LMFDB - Embedded newform 1050.3.p.f.451.2

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			451.2
Root			$-5.81071 + 4.13641i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.f.901.2

$q$-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} +(1.88399 - 6.74171i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.65702 - 2.87005i) q^{11} +(-3.00000 + 1.73205i) q^{12} +19.5077i q^{13} +(-9.58905 + 2.45970i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(7.30003 + 4.21467i) q^{17} +(2.12132 - 3.67423i) q^{18} +(0.704670 - 0.406841i) q^{19} +(8.66447 - 8.48098i) q^{21} -4.68677 q^{22} +(5.98556 + 10.3673i) q^{23} +(4.24264 + 2.44949i) q^{24} +(23.8919 - 13.7940i) q^{26} +5.19615i q^{27} +(9.79299 + 10.0049i) q^{28} +4.68677 q^{29} +(27.9363 + 16.1291i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(4.97107 - 2.87005i) q^{33} -11.9209i q^{34} -6.00000 q^{36} +(-3.01293 - 5.21854i) q^{37} +(-0.996554 - 0.575361i) q^{38} +(-16.8942 + 29.2615i) q^{39} -19.6861i q^{41} +(-16.5137 - 4.61481i) q^{42} -2.53339 q^{43} +(3.31404 + 5.74009i) q^{44} +(8.46486 - 14.6616i) q^{46} +(-15.8328 + 9.14110i) q^{47} -6.92820i q^{48} +(-41.9012 - 25.4026i) q^{49} +(7.30003 + 12.6440i) q^{51} +(-33.7883 - 19.5077i) q^{52} +(15.9837 - 27.6846i) q^{53} +(6.36396 - 3.67423i) q^{54} +(5.32872 - 19.0684i) q^{56} +1.40934 q^{57} +(-3.31404 - 5.74009i) q^{58} +(64.3758 + 37.1674i) q^{59} +(95.1577 - 54.9393i) q^{61} -45.6199i q^{62} +(20.3414 - 5.21781i) q^{63} +8.00000 q^{64} +(-7.03015 - 4.05886i) q^{66} +(-47.3405 + 81.9962i) q^{67} +(-14.6001 + 8.42935i) q^{68} +20.7346i q^{69} +98.0047 q^{71} +(4.24264 + 7.34847i) q^{72} +(-9.62690 - 5.55809i) q^{73} +(-4.26092 + 7.38013i) q^{74} +1.62737i q^{76} +(-16.2272 - 16.5783i) q^{77} +47.7839 q^{78} +(-0.500763 - 0.867346i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-24.1105 + 13.9202i) q^{82} +66.8044i q^{83} +(6.02501 + 23.4883i) q^{84} +(1.79138 + 3.10276i) q^{86} +(7.03015 + 4.05886i) q^{87} +(4.68677 - 8.11772i) q^{88} +(133.528 - 77.0927i) q^{89} +(131.515 + 36.7523i) q^{91} -23.9422 q^{92} +(27.9363 + 48.3872i) q^{93} +(22.3910 + 12.9275i) q^{94} +(-8.48528 + 4.89898i) q^{96} +132.023i q^{97} +(-1.48309 + 69.2806i) q^{98} +9.94213 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
$7$	1.88399	−	6.74171i	0.269141	−	0.963101i
$7$	1.88399	−	6.74171i	0.269141	−	0.963101i
$8$	2.82843			0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	1.65702	−	2.87005i	0.150638	−	0.260913i	−0.780824	−	0.624751i	$-0.785200\pi$
$11$	1.65702	−	2.87005i	0.150638	−	0.260913i	0.931462	+	0.363838i	$0.118534\pi$
$12$	−3.00000	+	1.73205i	−0.250000	+	0.144338i
$13$			19.5077i			1.50059i	0.661103	+	0.750296i	$0.270089\pi$
$13$			19.5077i			1.50059i	−0.661103	+	0.750296i	$0.729911\pi$
$14$	−9.58905	+	2.45970i	−0.684932	+	0.175693i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	7.30003	+	4.21467i	0.429414	+	0.247922i	0.699097	−	0.715027i	$-0.253586\pi$
$17$	7.30003	+	4.21467i	0.429414	+	0.247922i	−0.269683	+	0.962949i	$0.586919\pi$
$18$	2.12132	−	3.67423i	0.117851	−	0.204124i
$19$	0.704670	−	0.406841i	0.0370879	−	0.0214127i	−0.481341	−	0.876533i	$-0.659850\pi$
$19$	0.704670	−	0.406841i	0.0370879	−	0.0214127i	0.518429	+	0.855120i	$0.326517\pi$
$20$		0			0
$21$	8.66447	−	8.48098i	0.412594	−	0.403856i
$22$	−4.68677			−0.213035
$23$	5.98556	+	10.3673i	0.260242	+	0.450752i	0.966306	−	0.257396i	$-0.0828644\pi$
$23$	5.98556	+	10.3673i	0.260242	+	0.450752i	−0.706064	+	0.708148i	$0.749531\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	23.8919	−	13.7940i	0.918921	−	0.530539i
$27$			5.19615i			0.192450i
$28$	9.79299	+	10.0049i	0.349750	+	0.357317i
$29$	4.68677			0.161613			0.0808063	−	0.996730i	$-0.474250\pi$
$29$	4.68677			0.161613			0.0808063	+	0.996730i	$0.474250\pi$
$30$		0			0
$31$	27.9363	+	16.1291i	0.901172	+	0.520292i	0.877580	−	0.479430i	$-0.159156\pi$
$31$	27.9363	+	16.1291i	0.901172	+	0.520292i	0.0235920	+	0.999722i	$0.492490\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	4.97107	−	2.87005i	0.150638	−	0.0869711i
$34$		−	11.9209i		−	0.350615i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−3.01293	−	5.21854i	−0.0814304	−	0.141042i	0.822434	−	0.568860i	$-0.192616\pi$
$37$	−3.01293	−	5.21854i	−0.0814304	−	0.141042i	−0.903865	+	0.427819i	$0.859282\pi$
$38$	−0.996554	−	0.575361i	−0.0262251	−	0.0151411i
$39$	−16.8942	+	29.2615i	−0.433183	+	0.750296i
$40$		0			0
$41$		−	19.6861i		−	0.480150i	−0.970754	−	0.240075i	$-0.922828\pi$
$41$		−	19.6861i		−	0.480150i	0.970754	−	0.240075i	$-0.0771720\pi$
$42$	−16.5137	−	4.61481i	−0.393184	−	0.109876i
$43$	−2.53339			−0.0589160			−0.0294580	−	0.999566i	$-0.509378\pi$
$43$	−2.53339			−0.0589160			−0.0294580	+	0.999566i	$0.509378\pi$
$44$	3.31404	+	5.74009i	0.0753192	+	0.130457i
$45$		0			0
$46$	8.46486	−	14.6616i	0.184019	−	0.318730i
$47$	−15.8328	+	9.14110i	−0.336869	+	0.194491i	−0.658887	−	0.752242i	$-0.728972\pi$
$47$	−15.8328	+	9.14110i	−0.336869	+	0.194491i	0.322018	+	0.946734i	$0.395639\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−41.9012	−	25.4026i	−0.855126	−	0.518420i
$50$		0			0
$51$	7.30003	+	12.6440i	0.143138	+	0.247922i
$52$	−33.7883	−	19.5077i	−0.649775	−	0.375148i
$53$	15.9837	−	27.6846i	0.301580	−	0.522351i	−0.674914	−	0.737896i	$-0.735819\pi$
$53$	15.9837	−	27.6846i	0.301580	−	0.522351i	0.976494	+	0.215545i	$0.0691528\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	5.32872	−	19.0684i	0.0951558	−	0.340508i
$57$	1.40934			0.0247253
$58$	−3.31404	−	5.74009i	−0.0571387	−	0.0989671i
$59$	64.3758	+	37.1674i	1.09111	+	0.629956i	0.933873	−	0.357605i	$-0.116406\pi$
$59$	64.3758	+	37.1674i	1.09111	+	0.629956i	0.157242	+	0.987560i	$0.449740\pi$
$60$		0			0
$61$	95.1577	−	54.9393i	1.55996	−	0.900645i	0.562704	−	0.826659i	$-0.309761\pi$
$61$	95.1577	−	54.9393i	1.55996	−	0.900645i	0.997259	−	0.0739862i	$-0.0235721\pi$
$62$		−	45.6199i		−	0.735804i
$63$	20.3414	−	5.21781i	0.322880	−	0.0828224i
$64$	8.00000			0.125000
$65$		0			0
$66$	−7.03015	−	4.05886i	−0.106517	−	0.0614979i
$67$	−47.3405	+	81.9962i	−0.706575	+	1.22382i	0.259545	+	0.965731i	$0.416428\pi$
$67$	−47.3405	+	81.9962i	−0.706575	+	1.22382i	−0.966120	+	0.258093i	$0.916906\pi$
$68$	−14.6001	+	8.42935i	−0.214707	+	0.123961i
$69$			20.7346i			0.300501i
$70$		0			0
$71$	98.0047			1.38035			0.690174	−	0.723643i	$-0.257534\pi$
$71$	98.0047			1.38035			0.690174	+	0.723643i	$0.257534\pi$
$72$	4.24264	+	7.34847i	0.0589256	+	0.102062i
$73$	−9.62690	−	5.55809i	−0.131875	−	0.0761383i	0.432611	−	0.901581i	$-0.357592\pi$
$73$	−9.62690	−	5.55809i	−0.131875	−	0.0761383i	−0.564486	+	0.825442i	$0.690926\pi$
$74$	−4.26092	+	7.38013i	−0.0575800	+	0.0997315i
$75$		0			0
$76$			1.62737i			0.0214127i
$77$	−16.2272	−	16.5783i	−0.210743	−	0.215302i
$78$	47.7839			0.612614
$79$	−0.500763	−	0.867346i	−0.00633877	−	0.0109791i	0.862839	−	0.505479i	$-0.168684\pi$
$79$	−0.500763	−	0.867346i	−0.00633877	−	0.0109791i	−0.869177	+	0.494500i	$0.835351\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−24.1105	+	13.9202i	−0.294031	+	0.169759i
$83$			66.8044i			0.804872i	0.915448	+	0.402436i	$0.131836\pi$
$83$			66.8044i			0.804872i	−0.915448	+	0.402436i	$0.868164\pi$
$84$	6.02501	+	23.4883i	0.0717263	+	0.279622i
$85$		0			0
$86$	1.79138	+	3.10276i	0.0208300	+	0.0360786i
$87$	7.03015	+	4.05886i	0.0808063	+	0.0466536i
$88$	4.68677	−	8.11772i	0.0532587	−	0.0922468i
$89$	133.528	−	77.0927i	1.50032	−	0.866210i	0.500319	−	0.865841i	$-0.333216\pi$
