LMFDB - Embedded newform 483.2.d.c.461.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.4
Root			$0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	483.461
Dual form			483.2.d.c.461.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.923880 - 1.46508i) q^{3} +1.00000 q^{4} -3.37849 q^{5} +(-1.46508 - 0.923880i) q^{6} +(-2.41421 + 1.08239i) q^{7} -3.00000i q^{8} +(-1.29289 - 2.70711i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.923880 - 1.46508i) q^{3} +1.00000 q^{4} -3.37849 q^{5} +(-1.46508 - 0.923880i) q^{6} +(-2.41421 + 1.08239i) q^{7} -3.00000i q^{8} +(-1.29289 - 2.70711i) q^{9} +3.37849i q^{10} -3.41421i q^{11} +(0.923880 - 1.46508i) q^{12} +3.69552i q^{13} +(1.08239 + 2.41421i) q^{14} +(-3.12132 + 4.94975i) q^{15} -1.00000 q^{16} -4.46088 q^{17} +(-2.70711 + 1.29289i) q^{18} -5.22625i q^{19} -3.37849 q^{20} +(-0.644656 + 4.53701i) q^{21} -3.41421 q^{22} -1.00000i q^{23} +(-4.39523 - 2.77164i) q^{24} +6.41421 q^{25} +3.69552 q^{26} +(-5.16059 - 0.606854i) q^{27} +(-2.41421 + 1.08239i) q^{28} +4.24264i q^{29} +(4.94975 + 3.12132i) q^{30} -4.90923i q^{31} -5.00000i q^{32} +(-5.00208 - 3.15432i) q^{33} +4.46088i q^{34} +(8.15640 - 3.65685i) q^{35} +(-1.29289 - 2.70711i) q^{36} +10.4853 q^{37} -5.22625 q^{38} +(5.41421 + 3.41421i) q^{39} +10.1355i q^{40} +8.28772 q^{41} +(4.53701 + 0.644656i) q^{42} -9.65685 q^{43} -3.41421i q^{44} +(4.36803 + 9.14594i) q^{45} -1.00000 q^{46} +5.99162 q^{47} +(-0.923880 + 1.46508i) q^{48} +(4.65685 - 5.22625i) q^{49} -6.41421i q^{50} +(-4.12132 + 6.53553i) q^{51} +3.69552i q^{52} -0.828427i q^{53} +(-0.606854 + 5.16059i) q^{54} +11.5349i q^{55} +(3.24718 + 7.24264i) q^{56} +(-7.65685 - 4.82843i) q^{57} +4.24264 q^{58} -8.60474 q^{59} +(-3.12132 + 4.94975i) q^{60} -7.25972i q^{61} -4.90923 q^{62} +(6.05147 + 5.13612i) q^{63} -7.00000 q^{64} -12.4853i q^{65} +(-3.15432 + 5.00208i) q^{66} +14.7279 q^{67} -4.46088 q^{68} +(-1.46508 - 0.923880i) q^{69} +(-3.65685 - 8.15640i) q^{70} -1.65685i q^{71} +(-8.12132 + 3.87868i) q^{72} -6.75699i q^{73} -10.4853i q^{74} +(5.92596 - 9.39731i) q^{75} -5.22625i q^{76} +(3.69552 + 8.24264i) q^{77} +(3.41421 - 5.41421i) q^{78} -10.7279 q^{79} +3.37849 q^{80} +(-5.65685 + 7.00000i) q^{81} -8.28772i q^{82} +0.634051 q^{83} +(-0.644656 + 4.53701i) q^{84} +15.0711 q^{85} +9.65685i q^{86} +(6.21579 + 3.91969i) q^{87} -10.2426 q^{88} +8.79045 q^{89} +(9.14594 - 4.36803i) q^{90} +(-4.00000 - 8.92177i) q^{91} -1.00000i q^{92} +(-7.19239 - 4.53553i) q^{93} -5.99162i q^{94} +17.6569i q^{95} +(-7.32538 - 4.61940i) q^{96} +11.8519i q^{97} +(-5.22625 - 4.65685i) q^{98} +(-9.24264 + 4.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9	$ 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9} - 8 q^{15} - 8 q^{16} - 16 q^{18} + 24 q^{21} - 16 q^{22} + 40 q^{25} - 8 q^{28} - 16 q^{36} + 16 q^{37} + 32 q^{39} + 8 q^{42} - 32 q^{43} - 8 q^{46} - 8 q^{49} - 16 q^{51} - 16 q^{57} - 8 q^{60} + 8 q^{63} - 56 q^{64} + 16 q^{67} + 16 q^{70} - 48 q^{72} + 16 q^{78} + 16 q^{79} + 24 q^{84} + 64 q^{85} - 48 q^{88} - 32 q^{91} + 16 q^{93} - 40 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9 - 8 * q^15 - 8 * q^16 - 16 * q^18 + 24 * q^21 - 16 * q^22 + 40 * q^25 - 8 * q^28 - 16 * q^36 + 16 * q^37 + 32 * q^39 + 8 * q^42 - 32 * q^43 - 8 * q^46 - 8 * q^49 - 16 * q^51 - 16 * q^57 - 8 * q^60 + 8 * q^63 - 56 * q^64 + 16 * q^67 + 16 * q^70 - 48 * q^72 + 16 * q^78 + 16 * q^79 + 24 * q^84 + 64 * q^85 - 48 * q^88 - 32 * q^91 + 16 * q^93 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$	0.923880	−	1.46508i	0.533402	−	0.845862i
$3$	0.923880	−	1.46508i	0.533402	−	0.845862i
$4$	1.00000			0.500000
$5$	−3.37849			−1.51091			−0.755454	−	0.655202i	$-0.772584\pi$
$5$	−3.37849			−1.51091			−0.755454	+	0.655202i	$0.772584\pi$
$6$	−1.46508	−	0.923880i	−0.598115	−	0.377172i
$7$	−2.41421	+	1.08239i	−0.912487	+	0.409106i
$7$	−2.41421	+	1.08239i	−0.912487	+	0.409106i
$8$		−	3.00000i		−	1.06066i
$9$	−1.29289	−	2.70711i	−0.430964	−	0.902369i
$10$			3.37849i			1.06837i
$11$		−	3.41421i		−	1.02942i	−0.857363	−	0.514712i	$-0.827899\pi$
$11$		−	3.41421i		−	1.02942i	0.857363	−	0.514712i	$-0.172101\pi$
$12$	0.923880	−	1.46508i	0.266701	−	0.422931i
$13$			3.69552i			1.02495i	0.858701	+	0.512476i	$0.171272\pi$
$13$			3.69552i			1.02495i	−0.858701	+	0.512476i	$0.828728\pi$
$14$	1.08239	+	2.41421i	0.289281	+	0.645226i
$15$	−3.12132	+	4.94975i	−0.805921	+	1.27802i
$16$	−1.00000			−0.250000
$17$	−4.46088			−1.08192			−0.540962	−	0.841047i	$-0.681940\pi$
$17$	−4.46088			−1.08192			−0.540962	+	0.841047i	$0.681940\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$		−	5.22625i		−	1.19898i	−0.800381	−	0.599492i	$-0.795369\pi$
$19$		−	5.22625i		−	1.19898i	0.800381	−	0.599492i	$-0.204631\pi$
$20$	−3.37849			−0.755454
$21$	−0.644656	+	4.53701i	−0.140675	+	0.990056i
$22$	−3.41421			−0.727913
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	−4.39523	−	2.77164i	−0.897172	−	0.565758i
$25$	6.41421			1.28284
$26$	3.69552			0.724751
$27$	−5.16059	−	0.606854i	−0.993157	−	0.116789i
$28$	−2.41421	+	1.08239i	−0.456243	+	0.204553i
$29$			4.24264i			0.787839i	0.919145	+	0.393919i	$0.128881\pi$
$29$			4.24264i			0.787839i	−0.919145	+	0.393919i	$0.871119\pi$
$30$	4.94975	+	3.12132i	0.903696	+	0.569873i
$31$		−	4.90923i		−	0.881723i	−0.897575	−	0.440862i	$-0.854673\pi$
$31$		−	4.90923i		−	0.881723i	0.897575	−	0.440862i	$-0.145327\pi$
$32$		−	5.00000i		−	0.883883i
$33$	−5.00208	−	3.15432i	−0.870751	−	0.549097i
$34$			4.46088i			0.765035i
$35$	8.15640	−	3.65685i	1.37868	−	0.618121i
$36$	−1.29289	−	2.70711i	−0.215482	−	0.451184i
$37$	10.4853			1.72377			0.861885	−	0.507104i	$-0.169284\pi$
$37$	10.4853			1.72377			0.861885	+	0.507104i	$0.169284\pi$
$38$	−5.22625			−0.847810
$39$	5.41421	+	3.41421i	0.866968	+	0.546712i
$40$			10.1355i			1.60256i
$41$	8.28772			1.29432			0.647162	−	0.762352i	$-0.275956\pi$
$41$	8.28772			1.29432			0.647162	+	0.762352i	$0.275956\pi$
$42$	4.53701	+	0.644656i	0.700075	+	0.0994726i
$43$	−9.65685			−1.47266			−0.736328	−	0.676625i	$-0.763442\pi$
$43$	−9.65685			−1.47266			−0.736328	+	0.676625i	$0.763442\pi$
$44$		−	3.41421i		−	0.514712i
$45$	4.36803	+	9.14594i	0.651148	+	1.36340i
$46$	−1.00000			−0.147442
$47$	5.99162			0.873967			0.436984	−	0.899469i	$-0.356047\pi$
$47$	5.99162			0.873967			0.436984	+	0.899469i	$0.356047\pi$
$48$	−0.923880	+	1.46508i	−0.133351	+	0.211465i
$49$	4.65685	−	5.22625i	0.665265	−	0.746607i
$50$		−	6.41421i		−	0.907107i
$51$	−4.12132	+	6.53553i	−0.577100	+	0.915158i
$52$			3.69552i			0.512476i
$53$		−	0.828427i		−	0.113793i	−0.998380	−	0.0568966i	$-0.981879\pi$
$53$		−	0.828427i		−	0.113793i	0.998380	−	0.0568966i	$-0.0181205\pi$
$54$	−0.606854	+	5.16059i	−0.0825824	+	0.702268i
$55$			11.5349i			1.55537i
$56$	3.24718	+	7.24264i	0.433922	+	0.967839i
$57$	−7.65685	−	4.82843i	−1.01418	−	0.639541i
$58$	4.24264			0.557086
$59$	−8.60474			−1.12024			−0.560121	−	0.828411i	$-0.689245\pi$
$59$	−8.60474			−1.12024			−0.560121	+	0.828411i	$0.689245\pi$
$60$	−3.12132	+	4.94975i	−0.402961	+	0.639010i
$61$		−	7.25972i		−	0.929512i	−0.885439	−	0.464756i	$-0.846142\pi$
$61$		−	7.25972i		−	0.929512i	0.885439	−	0.464756i	$-0.153858\pi$
$62$	−4.90923			−0.623472
$63$	6.05147	+	5.13612i	0.762414	+	0.647090i
$64$	−7.00000			−0.875000
$65$		−	12.4853i		−	1.54861i
$66$	−3.15432	+	5.00208i	−0.388270	+	0.615714i
$67$	14.7279			1.79930			0.899651	−	0.436610i	$-0.143821\pi$
$67$	14.7279			1.79930			0.899651	+	0.436610i	$0.143821\pi$
$68$	−4.46088			−0.540962
$69$	−1.46508	−	0.923880i	−0.176374	−	0.111222i
