LMFDB - Embedded newform 1050.2.i.j.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.i (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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.151
Dual form			1050.2.i.j.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(2.00000 - 1.73205i) q^{21} -2.00000 q^{22} +(2.50000 + 4.33013i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(5.50000 - 9.52628i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +5.00000 q^{34} +1.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} +5.00000 q^{41} +(-2.50000 - 0.866025i) q^{42} +(1.00000 + 1.73205i) q^{44} +(2.50000 - 4.33013i) q^{46} +(-0.500000 - 0.866025i) q^{47} -1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(2.50000 + 4.33013i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(6.00000 - 10.3923i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} +4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(1.00000 - 1.73205i) q^{59} +(-5.00000 - 8.66025i) q^{61} -11.0000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-2.50000 - 4.33013i) q^{68} +5.00000 q^{69} -1.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} -4.00000 q^{76} +(4.00000 - 3.46410i) q^{77} -4.00000 q^{78} +(-4.50000 - 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -6.00000 q^{83} +(0.500000 + 2.59808i) q^{84} +(-3.00000 + 5.19615i) q^{87} +(1.00000 - 1.73205i) q^{88} +(-5.50000 - 9.52628i) q^{89} +(10.0000 + 3.46410i) q^{91} -5.00000 q^{92} +(-5.50000 - 9.52628i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000 q^{97} +(1.00000 - 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9} + 2 q^{11} + q^{12} + 8 q^{13} - q^{14} - q^{16} - 5 q^{17} - q^{18} + 4 q^{19} + 4 q^{21} - 4 q^{22} + 5 q^{23} + q^{24} - 4 q^{26} - 2 q^{27} - 4 q^{28} - 12 q^{29} + 11 q^{31} - q^{32} - 2 q^{33} + 10 q^{34} + 2 q^{36} + 8 q^{37} + 4 q^{38} + 4 q^{39} + 10 q^{41} - 5 q^{42} + 2 q^{44} + 5 q^{46} - q^{47} - 2 q^{48} + 11 q^{49} + 5 q^{51} - 4 q^{52} + 12 q^{53} + q^{54} + 5 q^{56} + 8 q^{57} + 6 q^{58} + 2 q^{59} - 10 q^{61} - 22 q^{62} - q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{68} + 10 q^{69} - 2 q^{71} - q^{72} + 2 q^{73} + 8 q^{74} - 8 q^{76} + 8 q^{77} - 8 q^{78} - 9 q^{79} - q^{81} - 5 q^{82} - 12 q^{83} + q^{84} - 6 q^{87} + 2 q^{88} - 11 q^{89} + 20 q^{91} - 10 q^{92} - 11 q^{93} - q^{94} + q^{96} + 2 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9 + 2 * q^11 + q^12 + 8 * q^13 - q^14 - q^16 - 5 * q^17 - q^18 + 4 * q^19 + 4 * q^21 - 4 * q^22 + 5 * q^23 + q^24 - 4 * q^26 - 2 * q^27 - 4 * q^28 - 12 * q^29 + 11 * q^31 - q^32 - 2 * q^33 + 10 * q^34 + 2 * q^36 + 8 * q^37 + 4 * q^38 + 4 * q^39 + 10 * q^41 - 5 * q^42 + 2 * q^44 + 5 * q^46 - q^47 - 2 * q^48 + 11 * q^49 + 5 * q^51 - 4 * q^52 + 12 * q^53 + q^54 + 5 * q^56 + 8 * q^57 + 6 * q^58 + 2 * q^59 - 10 * q^61 - 22 * q^62 - q^63 + 2 * q^64 - 2 * q^66 - 5 * q^68 + 10 * q^69 - 2 * q^71 - q^72 + 2 * q^73 + 8 * q^74 - 8 * q^76 + 8 * q^77 - 8 * q^78 - 9 * q^79 - q^81 - 5 * q^82 - 12 * q^83 + q^84 - 6 * q^87 + 2 * q^88 - 11 * q^89 + 20 * q^91 - 10 * q^92 - 11 * q^93 - q^94 + q^96 + 2 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		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	$0.0691756\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$		0			0
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$	−2.00000			−0.426401
$23$	2.50000	+	4.33013i	0.521286	+	0.902894i	0.999694	+	0.0247559i	$0.00788087\pi$
$23$	2.50000	+	4.33013i	0.521286	+	0.902894i	−0.478407	+	0.878138i	$0.658786\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$	−1.00000			−0.192450
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	5.50000	−	9.52628i	0.987829	−	1.71097i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	5.50000	−	9.52628i	0.987829	−	1.71097i	0.628619	−	0.777714i	$-0.283621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	5.00000			0.857493
$35$		0			0
$36$	1.00000			0.166667
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$	−2.50000	−	0.866025i	−0.385758	−	0.133631i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	2.50000	−	4.33013i	0.368605	−	0.638442i
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	0.827253	−	0.561830i	$-0.189902\pi$
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	−0.900185	+	0.435507i	$0.856569\pi$
$48$	−1.00000			−0.144338
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	2.50000	+	4.33013i	0.350070	+	0.606339i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$	4.00000			0.529813
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	−0.793560	−	0.608492i	$-0.791775\pi$
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	0.923749	+	0.382998i	$0.125108\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−11.0000			−1.39700
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$	5.00000			0.601929
$70$		0			0
$71$	−1.00000			−0.118678			−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000			−0.118678			−0.0593391	+	0.998238i	$0.518899\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	−4.00000			−0.458831
$77$	4.00000	−	3.46410i	0.455842	−	0.394771i
$78$	−4.00000			−0.452911
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	−0.999974	−	0.00727784i	$-0.997683\pi$
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	0.493684	−	0.869641i	$-0.335650\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	0.500000	+	2.59808i	0.0545545	+	0.283473i
$85$		0			0
$86$		0			0
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	−5.50000	−	9.52628i	−0.582999	−	1.00978i	−0.995122	−	0.0986553i	$-0.968546\pi$
$89$	−5.50000	−	9.52628i	−0.582999	−	1.00978i	0.412123	−	0.911128i	$-0.364787\pi$
$90$		0			0
$91$	10.0000	+	3.46410i	1.04828	+	0.363137i
$92$	−5.00000			−0.521286
$93$	−5.50000	−	9.52628i	−0.570323	−	0.987829i
$94$	−0.500000	+	0.866025i	−0.0515711	+	0.0893237i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	1.00000			0.101535			0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000			0.101535			0.0507673	+	0.998711i	$0.483833\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	2.50000	−	4.33013i	0.247537	−	0.428746i
