LMFDB - Embedded newform 156.3.e.c.103.12

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			103.12
Character	$\chi$	$=$	156.103
Dual form			156.3.e.c.103.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0830862 + 1.99827i) q^{2} -1.73205i q^{3} +(-3.98619 - 0.332058i) q^{4} -0.451006i q^{5} +(3.46111 + 0.143910i) q^{6} +9.24405 q^{7} +(0.994741 - 7.93791i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.0830862 + 1.99827i) q^{2} -1.73205i q^{3} +(-3.98619 - 0.332058i) q^{4} -0.451006i q^{5} +(3.46111 + 0.143910i) q^{6} +9.24405 q^{7} +(0.994741 - 7.93791i) q^{8} -3.00000 q^{9} +(0.901234 + 0.0374724i) q^{10} +11.2653 q^{11} +(-0.575141 + 6.90429i) q^{12} +(8.66010 + 9.69550i) q^{13} +(-0.768053 + 18.4721i) q^{14} -0.781166 q^{15} +(15.7795 + 2.64730i) q^{16} -5.48353 q^{17} +(0.249259 - 5.99482i) q^{18} +15.6424 q^{19} +(-0.149760 + 1.79780i) q^{20} -16.0112i q^{21} +(-0.935990 + 22.5111i) q^{22} -15.8759i q^{23} +(-13.7489 - 1.72294i) q^{24} +24.7966 q^{25} +(-20.0938 + 16.4997i) q^{26} +5.19615i q^{27} +(-36.8486 - 3.06956i) q^{28} -41.4435 q^{29} +(0.0649041 - 1.56098i) q^{30} -13.7377 q^{31} +(-6.60108 + 31.3118i) q^{32} -19.5121i q^{33} +(0.455606 - 10.9576i) q^{34} -4.16912i q^{35} +(11.9586 + 0.996174i) q^{36} +1.35152i q^{37} +(-1.29967 + 31.2579i) q^{38} +(16.7931 - 14.9997i) q^{39} +(-3.58005 - 0.448634i) q^{40} +31.3221i q^{41} +(31.9947 + 1.33031i) q^{42} -78.9583i q^{43} +(-44.9056 - 3.74073i) q^{44} +1.35302i q^{45} +(31.7243 + 1.31907i) q^{46} +39.5689 q^{47} +(4.58525 - 27.3309i) q^{48} +36.4524 q^{49} +(-2.06026 + 49.5504i) q^{50} +9.49775i q^{51} +(-31.3014 - 41.5238i) q^{52} -67.3481 q^{53} +(-10.3833 - 0.431729i) q^{54} -5.08071i q^{55} +(9.19543 - 73.3785i) q^{56} -27.0935i q^{57} +(3.44338 - 82.8153i) q^{58} -59.4363 q^{59} +(3.11388 + 0.259392i) q^{60} +36.6282 q^{61} +(1.14141 - 27.4516i) q^{62} -27.7321 q^{63} +(-62.0210 - 15.7923i) q^{64} +(4.37273 - 3.90576i) q^{65} +(38.9904 + 1.62118i) q^{66} -66.2481 q^{67} +(21.8584 + 1.82085i) q^{68} -27.4978 q^{69} +(8.33105 + 0.346397i) q^{70} +66.8261 q^{71} +(-2.98422 + 23.8137i) q^{72} +82.4828i q^{73} +(-2.70070 - 0.112292i) q^{74} -42.9490i q^{75} +(-62.3538 - 5.19420i) q^{76} +104.137 q^{77} +(28.5783 + 34.8035i) q^{78} +91.4509i q^{79} +(1.19395 - 7.11664i) q^{80} +9.00000 q^{81} +(-62.5900 - 2.60243i) q^{82} -121.470 q^{83} +(-5.31663 + 63.8236i) q^{84} +2.47311i q^{85} +(157.780 + 6.56035i) q^{86} +71.7822i q^{87} +(11.2060 - 89.4229i) q^{88} -69.6007i q^{89} +(-2.70370 - 0.112417i) q^{90} +(80.0544 + 89.6256i) q^{91} +(-5.27171 + 63.2843i) q^{92} +23.7943i q^{93} +(-3.28763 + 79.0695i) q^{94} -7.05484i q^{95} +(54.2335 + 11.4334i) q^{96} -92.5018i q^{97} +(-3.02870 + 72.8419i) q^{98} -33.7959 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 $

$2$	−0.0830862	+	1.99827i	−0.0415431	+	0.999137i
$2$	−0.0830862	+	1.99827i	−0.0415431	+	0.999137i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.98619	−	0.332058i	−0.996548	−	0.0830145i
$5$		−	0.451006i		−	0.0902012i	−0.998982	−	0.0451006i	$-0.985639\pi$
$5$		−	0.451006i		−	0.0902012i	0.998982	−	0.0451006i	$-0.0143608\pi$
$6$	3.46111	+	0.143910i	0.576852	+	0.0239849i
$7$	9.24405			1.32058			0.660289	−	0.751011i	$-0.270434\pi$
$7$	9.24405			1.32058			0.660289	+	0.751011i	$0.270434\pi$
$8$	0.994741	−	7.93791i	0.124343	−	0.992239i
$9$	−3.00000			−0.333333
$10$	0.901234	+	0.0374724i	0.0901234	+	0.00374724i
$11$	11.2653			1.02412			0.512059	−	0.858951i	$-0.328883\pi$
$11$	11.2653			1.02412			0.512059	+	0.858951i	$0.328883\pi$
$12$	−0.575141	+	6.90429i	−0.0479284	+	0.575357i
$13$	8.66010	+	9.69550i	0.666162	+	0.745807i
$13$	8.66010	+	9.69550i	0.666162	+	0.745807i
$14$	−0.768053	+	18.4721i	−0.0548609	+	1.31944i
$15$	−0.781166			−0.0520777
$16$	15.7795	+	2.64730i	0.986217	+	0.165456i
$17$	−5.48353			−0.322561			−0.161280	−	0.986909i	$-0.551562\pi$
$17$	−5.48353			−0.322561			−0.161280	+	0.986909i	$0.551562\pi$
$18$	0.249259	−	5.99482i	0.0138477	−	0.333046i
$19$	15.6424			0.823286			0.411643	−	0.911345i	$-0.364955\pi$
$19$	15.6424			0.823286			0.411643	+	0.911345i	$0.364955\pi$
$20$	−0.149760	+	1.79780i	−0.00748801	+	0.0898899i
$21$		−	16.0112i		−	0.762436i
$22$	−0.935990	+	22.5111i	−0.0425450	+	1.02323i
$23$		−	15.8759i		−	0.690255i	−0.938556	−	0.345128i	$-0.887836\pi$
$23$		−	15.8759i		−	0.690255i	0.938556	−	0.345128i	$-0.112164\pi$
$24$	−13.7489	−	1.72294i	−0.572870	−	0.0717892i
$25$	24.7966			0.991864
$26$	−20.0938	+	16.4997i	−0.772838	+	0.634603i
$27$			5.19615i			0.192450i
$28$	−36.8486	−	3.06956i	−1.31602	−	0.109627i
$29$	−41.4435			−1.42908			−0.714542	−	0.699592i	$-0.753365\pi$
$29$	−41.4435			−1.42908			−0.714542	+	0.699592i	$0.753365\pi$
$30$	0.0649041	−	1.56098i	0.00216347	−	0.0520328i
$31$	−13.7377			−0.443151			−0.221575	−	0.975143i	$-0.571120\pi$
$31$	−13.7377			−0.443151			−0.221575	+	0.975143i	$0.571120\pi$
$32$	−6.60108	+	31.3118i	−0.206284	+	0.978492i
$33$		−	19.5121i		−	0.591274i
$34$	0.455606	−	10.9576i	0.0134002	−	0.322282i
$35$		−	4.16912i		−	0.119118i
$36$	11.9586	+	0.996174i	0.332183	+	0.0276715i
$37$			1.35152i			0.0365275i	0.999833	+	0.0182637i	$0.00581385\pi$
$37$			1.35152i			0.0365275i	−0.999833	+	0.0182637i	$0.994186\pi$
$38$	−1.29967	+	31.2579i	−0.0342019	+	0.822575i
$39$	16.7931	−	14.9997i	0.430592	−	0.384609i
$40$	−3.58005	−	0.448634i	−0.0895012	−	0.0112159i
$41$			31.3221i			0.763952i	0.924172	+	0.381976i	$0.124756\pi$
$41$			31.3221i			0.763952i	−0.924172	+	0.381976i	$0.875244\pi$
$42$	31.9947	+	1.33031i	0.761778	+	0.0316740i
$43$		−	78.9583i		−	1.83624i	−0.396304	−	0.918120i	$-0.629707\pi$
$43$		−	78.9583i		−	1.83624i	0.396304	−	0.918120i	$-0.370293\pi$
$44$	−44.9056	−	3.74073i	−1.02058	−	0.0850166i
$45$			1.35302i			0.0300671i
$46$	31.7243	+	1.31907i	0.689659	+	0.0286754i
$47$	39.5689			0.841892			0.420946	−	0.907086i	$-0.361698\pi$
$47$	39.5689			0.841892			0.420946	+	0.907086i	$0.361698\pi$
$48$	4.58525	−	27.3309i	0.0955260	−	0.569393i
$49$	36.4524			0.743927
$50$	−2.06026	+	49.5504i	−0.0412051	+	0.991007i
$51$			9.49775i			0.186230i
$52$	−31.3014	−	41.5238i	−0.601949	−	0.798534i
$53$	−67.3481			−1.27072			−0.635359	−	0.772217i	$-0.719148\pi$
$53$	−67.3481			−1.27072			−0.635359	+	0.772217i	$0.719148\pi$
$54$	−10.3833	−	0.431729i	−0.192284	−	0.00799498i
$55$		−	5.08071i		−	0.0923766i
$56$	9.19543	−	73.3785i	0.164204	−	1.31033i
$57$		−	27.0935i		−	0.475324i
$58$	3.44338	−	82.8153i	0.0593686	−	1.42785i
$59$	−59.4363			−1.00740			−0.503698	−	0.863880i	$-0.668027\pi$
$59$	−59.4363			−1.00740			−0.503698	+	0.863880i	$0.668027\pi$
$60$	3.11388	+	0.259392i	0.0518980	+	0.00432321i
$61$	36.6282			0.600462			0.300231	−	0.953866i	$-0.402936\pi$
$61$	36.6282			0.600462			0.300231	+	0.953866i	$0.402936\pi$
$62$	1.14141	−	27.4516i	0.0184099	−	0.442768i
$63$	−27.7321			−0.440193
$64$	−62.0210	−	15.7923i	−0.969078	−	0.246755i
$65$	4.37273	−	3.90576i	0.0672728	−	0.0600886i
$66$	38.9904	+	1.62118i	0.590764	+	0.0245634i
$67$	−66.2481			−0.988777			−0.494389	−	0.869241i	$-0.664608\pi$
$67$	−66.2481			−0.988777			−0.494389	+	0.869241i	$0.664608\pi$
$68$	21.8584	+	1.82085i	0.321447	+	0.0267772i
$69$	−27.4978			−0.398519
$70$	8.33105	+	0.346397i	0.119015	+	0.00494853i
$71$	66.8261			0.941212			0.470606	−	0.882343i	$-0.344035\pi$
$71$	66.8261			0.941212			0.470606	+	0.882343i	$0.344035\pi$
$72$	−2.98422	+	23.8137i	−0.0414475	+	0.330746i
$73$			82.4828i			1.12990i	0.825125	+	0.564950i	$0.191105\pi$
$73$			82.4828i			1.12990i	−0.825125	+	0.564950i	$0.808895\pi$
$74$	−2.70070	−	0.112292i	−0.0364959	−	0.00151746i
$75$		−	42.9490i		−	0.572653i
$76$	−62.3538	−	5.19420i	−0.820444	−	0.0683447i
$77$	104.137			1.35243
$78$	28.5783	+	34.8035i	0.366388	+	0.446198i
$79$			91.4509i			1.15761i	0.815467	+	0.578803i	$0.196480\pi$
