LMFDB - Embedded newform 350.2.e.g.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(51,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.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:	$2.79476407074$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.151
Dual form			350.2.e.g.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{12} +2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(3.00000 - 5.19615i) q^{18} +(1.00000 + 1.73205i) q^{19} +(1.50000 - 7.79423i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(1.50000 - 2.59808i) q^{24} +(1.00000 + 1.73205i) q^{26} +9.00000 q^{27} +(0.500000 - 2.59808i) q^{28} -1.00000 q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} -2.00000 q^{34} +6.00000 q^{36} +(-4.00000 - 6.92820i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-3.00000 + 5.19615i) q^{39} -3.00000 q^{41} +(7.50000 - 2.59808i) q^{42} -5.00000 q^{43} +(0.500000 - 0.866025i) q^{46} +(4.00000 + 6.92820i) q^{47} +3.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(4.50000 + 7.79423i) q^{54} +(2.50000 - 0.866025i) q^{56} -6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(4.50000 + 7.79423i) q^{61} -10.0000 q^{62} +(12.0000 + 10.3923i) q^{63} +1.00000 q^{64} +(-3.50000 + 6.06218i) q^{67} +(-1.00000 - 1.73205i) q^{68} +3.00000 q^{69} +6.00000 q^{71} +(3.00000 + 5.19615i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(4.00000 - 6.92820i) q^{74} -2.00000 q^{76} -6.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(6.00000 + 5.19615i) q^{84} +(-2.50000 - 4.33013i) q^{86} +(1.50000 - 2.59808i) q^{87} +(3.50000 + 6.06218i) q^{89} +(-5.00000 + 1.73205i) q^{91} +1.00000 q^{92} +(-15.0000 - 25.9808i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(1.50000 + 2.59808i) q^{96} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{6} - 5 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^6 - 5 * q^7 - 2 * q^8 - 6 * q^9	$ 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{6} - 5 q^{7} - 2 q^{8} - 6 q^{9} - 3 q^{12} + 4 q^{13} - 4 q^{14} - q^{16} - 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{21} - q^{23} + 3 q^{24} + 2 q^{26} + 18 q^{27} + q^{28} - 2 q^{29} - 10 q^{31} + q^{32} - 4 q^{34} + 12 q^{36} - 8 q^{37} - 2 q^{38} - 6 q^{39} - 6 q^{41} + 15 q^{42} - 10 q^{43} + q^{46} + 8 q^{47} + 6 q^{48} + 11 q^{49} - 6 q^{51} - 2 q^{52} - 6 q^{53} + 9 q^{54} + 5 q^{56} - 12 q^{57} - q^{58} - 2 q^{59} + 9 q^{61} - 20 q^{62} + 24 q^{63} + 2 q^{64} - 7 q^{67} - 2 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} - 10 q^{73} + 8 q^{74} - 4 q^{76} - 12 q^{78} + 10 q^{79} - 9 q^{81} - 3 q^{82} + 18 q^{83} + 12 q^{84} - 5 q^{86} + 3 q^{87} + 7 q^{89} - 10 q^{91} + 2 q^{92} - 30 q^{93} - 8 q^{94} + 3 q^{96} + 13 q^{98}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^6 - 5 * q^7 - 2 * q^8 - 6 * q^9 - 3 * q^12 + 4 * q^13 - 4 * q^14 - q^16 - 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^21 - q^23 + 3 * q^24 + 2 * q^26 + 18 * q^27 + q^28 - 2 * q^29 - 10 * q^31 + q^32 - 4 * q^34 + 12 * q^36 - 8 * q^37 - 2 * q^38 - 6 * q^39 - 6 * q^41 + 15 * q^42 - 10 * q^43 + q^46 + 8 * q^47 + 6 * q^48 + 11 * q^49 - 6 * q^51 - 2 * q^52 - 6 * q^53 + 9 * q^54 + 5 * q^56 - 12 * q^57 - q^58 - 2 * q^59 + 9 * q^61 - 20 * q^62 + 24 * q^63 + 2 * q^64 - 7 * q^67 - 2 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 - 10 * q^73 + 8 * q^74 - 4 * q^76 - 12 * q^78 + 10 * q^79 - 9 * q^81 - 3 * q^82 + 18 * q^83 + 12 * q^84 - 5 * q^86 + 3 * q^87 + 7 * q^89 - 10 * q^91 + 2 * q^92 - 30 * q^93 - 8 * q^94 + 3 * q^96 + 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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	+	2.59808i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−3.00000			−1.22474
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−1.50000	−	2.59808i	−0.433013	−	0.750000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	3.00000	−	5.19615i	0.707107	−	1.22474i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$	1.50000	−	7.79423i	0.327327	−	1.70084i
$22$		0			0
$23$	−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	−	2.59808i	0.306186	−	0.530330i
$25$		0			0
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	9.00000			1.73205
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	6.00000			1.00000
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	−3.00000	+	5.19615i	−0.480384	+	0.832050i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	7.50000	−	2.59808i	1.15728	−	0.400892i
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$		0			0
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$	3.00000			0.433013
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$		0			0
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$	−6.00000			−0.794719
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	−0.923749	−	0.382998i	$-0.874892\pi$
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	0.793560	+	0.608492i	$0.208225\pi$
$60$		0			0
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$	−10.0000			−1.27000
$63$	12.0000	+	10.3923i	1.51186	+	1.30931i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	3.00000			0.361158
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	3.00000	+	5.19615i	0.353553	+	0.612372i
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	−2.00000			−0.229416
$77$		0			0
$78$	−6.00000			−0.679366
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	6.00000	+	5.19615i	0.654654	+	0.566947i
$85$		0			0
$86$	−2.50000	−	4.33013i	−0.269582	−	0.466930i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		0			0
$91$	−5.00000	+	1.73205i	−0.524142	+	0.181568i
$92$	1.00000			0.104257
$93$	−15.0000	−	25.9808i	−1.55543	−	2.69408i
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$		0			0
$96$	1.50000	+	2.59808i	0.153093	+	0.265165i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	6.50000	+	2.59808i	0.656599	+	0.262445i
$99$		0			0
$100$		0			0
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	−0.998793	−	0.0491146i	$-0.984360\pi$
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	0.456862	−	0.889538i	$-0.348973\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−3.50000	−	6.06218i	−0.338358	−	0.586053i	0.645766	−	0.763535i	$-0.276538\pi$
