LMFDB - Embedded newform 525.2.i.e.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.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:	$4.19214610612$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	525.151
Dual form			525.2.i.e.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{12} -1.00000 q^{13} +(1.00000 + 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(2.00000 - 1.73205i) q^{21} +4.00000 q^{22} +(-1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(-4.00000 + 3.46410i) q^{28} +4.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(-1.00000 - 1.73205i) q^{33} +2.00000 q^{36} +(1.50000 + 2.59808i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 + 0.866025i) q^{39} -10.0000 q^{41} +(5.00000 + 1.73205i) q^{42} -5.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-3.00000 - 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(1.00000 - 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-1.00000 - 1.73205i) q^{54} -1.00000 q^{57} +(4.00000 + 6.92820i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} -18.0000 q^{62} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(2.00000 - 3.46410i) q^{66} +(-2.50000 + 4.33013i) q^{67} -6.00000 q^{71} +(-1.50000 + 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +2.00000 q^{76} +(4.00000 - 3.46410i) q^{77} -2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-10.0000 - 17.3205i) q^{82} -6.00000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(2.00000 - 3.46410i) q^{87} +(-8.00000 - 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(4.50000 + 7.79423i) q^{93} +(6.00000 - 10.3923i) q^{94} +(4.00000 + 6.92820i) q^{96} +6.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9	$ 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9} + 2 q^{11} + 2 q^{12} - 2 q^{13} + 2 q^{14} + 4 q^{16} + 2 q^{18} - q^{19} + 4 q^{21} + 8 q^{22} - 2 q^{26} - 2 q^{27} - 8 q^{28} + 8 q^{29} - 9 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{36} + 3 q^{37} + 2 q^{38} - q^{39} - 20 q^{41} + 10 q^{42} - 10 q^{43} + 4 q^{44} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 2 q^{52} + 12 q^{53} - 2 q^{54} - 2 q^{57} + 8 q^{58} + 12 q^{59} - 10 q^{61} - 36 q^{62} - q^{63} - 16 q^{64} + 4 q^{66} - 5 q^{67} - 12 q^{71} - 3 q^{73} - 6 q^{74} + 4 q^{76} + 8 q^{77} - 4 q^{78} + q^{79} - q^{81} - 20 q^{82} - 12 q^{83} + 2 q^{84} - 10 q^{86} + 4 q^{87} - 16 q^{89} - 5 q^{91} + 9 q^{93} + 12 q^{94} + 8 q^{96} + 12 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9 + 2 * q^11 + 2 * q^12 - 2 * q^13 + 2 * q^14 + 4 * q^16 + 2 * q^18 - q^19 + 4 * q^21 + 8 * q^22 - 2 * q^26 - 2 * q^27 - 8 * q^28 + 8 * q^29 - 9 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^36 + 3 * q^37 + 2 * q^38 - q^39 - 20 * q^41 + 10 * q^42 - 10 * q^43 + 4 * q^44 - 6 * q^47 + 8 * q^48 + 11 * q^49 + 2 * q^52 + 12 * q^53 - 2 * q^54 - 2 * q^57 + 8 * q^58 + 12 * q^59 - 10 * q^61 - 36 * q^62 - q^63 - 16 * q^64 + 4 * q^66 - 5 * q^67 - 12 * q^71 - 3 * q^73 - 6 * q^74 + 4 * q^76 + 8 * q^77 - 4 * q^78 + q^79 - q^81 - 20 * q^82 - 12 * q^83 + 2 * q^84 - 10 * q^86 + 4 * q^87 - 16 * q^89 - 5 * q^91 + 9 * q^93 + 12 * q^94 + 8 * q^96 + 12 * q^97 - 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$		0			0
$5$		0			0
$6$	2.00000			0.816497
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$	−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	$0.0691756\pi$
$12$	1.00000	+	1.73205i	0.288675	+	0.500000i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	1.00000	+	5.19615i	0.267261	+	1.38873i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	1.00000	−	1.73205i	0.235702	−	0.408248i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$	4.00000			0.852803
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$		0			0
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	−1.00000			−0.192450
$28$	−4.00000	+	3.46410i	−0.755929	+	0.654654i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	0.105869	+	0.994380i	$0.466238\pi$
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	−0.914093	+	0.405505i	$0.867096\pi$
$32$	−4.00000	+	6.92820i	−0.707107	+	1.22474i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$		0			0
$35$		0			0
$36$	2.00000			0.333333
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$		0			0
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$	5.00000	+	1.73205i	0.771517	+	0.267261i
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	4.00000			0.577350
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	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	$-0.141688\pi$
$54$	−1.00000	−	1.73205i	−0.136083	−	0.235702i
$55$		0			0
$56$		0			0
$57$	−1.00000			−0.132453
$58$	4.00000	+	6.92820i	0.525226	+	0.909718i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		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	$-0.387809\pi$
$62$	−18.0000			−2.28600
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	−8.00000			−1.00000
$65$		0			0
$66$	2.00000	−	3.46410i	0.246183	−	0.426401i
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	−0.940356	−	0.340193i	$-0.889507\pi$
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	0.764794	+	0.644275i	$0.222841\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	2.00000			0.229416
$77$	4.00000	−	3.46410i	0.455842	−	0.394771i
$78$	−2.00000			−0.226455
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−10.0000	−	17.3205i	−1.10432	−	1.91273i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	1.00000	+	5.19615i	0.109109	+	0.566947i
$85$		0			0
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	2.00000	−	3.46410i	0.214423	−	0.371391i
$88$		0			0
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	0.0349934	−	0.999388i	$-0.488859\pi$
$90$		0			0