$70$	−3.65685	−	8.15640i	−0.437078	−	0.974877i
$71$		−	1.65685i		−	0.196632i	−0.995155	−	0.0983162i	$-0.968654\pi$
$71$		−	1.65685i		−	0.196632i	0.995155	−	0.0983162i	$-0.0313457\pi$
$72$	−8.12132	+	3.87868i	−0.957107	+	0.457107i
$73$		−	6.75699i		−	0.790845i	−0.918499	−	0.395423i	$-0.870598\pi$
$73$		−	6.75699i		−	0.790845i	0.918499	−	0.395423i	$-0.129402\pi$
$74$		−	10.4853i		−	1.21889i
$75$	5.92596	−	9.39731i	0.684271	−	1.08511i
$76$		−	5.22625i		−	0.599492i
$77$	3.69552	+	8.24264i	0.421143	+	0.939336i
$78$	3.41421	−	5.41421i	0.386584	−	0.613039i
$79$	−10.7279			−1.20699			−0.603493	−	0.797368i	$-0.706225\pi$
$79$	−10.7279			−1.20699			−0.603493	+	0.797368i	$0.706225\pi$
$80$	3.37849			0.377727
$81$	−5.65685	+	7.00000i	−0.628539	+	0.777778i
$82$		−	8.28772i		−	0.915225i
$83$	0.634051			0.0695961			0.0347981	−	0.999394i	$-0.488921\pi$
$83$	0.634051			0.0695961			0.0347981	+	0.999394i	$0.488921\pi$
$84$	−0.644656	+	4.53701i	−0.0703377	+	0.495028i
$85$	15.0711			1.63469
$86$			9.65685i			1.04133i
$87$	6.21579	+	3.91969i	0.666403	+	0.420235i
$88$	−10.2426			−1.09187
$89$	8.79045			0.931786			0.465893	−	0.884841i	$-0.345733\pi$
$89$	8.79045			0.931786			0.465893	+	0.884841i	$0.345733\pi$
$90$	9.14594	−	4.36803i	0.964067	−	0.460431i
$91$	−4.00000	−	8.92177i	−0.419314	−	0.935256i
$92$		−	1.00000i		−	0.104257i
$93$	−7.19239	−	4.53553i	−0.745816	−	0.470313i
$94$		−	5.99162i		−	0.617988i
$95$			17.6569i			1.81156i
$96$	−7.32538	−	4.61940i	−0.747643	−	0.471465i
$97$			11.8519i			1.20338i	0.798730	+	0.601690i	$0.205506\pi$
$97$			11.8519i			1.20338i	−0.798730	+	0.601690i	$0.794494\pi$
$98$	−5.22625	−	4.65685i	−0.527931	−	0.470413i
$99$	−9.24264	+	4.41421i	−0.928920	+	0.443645i
$100$	6.41421			0.641421
$101$	2.42742			0.241537			0.120768	−	0.992681i	$-0.461464\pi$
$101$	2.42742			0.241537			0.120768	+	0.992681i	$0.461464\pi$
$102$	6.53553	+	4.12132i	0.647114	+	0.408072i
$103$		−	7.39104i		−	0.728260i	−0.931348	−	0.364130i	$-0.881366\pi$
$103$		−	7.39104i		−	0.728260i	0.931348	−	0.364130i	$-0.118634\pi$
$104$	11.0866			1.08713
$105$	2.17797	−	15.3282i	0.212548	−	1.49588i
$106$	−0.828427			−0.0804640
$107$		−	4.82843i		−	0.466782i	−0.972383	−	0.233391i	$-0.925018\pi$
$107$		−	4.82843i		−	0.466782i	0.972383	−	0.233391i	$-0.0749821\pi$
$108$	−5.16059	−	0.606854i	−0.496578	−	0.0583946i
$109$	−7.65685			−0.733394			−0.366697	−	0.930341i	$-0.619511\pi$
$109$	−7.65685			−0.733394			−0.366697	+	0.930341i	$0.619511\pi$
$110$	11.5349			1.09981
$111$	9.68714	−	15.3617i	0.919462	−	1.45807i
$112$	2.41421	−	1.08239i	0.228122	−	0.102276i
$113$			8.82843i			0.830509i	0.909705	+	0.415254i	$0.136307\pi$
$113$			8.82843i			0.830509i	−0.909705	+	0.415254i	$0.863693\pi$
$114$	−4.82843	+	7.65685i	−0.452224	+	0.717130i
$115$			3.37849i			0.315046i
$116$			4.24264i			0.393919i
$117$	10.0042	−	4.77791i	0.924885	−	0.441718i
$118$			8.60474i			0.792131i
$119$	10.7695	−	4.82843i	0.987241	−	0.442621i
$120$	14.8492	+	9.36396i	1.35554	+	0.854809i
$121$	−0.656854			−0.0597140
$122$	−7.25972			−0.657264
$123$	7.65685	−	12.1421i	0.690395	−	1.09482i
$124$		−	4.90923i		−	0.440862i
$125$	−4.77791			−0.427349
$126$	5.13612	−	6.05147i	0.457562	−	0.539108i
$127$	6.82843			0.605925			0.302962	−	0.953002i	$-0.402024\pi$
$127$	6.82843			0.605925			0.302962	+	0.953002i	$0.402024\pi$
$128$		−	3.00000i		−	0.265165i
$129$	−8.92177	+	14.1480i	−0.785518	+	1.24566i
$130$	−12.4853			−1.09503
$131$	−1.66205			−0.145214			−0.0726070	−	0.997361i	$-0.523132\pi$
$131$	−1.66205			−0.145214			−0.0726070	+	0.997361i	$0.523132\pi$
$132$	−5.00208	−	3.15432i	−0.435375	−	0.274548i
$133$	5.65685	+	12.6173i	0.490511	+	1.09406i
$134$		−	14.7279i		−	1.27230i
$135$	17.4350	+	2.05025i	1.50057	+	0.176458i
$136$			13.3827i			1.14755i
$137$			3.65685i			0.312426i	0.987723	+	0.156213i	$0.0499287\pi$
$137$			3.65685i			0.312426i	−0.987723	+	0.156213i	$0.950071\pi$
$138$	−0.923880	+	1.46508i	−0.0786458	+	0.124716i
$139$		−	19.2430i		−	1.63217i	−0.577934	−	0.816083i	$-0.696141\pi$
$139$		−	19.2430i		−	1.63217i	0.577934	−	0.816083i	$-0.303859\pi$
$140$	8.15640	−	3.65685i	0.689342	−	0.309061i
$141$	5.53553	−	8.77817i	0.466176	−	0.739256i
$142$	−1.65685			−0.139040
$143$	12.6173			1.05511
$144$	1.29289	+	2.70711i	0.107741	+	0.225592i
$145$		−	14.3337i		−	1.19035i
$146$	−6.75699			−0.559212
$147$	−3.35448	−	11.6511i	−0.276673	−	0.960964i
$148$	10.4853			0.861885
$149$		−	5.51472i		−	0.451783i	−0.974152	−	0.225892i	$-0.927470\pi$
$149$		−	5.51472i		−	0.451783i	0.974152	−	0.225892i	$-0.0725295\pi$
$150$	−9.39731	−	5.92596i	−0.767287	−	0.483853i
$151$	5.17157			0.420857			0.210428	−	0.977609i	$-0.432514\pi$
$151$	5.17157			0.420857			0.210428	+	0.977609i	$0.432514\pi$
$152$	−15.6788			−1.27172
$153$	5.76745	+	12.0761i	0.466271	+	0.976294i
$154$	8.24264	−	3.69552i	0.664211	−	0.297793i
$155$			16.5858i			1.33220i
$156$	5.41421	+	3.41421i	0.433484	+	0.273356i
$157$			8.34211i			0.665773i	0.942967	+	0.332887i	$0.108023\pi$
$157$			8.34211i			0.665773i	−0.942967	+	0.332887i	$0.891977\pi$
$158$			10.7279i			0.853468i
$159$	−1.21371	−	0.765367i	−0.0962533	−	0.0606975i
$160$			16.8925i			1.33547i
$161$	1.08239	+	2.41421i	0.0853045	+	0.190267i
$162$	7.00000	+	5.65685i	0.549972	+	0.444444i
$163$	−14.1421			−1.10770			−0.553849	−	0.832617i	$-0.686841\pi$
$163$	−14.1421			−1.10770			−0.553849	+	0.832617i	$0.686841\pi$
$164$	8.28772			0.647162
$165$	16.8995	+	10.6569i	1.31562	+	0.829635i
$166$		−	0.634051i		−	0.0492119i
$167$	−11.5893			−0.896806			−0.448403	−	0.893831i	$-0.648007\pi$
$167$	−11.5893			−0.896806			−0.448403	+	0.893831i	$0.648007\pi$
$168$	13.6110	+	1.93397i	1.05011	+	0.149209i
$169$	−0.656854			−0.0505272
$170$		−	15.0711i		−	1.15590i
$171$	−14.1480	+	6.75699i	−1.08193	+	0.516720i
$172$	−9.65685			−0.736328
$173$	4.32957			0.329171			0.164586	−	0.986363i	$-0.447371\pi$
$173$	4.32957			0.329171			0.164586	+	0.986363i	$0.447371\pi$
$174$	3.91969	−	6.21579i	0.297151	−	0.471218i
$175$	−15.4853	+	6.94269i	−1.17058	+	0.524818i
$176$			3.41421i			0.257356i
$177$	−7.94975	+	12.6066i	−0.597540	+	0.947570i
$178$		−	8.79045i		−	0.658872i
$179$		−	23.7990i		−	1.77882i	−0.457110	−	0.889410i	$-0.651116\pi$
$179$		−	23.7990i		−	1.77882i	0.457110	−	0.889410i	$-0.348884\pi$
$180$	4.36803	+	9.14594i	0.325574	+	0.681698i
$181$		−	11.4036i		−	0.847621i	−0.905751	−	0.423811i	$-0.860692\pi$
$181$		−	11.4036i		−	0.847621i	0.905751	−	0.423811i	$-0.139308\pi$
$182$	−8.92177	+	4.00000i	−0.661326	+	0.296500i
$183$	−10.6360	−	6.70711i	−0.786239	−	0.495804i
$184$	−3.00000			−0.221163
$185$	−35.4244			−2.60446
$186$	−4.53553	+	7.19239i	−0.332561	+	0.527371i
$187$			15.2304i			1.11376i
$188$	5.99162			0.436984
$189$	13.1156	−	4.12071i	0.954022	−	0.299738i
$190$	17.6569			1.28096
$191$			22.4853i			1.62698i	0.581580	+	0.813489i	$0.302435\pi$
$191$			22.4853i			1.62698i	−0.581580	+	0.813489i	$0.697565\pi$
$192$	−6.46716	+	10.2555i	−0.466727	+	0.740129i
$193$	−14.3431			−1.03244			−0.516221	−	0.856455i	$-0.672662\pi$
$193$	−14.3431			−1.03244			−0.516221	+	0.856455i	$0.672662\pi$
$194$	11.8519			0.850918
$195$	−18.2919	−	11.5349i	−1.30991	−	0.826031i
$196$	4.65685	−	5.22625i	0.332632	−	0.373304i
$197$		−	0.686292i		−	0.0488962i	−0.999701	−	0.0244481i	$-0.992217\pi$
$197$		−	0.686292i		−	0.0488962i	0.999701	−	0.0244481i	$-0.00778285\pi$
$198$	4.41421	+	9.24264i	0.313704	+	0.656846i
$199$		−	9.55582i		−	0.677394i	−0.940895	−	0.338697i	$-0.890014\pi$
$199$		−	9.55582i		−	0.677394i	0.940895	−	0.338697i	$-0.109986\pi$
$200$		−	19.2426i		−	1.36066i