$79$			91.4509i			1.15761i	−0.815467	+	0.578803i	$0.803520\pi$
$80$	1.19395	−	7.11664i	0.0149243	−	0.0889580i
$81$	9.00000			0.111111
$82$	−62.5900	−	2.60243i	−0.763293	−	0.0317370i
$83$	−121.470			−1.46349			−0.731746	−	0.681578i	$-0.761294\pi$
$83$	−121.470			−1.46349			−0.731746	+	0.681578i	$0.761294\pi$
$84$	−5.31663	+	63.8236i	−0.0632933	+	0.759805i
$85$			2.47311i			0.0290954i
$86$	157.780	+	6.56035i	1.83465	+	0.0762831i
$87$			71.7822i			0.825082i
$88$	11.2060	−	89.4229i	0.127341	−	1.01617i
$89$		−	69.6007i		−	0.782030i	−0.920384	−	0.391015i	$-0.872124\pi$
$89$		−	69.6007i		−	0.782030i	0.920384	−	0.391015i	$-0.127876\pi$
$90$	−2.70370	−	0.112417i	−0.0300411	−	0.00124908i
$91$	80.0544	+	89.6256i	0.879719	+	0.984897i
$92$	−5.27171	+	63.2843i	−0.0573012	+	0.687873i
$93$			23.7943i			0.255853i
$94$	−3.28763	+	79.0695i	−0.0349748	+	0.841165i
$95$		−	7.05484i		−	0.0742614i
$96$	54.2335	+	11.4334i	0.564933	+	0.119098i
$97$		−	92.5018i		−	0.953627i	−0.879005	−	0.476813i	$-0.841792\pi$
$97$		−	92.5018i		−	0.953627i	0.879005	−	0.476813i	$-0.158208\pi$
$98$	−3.02870	+	72.8419i	−0.0309051	+	0.743285i
$99$	−33.7959			−0.341372
$100$	−98.8440	−	8.23391i	−0.988440	−	0.0823391i
$101$	−86.9141			−0.860535			−0.430268	−	0.902701i	$-0.641581\pi$
$101$	−86.9141			−0.860535			−0.430268	+	0.902701i	$0.641581\pi$
$102$	−18.9791	−	0.789133i	−0.186070	−	0.00773659i
$103$			110.505i			1.07286i	0.843944	+	0.536431i	$0.180228\pi$
$103$			110.505i			1.07286i	−0.843944	+	0.536431i	$0.819772\pi$
$104$	85.5766	−	59.0986i	0.822852	−	0.568256i
$105$	−7.22113			−0.0687727
$106$	5.59570	−	134.580i	0.0527896	−	1.26962i
$107$			210.444i			1.96677i	0.181535	+	0.983384i	$0.441893\pi$
$107$			210.444i			1.96677i	−0.181535	+	0.983384i	$0.558107\pi$
$108$	1.72542	−	20.7129i	0.0159761	−	0.191786i
$109$			178.380i			1.63651i	0.574852	+	0.818257i	$0.305060\pi$
$109$			178.380i			1.63651i	−0.574852	+	0.818257i	$0.694940\pi$
$110$	10.1527	+	0.422137i	0.0922969	+	0.00383761i
$111$	2.34089			0.0210891
$112$	145.866	+	24.4717i	1.30238	+	0.218498i
$113$	−8.85742			−0.0783843			−0.0391921	−	0.999232i	$-0.512478\pi$
$113$	−8.85742			−0.0783843			−0.0391921	+	0.999232i	$0.512478\pi$
$114$	54.1402	+	2.25110i	0.474914	+	0.0197465i
$115$	−7.16012			−0.0622619
$116$	165.202	+	13.7616i	1.42415	+	0.118635i
$117$	−25.9803	−	29.0865i	−0.222054	−	0.248602i
$118$	4.93834	−	118.770i	0.0418504	−	1.00653i
$119$	−50.6900			−0.425967
$120$	−0.777057	+	6.20083i	−0.00647548	+	0.0516736i
$121$	5.90670			0.0488157
$122$	−3.04330	+	73.1932i	−0.0249451	+	0.599944i
$123$	54.2514			0.441068
$124$	54.7610	+	4.56170i	0.441621	+	0.0367879i
$125$		−	22.4586i		−	0.179669i
$126$	2.30416	−	55.4164i	0.0182870	−	0.439813i
$127$			4.75632i			0.0374514i	0.999825	+	0.0187257i	$0.00596092\pi$
$127$			4.75632i			0.0374514i	−0.999825	+	0.0187257i	$0.994039\pi$
$128$	36.7105	−	122.623i	0.286801	−	0.957990i
$129$	−136.760			−1.06015
$130$	7.44146	+	9.06242i	0.0572420	+	0.0697109i
$131$		−	136.014i		−	1.03827i	−0.854691	−	0.519137i	$-0.826254\pi$
$131$		−	136.014i		−	1.03827i	0.854691	−	0.519137i	$-0.173746\pi$
$132$	−6.47913	+	77.7788i	−0.0490843	+	0.589233i
$133$	144.599			1.08721
$134$	5.50430	−	132.382i	0.0410769	−	0.987924i
$135$	2.34350			0.0173592
$136$	−5.45469	+	43.5278i	−0.0401080	+	0.320057i
$137$		−	140.844i		−	1.02806i	−0.857772	−	0.514030i	$-0.828152\pi$
$137$		−	140.844i		−	1.02806i	0.857772	−	0.514030i	$-0.171848\pi$
$138$	2.28469	−	54.9482i	0.0165557	−	0.398175i
$139$		−	249.944i		−	1.79816i	−0.437789	−	0.899078i	$-0.644238\pi$
$139$		−	249.944i		−	1.79816i	0.437789	−	0.899078i	$-0.355762\pi$
$140$	−1.38439	+	16.6189i	−0.00988851	+	0.118707i
$141$		−	68.5354i		−	0.486067i
$142$	−5.55233	+	133.537i	−0.0391009	+	0.940400i
$143$	97.5585	+	109.223i	0.682227	+	0.763794i
$144$	−47.3384	−	7.94189i	−0.328739	−	0.0551520i
$145$			18.6913i			0.128905i
$146$	−164.823	−	6.85318i	−1.12893	−	0.0469396i
$147$		−	63.1375i		−	0.429507i
$148$	0.448782	−	5.38741i	0.00303231	−	0.0364014i
$149$			42.7430i			0.286866i	0.989660	+	0.143433i	$0.0458141\pi$
$149$			42.7430i			0.286866i	−0.989660	+	0.143433i	$0.954186\pi$
$150$	85.8238	+	3.56847i	0.572158	+	0.0237898i
$151$	−97.5689			−0.646152			−0.323076	−	0.946373i	$-0.604717\pi$
$151$	−97.5689			−0.646152			−0.323076	+	0.946373i	$0.604717\pi$
$152$	15.5602	−	124.168i	0.102370	−	0.816897i
$153$	16.4506			0.107520
$154$	−8.65234	+	208.094i	−0.0561840	+	1.35126i
$155$			6.19578i			0.0399727i
$156$	−71.9213	+	54.2156i	−0.461034	+	0.347536i
$157$	113.388			0.722218			0.361109	−	0.932524i	$-0.382398\pi$
$157$	113.388			0.722218			0.361109	+	0.932524i	$0.382398\pi$
$158$	−182.744	−	7.59831i	−1.15661	−	0.0480906i
$159$			116.650i			0.733650i
$160$	14.1218	+	2.97713i	0.0882612	+	0.0186070i
$161$		−	146.757i		−	0.911536i
$162$	−0.747776	+	17.9845i	−0.00461590	+	0.111015i
$163$	−177.456			−1.08868			−0.544342	−	0.838863i	$-0.683221\pi$
$163$	−177.456			−1.08868			−0.544342	+	0.838863i	$0.683221\pi$
$164$	10.4007	−	124.856i	0.0634191	−	0.761316i
$165$	−8.80006			−0.0533337
$166$	10.0925	−	242.730i	0.0607980	−	1.46223i
$167$	129.955			0.778171			0.389086	−	0.921202i	$-0.372791\pi$
$167$	129.955			0.778171			0.389086	+	0.921202i	$0.372791\pi$
$168$	−127.095	−	15.9270i	−0.756519	−	0.0948033i
$169$	−19.0053	+	167.928i	−0.112457	+	0.993657i
$170$	−4.94194	−	0.205481i	−0.0290702	−	0.00120871i
$171$	−46.9273			−0.274429
$172$	−26.2187	+	314.743i	−0.152434	+	1.82990i
$173$	118.409			0.684443			0.342222	−	0.939619i	$-0.388821\pi$
$173$	118.409			0.684443			0.342222	+	0.939619i	$0.388821\pi$
$174$	−143.440	−	5.96411i	−0.824370	−	0.0342765i
$175$	229.221			1.30983
$176$	177.760	+	29.8225i	1.01000	+	0.169446i
$177$			102.947i			0.581620i
$178$	139.081	+	5.78286i	0.781355	+	0.0324880i
$179$		−	260.347i		−	1.45445i	−0.686398	−	0.727226i	$-0.740809\pi$
$179$		−	260.347i		−	1.45445i	0.686398	−	0.727226i	$-0.259191\pi$
$180$	0.449281	−	5.39339i	0.00249600	−	0.0299633i
$181$	−269.411			−1.48846			−0.744229	−	0.667925i	$-0.767183\pi$
$181$	−269.411			−1.48846			−0.744229	+	0.667925i	$0.767183\pi$
$182$	−185.748	+	152.524i	−1.02059	+	0.838043i
$183$		−	63.4419i		−	0.346677i
$184$	−126.021	−	15.7924i	−0.684898	−	0.0858281i
$185$	0.609542			0.00329482
$186$	−47.5476	−	1.97698i	−0.255632	−	0.0106289i
$187$	−61.7735			−0.330340
$188$	−157.729	−	13.1392i	−0.838986	−	0.0698892i
$189$			48.0335i			0.254145i
$190$	14.0975	+	0.586160i	0.0741973	+	0.00308505i
$191$		−	70.8815i		−	0.371107i	−0.982634	−	0.185554i	$-0.940592\pi$
$191$		−	70.8815i		−	0.371107i	0.982634	−	0.185554i	$-0.0594079\pi$
$192$	−27.3531	+	107.423i	−0.142464	+	0.559497i
$193$			101.778i			0.527347i	0.964612	+	0.263674i	$0.0849342\pi$
$193$			101.778i			0.527347i	−0.964612	+	0.263674i	$0.915066\pi$
$194$	184.844	+	7.68563i	0.952803	+	0.0396166i
$195$	−6.76497	−	7.57379i	−0.0346922	−	0.0388399i
$196$	−145.306	−	12.1043i	−0.741359	−	0.0617567i
$197$			110.548i			0.561159i	0.959831	+	0.280579i	$0.0905266\pi$
$197$			110.548i			0.561159i	−0.959831	+	0.280579i	$0.909473\pi$
$198$	2.80797	−	67.5334i	0.0141817	−	0.341078i
$199$		−	172.019i		−	0.864418i	−0.901773	−	0.432209i	$-0.857734\pi$
$199$		−	172.019i		−	0.864418i	0.901773	−	0.432209i	$-0.142266\pi$
$200$	24.6662	−	196.833i	0.123331	−	0.984166i
$201$			114.745i			0.570871i
$202$	7.22136	−	173.678i	0.0357493	−	0.859792i
$203$	−383.105			−1.88722
$204$	3.15381	−	37.8599i	0.0154598	−	0.185588i
$205$	14.1264			0.0689095
$206$	−220.819	−	9.18143i	−1.07194	−	0.0445700i
$207$			47.6276i			0.230085i
$208$	110.985	+	175.916i	0.533582	+	0.845748i
$209$	176.217			0.843141
$210$	0.599977	−	14.4298i	0.00285703	−	0.0687133i
$211$		−	16.2184i		−	0.0768647i	−0.999261	−	0.0384323i	$-0.987764\pi$
$211$		−	16.2184i		−	0.0768647i	0.999261	−	0.0384323i	$-0.0122364\pi$