$107$	−3.50000	−	6.06218i	−0.338358	−	0.586053i	−0.984124	+	0.177482i	$0.943205\pi$
$108$	−4.50000	+	7.79423i	−0.433013	+	0.750000i
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$	24.0000			2.27798
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	−3.00000	−	5.19615i	−0.280976	−	0.486664i
$115$		0			0
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	−6.00000	−	10.3923i	−0.554700	−	0.960769i
$118$	−2.00000			−0.184115
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−4.50000	+	7.79423i	−0.407411	+	0.705656i
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	−5.00000	−	8.66025i	−0.449013	−	0.777714i
$125$		0			0
$126$	−3.00000	+	15.5885i	−0.267261	+	1.38873i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	7.50000	−	12.9904i	0.660338	−	1.14374i
$130$		0			0
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.858137	−	0.513421i	$-0.828378\pi$
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.0155672	−	0.999879i	$-0.504955\pi$
$132$		0			0
$133$	−4.00000	−	3.46410i	−0.346844	−	0.300376i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	0.973910	−	0.226935i	$-0.0728704\pi$
$138$	1.50000	+	2.59808i	0.127688	+	0.221163i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$		0			0
$144$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$145$		0			0
$146$	−10.0000			−0.827606
$147$	3.00000	+	20.7846i	0.247436	+	1.71429i
$148$	8.00000			0.657596
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		0			0
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	−0.961888	−	0.273442i	$-0.911838\pi$
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	0.717752	+	0.696299i	$0.245171\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$	12.0000			0.970143
$154$		0			0
$155$		0			0
$156$	−3.00000	−	5.19615i	−0.240192	−	0.416025i
$157$	−6.00000	+	10.3923i	−0.478852	+	0.829396i	−0.999706	−	0.0242497i	$-0.992280\pi$
$157$	−6.00000	+	10.3923i	−0.478852	+	0.829396i	0.520854	+	0.853646i	$0.325614\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$		0			0
$161$	2.00000	+	1.73205i	0.157622	+	0.136505i
$162$	−9.00000			−0.707107
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	0.999410	−	0.0343508i	$-0.0109363\pi$
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	−0.529454	+	0.848339i	$0.677603\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$		0			0
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	9.00000			0.696441			0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000			0.696441			0.348220	+	0.937413i	$0.386786\pi$
$168$	−1.50000	+	7.79423i	−0.115728	+	0.601338i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	6.00000	−	10.3923i	0.458831	−	0.794719i
$172$	2.50000	−	4.33013i	0.190623	−	0.330169i
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$	3.00000			0.227429
$175$		0			0
$176$		0			0
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	−3.50000	+	6.06218i	−0.262336	+	0.454379i
$179$	13.0000	−	22.5167i	0.971666	−	1.68297i	0.281139	−	0.959667i	$-0.409288\pi$
$179$	13.0000	−	22.5167i	0.971666	−	1.68297i	0.690526	−	0.723307i	$-0.257379\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	−4.00000	−	3.46410i	−0.296500	−	0.256776i
$183$	−27.0000			−1.99590
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$		0			0
$186$	15.0000	−	25.9808i	1.09985	−	1.90500i
$187$		0			0
$188$	−8.00000			−0.583460
$189$	−22.5000	+	7.79423i	−1.63663	+	0.566947i
$190$		0			0
$191$	10.0000	+	17.3205i	0.723575	+	1.25327i	0.959558	+	0.281511i	$0.0908356\pi$
$191$	10.0000	+	17.3205i	0.723575	+	1.25327i	−0.235983	+	0.971757i	$0.575831\pi$
$192$	−1.50000	+	2.59808i	−0.108253	+	0.187500i
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	−0.241257	−	0.970461i	$-0.577560\pi$
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	0.961073	−	0.276296i	$-0.0891071\pi$
$194$		0			0
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$		0			0
$199$	−6.00000	+	10.3923i	−0.425329	+	0.736691i	−0.996451	−	0.0841740i	$-0.973175\pi$
$199$	−6.00000	+	10.3923i	−0.425329	+	0.736691i	0.571122	+	0.820865i	$0.306508\pi$
$200$		0			0
$201$	−10.5000	−	18.1865i	−0.740613	−	1.28278i
$202$	15.0000			1.05540
$203$	2.50000	−	0.866025i	0.175466	−	0.0607831i
$204$	6.00000			0.420084
$205$		0			0
$206$	5.50000	−	9.52628i	0.383203	−	0.663727i
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	−9.00000	+	15.5885i	−0.616670	+	1.06810i
$214$	3.50000	−	6.06218i	0.239255	−	0.414402i
$215$		0			0
$216$	−9.00000			−0.612372
$217$	5.00000	−	25.9808i	0.339422	−	1.76369i
$218$	−5.00000			−0.338643
$219$	−15.0000	−	25.9808i	−1.01361	−	1.75562i
$220$		0			0
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$	12.0000	+	20.7846i	0.805387	+	1.39497i
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	5.00000	+	8.66025i	0.332595	+	0.576072i
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$	3.00000	−	5.19615i	0.198680	−	0.344124i
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$		0			0
$231$		0			0
$232$	1.00000			0.0656532
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	0.540301	−	0.841472i	$-0.318310\pi$
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	−0.998886	+	0.0471787i	$0.984977\pi$
$234$	6.00000	−	10.3923i	0.392232	−	0.679366i
$235$		0			0
$236$	−1.00000	−	1.73205i	−0.0650945	−	0.112747i
$237$	−30.0000			−1.94871
$238$	5.00000	−	1.73205i	0.324102	−	0.112272i
$239$	−10.0000			−0.646846			−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000			−0.646846			−0.323423	+	0.946254i	$0.604834\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	−5.50000	+	9.52628i	−0.353553	+	0.612372i
$243$		0			0
$244$	−9.00000			−0.576166
$245$		0			0
$246$	9.00000			0.573819
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$	5.00000	−	8.66025i	0.317500	−	0.549927i
$249$	−13.5000	+	23.3827i	−0.855528	+	1.48182i
$250$		0			0
$251$	−10.0000			−0.631194			−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000			−0.631194			−0.315597	+	0.948893i	$0.602205\pi$
$252$	−15.0000	+	5.19615i	−0.944911	+	0.327327i
$253$		0			0
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	0.990217	−	0.139533i	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$	15.0000			0.933859
$259$	16.0000	+	13.8564i	0.994192	+	0.860995i
