LMFDB - Embedded newform 276.3.f.b.139.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,3,Mod(139,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, 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("276.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	276.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:	$7.52045529634$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.20
Character	$\chi$	$=$	276.139
Dual form			276.3.f.b.139.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.268173 + 1.98194i) q^{2} -1.73205i q^{3} +(-3.85617 + 1.06301i) q^{4} -0.0477853 q^{5} +(3.43282 - 0.464490i) q^{6} +3.46303i q^{7} +(-3.14094 - 7.35762i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.268173 + 1.98194i) q^{2} -1.73205i q^{3} +(-3.85617 + 1.06301i) q^{4} -0.0477853 q^{5} +(3.43282 - 0.464490i) q^{6} +3.46303i q^{7} +(-3.14094 - 7.35762i) q^{8} -3.00000 q^{9} +(-0.0128147 - 0.0947075i) q^{10} +9.73090i q^{11} +(1.84118 + 6.67908i) q^{12} -17.8630 q^{13} +(-6.86352 + 0.928694i) q^{14} +0.0827666i q^{15} +(13.7400 - 8.19826i) q^{16} -15.4176 q^{17} +(-0.804520 - 5.94582i) q^{18} +17.2928i q^{19} +(0.184268 - 0.0507961i) q^{20} +5.99815 q^{21} +(-19.2861 + 2.60957i) q^{22} -4.79583i q^{23} +(-12.7438 + 5.44026i) q^{24} -24.9977 q^{25} +(-4.79039 - 35.4034i) q^{26} +5.19615i q^{27} +(-3.68123 - 13.3540i) q^{28} -54.9443 q^{29} +(-0.164038 + 0.0221958i) q^{30} -14.9860i q^{31} +(19.9332 + 25.0334i) q^{32} +16.8544 q^{33} +(-4.13460 - 30.5568i) q^{34} -0.165482i q^{35} +(11.5685 - 3.18902i) q^{36} +70.4174 q^{37} +(-34.2734 + 4.63748i) q^{38} +30.9397i q^{39} +(0.150091 + 0.351586i) q^{40} -48.9510 q^{41} +(1.60854 + 11.8880i) q^{42} +3.95048i q^{43} +(-10.3440 - 37.5240i) q^{44} +0.143356 q^{45} +(9.50505 - 1.28611i) q^{46} +63.2190i q^{47} +(-14.1998 - 23.7984i) q^{48} +37.0074 q^{49} +(-6.70372 - 49.5440i) q^{50} +26.7041i q^{51} +(68.8828 - 18.9885i) q^{52} +32.2548 q^{53} +(-10.2985 + 1.39347i) q^{54} -0.464994i q^{55} +(25.4797 - 10.8772i) q^{56} +29.9521 q^{57} +(-14.7346 - 108.896i) q^{58} -14.3028i q^{59} +(-0.0879814 - 0.319162i) q^{60} +28.1047 q^{61} +(29.7014 - 4.01886i) q^{62} -10.3891i q^{63} +(-44.2690 + 46.2196i) q^{64} +0.853590 q^{65} +(4.51991 + 33.4044i) q^{66} -100.265i q^{67} +(59.4530 - 16.3891i) q^{68} -8.30662 q^{69} +(0.327975 - 0.0443779i) q^{70} +38.2226i q^{71} +(9.42281 + 22.0728i) q^{72} +32.9813 q^{73} +(18.8841 + 139.563i) q^{74} +43.2973i q^{75} +(-18.3824 - 66.6841i) q^{76} -33.6984 q^{77} +(-61.3206 + 8.29720i) q^{78} +72.2216i q^{79} +(-0.656571 + 0.391756i) q^{80} +9.00000 q^{81} +(-13.1274 - 97.0178i) q^{82} +96.0812i q^{83} +(-23.1299 + 6.37608i) q^{84} +0.736736 q^{85} +(-7.82961 + 1.05941i) q^{86} +95.1663i q^{87} +(71.5962 - 30.5641i) q^{88} -98.6750 q^{89} +(0.0384442 + 0.284123i) q^{90} -61.8603i q^{91} +(5.09800 + 18.4935i) q^{92} -25.9566 q^{93} +(-125.296 + 16.9537i) q^{94} -0.826344i q^{95} +(43.3590 - 34.5253i) q^{96} +35.5346 q^{97} +(9.92440 + 73.3464i) q^{98} -29.1927i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.268173	+	1.98194i	0.134087	+	0.990970i
$2$	0.268173	+	1.98194i	0.134087	+	0.990970i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.85617	+	1.06301i	−0.964041	+	0.265752i
$5$	−0.0477853			−0.00955706			−0.00477853	−	0.999989i	$-0.501521\pi$
$5$	−0.0477853			−0.00955706			−0.00477853	+	0.999989i	$0.501521\pi$
$6$	3.43282	−	0.464490i	0.572137	−	0.0774150i
$7$			3.46303i			0.494719i	0.968924	+	0.247360i	$0.0795629\pi$
$7$			3.46303i			0.494719i	−0.968924	+	0.247360i	$0.920437\pi$
$8$	−3.14094	−	7.35762i	−0.392617	−	0.919702i
$9$	−3.00000			−0.333333
$10$	−0.0128147	−	0.0947075i	−0.00128147	−	0.00947075i
$11$			9.73090i			0.884627i	0.896860	+	0.442314i	$0.145842\pi$
$11$			9.73090i			0.884627i	−0.896860	+	0.442314i	$0.854158\pi$
$12$	1.84118	+	6.67908i	0.153432	+	0.556590i
$13$	−17.8630			−1.37408			−0.687040	−	0.726620i	$-0.741090\pi$
$13$	−17.8630			−1.37408			−0.687040	+	0.726620i	$0.741090\pi$
$14$	−6.86352	+	0.928694i	−0.490252	+	0.0663353i
$15$			0.0827666i			0.00551777i
$16$	13.7400	−	8.19826i	0.858752	−	0.512391i
$17$	−15.4176			−0.906920			−0.453460	−	0.891277i	$-0.649811\pi$
$17$	−15.4176			−0.906920			−0.453460	+	0.891277i	$0.649811\pi$
$18$	−0.804520	−	5.94582i	−0.0446956	−	0.330323i
$19$			17.2928i			0.910150i	0.890453	+	0.455075i	$0.150388\pi$
$19$			17.2928i			0.910150i	−0.890453	+	0.455075i	$0.849612\pi$
$20$	0.184268	−	0.0507961i	0.00921340	−	0.00253981i
$21$	5.99815			0.285626
$22$	−19.2861	+	2.60957i	−0.876639	+	0.118617i
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	−12.7438	+	5.44026i	−0.530990	+	0.226678i
$25$	−24.9977			−0.999909
$26$	−4.79039	−	35.4034i	−0.184246	−	1.36167i
$27$			5.19615i			0.192450i
$28$	−3.68123	−	13.3540i	−0.131472	−	0.476930i
$29$	−54.9443			−1.89463			−0.947315	−	0.320304i	$-0.896215\pi$
$29$	−54.9443			−1.89463			−0.947315	+	0.320304i	$0.896215\pi$
$30$	−0.164038	+	0.0221958i	−0.00546794	+	0.000739860i
$31$		−	14.9860i		−	0.483421i	−0.970348	−	0.241710i	$-0.922292\pi$
$31$		−	14.9860i		−	0.483421i	0.970348	−	0.241710i	$-0.0777084\pi$
$32$	19.9332	+	25.0334i	0.622912	+	0.782292i
$33$	16.8544			0.510740
$34$	−4.13460	−	30.5568i	−0.121606	−	0.898730i
$35$		−	0.165482i		−	0.00472806i
$36$	11.5685	−	3.18902i	0.321347	−	0.0885839i
$37$	70.4174			1.90317			0.951586	−	0.307383i	$-0.0994533\pi$
$37$	70.4174			1.90317			0.951586	+	0.307383i	$0.0994533\pi$
$38$	−34.2734	+	4.63748i	−0.901931	+	0.122039i
$39$			30.9397i			0.793325i
$40$	0.150091	+	0.351586i	0.00375226	+	0.00878965i
$41$	−48.9510			−1.19393			−0.596963	−	0.802269i	$-0.703626\pi$
$41$	−48.9510			−1.19393			−0.596963	+	0.802269i	$0.703626\pi$
$42$	1.60854	+	11.8880i	0.0382987	+	0.283047i
$43$			3.95048i			0.0918716i	0.998944	+	0.0459358i	$0.0146270\pi$
$43$			3.95048i			0.0918716i	−0.998944	+	0.0459358i	$0.985373\pi$
$44$	−10.3440	−	37.5240i	−0.235091	−	0.852817i
$45$	0.143356			0.00318569
$46$	9.50505	−	1.28611i	0.206631	−	0.0279590i
$47$			63.2190i			1.34509i	0.740058	+	0.672543i	$0.234798\pi$
$47$			63.2190i			1.34509i	−0.740058	+	0.672543i	$0.765202\pi$
$48$	−14.1998	−	23.7984i	−0.295829	−	0.495801i
$49$	37.0074			0.755253
$50$	−6.70372	−	49.5440i	−0.134074	−	0.990879i
$51$			26.7041i			0.523610i
$52$	68.8828	−	18.9885i	1.32467	−	0.365164i
$53$	32.2548			0.608581			0.304291	−	0.952579i	$-0.401581\pi$
$53$	32.2548			0.608581			0.304291	+	0.952579i	$0.401581\pi$
$54$	−10.2985	+	1.39347i	−0.190712	+	0.0258050i
$55$		−	0.464994i		−	0.00845443i
$56$	25.4797	−	10.8772i	0.454994	−	0.194235i
$57$	29.9521			0.525475
$58$	−14.7346	−	108.896i	−0.254045	−	1.87752i
$59$		−	14.3028i		−	0.242420i	−0.992627	−	0.121210i	$-0.961323\pi$
$59$		−	14.3028i		−	0.242420i	0.992627	−	0.121210i	$-0.0386775\pi$
$60$	−0.0879814	−	0.319162i	−0.00146636	−	0.00531936i
$61$	28.1047			0.460733			0.230366	−	0.973104i	$-0.426008\pi$
$61$	28.1047			0.460733			0.230366	+	0.973104i	$0.426008\pi$
$62$	29.7014	−	4.01886i	0.479055	−	0.0648203i
$63$		−	10.3891i		−	0.164906i
$64$	−44.2690	+	46.2196i	−0.691704	+	0.722182i
$65$	0.853590			0.0131322
$66$	4.51991	+	33.4044i	0.0684834	+	0.506128i
$67$		−	100.265i		−	1.49649i	−0.663422	−	0.748246i	$-0.730896\pi$
$67$		−	100.265i		−	1.49649i	0.663422	−	0.748246i	$-0.269104\pi$
$68$	59.4530	−	16.3891i	0.874308	−	0.241016i
$69$	−8.30662			−0.120386
$70$	0.327975	−	0.0443779i	0.00468536	−	0.000633970i
$71$			38.2226i			0.538347i	0.963092	+	0.269173i	$0.0867505\pi$
$71$			38.2226i			0.538347i	−0.963092	+	0.269173i	$0.913250\pi$
$72$	9.42281	+	22.0728i	0.130872	+	0.306567i
$73$	32.9813			0.451799			0.225899	−	0.974151i	$-0.427468\pi$
$73$	32.9813			0.451799			0.225899	+	0.974151i	$0.427468\pi$
