LMFDB - Embedded newform 156.3.e.c.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(103,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("156.103");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	156.103
Dual form			156.3.e.c.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86766 - 0.715427i) q^{2} -1.73205i q^{3} +(2.97633 + 2.67235i) q^{4} +4.65917i q^{5} +(-1.23916 + 3.23489i) q^{6} -2.30148 q^{7} +(-3.64691 - 7.12040i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.86766 - 0.715427i) q^{2} -1.73205i q^{3} +(2.97633 + 2.67235i) q^{4} +4.65917i q^{5} +(-1.23916 + 3.23489i) q^{6} -2.30148 q^{7} +(-3.64691 - 7.12040i) q^{8} -3.00000 q^{9} +(3.33330 - 8.70176i) q^{10} -18.8569 q^{11} +(4.62865 - 5.15515i) q^{12} +(-5.93827 + 11.5645i) q^{13} +(4.29838 + 1.64654i) q^{14} +8.06992 q^{15} +(1.71708 + 15.9076i) q^{16} -7.23481 q^{17} +(5.60299 + 2.14628i) q^{18} +17.0136 q^{19} +(-12.4509 + 13.8672i) q^{20} +3.98628i q^{21} +(35.2183 + 13.4907i) q^{22} +43.7479i q^{23} +(-12.3329 + 6.31663i) q^{24} +3.29211 q^{25} +(19.3642 - 17.3501i) q^{26} +5.19615i q^{27} +(-6.84996 - 6.15036i) q^{28} -52.6383 q^{29} +(-15.0719 - 5.77344i) q^{30} -10.5577 q^{31} +(8.17380 - 30.9385i) q^{32} +32.6611i q^{33} +(13.5122 + 5.17598i) q^{34} -10.7230i q^{35} +(-8.92899 - 8.01705i) q^{36} +12.2916i q^{37} +(-31.7756 - 12.1720i) q^{38} +(20.0302 + 10.2854i) q^{39} +(33.1752 - 16.9916i) q^{40} -38.5108i q^{41} +(2.85189 - 7.44502i) q^{42} -12.0510i q^{43} +(-56.1243 - 50.3922i) q^{44} -13.9775i q^{45} +(31.2984 - 81.7064i) q^{46} +62.7999 q^{47} +(27.5528 - 2.97406i) q^{48} -43.7032 q^{49} +(-6.14854 - 2.35526i) q^{50} +12.5311i q^{51} +(-48.5786 + 18.5505i) q^{52} +74.8604 q^{53} +(3.71747 - 9.70466i) q^{54} -87.8574i q^{55} +(8.39328 + 16.3874i) q^{56} -29.4683i q^{57} +(98.3106 + 37.6588i) q^{58} -11.4508 q^{59} +(24.0188 + 21.5657i) q^{60} -32.1927 q^{61} +(19.7183 + 7.55328i) q^{62} +6.90443 q^{63} +(-37.4001 + 51.9349i) q^{64} +(-53.8809 - 27.6674i) q^{65} +(23.3666 - 60.9999i) q^{66} -60.8491 q^{67} +(-21.5332 - 19.3340i) q^{68} +75.7737 q^{69} +(-7.67151 + 20.0269i) q^{70} -8.07712 q^{71} +(10.9407 + 21.3612i) q^{72} +58.3386i q^{73} +(8.79373 - 22.9566i) q^{74} -5.70210i q^{75} +(50.6380 + 45.4662i) q^{76} +43.3987 q^{77} +(-30.0513 - 33.5398i) q^{78} -59.0233i q^{79} +(-74.1162 + 8.00016i) q^{80} +9.00000 q^{81} +(-27.5517 + 71.9252i) q^{82} -48.7775 q^{83} +(-10.6527 + 11.8645i) q^{84} -33.7082i q^{85} +(-8.62162 + 22.5073i) q^{86} +91.1722i q^{87} +(68.7693 + 134.268i) q^{88} -80.5117i q^{89} +(-9.99989 + 26.1053i) q^{90} +(13.6668 - 26.6154i) q^{91} +(-116.910 + 130.208i) q^{92} +18.2865i q^{93} +(-117.289 - 44.9287i) q^{94} +79.2691i q^{95} +(-53.5870 - 14.1574i) q^{96} -15.3235i q^{97} +(81.6229 + 31.2664i) q^{98} +56.5706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 72 q^{9}+O(q^{10}) $ 24 * q + 8 * q^4 - 72 * q^9	$ 24 q + 8 q^{4} - 72 q^{9} + 28 q^{10} + 36 q^{12} + 48 q^{13} - 40 q^{14} + 100 q^{16} + 32 q^{17} + 84 q^{22} - 312 q^{25} - 16 q^{26} - 80 q^{29} + 60 q^{30} - 24 q^{36} + 120 q^{38} - 204 q^{40} - 96 q^{42} - 144 q^{48} + 392 q^{49} + 28 q^{52} - 224 q^{53} + 800 q^{56} - 96 q^{61} - 352 q^{62} - 184 q^{64} - 112 q^{65} + 252 q^{66} - 344 q^{68} + 144 q^{69} + 232 q^{74} - 16 q^{77} - 168 q^{78} + 216 q^{81} + 20 q^{82} - 92 q^{88} - 84 q^{90} - 616 q^{92} - 684 q^{94}+O(q^{100}) $ 24 * q + 8 * q^4 - 72 * q^9 + 28 * q^10 + 36 * q^12 + 48 * q^13 - 40 * q^14 + 100 * q^16 + 32 * q^17 + 84 * q^22 - 312 * q^25 - 16 * q^26 - 80 * q^29 + 60 * q^30 - 24 * q^36 + 120 * q^38 - 204 * q^40 - 96 * q^42 - 144 * q^48 + 392 * q^49 + 28 * q^52 - 224 * q^53 + 800 * q^56 - 96 * q^61 - 352 * q^62 - 184 * q^64 - 112 * q^65 + 252 * q^66 - 344 * q^68 + 144 * q^69 + 232 * q^74 - 16 * q^77 - 168 * q^78 + 216 * q^81 + 20 * q^82 - 92 * q^88 - 84 * q^90 - 616 * q^92 - 684 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.86766	−	0.715427i	−0.933831	−	0.357713i
$2$	−1.86766	−	0.715427i	−0.933831	−	0.357713i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.97633	+	2.67235i	0.744082	+	0.668088i
$5$			4.65917i			0.931835i	0.884828	+	0.465917i	$0.154276\pi$
$5$			4.65917i			0.931835i	−0.884828	+	0.465917i	$0.845724\pi$
$6$	−1.23916	+	3.23489i	−0.206526	+	0.539148i
$7$	−2.30148			−0.328782			−0.164391	−	0.986395i	$-0.552566\pi$
$7$	−2.30148			−0.328782			−0.164391	+	0.986395i	$0.552566\pi$
$8$	−3.64691	−	7.12040i	−0.455864	−	0.890050i
$9$	−3.00000			−0.333333
$10$	3.33330	−	8.70176i	0.333330	−	0.870176i
$11$	−18.8569			−1.71426			−0.857131	−	0.515099i	$-0.827755\pi$
$11$	−18.8569			−1.71426			−0.857131	+	0.515099i	$0.827755\pi$
$12$	4.62865	−	5.15515i	0.385721	−	0.429596i
$13$	−5.93827	+	11.5645i	−0.456790	+	0.889574i
$13$	−5.93827	+	11.5645i	−0.456790	+	0.889574i
$14$	4.29838	+	1.64654i	0.307027	+	0.117610i
$15$	8.06992			0.537995
$16$	1.71708	+	15.9076i	0.107317	+	0.994225i
$17$	−7.23481			−0.425577			−0.212789	−	0.977098i	$-0.568255\pi$
$17$	−7.23481			−0.425577			−0.212789	+	0.977098i	$0.568255\pi$
$18$	5.60299	+	2.14628i	0.311277	+	0.119238i
$19$	17.0136			0.895450			0.447725	−	0.894171i	$-0.352234\pi$
$19$	17.0136			0.895450			0.447725	+	0.894171i	$0.352234\pi$
$20$	−12.4509	+	13.8672i	−0.622547	+	0.693362i
$21$			3.98628i			0.189823i
$22$	35.2183	+	13.4907i	1.60083	+	0.613214i
$23$			43.7479i			1.90208i	0.309061	+	0.951042i	$0.399985\pi$
$23$			43.7479i			1.90208i	−0.309061	+	0.951042i	$0.600015\pi$
$24$	−12.3329	+	6.31663i	−0.513870	+	0.263193i
$25$	3.29211			0.131684
$26$	19.3642	−	17.3501i	0.744778	−	0.667313i
$27$			5.19615i			0.192450i
$28$	−6.84996	−	6.15036i	−0.244641	−	0.219656i
$29$	−52.6383			−1.81511			−0.907557	−	0.419930i	$-0.862055\pi$
$29$	−52.6383			−1.81511			−0.907557	+	0.419930i	$0.862055\pi$
$30$	−15.0719	−	5.77344i	−0.502397	−	0.192448i
$31$	−10.5577			−0.340572			−0.170286	−	0.985395i	$-0.554469\pi$
$31$	−10.5577			−0.340572			−0.170286	+	0.985395i	$0.554469\pi$
$32$	8.17380	−	30.9385i	0.255431	−	0.966827i
$33$			32.6611i			0.989729i
$34$	13.5122	+	5.17598i	0.397417	+	0.152235i
$35$		−	10.7230i		−	0.306371i
$36$	−8.92899	−	8.01705i	−0.248027	−	0.222696i
$37$			12.2916i			0.332205i	0.986108	+	0.166103i	$0.0531183\pi$
$37$			12.2916i			0.332205i	−0.986108	+	0.166103i	$0.946882\pi$
$38$	−31.7756	−	12.1720i	−0.836200	−	0.320314i
$39$	20.0302	+	10.2854i	0.513596	+	0.263728i
$40$	33.1752	−	16.9916i	0.829379	−	0.424790i
$41$		−	38.5108i		−	0.939288i	−0.882856	−	0.469644i	$-0.844382\pi$
$41$		−	38.5108i		−	0.939288i	0.882856	−	0.469644i	$-0.155618\pi$
$42$	2.85189	−	7.44502i	0.0679021	−	0.177262i
$43$		−	12.0510i		−	0.280256i	−0.990133	−	0.140128i	$-0.955249\pi$
$43$		−	12.0510i		−	0.280256i	0.990133	−	0.140128i	$-0.0447515\pi$
$44$	−56.1243	−	50.3922i	−1.27555	−	1.14528i
$45$		−	13.9775i		−	0.310612i
$46$	31.2984	−	81.7064i	0.680401	−	1.77623i
$47$	62.7999			1.33617			0.668084	−	0.744086i	$-0.267115\pi$
$47$	62.7999			1.33617			0.668084	+	0.744086i	$0.267115\pi$
$48$	27.5528	−	2.97406i	0.574016	−	0.0619597i
$49$	−43.7032			−0.891902
$50$	−6.14854	−	2.35526i	−0.122971	−	0.0471052i
$51$			12.5311i			0.245707i
$52$	−48.5786	+	18.5505i	−0.934203	+	0.356741i
$53$	74.8604			1.41246			0.706230	−	0.707982i	$-0.250394\pi$
$53$	74.8604			1.41246			0.706230	+	0.707982i	$0.250394\pi$
$54$	3.71747	−	9.70466i	0.0688420	−	0.179716i
$55$		−	87.8574i		−	1.59741i
$56$	8.39328	+	16.3874i	0.149880	+	0.292633i
$57$		−	29.4683i		−	0.516989i
$58$	98.3106	+	37.6588i	1.69501	+	0.649290i
$59$	−11.4508			−0.194082			−0.0970410	−	0.995280i	$-0.530938\pi$
$59$	−11.4508			−0.194082			−0.0970410	+	0.995280i	$0.530938\pi$
$60$	24.0188	+	21.5657i	0.400313	+	0.359428i
$61$	−32.1927			−0.527749			−0.263874	−	0.964557i	$-0.585000\pi$
$61$	−32.1927			−0.527749			−0.263874	+	0.964557i	$0.585000\pi$
$62$	19.7183	+	7.55328i	0.318037	+	0.121827i
$63$	6.90443			0.109594
$64$	−37.4001	+	51.9349i	−0.584377	+	0.811483i
$65$	−53.8809	−	27.6674i	−0.828936	−	0.425653i
