LMFDB - Embedded newform 546.2.bk.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(25,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("546.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.4
Root			$2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	546.25
Dual form			546.2.bk.a.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.60464 - 2.08114i) q^{5} +1.00000i q^{6} +(2.59808 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.60464 - 2.08114i) q^{5} +1.00000i q^{6} +(2.59808 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.08114 - 3.60464i) q^{10} +(-1.87259 - 1.08114i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.58114 + 0.418861i) q^{13} +(2.00000 - 1.73205i) q^{14} +4.16228i q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.581139 - 1.00656i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-5.47723 + 3.16228i) q^{19} -4.16228i q^{20} +(-0.866025 + 2.50000i) q^{21} -2.16228 q^{22} +(2.58114 + 4.47066i) q^{23} +(0.866025 + 0.500000i) q^{24} +(6.16228 - 10.6734i) q^{25} +(-2.89193 + 2.15331i) q^{26} +1.00000 q^{27} +(0.866025 - 2.50000i) q^{28} -2.16228 q^{29} +(2.08114 + 3.60464i) q^{30} +(7.79423 + 4.50000i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.87259 - 1.08114i) q^{33} -1.16228i q^{34} +(8.32456 - 7.20928i) q^{35} -1.00000 q^{36} +(-5.47723 + 3.16228i) q^{37} +(-3.16228 + 5.47723i) q^{38} +(1.42783 - 3.31079i) q^{39} +(-2.08114 - 3.60464i) q^{40} +(0.500000 + 2.59808i) q^{42} -2.83772 q^{43} +(-1.87259 + 1.08114i) q^{44} +(-3.60464 - 2.08114i) q^{45} +(4.47066 + 2.58114i) q^{46} +(4.75174 - 2.74342i) q^{47} +1.00000 q^{48} +(6.50000 - 2.59808i) q^{49} -12.3246i q^{50} +(0.581139 + 1.00656i) q^{51} +(-1.42783 + 3.31079i) q^{52} +(-0.0811388 + 0.140537i) q^{53} +(0.866025 - 0.500000i) q^{54} -9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} -6.32456i q^{57} +(-1.87259 + 1.08114i) q^{58} +(7.06874 + 4.08114i) q^{59} +(3.60464 + 2.08114i) q^{60} +(1.74342 + 3.01969i) q^{61} +9.00000 q^{62} +(-1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(-12.0370 + 8.96269i) q^{65} +(1.08114 - 1.87259i) q^{66} +(-7.93477 - 4.58114i) q^{67} +(-0.581139 - 1.00656i) q^{68} -5.16228 q^{69} +(3.60464 - 10.4057i) q^{70} +16.3246i q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.47723 + 3.16228i) q^{73} +(-3.16228 + 5.47723i) q^{74} +(6.16228 + 10.6734i) q^{75} +6.32456i q^{76} +(-5.40569 - 1.87259i) q^{77} +(-0.418861 - 3.58114i) q^{78} +(-4.50000 - 7.79423i) q^{79} +(-3.60464 - 2.08114i) q^{80} +(-0.500000 + 0.866025i) q^{81} +14.8114i q^{83} +(1.73205 + 2.00000i) q^{84} -4.83772i q^{85} +(-2.45754 + 1.41886i) q^{86} +(1.08114 - 1.87259i) q^{87} +(-1.08114 + 1.87259i) q^{88} +(2.73861 - 1.58114i) q^{89} -4.16228 q^{90} +(-9.09464 + 2.87880i) q^{91} +5.16228 q^{92} +(-7.79423 + 4.50000i) q^{93} +(2.74342 - 4.75174i) q^{94} +(-13.1623 + 22.7977i) q^{95} +(0.866025 - 0.500000i) q^{96} -11.0000i q^{97} +(4.33013 - 5.50000i) q^{98} +2.16228i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} + 4 q^{10} + 4 q^{12} - 16 q^{13} + 16 q^{14} - 4 q^{16} - 8 q^{17} + 8 q^{22} + 8 q^{23} + 24 q^{25} + 8 q^{26} + 8 q^{27} + 8 q^{29} + 4 q^{30} + 16 q^{35} - 8 q^{36} + 8 q^{39} - 4 q^{40} + 4 q^{42} - 48 q^{43} + 8 q^{48} + 52 q^{49} - 8 q^{51} - 8 q^{52} + 12 q^{53} - 72 q^{55} - 4 q^{56} - 24 q^{61} + 72 q^{62} - 8 q^{64} - 12 q^{65} - 4 q^{66} + 8 q^{68} - 16 q^{69} + 24 q^{75} + 20 q^{77} - 16 q^{78} - 36 q^{79} - 4 q^{81} - 4 q^{87} + 4 q^{88} - 8 q^{90} + 8 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 + 4 * q^10 + 4 * q^12 - 16 * q^13 + 16 * q^14 - 4 * q^16 - 8 * q^17 + 8 * q^22 + 8 * q^23 + 24 * q^25 + 8 * q^26 + 8 * q^27 + 8 * q^29 + 4 * q^30 + 16 * q^35 - 8 * q^36 + 8 * q^39 - 4 * q^40 + 4 * q^42 - 48 * q^43 + 8 * q^48 + 52 * q^49 - 8 * q^51 - 8 * q^52 + 12 * q^53 - 72 * q^55 - 4 * q^56 - 24 * q^61 + 72 * q^62 - 8 * q^64 - 12 * q^65 - 4 * q^66 + 8 * q^68 - 16 * q^69 + 24 * q^75 + 20 * q^77 - 16 * q^78 - 36 * q^79 - 4 * q^81 - 4 * q^87 + 4 * q^88 - 8 * q^90 + 8 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.60464	−	2.08114i	1.61204	−	0.930714i	0.623147	−	0.782105i	$-0.285854\pi$
$5$	3.60464	−	2.08114i	1.61204	−	0.930714i	0.988896	−	0.148609i	$-0.0474796\pi$
$6$			1.00000i			0.408248i
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.08114	−	3.60464i	0.658114	−	1.13989i
$11$	−1.87259	−	1.08114i	−0.564606	−	0.325976i	0.190386	−	0.981709i	$-0.439026\pi$
$11$	−1.87259	−	1.08114i	−0.564606	−	0.325976i	−0.754992	+	0.655734i	$0.772359\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.58114	+	0.418861i	−0.993229	+	0.116171i
$13$	−3.58114	+	0.418861i	−0.993229	+	0.116171i
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$			4.16228i			1.07470i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.581139	−	1.00656i	0.140947	−	0.244127i	−0.786907	−	0.617072i	$-0.788319\pi$
$17$	0.581139	−	1.00656i	0.140947	−	0.244127i	0.927853	+	0.372945i	$0.121652\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−5.47723	+	3.16228i	−1.25656	+	0.725476i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−5.47723	+	3.16228i	−1.25656	+	0.725476i	−0.284157	+	0.958778i	$0.591714\pi$
$20$		−	4.16228i		−	0.930714i
$21$	−0.866025	+	2.50000i	−0.188982	+	0.545545i
$22$	−2.16228			−0.460999
$23$	2.58114	+	4.47066i	0.538205	+	0.932198i	0.999001	+	0.0446918i	$0.0142306\pi$
$23$	2.58114	+	4.47066i	0.538205	+	0.932198i	−0.460796	+	0.887506i	$0.652436\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	6.16228	−	10.6734i	1.23246	−	2.13468i
$26$	−2.89193	+	2.15331i	−0.567153	+	0.422300i
$27$	1.00000			0.192450
$28$	0.866025	−	2.50000i	0.163663	−	0.472456i
$29$	−2.16228			−0.401525			−0.200762	−	0.979640i	$-0.564342\pi$
$29$	−2.16228			−0.401525			−0.200762	+	0.979640i	$0.564342\pi$
$30$	2.08114	+	3.60464i	0.379962	+	0.658114i
$31$	7.79423	+	4.50000i	1.39988	+	0.808224i	0.994380	−	0.105869i	$-0.0337625\pi$
$31$	7.79423	+	4.50000i	1.39988	+	0.808224i	0.405505	+	0.914093i	$0.367096\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.87259	−	1.08114i	0.325976	−	0.188202i
$34$		−	1.16228i		−	0.199329i
$35$	8.32456	−	7.20928i	1.40711	−	1.21859i
$36$	−1.00000			−0.166667
$37$	−5.47723	+	3.16228i	−0.900450	+	0.519875i	−0.877346	−	0.479858i	$-0.840688\pi$
$37$	−5.47723	+	3.16228i	−0.900450	+	0.519875i	−0.0231041	+	0.999733i	$0.507355\pi$
$38$	−3.16228	+	5.47723i	−0.512989	+	0.888523i
$39$	1.42783	−	3.31079i	0.228635	−	0.530150i
$40$	−2.08114	−	3.60464i	−0.329057	−	0.569943i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	0.500000	+	2.59808i	0.0771517	+	0.400892i
$43$	−2.83772			−0.432749			−0.216374	−	0.976310i	$-0.569423\pi$
$43$	−2.83772			−0.432749			−0.216374	+	0.976310i	$0.569423\pi$
$44$	−1.87259	+	1.08114i	−0.282303	+	0.162988i
$45$	−3.60464	−	2.08114i	−0.537348	−	0.310238i
$46$	4.47066	+	2.58114i	0.659163	+	0.380568i
$47$	4.75174	−	2.74342i	0.693112	−	0.400168i	−0.111665	−	0.993746i	$-0.535618\pi$
$47$	4.75174	−	2.74342i	0.693112	−	0.400168i	0.804777	+	0.593578i	$0.202285\pi$
$48$	1.00000			0.144338
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		−	12.3246i		−	1.74296i
$51$	0.581139	+	1.00656i	0.0813757	+	0.140947i
$52$	−1.42783	+	3.31079i	−0.198004	+	0.459124i
$53$	−0.0811388	+	0.140537i	−0.0111453	+	0.0193042i	−0.871544	−	0.490317i	$-0.836881\pi$
$53$	−0.0811388	+	0.140537i	−0.0111453	+	0.0193042i	0.860399	+	0.509621i	$0.170214\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−9.00000			−1.21356
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		−	6.32456i		−	0.837708i
$58$	−1.87259	+	1.08114i	−0.245883	+	0.141960i
$59$	7.06874	+	4.08114i	0.920272	+	0.531319i	0.883722	−	0.468013i	$-0.155030\pi$
$59$	7.06874	+	4.08114i	0.920272	+	0.531319i	0.0365499	+	0.999332i	$0.488363\pi$
$60$	3.60464	+	2.08114i	0.465357	+	0.268674i
$61$	1.74342	+	3.01969i	0.223222	+	0.386631i	0.955784	−	0.294068i	$-0.0950093\pi$
$61$	1.74342	+	3.01969i	0.223222	+	0.386631i	−0.732563	+	0.680699i	$0.761676\pi$
$62$	9.00000			1.14300
$63$	−1.73205	−	2.00000i	−0.218218	−	0.251976i
$64$	−1.00000			−0.125000
$65$	−12.0370	+	8.96269i	−1.49301	+	1.11168i
$66$	1.08114	−	1.87259i	0.133079	−	0.230500i
$67$	−7.93477	−	4.58114i	−0.969386	−	0.559675i	−0.0703369	−	0.997523i	$-0.522407\pi$
$67$	−7.93477	−	4.58114i	−0.969386	−	0.559675i	−0.899049	+	0.437848i	$0.855741\pi$
$68$	−0.581139	−	1.00656i	−0.0704734	−	0.122064i
$69$	−5.16228			−0.621465
$70$	3.60464	−	10.4057i	0.430837	−	1.24372i
$71$			16.3246i			1.93737i	0.248296	+	0.968684i	$0.420129\pi$
