LMFDB - Embedded newform 450.2.e.g.301.1

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:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	450.301
Dual form			450.2.e.g.151.1

$q$-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} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.00000 + 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(-3.00000 + 5.19615i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} +6.00000 q^{19} -1.73205i q^{21} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-1.50000 - 0.866025i) q^{24} -6.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(-4.50000 - 7.79423i) q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +3.46410i q^{33} +(1.00000 + 1.73205i) q^{34} -3.00000 q^{36} -2.00000 q^{37} +(3.00000 + 5.19615i) q^{38} +(-9.00000 + 5.19615i) q^{39} +(5.50000 - 9.52628i) q^{41} +(1.50000 - 0.866025i) q^{42} +(-2.00000 - 3.46410i) q^{43} -2.00000 q^{44} +1.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} -1.73205i q^{48} +(3.00000 - 5.19615i) q^{49} +(3.00000 + 1.73205i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(-4.50000 + 2.59808i) q^{54} +(0.500000 + 0.866025i) q^{56} +(9.00000 + 5.19615i) q^{57} +(4.50000 - 7.79423i) q^{58} +(2.00000 - 3.46410i) q^{59} +(3.50000 + 6.06218i) q^{61} +2.00000 q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 1.73205i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(1.50000 - 0.866025i) q^{69} -6.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +4.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(1.00000 - 1.73205i) q^{77} +(-9.00000 - 5.19615i) q^{78} +(6.00000 + 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +11.0000 q^{82} +(-5.50000 - 9.52628i) q^{83} +(1.50000 + 0.866025i) q^{84} +(2.00000 - 3.46410i) q^{86} -15.5885i q^{87} +(-1.00000 - 1.73205i) q^{88} +1.00000 q^{89} +6.00000 q^{91} +(0.500000 + 0.866025i) q^{92} +(3.00000 - 1.73205i) q^{93} +(3.50000 - 6.06218i) q^{94} +(1.50000 - 0.866025i) q^{96} +(-4.00000 - 6.92820i) q^{97} +6.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} - q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{11} - 3 q^{12} - 6 q^{13} + q^{14} - q^{16} + 4 q^{17} - 3 q^{18} + 12 q^{19} - 2 q^{22} + q^{23} - 3 q^{24} - 12 q^{26} + 2 q^{28}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 - q^7 - 2 * q^8 + 3 * q^9 + 2 * q^11 - 3 * q^12 - 6 * q^13 + q^14 - q^16 + 4 * q^17 - 3 * q^18 + 12 * q^19 - 2 * q^22 + q^23 - 3 * q^24 - 12 * q^26 + 2 * q^28 - 9 * q^29 + 2 * q^31 + q^32 + 2 * q^34 - 6 * q^36 - 4 * q^37 + 6 * q^38 - 18 * q^39 + 11 * q^41 + 3 * q^42 - 4 * q^43 - 4 * q^44 + 2 * q^46 - 7 * q^47 + 6 * q^49 + 6 * q^51 - 6 * q^52 - 9 * q^54 + q^56 + 18 * q^57 + 9 * q^58 + 4 * q^59 + 7 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 - 6 * q^66 - 11 * q^67 - 2 * q^68 + 3 * q^69 - 12 * q^71 - 3 * q^72 + 8 * q^73 - 2 * q^74 - 6 * q^76 + 2 * q^77 - 18 * q^78 + 12 * q^79 - 9 * q^81 + 22 * q^82 - 11 * q^83 + 3 * q^84 + 4 * q^86 - 2 * q^88 + 2 * q^89 + 12 * q^91 + q^92 + 6 * q^93 + 7 * q^94 + 3 * q^96 - 8 * q^97 + 12 * q^98 - 6 * q^99

Character values

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

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

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
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			1.73205i			0.707107i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	0.0643593	+	0.997927i	$0.479500\pi$
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	−0.896410	+	0.443227i	$0.853834\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$		0			0
$21$		−	1.73205i		−	0.377964i
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$		0			0
$26$	−6.00000			−1.17670
$27$			5.19615i			1.00000i
$28$	1.00000			0.188982
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$			3.46410i			0.603023i
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$	−9.00000	+	5.19615i	−1.44115	+	0.832050i
$40$		0			0
$41$	5.50000	−	9.52628i	0.858956	−	1.48775i	−0.0139704	−	0.999902i	$-0.504447\pi$
$41$	5.50000	−	9.52628i	0.858956	−	1.48775i	0.872926	−	0.487852i	$-0.162220\pi$
$42$	1.50000	−	0.866025i	0.231455	−	0.133631i
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	1.00000			0.147442
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$		−	1.73205i		−	0.250000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	3.00000	+	1.73205i	0.420084	+	0.242536i
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$		0			0
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	9.00000	+	5.19615i	1.19208	+	0.688247i
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	2.00000			0.254000
$63$	1.50000	−	2.59808i	0.188982	−	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.00000	+	1.73205i	−0.369274	+	0.213201i