$212$	268.463	+	22.3635i	1.26633	+	0.105488i
$213$		−	115.746i		−	0.543409i
$214$	−420.525	−	17.4850i	−1.96507	−	0.0817057i
$215$	−35.6107			−0.165631
$216$	41.2466	+	5.16882i	0.190957	+	0.0239297i
$217$	−126.992			−0.585215
$218$	−356.452	−	14.8209i	−1.63510	−	0.0679859i
$219$	142.864			0.652349
$220$	−1.68709	+	20.2527i	−0.00766860	+	0.0920578i
$221$	−47.4879	−	53.1655i	−0.214877	−	0.240568i
$222$	−0.194496	+	4.67775i	−0.000876109	+	0.0210709i
$223$	204.961			0.919107			0.459553	−	0.888150i	$-0.348009\pi$
$223$	204.961			0.919107			0.459553	+	0.888150i	$0.348009\pi$
$224$	−61.0207	+	289.447i	−0.272414	+	1.29218i
$225$	−74.3898			−0.330621
$226$	0.735930	−	17.6996i	0.00325633	−	0.0783166i
$227$	247.892			1.09204			0.546018	−	0.837773i	$-0.316143\pi$
$227$	247.892			1.09204			0.546018	+	0.837773i	$0.316143\pi$
$228$	−8.99661	+	108.000i	−0.0394588	+	0.473684i
$229$		−	341.405i		−	1.49085i	−0.666589	−	0.745425i	$-0.732246\pi$
$229$		−	341.405i		−	1.49085i	0.666589	−	0.745425i	$-0.267754\pi$
$230$	0.594907	−	14.3079i	0.00258655	−	0.0622081i
$231$		−	180.370i		−	0.780824i
$232$	−41.2255	+	328.975i	−0.177696	+	1.41799i
$233$	174.456			0.748739			0.374369	−	0.927280i	$-0.377859\pi$
$233$	174.456			0.748739			0.374369	+	0.927280i	$0.377859\pi$
$234$	60.2814	−	49.4991i	0.257613	−	0.211534i
$235$		−	17.8458i		−	0.0759397i
$236$	236.925	+	19.7363i	1.00392	+	0.0836285i
$237$	158.398			0.668344
$238$	4.21164	−	101.293i	0.0176960	−	0.425599i
$239$	130.623			0.546540			0.273270	−	0.961937i	$-0.411895\pi$
$239$	130.623			0.546540			0.273270	+	0.961937i	$0.411895\pi$
$240$	−12.3264	−	2.06798i	−0.0513599	−	0.00861657i
$241$		−	204.639i		−	0.849124i	−0.905399	−	0.424562i	$-0.860428\pi$
$241$		−	204.639i		−	0.849124i	0.905399	−	0.424562i	$-0.139572\pi$
$242$	−0.490766	+	11.8032i	−0.00202796	+	0.0487736i
$243$		−	15.5885i		−	0.0641500i
$244$	−146.007	−	12.1627i	−0.598390	−	0.0498471i
$245$		−	16.4403i		−	0.0671031i
$246$	−4.50754	+	108.409i	−0.0183233	+	0.440687i
$247$	135.465	+	151.661i	0.548442	+	0.614013i
$248$	−13.6654	+	109.048i	−0.0551025	+	0.439712i
$249$			210.392i			0.844947i
$250$	44.8784	+	1.86600i	0.179513	+	0.00746399i
$251$		−	338.998i		−	1.35059i	−0.737548	−	0.675295i	$-0.764017\pi$
$251$		−	338.998i		−	1.35059i	0.737548	−	0.675295i	$-0.235983\pi$
$252$	110.546	+	9.20868i	0.438673	+	0.0365424i
$253$		−	178.846i		−	0.706902i
$254$	−9.50444	−	0.395185i	−0.0374190	−	0.00155585i
$255$	4.28355			0.0167982
$256$	241.984	+	83.5459i	0.945249	+	0.326351i
$257$	−22.5409			−0.0877078			−0.0438539	−	0.999038i	$-0.513964\pi$
$257$	−22.5409			−0.0877078			−0.0438539	+	0.999038i	$0.513964\pi$
$258$	11.3629	−	273.283i	0.0440421	−	1.05924i
$259$			12.4935i			0.0482374i
$260$	−18.7275	+	14.1171i	−0.0720288	+	0.0542966i
$261$	124.330			0.476362
$262$	271.793	+	11.3009i	1.03738	+	0.0431331i
$263$			164.263i			0.624575i	0.949988	+	0.312288i	$0.101095\pi$
$263$			164.263i			0.624575i	−0.949988	+	0.312288i	$0.898905\pi$
$264$	−154.885	−	19.4094i	−0.586686	−	0.0735206i
$265$			30.3744i			0.114620i
$266$	−12.0142	+	288.949i	−0.0451663	+	1.08628i
$267$	−120.552			−0.451505
$268$	264.078	+	21.9982i	0.985364	+	0.0820829i
$269$	−354.196			−1.31671			−0.658357	−	0.752706i	$-0.728748\pi$
$269$	−354.196			−1.31671			−0.658357	+	0.752706i	$0.728748\pi$
$270$	−0.194712	+	4.68295i	−0.000721157	+	0.0173443i
$271$	460.038			1.69756			0.848779	−	0.528747i	$-0.177338\pi$
$271$	460.038			1.69756			0.848779	+	0.528747i	$0.177338\pi$
$272$	−86.5272	−	14.5165i	−0.318115	−	0.0533696i
$273$	155.236	−	138.658i	0.568631	−	0.507906i
$274$	281.445	+	11.7022i	1.02717	+	0.0427088i
$275$	279.341			1.01578
$276$	109.612	+	9.13087i	0.397144	+	0.0330829i
$277$	−320.964			−1.15871			−0.579357	−	0.815074i	$-0.696696\pi$
$277$	−320.964			−1.15871			−0.579357	+	0.815074i	$0.696696\pi$
$278$	499.456	+	20.7669i	1.79660	+	0.0747010i
$279$	41.2130			0.147717
$280$	−33.0941	−	4.14720i	−0.118193	−	0.0148114i
$281$			392.202i			1.39574i	0.716226	+	0.697869i	$0.245868\pi$
$281$			392.202i			1.39574i	−0.716226	+	0.697869i	$0.754132\pi$
$282$	136.952	+	5.69435i	0.485647	+	0.0201927i
$283$			98.5400i			0.348198i	0.984728	+	0.174099i	$0.0557013\pi$
$283$			98.5400i			0.348198i	−0.984728	+	0.174099i	$0.944299\pi$
$284$	−266.382	−	22.1901i	−0.937964	−	0.0781343i
$285$	−12.2193			−0.0428749
$286$	−226.362	+	185.874i	−0.791477	+	0.649908i
$287$			289.543i			1.00886i
$288$	19.8032	−	93.9353i	0.0687612	−	0.326164i
$289$	−258.931			−0.895955
$290$	−37.3502	−	1.55299i	−0.128794	−	0.00535512i
$291$	−160.218			−0.550577
$292$	27.3891	−	328.792i	0.0937982	−	1.12600i
$293$			480.251i			1.63908i	0.573021	+	0.819541i	$0.305772\pi$
$293$			480.251i			1.63908i	−0.573021	+	0.819541i	$0.694228\pi$
$294$	126.166	+	5.24585i	0.429136	+	0.0178430i
$295$			26.8062i			0.0908683i
$296$	10.7282	+	1.34441i	0.0362440	+	0.00454192i
$297$			58.5362i			0.197091i
$298$	−85.4122	−	3.55135i	−0.286618	−	0.0119173i
$299$	153.924	−	137.487i	0.514798	−	0.459822i
$300$	−14.2615	+	171.203i	−0.0475385	+	0.570676i
$301$		−	729.894i		−	2.42490i
$302$	8.10663	−	194.969i	0.0268432	−	0.645594i
$303$			150.540i			0.496830i
$304$	246.829	+	41.4101i	0.811939	+	0.136218i
$305$		−	16.5195i		−	0.0541625i
$306$	−1.36682	+	32.8728i	−0.00446672	+	0.107427i
$307$	−555.279			−1.80873			−0.904363	−	0.426764i	$-0.859653\pi$
$307$	−555.279			−1.80873			−0.904363	+	0.426764i	$0.859653\pi$
$308$	−415.110	−	34.5795i	−1.34776	−	0.112271i
$309$	191.400			0.619417
$310$	−12.3809	−	0.514784i	−0.0399382	−	0.00166059i
$311$			290.366i			0.933654i	0.884349	+	0.466827i	$0.154603\pi$
$311$			290.366i			0.933654i	−0.884349	+	0.466827i	$0.845397\pi$
$312$	−102.362	−	148.223i	−0.328083	−	0.475074i
$313$	−239.279			−0.764470			−0.382235	−	0.924065i	$-0.624845\pi$
$313$	−239.279			−0.764470			−0.382235	+	0.924065i	$0.624845\pi$
$314$	−9.42100	+	226.581i	−0.0300032	+	0.721594i
$315$			12.5074i			0.0397059i
$316$	30.3670	−	364.541i	0.0960981	−	1.15361i
$317$			171.315i			0.540427i	0.962800	+	0.270214i	$0.0870943\pi$
$317$			171.315i			0.540427i	−0.962800	+	0.270214i	$0.912906\pi$
$318$	−233.099	−	9.69204i	−0.733016	−	0.0304781i
$319$	−466.872			−1.46355
$320$	−7.12244	+	27.9718i	−0.0222576	+	0.0874120i
$321$	364.500			1.13551
$322$	293.261	+	12.1935i	0.910749	+	0.0378681i
$323$	−85.7758			−0.265560
$324$	−35.8757	−	2.98852i	−0.110728	−	0.00922383i
$325$	214.741	+	240.415i	0.660742	+	0.739739i
$326$	14.7441	−	354.605i	0.0452273	−	1.08774i
$327$	308.963			0.944842
$328$	248.632	+	31.1573i	0.758024	+	0.0949918i
$329$	365.777			1.11178
$330$	0.731164	−	17.5849i	0.00221565	−	0.0532876i
$331$	−21.8179			−0.0659152			−0.0329576	−	0.999457i	$-0.510493\pi$
$331$	−21.8179			−0.0659152			−0.0329576	+	0.999457i	$0.510493\pi$
$332$	484.202	+	40.3350i	1.45844	+	0.121491i
$333$		−	4.05455i		−	0.0121758i
$334$	−10.7974	+	259.685i	−0.0323277	+	0.777499i
$335$			29.8783i			0.0891889i
$336$	42.3863	−	252.648i	0.126150	−	0.751928i
$337$	−58.7892			−0.174449			−0.0872243	−	0.996189i	$-0.527800\pi$
$337$	−58.7892			−0.174449			−0.0872243	+	0.996189i	$0.527800\pi$
$338$	−333.987	−	51.9303i	−0.988127	−	0.153640i
$339$			15.3415i			0.0452552i
$340$	0.821215	−	9.85828i	0.00241534	−	0.0289949i
$341$	−154.759			−0.453838
$342$	3.89901	−	93.7736i	0.0114006	−	0.274192i
$343$	−115.990			−0.338164
$344$	−626.764	−	78.5430i	−1.82199	−	0.228323i
$345$			12.4017i			0.0359469i
$346$	−9.83813	+	236.613i	−0.0284339	+	0.683852i
$347$			361.864i			1.04284i	0.853302	+	0.521418i	$0.174597\pi$
$347$			361.864i			1.04284i	−0.853302	+	0.521418i	$0.825403\pi$
$348$	23.8358	−	286.138i	0.0684938	−	0.822234i
$349$		−	318.629i		−	0.912977i	−0.889729	−	0.456489i	$-0.849107\pi$
$349$		−	318.629i		−	0.912977i	0.889729	−	0.456489i	$-0.150893\pi$
