LMFDB - Embedded newform 1050.3.q.e.199.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.7
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.e.649.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(4.61524 - 5.26304i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(4.61524 - 5.26304i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.41099 - 9.37211i) q^{11} +(1.73205 + 3.00000i) q^{12} -19.2715 q^{13} +(-1.93096 + 9.70935i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(5.13686 - 8.89730i) q^{17} +(3.67423 + 2.12132i) q^{18} +(18.0756 - 10.4359i) q^{19} +(3.89764 + 11.4808i) q^{21} +15.3046i q^{22} +(-18.2511 + 10.5373i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(23.6026 - 13.6270i) q^{26} +5.19615 q^{27} +(-4.50061 - 13.2569i) q^{28} -19.0888 q^{29} +(-34.6556 - 20.0084i) q^{31} +(4.89898 + 2.82843i) q^{32} +(9.37211 + 16.2330i) q^{33} +14.5292i q^{34} -6.00000 q^{36} +(-43.6177 + 25.1827i) q^{37} +(-14.7586 + 25.5627i) q^{38} +(16.6896 - 28.9072i) q^{39} +22.7706i q^{41} +(-12.8918 - 11.3050i) q^{42} +48.4307i q^{43} +(-10.8220 - 18.7442i) q^{44} +(14.9020 - 25.8110i) q^{46} +(33.2690 + 57.6236i) q^{47} +6.92820 q^{48} +(-6.39913 - 48.5804i) q^{49} +(8.89730 + 15.4106i) q^{51} +(-19.2715 + 33.3792i) q^{52} +(4.28736 + 2.47531i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(14.8861 + 13.0539i) q^{56} +36.1511i q^{57} +(23.3789 - 13.4978i) q^{58} +(24.4105 + 14.0934i) q^{59} +(-60.6988 + 35.0445i) q^{61} +56.5924 q^{62} +(-20.5966 - 4.09619i) q^{63} -8.00000 q^{64} +(-22.9569 - 13.2542i) q^{66} +(-16.7193 - 9.65287i) q^{67} +(-10.2737 - 17.7946i) q^{68} -36.5023i q^{69} +49.4968 q^{71} +(7.34847 - 4.24264i) q^{72} +(-66.4872 + 115.159i) q^{73} +(35.6137 - 61.6848i) q^{74} -41.7437i q^{76} +(-24.3527 - 71.7328i) q^{77} +47.2053i q^{78} +(-45.0404 - 78.0122i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-16.1013 - 27.8882i) q^{82} -101.045 q^{83} +(23.7829 + 4.72987i) q^{84} +(-34.2456 - 59.3152i) q^{86} +(16.5314 - 28.6332i) q^{87} +(26.5083 + 15.3046i) q^{88} +(-34.3077 + 19.8075i) q^{89} +(-88.9425 + 101.427i) q^{91} +42.1492i q^{92} +(60.0253 - 34.6556i) q^{93} +(-81.4920 - 47.0495i) q^{94} +(-8.48528 + 4.89898i) q^{96} -68.6944 q^{97} +(42.1888 + 54.9737i) q^{98} -32.4659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 48 * q^9	$ 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	4.61524	−	5.26304i	0.659320	−	0.751863i
$7$	4.61524	−	5.26304i	0.659320	−	0.751863i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	5.41099	−	9.37211i	0.491908	−	0.852010i	−0.508049	−	0.861328i	$-0.669633\pi$
$11$	5.41099	−	9.37211i	0.491908	−	0.852010i	0.999957	+	0.00931868i	$0.00296627\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	−19.2715			−1.48242			−0.741211	−	0.671273i	$-0.765748\pi$
$13$	−19.2715			−1.48242			−0.741211	+	0.671273i	$0.765748\pi$
$14$	−1.93096	+	9.70935i	−0.137926	+	0.693525i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	5.13686	−	8.89730i	0.302168	−	0.523371i	−0.674459	−	0.738313i	$-0.735623\pi$
$17$	5.13686	−	8.89730i	0.302168	−	0.523371i	0.976627	+	0.214942i	$0.0689562\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	18.0756	−	10.4359i	0.951346	−	0.549260i	0.0578471	−	0.998325i	$-0.481576\pi$
$19$	18.0756	−	10.4359i	0.951346	−	0.549260i	0.893499	+	0.449066i	$0.148243\pi$
$20$		0			0
$21$	3.89764	+	11.4808i	0.185602	+	0.546704i
$22$			15.3046i			0.695663i
$23$	−18.2511	+	10.5373i	−0.793527	+	0.458143i	−0.841203	−	0.540720i	$-0.818152\pi$
$23$	−18.2511	+	10.5373i	−0.793527	+	0.458143i	0.0476755	+	0.998863i	$0.484819\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	23.6026	−	13.6270i	0.907794	−	0.524115i
$27$	5.19615			0.192450
$28$	−4.50061	−	13.2569i	−0.160736	−	0.473460i
$29$	−19.0888			−0.658235			−0.329118	−	0.944289i	$-0.606751\pi$
$29$	−19.0888			−0.658235			−0.329118	+	0.944289i	$0.606751\pi$
$30$		0			0
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.177054	−	0.984201i	$-0.556657\pi$
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.940870	+	0.338768i	$0.889990\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	9.37211	+	16.2330i	0.284003	+	0.491908i
$34$			14.5292i			0.427330i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−43.6177	+	25.1827i	−1.17886	+	0.680614i	−0.955750	−	0.294180i	$-0.904953\pi$
$37$	−43.6177	+	25.1827i	−1.17886	+	0.680614i	−0.223107	+	0.974794i	$0.571620\pi$
$38$	−14.7586	+	25.5627i	−0.388385	+	0.672703i
$39$	16.6896	−	28.9072i	0.427938	−	0.741211i
$40$		0			0
$41$			22.7706i			0.555382i	0.960671	+	0.277691i	$0.0895691\pi$
$41$			22.7706i			0.555382i	−0.960671	+	0.277691i	$0.910431\pi$
$42$	−12.8918	−	11.3050i	−0.306947	−	0.269166i
$43$			48.4307i			1.12629i	0.826357	+	0.563147i	$0.190410\pi$
$43$			48.4307i			1.12629i	−0.826357	+	0.563147i	$0.809590\pi$
$44$	−10.8220	−	18.7442i	−0.245954	−	0.426005i
$45$		0			0
$46$	14.9020	−	25.8110i	0.323956	−	0.561109i
$47$	33.2690	+	57.6236i	0.707851	+	1.22603i	0.965653	+	0.259836i	$0.0836685\pi$
$47$	33.2690	+	57.6236i	0.707851	+	1.22603i	−0.257802	+	0.966198i	$0.582998\pi$
$48$	6.92820			0.144338
$49$	−6.39913	−	48.5804i	−0.130595	−	0.991436i
$50$		0			0
$51$	8.89730	+	15.4106i	0.174457	+	0.302168i
$52$	−19.2715	+	33.3792i	−0.370605	+	0.641907i
$53$	4.28736	+	2.47531i	0.0808937	+	0.0467040i	0.539901	−	0.841728i	$-0.318462\pi$
$53$	4.28736	+	2.47531i	0.0808937	+	0.0467040i	−0.459008	+	0.888432i	$0.651795\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	14.8861	+	13.0539i	0.265824	+	0.233105i
$57$			36.1511i			0.634231i
$58$	23.3789	−	13.4978i	0.403085	−	0.232721i
$59$	24.4105	+	14.0934i	0.413737	+	0.238871i	0.692394	−	0.721520i	$-0.256556\pi$
$59$	24.4105	+	14.0934i	0.413737	+	0.238871i	−0.278657	+	0.960391i	$0.589889\pi$
$60$		0			0
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.906784	−	0.421596i	$-0.861470\pi$
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.0882785	+	0.996096i	$0.528137\pi$
$62$	56.5924			0.912781
$63$	−20.5966	−	4.09619i	−0.326931	−	0.0650188i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−22.9569	−	13.2542i	−0.347832	−	0.200821i
$67$	−16.7193	−	9.65287i	−0.249541	−	0.144073i	0.370013	−	0.929027i	$-0.379353\pi$
$67$	−16.7193	−	9.65287i	−0.249541	−	0.144073i	−0.619554	+	0.784954i	$0.712687\pi$
$68$	−10.2737	−	17.7946i	−0.151084	−	0.261685i
$69$		−	36.5023i		−	0.529018i
$70$		0			0
$71$	49.4968			0.697138			0.348569	−	0.937283i	$-0.386668\pi$
$71$	49.4968			0.697138			0.348569	+	0.937283i	$0.386668\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	−66.4872	+	115.159i	−0.910783	+	1.57752i	−0.0978221	+	0.995204i	$0.531188\pi$
$73$	−66.4872	+	115.159i	−0.910783	+	1.57752i	−0.812961	+	0.582318i	$0.802146\pi$
$74$	35.6137	−	61.6848i	0.481266	−	0.833578i
$75$		0			0
$76$		−	41.7437i		−	0.549260i
$77$	−24.3527	−	71.7328i	−0.316269	−	0.931594i
$78$			47.2053i			0.605196i
$79$	−45.0404	−	78.0122i	−0.570132	−	0.987497i	−0.996552	−	0.0829717i	$-0.973559\pi$
$79$	−45.0404	−	78.0122i	−0.570132	−	0.987497i	0.426420	−	0.904525i	$-0.359774\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−16.1013	−	27.8882i	−0.196357	−	0.340100i
$83$	−101.045			−1.21741			−0.608706	−	0.793396i	$-0.708311\pi$
$83$	−101.045			−1.21741			−0.608706	+	0.793396i	$0.708311\pi$
$84$	23.7829	+	4.72987i	0.283130	+	0.0563080i
$85$		0			0
$86$	−34.2456	−	59.3152i	−0.398205	−	0.689712i
$87$	16.5314	−	28.6332i	0.190016	−	0.329118i
$88$	26.5083	+	15.3046i	0.301231	+	0.173916i
$89$	−34.3077	+	19.8075i	−0.385479	+	0.222557i	−0.680200	−	0.733027i	$-0.738107\pi$