$89$	133.528	−	77.0927i	1.50032	−	0.866210i	1.00000		0.000368641i	$-0.000117342\pi$
$90$		0			0
$91$	131.515	+	36.7523i	1.44522	+	0.403871i
$92$	−23.9422			−0.260242
$93$	27.9363	+	48.3872i	0.300391	+	0.520292i
$94$	22.3910	+	12.9275i	0.238202	+	0.137526i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$			132.023i			1.36107i	0.732717	+	0.680533i	$0.238252\pi$
$97$			132.023i			1.36107i	−0.732717	+	0.680533i	$0.761748\pi$
$98$	−1.48309	+	69.2806i	−0.0151336	+	0.706945i
$99$	9.94213			0.100426
$100$		0			0
$101$	−15.3107	−	8.83965i	−0.151591	−	0.0875213i	0.422286	−	0.906463i	$-0.361228\pi$
$101$	−15.3107	−	8.83965i	−0.151591	−	0.0875213i	−0.573877	+	0.818942i	$0.694561\pi$
$102$	10.3238	−	17.8813i	0.101214	−	0.175307i
$103$	33.9450	−	19.5981i	0.329563	−	0.190273i	−0.326084	−	0.945341i	$-0.605729\pi$
$103$	33.9450	−	19.5981i	0.329563	−	0.190273i	0.655647	+	0.755067i	$0.272396\pi$
$104$			55.1761i			0.530539i
$105$		0			0
$106$	−45.2088			−0.426498
$107$	66.5000	+	115.181i	0.621495	+	1.07646i	0.989207	+	0.146522i	$0.0468078\pi$
$107$	66.5000	+	115.181i	0.621495	+	1.07646i	−0.367712	+	0.929940i	$0.619859\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	24.5640	−	42.5461i	0.225358	−	0.390332i	−0.731069	−	0.682304i	$-0.760978\pi$
$109$	24.5640	−	42.5461i	0.225358	−	0.390332i	0.956427	+	0.291972i	$0.0943115\pi$
$110$		0			0
$111$		−	10.4371i		−	0.0940278i
$112$	−27.1219	+	6.95708i	−0.242160	+	0.0621168i
$113$	141.909			1.25583			0.627915	−	0.778282i	$-0.283908\pi$
$113$	141.909			1.25583			0.627915	+	0.778282i	$0.283908\pi$
$114$	−0.996554	−	1.72608i	−0.00874170	−	0.0151411i
$115$		0			0
$116$	−4.68677	+	8.11772i	−0.0404032	+	0.0699803i
$117$	−50.6825	+	29.2615i	−0.433183	+	0.250099i
$118$		−	105.125i		−	0.890892i
$119$	42.1673	−	41.2742i	0.354347	−	0.346842i
$120$		0			0
$121$	55.0086	+	95.2776i	0.454616	+	0.787418i
$122$	−134.573	−	77.6960i	−1.10306	−	0.636852i
$123$	17.0487	−	29.5292i	0.138607	−	0.240075i
$124$	−55.8727	+	32.2581i	−0.450586	+	0.260146i
$125$		0			0
$126$	−20.7741	−	21.2235i	−0.164874	−	0.168441i
$127$	−87.2663			−0.687137			−0.343568	−	0.939128i	$-0.611636\pi$
$127$	−87.2663			−0.687137			−0.343568	+	0.939128i	$0.611636\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	−3.80008	−	2.19398i	−0.0294580	−	0.0170076i
$130$		0			0
$131$	95.2814	−	55.0107i	0.727339	−	0.419929i	−0.0901091	−	0.995932i	$-0.528722\pi$
$131$	95.2814	−	55.0107i	0.727339	−	0.419929i	0.817448	+	0.576003i	$0.195388\pi$
$132$			11.4802i			0.0869711i
$133$	−1.41521	−	5.51716i	−0.0106407	−	0.0414824i
$134$	133.899			0.999248
$135$		0			0
$136$	20.6476	+	11.9209i	0.151821	+	0.0876537i
$137$	68.8331	−	119.222i	0.502431	−	0.870237i	−0.497565	−	0.867427i	$-0.665772\pi$
$137$	68.8331	−	119.222i	0.502431	−	0.870237i	0.999996	−	0.00280972i	$-0.000894362\pi$
$138$	25.3946	−	14.6616i	0.184019	−	0.106243i
$139$			68.6829i			0.494122i	0.969000	+	0.247061i	$0.0794648\pi$
$139$			68.6829i			0.494122i	−0.969000	+	0.247061i	$0.920535\pi$
$140$		0			0
$141$	−31.6657			−0.224579
$142$	−69.2998	−	120.031i	−0.488027	−	0.845287i
$143$	55.9880	+	32.3247i	0.391524	+	0.226047i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$			15.7207i			0.107676i
$147$	−40.8525	−	74.3914i	−0.277908	−	0.506064i
$148$	12.0517			0.0814304
$149$	−91.7993	−	159.001i	−0.616102	−	1.06712i	−0.990190	−	0.139727i	$-0.955377\pi$
$149$	−91.7993	−	159.001i	−0.616102	−	1.06712i	0.374088	−	0.927393i	$-0.377956\pi$
$150$		0			0
$151$	−70.7469	+	122.537i	−0.468523	+	0.811505i	−0.999353	−	0.0359734i	$-0.988547\pi$
$151$	−70.7469	+	122.537i	−0.468523	+	0.811505i	0.530830	+	0.847478i	$0.321880\pi$
$152$	1.99311	−	1.15072i	0.0131126	−	0.00757054i
$153$			25.2880i			0.165281i
$154$	−8.82982	+	31.5968i	−0.0573365	+	0.205174i
$155$		0			0
$156$	−33.7883	−	58.5231i	−0.216592	−	0.375148i
$157$	−148.618	−	85.8044i	−0.946609	−	0.546525i	−0.0545830	−	0.998509i	$-0.517383\pi$
$157$	−148.618	−	85.8044i	−0.946609	−	0.546525i	−0.892026	+	0.451984i	$0.850716\pi$
$158$	−0.708185	+	1.22661i	−0.00448219	+	0.00776337i
$159$	47.9511	−	27.6846i	0.301580	−	0.174117i
$160$		0			0
$161$	81.1699	−	20.8210i	0.504161	−	0.129323i
$162$	12.7279			0.0785674
$163$	−147.728	−	255.872i	−0.906306	−	1.56977i	−0.819154	−	0.573573i	$-0.805557\pi$
$163$	−147.728	−	255.872i	−0.906306	−	1.56977i	−0.0871517	−	0.996195i	$-0.527776\pi$
$164$	34.0974	+	19.6861i	0.207911	+	0.120037i
$165$		0			0
$166$	81.8183	−	47.2378i	0.492882	−	0.284565i
$167$			168.538i			1.00921i	0.863351	+	0.504604i	$0.168361\pi$
$167$			168.538i			1.00921i	−0.863351	+	0.504604i	$0.831639\pi$
$168$	24.5068	−	23.9878i	0.145874	−	0.142785i
$169$	−211.550			−1.25177
$170$		0			0
$171$	2.11401	+	1.22052i	0.0123626	+	0.00713757i
$172$	2.53339	−	4.38796i	0.0147290	−	0.0255114i
$173$	129.098	−	74.5349i	0.746232	−	0.430838i	−0.0780985	−	0.996946i	$-0.524885\pi$
$173$	129.098	−	74.5349i	0.746232	−	0.430838i	0.824331	+	0.566108i	$0.191552\pi$
$174$		−	11.4802i		−	0.0659781i
$175$		0			0
$176$	−13.2562			−0.0753192
$177$	64.3758	+	111.502i	0.363705	+	0.629956i
$178$	−188.838	−	109.025i	−1.06089	−	0.612503i
$179$	141.413	−	244.935i	0.790018	−	1.36835i	−0.135937	−	0.990718i	$-0.543404\pi$
$179$	141.413	−	244.935i	0.790018	−	1.36835i	0.925955	−	0.377634i	$-0.123262\pi$
$180$		0			0
$181$			305.418i			1.68739i	0.536820	+	0.843697i	$0.319625\pi$
$181$			305.418i			1.68739i	−0.536820	+	0.843697i	$0.680375\pi$
$182$	−47.9831	−	187.060i	−0.263643	−	1.02780i
$183$	190.315			1.03998
$184$	16.9297	+	29.3231i	0.0920093	+	0.159365i
$185$		0			0
$186$	39.5080	−	68.4298i	0.212408	−	0.367902i
$187$	24.1926	−	13.9676i	0.129372	−	0.0746931i
$188$		−	36.5644i		−	0.194491i
$189$	35.0309	+	9.78949i	0.185349	+	0.0517963i
$190$		0			0
$191$	−24.3372	−	42.1533i	−0.127420	−	0.220698i	0.795256	−	0.606273i	$-0.207336\pi$
$191$	−24.3372	−	42.1533i	−0.127420	−	0.220698i	−0.922676	+	0.385576i	$0.874003\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	−74.7666	+	129.500i	−0.387392	+	0.670982i	−0.992098	−	0.125467i	$-0.959957\pi$
$193$	−74.7666	+	129.500i	−0.387392	+	0.670982i	0.604706	+	0.796449i	$0.293291\pi$
$194$	161.695	−	93.3547i	0.833479	−	0.481210i
$195$		0			0
$196$	85.8998	−	47.1724i	0.438264	−	0.240675i
$197$	219.479			1.11411			0.557053	−	0.830477i	$-0.311932\pi$
$197$	219.479			1.11411			0.557053	+	0.830477i	$0.311932\pi$
$198$	−7.03015	−	12.1766i	−0.0355058	−	0.0614979i
$199$	−254.396	−	146.875i	−1.27837	−	0.738067i	−0.301821	−	0.953365i	$-0.597595\pi$
$199$	−254.396	−	146.875i	−1.27837	−	0.738067i	−0.976548	+	0.215298i	$0.930928\pi$
$200$		0			0
$201$	−142.022	+	81.9962i	−0.706575	+	0.407941i
$202$			25.0023i			0.123774i
$203$	8.82982	−	31.5968i	0.0434966	−	0.155649i
$204$	−29.2001			−0.143138
$205$		0			0
$206$	−48.0055	−	27.7160i	−0.233036	−	0.134544i
$207$	−17.9567	+	31.1019i	−0.0867472	+	0.150251i
$208$	67.5766	−	39.0154i	0.324888	−	0.187574i
$209$		−	2.69658i		−	0.0129023i
$210$		0			0
$211$	122.768			0.581841			0.290920	−	0.956747i	$-0.406039\pi$
$211$	122.768			0.581841			0.290920	+	0.956747i	$0.406039\pi$
$212$	31.9674	+	55.3692i	0.150790	+	0.261176i
$213$	147.007	+	84.8746i	0.690174	+	0.398472i
$214$	94.0452	−	162.891i	0.439463	−	0.761173i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	161.369	−	157.952i	0.743636	−	0.727888i
$218$	−69.4776			−0.318704
$219$	−9.62690	−	16.6743i	−0.0439585	−	0.0761383i
$220$		0			0
$221$	−82.2185	+	142.407i	−0.372030	+	0.644374i
$222$	−12.7828	+	7.38013i	−0.0575800	+	0.0332438i
$223$		−	3.70845i		−	0.0166298i	−0.999965	−	0.00831491i	$-0.997353\pi$