$91$	−2.50000	−	0.866025i	−0.262071	−	0.0907841i
$92$		0			0
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$		0			0
$96$	4.00000	+	6.92820i	0.408248	+	0.707107i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	−2.00000	+	13.8564i	−0.202031	+	1.39971i
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$		0			0
$106$	24.0000			2.33109
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	1.00000	−	1.73205i	0.0962250	−	0.166667i
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$		0			0
$111$	3.00000			0.284747
$112$	2.00000	+	10.3923i	0.188982	+	0.981981i
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$	24.0000			2.20938
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	10.0000	−	17.3205i	0.905357	−	1.56813i
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	−9.00000	−	15.5885i	−0.808224	−	1.39988i
$125$		0			0
$126$	4.00000	−	3.46410i	0.356348	−	0.308607i
$127$	15.0000			1.33103			0.665517	−	0.746382i	$-0.268211\pi$
$127$	15.0000			1.33103			0.665517	+	0.746382i	$0.268211\pi$
$128$		0			0
$129$	−2.50000	+	4.33013i	−0.220113	+	0.381246i
$130$		0			0
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	0.990972	+	0.134069i	$0.0428042\pi$
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	−0.379379	+	0.925241i	$0.623862\pi$
$132$	4.00000			0.348155
$133$	−0.500000	−	2.59808i	−0.0433555	−	0.225282i
$134$	−10.0000			−0.863868
$135$		0			0
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−3.00000			−0.254457			−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000			−0.254457			−0.127228	+	0.991873i	$0.540608\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	−6.00000	−	10.3923i	−0.503509	−	0.872103i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$	2.00000	−	3.46410i	0.166667	−	0.288675i
$145$		0			0
$146$	−6.00000			−0.496564
$147$	6.50000	−	2.59808i	0.536111	−	0.214286i
$148$	−6.00000			−0.493197
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		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	$-0.0589965\pi$
$152$		0			0
$153$		0			0
$154$	10.0000	+	3.46410i	0.805823	+	0.279145i
$155$		0			0
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−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	$0.977982\pi$
$158$	−1.00000	+	1.73205i	−0.0795557	+	0.137795i
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$		0			0
$162$	−2.00000			−0.157135
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	10.0000	−	17.3205i	0.780869	−	1.35250i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$	8.00000			0.606478
$175$		0			0
$176$	8.00000			0.603023
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	16.0000	−	27.7128i	1.19925	−	2.07716i
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	−0.900975	−	0.433872i	$-0.857147\pi$
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	0.826231	+	0.563331i	$0.190480\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	−1.00000	−	5.19615i	−0.0741249	−	0.385164i
$183$	−10.0000			−0.739221
$184$		0			0
$185$		0			0
$186$	−9.00000	+	15.5885i	−0.659912	+	1.14300i
$187$		0			0
$188$	12.0000			0.875190
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	0.626468	−	0.779447i	$-0.284500\pi$
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	−0.988255	+	0.152813i	$0.951167\pi$
$192$	−4.00000	+	6.92820i	−0.288675	+	0.500000i
$193$	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	$0.0370998\pi$
$194$	6.00000	+	10.3923i	0.430775	+	0.746124i
$195$		0			0
$196$	−13.0000	+	5.19615i	−0.928571	+	0.371154i
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$	−2.00000	−	3.46410i	−0.142134	−	0.246183i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$	2.50000	+	4.33013i	0.176336	+	0.305424i
$202$	−4.00000			−0.281439
$203$	10.0000	+	3.46410i	0.701862	+	0.243132i
$204$		0			0
$205$		0			0
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$		0			0
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$	−2.00000			−0.138343
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	12.0000	+	20.7846i	0.824163	+	1.42749i
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	8.00000	−	13.8564i	0.546869	−	0.947204i
$215$		0			0
$216$		0			0
$217$	−18.0000	+	15.5885i	−1.22192	+	1.05821i
$218$	−18.0000			−1.21911
$219$	1.50000	+	2.59808i	0.101361	+	0.175562i
$220$		0			0
$221$		0			0
$222$	3.00000	+	5.19615i	0.201347	+	0.348743i
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$	−16.0000	+	13.8564i	−1.06904	+	0.925820i
$225$		0			0
$226$	−10.0000	−	17.3205i	−0.665190	−	1.15214i
$227$	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	$-0.0371134\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$		0			0
$231$	−1.00000	−	5.19615i	−0.0657952	−	0.341882i
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$		0			0
$236$	12.0000	+	20.7846i	0.781133	+	1.35296i
$237$	1.00000			0.0649570
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	20.0000			1.28037
$245$		0			0
$246$	−20.0000			−1.27515
$247$	0.500000	+	0.866025i	0.0318142	+	0.0551039i
$248$		0			0
$249$	−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	$0.581245\pi$
$252$	5.00000	+	1.73205i	0.314970	+	0.109109i
$253$		0			0
$254$	15.0000	+	25.9808i	0.941184	+	1.63018i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	0.912222	+	0.409695i	$0.134365\pi$
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	−0.101305	+	0.994855i	$0.532302\pi$
$258$	−10.0000			−0.622573
$259$	1.50000	+	7.79423i	0.0932055	+	0.484310i
$260$		0			0
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	−14.0000	+	24.2487i	−0.864923	+	1.49809i
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	−0.797752	−	0.602986i	$-0.793977\pi$
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	0.921077	+	0.389380i	$0.127311\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$	−16.0000			−0.979184