$71$			16.3246i			1.93737i	−0.248296	+	0.968684i	$0.579871\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	5.47723	+	3.16228i	0.641061	+	0.370117i	0.785023	−	0.619467i	$-0.212651\pi$
$73$	5.47723	+	3.16228i	0.641061	+	0.370117i	−0.143962	+	0.989583i	$0.545984\pi$
$74$	−3.16228	+	5.47723i	−0.367607	+	0.636715i
$75$	6.16228	+	10.6734i	0.711559	+	1.23246i
$76$			6.32456i			0.725476i
$77$	−5.40569	−	1.87259i	−0.616036	−	0.213401i
$78$	−0.418861	−	3.58114i	−0.0474267	−	0.405484i
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	−0.999974	−	0.00727784i	$-0.997683\pi$
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	0.493684	−	0.869641i	$-0.335650\pi$
$80$	−3.60464	−	2.08114i	−0.403011	−	0.232678i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			14.8114i			1.62576i	0.582430	+	0.812881i	$0.302102\pi$
$83$			14.8114i			1.62576i	−0.582430	+	0.812881i	$0.697898\pi$
$84$	1.73205	+	2.00000i	0.188982	+	0.218218i
$85$		−	4.83772i		−	0.524725i
$86$	−2.45754	+	1.41886i	−0.265003	+	0.153000i
$87$	1.08114	−	1.87259i	0.115910	−	0.200762i
$88$	−1.08114	+	1.87259i	−0.115250	+	0.199618i
$89$	2.73861	−	1.58114i	0.290292	−	0.167600i	−0.347781	−	0.937576i	$-0.613065\pi$
$89$	2.73861	−	1.58114i	0.290292	−	0.167600i	0.638074	+	0.769975i	$0.279732\pi$
$90$	−4.16228			−0.438743
$91$	−9.09464	+	2.87880i	−0.953377	+	0.301781i
$92$	5.16228			0.538205
$93$	−7.79423	+	4.50000i	−0.808224	+	0.466628i
$94$	2.74342	−	4.75174i	0.282962	−	0.490104i
$95$	−13.1623	+	22.7977i	−1.35042	+	2.33900i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	11.0000i		−	1.11688i	−0.829545	−	0.558440i	$-0.811400\pi$
$97$		−	11.0000i		−	1.11688i	0.829545	−	0.558440i	$-0.188600\pi$
$98$	4.33013	−	5.50000i	0.437409	−	0.555584i
$99$			2.16228i			0.217317i
$100$	−6.16228	−	10.6734i	−0.616228	−	1.06734i
$101$	−1.83772	+	3.18303i	−0.182860	+	0.316723i	−0.942853	−	0.333208i	$-0.891869\pi$
$101$	−1.83772	+	3.18303i	−0.182860	+	0.316723i	0.759993	+	0.649931i	$0.225202\pi$
$102$	1.00656	+	0.581139i	0.0996645	+	0.0575413i
$103$	−0.162278	−	0.281073i	−0.0159897	−	0.0276950i	0.857920	−	0.513784i	$-0.171757\pi$
$103$	−0.162278	−	0.281073i	−0.0159897	−	0.0276950i	−0.873910	+	0.486089i	$0.838423\pi$
$104$	0.418861	+	3.58114i	0.0410727	+	0.351160i
$105$	2.08114	+	10.8139i	0.203098	+	1.05533i
$106$			0.162278i			0.0157618i
$107$	3.24342	+	5.61776i	0.313553	+	0.543090i	0.979129	−	0.203241i	$-0.0651474\pi$
$107$	3.24342	+	5.61776i	0.313553	+	0.543090i	−0.665576	+	0.746330i	$0.731814\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−13.4120	−	7.74342i	−1.28464	−	0.741685i	−0.306944	−	0.951728i	$-0.599306\pi$
$109$	−13.4120	−	7.74342i	−1.28464	−	0.741685i	−0.977692	+	0.210043i	$0.932640\pi$
$110$	−7.79423	+	4.50000i	−0.743151	+	0.429058i
$111$		−	6.32456i		−	0.600300i
$112$	−1.73205	−	2.00000i	−0.163663	−	0.188982i
$113$	−14.3246			−1.34754			−0.673770	−	0.738941i	$-0.735326\pi$
$113$	−14.3246			−1.34754			−0.673770	+	0.738941i	$0.735326\pi$
$114$	−3.16228	−	5.47723i	−0.296174	−	0.512989i
$115$	18.6081	+	10.7434i	1.73522	+	1.00183i
$116$	−1.08114	+	1.87259i	−0.100381	+	0.173865i
$117$	2.15331	+	2.89193i	0.199074	+	0.267359i
$118$	8.16228			0.751399
$119$	1.00656	−	2.90569i	0.0922714	−	0.266365i
$120$	4.16228			0.379962
$121$	−3.16228	−	5.47723i	−0.287480	−	0.497930i
$122$	3.01969	+	1.74342i	0.273390	+	0.157842i
$123$		0			0
$124$	7.79423	−	4.50000i	0.699942	−	0.404112i
$125$		−	30.4868i		−	2.72683i
$126$	−2.50000	−	0.866025i	−0.222718	−	0.0771517i
$127$	−21.9737			−1.94985			−0.974924	−	0.222539i	$-0.928566\pi$
$127$	−21.9737			−1.94985			−0.974924	+	0.222539i	$0.928566\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.41886	−	2.45754i	0.124924	−	0.216374i
$130$	−5.94300	+	13.7804i	−0.521236	+	1.20862i
$131$	−1.08114	−	1.87259i	−0.0944595	−	0.163609i	0.814923	−	0.579569i	$-0.196779\pi$
$131$	−1.08114	−	1.87259i	−0.0944595	−	0.163609i	−0.909383	+	0.415960i	$0.863446\pi$
$132$		−	2.16228i		−	0.188202i
$133$	−12.6491	+	10.9545i	−1.09682	+	0.949871i
$134$	−9.16228			−0.791500
$135$	3.60464	−	2.08114i	0.310238	−	0.179116i
$136$	−1.00656	−	0.581139i	−0.0863120	−	0.0498322i
$137$	6.20271	+	3.58114i	0.529934	+	0.305957i	0.740989	−	0.671517i	$-0.234357\pi$
$137$	6.20271	+	3.58114i	0.529934	+	0.305957i	−0.211056	+	0.977474i	$0.567690\pi$
$138$	−4.47066	+	2.58114i	−0.380568	+	0.219721i
$139$	−7.48683			−0.635025			−0.317512	−	0.948254i	$-0.602848\pi$
$139$	−7.48683			−0.635025			−0.317512	+	0.948254i	$0.602848\pi$
$140$	−2.08114	−	10.8139i	−0.175888	−	0.913943i
$141$			5.48683i			0.462075i
$142$	8.16228	+	14.1375i	0.684963	+	1.18639i
$143$	7.15884	+	3.08735i	0.598652	+	0.258178i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−7.79423	+	4.50000i	−0.647275	+	0.373705i
$146$	6.32456			0.523424
$147$	−1.00000	+	6.92820i	−0.0824786	+	0.571429i
$148$			6.32456i			0.519875i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$	10.6734	+	6.16228i	0.871478	+	0.503148i
$151$	2.59808	+	1.50000i	0.211428	+	0.122068i	0.601975	−	0.798515i	$-0.294381\pi$
$151$	2.59808	+	1.50000i	0.211428	+	0.122068i	−0.390547	+	0.920583i	$0.627714\pi$
$152$	3.16228	+	5.47723i	0.256495	+	0.444262i
$153$	−1.16228			−0.0939646
$154$	−5.61776	+	1.08114i	−0.452692	+	0.0871206i
$155$	37.4605			3.00890
$156$	−2.15331	−	2.89193i	−0.172403	−	0.231539i
$157$	7.58114	−	13.1309i	0.605041	−	1.04796i	−0.387004	−	0.922078i	$-0.626490\pi$
$157$	7.58114	−	13.1309i	0.605041	−	1.04796i	0.992045	−	0.125883i	$-0.0401765\pi$
$158$	−7.79423	−	4.50000i	−0.620076	−	0.358001i
$159$	−0.0811388	−	0.140537i	−0.00643473	−	0.0111453i
$160$	−4.16228			−0.329057
$161$	8.94133	+	10.3246i	0.704675	+	0.813689i
$162$			1.00000i			0.0785674i
$163$	10.9545	−	6.32456i	0.858019	−	0.495377i	−0.00532951	−	0.999986i	$-0.501696\pi$
$163$	10.9545	−	6.32456i	0.858019	−	0.495377i	0.863348	+	0.504608i	$0.168363\pi$
$164$		0			0
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$	7.40569	+	12.8270i	0.574793	+	0.995571i
$167$		−	11.1623i		−	0.863763i	−0.901930	−	0.431881i	$-0.857850\pi$
$167$		−	11.1623i		−	0.863763i	0.901930	−	0.431881i	$-0.142150\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	12.6491	−	3.00000i	0.973009	−	0.230769i
$170$	−2.41886	−	4.18959i	−0.185518	−	0.321327i
$171$	5.47723	+	3.16228i	0.418854	+	0.241825i
$172$	−1.41886	+	2.45754i	−0.108187	+	0.187386i
$173$	5.16228	+	8.94133i	0.392481	+	0.679797i	0.992776	−	0.119982i	$-0.0382836\pi$
$173$	5.16228	+	8.94133i	0.392481	+	0.679797i	−0.600295	+	0.799778i	$0.704950\pi$
$174$		−	2.16228i		−	0.163922i
$175$	10.6734	−	30.8114i	0.806832	−	2.32912i
$176$			2.16228i			0.162988i
$177$	−7.06874	+	4.08114i	−0.531319	+	0.306757i
$178$	1.58114	−	2.73861i	0.118511	−	0.205268i
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	−0.676927	−	0.736050i	$-0.736689\pi$
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	0.975901	+	0.218212i	$0.0700223\pi$
$180$	−3.60464	+	2.08114i	−0.268674	+	0.155119i
$181$	10.3246			0.767418			0.383709	−	0.923454i	$-0.374647\pi$
$181$	10.3246			0.767418			0.383709	+	0.923454i	$0.374647\pi$
$182$	−6.43679	+	7.04044i	−0.477127	+	0.521872i
$183$	−3.48683			−0.257754
$184$	4.47066	−	2.58114i	0.329582	−	0.190284i
$185$	−13.1623	+	22.7977i	−0.967710	+	1.67612i
$186$	−4.50000	+	7.79423i	−0.329956	+	0.571501i
$187$	−2.17647	+	1.25658i	−0.159159	+	0.0918905i
$188$		−	5.48683i		−	0.400168i
$189$	2.59808	−	0.500000i	0.188982	−	0.0363696i
$190$			26.3246i			1.90978i
$191$	−11.7434	−	20.3402i	−0.849724	−	1.47176i	−0.881455	−	0.472268i	$-0.843435\pi$
$191$	−11.7434	−	20.3402i	−0.849724	−	1.47176i	0.0317310	−	0.999496i	$-0.489898\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	2.31700	+	1.33772i	0.166782	+	0.0962914i	0.581067	−	0.813855i	$-0.302635\pi$
$193$	2.31700	+	1.33772i	0.166782	+	0.0962914i	−0.414286	+	0.910147i	$0.635969\pi$
$194$	−5.50000	−	9.52628i	−0.394877	−	0.683947i
$195$	−1.74342	−	14.9057i	−0.124849	−	1.06742i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$			13.6754i			0.974335i	0.873309	+	0.487168i	$0.161970\pi$
$197$			13.6754i			0.974335i	−0.873309	+	0.487168i	$0.838030\pi$
$198$	1.08114	+	1.87259i	0.0768332	+	0.133079i
$199$	3.32456	−	5.75830i	0.235671	−	0.408195i	−0.723796	−	0.690014i	$-0.757604\pi$
$199$	3.32456	−	5.75830i	0.235671	−	0.408195i	0.959468	+	0.281819i	$0.0909377\pi$
$200$	−10.6734	−	6.16228i	−0.754722	−	0.435739i
$201$	7.93477	−	4.58114i	0.559675	−	0.323129i
$202$			3.67544i			0.258603i
$203$	−5.61776	+	1.08114i	−0.394290	+	0.0758811i
$204$	1.16228			0.0813757
$205$		0			0
$206$	−0.281073	−	0.162278i	−0.0195833	−	0.0113064i
$207$	2.58114	−	4.47066i	0.179402	−	0.310733i
$208$	2.15331	+	2.89193i	0.149305	+	0.200519i
$209$	13.6754			0.945950
