LMFDB - Embedded newform 1050.3.p.f.451.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,3,Mod(451,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.451"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,18,-12,0,0,8,0,18,0,-4,-36,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + \cdots + 6882692292 $ x^12 - 4x^11 + 56x^10 + 300x^9 + 1007x^8 + 12456x^7 + 209990x^6 - 250384x^5 + 4799806x^4 + 51487320x^3 - 123648876x^2 + 379489320*x + 6882692292
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.4
Root			$-0.0663422 - 7.58000i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.f.901.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-6.80475 + 1.64177i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(8.87741 - 15.3761i) q^{11} +(-3.00000 + 1.73205i) q^{12} +2.00882i q^{13} +(-6.82244 - 7.17317i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-18.3681 - 10.6048i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-5.70198 + 3.29204i) q^{19} +(-11.6289 - 3.43042i) q^{21} +25.1091 q^{22} +(-19.7033 - 34.1271i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-2.46029 + 1.42045i) q^{26} +5.19615i q^{27} +(3.96111 - 13.4279i) q^{28} -25.1091 q^{29} +(4.76798 + 2.75280i) q^{31} +(2.82843 - 4.89898i) q^{32} +(26.6322 - 15.3761i) q^{33} -29.9950i q^{34} -6.00000 q^{36} +(-5.87580 - 10.1772i) q^{37} +(-8.06382 - 4.65565i) q^{38} +(-1.73969 + 3.01323i) q^{39} +16.8812i q^{41} +(-4.02151 - 16.6682i) q^{42} -27.7474 q^{43} +(17.7548 + 30.7523i) q^{44} +(27.8647 - 48.2631i) q^{46} +(-39.5579 + 22.8388i) q^{47} -6.92820i q^{48} +(43.6092 - 22.3437i) q^{49} +(-18.3681 - 31.8145i) q^{51} +(-3.47938 - 2.00882i) q^{52} +(49.2261 - 85.2621i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(19.2467 - 4.64364i) q^{56} -11.4040 q^{57} +(-17.7548 - 30.7523i) q^{58} +(10.9872 + 6.34348i) q^{59} +(82.0429 - 47.3675i) q^{61} +7.78609i q^{62} +(-14.4726 - 15.2166i) q^{63} +8.00000 q^{64} +(37.6637 + 21.7451i) q^{66} +(4.17603 - 7.23310i) q^{67} +(36.7362 - 21.2096i) q^{68} -68.2543i q^{69} +71.8225 q^{71} +(-4.24264 - 7.34847i) q^{72} +(0.697968 + 0.402972i) q^{73} +(8.30963 - 14.3927i) q^{74} -13.1682i q^{76} +(-35.1644 + 119.205i) q^{77} -4.92058 q^{78} +(-58.1846 - 100.779i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-20.6752 + 11.9368i) q^{82} -50.1243i q^{83} +(17.5706 - 16.7115i) q^{84} +(-19.6204 - 33.9835i) q^{86} +(-37.6637 - 21.7451i) q^{87} +(-25.1091 + 43.4903i) q^{88} +(74.9322 - 43.2621i) q^{89} +(-3.29803 - 13.6695i) q^{91} +78.8133 q^{92} +(4.76798 + 8.25839i) q^{93} +(-55.9433 - 32.2989i) q^{94} +(8.48528 - 4.89898i) q^{96} +165.642i q^{97} +(58.2017 + 37.6107i) q^{98} +53.2645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−6.80475	+	1.64177i	−0.972107	+	0.234539i
$7$	−6.80475	+	1.64177i	−0.972107	+	0.234539i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	8.87741	−	15.3761i	0.807038	−	1.39783i	−0.107869	−	0.994165i	$-0.534403\pi$
$11$	8.87741	−	15.3761i	0.807038	−	1.39783i	0.914907	−	0.403665i	$-0.132264\pi$
$12$	−3.00000	+	1.73205i	−0.250000	+	0.144338i
$13$			2.00882i			0.154525i	0.997011	+	0.0772623i	$0.0246179\pi$
$13$			2.00882i			0.154525i	−0.997011	+	0.0772623i	$0.975382\pi$
$14$	−6.82244	−	7.17317i	−0.487317	−	0.512369i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−18.3681	−	10.6048i	−1.08048	−	0.623813i	−0.149451	−	0.988769i	$-0.547751\pi$
$17$	−18.3681	−	10.6048i	−1.08048	−	0.623813i	−0.931025	+	0.364956i	$0.881084\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	−5.70198	+	3.29204i	−0.300104	+	0.173265i	−0.642490	−	0.766294i	$-0.722098\pi$
$19$	−5.70198	+	3.29204i	−0.300104	+	0.173265i	0.342386	+	0.939560i	$0.388765\pi$
$20$		0			0
$21$	−11.6289	−	3.43042i	−0.553759	−	0.163353i
$22$	25.1091			1.14132
$23$	−19.7033	−	34.1271i	−0.856666	−	1.48379i	−0.875091	−	0.483959i	$-0.839199\pi$
$23$	−19.7033	−	34.1271i	−0.856666	−	1.48379i	0.0184250	−	0.999830i	$-0.494135\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−2.46029	+	1.42045i	−0.0946266	+	0.0546327i
$27$			5.19615i			0.192450i
$28$	3.96111	−	13.4279i	0.141468	−	0.479569i
$29$	−25.1091			−0.865832			−0.432916	−	0.901434i	$-0.642515\pi$
$29$	−25.1091			−0.865832			−0.432916	+	0.901434i	$0.642515\pi$
$30$		0			0
$31$	4.76798	+	2.75280i	0.153806	+	0.0887999i	0.574928	−	0.818204i	$-0.305030\pi$
$31$	4.76798	+	2.75280i	0.153806	+	0.0887999i	−0.421122	+	0.907004i	$0.638363\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	26.6322	−	15.3761i	0.807038	−	0.465943i
$34$		−	29.9950i		−	0.882205i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−5.87580	−	10.1772i	−0.158805	−	0.275059i	0.775633	−	0.631184i	$-0.217431\pi$
$37$	−5.87580	−	10.1772i	−0.158805	−	0.275059i	−0.934438	+	0.356125i	$0.884098\pi$
$38$	−8.06382	−	4.65565i	−0.212206	−	0.122517i
$39$	−1.73969	+	3.01323i	−0.0446074	+	0.0772623i
$40$		0			0
$41$			16.8812i			0.411737i	0.978580	+	0.205868i	$0.0660019\pi$
$41$			16.8812i			0.411737i	−0.978580	+	0.205868i	$0.933998\pi$
$42$	−4.02151	−	16.6682i	−0.0957502	−	0.396861i
$43$	−27.7474			−0.645290			−0.322645	−	0.946520i	$-0.604572\pi$
$43$	−27.7474			−0.645290			−0.322645	+	0.946520i	$0.604572\pi$
$44$	17.7548	+	30.7523i	0.403519	+	0.698915i
$45$		0			0
$46$	27.8647	−	48.2631i	0.605754	−	1.04920i
$47$	−39.5579	+	22.8388i	−0.841657	+	0.485931i	−0.857827	−	0.513938i	$-0.828186\pi$
$47$	−39.5579	+	22.8388i	−0.841657	+	0.485931i	0.0161700	+	0.999869i	$0.494853\pi$
$48$		−	6.92820i		−	0.144338i
$49$	43.6092	−	22.3437i	0.889983	−	0.455994i
$50$		0			0
$51$	−18.3681	−	31.8145i	−0.360159	−	0.623813i
$52$	−3.47938	−	2.00882i	−0.0669111	−	0.0386311i
$53$	49.2261	−	85.2621i	0.928794	−	1.60872i	0.143451	−	0.989657i	$-0.454180\pi$
$53$	49.2261	−	85.2621i	0.928794	−	1.60872i	0.785343	−	0.619061i	$-0.212487\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	19.2467	−	4.64364i	0.343692	−	0.0829221i
$57$	−11.4040			−0.200069
$58$	−17.7548	−	30.7523i	−0.306118	−	0.530211i
$59$	10.9872	+	6.34348i	0.186224	+	0.107517i	0.590214	−	0.807247i	$-0.299043\pi$
$59$	10.9872	+	6.34348i	0.186224	+	0.107517i	−0.403990	+	0.914764i	$0.632377\pi$
$60$		0			0
$61$	82.0429	−	47.3675i	1.34497	−	0.776517i	0.357435	−	0.933938i	$-0.383652\pi$
$61$	82.0429	−	47.3675i	1.34497	−	0.776517i	0.987531	+	0.157422i	$0.0503182\pi$
$62$			7.78609i			0.125582i
$63$	−14.4726	−	15.2166i	−0.229723	−	0.241533i
$64$	8.00000			0.125000
$65$		0			0
$66$	37.6637	+	21.7451i	0.570662	+	0.329472i
$67$	4.17603	−	7.23310i	0.0623289	−	0.107957i	−0.833177	−	0.553006i	$-0.813481\pi$
$67$	4.17603	−	7.23310i	0.0623289	−	0.107957i	0.895506	+	0.445049i	$0.146814\pi$
$68$	36.7362	−	21.2096i	0.540238	−	0.311907i
$69$		−	68.2543i		−	0.989193i
$70$		0			0
$71$	71.8225			1.01158			0.505792	−	0.862655i	$-0.331200\pi$
$71$	71.8225			1.01158			0.505792	+	0.862655i	$0.331200\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	0.697968	+	0.402972i	0.00956121	+	0.00552017i	0.504773	−	0.863252i	$-0.331576\pi$
$73$	0.697968	+	0.402972i	0.00956121	+	0.00552017i	−0.495212	+	0.868772i	$0.664910\pi$
$74$	8.30963	−	14.3927i	0.112292	−	0.194496i
$75$		0			0
$76$		−	13.1682i		−	0.173265i
$77$	−35.1644	+	119.205i	−0.456681	+	1.54812i
$78$	−4.92058			−0.0630844
$79$	−58.1846	−	100.779i	−0.736514	−	1.27568i	−0.954056	−	0.299628i	$-0.903137\pi$
$79$	−58.1846	−	100.779i	−0.736514	−	1.27568i	0.217542	−	0.976051i	$-0.430196\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−20.6752	+	11.9368i	−0.252136	+	0.145571i
$83$		−	50.1243i		−	0.603907i	−0.953323	−	0.301953i	$-0.902361\pi$