$89$	−34.3077	+	19.8075i	−0.385479	+	0.222557i	0.294720	+	0.955584i	$0.404774\pi$
$90$		0			0
$91$	−88.9425	+	101.427i	−0.977390	+	1.11458i
$92$			42.1492i			0.458143i
$93$	60.0253	−	34.6556i	0.645434	−	0.372641i
$94$	−81.4920	−	47.0495i	−0.866937	−	0.500526i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	−68.6944			−0.708190			−0.354095	−	0.935210i	$-0.615211\pi$
$97$	−68.6944			−0.708190			−0.354095	+	0.935210i	$0.615211\pi$
$98$	42.1888	+	54.9737i	0.430498	+	0.560956i
$99$	−32.4659			−0.327939
$100$		0			0
$101$	−6.96199	−	4.01951i	−0.0689306	−	0.0397971i	0.465139	−	0.885238i	$-0.346004\pi$
$101$	−6.96199	−	4.01951i	−0.0689306	−	0.0397971i	−0.534069	+	0.845441i	$0.679338\pi$
$102$	−21.7939	−	12.5827i	−0.213665	−	0.123360i
$103$	−102.282	−	177.158i	−0.993033	−	1.71998i	−0.598568	−	0.801072i	$-0.704263\pi$
$103$	−102.282	−	177.158i	−0.993033	−	1.71998i	−0.394465	−	0.918911i	$-0.629070\pi$
$104$		−	54.5080i		−	0.524115i
$105$		0			0
$106$	−7.00124			−0.0660494
$107$	142.508	−	82.2769i	1.33185	−	0.768943i	0.346266	−	0.938136i	$-0.387449\pi$
$107$	142.508	−	82.2769i	1.33185	−	0.768943i	0.985583	+	0.169193i	$0.0541161\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	−39.5050	+	68.4247i	−0.362432	+	0.627750i	−0.988360	−	0.152130i	$-0.951387\pi$
$109$	−39.5050	+	68.4247i	−0.362432	+	0.627750i	0.625929	+	0.779880i	$0.284720\pi$
$110$		0			0
$111$		−	87.2354i		−	0.785905i
$112$	−27.4622	−	5.46158i	−0.245198	−	0.0487641i
$113$		−	84.5690i		−	0.748398i	−0.927348	−	0.374199i	$-0.877918\pi$
$113$		−	84.5690i		−	0.748398i	0.927348	−	0.374199i	$-0.122082\pi$
$114$	−25.5627	−	44.2759i	−0.224234	−	0.388385i
$115$		0			0
$116$	−19.0888	+	33.0628i	−0.164559	+	0.285024i
$117$	28.9072	+	50.0688i	0.247070	+	0.427938i
$118$	−39.8621			−0.337815
$119$	−23.1190	−	68.0987i	−0.194277	−	0.572258i
$120$		0			0
$121$	1.94240	+	3.36434i	0.0160529	+	0.0278044i
$122$	49.5603	−	85.8410i	0.406232	−	0.703615i
$123$	−34.1560	−	19.7200i	−0.277691	−	0.160325i
$124$	−69.3113	+	40.0169i	−0.558962	+	0.322717i
$125$		0			0
$126$	28.1221	−	9.54723i	0.223191	−	0.0757717i
$127$		−	101.777i		−	0.801393i	−0.916211	−	0.400697i	$-0.868768\pi$
$127$		−	101.777i		−	0.801393i	0.916211	−	0.400697i	$-0.131232\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−72.6460	−	41.9422i	−0.563147	−	0.325133i
$130$		0			0
$131$	61.2264	−	35.3491i	0.467377	−	0.269840i	−0.247764	−	0.968820i	$-0.579696\pi$
$131$	61.2264	−	35.3491i	0.467377	−	0.269840i	0.715141	+	0.698980i	$0.246362\pi$
$132$	37.4884			0.284003
$133$	28.4984	−	143.297i	0.214273	−	1.07742i
$134$	27.3024			0.203750
$135$		0			0
$136$	25.1654	+	14.5292i	0.185039	+	0.106833i
$137$	102.042	+	58.9138i	0.744829	+	0.430027i	0.823823	−	0.566848i	$-0.191837\pi$
$137$	102.042	+	58.9138i	0.744829	+	0.430027i	−0.0789932	+	0.996875i	$0.525171\pi$
$138$	25.8110	+	44.7060i	0.187036	+	0.323956i
$139$			158.507i			1.14034i	0.821528	+	0.570168i	$0.193122\pi$
$139$			158.507i			1.14034i	−0.821528	+	0.570168i	$0.806878\pi$
$140$		0			0
$141$	−115.247			−0.817356
$142$	−60.6209	+	34.9995i	−0.426908	+	0.246475i
$143$	−104.278	+	180.614i	−0.729215	+	1.26304i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$		−	188.054i		−	1.28804i
$147$	78.4123	+	32.4731i	0.533417	+	0.220906i
$148$			100.731i			0.680614i
$149$	−147.948	−	256.254i	−0.992940	−	1.71982i	−0.599193	−	0.800604i	$-0.704512\pi$
$149$	−147.948	−	256.254i	−0.992940	−	1.71982i	−0.393747	−	0.919219i	$-0.628821\pi$
$150$		0			0
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	−0.580530	−	0.814239i	$-0.697155\pi$
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	0.995417	+	0.0956344i	$0.0304880\pi$
$152$	29.5173	+	51.1254i	0.194193	+	0.336352i
$153$	−30.8212			−0.201445
$154$	80.5486	+	70.6343i	0.523043	+	0.458665i
$155$		0			0
$156$	−33.3792	−	57.8144i	−0.213969	−	0.370605i
$157$	−2.66684	+	4.61909i	−0.0169862	+	0.0294210i	−0.874394	−	0.485217i	$-0.838740\pi$
$157$	−2.66684	+	4.61909i	−0.0169862	+	0.0294210i	0.857407	+	0.514638i	$0.172074\pi$
$158$	110.326	+	63.6967i	0.698266	+	0.403144i
$159$	−7.42593	+	4.28736i	−0.0467040	+	0.0269646i
$160$		0			0
$161$	−28.7752	+	144.689i	−0.178728	+	0.898686i
$162$		−	12.7279i		−	0.0785674i
$163$	−207.193	+	119.623i	−1.27112	+	0.733883i	−0.975199	−	0.221329i	$-0.928961\pi$
$163$	−207.193	+	119.623i	−1.27112	+	0.733883i	−0.295923	+	0.955212i	$0.595627\pi$
$164$	39.4399	+	22.7706i	0.240487	+	0.138845i
$165$		0			0
$166$	123.754	−	71.4497i	0.745509	−	0.430420i
$167$	−310.440			−1.85892			−0.929462	−	0.368918i	$-0.879728\pi$
$167$	−310.440			−1.85892			−0.929462	+	0.368918i	$0.879728\pi$
$168$	−32.4726	+	11.0242i	−0.193289	+	0.0656202i
$169$	202.390			1.19757
$170$		0			0
$171$	−54.2267	−	31.3078i	−0.317115	−	0.183087i
$172$	83.8844	+	48.4307i	0.487700	+	0.281574i
$173$	−45.4539	−	78.7285i	−0.262739	−	0.455078i	0.704230	−	0.709972i	$-0.251293\pi$
$173$	−45.4539	−	78.7285i	−0.262739	−	0.455078i	−0.966969	+	0.254894i	$0.917959\pi$
$174$			46.7579i			0.268723i
$175$		0			0
$176$	−43.2879			−0.245954
$177$	−42.2802	+	24.4105i	−0.238871	+	0.137912i
$178$	28.0121	−	48.5184i	0.157371	−	0.272575i
$179$	−121.577	+	210.577i	−0.679200	+	1.17641i	0.296022	+	0.955181i	$0.404340\pi$
$179$	−121.577	+	210.577i	−0.679200	+	1.17641i	−0.975222	+	0.221228i	$0.928993\pi$
$180$		0			0
$181$		−	245.993i		−	1.35907i	−0.733641	−	0.679537i	$-0.762181\pi$
$181$		−	245.993i		−	1.35907i	0.733641	−	0.679537i	$-0.237819\pi$
$182$	37.2125	−	187.113i	0.204464	−	1.02810i
$183$		−	121.398i		−	0.663375i
$184$	−29.8040	−	51.6220i	−0.161978	−	0.280554i
$185$		0			0
$186$	−49.0105	+	84.8886i	−0.263497	+	0.456390i
$187$	−55.5910	−	96.2864i	−0.297278	−	0.514901i
$188$	133.076			0.707851
$189$	23.9815	−	27.3475i	0.126886	−	0.144696i
$190$		0			0
$191$	20.6108	+	35.6989i	0.107910	+	0.186905i	0.914923	−	0.403628i	$-0.132251\pi$
$191$	20.6108	+	35.6989i	0.107910	+	0.186905i	−0.807014	+	0.590533i	$0.798918\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	−164.324	−	94.8727i	−0.851422	−	0.491568i	0.00970872	−	0.999953i	$-0.496910\pi$
$193$	−164.324	−	94.8727i	−0.851422	−	0.491568i	−0.861130	+	0.508384i	$0.830243\pi$
$194$	84.1331	−	48.5743i	0.433676	−	0.250383i
$195$		0			0
$196$	−90.5428	−	37.4967i	−0.461953	−	0.191310i
$197$		−	362.318i		−	1.83918i	−0.392882	−	0.919589i	$-0.628522\pi$
$197$		−	362.318i		−	1.83918i	0.392882	−	0.919589i	$-0.371478\pi$
$198$	39.7625	−	22.9569i	0.200821	−	0.115944i
$199$	33.4433	+	19.3085i	0.168057	+	0.0970278i	0.581669	−	0.813425i	$-0.302400\pi$
$199$	33.4433	+	19.3085i	0.168057	+	0.0970278i	−0.413612	+	0.910453i	$0.635733\pi$
$200$		0			0
$201$	28.9586	−	16.7193i	0.144073	−	0.0831804i
$202$	11.3689			0.0562816
$203$	−88.0995	+	100.465i	−0.433987	+	0.494902i
$204$	35.5892			0.174457
$205$		0			0
$206$	250.540	+	144.649i	1.21621	+	0.702180i
$207$	54.7534	+	31.6119i	0.264509	+	0.152714i
$208$	38.5430	+	66.7584i	0.185303	+	0.320954i
$209$		−	225.875i		−	1.08074i
$210$		0			0
$211$	−136.551			−0.647163			−0.323581	−	0.946200i	$-0.604887\pi$
$211$	−136.551			−0.647163			−0.323581	+	0.946200i	$0.604887\pi$
$212$	8.57473	−	4.95062i	0.0404468	−	0.0233520i
$213$	−42.8655	+	74.2452i	−0.201246	+	0.348569i
$214$	−116.357	+	201.537i	−0.543725	+	0.941760i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−265.249	+	90.0502i	−1.22235	+	0.414978i
$218$		−	111.737i		−	0.512556i
$219$	−115.159	−	199.461i	−0.525841	−	0.910783i
$220$		0			0
$221$	−98.9949	+	171.464i	−0.447941	+	0.775856i
$222$	61.6848	+	106.841i	0.277859	+	0.481266i
$223$	154.949			0.694839			0.347419	−	0.937710i	$-0.387058\pi$
