LMFDB - Embedded newform 450.2.e.b.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:	no (minimal twist has level 90)
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.b.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} +(-1.50000 + 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

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

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
$3$	−1.50000	+	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	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	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	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	0.896410	+	0.443227i	$0.146166\pi$
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	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	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	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	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$	−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	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−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	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−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	0.872926	+	0.487852i	$0.162220\pi$
$41$	5.50000	+	9.52628i	0.858956	+	1.48775i	−0.0139704	+	0.999902i	$0.504447\pi$
$42$	−1.50000	−	0.866025i	−0.231455	−	0.133631i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	1.00000			0.147442
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	−0.489398	−	0.872060i	$-0.662783\pi$
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	0.999926	−	0.0121990i	$-0.00388317\pi$
$48$		−	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	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	−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	0.977356	+	0.211604i	$0.0678686\pi$
$67$	5.50000	+	9.52628i	0.671932	+	1.16382i	−0.305424	+	0.952217i	$0.598798\pi$
$68$	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	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	−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	−0.301401	−	0.953498i	$-0.597454\pi$
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	0.976453	−	0.215728i	$-0.0692125\pi$
$80$		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	−0.388552	−	0.921427i	$-0.627024\pi$
$83$	5.50000	−	9.52628i	0.603703	−	1.04565i	0.992255	−	0.124218i	$-0.0396422\pi$
$84$	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	$-0.700208\pi$
$97$	4.00000	−	6.92820i	0.406138	−	0.703452i	0.994453	+	0.105180i	$0.0335417\pi$
$98$	−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	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$			3.46410i			0.342997i
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$		0			0
$106$		0			0
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	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	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$		−	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	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	−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	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	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	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	−1.50000	+	0.866025i	−0.127688	+	0.0737210i
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		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	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$		0			0
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	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	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	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	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	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	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$			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	$-0.784744\pi$