$83$		−	50.1243i		−	0.603907i	0.953323	−	0.301953i	$-0.0976387\pi$
$84$	17.5706	−	16.7115i	0.209174	−	0.198946i
$85$		0			0
$86$	−19.6204	−	33.9835i	−0.228144	−	0.395158i
$87$	−37.6637	−	21.7451i	−0.432916	−	0.249944i
$88$	−25.1091	+	43.4903i	−0.285331	+	0.494208i
$89$	74.9322	−	43.2621i	0.841935	−	0.486091i	−0.0159868	−	0.999872i	$-0.505089\pi$
$89$	74.9322	−	43.2621i	0.841935	−	0.486091i	0.857921	+	0.513781i	$0.171756\pi$
$90$		0			0
$91$	−3.29803	−	13.6695i	−0.0362420	−	0.150214i
$92$	78.8133			0.856666
$93$	4.76798	+	8.25839i	0.0512687	+	0.0887999i
$94$	−55.9433	−	32.2989i	−0.595141	−	0.343605i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$			165.642i			1.70765i	0.520563	+	0.853823i	$0.325722\pi$
$97$			165.642i			1.70765i	−0.520563	+	0.853823i	$0.674278\pi$
$98$	58.2017	+	37.6107i	0.593895	+	0.383783i
$99$	53.2645			0.538025
$100$		0			0
$101$	−170.953	−	98.7000i	−1.69261	−	0.977227i	−0.952401	−	0.304847i	$-0.901395\pi$
$101$	−170.953	−	98.7000i	−1.69261	−	0.977227i	−0.740206	−	0.672380i	$-0.765272\pi$
$102$	25.9764	−	44.9925i	0.254671	−	0.441103i
$103$	−61.2474	+	35.3612i	−0.594635	+	0.343313i	−0.766928	−	0.641733i	$-0.778216\pi$
$103$	−61.2474	+	35.3612i	−0.594635	+	0.343313i	0.172293	+	0.985046i	$0.444882\pi$
$104$		−	5.68180i		−	0.0546327i
$105$		0			0
$106$	139.232			1.31351
$107$	15.9804	+	27.6788i	0.149349	+	0.258680i	0.930987	−	0.365052i	$-0.118949\pi$
$107$	15.9804	+	27.6788i	0.149349	+	0.258680i	−0.781638	+	0.623732i	$0.785615\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	−106.026	+	183.643i	−0.972717	+	1.68479i	−0.285444	+	0.958396i	$0.592141\pi$
$109$	−106.026	+	183.643i	−0.972717	+	1.68479i	−0.687273	+	0.726399i	$0.741192\pi$
$110$		0			0
$111$		−	20.3544i		−	0.183373i
$112$	19.2968	+	20.2888i	0.172293	+	0.181150i
$113$	−91.0393			−0.805657			−0.402829	−	0.915275i	$-0.631973\pi$
$113$	−91.0393			−0.805657			−0.402829	+	0.915275i	$0.631973\pi$
$114$	−8.06382	−	13.9669i	−0.0707352	−	0.122517i
$115$		0			0
$116$	25.1091	−	43.4903i	0.216458	−	0.374916i
$117$	−5.21906	+	3.01323i	−0.0446074	+	0.0257541i
$118$			17.9421i			0.152051i
$119$	142.401	+	42.0069i	1.19665	+	0.352999i
$120$		0			0
$121$	−97.1170	−	168.212i	−0.802620	−	1.39018i
$122$	116.026	+	66.9878i	0.951035	+	0.549080i
$123$	−14.6195	+	25.3218i	−0.118858	+	0.205868i
$124$	−9.53597	+	5.50559i	−0.0769030	+	0.0444000i
$125$		0			0
$126$	8.40279	−	28.4850i	0.0666888	−	0.226071i
$127$	−160.943			−1.26727			−0.633635	−	0.773632i	$-0.718438\pi$
$127$	−160.943			−1.26727			−0.633635	+	0.773632i	$0.718438\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−41.6212	−	24.0300i	−0.322645	−	0.186279i
$130$		0			0
$131$	−14.4620	+	8.34962i	−0.110397	+	0.0637375i	−0.554182	−	0.832396i	$-0.686969\pi$
$131$	−14.4620	+	8.34962i	−0.110397	+	0.0637375i	0.443785	+	0.896133i	$0.353635\pi$
$132$			61.5045i			0.465943i
$133$	33.3957	−	31.7629i	0.251096	−	0.238818i
$134$	11.8116			0.0881463
$135$		0			0
$136$	51.9528	+	29.9950i	0.382006	+	0.220551i
$137$	−63.2788	+	109.602i	−0.461889	+	0.800015i	−0.999055	−	0.0434613i	$-0.986161\pi$
$137$	−63.2788	+	109.602i	−0.461889	+	0.800015i	0.537166	+	0.843476i	$0.319495\pi$
$138$	83.5941	−	48.2631i	0.605754	−	0.349732i
$139$		−	135.361i		−	0.973820i	−0.873452	−	0.486910i	$-0.838124\pi$
$139$		−	135.361i		−	0.973820i	0.873452	−	0.486910i	$-0.161876\pi$
$140$		0			0
$141$	−79.1158			−0.561105
$142$	50.7862	+	87.9643i	0.357649	+	0.619467i
$143$	30.8879	+	17.8331i	0.215999	+	0.124707i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$			1.13978i			0.00780669i
$147$	84.7640	+	4.25108i	0.576626	+	0.0289189i
$148$	23.5032			0.158805
$149$	40.3068	+	69.8135i	0.270516	+	0.468547i	0.968994	−	0.247084i	$-0.0794725\pi$
$149$	40.3068	+	69.8135i	0.270516	+	0.468547i	−0.698478	+	0.715631i	$0.746139\pi$
$150$		0			0
$151$	6.96796	−	12.0689i	0.0461454	−	0.0799262i	−0.842030	−	0.539430i	$-0.818640\pi$
$151$	6.96796	−	12.0689i	0.0461454	−	0.0799262i	0.888176	+	0.459504i	$0.151973\pi$
$152$	16.1276	−	9.31129i	0.106103	−	0.0612585i
$153$		−	63.6289i		−	0.415875i
$154$	−170.861	+	41.2235i	−1.10949	+	0.267685i
$155$		0			0
$156$	−3.47938	−	6.02646i	−0.0223037	−	0.0386311i
$157$	21.8815	+	12.6333i	0.139373	+	0.0804669i	0.568065	−	0.822984i	$-0.307692\pi$
$157$	21.8815	+	12.6333i	0.139373	+	0.0804669i	−0.428692	+	0.903451i	$0.641026\pi$
$158$	82.2854	−	142.523i	0.520794	−	0.902041i
$159$	147.678	−	85.2621i	0.928794	−	0.536239i
$160$		0			0
$161$	190.105	+	199.878i	1.18078	+	1.24148i
$162$	−12.7279			−0.0785674
$163$	27.8663	+	48.2658i	0.170959	+	0.296109i	0.938755	−	0.344585i	$-0.111980\pi$
$163$	27.8663	+	48.2658i	0.170959	+	0.296109i	−0.767797	+	0.640694i	$0.778647\pi$
$164$	−29.2391	−	16.8812i	−0.178287	−	0.102934i
$165$		0			0
$166$	61.3895	−	35.4432i	0.369816	−	0.213513i
$167$		−	262.461i		−	1.57163i	−0.618464	−	0.785813i	$-0.712245\pi$
$167$		−	262.461i		−	1.57163i	0.618464	−	0.785813i	$-0.287755\pi$
$168$	32.8916	+	9.70270i	0.195783	+	0.0577542i
$169$	164.965			0.976122
$170$		0			0
$171$	−17.1059	−	9.87612i	−0.100035	−	0.0577551i
$172$	27.7474	−	48.0600i	0.161322	−	0.279419i
$173$	137.125	−	79.1694i	0.792632	−	0.457627i	−0.0482560	−	0.998835i	$-0.515366\pi$
$173$	137.125	−	79.1694i	0.792632	−	0.457627i	0.840888	+	0.541208i	$0.182033\pi$
$174$		−	61.5045i		−	0.353474i
$175$		0			0
$176$	−71.0193			−0.403519
$177$	10.9872	+	19.0304i	0.0620747	+	0.107517i
$178$	105.970	+	61.1819i	0.595338	+	0.343718i
$179$	5.01415	−	8.68475i	0.0280120	−	0.0485182i	−0.851680	−	0.524063i	$-0.824416\pi$
$179$	5.01415	−	8.68475i	0.0280120	−	0.0485182i	0.879692	+	0.475545i	$0.157749\pi$
$180$		0			0
$181$		−	318.143i		−	1.75770i	−0.477101	−	0.878848i	$-0.658312\pi$
$181$		−	318.143i		−	1.75770i	0.477101	−	0.878848i	$-0.341688\pi$
$182$	14.4096	−	13.7050i	0.0791736	−	0.0753024i
$183$	164.086			0.896644
$184$	55.7294	+	96.5261i	0.302877	+	0.524599i
$185$		0			0
$186$	−6.74295	+	11.6791i	−0.0362524	+	0.0627910i
$187$	−326.122	+	188.287i	−1.74397	+	1.00688i
$188$		−	91.3550i		−	0.485931i
$189$	−8.53091	−	35.3585i	−0.0451371	−	0.187082i
$190$		0			0
$191$	1.85642	+	3.21541i	0.00971946	+	0.0168346i	0.870844	−	0.491559i	$-0.163573\pi$
$191$	1.85642	+	3.21541i	0.00971946	+	0.0168346i	−0.861125	+	0.508394i	$0.830239\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	−147.770	+	255.946i	−0.765649	+	1.32614i	0.174253	+	0.984701i	$0.444249\pi$
$193$	−147.770	+	255.946i	−0.765649	+	1.32614i	−0.939903	+	0.341443i	$0.889084\pi$
$194$	−202.869	+	117.126i	−1.04572	+	0.603744i
$195$		0			0
$196$	−4.90872	+	97.8770i	−0.0250445	+	0.499372i
$197$	−231.134			−1.17327			−0.586635	−	0.809852i	$-0.699548\pi$
$197$	−231.134			−1.17327			−0.586635	+	0.809852i	$0.699548\pi$
$198$	37.6637	+	65.2354i	0.190221	+	0.329472i
$199$	−25.3639	−	14.6438i	−0.127457	−	0.0735871i	0.434916	−	0.900471i	$-0.356778\pi$
$199$	−25.3639	−	14.6438i	−0.127457	−	0.0735871i	−0.562373	+	0.826884i	$0.690111\pi$
$200$		0			0
$201$	12.5281	−	7.23310i	0.0623289	−	0.0359856i
$202$		−	279.166i		−	1.38201i
$203$	170.861	−	41.2235i	0.841681	−	0.203071i
$204$	73.4724			0.360159
$205$		0			0
$206$	−86.6169	−	50.0083i	−0.420470	−	0.242759i
$207$	59.1099	−	102.381i	0.285555	−	0.494596i
$208$	6.95875	−	4.01764i	0.0334555	−	0.0193156i
$209$			116.899i			0.559326i
$210$		0			0
$211$	−254.413			−1.20575			−0.602874	−	0.797836i	$-0.705978\pi$
$211$	−254.413			−1.20575			−0.602874	+	0.797836i	$0.705978\pi$
$212$	98.4522	+	170.524i	0.464397	+	0.804359i
$213$	107.734	+	62.2001i	0.505792	+	0.292019i