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	−12.0000			−1.16554
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−5.00000			−0.470360			−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000			−0.470360			−0.235180	+	0.971952i	$0.575568\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	−2.00000			−0.184115
$119$	−10.0000	+	8.66025i	−0.916698	+	0.793884i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$	2.50000	−	4.33013i	0.225417	−	0.390434i
$124$	5.50000	+	9.52628i	0.493915	+	0.855485i
$125$		0			0
$126$	−2.00000	+	1.73205i	−0.178174	+	0.154303i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$	2.00000			0.174078
$133$	2.00000	+	10.3923i	0.173422	+	0.901127i
$134$		0			0
$135$		0			0
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	11.5000	−	19.9186i	0.982511	−	1.70176i	0.329999	−	0.943981i	$-0.392952\pi$
$137$	11.5000	−	19.9186i	0.982511	−	1.70176i	0.652512	−	0.757778i	$-0.273715\pi$
$138$	−2.50000	−	4.33013i	−0.212814	−	0.368605i
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$	−1.00000			−0.0842152
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$	4.00000	−	6.92820i	0.334497	−	0.579365i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	6.50000	−	2.59808i	0.536111	−	0.214286i
$148$	−8.00000			−0.657596
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	5.00000			0.404226
$154$	−5.00000	−	1.73205i	−0.402911	−	0.139573i
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−4.50000	+	7.79423i	−0.358001	+	0.620076i
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$	2.50000	+	12.9904i	0.197028	+	1.02379i
$162$	1.00000			0.0785674
$163$	12.0000	+	20.7846i	0.939913	+	1.62798i	0.765631	+	0.643280i	$0.222427\pi$
$163$	12.0000	+	20.7846i	0.939913	+	1.62798i	0.174282	+	0.984696i	$0.444240\pi$
$164$	−2.50000	+	4.33013i	−0.195217	+	0.338126i
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	−16.0000			−1.23812			−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000			−1.23812			−0.619059	+	0.785345i	$0.712486\pi$
$168$	2.00000	−	1.73205i	0.154303	−	0.133631i
$169$	3.00000			0.230769
$170$		0			0
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$		0			0
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	0.825505	−	0.564396i	$-0.190891\pi$
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	−0.901533	+	0.432710i	$0.857557\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$	−2.00000			−0.150756
$177$	−1.00000	−	1.73205i	−0.0751646	−	0.130189i
$178$	−5.50000	+	9.52628i	−0.412242	+	0.714025i
$179$	−11.0000	+	19.0526i	−0.822179	+	1.42406i	0.0818780	+	0.996642i	$0.473908\pi$
$179$	−11.0000	+	19.0526i	−0.822179	+	1.42406i	−0.904057	+	0.427413i	$0.859425\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−2.00000	−	10.3923i	−0.148250	−	0.770329i
$183$	−10.0000			−0.739221
$184$	2.50000	+	4.33013i	0.184302	+	0.319221i
$185$		0			0
$186$	−5.50000	+	9.52628i	−0.403280	+	0.698501i
$187$	5.00000	+	8.66025i	0.365636	+	0.633300i
$188$	1.00000			0.0729325
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	12.5000	+	21.6506i	0.904468	+	1.56658i	0.821629	+	0.570022i	$0.193065\pi$
$191$	12.5000	+	21.6506i	0.904468	+	1.56658i	0.0828388	+	0.996563i	$0.473601\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$	−0.500000	−	0.866025i	−0.0358979	−	0.0621770i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	24.0000			1.70993			0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000			1.70993			0.854965	+	0.518686i	$0.173579\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	−0.940927	−	0.338608i	$-0.890044\pi$
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	0.763707	+	0.645563i	$0.223377\pi$
$200$		0			0
$201$		0			0
$202$	12.0000			0.844317
$203$	−15.0000	−	5.19615i	−1.05279	−	0.364698i
$204$	−5.00000			−0.350070
$205$		0			0
$206$	6.50000	−	11.2583i	0.452876	−	0.784405i
$207$	2.50000	−	4.33013i	0.173762	−	0.300965i
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$	8.00000			0.553372
$210$		0			0
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$	−0.500000	+	0.866025i	−0.0342594	+	0.0593391i
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	22.0000	−	19.0526i	1.49346	−	1.29337i
$218$	4.00000			0.270914
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$		0			0
$221$	−10.0000	+	17.3205i	−0.672673	+	1.16510i
$222$	−4.00000	−	6.92820i	−0.268462	−	0.464991i
$223$	−21.0000			−1.40626			−0.703132	−	0.711059i	$-0.748216\pi$
$223$	−21.0000			−1.40626			−0.703132	+	0.711059i	$0.748216\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	2.50000	+	4.33013i	0.166298	+	0.288036i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$	−1.00000	−	5.19615i	−0.0657952	−	0.341882i
$232$	−6.00000			−0.393919
$233$	13.0000	+	22.5167i	0.851658	+	1.47512i	0.879711	+	0.475509i	$0.157736\pi$
$233$	13.0000	+	22.5167i	0.851658	+	1.47512i	−0.0280525	+	0.999606i	$0.508931\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$		0			0
$236$	1.00000	+	1.73205i	0.0650945	+	0.112747i
$237$	−9.00000			−0.584613
$238$	12.5000	+	4.33013i	0.810255	+	0.280680i
$239$	11.0000			0.711531			0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000			0.711531			0.355765	+	0.934575i	$0.384220\pi$
$240$		0			0
$241$	3.00000	−	5.19615i	0.193247	−	0.334714i	−0.753077	−	0.657932i	$-0.771431\pi$
$241$	3.00000	−	5.19615i	0.193247	−	0.334714i	0.946324	+	0.323218i	$0.104765\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	10.0000			0.640184
$245$		0			0
$246$	−5.00000			−0.318788
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$	5.50000	−	9.52628i	0.349250	−	0.604919i
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$		0			0
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$	2.50000	+	0.866025i	0.157485	+	0.0545545i
$253$	10.0000			0.628695
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$		0			0
$259$	4.00000	+	20.7846i	0.248548	+	1.29149i
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$		0			0
$266$	8.00000	−	6.92820i	0.490511	−	0.424795i