$350$	−19.0451	+	458.046i	−0.0544146	+	1.30870i
$351$	−50.3793	+	44.9992i	−0.143531	+	0.128203i
$352$	−74.3630	+	352.736i	−0.211259	+	1.00209i
$353$			162.240i			0.459602i	0.973238	+	0.229801i	$0.0738076\pi$
$353$			162.240i			0.459602i	−0.973238	+	0.229801i	$0.926192\pi$
$354$	−205.716	−	8.55346i	−0.581118	−	0.0241623i
$355$		−	30.1390i		−	0.0848985i
$356$	−23.1115	+	277.442i	−0.0649198	+	0.779331i
$357$			87.7977i			0.245932i
$358$	520.244	+	21.6312i	1.45320	+	0.0604225i
$359$	−624.831			−1.74048			−0.870238	−	0.492632i	$-0.836035\pi$
$359$	−624.831			−1.74048			−0.870238	+	0.492632i	$0.836035\pi$
$360$	10.7401	+	1.34590i	0.0298337	+	0.00373862i
$361$	−116.314			−0.322200
$362$	22.3843	−	538.356i	0.0618352	−	1.48717i
$363$		−	10.2307i		−	0.0281838i
$364$	−289.351	−	383.848i	−0.794921	−	1.05453i
$365$	37.2002			0.101918
$366$	126.774	+	5.27115i	0.346378	+	0.0144020i
$367$			249.912i			0.680958i	0.940252	+	0.340479i	$0.110589\pi$
$367$			249.912i			0.680958i	−0.940252	+	0.340479i	$0.889411\pi$
$368$	42.0281	−	250.513i	0.114207	−	0.680742i
$369$		−	93.9662i		−	0.254651i
$370$	−0.0506446	+	1.21803i	−0.000136877	+	0.00329198i
$371$	−622.569			−1.67808
$372$	7.90110	−	94.8489i	0.0212395	−	0.254970i
$373$	511.549			1.37144			0.685722	−	0.727863i	$-0.259486\pi$
$373$	511.549			1.37144			0.685722	+	0.727863i	$0.259486\pi$
$374$	5.13253	−	123.440i	0.0137233	−	0.330055i
$375$	−38.8994			−0.103732
$376$	39.3608	−	314.095i	0.104683	−	0.835358i
$377$	−358.904	−	401.815i	−0.952001	−	1.06582i
$378$	−95.9840	−	3.99092i	−0.253926	−	0.0105580i
$379$	−28.7478			−0.0758517			−0.0379258	−	0.999281i	$-0.512075\pi$
$379$	−28.7478			−0.0758517			−0.0379258	+	0.999281i	$0.512075\pi$
$380$	−2.34261	+	28.1219i	−0.00616478	+	0.0740051i
$381$	8.23820			0.0216226
$382$	141.641	+	5.88928i	0.370787	+	0.0154170i
$383$	259.475			0.677479			0.338740	−	0.940880i	$-0.389999\pi$
$383$	259.475			0.677479			0.338740	+	0.940880i	$0.389999\pi$
$384$	−212.389	−	63.5844i	−0.553096	−	0.165584i
$385$		−	46.9664i		−	0.121991i
$386$	−203.380	−	8.45636i	−0.526892	−	0.0219077i
$387$			236.875i			0.612080i
$388$	−30.7160	+	368.730i	−0.0791648	+	0.950335i
$389$	634.076			1.63002			0.815008	−	0.579450i	$-0.196733\pi$
$389$	634.076			1.63002			0.815008	+	0.579450i	$0.196733\pi$
$390$	15.6966	−	12.8890i	0.0402476	−	0.0330487i
$391$			87.0558i			0.222649i
$392$	36.2607	−	289.356i	0.0925018	−	0.738154i
$393$	−235.583			−0.599447
$394$	−220.906	−	9.18504i	−0.560674	−	0.0233123i
$395$	41.2449			0.104418
$396$	134.717	+	11.2222i	0.340194	+	0.0283389i
$397$			458.005i			1.15367i	0.816862	+	0.576833i	$0.195712\pi$
$397$			458.005i			1.15367i	−0.816862	+	0.576833i	$0.804288\pi$
$398$	343.742	+	14.2924i	0.863672	+	0.0359106i
$399$		−	250.454i		−	0.627703i
$400$	391.277	+	65.6439i	0.978193	+	0.164110i
$401$			384.993i			0.960083i	0.877246	+	0.480042i	$0.159378\pi$
$401$			384.993i			0.960083i	−0.877246	+	0.480042i	$0.840622\pi$
$402$	−229.292	−	9.53373i	−0.570378	−	0.0237158i
$403$	−118.970	−	133.194i	−0.295210	−	0.330505i
$404$	346.456	+	28.8605i	0.857565	+	0.0714369i
$405$		−	4.05906i		−	0.0100224i
$406$	31.8308	−	765.549i	0.0784009	−	1.88559i
$407$			15.2252i			0.0374084i
$408$	75.3924	+	9.44780i	0.184785	+	0.0231564i
$409$		−	227.989i		−	0.557431i	−0.960374	−	0.278716i	$-0.910091\pi$
$409$		−	227.989i		−	0.557431i	0.960374	−	0.278716i	$-0.0899087\pi$
$410$	−1.17371	+	28.2285i	−0.00286271	+	0.0688500i
$411$	−243.949			−0.593550
$412$	36.6940	−	440.493i	0.0890631	−	1.06916i
$413$	−549.432			−1.33034
$414$	−95.1730	−	3.95720i	−0.229886	−	0.00955845i
$415$			54.7836i			0.132009i
$416$	−360.749	+	207.162i	−0.867185	+	0.497986i
$417$	−432.915			−1.03817
$418$	−14.6412	+	352.129i	−0.0350267	+	0.842413i
$419$		−	698.831i		−	1.66785i	−0.551875	−	0.833927i	$-0.686087\pi$
$419$		−	698.831i		−	1.66785i	0.551875	−	0.833927i	$-0.313913\pi$
$420$	28.7848	+	2.39784i	0.0685353	+	0.00570913i
$421$			559.647i			1.32933i	0.747142	+	0.664664i	$0.231425\pi$
$421$			559.647i			1.32933i	−0.747142	+	0.664664i	$0.768575\pi$
$422$	32.4089	+	1.34753i	0.0767983	+	0.00319320i
$423$	−118.707			−0.280631
$424$	−66.9939	+	534.603i	−0.158004	+	1.26086i
$425$	−135.973			−0.319936
$426$	231.292	+	9.61691i	0.542940	+	0.0225749i
$427$	338.593			0.792958
$428$	69.8797	−	838.872i	0.163270	−	1.95998i
$429$	189.179	−	168.976i	0.440977	−	0.393884i
$430$	2.95876	−	71.1599i	0.00688083	−	0.165488i
$431$	−134.369			−0.311762			−0.155881	−	0.987776i	$-0.549822\pi$
$431$	−134.369			−0.311762			−0.155881	+	0.987776i	$0.549822\pi$
$432$	−13.7557	+	81.9926i	−0.0318420	+	0.189798i
$433$	58.1735			0.134350			0.0671749	−	0.997741i	$-0.478601\pi$
$433$	58.1735			0.134350			0.0671749	+	0.997741i	$0.478601\pi$
$434$	10.5513	−	253.764i	0.0243117	−	0.584710i
$435$	32.3742			0.0744235
$436$	59.2325	−	711.058i	0.135854	−	1.63087i
$437$		−	248.337i		−	0.568278i
$438$	−11.8701	+	285.482i	−0.0271006	+	0.651785i
$439$		−	534.300i		−	1.21709i	−0.793521	−	0.608543i	$-0.791754\pi$
$439$		−	534.300i		−	1.21709i	0.793521	−	0.608543i	$-0.208246\pi$
$440$	−40.3303	−	5.05399i	−0.0916597	−	0.0114863i
$441$	−109.357			−0.247976
$442$	110.185	−	90.4765i	0.249287	−	0.204698i
$443$			244.149i			0.551127i	0.961283	+	0.275563i	$0.0888644\pi$
$443$			244.149i			0.551127i	−0.961283	+	0.275563i	$0.911136\pi$
$444$	−9.33126	−	0.777313i	−0.0210164	−	0.00175070i
$445$	−31.3903			−0.0705401
$446$	−17.0294	+	409.568i	−0.0381826	+	0.918313i
$447$	74.0330			0.165622
$448$	−573.325	−	145.985i	−1.27974	−	0.325860i
$449$		−	570.002i		−	1.26949i	−0.772721	−	0.634746i	$-0.781105\pi$
$449$		−	570.002i		−	1.26949i	0.772721	−	0.634746i	$-0.218895\pi$
$450$	6.18077	−	148.651i	0.0137350	−	0.330336i
$451$			352.852i			0.782377i
$452$	35.3074	+	2.94118i	0.0781137	+	0.00650703i
$453$			168.994i			0.373056i
$454$	−20.5964	+	495.356i	−0.0453666	+	1.09109i
$455$	40.4217	−	36.1050i	0.0888389	−	0.0793517i
$456$	−215.066	−	26.9510i	−0.471636	−	0.0591031i
$457$		−	142.300i		−	0.311379i	−0.987806	−	0.155690i	$-0.950240\pi$
$457$		−	142.300i		−	0.311379i	0.987806	−	0.155690i	$-0.0497600\pi$
$458$	682.220	+	28.3660i	1.48956	+	0.0619346i
$459$		−	28.4933i		−	0.0620768i
$460$	28.5416	+	2.37757i	0.0620470	+	0.00516864i
$461$			687.268i			1.49082i	0.666607	+	0.745410i	$0.267746\pi$
$461$			687.268i			1.49082i	−0.666607	+	0.745410i	$0.732254\pi$
$462$	360.429	+	14.9863i	0.780150	+	0.0324379i
$463$	−675.771			−1.45955			−0.729774	−	0.683688i	$-0.760375\pi$
$463$	−675.771			−1.45955			−0.729774	+	0.683688i	$0.760375\pi$
$464$	−653.956	−	109.713i	−1.40939	−	0.236451i
$465$	10.7314			0.0230783
$466$	−14.4949	+	348.611i	−0.0311049	+	0.748093i
$467$		−	374.263i		−	0.801421i	−0.916205	−	0.400710i	$-0.868763\pi$
$467$		−	374.263i		−	0.801421i	0.916205	−	0.400710i	$-0.131237\pi$
$468$	93.9041	+	124.571i	0.200650	+	0.266178i
$469$	−612.400			−1.30576
$470$	35.6608	+	1.48274i	0.0758741	+	0.00315477i
$471$		−	196.394i		−	0.416973i
$472$	−59.1237	+	471.801i	−0.125262	+	0.999578i
$473$		−	889.488i		−	1.88052i
$474$	−13.1607	+	316.522i	−0.0277651	+	0.667767i
$475$	387.879			0.816588
$476$	202.060	+	16.8320i	0.424496	+	0.0353614i
$477$	202.044			0.423573
$478$	−10.8530	+	261.020i	−0.0227050	+	0.546068i
$479$	769.059			1.60555			0.802775	−	0.596282i	$-0.203356\pi$
$479$	769.059			1.60555			0.802775	+	0.596282i	$0.203356\pi$
$480$	5.15653	−	24.4597i	0.0107428	−	0.0509576i
$481$	−13.1036	+	11.7043i	−0.0272425	+	0.0243332i
$482$	408.924	+	17.0027i	0.848391	+	0.0352753i
$483$	−254.191			−0.526276
$484$	−23.5453	−	1.96137i	−0.0486472	−	0.00405241i
$485$	−41.7189			−0.0860183
$486$	31.1500	+	1.29519i	0.0640946	+	0.00266499i
$487$	730.527			1.50006			0.750028	−	0.661406i	$-0.230040\pi$
$487$	730.527			1.50006			0.750028	+	0.661406i	$0.230040\pi$
$488$	36.4356	−	290.752i	0.0746630	−	0.595802i
