LMFDB - Embedded newform 85.3.p.a.14.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,3,Mod(14,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("85.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	85.p (of order $16$, degree $8$, 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:	$2.31608224706$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			14.14
Character	$\chi$	$=$	85.14
Dual form			85.3.p.a.79.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20149 + 2.90065i) q^{2} +(3.75496 + 0.746907i) q^{3} +(-4.14176 + 4.14176i) q^{4} +(-4.40427 - 2.36695i) q^{5} +(2.34502 + 11.7892i) q^{6} +(-0.580455 + 0.868712i) q^{7} +(-5.38745 - 2.23156i) q^{8} +(5.22691 + 2.16506i) q^{9} +(1.57401 - 15.6191i) q^{10} +(4.88661 - 0.972007i) q^{11} +(-18.6456 + 12.4586i) q^{12} +(13.2648 - 13.2648i) q^{13} +(-3.21723 - 0.639948i) q^{14} +(-14.7699 - 12.1774i) q^{15} +5.12102i q^{16} +(-8.60301 - 14.6625i) q^{17} +17.7627i q^{18} +(-17.6068 + 7.29299i) q^{19} +(28.0447 - 8.43807i) q^{20} +(-2.82843 + 2.82843i) q^{21} +(8.69065 + 13.0065i) q^{22} +(8.83254 - 1.75690i) q^{23} +(-18.5629 - 12.4033i) q^{24} +(13.7951 + 20.8493i) q^{25} +(54.4141 + 22.5391i) q^{26} +(-10.6400 - 7.10940i) q^{27} +(-1.19389 - 6.00209i) q^{28} +(-5.27556 - 7.89544i) q^{29} +(17.5764 - 57.4733i) q^{30} +(-26.3385 - 5.23906i) q^{31} +(-36.4041 + 15.0791i) q^{32} +19.0750 q^{33} +(32.1943 - 42.5711i) q^{34} +(4.61267 - 2.45213i) q^{35} +(-30.6157 + 12.6814i) q^{36} +(71.0039 + 14.1236i) q^{37} +(-42.3088 - 42.3088i) q^{38} +(59.7164 - 39.9012i) q^{39} +(18.4458 + 22.5802i) q^{40} +(-26.0834 - 17.4284i) q^{41} +(-11.6026 - 4.80595i) q^{42} +(-14.7645 + 35.6447i) q^{43} +(-16.2133 + 24.2650i) q^{44} +(-17.8961 - 21.9073i) q^{45} +(15.7083 + 23.5092i) q^{46} +(-49.2053 + 49.2053i) q^{47} +(-3.82493 + 19.2292i) q^{48} +(18.3338 + 44.2616i) q^{49} +(-43.9019 + 65.0650i) q^{50} +(-21.3524 - 61.4826i) q^{51} +109.879i q^{52} +(-30.2734 - 73.0866i) q^{53} +(7.83807 - 39.4046i) q^{54} +(-23.8226 - 7.28537i) q^{55} +(5.06575 - 3.38483i) q^{56} +(-71.5601 + 14.2342i) q^{57} +(16.5634 - 24.7888i) q^{58} +(-36.6614 + 88.5085i) q^{59} +(111.609 - 10.7378i) q^{60} +(-3.34491 + 5.00601i) q^{61} +(-16.4487 - 82.6934i) q^{62} +(-4.91479 + 3.28396i) q^{63} +(-72.9937 - 72.9937i) q^{64} +(-89.8189 + 27.0246i) q^{65} +(22.9184 + 55.3298i) q^{66} +36.9104 