$268$	−5.00000	−	8.66025i	−0.305424	−	0.529009i
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	−2.00000	+	1.73205i	−0.121046	+	0.104828i
$274$	−24.0000			−1.44989
$275$		0			0
$276$		0			0
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	−0.601975	−	0.798515i	$-0.705619\pi$
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	0.992522	+	0.122068i	$0.0389525\pi$
$278$	−3.00000	−	5.19615i	−0.179928	−	0.311645i
$279$	9.00000			0.538816
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	−6.00000	−	10.3923i	−0.357295	−	0.618853i
$283$	−5.50000	+	9.52628i	−0.326941	+	0.566279i	−0.981903	−	0.189383i	$-0.939351\pi$
$283$	−5.50000	+	9.52628i	−0.326941	+	0.566279i	0.654962	+	0.755662i	$0.272685\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$	−4.00000			−0.236525
$287$	−25.0000	−	8.66025i	−1.47570	−	0.511199i
$288$	8.00000			0.471405
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	3.00000	−	5.19615i	0.175863	−	0.304604i
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$	−8.00000			−0.467365			−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000			−0.467365			−0.233682	+	0.972313i	$0.575078\pi$
$294$	11.0000	+	8.66025i	0.641533	+	0.505076i
$295$		0			0
$296$		0			0
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	−12.0000	+	20.7846i	−0.695141	+	1.20402i
$299$		0			0
$300$		0			0
$301$	−12.5000	−	4.33013i	−0.720488	−	0.249584i
$302$	32.0000			1.84139
$303$	1.00000	+	1.73205i	0.0574485	+	0.0995037i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		0			0
$306$		0			0
$307$	17.0000			0.970241			0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000			0.970241			0.485121	+	0.874447i	$0.338776\pi$
$308$	2.00000	+	10.3923i	0.113961	+	0.592157i
$309$	−7.00000			−0.398216
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	−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	$0.842331\pi$
$314$	−28.0000			−1.58013
$315$		0			0
$316$	−2.00000			−0.112509
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$	12.0000	−	20.7846i	0.672927	−	1.16554i
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$		0			0
$321$	−8.00000			−0.446516
$322$		0			0
$323$		0			0
$324$	−1.00000	−	1.73205i	−0.0555556	−	0.0962250i
$325$		0			0
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$	4.50000	+	7.79423i	0.248851	+	0.431022i
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$		0			0
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	0.972784	+	0.231714i	$0.0744333\pi$
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	−0.285722	+	0.958313i	$0.592233\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$	1.50000	−	2.59808i	0.0821995	−	0.142374i
$334$	14.0000	+	24.2487i	0.766046	+	1.32683i
$335$		0			0
$336$	10.0000	+	3.46410i	0.545545	+	0.188982i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	−12.0000	−	20.7846i	−0.652714	−	1.13053i
$339$	−5.00000	+	8.66025i	−0.271563	+	0.470360i
$340$		0			0
$341$	9.00000	+	15.5885i	0.487377	+	0.844162i
$342$	−2.00000			−0.108148
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$	−8.00000	+	13.8564i	−0.430083	+	0.744925i
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	−0.0140303	−	0.999902i	$-0.504466\pi$
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	0.872955	−	0.487800i	$-0.162201\pi$
$348$	4.00000	+	6.92820i	0.214423	+	0.371391i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$	8.00000	+	13.8564i	0.426401	+	0.738549i
$353$	17.0000	−	29.4449i	0.904819	−	1.56719i	0.0836583	−	0.996495i	$-0.473340\pi$
$353$	17.0000	−	29.4449i	0.904819	−	1.56719i	0.821160	−	0.570697i	$-0.193327\pi$
$354$	12.0000	−	20.7846i	0.637793	−	1.10469i
$355$		0			0
$356$	32.0000			1.69600
$357$		0			0
$358$	−4.00000			−0.211407
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	13.0000	+	22.5167i	0.683265	+	1.18345i
$363$	7.00000			0.367405
$364$	4.00000	−	3.46410i	0.209657	−	0.181568i
$365$		0			0
$366$	−10.0000	−	17.3205i	−0.522708	−	0.905357i
$367$	−4.50000	+	7.79423i	−0.234898	+	0.406855i	−0.959243	−	0.282582i	$-0.908809\pi$
$367$	−4.50000	+	7.79423i	−0.234898	+	0.406855i	0.724345	+	0.689438i	$0.242142\pi$
$368$		0			0
$369$	5.00000	+	8.66025i	0.260290	+	0.450835i
$370$		0			0
$371$	24.0000	−	20.7846i	1.24602	−	1.07908i
$372$	−18.0000			−0.933257
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.00000			−0.206010
$378$	−1.00000	−	5.19615i	−0.0514344	−	0.267261i
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$		0			0
$381$	7.50000	−	12.9904i	0.384237	−	0.665517i
$382$	10.0000	−	17.3205i	0.511645	−	0.886194i
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$		0			0
$385$		0			0
$386$	22.0000			1.11977
$387$	2.50000	+	4.33013i	0.127082	+	0.220113i
$388$	−6.00000	+	10.3923i	−0.304604	+	0.527589i
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	14.0000			0.706207
$394$	−16.0000	−	27.7128i	−0.806068	−	1.39615i
$395$		0			0
$396$	2.00000	−	3.46410i	0.100504	−	0.174078i
$397$	−4.50000	−	7.79423i	−0.225849	−	0.391181i	0.730725	−	0.682672i	$-0.239182\pi$
$397$	−4.50000	−	7.79423i	−0.225849	−	0.391181i	−0.956574	+	0.291491i	$0.905849\pi$
$398$		0			0
$399$	−2.50000	−	0.866025i	−0.125157	−	0.0433555i
$400$		0			0
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.828932	+	0.559350i	$0.188949\pi$
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.0699455	+	0.997551i	$0.477717\pi$
$402$	−5.00000	+	8.66025i	−0.249377	+	0.431934i
$403$	4.50000	−	7.79423i	0.224161	−	0.388258i
$404$	−2.00000	−	3.46410i	−0.0995037	−	0.172345i
$405$		0			0
$406$	4.00000	+	20.7846i	0.198517	+	1.03152i
$407$	6.00000			0.297409
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	6.00000	+	10.3923i	0.295958	+	0.512615i
$412$	14.0000			0.689730
$413$	24.0000	−	20.7846i	1.18096	−	1.02274i