$173$	2.00000	−	3.46410i	0.152057	−	0.263371i	0.931984	+	0.362500i	$0.118077\pi$
$174$	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	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	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	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$	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	−0.989561	−	0.144112i	$-0.953967\pi$
$211$	−9.00000	−	15.5885i	−0.619586	−	1.07315i	0.369976	−	0.929041i	$-0.379366\pi$
$212$		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	0.167412	+	0.985887i	$0.446459\pi$
$223$	−11.5000	+	19.9186i	−0.770097	+	1.33385i	−0.937509	+	0.347960i	$0.886874\pi$
$224$	−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	$-0.747800\pi$
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	0.967692	+	0.252136i	$0.0811332\pi$
$228$	9.00000	+	5.19615i	0.596040	+	0.344124i
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		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	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$	−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	−0.820130	−	0.572177i	$-0.806099\pi$
$239$	−14.0000	−	24.2487i	−0.905585	−	1.56852i	−0.0854543	−	0.996342i	$-0.527234\pi$
$240$		0			0
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$	−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	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$	−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	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$			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	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$	16.0000			0.959616
$279$	6.00000			0.359211
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$	−10.5000	−	6.06218i	−0.625266	−	0.360997i
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$	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	0.999549	+	0.0300351i	$0.00956192\pi$
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	−0.473763	+	0.880652i	$0.657105\pi$
$294$	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	$-0.582678\pi$
$307$	−9.00000			−0.513657			−0.256829	+	0.966457i	$0.582678\pi$
$308$	−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	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$	−9.00000	−	5.19615i	−0.509525	−	0.294174i
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$	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	$-0.815446\pi$
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	0.892741	+	0.450570i	$0.148779\pi$
$318$		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	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	−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	$-0.236585\pi$
$337$	−4.00000	−	6.92820i	−0.217894	−	0.377403i	−0.954164	+	0.299285i	$0.903252\pi$
$338$	−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	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	−13.5000	+	7.79423i	−0.723676	+	0.417815i
$349$	5.50000	−	9.52628i	0.294408	−	0.509930i	−0.680439	−	0.732805i	$-0.738211\pi$
$349$	5.50000	−	9.52628i	0.294408	−	0.509930i	0.974847	+	0.222875i	$0.0715441\pi$
$350$		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	$-0.693327\pi$
$353$	8.00000	−	13.8564i	0.425797	−	0.737502i	0.996495	+	0.0836583i	$0.0266604\pi$
$354$	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	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$	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	$-0.267219\pi$
$373$	−6.00000	−	10.3923i	−0.310668	−	0.538093i	−0.978507	+	0.206213i	$0.933886\pi$
$374$	−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	−0.907474	−	0.420109i	$-0.861992\pi$
$383$	−16.0000	−	27.7128i	−0.817562	−	1.41606i	0.0899119	−	0.995950i	$-0.471341\pi$
$384$		−	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	−0.999779	−	0.0210389i	$-0.993303\pi$
$389$	−9.50000	+	16.4545i	−0.481669	+	0.834275i	0.518110	+	0.855314i	$0.326636\pi$