q^{67} +(96.3600 + 25.0968i) q^{68} +34.4780 q^{69} +(12.6548 + 10.4335i) q^{70} +(14.0080 - 70.4230i) q^{71} +(-23.3283 - 23.3283i) q^{72} +(-14.8948 - 22.2917i) q^{73} +(44.3429 + 222.927i) q^{74} +(36.2275 + 88.5920i) q^{75} +(42.7174 - 103.129i) q^{76} +(-1.99206 + 4.80926i) q^{77} +(187.488 + 125.275i) q^{78} +(110.235 - 21.9271i) q^{79} +(12.1212 - 22.5543i) q^{80} +(-70.6471 - 70.6471i) q^{81} +(19.2147 - 96.5989i) q^{82} +(29.0278 - 12.0237i) q^{83} -23.4293i q^{84} +(3.18463 + 84.9403i) q^{85} -121.132 q^{86} +(-13.9124 - 33.5874i) q^{87} +(-28.4955 - 5.66810i) q^{88} +(1.37917 - 1.37917i) q^{89} +(42.0434 - 78.2317i) q^{90} +(3.82368 + 19.2229i) q^{91} +(-29.3056 + 43.8589i) q^{92} +(-94.9869 - 39.3449i) q^{93} +(-201.847 - 83.6077i) q^{94} +(94.8073 + 9.55420i) q^{95} +(-147.958 + 29.4308i) q^{96} +(-18.0086 + 12.0330i) q^{97} +(-106.360 + 106.360i) q^{98} +(27.6463 + 5.49919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{4} - 8 q^{5} - 16 q^{6} - 16 q^{9} + 16 q^{10} - 96 q^{11} - 16 q^{14} + 16 q^{15} - 16 q^{19} - 120 q^{20} + 224 q^{21} - 160 q^{24} - 240 q^{25} + 288 q^{26} - 176 q^{29} - 200 q^{30} + 48 q^{31}+ \cdots - 1664 q^{99}+O(q^{100}) $ 128 * q - 16 * q^4 - 8 * q^5 - 16 * q^6 - 16 * q^9 + 16 * q^10 - 96 * q^11 - 16 * q^14 + 16 * q^15 - 16 * q^19 - 120 * q^20 + 224 * q^21 - 160 * q^24 - 240 * q^25 + 288 * q^26 - 176 * q^29 - 200 * q^30 + 48 * q^31 + 48 * q^34 + 48 * q^35 - 144 * q^36 + 440 * q^40 - 336 * q^41 - 48 * q^44 + 232 * q^45 - 224 * q^46 - 48 * q^49 - 16 * q^51 + 512 * q^54 - 392 * q^55 - 16 * q^56 + 272 * q^59 - 736 * q^60 - 16 * q^61 + 688 * q^64 - 128 * q^65 - 80 * q^66 + 448 * q^69 + 736 * q^70 + 192 * q^71 + 704 * q^74 + 1048 * q^75 + 496 * q^76 + 304 * q^79 + 1240 * q^80 + 128 * q^81 + 672 * q^85 - 2496 * q^86 - 256 * q^89 + 1104 * q^90 - 1632 * q^91 - 1296 * q^94 + 120 * q^95 - 1728 * q^96 - 1664 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	1.20149	+	2.90065i	0.600744	+	1.45032i	0.872817	+	0.488047i	$0.162291\pi$
$2$	1.20149	+	2.90065i	0.600744	+	1.45032i	−0.272073	+	0.962276i	$0.587709\pi$
$3$	3.75496	+	0.746907i	1.25165	+	0.248969i	0.776039	−	0.630685i	$-0.217226\pi$
$3$	3.75496	+	0.746907i	1.25165	+	0.248969i	0.475613	+	0.879654i	$0.342226\pi$
$4$	−4.14176	+	4.14176i	−1.03544	+	1.03544i
$5$	−4.40427	−	2.36695i	−0.880853	−	0.473390i