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	10.0000	−	17.3205i	0.617802	−	1.07006i
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	−0.336270	−	0.941766i	$-0.609166\pi$
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	0.983728	−	0.179664i	$-0.0575011\pi$
$264$		0			0
$265$		0			0
$266$	1.00000	−	5.19615i	0.0613139	−	0.318597i
$267$	−21.0000			−1.28518
$268$	−3.50000	−	6.06218i	−0.213797	−	0.370306i
$269$	−2.50000	+	4.33013i	−0.152428	+	0.264013i	−0.932119	−	0.362151i	$-0.882042\pi$
$269$	−2.50000	+	4.33013i	−0.152428	+	0.264013i	0.779692	+	0.626164i	$0.215376\pi$
$270$		0			0
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$	2.00000			0.121268
$273$	3.00000	−	15.5885i	0.181568	−	0.943456i
$274$	16.0000			0.966595
$275$		0			0
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−4.00000	−	6.92820i	−0.239904	−	0.415526i
$279$	60.0000			3.59211
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−12.0000	−	20.7846i	−0.714590	−	1.23771i
$283$	4.00000	−	6.92820i	0.237775	−	0.411839i	−0.722300	−	0.691580i	$-0.756915\pi$
$283$	4.00000	−	6.92820i	0.237775	−	0.411839i	0.960076	+	0.279741i	$0.0902485\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$		0			0
$287$	7.50000	−	2.59808i	0.442711	−	0.153360i
$288$	−6.00000			−0.353553
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$	−16.5000	+	12.9904i	−0.962300	+	0.757614i
$295$		0			0
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$		0			0
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$	12.5000	−	4.33013i	0.720488	−	0.249584i
$302$	−6.00000			−0.345261
$303$	22.5000	+	38.9711i	1.29259	+	2.23883i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$		0			0
$306$	6.00000	+	10.3923i	0.342997	+	0.594089i
$307$	19.0000			1.08439			0.542194	−	0.840254i	$-0.317594\pi$
$307$	19.0000			1.08439			0.542194	+	0.840254i	$0.317594\pi$
$308$		0			0
$309$	33.0000			1.87730
$310$		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	$0.221080\pi$
$312$	3.00000	−	5.19615i	0.169842	−	0.294174i
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	0.956647	−	0.291250i	$-0.0940712\pi$
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	−0.730554	+	0.682855i	$0.760738\pi$
$314$	−12.0000			−0.677199
$315$		0			0
$316$	−10.0000			−0.562544
$317$	11.0000	+	19.0526i	0.617822	+	1.07010i	0.989882	+	0.141890i	$0.0453179\pi$
$317$	11.0000	+	19.0526i	0.617822	+	1.07010i	−0.372061	+	0.928208i	$0.621349\pi$
$318$	9.00000	−	15.5885i	0.504695	−	0.874157i
$319$		0			0
$320$		0			0
$321$	21.0000			1.17211
$322$	−0.500000	+	2.59808i	−0.0278639	+	0.144785i
$323$	−4.00000			−0.222566
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	−7.50000	−	12.9904i	−0.414751	−	0.718370i
$328$	3.00000			0.165647
$329$	−16.0000	−	13.8564i	−0.882109	−	0.763928i
$330$		0			0
$331$	−7.00000	−	12.1244i	−0.384755	−	0.666415i	0.606980	−	0.794717i	$-0.292381\pi$
$331$	−7.00000	−	12.1244i	−0.384755	−	0.666415i	−0.991735	+	0.128302i	$0.959047\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	−24.0000	+	41.5692i	−1.31519	+	2.27798i
$334$	4.50000	+	7.79423i	0.246229	+	0.426481i
$335$		0			0
$336$	−7.50000	+	2.59808i	−0.409159	+	0.141737i
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	−15.0000	+	25.9808i	−0.814688	+	1.41108i
$340$		0			0
$341$		0			0
$342$	12.0000			0.648886
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	5.00000			0.269582
$345$		0			0
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	10.5000	−	18.1865i	0.563670	−	0.976304i	−0.433503	−	0.901152i	$-0.642722\pi$
$347$	10.5000	−	18.1865i	0.563670	−	0.976304i	0.997172	−	0.0751519i	$-0.0239442\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	−9.00000			−0.481759			−0.240879	−	0.970555i	$-0.577436\pi$
$349$	−9.00000			−0.481759			−0.240879	+	0.970555i	$0.577436\pi$
$350$		0			0
$351$	18.0000			0.960769
$352$		0			0
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$		0			0
$356$	−7.00000			−0.370999
$357$	12.0000	+	10.3923i	0.635107	+	0.550019i
$358$	26.0000			1.37414
$359$	7.00000	+	12.1244i	0.369446	+	0.639899i	0.989479	−	0.144677i	$-0.0462142\pi$
$359$	7.00000	+	12.1244i	0.369446	+	0.639899i	−0.620033	+	0.784576i	$0.712881\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	2.50000	+	4.33013i	0.131397	+	0.227586i
$363$	−33.0000			−1.73205
$364$	1.00000	−	5.19615i	0.0524142	−	0.272352i
$365$		0			0
$366$	−13.5000	−	23.3827i	−0.705656	−	1.22223i
$367$	−11.5000	+	19.9186i	−0.600295	+	1.03974i	0.392481	+	0.919760i	$0.371617\pi$
$367$	−11.5000	+	19.9186i	−0.600295	+	1.03974i	−0.992776	+	0.119982i	$0.961716\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	9.00000	+	15.5885i	0.468521	+	0.811503i
$370$		0			0
$371$	3.00000	−	15.5885i	0.155752	−	0.809312i
$372$	30.0000			1.55543
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	0.950804	−	0.309794i	$-0.100260\pi$
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	−0.743691	+	0.668523i	$0.766927\pi$
$374$		0			0
$375$		0			0
$376$	−4.00000	−	6.92820i	−0.206284	−	0.357295i
$377$	−2.00000			−0.103005
$378$	−18.0000	−	15.5885i	−0.925820	−	0.801784i
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$		0			0
$381$	−12.0000	+	20.7846i	−0.614779	+	1.06483i
$382$	−10.0000	+	17.3205i	−0.511645	+	0.886194i
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	0.727851	−	0.685736i	$-0.240519\pi$
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	−0.957790	+	0.287469i	$0.907186\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	20.0000			1.01797
$387$	15.0000	+	25.9808i	0.762493	+	1.32068i
$388$		0			0
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$	60.0000			3.02660
$394$	4.00000	+	6.92820i	0.201517	+	0.349038i
$395$		0			0
$396$		0			0
$397$	−16.0000	−	27.7128i	−0.803017	−	1.39087i	−0.917622	−	0.397455i	$-0.869893\pi$
$397$	−16.0000	−	27.7128i	−0.803017	−	1.39087i	0.114605	−	0.993411i	$-0.463440\pi$
$398$	−12.0000			−0.601506
$399$	15.0000	−	5.19615i	0.750939	−	0.260133i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$	10.5000	−	18.1865i	0.523692	−	0.907062i
$403$	−10.0000	+	17.3205i	−0.498135	+	0.862796i
$404$	7.50000	+	12.9904i	0.373139	+	0.646296i
$405$		0			0
$406$	2.00000	+	1.73205i	0.0992583	+	0.0859602i
$407$		0			0
$408$	3.00000	+	5.19615i	0.148522	+	0.257248i
