LMFDB - Embedded newform 1140.2.b.c.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1140,2,Mod(151,1140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1140, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1140.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1140.b (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:	$9.10294583043$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} - x^{16} + 3 x^{15} - x^{14} - x^{13} - x^{12} - x^{11} + 6 x^{10} - 4 x^{9} + \cdots + 512 $ x^18 - x^17 - x^16 + 3x^15 - x^14 - x^13 - x^12 - x^11 + 6x^10 - 4x^9 + 12x^8 - 4x^7 - 8x^6 - 16x^5 - 32x^4 + 192x^3 - 128x^2 - 256*x + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.5
Root			$0.891738 - 1.09763i$ of defining polynomial
Character	$\chi$	$=$	1140.151
Dual form			1140.2.b.c.151.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891738 - 1.09763i) q^{2} -1.00000 q^{3} +(-0.409605 + 1.95761i) q^{4} -1.00000 q^{5} +(0.891738 + 1.09763i) q^{6} -1.17043i q^{7} +(2.51400 - 1.29608i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.891738 - 1.09763i) q^{2} -1.00000 q^{3} +(-0.409605 + 1.95761i) q^{4} -1.00000 q^{5} +(0.891738 + 1.09763i) q^{6} -1.17043i q^{7} +(2.51400 - 1.29608i) q^{8} +1.00000 q^{9} +(0.891738 + 1.09763i) q^{10} +3.13926i q^{11} +(0.409605 - 1.95761i) q^{12} -3.97396i q^{13} +(-1.28471 + 1.04372i) q^{14} +1.00000 q^{15} +(-3.66445 - 1.60369i) q^{16} -3.09629 q^{17} +(-0.891738 - 1.09763i) q^{18} +(1.39920 + 4.12822i) q^{19} +(0.409605 - 1.95761i) q^{20} +1.17043i q^{21} +(3.44576 - 2.79940i) q^{22} +0.396883i q^{23} +(-2.51400 + 1.29608i) q^{24} +1.00000 q^{25} +(-4.36196 + 3.54374i) q^{26} -1.00000 q^{27} +(2.29124 + 0.479414i) q^{28} -1.25128i q^{29} +(-0.891738 - 1.09763i) q^{30} -4.36145 q^{31} +(1.50746 + 5.45230i) q^{32} -3.13926i q^{33} +(2.76108 + 3.39860i) q^{34} +1.17043i q^{35} +(-0.409605 + 1.95761i) q^{36} -5.87132i q^{37} +(3.28356 - 5.21711i) q^{38} +3.97396i q^{39} +(-2.51400 + 1.29608i) q^{40} +4.20164i q^{41} +(1.28471 - 1.04372i) q^{42} +0.543447i q^{43} +(-6.14544 - 1.28586i) q^{44} -1.00000 q^{45} +(0.435632 - 0.353915i) q^{46} +13.0439i q^{47} +(3.66445 + 1.60369i) q^{48} +5.63009 q^{49} +(-0.891738 - 1.09763i) q^{50} +3.09629 q^{51} +(7.77946 + 1.62776i) q^{52} +7.43354i q^{53} +(0.891738 + 1.09763i) q^{54} -3.13926i q^{55} +(-1.51697 - 2.94246i) q^{56} +(-1.39920 - 4.12822i) q^{57} +(-1.37345 + 1.11581i) q^{58} +11.5951 q^{59} +(-0.409605 + 1.95761i) q^{60} +4.96696 q^{61} +(3.88928 + 4.78729i) q^{62} -1.17043i q^{63} +(4.64037 - 6.51667i) q^{64} +3.97396i q^{65} +(-3.44576 + 2.79940i) q^{66} +16.2343 q^{67} +(1.26826 - 6.06132i) q^{68} -0.396883i q^{69} +(1.28471 - 1.04372i) q^{70} -9.75420 q^{71} +(2.51400 - 1.29608i) q^{72} +16.3058 q^{73} +(-6.44456 + 5.23568i) q^{74} -1.00000 q^{75} +(-8.65456 + 1.04814i) q^{76} +3.67429 q^{77} +(4.36196 - 3.54374i) q^{78} +3.53913 q^{79} +(3.66445 + 1.60369i) q^{80} +1.00000 q^{81} +(4.61186 - 3.74676i) q^{82} -5.79825i q^{83} +(-2.29124 - 0.479414i) q^{84} +3.09629 q^{85} +(0.596507 - 0.484613i) q^{86} +1.25128i q^{87} +(4.06872 + 7.89210i) q^{88} +16.9120i q^{89} +(0.891738 + 1.09763i) q^{90} -4.65125 q^{91} +(-0.776940 - 0.162565i) q^{92} +4.36145 q^{93} +(14.3174 - 11.6317i) q^{94} +(-1.39920 - 4.12822i) q^{95} +(-1.50746 - 5.45230i) q^{96} +11.8020i q^{97} +(-5.02057 - 6.17979i) q^{98} +3.13926i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{2} - 18 q^{3} + 3 q^{4} - 18 q^{5} + q^{6} + 5 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - q^2 - 18 * q^3 + 3 * q^4 - 18 * q^5 + q^6 + 5 * q^8 + 18 * q^9	$ 18 q - q^{2} - 18 q^{3} + 3 q^{4} - 18 q^{5} + q^{6} + 5 q^{8} + 18 q^{9} + q^{10} - 3 q^{12} + 18 q^{15} - q^{16} - 20 q^{17} - q^{18} - 8 q^{19} - 3 q^{20} + 32 q^{22} - 5 q^{24} + 18 q^{25} + 18 q^{26} - 18 q^{27} - 4 q^{28} - q^{30} + 16 q^{31} + 9 q^{32} - 22 q^{34} + 3 q^{36} - 21 q^{38} - 5 q^{40} + 16 q^{44} - 18 q^{45} - 26 q^{46} + q^{48} - 42 q^{49} - q^{50} + 20 q^{51} - 6 q^{52} + q^{54} - 4 q^{56} + 8 q^{57} - 34 q^{58} - 32 q^{59} + 3 q^{60} - 4 q^{61} + 36 q^{62} + 15 q^{64} - 32 q^{66} + 34 q^{68} - 16 q^{71} + 5 q^{72} + 20 q^{73} + 26 q^{74} - 18 q^{75} + 3 q^{76} + 16 q^{77} - 18 q^{78} - 16 q^{79} + q^{80} + 18 q^{81} - 34 q^{82} + 4 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + q^{90} - 8 q^{91} - 6 q^{92} - 16 q^{93} + 22 q^{94} + 8 q^{95} - 9 q^{96} + 65 q^{98}+O(q^{100}) $ 18 * q - q^2 - 18 * q^3 + 3 * q^4 - 18 * q^5 + q^6 + 5 * q^8 + 18 * q^9 + q^10 - 3 * q^12 + 18 * q^15 - q^16 - 20 * q^17 - q^18 - 8 * q^19 - 3 * q^20 + 32 * q^22 - 5 * q^24 + 18 * q^25 + 18 * q^26 - 18 * q^27 - 4 * q^28 - q^30 + 16 * q^31 + 9 * q^32 - 22 * q^34 + 3 * q^36 - 21 * q^38 - 5 * q^40 + 16 * q^44 - 18 * q^45 - 26 * q^46 + q^48 - 42 * q^49 - q^50 + 20 * q^51 - 6 * q^52 + q^54 - 4 * q^56 + 8 * q^57 - 34 * q^58 - 32 * q^59 + 3 * q^60 - 4 * q^61 + 36 * q^62 + 15 * q^64 - 32 * q^66 + 34 * q^68 - 16 * q^71 + 5 * q^72 + 20 * q^73 + 26 * q^74 - 18 * q^75 + 3 * q^76 + 16 * q^77 - 18 * q^78 - 16 * q^79 + q^80 + 18 * q^81 - 34 * q^82 + 4 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + q^90 - 8 * q^91 - 6 * q^92 - 16 * q^93 + 22 * q^94 + 8 * q^95 - 9 * q^96 + 65 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1140\mathbb{Z}\right)^\times$.

$n$	$457$	$571$	$761$	$781$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	−0.891738	−	1.09763i	−0.630554	−	0.776145i
$2$	−0.891738	−	1.09763i	−0.630554	−	0.776145i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.409605	+	1.95761i	−0.204803	+	0.978803i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.891738	+	1.09763i	0.364051	+	0.448108i
$7$		−	1.17043i		−	0.442381i	−0.975231	−	0.221191i	$-0.929006\pi$
$7$		−	1.17043i		−	0.442381i	0.975231	−	0.221191i	$-0.0709943\pi$
$8$	2.51400	−	1.29608i	0.888833	−	0.458232i
$9$	1.00000			0.333333
$10$	0.891738	+	1.09763i	0.281992	+	0.347103i
$11$			3.13926i			0.946523i	0.880922	+	0.473261i	$0.156923\pi$
$11$			3.13926i			0.946523i	−0.880922	+	0.473261i	$0.843077\pi$
$12$	0.409605	−	1.95761i	0.118243	−	0.565112i
$13$		−	3.97396i		−	1.10218i	−0.834446	−	0.551090i	$-0.814212\pi$
$13$		−	3.97396i		−	1.10218i	0.834446	−	0.551090i	$-0.185788\pi$
$14$	−1.28471	+	1.04372i	−0.343352	+	0.278945i
$15$	1.00000			0.258199
$16$	−3.66445	−	1.60369i	−0.916112	−	0.400923i
$17$	−3.09629			−0.750961			−0.375480	−	0.926830i	$-0.622522\pi$
$17$	−3.09629			−0.750961			−0.375480	+	0.926830i	$0.622522\pi$
$18$	−0.891738	−	1.09763i	−0.210185	−	0.258715i
$19$	1.39920	+	4.12822i	0.320998	+	0.947080i
$19$	1.39920	+	4.12822i	0.320998	+	0.947080i
$20$	0.409605	−	1.95761i	0.0915905	−	0.437734i
$21$			1.17043i			0.255409i
$22$	3.44576	−	2.79940i	0.734639	−	0.596834i
$23$			0.396883i			0.0827557i	0.999144	+	0.0413779i	$0.0131747\pi$
$23$			0.396883i			0.0827557i	−0.999144	+	0.0413779i	$0.986825\pi$
$24$	−2.51400	+	1.29608i	−0.513168	+	0.264560i
$25$	1.00000			0.200000
$26$	−4.36196	+	3.54374i	−0.855451	+	0.694984i
$27$	−1.00000			−0.192450
$28$	2.29124	+	0.479414i	0.433004	+	0.0906008i
$29$		−	1.25128i		−	0.232357i	−0.993228	−	0.116178i	$-0.962936\pi$
$29$		−	1.25128i		−	0.232357i	0.993228	−	0.116178i	$-0.0370644\pi$
$30$	−0.891738	−	1.09763i	−0.162808	−	0.200400i
$31$	−4.36145			−0.783340			−0.391670	−	0.920106i	$-0.628103\pi$
$31$	−4.36145			−0.783340			−0.391670	+	0.920106i	$0.628103\pi$
$32$	1.50746	+	5.45230i	0.266484	+	0.963839i
$33$		−	3.13926i		−	0.546475i
$34$	2.76108	+	3.39860i	0.473521	+	0.582854i
$35$			1.17043i			0.197839i
$36$	−0.409605	+	1.95761i	−0.0682675	+	0.326268i
$37$		−	5.87132i		−	0.965239i	−0.875830	−	0.482619i	$-0.839685\pi$
$37$		−	5.87132i		−	0.965239i	0.875830	−	0.482619i	$-0.160315\pi$
$38$	3.28356	−	5.21711i	0.532664	−	0.846327i
$39$			3.97396i			0.636344i
$40$	−2.51400	+	1.29608i	−0.397498	+	0.204928i
$41$			4.20164i			0.656186i	0.944646	+	0.328093i	$0.106406\pi$
$41$			4.20164i			0.656186i	−0.944646	+	0.328093i	$0.893594\pi$
$42$	1.28471	−	1.04372i	0.198234	−	0.161049i
$43$			0.543447i			0.0828750i	0.999141	+	0.0414375i	$0.0131937\pi$
$43$			0.543447i			0.0828750i	−0.999141	+	0.0414375i	$0.986806\pi$
$44$	−6.14544	−	1.28586i	−0.926460	−	0.193850i
$45$	−1.00000			−0.149071
