LMFDB - Embedded newform 450.2.p.g.407.2

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			407.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.407
Dual form			450.2.p.g.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 + 1.73205i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(3.34607 + 0.896575i) q^{13} +(0.500000 - 0.866025i) q^{16} +(4.24264 - 4.24264i) q^{17} +(2.89778 - 0.776457i) q^{18} +5.00000i q^{19} +(-0.896575 + 3.34607i) q^{22} +(1.55291 - 5.79555i) q^{23} -1.73205 q^{24} +3.46410i q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.46410 + 6.00000i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.965926 + 0.258819i) q^{32} +(5.79555 - 1.55291i) q^{33} +(5.19615 + 3.00000i) q^{34} +(1.50000 + 2.59808i) q^{36} +(-4.89898 - 4.89898i) q^{37} +(-4.82963 + 1.29410i) q^{38} +(5.19615 - 3.00000i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(3.13801 + 11.7112i) q^{43} -3.46410 q^{44} +6.00000 q^{46} +(-1.55291 - 5.79555i) q^{47} +(-0.448288 - 1.67303i) q^{48} +(-6.06218 + 3.50000i) q^{49} -10.3923i q^{51} +(-3.34607 + 0.896575i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(2.59808 - 4.50000i) q^{54} +(6.12372 + 6.12372i) q^{57} +(-6.69213 - 1.79315i) q^{58} +(0.866025 + 1.50000i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(3.00000 + 5.19615i) q^{66} +(-2.24144 + 8.36516i) q^{67} +(-1.55291 + 5.79555i) q^{68} +(-5.19615 - 9.00000i) q^{69} -6.92820i q^{71} +(-2.12132 + 2.12132i) q^{72} +(-8.57321 + 8.57321i) q^{73} +(3.46410 - 6.00000i) q^{74} +(-2.50000 - 4.33013i) q^{76} +(4.24264 + 4.24264i) q^{78} +(12.1244 + 7.00000i) q^{79} -9.00000 q^{81} +(-1.22474 - 1.22474i) q^{82} +(-8.69333 + 2.32937i) q^{83} +(-10.5000 + 6.06218i) q^{86} +(3.10583 + 11.5911i) q^{87} +(-0.896575 - 3.34607i) q^{88} -12.1244 q^{89} +(1.55291 + 5.79555i) q^{92} +(-6.69213 - 1.79315i) q^{93} +(5.19615 - 3.00000i) q^{94} +(1.50000 - 0.866025i) q^{96} +(5.01910 - 1.34486i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(5.19615 - 9.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{6}+O(q^{10}) $ 8 * q + 12 * q^6	$ 8 q + 12 q^{6} + 24 q^{11} + 4 q^{16} - 16 q^{31} + 12 q^{36} - 12 q^{41} + 48 q^{46} - 32 q^{61} + 24 q^{66} - 20 q^{76} - 72 q^{81} - 84 q^{86} + 12 q^{96}+O(q^{100}) $ 8 * q + 12 * q^6 + 24 * q^11 + 4 * q^16 - 16 * q^31 + 12 * q^36 - 12 * q^41 + 48 * q^46 - 32 * q^61 + 24 * q^66 - 20 * q^76 - 72 * q^81 - 84 * q^86 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$4$	−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			0		−0.258819	−	0.965926i	$-0.583333\pi$
$7$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	3.00000i		−	1.00000i
$10$		0			0
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$	−0.448288	+	1.67303i	−0.129410	+	0.482963i
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.691015	−	0.722840i	$-0.257164\pi$
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.237016	+	0.971506i	$0.423830\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.0294245	−	0.999567i	$-0.490633\pi$
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.999567	−	0.0294245i	$-0.00936746\pi$
$18$	2.89778	−	0.776457i	0.683013	−	0.183013i
$19$			5.00000i			1.14708i	0.819178	+	0.573539i	$0.194430\pi$
$19$			5.00000i			1.14708i	−0.819178	+	0.573539i	$0.805570\pi$
$20$		0			0
$21$		0			0
$22$	−0.896575	+	3.34607i	−0.191151	+	0.713384i
$23$	1.55291	−	5.79555i	0.323805	−	1.20846i	−0.591703	−	0.806156i	$-0.701544\pi$
$23$	1.55291	−	5.79555i	0.323805	−	1.20846i	0.915508	−	0.402300i	$-0.131789\pi$
$24$	−1.73205			−0.353553
$25$		0			0
$26$			3.46410i			0.679366i
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$		0			0
$29$	−3.46410	+	6.00000i	−0.643268	+	1.11417i	0.341431	+	0.939907i	$0.389088\pi$
$29$	−3.46410	+	6.00000i	−0.643268	+	1.11417i	−0.984699	+	0.174265i	$0.944245\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	5.79555	−	1.55291i	1.00888	−	0.270328i
$34$	5.19615	+	3.00000i	0.891133	+	0.514496i
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	0.178545	−	0.983932i	$-0.442861\pi$
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	−0.983932	+	0.178545i	$0.942861\pi$
$38$	−4.82963	+	1.29410i	−0.783469	+	0.209930i
$39$	5.19615	−	3.00000i	0.832050	−	0.480384i
$40$		0			0
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	−0.612536	−	0.790443i	$-0.709851\pi$
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	0.378275	+	0.925693i	$0.376517\pi$
$42$		0			0
$43$	3.13801	+	11.7112i	0.478543	+	1.78595i	0.607527	+	0.794299i	$0.292162\pi$
$43$	3.13801	+	11.7112i	0.478543	+	1.78595i	−0.128984	+	0.991647i	$0.541172\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	6.00000			0.884652
$47$	−1.55291	−	5.79555i	−0.226516	−	0.845369i	−0.981792	−	0.189961i	$-0.939164\pi$
$47$	−1.55291	−	5.79555i	−0.226516	−	0.845369i	0.755276	−	0.655407i	$-0.227503\pi$
$48$	−0.448288	−	1.67303i	−0.0647048	−	0.241481i
$49$	−6.06218	+	3.50000i	−0.866025	+	0.500000i
$50$		0			0
$51$		−	10.3923i		−	1.45521i
$52$	−3.34607	+	0.896575i	−0.464016	+	0.124333i
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$	2.59808	−	4.50000i	0.353553	−	0.612372i
$55$		0			0
$56$		0			0
$57$	6.12372	+	6.12372i	0.811107	+	0.811107i
$58$	−6.69213	−	1.79315i	−0.878720	−	0.235452i
$59$	0.866025	+	1.50000i	0.112747	+	0.195283i	0.916877	−	0.399170i	$-0.130702\pi$
$59$	0.866025	+	1.50000i	0.112747	+	0.195283i	−0.804130	+	0.594454i	$0.797368\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	2.82843	−	2.82843i	0.359211	−	0.359211i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	−2.24144	+	8.36516i	−0.273835	+	1.02197i	0.682783	+	0.730622i	$0.260770\pi$
$67$	−2.24144	+	8.36516i	−0.273835	+	1.02197i	−0.956618	+	0.291346i	$0.905897\pi$
$68$	−1.55291	+	5.79555i	−0.188319	+	0.702814i
$69$	−5.19615	−	9.00000i	−0.625543	−	1.08347i
$70$		0			0
$71$		−	6.92820i		−	0.822226i	−0.911584	−	0.411113i	$-0.865140\pi$
$71$		−	6.92820i		−	0.822226i	0.911584	−	0.411113i	$-0.134860\pi$
$72$	−2.12132	+	2.12132i	−0.250000	+	0.250000i
$73$	−8.57321	+	8.57321i	−1.00342	+	1.00342i	−0.00342468	+	0.999994i	$0.501090\pi$
$73$	−8.57321	+	8.57321i	−1.00342	+	1.00342i	−0.999994	+	0.00342468i	$0.998910\pi$
$74$	3.46410	−	6.00000i	0.402694	−	0.697486i
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$		0			0
$78$	4.24264	+	4.24264i	0.480384	+	0.480384i
$79$	12.1244	+	7.00000i	1.36410	+	0.787562i	0.990166	−	0.139895i	$-0.0446766\pi$
$79$	12.1244	+	7.00000i	1.36410	+	0.787562i	0.373930	+	0.927457i	$0.378010\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	−1.22474	−	1.22474i	−0.135250	−	0.135250i
$83$	−8.69333	+	2.32937i	−0.954217	+	0.255682i	−0.702151	−	0.712028i	$-0.747777\pi$
$83$	−8.69333	+	2.32937i	−0.954217	+	0.255682i	−0.252066	+	0.967710i	$0.581110\pi$
$84$		0			0
$85$		0			0
$86$	−10.5000	+	6.06218i	−1.13224	+	0.653701i
$87$	3.10583	+	11.5911i	0.332980	+	1.24270i
$88$	−0.896575	−	3.34607i	−0.0955753	−	0.356692i
$89$	−12.1244			−1.28518			−0.642590	−	0.766211i	$-0.722140\pi$