$210$	7.20928	+	8.32456i	0.497487	+	0.574449i
$211$	−0.513167			−0.0353279			−0.0176639	−	0.999844i	$-0.505623\pi$
$211$	−0.513167			−0.0353279			−0.0176639	+	0.999844i	$0.505623\pi$
$212$	0.0811388	+	0.140537i	0.00557264	+	0.00965209i
$213$	−14.1375	−	8.16228i	−0.968684	−	0.559270i
$214$	5.61776	+	3.24342i	0.384022	+	0.221715i
$215$	−10.2290	+	5.90569i	−0.697609	+	0.402765i
$216$		−	1.00000i		−	0.0680414i
$217$	22.5000	+	7.79423i	1.52740	+	0.529107i
$218$	−15.4868			−1.04890
$219$	−5.47723	+	3.16228i	−0.370117	+	0.213687i
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$	−1.65953	+	3.84805i	−0.111632	+	0.258848i
$222$	−3.16228	−	5.47723i	−0.212238	−	0.367607i
$223$			25.9737i			1.73933i	0.493646	+	0.869663i	$0.335664\pi$
$223$			25.9737i			1.73933i	−0.493646	+	0.869663i	$0.664336\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	−12.3246			−0.821637
$226$	−12.4054	+	7.16228i	−0.825197	+	0.476428i
$227$	9.08186	+	5.24342i	0.602784	+	0.348018i	0.770136	−	0.637879i	$-0.220188\pi$
$227$	9.08186	+	5.24342i	0.602784	+	0.348018i	−0.167352	+	0.985897i	$0.553522\pi$
$228$	−5.47723	−	3.16228i	−0.362738	−	0.209427i
$229$	−19.1703	+	11.0680i	−1.26681	+	0.731392i	−0.974383	−	0.224896i	$-0.927796\pi$
$229$	−19.1703	+	11.0680i	−1.26681	+	0.731392i	−0.292426	+	0.956288i	$0.594462\pi$
$230$	21.4868			1.41680
$231$	4.32456	−	3.74517i	0.284535	−	0.246414i
$232$			2.16228i			0.141960i
$233$	−12.9057	−	22.3533i	−0.845480	−	1.46441i	−0.885204	−	0.465204i	$-0.845981\pi$
$233$	−12.9057	−	22.3533i	−0.845480	−	1.46441i	0.0397235	−	0.999211i	$-0.487352\pi$
$234$	3.31079	+	1.42783i	0.216433	+	0.0933398i
$235$	11.4189	−	19.7780i	0.744884	−	1.29018i
$236$	7.06874	−	4.08114i	0.460136	−	0.265660i
$237$	9.00000			0.584613
$238$	−0.581139	−	3.01969i	−0.0376696	−	0.195737i
$239$			2.83772i			0.183557i	0.995779	+	0.0917785i	$0.0292552\pi$
$239$			2.83772i			0.183557i	−0.995779	+	0.0917785i	$0.970745\pi$
$240$	3.60464	−	2.08114i	0.232678	−	0.134337i
$241$	−22.4939	−	12.9868i	−1.44896	−	0.836555i	−0.450537	−	0.892758i	$-0.648768\pi$
$241$	−22.4939	−	12.9868i	−1.44896	−	0.836555i	−0.998419	+	0.0562022i	$0.982101\pi$
$242$	−5.47723	−	3.16228i	−0.352089	−	0.203279i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.48683			0.223222
$245$	18.0232	−	22.8925i	1.15146	−	1.46255i
$246$		0			0
$247$	18.2901	−	13.6188i	1.16377	−	0.866540i
$248$	4.50000	−	7.79423i	0.285750	−	0.494934i
$249$	−12.8270	−	7.40569i	−0.812881	−	0.469317i
$250$	−15.2434	−	26.4024i	−0.964078	−	1.66983i
$251$	−16.4868			−1.04064			−0.520320	−	0.853971i	$-0.674187\pi$
$251$	−16.4868			−1.04064			−0.520320	+	0.853971i	$0.674187\pi$
$252$	−2.59808	+	0.500000i	−0.163663	+	0.0314970i
$253$		−	11.1623i		−	0.701766i
$254$	−19.0298	+	10.9868i	−1.19403	+	0.689375i
$255$	4.18959	+	2.41886i	0.262362	+	0.151475i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.4868	+	21.6278i	0.778907	+	1.34911i	0.932572	+	0.360984i	$0.117559\pi$
$257$	12.4868	+	21.6278i	0.778907	+	1.34911i	−0.153665	+	0.988123i	$0.549108\pi$
$258$		−	2.83772i		−	0.176669i
$259$	−12.6491	+	10.9545i	−0.785977	+	0.680676i
$260$	1.74342	+	14.9057i	0.108122	+	0.924412i
$261$	1.08114	+	1.87259i	0.0669208	+	0.115910i
$262$	−1.87259	−	1.08114i	−0.115689	−	0.0667930i
$263$	6.48683	−	11.2355i	0.399995	−	0.692812i	−0.593730	−	0.804665i	$-0.702345\pi$
$263$	6.48683	−	11.2355i	0.399995	−	0.692812i	0.993725	+	0.111853i	$0.0356784\pi$
$264$	−1.08114	−	1.87259i	−0.0665395	−	0.115250i
$265$			0.675445i			0.0414922i
$266$	−5.47723	+	15.8114i	−0.335830	+	0.969458i
$267$			3.16228i			0.193528i
$268$	−7.93477	+	4.58114i	−0.484693	+	0.279838i
$269$	14.0811	−	24.3892i	0.858542	−	1.48704i	−0.0147773	−	0.999891i	$-0.504704\pi$
$269$	14.0811	−	24.3892i	0.858542	−	1.48704i	0.873319	−	0.487148i	$-0.161963\pi$
$270$	2.08114	−	3.60464i	0.126654	−	0.219371i
$271$	−12.9904	+	7.50000i	−0.789109	+	0.455593i	−0.839649	−	0.543130i	$-0.817239\pi$
$271$	−12.9904	+	7.50000i	−0.789109	+	0.455593i	0.0505395	+	0.998722i	$0.483906\pi$
$272$	−1.16228			−0.0704734
$273$	2.05420	−	9.31559i	0.124326	−	0.563805i
$274$	7.16228			0.432689
$275$	−23.0788	+	13.3246i	−1.39170	+	0.803501i
$276$	−2.58114	+	4.47066i	−0.155366	+	0.269102i
$277$	−7.90569	+	13.6931i	−0.475007	+	0.822736i	−0.999590	−	0.0286227i	$-0.990888\pi$
$277$	−7.90569	+	13.6931i	−0.475007	+	0.822736i	0.524583	+	0.851359i	$0.324221\pi$
$278$	−6.48379	+	3.74342i	−0.388872	+	0.224515i
$279$		−	9.00000i		−	0.538816i
$280$	−7.20928	−	8.32456i	−0.430837	−	0.497487i
$281$		−	11.1623i		−	0.665886i	−0.942947	−	0.332943i	$-0.891958\pi$
$281$		−	11.1623i		−	0.665886i	0.942947	−	0.332943i	$-0.108042\pi$
$282$	2.74342	+	4.75174i	0.163368	+	0.282962i
$283$	8.48683	−	14.6996i	0.504490	−	0.873802i	−0.495497	−	0.868610i	$-0.665014\pi$
$283$	8.48683	−	14.6996i	0.504490	−	0.873802i	0.999987	−	0.00519222i	$-0.00165274\pi$
$284$	14.1375	+	8.16228i	0.838905	+	0.484342i
$285$	−13.1623	−	22.7977i	−0.779666	−	1.35042i
$286$	7.74342	−	0.905694i	0.457878	−	0.0535548i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	7.82456	+	13.5525i	0.460268	+	0.797207i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	9.52628	+	5.50000i	0.558440	+	0.322416i
$292$	5.47723	−	3.16228i	0.320530	−	0.185058i
$293$			0.486833i			0.0284411i	0.999899	+	0.0142205i	$0.00452669\pi$
$293$			0.486833i			0.0284411i	−0.999899	+	0.0142205i	$0.995473\pi$
$294$	2.59808	+	6.50000i	0.151523	+	0.379088i
$295$	33.9737			1.97802
$296$	3.16228	+	5.47723i	0.183804	+	0.318357i
$297$	−1.87259	−	1.08114i	−0.108659	−	0.0627340i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−11.1160	−	14.9289i	−0.642855	−	0.863362i
$300$	12.3246			0.711559
$301$	−7.37262	+	1.41886i	−0.424951	+	0.0817818i
$302$	3.00000			0.172631
$303$	−1.83772	−	3.18303i	−0.105574	−	0.182860i
$304$	5.47723	+	3.16228i	0.314140	+	0.181369i
$305$	12.5688	+	7.25658i	0.719686	+	0.415511i
$306$	−1.00656	+	0.581139i	−0.0575413	+	0.0332215i
$307$		−	8.83772i		−	0.504395i	−0.967676	−	0.252198i	$-0.918847\pi$
$307$		−	8.83772i		−	0.504395i	0.967676	−	0.252198i	$-0.0811533\pi$
$308$	−4.32456	+	3.74517i	−0.246414	+	0.213401i
$309$	0.324555			0.0184633
$310$	32.4417	−	18.7302i	1.84257	−	1.06381i
$311$	−6.06797	+	10.5100i	−0.344083	+	0.595969i	−0.985187	−	0.171485i	$-0.945144\pi$
$311$	−6.06797	+	10.5100i	−0.344083	+	0.595969i	0.641104	+	0.767454i	$0.278477\pi$
$312$	−3.31079	−	1.42783i	−0.187436	−	0.0808347i
$313$	−7.50000	−	12.9904i	−0.423925	−	0.734260i	0.572394	−	0.819979i	$-0.306015\pi$
$313$	−7.50000	−	12.9904i	−0.423925	−	0.734260i	−0.996319	+	0.0857188i	$0.972681\pi$
$314$		−	15.1623i		−	0.855657i
$315$	−10.4057	−	3.60464i	−0.586294	−	0.203098i
$316$	−9.00000			−0.506290
$317$	−16.2911	+	9.40569i	−0.915002	+	0.528276i	−0.882037	−	0.471180i	$-0.843828\pi$
$317$	−16.2911	+	9.40569i	−0.915002	+	0.528276i	−0.0329646	+	0.999457i	$0.510495\pi$
$318$	−0.140537	−	0.0811388i	−0.00788090	−	0.00455004i
$319$	4.04905	+	2.33772i	0.226703	+	0.130887i
$320$	−3.60464	+	2.08114i	−0.201505	+	0.116339i
$321$	−6.48683			−0.362060
$322$	12.9057	+	4.47066i	0.719206	+	0.249140i
$323$			7.35089i			0.409014i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−17.5973	+	40.8040i	−0.976123	+	2.26340i
$326$	6.32456	−	10.9545i	0.350285	−	0.606711i
$327$	13.4120	−	7.74342i	0.741685	−	0.428212i
$328$		0			0
$329$	10.9737	−	9.50347i	0.604998	−	0.523943i
$330$		−	9.00000i		−	0.495434i
$331$	6.92820	−	4.00000i	0.380808	−	0.219860i	−0.297361	−	0.954765i	$-0.596107\pi$
$331$	6.92820	−	4.00000i	0.380808	−	0.219860i	0.678170	+	0.734905i	$0.262773\pi$
$332$	12.8270	+	7.40569i	0.703975	+	0.406440i
$333$	5.47723	+	3.16228i	0.300150	+	0.173292i
$334$	−5.58114	−	9.66682i	−0.305386	−	0.528945i
$335$	−38.1359			−2.08359
$336$	2.59808	−	0.500000i	0.141737	−	0.0272772i
$337$	−17.3246			−0.943729			−0.471864	−	0.881671i	$-0.656419\pi$
$337$	−17.3246			−0.943729			−0.471864	+	0.881671i	$0.656419\pi$
$338$	9.45445	−	8.92263i	0.514254	−	0.485327i
$339$	7.16228	−	12.4054i	0.389002	−	0.673770i
$340$	−4.18959	−	2.41886i	−0.227212	−	0.131181i
$341$	−9.73025	−	16.8533i	−0.526923	−	0.912657i
$342$	6.32456			0.341993
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$			2.83772i			0.153000i
$345$	−18.6081	+	10.7434i	−1.00183	+	0.578406i
$346$	8.94133	+	5.16228i	0.480689	+	0.277526i
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	−0.614664	−	0.788789i	$-0.710708\pi$
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	0.990443	+	0.137920i	$0.0440416\pi$
$348$	−1.08114	−	1.87259i	−0.0579551	−	0.100381i
$349$		−	16.9737i		−	0.908580i	−0.890854	−	0.454290i	$-0.849893\pi$
$349$		−	16.9737i		−	0.908580i	0.890854	−	0.454290i	$-0.150107\pi$