$214$	−22.5996	+	39.1437i	−0.105606	+	0.182915i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−36.9644	−	10.9041i	−0.170343	−	0.0502495i
$218$	−299.887			−1.37563
$219$	0.697968	+	1.20892i	0.00318707	+	0.00552017i
$220$		0			0
$221$	21.3032	−	36.8982i	0.0963944	−	0.166960i
$222$	24.9289	−	14.3927i	0.112292	−	0.0648320i
$223$			197.116i			0.883927i	0.897033	+	0.441964i	$0.145718\pi$
$223$			197.116i			0.883927i	−0.897033	+	0.441964i	$0.854282\pi$
$224$	−11.2037	+	37.9800i	−0.0500166	+	0.169553i
$225$		0			0
$226$	−64.3745	−	111.500i	−0.284843	−	0.493362i
$227$	248.054	+	143.214i	1.09275	+	0.630900i	0.934308	−	0.356468i	$-0.116019\pi$
$227$	248.054	+	143.214i	1.09275	+	0.630900i	0.158443	+	0.987368i	$0.449352\pi$
$228$	11.4040	−	19.7522i	0.0500174	−	0.0866326i
$229$	−178.628	+	103.131i	−0.780034	+	0.450353i	−0.836442	−	0.548055i	$-0.815368\pi$
$229$	−178.628	+	103.131i	−0.780034	+	0.450353i	0.0564084	+	0.998408i	$0.482035\pi$
$230$		0			0
$231$	−155.982	+	148.355i	−0.675245	+	0.642229i
$232$	71.0193			0.306118
$233$	3.44650	+	5.96951i	0.0147918	+	0.0256202i	0.873327	−	0.487135i	$-0.161958\pi$
$233$	3.44650	+	5.96951i	0.0147918	+	0.0256202i	−0.858535	+	0.512755i	$0.828625\pi$
$234$	−7.38087	−	4.26135i	−0.0315422	−	0.0182109i
$235$		0			0
$236$	−21.9744	+	12.6870i	−0.0931121	+	0.0537583i
$237$		−	201.557i		−	0.850453i
$238$	49.2450	+	204.108i	0.206912	+	0.857598i
$239$	289.962			1.21323			0.606615	−	0.794995i	$-0.292527\pi$
$239$	289.962			1.21323			0.606615	+	0.794995i	$0.292527\pi$
$240$		0			0
$241$	282.791	+	163.270i	1.17341	+	0.677467i	0.954480	−	0.298274i	$-0.0964110\pi$
$241$	282.791	+	163.270i	1.17341	+	0.677467i	0.218927	+	0.975741i	$0.429744\pi$
$242$	137.344	−	237.887i	0.567538	−	0.983004i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			189.470i			0.776517i
$245$		0			0
$246$	−41.3503			−0.168091
$247$	−6.61311	−	11.4542i	−0.0267737	−	0.0463735i
$248$	−13.4859	−	7.78609i	−0.0543786	−	0.0313955i
$249$	43.4089	−	75.1864i	0.174333	−	0.301953i
$250$		0			0
$251$			341.759i			1.36159i	0.732474	+	0.680795i	$0.238366\pi$
$251$			341.759i			1.36159i	−0.732474	+	0.680795i	$0.761634\pi$
$252$	40.8285	−	9.85064i	0.162018	−	0.0390898i
$253$	−699.658			−2.76545
$254$	−113.804	−	197.115i	−0.448048	−	0.776042i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−168.741	+	97.4226i	−0.656579	+	0.379076i	−0.790972	−	0.611852i	$-0.790425\pi$
$257$	−168.741	+	97.4226i	−0.656579	+	0.379076i	0.134393	+	0.990928i	$0.457092\pi$
$258$		−	67.9671i		−	0.263438i
$259$	56.6920	+	59.6064i	0.218888	+	0.230141i
$260$		0			0
$261$	−37.6637	−	65.2354i	−0.144305	−	0.249944i
$262$	−20.4523	−	11.8081i	−0.0780622	−	0.0450692i
$263$	69.0324	−	119.568i	0.262481	−	0.454630i	−0.704420	−	0.709783i	$-0.748793\pi$
$263$	69.0324	−	119.568i	0.262481	−	0.454630i	0.966900	+	0.255154i	$0.0821261\pi$
$264$	−75.3274	+	43.4903i	−0.285331	+	0.164736i
$265$		0			0
$266$	62.5157	+	18.4415i	0.235022	+	0.0693291i
$267$	149.864			0.561290
$268$	8.35207	+	14.4662i	0.0311644	+	0.0539784i
$269$	8.57284	+	4.94953i	0.0318693	+	0.0183998i	0.515850	−	0.856679i	$-0.327476\pi$
$269$	8.57284	+	4.94953i	0.0318693	+	0.0183998i	−0.483981	+	0.875079i	$0.660810\pi$
$270$		0			0
$271$	−16.4712	+	9.50963i	−0.0607792	+	0.0350909i	−0.530082	−	0.847947i	$-0.677839\pi$
$271$	−16.4712	+	9.50963i	−0.0607792	+	0.0350909i	0.469302	+	0.883037i	$0.344505\pi$
$272$			84.8386i			0.311907i
$273$	6.89110	−	23.3604i	0.0252421	−	0.0855693i
$274$	−178.979			−0.653210
$275$		0			0
$276$	118.220	+	68.2543i	0.428333	+	0.247298i
$277$	102.731	−	177.936i	0.370871	−	0.642367i	−0.618829	−	0.785526i	$-0.712393\pi$
$277$	102.731	−	177.936i	0.370871	−	0.642367i	0.989700	+	0.143159i	$0.0457260\pi$
$278$	165.783	−	95.7147i	0.596340	−	0.344297i
$279$			16.5168i			0.0591999i
$280$		0			0
$281$	−449.661			−1.60022			−0.800109	−	0.599854i	$-0.795225\pi$
$281$	−449.661			−1.60022			−0.800109	+	0.599854i	$0.795225\pi$
$282$	−55.9433	−	96.8966i	−0.198380	−	0.343605i
$283$	−137.762	−	79.5371i	−0.486792	−	0.281050i	0.236450	−	0.971644i	$-0.424016\pi$
$283$	−137.762	−	79.5371i	−0.486792	−	0.281050i	−0.723243	+	0.690594i	$0.757349\pi$
$284$	−71.8225	+	124.400i	−0.252896	+	0.438029i
$285$		0			0
$286$			50.4397i			0.176363i
$287$	−27.7151	−	114.872i	−0.0965683	−	0.400252i
$288$	16.9706			0.0589256
$289$	80.4246	+	139.300i	0.278286	+	0.482005i
$290$		0			0
$291$	−143.450	+	248.463i	−0.492955	+	0.853823i
$292$	−1.39594	+	0.805944i	−0.00478060	+	0.00276008i
$293$			451.939i			1.54245i	0.636560	+	0.771227i	$0.280357\pi$
$293$			451.939i			1.54245i	−0.636560	+	0.771227i	$0.719643\pi$
$294$	54.7307	+	106.820i	0.186159	+	0.363334i
$295$		0			0
$296$	16.6193	+	28.7854i	0.0561462	+	0.0972480i
$297$	79.8967	+	46.1284i	0.269013	+	0.155314i
$298$	−57.0024	+	98.7311i	−0.191283	+	0.331313i
$299$	68.5553	−	39.5804i	0.229282	−	0.132376i
$300$		0			0
$301$	188.814	−	45.5550i	0.627290	−	0.151346i
$302$	19.7084			0.0652595
$303$	−170.953	−	296.100i	−0.564202	−	0.977227i
$304$	22.8079	+	13.1682i	0.0750260	+	0.0433163i
$305$		0			0
$306$	77.9292	−	44.9925i	0.254671	−	0.147034i
$307$		−	555.454i		−	1.80930i	−0.426158	−	0.904649i	$-0.640133\pi$
$307$		−	555.454i		−	1.80930i	0.426158	−	0.904649i	$-0.359867\pi$
$308$	−171.305	−	180.112i	−0.556186	−	0.584779i
$309$	−122.495			−0.396423
$310$		0			0
$311$	146.444	+	84.5493i	0.470880	+	0.271863i	0.716608	−	0.697476i	$-0.245694\pi$
$311$	146.444	+	84.5493i	0.470880	+	0.271863i	−0.245728	+	0.969339i	$0.579027\pi$
$312$	4.92058	−	8.52270i	0.0157711	−	0.0273163i
$313$	−507.192	+	292.828i	−1.62042	+	0.935552i	−0.633617	+	0.773647i	$0.718430\pi$
$313$	−507.192	+	292.828i	−1.62042	+	0.935552i	−0.986806	+	0.161905i	$0.948236\pi$
$314$			35.7324i			0.113797i
$315$		0			0
$316$	232.738			0.736514
$317$	−130.614	−	226.230i	−0.412032	−	0.713660i	0.583080	−	0.812415i	$-0.301847\pi$
$317$	−130.614	−	226.230i	−0.412032	−	0.713660i	−0.995112	+	0.0987546i	$0.968514\pi$
$318$	208.849	+	120.579i	0.656756	+	0.379179i
$319$	−222.904	+	386.081i	−0.698759	+	1.21029i
$320$		0			0
$321$			55.3576i			0.172454i
$322$	−110.375	+	374.165i	−0.342780	+	1.16200i
$323$	139.646			0.432341
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−39.4088	+	68.2581i	−0.120886	+	0.209381i
$327$	−318.078	+	183.643i	−0.972717	+	0.561598i
$328$		−	47.7472i		−	0.145571i
$329$	231.685	−	220.357i	0.704211	−	0.669778i
$330$		0			0
$331$	−95.4984	−	165.408i	−0.288515	−	0.499722i	0.684941	−	0.728599i	$-0.259828\pi$
$331$	−95.4984	−	165.408i	−0.288515	−	0.499722i	−0.973455	+	0.228877i	$0.926495\pi$
$332$	86.8178	+	50.1243i	0.261499	+	0.150977i
$333$	17.6274	−	30.5315i	0.0529351	−	0.0916863i
$334$	321.448	−	185.588i	0.962420	−	0.555654i
$335$		0			0
$336$	11.3745	+	47.1447i	0.0338528	+	0.140312i
$337$	−226.109			−0.670947			−0.335474	−	0.942050i	$-0.608896\pi$
$337$	−226.109			−0.670947			−0.335474	+	0.942050i	$0.608896\pi$
$338$	116.648	+	202.040i	0.345111	+	0.597750i
$339$	−136.559	−	78.8423i	−0.402829	−	0.232573i
$340$		0			0
$341$	84.6548	−	48.8754i	0.248254	−	0.143330i
$342$		−	27.9339i		−	0.0816780i
$343$	−260.066	+	223.640i	−0.758210	+	0.652011i
$344$	78.4816			0.228144
$345$		0			0
$346$	193.925	+	111.962i	0.560476	+	0.323591i
$347$	331.636	−	574.410i	0.955723	−	1.65536i	0.223020	−	0.974814i	$-0.428409\pi$
$347$	331.636	−	574.410i	0.955723	−	1.65536i	0.732704	−	0.680548i	$-0.238258\pi$
$348$	75.3274	−	43.4903i	0.216458	−	0.124972i
$349$		−	293.777i		−	0.841769i	−0.907114	−	0.420884i	$-0.861720\pi$
$349$		−	293.777i		−	0.841769i	0.907114	−	0.420884i	$-0.138280\pi$
$350$		0			0