$89$	−12.1244			−1.28518			−0.642590	+	0.766211i	$0.722140\pi$
$90$		0			0
$91$		0			0
$92$	1.55291	+	5.79555i	0.161903	+	0.604228i
$93$	−6.69213	−	1.79315i	−0.693942	−	0.185941i
$94$	5.19615	−	3.00000i	0.535942	−	0.309426i
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	5.01910	−	1.34486i	0.509612	−	0.136550i	0.00515471	−	0.999987i	$-0.498359\pi$
$97$	5.01910	−	1.34486i	0.509612	−	0.136550i	0.504457	+	0.863437i	$0.331693\pi$
$98$	−4.94975	−	4.94975i	−0.500000	−	0.500000i
$99$	5.19615	−	9.00000i	0.522233	−	0.904534i
$100$		0			0
$101$	3.00000	+	1.73205i	0.298511	+	0.172345i	0.641774	−	0.766894i	$-0.278199\pi$
$101$	3.00000	+	1.73205i	0.298511	+	0.172345i	−0.343263	+	0.939239i	$0.611532\pi$
$102$	10.0382	−	2.68973i	0.993929	−	0.266323i
$103$	3.34607	+	0.896575i	0.329698	+	0.0883422i	0.419871	−	0.907584i	$-0.362075\pi$
$103$	3.34607	+	0.896575i	0.329698	+	0.0883422i	−0.0901732	+	0.995926i	$0.528742\pi$
$104$	−1.73205	−	3.00000i	−0.169842	−	0.294174i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	2.12132	−	2.12132i	0.205076	−	0.205076i	−0.597095	−	0.802171i	$-0.703678\pi$
$107$	2.12132	−	2.12132i	0.205076	−	0.205076i	0.802171	+	0.597095i	$0.203678\pi$
$108$	5.01910	+	1.34486i	0.482963	+	0.129410i
$109$		−	20.0000i		−	1.91565i	−0.287348	−	0.957826i	$-0.592774\pi$
$109$		−	20.0000i		−	1.91565i	0.287348	−	0.957826i	$-0.407226\pi$
$110$		0			0
$111$	−12.0000			−1.13899
$112$		0			0
$113$	3.88229	−	14.4889i	0.365215	−	1.36300i	−0.501915	−	0.864917i	$-0.667371\pi$
$113$	3.88229	−	14.4889i	0.365215	−	1.36300i	0.867129	−	0.498083i	$-0.165962\pi$
$114$	−4.33013	+	7.50000i	−0.405554	+	0.702439i
$115$		0			0
$116$		−	6.92820i		−	0.643268i
$117$	2.68973	−	10.0382i	0.248665	−	0.928032i
$118$	−1.22474	+	1.22474i	−0.112747	+	0.112747i
$119$		0			0
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	−7.72741	−	2.07055i	−0.699607	−	0.187459i
$123$	−0.776457	+	2.89778i	−0.0700108	+	0.261284i
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$		0			0
$126$		0			0
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	0.301420	−	0.953491i	$-0.402539\pi$
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	−0.953491	+	0.301420i	$0.902539\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	18.1865	+	10.5000i	1.60123	+	0.924473i
$130$		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	$0.284978\pi$
$132$	−4.24264	+	4.24264i	−0.369274	+	0.369274i
$133$		0			0
$134$	−8.66025			−0.748132
$135$		0			0
$136$	−6.00000			−0.514496
$137$	2.32937	+	8.69333i	0.199012	+	0.742722i	0.991192	+	0.132434i	$0.0422793\pi$
$137$	2.32937	+	8.69333i	0.199012	+	0.742722i	−0.792180	+	0.610287i	$0.791054\pi$
$138$	7.34847	−	7.34847i	0.625543	−	0.625543i
$139$	−3.46410	+	2.00000i	−0.293821	+	0.169638i	−0.639664	−	0.768655i	$-0.720926\pi$
$139$	−3.46410	+	2.00000i	−0.293821	+	0.169638i	0.345843	+	0.938293i	$0.387593\pi$
$140$		0			0
$141$	−9.00000	−	5.19615i	−0.757937	−	0.437595i
$142$	6.69213	−	1.79315i	0.561591	−	0.150478i
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$	−2.59808	−	1.50000i	−0.216506	−	0.125000i
$145$		0			0
$146$	−10.5000	−	6.06218i	−0.868986	−	0.501709i
$147$	−3.13801	+	11.7112i	−0.258819	+	0.965926i
$148$	6.69213	+	1.79315i	0.550090	+	0.147396i
$149$	−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
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	0.331842	+	0.943335i	$0.392330\pi$
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	−0.982873	+	0.184284i	$0.941004\pi$
$152$	3.53553	−	3.53553i	0.286770	−	0.286770i
$153$	−12.7279	−	12.7279i	−1.02899	−	1.02899i
$154$		0			0
$155$		0			0
$156$	−3.00000	+	5.19615i	−0.240192	+	0.416025i
$157$	0.896575	−	3.34607i	0.0715545	−	0.267045i	−0.920875	−	0.389857i	$-0.872524\pi$
$157$	0.896575	−	3.34607i	0.0715545	−	0.267045i	0.992430	+	0.122812i	$0.0391911\pi$
$158$	−3.62347	+	13.5230i	−0.288268	+	1.07583i
$159$	−10.3923			−0.824163
$160$		0			0
$161$		0			0
$162$	−2.32937	−	8.69333i	−0.183013	−	0.683013i
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	−0.753443	−	0.657513i	$-0.771608\pi$
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	0.657513	+	0.753443i	$0.271608\pi$
$164$	0.866025	−	1.50000i	0.0676252	−	0.117130i
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	−11.5911	−	3.10583i	−0.896947	−	0.240336i	−0.219242	−	0.975670i	$-0.570359\pi$
$167$	−11.5911	−	3.10583i	−0.896947	−	0.240336i	−0.677705	+	0.735334i	$0.737025\pi$
$168$		0			0
$169$	−0.866025	−	0.500000i	−0.0666173	−	0.0384615i
$170$		0			0
$171$	15.0000			1.14708
$172$	−8.57321	−	8.57321i	−0.653701	−	0.653701i
$173$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$173$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$174$	−10.3923	+	6.00000i	−0.787839	+	0.454859i
$175$		0			0
$176$	3.00000	−	1.73205i	0.226134	−	0.130558i
$177$	2.89778	+	0.776457i	0.217810	+	0.0583621i
$178$	−3.13801	−	11.7112i	−0.235204	−	0.877794i
$179$	22.5167			1.68297			0.841487	−	0.540277i	$-0.181681\pi$
$179$	22.5167			1.68297			0.841487	+	0.540277i	$0.181681\pi$
$180$		0			0
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$		0			0
$183$	3.58630	+	13.3843i	0.265107	+	0.989393i
$184$	−5.19615	+	3.00000i	−0.383065	+	0.221163i
$185$		0			0
$186$		−	6.92820i		−	0.508001i
$187$	20.0764	−	5.37945i	1.46813	−	0.393385i
$188$	4.24264	+	4.24264i	0.309426	+	0.309426i
$189$		0			0
$190$		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	$0.326017\pi$
$192$	1.22474	+	1.22474i	0.0883883	+	0.0883883i
$193$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$193$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$194$	2.59808	+	4.50000i	0.186531	+	0.323081i
$195$		0			0
$196$	3.50000	−	6.06218i	0.250000	−	0.433013i
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.237785	+	0.971318i	$0.576421\pi$
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.971318	+	0.237785i	$0.923579\pi$
$198$	10.0382	+	2.68973i	0.713384	+	0.191151i
$199$		−	8.00000i		−	0.567105i	−0.958957	−	0.283552i	$-0.908487\pi$
$199$		−	8.00000i		−	0.567105i	0.958957	−	0.283552i	$-0.0915130\pi$
$200$		0			0
$201$	7.50000	+	12.9904i	0.529009	+	0.916271i
$202$	−0.896575	+	3.34607i	−0.0630828	+	0.235428i
$203$		0			0
$204$	5.19615	+	9.00000i	0.363803	+	0.630126i
$205$		0			0
$206$			3.46410i			0.241355i
$207$	−17.3867	−	4.65874i	−1.20846	−	0.323805i
$208$	2.44949	−	2.44949i	0.169842	−	0.169842i
$209$	−8.66025	+	15.0000i	−0.599042	+	1.03757i
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$	5.79555	+	1.55291i	0.398040	+	0.106655i
$213$	−8.48528	−	8.48528i	−0.581402	−	0.581402i
$214$	2.59808	+	1.50000i	0.177601	+	0.102538i
$215$		0			0
$216$			5.19615i			0.353553i
$217$		0			0
$218$	19.3185	−	5.17638i	1.30842	−	0.350589i
$219$			21.0000i			1.41905i
$220$		0			0
$221$	18.0000	−	10.3923i	1.21081	−	0.699062i
$222$	−3.10583	−	11.5911i	−0.208450	−	0.777944i
$223$	−1.79315	−	6.69213i	−0.120078	−	0.448138i	0.879538	−	0.475828i	$-0.157852\pi$
