LMFDB - Embedded newform 105.2.s.d.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.838429221223$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	105.26
Dual form			105.2.s.d.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78651 - 1.03144i) q^{2} +(1.08415 + 1.35078i) q^{3} +(1.12774 + 1.95330i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} +(-0.00953166 + 2.64573i) q^{7} -0.527019i q^{8} +(-0.649237 + 2.92891i) q^{9} +O(q^{10})$	\(q+(-1.78651 - 1.03144i) q^{2} +(1.08415 + 1.35078i) q^{3} +(1.12774 + 1.95330i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} +(-0.00953166 + 2.64573i) q^{7} -0.527019i q^{8} +(-0.649237 + 2.92891i) q^{9} +(1.78651 - 1.03144i) q^{10} +(4.06348 - 2.34605i) q^{11} +(-1.41585 + 3.64100i) q^{12} -0.638688i q^{13} +(2.74595 - 4.71679i) q^{14} +(-1.71189 + 0.263509i) q^{15} +(1.71189 - 2.96508i) q^{16} +(2.07462 + 3.59334i) q^{17} +(4.18086 - 4.56286i) q^{18} +(-0.776975 - 0.448587i) q^{19} -2.25548 q^{20} +(-3.58415 + 2.85550i) q^{21} -9.67925 q^{22} +(-5.89275 - 3.40218i) q^{23} +(0.711889 - 0.571367i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.658769 + 1.14102i) q^{26} +(-4.66019 + 2.29839i) q^{27} +(-5.17866 + 2.96508i) q^{28} -2.14740i q^{29} +(3.33010 + 1.29495i) q^{30} +(-2.02453 + 1.16886i) q^{31} +(-7.02943 + 4.05844i) q^{32} +(7.57444 + 2.94542i) q^{33} -8.55938i q^{34} +(-2.28651 - 1.33112i) q^{35} +(-6.45320 + 2.03489i) q^{36} +(5.69122 - 9.85748i) q^{37} +(0.925382 + 1.60281i) q^{38} +(0.862730 - 0.692434i) q^{39} +(0.456412 + 0.263509i) q^{40} +4.10624 q^{41} +(9.34839 - 1.40453i) q^{42} +3.14924 q^{43} +(9.16509 + 5.29147i) q^{44} +(-2.21189 - 2.02671i) q^{45} +(7.01829 + 12.1560i) q^{46} +(3.40471 - 5.89714i) q^{47} +(5.86113 - 0.902197i) q^{48} +(-6.99982 - 0.0504365i) q^{49} +2.06288i q^{50} +(-2.60464 + 6.69809i) q^{51} +(1.24755 - 0.720273i) q^{52} +(-1.96187 + 1.13269i) q^{53} +(10.6961 + 0.700610i) q^{54} +4.69211i q^{55} +(1.39435 + 0.00502336i) q^{56} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 + 3.83635i) q^{58} +(0.254055 + 0.440035i) q^{59} +(-2.44528 - 3.04666i) q^{60} +(4.48946 + 2.59199i) q^{61} +4.82244 q^{62} +(-7.74292 - 1.74563i) q^{63} +9.89660 q^{64} +(0.553120 + 0.319344i) q^{65} +(-10.4938 - 13.0746i) q^{66} +(-2.41425 - 4.18160i) q^{67} +(-4.67925 + 8.10471i) q^{68} +(-1.79301 - 11.6483i) q^{69} +(2.71189 + 4.73645i) q^{70} +1.22800i q^{71} +(1.54359 + 0.342160i) q^{72} +(12.5197 - 7.22826i) q^{73} +(-20.3348 + 11.7403i) q^{74} +(0.627739 - 1.61429i) q^{75} -2.02356i q^{76} +(6.16830 + 10.7733i) q^{77} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 + 7.86448i) q^{79} +(1.71189 + 2.96508i) q^{80} +(-8.15698 - 3.80311i) q^{81} +(-7.33583 - 4.23534i) q^{82} -2.76359 q^{83} +(-9.61963 - 3.78067i) q^{84} -4.14924 q^{85} +(-5.62613 - 3.24825i) q^{86} +(2.90067 - 2.32810i) q^{87} +(-1.23641 - 2.14153i) q^{88} +(6.90067 - 11.9523i) q^{89} +(1.86113 + 5.90216i) q^{90} +(1.68980 + 0.00608775i) q^{91} -15.3471i q^{92} +(-3.77377 - 1.46748i) q^{93} +(-12.1651 + 7.02352i) q^{94} +(0.776975 - 0.448587i) q^{95} +(-13.1030 - 5.09528i) q^{96} +12.9085i q^{97} +(12.4532 + 7.31000i) q^{98} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 2 q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 + 2 * q^7 + 4 * q^9	$ 8 q + 3 q^{2} + 2 q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} + 2 q^{7} + 4 q^{9} - 3 q^{10} - 18 q^{12} + 12 q^{14} - q^{15} + q^{16} + 12 q^{17} + 26 q^{18} + 9 q^{19} - 6 q^{20} - 22 q^{21} - 40 q^{22} - 27 q^{23} - 7 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} + 3 q^{28} + 10 q^{30} - 21 q^{31} - 21 q^{32} + 4 q^{33} - q^{35} + 9 q^{36} + 7 q^{37} + 12 q^{38} + 15 q^{39} + 3 q^{40} + 30 q^{41} - 5 q^{42} + 16 q^{43} - 5 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} + 12 q^{51} + 30 q^{52} - 24 q^{53} + 7 q^{54} + 21 q^{56} + 6 q^{57} - 13 q^{58} + 12 q^{59} + 9 q^{60} + 15 q^{61} - 24 q^{62} - 44 q^{63} + 38 q^{64} + 3 q^{65} - 16 q^{66} + 4 q^{67} + 13 q^{69} + 9 q^{70} + 13 q^{72} + 15 q^{73} - 54 q^{74} - q^{75} + 36 q^{77} - 6 q^{78} - 29 q^{79} + q^{80} + 28 q^{81} + 27 q^{82} - 30 q^{83} - 51 q^{84} - 24 q^{85} - 9 q^{86} - 29 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 3 q^{91} + 45 q^{93} - 24 q^{94} - 9 q^{95} - 42 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 + 2 * q^7 + 4 * q^9 - 3 * q^10 - 18 * q^12 + 12 * q^14 - q^15 + q^16 + 12 * q^17 + 26 * q^18 + 9 * q^19 - 6 * q^20 - 22 * q^21 - 40 * q^22 - 27 * q^23 - 7 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 + 3 * q^28 + 10 * q^30 - 21 * q^31 - 21 * q^32 + 4 * q^33 - q^35 + 9 * q^36 + 7 * q^37 + 12 * q^38 + 15 * q^39 + 3 * q^40 + 30 * q^41 - 5 * q^42 + 16 * q^43 - 5 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 + 12 * q^51 + 30 * q^52 - 24 * q^53 + 7 * q^54 + 21 * q^56 + 6 * q^57 - 13 * q^58 + 12 * q^59 + 9 * q^60 + 15 * q^61 - 24 * q^62 - 44 * q^63 + 38 * q^64 + 3 * q^65 - 16 * q^66 + 4 * q^67 + 13 * q^69 + 9 * q^70 + 13 * q^72 + 15 * q^73 - 54 * q^74 - q^75 + 36 * q^77 - 6 * q^78 - 29 * q^79 + q^80 + 28 * q^81 + 27 * q^82 - 30 * q^83 - 51 * q^84 - 24 * q^85 - 9 * q^86 - 29 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 3 * q^91 + 45 * q^93 - 24 * q^94 - 9 * q^95 - 42 * q^96 + 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.593505\pi$
$2$	−1.78651	−	1.03144i	−1.26325	−	0.729338i	−0.973702	+	0.227825i	$0.926839\pi$
$3$	1.08415	+	1.35078i	0.625934	+	0.779876i
$3$	1.08415	+	1.35078i	0.625934	+	0.779876i
$4$	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
$7$	−0.00953166	+	2.64573i	−0.00360263	+	0.999994i
$7$	−0.00953166	+	2.64573i	−0.00360263	+	0.999994i
$8$		−	0.527019i		−	0.186329i
$9$	−0.649237	+	2.92891i	−0.216412	+	0.976302i
$10$	1.78651	−	1.03144i	0.564943	−	0.326170i
$11$	4.06348	−	2.34605i	1.22519	−	0.707362i	0.259167	−	0.965833i	$-0.416552\pi$
$11$	4.06348	−	2.34605i	1.22519	−	0.707362i	0.966019	+	0.258471i	$0.0832186\pi$
$12$	−1.41585	+	3.64100i	−0.408721	+	1.05107i
$13$		−	0.638688i		−	0.177140i	−0.996070	−	0.0885701i	$-0.971770\pi$
$13$		−	0.638688i		−	0.177140i	0.996070	−	0.0885701i	$-0.0282297\pi$
$14$	2.74595	−	4.71679i	0.733885	−	1.26062i
$15$	−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	0.999993	+	0.00366299i	$0.00116597\pi$
$17$	2.07462	+	3.59334i	0.503169	+	0.871514i	−0.496824	+	0.867851i	$0.665501\pi$
$18$	4.18086	−	4.56286i	0.985438	−	1.07548i
$19$	−0.776975	−	0.448587i	−0.178250	−	0.102913i	0.408220	−	0.912884i	$-0.366150\pi$
$19$	−0.776975	−	0.448587i	−0.178250	−	0.102913i	−0.586470	+	0.809971i	$0.699483\pi$
$20$	−2.25548			−0.504340
$21$	−3.58415	+	2.85550i	−0.782126	+	0.623121i
$22$	−9.67925			−2.06362
$23$	−5.89275	−	3.40218i	−1.22872	−	0.709403i	−0.261960	−	0.965079i	$-0.584369\pi$
$23$	−5.89275	−	3.40218i	−1.22872	−	0.709403i	−0.966763	+	0.255675i	$0.917702\pi$
$24$	0.711889	−	0.571367i	0.145314	−	0.116630i
$25$	−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
$28$	−5.17866	+	2.96508i	−0.978675	+	0.560347i
$29$		−	2.14740i		−	0.398762i	−0.979922	−	0.199381i	$-0.936107\pi$
$29$		−	2.14740i		−	0.398762i	0.979922	−	0.199381i	$-0.0638932\pi$
$30$	3.33010	+	1.29495i	0.607989	+	0.236424i
$31$	−2.02453	+	1.16886i	−0.363615	+	0.209933i	−0.670666	−	0.741760i	$-0.733991\pi$
$31$	−2.02453	+	1.16886i	−0.363615	+	0.209933i	0.307050	+	0.951693i	$0.400658\pi$
$32$	−7.02943	+	4.05844i	−1.24264	+	0.717438i
$33$	7.57444	+	2.94542i	1.31854	+	0.512731i
$34$		−	8.55938i		−	1.46792i
$35$	−2.28651	−	1.33112i	−0.386490	−	0.225001i
$36$	−6.45320	+	2.03489i	−1.07553	+	0.339148i
$37$	5.69122	−	9.85748i	0.935631	−	1.62056i	0.162126	−	0.986770i	$-0.448165\pi$
$37$	5.69122	−	9.85748i	0.935631	−	1.62056i	0.773505	−	0.633790i	$-0.218502\pi$
$38$	0.925382	+	1.60281i	0.150117	+	0.260010i
$39$	0.862730	−	0.692434i	0.138147	−	0.110878i
$40$	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	$0.396101\pi$
$42$	9.34839	−	1.40453i	1.44249	−	0.216724i
$43$	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
$45$	−2.21189	−	2.02671i	−0.329729	−	0.302124i
$46$	7.01829	+	12.1560i	1.03479	+	1.79231i
$47$	3.40471	−	5.89714i	0.496629	−	0.860186i	−0.503364	−	0.864075i	$-0.667904\pi$
$47$	3.40471	−	5.89714i	0.496629	−	0.860186i	0.999992	+	0.00388861i	$0.00123779\pi$
$48$	5.86113	−	0.902197i	0.845981	−	0.130221i
$49$	−6.99982	−	0.0504365i	−0.999974	−	0.00720521i
$50$			2.06288i			0.291735i
$51$	−2.60464	+	6.69809i	−0.364722	+	0.937920i
$52$	1.24755	−	0.720273i	0.173004	−	0.0998839i