$390$		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	$-0.532005\pi$
$397$	−4.00000			−0.200754			−0.100377	+	0.994949i	$0.532005\pi$
$398$	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	0.963439	−	0.267927i	$-0.0863386\pi$
$401$	5.00000	+	8.66025i	0.249688	+	0.432472i	−0.713751	+	0.700399i	$0.753005\pi$
$402$	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	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	−19.0000	−	32.9090i	−0.939490	−	1.62724i	−0.173064	−	0.984911i	$-0.555367\pi$
$410$		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	−0.897639	−	0.440732i	$-0.854719\pi$
$419$	−17.0000	−	29.4449i	−0.830504	−	1.43848i	0.0671345	−	0.997744i	$-0.478614\pi$
$420$		0			0
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	0.463002	+	0.886357i	$0.346772\pi$
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	−0.999109	+	0.0422075i	$0.986561\pi$
$422$	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	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	−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	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$		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	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$	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	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−7.00000			−0.327089
$459$		−	10.3923i		−	0.485071i
$460$		0			0
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	−0.510887	−	0.859648i	$-0.670683\pi$
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	0.999920	+	0.0126168i	$0.00401615\pi$
$462$	−3.00000	+	1.73205i	−0.139573	+	0.0805823i
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	−0.892778	−	0.450497i	$-0.851247\pi$
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	0.0562469	−	0.998417i	$-0.482087\pi$
$464$	−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	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$	−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	0.345827	+	0.938298i	$0.387598\pi$
$479$	−14.0000	+	24.2487i	−0.639676	+	1.10795i	−0.985504	+	0.169654i	$0.945735\pi$
$480$		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	$-0.587647\pi$
$487$	−12.0000			−0.543772			−0.271886	+	0.962329i	$0.587647\pi$
$488$	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	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$			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	0.999054	+	0.0434940i	$0.0138489\pi$
$499$	12.0000	+	20.7846i	0.537194	+	0.930447i	−0.461860	+	0.886953i	$0.652818\pi$
$500$		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	$-0.294397\pi$
$503$	27.0000			1.20387			0.601935	+	0.798545i	$0.294397\pi$
$504$	−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	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$		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	$-0.718605\pi$
$523$	−29.0000			−1.26808			−0.634041	+	0.773300i	$0.718605\pi$
$524$	−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	0.200417	+	0.979711i	$0.435770\pi$
$547$	−17.5000	+	30.3109i	−0.748246	+	1.29600i	−0.948663	+	0.316289i	$0.897563\pi$
$548$	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	$-0.669784\pi$
$557$	−24.0000			−1.01691			−0.508456	+	0.861088i	$0.669784\pi$
$558$	−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	0.932125	+	0.362137i	$0.117953\pi$
$563$	18.5000	+	32.0429i	0.779682	+	1.35045i	−0.152443	+	0.988312i	$0.548714\pi$
$564$	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	−0.844303	−	0.535866i	$-0.819985\pi$
$569$	1.00000	−	1.73205i	0.0419222	−	0.0726113i	0.886225	+	0.463255i	$0.153319\pi$
$570$		0			0
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$	−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	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$	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	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$			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	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$	−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	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	−0.549602	−	0.835426i	$-0.685221\pi$