$350$	−6.16228	−	32.0201i	−0.329388	−	1.71155i
$351$	−3.58114	+	0.418861i	−0.191147	+	0.0223572i
$352$	1.08114	+	1.87259i	0.0576249	+	0.0998092i
$353$	23.8043	+	13.7434i	1.26697	+	0.731488i	0.974414	−	0.224759i	$-0.0721594\pi$
$353$	23.8043	+	13.7434i	1.26697	+	0.731488i	0.292560	+	0.956247i	$0.405493\pi$
$354$	−4.08114	+	7.06874i	−0.216910	+	0.375699i
$355$	33.9737	+	58.8441i	1.80313	+	3.12312i
$356$		−	3.16228i		−	0.167600i
$357$	2.01312	+	2.32456i	0.106546	+	0.123029i
$358$		−	8.00000i		−	0.422813i
$359$	17.0394	−	9.83772i	0.899307	−	0.519215i	0.0223317	−	0.999751i	$-0.492891\pi$
$359$	17.0394	−	9.83772i	0.899307	−	0.519215i	0.876975	+	0.480535i	$0.159558\pi$
$360$	−2.08114	+	3.60464i	−0.109686	+	0.189981i
$361$	10.5000	−	18.1865i	0.552632	−	0.957186i
$362$	8.94133	−	5.16228i	0.469946	−	0.271323i
$363$	6.32456			0.331953
$364$	−2.05420	+	9.31559i	−0.107670	+	0.488270i
$365$	26.3246			1.37789
$366$	−3.01969	+	1.74342i	−0.157842	+	0.0911298i
$367$	−10.6623	+	18.4676i	−0.556566	+	0.964001i	0.441213	+	0.897402i	$0.354548\pi$
$367$	−10.6623	+	18.4676i	−0.556566	+	0.964001i	−0.997780	+	0.0665990i	$0.978785\pi$
$368$	2.58114	−	4.47066i	0.134551	−	0.233049i
$369$		0			0
$370$			26.3246i			1.36855i
$371$	−0.140537	+	0.405694i	−0.00729630	+	0.0210626i
$372$			9.00000i			0.466628i
$373$	8.74342	+	15.1440i	0.452717	+	0.784129i	0.998554	−	0.0537628i	$-0.0171215\pi$
$373$	8.74342	+	15.1440i	0.452717	+	0.784129i	−0.545837	+	0.837892i	$0.683788\pi$
$374$	−1.25658	+	2.17647i	−0.0649764	+	0.112542i
$375$	26.4024	+	15.2434i	1.36341	+	0.787167i
$376$	−2.74342	−	4.75174i	−0.141481	−	0.245052i
$377$	7.74342	−	0.905694i	0.398806	−	0.0466456i
$378$	2.00000	−	1.73205i	0.102869	−	0.0890871i
$379$		−	14.9737i		−	0.769146i	−0.923095	−	0.384573i	$-0.874349\pi$
$379$		−	14.9737i		−	0.769146i	0.923095	−	0.384573i	$-0.125651\pi$
$380$	13.1623	+	22.7977i	0.675211	+	1.16950i
$381$	10.9868	−	19.0298i	0.562873	−	0.974924i
$382$	−20.3402	−	11.7434i	−1.04069	−	0.600845i
$383$	12.6865	−	7.32456i	0.648250	−	0.374267i	−0.139535	−	0.990217i	$-0.544561\pi$
$383$	12.6865	−	7.32456i	0.648250	−	0.374267i	0.787785	+	0.615950i	$0.211228\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−23.3827	+	4.50000i	−1.19169	+	0.229341i
$386$	2.67544			0.136177
$387$	1.41886	+	2.45754i	0.0721248	+	0.124924i
$388$	−9.52628	−	5.50000i	−0.483624	−	0.279220i
$389$	10.1623	−	17.6016i	0.515248	−	0.892436i	−0.484595	−	0.874738i	$-0.661033\pi$
$389$	10.1623	−	17.6016i	0.515248	−	0.892436i	0.999843	−	0.0176972i	$-0.00563349\pi$
$390$	−8.96269	−	12.0370i	−0.453843	−	0.609517i
$391$	6.00000			0.303433
$392$	−2.59808	−	6.50000i	−0.131223	−	0.328300i
$393$	2.16228			0.109072
$394$	6.83772	+	11.8433i	0.344479	+	0.596656i
$395$	−32.4417	−	18.7302i	−1.63232	−	0.942421i
$396$	1.87259	+	1.08114i	0.0941011	+	0.0543293i
$397$	−2.17647	+	1.25658i	−0.109234	+	0.0630661i	−0.553622	−	0.832768i	$-0.686755\pi$
$397$	−2.17647	+	1.25658i	−0.109234	+	0.0630661i	0.444388	+	0.895835i	$0.353421\pi$
$398$		−	6.64911i		−	0.333290i
$399$	−3.16228	−	16.4317i	−0.158312	−	0.822613i
$400$	−12.3246			−0.616228
$401$	−3.01969	+	1.74342i	−0.150796	+	0.0870621i	−0.573499	−	0.819206i	$-0.694415\pi$
$401$	−3.01969	+	1.74342i	−0.150796	+	0.0870621i	0.422703	+	0.906268i	$0.361081\pi$
$402$	4.58114	−	7.93477i	0.228486	−	0.395750i
$403$	−29.7971	−	12.8504i	−1.48430	−	0.640125i
$404$	1.83772	+	3.18303i	0.0914301	+	0.158362i
$405$			4.16228i			0.206825i
$406$	−4.32456	+	3.74517i	−0.214624	+	0.185870i
$407$	13.6754			0.677867
$408$	1.00656	−	0.581139i	0.0498322	−	0.0287707i
$409$	29.9842	+	17.3114i	1.48262	+	0.855993i	0.999805	−	0.0197276i	$-0.00627990\pi$
$409$	29.9842	+	17.3114i	1.48262	+	0.855993i	0.482818	+	0.875721i	$0.339613\pi$
$410$		0			0
$411$	−6.20271	+	3.58114i	−0.305957	+	0.176645i
$412$	−0.324555			−0.0159897
$413$	20.4057	+	7.06874i	1.00410	+	0.347830i
$414$		−	5.16228i		−	0.253712i
$415$	30.8246	+	53.3897i	1.51312	+	2.62080i
$416$	3.31079	+	1.42783i	0.162325	+	0.0700049i
$417$	3.74342	−	6.48379i	0.183316	−	0.317512i
$418$	11.8433	−	6.83772i	0.579274	−	0.334444i
$419$	−30.6491			−1.49731			−0.748654	−	0.662961i	$-0.769299\pi$
$419$	−30.6491			−1.49731			−0.748654	+	0.662961i	$0.769299\pi$
$420$	10.4057	+	3.60464i	0.507746	+	0.175888i
$421$			39.4868i			1.92447i	0.272219	+	0.962235i	$0.412242\pi$
$421$			39.4868i			1.92447i	−0.272219	+	0.962235i	$0.587758\pi$
$422$	−0.444416	+	0.256584i	−0.0216338	+	0.0124903i
$423$	−4.75174	−	2.74342i	−0.231037	−	0.133389i
$424$	0.140537	+	0.0811388i	0.00682506	+	0.00394045i
$425$	−7.16228	−	12.4054i	−0.347421	−	0.601752i
$426$	−16.3246			−0.790927
$427$	6.03937	+	6.97367i	0.292266	+	0.337479i
$428$	6.48683			0.313553
$429$	−6.25315	+	4.65606i	−0.301905	+	0.224797i
$430$	−5.90569	+	10.2290i	−0.284798	+	0.493284i
$431$	3.01969	+	1.74342i	0.145453	+	0.0839774i	0.570960	−	0.820978i	$-0.306571\pi$
$431$	3.01969	+	1.74342i	0.145453	+	0.0839774i	−0.425507	+	0.904955i	$0.639904\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−20.0000			−0.961139			−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000			−0.961139			−0.480569	+	0.876957i	$0.659570\pi$
$434$	23.3827	−	4.50000i	1.12240	−	0.216007i
$435$		−	9.00000i		−	0.431517i
$436$	−13.4120	+	7.74342i	−0.642318	+	0.370842i
$437$	−28.2750	−	16.3246i	−1.35257	−	0.780909i
$438$	−3.16228	+	5.47723i	−0.151099	+	0.261712i
$439$	−16.9868	−	29.4221i	−0.810737	−	1.40424i	−0.912349	−	0.409414i	$-0.865733\pi$
$439$	−16.9868	−	29.4221i	−0.810737	−	1.40424i	0.101611	−	0.994824i	$-0.467600\pi$
$440$			9.00000i			0.429058i
$441$	−5.50000	−	4.33013i	−0.261905	−	0.206197i
$442$	0.486833	+	4.16228i	0.0231563	+	0.197979i
$443$	5.56797	+	9.64401i	0.264542	+	0.458201i	0.967444	−	0.253087i	$-0.0814458\pi$
$443$	5.56797	+	9.64401i	0.264542	+	0.458201i	−0.702901	+	0.711287i	$0.748112\pi$
$444$	−5.47723	−	3.16228i	−0.259938	−	0.150075i
$445$	6.58114	−	11.3989i	0.311976	−	0.540358i
$446$	12.9868	+	22.4939i	0.614944	+	1.06511i
$447$			6.00000i			0.283790i
$448$	−2.59808	+	0.500000i	−0.122748	+	0.0236228i
$449$		−	38.3246i		−	1.80865i	−0.426847	−	0.904324i	$-0.640376\pi$
$449$		−	38.3246i		−	1.80865i	0.426847	−	0.904324i	$-0.359624\pi$
$450$	−10.6734	+	6.16228i	−0.503148	+	0.290493i
$451$		0			0
$452$	−7.16228	+	12.4054i	−0.336885	+	0.583502i
$453$	−2.59808	+	1.50000i	−0.122068	+	0.0704761i
$454$	10.4868			0.492171
$455$	−26.7917	+	29.3043i	−1.25601	+	1.37380i
$456$	−6.32456			−0.296174
$457$	−6.06218	+	3.50000i	−0.283577	+	0.163723i	−0.635042	−	0.772478i	$-0.719017\pi$
$457$	−6.06218	+	3.50000i	−0.283577	+	0.163723i	0.351465	+	0.936201i	$0.385684\pi$
$458$	−11.0680	+	19.1703i	−0.517172	+	0.895769i
$459$	0.581139	−	1.00656i	0.0271252	−	0.0469823i
$460$	18.6081	−	10.7434i	0.867609	−	0.500914i
$461$		−	10.6491i		−	0.495979i	−0.968763	−	0.247989i	$-0.920230\pi$
$461$		−	10.6491i		−	0.495979i	0.968763	−	0.247989i	$-0.0797698\pi$
$462$	1.87259	−	5.40569i	0.0871206	−	0.251496i
$463$			11.6754i			0.542604i	0.962494	+	0.271302i	$0.0874542\pi$
$463$			11.6754i			0.542604i	−0.962494	+	0.271302i	$0.912546\pi$
$464$	1.08114	+	1.87259i	0.0501906	+	0.0869327i
$465$	−18.7302	+	32.4417i	−0.868595	+	1.50445i
$466$	−22.3533	−	12.9057i	−1.03550	−	0.597845i
$467$	4.32456	+	7.49035i	0.200117	+	0.346612i	0.948566	−	0.316580i	$-0.102535\pi$
$467$	4.32456	+	7.49035i	0.200117	+	0.346612i	−0.748449	+	0.663192i	$0.769201\pi$
$468$	3.58114	−	0.418861i	0.165538	−	0.0193619i
$469$	−22.9057	−	7.93477i	−1.05769	−	0.366393i
$470$		−	22.8377i		−	1.05343i
$471$	7.58114	+	13.1309i	0.349320	+	0.605041i
$472$	4.08114	−	7.06874i	0.187850	−	0.325365i
$473$	5.31388	+	3.06797i	0.244333	+	0.141065i
$474$	7.79423	−	4.50000i	0.358001	−	0.206692i
$475$			77.9473i			3.57647i
$476$	−2.01312	−	2.32456i	−0.0922714	−	0.106546i
$477$	0.162278			0.00743018
$478$	1.41886	+	2.45754i	0.0648972	+	0.112405i
$479$	−13.5753	−	7.83772i	−0.620273	−	0.358115i	0.156702	−	0.987646i	$-0.449914\pi$
$479$	−13.5753	−	7.83772i	−0.620273	−	0.358115i	−0.776975	+	0.629531i	$0.783247\pi$
$480$	2.08114	−	3.60464i	0.0949906	−	0.164528i
$481$	18.2901	−	13.6188i	0.833959	−	0.620962i
$482$	−25.9737			−1.18307
$483$	−13.4120	+	2.58114i	−0.610267	+	0.117446i
$484$	−6.32456			−0.287480
$485$	−22.8925	−	39.6510i	−1.03950	−	1.80046i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−16.4545	−	9.50000i	−0.745624	−	0.430486i	0.0784867	−	0.996915i	$-0.474991\pi$
$487$	−16.4545	−	9.50000i	−0.745624	−	0.430486i	−0.824110	+	0.566429i	$0.808325\pi$
$488$	3.01969	−	1.74342i	0.136695	−	0.0789208i
$489$			12.6491i			0.572013i
$490$	4.16228	−	28.8371i	0.188033	−	1.30273i