$223$	154.949			0.694839			0.347419	+	0.937710i	$0.387058\pi$
$224$	37.4961	−	12.7296i	0.167393	−	0.0568288i
$225$		0			0
$226$	59.7993	+	103.575i	0.264599	+	0.458299i
$227$	−11.1769	+	19.3590i	−0.0492375	+	0.0852818i	−0.889594	−	0.456753i	$-0.849012\pi$
$227$	−11.1769	+	19.3590i	−0.0492375	+	0.0852818i	0.840356	+	0.542034i	$0.182346\pi$
$228$	62.6156	+	36.1511i	0.274630	+	0.158558i
$229$	−25.9105	+	14.9594i	−0.113146	+	0.0653250i	−0.555505	−	0.831513i	$-0.687475\pi$
$229$	−25.9105	+	14.9594i	−0.113146	+	0.0653250i	0.442359	+	0.896838i	$0.354142\pi$
$230$		0			0
$231$	128.689	+	25.5933i	0.557096	+	0.110793i
$232$		−	53.9913i		−	0.232721i
$233$	219.176	−	126.541i	0.940669	−	0.543095i	0.0504987	−	0.998724i	$-0.483919\pi$
$233$	219.176	−	126.541i	0.940669	−	0.543095i	0.890170	+	0.455629i	$0.150586\pi$
$234$	−70.8079	−	40.8810i	−0.302598	−	0.174705i
$235$		0			0
$236$	48.8209	−	28.1868i	0.206868	−	0.119436i
$237$	156.024			0.658331
$238$	76.4679	+	67.0559i	0.321294	+	0.281747i
$239$	−121.009			−0.506315			−0.253158	−	0.967425i	$-0.581469\pi$
$239$	−121.009			−0.506315			−0.253158	+	0.967425i	$0.581469\pi$
$240$		0			0
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.918791	−	0.394745i	$-0.129167\pi$
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.117536	+	0.993069i	$0.462501\pi$
$242$	−4.75789	−	2.74697i	−0.0196607	−	0.0113511i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			140.178i			0.574499i
$245$		0			0
$246$	55.7765			0.226734
$247$	−348.343	+	201.116i	−1.41030	+	0.814234i
$248$	56.5924	−	98.0209i	0.228195	−	0.395246i
$249$	87.5076	−	151.568i	0.351436	−	0.608706i
$250$		0			0
$251$			422.260i			1.68231i	0.540795	+	0.841155i	$0.318124\pi$
$251$			422.260i			1.68231i	−0.540795	+	0.841155i	$0.681876\pi$
$252$	−27.6914	+	31.5782i	−0.109887	+	0.125310i
$253$			228.069i			0.901457i
$254$	71.9672	+	124.651i	0.283335	+	0.490751i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	37.2435	+	64.5077i	0.144916	+	0.251003i	0.929342	−	0.369221i	$-0.120375\pi$
$257$	37.2435	+	64.5077i	0.144916	+	0.251003i	−0.784425	+	0.620223i	$0.787042\pi$
$258$	118.630			0.459808
$259$	−68.7687	+	345.786i	−0.265516	+	1.33508i
$260$		0			0
$261$	28.6332	+	49.5942i	0.109706	+	0.190016i
$262$	−49.9911	+	86.5872i	−0.190806	+	0.330486i
$263$	271.304	+	156.637i	1.03157	+	0.595579i	0.917435	−	0.397885i	$-0.130256\pi$
$263$	271.304	+	156.637i	1.03157	+	0.595579i	0.114139	+	0.993465i	$0.463589\pi$
$264$	−45.9138	+	26.5083i	−0.173916	+	0.100410i
$265$		0			0
$266$	66.4229	+	195.653i	0.249710	+	0.735539i
$267$		−	68.6153i		−	0.256986i
$268$	−33.4385	+	19.3057i	−0.124771	+	0.0720363i
$269$	138.011	+	79.6809i	0.513053	+	0.296211i	0.734088	−	0.679055i	$-0.237610\pi$
$269$	138.011	+	79.6809i	0.513053	+	0.296211i	−0.221035	+	0.975266i	$0.570943\pi$
$270$		0			0
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	−0.769682	−	0.638427i	$-0.779585\pi$
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	0.168053	+	0.985778i	$0.446252\pi$
$272$	−41.0949			−0.151084
$273$	−75.1133	−	221.252i	−0.275140	−	0.810446i
$274$	−166.633			−0.608151
$275$		0			0
$276$	−63.2238	−	36.5023i	−0.229072	−	0.132255i
$277$	−6.10326	−	3.52372i	−0.0220334	−	0.0127210i	0.488943	−	0.872316i	$-0.337383\pi$
$277$	−6.10326	−	3.52372i	−0.0220334	−	0.0127210i	−0.510976	+	0.859595i	$0.670716\pi$
$278$	−112.081	−	194.130i	−0.403170	−	0.698311i
$279$			120.051i			0.430289i
$280$		0			0
$281$	198.386			0.705998			0.352999	−	0.935624i	$-0.385162\pi$
$281$	198.386			0.705998			0.352999	+	0.935624i	$0.385162\pi$
$282$	141.148	−	81.4920i	0.500526	−	0.288979i
$283$	−94.5641	+	163.790i	−0.334149	+	0.578763i	−0.983321	−	0.181879i	$-0.941782\pi$
$283$	−94.5641	+	163.790i	−0.334149	+	0.578763i	0.649172	+	0.760641i	$0.275115\pi$
$284$	49.4968	−	85.7309i	0.174284	−	0.301869i
$285$		0			0
$286$		−	294.942i		−	1.03127i
$287$	119.843	+	105.092i	0.417571	+	0.366174i
$288$		−	16.9706i		−	0.0589256i
$289$	91.7253	+	158.873i	0.317389	+	0.549733i
$290$		0			0
$291$	59.4911	−	103.042i	0.204437	−	0.354095i
$292$	132.974	+	230.318i	0.455391	+	0.788761i
$293$	486.090			1.65901			0.829505	−	0.558499i	$-0.188622\pi$
$293$	486.090			1.65901			0.829505	+	0.558499i	$0.188622\pi$
$294$	−118.997	+	15.6746i	−0.404752	+	0.0533150i
$295$		0			0
$296$	−71.2274	−	123.370i	−0.240633	−	0.416789i
$297$	28.1163	−	48.6989i	0.0946678	−	0.163969i
$298$	362.397	+	209.230i	1.21610	+	0.702115i
$299$	351.726	−	203.069i	1.17634	−	0.679161i
$300$		0			0
$301$	254.892	+	223.519i	0.846818	+	0.742588i
$302$			177.195i			0.586738i
$303$	12.0585	−	6.96199i	0.0397971	−	0.0229769i
$304$	−72.3023	−	41.7437i	−0.237836	−	0.137315i
$305$		0			0
$306$	37.7481	−	21.7939i	0.123360	−	0.0712217i
$307$	−427.589			−1.39280			−0.696399	−	0.717655i	$-0.745216\pi$
$307$	−427.589			−1.39280			−0.696399	+	0.717655i	$0.745216\pi$
$308$	−148.598	−	29.5526i	−0.482460	−	0.0959499i
$309$	354.317			1.14666
$310$		0			0
$311$	−311.852	−	180.048i	−1.00274	−	0.578931i	−0.0936811	−	0.995602i	$-0.529863\pi$
$311$	−311.852	−	180.048i	−1.00274	−	0.578931i	−0.909057	+	0.416671i	$0.863197\pi$
$312$	81.7620	+	47.2053i	0.262058	+	0.151299i
$313$	−291.964	−	505.696i	−0.932792	−	1.61564i	−0.778525	−	0.627614i	$-0.784032\pi$
$313$	−291.964	−	505.696i	−0.932792	−	1.61564i	−0.154267	−	0.988029i	$-0.549302\pi$
$314$		−	7.54295i		−	0.0240221i
$315$		0			0
$316$	−180.162			−0.570132
$317$	312.982	−	180.700i	0.987324	−	0.570032i	0.0828508	−	0.996562i	$-0.473597\pi$
$317$	312.982	−	180.700i	0.987324	−	0.570032i	0.904473	+	0.426530i	$0.140264\pi$
$318$	6.06325	−	10.5019i	0.0190668	−	0.0330247i
$319$	−103.289	+	178.902i	−0.323791	+	0.560823i
$320$		0			0
$321$			285.016i			0.887899i
$322$	−67.0680	−	197.554i	−0.208286	−	0.613521i
$323$		−	214.432i		−	0.663875i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	169.172	−	293.015i	0.518934	−	0.898819i
$327$	−68.4247	−	118.515i	−0.209250	−	0.362432i
$328$	−64.4051			−0.196357
$329$	456.819	+	90.8507i	1.38851	+	0.276142i
$330$		0			0
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	0.551088	−	0.834447i	$-0.314213\pi$
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	−0.998196	+	0.0600326i	$0.980880\pi$
$332$	−101.045	+	175.015i	−0.304353	+	0.527154i
$333$	130.853	+	75.5481i	0.392952	+	0.226871i
$334$	380.210	−	219.514i	1.13835	−	0.657229i
$335$		0			0
$336$	31.9753	−	36.4634i	0.0951646	−	0.108522i
$337$		−	22.0162i		−	0.0653300i	−0.999466	−	0.0326650i	$-0.989601\pi$
$337$		−	22.0162i		−	0.0653300i	0.999466	−	0.0326650i	$-0.0103994\pi$
$338$	−247.876	+	143.111i	−0.733361	+	0.423406i
$339$	126.854	+	73.2389i	0.374199	+	0.216044i
$340$		0			0
$341$	−375.043	+	216.531i	−1.09983	+	0.634988i
$342$	88.5519			0.258924
$343$	−285.214	−	190.531i	−0.831527	−	0.555484i
$344$	−136.983			−0.398205
$345$		0			0
$346$	111.339	+	64.2815i	0.321789	+	0.185785i
$347$	245.870	+	141.953i	0.708559	+	0.409086i	0.810527	−	0.585701i	$-0.199181\pi$
$347$	245.870	+	141.953i	0.708559	+	0.409086i	−0.101969	+	0.994788i	$0.532514\pi$
$348$	−33.0628	−	57.2665i	−0.0950080	−	0.164559i
$349$			317.175i			0.908811i	0.890795	+	0.454406i	$0.150148\pi$
$349$			317.175i			0.908811i	−0.890795	+	0.454406i	$0.849852\pi$
$350$		0			0
$351$	−100.138			−0.285292
$352$	53.0166	−	30.6092i	0.150615	−	0.0869579i
$353$	−58.4712	+	101.275i	−0.165641	+	0.286898i	−0.936883	−	0.349644i	$-0.886303\pi$
$353$	−58.4712	+	101.275i	−0.165641	+	0.286898i	0.771242	+	0.636542i	$0.219636\pi$
$354$	34.5216	−	59.7932i	0.0975187	−	0.168907i
$355$		0			0
$356$			79.2302i			0.222557i
