LMFDB - Embedded newform 156.3.f.a.79.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(79,156)]

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, 0]))

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

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

chi := DirichletCharacter("156.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.f (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			79.17
Character	$\chi$	$=$	156.79
Dual form			156.3.f.a.79.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41412 - 1.41431i) q^{2} -1.73205i q^{3} +(-0.000546494 - 4.00000i) q^{4} -9.54425 q^{5} +(-2.44966 - 2.44932i) q^{6} +4.66845i q^{7} +(-5.65801 - 5.65569i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.41412 - 1.41431i) q^{2} -1.73205i q^{3} +(-0.000546494 - 4.00000i) q^{4} -9.54425 q^{5} +(-2.44966 - 2.44932i) q^{6} +4.66845i q^{7} +(-5.65801 - 5.65569i) q^{8} -3.00000 q^{9} +(-13.4967 + 13.4985i) q^{10} -13.9274i q^{11} +(-6.92820 + 0.000946555i) q^{12} +3.60555 q^{13} +(6.60264 + 6.60174i) q^{14} +16.5311i q^{15} +(-16.0000 + 0.00437195i) q^{16} +13.3909 q^{17} +(-4.24235 + 4.24293i) q^{18} -11.4523i q^{19} +(0.00521587 + 38.1770i) q^{20} +8.08600 q^{21} +(-19.6976 - 19.6949i) q^{22} -33.8211i q^{23} +(-9.79595 + 9.79997i) q^{24} +66.0927 q^{25} +(5.09867 - 5.09937i) q^{26} +5.19615i q^{27} +(18.6738 - 0.00255128i) q^{28} -32.7005 q^{29} +(23.3801 + 23.3769i) q^{30} -5.21783i q^{31} +(-22.6197 + 22.6351i) q^{32} -24.1229 q^{33} +(18.9364 - 18.9389i) q^{34} -44.5569i q^{35} +(0.00163948 + 12.0000i) q^{36} -36.7066 q^{37} +(-16.1971 - 16.1949i) q^{38} -6.24500i q^{39} +(54.0015 + 53.9794i) q^{40} +13.6934 q^{41} +(11.4345 - 11.4361i) q^{42} +3.89060i q^{43} +(-55.7095 + 0.00761122i) q^{44} +28.6328 q^{45} +(-47.8335 - 47.8270i) q^{46} +54.8761i q^{47} +(0.00757244 + 27.7128i) q^{48} +27.2056 q^{49} +(93.4628 - 93.4756i) q^{50} -23.1938i q^{51} +(-0.00197041 - 14.4222i) q^{52} +68.4612 q^{53} +(7.34897 + 7.34797i) q^{54} +132.926i q^{55} +(26.4033 - 26.4142i) q^{56} -19.8359 q^{57} +(-46.2424 + 46.2487i) q^{58} -86.6934i q^{59} +(66.1245 - 0.00903416i) q^{60} +67.1764 q^{61} +(-7.37963 - 7.37862i) q^{62} -14.0054i q^{63} +(0.0262317 + 64.0000i) q^{64} -34.4123 q^{65} +(-34.1126 + 34.1173i) q^{66} -27.0455i q^{67} +(-0.00731806 - 53.5638i) q^{68} -58.5799 q^{69} +(-63.0172 - 63.0086i) q^{70} -56.1681i q^{71} +(16.9740 + 16.9671i) q^{72} -19.3068 q^{73} +(-51.9074 + 51.9145i) q^{74} -114.476i q^{75} +(-45.8091 + 0.00625859i) q^{76} +65.0192 q^{77} +(-8.83236 - 8.83116i) q^{78} +85.7311i q^{79} +(152.708 - 0.0417270i) q^{80} +9.00000 q^{81} +(19.3641 - 19.3667i) q^{82} +132.435i q^{83} +(-0.00441895 - 32.3440i) q^{84} -127.806 q^{85} +(5.50251 + 5.50176i) q^{86} +56.6390i q^{87} +(-78.7689 + 78.8012i) q^{88} -72.4666 q^{89} +(40.4901 - 40.4956i) q^{90} +16.8323i q^{91} +(-135.284 + 0.0184830i) q^{92} -9.03755 q^{93} +(77.6119 + 77.6013i) q^{94} +109.303i q^{95} +(39.2052 + 39.1784i) q^{96} +129.163 q^{97} +(38.4718 - 38.4771i) q^{98} +41.7821i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

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 $

$2$	1.41412	−	1.41431i	0.707058	−	0.707155i
$2$	1.41412	−	1.41431i	0.707058	−	0.707155i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−0.000546494	−	4.00000i	−0.000136623	−	1.00000i
$5$	−9.54425			−1.90885			−0.954425	−	0.298451i	$-0.903530\pi$
$5$	−9.54425			−1.90885			−0.954425	+	0.298451i	$0.903530\pi$
$6$	−2.44966	−	2.44932i	−0.408276	−	0.408220i
$7$			4.66845i			0.666922i	0.942764	+	0.333461i	$0.108216\pi$
$7$			4.66845i			0.666922i	−0.942764	+	0.333461i	$0.891784\pi$
$8$	−5.65801	−	5.65569i	−0.707252	−	0.706962i
$9$	−3.00000			−0.333333
$10$	−13.4967	+	13.4985i	−1.34967	+	1.34985i
$11$		−	13.9274i		−	1.26612i	−0.774101	−	0.633062i	$-0.781798\pi$
$11$		−	13.9274i		−	1.26612i	0.774101	−	0.633062i	$-0.218202\pi$
$12$	−6.92820		0.000946555i	−0.577350		7.88796e-5i
$13$	3.60555			0.277350
$13$	3.60555			0.277350
$14$	6.60264	+	6.60174i	0.471617	+	0.471553i
$15$			16.5311i			1.10208i
$16$	−16.0000	+	0.00437195i	−1.00000	+	0.000273247i
$17$	13.3909			0.787702			0.393851	−	0.919174i	$-0.371143\pi$
$17$	13.3909			0.787702			0.393851	+	0.919174i	$0.371143\pi$
$18$	−4.24235	+	4.24293i	−0.235686	+	0.235718i
$19$		−	11.4523i		−	0.602751i	−0.953506	−	0.301376i	$-0.902554\pi$
$19$		−	11.4523i		−	0.602751i	0.953506	−	0.301376i	$-0.0974458\pi$
$20$	0.00521587	+	38.1770i	0.000260794	+	1.90885i
$21$	8.08600			0.385047
$22$	−19.6976	−	19.6949i	−0.895346	−	0.895224i
$23$		−	33.8211i		−	1.47048i	−0.677805	−	0.735241i	$-0.737069\pi$
$23$		−	33.8211i		−	1.47048i	0.677805	−	0.735241i	$-0.262931\pi$
$24$	−9.79595	+	9.79997i	−0.408165	+	0.408332i
$25$	66.0927			2.64371
$26$	5.09867	−	5.09937i	0.196103	−	0.196130i
$27$			5.19615i			0.192450i
$28$	18.6738	−	0.00255128i	0.666922	−	9.11171e-5i
$29$	−32.7005			−1.12760			−0.563802	−	0.825910i	$-0.690662\pi$
$29$	−32.7005			−1.12760			−0.563802	+	0.825910i	$0.690662\pi$
$30$	23.3801	+	23.3769i	0.779338	+	0.779232i
$31$		−	5.21783i		−	0.168317i	−0.996452	−	0.0841585i	$-0.973180\pi$
$31$		−	5.21783i		−	0.168317i	0.996452	−	0.0841585i	$-0.0268202\pi$
$32$	−22.6197	+	22.6351i	−0.706865	+	0.707348i
$33$	−24.1229			−0.730997
$34$	18.9364	−	18.9389i	0.556952	−	0.557028i
$35$		−	44.5569i		−	1.27305i
$36$	0.00163948	+	12.0000i	4.55411e−5	+	0.333333i
$37$	−36.7066			−0.992071			−0.496035	−	0.868302i	$-0.665211\pi$
$37$	−36.7066			−0.992071			−0.496035	+	0.868302i	$0.665211\pi$
$38$	−16.1971	−	16.1949i	−0.426239	−	0.426180i
$39$		−	6.24500i		−	0.160128i
$40$	54.0015	+	53.9794i	1.35004	+	1.34948i
$41$	13.6934			0.333986			0.166993	−	0.985958i	$-0.446594\pi$
$41$	13.6934			0.333986			0.166993	+	0.985958i	$0.446594\pi$
$42$	11.4345	−	11.4361i	0.272251	−	0.272288i
$43$			3.89060i			0.0904790i	0.998976	+	0.0452395i	$0.0144051\pi$
$43$			3.89060i			0.0904790i	−0.998976	+	0.0452395i	$0.985595\pi$
$44$	−55.7095	+	0.00761122i	−1.26612	+	0.000172982i
$45$	28.6328			0.636283
$46$	−47.8335	−	47.8270i	−1.03986	−	1.03972i
$47$			54.8761i			1.16758i	0.811906	+	0.583789i	$0.198430\pi$
$47$			54.8761i			1.16758i	−0.811906	+	0.583789i	$0.801570\pi$
$48$	0.00757244	+	27.7128i	0.000157759	+	0.577350i
$49$	27.2056			0.555216
$50$	93.4628	−	93.4756i	1.86926	−	1.86951i
$51$		−	23.1938i		−	0.454780i
$52$	−0.00197041	−	14.4222i	−3.78925e−5	−	0.277350i
$53$	68.4612			1.29172			0.645860	−	0.763455i	$-0.276499\pi$
$53$	68.4612			1.29172			0.645860	+	0.763455i	$0.276499\pi$
$54$	7.34897	+	7.34797i	0.136092	+	0.136073i
$55$			132.926i			2.41684i
$56$	26.4033	−	26.4142i	0.471488	−	0.471681i
$57$	−19.8359			−0.347999
$58$	−46.2424	+	46.2487i	−0.797282	+	0.797391i
$59$		−	86.6934i		−	1.46938i	−0.678403	−	0.734690i	$-0.737328\pi$
$59$		−	86.6934i		−	1.46938i	0.678403	−	0.734690i	$-0.262672\pi$
$60$	66.1245	−	0.00903416i	1.10208	−	0.000150569i
$61$	67.1764			1.10125			0.550626	−	0.834752i	$-0.314389\pi$
$61$	67.1764			1.10125			0.550626	+	0.834752i	$0.314389\pi$
$62$	−7.37963	−	7.37862i	−0.119026	−	0.119010i
$63$		−	14.0054i		−	0.222307i
$64$	0.0262317	+	64.0000i	0.000409870	+	1.00000i
$65$	−34.4123			−0.529420
$66$	−34.1126	+	34.1173i	−0.516858	+	0.516928i
$67$		−	27.0455i		−	0.403664i	−0.979420	−	0.201832i	$-0.935311\pi$
$67$		−	27.0455i		−	0.403664i	0.979420	−	0.201832i	$-0.0646895\pi$
$68$	−0.00731806	−	53.5638i	−0.000107619	−	0.787702i
$69$	−58.5799			−0.848983
$70$	−63.0172	−	63.0086i	−0.900246	−	0.900123i
$71$		−	56.1681i		−	0.791099i	−0.918445	−	0.395550i	$-0.870554\pi$
$71$		−	56.1681i		−	0.791099i	0.918445	−	0.395550i	$-0.129446\pi$
$72$	16.9740	+	16.9671i	0.235751	+	0.235654i
$73$	−19.3068			−0.264477			−0.132238	−	0.991218i	$-0.542216\pi$