$223$	−1.79315	−	6.69213i	−0.120078	−	0.448138i	−0.999617	+	0.0276899i	$0.991185\pi$
$224$		0			0
$225$		0			0
$226$	15.0000			0.997785
$227$	0.776457	+	2.89778i	0.0515353	+	0.192332i	0.986894	−	0.161367i	$-0.0515903\pi$
$227$	0.776457	+	2.89778i	0.0515353	+	0.192332i	−0.935359	+	0.353699i	$0.884924\pi$
$228$	−8.36516	−	2.24144i	−0.553996	−	0.148443i
$229$	−13.8564	+	8.00000i	−0.915657	+	0.528655i	−0.882247	−	0.470787i	$-0.843970\pi$
$229$	−13.8564	+	8.00000i	−0.915657	+	0.528655i	−0.0334101	+	0.999442i	$0.510637\pi$
$230$		0			0
$231$		0			0
$232$	6.69213	−	1.79315i	0.439360	−	0.117726i
$233$	6.36396	+	6.36396i	0.416917	+	0.416917i	0.884140	−	0.467223i	$-0.154745\pi$
$233$	6.36396	+	6.36396i	0.416917	+	0.416917i	−0.467223	+	0.884140i	$0.654745\pi$
$234$	10.3923			0.679366
$235$		0			0
$236$	−1.50000	−	0.866025i	−0.0976417	−	0.0563735i
$237$	23.4225	−	6.27603i	1.52145	−	0.407672i
$238$		0			0
$239$	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	$0.156413\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$	−11.0227	+	11.0227i	−0.707107	+	0.707107i
$244$		−	8.00000i		−	0.512148i
$245$		0			0
$246$	−3.00000			−0.191273
$247$	−4.48288	+	16.7303i	−0.285239	+	1.06453i
$248$	−1.03528	+	3.86370i	−0.0657401	+	0.245345i
$249$	−7.79423	+	13.5000i	−0.493939	+	0.855528i
$250$		0			0
$251$			5.19615i			0.327978i	0.986462	+	0.163989i	$0.0524362\pi$
$251$			5.19615i			0.327978i	−0.986462	+	0.163989i	$0.947564\pi$
$252$		0			0
$253$	14.6969	−	14.6969i	0.923989	−	0.923989i
$254$	5.19615	−	9.00000i	0.326036	−	0.564710i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.4889	+	3.88229i	0.903792	+	0.242170i	0.680644	−	0.732614i	$-0.261700\pi$
$257$	14.4889	+	3.88229i	0.903792	+	0.242170i	0.223148	+	0.974785i	$0.428367\pi$
$258$	−5.43520	+	20.2844i	−0.338381	+	1.26285i
$259$		0			0
$260$		0			0
$261$	18.0000	+	10.3923i	1.11417	+	0.643268i
$262$	2.44949	+	2.44949i	0.151330	+	0.151330i
$263$	11.5911	−	3.10583i	0.714738	−	0.191514i	0.116916	−	0.993142i	$-0.462699\pi$
$263$	11.5911	−	3.10583i	0.714738	−	0.191514i	0.597823	+	0.801628i	$0.296033\pi$
$264$	−5.19615	−	3.00000i	−0.319801	−	0.184637i
$265$		0			0
$266$		0			0
$267$	−14.8492	+	14.8492i	−0.908759	+	0.908759i
$268$	−2.24144	−	8.36516i	−0.136918	−	0.510984i
$269$	13.8564			0.844840			0.422420	−	0.906400i	$-0.361181\pi$
$269$	13.8564			0.844840			0.422420	+	0.906400i	$0.361181\pi$
$270$		0			0
$271$	−10.0000			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$272$	−1.55291	−	5.79555i	−0.0941593	−	0.351407i
$273$		0			0
$274$	−7.79423	+	4.50000i	−0.470867	+	0.271855i
$275$		0			0
$276$	9.00000	+	5.19615i	0.541736	+	0.312772i
$277$	−6.69213	+	1.79315i	−0.402091	+	0.107740i	−0.454196	−	0.890902i	$-0.650074\pi$
$277$	−6.69213	+	1.79315i	−0.402091	+	0.107740i	0.0521052	+	0.998642i	$0.483407\pi$
$278$	−2.82843	−	2.82843i	−0.169638	−	0.169638i
$279$	−10.3923	+	6.00000i	−0.622171	+	0.359211i
$280$		0			0
$281$	−18.0000	−	10.3923i	−1.07379	−	0.619953i	−0.144575	−	0.989494i	$-0.546182\pi$
$281$	−18.0000	−	10.3923i	−1.07379	−	0.619953i	−0.929214	+	0.369541i	$0.879515\pi$
$282$	2.68973	−	10.0382i	0.160171	−	0.597766i
$283$	11.7112	+	3.13801i	0.696160	+	0.186536i	0.589510	−	0.807761i	$-0.299321\pi$
$283$	11.7112	+	3.13801i	0.696160	+	0.186536i	0.106650	+	0.994297i	$0.465988\pi$
$284$	3.46410	+	6.00000i	0.205557	+	0.356034i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		0			0
$288$	0.776457	−	2.89778i	0.0457532	−	0.170753i
$289$		−	19.0000i		−	1.11765i
$290$		0			0
$291$	4.50000	−	7.79423i	0.263795	−	0.456906i
$292$	3.13801	−	11.7112i	0.183638	−	0.685348i
$293$	1.55291	−	5.79555i	0.0907222	−	0.338580i	−0.905614	−	0.424103i	$-0.860589\pi$
$293$	1.55291	−	5.79555i	0.0907222	−	0.338580i	0.996336	+	0.0855230i	$0.0272561\pi$
$294$	−12.1244			−0.707107
$295$		0			0
$296$			6.92820i			0.402694i
$297$	−4.65874	−	17.3867i	−0.270328	−	1.00888i
$298$	7.34847	−	7.34847i	0.425685	−	0.425685i
$299$	10.3923	−	18.0000i	0.601003	−	1.04097i
$300$		0			0
$301$		0			0
$302$	−15.4548	−	4.14110i	−0.889325	−	0.238294i
$303$	5.79555	−	1.55291i	0.332946	−	0.0892126i
$304$	4.33013	+	2.50000i	0.248350	+	0.143385i
$305$		0			0
$306$	9.00000	−	15.5885i	0.514496	−	0.891133i
$307$	17.1464	+	17.1464i	0.978598	+	0.978598i	0.999776	−	0.0211774i	$-0.00674148\pi$
$307$	17.1464	+	17.1464i	0.978598	+	0.978598i	−0.0211774	+	0.999776i	$0.506741\pi$
$308$		0			0
$309$	5.19615	−	3.00000i	0.295599	−	0.170664i
$310$		0			0
$311$	−21.0000	+	12.1244i	−1.19080	+	0.687509i	−0.958488	−	0.285132i	$-0.907963\pi$
$311$	−21.0000	+	12.1244i	−1.19080	+	0.687509i	−0.232313	+	0.972641i	$0.574629\pi$
$312$	−5.79555	−	1.55291i	−0.328109	−	0.0879165i
$313$	−8.51747	−	31.7876i	−0.481436	−	1.79674i	−0.595601	−	0.803281i	$-0.703086\pi$
$313$	−8.51747	−	31.7876i	−0.481436	−	1.79674i	0.114165	−	0.993462i	$-0.463581\pi$
$314$	3.46410			0.195491
$315$		0			0
$316$	−14.0000			−0.787562
$317$	−3.10583	−	11.5911i	−0.174441	−	0.651022i	−0.996646	−	0.0818309i	$-0.973923\pi$
$317$	−3.10583	−	11.5911i	−0.174441	−	0.651022i	0.822206	−	0.569191i	$-0.192743\pi$
$318$	−2.68973	−	10.0382i	−0.150832	−	0.562914i
$319$	−20.7846	+	12.0000i	−1.16371	+	0.671871i
$320$		0			0
$321$		−	5.19615i		−	0.290021i
$322$		0			0
$323$	21.2132	+	21.2132i	1.18033	+	1.18033i
$324$	7.79423	−	4.50000i	0.433013	−	0.250000i
$325$		0			0
$326$	−1.50000	−	0.866025i	−0.0830773	−	0.0479647i
$327$	−24.4949	−	24.4949i	−1.35457	−	1.35457i
$328$	1.67303	+	0.448288i	0.0923778	+	0.0247525i
$329$		0			0
$330$		0			0
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	0.879440	+	0.476011i	$0.157918\pi$
$332$	6.36396	−	6.36396i	0.349268	−	0.349268i
$333$	−14.6969	+	14.6969i	−0.805387	+	0.805387i
$334$		−	12.0000i		−	0.656611i
$335$		0			0
$336$		0			0
$337$	−1.79315	+	6.69213i	−0.0976792	+	0.364544i	−0.997412	−	0.0718974i	$-0.977095\pi$
$337$	−1.79315	+	6.69213i	−0.0976792	+	0.364544i	0.899733	+	0.436441i	$0.143761\pi$
$338$	0.258819	−	0.965926i	0.0140779	−	0.0525394i
$339$	−12.9904	−	22.5000i	−0.705541	−	1.22203i
$340$		0			0
$341$		−	13.8564i		−	0.750366i
$342$	3.88229	+	14.4889i	0.209930	+	0.783469i
$343$		0			0
$344$	6.06218	−	10.5000i	0.326851	−	0.566122i
$345$		0			0
$346$		0			0
$347$	11.5911	+	3.10583i	0.622243	+	0.166730i	0.556147	−	0.831084i	$-0.312279\pi$
$347$	11.5911	+	3.10583i	0.622243	+	0.166730i	0.0660960	+	0.997813i	$0.478946\pi$
$348$	−8.48528	−	8.48528i	−0.454859	−	0.454859i
$349$	−22.5167	−	13.0000i	−1.20529	−	0.695874i	−0.243563	−	0.969885i	$-0.578316\pi$
$349$	−22.5167	−	13.0000i	−1.20529	−	0.695874i	−0.961727	+	0.274011i	$0.911649\pi$
$350$		0			0
$351$	−9.00000	−	15.5885i	−0.480384	−	0.832050i
$352$	2.44949	+	2.44949i	0.130558	+	0.130558i
$353$	8.69333	−	2.32937i	0.462699	−	0.123980i	−0.0199361	−	0.999801i	$-0.506346\pi$
$353$	8.69333	−	2.32937i	0.462699	−	0.123980i	0.482635	+	0.875821i	$0.339680\pi$
$354$			3.00000i			0.159448i
$355$		0			0
$356$	10.5000	−	6.06218i	0.556499	−	0.321295i
$357$		0			0
$358$	5.82774	+	21.7494i	0.308006	+	1.14949i