$357$	122.170	+	24.2967i	0.342212	+	0.0680579i
$358$		−	343.871i		−	0.960534i
$359$	116.793	+	202.291i	0.325329	+	0.563486i	0.981579	−	0.191058i	$-0.0611918\pi$
$359$	116.793	+	202.291i	0.325329	+	0.563486i	−0.656250	+	0.754543i	$0.727858\pi$
$360$		0			0
$361$	37.3175	−	64.6359i	0.103373	−	0.179047i
$362$	173.943	+	301.278i	0.480505	+	0.832260i
$363$	−6.72867			−0.0185363
$364$	86.7334	+	255.479i	0.238279	+	0.701866i
$365$		0			0
$366$	85.8410	+	148.681i	0.234538	+	0.406232i
$367$	−256.037	+	443.469i	−0.697648	+	1.20836i	0.271632	+	0.962401i	$0.412437\pi$
$367$	−256.037	+	443.469i	−0.697648	+	1.20836i	−0.969280	+	0.245960i	$0.920897\pi$
$368$	73.0045	+	42.1492i	0.198382	+	0.114536i
$369$	59.1599	−	34.1560i	0.160325	−	0.0925636i
$370$		0			0
$371$	32.8149	−	11.1404i	0.0884498	−	0.0300280i
$372$		−	138.623i		−	0.372641i
$373$	481.863	−	278.204i	1.29186	−	0.745854i	0.312874	−	0.949795i	$-0.398708\pi$
$373$	481.863	−	278.204i	1.29186	−	0.745854i	0.978983	+	0.203941i	$0.0653749\pi$
$374$	136.170	+	78.6175i	0.364090	+	0.210207i
$375$		0			0
$376$	−162.984	+	94.0989i	−0.433468	+	0.250263i
$377$	367.870			0.975782
$378$	−10.0336	+	50.4512i	−0.0265438	+	0.133469i
$379$	536.301			1.41504			0.707521	−	0.706692i	$-0.249813\pi$
$379$	536.301			1.41504			0.707521	+	0.706692i	$0.249813\pi$
$380$		0			0
$381$	152.665	+	88.1414i	0.400697	+	0.231342i
$382$	−50.4859	−	29.1480i	−0.132162	−	0.0763038i
$383$	−14.6753	−	25.4184i	−0.0383168	−	0.0663666i	0.846231	−	0.532816i	$-0.178866\pi$
$383$	−14.6753	−	25.4184i	−0.0383168	−	0.0663666i	−0.884548	+	0.466450i	$0.845533\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	268.341			0.695183
$387$	125.827	−	72.6460i	0.325133	−	0.187716i
$388$	−68.6944	+	118.982i	−0.177047	+	0.306655i
$389$	−349.242	+	604.905i	−0.897795	+	1.55503i	−0.0674875	+	0.997720i	$0.521498\pi$
$389$	−349.242	+	604.905i	−0.897795	+	1.55503i	−0.830307	+	0.557306i	$0.811835\pi$
$390$		0			0
$391$			216.514i			0.553745i
$392$	137.406	−	18.0995i	0.350526	−	0.0461721i
$393$			122.453i			0.311585i
$394$	256.198	+	443.747i	0.650248	+	1.12626i
$395$		0			0
$396$	−32.4659	+	56.2326i	−0.0819847	+	0.142002i
$397$	−102.347	−	177.270i	−0.257801	−	0.446525i	0.707851	−	0.706361i	$-0.249665\pi$
$397$	−102.347	−	177.270i	−0.257801	−	0.446525i	−0.965653	+	0.259837i	$0.916331\pi$
$398$	−54.6127			−0.137218
$399$	190.265	+	166.846i	0.476854	+	0.418161i
$400$		0			0
$401$	−214.984	−	372.363i	−0.536119	−	0.928585i	−0.999108	−	0.0422215i	$-0.986556\pi$
$401$	−214.984	−	372.363i	−0.536119	−	0.928585i	0.462989	−	0.886364i	$-0.346777\pi$
$402$	−23.6446	+	40.9537i	−0.0588174	+	0.101875i
$403$	667.865	+	385.592i	1.65723	+	0.956805i
$404$	−13.9240	+	8.03902i	−0.0344653	+	0.0198986i
$405$		0			0
$406$	36.8598	−	185.340i	0.0907876	−	0.456502i
$407$			545.053i			1.33920i
$408$	−43.5877	+	25.1654i	−0.106833	+	0.0616798i
$409$	−15.3567	−	8.86618i	−0.0375469	−	0.0216777i	0.481109	−	0.876661i	$-0.340234\pi$
$409$	−15.3567	−	8.86618i	−0.0375469	−	0.0216777i	−0.518656	+	0.854983i	$0.673567\pi$
$410$		0			0
$411$	−176.741	+	102.042i	−0.430027	+	0.248276i
$412$	−409.129			−0.993033
$413$	186.834	−	63.4289i	0.452383	−	0.153581i
$414$	−89.4119			−0.215971
$415$		0			0
$416$	−94.4106	−	54.5080i	−0.226948	−	0.131029i
$417$	−237.760	−	137.271i	−0.570168	−	0.329187i
$418$	159.718	+	276.639i	0.382100	+	0.661816i
$419$			440.768i			1.05195i	0.850499	+	0.525977i	$0.176300\pi$
$419$			440.768i			1.05195i	−0.850499	+	0.525977i	$0.823700\pi$
$420$		0			0
$421$	−143.012			−0.339696			−0.169848	−	0.985470i	$-0.554328\pi$
$421$	−143.012			−0.339696			−0.169848	+	0.985470i	$0.554328\pi$
$422$	167.241	−	96.5564i	0.396305	−	0.228807i
$423$	99.8070	−	172.871i	0.235950	−	0.408678i
$424$	−7.00124	+	12.1265i	−0.0165123	+	0.0286002i
$425$		0			0
$426$		−	121.242i		−	0.284605i
$427$	−95.6991	+	481.199i	−0.224120	+	1.12693i
$428$		−	329.108i		−	0.768943i
$429$	−180.614	−	312.833i	−0.421012	−	0.729215i
$430$		0			0
$431$	391.608	−	678.285i	0.908604	−	1.57375i	0.0925988	−	0.995704i	$-0.470483\pi$
$431$	391.608	−	678.285i	0.908604	−	1.57375i	0.816005	−	0.578045i	$-0.196184\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	−286.669			−0.662053			−0.331026	−	0.943622i	$-0.607395\pi$
$433$	−286.669			−0.662053			−0.331026	+	0.943622i	$0.607395\pi$
$434$	261.188	−	297.848i	0.601815	−	0.686286i
$435$		0			0
$436$	79.0101	+	136.849i	0.181216	+	0.313875i
$437$	−219.933	+	380.935i	−0.503279	+	0.871705i
$438$	282.081	+	162.860i	0.644021	+	0.371826i
$439$	295.016	−	170.328i	0.672018	−	0.387990i	−0.124823	−	0.992179i	$-0.539836\pi$
$439$	295.016	−	170.328i	0.672018	−	0.387990i	0.796841	+	0.604189i	$0.206503\pi$
$440$		0			0
$441$	−116.617	+	89.4960i	−0.264437	+	0.202939i
$442$		−	280.000i		−	0.633484i
$443$	−342.304	+	197.629i	−0.772696	+	0.446116i	−0.833835	−	0.552013i	$-0.813860\pi$
$443$	−342.304	+	197.629i	−0.772696	+	0.446116i	0.0611396	+	0.998129i	$0.480527\pi$
$444$	−151.096	−	87.2354i	−0.340307	−	0.196476i
$445$		0			0
$446$	−189.773	+	109.566i	−0.425500	+	0.245663i
$447$	512.507			1.14655
$448$	−36.9219	+	42.1043i	−0.0824150	+	0.0939828i
$449$	−665.078			−1.48124			−0.740621	−	0.671923i	$-0.765469\pi$
$449$	−665.078			−1.48124			−0.740621	+	0.671923i	$0.765469\pi$
$450$		0			0
$451$	213.409	+	123.212i	0.473190	+	0.273197i
$452$	−146.478	−	84.5690i	−0.324066	−	0.187100i
$453$	108.509	+	187.944i	0.239535	+	0.414886i
$454$		−	31.6131i		−	0.0696323i
$455$		0			0
$456$	−102.251			−0.224234
$457$	442.484	−	255.468i	0.968236	−	0.559012i	0.0695382	−	0.997579i	$-0.477847\pi$
$457$	442.484	−	255.468i	0.968236	−	0.559012i	0.898698	+	0.438568i	$0.144514\pi$
$458$	21.1558	−	36.6429i	0.0461917	−	0.0800064i
$459$	26.6919	−	46.2317i	0.0581523	−	0.100723i
$460$		0			0
$461$			174.303i			0.378097i	0.981968	+	0.189049i	$0.0605404\pi$
$461$			174.303i			0.378097i	−0.981968	+	0.189049i	$0.939460\pi$
$462$	−175.709	+	59.6518i	−0.380322	+	0.129116i
$463$		−	755.187i		−	1.63107i	−0.578705	−	0.815537i	$-0.696442\pi$
$463$		−	755.187i		−	1.63107i	0.578705	−	0.815537i	$-0.303558\pi$
$464$	38.1776	+	66.1256i	0.0822794	+	0.142512i
$465$		0			0
$466$	−178.956	+	309.961i	−0.384026	+	0.665153i
$467$	−283.286	−	490.666i	−0.606609	−	1.05068i	−0.991795	−	0.127839i	$-0.959196\pi$
$467$	−283.286	−	490.666i	−0.606609	−	1.05068i	0.385186	−	0.922839i	$-0.374137\pi$
$468$	115.629			0.247070
$469$	−127.967	+	43.4438i	−0.272850	+	0.0926307i
$470$		0			0
$471$	−4.61909	−	8.00051i	−0.00980699	−	0.0169862i
$472$	−39.8621	+	69.0432i	−0.0844537	+	0.146278i
$473$	453.897	+	262.058i	0.959614	+	0.554033i
$474$	−191.090	+	110.326i	−0.403144	+	0.232755i
$475$		0			0
$476$	−141.069	−	28.0554i	−0.296364	−	0.0589399i
$477$		−	14.8519i		−	0.0311360i
$478$	148.206	−	85.5665i	0.310053	−	0.179009i
$479$	−445.286	−	257.086i	−0.929615	−	0.536714i	−0.0429255	−	0.999078i	$-0.513668\pi$
$479$	−445.286	−	257.086i	−0.929615	−	0.536714i	−0.886690	+	0.462365i	$0.847001\pi$
$480$		0			0
$481$	840.578	−	485.308i	1.74756	−	1.00896i
$482$	−407.848			−0.846157
$483$	−192.113	−	168.467i	−0.397749	−	0.348792i
$484$	7.76960			0.0160529
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−283.473	−	163.663i	−0.582081	−	0.336064i	0.179879	−	0.983689i	$-0.442429\pi$
$487$	−283.473	−	163.663i	−0.582081	−	0.336064i	−0.761960	+	0.647624i	$0.775763\pi$
$488$	−99.1207	−	171.682i	−0.203116	−	0.351808i
$489$		−	414.386i		−	0.847415i
$490$		0			0
$491$	−41.8889			−0.0853134			−0.0426567	−	0.999090i	$-0.513582\pi$
$491$	−41.8889			−0.0853134			−0.0426567	+	0.999090i	$0.513582\pi$
