LMFDB - Embedded newform 735.2.s.k.521.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(521,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("735.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.s (of order $6$, degree $2$, not 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.4
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	735.521
Dual form			735.2.s.k.656.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78651 - 1.03144i) q^{2} +(0.627739 - 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +O(q^{10})$	\(q+(1.78651 - 1.03144i) q^{2} +(0.627739 - 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +(-1.78651 - 1.03144i) q^{10} +(-4.06348 - 2.34605i) q^{11} +(-2.44528 - 3.04666i) q^{12} -0.638688i q^{13} +(-1.71189 + 0.263509i) q^{15} +(1.71189 + 2.96508i) q^{16} +(2.07462 - 3.59334i) q^{17} +(-6.04198 - 1.33930i) q^{18} +(0.776975 - 0.448587i) q^{19} -2.25548 q^{20} -9.67925 q^{22} +(5.89275 - 3.40218i) q^{23} +(-0.850763 - 0.330830i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.658769 - 1.14102i) q^{26} +(-4.66019 + 2.29839i) q^{27} -2.14740i q^{29} +(-2.78651 + 2.23647i) q^{30} +(2.02453 + 1.16886i) q^{31} +(7.02943 + 4.05844i) q^{32} +(-6.33802 + 5.08695i) q^{33} -8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} +(5.69122 + 9.85748i) q^{37} +(0.925382 - 1.60281i) q^{38} +(-1.03103 - 0.400929i) q^{39} +(-0.456412 + 0.263509i) q^{40} +4.10624 q^{41} +3.14924 q^{43} +(-9.16509 + 5.29147i) q^{44} +(-0.649237 + 2.92891i) q^{45} +(7.01829 - 12.1560i) q^{46} +(3.40471 + 5.89714i) q^{47} +(5.86113 - 0.902197i) q^{48} +2.06288i q^{50} +(-4.49840 - 5.60472i) q^{51} +(-1.24755 - 0.720273i) q^{52} +(1.96187 + 1.13269i) q^{53} +(-5.95481 + 8.91281i) q^{54} +4.69211i q^{55} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 - 3.83635i) q^{58} +(0.254055 - 0.440035i) q^{59} +(-1.41585 + 3.64100i) q^{60} +(-4.48946 + 2.59199i) q^{61} +4.82244 q^{62} +9.89660 q^{64} +(-0.553120 + 0.319344i) q^{65} +(-6.07604 + 15.6252i) q^{66} +(-2.41425 + 4.18160i) q^{67} +(-4.67925 - 8.10471i) q^{68} +(-1.79301 - 11.6483i) q^{69} +1.22800i q^{71} +(-1.06811 + 1.16571i) q^{72} +(-12.5197 - 7.22826i) q^{73} +(20.3348 + 11.7403i) q^{74} +(1.08415 + 1.35078i) q^{75} -2.02356i q^{76} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 - 7.86448i) q^{79} +(1.71189 - 2.96508i) q^{80} +(0.784903 + 8.96571i) q^{81} +(7.33583 - 4.23534i) q^{82} -2.76359 q^{83} -4.14924 q^{85} +(5.62613 - 3.24825i) q^{86} +(-3.46653 - 1.34801i) q^{87} +(-1.23641 + 2.14153i) q^{88} +(6.90067 + 11.9523i) q^{89} +(1.86113 + 5.90216i) q^{90} -15.3471i q^{92} +(3.15776 - 2.53444i) q^{93} +(12.1651 + 7.02352i) q^{94} +(-0.776975 - 0.448587i) q^{95} +(10.9642 - 8.79992i) q^{96} +12.9085i q^{97} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	1.78651	−	1.03144i	1.26325	−	0.729338i	0.289549	−	0.957163i	$-0.406495\pi$
$2$	1.78651	−	1.03144i	1.26325	−	0.729338i	0.973702	+	0.227825i	$0.0731613\pi$
$3$	0.627739	−	1.61429i	0.362425	−	0.932013i
$3$	0.627739	−	1.61429i	0.362425	−	0.932013i
$4$	1.12774	−	1.95330i	0.563869	−	0.976650i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.543588	−	3.53142i	−0.221919	−	1.44170i
$7$		0			0
$7$		0			0
$8$		−	0.527019i		−	0.186329i
$9$	−2.21189	−	2.02671i	−0.737296	−	0.675570i
$10$	−1.78651	−	1.03144i	−0.564943	−	0.326170i
$11$	−4.06348	−	2.34605i	−1.22519	−	0.707362i	−0.259167	−	0.965833i	$-0.583448\pi$
$11$	−4.06348	−	2.34605i	−1.22519	−	0.707362i	−0.966019	+	0.258471i	$0.916781\pi$
$12$	−2.44528	−	3.04666i	−0.705890	−	0.879496i
$13$		−	0.638688i		−	0.177140i	−0.996070	−	0.0885701i	$-0.971770\pi$
$13$		−	0.638688i		−	0.177140i	0.996070	−	0.0885701i	$-0.0282297\pi$
$14$		0			0
$15$	−1.71189	+	0.263509i	−0.442008	+	0.0680378i
$16$	1.71189	+	2.96508i	0.427972	+	0.741270i
$17$	2.07462	−	3.59334i	0.503169	−	0.871514i	−0.496824	−	0.867851i	$-0.665501\pi$
$17$	2.07462	−	3.59334i	0.503169	−	0.871514i	0.999993	−	0.00366299i	$-0.00116597\pi$
$18$	−6.04198	−	1.33930i	−1.42411	−	0.315676i
$19$	0.776975	−	0.448587i	0.178250	−	0.102913i	−0.408220	−	0.912884i	$-0.633850\pi$
$19$	0.776975	−	0.448587i	0.178250	−	0.102913i	0.586470	+	0.809971i	$0.300517\pi$
$20$	−2.25548			−0.504340
$21$		0			0
$22$	−9.67925			−2.06362
$23$	5.89275	−	3.40218i	1.22872	−	0.709403i	0.261960	−	0.965079i	$-0.415631\pi$
$23$	5.89275	−	3.40218i	1.22872	−	0.709403i	0.966763	+	0.255675i	$0.0822978\pi$
$24$	−0.850763	−	0.330830i	−0.173661	−	0.0675304i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.658769	−	1.14102i	−0.129195	−	0.223773i
$27$	−4.66019	+	2.29839i	−0.896854	+	0.442326i
$28$		0			0
$29$		−	2.14740i		−	0.398762i	−0.979922	−	0.199381i	$-0.936107\pi$
$29$		−	2.14740i		−	0.398762i	0.979922	−	0.199381i	$-0.0638932\pi$
$30$	−2.78651	+	2.23647i	−0.508744	+	0.408322i
$31$	2.02453	+	1.16886i	0.363615	+	0.209933i	0.670666	−	0.741760i	$-0.266009\pi$
$31$	2.02453	+	1.16886i	0.363615	+	0.209933i	−0.307050	+	0.951693i	$0.599342\pi$
$32$	7.02943	+	4.05844i	1.24264	+	0.717438i
$33$	−6.33802	+	5.08695i	−1.10331	+	0.885524i
$34$		−	8.55938i		−	1.46792i
$35$		0			0
$36$	−6.45320	+	2.03489i	−1.07553	+	0.339148i
$37$	5.69122	+	9.85748i	0.935631	+	1.62056i	0.773505	+	0.633790i	$0.218502\pi$
$37$	5.69122	+	9.85748i	0.935631	+	1.62056i	0.162126	+	0.986770i	$0.448165\pi$
$38$	0.925382	−	1.60281i	0.150117	−	0.260010i
$39$	−1.03103	−	0.400929i	−0.165097	−	0.0642000i
$40$	−0.456412	+	0.263509i	−0.0721650	+	0.0416645i
$41$	4.10624			0.641287			0.320643	−	0.947200i	$-0.396101\pi$
$41$	4.10624			0.641287			0.320643	+	0.947200i	$0.396101\pi$
$42$		0			0
$43$	3.14924			0.480254			0.240127	−	0.970741i	$-0.422811\pi$
$43$	3.14924			0.480254			0.240127	+	0.970741i	$0.422811\pi$
$44$	−9.16509	+	5.29147i	−1.38169	+	0.797719i
$45$	−0.649237	+	2.92891i	−0.0967825	+	0.436616i
$46$	7.01829	−	12.1560i	1.03479	−	1.79231i
$47$	3.40471	+	5.89714i	0.496629	+	0.860186i	0.999992	−	0.00388861i	$-0.00123779\pi$
$47$	3.40471	+	5.89714i	0.496629	+	0.860186i	−0.503364	+	0.864075i	$0.667904\pi$
$48$	5.86113	−	0.902197i	0.845981	−	0.130221i
$49$		0			0
$50$			2.06288i			0.291735i
$51$	−4.49840	−	5.60472i	−0.629901	−	0.784818i
$52$	−1.24755	−	0.720273i	−0.173004	−	0.0998839i
$53$	1.96187	+	1.13269i	0.269484	+	0.155587i	0.628653	−	0.777686i	$-0.283607\pi$
$53$	1.96187	+	1.13269i	0.269484	+	0.155587i	−0.359169	+	0.933272i	$0.616940\pi$
$54$	−5.95481	+	8.91281i	−0.810347	+	1.21288i
$55$			4.69211i			0.632683i
$56$		0			0
$57$	−0.236414	−	1.53586i	−0.0313138	−	0.203430i
$58$	−2.21492	−	3.83635i	−0.290833	−	0.503737i
$59$	0.254055	−	0.440035i	0.0330751	−	0.0572877i	−0.849014	−	0.528370i	$-0.822803\pi$
$59$	0.254055	−	0.440035i	0.0330751	−	0.0572877i	0.882089	+	0.471083i	$0.156137\pi$
$60$	−1.41585	+	3.64100i	−0.182785	+	0.470051i
$61$	−4.48946	+	2.59199i	−0.574816	+	0.331870i	−0.759070	−	0.651008i	$-0.774346\pi$
$61$	−4.48946	+	2.59199i	−0.574816	+	0.331870i	0.184255	+	0.982879i	$0.441013\pi$
$62$	4.82244			0.612450
$63$		0			0
$64$	9.89660			1.23708
$65$	−0.553120	+	0.319344i	−0.0686061	+	0.0396097i
$66$	−6.07604	+	15.6252i	−0.747909	+	1.92332i
$67$	−2.41425	+	4.18160i	−0.294947	+	0.510863i	−0.974973	−	0.222325i	$-0.928635\pi$
$67$	−2.41425	+	4.18160i	−0.294947	+	0.510863i	0.680026	+	0.733188i	$0.261969\pi$
$68$	−4.67925	−	8.10471i	−0.567443	−	0.982840i
$69$	−1.79301	−	11.6483i	−0.215853	−	1.40229i
$70$		0			0
$71$			1.22800i			0.145737i	0.997342	+	0.0728686i	$0.0232154\pi$
$71$			1.22800i			0.145737i	−0.997342	+	0.0728686i	$0.976785\pi$
$72$	−1.06811	+	1.16571i	−0.125878	+	0.137380i
$73$	−12.5197	−	7.22826i	−1.46532	−	0.846004i	−0.466072	−	0.884747i	$-0.654331\pi$
$73$	−12.5197	−	7.22826i	−1.46532	−	0.846004i	−0.999249	+	0.0387429i	$0.987665\pi$
$74$	20.3348	+	11.7403i	2.36387	+	1.36478i
$75$	1.08415	+	1.35078i	0.125187	+	0.155975i
$76$		−	2.02356i		−	0.232118i
$77$		0			0
$78$	−2.25548	+	0.347183i	−0.255382	+	0.0393108i
$79$	−4.54056	−	7.86448i	−0.510853	−	0.884824i	−0.999921	−	0.0125778i	$-0.995996\pi$
$79$	−4.54056	−	7.86448i	−0.510853	−	0.884824i	0.489068	−	0.872246i	$-0.337337\pi$
$80$	1.71189	−	2.96508i	0.191395	−	0.331506i