$46$	0.435632	−	0.353915i	0.0642305	−	0.0521820i
$47$			13.0439i			1.90264i	0.308198	+	0.951322i	$0.400274\pi$
$47$			13.0439i			1.90264i	−0.308198	+	0.951322i	$0.599726\pi$
$48$	3.66445	+	1.60369i	0.528917	+	0.231473i
$49$	5.63009			0.804299
$50$	−0.891738	−	1.09763i	−0.126111	−	0.155229i
$51$	3.09629			0.433567
$52$	7.77946	+	1.62776i	1.07882	+	0.225729i
$53$			7.43354i			1.02108i	0.859855	+	0.510538i	$0.170554\pi$
$53$			7.43354i			1.02108i	−0.859855	+	0.510538i	$0.829446\pi$
$54$	0.891738	+	1.09763i	0.121350	+	0.149369i
$55$		−	3.13926i		−	0.423298i
$56$	−1.51697	−	2.94246i	−0.202713	−	0.393203i
$57$	−1.39920	−	4.12822i	−0.185328	−	0.546797i
$58$	−1.37345	+	1.11581i	−0.180342	+	0.146513i
$59$	11.5951			1.50956			0.754778	−	0.655980i	$-0.227744\pi$
$59$	11.5951			1.50956			0.754778	+	0.655980i	$0.227744\pi$
$60$	−0.409605	+	1.95761i	−0.0528798	+	0.252726i
$61$	4.96696			0.635954			0.317977	−	0.948099i	$-0.396997\pi$
$61$	4.96696			0.635954			0.317977	+	0.948099i	$0.396997\pi$
$62$	3.88928	+	4.78729i	0.493939	+	0.607986i
$63$		−	1.17043i		−	0.147460i
$64$	4.64037	−	6.51667i	0.580047	−	0.814583i
$65$			3.97396i			0.492910i
$66$	−3.44576	+	2.79940i	−0.424144	+	0.344582i
$67$	16.2343			1.98334			0.991670	−	0.128801i	$-0.0411128\pi$
$67$	16.2343			1.98334			0.991670	+	0.128801i	$0.0411128\pi$
$68$	1.26826	−	6.06132i	0.153799	−	0.735043i
$69$		−	0.396883i		−	0.0477790i
$70$	1.28471	−	1.04372i	0.153552	−	0.124748i
$71$	−9.75420			−1.15761			−0.578806	−	0.815466i	$-0.696481\pi$
$71$	−9.75420			−1.15761			−0.578806	+	0.815466i	$0.696481\pi$
$72$	2.51400	−	1.29608i	0.296278	−	0.152744i
$73$	16.3058			1.90845			0.954225	−	0.299088i	$-0.0966825\pi$
$73$	16.3058			1.90845			0.954225	+	0.299088i	$0.0966825\pi$
$74$	−6.44456	+	5.23568i	−0.749165	+	0.608635i
$75$	−1.00000			−0.115470
$76$	−8.65456	+	1.04814i	−0.992746	+	0.120230i
$77$	3.67429			0.418724
$78$	4.36196	−	3.54374i	0.493895	−	0.401249i
$79$	3.53913			0.398183			0.199092	−	0.979981i	$-0.436201\pi$
$79$	3.53913			0.398183			0.199092	+	0.979981i	$0.436201\pi$
$80$	3.66445	+	1.60369i	0.409698	+	0.179298i
$81$	1.00000			0.111111
$82$	4.61186	−	3.74676i	0.509295	−	0.413761i
$83$		−	5.79825i		−	0.636441i	−0.948017	−	0.318220i	$-0.896915\pi$
$83$		−	5.79825i		−	0.636441i	0.948017	−	0.318220i	$-0.103085\pi$
$84$	−2.29124	−	0.479414i	−0.249995	−	0.0523084i
$85$	3.09629			0.335840
$86$	0.596507	−	0.484613i	0.0643230	−	0.0522572i
$87$			1.25128i			0.134151i
$88$	4.06872	+	7.89210i	0.433727	+	0.841300i
$89$			16.9120i			1.79267i	0.443382	+	0.896333i	$0.353778\pi$
$89$			16.9120i			1.79267i	−0.443382	+	0.896333i	$0.646222\pi$
$90$	0.891738	+	1.09763i	0.0939975	+	0.115701i
$91$	−4.65125			−0.487583
$92$	−0.776940	−	0.162565i	−0.0810016	−	0.0169486i
$93$	4.36145			0.452262
$94$	14.3174	−	11.6317i	1.47673	−	1.19972i
$95$	−1.39920	−	4.12822i	−0.143555	−	0.423547i
$96$	−1.50746	−	5.45230i	−0.153855	−	0.556473i
$97$			11.8020i			1.19831i	0.800634	+	0.599154i	$0.204496\pi$
$97$			11.8020i			1.19831i	−0.800634	+	0.599154i	$0.795504\pi$
$98$	−5.02057	−	6.17979i	−0.507154	−	0.624253i
$99$			3.13926i			0.315508i
$100$	−0.409605	+	1.95761i	−0.0409605	+	0.195761i
$101$	2.12111			0.211059			0.105529	−	0.994416i	$-0.466346\pi$
$101$	2.12111			0.211059			0.105529	+	0.994416i	$0.466346\pi$
$102$	−2.76108	−	3.39860i	−0.273388	−	0.336511i
$103$	−4.85962			−0.478833			−0.239416	−	0.970917i	$-0.576956\pi$
$103$	−4.85962			−0.478833			−0.239416	+	0.970917i	$0.576956\pi$
$104$	−5.15056	−	9.99054i	−0.505054	−	0.979653i
$105$		−	1.17043i		−	0.114222i
$106$	8.15932	−	6.62878i	0.792503	−	0.643844i
$107$	−2.40698			−0.232691			−0.116346	−	0.993209i	$-0.537118\pi$
$107$	−2.40698			−0.232691			−0.116346	+	0.993209i	$0.537118\pi$
$108$	0.409605	−	1.95761i	0.0394143	−	0.188371i
$109$			2.88193i			0.276039i	0.990429	+	0.138020i	$0.0440737\pi$
$109$			2.88193i			0.276039i	−0.990429	+	0.138020i	$0.955926\pi$
$110$	−3.44576	+	2.79940i	−0.328541	+	0.266912i
$111$			5.87132i			0.557281i
$112$	−1.87701	+	4.28898i	−0.177361	+	0.405271i
$113$		−	6.62143i		−	0.622892i	−0.950264	−	0.311446i	$-0.899187\pi$
$113$		−	6.62143i		−	0.622892i	0.950264	−	0.311446i	$-0.100813\pi$
$114$	−3.28356	+	5.21711i	−0.307534	+	0.488627i
$115$		−	0.396883i		−	0.0370095i
$116$	2.44951	+	0.512530i	0.227431	+	0.0475872i
$117$		−	3.97396i		−	0.367393i
$118$	−10.3398	−	12.7272i	−0.951857	−	1.17164i
$119$			3.62399i			0.332211i
$120$	2.51400	−	1.29608i	0.229496	−	0.118315i
$121$	1.14504			0.104094
$122$	−4.42923	−	5.45190i	−0.401003	−	0.493592i
$123$		−	4.20164i		−	0.378849i
$124$	1.78647	−	8.53801i	0.160430	−	0.766736i
$125$	−1.00000			−0.0894427
$126$	−1.28471	+	1.04372i	−0.114451	+	0.0929818i
$127$	−9.20537			−0.816845			−0.408422	−	0.912793i	$-0.633921\pi$
$127$	−9.20537			−0.816845			−0.408422	+	0.912793i	$0.633921\pi$
$128$	−11.2909	+	0.717726i	−0.997986	+	0.0634387i
$129$		−	0.543447i		−	0.0478479i
$130$	4.36196	−	3.54374i	0.382569	−	0.310806i
$131$			2.33709i			0.204192i	0.994775	+	0.102096i	$0.0325549\pi$
$131$			2.33709i			0.204192i	−0.994775	+	0.102096i	$0.967445\pi$
$132$	6.14544	+	1.28586i	0.534892	+	0.111920i
$133$	4.83180	−	1.63767i	0.418970	−	0.142004i
$134$	−14.4768	−	17.8194i	−1.25060	−	1.53936i
$135$	1.00000			0.0860663
$136$	−7.78407	+	4.01303i	−0.667478	+	0.344114i
$137$	13.1124			1.12027			0.560135	−	0.828401i	$-0.310749\pi$
$137$	13.1124			1.12027			0.560135	+	0.828401i	$0.310749\pi$
$138$	−0.435632	+	0.353915i	−0.0370835	+	0.0301273i
$139$			11.9583i			1.01429i	0.861861	+	0.507145i	$0.169299\pi$
$139$			11.9583i			1.01429i	−0.861861	+	0.507145i	$0.830701\pi$
$140$	−2.29124	−	0.479414i	−0.193645	−	0.0405179i
$141$		−	13.0439i		−	1.09849i
$142$	8.69820	+	10.7066i	0.729937	+	0.898474i
$143$	12.4753			1.04324
$144$	−3.66445	−	1.60369i	−0.305371	−	0.133641i
$145$			1.25128i			0.103913i
$146$	−14.5405	−	17.8978i	−1.20338	−	1.48123i
$147$	−5.63009			−0.464362
$148$	11.4937	+	2.40492i	0.944779	+	0.197683i
$149$	5.07903			0.416090			0.208045	−	0.978119i	$-0.433290\pi$
$149$	5.07903			0.416090			0.208045	+	0.978119i	$0.433290\pi$
$150$	0.891738	+	1.09763i	0.0728101	+	0.0896215i
$151$	−15.4021			−1.25341			−0.626703	−	0.779259i	$-0.715596\pi$
$151$	−15.4021			−1.25341			−0.626703	+	0.779259i	$0.715596\pi$
$152$	8.86808	+	8.56488i	0.719296	+	0.694704i
$153$	−3.09629			−0.250320
$154$	−3.27650	−	4.03303i	−0.264028	−	0.324991i
$155$	4.36145			0.350320
$156$	−7.77946	−	1.62776i	−0.622855	−	0.130325i
$157$	15.8201			1.26258			0.631291	−	0.775546i	$-0.282525\pi$
$157$	15.8201			1.26258			0.631291	+	0.775546i	$0.282525\pi$
$158$	−3.15598	−	3.88467i	−0.251076	−	0.309048i
$159$		−	7.43354i		−	0.589518i
$160$	−1.50746	−	5.45230i	−0.119175	−	0.431042i
$161$	0.464523			0.0366096
$162$	−0.891738	−	1.09763i	−0.0700616	−	0.0862383i
$163$			0.193191i			0.0151319i	0.999971	+	0.00756593i	$0.00240833\pi$
$163$			0.193191i			0.0151319i	−0.999971	+	0.00756593i	$0.997592\pi$
$164$	−8.22515	−	1.72101i	−0.642277	−	0.134388i
$165$			3.13926i			0.244391i
$166$	−6.36437	+	5.17053i	−0.493971	+	0.401311i
$167$	19.6611			1.52142			0.760712	−	0.649089i	$-0.224850\pi$
$167$	19.6611			1.52142			0.760712	+	0.649089i	$0.224850\pi$
$168$	1.51697	+	2.94246i	0.117037	+	0.227016i
$169$	−2.79239			−0.214800
$170$	−2.76108	−	3.39860i	−0.211765	−	0.260660i
$171$	1.39920	+	4.12822i	0.106999	+	0.315693i
$172$	−1.06386	−	0.222599i	−0.0811183	−	0.0169730i
$173$		−	3.77834i		−	0.287262i	−0.989631	−	0.143631i	$-0.954122\pi$
$173$		−	3.77834i		−	0.287262i	0.989631	−	0.143631i	$-0.0458778\pi$
$174$	1.37345	−	1.11581i	0.104121	−	0.0845896i
$175$		−	1.17043i		−	0.0884762i
$176$	5.03441	−	11.5037i	0.379483	−	0.867121i
$177$	−11.5951			−0.871543
$178$	18.5632	−	15.0811i	1.39137	−	1.13037i
$179$	0.263723			0.0197116			0.00985580	−	0.999951i	$-0.496863\pi$
$179$	0.263723			0.0197116			0.00985580	+	0.999951i	$0.496863\pi$
$180$	0.409605	−	1.95761i	0.0305302	−	0.145911i
$181$		−	14.2283i		−	1.05758i	−0.848752	−	0.528791i	$-0.822646\pi$
$181$		−	14.2283i		−	1.05758i	0.848752	−	0.528791i	$-0.177354\pi$
$182$	4.14770	+	5.10537i	0.307448	+	0.378435i
$183$	−4.96696			−0.367168
$184$	0.514390	+	0.997762i	0.0379213	+	0.0735560i
$185$			5.87132i			0.431668i
$186$	−3.88928	−	4.78729i	−0.285176	−	0.351021i