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	1.50000	−	0.866025i	0.180579	−	0.104257i
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	1.00000	−	1.73205i	0.113961	−	0.197386i
$78$	−9.00000	−	5.19615i	−1.01905	−	0.588348i
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	0.976453	+	0.215728i	$0.0692125\pi$
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	−0.301401	+	0.953498i	$0.597454\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	11.0000			1.21475
$83$	−5.50000	−	9.52628i	−0.603703	−	1.04565i	−0.992255	−	0.124218i	$-0.960358\pi$
$83$	−5.50000	−	9.52628i	−0.603703	−	1.04565i	0.388552	−	0.921427i	$-0.372976\pi$
$84$	1.50000	+	0.866025i	0.163663	+	0.0944911i
$85$		0			0
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$		−	15.5885i		−	1.67126i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	6.00000			0.628971
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$	3.00000	−	1.73205i	0.311086	−	0.179605i
$94$	3.50000	−	6.06218i	0.360997	−	0.625266i
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	6.00000			0.606092
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$		0			0
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$			3.46410i			0.342997i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	3.00000	−	5.19615i	0.294174	−	0.509525i
$105$		0			0
$106$		0			0
$107$	−3.00000			−0.290021			−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000			−0.290021			−0.145010	+	0.989430i	$0.546322\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$		0			0
$111$	−3.00000	−	1.73205i	−0.284747	−	0.164399i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	−0.432670	−	0.901553i	$-0.642428\pi$
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	0.997102	−	0.0760733i	$-0.0242383\pi$
$114$			10.3923i			0.973329i
$115$		0			0
$116$	9.00000			0.835629
$117$	−18.0000			−1.66410
$118$	4.00000			0.368230
$119$	−1.00000	−	1.73205i	−0.0916698	−	0.158777i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−3.50000	+	6.06218i	−0.316875	+	0.548844i
$123$	16.5000	−	9.52628i	1.48775	−	0.858956i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$		0			0
$126$	3.00000			0.267261
$127$	19.0000			1.68598			0.842989	−	0.537931i	$-0.180794\pi$
$127$	19.0000			1.68598			0.842989	+	0.537931i	$0.180794\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		−	6.92820i		−	0.609994i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−3.00000	−	1.73205i	−0.261116	−	0.150756i
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$	−11.0000			−0.950255
$135$		0			0
$136$	−2.00000			−0.171499
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	1.50000	+	0.866025i	0.127688	+	0.0737210i
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$		−	12.1244i		−	1.02105i
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−12.0000			−1.00349
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$		0			0
$146$	2.00000	+	3.46410i	0.165521	+	0.286691i
$147$	9.00000	−	5.19615i	0.742307	−	0.428571i
$148$	1.00000	−	1.73205i	0.0821995	−	0.142374i
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	−6.00000			−0.486664
$153$	3.00000	+	5.19615i	0.242536	+	0.420084i
$154$	2.00000			0.161165
$155$		0			0
$156$		−	10.3923i		−	0.832050i
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	−6.00000	+	10.3923i	−0.477334	+	0.826767i
$159$		0			0
$160$		0			0
$161$	−1.00000			−0.0788110
$162$	−9.00000			−0.707107
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	5.50000	+	9.52628i	0.429478	+	0.743877i
$165$		0			0
$166$	5.50000	−	9.52628i	0.426883	−	0.739383i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$			1.73205i			0.133631i
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$		0			0
$171$	9.00000	+	15.5885i	0.688247	+	1.19208i
$172$	4.00000			0.304997
$173$	−2.00000	−	3.46410i	−0.152057	−	0.263371i	0.779926	−	0.625871i	$-0.215256\pi$
$173$	−2.00000	−	3.46410i	−0.152057	−	0.263371i	−0.931984	+	0.362500i	$0.881923\pi$
$174$	13.5000	−	7.79423i	1.02343	−	0.590879i
$175$		0			0
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$	6.00000	−	3.46410i	0.450988	−	0.260378i
$178$	0.500000	+	0.866025i	0.0374766	+	0.0649113i
$179$	2.00000			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$180$		0			0
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$	3.00000	+	5.19615i	0.222375	+	0.385164i
$183$			12.1244i			0.896258i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$		0			0
$186$	3.00000	+	1.73205i	0.219971	+	0.127000i
$187$	2.00000	+	3.46410i	0.146254	+	0.253320i
$188$	7.00000			0.510527
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$		0			0
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$	−6.00000			−0.426401
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$		0			0