$66$	23.3666	−	60.9999i	0.354039	−	0.924240i
$67$	−60.8491			−0.908195			−0.454098	−	0.890952i	$-0.650038\pi$
$67$	−60.8491			−0.908195			−0.454098	+	0.890952i	$0.650038\pi$
$68$	−21.5332	−	19.3340i	−0.316665	−	0.284323i
$69$	75.7737			1.09817
$70$	−7.67151	+	20.0269i	−0.109593	+	0.286099i
$71$	−8.07712			−0.113762			−0.0568811	−	0.998381i	$-0.518116\pi$
$71$	−8.07712			−0.113762			−0.0568811	+	0.998381i	$0.518116\pi$
$72$	10.9407	+	21.3612i	0.151955	+	0.296683i
$73$			58.3386i			0.799159i	0.916699	+	0.399579i	$0.130844\pi$
$73$			58.3386i			0.799159i	−0.916699	+	0.399579i	$0.869156\pi$
$74$	8.79373	−	22.9566i	0.118834	−	0.310224i
$75$		−	5.70210i		−	0.0760279i
$76$	50.6380	+	45.4662i	0.666289	+	0.598239i
$77$	43.3987			0.563619
$78$	−30.0513	−	33.5398i	−0.385273	−	0.429998i
$79$		−	59.0233i		−	0.747131i	−0.927604	−	0.373565i	$-0.878135\pi$
$79$		−	59.0233i		−	0.747131i	0.927604	−	0.373565i	$-0.121865\pi$
$80$	−74.1162	+	8.00016i	−0.926453	+	0.100002i
$81$	9.00000			0.111111
$82$	−27.5517	+	71.9252i	−0.335996	+	0.877137i
$83$	−48.7775			−0.587681			−0.293841	−	0.955854i	$-0.594934\pi$
$83$	−48.7775			−0.587681			−0.293841	+	0.955854i	$0.594934\pi$
$84$	−10.6527	+	11.8645i	−0.126818	+	0.141244i
$85$		−	33.7082i		−	0.396568i
$86$	−8.62162	+	22.5073i	−0.100251	+	0.261712i
$87$			91.1722i			1.04796i
$88$	68.7693	+	134.268i	0.781469	+	1.52578i
$89$		−	80.5117i		−	0.904626i	−0.891859	−	0.452313i	$-0.850599\pi$
$89$		−	80.5117i		−	0.904626i	0.891859	−	0.452313i	$-0.149401\pi$
$90$	−9.99989	+	26.1053i	−0.111110	+	0.290059i
$91$	13.6668	−	26.6154i	0.150185	−	0.292476i
$92$	−116.910	+	130.208i	−1.27076	+	1.41531i
$93$			18.2865i			0.196629i
$94$	−117.289	−	44.9287i	−1.24776	−	0.477965i
$95$			79.2691i			0.834412i
$96$	−53.5870	−	14.1574i	−0.558198	−	0.147473i
$97$		−	15.3235i		−	0.157975i	−0.996876	−	0.0789873i	$-0.974831\pi$
$97$		−	15.3235i		−	0.157975i	0.996876	−	0.0789873i	$-0.0251687\pi$
$98$	81.6229	+	31.2664i	0.832886	+	0.319045i
$99$	56.5706			0.571420
$100$	9.79839	+	8.79766i	0.0979839	+	0.0879766i
$101$	82.3254			0.815103			0.407552	−	0.913182i	$-0.366383\pi$
$101$	82.3254			0.815103			0.407552	+	0.913182i	$0.366383\pi$
$102$	8.96506	−	23.4038i	0.0878927	−	0.229449i
$103$		−	110.613i		−	1.07391i	−0.843610	−	0.536956i	$-0.819574\pi$
$103$		−	110.613i		−	1.07391i	0.843610	−	0.536956i	$-0.180426\pi$
$104$	104.000	+	0.108306i	0.999999	+	0.00104140i
$105$	−18.5727			−0.176883
$106$	−139.814	−	53.5571i	−1.31900	−	0.505256i
$107$			115.897i			1.08315i	0.840653	+	0.541575i	$0.182172\pi$
$107$			115.897i			1.08315i	−0.840653	+	0.541575i	$0.817828\pi$
$108$	−13.8859	+	15.4655i	−0.128574	+	0.143199i
$109$			74.5767i			0.684190i	0.939665	+	0.342095i	$0.111136\pi$
$109$			74.5767i			0.684190i	−0.939665	+	0.342095i	$0.888864\pi$
$110$	−62.8555	+	164.088i	−0.571414	+	1.49171i
$111$	21.2897			0.191799
$112$	−3.95181	−	36.6110i	−0.0352840	−	0.326884i
$113$	129.161			1.14302			0.571510	−	0.820595i	$-0.306358\pi$
$113$	129.161			1.14302			0.571510	+	0.820595i	$0.306358\pi$
$114$	−21.0824	+	55.0369i	−0.184934	+	0.482780i
$115$	−203.829			−1.77243
$116$	−156.669	−	140.668i	−1.35059	−	1.21266i
$117$	17.8148	−	34.6934i	0.152263	−	0.296525i
$118$	21.3863	+	8.19224i	0.181240	+	0.0694257i
$119$	16.6508			0.139922
$120$	−29.4303	−	57.4611i	−0.245252	−	0.478842i
$121$	234.582			1.93869
$122$	60.1251	+	23.0315i	0.492828	+	0.188783i
$123$	−66.7027			−0.542298
$124$	−31.4233	−	28.2140i	−0.253413	−	0.227532i
$125$			131.818i			1.05454i
$126$	−12.8952	−	4.93961i	−0.102342	−	0.0392033i
$127$		−	12.8779i		−	0.101401i	−0.998714	−	0.0507003i	$-0.983855\pi$
$127$		−	12.8779i		−	0.101401i	0.998714	−	0.0507003i	$-0.0161453\pi$
$128$	107.006	−	70.2398i	0.835987	−	0.548749i
$129$	−20.8730			−0.161806
$130$	80.8372	+	90.2213i	0.621825	+	0.694010i
$131$		−	67.0067i		−	0.511502i	−0.966743	−	0.255751i	$-0.917677\pi$
$131$		−	67.0067i		−	0.511502i	0.966743	−	0.255751i	$-0.0823227\pi$
$132$	−87.2818	+	97.2101i	−0.661226	+	0.736440i
$133$	−39.1563			−0.294408
$134$	113.646	+	43.5331i	0.848102	+	0.324874i
$135$	−24.2098			−0.179332
$136$	26.3847	+	51.5147i	0.194005	+	0.378785i
$137$			250.997i			1.83209i	0.401072	+	0.916047i	$0.368638\pi$
$137$			250.997i			1.83209i	−0.401072	+	0.916047i	$0.631362\pi$
$138$	−141.520	−	54.2105i	−1.02550	−	0.392830i
$139$			118.887i			0.855299i	0.903945	+	0.427650i	$0.140658\pi$
$139$			118.887i			0.855299i	−0.903945	+	0.427650i	$0.859342\pi$
$140$	28.6556	−	31.9151i	0.204683	−	0.227965i
$141$		−	108.773i		−	0.771437i
$142$	15.0853	+	5.77859i	0.106235	+	0.0406943i
$143$	111.977	−	218.070i	0.783058	−	1.52496i
$144$	−5.15123	−	47.7228i	−0.0357724	−	0.331408i
$145$		−	245.251i		−	1.69139i
$146$	41.7370	−	108.957i	0.285870	−	0.746279i
$147$			75.6962i			0.514940i
$148$	−32.8475	+	36.5838i	−0.221942	+	0.247188i
$149$		−	93.2446i		−	0.625803i	−0.949786	−	0.312901i	$-0.898699\pi$
$149$		−	93.2446i		−	0.625803i	0.949786	−	0.312901i	$-0.101301\pi$
$150$	−4.07943	+	10.6496i	−0.0271962	+	0.0709973i
$151$	157.498			1.04303			0.521517	−	0.853241i	$-0.325366\pi$
$151$	157.498			1.04303			0.521517	+	0.853241i	$0.325366\pi$
$152$	−62.0469	−	121.143i	−0.408203	−	0.796995i
$153$	21.7044			0.141859
$154$	−81.0541	−	31.0486i	−0.526325	−	0.201614i
$155$		−	49.1903i		−	0.317357i
$156$	32.1304	+	84.1406i	0.205964	+	0.539363i
$157$	−131.405			−0.836972			−0.418486	−	0.908223i	$-0.637439\pi$
$157$	−131.405			−0.836972			−0.418486	+	0.908223i	$0.637439\pi$
$158$	−42.2269	+	110.236i	−0.267259	+	0.697694i
$159$		−	129.662i		−	0.815484i
$160$	144.148	+	38.0831i	0.900923	+	0.238020i
$161$		−	100.685i		−	0.625372i
$162$	−16.8090	−	6.43884i	−0.103759	−	0.0397459i
$163$	−112.410			−0.689632			−0.344816	−	0.938670i	$-0.612059\pi$
$163$	−112.410			−0.689632			−0.344816	+	0.938670i	$0.612059\pi$
$164$	102.914	−	114.621i	0.627527	−	0.698908i
$165$	−152.174			−0.922264
$166$	91.1000	+	34.8968i	0.548795	+	0.210221i
$167$	83.8946			0.502363			0.251181	−	0.967940i	$-0.419181\pi$
$167$	83.8946			0.502363			0.251181	+	0.967940i	$0.419181\pi$
$168$	28.3839	−	14.5376i	0.168952	−	0.0865333i
$169$	−98.4738	−	137.346i	−0.582685	−	0.812698i
$170$	−24.1158	+	62.9556i	−0.141857	+	0.370327i
$171$	−51.0407			−0.298483
$172$	32.2046	−	35.8678i	0.187236	−	0.208534i
$173$	−57.0962			−0.330036			−0.165018	−	0.986291i	$-0.552768\pi$
$173$	−57.0962			−0.330036			−0.165018	+	0.986291i	$0.552768\pi$
$174$	65.2270	−	170.279i	0.374868	−	0.978614i
$175$	−7.57671			−0.0432955
$176$	−32.3787	−	299.968i	−0.183970	−	1.70436i
$177$			19.8334i			0.112053i
$178$	−57.6002	+	150.369i	−0.323597	+	0.844768i
$179$			258.829i			1.44597i	0.690862	+	0.722987i	$0.257231\pi$
$179$			258.829i			1.44597i	−0.690862	+	0.722987i	$0.742769\pi$
$180$	37.3528	−	41.6017i	0.207516	−	0.231121i
$181$	−173.429			−0.958172			−0.479086	−	0.877768i	$-0.659032\pi$
$181$	−173.429			−0.958172			−0.479086	+	0.877768i	$0.659032\pi$
$182$	−44.5663	+	39.9309i	−0.244870	+	0.219401i
$183$			55.7594i			0.304696i
$184$	311.503	−	159.545i	1.69295	−	0.867091i
$185$	−57.2687			−0.309560
$186$	13.0827	−	34.1530i	0.0703369	−	0.183619i
$187$	136.426			0.729551
$188$	186.913	+	167.823i	0.994219	+	0.892677i
$189$		−	11.9588i		−	0.0632742i
$190$	56.7112	−	148.048i	0.298480	−	0.779200i
$191$		−	175.865i		−	0.920761i	−0.887722	−	0.460380i	$-0.847713\pi$
$191$		−	175.865i		−	0.920761i	0.887722	−	0.460380i	$-0.152287\pi$
$192$	89.9539	+	64.7789i	0.468510	+	0.337390i
$193$			132.333i			0.685665i	0.939397	+	0.342832i	$0.111386\pi$
$193$			132.333i			0.685665i	−0.939397	+	0.342832i	$0.888614\pi$
$194$	−10.9629	+	28.6192i	−0.0565096	+	0.147522i
$195$	−47.9214	+	93.3244i	−0.245751	+	0.478587i
$196$	−130.075	−	116.790i	−0.663649	−	0.595869i
$197$			238.024i			1.20825i	0.796891	+	0.604123i	$0.206476\pi$
$197$			238.024i			1.20825i	−0.796891	+	0.604123i	$0.793524\pi$
$198$	−105.655	−	40.4721i	−0.533610	−	0.204405i
$199$			241.516i			1.21365i	0.794836	+	0.606824i	$0.207557\pi$