$74$	18.8841	+	139.563i	0.255190	+	1.88599i
$75$			43.2973i			0.577298i
$76$	−18.3824	−	66.6841i	−0.241874	−	0.877422i
$77$	−33.6984			−0.437642
$78$	−61.3206	+	8.29720i	−0.786161	+	0.106374i
$79$			72.2216i			0.914197i	0.889416	+	0.457099i	$0.151111\pi$
$79$			72.2216i			0.914197i	−0.889416	+	0.457099i	$0.848889\pi$
$80$	−0.656571	+	0.391756i	−0.00820714	+	0.00489696i
$81$	9.00000			0.111111
$82$	−13.1274	−	97.0178i	−0.160090	−	1.18314i
$83$			96.0812i			1.15760i	0.815468	+	0.578802i	$0.196480\pi$
$83$			96.0812i			1.15760i	−0.815468	+	0.578802i	$0.803520\pi$
$84$	−23.1299	+	6.37608i	−0.275355	+	0.0759057i
$85$	0.736736			0.00866749
$86$	−7.82961	+	1.05941i	−0.0910420	+	0.0123188i
$87$			95.1663i			1.09387i
$88$	71.5962	−	30.5641i	0.813593	−	0.347320i
$89$	−98.6750			−1.10871			−0.554354	−	0.832281i	$-0.687035\pi$
$89$	−98.6750			−1.10871			−0.554354	+	0.832281i	$0.687035\pi$
$90$	0.0384442	+	0.284123i	0.000427158	+	0.00315692i
$91$		−	61.8603i		−	0.679783i
$92$	5.09800	+	18.4935i	0.0554131	+	0.201017i
$93$	−25.9566			−0.279103
$94$	−125.296	+	16.9537i	−1.33294	+	0.180358i
$95$		−	0.826344i		−	0.00869836i
$96$	43.3590	−	34.5253i	0.451657	−	0.359638i
$97$	35.5346			0.366336			0.183168	−	0.983082i	$-0.441365\pi$
$97$	35.5346			0.366336			0.183168	+	0.983082i	$0.441365\pi$
$98$	9.92440	+	73.3464i	0.101269	+	0.748433i
$99$		−	29.1927i		−	0.294876i
$100$	96.3953	−	26.5728i	0.963953	−	0.265728i
$101$	157.866			1.56303			0.781517	−	0.623884i	$-0.214446\pi$
$101$	157.866			1.56303			0.781517	+	0.623884i	$0.214446\pi$
$102$	−52.9260	+	7.16134i	−0.518882	+	0.0702092i
$103$			93.1482i			0.904352i	0.891929	+	0.452176i	$0.149352\pi$
$103$			93.1482i			0.904352i	−0.891929	+	0.452176i	$0.850648\pi$
$104$	56.1067	+	131.429i	0.539487	+	1.26374i
$105$	−0.286623			−0.00272975
$106$	8.64988	+	63.9270i	0.0816027	+	0.603085i
$107$		−	14.8736i		−	0.139005i	−0.997582	−	0.0695026i	$-0.977859\pi$
$107$		−	14.8736i		−	0.139005i	0.997582	−	0.0695026i	$-0.0221412\pi$
$108$	−5.52355	−	20.0372i	−0.0511440	−	0.185530i
$109$	−13.8388			−0.126961			−0.0634807	−	0.997983i	$-0.520220\pi$
$109$	−13.8388			−0.126961			−0.0634807	+	0.997983i	$0.520220\pi$
$110$	0.921590	−	0.124699i	0.00837809	−	0.00113363i
$111$		−	121.966i		−	1.09880i
$112$	28.3909	+	47.5822i	0.253490	+	0.424841i
$113$	−11.2180			−0.0992746			−0.0496373	−	0.998767i	$-0.515807\pi$
$113$	−11.2180			−0.0992746			−0.0496373	+	0.998767i	$0.515807\pi$
$114$	8.03236	+	59.3632i	0.0704593	+	0.520730i
$115$			0.229170i			0.00199278i
$116$	211.874	−	58.4061i	1.82650	−	0.503501i
$117$	53.5891			0.458026
$118$	28.3473	−	3.83563i	0.240231	−	0.0325053i
$119$		−	53.3918i		−	0.448671i
$120$	0.608965	−	0.259965i	0.00507470	−	0.00216637i
$121$	26.3096			0.217435
$122$	7.53694	+	55.7018i	0.0617782	+	0.456572i
$123$			84.7856i			0.689314i
$124$	15.9303	+	57.7886i	0.128470	+	0.466037i
$125$	2.38916			0.0191132
$126$	20.5906	−	2.78608i	0.163417	−	0.0221118i
$127$			159.175i			1.25334i	0.779283	+	0.626672i	$0.215583\pi$
$127$			159.175i			1.25334i	−0.779283	+	0.626672i	$0.784417\pi$
$128$	−103.476	−	75.3437i	−0.808408	−	0.588622i
$129$	6.84243			0.0530421
$130$	0.228910	+	1.69176i	0.00176085	+	0.0130136i
$131$		−	26.5378i		−	0.202579i	−0.994857	−	0.101289i	$-0.967703\pi$
$131$		−	26.5378i		−	0.202579i	0.994857	−	0.101289i	$-0.0322968\pi$
$132$	−64.9934	+	17.9164i	−0.492374	+	0.135730i
$133$	−59.8857			−0.450268
$134$	198.719	−	26.8884i	1.48298	−	0.200660i
$135$		−	0.248300i		−	0.00183926i
$136$	48.4258	+	113.437i	0.356072	+	0.834096i
$137$	−220.854			−1.61207			−0.806037	−	0.591866i	$-0.798392\pi$
$137$	−220.854			−1.61207			−0.806037	+	0.591866i	$0.798392\pi$
$138$	−2.22762	−	16.4632i	−0.0161421	−	0.119299i
$139$		−	165.617i		−	1.19149i	−0.803174	−	0.595744i	$-0.796857\pi$
$139$		−	165.617i		−	1.19149i	0.803174	−	0.595744i	$-0.203143\pi$
$140$	0.175909	+	0.638126i	0.00125649	+	0.00455804i
$141$	109.499			0.776586
$142$	−75.7549	+	10.2503i	−0.533485	+	0.0721852i
$143$		−	173.823i		−	1.21555i
$144$	−41.2201	+	24.5948i	−0.286251	+	0.170797i
$145$	2.62553			0.0181071
$146$	8.84471	+	65.3670i	0.0605802	+	0.447719i
$147$		−	64.0987i		−	0.436046i
$148$	−271.541	+	74.8541i	−1.83474	+	0.505771i
$149$	−183.570			−1.23201			−0.616007	−	0.787740i	$-0.711251\pi$
$149$	−183.570			−1.23201			−0.616007	+	0.787740i	$0.711251\pi$
$150$	−85.8126	+	11.6112i	−0.572084	+	0.0774079i
$151$		−	191.991i		−	1.27146i	−0.771910	−	0.635732i	$-0.780699\pi$
$151$		−	191.991i		−	1.27146i	0.771910	−	0.635732i	$-0.219301\pi$
$152$	127.234	−	54.3157i	0.837067	−	0.357340i
$153$	46.2529			0.302307
$154$	−9.03703	−	66.7882i	−0.0586820	−	0.433690i
$155$			0.716112i			0.00462008i
$156$	−32.8891	−	119.309i	−0.210828	−	0.764798i
$157$	94.5731			0.602376			0.301188	−	0.953565i	$-0.402617\pi$
$157$	94.5731			0.602376			0.301188	+	0.953565i	$0.402617\pi$
$158$	−143.139	+	19.3679i	−0.905941	+	0.122582i
$159$		−	55.8669i		−	0.351364i
$160$	−0.952512	−	1.19623i	−0.00595320	−	0.00747641i
$161$	16.6081			0.103156
$162$	2.41356	+	17.8375i	0.0148985	+	0.110108i
$163$		−	239.775i		−	1.47101i	−0.677517	−	0.735507i	$-0.736944\pi$
$163$		−	239.775i		−	1.47101i	0.677517	−	0.735507i	$-0.263056\pi$
$164$	188.763	−	52.0352i	1.15099	−	0.317288i
$165$	−0.805393			−0.00488117
$166$	−190.427	+	25.7664i	−1.14715	+	0.155219i
$167$			111.442i			0.667319i	0.942694	+	0.333659i	$0.108284\pi$
$167$			111.442i			0.667319i	−0.942694	+	0.333659i	$0.891716\pi$
$168$	−18.8398	−	44.1321i	−0.112142	−	0.262691i
$169$	150.088			0.888094
$170$	0.197573	+	1.46017i	0.00116220	+	0.00858922i
$171$		−	51.8785i		−	0.303383i
$172$	−4.19939	−	15.2337i	−0.0244150	−	0.0885680i
$173$	31.4380			0.181723			0.0908614	−	0.995864i	$-0.471038\pi$
$173$	31.4380			0.181723			0.0908614	+	0.995864i	$0.471038\pi$
$174$	−188.614	+	25.5211i	−1.08399	+	0.146673i
$175$		−	86.5679i		−	0.494674i
$176$	79.7765	+	133.703i	0.453275	+	0.759675i
$177$	−24.7732			−0.139961
$178$	−26.4620	−	195.568i	−0.148663	−	1.09870i
$179$		−	8.30300i		−	0.0463855i	−0.999731	−	0.0231927i	$-0.992617\pi$
$179$		−	8.30300i		−	0.0463855i	0.999731	−	0.0231927i	$-0.00738314\pi$
$180$	−0.552804	+	0.152388i	−0.00307113	+	0.000846602i
$181$	−38.4719			−0.212552			−0.106276	−	0.994337i	$-0.533893\pi$
$181$	−38.4719			−0.212552			−0.106276	+	0.994337i	$0.533893\pi$
$182$	122.603	−	16.5893i	0.673645	−	0.0911499i
$183$		−	48.6788i		−	0.266004i
$184$	−35.2859	+	15.0634i	−0.191771	+	0.0818663i
$185$	−3.36491			−0.0181887
$186$	−6.96087	−	51.4444i	−0.0374240	−	0.276583i
$187$		−	150.028i		−	0.802286i
$188$	−67.2023	−	243.783i	−0.357459	−	1.29672i
$189$	−17.9944			−0.0952087
$190$	1.63776	−	0.221604i	0.00861981	−	0.00116633i
$191$		−	338.592i		−	1.77273i	−0.462984	−	0.886367i	$-0.653221\pi$
$191$		−	338.592i		−	1.77273i	0.462984	−	0.886367i	$-0.346779\pi$
$192$	80.0547	+	76.6762i	0.416952	+	0.399355i
$193$	−219.086			−1.13516			−0.567580	−	0.823318i	$-0.692120\pi$
$193$	−219.086			−1.13516			−0.567580	+	0.823318i	$0.692120\pi$
$194$	9.52942	+	70.4273i	0.0491207	+	0.363027i
$195$		−	1.47846i		−	0.00758185i
$196$	−142.707	+	39.3391i	−0.728095	+	0.200710i
$197$	−123.819			−0.628522			−0.314261	−	0.949337i	$-0.601757\pi$
$197$	−123.819			−0.628522			−0.314261	+	0.949337i	$0.601757\pi$
$198$	57.8582	−	7.82871i	0.292213	−	0.0395389i
$199$			221.174i			1.11143i	0.831374	+	0.555713i	$0.187555\pi$
$199$			221.174i			1.11143i	−0.831374	+	0.555713i	$0.812445\pi$
$200$	78.5163	+	183.924i	0.392581	+	0.919618i
$201$	−173.664			−0.864000
$202$	42.3356	+	312.882i	0.209582	+	1.54892i
$203$		−	190.274i		−	0.937309i
$204$	−28.3867	−	102.976i	−0.139150	−	0.504782i
$205$	2.33914			0.0114104
