LMFDB - Embedded newform 450.2.e.f.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(151,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("450.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.e (of order $3$, degree $2$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	450.151
Dual form			450.2.e.f.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(-1.50000 + 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} -7.00000 q^{19} +(-3.00000 - 1.73205i) q^{21} +1.73205i q^{24} -4.00000 q^{26} +5.19615i q^{27} -2.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(5.00000 + 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{34} +(1.50000 + 2.59808i) q^{36} -2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +(-6.00000 + 3.46410i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(-3.00000 + 1.73205i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{47} +(1.50000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} -10.3923i q^{51} +(-2.00000 + 3.46410i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +(-1.00000 + 1.73205i) q^{56} +12.1244i q^{57} +(-3.00000 - 5.19615i) q^{58} +(4.50000 + 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +10.0000 q^{62} +(-3.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(-6.50000 - 11.2583i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{71} +3.00000 q^{72} +1.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +6.92820i q^{78} +(-1.00000 + 1.73205i) q^{79} +9.00000 q^{81} -9.00000 q^{82} +(4.50000 - 7.79423i) q^{83} +3.46410i q^{84} +(0.500000 + 0.866025i) q^{86} +(-9.00000 - 5.19615i) q^{87} +15.0000 q^{89} -8.00000 q^{91} +(15.0000 - 8.66025i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(1.50000 - 0.866025i) q^{96} +(8.50000 - 14.7224i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 3 q^{6} + 2 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^4 - 3 * q^6 + 2 * q^7 - 2 * q^8 - 6 * q^9	$ 2 q + q^{2} - q^{4} - 3 q^{6} + 2 q^{7} - 2 q^{8} - 6 q^{9} - 3 q^{12} - 4 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 3 q^{18} - 14 q^{19} - 6 q^{21} - 8 q^{26} - 4 q^{28} + 6 q^{29} + 10 q^{31} + q^{32} + 6 q^{34} + 3 q^{36} - 4 q^{37} - 7 q^{38} - 12 q^{39} - 9 q^{41} - 6 q^{42} - q^{43} + 6 q^{47} + 3 q^{48} + 3 q^{49} - 4 q^{52} + 24 q^{53} + 9 q^{54} - 2 q^{56} - 6 q^{58} + 9 q^{59} + 4 q^{61} + 20 q^{62} - 6 q^{63} + 2 q^{64} - 13 q^{67} - 6 q^{68} + 12 q^{71} + 6 q^{72} + 2 q^{73} - 2 q^{74} + 7 q^{76} - 2 q^{79} + 18 q^{81} - 18 q^{82} + 9 q^{83} + q^{86} - 18 q^{87} + 30 q^{89} - 16 q^{91} + 30 q^{93} - 6 q^{94} + 3 q^{96} + 17 q^{97} + 6 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 3 * q^6 + 2 * q^7 - 2 * q^8 - 6 * q^9 - 3 * q^12 - 4 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 3 * q^18 - 14 * q^19 - 6 * q^21 - 8 * q^26 - 4 * q^28 + 6 * q^29 + 10 * q^31 + q^32 + 6 * q^34 + 3 * q^36 - 4 * q^37 - 7 * q^38 - 12 * q^39 - 9 * q^41 - 6 * q^42 - q^43 + 6 * q^47 + 3 * q^48 + 3 * q^49 - 4 * q^52 + 24 * q^53 + 9 * q^54 - 2 * q^56 - 6 * q^58 + 9 * q^59 + 4 * q^61 + 20 * q^62 - 6 * q^63 + 2 * q^64 - 13 * q^67 - 6 * q^68 + 12 * q^71 + 6 * q^72 + 2 * q^73 - 2 * q^74 + 7 * q^76 - 2 * q^79 + 18 * q^81 - 18 * q^82 + 9 * q^83 + q^86 - 18 * q^87 + 30 * q^89 - 16 * q^91 + 30 * q^93 - 6 * q^94 + 3 * q^96 + 17 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	−1.00000			−0.353553
$9$	−3.00000			−1.00000
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−1.00000	−	1.73205i	−0.267261	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−3.00000	−	1.73205i	−0.654654	−	0.377964i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$			1.73205i			0.353553i
$25$		0			0
$26$	−4.00000			−0.784465
$27$			5.19615i			1.00000i
$28$	−2.00000			−0.377964
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.830014	+	0.557743i	$0.188333\pi$
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	−3.50000	+	6.06218i	−0.567775	+	0.983415i
$39$	−6.00000	+	3.46410i	−0.960769	+	0.554700i
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−3.00000	+	1.73205i	−0.462910	+	0.267261i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	1.50000	+	0.866025i	0.216506	+	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$		0			0
$51$		−	10.3923i		−	1.45521i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$		0			0
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$			12.1244i			1.60591i
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		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	$0.0842377\pi$
$62$	10.0000			1.27000
$63$	−3.00000	+	5.19615i	−0.377964	+	0.654654i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	−0.923408	−	0.383819i	$-0.874609\pi$
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	0.129307	−	0.991605i	$-0.458725\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	3.00000			0.353553
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$		0			0
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$		0			0
$78$			6.92820i			0.784465i
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$	−9.00000			−0.993884
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$			3.46410i			0.377964i
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	−9.00000	−	5.19615i	−0.964901	−	0.557086i
$88$		0			0
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$		0			0
$93$	15.0000	−	8.66025i	1.55543	−	0.898027i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	−0.00593185	−	0.999982i	$-0.501888\pi$
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	0.868976	−	0.494854i	$-0.164778\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	−9.00000	−	5.19615i	−0.891133	−	0.514496i
$103$	1.00000	+	1.73205i	0.0985329	+	0.170664i	0.911078	−	0.412235i	$-0.135252\pi$