$414$		0			0
$415$		0			0
$416$	4.00000	−	6.92820i	0.196116	−	0.339683i
$417$	−1.50000	+	2.59808i	−0.0734553	+	0.127228i
$418$	−2.00000	−	3.46410i	−0.0978232	−	0.169435i
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$		0			0
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	−5.00000	−	25.9808i	−0.241967	−	1.25730i
$428$	16.0000			0.773389
$429$	1.00000	+	1.73205i	0.0482805	+	0.0836242i
$430$		0			0
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	0.997173	+	0.0751385i	$0.0239399\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	−31.0000			−1.48976			−0.744882	−	0.667196i	$-0.767494\pi$
$433$	−31.0000			−1.48976			−0.744882	+	0.667196i	$0.767494\pi$
$434$	−45.0000	−	15.5885i	−2.16007	−	0.748270i
$435$		0			0
$436$	−9.00000	−	15.5885i	−0.431022	−	0.746552i
$437$		0			0
$438$	−3.00000	+	5.19615i	−0.143346	+	0.248282i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$	−3.00000	+	5.19615i	−0.142374	+	0.246598i
$445$		0			0
$446$	−16.0000	−	27.7128i	−0.757622	−	1.31224i
$447$	12.0000			0.567581
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−10.0000	+	17.3205i	−0.470882	+	0.815591i
$452$	10.0000	−	17.3205i	0.470360	−	0.814688i
$453$	−8.00000	−	13.8564i	−0.375873	−	0.651031i
$454$	36.0000			1.68956
$455$		0			0
$456$		0			0
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$	−19.0000	+	32.9090i	−0.887812	+	1.53773i
$459$		0			0
$460$		0			0
$461$	20.0000			0.931493			0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000			0.931493			0.465746	+	0.884918i	$0.345786\pi$
$462$	8.00000	−	6.92820i	0.372194	−	0.322329i
$463$	17.0000			0.790057			0.395029	−	0.918669i	$-0.370735\pi$
$463$	17.0000			0.790057			0.395029	+	0.918669i	$0.370735\pi$
$464$	8.00000	+	13.8564i	0.371391	+	0.643268i
$465$		0			0
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	0.927052	−	0.374934i	$-0.122335\pi$
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	−0.788228	+	0.615383i	$0.789001\pi$
$468$	−2.00000			−0.0924500
$469$	−10.0000	+	8.66025i	−0.461757	+	0.399893i
$470$		0			0
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$		0			0
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$	1.00000	+	1.73205i	0.0459315	+	0.0795557i
$475$		0			0
$476$		0			0
$477$	−12.0000			−0.549442
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	−14.0000			−0.636364
$485$		0			0
$486$	−1.00000	+	1.73205i	−0.0453609	+	0.0785674i
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	−0.265260	−	0.964177i	$-0.585458\pi$
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	0.967632	−	0.252367i	$-0.0812090\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$	−10.0000	−	17.3205i	−0.450835	−	0.780869i
$493$		0			0
$494$	−1.00000	+	1.73205i	−0.0449921	+	0.0779287i
$495$		0			0
$496$	−36.0000			−1.61645
$497$	−15.0000	−	5.19615i	−0.672842	−	0.233079i
$498$	−12.0000			−0.537733
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	−0.899469	−	0.436984i	$-0.856047\pi$
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	0.0712957	−	0.997455i	$-0.477287\pi$
$500$		0			0
$501$	7.00000	−	12.1244i	0.312737	−	0.541676i
$502$	−8.00000	−	13.8564i	−0.357057	−	0.618442i
$503$	42.0000			1.87269			0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000			1.87269			0.936344	+	0.351085i	$0.114187\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$	−15.0000	+	25.9808i	−0.665517	+	1.15271i
$509$	−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
$511$	−6.00000	+	5.19615i	−0.265424	+	0.229864i
$512$	−32.0000			−1.41421
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	−26.0000	+	45.0333i	−1.14681	+	1.98633i
$515$		0			0
$516$	−5.00000	−	8.66025i	−0.220113	−	0.381246i
$517$	−12.0000			−0.527759
$518$	−12.0000	+	10.3923i	−0.527250	+	0.456612i
$519$	8.00000			0.351161
$520$		0			0
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	−0.967002	−	0.254769i	$-0.918001\pi$
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	0.704137	+	0.710064i	$0.251334\pi$
$522$	4.00000	−	6.92820i	0.175075	−	0.303239i
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	0.975652	+	0.219326i	$0.0703858\pi$
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	−0.297884	+	0.954602i	$0.596281\pi$
$524$	−28.0000			−1.22319
$525$		0			0
$526$	8.00000			0.348817
$527$		0			0
$528$	4.00000	−	6.92820i	0.174078	−	0.301511i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	−12.0000			−0.520756
$532$	5.00000	+	1.73205i	0.216777	+	0.0750939i
$533$	10.0000			0.433148
$534$	−16.0000	−	27.7128i	−0.692388	−	1.19925i
$535$		0			0
$536$		0			0
$537$	1.00000	+	1.73205i	0.0431532	+	0.0747435i
$538$	−12.0000			−0.517357
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$		0			0
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	16.0000	−	27.7128i	0.687259	−	1.19037i
$543$	6.50000	−	11.2583i	0.278942	−	0.483141i
$544$		0			0
$545$		0			0
$546$	−5.00000	−	1.73205i	−0.213980	−	0.0741249i
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−12.0000	−	20.7846i	−0.512615	−	0.887875i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$		0			0
$551$	−2.00000	−	3.46410i	−0.0852029	−	0.147576i
$552$		0			0
$553$	0.500000	+	2.59808i	0.0212622	+	0.110481i
$554$	26.0000			1.10463
$555$		0			0
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$	9.00000	+	15.5885i	0.381000	+	0.659912i
$559$	5.00000			0.211477
$560$		0			0
$561$		0			0
$562$	−4.00000	−	6.92820i	−0.168730	−	0.292249i
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	0.450535	+	0.892759i	$0.351233\pi$
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	−0.998419	+	0.0562051i	$0.982100\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$		0			0
$566$	−22.0000			−0.924729
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$		0			0