$199$			241.516i			1.21365i	−0.794836	+	0.606824i	$0.792443\pi$
$200$	−12.0060	−	23.4411i	−0.0600301	−	0.117206i
$201$			105.394i			0.524347i
$202$	−153.756	−	58.8978i	−0.761169	−	0.291573i
$203$	121.146			0.596777
$204$	−33.4874	+	37.2966i	−0.164154	+	0.182826i
$205$	179.429			0.875261
$206$	−79.1354	+	206.588i	−0.384153	+	1.00285i
$207$		−	131.244i		−	0.634028i
$208$	−194.159	−	74.6066i	−0.933458	−	0.358686i
$209$	−320.822			−1.53504
$210$	34.6876	+	13.2874i	0.165179	+	0.0632735i
$211$		−	218.961i		−	1.03773i	−0.854857	−	0.518864i	$-0.826355\pi$
$211$		−	218.961i		−	1.03773i	0.854857	−	0.518864i	$-0.173645\pi$
$212$	222.809	+	200.053i	1.05099	+	0.943648i
$213$			13.9900i			0.0656807i
$214$	82.9158	−	216.457i	0.387457	−	1.01148i
$215$	56.1478			0.261153
$216$	36.9987	−	18.9499i	0.171290	−	0.0877310i
$217$	24.2984			0.111974
$218$	53.3541	−	139.284i	0.244744	−	0.638918i
$219$	101.045			0.461394
$220$	234.786	−	261.493i	1.06721	−	1.18860i
$221$	42.9623	−	83.6668i	0.194400	−	0.378583i
$222$	−39.7619	−	15.2312i	−0.179108	−	0.0686090i
$223$	282.087			1.26496			0.632482	−	0.774575i	$-0.282036\pi$
$223$	282.087			1.26496			0.632482	+	0.774575i	$0.282036\pi$
$224$	−18.8118	+	71.2042i	−0.0839813	+	0.317876i
$225$	−9.87632			−0.0438947
$226$	−241.230	−	92.4055i	−1.06739	−	0.408874i
$227$	−241.629			−1.06445			−0.532223	−	0.846604i	$-0.678643\pi$
$227$	−241.629			−1.06445			−0.532223	+	0.846604i	$0.678643\pi$
$228$	78.7498	−	87.7075i	0.345394	−	0.384682i
$229$			423.757i			1.85047i	0.379396	+	0.925234i	$0.376132\pi$
$229$			423.757i			1.85047i	−0.379396	+	0.925234i	$0.623868\pi$
$230$	380.684	+	145.825i	1.65515	+	0.634021i
$231$		−	75.1687i		−	0.325406i
$232$	191.967	+	374.805i	0.827444	+	1.61554i
$233$	−398.396			−1.70985			−0.854926	−	0.518750i	$-0.826398\pi$
$233$	−398.396			−1.70985			−0.854926	+	0.518750i	$0.826398\pi$
$234$	−58.0927	+	52.0504i	−0.248259	+	0.222438i
$235$			292.596i			1.24509i
$236$	−34.0815	−	30.6007i	−0.144413	−	0.129664i
$237$	−102.231			−0.431356
$238$	−31.0980	−	11.9124i	−0.130664	−	0.0500521i
$239$	83.0358			0.347430			0.173715	−	0.984796i	$-0.444423\pi$
$239$	83.0358			0.347430			0.173715	+	0.984796i	$0.444423\pi$
$240$	13.8567	+	128.373i	0.0577362	+	0.534888i
$241$			321.181i			1.33270i	0.745639	+	0.666350i	$0.232144\pi$
$241$			321.181i			1.33270i	−0.745639	+	0.666350i	$0.767856\pi$
$242$	−438.120	−	167.826i	−1.81041	−	0.693496i
$243$		−	15.5885i		−	0.0641500i
$244$	−95.8160	−	86.0301i	−0.392689	−	0.352583i
$245$		−	203.621i		−	0.831105i
$246$	124.578	+	47.7209i	0.506415	+	0.193987i
$247$	−101.031	+	196.753i	−0.409033	+	0.796570i
$248$	38.5031	+	75.1752i	0.155254	+	0.303126i
$249$			84.4852i			0.339298i
$250$	94.3060	−	246.191i	0.377224	−	0.984765i
$251$			178.799i			0.712345i	0.934420	+	0.356172i	$0.115918\pi$
$251$			178.799i			0.712345i	−0.934420	+	0.356172i	$0.884082\pi$
$252$	20.5499	+	18.4511i	0.0815471	+	0.0732185i
$253$		−	824.949i		−	3.26067i
$254$	−9.21318	+	24.0515i	−0.0362724	+	0.0946911i
$255$	−58.3844			−0.228958
$256$	−250.103	+	54.6291i	−0.976966	+	0.213395i
$257$	402.707			1.56695			0.783476	−	0.621422i	$-0.213445\pi$
$257$	402.707			1.56695			0.783476	+	0.621422i	$0.213445\pi$
$258$	38.9837	+	14.9331i	0.151100	+	0.0578802i
$259$		−	28.2888i		−	0.109223i
$260$	−86.4300	−	226.336i	−0.332423	−	0.870523i
$261$	157.915			0.605038
$262$	−47.9384	+	125.146i	−0.182971	+	0.477656i
$263$		−	282.633i		−	1.07465i	−0.843375	−	0.537325i	$-0.819435\pi$
$263$		−	282.633i		−	1.07465i	0.843375	−	0.537325i	$-0.180565\pi$
$264$	232.560	−	119.112i	0.880908	−	0.451182i
$265$			348.788i			1.31618i
$266$	73.1308	+	28.0135i	0.274928	+	0.105314i
$267$	−139.450			−0.522286
$268$	−181.107	−	162.610i	−0.675772	−	0.606754i
$269$	158.866			0.590579			0.295289	−	0.955408i	$-0.404584\pi$
$269$	158.866			0.590579			0.295289	+	0.955408i	$0.404584\pi$
$270$	45.2157	+	17.3203i	0.167466	+	0.0641493i
$271$	−256.327			−0.945855			−0.472928	−	0.881101i	$-0.656803\pi$
$271$	−256.327			−0.945855			−0.472928	+	0.881101i	$0.656803\pi$
$272$	−12.4227	−	115.088i	−0.0456718	−	0.423119i
$273$	−46.0992	−	23.6716i	−0.168861	−	0.0867092i
$274$	179.570	−	468.777i	0.655364	−	1.71087i
$275$	−62.0788			−0.225741
$276$	225.527	+	202.494i	0.817128	+	0.733673i
$277$	−108.906			−0.393163			−0.196582	−	0.980487i	$-0.562984\pi$
$277$	−108.906			−0.393163			−0.196582	+	0.980487i	$0.562984\pi$
$278$	85.0546	−	222.040i	0.305952	−	0.798705i
$279$	31.6732			0.113524
$280$	−76.3519	+	39.1057i	−0.272685	+	0.139663i
$281$			52.2572i			0.185969i	0.995668	+	0.0929844i	$0.0296407\pi$
$281$			52.2572i			0.185969i	−0.995668	+	0.0929844i	$0.970359\pi$
$282$	−77.8188	+	203.151i	−0.275953	+	0.720392i
$283$			233.514i			0.825140i	0.910926	+	0.412570i	$0.135369\pi$
$283$			233.514i			0.825140i	−0.910926	+	0.412570i	$0.864631\pi$
$284$	−24.0402	−	21.5849i	−0.0846485	−	0.0760032i
$285$	137.298			0.481748
$286$	−365.149	+	327.169i	−1.27674	+	1.14395i
$287$			88.6318i			0.308822i
$288$	−24.5214	+	92.8154i	−0.0851437	+	0.322276i
$289$	−236.657			−0.818884
$290$	−175.459	+	458.046i	−0.605031	+	1.57947i
$291$	−26.5412			−0.0912067
$292$	−155.901	+	173.635i	−0.533908	+	0.594640i
$293$			0.918517i			0.00313487i	0.999999	+	0.00156744i	$0.000498930\pi$
$293$			0.918517i			0.00313487i	−0.999999	+	0.00156744i	$0.999501\pi$
$294$	54.1550	−	141.375i	0.184201	−	0.480867i
$295$		−	53.3514i		−	0.180852i
$296$	87.5210	−	44.8263i	0.295679	−	0.151440i
$297$		−	97.9832i		−	0.329910i
$298$	−66.7096	+	174.149i	−0.223858	+	0.584394i
$299$	−505.922	−	259.787i	−1.69205	−	0.868854i
$300$	15.2380	−	16.9713i	0.0507933	−	0.0565711i
$301$			27.7352i			0.0921434i
$302$	−294.153	−	112.678i	−0.974018	−	0.373107i
$303$		−	142.592i		−	0.470600i
$304$	29.2136	+	270.645i	0.0960973	+	0.890279i
$305$		−	149.991i		−	0.491775i
$306$	−40.5366	−	15.5279i	−0.132472	−	0.0507449i
$307$	−442.913			−1.44271			−0.721356	−	0.692564i	$-0.756481\pi$
$307$	−442.913			−1.44271			−0.721356	+	0.692564i	$0.756481\pi$
$308$	129.169	+	115.976i	0.419379	+	0.376547i
$309$	−191.587			−0.620023
$310$	−35.1920	+	91.8708i	−0.113523	+	0.296358i
$311$			461.751i			1.48473i	0.669995	+	0.742366i	$0.266296\pi$
$311$			461.751i			1.48473i	−0.669995	+	0.742366i	$0.733704\pi$
$312$	0.187591	−	180.133i	0.000601252	−	0.577350i
$313$	452.776			1.44657			0.723284	−	0.690551i	$-0.242632\pi$
$313$	452.776			1.44657			0.723284	+	0.690551i	$0.242632\pi$
$314$	245.420	+	94.0104i	0.781591	+	0.299396i
$315$			32.1689i			0.102124i
$316$	157.731	−	175.673i	0.499149	−	0.555927i
$317$			429.708i			1.35555i	0.735271	+	0.677773i	$0.237055\pi$
$317$			429.708i			1.35555i	−0.735271	+	0.677773i	$0.762945\pi$
$318$	−92.7636	+	242.165i	−0.291710	+	0.761525i
$319$	992.593			3.11158
$320$	−241.974	−	174.254i	−0.756168	−	0.544542i
$321$	200.740			0.625357
$322$	−72.0327	+	188.045i	−0.223704	+	0.583992i
$323$	−123.090			−0.381083
$324$	26.7870	+	24.0512i	0.0826758	+	0.0742320i
$325$	−19.5494	+	38.0715i	−0.0601521	+	0.117143i
$326$	209.944	+	80.4211i	0.644000	+	0.246690i
$327$	129.171			0.395017
$328$	−274.212	+	140.445i	−0.836013	+	0.428187i
$329$	−144.533			−0.439309
$330$	284.209	+	108.869i	0.861239	+	0.329906i
$331$	168.515			0.509110			0.254555	−	0.967058i	$-0.418071\pi$
$331$	168.515			0.509110			0.254555	+	0.967058i	$0.418071\pi$
$332$	−145.178	−	130.351i	−0.437283	−	0.392623i
$333$		−	36.8748i		−	0.110735i
$334$	−156.687	−	60.0204i	−0.469122	−	0.179702i
$335$		−	283.506i		−	0.846288i
$336$	−63.4121	+	6.84474i	−0.188726	+	0.0203712i
$337$	367.985			1.09195			0.545973	−	0.837803i	$-0.316160\pi$
$337$	367.985			1.09195			0.545973	+	0.837803i	$0.316160\pi$
$338$	85.6549	+	326.967i	0.253417	+	0.967357i
$339$		−	223.714i		−	0.659923i
$340$	90.0803	−	100.327i	0.264942	−	0.295079i
$341$	199.086			0.583829
$342$	95.3268	+	36.5159i	0.278733	+	0.106771i
$343$	213.354			0.622024
$344$	−85.8081	+	43.9490i	−0.249442	+	0.127759i
$345$			353.043i			1.02331i
$346$	106.636	+	40.8481i	0.308198	+	0.118058i