$201$	13.6068	−	21.5775i	0.959751	−	1.52196i
$202$		−	2.42742i		−	0.170792i
$203$	−4.59220	−	10.2426i	−0.322309	−	0.718892i
$204$	−4.12132	+	6.53553i	−0.288550	+	0.457579i
$205$	−28.0000			−1.95560
$206$	−7.39104			−0.514958
$207$	−2.70711	+	1.29289i	−0.188157	+	0.0898623i
$208$		−	3.69552i		−	0.256238i
$209$	−17.8435			−1.23426
$210$	−15.3282	−	2.17797i	−1.05775	−	0.150294i
$211$	3.51472			0.241963			0.120982	−	0.992655i	$-0.461396\pi$
$211$	3.51472			0.241963			0.120982	+	0.992655i	$0.461396\pi$
$212$		−	0.828427i		−	0.0568966i
$213$	−2.42742	−	1.53073i	−0.166324	−	0.104884i
$214$	−4.82843			−0.330064
$215$	32.6256			2.22505
$216$	−1.82056	+	15.4818i	−0.123874	+	1.05340i
$217$	5.31371	+	11.8519i	0.360718	+	0.804561i
$218$			7.65685i			0.518588i
$219$	−9.89949	−	6.24264i	−0.668946	−	0.421839i
$220$			11.5349i			0.777683i
$221$		−	16.4853i		−	1.10892i
$222$	−15.3617	−	9.68714i	−1.03101	−	0.650158i
$223$			16.1815i			1.08359i	0.840510	+	0.541796i	$0.182256\pi$
$223$			16.1815i			1.08359i	−0.840510	+	0.541796i	$0.817744\pi$
$224$	5.41196	+	12.0711i	0.361602	+	0.806532i
$225$	−8.29289	−	17.3640i	−0.552860	−	1.15760i
$226$	8.82843			0.587258
$227$	13.5140			0.896954			0.448477	−	0.893794i	$-0.351967\pi$
$227$	13.5140			0.896954			0.448477	+	0.893794i	$0.351967\pi$
$228$	−7.65685	−	4.82843i	−0.507088	−	0.319770i
$229$			21.2220i			1.40239i	0.712969	+	0.701196i	$0.247350\pi$
$229$			21.2220i			1.40239i	−0.712969	+	0.701196i	$0.752650\pi$
$230$	3.37849			0.222771
$231$	15.4903	+	2.20099i	1.01919	+	0.144815i
$232$	12.7279			0.835629
$233$			25.2132i			1.65177i	0.563837	+	0.825886i	$0.309325\pi$
$233$			25.2132i			1.65177i	−0.563837	+	0.825886i	$0.690675\pi$
$234$	−4.77791	−	10.0042i	−0.312342	−	0.653993i
$235$	−20.2426			−1.32048
$236$	−8.60474			−0.560121
$237$	−9.91131	+	15.7172i	−0.643809	+	1.02094i
$238$	−4.82843	−	10.7695i	−0.312980	−	0.698085i
$239$			22.8284i			1.47665i	0.674446	+	0.738324i	$0.264382\pi$
$239$			22.8284i			1.47665i	−0.674446	+	0.738324i	$0.735618\pi$
$240$	3.12132	−	4.94975i	0.201480	−	0.319505i
$241$		−	5.80591i		−	0.373992i	−0.982361	−	0.186996i	$-0.940125\pi$
$241$		−	5.80591i		−	0.373992i	0.982361	−	0.186996i	$-0.0598751\pi$
$242$			0.656854i			0.0422242i
$243$	5.02928	+	14.7549i	0.322628	+	0.946526i
$244$		−	7.25972i		−	0.464756i
$245$	−15.7331	+	17.6569i	−1.00515	+	1.12806i
$246$	−12.1421	−	7.65685i	−0.774154	−	0.488183i
$247$	19.3137			1.22890
$248$	−14.7277			−0.935209
$249$	0.585786	−	0.928932i	0.0371227	−	0.0588687i
$250$			4.77791i			0.302182i
$251$	24.3379			1.53619			0.768097	−	0.640333i	$-0.221204\pi$
$251$	24.3379			1.53619			0.768097	+	0.640333i	$0.221204\pi$
$252$	6.05147	+	5.13612i	0.381207	+	0.323545i
$253$	−3.41421			−0.214650
$254$		−	6.82843i		−	0.428454i
$255$	13.9239	−	22.0803i	0.871945	−	1.38272i
$256$	−17.0000			−1.06250
$257$	−10.4525			−0.652009			−0.326005	−	0.945368i	$-0.605703\pi$
$257$	−10.4525			−0.652009			−0.326005	+	0.945368i	$0.605703\pi$
$258$	14.1480	+	8.92177i	0.880817	+	0.555445i
$259$	−25.3137	+	11.3492i	−1.57292	+	0.705204i
$260$		−	12.4853i		−	0.774304i
$261$	11.4853	−	5.48528i	0.710921	−	0.339530i
$262$			1.66205i			0.102682i
$263$		−	10.9289i		−	0.673907i	−0.941521	−	0.336953i	$-0.890604\pi$
$263$		−	10.9289i		−	0.673907i	0.941521	−	0.336953i	$-0.109396\pi$
$264$	−9.46297	+	15.0062i	−0.582405	+	0.923570i
$265$			2.79884i			0.171931i
$266$	12.6173	−	5.65685i	0.773616	−	0.346844i
$267$	8.12132	−	12.8787i	0.497017	−	0.788162i
$268$	14.7279			0.899651
$269$	−27.3994			−1.67057			−0.835284	−	0.549818i	$-0.814697\pi$
$269$	−27.3994			−1.67057			−0.835284	+	0.549818i	$0.814697\pi$
$270$	2.05025	−	17.4350i	0.124774	−	1.06106i
$271$		−	5.99162i		−	0.363965i	−0.983302	−	0.181982i	$-0.941749\pi$
$271$		−	5.99162i		−	0.363965i	0.983302	−	0.181982i	$-0.0582514\pi$
$272$	4.46088			0.270481
$273$	−16.7666	−	2.38234i	−1.01476	−	0.144186i
$274$	3.65685			0.220919
$275$		−	21.8995i		−	1.32059i
$276$	−1.46508	−	0.923880i	−0.0881872	−	0.0556110i
$277$	14.5858			0.876375			0.438187	−	0.898884i	$-0.355621\pi$
$277$	14.5858			0.876375			0.438187	+	0.898884i	$0.355621\pi$
$278$	−19.2430			−1.15412
$279$	−13.2898	+	6.34711i	−0.795640	+	0.379991i
$280$	−10.9706	−	24.4692i	−0.655617	−	1.46231i
$281$			5.51472i			0.328981i	0.986379	+	0.164490i	$0.0525979\pi$
$281$			5.51472i			0.328981i	−0.986379	+	0.164490i	$0.947402\pi$
$282$	−8.77817	−	5.53553i	−0.522733	−	0.329636i
$283$			18.7402i			1.11399i	0.830516	+	0.556995i	$0.188046\pi$
$283$			18.7402i			1.11399i	−0.830516	+	0.556995i	$0.811954\pi$
$284$		−	1.65685i		−	0.0983162i
$285$	25.8686	+	16.3128i	1.53233	+	0.966287i
$286$		−	12.6173i		−	0.746076i
$287$	−20.0083	+	8.97056i	−1.18105	+	0.529516i
$288$	−13.5355	+	6.46447i	−0.797589	+	0.380922i
$289$	2.89949			0.170559
$290$	−14.3337			−0.841706
$291$	17.3640	+	10.9497i	1.01789	+	0.641886i
$292$		−	6.75699i		−	0.395423i
$293$	1.47634			0.0862487			0.0431244	−	0.999070i	$-0.486269\pi$
$293$	1.47634			0.0862487			0.0431244	+	0.999070i	$0.486269\pi$
$294$	−11.6511	+	3.35448i	−0.679504	+	0.195637i
$295$	29.0711			1.69258
$296$		−	31.4558i		−	1.82833i
$297$	−2.07193	+	17.6194i	−0.120226	+	1.02238i
$298$	−5.51472			−0.319459
$299$	3.69552			0.213717
$300$	5.92596	−	9.39731i	0.342135	−	0.542554i
$301$	23.3137	−	10.4525i	1.34378	−	0.602472i
$302$		−	5.17157i		−	0.297591i
$303$	2.24264	−	3.55635i	0.128836	−	0.204307i
$304$			5.22625i			0.299746i
$305$			24.5269i			1.40441i
$306$	12.0761	−	5.76745i	0.690344	−	0.329703i
$307$		−	20.9594i		−	1.19622i	−0.801415	−	0.598108i	$-0.795919\pi$
$307$		−	20.9594i		−	1.19622i	0.801415	−	0.598108i	$-0.204081\pi$
$308$	3.69552	+	8.24264i	0.210572	+	0.469668i
$309$	−10.8284	−	6.82843i	−0.616008	−	0.388456i
$310$	16.5858			0.942009
$311$	−3.11586			−0.176684			−0.0883421	−	0.996090i	$-0.528157\pi$
$311$	−3.11586			−0.176684			−0.0883421	+	0.996090i	$0.528157\pi$
$312$	10.2426	−	16.2426i	0.579875	−	0.919558i
$313$			4.01254i			0.226802i	0.993549	+	0.113401i	$0.0361745\pi$
$313$			4.01254i			0.226802i	−0.993549	+	0.113401i	$0.963825\pi$
$314$	8.34211			0.470773
$315$	−20.4449	−	17.3523i	−1.15194	−	0.977693i
$316$	−10.7279			−0.603493
$317$			13.2132i			0.742127i	0.928607	+	0.371064i	$0.121007\pi$
$317$			13.2132i			0.742127i	−0.928607	+	0.371064i	$0.878993\pi$
$318$	−0.765367	+	1.21371i	−0.0429196	+	0.0680614i
$319$	14.4853			0.811020
$320$	23.6494			1.32204
$321$	−7.07401	−	4.46088i	−0.394833	−	0.248982i
$322$	2.41421	−	1.08239i	0.134539	−	0.0603194i
$323$			23.3137i			1.29721i
$324$	−5.65685	+	7.00000i	−0.314270	+	0.388889i
$325$			23.7038i			1.31485i
$326$			14.1421i			0.783260i
$327$	−7.07401	+	11.2179i	−0.391194	+	0.620350i
$328$		−	24.8632i		−	1.37284i
$329$	−14.4650	+	6.48528i	−0.797484	+	0.357545i
$330$	10.6569	−	16.8995i	0.586641	−	0.930287i
$331$	16.9706			0.932786			0.466393	−	0.884577i	$-0.345553\pi$
$331$	16.9706			0.932786			0.466393	+	0.884577i	$0.345553\pi$
$332$	0.634051			0.0347981
$333$	−13.5563	−	28.3848i	−0.742883	−	1.55548i
$334$			11.5893i			0.634138i
$335$	−49.7582			−2.71858
$336$	0.644656	−	4.53701i	0.0351689	−	0.247514i
$337$	−14.9706			−0.815499			−0.407749	−	0.913094i	$-0.633686\pi$
$337$	−14.9706			−0.815499			−0.407749	+	0.913094i	$0.633686\pi$
$338$			0.656854i			0.0357282i
$339$	12.9343	+	8.15640i	0.702495	+	0.442995i
$340$	15.0711			0.817343
$341$	−16.7611			−0.907667
$342$	6.75699	+	14.1480i	0.365376	+	0.765037i
$343$	−5.58579	+	17.6578i	−0.301604	+	0.953433i
$344$			28.9706i			1.56199i
$345$	4.94975	+	3.12132i	0.266485	+	0.168046i
$346$		−	4.32957i		−	0.232759i