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	0.998608	+	0.0527519i	$0.0167993\pi$
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	−0.453619	+	0.891196i	$0.649867\pi$
$570$		0			0
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$	−10.0000			−0.417756
$574$	−10.0000	−	51.9615i	−0.417392	−	2.16883i
$575$		0			0
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	−8.50000	+	14.7224i	−0.353860	+	0.612903i	−0.986922	−	0.161198i	$-0.948464\pi$
$577$	−8.50000	+	14.7224i	−0.353860	+	0.612903i	0.633062	+	0.774101i	$0.281798\pi$
$578$	−17.0000	+	29.4449i	−0.707107	+	1.22474i
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$	−15.0000	−	5.19615i	−0.622305	−	0.215573i
$582$	12.0000			0.497416
$583$	−12.0000	−	20.7846i	−0.496989	−	0.860811i
$584$		0			0
$585$		0			0
$586$	−8.00000	−	13.8564i	−0.330477	−	0.572403i
$587$	−16.0000			−0.660391			−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000			−0.660391			−0.330195	+	0.943913i	$0.607115\pi$
$588$	−2.00000	+	13.8564i	−0.0824786	+	0.571429i
$589$	9.00000			0.370839
$590$		0			0
$591$	−8.00000	+	13.8564i	−0.329076	+	0.569976i
$592$	−6.00000	+	10.3923i	−0.246598	+	0.427121i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−24.0000			−0.983078
$597$		0			0
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	−9.00000			−0.367118			−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000			−0.367118			−0.183559	+	0.983009i	$0.558762\pi$
$602$	−5.00000	−	25.9808i	−0.203785	−	1.05890i
$603$	5.00000			0.203616
$604$	16.0000	+	27.7128i	0.651031	+	1.12762i
$605$		0			0
$606$	−2.00000	+	3.46410i	−0.0812444	+	0.140720i
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$	8.00000			0.324443
$609$	8.00000	−	6.92820i	0.324176	−	0.280745i
$610$		0			0
$611$	3.00000	+	5.19615i	0.121367	+	0.210214i
$612$		0			0
$613$	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	$-0.0742412\pi$
$614$	17.0000	+	29.4449i	0.686064	+	1.18830i
$615$		0			0
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	−7.00000	−	12.1244i	−0.281581	−	0.487713i
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	−0.412341	−	0.911030i	$-0.635289\pi$
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	0.995145	−	0.0984169i	$-0.0313779\pi$
$620$		0			0
$621$		0			0
$622$	12.0000			0.481156
$623$	−8.00000	−	41.5692i	−0.320513	−	1.66544i
$624$	−4.00000			−0.160128
$625$		0			0
$626$	1.00000	−	1.73205i	0.0399680	−	0.0692267i
$627$	−1.00000	+	1.73205i	−0.0399362	+	0.0691714i
$628$	−14.0000	−	24.2487i	−0.558661	−	0.967629i
$629$		0			0
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$	−24.0000	+	41.5692i	−0.953162	+	1.65092i
$635$		0			0
$636$	24.0000			0.951662
$637$	−5.50000	−	4.33013i	−0.217918	−	0.171566i
$638$	16.0000			0.633446
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$	−8.00000	−	13.8564i	−0.315735	−	0.546869i
$643$	19.0000			0.749287			0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000			0.749287			0.374643	+	0.927169i	$0.377765\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.00000	−	1.73205i	0.0393141	−	0.0680939i	−0.845699	−	0.533660i	$-0.820816\pi$
$647$	1.00000	−	1.73205i	0.0393141	−	0.0680939i	0.885013	+	0.465566i	$0.154149\pi$
$648$		0			0
$649$	−12.0000	−	20.7846i	−0.471041	−	0.815867i
$650$		0			0
$651$	4.50000	+	23.3827i	0.176369	+	0.916440i
$652$	−8.00000			−0.313304
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$	−9.00000	+	15.5885i	−0.351928	+	0.609557i
$655$		0			0
$656$	−20.0000	−	34.6410i	−0.780869	−	1.35250i
$657$	3.00000			0.117041
$658$	24.0000	−	20.7846i	0.935617	−	0.810268i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		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	$-0.127103\pi$
$662$	−25.0000	+	43.3013i	−0.971653	+	1.68295i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	6.00000			0.232495
$667$		0			0
$668$	−14.0000	+	24.2487i	−0.541676	+	0.938211i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$		0			0
$671$	−20.0000			−0.772091
$672$	4.00000	+	20.7846i	0.154303	+	0.801784i
$673$	41.0000			1.58043			0.790217	−	0.612827i	$-0.209968\pi$
$673$	41.0000			1.58043			0.790217	+	0.612827i	$0.209968\pi$
$674$	−13.0000	−	22.5167i	−0.500741	−	0.867309i
$675$		0			0
$676$	12.0000	−	20.7846i	0.461538	−	0.799408i
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	0.957984	−	0.286820i	$-0.0925982\pi$
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	−0.727386	+	0.686229i	$0.759265\pi$
$678$	−20.0000			−0.768095
$679$	15.0000	+	5.19615i	0.575647	+	0.199410i
$680$		0			0
$681$	−9.00000	−	15.5885i	−0.344881	−	0.597351i
$682$	−18.0000	+	31.1769i	−0.689256	+	1.19383i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$		0			0
$686$	−17.0000	+	32.9090i	−0.649063	+	1.25647i
$687$	19.0000			0.724895
$688$	−10.0000	−	17.3205i	−0.381246	−	0.660338i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	18.5000	+	32.0429i	0.703773	+	1.21897i	0.967132	+	0.254273i	$0.0818362\pi$
$691$	18.5000	+	32.0429i	0.703773	+	1.21897i	−0.263359	+	0.964698i	$0.584830\pi$
$692$	−16.0000			−0.608229
$693$	−5.00000	−	1.73205i	−0.189934	−	0.0657952i
$694$	64.0000			2.42941
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−14.0000	−	24.2487i	−0.529908	−	0.917827i
$699$	6.00000			0.226941
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	1.00000	+	1.73205i	0.0377426	+	0.0653720i
$703$	1.50000	−	2.59808i	0.0565736	−	0.0979883i
$704$	−8.00000	+	13.8564i	−0.301511	+	0.522233i
$705$		0			0
$706$	68.0000			2.55921
$707$	−4.00000	+	3.46410i	−0.150435	+	0.130281i
$708$	24.0000			0.901975
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	−0.997202	−	0.0747503i	$-0.976184\pi$
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	0.433865	−	0.900978i	$-0.357149\pi$
$710$		0			0