$81$	0.784903	+	8.96571i	0.0872114	+	0.996190i
$82$	7.33583	−	4.23534i	0.810107	−	0.467715i
$83$	−2.76359			−0.303343			−0.151671	−	0.988431i	$-0.548466\pi$
$83$	−2.76359			−0.303343			−0.151671	+	0.988431i	$0.548466\pi$
$84$		0			0
$85$	−4.14924			−0.450048
$86$	5.62613	−	3.24825i	0.606682	−	0.350268i
$87$	−3.46653	−	1.34801i	−0.371652	−	0.144521i
$88$	−1.23641	+	2.14153i	−0.131802	+	0.228288i
$89$	6.90067	+	11.9523i	0.731470	+	1.26694i	0.956255	+	0.292535i	$0.0944988\pi$
$89$	6.90067	+	11.9523i	0.731470	+	1.26694i	−0.224785	+	0.974408i	$0.572168\pi$
$90$	1.86113	+	5.90216i	0.196180	+	0.622142i
$91$		0			0
$92$		−	15.3471i		−	1.60004i
$93$	3.15776	−	2.53444i	0.327444	−	0.262809i
$94$	12.1651	+	7.02352i	1.25473	+	0.724421i
$95$	−0.776975	−	0.448587i	−0.0797160	−	0.0460241i
$96$	10.9642	−	8.79992i	1.11902	−	0.898138i
$97$			12.9085i			1.31066i	0.755344	+	0.655329i	$0.227470\pi$
$97$			12.9085i			1.31066i	−0.755344	+	0.655329i	$0.772530\pi$
$98$		0			0
$99$	4.23321	+	13.4247i	0.425453	+	1.34923i
$100$	1.12774	+	1.95330i	0.112774	+	0.195330i
$101$	4.51989	−	7.82869i	0.449746	−	0.778983i	−0.548623	−	0.836070i	$-0.684848\pi$
$101$	4.51989	−	7.82869i	0.449746	−	0.778983i	0.998369	+	0.0570865i	$0.0181811\pi$
$102$	−13.8174	−	5.37305i	−1.36812	−	0.532012i
$103$	13.4412	−	7.76030i	1.32440	−	0.764645i	0.339976	−	0.940434i	$-0.389581\pi$
$103$	13.4412	−	7.76030i	1.32440	−	0.764645i	0.984428	+	0.175789i	$0.0562476\pi$
$104$	−0.336601			−0.0330064
$105$		0			0
$106$	4.67320			0.453901
$107$	−4.64012	+	2.67897i	−0.448577	+	0.258986i	−0.707229	−	0.706985i	$-0.750055\pi$
$107$	−4.64012	+	2.67897i	−0.448577	+	0.258986i	0.258652	+	0.965971i	$0.416722\pi$
$108$	−0.766021	+	11.6947i	−0.0737104	+	1.12533i
$109$	−0.679436	+	1.17682i	−0.0650782	+	0.112719i	−0.896729	−	0.442581i	$-0.854063\pi$
$109$	−0.679436	+	1.17682i	−0.0650782	+	0.112719i	0.831650	+	0.555299i	$0.187396\pi$
$110$	4.83963	+	8.38248i	0.461440	+	0.799238i
$111$	19.4855	−	2.99938i	1.84948	−	0.284689i
$112$		0			0
$113$		−	11.9390i		−	1.12312i	−0.827435	−	0.561562i	$-0.810201\pi$
$113$		−	11.9390i		−	1.12312i	0.827435	−	0.561562i	$-0.189799\pi$
$114$	−2.00650	−	2.49998i	−0.187926	−	0.234145i
$115$	−5.89275	−	3.40218i	−0.549502	−	0.317255i
$116$	−4.19452	−	2.42171i	−0.389451	−	0.224850i
$117$	−1.29443	+	1.41271i	−0.119671	+	0.130605i
$118$		−	1.04817i		−	0.0964917i
$119$		0			0
$120$	0.138874	+	0.902197i	0.0126774	+	0.0823590i
$121$	5.50793	+	9.54001i	0.500721	+	0.867274i
$122$	−5.34696	+	9.26121i	−0.484091	+	0.838471i
$123$	2.57765	−	6.62868i	0.232418	−	0.597688i
$124$	4.56627	−	2.63634i	0.410063	−	0.236750i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−16.8492			−1.49513			−0.747563	−	0.664191i	$-0.768776\pi$
$127$	−16.8492			−1.49513			−0.747563	+	0.664191i	$0.768776\pi$
$128$	3.62150	−	2.09088i	0.320099	−	0.184809i
$129$	1.97690	−	5.08379i	0.174056	−	0.447603i
$130$	−0.658769	+	1.14102i	−0.0577778	+	0.100074i
$131$	−6.93473	−	12.0113i	−0.605890	−	1.04943i	−0.991910	−	0.126942i	$-0.959484\pi$
$131$	−6.93473	−	12.0113i	−0.605890	−	1.04943i	0.386020	−	0.922490i	$-0.373850\pi$
$132$	2.78870	+	18.1168i	0.242725	+	1.57687i
$133$		0			0
$134$			9.96060i			0.860465i
$135$	4.32056	+	2.88665i	0.371855	+	0.248443i
$136$	−1.89376	−	1.09336i	−0.162389	−	0.0937551i
$137$	−3.75708	−	2.16915i	−0.320989	−	0.185323i	0.330844	−	0.943685i	$-0.392667\pi$
$137$	−3.75708	−	2.16915i	−0.320989	−	0.185323i	−0.651833	+	0.758362i	$0.726000\pi$
$138$	−15.2178	−	18.9604i	−1.29542	−	1.61402i
$139$			10.9631i			0.929881i	0.885342	+	0.464941i	$0.153924\pi$
$139$			10.9631i			0.929881i	−0.885342	+	0.464941i	$0.846076\pi$
$140$		0			0
$141$	11.6570	−	1.79435i	0.981695	−	0.151111i
$142$	1.26661	+	2.19384i	0.106292	+	0.184103i
$143$	−1.49840	+	2.59530i	−0.125302	+	0.217030i
$144$	2.22284	−	10.0279i	0.185237	−	0.835660i
$145$	−1.85970	+	1.07370i	−0.154440	+	0.0891659i
$146$	−29.8221			−2.46809
$147$		0			0
$148$	25.6728			2.11029
$149$	7.50546	−	4.33328i	0.614871	−	0.354996i	−0.159998	−	0.987117i	$-0.551149\pi$
$149$	7.50546	−	4.33328i	0.614871	−	0.354996i	0.774870	+	0.632121i	$0.217816\pi$
$150$	3.33010	+	1.29495i	0.271901	+	0.105732i
$151$	−6.73018	+	11.6570i	−0.547694	+	0.948634i	0.450738	+	0.892656i	$0.351161\pi$
$151$	−6.73018	+	11.6570i	−0.547694	+	0.948634i	−0.998432	+	0.0559778i	$0.982172\pi$
$152$	−0.236414	−	0.409481i	−0.0191757	−	0.0332133i
$153$	−11.8715	+	3.74343i	−0.959753	+	0.302638i
$154$		0			0
$155$		−	2.33772i		−	0.187770i
$156$	−1.94587	+	1.56177i	−0.155794	+	0.125042i
$157$	6.76643	+	3.90660i	0.540020	+	0.311781i	0.745087	−	0.666967i	$-0.232408\pi$
$157$	6.76643	+	3.90660i	0.540020	+	0.311781i	−0.205067	+	0.978748i	$0.565741\pi$
$158$	−16.2235	−	9.36664i	−1.29067	−	0.745170i
$159$	3.06003	−	2.45601i	0.242677	−	0.194774i
$160$		−	8.11688i		−	0.641696i
$161$		0			0
$162$	10.6498	+	15.2077i	0.836730	+	1.19483i
$163$	−8.33945	−	14.4443i	−0.653196	−	1.13137i	−0.982343	−	0.187090i	$-0.940095\pi$
$163$	−8.33945	−	14.4443i	−0.653196	−	1.13137i	0.329147	−	0.944279i	$-0.393239\pi$
$164$	4.63077	−	8.02072i	0.361602	−	0.626313i
$165$	7.57444	+	2.94542i	0.589669	+	0.229300i
$166$	−4.93717	+	2.85047i	−0.383198	+	0.221240i
$167$	−0.465112			−0.0359915			−0.0179957	−	0.999838i	$-0.505729\pi$
$167$	−0.465112			−0.0359915			−0.0179957	+	0.999838i	$0.505729\pi$
$168$		0			0
$169$	12.5921			0.968621
$170$	−7.41264	+	4.27969i	−0.568524	+	0.328237i
$171$	−2.62774	−	0.582479i	−0.200948	−	0.0445432i
$172$	3.55152	−	6.15141i	0.270801	−	0.469040i
$173$	−5.59208	−	9.68576i	−0.425158	−	0.736395i	0.571277	−	0.820757i	$-0.306448\pi$
$173$	−5.59208	−	9.68576i	−0.425158	−	0.736395i	−0.996435	+	0.0843622i	$0.973115\pi$
$174$	−7.58338	+	1.16730i	−0.574894	+	0.0884929i
$175$		0			0
$176$		−	16.0647i		−	1.21092i
$177$	−0.550867	−	0.686346i	−0.0414057	−	0.0515889i
$178$	24.6562	+	14.2353i	1.84806	+	1.06698i
$179$	−0.214505	−	0.123845i	−0.0160329	−	0.00925660i	0.491962	−	0.870617i	$-0.336280\pi$
$179$	−0.214505	−	0.123845i	−0.0160329	−	0.00925660i	−0.507995	+	0.861360i	$0.669613\pi$
$180$	4.98886	+	4.57120i	0.371848	+	0.340717i
$181$			14.3385i			1.06578i	0.846186	+	0.532888i	$0.178893\pi$
$181$			14.3385i			1.06578i	−0.846186	+	0.532888i	$0.821107\pi$
$182$		0			0
$183$	1.36603	+	8.87439i	0.100980	+	0.656014i
$184$	−1.79301	−	3.10559i	−0.132183	−	0.228947i
$185$	5.69122	−	9.85748i	0.418427	−	0.724737i
$186$	3.02723	−	7.78483i	0.221967	−	0.570812i
$187$	−16.8604	+	9.73433i	−1.23295	+	0.711845i
$188$	15.3585			1.12013
$189$		0			0
$190$	−1.85076			−0.134268
$191$	14.7572	−	8.52006i	1.06779	−	0.616490i	0.140214	−	0.990121i	$-0.455221\pi$
$191$	14.7572	−	8.52006i	1.06779	−	0.616490i	0.927577	+	0.373632i	$0.121888\pi$
$192$	6.21248	−	15.9760i	0.448347	−	1.15297i
$193$	−1.41181	+	2.44533i	−0.101624	+	0.176019i	−0.912354	−	0.409402i	$-0.865737\pi$
$193$	−1.41181	+	2.44533i	−0.101624	+	0.176019i	0.810730	+	0.585421i	$0.199071\pi$
$194$	13.3143	+	23.0611i	0.955913	+	1.65569i
$195$	0.168300	+	1.09336i	0.0120522	+	0.0782973i
$196$		0			0
$197$			9.59675i			0.683740i	0.939747	+	0.341870i	$0.111060\pi$
$197$			9.59675i			0.683740i	−0.939747	+	0.341870i	$0.888940\pi$
$198$	21.4094	+	19.6170i	1.52150	+	1.39412i
$199$	−10.5777	−	6.10706i	−0.749836	−	0.432918i	0.0757989	−	0.997123i	$-0.475849\pi$
$199$	−10.5777	−	6.10706i	−0.749836	−	0.432918i	−0.825635	+	0.564205i	$0.809183\pi$
$200$	0.456412	+	0.263509i	0.0322732	+	0.0186329i
$201$	5.23481	+	6.52225i	0.369235	+	0.460044i
$202$		−	18.6480i		−	1.31207i
$203$		0			0
$204$	−16.0207	+	2.46605i	−1.12168	+	0.172658i
$205$	−2.05312	−	3.55611i	−0.143396	−	0.248369i
$206$	16.0086	−	27.7277i	1.11537	−	1.93188i
$207$	−19.9293	−	4.41764i	−1.38518	−	0.307047i
$208$	1.89376	−	1.09336i	0.131309	−	0.0758111i
$209$	−4.20964			−0.291187
$210$		0			0
$211$	5.64113			0.388351			0.194176	−	0.980967i	$-0.437797\pi$
$211$	5.64113			0.388351			0.194176	+	0.980967i	$0.437797\pi$
$212$	4.42496	−	2.55475i	0.303908	−	0.175461i
$213$	1.98236	+	0.770865i	0.135829	+	0.0528188i
$214$	−5.52640	+	9.57200i	−0.377777	+	0.654329i
$215$	−1.57462	−	2.72732i	−0.107388	−	0.186002i