$347$			9.17157i			0.492356i	0.969225	+	0.246178i	$0.0791748\pi$
$347$			9.17157i			0.492356i	−0.969225	+	0.246178i	$0.920825\pi$
$348$	6.21579	+	3.91969i	0.333201	+	0.210117i
$349$		−	8.65914i		−	0.463513i	−0.972774	−	0.231757i	$-0.925553\pi$
$349$		−	8.65914i		−	0.463513i	0.972774	−	0.231757i	$-0.0744473\pi$
$350$	6.94269	+	15.4853i	0.371103	+	0.827723i
$351$	2.24264	−	19.0711i	0.119703	−	1.01794i
$352$	−17.0711			−0.909891
$353$	18.1062			0.963694			0.481847	−	0.876255i	$-0.339966\pi$
$353$	18.1062			0.963694			0.481847	+	0.876255i	$0.339966\pi$
$354$	12.6066	+	7.94975i	0.670033	+	0.422524i
$355$			5.59767i			0.297093i
$356$	8.79045			0.465893
$357$	2.87574	−	20.2391i	0.152200	−	1.07116i
$358$	−23.7990			−1.25782
$359$		−	15.4142i		−	0.813531i	−0.913533	−	0.406766i	$-0.866657\pi$
$359$		−	15.4142i		−	0.813531i	0.913533	−	0.406766i	$-0.133343\pi$
$360$	27.4378	−	13.1041i	1.44610	−	0.690646i
$361$	−8.31371			−0.437564
$362$	−11.4036			−0.599359
$363$	−0.606854	+	0.962341i	−0.0318516	+	0.0505098i
$364$	−4.00000	−	8.92177i	−0.209657	−	0.467628i
$365$			22.8284i			1.19489i
$366$	−6.70711	+	10.6360i	−0.350586	+	0.555955i
$367$			9.29319i			0.485100i	0.970139	+	0.242550i	$0.0779839\pi$
$367$			9.29319i			0.485100i	−0.970139	+	0.242550i	$0.922016\pi$
$368$			1.00000i			0.0521286i
$369$	−10.7151	−	22.4357i	−0.557808	−	1.16796i
$370$			35.4244i			1.84163i
$371$	0.896683	+	2.00000i	0.0465535	+	0.103835i
$372$	−7.19239	−	4.53553i	−0.372908	−	0.235156i
$373$	10.9706			0.568034			0.284017	−	0.958819i	$-0.408333\pi$
$373$	10.9706			0.568034			0.284017	+	0.958819i	$0.408333\pi$
$374$	15.2304			0.787546
$375$	−4.41421	+	7.00000i	−0.227949	+	0.361478i
$376$		−	17.9749i		−	0.926982i
$377$	−15.6788			−0.807497
$378$	−4.12071	−	13.1156i	−0.211946	−	0.674595i
$379$	25.0711			1.28781			0.643907	−	0.765104i	$-0.277312\pi$
$379$	25.0711			1.28781			0.643907	+	0.765104i	$0.277312\pi$
$380$			17.6569i			0.905778i
$381$	6.30864	−	10.0042i	0.323202	−	0.512529i
$382$	22.4853			1.15045
$383$	1.15932			0.0592383			0.0296191	−	0.999561i	$-0.490571\pi$
$383$	1.15932			0.0592383			0.0296191	+	0.999561i	$0.490571\pi$
$384$	−4.39523	−	2.77164i	−0.224293	−	0.141440i
$385$	−12.4853	−	27.8477i	−0.636309	−	1.41925i
$386$			14.3431i			0.730047i
$387$	12.4853	+	26.1421i	0.634663	+	1.32888i
$388$			11.8519i			0.601690i
$389$			7.17157i			0.363613i	0.983334	+	0.181807i	$0.0581945\pi$
$389$			7.17157i			0.363613i	−0.983334	+	0.181807i	$0.941806\pi$
$390$	−11.5349	+	18.2919i	−0.584092	+	0.926245i
$391$			4.46088i			0.225597i
$392$	−15.6788	−	13.9706i	−0.791897	−	0.705620i
$393$	−1.53553	+	2.43503i	−0.0774574	+	0.122831i
$394$	−0.686292			−0.0345749
$395$	36.2442			1.82364
$396$	−9.24264	+	4.41421i	−0.464460	+	0.221823i
$397$		−	16.3128i		−	0.818716i	−0.912374	−	0.409358i	$-0.865753\pi$
$397$		−	16.3128i		−	0.818716i	0.912374	−	0.409358i	$-0.134247\pi$
$398$	−9.55582			−0.478990
$399$	23.7115	+	3.36913i	1.18706	+	0.168668i
$400$	−6.41421			−0.320711
$401$		−	28.8284i		−	1.43962i	−0.694170	−	0.719811i	$-0.744228\pi$
$401$		−	28.8284i		−	1.43962i	0.694170	−	0.719811i	$-0.255772\pi$
$402$	−21.5775	−	13.6068i	−1.07619	−	0.678647i
$403$	18.1421			0.903724
$404$	2.42742			0.120768
$405$	19.1116	−	23.6494i	0.949665	−	1.17515i
$406$	−10.2426	+	4.59220i	−0.508334	+	0.227907i
$407$		−	35.7990i		−	1.77449i
$408$	19.6066	+	12.3640i	0.970671	+	0.612107i
$409$			23.7038i			1.17208i	0.810282	+	0.586040i	$0.199314\pi$
$409$			23.7038i			1.17208i	−0.810282	+	0.586040i	$0.800686\pi$
$410$			28.0000i			1.38282i
$411$	5.35757	+	3.37849i	0.264269	+	0.166649i
$412$		−	7.39104i		−	0.364130i
$413$	20.7737	−	9.31371i	1.02221	−	0.458298i
$414$	1.29289	+	2.70711i	0.0635422	+	0.133047i
$415$	−2.14214			−0.105153
$416$	18.4776			0.905938
$417$	−28.1924	−	17.7782i	−1.38059	−	0.870601i
$418$			17.8435i			0.872756i
$419$	−13.8854			−0.678346			−0.339173	−	0.940724i	$-0.610147\pi$
$419$	−13.8854			−0.678346			−0.339173	+	0.940724i	$0.610147\pi$
$420$	2.17797	−	15.3282i	0.106274	−	0.747942i
$421$	12.3431			0.601568			0.300784	−	0.953692i	$-0.402752\pi$
$421$	12.3431			0.601568			0.300784	+	0.953692i	$0.402752\pi$
$422$		−	3.51472i		−	0.171094i
$423$	−7.74652	−	16.2200i	−0.376649	−	0.788641i
$424$	−2.48528			−0.120696
$425$	−28.6131			−1.38794
$426$	−1.53073	+	2.42742i	−0.0741643	+	0.117609i
$427$	7.85786	+	17.5265i	0.380269	+	0.848167i
$428$		−	4.82843i		−	0.233391i
$429$	11.6569	−	18.4853i	0.562798	−	0.892478i
$430$		−	32.6256i		−	1.57335i
$431$		−	39.5980i		−	1.90737i	−0.300811	−	0.953684i	$-0.597257\pi$
$431$		−	39.5980i		−	1.90737i	0.300811	−	0.953684i	$-0.402743\pi$
$432$	5.16059	+	0.606854i	0.248289	+	0.0291973i
$433$		−	2.93015i		−	0.140814i	−0.997518	−	0.0704070i	$-0.977570\pi$
$433$		−	2.93015i		−	0.140814i	0.997518	−	0.0704070i	$-0.0224298\pi$
$434$	11.8519	−	5.31371i	0.568910	−	0.255066i
$435$	−21.0000	−	13.2426i	−1.00687	−	0.634936i
$436$	−7.65685			−0.366697
$437$	−5.22625			−0.250006
$438$	−6.24264	+	9.89949i	−0.298285	+	0.473016i
$439$			2.93015i			0.139848i	0.997552	+	0.0699242i	$0.0222758\pi$
$439$			2.93015i			0.139848i	−0.997552	+	0.0699242i	$0.977724\pi$
$440$	34.6047			1.64971
$441$	−20.1688	−	5.84962i	−0.960421	−	0.278553i
$442$	−16.4853			−0.784125
$443$		−	15.7990i		−	0.750633i	−0.926897	−	0.375316i	$-0.877534\pi$
$443$		−	15.7990i		−	0.750633i	0.926897	−	0.375316i	$-0.122466\pi$
$444$	9.68714	−	15.3617i	0.459731	−	0.729035i
$445$	−29.6985			−1.40784
$446$	16.1815			0.766216
$447$	−8.07948	−	5.09494i	−0.382146	−	0.240982i
$448$	16.8995	−	7.57675i	0.798426	−	0.357968i
$449$		−	11.0711i		−	0.522476i	−0.965274	−	0.261238i	$-0.915869\pi$
$449$		−	11.0711i		−	0.522476i	0.965274	−	0.261238i	$-0.0841307\pi$
$450$	−17.3640	+	8.29289i	−0.818545	+	0.390931i
$451$		−	28.2960i		−	1.33241i
$452$			8.82843i			0.415254i
$453$	4.77791	−	7.57675i	0.224486	−	0.355987i
$454$		−	13.5140i		−	0.634242i
$455$	13.5140	+	30.1421i	0.633545	+	1.41309i
$456$	−14.4853	+	22.9706i	−0.678335	+	1.07570i
$457$	−30.4853			−1.42604			−0.713021	−	0.701143i	$-0.752673\pi$
$457$	−30.4853			−1.42604			−0.713021	+	0.701143i	$0.752673\pi$
$458$	21.2220			0.991640
$459$	23.0208	+	2.70711i	1.07452	+	0.126357i
$460$			3.37849i			0.157523i
$461$	−3.95815			−0.184349			−0.0921747	−	0.995743i	$-0.529382\pi$
$461$	−3.95815			−0.184349			−0.0921747	+	0.995743i	$0.529382\pi$
$462$	2.20099	−	15.4903i	0.102399	−	0.720674i
$463$	26.6274			1.23748			0.618741	−	0.785595i	$-0.287643\pi$
$463$	26.6274			1.23748			0.618741	+	0.785595i	$0.287643\pi$
$464$		−	4.24264i		−	0.196960i
$465$	24.2994	+	15.3233i	1.12686	+	0.710600i
$466$	25.2132			1.16798
$467$	16.0502			0.742713			0.371357	−	0.928490i	$-0.378893\pi$
$467$	16.0502			0.742713			0.371357	+	0.928490i	$0.378893\pi$
$468$	10.0042	−	4.77791i	0.462443	−	0.220859i
$469$	−35.5563	+	15.9414i	−1.64184	+	0.736105i
$470$			20.2426i			0.933723i
$471$	12.2218	+	7.70711i	0.563152	+	0.355125i
$472$			25.8142i			1.18820i
$473$			32.9706i			1.51599i
$474$	15.7172	+	9.91131i	0.721916	+	0.455241i
$475$		−	33.5223i		−	1.53811i
$476$	10.7695	−	4.82843i	0.493621	−	0.221311i
$477$	−2.24264	+	1.07107i	−0.102683	+	0.0490408i
$478$	22.8284			1.04415
$479$	−11.3492			−0.518558			−0.259279	−	0.965803i	$-0.583485\pi$
$479$	−11.3492			−0.518558			−0.259279	+	0.965803i	$0.583485\pi$
$480$	24.7487	+	15.6066i	1.12962	+	0.712341i
$481$			38.7485i			1.76678i
$482$	−5.80591			−0.264452
$483$	4.53701	+	0.644656i	0.206441	+	0.0293329i
$484$	−0.656854			−0.0298570
$485$		−	40.0416i		−	1.81820i
$486$	14.7549	−	5.02928i	0.669295	−	0.228133i