$103$	1.00000	+	1.73205i	0.0985329	+	0.170664i	−0.812545	+	0.582899i	$0.801918\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$		0			0
$106$	6.00000	−	10.3923i	0.582772	−	1.00939i
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$			3.46410i			0.328798i
$112$	1.00000	+	1.73205i	0.0944911	+	0.163663i
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	0.927914	−	0.372794i	$-0.121600\pi$
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	−0.786806	+	0.617200i	$0.788267\pi$
$114$	10.5000	+	6.06218i	0.983415	+	0.567775i
$115$		0			0
$116$	−6.00000			−0.557086
$117$	6.00000	+	10.3923i	0.554700	+	0.960769i
$118$	9.00000			0.828517
$119$	6.00000	−	10.3923i	0.550019	−	0.952661i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−2.00000	−	3.46410i	−0.181071	−	0.313625i
$123$	−13.5000	+	7.79423i	−1.21725	+	0.702782i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$		0			0
$126$	3.00000	+	5.19615i	0.267261	+	0.462910i
$127$	−20.0000			−1.77471			−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000			−1.77471			−0.887357	+	0.461084i	$0.847461\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	1.50000	+	0.866025i	0.132068	+	0.0762493i
$130$		0			0
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$	−7.00000	+	12.1244i	−0.606977	+	1.05131i
$134$	−13.0000			−1.12303
$135$		0			0
$136$	−6.00000			−0.514496
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$	−9.00000	−	5.19615i	−0.757937	−	0.437595i
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$		0			0
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$		0			0
$146$	0.500000	−	0.866025i	0.0413803	−	0.0716728i
$147$	4.50000	−	2.59808i	0.371154	−	0.214286i
$148$	1.00000	+	1.73205i	0.0821995	+	0.142374i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	7.00000			0.567775
$153$	−18.0000			−1.45521
$154$		0			0
$155$		0			0
$156$	6.00000	+	3.46410i	0.480384	+	0.277350i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$		−	20.7846i		−	1.64833i
$160$		0			0
$161$		0			0
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	7.00000			0.548282			0.274141	−	0.961689i	$-0.411606\pi$
$163$	7.00000			0.548282			0.274141	+	0.961689i	$0.411606\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$	3.00000	+	1.73205i	0.231455	+	0.133631i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$		0			0
$171$	21.0000			1.60591
$172$	1.00000			0.0762493
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$	−9.00000	+	5.19615i	−0.682288	+	0.393919i
$175$		0			0
$176$		0			0
$177$	13.5000	−	7.79423i	1.01472	−	0.585850i
$178$	7.50000	−	12.9904i	0.562149	−	0.973670i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−4.00000	+	6.92820i	−0.296500	+	0.513553i
$183$	−6.00000	−	3.46410i	−0.443533	−	0.256074i
$184$		0			0
$185$		0			0
$186$		−	17.3205i		−	1.27000i
$187$		0			0
$188$	−6.00000			−0.437595
$189$	9.00000	+	5.19615i	0.654654	+	0.377964i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		−	1.73205i		−	0.125000i
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−8.50000	−	14.7224i	−0.610264	−	1.05701i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$		0			0
$201$	−19.5000	+	11.2583i	−1.37542	+	0.794101i
$202$	6.00000	+	10.3923i	0.422159	+	0.731200i
$203$	−6.00000	−	10.3923i	−0.421117	−	0.729397i
$204$	−9.00000	+	5.19615i	−0.630126	+	0.363803i
$205$		0			0
$206$	2.00000			0.139347
$207$		0			0
$208$	4.00000			0.277350
$209$		0			0
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$		−	10.3923i		−	0.712069i
$214$	−4.50000	+	7.79423i	−0.307614	+	0.532803i
$215$		0			0
$216$		−	5.19615i		−	0.353553i
$217$	20.0000			1.35769
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$		−	1.73205i		−	0.117041i
$220$		0			0
$221$	−12.0000	−	20.7846i	−0.807207	−	1.39812i
$222$	3.00000	+	1.73205i	0.201347	+	0.116248i
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	3.00000			0.199557
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$	10.5000	−	6.06218i	0.695379	−	0.401478i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$		0			0
$231$		0			0
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$	12.0000			0.784465
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	3.00000	+	1.73205i	0.194871	+	0.112509i
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	−0.378963	−	0.925412i	$-0.623719\pi$
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	0.990912	−	0.134515i	$-0.0429475\pi$
$242$	11.0000			0.707107
$243$		−	15.5885i		−	1.00000i
$244$	−4.00000			−0.256074
$245$		0			0
$246$			15.5885i			0.993884i
$247$	14.0000	+	24.2487i	0.890799	+	1.54291i
$248$	−5.00000	−	8.66025i	−0.317500	−	0.549927i
$249$	−13.5000	−	7.79423i	−0.855528	−	0.493939i
$250$		0			0
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$	6.00000			0.377964
$253$		0			0
$254$	−10.0000	+	17.3205i	−0.627456	+	1.08679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	1.50000	−	0.866025i	0.0933859	−	0.0539164i
$259$	−2.00000	+	3.46410i	−0.124274	+	0.215249i
$260$		0			0
$261$	−9.00000	+	15.5885i	−0.557086	+	0.964901i
$262$	12.0000			0.741362
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$		0			0
$265$		0			0
$266$	7.00000	+	12.1244i	0.429198	+	0.743392i
$267$		−	25.9808i		−	1.59000i
$268$	−6.50000	+	11.2583i	−0.397051	+	0.687712i
$269$	−30.0000			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$			13.8564i			0.838628i
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$		0			0
$276$		0			0
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	4.00000			0.239904
$279$	−15.0000	−	25.9808i	−0.898027	−	1.55543i
$280$		0			0
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$	−9.00000	+	5.19615i	−0.535942	+	0.309426i
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	−0.997076	−	0.0764162i	$-0.975652\pi$