$489$			307.362i			0.628552i
$490$	32.8522	+	1.36596i	0.0670452	+	0.00278767i
$491$			700.539i			1.42676i	0.700777	+	0.713380i	$0.252837\pi$
$491$			700.539i			1.42676i	−0.700777	+	0.713380i	$0.747163\pi$
$492$	−216.257	−	18.0146i	−0.439546	−	0.0366151i
$493$	227.256			0.460966
$494$	−314.316	+	258.095i	−0.636267	+	0.522460i
$495$			15.2421i			0.0307922i
$496$	−216.773	−	36.3677i	−0.437043	−	0.0733219i
$497$	617.743			1.24294
$498$	−420.420	−	17.4807i	−0.844218	−	0.0351017i
$499$	86.4734			0.173293			0.0866466	−	0.996239i	$-0.472385\pi$
$499$	86.4734			0.173293			0.0866466	+	0.996239i	$0.472385\pi$
$500$	−7.45755	+	89.5242i	−0.0149151	+	0.179048i
$501$		−	225.088i		−	0.449277i
$502$	677.410	+	28.1661i	1.34942	+	0.0561077i
$503$		−	157.257i		−	0.312637i	−0.987707	−	0.156319i	$-0.950037\pi$
$503$		−	157.257i		−	0.312637i	0.987707	−	0.156319i	$-0.0499627\pi$
$504$	−27.5863	+	220.135i	−0.0547347	+	0.436777i
$505$			39.1988i			0.0776214i
$506$	357.384	+	14.8597i	0.706292	+	0.0293669i
$507$	290.860	+	32.9181i	0.573688	+	0.0649273i
$508$	1.57938	−	18.9596i	0.00310901	−	0.0373221i
$509$		−	260.990i		−	0.512751i	−0.966577	−	0.256375i	$-0.917472\pi$
$509$		−	260.990i		−	0.512751i	0.966577	−	0.256375i	$-0.0825283\pi$
$510$	−0.355904	+	8.55970i	−0.000697850	+	0.0167837i
$511$			762.475i			1.49212i
$512$	−187.053	+	476.608i	−0.365338	+	0.930875i
$513$			81.2805i			0.158441i
$514$	1.87284	−	45.0429i	0.00364365	−	0.0876320i
$515$	49.8383			0.0967735
$516$	545.151	+	45.4122i	1.05649	+	0.0880081i
$517$	445.755			0.862196
$518$	−24.9654	−	1.03804i	−0.0481957	−	0.00200393i
$519$		−	205.090i		−	0.395163i
$520$	−26.6539	−	38.5956i	−0.0512574	−	0.0742222i
$521$	328.800			0.631095			0.315547	−	0.948910i	$-0.397812\pi$
$521$	328.800			0.631095			0.315547	+	0.948910i	$0.397812\pi$
$522$	−10.3301	+	248.446i	−0.0197895	+	0.475950i
$523$			235.465i			0.450220i	0.974333	+	0.225110i	$0.0722742\pi$
$523$			235.465i			0.450220i	−0.974333	+	0.225110i	$0.927726\pi$
$524$	−45.1645	+	542.177i	−0.0861918	+	1.03469i
$525$		−	397.022i		−	0.756233i
$526$	−328.243	−	13.6480i	−0.624036	−	0.0259468i
$527$	75.3309			0.142943
$528$	51.6542	−	307.890i	0.0978298	−	0.583125i
$529$	276.957			0.523548
$530$	−60.6964	−	2.52370i	−0.114521	−	0.00476169i
$531$	178.309			0.335799
$532$	−576.401	−	48.0154i	−1.08346	−	0.0902545i
$533$	−303.683	+	271.252i	−0.569761	+	0.508916i
$534$	10.0162	−	240.896i	0.0187569	−	0.451115i
$535$	94.9117			0.177405
$536$	−65.8997	+	525.872i	−0.122947	+	0.981104i
$537$	−450.934			−0.839728
$538$	29.4288	−	707.780i	0.0547004	−	1.31558i
$539$	410.647			0.761868
$540$	−9.34163	−	0.778177i	−0.0172993	−	0.00144107i
$541$		−	497.494i		−	0.919582i	−0.888027	−	0.459791i	$-0.847924\pi$
$541$		−	497.494i		−	0.919582i	0.888027	−	0.459791i	$-0.152076\pi$
$542$	−38.2229	+	919.283i	−0.0705219	+	1.69609i
$543$			466.633i			0.859361i
$544$	36.1972	−	171.699i	0.0665390	−	0.315623i
$545$	80.4505			0.147616
$546$	264.179	+	321.725i	0.483845	+	0.589240i
$547$		−	759.042i		−	1.38764i	−0.720146	−	0.693822i	$-0.755925\pi$
$547$		−	759.042i		−	1.38764i	0.720146	−	0.693822i	$-0.244075\pi$
$548$	−46.7684	+	561.432i	−0.0853438	+	1.02451i
$549$	−109.885			−0.200154
$550$	−23.2094	+	558.199i	−0.0421989	+	1.01491i
$551$	−648.277			−1.17655
$552$	−27.3532	+	218.275i	−0.0495529	+	0.395426i
$553$			845.377i			1.52871i
$554$	26.6677	−	641.374i	0.0481366	−	1.15771i
$555$		−	1.05576i		−	0.00190227i
$556$	−82.9958	+	996.324i	−0.149273	+	1.79195i
$557$			135.121i			0.242586i	0.992617	+	0.121293i	$0.0387041\pi$
$557$			135.121i			0.242586i	−0.992617	+	0.121293i	$0.961296\pi$
$558$	−3.42423	+	82.3549i	−0.00613662	+	0.147589i
$559$	765.540	−	683.787i	1.36948	−	1.22323i
$560$	11.0369	−	65.7866i	0.0197087	−	0.117476i
$561$			106.995i			0.190722i
$562$	−783.727	−	32.5866i	−1.39453	−	0.0579833i
$563$			352.278i			0.625715i	0.949800	+	0.312858i	$0.101286\pi$
$563$			352.278i			0.625715i	−0.949800	+	0.312858i	$0.898714\pi$
$564$	−22.7577	+	273.195i	−0.0403506	+	0.484389i
$565$			3.99475i			0.00707036i
$566$	−196.910	−	8.18732i	−0.347897	−	0.0144652i
$567$	83.1964			0.146731
$568$	66.4746	−	530.460i	0.117033	−	0.933908i
$569$	646.281			1.13582			0.567909	−	0.823091i	$-0.307753\pi$
$569$	646.281			1.13582			0.567909	+	0.823091i	$0.307753\pi$
$570$	1.01526	−	24.4176i	0.00178116	−	0.0428378i
$571$		−	497.031i		−	0.870456i	−0.900320	−	0.435228i	$-0.856668\pi$
$571$		−	497.031i		−	0.870456i	0.900320	−	0.435228i	$-0.143332\pi$
$572$	−352.619	−	467.777i	−0.616467	−	0.817793i
$573$	−122.770			−0.214259
$574$	−578.585	−	24.0570i	−1.00799	−	0.0419112i
$575$		−	393.668i		−	0.684639i
$576$	186.063	+	47.3770i	0.323026	+	0.0822517i
$577$			916.695i			1.58873i	0.607443	+	0.794363i	$0.292195\pi$
$577$			916.695i			1.58873i	−0.607443	+	0.794363i	$0.707805\pi$
$578$	21.5136	−	517.415i	0.0372208	−	0.895181i
$579$	176.285			0.304464
$580$	6.20658	−	74.5070i	0.0107010	−	0.128460i
$581$	−1122.87			−1.93266
$582$	13.3119	−	320.159i	0.0228727	−	0.550101i
$583$	−758.696			−1.30136
$584$	654.741	+	82.0489i	1.12113	+	0.140495i
$585$	−13.1182	+	11.7173i	−0.0224243	+	0.0200295i
$586$	−959.673	−	39.9022i	−1.63767	−	0.0680926i
$587$	507.493			0.864554			0.432277	−	0.901741i	$-0.357710\pi$
$587$	507.493			0.864554			0.432277	+	0.901741i	$0.357710\pi$
$588$	−20.9653	+	251.678i	−0.0356553	+	0.428024i
$589$	−214.891			−0.364840
$590$	−53.5660	−	2.22722i	−0.0907899	−	0.00377495i
$591$	191.475			0.323985
$592$	−3.57786	+	21.3262i	−0.00604369	+	0.0360240i
$593$		−	480.305i		−	0.809959i	−0.914326	−	0.404979i	$-0.867279\pi$
$593$		−	480.305i		−	0.809959i	0.914326	−	0.404979i	$-0.132721\pi$
$594$	−116.971	−	4.86355i	−0.196921	−	0.00818779i
$595$			22.8615i			0.0384227i
$596$	14.1932	−	170.382i	0.0238140	−	0.285876i
$597$	−297.946			−0.499072
$598$	261.947	+	319.006i	0.438038	+	0.533456i
$599$		−	825.195i		−	1.37762i	−0.724941	−	0.688810i	$-0.758133\pi$
$599$		−	825.195i		−	1.37762i	0.724941	−	0.688810i	$-0.241867\pi$
$600$	−340.925	−	42.7231i	−0.568209	−	0.0712051i
$601$	−80.2976			−0.133607			−0.0668033	−	0.997766i	$-0.521280\pi$
$601$	−80.2976			−0.133607			−0.0668033	+	0.997766i	$0.521280\pi$
$602$	1458.53	+	60.6442i	2.42280	+	0.100738i
$603$	198.744			0.329592
$604$	388.929	+	32.3985i	0.643921	+	0.0536400i
$605$		−	2.66396i		−	0.00440324i
$606$	−300.819	−	12.5078i	−0.496401	−	0.0206399i
$607$			59.4403i			0.0979247i	0.998801	+	0.0489623i	$0.0155914\pi$
$607$			59.4403i			0.0979247i	−0.998801	+	0.0489623i	$0.984409\pi$
$608$	−103.257	+	489.792i	−0.169830	+	0.805579i
$609$			663.558i			1.08959i
$610$	33.0106	+	1.37255i	0.0541157	+	0.00225008i
$611$	342.671	+	383.640i	0.560836	+	0.627889i
$612$	−65.5752	−	5.46255i	−0.107149	−	0.00892574i
$613$			269.847i			0.440207i	0.975476	+	0.220104i	$0.0706396\pi$
$613$			269.847i			0.440207i	−0.975476	+	0.220104i	$0.929360\pi$
$614$	46.1360	−	1109.60i	0.0751401	−	1.80716i
$615$		−	24.4677i		−	0.0397849i
$616$	103.589	−	826.630i	0.168164	−	1.34193i
$617$		−	759.186i		−	1.23045i	−0.788352	−	0.615224i	$-0.789066\pi$
$617$		−	759.186i		−	1.23045i	0.788352	−	0.615224i	$-0.210934\pi$
$618$	−15.9027	+	382.469i	−0.0257325	+	0.618882i
$619$	890.555			1.43870			0.719350	−	0.694648i	$-0.244440\pi$
$619$	890.555			1.43870			0.719350	+	0.694648i	$0.244440\pi$
$620$	2.05736	−	24.6976i	0.00331832	−	0.0398348i
$621$	82.4935			0.132840
$622$	−580.231	−	24.1255i	−0.932848	−	0.0387869i
$623$		−	643.392i		−	1.03273i
$624$	304.695	−	192.232i	0.488293	−	0.308064i
$625$	609.786			0.975657
$626$	19.8808	−	478.145i	0.0317585	−	0.763810i
$627$		−	305.216i		−	0.486788i
$628$	−451.987	−	37.6515i	−0.719725	−	0.0599545i
$629$		−	7.41108i		−	0.0117823i
$630$	−24.9931	−	1.03919i	−0.0396717	−	0.00164951i
$631$	−915.214			−1.45042			−0.725209	−	0.688528i	$-0.758257\pi$