$201$	−16.5000	+	9.52628i	−1.16382	+	0.671932i
$202$	1.00000	−	1.73205i	0.0703598	−	0.121867i
$203$	−4.50000	+	7.79423i	−0.315838	+	0.547048i
$204$	−3.00000	+	1.73205i	−0.210042	+	0.121268i
$205$		0			0
$206$	−8.00000			−0.557386
$207$	3.00000			0.208514
$208$	6.00000			0.416025
$209$	6.00000	+	10.3923i	0.415029	+	0.718851i
$210$		0			0
$211$	−9.00000	+	15.5885i	−0.619586	+	1.07315i	0.369976	+	0.929041i	$0.379366\pi$
$211$	−9.00000	+	15.5885i	−0.619586	+	1.07315i	−0.989561	+	0.144112i	$0.953967\pi$
$212$		0			0
$213$	−9.00000	−	5.19615i	−0.616670	−	0.356034i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$		0			0
$216$		−	5.19615i		−	0.353553i
$217$	−2.00000			−0.135769
$218$	3.50000	+	6.06218i	0.237050	+	0.410582i
$219$	6.00000	+	3.46410i	0.405442	+	0.234082i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		−	3.46410i		−	0.232495i
$223$	11.5000	+	19.9186i	0.770097	+	1.33385i	0.937509	+	0.347960i	$0.113126\pi$
$223$	11.5000	+	19.9186i	0.770097	+	1.33385i	−0.167412	+	0.985887i	$0.553541\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	12.0000			0.798228
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	0.702202	−	0.711977i	$-0.252200\pi$
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	−0.967692	+	0.252136i	$0.918867\pi$
$228$	−9.00000	+	5.19615i	−0.596040	+	0.344124i
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$	3.00000	−	1.73205i	0.197386	−	0.113961i
$232$	4.50000	+	7.79423i	0.295439	+	0.511716i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$	−9.00000	−	15.5885i	−0.588348	−	1.01905i
$235$		0			0
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$			20.7846i			1.35011i
$238$	1.00000	−	1.73205i	0.0648204	−	0.112272i
$239$	−14.0000	+	24.2487i	−0.905585	+	1.56852i	−0.0854543	+	0.996342i	$0.527234\pi$
$239$	−14.0000	+	24.2487i	−0.905585	+	1.56852i	−0.820130	+	0.572177i	$0.806099\pi$
$240$		0			0
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$	7.00000			0.449977
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−7.00000			−0.448129
$245$		0			0
$246$	16.5000	+	9.52628i	1.05200	+	0.607373i
$247$	−18.0000	+	31.1769i	−1.14531	+	1.98374i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$		−	19.0526i		−	1.20741i
$250$		0			0
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	1.50000	+	2.59808i	0.0944911	+	0.163663i
$253$	2.00000			0.125739
$254$	9.50000	+	16.4545i	0.596083	+	1.03245i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$	6.00000	−	3.46410i	0.373544	−	0.215666i
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$		0			0
$261$	13.5000	−	23.3827i	0.835629	−	1.44735i
$262$	−12.0000			−0.741362
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		−	3.46410i		−	0.213201i
$265$		0			0
$266$	3.00000	−	5.19615i	0.183942	−	0.318597i
$267$	1.50000	+	0.866025i	0.0917985	+	0.0529999i
$268$	−5.50000	−	9.52628i	−0.335966	−	0.581910i
$269$	3.00000			0.182913			0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000			0.182913			0.0914566	+	0.995809i	$0.470848\pi$
$270$		0			0
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$	9.00000	+	5.19615i	0.544705	+	0.314485i
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$			1.73205i			0.104257i
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	−16.0000			−0.959616
$279$	6.00000			0.359211
$280$		0			0
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	0.907293	−	0.420500i	$-0.138145\pi$
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	−0.817810	+	0.575488i	$0.804812\pi$
$282$	10.5000	−	6.06218i	0.625266	−	0.360997i
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	−0.850782	−	0.525519i	$-0.823871\pi$
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	0.880504	+	0.474039i	$0.157204\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$	−11.0000			−0.649309
$288$	3.00000			0.176777
$289$	−13.0000			−0.764706
$290$		0			0
$291$		−	13.8564i		−	0.812277i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$	9.00000	+	5.19615i	0.524891	+	0.303046i
$295$		0			0
$296$	2.00000			0.116248
$297$	−9.00000	+	5.19615i	−0.522233	+	0.301511i
$298$	1.00000			0.0579284
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$	5.00000	−	8.66025i	0.287718	−	0.498342i
$303$		−	3.46410i		−	0.199007i
$304$	−3.00000	−	5.19615i	−0.172062	−	0.298020i
$305$		0			0
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$	9.00000			0.513657			0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000			0.513657			0.256829	+	0.966457i	$0.417322\pi$
$308$	1.00000	+	1.73205i	0.0569803	+	0.0986928i
$309$	−12.0000	+	6.92820i	−0.682656	+	0.394132i
$310$		0			0
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	−0.938460	−	0.345389i	$-0.887747\pi$
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	0.768345	+	0.640036i	$0.221080\pi$