$351$	−10.4381			−0.0297383
$352$	−50.2182	−	86.9805i	−0.142665	−	0.247104i
$353$	310.089	+	179.030i	0.878439	+	0.507167i	0.870144	−	0.492798i	$-0.164026\pi$
$353$	310.089	+	179.030i	0.878439	+	0.507167i	0.00829580	+	0.999966i	$0.497359\pi$
$354$	−15.5383	+	26.9131i	−0.0438934	+	0.0760257i
$355$		0			0
$356$			173.048i			0.486091i
$357$	177.222	+	186.333i	0.496421	+	0.521942i
$358$	14.1821			0.0396149
$359$	28.2996	+	49.0164i	0.0788291	+	0.136536i	0.902745	−	0.430176i	$-0.141549\pi$
$359$	28.2996	+	49.0164i	0.0788291	+	0.136536i	−0.823916	+	0.566712i	$0.808215\pi$
$360$		0			0
$361$	−158.825	+	275.093i	−0.439958	+	0.762030i
$362$	389.644	−	224.961i	1.07637	−	0.621440i
$363$		−	336.423i		−	0.926785i
$364$	26.9743	+	7.95716i	0.0741052	+	0.0218603i
$365$		0			0
$366$	116.026	+	200.963i	0.317012	+	0.549080i
$367$	419.473	+	242.183i	1.14298	+	0.659898i	0.947166	−	0.320743i	$-0.103933\pi$
$367$	419.473	+	242.183i	1.14298	+	0.659898i	0.195811	+	0.980642i	$0.437266\pi$
$368$	−78.8133	+	136.509i	−0.214166	+	0.370947i
$369$	−43.8586	+	25.3218i	−0.118858	+	0.0686228i
$370$		0			0
$371$	−194.990	+	661.005i	−0.525579	+	1.78168i
$372$	−19.0719			−0.0512687
$373$	−176.452	−	305.623i	−0.473061	−	0.819365i	0.526464	−	0.850198i	$-0.323518\pi$
$373$	−176.452	−	305.623i	−0.473061	−	0.819365i	−0.999525	+	0.0308322i	$0.990184\pi$
$374$	−461.207	−	266.278i	−1.23317	−	0.711973i
$375$		0			0
$376$	111.887	−	64.5978i	0.297571	−	0.171803i
$377$		−	50.4397i		−	0.133792i
$378$	37.2729	−	35.4504i	0.0986055	−	0.0937842i
$379$	−129.666			−0.342126			−0.171063	−	0.985260i	$-0.554720\pi$
$379$	−129.666			−0.342126			−0.171063	+	0.985260i	$0.554720\pi$
$380$		0			0
$381$	−241.415	−	139.381i	−0.633635	−	0.365830i
$382$	−2.62537	+	4.54727i	−0.00687269	+	0.0119039i
$383$	363.416	−	209.819i	0.948868	−	0.547829i	0.0561389	−	0.998423i	$-0.482121\pi$
$383$	363.416	−	209.819i	0.948868	−	0.547829i	0.892729	+	0.450594i	$0.148788\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−417.958			−1.08279
$387$	−41.6212	−	72.0900i	−0.107548	−	0.186279i
$388$	−286.900	−	165.642i	−0.739433	−	0.426912i
$389$	−49.2202	+	85.2518i	−0.126530	+	0.219156i	−0.922330	−	0.386403i	$-0.873717\pi$
$389$	−49.2202	+	85.2518i	−0.126530	+	0.219156i	0.795800	+	0.605560i	$0.207051\pi$
$390$		0			0
$391$			835.801i			2.13760i
$392$	−123.345	+	63.1975i	−0.314656	+	0.161218i
$393$	−28.9239			−0.0735978
$394$	−163.437	−	283.080i	−0.414814	−	0.718478i
$395$		0			0
$396$	−53.2645	+	92.2568i	−0.134506	+	0.232972i
$397$	160.707	−	92.7842i	0.404804	−	0.233713i	−0.283751	−	0.958898i	$-0.591579\pi$
$397$	160.707	−	92.7842i	0.404804	−	0.233713i	0.688555	+	0.725185i	$0.258246\pi$
$398$		−	41.4190i		−	0.104068i
$399$	77.6010	−	18.7227i	0.194489	−	0.0469241i
$400$		0			0
$401$	93.6753	+	162.250i	0.233604	+	0.404614i	0.958866	−	0.283859i	$-0.0916147\pi$
$401$	93.6753	+	162.250i	0.233604	+	0.404614i	−0.725262	+	0.688473i	$0.758281\pi$
$402$	17.7174	+	10.2292i	0.0440732	+	0.0254457i
$403$	−5.52987	+	9.57802i	−0.0137218	+	0.0237668i
$404$	341.907	−	197.400i	0.846304	−	0.488614i
$405$		0			0
$406$	171.305	+	180.112i	0.421934	+	0.443626i
$407$	−208.648			−0.512648
$408$	51.9528	+	89.9849i	0.127335	+	0.220551i
$409$	−182.953	−	105.628i	−0.447319	−	0.258260i	0.259378	−	0.965776i	$-0.416482\pi$
$409$	−182.953	−	105.628i	−0.447319	−	0.258260i	−0.706697	+	0.707516i	$0.749816\pi$
$410$		0			0
$411$	−189.836	+	109.602i	−0.461889	+	0.266672i
$412$		−	141.445i		−	0.343313i
$413$	−85.1798	−	25.1272i	−0.206247	−	0.0608407i
$414$	167.188			0.403836
$415$		0			0
$416$	9.84116	+	5.68180i	0.0236566	+	0.0136582i
$417$	117.226	−	203.041i	0.281118	−	0.486910i
$418$	−143.172	+	82.6602i	−0.342516	+	0.197752i
$419$		−	48.9505i		−	0.116827i	−0.998292	−	0.0584134i	$-0.981396\pi$
$419$		−	48.9505i		−	0.116827i	0.998292	−	0.0584134i	$-0.0186042\pi$
$420$		0			0
$421$	−166.539			−0.395581			−0.197790	−	0.980244i	$-0.563376\pi$
$421$	−166.539			−0.395581			−0.197790	+	0.980244i	$0.563376\pi$
$422$	−179.897	−	311.591i	−0.426297	−	0.738367i
$423$	−118.674	−	68.5163i	−0.280552	−	0.161977i
$424$	−139.232	+	241.158i	−0.328378	+	0.568768i
$425$		0			0
$426$			175.929i			0.412978i
$427$	−480.515	+	457.020i	−1.12533	+	1.07030i
$428$	−63.9214			−0.149349
$429$	30.8879	+	53.4994i	0.0719997	+	0.124707i
$430$		0			0
$431$	−95.9137	+	166.127i	−0.222538	+	0.385446i	−0.955578	−	0.294739i	$-0.904767\pi$
$431$	−95.9137	+	166.127i	−0.222538	+	0.385446i	0.733040	+	0.680185i	$0.238101\pi$
$432$	18.0000	−	10.3923i	0.0416667	−	0.0240563i
$433$			509.172i			1.17592i	0.808891	+	0.587958i	$0.200068\pi$
$433$			509.172i			1.17592i	−0.808891	+	0.587958i	$0.799932\pi$
$434$	−12.7830	−	52.9823i	−0.0294539	−	0.122079i
$435$		0			0
$436$	−212.052	−	367.285i	−0.486358	−	0.842397i
$437$	224.696	+	129.728i	0.514178	+	0.296861i
$438$	−0.987076	+	1.70967i	−0.00225360	+	0.00390335i
$439$	−459.149	+	265.090i	−1.04590	+	0.603849i	−0.921498	−	0.388383i	$-0.873034\pi$
$439$	−459.149	+	265.090i	−1.04590	+	0.603849i	−0.124400	+	0.992232i	$0.539701\pi$
$440$		0			0
$441$	123.464	+	79.7844i	0.279965	+	0.180917i
$442$	60.2545			0.136322
$443$	−212.946	−	368.834i	−0.480692	−	0.832583i	0.519063	−	0.854736i	$-0.326281\pi$
$443$	−212.946	−	368.834i	−0.480692	−	0.832583i	−0.999755	+	0.0221535i	$0.992948\pi$
$444$	35.2548	+	20.3544i	0.0794027	+	0.0458432i
$445$		0			0
$446$	−241.417	+	139.382i	−0.541293	+	0.312516i
$447$			139.627i			0.312364i
$448$	−54.4380	+	13.1342i	−0.121513	+	0.0293174i
$449$	−294.520			−0.655946			−0.327973	−	0.944687i	$-0.606365\pi$
$449$	−294.520			−0.655946			−0.327973	+	0.944687i	$0.606365\pi$
$450$		0			0
$451$	259.568	+	149.861i	0.575538	+	0.332287i
$452$	91.0393	−	157.685i	0.201414	−	0.348860i
$453$	20.9039	−	12.0689i	0.0461454	−	0.0266421i
$454$			405.071i			0.892227i
$455$		0			0
$456$	32.2553			0.0707352
$457$	40.9206	+	70.8765i	0.0895418	+	0.155091i	0.907318	−	0.420446i	$-0.138126\pi$
$457$	40.9206	+	70.8765i	0.0895418	+	0.155091i	−0.817776	+	0.575537i	$0.804793\pi$
$458$	−252.618	−	145.849i	−0.551567	−	0.318448i
$459$	55.1043	−	95.4434i	0.120053	−	0.207938i
$460$		0			0
$461$		−	759.149i		−	1.64674i	−0.567502	−	0.823372i	$-0.692090\pi$
$461$		−	759.149i		−	1.64674i	0.567502	−	0.823372i	$-0.307910\pi$
$462$	−291.992	−	86.1349i	−0.632018	−	0.186439i
$463$	394.988			0.853105			0.426552	−	0.904463i	$-0.359728\pi$
$463$	394.988			0.853105			0.426552	+	0.904463i	$0.359728\pi$
$464$	50.2182	+	86.9805i	0.108229	+	0.187458i
$465$		0			0
$466$	−4.87409	+	8.44217i	−0.0104594	+	0.0181162i
$467$	−232.364	+	134.156i	−0.497568	+	0.287271i	−0.727709	−	0.685886i	$-0.759415\pi$
$467$	−232.364	+	134.156i	−0.497568	+	0.287271i	0.230140	+	0.973157i	$0.426081\pi$
$468$		−	12.0529i		−	0.0257541i
$469$	−16.5417	+	56.0755i	−0.0352702	+	0.119564i
$470$		0			0
$471$	21.8815	+	37.8999i	0.0464576	+	0.0804669i
$472$	−31.0766	−	17.9421i	−0.0658402	−	0.0380128i
$473$	−246.326	+	426.648i	−0.520773	+	0.902005i
$474$	246.856	−	142.523i	0.520794	−	0.300680i
$475$		0			0
$476$	−215.159	+	204.639i	−0.452015	+	0.429913i
$477$	295.356			0.619196
$478$	205.034	+	355.130i	0.428942	+	0.742949i
$479$	−470.659	−	271.735i	−0.982586	−	0.567296i	−0.0795360	−	0.996832i	$-0.525344\pi$
$479$	−470.659	−	271.735i	−0.982586	−	0.567296i	−0.903050	+	0.429536i	$0.858677\pi$
$480$		0			0
$481$	20.4441	−	11.8034i	0.0425034	−	0.0245393i
$482$			461.796i			0.958083i
$483$	112.058	+	464.453i	0.232004	+	0.961601i
$484$	388.468			0.802620
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	198.261	−	343.398i	0.407107	−	0.705130i	−0.587457	−	0.809255i	$-0.699871\pi$