$216$	1.21130	+	2.45601i	0.0824183	+	0.167110i
$217$		0			0
$218$			2.80319i			0.189856i
$219$	−19.5276	+	15.6730i	−1.31956	+	1.05909i
$220$	9.16509	+	5.29147i	0.617910	+	0.356751i
$221$	−2.29503	−	1.32503i	−0.154380	−	0.0891314i
$222$	31.7173	−	25.4565i	2.12872	−	1.70853i
$223$			0.392378i			0.0262755i	0.999914	+	0.0131378i	$0.00418200\pi$
$223$			0.392378i			0.0262755i	−0.999914	+	0.0131378i	$0.995818\pi$
$224$		0			0
$225$	2.86113	−	0.902197i	0.190742	−	0.0601465i
$226$	−12.3143	−	21.3290i	−0.819137	−	1.41879i
$227$	−11.7125	+	20.2867i	−0.777388	+	1.34648i	0.156054	+	0.987749i	$0.450123\pi$
$227$	−11.7125	+	20.2867i	−0.777388	+	1.34648i	−0.933442	+	0.358728i	$0.883211\pi$
$228$	−3.26661	−	1.27026i	−0.216337	−	0.0841253i
$229$	−6.69286	+	3.86412i	−0.442276	+	0.255348i	−0.704563	−	0.709642i	$-0.748857\pi$
$229$	−6.69286	+	3.86412i	−0.442276	+	0.255348i	0.262286	+	0.964990i	$0.415523\pi$
$230$	−14.0366			−0.925545
$231$		0			0
$232$	−1.13172			−0.0743011
$233$	3.53323	−	2.03991i	0.231469	−	0.133639i	−0.379780	−	0.925077i	$-0.624000\pi$
$233$	3.53323	−	2.03991i	0.231469	−	0.133639i	0.611250	+	0.791438i	$0.290667\pi$
$234$	−0.855394	+	3.85894i	−0.0559188	+	0.252267i
$235$	3.40471	−	5.89714i	0.222099	−	0.384687i
$236$	−0.573014	−	0.992490i	−0.0373001	−	0.0646056i
$237$	−15.5459	+	2.39296i	−1.00981	+	0.155440i
$238$		0			0
$239$			5.76281i			0.372765i	0.982477	+	0.186383i	$0.0596764\pi$
$239$			5.76281i			0.372765i	−0.982477	+	0.186383i	$0.940324\pi$
$240$	−3.71189	−	4.62479i	−0.239601	−	0.298529i
$241$	17.6840	+	10.2098i	1.13912	+	0.657674i	0.946214	−	0.323542i	$-0.104874\pi$
$241$	17.6840	+	10.2098i	1.13912	+	0.657674i	0.192911	+	0.981216i	$0.438207\pi$
$242$	19.6799	+	11.3622i	1.26507	+	0.730390i
$243$	14.9660	+	4.36106i	0.960069	+	0.279762i
$244$			11.6923i			0.748525i
$245$		0			0
$246$	−2.23210	−	14.5009i	−0.142314	−	0.924542i
$247$	−0.286507	−	0.496245i	−0.0182300	−	0.0315753i
$248$	0.616011	−	1.06696i	0.0391167	−	0.0677522i
$249$	−1.73481	+	4.46124i	−0.109939	+	0.282720i
$250$	1.78651	−	1.03144i	0.112989	−	0.0652340i
$251$	−4.42544			−0.279331			−0.139666	−	0.990199i	$-0.544603\pi$
$251$	−4.42544			−0.279331			−0.139666	+	0.990199i	$0.544603\pi$
$252$		0			0
$253$	−31.9268			−2.00722
$254$	−30.1012	+	17.3790i	−1.88872	+	1.09045i
$255$	−2.60464	+	6.69809i	−0.163109	+	0.419450i
$256$	−5.58338	+	9.67069i	−0.348961	+	0.604418i
$257$	−12.7539	−	22.0904i	−0.795565	−	1.37796i	−0.922480	−	0.386045i	$-0.873841\pi$
$257$	−12.7539	−	22.0904i	−0.795565	−	1.37796i	0.126915	−	0.991914i	$-0.459492\pi$
$258$	−1.71189	−	11.1213i	−0.106578	−	0.692381i
$259$		0			0
$260$			1.44055i			0.0893389i
$261$	−4.35215	+	4.74981i	−0.269392	+	0.294006i
$262$	−24.7779	−	14.3055i	−1.53078	−	0.883798i
$263$	0.310020	+	0.178990i	0.0191166	+	0.0110370i	0.509528	−	0.860454i	$-0.329820\pi$
$263$	0.310020	+	0.178990i	0.0191166	+	0.0110370i	−0.490411	+	0.871491i	$0.663153\pi$
$264$	2.68092	+	3.34026i	0.164999	+	0.205579i
$265$		−	2.26538i		−	0.139161i
$266$		0			0
$267$	23.6264	−	3.63678i	1.44591	−	0.222568i
$268$	5.44528	+	9.43149i	0.332623	+	0.576120i
$269$	−4.26905	+	7.39421i	−0.260288	+	0.450833i	−0.966319	−	0.257349i	$-0.917151\pi$
$269$	−4.26905	+	7.39421i	−0.260288	+	0.450833i	0.706030	+	0.708182i	$0.250484\pi$
$270$	10.6961	+	0.700610i	0.650945	+	0.0426378i
$271$	7.30474	−	4.21739i	0.443731	−	0.256188i	−0.261448	−	0.965218i	$-0.584200\pi$
$271$	7.30474	−	4.21739i	0.443731	−	0.256188i	0.705179	+	0.709029i	$0.250867\pi$
$272$	14.2061			0.861369
$273$		0			0
$274$	−8.94940			−0.540653
$275$	4.06348	−	2.34605i	0.245037	−	0.141472i
$276$	−24.7747	−	9.63395i	−1.49126	−	0.579896i
$277$	−5.05294	+	8.75195i	−0.303602	+	0.525853i	−0.976949	−	0.213473i	$-0.931523\pi$
$277$	−5.05294	+	8.75195i	−0.303602	+	0.525853i	0.673347	+	0.739326i	$0.264856\pi$
$278$	11.3078	+	19.5857i	0.678198	+	1.17467i
$279$	−2.10909	−	6.68851i	−0.126268	−	0.400431i
$280$		0			0
$281$			15.1554i			0.904094i	0.891994	+	0.452047i	$0.149306\pi$
$281$			15.1554i			0.904094i	−0.891994	+	0.452047i	$0.850694\pi$
$282$	18.9745	−	15.2291i	1.12992	−	0.906880i
$283$	−20.7322	−	11.9697i	−1.23240	−	0.711527i	−0.264871	−	0.964284i	$-0.585329\pi$
$283$	−20.7322	−	11.9697i	−1.23240	−	0.711527i	−0.967530	+	0.252757i	$0.918663\pi$
$284$	2.39866	+	1.38487i	0.142334	+	0.0821768i
$285$	−1.21189	+	0.972671i	−0.0717861	+	0.0576161i
$286$			6.18202i			0.365551i
$287$		0			0
$288$	−7.32303	−	23.2234i	−0.431514	−	1.36845i
$289$	−0.108084	−	0.187206i	−0.00635786	−	0.0110121i
$290$	−2.21492	+	3.83635i	−0.130064	+	0.225278i
$291$	20.8381	+	8.10315i	1.22155	+	0.475015i
$292$	−28.2379	+	16.3032i	−1.65250	+	0.954071i
$293$	21.2223			1.23982			0.619909	−	0.784673i	$-0.287169\pi$
$293$	21.2223			1.23982			0.619909	+	0.784673i	$0.287169\pi$
$294$		0			0
$295$	−0.508109			−0.0295833
$296$	5.19508	−	2.99938i	0.301958	−	0.174335i
$297$	24.3288	+	1.59357i	1.41170	+	0.0924681i
$298$	8.93904	−	15.4829i	0.517825	−	0.896899i
$299$	−2.17293	−	3.76363i	−0.125664	−	0.217656i
$300$	3.86113	−	0.594339i	0.222922	−	0.0343142i
$301$		0			0
$302$			27.7671i			1.59782i
$303$	−9.80049	−	12.2108i	−0.563023	−	0.701492i
$304$	2.66019	+	1.53586i	0.152572	+	0.0880877i
$305$	4.48946	+	2.59199i	0.257065	+	0.148417i
$306$	−17.3474	+	18.9324i	−0.991683	+	1.08229i
$307$		−	24.2817i		−	1.38583i	−0.721019	−	0.692916i	$-0.756326\pi$
$307$		−	24.2817i		−	1.38583i	0.721019	−	0.692916i	$-0.243674\pi$
$308$		0			0
$309$	−4.08982	−	26.5695i	−0.232662	−	1.51149i
$310$	−2.41122	−	4.17635i	−0.136948	−	0.237201i
$311$	−3.55858	+	6.16364i	−0.201789	+	0.349508i	−0.949105	−	0.314960i	$-0.898009\pi$
$311$	−3.55858	+	6.16364i	−0.201789	+	0.349508i	0.747316	+	0.664469i	$0.231342\pi$
$312$	−0.211297	+	0.543372i	−0.0119623	+	0.0307624i
$313$	−3.07200	+	1.77362i	−0.173640	+	0.100251i	−0.584301	−	0.811537i	$-0.698631\pi$
$313$	−3.07200	+	1.77362i	−0.173640	+	0.100251i	0.410661	+	0.911788i	$0.365298\pi$
$314$	16.1177			0.909575
$315$		0			0
$316$	−20.4823			−1.15222
$317$	−18.2527	+	10.5382i	−1.02517	+	0.591885i	−0.915599	−	0.402093i	$-0.868283\pi$
$317$	−18.2527	+	10.5382i	−1.02517	+	0.591885i	−0.109576	+	0.993978i	$0.534949\pi$
$318$	2.93355	−	7.54392i	0.164505	−	0.423042i
$319$	−5.03791	+	8.72592i	−0.282069	+	0.488558i
$320$	−4.94830	−	8.57071i	−0.276619	−	0.479117i
$321$	1.41187	+	9.17220i	0.0788028	+	0.511942i
$322$		0			0
$323$		−	3.72259i		−	0.207130i
$324$	18.3979	+	8.57782i	1.02210	+	0.476546i
$325$	0.553120	+	0.319344i	0.0306816	+	0.0177140i
$326$	−29.7970	−	17.2033i	−1.65030	−	0.952802i
$327$	1.47322	+	1.83554i	0.0814693	+	0.101506i
$328$		−	2.16407i		−	0.119491i
$329$		0			0
$330$	16.5698	−	2.55057i	0.912138	−	0.140404i
$331$	7.40412	+	12.8243i	0.406967	+	0.704888i	0.994548	−	0.104277i	$-0.0332529\pi$
$331$	7.40412	+	12.8243i	0.406967	+	0.704888i	−0.587581	+	0.809165i	$0.699920\pi$
$332$	−3.11660	+	5.39811i	−0.171046	+	0.296260i
$333$	7.38990	−	33.3381i	0.404964	−	1.82692i
$334$	−0.830926	+	0.479736i	−0.0454663	+	0.0262500i
$335$	4.82849			0.263809
$336$		0			0
$337$	20.5062			1.11704			0.558522	−	0.829490i	$-0.311369\pi$
$337$	20.5062			1.11704			0.558522	+	0.829490i	$0.311369\pi$
$338$	22.4958	−	12.9880i	1.22361	−	0.706453i
$339$	−19.2730	−	7.49455i	−1.04677	−	0.407048i
$340$	−4.67925	+	8.10471i	−0.253768	+	0.439539i
$341$	−5.48442	−	9.49929i	−0.296998	−	0.514415i
$342$	−5.29527	+	1.66975i	−0.286335	+	0.0902899i
$343$		0			0
$344$		−	1.65971i		−	0.0894854i
$345$	−9.19122	+	7.37695i	−0.494839	+	0.397161i
$346$	−19.9806	−	11.5358i	−1.07416	−	0.620168i
$347$	13.7103	+	7.91567i	0.736010	+	0.424935i	0.820617	−	0.571479i	$-0.193630\pi$
$347$	13.7103	+	7.91567i	0.736010	+	0.424935i	−0.0846070	+	0.996414i	$0.526963\pi$
$348$	−6.54241	+	5.25099i	−0.350710	+	0.281482i
$349$			8.96019i			0.479628i	0.970819	+	0.239814i	$0.0770865\pi$
$349$			8.96019i			0.479628i	−0.970819	+	0.239814i	$0.922914\pi$
$350$		0			0
$351$	1.46796	+	2.97641i	0.0783538	+	0.158869i
$352$	−19.0426	−	32.9828i	−1.01498	−	1.75799i
$353$	−6.72876	+	11.6545i	−0.358136	+	0.620309i	−0.987649	−	0.156680i	$-0.949921\pi$
$353$	−6.72876	+	11.6545i	−0.358136	+	0.620309i	0.629514	+	0.776989i	$0.283254\pi$