$223$		−	3.70845i		−	0.0166298i	0.999965	−	0.00831491i	$-0.00264675\pi$
$224$	27.6988	+	28.2980i	0.123655	+	0.126331i
$225$		0			0
$226$	−100.345	−	173.802i	−0.444003	−	0.769036i
$227$	131.877	+	76.1393i	0.580957	+	0.335416i	0.761514	−	0.648149i	$-0.224457\pi$
$227$	131.877	+	76.1393i	0.580957	+	0.335416i	−0.180557	+	0.983565i	$0.557790\pi$
$228$	−1.40934	+	2.44105i	−0.00618132	+	0.0107064i
$229$	−123.917	+	71.5435i	−0.541123	+	0.312417i	−0.745534	−	0.666468i	$-0.767805\pi$
$229$	−123.917	+	71.5435i	−0.541123	+	0.312417i	0.204411	+	0.978885i	$0.434472\pi$
$230$		0			0
$231$	−9.98358	−	38.9206i	−0.0432189	−	0.168487i
$232$	13.2562			0.0571387
$233$	−35.9752	−	62.3109i	−0.154400	−	0.267429i	0.778440	−	0.627719i	$-0.216011\pi$
$233$	−35.9752	−	62.3109i	−0.154400	−	0.267429i	−0.932840	+	0.360290i	$0.882678\pi$
$234$	71.6758	+	41.3820i	0.306307	+	0.176846i
$235$		0			0
$236$	−128.752	+	74.3347i	−0.545557	+	0.314978i
$237$		−	1.73469i		−	0.00731938i
$238$	−80.3672	−	22.4588i	−0.337677	−	0.0943649i
$239$	−453.719			−1.89840			−0.949202	−	0.314667i	$-0.898107\pi$
$239$	−453.719			−1.89840			−0.949202	+	0.314667i	$0.898107\pi$
$240$		0			0
$241$	−163.281	−	94.2706i	−0.677516	−	0.391164i	0.121402	−	0.992603i	$-0.461261\pi$
$241$	−163.281	−	94.2706i	−0.677516	−	0.391164i	−0.798919	+	0.601439i	$0.794594\pi$
$242$	77.7938	−	134.743i	0.321462	−	0.556789i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			219.757i			0.900645i
$245$		0			0
$246$	−48.2210			−0.196020
$247$	7.93653	+	13.7465i	0.0321317	+	0.0556538i
$248$	79.0159	+	45.6199i	0.318613	+	0.183951i
$249$	−57.8543	+	100.207i	−0.232347	+	0.402436i
$250$		0			0
$251$		−	233.911i		−	0.931917i	−0.884807	−	0.465958i	$-0.845710\pi$
$251$		−	233.911i		−	0.931917i	0.884807	−	0.465958i	$-0.154290\pi$
$252$	−11.3039	+	40.4502i	−0.0448569	+	0.160517i
$253$	39.6728			0.156810
$254$	61.7066	+	106.879i	0.242939	+	0.420783i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	162.902	−	94.0516i	0.633861	−	0.365960i	−0.148385	−	0.988930i	$-0.547408\pi$
$257$	162.902	−	94.0516i	0.633861	−	0.365960i	0.782246	+	0.622970i	$0.214074\pi$
$258$			6.20551i			0.0240524i
$259$	−40.8582	+	10.4806i	−0.157754	+	0.0404656i
$260$		0			0
$261$	7.03015	+	12.1766i	0.0269354	+	0.0466536i
$262$	−134.748	−	77.7969i	−0.514306	−	0.296935i
$263$	−169.290	+	293.219i	−0.643688	+	1.11490i	0.340915	+	0.940094i	$0.389263\pi$
$263$	−169.290	+	293.219i	−0.643688	+	1.11490i	−0.984603	+	0.174806i	$0.944070\pi$
$264$	14.0603	−	8.11772i	0.0532587	−	0.0307489i
$265$		0			0
$266$	−5.75641	+	5.63450i	−0.0216406	+	0.0211823i
$267$	267.057			1.00021
$268$	−94.6811	−	163.992i	−0.353288	−	0.611912i
$269$	453.034	+	261.559i	1.68414	+	0.972340i	0.958856	+	0.283893i	$0.0916259\pi$
$269$	453.034	+	261.559i	1.68414	+	0.972340i	0.725286	+	0.688448i	$0.241707\pi$
$270$		0			0
$271$	385.799	−	222.741i	1.42361	−	0.821923i	0.427006	−	0.904249i	$-0.359568\pi$
$271$	385.799	−	222.741i	1.42361	−	0.821923i	0.996605	+	0.0823259i	$0.0262348\pi$
$272$		−	33.7174i		−	0.123961i
$273$	165.444	+	169.024i	0.606023	+	0.619135i
$274$	−194.689			−0.710545
$275$		0			0
$276$	−35.9133	−	20.7346i	−0.130121	−	0.0751253i
$277$	−7.26684	+	12.5865i	−0.0262341	+	0.0454388i	−0.878844	−	0.477109i	$-0.841685\pi$
$277$	−7.26684	+	12.5865i	−0.0262341	+	0.0454388i	0.852610	+	0.522547i	$0.175018\pi$
$278$	84.1191	−	48.5662i	0.302587	−	0.174698i
$279$			96.7743i			0.346861i
$280$		0			0
$281$	−526.257			−1.87280			−0.936400	−	0.350933i	$-0.885864\pi$
$281$	−526.257			−1.87280			−0.936400	+	0.350933i	$0.885864\pi$
$282$	22.3910	+	38.7824i	0.0794008	+	0.137526i
$283$	−436.617	−	252.081i	−1.54282	−	0.890746i	−0.998659	−	0.0517626i	$-0.983516\pi$
$283$	−436.617	−	252.081i	−1.54282	−	0.890746i	−0.544157	−	0.838983i	$-0.683151\pi$
$284$	−98.0047	+	169.749i	−0.345087	+	0.597708i
$285$		0			0
$286$		−	91.4280i		−	0.319678i
$287$	−132.718	−	37.0885i	−0.462433	−	0.129228i
$288$	−16.9706			−0.0589256
$289$	−108.973	−	188.747i	−0.377069	−	0.653103i
$290$		0			0
$291$	−114.336	+	198.035i	−0.392906	+	0.680533i
$292$	19.2538	−	11.1162i	0.0659377	−	0.0380691i
$293$			220.145i			0.751348i	0.926752	+	0.375674i	$0.122589\pi$
$293$			220.145i			0.751348i	−0.926752	+	0.375674i	$0.877411\pi$
$294$	−62.2234	+	102.636i	−0.211644	+	0.349104i
$295$		0			0
$296$	−8.52184	−	14.7603i	−0.0287900	−	0.0498657i
$297$	14.9132	+	8.61014i	0.0502128	+	0.0289904i
$298$	−129.824	+	224.861i	−0.435650	+	0.754568i
$299$	−202.242	+	116.764i	−0.676394	+	0.390516i
$300$		0			0
$301$	−4.77288	+	17.0794i	−0.0158567	+	0.0567421i
$302$	200.102			0.662591
$303$	−15.3107	−	26.5190i	−0.0505305	−	0.0875213i
$304$	−2.81868	−	1.62737i	−0.00927197	−	0.00535318i
$305$		0			0
$306$	30.9714	−	17.8813i	0.101214	−	0.0584358i
$307$		−	183.623i		−	0.598120i	−0.954234	−	0.299060i	$-0.903327\pi$
$307$		−	183.623i		−	0.598120i	0.954234	−	0.299060i	$-0.0966731\pi$
$308$	44.9416	−	11.5280i	0.145914	−	0.0374287i
$309$	67.8900			0.219709
$310$		0			0
$311$	−195.658	−	112.963i	−0.629126	−	0.363226i	0.151288	−	0.988490i	$-0.451658\pi$
$311$	−195.658	−	112.963i	−0.629126	−	0.363226i	−0.780414	+	0.625264i	$0.784991\pi$
$312$	−47.7839	+	82.7641i	−0.153153	+	0.265270i
$313$	−231.701	+	133.773i	−0.740258	+	0.427388i	−0.822163	−	0.569252i	$-0.807233\pi$
$313$	−231.701	+	133.773i	−0.740258	+	0.427388i	0.0819050	+	0.996640i	$0.473900\pi$
$314$			242.692i			0.772903i
$315$		0			0
$316$	2.00305			0.00633877
$317$	264.896	+	458.814i	0.835635	+	1.44736i	0.893513	+	0.449038i	$0.148233\pi$
$317$	264.896	+	458.814i	0.835635	+	1.44736i	−0.0578777	+	0.998324i	$0.518433\pi$
$318$	−67.8132	−	39.1519i	−0.213249	−	0.123119i
$319$	7.76608	−	13.4512i	0.0243451	−	0.0421669i
$320$		0			0
$321$			230.363i			0.717641i
$322$	−82.8962	−	84.6898i	−0.257442	−	0.263012i
$323$	6.85882			0.0212347
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−208.919	+	361.858i	−0.640855	+	1.10999i
$327$	73.6921	−	42.5461i	0.225358	−	0.130111i
$328$		−	55.6808i		−	0.169759i
$329$	31.7977	+	123.962i	0.0966495	+	0.376784i
$330$		0			0
$331$	102.815	+	178.081i	0.310619	+	0.538008i	0.978497	−	0.206263i	$-0.0661302\pi$
$331$	102.815	+	178.081i	0.310619	+	0.538008i	−0.667877	+	0.744271i	$0.732797\pi$
$332$	−115.709	−	66.8044i	−0.348520	−	0.201218i
$333$	9.03878	−	15.6556i	0.0271435	−	0.0470139i
$334$	206.416	−	119.174i	0.618011	−	0.356809i
$335$		0			0
$336$	−46.7079	−	13.0527i	−0.139012	−	0.0388472i
$337$	333.809			0.990530			0.495265	−	0.868742i	$-0.335071\pi$
$337$	333.809			0.990530			0.495265	+	0.868742i	$0.335071\pi$
$338$	149.588	+	259.094i	0.442569	+	0.766552i
$339$	212.863	+	122.897i	0.627915	+	0.362527i
$340$		0			0
$341$	92.5823	−	53.4524i	0.271502	−	0.156752i
$342$		−	3.45216i		−	0.0100940i
$343$	−250.198	+	234.627i	−0.729441	+	0.684044i
$344$	−7.16551			−0.0208300
$345$		0			0
$346$	−182.572	−	105.408i	−0.527666	−	0.304648i
$347$	−326.532	+	565.569i	−0.941013	+	1.62988i	−0.177470	+	0.984126i	$0.556791\pi$
$347$	−326.532	+	565.569i	−0.941013	+	1.62988i	−0.763543	+	0.645757i	$0.776542\pi$
$348$	−14.0603	+	8.11772i	−0.0404032	+	0.0233268i
$349$		−	244.056i		−	0.699301i	−0.936880	−	0.349651i	$-0.886300\pi$
$349$		−	244.056i		−	0.699301i	0.936880	−	0.349651i	$-0.113700\pi$
$350$		0			0
$351$	−101.365			−0.288789
$352$	9.37353	+	16.2354i	0.0266294	+	0.0461234i
$353$	−361.582	−	208.759i	−1.02431	−	0.591387i	−0.108962	−	0.994046i	$-0.534753\pi$
$353$	−361.582	−	208.759i	−1.02431	−	0.591387i	−0.915350	+	0.402659i	$0.868086\pi$
$354$	91.0411	−	157.688i	0.257178	−	0.445446i