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	−0.575670	−	0.817682i	$-0.695259\pi$
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	0.995968	+	0.0897044i	$0.0285922\pi$
$410$		0			0
$411$	24.0000	+	41.5692i	1.18383	+	2.05046i
$412$	11.0000			0.541931
$413$	1.00000	−	5.19615i	0.0492068	−	0.255686i
$414$	−6.00000			−0.294884
$415$		0			0
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	12.0000	−	20.7846i	0.587643	−	1.01783i
$418$		0			0
$419$	−40.0000			−1.95413			−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000			−1.95413			−0.977064	+	0.212946i	$0.931694\pi$
$420$		0			0
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$	−9.00000	−	15.5885i	−0.438113	−	0.758834i
$423$	24.0000	−	41.5692i	1.16692	−	2.02116i
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$		0			0
$426$	−18.0000			−0.872103
$427$	−18.0000	−	15.5885i	−0.871081	−	0.754378i
$428$	7.00000			0.338358
$429$		0			0
$430$		0			0
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	0.166491	+	0.986043i	$0.446756\pi$
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	−0.937184	+	0.348836i	$0.886577\pi$
$432$	−4.50000	−	7.79423i	−0.216506	−	0.375000i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	25.0000	−	8.66025i	1.20004	−	0.415705i
$435$		0			0
$436$	−2.50000	−	4.33013i	−0.119728	−	0.207375i
$437$	1.00000	−	1.73205i	0.0478365	−	0.0828552i
$438$	15.0000	−	25.9808i	0.716728	−	1.24141i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$	−39.0000	−	15.5885i	−1.85714	−	0.742307i
$442$	−4.00000			−0.190261
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	0.828190	−	0.560448i	$-0.189371\pi$
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	−0.899457	+	0.437009i	$0.856038\pi$
$444$	−12.0000	+	20.7846i	−0.569495	+	0.986394i
$445$		0			0
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$	−45.0000			−2.12843
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$		0			0
$451$		0			0
$452$	−5.00000	+	8.66025i	−0.235180	+	0.407344i
$453$	−9.00000	−	15.5885i	−0.422857	−	0.732410i
$454$	12.0000			0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	0.948566	+	0.316579i	$0.102534\pi$
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	−0.200118	+	0.979772i	$0.564132\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$	−25.0000			−1.16185			−0.580924	−	0.813958i	$-0.697309\pi$
$463$	−25.0000			−1.16185			−0.580924	+	0.813958i	$0.697309\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$		0			0
$466$	7.00000	−	12.1244i	0.324269	−	0.561650i
$467$	0.500000	+	0.866025i	0.0231372	+	0.0400749i	0.877362	−	0.479829i	$-0.159301\pi$
$467$	0.500000	+	0.866025i	0.0231372	+	0.0400749i	−0.854225	+	0.519904i	$0.825968\pi$
$468$	12.0000			0.554700
$469$	3.50000	−	18.1865i	0.161615	−	0.839776i
$470$		0			0
$471$	−18.0000	−	31.1769i	−0.829396	−	1.43656i
$472$	1.00000	−	1.73205i	0.0460287	−	0.0797241i
$473$		0			0
$474$	−15.0000	−	25.9808i	−0.688973	−	1.19334i
$475$		0			0
$476$	4.00000	+	3.46410i	0.183340	+	0.158777i
$477$	36.0000			1.64833
$478$	−5.00000	−	8.66025i	−0.228695	−	0.396111i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$	−18.0000			−0.819878
$483$	−7.50000	+	2.59808i	−0.341262	+	0.118217i
$484$	−11.0000			−0.500000
$485$		0			0
$486$		0			0
$487$	2.00000	−	3.46410i	0.0906287	−	0.156973i	−0.817147	−	0.576429i	$-0.804446\pi$
$487$	2.00000	−	3.46410i	0.0906287	−	0.156973i	0.907776	+	0.419456i	$0.137779\pi$
$488$	−4.50000	−	7.79423i	−0.203705	−	0.352828i
$489$	−36.0000			−1.62798
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	4.50000	+	7.79423i	0.202876	+	0.351391i
$493$	1.00000	−	1.73205i	0.0450377	−	0.0780076i
$494$	−2.00000	+	3.46410i	−0.0899843	+	0.155857i
$495$		0			0
$496$	10.0000			0.449013
$497$	−15.0000	+	5.19615i	−0.672842	+	0.233079i
$498$	−27.0000			−1.20990
$499$	−8.00000	−	13.8564i	−0.358129	−	0.620298i	0.629519	−	0.776985i	$-0.283252\pi$
$499$	−8.00000	−	13.8564i	−0.358129	−	0.620298i	−0.987648	+	0.156687i	$0.949919\pi$
$500$		0			0
$501$	−13.5000	+	23.3827i	−0.603136	+	1.04466i
$502$	−5.00000	−	8.66025i	−0.223161	−	0.386526i
$503$	5.00000			0.222939			0.111469	−	0.993768i	$-0.464444\pi$
$503$	5.00000			0.222939			0.111469	+	0.993768i	$0.464444\pi$
$504$	−12.0000	−	10.3923i	−0.534522	−	0.462910i
$505$		0			0
$506$		0			0
$507$	13.5000	−	23.3827i	0.599556	−	1.03846i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−17.5000	−	30.3109i	−0.775674	−	1.34351i	−0.934415	−	0.356186i	$-0.884077\pi$
$509$	−17.5000	−	30.3109i	−0.775674	−	1.34351i	0.158741	−	0.987320i	$-0.449256\pi$
$510$		0			0
$511$	5.00000	−	25.9808i	0.221187	−	1.14932i
$512$	−1.00000			−0.0441942
$513$	9.00000	+	15.5885i	0.397360	+	0.688247i
$514$	−6.00000	+	10.3923i	−0.264649	+	0.458385i
$515$		0			0
$516$	7.50000	+	12.9904i	0.330169	+	0.571870i
$517$		0			0
$518$	−4.00000	+	20.7846i	−0.175750	+	0.913223i
$519$	−36.0000			−1.58022
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	21.0000			0.915644
$527$	−10.0000	−	17.3205i	−0.435607	−	0.754493i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$	12.0000			0.520756
$532$	5.00000	−	1.73205i	0.216777	−	0.0750939i
$533$	−6.00000			−0.259889
$534$	−10.5000	−	18.1865i	−0.454379	−	0.787008i
$535$		0			0
$536$	3.50000	−	6.06218i	0.151177	−	0.261846i
$537$	39.0000	+	67.5500i	1.68297	+	2.91500i
$538$	−5.00000			−0.215565
$539$		0			0
$540$		0			0
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	0.807267	−	0.590187i	$-0.200946\pi$
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	−0.914750	+	0.404020i	$0.867613\pi$
$542$	3.00000	−	5.19615i	0.128861	−	0.223194i
$543$	−7.50000	+	12.9904i	−0.321856	+	0.557471i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$		0			0
$546$	15.0000	−	5.19615i	0.641941	−	0.222375i
$547$	−37.0000			−1.58201			−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000			−1.58201			−0.791003	+	0.611812i	$0.790441\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	27.0000	−	46.7654i	1.15233	−	1.99590i
$550$		0			0
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$	−3.00000			−0.127688
$553$	−20.0000	−	17.3205i	−0.850487	−	0.736543i
$554$	−26.0000			−1.10463
$555$		0			0
$556$	4.00000	−	6.92820i	0.169638	−	0.293821i
$557$	−2.00000	+	3.46410i	−0.0847427	+	0.146779i	−0.905282	−	0.424812i	$-0.860340\pi$