$354$	−1.69205	−	0.657976i	−0.0899316	−	0.0349710i
$355$	1.06348	−	0.614002i	0.0564438	−	0.0325878i
$356$	31.1286			1.64981
$357$		0			0
$358$	−0.510954			−0.0270048
$359$	−4.85824	+	2.80491i	−0.256408	+	0.148037i	−0.622695	−	0.782465i	$-0.713962\pi$
$359$	−4.85824	+	2.80491i	−0.256408	+	0.148037i	0.366287	+	0.930502i	$0.380629\pi$
$360$	1.54359	+	0.342160i	0.0813543	+	0.0180334i
$361$	−9.09754	+	15.7574i	−0.478818	+	0.829337i
$362$	14.7894	+	25.6159i	0.777311	+	1.34634i
$363$	18.8579	−	2.90278i	0.989784	−	0.152356i
$364$		0			0
$365$			14.4565i			0.756689i
$366$	11.5938	+	14.4452i	0.606019	+	0.755062i
$367$	1.71154	+	0.988156i	0.0893415	+	0.0515813i	0.544005	−	0.839082i	$-0.316907\pi$
$367$	1.71154	+	0.988156i	0.0893415	+	0.0515813i	−0.454664	+	0.890663i	$0.650241\pi$
$368$	20.1755	+	11.6483i	1.05172	+	0.607210i
$369$	−9.08255	−	8.32215i	−0.472818	−	0.433234i
$370$		−	23.4806i		−	1.22070i
$371$		0			0
$372$	−1.38940	−	9.02623i	−0.0720370	−	0.467988i
$373$	11.5467	+	19.9995i	0.597866	+	1.03553i	0.993136	+	0.116969i	$0.0373177\pi$
$373$	11.5467	+	19.9995i	0.597866	+	1.03553i	−0.395270	+	0.918565i	$0.629349\pi$
$374$	−20.0808	+	34.7809i	−1.03835	+	1.79848i
$375$	0.627739	−	1.61429i	0.0324163	−	0.0833618i
$376$	3.10790	−	1.79435i	0.160278	−	0.0925364i
$377$	−1.37152			−0.0706368
$378$		0			0
$379$	−17.0645			−0.876547			−0.438273	−	0.898842i	$-0.644410\pi$
$379$	−17.0645			−0.876547			−0.438273	+	0.898842i	$0.644410\pi$
$380$	−1.75245	+	1.01178i	−0.0898988	+	0.0519031i
$381$	−10.5769	+	27.1996i	−0.541871	+	1.39348i
$382$	17.5759	−	30.4423i	0.899259	−	1.55756i
$383$	−13.3056	−	23.0460i	−0.679886	−	1.17760i	−0.975015	−	0.222139i	$-0.928696\pi$
$383$	−13.3056	−	23.0460i	−0.679886	−	1.17760i	0.295129	−	0.955457i	$-0.404637\pi$
$384$	−1.10193	−	7.15869i	−0.0562327	−	0.365316i
$385$		0			0
$386$			5.82479i			0.296474i
$387$	−6.96576	−	6.38259i	−0.354090	−	0.324445i
$388$	25.2141	+	14.5574i	1.28005	+	0.739040i
$389$	8.20951	+	4.73976i	0.416239	+	0.240316i	0.693467	−	0.720489i	$-0.256082\pi$
$389$	8.20951	+	4.73976i	0.416239	+	0.240316i	−0.277228	+	0.960804i	$0.589416\pi$
$390$	1.42841	+	1.77971i	0.0723303	+	0.0901191i
$391$		−	28.2329i		−	1.42780i
$392$		0			0
$393$	−23.7430	+	3.65473i	−1.19767	+	0.184357i
$394$	9.89848	+	17.1447i	0.498678	+	0.863736i
$395$	−4.54056	+	7.86448i	−0.228460	+	0.395705i
$396$	30.9964	+	6.87083i	1.55763	+	0.345272i
$397$	−10.7042	+	6.18009i	−0.537230	+	0.310170i	−0.743956	−	0.668229i	$-0.767053\pi$
$397$	−10.7042	+	6.18009i	−0.537230	+	0.310170i	0.206726	+	0.978399i	$0.433719\pi$
$398$	−25.1963			−1.26297
$399$		0			0
$400$	−3.42378			−0.171189
$401$	7.11494	−	4.10781i	0.355303	−	0.205134i	−0.311715	−	0.950176i	$-0.600904\pi$
$401$	7.11494	−	4.10781i	0.355303	−	0.205134i	0.667019	+	0.745041i	$0.267570\pi$
$402$	16.0793	+	6.25265i	0.801964	+	0.311854i
$403$	0.746537	−	1.29304i	0.0371877	−	0.0644109i
$404$	−10.1945	−	17.6574i	−0.507196	−	0.878490i
$405$	7.37208	−	5.16260i	0.366322	−	0.256532i
$406$		0			0
$407$		−	53.4076i		−	2.64732i
$408$	−2.95379	+	2.37074i	−0.146235	+	0.117369i
$409$	17.9575	+	10.3678i	0.887942	+	0.512653i	0.873269	−	0.487239i	$-0.161996\pi$
$409$	17.9575	+	10.3678i	0.887942	+	0.512653i	0.0146731	+	0.999892i	$0.495329\pi$
$410$	−7.33583	−	4.23534i	−0.362291	−	0.209169i
$411$	−5.86011	+	4.70337i	−0.289058	+	0.232000i
$412$		−	35.0064i		−	1.72464i
$413$		0			0
$414$	−40.1604	+	12.6638i	−1.97378	+	0.622390i
$415$	1.38179	+	2.39334i	0.0678296	+	0.117484i
$416$	2.59208	−	4.48961i	0.127087	−	0.220121i
$417$	17.6977	+	6.88198i	0.866661	+	0.337012i
$418$	−7.52054	+	4.34199i	−0.367842	+	0.212374i
$419$	−6.93924			−0.339004			−0.169502	−	0.985530i	$-0.554216\pi$
$419$	−6.93924			−0.339004			−0.169502	+	0.985530i	$0.554216\pi$
$420$		0			0
$421$	−15.2162			−0.741594			−0.370797	−	0.928714i	$-0.620915\pi$
$421$	−15.2162			−0.741594			−0.370797	+	0.928714i	$0.620915\pi$
$422$	10.0779	−	5.81849i	0.490585	−	0.283240i
$423$	4.42093	−	19.9442i	0.214953	−	0.969719i
$424$	0.596948	−	1.03394i	0.0289904	−	0.0502128i
$425$	2.07462	+	3.59334i	0.100634	+	0.174303i
$426$	4.33660	−	0.667529i	0.210109	−	0.0323419i
$427$		0			0
$428$			12.0847i			0.584137i
$429$	3.24897	+	4.04802i	0.156862	+	0.195440i
$430$	−5.62613	−	3.24825i	−0.271316	−	0.156645i
$431$	−26.9043	−	15.5332i	−1.29594	−	0.748209i	−0.316236	−	0.948681i	$-0.602419\pi$
$431$	−26.9043	−	15.5332i	−1.29594	−	0.748209i	−0.979699	+	0.200472i	$0.935752\pi$
$432$	−14.7926	−	9.88323i	−0.711712	−	0.475507i
$433$			22.3083i			1.07207i	0.844196	+	0.536034i	$0.180078\pi$
$433$			22.3083i			1.07207i	−0.844196	+	0.536034i	$0.819922\pi$
$434$		0			0
$435$	0.565860	+	3.67611i	0.0271309	+	0.176256i
$436$	1.53245	+	2.65429i	0.0733912	+	0.127117i
$437$	3.05235	−	5.28682i	0.146014	−	0.252903i
$438$	−18.7205	+	48.1416i	−0.894498	+	2.30029i
$439$	22.4126	−	12.9399i	1.06970	−	0.617590i	0.141598	−	0.989924i	$-0.454776\pi$
$439$	22.4126	−	12.9399i	1.06970	−	0.617590i	0.928099	+	0.372334i	$0.121443\pi$
$440$	2.47283			0.117887
$441$		0			0
$442$	−5.46677			−0.260028
$443$	−26.8166	+	15.4826i	−1.27409	+	0.735599i	−0.975756	−	0.218862i	$-0.929766\pi$
$443$	−26.8166	+	15.4826i	−1.27409	+	0.735599i	−0.298338	+	0.954460i	$0.596432\pi$
$444$	16.1158	−	41.4435i	0.764823	−	1.96682i
$445$	6.90067	−	11.9523i	0.327123	−	0.566594i
$446$	0.404714	+	0.700985i	0.0191638	+	0.0331926i
$447$	−2.28372	−	14.8362i	−0.108016	−	0.701728i
$448$		0			0
$449$		−	24.2032i		−	1.14222i	−0.820874	−	0.571110i	$-0.806513\pi$
$449$		−	24.2032i		−	1.14222i	0.820874	−	0.571110i	$-0.193487\pi$
$450$	4.18086	−	4.56286i	0.197088	−	0.215095i
$451$	−16.6856	−	9.63346i	−0.785696	−	0.453622i
$452$	−23.3204	−	13.4640i	−1.09690	−	0.633295i
$453$	14.5930	+	18.1820i	0.685641	+	0.854267i
$454$			48.3231i			2.26792i
$455$		0			0
$456$	−0.809428	+	0.124594i	−0.0379049	+	0.00583467i
$457$	1.20726	+	2.09103i	0.0564731	+	0.0978143i	0.892880	−	0.450295i	$-0.148681\pi$
$457$	1.20726	+	2.09103i	0.0564731	+	0.0978143i	−0.836407	+	0.548109i	$0.815348\pi$
$458$	−7.97122	+	13.8066i	−0.372471	+	0.645138i
$459$	−1.40919	+	21.5140i	−0.0657755	+	1.00419i
$460$	−13.2910	+	7.67354i	−0.619694	+	0.357781i
$461$	−7.45376			−0.347156			−0.173578	−	0.984820i	$-0.555533\pi$
$461$	−7.45376			−0.347156			−0.173578	+	0.984820i	$0.555533\pi$
$462$		0			0
$463$	13.8862			0.645345			0.322672	−	0.946511i	$-0.395419\pi$
$463$	13.8862			0.645345			0.322672	+	0.946511i	$0.395419\pi$
$464$	6.36721	−	3.67611i	0.295590	−	0.170659i
$465$	−3.77377	−	1.46748i	−0.175004	−	0.0680526i
$466$	4.20809	−	7.28862i	0.194936	−	0.337639i
$467$	10.0692	+	17.4404i	0.465948	+	0.807045i	0.999244	−	0.0388836i	$-0.0123802\pi$
$467$	10.0692	+	17.4404i	0.465948	+	0.807045i	−0.533296	+	0.845929i	$0.679047\pi$
$468$	1.29966	+	4.12158i	0.0600767	+	0.190520i
$469$		0			0
$470$		−	14.0470i		−	0.647942i
$471$	10.5540	−	8.47068i	0.486300	−	0.390309i
$472$	−0.231907	−	0.133892i	−0.0106744	−	0.00616286i
$473$	−12.7969	−	7.38828i	−0.588401	−	0.339713i
$474$	−25.3046	+	20.3097i	−1.16228	+	0.932855i
$475$			0.897174i			0.0411652i
$476$		0			0
$477$	−2.04382	−	6.48153i	−0.0935799	−	0.296769i
$478$	5.94399	+	10.2953i	0.271872	+	0.470896i
$479$	16.6189	−	28.7847i	0.759335	−	1.31521i	−0.183855	−	0.982953i	$-0.558858\pi$
$479$	16.6189	−	28.7847i	0.759335	−	1.31521i	0.943190	−	0.332253i	$-0.107809\pi$
$480$	−13.1030	−	5.09528i	−0.598069	−	0.232567i
$481$	6.29586	−	3.63491i	0.287066	−	0.165738i
$482$	42.1234			1.91867
$483$		0			0
$484$	24.8460			1.12936
$485$	11.1791	−	6.45424i	0.507616	−	0.293072i
$486$	31.2350	−	7.64548i	1.41685	−	0.346806i
$487$	16.1039	−	27.8927i	0.729736	−	1.26394i	−0.227259	−	0.973834i	$-0.572976\pi$
$487$	16.1039	−	27.8927i	0.729736	−	1.26394i	0.956995	−	0.290105i	$-0.0936902\pi$
$488$	1.36603	+	2.36603i	0.0618371	+	0.107105i
$489$	−28.5524	+	4.39504i	−1.29118	+	0.198751i
$490$		0			0
$491$			22.5003i			1.01542i	0.861527	+	0.507712i	$0.169509\pi$
$491$			22.5003i			1.01542i	−0.861527	+	0.507712i	$0.830491\pi$
$492$	−10.0409	−	12.5103i	−0.452678	−	0.564009i
$493$	−7.71635	−	4.45504i	−0.347527	−	0.200645i