$53$	−1.96187	+	1.13269i	−0.269484	+	0.155587i	−0.628653	−	0.777686i	$-0.716393\pi$
$53$	−1.96187	+	1.13269i	−0.269484	+	0.155587i	0.359169	+	0.933272i	$0.383060\pi$
$54$	10.6961	+	0.700610i	1.45556	+	0.0953410i
$55$			4.69211i			0.632683i
$56$	1.39435	+	0.00502336i	0.186328	+	0.000671275i
$57$	−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	0.882089	−	0.471083i	$-0.156137\pi$
$59$	0.254055	+	0.440035i	0.0330751	+	0.0572877i	−0.849014	+	0.528370i	$0.822803\pi$
$60$	−2.44528	−	3.04666i	−0.315684	−	0.393323i
$61$	4.48946	+	2.59199i	0.574816	+	0.331870i	0.759070	−	0.651008i	$-0.225654\pi$
$61$	4.48946	+	2.59199i	0.574816	+	0.331870i	−0.184255	+	0.982879i	$0.558987\pi$
$62$	4.82244			0.612450
$63$	−7.74292	−	1.74563i	−0.975516	−	0.219928i
$64$	9.89660			1.23708
$65$	0.553120	+	0.319344i	0.0686061	+	0.0396097i
$66$	−10.4938	−	13.0746i	−1.29169	−	1.60937i
$67$	−2.41425	−	4.18160i	−0.294947	−	0.510863i	0.680026	−	0.733188i	$-0.261969\pi$
$67$	−2.41425	−	4.18160i	−0.294947	−	0.510863i	−0.974973	+	0.222325i	$0.928635\pi$
$68$	−4.67925	+	8.10471i	−0.567443	+	0.982840i
$69$	−1.79301	−	11.6483i	−0.215853	−	1.40229i
$70$	2.71189	+	4.73645i	0.324133	+	0.566115i
$71$			1.22800i			0.145737i	0.997342	+	0.0728686i	$0.0232154\pi$
$71$			1.22800i			0.145737i	−0.997342	+	0.0728686i	$0.976785\pi$
$72$	1.54359	+	0.342160i	0.181914	+	0.0403239i
$73$	12.5197	−	7.22826i	1.46532	−	0.846004i	0.466072	−	0.884747i	$-0.345669\pi$
$73$	12.5197	−	7.22826i	1.46532	−	0.846004i	0.999249	+	0.0387429i	$0.0123353\pi$
$74$	−20.3348	+	11.7403i	−2.36387	+	1.36478i
$75$	0.627739	−	1.61429i	0.0724850	−	0.186403i
$76$		−	2.02356i		−	0.232118i
$77$	6.16830	+	10.7733i	0.702943	+	1.22773i
$78$	−2.25548	+	0.347183i	−0.255382	+	0.0393108i
$79$	−4.54056	+	7.86448i	−0.510853	+	0.884824i	0.489068	+	0.872246i	$0.337337\pi$
$79$	−4.54056	+	7.86448i	−0.510853	+	0.884824i	−0.999921	+	0.0125778i	$0.995996\pi$
$80$	1.71189	+	2.96508i	0.191395	+	0.331506i
$81$	−8.15698	−	3.80311i	−0.906331	−	0.422568i
$82$	−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	$0.548466\pi$
$84$	−9.61963	−	3.78067i	−1.04959	−	0.412505i
$85$	−4.14924			−0.450048
$86$	−5.62613	−	3.24825i	−0.606682	−	0.350268i
$87$	2.90067	−	2.32810i	0.310985	−	0.249599i
$88$	−1.23641	−	2.14153i	−0.131802	−	0.228288i
$89$	6.90067	−	11.9523i	0.731470	−	1.26694i	−0.224785	−	0.974408i	$-0.572168\pi$
$89$	6.90067	−	11.9523i	0.731470	−	1.26694i	0.956255	−	0.292535i	$-0.0944988\pi$
$90$	1.86113	+	5.90216i	0.196180	+	0.622142i
$91$	1.68980	+	0.00608775i	0.177139	+	0.000638170i
$92$		−	15.3471i		−	1.60004i
$93$	−3.77377	−	1.46748i	−0.391321	−	0.152170i
$94$	−12.1651	+	7.02352i	−1.25473	+	0.724421i
$95$	0.776975	−	0.448587i	0.0797160	−	0.0460241i
$96$	−13.1030	−	5.09528i	−1.33732	−	0.520035i
$97$			12.9085i			1.31066i	0.755344	+	0.655329i	$0.227470\pi$
$97$			12.9085i			1.31066i	−0.755344	+	0.655329i	$0.772530\pi$
$98$	12.4532	+	7.31000i	1.25796	+	0.738422i
$99$	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	0.998369	−	0.0570865i	$-0.0181811\pi$
$101$	4.51989	+	7.82869i	0.449746	+	0.778983i	−0.548623	+	0.836070i	$0.684848\pi$
$102$	11.5619	−	9.27965i	1.14480	−	0.918823i
$103$	−13.4412	−	7.76030i	−1.32440	−	0.764645i	−0.339976	−	0.940434i	$-0.610419\pi$
$103$	−13.4412	−	7.76030i	−1.32440	−	0.764645i	−0.984428	+	0.175789i	$0.943752\pi$
$104$	−0.336601			−0.0330064
$105$	−0.680859	−	4.53171i	−0.0664450	−	0.442250i
$106$	4.67320			0.453901
$107$	4.64012	+	2.67897i	0.448577	+	0.258986i	0.707229	−	0.706985i	$-0.249945\pi$
$107$	4.64012	+	2.67897i	0.448577	+	0.258986i	−0.258652	+	0.965971i	$0.583278\pi$
$108$	−9.74493	−	6.51076i	−0.937707	−	0.626499i
$109$	−0.679436	−	1.17682i	−0.0650782	−	0.112719i	0.831650	−	0.555299i	$-0.187396\pi$
$109$	−0.679436	−	1.17682i	−0.0650782	−	0.112719i	−0.896729	+	0.442581i	$0.854063\pi$
$110$	4.83963	−	8.38248i	0.461440	−	0.799238i
$111$	19.4855	−	2.99938i	1.84948	−	0.284689i
$112$	7.82849	+	4.55746i	0.739723	+	0.430640i
$113$		−	11.9390i		−	1.12312i	−0.827435	−	0.561562i	$-0.810201\pi$
$113$		−	11.9390i		−	1.12312i	0.827435	−	0.561562i	$-0.189799\pi$
$114$	−1.16180	+	2.98768i	−0.108812	+	0.279821i
$115$	5.89275	−	3.40218i	0.549502	−	0.317255i
$116$	4.19452	−	2.42171i	0.389451	−	0.224850i
$117$	1.87066	+	0.414660i	0.172942	+	0.0383353i
$118$		−	1.04817i		−	0.0964917i
$119$	−9.52681	+	5.45464i	−0.873321	+	0.500026i
$120$	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
$123$	4.45178	+	5.54665i	0.401404	+	0.500124i
$124$	−4.56627	−	2.63634i	−0.410063	−	0.236750i
$125$	1.00000			0.0894427
$126$	12.0323	+	11.1049i	1.07192	+	0.989306i
$127$	−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
$129$	3.41425	+	4.25394i	0.300608	+	0.374539i
$130$	−0.658769	−	1.14102i	−0.0577778	−	0.100074i
$131$	−6.93473	+	12.0113i	−0.605890	+	1.04943i	0.386020	+	0.922490i	$0.373850\pi$
$131$	−6.93473	+	12.0113i	−0.605890	+	1.04943i	−0.991910	+	0.126942i	$0.959484\pi$
$132$	2.78870	+	18.1168i	0.242725	+	1.57687i
$133$	1.19425	−	2.05139i	0.103554	−	0.177878i
$134$			9.96060i			0.860465i
$135$	0.339627	−	5.18504i	0.0292305	−	0.446257i
$136$	1.89376	−	1.09336i	0.162389	−	0.0937551i
$137$	3.75708	−	2.16915i	0.320989	−	0.185323i	−0.330844	−	0.943685i	$-0.607333\pi$
$137$	3.75708	−	2.16915i	0.320989	−	0.185323i	0.651833	+	0.758362i	$0.274000\pi$
$138$	−8.81130	+	22.6592i	−0.750068	+	1.92888i
$139$			10.9631i			0.929881i	0.885342	+	0.464941i	$0.153924\pi$
$139$			10.9631i			0.929881i	−0.885342	+	0.464941i	$0.846076\pi$
$140$	0.0214984	−	5.96739i	0.00181695	−	0.504337i
$141$	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
$144$	7.57301	+	6.93900i	0.631085	+	0.578250i
$145$	1.85970	+	1.07370i	0.154440	+	0.0891659i
$146$	−29.8221			−2.46809
$147$	−7.52073	−	9.50993i	−0.620299	−	0.784365i
$148$	25.6728			2.11029
$149$	−7.50546	−	4.33328i	−0.614871	−	0.354996i	0.159998	−	0.987117i	$-0.448851\pi$
$149$	−7.50546	−	4.33328i	−0.614871	−	0.354996i	−0.774870	+	0.632121i	$0.782184\pi$
$150$	−2.78651	+	2.23647i	−0.227517	+	0.182607i
$151$	−6.73018	−	11.6570i	−0.547694	−	0.948634i	−0.998432	−	0.0559778i	$-0.982172\pi$
$151$	−6.73018	−	11.6570i	−0.547694	−	0.948634i	0.450738	−	0.892656i	$-0.351161\pi$
$152$	−0.236414	+	0.409481i	−0.0191757	+	0.0332133i
$153$	−11.8715	+	3.74343i	−0.959753	+	0.302638i
$154$	0.0922593	−	25.6087i	0.00743447	−	2.06361i
$155$		−	2.33772i		−	0.187770i
$156$	2.32546	+	0.904286i	0.186186	+	0.0724009i
$157$	−6.76643	+	3.90660i	−0.540020	+	0.311781i	−0.745087	−	0.666967i	$-0.767592\pi$
$157$	−6.76643	+	3.90660i	−0.540020	+	0.311781i	0.205067	+	0.978748i	$0.434259\pi$
$158$	16.2235	−	9.36664i	1.29067	−	0.745170i
$159$	−3.65698	−	1.42206i	−0.290018	−	0.112777i
$160$		−	8.11688i		−	0.641696i
$161$	9.05743	−	15.5582i	0.713825	−	1.22616i
$162$	10.6498	+	15.2077i	0.836730	+	1.19483i
$163$	−8.33945	+	14.4443i	−0.653196	+	1.13137i	0.329147	+	0.944279i	$0.393239\pi$
$163$	−8.33945	+	14.4443i	−0.653196	+	1.13137i	−0.982343	+	0.187090i	$0.940095\pi$
$164$	4.63077	+	8.02072i	0.361602	+	0.626313i
$165$	−6.33802	+	5.08695i	−0.493414	+	0.396018i
$166$	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	$0.505729\pi$
$168$	1.50490	+	1.88891i	0.116106	+	0.145733i
$169$	12.5921			0.968621
$170$	7.41264	+	4.27969i	0.568524	+	0.328237i
$171$	1.81831	−	1.98445i	0.139050	−	0.151755i
$172$	3.55152	+	6.15141i	0.270801	+	0.469040i
$173$	−5.59208	+	9.68576i	−0.425158	+	0.736395i	−0.996435	−	0.0843622i	$-0.973115\pi$
$173$	−5.59208	+	9.68576i	−0.425158	+	0.736395i	0.571277	+	0.820757i	$0.306448\pi$
$174$	−7.58338	+	1.16730i	−0.574894	+	0.0884929i
$175$	2.29604	−	1.31461i	0.173564	−	0.0993754i
$176$		−	16.0647i		−	1.21092i
$177$	−0.318960	+	0.820237i	−0.0239745	+	0.0616528i
$178$	−24.6562	+	14.2353i	−1.84806	+	1.06698i
$179$	0.214505	−	0.123845i	0.0160329	−	0.00925660i	−0.491962	−	0.870617i	$-0.663720\pi$
$179$	0.214505	−	0.123845i	0.0160329	−	0.00925660i	0.507995	+	0.861360i	$0.330387\pi$
$180$	1.46434	−	6.60608i	0.109145	−	0.492388i
$181$			14.3385i			1.06578i	0.846186	+	0.532888i	$0.178893\pi$
$181$			14.3385i			1.06578i	−0.846186	+	0.532888i	$0.821107\pi$
$182$	−3.01256	−	1.75380i	−0.223306	−	0.130000i
$183$	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
$186$	5.22825	+	6.51407i	0.383354	+	0.477635i
$187$	16.8604	+	9.73433i	1.23295	+	0.711845i
$188$	15.3585			1.12013
$189$	−6.03652	−	12.3515i	−0.439092	−	0.898442i
$190$	−1.85076			−0.134268
$191$	−14.7572	−	8.52006i	−1.06779	−	0.616490i	−0.140214	−	0.990121i	$-0.544779\pi$