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	0.432360	−	0.901701i	$-0.357681\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$		0			0
$287$	−18.0000			−1.06251
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	19.0000			1.11765
$290$		0			0
$291$	−25.5000	−	14.7224i	−1.49484	−	0.863044i
$292$	−0.500000	−	0.866025i	−0.0292603	−	0.0506803i
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	0.986341	−	0.164714i	$-0.0526703\pi$
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	−0.635818	+	0.771839i	$0.719337\pi$
$294$		−	5.19615i		−	0.303046i
$295$		0			0
$296$	2.00000			0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$		0			0
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	−2.00000	−	3.46410i	−0.115087	−	0.199337i
$303$	18.0000	+	10.3923i	1.03407	+	0.597022i
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$		0			0
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	3.00000	−	1.73205i	0.170664	−	0.0985329i
$310$		0			0
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	6.00000	−	3.46410i	0.339683	−	0.196116i
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	2.00000			0.112509
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$	−18.0000	−	10.3923i	−1.00939	−	0.582772i
$319$		0			0
$320$		0			0
$321$			15.5885i			0.870063i
$322$		0			0
$323$	−42.0000			−2.33694
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	3.50000	−	6.06218i	0.193847	−	0.335753i
$327$		−	3.46410i		−	0.191565i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	−0.976658	−	0.214799i	$-0.931090\pi$
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	0.674351	+	0.738411i	$0.264424\pi$
$332$	−9.00000			−0.493939
$333$	6.00000			0.328798
$334$	12.0000			0.656611
$335$		0			0
$336$	3.00000	−	1.73205i	0.163663	−	0.0944911i
$337$	7.00000	+	12.1244i	0.381314	+	0.660456i	0.991250	−	0.131995i	$-0.0421382\pi$
$337$	7.00000	+	12.1244i	0.381314	+	0.660456i	−0.609936	+	0.792451i	$0.708805\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$	4.50000	−	2.59808i	0.244406	−	0.141108i
$340$		0			0
$341$		0			0
$342$	10.5000	−	18.1865i	0.567775	−	0.983415i
$343$	20.0000			1.07990
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$		0			0
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$			10.3923i			0.557086i
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$		0			0
$351$	18.0000	−	10.3923i	0.960769	−	0.554700i
$352$		0			0
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	−0.594441	−	0.804139i	$-0.702627\pi$
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	0.993626	+	0.112731i	$0.0359599\pi$
$354$		−	15.5885i		−	0.828517i
$355$		0			0
$356$	−7.50000	−	12.9904i	−0.397499	−	0.688489i
$357$	−18.0000	−	10.3923i	−0.952661	−	0.550019i
$358$	−4.50000	+	7.79423i	−0.237832	+	0.411938i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$	−8.00000	+	13.8564i	−0.420471	+	0.728277i
$363$	16.5000	−	9.52628i	0.866025	−	0.500000i
$364$	4.00000	+	6.92820i	0.209657	+	0.363137i
$365$		0			0
$366$	−6.00000	+	3.46410i	−0.313625	+	0.181071i
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	−0.966507	−	0.256639i	$-0.917385\pi$
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	0.705509	+	0.708700i	$0.250718\pi$
$368$		0			0
$369$	13.5000	+	23.3827i	0.702782	+	1.21725i
$370$		0			0
$371$	12.0000	−	20.7846i	0.623009	−	1.07908i
$372$	−15.0000	−	8.66025i	−0.777714	−	0.449013i
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	−24.0000			−1.23606
$378$	9.00000	−	5.19615i	0.462910	−	0.267261i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$			34.6410i			1.77471i
$382$	3.00000	+	5.19615i	0.153493	+	0.265858i
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$		0			0
$386$	2.00000			0.101797
$387$	1.50000	−	2.59808i	0.0762493	−	0.132068i
$388$	−17.0000			−0.863044
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$	18.0000	−	10.3923i	0.907980	−	0.524222i
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$		0			0
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	−8.00000	+	13.8564i	−0.401004	+	0.694559i
$399$	21.0000	+	12.1244i	1.05131	+	0.606977i
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$			22.5167i			1.12303i
$403$	20.0000	−	34.6410i	0.996271	−	1.72559i
$404$	12.0000			0.597022
$405$		0			0
$406$	−12.0000			−0.595550
$407$		0			0
$408$			10.3923i			0.514496i
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	0.939490	+	0.342578i	$0.111300\pi$
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	−0.173064	+	0.984911i	$0.555367\pi$
$410$		0			0
$411$	4.50000	+	2.59808i	0.221969	+	0.128154i
$412$	1.00000	−	1.73205i	0.0492665	−	0.0853320i
$413$	18.0000			0.885722
$414$		0			0
$415$		0			0
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$	6.00000	−	3.46410i	0.293821	−	0.169638i
$418$		0			0
$419$	−1.50000	−	2.59808i	−0.0732798	−	0.126924i	0.827057	−	0.562118i	$-0.190013\pi$
$419$	−1.50000	−	2.59808i	−0.0732798	−	0.126924i	−0.900337	+	0.435194i	$0.856680\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	−5.00000			−0.243396
$423$	−9.00000	+	15.5885i	−0.437595	+	0.757937i
$424$	−12.0000			−0.582772
$425$		0			0
$426$	−9.00000	−	5.19615i	−0.436051	−	0.251754i
$427$	−4.00000	−	6.92820i	−0.193574	−	0.335279i
$428$	4.50000	+	7.79423i	0.217516	+	0.376748i
$429$		0			0
$430$		0			0
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	10.0000	−	17.3205i	0.480015	−	0.831411i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$		0			0
$438$	−1.50000	−	0.866025i	−0.0716728	−	0.0413803i
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$	−24.0000			−1.14156
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$	3.00000	−	1.73205i	0.142374	−	0.0821995i
$445$		0			0
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$	9.00000	−	5.19615i	0.425685	−	0.245770i