$359$	27.7128			1.46263			0.731313	−	0.682042i	$-0.238908\pi$
$359$	27.7128			1.46263			0.731313	+	0.682042i	$0.238908\pi$
$360$		0			0
$361$	−6.00000			−0.315789
$362$	4.14110	+	15.4548i	0.217652	+	0.812287i
$363$	1.67303	+	0.448288i	0.0878114	+	0.0235290i
$364$		0			0
$365$		0			0
$366$	−12.0000	+	6.92820i	−0.627250	+	0.362143i
$367$	16.7303	−	4.48288i	0.873316	−	0.234004i	0.205795	−	0.978595i	$-0.434022\pi$
$367$	16.7303	−	4.48288i	0.873316	−	0.234004i	0.667521	+	0.744591i	$0.267355\pi$
$368$	−4.24264	−	4.24264i	−0.221163	−	0.221163i
$369$	2.59808	+	4.50000i	0.135250	+	0.234261i
$370$		0			0
$371$		0			0
$372$	6.69213	−	1.79315i	0.346971	−	0.0929705i
$373$	−20.0764	−	5.37945i	−1.03952	−	0.278538i	−0.301603	−	0.953434i	$-0.597522\pi$
$373$	−20.0764	−	5.37945i	−1.03952	−	0.278538i	−0.737913	+	0.674896i	$0.764188\pi$
$374$	10.3923	+	18.0000i	0.537373	+	0.930758i
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	−16.9706	+	16.9706i	−0.874028	+	0.874028i
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$	−6.27603	+	23.4225i	−0.321110	+	1.19840i
$383$	−1.55291	+	5.79555i	−0.0793502	+	0.296139i	−0.994184	−	0.107691i	$-0.965654\pi$
$383$	−1.55291	+	5.79555i	−0.0793502	+	0.296139i	0.914834	+	0.403830i	$0.132321\pi$
$384$	−0.866025	+	1.50000i	−0.0441942	+	0.0765466i
$385$		0			0
$386$		0			0
$387$	35.1337	−	9.41404i	1.78595	−	0.478543i
$388$	−3.67423	+	3.67423i	−0.186531	+	0.186531i
$389$	−5.19615	+	9.00000i	−0.263455	+	0.456318i	−0.967158	−	0.254177i	$-0.918196\pi$
$389$	−5.19615	+	9.00000i	−0.263455	+	0.456318i	0.703702	+	0.710495i	$0.251529\pi$
$390$		0			0
$391$	−18.0000	−	31.1769i	−0.910299	−	1.57668i
$392$	6.76148	+	1.81173i	0.341506	+	0.0915064i
$393$	1.55291	−	5.79555i	0.0783342	−	0.292347i
$394$	−20.7846	−	12.0000i	−1.04711	−	0.604551i
$395$		0			0
$396$			10.3923i			0.522233i
$397$	−17.1464	−	17.1464i	−0.860555	−	0.860555i	0.130848	−	0.991402i	$-0.458230\pi$
$397$	−17.1464	−	17.1464i	−0.860555	−	0.860555i	−0.991402	+	0.130848i	$0.958230\pi$
$398$	7.72741	−	2.07055i	0.387340	−	0.103787i
$399$		0			0
$400$		0			0
$401$	−18.0000	+	10.3923i	−0.898877	+	0.518967i	−0.876836	−	0.480790i	$-0.840350\pi$
$401$	−18.0000	+	10.3923i	−0.898877	+	0.518967i	−0.0220414	+	0.999757i	$0.507017\pi$
$402$	−10.6066	+	10.6066i	−0.529009	+	0.529009i
$403$	−3.58630	−	13.3843i	−0.178646	−	0.666718i
$404$	−3.46410			−0.172345
$405$		0			0
$406$		0			0
$407$	−6.21166	−	23.1822i	−0.307900	−	1.14910i
$408$	−7.34847	+	7.34847i	−0.363803	+	0.363803i
$409$	25.1147	−	14.5000i	1.24184	−	0.716979i	0.272374	−	0.962191i	$-0.412191\pi$
$409$	25.1147	−	14.5000i	1.24184	−	0.716979i	0.969469	+	0.245212i	$0.0788577\pi$
$410$		0			0
$411$	13.5000	+	7.79423i	0.665906	+	0.384461i
$412$	−3.34607	+	0.896575i	−0.164849	+	0.0441711i
$413$		0			0
$414$		−	18.0000i		−	0.884652i
$415$		0			0
$416$	3.00000	+	1.73205i	0.147087	+	0.0849208i
$417$	−1.79315	+	6.69213i	−0.0878110	+	0.327715i
$418$	−16.7303	−	4.48288i	−0.818307	−	0.219265i
$419$	−12.9904	−	22.5000i	−0.634622	−	1.09920i	−0.986595	−	0.163187i	$-0.947823\pi$
$419$	−12.9904	−	22.5000i	−0.634622	−	1.09920i	0.351974	−	0.936010i	$-0.385511\pi$
$420$		0			0
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	−9.19239	+	9.19239i	−0.447478	+	0.447478i
$423$	−17.3867	+	4.65874i	−0.845369	+	0.226516i
$424$			6.00000i			0.291386i
$425$		0			0
$426$	6.00000	−	10.3923i	0.290701	−	0.503509i
$427$		0			0
$428$	−0.776457	+	2.89778i	−0.0375315	+	0.140069i
$429$	20.7846			1.00349
$430$		0			0
$431$			13.8564i			0.667440i	0.942672	+	0.333720i	$0.108304\pi$
$431$			13.8564i			0.667440i	−0.942672	+	0.333720i	$0.891696\pi$
$432$	−5.01910	+	1.34486i	−0.241481	+	0.0647048i
$433$	−4.89898	+	4.89898i	−0.235430	+	0.235430i	−0.814955	−	0.579525i	$-0.803238\pi$
$433$	−4.89898	+	4.89898i	−0.235430	+	0.235430i	0.579525	+	0.814955i	$0.303238\pi$
$434$		0			0
$435$		0			0
$436$	10.0000	+	17.3205i	0.478913	+	0.829502i
$437$	28.9778	+	7.76457i	1.38619	+	0.371430i
$438$	−20.2844	+	5.43520i	−0.969228	+	0.259704i
$439$	22.5167	+	13.0000i	1.07466	+	0.620456i	0.929451	−	0.368945i	$-0.120281\pi$
$439$	22.5167	+	13.0000i	1.07466	+	0.620456i	0.145210	+	0.989401i	$0.453614\pi$
$440$		0			0
$441$	10.5000	+	18.1865i	0.500000	+	0.866025i
$442$	14.6969	+	14.6969i	0.699062	+	0.699062i
$443$	−34.7733	+	9.31749i	−1.65213	+	0.442687i	−0.960208	−	0.279285i	$-0.909903\pi$
$443$	−34.7733	+	9.31749i	−1.65213	+	0.442687i	−0.691922	+	0.721972i	$0.743236\pi$
$444$	10.3923	−	6.00000i	0.493197	−	0.284747i
$445$		0			0
$446$	6.00000	−	3.46410i	0.284108	−	0.164030i
$447$	−17.3867	−	4.65874i	−0.822361	−	0.220351i
$448$		0			0
$449$	8.66025			0.408703			0.204351	−	0.978898i	$-0.434492\pi$
$449$	8.66025			0.408703			0.204351	+	0.978898i	$0.434492\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	3.88229	+	14.4889i	0.182607	+	0.681500i
$453$	7.17260	+	26.7685i	0.336998	+	1.25769i
$454$	−2.59808	+	1.50000i	−0.121934	+	0.0703985i
$455$		0			0
$456$		−	8.66025i		−	0.405554i
$457$	5.01910	−	1.34486i	0.234783	−	0.0629100i	−0.139509	−	0.990221i	$-0.544552\pi$
$457$	5.01910	−	1.34486i	0.234783	−	0.0629100i	0.374292	+	0.927311i	$0.377886\pi$
$458$	−11.3137	−	11.3137i	−0.528655	−	0.528655i
$459$	−31.1769			−1.45521
$460$		0			0
$461$	−30.0000	−	17.3205i	−1.39724	−	0.806696i	−0.403137	−	0.915140i	$-0.632080\pi$
$461$	−30.0000	−	17.3205i	−1.39724	−	0.806696i	−0.994103	+	0.108443i	$0.965413\pi$
$462$		0			0
$463$	6.69213	+	1.79315i	0.311010	+	0.0833348i	0.410948	−	0.911659i	$-0.365198\pi$
$463$	6.69213	+	1.79315i	0.311010	+	0.0833348i	−0.0999382	+	0.994994i	$0.531864\pi$
$464$	3.46410	+	6.00000i	0.160817	+	0.278543i
$465$		0			0
$466$	−4.50000	+	7.79423i	−0.208458	+	0.361061i
$467$	14.8492	−	14.8492i	0.687141	−	0.687141i	−0.274458	−	0.961599i	$-0.588498\pi$
$467$	14.8492	−	14.8492i	0.687141	−	0.687141i	0.961599	+	0.274458i	$0.0884985\pi$
$468$	2.68973	+	10.0382i	0.124333	+	0.464016i
$469$		0			0
$470$		0			0
$471$	−3.00000	−	5.19615i	−0.138233	−	0.239426i
$472$	0.448288	−	1.67303i	0.0206341	−	0.0770076i
$473$	−10.8704	+	40.5689i	−0.499822	+	1.86536i
$474$	12.1244	+	21.0000i	0.556890	+	0.964562i
$475$		0			0
$476$		0			0
$477$	−12.7279	+	12.7279i	−0.582772	+	0.582772i
$478$	−7.34847	+	7.34847i	−0.336111	+	0.336111i
$479$	8.66025	−	15.0000i	0.395697	−	0.685367i	−0.597493	−	0.801874i	$-0.703836\pi$
$479$	8.66025	−	15.0000i	0.395697	−	0.685367i	0.993190	+	0.116507i	$0.0371697\pi$
$480$		0			0
$481$	−12.0000	−	20.7846i	−0.547153	−	0.947697i
$482$	0.965926	+	0.258819i	0.0439967	+	0.0117889i
$483$		0			0
$484$	−0.866025	−	0.500000i	−0.0393648	−	0.0227273i
$485$		0			0
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	4.89898	+	4.89898i	0.221994	+	0.221994i	0.809338	−	0.587344i	$-0.199826\pi$
$487$	4.89898	+	4.89898i	0.221994	+	0.221994i	−0.587344	+	0.809338i	$0.699826\pi$
$488$	7.72741	−	2.07055i	0.349803	−	0.0937295i
$489$			3.00000i			0.135665i
$490$		0			0
$491$	25.5000	−	14.7224i	1.15080	−	0.664414i	0.201717	−	0.979444i	$-0.435348\pi$