$491$	−17.8377			−0.805005			−0.402503	−	0.915419i	$-0.631860\pi$
$491$	−17.8377			−0.805005			−0.402503	+	0.915419i	$0.631860\pi$
$492$		0			0
$493$	−1.25658	+	2.17647i	−0.0565937	+	0.0980231i
$494$	9.03036	−	20.9393i	0.406295	−	0.942102i
$495$	4.50000	+	7.79423i	0.202260	+	0.350325i
$496$		−	9.00000i		−	0.404112i
$497$	8.16228	+	42.4124i	0.366128	+	1.90246i
$498$	−14.8114			−0.663714
$499$	9.94789	−	5.74342i	0.445329	−	0.257111i	−0.260527	−	0.965467i	$-0.583896\pi$
$499$	9.94789	−	5.74342i	0.445329	−	0.257111i	0.705855	+	0.708356i	$0.250563\pi$
$500$	−26.4024	−	15.2434i	−1.18075	−	0.681706i
$501$	9.66682	+	5.58114i	0.431881	+	0.249347i
$502$	−14.2780	+	8.24342i	−0.637259	+	0.367922i
$503$	15.4868			0.690524			0.345262	−	0.938506i	$-0.387790\pi$
$503$	15.4868			0.690524			0.345262	+	0.938506i	$0.387790\pi$
$504$	−2.00000	+	1.73205i	−0.0890871	+	0.0771517i
$505$			15.2982i			0.680762i
$506$	−5.58114	−	9.66682i	−0.248112	−	0.429742i
$507$	−3.72648	+	12.4545i	−0.165499	+	0.553122i
$508$	−10.9868	+	19.0298i	−0.487462	+	0.844309i
$509$	20.9251	−	12.0811i	0.927491	−	0.535487i	0.0414737	−	0.999140i	$-0.486795\pi$
$509$	20.9251	−	12.0811i	0.927491	−	0.535487i	0.886017	+	0.463653i	$0.153461\pi$
$510$	4.83772			0.214218
$511$	15.8114	+	5.47723i	0.699455	+	0.242298i
$512$			1.00000i			0.0441942i
$513$	−5.47723	+	3.16228i	−0.241825	+	0.139618i
$514$	21.6278	+	12.4868i	0.953963	+	0.550771i
$515$	−1.16990	−	0.675445i	−0.0515522	−	0.0297636i
$516$	−1.41886	−	2.45754i	−0.0624619	−	0.108187i
$517$	−11.8641			−0.521781
$518$	−5.47723	+	15.8114i	−0.240655	+	0.694713i
$519$	−10.3246			−0.453198
$520$	8.96269	+	12.0370i	0.393040	+	0.527857i
$521$	10.7434	−	18.6081i	0.470678	−	0.815238i	−0.528760	−	0.848771i	$-0.677343\pi$
$521$	10.7434	−	18.6081i	0.470678	−	0.815238i	0.999438	+	0.0335339i	$0.0106762\pi$
$522$	1.87259	+	1.08114i	0.0819609	+	0.0473202i
$523$	−18.3246	−	31.7391i	−0.801277	−	1.38785i	−0.918776	−	0.394779i	$-0.870821\pi$
$523$	−18.3246	−	31.7391i	−0.801277	−	1.38785i	0.117499	−	0.993073i	$-0.462512\pi$
$524$	−2.16228			−0.0944595
$525$	21.3468	+	24.6491i	0.931649	+	1.07578i
$526$		−	12.9737i		−	0.565679i
$527$	9.05906	−	5.23025i	0.394619	−	0.227833i
$528$	−1.87259	−	1.08114i	−0.0814939	−	0.0470505i
$529$	−1.82456	+	3.16022i	−0.0793285	+	0.137401i
$530$	0.337722	+	0.584952i	0.0146697	+	0.0254087i
$531$		−	8.16228i		−	0.354213i
$532$	3.16228	+	16.4317i	0.137102	+	0.712404i
$533$		0			0
$534$	1.58114	+	2.73861i	0.0684226	+	0.118511i
$535$	23.3827	+	13.5000i	1.01092	+	0.583656i
$536$	−4.58114	+	7.93477i	−0.197875	+	0.342730i
$537$	4.00000	+	6.92820i	0.172613	+	0.298974i
$538$		−	28.1623i		−	1.21416i
$539$	−14.9807	−	2.16228i	−0.645264	−	0.0931359i
$540$		−	4.16228i		−	0.179116i
$541$	40.2360	−	23.2302i	1.72988	−	0.998746i	0.839912	−	0.542723i	$-0.182607\pi$
$541$	40.2360	−	23.2302i	1.72988	−	0.998746i	0.889968	−	0.456024i	$-0.150727\pi$
$542$	−7.50000	+	12.9904i	−0.322153	+	0.557985i
$543$	−5.16228	+	8.94133i	−0.221535	+	0.383709i
$544$	−1.00656	+	0.581139i	−0.0431560	+	0.0249161i
$545$	−64.4605			−2.76118
$546$	−2.87880	−	9.09464i	−0.123201	−	0.389215i
$547$	8.64911			0.369809			0.184905	−	0.982756i	$-0.440802\pi$
$547$	8.64911			0.369809			0.184905	+	0.982756i	$0.440802\pi$
$548$	6.20271	−	3.58114i	0.264967	−	0.152979i
$549$	1.74342	−	3.01969i	0.0744072	−	0.128877i
$550$	−13.3246	+	23.0788i	−0.568161	+	0.984084i
$551$	11.8433	−	6.83772i	0.504541	−	0.291297i
$552$			5.16228i			0.219721i
$553$	−15.5885	−	18.0000i	−0.662889	−	0.765438i
$554$			15.8114i			0.671762i
$555$	−13.1623	−	22.7977i	−0.558708	−	0.967710i
$556$	−3.74342	+	6.48379i	−0.158756	+	0.274974i
$557$	12.2649	+	7.08114i	0.519680	+	0.300037i	0.736804	−	0.676107i	$-0.236334\pi$
$557$	12.2649	+	7.08114i	0.519680	+	0.300037i	−0.217124	+	0.976144i	$0.569667\pi$
$558$	−4.50000	−	7.79423i	−0.190500	−	0.329956i
$559$	10.1623	−	1.18861i	0.429819	−	0.0502729i
$560$	−10.4057	−	3.60464i	−0.439721	−	0.152324i
$561$		−	2.51317i		−	0.106106i
$562$	−5.58114	−	9.66682i	−0.235426	−	0.407770i
$563$	−10.4057	+	18.0232i	−0.438548	+	0.759587i	−0.997578	−	0.0695605i	$-0.977840\pi$
$563$	−10.4057	+	18.0232i	−0.438548	+	0.759587i	0.559030	+	0.829147i	$0.311174\pi$
$564$	4.75174	+	2.74342i	0.200084	+	0.115519i
$565$	−51.6348	+	29.8114i	−2.17229	+	1.25417i
$566$		−	16.9737i		−	0.713456i
$567$	−0.866025	+	2.50000i	−0.0363696	+	0.104990i
$568$	16.3246			0.684963
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$	−22.7977	−	13.1623i	−0.954892	−	0.551307i
$571$	−12.9057	+	22.3533i	−0.540086	+	0.935457i	0.458812	+	0.888533i	$0.348275\pi$
$571$	−12.9057	+	22.3533i	−0.540086	+	0.935457i	−0.998898	+	0.0469239i	$0.985058\pi$
$572$	6.25315	−	4.65606i	0.261457	−	0.194680i
$573$	23.4868			0.981177
$574$		0			0
$575$	63.6228			2.65325
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	12.1015	+	6.98683i	0.503794	+	0.290866i	0.730279	−	0.683149i	$-0.239390\pi$
$577$	12.1015	+	6.98683i	0.503794	+	0.290866i	−0.226485	+	0.974015i	$0.572723\pi$
$578$	13.5525	+	7.82456i	0.563711	+	0.325459i
$579$	−2.31700	+	1.33772i	−0.0962914	+	0.0555938i
$580$			9.00000i			0.373705i
$581$	7.40569	+	38.4811i	0.307240	+	1.59647i
$582$	11.0000			0.455965
$583$	0.303879	−	0.175445i	0.0125854	−	0.00726618i
$584$	3.16228	−	5.47723i	0.130856	−	0.226649i
$585$	13.7804	+	5.94300i	0.569750	+	0.245713i
$586$	0.243416	+	0.421610i	0.0100554	+	0.0174165i
$587$		−	14.1623i		−	0.584540i	−0.956336	−	0.292270i	$-0.905589\pi$
$587$		−	14.1623i		−	0.584540i	0.956336	−	0.292270i	$-0.0944106\pi$
$588$	5.50000	+	4.33013i	0.226816	+	0.178571i
$589$	−56.9210			−2.34539
$590$	29.4221	−	16.9868i	1.21129	−	0.699337i
$591$	−11.8433	−	6.83772i	−0.487168	−	0.281266i
$592$	5.47723	+	3.16228i	0.225113	+	0.129969i
$593$	20.7846	−	12.0000i	0.853522	−	0.492781i	−0.00831589	−	0.999965i	$-0.502647\pi$
$593$	20.7846	−	12.0000i	0.853522	−	0.492781i	0.861838	+	0.507184i	$0.169314\pi$
$594$	−2.16228			−0.0887193
$595$	−2.41886	−	12.5688i	−0.0991636	−	0.515269i
$596$		−	6.00000i		−	0.245770i
$597$	3.32456	+	5.75830i	0.136065	+	0.235671i
$598$	−17.0912	−	7.37083i	−0.698911	−	0.301416i
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	−0.920783	−	0.390075i	$-0.872449\pi$
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	0.798206	+	0.602384i	$0.205782\pi$
$600$	10.6734	−	6.16228i	0.435739	−	0.251574i
$601$	28.9473			1.18079			0.590393	−	0.807116i	$-0.298973\pi$
$601$	28.9473			1.18079			0.590393	+	0.807116i	$0.298973\pi$
$602$	−5.67544	+	4.91508i	−0.231314	+	0.200324i
$603$			9.16228i			0.373117i
$604$	2.59808	−	1.50000i	0.105714	−	0.0610341i
$605$	−22.7977	−	13.1623i	−0.926860	−	0.535123i
$606$	−3.18303	−	1.83772i	−0.129302	−	0.0746524i
$607$	23.8246	+	41.2653i	0.967009	+	1.67491i	0.704118	+	0.710083i	$0.251343\pi$
$607$	23.8246	+	41.2653i	0.967009	+	1.67491i	0.262891	+	0.964826i	$0.415324\pi$
$608$	6.32456			0.256495
$609$	1.87259	−	5.40569i	0.0758811	−	0.219050i
$610$	14.5132			0.587621
$611$	−15.8675	+	11.8149i	−0.641931	+	0.477979i
$612$	−0.581139	+	1.00656i	−0.0234911	+	0.0406879i
$613$	6.36606	+	3.67544i	0.257123	+	0.148450i	0.623021	−	0.782205i	$-0.285905\pi$
$613$	6.36606	+	3.67544i	0.257123	+	0.148450i	−0.365899	+	0.930655i	$0.619238\pi$
$614$	−4.41886	−	7.65369i	−0.178331	−	0.308878i
$615$		0			0
$616$	−1.87259	+	5.40569i	−0.0754487	+	0.217802i
$617$			11.1623i			0.449376i	0.974431	+	0.224688i	$0.0721364\pi$
$617$			11.1623i			0.449376i	−0.974431	+	0.224688i	$0.927864\pi$
$618$	0.281073	−	0.162278i	0.0113064	−	0.00652776i
$619$	−18.8892	−	10.9057i	−0.759222	−	0.438337i	0.0697945	−	0.997561i	$-0.477766\pi$
$619$	−18.8892	−	10.9057i	−0.759222	−	0.438337i	−0.829016	+	0.559225i	$0.811099\pi$
$620$	18.7302	−	32.4417i	0.752225	−	1.30289i
$621$	2.58114	+	4.47066i	0.103578	+	0.179402i
$622$			12.1359i			0.486607i
$623$	6.32456	−	5.47723i	0.253388	−	0.219440i
$624$	−3.58114	+	0.418861i	−0.143360	+	0.0167679i
$625$	−32.6359	−	56.5271i	−1.30544	−	2.26108i
$626$	−12.9904	−	7.50000i	−0.519200	−	0.299760i
$627$	−6.83772	+	11.8433i	−0.273072	+	0.472975i
$628$	−7.58114	−	13.1309i	−0.302520	−	0.523981i
$629$			7.35089i			0.293099i
$630$	−10.8139	+	2.08114i	−0.430837	+	0.0829146i
$631$		−	22.2982i		−	0.887678i	−0.896107	−	0.443839i	$-0.853616\pi$
$631$		−	22.2982i		−	0.887678i	0.896107	−	0.443839i	$-0.146384\pi$
$632$	−7.79423	+	4.50000i	−0.310038	+	0.179000i
$633$	0.256584	−	0.444416i	0.0101983	−	0.0176639i
$634$	−9.40569	+	16.2911i	−0.373548	+	0.647004i
$635$	−79.2071	+	45.7302i	−3.14324	+	1.81475i
$636$	−0.162278			−0.00643473
$637$	−22.1892	+	12.0267i	−0.879167	+	0.476514i
$638$	4.67544			0.185103