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$		0			0
$451$		0			0
$452$	1.50000	−	2.59808i	0.0705541	−	0.122203i
$453$	−6.00000	−	3.46410i	−0.281905	−	0.162758i
$454$	7.50000	+	12.9904i	0.351992	+	0.609669i
$455$		0			0
$456$		−	12.1244i		−	0.567775i
$457$	−9.50000	+	16.4545i	−0.444391	+	0.769708i	−0.998010	−	0.0630623i	$-0.979913\pi$
$457$	−9.50000	+	16.4545i	−0.444391	+	0.769708i	0.553618	+	0.832771i	$0.313247\pi$
$458$	10.0000			0.467269
$459$			31.1769i			1.45521i
$460$		0			0
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	−0.927392	−	0.374091i	$-0.877955\pi$
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	0.787668	+	0.616100i	$0.211288\pi$
$462$		0			0
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	0.992183	+	0.124788i	$0.0398251\pi$
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	−0.388022	+	0.921650i	$0.626842\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−1.50000	+	2.59808i	−0.0694862	+	0.120354i
$467$	15.0000			0.694117			0.347059	−	0.937843i	$-0.387180\pi$
$467$	15.0000			0.694117			0.347059	+	0.937843i	$0.387180\pi$
$468$	6.00000	−	10.3923i	0.277350	−	0.480384i
$469$	−26.0000			−1.20057
$470$		0			0
$471$	21.0000	−	12.1244i	0.967629	−	0.558661i
$472$	−4.50000	−	7.79423i	−0.207129	−	0.358758i
$473$		0			0
$474$	3.00000	−	1.73205i	0.137795	−	0.0795557i
$475$		0			0
$476$	−12.0000			−0.550019
$477$	−36.0000			−1.64833
$478$		0			0
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	−9.50000	−	16.4545i	−0.432713	−	0.749481i
$483$		0			0
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$		0			0
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−2.00000	+	3.46410i	−0.0905357	+	0.156813i
$489$		−	12.1244i		−	0.548282i
$490$		0			0
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	0.897886	−	0.440228i	$-0.145102\pi$
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	−0.830192	+	0.557478i	$0.811769\pi$
$492$	13.5000	+	7.79423i	0.608627	+	0.351391i
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$	28.0000			1.25978
$495$		0			0
$496$	−10.0000			−0.449013
$497$	6.00000	−	10.3923i	0.269137	−	0.466159i
$498$	−13.5000	+	7.79423i	−0.604949	+	0.349268i
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	0.716258	−	0.697835i	$-0.245853\pi$
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	−0.962472	+	0.271380i	$0.912520\pi$
$500$		0			0
$501$	18.0000	−	10.3923i	0.804181	−	0.464294i
$502$	7.50000	−	12.9904i	0.334741	−	0.579789i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$		0			0
$506$		0			0
$507$	4.50000	+	2.59808i	0.199852	+	0.115385i
$508$	10.0000	+	17.3205i	0.443678	+	0.768473i
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	0.921023	+	0.389509i	$0.127355\pi$
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	−0.123187	+	0.992384i	$0.539311\pi$
$510$		0			0
$511$	1.00000	−	1.73205i	0.0442374	−	0.0766214i
$512$	−1.00000			−0.0441942
$513$		−	36.3731i		−	1.60591i
$514$	3.00000			0.132324
$515$		0			0
$516$		−	1.73205i		−	0.0762493i
$517$		0			0
$518$	2.00000	+	3.46410i	0.0878750	+	0.152204i
$519$	18.0000	+	10.3923i	0.790112	+	0.456172i
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	1.00000			0.0437269			0.0218635	−	0.999761i	$-0.493040\pi$
$523$	1.00000			0.0437269			0.0218635	+	0.999761i	$0.493040\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$		0			0
$526$	3.00000	+	5.19615i	0.130806	+	0.226563i
$527$	30.0000	+	51.9615i	1.30682	+	2.26348i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	−13.5000	−	23.3827i	−0.585850	−	1.01472i
$532$	14.0000			0.606977
$533$	−18.0000	+	31.1769i	−0.779667	+	1.35042i
$534$	−22.5000	−	12.9904i	−0.973670	−	0.562149i
$535$		0			0
$536$	6.50000	+	11.2583i	0.280757	+	0.486286i
$537$			15.5885i			0.672692i
$538$	−15.0000	+	25.9808i	−0.646696	+	1.12011i
$539$		0			0
$540$		0			0
$541$	32.0000			1.37579			0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000			1.37579			0.687894	+	0.725811i	$0.258536\pi$
$542$	−14.0000	+	24.2487i	−0.601351	+	1.04157i
$543$			27.7128i			1.18927i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$		0			0
$546$	12.0000	+	6.92820i	0.513553	+	0.296500i
$547$	2.50000	−	4.33013i	0.106892	−	0.185143i	−0.807617	−	0.589707i	$-0.799243\pi$
$547$	2.50000	−	4.33013i	0.106892	−	0.185143i	0.914510	+	0.404564i	$0.132577\pi$
$548$	3.00000			0.128154
$549$	−6.00000	+	10.3923i	−0.256074	+	0.443533i
$550$		0			0
$551$	−21.0000	+	36.3731i	−0.894630	+	1.54954i
$552$		0			0
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$	−30.0000			−1.27000
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	−9.00000	−	15.5885i	−0.379642	−	0.657559i
$563$	4.50000	+	7.79423i	0.189652	+	0.328488i	0.945134	−	0.326682i	$-0.105931\pi$
$563$	4.50000	+	7.79423i	0.189652	+	0.328488i	−0.755482	+	0.655169i	$0.772597\pi$
$564$			10.3923i			0.437595i
$565$		0			0
$566$	−19.0000			−0.798630
$567$	9.00000	−	15.5885i	0.377964	−	0.654654i
$568$	−6.00000			−0.251754
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.850935	−	0.525271i	$-0.176036\pi$
$570$		0			0
$571$	−17.5000	−	30.3109i	−0.732352	−	1.26847i	−0.955875	−	0.293773i	$-0.905089\pi$
$571$	−17.5000	−	30.3109i	−0.732352	−	1.26847i	0.223523	−	0.974699i	$-0.428244\pi$
$572$		0			0
$573$	9.00000	+	5.19615i	0.375980	+	0.217072i
$574$	−9.00000	+	15.5885i	−0.375653	+	0.650650i
$575$		0			0
$576$	−3.00000			−0.125000
$577$	−35.0000			−1.45707			−0.728535	−	0.685009i	$-0.759798\pi$
$577$	−35.0000			−1.45707			−0.728535	+	0.685009i	$0.759798\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	3.00000	−	1.73205i	0.124676	−	0.0719816i
$580$		0			0
$581$	−9.00000	−	15.5885i	−0.373383	−	0.646718i
$582$	−25.5000	+	14.7224i	−1.05701	+	0.610264i
$583$		0			0
$584$	−1.00000			−0.0413803
$585$		0			0