$187$		−	9.72006i		−	0.710801i
$188$	−25.5348	−	5.34284i	−1.86231	−	0.389666i
$189$			1.17043i			0.0851363i
$190$	−3.28356	+	5.21711i	−0.238215	+	0.378489i
$191$		−	6.79318i		−	0.491537i	−0.969329	−	0.245769i	$-0.920960\pi$
$191$		−	6.79318i		−	0.491537i	0.969329	−	0.245769i	$-0.0790404\pi$
$192$	−4.64037	+	6.51667i	−0.334890	+	0.470300i
$193$			16.9319i			1.21879i	0.792869	+	0.609393i	$0.208587\pi$
$193$			16.9319i			1.21879i	−0.792869	+	0.609393i	$0.791413\pi$
$194$	12.9542	−	10.5243i	0.930061	−	0.755598i
$195$		−	3.97396i		−	0.284582i
$196$	−2.30611	+	11.0215i	−0.164722	+	0.787250i
$197$	−23.5897			−1.68069			−0.840347	−	0.542048i	$-0.817649\pi$
$197$	−23.5897			−1.68069			−0.840347	+	0.542048i	$0.817649\pi$
$198$	3.44576	−	2.79940i	0.244880	−	0.198945i
$199$			18.6434i			1.32160i	0.750564	+	0.660798i	$0.229782\pi$
$199$			18.6434i			1.32160i	−0.750564	+	0.660798i	$0.770218\pi$
$200$	2.51400	−	1.29608i	0.177767	−	0.0916464i
$201$	−16.2343			−1.14508
$202$	−1.89148	−	2.32821i	−0.133084	−	0.163812i
$203$	−1.46453			−0.102790
$204$	−1.26826	+	6.06132i	−0.0887957	+	0.424377i
$205$		−	4.20164i		−	0.293455i
$206$	4.33351	+	5.33409i	0.301930	+	0.371644i
$207$			0.396883i			0.0275852i
$208$	−6.37301	+	14.5624i	−0.441889	+	1.00972i
$209$	−12.9596	+	4.39245i	−0.896433	+	0.303832i
$210$	−1.28471	+	1.04372i	−0.0886531	+	0.0720234i
$211$	−18.2006			−1.25298			−0.626491	−	0.779428i	$-0.715510\pi$
$211$	−18.2006			−1.25298			−0.626491	+	0.779428i	$0.715510\pi$
$212$	−14.5520	−	3.04482i	−0.999432	−	0.209119i
$213$	9.75420			0.668347
$214$	2.14639	+	2.64198i	0.146724	+	0.180602i
$215$		−	0.543447i		−	0.0370628i
$216$	−2.51400	+	1.29608i	−0.171056	+	0.0881868i
$217$			5.10478i			0.346535i
$218$	3.16331	−	2.56993i	0.214246	−	0.174058i
$219$	−16.3058			−1.10184
$220$	6.14544	+	1.28586i	0.414325	+	0.0866925i
$221$			12.3045i			0.827693i
$222$	6.44456	−	5.23568i	0.432531	−	0.351396i
$223$	−6.29777			−0.421730			−0.210865	−	0.977515i	$-0.567628\pi$
$223$	−6.29777			−0.421730			−0.210865	+	0.977515i	$0.567628\pi$
$224$	6.38154	−	1.76438i	0.426384	−	0.117887i
$225$	1.00000			0.0666667
$226$	−7.26792	+	5.90459i	−0.483455	+	0.392767i
$227$	3.09821			0.205636			0.102818	−	0.994700i	$-0.467214\pi$
$227$	3.09821			0.205636			0.102818	+	0.994700i	$0.467214\pi$
$228$	8.65456	−	1.04814i	0.573162	−	0.0694148i
$229$	18.6275			1.23094			0.615471	−	0.788160i	$-0.288966\pi$
$229$	18.6275			1.23094			0.615471	+	0.788160i	$0.288966\pi$
$230$	−0.435632	+	0.353915i	−0.0287247	+	0.0233365i
$231$	−3.67429			−0.241750
$232$	−1.62175	−	3.14571i	−0.106473	−	0.206526i
$233$	−9.15711			−0.599902			−0.299951	−	0.953955i	$-0.596970\pi$
$233$	−9.15711			−0.599902			−0.299951	+	0.953955i	$0.596970\pi$
$234$	−4.36196	+	3.54374i	−0.285150	+	0.231661i
$235$		−	13.0439i		−	0.850888i
$236$	−4.74942	+	22.6987i	−0.309161	+	1.47756i
$237$	−3.53913			−0.229891
$238$	3.97782	−	3.23165i	0.257844	−	0.209477i
$239$			14.4117i			0.932216i	0.884728	+	0.466108i	$0.154344\pi$
$239$			14.4117i			0.932216i	−0.884728	+	0.466108i	$0.845656\pi$
$240$	−3.66445	−	1.60369i	−0.236539	−	0.103518i
$241$			7.30810i			0.470756i	0.971904	+	0.235378i	$0.0756328\pi$
$241$			7.30810i			0.470756i	−0.971904	+	0.235378i	$0.924367\pi$
$242$	−1.02107	−	1.25683i	−0.0656371	−	0.0807922i
$243$	−1.00000			−0.0641500
$244$	−2.03449	+	9.72335i	−0.130245	+	0.622473i
$245$	−5.63009			−0.359693
$246$	−4.61186	+	3.74676i	−0.294042	+	0.238885i
$247$	16.4054	−	5.56037i	1.04385	−	0.353798i
$248$	−10.9647	+	5.65278i	−0.696258	+	0.358952i
$249$			5.79825i			0.367449i
$250$	0.891738	+	1.09763i	0.0563985	+	0.0694205i
$251$			6.59663i			0.416376i	0.978089	+	0.208188i	$0.0667566\pi$
$251$			6.59663i			0.416376i	−0.978089	+	0.208188i	$0.933243\pi$
$252$	2.29124	+	0.479414i	0.144335	+	0.0302003i
$253$	−1.24592			−0.0783302
$254$	8.20879	+	10.1041i	0.515065	+	0.633990i
$255$	−3.09629			−0.193897
$256$	10.8563	+	11.7533i	0.678522	+	0.734580i
$257$		−	5.17351i		−	0.322715i	−0.986896	−	0.161357i	$-0.948413\pi$
$257$		−	5.17351i		−	0.322715i	0.986896	−	0.161357i	$-0.0515872\pi$
$258$	−0.596507	+	0.484613i	−0.0371369	+	0.0301707i
$259$	−6.87197			−0.427003
$260$	−7.77946	−	1.62776i	−0.482462	−	0.100949i
$261$		−	1.25128i		−	0.0774522i
$262$	2.56527	−	2.08407i	0.158483	−	0.128754i
$263$			28.8491i			1.77891i	0.457022	+	0.889455i	$0.348916\pi$
$263$			28.8491i			1.77891i	−0.457022	+	0.889455i	$0.651084\pi$
$264$	−4.06872	−	7.89210i	−0.250413	−	0.485725i
$265$		−	7.43354i		−	0.456639i
$266$	−6.10626	−	3.84318i	−0.374399	−	0.235641i
$267$		−	16.9120i		−	1.03500i
$268$	−6.64967	+	31.7805i	−0.406193	+	1.94130i
$269$		−	12.0009i		−	0.731709i	−0.930672	−	0.365854i	$-0.880777\pi$
$269$		−	12.0009i		−	0.731709i	0.930672	−	0.365854i	$-0.119223\pi$
$270$	−0.891738	−	1.09763i	−0.0542695	−	0.0667999i
$271$		−	4.41695i		−	0.268311i	−0.990960	−	0.134155i	$-0.957168\pi$
$271$		−	4.41695i		−	0.268311i	0.990960	−	0.134155i	$-0.0428321\pi$
$272$	11.3462	+	4.96549i	0.687964	+	0.301077i
$273$	4.65125			0.281506
$274$	−11.6929	−	14.3927i	−0.706391	−	0.869493i
$275$			3.13926i			0.189305i
$276$	0.776940	+	0.162565i	0.0467663	+	0.00978527i
$277$	−31.8246			−1.91215			−0.956076	−	0.293119i	$-0.905307\pi$
$277$	−31.8246			−1.91215			−0.956076	+	0.293119i	$0.905307\pi$
$278$	13.1259	−	10.6637i	0.787236	−	0.639565i
$279$	−4.36145			−0.261113
$280$	1.51697	+	2.94246i	0.0906561	+	0.175846i
$281$			27.6843i			1.65151i	0.564030	+	0.825755i	$0.309250\pi$
$281$			27.6843i			1.65151i	−0.564030	+	0.825755i	$0.690750\pi$
$282$	−14.3174	+	11.6317i	−0.852589	+	0.692659i
$283$		−	0.779861i		−	0.0463579i	−0.999731	−	0.0231790i	$-0.992621\pi$
$283$		−	0.779861i		−	0.0463579i	0.999731	−	0.0231790i	$-0.00737875\pi$
$284$	3.99537	−	19.0949i	0.237082	−	1.13307i
$285$	1.39920	+	4.12822i	0.0828814	+	0.244535i
$286$	−11.1247	−	13.6933i	−0.657818	−	0.809704i
$287$	4.91772			0.290284
$288$	1.50746	+	5.45230i	0.0888280	+	0.321280i
$289$	−7.41299			−0.436058
$290$	1.37345	−	1.11581i	0.0806516	−	0.0655228i
$291$		−	11.8020i		−	0.691843i
$292$	−6.67894	+	31.9204i	−0.390856	+	1.86800i
$293$		−	0.203408i		−	0.0118832i	−0.999982	−	0.00594161i	$-0.998109\pi$
$293$		−	0.203408i		−	0.0118832i	0.999982	−	0.00594161i	$-0.00189128\pi$
$294$	5.02057	+	6.17979i	0.292806	+	0.360412i
$295$	−11.5951			−0.675094
$296$	−7.60967	−	14.7605i	−0.442303	−	0.857936i
$297$		−	3.13926i		−	0.182158i
$298$	−4.52917	−	5.57492i	−0.262368	−	0.322947i
$299$	1.57720			0.0912117
$300$	0.409605	−	1.95761i	0.0236486	−	0.113022i
$301$	0.636068			0.0366623
$302$	13.7346	+	16.9059i	0.790340	+	0.972824i
$303$	−2.12111			−0.121855
$304$	1.49311	−	17.3715i	0.0856355	−	0.996327i
$305$	−4.96696			−0.284407
$306$	2.76108	+	3.39860i	0.157840	+	0.194285i
$307$	−2.79704			−0.159636			−0.0798179	−	0.996809i	$-0.525434\pi$
$307$	−2.79704			−0.159636			−0.0798179	+	0.996809i	$0.525434\pi$
$308$	−1.50501	+	7.19281i	−0.0857557	+	0.409848i
$309$	4.85962			0.276454
$310$	−3.88928	−	4.78729i	−0.220896	−	0.271900i
$311$			3.60350i			0.204335i	0.994767	+	0.102168i	$0.0325778\pi$
$311$			3.60350i			0.204335i	−0.994767	+	0.102168i	$0.967422\pi$
$312$	5.15056	+	9.99054i	0.291593	+	0.565603i
$313$	13.9263			0.787163			0.393582	−	0.919290i	$-0.371236\pi$
$313$	13.9263			0.787163			0.393582	+	0.919290i	$0.371236\pi$
$314$	−14.1074	−	17.3647i	−0.796127	−	0.979948i
$315$			1.17043i			0.0659463i
$316$	−1.44965	+	6.92823i	−0.0815490	+	0.389743i
$317$		−	20.5047i		−	1.15166i	−0.817570	−	0.575830i	$-0.804679\pi$
$317$		−	20.5047i		−	1.15166i	0.817570	−	0.575830i	$-0.195321\pi$
$318$	−8.15932	+	6.62878i	−0.457552	+	0.371723i
$319$	3.92809			0.219931
$320$	−4.64037	+	6.51667i	−0.259405	+	0.364293i
$321$	2.40698			0.134344
$322$	−0.414233	−	0.509877i	−0.0230843	−	0.0284143i
$323$	−4.33233	−	12.7822i	−0.241057	−	0.711219i
$324$	−0.409605	+	1.95761i	−0.0227558	+	0.108756i
$325$		−	3.97396i		−	0.220436i
$326$	0.212053	−	0.172275i	0.0117445	−	0.00954145i
$327$		−	2.88193i		−	0.159371i
$328$	5.44564	+	10.5629i	0.300685	+	0.583239i
$329$	15.2669			0.841694
$330$	3.44576	−	2.79940i	0.189683	−	0.154102i
$331$	−23.3548			−1.28369			−0.641847	−	0.766832i	$-0.721832\pi$
$331$	−23.3548			−1.28369			−0.641847	+	0.766832i	$0.721832\pi$
