pi$
$998$	−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.443.2	yes	8
3.2	odd	2		1350.2.q.f.143.1		8
5.2	odd	4	inner	450.2.p.f.407.2	yes	8
5.3	odd	4	inner	450.2.p.f.407.1	yes	8
5.4	even	2	inner	450.2.p.f.443.1	yes	8
9.4	even	3		1350.2.q.f.1043.1		8
9.5	odd	6	inner	450.2.p.f.293.2	yes	8
15.2	even	4		1350.2.q.f.1007.1		8
15.8	even	4		1350.2.q.f.1007.2		8
15.14	odd	2		1350.2.q.f.143.2		8
45.4	even	6		1350.2.q.f.1043.2		8
45.13	odd	12		1350.2.q.f.557.2		8
45.14	odd	6	inner	450.2.p.f.293.1	yes	8
45.22	odd	12		1350.2.q.f.557.1		8
45.23	even	12	inner	450.2.p.f.257.1	✓	8
45.32	even	12	inner	450.2.p.f.257.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.f.257.1	✓	8	45.23	even	12	inner
450.2.p.f.257.2	yes	8	45.32	even	12	inner
450.2.p.f.293.1	yes	8	45.14	odd	6	inner
450.2.p.f.293.2	yes	8	9.5	odd	6	inner
450.2.p.f.407.1	yes	8	5.3	odd	4	inner
450.2.p.f.407.2	yes	8	5.2	odd	4	inner
450.2.p.f.443.1	yes	8	5.4	even	2	inner
450.2.p.f.443.2	yes	8	1.1	even	1	trivial
1350.2.q.f.143.1		8	3.2	odd	2
1350.2.q.f.143.2		8	15.14	odd	2
1350.2.q.f.557.1		8	45.22	odd	12
1350.2.q.f.557.2		8	45.13	odd	12
1350.2.q.f.1007.1		8	15.2	even	4
1350.2.q.f.1007.2		8	15.8	even	4
1350.2.q.f.1043.1		8	9.4	even	3
1350.2.q.f.1043.2		8	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-0.896575 - 3.34607i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-0.896575 - 3.34607i) 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} +(-0.896575 + 3.34607i) 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} +(-1.67303 - 0.448288i) q^{22} +(5.79555 + 1.55291i) 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} +(0.258819 - 0.965926i) q^{32} +(-2.89778 - 0.776457i) q^{33} +(-2.59808 - 1.50000i) q^{34} +(1.50000 - 2.59808i) q^{36} +(4.89898 - 4.89898i) q^{37} +(1.81173 + 6.76148i) q^{38} +6.00000i q^{39} +(-10.5000 + 6.06218i) q^{41} +(-4.24264 - 4.24264i) q^{42} +(5.01910 - 1.34486i) q^{43} -1.73205 q^{44} +6.00000 q^{46} +(-5.79555 + 1.55291i) q^{47} +(0.448288 - 1.67303i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(-4.50000 - 2.59808i) q^{51} +(0.896575 + 3.34607i) q^{52} +(2.59808 - 4.50000i) q^{54} +(-3.00000 - 1.73205i) q^{56} +(3.13801 + 11.7112i) q^{57} +(-0.896575 + 3.34607i) 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} +(-1.67303 - 0.448288i) q^{67} +(-2.89778 - 0.776457i) q^{68} +10.3923 q^{69} +13.8564i q^{71} +(0.776457 - 2.89778i) q^{72} +(-6.12372 - 6.12372i) q^{73} +(3.46410 - 6.00000i) q^{74} +(3.50000 + 6.06218i) q^{76} +(-1.55291 + 5.79555i) q^{77} +(1.55291 + 5.79555i) q^{78} +(3.46410 + 2.00000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(-8.57321 + 8.57321i) q^{82} +(-3.10583 - 11.5911i) q^{83} +(-5.19615 - 3.00000i) q^{84} +(4.50000 - 2.59808i) q^{86} +(-1.55291 + 5.79555i) q^{87} +(-1.67303 + 0.448288i) q^{88} +6.92820 q^{89} +12.0000 q^{91} +(5.79555 - 1.55291i) q^{92} +(9.79796 + 9.79796i) q^{93} +(-5.19615 + 3.00000i) q^{94} -1.73205i q^{96} +(2.24144 + 8.36516i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more