$312$	9.00000	−	5.19615i	0.509525	−	0.294174i
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	0.367402	−	0.930062i	$-0.380247\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−12.0000			−0.675053
$317$	−1.00000	−	1.73205i	−0.0561656	−	0.0972817i	0.836576	−	0.547852i	$-0.184554\pi$
$317$	−1.00000	−	1.73205i	−0.0561656	−	0.0972817i	−0.892741	+	0.450570i	$0.851221\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$	−0.500000	−	0.866025i	−0.0278639	−	0.0482617i
$323$	12.0000			0.667698
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$	10.5000	+	6.06218i	0.580651	+	0.335239i
$328$	−5.50000	+	9.52628i	−0.303687	+	0.526001i
$329$	−3.50000	+	6.06218i	−0.192961	+	0.334219i
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	11.0000			0.603703
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$	−3.00000			−0.164153
$335$		0			0
$336$	−1.50000	+	0.866025i	−0.0818317	+	0.0472456i
$337$	4.00000	−	6.92820i	0.217894	−	0.377403i	−0.736270	−	0.676688i	$-0.763415\pi$
$337$	4.00000	−	6.92820i	0.217894	−	0.377403i	0.954164	+	0.299285i	$0.0967480\pi$
$338$	11.5000	−	19.9186i	0.625518	−	1.08343i
$339$	18.0000	−	10.3923i	0.977626	−	0.564433i
$340$		0			0
$341$	4.00000			0.216612
$342$	−9.00000	+	15.5885i	−0.486664	+	0.842927i
$343$	−13.0000			−0.701934
$344$	2.00000	+	3.46410i	0.107833	+	0.186772i
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$	13.5000	+	7.79423i	0.723676	+	0.417815i
$349$	5.50000	+	9.52628i	0.294408	+	0.509930i	0.974847	−	0.222875i	$-0.0715441\pi$
$349$	5.50000	+	9.52628i	0.294408	+	0.509930i	−0.680439	+	0.732805i	$0.738211\pi$
$350$		0			0
$351$	−27.0000	−	15.5885i	−1.44115	−	0.832050i
$352$	2.00000			0.106600
$353$	−8.00000	−	13.8564i	−0.425797	−	0.737502i	0.570697	−	0.821160i	$-0.306673\pi$
$353$	−8.00000	−	13.8564i	−0.425797	−	0.737502i	−0.996495	+	0.0836583i	$0.973340\pi$
$354$	6.00000	+	3.46410i	0.318896	+	0.184115i
$355$		0			0
$356$	−0.500000	+	0.866025i	−0.0264999	+	0.0458993i
$357$		−	3.46410i		−	0.183340i
$358$	1.00000	+	1.73205i	0.0528516	+	0.0915417i
$359$	30.0000			1.58334			0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000			1.58334			0.791670	+	0.610949i	$0.209212\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−6.50000	−	11.2583i	−0.341632	−	0.591725i
$363$	10.5000	−	6.06218i	0.551107	−	0.318182i
$364$	−3.00000	+	5.19615i	−0.157243	+	0.272352i
$365$		0			0
$366$	−10.5000	+	6.06218i	−0.548844	+	0.316875i
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$	−1.00000			−0.0521286
$369$	33.0000			1.71791
$370$		0			0
$371$		0			0
$372$			3.46410i			0.179605i
$373$	6.00000	−	10.3923i	0.310668	−	0.538093i	−0.667839	−	0.744306i	$-0.732781\pi$
$373$	6.00000	−	10.3923i	0.310668	−	0.538093i	0.978507	+	0.206213i	$0.0661139\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$		0			0
$376$	3.50000	+	6.06218i	0.180499	+	0.312633i
$377$	54.0000			2.78114
$378$	4.50000	+	2.59808i	0.231455	+	0.133631i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	28.5000	+	16.4545i	1.46010	+	0.842989i
$382$	3.00000	−	5.19615i	0.153493	−	0.265858i
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	−0.0899119	−	0.995950i	$-0.528659\pi$
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	0.907474	−	0.420109i	$-0.138008\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$	−10.0000			−0.508987
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$	8.00000			0.406138
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$390$		0			0
$391$	1.00000	−	1.73205i	0.0505722	−	0.0875936i
$392$	−3.00000	+	5.19615i	−0.151523	+	0.262445i
$393$	−18.0000	+	10.3923i	−0.907980	+	0.524222i
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$		0			0
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	4.00000			0.200754			0.100377	−	0.994949i	$-0.467995\pi$
$397$	4.00000			0.200754			0.100377	+	0.994949i	$0.467995\pi$
$398$	−9.00000	−	15.5885i	−0.451129	−	0.781379i
$399$		−	10.3923i		−	0.520266i
$400$		0			0
$401$	5.00000	−	8.66025i	0.249688	−	0.432472i	−0.713751	−	0.700399i	$-0.753005\pi$
$401$	5.00000	−	8.66025i	0.249688	−	0.432472i	0.963439	+	0.267927i	$0.0863386\pi$
$402$	−16.5000	−	9.52628i	−0.822945	−	0.475128i
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	2.00000			0.0995037
$405$		0			0
$406$	−9.00000			−0.446663
$407$	−2.00000	−	3.46410i	−0.0991363	−	0.171709i
$408$	−3.00000	−	1.73205i	−0.148522	−	0.0857493i
$409$	−19.0000	+	32.9090i	−0.939490	+	1.62724i	−0.173064	+	0.984911i	$0.555367\pi$
$409$	−19.0000	+	32.9090i	−0.939490	+	1.62724i	−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	−4.00000			−0.196827
$414$	1.50000	+	2.59808i	0.0737210	+	0.127688i
$415$		0			0
$416$	3.00000	+	5.19615i	0.147087	+	0.254762i
$417$	−24.0000	+	13.8564i	−1.17529	+	0.678551i