$332$	11.3507	+	2.37499i	0.622951	+	0.130345i
$333$		−	5.87132i		−	0.321746i
$334$	−17.5326	−	21.5808i	−0.959341	−	1.18085i
$335$	−16.2343			−0.886977
$336$	1.87701	−	4.28898i	0.102399	−	0.233983i
$337$		−	11.5134i		−	0.627175i	−0.949559	−	0.313587i	$-0.898469\pi$
$337$		−	11.5134i		−	0.627175i	0.949559	−	0.313587i	$-0.101531\pi$
$338$	2.49008	+	3.06503i	0.135443	+	0.166716i
$339$			6.62143i			0.359627i
$340$	−1.26826	+	6.06132i	−0.0687808	+	0.328721i
$341$		−	13.6917i		−	0.741450i
$342$	3.28356	−	5.21711i	0.177555	−	0.282109i
$343$		−	14.7826i		−	0.798188i
$344$	0.704349	+	1.36623i	0.0379760	+	0.0736620i
$345$			0.396883i			0.0213674i
$346$	−4.14724	+	3.36929i	−0.222957	+	0.181134i
$347$		−	21.8079i		−	1.17071i	−0.810778	−	0.585354i	$-0.800956\pi$
$347$		−	21.8079i		−	1.17071i	0.810778	−	0.585354i	$-0.199044\pi$
$348$	−2.44951	−	0.512530i	−0.131308	−	0.0274745i
$349$	33.1288			1.77334			0.886672	−	0.462399i	$-0.153011\pi$
$349$	33.1288			1.77334			0.886672	+	0.462399i	$0.153011\pi$
$350$	−1.28471	+	1.04372i	−0.0686704	+	0.0557891i
$351$			3.97396i			0.212115i
$352$	−17.1162	+	4.73231i	−0.912296	+	0.252233i
$353$	−20.0876			−1.06915			−0.534577	−	0.845120i	$-0.679529\pi$
$353$	−20.0876			−1.06915			−0.534577	+	0.845120i	$0.679529\pi$
$354$	10.3398	+	12.7272i	0.549555	+	0.676444i
$355$	9.75420			0.517699
$356$	−33.1070	−	6.92723i	−1.75467	−	0.367142i
$357$		−	3.62399i		−	0.191802i
$358$	−0.235172	−	0.289472i	−0.0124292	−	0.0152991i
$359$		−	30.4684i		−	1.60806i	−0.594588	−	0.804030i	$-0.702685\pi$
$359$		−	30.4684i		−	1.60806i	0.594588	−	0.804030i	$-0.297315\pi$
$360$	−2.51400	+	1.29608i	−0.132499	+	0.0683092i
$361$	−15.0845	+	11.5524i	−0.793920	+	0.608022i
$362$	−15.6175	+	12.6879i	−0.820837	+	0.666863i
$363$	−1.14504			−0.0600988
$364$	1.90518	−	9.10532i	0.0998583	−	0.477248i
$365$	−16.3058			−0.853485
$366$	4.42923	+	5.45190i	0.231519	+	0.284976i
$367$		−	10.9037i		−	0.569170i	−0.958651	−	0.284585i	$-0.908144\pi$
$367$		−	10.9037i		−	0.569170i	0.958651	−	0.284585i	$-0.0918557\pi$
$368$	0.636477	−	1.45436i	0.0331787	−	0.0758135i
$369$			4.20164i			0.218729i
$370$	6.44456	−	5.23568i	0.335037	−	0.272190i
$371$	8.70045			0.451705
$372$	−1.78647	+	8.53801i	−0.0926244	+	0.442675i
$373$			18.5174i			0.958797i	0.877597	+	0.479399i	$0.159145\pi$
$373$			18.5174i			0.958797i	−0.877597	+	0.479399i	$0.840855\pi$
$374$	−10.6691	+	8.66775i	−0.551685	+	0.448199i
$375$	1.00000			0.0516398
$376$	16.9059	+	32.7923i	0.871853	+	1.69113i
$377$	−4.97254			−0.256099
$378$	1.28471	−	1.04372i	0.0660781	−	0.0536831i
$379$	25.8447			1.32755			0.663777	−	0.747931i	$-0.268953\pi$
$379$	25.8447			1.32755			0.663777	+	0.747931i	$0.268953\pi$
$380$	8.65456	−	1.04814i	0.443970	−	0.0537685i
$381$	9.20537			0.471606
$382$	−7.45643	+	6.05774i	−0.381504	+	0.309941i
$383$	−5.68429			−0.290454			−0.145227	−	0.989398i	$-0.546391\pi$
$383$	−5.68429			−0.290454			−0.145227	+	0.989398i	$0.546391\pi$
$384$	11.2909	−	0.717726i	0.576187	−	0.0366263i
$385$	−3.67429			−0.187259
$386$	18.5850	−	15.0988i	0.945954	−	0.768510i
$387$			0.543447i			0.0276250i
$388$	−23.1036	−	4.83414i	−1.17291	−	0.245416i
$389$	17.6467			0.894723			0.447361	−	0.894353i	$-0.352364\pi$
$389$	17.6467			0.894723			0.447361	+	0.894353i	$0.352364\pi$
$390$	−4.36196	+	3.54374i	−0.220877	+	0.179444i
$391$		−	1.22886i		−	0.0621463i
$392$	14.1540	−	7.29703i	0.714887	−	0.368556i
$393$		−	2.33709i		−	0.117890i
$394$	21.0358	+	25.8928i	1.05977	+	1.30446i
$395$	−3.53913			−0.178073
$396$	−6.14544	−	1.28586i	−0.308820	−	0.0646168i
$397$	−10.7173			−0.537884			−0.268942	−	0.963156i	$-0.586674\pi$
$397$	−10.7173			−0.537884			−0.268942	+	0.963156i	$0.586674\pi$
$398$	20.4637	−	16.6250i	1.02575	−	0.833338i
$399$	−4.83180	+	1.63767i	−0.241893	+	0.0819858i
$400$	−3.66445	−	1.60369i	−0.183222	−	0.0801846i
$401$			0.149076i			0.00744449i	0.999993	+	0.00372224i	$0.00118483\pi$
$401$			0.149076i			0.00744449i	−0.999993	+	0.00372224i	$0.998815\pi$
$402$	14.4768	+	17.8194i	0.722037	+	0.888750i
$403$			17.3323i			0.863382i
$404$	−0.868818	+	4.15230i	−0.0432253	+	0.206585i
$405$	−1.00000			−0.0496904
$406$	1.30598	+	1.60752i	0.0648148	+	0.0797801i
$407$	18.4316			0.913621
$408$	7.78407	−	4.01303i	0.385369	−	0.198674i
$409$		−	28.6492i		−	1.41661i	−0.705906	−	0.708305i	$-0.749460\pi$
$409$		−	28.6492i		−	1.41661i	0.705906	−	0.708305i	$-0.250540\pi$
$410$	−4.61186	+	3.74676i	−0.227764	+	0.185039i
$411$	−13.1124			−0.646789
$412$	1.99053	−	9.51323i	0.0980662	−	0.468683i
$413$		−	13.5713i		−	0.667799i
$414$	0.435632	−	0.353915i	0.0214102	−	0.0173940i
$415$			5.79825i			0.284625i
$416$	21.6672	−	5.99060i	1.06232	−	0.293713i
$417$		−	11.9583i		−	0.585601i
$418$	16.3779	+	10.3080i	0.801068	+	0.504179i
$419$			10.8711i			0.531087i	0.964099	+	0.265544i	$0.0855514\pi$
$419$			10.8711i			0.531087i	−0.964099	+	0.265544i	$0.914449\pi$
$420$	2.29124	+	0.479414i	0.111801	+	0.0233930i
$421$		−	4.65918i		−	0.227075i	−0.993534	−	0.113537i	$-0.963782\pi$
$421$		−	4.65918i		−	0.227075i	0.993534	−	0.113537i	$-0.0362181\pi$
$422$	16.2302	+	19.9776i	0.790074	+	0.972496i
$423$			13.0439i			0.634215i
$424$	9.63444	+	18.6879i	0.467890	+	0.907565i
$425$	−3.09629			−0.150192
$426$	−8.69820	−	10.7066i	−0.421429	−	0.518734i
$427$		−	5.81348i		−	0.281334i
$428$	0.985909	−	4.71191i	0.0476557	−	0.227759i
$429$	−12.4753			−0.602314
$430$	−0.596507	+	0.484613i	−0.0287661	+	0.0233701i
$431$	10.6517			0.513074			0.256537	−	0.966534i	$-0.417418\pi$
$431$	10.6517			0.513074			0.256537	+	0.966534i	$0.417418\pi$
$432$	3.66445	+	1.60369i	0.176306	+	0.0771576i
$433$			8.44211i			0.405702i	0.979210	+	0.202851i	$0.0650207\pi$
$433$			8.44211i			0.405702i	−0.979210	+	0.202851i	$0.934979\pi$
$434$	5.60318	−	4.55213i	0.268961	−	0.218509i
$435$		−	1.25128i		−	0.0599942i
$436$	−5.64169	−	1.18045i	−0.270188	−	0.0565335i
$437$	−1.63842	+	0.555318i	−0.0783763	+	0.0265645i
$438$	14.5405	+	17.8978i	0.694773	+	0.855191i
$439$	0.610242			0.0291253			0.0145626	−	0.999894i	$-0.495364\pi$
$439$	0.610242			0.0291253			0.0145626	+	0.999894i	$0.495364\pi$
$440$	−4.06872	−	7.89210i	−0.193969	−	0.376241i
$441$	5.63009			0.268100
$442$	13.5059	−	10.9724i	0.642410	−	0.521906i
$443$			22.8942i			1.08774i	0.839171	+	0.543868i	$0.183041\pi$
$443$			22.8942i			1.08774i	−0.839171	+	0.543868i	$0.816959\pi$
$444$	−11.4937	−	2.40492i	−0.545468	−	0.114133i
$445$		−	16.9120i		−	0.801704i
$446$	5.61596	+	6.91265i	0.265923	+	0.327323i
$447$	−5.07903			−0.240230
$448$	−7.62731	−	5.43123i	−0.360356	−	0.256602i
$449$			14.3870i			0.678965i	0.940612	+	0.339482i	$0.110252\pi$
$449$			14.3870i			0.678965i	−0.940612	+	0.339482i	$0.889748\pi$
$450$	−0.891738	−	1.09763i	−0.0420370	−	0.0517430i
$451$	−13.1900			−0.621095
$452$	12.9622	+	2.71217i	0.609689	+	0.127570i
$453$	15.4021			0.723654
$454$	−2.76280	−	3.40071i	−0.129664	−	0.159603i
$455$	4.65125			0.218054
$456$	−8.86808	−	8.56488i	−0.415286	−	0.401087i
$457$	−41.4946			−1.94103			−0.970517	−	0.241031i	$-0.922515\pi$
$457$	−41.4946			−1.94103			−0.970517	+	0.241031i	$0.922515\pi$
$458$	−16.6109	−	20.4462i	−0.776175	−	0.955389i
$459$	3.09629			0.144522
$460$	0.776940	+	0.162565i	0.0362250	+	0.00757964i
$461$	33.3293			1.55230			0.776150	−	0.630548i	$-0.217170\pi$
$461$	33.3293			1.55230			0.776150	+	0.630548i	$0.217170\pi$
$462$	3.27650	+	4.03303i	0.152437	+	0.187633i
$463$		−	15.8076i		−	0.734643i	−0.930094	−	0.367321i	$-0.880275\pi$
$463$		−	15.8076i		−	0.734643i	0.930094	−	0.367321i	$-0.119725\pi$
$464$	−2.00666	+	4.58524i	−0.0931570	+	0.212865i
$465$	−4.36145			−0.202258
$466$	8.16575	+	10.0512i	0.378271	+	0.465611i
$467$			8.37256i			0.387436i	0.981057	+	0.193718i	$0.0620547\pi$
$467$			8.37256i			0.387436i	−0.981057	+	0.193718i	$0.937945\pi$
$468$	7.77946	+	1.62776i	0.359606	+	0.0752430i
$469$		−	19.0012i		−	0.877393i
$470$	−14.3174	+	11.6317i	−0.660413	+	0.536531i
$471$	−15.8201			−0.728953
$472$	29.1501	−	15.0282i	1.34174	−	0.691727i
$473$	−1.70602			−0.0784431
$474$	3.15598	+	3.88467i	0.144959	+	0.178429i
$475$	1.39920	+	4.12822i	0.0641997	+	0.189416i
$476$	−7.09435	−	1.48441i	−0.325169	−	0.0680376i
$477$			7.43354i			0.340359i
$478$	15.8188	−	12.8515i	0.723535	−	0.587813i
$479$			9.78088i			0.446900i	0.974715	+	0.223450i	$0.0717319\pi$