$711$	0.500000	−	0.866025i	0.0187515	−	0.0324785i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$	3.00000	−	5.19615i	0.112037	−	0.194054i
$718$	20.0000	−	34.6410i	0.746393	−	1.29279i
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$		0			0
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$	36.0000			1.33978
$723$	7.00000	+	12.1244i	0.260333	+	0.450910i
$724$	−13.0000	+	22.5167i	−0.483141	+	0.836825i
$725$		0			0
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	10.0000	−	17.3205i	0.369611	−	0.640184i
$733$	−7.50000	−	12.9904i	−0.277019	−	0.479811i	0.693624	−	0.720338i	$-0.256013\pi$
$733$	−7.50000	−	12.9904i	−0.277019	−	0.479811i	−0.970642	+	0.240527i	$0.922680\pi$
$734$	−18.0000			−0.664392
$735$		0			0
$736$		0			0
$737$	5.00000	+	8.66025i	0.184177	+	0.319005i
$738$	−10.0000	+	17.3205i	−0.368105	+	0.637577i
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$		0			0
$741$	1.00000			0.0367359
$742$	60.0000	+	20.7846i	2.20267	+	0.763027i
$743$	−42.0000			−1.54083			−0.770415	−	0.637542i	$-0.779951\pi$
$743$	−42.0000			−1.54083			−0.770415	+	0.637542i	$0.779951\pi$
$744$		0			0
$745$		0			0
$746$	−23.0000	+	39.8372i	−0.842090	+	1.45854i
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$		0			0
$749$	−4.00000	−	20.7846i	−0.146157	−	0.759453i
$750$		0			0
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	0.722718	−	0.691143i	$-0.242893\pi$
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	−0.959906	+	0.280321i	$0.909559\pi$
$752$	12.0000	−	20.7846i	0.437595	−	0.757937i
$753$	−4.00000	+	6.92820i	−0.145768	+	0.252478i
$754$	−4.00000	−	6.92820i	−0.145671	−	0.252310i
$755$		0			0
$756$	4.00000	−	3.46410i	0.145479	−	0.125988i
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	3.00000	+	5.19615i	0.108965	+	0.188733i
$759$		0			0
$760$		0			0
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$	30.0000			1.08679
$763$	−18.0000	+	15.5885i	−0.651644	+	0.564340i
$764$	20.0000			0.723575
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$	8.00000	+	13.8564i	0.288675	+	0.500000i
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	26.0000			0.936367
$772$	11.0000	+	19.0526i	0.395899	+	0.685717i
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	0.379549	+	0.925172i	$0.376079\pi$
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	−0.990997	+	0.133887i	$0.957254\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$		0			0
$776$		0			0
$777$	7.50000	+	2.59808i	0.269061	+	0.0932055i
$778$	12.0000			0.430221
$779$	5.00000	+	8.66025i	0.179144	+	0.310286i
$780$		0			0
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$		0			0
$783$	−4.00000			−0.142948
$784$	−4.00000	+	27.7128i	−0.142857	+	0.989743i
$785$		0			0
$786$	14.0000	+	24.2487i	0.499363	+	0.864923i
$787$	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	$-0.0859624\pi$
$788$	16.0000	−	27.7128i	0.569976	−	0.987228i
$789$	−2.00000	−	3.46410i	−0.0712019	−	0.123325i
$790$		0			0
$791$	−25.0000	−	8.66025i	−0.888898	−	0.307923i
$792$		0			0
$793$	5.00000	+	8.66025i	0.177555	+	0.307535i
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$		0			0
$796$		0			0
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$	−1.00000	−	5.19615i	−0.0353996	−	0.183942i
$799$		0			0
$800$		0			0
$801$	−8.00000	+	13.8564i	−0.282666	+	0.489592i
$802$	−36.0000	+	62.3538i	−1.27120	+	2.20179i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$	−10.0000			−0.352673
$805$		0			0
$806$	18.0000			0.634023
$807$	3.00000	+	5.19615i	0.105605	+	0.182913i
$808$		0			0
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	−16.0000	+	13.8564i	−0.561490	+	0.486265i
$813$	−16.0000			−0.561144
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$		0			0
$816$		0			0
$817$	2.50000	+	4.33013i	0.0874639	+	0.151492i
$818$	−10.0000			−0.349642
$819$	0.500000	+	2.59808i	0.0174714	+	0.0907841i
$820$		0			0
$821$	−1.00000	−	1.73205i	−0.0349002	−	0.0604490i	0.848048	−	0.529920i	$-0.177778\pi$
$821$	−1.00000	−	1.73205i	−0.0349002	−	0.0604490i	−0.882948	+	0.469471i	$0.844445\pi$
$822$	−12.0000	+	20.7846i	−0.418548	+	0.724947i
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$		0			0
$826$	60.0000	+	20.7846i	2.08767	+	0.723189i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$		0			0
$831$	−6.50000	−	11.2583i	−0.225483	−	0.390547i
$832$	8.00000			0.277350
$833$		0			0
$834$	−6.00000			−0.207763
$835$		0			0
$836$	2.00000	−	3.46410i	0.0691714	−	0.119808i
$837$	4.50000	−	7.79423i	0.155543	−	0.269408i
$838$	30.0000	+	51.9615i	1.03633	+	1.79498i
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−7.00000	−	12.1244i	−0.241236	−	0.417833i
$843$	−2.00000	+	3.46410i	−0.0688837	+	0.119310i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$		0			0
$846$	−12.0000			−0.412568
$847$	3.50000	+	18.1865i	0.120261	+	0.624897i
$848$	48.0000			1.64833
$849$	5.50000	+	9.52628i	0.188760	+	0.326941i
$850$		0			0
$851$		0			0
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	−35.0000			−1.19838			−0.599189	−	0.800608i	$-0.704510\pi$
$853$	−35.0000			−1.19838			−0.599189	+	0.800608i	$0.704510\pi$
$854$	40.0000	−	34.6410i	1.36877	−	1.18539i
$855$		0			0
$856$		0			0
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	0.451958	+	0.892039i	$0.350726\pi$
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	−0.998508	+	0.0546125i	$0.982608\pi$
$858$	−2.00000	+	3.46410i	−0.0682789	+	0.118262i
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	0.974249	+	0.225475i	$0.0723932\pi$
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	−0.291858	+	0.956462i	$0.594273\pi$
$860$		0			0
$861$	−20.0000	+	17.3205i	−0.681598	+	0.590281i
$862$	36.0000			1.22616
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.800799	−	0.598933i	$-0.795592\pi$