$191$	−14.7572	−	8.52006i	−1.06779	−	0.616490i	−0.927577	+	0.373632i	$0.878112\pi$
$192$	10.7294	+	13.3682i	0.774328	+	0.964765i
$193$	−1.41181	−	2.44533i	−0.101624	−	0.176019i	0.810730	−	0.585421i	$-0.199071\pi$
$193$	−1.41181	−	2.44533i	−0.101624	−	0.176019i	−0.912354	+	0.409402i	$0.865737\pi$
$194$	13.3143	−	23.0611i	0.955913	−	1.65569i
$195$	0.168300	+	1.09336i	0.0120522	+	0.0782973i
$196$	−7.79545	−	13.7296i	−0.556818	−	0.980688i
$197$			9.59675i			0.683740i	0.939747	+	0.341870i	$0.111060\pi$
$197$			9.59675i			0.683740i	−0.939747	+	0.341870i	$0.888940\pi$
$198$	6.28413	−	28.3496i	0.446594	−	2.01472i
$199$	10.5777	−	6.10706i	0.749836	−	0.432918i	−0.0757989	−	0.997123i	$-0.524151\pi$
$199$	10.5777	−	6.10706i	0.749836	−	0.432918i	0.825635	+	0.564205i	$0.190817\pi$
$200$	−0.456412	+	0.263509i	−0.0322732	+	0.0186329i
$201$	3.03103	−	7.79460i	0.213792	−	0.549789i
$202$		−	18.6480i		−	1.31207i
$203$	5.68145	+	0.0204683i	0.398760	+	0.00143659i
$204$	−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
$207$	13.7905	−	15.0505i	0.958503	−	1.04608i
$208$	−1.89376	−	1.09336i	−0.131309	−	0.0758111i
$209$	−4.20964			−0.291187
$210$	−3.45783	+	8.79820i	−0.238613	+	0.607134i
$211$	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
$213$	−1.65877	+	1.33134i	−0.113657	+	0.0912220i
$214$	−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
$217$	−3.07320	−	5.36750i	−0.208622	−	0.364369i
$218$			2.80319i			0.189856i
$219$	23.3371	+	9.07491i	1.57697	+	0.613226i
$220$	−9.16509	+	5.29147i	−0.617910	+	0.356751i
$221$	2.29503	−	1.32503i	0.154380	−	0.0891314i
$222$	−37.9046	−	14.7397i	−2.54399	−	0.989263i
$223$			0.392378i			0.0262755i	0.999914	+	0.0131378i	$0.00418200\pi$
$223$			0.392378i			0.0262755i	−0.999914	+	0.0131378i	$0.995818\pi$
$224$	−10.6706	−	18.6367i	−0.712956	−	1.24522i
$225$	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	−0.933442	−	0.358728i	$-0.883211\pi$
$227$	−11.7125	−	20.2867i	−0.777388	−	1.34648i	0.156054	−	0.987749i	$-0.450123\pi$
$228$	2.73339	−	2.19384i	0.181023	−	0.145290i
$229$	6.69286	+	3.86412i	0.442276	+	0.255348i	0.704563	−	0.709642i	$-0.251143\pi$
$229$	6.69286	+	3.86412i	0.442276	+	0.255348i	−0.262286	+	0.964990i	$0.584477\pi$
$230$	−14.0366			−0.925545
$231$	−7.86498	+	20.0119i	−0.517478	+	1.31668i
$232$	−1.13172			−0.0743011
$233$	−3.53323	−	2.03991i	−0.231469	−	0.133639i	0.379780	−	0.925077i	$-0.376000\pi$
$233$	−3.53323	−	2.03991i	−0.231469	−	0.133639i	−0.611250	+	0.791438i	$0.709333\pi$
$234$	−2.91425	−	2.67026i	−0.190510	−	0.174561i
$235$	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
$238$	22.6458	+	0.0815851i	1.46791	+	0.00528837i
$239$			5.76281i			0.372765i	0.982477	+	0.186383i	$0.0596764\pi$
$239$			5.76281i			0.372765i	−0.982477	+	0.186383i	$0.940324\pi$
$240$	−2.14924	+	5.52698i	−0.138733	+	0.356765i
$241$	−17.6840	+	10.2098i	−1.13912	+	0.657674i	−0.946214	−	0.323542i	$-0.895126\pi$
$241$	−17.6840	+	10.2098i	−1.13912	+	0.657674i	−0.192911	+	0.981216i	$0.561793\pi$
$242$	−19.6799	+	11.3622i	−1.26507	+	0.730390i
$243$	−3.70621	−	15.1415i	−0.237754	−	0.971325i
$244$			11.6923i			0.748525i
$245$	3.54359	−	6.03680i	0.226392	−	0.385677i
$246$	−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
$249$	−2.99614	−	3.73301i	−0.189873	−	0.236570i
$250$	−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	$0.544603\pi$
$252$	−5.32226	−	17.0929i	−0.335271	−	1.07675i
$253$	−31.9268			−2.00722
$254$	30.1012	+	17.3790i	1.88872	+	1.09045i
$255$	−4.49840	−	5.60472i	−0.281700	−	0.350981i
$256$	−5.58338	−	9.67069i	−0.348961	−	0.604418i
$257$	−12.7539	+	22.0904i	−0.795565	+	1.37796i	0.126915	+	0.991914i	$0.459492\pi$
$257$	−12.7539	+	22.0904i	−0.795565	+	1.37796i	−0.922480	+	0.386045i	$0.873841\pi$
$258$	−1.71189	−	11.1213i	−0.106578	−	0.692381i
$259$	26.0260	+	15.1514i	1.61718	+	0.941463i
$260$			1.44055i			0.0893389i
$261$	6.28953	+	1.39417i	0.389312	+	0.0862971i
$262$	24.7779	−	14.3055i	1.53078	−	0.883798i
$263$	−0.310020	+	0.178990i	−0.0191166	+	0.0110370i	−0.509528	−	0.860454i	$-0.670180\pi$
$263$	−0.310020	+	0.178990i	−0.0191166	+	0.0110370i	0.490411	+	0.871491i	$0.336847\pi$
$264$	1.55229	−	3.99187i	0.0955368	−	0.245683i
$265$		−	2.26538i		−	0.139161i
$266$	−4.24942	+	2.43304i	−0.260549	+	0.149179i
$267$	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	0.706030	−	0.708182i	$-0.250484\pi$
$269$	−4.26905	−	7.39421i	−0.260288	−	0.450833i	−0.966319	+	0.257349i	$0.917151\pi$
$270$	−5.95481	+	8.91281i	−0.362398	+	0.542416i
$271$	−7.30474	−	4.21739i	−0.443731	−	0.256188i	0.261448	−	0.965218i	$-0.415800\pi$
$271$	−7.30474	−	4.21739i	−0.443731	−	0.256188i	−0.705179	+	0.709029i	$0.749133\pi$
$272$	14.2061			0.861369
$273$	1.82377	+	2.28915i	0.110380	+	0.138546i
$274$	−8.94940			−0.540653
$275$	−4.06348	−	2.34605i	−0.245037	−	0.141472i
$276$	20.7306	−	16.6385i	1.24783	−	1.00152i
$277$	−5.05294	−	8.75195i	−0.303602	−	0.525853i	0.673347	−	0.739326i	$-0.264856\pi$
$277$	−5.05294	−	8.75195i	−0.303602	−	0.525853i	−0.976949	+	0.213473i	$0.931523\pi$
$278$	11.3078	−	19.5857i	0.678198	−	1.17467i
$279$	−2.10909	−	6.68851i	−0.126268	−	0.400431i
$280$	−0.701526	+	1.20503i	−0.0419242	+	0.0720144i
$281$			15.1554i			0.904094i	0.891994	+	0.452047i	$0.149306\pi$
$281$			15.1554i			0.904094i	−0.891994	+	0.452047i	$0.850694\pi$
$282$	−22.6760	−	8.81787i	−1.35034	−	0.525096i
$283$	20.7322	−	11.9697i	1.23240	−	0.711527i	0.264871	−	0.964284i	$-0.414671\pi$
$283$	20.7322	−	11.9697i	1.23240	−	0.711527i	0.967530	+	0.252757i	$0.0813373\pi$
$284$	−2.39866	+	1.38487i	−0.142334	+	0.0821768i
$285$	1.44830	+	0.563191i	0.0857900	+	0.0333605i
$286$			6.18202i			0.365551i
$287$	−0.0391393	+	10.8640i	−0.00231032	+	0.641283i
$288$	−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
$291$	−17.4366	+	13.9947i	−1.02215	+	0.820386i
$292$	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	$0.287169\pi$
$294$	3.62691	+	24.7467i	0.211526	+	1.44326i
$295$	−0.508109			−0.0295833
$296$	−5.19508	−	2.99938i	−0.301958	−	0.174335i
$297$	−13.5444	+	20.2725i	−0.785929	+	1.17633i
$298$	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
$301$	−0.0300174	+	8.33204i	−0.00173018	+	0.480251i
$302$			27.7671i			1.59782i
$303$	−5.67462	+	14.5929i	−0.325999	+	0.838339i
$304$	−2.66019	+	1.53586i	−0.152572	+	0.0880877i
$305$	−4.48946	+	2.59199i	−0.257065	+	0.148417i
$306$	25.0696	+	5.55707i	1.43314	+	0.317676i
$307$		−	24.2817i		−	1.38583i	−0.721019	−	0.692916i	$-0.756326\pi$
$307$		−	24.2817i		−	1.38583i	0.721019	−	0.692916i	$-0.243674\pi$
$308$	−14.0872	+	24.1980i	−0.802691	+	1.37881i
$309$	−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	0.747316	−	0.664469i	$-0.231342\pi$
$311$	−3.55858	−	6.16364i	−0.201789	−	0.349508i	−0.949105	+	0.314960i	$0.898009\pi$
$312$	−0.364926	−	0.454675i	−0.0206598	−	0.0257409i
$313$	3.07200	+	1.77362i	0.173640	+	0.100251i	0.584301	−	0.811537i	$-0.301369\pi$
$313$	3.07200	+	1.77362i	0.173640	+	0.100251i	−0.410661	+	0.911788i	$0.634702\pi$
$314$	16.1177			0.909575
$315$	5.38322	−	5.83275i	0.303310	−	0.328638i
$316$	−20.4823			−1.15222
$317$	18.2527	+	10.5382i	1.02517	+	0.591885i	0.915599	−	0.402093i	$-0.131717\pi$
$317$	18.2527	+	10.5382i	1.02517	+	0.591885i	0.109576	+	0.993978i	$0.465051\pi$
$318$	5.06645	+	6.31249i	0.284112	+	0.353987i
$319$	−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
$322$	−32.2285	+	18.4527i	−1.79603	+	1.02833i
$323$		−	3.72259i		−	0.207130i
$324$	−1.77033	−	20.2219i	−0.0983517	−	1.12344i
$325$	−0.553120	+	0.319344i	−0.0306816	+	0.0177140i
$326$	29.7970	−	17.2033i	1.65030	−	0.952802i
$327$	0.853016	−	2.19362i	0.0471719	−	0.121307i
$328$		−	2.16407i		−	0.119491i
$329$	15.5698	+	9.06418i	0.858391	+	0.499724i
$330$	16.5698	−	2.55057i	0.912138	−	0.140404i
$331$	7.40412	−	12.8243i	0.406967	−	0.704888i	−0.587581	−	0.809165i	$-0.699920\pi$
$331$	7.40412	−	12.8243i	0.406967	−	0.704888i	0.994548	+	0.104277i	$0.0332529\pi$
$332$	−3.11660	−	5.39811i	−0.171046	−	0.296260i
$333$	25.1767	+	23.0689i	1.37967	+	1.26417i
$334$	0.830926	+	0.479736i	0.0454663	+	0.0262500i
$335$	4.82849			0.263809
$336$	2.33111	+	15.5156i	0.127172	+	0.846444i
$337$	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
$339$	16.1270	−	12.9436i	0.875897	−	0.703001i
$340$	−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
$343$	0.200161	−	18.5192i	0.0108077	−	0.999942i
$344$		−	1.65971i		−	0.0894854i
$345$	10.9842	+	4.27136i	0.591371	+	0.229962i
$346$	19.9806	−	11.5358i	1.07416	−	0.620168i