$487$	7.31371			0.331416			0.165708	−	0.986175i	$-0.447009\pi$
$487$	7.31371			0.331416			0.165708	+	0.986175i	$0.447009\pi$
$488$	−21.7792			−0.985896
$489$	−13.0656	+	20.7193i	−0.590848	+	0.936959i
$490$	17.6569	+	15.7331i	0.797655	+	0.710751i
$491$			19.3137i			0.871615i	0.900040	+	0.435808i	$0.143537\pi$
$491$			19.3137i			0.871615i	−0.900040	+	0.435808i	$0.856463\pi$
$492$	7.65685	−	12.1421i	0.345198	−	0.547410i
$493$		−	18.9259i		−	0.852381i
$494$		−	19.3137i		−	0.868965i
$495$	31.2262	−	14.9134i	1.40351	−	0.670307i
$496$			4.90923i			0.220431i
$497$	1.79337	+	4.00000i	0.0804435	+	0.179425i
$498$	−0.928932	−	0.585786i	−0.0416264	−	0.0262497i
$499$	2.34315			0.104894			0.0524468	−	0.998624i	$-0.483298\pi$
$499$	2.34315			0.104894			0.0524468	+	0.998624i	$0.483298\pi$
$500$	−4.77791			−0.213675
$501$	−10.7071	+	16.9792i	−0.478358	+	0.758574i
$502$		−	24.3379i		−	1.08625i
$503$	17.8435			0.795604			0.397802	−	0.917471i	$-0.369773\pi$
$503$	17.8435			0.795604			0.397802	+	0.917471i	$0.369773\pi$
$504$	15.4083	−	18.1544i	0.686342	−	0.808662i
$505$	−8.20101			−0.364940
$506$			3.41421i			0.151780i
$507$	−0.606854	+	0.962341i	−0.0269513	+	0.0427391i
$508$	6.82843			0.302962
$509$	20.9050			0.926598			0.463299	−	0.886202i	$-0.346666\pi$
$509$	20.9050			0.926598			0.463299	+	0.886202i	$0.346666\pi$
$510$	−22.0803	−	13.9239i	−0.977730	−	0.616558i
$511$	7.31371	+	16.3128i	0.323539	+	0.721636i
$512$			11.0000i			0.486136i
$513$	−3.17157	+	26.9706i	−0.140028	+	1.19078i
$514$			10.4525i			0.461040i
$515$			24.9706i			1.10033i
$516$	−8.92177	+	14.1480i	−0.392759	+	0.622832i
$517$		−	20.4567i		−	0.899683i
$518$	11.3492	+	25.3137i	0.498655	+	1.11222i
$519$	4.00000	−	6.34315i	0.175581	−	0.278433i
$520$	−37.4558			−1.64255
$521$	5.28064			0.231349			0.115675	−	0.993287i	$-0.463097\pi$
$521$	5.28064			0.231349			0.115675	+	0.993287i	$0.463097\pi$
$522$	−5.48528	−	11.4853i	−0.240084	−	0.502697i
$523$		−	7.39104i		−	0.323187i	−0.986857	−	0.161594i	$-0.948337\pi$
$523$		−	7.39104i		−	0.323187i	0.986857	−	0.161594i	$-0.0516634\pi$
$524$	−1.66205			−0.0726070
$525$	−4.13496	+	29.1013i	−0.180465	+	1.27009i
$526$	−10.9289			−0.476524
$527$			21.8995i			0.953957i
$528$	5.00208	+	3.15432i	0.217688	+	0.137274i
$529$	−1.00000			−0.0434783
$530$	2.79884			0.121574
$531$	11.1250	+	23.2940i	0.482785	+	1.01087i
$532$	5.65685	+	12.6173i	0.245256	+	0.547029i
$533$			30.6274i			1.32662i
$534$	−12.8787	−	8.12132i	−0.557315	−	0.351444i
$535$			16.3128i			0.705264i
$536$		−	44.1838i		−	1.90845i
$537$	−34.8673	−	21.9874i	−1.50464	−	0.948826i
$538$			27.3994i			1.18127i
$539$	−17.8435	−	15.8995i	−0.768576	−	0.684840i
$540$	17.4350	+	2.05025i	0.750284	+	0.0882288i
$541$	6.10051			0.262281			0.131141	−	0.991364i	$-0.458136\pi$
$541$	6.10051			0.262281			0.131141	+	0.991364i	$0.458136\pi$
$542$	−5.99162			−0.257362
$543$	−16.7071	−	10.5355i	−0.716971	−	0.452123i
$544$			22.3044i			0.956294i
$545$	25.8686			1.10809
$546$	−2.38234	+	16.7666i	−0.101955	+	0.717544i
$547$	−29.1716			−1.24729			−0.623643	−	0.781709i	$-0.714348\pi$
$547$	−29.1716			−1.24729			−0.623643	+	0.781709i	$0.714348\pi$
$548$			3.65685i			0.156213i
$549$	−19.6528	+	9.38604i	−0.838763	+	0.400587i
$550$	−21.8995			−0.933798
$551$	22.1731			0.944606
$552$	−2.77164	+	4.39523i	−0.117969	+	0.187073i
$553$	25.8995	−	11.6118i	1.10136	−	0.493785i
$554$		−	14.5858i		−	0.619691i
$555$	−32.7279	+	51.8995i	−1.38922	+	2.20301i
$556$		−	19.2430i		−	0.816083i
$557$		−	26.4853i		−	1.12222i	−0.827742	−	0.561109i	$-0.810375\pi$
$557$		−	26.4853i		−	1.12222i	0.827742	−	0.561109i	$-0.189625\pi$
$558$	6.34711	+	13.2898i	0.268694	+	0.562602i
$559$		−	35.6871i		−	1.50940i
$560$	−8.15640	+	3.65685i	−0.344671	+	0.154530i
$561$	22.3137	+	14.0711i	0.942086	+	0.594081i
$562$	5.51472			0.232624
$563$	24.3379			1.02572			0.512860	−	0.858472i	$-0.328586\pi$
$563$	24.3379			1.02572			0.512860	+	0.858472i	$0.328586\pi$
$564$	5.53553	−	8.77817i	0.233088	−	0.369628i
$565$		−	29.8268i		−	1.25482i
$566$	18.7402			0.787710
$567$	6.08011	−	23.0224i	0.255341	−	0.966851i
$568$	−4.97056			−0.208560
$569$		−	47.6569i		−	1.99788i	−0.0460393	−	0.998940i	$-0.514660\pi$
$569$		−	47.6569i		−	1.99788i	0.0460393	−	0.998940i	$-0.485340\pi$
$570$	16.3128	−	25.8686i	0.683268	−	1.08352i
$571$	9.65685			0.404127			0.202063	−	0.979372i	$-0.435235\pi$
$571$	9.65685			0.404127			0.202063	+	0.979372i	$0.435235\pi$
$572$	12.6173			0.527555
$573$	32.9426	+	20.7737i	1.37620	+	0.867833i
$574$	8.97056	+	20.0083i	0.374424	+	0.835131i
$575$		−	6.41421i		−	0.267491i
$576$	9.05025	+	18.9497i	0.377094	+	0.789573i
$577$		−	22.8072i		−	0.949474i	−0.880128	−	0.474737i	$-0.842543\pi$
$577$		−	22.8072i		−	0.949474i	0.880128	−	0.474737i	$-0.157457\pi$
$578$		−	2.89949i		−	0.120603i
$579$	−13.2513	+	21.0138i	−0.550707	+	0.873303i
$580$		−	14.3337i		−	0.595176i
$581$	−1.53073	+	0.686292i	−0.0635055	+	0.0284722i
$582$	10.9497	−	17.3640i	0.453882	−	0.719759i
$583$	−2.82843			−0.117141
$584$	−20.2710			−0.838818
$585$	−33.7990	+	16.1421i	−1.39742	+	0.667395i
$586$		−	1.47634i		−	0.0609871i
$587$	14.7277			0.607876			0.303938	−	0.952692i	$-0.401698\pi$
$587$	14.7277			0.607876			0.303938	+	0.952692i	$0.401698\pi$
$588$	−3.35448	−	11.6511i	−0.138337	−	0.480482i
$589$	−25.6569			−1.05717
$590$		−	29.0711i		−	1.19684i
$591$	−1.00547	−	0.634051i	−0.0413595	−	0.0260814i
$592$	−10.4853			−0.430942
$593$	−34.4190			−1.41342			−0.706709	−	0.707504i	$-0.749821\pi$
$593$	−34.4190			−1.41342			−0.706709	+	0.707504i	$0.749821\pi$
$594$	17.6194	+	2.07193i	0.722931	+	0.0850123i
$595$	−36.3848	+	16.3128i	−1.49163	+	0.668760i
$596$		−	5.51472i		−	0.225892i
$597$	−14.0000	−	8.82843i	−0.572982	−	0.361323i
$598$		−	3.69552i		−	0.151121i
$599$			35.1127i			1.43467i	0.696731	+	0.717333i	$0.254637\pi$
$599$			35.1127i			1.43467i	−0.696731	+	0.717333i	$0.745363\pi$
$600$	−28.1919	−	17.7779i	−1.15093	−	0.725779i
$601$			1.90215i			0.0775904i	0.999247	+	0.0387952i	$0.0123520\pi$
$601$			1.90215i			0.0775904i	−0.999247	+	0.0387952i	$0.987648\pi$
$602$	−10.4525	−	23.3137i	−0.426012	−	0.950196i
$603$	−19.0416	−	39.8701i	−0.775435	−	1.62363i
$604$	5.17157			0.210428
$605$	2.21918			0.0902224
$606$	−3.55635	−	2.24264i	−0.144467	−	0.0911011i
$607$		−	3.74991i		−	0.152204i	−0.997100	−	0.0761021i	$-0.975753\pi$
$607$		−	3.74991i		−	0.152204i	0.997100	−	0.0761021i	$-0.0242475\pi$
$608$	−26.1313			−1.05976
$609$	−19.2489	−	2.73504i	−0.780004	−	0.110830i
$610$	24.5269			0.993066
$611$			22.1421i			0.895775i
$612$	5.76745	+	12.0761i	0.233135	+	0.488147i
$613$	23.6569			0.955491			0.477746	−	0.878498i	$-0.341454\pi$
$613$	23.6569			0.955491			0.477746	+	0.878498i	$0.341454\pi$
$614$	−20.9594			−0.845853
$615$	−25.8686	+	41.0221i	−1.04312	+	1.65417i
$616$	24.7279	−	11.0866i	0.996316	−	0.446690i
$617$		−	10.0000i		−	0.402585i	−0.979531	−	0.201292i	$-0.935486\pi$
$617$		−	10.0000i		−	0.402585i	0.979531	−	0.201292i	$-0.0645141\pi$
$618$	−6.82843	+	10.8284i	−0.274680	+	0.435583i
$619$		−	28.0334i		−	1.12676i	−0.826199	−	0.563379i	$-0.809501\pi$
$619$		−	28.0334i		−	1.12676i	0.826199	−	0.563379i	$-0.190499\pi$
$620$			16.5858i			0.666101i
$621$	−0.606854	+	5.16059i	−0.0243522	+	0.207087i
$622$			3.11586i			0.124935i
$623$	−21.2220	+	9.51472i	−0.850243	+	0.381199i
$624$	−5.41421	−	3.41421i	−0.216742	−	0.136678i
$625$	−15.9289			−0.637157
$626$	4.01254			0.160373
$627$	−16.4853	+	26.1421i	−0.658359	+	1.04402i
$628$			8.34211i			0.332887i
$629$	−46.7736			−1.86499
$630$	−17.3523	+	20.4449i	−0.691333	+	0.814542i
$631$	14.0416			0.558988			0.279494	−	0.960147i	$-0.409833\pi$