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.118291	−	0.992979i	$-0.537742\pi$
$864$	4.00000	−	6.92820i	0.136083	−	0.235702i
$865$		0			0
$866$	−31.0000	−	53.6936i	−1.05342	−	1.82458i
$867$	17.0000			0.577350
$868$	−9.00000	−	46.7654i	−0.305480	−	1.58732i
$869$	2.00000			0.0678454
$870$		0			0
$871$	2.50000	−	4.33013i	0.0847093	−	0.146721i
$872$		0			0
$873$	−3.00000	−	5.19615i	−0.101535	−	0.175863i
$874$		0			0
$875$		0			0
$876$	−6.00000			−0.202721
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$		0			0
$879$	−4.00000	+	6.92820i	−0.134917	+	0.233682i
$880$		0			0
$881$	24.0000			0.808581			0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000			0.808581			0.404290	+	0.914631i	$0.367519\pi$
$882$	13.0000	−	5.19615i	0.437733	−	0.174964i
$883$	13.0000			0.437485			0.218742	−	0.975783i	$-0.429805\pi$
$883$	13.0000			0.437485			0.218742	+	0.975783i	$0.429805\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	−17.0000	−	29.4449i	−0.570804	−	0.988662i	−0.996484	−	0.0837878i	$-0.973298\pi$
$887$	−17.0000	−	29.4449i	−0.570804	−	0.988662i	0.425679	−	0.904874i	$-0.360035\pi$
$888$		0			0
$889$	37.5000	+	12.9904i	1.25771	+	0.435683i
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	16.0000	−	27.7128i	0.535720	−	0.927894i
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$	12.0000	+	20.7846i	0.401340	+	0.695141i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−18.0000	−	31.1769i	−0.600668	−	1.04039i
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$		0			0
$902$	−40.0000			−1.33185
$903$	−10.0000	+	8.66025i	−0.332779	+	0.288195i
$904$		0			0
$905$		0			0
$906$	16.0000	−	27.7128i	0.531564	−	0.920697i
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	0.376228	+	0.926527i	$0.377221\pi$
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	−0.990510	+	0.137441i	$0.956112\pi$
$908$	18.0000	+	31.1769i	0.597351	+	1.03464i
$909$	2.00000			0.0663358
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$		0			0
$916$	−38.0000			−1.25556
$917$	7.00000	+	36.3731i	0.231160	+	1.20114i
$918$		0			0
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	0.611618	−	0.791153i	$-0.290519\pi$
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	−0.990968	+	0.134100i	$0.957186\pi$
$920$		0			0
$921$	8.50000	−	14.7224i	0.280085	−	0.485121i
$922$	20.0000	+	34.6410i	0.658665	+	1.14084i
$923$	6.00000			0.197492
$924$	10.0000	+	3.46410i	0.328976	+	0.113961i
$925$		0			0
$926$	17.0000	+	29.4449i	0.558655	+	0.967618i
$927$	−3.50000	+	6.06218i	−0.114955	+	0.199108i
$928$	−16.0000	+	27.7128i	−0.525226	+	0.909718i
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$	−12.0000			−0.393073
$933$	−3.00000	−	5.19615i	−0.0982156	−	0.170114i
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	−15.0000			−0.490029			−0.245014	−	0.969519i	$-0.578793\pi$
$937$	−15.0000			−0.490029			−0.245014	+	0.969519i	$0.578793\pi$
$938$	−25.0000	−	8.66025i	−0.816279	−	0.282767i
$939$	−1.00000			−0.0326338
$940$		0			0
$941$	2.00000	−	3.46410i	0.0651981	−	0.112926i	−0.831584	−	0.555399i	$-0.812565\pi$
$941$	2.00000	−	3.46410i	0.0651981	−	0.112926i	0.896782	+	0.442473i	$0.145899\pi$
$942$	−14.0000	+	24.2487i	−0.456145	+	0.790066i
$943$		0			0
$944$	48.0000			1.56227
$945$		0			0
$946$	−20.0000			−0.650256
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	0.773279	−	0.634066i	$-0.218615\pi$
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	−0.935757	+	0.352646i	$0.885282\pi$
$948$	−1.00000	+	1.73205i	−0.0324785	+	0.0562544i
$949$	1.50000	−	2.59808i	0.0486921	−	0.0843371i
$950$		0			0
$951$	24.0000			0.778253
$952$		0			0
$953$	−44.0000			−1.42530			−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000			−1.42530			−0.712650	+	0.701520i	$0.752505\pi$
$954$	−12.0000	−	20.7846i	−0.388514	−	0.672927i
$955$		0			0
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$	−4.00000	−	6.92820i	−0.129302	−	0.223957i
$958$	56.0000			1.80928
$959$	−24.0000	+	20.7846i	−0.775000	+	0.671170i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$	3.00000	−	5.19615i	0.0967239	−	0.167531i
$963$	−4.00000	+	6.92820i	−0.128898	+	0.223258i
$964$	−14.0000	−	24.2487i	−0.450910	−	0.780998i
$965$		0			0
$966$		0			0
$967$	−19.0000			−0.610999			−0.305499	−	0.952192i	$-0.598823\pi$
$967$	−19.0000			−0.610999			−0.305499	+	0.952192i	$0.598823\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$	−2.00000			−0.0641500
$973$	−7.50000	−	2.59808i	−0.240439	−	0.0832905i
$974$	62.0000			1.98661
$975$		0			0
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$	4.00000	+	6.92820i	0.127906	+	0.221540i
$979$	−32.0000			−1.02272
$980$		0			0
$981$	9.00000			0.287348
$982$	−28.0000	−	48.4974i	−0.893516	−	1.54761i
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−15.0000	−	5.19615i	−0.477455	−	0.165395i
$988$	−2.00000			−0.0636285
$989$		0			0
$990$		0			0
$991$	−8.50000	+	14.7224i	−0.270011	+	0.467673i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−8.50000	+	14.7224i	−0.270011	+	0.467673i	0.698853	+	0.715265i	$0.253694\pi$
$992$	−36.0000	−	62.3538i	−1.14300	−	1.97974i
$993$	25.0000			0.793351
$994$	−6.00000	−	31.1769i	−0.190308	−	0.988872i
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	9.50000	−	16.4545i	0.300868	−	0.521119i	−0.675465	−	0.737392i	$-0.736057\pi$
$997$	9.50000	−	16.4545i	0.300868	−	0.521119i	0.976333	+	0.216274i	$0.0693903\pi$
$998$	37.0000	−	64.0859i	1.17121	−	2.02860i
$999$	−1.50000	−	2.59808i	−0.0474579	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.e.151.1		2
5.2	odd	4		525.2.r.e.424.1		4
5.3	odd	4		525.2.r.e.424.2		4
5.4	even	2		21.2.e.a.4.1	✓	2
7.2	even	3	inner	525.2.i.e.226.1		2
7.3	odd	6		3675.2.a.c.1.1		1
7.4	even	3		3675.2.a.a.1.1		1
15.14	odd	2		63.2.e.b.46.1		2
20.19	odd	2		336.2.q.f.193.1		2