$631$	−915.214			−1.45042			−0.725209	+	0.688528i	$0.758257\pi$
$632$	725.929	+	90.9699i	1.14862	+	0.143940i
$633$	−28.0912			−0.0443778
$634$	−342.335	−	14.2339i	−0.539960	−	0.0224510i
$635$	2.14513			0.00337816
$636$	38.7347	−	464.991i	0.0609036	−	0.731117i
$637$	315.682	+	353.424i	0.495576	+	0.554826i
$638$	38.7907	−	932.939i	0.0608004	−	1.46229i
$639$	−200.478			−0.313737
$640$	−55.3036	−	16.5567i	−0.0864119	−	0.0258698i
$641$	1079.76			1.68449			0.842243	−	0.539099i	$-0.181235\pi$
$641$	1079.76			1.68449			0.842243	+	0.539099i	$0.181235\pi$
$642$	−30.2849	+	728.371i	−0.0471728	+	1.13453i
$643$	8.94154			0.0139060			0.00695299	−	0.999976i	$-0.497787\pi$
$643$	8.94154			0.0139060			0.00695299	+	0.999976i	$0.497787\pi$
$644$	−48.7319	+	585.003i	−0.0756707	+	0.908390i
$645$			61.6795i			0.0956271i
$646$	7.12679	−	171.403i	0.0110322	−	0.265330i
$647$			128.346i			0.198372i	0.995069	+	0.0991858i	$0.0316238\pi$
$647$			128.346i			0.198372i	−0.995069	+	0.0991858i	$0.968376\pi$
$648$	8.95267	−	71.4412i	0.0138158	−	0.110249i
$649$	−669.567			−1.03169
$650$	−498.257	+	409.136i	−0.766550	+	0.629440i
$651$			219.956i			0.337874i
$652$	707.372	+	58.9255i	1.08493	+	0.0903766i
$653$	−218.498			−0.334607			−0.167304	−	0.985905i	$-0.553506\pi$
$653$	−218.498			−0.334607			−0.167304	+	0.985905i	$0.553506\pi$
$654$	−25.6706	+	617.393i	−0.0392517	+	0.944026i
$655$	−61.3431			−0.0936535
$656$	−82.9187	+	494.246i	−0.126400	+	0.753423i
$657$		−	247.448i		−	0.376634i
$658$	−30.3910	+	730.922i	−0.0461870	+	1.11082i
$659$		−	445.749i		−	0.676402i	−0.941074	−	0.338201i	$-0.890182\pi$
$659$		−	445.749i		−	0.676402i	0.941074	−	0.338201i	$-0.109818\pi$
$660$	35.0787	+	2.92213i	0.0531496	+	0.00442747i
$661$		−	1213.03i		−	1.83515i	−0.397567	−	0.917573i	$-0.630145\pi$
$661$		−	1213.03i		−	1.83515i	0.397567	−	0.917573i	$-0.369855\pi$
$662$	1.81277	−	43.5982i	0.00273832	−	0.0658583i
$663$	−92.0854	+	82.2515i	−0.138892	+	0.124060i
$664$	−120.831	+	964.217i	−0.181974	+	1.45213i
$665$		−	65.2152i		−	0.0980680i
$666$	8.10210	+	0.336877i	0.0121653	+	0.000505822i
$667$			657.951i			0.986433i
$668$	−518.024	−	43.1525i	−0.775485	−	0.0645995i
$669$		−	355.003i		−	0.530647i
$670$	−59.7050	−	2.48248i	−0.0891120	−	0.00370519i
$671$	412.627			0.614944
$672$	501.338	+	105.691i	0.746038	+	0.157278i
$673$	414.657			0.616132			0.308066	−	0.951365i	$-0.400318\pi$
$673$	414.657			0.616132			0.308066	+	0.951365i	$0.400318\pi$
$674$	4.88457	−	117.477i	0.00724714	−	0.174298i
$675$			128.847i			0.190884i
$676$	131.521	−	663.082i	0.194557	−	0.980891i
$677$	784.713			1.15910			0.579552	−	0.814935i	$-0.303228\pi$
$677$	784.713			1.15910			0.579552	+	0.814935i	$0.303228\pi$
$678$	−30.6565	−	1.27467i	−0.0452161	−	0.00188004i
$679$		−	855.091i		−	1.25934i
$680$	19.6313	+	2.46010i	0.0288696	+	0.00361779i
$681$		−	429.362i		−	0.630487i
$682$	12.8583	−	309.250i	0.0188539	−	0.453446i
$683$	−340.606			−0.498691			−0.249346	−	0.968415i	$-0.580216\pi$
$683$	−340.606			−0.498691			−0.249346	+	0.968415i	$0.580216\pi$
$684$	187.061	+	15.5826i	0.273481	+	0.0227816i
$685$	−63.5216			−0.0927322
$686$	9.63720	−	231.780i	0.0140484	−	0.337872i
$687$	−591.331			−0.860743
$688$	209.026	−	1245.92i	0.303817	−	1.81093i
$689$	−583.241	−	652.973i	−0.846504	−	0.947711i
$690$	−24.7820	−	1.03041i	−0.0359159	−	0.00149335i
$691$	−604.139			−0.874297			−0.437148	−	0.899389i	$-0.644012\pi$
$691$	−604.139			−0.874297			−0.437148	+	0.899389i	$0.644012\pi$
$692$	−472.000	−	39.3186i	−0.682081	−	0.0568187i
$693$	−312.411			−0.450809
$694$	−723.103	−	30.0659i	−1.04194	−	0.0433226i
$695$	−112.726			−0.162196
$696$	569.801	+	71.4046i	0.818679	+	0.102593i
$697$		−	171.755i		−	0.246421i
$698$	636.708	+	26.4737i	0.912189	+	0.0379279i
$699$		−	302.167i		−	0.432285i
$700$	−913.719	−	76.1146i	−1.30531	−	0.108735i
$701$	−546.639			−0.779799			−0.389900	−	0.920857i	$-0.627490\pi$
$701$	−546.639			−0.779799			−0.389900	+	0.920857i	$0.627490\pi$
$702$	−85.7349	−	104.410i	−0.122129	−	0.148733i
$703$			21.1410i			0.0300726i
$704$	−698.684	−	177.905i	−0.992449	−	0.252706i
$705$	−30.9099			−0.0438438
$706$	−324.199	−	13.4799i	−0.459205	−	0.0190933i
$707$	−803.438			−1.13640
$708$	34.1843	−	410.366i	0.0482829	−	0.579613i
$709$			467.889i			0.659928i	0.943993	+	0.329964i	$0.107037\pi$
$709$			467.889i			0.659928i	−0.943993	+	0.329964i	$0.892963\pi$
$710$	60.2259	+	2.50413i	0.0848252	+	0.00352695i
$711$		−	274.353i		−	0.385869i
$712$	−552.484	−	69.2346i	−0.775961	−	0.0972396i
$713$			218.098i			0.305887i
$714$	−175.444	−	7.29478i	−0.245720	−	0.0102168i
$715$	49.2601	−	43.9995i	0.0688952	−	0.0615378i
$716$	−86.4503	+	1037.79i	−0.120741	+	1.44943i
$717$		−	226.246i		−	0.315545i
$718$	51.9148	−	1248.58i	0.0723048	−	1.73897i
$719$			1115.45i			1.55139i	0.631106	+	0.775697i	$0.282601\pi$
$719$			1115.45i			1.55139i	−0.631106	+	0.775697i	$0.717399\pi$
$720$	−3.58184	+	21.3499i	−0.00497478	+	0.0296527i
$721$			1021.51i			1.41680i
$722$	9.66411	−	232.428i	0.0133852	−	0.321922i
$723$	−354.445			−0.490242
$724$	1073.92	+	89.4600i	1.48332	+	0.123564i
$725$	−1027.66			−1.41746
$726$	20.4437	+	0.850031i	0.0281594	+	0.00117084i
$727$		−	279.653i		−	0.384666i	−0.981330	−	0.192333i	$-0.938395\pi$
$727$		−	279.653i		−	0.384666i	0.981330	−	0.192333i	$-0.0616054\pi$
$728$	791.074	−	546.311i	1.08664	−	0.750427i
$729$	−27.0000			−0.0370370
$730$	−3.09083	+	74.3362i	−0.00423401	+	0.101830i
$731$			432.970i			0.592298i
$732$	−21.0664	+	252.892i	−0.0287792	+	0.345481i
$733$			468.555i			0.639229i	0.947548	+	0.319614i	$0.103553\pi$
$733$			468.555i			0.639229i	−0.947548	+	0.319614i	$0.896447\pi$
$734$	−499.392	−	20.7642i	−0.680370	−	0.0282891i
$735$	−28.4754			−0.0387420
$736$	497.101	+	104.798i	0.675409	+	0.142388i
$737$	−746.304			−1.01262
$738$	187.770	+	7.80729i	0.254431	+	0.0105790i
$739$	108.879			0.147333			0.0736666	−	0.997283i	$-0.476530\pi$
$739$	108.879			0.147333			0.0736666	+	0.997283i	$0.476530\pi$
$740$	−2.42975	−	0.202403i	−0.00328345	−	0.000273518i
$741$	262.685	−	234.632i	0.354500	−	0.316643i
$742$	51.7269	−	1244.06i	0.0697128	−	1.67663i
$743$	−1383.12			−1.86153			−0.930765	−	0.365619i	$-0.880857\pi$
$743$	−1383.12			−1.86153			−0.930765	+	0.365619i	$0.880857\pi$
$744$	188.877	+	23.6692i	0.253868	+	0.0318134i
$745$	19.2774			0.0258756
$746$	−42.5027	+	1022.21i	−0.0569741	+	1.37026i
$747$	364.409			0.487831
$748$	246.241	+	20.5124i	0.329200	+	0.0274230i
$749$			1945.36i			2.59727i
$750$	3.23200	−	77.7316i	0.00430934	−	0.103642i
$751$			884.139i			1.17728i	0.808394	+	0.588641i	$0.200337\pi$
$751$			884.139i			1.17728i	−0.808394	+	0.588641i	$0.799663\pi$
$752$	624.377	+	104.751i	0.830288	+	0.139296i
$753$	−587.162			−0.779763
$754$	832.756	−	683.804i	1.10445	−	0.906902i
$755$			44.0042i			0.0582837i
$756$	15.9499	−	191.471i	0.0210978	−	0.253268i
$757$	1396.91			1.84532			0.922661	−	0.385613i	$-0.126010\pi$
$757$	1396.91			1.84532			0.922661	+	0.385613i	$0.126010\pi$
$758$	2.38855	−	57.4459i	0.00315111	−	0.0757862i
$759$	−309.771			−0.408130
$760$	−56.0007	−	7.01773i	−0.0736851	−	0.00923386i
$761$		−	138.688i		−	0.182244i	−0.995840	−	0.0911220i	$-0.970955\pi$
$761$		−	138.688i		−	0.182244i	0.995840	−	0.0911220i	$-0.0290453\pi$
$762$	−0.684481	+	16.4622i	−0.000898269	+	0.0216039i
$763$			1648.95i			2.16115i
$764$	−23.5368	+	282.547i	−0.0308073	+	0.369826i
$765$		−	7.41932i		−	0.00969846i
$766$	−21.5588	+	518.501i	−0.0281446	+	0.676895i
$767$	−514.725	−	576.265i	−0.671088	−	0.751323i
$768$	144.706	−	419.128i	0.188419	−	0.545740i
$769$			250.681i			0.325983i	0.986627	+	0.162992i	$0.0521143\pi$
$769$			250.681i			0.325983i	−0.986627	+	0.162992i	$0.947886\pi$
$770$	93.8517	+	3.90226i	0.121885	+	0.00506787i
$771$			39.0420i			0.0506381i
$772$	33.7962	−	405.707i	0.0437775	−	0.525527i