$479$			9.78088i			0.446900i	−0.974715	+	0.223450i	$0.928268\pi$
$480$	1.50746	+	5.45230i	0.0688059	+	0.248862i
$481$	−23.3324			−1.06387
$482$	8.02162	−	6.51691i	0.365375	−	0.296837i
$483$	−0.464523			−0.0211365
$484$	−0.469013	+	2.24153i	−0.0213188	+	0.101888i
$485$		−	11.8020i		−	0.535900i
$486$	0.891738	+	1.09763i	0.0404501	+	0.0497897i
$487$	25.8082			1.16948			0.584740	−	0.811220i	$-0.301196\pi$
$487$	25.8082			1.16948			0.584740	+	0.811220i	$0.301196\pi$
$488$	12.4869	−	6.43755i	0.565256	−	0.291414i
$489$		−	0.193191i		−	0.00873638i
$490$	5.02057	+	6.17979i	0.226806	+	0.279174i
$491$		−	31.1973i		−	1.40791i	−0.710242	−	0.703957i	$-0.751415\pi$
$491$		−	31.1973i		−	1.40791i	0.710242	−	0.703957i	$-0.248585\pi$
$492$	8.22515	+	1.72101i	0.370819	+	0.0775892i
$493$			3.87432i			0.174491i
$494$	−20.7326	−	13.0488i	−0.932804	−	0.587092i
$495$		−	3.13926i		−	0.141099i
$496$	15.9823	+	6.99443i	0.717627	+	0.314059i
$497$			11.4166i			0.512105i
$498$	6.36437	−	5.17053i	0.285194	−	0.231697i
$499$		−	19.2167i		−	0.860257i	−0.902768	−	0.430129i	$-0.858468\pi$
$499$		−	19.2167i		−	0.860257i	0.902768	−	0.430129i	$-0.141532\pi$
$500$	0.409605	−	1.95761i	0.0183181	−	0.0875468i
$501$	−19.6611			−0.878395
$502$	7.24070	−	5.88247i	0.323168	−	0.262548i
$503$		−	15.4853i		−	0.690458i	−0.938519	−	0.345229i	$-0.887801\pi$
$503$		−	15.4853i		−	0.690458i	0.938519	−	0.345229i	$-0.112199\pi$
$504$	−1.51697	−	2.94246i	−0.0675711	−	0.131068i
$505$	−2.12111			−0.0943883
$506$	1.11103	+	1.36756i	0.0493914	+	0.0607956i
$507$	2.79239			0.124015
$508$	3.77057	−	18.0205i	0.167292	−	0.799530i
$509$			24.1225i			1.06921i	0.845101	+	0.534606i	$0.179540\pi$
$509$			24.1225i			1.06921i	−0.845101	+	0.534606i	$0.820460\pi$
$510$	2.76108	+	3.39860i	0.122263	+	0.150492i
$511$		−	19.0848i		−	0.844263i
$512$	3.21979	−	22.3972i	0.142296	−	0.989824i
$513$	−1.39920	−	4.12822i	−0.0617762	−	0.182266i
$514$	−5.67863	+	4.61342i	−0.250473	+	0.203489i
$515$	4.85962			0.214141
$516$	1.06386	+	0.222599i	0.0468337	+	0.00979937i
$517$	−40.9481			−1.80090
$518$	6.12800	+	7.54291i	0.269249	+	0.331417i
$519$			3.77834i			0.165851i
$520$	5.15056	+	9.99054i	0.225867	+	0.438114i
$521$		−	16.8118i		−	0.736538i	−0.929719	−	0.368269i	$-0.879951\pi$
$521$		−	16.8118i		−	0.736538i	0.929719	−	0.368269i	$-0.120049\pi$
$522$	−1.37345	+	1.11581i	−0.0601141	+	0.0488378i
$523$	0.876796			0.0383396			0.0191698	−	0.999816i	$-0.493898\pi$
$523$	0.876796			0.0383396			0.0191698	+	0.999816i	$0.493898\pi$
$524$	−4.57510	−	0.957283i	−0.199864	−	0.0418191i
$525$			1.17043i			0.0510818i
$526$	31.6658	−	25.7258i	1.38069	−	1.12170i
$527$	13.5043			0.588258
$528$	−5.03441	+	11.5037i	−0.219094	+	0.500632i
$529$	22.8425			0.993151
$530$	−8.15932	+	6.62878i	−0.354418	+	0.287936i
$531$	11.5951			0.503186
$532$	1.22678	+	10.1296i	0.0531875	+	0.439172i
$533$	16.6972			0.723234
$534$	−18.5632	+	15.0811i	−0.803307	+	0.652621i
$535$	2.40698			0.104063
$536$	40.8131	−	21.0409i	1.76286	−	0.908831i
$537$	−0.263723			−0.0113805
$538$	−13.1726	+	10.7017i	−0.567912	+	0.461382i
$539$			17.6743i			0.761287i
$540$	−0.409605	+	1.95761i	−0.0176266	+	0.0842420i
$541$	4.97090			0.213716			0.106858	−	0.994274i	$-0.465921\pi$
$541$	4.97090			0.213716			0.106858	+	0.994274i	$0.465921\pi$
$542$	−4.84820	+	3.93877i	−0.208248	+	0.169185i
$543$			14.2283i			0.610595i
$544$	−4.66754	−	16.8819i	−0.200119	−	0.723805i
$545$		−	2.88193i		−	0.123448i
$546$	−4.14770	−	5.10537i	−0.177505	−	0.218490i
$547$	−4.12750			−0.176479			−0.0882396	−	0.996099i	$-0.528124\pi$
$547$	−4.12750			−0.176479			−0.0882396	+	0.996099i	$0.528124\pi$
$548$	−5.37092	+	25.6690i	−0.229434	+	1.09652i
$549$	4.96696			0.211985
$550$	3.44576	−	2.79940i	0.146928	−	0.119367i
$551$	5.16556	−	1.75079i	0.220060	−	0.0745861i
$552$	−0.514390	−	0.997762i	−0.0218939	−	0.0424676i
$553$		−	4.14231i		−	0.176149i
$554$	28.3792	+	34.9317i	1.20572	+	1.48411i
$555$		−	5.87132i		−	0.249224i
$556$	−23.4097	−	4.89818i	−0.992790	−	0.207729i
$557$	−22.5425			−0.955155			−0.477577	−	0.878590i	$-0.658485\pi$
$557$	−22.5425			−0.955155			−0.477577	+	0.878590i	$0.658485\pi$
$558$	3.88928	+	4.78729i	0.164646	+	0.202662i
$559$	2.15964			0.0913431
$560$	1.87701	−	4.28898i	0.0793181	−	0.181243i
$561$			9.72006i			0.410381i
$562$	30.3873	−	24.6872i	1.28181	−	1.04137i
$563$	30.3146			1.27761			0.638804	−	0.769369i	$-0.279429\pi$
$563$	30.3146			1.27761			0.638804	+	0.769369i	$0.279429\pi$
$564$	25.5348	+	5.34284i	1.07521	+	0.224974i
$565$			6.62143i			0.278566i
$566$	−0.856003	+	0.695432i	−0.0359805	+	0.0292312i
$567$		−	1.17043i		−	0.0491535i
$568$	−24.5220	+	12.6422i	−1.02892	+	0.530455i
$569$		−	15.5447i		−	0.651666i	−0.945427	−	0.325833i	$-0.894355\pi$
$569$		−	15.5447i		−	0.651666i	0.945427	−	0.325833i	$-0.105645\pi$
$570$	3.28356	−	5.21711i	0.137533	−	0.218521i
$571$		−	42.4039i		−	1.77455i	−0.461244	−	0.887273i	$-0.652597\pi$
$571$		−	42.4039i		−	1.77455i	0.461244	−	0.887273i	$-0.347403\pi$
$572$	−5.10995	+	24.4218i	−0.213658	+	1.02112i
$573$			6.79318i			0.283789i
$574$	−4.38532	−	5.39787i	−0.183040	−	0.225303i
$575$			0.396883i			0.0165511i
$576$	4.64037	−	6.51667i	0.193349	−	0.271528i
$577$	4.67066			0.194442			0.0972211	−	0.995263i	$-0.469005\pi$
$577$	4.67066			0.194442			0.0972211	+	0.995263i	$0.469005\pi$
$578$	6.61045	+	8.13676i	0.274958	+	0.338445i
$579$		−	16.9319i		−	0.703666i
$580$	−2.44951	−	0.512530i	−0.101710	−	0.0212816i
$581$	−6.78645			−0.281549
$582$	−12.9542	+	10.5243i	−0.536971	+	0.436245i
$583$	−23.3358			−0.966472
$584$	40.9928	−	21.1336i	1.69629	−	0.874514i
$585$			3.97396i			0.164303i
$586$	−0.223268	+	0.181387i	−0.00922310	+	0.00749301i
$587$		−	38.2783i		−	1.57991i	−0.613162	−	0.789957i	$-0.710103\pi$
$587$		−	38.2783i		−	1.57991i	0.613162	−	0.789957i	$-0.289897\pi$
$588$	2.30611	−	11.0215i	0.0951026	−	0.454519i
$589$	−6.10255	−	18.0051i	−0.251451	−	0.741886i
$590$	10.3398	+	12.7272i	0.425684	+	0.523971i
$591$	23.5897			0.970349
$592$	−9.41578	+	21.5151i	−0.386986	+	0.884267i
$593$	−35.6631			−1.46451			−0.732255	−	0.681031i	$-0.761532\pi$
$593$	−35.6631			−1.46451			−0.732255	+	0.681031i	$0.761532\pi$
$594$	−3.44576	+	2.79940i	−0.141381	+	0.114861i
$595$		−	3.62399i		−	0.148569i
$596$	−2.08040	+	9.94274i	−0.0852164	+	0.407271i
$597$		−	18.6434i		−	0.763024i
$598$	−1.40645	−	1.73119i	−0.0575139	−	0.0707935i
$599$	35.0394			1.43167			0.715835	−	0.698270i	$-0.246046\pi$
$599$	35.0394			1.43167			0.715835	+	0.698270i	$0.246046\pi$
$600$	−2.51400	+	1.29608i	−0.102634	+	0.0529121i
$601$		−	10.8232i		−	0.441486i	−0.975332	−	0.220743i	$-0.929152\pi$
$601$		−	10.8232i		−	0.441486i	0.975332	−	0.220743i	$-0.0708481\pi$
$602$	−0.567206	−	0.698170i	−0.0231176	−	0.0284553i
$603$	16.2343			0.661114
$604$	6.30878	−	30.1513i	0.256701	−	1.22684i
$605$	−1.14504			−0.0465524
$606$	1.89148	+	2.32821i	0.0768360	+	0.0945770i
$607$	8.27197			0.335749			0.167874	−	0.985808i	$-0.446310\pi$
$607$	8.27197			0.335749			0.167874	+	0.985808i	$0.446310\pi$
$608$	−20.3991	+	13.8520i	−0.827292	+	0.561772i
$609$	1.46453			0.0593459
$610$	4.42923	+	5.45190i	0.179334	+	0.220741i
$611$	51.8359			2.09706
$612$	1.26826	−	6.06132i	0.0512662	−	0.245014i
$613$	−33.8556			−1.36742			−0.683708	−	0.729756i	$-0.739634\pi$
$613$	−33.8556			−1.36742			−0.683708	+	0.729756i	$0.739634\pi$
$614$	2.49423	+	3.07013i	0.100659	+	0.123900i
$615$			4.20164i			0.169426i
$616$	9.23715	−	4.76216i	0.372175	−	0.191873i
$617$	12.2279			0.492276			0.246138	−	0.969235i	$-0.420838\pi$
$617$	12.2279			0.492276			0.246138	+	0.969235i	$0.420838\pi$
$618$	−4.33351	−	5.33409i	−0.174319	−	0.214569i
$619$		−	3.36824i		−	0.135381i	−0.997706	−	0.0676905i	$-0.978437\pi$
$619$		−	3.36824i		−	0.135381i	0.997706	−	0.0676905i	$-0.0215631\pi$
$620$	−1.78647	+	8.53801i	−0.0717465	+	0.342895i
$621$		−	0.396883i		−	0.0159263i
$622$	3.95532	−	3.21338i	0.158594	−	0.128845i
$623$	19.7943			0.793041
$624$	6.37301	−	14.5624i	0.255125	−	0.582962i
$625$	1.00000			0.0400000
$626$	−12.4187	−	15.2860i	−0.496349	−	0.610953i
$627$	12.9596	−	4.39245i	0.517556	−	0.175418i
$628$	−6.48000	+	30.9696i	−0.258580	+	1.23582i
$629$			18.1793i			0.724856i
$630$	1.28471	−	1.04372i	0.0511839	−	0.0415827i