$355$		0			0
$356$			308.371i			0.866210i
$357$	98.9954	−	25.3935i	0.277298	−	0.0711301i
$358$	−399.977			−1.11725
$359$	−147.477	−	255.438i	−0.410800	−	0.711527i	0.584177	−	0.811626i	$-0.301417\pi$
$359$	−147.477	−	255.438i	−0.410800	−	0.711527i	−0.994977	+	0.100099i	$0.968084\pi$
$360$		0			0
$361$	−180.169	+	312.062i	−0.499083	+	0.864437i
$362$	374.059	−	215.963i	1.03331	−	0.596584i
$363$			190.555i			0.524946i
$364$	−195.172	+	191.039i	−0.536186	+	0.524831i
$365$		0			0
$366$	−134.573	−	233.088i	−0.367687	−	0.636852i
$367$	−20.4635	−	11.8146i	−0.0557589	−	0.0321924i	0.471861	−	0.881673i	$-0.343582\pi$
$367$	−20.4635	−	11.8146i	−0.0557589	−	0.0321924i	−0.527620	+	0.849480i	$0.676916\pi$
$368$	23.9422	−	41.4692i	0.0650604	−	0.112688i
$369$	51.1461	−	29.5292i	0.138607	−	0.0800250i
$370$		0			0
$371$	−156.528	−	159.915i	−0.421909	−	0.431038i
$372$	−111.745			−0.300391
$373$	−82.9807	−	143.727i	−0.222468	−	0.385326i	0.733089	−	0.680133i	$-0.238078\pi$
$373$	−82.9807	−	143.727i	−0.222468	−	0.385326i	−0.955557	+	0.294807i	$0.904745\pi$
$374$	−34.2135	−	19.7532i	−0.0914800	−	0.0528160i
$375$		0			0
$376$	−44.7820	+	25.8549i	−0.119101	+	0.0687631i
$377$			91.4280i			0.242515i
$378$	−12.7810	−	49.8262i	−0.0338121	−	0.131815i
$379$	−456.876			−1.20548			−0.602739	−	0.797938i	$-0.705924\pi$
$379$	−456.876			−1.20548			−0.602739	+	0.797938i	$0.705924\pi$
$380$		0			0
$381$	−130.900	−	75.5749i	−0.343568	−	0.198359i
$382$	−34.4180	+	59.6137i	−0.0900995	+	0.156057i
$383$	5.78050	−	3.33737i	0.0150927	−	0.00871377i	−0.492435	−	0.870349i	$-0.663893\pi$
$383$	5.78050	−	3.33737i	0.0150927	−	0.00871377i	0.507527	+	0.861636i	$0.330560\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	211.472			0.547855
$387$	−3.80008	−	6.58194i	−0.00981934	−	0.0170076i
$388$	−228.671	−	132.023i	−0.589359	−	0.340267i
$389$	−106.375	+	184.246i	−0.273456	+	0.473640i	−0.969745	−	0.244122i	$-0.921500\pi$
$389$	−106.375	+	184.246i	−0.273456	+	0.473640i	0.696288	+	0.717762i	$0.254834\pi$
$390$		0			0
$391$			100.909i			0.258079i
$392$	−118.514	−	71.8494i	−0.302333	−	0.183289i
$393$	190.563			0.484892
$394$	−155.195	−	268.806i	−0.393896	−	0.682248i
$395$		0			0
$396$	−9.94213	+	17.2203i	−0.0251064	+	0.0434856i
$397$	−219.812	+	126.909i	−0.553684	+	0.319669i	−0.750606	−	0.660750i	$-0.770238\pi$
$397$	−219.812	+	126.909i	−0.553684	+	0.319669i	0.196923	+	0.980419i	$0.436905\pi$
$398$			415.426i			1.04378i
$399$	2.65518	−	9.50135i	0.00665459	−	0.0238129i
$400$		0			0
$401$	−275.993	−	478.033i	−0.688261	−	1.19210i	−0.972400	−	0.233319i	$-0.925041\pi$
$401$	−275.993	−	478.033i	−0.688261	−	1.19210i	0.284140	−	0.958783i	$-0.408292\pi$
$402$	200.849	+	115.960i	0.499624	+	0.288458i
$403$	−314.641	+	544.973i	−0.780746	+	1.35229i
$404$	30.6215	−	17.6793i	0.0757957	−	0.0437607i
$405$		0			0
$406$	−44.9416	+	11.5280i	−0.110694	+	0.0283942i
$407$	−19.9699			−0.0490662
$408$	20.6476	+	35.7627i	0.0506069	+	0.0876537i
$409$	135.412	+	78.1800i	0.331080	+	0.191149i	0.656320	−	0.754482i	$-0.272112\pi$
$409$	135.412	+	78.1800i	0.331080	+	0.191149i	−0.325241	+	0.945631i	$0.605445\pi$
$410$		0			0
$411$	206.499	−	119.222i	0.502431	−	0.290079i
$412$			78.3926i			0.190273i
$413$	371.855	−	363.980i	0.900375	−	0.881307i
$414$	50.7891			0.122679
$415$		0			0
$416$	−95.5677	−	55.1761i	−0.229730	−	0.132635i
$417$	−59.4812	+	103.024i	−0.142641	+	0.247061i
$418$	−3.30262	+	1.90677i	−0.00790101	+	0.00456165i
$419$		−	57.3609i		−	0.136899i	−0.997655	−	0.0684497i	$-0.978195\pi$
$419$		−	57.3609i		−	0.136899i	0.997655	−	0.0684497i	$-0.0218053\pi$
$420$		0			0
$421$	−334.545			−0.794644			−0.397322	−	0.917679i	$-0.630060\pi$
$421$	−334.545			−0.794644			−0.397322	+	0.917679i	$0.630060\pi$
$422$	−86.8104	−	150.360i	−0.205712	−	0.356303i
$423$	−47.4985	−	27.4233i	−0.112290	−	0.0648305i
$424$	45.2088	−	78.3039i	0.106624	−	0.184679i
$425$		0			0
$426$		−	240.062i		−	0.563525i
$427$	−191.109	−	745.030i	−0.447562	−	1.74480i
$428$	−266.000			−0.621495
$429$	55.9880	+	96.9740i	0.130508	+	0.226047i
$430$		0			0
$431$	−223.891	+	387.791i	−0.519469	+	0.899746i	0.480275	+	0.877118i	$0.340537\pi$
$431$	−223.891	+	387.791i	−0.519469	+	0.899746i	−0.999744	+	0.0226285i	$0.992797\pi$
$432$	18.0000	−	10.3923i	0.0416667	−	0.0240563i
$433$		−	236.914i		−	0.547146i	−0.961851	−	0.273573i	$-0.911795\pi$
$433$		−	236.914i		−	0.547146i	0.961851	−	0.273573i	$-0.0882055\pi$
$434$	−307.556	−	85.9473i	−0.708654	−	0.198035i
$435$		0			0
$436$	49.1281	+	85.0923i	0.112679	+	0.195166i
$437$	8.43569	+	4.87035i	0.0193036	+	0.0111450i
$438$	−13.6145	+	23.5810i	−0.0310833	+	0.0538379i
$439$	−176.852	+	102.105i	−0.402852	+	0.232586i	−0.687714	−	0.725982i	$-0.741386\pi$
$439$	−176.852	+	102.105i	−0.402852	+	0.232586i	0.284862	+	0.958569i	$0.408052\pi$
$440$		0			0
$441$	3.14611	−	146.966i	0.00713403	−	0.333257i
$442$	232.549			0.526129
$443$	−76.8057	−	133.031i	−0.173376	−	0.300297i	0.766222	−	0.642576i	$-0.222134\pi$
$443$	−76.8057	−	133.031i	−0.173376	−	0.300297i	−0.939598	+	0.342279i	$0.888801\pi$
$444$	18.0776	+	10.4371i	0.0407152	+	0.0235069i
$445$		0			0
$446$	−4.54191	+	2.62227i	−0.0101836	+	0.00587953i
$447$		−	318.002i		−	0.711414i
$448$	15.0719	−	53.9336i	0.0336427	−	0.120388i
$449$	−200.642			−0.446864			−0.223432	−	0.974720i	$-0.571726\pi$
$449$	−200.642			−0.446864			−0.223432	+	0.974720i	$0.571726\pi$
$450$		0			0
$451$	−56.5002	−	32.6204i	−0.125278	−	0.0723290i
$452$	−141.909	+	245.793i	−0.313958	+	0.543791i
$453$	−212.241	+	122.537i	−0.468523	+	0.270502i
$454$		−	215.355i		−	0.474349i
$455$		0			0
$456$	3.98622			0.00874170
$457$	198.447	+	343.720i	0.434238	+	0.752122i	0.997233	−	0.0743379i	$-0.0236843\pi$
$457$	198.447	+	343.720i	0.434238	+	0.752122i	−0.562995	+	0.826460i	$0.690351\pi$
$458$	175.245	+	101.178i	0.382631	+	0.220912i
$459$	−21.9001	+	37.9321i	−0.0477126	+	0.0826407i
$460$		0			0
$461$		−	337.389i		−	0.731864i	−0.930642	−	0.365932i	$-0.880750\pi$
$461$		−	337.389i		−	0.731864i	0.930642	−	0.365932i	$-0.119250\pi$
$462$	−40.6084	+	39.7484i	−0.0878969	+	0.0860354i
$463$	−270.743			−0.584759			−0.292379	−	0.956302i	$-0.594447\pi$
$463$	−270.743			−0.584759			−0.292379	+	0.956302i	$0.594447\pi$
$464$	−9.37353	−	16.2354i	−0.0202016	−	0.0349902i
$465$		0			0
$466$	−50.8766	+	88.1209i	−0.109177	+	0.189101i
$467$	−22.2896	+	12.8689i	−0.0477292	+	0.0275565i	−0.523675	−	0.851918i	$-0.675439\pi$
$467$	−22.2896	+	12.8689i	−0.0477292	+	0.0275565i	0.475946	+	0.879475i	$0.342106\pi$
$468$		−	117.046i		−	0.250099i
$469$	463.605	+	473.636i	0.988498	+	1.00988i
$470$		0			0
$471$	−148.618	−	257.413i	−0.315536	−	0.546525i
$472$	182.082	+	105.125i	0.385767	+	0.222723i
$473$	−4.19788	+	7.27095i	−0.00887502	+	0.0153720i
$474$	−2.12456	+	1.22661i	−0.00448219	+	0.00258779i
$475$		0			0
$476$	29.3218	+	114.310i	0.0616005	+	0.240147i
$477$	95.9023			0.201053
$478$	320.828	+	555.690i	0.671187	+	1.16253i
$479$	162.828	+	94.0089i	0.339934	+	0.196261i	0.660243	−	0.751052i	$-0.270453\pi$
$479$	162.828	+	94.0089i	0.339934	+	0.196261i	−0.320309	+	0.947313i	$0.603787\pi$
$480$		0			0
$481$	101.802	−	58.7752i	0.211646	−	0.122194i
$482$			266.637i			0.553190i
$483$	139.786	+	39.0637i	0.289413	+	0.0808773i
$484$	−220.034			−0.454616
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−149.889	+	259.615i	−0.307780	+	0.533091i	−0.977876	−	0.209183i	$-0.932919\pi$
$487$	−149.889	+	259.615i	−0.307780	+	0.533091i	0.670096	+	0.742274i	$0.266253\pi$
$488$	269.147	−	155.392i	0.551530	−	0.318426i
$489$		−	511.744i		−	1.04651i