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	0.998302	+	0.0582563i	$0.0185541\pi$
$602$	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	$-0.173127\pi$
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	−0.875994	+	0.482322i	$0.839794\pi$
$608$	−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	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$	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	0.984500	+	0.175382i	$0.0561162\pi$
$617$	16.0000	+	27.7128i	0.644136	+	1.11568i	−0.340365	+	0.940294i	$0.610551\pi$
$618$	12.0000	−	6.92820i	0.482711	−	0.278693i
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		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	−0.965365	−	0.260902i	$-0.915980\pi$
$641$	−6.50000	+	11.2583i	−0.256735	+	0.444677i	0.708631	+	0.705580i	$0.249313\pi$
$642$		−	5.19615i		−	0.205076i
$643$	16.5000	+	28.5788i	0.650696	+	1.12704i	0.982954	+	0.183851i	$0.0588563\pi$
$643$	16.5000	+	28.5788i	0.650696	+	1.12704i	−0.332258	+	0.943189i	$0.607810\pi$
$644$	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	$-0.275321\pi$
$647$	33.0000			1.29736			0.648682	+	0.761060i	$0.275321\pi$
$648$	−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	0.999949	+	0.0101092i	$0.00321793\pi$
$653$	13.0000	+	22.5167i	0.508729	+	0.881145i	−0.491220	+	0.871036i	$0.663449\pi$
$654$		−	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	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	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	$-0.870226\pi$
$673$	−3.00000	+	5.19615i	−0.115642	+	0.200297i	0.802395	+	0.596794i	$0.203559\pi$
$674$	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	$-0.972274\pi$
$677$	−11.0000	+	19.0526i	−0.422764	+	0.732249i	0.573444	+	0.819244i	$0.305607\pi$
$678$	−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	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$	−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	−0.0555386	−	0.998457i	$-0.517688\pi$
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	0.892458	−	0.451130i	$-0.148979\pi$
$692$	−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	−0.492964	−	0.870050i	$-0.664087\pi$
$709$	13.5000	−	23.3827i	0.507003	−	0.878155i	0.999967	−	0.00810550i	$-0.00258009\pi$
$710$		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	$-0.960659\pi$
$727$	−10.5000	+	18.1865i	−0.389423	+	0.674501i	0.602949	+	0.797780i	$0.293992\pi$
$728$	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	$-0.190202\pi$
$733$	−2.00000	−	3.46410i	−0.0738717	−	0.127950i	−0.900595	+	0.434659i	$0.856869\pi$
$734$	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	$-0.0779397\pi$
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	−0.695024	+	0.718986i	$0.744606\pi$
$744$	−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	0.525193	−	0.850983i	$-0.323993\pi$
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	−0.999570	+	0.0293387i	$0.990660\pi$
$752$	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	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	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	0.935988	−	0.352032i	$-0.114509\pi$
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$762$			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	0.968979	−	0.247143i	$-0.0794919\pi$
$769$	7.50000	+	12.9904i	0.270457	+	0.468445i	−0.698522	+	0.715589i	$0.746159\pi$
$770$		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	$-0.430762\pi$
$773$	12.0000			0.431610			0.215805	+	0.976436i	$0.430762\pi$
$774$	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	+	10.3923i	−0.214697	+	0.371866i
$782$	−2.00000			−0.0715199
$783$	−40.5000	−	23.3827i	−1.44735	−	0.835629i