$773$		−	885.091i		−	1.14501i	−0.819902	−	0.572504i	$-0.805972\pi$
$773$		−	885.091i		−	1.14501i	0.819902	−	0.572504i	$-0.194028\pi$
$774$	−473.341	−	19.6810i	−0.611551	−	0.0254277i
$775$	−340.647			−0.439545
$776$	−734.271	−	92.0153i	−0.946226	−	0.118576i
$777$	21.6393			0.0278499
$778$	−52.6830	+	1267.06i	−0.0677159	+	1.62861i
$779$			489.953i			0.628951i
$780$	24.4516	+	32.4370i	0.0313481	+	0.0415858i
$781$	752.815			0.963912
$782$	−173.961	−	7.23314i	−0.222457	−	0.00924954i
$783$		−	215.346i		−	0.275027i
$784$	575.200	+	96.5003i	0.733674	+	0.123087i
$785$		−	51.1388i		−	0.0651449i
$786$	19.5737	−	470.759i	0.0249029	−	0.598930i
$787$	753.982			0.958046			0.479023	−	0.877802i	$-0.340991\pi$
$787$	753.982			0.958046			0.479023	+	0.877802i	$0.340991\pi$
$788$	36.7084	−	440.667i	0.0465843	−	0.559222i
$789$	284.512			0.360599
$790$	−3.42689	+	82.4186i	−0.00433783	+	0.104327i
$791$	−81.8784			−0.103513
$792$	−33.6181	+	268.269i	−0.0424471	+	0.338723i
$793$	317.204	+	355.129i	0.400005	+	0.447829i
$794$	−915.220	−	38.0539i	−1.15267	−	0.0479269i
$795$	52.6100			0.0661761
$796$	−57.1204	+	685.702i	−0.0717593	+	0.861435i
$797$	−354.297			−0.444538			−0.222269	−	0.974985i	$-0.571346\pi$
$797$	−354.297			−0.444538			−0.222269	+	0.974985i	$0.571346\pi$
$798$	500.475	+	20.8092i	0.627161	+	0.0260767i
$799$	−216.977			−0.271561
$800$	−163.684	+	776.425i	−0.204605	+	0.970531i
$801$			208.802i			0.260677i
$802$	−769.322	−	31.9876i	−0.959254	−	0.0398848i
$803$			929.192i			1.15715i
$804$	38.1020	−	457.396i	0.0473906	−	0.568900i
$805$	−66.1885			−0.0822217
$806$	276.042	−	226.667i	0.342484	−	0.281225i
$807$			613.485i			0.760205i
$808$	−86.4570	+	689.917i	−0.107001	+	0.853857i
$809$	−770.844			−0.952836			−0.476418	−	0.879219i	$-0.658065\pi$
$809$	−770.844			−0.952836			−0.476418	+	0.879219i	$0.658065\pi$
$810$	8.11110	+	0.337252i	0.0100137	+	0.000416360i
$811$	−288.795			−0.356098			−0.178049	−	0.984022i	$-0.556979\pi$
$811$	−288.795			−0.356098			−0.178049	+	0.984022i	$0.556979\pi$
$812$	1527.13	+	127.213i	1.88070	+	0.156666i
$813$		−	796.810i		−	0.980086i
$814$	−30.4242	−	1.26501i	−0.0373761	−	0.00155406i
$815$			80.0336i			0.0982007i
$816$	−25.1434	+	149.870i	−0.0308129	+	0.183664i
$817$		−	1235.10i		−	1.51175i
$818$	455.585	+	18.9428i	0.556950	+	0.0231574i
$819$	−240.163	−	268.877i	−0.293240	−	0.328299i
$820$	−56.3107	−	4.69080i	−0.0686716	−	0.00572049i
$821$			809.780i			0.986334i	0.869935	+	0.493167i	$0.164161\pi$
$821$			809.780i			0.986334i	−0.869935	+	0.493167i	$0.835839\pi$
$822$	20.2688	−	487.477i	0.0246579	−	0.593038i
$823$		−	194.010i		−	0.235735i	−0.993029	−	0.117868i	$-0.962394\pi$
$823$		−	194.010i		−	0.235735i	0.993029	−	0.117868i	$-0.0376058\pi$
$824$	877.178	+	109.924i	1.06454	+	0.133402i
$825$		−	483.832i		−	0.586463i
$826$	45.6503	−	1097.92i	0.0552667	−	1.32920i
$827$	663.097			0.801810			0.400905	−	0.916120i	$-0.368696\pi$
$827$	663.097			0.801810			0.400905	+	0.916120i	$0.368696\pi$
$828$	15.8151	−	189.853i	0.0191004	−	0.229291i
$829$	−88.1628			−0.106348			−0.0531742	−	0.998585i	$-0.516934\pi$
$829$	−88.1628			−0.106348			−0.0531742	+	0.998585i	$0.516934\pi$
$830$	−109.473	−	4.55177i	−0.131895	−	0.00548406i
$831$			555.926i			0.668984i
$832$	−383.993	−	738.087i	−0.461531	−	0.887124i
$833$	−199.888			−0.239962
$834$	35.9693	−	865.083i	0.0431286	−	1.03727i
$835$		−	58.6103i		−	0.0701920i
$836$	−702.433	−	58.5141i	−0.840231	−	0.0699930i
$837$		−	71.3830i		−	0.0852844i
$838$	1396.46	+	58.0632i	1.66641	+	0.0692879i
$839$	719.761			0.857879			0.428940	−	0.903333i	$-0.358887\pi$
$839$	719.761			0.857879			0.428940	+	0.903333i	$0.358887\pi$
$840$	−7.18315	+	57.3207i	−0.00855137	+	0.0682390i
$841$	876.560			1.04228
$842$	−1118.33	−	46.4990i	−1.32818	−	0.0552244i
$843$	679.314			0.805830
$844$	−5.38547	+	64.6499i	−0.00638088	+	0.0765994i
$845$	75.7366	+	8.57151i	0.0896291	+	0.0101438i
$846$	9.86290	−	237.209i	0.0116583	−	0.280388i
$847$	54.6018			0.0644650
$848$	−1062.72	−	178.290i	−1.25320	−	0.210248i
$849$	170.676			0.201032
$850$	11.2975	−	271.711i	0.0132911	−	0.319660i
$851$	21.4565			0.0252133
$852$	−38.4344	+	461.387i	−0.0451108	+	0.541533i
$853$		−	1206.29i		−	1.41417i	−0.707129	−	0.707085i	$-0.750010\pi$
$853$		−	1206.29i		−	1.41417i	0.707129	−	0.707085i	$-0.249990\pi$
$854$	−28.1324	+	676.601i	−0.0329419	+	0.792273i
$855$			21.1645i			0.0247538i
$856$	1670.49	+	209.337i	1.95151	+	0.244553i
$857$	1229.54			1.43470			0.717352	−	0.696711i	$-0.245354\pi$
$857$	1229.54			1.43470			0.717352	+	0.696711i	$0.245354\pi$
$858$	321.943	+	392.071i	0.375225	+	0.456959i
$859$			754.293i			0.878106i	0.898461	+	0.439053i	$0.144686\pi$
$859$			754.293i			0.878106i	−0.898461	+	0.439053i	$0.855314\pi$
$860$	141.951	+	11.8248i	0.165059	+	0.0137498i
$861$	501.502			0.582465
$862$	11.1642	−	268.506i	0.0129515	−	0.311492i
$863$	698.704			0.809622			0.404811	−	0.914400i	$-0.367337\pi$
$863$	698.704			0.809622			0.404811	+	0.914400i	$0.367337\pi$
$864$	−162.701	−	34.3002i	−0.188311	−	0.0396993i
$865$		−	53.4030i		−	0.0617376i
$866$	−4.83341	+	116.246i	−0.00558131	+	0.134234i
$867$			448.481i			0.517280i
$868$	506.213	+	42.1686i	0.583195	+	0.0485814i
$869$			1030.22i			1.18552i
$870$	−2.68985	+	64.6925i	−0.00309178	+	0.0743592i
$871$	−573.715	−	642.308i	−0.658686	−	0.737438i
$872$	1415.97	+	177.442i	1.62381	+	0.203488i
$873$			277.505i			0.317876i
$874$	496.246	+	20.6334i	0.567787	+	0.0236080i
$875$		−	207.608i		−	0.237266i
$876$	−569.485	−	47.4392i	−0.650097	−	0.0541544i
$877$			883.451i			1.00736i	0.863892	+	0.503678i	$0.168020\pi$
$877$			883.451i			1.00736i	−0.863892	+	0.503678i	$0.831980\pi$
$878$	1067.68	+	44.3930i	1.21603	+	0.0505615i
$879$	831.819			0.946324
$880$	13.4502	−	80.1710i	0.0152843	−	0.0911034i
$881$	−736.089			−0.835515			−0.417757	−	0.908559i	$-0.637184\pi$
$881$	−736.089			−0.835515			−0.417757	+	0.908559i	$0.637184\pi$
$882$	9.08609	−	218.526i	0.0103017	−	0.247762i
$883$		−	161.432i		−	0.182822i	−0.995813	−	0.0914112i	$-0.970862\pi$
$883$		−	161.432i		−	0.182822i	0.995813	−	0.0914112i	$-0.0291378\pi$
$884$	171.642	+	227.697i	0.194165	+	0.257576i
$885$	46.4296			0.0524629
$886$	−487.877	−	20.2854i	−0.550651	−	0.0228955i
$887$		−	691.631i		−	0.779741i	−0.920870	−	0.389871i	$-0.872520\pi$
$887$		−	691.631i		−	0.779741i	0.920870	−	0.389871i	$-0.127480\pi$
$888$	2.32858	−	18.5818i	0.00262228	−	0.0209255i
$889$			43.9677i			0.0494575i
$890$	2.60810	−	62.7265i	0.00293045	−	0.0704792i
$891$	101.388			0.113791
$892$	−817.014	−	68.0589i	−0.915934	−	0.0762992i
$893$	618.954			0.693118
$894$	−6.15113	+	147.938i	−0.00688045	+	0.165479i
$895$	−117.418			−0.131193
$896$	339.354	−	1133.53i	0.378743	−	1.26510i
$897$	−238.134	−	266.605i	−0.265478	−	0.297218i
$898$	1139.02	+	47.3593i	1.26840	+	0.0527387i
$899$	569.337			0.633300
$900$	296.532	+	24.7017i	0.329480	+	0.0274464i
$901$	369.305			0.409884
$902$	−705.095	−	29.3171i	−0.781701	−	0.0325024i
$903$	−1264.21			−1.40002
$904$	−8.81084	+	70.3095i	−0.00974650	+	0.0777760i
$905$			121.506i			0.134261i
$906$	−337.697	−	14.0411i	−0.372734	−	0.0154979i
$907$			82.2700i			0.0907056i	0.998971	+	0.0453528i	$0.0144412\pi$
$907$			82.2700i			0.0907056i	−0.998971	+	0.0453528i	$0.985559\pi$
$908$	−988.146	−	82.3146i	−1.08827	−	0.0906548i
$909$	260.742			0.286845
$910$	68.7892	+	83.7735i	0.0755926	+	0.0920588i
$911$			659.385i			0.723804i	0.932216	+	0.361902i	$0.117872\pi$
$911$			659.385i			0.723804i	−0.932216	+	0.361902i	$0.882128\pi$
$912$	71.7245	−	427.521i	0.0786453	−	0.468773i
$913$	−1368.39			−1.49879
$914$	284.355	+	11.8232i	0.311110	+	0.0129357i
$915$	−28.6127			−0.0312707
$916$	−113.366	+	1360.91i	−0.123762	+	1.48570i
$917$		−	1257.32i		−	1.37112i
$918$	56.9373	+	2.36740i	0.0620232	+	0.00257886i
$919$		−	742.422i		−	0.807859i	−0.914790	−	0.403929i	$-0.867644\pi$