$73$	−19.3068			−0.264477			−0.132238	+	0.991218i	$0.542216\pi$
$74$	−51.9074	+	51.9145i	−0.701452	+	0.701548i
$75$		−	114.476i		−	1.52635i
$76$	−45.8091	+	0.00625859i	−0.602751	+	8.23499e-5i
$77$	65.0192			0.844406
$78$	−8.83236	−	8.83116i	−0.113235	−	0.113220i
$79$			85.7311i			1.08520i	0.839990	+	0.542602i	$0.182561\pi$
$79$			85.7311i			1.08520i	−0.839990	+	0.542602i	$0.817439\pi$
$80$	152.708	−	0.0417270i	1.90885	−	0.000521587i
$81$	9.00000			0.111111
$82$	19.3641	−	19.3667i	0.236147	−	0.236180i
$83$			132.435i			1.59560i	0.602925	+	0.797798i	$0.294002\pi$
$83$			132.435i			1.59560i	−0.602925	+	0.797798i	$0.705998\pi$
$84$	−0.00441895	−	32.3440i	−5.26065e−5	−	0.385047i
$85$	−127.806			−1.50361
$86$	5.50251	+	5.50176i	0.0639827	+	0.0639740i
$87$			56.6390i			0.651023i
$88$	−78.7689	+	78.8012i	−0.895102	+	0.895468i
$89$	−72.4666			−0.814232			−0.407116	−	0.913376i	$-0.633466\pi$
$89$	−72.4666			−0.814232			−0.407116	+	0.913376i	$0.633466\pi$
$90$	40.4901	−	40.4956i	0.449890	−	0.449951i
$91$			16.8323i			0.184971i
$92$	−135.284	+	0.0184830i	−1.47048	+	0.000200902i
$93$	−9.03755			−0.0971779
$94$	77.6119	+	77.6013i	0.825658	+	0.825545i
$95$			109.303i			1.15056i
$96$	39.2052	+	39.1784i	0.408388	+	0.408109i
$97$	129.163			1.33158			0.665790	−	0.746139i	$-0.268095\pi$
$97$	129.163			1.33158			0.665790	+	0.746139i	$0.268095\pi$
$98$	38.4718	−	38.4771i	0.392570	−	0.392623i
$99$			41.7821i			0.422041i
$100$	−0.0361193	−	264.371i	−0.000361193	−	2.64371i
$101$	24.9436			0.246966			0.123483	−	0.992347i	$-0.460594\pi$
$101$	24.9436			0.246966			0.123483	+	0.992347i	$0.460594\pi$
$102$	−32.8032	−	32.7987i	−0.321600	−	0.321556i
$103$		−	29.9800i		−	0.291068i	−0.989353	−	0.145534i	$-0.953510\pi$
$103$		−	29.9800i		−	0.291068i	0.989353	−	0.145534i	$-0.0464900\pi$
$104$	−20.4003	−	20.3919i	−0.196156	−	0.196076i
$105$	−77.1748			−0.734998
$106$	96.8122	−	96.8254i	0.913322	−	0.913447i
$107$		−	159.793i		−	1.49339i	−0.665168	−	0.746694i	$-0.731640\pi$
$107$		−	159.793i		−	1.49339i	0.665168	−	0.746694i	$-0.268360\pi$
$108$	20.7846	−	0.00283966i	0.192450	−	2.62932e-5i
$109$	−110.483			−1.01361			−0.506804	−	0.862061i	$-0.669173\pi$
$109$	−110.483			−1.01361			−0.506804	+	0.862061i	$0.669173\pi$
$110$	187.999	+	187.973i	1.70908	+	1.70885i
$111$			63.5777i			0.572772i
$112$	−0.0204102	−	74.6952i	−0.000182234	−	0.666922i
$113$	−158.804			−1.40534			−0.702672	−	0.711514i	$-0.748010\pi$
$113$	−158.804			−1.40534			−0.702672	+	0.711514i	$0.748010\pi$
$114$	−28.0503	+	28.0541i	−0.246055	+	0.246089i
$115$			322.797i			2.80693i
$116$	0.0178706	+	130.802i	0.000154057	+	1.12760i
$117$	−10.8167			−0.0924500
$118$	−122.611	−	122.595i	−1.03908	−	1.03894i
$119$			62.5150i			0.525336i
$120$	93.4950	−	93.5333i	0.779125	−	0.779445i
$121$	−72.9715			−0.603071
$122$	94.9953	−	95.0083i	0.778650	−	0.778756i
$123$		−	23.7177i		−	0.192827i
$124$	−20.8713	+	0.00285151i	−0.168317	+	2.29961e-5i
$125$	−392.199			−3.13759
$126$	−19.8079	−	19.8052i	−0.157206	−	0.157184i
$127$		−	151.781i		−	1.19513i	−0.801822	−	0.597564i	$-0.796136\pi$
$127$		−	151.781i		−	1.19513i	0.801822	−	0.597564i	$-0.203864\pi$
$128$	90.5529	+	90.4664i	0.707445	+	0.706769i
$129$	6.73871			0.0522381
$130$	−48.6630	+	48.6696i	−0.374331	+	0.374382i
$131$			26.4426i			0.201852i	0.994894	+	0.100926i	$0.0321805\pi$
$131$			26.4426i			0.201852i	−0.994894	+	0.100926i	$0.967819\pi$
$132$	0.0131830	+	96.4916i	9.98713e−5	+	0.730997i
$133$	53.4644			0.401988
$134$	−38.2507	−	38.2455i	−0.285453	−	0.285414i
$135$		−	49.5934i		−	0.367358i
$136$	−75.7661	−	75.7351i	−0.557104	−	0.556876i
$137$	−42.3403			−0.309053			−0.154527	−	0.987989i	$-0.549385\pi$
$137$	−42.3403			−0.309053			−0.154527	+	0.987989i	$0.549385\pi$
$138$	−82.8388	+	82.8501i	−0.600281	+	0.600363i
$139$		−	176.028i		−	1.26639i	−0.773993	−	0.633194i	$-0.781743\pi$
$139$		−	176.028i		−	1.26639i	0.773993	−	0.633194i	$-0.218257\pi$
$140$	−178.227	+	0.0243500i	−1.27305	+	0.000173929i
$141$	95.0482			0.674101
$142$	−79.4391	−	79.4282i	−0.559430	−	0.559354i
$143$		−	50.2158i		−	0.351160i
$144$	48.0000	−	0.0131158i	0.333333	−	9.10823e-5i
$145$	312.102			2.15243
$146$	−27.3021	+	27.3058i	−0.187001	+	0.187026i
$147$		−	47.1214i		−	0.320554i
$148$	0.0200599	+	146.826i	0.000135540	+	0.992071i
$149$	−76.5599			−0.513825			−0.256912	−	0.966435i	$-0.582705\pi$
$149$	−76.5599			−0.513825			−0.256912	+	0.966435i	$0.582705\pi$
$150$	−161.905	−	161.882i	−1.07936	−	1.07922i
$151$		−	34.8507i		−	0.230799i	−0.993319	−	0.115400i	$-0.963185\pi$
$151$		−	34.8507i		−	0.230799i	0.993319	−	0.115400i	$-0.0368148\pi$
$152$	−64.7706	+	64.7971i	−0.426122	+	0.426297i
$153$	−40.1728			−0.262567
$154$	91.9448	−	91.9574i	0.597044	−	0.597126i
$155$			49.8003i			0.321292i
$156$	−24.9800	+	0.00341285i	−0.160128	+	2.18773e-5i
$157$	14.2896			0.0910165			0.0455083	−	0.998964i	$-0.485509\pi$
$157$	14.2896			0.0910165			0.0455083	+	0.998964i	$0.485509\pi$
$158$	121.250	+	121.234i	0.767407	+	0.767302i
$159$		−	118.578i		−	0.745775i
$160$	215.888	−	216.035i	1.34930	−	1.35022i
$161$	157.892			0.980697
$162$	12.7271	−	12.7288i	0.0785621	−	0.0785728i
$163$		−	174.548i		−	1.07085i	−0.844583	−	0.535425i	$-0.820152\pi$
$163$		−	174.548i		−	1.07085i	0.844583	−	0.535425i	$-0.179848\pi$
$164$	−0.00748336	−	54.7736i	−4.56302e−5	−	0.333986i
$165$	230.235			1.39536
$166$	187.303	+	187.278i	1.12833	+	1.12818i
$167$		−	52.8583i		−	0.316517i	−0.987398	−	0.158258i	$-0.949412\pi$
$167$		−	52.8583i		−	0.316517i	0.987398	−	0.158258i	$-0.0505879\pi$
$168$	−45.7507	−	45.7319i	−0.272325	−	0.272214i
$169$	13.0000			0.0769231
$170$	−180.733	+	180.758i	−1.06314	+	1.06328i
$171$			34.3568i			0.200917i
$172$	15.5624	−	0.00212619i	0.0904790	−	1.23616e-5i
$173$	247.032			1.42793			0.713965	−	0.700182i	$-0.246898\pi$
$173$	247.032			1.42793			0.713965	+	0.700182i	$0.246898\pi$
$174$	80.1051	+	80.0942i	0.460374	+	0.460311i
$175$			308.551i			1.76315i
$176$	0.0608897	+	222.838i	0.000345964	+	1.26612i
$177$	−150.157			−0.848347
$178$	−102.476	+	102.490i	−0.575710	+	0.575788i
$179$			207.209i			1.15759i	0.815471	+	0.578797i	$0.196478\pi$
$179$			207.209i			1.15759i	−0.815471	+	0.578797i	$0.803522\pi$
$180$	−0.0156476	−	114.531i	−8.69312e−5	−	0.636283i
$181$	162.280			0.896572			0.448286	−	0.893890i	$-0.352035\pi$
$181$	162.280			0.896572			0.448286	+	0.893890i	$0.352035\pi$
$182$	23.8062	+	23.8029i	0.130803	+	0.130785i
$183$		−	116.353i		−	0.635808i
$184$	−191.282	+	191.360i	−1.03958	+	1.04000i
$185$	350.337			1.89371
$186$	−12.7801	+	12.7819i	−0.0687105	+	0.0687198i
$187$		−	186.501i		−	0.997329i
$188$	219.504	−	0.0299895i	1.16758	−	0.000159518i
$189$	−24.2580			−0.128349
$190$	154.589	+	154.568i	0.813625	+	0.813514i
$191$			138.884i			0.727140i	0.931567	+	0.363570i	$0.118442\pi$
$191$			138.884i			0.727140i	−0.931567	+	0.363570i	$0.881558\pi$
$192$	110.851	−	0.0454346i	0.577350	−	0.000236639i
$193$	−108.263			−0.560948			−0.280474	−	0.959862i	$-0.590492\pi$
$193$	−108.263			−0.560948			−0.280474	+	0.959862i	$0.590492\pi$
$194$	182.652	−	182.677i	0.941505	−	0.941634i
$195$			59.6038i			0.305661i
$196$	−0.0148677	−	108.822i	−7.58554e−5	−	0.555216i
$197$	368.999			1.87309			0.936547	−	0.350542i	$-0.114003\pi$
$197$	368.999			1.87309			0.936547	+	0.350542i	$0.114003\pi$
$198$	59.0928	+	59.0848i	0.298449	+	0.298408i
$199$			6.70442i			0.0336906i	0.999858	+	0.0168453i	$0.00536227\pi$
$199$			6.70442i			0.0336906i	−0.999858	+	0.0168453i	$0.994638\pi$
$200$	−373.954	−	373.800i	−1.86977	−	1.86900i
$201$	−46.8442			−0.233055
$202$	35.2732	−	35.2780i	0.174620	−	0.174643i
$203$		−	152.661i		−	0.752024i
$204$	−92.7752	+	0.0126753i	−0.454780	+	6.21336e-5i
$205$	−130.693			−0.637528