$784$	−6.00000			−0.214286
$785$		0			0
$786$	−18.0000	+	10.3923i	−0.642039	+	0.370681i
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	−0.929467	−	0.368906i	$-0.879732\pi$
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	0.145251	−	0.989395i	$-0.453601\pi$
$788$	−4.00000	−	6.92820i	−0.142494	−	0.246807i
$789$		−	27.7128i		−	0.986602i
$790$		0			0
$791$	−12.0000			−0.426671
$792$	−3.00000	−	5.19615i	−0.106600	−	0.184637i
$793$	42.0000			1.49146
$794$	2.00000	−	3.46410i	0.0709773	−	0.122936i
$795$		0			0
$796$	9.00000	+	15.5885i	0.318997	+	0.552518i
$797$	1.00000	+	1.73205i	0.0354218	+	0.0613524i	0.883193	−	0.469010i	$-0.155389\pi$
$797$	1.00000	+	1.73205i	0.0354218	+	0.0613524i	−0.847771	+	0.530362i	$0.822056\pi$
$798$	−9.00000	−	5.19615i	−0.318597	−	0.183942i
$799$	−7.00000	+	12.1244i	−0.247642	+	0.428929i
$800$		0			0
$801$	1.50000	−	2.59808i	0.0529999	−	0.0917985i
$802$	−10.0000			−0.353112
$803$	−4.00000	+	6.92820i	−0.141157	+	0.244491i
$804$			19.0526i			0.671932i
$805$		0			0
$806$	−6.00000	−	10.3923i	−0.211341	−	0.366053i
$807$	−4.50000	+	2.59808i	−0.158408	+	0.0914566i
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$	4.50000	−	7.79423i	0.157919	−	0.273524i
$813$	21.0000	−	12.1244i	0.736502	−	0.425220i
$814$	2.00000	+	3.46410i	0.0701000	+	0.121417i
$815$		0			0
$816$			3.46410i			0.121268i
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$	38.0000			1.32864
$819$	9.00000	−	15.5885i	0.314485	−	0.544705i
$820$		0			0
$821$	15.5000	−	26.8468i	0.540954	−	0.936959i	−0.457896	−	0.889006i	$-0.651397\pi$
$821$	15.5000	−	26.8468i	0.540954	−	0.936959i	0.998850	−	0.0479535i	$-0.0152699\pi$
$822$	18.0000	+	10.3923i	0.627822	+	0.362473i
$823$	−7.50000	−	12.9904i	−0.261434	−	0.452816i	0.705190	−	0.709019i	$-0.250862\pi$
$823$	−7.50000	−	12.9904i	−0.261434	−	0.452816i	−0.966623	+	0.256203i	$0.917529\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	−2.00000	+	3.46410i	−0.0695889	+	0.120532i
$827$	−35.0000			−1.21707			−0.608535	−	0.793527i	$-0.708242\pi$
$827$	−35.0000			−1.21707			−0.608535	+	0.793527i	$0.708242\pi$
$828$	1.50000	+	2.59808i	0.0521286	+	0.0902894i
$829$	15.0000			0.520972			0.260486	−	0.965478i	$-0.416117\pi$
$829$	15.0000			0.520972			0.260486	+	0.965478i	$0.416117\pi$
$830$		0			0
$831$			38.1051i			1.32185i
$832$	3.00000	+	5.19615i	0.104006	+	0.180144i
$833$	−6.00000	−	10.3923i	−0.207888	−	0.360072i
$834$	−24.0000	+	13.8564i	−0.831052	+	0.479808i
$835$		0			0
$836$	−12.0000			−0.415029
$837$	−9.00000	+	5.19615i	−0.311086	+	0.179605i
$838$	34.0000			1.17451
$839$	−19.0000	+	32.9090i	−0.655953	+	1.13614i	0.325701	+	0.945473i	$0.394400\pi$
$839$	−19.0000	+	32.9090i	−0.655953	+	1.13614i	−0.981654	+	0.190671i	$0.938934\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	−11.0000	−	19.0526i	−0.379085	−	0.656595i
$843$			5.19615i			0.178965i
$844$	−9.00000	+	15.5885i	−0.309793	+	0.536577i
$845$		0			0
$846$	21.0000			0.721995
$847$	7.00000			0.240523
$848$		0			0
$849$	1.50000	+	0.866025i	0.0514799	+	0.0297219i
$850$		0			0
$851$	−1.00000	−	1.73205i	−0.0342796	−	0.0593739i
$852$	−9.00000	−	5.19615i	−0.308335	−	0.178017i
$853$	−23.0000	+	39.8372i	−0.787505	+	1.36400i	0.139986	+	0.990153i	$0.455294\pi$
$853$	−23.0000	+	39.8372i	−0.787505	+	1.36400i	−0.927491	+	0.373845i	$0.878039\pi$
$854$	7.00000			0.239535
$855$		0			0
$856$	3.00000			0.102538
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		−	20.7846i		−	0.709575i
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$		0			0
$861$	−16.5000	+	9.52628i	−0.562318	+	0.324655i
$862$	−8.00000	+	13.8564i	−0.272481	+	0.471951i
$863$	−45.0000			−1.53182			−0.765909	−	0.642949i	$-0.777711\pi$
$863$	−45.0000			−1.53182			−0.765909	+	0.642949i	$0.777711\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$		0			0
$866$	−1.00000	+	1.73205i	−0.0339814	+	0.0588575i
$867$	19.5000	−	11.2583i	0.662255	−	0.382353i