$267$	−11.0000			−0.673189
$268$		0			0
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$		0			0
$271$	4.50000	+	7.79423i	0.273356	+	0.473466i	0.969719	−	0.244224i	$-0.0785331\pi$
$271$	4.50000	+	7.79423i	0.273356	+	0.473466i	−0.696363	+	0.717689i	$0.745200\pi$
$272$	5.00000			0.303170
$273$	8.00000	−	6.92820i	0.484182	−	0.419314i
$274$	−23.0000			−1.38948
$275$		0			0
$276$	−2.50000	+	4.33013i	−0.150482	+	0.260643i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$	−11.0000			−0.658553
$280$		0			0
$281$	−29.0000			−1.72999			−0.864997	−	0.501776i	$-0.832680\pi$
$281$	−29.0000			−1.72999			−0.864997	+	0.501776i	$0.832680\pi$
$282$	0.500000	+	0.866025i	0.0297746	+	0.0515711i
$283$	−13.0000	+	22.5167i	−0.772770	+	1.33848i	0.163270	+	0.986581i	$0.447796\pi$
$283$	−13.0000	+	22.5167i	−0.772770	+	1.33848i	−0.936039	+	0.351895i	$0.885537\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$		0			0
$286$	−8.00000			−0.473050
$287$	12.5000	+	4.33013i	0.737852	+	0.255599i
$288$	1.00000			0.0589256
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$	0.500000	−	0.866025i	0.0293105	−	0.0507673i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$	−5.50000	−	4.33013i	−0.320767	−	0.252538i
$295$		0			0
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$	10.0000	+	17.3205i	0.578315	+	1.00167i
$300$		0			0
$301$		0			0
$302$	−16.0000			−0.920697
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		0			0
$306$	−2.50000	−	4.33013i	−0.142915	−	0.247537i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	1.00000	+	5.19615i	0.0569803	+	0.296078i
$309$	13.0000			0.739544
$310$		0			0
$311$	−14.5000	+	25.1147i	−0.822220	+	1.42413i	0.0818063	+	0.996648i	$0.473931\pi$
$311$	−14.5000	+	25.1147i	−0.822220	+	1.42413i	−0.904026	+	0.427478i	$0.859402\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	9.00000			0.506290
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	0.916710	−	0.399554i	$-0.130835\pi$
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	−0.804379	+	0.594117i	$0.797502\pi$
$318$	−6.00000	+	10.3923i	−0.336463	+	0.582772i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$	2.00000			0.111629
$322$	10.0000	−	8.66025i	0.557278	−	0.482617i
$323$	−20.0000			−1.11283
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	12.0000	−	20.7846i	0.664619	−	1.15115i
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	5.00000			0.276079
$329$	−0.500000	−	2.59808i	−0.0275659	−	0.143237i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	4.00000	−	6.92820i	0.219199	−	0.379663i
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$		0			0
$336$	−2.50000	−	0.866025i	−0.136386	−	0.0472456i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	−2.50000	+	4.33013i	−0.135781	+	0.235180i
$340$		0			0
$341$	−11.0000	−	19.0526i	−0.595683	−	1.03175i
$342$	−4.00000			−0.216295
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$	−1.00000	+	1.73205i	−0.0537603	+	0.0931156i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	0.960574	+	0.278024i	$0.0896796\pi$
$354$	−1.00000	+	1.73205i	−0.0531494	+	0.0920575i
$355$		0			0
$356$	11.0000			0.582999
$357$	2.50000	+	12.9904i	0.132314	+	0.687524i
$358$	22.0000			1.16274
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	11.0000	+	19.0526i	0.578147	+	1.00138i
$363$	7.00000			0.367405
$364$	−8.00000	+	6.92820i	−0.419314	+	0.363137i
$365$		0			0
$366$	5.00000	+	8.66025i	0.261354	+	0.452679i
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	0.809093	+	0.587680i	$0.199959\pi$
$368$	2.50000	−	4.33013i	0.130322	−	0.225723i
$369$	−2.50000	−	4.33013i	−0.130145	−	0.225417i
$370$		0			0
$371$	24.0000	−	20.7846i	1.24602	−	1.07908i
$372$	11.0000			0.570323
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	−0.899255	−	0.437425i	$-0.855891\pi$
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	0.0708063	−	0.997490i	$-0.477443\pi$
$374$	5.00000	−	8.66025i	0.258544	−	0.447811i
$375$		0			0
$376$	−0.500000	−	0.866025i	−0.0257855	−	0.0446619i
$377$	−24.0000			−1.23606
$378$	0.500000	+	2.59808i	0.0257172	+	0.133631i
$379$	−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
$381$		0			0
$382$	12.5000	−	21.6506i	0.639556	−	1.10774i
$383$	1.50000	+	2.59808i	0.0766464	+	0.132755i	0.901801	−	0.432151i	$-0.142245\pi$
$383$	1.50000	+	2.59808i	0.0766464	+	0.132755i	−0.825155	+	0.564907i	$0.808912\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−11.0000			−0.559885
$387$		0			0
$388$	−0.500000	+	0.866025i	−0.0253837	+	0.0439658i
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	0.383076	+	0.923717i	$0.374865\pi$
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	−0.991500	+	0.130105i	$0.958469\pi$
$390$		0			0
$391$	−25.0000			−1.26430
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$	−6.00000			−0.302660
$394$	−12.0000	−	20.7846i	−0.604551	−	1.04711i
$395$		0			0
$396$	1.00000	−	1.73205i	0.0502519	−	0.0870388i
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	0.0250943	−	0.999685i	$-0.492011\pi$
$398$	5.00000			0.250627
$399$	10.0000	+	3.46410i	0.500626	+	0.173422i
$400$		0			0
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$		0			0
$403$	22.0000	−	38.1051i	1.09590	−	1.89815i
$404$	−6.00000	−	10.3923i	−0.298511	−	0.517036i
$405$		0			0
$406$	3.00000	+	15.5885i	0.148888	+	0.773642i
$407$	16.0000			0.793091
$408$	2.50000	+	4.33013i	0.123768	+	0.214373i
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	−0.00141047	−	0.999999i	$-0.500449\pi$
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	0.866730	−	0.498778i	$-0.166218\pi$
$410$		0			0
$411$	−11.5000	−	19.9186i	−0.567253	−	0.982511i
$412$	−13.0000			−0.640464
$413$	4.00000	−	3.46410i	0.196827	−	0.170457i
$414$	−5.00000			−0.245737
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	1.00000	−	1.73205i	0.0489702	−	0.0848189i
$418$	−4.00000	−	6.92820i	−0.195646	−	0.338869i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	28.0000			1.36464			0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000			1.36464			0.682318	+	0.731055i	$0.260972\pi$