$206$	−42.4010	−	42.3952i	−0.205830	−	0.205802i
$207$			101.463i			0.490161i
$208$	−57.6888	+	0.0157633i	−0.277350	+	7.57850e-5i
$209$	−159.500			−0.763158
$210$	−109.134	+	109.149i	−0.519686	+	0.519757i
$211$			17.0366i			0.0807420i	0.999185	+	0.0403710i	$0.0128540\pi$
$211$			17.0366i			0.0807420i	−0.999185	+	0.0403710i	$0.987146\pi$
$212$	−0.0374136	−	273.845i	−0.000176479	−	1.29172i
$213$	−97.2859			−0.456742
$214$	−225.996	−	225.965i	−1.05606	−	1.05591i
$215$		−	37.1328i		−	0.172711i
$216$	29.3879	−	29.3999i	0.136055	−	0.136111i
$217$	24.3592			0.112254
$218$	−156.236	+	156.258i	−0.716680	+	0.716778i
$219$			33.4404i			0.152696i
$220$	531.705	−	0.0726434i	2.41684	−	0.000330197i
$221$	48.2817			0.218469
$222$	89.9186	+	89.9063i	0.405039	+	0.404983i
$223$		−	175.922i		−	0.788890i	−0.918920	−	0.394445i	$-0.870937\pi$
$223$		−	175.922i		−	0.788890i	0.918920	−	0.394445i	$-0.129063\pi$
$224$	−105.671	−	105.599i	−0.471746	−	0.471424i
$225$	−198.278			−0.881236
$226$	−224.567	+	224.598i	−0.993660	+	0.993796i
$227$			144.674i			0.637332i	0.947867	+	0.318666i	$0.103235\pi$
$227$			144.674i			0.637332i	−0.947867	+	0.318666i	$0.896765\pi$
$228$	0.0108402	+	79.3437i	4.75448e−5	+	0.347999i
$229$	188.811			0.824503			0.412252	−	0.911070i	$-0.364742\pi$
$229$	188.811			0.824503			0.412252	+	0.911070i	$0.364742\pi$
$230$	456.535	+	456.473i	1.98494	+	1.98466i
$231$		−	112.617i		−	0.487518i
$232$	185.020	+	184.944i	0.797500	+	0.797173i
$233$	160.421			0.688504			0.344252	−	0.938877i	$-0.388133\pi$
$233$	160.421			0.688504			0.344252	+	0.938877i	$0.388133\pi$
$234$	−15.2960	+	15.2981i	−0.0653676	+	0.0653765i
$235$		−	523.752i		−	2.22873i
$236$	−346.774	+	0.0473774i	−1.46938	+	0.000200752i
$237$	148.491			0.626542
$238$	88.4155	+	88.4035i	0.371494	+	0.371443i
$239$			284.652i			1.19101i	0.803350	+	0.595507i	$0.203049\pi$
$239$			284.652i			1.19101i	−0.803350	+	0.595507i	$0.796951\pi$
$240$	−0.0722733	−	264.498i	−0.000301139	−	1.10208i
$241$	40.3734			0.167524			0.0837622	−	0.996486i	$-0.473306\pi$
$241$	40.3734			0.167524			0.0837622	+	0.996486i	$0.473306\pi$
$242$	−103.190	+	103.204i	−0.426406	+	0.426464i
$243$		−	15.5885i		−	0.0641500i
$244$	−0.0367115	−	268.706i	−0.000150457	−	1.10125i
$245$	−259.657			−1.05982
$246$	−33.5442	−	33.5396i	−0.136358	−	0.136340i
$247$		−	41.2918i		−	0.167173i
$248$	−29.5104	+	29.5225i	−0.118994	+	0.119043i
$249$	229.383			0.921218
$250$	−554.616	+	554.691i	−2.21846	+	2.21877i
$251$			364.370i			1.45167i	0.687868	+	0.725836i	$0.258547\pi$
$251$			364.370i			1.45167i	−0.687868	+	0.725836i	$0.741453\pi$
$252$	−56.0214	+	0.00765384i	−0.222307	+	3.03724e-5i
$253$	−471.039			−1.86181
$254$	−214.666	−	214.636i	−0.845140	−	0.845025i
$255$			221.367i			0.868107i
$256$	256.000	−	0.139902i	1.00000	−	0.000546494i
$257$	346.956			1.35002			0.675012	−	0.737807i	$-0.264138\pi$
$257$	346.956			1.35002			0.675012	+	0.737807i	$0.264138\pi$
$258$	9.52933	−	9.53063i	0.0369354	−	0.0369404i
$259$		−	171.363i		−	0.661633i
$260$	0.0188061	+	137.649i	7.23311e−5	+	0.529420i
$261$	98.1016			0.375868
$262$	37.3981	+	37.3929i	0.142741	+	0.142721i
$263$		−	509.485i		−	1.93720i	−0.248617	−	0.968602i	$-0.579976\pi$
$263$		−	509.485i		−	1.93720i	0.248617	−	0.968602i	$-0.420024\pi$
$264$	136.488	+	136.432i	0.516999	+	0.516787i
$265$	−653.411			−2.46570
$266$	75.6049	−	75.6152i	0.284229	−	0.284268i
$267$			125.516i			0.470097i
$268$	−108.182	+	0.0147802i	−0.403664	+	5.51499e-5i
$269$	−307.157			−1.14185			−0.570923	−	0.821004i	$-0.693415\pi$
$269$	−307.157			−1.14185			−0.570923	+	0.821004i	$0.693415\pi$
$270$	−70.1404	−	70.1308i	−0.259779	−	0.259744i
$271$		−	149.197i		−	0.550543i	−0.961367	−	0.275272i	$-0.911232\pi$
$271$		−	149.197i		−	0.550543i	0.961367	−	0.275272i	$-0.0887678\pi$
$272$	−214.255	+	0.0585445i	−0.787702	+	0.000215237i
$273$	29.1545			0.106793
$274$	−59.8741	+	59.8823i	−0.218519	+	0.218549i
$275$		−	920.498i		−	3.34726i
$276$	0.0320135	+	234.319i	0.000115991	+	0.848983i
$277$	148.101			0.534660			0.267330	−	0.963605i	$-0.413859\pi$
$277$	148.101			0.534660			0.267330	+	0.963605i	$0.413859\pi$
$278$	−248.958	−	248.924i	−0.895533	−	0.895410i
$279$			15.6535i			0.0561057i
$280$	−252.000	+	252.103i	−0.900000	+	0.900369i
$281$	222.764			0.792753			0.396377	−	0.918088i	$-0.370267\pi$
$281$	222.764			0.792753			0.396377	+	0.918088i	$0.370267\pi$
$282$	134.409	−	134.428i	0.476629	−	0.476694i
$283$		−	268.898i		−	0.950169i	−0.879940	−	0.475085i	$-0.842417\pi$
$283$		−	268.898i		−	0.950169i	0.879940	−	0.475085i	$-0.157583\pi$
$284$	−224.672	+	0.0306955i	−0.791099	+	0.000108083i
$285$	189.319			0.664277
$286$	−71.0208	−	71.0111i	−0.248324	−	0.248290i
$287$			63.9270i			0.222742i
$288$	67.8591	−	67.9054i	0.235622	−	0.235783i
$289$	−109.683			−0.379525
$290$	441.349	−	441.409i	1.52189	−	1.52210i
$291$		−	223.717i		−	0.768789i
$292$	0.0105510	+	77.2272i	3.61337e−5	+	0.264477i
$293$	−186.635			−0.636981			−0.318490	−	0.947926i	$-0.603176\pi$
$293$	−186.635			−0.636981			−0.318490	+	0.947926i	$0.603176\pi$
$294$	−66.6443	−	66.6352i	−0.226681	−	0.226650i
$295$			827.424i			2.80483i
$296$	207.686	+	207.601i	0.701644	+	0.701356i
$297$	72.3687			0.243666
$298$	−108.265	+	108.279i	−0.363304	+	0.363354i
$299$		−	121.944i		−	0.407838i
$300$	−457.904	+	0.0625604i	−1.52635	+	0.000208535i
$301$	−18.1631			−0.0603424
$302$	−49.2896	−	49.2829i	−0.163211	−	0.163188i
$303$		−	43.2036i		−	0.142586i
$304$	0.0500688	+	183.236i	0.000164700	+	0.602751i
$305$	−641.148			−2.10213
$306$	−56.8091	+	56.8168i	−0.185651	+	0.185676i
$307$			58.0094i			0.188956i	0.995527	+	0.0944779i	$0.0301182\pi$
$307$			58.0094i			0.188956i	−0.995527	+	0.0944779i	$0.969882\pi$
$308$	−0.0355326	−	260.077i	−0.000115366	−	0.844406i
$309$	−51.9268			−0.168048
$310$	70.4330	+	70.4234i	0.227203	+	0.227172i
$311$			478.345i			1.53809i	0.639196	+	0.769044i	$0.279267\pi$
$311$			478.345i			1.53809i	−0.639196	+	0.769044i	$0.720733\pi$
$312$	−35.3198	+	35.3343i	−0.113204	+	0.113251i
$313$	−54.2493			−0.173320			−0.0866602	−	0.996238i	$-0.527619\pi$
$313$	−54.2493			−0.173320			−0.0866602	+	0.996238i	$0.527619\pi$
$314$	20.2072	−	20.2099i	0.0643540	−	0.0643628i
$315$			133.671i			0.424351i
$316$	342.924	−	0.0468515i	1.08520	−	0.000148264i
$317$	253.398			0.799362			0.399681	−	0.916654i	$-0.369121\pi$
$317$	253.398			0.799362			0.399681	+	0.916654i	$0.369121\pi$
$318$	−167.706	−	167.684i	−0.527379	−	0.527307i
$319$			455.432i			1.42769i
$320$	−0.250362	−	610.832i	−0.000782381	−	1.90885i
$321$	−276.769			−0.862208
$322$	223.278	−	223.308i	0.693410	−	0.693505i
$323$		−	153.357i		−	0.474789i
$324$	−0.00491844	−	36.0000i	−1.51804e−5	−	0.111111i
$325$	238.301			0.733233
$326$	−246.866	−	246.832i	−0.757257	−	0.757153i
$327$			191.363i			0.585207i
$328$	−77.4775	−	77.4457i	−0.236212	−	0.236115i
$329$	−256.187			−0.778682
$330$	325.579	−	325.624i	0.986604	−	0.986739i
$331$			53.8671i			0.162740i	0.996684	+	0.0813702i	$0.0259296\pi$
$331$			53.8671i			0.162740i	−0.996684	+	0.0813702i	$0.974070\pi$
$332$	529.738	−	0.0723746i	1.59560	−	0.000217996i
$333$	110.120			0.330690
$334$	−74.7580	−	74.7478i	−0.223826	−	0.223796i
$335$			258.129i			0.770534i
$336$	−129.376	+	0.0353516i	−0.385047	+	0.000105213i
$337$	−173.807			−0.515747			−0.257874	−	0.966179i	$-0.583022\pi$
$337$	−173.807			−0.515747			−0.257874	+	0.966179i	$0.583022\pi$
$338$	18.3835	−	18.3860i	0.0543891	−	0.0543965i
$339$			275.056i			0.811376i
$340$	0.0698454	+	511.226i	0.000205428	+	1.50361i
$341$	−72.6706			−0.213110
$342$	48.5912	+	48.5846i	0.142080	+	0.142060i
$343$			355.762i			1.03721i
$344$	22.0040	−	22.0131i	0.0639652	−	0.0639914i
$345$	559.101			1.62058
$346$	349.332	−	349.380i	1.00963	−	1.00977i