$557$	−2.00000	+	3.46410i	−0.0847427	+	0.146779i	0.820539	+	0.571591i	$0.193674\pi$
$558$	30.0000	+	51.9615i	1.27000	+	2.19971i
$559$	−10.0000			−0.422955
$560$		0			0
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	5.50000	−	9.52628i	0.231797	−	0.401485i	−0.726540	−	0.687124i	$-0.758873\pi$
$563$	5.50000	−	9.52628i	0.231797	−	0.401485i	0.958337	+	0.285640i	$0.0922060\pi$
$564$	12.0000	−	20.7846i	0.505291	−	0.875190i
$565$		0			0
$566$	8.00000			0.336265
$567$	4.50000	−	23.3827i	0.188982	−	0.981981i
$568$	−6.00000			−0.251754
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	5.00000	−	8.66025i	0.209243	−	0.362420i	−0.742233	−	0.670142i	$-0.766233\pi$
$571$	5.00000	−	8.66025i	0.209243	−	0.362420i	0.951476	+	0.307722i	$0.0995665\pi$
$572$		0			0
$573$	−60.0000			−2.50654
$574$	6.00000	+	5.19615i	0.250435	+	0.216883i
$575$		0			0
$576$	−3.00000	−	5.19615i	−0.125000	−	0.216506i
$577$	−8.00000	+	13.8564i	−0.333044	+	0.576850i	−0.983107	−	0.183031i	$-0.941409\pi$
$577$	−8.00000	+	13.8564i	−0.333044	+	0.576850i	0.650063	+	0.759880i	$0.274743\pi$
$578$	−6.50000	+	11.2583i	−0.270364	+	0.468285i
$579$	30.0000	+	51.9615i	1.24676	+	2.15945i
$580$		0			0
$581$	−22.5000	+	7.79423i	−0.933457	+	0.323359i
$582$		0			0
$583$		0			0
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$		0			0
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$	−28.0000			−1.15568			−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000			−1.15568			−0.577842	+	0.816149i	$0.696105\pi$
$588$	−19.5000	−	7.79423i	−0.804166	−	0.321429i
$589$	−20.0000			−0.824086
$590$		0			0
$591$	−12.0000	+	20.7846i	−0.493614	+	0.854965i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	0.869638	+	0.493689i	$0.164352\pi$
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	−0.00727173	+	0.999974i	$0.502315\pi$
$594$		0			0
$595$		0			0
$596$	−15.0000			−0.614424
$597$	−18.0000	−	31.1769i	−0.736691	−	1.27599i
$598$	1.00000	−	1.73205i	0.0408930	−	0.0708288i
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	0.219061	+	0.975711i	$0.429701\pi$
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	−0.954521	+	0.298143i	$0.903633\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	10.0000	+	8.66025i	0.407570	+	0.352966i
$603$	42.0000			1.71037
$604$	−3.00000	−	5.19615i	−0.122068	−	0.211428i
$605$		0			0
$606$	−22.5000	+	38.9711i	−0.914000	+	1.58309i
$607$	2.50000	+	4.33013i	0.101472	+	0.175754i	0.912291	−	0.409542i	$-0.134311\pi$
$607$	2.50000	+	4.33013i	0.101472	+	0.175754i	−0.810819	+	0.585296i	$0.800978\pi$
$608$	2.00000			0.0811107
$609$	−1.50000	+	7.79423i	−0.0607831	+	0.315838i
$610$		0			0
$611$	8.00000	+	13.8564i	0.323645	+	0.560570i
$612$	−6.00000	+	10.3923i	−0.242536	+	0.420084i
$613$	9.00000	−	15.5885i	0.363507	−	0.629612i	−0.625029	−	0.780602i	$-0.714913\pi$
$613$	9.00000	−	15.5885i	0.363507	−	0.629612i	0.988535	+	0.150990i	$0.0482461\pi$
$614$	9.50000	+	16.4545i	0.383389	+	0.664049i
$615$		0			0
$616$		0			0
$617$	−20.0000			−0.805170			−0.402585	−	0.915383i	$-0.631888\pi$
$617$	−20.0000			−0.805170			−0.402585	+	0.915383i	$0.631888\pi$
$618$	16.5000	+	28.5788i	0.663727	+	1.14961i
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$		0			0
$621$	−4.50000	−	7.79423i	−0.180579	−	0.312772i
$622$	−6.00000			−0.240578
$623$	−14.0000	−	12.1244i	−0.560898	−	0.485752i
$624$	6.00000			0.240192
$625$		0			0
$626$	−4.00000	+	6.92820i	−0.159872	+	0.276907i
$627$		0			0
$628$	−6.00000	−	10.3923i	−0.239426	−	0.414698i
$629$	16.0000			0.637962
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	27.0000	−	46.7654i	1.07315	−	1.85876i
$634$	−11.0000	+	19.0526i	−0.436866	+	0.756674i
$635$		0			0
$636$	18.0000			0.713746
$637$	11.0000	−	8.66025i	0.435836	−	0.343132i
$638$		0			0
$639$	−18.0000	−	31.1769i	−0.712069	−	1.23334i
$640$		0			0
$641$	17.5000	−	30.3109i	0.691208	−	1.19721i	−0.280234	−	0.959932i	$-0.590412\pi$
$641$	17.5000	−	30.3109i	0.691208	−	1.19721i	0.971442	−	0.237276i	$-0.0762547\pi$
$642$	10.5000	+	18.1865i	0.414402	+	0.717765i
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$	−2.50000	+	0.866025i	−0.0985138	+	0.0341262i
$645$		0			0
$646$	−2.00000	−	3.46410i	−0.0786889	−	0.136293i
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	−0.582397	−	0.812905i	$-0.697885\pi$
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	0.995194	+	0.0979182i	$0.0312184\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$		0			0
$650$		0			0
$651$	60.0000	+	51.9615i	2.35159	+	2.03653i
$652$	−12.0000			−0.469956
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	0.904345	+	0.426801i	$0.140360\pi$
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	−0.0825519	+	0.996587i	$0.526307\pi$
$654$	7.50000	−	12.9904i	0.293273	−	0.507964i
$655$		0			0
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	60.0000			2.34082
$658$	4.00000	−	20.7846i	0.155936	−	0.810268i
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	−0.123974	−	0.992286i	$-0.539564\pi$
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	0.921331	−	0.388778i	$-0.127103\pi$
$662$	7.00000	−	12.1244i	0.272063	−	0.471226i
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$	−9.00000			−0.349268
$665$		0			0
$666$	−48.0000			−1.85996
$667$	0.500000	+	0.866025i	0.0193601	+	0.0335326i
$668$	−4.50000	+	7.79423i	−0.174110	+	0.301568i
$669$	−12.0000	+	20.7846i	−0.463947	+	0.803579i
$670$		0			0
$671$		0			0
$672$	−6.00000	−	5.19615i	−0.231455	−	0.200446i
$673$	−20.0000			−0.770943			−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000			−0.770943			−0.385472	+	0.922720i	$0.625961\pi$
$674$	1.00000	+	1.73205i	0.0385186	+	0.0667161i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−1.00000	−	1.73205i	−0.0384331	−	0.0665681i	0.846169	−	0.532915i	$-0.178903\pi$
$677$	−1.00000	−	1.73205i	−0.0384331	−	0.0665681i	−0.884602	+	0.466347i	$0.845570\pi$
$678$	−30.0000			−1.15214
$679$		0			0
$680$		0			0
$681$	18.0000	+	31.1769i	0.689761	+	1.19470i
$682$		0			0
$683$	12.5000	−	21.6506i	0.478299	−	0.828439i	−0.521391	−	0.853318i	$-0.674587\pi$
$683$	12.5000	−	21.6506i	0.478299	−	0.828439i	0.999690	+	0.0248792i	$0.00792011\pi$
$684$	6.00000	+	10.3923i	0.229416	+	0.397360i