$491$	25.5000	−	14.7224i	1.15080	−	0.664414i	0.949082	+	0.315030i	$0.102015\pi$
$492$	−0.776457	−	2.89778i	−0.0350054	−	0.130642i
$493$	10.7589	+	40.1528i	0.484557	+	1.80839i
$494$	−17.3205			−0.779287
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$	−15.0573	−	4.03459i	−0.674733	−	0.180794i
$499$	11.2583	−	6.50000i	0.503992	−	0.290980i	−0.226369	−	0.974042i	$-0.572685\pi$
$499$	11.2583	−	6.50000i	0.503992	−	0.290980i	0.730361	+	0.683062i	$0.239352\pi$
$500$		0			0
$501$	−18.0000	+	10.3923i	−0.804181	+	0.464294i
$502$	−5.01910	+	1.34486i	−0.224013	+	0.0600242i
$503$	−29.6985	−	29.6985i	−1.32419	−	1.32419i	−0.910349	−	0.413841i	$-0.864187\pi$
$503$	−29.6985	−	29.6985i	−1.32419	−	1.32419i	−0.413841	−	0.910349i	$-0.635813\pi$
$504$		0			0
$505$		0			0
$506$	18.0000	+	10.3923i	0.800198	+	0.461994i
$507$	−1.67303	+	0.448288i	−0.0743020	+	0.0199092i
$508$	10.0382	+	2.68973i	0.445373	+	0.119337i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	18.3712	−	18.3712i	0.811107	−	0.811107i
$514$			15.0000i			0.661622i
$515$		0			0
$516$	−21.0000			−0.924473
$517$	5.37945	−	20.0764i	0.236588	−	0.882959i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			20.7846i			0.910590i	0.890341	+	0.455295i	$0.150466\pi$
$521$			20.7846i			0.910590i	−0.890341	+	0.455295i	$0.849534\pi$
$522$	−5.37945	+	20.0764i	−0.235452	+	0.878720i
$523$	3.67423	−	3.67423i	0.160663	−	0.160663i	−0.622197	−	0.782860i	$-0.713760\pi$
$523$	3.67423	−	3.67423i	0.160663	−	0.160663i	0.782860	+	0.622197i	$0.213760\pi$
$524$	−1.73205	+	3.00000i	−0.0756650	+	0.131056i
$525$		0			0
$526$	6.00000	+	10.3923i	0.261612	+	0.453126i
$527$	−23.1822	−	6.21166i	−1.00983	−	0.270584i
$528$	1.55291	−	5.79555i	0.0675819	−	0.252219i
$529$	−11.2583	−	6.50000i	−0.489493	−	0.282609i
$530$		0			0
$531$	4.50000	−	2.59808i	0.195283	−	0.112747i
$532$		0			0
$533$	−5.79555	+	1.55291i	−0.251033	+	0.0672642i
$534$	−18.1865	−	10.5000i	−0.787008	−	0.454379i
$535$		0			0
$536$	7.50000	−	4.33013i	0.323951	−	0.187033i
$537$	27.5772	−	27.5772i	1.19004	−	1.19004i
$538$	3.58630	+	13.3843i	0.154616	+	0.577036i
$539$	−24.2487			−1.04447
$540$		0			0
$541$	32.0000			1.37579			0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000			1.37579			0.687894	+	0.725811i	$0.258536\pi$
$542$	−2.58819	−	9.65926i	−0.111172	−	0.414901i
$543$	19.5959	−	19.5959i	0.840941	−	0.840941i
$544$	5.19615	−	3.00000i	0.222783	−	0.128624i
$545$		0			0
$546$		0			0
$547$	−21.7494	+	5.82774i	−0.929938	+	0.249176i	−0.691828	−	0.722062i	$-0.743195\pi$
$547$	−21.7494	+	5.82774i	−0.929938	+	0.249176i	−0.238110	+	0.971238i	$0.576528\pi$
$548$	−6.36396	−	6.36396i	−0.271855	−	0.271855i
$549$	20.7846	+	12.0000i	0.887066	+	0.512148i
$550$		0			0
$551$	−30.0000	−	17.3205i	−1.27804	−	0.737878i
$552$	−2.68973	+	10.0382i	−0.114482	+	0.427254i
$553$		0			0
$554$	−3.46410	−	6.00000i	−0.147176	−	0.254916i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−16.9706	+	16.9706i	−0.719066	+	0.719066i	−0.968414	−	0.249348i	$-0.919784\pi$
$557$	−16.9706	+	16.9706i	−0.719066	+	0.719066i	0.249348	+	0.968414i	$0.419784\pi$
$558$	−8.48528	−	8.48528i	−0.359211	−	0.359211i
$559$			42.0000i			1.77641i
$560$		0			0
$561$	18.0000	−	31.1769i	0.759961	−	1.31629i
$562$	5.37945	−	20.0764i	0.226919	−	0.846871i
$563$	5.43520	−	20.2844i	0.229066	−	0.854887i	−0.751668	−	0.659542i	$-0.770750\pi$
$563$	5.43520	−	20.2844i	0.229066	−	0.854887i	0.980734	−	0.195346i	$-0.0625829\pi$
$564$	10.3923			0.437595
$565$		0			0
$566$			12.1244i			0.509625i
$567$		0			0
$568$	−4.89898	+	4.89898i	−0.205557	+	0.205557i
$569$	−17.3205	+	30.0000i	−0.726113	+	1.25767i	0.232401	+	0.972620i	$0.425342\pi$
$569$	−17.3205	+	30.0000i	−0.726113	+	1.25767i	−0.958514	+	0.285045i	$0.907991\pi$
$570$		0			0
$571$	0.500000	+	0.866025i	0.0209243	+	0.0362420i	0.876298	−	0.481770i	$-0.160006\pi$
$571$	0.500000	+	0.866025i	0.0209243	+	0.0362420i	−0.855374	+	0.518012i	$0.826672\pi$
$572$	−11.5911	−	3.10583i	−0.484649	−	0.129861i
$573$	40.5689	−	10.8704i	1.69479	−	0.454117i
$574$		0			0
$575$		0			0
$576$	3.00000			0.125000
$577$	−25.7196	−	25.7196i	−1.07072	−	1.07072i	−0.997301	−	0.0734217i	$-0.976608\pi$
$577$	−25.7196	−	25.7196i	−1.07072	−	1.07072i	−0.0734217	−	0.997301i	$-0.523392\pi$
$578$	18.3526	−	4.91756i	0.763367	−	0.204544i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	8.69333	+	2.32937i	0.360350	+	0.0965556i
$583$	−5.37945	−	20.0764i	−0.222794	−	0.831479i
$584$	12.1244			0.501709
$585$		0			0
$586$	6.00000			0.247858
$587$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$587$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$588$	−3.13801	−	11.7112i	−0.129410	−	0.482963i
$589$	17.3205	−	10.0000i	0.713679	−	0.412043i
$590$		0			0
$591$			41.5692i			1.70993i
$592$	−6.69213	+	1.79315i	−0.275045	+	0.0736980i
$593$	23.3345	+	23.3345i	0.958234	+	0.958234i	0.999162	−	0.0409281i	$-0.0130314\pi$
$593$	23.3345	+	23.3345i	0.958234	+	0.958234i	−0.0409281	+	0.999162i	$0.513031\pi$
$594$	15.5885	−	9.00000i	0.639602	−	0.369274i
$595$		0			0
$596$	9.00000	+	5.19615i	0.368654	+	0.212843i
$597$	−9.79796	−	9.79796i	−0.401004	−	0.401004i
$598$	20.0764	+	5.37945i	0.820985	+	0.219982i
$599$	−13.8564	−	24.0000i	−0.566157	−	0.980613i	−0.996941	−	0.0781581i	$-0.975096\pi$
$599$	−13.8564	−	24.0000i	−0.566157	−	0.980613i	0.430784	−	0.902455i	$-0.358237\pi$
$600$		0			0
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$	25.0955	+	6.72432i	1.02197	+	0.273835i
$604$		−	16.0000i		−	0.651031i
$605$		0			0
$606$	3.00000	+	5.19615i	0.121867	+	0.211079i
$607$	6.27603	−	23.4225i	0.254736	−	0.950688i	−0.713501	−	0.700654i	$-0.752892\pi$
$607$	6.27603	−	23.4225i	0.254736	−	0.950688i	0.968237	−	0.250034i	$-0.0804418\pi$
$608$	−1.29410	+	4.82963i	−0.0524825	+	0.195867i
$609$		0			0
$610$		0			0
$611$		−	20.7846i		−	0.840855i
$612$	17.3867	+	4.65874i	0.702814	+	0.188319i
$613$	−2.44949	+	2.44949i	−0.0989340	+	0.0989340i	−0.754841	−	0.655907i	$-0.772286\pi$
$613$	−2.44949	+	2.44949i	−0.0989340	+	0.0989340i	0.655907	+	0.754841i	$0.272286\pi$
$614$	−12.1244	+	21.0000i	−0.489299	+	0.847491i
$615$		0			0
$616$		0			0
$617$	8.69333	+	2.32937i	0.349980	+	0.0937770i	0.429527	−	0.903054i	$-0.358680\pi$
$617$	8.69333	+	2.32937i	0.349980	+	0.0937770i	−0.0795462	+	0.996831i	$0.525347\pi$
$618$	4.24264	+	4.24264i	0.170664	+	0.170664i
$619$	14.7224	+	8.50000i	0.591744	+	0.341644i	0.765787	−	0.643094i	$-0.222350\pi$
$619$	14.7224	+	8.50000i	0.591744	+	0.341644i	−0.174042	+	0.984738i	$0.555683\pi$
$620$		0			0
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$	−17.1464	−	17.1464i	−0.687509	−	0.687509i
$623$		0			0
$624$		−	6.00000i		−	0.240192i
$625$		0			0
$626$	28.5000	−	16.4545i	1.13909	−	0.657653i
$627$	7.76457	+	28.9778i	0.310087	+	1.15726i
$628$	0.896575	+	3.34607i	0.0357773	+	0.133523i
$629$	−41.5692			−1.65747
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	−3.62347	−	13.5230i	−0.144134	−	0.537915i
$633$	21.7494	+	5.82774i	0.864462	+	0.231632i