$422$	8.00000	+	13.8564i	0.389434	+	0.674519i
$423$	−0.500000	+	0.866025i	−0.0243108	+	0.0421076i
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$		0			0
$426$	1.00000			0.0484502
$427$	−5.00000	−	25.9808i	−0.241967	−	1.25730i
$428$	−2.00000			−0.0966736
$429$	−4.00000	−	6.92820i	−0.193122	−	0.334497i
$430$		0			0
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	9.00000			0.432512			0.216256	−	0.976337i	$-0.430615\pi$
$433$	9.00000			0.432512			0.216256	+	0.976337i	$0.430615\pi$
$434$	−27.5000	−	9.52628i	−1.32004	−	0.457276i
$435$		0			0
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	−10.0000	+	17.3205i	−0.478365	+	0.828552i
$438$	−1.00000	+	1.73205i	−0.0477818	+	0.0827606i
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	20.0000			0.951303
$443$	−4.00000	−	6.92820i	−0.190046	−	0.329169i	0.755219	−	0.655472i	$-0.227530\pi$
$443$	−4.00000	−	6.92820i	−0.190046	−	0.329169i	−0.945265	+	0.326303i	$0.894197\pi$
$444$	−4.00000	+	6.92820i	−0.189832	+	0.328798i
$445$		0			0
$446$	10.5000	+	18.1865i	0.497189	+	0.861157i
$447$	−18.0000			−0.851371
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	37.0000			1.74614			0.873069	−	0.487597i	$-0.162126\pi$
$449$	37.0000			1.74614			0.873069	+	0.487597i	$0.162126\pi$
$450$		0			0
$451$	5.00000	−	8.66025i	0.235441	−	0.407795i
$452$	2.50000	−	4.33013i	0.117590	−	0.203672i
$453$	−8.00000	−	13.8564i	−0.375873	−	0.651031i
$454$	−18.0000			−0.844782
$455$		0			0
$456$	4.00000			0.187317
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	0.982004	−	0.188858i	$-0.0604787\pi$
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	−0.654558	+	0.756012i	$0.727145\pi$
$458$	7.00000	−	12.1244i	0.327089	−	0.566534i
$459$	2.50000	−	4.33013i	0.116690	−	0.202113i
$460$		0			0
$461$	20.0000			0.931493			0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000			0.931493			0.465746	+	0.884918i	$0.345786\pi$
$462$	−4.00000	+	3.46410i	−0.186097	+	0.161165i
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	13.0000	−	22.5167i	0.602213	−	1.04306i
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	−0.927999	−	0.372584i	$-0.878472\pi$
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	0.141332	−	0.989962i	$-0.454861\pi$
$468$	4.00000			0.184900
$469$		0			0
$470$		0			0
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$	1.00000	−	1.73205i	0.0460287	−	0.0797241i
$473$		0			0
$474$	4.50000	+	7.79423i	0.206692	+	0.358001i
$475$		0			0
$476$	−2.50000	−	12.9904i	−0.114587	−	0.595413i
$477$	−12.0000			−0.549442
$478$	−5.50000	−	9.52628i	−0.251564	−	0.435722i
$479$	1.50000	−	2.59808i	0.0685367	−	0.118709i	−0.829721	−	0.558179i	$-0.811500\pi$
$479$	1.50000	−	2.59808i	0.0685367	−	0.118709i	0.898257	+	0.439470i	$0.144834\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	−6.00000			−0.273293
$483$	12.5000	+	4.33013i	0.568770	+	0.197028i
$484$	−7.00000			−0.318182
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−19.5000	+	33.7750i	−0.883629	+	1.53049i	−0.0363527	+	0.999339i	$0.511574\pi$
$487$	−19.5000	+	33.7750i	−0.883629	+	1.53049i	−0.847277	+	0.531152i	$0.821759\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$	24.0000			1.08532
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	2.50000	+	4.33013i	0.112709	+	0.195217i
$493$	15.0000	−	25.9808i	0.675566	−	1.17011i
$494$	8.00000	−	13.8564i	0.359937	−	0.623429i
$495$		0			0
$496$	−11.0000			−0.493915
$497$	−2.50000	−	0.866025i	−0.112140	−	0.0388465i
$498$	6.00000			0.268866
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	0.507534	−	0.861632i	$-0.330557\pi$
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	−0.999962	+	0.00872186i	$0.997224\pi$
$500$		0			0
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$	4.00000	+	6.92820i	0.178529	+	0.309221i
$503$	−8.00000			−0.356702			−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000			−0.356702			−0.178351	+	0.983967i	$0.557076\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$		0			0
$506$	−5.00000	−	8.66025i	−0.222277	−	0.384995i
$507$	1.50000	−	2.59808i	0.0666173	−	0.115385i
$508$		0			0
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	0.843012	−	0.537895i	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$		0			0
$511$	4.00000	−	3.46410i	0.176950	−	0.153243i
$512$	1.00000			0.0441942
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$	−7.00000	+	12.1244i	−0.308757	+	0.534782i
$515$		0			0
$516$		0			0
$517$	−2.00000			−0.0879599
$518$	16.0000	−	13.8564i	0.703000	−	0.608816i
$519$	−2.00000			−0.0877903
$520$		0			0
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	−0.831295	−	0.555831i	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	0.671414	−	0.741082i	$-0.265687\pi$
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	−0.977503	+	0.210921i	$0.932354\pi$
$524$	6.00000			0.262111
$525$		0			0
$526$	21.0000			0.915644
$527$	27.5000	+	47.6314i	1.19792	+	2.07486i
$528$	−1.00000	+	1.73205i	−0.0435194	+	0.0753778i
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	−2.00000			−0.0867926
$532$	−10.0000	−	3.46410i	−0.433555	−	0.150188i
$533$	20.0000			0.866296
$534$	5.50000	+	9.52628i	0.238008	+	0.412242i
$535$		0			0
$536$		0			0
$537$	11.0000	+	19.0526i	0.474685	+	0.822179i
$538$	−24.0000			−1.03471
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$		0			0
$541$	2.00000	+	3.46410i	0.0859867	+	0.148933i	0.905811	−	0.423681i	$-0.139262\pi$
$541$	2.00000	+	3.46410i	0.0859867	+	0.148933i	−0.819825	+	0.572615i	$0.805929\pi$
$542$	4.50000	−	7.79423i	0.193292	−	0.334791i
$543$	−11.0000	+	19.0526i	−0.472055	+	0.817624i
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$		0			0
$546$	−10.0000	−	3.46410i	−0.427960	−	0.148250i
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$	11.5000	+	19.9186i	0.491256	+	0.850880i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$	5.00000			0.212814
$553$	−4.50000	−	23.3827i	−0.191359	−	0.994333i
$554$	2.00000			0.0849719
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	19.0000	−	32.9090i	0.805056	−	1.39440i	−0.111198	−	0.993798i	$-0.535469\pi$