$347$		−	120.208i		−	0.346421i	−0.984885	−	0.173210i	$-0.944586\pi$
$347$		−	120.208i		−	0.346421i	0.984885	−	0.173210i	$-0.0554140\pi$
$348$	−243.644	+	271.358i	−0.700127	+	0.779766i
$349$		−	188.549i		−	0.540255i	−0.962825	−	0.270127i	$-0.912934\pi$
$349$		−	188.549i		−	0.540255i	0.962825	−	0.270127i	$-0.0870658\pi$
$350$	14.1507	+	5.42058i	0.0404307	+	0.0154874i
$351$	−60.0907	−	30.8562i	−0.171199	−	0.0879093i
$352$	−154.132	+	583.403i	−0.437876	+	1.65739i
$353$		−	433.581i		−	1.22828i	−0.789199	−	0.614138i	$-0.789504\pi$
$353$		−	433.581i		−	1.22828i	0.789199	−	0.614138i	$-0.210496\pi$
$354$	14.1894	−	37.0422i	0.0400830	−	0.104639i
$355$		−	37.6327i		−	0.106008i
$356$	215.156	−	239.629i	0.604370	−	0.673116i
$357$		−	28.8400i		−	0.0807842i
$358$	185.173	−	483.406i	0.517244	−	1.35030i
$359$	−85.1287			−0.237127			−0.118564	−	0.992946i	$-0.537829\pi$
$359$	−85.1287			−0.237127			−0.118564	+	0.992946i	$0.537829\pi$
$360$	−99.5255	+	50.9747i	−0.276460	+	0.141597i
$361$	−71.5389			−0.198169
$362$	323.907	+	124.076i	0.894771	+	0.342751i
$363$		−	406.307i		−	1.11930i
$364$	111.803	−	42.6936i	0.307150	−	0.117290i
$365$	−271.810			−0.744684
$366$	39.8917	−	104.140i	0.108994	−	0.284535i
$367$			457.599i			1.24686i	0.781878	+	0.623432i	$0.214262\pi$
$367$			457.599i			1.24686i	−0.781878	+	0.623432i	$0.785738\pi$
$368$	−695.925	+	75.1186i	−1.89110	+	0.204127i
$369$			115.532i			0.313096i
$370$	106.959	+	40.9715i	0.289077	+	0.110734i
$371$	−172.290			−0.464392
$372$	−48.8680	+	54.4267i	−0.131366	+	0.146308i
$373$	479.627			1.28586			0.642932	−	0.765923i	$-0.277718\pi$
$373$	479.627			1.28586			0.642932	+	0.765923i	$0.277718\pi$
$374$	−254.798	−	97.6028i	−0.681277	−	0.260970i
$375$	228.315			0.608840
$376$	−229.025	−	447.160i	−0.609110	−	1.18926i
$377$	312.581	−	608.734i	0.829126	−	1.61468i
$378$	−8.55566	+	22.3351i	−0.0226340	+	0.0590875i
$379$	−138.067			−0.364292			−0.182146	−	0.983271i	$-0.558304\pi$
$379$	−138.067			−0.364292			−0.182146	+	0.983271i	$0.558304\pi$
$380$	−211.835	+	235.931i	−0.557460	+	0.620871i
$381$	−22.3051			−0.0585437
$382$	−125.819	+	328.457i	−0.329368	+	0.859835i
$383$	−376.647			−0.983414			−0.491707	−	0.870761i	$-0.663627\pi$
$383$	−376.647			−0.983414			−0.491707	+	0.870761i	$0.663627\pi$
$384$	−121.659	−	185.340i	−0.316820	−	0.482658i
$385$			202.202i			0.525200i
$386$	94.6747	−	247.154i	0.245271	−	0.640295i
$387$			36.1531i			0.0934188i
$388$	40.9499	−	45.6079i	0.105541	−	0.117546i
$389$	−247.664			−0.636669			−0.318334	−	0.947978i	$-0.603123\pi$
$389$	−247.664			−0.636669			−0.318334	+	0.947978i	$0.603123\pi$
$390$	156.268	−	140.014i	0.400687	−	0.359011i
$391$		−	316.508i		−	0.809484i
$392$	159.382	+	311.184i	0.406586	+	0.793837i
$393$	−116.059			−0.295316
$394$	170.289	−	444.549i	0.432205	−	1.12830i
$395$	275.000			0.696202
$396$	168.373	+	151.177i	0.425184	+	0.381759i
$397$		−	107.924i		−	0.271848i	−0.990719	−	0.135924i	$-0.956600\pi$
$397$		−	107.924i		−	0.271848i	0.990719	−	0.135924i	$-0.0434003\pi$
$398$	172.787	−	451.070i	0.434138	−	1.13334i
$399$			67.8207i			0.169977i
$400$	5.65280	+	52.3695i	0.0141320	+	0.130924i
$401$		−	533.051i		−	1.32930i	−0.747153	−	0.664652i	$-0.768580\pi$
$401$		−	533.051i		−	1.32930i	0.747153	−	0.664652i	$-0.231420\pi$
$402$	75.4015	−	196.840i	0.187566	−	0.489652i
$403$	62.6947	−	122.094i	0.155570	−	0.302964i
$404$	245.028	+	220.003i	0.606504	+	0.544561i
$405$			41.9326i			0.103537i
$406$	−226.260	−	86.6709i	−0.557290	−	0.213475i
$407$		−	231.781i		−	0.569487i
$408$	89.2261	−	45.6997i	0.218692	−	0.112009i
$409$		−	628.025i		−	1.53551i	−0.640742	−	0.767756i	$-0.721373\pi$
$409$		−	628.025i		−	1.53551i	0.640742	−	0.767756i	$-0.278627\pi$
$410$	−335.112	−	128.368i	−0.817347	−	0.313093i
$411$	434.739			1.05776
$412$	295.597	−	329.221i	0.717468	−	0.799079i
$413$	26.3539			0.0638108
$414$	−93.8953	+	245.119i	−0.226800	+	0.592075i
$415$		−	227.263i		−	0.547622i
$416$	309.249	+	278.247i	0.743386	+	0.668862i
$417$	205.918			0.493807
$418$	599.188	+	229.525i	1.43346	+	0.549103i
$419$		−	154.533i		−	0.368814i	−0.982850	−	0.184407i	$-0.940964\pi$
$419$		−	154.533i		−	0.368814i	0.982850	−	0.184407i	$-0.0590365\pi$
$420$	−55.2786	−	49.6329i	−0.131616	−	0.118174i
$421$		−	448.868i		−	1.06620i	−0.846054	−	0.533098i	$-0.821028\pi$
$421$		−	448.868i		−	1.06620i	0.846054	−	0.533098i	$-0.178972\pi$
$422$	−156.650	+	408.945i	−0.371209	+	0.969063i
$423$	−188.400			−0.445389
$424$	−273.009	−	533.036i	−0.643889	−	1.25716i
$425$	−23.8178			−0.0560418
$426$	10.0088	−	26.1286i	0.0234949	−	0.0613347i
$427$	74.0907			0.173515
$428$	−309.718	+	344.948i	−0.723639	+	0.805953i
$429$	−377.708	−	193.950i	−0.880438	−	0.452099i
$430$	−104.865	−	40.1696i	−0.243873	−	0.0934177i
$431$	106.337			0.246722			0.123361	−	0.992362i	$-0.460633\pi$
$431$	106.337			0.246722			0.123361	+	0.992362i	$0.460633\pi$
$432$	−82.6583	+	8.92219i	−0.191339	+	0.0206532i
$433$	86.2231			0.199130			0.0995648	−	0.995031i	$-0.468255\pi$
$433$	86.2231			0.199130			0.0995648	+	0.995031i	$0.468255\pi$
$434$	−45.3812	−	17.3837i	−0.104565	−	0.0400546i
$435$	−424.787			−0.976522
$436$	−199.295	+	221.965i	−0.457099	+	0.509094i
$437$			744.308i			1.70322i
$438$	−188.719	−	72.2905i	−0.430865	−	0.165047i
$439$		−	128.927i		−	0.293683i	−0.989160	−	0.146841i	$-0.953089\pi$
$439$		−	128.927i		−	0.293683i	0.989160	−	0.146841i	$-0.0469107\pi$
$440$	−625.580	+	320.408i	−1.42177	+	0.728200i
$441$	131.110			0.297301
$442$	−140.097	+	125.525i	−0.316960	+	0.283993i
$443$		−	359.734i		−	0.812040i	−0.913864	−	0.406020i	$-0.866916\pi$
$443$		−	359.734i		−	0.812040i	0.913864	−	0.406020i	$-0.133084\pi$
$444$	63.3651	+	56.8935i	0.142714	+	0.128138i
$445$	375.118			0.842962
$446$	−526.843	−	201.812i	−1.18126	−	0.452494i
$447$	−161.504			−0.361307
$448$	86.0755	−	119.527i	0.192133	−	0.266801i
$449$			274.459i			0.611266i	0.952149	+	0.305633i	$0.0988681\pi$
$449$			274.459i			0.611266i	−0.952149	+	0.305633i	$0.901132\pi$
$450$	18.4456	+	7.06578i	0.0409903	+	0.0157017i
$451$			726.194i			1.61019i
$452$	384.427	+	345.165i	0.850502	+	0.763638i
$453$		−	272.795i		−	0.602196i
$454$	451.282	+	172.868i	0.994014	+	0.380767i
$455$	124.006	+	63.6760i	0.272540	+	0.139947i
$456$	−209.826	+	107.468i	−0.460145	+	0.235676i
$457$			489.942i			1.07208i	0.844191	+	0.536042i	$0.180081\pi$
$457$			489.942i			1.07208i	−0.844191	+	0.536042i	$0.819919\pi$
$458$	303.167	−	791.436i	0.661937	−	1.72803i
$459$		−	37.5932i		−	0.0819024i
$460$	−606.663	−	544.703i	−1.31883	−	1.18414i
$461$		−	14.8651i		−	0.0322452i	−0.999870	−	0.0161226i	$-0.994868\pi$
$461$		−	14.8651i		−	0.0322452i	0.999870	−	0.0161226i	$-0.00513221\pi$
$462$	−53.7777	+	140.390i	−0.116402	+	0.303874i
$463$	−176.877			−0.382024			−0.191012	−	0.981588i	$-0.561177\pi$
$463$	−176.877			−0.382024			−0.191012	+	0.981588i	$0.561177\pi$
$464$	−90.3839	−	837.349i	−0.194793	−	1.80463i
$465$	−85.2000			−0.183226
$466$	744.069	+	285.023i	1.59671	+	0.611637i
$467$			826.653i			1.77013i	0.465463	+	0.885067i	$0.345888\pi$
$467$			826.653i			1.77013i	−0.465463	+	0.885067i	$0.654112\pi$
$468$	145.736	−	55.6515i	0.311401	−	0.118914i
$469$	140.043			0.298599
$470$	209.331	−	546.470i	0.445384	−	1.16270i
$471$			227.600i			0.483226i
$472$	41.7602	+	81.5345i	0.0884750	+	0.172743i
$473$			227.245i			0.480433i
$474$	190.934	+	73.1391i	0.402814	+	0.154302i
$475$	56.0104			0.117917
$476$	49.5581	+	44.4967i	0.104114	+	0.0934804i
$477$	−224.581			−0.470820
$478$	−155.083	−	59.4060i	−0.324441	−	0.124280i
$479$	773.623			1.61508			0.807539	−	0.589814i	$-0.200799\pi$
$479$	773.623			1.61508			0.807539	+	0.589814i	$0.200799\pi$
$480$	65.9619	−	249.671i	0.137421	−	0.520148i
$481$	−142.146	−	72.9909i	−0.295521	−	0.151748i
$482$	229.781	−	599.858i	0.476725	−	1.24452i
$483$	−174.391			−0.361059
$484$	698.192	+	626.885i	1.44255	+	1.29522i
$485$	71.3950			0.147206
$486$	−11.1524	+	29.1140i	−0.0229473	+	0.0599053i
$487$	−732.143			−1.50337			−0.751687	−	0.659520i	$-0.770759\pi$
$487$	−732.143			−1.50337			−0.751687	+	0.659520i	$0.770759\pi$