$5$	−4.40427	−	2.36695i	−0.880853	−	0.473390i
$6$	2.34502	+	11.7892i	0.390836	+	1.96487i
$7$	−0.580455	+	0.868712i	−0.0829221	+	0.124102i	−0.870612	−	0.491970i	$-0.836277\pi$
$7$	−0.580455	+	0.868712i	−0.0829221	+	0.124102i	0.787690	+	0.616072i	$0.211277\pi$
$8$	−5.38745	−	2.23156i	−0.673432	−	0.278945i
$9$	5.22691	+	2.16506i	0.580768	+	0.240562i
$10$	1.57401	−	15.6191i	0.157401	−	1.56191i
$11$	4.88661	−	0.972007i	0.444237	−	0.0883643i	0.0320970	−	0.999485i	$-0.489781\pi$
$11$	4.88661	−	0.972007i	0.444237	−	0.0883643i	0.412140	+	0.911121i	$0.364781\pi$
$12$	−18.6456	+	12.4586i	−1.55380	+	1.03822i
$13$	13.2648	−	13.2648i	1.02037	−	1.02037i	0.0205827	−	0.999788i	$-0.493448\pi$
$13$	13.2648	−	13.2648i	1.02037	−	1.02037i	0.999788	−	0.0205827i	$-0.00655215\pi$
$14$	−3.21723	−	0.639948i	−0.229802	−	0.0457106i
$15$	−14.7699	−	12.1774i	−0.984662	−	0.811824i
$16$			5.12102i			0.320064i
$17$	−8.60301	−	14.6625i	−0.506060	−	0.862499i
$17$	−8.60301	−	14.6625i	−0.506060	−	0.862499i
$18$			17.7627i			0.986817i
$19$	−17.6068	+	7.29299i	−0.926675	+	0.383841i	−0.794416	−	0.607374i	$-0.792223\pi$
$19$	−17.6068	+	7.29299i	−0.926675	+	0.383841i	−0.132259	+	0.991215i	$0.542223\pi$
$20$	28.0447	−	8.43807i	1.40224	−	0.421904i
$21$	−2.82843	+	2.82843i	−0.134687	+	0.134687i
$22$	8.69065	+	13.0065i	0.395029	+	0.591203i
$23$	8.83254	−	1.75690i	0.384024	−	0.0763870i	0.000696607	−	1.00000i	$-0.499778\pi$
$23$	8.83254	−	1.75690i	0.384024	−	0.0763870i	0.383327	+	0.923613i	$0.374778\pi$
$24$	−18.5629	−	12.4033i	−0.773454	−	0.516805i
$25$	13.7951	+	20.8493i	0.551804	+	0.833974i
$26$	54.4141	+	22.5391i	2.09285	+	0.866887i
$27$	−10.6400	−	7.10940i	−0.394073	−	0.263311i
$28$	−1.19389	−	6.00209i	−0.0426389	−	0.214360i
$29$	−5.27556	−	7.89544i	−0.181916	−	0.272257i	0.729292	−	0.684202i	$-0.239849\pi$
$29$	−5.27556	−	7.89544i	−0.181916	−	0.272257i	−0.911208	+	0.411946i	$0.864849\pi$
$30$	17.5764	−	57.4733i	0.585878	−	1.91578i
$31$	−26.3385	−	5.23906i	−0.849630	−	0.169002i	−0.248974	−	0.968510i	$-0.580094\pi$
$31$	−26.3385	−	5.23906i	−0.849630	−	0.169002i	−0.600655	+	0.799508i	$0.705094\pi$
$32$	−36.4041	+	15.0791i	−1.13763	+	0.471221i
$33$	19.0750			0.578030
$34$	32.1943	−	42.5711i	0.946890	−	1.25209i
$35$	4.61267	−	2.45213i	0.131791	−	0.0700609i
$36$	−30.6157	+	12.6814i	−0.850437	+	0.352262i
$37$	71.0039	+	14.1236i	1.91902	+	0.381718i	0.999924	−	0.0123055i	$-0.00391705\pi$