$206$	−184.614	+	24.9799i	−0.896185	+	0.121262i
$207$			14.3875i			0.0695048i
$208$	−245.439	+	146.446i	−1.17999	+	0.704067i
$209$	−168.275			−0.805143
$210$	−0.0768648	−	0.568070i	−0.000366023	−	0.00270510i
$211$			282.454i			1.33864i	0.742973	+	0.669322i	$0.233415\pi$
$211$			282.454i			1.33864i	−0.742973	+	0.669322i	$0.766585\pi$
$212$	−124.380	+	34.2871i	−0.586697	+	0.161731i
$213$	66.2035			0.310815
$214$	29.4785	−	3.98870i	0.137750	−	0.0186388i
$215$		−	0.188775i		−	0.000878022i
$216$	38.2313	−	16.3208i	0.176997	−	0.0755592i
$217$	51.8971			0.239157
$218$	−3.71120	−	27.4276i	−0.0170238	−	0.125815i
$219$		−	57.1253i		−	0.260846i
$220$	0.494292	+	1.79309i	0.00224678	+	0.00815043i
$221$	275.406			1.24618
$222$	241.730	−	32.7082i	1.08887	−	0.147334i
$223$			65.0684i			0.291787i	0.989300	+	0.145893i	$0.0466056\pi$
$223$			65.0684i			0.291787i	−0.989300	+	0.145893i	$0.953394\pi$
$224$	−86.6913	+	69.0292i	−0.387015	+	0.308166i
$225$	74.9931			0.333303
$226$	−3.00838	−	22.2335i	−0.0133114	−	0.0983781i
$227$			226.622i			0.998335i	0.866506	+	0.499167i	$0.166361\pi$
$227$			226.622i			0.998335i	−0.866506	+	0.499167i	$0.833639\pi$
$228$	−115.500	+	31.8393i	−0.506580	+	0.139646i
$229$	133.767			0.584138			0.292069	−	0.956397i	$-0.405656\pi$
$229$	133.767			0.584138			0.292069	+	0.956397i	$0.405656\pi$
$230$	−0.454201	+	0.0614574i	−0.00197479	+	0.000267206i
$231$			58.3674i			0.252673i
$232$	172.576	+	404.259i	0.743864	+	1.74249i
$233$	−29.5526			−0.126835			−0.0634177	−	0.997987i	$-0.520200\pi$
$233$	−29.5526			−0.126835			−0.0634177	+	0.997987i	$0.520200\pi$
$234$	14.3712	+	106.210i	0.0614153	+	0.453890i
$235$		−	3.02094i		−	0.0128551i
$236$	15.2040	+	55.1539i	0.0644236	+	0.233703i
$237$	125.091			0.527812
$238$	105.819	−	14.3183i	0.444619	−	0.0601608i
$239$			94.9825i			0.397416i	0.980059	+	0.198708i	$0.0636746\pi$
$239$			94.9825i			0.397416i	−0.980059	+	0.198708i	$0.936325\pi$
$240$	0.678542	+	1.13722i	0.00282726	+	0.00473840i
$241$	−314.015			−1.30297			−0.651483	−	0.758663i	$-0.725853\pi$
$241$	−314.015			−1.30297			−0.651483	+	0.758663i	$0.725853\pi$
$242$	7.05553	+	52.1440i	0.0291551	+	0.215471i
$243$		−	15.5885i		−	0.0641500i
$244$	−108.376	+	29.8755i	−0.444166	+	0.122441i
$245$	−1.76841			−0.00721800
$246$	−168.040	+	22.7372i	−0.683089	+	0.0924278i
$247$		−	308.903i		−	1.25062i
$248$	−110.262	+	47.0702i	−0.444603	+	0.189799i
$249$	166.418			0.668344
$250$	0.640708	+	4.73516i	0.00256283	+	0.0189406i
$251$		−	216.740i		−	0.863505i	−0.901992	−	0.431752i	$-0.857895\pi$
$251$		−	216.740i		−	0.863505i	0.901992	−	0.431752i	$-0.142105\pi$
$252$	11.0437	+	40.0621i	0.0438242	+	0.158977i
$253$	46.6678			0.184458
$254$	−315.474	+	42.6864i	−1.24203	+	0.168057i
$255$		−	1.27606i		−	0.00500418i
$256$	121.577	−	225.289i	0.474910	−	0.880034i
$257$	−211.672			−0.823626			−0.411813	−	0.911268i	$-0.635104\pi$
$257$	−211.672			−0.823626			−0.411813	+	0.911268i	$0.635104\pi$
$258$	1.83496	+	13.5613i	0.00711224	+	0.0525631i
$259$			243.858i			0.941535i
$260$	−3.29159	+	0.907373i	−0.0126599	+	0.00348989i
$261$	164.833			0.631543
$262$	52.5964	−	7.11674i	0.200749	−	0.0271631i
$263$		−	16.6494i		−	0.0633056i	−0.999499	−	0.0316528i	$-0.989923\pi$
$263$		−	16.6494i		−	0.0633056i	0.999499	−	0.0316528i	$-0.0100771\pi$
$264$	−52.9386	−	124.008i	−0.200525	−	0.469728i
$265$	−1.54130			−0.00581624
$266$	−16.0598	−	118.690i	−0.0603750	−	0.446202i
$267$			170.910i			0.640113i
$268$	106.582	+	386.638i	0.397695	+	1.44268i
$269$	59.6939			0.221911			0.110955	−	0.993825i	$-0.464609\pi$
$269$	59.6939			0.221911			0.110955	+	0.993825i	$0.464609\pi$
$270$	0.492115	−	0.0665874i	0.00182265	−	0.000246620i
$271$			299.684i			1.10585i	0.833232	+	0.552923i	$0.186488\pi$
$271$			299.684i			1.10585i	−0.833232	+	0.552923i	$0.813512\pi$
$272$	−211.839	+	126.398i	−0.778819	+	0.464698i
$273$	−107.145			−0.392473
$274$	−59.2272	−	437.719i	−0.216158	−	1.59752i
$275$		−	243.250i		−	0.884546i
$276$	32.0317	−	8.83000i	0.116057	−	0.0319928i
$277$	497.444			1.79583			0.897914	−	0.440171i	$-0.145082\pi$
$277$	497.444			1.79583			0.897914	+	0.440171i	$0.145082\pi$
$278$	328.243	−	44.4141i	1.18073	−	0.159763i
$279$			44.9581i			0.161140i
$280$	−1.21755	+	0.519769i	−0.00434840	+	0.00185632i
$281$	−507.767			−1.80700			−0.903500	−	0.428588i	$-0.859011\pi$
$281$	−507.767			−1.80700			−0.903500	+	0.428588i	$0.859011\pi$
$282$	29.3646	+	217.020i	0.104130	+	0.769573i
$283$			517.680i			1.82926i	0.404295	+	0.914629i	$0.367517\pi$
$283$			517.680i			1.82926i	−0.404295	+	0.914629i	$0.632483\pi$
$284$	−40.6309	−	147.393i	−0.143067	−	0.518989i
$285$	−1.43127			−0.00502200
$286$	344.507	−	46.6148i	1.20457	−	0.162989i
$287$		−	169.519i		−	0.590658i
$288$	−59.7995	−	75.1001i	−0.207637	−	0.260764i
$289$	−51.2964			−0.177496
$290$	0.704097	+	5.20364i	0.00242792	+	0.0179436i
$291$		−	61.5476i		−	0.211504i
$292$	−127.181	+	35.0594i	−0.435553	+	0.120066i
$293$	281.369			0.960304			0.480152	−	0.877185i	$-0.340581\pi$
$293$	281.369			0.960304			0.480152	+	0.877185i	$0.340581\pi$
$294$	127.040	−	17.1896i	0.432108	−	0.0584679i
$295$			0.683463i			0.00231682i
$296$	−221.176	−	518.104i	−0.747218	−	1.75035i
$297$	−50.5632			−0.170247
$298$	−49.2286	−	363.825i	−0.165197	−	1.22089i
$299$			85.6681i			0.286515i
$300$	−46.0254	−	166.962i	−0.153418	−	0.556539i
$301$	−13.6806			−0.0454506
$302$	380.514	−	51.4869i	1.25998	−	0.170486i
$303$		−	273.433i		−	0.902418i
$304$	141.771	+	237.604i	0.466353	+	0.781593i
$305$	−1.34299			−0.00440325
$306$	12.4038	+	91.6705i	0.0405353	+	0.299577i
$307$			183.035i			0.596207i	0.954534	+	0.298103i	$0.0963540\pi$
$307$			183.035i			0.596207i	−0.954534	+	0.298103i	$0.903646\pi$
$308$	129.947	−	35.8217i	0.421905	−	0.116304i
$309$	161.337			0.522128
$310$	−1.41929	+	0.192042i	−0.00457836	+	0.000619491i
$311$			587.863i			1.89023i	0.326733	+	0.945117i	$0.394052\pi$
$311$			587.863i			1.89023i	−0.326733	+	0.945117i	$0.605948\pi$
$312$	227.642	−	97.1796i	0.729623	−	0.311473i
$313$	270.236			0.863375			0.431688	−	0.902023i	$-0.357918\pi$
$313$	270.236			0.863375			0.431688	+	0.902023i	$0.357918\pi$
$314$	25.3620	+	187.438i	0.0807707	+	0.596937i
$315$			0.496446i			0.00157602i
$316$	−76.7720	−	278.498i	−0.242949	−	0.881324i
$317$	−136.489			−0.430564			−0.215282	−	0.976552i	$-0.569067\pi$
$317$	−136.489			−0.430564			−0.215282	+	0.976552i	$0.569067\pi$
$318$	110.725	−	14.9820i	0.348191	−	0.0471133i
$319$		−	534.657i		−	1.67604i
$320$	2.11541	−	2.20862i	0.00661065	−	0.00690193i
$321$	−25.7618			−0.0802547
$322$	4.45386	+	32.9163i	0.0138319	+	0.102225i
$323$		−	266.615i		−	0.825433i
$324$	−34.7055	+	9.56706i	−0.107116	+	0.0295280i
$325$	446.535			1.37395
$326$	475.220	−	64.3014i	1.45773	−	0.197243i
$327$			23.9695i			0.0733012i
$328$	153.752	+	360.162i	0.468756	+	1.09806i
$329$	−218.930			−0.665440
$330$	−0.215985	−	1.59624i	−0.000654500	−	0.00483709i
$331$			243.989i			0.737127i	0.929603	+	0.368563i	$0.120150\pi$
$331$			243.989i			0.737127i	−0.929603	+	0.368563i	$0.879850\pi$
$332$	−102.135	−	370.505i	−0.307636	−	1.11598i
$333$	−211.252			−0.634391
$334$	−220.872	+	29.8858i	−0.661292	+	0.0894786i
$335$			4.79119i			0.0143021i
$336$	82.4148	−	49.1744i	0.245282	−	0.146352i
$337$	−275.255			−0.816779			−0.408390	−	0.912808i	$-0.633910\pi$
$337$	−275.255			−0.816779			−0.408390	+	0.912808i	$0.633910\pi$
$338$	40.2496	+	297.465i	0.119082	+	0.880075i
$339$			19.4302i			0.0573162i
$340$	−2.84098	+	0.783156i	−0.00835582	+	0.00230340i
$341$	145.828			0.427647
$342$	102.820	−	13.9125i	0.300644	−	0.0406797i
$343$			297.846i			0.868357i
$344$	29.0661	−	12.4082i	0.0844945	−	0.0360704i
$345$	0.396934			0.00115053
$346$	8.43085	+	62.3083i	0.0243666	+	0.180082i