$492$	−68.3119	+	39.4399i	−0.138845	+	0.0801624i
$493$	−98.0566	+	169.839i	−0.198898	+	0.344501i
$494$	284.421	−	492.631i	0.575751	−	0.997229i
$495$		0			0
$496$			160.068i			0.322717i
$497$	228.439	−	260.503i	0.459637	−	0.524152i
$498$			247.509i			0.497006i
$499$	207.685	+	359.721i	0.416203	+	0.720885i	0.995554	−	0.0941936i	$-0.0300273\pi$
$499$	207.685	+	359.721i	0.416203	+	0.720885i	−0.579351	+	0.815078i	$0.696694\pi$
$500$		0			0
$501$	268.849	−	465.660i	0.536625	−	0.929462i
$502$	−298.583	−	517.160i	−0.594786	−	1.03020i
$503$	51.7604			0.102903			0.0514517	−	0.998675i	$-0.483615\pi$
$503$	51.7604			0.102903			0.0514517	+	0.998675i	$0.483615\pi$
$504$	11.5858	−	58.2561i	0.0229876	−	0.115587i
$505$		0			0
$506$	−161.269	−	279.326i	−0.318713	−	0.552028i
$507$	−175.275	+	303.585i	−0.345709	+	0.598786i
$508$	−176.283	−	101.777i	−0.347014	−	0.200348i
$509$	−136.916	+	79.0486i	−0.268991	+	0.155302i	−0.628429	−	0.777867i	$-0.716302\pi$
$509$	−136.916	+	79.0486i	−0.268991	+	0.155302i	0.359438	+	0.933169i	$0.382968\pi$
$510$		0			0
$511$	299.233	+	881.411i	0.585583	+	1.72488i
$512$		−	22.6274i		−	0.0441942i
$513$	93.9234	−	54.2267i	0.183087	−	0.105705i
$514$	−91.2276	−	52.6703i	−0.177486	−	0.102471i
$515$		0			0
$516$	−145.292	+	83.8844i	−0.281574	+	0.162567i
$517$	720.073			1.39279
$518$	−160.283	−	472.126i	−0.309428	−	0.911441i
$519$	157.457			0.303385
$520$		0			0
$521$	306.214	+	176.793i	0.587744	+	0.339334i	0.764205	−	0.644974i	$-0.223132\pi$
$521$	306.214	+	176.793i	0.587744	+	0.339334i	−0.176461	+	0.984308i	$0.556465\pi$
$522$	−70.1368	−	40.4935i	−0.134362	−	0.0775737i
$523$	59.7756	+	103.534i	0.114294	+	0.197962i	0.917497	−	0.397742i	$-0.130206\pi$
$523$	59.7756	+	103.534i	0.114294	+	0.197962i	−0.803204	+	0.595705i	$0.796873\pi$
$524$		−	141.396i		−	0.269840i
$525$		0			0
$526$	−443.037			−0.842277
$527$	−356.042	+	205.561i	−0.675602	+	0.390059i
$528$	37.4884	−	64.9319i	0.0710008	−	0.122977i
$529$	−42.4308	+	73.4924i	−0.0802095	+	0.138927i
$530$		0			0
$531$		−	84.5604i		−	0.159247i
$532$	−219.699	−	192.657i	−0.412968	−	0.362138i
$533$		−	438.824i		−	0.823309i
$534$	48.5184	+	84.0363i	0.0908584	+	0.157371i
$535$		0			0
$536$	27.3024	−	47.2892i	0.0509374	−	0.0882261i
$537$	−210.577	−	364.731i	−0.392136	−	0.679200i
$538$	−225.372			−0.418906
$539$	−489.926	−	202.894i	−0.908954	−	0.376427i
$540$		0			0
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	−0.999989	−	0.00468349i	$-0.998509\pi$
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	0.495938	−	0.868358i	$-0.334824\pi$
$542$	133.123	−	230.575i	0.245614	−	0.425416i
$543$	368.989	+	213.036i	0.679537	+	0.392331i
$544$	50.3307	−	29.0585i	0.0925197	−	0.0534163i
$545$		0			0
$546$	248.443	+	217.864i	0.455024	+	0.399018i
$547$		−	117.783i		−	0.215325i	−0.994188	−	0.107663i	$-0.965663\pi$
$547$		−	117.783i		−	0.215325i	0.994188	−	0.107663i	$-0.0343366\pi$
$548$	204.083	−	117.828i	0.372415	−	0.215014i
$549$	182.096	+	105.133i	0.331687	+	0.191500i
$550$		0			0
$551$	−345.041	+	199.210i	−0.626209	+	0.361542i
$552$	103.244			0.187036
$553$	−618.454	−	122.996i	−1.11836	−	0.222416i
$554$	9.96659			0.0179902
$555$		0			0
$556$	274.542	+	158.507i	0.493780	+	0.285084i
$557$	533.028	+	307.744i	0.956963	+	0.552503i	0.895237	−	0.445590i	$-0.147006\pi$
$557$	533.028	+	307.744i	0.956963	+	0.552503i	0.0617258	+	0.998093i	$0.480340\pi$
$558$	−84.8886	−	147.031i	−0.152130	−	0.263497i
$559$		−	933.330i		−	1.66964i
$560$		0			0
$561$	192.573			0.343267
$562$	−242.972	+	140.280i	−0.432334	+	0.249608i
$563$	−239.628	+	415.047i	−0.425626	+	0.737207i	−0.996479	−	0.0838462i	$-0.973280\pi$
$563$	−239.628	+	415.047i	−0.425626	+	0.737207i	0.570852	+	0.821053i	$0.306613\pi$
$564$	−115.247	+	199.614i	−0.204339	+	0.353925i
$565$		0			0
$566$		−	267.468i		−	0.472558i
$567$	20.2527	+	59.6559i	0.0357191	+	0.105213i
$568$			139.998i			0.246475i
$569$	−228.674	−	396.074i	−0.401887	−	0.696088i	0.592067	−	0.805889i	$-0.298312\pi$
$569$	−228.674	−	396.074i	−0.401887	−	0.696088i	−0.993954	+	0.109800i	$0.964979\pi$
$570$		0			0
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	−0.981874	−	0.189532i	$-0.939303\pi$
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	0.655077	+	0.755562i	$0.272636\pi$
$572$	208.555	+	361.229i	0.364607	+	0.631519i
$573$	−71.3978			−0.124604
$574$	−221.088	−	43.9692i	−0.385171	−	0.0766014i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	445.777	−	772.108i	0.772577	−	1.33814i	−0.163569	−	0.986532i	$-0.552301\pi$
$577$	445.777	−	772.108i	0.772577	−	1.33814i	0.936146	−	0.351611i	$-0.114366\pi$
$578$	−224.680	−	129.719i	−0.388720	−	0.224428i
$579$	284.618	−	164.324i	0.491568	−	0.283807i
$580$		0			0
$581$	−466.347	+	531.804i	−0.802663	+	0.915326i
$582$			168.266i			0.289117i
$583$	46.3978	−	26.7878i	0.0795845	−	0.0459481i
$584$	−325.719	−	188.054i	−0.557738	−	0.322010i
$585$		0			0
$586$	−595.336	+	343.718i	−1.01593	+	0.586549i
$587$	−786.758			−1.34030			−0.670151	−	0.742224i	$-0.733771\pi$
$587$	−786.758			−1.34030			−0.670151	+	0.742224i	$0.733771\pi$
$588$	134.657	−	103.341i	0.229009	−	0.175750i
$589$	−835.227			−1.41804
$590$		0			0
$591$	543.477	+	313.777i	0.919589	+	0.530925i
$592$	174.471	+	100.731i	0.294714	+	0.170153i
$593$	312.676	+	541.571i	0.527278	+	0.913273i	0.999495	+	0.0317903i	$0.0101209\pi$
$593$	312.676	+	541.571i	0.527278	+	0.913273i	−0.472216	+	0.881483i	$0.656546\pi$
$594$			79.5250i			0.133880i
$595$		0			0
$596$	−591.792			−0.992940
$597$	−57.9256	+	33.4433i	−0.0970278	+	0.0560190i
$598$	−287.183	+	497.416i	−0.480240	+	0.831799i
$599$	75.2476	−	130.333i	0.125622	−	0.217584i	−0.796354	−	0.604831i	$-0.793241\pi$
$599$	75.2476	−	130.333i	0.125622	−	0.217584i	0.921976	+	0.387247i	$0.126574\pi$
$600$		0			0
$601$		−	521.601i		−	0.867888i	−0.900940	−	0.433944i	$-0.857122\pi$
$601$		−	521.601i		−	0.867888i	0.900940	−	0.433944i	$-0.142878\pi$
$602$	−470.230	−	93.5177i	−0.781113	−	0.155345i
$603$			57.9172i			0.0960485i
$604$	−125.296	−	217.019i	−0.207443	−	0.359302i
$605$		0			0
$606$	−9.84575	+	17.0533i	−0.0162471	+	0.0281408i
$607$	−348.375	−	603.404i	−0.573930	−	0.994075i	−0.996157	−	0.0875852i	$-0.972085\pi$
$607$	−348.375	−	603.404i	−0.573930	−	0.994075i	0.422228	−	0.906490i	$-0.361248\pi$
$608$	118.069			0.194193
$609$	−74.4014	−	219.155i	−0.122170	−	0.359860i
$610$		0			0
$611$	−641.143	−	1110.49i	−1.04933	−	1.81750i
$612$	−30.8212	+	53.3838i	−0.0503614	+	0.0872285i
$613$	46.9809	+	27.1244i	0.0766410	+	0.0442487i	0.537831	−	0.843053i	$-0.319244\pi$
$613$	46.9809	+	27.1244i	0.0766410	+	0.0442487i	−0.461190	+	0.887302i	$0.652577\pi$
$614$	523.687	−	302.351i	0.852911	−	0.492428i
$615$		0			0
$616$	202.891	−	68.8800i	0.329368	−	0.111818i
$617$		−	969.852i		−	1.57188i	−0.618301	−	0.785941i	$-0.712179\pi$
$617$		−	969.852i		−	1.57188i	0.618301	−	0.785941i	$-0.287821\pi$
$618$	−433.947	+	250.540i	−0.702180	+	0.405404i
$619$	111.240	+	64.2247i	0.179710	+	0.103756i	0.587156	−	0.809474i	$-0.300247\pi$
$619$	111.240	+	64.2247i	0.179710	+	0.103756i	−0.407446	+	0.913229i	$0.633581\pi$
$620$		0			0
$621$	−94.8357	+	54.7534i	−0.152714	+	0.0881697i
$622$	509.252			0.818733
$623$	−54.0903	+	271.979i	−0.0868223	+	0.436564i
$624$	−133.517			−0.213969
$625$		0			0
$626$	715.163	+	412.899i	1.14243	+	0.659584i
$627$	338.812	+	195.613i	0.540371	+	0.311983i
$628$	5.33367	+	9.23819i	0.00849311	+	0.0147105i
$629$			517.440i			0.822639i
$630$		0			0
$631$	115.457			0.182975			0.0914877	−	0.995806i	$-0.470838\pi$
$631$	115.457			0.182975			0.0914877	+	0.995806i	$0.470838\pi$
$632$	220.652	−	127.393i	0.349133	−	0.201572i