$487$	198.261	−	343.398i	0.407107	−	0.705130i	0.994564	+	0.104125i	$0.0332043\pi$
$488$	−232.052	+	133.976i	−0.475517	+	0.274540i
$489$			96.5315i			0.197406i
$490$		0			0
$491$	750.658			1.52883			0.764417	−	0.644722i	$-0.223027\pi$
$491$	750.658			1.52883			0.764417	+	0.644722i	$0.223027\pi$
$492$	−29.2391	−	50.6436i	−0.0594291	−	0.102934i
$493$	461.207	+	266.278i	0.935511	+	0.540117i
$494$	9.35235	−	16.1987i	0.0189319	−	0.0327910i
$495$		0			0
$496$		−	22.0224i		−	0.0444000i
$497$	−488.734	+	117.916i	−0.983368	+	0.237256i
$498$	122.779			0.246544
$499$	66.6787	+	115.491i	0.133625	+	0.231445i	0.925071	−	0.379794i	$-0.124005\pi$
$499$	66.6787	+	115.491i	0.133625	+	0.231445i	−0.791447	+	0.611238i	$0.790672\pi$
$500$		0			0
$501$	227.298	−	393.692i	0.453689	−	0.785813i
$502$	−418.568	+	241.660i	−0.833800	+	0.481395i
$503$			226.683i			0.450661i	0.974282	+	0.225331i	$0.0723462\pi$
$503$			226.683i			0.450661i	−0.974282	+	0.225331i	$0.927654\pi$
$504$	40.9346	+	43.0390i	0.0812195	+	0.0853949i
$505$		0			0
$506$	−494.733	−	856.903i	−0.977733	−	1.69348i
$507$	247.447	+	142.864i	0.488061	+	0.281782i
$508$	160.943	−	278.762i	0.316818	−	0.548744i
$509$	17.6930	−	10.2151i	0.0347603	−	0.0200689i	−0.482519	−	0.875885i	$-0.660278\pi$
$509$	17.6930	−	10.2151i	0.0347603	−	0.0200689i	0.517279	+	0.855817i	$0.326945\pi$
$510$		0			0
$511$	−5.41109	−	1.59622i	−0.0105892	−	0.00312371i
$512$	−22.6274			−0.0441942
$513$	−17.1059	−	29.6284i	−0.0333449	−	0.0577551i
$514$	−238.636	−	137.776i	−0.464272	−	0.268047i
$515$		0			0
$516$	83.2423	−	48.0600i	0.161322	−	0.0931395i
$517$			810.996i			1.56866i
$518$	−32.9154	+	111.581i	−0.0635432	+	0.215408i
$519$	274.251			0.528422
$520$		0			0
$521$	775.322	+	447.632i	1.48814	+	0.859179i	0.999908	−	0.0135342i	$-0.00430819\pi$
$521$	775.322	+	447.632i	1.48814	+	0.859179i	0.488233	+	0.872713i	$0.337642\pi$
$522$	53.2645	−	92.2568i	0.102039	−	0.176737i
$523$	244.761	−	141.313i	0.467995	−	0.270197i	−0.247405	−	0.968912i	$-0.579578\pi$
$523$	244.761	−	141.313i	0.467995	−	0.270197i	0.715400	+	0.698715i	$0.246244\pi$
$524$		−	33.3985i		−	0.0637375i
$525$		0			0
$526$	195.253			0.371204
$527$	−58.3859	−	101.127i	−0.110789	−	0.191892i
$528$	−106.529	−	61.5045i	−0.201759	−	0.116486i
$529$	−511.941	+	886.708i	−0.967753	+	1.67620i
$530$		0			0
$531$			38.0609i			0.0716777i
$532$	21.6191	+	89.6060i	0.0406375	+	0.168432i
$533$	−33.9113			−0.0636234
$534$	105.970	+	183.546i	0.198446	+	0.343718i
$535$		0			0
$536$	−11.8116	+	20.4583i	−0.0220366	+	0.0381685i
$537$	15.0424	−	8.68475i	0.0280120	−	0.0161727i
$538$			13.9994i			0.0260212i
$539$	43.5768	−	868.895i	0.0808474	−	1.61205i
$540$		0			0
$541$	−178.897	−	309.858i	−0.330678	−	0.572751i	0.651967	−	0.758247i	$-0.273944\pi$
$541$	−178.897	−	309.858i	−0.330678	−	0.572751i	−0.982645	+	0.185496i	$0.940611\pi$
$542$	−23.2937	−	13.4486i	−0.0429774	−	0.0248130i
$543$	275.520	−	477.215i	0.507403	−	0.878848i
$544$	−103.906	+	59.9899i	−0.191003	+	0.110276i
$545$		0			0
$546$	33.4833	−	8.07848i	0.0613247	−	0.0147958i
$547$	−251.048			−0.458954			−0.229477	−	0.973314i	$-0.573702\pi$
$547$	−251.048			−0.458954			−0.229477	+	0.973314i	$0.573702\pi$
$548$	−126.558	−	219.204i	−0.230944	−	0.400008i
$549$	246.129	+	142.103i	0.448322	+	0.258839i
$550$		0			0
$551$	143.172	−	82.6602i	0.259840	−	0.150019i
$552$			193.052i			0.349732i
$553$	561.387	+	590.247i	1.01517	+	1.06736i
$554$	290.568			0.524490
$555$		0			0
$556$	234.452	+	135.361i	0.421676	+	0.243455i
$557$	347.274	−	601.496i	0.623472	−	1.07989i	−0.365362	−	0.930866i	$-0.619055\pi$
$557$	347.274	−	601.496i	0.623472	−	1.07989i	0.988834	−	0.149020i	$-0.0476120\pi$
$558$	−20.2288	+	11.6791i	−0.0362524	+	0.0209303i
$559$		−	55.7396i		−	0.0997131i
$560$		0			0
$561$	−652.245			−1.16265
$562$	−317.959	−	550.721i	−0.565763	−	0.979930i
$563$	483.826	+	279.337i	0.859371	+	0.496158i	0.863802	−	0.503832i	$-0.168077\pi$
$563$	483.826	+	279.337i	0.859371	+	0.496158i	−0.00443074	+	0.999990i	$0.501410\pi$
$564$	79.1158	−	137.033i	0.140276	−	0.242965i
$565$		0			0
$566$		−	224.965i		−	0.397464i
$567$	17.8250	−	60.4257i	0.0314374	−	0.106571i
$568$	−203.145			−0.357649
$569$	270.266	+	468.114i	0.474983	+	0.822696i	0.999590	−	0.0286496i	$-0.00912069\pi$
$569$	270.266	+	468.114i	0.474983	+	0.822696i	−0.524606	+	0.851345i	$0.675787\pi$
$570$		0			0
$571$	462.071	−	800.331i	0.809232	−	1.40163i	−0.104164	−	0.994560i	$-0.533217\pi$
$571$	462.071	−	800.331i	0.809232	−	1.40163i	0.913397	−	0.407071i	$-0.133450\pi$
$572$	−61.7757	+	35.6662i	−0.108000	+	0.0623536i
$573$			6.43081i			0.0112231i
$574$	121.092	−	115.171i	0.210961	−	0.200646i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	838.835	+	484.302i	1.45379	+	0.839344i	0.998694	−	0.0510997i	$-0.0162726\pi$
$577$	838.835	+	484.302i	1.45379	+	0.839344i	0.455093	+	0.890444i	$0.349606\pi$
$578$	−113.738	+	196.999i	−0.196778	+	0.340829i
$579$	−443.311	+	255.946i	−0.765649	+	0.442048i
$580$		0			0
$581$	82.2927	+	341.083i	0.141640	+	0.587062i
$582$	−405.738			−0.697144
$583$	−874.001	−	1513.81i	−1.49914	−	2.59659i
$584$	−1.97415	−	1.13978i	−0.00338040	−	0.00195167i
$585$		0			0
$586$	−553.510	+	319.569i	−0.944556	+	0.545340i
$587$		−	698.278i		−	1.18957i	−0.803885	−	0.594785i	$-0.797237\pi$
$587$		−	698.278i		−	1.18957i	0.803885	−	0.594785i	$-0.202763\pi$
$588$	−92.1270	+	142.564i	−0.156679	+	0.242456i
$589$	−36.2493			−0.0615437
$590$		0			0
$591$	−346.701	−	200.168i	−0.586635	−	0.338694i
$592$	−23.5032	+	40.7087i	−0.0397013	+	0.0687647i
$593$	607.963	−	351.007i	1.02523	−	0.591918i	0.109617	−	0.993974i	$-0.465038\pi$
$593$	607.963	−	351.007i	1.02523	−	0.591918i	0.915615	+	0.402056i	$0.131704\pi$
$594$			130.471i			0.219648i
$595$		0			0
$596$	−161.227			−0.270516
$597$	−25.3639	−	43.9315i	−0.0424855	−	0.0735871i
$598$	96.9518	+	55.9751i	0.162127	+	0.0936039i
$599$	83.1873	−	144.085i	0.138877	−	0.240542i	−0.788195	−	0.615426i	$-0.788984\pi$
$599$	83.1873	−	144.085i	0.138877	−	0.240542i	0.927072	+	0.374884i	$0.122317\pi$
$600$		0			0
$601$		−	952.482i		−	1.58483i	−0.609983	−	0.792415i	$-0.708824\pi$
$601$		−	952.482i		−	1.58483i	0.609983	−	0.792415i	$-0.291176\pi$
$602$	189.305	+	199.037i	0.314460	+	0.330627i
$603$	25.0562			0.0415526
$604$	13.9359	+	24.1377i	0.0230727	+	0.0399631i
$605$		0			0
$606$	241.765	−	418.748i	0.398951	−	0.691004i
$607$	694.188	−	400.790i	1.14364	−	0.660279i	0.196309	−	0.980542i	$-0.437105\pi$
$607$	694.188	−	400.790i	1.14364	−	0.660279i	0.947329	+	0.320263i	$0.103771\pi$
$608$			37.2452i			0.0612585i
$609$	291.992	+	86.1349i	0.479462	+	0.141437i
$610$		0			0
$611$	−45.8789	−	79.4646i	−0.0750883	−	0.130057i
$612$	110.209	+	63.6289i	0.180079	+	0.103969i
$613$	368.775	−	638.737i	0.601591	−	1.04199i	−0.390990	−	0.920395i	$-0.627867\pi$
$613$	368.775	−	638.737i	0.601591	−	1.04199i	0.992580	−	0.121590i	$-0.0387994\pi$
$614$	680.290	−	392.766i	1.10796	−	0.639683i
$615$		0			0
$616$	99.4600	−	337.164i	0.161461	−	0.547344i
$617$	−244.329			−0.395995			−0.197997	−	0.980203i	$-0.563444\pi$
$617$	−244.329			−0.395995			−0.197997	+	0.980203i	$0.563444\pi$
$618$	−86.6169	−	150.025i	−0.140157	−	0.242759i
$619$	409.586	+	236.475i	0.661690	+	0.382027i	0.792920	−	0.609325i	$-0.208560\pi$
$619$	409.586	+	236.475i	0.661690	+	0.382027i	−0.131231	+	0.991352i	$0.541893\pi$
$620$		0			0
$621$	177.330	−	102.381i	0.285555	−	0.164865i
$622$			239.142i			0.384472i
$623$	−438.868	+	417.409i	−0.704443	+	0.669999i
$624$	13.9175			0.0223037
$625$		0			0