$488$	117.404	+	229.225i	0.240582	+	0.469723i
$489$			194.700i			0.398159i
$490$	−145.676	+	380.295i	−0.297297	+	0.776112i
$491$		−	427.549i		−	0.870771i	−0.900244	−	0.435386i	$-0.856612\pi$
$491$		−	427.549i		−	0.870771i	0.900244	−	0.435386i	$-0.143388\pi$
$492$	−198.529	−	178.253i	−0.403515	−	0.362303i
$493$	380.828			0.772471
$494$	329.454	−	295.187i	0.666912	−	0.597545i
$495$			263.572i			0.532469i
$496$	−18.1284	−	167.948i	−0.0365492	−	0.338605i
$497$	18.5893			0.0374030
$498$	60.4430	−	157.790i	0.121371	−	0.316847i
$499$	394.459			0.790499			0.395250	−	0.918574i	$-0.370658\pi$
$499$	394.459			0.790499			0.395250	+	0.918574i	$0.370658\pi$
$500$	−352.264	+	392.333i	−0.704527	+	0.784667i
$501$		−	145.310i		−	0.290039i
$502$	127.917	−	333.935i	0.254815	−	0.665210i
$503$			28.4159i			0.0564929i	0.999601	+	0.0282464i	$0.00899232\pi$
$503$			28.4159i			0.0564929i	−0.999601	+	0.0282464i	$0.991008\pi$
$504$	−25.1798	−	49.1623i	−0.0499600	−	0.0975442i
$505$			383.569i			0.759542i
$506$	−590.191	+	1540.73i	−1.16638	+	3.04492i
$507$	−237.890	+	170.562i	−0.469211	+	0.336413i
$508$	34.4142	−	38.3288i	0.0677445	−	0.0754504i
$509$			545.639i			1.07198i	0.844223	+	0.535992i	$0.180062\pi$
$509$			545.639i			1.07198i	−0.844223	+	0.535992i	$0.819938\pi$
$510$	109.042	+	41.7697i	0.213809	+	0.0819015i
$511$		−	134.265i		−	0.262749i
$512$	506.192	+	76.9018i	0.988656	+	0.150199i
$513$			88.4050i			0.172330i
$514$	−752.121	−	288.107i	−1.46327	−	0.560520i
$515$	515.365			1.00071
$516$	−62.1249	−	55.7800i	−0.120397	−	0.108101i
$517$	−1184.21			−2.29054
$518$	−20.2386	+	52.8340i	−0.0390706	+	0.101996i
$519$			98.8935i			0.190546i
$520$	−0.504614	+	484.554i	−0.000970412	+	0.931834i
$521$	52.0278			0.0998614			0.0499307	−	0.998753i	$-0.484100\pi$
$521$	52.0278			0.0998614			0.0499307	+	0.998753i	$0.484100\pi$
$522$	−294.932	−	112.976i	−0.565003	−	0.216430i
$523$			224.257i			0.428789i	0.976747	+	0.214394i	$0.0687778\pi$
$523$			224.257i			0.428789i	−0.976747	+	0.214394i	$0.931222\pi$
$524$	179.066	−	199.434i	0.341728	−	0.380599i
$525$			13.1232i			0.0249967i
$526$	−202.203	+	527.863i	−0.384417	+	1.00354i
$527$	76.3832			0.144940
$528$	−519.559	+	56.0815i	−0.984013	+	0.106215i
$529$	−1384.88			−2.61793
$530$	249.532	−	651.418i	0.470815	−	1.22909i
$531$	34.3525			0.0646940
$532$	−116.542	−	104.639i	−0.219064	−	0.196691i
$533$	445.357	+	228.688i	0.835567	+	0.429058i
$534$	260.446	+	99.7665i	0.487727	+	0.186829i
$535$	−539.984			−1.00932
$536$	221.911	+	433.270i	0.414013	+	0.808339i
$537$	448.305			0.834833
$538$	−296.707	−	113.657i	−0.551501	−	0.211258i
$539$	824.106			1.52895
$540$	−72.0563	−	64.6970i	−0.133438	−	0.119809i
$541$			481.809i			0.890589i	0.895384	+	0.445295i	$0.146901\pi$
$541$			481.809i			0.890589i	−0.895384	+	0.445295i	$0.853099\pi$
$542$	478.732	+	183.383i	0.883270	+	0.338345i
$543$			300.388i			0.553201i
$544$	−59.1359	+	223.834i	−0.108706	+	0.411460i
$545$	−347.466			−0.637552
$546$	69.1624	+	77.1911i	0.126671	+	0.141376i
$547$		−	132.674i		−	0.242548i	−0.992619	−	0.121274i	$-0.961302\pi$
$547$		−	132.674i		−	0.242548i	0.992619	−	0.121274i	$-0.0386980\pi$
$548$	−670.752	+	747.049i	−1.22400	+	1.36323i
$549$	96.5780			0.175916
$550$	115.942	+	44.4128i	0.210804	+	0.0807506i
$551$	−895.564			−1.62534
$552$	−276.340	−	539.539i	−0.500615	−	0.977425i
$553$			135.841i			0.245644i
$554$	203.400	+	77.9144i	0.367148	+	0.140640i
$555$			99.1923i			0.178725i
$556$	−317.707	+	353.846i	−0.571415	+	0.636413i
$557$		−	36.8507i		−	0.0661593i	−0.999453	−	0.0330796i	$-0.989468\pi$
$557$		−	36.8507i		−	0.0661593i	0.999453	−	0.0330796i	$-0.0105315\pi$
$558$	−59.1548	−	22.6598i	−0.106012	−	0.0406090i
$559$	139.364	+	71.5623i	0.249309	+	0.128018i
$560$	170.577	−	18.4122i	0.304602	−	0.0328789i
$561$		−	236.297i		−	0.421206i
$562$	37.3862	−	97.5989i	0.0665235	−	0.173663i
$563$			206.073i			0.366026i	0.983110	+	0.183013i	$0.0585851\pi$
$563$			206.073i			0.366026i	−0.983110	+	0.183013i	$0.941415\pi$
$564$	290.679	−	323.743i	0.515388	−	0.574013i
$565$			601.785i			1.06511i
$566$	167.062	−	436.126i	0.295163	−	0.770541i
$567$	−20.7133			−0.0365314
$568$	29.4565	+	57.5123i	0.0518601	+	0.101254i
$569$	−325.540			−0.572126			−0.286063	−	0.958211i	$-0.592347\pi$
$569$	−325.540			−0.572126			−0.286063	+	0.958211i	$0.592347\pi$
$570$	−256.427	−	98.2267i	−0.449871	−	0.172328i
$571$		−	436.353i		−	0.764191i	−0.924123	−	0.382095i	$-0.875203\pi$
$571$		−	436.353i		−	0.764191i	0.924123	−	0.382095i	$-0.124797\pi$
$572$	916.040	−	349.805i	1.60147	−	0.611547i
$573$	−304.608			−0.531601
$574$	63.4095	−	165.534i	0.110470	−	0.288387i
$575$			144.023i			0.250475i
$576$	112.200	−	155.805i	0.194792	−	0.270494i
$577$			69.7493i			0.120883i	0.998172	+	0.0604413i	$0.0192508\pi$
$577$			69.7493i			0.120883i	−0.998172	+	0.0604413i	$0.980749\pi$
$578$	441.996	+	169.311i	0.764700	+	0.292926i
$579$	229.208			0.395869
$580$	655.396	−	729.947i	1.12999	−	1.25853i
$581$	112.260			0.193219
$582$	49.5699	+	18.9882i	0.0851717	+	0.0326259i
$583$	−1411.63			−2.42133
$584$	415.394	−	212.755i	0.711291	−	0.364307i
$585$	161.643	+	83.0023i	0.276312	+	0.141884i
$586$	0.657132	−	1.71548i	0.00112138	−	0.00292744i
$587$	−199.126			−0.339226			−0.169613	−	0.985511i	$-0.554252\pi$
$587$	−199.126			−0.339226			−0.169613	+	0.985511i	$0.554252\pi$
$588$	−202.287	+	225.297i	−0.344025	+	0.383158i
$589$	−179.624			−0.304965
$590$	−38.1690	+	99.6425i	−0.0646933	+	0.168886i
$591$	412.270			0.697581
$592$	−195.530	+	21.1056i	−0.330287	+	0.0356514i
$593$		−	83.9053i		−	0.141493i	−0.997494	−	0.0707465i	$-0.977462\pi$
$593$		−	83.9053i		−	0.141493i	0.997494	−	0.0707465i	$-0.0225381\pi$
$594$	−70.0998	+	183.000i	−0.118013	+	0.308080i
$595$			77.5788i			0.130384i
$596$	249.182	−	277.527i	0.418091	−	0.465649i
$597$	418.318			0.700700
$598$	759.032	+	847.145i	1.26929	+	1.41663i
$599$			624.842i			1.04314i	0.853208	+	0.521571i	$0.174654\pi$
$599$			624.842i			1.04314i	−0.853208	+	0.521571i	$0.825346\pi$
$600$	−40.6012	+	20.7950i	−0.0676686	+	0.0346584i
$601$	−320.409			−0.533126			−0.266563	−	0.963817i	$-0.585888\pi$
$601$	−320.409			−0.533126			−0.266563	+	0.963817i	$0.585888\pi$
$602$	19.8425	−	51.7999i	0.0329609	−	0.0860464i
$603$	182.547			0.302732
$604$	468.766	+	420.890i	0.776103	+	0.696838i
$605$			1092.96i			1.80654i
$606$	−102.014	+	266.314i	−0.168340	+	0.439461i
$607$		−	1088.74i		−	1.79364i	−0.442399	−	0.896818i	$-0.645873\pi$
$607$		−	1088.74i		−	1.79364i	0.442399	−	0.896818i	$-0.354127\pi$
$608$	139.065	−	526.373i	0.228726	−	0.865746i
$609$		−	209.831i		−	0.344550i
$610$	−107.308	+	280.133i	−0.175914	+	0.459235i
$611$	−372.923	+	726.247i	−0.610348	+	1.18862i
$612$	64.5996	+	58.0019i	0.105555	+	0.0947743i
$613$		−	845.844i		−	1.37984i	−0.723884	−	0.689922i	$-0.757645\pi$
$613$		−	845.844i		−	1.37984i	0.723884	−	0.689922i	$-0.242355\pi$
$614$	827.212	+	316.871i	1.34725	+	0.516077i
$615$		−	310.779i		−	0.505332i
$616$	−158.271	−	309.016i	−0.256933	−	0.501649i
$617$		−	1044.18i		−	1.69234i	−0.532910	−	0.846172i	$-0.678902\pi$
$617$		−	1044.18i		−	1.69234i	0.532910	−	0.846172i	$-0.321098\pi$
$618$	357.820	+	137.067i	0.578997	+	0.221791i
$619$	−403.053			−0.651135			−0.325568	−	0.945519i	$-0.605555\pi$
$619$	−403.053			−0.651135			−0.325568	+	0.945519i	$0.605555\pi$
$620$	131.454	−	146.406i	0.212022	−	0.236139i
$621$	−227.321			−0.366056
$622$	330.349	−	862.396i	0.531108	−	1.38649i
$623$			185.296i			0.297425i
$624$	−129.222	+	336.294i	−0.207087	+	0.538932i
$625$	−531.859			−0.850975
$626$	−845.633	−	323.928i	−1.35085	−	0.517457i
$627$			555.681i			0.886253i
$628$	−391.104	−	351.159i	−0.622776	−	0.559171i
$629$		−	88.9274i		−	0.141379i
$630$	23.0145	−	60.0807i	0.0365310	−	0.0953663i
$631$	433.317			0.686715			0.343357	−	0.939205i	$-0.388436\pi$
$631$	433.317			0.686715			0.343357	+	0.939205i	$0.388436\pi$
$632$	−420.270	+	215.253i	−0.664984	+	0.340590i
$633$	−379.251			−0.599133
$634$	307.425	−	802.550i	0.484897	−	1.26585i