$633$	118.257	−	204.827i	0.186820	−	0.323581i
$634$	−255.549	+	442.623i	−0.403073	+	0.698144i
$635$		0			0
$636$			17.1495i			0.0269646i
$637$	123.321	+	936.215i	0.193596	+	1.46973i
$638$		−	292.146i		−	0.457910i
$639$	−74.2452	−	128.596i	−0.116190	−	0.201246i
$640$		0			0
$641$	476.249	−	824.887i	0.742978	−	1.28688i	−0.208156	−	0.978096i	$-0.566746\pi$
$641$	476.249	−	824.887i	0.742978	−	1.28688i	0.951134	−	0.308780i	$-0.0999206\pi$
$642$	−201.537	−	349.072i	−0.313920	−	0.543725i
$643$	253.254			0.393863			0.196931	−	0.980417i	$-0.436902\pi$
$643$	253.254			0.393863			0.196931	+	0.980417i	$0.436902\pi$
$644$	221.833	+	194.529i	0.344461	+	0.302063i
$645$		0			0
$646$	151.626	+	262.624i	0.234715	+	0.406539i
$647$	−502.388	+	870.161i	−0.776488	+	1.34492i	0.157466	+	0.987524i	$0.449668\pi$
$647$	−502.388	+	870.161i	−0.776488	+	1.34492i	−0.933954	+	0.357393i	$0.883666\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	264.170	−	152.518i	0.407041	−	0.235005i
$650$		0			0
$651$	94.6373	−	475.860i	0.145372	−	0.730967i
$652$			478.492i			0.733883i
$653$	−922.831	+	532.797i	−1.41322	+	0.815922i	−0.995690	−	0.0927422i	$-0.970437\pi$
$653$	−922.831	+	532.797i	−1.41322	+	0.815922i	−0.417528	+	0.908664i	$0.637103\pi$
$654$	167.606	+	96.7672i	0.256278	+	0.147962i
$655$		0			0
$656$	78.8798	−	45.5413i	0.120244	−	0.0694227i
$657$	398.923			0.607189
$658$	−623.728	+	211.751i	−0.947915	+	0.321810i
$659$	−432.265			−0.655941			−0.327970	−	0.944688i	$-0.606365\pi$
$659$	−432.265			−0.655941			−0.327970	+	0.944688i	$0.606365\pi$
$660$		0			0
$661$	327.626	+	189.155i	0.495652	+	0.286165i	0.726916	−	0.686726i	$-0.240953\pi$
$661$	327.626	+	189.155i	0.495652	+	0.286165i	−0.231264	+	0.972891i	$0.574286\pi$
$662$	362.507	+	209.294i	0.547594	+	0.316153i
$663$	−171.464	−	296.985i	−0.258619	−	0.447941i
$664$		−	285.799i		−	0.430420i
$665$		0			0
$666$	−213.682			−0.320844
$667$	348.392	−	201.144i	0.522328	−	0.301566i
$668$	−310.440	+	537.698i	−0.464731	+	0.804937i
$669$	−134.190	+	232.424i	−0.200583	+	0.347419i
$670$		0			0
$671$			758.501i			1.13040i
$672$	−13.3781	+	67.2683i	−0.0199079	+	0.100102i
$673$			689.666i			1.02476i	0.858758	+	0.512382i	$0.171237\pi$
$673$			689.666i			1.02476i	−0.858758	+	0.512382i	$0.828763\pi$
$674$	15.5678	+	26.9642i	0.0230976	+	0.0400063i
$675$		0			0
$676$	202.390	−	350.549i	0.299393	−	0.518564i
$677$	189.754	+	328.663i	0.280286	+	0.485470i	0.971455	−	0.237223i	$-0.0762373\pi$
$677$	189.754	+	328.663i	0.280286	+	0.485470i	−0.691169	+	0.722693i	$0.742904\pi$
$678$	−207.151			−0.305532
$679$	−317.041	+	361.541i	−0.466924	+	0.532461i
$680$		0			0
$681$	−19.3590	−	33.5307i	−0.0284273	−	0.0492375i
$682$	306.221	−	530.390i	0.449004	−	0.777698i
$683$	647.360	+	373.753i	0.947818	+	0.547223i	0.892403	−	0.451240i	$-0.149018\pi$
$683$	647.360	+	373.753i	0.947818	+	0.547223i	0.0554159	+	0.998463i	$0.482352\pi$
$684$	−108.453	+	62.6156i	−0.158558	+	0.0915433i
$685$		0			0
$686$	484.040	+	31.6754i	0.705598	+	0.0461740i
$687$		−	51.8209i		−	0.0754308i
$688$	167.769	−	96.8613i	0.243850	−	0.140787i
$689$	−82.6238	−	47.7029i	−0.119918	−	0.0692350i
$690$		0			0
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.175483	−	0.984482i	$-0.443851\pi$
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.940328	+	0.340268i	$0.110518\pi$
$692$	−181.816			−0.262739
$693$	−149.838	+	170.869i	−0.216217	+	0.246565i
$694$	−401.504			−0.578536
$695$		0			0
$696$	80.9870	+	46.7579i	0.116361	+	0.0671808i
$697$	202.597	+	116.970i	0.290670	+	0.167819i
$698$	−224.277	−	388.459i	−0.321313	−	0.556531i
$699$			438.352i			0.627112i
$700$		0			0
$701$	−650.703			−0.928250			−0.464125	−	0.885770i	$-0.653631\pi$
$701$	−650.703			−0.928250			−0.464125	+	0.885770i	$0.653631\pi$
$702$	122.643	−	70.8079i	0.174705	−	0.100866i
$703$	−525.610	+	910.384i	−0.747667	+	1.29500i
$704$	−43.2879	+	74.9769i	−0.0614885	+	0.106501i
$705$		0			0
$706$		−	165.382i		−	0.234251i
$707$	−53.2861	+	18.0902i	−0.0753693	+	0.0255873i
$708$			97.6419i			0.137912i
$709$	−196.427	−	340.222i	−0.277048	−	0.479862i	0.693602	−	0.720359i	$-0.256023\pi$
$709$	−196.427	−	340.222i	−0.277048	−	0.479862i	−0.970650	+	0.240497i	$0.922690\pi$
$710$		0			0
$711$	−135.121	+	234.037i	−0.190044	+	0.329166i
$712$	−56.0242	−	97.0368i	−0.0786857	−	0.136288i
$713$	843.339			1.18280
$714$	−166.807	+	56.6298i	−0.233623	+	0.0793134i
$715$		0			0
$716$	243.154	+	421.155i	0.339600	+	0.588205i
$717$	104.797	−	181.514i	0.146161	−	0.253158i
$718$	−286.083	−	165.170i	−0.398444	−	0.230042i
$719$	−899.919	+	519.569i	−1.25163	+	0.722627i	−0.971432	−	0.237317i	$-0.923732\pi$
$719$	−899.919	+	519.569i	−1.25163	+	0.722627i	−0.280194	+	0.959943i	$0.590399\pi$
$720$		0			0
$721$	−1404.45	−	279.312i	−1.94792	−	0.387395i
$722$			105.550i			0.146191i
$723$	−432.588	+	249.755i	−0.598323	+	0.345442i
$724$	−426.072	−	245.993i	−0.588497	−	0.339769i
$725$		0			0
$726$	8.24091	−	4.75789i	0.0113511	−	0.00655357i
$727$	610.568			0.839846			0.419923	−	0.907560i	$-0.362057\pi$
$727$	610.568			0.839846			0.419923	+	0.907560i	$0.362057\pi$
$728$	−286.877	−	251.567i	−0.394062	−	0.345559i
$729$	27.0000			0.0370370
$730$		0			0
$731$	430.902	+	248.781i	0.589469	+	0.340330i
$732$	−210.267	−	121.398i	−0.287250	−	0.165844i
$733$	−539.576	−	934.574i	−0.736121	−	1.27500i	−0.954230	−	0.299074i	$-0.903322\pi$
$733$	−539.576	−	934.574i	−0.736121	−	1.27500i	0.218109	−	0.975924i	$-0.430011\pi$
$734$		−	724.181i		−	0.986623i
$735$		0			0
$736$	−119.216			−0.161978
$737$	−180.935	+	104.463i	−0.245503	+	0.141741i
$738$	−48.3038	+	83.6647i	−0.0654523	+	0.113367i
$739$	378.082	−	654.857i	0.511613	−	0.886139i	−0.488297	−	0.872678i	$-0.662382\pi$
$739$	378.082	−	654.857i	0.511613	−	0.886139i	0.999909	−	0.0134615i	$-0.00428507\pi$
$740$		0			0
$741$		−	696.686i		−	0.940197i
$742$	−32.3124	+	36.8478i	−0.0435477	+	0.0496601i
$743$		−	963.993i		−	1.29743i	−0.761030	−	0.648717i	$-0.775306\pi$
$743$		−	963.993i		−	1.29743i	0.761030	−	0.648717i	$-0.224694\pi$
$744$	98.0209	+	169.777i	0.131749	+	0.228195i
$745$		0			0
$746$	−393.439	+	681.457i	−0.527398	+	0.913481i
$747$	151.568	+	262.523i	0.202902	+	0.351436i
$748$	−222.364			−0.297278
$749$	224.681	−	1129.75i	0.299975	−	1.50835i
$750$		0			0
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	−0.997903	−	0.0647203i	$-0.979384\pi$
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	0.442902	−	0.896570i	$-0.353949\pi$
$752$	133.076	−	230.494i	0.176963	−	0.306508i
$753$	−633.389	−	365.688i	−0.841155	−	0.485641i
$754$	−450.547	+	260.123i	−0.597542	+	0.344991i
$755$		0			0
$756$	−23.3859	−	68.8847i	−0.0309337	−	0.0911173i
$757$		−	744.966i		−	0.984103i	−0.870566	−	0.492051i	$-0.836247\pi$
$757$		−	744.966i		−	0.984103i	0.870566	−	0.492051i	$-0.163753\pi$
$758$	−656.832	+	379.222i	−0.866533	+	0.500293i
$759$	−342.103	−	197.513i	−0.450729	−	0.260228i
$760$		0			0
$761$	−64.1518	+	37.0381i	−0.0842993	+	0.0486702i	−0.541557	−	0.840664i	$-0.682165\pi$
$761$	−64.1518	+	37.0381i	−0.0842993	+	0.0486702i	0.457258	+	0.889334i	$0.348832\pi$
$762$	−249.302			−0.327167
$763$	177.797	+	523.713i	0.233023	+	0.686387i
$764$	82.4431			0.107910
$765$		0			0
$766$	35.9471	+	20.7540i	0.0469283	+	0.0270941i
$767$	−470.426	−	271.601i	−0.613332	−	0.354108i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$		−	961.553i		−	1.25039i	−0.780467	−	0.625197i	$-0.785019\pi$
$769$		−	961.553i		−	1.25039i	0.780467	−	0.625197i	$-0.214981\pi$
$770$		0			0
$771$	−129.015			−0.167335
$772$	−328.649	+	189.745i	−0.425711	+	0.245784i