$347$		−	228.856i		−	0.659527i	−0.944064	−	0.329764i	$-0.893031\pi$
$347$		−	228.856i		−	0.659527i	0.944064	−	0.329764i	$-0.106969\pi$
$348$	−101.162	−	366.977i	−0.290697	−	1.05453i
$349$	−594.848			−1.70444			−0.852218	−	0.523186i	$-0.824743\pi$
$349$	−594.848			−1.70444			−0.852218	+	0.523186i	$0.824743\pi$
$350$	171.572	−	23.2152i	0.490207	−	0.0663292i
$351$		−	92.8190i		−	0.264442i
$352$	−243.597	+	193.968i	−0.692037	+	0.551045i
$353$	292.268			0.827956			0.413978	−	0.910287i	$-0.364139\pi$
$353$	292.268			0.827956			0.413978	+	0.910287i	$0.364139\pi$
$354$	−6.64350	−	49.0989i	−0.0187670	−	0.138697i
$355$		−	1.82648i		−	0.00514501i
$356$	380.507	−	104.892i	1.06884	−	0.294641i
$357$	−92.4773			−0.259040
$358$	16.4560	−	2.22664i	0.0459666	−	0.00621968i
$359$		−	260.326i		−	0.725142i	−0.931956	−	0.362571i	$-0.881899\pi$
$359$		−	260.326i		−	0.725142i	0.931956	−	0.362571i	$-0.118101\pi$
$360$	−0.450272	−	1.05476i	−0.00125075	−	0.00292988i
$361$	61.9574			0.171627
$362$	−10.3171	−	76.2490i	−0.0285004	−	0.210632i
$363$		−	45.5695i		−	0.125536i
$364$	65.7579	+	238.543i	0.180654	+	0.655339i
$365$	−1.57602			−0.00431787
$366$	96.4784	−	13.0544i	0.263602	−	0.0356676i
$367$			368.601i			1.00436i	0.864763	+	0.502181i	$0.167469\pi$
$367$			368.601i			1.00436i	−0.864763	+	0.502181i	$0.832531\pi$
$368$	−39.3175	−	65.8949i	−0.106841	−	0.179062i
$369$	146.853			0.397975
$370$	−0.902381	−	6.66905i	−0.00243887	−	0.0180245i
$371$			111.699i			0.301077i
$372$	100.093	−	27.5920i	0.269067	−	0.0741721i
$373$	−439.176			−1.17742			−0.588708	−	0.808346i	$-0.700363\pi$
$373$	−439.176			−1.17742			−0.588708	+	0.808346i	$0.700363\pi$
$374$	297.345	−	40.2334i	0.795041	−	0.107576i
$375$		−	4.13814i		−	0.0110350i
$376$	465.141	−	198.567i	1.23708	−	0.528104i
$377$	981.471			2.60337
$378$	−4.82563	−	35.6639i	−0.0127662	−	0.0943489i
$379$		−	226.718i		−	0.598201i	−0.954222	−	0.299101i	$-0.903313\pi$
$379$		−	226.718i		−	0.598201i	0.954222	−	0.299101i	$-0.0966866\pi$
$380$	0.878409	+	3.18652i	0.00231160	+	0.00838558i
$381$	275.698			0.723618
$382$	671.069	−	90.8014i	1.75672	−	0.237700i
$383$			469.477i			1.22579i	0.790165	+	0.612895i	$0.209995\pi$
$383$			469.477i			1.22579i	−0.790165	+	0.612895i	$0.790005\pi$
$384$	−130.499	+	179.226i	−0.339841	+	0.466735i
$385$	1.61029			0.00418257
$386$	−58.7531	−	434.215i	−0.152210	−	1.12491i
$387$		−	11.8514i		−	0.0306239i
$388$	−137.027	+	37.7735i	−0.353163	+	0.0973543i
$389$	−57.1286			−0.146860			−0.0734301	−	0.997300i	$-0.523395\pi$
$389$	−57.1286			−0.146860			−0.0734301	+	0.997300i	$0.523395\pi$
$390$	2.93022	−	0.396484i	0.00751339	−	0.00101663i
$391$			73.9404i			0.189106i
$392$	−116.238	−	272.286i	−0.296525	−	0.694608i
$393$	−45.9649			−0.116959
$394$	−33.2049	−	245.401i	−0.0842764	−	0.622846i
$395$		−	3.45113i		−	0.00873703i
$396$	31.0320	+	112.572i	0.0783638	+	0.284272i
$397$	−10.4521			−0.0263278			−0.0131639	−	0.999913i	$-0.504190\pi$
$397$	−10.4521			−0.0263278			−0.0131639	+	0.999913i	$0.504190\pi$
$398$	−438.353	+	59.3129i	−1.10139	+	0.149027i
$399$			103.725i			0.259963i
$400$	−343.469	+	204.938i	−0.858674	+	0.512345i
$401$	−83.8175			−0.209021			−0.104511	−	0.994524i	$-0.533328\pi$
$401$	−83.8175			−0.209021			−0.104511	+	0.994524i	$0.533328\pi$
$402$	−46.5721	−	344.191i	−0.115851	−	0.856197i
$403$			267.696i			0.664258i
$404$	−608.759	+	167.813i	−1.50683	+	0.415379i
$405$	−0.430068			−0.00106190
$406$	377.111	−	51.0264i	0.928845	−	0.125681i
$407$			685.224i			1.68360i
$408$	196.479	−	83.8760i	0.481566	−	0.205578i
$409$	−71.5858			−0.175026			−0.0875132	−	0.996163i	$-0.527892\pi$
$409$	−71.5858			−0.175026			−0.0875132	+	0.996163i	$0.527892\pi$
$410$	0.627294	+	4.63603i	0.00152999	+	0.0113074i
$411$			382.530i			0.930731i
$412$	−99.0172	−	359.195i	−0.240333	−	0.871833i
$413$	49.5310			0.119930
$414$	−28.5151	+	3.85834i	−0.0688771	+	0.00931967i
$415$		−	4.59127i		−	0.0110633i
$416$	−356.067	−	447.172i	−0.855930	−	1.07493i
$417$	−286.857			−0.687906
$418$	−45.1269	−	333.511i	−0.107959	−	0.797873i
$419$			829.838i			1.98052i	0.139226	+	0.990261i	$0.455538\pi$
$419$			829.838i			1.98052i	−0.139226	+	0.990261i	$0.544462\pi$
$420$	1.10527	−	0.304683i	0.00263159	−	0.000725435i
$421$	272.371			0.646962			0.323481	−	0.946235i	$-0.395147\pi$
$421$	272.371			0.646962			0.323481	+	0.946235i	$0.395147\pi$
$422$	−559.806	+	75.7466i	−1.32655	+	0.179494i
$423$		−	189.657i		−	0.448362i
$424$	−101.310	−	237.318i	−0.238939	−	0.559713i
$425$	385.406			0.906837
$426$	17.7540	+	131.211i	0.0416761	+	0.308008i
$427$			97.3275i			0.227933i
$428$	15.8107	+	57.3549i	0.0369409	+	0.134007i
$429$	−301.071			−0.701797
$430$	0.374140	−	0.0506244i	0.000870093	−	0.000117731i
$431$		−	610.627i		−	1.41677i	−0.705827	−	0.708384i	$-0.749424\pi$
$431$		−	610.627i		−	1.41677i	0.705827	−	0.708384i	$-0.250576\pi$
$432$	42.5994	+	71.3953i	0.0986098	+	0.165267i
$433$	−289.438			−0.668448			−0.334224	−	0.942494i	$-0.608474\pi$
$433$	−289.438			−0.668448			−0.334224	+	0.942494i	$0.608474\pi$
$434$	13.9174	+	102.857i	0.0320678	+	0.236998i
$435$		−	4.54755i		−	0.0104541i
$436$	53.3647	−	14.7107i	0.122396	−	0.0337402i
$437$	82.9336			0.189779
$438$	113.219	−	15.3195i	0.258491	−	0.0349760i
$439$		−	223.686i		−	0.509536i	−0.967002	−	0.254768i	$-0.918001\pi$
$439$		−	223.686i		−	0.509536i	0.967002	−	0.254768i	$-0.0819991\pi$
$440$	−3.42125	+	1.46052i	−0.00777556	+	0.00331936i
$441$	−111.022			−0.251751
$442$	73.8565	+	545.838i	0.167096	+	1.23493i
$443$			640.324i			1.44543i	0.691147	+	0.722714i	$0.257105\pi$
$443$			640.324i			1.44543i	−0.691147	+	0.722714i	$0.742895\pi$
$444$	129.651	+	470.323i	0.292007	+	1.05929i
$445$	4.71521			0.0105960
$446$	−128.962	+	17.4496i	−0.289152	+	0.0391247i
$447$			317.953i			0.711304i
$448$	−160.060	−	153.305i	−0.357277	−	0.342199i
$449$	29.5031			0.0657085			0.0328543	−	0.999460i	$-0.489540\pi$
$449$	29.5031			0.0657085			0.0328543	+	0.999460i	$0.489540\pi$
$450$	20.1112	+	148.632i	0.0446915	+	0.330293i
$451$		−	476.337i		−	1.05618i
$452$	43.2586	−	11.9248i	0.0957048	−	0.0263824i
$453$	−332.538			−0.734080
$454$	−449.151	+	60.7740i	−0.989320	+	0.133863i
$455$			2.95601i			0.00649673i
$456$	−94.0776	−	220.376i	−0.206311	−	0.483281i
$457$	−470.582			−1.02972			−0.514860	−	0.857275i	$-0.672156\pi$
$457$	−470.582			−1.02972			−0.514860	+	0.857275i	$0.672156\pi$
$458$	35.8729	+	265.119i	0.0783251	+	0.578863i
$459$		−	80.1124i		−	0.174537i
$460$	−0.243610	−	0.883718i	−0.000529586	−	0.00192113i
$461$	190.008			0.412164			0.206082	−	0.978535i	$-0.433929\pi$
$461$	190.008			0.412164			0.206082	+	0.978535i	$0.433929\pi$
$462$	−115.681	+	15.6526i	−0.250391	+	0.0338801i
$463$			300.412i			0.648839i	0.945913	+	0.324419i	$0.105169\pi$
$463$			300.412i			0.648839i	−0.945913	+	0.324419i	$0.894831\pi$
$464$	−754.936	+	450.448i	−1.62702	+	0.970792i
$465$	1.24034			0.00266740
$466$	−7.92523	−	58.5715i	−0.0170069	−	0.125690i
$467$			226.500i			0.485011i	0.970150	+	0.242505i	$0.0779692\pi$
$467$			226.500i			0.485011i	−0.970150	+	0.242505i	$0.922031\pi$
$468$	−206.648	+	56.9656i	−0.441557	+	0.121721i
$469$	347.221			0.740343
$470$	5.98732	−	0.810136i	0.0127390	−	0.00172369i
$471$		−	163.805i		−	0.347782i
$472$	−105.234	+	44.9241i	−0.222954	+	0.0951783i
$473$	−38.4417			−0.0812721
$474$	33.5462	+	247.924i	0.0707726	+	0.523046i
$475$		−	432.282i		−	0.910067i
$476$	56.7559	+	205.888i	0.119235	+	0.432537i
$477$	−96.7644			−0.202860
$478$	−188.249	+	25.4718i	−0.393827	+	0.0532882i
$479$		−	804.128i		−	1.67876i	−0.543541	−	0.839382i	$-0.682917\pi$
$479$		−	804.128i		−	1.67876i	0.543541	−	0.839382i	$-0.317083\pi$
$480$	−2.07192	+	1.64980i	−0.00431651	+	0.00343708i