$586$	12.0000			0.495715
$587$	18.0000	−	31.1769i	0.742940	−	1.28681i	−0.208212	−	0.978084i	$-0.566764\pi$
$587$	18.0000	−	31.1769i	0.742940	−	1.28681i	0.951151	−	0.308725i	$-0.0999023\pi$
$588$	−4.50000	−	2.59808i	−0.185577	−	0.107143i
$589$	−35.0000	−	60.6218i	−1.44215	−	2.49788i
$590$		0			0
$591$			31.1769i			1.28245i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	9.00000			0.369586			0.184793	−	0.982777i	$-0.440839\pi$
$593$	9.00000			0.369586			0.184793	+	0.982777i	$0.440839\pi$
$594$		0			0
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$			27.7128i			1.13421i
$598$		0			0
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	−0.745845	−	0.666120i	$-0.767954\pi$
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	0.949799	+	0.312861i	$0.101287\pi$
$602$	2.00000			0.0815139
$603$	19.5000	+	33.7750i	0.794101	+	1.37542i
$604$	−4.00000			−0.162758
$605$		0			0
$606$	18.0000	−	10.3923i	0.731200	−	0.422159i
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	−0.911621	−	0.411033i	$-0.865168\pi$
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	0.0998457	−	0.995003i	$-0.468165\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$	−18.0000	+	10.3923i	−0.729397	+	0.421117i
$610$		0			0
$611$	−24.0000			−0.970936
$612$	9.00000	+	15.5885i	0.363803	+	0.630126i
$613$	−44.0000			−1.77714			−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000			−1.77714			−0.888572	+	0.458738i	$0.848302\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$		0			0
$616$		0			0
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	0.761114	−	0.648618i	$-0.224653\pi$
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	−0.942277	+	0.334835i	$0.891320\pi$
$618$		−	3.46410i		−	0.139347i
$619$	−11.5000	+	19.9186i	−0.462224	+	0.800595i	−0.999071	−	0.0430838i	$-0.986282\pi$
$619$	−11.5000	+	19.9186i	−0.462224	+	0.800595i	0.536847	+	0.843679i	$0.319615\pi$
$620$		0			0
$621$		0			0
$622$	30.0000			1.20289
$623$	15.0000	−	25.9808i	0.600962	−	1.04090i
$624$		−	6.92820i		−	0.277350i
$625$		0			0
$626$	9.50000	+	16.4545i	0.379696	+	0.657653i
$627$		0			0
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	1.00000	−	1.73205i	0.0397779	−	0.0688973i
$633$	−7.50000	+	4.33013i	−0.298098	+	0.172107i
$634$	−15.0000	−	25.9808i	−0.595726	−	1.03183i
$635$		0			0
$636$	−18.0000	+	10.3923i	−0.713746	+	0.412082i
$637$	6.00000	−	10.3923i	0.237729	−	0.411758i
$638$		0			0
$639$	−18.0000			−0.712069
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$	13.5000	+	7.79423i	0.532803	+	0.307614i
$643$	−6.50000	−	11.2583i	−0.256335	−	0.443985i	0.708922	−	0.705287i	$-0.249182\pi$
$643$	−6.50000	−	11.2583i	−0.256335	−	0.443985i	−0.965257	+	0.261301i	$0.915848\pi$
$644$		0			0
$645$		0			0
$646$	−21.0000	+	36.3731i	−0.826234	+	1.43108i
$647$	48.0000			1.88707			0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000			1.88707			0.943537	+	0.331266i	$0.107476\pi$
$648$	−9.00000			−0.353553
$649$		0			0
$650$		0			0
$651$		−	34.6410i		−	1.35769i
$652$	−3.50000	−	6.06218i	−0.137071	−	0.237413i
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	−0.966910	−	0.255119i	$-0.917885\pi$
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	0.262515	−	0.964928i	$-0.415448\pi$
$654$	−3.00000	−	1.73205i	−0.117309	−	0.0677285i
$655$		0			0
$656$	9.00000			0.351391
$657$	−3.00000			−0.117041
$658$	−12.0000			−0.467809
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	0.342068	+	0.939675i	$0.388873\pi$
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	−0.984817	+	0.173598i	$0.944461\pi$
$660$		0			0
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	0.845922	−	0.533306i	$-0.179051\pi$
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	−0.884818	+	0.465937i	$0.845717\pi$
$662$	5.50000	+	9.52628i	0.213764	+	0.370249i
$663$	−36.0000	+	20.7846i	−1.39812	+	0.807207i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$		0			0
$666$	3.00000	−	5.19615i	0.116248	−	0.201347i
$667$		0			0
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	24.0000	+	13.8564i	0.927894	+	0.535720i
$670$		0			0
$671$		0			0
$672$		−	3.46410i		−	0.133631i
$673$	1.00000	−	1.73205i	0.0385472	−	0.0667657i	−0.846108	−	0.533011i	$-0.821060\pi$
$673$	1.00000	−	1.73205i	0.0385472	−	0.0667657i	0.884655	+	0.466246i	$0.154394\pi$
$674$	14.0000			0.539260
$675$		0			0
$676$	3.00000			0.115385
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	−0.957984	−	0.286820i	$-0.907402\pi$
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	0.727386	+	0.686229i	$0.240735\pi$
$678$		−	5.19615i		−	0.199557i
$679$	−17.0000	−	29.4449i	−0.652400	−	1.12999i
$680$		0			0
$681$	22.5000	+	12.9904i	0.862202	+	0.497792i
$682$		0			0
$683$	3.00000			0.114792			0.0573959	−	0.998351i	$-0.481720\pi$
$683$	3.00000			0.114792			0.0573959	+	0.998351i	$0.481720\pi$
$684$	−10.5000	−	18.1865i	−0.401478	−	0.695379i
$685$		0			0
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	15.0000	−	8.66025i	0.572286	−	0.330409i
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	−24.0000	−	41.5692i	−0.914327	−	1.58366i
$690$		0			0
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	0.313355	+	0.949636i	$0.398547\pi$
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	−0.979086	+	0.203445i	$0.934786\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$	−27.0000	−	46.7654i	−1.02270	−	1.77136i
$698$	−5.00000	−	8.66025i	−0.189253	−	0.327795i
$699$			5.19615i			0.196537i
$700$		0			0
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$		−	20.7846i		−	0.784465i
$703$	14.0000			0.528020
$704$		0			0
$705$		0			0
$706$	−7.50000	−	12.9904i	−0.282266	−	0.488899i
$707$	12.0000	+	20.7846i	0.451306	+	0.781686i
$708$	−13.5000	−	7.79423i	−0.507361	−	0.292925i