$557$	19.0000	−	32.9090i	0.805056	−	1.39440i	0.916253	−	0.400599i	$-0.131198\pi$
$558$	5.50000	+	9.52628i	0.232834	+	0.403280i
$559$		0			0
$560$		0			0
$561$	10.0000			0.422200
$562$	14.5000	+	25.1147i	0.611646	+	1.05940i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	0.500000	−	0.866025i	0.0210538	−	0.0364662i
$565$		0			0
$566$	26.0000			1.09286
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$	−1.00000			−0.0419591
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	0.756151	−	0.654398i	$-0.227078\pi$
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	−0.944800	+	0.327647i	$0.893744\pi$
$570$		0			0
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.122292	−	0.992494i	$-0.460975\pi$
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.798379	−	0.602155i	$-0.205691\pi$
$572$	4.00000	+	6.92820i	0.167248	+	0.289683i
$573$	25.0000			1.04439
$574$	−2.50000	−	12.9904i	−0.104348	−	0.542208i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$	−15.0000	−	5.19615i	−0.622305	−	0.215573i
$582$	−1.00000			−0.0414513
$583$	−12.0000	−	20.7846i	−0.496989	−	0.860811i
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$		0			0
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$	−6.00000			−0.247647			−0.123823	−	0.992304i	$-0.539516\pi$
$587$	−6.00000			−0.247647			−0.123823	+	0.992304i	$0.539516\pi$
$588$	−1.00000	+	6.92820i	−0.0412393	+	0.285714i
$589$	44.0000			1.81299
$590$		0			0
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	0.943507	−	0.331353i	$-0.107505\pi$
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	−0.758714	+	0.651424i	$0.774172\pi$
$594$	2.00000			0.0820610
$595$		0			0
$596$	18.0000			0.737309
$597$	2.50000	+	4.33013i	0.102318	+	0.177220i
$598$	10.0000	−	17.3205i	0.408930	−	0.708288i
$599$	−8.50000	+	14.7224i	−0.347301	+	0.601542i	−0.985769	−	0.168106i	$-0.946235\pi$
$599$	−8.50000	+	14.7224i	−0.347301	+	0.601542i	0.638468	+	0.769648i	$0.279568\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$		0			0
$603$		0			0
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$		0			0
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	−0.998415	−	0.0562808i	$-0.982076\pi$
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	0.450467	−	0.892793i	$-0.351258\pi$
$608$	−4.00000			−0.162221
$609$	−12.0000	+	10.3923i	−0.486265	+	0.421117i
$610$		0			0
$611$	−2.00000	−	3.46410i	−0.0809113	−	0.140143i
$612$	−2.50000	+	4.33013i	−0.101057	+	0.175035i
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	4.00000	−	3.46410i	0.161165	−	0.139573i
$617$	−29.0000			−1.16750			−0.583748	−	0.811935i	$-0.698414\pi$
$617$	−29.0000			−1.16750			−0.583748	+	0.811935i	$0.698414\pi$
$618$	−6.50000	−	11.2583i	−0.261468	−	0.452876i
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	−0.690365	−	0.723462i	$-0.742550\pi$
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	0.971718	+	0.236143i	$0.0758832\pi$
$620$		0			0
$621$	−2.50000	−	4.33013i	−0.100322	−	0.173762i
$622$	29.0000			1.16279
$623$	−5.50000	−	28.5788i	−0.220353	−	1.14499i
$624$	−4.00000			−0.160128
$625$		0			0
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$	4.00000	−	6.92820i	0.159745	−	0.276686i
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	−40.0000			−1.59490
$630$		0			0
$631$	33.0000			1.31371			0.656855	−	0.754017i	$-0.271887\pi$
$631$	33.0000			1.31371			0.656855	+	0.754017i	$0.271887\pi$
$632$	−4.50000	−	7.79423i	−0.179000	−	0.310038i
$633$	−8.00000	+	13.8564i	−0.317971	+	0.550743i
$634$	2.00000	−	3.46410i	0.0794301	−	0.137577i
$635$		0			0
$636$	12.0000			0.475831
$637$	22.0000	+	17.3205i	0.871672	+	0.686264i
$638$	12.0000			0.475085
$639$	0.500000	+	0.866025i	0.0197797	+	0.0342594i
$640$		0			0
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	−0.679039	−	0.734103i	$-0.737603\pi$
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	0.975271	+	0.221013i	$0.0709364\pi$
$642$	−1.00000	−	1.73205i	−0.0394669	−	0.0683586i
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$	−12.5000	−	4.33013i	−0.492569	−	0.170631i
$645$		0			0
$646$	10.0000	+	17.3205i	0.393445	+	0.681466i
$647$	−14.0000	+	24.2487i	−0.550397	+	0.953315i	0.447849	+	0.894109i	$0.352190\pi$
$647$	−14.0000	+	24.2487i	−0.550397	+	0.953315i	−0.998246	+	0.0592060i	$0.981143\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−2.00000	−	3.46410i	−0.0785069	−	0.135978i
$650$		0			0
$651$	−5.50000	−	28.5788i	−0.215562	−	1.12009i
$652$	−24.0000			−0.939913
$653$	14.0000	+	24.2487i	0.547862	+	0.948925i	0.998421	+	0.0561784i	$0.0178916\pi$
$653$	14.0000	+	24.2487i	0.547862	+	0.948925i	−0.450558	+	0.892747i	$0.648775\pi$
$654$	2.00000	−	3.46410i	0.0782062	−	0.135457i
$655$		0			0
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$	−2.00000			−0.0780274
$658$	−2.00000	+	1.73205i	−0.0779681	+	0.0675224i
$659$	−14.0000			−0.545363			−0.272681	−	0.962104i	$-0.587910\pi$
$659$	−14.0000			−0.545363			−0.272681	+	0.962104i	$0.587910\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−5.00000	+	8.66025i	−0.194331	+	0.336590i
$663$	10.0000	+	17.3205i	0.388368	+	0.672673i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−15.0000	−	25.9808i	−0.580802	−	1.00598i
$668$	8.00000	−	13.8564i	0.309529	−	0.536120i
$669$	−10.5000	+	18.1865i	−0.405953	+	0.703132i
$670$		0			0
$671$	−20.0000			−0.772091
$672$	0.500000	+	2.59808i	0.0192879	+	0.100223i
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	6.50000	+	11.2583i	0.250371	+	0.433655i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$	5.00000			0.192024
$679$	2.50000	+	0.866025i	0.0959412	+	0.0332350i
$680$		0			0
$681$	−9.00000	−	15.5885i	−0.344881	−	0.597351i
$682$	−11.0000	+	19.0526i	−0.421212	+	0.729560i
$683$	−1.00000	+	1.73205i	−0.0382639	+	0.0662751i	−0.884523	−	0.466496i	$-0.845516\pi$
$683$	−1.00000	+	1.73205i	−0.0382639	+	0.0662751i	0.846259	+	0.532771i	$0.178849\pi$
$684$	2.00000	+	3.46410i	0.0764719	+	0.132453i
$685$		0			0
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	14.0000			0.534133