$639$	14.1375	−	8.16228i	0.559270	−	0.322895i
$640$	−2.08114	+	3.60464i	−0.0822642	+	0.142486i
$641$	−17.5811	+	30.4514i	−0.694413	+	1.20276i	0.275965	+	0.961168i	$0.411003\pi$
$641$	−17.5811	+	30.4514i	−0.694413	+	1.20276i	−0.970378	+	0.241591i	$0.922331\pi$
$642$	−5.61776	+	3.24342i	−0.221715	+	0.128007i
$643$			21.1623i			0.834559i	0.908778	+	0.417279i	$0.137016\pi$
$643$			21.1623i			0.834559i	−0.908778	+	0.417279i	$0.862984\pi$
$644$	13.4120	−	2.58114i	0.528506	−	0.101711i
$645$		−	11.8114i		−	0.465073i
$646$	3.67544	+	6.36606i	0.144608	+	0.250469i
$647$	18.2302	−	31.5757i	0.716705	−	1.24137i	−0.245593	−	0.969373i	$-0.578983\pi$
$647$	18.2302	−	31.5757i	0.716705	−	1.24137i	0.962298	−	0.271997i	$-0.0876839\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−8.82456	−	15.2846i	−0.346394	−	0.599972i
$650$	5.16228	+	44.1359i	0.202481	+	1.73115i
$651$	−18.0000	+	15.5885i	−0.705476	+	0.610960i
$652$		−	12.6491i		−	0.495377i
$653$	−6.56797	−	11.3761i	−0.257025	−	0.445180i	0.708419	−	0.705792i	$-0.249409\pi$
$653$	−6.56797	−	11.3761i	−0.257025	−	0.445180i	−0.965443	+	0.260613i	$0.916075\pi$
$654$	7.74342	−	13.4120i	0.302792	−	0.524450i
$655$	−7.79423	−	4.50000i	−0.304546	−	0.175830i
$656$		0			0
$657$		−	6.32456i		−	0.246744i
$658$	4.75174	−	13.7171i	0.185242	−	0.534748i
$659$	−40.2719			−1.56877			−0.784385	−	0.620274i	$-0.787021\pi$
$659$	−40.2719			−1.56877			−0.784385	+	0.620274i	$0.787021\pi$
$660$	−4.50000	−	7.79423i	−0.175162	−	0.303390i
$661$	−5.75830	−	3.32456i	−0.223972	−	0.129310i	0.383816	−	0.923410i	$-0.374610\pi$
$661$	−5.75830	−	3.32456i	−0.223972	−	0.129310i	−0.607788	+	0.794099i	$0.707943\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$	−2.50275	−	3.36122i	−0.0971987	−	0.130539i
$664$	14.8114			0.574793
$665$	−22.7977	+	65.8114i	−0.884058	+	2.55206i
$666$	6.32456			0.245072
$667$	−5.58114	−	9.66682i	−0.216103	−	0.374301i
$668$	−9.66682	−	5.58114i	−0.374020	−	0.215941i
$669$	−22.4939	−	12.9868i	−0.869663	−	0.502100i
$670$	−33.0267	+	19.0680i	−1.27593	+	0.736660i
$671$		−	7.53950i		−	0.291059i
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$	9.32456			0.359435			0.179718	−	0.983718i	$-0.442482\pi$
$673$	9.32456			0.359435			0.179718	+	0.983718i	$0.442482\pi$
$674$	−15.0035	+	8.66228i	−0.577913	+	0.333658i
$675$	6.16228	−	10.6734i	0.237186	−	0.410819i
$676$	3.72648	−	12.4545i	0.143326	−	0.479017i
$677$	11.2434	+	19.4742i	0.432120	+	0.748453i	0.997056	−	0.0766816i	$-0.0244325\pi$
$677$	11.2434	+	19.4742i	0.432120	+	0.748453i	−0.564936	+	0.825135i	$0.691099\pi$
$678$		−	14.3246i		−	0.550131i
$679$	−5.50000	−	28.5788i	−0.211071	−	1.09676i
$680$	−4.83772			−0.185518
$681$	−9.08186	+	5.24342i	−0.348018	+	0.200928i
$682$	−16.8533	−	9.73025i	−0.645346	−	0.372591i
$683$	16.8989	+	9.75658i	0.646618	+	0.373325i	0.787159	−	0.616750i	$-0.211551\pi$
$683$	16.8989	+	9.75658i	0.646618	+	0.373325i	−0.140541	+	0.990075i	$0.544884\pi$
$684$	5.47723	−	3.16228i	0.209427	−	0.120913i
$685$	29.8114			1.13903
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		−	22.1359i		−	0.844539i
$688$	1.41886	+	2.45754i	0.0540936	+	0.0936928i
$689$	0.231704	−	0.537267i	0.00882722	−	0.0204682i
$690$	−10.7434	+	18.6081i	−0.408995	+	0.708400i
$691$	6.92820	−	4.00000i	0.263561	−	0.152167i	−0.362397	−	0.932024i	$-0.618041\pi$
$691$	6.92820	−	4.00000i	0.263561	−	0.152167i	0.625958	+	0.779857i	$0.284708\pi$
$692$	10.3246			0.392481
$693$	1.08114	+	5.61776i	0.0410691	+	0.213401i
$694$		−	14.0000i		−	0.531433i
$695$	−26.9873	+	15.5811i	−1.02369	+	0.591026i
$696$	−1.87259	−	1.08114i	−0.0709802	−	0.0409805i
$697$		0			0
$698$	−8.48683	−	14.6996i	−0.321231	−	0.556389i
$699$	25.8114			0.976276
$700$	−21.3468	−	24.6491i	−0.806832	−	0.931649i
$701$	40.8114			1.54142			0.770712	−	0.637183i	$-0.219901\pi$
$701$	40.8114			1.54142			0.770712	+	0.637183i	$0.219901\pi$
$702$	−2.89193	+	2.15331i	−0.109149	+	0.0812716i
$703$	20.0000	−	34.6410i	0.754314	−	1.30651i
$704$	1.87259	+	1.08114i	0.0705758	+	0.0407470i
$705$	11.4189	+	19.7780i	0.430059	+	0.744884i
$706$	27.4868			1.03448
$707$	−3.18303	+	9.18861i	−0.119710	+	0.345573i
$708$			8.16228i			0.306757i
$709$	10.6734	−	6.16228i	0.400847	−	0.231429i	−0.286002	−	0.958229i	$-0.592327\pi$
$709$	10.6734	−	6.16228i	0.400847	−	0.231429i	0.686849	+	0.726800i	$0.258993\pi$
$710$	58.8441	+	33.9737i	2.20838	+	1.27501i
$711$	−4.50000	+	7.79423i	−0.168763	+	0.292306i
$712$	−1.58114	−	2.73861i	−0.0592557	−	0.102634i
$713$			46.4605i			1.73996i
$714$	2.90569	+	1.00656i	0.108743	+	0.0376696i
$715$	32.2302	−	3.76975i	1.20534	−	0.140981i
$716$	−4.00000	−	6.92820i	−0.149487	−	0.258919i
$717$	−2.45754	−	1.41886i	−0.0917785	−	0.0529883i
$718$	9.83772	−	17.0394i	0.367141	−	0.635906i
$719$	12.8114	+	22.1900i	0.477784	+	0.827546i	0.999676	−	0.0254654i	$-0.00810677\pi$
$719$	12.8114	+	22.1900i	0.477784	+	0.827546i	−0.521892	+	0.853012i	$0.674773\pi$
$720$			4.16228i			0.155119i
$721$	−0.562146	−	0.649111i	−0.0209354	−	0.0241741i
$722$		−	21.0000i		−	0.781539i
$723$	22.4939	−	12.9868i	0.836555	−	0.482986i
$724$	5.16228	−	8.94133i	0.191855	−	0.332302i
$725$	−13.3246	+	23.0788i	−0.494862	+	0.857125i
$726$	5.47723	−	3.16228i	0.203279	−	0.117363i
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	2.87880	+	9.09464i	0.106696	+	0.337070i
$729$	1.00000			0.0370370
$730$	22.7977	−	13.1623i	0.843782	−	0.487158i
$731$	−1.64911	+	2.85634i	−0.0609946	+	0.105646i
$732$	−1.74342	+	3.01969i	−0.0644385	+	0.111611i
$733$	11.5622	−	6.67544i	0.427060	−	0.246563i	−0.271033	−	0.962570i	$-0.587365\pi$
$733$	11.5622	−	6.67544i	0.427060	−	0.246563i	0.698093	+	0.716007i	$0.254032\pi$
$734$			21.3246i			0.787104i
$735$	10.8139	+	27.0548i	0.398877	+	0.997932i
$736$		−	5.16228i		−	0.190284i
$737$	9.90569	+	17.1572i	0.364881	+	0.631992i
$738$		0			0
$739$	−13.2486	−	7.64911i	−0.487359	−	0.281377i	0.236119	−	0.971724i	$-0.424125\pi$
$739$	−13.2486	−	7.64911i	−0.487359	−	0.281377i	−0.723478	+	0.690347i	$0.757458\pi$
$740$	13.1623	+	22.7977i	0.483855	+	0.838061i
$741$	2.64911	+	22.6491i	0.0973175	+	0.832036i
$742$	0.0811388	+	0.421610i	0.00297870	+	0.0154778i
$743$			27.1623i			0.996487i	0.867037	+	0.498244i	$0.166021\pi$
$743$			27.1623i			0.996487i	−0.867037	+	0.498244i	$0.833979\pi$
$744$	4.50000	+	7.79423i	0.164978	+	0.285750i
$745$	12.4868	−	21.6278i	0.457482	−	0.792382i
$746$	15.1440	+	8.74342i	0.554463	+	0.320119i
$747$	12.8270	−	7.40569i	0.469317	−	0.270960i
$748$			2.51317i			0.0918905i
$749$	11.2355	+	12.9737i	0.410537	+	0.474047i
$750$	30.4868			1.11322
$751$	−11.4737	−	19.8730i	−0.418680	−	0.725175i	0.577127	−	0.816654i	$-0.304174\pi$
$751$	−11.4737	−	19.8730i	−0.418680	−	0.725175i	−0.995807	+	0.0914794i	$0.970840\pi$
$752$	−4.75174	−	2.74342i	−0.173278	−	0.100042i
$753$	8.24342	−	14.2780i	0.300407	−	0.520320i
$754$	6.25315	−	4.65606i	0.227726	−	0.169564i
$755$	12.4868			0.454442
$756$	0.866025	−	2.50000i	0.0314970	−	0.0909241i
$757$	0.973666			0.0353885			0.0176942	−	0.999843i	$-0.494367\pi$
$757$	0.973666			0.0353885			0.0176942	+	0.999843i	$0.494367\pi$
$758$	−7.48683	−	12.9676i	−0.271934	−	0.471004i
$759$	9.66682	+	5.58114i	0.350883	+	0.202583i
$760$	22.7977	+	13.1623i	0.826961	+	0.477446i
$761$	18.4448	−	10.6491i	0.668624	−	0.386030i	−0.126931	−	0.991912i	$-0.540513\pi$
$761$	18.4448	−	10.6491i	0.668624	−	0.386030i	0.795555	+	0.605882i	$0.207179\pi$
$762$		−	21.9737i		−	0.796022i
$763$	−38.7171	−	13.4120i	−1.40165	−	0.485547i
$764$	−23.4868			−0.849724
$765$	−4.18959	+	2.41886i	−0.151475	+	0.0874541i
$766$	7.32456	−	12.6865i	0.264647	−	0.458382i
$767$	−27.0236	−	11.6543i	−0.975765	−	0.420813i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	21.3246i		−	0.768983i	−0.923129	−	0.384492i	$-0.874377\pi$
$769$		−	21.3246i		−	0.768983i	0.923129	−	0.384492i	$-0.125623\pi$
$770$	−18.0000	+	15.5885i	−0.648675	+	0.561769i
$771$	−24.9737			−0.899405
$772$	2.31700	−	1.33772i	0.0833908	−	0.0481457i
$773$	17.6016	+	10.1623i	0.633085	+	0.365512i	0.781946	−	0.623346i	$-0.214227\pi$
$773$	17.6016	+	10.1623i	0.633085	+	0.365512i	−0.148861	+	0.988858i	$0.547561\pi$
$774$	2.45754	+	1.41886i	0.0883344	+	0.0509999i
$775$	96.0604	−	55.4605i	3.45059	−	1.99220i
$776$	−11.0000			−0.394877
$777$	−3.16228	−	16.4317i	−0.113446	−	0.589483i
$778$		−	20.3246i		−	0.728671i
$779$		0			0
$780$	−13.7804	−	5.94300i	−0.493418	−	0.212794i
$781$	17.6491	−	30.5692i	0.631535	−	1.09385i
$782$	5.19615	−	3.00000i	0.185814	−	0.107280i
$783$	−2.16228			−0.0772735
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$		−	63.1096i		−	2.25248i
$786$	1.87259	−	1.08114i	0.0667930	−	0.0385629i