$631$	14.0416			0.558988			0.279494	+	0.960147i	$0.409833\pi$
$632$			32.1838i			1.28020i
$633$	3.24718	−	5.14933i	0.129064	−	0.204667i
$634$	13.2132			0.524763
$635$	−23.0698			−0.915497
$636$	−1.21371	−	0.765367i	−0.0481267	−	0.0303488i
$637$	19.3137	+	17.2095i	0.765237	+	0.681865i
$638$		−	14.4853i		−	0.573478i
$639$	−4.48528	+	2.14214i	−0.177435	+	0.0847416i
$640$			10.1355i			0.400640i
$641$			6.28427i			0.248214i	0.992269	+	0.124107i	$0.0396066\pi$
$641$			6.28427i			0.248214i	−0.992269	+	0.124107i	$0.960393\pi$
$642$	−4.46088	+	7.07401i	−0.176057	+	0.279189i
$643$			45.2429i			1.78421i	0.451832	+	0.892103i	$0.350771\pi$
$643$			45.2429i			1.78421i	−0.451832	+	0.892103i	$0.649229\pi$
$644$	1.08239	+	2.41421i	0.0426522	+	0.0951333i
$645$	30.1421	−	47.7990i	1.18685	−	1.88208i
$646$	23.3137			0.917266
$647$	3.93562			0.154725			0.0773626	−	0.997003i	$-0.475350\pi$
$647$	3.93562			0.154725			0.0773626	+	0.997003i	$0.475350\pi$
$648$	21.0000	+	16.9706i	0.824958	+	0.666667i
$649$			29.3784i			1.15320i
$650$	23.7038			0.929741
$651$	22.2732	+	3.16476i	0.872955	+	0.124037i
$652$	−14.1421			−0.553849
$653$		−	3.31371i		−	0.129675i	−0.997896	−	0.0648377i	$-0.979347\pi$
$653$		−	3.31371i		−	0.129675i	0.997896	−	0.0648377i	$-0.0206530\pi$
$654$	11.2179	+	7.07401i	0.438653	+	0.276616i
$655$	5.61522			0.219405
$656$	−8.28772			−0.323581
$657$	−18.2919	+	8.73606i	−0.713634	+	0.340826i
$658$	6.48528	+	14.4650i	0.252823	+	0.563906i
$659$		−	28.0000i		−	1.09073i	−0.838200	−	0.545363i	$-0.816392\pi$
$659$		−	28.0000i		−	1.09073i	0.838200	−	0.545363i	$-0.183608\pi$
$660$	16.8995	+	10.6569i	0.657812	+	0.414817i
$661$		−	35.2931i		−	1.37274i	−0.727251	−	0.686372i	$-0.759202\pi$
$661$		−	35.2931i		−	1.37274i	0.727251	−	0.686372i	$-0.240798\pi$
$662$		−	16.9706i		−	0.659580i
$663$	−24.1522	−	15.2304i	−0.937993	−	0.591500i
$664$		−	1.90215i		−	0.0738178i
$665$	−19.1116	−	42.6274i	−0.741118	−	1.65302i
$666$	−28.3848	+	13.5563i	−1.09989	+	0.525298i
$667$	4.24264			0.164276
$668$	−11.5893			−0.448403
$669$	23.7071	+	14.9497i	0.916570	+	0.577991i
$670$			49.7582i			1.92233i
$671$	−24.7862			−0.956862
$672$	22.6850	+	3.22328i	0.875094	+	0.124341i
$673$	5.41421			0.208703			0.104351	−	0.994541i	$-0.466723\pi$
$673$	5.41421			0.208703			0.104351	+	0.994541i	$0.466723\pi$
$674$			14.9706i			0.576645i
$675$	−33.1012	−	3.89249i	−1.27406	−	0.149822i
$676$	−0.656854			−0.0252636
$677$	48.8840			1.87877			0.939383	−	0.342870i	$-0.111399\pi$
$677$	48.8840			1.87877			0.939383	+	0.342870i	$0.111399\pi$
$678$	8.15640	−	12.9343i	0.313245	−	0.496739i
$679$	−12.8284	−	28.6131i	−0.492310	−	1.09807i
$680$		−	45.2132i		−	1.73385i
$681$	12.4853	−	19.7990i	0.478437	−	0.758699i
$682$			16.7611i			0.641818i
$683$		−	31.7990i		−	1.21675i	−0.793648	−	0.608377i	$-0.791821\pi$
$683$		−	31.7990i		−	1.21675i	0.793648	−	0.608377i	$-0.208179\pi$
$684$	−14.1480	+	6.75699i	−0.540963	+	0.258360i
$685$		−	12.3547i		−	0.472047i
$686$	17.6578	+	5.58579i	0.674179	+	0.213266i
$687$	31.0919	+	19.6066i	1.18623	+	0.748039i
$688$	9.65685			0.368164
$689$	3.06147			0.116633
$690$	3.12132	−	4.94975i	0.118827	−	0.188434i
$691$		−	30.7779i		−	1.17084i	−0.810728	−	0.585422i	$-0.800929\pi$
$691$		−	30.7779i		−	1.17084i	0.810728	−	0.585422i	$-0.199071\pi$
$692$	4.32957			0.164586
$693$	17.5358	−	20.6610i	0.666130	−	0.784847i
$694$	9.17157			0.348148
$695$			65.0122i			2.46605i
$696$	11.7591	−	18.6474i	0.445726	−	0.706827i
$697$	−36.9706			−1.40036
$698$	−8.65914			−0.327753
$699$	36.9392	+	23.2940i	1.39717	+	0.881059i
$700$	−15.4853	+	6.94269i	−0.585289	+	0.262409i
$701$			5.02944i			0.189959i	0.995479	+	0.0949796i	$0.0302786\pi$
$701$			5.02944i			0.189959i	−0.995479	+	0.0949796i	$0.969721\pi$
$702$	−19.0711	−	2.24264i	−0.719791	−	0.0846430i
$703$		−	54.7987i		−	2.06677i
$704$			23.8995i			0.900746i
$705$	−18.7018	+	29.6570i	−0.704349	+	1.11695i
$706$		−	18.1062i		−	0.681435i
$707$	−5.86030	+	2.62742i	−0.220399	+	0.0988142i
$708$	−7.94975	+	12.6066i	−0.298770	+	0.473785i
$709$	−34.2843			−1.28757			−0.643786	−	0.765205i	$-0.722637\pi$
$709$	−34.2843			−1.28757			−0.643786	+	0.765205i	$0.722637\pi$
$710$	5.59767			0.210077
$711$	13.8701	+	29.0416i	0.520168	+	1.08915i
$712$		−	26.3714i		−	0.988309i
$713$	−4.90923			−0.183852
$714$	−20.2391	−	2.87574i	−0.757428	−	0.107622i
$715$	−42.6274			−1.59418
$716$		−	23.7990i		−	0.889410i
$717$	33.4454	+	21.0907i	1.24904	+	0.787647i
$718$	−15.4142			−0.575253
$719$	−11.8519			−0.442002			−0.221001	−	0.975274i	$-0.570932\pi$
$719$	−11.8519			−0.442002			−0.221001	+	0.975274i	$0.570932\pi$
$720$	−4.36803	−	9.14594i	−0.162787	−	0.340849i
$721$	8.00000	+	17.8435i	0.297936	+	0.664528i
$722$			8.31371i			0.309404i
$723$	−8.50610	−	5.36396i	−0.316345	−	0.199488i
$724$		−	11.4036i		−	0.423811i
$725$			27.2132i			1.01067i
$726$	0.962341	+	0.606854i	0.0357158	+	0.0225225i
$727$			30.0894i			1.11595i	0.829856	+	0.557977i	$0.188422\pi$
$727$			30.0894i			1.11595i	−0.829856	+	0.557977i	$0.811578\pi$
$728$	−26.7653	+	12.0000i	−0.991988	+	0.444750i
$729$	26.2635	+	6.26346i	0.972721	+	0.231980i
$730$	22.8284			0.844918
$731$	43.0781			1.59330
$732$	−10.6360	−	6.70711i	−0.393119	−	0.247902i
$733$		−	18.7177i		−	0.691354i	−0.938354	−	0.345677i	$-0.887649\pi$
$733$		−	18.7177i		−	0.691354i	0.938354	−	0.345677i	$-0.112351\pi$
$734$	9.29319			0.343018
$735$	11.3331	+	39.3631i	0.418027	+	1.45193i
$736$	−5.00000			−0.184302
$737$		−	50.2843i		−	1.85224i
$738$	−22.4357	+	10.7151i	−0.825871	+	0.394430i
$739$	20.9706			0.771415			0.385707	−	0.922621i	$-0.373957\pi$
$739$	20.9706			0.771415			0.385707	+	0.922621i	$0.373957\pi$
$740$	−35.4244			−1.30223
$741$	17.8435	−	28.2960i	0.655499	−	1.03948i
$742$	2.00000	−	0.896683i	0.0734223	−	0.0329183i
$743$		−	33.5563i		−	1.23106i	−0.788112	−	0.615532i	$-0.788941\pi$
$743$		−	33.5563i		−	1.23106i	0.788112	−	0.615532i	$-0.211059\pi$
$744$	−13.6066	+	21.5772i	−0.498842	+	0.791057i
$745$			18.6314i			0.682603i
$746$		−	10.9706i		−	0.401661i
$747$	−0.819760	−	1.71644i	−0.0299934	−	0.0628014i
$748$			15.2304i			0.556879i
$749$	5.22625	+	11.6569i	0.190963	+	0.425932i
$750$	7.00000	+	4.41421i	0.255604	+	0.161184i
$751$	−37.8406			−1.38082			−0.690412	−	0.723416i	$-0.742571\pi$
$751$	−37.8406			−1.38082			−0.690412	+	0.723416i	$0.742571\pi$
$752$	−5.99162			−0.218492
$753$	22.4853	−	35.6569i	0.819409	−	1.29941i
$754$			15.6788i			0.570987i
$755$	−17.4721			−0.635876
$756$	13.1156	−	4.12071i	0.477011	−	0.149869i
$757$	−18.4853			−0.671859			−0.335929	−	0.941887i	$-0.609050\pi$
$757$	−18.4853			−0.671859			−0.335929	+	0.941887i	$0.609050\pi$
$758$		−	25.0711i		−	0.910622i
$759$	−3.15432	+	5.00208i	−0.114495	+	0.181564i
$760$	52.9706			1.92144
$761$	14.1480			0.512865			0.256433	−	0.966562i	$-0.417453\pi$
$761$	14.1480			0.512865			0.256433	+	0.966562i	$0.417453\pi$
$762$	−10.0042	−	6.30864i	−0.362413	−	0.228538i
$763$	18.4853	−	8.28772i	0.669212	−	0.300036i
$764$			22.4853i			0.813489i
$765$	−19.4853	−	40.7990i	−0.704492	−	1.47509i
$766$		−	1.15932i		−	0.0418878i
$767$		−	31.7990i		−	1.14819i
$768$	−15.7060	+	24.9063i	−0.566740	+	0.898728i
$769$			5.80591i			0.209366i	0.994506	+	0.104683i	$0.0333829\pi$
$769$			5.80591i			0.209366i	−0.994506	+	0.104683i	$0.966617\pi$
$770$	−27.8477	+	12.4853i	−1.00356	+	0.449938i
$771$	−9.65685	+	15.3137i	−0.347783	+	0.551510i
$772$	−14.3431			−0.516221
$773$	17.7122			0.637064			0.318532	−	0.947912i	$-0.396810\pi$
$773$	17.7122			0.637064			0.318532	+	0.947912i	$0.396810\pi$
$774$	26.1421	−	12.4853i	0.939660	−	0.448774i