$634$	10.3923	−	6.00000i	0.412731	−	0.238290i
$635$		0			0
$636$	9.00000	−	5.19615i	0.356873	−	0.206041i
$637$	−23.4225	+	6.27603i	−0.928032	+	0.248665i
$638$	−16.9706	−	16.9706i	−0.671871	−	0.671871i
$639$	−20.7846			−0.822226
$640$		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
$643$	−45.1719	−	12.1038i	−1.78141	−	0.477326i	−0.790566	−	0.612376i	$-0.790214\pi$
$643$	−45.1719	−	12.1038i	−1.78141	−	0.477326i	−0.990839	+	0.135050i	$0.956880\pi$
$644$		0			0
$645$		0			0
$646$	−15.0000	+	25.9808i	−0.590167	+	1.02220i
$647$	29.6985	−	29.6985i	1.16757	−	1.16757i	0.184790	−	0.982778i	$-0.440840\pi$
$647$	29.6985	−	29.6985i	1.16757	−	1.16757i	0.982778	−	0.184790i	$-0.0591604\pi$
$648$	6.36396	+	6.36396i	0.250000	+	0.250000i
$649$			6.00000i			0.235521i
$650$		0			0
$651$		0			0
$652$	0.448288	−	1.67303i	0.0175563	−	0.0655210i
$653$	7.76457	−	28.9778i	0.303851	−	1.13399i	−0.630079	−	0.776531i	$-0.716977\pi$
$653$	7.76457	−	28.9778i	0.303851	−	1.13399i	0.933930	−	0.357457i	$-0.116356\pi$
$654$	17.3205	−	30.0000i	0.677285	−	1.17309i
$655$		0			0
$656$			1.73205i			0.0676252i
$657$	25.7196	+	25.7196i	1.00342	+	1.00342i
$658$		0			0
$659$	−7.79423	+	13.5000i	−0.303620	+	0.525885i	−0.976953	−	0.213454i	$-0.931529\pi$
$659$	−7.79423	+	13.5000i	−0.303620	+	0.525885i	0.673333	+	0.739339i	$0.264862\pi$
$660$		0			0
$661$	25.0000	+	43.3013i	0.972387	+	1.68422i	0.688301	+	0.725426i	$0.258357\pi$
$661$	25.0000	+	43.3013i	0.972387	+	1.68422i	0.284087	+	0.958799i	$0.408310\pi$
$662$	0.965926	+	0.258819i	0.0375418	+	0.0100593i
$663$	9.31749	−	34.7733i	0.361861	−	1.35048i
$664$	7.79423	+	4.50000i	0.302475	+	0.174634i
$665$		0			0
$666$	−18.0000	−	10.3923i	−0.697486	−	0.402694i
$667$	29.3939	+	29.3939i	1.13814	+	1.13814i
$668$	11.5911	−	3.10583i	0.448474	−	0.120168i
$669$	−10.3923	−	6.00000i	−0.401790	−	0.231973i
$670$		0			0
$671$	−24.0000	+	13.8564i	−0.926510	+	0.534921i
$672$		0			0
$673$	8.96575	+	33.4607i	0.345604	+	1.28981i	0.891904	+	0.452224i	$0.149369\pi$
$673$	8.96575	+	33.4607i	0.345604	+	1.28981i	−0.546300	+	0.837590i	$0.683964\pi$
$674$	−6.92820			−0.266864
$675$		0			0
$676$	1.00000			0.0384615
$677$	−1.55291	−	5.79555i	−0.0596833	−	0.222741i	0.929642	−	0.368464i	$-0.120116\pi$
$677$	−1.55291	−	5.79555i	−0.0596833	−	0.222741i	−0.989326	+	0.145722i	$0.953449\pi$
$678$	18.3712	−	18.3712i	0.705541	−	0.705541i
$679$		0			0
$680$		0			0
$681$	4.50000	+	2.59808i	0.172440	+	0.0995585i
$682$	13.3843	−	3.58630i	0.512510	−	0.137327i
$683$	2.12132	+	2.12132i	0.0811701	+	0.0811701i	0.746526	−	0.665356i	$-0.231720\pi$
$683$	2.12132	+	2.12132i	0.0811701	+	0.0811701i	−0.665356	+	0.746526i	$0.731720\pi$
$684$	−12.9904	+	7.50000i	−0.496700	+	0.286770i
$685$		0			0
$686$		0			0
$687$	−7.17260	+	26.7685i	−0.273652	+	1.02128i
$688$	11.7112	+	3.13801i	0.446486	+	0.119636i
$689$	−10.3923	−	18.0000i	−0.395915	−	0.685745i
$690$		0			0
$691$	17.5000	−	30.3109i	0.665731	−	1.15308i	−0.313355	−	0.949636i	$-0.601453\pi$
$691$	17.5000	−	30.3109i	0.665731	−	1.15308i	0.979086	−	0.203445i	$-0.0652137\pi$
$692$		0			0
$693$		0			0
$694$			12.0000i			0.455514i
$695$		0			0
$696$	6.00000	−	10.3923i	0.227429	−	0.393919i
$697$	−2.68973	+	10.0382i	−0.101881	+	0.380224i
$698$	6.72930	−	25.1141i	0.254708	−	0.950582i
$699$	15.5885			0.589610
$700$		0			0
$701$			6.92820i			0.261675i	0.991404	+	0.130837i	$0.0417666\pi$
$701$			6.92820i			0.261675i	−0.991404	+	0.130837i	$0.958233\pi$
$702$	12.7279	−	12.7279i	0.480384	−	0.480384i
$703$	24.4949	−	24.4949i	0.923843	−	0.923843i
$704$	−1.73205	+	3.00000i	−0.0652791	+	0.113067i
$705$		0			0
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$		0			0
$708$	−2.89778	+	0.776457i	−0.108905	+	0.0291810i
$709$	39.8372	+	23.0000i	1.49612	+	0.863783i	0.999990	−	0.00446726i	$-0.00142198\pi$
$709$	39.8372	+	23.0000i	1.49612	+	0.863783i	0.496126	+	0.868250i	$0.334755\pi$
$710$		0			0
$711$	21.0000	−	36.3731i	0.787562	−	1.36410i
$712$	8.57321	+	8.57321i	0.321295	+	0.321295i
$713$	−23.1822	+	6.21166i	−0.868181	+	0.232628i
$714$		0			0
$715$		0			0
$716$	−19.5000	+	11.2583i	−0.728749	+	0.420744i
$717$	17.3867	+	4.65874i	0.649317	+	0.173984i
$718$	7.17260	+	26.7685i	0.267679	+	0.998992i
$719$	−6.92820			−0.258378			−0.129189	−	0.991620i	$-0.541237\pi$
$719$	−6.92820			−0.258378			−0.129189	+	0.991620i	$0.541237\pi$
$720$		0			0
$721$		0			0
$722$	−1.55291	−	5.79555i	−0.0577935	−	0.215688i
$723$	−0.448288	−	1.67303i	−0.0166720	−	0.0622208i
$724$	−13.8564	+	8.00000i	−0.514969	+	0.297318i
$725$		0			0
$726$			1.73205i			0.0642824i
$727$	−33.4607	+	8.96575i	−1.24099	+	0.332521i	−0.818848	−	0.574010i	$-0.805387\pi$
$727$	−33.4607	+	8.96575i	−1.24099	+	0.332521i	−0.422139	+	0.906531i	$0.638720\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	63.0000	+	36.3731i	2.33014	+	1.34531i
$732$	−9.79796	−	9.79796i	−0.362143	−	0.362143i
$733$	30.1146	+	8.06918i	1.11231	+	0.298042i	0.767767	−	0.640729i	$-0.221368\pi$
$733$	30.1146	+	8.06918i	1.11231	+	0.298042i	0.344541	+	0.938771i	$0.388035\pi$
$734$	8.66025	+	15.0000i	0.319656	+	0.553660i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−21.2132	+	21.2132i	−0.781398	+	0.781398i
$738$	−3.67423	+	3.67423i	−0.135250	+	0.135250i
$739$			23.0000i			0.846069i	0.906114	+	0.423034i	$0.139035\pi$
$739$			23.0000i			0.846069i	−0.906114	+	0.423034i	$0.860965\pi$
$740$		0			0
$741$	15.0000	+	25.9808i	0.551039	+	0.954427i
$742$		0			0
$743$	3.10583	−	11.5911i	0.113942	−	0.425237i	−0.885264	−	0.465089i	$-0.846022\pi$
$743$	3.10583	−	11.5911i	0.113942	−	0.425237i	0.999206	+	0.0398527i	$0.0126889\pi$
$744$	3.46410	+	6.00000i	0.127000	+	0.219971i
$745$		0			0
$746$		−	20.7846i		−	0.760979i
$747$	6.98811	+	26.0800i	0.255682	+	0.954217i
$748$	−14.6969	+	14.6969i	−0.537373	+	0.537373i
$749$		0			0
$750$		0			0
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$	−5.79555	−	1.55291i	−0.211342	−	0.0566290i
$753$	6.36396	+	6.36396i	0.231916	+	0.231916i
$754$	−20.7846	−	12.0000i	−0.756931	−	0.437014i
$755$		0			0
$756$		0			0
$757$	14.6969	+	14.6969i	0.534169	+	0.534169i	0.921810	−	0.387641i	$-0.126710\pi$
$757$	14.6969	+	14.6969i	0.534169	+	0.534169i	−0.387641	+	0.921810i	$0.626710\pi$
$758$	−7.72741	+	2.07055i	−0.280672	+	0.0752058i
$759$		−	36.0000i		−	1.30672i
$760$		0			0
$761$	1.50000	−	0.866025i	0.0543750	−	0.0313934i	−0.472566	−	0.881295i	$-0.656672\pi$
$761$	1.50000	−	0.866025i	0.0543750	−	0.0313934i	0.526941	+	0.849902i	$0.323339\pi$
$762$	−4.65874	−	17.3867i	−0.168768	−	0.629852i
$763$		0			0
$764$	−24.2487			−0.877288
$765$		0			0
$766$	−6.00000			−0.216789
$767$	1.55291	+	5.79555i	0.0560725	+	0.209265i
$768$	−1.67303	−	0.448288i	−0.0603704	−	0.0161762i
$769$	42.4352	−	24.5000i	1.53025	−	0.883493i	0.530904	−	0.847432i	$-0.321852\pi$
$769$	42.4352	−	24.5000i	1.53025	−	0.883493i	0.999350	−	0.0360609i	$-0.0114810\pi$
$770$		0			0
$771$	22.5000	−	12.9904i	0.810318	−	0.467837i
$772$		0			0