$494$	−1.02369	−	0.591030i	−0.0460582	−	0.0265917i
$495$	9.50953	−	10.3784i	0.427422	−	0.466475i
$496$			8.00383i			0.359383i
$497$		0			0
$498$	1.50225	+	9.75939i	0.0673176	+	0.437329i
$499$	−3.20702	−	5.55472i	−0.143566	−	0.248663i	0.785271	−	0.619152i	$-0.212524\pi$
$499$	−3.20702	−	5.55472i	−0.143566	−	0.248663i	−0.928837	+	0.370489i	$0.879190\pi$
$500$	1.12774	−	1.95330i	0.0504340	−	0.0873543i
$501$	−0.291969	+	0.750828i	−0.0130442	+	0.0335445i
$502$	−7.90608	+	4.56458i	−0.352866	+	0.203727i
$503$	−38.0103			−1.69479			−0.847397	−	0.530960i	$-0.821831\pi$
$503$	−38.0103			−1.69479			−0.847397	+	0.530960i	$0.821831\pi$
$504$		0			0
$505$	−9.03979			−0.402265
$506$	−57.0374	+	32.9306i	−2.53562	+	1.46394i
$507$	7.90453	−	20.3273i	0.351053	−	0.902768i
$508$	−19.0015	+	32.9116i	−0.843056	+	1.46022i
$509$	6.34981	+	10.9982i	0.281450	+	0.487486i	0.971742	−	0.236045i	$-0.0758512\pi$
$509$	6.34981	+	10.9982i	0.281450	+	0.487486i	−0.690292	+	0.723531i	$0.742518\pi$
$510$	2.25548	+	14.6527i	0.0998742	+	0.648833i
$511$		0			0
$512$			31.3992i			1.38766i
$513$	−2.58982	+	3.87630i	−0.114344	+	0.171143i
$514$	−45.5698	−	26.3097i	−2.01000	−	1.16047i
$515$	−13.4412	−	7.76030i	−0.592292	−	0.341960i
$516$	−7.70075	−	9.59466i	−0.339007	−	0.422382i
$517$		−	31.9506i		−	1.40518i
$518$		0			0
$519$	−19.1460	+	2.94713i	−0.840417	+	0.129365i
$520$	0.168300	+	0.291505i	0.00738046	+	0.0127833i
$521$	−18.0970	+	31.3449i	−0.792843	+	1.37324i	0.131357	+	0.991335i	$0.458067\pi$
$521$	−18.0970	+	31.3449i	−0.792843	+	1.37324i	−0.924200	+	0.381909i	$0.875267\pi$
$522$	−2.87601	+	12.9746i	−0.125880	+	0.567881i
$523$	4.27382	−	2.46749i	0.186881	−	0.107896i	−0.403640	−	0.914918i	$-0.632255\pi$
$523$	4.27382	−	2.46749i	0.186881	−	0.107896i	0.590522	+	0.807022i	$0.298922\pi$
$524$	−31.2823			−1.36657
$525$		0			0
$526$	0.738470			0.0321988
$527$	8.40023	−	4.84988i	0.365920	−	0.211264i
$528$	−25.9332	−	10.0844i	−1.12860	−	0.438869i
$529$	11.6496	−	20.1778i	0.506506	−	0.877295i
$530$	−2.33660	−	4.04711i	−0.101495	−	0.175795i
$531$	−1.45376	+	0.458415i	−0.0630880	+	0.0198935i
$532$		0			0
$533$		−	2.62261i		−	0.113598i
$534$	38.4576	−	30.8663i	1.66422	−	1.33572i
$535$	4.64012	+	2.67897i	0.200610	+	0.115822i
$536$	2.20378	+	1.27235i	0.0951888	+	0.0549573i
$537$	−0.334575	+	0.268533i	−0.0144380	+	0.0115880i
$538$			17.6131i			0.759354i
$539$		0			0
$540$	10.5110	−	5.18398i	0.452319	−	0.223083i
$541$	−8.32849	−	14.4254i	−0.358070	−	0.620195i	0.629569	−	0.776945i	$-0.283232\pi$
$541$	−8.32849	−	14.4254i	−0.358070	−	0.620195i	−0.987638	+	0.156750i	$0.949898\pi$
$542$	8.69998	−	15.0688i	0.373696	−	0.647261i
$543$	23.1466	+	9.00086i	0.993317	+	0.386264i
$544$	29.1668	−	16.8394i	1.25051	−	0.721985i
$545$	1.35887			0.0582077
$546$		0			0
$547$	21.2868			0.910159			0.455079	−	0.890451i	$-0.349611\pi$
$547$	21.2868			0.910159			0.455079	+	0.890451i	$0.349611\pi$
$548$	−8.47401	+	4.89247i	−0.361992	+	0.208996i
$549$	15.1834	+	3.36563i	0.648011	+	0.143642i
$550$	4.83963	−	8.38248i	0.206362	−	0.357430i
$551$	−0.963296	−	1.66848i	−0.0410378	−	0.0710795i
$552$	−6.13887	+	0.944951i	−0.261288	+	0.0402198i
$553$		0			0
$554$			20.8472i			0.885713i
$555$	−12.3403	−	15.3752i	−0.523816	−	0.652642i
$556$	21.4143	+	12.3636i	0.908169	+	0.524331i
$557$	−16.5937	−	9.58040i	−0.703099	−	0.405935i	0.105401	−	0.994430i	$-0.466387\pi$
$557$	−16.5937	−	9.58040i	−0.703099	−	0.405935i	−0.808501	+	0.588495i	$0.799721\pi$
$558$	−10.6667	−	9.77368i	−0.451557	−	0.413753i
$559$		−	2.01138i		−	0.0850723i
$560$		0			0
$561$	5.13017	+	33.3282i	0.216596	+	1.40712i
$562$	15.6319	+	27.0752i	0.659390	+	1.14210i
$563$	13.6243	−	23.5981i	0.574198	−	0.994540i	−0.421930	−	0.906628i	$-0.638647\pi$
$563$	13.6243	−	23.5981i	0.574198	−	0.994540i	0.996128	−	0.0879116i	$-0.0280193\pi$
$564$	9.64113	−	24.7931i	0.405965	−	1.04398i
$565$	−10.3394	+	5.96948i	−0.434984	+	0.251138i
$566$	−49.3843			−2.07578
$567$		0			0
$568$	0.647181			0.0271551
$569$	22.7124	−	13.1130i	0.952153	−	0.549726i	0.0584038	−	0.998293i	$-0.481399\pi$
$569$	22.7124	−	13.1130i	0.952153	−	0.549726i	0.893749	+	0.448567i	$0.148066\pi$
$570$	−1.16180	+	2.98768i	−0.0486622	+	0.125140i
$571$	13.4388	−	23.2767i	0.562397	−	0.974101i	−0.434889	−	0.900484i	$-0.643212\pi$
$571$	13.4388	−	23.2767i	0.562397	−	0.974101i	0.997287	−	0.0736170i	$-0.0234542\pi$
$572$	3.37960	+	5.85363i	0.141308	+	0.244753i
$573$	−4.49023	−	29.1708i	−0.187582	−	1.21863i
$574$		0			0
$575$			6.80436i			0.283761i
$576$	−21.8902	−	20.0575i	−0.912091	−	0.835731i
$577$	8.93069	+	5.15614i	0.371790	+	0.214653i	0.674240	−	0.738512i	$-0.264471\pi$
$577$	8.93069	+	5.15614i	0.371790	+	0.214653i	−0.302450	+	0.953165i	$0.597805\pi$
$578$	−0.386185	−	0.222964i	−0.0160632	−	0.00927407i
$579$	3.06123	+	3.81410i	0.127220	+	0.158509i
$580$			4.84341i			0.201112i
$581$		0			0
$582$	45.5853	−	7.01690i	1.88957	−	0.290860i
$583$	−5.31469	−	9.20532i	−0.220112	−	0.381245i
$584$	−3.80943	+	6.59812i	−0.157635	+	0.273032i
$585$	1.87066	+	0.414660i	0.0773422	+	0.0171441i
$586$	37.9138	−	21.8895i	1.56620	−	0.904248i
$587$	−22.1492			−0.914197			−0.457098	−	0.889416i	$-0.651111\pi$
$587$	−22.1492			−0.914197			−0.457098	+	0.889416i	$0.651111\pi$
$588$		0			0
$589$	2.09734			0.0864195
$590$	−0.907741	+	0.524084i	−0.0373711	+	0.0215762i
$591$	15.4920	+	6.02425i	0.637255	+	0.247805i
$592$	−19.4855	+	33.7498i	−0.800848	+	1.38711i
$593$	−1.45861	−	2.52638i	−0.0598978	−	0.103746i	0.834522	−	0.550975i	$-0.185744\pi$
$593$	−1.45861	−	2.52638i	−0.0598978	−	0.103746i	−0.894419	+	0.447229i	$0.852411\pi$
$594$	45.1072	−	22.2467i	1.85077	−	0.912795i
$595$		0			0
$596$		−	19.5472i		−	0.800686i
$597$	−16.4986	+	13.2419i	−0.675244	+	0.541956i
$598$	−7.76391	−	4.48250i	−0.317490	−	0.183303i
$599$	−31.4551	−	18.1606i	−1.28522	−	0.742023i	−0.307424	−	0.951573i	$-0.599467\pi$
$599$	−31.4551	−	18.1606i	−1.28522	−	0.742023i	−0.977798	+	0.209550i	$0.932800\pi$
$600$	0.711889	−	0.571367i	0.0290627	−	0.0233260i
$601$		−	7.15198i		−	0.291735i	−0.989304	−	0.145868i	$-0.953403\pi$
$601$		−	7.15198i		−	0.291735i	0.989304	−	0.145868i	$-0.0465974\pi$
$602$		0			0
$603$	13.8149	−	4.35625i	0.562587	−	0.177400i
$604$	15.1798	+	26.2921i	0.617656	+	1.06981i
$605$	5.50793	−	9.54001i	0.223929	−	0.387857i
$606$	−30.1034	−	11.7061i	−1.22287	−	0.475527i
$607$	37.8248	−	21.8382i	1.53526	−	0.886384i	0.536156	−	0.844119i	$-0.319876\pi$
$607$	37.8248	−	21.8382i	1.53526	−	0.886384i	0.999106	−	0.0422651i	$-0.0134574\pi$
$608$	7.28226			0.295334
$609$		0			0
$610$	10.6939			0.432984
$611$	3.76643	−	2.17455i	0.152373	−	0.0879729i
$612$	−6.07589	+	27.4102i	−0.245603	+	1.10799i
$613$	7.27926	−	12.6080i	0.294007	−	0.509234i	−0.680747	−	0.732519i	$-0.738345\pi$
$613$	7.27926	−	12.6080i	0.294007	−	0.509234i	0.974753	+	0.223285i	$0.0716779\pi$
$614$	−25.0452	−	43.3795i	−1.01074	−	1.75065i
$615$	−7.02943	+	1.08203i	−0.283454	+	0.0436318i
$616$		0			0
$617$		−	4.68442i		−	0.188588i	−0.995544	−	0.0942938i	$-0.969941\pi$
$617$		−	4.68442i		−	0.188588i	0.995544	−	0.0942938i	$-0.0300593\pi$
$618$	−34.7114	−	43.2483i	−1.39630	−	1.73970i
$619$	33.0429	+	19.0773i	1.32810	+	0.766782i	0.985006	−	0.172518i	$-0.0551902\pi$
$619$	33.0429	+	19.0773i	1.32810	+	0.766782i	0.343098	+	0.939299i	$0.388524\pi$
$620$	−4.56627	−	2.63634i	−0.183386	−	0.105878i
$621$	−19.6418	+	29.3987i	−0.788197	+	1.17973i
$622$			14.6819i			0.588689i
$623$		0			0
$624$	−0.576223	−	3.74343i	−0.0230674	−	0.149857i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.65877	+	6.33717i	−0.146234	+	0.253284i
$627$	−2.64255	+	6.79559i	−0.105533	+	0.271390i
$628$	15.2615	−	8.81125i	0.609001	−	0.351607i
$629$	47.2285			1.88312
$630$		0			0
$631$	23.9959			0.955264			0.477632	−	0.878560i	$-0.341495\pi$
$631$	23.9959			0.955264			0.477632	+	0.878560i	$0.341495\pi$
$632$	−4.14473	+	2.39296i	−0.164869	+	0.0951869i
$633$	3.54115	−	9.10644i	0.140748	−	0.361948i
$634$	−21.7391	+	37.6532i	−0.863369	+	1.49540i
$635$	8.42461	+	14.5918i	0.334320	+	0.579060i
$636$	−1.34640	−	8.74690i	−0.0533883	−	0.346837i
$637$		0			0
$638$			20.7852i			0.822895i
$639$	2.48881	−	2.71621i	0.0984557	−	0.107452i