$347$	−13.7103	+	7.91567i	−0.736010	+	0.424935i	−0.820617	−	0.571479i	$-0.806370\pi$
$347$	−13.7103	+	7.91567i	−0.736010	+	0.424935i	0.0846070	+	0.996414i	$0.473037\pi$
$348$	7.81869	+	3.04040i	0.419126	+	0.162982i
$349$			8.96019i			0.479628i	0.970819	+	0.239814i	$0.0770865\pi$
$349$			8.96019i			0.479628i	−0.970819	+	0.239814i	$0.922914\pi$
$350$	−5.45783	−	0.0196627i	−0.291734	−	0.00105101i
$351$	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	0.629514	−	0.776989i	$-0.283254\pi$
$353$	−6.72876	−	11.6545i	−0.358136	−	0.620309i	−0.987649	+	0.156680i	$0.949921\pi$
$354$	1.41585	−	1.13637i	0.0752516	−	0.0603975i
$355$	−1.06348	−	0.614002i	−0.0564438	−	0.0325878i
$356$	31.1286			1.64981
$357$	−17.6965	−	6.95502i	−0.936600	−	0.368099i
$358$	−0.510954			−0.0270048
$359$	4.85824	+	2.80491i	0.256408	+	0.148037i	0.622695	−	0.782465i	$-0.286038\pi$
$359$	4.85824	+	2.80491i	0.256408	+	0.148037i	−0.366287	+	0.930502i	$0.619371\pi$
$360$	−1.06811	+	1.16571i	−0.0562945	+	0.0614381i
$361$	−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
$364$	1.89376	+	3.30755i	0.0992600	+	0.173363i
$365$			14.4565i			0.756689i
$366$	6.71299	−	17.2631i	0.350894	−	0.902359i
$367$	−1.71154	+	0.988156i	−0.0893415	+	0.0515813i	−0.544005	−	0.839082i	$-0.683093\pi$
$367$	−1.71154	+	0.988156i	−0.0893415	+	0.0515813i	0.454664	+	0.890663i	$0.349759\pi$
$368$	−20.1755	+	11.6483i	−1.05172	+	0.607210i
$369$	−2.66592	+	12.0268i	−0.138782	+	0.626090i
$370$		−	23.4806i		−	1.22070i
$371$	−2.97809	−	5.20139i	−0.154615	−	0.270043i
$372$	−1.38940	−	9.02623i	−0.0720370	−	0.467988i
$373$	11.5467	−	19.9995i	0.597866	−	1.03553i	−0.395270	−	0.918565i	$-0.629349\pi$
$373$	11.5467	−	19.9995i	0.597866	−	1.03553i	0.993136	−	0.116969i	$-0.0373177\pi$
$374$	−20.0808	−	34.7809i	−1.03835	−	1.79848i
$375$	1.08415	+	1.35078i	0.0559853	+	0.0697542i
$376$	−3.10790	−	1.79435i	−0.160278	−	0.0925364i
$377$	−1.37152			−0.0706368
$378$	−1.95558	+	28.2924i	−0.100584	+	1.45520i
$379$	−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
$381$	−18.2671	−	22.7597i	−0.935851	−	1.16601i
$382$	17.5759	+	30.4423i	0.899259	+	1.55756i
$383$	−13.3056	+	23.0460i	−0.679886	+	1.17760i	0.295129	+	0.955457i	$0.404637\pi$
$383$	−13.3056	+	23.0460i	−0.679886	+	1.17760i	−0.975015	+	0.222139i	$0.928696\pi$
$384$	−1.10193	−	7.15869i	−0.0562327	−	0.365316i
$385$	−12.4141	−	0.0447235i	−0.632679	−	0.00227932i
$386$			5.82479i			0.296474i
$387$	−2.04460	+	9.22382i	−0.103933	+	0.468873i
$388$	−25.2141	+	14.5574i	−1.28005	+	0.739040i
$389$	−8.20951	+	4.73976i	−0.416239	+	0.240316i	−0.693467	−	0.720489i	$-0.743918\pi$
$389$	−8.20951	+	4.73976i	−0.416239	+	0.240316i	0.277228	+	0.960804i	$0.410584\pi$
$390$	0.827069	−	2.12689i	0.0418803	−	0.107699i
$391$		−	28.2329i		−	1.42780i
$392$	−0.0265810	+	3.68904i	−0.00134254	+	0.186324i
$393$	−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
$396$	−21.4485	+	23.4083i	−1.07783	+	1.17631i
$397$	10.7042	+	6.18009i	0.537230	+	0.310170i	0.743956	−	0.668229i	$-0.232947\pi$
$397$	10.7042	+	6.18009i	0.537230	+	0.310170i	−0.206726	+	0.978399i	$0.566281\pi$
$398$	−25.1963			−1.26297
$399$	4.06574	−	0.610849i	0.203541	−	0.0305807i
$400$	−3.42378			−0.171189
$401$	−7.11494	−	4.10781i	−0.355303	−	0.205134i	0.311715	−	0.950176i	$-0.399096\pi$
$401$	−7.11494	−	4.10781i	−0.355303	−	0.205134i	−0.667019	+	0.745041i	$0.732430\pi$
$402$	−13.4546	+	10.7988i	−0.671056	+	0.538595i
$403$	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
$406$	−10.1288	−	5.89664i	−0.502686	−	0.292646i
$407$		−	53.4076i		−	2.64732i
$408$	3.53002	+	1.37269i	0.174762	+	0.0679584i
$409$	−17.9575	+	10.3678i	−0.887942	+	0.512653i	−0.873269	−	0.487239i	$-0.838004\pi$
$409$	−17.9575	+	10.3678i	−0.887942	+	0.512653i	−0.0146731	+	0.999892i	$0.504671\pi$
$410$	7.33583	−	4.23534i	0.362291	−	0.209169i
$411$	7.00330	+	2.72332i	0.345447	+	0.134331i
$412$		−	35.0064i		−	1.72464i
$413$	−1.16664	+	0.667967i	−0.0574065	+	0.0328685i
$414$	−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
$417$	−14.8088	+	11.8857i	−0.725192	+	0.582045i
$418$	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	$0.554216\pi$
$420$	8.08397	−	6.44051i	0.394457	−	0.314265i
$421$	−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
$423$	15.0617	+	13.8007i	0.732325	+	0.671014i
$424$	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
$427$	−6.90050	+	11.8532i	−0.333939	+	0.573617i
$428$			12.0847i			0.584137i
$429$	1.88120	−	4.83770i	0.0908253	−	0.233566i
$430$	5.62613	−	3.24825i	0.271316	−	0.156645i
$431$	26.9043	−	15.5332i	1.29594	−	0.748209i	0.316236	−	0.948681i	$-0.397581\pi$
$431$	26.9043	−	15.5332i	1.29594	−	0.748209i	0.979699	+	0.200472i	$0.0642475\pi$
$432$	−1.16281	+	17.7524i	−0.0559456	+	0.854114i
$433$			22.3083i			1.07207i	0.844196	+	0.536034i	$0.180078\pi$
$433$			22.3083i			1.07207i	−0.844196	+	0.536034i	$0.819922\pi$
$434$	−0.0459658	+	12.7589i	−0.00220643	+	0.612446i
$435$	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
$438$	−32.3316	−	40.2832i	−1.54486	−	1.92481i
$439$	−22.4126	−	12.9399i	−1.06970	−	0.617590i	−0.141598	−	0.989924i	$-0.545224\pi$
$439$	−22.4126	−	12.9399i	−1.06970	−	0.617590i	−0.928099	+	0.372334i	$0.878557\pi$
$440$	2.47283			0.117887
$441$	4.69226	−	20.4691i	0.223441	−	0.974717i
$442$	−5.46677			−0.260028
$443$	26.8166	+	15.4826i	1.27409	+	0.735599i	0.975756	−	0.218862i	$-0.0702343\pi$
$443$	26.8166	+	15.4826i	1.27409	+	0.735599i	0.298338	+	0.954460i	$0.403568\pi$
$444$	27.8332	+	34.6785i	1.32091	+	1.64577i
$445$	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
$448$	−0.0943310	+	26.1838i	−0.00445672	+	1.23707i
$449$		−	24.2032i		−	1.14222i	−0.820874	−	0.571110i	$-0.806513\pi$
$449$		−	24.2032i		−	1.14222i	0.820874	−	0.571110i	$-0.193487\pi$
$450$	−6.04198	−	1.33930i	−0.284822	−	0.0631351i
$451$	16.6856	−	9.63346i	0.785696	−	0.453622i
$452$	23.3204	−	13.4640i	1.09690	−	0.633295i
$453$	8.44959	−	21.7290i	0.396996	−	1.02092i
$454$			48.3231i			2.26792i
$455$	−0.850172	+	1.46036i	−0.0398567	+	0.0684630i
$456$	−0.809428	+	0.124594i	−0.0379049	+	0.00583467i
$457$	1.20726	−	2.09103i	0.0564731	−	0.0978143i	−0.836407	−	0.548109i	$-0.815348\pi$
$457$	1.20726	−	2.09103i	0.0564731	−	0.0978143i	0.892880	+	0.450295i	$0.148681\pi$
$458$	−7.97122	−	13.8066i	−0.372471	−	0.645138i
$459$	−17.9270	−	11.9774i	−0.836763	−	0.559056i
$460$	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	$0.555533\pi$
$462$	34.6919	−	27.6391i	1.61401	−	1.28589i
$463$	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
$465$	3.15776	−	2.53444i	0.146437	−	0.117532i
$466$	4.20809	+	7.28862i	0.194936	+	0.337639i
$467$	10.0692	−	17.4404i	0.465948	−	0.807045i	−0.533296	−	0.845929i	$-0.679047\pi$
$467$	10.0692	−	17.4404i	0.465948	−	0.807045i	0.999244	+	0.0388836i	$0.0123802\pi$
$468$	1.29966	+	4.12158i	0.0600767	+	0.190520i
$469$	11.0864	−	6.34759i	0.511923	−	0.293105i
$470$		−	14.0470i		−	0.647942i
$471$	−12.6128	−	4.90465i	−0.581167	−	0.225994i
$472$	0.231907	−	0.133892i	0.0106744	−	0.00616286i
$473$	12.7969	−	7.38828i	0.588401	−	0.339713i
$474$	30.2410	+	11.7596i	1.38902	+	0.540136i
$475$			0.897174i			0.0411652i
$476$	−21.3983	−	12.4573i	−0.980789	−	0.570980i
$477$	−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	0.943190	+	0.332253i	$0.107809\pi$
$479$	16.6189	+	28.7847i	0.759335	+	1.31521i	−0.183855	+	0.982953i	$0.558858\pi$
$480$	10.9642	−	8.79992i	0.500443	−	0.401659i
$481$	−6.29586	−	3.63491i	−0.287066	−	0.165738i
$482$	42.1234			1.91867
$483$	30.8354	−	4.63281i	1.40306	−	0.210800i
$484$	24.8460			1.12936
$485$	−11.1791	−	6.45424i	−0.507616	−	0.293072i
$486$	−8.99634	+	30.8731i	−0.408082	+	1.40043i
$487$	16.1039	+	27.8927i	0.729736	+	1.26394i	0.956995	+	0.290105i	$0.0936902\pi$
$487$	16.1039	+	27.8927i	0.729736	+	1.26394i	−0.227259	+	0.973834i	$0.572976\pi$
$488$	1.36603	−	2.36603i	0.0618371	−	0.107105i
$489$	−28.5524	+	4.39504i	−1.29118	+	0.198751i
$490$	−12.5572	+	7.12979i	−0.567279	+	0.322091i
$491$			22.5003i			1.01542i	0.861527	+	0.507712i	$0.169509\pi$
$491$			22.5003i			1.01542i	−0.861527	+	0.507712i	$0.830491\pi$
$492$	−5.81382	+	14.9508i	−0.262107	+	0.674036i
$493$	7.71635	−	4.45504i	0.347527	−	0.200645i
$494$	1.02369	−	0.591030i	0.0460582	−	0.0265917i
$495$	−13.7427	−	3.04629i	−0.617690	−	0.136920i
$496$			8.00383i			0.359383i
$497$	−3.24897	−	0.0117049i	−0.145736	−	0.000525037i
$498$	1.50225	+	9.75939i	0.0673176	+	0.437329i
$499$	−3.20702	+	5.55472i	−0.143566	+	0.248663i	−0.928837	−	0.370489i	$-0.879190\pi$