35.2	odd	12		525.2.r.e.499.2		4
35.4	even	6		147.2.a.c.1.1		1
35.9	even	6		21.2.e.a.16.1	yes	2
35.19	odd	6		147.2.e.a.79.1		2
35.23	odd	12		525.2.r.e.499.1		4
35.24	odd	6		147.2.a.b.1.1		1
35.34	odd	2		147.2.e.a.67.1		2
40.19	odd	2		1344.2.q.c.193.1		2
40.29	even	2		1344.2.q.m.193.1		2
45.4	even	6		567.2.h.f.298.1		2
45.14	odd	6		567.2.h.a.298.1		2
45.29	odd	6		567.2.g.f.109.1		2
45.34	even	6		567.2.g.a.109.1		2
60.59	even	2		1008.2.s.d.865.1		2
105.44	odd	6		63.2.e.b.37.1		2
105.59	even	6		441.2.a.a.1.1		1
105.74	odd	6		441.2.a.b.1.1		1
105.89	even	6		441.2.e.e.226.1		2
105.104	even	2		441.2.e.e.361.1		2
140.19	even	6		2352.2.q.c.961.1		2
140.39	odd	6		2352.2.a.d.1.1		1
140.59	even	6		2352.2.a.w.1.1		1
140.79	odd	6		336.2.q.f.289.1		2
140.139	even	2		2352.2.q.c.1537.1		2
280.59	even	6		9408.2.a.k.1.1		1
280.109	even	6		9408.2.a.bg.1.1		1
280.149	even	6		1344.2.q.m.961.1		2
280.179	odd	6		9408.2.a.cv.1.1		1
280.219	odd	6		1344.2.q.c.961.1		2
280.269	odd	6		9408.2.a.bz.1.1		1
315.79	even	6		567.2.h.f.352.1		2
315.149	odd	6		567.2.g.f.541.1		2
315.184	even	6		567.2.g.a.541.1		2
315.254	odd	6		567.2.h.a.352.1		2
420.59	odd	6		7056.2.a.m.1.1		1
420.179	even	6		7056.2.a.bp.1.1		1
420.359	even	6		1008.2.s.d.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.e.a.4.1	✓	2	5.4	even	2
21.2.e.a.16.1	yes	2	35.9	even	6
63.2.e.b.37.1		2	105.44	odd	6
63.2.e.b.46.1		2	15.14	odd	2
147.2.a.b.1.1		1	35.24	odd	6
147.2.a.c.1.1		1	35.4	even	6
147.2.e.a.67.1		2	35.34	odd	2
147.2.e.a.79.1		2	35.19	odd	6
336.2.q.f.193.1		2	20.19	odd	2
336.2.q.f.289.1		2	140.79	odd	6
441.2.a.a.1.1		1	105.59	even	6
441.2.a.b.1.1		1	105.74	odd	6
441.2.e.e.226.1		2	105.89	even	6
441.2.e.e.361.1		2	105.104	even	2
525.2.i.e.151.1		2	1.1	even	1	trivial
525.2.i.e.226.1		2	7.2	even	3	inner
525.2.r.e.424.1		4	5.2	odd	4
525.2.r.e.424.2		4	5.3	odd	4
525.2.r.e.499.1		4	35.23	odd	12
525.2.r.e.499.2		4	35.2	odd	12
567.2.g.a.109.1		2	45.34	even	6
567.2.g.a.541.1		2	315.184	even	6
567.2.g.f.109.1		2	45.29	odd	6
567.2.g.f.541.1		2	315.149	odd	6
567.2.h.a.298.1		2	45.14	odd	6
567.2.h.a.352.1		2	315.254	odd	6
567.2.h.f.298.1		2	45.4	even	6
567.2.h.f.352.1		2	315.79	even	6
1008.2.s.d.289.1		2	420.359	even	6
1008.2.s.d.865.1		2	60.59	even	2
1344.2.q.c.193.1		2	40.19	odd	2
1344.2.q.c.961.1		2	280.219	odd	6
1344.2.q.m.193.1		2	40.29	even	2
1344.2.q.m.961.1		2	280.149	even	6
2352.2.a.d.1.1		1	140.39	odd	6
2352.2.a.w.1.1		1	140.59	even	6
2352.2.q.c.961.1		2	140.19	even	6
2352.2.q.c.1537.1		2	140.139	even	2
3675.2.a.a.1.1		1	7.4	even	3
3675.2.a.c.1.1		1	7.3	odd	6
7056.2.a.m.1.1		1	420.59	odd	6
7056.2.a.bp.1.1		1	420.179	even	6
9408.2.a.k.1.1		1	280.59	even	6
9408.2.a.bg.1.1		1	280.109	even	6
9408.2.a.bz.1.1		1	280.269	odd	6
9408.2.a.cv.1.1		1	280.179	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{12} -1.00000 q^{13} +(1.00000 + 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(2.00000 - 1.73205i) q^{21} +4.00000 q^{22} +(-1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(-4.00000 + 3.46410i) q^{28} +4.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(-1.00000 - 1.73205i) q^{33} +2.00000 q^{36} +(1.50000 + 2.59808i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 + 0.866025i) q^{39} -10.0000 q^{41} +(5.00000 + 1.73205i) q^{42} -5.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-3.00000 - 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(1.00000 - 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-1.00000 - 1.73205i) q^{54} -1.00000 q^{57} +(4.00000 + 6.92820i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} -18.0000 q^{62} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(2.00000 - 3.46410i) q^{66} +(-2.50000 + 4.33013i) q^{67} -6.00000 q^{71} +(-1.50000 + 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +2.00000 q^{76} +(4.00000 - 3.46410i) q^{77} -2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-10.0000 - 17.3205i) q^{82} -6.00000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(2.00000 - 3.46410i) q^{87} +(-8.00000 - 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(4.50000 + 7.79423i) q^{93} +(6.00000 - 10.3923i) q^{94} +(4.00000 + 6.92820i) q^{96} +6.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9	\( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9} + 2 q^{11} + 2 q^{12} - 2 q^{13} + 2 q^{14} + 4 q^{16} + 2 q^{18} - q^{19} + 4 q^{21} + 8 q^{22} - 2 q^{26} - 2 q^{27} - 8 q^{28} + 8 q^{29} - 9 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{36} + 3 q^{37} + 2 q^{38} - q^{39} - 20 q^{41} + 10 q^{42} - 10 q^{43} + 4 q^{44} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 2 q^{52} + 12 q^{53} - 2 q^{54} - 2 q^{57} + 8 q^{58} + 12 q^{59} - 10 q^{61} - 36 q^{62} - q^{63} - 16 q^{64} + 4 q^{66} - 5 q^{67} - 12 q^{71} - 3 q^{73} - 6 q^{74} + 4 q^{76} + 8 q^{77} - 4 q^{78} + q^{79} - q^{81} - 20 q^{82} - 12 q^{83} + 2 q^{84} - 10 q^{86} + 4 q^{87} - 16 q^{89} - 5 q^{91} + 9 q^{93} + 12 q^{94} + 8 q^{96} + 12 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9 + 2 * q^11 + 2 * q^12 - 2 * q^13 + 2 * q^14 + 4 * q^16 + 2 * q^18 - q^19 + 4 * q^21 + 8 * q^22 - 2 * q^26 - 2 * q^27 - 8 * q^28 + 8 * q^29 - 9 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^36 + 3 * q^37 + 2 * q^38 - q^39 - 20 * q^41 + 10 * q^42 - 10 * q^43 + 4 * q^44 - 6 * q^47 + 8 * q^48 + 11 * q^49 + 2 * q^52 + 12 * q^53 - 2 * q^54 - 2 * q^57 + 8 * q^58 + 12 * q^59 - 10 * q^61 - 36 * q^62 - q^63 - 16 * q^64 + 4 * q^66 - 5 * q^67 - 12 * q^71 - 3 * q^73 - 6 * q^74 + 4 * q^76 + 8 * q^77 - 4 * q^78 + q^79 - q^81 - 20 * q^82 - 12 * q^83 + 2 * q^84 - 10 * q^86 + 4 * q^87 - 16 * q^89 - 5 * q^91 + 9 * q^93 + 12 * q^94 + 8 * q^96 + 12 * q^97 - 4 * q^98 - 4 * q^99

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