$775$		−	31.4888i		−	1.13111i
$776$	35.5558			1.27638
$777$	−6.75940	+	47.5718i	−0.242492	+	1.70663i
$778$	7.17157			0.257113
$779$		−	43.3137i		−	1.55187i
$780$	−18.2919	−	11.5349i	−0.654954	−	0.413016i
$781$	−5.65685			−0.202418
$782$	4.46088			0.159521
$783$	2.57466	−	21.8945i	0.0920110	−	0.782447i
$784$	−4.65685	+	5.22625i	−0.166316	+	0.186652i
$785$		−	28.1838i		−	1.00592i
$786$	2.43503	+	1.53553i	0.0868546	+	0.0547707i
$787$		−	21.1676i		−	0.754545i	−0.926102	−	0.377272i	$-0.876862\pi$
$787$		−	21.1676i		−	0.754545i	0.926102	−	0.377272i	$-0.123138\pi$
$788$		−	0.686292i		−	0.0244481i
$789$	−16.0117	−	10.0970i	−0.570032	−	0.359463i
$790$		−	36.2442i		−	1.28951i
$791$	−9.55582	−	21.3137i	−0.339766	−	0.757828i
$792$	13.2426	+	27.7279i	0.470557	+	0.985269i
$793$	26.8284			0.952705
$794$	−16.3128			−0.578920
$795$	4.10051	+	2.58579i	0.145430	+	0.0917084i
$796$		−	9.55582i		−	0.338697i
$797$	2.40489			0.0851855			0.0425927	−	0.999093i	$-0.486438\pi$
$797$	2.40489			0.0851855			0.0425927	+	0.999093i	$0.486438\pi$
$798$	3.36913	−	23.7115i	0.119266	−	0.839379i
$799$	−26.7279			−0.945566
$800$		−	32.0711i		−	1.13388i
$801$	−11.3651	−	23.7967i	−0.401567	−	0.840815i
$802$	−28.8284			−1.01797
$803$	−23.0698			−0.814115
$804$	13.6068	−	21.5775i	0.479876	−	0.760980i
$805$	−3.65685	−	8.15640i	−0.128887	−	0.287475i
$806$		−	18.1421i		−	0.639029i
$807$	−25.3137	+	40.1421i	−0.891085	+	1.41307i
$808$		−	7.28225i		−	0.256189i
$809$		−	6.68629i		−	0.235077i	−0.993068	−	0.117539i	$-0.962500\pi$
$809$		−	6.68629i		−	0.235077i	0.993068	−	0.117539i	$-0.0375004\pi$
$810$	−23.6494	−	19.1116i	−0.830957	−	0.671515i
$811$			35.1074i			1.23279i	0.787438	+	0.616394i	$0.211407\pi$
$811$			35.1074i			1.23279i	−0.787438	+	0.616394i	$0.788593\pi$
$812$	−4.59220	−	10.2426i	−0.161155	−	0.359446i
$813$	−8.77817	−	5.53553i	−0.307864	−	0.194140i
$814$	−35.7990			−1.25475
$815$	47.7791			1.67363
$816$	4.12132	−	6.53553i	0.144275	−	0.228789i
$817$			50.4692i			1.76569i
$818$	23.7038			0.828785
$819$	−18.9806	+	22.3633i	−0.663236	+	0.781438i
$820$	−28.0000			−0.977802
$821$			39.7574i			1.38754i	0.720196	+	0.693771i	$0.244052\pi$
$821$			39.7574i			1.38754i	−0.720196	+	0.693771i	$0.755948\pi$
$822$	3.37849	−	5.35757i	0.117838	−	0.186867i
$823$	−35.1127			−1.22395			−0.611976	−	0.790876i	$-0.709625\pi$
$823$	−35.1127			−1.22395			−0.611976	+	0.790876i	$0.709625\pi$
$824$	−22.1731			−0.772437
$825$	−32.0844	−	20.2325i	−1.11704	−	0.704405i
$826$	−9.31371	−	20.7737i	−0.324065	−	0.722809i
$827$		−	10.6274i		−	0.369551i	−0.982781	−	0.184776i	$-0.940844\pi$
$827$		−	10.6274i		−	0.369551i	0.982781	−	0.184776i	$-0.0591559\pi$
$828$	−2.70711	+	1.29289i	−0.0940785	+	0.0449311i
$829$			37.3266i			1.29641i	0.761467	+	0.648203i	$0.224479\pi$
$829$			37.3266i			1.29641i	−0.761467	+	0.648203i	$0.775521\pi$
$830$			2.14214i			0.0743546i
$831$	13.4755	−	21.3693i	0.467460	−	0.741292i
$832$		−	25.8686i		−	0.896833i
$833$	−20.7737	+	23.3137i	−0.719766	+	0.807772i
$834$	−17.7782	+	28.1924i	−0.615608	+	0.976223i
$835$	39.1543			1.35499
$836$	−17.8435			−0.617132
$837$	−2.97918	+	25.3345i	−0.102976	+	0.875689i
$838$			13.8854i			0.479663i
$839$	1.53073			0.0528468			0.0264234	−	0.999651i	$-0.491588\pi$
$839$	1.53073			0.0528468			0.0264234	+	0.999651i	$0.491588\pi$
$840$	−45.9847	−	6.53390i	−1.58662	−	0.225441i
$841$	11.0000			0.379310
$842$		−	12.3431i		−	0.425373i
$843$	8.07948	+	5.09494i	0.278272	+	0.175479i
$844$	3.51472			0.120982
$845$	2.21918			0.0763420
$846$	−16.2200	+	7.74652i	−0.557653	+	0.266331i
$847$	1.58579	−	0.710974i	0.0544883	−	0.0244294i
$848$			0.828427i			0.0284483i
$849$	27.4558	+	17.3137i	0.942282	+	0.594205i
$850$			28.6131i			0.981420i
$851$		−	10.4853i		−	0.359431i
$852$	−2.42742	−	1.53073i	−0.0831619	−	0.0524421i
$853$		−	42.9693i		−	1.47124i	−0.677393	−	0.735621i	$-0.736891\pi$
$853$		−	42.9693i		−	1.47124i	0.677393	−	0.735621i	$-0.263109\pi$
$854$	17.5265	−	7.85786i	0.599745	−	0.268891i
$855$	47.7990	−	22.8284i	1.63469	−	0.780716i
$856$	−14.4853			−0.495097
$857$	−24.3379			−0.831367			−0.415683	−	0.909509i	$-0.636458\pi$
$857$	−24.3379			−0.831367			−0.415683	+	0.909509i	$0.636458\pi$
$858$	−18.4853	−	11.6569i	−0.631077	−	0.397958i
$859$			24.3604i			0.831167i	0.909555	+	0.415583i	$0.136423\pi$
$859$			24.3604i			0.831167i	−0.909555	+	0.415583i	$0.863577\pi$
$860$	32.6256			1.11252
$861$	−5.34273	+	37.6014i	−0.182080	+	1.28145i
$862$	−39.5980			−1.34871
$863$		−	22.6274i		−	0.770246i	−0.922865	−	0.385123i	$-0.874159\pi$
$863$		−	22.6274i		−	0.770246i	0.922865	−	0.385123i	$-0.125841\pi$
$864$	−3.03427	+	25.8030i	−0.103228	+	0.877835i
$865$	−14.6274			−0.497347
$866$	−2.93015			−0.0995706
$867$	2.67878	−	4.24798i	0.0909763	−	0.144269i
$868$	5.31371	+	11.8519i	0.180359	+	0.402280i
$869$			36.6274i			1.24250i
$870$	−13.2426	+	21.0000i	−0.448968	+	0.711967i
$871$			54.4273i			1.84420i
$872$			22.9706i			0.777881i
$873$	32.0844	−	15.3233i	1.08589	−	0.518614i
$874$			5.22625i			0.176781i
$875$	11.5349	−	5.17157i	0.389951	−	0.174831i
$876$	−9.89949	−	6.24264i	−0.334473	−	0.210919i
$877$	2.87006			0.0969150			0.0484575	−	0.998825i	$-0.484569\pi$
$877$	2.87006			0.0969150			0.0484575	+	0.998825i	$0.484569\pi$
$878$	2.93015			0.0988878
$879$	1.36396	−	2.16295i	0.0460053	−	0.0729545i
$880$		−	11.5349i		−	0.388841i
$881$	47.2764			1.59278			0.796391	−	0.604783i	$-0.206740\pi$
$881$	47.2764			1.59278			0.796391	+	0.604783i	$0.206740\pi$
$882$	−5.84962	+	20.1688i	−0.196967	+	0.679120i
$883$	−40.4853			−1.36244			−0.681219	−	0.732080i	$-0.738550\pi$
$883$	−40.4853			−1.36244			−0.681219	+	0.732080i	$0.738550\pi$
$884$		−	16.4853i		−	0.554460i
$885$	26.8582	−	42.5913i	0.902827	−	1.43169i
$886$	−15.7990			−0.530777
$887$	−35.6327			−1.19643			−0.598214	−	0.801336i	$-0.704123\pi$
$887$	−35.6327			−1.19643			−0.598214	+	0.801336i	$0.704123\pi$
$888$	−46.0852	−	29.0614i	−1.54652	−	0.975237i
$889$	−16.4853	+	7.39104i	−0.552899	+	0.247887i
$890$			29.6985i			0.995495i
$891$	23.8995	+	19.3137i	0.800663	+	0.647034i
$892$			16.1815i			0.541796i
$893$		−	31.3137i		−	1.04787i
$894$	−5.09494	+	8.07948i	−0.170400	+	0.270218i
$895$			80.4047i			2.68763i
$896$	3.24718	+	7.24264i	0.108481	+	0.241960i
$897$	3.41421	−	5.41421i	0.113997	−	0.180775i
$898$	−11.0711			−0.369446
$899$	20.8281			0.694656
$900$	−8.29289	−	17.3640i	−0.276430	−	0.578799i
$901$			3.69552i			0.123116i
$902$	−28.2960			−0.942155
$903$	6.22535	−	43.8132i	0.207167	−	1.45801i
$904$	26.4853			0.880887
$905$			38.5269i			1.28068i
$906$	−7.57675	−	4.77791i	−0.251721	−	0.158735i
$907$	49.1127			1.63076			0.815380	−	0.578926i	$-0.196528\pi$
$907$	49.1127			1.63076			0.815380	+	0.578926i	$0.196528\pi$
$908$	13.5140			0.448477
$909$	−3.13839	−	6.57128i	−0.104094	−	0.217955i
$910$	30.1421	−	13.5140i	0.999202	−	0.447984i
$911$			50.7279i			1.68069i	0.542051	+	0.840346i	$0.317648\pi$
$911$			50.7279i			1.68069i	−0.542051	+	0.840346i	$0.682352\pi$
$912$	7.65685	+	4.82843i	0.253544	+	0.159885i
$913$		−	2.16478i		−	0.0716439i
$914$			30.4853i			1.00836i
$915$	35.9338	+	22.6599i	1.18793	+	0.749114i
$916$			21.2220i			0.701196i
$917$	4.01254	−	1.79899i	0.132506	−	0.0594079i
$918$	2.70711	−	23.0208i	0.0893478	−	0.759800i
$919$	33.5563			1.10692			0.553461	−	0.832875i	$-0.313307\pi$
$919$	33.5563			1.10692			0.553461	+	0.832875i	$0.313307\pi$
$920$	10.1355			0.334157
$921$	−30.7071	−	19.3640i	−1.01183	−	0.638064i
$922$			3.95815i			0.130355i
$923$	6.12293			0.201539
$924$	15.4903	+	2.20099i	0.509594	+	0.0724074i
$925$	67.2548			2.21133