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.997499	−	0.0706813i	$-0.977483\pi$
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.0706813	−	0.997499i	$-0.522517\pi$
$774$	18.1865	+	31.5000i	0.653701	+	1.13224i
$775$		0			0
$776$	−4.50000	−	2.59808i	−0.161541	−	0.0932655i
$777$		0			0
$778$	−10.0382	−	2.68973i	−0.359887	−	0.0964314i
$779$	−4.33013	−	7.50000i	−0.155143	−	0.268715i
$780$		0			0
$781$	12.0000	−	20.7846i	0.429394	−	0.743732i
$782$	25.4558	−	25.4558i	0.910299	−	0.910299i
$783$	34.7733	−	9.31749i	1.24270	−	0.332980i
$784$			7.00000i			0.250000i
$785$		0			0
$786$	6.00000			0.214013
$787$	8.06918	−	30.1146i	0.287635	−	1.07347i	−0.659257	−	0.751918i	$-0.729129\pi$
$787$	8.06918	−	30.1146i	0.287635	−	1.07347i	0.946892	−	0.321551i	$-0.104204\pi$
$788$	6.21166	−	23.1822i	0.221281	−	0.825832i
$789$	10.3923	−	18.0000i	0.369976	−	0.640817i
$790$		0			0
$791$		0			0
$792$	−10.0382	+	2.68973i	−0.356692	+	0.0955753i
$793$	−19.5959	+	19.5959i	−0.695871	+	0.695871i
$794$	12.1244	−	21.0000i	0.430277	−	0.745262i
$795$		0			0
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	5.79555	+	1.55291i	0.205289	+	0.0550070i	0.359998	−	0.932953i	$-0.382777\pi$
$797$	5.79555	+	1.55291i	0.205289	+	0.0550070i	−0.154709	+	0.987960i	$0.549444\pi$
$798$		0			0
$799$	−31.1769	−	18.0000i	−1.10296	−	0.636794i
$800$		0			0
$801$			36.3731i			1.28518i
$802$	−14.6969	−	14.6969i	−0.518967	−	0.518967i
$803$	−40.5689	+	10.8704i	−1.43164	+	0.383608i
$804$	−12.9904	−	7.50000i	−0.458135	−	0.264505i
$805$		0			0
$806$	12.0000	−	6.92820i	0.422682	−	0.244036i
$807$	16.9706	−	16.9706i	0.597392	−	0.597392i
$808$	−0.896575	−	3.34607i	−0.0315414	−	0.117714i
$809$	−29.4449			−1.03523			−0.517613	−	0.855615i	$-0.673179\pi$
$809$	−29.4449			−1.03523			−0.517613	+	0.855615i	$0.673179\pi$
$810$		0			0
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$		0			0
$813$	−12.2474	+	12.2474i	−0.429537	+	0.429537i
$814$	20.7846	−	12.0000i	0.728500	−	0.420600i
$815$		0			0
$816$	−9.00000	−	5.19615i	−0.315063	−	0.181902i
$817$	−58.5561	+	15.6901i	−2.04862	+	0.548926i
$818$	20.5061	+	20.5061i	0.716979	+	0.716979i
$819$		0			0
$820$		0			0
$821$	−48.0000	−	27.7128i	−1.67521	−	0.967184i	−0.964645	−	0.263554i	$-0.915105\pi$
$821$	−48.0000	−	27.7128i	−1.67521	−	0.967184i	−0.710567	−	0.703630i	$-0.751561\pi$
$822$	−4.03459	+	15.0573i	−0.140722	+	0.525183i
$823$	−3.34607	−	0.896575i	−0.116637	−	0.0312527i	0.200029	−	0.979790i	$-0.435896\pi$
$823$	−3.34607	−	0.896575i	−0.116637	−	0.0312527i	−0.316665	+	0.948537i	$0.602563\pi$
$824$	−1.73205	−	3.00000i	−0.0603388	−	0.104510i
$825$		0			0
$826$		0			0
$827$	10.6066	−	10.6066i	0.368828	−	0.368828i	−0.498222	−	0.867050i	$-0.666014\pi$
$827$	10.6066	−	10.6066i	0.368828	−	0.368828i	0.867050	+	0.498222i	$0.166014\pi$
$828$	17.3867	−	4.65874i	0.604228	−	0.161903i
$829$			38.0000i			1.31979i	0.751356	+	0.659897i	$0.229400\pi$
$829$			38.0000i			1.31979i	−0.751356	+	0.659897i	$0.770600\pi$
$830$		0			0
$831$	−6.00000	+	10.3923i	−0.208138	+	0.360505i
$832$	−0.896575	+	3.34607i	−0.0310832	+	0.116004i
$833$	−10.8704	+	40.5689i	−0.376637	+	1.40563i
$834$	−6.92820			−0.239904
$835$		0			0
$836$		−	17.3205i		−	0.599042i
$837$	−5.37945	+	20.0764i	−0.185941	+	0.693942i
$838$	18.3712	−	18.3712i	0.634622	−	0.634622i
$839$	−6.92820	+	12.0000i	−0.239188	+	0.414286i	−0.960482	−	0.278344i	$-0.910215\pi$
$839$	−6.92820	+	12.0000i	−0.239188	+	0.414286i	0.721293	+	0.692630i	$0.243548\pi$
$840$		0			0
$841$	−9.50000	−	16.4545i	−0.327586	−	0.567396i
$842$	7.72741	+	2.07055i	0.266304	+	0.0713559i
$843$	−34.7733	+	9.31749i	−1.19766	+	0.320911i
$844$	−11.2583	−	6.50000i	−0.387528	−	0.223739i
$845$		0			0
$846$	−9.00000	−	15.5885i	−0.309426	−	0.535942i
$847$		0			0
$848$	−5.79555	+	1.55291i	−0.199020	+	0.0533273i
$849$	18.1865	−	10.5000i	0.624160	−	0.360359i
$850$		0			0
$851$	−36.0000	+	20.7846i	−1.23406	+	0.712487i
$852$	11.5911	+	3.10583i	0.397105	+	0.106404i
$853$	−0.896575	−	3.34607i	−0.0306982	−	0.114567i	0.948877	−	0.315647i	$-0.102222\pi$
$853$	−0.896575	−	3.34607i	−0.0306982	−	0.114567i	−0.979575	+	0.201080i	$0.935555\pi$
$854$		0			0
$855$		0			0
$856$	−3.00000			−0.102538
$857$	−3.88229	−	14.4889i	−0.132616	−	0.494931i	0.867380	−	0.497646i	$-0.165802\pi$
$857$	−3.88229	−	14.4889i	−0.132616	−	0.494931i	−0.999996	+	0.00271550i	$0.999136\pi$
$858$	5.37945	+	20.0764i	0.183651	+	0.685397i
$859$	11.2583	−	6.50000i	0.384129	−	0.221777i	−0.295484	−	0.955348i	$-0.595481\pi$
$859$	11.2583	−	6.50000i	0.384129	−	0.221777i	0.679613	+	0.733571i	$0.262148\pi$
$860$		0			0
$861$		0			0
$862$	−13.3843	+	3.58630i	−0.455870	+	0.122150i
$863$	−4.24264	−	4.24264i	−0.144421	−	0.144421i	0.631199	−	0.775621i	$-0.282563\pi$
$863$	−4.24264	−	4.24264i	−0.144421	−	0.144421i	−0.775621	+	0.631199i	$0.782563\pi$
$864$	−2.59808	−	4.50000i	−0.0883883	−	0.153093i
$865$		0			0
$866$	−6.00000	−	3.46410i	−0.203888	−	0.117715i
$867$	−23.2702	−	23.2702i	−0.790296	−	0.790296i
$868$		0			0
$869$	24.2487	+	42.0000i	0.822581	+	1.42475i
$870$		0			0
$871$	−15.0000	+	25.9808i	−0.508256	+	0.880325i
$872$	−14.1421	+	14.1421i	−0.478913	+	0.478913i
$873$	−4.03459	−	15.0573i	−0.136550	−	0.509612i
$874$			30.0000i			1.01477i
$875$		0			0
$876$	−10.5000	−	18.1865i	−0.354762	−	0.614466i
$877$	−2.68973	+	10.0382i	−0.0908256	+	0.338966i	−0.996354	−	0.0853209i	$-0.972808\pi$
$877$	−2.68973	+	10.0382i	−0.0908256	+	0.338966i	0.905528	+	0.424287i	$0.139475\pi$
$878$	−6.72930	+	25.1141i	−0.227103	+	0.847559i
$879$	−5.19615	−	9.00000i	−0.175262	−	0.303562i
$880$		0			0
$881$			6.92820i			0.233417i	0.993166	+	0.116709i	$0.0372343\pi$
$881$			6.92820i			0.233417i	−0.993166	+	0.116709i	$0.962766\pi$
$882$	−14.8492	+	14.8492i	−0.500000	+	0.500000i
$883$	−36.7423	+	36.7423i	−1.23648	+	1.23648i	−0.275048	+	0.961431i	$0.588694\pi$
$883$	−36.7423	+	36.7423i	−1.23648	+	1.23648i	−0.961431	+	0.275048i	$0.911306\pi$
$884$	−10.3923	+	18.0000i	−0.349531	+	0.605406i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−5.79555	−	1.55291i	−0.194596	−	0.0521418i	0.160205	−	0.987084i	$-0.448785\pi$
$887$	−5.79555	−	1.55291i	−0.194596	−	0.0521418i	−0.354800	+	0.934942i	$0.615451\pi$
$888$	8.48528	+	8.48528i	0.284747	+	0.284747i
$889$		0			0
$890$		0			0
$891$	−27.0000	−	15.5885i	−0.904534	−	0.522233i
$892$	4.89898	+	4.89898i	0.164030	+	0.164030i
$893$	28.9778	−	7.76457i	0.969704	−	0.259831i
$894$		−	18.0000i		−	0.602010i
$895$		0			0
$896$		0			0
$897$	−9.31749	−	34.7733i	−0.311102	−	1.16105i
$898$	2.24144	+	8.36516i	0.0747978	+	0.279149i
$899$	27.7128			0.924274
$900$		0			0
$901$	−36.0000			−1.19933
$902$	−1.55291	−	5.79555i	−0.0517064	−	0.192971i
$903$		0			0
$904$	−12.9904	+	7.50000i	−0.432054	+	0.249446i
$905$		0			0
$906$	−24.0000	+	13.8564i	−0.797347	+	0.460348i
$907$	31.7876	−	8.51747i	1.05549	−	0.282818i	0.310972	−	0.950419i	$-0.399346\pi$
$907$	31.7876	−	8.51747i	1.05549	−	0.282818i	0.744519	+	0.667601i	$0.232679\pi$
$908$	−2.12132	−	2.12132i	−0.0703985	−	0.0703985i