$418$	−6.00000	+	10.3923i	−0.293470	+	0.508304i
$419$	−17.0000	+	29.4449i	−0.830504	+	1.43848i	0.0671345	+	0.997744i	$0.478614\pi$
$419$	−17.0000	+	29.4449i	−0.830504	+	1.43848i	−0.897639	+	0.440732i	$0.854719\pi$
$420$		0			0
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	0.463002	−	0.886357i	$-0.346772\pi$
$422$	−18.0000			−0.876226
$423$	10.5000	−	18.1865i	0.510527	−	0.884260i
$424$		0			0
$425$		0			0
$426$		−	10.3923i		−	0.503509i
$427$	3.50000	−	6.06218i	0.169377	−	0.293369i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$	−18.0000	−	10.3923i	−0.869048	−	0.501745i
$430$		0			0
$431$	16.0000			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$432$	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	$0.515303\pi$
$434$	−1.00000	−	1.73205i	−0.0480015	−	0.0831411i
$435$		0			0
$436$	−3.50000	+	6.06218i	−0.167620	+	0.290326i
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$			6.92820i			0.331042i
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$	−12.0000			−0.570782
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	0.739100	−	0.673596i	$-0.235251\pi$
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	−0.952901	+	0.303281i	$0.901918\pi$
$444$	3.00000	−	1.73205i	0.142374	−	0.0821995i
$445$		0			0
$446$	−11.5000	+	19.9186i	−0.544541	+	0.943172i
$447$	1.50000	−	0.866025i	0.0709476	−	0.0409616i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	22.0000			1.03594
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$		−	17.3205i		−	0.813788i
$454$	4.00000	−	6.92820i	0.187729	−	0.325157i
$455$		0			0
$456$	−9.00000	−	5.19615i	−0.421464	−	0.243332i
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	7.00000			0.327089
$459$			10.3923i			0.485071i
$460$		0			0
$461$	10.5000	+	18.1865i	0.489034	+	0.847031i	0.999920	−	0.0126168i	$-0.00401615\pi$
$461$	10.5000	+	18.1865i	0.489034	+	0.847031i	−0.510887	+	0.859648i	$0.670683\pi$
$462$	3.00000	+	1.73205i	0.139573	+	0.0805823i
$463$	18.0000	−	31.1769i	0.836531	−	1.44891i	−0.0562469	−	0.998417i	$-0.517913\pi$
$463$	18.0000	−	31.1769i	0.836531	−	1.44891i	0.892778	−	0.450497i	$-0.148753\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	5.00000	+	8.66025i	0.231621	+	0.401179i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$	9.00000	−	15.5885i	0.416025	−	0.720577i
$469$	11.0000			0.507933
$470$		0			0
$471$	6.00000	−	3.46410i	0.276465	−	0.159617i
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	4.00000	−	6.92820i	0.183920	−	0.318559i
$474$	−18.0000	+	10.3923i	−0.826767	+	0.477334i
$475$		0			0
$476$	2.00000			0.0916698
$477$		0			0
$478$	−28.0000			−1.28069
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	0.500000	−	0.866025i	0.0227744	−	0.0394464i
$483$	−1.50000	−	0.866025i	−0.0682524	−	0.0394055i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$		0			0
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	12.0000			0.543772			0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000			0.543772			0.271886	+	0.962329i	$0.412353\pi$
$488$	−3.50000	−	6.06218i	−0.158438	−	0.274422i
$489$	−6.00000	−	3.46410i	−0.271329	−	0.156652i
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$			19.0526i			0.858956i
$493$	−9.00000	−	15.5885i	−0.405340	−	0.702069i
$494$	−36.0000			−1.61972
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$	16.5000	−	9.52628i	0.739383	−	0.426883i
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	−0.461860	−	0.886953i	$-0.652818\pi$
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	0.999054	−	0.0434940i	$-0.0138489\pi$
$500$		0			0
$501$	−4.50000	+	2.59808i	−0.201045	+	0.116073i
$502$	9.00000	+	15.5885i	0.401690	+	0.695747i
$503$	−27.0000			−1.20387			−0.601935	−	0.798545i	$-0.705603\pi$
$503$	−27.0000			−1.20387			−0.601935	+	0.798545i	$0.705603\pi$
$504$	−1.50000	+	2.59808i	−0.0668153	+	0.115728i
$505$		0			0
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$		−	39.8372i		−	1.76923i
$508$	−9.50000	+	16.4545i	−0.421494	+	0.730050i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	−1.00000			−0.0441942
$513$			31.1769i			1.37649i
$514$	12.0000			0.529297
$515$		0			0
$516$	6.00000	+	3.46410i	0.264135	+	0.152499i
$517$	7.00000	−	12.1244i	0.307860	−	0.533229i
$518$	−1.00000	+	1.73205i	−0.0439375	+	0.0761019i
$519$		−	6.92820i		−	0.304114i
$520$		0			0
$521$	−37.0000			−1.62100			−0.810500	−	0.585739i	$-0.800804\pi$
$521$	−37.0000			−1.62100			−0.810500	+	0.585739i	$0.800804\pi$
$522$	27.0000			1.18176
$523$	29.0000			1.26808			0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000			1.26808			0.634041	+	0.773300i	$0.281395\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	−8.00000	+	13.8564i	−0.348817	+	0.604168i