$347$		−	680.781i		−	1.96190i	−0.194248	−	0.980952i	$-0.562227\pi$
$347$		−	680.781i		−	1.96190i	0.194248	−	0.980952i	$-0.437773\pi$
$348$	226.556	−	0.0309528i	0.651023	−	8.89450e-5i
$349$	−521.503			−1.49428			−0.747139	−	0.664668i	$-0.768573\pi$
$349$	−521.503			−1.49428			−0.747139	+	0.664668i	$0.768573\pi$
$350$	436.386	+	436.327i	1.24682	+	1.24665i
$351$			18.7350i			0.0533761i
$352$	315.248	+	315.033i	0.895591	+	0.894979i
$353$	323.124			0.915364			0.457682	−	0.889116i	$-0.348680\pi$
$353$	323.124			0.915364			0.457682	+	0.889116i	$0.348680\pi$
$354$	−212.340	+	212.369i	−0.599831	+	0.599913i
$355$			536.082i			1.51009i
$356$	0.0396026	+	289.867i	0.000111243	+	0.814232i
$357$	108.279			0.303303
$358$	293.058	+	293.018i	0.818599	+	0.818487i
$359$			204.176i			0.568737i	0.958715	+	0.284368i	$0.0917839\pi$
$359$			204.176i			0.568737i	−0.958715	+	0.284368i	$0.908216\pi$
$360$	−162.004	−	161.938i	−0.450012	−	0.449828i
$361$	229.845			0.636691
$362$	229.482	−	229.514i	0.633929	−	0.634015i
$363$			126.390i			0.348183i
$364$	67.3294	−	0.00919877i	0.184971	−	2.52713e-5i
$365$	184.269			0.504847
$366$	−164.559	−	164.537i	−0.449615	−	0.449554i
$367$		−	232.975i		−	0.634809i	−0.948290	−	0.317404i	$-0.897189\pi$
$367$		−	232.975i		−	0.634809i	0.948290	−	0.317404i	$-0.102811\pi$
$368$	0.147864	+	541.138i	0.000401805	+	1.47048i
$369$	−41.0802			−0.111329
$370$	495.418	−	495.485i	1.33897	−	1.33915i
$371$			319.608i			0.861477i
$372$	0.00493896	+	36.1502i	1.32768e−5	+	0.0971779i
$373$	507.293			1.36004			0.680018	−	0.733196i	$-0.261972\pi$
$373$	507.293			1.36004			0.680018	+	0.733196i	$0.261972\pi$
$374$	−263.770	−	263.734i	−0.705266	−	0.705170i
$375$			679.309i			1.81149i
$376$	310.363	−	310.490i	0.825432	−	0.825771i
$377$	−117.903			−0.312741
$378$	−34.3036	+	34.3083i	−0.0907503	+	0.0907627i
$379$		−	141.793i		−	0.374124i	−0.982348	−	0.187062i	$-0.940103\pi$
$379$		−	141.793i		−	0.374124i	0.982348	−	0.187062i	$-0.0598966\pi$
$380$	437.213	−	0.0597336i	1.15056	−	0.000157194i
$381$	−262.893			−0.690007
$382$	196.425	+	196.398i	0.514201	+	0.514130i
$383$			348.810i			0.910731i	0.890305	+	0.455366i	$0.150491\pi$
$383$			348.810i			0.910731i	−0.890305	+	0.455366i	$0.849509\pi$
$384$	156.692	−	156.842i	0.408053	−	0.408443i
$385$	−620.560			−1.61184
$386$	−153.097	+	153.117i	−0.396623	+	0.396677i
$387$		−	11.6718i		−	0.0301597i
$388$	−0.0705869	−	516.653i	−0.000181925	−	1.33158i
$389$	−527.083			−1.35497			−0.677484	−	0.735537i	$-0.736930\pi$
$389$	−527.083			−1.35497			−0.677484	+	0.735537i	$0.736930\pi$
$390$	84.2983	+	84.2868i	0.216149	+	0.216120i
$391$		−	452.896i		−	1.15830i
$392$	−153.929	−	153.866i	−0.392677	−	0.392516i
$393$	45.7999			0.116539
$394$	521.808	−	521.880i	1.32439	−	1.32457i
$395$		−	818.239i		−	2.07149i
$396$	167.128	−	0.0228337i	0.422041	−	5.76607e-5i
$397$	41.3192			0.104079			0.0520393	−	0.998645i	$-0.483428\pi$
$397$	41.3192			0.104079			0.0520393	+	0.998645i	$0.483428\pi$
$398$	9.48213	+	9.48083i	0.0238244	+	0.0238212i
$399$		−	92.6030i		−	0.232088i
$400$	−1057.48	+	0.288954i	−2.64371	+	0.000722385i
$401$	207.329			0.517029			0.258515	−	0.966007i	$-0.416767\pi$
$401$	207.329			0.517029			0.258515	+	0.966007i	$0.416767\pi$
$402$	−66.2431	+	66.2522i	−0.164784	+	0.164806i
$403$		−	18.8132i		−	0.0466828i
$404$	−0.0136315	−	99.7744i	−3.37414e−5	−	0.246966i
$405$	−85.8983			−0.212094
$406$	−215.910	−	215.880i	−0.531798	−	0.531725i
$407$			511.226i			1.25608i
$408$	−131.177	+	131.231i	−0.321512	+	0.321644i
$409$	3.86838			0.00945814			0.00472907	−	0.999989i	$-0.498495\pi$
$409$	3.86838			0.00945814			0.00472907	+	0.999989i	$0.498495\pi$
$410$	−184.816	+	184.841i	−0.450770	+	0.450831i
$411$			73.3355i			0.178432i
$412$	−119.920	+	0.0163839i	−0.291068	+	3.97667e-5i
$413$	404.724			0.979961
$414$	143.501	+	143.481i	0.346620	+	0.346572i
$415$		−	1263.99i		−	3.04575i
$416$	−81.5564	+	81.6122i	−0.196049	+	0.196183i
$417$	−304.889			−0.731150
$418$	−225.552	+	225.582i	−0.539597	+	0.539671i
$419$			742.432i			1.77191i	0.463767	+	0.885957i	$0.346498\pi$
$419$			742.432i			1.77191i	−0.463767	+	0.885957i	$0.653502\pi$
$420$	0.0421755	+	308.699i	0.000100418	+	0.734998i
$421$	180.675			0.429158			0.214579	−	0.976707i	$-0.431162\pi$
$421$	180.675			0.429158			0.214579	+	0.976707i	$0.431162\pi$
$422$	24.0950	+	24.0917i	0.0570971	+	0.0570893i
$423$		−	164.628i		−	0.389192i
$424$	−387.354	−	387.196i	−0.913572	−	0.913197i
$425$	885.044			2.08246
$426$	−137.574	+	137.592i	−0.322943	+	0.322987i
$427$			313.610i			0.734449i
$428$	−639.170	+	0.0873256i	−1.49339	+	0.000204032i
$429$	−86.9764			−0.202742
$430$	−52.5174	−	52.5102i	−0.122133	−	0.122117i
$431$		−	451.173i		−	1.04681i	−0.852086	−	0.523403i	$-0.824662\pi$
$431$		−	451.173i		−	1.04681i	0.852086	−	0.523403i	$-0.175338\pi$
$432$	−0.0227173	−	83.1384i	−5.25864e−5	−	0.192450i
$433$	−223.504			−0.516176			−0.258088	−	0.966121i	$-0.583093\pi$
$433$	−223.504			−0.516176			−0.258088	+	0.966121i	$0.583093\pi$
$434$	34.4467	−	34.4514i	0.0793703	−	0.0793812i
$435$		−	540.577i		−	1.24271i
$436$	0.0603784	+	441.933i	0.000138483	+	1.01361i
$437$	−387.328			−0.886335
$438$	47.2951	+	47.2886i	0.107980	+	0.107965i
$439$		−	239.581i		−	0.545742i	−0.962051	−	0.272871i	$-0.912027\pi$
$439$		−	239.581i		−	0.545742i	0.962051	−	0.272871i	$-0.0879732\pi$
$440$	751.790	−	752.099i	1.70861	−	1.70932i
$441$	−81.6167			−0.185072
$442$	68.2760	−	68.2853i	0.154471	−	0.154492i
$443$		−	19.7086i		−	0.0444890i	−0.999753	−	0.0222445i	$-0.992919\pi$
$443$		−	19.7086i		−	0.0444890i	0.999753	−	0.0222445i	$-0.00708123\pi$
$444$	254.311	−	0.0347448i	0.572772	−	7.82541e-5i
$445$	691.640			1.55425
$446$	−248.809	−	248.775i	−0.557868	−	0.557791i
$447$			132.606i			0.296657i
$448$	−298.781	+	0.122461i	−0.666922	+	0.000273351i
$449$	104.457			0.232644			0.116322	−	0.993212i	$-0.462890\pi$
$449$	104.457			0.232644			0.116322	+	0.993212i	$0.462890\pi$
$450$	−280.389	+	280.427i	−0.623086	+	0.623171i
$451$		−	190.713i		−	0.422867i
$452$	0.0867853	+	635.215i	0.000192003	+	1.40534i
$453$	−60.3631			−0.133252
$454$	204.614	+	204.586i	0.450692	+	0.450631i
$455$		−	160.652i		−	0.353082i
$456$	112.232	+	112.186i	0.246123	+	0.246022i
$457$	42.0539			0.0920217			0.0460109	−	0.998941i	$-0.485349\pi$
$457$	42.0539			0.0920217			0.0460109	+	0.998941i	$0.485349\pi$
$458$	267.001	−	267.038i	0.582972	−	0.583052i
$459$			69.5814i			0.151593i
$460$	1291.19	−	0.176407i	2.80693	−	0.000383493i
$461$	237.213			0.514563			0.257281	−	0.966337i	$-0.417173\pi$
$461$	237.213			0.514563			0.257281	+	0.966337i	$0.417173\pi$
$462$	−159.275	−	159.253i	−0.344751	−	0.344704i
$463$			386.947i			0.835738i	0.908507	+	0.417869i	$0.137223\pi$
$463$			386.947i			0.835738i	−0.908507	+	0.417869i	$0.862777\pi$
$464$	523.209	−	0.142965i	1.12760	−	0.000308114i
$465$	86.2566			0.185498
$466$	226.855	−	226.886i	0.486813	−	0.486879i
$467$			559.994i			1.19913i	0.800326	+	0.599565i	$0.204660\pi$
$467$			559.994i			1.19913i	−0.800326	+	0.599565i	$0.795340\pi$
$468$	0.00591123	+	43.2666i	1.26308e−5	+	0.0924500i
$469$	126.261			0.269212
$470$	−740.747	−	740.646i	−1.57606	−	1.57584i
$471$		−	24.7503i		−	0.0525484i
$472$	−490.312	+	490.513i	−1.03880	+	1.03922i
$473$	54.1858			0.114558
$474$	209.983	−	210.012i	0.443002	−	0.443063i
$475$		−	756.912i		−	1.59350i
$476$	250.060	−	0.0341640i	0.525336	−	7.17732e-5i
$477$	−205.384			−0.430574
$478$	402.587	+	402.532i	0.842231	+	0.842116i
$479$			82.9812i			0.173238i	0.996241	+	0.0866192i	$0.0276064\pi$
$479$			82.9812i			0.173238i	−0.996241	+	0.0866192i	$0.972394\pi$
$480$	−374.184	−	373.929i	−0.779551	−	0.779019i
$481$	−132.348			−0.275151
$482$	57.0927	−	57.1005i	0.118450	−	0.118466i
$483$		−	273.477i		−	0.566205i