$626$	−717.278	−	414.121i	−1.14581	−	0.661535i
$627$	−101.238	+	175.349i	−0.161464	+	0.279663i
$628$	−43.7630	+	25.2666i	−0.0696863	+	0.0402334i
$629$			249.247i			0.396260i
$630$		0			0
$631$	−1204.19			−1.90839			−0.954193	−	0.299191i	$-0.903283\pi$
$631$	−1204.19			−1.90839			−0.954193	+	0.299191i	$0.903283\pi$
$632$	164.571	+	285.045i	0.260397	+	0.451021i
$633$	−381.620	−	220.328i	−0.602874	−	0.348070i
$634$	184.716	−	319.938i	0.291351	−	0.504634i
$635$		0			0
$636$			341.048i			0.536239i
$637$	44.8845	+	87.6029i	0.0704623	+	0.137524i
$638$	−630.468			−0.988194
$639$	107.734	+	186.600i	0.168597	+	0.292019i
$640$		0			0
$641$	273.033	−	472.908i	0.425949	−	0.737766i	−0.570559	−	0.821256i	$-0.693274\pi$
$641$	273.033	−	472.908i	0.425949	−	0.737766i	0.996509	+	0.0834907i	$0.0266069\pi$
$642$	−67.7989	+	39.1437i	−0.105606	+	0.0609715i
$643$		−	193.418i		−	0.300805i	−0.988625	−	0.150403i	$-0.951943\pi$
$643$		−	193.418i		−	0.300805i	0.988625	−	0.150403i	$-0.0480570\pi$
$644$	−536.304	+	129.394i	−0.832771	+	0.200922i
$645$		0			0
$646$	98.7446	+	171.031i	0.152855	+	0.264753i
$647$	−103.099	−	59.5245i	−0.159350	−	0.0920007i	0.418205	−	0.908353i	$-0.362660\pi$
$647$	−103.099	−	59.5245i	−0.159350	−	0.0920007i	−0.577554	+	0.816352i	$0.695993\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	195.076	−	112.627i	0.300580	−	0.173540i
$650$		0			0
$651$	−46.0033	−	48.3683i	−0.0706657	−	0.0742985i
$652$	−111.465			−0.170959
$653$	293.854	+	508.970i	0.450006	+	0.779433i	0.998386	−	0.0567963i	$-0.0180886\pi$
$653$	293.854	+	508.970i	0.450006	+	0.779433i	−0.548380	+	0.836229i	$0.684755\pi$
$654$	−449.831	−	259.710i	−0.687815	−	0.397110i
$655$		0			0
$656$	58.4782	−	33.7624i	0.0891436	−	0.0514671i
$657$			2.41783i			0.00368011i
$658$	433.707	+	127.939i	0.659130	+	0.194437i
$659$	−36.3580			−0.0551714			−0.0275857	−	0.999619i	$-0.508782\pi$
$659$	−36.3580			−0.0551714			−0.0275857	+	0.999619i	$0.508782\pi$
$660$		0			0
$661$	279.780	+	161.531i	0.423268	+	0.244374i	0.696475	−	0.717582i	$-0.254751\pi$
$661$	279.780	+	161.531i	0.423268	+	0.244374i	−0.273207	+	0.961955i	$0.588084\pi$
$662$	135.055	−	233.922i	0.204011	−	0.353357i
$663$	63.9095	−	36.8982i	0.0963944	−	0.0556534i
$664$			141.773i			0.213513i
$665$		0			0
$666$	49.8578			0.0748616
$667$	494.733	+	856.903i	0.741729	+	1.28471i
$668$	454.597	+	262.461i	0.680534	+	0.392906i
$669$	−170.707	+	295.674i	−0.255168	+	0.441964i
$670$		0			0
$671$		−	1682.00i		−	2.50671i
$672$	−49.6972	+	47.2672i	−0.0739541	+	0.0703381i
$673$	705.426			1.04818			0.524091	−	0.851663i	$-0.324405\pi$
$673$	705.426			1.04818			0.524091	+	0.851663i	$0.324405\pi$
$674$	−159.883	−	276.926i	−0.237216	−	0.410870i
$675$		0			0
$676$	−164.965	+	285.727i	−0.244031	+	0.422673i
$677$	−720.152	+	415.780i	−1.06374	+	0.614151i	−0.926465	−	0.376382i	$-0.877168\pi$
$677$	−720.152	+	415.780i	−1.06374	+	0.614151i	−0.137276	+	0.990533i	$0.543835\pi$
$678$		−	223.000i		−	0.328908i
$679$	−271.946	−	1127.15i	−0.400510	−	1.66001i
$680$		0			0
$681$	248.054	+	429.643i	0.364250	+	0.630900i
$682$	119.720	+	69.1203i	0.175542	+	0.101349i
$683$	486.271	−	842.246i	0.711964	−	1.23316i	−0.252155	−	0.967687i	$-0.581139\pi$
$683$	486.271	−	842.246i	0.711964	−	1.23316i	0.964119	−	0.265470i	$-0.0855272\pi$
$684$	34.2119	−	19.7522i	0.0500174	−	0.0288775i
$685$		0			0
$686$	−457.796	−	160.377i	−0.667341	−	0.233786i
$687$	−357.256			−0.520023
$688$	55.4949	+	96.1200i	0.0806612	+	0.139709i
$689$	171.276	+	98.8863i	0.248586	+	0.143521i
$690$		0			0
$691$	443.849	−	256.256i	0.642328	−	0.370848i	−0.143183	−	0.989696i	$-0.545734\pi$
$691$	443.849	−	256.256i	0.642328	−	0.370848i	0.785511	+	0.618848i	$0.212400\pi$
$692$			316.678i			0.457627i
$693$	−362.451	+	87.4482i	−0.523018	+	0.126188i
$694$	938.008			1.35160
$695$		0			0
$696$	106.529	+	61.5045i	0.153059	+	0.0883686i
$697$	179.022	−	310.076i	0.256847	−	0.444872i
$698$	359.802	−	207.732i	0.515476	−	0.297610i
$699$			11.9390i			0.0170802i
$700$		0			0
$701$	−259.526			−0.370223			−0.185111	−	0.982718i	$-0.559265\pi$
$701$	−259.526			−0.370223			−0.185111	+	0.982718i	$0.559265\pi$
$702$	−7.38087	−	12.7840i	−0.0105141	−	0.0182109i
$703$	67.0074	+	38.6867i	0.0953163	+	0.0550309i
$704$	71.0193	−	123.009i	0.100880	−	0.174729i
$705$		0			0
$706$			506.373i			0.717243i
$707$	1325.34	+	390.962i	1.87459	+	0.552987i
$708$	−43.9489			−0.0620747
$709$	−138.685	−	240.210i	−0.195607	−	0.338801i	0.751492	−	0.659742i	$-0.229334\pi$
$709$	−138.685	−	240.210i	−0.195607	−	0.338801i	−0.947099	+	0.320941i	$0.896001\pi$
$710$		0			0
$711$	174.554	−	302.336i	0.245505	−	0.425226i
$712$	−211.940	+	122.364i	−0.297669	+	0.171859i
$713$		−	216.957i		−	0.304287i
$714$	−102.895	+	348.810i	−0.144111	+	0.488529i
$715$		0			0
$716$	10.0283	+	17.3695i	0.0140060	+	0.0242591i
$717$	434.943	+	251.115i	0.606615	+	0.350230i
$718$	−40.0217	+	69.3197i	−0.0557406	+	0.0965455i
$719$	1165.19	−	672.723i	1.62057	−	0.935638i	0.633805	−	0.773493i	$-0.281492\pi$
$719$	1165.19	−	672.723i	1.62057	−	0.935638i	0.986767	−	0.162144i	$-0.0518410\pi$
$720$		0			0
$721$	358.718	−	341.178i	0.497528	−	0.473202i
$722$	−449.225			−0.622195
$723$	282.791	+	489.809i	0.391136	+	0.677467i
$724$	551.040	+	318.143i	0.761105	+	0.439424i
$725$		0			0
$726$	412.032	−	237.887i	0.567538	−	0.327668i
$727$		−	1143.24i		−	1.57255i	−0.617876	−	0.786275i	$-0.712007\pi$
$727$		−	1143.24i		−	1.57255i	0.617876	−	0.786275i	$-0.287993\pi$
$728$	9.32823	+	38.6632i	0.0128135	+	0.0531088i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	509.668	+	294.257i	0.697220	+	0.402540i
$732$	−164.086	+	284.205i	−0.224161	+	0.388258i
$733$	−1181.32	+	682.037i	−1.61163	+	0.930474i	−0.622634	+	0.782513i	$0.713938\pi$
$733$	−1181.32	+	682.037i	−1.61163	+	0.930474i	−0.988993	+	0.147961i	$0.952729\pi$
$734$			684.996i			0.933237i
$735$		0			0
$736$	−222.918			−0.302877
$737$	−74.1448	−	128.423i	−0.100603	−	0.174250i
$738$	−62.0255	−	35.8104i	−0.0840454	−	0.0485236i
$739$	101.096	−	175.103i	0.136801	−	0.236946i	−0.789483	−	0.613772i	$-0.789651\pi$
$739$	101.096	−	175.103i	0.136801	−	0.236946i	0.926284	+	0.376827i	$0.122985\pi$
$740$		0			0
$741$		−	22.9085i		−	0.0309156i
$742$	−947.441	+	228.588i	−1.27687	+	0.308070i
$743$	344.793			0.464055			0.232028	−	0.972709i	$-0.425464\pi$
$743$	344.793			0.464055			0.232028	+	0.972709i	$0.425464\pi$
$744$	−13.4859	−	23.3583i	−0.0181262	−	0.0313955i
$745$		0			0
$746$	249.540	−	432.217i	0.334505	−	0.579379i
$747$	130.227	−	75.1864i	0.174333	−	0.100651i
$748$		−	753.147i		−	1.00688i
$749$	−154.185	−	162.111i	−0.205854	−	0.216437i
$750$		0			0
$751$	−110.795	−	191.903i	−0.147530	−	0.255530i	0.782784	−	0.622294i	$-0.213799\pi$
$751$	−110.795	−	191.903i	−0.147530	−	0.255530i	−0.930314	+	0.366764i	$0.880466\pi$
$752$	158.232	+	91.3550i	0.210414	+	0.121483i
$753$	−295.972	+	512.639i	−0.393057	+	0.680795i
$754$	61.7757	−	35.6662i	0.0819307	−	0.0473027i
$755$		0			0
$756$	69.7736	+	20.5825i	0.0922932	+	0.0272256i
$757$	−1006.02			−1.32895			−0.664476	−	0.747310i	$-0.731345\pi$
$757$	−1006.02			−1.32895			−0.664476	+	0.747310i	$0.731345\pi$
$758$	−91.6875	−	158.807i	−0.120960	−	0.209508i
$759$	−1049.49	−	605.922i	−1.38272	−	0.798316i
$760$		0			0
$761$	981.832	−	566.861i	1.29019	−	0.744889i	0.311499	−	0.950246i	$-0.399169\pi$
$761$	981.832	−	566.861i	1.29019	−	0.744889i	0.978687	+	0.205357i	$0.0658355\pi$
$762$		−	394.229i		−	0.517361i
$763$	419.981	−	1423.71i	0.550434	−	1.86594i
$764$	−7.42566			−0.00971946
$765$		0			0
$766$	513.948	+	296.728i	0.670951	+	0.387374i