$926$		−	26.6274i		−	0.875031i
$927$	−20.0083	+	9.55582i	−0.657160	+	0.313854i
$928$	21.2132			0.696358
$929$	−1.63952			−0.0537909			−0.0268954	−	0.999638i	$-0.508562\pi$
$929$	−1.63952			−0.0537909			−0.0268954	+	0.999638i	$0.508562\pi$
$930$	15.3233	−	24.2994i	0.502470	−	0.796810i
$931$	−27.3137	−	24.3379i	−0.895171	−	0.797642i
$932$			25.2132i			0.825886i
$933$	−2.87868	+	4.56497i	−0.0942437	+	0.149450i
$934$		−	16.0502i		−	0.525178i
$935$		−	51.4558i		−	1.68279i
$936$	−14.3337	−	30.0125i	−0.468513	−	0.980989i
$937$			56.9091i			1.85914i	0.368646	+	0.929570i	$0.379821\pi$
$937$			56.9091i			1.85914i	−0.368646	+	0.929570i	$0.620179\pi$
$938$	15.9414	+	35.5563i	0.520505	+	1.16096i
$939$	5.87868	+	3.70711i	0.191843	+	0.120977i
$940$	−20.2426			−0.660242
$941$	−10.0586			−0.327900			−0.163950	−	0.986469i	$-0.552423\pi$
$941$	−10.0586			−0.327900			−0.163950	+	0.986469i	$0.552423\pi$
$942$	7.70711	−	12.2218i	0.251111	−	0.398209i
$943$		−	8.28772i		−	0.269885i
$944$	8.60474			0.280061
$945$	−44.3111	+	13.9218i	−1.44144	+	0.452876i
$946$	32.9706			1.07197
$947$		−	8.28427i		−	0.269203i	−0.990900	−	0.134601i	$-0.957025\pi$
$947$		−	8.28427i		−	0.269203i	0.990900	−	0.134601i	$-0.0429754\pi$
$948$	−9.91131	+	15.7172i	−0.321904	+	0.510471i
$949$	24.9706			0.810579
$950$	−33.5223			−1.08761
$951$	19.3583	+	12.2074i	0.627737	+	0.395852i
$952$	−14.4853	−	32.3086i	−0.469471	−	1.04713i
$953$			16.3431i			0.529406i	0.964330	+	0.264703i	$0.0852740\pi$
$953$			16.3431i			0.529406i	−0.964330	+	0.264703i	$0.914726\pi$
$954$	1.07107	+	2.24264i	0.0346771	+	0.0726082i
$955$		−	75.9664i		−	2.45821i
$956$			22.8284i			0.738324i
$957$	13.3827	−	21.2220i	0.432600	−	0.686011i
$958$			11.3492i			0.366676i
$959$	−3.95815	−	8.82843i	−0.127815	−	0.285085i
$960$	21.8492	−	34.6482i	0.705181	−	1.11827i
$961$	6.89949			0.222564
$962$	38.7485			1.24930
$963$	−13.0711	+	6.24264i	−0.421209	+	0.201166i
$964$		−	5.80591i		−	0.186996i
$965$	48.4582			1.55993
$966$	0.644656	−	4.53701i	0.0207415	−	0.145976i
$967$	−2.82843			−0.0909561			−0.0454780	−	0.998965i	$-0.514481\pi$
$967$	−2.82843			−0.0909561			−0.0454780	+	0.998965i	$0.514481\pi$
$968$			1.97056i			0.0633363i
$969$	34.1563	+	21.5391i	1.09726	+	0.691934i
$970$	−40.0416			−1.28566
$971$	60.8129			1.95158			0.975789	−	0.218714i	$-0.0701863\pi$
$971$	60.8129			1.95158			0.975789	+	0.218714i	$0.0701863\pi$
$972$	5.02928	+	14.7549i	0.161314	+	0.473263i
$973$	20.8284	+	46.4566i	0.667729	+	1.48933i
$974$		−	7.31371i		−	0.234346i
$975$	34.7279	+	21.8995i	1.11218	+	0.701345i
$976$			7.25972i			0.232378i
$977$		−	44.4264i		−	1.42133i	−0.703532	−	0.710663i	$-0.748395\pi$
$977$		−	44.4264i		−	1.42133i	0.703532	−	0.710663i	$-0.251605\pi$
$978$	20.7193	+	13.0656i	0.662530	+	0.417793i
$979$		−	30.0125i		−	0.959203i
$980$	−15.7331	+	17.6569i	−0.502577	+	0.564028i
$981$	9.89949	+	20.7279i	0.316067	+	0.661792i
$982$	19.3137			0.616325
$983$	−38.1145			−1.21566			−0.607832	−	0.794066i	$-0.707961\pi$
$983$	−38.1145			−1.21566			−0.607832	+	0.794066i	$0.707961\pi$
$984$	−36.4264	−	22.9706i	−1.16123	−	0.732275i
$985$			2.31863i			0.0738777i
$986$	−18.9259			−0.602724
$987$	−3.86253	+	27.1840i	−0.122946	+	0.865276i
$988$	19.3137			0.614451
$989$			9.65685i			0.307070i
$990$	−14.9134	−	31.2262i	−0.473979	−	0.992434i
$991$	33.9411			1.07818			0.539088	−	0.842250i	$-0.318769\pi$
$991$	33.9411			1.07818			0.539088	+	0.842250i	$0.318769\pi$
$992$	−24.5461			−0.779340
$993$	15.6788	−	24.8632i	0.497550	−	0.789008i
$994$	4.00000	−	1.79337i	0.126872	−	0.0568821i
$995$			32.2843i			1.02348i
$996$	0.585786	−	0.928932i	0.0185614	−	0.0294343i
$997$			25.2346i			0.799187i	0.916692	+	0.399594i	$0.130849\pi$
$997$			25.2346i			0.799187i	−0.916692	+	0.399594i	$0.869151\pi$
$998$		−	2.34315i		−	0.0741710i
$999$	−54.1103	−	6.36304i	−1.71197	−	0.201318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.c.461.4	yes	8
3.2	odd	2	inner	483.2.d.c.461.5	yes	8
7.6	odd	2	inner	483.2.d.c.461.1	✓	8
21.20	even	2	inner	483.2.d.c.461.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.c.461.1	✓	8	7.6	odd	2	inner
483.2.d.c.461.4	yes	8	1.1	even	1	trivial
483.2.d.c.461.5	yes	8	3.2	odd	2	inner
483.2.d.c.461.8	yes	8	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.923880 - 1.46508i) q^{3} +1.00000 q^{4} -3.37849 q^{5} +(-1.46508 - 0.923880i) q^{6} +(-2.41421 + 1.08239i) q^{7} -3.00000i q^{8} +(-1.29289 - 2.70711i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.923880 - 1.46508i) q^{3} +1.00000 q^{4} -3.37849 q^{5} +(-1.46508 - 0.923880i) q^{6} +(-2.41421 + 1.08239i) q^{7} -3.00000i q^{8} +(-1.29289 - 2.70711i) q^{9} +3.37849i q^{10} -3.41421i q^{11} +(0.923880 - 1.46508i) q^{12} +3.69552i q^{13} +(1.08239 + 2.41421i) q^{14} +(-3.12132 + 4.94975i) q^{15} -1.00000 q^{16} -4.46088 q^{17} +(-2.70711 + 1.29289i) q^{18} -5.22625i q^{19} -3.37849 q^{20} +(-0.644656 + 4.53701i) q^{21} -3.41421 q^{22} -1.00000i q^{23} +(-4.39523 - 2.77164i) q^{24} +6.41421 q^{25} +3.69552 q^{26} +(-5.16059 - 0.606854i) q^{27} +(-2.41421 + 1.08239i) q^{28} +4.24264i q^{29} +(4.94975 + 3.12132i) q^{30} -4.90923i q^{31} -5.00000i q^{32} +(-5.00208 - 3.15432i) q^{33} +4.46088i q^{34} +(8.15640 - 3.65685i) q^{35} +(-1.29289 - 2.70711i) q^{36} +10.4853 q^{37} -5.22625 q^{38} +(5.41421 + 3.41421i) q^{39} +10.1355i q^{40} +8.28772 q^{41} +(4.53701 + 0.644656i) q^{42} -9.65685 q^{43} -3.41421i q^{44} +(4.36803 + 9.14594i) q^{45} -1.00000 q^{46} +5.99162 q^{47} +(-0.923880 + 1.46508i) q^{48} +(4.65685 - 5.22625i) q^{49} -6.41421i q^{50} +(-4.12132 + 6.53553i) q^{51} +3.69552i q^{52} -0.828427i q^{53} +(-0.606854 + 5.16059i) q^{54} +11.5349i q^{55} +(3.24718 + 7.24264i) q^{56} +(-7.65685 - 4.82843i) q^{57} +4.24264 q^{58} -8.60474 q^{59} +(-3.12132 + 4.94975i) q^{60} -7.25972i q^{61} -4.90923 q^{62} +(6.05147 + 5.13612i) q^{63} -7.00000 q^{64} -12.4853i q^{65} +(-3.15432 + 5.00208i) q^{66} +14.7279 q^{67} -4.46088 q^{68} +(-1.46508 - 0.923880i) q^{69} +(-3.65685 - 8.15640i) q^{70} -1.65685i q^{71} +(-8.12132 + 3.87868i) q^{72} -6.75699i q^{73} -10.4853i q^{74} +(5.92596 - 9.39731i) q^{75} -5.22625i q^{76} +(3.69552 + 8.24264i) q^{77} +(3.41421 - 5.41421i) q^{78} -10.7279 q^{79} +3.37849 q^{80} +(-5.65685 + 7.00000i) q^{81} -8.28772i q^{82} +0.634051 q^{83} +(-0.644656 + 4.53701i) q^{84} +15.0711 q^{85} +9.65685i q^{86} +(6.21579 + 3.91969i) q^{87} -10.2426 q^{88} +8.79045 q^{89} +(9.14594 - 4.36803i) q^{90} +(-4.00000 - 8.92177i) q^{91} -1.00000i q^{92} +(-7.19239 - 4.53553i) q^{93} -5.99162i q^{94} +17.6569i q^{95} +(-7.32538 - 4.61940i) q^{96} +11.8519i q^{97} +(-5.22625 - 4.65685i) q^{98} +(-9.24264 + 4.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9	\( 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9} - 8 q^{15} - 8 q^{16} - 16 q^{18} + 24 q^{21} - 16 q^{22} + 40 q^{25} - 8 q^{28} - 16 q^{36} + 16 q^{37} + 32 q^{39} + 8 q^{42} - 32 q^{43} - 8 q^{46} - 8 q^{49} - 16 q^{51} - 16 q^{57} - 8 q^{60} + 8 q^{63} - 56 q^{64} + 16 q^{67} + 16 q^{70} - 48 q^{72} + 16 q^{78} + 16 q^{79} + 24 q^{84} + 64 q^{85} - 48 q^{88} - 32 q^{91} + 16 q^{93} - 40 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9 - 8 * q^15 - 8 * q^16 - 16 * q^18 + 24 * q^21 - 16 * q^22 + 40 * q^25 - 8 * q^28 - 16 * q^36 + 16 * q^37 + 32 * q^39 + 8 * q^42 - 32 * q^43 - 8 * q^46 - 8 * q^49 - 16 * q^51 - 16 * q^57 - 8 * q^60 + 8 * q^63 - 56 * q^64 + 16 * q^67 + 16 * q^70 - 48 * q^72 + 16 * q^78 + 16 * q^79 + 24 * q^84 + 64 * q^85 - 48 * q^88 - 32 * q^91 + 16 * q^93 - 40 * q^99

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