$490$		0			0
$491$	461.533			0.939985			0.469993	−	0.882670i	$-0.344257\pi$
$491$	461.533			0.939985			0.469993	+	0.882670i	$0.344257\pi$
$492$	34.0974	+	59.0584i	0.0693037	+	0.120037i
$493$	34.2135	+	19.7532i	0.0693987	+	0.0400673i
$494$	11.2240	−	19.4405i	0.0227206	−	0.0393532i
$495$		0			0
$496$		−	129.032i		−	0.260146i
$497$	184.640	−	660.719i	0.371509	−	1.32941i
$498$	163.637			0.328588
$499$	86.9948	+	150.679i	0.174338	+	0.301963i	0.939932	−	0.341362i	$-0.110888\pi$
$499$	86.9948	+	150.679i	0.174338	+	0.301963i	−0.765594	+	0.643324i	$0.777555\pi$
$500$		0			0
$501$	−145.958	+	252.807i	−0.291333	+	0.504604i
$502$	−286.481	+	165.400i	−0.570680	+	0.329482i
$503$			26.5806i			0.0528442i	0.999651	+	0.0264221i	$0.00841139\pi$
$503$			26.5806i			0.0528442i	−0.999651	+	0.0264221i	$0.991589\pi$
$504$	57.5343	−	14.7582i	0.114155	−	0.0292821i
$505$		0			0
$506$	−28.0529	−	48.5891i	−0.0554405	−	0.0960258i
$507$	−317.325	−	183.207i	−0.625887	−	0.361356i
$508$	87.2663	−	151.150i	0.171784	−	0.297539i
$509$	74.1139	−	42.7897i	0.145607	−	0.0840662i	−0.425427	−	0.904993i	$-0.639876\pi$
$509$	74.1139	−	42.7897i	0.145607	−	0.0840662i	0.571034	+	0.820927i	$0.306543\pi$
$510$		0			0
$511$	−55.6080	+	54.4304i	−0.108822	+	0.106517i
$512$	22.6274			0.0441942
$513$	2.11401	+	3.66157i	0.00412088	+	0.00713757i
$514$	−230.378	−	133.009i	−0.448207	−	0.258772i
$515$		0			0
$516$	7.60017	−	4.38796i	0.0147290	−	0.00850380i
$517$			60.5880i			0.117192i
$518$	41.7271	+	42.6300i	0.0805543	+	0.0822972i
$519$	258.196			0.497488
$520$		0			0
$521$	−698.846	−	403.479i	−1.34136	−	0.774432i	−0.354349	−	0.935113i	$-0.615297\pi$
$521$	−698.846	−	403.479i	−1.34136	−	0.774432i	−0.987006	+	0.160682i	$0.948631\pi$
$522$	9.94213	−	17.2203i	0.0190462	−	0.0329890i
$523$	−216.841	+	125.193i	−0.414610	+	0.239375i	−0.692768	−	0.721160i	$-0.743609\pi$
$523$	−216.841	+	125.193i	−0.414610	+	0.239375i	0.278159	+	0.960535i	$0.410276\pi$
$524$			220.043i			0.419929i
$525$		0			0
$526$	478.824			0.910312
$527$	135.957	+	235.485i	0.257984	+	0.446841i
$528$	−19.8843	−	11.4802i	−0.0376596	−	0.0217428i
$529$	192.846	−	334.019i	0.364549	−	0.631417i
$530$		0			0
$531$			223.004i			0.419970i
$532$	10.9712	+	3.06594i	0.0206226	+	0.00576304i
$533$	384.031			0.720509
$534$	−188.838	−	327.076i	−0.353629	−	0.612503i
$535$		0			0
$536$	−133.899	+	231.920i	−0.249812	+	0.432687i
$537$	424.240	−	244.935i	0.790018	−	0.456117i
$538$		−	739.802i		−	1.37510i
$539$	−142.338	+	78.1657i	−0.264078	+	0.145020i
$540$		0			0
$541$	421.926	+	730.798i	0.779901	+	1.35083i	0.931998	+	0.362462i	$0.118064\pi$
$541$	421.926	+	730.798i	0.779901	+	1.35083i	−0.152098	+	0.988365i	$0.548603\pi$
$542$	−545.602	−	315.003i	−1.00665	−	0.581187i
$543$	−264.500	+	458.127i	−0.487109	+	0.843697i
$544$	−41.2952	+	23.8418i	−0.0759103	+	0.0438268i
$545$		0			0
$546$	90.0243	−	322.145i	0.164880	−	0.590009i
$547$	674.572			1.23322			0.616611	−	0.787268i	$-0.288505\pi$
$547$	674.572			1.23322			0.616611	+	0.787268i	$0.288505\pi$
$548$	137.666	+	238.445i	0.251216	+	0.435118i
$549$	285.473	+	164.818i	0.519988	+	0.300215i
$550$		0			0
$551$	3.30262	−	1.90677i	0.00599387	−	0.00346056i
$552$			58.6463i			0.106243i
$553$	−6.79083	+	1.74192i	−0.0122800	+	0.00314995i
$554$	20.5537			0.0371006
$555$		0			0
$556$	−118.962	−	68.6829i	−0.213961	−	0.123530i
$557$	−292.958	+	507.418i	−0.525957	+	0.910984i	0.473586	+	0.880748i	$0.342959\pi$
$557$	−292.958	+	507.418i	−0.525957	+	0.910984i	−0.999543	+	0.0302363i	$0.990374\pi$
$558$	118.524	−	68.4298i	0.212408	−	0.122634i
$559$		−	49.4206i		−	0.0884089i
$560$		0			0
$561$	48.3852			0.0862482
$562$	372.120	+	644.531i	0.662135	+	1.14685i
$563$	118.176	+	68.2288i	0.209904	+	0.121188i	0.601267	−	0.799048i	$-0.294663\pi$
$563$	118.176	+	68.2288i	0.209904	+	0.121188i	−0.391363	+	0.920236i	$0.627996\pi$
$564$	31.6657	−	54.8466i	0.0561448	−	0.0972457i
$565$		0			0
$566$			712.993i			1.25970i
$567$	44.0684	+	45.0219i	0.0777221	+	0.0794037i
$568$	277.199			0.488027
$569$	284.763	+	493.225i	0.500463	+	0.866827i	1.00000		0.000534692i	$0.000170198\pi$
$569$	284.763	+	493.225i	0.500463	+	0.866827i	−0.499537	+	0.866293i	$0.666496\pi$
$570$		0			0
$571$	38.9272	−	67.4238i	0.0681737	−	0.118080i	−0.829924	−	0.557877i	$-0.811616\pi$
$571$	38.9272	−	67.4238i	0.0681737	−	0.118080i	0.898097	+	0.439797i	$0.144949\pi$
$572$	−111.976	+	64.6493i	−0.195762	+	0.113023i
$573$		−	84.3065i		−	0.147132i
$574$	48.4220	+	188.771i	0.0843589	+	0.328870i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−849.557	−	490.492i	−1.47237	−	0.850073i	−0.472853	−	0.881142i	$-0.656776\pi$
$577$	−849.557	−	490.492i	−1.47237	−	0.850073i	−0.999517	+	0.0310685i	$0.990109\pi$
$578$	−154.111	+	266.928i	−0.266628	+	0.461814i
$579$	−224.300	+	129.500i	−0.387392	+	0.223661i
$580$		0			0
$581$	450.376	+	125.859i	0.775173	+	0.216624i
$582$	323.390			0.555653
$583$	−52.9707	−	91.7480i	−0.0908589	−	0.157372i
$584$	−27.2290	−	15.7207i	−0.0466250	−	0.0269189i
$585$		0			0
$586$	269.621	−	155.666i	0.460105	−	0.265642i
$587$		−	894.491i		−	1.52384i	−0.647674	−	0.761918i	$-0.724258\pi$
$587$		−	894.491i		−	1.52384i	0.647674	−	0.761918i	$-0.275742\pi$
$588$	169.702	+	3.63281i	0.288609	+	0.00617825i
$589$	26.2479			0.0445635
$590$		0			0
$591$	329.218	+	190.074i	0.557053	+	0.321615i
$592$	−12.0517	+	20.8742i	−0.0203576	+	0.0352604i
$593$	877.978	−	506.901i	1.48057	−	0.854808i	0.480813	−	0.876823i	$-0.340342\pi$
$593$	877.978	−	506.901i	1.48057	−	0.854808i	0.999758	+	0.0220156i	$0.00700833\pi$
$594$		−	24.3532i		−	0.0409986i
$595$		0			0
$596$	367.197			0.616102
$597$	−254.396	−	440.626i	−0.426123	−	0.738067i
$598$	286.013	+	165.130i	0.478283	+	0.276137i
$599$	339.723	−	588.418i	0.567151	−	0.982334i	−0.429695	−	0.902974i	$-0.641379\pi$
$599$	339.723	−	588.418i	0.567151	−	0.982334i	0.996846	−	0.0793601i	$-0.0252877\pi$
$600$		0			0
$601$		−	13.9775i		−	0.0232571i	−0.999932	−	0.0116285i	$-0.996298\pi$
$601$		−	13.9775i		−	0.0232571i	0.999932	−	0.0116285i	$-0.00370156\pi$
$602$	24.2928	−	6.23138i	0.0403535	−	0.0103511i
$603$	−284.043			−0.471050
$604$	−141.494	−	245.074i	−0.234261	−	0.405752i
$605$		0			0
$606$	−21.6526	+	37.5035i	−0.0357304	+	0.0618869i
$607$	−795.111	+	459.058i	−1.30990	+	0.756273i	−0.982080	−	0.188466i	$-0.939648\pi$
$607$	−795.111	+	459.058i	−1.30990	+	0.756273i	−0.327823	+	0.944739i	$0.606315\pi$
$608$			4.60289i			0.00757054i
$609$	40.6084	−	39.7484i	0.0666804	−	0.0652682i
$610$		0			0
$611$	−178.322	−	308.862i	−0.291852	−	0.505503i
$612$	−43.8002	−	25.2880i	−0.0715689	−	0.0413203i
$613$	312.457	−	541.192i	0.509718	−	0.882858i	−0.490219	−	0.871600i	$-0.663083\pi$
$613$	312.457	−	541.192i	0.509718	−	0.882858i	0.999937	−	0.0112580i	$-0.00358362\pi$
$614$	−224.891	+	129.841i	−0.366272	+	0.211467i
$615$		0			0
$616$	−45.8974	−	46.8905i	−0.0745088	−	0.0761209i
$617$	−11.2800			−0.0182821			−0.00914103	−	0.999958i	$-0.502910\pi$
$617$	−11.2800			−0.0182821			−0.00914103	+	0.999958i	$0.502910\pi$
$618$	−48.0055	−	83.1479i	−0.0776787	−	0.134544i
$619$	130.107	+	75.1176i	0.210190	+	0.121353i	0.601400	−	0.798948i	$-0.294610\pi$
$619$	130.107	+	75.1176i	0.210190	+	0.121353i	−0.391210	+	0.920302i	$0.627943\pi$
$620$		0			0
$621$	−53.8700	+	31.1019i	−0.0867472	+	0.0500835i
$622$			319.508i			0.513679i
$623$	−268.170	−	1045.45i	−0.430449	−	1.67809i
$624$	135.153			0.216592
$625$		0			0
$626$	327.674	+	189.183i	0.523442	+	0.302209i
$627$	2.33531	−	4.04487i	0.00372457	−	0.00645115i
$628$	297.235	−	171.609i	0.473304	−	0.273262i