$767$	−12.7429	+	22.0713i	−0.0166139	+	0.0287762i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$			206.796i			0.268915i	0.990919	+	0.134458i	$0.0429292\pi$
$769$			206.796i			0.268915i	−0.990919	+	0.134458i	$0.957071\pi$
$770$		0			0
$771$	−337.482			−0.437719
$772$	−295.541	−	511.891i	−0.382825	−	0.663072i
$773$	663.637	+	383.151i	0.858521	+	0.495668i	0.863517	−	0.504320i	$-0.168257\pi$
$773$	663.637	+	383.151i	0.858521	+	0.495668i	−0.00499551	+	0.999988i	$0.501590\pi$
$774$	58.8612	−	101.951i	0.0760481	−	0.131719i
$775$		0			0
$776$		−	468.506i		−	0.603744i
$777$	33.4173	+	138.506i	0.0430081	+	0.178258i
$778$	−139.216			−0.178940
$779$	−55.5736	−	96.2563i	−0.0713396	−	0.123564i
$780$		0			0
$781$	637.598	−	1104.35i	0.816387	−	1.41402i
$782$	−1023.64	+	591.000i	−1.30901	+	0.755755i
$783$		−	130.471i		−	0.166629i
$784$	−164.619	−	106.379i	−0.209973	−	0.135688i
$785$		0			0
$786$	−20.4523	−	35.4244i	−0.0260207	−	0.0450692i
$787$	763.935	+	441.058i	0.970693	+	0.560430i	0.899447	−	0.437029i	$-0.143969\pi$
$787$	763.935	+	441.058i	0.970693	+	0.560430i	0.0712454	+	0.997459i	$0.477303\pi$
$788$	231.134	−	400.336i	0.293317	−	0.508041i
$789$	207.097	−	119.568i	0.262481	−	0.151543i
$790$		0			0
$791$	619.499	−	149.466i	0.783185	−	0.188958i
$792$	−150.655			−0.190221
$793$	95.1527	+	164.809i	0.119991	+	0.207830i
$794$	227.274	+	131.217i	0.286239	+	0.165260i
$795$		0			0
$796$	50.7277	−	29.2877i	0.0637283	−	0.0367936i
$797$			1202.53i			1.50882i	0.656406	+	0.754408i	$0.272076\pi$
$797$			1202.53i			1.50882i	−0.656406	+	0.754408i	$0.727924\pi$
$798$	77.8028	+	81.8025i	0.0974972	+	0.102509i
$799$	968.804			1.21252
$800$		0			0
$801$	224.797	+	129.786i	0.280645	+	0.162030i
$802$	−132.477	+	229.457i	−0.165183	+	0.286106i
$803$	12.3923	−	7.15470i	0.0154325	−	0.00890997i
$804$			28.9324i			0.0359856i
$805$		0			0
$806$	−15.6408			−0.0194055
$807$	8.57284	+	14.8486i	0.0106231	+	0.0183998i
$808$	483.529	+	279.166i	0.598427	+	0.345502i
$809$	−693.426	+	1201.05i	−0.857140	+	1.48461i	0.0175061	+	0.999847i	$0.494427\pi$
$809$	−693.426	+	1201.05i	−0.857140	+	1.48461i	−0.874646	+	0.484763i	$0.838906\pi$
$810$		0			0
$811$			987.281i			1.21736i	0.793415	+	0.608681i	$0.208301\pi$
$811$			987.281i			1.21736i	−0.793415	+	0.608681i	$0.791699\pi$
$812$	−99.4600	+	337.164i	−0.122488	+	0.415226i
$813$	−32.9423			−0.0405195
$814$	−147.536	−	255.540i	−0.181248	−	0.313931i
$815$		0			0
$816$	−73.4724	+	127.258i	−0.0900397	+	0.155953i
$817$	158.215	−	91.3457i	0.193654	−	0.111806i
$818$		−	298.762i		−	0.365234i
$819$	30.5674	−	29.0728i	0.0373228	−	0.0354979i
$820$		0			0
$821$	223.132	+	386.477i	0.271781	+	0.470739i	0.969318	−	0.245810i	$-0.0790539\pi$
$821$	223.132	+	386.477i	0.271781	+	0.470739i	−0.697537	+	0.716549i	$0.745721\pi$
$822$	−268.469	−	155.001i	−0.326605	−	0.188565i
$823$	413.931	−	716.949i	0.502954	−	0.871141i	−0.497040	−	0.867727i	$-0.665580\pi$
$823$	413.931	−	716.949i	0.502954	−	0.871141i	0.999994	−	0.00341406i	$-0.00108673\pi$
$824$	173.234	−	100.017i	0.210235	−	0.121379i
$825$		0			0
$826$	−29.4568	−	122.091i	−0.0356620	−	0.147810i
$827$	−1333.16			−1.61204			−0.806022	−	0.591885i	$-0.798384\pi$
$827$	−1333.16			−1.61204			−0.806022	+	0.591885i	$0.798384\pi$
$828$	118.220	+	204.763i	0.142778	+	0.247298i
$829$	−1257.72	−	726.147i	−1.51716	−	0.875931i	−0.999797	−	0.0201631i	$-0.993581\pi$
$829$	−1257.72	−	726.147i	−1.51716	−	0.875931i	−0.517360	−	0.855768i	$-0.673085\pi$
$830$		0			0
$831$	308.194	−	177.936i	0.370871	−	0.214122i
$832$			16.0706i			0.0193156i
$833$	−1037.97	−	52.0561i	−1.24606	−	0.0624924i
$834$	331.565			0.397560
$835$		0			0
$836$	−202.475	−	116.899i	−0.242195	−	0.139832i
$837$	−14.3040	+	24.7752i	−0.0170896	+	0.0296000i
$838$	59.9518	−	34.6132i	0.0715416	−	0.0413045i
$839$			602.259i			0.717830i	0.933370	+	0.358915i	$0.116853\pi$
$839$			602.259i			0.717830i	−0.933370	+	0.358915i	$0.883147\pi$
$840$		0			0
$841$	−210.532			−0.250335
$842$	−117.761	−	203.968i	−0.139859	−	0.242243i
$843$	−674.492	−	389.418i	−0.800109	−	0.461943i
$844$	254.413	−	440.656i	0.301437	−	0.522105i
$845$		0			0
$846$		−	193.793i		−	0.229070i
$847$	937.022	+	985.193i	1.10628	+	1.16316i
$848$	−393.809			−0.464397
$849$	−137.762	−	238.611i	−0.162264	−	0.281050i
$850$		0			0
$851$	−231.545	+	401.048i	−0.272086	+	0.471267i
$852$	−215.468	+	124.400i	−0.252896	+	0.146010i
$853$			487.049i			0.570983i	0.958381	+	0.285492i	$0.0921569\pi$
$853$			487.049i			0.570983i	−0.958381	+	0.285492i	$0.907843\pi$
$854$	−899.508	−	265.346i	−1.05329	−	0.310710i
$855$		0			0
$856$	−45.1993	−	78.2875i	−0.0528029	−	0.0914573i
$857$	1199.88	+	692.754i	1.40010	+	0.808347i	0.994402	−	0.105661i	$-0.0336957\pi$
$857$	1199.88	+	692.754i	1.40010	+	0.808347i	0.405696	+	0.914008i	$0.367029\pi$
$858$	−43.6820	+	75.6595i	−0.0509115	+	0.0881813i
$859$	1165.46	−	672.881i	1.35677	−	0.783331i	0.367582	−	0.929991i	$-0.380186\pi$
$859$	1165.46	−	672.881i	1.35677	−	0.783331i	0.989187	+	0.146660i	$0.0468523\pi$
$860$		0			0
$861$	57.9097	−	196.310i	0.0672586	−	0.228003i
$862$	−271.285			−0.314716
$863$	−124.905	−	216.341i	−0.144733	−	0.250685i	0.784540	−	0.620078i	$-0.212899\pi$
$863$	−124.905	−	216.341i	−0.144733	−	0.250685i	−0.929273	+	0.369393i	$0.879566\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	−623.605	+	360.039i	−0.720099	+	0.415749i
$867$			278.599i			0.321337i
$868$	55.8509	−	53.1201i	0.0643444	−	0.0611983i
$869$	−2066.11			−2.37758
$870$		0			0
$871$	14.5300	+	8.38890i	0.0166820	+	0.00963134i
$872$	299.887	−	519.420i	0.343907	−	0.595665i
$873$	−430.350	+	248.463i	−0.492955	+	0.284608i
$874$			366.927i			0.419825i
$875$		0			0
$876$	−2.79187			−0.00318707
$877$	354.104	+	613.327i	0.403768	+	0.699346i	0.994177	−	0.107757i	$-0.0343670\pi$
$877$	354.104	+	613.327i	0.403768	+	0.699346i	−0.590409	+	0.807104i	$0.701034\pi$
$878$	−649.335	−	374.894i	−0.739562	−	0.426986i
$879$	−391.391	+	677.908i	−0.445268	+	0.771227i
$880$		0			0
$881$			83.7844i			0.0951014i	0.998869	+	0.0475507i	$0.0151416\pi$
$881$			83.7844i			0.0951014i	−0.998869	+	0.0475507i	$0.984858\pi$
$882$	−10.4130	+	207.628i	−0.0118061	+	0.235406i
$883$	1155.05			1.30810			0.654051	−	0.756450i	$-0.273068\pi$
$883$	1155.05			1.30810			0.654051	+	0.756450i	$0.273068\pi$
$884$	42.6063	+	73.7964i	0.0481972	+	0.0834800i
$885$		0			0
$886$	301.152	−	521.610i	0.339900	−	0.588725i
$887$	278.227	−	160.634i	0.313672	−	0.181098i	−0.334897	−	0.942255i	$-0.608701\pi$
$887$	278.227	−	160.634i	0.313672	−	0.181098i	0.648568	+	0.761157i	$0.275368\pi$
$888$			57.5708i			0.0648320i
$889$	1095.18	−	264.233i	1.23192	−	0.297225i
$890$		0			0
$891$	79.8967	+	138.385i	0.0896709	+	0.155314i
$892$	−341.415	−	197.116i	−0.382752	−	0.220982i
$893$	150.372	−	260.452i	0.168390	−	0.291660i
$894$	−171.007	+	98.7311i	−0.191283	+	0.110438i
$895$		0			0
$896$	−54.5795	−	57.3854i	−0.0609146	−	0.0640462i
$897$	137.111			0.152855
$898$	−208.257	−	360.711i	−0.231912	−	0.401683i
$899$	−119.720	−	69.1203i	−0.133170	−	0.0768858i
$900$		0			0
$901$	−1808.38	+	1044.07i	−2.00708	+	1.15879i
$902$			423.872i			0.469925i
$903$	322.673	+	95.1855i	0.357335	+	0.105410i
$904$	257.498			0.284843
$905$		0			0
$906$	29.5625	+	17.0679i	0.0326297	+	0.0188388i
$907$	192.833	−	333.996i	0.212605	−	0.368243i	−0.739924	−	0.672690i	$-0.765139\pi$
$907$	192.833	−	333.996i	0.212605	−	0.368243i	0.952529	+	0.304448i	$0.0984719\pi$
$908$	−496.109	+	286.429i	−0.546376	+	0.315450i
$909$		−	592.200i		−	0.651485i
$910$		0			0
$911$	544.040			0.597190			0.298595	−	0.954380i	$-0.403482\pi$