$640$	−3.62150	−	2.09088i	−0.143152	−	0.0826491i
$641$	20.0037	+	11.5491i	0.790099	+	0.456164i	0.839997	−	0.542590i	$-0.182556\pi$
$641$	20.0037	+	11.5491i	0.790099	+	0.456164i	−0.0498985	+	0.998754i	$0.515890\pi$
$642$	11.9829	+	14.9299i	0.472927	+	0.589238i
$643$			22.7592i			0.897536i	0.893648	+	0.448768i	$0.148137\pi$
$643$			22.7592i			0.897536i	−0.893648	+	0.448768i	$0.851863\pi$
$644$		0			0
$645$	−5.39114	+	0.829853i	−0.212276	+	0.0326754i
$646$	−3.83963	−	6.65043i	−0.151068	−	0.261658i
$647$	−1.21349	+	2.10183i	−0.0477073	+	0.0826315i	−0.888893	−	0.458115i	$-0.848525\pi$
$647$	−1.21349	+	2.10183i	−0.0477073	+	0.0826315i	0.841186	+	0.540746i	$0.181858\pi$
$648$	4.72510	−	0.413659i	0.185619	−	0.0162500i
$649$	−2.06469	+	1.19205i	−0.0810463	+	0.0467921i
$650$	1.31754			0.0516781
$651$		0			0
$652$	−37.6189			−1.47327
$653$	−34.7760	+	20.0779i	−1.36089	+	0.785709i	−0.989742	−	0.142865i	$-0.954368\pi$
$653$	−34.7760	+	20.0779i	−1.36089	+	0.785709i	−0.371146	+	0.928574i	$0.621035\pi$
$654$	4.52517	+	1.75967i	0.176948	+	0.0688086i
$655$	−6.93473	+	12.0113i	−0.270962	+	0.469321i
$656$	7.02943	+	12.1753i	0.274453	+	0.475366i
$657$	13.0426	+	41.3619i	0.508842	+	1.61368i
$658$		0			0
$659$		−	0.627454i		−	0.0244421i	−0.999925	−	0.0122211i	$-0.996110\pi$
$659$		−	0.627454i		−	0.0244421i	0.999925	−	0.0122211i	$-0.00389018\pi$
$660$	14.2953	−	11.4735i	0.556442	−	0.446605i
$661$	28.5745	+	16.4975i	1.11142	+	0.641678i	0.939197	−	0.343380i	$-0.111572\pi$
$661$	28.5745	+	16.4975i	1.11142	+	0.641678i	0.172222	+	0.985058i	$0.444905\pi$
$662$	26.4550	+	15.2738i	1.02820	+	0.593634i
$663$	−3.57967	+	2.87307i	−0.139023	+	0.111581i
$664$			1.45646i			0.0565217i
$665$		0			0
$666$	−21.1842	−	67.1810i	−0.820869	−	2.60321i
$667$	−7.30584	−	12.6541i	−0.282883	−	0.489968i
$668$	−0.524525	+	0.908504i	−0.0202945	+	0.0351511i
$669$	0.633413	+	0.246310i	0.0244891	+	0.00952291i
$670$	8.62613	−	4.98030i	0.333257	−	0.192406i
$671$	24.3238			0.939009
$672$		0			0
$673$	1.14437			0.0441121			0.0220560	−	0.999757i	$-0.492979\pi$
$673$	1.14437			0.0441121			0.0220560	+	0.999757i	$0.492979\pi$
$674$	36.6345	−	21.1509i	1.41111	−	0.814703i
$675$	0.339627	−	5.18504i	0.0130723	−	0.199572i
$676$	14.2006	−	24.5961i	0.546176	−	0.946004i
$677$	−7.98910	−	13.8375i	−0.307046	−	0.531820i	0.670669	−	0.741757i	$-0.266007\pi$
$677$	−7.98910	−	13.8375i	−0.307046	−	0.531820i	−0.977715	+	0.209938i	$0.932674\pi$
$678$	−42.1615	+	6.48988i	−1.61920	+	0.249242i
$679$		0			0
$680$			2.18673i			0.0838571i
$681$	25.3963	+	31.6422i	0.973188	+	1.21253i
$682$	−19.5959	−	11.3137i	−0.750366	−	0.433224i
$683$	−1.96122	−	1.13231i	−0.0750442	−	0.0433268i	0.462008	−	0.886876i	$-0.347129\pi$
$683$	−1.96122	−	1.13231i	−0.0750442	−	0.0433268i	−0.537053	+	0.843549i	$0.680462\pi$
$684$	−4.10116	+	4.47588i	−0.156812	+	0.171140i
$685$			4.33830i			0.165758i
$686$		0			0
$687$	2.03646	+	13.2299i	0.0776960	+	0.504752i
$688$	5.39114	+	9.33773i	0.205535	+	0.355998i
$689$	0.723434	−	1.25303i	0.0275607	−	0.0477365i
$690$	−8.81130	+	22.6592i	−0.335441	+	0.862620i
$691$	2.40044	−	1.38589i	0.0913169	−	0.0527218i	−0.453646	−	0.891182i	$-0.649877\pi$
$691$	2.40044	−	1.38589i	0.0913169	−	0.0527218i	0.544963	+	0.838460i	$0.316544\pi$
$692$	−25.2256			−0.958934
$693$		0			0
$694$	32.6582			1.23969
$695$	9.49436	−	5.48157i	0.360141	−	0.207928i
$696$	−0.710424	+	1.82693i	−0.0269286	+	0.0692496i
$697$	8.51888	−	14.7551i	0.322676	−	0.558891i
$698$	9.24191	+	16.0075i	0.349811	+	0.605891i
$699$	−1.07507	−	6.98419i	−0.0406629	−	0.264166i
$700$		0			0
$701$			23.1184i			0.873169i	0.899663	+	0.436585i	$0.143812\pi$
$701$			23.1184i			0.873169i	−0.899663	+	0.436585i	$0.856188\pi$
$702$	5.69250	+	3.80326i	0.214850	+	0.143545i
$703$	8.84388	+	5.10602i	0.333553	+	0.192577i
$704$	−40.2147	−	23.2180i	−1.51565	−	0.875060i
$705$	−7.38244	−	9.19807i	−0.278039	−	0.346419i
$706$			27.7612i			1.04481i
$707$		0			0
$708$	−1.96187	+	0.301989i	−0.0737317	+	0.0113495i
$709$	18.0134	+	31.2002i	0.676508	+	1.17175i	0.976026	+	0.217656i	$0.0698410\pi$
$709$	18.0134	+	31.2002i	0.676508	+	1.17175i	−0.299517	+	0.954091i	$0.596826\pi$
$710$	1.26661	−	2.19384i	0.0475351	−	0.0823333i
$711$	−5.89580	+	26.5978i	−0.221110	+	0.997494i
$712$	6.29910	−	3.63678i	0.236069	−	0.136294i
$713$	15.9067			0.595710
$714$		0			0
$715$	2.99679			0.112074
$716$	−0.483812	+	0.279329i	−0.0180809	+	0.0104390i
$717$	9.30287	+	3.61754i	0.347422	+	0.135099i
$718$	−5.78619	+	10.0220i	−0.215939	+	0.374017i
$719$	−8.57099	−	14.8454i	−0.319644	−	0.553640i	0.660770	−	0.750589i	$-0.270230\pi$
$719$	−8.57099	−	14.8454i	−0.319644	−	0.553640i	−0.980414	+	0.196949i	$0.936897\pi$
$720$	−9.79586	+	3.08892i	−0.365070	+	0.115117i
$721$		0			0
$722$			37.5343i			1.39688i
$723$	27.5826	−	22.1380i	1.02581	−	0.823322i
$724$	28.0075	+	16.1701i	1.04089	+	0.600958i
$725$	1.85970	+	1.07370i	0.0690676	+	0.0398762i
$726$	30.6958	−	24.6367i	1.13923	−	0.914352i
$727$			16.6832i			0.618747i	0.950941	+	0.309374i	$0.100119\pi$
$727$			16.6832i			0.618747i	−0.950941	+	0.309374i	$0.899881\pi$
$728$		0			0
$729$	16.4348	−	21.4219i	0.608695	−	0.793404i
$730$	14.9110	+	25.8267i	0.551882	+	0.955888i
$731$	6.53347	−	11.3163i	0.241649	−	0.418548i
$732$	18.8749	+	7.33973i	0.697635	+	0.271284i
$733$	−32.9814	+	19.0418i	−1.21820	+	0.703326i	−0.964532	−	0.263967i	$-0.914969\pi$
$733$	−32.9814	+	19.0418i	−1.21820	+	0.703326i	−0.253664	+	0.967292i	$0.581636\pi$
$734$	4.07690			0.150481
$735$		0			0
$736$	55.2302			2.03581
$737$	19.6205	−	11.3279i	0.722730	−	0.417268i
$738$	−24.8098	−	5.49948i	−0.913263	−	0.202439i
$739$	11.2186	−	19.4312i	0.412684	−	0.714790i	−0.582498	−	0.812832i	$-0.697925\pi$
$739$	11.2186	−	19.4312i	0.412684	−	0.714790i	0.995182	+	0.0980422i	$0.0312580\pi$
$740$	−12.8364	−	22.2333i	−0.471876	−	0.817313i
$741$	−0.980937	+	0.150995i	−0.0360356	+	0.00554693i
$742$		0			0
$743$		−	6.39189i		−	0.234496i	−0.993103	−	0.117248i	$-0.962593\pi$
$743$		−	6.39189i		−	0.234496i	0.993103	−	0.117248i	$-0.0374072\pi$
$744$	−1.33570	−	1.66420i	−0.0489690	−	0.0610124i
$745$	−7.50546	−	4.33328i	−0.274979	−	0.158759i
$746$	41.2565	+	23.8195i	1.51051	+	0.872093i
$747$	6.11275	+	5.60098i	0.223654	+	0.204929i
$748$			43.9111i			1.60555i
$749$		0			0
$750$	−0.543588	−	3.53142i	−0.0198490	−	0.128949i
$751$	5.49944	+	9.52531i	0.200677	+	0.347583i	0.948747	−	0.316037i	$-0.102352\pi$
$751$	5.49944	+	9.52531i	0.200677	+	0.347583i	−0.748069	+	0.663620i	$0.769019\pi$
$752$	−11.6570	+	20.1905i	−0.425086	+	0.736271i
$753$	−2.77802	+	7.14396i	−0.101237	+	0.260340i
$754$	−2.45023	+	1.41464i	−0.0892320	+	0.0515181i
$755$	13.4604			0.489873
$756$		0			0
$757$	−27.8216			−1.01119			−0.505597	−	0.862770i	$-0.668728\pi$
$757$	−27.8216			−1.01119			−0.505597	+	0.862770i	$0.668728\pi$
$758$	−30.4859	+	17.6011i	−1.10730	+	0.639299i
$759$	−20.0417	+	51.5392i	−0.727466	+	1.87075i
$760$	−0.236414	+	0.409481i	−0.00857563	+	0.0148534i
$761$	6.54766	+	11.3409i	0.237352	+	0.411106i	0.959954	−	0.280159i	$-0.0903871\pi$
$761$	6.54766	+	11.3409i	0.237352	+	0.411106i	−0.722601	+	0.691265i	$0.757054\pi$
$762$	9.15904	+	59.5017i	0.331797	+	2.15552i
$763$		0			0
$764$		−	38.4336i		−	1.39048i
$765$	9.17765	+	8.40930i	0.331819	+	0.304039i
$766$	−47.5412	−	27.4479i	−1.71773	−	0.991734i
$767$	−0.281045	−	0.162262i	−0.0101480	−	0.00585893i
$768$	12.1064	+	15.0839i	0.436853	+	0.544293i
$769$			7.74247i			0.279201i	0.990208	+	0.139600i	$0.0445818\pi$
$769$			7.74247i			0.279201i	−0.990208	+	0.139600i	$0.955418\pi$
$770$		0			0
$771$	−43.6664	+	6.72153i	−1.57261	+	0.242070i
$772$	3.18431	+	5.51538i	0.114606	+	0.198503i
$773$	−19.1733	+	33.2091i	−0.689614	+	1.19445i	0.282349	+	0.959312i	$0.408887\pi$
$773$	−19.1733	+	33.2091i	−0.689614	+	1.19445i	−0.971963	+	0.235135i	$0.924447\pi$
$774$	−19.0276	−	4.21777i	−0.683934	−	0.151605i
$775$	−2.02453	+	1.16886i	−0.0727231	+	0.0419867i
$776$	6.80301			0.244214
$777$		0			0
$778$	19.5551			0.701086
$779$	3.19045	−	1.84201i	0.114310	−	0.0659967i
$780$	2.32546	+	0.904286i	0.0832650	+	0.0323786i
$781$	2.88096	−	4.98997i	0.103089	−	0.178555i