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	30.0000			1.14457
$688$	2.50000	+	4.33013i	0.0953116	+	0.165085i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	21.0000			0.797149
$695$		0			0
$696$	−1.50000	+	2.59808i	−0.0568574	+	0.0984798i
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	−4.50000	−	7.79423i	−0.170328	−	0.295016i
$699$	42.0000			1.58859
$700$		0			0
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$	9.00000	+	15.5885i	0.339683	+	0.588348i
$703$	8.00000	−	13.8564i	0.301726	−	0.522604i
$704$		0			0
$705$		0			0
$706$	−6.00000			−0.225813
$707$	−7.50000	+	38.9711i	−0.282067	+	1.46566i
$708$	6.00000			0.225494
$709$	4.50000	+	7.79423i	0.169001	+	0.292718i	0.938069	−	0.346449i	$-0.112613\pi$
$709$	4.50000	+	7.79423i	0.169001	+	0.292718i	−0.769068	+	0.639167i	$0.779279\pi$
$710$		0			0
$711$	30.0000	−	51.9615i	1.12509	−	1.94871i
$712$	−3.50000	−	6.06218i	−0.131168	−	0.227190i
$713$	10.0000			0.374503
$714$	−3.00000	+	15.5885i	−0.112272	+	0.583383i
$715$		0			0
$716$	13.0000	+	22.5167i	0.485833	+	0.841487i
$717$	15.0000	−	25.9808i	0.560185	−	0.970269i
$718$	−7.00000	+	12.1244i	−0.261238	+	0.452477i
$719$	−10.0000	−	17.3205i	−0.372937	−	0.645946i	0.617079	−	0.786901i	$-0.288316\pi$
$719$	−10.0000	−	17.3205i	−0.372937	−	0.645946i	−0.990016	+	0.140955i	$0.954983\pi$
$720$		0			0
$721$	22.0000	+	19.0526i	0.819323	+	0.709554i
$722$	15.0000			0.558242
$723$	−27.0000	−	46.7654i	−1.00414	−	1.73922i
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$		0			0
$726$	−16.5000	−	28.5788i	−0.612372	−	1.06066i
$727$	29.0000			1.07555			0.537775	−	0.843088i	$-0.319265\pi$
$727$	29.0000			1.07555			0.537775	+	0.843088i	$0.319265\pi$
$728$	5.00000	−	1.73205i	0.185312	−	0.0641941i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	5.00000	−	8.66025i	0.184932	−	0.320311i
$732$	13.5000	−	23.3827i	0.498974	−	0.864249i
$733$	−8.00000	−	13.8564i	−0.295487	−	0.511798i	0.679611	−	0.733572i	$-0.262148\pi$
$733$	−8.00000	−	13.8564i	−0.295487	−	0.511798i	−0.975098	+	0.221774i	$0.928815\pi$
$734$	−23.0000			−0.848945
$735$		0			0
$736$	−1.00000			−0.0368605
$737$		0			0
$738$	−9.00000	+	15.5885i	−0.331295	+	0.573819i
$739$	16.0000	−	27.7128i	0.588570	−	1.01943i	−0.405851	−	0.913939i	$-0.633025\pi$
$739$	16.0000	−	27.7128i	0.588570	−	1.01943i	0.994420	−	0.105493i	$-0.0336420\pi$
$740$		0			0
$741$	−12.0000			−0.440831
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	3.00000			0.110059			0.0550297	−	0.998485i	$-0.482475\pi$
$743$	3.00000			0.110059			0.0550297	+	0.998485i	$0.482475\pi$
$744$	15.0000	+	25.9808i	0.549927	+	0.952501i
$745$		0			0
$746$	−4.00000	+	6.92820i	−0.146450	+	0.253660i
$747$	−27.0000	−	46.7654i	−0.987878	−	1.71106i
$748$		0			0
$749$	14.0000	+	12.1244i	0.511549	+	0.443014i
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$	15.0000	−	25.9808i	0.546630	−	0.946792i
$754$	−1.00000	−	1.73205i	−0.0364179	−	0.0630776i
$755$		0			0
$756$	4.50000	−	23.3827i	0.163663	−	0.850420i
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$	−1.00000	−	1.73205i	−0.0363216	−	0.0629109i
$759$		0			0
$760$		0			0
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.819231	+	0.573463i	$0.194400\pi$
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.0870179	+	0.996207i	$0.472266\pi$
$762$	−24.0000			−0.869428
$763$	2.50000	−	12.9904i	0.0905061	−	0.470283i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	4.50000	−	7.79423i	0.162592	−	0.281617i
$767$	−2.00000	+	3.46410i	−0.0722158	+	0.125081i
$768$	−1.50000	−	2.59808i	−0.0541266	−	0.0937500i
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$	10.0000	+	17.3205i	0.359908	+	0.623379i
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$	−15.0000	+	25.9808i	−0.539164	+	0.933859i
$775$		0			0
$776$		0			0
$777$	−60.0000	+	20.7846i	−2.15249	+	0.745644i
$778$	18.0000			0.645331
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$		0			0
$781$		0			0
$782$	1.00000	+	1.73205i	0.0357599	+	0.0619380i
$783$	−9.00000			−0.321634
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$	30.0000	+	51.9615i	1.07006	+	1.85341i
$787$	10.5000	−	18.1865i	0.374285	−	0.648280i	−0.615935	−	0.787797i	$-0.711222\pi$
$787$	10.5000	−	18.1865i	0.374285	−	0.648280i	0.990220	+	0.139517i	$0.0445550\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$	31.5000	+	54.5596i	1.12143	+	1.94237i
$790$		0			0
$791$	−25.0000	+	8.66025i	−0.888898	+	0.307923i
$792$		0			0
$793$	9.00000	+	15.5885i	0.319599	+	0.553562i
$794$	16.0000	−	27.7128i	0.567819	−	0.983491i
$795$		0			0
$796$	−6.00000	−	10.3923i	−0.212664	−	0.368345i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$	12.0000	+	10.3923i	0.424795	+	0.367884i
$799$	−16.0000			−0.566039
$800$		0			0
$801$	21.0000	−	36.3731i	0.741999	−	1.28518i
$802$	1.50000	−	2.59808i	0.0529668	−	0.0917413i
$803$		0			0
$804$	21.0000			0.740613
$805$		0			0
$806$	−20.0000			−0.704470
$807$	−7.50000	−	12.9904i	−0.264013	−	0.457283i
$808$	−7.50000	+	12.9904i	−0.263849	+	0.457000i
$809$	−12.5000	+	21.6506i	−0.439477	+	0.761196i	−0.997649	−	0.0685291i	$-0.978169\pi$
$809$	−12.5000	+	21.6506i	−0.439477	+	0.761196i	0.558173	+	0.829725i	$0.311503\pi$
$810$		0			0
$811$	6.00000			0.210688			0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000			0.210688			0.105344	+	0.994436i	$0.466406\pi$
$812$	−0.500000	+	2.59808i	−0.0175466	+	0.0911746i
$813$	18.0000			0.631288
$814$		0			0
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−5.00000	−	8.66025i	−0.174928	−	0.302984i
$818$	17.0000			0.594391
$819$	24.0000	+	20.7846i	0.838628	+	0.726273i
$820$		0			0
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$	−24.0000	+	41.5692i	−0.837096	+	1.44989i
$823$	−22.5000	+	38.9711i	−0.784301	+	1.35845i	0.145115	+	0.989415i	$0.453645\pi$
$823$	−22.5000	+	38.9711i	−0.784301	+	1.35845i	−0.929416	+	0.369034i	$0.879689\pi$
$824$	5.50000	+	9.52628i	0.191602	+	0.331864i
$825$		0			0
$826$	5.00000	−	1.73205i	0.173972	−	0.0602658i
$827$	37.0000			1.28662			0.643308	−	0.765607i	$-0.277561\pi$
$827$	37.0000			1.28662			0.643308	+	0.765607i	$0.277561\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	0.403739	+	0.914874i	$0.367710\pi$
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$830$		0			0