$911$	544.040			0.597190			0.298595	+	0.954380i	$0.403482\pi$
$912$	22.8079	+	39.5045i	0.0250087	+	0.0433163i
$913$	−770.718	−	444.974i	−0.844159	−	0.487376i
$914$	−57.8704	+	100.235i	−0.0633156	+	0.109666i
$915$		0			0
$916$		−	412.523i		−	0.450353i
$917$	84.7018	−	80.5603i	0.0923684	−	0.0878520i
$918$	155.858			0.169780
$919$	−305.574	−	529.269i	−0.332507	−	0.575919i	0.650496	−	0.759510i	$-0.274561\pi$
$919$	−305.574	−	529.269i	−0.332507	−	0.575919i	−0.983003	+	0.183591i	$0.941228\pi$
$920$		0			0
$921$	481.038	−	833.182i	0.522299	−	0.904649i
$922$	929.764	−	536.799i	1.00842	−	0.582212i
$923$			144.278i			0.156315i
$924$	−100.977	−	418.523i	−0.109282	−	0.452947i
$925$		0			0
$926$	279.298	+	483.759i	0.301618	+	0.522418i
$927$	−183.742	−	106.084i	−0.198212	−	0.114438i
$928$	−71.0193	+	123.009i	−0.0765294	+	0.132553i
$929$	−744.000	+	429.549i	−0.800862	+	0.462378i	−0.843772	−	0.536701i	$-0.819670\pi$
$929$	−744.000	+	429.549i	−0.800862	+	0.462378i	0.0429108	+	0.999079i	$0.486337\pi$
$930$		0			0
$931$	−175.102	+	270.966i	−0.188080	+	0.291049i
$932$	−13.7860			−0.0147918
$933$	146.444	+	253.648i	0.156960	+	0.271863i
$934$	−328.613	−	189.725i	−0.351834	−	0.203131i
$935$		0			0
$936$	14.7617	−	8.52270i	0.0157711	−	0.00910545i
$937$		−	1665.22i		−	1.77718i	−0.458700	−	0.888591i	$-0.651685\pi$
$937$		−	1665.22i		−	1.77718i	0.458700	−	0.888591i	$-0.348315\pi$
$938$	−80.3750	+	19.3920i	−0.0856876	+	0.0206738i
$939$	−1014.38			−1.08028
$940$		0			0
$941$	946.705	+	546.581i	1.00606	+	0.580851i	0.910037	−	0.414528i	$-0.136053\pi$
$941$	946.705	+	546.581i	1.00606	+	0.580851i	0.0960266	+	0.995379i	$0.469387\pi$
$942$	−30.9451	+	53.5985i	−0.0328505	+	0.0568987i
$943$	576.107	−	332.616i	0.610930	−	0.352721i
$944$		−	50.7478i		−	0.0537583i
$945$		0			0
$946$	−696.714			−0.736484
$947$	−702.226	−	1216.29i	−0.741527	−	1.28436i	−0.951800	−	0.306720i	$-0.900769\pi$
$947$	−702.226	−	1216.29i	−0.741527	−	1.28436i	0.210273	−	0.977643i	$-0.432565\pi$
$948$	349.108	+	201.557i	0.368257	+	0.212613i
$949$	−0.809498	+	1.40209i	−0.000853001	+	0.00147744i
$950$		0			0
$951$		−	452.461i		−	0.475773i
$952$	−402.771	−	118.813i	−0.423079	−	0.124804i
$953$	−1284.11			−1.34744			−0.673722	−	0.738985i	$-0.735305\pi$
$953$	−1284.11			−1.34744			−0.673722	+	0.738985i	$0.735305\pi$
$954$	208.849	+	361.736i	0.218919	+	0.379179i
$955$		0			0
$956$	−289.962	+	502.229i	−0.303308	+	0.525344i
$957$	−668.712	+	386.081i	−0.698759	+	0.403429i
$958$		−	768.582i		−	0.802278i
$959$	250.654	−	849.704i	0.261371	−	0.886031i
$960$		0			0
$961$	−465.344	−	806.000i	−0.484229	−	0.838709i
$962$	28.9123	+	16.6926i	0.0300544	+	0.0173519i
$963$	−47.9411	+	83.0364i	−0.0497831	+	0.0862268i
$964$	−565.582	+	326.539i	−0.586704	+	0.338733i
$965$		0			0
$966$	−489.600	+	465.661i	−0.506832	+	0.482050i
$967$	−437.417			−0.452344			−0.226172	−	0.974087i	$-0.572621\pi$
$967$	−437.417			−0.452344			−0.226172	+	0.974087i	$0.572621\pi$
$968$	274.688	+	475.774i	0.283769	+	0.491502i
$969$	209.469	+	120.937i	0.216170	+	0.124806i
$970$		0			0
$971$	−277.241	+	160.065i	−0.285521	+	0.164846i	−0.635920	−	0.771755i	$-0.719379\pi$
$971$	−277.241	+	160.065i	−0.285521	+	0.164846i	0.350399	+	0.936601i	$0.386046\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	222.232	+	921.097i	0.228399	+	0.946657i
$974$	560.767			0.575736
$975$		0			0
$976$	−328.172	−	189.470i	−0.336242	−	0.194129i
$977$	−109.535	+	189.720i	−0.112114	+	0.194187i	−0.916622	−	0.399754i	$-0.869095\pi$
$977$	−109.535	+	189.720i	−0.112114	+	0.194187i	0.804509	+	0.593941i	$0.202429\pi$
$978$	−118.227	+	68.2581i	−0.120886	+	0.0697936i
$979$		−	1536.22i		−	1.56918i
$980$		0			0
$981$	−636.157			−0.648478
$982$	530.795	+	919.364i	0.540525	+	0.936216i
$983$	−188.528	−	108.847i	−0.191789	−	0.110729i	0.401031	−	0.916064i	$-0.368652\pi$
$983$	−188.528	−	108.847i	−0.191789	−	0.110729i	−0.592820	+	0.805335i	$0.701985\pi$
$984$	41.3503	−	71.6209i	0.0420227	−	0.0727854i
$985$		0			0
$986$			753.147i			0.763841i
$987$	538.363	−	129.890i	0.545454	−	0.131601i
$988$	26.4524			0.0267737
$989$	546.717	+	946.941i	0.552798	+	0.957473i
$990$		0			0
$991$	−566.322	+	980.899i	−0.571466	+	0.989808i	0.424950	+	0.905217i	$0.360292\pi$
$991$	−566.322	+	980.899i	−0.571466	+	0.989808i	−0.996416	+	0.0845907i	$0.973042\pi$
$992$	26.9718	−	15.5722i	0.0271893	−	0.0156978i
$993$		−	330.816i		−	0.333148i
$994$	−490.005	−	515.195i	−0.492962	−	0.518305i
$995$		0			0
$996$	86.8178	+	150.373i	0.0871665	+	0.150977i
$997$	−1350.51	−	779.718i	−1.35458	−	0.782065i	−0.365689	−	0.930737i	$-0.619167\pi$
$997$	−1350.51	−	779.718i	−1.35458	−	0.782065i	−0.988887	+	0.148672i	$0.952500\pi$
$998$	−94.2980	+	163.329i	−0.0944869	+	0.163656i
$999$	52.8822	−	30.5315i	0.0529351	−	0.0305621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.f.451.4	yes	12
5.2	odd	4		1050.3.q.d.199.2		24
5.3	odd	4		1050.3.q.d.199.8		24
5.4	even	2		1050.3.p.e.451.3	✓	12
7.5	odd	6	inner	1050.3.p.f.901.4	yes	12
35.12	even	12		1050.3.q.d.649.8		24
35.19	odd	6		1050.3.p.e.901.3	yes	12
35.33	even	12		1050.3.q.d.649.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.3	✓	12	5.4	even	2
1050.3.p.e.901.3	yes	12	35.19	odd	6
1050.3.p.f.451.4	yes	12	1.1	even	1	trivial
1050.3.p.f.901.4	yes	12	7.5	odd	6	inner
1050.3.q.d.199.2		24	5.2	odd	4
1050.3.q.d.199.8		24	5.3	odd	4
1050.3.q.d.649.2		24	35.33	even	12
1050.3.q.d.649.8		24	35.12	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-6.80475 + 1.64177i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(8.87741 - 15.3761i) q^{11} +(-3.00000 + 1.73205i) q^{12} +2.00882i q^{13} +(-6.82244 - 7.17317i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-18.3681 - 10.6048i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-5.70198 + 3.29204i) q^{19} +(-11.6289 - 3.43042i) q^{21} +25.1091 q^{22} +(-19.7033 - 34.1271i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-2.46029 + 1.42045i) q^{26} +5.19615i q^{27} +(3.96111 - 13.4279i) q^{28} -25.1091 q^{29} +(4.76798 + 2.75280i) q^{31} +(2.82843 - 4.89898i) q^{32} +(26.6322 - 15.3761i) q^{33} -29.9950i q^{34} -6.00000 q^{36} +(-5.87580 - 10.1772i) q^{37} +(-8.06382 - 4.65565i) q^{38} +(-1.73969 + 3.01323i) q^{39} +16.8812i q^{41} +(-4.02151 - 16.6682i) q^{42} -27.7474 q^{43} +(17.7548 + 30.7523i) q^{44} +(27.8647 - 48.2631i) q^{46} +(-39.5579 + 22.8388i) q^{47} -6.92820i q^{48} +(43.6092 - 22.3437i) q^{49} +(-18.3681 - 31.8145i) q^{51} +(-3.47938 - 2.00882i) q^{52} +(49.2261 - 85.2621i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(19.2467 - 4.64364i) q^{56} -11.4040 q^{57} +(-17.7548 - 30.7523i) q^{58} +(10.9872 + 6.34348i) q^{59} +(82.0429 - 47.3675i) q^{61} +7.78609i q^{62} +(-14.4726 - 15.2166i) q^{63} +8.00000 q^{64} +(37.6637 + 21.7451i) q^{66} +(4.17603 - 7.23310i) q^{67} +(36.7362 - 21.2096i) q^{68} -68.2543i q^{69} +71.8225 q^{71} +(-4.24264 - 7.34847i) q^{72} +(0.697968 + 0.402972i) q^{73} +(8.30963 - 14.3927i) q^{74} -13.1682i q^{76} +(-35.1644 + 119.205i) q^{77} -4.92058 q^{78} +(-58.1846 - 100.779i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-20.6752 + 11.9368i) q^{82} -50.1243i q^{83} +(17.5706 - 16.7115i) q^{84} +(-19.6204 - 33.9835i) q^{86} +(-37.6637 - 21.7451i) q^{87} +(-25.1091 + 43.4903i) q^{88} +(74.9322 - 43.2621i) q^{89} +(-3.29803 - 13.6695i) q^{91} +78.8133 q^{92} +(4.76798 + 8.25839i) q^{93} +(-55.9433 - 32.2989i) q^{94} +(8.48528 - 4.89898i) q^{96} +165.642i q^{97} +(58.2017 + 37.6107i) q^{98} +53.2645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

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