$782$	−29.1205	−	50.4383i	−1.04135	−	1.80367i
$783$	4.93557	+	10.0073i	0.176383	+	0.357632i
$784$		0			0
$785$		−	7.81320i		−	0.278865i
$786$	−38.6474	+	31.0187i	−1.37851	+	1.10640i
$787$	21.6178	+	12.4811i	0.770592	+	0.444901i	0.833086	−	0.553144i	$-0.186572\pi$
$787$	21.6178	+	12.4811i	0.770592	+	0.444901i	−0.0624938	+	0.998045i	$0.519905\pi$
$788$	18.7453	+	10.8226i	0.667775	+	0.385540i
$789$	0.483554	−	0.388104i	0.0172150	−	0.0138169i
$790$			18.7333i			0.666500i
$791$		0			0
$792$	7.07507	−	2.23098i	0.251402	−	0.0792744i
$793$	1.65547	+	2.86736i	0.0587875	+	0.101823i
$794$	−12.7488	+	22.0816i	−0.452438	+	0.783645i
$795$	−3.65698	−	1.42206i	−0.129700	−	0.0504354i
$796$	−23.8578	+	13.7743i	−0.845619	+	0.488218i
$797$	−5.81191			−0.205868			−0.102934	−	0.994688i	$-0.532823\pi$
$797$	−5.81191			−0.205868			−0.102934	+	0.994688i	$0.532823\pi$
$798$		0			0
$799$	28.2539			0.999552
$800$	−7.02943	+	4.05844i	−0.248528	+	0.143488i
$801$	8.96035	−	40.4229i	0.316598	−	1.42827i
$802$	8.47393	−	14.6773i	0.299225	−	0.518273i
$803$	33.9158	+	58.7438i	1.19686	+	2.07302i
$804$	18.6434	−	2.86976i	0.657502	−	0.101209i
$805$		0			0
$806$		−	3.08003i		−	0.108490i
$807$	9.25658	+	11.5331i	0.325847	+	0.405985i
$808$	−4.12586	−	2.38207i	−0.145147	−	0.0838009i
$809$	1.51563	+	0.875048i	0.0532866	+	0.0307650i	0.526407	−	0.850233i	$-0.323539\pi$
$809$	1.51563	+	0.875048i	0.0532866	+	0.0307650i	−0.473120	+	0.880998i	$0.656872\pi$
$810$	7.84536	−	16.8269i	0.275658	−	0.591236i
$811$		−	28.4479i		−	0.998940i	−0.866331	−	0.499470i	$-0.833528\pi$
$811$		−	28.4479i		−	0.998940i	0.866331	−	0.499470i	$-0.166472\pi$
$812$		0			0
$813$	−2.22265	−	14.4394i	−0.0779516	−	0.506412i
$814$	−55.0868	−	95.4131i	−1.93079	−	3.34423i
$815$	−8.33945	+	14.4443i	−0.292118	+	0.505963i
$816$	8.91769	−	22.9328i	0.312182	−	0.802807i
$817$	2.44688	−	1.41271i	0.0856055	−	0.0494244i
$818$	42.7750			1.49559
$819$		0			0
$820$	−9.26153			−0.323427
$821$	25.9378	−	14.9752i	0.905236	−	0.522638i	0.0263407	−	0.999653i	$-0.491615\pi$
$821$	25.9378	−	14.9752i	0.905236	−	0.522638i	0.878895	+	0.477015i	$0.158281\pi$
$822$	−5.61789	+	14.4470i	−0.195946	+	0.503896i
$823$	−8.06283	+	13.9652i	−0.281053	+	0.486798i	−0.971644	−	0.236447i	$-0.924017\pi$
$823$	−8.06283	+	13.9652i	−0.281053	+	0.486798i	0.690592	+	0.723245i	$0.257350\pi$
$824$	−4.08982	−	7.08378i	−0.142476	−	0.246775i
$825$	−1.23641	−	8.03236i	−0.0430464	−	0.279651i
$826$		0			0
$827$		−	15.9844i		−	0.555831i	−0.960605	−	0.277916i	$-0.910356\pi$
$827$		−	15.9844i		−	0.555831i	0.960605	−	0.277916i	$-0.0896436\pi$
$828$	−31.1041	+	33.9460i	−1.08094	+	1.17971i
$829$	−18.0763	−	10.4363i	−0.627815	−	0.362469i	0.152091	−	0.988367i	$-0.451399\pi$
$829$	−18.0763	−	10.4363i	−0.627815	−	0.362469i	−0.779905	+	0.625898i	$0.784733\pi$
$830$	4.93717	+	2.85047i	0.171372	+	0.0989414i
$831$	10.9563	+	13.6509i	0.380069	+	0.473543i
$832$		−	6.32084i		−	0.219136i
$833$		0			0
$834$	38.7155	−	5.95943i	1.34061	−	0.206358i
$835$	0.232556	+	0.402799i	0.00804794	+	0.0139394i
$836$	−4.74737	+	8.22268i	−0.164191	+	0.284387i
$837$	−12.1212	−	0.793953i	−0.418969	−	0.0274430i
$838$	−12.3970	+	7.15741i	−0.428247	+	0.247249i
$839$	14.2504			0.491977			0.245989	−	0.969273i	$-0.420887\pi$
$839$	14.2504			0.491977			0.245989	+	0.969273i	$0.420887\pi$
$840$		0			0
$841$	24.3887			0.840989
$842$	−27.1839	+	15.6946i	−0.936819	+	0.540873i
$843$	24.4652	+	9.51361i	0.842627	+	0.327666i
$844$	6.36172	−	11.0188i	0.218979	−	0.379283i
$845$	−6.29604	−	10.9051i	−0.216590	−	0.375145i
$846$	−12.6732	−	40.1903i	−0.435714	−	1.38177i
$847$		0			0
$848$			7.75614i			0.266347i
$849$	−32.3371	+	25.9540i	−1.10981	+	0.890738i
$850$	7.41264	+	4.27969i	0.254252	+	0.146792i
$851$	67.0739	+	38.7251i	2.29926	+	1.32748i
$852$	3.74131	−	3.00281i	0.128175	−	0.102875i
$853$		−	49.6034i		−	1.69839i	−0.528081	−	0.849194i	$-0.677088\pi$
$853$		−	49.6034i		−	1.69839i	0.528081	−	0.849194i	$-0.322912\pi$
$854$		0			0
$855$	0.809428	+	2.56693i	0.0276819	+	0.0877871i
$856$	1.41187	+	2.44543i	0.0482567	+	0.0835830i
$857$	−2.62252	+	4.54233i	−0.0895834	+	0.155163i	−0.907335	−	0.420408i	$-0.861887\pi$
$857$	−2.62252	+	4.54233i	−0.0895834	+	0.155163i	0.817752	+	0.575571i	$0.195220\pi$
$858$	9.97960	+	3.88069i	0.340698	+	0.132485i
$859$	10.1722	−	5.87292i	0.347071	−	0.200382i	−0.316323	−	0.948651i	$-0.602448\pi$
$859$	10.1722	−	5.87292i	0.347071	−	0.200382i	0.663394	+	0.748270i	$0.269115\pi$
$860$	−7.10303			−0.242211
$861$		0			0
$862$	−64.0863			−2.18279
$863$	30.3896	−	17.5454i	1.03447	−	0.597254i	0.116211	−	0.993225i	$-0.462925\pi$
$863$	30.3896	−	17.5454i	1.03447	−	0.597254i	0.918263	+	0.395971i	$0.129592\pi$
$864$	−42.0864	−	2.75671i	−1.43181	−	0.0937853i
$865$	−5.59208	+	9.68576i	−0.190136	+	0.329326i
$866$	23.0097	+	39.8539i	0.781901	+	1.35429i
$867$	−0.370054	+	0.0569621i	−0.0125677	+	0.00193454i
$868$		0			0
$869$			42.6096i			1.44543i
$870$	4.80260	+	5.98375i	0.162823	+	0.202868i
$871$	2.67074	+	1.54195i	0.0904944	+	0.0522470i
$872$	0.620205	+	0.358076i	0.0210028	+	0.0121260i
$873$	26.1617	−	28.5521i	0.885440	−	0.966343i
$874$		−	12.5933i		−	0.425973i
$875$		0			0
$876$	8.59208	+	55.8184i	0.290299	+	1.88593i
$877$	8.42662	+	14.5953i	0.284547	+	0.492850i	0.972499	−	0.232906i	$-0.0748235\pi$
$877$	8.42662	+	14.5953i	0.284547	+	0.492850i	−0.687952	+	0.725756i	$0.741490\pi$
$878$	26.6936	−	46.2346i	0.900864	−	1.56034i
$879$	13.3220	−	34.2590i	0.449341	−	1.15553i
$880$	−13.9125	+	8.03236i	−0.468989	+	0.270771i
$881$	51.9437			1.75003			0.875015	−	0.484096i	$-0.160852\pi$
$881$	51.9437			1.75003			0.875015	+	0.484096i	$0.160852\pi$
$882$		0			0
$883$	14.9096			0.501748			0.250874	−	0.968020i	$-0.419282\pi$
$883$	14.9096			0.501748			0.250874	+	0.968020i	$0.419282\pi$
$884$	−5.17638	+	2.98858i	−0.174100	+	0.100517i
$885$	−0.318960	+	0.820237i	−0.0107217	+	0.0275720i
$886$	−31.9387	+	55.3194i	−1.07300	+	1.85849i
$887$	6.59427	+	11.4216i	0.221414	+	0.383500i	0.955238	−	0.295840i	$-0.0955994\pi$
$887$	6.59427	+	11.4216i	0.221414	+	0.383500i	−0.733824	+	0.679340i	$0.762266\pi$
$888$	−1.58073	−	10.2692i	−0.0530458	−	0.344612i
$889$		0			0
$890$		−	28.4705i		−	0.954335i
$891$	17.8446	−	38.2734i	0.597816	−	1.28221i
$892$	0.766431	+	0.442499i	0.0256620	+	0.0148160i
$893$	5.29076	+	3.05462i	0.177048	+	0.102219i
$894$	−19.3825	−	24.1494i	−0.648249	−	0.807678i
$895$			0.247690i			0.00827935i
$896$		0			0
$897$	−7.43963	+	1.14518i	−0.248402	+	0.0382363i
$898$	−24.9642	−	43.2392i	−0.833065	−	1.44291i
$899$	2.51001	−	4.34747i	0.0837135	−	0.144996i
$900$	1.46434	−	6.60608i	0.0488113	−	0.220203i
$901$	8.14028	−	4.69979i	0.271192	−	0.156573i
$902$	−39.7453			−1.32338
$903$		0			0
$904$	−6.29206			−0.209271
$905$	12.4175	−	7.16927i	0.412773	−	0.238315i
$906$	44.8243	+	17.4305i	1.48919	+	0.579089i
$907$	−23.4709	+	40.6527i	−0.779337	+	1.34985i	0.152987	+	0.988228i	$0.451111\pi$
$907$	−23.4709	+	40.6527i	−0.779337	+	1.34985i	−0.932324	+	0.361623i	$0.882223\pi$
$908$	26.4174	+	45.7562i	0.876691	+	1.51847i
$909$	−25.8640	+	8.15567i	−0.857854	+	0.270507i
$910$		0			0
$911$		−	45.2977i		−	1.50078i	−0.660996	−	0.750389i	$-0.729866\pi$
$911$		−	45.2977i		−	1.50078i	0.660996	−	0.750389i	$-0.270134\pi$
$912$	4.14924	−	3.33021i	0.137395	−	0.110274i
$913$	11.2298	+	6.48352i	0.371652	+	0.214573i
$914$	4.31355	+	2.49043i	0.142680	+	0.0823761i
$915$	7.00244	−	5.62021i	0.231493	−	0.185798i
$916$			17.4309i			0.575932i
$917$		0			0
$918$	19.6728	+	39.8884i	0.649300	+	1.31651i
$919$	−21.5911	−	37.3969i	−0.712225	−	1.23361i	−0.964020	−	0.265830i	$-0.914354\pi$
$919$	−21.5911	−	37.3969i	−0.712225	−	1.23361i	0.251795	−	0.967781i	$-0.418979\pi$
$920$	−1.79301	+	3.10559i	−0.0591139	+	0.102388i
$921$	−39.1978	−	15.2426i	−1.29161	−	0.502260i
$922$	−13.3162	+	7.68811i	−0.438546	+	0.253195i
$923$	0.784311			0.0258159
$924$		0			0
$925$	−11.3824			−0.374252
$926$	24.8077	−	14.3227i	0.815232	−	0.470675i
$927$	−45.4584	−	10.0765i	−1.49305	−	0.330957i
$928$	8.71510	−	15.0950i	0.286087	−	0.495517i
$929$	4.50570	+	7.80410i	0.147827	+	0.256044i	0.930424	−	0.366484i	$-0.119439\pi$