$831$	−39.0000	−	67.5500i	−1.35290	−	2.34328i
$832$	2.00000			0.0693375
$833$	2.00000	+	13.8564i	0.0692959	+	0.480096i
$834$	24.0000			0.831052
$835$		0			0
$836$		0			0
$837$	−45.0000	+	77.9423i	−1.55543	+	2.69408i
$838$	−20.0000	−	34.6410i	−0.690889	−	1.19665i
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	15.5000	+	26.8468i	0.534165	+	0.925201i
$843$	−27.0000	+	46.7654i	−0.929929	+	1.61068i
$844$	9.00000	−	15.5885i	0.309793	−	0.536577i
$845$		0			0
$846$	48.0000			1.65027
$847$	−22.0000	−	19.0526i	−0.755929	−	0.654654i
$848$	6.00000			0.206041
$849$	12.0000	+	20.7846i	0.411839	+	0.713326i
$850$		0			0
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$	−9.00000	−	15.5885i	−0.308335	−	0.534052i
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$	4.50000	−	23.3827i	0.153987	−	0.800139i
$855$		0			0
$856$	3.50000	+	6.06218i	0.119628	+	0.207201i
$857$	−2.00000	+	3.46410i	−0.0683187	+	0.118331i	−0.898161	−	0.439666i	$-0.855097\pi$
$857$	−2.00000	+	3.46410i	−0.0683187	+	0.118331i	0.829843	+	0.557998i	$0.188430\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$		0			0
$861$	−4.50000	+	23.3827i	−0.153360	+	0.796880i
$862$	−32.0000			−1.08992
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	0.757101	−	0.653298i	$-0.226615\pi$
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	−0.944323	+	0.329020i	$0.893282\pi$
$864$	4.50000	−	7.79423i	0.153093	−	0.265165i
$865$		0			0
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$	−39.0000			−1.32451
$868$	20.0000	+	17.3205i	0.678844	+	0.587896i
$869$		0			0
$870$		0			0
$871$	−7.00000	+	12.1244i	−0.237186	+	0.410818i
$872$	2.50000	−	4.33013i	0.0846607	−	0.146637i
$873$		0			0
$874$	2.00000			0.0676510
$875$		0			0
$876$	30.0000			1.01361
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$	36.0000	−	62.3538i	1.21425	−	2.10314i
$880$		0			0
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$	−6.00000	−	41.5692i	−0.202031	−	1.39971i
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$		0			0
$886$	1.50000	−	2.59808i	0.0503935	−	0.0872841i
$887$	4.50000	+	7.79423i	0.151095	+	0.261705i	0.931630	−	0.363407i	$-0.118387\pi$
$887$	4.50000	+	7.79423i	0.151095	+	0.261705i	−0.780535	+	0.625112i	$0.785053\pi$
$888$	−24.0000			−0.805387
$889$	−20.0000	+	6.92820i	−0.670778	+	0.232364i
$890$		0			0
$891$		0			0
$892$	−4.00000	+	6.92820i	−0.133930	+	0.231973i
$893$	−8.00000	+	13.8564i	−0.267710	+	0.463687i
$894$	−22.5000	−	38.9711i	−0.752513	−	1.30339i
$895$		0			0
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$	6.00000			0.200334
$898$	11.5000	+	19.9186i	0.383760	+	0.664692i
$899$	5.00000	−	8.66025i	0.166759	−	0.288836i
$900$		0			0
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$		0			0
$903$	−7.50000	+	38.9711i	−0.249584	+	1.29688i
$904$	−10.0000			−0.332595
$905$		0			0
$906$	9.00000	−	15.5885i	0.299005	−	0.517892i
$907$	−12.5000	+	21.6506i	−0.415056	+	0.718898i	−0.995434	−	0.0954492i	$-0.969571\pi$
$907$	−12.5000	+	21.6506i	−0.415056	+	0.718898i	0.580379	+	0.814347i	$0.302905\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	−90.0000			−2.98511
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$	3.00000	+	5.19615i	0.0993399	+	0.172062i
$913$		0			0
$914$	−16.0000	+	27.7128i	−0.529233	+	0.916658i
$915$		0			0
$916$	10.0000			0.330409
$917$	40.0000	+	34.6410i	1.32092	+	1.14395i
$918$	−18.0000			−0.594089
$919$	−13.0000	−	22.5167i	−0.428830	−	0.742756i	0.567939	−	0.823071i	$-0.307741\pi$
$919$	−13.0000	−	22.5167i	−0.428830	−	0.742756i	−0.996770	+	0.0803145i	$0.974408\pi$
$920$		0			0
$921$	−28.5000	+	49.3634i	−0.939107	+	1.62658i
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$	12.0000			0.394985
$924$		0			0
$925$		0			0
$926$	−12.5000	−	21.6506i	−0.410775	−	0.711484i
$927$	−33.0000	+	57.1577i	−1.08386	+	1.87730i
$928$	−0.500000	+	0.866025i	−0.0164133	+	0.0284287i
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	13.0000	+	5.19615i	0.426058	+	0.170297i
$932$	14.0000			0.458585
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$	−0.500000	+	0.866025i	−0.0163605	+	0.0283372i
$935$		0			0
$936$	6.00000	+	10.3923i	0.196116	+	0.339683i
$937$	56.0000			1.82944			0.914720	−	0.404088i	$-0.132411\pi$
$937$	56.0000			1.82944			0.914720	+	0.404088i	$0.132411\pi$
$938$	17.5000	−	6.06218i	0.571395	−	0.197937i
$939$	−24.0000			−0.783210
$940$		0			0
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	−0.957273	−	0.289187i	$-0.906615\pi$
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	0.729079	+	0.684429i	$0.239949\pi$
$942$	18.0000	−	31.1769i	0.586472	−	1.01580i
$943$	1.50000	+	2.59808i	0.0488467	+	0.0846050i
$944$	2.00000			0.0650945
$945$		0			0
$946$		0			0
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	0.840624	−	0.541619i	$-0.182188\pi$
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	−0.889368	+	0.457193i	$0.848855\pi$
$948$	15.0000	−	25.9808i	0.487177	−	0.843816i
$949$	−10.0000	+	17.3205i	−0.324614	+	0.562247i
$950$		0			0
$951$	−66.0000			−2.14020
$952$	−1.00000	+	5.19615i	−0.0324102	+	0.168408i
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$	18.0000	+	31.1769i	0.582772	+	1.00939i
$955$		0			0
$956$	5.00000	−	8.66025i	0.161712	−	0.280093i
$957$		0			0
$958$	−18.0000			−0.581554
$959$	−8.00000	+	41.5692i	−0.258333	+	1.34234i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	8.00000	−	13.8564i	0.257930	−	0.446748i
$963$	−21.0000	+	36.3731i	−0.676716	+	1.17211i
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$		0			0
$966$	−6.00000	−	5.19615i	−0.193047	−	0.167183i
$967$	−17.0000			−0.546683			−0.273342	−	0.961917i	$-0.588129\pi$
$967$	−17.0000			−0.546683			−0.273342	+	0.961917i	$0.588129\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$	6.00000	−	10.3923i	0.192748	−	0.333849i
$970$		0			0
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$		0			0
$973$	20.0000	−	6.92820i	0.641171	−	0.222108i
$974$	4.00000			0.128168
$975$		0			0
$976$	4.50000	−	7.79423i	0.144041	−	0.249487i
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	−0.420075	−	0.907489i	$-0.637996\pi$
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	0.995946	−	0.0899487i	$-0.0286703\pi$
$978$	−18.0000	−	31.1769i	−0.575577	−	0.996928i