$484$	0.0398785	+	291.886i	8.23936e−5	+	0.603071i
$485$	−1232.77			−2.54179
$486$	−22.0469	−	22.0439i	−0.0453640	−	0.0453578i
$487$		−	432.482i		−	0.888054i	−0.896014	−	0.444027i	$-0.853549\pi$
$487$		−	432.482i		−	0.888054i	0.896014	−	0.444027i	$-0.146451\pi$
$488$	−380.085	−	379.929i	−0.778863	−	0.778543i
$489$	−302.327			−0.618255
$490$	−367.185	+	367.235i	−0.749357	+	0.749459i
$491$			297.130i			0.605153i	0.953125	+	0.302576i	$0.0978468\pi$
$491$			297.130i			0.605153i	−0.953125	+	0.302576i	$0.902153\pi$
$492$	−94.8707	+	0.0129616i	−0.192827	+	2.63446e-5i
$493$	−437.891			−0.888217
$494$	−58.3993	−	58.3914i	−0.118217	−	0.118201i
$495$		−	398.779i		−	0.805614i
$496$	0.0228121	+	83.4853i	4.59921e−5	+	0.168317i
$497$	262.218			0.527601
$498$	324.375	−	324.419i	0.651355	−	0.651444i
$499$			409.472i			0.820585i	0.911954	+	0.410292i	$0.134573\pi$
$499$			409.472i			0.820585i	−0.911954	+	0.410292i	$0.865427\pi$
$500$	0.214334	+	1568.80i	0.000428669	+	3.13759i
$501$	−91.5532			−0.182741
$502$	515.332	+	515.261i	1.02656	+	1.02642i
$503$			705.998i			1.40358i	0.712386	+	0.701788i	$0.247614\pi$
$503$			705.998i			1.40358i	−0.712386	+	0.701788i	$0.752386\pi$
$504$	−79.2100	+	79.2425i	−0.157163	+	0.157227i
$505$	−238.068			−0.471422
$506$	−666.104	+	666.195i	−1.31641	+	1.31659i
$507$		−	22.5167i		−	0.0444116i
$508$	−607.125	+	0.0829474i	−1.19513	+	0.000163282i
$509$	−862.589			−1.69467			−0.847337	−	0.531055i	$-0.821796\pi$
$509$	−862.589			−1.69467			−0.847337	+	0.531055i	$0.821796\pi$
$510$	313.082	+	313.039i	0.613886	+	0.613803i
$511$		−	90.1329i		−	0.176385i
$512$	361.816	−	362.261i	0.706672	−	0.707541i
$513$	59.5077			0.116000
$514$	490.637	−	490.704i	0.954546	−	0.954677i
$515$			286.136i			0.555605i
$516$	−0.00368266	−	26.9549i	−7.13695e−6	−	0.0522381i
$517$	764.280			1.47830
$518$	−242.360	−	242.327i	−0.467877	−	0.467813i
$519$		−	427.872i		−	0.824415i
$520$	194.705	+	194.625i	0.374433	+	0.374280i
$521$	−48.8947			−0.0938478			−0.0469239	−	0.998898i	$-0.514942\pi$
$521$	−48.8947			−0.0938478			−0.0469239	+	0.998898i	$0.514942\pi$
$522$	138.727	−	138.746i	0.265761	−	0.265797i
$523$			783.325i			1.49775i	0.662710	+	0.748876i	$0.269406\pi$
$523$			783.325i			1.49775i	−0.662710	+	0.748876i	$0.730594\pi$
$524$	105.770	−	0.0144507i	0.201852	−	2.75777e-5i
$525$	534.425			1.01795
$526$	−720.569	−	720.471i	−1.36990	−	1.36972i
$527$		−	69.8716i		−	0.132584i
$528$	385.966	−	0.105464i	0.730997	−	0.000199743i
$529$	−614.867			−1.16232
$530$	−924.000	+	924.126i	−1.74340	+	1.74363i
$531$			260.080i			0.489793i
$532$	−0.0292179	−	213.857i	−5.49209e−5	−	0.401988i
$533$	49.3723			0.0926309
$534$	177.518	+	177.494i	0.332432	+	0.332386i
$535$			1525.10i			2.85065i
$536$	−152.961	+	153.024i	−0.285375	+	0.285492i
$537$	358.897			0.668338
$538$	−434.355	+	434.415i	−0.807352	+	0.807462i
$539$		−	378.902i		−	0.702972i
$540$	−198.374	+	0.0271025i	−0.367358	+	5.01898e-5i
$541$	184.830			0.341646			0.170823	−	0.985302i	$-0.445357\pi$
$541$	184.830			0.341646			0.170823	+	0.985302i	$0.445357\pi$
$542$	−211.011	−	210.982i	−0.389319	−	0.389266i
$543$		−	281.076i		−	0.517636i
$544$	−302.899	+	303.106i	−0.556799	+	0.557180i
$545$	1054.48			1.93483
$546$	41.2278	−	41.2335i	0.0755088	−	0.0755192i
$547$			351.962i			0.643441i	0.946835	+	0.321720i	$0.104261\pi$
$547$			351.962i			0.643441i	−0.946835	+	0.321720i	$0.895739\pi$
$548$	0.0231387	+	169.361i	4.22239e−5	+	0.309053i
$549$	−201.529			−0.367084
$550$	−1301.87	−	1301.69i	−2.36703	−	2.36671i
$551$			374.495i			0.679665i
$552$	331.446	+	331.310i	0.600445	+	0.600199i
$553$	−400.231			−0.723746
$554$	209.432	−	209.460i	0.378036	−	0.378087i
$555$		−	606.802i		−	1.09334i
$556$	−704.112	+	0.0961982i	−1.26639	+	0.000173018i
$557$	−222.372			−0.399232			−0.199616	−	0.979874i	$-0.563970\pi$
$557$	−222.372			−0.399232			−0.199616	+	0.979874i	$0.563970\pi$
$558$	22.1389	+	22.1359i	0.0396754	+	0.0396700i
$559$			14.0278i			0.0250944i
$560$	0.194800	+	712.910i	0.000347858	+	1.27305i
$561$	−323.028			−0.575808
$562$	315.014	−	315.057i	0.560523	−	0.560599i
$563$		−	683.716i		−	1.21442i	−0.794543	−	0.607208i	$-0.792290\pi$
$563$		−	683.716i		−	1.21442i	0.794543	−	0.607208i	$-0.207710\pi$
$564$	−0.0519433	−	380.193i	−9.20980e−5	−	0.674101i
$565$	1515.66			2.68259
$566$	−380.305	−	380.253i	−0.671917	−	0.671825i
$567$			42.0161i			0.0741024i
$568$	−317.669	+	317.800i	−0.559277	+	0.559506i
$569$	609.276			1.07078			0.535392	−	0.844604i	$-0.320164\pi$
$569$	609.276			1.07078			0.535392	+	0.844604i	$0.320164\pi$
$570$	267.719	−	267.756i	0.469683	−	0.469747i
$571$		−	231.045i		−	0.404632i	−0.979320	−	0.202316i	$-0.935153\pi$
$571$		−	231.045i		−	0.404632i	0.979320	−	0.202316i	$-0.0648467\pi$
$572$	−200.863	+	0.0274426i	−0.351160	+	4.79766e-5i
$573$	240.554			0.419814
$574$	90.4126	+	90.4003i	0.157513	+	0.157492i
$575$		−	2235.33i		−	3.88753i
$576$	−0.0786951	−	192.000i	−0.000136623	−	0.333333i
$577$	138.981			0.240867			0.120434	−	0.992721i	$-0.461571\pi$
$577$	138.981			0.240867			0.120434	+	0.992721i	$0.461571\pi$
$578$	−155.104	+	155.125i	−0.268346	+	0.268383i
$579$			187.517i			0.323864i
$580$	−0.170562	−	1248.41i	−0.000294072	−	2.15243i
$581$	−618.264			−1.06414
$582$	−316.406	−	316.363i	−0.543653	−	0.543578i
$583$		−	953.484i		−	1.63548i
$584$	109.238	+	109.193i	0.187052	+	0.186975i
$585$	103.237			0.176473
$586$	−263.924	+	263.960i	−0.450383	+	0.450444i
$587$			503.355i			0.857504i	0.903422	+	0.428752i	$0.141047\pi$
$587$			503.355i			0.857504i	−0.903422	+	0.428752i	$0.858953\pi$
$588$	−188.486	+	0.0257516i	−0.320554	+	4.37952e-5i
$589$	−59.7560			−0.101453
$590$	1170.23	+	1170.07i	1.98345	+	1.98318i
$591$		−	639.126i		−	1.08143i
$592$	587.306	−	0.160479i	0.992071	−	0.000271080i
$593$	736.464			1.24193			0.620965	−	0.783838i	$-0.286741\pi$
$593$	736.464			1.24193			0.620965	+	0.783838i	$0.286741\pi$
$594$	102.338	−	102.352i	0.172286	−	0.172309i
$595$		−	596.658i		−	1.00279i
$596$	0.0418395	+	306.240i	7.02005e−5	+	0.513825i
$597$	11.6124			0.0194513
$598$	−172.466	−	172.443i	−0.288405	−	0.288366i
$599$		−	564.470i		−	0.942354i	−0.882039	−	0.471177i	$-0.843829\pi$
$599$		−	564.470i		−	0.942354i	0.882039	−	0.471177i	$-0.156171\pi$
$600$	−647.441	+	647.707i	−1.07907	+	1.07951i
$601$	−665.206			−1.10683			−0.553416	−	0.832905i	$-0.686676\pi$
$601$	−665.206			−1.10683			−0.553416	+	0.832905i	$0.686676\pi$
$602$	−25.6847	+	25.6882i	−0.0426656	+	0.0426715i
$603$			81.1365i			0.134555i
$604$	−139.403	+	0.0190457i	−0.230799	+	3.15326e-5i
$605$	696.459			1.15117
$606$	−61.1032	−	61.0949i	−0.100830	−	0.100817i
$607$		−	835.470i		−	1.37639i	−0.725525	−	0.688196i	$-0.758403\pi$
$607$		−	835.470i		−	1.37639i	0.725525	−	0.688196i	$-0.241597\pi$
$608$	259.224	+	259.047i	0.426355	+	0.426064i
$609$	−264.416			−0.434181
$610$	−906.659	+	906.783i	−1.48633	+	1.48653i
$611$			197.859i			0.323828i
$612$	0.0219542	+	160.691i	3.58729e−5	+	0.262567i
$613$	−21.0659			−0.0343652			−0.0171826	−	0.999852i	$-0.505470\pi$
$613$	−21.0659			−0.0343652			−0.0171826	+	0.999852i	$0.505470\pi$
$614$	82.0433	+	82.0321i	0.133621	+	0.133603i
$615$			226.367i			0.368077i
$616$	−367.880	−	367.729i	−0.597207	−	0.596963i
$617$	316.590			0.513112			0.256556	−	0.966529i	$-0.417412\pi$
$617$	316.590			0.513112			0.256556	+	0.966529i	$0.417412\pi$
$618$	−73.4306	+	73.4406i	−0.118820	+	0.118836i
$619$			1153.52i			1.86353i	0.363063	+	0.931764i	$0.381731\pi$
$619$			1153.52i			1.86353i	−0.363063	+	0.931764i	$0.618269\pi$
$620$	199.201	−	0.0272155i	0.321292	−	4.38960e-5i
$621$	175.740			0.282994
$622$	676.529	+	676.436i	1.08767	+	1.08752i
$623$		−	338.307i		−	0.543029i
$624$	0.0273028	+	99.9200i	4.37545e−5	+	0.160128i
$625$	2090.93			3.34549