$787$	−14.8630	−	8.58114i	−0.529808	−	0.305885i	0.211131	−	0.977458i	$-0.432285\pi$
$787$	−14.8630	−	8.58114i	−0.529808	−	0.305885i	−0.740938	+	0.671573i	$0.765619\pi$
$788$	11.8433	+	6.83772i	0.421899	+	0.243584i
$789$	6.48683	+	11.2355i	0.230937	+	0.399995i
$790$	−37.4605			−1.33278
$791$	−37.2163	+	7.16228i	−1.32326	+	0.254661i
$792$	2.16228			0.0768332
$793$	−7.50825	−	10.0837i	−0.266626	−	0.358081i
$794$	−1.25658	+	2.17647i	−0.0445945	+	0.0772399i
$795$	−0.584952	−	0.337722i	−0.0207461	−	0.0119778i
$796$	−3.32456	−	5.75830i	−0.117836	−	0.204097i
$797$	42.4868			1.50496			0.752480	−	0.658615i	$-0.228857\pi$
$797$	42.4868			1.50496			0.752480	+	0.658615i	$0.228857\pi$
$798$	−10.9545	−	12.6491i	−0.387783	−	0.447774i
$799$		−	6.37722i		−	0.225610i
$800$	−10.6734	+	6.16228i	−0.377361	+	0.217869i
$801$	−2.73861	−	1.58114i	−0.0967641	−	0.0558668i
$802$	−1.74342	+	3.01969i	−0.0615622	+	0.106629i
$803$	−6.83772	−	11.8433i	−0.241298	−	0.417940i
$804$		−	9.16228i		−	0.323129i
$805$	53.7171	+	18.6081i	1.89328	+	0.655851i
$806$	−32.2302	+	3.76975i	−1.13526	+	0.132784i
$807$	14.0811	+	24.3892i	0.495680	+	0.858542i
$808$	3.18303	+	1.83772i	0.111979	+	0.0646508i
$809$	13.1623	−	22.7977i	0.462761	−	0.801526i	−0.536336	−	0.844004i	$-0.680192\pi$
$809$	13.1623	−	22.7977i	0.462761	−	0.801526i	0.999097	+	0.0424787i	$0.0135255\pi$
$810$	2.08114	+	3.60464i	0.0731238	+	0.126654i
$811$			47.4868i			1.66749i	0.552151	+	0.833744i	$0.313807\pi$
$811$			47.4868i			1.66749i	−0.552151	+	0.833744i	$0.686193\pi$
$812$	−1.87259	+	5.40569i	−0.0657149	+	0.189703i
$813$		−	15.0000i		−	0.526073i
$814$	11.8433	−	6.83772i	0.415107	−	0.239662i
$815$	26.3246	−	45.5955i	0.922109	−	1.59714i
$816$	0.581139	−	1.00656i	0.0203439	−	0.0352367i
$817$	15.5428	−	8.97367i	0.543775	−	0.313949i
$818$	34.6228			1.21056
$819$	7.04044	+	6.43679i	0.246013	+	0.224920i
$820$		0			0
$821$	43.4418	−	25.0811i	1.51613	−	0.875338i	0.516309	−	0.856402i	$-0.327306\pi$
$821$	43.4418	−	25.0811i	1.51613	−	0.875338i	0.999821	−	0.0189353i	$-0.00602765\pi$
$822$	−3.58114	+	6.20271i	−0.124907	+	0.216345i
$823$	3.64911	−	6.32045i	0.127200	−	0.220317i	−0.795391	−	0.606097i	$-0.792734\pi$
$823$	3.64911	−	6.32045i	0.127200	−	0.220317i	0.922591	+	0.385780i	$0.126068\pi$
$824$	−0.281073	+	0.162278i	−0.00979165	+	0.00565321i
$825$		−	26.6491i		−	0.927803i
$826$	21.2062	−	4.08114i	0.737859	−	0.142001i
$827$		−	12.8114i		−	0.445496i	−0.974876	−	0.222748i	$-0.928497\pi$
$827$		−	12.8114i		−	0.445496i	0.974876	−	0.222748i	$-0.0715026\pi$
$828$	−2.58114	−	4.47066i	−0.0897008	−	0.155366i
$829$	−14.7434	+	25.5363i	−0.512060	+	0.886914i	0.487842	+	0.872932i	$0.337784\pi$
$829$	−14.7434	+	25.5363i	−0.512060	+	0.886914i	−0.999902	+	0.0139822i	$0.995549\pi$
$830$	53.3897	+	30.8246i	1.85318	+	1.06994i
$831$	−7.90569	−	13.6931i	−0.274245	−	0.475007i
$832$	3.58114	−	0.418861i	0.124154	−	0.0145214i
$833$	1.16228	−	8.05250i	0.0402705	−	0.279002i
$834$		−	7.48683i		−	0.259248i
$835$	−23.2302	−	40.2360i	−0.803916	−	1.39242i
$836$	6.83772	−	11.8433i	0.236488	−	0.409608i
$837$	7.79423	+	4.50000i	0.269408	+	0.155543i
$838$	−26.5429	+	15.3246i	−0.916910	+	0.529378i
$839$			7.35089i			0.253781i	0.991917	+	0.126890i	$0.0404997\pi$
$839$			7.35089i			0.253781i	−0.991917	+	0.126890i	$0.959500\pi$
$840$	10.8139	−	2.08114i	0.373116	−	0.0718061i
$841$	−24.3246			−0.838778
$842$	19.7434	+	34.1966i	0.680403	+	1.17849i
$843$	9.66682	+	5.58114i	0.332943	+	0.192225i
$844$	−0.256584	+	0.444416i	−0.00883197	+	0.0152974i
$845$	39.3521	−	37.1385i	1.35375	−	1.27760i
$846$	−5.48683			−0.188641
$847$	−10.9545	−	12.6491i	−0.376399	−	0.434629i
$848$	0.162278			0.00557264
$849$	8.48683	+	14.6996i	0.291267	+	0.504490i
$850$	−12.4054	−	7.16228i	−0.425503	−	0.245664i
$851$	−28.2750	−	16.3246i	−0.969253	−	0.559599i
$852$	−14.1375	+	8.16228i	−0.484342	+	0.279635i
$853$			12.3246i			0.421985i	0.977488	+	0.210992i	$0.0676695\pi$
$853$			12.3246i			0.421985i	−0.977488	+	0.210992i	$0.932330\pi$
$854$	8.71708	+	3.01969i	0.298292	+	0.103332i
$855$	26.3246			0.900281
$856$	5.61776	−	3.24342i	0.192011	−	0.110858i
$857$	−6.48683	+	11.2355i	−0.221586	+	0.383798i	−0.955290	−	0.295671i	$-0.904457\pi$
$857$	−6.48683	+	11.2355i	−0.221586	+	0.383798i	0.733704	+	0.679470i	$0.237790\pi$
$858$	−3.08735	+	7.15884i	−0.105401	+	0.244399i
$859$	−3.93203	−	6.81047i	−0.134159	−	0.232370i	0.791117	−	0.611665i	$-0.209500\pi$
$859$	−3.93203	−	6.81047i	−0.134159	−	0.232370i	−0.925276	+	0.379295i	$0.876167\pi$
$860$			11.8114i			0.402765i
$861$		0			0
$862$	3.48683			0.118762
$863$	10.2290	−	5.90569i	0.348198	−	0.201032i	−0.315693	−	0.948861i	$-0.602237\pi$
$863$	10.2290	−	5.90569i	0.348198	−	0.201032i	0.663891	+	0.747829i	$0.268904\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	37.2163	+	21.4868i	1.26539	+	0.730574i
$866$	−17.3205	+	10.0000i	−0.588575	+	0.339814i
$867$	−15.6491			−0.531472
$868$	18.0000	−	15.5885i	0.610960	−	0.529107i
$869$			19.4605i			0.660152i
$870$	−4.50000	−	7.79423i	−0.152564	−	0.264249i
$871$	30.3344	+	13.0821i	1.02784	+	0.443271i
$872$	−7.74342	+	13.4120i	−0.262225	+	0.454187i
$873$	−9.52628	+	5.50000i	−0.322416	+	0.186147i
$874$	−32.6491			−1.10437
$875$	−15.2434	−	79.2071i	−0.515322	−	2.67769i
$876$			6.32456i			0.213687i
$877$	33.9155	−	19.5811i	1.14525	−	0.661208i	0.197522	−	0.980299i	$-0.436711\pi$
$877$	33.9155	−	19.5811i	1.14525	−	0.661208i	0.947724	+	0.319090i	$0.103377\pi$
$878$	−29.4221	−	16.9868i	−0.992946	−	0.573278i
$879$	−0.421610	−	0.243416i	−0.0142205	−	0.00821023i
$880$	4.50000	+	7.79423i	0.151695	+	0.262743i
$881$	17.3509			0.584566			0.292283	−	0.956332i	$-0.405585\pi$
$881$	17.3509			0.584566			0.292283	+	0.956332i	$0.405585\pi$
$882$	−6.92820	−	1.00000i	−0.233285	−	0.0336718i
$883$	−12.4605			−0.419329			−0.209665	−	0.977773i	$-0.567237\pi$
$883$	−12.4605			−0.419329			−0.209665	+	0.977773i	$0.567237\pi$
$884$	2.50275	+	3.36122i	0.0841765	+	0.113050i
$885$	−16.9868	+	29.4221i	−0.571006	+	0.989012i
$886$	9.64401	+	5.56797i	0.323997	+	0.187060i
$887$	8.83772	+	15.3074i	0.296742	+	0.513972i	0.975389	−	0.220493i	$-0.0707666\pi$
$887$	8.83772	+	15.3074i	0.296742	+	0.513972i	−0.678647	+	0.734465i	$0.737433\pi$
$888$	−6.32456			−0.212238
$889$	−57.0893	+	10.9868i	−1.91471	+	0.368487i
$890$		−	13.1623i		−	0.441201i
$891$	1.87259	−	1.08114i	0.0627340	−	0.0362195i
$892$	22.4939	+	12.9868i	0.753150	+	0.434831i
$893$	−17.3509	+	30.0526i	−0.580625	+	1.00567i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$		−	33.2982i		−	1.11304i
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$	18.4868	−	2.16228i	0.617257	−	0.0721963i
$898$	−19.1623	−	33.1900i	−0.639453	−	1.10757i
$899$	−16.8533	−	9.73025i	−0.562089	−	0.324522i
$900$	−6.16228	+	10.6734i	−0.205409	+	0.355779i
$901$	0.0943058	+	0.163343i	0.00314178	+	0.00544173i
$902$		0			0
$903$	2.45754	−	7.09431i	0.0817818	−	0.236084i
$904$			14.3246i			0.476428i
$905$	37.2163	−	21.4868i	1.23711	−	0.714246i
$906$	−1.50000	+	2.59808i	−0.0498342	+	0.0863153i
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	−0.595082	−	0.803665i	$-0.702880\pi$
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	0.993535	+	0.113523i	$0.0362137\pi$
$908$	9.08186	−	5.24342i	0.301392	−	0.174009i
$909$	3.67544			0.121907
$910$	−8.55017	+	38.7741i	−0.283435	+	1.28535i
$911$	−36.3246			−1.20349			−0.601743	−	0.798690i	$-0.705527\pi$
$911$	−36.3246			−1.20349			−0.601743	+	0.798690i	$0.705527\pi$
$912$	−5.47723	+	3.16228i	−0.181369	+	0.104713i
$913$	16.0132	−	27.7356i	0.529958	−	0.917915i
$914$	−3.50000	+	6.06218i	−0.115770	+	0.200519i
$915$	−12.5688	+	7.25658i	−0.415511	+	0.239895i
$916$			22.1359i			0.731392i
$917$	−3.74517	−	4.32456i	−0.123677	−	0.142809i
$918$		−	1.16228i		−	0.0383609i
$919$	−2.48683	−	4.30732i	−0.0820331	−	0.142085i	0.822090	−	0.569358i	$-0.192808\pi$
$919$	−2.48683	−	4.30732i	−0.0820331	−	0.142085i	−0.904123	+	0.427272i	$0.859475\pi$
$920$	10.7434	−	18.6081i	0.354200	−	0.613492i
$921$	7.65369	+	4.41886i	0.252198	+	0.145606i
$922$	−5.32456	−	9.22240i	−0.175355	−	0.303724i
$923$	−6.83772	−	58.4605i	−0.225066	−	1.92425i
$924$	−1.08114	−	5.61776i	−0.0355669	−	0.184811i
$925$			77.9473i			2.56289i
$926$	5.83772	+	10.1112i	0.191839	+	0.332276i
$927$	−0.162278	+	0.281073i	−0.00532990	+	0.00923165i
$928$	1.87259	+	1.08114i	0.0614707	+	0.0354901i
$929$	−35.0398	+	20.2302i	−1.14962	+	0.663733i	−0.948794	−	0.315894i	$-0.897696\pi$
$929$	−35.0398	+	20.2302i	−1.14962	+	0.663733i	−0.200825	+	0.979627i	$0.564362\pi$
$930$			37.4605i			1.22838i
$931$	−27.3861	+	34.7851i	−0.897544	+	1.14003i
$932$	−25.8114			−0.845480
$933$	−6.06797	−	10.5100i	−0.198656	−	0.344083i