$499$	−3.20702	+	5.55472i	−0.143566	+	0.248663i	0.785271	+	0.619152i	$0.212524\pi$
$500$	1.12774	+	1.95330i	0.0504340	+	0.0873543i
$501$	−0.504252	−	0.628266i	−0.0225283	−	0.0280689i
$502$	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	$0.821831\pi$
$504$	−0.919977	+	4.08066i	−0.0409791	+	0.181767i
$505$	−9.03979			−0.402265
$506$	57.0374	+	32.9306i	2.53562	+	1.46394i
$507$	13.6517	+	17.0092i	0.606293	+	0.755404i
$508$	−19.0015	−	32.9116i	−0.843056	−	1.46022i
$509$	6.34981	−	10.9982i	0.281450	−	0.487486i	−0.690292	−	0.723531i	$-0.742518\pi$
$509$	6.34981	−	10.9982i	0.281450	−	0.487486i	0.971742	+	0.236045i	$0.0758512\pi$
$510$	2.25548	+	14.6527i	0.0998742	+	0.648833i
$511$	19.0047	+	33.1927i	0.840719	+	1.46836i
$512$			31.3992i			1.38766i
$513$	4.65188	+	0.304705i	0.205386	+	0.0134530i
$514$	45.5698	−	26.3097i	2.01000	−	1.16047i
$515$	13.4412	−	7.76030i	0.592292	−	0.341960i
$516$	−4.45885	+	11.4664i	−0.196290	+	0.504779i
$517$		−	31.9506i		−	1.40518i
$518$	−30.8679	−	53.9124i	−1.35626	−	2.36878i
$519$	−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	−0.924200	−	0.381909i	$-0.875267\pi$
$521$	−18.0970	−	31.3449i	−0.792843	−	1.37324i	0.131357	−	0.991335i	$-0.458067\pi$
$522$	−9.79829	−	8.97798i	−0.428860	−	0.392955i
$523$	−4.27382	−	2.46749i	−0.186881	−	0.107896i	0.403640	−	0.914918i	$-0.367745\pi$
$523$	−4.27382	−	2.46749i	−0.186881	−	0.107896i	−0.590522	+	0.807022i	$0.701078\pi$
$524$	−31.2823			−1.36657
$525$	4.26501	+	1.67622i	0.186140	+	0.0731561i
$526$	0.738470			0.0321988
$527$	−8.40023	−	4.84988i	−0.365920	−	0.211264i
$528$	21.7000	−	17.4166i	0.944370	−	0.757959i
$529$	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
$532$	5.35379	+	0.0192878i	0.232116	+	0.000836234i
$533$		−	2.62261i		−	0.113598i
$534$	−45.9598	−	17.8721i	−1.98888	−	0.773399i
$535$	−4.64012	+	2.67897i	−0.200610	+	0.115822i
$536$	−2.20378	+	1.27235i	−0.0951888	+	0.0549573i
$537$	0.399844	+	0.155484i	0.0172545	+	0.00670964i
$538$			17.6131i			0.759354i
$539$	−28.5620	+	16.2170i	−1.23025	+	0.698515i
$540$	10.5110	−	5.18398i	0.452319	−	0.223083i
$541$	−8.32849	+	14.4254i	−0.358070	+	0.620195i	−0.987638	−	0.156750i	$-0.949898\pi$
$541$	−8.32849	+	14.4254i	−0.358070	+	0.620195i	0.629569	+	0.776945i	$0.283232\pi$
$542$	8.69998	+	15.0688i	0.373696	+	0.647261i
$543$	−19.3683	+	15.5451i	−0.831172	+	0.667106i
$544$	−29.1668	−	16.8394i	−1.25051	−	0.721985i
$545$	1.35887			0.0582077
$546$	−0.897057	−	5.97070i	−0.0383905	−	0.255522i
$547$	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
$549$	−10.5064	+	11.4664i	−0.448403	+	0.489373i
$550$	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
$553$	−20.7641	−	12.0881i	−0.882977	−	0.514037i
$554$			20.8472i			0.885713i
$555$	−7.14520	+	18.3746i	−0.303297	+	0.779959i
$556$	−21.4143	+	12.3636i	−0.908169	+	0.524331i
$557$	16.5937	−	9.58040i	0.703099	−	0.405935i	−0.105401	−	0.994430i	$-0.533613\pi$
$557$	16.5937	−	9.58040i	0.703099	−	0.405935i	0.808501	+	0.588495i	$0.200279\pi$
$558$	−3.13091	+	14.1245i	−0.132542	+	0.597936i
$559$		−	2.01138i		−	0.0850723i
$560$	−7.86113	+	4.50094i	−0.332193	+	0.190199i
$561$	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	0.996128	+	0.0879116i	$0.0280193\pi$
$563$	13.6243	+	23.5981i	0.574198	+	0.994540i	−0.421930	+	0.906628i	$0.638647\pi$
$564$	16.6509	+	20.7460i	0.701131	+	0.873566i
$565$	10.3394	+	5.96948i	0.434984	+	0.251138i
$566$	−49.3843			−2.07578
$567$	10.1398	−	21.5450i	0.425830	−	0.904803i
$568$	0.647181			0.0271551
$569$	−22.7124	−	13.1130i	−0.952153	−	0.549726i	−0.0584038	−	0.998293i	$-0.518601\pi$
$569$	−22.7124	−	13.1130i	−0.952153	−	0.549726i	−0.893749	+	0.448567i	$0.851934\pi$
$570$	−2.00650	−	2.49998i	−0.0840432	−	0.104713i
$571$	13.4388	+	23.2767i	0.562397	+	0.974101i	0.997287	+	0.0736170i	$0.0234542\pi$
$571$	13.4388	+	23.2767i	0.562397	+	0.974101i	−0.434889	+	0.900484i	$0.643212\pi$
$572$	3.37960	−	5.85363i	0.141308	−	0.244753i
$573$	−4.49023	−	29.1708i	−0.187582	−	1.21863i
$574$	11.2755	−	19.3683i	0.470631	−	0.808416i
$575$			6.80436i			0.283761i
$576$	−6.42524	+	28.9862i	−0.267718	+	1.20776i
$577$	−8.93069	+	5.15614i	−0.371790	+	0.214653i	−0.674240	−	0.738512i	$-0.735529\pi$
$577$	−8.93069	+	5.15614i	−0.371790	+	0.214653i	0.302450	+	0.953165i	$0.402195\pi$
$578$	0.386185	−	0.222964i	0.0160632	−	0.00927407i
$579$	1.77250	−	4.55815i	0.0736624	−	0.189430i
$580$			4.84341i			0.201112i
$581$	0.0263416	−	7.31171i	0.00109283	−	0.303341i
$582$	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
$585$	−1.29443	+	1.41271i	−0.0535183	+	0.0584082i
$586$	−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	$0.651111\pi$
$588$	10.0943	−	25.4149i	0.416283	−	1.04809i
$589$	2.09734			0.0864195
$590$	0.907741	+	0.524084i	0.0373711	+	0.0215762i
$591$	−12.9631	+	10.4043i	−0.533233	+	0.427977i
$592$	−19.4855	−	33.7498i	−0.800848	−	1.38711i
$593$	−1.45861	+	2.52638i	−0.0598978	+	0.103746i	−0.894419	−	0.447229i	$-0.852411\pi$
$593$	−1.45861	+	2.52638i	−0.0598978	+	0.103746i	0.834522	+	0.550975i	$0.185744\pi$
$594$	45.1072	−	22.2467i	1.85077	−	0.912795i
$595$	0.0395491	−	10.9778i	0.00162135	−	0.450045i
$596$		−	19.5472i		−	0.800686i
$597$	19.7172	+	7.66727i	0.806970	+	0.313800i
$598$	7.76391	−	4.48250i	0.317490	−	0.183303i
$599$	31.4551	−	18.1606i	1.28522	−	0.742023i	0.307424	−	0.951573i	$-0.400533\pi$
$599$	31.4551	−	18.1606i	1.28522	−	0.742023i	0.977798	+	0.209550i	$0.0671998\pi$
$600$	−0.850763	−	0.330830i	−0.0347323	−	0.0135061i
$601$		−	7.15198i		−	0.291735i	−0.989304	−	0.145868i	$-0.953403\pi$
$601$		−	7.15198i		−	0.291735i	0.989304	−	0.145868i	$-0.0465974\pi$
$602$	8.64763	−	14.8543i	0.352451	−	0.605416i
$603$	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
$606$	25.1894	−	20.2172i	1.02325	−	0.821269i
$607$	−37.8248	−	21.8382i	−1.53526	−	0.886384i	−0.999106	−	0.0422651i	$-0.986543\pi$
$607$	−37.8248	−	21.8382i	−1.53526	−	0.886384i	−0.536156	−	0.844119i	$-0.680124\pi$
$608$	7.28226			0.295334
$609$	6.13190	+	7.69660i	0.248477	+	0.311882i
$610$	10.6939			0.432984
$611$	−3.76643	−	2.17455i	−0.152373	−	0.0879729i
$612$	−20.7000	−	18.9670i	−0.836747	−	0.766694i
$613$	7.27926	+	12.6080i	0.294007	+	0.509234i	0.974753	−	0.223285i	$-0.0716779\pi$
$613$	7.27926	+	12.6080i	0.294007	+	0.509234i	−0.680747	+	0.732519i	$0.738345\pi$
$614$	−25.0452	+	43.3795i	−1.01074	+	1.75065i
$615$	−7.02943	+	1.08203i	−0.283454	+	0.0436318i
$616$	5.67771	−	3.25081i	0.228761	−	0.130979i
$617$		−	4.68442i		−	0.188588i	−0.995544	−	0.0942938i	$-0.969941\pi$
$617$		−	4.68442i		−	0.188588i	0.995544	−	0.0942938i	$-0.0300593\pi$
$618$	−20.0984	+	51.6851i	−0.808476	+	2.07908i
$619$	−33.0429	+	19.0773i	−1.32810	+	0.766782i	−0.985006	−	0.172518i	$-0.944810\pi$
$619$	−33.0429	+	19.0773i	−1.32810	+	0.766782i	−0.343098	+	0.939299i	$0.611476\pi$
$620$	4.56627	−	2.63634i	0.183386	−	0.105878i
$621$	35.2809	+	2.31095i	1.41577	+	0.0927350i
$622$			14.6819i			0.588689i
$623$	31.5569	+	18.3713i	1.26430	+	0.736030i
$624$	−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
$627$	−4.56388	−	5.68631i	−0.182264	−	0.227089i
$628$	−15.2615	−	8.81125i	−0.609001	−	0.351607i
$629$	47.2285			1.88312
$630$	−15.6333	+	4.86779i	−0.622845	+	0.193937i
$631$	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
$633$	6.11583	+	7.61995i	0.243082	+	0.302866i
$634$	−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
$637$	−0.0322132	+	4.47070i	−0.00127633	+	0.177136i
$638$			20.7852i			0.822895i
$639$	−3.59671	−	0.797266i	−0.142284	−	0.0315393i
$640$	3.62150	−	2.09088i	0.143152	−	0.0826491i
$641$	−20.0037	+	11.5491i	−0.790099	+	0.456164i	−0.839997	−	0.542590i	$-0.817444\pi$
$641$	−20.0037	+	11.5491i	−0.790099	+	0.456164i	0.0498985	+	0.998754i	$0.484110\pi$
$642$	6.93827	−	17.8425i	0.273832	−	0.704186i
$643$			22.7592i			0.897536i	0.893648	+	0.448768i	$0.148137\pi$
$643$			22.7592i			0.897536i	−0.893648	+	0.448768i	$0.851863\pi$
$644$	40.6043	+	0.146283i	1.60003	+	0.00576436i
$645$	−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	0.841186	−	0.540746i	$-0.181858\pi$
$647$	−1.21349	−	2.10183i	−0.0477073	−	0.0826315i	−0.888893	+	0.458115i	$0.848525\pi$
$648$	−2.00431	+	4.29888i	−0.0787367	+	0.168876i
$649$	2.06469	+	1.19205i	0.0810463	+	0.0467921i
$650$	1.31754			0.0516781
$651$	3.91852	−	9.97040i	0.153579	−	0.390771i
$652$	−37.6189			−1.47327
$653$	34.7760	+	20.0779i	1.36089	+	0.785709i	0.989742	−	0.142865i	$-0.0456315\pi$
$653$	34.7760	+	20.0779i	1.36089	+	0.785709i	0.371146	+	0.928574i	$0.378965\pi$