$919$		−	742.422i		−	0.807859i	0.914790	−	0.403929i	$-0.132356\pi$
$920$	−7.12246	+	56.8364i	−0.00774180	+	0.0617787i
$921$			961.771i			1.04427i
$922$	−1373.35	−	57.1025i	−1.48953	−	0.0619333i
$923$	578.721	+	647.912i	0.626999	+	0.701963i
$924$	−59.8934	+	718.991i	−0.0648197	+	0.778129i
$925$			33.5130i			0.0362303i
$926$	56.1473	−	1350.38i	0.0606342	−	1.45829i
$927$		−	331.514i		−	0.357621i
$928$	273.571	−	1297.67i	0.294797	−	1.39835i
$929$			161.647i			0.174001i	0.996208	+	0.0870003i	$0.0277281\pi$
$929$			161.647i			0.174001i	−0.996208	+	0.0870003i	$0.972272\pi$
$930$	−0.891631	+	21.4443i	−0.000958744	+	0.0230584i
$931$	570.205			0.612465
$932$	−695.416	−	57.9296i	−0.746155	−	0.0621562i
$933$	502.929			0.539045
$934$	747.881	+	31.0961i	0.800729	+	0.0332935i
$935$			27.8603i			0.0297971i
$936$	−256.730	+	177.296i	−0.274284	+	0.189419i
$937$	−1303.54			−1.39118			−0.695590	−	0.718439i	$-0.744857\pi$
$937$	−1303.54			−1.39118			−0.695590	+	0.718439i	$0.744857\pi$
$938$	50.8821	−	1223.74i	0.0542453	−	1.30463i
$939$			414.443i			0.441367i
$940$	−5.92585	+	71.1369i	−0.00630410	+	0.0756776i
$941$			483.653i			0.513978i	0.966414	+	0.256989i	$0.0827304\pi$
$941$			483.653i			0.513978i	−0.966414	+	0.256989i	$0.917270\pi$
$942$	392.449	+	16.3176i	0.416613	+	0.0173223i
$943$	497.265			0.527322
$944$	−937.874	−	157.346i	−0.993511	−	0.166680i
$945$	21.6634			0.0229242
$946$	1777.44	+	73.9042i	1.87890	+	0.0781228i
$947$	−1203.23			−1.27057			−0.635286	−	0.772277i	$-0.719118\pi$
$947$	−1203.23			−1.27057			−0.635286	+	0.772277i	$0.719118\pi$
$948$	−631.404	−	52.5972i	−0.666037	−	0.0554823i
$949$	−799.711	+	714.309i	−0.842688	+	0.752697i
$950$	−32.2274	+	775.089i	−0.0339236	+	0.815883i
$951$	296.727			0.312016
$952$	−50.4234	+	402.373i	−0.0529658	+	0.422661i
$953$	409.611			0.429812			0.214906	−	0.976635i	$-0.431056\pi$
$953$	409.611			0.429812			0.214906	+	0.976635i	$0.431056\pi$
$954$	−16.7871	+	403.740i	−0.0175965	+	0.423207i
$955$	−31.9680			−0.0334743
$956$	−520.688	−	43.3744i	−0.544653	−	0.0453707i
$957$			808.647i			0.844981i
$958$	−63.8982	+	1536.79i	−0.0666996	+	1.60416i
$959$		−	1301.97i		−	1.35763i
$960$	48.4487	+	12.3364i	0.0504674	+	0.0128504i
$961$	−772.276			−0.803617
$962$	−22.2996	−	27.1571i	−0.0231805	−	0.0282298i
$963$		−	631.333i		−	0.655590i
$964$	−67.9520	+	815.730i	−0.0704896	+	0.846193i
$965$	45.9025			0.0475674
$966$	21.1198	−	507.943i	0.0218631	−	0.525821i
$967$	−493.084			−0.509911			−0.254956	−	0.966953i	$-0.582061\pi$
$967$	−493.084			−0.509911			−0.254956	+	0.966953i	$0.582061\pi$
$968$	5.87563	−	46.8869i	0.00606987	−	0.0484369i
$969$			148.568i			0.153321i
$970$	3.46626	−	83.3657i	0.00357347	−	0.0859440i
$971$			749.707i			0.772097i	0.922478	+	0.386049i	$0.126160\pi$
$971$			749.707i			0.772097i	−0.922478	+	0.386049i	$0.873840\pi$
$972$	−5.17627	+	62.1386i	−0.00532538	+	0.0639286i
$973$		−	2310.49i		−	2.37461i
$974$	−60.6967	+	1459.79i	−0.0623170	+	1.49876i
$975$	416.411	−	371.942i	0.427089	−	0.381479i
$976$	577.974	+	96.9657i	0.592186	+	0.0993501i
$977$		−	442.080i		−	0.452487i	−0.974071	−	0.226243i	$-0.927356\pi$
$977$		−	442.080i		−	0.452487i	0.974071	−	0.226243i	$-0.0726445\pi$
$978$	−614.193	−	25.5376i	−0.628010	−	0.0261120i
$979$		−	784.071i		−	0.800890i
$980$	−5.45912	+	65.5341i	−0.00557054	+	0.0668715i
$981$		−	535.140i		−	0.545505i
$982$	−1399.87	−	58.2052i	−1.42553	−	0.0592721i
$983$	−179.850			−0.182960			−0.0914801	−	0.995807i	$-0.529160\pi$
$983$	−179.850			−0.182960			−0.0914801	+	0.995807i	$0.529160\pi$
$984$	53.9661	−	430.643i	0.0548436	−	0.437645i
$985$	49.8580			0.0506172
$986$	−18.8819	+	454.120i	−0.0191500	+	0.460568i
$987$		−	633.544i		−	0.641889i
$988$	−489.630	−	649.533i	−0.495577	−	0.657422i
$989$	−1253.53			−1.26747
$990$	−30.4580	−	1.26641i	−0.0307656	−	0.00127920i
$991$		−	652.511i		−	0.658437i	−0.944254	−	0.329219i	$-0.893215\pi$
$991$		−	652.511i		−	0.658437i	0.944254	−	0.329219i	$-0.106785\pi$
$992$	90.6834	−	430.151i	0.0914147	−	0.433620i
$993$			37.7898i			0.0380562i
$994$	−51.3260	+	1234.42i	−0.0516358	+	1.24187i
$995$	−77.5818			−0.0779716
$996$	69.8623	−	838.663i	0.0701429	−	0.842031i
$997$	−435.535			−0.436845			−0.218423	−	0.975854i	$-0.570091\pi$
$997$	−435.535			−0.436845			−0.218423	+	0.975854i	$0.570091\pi$
$998$	−7.18475	+	172.797i	−0.00719914	+	0.173144i
$999$	−7.02268			−0.00702971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.e.c.103.12	yes	24
3.2	odd	2		468.3.e.m.415.13		24
4.3	odd	2	inner	156.3.e.c.103.14	yes	24
12.11	even	2		468.3.e.m.415.11		24
13.12	even	2	inner	156.3.e.c.103.13	yes	24
39.38	odd	2		468.3.e.m.415.12		24
52.51	odd	2	inner	156.3.e.c.103.11	✓	24
156.155	even	2		468.3.e.m.415.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.e.c.103.11	✓	24	52.51	odd	2	inner
156.3.e.c.103.12	yes	24	1.1	even	1	trivial
156.3.e.c.103.13	yes	24	13.12	even	2	inner
156.3.e.c.103.14	yes	24	4.3	odd	2	inner
468.3.e.m.415.11		24	12.11	even	2
468.3.e.m.415.12		24	39.38	odd	2
468.3.e.m.415.13		24	3.2	odd	2
468.3.e.m.415.14		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)

\(f(q)\)	\(=\)	\(q+(-0.0830862 + 1.99827i) q^{2} -1.73205i q^{3} +(-3.98619 - 0.332058i) q^{4} -0.451006i q^{5} +(3.46111 + 0.143910i) q^{6} +9.24405 q^{7} +(0.994741 - 7.93791i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.0830862 + 1.99827i) q^{2} -1.73205i q^{3} +(-3.98619 - 0.332058i) q^{4} -0.451006i q^{5} +(3.46111 + 0.143910i) q^{6} +9.24405 q^{7} +(0.994741 - 7.93791i) q^{8} -3.00000 q^{9} +(0.901234 + 0.0374724i) q^{10} +11.2653 q^{11} +(-0.575141 + 6.90429i) q^{12} +(8.66010 + 9.69550i) q^{13} +(-0.768053 + 18.4721i) q^{14} -0.781166 q^{15} +(15.7795 + 2.64730i) q^{16} -5.48353 q^{17} +(0.249259 - 5.99482i) q^{18} +15.6424 q^{19} +(-0.149760 + 1.79780i) q^{20} -16.0112i q^{21} +(-0.935990 + 22.5111i) q^{22} -15.8759i q^{23} +(-13.7489 - 1.72294i) q^{24} +24.7966 q^{25} +(-20.0938 + 16.4997i) q^{26} +5.19615i q^{27} +(-36.8486 - 3.06956i) q^{28} -41.4435 q^{29} +(0.0649041 - 1.56098i) q^{30} -13.7377 q^{31} +(-6.60108 + 31.3118i) q^{32} -19.5121i q^{33} +(0.455606 - 10.9576i) q^{34} -4.16912i q^{35} +(11.9586 + 0.996174i) q^{36} +1.35152i q^{37} +(-1.29967 + 31.2579i) q^{38} +(16.7931 - 14.9997i) q^{39} +(-3.58005 - 0.448634i) q^{40} +31.3221i q^{41} +(31.9947 + 1.33031i) q^{42} -78.9583i q^{43} +(-44.9056 - 3.74073i) q^{44} +1.35302i q^{45} +(31.7243 + 1.31907i) q^{46} +39.5689 q^{47} +(4.58525 - 27.3309i) q^{48} +36.4524 q^{49} +(-2.06026 + 49.5504i) q^{50} +9.49775i q^{51} +(-31.3014 - 41.5238i) q^{52} -67.3481 q^{53} +(-10.3833 - 0.431729i) q^{54} -5.08071i q^{55} +(9.19543 - 73.3785i) q^{56} -27.0935i q^{57} +(3.44338 - 82.8153i) q^{58} -59.4363 q^{59} +(3.11388 + 0.259392i) q^{60} +36.6282 q^{61} +(1.14141 - 27.4516i) q^{62} -27.7321 q^{63} +(-62.0210 - 15.7923i) q^{64} +(4.37273 - 3.90576i) q^{65} +(38.9904 + 1.62118i) q^{66} -66.2481 q^{67} +(21.8584 + 1.82085i) q^{68} -27.4978 q^{69} +(8.33105 + 0.346397i) q^{70} +66.8261 q^{71} +(-2.98422 + 23.8137i) q^{72} +82.4828i q^{73} +(-2.70070 - 0.112292i) q^{74} -42.9490i q^{75} +(-62.3538 - 5.19420i) q^{76} +104.137 q^{77} +(28.5783 + 34.8035i) q^{78} +91.4509i q^{79} +(1.19395 - 7.11664i) q^{80} +9.00000 q^{81} +(-62.5900 - 2.60243i) q^{82} -121.470 q^{83} +(-5.31663 + 63.8236i) q^{84} +2.47311i q^{85} +(157.780 + 6.56035i) q^{86} +71.7822i q^{87} +(11.2060 - 89.4229i) q^{88} -69.6007i q^{89} +(-2.70370 - 0.112417i) q^{90} +(80.0544 + 89.6256i) q^{91} +(-5.27171 + 63.2843i) q^{92} +23.7943i q^{93} +(-3.28763 + 79.0695i) q^{94} -7.05484i q^{95} +(54.2335 + 11.4334i) q^{96} -92.5018i q^{97} +(-3.02870 + 72.8419i) q^{98} -33.7959 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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