$688$		0			0
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$		0			0
$691$	1.00000	+	1.73205i	0.0380418	+	0.0658903i	0.884419	−	0.466693i	$-0.154555\pi$
$691$	1.00000	+	1.73205i	0.0380418	+	0.0658903i	−0.846378	+	0.532583i	$0.821221\pi$
$692$	2.00000			0.0760286
$693$	−5.00000	−	1.73205i	−0.189934	−	0.0657952i
$694$	18.0000			0.683271
$695$		0			0
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$	−12.5000	+	21.6506i	−0.473471	+	0.820076i
$698$	2.00000	+	3.46410i	0.0757011	+	0.131118i
$699$	26.0000			0.983410
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	2.00000	+	3.46410i	0.0754851	+	0.130744i
$703$	−16.0000	+	27.7128i	−0.603451	+	1.04521i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$		0			0
$706$	−9.00000			−0.338719
$707$	−24.0000	+	20.7846i	−0.902613	+	0.781686i
$708$	2.00000			0.0751646
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$		0			0
$711$	−4.50000	+	7.79423i	−0.168763	+	0.292306i
$712$	−5.50000	−	9.52628i	−0.206121	−	0.357012i
$713$	55.0000			2.05977
$714$	10.0000	−	8.66025i	0.374241	−	0.324102i
$715$		0			0
$716$	−11.0000	−	19.0526i	−0.411089	−	0.712028i
$717$	5.50000	−	9.52628i	0.205401	−	0.355765i
$718$	10.0000	−	17.3205i	0.373197	−	0.646396i
$719$	1.50000	+	2.59808i	0.0559406	+	0.0968919i	0.892640	−	0.450771i	$-0.148851\pi$
$719$	1.50000	+	2.59808i	0.0559406	+	0.0968919i	−0.836699	+	0.547663i	$0.815518\pi$
$720$		0			0
$721$	6.50000	+	33.7750i	0.242073	+	1.25785i
$722$	−3.00000			−0.111648
$723$	−3.00000	−	5.19615i	−0.111571	−	0.193247i
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$		0			0
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$	33.0000			1.22390			0.611951	−	0.790896i	$-0.290385\pi$
$727$	33.0000			1.22390			0.611951	+	0.790896i	$0.290385\pi$
$728$	10.0000	+	3.46410i	0.370625	+	0.128388i
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	5.00000	−	8.66025i	0.184805	−	0.320092i
$733$	15.0000	+	25.9808i	0.554038	+	0.959621i	0.997978	+	0.0635649i	$0.0202470\pi$
$733$	15.0000	+	25.9808i	0.554038	+	0.959621i	−0.443940	+	0.896056i	$0.646420\pi$
$734$	4.00000			0.147643
$735$		0			0
$736$	−5.00000			−0.184302
$737$		0			0
$738$	−2.50000	+	4.33013i	−0.0920263	+	0.159394i
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$		0			0
$741$	16.0000			0.587775
$742$	−30.0000	−	10.3923i	−1.10133	−	0.381514i
$743$	33.0000			1.21065			0.605326	−	0.795977i	$-0.293043\pi$
$743$	33.0000			1.21065			0.605326	+	0.795977i	$0.293043\pi$
$744$	−5.50000	−	9.52628i	−0.201640	−	0.349250i
$745$		0			0
$746$	−16.0000	+	27.7128i	−0.585802	+	1.01464i
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$	−10.0000			−0.365636
$749$	1.00000	+	5.19615i	0.0365392	+	0.189863i
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−0.500000	+	0.866025i	−0.0182331	+	0.0315807i
$753$	−4.00000	+	6.92820i	−0.145768	+	0.252478i
$754$	12.0000	+	20.7846i	0.437014	+	0.756931i
$755$		0			0
$756$	2.00000	−	1.73205i	0.0727393	−	0.0629941i
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	1.00000	+	1.73205i	0.0363216	+	0.0629109i
$759$	5.00000	−	8.66025i	0.181489	−	0.314347i
$760$		0			0
$761$	−8.50000	−	14.7224i	−0.308125	−	0.533688i	0.669827	−	0.742517i	$-0.266368\pi$
$761$	−8.50000	−	14.7224i	−0.308125	−	0.533688i	−0.977952	+	0.208829i	$0.933035\pi$
$762$		0			0
$763$	−8.00000	+	6.92820i	−0.289619	+	0.250818i
$764$	−25.0000			−0.904468
$765$		0			0
$766$	1.50000	−	2.59808i	0.0541972	−	0.0938723i
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$	5.50000	+	9.52628i	0.197949	+	0.342858i
$773$	−2.00000	+	3.46410i	−0.0719350	+	0.124595i	−0.899749	−	0.436407i	$-0.856251\pi$
$773$	−2.00000	+	3.46410i	−0.0719350	+	0.124595i	0.827814	+	0.561002i	$0.189584\pi$
$774$		0			0
$775$		0			0
$776$	1.00000			0.0358979
$777$	20.0000	+	6.92820i	0.717496	+	0.248548i
$778$	24.0000			0.860442
$779$	10.0000	+	17.3205i	0.358287	+	0.620572i
$780$		0			0
$781$	−1.00000	+	1.73205i	−0.0357828	+	0.0619777i
$782$	12.5000	+	21.6506i	0.446999	+	0.774225i
$783$	6.00000			0.214423
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$		0			0
$786$	3.00000	+	5.19615i	0.107006	+	0.185341i
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	−0.250832	−	0.968031i	$-0.580704\pi$
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	0.963755	−	0.266788i	$-0.0859624\pi$
$788$	−12.0000	+	20.7846i	−0.427482	+	0.740421i
$789$	10.5000	+	18.1865i	0.373810	+	0.647458i
$790$		0			0
$791$	−12.5000	−	4.33013i	−0.444449	−	0.153962i
$792$	−2.00000			−0.0710669
$793$	−20.0000	−	34.6410i	−0.710221	−	1.23014i
$794$	−17.0000	+	29.4449i	−0.603307	+	1.04496i
$795$		0			0
$796$	−2.50000	−	4.33013i	−0.0886102	−	0.153477i
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$	−2.00000	−	10.3923i	−0.0707992	−	0.367884i
$799$	5.00000			0.176887
$800$		0			0
$801$	−5.50000	+	9.52628i	−0.194333	+	0.336595i
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	−2.00000	−	3.46410i	−0.0705785	−	0.122245i
$804$		0			0
$805$		0			0
$806$	−44.0000			−1.54983
$807$	−12.0000	−	20.7846i	−0.422420	−	0.731653i
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	−0.940435	−	0.339975i	$-0.889582\pi$
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	0.764644	+	0.644453i	$0.222915\pi$
$810$		0			0
$811$	−48.0000			−1.68551			−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000			−1.68551			−0.842754	+	0.538299i	$0.819067\pi$
$812$	12.0000	−	10.3923i	0.421117	−	0.364698i
$813$	9.00000			0.315644
$814$	−8.00000	−	13.8564i	−0.280400	−	0.485667i
$815$		0			0
$816$	2.50000	−	4.33013i	0.0875175	−	0.151585i
$817$		0			0
$818$	−35.0000			−1.22375
$819$	−2.00000	−	10.3923i	−0.0698857	−	0.363137i
$820$		0			0
$821$	−26.0000	−	45.0333i	−0.907406	−	1.57167i	−0.817654	−	0.575710i	$-0.804726\pi$
$821$	−26.0000	−	45.0333i	−0.907406	−	1.57167i	−0.0897520	−	0.995964i	$-0.528607\pi$
$822$	−11.5000	+	19.9186i	−0.401109	+	0.694740i
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	−0.637419	−	0.770517i	$-0.719998\pi$
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	0.985997	+	0.166762i	$0.0533313\pi$