$654$	−3.78651	+	3.03908i	−0.148064	+	0.118837i
$655$	−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
$658$	−18.4664	−	32.2525i	−0.719896	−	1.25734i
$659$		−	0.627454i		−	0.0244421i	−0.999925	−	0.0122211i	$-0.996110\pi$
$659$		−	0.627454i		−	0.0244421i	0.999925	−	0.0122211i	$-0.00389018\pi$
$660$	−17.0840	−	6.64332i	−0.664993	−	0.258591i
$661$	−28.5745	+	16.4975i	−1.11142	+	0.641678i	−0.939197	−	0.343380i	$-0.888428\pi$
$661$	−28.5745	+	16.4975i	−1.11142	+	0.641678i	−0.172222	+	0.985058i	$0.555095\pi$
$662$	−26.4550	+	15.2738i	−1.02820	+	0.593634i
$663$	4.27799	+	1.66355i	0.166143	+	0.0646069i
$664$			1.45646i			0.0565217i
$665$	1.17944	+	2.05995i	0.0457366	+	0.0798813i
$666$	−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
$669$	−0.530017	+	0.425396i	−0.0204917	+	0.0164468i
$670$	−8.62613	−	4.98030i	−0.333257	−	0.192406i
$671$	24.3238			0.939009
$672$	13.6056	−	34.6186i	0.524849	−	1.33544i
$673$	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
$675$	4.32056	+	2.88665i	0.166299	+	0.111107i
$676$	14.2006	+	24.5961i	0.546176	+	0.946004i
$677$	−7.98910	+	13.8375i	−0.307046	+	0.531820i	−0.977715	−	0.209938i	$-0.932674\pi$
$677$	−7.98910	+	13.8375i	−0.307046	+	0.531820i	0.670669	+	0.741757i	$0.266007\pi$
$678$	−42.1615	+	6.48988i	−1.61920	+	0.249242i
$679$	−34.1524	−	0.123039i	−1.31065	−	0.00472181i
$680$			2.18673i			0.0838571i
$681$	14.7048	−	37.8150i	0.563490	−	1.44907i
$682$	19.5959	−	11.3137i	0.750366	−	0.433224i
$683$	1.96122	−	1.13231i	0.0750442	−	0.0433268i	−0.462008	−	0.886876i	$-0.652871\pi$
$683$	1.96122	−	1.13231i	0.0750442	−	0.0433268i	0.537053	+	0.843549i	$0.319538\pi$
$684$	5.92680	+	1.31377i	0.226617	+	0.0502331i
$685$			4.33830i			0.165758i
$686$	−19.4590	+	32.8782i	−0.742949	+	1.25530i
$687$	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
$690$	−15.2178	−	18.9604i	−0.579330	−	0.721810i
$691$	−2.40044	−	1.38589i	−0.0913169	−	0.0527218i	0.453646	−	0.891182i	$-0.350123\pi$
$691$	−2.40044	−	1.38589i	−0.0913169	−	0.0527218i	−0.544963	+	0.838460i	$0.683456\pi$
$692$	−25.2256			−0.958934
$693$	−35.5585	+	11.0720i	−1.35076	+	0.420590i
$694$	32.6582			1.23969
$695$	−9.49436	−	5.48157i	−0.360141	−	0.207928i
$696$	−1.22695	−	1.52871i	−0.0465076	−	0.0579456i
$697$	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
$700$	5.15716	+	3.00231i	0.194922	+	0.113477i
$701$			23.1184i			0.873169i	0.899663	+	0.436585i	$0.143812\pi$
$701$			23.1184i			0.873169i	−0.899663	+	0.436585i	$0.856188\pi$
$702$	0.447471	−	6.83148i	0.0168887	−	0.257838i
$703$	−8.84388	+	5.10602i	−0.333553	+	0.192577i
$704$	40.2147	−	23.2180i	1.51565	−	0.875060i
$705$	−4.27454	+	10.9924i	−0.160989	+	0.413998i
$706$			27.7612i			1.04481i
$707$	−20.7557	+	11.8838i	−0.780599	+	0.446937i
$708$	−1.96187	+	0.301989i	−0.0737317	+	0.0113495i
$709$	18.0134	−	31.2002i	0.676508	−	1.17175i	−0.299517	−	0.954091i	$-0.596826\pi$
$709$	18.0134	−	31.2002i	0.676508	−	1.17175i	0.976026	−	0.217656i	$-0.0698410\pi$
$710$	1.26661	+	2.19384i	0.0475351	+	0.0823333i
$711$	−20.0864	−	18.4048i	−0.753300	−	0.690234i
$712$	−6.29910	−	3.63678i	−0.236069	−	0.136294i
$713$	15.9067			0.595710
$714$	24.4413	+	30.6781i	0.914692	+	1.14810i
$715$	2.99679			0.112074
$716$	0.483812	+	0.279329i	0.0180809	+	0.0104390i
$717$	−7.78431	+	6.24775i	−0.290710	+	0.233326i
$718$	−5.78619	−	10.0220i	−0.215939	−	0.374017i
$719$	−8.57099	+	14.8454i	−0.319644	+	0.553640i	−0.980414	−	0.196949i	$-0.936897\pi$
$719$	−8.57099	+	14.8454i	−0.319644	+	0.553640i	0.660770	+	0.750589i	$0.270230\pi$
$720$	−9.79586	+	3.08892i	−0.365070	+	0.115117i
$721$	20.6598	−	35.4880i	0.769412	−	1.32164i
$722$			37.5343i			1.39688i
$723$	−32.9634	−	12.8182i	−1.22592	−	0.476715i
$724$	−28.0075	+	16.1701i	−1.04089	+	0.600958i
$725$	−1.85970	+	1.07370i	−0.0690676	+	0.0398762i
$726$	−36.6838	−	14.2650i	−1.36147	−	0.529423i
$727$			16.6832i			0.618747i	0.950941	+	0.309374i	$0.100119\pi$
$727$			16.6832i			0.618747i	−0.950941	+	0.309374i	$0.899881\pi$
$728$	0.00320836	−	0.890556i	0.000118910	−	0.0330062i
$729$	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
$732$	−15.7938	+	12.6763i	−0.583757	+	0.468528i
$733$	32.9814	+	19.0418i	1.21820	+	0.703326i	0.964532	−	0.263967i	$-0.0850309\pi$
$733$	32.9814	+	19.0418i	1.21820	+	0.703326i	0.253664	+	0.967292i	$0.418364\pi$
$734$	4.07690			0.150481
$735$	11.9962	−	1.75818i	0.442487	−	0.0648513i
$736$	55.2302			2.03581
$737$	−19.6205	−	11.3279i	−0.722730	−	0.417268i
$738$	17.1676	−	18.7362i	0.631948	−	0.689689i
$739$	11.2186	+	19.4312i	0.412684	+	0.714790i	0.995182	−	0.0980422i	$-0.0312580\pi$
$739$	11.2186	+	19.4312i	0.412684	+	0.714790i	−0.582498	+	0.812832i	$0.697925\pi$
$740$	−12.8364	+	22.2333i	−0.471876	+	0.817313i
$741$	−0.980937	+	0.150995i	−0.0360356	+	0.00554693i
$742$	−0.0445433	+	12.3640i	−0.00163524	+	0.453898i
$743$		−	6.39189i		−	0.234496i	−0.993103	−	0.117248i	$-0.962593\pi$
$743$		−	6.39189i		−	0.234496i	0.993103	−	0.117248i	$-0.0374072\pi$
$744$	−0.773388	+	1.98885i	−0.0283538	+	0.0729146i
$745$	7.50546	−	4.33328i	0.274979	−	0.158759i
$746$	−41.2565	+	23.8195i	−1.51051	+	0.872093i
$747$	1.79422	−	8.09428i	0.0656472	−	0.296154i
$748$			43.9111i			1.60555i
$749$	−7.13207	+	12.2510i	−0.260600	+	0.447641i
$750$	−0.543588	−	3.53142i	−0.0198490	−	0.128949i
$751$	5.49944	−	9.52531i	0.200677	−	0.347583i	−0.748069	−	0.663620i	$-0.769019\pi$
$751$	5.49944	−	9.52531i	0.200677	−	0.347583i	0.948747	+	0.316037i	$0.102352\pi$
$752$	−11.6570	−	20.1905i	−0.425086	−	0.736271i
$753$	−4.79784	−	5.97781i	−0.174843	−	0.217844i
$754$	2.45023	+	1.41464i	0.0892320	+	0.0515181i
$755$	13.4604			0.489873
$756$	17.3186	−	25.7204i	0.629873	−	0.935443i
$757$	−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
$759$	−34.6134	−	43.1262i	−1.25639	−	1.56538i
$760$	−0.236414	−	0.409481i	−0.00857563	−	0.0148534i
$761$	6.54766	−	11.3409i	0.237352	−	0.411106i	−0.722601	−	0.691265i	$-0.757054\pi$
$761$	6.54766	−	11.3409i	0.237352	−	0.411106i	0.959954	+	0.280159i	$0.0903871\pi$
$762$	9.15904	+	59.5017i	0.331797	+	2.15552i
$763$	3.12002	−	1.78639i	0.112952	−	0.0646717i
$764$		−	38.4336i		−	1.39048i
$765$	2.69384	−	12.1527i	0.0973959	−	0.439383i
$766$	47.5412	−	27.4479i	1.71773	−	0.991734i
$767$	0.281045	−	0.162262i	0.0101480	−	0.00585893i
$768$	7.00980	−	18.0264i	0.252944	−	0.650472i
$769$			7.74247i			0.279201i	0.990208	+	0.139600i	$0.0445818\pi$
$769$			7.74247i			0.279201i	−0.990208	+	0.139600i	$0.955418\pi$
$770$	22.1317	+	12.8843i	0.797571	+	0.464317i
$771$	−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	−0.971963	−	0.235135i	$-0.924447\pi$
$773$	−19.1733	−	33.2091i	−0.689614	−	1.19445i	0.282349	−	0.959312i	$-0.408887\pi$
$774$	13.1665	−	14.3695i	0.473261	−	0.516502i
$775$	2.02453	+	1.16886i	0.0727231	+	0.0419867i
$776$	6.80301			0.244214
$777$	7.74983	+	51.5820i	0.278024	+	1.85049i
$778$	19.5551			0.701086
$779$	−3.19045	−	1.84201i	−0.114310	−	0.0659967i
$780$	−1.94587	+	1.56177i	−0.0696732	+	0.0559203i
$781$	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
$784$	−12.1325	+	20.6687i	−0.433302	+	0.738167i
$785$		−	7.81320i		−	0.278865i
$786$	46.1866	+	17.9603i	1.64742	+	0.640621i
$787$	−21.6178	+	12.4811i	−0.770592	+	0.444901i	−0.833086	−	0.553144i	$-0.813428\pi$
$787$	−21.6178	+	12.4811i	−0.770592	+	0.444901i	0.0624938	+	0.998045i	$0.480095\pi$
$788$	−18.7453	+	10.8226i	−0.667775	+	0.385540i
$789$	−0.577885	−	0.224718i	−0.0205732	−	0.00800016i
$790$			18.7333i			0.666500i
$791$	31.5873	+	0.113798i	1.12312	+	0.00404619i
$792$	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
$795$	3.06003	−	2.45601i	0.108528	−	0.0871056i
$796$	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	$0.532823\pi$
$798$	−7.89352	−	3.10228i	−0.279428	−	0.109819i
$799$	28.2539			0.999552
$800$	7.02943	+	4.05844i	0.248528	+	0.143488i
$801$	30.5270	+	27.9713i	1.07862	+	0.988318i
$802$	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
$805$	8.94509	+	15.6231i	0.315273	+	0.550641i
$806$		−	3.08003i		−	0.108490i
$807$	5.35969	−	13.7830i	0.188670	−	0.485184i
$808$	4.12586	−	2.38207i	0.145147	−	0.0838009i
$809$	−1.51563	+	0.875048i	−0.0532866	+	0.0307650i	−0.526407	−	0.850233i	$-0.676461\pi$
$809$	−1.51563	+	0.875048i	−0.0532866	+	0.0307650i	0.473120	+	0.880998i	$0.343128\pi$
$810$	−18.4952	+	1.61916i	−0.649855	+	0.0568915i
$811$		−	28.4479i		−	0.998940i	−0.866331	−	0.499470i	$-0.833528\pi$
$811$		−	28.4479i		−	0.998940i	0.866331	−	0.499470i	$-0.166472\pi$
$812$	6.36721	+	11.1207i	0.223445	+	0.390259i