$934$	7.49035	+	4.32456i	0.245092	+	0.141504i
$935$	−5.23025	+	9.05906i	−0.171047	+	0.296263i
$936$	2.89193	−	2.15331i	0.0945256	−	0.0703833i
$937$	−21.6491			−0.707246			−0.353623	−	0.935388i	$-0.615050\pi$
$937$	−21.6491			−0.707246			−0.353623	+	0.935388i	$0.615050\pi$
$938$	−23.8043	+	4.58114i	−0.777238	+	0.149579i
$939$	15.0000			0.489506
$940$	−11.4189	−	19.7780i	−0.372442	−	0.645089i
$941$	−13.1537	−	7.59431i	−0.428799	−	0.247567i	0.270036	−	0.962850i	$-0.412964\pi$
$941$	−13.1537	−	7.59431i	−0.428799	−	0.247567i	−0.698835	+	0.715283i	$0.746298\pi$
$942$	13.1309	+	7.58114i	0.427828	+	0.247007i
$943$		0			0
$944$		−	8.16228i		−	0.265660i
$945$	8.32456	−	7.20928i	0.270798	−	0.234518i
$946$	6.13594			0.199497
$947$	−29.1638	+	16.8377i	−0.947696	+	0.547152i	−0.892364	−	0.451316i	$-0.850955\pi$
$947$	−29.1638	+	16.8377i	−0.947696	+	0.547152i	−0.0553314	+	0.998468i	$0.517622\pi$
$948$	4.50000	−	7.79423i	0.146153	−	0.253145i
$949$	−20.9393	−	9.03036i	−0.679717	−	0.293138i
$950$	38.9737	+	67.5044i	1.26447	+	2.19013i
$951$		−	18.8114i		−	0.610001i
$952$	−2.90569	−	1.00656i	−0.0941741	−	0.0326229i
$953$	18.7851			0.608508			0.304254	−	0.952591i	$-0.401593\pi$
$953$	18.7851			0.608508			0.304254	+	0.952591i	$0.401593\pi$
$954$	0.140537	−	0.0811388i	0.00455004	−	0.00262697i
$955$	−84.6615	−	48.8794i	−2.73958	−	1.58170i
$956$	2.45754	+	1.41886i	0.0794825	+	0.0458892i
$957$	−4.04905	+	2.33772i	−0.130887	+	0.0755678i
$958$	−15.6754			−0.506451
$959$	17.9057	+	6.20271i	0.578205	+	0.200296i
$960$		−	4.16228i		−	0.134337i
$961$	25.0000	+	43.3013i	0.806452	+	1.39682i
$962$	9.03036	−	20.9393i	0.291150	−	0.675109i
$963$	3.24342	−	5.61776i	0.104518	−	0.181030i
$964$	−22.4939	+	12.9868i	−0.724478	+	0.418278i
$965$	11.1359			0.358479
$966$	−10.3246	+	8.94133i	−0.332187	+	0.287682i
$967$			43.9737i			1.41410i	0.707165	+	0.707049i	$0.249974\pi$
$967$			43.9737i			1.41410i	−0.707165	+	0.707049i	$0.750026\pi$
$968$	−5.47723	+	3.16228i	−0.176045	+	0.101639i
$969$	−6.36606	−	3.67544i	−0.204507	−	0.118072i
$970$	−39.6510	−	22.8925i	−1.27312	−	0.735035i
$971$	−19.7302	−	34.1738i	−0.633174	−	1.09669i	−0.986899	−	0.161340i	$-0.948418\pi$
$971$	−19.7302	−	34.1738i	−0.633174	−	1.09669i	0.353725	−	0.935349i	$-0.384915\pi$
$972$	−1.00000			−0.0320750
$973$	−19.4514	+	3.74342i	−0.623582	+	0.120008i
$974$	−19.0000			−0.608799
$975$	−26.5386	−	35.6417i	−0.849917	−	1.14145i
$976$	1.74342	−	3.01969i	0.0558054	−	0.0966578i
$977$	−15.5885	−	9.00000i	−0.498719	−	0.287936i	0.229465	−	0.973317i	$-0.426302\pi$
$977$	−15.5885	−	9.00000i	−0.498719	−	0.287936i	−0.728184	+	0.685381i	$0.759636\pi$
$978$	6.32456	+	10.9545i	0.202237	+	0.350285i
$979$	−6.83772			−0.218535
$980$	−10.8139	−	27.0548i	−0.345438	−	0.864234i
$981$			15.4868i			0.494457i
$982$	−15.4479	+	8.91886i	−0.492963	+	0.284612i
$983$	−5.59496	−	3.23025i	−0.178451	−	0.103029i	0.408113	−	0.912931i	$-0.366187\pi$
$983$	−5.59496	−	3.23025i	−0.178451	−	0.103029i	−0.586565	+	0.809902i	$0.699520\pi$
$984$		0			0
$985$	28.4605	+	49.2950i	0.906827	+	1.57067i
$986$			2.51317i			0.0800355i
$987$	2.74342	+	14.2552i	0.0873239	+	0.453748i
$988$	−2.64911	−	22.6491i	−0.0842794	−	0.720564i
$989$	−7.32456	−	12.6865i	−0.232907	−	0.403407i
$990$	7.79423	+	4.50000i	0.247717	+	0.143019i
$991$	7.17544	−	12.4282i	0.227936	−	0.394796i	−0.729261	−	0.684236i	$-0.760136\pi$
$991$	7.17544	−	12.4282i	0.227936	−	0.394796i	0.957196	+	0.289440i	$0.0934691\pi$
$992$	−4.50000	−	7.79423i	−0.142875	−	0.247467i
$993$			8.00000i			0.253872i
$994$	28.2750	+	32.6491i	0.896827	+	1.03557i
$995$		−	27.6754i		−	0.877371i
$996$	−12.8270	+	7.40569i	−0.406440	+	0.234658i
$997$	−22.5811	+	39.1117i	−0.715152	+	1.23868i	0.247749	+	0.968824i	$0.420309\pi$
$997$	−22.5811	+	39.1117i	−0.715152	+	1.23868i	−0.962901	+	0.269855i	$0.913024\pi$
$998$	5.74342	−	9.94789i	0.181805	−	0.314895i
$999$	−5.47723	+	3.16228i	−0.173292	+	0.100050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.a.25.4	yes	8
3.2	odd	2		1638.2.dm.b.1117.1		8
7.2	even	3	inner	546.2.bk.a.415.1	yes	8
7.3	odd	6		3822.2.c.f.883.3		4
7.4	even	3		3822.2.c.g.883.4		4
13.12	even	2	inner	546.2.bk.a.25.1	✓	8
21.2	odd	6		1638.2.dm.b.415.4		8
39.38	odd	2		1638.2.dm.b.1117.4		8
91.25	even	6		3822.2.c.g.883.1		4
91.38	odd	6		3822.2.c.f.883.2		4
91.51	even	6	inner	546.2.bk.a.415.4	yes	8
273.233	odd	6		1638.2.dm.b.415.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.a.25.1	✓	8	13.12	even	2	inner
546.2.bk.a.25.4	yes	8	1.1	even	1	trivial
546.2.bk.a.415.1	yes	8	7.2	even	3	inner
546.2.bk.a.415.4	yes	8	91.51	even	6	inner
1638.2.dm.b.415.1		8	273.233	odd	6
1638.2.dm.b.415.4		8	21.2	odd	6
1638.2.dm.b.1117.1		8	3.2	odd	2
1638.2.dm.b.1117.4		8	39.38	odd	2
3822.2.c.f.883.2		4	91.38	odd	6
3822.2.c.f.883.3		4	7.3	odd	6
3822.2.c.g.883.1		4	91.25	even	6
3822.2.c.g.883.4		4	7.4	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.60464 - 2.08114i) q^{5} +1.00000i q^{6} +(2.59808 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.60464 - 2.08114i) q^{5} +1.00000i q^{6} +(2.59808 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.08114 - 3.60464i) q^{10} +(-1.87259 - 1.08114i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.58114 + 0.418861i) q^{13} +(2.00000 - 1.73205i) q^{14} +4.16228i q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.581139 - 1.00656i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-5.47723 + 3.16228i) q^{19} -4.16228i q^{20} +(-0.866025 + 2.50000i) q^{21} -2.16228 q^{22} +(2.58114 + 4.47066i) q^{23} +(0.866025 + 0.500000i) q^{24} +(6.16228 - 10.6734i) q^{25} +(-2.89193 + 2.15331i) q^{26} +1.00000 q^{27} +(0.866025 - 2.50000i) q^{28} -2.16228 q^{29} +(2.08114 + 3.60464i) q^{30} +(7.79423 + 4.50000i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.87259 - 1.08114i) q^{33} -1.16228i q^{34} +(8.32456 - 7.20928i) q^{35} -1.00000 q^{36} +(-5.47723 + 3.16228i) q^{37} +(-3.16228 + 5.47723i) q^{38} +(1.42783 - 3.31079i) q^{39} +(-2.08114 - 3.60464i) q^{40} +(0.500000 + 2.59808i) q^{42} -2.83772 q^{43} +(-1.87259 + 1.08114i) q^{44} +(-3.60464 - 2.08114i) q^{45} +(4.47066 + 2.58114i) q^{46} +(4.75174 - 2.74342i) q^{47} +1.00000 q^{48} +(6.50000 - 2.59808i) q^{49} -12.3246i q^{50} +(0.581139 + 1.00656i) q^{51} +(-1.42783 + 3.31079i) q^{52} +(-0.0811388 + 0.140537i) q^{53} +(0.866025 - 0.500000i) q^{54} -9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} -6.32456i q^{57} +(-1.87259 + 1.08114i) q^{58} +(7.06874 + 4.08114i) q^{59} +(3.60464 + 2.08114i) q^{60} +(1.74342 + 3.01969i) q^{61} +9.00000 q^{62} +(-1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(-12.0370 + 8.96269i) q^{65} +(1.08114 - 1.87259i) q^{66} +(-7.93477 - 4.58114i) q^{67} +(-0.581139 - 1.00656i) q^{68} -5.16228 q^{69} +(3.60464 - 10.4057i) q^{70} +16.3246i q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.47723 + 3.16228i) q^{73} +(-3.16228 + 5.47723i) q^{74} +(6.16228 + 10.6734i) q^{75} +6.32456i q^{76} +(-5.40569 - 1.87259i) q^{77} +(-0.418861 - 3.58114i) q^{78} +(-4.50000 - 7.79423i) q^{79} +(-3.60464 - 2.08114i) q^{80} +(-0.500000 + 0.866025i) q^{81} +14.8114i q^{83} +(1.73205 + 2.00000i) q^{84} -4.83772i q^{85} +(-2.45754 + 1.41886i) q^{86} +(1.08114 - 1.87259i) q^{87} +(-1.08114 + 1.87259i) q^{88} +(2.73861 - 1.58114i) q^{89} -4.16228 q^{90} +(-9.09464 + 2.87880i) q^{91} +5.16228 q^{92} +(-7.79423 + 4.50000i) q^{93} +(2.74342 - 4.75174i) q^{94} +(-13.1623 + 22.7977i) q^{95} +(0.866025 - 0.500000i) q^{96} -11.0000i q^{97} +(4.33013 - 5.50000i) q^{98} +2.16228i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} + 4 q^{10} + 4 q^{12} - 16 q^{13} + 16 q^{14} - 4 q^{16} - 8 q^{17} + 8 q^{22} + 8 q^{23} + 24 q^{25} + 8 q^{26} + 8 q^{27} + 8 q^{29} + 4 q^{30} + 16 q^{35} - 8 q^{36} + 8 q^{39} - 4 q^{40} + 4 q^{42} - 48 q^{43} + 8 q^{48} + 52 q^{49} - 8 q^{51} - 8 q^{52} + 12 q^{53} - 72 q^{55} - 4 q^{56} - 24 q^{61} + 72 q^{62} - 8 q^{64} - 12 q^{65} - 4 q^{66} + 8 q^{68} - 16 q^{69} + 24 q^{75} + 20 q^{77} - 16 q^{78} - 36 q^{79} - 4 q^{81} - 4 q^{87} + 4 q^{88} - 8 q^{90} + 8 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 + 4 * q^10 + 4 * q^12 - 16 * q^13 + 16 * q^14 - 4 * q^16 - 8 * q^17 + 8 * q^22 + 8 * q^23 + 24 * q^25 + 8 * q^26 + 8 * q^27 + 8 * q^29 + 4 * q^30 + 16 * q^35 - 8 * q^36 + 8 * q^39 - 4 * q^40 + 4 * q^42 - 48 * q^43 + 8 * q^48 + 52 * q^49 - 8 * q^51 - 8 * q^52 + 12 * q^53 - 72 * q^55 - 4 * q^56 - 24 * q^61 + 72 * q^62 - 8 * q^64 - 12 * q^65 - 4 * q^66 + 8 * q^68 - 16 * q^69 + 24 * q^75 + 20 * q^77 - 16 * q^78 - 36 * q^79 - 4 * q^81 - 4 * q^87 + 4 * q^88 - 8 * q^90 + 8 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more