LMFDB - Embedded newform 156.3.e.c.103.4

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

$q$-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	$-0.845724\pi$
$5$		−	4.65917i		−	0.931835i	0.884828	−	0.465917i	$-0.154276\pi$
$6$	−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	$-0.600015\pi$
$23$		−	43.7479i		−	1.90208i	0.309061	−	0.951042i	$-0.399985\pi$
$24$	−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	$-0.946882\pi$
$37$		−	12.2916i		−	0.332205i	0.986108	−	0.166103i	$-0.0531183\pi$
$38$	−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	$0.155618\pi$
$41$			38.5108i			0.939288i	−0.882856	+	0.469644i	$0.844382\pi$
$42$	2.85189	+	7.44502i	0.0679021	+	0.177262i
$43$			12.0510i			0.280256i	0.990133	+	0.140128i	$0.0447515\pi$
$43$			12.0510i			0.280256i	−0.990133	+	0.140128i	$0.955249\pi$
$44$	−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	$-0.869156\pi$
$73$		−	58.3386i		−	0.799159i	0.916699	−	0.399579i	$-0.130844\pi$
$74$	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	$0.121865\pi$
$79$			59.0233i			0.747131i	−0.927604	+	0.373565i	$0.878135\pi$
$80$	−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	$0.149401\pi$
$89$			80.5117i			0.904626i	−0.891859	+	0.452313i	$0.850599\pi$
$90$	−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	$0.0251687\pi$
$97$			15.3235i			0.157975i	−0.996876	+	0.0789873i	$0.974831\pi$
$98$	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	$0.180426\pi$
$103$			110.613i			1.07391i	−0.843610	+	0.536956i	$0.819574\pi$
$104$	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	$-0.817828\pi$
$107$		−	115.897i		−	1.08315i	0.840653	−	0.541575i	$-0.182172\pi$
$108$	−13.8859	−	15.4655i	−0.128574	−	0.143199i
$109$		−	74.5767i		−	0.684190i	−0.939665	−	0.342095i	$-0.888864\pi$
$109$		−	74.5767i		−	0.684190i	0.939665	−	0.342095i	$-0.111136\pi$
$110$	−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	$0.0161453\pi$
$127$			12.8779i			0.101401i	−0.998714	+	0.0507003i	$0.983855\pi$
$128$	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	$0.0823227\pi$
$131$			67.0067i			0.511502i	−0.966743	+	0.255751i	$0.917677\pi$
$132$	−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	$-0.631362\pi$
$137$		−	250.997i		−	1.83209i	0.401072	−	0.916047i	$-0.368638\pi$
$138$	−141.520	+	54.2105i	−1.02550	+	0.392830i
$139$		−	118.887i		−	0.855299i	−0.903945	−	0.427650i	$-0.859342\pi$
$139$		−	118.887i		−	0.855299i	0.903945	−	0.427650i	$-0.140658\pi$
$140$	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	$0.101301\pi$
$149$			93.2446i			0.625803i	−0.949786	+	0.312901i	$0.898699\pi$
$150$	−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	$-0.742769\pi$
$179$		−	258.829i		−	1.44597i	0.690862	−	0.722987i	$-0.257231\pi$
$180$	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	$0.152287\pi$
$191$			175.865i			0.920761i	−0.887722	+	0.460380i	$0.847713\pi$
$192$	89.9539	−	64.7789i	0.468510	−	0.337390i
$193$		−	132.333i		−	0.685665i	−0.939397	−	0.342832i	$-0.888614\pi$
$193$		−	132.333i		−	0.685665i	0.939397	−	0.342832i	$-0.111386\pi$
$194$	−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	$-0.793524\pi$
$197$		−	238.024i		−	1.20825i	0.796891	−	0.604123i	$-0.206476\pi$
$198$	−105.655	+	40.4721i	−0.533610	+	0.204405i
$199$		−	241.516i		−	1.21365i	−0.794836	−	0.606824i	$-0.792443\pi$
$199$		−	241.516i		−	1.21365i	0.794836	−	0.606824i	$-0.207557\pi$
$200$	−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	$0.173645\pi$
$211$			218.961i			1.03773i	−0.854857	+	0.518864i	$0.826355\pi$
$212$	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	$-0.623868\pi$
$229$		−	423.757i		−	1.85047i	0.379396	−	0.925234i	$-0.376132\pi$
$230$	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	$-0.767856\pi$
$241$		−	321.181i		−	1.33270i	0.745639	−	0.666350i	$-0.232144\pi$
$242$	−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	$-0.884082\pi$
$251$		−	178.799i		−	0.712345i	0.934420	−	0.356172i	$-0.115918\pi$
$252$	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	$0.180565\pi$
$263$			282.633i			1.07465i	−0.843375	+	0.537325i	$0.819435\pi$
$264$	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	$-0.970359\pi$
$281$		−	52.2572i		−	0.185969i	0.995668	−	0.0929844i	$-0.0296407\pi$
$282$	−77.8188	−	203.151i	−0.275953	−	0.720392i
$283$		−	233.514i		−	0.825140i	−0.910926	−	0.412570i	$-0.864631\pi$
$283$		−	233.514i		−	0.825140i	0.910926	−	0.412570i	$-0.135369\pi$
$284$	−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	$-0.999501\pi$