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$	3.00000	−	1.73205i	0.130558	−	0.0753778i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	12.0000			0.520756
$532$	6.00000			0.260133
$533$	33.0000	+	57.1577i	1.42939	+	2.47577i
$534$			1.73205i			0.0749532i
$535$		0			0
$536$	5.50000	−	9.52628i	0.237564	−	0.411473i
$537$	3.00000	+	1.73205i	0.129460	+	0.0747435i
$538$	1.50000	+	2.59808i	0.0646696	+	0.112011i
$539$	12.0000			0.516877
$540$		0			0
$541$	−17.0000			−0.730887			−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000			−0.730887			−0.365444	+	0.930834i	$0.619083\pi$
$542$	−7.00000	−	12.1244i	−0.300676	−	0.520786i
$543$	−19.5000	−	11.2583i	−0.836825	−	0.483141i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$		0			0
$546$			10.3923i			0.444750i
$547$	17.5000	+	30.3109i	0.748246	+	1.29600i	0.948663	+	0.316289i	$0.102437\pi$
$547$	17.5000	+	30.3109i	0.748246	+	1.29600i	−0.200417	+	0.979711i	$0.564230\pi$
$548$	−12.0000			−0.512615
$549$	−10.5000	+	18.1865i	−0.448129	+	0.776182i
$550$		0			0
$551$	−27.0000	−	46.7654i	−1.15024	−	1.99227i
$552$	−1.50000	+	0.866025i	−0.0638442	+	0.0368605i
$553$	6.00000	−	10.3923i	0.255146	−	0.441926i
$554$	11.0000	−	19.0526i	0.467345	−	0.809466i
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	24.0000			1.01691			0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000			1.01691			0.508456	+	0.861088i	$0.330216\pi$
$558$	3.00000	+	5.19615i	0.127000	+	0.219971i
$559$	24.0000			1.01509
$560$		0			0
$561$			6.92820i			0.292509i
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−18.5000	+	32.0429i	−0.779682	+	1.35045i	0.152443	+	0.988312i	$0.451286\pi$
$563$	−18.5000	+	32.0429i	−0.779682	+	1.35045i	−0.932125	+	0.362137i	$0.882047\pi$
$564$	10.5000	+	6.06218i	0.442130	+	0.255264i
$565$		0			0
$566$	1.00000			0.0420331
$567$	9.00000			0.377964
$568$	6.00000			0.251754
$569$	1.00000	+	1.73205i	0.0419222	+	0.0726113i	0.886225	−	0.463255i	$-0.153319\pi$
$569$	1.00000	+	1.73205i	0.0419222	+	0.0726113i	−0.844303	+	0.535866i	$0.819985\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$		−	10.3923i		−	0.434145i
$574$	−5.50000	−	9.52628i	−0.229566	−	0.397619i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−15.0000	+	8.66025i	−0.623379	+	0.359908i
$580$		0			0
$581$	−5.50000	+	9.52628i	−0.228178	+	0.395217i
$582$	12.0000	−	6.92820i	0.497416	−	0.287183i
$583$		0			0
$584$	−4.00000			−0.165521
$585$		0			0
$586$	−18.0000			−0.743573
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	0.895320	−	0.445424i	$-0.146947\pi$
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	−0.833408	+	0.552658i	$0.813614\pi$
$588$			10.3923i			0.428571i
$589$	6.00000	−	10.3923i	0.247226	−	0.428207i
$590$		0			0
$591$	−12.0000	−	6.92820i	−0.493614	−	0.284988i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	30.0000			1.23195			0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$	−9.00000	−	5.19615i	−0.369274	−	0.213201i
$595$		0			0
$596$	0.500000	+	0.866025i	0.0204808	+	0.0354738i
$597$	−27.0000	−	15.5885i	−1.10504	−	0.637993i
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$	−4.00000			−0.163028
$603$	−33.0000			−1.34386
$604$	10.0000			0.406894
$605$		0			0
$606$	3.00000	−	1.73205i	0.121867	−	0.0703598i
$607$	0.500000	−	0.866025i	0.0202944	−	0.0351509i	−0.855700	−	0.517472i	$-0.826873\pi$
$607$	0.500000	−	0.866025i	0.0202944	−	0.0351509i	0.875994	+	0.482322i	$0.160206\pi$
$608$	3.00000	−	5.19615i	0.121666	−	0.210732i
$609$	−13.5000	+	7.79423i	−0.547048	+	0.315838i
$610$		0			0
$611$	42.0000			1.69914
$612$	−6.00000			−0.242536
$613$	34.0000			1.37325			0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000			1.37325			0.686624	+	0.727013i	$0.259092\pi$
$614$	4.50000	+	7.79423i	0.181605	+	0.314549i
$615$		0			0
$616$	−1.00000	+	1.73205i	−0.0402911	+	0.0697863i
$617$	−16.0000	+	27.7128i	−0.644136	+	1.11568i	0.340365	+	0.940294i	$0.389449\pi$
$617$	−16.0000	+	27.7128i	−0.644136	+	1.11568i	−0.984500	+	0.175382i	$0.943884\pi$
$618$	−12.0000	−	6.92820i	−0.482711	−	0.278693i
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$		0			0
$621$	4.50000	+	2.59808i	0.180579	+	0.104257i
$622$	−6.00000			−0.240578
$623$	−0.500000	−	0.866025i	−0.0200321	−	0.0346966i
$624$	9.00000	+	5.19615i	0.360288	+	0.208013i
$625$		0			0
$626$	11.0000	−	19.0526i	0.439648	−	0.761493i
$627$			20.7846i			0.830057i
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	−4.00000			−0.159490
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−6.00000	−	10.3923i	−0.238667	−	0.413384i
$633$	−27.0000	+	15.5885i	−1.07315	+	0.619586i
$634$	1.00000	−	1.73205i	0.0397151	−	0.0687885i
$635$		0			0
$636$		0			0
$637$	18.0000	+	31.1769i	0.713186	+	1.23527i
$638$	18.0000			0.712627
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$		0			0