$629$		−	50.7940i		−	0.0807536i
$630$		0			0
$631$	768.570			1.21802			0.609009	−	0.793163i	$-0.291567\pi$
$631$	768.570			1.21802			0.609009	+	0.793163i	$0.291567\pi$
$632$	−1.41637	−	2.45323i	−0.00224109	−	0.00388169i
$633$	184.153	+	106.321i	0.290920	+	0.167963i
$634$	374.620	−	648.861i	0.590883	−	1.02344i
$635$		0			0
$636$			110.738i			0.174117i
$637$	495.546	−	817.395i	0.777937	−	1.28319i
$638$	−21.9658			−0.0344291
$639$	147.007	+	254.624i	0.230058	+	0.398472i
$640$		0			0
$641$	23.1711	−	40.1335i	0.0361484	−	0.0626108i	−0.847385	−	0.530979i	$-0.821824\pi$
$641$	23.1711	−	40.1335i	0.0361484	−	0.0626108i	0.883534	+	0.468368i	$0.155158\pi$
$642$	282.136	−	162.891i	0.439463	−	0.253724i
$643$		−	122.504i		−	0.190519i	−0.995452	−	0.0952597i	$-0.969632\pi$
$643$		−	122.504i		−	0.190519i	0.995452	−	0.0952597i	$-0.0303682\pi$
$644$	−45.1069	+	161.411i	−0.0700418	+	0.250639i
$645$		0			0
$646$	−4.84992	−	8.40030i	−0.00750761	−	0.0130036i
$647$	−746.689	−	431.101i	−1.15408	−	0.666308i	−0.204201	−	0.978929i	$-0.565460\pi$
$647$	−746.689	−	431.101i	−1.15408	−	0.666308i	−0.949878	+	0.312621i	$0.898793\pi$
$648$	−12.7279	+	22.0454i	−0.0196419	+	0.0340207i
$649$	213.344	−	123.174i	0.328728	−	0.189791i
$650$		0			0
$651$	378.844	−	97.1777i	0.581941	−	0.149275i
$652$	590.912			0.906306
$653$	−331.517	−	574.205i	−0.507683	−	0.879333i	−0.999960	−	0.00889466i	$-0.997169\pi$
$653$	−331.517	−	574.205i	−0.507683	−	0.879333i	0.492277	−	0.870438i	$-0.336165\pi$
$654$	−104.216	−	60.1693i	−0.159352	−	0.0920021i
$655$		0			0
$656$	−68.1948	+	39.3723i	−0.103956	+	0.0600187i
$657$		−	33.3486i		−	0.0507589i
$658$	129.338	−	126.598i	0.196562	−	0.192399i
$659$	−999.565			−1.51679			−0.758395	−	0.651795i	$-0.774016\pi$
$659$	−999.565			−1.51679			−0.758395	+	0.651795i	$0.774016\pi$
$660$		0			0
$661$	−653.320	−	377.195i	−0.988382	−	0.570642i	−0.0835916	−	0.996500i	$-0.526639\pi$
$661$	−653.320	−	377.195i	−0.988382	−	0.570642i	−0.904790	+	0.425858i	$0.859972\pi$
$662$	145.402	−	251.844i	0.219641	−	0.380429i
$663$	−246.656	+	142.407i	−0.372030	+	0.214791i
$664$			188.951i			0.284565i
$665$		0			0
$666$	−25.5655			−0.0383867
$667$	28.0529	+	48.5891i	0.0420583	+	0.0728472i
$668$	−291.916	−	168.538i	−0.437000	−	0.252302i
$669$	3.21161	−	5.56268i	0.00480062	−	0.00831491i
$670$		0			0
$671$		−	364.143i		−	0.542687i
$672$	17.0413	+	66.4349i	0.0253591	+	0.0988614i
$673$	838.745			1.24628			0.623139	−	0.782111i	$-0.285857\pi$
$673$	838.745			1.24628			0.623139	+	0.782111i	$0.285857\pi$
$674$	−236.038	−	408.830i	−0.350205	−	0.606573i
$675$		0			0
$676$	211.550	−	366.415i	0.312943	−	0.542034i
$677$	120.385	−	69.5041i	0.177821	−	0.102665i	−0.408448	−	0.912782i	$-0.633930\pi$
$677$	120.385	−	69.5041i	0.177821	−	0.102665i	0.586268	+	0.810117i	$0.300596\pi$
$678$		−	347.604i		−	0.512691i
$679$	890.063	+	248.731i	1.31084	+	0.366319i
$680$		0			0
$681$	131.877	+	228.418i	0.193652	+	0.335416i
$682$	−130.931	−	75.5931i	−0.191981	−	0.110840i
$683$	517.117	−	895.672i	0.757125	−	1.31138i	−0.187186	−	0.982325i	$-0.559937\pi$
$683$	517.117	−	895.672i	0.757125	−	1.31138i	0.944311	−	0.329055i	$-0.106730\pi$
$684$	−4.22802	+	2.44105i	−0.00618132	+	0.00356878i
$685$		0			0
$686$	464.275	+	140.522i	0.676786	+	0.204843i
$687$	−247.834			−0.360748
$688$	5.06678	+	8.77592i	0.00736450	+	0.0127557i
$689$	540.063	+	311.805i	0.783835	+	0.452548i
$690$		0			0
$691$	602.952	−	348.115i	0.872579	−	0.503784i	0.00437465	−	0.999990i	$-0.498608\pi$
$691$	602.952	−	348.115i	0.872579	−	0.503784i	0.868204	+	0.496207i	$0.165274\pi$
$692$			298.140i			0.430838i
$693$	18.7309	−	67.0269i	0.0270287	−	0.0967200i
$694$	923.571			1.33079
$695$		0			0
$696$	19.8843	+	11.4802i	0.0285694	+	0.0164945i
$697$	82.9707	−	143.709i	0.119040	−	0.206183i
$698$	−298.907	+	172.574i	−0.428233	+	0.247240i
$699$		−	124.622i		−	0.178286i
$700$		0			0
$701$	1001.00			1.42796			0.713979	−	0.700167i	$-0.246891\pi$
$701$	1001.00			1.42796			0.713979	+	0.700167i	$0.246891\pi$
$702$	71.6758	+	124.146i	0.102102	+	0.176846i
$703$	−4.24624	−	2.45157i	−0.00604017	−	0.00348729i
$704$	13.2562	−	22.9604i	0.0188298	−	0.0326142i
$705$		0			0
$706$			590.461i			0.836347i
$707$	−88.4396	+	86.5666i	−0.125091	+	0.122442i
$708$	−257.503			−0.363705
$709$	131.927	+	228.505i	0.186075	+	0.322291i	0.943938	−	0.330122i	$-0.107090\pi$
$709$	131.927	+	228.505i	0.186075	+	0.322291i	−0.757863	+	0.652414i	$0.773757\pi$
$710$		0			0
$711$	1.50229	−	2.60204i	0.00211292	−	0.00365969i
$712$	377.675	−	218.051i	0.530443	−	0.306251i
$713$			386.166i			0.541607i
$714$	−101.101	−	103.288i	−0.141598	−	0.144661i
$715$		0			0
$716$	282.827	+	489.870i	0.395009	+	0.684176i
$717$	−680.578	−	392.932i	−0.949202	−	0.548022i
$718$	−208.564	+	361.244i	−0.290479	+	0.503125i
$719$	−574.059	+	331.433i	−0.798413	+	0.460964i	−0.842916	−	0.538045i	$-0.819163\pi$
$719$	−574.059	+	331.433i	−0.798413	+	0.460964i	0.0445027	+	0.999009i	$0.485830\pi$
$720$		0			0
$721$	−68.1730	−	265.770i	−0.0945533	−	0.368613i
$722$	509.595			0.705810
$723$	−163.281	−	282.812i	−0.225839	−	0.391164i
$724$	−529.000	−	305.418i	−0.730663	−	0.421848i
$725$		0			0
$726$	233.382	−	134.743i	0.321462	−	0.185596i
$727$		−	73.2857i		−	0.100806i	−0.998729	−	0.0504028i	$-0.983949\pi$
$727$		−	73.2857i		−	0.100806i	0.998729	−	0.0504028i	$-0.0160505\pi$
$728$	371.981	+	103.951i	0.510963	+	0.142790i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−18.4938	−	10.6774i	−0.0252993	−	0.0146066i
$732$	−190.315	+	329.636i	−0.259994	+	0.450322i
$733$	1153.04	−	665.709i	1.57304	−	0.908198i	0.577251	−	0.816567i	$-0.304125\pi$
$733$	1153.04	−	665.709i	1.57304	−	0.908198i	0.995793	−	0.0916311i	$-0.0292080\pi$
$734$			33.4168i			0.0455269i
$735$		0			0
$736$	−67.7189			−0.0920093
$737$	156.889	+	271.739i	0.212875	+	0.368710i
$738$	−72.3315	−	41.7606i	−0.0980102	−	0.0565862i
$739$	−148.610	+	257.400i	−0.201096	+	0.348309i	−0.948882	−	0.315631i	$-0.897784\pi$
$739$	−148.610	+	257.400i	−0.201096	+	0.348309i	0.747786	+	0.663940i	$0.231117\pi$
$740$		0			0
$741$			27.4930i			0.0371025i
$742$	−85.1728	+	304.784i	−0.114788	+	0.410760i
$743$	−774.964			−1.04302			−0.521510	−	0.853245i	$-0.674631\pi$
$743$	−774.964			−1.04302			−0.521510	+	0.853245i	$0.674631\pi$
$744$	79.0159	+	136.860i	0.106204	+	0.183951i
$745$		0			0
$746$	−117.352	+	203.260i	−0.157309	+	0.272467i
$747$	−173.563	+	100.207i	−0.232347	+	0.134145i
$748$			55.8705i			0.0746931i
$749$	901.804	−	231.323i	1.20401	−	0.308842i
$750$		0			0
$751$	516.034	+	893.796i	0.687129	+	1.19014i	0.972763	+	0.231803i	$0.0744624\pi$
$751$	516.034	+	893.796i	0.687129	+	1.19014i	−0.285634	+	0.958339i	$0.592204\pi$
$752$	63.3314	+	36.5644i	0.0842173	+	0.0486229i
$753$	202.573	−	350.867i	0.269021	−	0.465958i
$754$	111.976	−	64.6493i	0.148509	−	0.0857418i
$755$		0			0
$756$	−51.9868	+	50.8859i	−0.0687656	+	0.0673093i
$757$	−450.128			−0.594621			−0.297310	−	0.954781i	$-0.596090\pi$
$757$	−450.128			−0.594621			−0.297310	+	0.954781i	$0.596090\pi$
$758$	323.060	+	559.557i	0.426201	+	0.738202i
$759$	59.5092	+	34.3577i	0.0784048	+	0.0452670i
$760$		0			0
$761$	−74.2627	+	42.8756i	−0.0975856	+	0.0563411i	−0.547999	−	0.836479i	$-0.684610\pi$
$761$	−74.2627	+	42.8756i	−0.0975856	+	0.0563411i	0.450413	+	0.892820i	$0.351277\pi$
$762$			213.758i			0.280522i
$763$	−240.555	−	245.760i	−0.315276	−	0.322097i
$764$	97.3488			0.127420
$765$		0			0
$766$	−8.17487	−	4.71976i	−0.0106721	−	0.00616157i
$767$	−725.049	+	1255.82i	−0.945306	+	1.63732i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$		−	959.716i		−	1.24800i	−0.781422	−	0.624002i	$-0.785506\pi$