$773$	−687.723	+	1191.17i	−0.889680	+	1.54097i	−0.0494271	+	0.998778i	$0.515740\pi$
$773$	−687.723	+	1191.17i	−0.889680	+	1.54097i	−0.840253	+	0.542194i	$0.817594\pi$
$774$	−102.737	+	177.946i	−0.132735	+	0.229904i
$775$		0			0
$776$		−	194.297i		−	0.250383i
$777$	−459.123	−	402.612i	−0.590892	−	0.518163i
$778$		−	987.806i		−	1.26967i
$779$	237.633	+	411.592i	0.305049	+	0.528360i
$780$		0			0
$781$	267.826	−	463.889i	0.342928	−	0.593968i
$782$	−153.099	−	265.175i	−0.195779	−	0.339098i
$783$	−99.1884			−0.126677
$784$	−155.489	+	119.328i	−0.198328	+	0.152204i
$785$		0			0
$786$	−86.5872	−	149.973i	−0.110162	−	0.190806i
$787$	−190.340	+	329.679i	−0.241856	+	0.418906i	−0.961243	−	0.275703i	$-0.911089\pi$
$787$	−190.340	+	329.679i	−0.241856	+	0.418906i	0.719387	+	0.694609i	$0.244423\pi$
$788$	−627.553	−	362.318i	−0.796387	−	0.459795i
$789$	−469.912	+	271.304i	−0.595579	+	0.343858i
$790$		0			0
$791$	−445.090	−	390.306i	−0.562693	−	0.493434i
$792$		−	91.8275i		−	0.115944i
$793$	1169.76	−	675.358i	1.47510	−	0.851650i
$794$	250.698	+	144.741i	0.315741	+	0.182293i
$795$		0			0
$796$	66.8867	−	38.6170i	0.0840285	−	0.0485139i
$797$	511.440			0.641706			0.320853	−	0.947129i	$-0.396030\pi$
$797$	511.440			0.641706			0.320853	+	0.947129i	$0.396030\pi$
$798$	−351.004	−	69.8064i	−0.439855	−	0.0874768i
$799$	683.593			0.855560
$800$		0			0
$801$	102.923	+	59.4226i	0.128493	+	0.0741856i
$802$	526.600	+	304.033i	0.656609	+	0.379093i
$803$	719.522	+	1246.25i	0.896043	+	1.55199i
$804$		−	66.8770i		−	0.0831804i
$805$		0			0
$806$	−1090.62			−1.35313
$807$	−239.043	+	138.011i	−0.296211	+	0.171018i
$808$	11.3689	−	19.6915i	0.0140704	−	0.0243707i
$809$	579.187	−	1003.18i	0.715930	−	1.24003i	−0.246670	−	0.969099i	$-0.579336\pi$
$809$	579.187	−	1003.18i	0.715930	−	1.24003i	0.962600	−	0.270927i	$-0.0873302\pi$
$810$		0			0
$811$			92.0692i			0.113526i	0.998388	+	0.0567628i	$0.0180779\pi$
$811$			92.0692i			0.113526i	−0.998388	+	0.0567628i	$0.981922\pi$
$812$	85.9113	+	253.058i	0.105802	+	0.311648i
$813$		−	326.083i		−	0.401086i
$814$	−385.411	−	667.551i	−0.473478	−	0.820088i
$815$		0			0
$816$	35.5892	−	61.6423i	0.0436142	−	0.0755421i
$817$	505.419	+	875.412i	0.618628	+	1.07150i
$818$	25.0774			0.0306569
$819$	396.928	+	78.9396i	0.484649	+	0.0963853i
$820$		0			0
$821$	493.467	+	854.711i	0.601057	+	1.04106i	0.992661	+	0.120927i	$0.0385867\pi$
$821$	493.467	+	854.711i	0.601057	+	1.04106i	−0.391605	+	0.920134i	$0.628080\pi$
$822$	144.309	−	249.950i	0.175558	−	0.304075i
$823$	481.074	+	277.748i	0.584537	+	0.337483i	0.762935	−	0.646476i	$-0.223758\pi$
$823$	481.074	+	277.748i	0.584537	+	0.337483i	−0.178397	+	0.983959i	$0.557091\pi$
$824$	501.079	−	289.298i	0.608106	−	0.351090i
$825$		0			0
$826$	−183.973	+	209.796i	−0.222728	+	0.253990i
$827$		−	1323.46i		−	1.60032i	−0.599787	−	0.800160i	$-0.704748\pi$
$827$		−	1323.46i		−	1.60032i	0.599787	−	0.800160i	$-0.295252\pi$
$828$	109.507	−	63.2238i	0.132255	−	0.0763572i
$829$	−911.903	−	526.488i	−1.10000	−	0.635088i	−0.163782	−	0.986497i	$-0.552369\pi$
$829$	−911.903	−	526.488i	−1.10000	−	0.635088i	−0.936222	+	0.351409i	$0.885703\pi$
$830$		0			0
$831$	10.5712	−	6.10326i	0.0127210	−	0.00734448i
$832$	154.172			0.185303
$833$	−465.106	−	192.615i	−0.558350	−	0.231231i
$834$	388.261			0.465540
$835$		0			0
$836$	−391.227	−	225.875i	−0.467975	−	0.270185i
$837$	−180.076	−	103.967i	−0.215145	−	0.124214i
$838$	−311.670	−	539.829i	−0.371922	−	0.644187i
$839$			1254.98i			1.49580i	0.663810	+	0.747901i	$0.268938\pi$
$839$			1254.98i			1.49580i	−0.663810	+	0.747901i	$0.731062\pi$
$840$		0			0
$841$	−476.617			−0.566727
$842$	175.153	−	101.125i	0.208020	−	0.120101i
$843$	−171.807	+	297.578i	−0.203804	+	0.352999i
$844$	−136.551	+	236.514i	−0.161791	+	0.280230i
$845$		0			0
$846$			282.297i			0.333684i
$847$	26.6713	+	5.30429i	0.0314891	+	0.00626244i
$848$		−	19.8025i		−	0.0233520i
$849$	−163.790	−	283.692i	−0.192921	−	0.334149i
$850$		0			0
$851$	530.715	−	919.226i	0.623637	−	1.08017i
$852$	85.7309	+	148.490i	0.100623	+	0.174284i
$853$	454.825			0.533207			0.266603	−	0.963806i	$-0.414099\pi$
$853$	454.825			0.533207			0.266603	+	0.963806i	$0.414099\pi$
$854$	−223.052	−	657.015i	−0.261185	−	0.769338i
$855$		0			0
$856$	232.714	+	403.073i	0.271863	+	0.470880i
$857$	84.3691	−	146.132i	0.0984470	−	0.170515i	−0.812595	−	0.582829i	$-0.801946\pi$
$857$	84.3691	−	146.132i	0.0984470	−	0.170515i	0.911042	+	0.412314i	$0.135279\pi$
$858$	442.413	+	255.427i	0.515633	+	0.297701i
$859$	707.715	−	408.599i	0.823882	−	0.475669i	−0.0278711	−	0.999612i	$-0.508873\pi$
$859$	707.715	−	408.599i	0.823882	−	0.475669i	0.851753	+	0.523943i	$0.175539\pi$
$860$		0			0
$861$	−261.425	+	88.7518i	−0.303629	+	0.103080i
$862$			1107.64i			1.28496i
$863$	1068.59	−	616.950i	1.23823	−	0.714890i	0.269495	−	0.963002i	$-0.413143\pi$
$863$	1068.59	−	616.950i	1.23823	−	0.714890i	0.968731	+	0.248112i	$0.0798100\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	351.096	−	202.705i	0.405423	−	0.234071i
$867$	−317.746			−0.366489
$868$	−109.278	+	549.475i	−0.125896	+	0.633036i
$869$	−974.852			−1.12181
$870$		0			0
$871$	322.205	+	186.025i	0.369925	+	0.213576i
$872$	−193.534	−	111.737i	−0.221943	−	0.128139i
$873$	103.042	+	178.473i	0.118032	+	0.204437i
$874$		−	622.065i		−	0.711744i
$875$		0			0
$876$	−460.637			−0.525841
$877$	64.9136	−	37.4779i	0.0740177	−	0.0427342i	−0.462534	−	0.886601i	$-0.653060\pi$
$877$	64.9136	−	37.4779i	0.0740177	−	0.0427342i	0.536552	+	0.843867i	$0.319726\pi$
$878$	−240.880	+	417.216i	−0.274350	+	0.475189i
$879$	−420.966	+	729.135i	−0.478915	+	0.829505i
$880$		0			0
$881$		−	461.343i		−	0.523658i	−0.965114	−	0.261829i	$-0.915674\pi$
$881$		−	461.343i		−	0.523658i	0.965114	−	0.261829i	$-0.0843257\pi$
$882$	79.5426	−	192.070i	0.0901843	−	0.217767i
$883$		−	237.840i		−	0.269354i	−0.990890	−	0.134677i	$-0.957000\pi$
$883$		−	237.840i		−	0.269354i	0.990890	−	0.134677i	$-0.0429997\pi$
$884$	197.990	+	342.928i	0.223970	+	0.387928i
$885$		0			0
$886$	279.490	−	484.091i	0.315452	−	0.546379i
$887$	4.55679	+	7.89260i	0.00513731	+	0.00889808i	0.868583	−	0.495544i	$-0.165031\pi$
$887$	4.55679	+	7.89260i	0.00513731	+	0.00889808i	−0.863445	+	0.504442i	$0.831698\pi$
$888$	246.739			0.277859
$889$	−535.656	−	469.725i	−0.602538	−	0.528375i
$890$		0			0
$891$	48.6989	+	84.3490i	0.0546565	+	0.0946678i
$892$	154.949	−	268.380i	0.173710	−	0.300874i
$893$	1202.71	+	694.386i	1.34682	+	0.777588i
$894$	−627.691	+	362.397i	−0.702115	+	0.405366i
$895$		0			0
$896$	15.4477	−	77.6748i	0.0172407	−	0.0866906i
$897$			703.452i			0.784228i
$898$	814.551	−	470.281i	0.907072	−	0.523698i
$899$	661.535	+	381.938i	0.735857	+	0.424847i
$900$		0			0
$901$	44.0472	−	25.4306i	0.0488870	−	0.0282249i
$902$	−348.495			−0.386358
$903$	−556.022	+	188.765i	−0.615750	+	0.209042i
$904$	239.197			0.264599
$905$		0			0
$906$	−265.792	−	153.455i	−0.293369	−	0.169377i
$907$	−728.070	−	420.352i	−0.802723	−	0.463453i	0.0416991	−	0.999130i	$-0.486723\pi$
$907$	−728.070	−	420.352i	−0.802723	−	0.463453i	−0.844423	+	0.535678i	$0.820056\pi$
$908$	22.3538	+	38.7179i	0.0246187	+	0.0426409i
$909$			24.1171i			0.0265314i
$910$		0			0
$911$	−35.4735			−0.0389390			−0.0194695	−	0.999810i	$-0.506198\pi$
$911$	−35.4735			−0.0389390			−0.0194695	+	0.999810i	$0.506198\pi$
$912$	125.231	−	72.3023i	0.137315	−	0.0792788i
$913$	−546.754	+	947.006i	−0.598854	+	1.03725i
$914$	−361.287	+	625.767i	−0.395281	+	0.684646i
$915$		0			0
$916$			59.8377i			0.0653250i
$917$	96.5310	−	485.381i	0.105268	−	0.529314i
$918$			75.4961i			0.0822398i