$631$			20.8330i			0.829350i	0.909970	+	0.414675i	$0.136105\pi$
$631$			20.8330i			0.829350i	−0.909970	+	0.414675i	$0.863895\pi$
$632$	8.89737	−	4.58698i	0.353918	−	0.182460i
$633$	18.2006			0.723410
$634$	−22.5067	+	18.2848i	−0.893855	+	0.726184i
$635$	9.20537			0.365304
$636$	14.5520	+	3.04482i	0.577023	+	0.120735i
$637$		−	22.3738i		−	0.886482i
$638$	−3.50283	−	4.31161i	−0.138678	−	0.170698i
$639$	−9.75420			−0.385870
$640$	11.2909	−	0.717726i	0.446313	−	0.0283706i
$641$			38.9434i			1.53817i	0.639145	+	0.769087i	$0.279289\pi$
$641$			38.9434i			1.53817i	−0.639145	+	0.769087i	$0.720711\pi$
$642$	−2.14639	−	2.64198i	−0.0847113	−	0.104271i
$643$			11.0122i			0.434278i	0.976141	+	0.217139i	$0.0696726\pi$
$643$			11.0122i			0.434278i	−0.976141	+	0.217139i	$0.930327\pi$
$644$	−0.190271	+	0.909354i	−0.00749773	+	0.0358336i
$645$			0.543447i			0.0213982i
$646$	−10.1669	+	16.1537i	−0.400010	+	0.635558i
$647$		−	4.62186i		−	0.181704i	−0.995864	−	0.0908520i	$-0.971041\pi$
$647$		−	4.62186i		−	0.181704i	0.995864	−	0.0908520i	$-0.0289590\pi$
$648$	2.51400	−	1.29608i	0.0987592	−	0.0509147i
$649$			36.4001i			1.42883i
$650$	−4.36196	+	3.54374i	−0.171090	+	0.138997i
$651$		−	5.10478i		−	0.200072i
$652$	−0.378191	−	0.0791318i	−0.0148111	−	0.00309904i
$653$	2.27550			0.0890472			0.0445236	−	0.999008i	$-0.485823\pi$
$653$	2.27550			0.0890472			0.0445236	+	0.999008i	$0.485823\pi$
$654$	−3.16331	+	2.56993i	−0.123695	+	0.100492i
$655$		−	2.33709i		−	0.0913175i
$656$	6.73813	−	15.3967i	0.263080	−	0.601139i
$657$	16.3058			0.636150
$658$	−13.6141	−	16.7575i	−0.530734	−	0.653277i
$659$	−33.8514			−1.31866			−0.659332	−	0.751852i	$-0.729161\pi$
$659$	−33.8514			−1.31866			−0.659332	+	0.751852i	$0.729161\pi$
$660$	−6.14544	−	1.28586i	−0.239211	−	0.0500519i
$661$		−	16.7964i		−	0.653305i	−0.945145	−	0.326652i	$-0.894079\pi$
$661$		−	16.7964i		−	0.653305i	0.945145	−	0.326652i	$-0.105921\pi$
$662$	20.8264	+	25.6350i	0.809439	+	0.996334i
$663$		−	12.3045i		−	0.477869i
$664$	−7.51498	−	14.5768i	−0.291638	−	0.565689i
$665$	−4.83180	+	1.63767i	−0.187369	+	0.0635060i
$666$	−6.44456	+	5.23568i	−0.249722	+	0.202878i
$667$	0.496610			0.0192288
$668$	−8.05330	+	38.4888i	−0.311592	+	1.48918i
$669$	6.29777			0.243486
$670$	14.4768	+	17.8194i	0.559287	+	0.688423i
$671$			15.5926i			0.601945i
$672$	−6.38154	+	1.76438i	−0.246173	+	0.0680624i
$673$			9.54745i			0.368027i	0.982924	+	0.184014i	$0.0589091\pi$
$673$			9.54745i			0.368027i	−0.982924	+	0.184014i	$0.941091\pi$
$674$	−12.6375	+	10.2669i	−0.486779	+	0.395468i
$675$	−1.00000			−0.0384900
$676$	1.14378	−	5.46641i	0.0439915	−	0.210246i
$677$		−	6.79061i		−	0.260984i	−0.991449	−	0.130492i	$-0.958344\pi$
$677$		−	6.79061i		−	0.260984i	0.991449	−	0.130492i	$-0.0416557\pi$
$678$	7.26792	−	5.90459i	0.279123	−	0.226764i
$679$	13.8134			0.530109
$680$	7.78407	−	4.01303i	0.298505	−	0.153893i
$681$	−3.09821			−0.118724
$682$	−15.0285	+	12.2095i	−0.575473	+	0.467524i
$683$	−24.4628			−0.936041			−0.468021	−	0.883717i	$-0.655033\pi$
$683$	−24.4628			−0.936041			−0.468021	+	0.883717i	$0.655033\pi$
$684$	−8.65456	+	1.04814i	−0.330915	+	0.0400766i
$685$	−13.1124			−0.501000
$686$	−16.2259	+	13.1823i	−0.619510	+	0.503301i
$687$	−18.6275			−0.710684
$688$	0.871522	−	1.99143i	0.0332265	−	0.0759227i
$689$	29.5406			1.12541
$690$	0.435632	−	0.353915i	0.0165842	−	0.0134733i
$691$			34.3740i			1.30765i	0.756646	+	0.653824i	$0.226836\pi$
$691$			34.3740i			1.30765i	−0.756646	+	0.653824i	$0.773164\pi$
$692$	7.39650	+	1.54763i	0.281173	+	0.0588320i
$693$	3.67429			0.139575
$694$	−23.9371	+	19.4469i	−0.908639	+	0.738195i
$695$		−	11.9583i		−	0.453604i
$696$	1.62175	+	3.14571i	0.0614724	+	0.119238i
$697$		−	13.0095i		−	0.492769i
$698$	−29.5422	−	36.3633i	−1.11819	−	1.37637i
$699$	9.15711			0.346354
$700$	2.29124	+	0.479414i	0.0866008	+	0.0181202i
$701$	−13.2500			−0.500446			−0.250223	−	0.968188i	$-0.580504\pi$
$701$	−13.2500			−0.500446			−0.250223	+	0.968188i	$0.580504\pi$
$702$	4.36196	−	3.54374i	0.164632	−	0.133750i
$703$	24.2381	−	8.21514i	0.914158	−	0.309840i
$704$	20.4575	+	14.5673i	0.771022	+	0.549027i
$705$			13.0439i			0.491261i
$706$	17.9129	+	22.0488i	0.674160	+	0.829819i
$707$		−	2.48261i		−	0.0933683i
$708$	4.74942	−	22.6987i	0.178494	−	0.853069i
$709$	−12.2149			−0.458742			−0.229371	−	0.973339i	$-0.573667\pi$
$709$	−12.2149			−0.458742			−0.229371	+	0.973339i	$0.573667\pi$
$710$	−8.69820	−	10.7066i	−0.326438	−	0.401810i
$711$	3.53913			0.132728
$712$	21.9192	+	42.5167i	0.821457	+	1.59338i
$713$		−	1.73099i		−	0.0648259i
$714$	−3.97782	+	3.23165i	−0.148866	+	0.120942i
$715$	−12.4753			−0.466550
$716$	−0.108022	+	0.516267i	−0.00403699	+	0.0192938i
$717$		−	14.4117i		−	0.538215i
$718$	−33.4432	+	27.1698i	−1.24809	+	1.01397i
$719$			24.3704i			0.908862i	0.890782	+	0.454431i	$0.150157\pi$
$719$			24.3704i			0.908862i	−0.890782	+	0.454431i	$0.849843\pi$
$720$	3.66445	+	1.60369i	0.136566	+	0.0597660i
$721$			5.68785i			0.211827i
$722$	26.1318	+	6.25552i	0.972523	+	0.232806i
$723$		−	7.30810i		−	0.271791i
$724$	27.8534	+	5.82799i	1.03516	+	0.216595i
$725$		−	1.25128i		−	0.0464713i
$726$	1.02107	+	1.25683i	0.0378956	+	0.0466454i
$727$			35.3857i			1.31238i	0.754594	+	0.656192i	$0.227834\pi$
$727$			35.3857i			1.31238i	−0.754594	+	0.656192i	$0.772166\pi$
$728$	−11.6932	+	6.02837i	−0.433380	+	0.223426i
$729$	1.00000			0.0370370
$730$	14.5405	+	17.8978i	0.538169	+	0.662428i
$731$		−	1.68267i		−	0.0622358i
$732$	2.03449	−	9.72335i	0.0751969	−	0.359385i
$733$	−2.21849			−0.0819418			−0.0409709	−	0.999160i	$-0.513045\pi$
$733$	−2.21849			−0.0819418			−0.0409709	+	0.999160i	$0.513045\pi$
$734$	−11.9683	+	9.72327i	−0.441758	+	0.358892i
$735$	5.63009			0.207669
$736$	−2.16392	+	0.598285i	−0.0797632	+	0.0220531i
$737$			50.9639i			1.87728i
$738$	4.61186	−	3.74676i	0.169765	−	0.137920i
$739$			22.8037i			0.838848i	0.907790	+	0.419424i	$0.137768\pi$
$739$			22.8037i			0.838848i	−0.907790	+	0.419424i	$0.862232\pi$
$740$	−11.4937	−	2.40492i	−0.422518	−	0.0884067i
$741$	−16.4054	+	5.56037i	−0.602668	+	0.204265i
$742$	−7.75852	−	9.54991i	−0.284824	−	0.350588i
$743$	0.214373			0.00786460			0.00393230	−	0.999992i	$-0.498748\pi$
$743$	0.214373			0.00786460			0.00393230	+	0.999992i	$0.498748\pi$
$744$	10.9647	−	5.65278i	0.401985	−	0.207241i
$745$	−5.07903			−0.186081
$746$	20.3254	−	16.5127i	0.744166	−	0.604574i
$747$		−	5.79825i		−	0.212147i
$748$	19.0281	+	3.98139i	0.695735	+	0.145574i
$749$			2.81720i			0.102938i
$750$	−0.891738	−	1.09763i	−0.0325617	−	0.0400800i
$751$	−18.4697			−0.673969			−0.336985	−	0.941510i	$-0.609407\pi$
$751$	−18.4697			−0.673969			−0.336985	+	0.941510i	$0.609407\pi$
$752$	20.9183	−	47.7986i	0.762813	−	1.74303i
$753$		−	6.59663i		−	0.240395i
$754$	4.43420	+	5.45803i	0.161484	+	0.198770i
$755$	15.4021			0.560540
$756$	−2.29124	−	0.479414i	−0.0833317	−	0.0174361i
$757$	17.2949			0.628592			0.314296	−	0.949325i	$-0.398231\pi$
$757$	17.2949			0.628592			0.314296	+	0.949325i	$0.398231\pi$
$758$	−23.0467	−	28.3681i	−0.837095	−	1.03037i
$759$	1.24592			0.0452240
$760$	−8.86808	−	8.56488i	−0.321679	−	0.310681i
$761$	30.2818			1.09771			0.548857	−	0.835916i	$-0.315063\pi$
$761$	30.2818			1.09771			0.548857	+	0.835916i	$0.315063\pi$
$762$	−8.20879	−	10.1041i	−0.297373	−	0.366034i
$763$	3.37310			0.122115
$764$	13.2984	+	2.78252i	0.481118	+	0.100668i
$765$	3.09629			0.111947
$766$	5.06890	+	6.23928i	0.183147	+	0.225434i
$767$		−	46.0786i		−	1.66380i
$768$	−10.8563	−	11.7533i	−0.391745	−	0.424110i
$769$	−29.4380			−1.06156			−0.530781	−	0.847509i	$-0.678101\pi$
$769$	−29.4380			−1.06156			−0.530781	+	0.847509i	$0.678101\pi$
$770$	3.27650	+	4.03303i	0.118077	+	0.145340i
$771$			5.17351i			0.186319i
$772$	−33.1460	−	6.93539i	−1.19295	−	0.249610i
$773$		−	36.4883i		−	1.31239i	−0.754590	−	0.656196i	$-0.772164\pi$
$773$		−	36.4883i		−	1.31239i	0.754590	−	0.656196i	$-0.227836\pi$
$774$	0.596507	−	0.484613i	0.0214410	−	0.0174191i
$775$	−4.36145			−0.156668
$776$	15.2962	+	29.6701i	0.549103	+	1.06510i
$777$	6.87197			0.246531
$778$	−15.7362	−	19.3696i	−0.564171	−	0.694435i
$779$	−17.3453	+	5.87893i	−0.621460	+	0.210634i
$780$	7.77946	+	1.62776i	0.278549	+	0.0582830i
$781$		−	30.6210i		−	1.09571i
$782$	−1.34884	+	1.09582i	−0.0482345	+	0.0391866i