$769$		−	959.716i		−	1.24800i	0.781422	−	0.624002i	$-0.214494\pi$
$770$		0			0
$771$	325.804			0.422574
$772$	−149.533	−	258.999i	−0.193696	−	0.335491i
$773$	879.534	+	507.799i	1.13782	+	0.656920i	0.945890	−	0.324488i	$-0.105192\pi$
$773$	879.534	+	507.799i	1.13782	+	0.656920i	0.191930	+	0.981409i	$0.438525\pi$
$774$	−5.37413	+	9.30827i	−0.00694332	+	0.0120262i
$775$		0			0
$776$			373.419i			0.481210i
$777$	−70.3637	−	19.6633i	−0.0905582	−	0.0253067i
$778$	300.873			0.386726
$779$	−8.00914	−	13.8722i	−0.0102813	−	0.0178077i
$780$		0			0
$781$	162.396	−	281.278i	0.207933	−	0.360151i
$782$	123.587	−	71.3532i	0.158040	−	0.0912445i
$783$			24.3532i			0.0311024i
$784$	−4.19481	+	195.955i	−0.00535052	+	0.249943i
$785$		0			0
$786$	−134.748	−	233.391i	−0.171435	−	0.296935i
$787$	−968.434	−	559.126i	−1.23054	−	0.710452i	−0.263396	−	0.964688i	$-0.584843\pi$
$787$	−968.434	−	559.126i	−1.23054	−	0.710452i	−0.967142	+	0.254236i	$0.918176\pi$
$788$	−219.479	+	380.148i	−0.278526	+	0.482422i
$789$	−507.870	+	293.219i	−0.643688	+	0.371633i
$790$		0			0
$791$	267.355	−	956.707i	0.337996	−	1.20949i
$792$	28.1206			0.0355058
$793$	1071.74	+	1856.31i	1.35150	+	2.34087i
$794$	310.862	+	179.476i	0.391513	+	0.226040i
$795$		0			0
$796$	508.791	−	293.751i	0.639185	−	0.369034i
$797$			803.162i			1.00773i	0.863782	+	0.503866i	$0.168089\pi$
$797$			803.162i			1.00773i	−0.863782	+	0.503866i	$0.831911\pi$
$798$	−13.5142	+	3.46655i	−0.0169351	+	0.00434405i
$799$	−154.107			−0.192875
$800$		0			0
$801$	400.585	+	231.278i	0.500106	+	0.288737i
$802$	−390.312	+	676.041i	−0.486674	+	0.842944i
$803$	−31.9040	+	18.4198i	−0.0397310	+	0.0229387i
$804$		−	327.985i		−	0.407941i
$805$		0			0
$806$	889.938			1.10414
$807$	453.034	+	784.678i	0.561381	+	0.972340i
$808$	−43.3053	−	25.0023i	−0.0535956	−	0.0309435i
$809$	255.382	−	442.334i	0.315676	−	0.546767i	−0.663905	−	0.747817i	$-0.731102\pi$
$809$	255.382	−	442.334i	0.315676	−	0.546767i	0.979581	+	0.201050i	$0.0644354\pi$
$810$		0			0
$811$		−	572.874i		−	0.706380i	−0.935552	−	0.353190i	$-0.885097\pi$
$811$		−	572.874i		−	0.706380i	0.935552	−	0.353190i	$-0.114903\pi$
$812$	45.8974	+	46.8905i	0.0565240	+	0.0577469i
$813$	771.598			0.949075
$814$	14.1209	+	24.4581i	0.0173475	+	0.0300468i
$815$		0			0
$816$	29.2001	−	50.5761i	0.0357845	−	0.0619805i
$817$	−1.78520	+	1.03069i	−0.00218507	+	0.00126155i
$818$		−	221.126i		−	0.270326i
$819$	101.787	+	396.815i	0.124283	+	0.484511i
$820$		0			0
$821$	−443.437	−	768.056i	−0.540119	−	0.935513i	−0.998897	−	0.0469621i	$-0.985046\pi$
$821$	−443.437	−	768.056i	−0.540119	−	0.935513i	0.458778	−	0.888551i	$-0.348287\pi$
$822$	−292.034	−	168.606i	−0.355273	−	0.205117i
$823$	−548.198	+	949.506i	−0.666097	+	1.15371i	0.312890	+	0.949789i	$0.398703\pi$
$823$	−548.198	+	949.506i	−0.666097	+	1.15371i	−0.978987	+	0.203924i	$0.934630\pi$
$824$	96.0109	−	55.4319i	0.116518	−	0.0672718i
$825$		0			0
$826$	−708.723	−	198.055i	−0.858018	−	0.239776i
$827$	−556.105			−0.672437			−0.336218	−	0.941784i	$-0.609148\pi$
$827$	−556.105			−0.672437			−0.336218	+	0.941784i	$0.609148\pi$
$828$	−35.9133	−	62.2037i	−0.0433736	−	0.0751253i
$829$	1002.59	+	578.843i	1.20939	+	0.698243i	0.962626	−	0.270833i	$-0.0872990\pi$
$829$	1002.59	+	578.843i	1.20939	+	0.698243i	0.246765	+	0.969075i	$0.420632\pi$
$830$		0			0
$831$	−21.8005	+	12.5865i	−0.0262341	+	0.0151463i
$832$			156.061i			0.187574i
$833$	−198.816	−	362.039i	−0.238675	−	0.434621i
$834$	168.238			0.201724
$835$		0			0
$836$	4.67062	+	2.69658i	0.00558686	+	0.00322558i
$837$	−83.8090	+	145.162i	−0.100130	+	0.173431i
$838$	−70.2524	+	40.5603i	−0.0838334	+	0.0484013i
$839$		−	313.727i		−	0.373930i	−0.982367	−	0.186965i	$-0.940135\pi$
$839$		−	313.727i		−	0.373930i	0.982367	−	0.186965i	$-0.0598651\pi$
$840$		0			0
$841$	−819.034			−0.973881
$842$	236.559	+	409.733i	0.280949	+	0.486618i
$843$	−789.386	−	455.752i	−0.936400	−	0.540631i
$844$	−122.768	+	212.641i	−0.145460	+	0.251944i
$845$		0			0
$846$			77.5648i			0.0916841i
$847$	745.969	−	191.350i	0.880719	−	0.225914i
$848$	−127.870			−0.150790
$849$	−436.617	−	756.243i	−0.514272	−	0.890746i
$850$		0			0
$851$	36.0681	−	62.4718i	0.0423832	−	0.0734098i
$852$	−294.014	+	169.749i	−0.345087	+	0.199236i
$853$			638.107i			0.748074i	0.927414	+	0.374037i	$0.122027\pi$
$853$			638.107i			0.748074i	−0.927414	+	0.374037i	$0.877973\pi$
$854$	−777.338	+	760.876i	−0.910232	+	0.890955i
$855$		0			0
$856$	188.090	+	325.782i	0.219732	+	0.380586i
$857$	−878.130	−	506.989i	−1.02466	−	0.591585i	−0.109207	−	0.994019i	$-0.534831\pi$
$857$	−878.130	−	506.989i	−1.02466	−	0.591585i	−0.915449	+	0.402434i	$0.868164\pi$
$858$	79.1789	−	137.142i	0.0922832	−	0.159839i
$859$	−211.106	+	121.882i	−0.245758	+	0.141888i	−0.617820	−	0.786319i	$-0.711984\pi$
$859$	−211.106	+	121.882i	−0.245758	+	0.141888i	0.372062	+	0.928208i	$0.378651\pi$
$860$		0			0
$861$	−166.958	−	170.570i	−0.193911	−	0.198107i
$862$	633.260			0.734640
$863$	−274.165	−	474.868i	−0.317688	−	0.550253i	0.662317	−	0.749224i	$-0.269573\pi$
$863$	−274.165	−	474.868i	−0.317688	−	0.550253i	−0.980005	+	0.198971i	$0.936240\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−290.159	+	167.524i	−0.335057	+	0.193445i
$867$		−	377.494i		−	0.435402i
$868$	112.211	+	437.451i	0.129276	+	0.503976i
$869$	−3.31910			−0.00381945
$870$		0			0
$871$	−1599.56	−	923.504i	−1.83646	−	1.06028i
$872$	69.4776	−	120.339i	0.0796761	−	0.138003i
$873$	−343.007	+	198.035i	−0.392906	+	0.226844i
$874$		−	13.7754i		−	0.0157613i
$875$		0			0
$876$	38.5076			0.0439585
$877$	−536.806	−	929.775i	−0.612094	−	1.06018i	−0.990887	−	0.134696i	$-0.956994\pi$
$877$	−536.806	−	929.775i	−0.612094	−	1.06018i	0.378793	−	0.925481i	$-0.376339\pi$
$878$	250.106	+	144.399i	0.284859	+	0.164463i
$879$	−190.651	+	330.217i	−0.216896	+	0.375674i
$880$		0			0
$881$		−	341.661i		−	0.387811i	−0.981020	−	0.193905i	$-0.937884\pi$
$881$		−	341.661i		−	0.387811i	0.981020	−	0.193905i	$-0.0621155\pi$
$882$	−182.221	+	100.068i	−0.206600	+	0.113455i
$883$	884.344			1.00152			0.500761	−	0.865585i	$-0.333053\pi$
$883$	884.344			1.00152			0.500761	+	0.865585i	$0.333053\pi$
$884$	−164.437	−	284.813i	−0.186015	−	0.322187i
$885$		0			0
$886$	−108.620	+	188.135i	−0.122596	+	0.212342i
$887$	145.147	−	83.8009i	0.163639	−	0.0944768i	−0.415944	−	0.909390i	$-0.636549\pi$
$887$	145.147	−	83.8009i	0.163639	−	0.0944768i	0.579583	+	0.814913i	$0.303216\pi$
$888$		−	29.5205i		−	0.0332438i
$889$	−164.409	+	588.324i	−0.184937	+	0.661782i
$890$		0			0
$891$	14.9132	+	25.8304i	0.0167376	+	0.0289904i
$892$	6.42323	+	3.70845i	0.00720093	+	0.00415746i
$893$	−7.43795	+	12.8829i	−0.00832918	+	0.0144266i
$894$	−389.471	+	224.861i	−0.435650	+	0.251523i
$895$		0			0
$896$	−76.7124	+	19.6776i	−0.0856165	+	0.0219616i
$897$	−404.484			−0.450929
$898$	141.875	+	245.735i	0.157990	+	0.273647i
$899$	130.931	+	75.5931i	0.145641	+	0.0840858i
$900$		0			0
$901$	233.363	−	134.732i	0.259005	−	0.149536i
$902$			92.2644i			0.102289i
$903$	−21.9505	+	21.4856i	−0.0243084	+	0.0237936i
$904$	401.379			0.444003
$905$		0			0
$906$	300.154	+	173.294i	0.331295	+	0.191274i
$907$	−298.562	+	517.124i	−0.329175	+	0.570148i	−0.982348	−	0.187060i	$-0.940104\pi$
$907$	−298.562	+	517.124i	−0.329175	+	0.570148i	0.653173	+	0.757209i	$0.273437\pi$
$908$	−263.754	+	152.279i	−0.290478	+	0.167708i
$909$		−	53.0379i		−	0.0583475i
$910$		0			0
$911$	1340.36			1.47131			0.735655	−	0.677357i	$-0.236875\pi$