$626$	−76.7148	+	76.7253i	−0.122548	+	0.122564i
$627$			276.262i			0.440609i
$628$	−0.00780917	−	57.1584i	−1.24350e−5	−	0.0910165i
$629$	−491.536			−0.781456
$630$	189.052	+	189.026i	0.300082	+	0.300041i
$631$		−	244.510i		−	0.387495i	−0.981051	−	0.193748i	$-0.937936\pi$
$631$		−	244.510i		−	0.387495i	0.981051	−	0.193748i	$-0.0620643\pi$
$632$	484.869	−	485.068i	0.767197	−	0.767512i
$633$	29.5082			0.0466164
$634$	358.334	−	358.383i	0.565195	−	0.565273i
$635$			1448.64i			2.28132i
$636$	−474.313	+	0.0648023i	−0.745775	+	0.000101890i
$637$	98.0910			0.153989
$638$	644.123	+	644.035i	1.00960	+	1.00946i
$639$			168.504i			0.263700i
$640$	−864.260	−	863.434i	−1.35041	−	1.34912i
$641$	−614.173			−0.958148			−0.479074	−	0.877775i	$-0.659027\pi$
$641$	−614.173			−0.958148			−0.479074	+	0.877775i	$0.659027\pi$
$642$	−391.383	+	391.437i	−0.609631	+	0.609715i
$643$			525.403i			0.817113i	0.912733	+	0.408556i	$0.133968\pi$
$643$			525.403i			0.817113i	−0.912733	+	0.408556i	$0.866032\pi$
$644$	−0.0862871	−	631.569i	−0.000133986	−	0.980697i
$645$	−64.3160			−0.0997147
$646$	−216.894	−	216.864i	−0.335749	−	0.335703i
$647$		−	784.350i		−	1.21229i	−0.795355	−	0.606144i	$-0.792716\pi$
$647$		−	784.350i		−	1.21229i	0.795355	−	0.606144i	$-0.207284\pi$
$648$	−50.9221	−	50.9013i	−0.0785835	−	0.0785513i
$649$	−1207.41			−1.86042
$650$	336.985	−	337.031i	0.518439	−	0.518509i
$651$		−	42.1913i		−	0.0648100i
$652$	−698.194	+	0.0953896i	−1.07085	+	0.000146303i
$653$	−977.235			−1.49653			−0.748266	−	0.663399i	$-0.769113\pi$
$653$	−977.235			−1.49653			−0.748266	+	0.663399i	$0.769113\pi$
$654$	270.646	+	270.609i	0.413832	+	0.413776i
$655$		−	252.375i		−	0.385305i
$656$	−219.095	+	0.0598669i	−0.333986	+	9.12605e-5i
$657$	57.9204			0.0881589
$658$	−362.278	+	362.327i	−0.550574	+	0.550649i
$659$		−	137.883i		−	0.209231i	−0.994513	−	0.104616i	$-0.966639\pi$
$659$		−	137.883i		−	0.209231i	0.994513	−	0.104616i	$-0.0333612\pi$
$660$	−0.125822	−	920.940i	−0.000190639	−	1.39536i
$661$	−399.473			−0.604347			−0.302173	−	0.953253i	$-0.597712\pi$
$661$	−399.473			−0.604347			−0.302173	+	0.953253i	$0.597712\pi$
$662$	76.1848	+	76.1744i	0.115083	+	0.115067i
$663$		−	83.6264i		−	0.126133i
$664$	749.009	−	749.316i	1.12803	−	1.12849i
$665$	−510.277			−0.767334
$666$	155.722	−	155.744i	0.233817	−	0.233849i
$667$			1105.97i			1.65812i
$668$	−211.433	+	0.0288867i	−0.316517	+	4.32436e-5i
$669$	−304.707			−0.455466
$670$	365.074	+	365.024i	0.544887	+	0.544813i
$671$		−	935.590i		−	1.39432i
$672$	−182.903	+	183.028i	−0.272177	+	0.272363i
$673$	394.376			0.585998			0.292999	−	0.956113i	$-0.405347\pi$
$673$	394.376			0.585998			0.292999	+	0.956113i	$0.405347\pi$
$674$	−245.783	+	245.817i	−0.364663	+	0.364713i
$675$			343.428i			0.508782i
$676$	−0.00710442	−	52.0000i	−1.05095e−5	−	0.0769231i
$677$	510.906			0.754661			0.377331	−	0.926079i	$-0.376842\pi$
$677$	510.906			0.754661			0.377331	+	0.926079i	$0.376842\pi$
$678$	389.015	+	388.962i	0.573768	+	0.573690i
$679$			602.993i			0.888060i
$680$	723.131	+	722.835i	1.06343	+	1.06299i
$681$	250.583			0.367964
$682$	−102.765	+	102.779i	−0.150681	+	0.150702i
$683$			209.942i			0.307382i	0.988119	+	0.153691i	$0.0491161\pi$
$683$			209.942i			0.307382i	−0.988119	+	0.153691i	$0.950884\pi$
$684$	137.427	−	0.0187758i	0.200917	−	2.74500e-5i
$685$	404.106			0.589936
$686$	503.158	+	503.089i	0.733466	+	0.733366i
$687$		−	327.031i		−	0.476027i
$688$	−0.0170095	−	62.2496i	−2.47231e−5	−	0.0904790i
$689$	246.840			0.358259
$690$	790.634	−	790.742i	1.14585	−	1.14600i
$691$		−	1089.15i		−	1.57620i	−0.615550	−	0.788098i	$-0.711066\pi$
$691$		−	1089.15i		−	1.57620i	0.615550	−	0.788098i	$-0.288934\pi$
$692$	−0.135001	−	988.127i	−0.000195089	−	1.42793i
$693$	−195.058			−0.281469
$694$	−962.835	−	962.704i	−1.38737	−	1.38718i
$695$			1680.05i			2.41735i
$696$	320.333	−	320.464i	0.460248	−	0.460437i
$697$	183.368			0.263081
$698$	−737.466	+	737.567i	−1.05654	+	1.05669i
$699$		−	277.858i		−	0.397508i
$700$	1234.20	−	0.168621i	1.76315	−	0.000240887i
$701$	44.0007			0.0627684			0.0313842	−	0.999507i	$-0.490008\pi$
$701$	44.0007			0.0627684			0.0313842	+	0.999507i	$0.490008\pi$
$702$	26.4971	+	26.4935i	0.0377451	+	0.0377400i
$703$			420.374i			0.597972i
$704$	891.351	−	0.365338i	1.26612	−	0.000518947i
$705$	−907.164			−1.28676
$706$	456.935	−	456.997i	0.647216	−	0.647304i
$707$			116.448i			0.164707i
$708$	0.0820601	+	600.630i	0.000115904	+	0.848347i
$709$	259.106			0.365453			0.182727	−	0.983164i	$-0.441508\pi$
$709$	259.106			0.365453			0.182727	+	0.983164i	$0.441508\pi$
$710$	758.186	+	758.083i	1.06787	+	1.06772i
$711$		−	257.193i		−	0.361734i
$712$	410.017	+	409.849i	0.575867	+	0.575631i
$713$	−176.473			−0.247507
$714$	153.119	−	153.140i	0.214453	−	0.214482i
$715$			479.273i			0.670311i
$716$	828.838	−	0.113239i	1.15759	−	0.000158155i
$717$	493.032			0.687632
$718$	288.769	+	288.729i	0.402185	+	0.402130i
$719$		−	792.204i		−	1.10181i	−0.834567	−	0.550907i	$-0.814282\pi$
$719$		−	792.204i		−	1.10181i	0.834567	−	0.550907i	$-0.185718\pi$
$720$	−458.124	+	0.125181i	−0.636283	+	0.000173862i
$721$	139.960			0.194119
$722$	325.028	−	325.073i	0.450178	−	0.450239i
$723$		−	69.9287i		−	0.0967203i
$724$	−0.0886847	−	649.118i	−0.000122493	−	0.896572i
$725$	−2161.27			−2.98106
$726$	178.755	+	178.731i	0.246219	+	0.246186i
$727$			548.563i			0.754557i	0.926100	+	0.377279i	$0.123140\pi$
$727$			548.563i			0.754557i	−0.926100	+	0.377279i	$0.876860\pi$
$728$	95.1986	−	95.2376i	0.130767	−	0.130821i
$729$	−27.0000			−0.0370370
$730$	260.578	−	260.614i	0.356956	−	0.357005i
$731$			52.0988i			0.0712705i
$732$	−465.412	+	0.0635861i	−0.635808	+	8.68663e-5i
$733$	590.980			0.806249			0.403124	−	0.915145i	$-0.367924\pi$
$733$	590.980			0.806249			0.403124	+	0.915145i	$0.367924\pi$
$734$	−329.499	−	329.454i	−0.448908	−	0.448847i
$735$			449.739i			0.611889i
$736$	765.545	+	765.023i	1.04014	+	1.03943i
$737$	−376.672			−0.511089
$738$	−58.0922	+	58.1002i	−0.0787158	+	0.0787265i
$739$			1190.39i			1.61082i	0.592720	+	0.805408i	$0.298054\pi$
$739$			1190.39i			1.61082i	−0.592720	+	0.805408i	$0.701946\pi$
$740$	−0.191457	−	1401.35i	−0.000258726	−	1.89371i
$741$	−71.5194			−0.0965174
$742$	452.025	+	451.963i	0.609198	+	0.609114i
$743$		−	318.588i		−	0.428786i	−0.976748	−	0.214393i	$-0.931223\pi$
$743$		−	318.588i		−	0.428786i	0.976748	−	0.214393i	$-0.0687773\pi$
$744$	51.1346	+	51.1136i	0.0687292	+	0.0687011i
$745$	730.707			0.980815
$746$	717.372	−	717.470i	0.961625	−	0.961756i
$747$		−	397.304i		−	0.531865i
$748$	−746.002	+	0.101921i	−0.997329	+	0.000136259i
$749$	745.984			0.995973
$750$	960.754	+	960.623i	1.28101	+	1.28083i
$751$			291.703i			0.388420i	0.980960	+	0.194210i	$0.0622143\pi$
$751$			291.703i			0.388420i	−0.980960	+	0.194210i	$0.937786\pi$
$752$	−0.239916	−	878.018i	−0.000319037	−	1.16758i
$753$	631.107			0.838123
$754$	−166.729	+	166.752i	−0.221126	+	0.221157i
$755$			332.623i			0.440561i
$756$	0.0132568	+	97.0319i	1.75355e−5	+	0.128349i
$757$	81.9589			0.108268			0.0541340	−	0.998534i	$-0.482760\pi$
$757$	81.9589			0.108268			0.0541340	+	0.998534i	$0.482760\pi$
$758$	−200.539	−	200.512i	−0.264564	−	0.264528i
$759$			815.863i			1.07492i
$760$	618.186	−	618.440i	0.813403	−	0.813737i
$761$	1050.21			1.38004			0.690021	−	0.723790i	$-0.257601\pi$
$761$	1050.21			1.38004			0.690021	+	0.723790i	$0.257601\pi$
$762$	−371.761	+	371.812i	−0.487875	+	0.487942i
$763$		−	515.786i		−	0.675997i
$764$	555.535	−	0.0758991i	0.727140	−	9.93443e-5i
$765$	383.419			0.501202
$766$	493.326	+	493.258i	0.644028	+	0.643940i
$767$		−	312.578i		−	0.407533i
$768$	−0.242318	−	443.405i	−0.000315518	−	0.577350i
$769$	−120.339			−0.156488			−0.0782441	−	0.996934i	$-0.524931\pi$