$919$	215.680	+	373.569i	0.234690	+	0.406495i	0.959182	−	0.282788i	$-0.0912592\pi$
$919$	215.680	+	373.569i	0.234690	+	0.406495i	−0.724493	+	0.689282i	$0.757926\pi$
$920$		0			0
$921$	370.303	−	641.384i	0.402066	−	0.696399i
$922$	−123.251	−	213.477i	−0.133678	−	0.231536i
$923$	−953.876			−1.03345
$924$	173.018	−	197.303i	0.187249	−	0.213531i
$925$		0			0
$926$	533.998	+	924.911i	0.576671	+	0.998824i
$927$	−306.847	+	531.475i	−0.331011	+	0.573328i
$928$	−93.5157	−	53.9913i	−0.100771	−	0.0581803i
$929$	−531.053	+	306.603i	−0.571639	+	0.330036i	−0.757804	−	0.652483i	$-0.773728\pi$
$929$	−531.053	+	306.603i	−0.571639	+	0.330036i	0.186165	+	0.982519i	$0.440394\pi$
$930$		0			0
$931$	−622.649	−	811.337i	−0.668796	−	0.871468i
$932$		−	506.165i		−	0.543095i
$933$	540.143	−	311.852i	0.578931	−	0.334246i
$934$	693.907	+	400.627i	0.742941	+	0.428937i
$935$		0			0
$936$	−141.616	+	81.7620i	−0.151299	+	0.0873525i
$937$	1360.68			1.45216			0.726081	−	0.687609i	$-0.241340\pi$
$937$	1360.68			1.45216			0.726081	+	0.687609i	$0.241340\pi$
$938$	126.007	−	143.694i	0.134336	−	0.153192i
$939$	1011.39			1.07710
$940$		0			0
$941$	−146.671	−	84.6806i	−0.155867	−	0.0899900i	0.420038	−	0.907507i	$-0.362017\pi$
$941$	−146.671	−	84.6806i	−0.155867	−	0.0899900i	−0.575905	+	0.817517i	$0.695350\pi$
$942$	11.3144	+	6.53239i	0.0120111	+	0.00693459i
$943$	−239.941	−	415.590i	−0.254444	−	0.440710i
$944$		−	112.747i		−	0.119436i
$945$		0			0
$946$	−741.211			−0.783521
$947$	−1107.79	+	639.583i	−1.16979	+	0.675378i	−0.953630	−	0.300981i	$-0.902686\pi$
$947$	−1107.79	+	639.583i	−1.16979	+	0.675378i	−0.216158	+	0.976358i	$0.569353\pi$
$948$	156.024	−	270.242i	0.164583	−	0.285066i
$949$	1281.31	−	2219.29i	1.35016	−	2.33855i
$950$		0			0
$951$			625.964i			0.658216i
$952$	192.612	−	65.3904i	0.202324	−	0.0686874i
$953$			1.43779i			0.00150870i	1.00000		0.000754349i	$0.000240117\pi$
$953$			1.43779i			0.00150870i	−1.00000		0.000754349i	$0.999760\pi$
$954$	10.5019	+	18.1897i	0.0110082	+	0.0190668i
$955$		0			0
$956$	−121.009	+	209.594i	−0.126579	+	0.219241i
$957$	−178.902	−	309.868i	−0.186941	−	0.323791i
$958$	727.149			0.759028
$959$	781.012	−	265.148i	0.814402	−	0.276484i
$960$		0			0
$961$	320.176	+	554.560i	0.333169	+	0.577066i
$962$	−686.329	+	1188.76i	−0.713440	+	1.23571i
$963$	−427.524	−	246.831i	−0.443950	−	0.256314i
$964$	499.509	−	288.392i	0.518163	−	0.299162i
$965$		0			0
$966$	354.413	+	70.4844i	0.366887	+	0.0729653i
$967$			486.815i			0.503428i	0.967802	+	0.251714i	$0.0809942\pi$
$967$			486.815i			0.503428i	−0.967802	+	0.251714i	$0.919006\pi$
$968$	−9.51578	+	5.49394i	−0.00983035	+	0.00567556i
$969$	321.648	+	185.703i	0.331938	+	0.191644i
$970$		0			0
$971$	378.215	−	218.362i	0.389511	−	0.224884i	−0.292437	−	0.956285i	$-0.594466\pi$
$971$	378.215	−	218.362i	0.389511	−	0.224884i	0.681948	+	0.731401i	$0.261133\pi$
$972$	−31.1769			−0.0320750
$973$	834.227	+	731.547i	0.857376	+	0.751847i
$974$	462.910			0.475267
$975$		0			0
$976$	242.795	+	140.178i	0.248766	+	0.143625i
$977$	−220.866	−	127.517i	−0.226066	−	0.130519i	0.382690	−	0.923877i	$-0.374998\pi$
$977$	−220.866	−	127.517i	−0.226066	−	0.130519i	−0.608756	+	0.793358i	$0.708331\pi$
$978$	293.015	+	507.517i	0.299606	+	0.518934i
$979$			428.714i			0.437910i
$980$		0			0
$981$	237.030			0.241621
$982$	51.3032	−	29.6199i	0.0522436	−	0.0301628i
$983$	690.443	−	1195.88i	0.702383	−	1.21656i	−0.265244	−	0.964181i	$-0.585453\pi$
$983$	690.443	−	1195.88i	0.702383	−	1.21656i	0.967628	−	0.252383i	$-0.0812141\pi$
$984$	55.7765	−	96.6077i	0.0566834	−	0.0981785i
$985$		0			0
$986$		−	277.346i		−	0.281284i
$987$	−531.893	+	606.550i	−0.538899	+	0.614539i
$988$			804.464i			0.814234i
$989$	−510.328	−	883.914i	−0.516004	−	0.893745i
$990$		0			0
$991$	311.554	−	539.628i	0.314384	−	0.544528i	−0.664923	−	0.746912i	$-0.731535\pi$
$991$	311.554	−	539.628i	0.314384	−	0.544528i	0.979306	+	0.202384i	$0.0648688\pi$
$992$	−113.185	−	196.042i	−0.114098	−	0.197623i
$993$	512.662			0.516276
$994$	−95.5763	+	480.581i	−0.0961533	+	0.483482i
$995$		0			0
$996$	−175.015	−	303.135i	−0.175718	−	0.304353i
$997$	−280.158	+	485.248i	−0.281001	+	0.486708i	−0.971632	−	0.236499i	$-0.924000\pi$
$997$	−280.158	+	485.248i	−0.281001	+	0.486708i	0.690630	+	0.723208i	$0.257333\pi$
$998$	−508.723	−	293.711i	−0.509742	−	0.294300i
$999$	−226.644	+	130.853i	−0.226871	+	0.130984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.e.199.7		32
5.2	odd	4		1050.3.p.i.451.3		16
5.3	odd	4		210.3.o.b.31.5	✓	16
5.4	even	2	inner	1050.3.q.e.199.16		32
7.5	odd	6	inner	1050.3.q.e.649.16		32
15.8	even	4		630.3.v.c.451.3		16
35.3	even	12		1470.3.f.d.391.3		16
35.12	even	12		1050.3.p.i.901.3		16
35.18	odd	12		1470.3.f.d.391.5		16
35.19	odd	6	inner	1050.3.q.e.649.7		32
35.33	even	12		210.3.o.b.61.5	yes	16
105.68	odd	12		630.3.v.c.271.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.5	✓	16	5.3	odd	4
210.3.o.b.61.5	yes	16	35.33	even	12
630.3.v.c.271.3		16	105.68	odd	12
630.3.v.c.451.3		16	15.8	even	4
1050.3.p.i.451.3		16	5.2	odd	4
1050.3.p.i.901.3		16	35.12	even	12
1050.3.q.e.199.7		32	1.1	even	1	trivial
1050.3.q.e.199.16		32	5.4	even	2	inner
1050.3.q.e.649.7		32	35.19	odd	6	inner
1050.3.q.e.649.16		32	7.5	odd	6	inner
1470.3.f.d.391.3		16	35.3	even	12
1470.3.f.d.391.5		16	35.18	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(4.61524 - 5.26304i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(4.61524 - 5.26304i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.41099 - 9.37211i) q^{11} +(1.73205 + 3.00000i) q^{12} -19.2715 q^{13} +(-1.93096 + 9.70935i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(5.13686 - 8.89730i) q^{17} +(3.67423 + 2.12132i) q^{18} +(18.0756 - 10.4359i) q^{19} +(3.89764 + 11.4808i) q^{21} +15.3046i q^{22} +(-18.2511 + 10.5373i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(23.6026 - 13.6270i) q^{26} +5.19615 q^{27} +(-4.50061 - 13.2569i) q^{28} -19.0888 q^{29} +(-34.6556 - 20.0084i) q^{31} +(4.89898 + 2.82843i) q^{32} +(9.37211 + 16.2330i) q^{33} +14.5292i q^{34} -6.00000 q^{36} +(-43.6177 + 25.1827i) q^{37} +(-14.7586 + 25.5627i) q^{38} +(16.6896 - 28.9072i) q^{39} +22.7706i q^{41} +(-12.8918 - 11.3050i) q^{42} +48.4307i q^{43} +(-10.8220 - 18.7442i) q^{44} +(14.9020 - 25.8110i) q^{46} +(33.2690 + 57.6236i) q^{47} +6.92820 q^{48} +(-6.39913 - 48.5804i) q^{49} +(8.89730 + 15.4106i) q^{51} +(-19.2715 + 33.3792i) q^{52} +(4.28736 + 2.47531i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(14.8861 + 13.0539i) q^{56} +36.1511i q^{57} +(23.3789 - 13.4978i) q^{58} +(24.4105 + 14.0934i) q^{59} +(-60.6988 + 35.0445i) q^{61} +56.5924 q^{62} +(-20.5966 - 4.09619i) q^{63} -8.00000 q^{64} +(-22.9569 - 13.2542i) q^{66} +(-16.7193 - 9.65287i) q^{67} +(-10.2737 - 17.7946i) q^{68} -36.5023i q^{69} +49.4968 q^{71} +(7.34847 - 4.24264i) q^{72} +(-66.4872 + 115.159i) q^{73} +(35.6137 - 61.6848i) q^{74} -41.7437i q^{76} +(-24.3527 - 71.7328i) q^{77} +47.2053i q^{78} +(-45.0404 - 78.0122i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-16.1013 - 27.8882i) q^{82} -101.045 q^{83} +(23.7829 + 4.72987i) q^{84} +(-34.2456 - 59.3152i) q^{86} +(16.5314 - 28.6332i) q^{87} +(26.5083 + 15.3046i) q^{88} +(-34.3077 + 19.8075i) q^{89} +(-88.9425 + 101.427i) q^{91} +42.1492i q^{92} +(60.0253 - 34.6556i) q^{93} +(-81.4920 - 47.0495i) q^{94} +(-8.48528 + 4.89898i) q^{96} -68.6944 q^{97} +(42.1888 + 54.9737i) q^{98} -32.4659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 48 * q^9	\( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

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