$911$	1340.36			1.47131			0.735655	+	0.677357i	$0.236875\pi$
$912$	−2.81868	−	4.88210i	−0.00309066	−	0.00535318i
$913$	191.732	+	110.696i	0.210002	+	0.121245i
$914$	280.646	−	486.093i	0.307053	−	0.531831i
$915$		0			0
$916$		−	286.174i		−	0.312417i
$917$	−191.357	−	745.998i	−0.208677	−	0.813521i
$918$	61.9428			0.0674758
$919$	480.400	+	832.078i	0.522743	+	0.905417i	0.999650	+	0.0264631i	$0.00842447\pi$
$919$	480.400	+	832.078i	0.522743	+	0.905417i	−0.476907	+	0.878954i	$0.658242\pi$
$920$		0			0
$921$	159.022	−	275.434i	0.172662	−	0.299060i
$922$	−413.216	+	238.570i	−0.448173	+	0.258753i
$923$			1911.85i			2.07134i
$924$	77.3960	+	21.6285i	0.0837619	+	0.0234075i
$925$		0			0
$926$	191.444	+	331.592i	0.206744	+	0.358090i
$927$	101.835	+	58.7944i	0.109854	+	0.0634244i
$928$	−13.2562	+	22.9604i	−0.0142847	+	0.0247418i
$929$	823.312	−	475.340i	0.886235	−	0.511668i	0.0135260	−	0.999909i	$-0.495694\pi$
$929$	823.312	−	475.340i	0.886235	−	0.511668i	0.872709	+	0.488240i	$0.162361\pi$
$930$		0			0
$931$	−39.8613	−	0.853311i	−0.0428156	−	0.000916553i
$932$	143.901			0.154400
$933$	−195.658	−	338.890i	−0.209709	−	0.363226i
$934$	31.5222	+	18.1993i	0.0337497	+	0.0194854i
$935$		0			0
$936$	−143.352	+	82.7641i	−0.153153	+	0.0884232i
$937$		−	236.656i		−	0.252568i	−0.991994	−	0.126284i	$-0.959695\pi$
$937$		−	236.656i		−	0.252568i	0.991994	−	0.126284i	$-0.0403050\pi$
$938$	252.265	−	902.709i	0.268939	−	0.962377i
$939$	−463.402			−0.493505
$940$		0			0
$941$	454.869	+	262.619i	0.483389	+	0.279085i	0.721828	−	0.692073i	$-0.243302\pi$
$941$	454.869	+	262.619i	0.483389	+	0.279085i	−0.238439	+	0.971158i	$0.576636\pi$
$942$	−210.177	+	364.037i	−0.223118	+	0.386451i
$943$	204.092	−	117.833i	0.216428	−	0.124955i
$944$		−	297.339i		−	0.314978i
$945$		0			0
$946$	11.8734			0.0125512
$947$	−666.313	−	1154.09i	−0.703604	−	1.21868i	−0.967193	−	0.254042i	$-0.918240\pi$
$947$	−666.313	−	1154.09i	−0.703604	−	1.21868i	0.263589	−	0.964635i	$-0.415094\pi$
$948$	3.00458	+	1.73469i	0.00316938	+	0.00182984i
$949$	108.426	−	187.799i	0.114252	−	0.197891i
$950$		0			0
$951$			917.627i			0.964908i
$952$	119.267	−	116.741i	0.125280	−	0.122627i
$953$	−1748.81			−1.83506			−0.917531	−	0.397665i	$-0.869821\pi$
$953$	−1748.81			−1.83506			−0.917531	+	0.397665i	$0.869821\pi$
$954$	−67.8132	−	117.456i	−0.0710830	−	0.123119i
$955$		0			0
$956$	453.719	−	785.864i	0.474601	−	0.822033i
$957$	23.2982	−	13.4512i	0.0243451	−	0.0140556i
$958$		−	265.897i		−	0.277555i
$959$	−674.082	−	688.666i	−0.702900	−	0.718108i
$960$		0			0
$961$	39.7929	+	68.9233i	0.0414078	+	0.0717204i
$962$	−143.969	−	83.1207i	−0.149656	−	0.0864040i
$963$	−199.500	+	345.544i	−0.207165	+	0.358820i
$964$	326.563	−	188.541i	0.338758	−	0.195582i
$965$		0			0
$966$	−51.0008	−	198.825i	−0.0527959	−	0.205823i
$967$	638.367			0.660152			0.330076	−	0.943954i	$-0.392926\pi$
$967$	638.367			0.660152			0.330076	+	0.943954i	$0.392926\pi$
$968$	155.588	+	269.486i	0.160731	+	0.278394i
$969$	10.2882	+	5.93991i	0.0106174	+	0.00612994i
$970$		0			0
$971$	−1222.24	+	705.662i	−1.25875	+	0.726737i	−0.972831	−	0.231518i	$-0.925631\pi$
$971$	−1222.24	+	705.662i	−1.25875	+	0.726737i	−0.285915	+	0.958255i	$0.592298\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	463.040	+	129.398i	0.475889	+	0.132989i
$974$	423.950			0.435267
$975$		0			0
$976$	−380.631	−	219.757i	−0.389991	−	0.225161i
$977$	−550.326	+	953.192i	−0.563281	+	0.975632i	0.433926	+	0.900949i	$0.357128\pi$
$977$	−550.326	+	953.192i	−0.563281	+	0.975632i	−0.997207	+	0.0746833i	$0.976205\pi$
$978$	−626.756	+	361.858i	−0.640855	+	0.369998i
$979$		−	510.977i		−	0.521938i
$980$		0			0
$981$	147.384			0.150239
$982$	−326.353	−	565.260i	−0.332335	−	0.575621i
$983$	−1209.68	−	698.409i	−1.23060	−	0.710488i	−0.263446	−	0.964674i	$-0.584859\pi$
$983$	−1209.68	−	698.409i	−1.23060	−	0.710488i	−0.967155	+	0.254187i	$0.918192\pi$
$984$	48.2210	−	83.5212i	0.0490051	−	0.0848793i
$985$		0			0
$986$		−	55.8705i		−	0.0566638i
$987$	−59.6578	+	213.481i	−0.0604436	+	0.216293i
$988$	−31.7461			−0.0321317
$989$	−15.1638	−	26.2644i	−0.0153324	−	0.0265565i
$990$		0			0
$991$	−464.607	+	804.723i	−0.468826	+	0.812031i	−0.999365	−	0.0356298i	$-0.988656\pi$
$991$	−464.607	+	804.723i	−0.468826	+	0.812031i	0.530539	+	0.847661i	$0.321990\pi$
$992$	−158.032	+	91.2397i	−0.159306	+	0.0919755i
$993$			356.162i			0.358672i
$994$	−939.772	+	241.062i	−0.945445	+	0.242517i
$995$		0			0
$996$	−115.709	−	200.413i	−0.116173	−	0.201218i
$997$	996.474	+	575.315i	0.999473	+	0.577046i	0.908092	−	0.418770i	$-0.137539\pi$
$997$	996.474	+	575.315i	0.999473	+	0.577046i	0.0913804	+	0.995816i	$0.470872\pi$
$998$	123.029	−	213.093i	0.123276	−	0.213520i
$999$	27.1163	−	15.6556i	0.0271435	−	0.0156713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.f.451.2	yes	12
5.2	odd	4		1050.3.q.d.199.11		24
5.3	odd	4		1050.3.q.d.199.3		24
5.4	even	2		1050.3.p.e.451.5	✓	12
7.5	odd	6	inner	1050.3.p.f.901.2	yes	12
35.12	even	12		1050.3.q.d.649.3		24
35.19	odd	6		1050.3.p.e.901.5	yes	12
35.33	even	12		1050.3.q.d.649.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.5	✓	12	5.4	even	2
1050.3.p.e.901.5	yes	12	35.19	odd	6
1050.3.p.f.451.2	yes	12	1.1	even	1	trivial
1050.3.p.f.901.2	yes	12	7.5	odd	6	inner
1050.3.q.d.199.3		24	5.3	odd	4
1050.3.q.d.199.11		24	5.2	odd	4
1050.3.q.d.649.3		24	35.12	even	12
1050.3.q.d.649.11		24	35.33	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} +(1.88399 - 6.74171i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.65702 - 2.87005i) q^{11} +(-3.00000 + 1.73205i) q^{12} +19.5077i q^{13} +(-9.58905 + 2.45970i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(7.30003 + 4.21467i) q^{17} +(2.12132 - 3.67423i) q^{18} +(0.704670 - 0.406841i) q^{19} +(8.66447 - 8.48098i) q^{21} -4.68677 q^{22} +(5.98556 + 10.3673i) q^{23} +(4.24264 + 2.44949i) q^{24} +(23.8919 - 13.7940i) q^{26} +5.19615i q^{27} +(9.79299 + 10.0049i) q^{28} +4.68677 q^{29} +(27.9363 + 16.1291i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(4.97107 - 2.87005i) q^{33} -11.9209i q^{34} -6.00000 q^{36} +(-3.01293 - 5.21854i) q^{37} +(-0.996554 - 0.575361i) q^{38} +(-16.8942 + 29.2615i) q^{39} -19.6861i q^{41} +(-16.5137 - 4.61481i) q^{42} -2.53339 q^{43} +(3.31404 + 5.74009i) q^{44} +(8.46486 - 14.6616i) q^{46} +(-15.8328 + 9.14110i) q^{47} -6.92820i q^{48} +(-41.9012 - 25.4026i) q^{49} +(7.30003 + 12.6440i) q^{51} +(-33.7883 - 19.5077i) q^{52} +(15.9837 - 27.6846i) q^{53} +(6.36396 - 3.67423i) q^{54} +(5.32872 - 19.0684i) q^{56} +1.40934 q^{57} +(-3.31404 - 5.74009i) q^{58} +(64.3758 + 37.1674i) q^{59} +(95.1577 - 54.9393i) q^{61} -45.6199i q^{62} +(20.3414 - 5.21781i) q^{63} +8.00000 q^{64} +(-7.03015 - 4.05886i) q^{66} +(-47.3405 + 81.9962i) q^{67} +(-14.6001 + 8.42935i) q^{68} +20.7346i q^{69} +98.0047 q^{71} +(4.24264 + 7.34847i) q^{72} +(-9.62690 - 5.55809i) q^{73} +(-4.26092 + 7.38013i) q^{74} +1.62737i q^{76} +(-16.2272 - 16.5783i) q^{77} +47.7839 q^{78} +(-0.500763 - 0.867346i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-24.1105 + 13.9202i) q^{82} +66.8044i q^{83} +(6.02501 + 23.4883i) q^{84} +(1.79138 + 3.10276i) q^{86} +(7.03015 + 4.05886i) q^{87} +(4.68677 - 8.11772i) q^{88} +(133.528 - 77.0927i) q^{89} +(131.515 + 36.7523i) q^{91} -23.9422 q^{92} +(27.9363 + 48.3872i) q^{93} +(22.3910 + 12.9275i) q^{94} +(-8.48528 + 4.89898i) q^{96} +132.023i q^{97} +(-1.48309 + 69.2806i) q^{98} +9.94213 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

Introduction

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