$769$	−120.339			−0.156488			−0.0782441	+	0.996934i	$0.524931\pi$
$770$	−877.544	+	877.664i	−1.13967	+	1.13982i
$771$		−	600.946i		−	0.779437i
$772$	0.0591650	+	433.052i	7.66387e−5	+	0.560948i
$773$	559.158			0.723361			0.361680	−	0.932302i	$-0.382203\pi$
$773$	559.158			0.723361			0.361680	+	0.932302i	$0.382203\pi$
$774$	−16.5075	−	16.5053i	−0.0213276	−	0.0213247i
$775$		−	344.861i		−	0.444981i
$776$	−730.808	−	730.508i	−0.941763	−	0.941377i
$777$	−296.809			−0.381994
$778$	−745.357	+	745.459i	−0.958042	+	0.958173i
$779$		−	156.821i		−	0.201310i
$780$	238.415	−	0.0325731i	0.305661	−	4.17604e-5i
$781$	−782.273			−1.00163
$782$	−640.536	−	640.448i	−0.819100	−	0.818988i
$783$		−	169.917i		−	0.217008i
$784$	−435.289	+	0.118941i	−0.555216	+	0.000151711i
$785$	−136.383			−0.173737
$786$	64.7665	−	64.7753i	0.0824001	−	0.0824114i
$787$		−	960.138i		−	1.22000i	−0.792402	−	0.609999i	$-0.791170\pi$
$787$		−	960.138i		−	1.22000i	0.792402	−	0.609999i	$-0.208830\pi$
$788$	−0.201656	−	1476.00i	−0.000255908	−	1.87309i
$789$	−882.453			−1.11845
$790$	−1157.24	−	1157.09i	−1.46487	−	1.46467i
$791$		−	741.368i		−	0.937254i
$792$	236.307	−	236.404i	0.298367	−	0.298489i
$793$	242.208			0.305432
$794$	58.4301	−	58.4381i	0.0735896	−	0.0735997i
$795$			1131.74i			1.42357i
$796$	26.8177	−	0.00366392i	0.0336906	−	4.60292e-6i
$797$	−764.400			−0.959097			−0.479548	−	0.877515i	$-0.659199\pi$
$797$	−764.400			−0.959097			−0.479548	+	0.877515i	$0.659199\pi$
$798$	−130.969	−	130.951i	−0.164122	−	0.164100i
$799$			734.843i			0.919703i
$800$	−1495.00	+	1496.02i	−1.86875	+	1.87002i
$801$	217.400			0.271411
$802$	293.187	−	293.227i	0.365570	−	0.365620i
$803$			268.893i			0.334860i
$804$	0.0256000	+	187.377i	3.18408e−5	+	0.233055i
$805$	−1506.96			−1.87200
$806$	−26.6076	−	26.6040i	−0.0330119	−	0.0330074i
$807$			532.011i			0.659245i
$808$	−141.131	−	141.073i	−0.174667	−	0.174596i
$809$	−441.739			−0.546031			−0.273015	−	0.962010i	$-0.588021\pi$
$809$	−441.739			−0.546031			−0.273015	+	0.962010i	$0.588021\pi$
$810$	−121.470	+	121.487i	−0.149963	+	0.149984i
$811$		−	961.536i		−	1.18562i	−0.805343	−	0.592809i	$-0.798019\pi$
$811$		−	961.536i		−	1.18562i	0.805343	−	0.592809i	$-0.201981\pi$
$812$	−610.643	+	0.0834282i	−0.752024	+	0.000102744i
$813$	−258.417			−0.317856
$814$	723.033	+	722.934i	0.888247	+	0.888125i
$815$			1665.93i			2.04409i
$816$	0.101402	+	371.101i	0.000124267	+	0.454780i
$817$	44.5562			0.0545363
$818$	5.47034	−	5.47109i	0.00668746	−	0.00668837i
$819$		−	50.4970i		−	0.0616569i
$820$	0.0714231	+	522.773i	8.71013e−5	+	0.637528i
$821$	284.806			0.346902			0.173451	−	0.984843i	$-0.444508\pi$
$821$	284.806			0.346902			0.173451	+	0.984843i	$0.444508\pi$
$822$	103.719	+	103.705i	0.126179	+	0.126162i
$823$			1029.58i			1.25101i	0.780220	+	0.625505i	$0.215107\pi$
$823$			1029.58i			1.25101i	−0.780220	+	0.625505i	$0.784893\pi$
$824$	−169.558	+	169.627i	−0.205774	+	0.205858i
$825$	−1594.35			−1.93254
$826$	572.327	−	572.405i	0.692890	−	0.692985i
$827$		−	198.690i		−	0.240254i	−0.992759	−	0.120127i	$-0.961670\pi$
$827$		−	198.690i		−	0.240254i	0.992759	−	0.120127i	$-0.0383302\pi$
$828$	405.853	−	0.0554491i	0.490161	−	6.69675e-5i
$829$	700.900			0.845476			0.422738	−	0.906252i	$-0.361069\pi$
$829$	700.900			0.845476			0.422738	+	0.906252i	$0.361069\pi$
$830$	−1787.67	−	1787.43i	−2.15382	−	2.15353i
$831$		−	256.518i		−	0.308686i
$832$	0.0945797	+	230.755i	0.000113678	+	0.277350i
$833$	364.308			0.437345
$834$	−431.149	+	431.208i	−0.516965	+	0.517036i
$835$			504.493i			0.604183i
$836$	0.0871657	+	638.000i	0.000104265	+	0.763158i
$837$	27.1126			0.0323926
$838$	1050.03	+	1049.89i	1.25302	+	1.25285i
$839$			506.234i			0.603378i	0.953406	+	0.301689i	$0.0975504\pi$
$839$			506.234i			0.603378i	−0.953406	+	0.301689i	$0.902450\pi$
$840$	436.656	+	436.477i	0.519828	+	0.519615i
$841$	228.325			0.271492
$842$	255.496	−	255.531i	0.303439	−	0.303481i
$843$		−	385.838i		−	0.457696i
$844$	68.1463	−	0.00931038i	0.0807420	−	1.10313e-5i
$845$	−124.075			−0.146835
$846$	−232.836	−	232.804i	−0.275219	−	0.275182i
$847$		−	340.664i		−	0.402201i
$848$	−1095.38	+	0.299309i	−1.29172	+	0.000352959i
$849$	−465.745			−0.548580
$850$	1251.56	−	1251.73i	1.47242	−	1.47262i
$851$			1241.46i			1.45882i
$852$	0.0531662	+	389.144i	6.24016e−5	+	0.456742i
$853$	70.7418			0.0829329			0.0414665	−	0.999140i	$-0.486797\pi$
$853$	70.7418			0.0829329			0.0414665	+	0.999140i	$0.486797\pi$
$854$	443.541	+	443.481i	0.519369	+	0.519298i
$855$		−	327.910i		−	0.383521i
$856$	−903.738	+	904.108i	−1.05577	+	1.05620i
$857$	362.632			0.423141			0.211570	−	0.977363i	$-0.432142\pi$
$857$	362.632			0.423141			0.211570	+	0.977363i	$0.432142\pi$
$858$	−122.995	+	123.012i	−0.143351	+	0.143370i
$859$			286.846i			0.333930i	0.985963	+	0.166965i	$0.0533966\pi$
$859$			286.846i			0.333930i	−0.985963	+	0.166965i	$0.946603\pi$
$860$	−148.531	+	0.0202929i	−0.172711	+	2.35964e-5i
$861$	110.725			0.128600
$862$	−638.099	−	638.011i	−0.740253	−	0.740152i
$863$		−	1459.97i		−	1.69174i	−0.533390	−	0.845869i	$-0.679082\pi$
$863$		−	1459.97i		−	1.69174i	0.533390	−	0.845869i	$-0.320918\pi$
$864$	−117.616	−	117.535i	−0.136129	−	0.136036i
$865$	−2357.73			−2.72570
$866$	−316.061	+	316.104i	−0.364967	+	0.365017i
$867$			189.976i			0.219119i
$868$	−0.0133121	−	97.4367i	−1.53366e−5	−	0.112254i
$869$	1194.01			1.37400
$870$	−764.543	−	764.439i	−0.878785	−	0.878665i
$871$		−	97.5139i		−	0.111956i
$872$	625.116	+	624.860i	0.716876	+	0.716582i
$873$	−387.490			−0.443860
$874$	−547.728	+	547.802i	−0.626691	+	0.626776i
$875$		−	1830.96i		−	2.09253i
$876$	133.761	−	0.0182750i	0.152696	−	2.08618e-5i
$877$	−1433.24			−1.63426			−0.817129	−	0.576455i	$-0.804436\pi$
$877$	−1433.24			−1.63426			−0.817129	+	0.576455i	$0.804436\pi$
$878$	−338.842	−	338.795i	−0.385924	−	0.385872i
$879$			323.262i			0.367761i
$880$	−0.581147	−	2126.82i	−0.000660394	−	2.41684i
$881$	−1560.67			−1.77148			−0.885739	−	0.464184i	$-0.846348\pi$
$881$	−1560.67			−1.77148			−0.885739	+	0.464184i	$0.846348\pi$
$882$	−115.416	+	115.431i	−0.130857	+	0.130874i
$883$		−	108.615i		−	0.123007i	−0.998107	−	0.0615035i	$-0.980410\pi$
$883$		−	108.615i		−	0.123007i	0.998107	−	0.0615035i	$-0.0195895\pi$
$884$	−0.0263857	−	193.127i	−2.98480e−5	−	0.218469i
$885$	1433.14			1.61937
$886$	−27.8741	−	27.8703i	−0.0314606	−	0.0314563i
$887$			77.6756i			0.0875712i	0.999041	+	0.0437856i	$0.0139418\pi$
$887$			77.6756i			0.0875712i	−0.999041	+	0.0437856i	$0.986058\pi$
$888$	359.576	−	359.724i	0.404928	−	0.405094i
$889$	708.583			0.797056
$890$	978.060	−	978.193i	1.09894	−	1.09909i
$891$		−	125.346i		−	0.140680i
$892$	−703.690	+	0.0961405i	−0.788890	+	0.000107781i
$893$	628.456			0.703758
$894$	187.546	+	187.520i	0.209782	+	0.209754i
$895$		−	1977.66i		−	2.20968i
$896$	−422.338	+	422.742i	−0.471359	+	0.471810i
$897$	−211.213			−0.235466
$898$	147.714	−	147.735i	0.164493	−	0.164515i
$899$			170.626i			0.189795i
$900$	0.108358	+	793.113i	0.000120398	+	0.881236i
$901$	916.760			1.01749
$902$	−269.727	−	269.691i	−0.299033	−	0.298992i
$903$			31.4594i			0.0348387i
$904$	898.514	+	898.146i	0.993932	+	0.993524i
$905$	−1548.84			−1.71142
$906$	−85.3605	+	85.3722i	−0.0942169	+	0.0942298i
$907$			1361.82i			1.50146i	0.660612	+	0.750728i	$0.270297\pi$
$907$			1361.82i			1.50146i	−0.660612	+	0.750728i	$0.729703\pi$
$908$	578.697	−	0.0790636i	0.637332	−	8.70744e-5i
$909$	−74.8308			−0.0823221
$910$	−227.212	−	227.181i	−0.249683	−	0.249649i
$911$			384.257i			0.421797i	0.977508	+	0.210898i	$0.0676389\pi$
$911$			384.257i			0.421797i	−0.977508	+	0.210898i	$0.932361\pi$
$912$	317.375	−	0.0867216i	0.347999	−	9.50895e-5i
$913$	1844.46			2.02022
$914$	59.4692	−	59.4773i	0.0650647	−	0.0650736i