$909$	5.19615	−	9.00000i	0.172345	−	0.298511i
$910$		0			0
$911$	15.0000	+	8.66025i	0.496972	+	0.286927i	0.727462	−	0.686148i	$-0.240700\pi$
$911$	15.0000	+	8.66025i	0.496972	+	0.286927i	−0.230490	+	0.973075i	$0.574033\pi$
$912$	8.36516	−	2.24144i	0.276998	−	0.0742215i
$913$	−30.1146	−	8.06918i	−0.996647	−	0.267051i
$914$	2.59808	+	4.50000i	0.0859367	+	0.148847i
$915$		0			0
$916$	8.00000	−	13.8564i	0.264327	−	0.457829i
$917$		0			0
$918$	−8.06918	−	30.1146i	−0.266323	−	0.993929i
$919$			2.00000i			0.0659739i	0.999456	+	0.0329870i	$0.0105020\pi$
$919$			2.00000i			0.0659739i	−0.999456	+	0.0329870i	$0.989498\pi$
$920$		0			0
$921$	42.0000			1.38395
$922$	8.96575	−	33.4607i	0.295271	−	1.10197i
$923$	6.21166	−	23.1822i	0.204459	−	0.763052i
$924$		0			0
$925$		0			0
$926$			6.92820i			0.227675i
$927$	2.68973	−	10.0382i	0.0883422	−	0.329698i
$928$	−4.89898	+	4.89898i	−0.160817	+	0.160817i
$929$	27.7128	−	48.0000i	0.909228	−	1.57483i	0.0940887	−	0.995564i	$-0.470006\pi$
$929$	27.7128	−	48.0000i	0.909228	−	1.57483i	0.815139	−	0.579265i	$-0.196660\pi$
$930$		0			0
$931$	−17.5000	−	30.3109i	−0.573539	−	0.993399i
$932$	−8.69333	−	2.32937i	−0.284760	−	0.0763011i
$933$	−10.8704	+	40.5689i	−0.355881	+	1.32817i
$934$	18.1865	+	10.5000i	0.595082	+	0.343570i
$935$		0			0
$936$	−9.00000	+	5.19615i	−0.294174	+	0.169842i
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	0.644539	−	0.764571i	$-0.277049\pi$
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	−0.764571	+	0.644539i	$0.777049\pi$
$938$		0			0
$939$	−49.3634	−	28.5000i	−1.61092	−	0.930062i
$940$		0			0
$941$	36.0000	−	20.7846i	1.17357	−	0.677559i	0.219049	−	0.975714i	$-0.429705\pi$
$941$	36.0000	−	20.7846i	1.17357	−	0.677559i	0.954517	+	0.298155i	$0.0963712\pi$
$942$	4.24264	−	4.24264i	0.138233	−	0.138233i
$943$	2.68973	+	10.0382i	0.0875895	+	0.326889i
$944$	1.73205			0.0563735
$945$		0			0
$946$	−42.0000			−1.36554
$947$	3.88229	+	14.4889i	0.126157	+	0.470826i	0.999878	−	0.0156019i	$-0.00496644\pi$
$947$	3.88229	+	14.4889i	0.126157	+	0.470826i	−0.873721	+	0.486427i	$0.838300\pi$
$948$	−17.1464	+	17.1464i	−0.556890	+	0.556890i
$949$	−36.3731	+	21.0000i	−1.18072	+	0.681689i
$950$		0			0
$951$	−18.0000	−	10.3923i	−0.583690	−	0.336994i
$952$		0			0
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	0.635044	−	0.772476i	$-0.280982\pi$
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	−0.772476	+	0.635044i	$0.780982\pi$
$954$	−15.5885	−	9.00000i	−0.504695	−	0.291386i
$955$		0			0
$956$	−9.00000	−	5.19615i	−0.291081	−	0.168056i
$957$	−10.7589	+	40.1528i	−0.347786	+	1.29796i
$958$	16.7303	+	4.48288i	0.540532	+	0.144835i
$959$		0			0
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	16.9706	−	16.9706i	0.547153	−	0.547153i
$963$	−6.36396	−	6.36396i	−0.205076	−	0.205076i
$964$			1.00000i			0.0322078i
$965$		0			0
$966$		0			0
$967$	−1.79315	+	6.69213i	−0.0576638	+	0.215204i	−0.988746	−	0.149606i	$-0.952200\pi$
$967$	−1.79315	+	6.69213i	−0.0576638	+	0.215204i	0.931082	+	0.364810i	$0.118866\pi$
$968$	0.258819	−	0.965926i	0.00831876	−	0.0310460i
$969$	51.9615			1.66924
$970$		0			0
$971$			22.5167i			0.722594i	0.932451	+	0.361297i	$0.117666\pi$
$971$			22.5167i			0.722594i	−0.932451	+	0.361297i	$0.882334\pi$
$972$	4.03459	−	15.0573i	0.129410	−	0.482963i
$973$		0			0
$974$	−3.46410	+	6.00000i	−0.110997	+	0.192252i
$975$		0			0
$976$	4.00000	+	6.92820i	0.128037	+	0.221766i
$977$	2.89778	+	0.776457i	0.0927081	+	0.0248411i	0.304875	−	0.952392i	$-0.401385\pi$
$977$	2.89778	+	0.776457i	0.0927081	+	0.0248411i	−0.212167	+	0.977233i	$0.568052\pi$
$978$	−2.89778	+	0.776457i	−0.0926607	+	0.0248284i
$979$	−36.3731	−	21.0000i	−1.16249	−	0.671163i
$980$		0			0
$981$	−60.0000			−1.91565
$982$	20.8207	+	20.8207i	0.664414	+	0.664414i
$983$	−40.5689	+	10.8704i	−1.29395	+	0.346712i	−0.839158	−	0.543888i	$-0.816952\pi$
$983$	−40.5689	+	10.8704i	−1.29395	+	0.346712i	−0.454788	+	0.890600i	$0.650285\pi$
$984$	2.59808	−	1.50000i	0.0828236	−	0.0478183i
$985$		0			0
$986$	−36.0000	+	20.7846i	−1.14647	+	0.661917i
$987$		0			0
$988$	−4.48288	−	16.7303i	−0.142619	−	0.532263i
$989$	72.7461			2.31319
$990$		0			0
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	−1.03528	−	3.86370i	−0.0328701	−	0.122673i
$993$	−0.448288	−	1.67303i	−0.0142260	−	0.0530921i
$994$		0			0
$995$		0			0
$996$		−	15.5885i		−	0.493939i
$997$	10.0382	−	2.68973i	0.317913	−	0.0851845i	−0.0963340	−	0.995349i	$-0.530712\pi$
$997$	10.0382	−	2.68973i	0.317913	−	0.0851845i	0.414247	+	0.910165i	$0.364045\pi$
$998$	9.19239	+	9.19239i	0.290980	+	0.290980i
$999$			36.0000i			1.13899i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50000 + 0.866025i) q^{6} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 + 1.73205i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(3.34607 + 0.896575i) q^{13} +(0.500000 - 0.866025i) q^{16} +(4.24264 - 4.24264i) q^{17} +(2.89778 - 0.776457i) q^{18} +5.00000i q^{19} +(-0.896575 + 3.34607i) q^{22} +(1.55291 - 5.79555i) q^{23} -1.73205 q^{24} +3.46410i q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.46410 + 6.00000i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.965926 + 0.258819i) q^{32} +(5.79555 - 1.55291i) q^{33} +(5.19615 + 3.00000i) q^{34} +(1.50000 + 2.59808i) q^{36} +(-4.89898 - 4.89898i) q^{37} +(-4.82963 + 1.29410i) q^{38} +(5.19615 - 3.00000i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(3.13801 + 11.7112i) q^{43} -3.46410 q^{44} +6.00000 q^{46} +(-1.55291 - 5.79555i) q^{47} +(-0.448288 - 1.67303i) q^{48} +(-6.06218 + 3.50000i) q^{49} -10.3923i q^{51} +(-3.34607 + 0.896575i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(2.59808 - 4.50000i) q^{54} +(6.12372 + 6.12372i) q^{57} +(-6.69213 - 1.79315i) q^{58} +(0.866025 + 1.50000i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(3.00000 + 5.19615i) q^{66} +(-2.24144 + 8.36516i) q^{67} +(-1.55291 + 5.79555i) q^{68} +(-5.19615 - 9.00000i) q^{69} -6.92820i q^{71} +(-2.12132 + 2.12132i) q^{72} +(-8.57321 + 8.57321i) q^{73} +(3.46410 - 6.00000i) q^{74} +(-2.50000 - 4.33013i) q^{76} +(4.24264 + 4.24264i) q^{78} +(12.1244 + 7.00000i) q^{79} -9.00000 q^{81} +(-1.22474 - 1.22474i) q^{82} +(-8.69333 + 2.32937i) q^{83} +(-10.5000 + 6.06218i) q^{86} +(3.10583 + 11.5911i) q^{87} +(-0.896575 - 3.34607i) q^{88} -12.1244 q^{89} +(1.55291 + 5.79555i) q^{92} +(-6.69213 - 1.79315i) q^{93} +(5.19615 - 3.00000i) q^{94} +(1.50000 - 0.866025i) q^{96} +(5.01910 - 1.34486i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(5.19615 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{6}+O(q^{10}) \) 8 * q + 12 * q^6	\( 8 q + 12 q^{6} + 24 q^{11} + 4 q^{16} - 16 q^{31} + 12 q^{36} - 12 q^{41} + 48 q^{46} - 32 q^{61} + 24 q^{66} - 20 q^{76} - 72 q^{81} - 84 q^{86} + 12 q^{96}+O(q^{100}) \) 8 * q + 12 * q^6 + 24 * q^11 + 4 * q^16 - 16 * q^31 + 12 * q^36 - 12 * q^41 + 48 * q^46 - 32 * q^61 + 24 * q^66 - 20 * q^76 - 72 * q^81 - 84 * q^86 + 12 * q^96

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