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	−33.0000	+	57.1577i	−1.11816	+	1.93671i
$872$	7.00000			0.237050
$873$	−12.0000	−	20.7846i	−0.406138	−	0.703452i
$874$	6.00000			0.202953
$875$		0			0
$876$	−6.00000	−	3.46410i	−0.202721	−	0.117041i
$877$	−23.0000	−	39.8372i	−0.776655	−	1.34521i	−0.933860	−	0.357640i	$-0.883582\pi$
$877$	−23.0000	−	39.8372i	−0.776655	−	1.34521i	0.157205	−	0.987566i	$-0.449752\pi$
$878$	−12.0000	−	20.7846i	−0.404980	−	0.701447i
$879$	−27.0000	−	15.5885i	−0.910687	−	0.525786i
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$	−9.00000	+	15.5885i	−0.303046	+	0.524891i
$883$	3.00000			0.100958			0.0504790	−	0.998725i	$-0.483925\pi$
$883$	3.00000			0.100958			0.0504790	+	0.998725i	$0.483925\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	4.50000	+	7.79423i	0.151180	+	0.261852i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	−3.00000	+	1.73205i	−0.100673	+	0.0581238i
$889$	−9.50000	+	16.4545i	−0.318620	+	0.551866i
$890$		0			0
$891$	−18.0000			−0.603023
$892$	23.0000			0.770097
$893$	21.0000	−	36.3731i	0.702738	−	1.21718i
$894$	1.50000	−	0.866025i	0.0501675	−	0.0289642i
$895$		0			0
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$			10.3923i			0.346989i
$898$	−9.00000	+	15.5885i	−0.300334	+	0.520194i
$899$	−18.0000			−0.600334
$900$		0			0
$901$		0			0
$902$	−11.0000	+	19.0526i	−0.366260	+	0.634381i
$903$	6.00000	+	3.46410i	0.199667	+	0.115278i
$904$	−6.00000	−	10.3923i	−0.199557	−	0.345643i
$905$		0			0
$906$	15.0000	+	8.66025i	0.498342	+	0.287718i
$907$	−16.5000	+	28.5788i	−0.547874	+	0.948945i	0.450546	+	0.892753i	$0.351229\pi$
$907$	−16.5000	+	28.5788i	−0.547874	+	0.948945i	−0.998420	+	0.0561918i	$0.982104\pi$
$908$	−8.00000			−0.265489
$909$	3.00000	+	5.19615i	0.0995037	+	0.172345i
$910$		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	$0.230367\pi$
$912$		−	10.3923i		−	0.344124i
$913$	−11.0000	−	19.0526i	−0.364047	−	0.630548i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		0			0
$916$	3.50000	−	6.06218i	0.115643	−	0.200300i
$917$	−12.0000			−0.396275
$918$	9.00000	+	5.19615i	0.297044	+	0.171499i
$919$	−36.0000			−1.18753			−0.593765	−	0.804638i	$-0.702359\pi$
$919$	−36.0000			−1.18753			−0.593765	+	0.804638i	$0.702359\pi$
$920$		0			0
$921$	13.5000	−	7.79423i	0.444840	−	0.256829i
$922$	10.5000	+	18.1865i	0.345799	+	0.598942i
$923$	−18.0000	−	31.1769i	−0.592477	−	1.02620i
$924$		−	3.46410i		−	0.113961i
$925$		0			0
$926$	36.0000			1.18303
$927$	24.0000			0.788263
$928$	9.00000			0.295439
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		0			0
$931$	18.0000	+	31.1769i	0.589926	+	1.02178i
$932$	5.00000	+	8.66025i	0.163780	+	0.283676i
$933$	9.00000	+	5.19615i	0.294647	+	0.170114i
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$		0			0
$936$	18.0000			0.588348
$937$	52.0000			1.69877			0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000			1.69877			0.849383	+	0.527777i	$0.176974\pi$
$938$	−5.50000	+	9.52628i	−0.179581	+	0.311044i
$939$			38.1051i			1.24351i
$940$		0			0
$941$	20.5000	+	35.5070i	0.668281	+	1.15750i	0.978385	+	0.206794i	$0.0663029\pi$
$941$	20.5000	+	35.5070i	0.668281	+	1.15750i	−0.310104	+	0.950703i	$0.600364\pi$
$942$	−6.00000	+	3.46410i	−0.195491	+	0.112867i
$943$	5.50000	−	9.52628i	0.179105	−	0.310218i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	8.00000			0.260102
$947$	25.5000	−	44.1673i	0.828639	−	1.43524i	−0.0704677	−	0.997514i	$-0.522449\pi$
$947$	25.5000	−	44.1673i	0.828639	−	1.43524i	0.899106	−	0.437730i	$-0.144217\pi$
$948$	18.0000	−	10.3923i	0.584613	−	0.337526i
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$			3.46410i			0.112331i
$952$	−1.00000	+	1.73205i	−0.0324102	+	0.0561361i
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$		0			0
$955$		0			0
$956$	−14.0000	+	24.2487i	−0.452792	+	0.784259i
$957$	−27.0000	−	15.5885i	−0.872786	−	0.503903i
$958$	−14.0000	−	24.2487i	−0.452319	−	0.783440i
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−12.0000			−0.386896