$293$		−	0.918517i		−	0.00313487i	0.999999	−	0.00156744i	$-0.000498930\pi$
$294$	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	$-0.733704\pi$
$311$		−	461.751i		−	1.48473i	0.669995	−	0.742366i	$-0.266296\pi$
$312$	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	$-0.762945\pi$
$317$		−	429.708i		−	1.35555i	0.735271	−	0.677773i	$-0.237055\pi$
$318$	−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	$0.0554140\pi$
$347$			120.208i			0.346421i	−0.984885	+	0.173210i	$0.944586\pi$
$348$	−243.644	−	271.358i	−0.700127	−	0.779766i
$349$			188.549i			0.540255i	0.962825	+	0.270127i	$0.0870658\pi$
$349$			188.549i			0.540255i	−0.962825	+	0.270127i	$0.912934\pi$
$350$	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	$0.210496\pi$
$353$			433.581i			1.22828i	−0.789199	+	0.614138i	$0.789504\pi$
$354$	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	$-0.785738\pi$
$367$		−	457.599i		−	1.24686i	0.781878	−	0.623432i	$-0.214262\pi$
$368$	−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	$0.0434003\pi$
$397$			107.924i			0.271848i	−0.990719	+	0.135924i	$0.956600\pi$
$398$	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	$0.231420\pi$
$401$			533.051i			1.32930i	−0.747153	+	0.664652i	$0.768580\pi$
$402$	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	$0.278627\pi$
$409$			628.025i			1.53551i	−0.640742	+	0.767756i	$0.721373\pi$
$410$	−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	$0.0590365\pi$
$419$			154.533i			0.368814i	−0.982850	+	0.184407i	$0.940964\pi$
$420$	−55.2786	+	49.6329i	−0.131616	+	0.118174i
$421$			448.868i			1.06620i	0.846054	+	0.533098i	$0.178972\pi$
$421$			448.868i			1.06620i	−0.846054	+	0.533098i	$0.821028\pi$
$422$	−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	$0.0469107\pi$
$439$			128.927i			0.293683i	−0.989160	+	0.146841i	$0.953089\pi$
$440$	−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	$0.133084\pi$
$443$			359.734i			0.812040i	−0.913864	+	0.406020i	$0.866916\pi$
$444$	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	$-0.901132\pi$
$449$		−	274.459i		−	0.611266i	0.952149	−	0.305633i	$-0.0988681\pi$
$450$	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	$-0.819919\pi$
$457$		−	489.942i		−	1.07208i	0.844191	−	0.536042i	$-0.180081\pi$
$458$	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	$0.00513221\pi$
$461$			14.8651i			0.0322452i	−0.999870	+	0.0161226i	$0.994868\pi$
$462$	−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	$-0.654112\pi$
$467$		−	826.653i		−	1.77013i	0.465463	−	0.885067i	$-0.345888\pi$
$468$	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	$0.143388\pi$
$491$			427.549i			0.870771i	−0.900244	+	0.435386i	$0.856612\pi$
$492$	−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	$-0.991008\pi$
$503$		−	28.4159i		−	0.0564929i	0.999601	−	0.0282464i	$-0.00899232\pi$
$504$	−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	$-0.819938\pi$
$509$		−	545.639i		−	1.07198i	0.844223	−	0.535992i	$-0.180062\pi$
$510$	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	$-0.931222\pi$
$523$		−	224.257i		−	0.428789i	0.976747	−	0.214394i	$-0.0687778\pi$
$524$	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	$-0.853099\pi$
$541$		−	481.809i		−	0.890589i	0.895384	−	0.445295i	$-0.146901\pi$
$542$	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	$0.0386980\pi$
$547$			132.674i			0.242548i	−0.992619	+	0.121274i	$0.961302\pi$
$548$	−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	$0.0105315\pi$
$557$			36.8507i			0.0661593i	−0.999453	+	0.0330796i	$0.989468\pi$
$558$	−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	$-0.941415\pi$
$563$		−	206.073i		−	0.366026i	0.983110	−	0.183013i	$-0.0585851\pi$
$564$	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	$0.124797\pi$
$571$			436.353i			0.764191i	−0.924123	+	0.382095i	$0.875203\pi$
$572$	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	$-0.980749\pi$
$577$		−	69.7493i		−	0.120883i	0.998172	−	0.0604413i	$-0.0192508\pi$
$578$	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	$0.0225381\pi$
$593$			83.9053i			0.141493i	−0.997494	+	0.0707465i	$0.977462\pi$
$594$	−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	$-0.825346\pi$
$599$		−	624.842i		−	1.04314i	0.853208	−	0.521571i	$-0.174654\pi$
$600$	−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	$0.354127\pi$
$607$			1088.74i			1.79364i	−0.442399	+	0.896818i	$0.645873\pi$