$481$	−1257.87			−2.61511
$482$	−84.2105	−	622.359i	−0.174711	−	1.29120i
$483$		−	28.7661i		−	0.0595572i
$484$	−101.454	+	27.9673i	−0.209616	+	0.0577836i
$485$	−1.69803			−0.00350109
$486$	30.8954	−	4.18041i	0.0635707	−	0.00860167i
$487$			400.568i			0.822522i	0.911518	+	0.411261i	$0.134911\pi$
$487$			400.568i			0.822522i	−0.911518	+	0.411261i	$0.865089\pi$
$488$	−88.2751	−	206.784i	−0.180892	−	0.423737i
$489$	−415.303			−0.849290
$490$	−0.474241	−	3.50488i	−0.000967838	−	0.00715282i
$491$			31.0832i			0.0633058i	0.999499	+	0.0316529i	$0.0100771\pi$
$491$			31.0832i			0.0633058i	−0.999499	+	0.0316529i	$0.989923\pi$
$492$	−90.1277	−	326.947i	−0.183186	−	0.664527i
$493$	847.111			1.71828
$494$	612.226	−	82.8395i	1.23932	−	0.167691i
$495$			1.39498i			0.00281814i
$496$	−122.859	−	205.909i	−0.247701	−	0.415138i
$497$	−132.366			−0.266330
$498$	44.6288	+	329.829i	0.0896160	+	0.662308i
$499$		−	474.845i		−	0.951592i	−0.879556	−	0.475796i	$-0.842160\pi$
$499$		−	474.845i		−	0.951592i	0.879556	−	0.475796i	$-0.157840\pi$
$500$	−9.21298	+	2.53969i	−0.0184260	+	0.00507938i
$501$	193.024			0.385277
$502$	429.565	−	58.1238i	0.855707	−	0.115785i
$503$			228.040i			0.453360i	0.973969	+	0.226680i	$0.0727871\pi$
$503$			228.040i			0.453360i	−0.973969	+	0.226680i	$0.927213\pi$
$504$	−76.4390	+	32.6315i	−0.151665	+	0.0647451i
$505$	−7.54369			−0.0149380
$506$	12.5151	+	92.4927i	0.0247333	+	0.182792i
$507$		−	259.960i		−	0.512742i
$508$	−169.204	−	613.804i	−0.333078	−	1.20827i
$509$	41.8631			0.0822457			0.0411229	−	0.999154i	$-0.486906\pi$
$509$	41.8631			0.0822457			0.0411229	+	0.999154i	$0.486906\pi$
$510$	2.52908	−	0.342207i	0.00495899	−	0.000670994i
$511$			114.215i			0.223513i
$512$	479.112	+	180.542i	0.935766	+	0.352620i
$513$	−89.8563			−0.175158
$514$	−56.7648	−	419.521i	−0.110437	−	0.816188i
$515$		−	4.45112i		−	0.00864294i
$516$	−26.3855	+	7.27355i	−0.0511348	+	0.0140960i
$517$	−615.178			−1.18990
$518$	−483.311	+	65.3961i	−0.933033	+	0.126247i
$519$		−	54.4523i		−	0.104918i
$520$	−2.68107	−	6.28039i	−0.00515591	−	0.0120777i
$521$	−655.856			−1.25884			−0.629420	−	0.777065i	$-0.716708\pi$
$521$	−655.856			−1.25884			−0.629420	+	0.777065i	$0.716708\pi$
$522$	44.2038	+	326.689i	0.0846816	+	0.625840i
$523$		−	957.377i		−	1.83055i	−0.402831	−	0.915274i	$-0.631974\pi$
$523$		−	957.377i		−	1.83055i	0.402831	−	0.915274i	$-0.368026\pi$
$524$	28.2099	+	102.334i	0.0538357	+	0.195294i
$525$	−149.940			−0.285600
$526$	32.9981	−	4.46492i	0.0627340	−	0.00848845i
$527$			231.049i			0.438424i
$528$	231.580	−	138.177i	0.438599	−	0.261699i
$529$	−23.0000			−0.0434783
$530$	−0.413337	−	3.05477i	−0.000779881	−	0.00576372i
$531$			42.9084i			0.0808067i
$532$	230.929	−	63.6589i	0.434077	−	0.119660i
$533$	874.413			1.64055
$534$	−338.733	+	45.8336i	−0.634332	+	0.0858306i
$535$			0.710738i			0.00132848i
$536$	−737.711	+	314.926i	−1.37633	+	0.587548i
$537$	−14.3812			−0.0267807
$538$	16.0083	+	118.310i	0.0297553	+	0.219907i
$539$			360.115i			0.668117i
$540$	0.263944	+	0.957485i	0.000488786	+	0.00177312i
$541$	316.460			0.584953			0.292477	−	0.956273i	$-0.405521\pi$
$541$	316.460			0.584953			0.292477	+	0.956273i	$0.405521\pi$
$542$	−593.956	+	80.3674i	−1.09586	+	0.148279i
$543$			66.6353i			0.122717i
$544$	−307.322	−	385.955i	−0.564931	−	0.709476i
$545$	0.661290			0.00121338
$546$	−28.7335	−	212.355i	−0.0526254	−	0.388929i
$547$		−	373.534i		−	0.682878i	−0.939904	−	0.341439i	$-0.889086\pi$
$547$		−	373.534i		−	0.682878i	0.939904	−	0.341439i	$-0.110914\pi$
$548$	851.650	−	234.769i	1.55411	−	0.428411i
$549$	−84.3141			−0.153578
$550$	482.107	−	65.2333i	0.876559	−	0.118606i
$551$		−	950.143i		−	1.72440i
$552$	26.0906	+	61.1169i	0.0472655	+	0.110719i
$553$	−250.106			−0.452271
$554$	133.401	+	985.904i	0.240797	+	1.77961i
$555$			5.82820i			0.0105013i
$556$	176.052	+	638.646i	0.316640	+	1.14864i
$557$	967.145			1.73635			0.868174	−	0.496261i	$-0.165294\pi$
$557$	967.145			1.73635			0.868174	+	0.496261i	$0.165294\pi$
$558$	−89.1042	+	12.0566i	−0.159685	+	0.0216068i
$559$		−	70.5675i		−	0.126239i
$560$	−1.35667	−	2.27373i	−0.00242262	−	0.00406023i
$561$	−259.855			−0.463200
$562$	−136.170	−	1006.36i	−0.242295	−	1.79068i
$563$			642.703i			1.14157i	0.821100	+	0.570784i	$0.193361\pi$
$563$			642.703i			1.14157i	−0.821100	+	0.570784i	$0.806639\pi$
$564$	−422.245	+	116.398i	−0.748661	+	0.206379i
$565$	0.536057			0.000948773
$566$	−1026.01	+	138.828i	−1.81274	+	0.245279i
$567$			31.1673i			0.0549688i
$568$	281.227	−	120.055i	0.495119	−	0.211364i
$569$	580.263			1.01980			0.509898	−	0.860235i	$-0.329683\pi$
$569$	580.263			1.01980			0.509898	+	0.860235i	$0.329683\pi$
$570$	−0.383829	−	2.83669i	−0.000673383	−	0.00497665i
$571$		−	145.311i		−	0.254485i	−0.991872	−	0.127243i	$-0.959387\pi$
$571$		−	145.311i		−	0.254485i	0.991872	−	0.127243i	$-0.0406127\pi$
$572$	184.775	+	670.292i	0.323034	+	1.17184i
$573$	−586.459			−1.02349
$574$	335.976	−	45.4605i	0.585324	−	0.0791994i
$575$			119.885i			0.208495i
$576$	132.807	−	138.659i	0.230568	−	0.240727i
$577$	476.475			0.825780			0.412890	−	0.910781i	$-0.364519\pi$
$577$	476.475			0.825780			0.412890	+	0.910781i	$0.364519\pi$
$578$	−13.7563	−	101.666i	−0.0237999	−	0.175893i
$579$			379.468i			0.655385i
$580$	−10.1245	+	2.79095i	−0.0174560	+	0.00481199i
$581$	−332.732			−0.572689
$582$	121.984	−	16.5054i	0.209594	−	0.0283599i
$583$			313.868i			0.538367i
$584$	−103.592	−	242.664i	−0.177384	−	0.415520i
$585$	−2.56077			−0.00437739
$586$	75.4557	+	557.656i	0.128764	+	0.951632i
$587$			352.005i			0.599668i	0.953991	+	0.299834i	$0.0969314\pi$
$587$			352.005i			0.599668i	−0.953991	+	0.299834i	$0.903069\pi$
$588$	68.1374	+	247.175i	0.115880	+	0.420366i
$589$	259.151			0.439985
$590$	−1.35458	+	0.183287i	−0.00229590	+	0.000310655i
$591$			214.460i			0.362877i
$592$	967.537	−	577.300i	1.63435	−	0.975169i
$593$	−250.648			−0.422678			−0.211339	−	0.977413i	$-0.567782\pi$
$593$	−250.648			−0.422678			−0.211339	+	0.977413i	$0.567782\pi$
$594$	−13.5597	−	100.213i	−0.0228278	−	0.168709i
$595$			2.55134i			0.00428797i
$596$	707.877	−	195.136i	1.18771	−	0.327410i
$597$	383.084			0.641682
$598$	−169.789	+	22.9739i	−0.283928	+	0.0384179i
$599$		−	262.165i		−	0.437671i	−0.975762	−	0.218836i	$-0.929774\pi$
$599$		−	262.165i		−	0.437671i	0.975762	−	0.218836i	$-0.0702258\pi$
$600$	318.565	−	135.994i	0.530942	−	0.226657i
$601$	−590.394			−0.982353			−0.491176	−	0.871060i	$-0.663433\pi$
$601$	−590.394			−0.982353			−0.491176	+	0.871060i	$0.663433\pi$
$602$	−3.66879	−	27.1142i	−0.00609433	−	0.0450402i
$603$			300.795i			0.498830i
$604$	204.088	+	740.349i	0.337894	+	1.22574i
$605$	−1.25721			−0.00207803
$606$	541.927	−	73.3274i	0.894269	−	0.121002i
$607$		−	232.303i		−	0.382707i	−0.981521	−	0.191354i	$-0.938712\pi$
$607$		−	232.303i		−	0.382707i	0.981521	−	0.191354i	$-0.0612877\pi$
$608$	−432.898	+	344.701i	−0.712003	+	0.566943i
$609$	−329.564			−0.541156
$610$	−0.360155	−	2.66173i	−0.000590418	−	0.00436349i
$611$		−	1129.28i		−	1.84826i
$612$	−178.359	+	49.1672i	−0.291436	+	0.0803385i
$613$	358.929			0.585529			0.292765	−	0.956185i	$-0.405425\pi$
$613$	358.929			0.585529			0.292765	+	0.956185i	$0.405425\pi$
$614$	−362.765	+	49.0853i	−0.590823	+	0.0799434i
$615$		−	4.05150i		−	0.00658781i
$616$	105.845	+	247.940i	0.171826	+	0.402500i
$617$	668.434			1.08336			0.541681	−	0.840584i	$-0.317788\pi$
$617$	668.434			1.08336			0.541681	+	0.840584i	$0.317788\pi$
$618$	43.2664	+	319.761i	0.0700104	+	0.517413i
$619$		−	955.717i		−	1.54397i	−0.635641	−	0.771985i	$-0.719264\pi$
$619$		−	955.717i		−	1.54397i	0.635641	−	0.771985i	$-0.280736\pi$
$620$	−0.761232	−	2.76145i	−0.00122779	−	0.00445395i