$824$	6.50000	+	11.2583i	0.226438	+	0.392203i
$825$		0			0
$826$	−5.00000	−	1.73205i	−0.173972	−	0.0602658i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$	2.50000	+	4.33013i	0.0868810	+	0.150482i
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	−0.998480	−	0.0551154i	$-0.982447\pi$
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	0.546971	+	0.837151i	$0.315781\pi$
$830$		0			0
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$	4.00000			0.138675
$833$	−32.5000	+	12.9904i	−1.12606	+	0.450090i
$834$	−2.00000			−0.0692543
$835$		0			0
$836$	−4.00000	+	6.92820i	−0.138343	+	0.239617i
$837$	−5.50000	+	9.52628i	−0.190108	+	0.329276i
$838$		0			0
$839$	−9.00000			−0.310715			−0.155357	−	0.987858i	$-0.549653\pi$
$839$	−9.00000			−0.310715			−0.155357	+	0.987858i	$0.549653\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−14.0000	−	24.2487i	−0.482472	−	0.835666i
$843$	−14.5000	+	25.1147i	−0.499407	+	0.864997i
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$		0			0
$846$	1.00000			0.0343807
$847$	3.50000	+	18.1865i	0.120261	+	0.624897i
$848$	−12.0000			−0.412082
$849$	13.0000	+	22.5167i	0.446159	+	0.772770i
$850$		0			0
$851$	−20.0000	+	34.6410i	−0.685591	+	1.18748i
$852$	−0.500000	−	0.866025i	−0.0171297	−	0.0296695i
$853$	−20.0000			−0.684787			−0.342393	−	0.939557i	$-0.611238\pi$
$853$	−20.0000			−0.684787			−0.342393	+	0.939557i	$0.611238\pi$
$854$	−20.0000	+	17.3205i	−0.684386	+	0.592696i
$855$		0			0
$856$	1.00000	+	1.73205i	0.0341793	+	0.0592003i
$857$	29.0000	−	50.2295i	0.990621	−	1.71581i	0.376979	−	0.926222i	$-0.376963\pi$
$857$	29.0000	−	50.2295i	0.990621	−	1.71581i	0.613642	−	0.789584i	$-0.289704\pi$
$858$	−4.00000	+	6.92820i	−0.136558	+	0.236525i
$859$	5.00000	+	8.66025i	0.170598	+	0.295484i	0.938629	−	0.344928i	$-0.112097\pi$
$859$	5.00000	+	8.66025i	0.170598	+	0.295484i	−0.768031	+	0.640412i	$0.778763\pi$
$860$		0			0
$861$	10.0000	−	8.66025i	0.340799	−	0.295141i
$862$	−3.00000			−0.102180
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.864007	+	0.503480i	$0.167947\pi$
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.00402340	+	0.999992i	$0.498719\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−4.50000	−	7.79423i	−0.152916	−	0.264859i
$867$	−8.00000			−0.271694
$868$	5.50000	+	28.5788i	0.186682	+	0.970029i
$869$	−18.0000			−0.610608
$870$		0			0
$871$		0			0
$872$	−2.00000	+	3.46410i	−0.0677285	+	0.117309i
$873$	−0.500000	−	0.866025i	−0.0169224	−	0.0293105i
$874$	20.0000			0.676510
$875$		0			0
$876$	2.00000			0.0675737
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	−17.5000	+	30.3109i	−0.590596	+	1.02294i
$879$	−9.00000	+	15.5885i	−0.303562	+	0.525786i
$880$		0			0
$881$	39.0000			1.31394			0.656972	−	0.753915i	$-0.271837\pi$
$881$	39.0000			1.31394			0.656972	+	0.753915i	$0.271837\pi$
$882$	−6.50000	+	2.59808i	−0.218866	+	0.0874818i
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$	−10.0000	−	17.3205i	−0.336336	−	0.582552i
$885$		0			0
$886$	−4.00000	+	6.92820i	−0.134383	+	0.232758i
$887$	28.0000	+	48.4974i	0.940148	+	1.62838i	0.765186	+	0.643809i	$0.222647\pi$
$887$	28.0000	+	48.4974i	0.940148	+	1.62838i	0.174962	+	0.984575i	$0.444020\pi$
$888$	8.00000			0.268462
$889$		0			0
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	10.5000	−	18.1865i	0.351566	−	0.608930i
$893$	2.00000	−	3.46410i	0.0669274	−	0.115922i
$894$	9.00000	+	15.5885i	0.301005	+	0.521356i
$895$		0			0
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	20.0000			0.667781
$898$	−18.5000	−	32.0429i	−0.617353	−	1.06929i
$899$	−33.0000	+	57.1577i	−1.10061	+	1.90632i
$900$		0			0
$901$	30.0000	+	51.9615i	0.999445	+	1.73109i
$902$	−10.0000			−0.332964
$903$		0			0
$904$	−5.00000			−0.166298
$905$		0			0
$906$	−8.00000	+	13.8564i	−0.265782	+	0.460348i
$907$	9.00000	−	15.5885i	0.298840	−	0.517606i	−0.677031	−	0.735955i	$-0.736734\pi$
$907$	9.00000	−	15.5885i	0.298840	−	0.517606i	0.975871	+	0.218348i	$0.0700669\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	12.0000			0.398015
$910$		0			0
$911$	51.0000			1.68971			0.844853	−	0.534999i	$-0.179688\pi$
$911$	51.0000			1.68971			0.844853	+	0.534999i	$0.179688\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	7.00000	−	12.1244i	0.231539	−	0.401038i
$915$		0			0
$916$	−14.0000			−0.462573
$917$	−3.00000	−	15.5885i	−0.0990687	−	0.514776i
$918$	−5.00000			−0.165025
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	−0.965147	−	0.261708i	$-0.915714\pi$
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	0.255927	−	0.966696i	$-0.417619\pi$
$920$		0			0
$921$	−14.0000	+	24.2487i	−0.461316	+	0.799022i
$922$	−10.0000	−	17.3205i	−0.329332	−	0.570421i
$923$	−4.00000			−0.131662
$924$	5.00000	+	1.73205i	0.164488	+	0.0569803i
$925$		0			0
$926$	6.50000	+	11.2583i	0.213603	+	0.369972i
$927$	6.50000	−	11.2583i	0.213488	−	0.369772i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	−0.997684	−	0.0680235i	$-0.978331\pi$
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	0.439932	−	0.898031i	$-0.355003\pi$
$930$		0			0
$931$	−4.00000	+	27.7128i	−0.131095	+	0.908251i
$932$	−26.0000			−0.851658
$933$	14.5000	+	25.1147i	0.474709	+	0.822220i
$934$	−17.0000	+	29.4449i	−0.556257	+	0.963465i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$		0			0
$939$	−1.00000			−0.0326338
$940$		0			0
$941$	−18.0000	+	31.1769i	−0.586783	+	1.01634i	0.407867	+	0.913041i	$0.366273\pi$
$941$	−18.0000	+	31.1769i	−0.586783	+	1.01634i	−0.994651	+	0.103297i	$0.967061\pi$
$942$	7.00000	−	12.1244i	0.228072	−	0.395033i
$943$	12.5000	+	21.6506i	0.407056	+	0.705042i
$944$	−2.00000			−0.0650945
$945$		0			0
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	4.50000	−	7.79423i	0.146153	−	0.253145i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$	4.00000			0.129709
$952$	−10.0000	+	8.66025i	−0.324102	+	0.280680i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	6.00000	+	10.3923i	0.194257	+	0.336463i
$955$		0			0
$956$	−5.50000	+	9.52628i	−0.177883	+	0.308102i
$957$	6.00000	+	10.3923i	0.193952	+	0.335936i