$608$	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	$0.242355\pi$
$613$			845.844i			1.37984i	−0.723884	+	0.689922i	$0.757645\pi$
$614$	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	$0.321098\pi$
$617$			1044.18i			1.69234i	−0.532910	+	0.846172i	$0.678902\pi$
$618$	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	$0.122910\pi$
$647$			487.331i			0.753216i	−0.926373	+	0.376608i	$0.877090\pi$
$648$	−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	$0.174810\pi$
$659$			687.981i			1.04398i	−0.852953	+	0.521988i	$0.825190\pi$
$660$	−452.919	+	406.661i	−0.686240	+	0.616153i
$661$		−	63.7781i		−	0.0964873i	−0.998836	−	0.0482437i	$-0.984638\pi$
$661$		−	63.7781i		−	0.0964873i	0.998836	−	0.0482437i	$-0.0153624\pi$
$662$	−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	$0.0174288\pi$
$709$			77.6026i			0.109454i	−0.998501	+	0.0547268i	$0.982571\pi$
$710$	−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	$-0.723496\pi$
$719$		−	1097.86i		−	1.52693i	0.645848	−	0.763466i	$-0.276504\pi$
$720$	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	$-0.867030\pi$
$727$		−	589.880i		−	0.811389i	0.914009	−	0.405694i	$-0.132970\pi$
$728$	−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	$0.110297\pi$
$733$			497.876i			0.679230i	−0.940565	+	0.339615i	$0.889703\pi$
$734$	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	$0.00608075\pi$
$751$			28.6913i			0.0382041i	−0.999818	+	0.0191021i	$0.993919\pi$
$752$	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	$0.335881\pi$
$761$			1324.14i			1.74000i	−0.493053	+	0.869999i	$0.664119\pi$
$762$	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	$-0.863894\pi$
$769$		−	637.778i		−	0.829360i	0.909967	−	0.414680i	$-0.136106\pi$
$770$	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	$-0.912671\pi$
$773$		−	418.846i		−	0.541845i	0.962601	−	0.270922i	$-0.0873287\pi$
$774$	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	$0.271793\pi$
$821$			1237.78i			1.50765i	−0.657075	+	0.753825i	$0.728207\pi$
$822$	−811.946	+	311.024i	−0.987769	+	0.378375i
$823$		−	684.583i		−	0.831814i	−0.909407	−	0.415907i	$-0.863464\pi$
$823$		−	684.583i		−	0.831814i	0.909407	−	0.415907i	$-0.136536\pi$
$824$	−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	$-0.949062\pi$
$853$		−	271.841i		−	0.318688i	0.987223	−	0.159344i	$-0.0509379\pi$
$854$	−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	$0.172714\pi$
$859$			887.108i			1.03272i	−0.856371	+	0.516361i	$0.827286\pi$
$860$	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	$-0.821206\pi$
$877$		−	934.224i		−	1.06525i	0.846351	−	0.532625i	$-0.178794\pi$
$878$	−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	$0.0453410\pi$
$883$			250.704i			0.283923i	−0.989872	+	0.141962i	$0.954659\pi$
$884$	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	$-0.852720\pi$
$887$		−	791.842i		−	0.892719i	0.894854	−	0.446360i	$-0.147280\pi$
$888$	−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	$0.186123\pi$
$907$			1001.27i			1.10394i	−0.833865	+	0.551968i	$0.813877\pi$
$908$	−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	$-0.964631\pi$
$911$		−	202.038i		−	0.221776i	0.993833	−	0.110888i	$-0.0353695\pi$
$912$	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	$-0.615950\pi$
$919$		−	1717.40i		−	1.86877i	0.356265	−	0.934385i	$-0.384050\pi$
$920$	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	$-0.758814\pi$
$929$		−	1276.92i		−	1.37452i	0.726414	−	0.687258i	$-0.241186\pi$
$930$	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	$-0.791681\pi$
$941$		−	1145.62i		−	1.21745i	0.793381	−	0.608725i	$-0.208319\pi$
$942$	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	$-0.895638\pi$
$971$		−	625.363i		−	0.644040i	0.946733	−	0.322020i	$-0.104362\pi$
$972$	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	$0.0635412\pi$
$977$			387.473i			0.396595i	−0.980142	+	0.198297i	$0.936459\pi$
$978$	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	$0.0665508\pi$
$991$			411.375i			0.415111i	−0.978223	+	0.207556i	$0.933449\pi$
$992$	−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.103.4	yes	24
3.2	odd	2		468.3.e.m.415.21		24
4.3	odd	2	inner	156.3.e.c.103.22	yes	24
12.11	even	2		468.3.e.m.415.3		24
13.12	even	2	inner	156.3.e.c.103.21	yes	24
39.38	odd	2		468.3.e.m.415.4		24
52.51	odd	2	inner	156.3.e.c.103.3	✓	24
156.155	even	2		468.3.e.m.415.22		24

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

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