$37$	71.0039	+	14.1236i	1.91902	+	0.381718i	0.919100	+	0.394023i	$0.128917\pi$
$38$	−42.3088	−	42.3088i	−1.11339	−	1.11339i
$39$	59.7164	−	39.9012i	1.53119	−	1.02311i
$40$	18.4458	+	22.5802i	0.461145	+	0.564505i
$41$	−26.0834	−	17.4284i	−0.636182	−	0.425083i	0.195217	−	0.980760i	$-0.437459\pi$
$41$	−26.0834	−	17.4284i	−0.636182	−	0.425083i	−0.831398	+	0.555677i	$0.812459\pi$
$42$	−11.6026	−	4.80595i	−0.276252	−	0.114427i
$43$	−14.7645	+	35.6447i	−0.343360	+	0.828945i	0.654011	+	0.756485i	$0.273085\pi$
$43$	−14.7645	+	35.6447i	−0.343360	+	0.828945i	−0.997371	+	0.0724602i	$0.976915\pi$
$44$	−16.2133	+	24.2650i	−0.368485	+	0.551476i
$45$	−17.8961	−	21.9073i	−0.397691	−	0.486829i
$46$	15.7083	+	23.5092i	0.341486	+	0.511069i
$47$	−49.2053	+	49.2053i	−1.04692	+	1.04692i	−0.0480776	+	0.998844i	$0.515309\pi$
$47$	−49.2053	+	49.2053i	−1.04692	+	1.04692i	−0.998844	+	0.0480776i	$0.984691\pi$
$48$	−3.82493	+	19.2292i	−0.0796860	+	0.400608i
$49$	18.3338	+	44.2616i	0.374158	+	0.903298i
$50$	−43.9019	+	65.0650i	−0.878039	+	1.30130i
$51$	−21.3524	−	61.4826i	−0.418675	−	1.20554i
$52$			109.879i			2.11306i
$53$	−30.2734	−	73.0866i	−0.571197	−	1.37899i	−0.900537	−	0.434780i	$-0.856826\pi$
$53$	−30.2734	−	73.0866i	−0.571197	−	1.37899i	0.329340	−	0.944212i	$-0.393174\pi$
$54$	7.83807	−	39.4046i	0.145149	−	0.729716i
$55$	−23.8226	−	7.28537i	−0.433138	−	0.132461i
$56$	5.06575	−	3.38483i	0.0904598	−	0.0604433i
$57$	−71.5601	+	14.2342i	−1.25544	+	0.249722i
$58$	16.5634	−	24.7888i	0.285575	−	0.427394i
$59$	−36.6614	+	88.5085i	−0.621380	+	1.50014i	0.228703	+	0.973496i	$0.426551\pi$
$59$	−36.6614	+	88.5085i	−0.621380	+	1.50014i	−0.850083	+	0.526648i	$0.823449\pi$
$60$	111.609	−	10.7378i	1.86015	−	0.178963i
$61$	−3.34491	+	5.00601i	−0.0548346	+	0.0820658i	−0.857874	−	0.513860i	$-0.828215\pi$
$61$	−3.34491	+	5.00601i	−0.0548346	+	0.0820658i	0.803039	+	0.595926i	$0.203215\pi$
$62$	−16.4487	−	82.6934i	−0.265302	−	1.33376i
$63$	−4.91479	+	3.28396i	−0.0780126	+	0.0521263i
$64$	−72.9937	−	72.9937i	−1.14053	−	1.14053i
$65$	−89.8189	+	27.0246i	−1.38183	+	0.415764i
$66$	22.9184	+	55.3298i	0.347248	+	0.838331i
$67$	36.9104			0.550901			0.275450	−	0.961315i	$-0.411173\pi$
$67$	36.9104			0.550901			0.275450	+	0.961315i	$0.411173\pi$
$68$	96.3600	+	25.0968i	1.41706	+	0.369071i
$69$	34.4780			0.499682