$635$	60.0003			0.0944886
$636$	346.502	−	385.917i	0.544815	−	0.606788i
$637$	259.522	−	505.404i	0.407412	−	0.793413i
$638$	−1853.83	−	710.128i	−2.90569	−	1.11305i
$639$	24.2314			0.0379208
$640$	327.260	+	498.561i	0.511343	+	0.779002i
$641$	−697.048			−1.08744			−0.543719	−	0.839267i	$-0.682984\pi$
$641$	−697.048			−1.08744			−0.543719	+	0.839267i	$0.682984\pi$
$642$	−374.914	−	143.614i	−0.583978	−	0.223698i
$643$	977.442			1.52013			0.760064	−	0.649848i	$-0.225168\pi$
$643$	977.442			1.52013			0.760064	+	0.649848i	$0.225168\pi$
$644$	269.065	−	299.671i	0.417803	−	0.465328i
$645$		−	97.2509i		−	0.150777i
$646$	229.890	+	88.0618i	0.355868	+	0.136319i
$647$		−	487.331i		−	0.753216i	−0.926373	−	0.376608i	$-0.877090\pi$
$647$		−	487.331i		−	0.753216i	0.926373	−	0.376608i	$-0.122910\pi$
$648$	−32.8222	−	64.0836i	−0.0506515	−	0.0988944i
$649$	215.927			0.332707
$650$	63.7491	−	57.1185i	0.0980755	−	0.0878746i
$651$		−	42.0860i		−	0.0646482i
$652$	−334.569	−	300.399i	−0.513143	−	0.460734i
$653$	865.011			1.32467			0.662336	−	0.749207i	$-0.269565\pi$
$653$	865.011			1.32467			0.662336	+	0.749207i	$0.269565\pi$
$654$	−241.247	−	92.4121i	−0.368879	−	0.141303i
$655$	312.196			0.476635
$656$	612.615	−	66.1260i	0.933864	−	0.100802i
$657$		−	175.016i		−	0.266386i
$658$	269.938	+	103.402i	0.410240	+	0.157146i
$659$		−	687.981i		−	1.04398i	−0.852953	−	0.521988i	$-0.825190\pi$
$659$		−	687.981i		−	1.04398i	0.852953	−	0.521988i	$-0.174810\pi$
$660$	−452.919	−	406.661i	−0.686240	−	0.616153i
$661$			63.7781i			0.0964873i	0.998836	+	0.0482437i	$0.0153624\pi$
$661$			63.7781i			0.0964873i	−0.998836	+	0.0482437i	$0.984638\pi$
$662$	−314.730	−	120.560i	−0.475423	−	0.182115i
$663$	−144.915	−	74.4129i	−0.218575	−	0.112237i
$664$	177.887	+	347.316i	0.267903	+	0.523066i
$665$		−	182.436i		−	0.274340i
$666$	−26.3812	+	68.8697i	−0.0396114	+	0.103408i
$667$		−	2302.82i		−	3.45250i
$668$	249.698	+	224.196i	0.373799	+	0.335622i
$669$		−	488.589i		−	0.730327i
$670$	−202.828	+	529.495i	−0.302728	+	0.790290i
$671$	607.053			0.904699
$672$	123.329	+	32.5830i	0.183526	+	0.0484866i
$673$	1008.38			1.49833			0.749164	−	0.662384i	$-0.230455\pi$
$673$	1008.38			1.49833			0.749164	+	0.662384i	$0.230455\pi$
$674$	−687.273	−	263.267i	−1.01969	−	0.390603i
$675$			17.1063i			0.0253426i
$676$	73.9462	−	671.943i	0.109388	−	0.993999i
$677$	512.221			0.756605			0.378302	−	0.925682i	$-0.376508\pi$
$677$	512.221			0.756605			0.378302	+	0.925682i	$0.376508\pi$
$678$	−160.051	+	417.822i	−0.236063	+	0.616257i
$679$			35.2668i			0.0519393i
$680$	−240.016	+	122.931i	−0.352965	+	0.180781i
$681$			418.514i			0.614559i
$682$	−371.825	−	142.431i	−0.545198	−	0.208843i
$683$	803.909			1.17703			0.588513	−	0.808488i	$-0.299713\pi$
$683$	803.909			1.17703			0.588513	+	0.808488i	$0.299713\pi$
$684$	−151.914	−	136.399i	−0.222096	−	0.199413i
$685$	−1169.44			−1.70721
$686$	−398.474	−	152.639i	−0.580866	−	0.222506i
$687$	733.969			1.06837
$688$	191.703	−	20.6925i	0.278638	−	0.0300763i
$689$	−444.542	+	865.721i	−0.645198	+	1.25649i
$690$	252.576	−	659.365i	0.366052	−	0.955601i
$691$	−562.395			−0.813885			−0.406943	−	0.913454i	$-0.633405\pi$
$691$	−562.395			−0.813885			−0.406943	+	0.913454i	$0.633405\pi$
$692$	−169.937	−	152.581i	−0.245574	−	0.220493i
$693$	−130.196			−0.187873
$694$	−86.0000	+	224.508i	−0.123919	+	0.323499i
$695$	−553.913			−0.796997
$696$	649.182	−	332.497i	0.932733	−	0.477725i
$697$			278.619i			0.399740i
$698$	−134.893	+	352.146i	−0.193256	+	0.504507i
$699$			690.041i			0.987184i
$700$	−22.5508	−	20.2476i	−0.0322154	−	0.0289252i
$701$	422.806			0.603146			0.301573	−	0.953443i	$-0.402488\pi$
$701$	422.806			0.603146			0.301573	+	0.953443i	$0.402488\pi$
$702$	90.1539	+	100.619i	0.128424	+	0.143333i
$703$			209.124i			0.297473i
$704$	705.249	−	979.330i	1.00177	−	1.39109i
$705$	506.790			0.718851
$706$	−310.196	+	809.784i	−0.439371	+	1.14700i
$707$	−189.470			−0.267992
$708$	−53.0019	+	59.0308i	−0.0748615	+	0.0833769i
$709$		−	77.6026i		−	0.109454i	−0.998501	−	0.0547268i	$-0.982571\pi$
$709$		−	77.6026i		−	0.109454i	0.998501	−	0.0547268i	$-0.0174288\pi$
$710$	−26.9234	+	70.2852i	−0.0379203	+	0.0989932i
$711$			177.070i			0.249044i
$712$	−573.275	+	293.619i	−0.805162	+	0.412386i
$713$		−	461.879i		−	0.647796i
$714$	−20.6329	+	53.8633i	−0.0288976	+	0.0754388i
$715$	1016.02	+	521.722i	1.42101	+	0.729680i
$716$	−691.682	+	770.361i	−0.966037	+	1.07592i
$717$		−	143.822i		−	0.200589i
$718$	158.992	+	60.9033i	0.221437	+	0.0848236i
$719$			1097.86i			1.52693i	0.645848	+	0.763466i	$0.276504\pi$
$719$			1097.86i			1.52693i	−0.645848	+	0.763466i	$0.723496\pi$
$720$	222.349	−	24.0005i	0.308818	−	0.0333340i
$721$			254.573i			0.353083i
$722$	133.611	+	51.1808i	0.185056	+	0.0708876i
$723$	556.302			0.769435
$724$	−516.182	−	463.463i	−0.712959	−	0.640143i
$725$	−173.291			−0.239022
$726$	−290.683	+	758.845i	−0.400390	+	1.04524i
$727$			589.880i			0.811389i	0.914009	+	0.405694i	$0.132970\pi$
$727$			589.880i			0.811389i	−0.914009	+	0.405694i	$0.867030\pi$
$728$	−239.354	−	0.249263i	−0.328782	−	0.000342394i
$729$	−27.0000			−0.0370370
$730$	507.649	+	194.460i	0.695409	+	0.266383i
$731$			87.1869i			0.119271i
$732$	−149.009	+	165.958i	−0.203564	+	0.226719i
$733$		−	497.876i		−	0.679230i	−0.940565	−	0.339615i	$-0.889703\pi$
$733$		−	497.876i		−	0.679230i	0.940565	−	0.339615i	$-0.110297\pi$
$734$	327.378	−	854.640i	0.446020	−	1.16436i
$735$	−352.682			−0.479839
$736$	1353.49	+	357.587i	1.83899	+	0.485852i
$737$	1147.42			1.55688
$738$	82.6550	−	215.776i	0.111999	−	0.292379i
$739$	−615.660			−0.833098			−0.416549	−	0.909113i	$-0.636761\pi$
$739$	−615.660			−0.833098			−0.416549	+	0.909113i	$0.636761\pi$
$740$	−170.450	−	153.042i	−0.230338	−	0.206814i
$741$	340.786	+	174.991i	0.459900	+	0.236155i
$742$	321.779	+	123.260i	0.433664	+	0.166119i
$743$	130.770			0.176002			0.0880010	−	0.996120i	$-0.471952\pi$
$743$	130.770			0.176002			0.0880010	+	0.996120i	$0.471952\pi$
$744$	130.207	−	66.6893i	0.175010	−	0.0896361i
$745$	434.443			0.583144
$746$	−895.782	−	343.138i	−1.20078	−	0.459971i
$747$	146.333			0.195894
$748$	406.049	+	364.578i	0.542846	+	0.487404i
$749$		−	266.734i		−	0.356121i
$750$	−426.416	−	163.343i	−0.568554	−	0.217790i
$751$		−	28.6913i		−	0.0382041i	−0.999818	−	0.0191021i	$-0.993919\pi$
$751$		−	28.6913i		−	0.0382041i	0.999818	−	0.0191021i	$-0.00608075\pi$
$752$	107.832	+	998.995i	0.143394	+	1.32845i
$753$	309.688			0.411272
$754$	−1019.30	+	913.281i	−1.35186	+	1.21125i
$755$			733.811i			0.971935i
$756$	31.9582	−	35.5934i	0.0422727	−	0.0470812i
$757$	455.353			0.601523			0.300761	−	0.953699i	$-0.402759\pi$
$757$	455.353			0.601523			0.300761	+	0.953699i	$0.402759\pi$
$758$	257.862	+	98.7767i	0.340188	+	0.130312i
$759$	−1428.85			−1.88255
$760$	564.427	−	289.087i	0.742668	−	0.380378i
$761$		−	1324.14i		−	1.74000i	−0.493053	−	0.869999i	$-0.664119\pi$
$761$		−	1324.14i		−	1.74000i	0.493053	−	0.869999i	$-0.335881\pi$
$762$	41.6585	+	15.9577i	0.0546699	+	0.0209419i
$763$		−	171.637i		−	0.224950i
$764$	469.974	−	523.433i	0.615149	−	0.685122i
$765$			101.125i			0.132189i
$766$	703.450	+	269.464i	0.918343	+	0.351780i
$767$	67.9982	−	132.423i	0.0886548	−	0.172650i
$768$	94.6204	+	433.192i	0.123204	+	0.564052i
$769$			637.778i			0.829360i	0.909967	+	0.414680i	$0.136106\pi$
$769$			637.778i			0.829360i	−0.909967	+	0.414680i	$0.863894\pi$
$770$	144.661	−	377.645i	0.187871	−	0.490448i
$771$		−	697.509i		−	0.904681i
$772$	−353.641	+	393.867i	−0.458084	+	0.510191i
$773$			418.846i			0.541845i	0.962601	+	0.270922i	$0.0873287\pi$
$773$			418.846i			0.541845i	−0.962601	+	0.270922i	$0.912671\pi$
$774$	25.8649	−	67.5218i	0.0334171	−	0.0872374i
$775$	−34.7572			−0.0448479
$776$	−109.110	+	55.8836i	−0.140605	+	0.0720149i
$777$	−48.9977			−0.0630601
$778$	462.553	+	177.186i	0.594541	+	0.227745i
$779$		−	655.206i		−	0.841086i
$780$	−392.025	+	149.701i	−0.502597	+	0.191925i
$781$	152.309			0.195018
$782$	−226.438	+	591.131i	−0.289563	+	0.755922i