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$	−9.00000	−	15.5885i	−0.287202	−	0.497448i
$983$	12.5000	−	21.6506i	0.398688	−	0.690548i	−0.594876	−	0.803817i	$-0.702799\pi$
$983$	12.5000	−	21.6506i	0.398688	−	0.690548i	0.993564	+	0.113269i	$0.0361323\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$		0			0
$986$	2.00000			0.0636930
$987$	60.0000	−	20.7846i	1.90982	−	0.661581i
$988$	−4.00000			−0.127257
$989$	2.50000	+	4.33013i	0.0794954	+	0.137690i
$990$		0			0
$991$	13.0000	−	22.5167i	0.412959	−	0.715265i	−0.582253	−	0.813008i	$-0.697829\pi$
$991$	13.0000	−	22.5167i	0.412959	−	0.715265i	0.995212	+	0.0977423i	$0.0311621\pi$
$992$	5.00000	+	8.66025i	0.158750	+	0.274963i
$993$	42.0000			1.33283
$994$	−12.0000	−	10.3923i	−0.380617	−	0.329624i
$995$		0			0
$996$	−13.5000	−	23.3827i	−0.427764	−	0.740909i
$997$	17.0000	−	29.4449i	0.538395	−	0.932528i	−0.460595	−	0.887610i	$-0.652364\pi$
$997$	17.0000	−	29.4449i	0.538395	−	0.932528i	0.998991	−	0.0449179i	$-0.0143026\pi$
$998$	8.00000	−	13.8564i	0.253236	−	0.438617i
$999$	−36.0000	−	62.3538i	−1.13899	−	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.e.g.151.1		2
5.2	odd	4		70.2.i.a.39.1	yes	4
5.3	odd	4		70.2.i.a.39.2	yes	4
5.4	even	2		350.2.e.f.151.1		2
7.2	even	3	inner	350.2.e.g.51.1		2
7.3	odd	6		2450.2.a.c.1.1		1
7.4	even	3		2450.2.a.r.1.1		1
15.2	even	4		630.2.u.b.109.2		4
15.8	even	4		630.2.u.b.109.1		4
20.3	even	4		560.2.bw.c.529.2		4
20.7	even	4		560.2.bw.c.529.1		4
35.2	odd	12		70.2.i.a.9.2	yes	4
35.3	even	12		490.2.c.b.99.2		2
35.4	even	6		2450.2.a.s.1.1		1
35.9	even	6		350.2.e.f.51.1		2
35.12	even	12		490.2.i.b.79.2		4
35.13	even	4		490.2.i.b.459.2		4
35.17	even	12		490.2.c.b.99.1		2
35.18	odd	12		490.2.c.c.99.2		2
35.23	odd	12		70.2.i.a.9.1	✓	4
35.24	odd	6		2450.2.a.bh.1.1		1
35.27	even	4		490.2.i.b.459.1		4
35.32	odd	12		490.2.c.c.99.1		2
35.33	even	12		490.2.i.b.79.1		4
105.2	even	12		630.2.u.b.289.1		4
105.23	even	12		630.2.u.b.289.2		4
140.23	even	12		560.2.bw.c.289.1		4
140.107	even	12		560.2.bw.c.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.a.9.1	✓	4	35.23	odd	12
70.2.i.a.9.2	yes	4	35.2	odd	12
70.2.i.a.39.1	yes	4	5.2	odd	4
70.2.i.a.39.2	yes	4	5.3	odd	4
350.2.e.f.51.1		2	35.9	even	6
350.2.e.f.151.1		2	5.4	even	2
350.2.e.g.51.1		2	7.2	even	3	inner
350.2.e.g.151.1		2	1.1	even	1	trivial
490.2.c.b.99.1		2	35.17	even	12
490.2.c.b.99.2		2	35.3	even	12
490.2.c.c.99.1		2	35.32	odd	12
490.2.c.c.99.2		2	35.18	odd	12
490.2.i.b.79.1		4	35.33	even	12
490.2.i.b.79.2		4	35.12	even	12
490.2.i.b.459.1		4	35.27	even	4
490.2.i.b.459.2		4	35.13	even	4
560.2.bw.c.289.1		4	140.23	even	12
560.2.bw.c.289.2		4	140.107	even	12
560.2.bw.c.529.1		4	20.7	even	4
560.2.bw.c.529.2		4	20.3	even	4
630.2.u.b.109.1		4	15.8	even	4
630.2.u.b.109.2		4	15.2	even	4
630.2.u.b.289.1		4	105.2	even	12
630.2.u.b.289.2		4	105.23	even	12
2450.2.a.c.1.1		1	7.3	odd	6
2450.2.a.r.1.1		1	7.4	even	3
2450.2.a.s.1.1		1	35.4	even	6
2450.2.a.bh.1.1		1	35.24	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{12} +2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(3.00000 - 5.19615i) q^{18} +(1.00000 + 1.73205i) q^{19} +(1.50000 - 7.79423i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(1.50000 - 2.59808i) q^{24} +(1.00000 + 1.73205i) q^{26} +9.00000 q^{27} +(0.500000 - 2.59808i) q^{28} -1.00000 q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} -2.00000 q^{34} +6.00000 q^{36} +(-4.00000 - 6.92820i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-3.00000 + 5.19615i) q^{39} -3.00000 q^{41} +(7.50000 - 2.59808i) q^{42} -5.00000 q^{43} +(0.500000 - 0.866025i) q^{46} +(4.00000 + 6.92820i) q^{47} +3.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(4.50000 + 7.79423i) q^{54} +(2.50000 - 0.866025i) q^{56} -6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(4.50000 + 7.79423i) q^{61} -10.0000 q^{62} +(12.0000 + 10.3923i) q^{63} +1.00000 q^{64} +(-3.50000 + 6.06218i) q^{67} +(-1.00000 - 1.73205i) q^{68} +3.00000 q^{69} +6.00000 q^{71} +(3.00000 + 5.19615i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(4.00000 - 6.92820i) q^{74} -2.00000 q^{76} -6.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(6.00000 + 5.19615i) q^{84} +(-2.50000 - 4.33013i) q^{86} +(1.50000 - 2.59808i) q^{87} +(3.50000 + 6.06218i) q^{89} +(-5.00000 + 1.73205i) q^{91} +1.00000 q^{92} +(-15.0000 - 25.9808i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(1.50000 + 2.59808i) q^{96} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{6} - 5 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^6 - 5 * q^7 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{6} - 5 q^{7} - 2 q^{8} - 6 q^{9} - 3 q^{12} + 4 q^{13} - 4 q^{14} - q^{16} - 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{21} - q^{23} + 3 q^{24} + 2 q^{26} + 18 q^{27} + q^{28} - 2 q^{29} - 10 q^{31} + q^{32} - 4 q^{34} + 12 q^{36} - 8 q^{37} - 2 q^{38} - 6 q^{39} - 6 q^{41} + 15 q^{42} - 10 q^{43} + q^{46} + 8 q^{47} + 6 q^{48} + 11 q^{49} - 6 q^{51} - 2 q^{52} - 6 q^{53} + 9 q^{54} + 5 q^{56} - 12 q^{57} - q^{58} - 2 q^{59} + 9 q^{61} - 20 q^{62} + 24 q^{63} + 2 q^{64} - 7 q^{67} - 2 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} - 10 q^{73} + 8 q^{74} - 4 q^{76} - 12 q^{78} + 10 q^{79} - 9 q^{81} - 3 q^{82} + 18 q^{83} + 12 q^{84} - 5 q^{86} + 3 q^{87} + 7 q^{89} - 10 q^{91} + 2 q^{92} - 30 q^{93} - 8 q^{94} + 3 q^{96} + 13 q^{98}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^6 - 5 * q^7 - 2 * q^8 - 6 * q^9 - 3 * q^12 + 4 * q^13 - 4 * q^14 - q^16 - 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^21 - q^23 + 3 * q^24 + 2 * q^26 + 18 * q^27 + q^28 - 2 * q^29 - 10 * q^31 + q^32 - 4 * q^34 + 12 * q^36 - 8 * q^37 - 2 * q^38 - 6 * q^39 - 6 * q^41 + 15 * q^42 - 10 * q^43 + q^46 + 8 * q^47 + 6 * q^48 + 11 * q^49 - 6 * q^51 - 2 * q^52 - 6 * q^53 + 9 * q^54 + 5 * q^56 - 12 * q^57 - q^58 - 2 * q^59 + 9 * q^61 - 20 * q^62 + 24 * q^63 + 2 * q^64 - 7 * q^67 - 2 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 - 10 * q^73 + 8 * q^74 - 4 * q^76 - 12 * q^78 + 10 * q^79 - 9 * q^81 - 3 * q^82 + 18 * q^83 + 12 * q^84 - 5 * q^86 + 3 * q^87 + 7 * q^89 - 10 * q^91 + 2 * q^92 - 30 * q^93 - 8 * q^94 + 3 * q^96 + 13 * q^98

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