$813$	−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
$816$	15.4015	+	19.1893i	0.539161	+	0.671761i
$817$	−2.44688	−	1.41271i	−0.0856055	−	0.0494244i
$818$	42.7750			1.49559
$819$	−1.11491	+	4.94531i	−0.0389581	+	0.172803i
$820$	−9.26153			−0.323427
$821$	−25.9378	−	14.9752i	−0.905236	−	0.522638i	−0.0263407	−	0.999653i	$-0.508385\pi$
$821$	−25.9378	−	14.9752i	−0.905236	−	0.522638i	−0.878895	+	0.477015i	$0.841719\pi$
$822$	−9.70250	−	12.0887i	−0.338413	−	0.421642i
$823$	−8.06283	−	13.9652i	−0.281053	−	0.486798i	0.690592	−	0.723245i	$-0.257350\pi$
$823$	−8.06283	−	13.9652i	−0.281053	−	0.486798i	−0.971644	+	0.236447i	$0.924017\pi$
$824$	−4.08982	+	7.08378i	−0.142476	+	0.246775i
$825$	−1.23641	−	8.03236i	−0.0430464	−	0.279651i
$826$	2.77318	+	0.00999078i	0.0964911	+	0.000347624i
$827$		−	15.9844i		−	0.555831i	−0.960605	−	0.277916i	$-0.910356\pi$
$827$		−	15.9844i		−	0.555831i	0.960605	−	0.277916i	$-0.0896436\pi$
$828$	44.9501	+	9.96389i	1.56213	+	0.346269i
$829$	18.0763	−	10.4363i	0.627815	−	0.362469i	−0.152091	−	0.988367i	$-0.548601\pi$
$829$	18.0763	−	10.4363i	0.627815	−	0.362469i	0.779905	+	0.625898i	$0.215267\pi$
$830$	−4.93717	+	2.85047i	−0.171372	+	0.0989414i
$831$	6.34385	−	16.3139i	0.220066	−	0.565921i
$832$		−	6.32084i		−	0.219136i
$833$	−14.3407	−	25.2574i	−0.496876	−	0.875117i
$834$	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
$837$	6.74817	−	10.1003i	0.233251	−	0.349116i
$838$	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	$0.420887\pi$
$840$	−2.38830	+	0.358825i	−0.0824041	+	0.0123806i
$841$	24.3887			0.840989
$842$	27.1839	+	15.6946i	0.936819	+	0.540873i
$843$	−20.4716	+	16.4307i	−0.705081	+	0.565903i
$844$	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
$847$	25.1878	+	14.6634i	0.865464	+	0.503842i
$848$			7.75614i			0.266347i
$849$	38.6453	+	15.0277i	1.32630	+	0.515750i
$850$	−7.41264	+	4.27969i	−0.254252	+	0.146792i
$851$	−67.0739	+	38.7251i	−2.29926	+	1.32748i
$852$	−4.47117	−	1.73867i	−0.153180	−	0.0595658i
$853$		−	49.6034i		−	1.69839i	−0.528081	−	0.849194i	$-0.677088\pi$
$853$		−	49.6034i		−	1.69839i	0.528081	−	0.849194i	$-0.322912\pi$
$854$	24.5537	−	14.0584i	0.840209	−	0.481067i
$855$	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	0.817752	−	0.575571i	$-0.195220\pi$
$857$	−2.62252	−	4.54233i	−0.0895834	−	0.155163i	−0.907335	+	0.420408i	$0.861887\pi$
$858$	−8.35058	+	6.70224i	−0.285084	+	0.228811i
$859$	−10.1722	−	5.87292i	−0.347071	−	0.200382i	0.316323	−	0.948651i	$-0.397552\pi$
$859$	−10.1722	−	5.87292i	−0.347071	−	0.200382i	−0.663394	+	0.748270i	$0.730885\pi$
$860$	−7.10303			−0.242211
$861$	−14.7174	+	11.7254i	−0.501567	+	0.399599i
$862$	−64.0863			−2.18279
$863$	−30.3896	−	17.5454i	−1.03447	−	0.597254i	−0.116211	−	0.993225i	$-0.537075\pi$
$863$	−30.3896	−	17.5454i	−1.03447	−	0.597254i	−0.918263	+	0.395971i	$0.870408\pi$
$864$	23.4306	−	35.0695i	0.797124	−	1.19309i
$865$	−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
$868$	7.01857	−	12.0560i	0.238226	−	0.409208i
$869$			42.6096i			1.44543i
$870$	2.78078	−	7.15105i	0.0942771	−	0.242443i
$871$	−2.67074	+	1.54195i	−0.0904944	+	0.0522470i
$872$	−0.620205	+	0.358076i	−0.0210028	+	0.0121260i
$873$	−37.8077	−	8.38066i	−1.27960	−	0.283642i
$874$		−	12.5933i		−	0.425973i
$875$	−0.00953166	+	2.64573i	−0.000322229	+	0.0894421i
$876$	8.59208	+	55.8184i	0.290299	+	1.88593i
$877$	8.42662	−	14.5953i	0.284547	−	0.492850i	−0.687952	−	0.725756i	$-0.741490\pi$
$877$	8.42662	−	14.5953i	0.284547	−	0.492850i	0.972499	+	0.232906i	$0.0748235\pi$
$878$	26.6936	+	46.2346i	0.900864	+	1.56034i
$879$	23.0081	+	28.6667i	0.776045	+	0.966905i
$880$	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	$0.160852\pi$
$882$	−29.4954	+	31.7283i	−0.993161	+	1.06835i
$883$	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
$885$	−0.550867	−	0.686346i	−0.0185172	−	0.0230713i
$886$	−31.9387	−	55.3194i	−1.07300	−	1.85849i
$887$	6.59427	−	11.4216i	0.221414	−	0.383500i	−0.733824	−	0.679340i	$-0.762266\pi$
$887$	6.59427	−	11.4216i	0.221414	−	0.383500i	0.955238	+	0.295840i	$0.0955994\pi$
$888$	−1.58073	−	10.2692i	−0.0530458	−	0.344612i
$889$	0.160601	−	44.5785i	0.00538638	−	1.49512i
$890$		−	28.4705i		−	0.954335i
$891$	−42.0681	+	3.68285i	−1.40933	+	0.123380i
$892$	−0.766431	+	0.442499i	−0.0256620	+	0.0148160i
$893$	−5.29076	+	3.05462i	−0.177048	+	0.102219i
$894$	−11.2228	+	28.8605i	−0.375345	+	0.965239i
$895$			0.247690i			0.00827935i
$896$	5.56642	−	9.56161i	0.185961	−	0.319431i
$897$	−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
$900$	4.98886	+	4.57120i	0.166295	+	0.152373i
$901$	−8.14028	−	4.69979i	−0.271192	−	0.156573i
$902$	−39.7453			−1.32338
$903$	−11.2873	+	8.99264i	−0.375619	+	0.299256i
$904$	−6.29206			−0.209271
$905$	−12.4175	−	7.16927i	−0.412773	−	0.238315i
$906$	−37.5074	+	30.1037i	−1.24610	+	1.00013i
$907$	−23.4709	−	40.6527i	−0.779337	−	1.34985i	−0.932324	−	0.361623i	$-0.882223\pi$
$907$	−23.4709	−	40.6527i	−0.779337	−	1.34985i	0.152987	−	0.988228i	$-0.451111\pi$
$908$	26.4174	−	45.7562i	0.876691	−	1.51847i
$909$	−25.8640	+	8.15567i	−0.857854	+	0.270507i
$910$	3.02512	−	1.73205i	0.100282	−	0.0574169i
$911$		−	45.2977i		−	1.50078i	−0.660996	−	0.750389i	$-0.729866\pi$
$911$		−	45.2977i		−	1.50078i	0.660996	−	0.750389i	$-0.270134\pi$
$912$	−4.95867	−	1.92824i	−0.164198	−	0.0638504i
$913$	−11.2298	+	6.48352i	−0.371652	+	0.214573i
$914$	−4.31355	+	2.49043i	−0.142680	+	0.0823761i
$915$	−8.36846	−	3.25418i	−0.276653	−	0.107580i
$916$			17.4309i			0.575932i
$917$	−31.7126	−	18.4619i	−1.04724	−	0.609667i
$918$	19.6728	+	39.8884i	0.649300	+	1.31651i
$919$	−21.5911	+	37.3969i	−0.712225	+	1.23361i	0.251795	+	0.967781i	$0.418979\pi$
$919$	−21.5911	+	37.3969i	−0.712225	+	1.23361i	−0.964020	+	0.265830i	$0.914354\pi$
$920$	−1.79301	−	3.10559i	−0.0591139	−	0.102388i
$921$	32.7994	−	26.3250i	1.08078	−	0.867440i
$922$	13.3162	+	7.68811i	0.438546	+	0.253195i
$923$	0.784311			0.0258159
$924$	−47.9588	+	7.20548i	−1.57773	+	0.237043i
$925$	−11.3824			−0.374252
$926$	−24.8077	−	14.3227i	−0.815232	−	0.470675i
$927$	31.4557	−	34.3298i	1.03314	−	1.12754i
$928$	8.71510	+	15.0950i	0.286087	+	0.495517i
$929$	4.50570	−	7.80410i	0.147827	−	0.256044i	−0.782597	−	0.622529i	$-0.786105\pi$
$929$	4.50570	−	7.80410i	0.147827	−	0.256044i	0.930424	+	0.366484i	$0.119439\pi$
$930$	−8.25548	+	1.27076i	−0.270708	+	0.0416698i
$931$	5.41606	+	3.17922i	0.177504	+	0.104195i
$932$		−	9.20194i		−	0.301419i
$933$	4.46772	−	11.4892i	0.146267	−	0.376139i
$934$	−35.9774	+	20.7716i	−1.17722	+	0.679667i
$935$	−16.8604	+	9.73433i	−0.551392	+	0.318347i
$936$	0.218534	−	0.985871i	0.00714299	−	0.0322242i
$937$		−	21.9677i		−	0.717654i	−0.933404	−	0.358827i	$-0.883177\pi$
$937$		−	21.9677i		−	0.717654i	0.933404	−	0.358827i	$-0.116823\pi$
$938$	−26.3531	−	0.0949410i	−0.860459	−	0.00309993i
$939$	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	0.852284	−	0.523079i	$-0.175217\pi$
$941$	−0.823861	−	1.42697i	−0.0268571	−	0.0465178i	−0.879142	+	0.476561i	$0.841883\pi$
$942$	17.4740	+	21.7715i	0.569334	+	0.709355i
$943$	−24.1970	−	13.9702i	−0.787964	−	0.454931i
$944$	1.73965			0.0566209
$945$	13.7150	+	0.947985i	0.446149	+	0.0308380i
$946$	−30.4823			−0.991064
$947$	23.6645	+	13.6627i	0.768994	+	0.443979i	0.832516	−	0.554002i	$-0.186900\pi$
$947$	23.6645	+	13.6627i	0.768994	+	0.443979i	−0.0635217	+	0.997980i	$0.520233\pi$
$948$	−22.2059	−	27.6671i	−0.721213	−	0.898586i
$949$	−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
$952$	2.87470	+	5.02081i	0.0931695	+	0.162725i
$953$			55.2380i			1.78933i	0.446734	+	0.894667i	$0.352587\pi$
$953$			55.2380i			1.78933i	−0.446734	+	0.894667i	$0.647413\pi$
$954$	−3.03401	+	13.6874i	−0.0982299	+	0.443145i
$955$	14.7572	−	8.52006i	0.477531	−	0.275703i
$956$	−11.2565	+	6.49894i	−0.364061	+	0.210191i
$957$	6.32499	−	16.2653i	0.204458	−	0.525784i
$958$		−	68.5654i		−	2.21525i
$959$	5.70319	+	9.96091i	0.184166	+	0.321655i
$960$	−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
$963$	−10.8590	+	11.8512i	−0.349926	+	0.381899i
$964$	−39.8858	−	23.0281i	−1.28464	−	0.741684i
$965$	2.82362			0.0908956
$966$	−59.8661	−	23.5283i	−1.92616	−	0.757012i
$967$	−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
$969$	5.02841	−	4.03584i	0.161536	−	0.129650i
$970$	13.3143	+	23.0611i	0.427497	+	0.740447i
$971$	−2.12246	+	3.67621i	−0.0681129	+	0.117975i	−0.898071	−	0.439851i	$-0.855031\pi$
$971$	−2.12246	+	3.67621i	−0.0681129	+	0.117975i	0.829958	+	0.557826i	$0.188364\pi$