$621$	24.9199			0.0401286
$622$	−1165.11	+	157.649i	−1.87316	+	0.253455i
$623$		−	341.715i		−	0.548499i
$624$	253.652	+	425.112i	0.406493	+	0.681270i
$625$	624.829			0.999726
$626$	72.4702	+	535.592i	0.115767	+	0.855578i
$627$			291.461i			0.464850i
$628$	−364.689	+	100.532i	−0.580716	+	0.160083i
$629$	−1085.67			−1.72602
$630$	−0.983926	+	0.133134i	−0.00156179	+	0.000211323i
$631$		−	1030.91i		−	1.63378i	−0.576796	−	0.816888i	$-0.695697\pi$
$631$		−	1030.91i		−	1.63378i	0.576796	−	0.816888i	$-0.304303\pi$
$632$	531.379	−	226.843i	0.840789	−	0.358929i
$633$	489.224			0.772866
$634$	−36.6027	−	270.512i	−0.0577329	−	0.426676i
$635$		−	7.60620i		−	0.0119783i
$636$	59.3870	+	215.432i	0.0933757	+	0.338730i
$637$	−661.064			−1.03778
$638$	1059.66	−	143.381i	1.66091	−	0.224735i
$639$		−	114.668i		−	0.179449i
$640$	4.94464	+	3.60032i	0.00772600	+	0.00562550i
$641$	−133.815			−0.208760			−0.104380	−	0.994538i	$-0.533286\pi$
$641$	−133.815			−0.208760			−0.104380	+	0.994538i	$0.533286\pi$
$642$	−6.90862	−	51.0583i	−0.0107611	−	0.0795300i
$643$		−	1169.73i		−	1.81918i	−0.415504	−	0.909592i	$-0.636395\pi$
$643$		−	1169.73i		−	1.81918i	0.415504	−	0.909592i	$-0.363605\pi$
$644$	−64.0437	+	17.6546i	−0.0994467	+	0.0274139i
$645$	−0.326968			−0.000506926
$646$	528.415	−	71.4990i	0.817979	−	0.110680i
$647$		−	832.481i		−	1.28668i	−0.765581	−	0.643340i	$-0.777548\pi$
$647$		−	832.481i		−	1.28668i	0.765581	−	0.643340i	$-0.222452\pi$
$648$	−28.2684	−	66.2185i	−0.0436241	−	0.102189i
$649$	139.179			0.214451
$650$	119.749	+	885.005i	0.184229	+	1.36155i
$651$		−	89.8885i		−	0.138078i
$652$	254.883	+	924.613i	0.390925	+	1.41812i
$653$	543.043			0.831612			0.415806	−	0.909453i	$-0.363500\pi$
$653$	543.043			0.831612			0.415806	+	0.909453i	$0.363500\pi$
$654$	−47.5061	+	6.42798i	−0.0726392	+	0.00982871i
$655$			1.26812i			0.00193606i
$656$	−672.588	+	401.313i	−1.02529	+	0.611758i
$657$	−98.9439			−0.150600
$658$	−58.7111	−	433.905i	−0.0892266	−	0.659431i
$659$		−	313.838i		−	0.476234i	−0.971236	−	0.238117i	$-0.923470\pi$
$659$		−	313.838i		−	0.476234i	0.971236	−	0.238117i	$-0.0765302\pi$
$660$	3.10573	−	0.856139i	0.00470565	−	0.00129718i
$661$	720.463			1.08996			0.544980	−	0.838449i	$-0.316537\pi$
$661$	720.463			1.08996			0.544980	+	0.838449i	$0.316537\pi$
$662$	−483.571	+	65.4314i	−0.730470	+	0.0988389i
$663$		−	477.017i		−	0.719482i
$664$	706.929	−	301.785i	1.06465	−	0.454496i
$665$	2.86166			0.00430324
$666$	−56.6522	−	418.689i	−0.0850634	−	0.628662i
$667$			263.503i			0.395058i
$668$	−118.464	−	429.740i	−0.177341	−	0.643323i
$669$	112.702			0.168463
$670$	−9.49584	+	1.28487i	−0.0141729	+	0.00191772i
$671$			273.484i			0.407577i
$672$	119.562	+	150.154i	0.177920	+	0.223443i
$673$	−1197.47			−1.77930			−0.889652	−	0.456639i	$-0.849053\pi$
$673$	−1197.47			−1.77930			−0.889652	+	0.456639i	$0.849053\pi$
$674$	−73.8160	−	545.538i	−0.109519	−	0.809403i
$675$		−	129.892i		−	0.192433i
$676$	−578.764	+	159.545i	−0.856160	+	0.236013i
$677$	867.721			1.28172			0.640858	−	0.767660i	$-0.278579\pi$
$677$	867.721			1.28172			0.640858	+	0.767660i	$0.278579\pi$
$678$	−38.5095	+	5.21066i	−0.0567986	+	0.00768535i
$679$			123.057i			0.181233i
$680$	−2.31404	−	5.42062i	−0.00340300	−	0.00797151i
$681$	392.521			0.576389
$682$	39.1071	+	289.022i	0.0573418	+	0.423785i
$683$			753.952i			1.10388i	0.833883	+	0.551941i	$0.186113\pi$
$683$			753.952i			1.10388i	−0.833883	+	0.551941i	$0.813887\pi$
$684$	55.1473	+	200.052i	0.0806247	+	0.292474i
$685$	10.5536			0.0154067
$686$	−590.314	+	79.8745i	−0.860515	+	0.116435i
$687$		−	231.692i		−	0.337252i
$688$	32.3871	+	54.2797i	0.0470742	+	0.0788949i
$689$	−576.168			−0.836239
$690$	0.106447	+	0.786700i	0.000154271	+	0.00114014i
$691$			1240.22i			1.79482i	0.441197	+	0.897411i	$0.354554\pi$
$691$			1240.22i			1.79482i	−0.441197	+	0.897411i	$0.645446\pi$
$692$	−121.230	+	33.4189i	−0.175188	+	0.0482931i
$693$	101.095			0.145881
$694$	453.579	−	61.3731i	0.653571	−	0.0884339i
$695$			7.91405i			0.0113871i
$696$	700.197	−	298.911i	1.00603	−	0.429470i
$697$	754.708			1.08280
$698$	−159.523	−	1178.95i	−0.228542	−	1.68904i
$699$			51.1867i			0.0732284i
$700$	92.0223	+	333.820i	0.131460	+	0.476886i
$701$	−287.623			−0.410304			−0.205152	−	0.978730i	$-0.565769\pi$
$701$	−287.623			−0.410304			−0.205152	+	0.978730i	$0.565769\pi$
$702$	183.962	−	24.8916i	0.262054	−	0.0354581i
$703$			1217.72i			1.73217i
$704$	−449.758	−	430.778i	−0.638861	−	0.611900i
$705$	−5.23242			−0.00742188
$706$	78.3786	+	579.258i	0.111018	+	0.820479i
$707$			546.697i			0.773263i
$708$	95.5294	−	26.3340i	0.134929	−	0.0371950i
$709$	−1292.74			−1.82333			−0.911663	−	0.410938i	$-0.865201\pi$
$709$	−1292.74			−1.82333			−0.911663	+	0.410938i	$0.865201\pi$
$710$	3.61997	−	0.489813i	0.00509855	−	0.000689878i
$711$		−	216.665i		−	0.304732i
$712$	309.932	+	726.013i	0.435298	+	1.01968i
$713$	−71.8705			−0.100800
$714$	−24.8000	−	183.284i	−0.0347338	−	0.256701i
$715$			8.30620i			0.0116171i
$716$	8.82615	+	32.0177i	0.0123270	+	0.0447175i
$717$	164.514			0.229448
$718$	515.950	−	69.8125i	0.718593	−	0.0972319i
$719$		−	750.529i		−	1.04385i	−0.852991	−	0.521926i	$-0.825214\pi$
$719$		−	750.529i		−	1.04385i	0.852991	−	0.521926i	$-0.174786\pi$
$720$	1.96971	−	1.17527i	0.00273571	−	0.00163232i
$721$	−322.575			−0.447400
$722$	16.6153	+	122.796i	0.0230129	+	0.170077i
$723$			543.890i			0.752268i
$724$	148.354	−	40.8959i	0.204909	−	0.0564861i
$725$	1373.48			1.89446
$726$	90.3160	−	12.2205i	0.124402	−	0.0168327i
$727$		−	1138.92i		−	1.56660i	−0.621644	−	0.783300i	$-0.713535\pi$
$727$		−	1138.92i		−	1.56660i	0.621644	−	0.783300i	$-0.286465\pi$
$728$	−455.144	+	194.299i	−0.625198	+	0.266895i
$729$	−27.0000			−0.0370370
$730$	−0.422647	−	3.12358i	−0.000578969	−	0.00427888i
$731$		−	60.9071i		−	0.0833202i
$732$	51.7459	+	187.713i	0.0706911	+	0.256439i
$733$	467.159			0.637325			0.318662	−	0.947868i	$-0.396766\pi$
$733$	467.159			0.637325			0.318662	+	0.947868i	$0.396766\pi$
$734$	−730.544	+	98.8489i	−0.995291	+	0.134672i
$735$			3.06298i			0.00416731i
$736$	120.056	−	95.5961i	0.163119	−	0.129886i
$737$	975.668			1.32384
$738$	39.3821	+	291.054i	0.0533632	+	0.394381i
$739$		−	732.224i		−	0.990831i	−0.868656	−	0.495416i	$-0.835016\pi$
$739$		−	732.224i		−	0.990831i	0.868656	−	0.495416i	$-0.164984\pi$
$740$	12.9757	−	3.57693i	0.0175347	−	0.00483369i
$741$	−535.035			−0.722045
$742$	−221.381	+	29.9548i	−0.298358	+	0.0403704i
$743$			534.020i			0.718735i	0.933196	+	0.359368i	$0.117008\pi$
$743$			534.020i			0.718735i	−0.933196	+	0.359368i	$0.882992\pi$
$744$	81.5280	+	190.979i	0.109581	+	0.256692i
$745$	8.77195			0.0117744
$746$	−117.775	−	870.421i	−0.157876	−	1.16678i
$747$		−	288.244i		−	0.385868i
$748$	159.480	+	578.531i	0.213209	+	0.773437i
$749$	51.5076			0.0687685
$750$	8.20154	−	1.10974i	0.0109354	−	0.00147965i
$751$			1001.88i			1.33406i	0.745029	+	0.667032i	$0.232435\pi$
$751$			1001.88i			1.33406i	−0.745029	+	0.667032i	$0.767565\pi$
$752$	518.286	+	868.632i	0.689211	+	1.15510i
$753$	−375.404			−0.498545
$754$	263.205	+	1945.22i	0.349078	+	2.57986i
$755$			9.17434i			0.0121514i
$756$	69.3896	−	19.1282i	0.0917852	−	0.0253019i
$757$	1388.43			1.83412			0.917059	−	0.398752i	$-0.130557\pi$
$757$	1388.43			1.83412			0.917059	+	0.398752i	$0.130557\pi$
$758$	449.342	−	60.7998i	0.592799	−	0.0802108i
$759$		−	80.8309i		−	0.106497i
$760$	−6.07992	+	2.59549i	−0.00799990	+	0.00341512i
$761$	−177.666			−0.233464			−0.116732	−	0.993163i	$-0.537242\pi$
$761$	−177.666			−0.233464			−0.116732	+	0.993163i	$0.537242\pi$
$762$	73.9350	+	546.418i	0.0970276	+	0.717084i
$763$		−	47.9242i		−	0.0628102i
$764$	359.926	+	1305.67i	0.471107	+	1.70899i