$641$	−6.50000	−	11.2583i	−0.256735	−	0.444677i	0.708631	−	0.705580i	$-0.249313\pi$
$641$	−6.50000	−	11.2583i	−0.256735	−	0.444677i	−0.965365	+	0.260902i	$0.915980\pi$
$642$		−	5.19615i		−	0.205076i
$643$	−16.5000	+	28.5788i	−0.650696	+	1.12704i	0.332258	+	0.943189i	$0.392190\pi$
$643$	−16.5000	+	28.5788i	−0.650696	+	1.12704i	−0.982954	+	0.183851i	$0.941144\pi$
$644$	0.500000	−	0.866025i	0.0197028	−	0.0341262i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	−33.0000			−1.29736			−0.648682	−	0.761060i	$-0.724679\pi$
$647$	−33.0000			−1.29736			−0.648682	+	0.761060i	$0.724679\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	8.00000			0.314027
$650$		0			0
$651$	−3.00000	−	1.73205i	−0.117579	−	0.0678844i
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	0.491220	+	0.871036i	$0.336551\pi$
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	−0.999949	+	0.0101092i	$0.996782\pi$
$654$			12.1244i			0.474100i
$655$		0			0
$656$	−11.0000			−0.429478
$657$	6.00000	+	10.3923i	0.234082	+	0.405442i
$658$	−7.00000			−0.272888
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	−4.00000	+	6.92820i	−0.155464	+	0.269272i
$663$	−18.0000	+	10.3923i	−0.699062	+	0.403604i
$664$	5.50000	+	9.52628i	0.213441	+	0.369691i
$665$		0			0
$666$	3.00000	−	5.19615i	0.116248	−	0.201347i
$667$	−9.00000			−0.348481
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$			39.8372i			1.54019i
$670$		0			0
$671$	−7.00000	+	12.1244i	−0.270232	+	0.468056i
$672$	−1.50000	−	0.866025i	−0.0578638	−	0.0334077i
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	0.918036	−	0.396497i	$-0.129774\pi$
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	−0.802395	+	0.596794i	$0.796441\pi$
$674$	8.00000			0.308148
$675$		0			0
$676$	23.0000			0.884615
$677$	11.0000	+	19.0526i	0.422764	+	0.732249i	0.996209	−	0.0869952i	$-0.0277265\pi$
$677$	11.0000	+	19.0526i	0.422764	+	0.732249i	−0.573444	+	0.819244i	$0.694393\pi$
$678$	18.0000	+	10.3923i	0.691286	+	0.399114i
$679$	−4.00000	+	6.92820i	−0.153506	+	0.265880i
$680$		0			0
$681$		−	13.8564i		−	0.530979i
$682$	2.00000	+	3.46410i	0.0765840	+	0.132647i
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−18.0000			−0.688247
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	10.5000	−	6.06218i	0.400600	−	0.231287i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$		0			0
$690$		0			0
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	0.892458	+	0.451130i	$0.148979\pi$
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	−0.0555386	+	0.998457i	$0.517688\pi$
$692$	4.00000			0.152057
$693$	6.00000			0.227921
$694$	−12.0000			−0.455514
$695$		0			0
$696$			15.5885i			0.590879i
$697$	11.0000	−	19.0526i	0.416655	−	0.721667i
$698$	−5.50000	+	9.52628i	−0.208178	+	0.360575i
$699$	15.0000	+	8.66025i	0.567352	+	0.327561i
$700$		0			0
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$		−	31.1769i		−	1.17670i
$703$	−12.0000			−0.452589
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$		0			0
$706$	8.00000	−	13.8564i	0.301084	−	0.521493i
$707$	−1.00000	+	1.73205i	−0.0376089	+	0.0651405i
$708$			6.92820i			0.260378i
$709$	13.5000	+	23.3827i	0.507003	+	0.878155i	0.999967	+	0.00810550i	$0.00258009\pi$
$709$	13.5000	+	23.3827i	0.507003	+	0.878155i	−0.492964	+	0.870050i	$0.664087\pi$
$710$		0			0
$711$	−18.0000	+	31.1769i	−0.675053	+	1.16923i
$712$	−1.00000			−0.0374766
$713$	−1.00000	−	1.73205i	−0.0374503	−	0.0648658i
$714$	3.00000	−	1.73205i	0.112272	−	0.0648204i
$715$		0			0
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	−42.0000	+	24.2487i	−1.56852	+	0.905585i
$718$	15.0000	+	25.9808i	0.559795	+	0.969593i
$719$	−44.0000			−1.64092			−0.820462	−	0.571702i	$-0.806283\pi$
$719$	−44.0000			−1.64092			−0.820462	+	0.571702i	$0.806283\pi$
$720$		0			0
$721$	8.00000			0.297936
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$		−	1.73205i		−	0.0644157i
$724$	6.50000	−	11.2583i	0.241571	−	0.418413i
$725$		0			0
$726$	10.5000	+	6.06218i	0.389692	+	0.224989i
$727$	10.5000	+	18.1865i	0.389423	+	0.674501i	0.992372	−	0.123279i	$-0.0393409\pi$
$727$	10.5000	+	18.1865i	0.389423	+	0.674501i	−0.602949	+	0.797780i	$0.706008\pi$
$728$	−6.00000			−0.222375
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$	−10.5000	−	6.06218i	−0.388091	−	0.224065i
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	−0.826723	−	0.562609i	$-0.809798\pi$
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	0.900595	+	0.434659i	$0.143131\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$		0			0
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	−22.0000			−0.810380
$738$	16.5000	+	28.5788i	0.607373	+	1.05200i
$739$	40.0000			1.47142			0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000			1.47142			0.735712	+	0.677295i	$0.236848\pi$