$958$	−3.00000			−0.0969256
$959$	46.0000	−	39.8372i	1.48542	−	1.28641i
$960$		0			0
$961$	−45.0000	−	77.9423i	−1.45161	−	2.51427i
$962$	16.0000	−	27.7128i	0.515861	−	0.893497i
$963$	1.00000	−	1.73205i	0.0322245	−	0.0558146i
$964$	3.00000	+	5.19615i	0.0966235	+	0.167357i
$965$		0			0
$966$	−2.50000	−	12.9904i	−0.0804362	−	0.417959i
$967$	1.00000			0.0321578			0.0160789	−	0.999871i	$-0.494882\pi$
$967$	1.00000			0.0321578			0.0160789	+	0.999871i	$0.494882\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	−10.0000	+	17.3205i	−0.321246	+	0.556415i
$970$		0			0
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	0.813865	−	0.581054i	$-0.197359\pi$
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	−0.910140	+	0.414301i	$0.864026\pi$
$972$	−1.00000			−0.0320750
$973$	5.00000	+	1.73205i	0.160293	+	0.0555270i
$974$	39.0000			1.24964
$975$		0			0
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	−16.5000	+	28.5788i	−0.527882	+	0.914318i	0.471590	+	0.881818i	$0.343680\pi$
$977$	−16.5000	+	28.5788i	−0.527882	+	0.914318i	−0.999472	+	0.0325001i	$0.989653\pi$
$978$	−12.0000	−	20.7846i	−0.383718	−	0.664619i
$979$	−22.0000			−0.703123
$980$		0			0
$981$	4.00000			0.127710
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	8.00000	−	13.8564i	0.255160	−	0.441951i	−0.709779	−	0.704425i	$-0.751205\pi$
$983$	8.00000	−	13.8564i	0.255160	−	0.441951i	0.964939	+	0.262474i	$0.0845384\pi$
$984$	2.50000	−	4.33013i	0.0796971	−	0.138039i
$985$		0			0
$986$	−30.0000			−0.955395
$987$	−2.50000	−	0.866025i	−0.0795759	−	0.0275659i
$988$	−16.0000			−0.509028
$989$		0			0
$990$		0			0
$991$	−18.5000	+	32.0429i	−0.587672	+	1.01788i	0.406865	+	0.913488i	$0.366622\pi$
$991$	−18.5000	+	32.0429i	−0.587672	+	1.01788i	−0.994537	+	0.104389i	$0.966711\pi$
$992$	5.50000	+	9.52628i	0.174625	+	0.302460i
$993$	−10.0000			−0.317340
$994$	0.500000	+	2.59808i	0.0158590	+	0.0824060i
$995$		0			0
$996$	−3.00000	−	5.19615i	−0.0950586	−	0.164646i
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	−0.832616	−	0.553851i	$-0.813158\pi$
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	0.895957	+	0.444141i	$0.146491\pi$
$998$	−11.0000	+	19.0526i	−0.348199	+	0.603098i
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.j.151.1	✓	2
5.2	odd	4		1050.2.o.f.949.2		4
5.3	odd	4		1050.2.o.f.949.1		4
5.4	even	2		1050.2.i.k.151.1	yes	2
7.2	even	3	inner	1050.2.i.j.751.1	yes	2
7.3	odd	6		7350.2.a.cn.1.1		1
7.4	even	3		7350.2.a.bt.1.1		1
35.2	odd	12		1050.2.o.f.499.1		4
35.4	even	6		7350.2.a.z.1.1		1
35.9	even	6		1050.2.i.k.751.1	yes	2
35.23	odd	12		1050.2.o.f.499.2		4
35.24	odd	6		7350.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.j.151.1	✓	2	1.1	even	1	trivial
1050.2.i.j.751.1	yes	2	7.2	even	3	inner
1050.2.i.k.151.1	yes	2	5.4	even	2
1050.2.i.k.751.1	yes	2	35.9	even	6
1050.2.o.f.499.1		4	35.2	odd	12
1050.2.o.f.499.2		4	35.23	odd	12
1050.2.o.f.949.1		4	5.3	odd	4
1050.2.o.f.949.2		4	5.2	odd	4
7350.2.a.h.1.1		1	35.24	odd	6
7350.2.a.z.1.1		1	35.4	even	6
7350.2.a.bt.1.1		1	7.4	even	3
7350.2.a.cn.1.1		1	7.3	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(2.00000 - 1.73205i) q^{21} -2.00000 q^{22} +(2.50000 + 4.33013i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(5.50000 - 9.52628i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +5.00000 q^{34} +1.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} +5.00000 q^{41} +(-2.50000 - 0.866025i) q^{42} +(1.00000 + 1.73205i) q^{44} +(2.50000 - 4.33013i) q^{46} +(-0.500000 - 0.866025i) q^{47} -1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(2.50000 + 4.33013i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(6.00000 - 10.3923i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} +4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(1.00000 - 1.73205i) q^{59} +(-5.00000 - 8.66025i) q^{61} -11.0000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-2.50000 - 4.33013i) q^{68} +5.00000 q^{69} -1.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} -4.00000 q^{76} +(4.00000 - 3.46410i) q^{77} -4.00000 q^{78} +(-4.50000 - 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -6.00000 q^{83} +(0.500000 + 2.59808i) q^{84} +(-3.00000 + 5.19615i) q^{87} +(1.00000 - 1.73205i) q^{88} +(-5.50000 - 9.52628i) q^{89} +(10.0000 + 3.46410i) q^{91} -5.00000 q^{92} +(-5.50000 - 9.52628i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000 q^{97} +(1.00000 - 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9} + 2 q^{11} + q^{12} + 8 q^{13} - q^{14} - q^{16} - 5 q^{17} - q^{18} + 4 q^{19} + 4 q^{21} - 4 q^{22} + 5 q^{23} + q^{24} - 4 q^{26} - 2 q^{27} - 4 q^{28} - 12 q^{29} + 11 q^{31} - q^{32} - 2 q^{33} + 10 q^{34} + 2 q^{36} + 8 q^{37} + 4 q^{38} + 4 q^{39} + 10 q^{41} - 5 q^{42} + 2 q^{44} + 5 q^{46} - q^{47} - 2 q^{48} + 11 q^{49} + 5 q^{51} - 4 q^{52} + 12 q^{53} + q^{54} + 5 q^{56} + 8 q^{57} + 6 q^{58} + 2 q^{59} - 10 q^{61} - 22 q^{62} - q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{68} + 10 q^{69} - 2 q^{71} - q^{72} + 2 q^{73} + 8 q^{74} - 8 q^{76} + 8 q^{77} - 8 q^{78} - 9 q^{79} - q^{81} - 5 q^{82} - 12 q^{83} + q^{84} - 6 q^{87} + 2 q^{88} - 11 q^{89} + 20 q^{91} - 10 q^{92} - 11 q^{93} - q^{94} + q^{96} + 2 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9 + 2 * q^11 + q^12 + 8 * q^13 - q^14 - q^16 - 5 * q^17 - q^18 + 4 * q^19 + 4 * q^21 - 4 * q^22 + 5 * q^23 + q^24 - 4 * q^26 - 2 * q^27 - 4 * q^28 - 12 * q^29 + 11 * q^31 - q^32 - 2 * q^33 + 10 * q^34 + 2 * q^36 + 8 * q^37 + 4 * q^38 + 4 * q^39 + 10 * q^41 - 5 * q^42 + 2 * q^44 + 5 * q^46 - q^47 - 2 * q^48 + 11 * q^49 + 5 * q^51 - 4 * q^52 + 12 * q^53 + q^54 + 5 * q^56 + 8 * q^57 + 6 * q^58 + 2 * q^59 - 10 * q^61 - 22 * q^62 - q^63 + 2 * q^64 - 2 * q^66 - 5 * q^68 + 10 * q^69 - 2 * q^71 - q^72 + 2 * q^73 + 8 * q^74 - 8 * q^76 + 8 * q^77 - 8 * q^78 - 9 * q^79 - q^81 - 5 * q^82 - 12 * q^83 + q^84 - 6 * q^87 + 2 * q^88 - 11 * q^89 + 20 * q^91 - 10 * q^92 - 11 * q^93 - q^94 + q^96 + 2 * q^97 + 2 * q^98 - 4 * q^99

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