$783$			1.25128i			0.0447170i
$784$	−20.6312	−	9.02893i	−0.736828	−	0.322462i
$785$	−15.8201			−0.564644
$786$	−2.56527	+	2.08407i	−0.0915001	+	0.0743363i
$787$	13.9431			0.497016			0.248508	−	0.968630i	$-0.420060\pi$
$787$	13.9431			0.497016			0.248508	+	0.968630i	$0.420060\pi$
$788$	9.66245	−	46.1793i	0.344210	−	1.64507i
$789$		−	28.8491i		−	1.02705i
$790$	3.15598	+	3.88467i	0.112285	+	0.138211i
$791$	−7.74993			−0.275556
$792$	4.06872	+	7.89210i	0.144576	+	0.280433i
$793$		−	19.7385i		−	0.700935i
$794$	9.55699	+	11.7636i	0.339165	+	0.417476i
$795$			7.43354i			0.263641i
$796$	−36.4965	−	7.63643i	−1.29358	−	0.270666i
$797$			7.02918i			0.248986i	0.992220	+	0.124493i	$0.0397305\pi$
$797$			7.02918i			0.248986i	−0.992220	+	0.124493i	$0.960270\pi$
$798$	6.10626	+	3.84318i	0.216159	+	0.136047i
$799$		−	40.3876i		−	1.42881i
$800$	1.50746	+	5.45230i	0.0532968	+	0.192768i
$801$			16.9120i			0.597555i
$802$	0.163631	−	0.132937i	0.00577800	−	0.00469415i
$803$			51.1882i			1.80639i
$804$	6.64967	−	31.7805i	0.234516	−	1.12081i
$805$	−0.464523			−0.0163723
$806$	19.0245	−	15.4558i	0.670110	−	0.544409i
$807$			12.0009i			0.422452i
$808$	5.33247	−	2.74912i	0.187596	−	0.0967138i
$809$	−21.7159			−0.763491			−0.381745	−	0.924268i	$-0.624677\pi$
$809$	−21.7159			−0.763491			−0.381745	+	0.924268i	$0.624677\pi$
$810$	0.891738	+	1.09763i	0.0313325	+	0.0385670i
$811$	12.1303			0.425951			0.212976	−	0.977058i	$-0.431685\pi$
$811$	12.1303			0.425951			0.212976	+	0.977058i	$0.431685\pi$
$812$	0.599881	−	2.86698i	0.0210517	−	0.100611i
$813$			4.41695i			0.154909i
$814$	−16.4362	−	20.2312i	−0.576087	−	0.709102i
$815$		−	0.193191i		−	0.00676717i
$816$	−11.3462	−	4.96549i	−0.397196	−	0.173827i
$817$	−2.24347	+	0.760391i	−0.0784892	+	0.0266027i
$818$	−31.4463	+	25.5476i	−1.09950	+	0.893250i
$819$	−4.65125			−0.162528
$820$	8.22515	+	1.72101i	0.287235	+	0.0601003i
$821$	36.1247			1.26076			0.630380	−	0.776286i	$-0.282899\pi$
$821$	36.1247			1.26076			0.630380	+	0.776286i	$0.282899\pi$
$822$	11.6929	+	14.3927i	0.407835	+	0.502002i
$823$			48.2428i			1.68164i	0.541317	+	0.840819i	$0.317926\pi$
$823$			48.2428i			1.68164i	−0.541317	+	0.840819i	$0.682074\pi$
$824$	−12.2171	+	6.29844i	−0.425602	+	0.219417i
$825$		−	3.13926i		−	0.109295i
$826$	−14.8963	+	12.1020i	−0.518309	+	0.421084i
$827$	−21.9189			−0.762193			−0.381097	−	0.924535i	$-0.624454\pi$
$827$	−21.9189			−0.762193			−0.381097	+	0.924535i	$0.624454\pi$
$828$	−0.776940	−	0.162565i	−0.0270005	−	0.00564953i
$829$			48.4638i			1.68322i	0.540089	+	0.841608i	$0.318391\pi$
$829$			48.4638i			1.68322i	−0.540089	+	0.841608i	$0.681609\pi$
$830$	6.36437	−	5.17053i	0.220910	−	0.179472i
$831$	31.8246			1.10398
$832$	−25.8970	−	18.4407i	−0.897817	−	0.639315i
$833$	−17.4324			−0.603997
$834$	−13.1259	+	10.6637i	−0.454511	+	0.369253i
$835$	−19.6611			−0.680402
$836$	−3.29039	−	27.1689i	−0.113800	−	0.939657i
$837$	4.36145			0.150754
$838$	11.9325	−	9.69416i	0.412201	−	0.334879i
$839$	−44.5261			−1.53721			−0.768606	−	0.639722i	$-0.779049\pi$
$839$	−44.5261			−1.53721			−0.768606	+	0.639722i	$0.779049\pi$
$840$	−1.51697	−	2.94246i	−0.0523403	−	0.101525i
$841$	27.4343			0.946010
$842$	−5.11408	+	4.15477i	−0.176243	+	0.143183i
$843$		−	27.6843i		−	0.953499i
$844$	7.45507	−	35.6297i	0.256614	−	1.22642i
$845$	2.79239			0.0960613
$846$	14.3174	−	11.6317i	0.492243	−	0.399907i
$847$		−	1.34019i		−	0.0460493i
$848$	11.9211	−	27.2398i	0.409373	−	0.935420i
$849$			0.779861i			0.0267648i
$850$	2.76108	+	3.39860i	0.0947043	+	0.116571i
$851$	2.33022			0.0798790
$852$	−3.99537	+	19.0949i	−0.136879	+	0.654180i
$853$	20.1342			0.689384			0.344692	−	0.938716i	$-0.387983\pi$
$853$	20.1342			0.689384			0.344692	+	0.938716i	$0.387983\pi$
$854$	−6.38108	+	5.18410i	−0.218356	+	0.177396i
$855$	−1.39920	−	4.12822i	−0.0478516	−	0.141182i
$856$	−6.05113	+	3.11962i	−0.206823	+	0.106627i
$857$		−	44.6087i		−	1.52381i	−0.647691	−	0.761903i	$-0.724265\pi$
$857$		−	44.6087i		−	1.52381i	0.647691	−	0.761903i	$-0.275735\pi$
$858$	11.1247	+	13.6933i	0.379792	+	0.467483i
$859$			49.0886i			1.67488i	0.546527	+	0.837441i	$0.315949\pi$
$859$			49.0886i			1.67488i	−0.546527	+	0.837441i	$0.684051\pi$
$860$	1.06386	+	0.222599i	0.0362772	+	0.00759056i
$861$	−4.91772			−0.167596
$862$	−9.49852	−	11.6917i	−0.323521	−	0.398220i
$863$	−9.24561			−0.314724			−0.157362	−	0.987541i	$-0.550299\pi$
$863$	−9.24561			−0.314724			−0.157362	+	0.987541i	$0.550299\pi$
$864$	−1.50746	−	5.45230i	−0.0512849	−	0.185491i
$865$			3.77834i			0.128467i
$866$	9.26636	−	7.52816i	0.314884	−	0.255817i
$867$	7.41299			0.251758
$868$	−9.99315	−	2.09094i	−0.339190	−	0.0709713i
$869$			11.1103i			0.376890i
$870$	−1.37345	+	1.11581i	−0.0465642	+	0.0378296i
$871$		−	64.5147i		−	2.18600i
$872$	3.73521	+	7.24518i	0.126490	+	0.245353i
$873$			11.8020i			0.399436i
$874$	2.07058	+	1.30319i	0.0700384	+	0.0440810i
$875$			1.17043i			0.0395678i
$876$	6.67894	−	31.9204i	0.225661	−	1.07849i
$877$			43.0694i			1.45435i	0.686452	+	0.727175i	$0.259167\pi$
$877$			43.0694i			1.45435i	−0.686452	+	0.727175i	$0.740833\pi$
$878$	−0.544176	−	0.669823i	−0.0183651	−	0.0226054i
$879$			0.203408i			0.00686078i
$880$	−5.03441	+	11.5037i	−0.169710	+	0.387788i
$881$	33.6190			1.13265			0.566327	−	0.824181i	$-0.308364\pi$
$881$	33.6190			1.13265			0.566327	+	0.824181i	$0.308364\pi$
$882$	−5.02057	−	6.17979i	−0.169051	−	0.208084i
$883$			25.3123i			0.851825i	0.904764	+	0.425913i	$0.140047\pi$
$883$			25.3123i			0.851825i	−0.904764	+	0.425913i	$0.859953\pi$
$884$	−24.0875	−	5.04000i	−0.810149	−	0.169514i
$885$	11.5951			0.389766
$886$	25.1295	−	20.4156i	0.844242	−	0.685877i
$887$	−44.3479			−1.48906			−0.744528	−	0.667591i	$-0.767325\pi$
$887$	−44.3479			−1.48906			−0.744528	+	0.667591i	$0.767325\pi$
$888$	7.60967	+	14.7605i	0.255364	+	0.495329i
$889$			10.7743i			0.361357i
$890$	−18.5632	+	15.0811i	−0.622239	+	0.505518i
$891$			3.13926i			0.105169i
$892$	2.57960	−	12.3285i	0.0863713	−	0.412790i
$893$	−53.8480	+	18.2510i	−1.80196	+	0.610746i
$894$	4.52917	+	5.57492i	0.151478	+	0.186453i
$895$	−0.263723			−0.00881530
$896$	0.840049	+	13.2152i	0.0280641	+	0.441490i
$897$	−1.57720			−0.0526611
$898$	15.7917	−	12.8294i	0.526975	−	0.428124i
$899$			5.45739i			0.182014i
$900$	−0.409605	+	1.95761i	−0.0136535	+	0.0652536i
$901$		−	23.0164i		−	0.766788i
$902$	11.7621	+	14.4778i	0.391634	+	0.482060i
$903$	−0.636068			−0.0211670
$904$	−8.58188	−	16.6463i	−0.285429	−	0.553647i
$905$			14.2283i			0.472965i
$906$	−13.7346	−	16.9059i	−0.456303	−	0.561660i
$907$	21.4988			0.713856			0.356928	−	0.934132i	$-0.383824\pi$
$907$	21.4988			0.713856			0.356928	+	0.934132i	$0.383824\pi$
$908$	−1.26904	+	6.06508i	−0.0421147	+	0.201277i
$909$	2.12111			0.0703529
$910$	−4.14770	−	5.10537i	−0.137495	−	0.169241i
$911$	−13.5230			−0.448038			−0.224019	−	0.974585i	$-0.571918\pi$
$911$	−13.5230			−0.448038			−0.224019	+	0.974585i	$0.571918\pi$
$912$	−1.49311	+	17.3715i	−0.0494417	+	0.575229i
$913$	18.2022			0.602406
$914$	37.0023	+	45.5459i	1.22393	+	1.50652i
$915$	4.96696			0.164203
$916$	−7.62993	+	36.4654i	−0.252100	+	1.20485i
$917$	2.73540			0.0903308
$918$	−2.76108	−	3.39860i	−0.0911292	−	0.112170i
$919$			8.55980i			0.282362i	0.989984	+	0.141181i	$0.0450899\pi$
$919$			8.55980i			0.282362i	−0.989984	+	0.141181i	$0.954910\pi$
$920$	−0.514390	−	0.997762i	−0.0169589	−	0.0328952i
$921$	2.79704			0.0921657
$922$	−29.7210	−	36.5834i	−0.978810	−	1.20481i
$923$			38.7629i			1.27590i
$924$	1.50501	−	7.19281i	0.0495111	−	0.236626i
$925$		−	5.87132i		−	0.193048i
$926$	−17.3510	+	14.0963i	−0.570189	+	0.463232i
$927$	−4.85962			−0.159611
$928$	6.82234	−	1.88625i	0.223954	−	0.0619193i
$929$	−0.674727			−0.0221371			−0.0110685	−	0.999939i	$-0.503523\pi$
$929$	−0.674727			−0.0221371			−0.0110685	+	0.999939i	$0.503523\pi$
$930$	3.88928	+	4.78729i	0.127534	+	0.156981i
$931$	7.87762	+	23.2423i	0.258179	+	0.761735i
$932$	3.75080	−	17.9260i	0.122861	−	0.587186i
$933$		−	3.60350i		−	0.117973i
$934$	9.19002	−	7.46614i	0.300707	−	0.244299i
$935$			9.72006i			0.317880i
$936$	−5.15056	−	9.99054i	−0.168351	−	0.326551i
$937$	−51.4891			−1.68208			−0.841039	−	0.540975i	$-0.818055\pi$
$937$	−51.4891			−1.68208			−0.841039	+	0.540975i	$0.818055\pi$