$740$		0			0
$741$	−54.0000	+	31.1769i	−1.98374	+	1.14531i
$742$		0			0
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	−0.970173	−	0.242415i	$-0.922060\pi$
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	0.695024	+	0.718986i	$0.255394\pi$
$744$	−3.00000	+	1.73205i	−0.109985	+	0.0635001i
$745$		0			0
$746$	12.0000			0.439351
$747$	16.5000	−	28.5788i	0.603703	−	1.04565i
$748$	−4.00000			−0.146254
$749$	1.50000	+	2.59808i	0.0548088	+	0.0949316i
$750$		0			0
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$	27.0000	+	15.5885i	0.983935	+	0.568075i
$754$	27.0000	+	46.7654i	0.983282	+	1.70309i
$755$		0			0
$756$			5.19615i			0.188982i
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$	3.00000	+	1.73205i	0.108893	+	0.0628695i
$760$		0			0
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	−0.772863	−	0.634573i	$-0.781176\pi$
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	0.935988	+	0.352032i	$0.114509\pi$
$762$			32.9090i			1.19217i
$763$	−3.50000	−	6.06218i	−0.126709	−	0.219466i
$764$	6.00000			0.217072
$765$		0			0
$766$	32.0000			1.15621
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	7.50000	−	12.9904i	0.270457	−	0.468445i	−0.698522	−	0.715589i	$-0.746159\pi$
$769$	7.50000	−	12.9904i	0.270457	−	0.468445i	0.968979	+	0.247143i	$0.0794919\pi$
$770$		0			0
$771$	18.0000	−	10.3923i	0.648254	−	0.374270i
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	−12.0000			−0.431610			−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000			−0.431610			−0.215805	+	0.976436i	$0.569238\pi$
$774$	12.0000			0.431331
$775$		0			0
$776$	4.00000	+	6.92820i	0.143592	+	0.248708i
$777$			3.46410i			0.124274i
$778$	9.50000	−	16.4545i	0.340592	−	0.589922i
$779$	33.0000	−	57.1577i	1.18235	−	2.04789i
$780$		0			0
$781$	−6.00000

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} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.00000 + 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(-3.00000 + 5.19615i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} +6.00000 q^{19} -1.73205i q^{21} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-1.50000 - 0.866025i) q^{24} -6.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(-4.50000 - 7.79423i) q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +3.46410i q^{33} +(1.00000 + 1.73205i) q^{34} -3.00000 q^{36} -2.00000 q^{37} +(3.00000 + 5.19615i) q^{38} +(-9.00000 + 5.19615i) q^{39} +(5.50000 - 9.52628i) q^{41} +(1.50000 - 0.866025i) q^{42} +(-2.00000 - 3.46410i) q^{43} -2.00000 q^{44} +1.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} -1.73205i q^{48} +(3.00000 - 5.19615i) q^{49} +(3.00000 + 1.73205i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(-4.50000 + 2.59808i) q^{54} +(0.500000 + 0.866025i) q^{56} +(9.00000 + 5.19615i) q^{57} +(4.50000 - 7.79423i) q^{58} +(2.00000 - 3.46410i) q^{59} +(3.50000 + 6.06218i) q^{61} +2.00000 q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 1.73205i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(1.50000 - 0.866025i) q^{69} -6.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +4.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(1.00000 - 1.73205i) q^{77} +(-9.00000 - 5.19615i) q^{78} +(6.00000 + 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +11.0000 q^{82} +(-5.50000 - 9.52628i) q^{83} +(1.50000 + 0.866025i) q^{84} +(2.00000 - 3.46410i) q^{86} -15.5885i q^{87} +(-1.00000 - 1.73205i) q^{88} +1.00000 q^{89} +6.00000 q^{91} +(0.500000 + 0.866025i) q^{92} +(3.00000 - 1.73205i) q^{93} +(3.50000 - 6.06218i) q^{94} +(1.50000 - 0.866025i) q^{96} +(-4.00000 - 6.92820i) q^{97} +6.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} - q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{11} - 3 q^{12} - 6 q^{13} + q^{14} - q^{16} + 4 q^{17} - 3 q^{18} + 12 q^{19} - 2 q^{22} + q^{23} - 3 q^{24} - 12 q^{26} + 2 q^{28}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - q^7 - 2 * q^8 + 3 * q^9 + 2 * q^11 - 3 * q^12 - 6 * q^13 + q^14 - q^16 + 4 * q^17 - 3 * q^18 + 12 * q^19 - 2 * q^22 + q^23 - 3 * q^24 - 12 * q^26 + 2 * q^28 - 9 * q^29 + 2 * q^31 + q^32 + 2 * q^34 - 6 * q^36 - 4 * q^37 + 6 * q^38 - 18 * q^39 + 11 * q^41 + 3 * q^42 - 4 * q^43 - 4 * q^44 + 2 * q^46 - 7 * q^47 + 6 * q^49 + 6 * q^51 - 6 * q^52 - 9 * q^54 + q^56 + 18 * q^57 + 9 * q^58 + 4 * q^59 + 7 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 - 6 * q^66 - 11 * q^67 - 2 * q^68 + 3 * q^69 - 12 * q^71 - 3 * q^72 + 8 * q^73 - 2 * q^74 - 6 * q^76 + 2 * q^77 - 18 * q^78 + 12 * q^79 - 9 * q^81 + 22 * q^82 - 11 * q^83 + 3 * q^84 + 4 * q^86 - 2 * q^88 + 2 * q^89 + 12 * q^91 + q^92 + 6 * q^93 + 7 * q^94 + 3 * q^96 - 8 * q^97 + 12 * q^98 - 6 * q^99

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