$709$	14.0000	−	24.2487i	0.525781	−	0.910679i	−0.473768	−	0.880650i	$-0.657106\pi$
$709$	14.0000	−	24.2487i	0.525781	−	0.910679i	0.999549	−	0.0300298i	$-0.00956021\pi$
$710$		0			0
$711$	3.00000	−	5.19615i	0.112509	−	0.194871i
$712$	−15.0000			−0.562149
$713$		0			0
$714$	−18.0000	+	10.3923i	−0.673633	+	0.388922i
$715$		0			0
$716$	4.50000	+	7.79423i	0.168173	+	0.291284i
$717$		0			0
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	18.0000			0.671287			0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000			0.671287			0.335643	+	0.941989i	$0.391046\pi$
$720$		0			0
$721$	4.00000			0.148968
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$	−28.5000	−	16.4545i	−1.05993	−	0.611949i
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$		0			0
$726$		−	19.0526i		−	0.707107i
$727$	−20.0000	+	34.6410i	−0.741759	+	1.28476i	0.209935	+	0.977715i	$0.432675\pi$
$727$	−20.0000	+	34.6410i	−0.741759	+	1.28476i	−0.951694	+	0.307049i	$0.900659\pi$
$728$	8.00000			0.296500
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$			6.92820i			0.256074i
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	5.00000	+	8.66025i	0.184553	+	0.319656i
$735$		0			0
$736$		0			0
$737$		0			0
$738$	27.0000			0.993884
$739$	−25.0000			−0.919640			−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000			−0.919640			−0.459820	+	0.888012i	$0.652086\pi$
$740$		0			0
$741$	42.0000	−	24.2487i	1.54291	−	0.890799i
$742$	−12.0000	−	20.7846i	−0.440534	−	0.763027i
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$	−15.0000	+	8.66025i	−0.549927	+	0.317500i
$745$		0			0
$746$	−4.00000			−0.146450
$747$	−13.5000	+	23.3827i	−0.493939	+	0.855528i
$748$		0			0
$749$	−9.00000	+	15.5885i	−0.328853	+	0.569590i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		−	25.9808i		−	0.946792i
$754$	−12.0000	+	20.7846i	−0.437014	+	0.756931i
$755$		0			0
$756$		−	10.3923i		−	0.377964i
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	10.0000	−	17.3205i	0.363216	−	0.629109i
$759$		0			0
$760$		0			0
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	0.610527	−	0.791995i	$-0.290958\pi$
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	−0.991152	+	0.132734i	$0.957624\pi$
$762$	30.0000	+	17.3205i	1.08679	+	0.627456i
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	6.00000			0.217072
$765$		0			0
$766$	24.0000			0.867155
$767$	18.0000	−	31.1769i	0.649942	−	1.12573i
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$		0			0
$771$	4.50000	−	2.59808i	0.162064	−	0.0935674i
$772$	1.00000	−	1.73205i	0.0359908	−	0.0623379i
$773$	−6.00000			−0.215805			−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$	−1.50000	−	2.59808i	−0.0539164	−	0.0933859i
$775$		0			0
$776$	−8.50000	+	14.7224i	−0.305132	+	0.528505i
$777$	6.00000	+	3.46410i	0.215249	+	0.124274i
$778$	3.00000	+	5.19615i	0.107555	+	0.186291i
$779$	31.5000	+	54.5596i	1.12860	+	1.95480i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	−3.00000			−0.107143
$785$		0			0
$786$		−	20.7846i		−	0.741362i
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$	9.00000	+	5.19615i	0.320408	+	0.184988i
$790$		0			0
$791$	6.00000			0.213335
$792$		0			0
$793$	−16.0000			−0.568177
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−18.0000	−	31.1769i	−0.637593	−	1.10434i	−0.985959	−	0.166985i	$-0.946597\pi$
$797$	−18.0000	−	31.1769i	−0.637593	−	1.10434i	0.348367	−	0.937358i	$-0.386736\pi$
$798$	21.0000	−	12.1244i	0.743392	−	0.429198i
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$		0			0
$801$	−45.0000			−1.59000
$802$	−18.0000			−0.635602
$803$		0			0
$804$	19.5000	+	11.2583i	0.687712	+	0.397051i
$805$		0			0
$806$	−20.0000	−	34.6410i	−0.704470	−	1.22018i
$807$			51.9615i			1.82913i
$808$	6.00000	−	10.3923i	0.211079	−	0.365600i
$809$	−39.0000			−1.37117			−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000			−1.37117			−0.685583	+	0.727994i	$0.740453\pi$
$810$		0			0
$811$	5.00000			0.175574			0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000			0.175574			0.0877869	+	0.996139i	$0.472021\pi$
$812$	−6.00000	+	10.3923i	−0.210559	+	0.364698i
$813$			48.4974i			1.70088i
$814$		0			0
$815$		0			0
$816$	9.00000	+	5.19615i	0.315063	+	0.181902i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	31.0000			1.08389
$819$	24.0000			0.838628
$820$		0			0
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	−0.577016	−	0.816733i	$-0.695783\pi$
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	0.995819	+	0.0913446i	$0.0291165\pi$
$822$	4.50000	−	2.59808i	0.156956	−	0.0906183i
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	0.961851	−	0.273573i	$-0.0882054\pi$
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	−0.717847	+	0.696201i	$0.754872\pi$
$824$	−1.00000	−	1.73205i	−0.0348367	−	0.0603388i
$825$		0			0
$826$	9.00000	−	15.5885i	0.313150	−	0.542392i
$827$	27.0000			0.938882			0.469441	−	0.882964i	$-0.344455\pi$
$827$	27.0000			0.938882			0.469441	+	0.882964i	$0.344455\pi$
$828$		0			0
$829$	32.0000			1.11141			0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000			1.11141			0.555703	+	0.831381i	$0.312449\pi$
$830$		0			0
$831$	−3.00000	−	1.73205i	−0.104069	−	0.0600842i
$832$	−2.00000	−	3.46410i	−0.0693375	−	0.120096i
$833$	9.00000	+	15.5885i	0.311832	+	0.540108i
$834$		−	6.92820i		−	0.239904i
$835$		0			0
$836$		0			0
$837$	−45.0000	+	25.9808i	−1.55543	+	0.898027i
$838$	−3.00000			−0.103633
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	−0.233973	−	0.972243i	$-0.575173\pi$
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	0.958974	−	0.283495i	$-0.0914938\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$	−27.0000	−	15.5885i	−0.929929	−	0.536895i
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$		0			0