$929$	4.50570	+	7.80410i	0.147827	+	0.256044i	−0.782597	+	0.622529i	$0.786105\pi$
$930$	−8.25548	+	1.27076i	−0.270708	+	0.0416698i
$931$		0			0
$932$		−	9.20194i		−	0.301419i
$933$	7.71607	+	9.61375i	0.252613	+	0.314740i
$934$	35.9774	+	20.7716i	1.17722	+	0.679667i
$935$	16.8604	+	9.73433i	0.551392	+	0.318347i
$936$	0.744523	+	0.682191i	0.0243355	+	0.0222981i
$937$		−	21.9677i		−	0.717654i	−0.933404	−	0.358827i	$-0.883177\pi$
$937$		−	21.9677i		−	0.717654i	0.933404	−	0.358827i	$-0.116823\pi$
$938$		0			0
$939$	0.934731	+	6.07248i	0.0305038	+	0.198168i
$940$	−7.67925	−	13.3009i	−0.250470	−	0.433826i
$941$	−0.823861	+	1.42697i	−0.0268571	+	0.0465178i	−0.879142	−	0.476561i	$-0.841883\pi$
$941$	−0.823861	+	1.42697i	−0.0268571	+	0.0465178i	0.852284	+	0.523079i	$0.175217\pi$
$942$	10.1177	−	26.0187i	0.329653	−	0.847735i
$943$	24.1970	−	13.9702i	0.787964	−	0.454931i
$944$	1.73965			0.0566209
$945$		0			0
$946$	−30.4823			−0.991064
$947$	−23.6645	+	13.6627i	−0.768994	+	0.443979i	−0.832516	−	0.554002i	$-0.813100\pi$
$947$	−23.6645	+	13.6627i	−0.768994	+	0.443979i	0.0635217	+	0.997980i	$0.479767\pi$
$948$	−12.8575	+	33.0644i	−0.417592	+	1.07388i
$949$	−4.61660	+	7.99619i	−0.149861	+	0.259567i
$950$	0.925382	+	1.60281i	0.0300233	+	0.0520020i
$951$	5.55384	+	36.0805i	0.180095	+	1.16999i
$952$		0			0
$953$			55.2380i			1.78933i	0.446734	+	0.894667i	$0.352587\pi$
$953$			55.2380i			1.78933i	−0.446734	+	0.894667i	$0.647413\pi$
$954$	−10.3366	−	9.47122i	−0.334660	−	0.306642i
$955$	−14.7572	−	8.52006i	−0.477531	−	0.275703i
$956$	11.2565	+	6.49894i	0.364061	+	0.210191i
$957$	10.9237	+	13.6103i	0.353113	+	0.439958i
$958$		−	68.5654i		−	2.21525i
$959$		0			0
$960$	−16.9419	+	2.60785i	−0.546797	+	0.0841679i
$961$	−12.7675	−	22.1140i	−0.411856	−	0.713355i
$962$	7.49840	−	12.9876i	0.241758	−	0.418737i
$963$	15.6929	+	3.47857i	0.505697	+	0.112096i
$964$	39.8858	−	23.0281i	1.28464	−	0.741684i
$965$	2.82362			0.0908956
$966$		0			0
$967$	−34.5930			−1.11244			−0.556218	−	0.831036i	$-0.687748\pi$
$967$	−34.5930			−1.11244			−0.556218	+	0.831036i	$0.687748\pi$
$968$	5.02776	−	2.90278i	0.161598	−	0.0932989i
$969$	−6.00935	−	2.33681i	−0.193048	−	0.0750692i
$970$	13.3143	−	23.0611i	0.427497	−	0.740447i
$971$	−2.12246	−	3.67621i	−0.0681129	−	0.117975i	0.829958	−	0.557826i	$-0.188364\pi$
$971$	−2.12246	−	3.67621i	−0.0681129	−	0.117975i	−0.898071	+	0.439851i	$0.855031\pi$
$972$	25.3962	−	24.3150i	0.814583	−	0.779903i
$973$		0			0
$974$		−	66.4407i		−	2.12890i
$975$	0.862730	−	0.692434i	0.0276295	−	0.0221756i
$976$	−15.3709	−	8.87439i	−0.492010	−	0.284062i
$977$	−33.6806	−	19.4455i	−1.07754	−	0.622118i	−0.147308	−	0.989091i	$-0.547061\pi$
$977$	−33.6806	−	19.4455i	−1.07754	−	0.622118i	−0.930232	+	0.366973i	$0.880394\pi$
$978$	−46.4758	+	37.3019i	−1.48613	+	1.19278i
$979$		−	64.7574i		−	2.06966i
$980$		0			0
$981$	3.88790	−	1.22597i	0.124131	−	0.0391422i
$982$	23.2077	+	40.1970i	0.740588	+	1.28274i
$983$	13.1884	−	22.8429i	0.420644	−	0.728577i	−0.575359	−	0.817901i	$-0.695138\pi$
$983$	13.1884	−	22.8429i	0.420644	−	0.728577i	0.996003	+	0.0893246i	$0.0284709\pi$
$984$	−3.49344	−	1.35847i	−0.111367	−	0.0433064i
$985$	8.31103	−	4.79838i	0.264812	−	0.152889i
$986$	−18.3804			−0.585352
$987$		0			0
$988$	−1.29242			−0.0411174
$989$	18.5577	−	10.7143i	0.590099	−	0.340694i
$990$	6.28413	−	28.3496i	0.199723	−	0.901010i
$991$	6.90833	−	11.9656i	0.219450	−	0.380099i	−0.735190	−	0.677861i	$-0.762907\pi$
$991$	6.90833	−	11.9656i	0.219450	−	0.380099i	0.954640	+	0.297762i	$0.0962403\pi$
$992$	9.48750	+	16.4328i	0.301228	+	0.521743i
$993$	25.3501	−	3.90211i	0.804460	−	0.123830i
$994$		0			0
$995$			12.2141i			0.387213i
$996$	6.75773	+	8.41972i	0.214127	+	0.266789i
$997$	−53.1001	−	30.6574i	−1.68170	−	0.970929i	−0.960533	−	0.278166i	$-0.910274\pi$
$997$	−53.1001	−	30.6574i	−1.68170	−	0.970929i	−0.721165	−	0.692763i	$-0.756393\pi$
$998$	−11.4587	−	6.61570i	−0.362720	−	0.209416i
$999$	−49.1786	−	32.8571i	−1.55594	−	1.03955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.k.521.4		8
3.2	odd	2		735.2.s.l.521.1		8
7.2	even	3		105.2.s.d.26.1	yes	8
7.3	odd	6		735.2.b.d.146.7		8
7.4	even	3		735.2.b.c.146.7		8
7.5	odd	6		735.2.s.l.656.1		8
7.6	odd	2		105.2.s.c.101.4	yes	8
21.2	odd	6		105.2.s.c.26.4	✓	8
21.5	even	6	inner	735.2.s.k.656.4		8
21.11	odd	6		735.2.b.d.146.2		8
21.17	even	6		735.2.b.c.146.2		8
21.20	even	2		105.2.s.d.101.1	yes	8
35.2	odd	12		525.2.q.e.299.7		16
35.9	even	6		525.2.t.f.26.4		8
35.13	even	4		525.2.q.f.374.2		16
35.23	odd	12		525.2.q.e.299.2		16
35.27	even	4		525.2.q.f.374.7		16
35.34	odd	2		525.2.t.g.101.1		8
105.2	even	12		525.2.q.f.299.2		16
105.23	even	12		525.2.q.f.299.7		16
105.44	odd	6		525.2.t.g.26.1		8
105.62	odd	4		525.2.q.e.374.2		16
105.83	odd	4		525.2.q.e.374.7		16
105.104	even	2		525.2.t.f.101.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.4	✓	8	21.2	odd	6
105.2.s.c.101.4	yes	8	7.6	odd	2
105.2.s.d.26.1	yes	8	7.2	even	3
105.2.s.d.101.1	yes	8	21.20	even	2
525.2.q.e.299.2		16	35.23	odd	12
525.2.q.e.299.7		16	35.2	odd	12
525.2.q.e.374.2		16	105.62	odd	4
525.2.q.e.374.7		16	105.83	odd	4
525.2.q.f.299.2		16	105.2	even	12
525.2.q.f.299.7		16	105.23	even	12
525.2.q.f.374.2		16	35.13	even	4
525.2.q.f.374.7		16	35.27	even	4
525.2.t.f.26.4		8	35.9	even	6
525.2.t.f.101.4		8	105.104	even	2
525.2.t.g.26.1		8	105.44	odd	6
525.2.t.g.101.1		8	35.34	odd	2
735.2.b.c.146.2		8	21.17	even	6
735.2.b.c.146.7		8	7.4	even	3
735.2.b.d.146.2		8	21.11	odd	6
735.2.b.d.146.7		8	7.3	odd	6
735.2.s.k.521.4		8	1.1	even	1	trivial
735.2.s.k.656.4		8	21.5	even	6	inner
735.2.s.l.521.1		8	3.2	odd	2
735.2.s.l.656.1		8	7.5	odd	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.78651 - 1.03144i) q^{2} +(0.627739 - 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +O(q^{10})\)	\(q+(1.78651 - 1.03144i) q^{2} +(0.627739 - 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +(-1.78651 - 1.03144i) q^{10} +(-4.06348 - 2.34605i) q^{11} +(-2.44528 - 3.04666i) q^{12} -0.638688i q^{13} +(-1.71189 + 0.263509i) q^{15} +(1.71189 + 2.96508i) q^{16} +(2.07462 - 3.59334i) q^{17} +(-6.04198 - 1.33930i) q^{18} +(0.776975 - 0.448587i) q^{19} -2.25548 q^{20} -9.67925 q^{22} +(5.89275 - 3.40218i) q^{23} +(-0.850763 - 0.330830i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.658769 - 1.14102i) q^{26} +(-4.66019 + 2.29839i) q^{27} -2.14740i q^{29} +(-2.78651 + 2.23647i) q^{30} +(2.02453 + 1.16886i) q^{31} +(7.02943 + 4.05844i) q^{32} +(-6.33802 + 5.08695i) q^{33} -8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} +(5.69122 + 9.85748i) q^{37} +(0.925382 - 1.60281i) q^{38} +(-1.03103 - 0.400929i) q^{39} +(-0.456412 + 0.263509i) q^{40} +4.10624 q^{41} +3.14924 q^{43} +(-9.16509 + 5.29147i) q^{44} +(-0.649237 + 2.92891i) q^{45} +(7.01829 - 12.1560i) q^{46} +(3.40471 + 5.89714i) q^{47} +(5.86113 - 0.902197i) q^{48} +2.06288i q^{50} +(-4.49840 - 5.60472i) q^{51} +(-1.24755 - 0.720273i) q^{52} +(1.96187 + 1.13269i) q^{53} +(-5.95481 + 8.91281i) q^{54} +4.69211i q^{55} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 - 3.83635i) q^{58} +(0.254055 - 0.440035i) q^{59} +(-1.41585 + 3.64100i) q^{60} +(-4.48946 + 2.59199i) q^{61} +4.82244 q^{62} +9.89660 q^{64} +(-0.553120 + 0.319344i) q^{65} +(-6.07604 + 15.6252i) q^{66} +(-2.41425 + 4.18160i) q^{67} +(-4.67925 - 8.10471i) q^{68} +(-1.79301 - 11.6483i) q^{69} +1.22800i q^{71} +(-1.06811 + 1.16571i) q^{72} +(-12.5197 - 7.22826i) q^{73} +(20.3348 + 11.7403i) q^{74} +(1.08415 + 1.35078i) q^{75} -2.02356i q^{76} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 - 7.86448i) q^{79} +(1.71189 - 2.96508i) q^{80} +(0.784903 + 8.96571i) q^{81} +(7.33583 - 4.23534i) q^{82} -2.76359 q^{83} -4.14924 q^{85} +(5.62613 - 3.24825i) q^{86} +(-3.46653 - 1.34801i) q^{87} +(-1.23641 + 2.14153i) q^{88} +(6.90067 + 11.9523i) q^{89} +(1.86113 + 5.90216i) q^{90} -15.3471i q^{92} +(3.15776 - 2.53444i) q^{93} +(12.1651 + 7.02352i) q^{94} +(-0.776975 - 0.448587i) q^{95} +(10.9642 - 8.79992i) q^{96} +12.9085i q^{97} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * q^96 - 34 * q^99

Introduction

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