$765$	−2.21021			−0.00288916
$766$	−930.475	+	125.901i	−1.21472	+	0.164362i
$767$			255.491i			0.333104i
$768$	−390.212	−	210.577i	−0.508088	−	0.274189i
$769$	1013.17			1.31752			0.658759	−	0.752354i	$-0.271082\pi$
$769$	1013.17			1.31752			0.658759	+	0.752354i	$0.271082\pi$
$770$	0.431837	+	3.19150i	0.000560827	+	0.00414480i
$771$			366.626i			0.475521i
$772$	844.832	−	232.890i	1.09434	−	0.301671i
$773$	258.809			0.334811			0.167405	−	0.985888i	$-0.446461\pi$
$773$	258.809			0.334811			0.167405	+	0.985888i	$0.446461\pi$
$774$	23.4888	−	3.17824i	0.0303473	−	0.00410626i
$775$			374.617i			0.483376i
$776$	−111.612	−	261.450i	−0.143830	−	0.336920i
$777$	422.374			0.543596
$778$	−15.3204	−	113.225i	−0.0196920	−	0.145534i
$779$		−	846.502i		−	1.08665i
$780$	1.57162	+	5.70119i	0.00201489	+	0.00730922i
$781$	−371.941			−0.476236
$782$	−146.545	+	19.8289i	−0.187398	+	0.0253566i
$783$		−	285.499i		−	0.364622i
$784$	508.483	−	303.396i	0.648575	−	0.386985i
$785$	−4.51920			−0.00575695
$786$	−12.3266	−	91.0996i	−0.0156826	−	0.115903i
$787$			485.896i			0.617403i	0.951159	+	0.308701i	$0.0998944\pi$
$787$			485.896i			0.617403i	−0.951159	+	0.308701i	$0.900106\pi$
$788$	477.466	−	131.620i	0.605921	−	0.167031i
$789$	−28.8376			−0.0365495
$790$	6.83993	−	0.925501i	0.00865814	−	0.00117152i
$791$		−	38.8484i		−	0.0491130i
$792$	−214.789	+	91.6924i	−0.271198	+	0.115773i
$793$	−502.035			−0.633084
$794$	−2.80299	−	20.7155i	−0.00353021	−	0.0260901i
$795$			2.66962i			0.00335801i
$796$	−235.109	−	852.883i	−0.295363	−	1.07146i
$797$	−963.799			−1.20928			−0.604642	−	0.796498i	$-0.706684\pi$
$797$	−963.799			−1.20928			−0.604642	+	0.796498i	$0.706684\pi$
$798$	−205.577	+	27.8163i	−0.257615	+	0.0348575i
$799$		−	974.688i		−	1.21989i
$800$	−498.284	−	625.777i	−0.622855	−	0.782221i
$801$	296.025			0.369569
$802$	−22.4776	−	166.121i	−0.0280270	−	0.207134i
$803$			320.938i			0.399674i
$804$	669.677	−	184.606i	0.832932	−	0.229609i
$805$	−0.793624			−0.000985868
$806$	−530.557	+	71.7890i	−0.658260	+	0.0890682i
$807$		−	103.393i		−	0.128120i
$808$	−495.848	−	1161.52i	−0.613674	−	1.43753i
$809$	−1376.58			−1.70159			−0.850793	−	0.525502i	$-0.823878\pi$
$809$	−1376.58			−1.70159			−0.850793	+	0.525502i	$0.823878\pi$
$810$	−0.115333	−	0.852368i	−0.000142386	−	0.00105231i
$811$			523.632i			0.645662i	0.946457	+	0.322831i	$0.104635\pi$
$811$			523.632i			0.645662i	−0.946457	+	0.322831i	$0.895365\pi$
$812$	202.262	+	733.727i	0.249092	+	0.903605i
$813$	519.069			0.638461
$814$	−1358.07	+	183.759i	−1.66839	+	0.225748i
$815$			11.4577i			0.0140586i
$816$	218.928	+	366.916i	0.268294	+	0.449652i
$817$	−68.3150			−0.0836169
$818$	−19.1974	−	141.879i	−0.0234687	−	0.173446i
$819$			185.581i			0.226594i
$820$	−9.02010	+	2.48652i	−0.0110001	+	0.00303234i
$821$	47.6370			0.0580231			0.0290116	−	0.999579i	$-0.490764\pi$
$821$	47.6370			0.0580231			0.0290116	+	0.999579i	$0.490764\pi$
$822$	−758.152	+	102.585i	−0.922326	+	0.124799i
$823$			1283.93i			1.56006i	0.625740	+	0.780031i	$0.284797\pi$
$823$			1283.93i			1.56006i	−0.625740	+	0.780031i	$0.715203\pi$
$824$	685.349	−	292.573i	0.831734	−	0.355064i
$825$	−421.322			−0.510693
$826$	13.2829	+	98.1675i	0.0160810	+	0.118847i
$827$			433.877i			0.524639i	0.964981	+	0.262320i	$0.0844875\pi$
$827$			433.877i			0.524639i	−0.964981	+	0.262320i	$0.915512\pi$
$828$	−15.2940	−	55.4806i	−0.0184710	−	0.0670055i
$829$	548.822			0.662029			0.331014	−	0.943626i	$-0.392609\pi$
$829$	548.822			0.662029			0.331014	+	0.943626i	$0.392609\pi$
$830$	9.09962	−	1.23126i	0.0109634	−	0.00148344i
$831$		−	861.599i		−	1.03682i
$832$	790.779	−	825.623i	0.950456	−	0.992335i
$833$	−570.567			−0.684954
$834$	−76.9274	−	568.533i	−0.0922391	−	0.681694i
$835$		−	5.32530i		−	0.00637760i
$836$	648.896	−	178.878i	0.776192	−	0.213968i
$837$	77.8697			0.0930343
$838$	−1644.69	+	222.541i	−1.96264	+	0.265562i
$839$		−	821.014i		−	0.978562i	−0.872126	−	0.489281i	$-0.837259\pi$
$839$		−	821.014i		−	0.978562i	0.872126	−	0.489281i	$-0.162741\pi$
$840$	0.900266	+	2.10886i	0.00107174	+	0.00251055i
$841$	2177.87			2.58962
$842$	73.0427	+	539.823i	0.0867491	+	0.641120i
$843$			879.478i			1.04327i
$844$	−300.250	−	1089.19i	−0.355747	−	1.29051i
$845$	−7.17200			−0.00848757
$846$	375.889	−	50.8610i	0.444313	−	0.0601194i
$847$			91.1110i			0.107569i
$848$	443.182	−	264.433i	0.522620	−	0.311832i
$849$	896.648			1.05612
$850$	103.356	+	763.851i	0.121595	+	0.898648i
$851$		−	337.710i		−	0.396839i
$852$	−255.292	+	70.3748i	−0.299638	+	0.0825996i
$853$	−957.346			−1.12233			−0.561164	−	0.827705i	$-0.689646\pi$
$853$	−957.346			−1.12233			−0.561164	+	0.827705i	$0.689646\pi$
$854$	−192.897	+	26.1007i	−0.225875	+	0.0305628i
$855$			2.47903i			0.00289945i
$856$	−109.434	+	46.7169i	−0.127843	+	0.0545758i
$857$	−1131.68			−1.32051			−0.660257	−	0.751040i	$-0.729553\pi$
$857$	−1131.68			−1.32051			−0.660257	+	0.751040i	$0.729553\pi$
$858$	−80.7392	−	596.704i	−0.0941017	−	0.695460i
$859$		−	1046.03i		−	1.21773i	−0.793276	−	0.608863i	$-0.791626\pi$
$859$		−	1046.03i		−	1.21773i	0.793276	−	0.608863i	$-0.208374\pi$
$860$	0.200669	+	0.727947i	0.000233336	+	0.000846450i
$861$	−293.615			−0.341017
$862$	1210.23	−	163.754i	1.40397	−	0.189970i
$863$		−	594.072i		−	0.688380i	−0.938900	−	0.344190i	$-0.888154\pi$
$863$		−	594.072i		−	0.688380i	0.938900	−	0.344190i	$-0.111846\pi$
$864$	−130.077	+	103.576i	−0.150552	+	0.119879i
$865$	−1.50228			−0.00173673
$866$	−77.6196	−	573.649i	−0.0896300	−	0.662412i
$867$			88.8480i			0.102477i
$868$	−200.124	+	55.1670i	−0.230558	+	0.0635565i
$869$	−702.781			−0.808724
$870$	9.01296	−	1.21953i	0.0103597	−	0.00140176i
$871$			1791.04i			2.05630i
$872$	43.4668	+	101.820i	0.0498472	+	0.116767i
$873$	−106.604			−0.122112
$874$	22.2406	+	164.369i	0.0254469	+	0.188066i
$875$			8.27372i			0.00945569i
$876$	60.7246	+	220.285i	0.0693203	+	0.251467i
$877$	−180.048			−0.205299			−0.102650	−	0.994718i	$-0.532732\pi$
$877$	−180.048			−0.205299			−0.102650	+	0.994718i	$0.532732\pi$
$878$	443.333	−	59.9867i	0.504935	−	0.0683220i
$879$		−	487.346i		−	0.554432i
$880$	−3.81214	−	6.38903i	−0.00433198	−	0.00726026i
$881$	902.358			1.02424			0.512121	−	0.858913i	$-0.328860\pi$
$881$	902.358			1.02424			0.512121	+	0.858913i	$0.328860\pi$
$882$	−29.7732	−	220.039i	−0.0337565	−	0.249478i
$883$			524.469i			0.593963i	0.954883	+	0.296981i	$0.0959800\pi$
$883$			524.469i			0.593963i	−0.954883	+	0.296981i	$0.904020\pi$
$884$	−1062.01	+	292.758i	−1.20137	+	0.331175i
$885$	1.18379			0.00133762
$886$	−1269.08	+	171.718i	−1.43237	+	0.193813i
$887$			1096.94i			1.23669i	0.785907	+	0.618345i	$0.212196\pi$
$887$			1096.94i			1.23669i	−0.785907	+	0.618345i	$0.787804\pi$
$888$	−897.382	+	383.089i	−1.01057	+	0.431406i
$889$	−551.227			−0.620053
$890$	1.26450	+	9.34527i	0.00142078	+	0.0105003i
$891$			87.5781i			0.0982919i
$892$	−69.1682	−	250.915i	−0.0775428	−	0.281294i
$893$	−1093.24			−1.22423
$894$	−630.163	+	85.2665i	−0.704881	+	0.0953764i
$895$			0.396761i			0.000443309i
$896$	260.918	−	358.342i	0.291203	−	0.399935i
$897$	148.381			0.165420
$898$	7.91196	+	58.4734i	0.00881064	+	0.0651152i
$899$			823.397i			0.915903i
$900$	−289.186	+	79.7183i	−0.321318	+	0.0885758i
$901$	−497.293			−0.551934
$902$	944.071	−	127.741i	1.04664	−	0.141620i
$903$			23.6956i			0.0262409i
$904$	35.2351	+	82.5380i	0.0389769	+	0.0913031i
$905$	1.83839			0.00203137
$906$	−89.1779	−	659.070i	−0.0984303	−	0.727451i
$907$		−	1161.30i		−	1.28038i	−0.768217	−	0.640189i	$-0.778856\pi$
$907$		−	1161.30i		−	1.28038i	0.768217	−	0.640189i	$-0.221144\pi$
$908$	−240.901	−	873.892i	−0.265309	−	0.962436i
$909$	−473.599			−0.521011
$910$	−5.85863	+	0.792724i	−0.00643806	+	0.000871125i