$846$	9.00000	+	15.5885i	0.309426	+	0.535942i
$847$	22.0000			0.755929
$848$	−6.00000	+	10.3923i	−0.206041	+	0.356873i
$849$	−28.5000	+	16.4545i	−0.978117	+	0.564716i
$850$		0			0
$851$		0			0
$852$	−9.00000	+	5.19615i	−0.308335	+	0.178017i
$853$	−5.00000	+	8.66025i	−0.171197	+	0.296521i	−0.938839	−	0.344358i	$-0.888097\pi$
$853$	−5.00000	+	8.66025i	−0.171197	+	0.296521i	0.767642	+	0.640879i	$0.221430\pi$
$854$	−8.00000			−0.273754
$855$		0			0
$856$	9.00000			0.307614
$857$	−19.5000	+	33.7750i	−0.666107	+	1.15373i	0.312877	+	0.949794i	$0.398707\pi$
$857$	−19.5000	+	33.7750i	−0.666107	+	1.15373i	−0.978984	+	0.203938i	$0.934626\pi$
$858$		0			0
$859$	15.5000	+	26.8468i	0.528853	+	0.916001i	0.999434	+	0.0336436i	$0.0107111\pi$
$859$	15.5000	+	26.8468i	0.528853	+	0.916001i	−0.470581	+	0.882357i	$0.655956\pi$
$860$		0			0
$861$			31.1769i			1.06251i
$862$	3.00000	−	5.19615i	0.102180	−	0.176982i
$863$	−12.0000			−0.408485			−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000			−0.408485			−0.204242	+	0.978920i	$0.565473\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$		0			0
$866$	−1.00000	+	1.73205i	−0.0339814	+	0.0588575i
$867$		−	32.9090i		−	1.11765i
$868$	−10.0000	−	17.3205i	−0.339422	−	0.587896i
$869$		0			0
$870$		0			0
$871$	−26.0000	+	45.0333i	−0.880976	+	1.52590i
$872$	−2.00000			−0.0677285
$873$	−25.5000	+	44.1673i	−0.863044	+	1.49484i
$874$		0			0
$875$		0			0
$876$	−1.50000	+	0.866025i	−0.0506803	+	0.0292603i
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	0.769174	−	0.639040i	$-0.220668\pi$
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	−0.938012	+	0.346604i	$0.887335\pi$
$878$	−2.00000	−	3.46410i	−0.0674967	−	0.116908i
$879$	18.0000	−	10.3923i	0.607125	−	0.350524i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	−9.00000			−0.303046
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	0.911986	−	0.410222i	$-0.134549\pi$
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	−0.811256	+	0.584692i	$0.801215\pi$
$888$		−	3.46410i		−	0.116248i
$889$	−20.0000	+	34.6410i	−0.670778	+	1.16182i
$890$		0			0
$891$		0			0
$892$	16.0000			0.535720
$893$	−21.0000	+	36.3731i	−0.702738	+	1.21718i
$894$		−	10.3923i		−	0.347571i
$895$		0			0
$896$	−1.00000	−	1.73205i	−0.0334077	−	0.0578638i
$897$		0			0
$898$	−7.50000	+	12.9904i	−0.250278	+	0.433495i
$899$	60.0000			2.00111
$900$		0			0
$901$	72.0000			2.39867
$902$		0			0
$903$	3.00000	−	1.73205i	0.0998337	−	0.0576390i
$904$	−1.50000	−	2.59808i	−0.0498893	−	0.0864107i
$905$		0			0
$906$	−6.00000	+	3.46410i	−0.199337	+	0.115087i
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$	15.0000			0.497792
$909$	18.0000	−	31.1769i	0.597022	−	1.03407i
$910$		0			0
$911$	−6.00000	+	10.3923i	−0.198789	+	0.344312i	−0.948136	−	0.317865i	$-0.897034\pi$
$911$	−6.00000	+	10.3923i	−0.198789	+	0.344312i	0.749347	+	0.662177i	$0.230367\pi$
$912$	−10.5000	−	6.06218i	−0.347690	−	0.200739i
$913$		0			0
$914$	9.50000	+	16.4545i	0.314232	+	0.544266i
$915$		0			0
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	24.0000			0.792550
$918$	27.0000	+	15.5885i	0.891133	+	0.514496i
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$		0			0
$921$			13.8564i			0.456584i
$922$	3.00000	+	5.19615i	0.0987997	+	0.171126i
$923$	−12.0000	−	20.7846i	−0.394985	−	0.684134i
$924$		0			0
$925$		0			0
$926$	26.0000			0.854413
$927$	−3.00000	−	5.19615i	−0.0985329	−	0.170664i
$928$	6.00000			0.196960
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.0410949	−	0.999155i	$-0.486915\pi$
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.844746	−	0.535167i	$-0.179751\pi$
$930$		0			0
$931$	−10.5000	−	18.1865i	−0.344124	−	0.596040i
$932$	1.50000	+	2.59808i	0.0491341	+	0.0851028i
$933$	45.0000	−	25.9808i	1.47323	−	0.850572i
$934$	7.50000	−	12.9904i	0.245407	−	0.425058i
$935$		0			0
$936$	−6.00000	−	10.3923i	−0.196116	−	0.339683i
$937$	−23.0000			−0.751377			−0.375689	−	0.926746i	$-0.622594\pi$
$937$	−23.0000			−0.751377			−0.375689	+	0.926746i	$0.622594\pi$
$938$	−13.0000	+	22.5167i	−0.424465	+	0.735195i
$939$	28.5000	+	16.4545i	0.930062	+	0.536972i
$940$		0			0
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$		−	24.2487i		−	0.790066i
$943$		0			0
$944$	−9.00000			−0.292925
$945$		0			0
$946$		0			0
$947$	−10.5000	+	18.1865i	−0.341204	+	0.590983i	−0.984657	−	0.174503i	$-0.944168\pi$
$947$	−10.5000	+	18.1865i	−0.341204	+	0.590983i	0.643452	+	0.765486i	$0.277501\pi$
$948$		−	3.46410i		−	0.112509i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	−45.0000	−	25.9808i	−1.45922	−	0.842484i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$	−18.0000	+	31.1769i	−0.582772	+	1.00939i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	18.0000	+	31.1769i	0.581554	+	1.00728i
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	8.00000			0.257930
$963$	27.0000			0.870063
$964$	−19.0000			−0.611949
$965$		0			0
$966$		0			0
$967$	10.0000	+	17.3205i	0.321578	+	0.556990i	0.980814	−	0.194946i	$-0.0624533\pi$
$967$	10.0000	+	17.3205i	0.321578	+	0.556990i	−0.659236	+	0.751936i	$0.729120\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$			72.7461i			2.33694i
$970$		0			0
$971$	−21.0000			−0.673922			−0.336961	−	0.941519i	$-0.609399\pi$
$971$	−21.0000			−0.673922			−0.336961	+	0.941519i	$0.609399\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	8.00000			0.256468
$974$	−1.00000	+	1.73205i	−0.0320421	+	0.0554985i
$975$		0			0
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	−7.50000	−	12.9904i	−0.239946	−	0.415599i	0.720752	−	0.693193i	$-0.243796\pi$
$977$	−7.50000	−	12.9904i	−0.239946	−	0.415599i	−0.960699	+	0.277594i	$0.910463\pi$
$978$	−10.5000	−	6.06218i	−0.335753	−	0.193847i
$979$		0			0
$980$		0			0
$981$	−6.00000			−0.191565
$982$	3.00000			0.0957338