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$	1.00000			0.0322078
$965$		0			0
$966$			1.73205i			0.0557278i
$967$	8.50000	+	14.7224i	0.273342	+	0.473441i	0.969715	−	0.244238i	$-0.0785377\pi$
$967$	8.50000	+	14.7224i	0.273342	+	0.473441i	−0.696374	+	0.717679i	$0.745204\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	18.0000	−	10.3923i	0.578243	−	0.333849i
$970$		0			0
$971$	−42.0000			−1.34784			−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000			−1.34784			−0.673922	+	0.738802i	$0.735392\pi$
$972$		−	15.5885i		−	0.500000i
$973$	−16.0000			−0.512936
$974$	6.00000	−	10.3923i	0.192252	−	0.332991i
$975$		0			0
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$		−	6.92820i		−	0.221540i
$979$	1.00000	−	1.73205i	0.0319601	−	0.0553566i
$980$		0			0
$981$	10.5000	−	18.1865i	0.335239	−	0.580651i
$982$		0			0
$983$	9.50000	−	16.4545i	0.303003	−	0.524816i	−0.673812	−	0.738903i	$-0.735344\pi$
$983$	9.50000	−	16.4545i	0.303003	−	0.524816i	0.976815	+	0.214087i	$0.0686775\pi$
$984$	−16.5000	−	9.52628i	−0.526001	−	0.303687i
$985$		0			0
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$	10.5000	+	6.06218i	0.334219	+	0.192961i
$988$	18.0000	−	31.1769i	0.572656	−	0.991870i
$989$	−4.00000			−0.127193
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$			13.8564i			0.439720i
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$	16.5000	−	9.52628i	0.522823	−	0.301852i
$997$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$997$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$998$	−24.0000			−0.759707
$999$			10.3923i			0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.e.b.151.1		2
3.2	odd	2		1350.2.e.i.451.1		2
5.2	odd	4		90.2.i.a.79.1	yes	4
5.3	odd	4		90.2.i.a.79.2	yes	4
5.4	even	2		450.2.e.g.151.1		2
9.2	odd	6		4050.2.a.g.1.1		1
9.4	even	3	inner	450.2.e.b.301.1		2
9.5	odd	6		1350.2.e.i.901.1		2
9.7	even	3		4050.2.a.x.1.1		1
15.2	even	4		270.2.i.a.19.2		4
15.8	even	4		270.2.i.a.19.1		4
15.14	odd	2		1350.2.e.a.451.1		2
20.3	even	4		720.2.by.a.529.2		4
20.7	even	4		720.2.by.a.529.1		4
45.2	even	12		810.2.c.c.649.1		2
45.4	even	6		450.2.e.g.301.1		2
45.7	odd	12		810.2.c.b.649.2		2
45.13	odd	12		90.2.i.a.49.1	✓	4
45.14	odd	6		1350.2.e.a.901.1		2
45.22	odd	12		90.2.i.a.49.2	yes	4
45.23	even	12		270.2.i.a.199.2		4
45.29	odd	6		4050.2.a.be.1.1		1
45.32	even	12		270.2.i.a.199.1		4
45.34	even	6		4050.2.a.j.1.1		1
45.38	even	12		810.2.c.c.649.2		2
45.43	odd	12		810.2.c.b.649.1		2
60.23	odd	4		2160.2.by.b.289.1		4
60.47	odd	4		2160.2.by.b.289.2		4
180.23	odd	12		2160.2.by.b.1009.2		4
180.67	even	12		720.2.by.a.49.2		4
180.103	even	12		720.2.by.a.49.1		4
180.167	odd	12		2160.2.by.b.1009.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.a.49.1	✓	4	45.13	odd	12
90.2.i.a.49.2	yes	4	45.22	odd	12
90.2.i.a.79.1	yes	4	5.2	odd	4
90.2.i.a.79.2	yes	4	5.3	odd	4
270.2.i.a.19.1		4	15.8	even	4
270.2.i.a.19.2		4	15.2	even	4
270.2.i.a.199.1		4	45.32	even	12
270.2.i.a.199.2		4	45.23	even	12
450.2.e.b.151.1		2	1.1	even	1	trivial
450.2.e.b.301.1		2	9.4	even	3	inner
450.2.e.g.151.1		2	5.4	even	2
450.2.e.g.301.1		2	45.4	even	6
720.2.by.a.49.1		4	180.103	even	12
720.2.by.a.49.2		4	180.67	even	12
720.2.by.a.529.1		4	20.7	even	4
720.2.by.a.529.2		4	20.3	even	4
810.2.c.b.649.1		2	45.43	odd	12
810.2.c.b.649.2		2	45.7	odd	12
810.2.c.c.649.1		2	45.2	even	12
810.2.c.c.649.2		2	45.38	even	12
1350.2.e.a.451.1		2	15.14	odd	2
1350.2.e.a.901.1		2	45.14	odd	6
1350.2.e.i.451.1		2	3.2	odd	2
1350.2.e.i.901.1		2	9.5	odd	6
2160.2.by.b.289.1		4	60.23	odd	4
2160.2.by.b.289.2		4	60.47	odd	4
2160.2.by.b.1009.1		4	180.167	odd	12
2160.2.by.b.1009.2		4	180.23	odd	12
4050.2.a.g.1.1		1	9.2	odd	6
4050.2.a.j.1.1		1	45.34	even	6
4050.2.a.x.1.1		1	9.7	even	3
4050.2.a.be.1.1		1	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.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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