$783$		−	273.517i		−	0.349319i
$784$	−75.0417	−	695.213i	−0.0957165	−	0.886751i
$785$		−	612.237i		−	0.779920i
$786$	216.759	+	83.0317i	0.275775	+	0.105638i
$787$	−1106.40			−1.40584			−0.702922	−	0.711267i	$-0.748122\pi$
$787$	−1106.40			−1.40584			−0.702922	+	0.711267i	$0.748122\pi$
$788$	−636.084	+	708.439i	−0.807214	+	0.899034i
$789$	−489.535			−0.620449
$790$	−513.607	−	196.742i	−0.650136	−	0.249041i
$791$	−297.262			−0.375805
$792$	−206.308	−	402.805i	−0.260490	−	0.508593i
$793$	191.169	−	372.291i	0.241071	−	0.469472i
$794$	−77.2114	+	201.565i	−0.0972436	+	0.253860i
$795$	604.118			0.759896
$796$	−645.415	+	718.831i	−0.810823	+	0.903054i
$797$	−1526.46			−1.91526			−0.957631	−	0.287997i	$-0.907011\pi$
$797$	−1526.46			−1.91526			−0.957631	+	0.287997i	$0.907011\pi$
$798$	48.5208	−	126.666i	0.0608029	−	0.158730i
$799$	−454.345			−0.568643
$800$	26.9090	−	101.853i	0.0336363	−	0.127316i
$801$			241.535i			0.301542i
$802$	−381.359	+	995.560i	−0.475510	+	1.24135i
$803$		−	1100.08i		−	1.36997i
$804$	−281.649	+	313.686i	−0.350310	+	0.390157i
$805$	469.108			0.582743
$806$	−204.442	+	183.178i	−0.253650	+	0.227268i
$807$		−	275.163i		−	0.340971i
$808$	−300.233	−	586.190i	−0.371576	−	0.725483i
$809$	−549.549			−0.679295			−0.339647	−	0.940553i	$-0.610308\pi$
$809$	−549.549			−0.679295			−0.339647	+	0.940553i	$0.610308\pi$
$810$	29.9997	−	78.3159i	0.0370366	−	0.0966863i
$811$	1157.72			1.42752			0.713760	−	0.700390i	$-0.246991\pi$
$811$	1157.72			1.42752			0.713760	+	0.700390i	$0.246991\pi$
$812$	360.570	+	323.744i	0.444052	+	0.398700i
$813$			443.971i			0.546090i
$814$	−165.822	+	432.889i	−0.203713	+	0.531805i
$815$		−	523.737i		−	0.642623i
$816$	−199.339	+	21.5168i	−0.244288	+	0.0263686i
$817$		−	205.031i		−	0.250956i
$818$	−449.306	+	1172.94i	−0.549273	+	1.43391i
$819$	−41.0004	+	79.8461i	−0.0500616	+	0.0974922i
$820$	534.039	+	479.496i	0.651267	+	0.584751i
$821$		−	1237.78i		−	1.50765i	−0.657075	−	0.753825i	$-0.728207\pi$
$821$		−	1237.78i		−	1.50765i	0.657075	−	0.753825i	$-0.271793\pi$
$822$	−811.946	−	311.024i	−0.987769	−	0.378375i
$823$			684.583i			0.831814i	0.909407	+	0.415907i	$0.136536\pi$
$823$			684.583i			0.831814i	−0.909407	+	0.415907i	$0.863464\pi$
$824$	−787.608	+	403.395i	−0.955835	+	0.489557i
$825$			107.524i			0.130332i
$826$	−49.2201	−	18.8542i	−0.0595885	−	0.0228260i
$827$	976.954			1.18132			0.590661	−	0.806920i	$-0.298867\pi$
$827$	976.954			1.18132			0.590661	+	0.806920i	$0.298867\pi$
$828$	350.730	−	390.625i	0.423587	−	0.471769i
$829$	276.950			0.334077			0.167039	−	0.985950i	$-0.446580\pi$
$829$	276.950			0.334077			0.167039	+	0.985950i	$0.446580\pi$
$830$	−162.590	+	424.451i	−0.195892	+	0.511386i
$831$			188.631i			0.226993i
$832$	−378.507	−	740.916i	−0.454937	−	0.890524i
$833$	316.184			0.379573
$834$	−384.585	−	147.319i	−0.461133	−	0.176641i
$835$			390.879i			0.468119i
$836$	−954.873	−	857.350i	−1.14219	−	1.02554i
$837$		−	54.8595i		−	0.0655431i
$838$	−110.557	+	288.616i	−0.131930	+	0.344410i
$839$	−1489.27			−1.77505			−0.887527	−	0.460755i	$-0.847579\pi$
$839$	−1489.27			−1.77505			−0.887527	+	0.460755i	$0.847579\pi$
$840$	67.7331	+	132.245i	0.0806347	+	0.157435i
$841$	1929.79			2.29464
$842$	−321.132	+	838.334i	−0.381392	+	0.995646i
$843$	90.5122			0.107369
$844$	585.140	−	651.699i	0.693293	−	0.772155i
$845$	639.919	−	458.806i	0.757300	−	0.542966i
$846$	351.867	+	134.786i	0.415918	+	0.159322i
$847$	−539.884			−0.637408
$848$	128.541	+	1190.85i	0.151581	+	1.40430i
$849$	404.459			0.476395
$850$	44.4836	+	17.0399i	0.0523336	+	0.0200469i
$851$	−537.732			−0.631883
$852$	−37.3862	+	41.6388i	−0.0438805	+	0.0488718i
$853$			271.841i			0.318688i	0.987223	+	0.159344i	$0.0509379\pi$
$853$			271.841i			0.318688i	−0.987223	+	0.159344i	$0.949062\pi$
$854$	−138.376	−	53.0065i	−0.162033	−	0.0620685i
$855$		−	237.807i		−	0.278137i
$856$	825.233	−	422.666i	0.964057	−	0.493769i
$857$	−303.126			−0.353705			−0.176853	−	0.984237i	$-0.556592\pi$
$857$	−303.126			−0.353705			−0.176853	+	0.984237i	$0.556592\pi$
$858$	566.674	+	632.456i	0.660459	+	0.737128i
$859$		−	887.108i		−	1.03272i	−0.856371	−	0.516361i	$-0.827286\pi$
$859$		−	887.108i		−	1.03272i	0.856371	−	0.516361i	$-0.172714\pi$
$860$	167.114	+	150.047i	0.194319	+	0.174473i
$861$	153.515			0.178298
$862$	−198.602	−	76.0765i	−0.230397	−	0.0882558i
$863$	−1174.90			−1.36141			−0.680706	−	0.732557i	$-0.738327\pi$
$863$	−1174.90			−1.36141			−0.680706	+	0.732557i	$0.738327\pi$
$864$	160.761	+	42.4723i	0.186066	+	0.0491578i
$865$		−	266.021i		−	0.307539i
$866$	−161.036	−	61.6863i	−0.185954	−	0.0712313i
$867$			409.903i			0.472783i
$868$	72.3199	+	64.9338i	0.0833179	+	0.0748085i
$869$			1113.00i			1.28078i
$870$	793.359	+	303.904i	0.911907	+	0.349315i
$871$	361.339	−	703.687i	0.414855	−	0.807907i
$872$	531.016	−	271.974i	0.608963	−	0.311897i
$873$			45.9706i			0.0526582i
$874$	532.498	−	1390.12i	0.609265	−	1.59052i
$875$		−	303.376i		−	0.346715i
$876$	300.744	+	270.029i	0.343315	+	0.308252i
$877$			934.224i			1.06525i	0.846351	+	0.532625i	$0.178794\pi$
$877$			934.224i			1.06525i	−0.846351	+	0.532625i	$0.821206\pi$
$878$	−92.2377	+	240.792i	−0.105054	+	0.274250i
$879$	1.59092			0.00180992
$880$	1397.60	−	150.858i	1.58818	−	0.171429i
$881$	−112.930			−0.128184			−0.0640920	−	0.997944i	$-0.520415\pi$
$881$	−112.930			−0.128184			−0.0640920	+	0.997944i	$0.520415\pi$
$882$	−244.869	−	93.7993i	−0.277629	−	0.106348i
$883$		−	250.704i		−	0.283923i	−0.989872	−	0.141962i	$-0.954659\pi$
$883$		−	250.704i		−	0.283923i	0.989872	−	0.141962i	$-0.0453410\pi$
$884$	351.457	−	134.209i	0.397576	−	0.151821i
$885$	−92.4074			−0.104415
$886$	−257.363	+	671.861i	−0.290477	+	0.758308i
$887$			791.842i			0.892719i	0.894854	+	0.446360i	$0.147280\pi$
$887$			791.842i			0.892719i	−0.894854	+	0.446360i	$0.852720\pi$
$888$	−77.6415	−	151.591i	−0.0874341	−	0.170710i
$889$			29.6382i			0.0333388i
$890$	−700.594	−	268.369i	−0.787184	−	0.301539i
$891$	−169.712			−0.190473
$892$	839.584	+	753.835i	0.941237	+	0.845107i
$893$	1068.45			1.19647
$894$	301.636	+	115.544i	0.337400	+	0.129244i
$895$	−1205.93			−1.34741
$896$	−246.273	+	161.655i	−0.274858	+	0.180419i
$897$	−449.965	+	876.282i	−0.501633	+	0.976903i
$898$	196.355	−	512.596i	0.218658	−	0.570820i
$899$	555.740			0.618176
$900$	−29.3952	−	26.3930i	−0.0326613	−	0.0293255i
$901$	−541.601			−0.601111
$902$	519.538	−	1356.29i	0.575985	−	1.50364i
$903$	48.0387			0.0531990
$904$	−471.040	−	919.680i	−0.521062	−	1.01735i
$905$		−	808.036i		−	0.892858i
$906$	−195.165	+	509.488i	−0.215413	+	0.562349i
$907$		−	1001.27i		−	1.10394i	−0.833865	−	0.551968i	$-0.813877\pi$
$907$		−	1001.27i		−	1.10394i	0.833865	−	0.551968i	$-0.186123\pi$
$908$	−719.169	−	645.719i	−0.792036	−	0.711144i
$909$	−246.976			−0.271701
$910$	−186.045	−	207.642i	−0.204445	−	0.228178i
$911$			202.038i			0.221776i	0.993833	+	0.110888i	$0.0353695\pi$
$911$			202.038i			0.221776i	−0.993833	+	0.110888i	$0.964631\pi$
$912$	468.771	−	50.5994i	0.514003	−	0.0554818i
$913$	919.792			1.00744
$914$	350.518	−	915.047i	0.383499	−	1.00115i
$915$	−259.792			−0.283926
$916$	−1132.43	+	1261.24i	−1.23628	+	1.37690i
$917$			154.214i			0.168173i
$918$	−26.8952	+	70.2114i	−0.0292976	+	0.0764830i
$919$			1717.40i			1.86877i	0.356265	+	0.934385i	$0.384050\pi$
$919$			1717.40i			1.86877i	−0.356265	+	0.934385i	$0.615950\pi$
$920$	743.347	+	1451.35i	0.807986	+	1.57755i
$921$			767.147i			0.832950i
$922$	−10.6349	+	27.7629i	−0.0115346	+	0.0301116i
$923$	47.9642	−	93.4076i	0.0519655	−	0.101200i
$924$	200.877	−	223.727i	0.217400	−	0.242129i
$925$			40.4652i			0.0437462i
$926$	330.347	+	126.543i	0.356746	+	0.136655i
$927$			331.839i			0.357971i
$928$	−430.255	+	1628.55i	−0.463636	+	1.75490i
$929$			1276.92i			1.37452i	0.726414	+	0.687258i	$0.241186\pi$
$929$			1276.92i			1.37452i	−0.726414	+	0.687258i	$0.758814\pi$
$930$	159.125	+	60.9544i	0.171102	+	0.0655423i
$931$	−743.547			−0.798654
$932$	−1185.76	−	1064.65i	−1.27227	−	1.14233i