$915$			1110.50i			1.21366i
$916$	−0.103184	−	755.245i	−0.000112646	−	0.824503i
$917$	−123.446			−0.134619
$918$	98.4096	+	98.3962i	0.107200	+	0.107185i
$919$			1063.32i			1.15704i	0.815668	+	0.578520i	$0.196369\pi$
$919$			1063.32i			1.15704i	−0.815668	+	0.578520i	$0.803631\pi$
$920$	1825.64	−	1826.39i	1.98439	−	1.98521i
$921$	100.475			0.109094
$922$	335.447	−	335.493i	0.363826	−	0.363876i
$923$		−	202.517i		−	0.219412i
$924$	−450.466	+	0.0615443i	−0.487518	+	6.66064e-5i
$925$	−2426.04			−2.62275
$926$	547.263	+	547.188i	0.590997	+	0.590916i
$927$			89.9399i			0.0970226i
$928$	739.676	−	740.181i	0.797065	−	0.797609i
$929$	−419.632			−0.451703			−0.225851	−	0.974162i	$-0.572516\pi$
$929$	−419.632			−0.451703			−0.225851	+	0.974162i	$0.572516\pi$
$930$	121.977	−	121.994i	0.131158	−	0.131176i
$931$		−	311.565i		−	0.334657i
$932$	−0.0876693	−	641.686i	−9.40658e−5	−	0.688504i
$933$	828.518			0.888015
$934$	792.005	+	791.897i	0.847971	+	0.847855i
$935$			1780.01i			1.90375i
$936$	61.2008	+	61.1757i	0.0653854	+	0.0653586i
$937$	−1388.53			−1.48189			−0.740947	−	0.671563i	$-0.765623\pi$
$937$	−1388.53			−1.48189			−0.740947	+	0.671563i	$0.765623\pi$
$938$	178.547	−	178.572i	0.190349	−	0.190375i
$939$			93.9625i			0.100067i
$940$	−2095.01	+	0.286227i	−2.22873	+	0.000304497i
$941$	−318.166			−0.338114			−0.169057	−	0.985606i	$-0.554072\pi$
$941$	−318.166			−0.338114			−0.169057	+	0.985606i	$0.554072\pi$
$942$	−35.0046	−	34.9998i	−0.0371599	−	0.0371548i
$943$		−	463.126i		−	0.491120i
$944$	0.379019	+	1387.09i	0.000401504	+	1.46938i
$945$	231.524			0.244999
$946$	76.6250	−	76.6355i	0.0809990	−	0.0810101i
$947$			234.256i			0.247367i	0.992322	+	0.123683i	$0.0394707\pi$
$947$			234.256i			0.247367i	−0.992322	+	0.123683i	$0.960529\pi$
$948$	−0.0811492	−	593.962i	−8.56004e−5	−	0.626542i
$949$	−69.6117			−0.0733527
$950$	−1070.51	−	1070.36i	−1.12685	−	1.12670i
$951$		−	438.898i		−	0.461512i
$952$	353.566	−	353.710i	0.371392	−	0.371545i
$953$	704.526			0.739272			0.369636	−	0.929177i	$-0.379482\pi$
$953$	704.526			0.739272			0.369636	+	0.929177i	$0.379482\pi$
$954$	−290.436	+	290.476i	−0.304441	+	0.304482i
$955$		−	1325.54i		−	1.38800i
$956$	1138.61	−	0.155561i	1.19101	−	0.000162720i
$957$	788.832			0.824276
$958$	117.361	+	117.345i	0.122506	+	0.122490i
$959$		−	197.664i		−	0.206114i
$960$	−1057.99	+	0.433640i	−1.10208	+	0.000451708i
$961$	933.774			0.971669
$962$	−187.155	+	187.181i	−0.194548	+	0.194574i
$963$			479.378i			0.497796i
$964$	−0.0220638	−	161.494i	−2.28878e−5	−	0.167524i
$965$	1033.29			1.07077
$966$	−386.782	−	386.729i	−0.400395	−	0.400340i
$967$		−	1017.81i		−	1.05254i	−0.850316	−	0.526272i	$-0.823589\pi$
$967$		−	1017.81i		−	1.05254i	0.850316	−	0.526272i	$-0.176411\pi$
$968$	412.874	+	412.705i	0.426523	+	0.426348i
$969$	−265.622			−0.274119
$970$	−1743.28	+	1743.52i	−1.79719	+	1.79744i
$971$		−	59.6241i		−	0.0614049i	−0.999529	−	0.0307024i	$-0.990226\pi$
$971$		−	59.6241i		−	0.0614049i	0.999529	−	0.0307024i	$-0.00977443\pi$
$972$	−62.3538	+	0.00851899i	−0.0641500	+	8.76440e-6i
$973$	821.778			0.844582
$974$	−611.664	−	611.580i	−0.627992	−	0.627906i
$975$		−	412.749i		−	0.423332i
$976$	−1074.82	+	0.293692i	−1.10125	+	0.000300914i
$977$	1577.08			1.61421			0.807105	−	0.590408i	$-0.201033\pi$
$977$	1577.08			1.61421			0.807105	+	0.590408i	$0.201033\pi$
$978$	−427.525	+	427.584i	−0.437143	+	0.437202i
$979$			1009.27i			1.03092i
$980$	0.141901	+	1038.63i	0.000144797	+	1.05982i
$981$	331.450			0.337869
$982$	420.234	+	420.177i	0.427937	+	0.427878i
$983$		−	1299.25i		−	1.32172i	−0.750508	−	0.660861i	$-0.770191\pi$
$983$		−	1299.25i		−	1.32172i	0.750508	−	0.660861i	$-0.229809\pi$
$984$	−134.140	+	134.195i	−0.136321	+	0.136377i
$985$	−3521.82			−3.57546
$986$	−619.229	+	619.314i	−0.628021	+	0.628107i
$987$			443.728i			0.449573i
$988$	−165.167	+	0.0225657i	−0.167173	+	2.28398e-5i
$989$	131.584			0.133048
$990$	−563.997	−	563.920i	−0.569694	−	0.569616i
$991$		−	169.450i		−	0.170988i	−0.996339	−	0.0854942i	$-0.972753\pi$
$991$		−	169.450i		−	0.170988i	0.996339	−	0.0854942i	$-0.0272469\pi$
$992$	118.106	+	118.026i	0.119059	+	0.118977i
$993$	93.3005			0.0939583
$994$	370.807	−	370.857i	0.373045	−	0.373096i
$995$		−	63.9887i		−	0.0643102i
$996$	−0.125357	−	917.533i	−0.000125860	−	0.921218i
$997$	368.693			0.369802			0.184901	−	0.982757i	$-0.440804\pi$
$997$	368.693			0.369802			0.184901	+	0.982757i	$0.440804\pi$
$998$	579.120	+	579.041i	0.580281	+	0.580202i
$999$		−	190.733i		−	0.190924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.f.a.79.17	✓	24
3.2	odd	2		468.3.f.b.235.8		24
4.3	odd	2	inner	156.3.f.a.79.18	yes	24
8.3	odd	2		2496.3.k.e.703.5		24
8.5	even	2		2496.3.k.e.703.6		24
12.11	even	2		468.3.f.b.235.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.f.a.79.17	✓	24	1.1	even	1	trivial
156.3.f.a.79.18	yes	24	4.3	odd	2	inner
468.3.f.b.235.7		24	12.11	even	2
468.3.f.b.235.8		24	3.2	odd	2
2496.3.k.e.703.5		24	8.3	odd	2
2496.3.k.e.703.6		24	8.5	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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41412 - 1.41431i) q^{2} -1.73205i q^{3} +(-0.000546494 - 4.00000i) q^{4} -9.54425 q^{5} +(-2.44966 - 2.44932i) q^{6} +4.66845i q^{7} +(-5.65801 - 5.65569i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.41412 - 1.41431i) q^{2} -1.73205i q^{3} +(-0.000546494 - 4.00000i) q^{4} -9.54425 q^{5} +(-2.44966 - 2.44932i) q^{6} +4.66845i q^{7} +(-5.65801 - 5.65569i) q^{8} -3.00000 q^{9} +(-13.4967 + 13.4985i) q^{10} -13.9274i q^{11} +(-6.92820 + 0.000946555i) q^{12} +3.60555 q^{13} +(6.60264 + 6.60174i) q^{14} +16.5311i q^{15} +(-16.0000 + 0.00437195i) q^{16} +13.3909 q^{17} +(-4.24235 + 4.24293i) q^{18} -11.4523i q^{19} +(0.00521587 + 38.1770i) q^{20} +8.08600 q^{21} +(-19.6976 - 19.6949i) q^{22} -33.8211i q^{23} +(-9.79595 + 9.79997i) q^{24} +66.0927 q^{25} +(5.09867 - 5.09937i) q^{26} +5.19615i q^{27} +(18.6738 - 0.00255128i) q^{28} -32.7005 q^{29} +(23.3801 + 23.3769i) q^{30} -5.21783i q^{31} +(-22.6197 + 22.6351i) q^{32} -24.1229 q^{33} +(18.9364 - 18.9389i) q^{34} -44.5569i q^{35} +(0.00163948 + 12.0000i) q^{36} -36.7066 q^{37} +(-16.1971 - 16.1949i) q^{38} -6.24500i q^{39} +(54.0015 + 53.9794i) q^{40} +13.6934 q^{41} +(11.4345 - 11.4361i) q^{42} +3.89060i q^{43} +(-55.7095 + 0.00761122i) q^{44} +28.6328 q^{45} +(-47.8335 - 47.8270i) q^{46} +54.8761i q^{47} +(0.00757244 + 27.7128i) q^{48} +27.2056 q^{49} +(93.4628 - 93.4756i) q^{50} -23.1938i q^{51} +(-0.00197041 - 14.4222i) q^{52} +68.4612 q^{53} +(7.34897 + 7.34797i) q^{54} +132.926i q^{55} +(26.4033 - 26.4142i) q^{56} -19.8359 q^{57} +(-46.2424 + 46.2487i) q^{58} -86.6934i q^{59} +(66.1245 - 0.00903416i) q^{60} +67.1764 q^{61} +(-7.37963 - 7.37862i) q^{62} -14.0054i q^{63} +(0.0262317 + 64.0000i) q^{64} -34.4123 q^{65} +(-34.1126 + 34.1173i) q^{66} -27.0455i q^{67} +(-0.00731806 - 53.5638i) q^{68} -58.5799 q^{69} +(-63.0172 - 63.0086i) q^{70} -56.1681i q^{71} +(16.9740 + 16.9671i) q^{72} -19.3068 q^{73} +(-51.9074 + 51.9145i) q^{74} -114.476i q^{75} +(-45.8091 + 0.00625859i) q^{76} +65.0192 q^{77} +(-8.83236 - 8.83116i) q^{78} +85.7311i q^{79} +(152.708 - 0.0417270i) q^{80} +9.00000 q^{81} +(19.3641 - 19.3667i) q^{82} +132.435i q^{83} +(-0.00441895 - 32.3440i) q^{84} -127.806 q^{85} +(5.50251 + 5.50176i) q^{86} +56.6390i q^{87} +(-78.7689 + 78.8012i) q^{88} -72.4666 q^{89} +(40.4901 - 40.4956i) q^{90} +16.8323i q^{91} +(-135.284 + 0.0184830i) q^{92} -9.03755 q^{93} +(77.6119 + 77.6013i) q^{94} +109.303i q^{95} +(39.2052 + 39.1784i) q^{96} +129.163 q^{97} +(38.4718 - 38.4771i) q^{98} +41.7821i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

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