$911$			1162.02i			1.27555i	0.770224	+	0.637774i	$0.220144\pi$
$911$			1162.02i			1.27555i	−0.770224	+	0.637774i	$0.779856\pi$
$912$	411.543	−	245.555i	0.451253	−	0.269249i
$913$	−934.957			−1.02405
$914$	−126.198	−	932.664i	−0.138072	−	1.02042i
$915$			2.32613i			0.00254222i
$916$	−515.830	+	142.196i	−0.563133	+	0.155236i
$917$	91.9014			0.100220
$918$	158.778	−	21.4840i	0.172961	−	0.0234031i
$919$		−	226.473i		−	0.246434i	−0.992380	−	0.123217i	$-0.960679\pi$
$919$		−	226.473i		−	0.246434i	0.992380	−	0.123217i	$-0.0393212\pi$
$920$	1.68615	−	0.719809i	0.00183277	−	0.000782401i
$921$	317.027			0.344220
$922$	50.9550	+	376.583i	0.0552657	+	0.408442i
$923$		−	682.772i		−	0.739731i
$924$	−62.0450	−	225.074i	−0.0671482	−	0.243587i
$925$	−1760.27			−1.90300
$926$	−595.399	+	80.5626i	−0.642979	+	0.0870007i
$927$		−	279.445i		−	0.301451i
$928$	−1095.21	−	1375.44i	−1.18019	−	1.48215i
$929$	783.472			0.843349			0.421675	−	0.906747i	$-0.361442\pi$
$929$	783.472			0.843349			0.421675	+	0.906747i	$0.361442\pi$
$930$	0.332627	+	2.45828i	0.000357663	+	0.00264332i
$931$			639.963i			0.687394i
$932$	113.960	−	31.4147i	0.122275	−	0.0337067i
$933$	1018.21			1.09133
$934$	−448.909	+	60.7413i	−0.480631	+	0.0650335i
$935$			7.16911i			0.00766750i
$936$	−168.320	−	394.288i	−0.179829	−	0.421248i
$937$	606.692			0.647483			0.323742	−	0.946146i	$-0.395059\pi$
$937$	606.692			0.647483			0.323742	+	0.946146i	$0.395059\pi$
$938$	93.1154	+	688.170i	0.0992701	+	0.733657i
$939$		−	468.063i		−	0.498470i
$940$	3.21128	+	11.6492i	0.00341626	+	0.0123928i
$941$	−1765.65			−1.87635			−0.938177	−	0.346155i	$-0.887487\pi$
$941$	−1765.65			−1.87635			−0.938177	+	0.346155i	$0.887487\pi$
$942$	324.652	−	43.9283i	0.344642	−	0.0466330i
$943$			234.761i			0.248951i
$944$	−117.258	−	196.521i	−0.124214	−	0.208179i
$945$	0.859870			0.000909915
$946$	−10.3091	−	76.1892i	−0.0108975	−	0.0805382i
$947$		−	1465.61i		−	1.54763i	−0.633411	−	0.773816i	$-0.718346\pi$
$947$		−	1465.61i		−	1.54763i	0.633411	−	0.773816i	$-0.281654\pi$
$948$	−482.373	+	132.973i	−0.508833	+	0.140267i
$949$	−589.146			−0.620807
$950$	856.756	−	115.926i	0.901849	−	0.122028i
$951$			236.405i			0.248586i
$952$	−392.836	+	167.700i	−0.412643	+	0.176156i
$953$	1423.94			1.49416			0.747082	−	0.664732i	$-0.231454\pi$
$953$	1423.94			1.49416			0.747082	+	0.664732i	$0.231454\pi$
$954$	−25.9496	−	191.781i	−0.0272009	−	0.201028i
$955$			16.1797i			0.0169421i
$956$	−100.967	−	366.268i	−0.105614	−	0.383126i
$957$	−926.053			−0.967663
$958$	1593.73	−	215.646i	1.66360	−	0.225100i
$959$		−	764.825i		−	0.797523i
$960$	−3.82544	−	3.66400i	−0.00398483	−	0.00381666i
$961$	736.419			0.766305
$962$	−337.327	−	2493.02i	−0.350651	−	2.59149i
$963$			44.6207i			0.0463351i
$964$	1210.89	−	333.800i	1.25611	−	0.346266i
$965$	10.4691			0.0108488
$966$	57.0127	−	7.71431i	0.0590193	−	0.00798583i
$967$			800.118i			0.827423i	0.910408	+	0.413711i	$0.135768\pi$
$967$			800.118i			0.827423i	−0.910408	+	0.413711i	$0.864232\pi$
$968$	−82.6367	−	193.576i	−0.0853685	−	0.199975i
$969$	−461.791			−0.476564
$970$	−0.455366	−	3.36539i	−0.000469450	−	0.00346947i
$971$			221.431i			0.228044i	0.993478	+	0.114022i	$0.0363734\pi$
$971$			221.431i			0.228044i	−0.993478	+	0.114022i	$0.963627\pi$
$972$	16.5706	+	60.1117i	0.0170480	+	0.0618433i
$973$	573.537			0.589452
$974$	−793.902	+	107.422i	−0.815094	+	0.110289i
$975$		−	773.421i		−	0.793253i
$976$	386.160	−	230.410i	0.395655	−	0.236076i
$977$	−633.198			−0.648105			−0.324052	−	0.946039i	$-0.605045\pi$
$977$	−633.198			−0.648105			−0.324052	+	0.946039i	$0.605045\pi$
$978$	−111.373	−	823.105i	−0.113879	−	0.841621i
$979$		−	960.197i		−	0.980793i
$980$	6.81928	−	1.87983i	0.00695845	−	0.00191820i
$981$	41.5164			0.0423204
$982$	−61.6049	+	8.33568i	−0.0627342	+	0.00848847i
$983$			1826.46i			1.85804i	0.370025	+	0.929022i	$0.379349\pi$
$983$			1826.46i			1.85804i	−0.370025	+	0.929022i	$0.620651\pi$
$984$	623.820	−	266.306i	0.633963	−	0.270636i
$985$	5.91671			0.00600682
$986$	227.173	+	1678.92i	0.230398	+	1.70276i
$987$			379.197i			0.384192i
$988$	328.366	+	1191.18i	0.332354	+	1.20565i
$989$	18.9458			0.0191566
$990$	−2.76477	+	0.374097i	−0.00279270	+	0.000377876i
$991$			1030.70i			1.04006i	0.854149	+	0.520028i	$0.174078\pi$
$991$			1030.70i			1.04006i	−0.854149	+	0.520028i	$0.825922\pi$
$992$	375.151	−	298.719i	0.378176	−	0.301128i
$993$	422.601			0.425580
$994$	−35.4971	−	262.342i	−0.0357114	−	0.263925i
$995$		−	10.5689i		−	0.0106220i
$996$	−641.734	+	176.903i	−0.644311	+	0.177613i
$997$	17.9073			0.0179612			0.00898061	−	0.999960i	$-0.497141\pi$
$997$	17.9073			0.0179612			0.00898061	+	0.999960i	$0.497141\pi$
$998$	941.113	−	127.341i	0.942999	−	0.127596i
$999$			365.899i			0.366266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.3.f.b.139.20	yes	40
4.3	odd	2	inner	276.3.f.b.139.19	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.3.f.b.139.19	✓	40	4.3	odd	2	inner
276.3.f.b.139.20	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	276.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.268173 + 1.98194i) q^{2} -1.73205i q^{3} +(-3.85617 + 1.06301i) q^{4} -0.0477853 q^{5} +(3.43282 - 0.464490i) q^{6} +3.46303i q^{7} +(-3.14094 - 7.35762i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.268173 + 1.98194i) q^{2} -1.73205i q^{3} +(-3.85617 + 1.06301i) q^{4} -0.0477853 q^{5} +(3.43282 - 0.464490i) q^{6} +3.46303i q^{7} +(-3.14094 - 7.35762i) q^{8} -3.00000 q^{9} +(-0.0128147 - 0.0947075i) q^{10} +9.73090i q^{11} +(1.84118 + 6.67908i) q^{12} -17.8630 q^{13} +(-6.86352 + 0.928694i) q^{14} +0.0827666i q^{15} +(13.7400 - 8.19826i) q^{16} -15.4176 q^{17} +(-0.804520 - 5.94582i) q^{18} +17.2928i q^{19} +(0.184268 - 0.0507961i) q^{20} +5.99815 q^{21} +(-19.2861 + 2.60957i) q^{22} -4.79583i q^{23} +(-12.7438 + 5.44026i) q^{24} -24.9977 q^{25} +(-4.79039 - 35.4034i) q^{26} +5.19615i q^{27} +(-3.68123 - 13.3540i) q^{28} -54.9443 q^{29} +(-0.164038 + 0.0221958i) q^{30} -14.9860i q^{31} +(19.9332 + 25.0334i) q^{32} +16.8544 q^{33} +(-4.13460 - 30.5568i) q^{34} -0.165482i q^{35} +(11.5685 - 3.18902i) q^{36} +70.4174 q^{37} +(-34.2734 + 4.63748i) q^{38} +30.9397i q^{39} +(0.150091 + 0.351586i) q^{40} -48.9510 q^{41} +(1.60854 + 11.8880i) q^{42} +3.95048i q^{43} +(-10.3440 - 37.5240i) q^{44} +0.143356 q^{45} +(9.50505 - 1.28611i) q^{46} +63.2190i q^{47} +(-14.1998 - 23.7984i) q^{48} +37.0074 q^{49} +(-6.70372 - 49.5440i) q^{50} +26.7041i q^{51} +(68.8828 - 18.9885i) q^{52} +32.2548 q^{53} +(-10.2985 + 1.39347i) q^{54} -0.464994i q^{55} +(25.4797 - 10.8772i) q^{56} +29.9521 q^{57} +(-14.7346 - 108.896i) q^{58} -14.3028i q^{59} +(-0.0879814 - 0.319162i) q^{60} +28.1047 q^{61} +(29.7014 - 4.01886i) q^{62} -10.3891i q^{63} +(-44.2690 + 46.2196i) q^{64} +0.853590 q^{65} +(4.51991 + 33.4044i) q^{66} -100.265i q^{67} +(59.4530 - 16.3891i) q^{68} -8.30662 q^{69} +(0.327975 - 0.0443779i) q^{70} +38.2226i q^{71} +(9.42281 + 22.0728i) q^{72} +32.9813 q^{73} +(18.8841 + 139.563i) q^{74} +43.2973i q^{75} +(-18.3824 - 66.6841i) q^{76} -33.6984 q^{77} +(-61.3206 + 8.29720i) q^{78} +72.2216i q^{79} +(-0.656571 + 0.391756i) q^{80} +9.00000 q^{81} +(-13.1274 - 97.0178i) q^{82} +96.0812i q^{83} +(-23.1299 + 6.37608i) q^{84} +0.736736 q^{85} +(-7.82961 + 1.05941i) q^{86} +95.1663i q^{87} +(71.5962 - 30.5641i) q^{88} -98.6750 q^{89} +(0.0384442 + 0.284123i) q^{90} -61.8603i q^{91} +(5.09800 + 18.4935i) q^{92} -25.9566 q^{93} +(-125.296 + 16.9537i) q^{94} -0.826344i q^{95} +(43.3590 - 34.5253i) q^{96} +35.5346 q^{97} +(9.92440 + 73.3464i) q^{98} -29.1927i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

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