$972$	25.3962	−	24.3150i	0.814583	−	0.779903i
$973$	−29.0056	−	0.104497i	−0.929875	−	0.00335002i
$974$		−	66.4407i		−	2.12890i
$975$	−1.03103	−	0.400929i	−0.0330194	−	0.0128400i
$976$	15.3709	−	8.87439i	0.492010	−	0.284062i
$977$	33.6806	−	19.4455i	1.07754	−	0.622118i	0.147308	−	0.989091i	$-0.452939\pi$
$977$	33.6806	−	19.4455i	1.07754	−	0.622118i	0.930232	+	0.366973i	$0.119606\pi$
$978$	55.5423	+	21.5983i	1.77605	+	0.690638i
$979$		−	64.7574i		−	2.06966i
$980$	15.7879	+	0.113758i	0.504327	+	0.00363387i
$981$	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	0.996003	−	0.0893246i	$-0.0284709\pi$
$983$	13.1884	+	22.8429i	0.420644	+	0.728577i	−0.575359	+	0.817901i	$0.695138\pi$
$984$	2.92319	−	2.34617i	0.0931878	−	0.0747932i
$985$	−8.31103	−	4.79838i	−0.264812	−	0.152889i
$986$	−18.3804			−0.585352
$987$	4.63626	+	30.8584i	0.147574	+	0.982233i
$988$	−1.29242			−0.0411174
$989$	−18.5577	−	10.7143i	−0.590099	−	0.340694i
$990$	21.4094	+	19.6170i	0.680436	+	0.623470i
$991$	6.90833	+	11.9656i	0.219450	+	0.380099i	0.954640	−	0.297762i	$-0.0962403\pi$
$991$	6.90833	+	11.9656i	0.219450	+	0.380099i	−0.735190	+	0.677861i	$0.762907\pi$
$992$	9.48750	−	16.4328i	0.301228	−	0.521743i
$993$	25.3501	−	3.90211i	0.804460	−	0.123830i
$994$	5.79224	+	3.37203i	0.183719	+	0.106954i
$995$			12.2141i			0.387213i
$996$	3.91282	−	10.0622i	0.123983	−	0.318834i
$997$	53.1001	−	30.6574i	1.68170	−	0.970929i	0.721165	−	0.692763i	$-0.243607\pi$
$997$	53.1001	−	30.6574i	1.68170	−	0.970929i	0.960533	−	0.278166i	$-0.0897265\pi$
$998$	11.4587	−	6.61570i	0.362720	−	0.209416i
$999$	−3.86579	+	59.0184i	−0.122308	+	1.86726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.s.d.26.1	yes	8
3.2	odd	2		105.2.s.c.26.4	✓	8
5.2	odd	4		525.2.q.e.299.7		16
5.3	odd	4		525.2.q.e.299.2		16
5.4	even	2		525.2.t.f.26.4		8
7.2	even	3		735.2.b.c.146.7		8
7.3	odd	6		105.2.s.c.101.4	yes	8
7.4	even	3		735.2.s.k.521.4		8
7.5	odd	6		735.2.b.d.146.7		8
7.6	odd	2		735.2.s.l.656.1		8
15.2	even	4		525.2.q.f.299.2		16
15.8	even	4		525.2.q.f.299.7		16
15.14	odd	2		525.2.t.g.26.1		8
21.2	odd	6		735.2.b.d.146.2		8
21.5	even	6		735.2.b.c.146.2		8
21.11	odd	6		735.2.s.l.521.1		8
21.17	even	6	inner	105.2.s.d.101.1	yes	8
21.20	even	2		735.2.s.k.656.4		8
35.3	even	12		525.2.q.f.374.2		16
35.17	even	12		525.2.q.f.374.7		16
35.24	odd	6		525.2.t.g.101.1		8
105.17	odd	12		525.2.q.e.374.2		16
105.38	odd	12		525.2.q.e.374.7		16
105.59	even	6		525.2.t.f.101.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.4	✓	8	3.2	odd	2
105.2.s.c.101.4	yes	8	7.3	odd	6
105.2.s.d.26.1	yes	8	1.1	even	1	trivial
105.2.s.d.101.1	yes	8	21.17	even	6	inner
525.2.q.e.299.2		16	5.3	odd	4
525.2.q.e.299.7		16	5.2	odd	4
525.2.q.e.374.2		16	105.17	odd	12
525.2.q.e.374.7		16	105.38	odd	12
525.2.q.f.299.2		16	15.2	even	4
525.2.q.f.299.7		16	15.8	even	4
525.2.q.f.374.2		16	35.3	even	12
525.2.q.f.374.7		16	35.17	even	12
525.2.t.f.26.4		8	5.4	even	2
525.2.t.f.101.4		8	105.59	even	6
525.2.t.g.26.1		8	15.14	odd	2
525.2.t.g.101.1		8	35.24	odd	6
735.2.b.c.146.2		8	21.5	even	6
735.2.b.c.146.7		8	7.2	even	3
735.2.b.d.146.2		8	21.2	odd	6
735.2.b.d.146.7		8	7.5	odd	6
735.2.s.k.521.4		8	7.4	even	3
735.2.s.k.656.4		8	21.20	even	2
735.2.s.l.521.1		8	21.11	odd	6
735.2.s.l.656.1		8	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78651 - 1.03144i) q^{2} +(1.08415 + 1.35078i) q^{3} +(1.12774 + 1.95330i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} +(-0.00953166 + 2.64573i) q^{7} -0.527019i q^{8} +(-0.649237 + 2.92891i) q^{9} +O(q^{10})\)	\(q+(-1.78651 - 1.03144i) q^{2} +(1.08415 + 1.35078i) q^{3} +(1.12774 + 1.95330i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.543588 - 3.53142i) q^{6} +(-0.00953166 + 2.64573i) q^{7} -0.527019i q^{8} +(-0.649237 + 2.92891i) q^{9} +(1.78651 - 1.03144i) q^{10} +(4.06348 - 2.34605i) q^{11} +(-1.41585 + 3.64100i) q^{12} -0.638688i q^{13} +(2.74595 - 4.71679i) q^{14} +(-1.71189 + 0.263509i) q^{15} +(1.71189 - 2.96508i) q^{16} +(2.07462 + 3.59334i) q^{17} +(4.18086 - 4.56286i) q^{18} +(-0.776975 - 0.448587i) q^{19} -2.25548 q^{20} +(-3.58415 + 2.85550i) q^{21} -9.67925 q^{22} +(-5.89275 - 3.40218i) q^{23} +(0.711889 - 0.571367i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.658769 + 1.14102i) q^{26} +(-4.66019 + 2.29839i) q^{27} +(-5.17866 + 2.96508i) q^{28} -2.14740i q^{29} +(3.33010 + 1.29495i) q^{30} +(-2.02453 + 1.16886i) q^{31} +(-7.02943 + 4.05844i) q^{32} +(7.57444 + 2.94542i) q^{33} -8.55938i q^{34} +(-2.28651 - 1.33112i) q^{35} +(-6.45320 + 2.03489i) q^{36} +(5.69122 - 9.85748i) q^{37} +(0.925382 + 1.60281i) q^{38} +(0.862730 - 0.692434i) q^{39} +(0.456412 + 0.263509i) q^{40} +4.10624 q^{41} +(9.34839 - 1.40453i) q^{42} +3.14924 q^{43} +(9.16509 + 5.29147i) q^{44} +(-2.21189 - 2.02671i) q^{45} +(7.01829 + 12.1560i) q^{46} +(3.40471 - 5.89714i) q^{47} +(5.86113 - 0.902197i) q^{48} +(-6.99982 - 0.0504365i) q^{49} +2.06288i q^{50} +(-2.60464 + 6.69809i) q^{51} +(1.24755 - 0.720273i) q^{52} +(-1.96187 + 1.13269i) q^{53} +(10.6961 + 0.700610i) q^{54} +4.69211i q^{55} +(1.39435 + 0.00502336i) q^{56} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 + 3.83635i) q^{58} +(0.254055 + 0.440035i) q^{59} +(-2.44528 - 3.04666i) q^{60} +(4.48946 + 2.59199i) q^{61} +4.82244 q^{62} +(-7.74292 - 1.74563i) q^{63} +9.89660 q^{64} +(0.553120 + 0.319344i) q^{65} +(-10.4938 - 13.0746i) q^{66} +(-2.41425 - 4.18160i) q^{67} +(-4.67925 + 8.10471i) q^{68} +(-1.79301 - 11.6483i) q^{69} +(2.71189 + 4.73645i) q^{70} +1.22800i q^{71} +(1.54359 + 0.342160i) q^{72} +(12.5197 - 7.22826i) q^{73} +(-20.3348 + 11.7403i) q^{74} +(0.627739 - 1.61429i) q^{75} -2.02356i q^{76} +(6.16830 + 10.7733i) q^{77} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 + 7.86448i) q^{79} +(1.71189 + 2.96508i) q^{80} +(-8.15698 - 3.80311i) q^{81} +(-7.33583 - 4.23534i) q^{82} -2.76359 q^{83} +(-9.61963 - 3.78067i) q^{84} -4.14924 q^{85} +(-5.62613 - 3.24825i) q^{86} +(2.90067 - 2.32810i) q^{87} +(-1.23641 - 2.14153i) q^{88} +(6.90067 - 11.9523i) q^{89} +(1.86113 + 5.90216i) q^{90} +(1.68980 + 0.00608775i) q^{91} -15.3471i q^{92} +(-3.77377 - 1.46748i) q^{93} +(-12.1651 + 7.02352i) q^{94} +(0.776975 - 0.448587i) q^{95} +(-13.1030 - 5.09528i) q^{96} +12.9085i q^{97} +(12.4532 + 7.31000i) q^{98} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 2 q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 + 2 * q^7 + 4 * q^9	\( 8 q + 3 q^{2} + 2 q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} + 2 q^{7} + 4 q^{9} - 3 q^{10} - 18 q^{12} + 12 q^{14} - q^{15} + q^{16} + 12 q^{17} + 26 q^{18} + 9 q^{19} - 6 q^{20} - 22 q^{21} - 40 q^{22} - 27 q^{23} - 7 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} + 3 q^{28} + 10 q^{30} - 21 q^{31} - 21 q^{32} + 4 q^{33} - q^{35} + 9 q^{36} + 7 q^{37} + 12 q^{38} + 15 q^{39} + 3 q^{40} + 30 q^{41} - 5 q^{42} + 16 q^{43} - 5 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} + 12 q^{51} + 30 q^{52} - 24 q^{53} + 7 q^{54} + 21 q^{56} + 6 q^{57} - 13 q^{58} + 12 q^{59} + 9 q^{60} + 15 q^{61} - 24 q^{62} - 44 q^{63} + 38 q^{64} + 3 q^{65} - 16 q^{66} + 4 q^{67} + 13 q^{69} + 9 q^{70} + 13 q^{72} + 15 q^{73} - 54 q^{74} - q^{75} + 36 q^{77} - 6 q^{78} - 29 q^{79} + q^{80} + 28 q^{81} + 27 q^{82} - 30 q^{83} - 51 q^{84} - 24 q^{85} - 9 q^{86} - 29 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 3 q^{91} + 45 q^{93} - 24 q^{94} - 9 q^{95} - 42 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 + 2 * q^7 + 4 * q^9 - 3 * q^10 - 18 * q^12 + 12 * q^14 - q^15 + q^16 + 12 * q^17 + 26 * q^18 + 9 * q^19 - 6 * q^20 - 22 * q^21 - 40 * q^22 - 27 * q^23 - 7 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 + 3 * q^28 + 10 * q^30 - 21 * q^31 - 21 * q^32 + 4 * q^33 - q^35 + 9 * q^36 + 7 * q^37 + 12 * q^38 + 15 * q^39 + 3 * q^40 + 30 * q^41 - 5 * q^42 + 16 * q^43 - 5 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 + 12 * q^51 + 30 * q^52 - 24 * q^53 + 7 * q^54 + 21 * q^56 + 6 * q^57 - 13 * q^58 + 12 * q^59 + 9 * q^60 + 15 * q^61 - 24 * q^62 - 44 * q^63 + 38 * q^64 + 3 * q^65 - 16 * q^66 + 4 * q^67 + 13 * q^69 + 9 * q^70 + 13 * q^72 + 15 * q^73 - 54 * q^74 - q^75 + 36 * q^77 - 6 * q^78 - 29 * q^79 + q^80 + 28 * q^81 + 27 * q^82 - 30 * q^83 - 51 * q^84 - 24 * q^85 - 9 * q^86 - 29 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 3 * q^91 + 45 * q^93 - 24 * q^94 - 9 * q^95 - 42 * q^96 + 39 * q^98 - 34 * q^99

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