$938$	−20.8564	+	16.9441i	−0.680984	+	0.553244i
$939$	−13.9263			−0.454469
$940$	25.5348	+	5.34284i	0.832852	+	0.174264i
$941$		−	7.28293i		−	0.237417i	−0.992929	−	0.118708i	$-0.962125\pi$
$941$		−	7.28293i		−	0.237417i	0.992929	−	0.118708i	$-0.0378754\pi$
$942$	14.1074	+	17.3647i	0.459644	+	0.565773i
$943$	−1.66756			−0.0543031
$944$	−42.4897	−	18.5950i	−1.38292	−	0.605216i
$945$		−	1.17043i		−	0.0380741i
$946$	1.52133	+	1.87259i	0.0494626	+	0.0608832i
$947$		−	42.8750i		−	1.39325i	−0.717436	−	0.696624i	$-0.754684\pi$
$947$		−	42.8750i		−	1.39325i	0.717436	−	0.696624i	$-0.245316\pi$
$948$	1.44965	−	6.92823i	0.0470823	−	0.225018i
$949$		−	64.7987i		−	2.10346i
$950$	3.28356	−	5.21711i	0.106533	−	0.169265i
$951$			20.5047i			0.664911i
$952$	4.69697	+	9.11071i	0.152230	+	0.295280i
$953$			13.0376i			0.422330i	0.977450	+	0.211165i	$0.0677257\pi$
$953$			13.0376i			0.422330i	−0.977450	+	0.211165i	$0.932274\pi$
$954$	8.15932	−	6.62878i	0.264168	−	0.214615i
$955$			6.79318i			0.219822i
$956$	−28.2125	−	5.90311i	−0.912456	−	0.190920i
$957$	−3.92809			−0.126977
$958$	10.7358	−	8.72199i	0.346859	−	0.281795i
$959$		−	15.3472i		−	0.495587i
$960$	4.64037	−	6.51667i	0.149767	−	0.210325i
$961$	−11.9777			−0.386378
$962$	20.8064	+	25.6105i	0.670825	+	0.825715i
$963$	−2.40698			−0.0775637
$964$	−14.3064	−	2.99343i	−0.460777	−	0.0964120i
$965$		−	16.9319i		−	0.545057i
$966$	0.414233	+	0.509877i	0.0133277	+	0.0164050i
$967$			16.8218i			0.540952i	0.962727	+	0.270476i	$0.0871811\pi$
$967$			16.8218i			0.540952i	−0.962727	+	0.270476i	$0.912819\pi$
$968$	2.87862	−	1.48405i	0.0925223	−	0.0476993i
$969$	4.33233	+	12.7822i	0.139174	+	0.410623i
$970$	−12.9542	+	10.5243i	−0.415936	+	0.337914i
$971$	39.5481			1.26916			0.634580	−	0.772857i	$-0.281173\pi$
$971$	39.5481			1.26916			0.634580	+	0.772857i	$0.281173\pi$
$972$	0.409605	−	1.95761i	0.0131381	−	0.0627903i
$973$	13.9964			0.448703
$974$	−23.0142	−	28.3280i	−0.737421	−	0.907687i
$975$			3.97396i			0.127269i
$976$	−18.2011	−	7.96546i	−0.582605	−	0.254968i
$977$			32.1625i			1.02897i	0.857500	+	0.514485i	$0.172017\pi$
$977$			32.1625i			1.02897i	−0.857500	+	0.514485i	$0.827983\pi$
$978$	−0.212053	+	0.172275i	−0.00678070	+	0.00550876i
$979$	−53.0911			−1.69680
$980$	2.30611	−	11.0215i	0.0736661	−	0.352069i
$981$			2.88193i			0.0920131i
$982$	−34.2433	+	27.8198i	−1.09275	+	0.887767i
$983$	−42.2994			−1.34914			−0.674570	−	0.738211i	$-0.735671\pi$
$983$	−42.2994			−1.34914			−0.674570	+	0.738211i	$0.735671\pi$
$984$	−5.44564	−	10.5629i	−0.173601	−	0.336733i
$985$	23.5897			0.751629
$986$	4.25259	−	3.45488i	0.135430	−	0.110026i
$987$	−15.2669			−0.485952
$988$	4.16527	+	34.3929i	0.132515	+	1.09418i
$989$	−0.215685			−0.00685838
$990$	−3.44576	+	2.79940i	−0.109514	+	0.0889708i
$991$	33.2252			1.05543			0.527716	−	0.849421i	$-0.323048\pi$
$991$	33.2252			1.05543			0.527716	+	0.849421i	$0.323048\pi$
$992$	−6.57472	−	23.7800i	−0.208748	−	0.755014i
$993$	23.3548			0.741142
$994$	12.5313	−	10.1806i	0.397468	−	0.322910i
$995$		−	18.6434i		−	0.591036i
$996$	−11.3507	−	2.37499i	−0.359661	−	0.0752546i
$997$	36.1098			1.14361			0.571805	−	0.820390i	$-0.306244\pi$
$997$	36.1098			1.14361			0.571805	+	0.820390i	$0.306244\pi$
$998$	−21.0929	+	17.1363i	−0.667685	+	0.542439i
$999$			5.87132i			0.185760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1140.2.b.c.151.5	✓	18
4.3	odd	2		1140.2.b.d.151.13	yes	18
19.18	odd	2		1140.2.b.d.151.14	yes	18
76.75	even	2	inner	1140.2.b.c.151.6	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1140.2.b.c.151.5	✓	18	1.1	even	1	trivial
1140.2.b.c.151.6	yes	18	76.75	even	2	inner
1140.2.b.d.151.13	yes	18	4.3	odd	2
1140.2.b.d.151.14	yes	18	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891738 - 1.09763i) q^{2} -1.00000 q^{3} +(-0.409605 + 1.95761i) q^{4} -1.00000 q^{5} +(0.891738 + 1.09763i) q^{6} -1.17043i q^{7} +(2.51400 - 1.29608i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.891738 - 1.09763i) q^{2} -1.00000 q^{3} +(-0.409605 + 1.95761i) q^{4} -1.00000 q^{5} +(0.891738 + 1.09763i) q^{6} -1.17043i q^{7} +(2.51400 - 1.29608i) q^{8} +1.00000 q^{9} +(0.891738 + 1.09763i) q^{10} +3.13926i q^{11} +(0.409605 - 1.95761i) q^{12} -3.97396i q^{13} +(-1.28471 + 1.04372i) q^{14} +1.00000 q^{15} +(-3.66445 - 1.60369i) q^{16} -3.09629 q^{17} +(-0.891738 - 1.09763i) q^{18} +(1.39920 + 4.12822i) q^{19} +(0.409605 - 1.95761i) q^{20} +1.17043i q^{21} +(3.44576 - 2.79940i) q^{22} +0.396883i q^{23} +(-2.51400 + 1.29608i) q^{24} +1.00000 q^{25} +(-4.36196 + 3.54374i) q^{26} -1.00000 q^{27} +(2.29124 + 0.479414i) q^{28} -1.25128i q^{29} +(-0.891738 - 1.09763i) q^{30} -4.36145 q^{31} +(1.50746 + 5.45230i) q^{32} -3.13926i q^{33} +(2.76108 + 3.39860i) q^{34} +1.17043i q^{35} +(-0.409605 + 1.95761i) q^{36} -5.87132i q^{37} +(3.28356 - 5.21711i) q^{38} +3.97396i q^{39} +(-2.51400 + 1.29608i) q^{40} +4.20164i q^{41} +(1.28471 - 1.04372i) q^{42} +0.543447i q^{43} +(-6.14544 - 1.28586i) q^{44} -1.00000 q^{45} +(0.435632 - 0.353915i) q^{46} +13.0439i q^{47} +(3.66445 + 1.60369i) q^{48} +5.63009 q^{49} +(-0.891738 - 1.09763i) q^{50} +3.09629 q^{51} +(7.77946 + 1.62776i) q^{52} +7.43354i q^{53} +(0.891738 + 1.09763i) q^{54} -3.13926i q^{55} +(-1.51697 - 2.94246i) q^{56} +(-1.39920 - 4.12822i) q^{57} +(-1.37345 + 1.11581i) q^{58} +11.5951 q^{59} +(-0.409605 + 1.95761i) q^{60} +4.96696 q^{61} +(3.88928 + 4.78729i) q^{62} -1.17043i q^{63} +(4.64037 - 6.51667i) q^{64} +3.97396i q^{65} +(-3.44576 + 2.79940i) q^{66} +16.2343 q^{67} +(1.26826 - 6.06132i) q^{68} -0.396883i q^{69} +(1.28471 - 1.04372i) q^{70} -9.75420 q^{71} +(2.51400 - 1.29608i) q^{72} +16.3058 q^{73} +(-6.44456 + 5.23568i) q^{74} -1.00000 q^{75} +(-8.65456 + 1.04814i) q^{76} +3.67429 q^{77} +(4.36196 - 3.54374i) q^{78} +3.53913 q^{79} +(3.66445 + 1.60369i) q^{80} +1.00000 q^{81} +(4.61186 - 3.74676i) q^{82} -5.79825i q^{83} +(-2.29124 - 0.479414i) q^{84} +3.09629 q^{85} +(0.596507 - 0.484613i) q^{86} +1.25128i q^{87} +(4.06872 + 7.89210i) q^{88} +16.9120i q^{89} +(0.891738 + 1.09763i) q^{90} -4.65125 q^{91} +(-0.776940 - 0.162565i) q^{92} +4.36145 q^{93} +(14.3174 - 11.6317i) q^{94} +(-1.39920 - 4.12822i) q^{95} +(-1.50746 - 5.45230i) q^{96} +11.8020i q^{97} +(-5.02057 - 6.17979i) q^{98} +3.13926i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{2} - 18 q^{3} + 3 q^{4} - 18 q^{5} + q^{6} + 5 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - q^2 - 18 * q^3 + 3 * q^4 - 18 * q^5 + q^6 + 5 * q^8 + 18 * q^9	\( 18 q - q^{2} - 18 q^{3} + 3 q^{4} - 18 q^{5} + q^{6} + 5 q^{8} + 18 q^{9} + q^{10} - 3 q^{12} + 18 q^{15} - q^{16} - 20 q^{17} - q^{18} - 8 q^{19} - 3 q^{20} + 32 q^{22} - 5 q^{24} + 18 q^{25} + 18 q^{26} - 18 q^{27} - 4 q^{28} - q^{30} + 16 q^{31} + 9 q^{32} - 22 q^{34} + 3 q^{36} - 21 q^{38} - 5 q^{40} + 16 q^{44} - 18 q^{45} - 26 q^{46} + q^{48} - 42 q^{49} - q^{50} + 20 q^{51} - 6 q^{52} + q^{54} - 4 q^{56} + 8 q^{57} - 34 q^{58} - 32 q^{59} + 3 q^{60} - 4 q^{61} + 36 q^{62} + 15 q^{64} - 32 q^{66} + 34 q^{68} - 16 q^{71} + 5 q^{72} + 20 q^{73} + 26 q^{74} - 18 q^{75} + 3 q^{76} + 16 q^{77} - 18 q^{78} - 16 q^{79} + q^{80} + 18 q^{81} - 34 q^{82} + 4 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + q^{90} - 8 q^{91} - 6 q^{92} - 16 q^{93} + 22 q^{94} + 8 q^{95} - 9 q^{96} + 65 q^{98}+O(q^{100}) \) 18 * q - q^2 - 18 * q^3 + 3 * q^4 - 18 * q^5 + q^6 + 5 * q^8 + 18 * q^9 + q^10 - 3 * q^12 + 18 * q^15 - q^16 - 20 * q^17 - q^18 - 8 * q^19 - 3 * q^20 + 32 * q^22 - 5 * q^24 + 18 * q^25 + 18 * q^26 - 18 * q^27 - 4 * q^28 - q^30 + 16 * q^31 + 9 * q^32 - 22 * q^34 + 3 * q^36 - 21 * q^38 - 5 * q^40 + 16 * q^44 - 18 * q^45 - 26 * q^46 + q^48 - 42 * q^49 - q^50 + 20 * q^51 - 6 * q^52 + q^54 - 4 * q^56 + 8 * q^57 - 34 * q^58 - 32 * q^59 + 3 * q^60 - 4 * q^61 + 36 * q^62 + 15 * q^64 - 32 * q^66 + 34 * q^68 - 16 * q^71 + 5 * q^72 + 20 * q^73 + 26 * q^74 - 18 * q^75 + 3 * q^76 + 16 * q^77 - 18 * q^78 - 16 * q^79 + q^80 + 18 * q^81 - 34 * q^82 + 4 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + q^90 - 8 * q^91 - 6 * q^92 - 16 * q^93 + 22 * q^94 + 8 * q^95 - 9 * q^96 + 65 * q^98

Introduction

L-functions

Modular forms

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