$933$	799.777			0.857210
$934$	591.409	−	1543.91i	0.633201	−	1.65301i
$935$			635.632i			0.679820i
$936$	−312.000	−	0.324917i	−0.333333	−	0.000347133i
$937$	−235.465			−0.251297			−0.125648	−	0.992075i	$-0.540101\pi$
$937$	−235.465			−0.251297			−0.125648	+	0.992075i	$0.540101\pi$
$938$	−261.553	−	100.190i	−0.278841	−	0.106813i
$939$		−	784.231i		−	0.835177i
$940$	−781.918	+	870.861i	−0.831828	+	0.926448i
$941$			1145.62i			1.21745i	0.793381	+	0.608725i	$0.208319\pi$
$941$			1145.62i			1.21745i	−0.793381	+	0.608725i	$0.791681\pi$
$942$	162.831	−	425.079i	0.172856	−	0.451252i
$943$	1684.77			1.78661
$944$	−19.6620	−	182.155i	−0.0208284	−	0.192961i
$945$	55.7182			0.0589611
$946$	162.577	−	424.416i	0.171857	−	0.448643i
$947$	381.016			0.402341			0.201170	−	0.979556i	$-0.435526\pi$
$947$	381.016			0.402341			0.201170	+	0.979556i	$0.435526\pi$
$948$	−304.274	−	273.198i	−0.320965	−	0.288184i
$949$	−674.655	−	346.430i	−0.710911	−	0.365048i
$950$	−104.609	−	40.0714i	−0.110114	−	0.0421804i
$951$	744.276			0.782625
$952$	−60.7238	−	118.560i	−0.0637855	−	0.124538i
$953$	−378.512			−0.397179			−0.198589	−	0.980083i	$-0.563636\pi$
$953$	−378.512			−0.397179			−0.198589	+	0.980083i	$0.563636\pi$
$954$	419.442	+	160.671i	0.439667	+	0.168419i
$955$	819.387			0.857997
$956$	247.142	+	221.901i	0.258517	+	0.232114i
$957$		−	1719.22i		−	1.79647i
$958$	−1444.87	−	553.470i	−1.50821	−	0.577735i
$959$		−	577.663i		−	0.602360i
$960$	−301.816	+	419.111i	−0.314392	+	0.436574i
$961$	−849.534			−0.884011
$962$	213.261	+	238.017i	0.221685	+	0.247419i
$963$		−	347.691i		−	0.361050i
$964$	−858.308	+	955.940i	−0.890361	+	0.991639i
$965$	−616.564			−0.638926
$966$	325.704	+	124.764i	0.337168	+	0.129156i
$967$	1283.14			1.32693			0.663464	−	0.748208i	$-0.269086\pi$
$967$	1283.14			1.32693			0.663464	+	0.748208i	$0.269086\pi$
$968$	−855.498	−	1670.31i	−0.883779	−	1.72553i
$969$			213.198i			0.220019i
$970$	−133.342	−	51.0779i	−0.137466	−	0.0526576i
$971$			625.363i			0.644040i	0.946733	+	0.322020i	$0.104362\pi$
$971$			625.363i			0.644040i	−0.946733	+	0.322020i	$0.895638\pi$
$972$	41.6578	−	46.3964i	0.0428579	−	0.0477329i
$973$		−	273.615i		−	0.281207i
$974$	1367.40	+	523.794i	1.40390	+	0.537777i
$975$	65.9417	+	33.8606i	0.0676325	+	0.0347288i
$976$	−55.2773	−	512.108i	−0.0566366	−	0.524701i
$977$		−	387.473i		−	0.396595i	−0.980142	−	0.198297i	$-0.936459\pi$
$977$		−	387.473i		−	0.396595i	0.980142	−	0.198297i	$-0.0635412\pi$
$978$	139.293	−	363.633i	0.142427	−	0.371813i
$979$			1518.20i			1.55077i
$980$	544.146	−	606.043i	0.555251	−	0.618411i
$981$		−	223.730i		−	0.228063i
$982$	−305.880	+	798.517i	−0.311486	+	0.813154i
$983$	−1600.35			−1.62802			−0.814012	−	0.580849i	$-0.802721\pi$
$983$	−1600.35			−1.62802			−0.814012	+	0.580849i	$0.802721\pi$
$984$	243.259	+	474.950i	0.247214	+	0.482672i
$985$	−1109.00			−1.12588
$986$	−711.259	−	272.455i	−0.721358	−	0.276323i
$987$			250.338i			0.253635i
$988$	−826.494	+	315.610i	−0.836533	+	0.319443i
$989$	527.208			0.533071
$990$	188.567	−	492.264i	0.190471	−	0.497237i
$991$		−	411.375i		−	0.415111i	−0.978223	−	0.207556i	$-0.933449\pi$
$991$		−	411.375i		−	0.415111i	0.978223	−	0.207556i	$-0.0665508\pi$
$992$	−86.2967	+	326.640i	−0.0869927	+	0.329274i
$993$		−	291.877i		−	0.293935i
$994$	−34.7186	−	13.2993i	−0.0349281	−	0.0133796i
$995$	−1125.26			−1.13092
$996$	−225.774	+	251.456i	−0.226681	+	0.252466i
$997$	−708.030			−0.710161			−0.355080	−	0.934836i	$-0.615546\pi$
$997$	−708.030			−0.710161			−0.355080	+	0.934836i	$0.615546\pi$
$998$	−736.717	−	282.206i	−0.738193	−	0.282772i
$999$	−63.8690			−0.0639329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.e.c.103.3	✓	24
3.2	odd	2		468.3.e.m.415.22		24
4.3	odd	2	inner	156.3.e.c.103.21	yes	24
12.11	even	2		468.3.e.m.415.4		24
13.12	even	2	inner	156.3.e.c.103.22	yes	24
39.38	odd	2		468.3.e.m.415.3		24
52.51	odd	2	inner	156.3.e.c.103.4	yes	24
156.155	even	2		468.3.e.m.415.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.e.c.103.3	✓	24	1.1	even	1	trivial
156.3.e.c.103.4	yes	24	52.51	odd	2	inner
156.3.e.c.103.21	yes	24	4.3	odd	2	inner
156.3.e.c.103.22	yes	24	13.12	even	2	inner
468.3.e.m.415.3		24	39.38	odd	2
468.3.e.m.415.4		24	12.11	even	2
468.3.e.m.415.21		24	156.155	even	2
468.3.e.m.415.22		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86766 - 0.715427i) q^{2} -1.73205i q^{3} +(2.97633 + 2.67235i) q^{4} +4.65917i q^{5} +(-1.23916 + 3.23489i) q^{6} -2.30148 q^{7} +(-3.64691 - 7.12040i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.86766 - 0.715427i) q^{2} -1.73205i q^{3} +(2.97633 + 2.67235i) q^{4} +4.65917i q^{5} +(-1.23916 + 3.23489i) q^{6} -2.30148 q^{7} +(-3.64691 - 7.12040i) q^{8} -3.00000 q^{9} +(3.33330 - 8.70176i) q^{10} -18.8569 q^{11} +(4.62865 - 5.15515i) q^{12} +(-5.93827 + 11.5645i) q^{13} +(4.29838 + 1.64654i) q^{14} +8.06992 q^{15} +(1.71708 + 15.9076i) q^{16} -7.23481 q^{17} +(5.60299 + 2.14628i) q^{18} +17.0136 q^{19} +(-12.4509 + 13.8672i) q^{20} +3.98628i q^{21} +(35.2183 + 13.4907i) q^{22} +43.7479i q^{23} +(-12.3329 + 6.31663i) q^{24} +3.29211 q^{25} +(19.3642 - 17.3501i) q^{26} +5.19615i q^{27} +(-6.84996 - 6.15036i) q^{28} -52.6383 q^{29} +(-15.0719 - 5.77344i) q^{30} -10.5577 q^{31} +(8.17380 - 30.9385i) q^{32} +32.6611i q^{33} +(13.5122 + 5.17598i) q^{34} -10.7230i q^{35} +(-8.92899 - 8.01705i) q^{36} +12.2916i q^{37} +(-31.7756 - 12.1720i) q^{38} +(20.0302 + 10.2854i) q^{39} +(33.1752 - 16.9916i) q^{40} -38.5108i q^{41} +(2.85189 - 7.44502i) q^{42} -12.0510i q^{43} +(-56.1243 - 50.3922i) q^{44} -13.9775i q^{45} +(31.2984 - 81.7064i) q^{46} +62.7999 q^{47} +(27.5528 - 2.97406i) q^{48} -43.7032 q^{49} +(-6.14854 - 2.35526i) q^{50} +12.5311i q^{51} +(-48.5786 + 18.5505i) q^{52} +74.8604 q^{53} +(3.71747 - 9.70466i) q^{54} -87.8574i q^{55} +(8.39328 + 16.3874i) q^{56} -29.4683i q^{57} +(98.3106 + 37.6588i) q^{58} -11.4508 q^{59} +(24.0188 + 21.5657i) q^{60} -32.1927 q^{61} +(19.7183 + 7.55328i) q^{62} +6.90443 q^{63} +(-37.4001 + 51.9349i) q^{64} +(-53.8809 - 27.6674i) q^{65} +(23.3666 - 60.9999i) q^{66} -60.8491 q^{67} +(-21.5332 - 19.3340i) q^{68} +75.7737 q^{69} +(-7.67151 + 20.0269i) q^{70} -8.07712 q^{71} +(10.9407 + 21.3612i) q^{72} +58.3386i q^{73} +(8.79373 - 22.9566i) q^{74} -5.70210i q^{75} +(50.6380 + 45.4662i) q^{76} +43.3987 q^{77} +(-30.0513 - 33.5398i) q^{78} -59.0233i q^{79} +(-74.1162 + 8.00016i) q^{80} +9.00000 q^{81} +(-27.5517 + 71.9252i) q^{82} -48.7775 q^{83} +(-10.6527 + 11.8645i) q^{84} -33.7082i q^{85} +(-8.62162 + 22.5073i) q^{86} +91.1722i q^{87} +(68.7693 + 134.268i) q^{88} -80.5117i q^{89} +(-9.99989 + 26.1053i) q^{90} +(13.6668 - 26.6154i) q^{91} +(-116.910 + 130.208i) q^{92} +18.2865i q^{93} +(-117.289 - 44.9287i) q^{94} +79.2691i q^{95} +(-53.5870 - 14.1574i) q^{96} -15.3235i q^{97} +(81.6229 + 31.2664i) q^{98} +56.5706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 72 q^{9}+O(q^{10}) \) 24 * q + 8 * q^4 - 72 * q^9	\( 24 q + 8 q^{4} - 72 q^{9} + 28 q^{10} + 36 q^{12} + 48 q^{13} - 40 q^{14} + 100 q^{16} + 32 q^{17} + 84 q^{22} - 312 q^{25} - 16 q^{26} - 80 q^{29} + 60 q^{30} - 24 q^{36} + 120 q^{38} - 204 q^{40} - 96 q^{42} - 144 q^{48} + 392 q^{49} + 28 q^{52} - 224 q^{53} + 800 q^{56} - 96 q^{61} - 352 q^{62} - 184 q^{64} - 112 q^{65} + 252 q^{66} - 344 q^{68} + 144 q^{69} + 232 q^{74} - 16 q^{77} - 168 q^{78} + 216 q^{81} + 20 q^{82} - 92 q^{88} - 84 q^{90} - 616 q^{92} - 684 q^{94}+O(q^{100}) \) 24 * q + 8 * q^4 - 72 * q^9 + 28 * q^10 + 36 * q^12 + 48 * q^13 - 40 * q^14 + 100 * q^16 + 32 * q^17 + 84 * q^22 - 312 * q^25 - 16 * q^26 - 80 * q^29 + 60 * q^30 - 24 * q^36 + 120 * q^38 - 204 * q^40 - 96 * q^42 - 144 * q^48 + 392 * q^49 + 28 * q^52 - 224 * q^53 + 800 * q^56 - 96 * q^61 - 352 * q^62 - 184 * q^64 - 112 * q^65 + 252 * q^66 - 344 * q^68 + 144 * q^69 + 232 * q^74 - 16 * q^77 - 168 * q^78 + 216 * q^81 + 20 * q^82 - 92 * q^88 - 84 * q^90 - 616 * q^92 - 684 * q^94

Introduction

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