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	−0.999694	−	0.0247352i	$-0.992126\pi$
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	0.521268	+	0.853393i	$0.325459\pi$
$984$	13.5000	−	7.79423i	0.430364	−	0.248471i
$985$		0			0
$986$	−18.0000	−	31.1769i	−0.573237	−	0.992875i
$987$	−18.0000	+	10.3923i	−0.572946	+	0.330791i
$988$	14.0000	−	24.2487i	0.445399	−	0.771454i
$989$		0			0
$990$		0			0
$991$	44.0000			1.39771			0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000			1.39771			0.698853	+	0.715265i	$0.253694\pi$
$992$	−5.00000	+	8.66025i	−0.158750	+	0.274963i
$993$	16.5000	+	9.52628i	0.523612	+	0.302307i
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$		0			0
$996$			15.5885i			0.493939i
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	−0.997938	−	0.0641836i	$-0.979556\pi$
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	0.554554	+	0.832148i	$0.312889\pi$
$998$	−11.0000			−0.348199
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.e.f.151.1	yes	2
3.2	odd	2		1350.2.e.d.451.1		2
5.2	odd	4		450.2.j.b.349.2		4
5.3	odd	4		450.2.j.b.349.1		4
5.4	even	2		450.2.e.c.151.1	✓	2
9.2	odd	6		4050.2.a.u.1.1		1
9.4	even	3	inner	450.2.e.f.301.1	yes	2
9.5	odd	6		1350.2.e.d.901.1		2
9.7	even	3		4050.2.a.d.1.1		1
15.2	even	4		1350.2.j.b.1099.1		4
15.8	even	4		1350.2.j.b.1099.2		4
15.14	odd	2		1350.2.e.h.451.1		2
45.2	even	12		4050.2.c.m.649.2		2
45.4	even	6		450.2.e.c.301.1	yes	2
45.7	odd	12		4050.2.c.h.649.1		2
45.13	odd	12		450.2.j.b.49.2		4
45.14	odd	6		1350.2.e.h.901.1		2
45.22	odd	12		450.2.j.b.49.1		4
45.23	even	12		1350.2.j.b.199.1		4
45.29	odd	6		4050.2.a.o.1.1		1
45.32	even	12		1350.2.j.b.199.2		4
45.34	even	6		4050.2.a.bg.1.1		1
45.38	even	12		4050.2.c.m.649.1		2
45.43	odd	12		4050.2.c.h.649.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.e.c.151.1	✓	2	5.4	even	2
450.2.e.c.301.1	yes	2	45.4	even	6
450.2.e.f.151.1	yes	2	1.1	even	1	trivial
450.2.e.f.301.1	yes	2	9.4	even	3	inner
450.2.j.b.49.1		4	45.22	odd	12
450.2.j.b.49.2		4	45.13	odd	12
450.2.j.b.349.1		4	5.3	odd	4
450.2.j.b.349.2		4	5.2	odd	4
1350.2.e.d.451.1		2	3.2	odd	2
1350.2.e.d.901.1		2	9.5	odd	6
1350.2.e.h.451.1		2	15.14	odd	2
1350.2.e.h.901.1		2	45.14	odd	6
1350.2.j.b.199.1		4	45.23	even	12
1350.2.j.b.199.2		4	45.32	even	12
1350.2.j.b.1099.1		4	15.2	even	4
1350.2.j.b.1099.2		4	15.8	even	4
4050.2.a.d.1.1		1	9.7	even	3
4050.2.a.o.1.1		1	45.29	odd	6
4050.2.a.u.1.1		1	9.2	odd	6
4050.2.a.bg.1.1		1	45.34	even	6
4050.2.c.h.649.1		2	45.7	odd	12
4050.2.c.h.649.2		2	45.43	odd	12
4050.2.c.m.649.1		2	45.38	even	12
4050.2.c.m.649.2		2	45.2	even	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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(-1.50000 + 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} -7.00000 q^{19} +(-3.00000 - 1.73205i) q^{21} +1.73205i q^{24} -4.00000 q^{26} +5.19615i q^{27} -2.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(5.00000 + 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{34} +(1.50000 + 2.59808i) q^{36} -2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +(-6.00000 + 3.46410i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(-3.00000 + 1.73205i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{47} +(1.50000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} -10.3923i q^{51} +(-2.00000 + 3.46410i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +(-1.00000 + 1.73205i) q^{56} +12.1244i q^{57} +(-3.00000 - 5.19615i) q^{58} +(4.50000 + 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +10.0000 q^{62} +(-3.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(-6.50000 - 11.2583i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{71} +3.00000 q^{72} +1.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +6.92820i q^{78} +(-1.00000 + 1.73205i) q^{79} +9.00000 q^{81} -9.00000 q^{82} +(4.50000 - 7.79423i) q^{83} +3.46410i q^{84} +(0.500000 + 0.866025i) q^{86} +(-9.00000 - 5.19615i) q^{87} +15.0000 q^{89} -8.00000 q^{91} +(15.0000 - 8.66025i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(1.50000 - 0.866025i) q^{96} +(8.50000 - 14.7224i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 3 q^{6} + 2 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^4 - 3 * q^6 + 2 * q^7 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} - q^{4} - 3 q^{6} + 2 q^{7} - 2 q^{8} - 6 q^{9} - 3 q^{12} - 4 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 3 q^{18} - 14 q^{19} - 6 q^{21} - 8 q^{26} - 4 q^{28} + 6 q^{29} + 10 q^{31} + q^{32} + 6 q^{34} + 3 q^{36} - 4 q^{37} - 7 q^{38} - 12 q^{39} - 9 q^{41} - 6 q^{42} - q^{43} + 6 q^{47} + 3 q^{48} + 3 q^{49} - 4 q^{52} + 24 q^{53} + 9 q^{54} - 2 q^{56} - 6 q^{58} + 9 q^{59} + 4 q^{61} + 20 q^{62} - 6 q^{63} + 2 q^{64} - 13 q^{67} - 6 q^{68} + 12 q^{71} + 6 q^{72} + 2 q^{73} - 2 q^{74} + 7 q^{76} - 2 q^{79} + 18 q^{81} - 18 q^{82} + 9 q^{83} + q^{86} - 18 q^{87} + 30 q^{89} - 16 q^{91} + 30 q^{93} - 6 q^{94} + 3 q^{96} + 17 q^{97} + 6 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 3 * q^6 + 2 * q^7 - 2 * q^8 - 6 * q^9 - 3 * q^12 - 4 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 3 * q^18 - 14 * q^19 - 6 * q^21 - 8 * q^26 - 4 * q^28 + 6 * q^29 + 10 * q^31 + q^32 + 6 * q^34 + 3 * q^36 - 4 * q^37 - 7 * q^38 - 12 * q^39 - 9 * q^41 - 6 * q^42 - q^43 + 6 * q^47 + 3 * q^48 + 3 * q^49 - 4 * q^52 + 24 * q^53 + 9 * q^54 - 2 * q^56 - 6 * q^58 + 9 * q^59 + 4 * q^61 + 20 * q^62 - 6 * q^63 + 2 * q^64 - 13 * q^67 - 6 * q^68 + 12 * q^71 + 6 * q^72 + 2 * q^73 - 2 * q^74 + 7 * q^76 - 2 * q^79 + 18 * q^81 - 18 * q^82 + 9 * q^83 + q^86 - 18 * q^87 + 30 * q^89 - 16 * q^91 + 30 * q^93 - 6 * q^94 + 3 * q^96 + 17 * q^97 + 6 * q^98

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