$70$	12.6548	+	10.4335i	0.180783	+	0.149050i
$71$	14.0080	−	70.4230i	0.197296	−	0.991874i	−0.747512	−	0.664249i	$-0.768752\pi$
$71$	14.0080	−	70.4230i	0.197296	−	0.991874i	0.944808	−	0.327625i	$-0.106248\pi$
$72$	−23.3283	−	23.3283i	−0.324004	−	0.324004i
$73$	−14.8948	−	22.2917i	−0.204039	−	0.305366i	0.715311	−	0.698806i	$-0.246285\pi$
$73$	−14.8948	−	22.2917i	−0.204039	−	0.305366i	−0.919350	+	0.393440i	$0.871285\pi$
$74$	44.3429	+	222.927i	0.599228	+	3.01252i
$75$	36.2275	+	88.5920i	0.483033	+	1.18123i
$76$	42.7174	−	103.129i	0.562071	−	1.35696i
$77$	−1.99206	+	4.80926i	−0.0258709	+	0.0624579i
$78$	187.488	+	125.275i	2.40369	+	1.60610i
$79$	110.235	−	21.9271i	1.39538	−	0.277559i	0.560576	−	0.828103i	$-0.310580\pi$
$79$	110.235	−	21.9271i	1.39538	−	0.277559i	0.834806	+	0.550544i	$0.185580\pi$
$80$	12.1212	−	22.5543i	0.151515	−	0.281929i
$81$	−70.6471	−	70.6471i	−0.872186	−	0.872186i
$82$	19.2147	−	96.5989i	0.234326	−	1.17804i
$83$	29.0278	−	12.0237i	0.349732	−	0.144864i	−0.200900	−	0.979612i	$-0.564387\pi$
$83$	29.0278	−	12.0237i	0.349732	−	0.144864i	0.550632	+	0.834748i	$0.314387\pi$
$84$		−	23.4293i		−	0.278920i
$85$	3.18463	+	84.9403i	0.0374663	+	0.999298i
$86$	−121.132			−1.40851
$87$	−13.9124	−	33.5874i	−0.159912	−	0.386062i
$88$	−28.4955	−	5.66810i	−0.323812	−	0.0644102i
$89$	1.37917	−	1.37917i	0.0154963	−	0.0154963i	−0.699316	−	0.714813i	$-0.746512\pi$
$89$	1.37917	−	1.37917i	0.0154963	−	0.0154963i	0.714813	+	0.699316i	$0.246512\pi$
$90$	42.0434	−	78.2317i	0.467149	−	0.869241i
$91$	3.82368	+	19.2229i	0.0420184	+	0.211241i
$92$	−29.3056	+	43.8589i	−0.318539	+	0.476727i
$93$	−94.9869	−	39.3449i	−1.02136	−	0.423063i
$94$	−201.847	−	83.6077i	−2.14731	−	0.889443i
$95$	94.8073	+	9.55420i	0.997971	+	0.100571i
$96$	−147.958	+	29.4308i	−1.54123	+	0.306570i
$97$	−18.0086	+	12.0330i	−0.185656	+	0.124051i	−0.644925	−	0.764246i	$-0.723111\pi$
$97$	−18.0086	+	12.0330i	−0.185656	+	0.124051i	0.459269	+	0.888297i	$0.348111\pi$
$98$	−106.360	+	106.360i	−1.08530	+	1.08530i
$99$	27.6463	+	5.49919i	0.279256	+	0.0555474i
$100$	−143.489	−	29.2169i	−1.43489	−	0.292169i
$101$		−	30.6576i		−	0.303540i	−0.988416	−	0.151770i	$-0.951503\pi$
$101$		−	30.6576i		−	0.303540i	0.988416	−	0.151770i	$-0.0484974\pi$
$102$	152.685	−	135.806i	1.49691	−	1.33144i
$103$		−	97.6583i		−	0.948138i	−0.880488	−	0.474069i	$-0.842785\pi$
$103$		−	97.6583i		−	0.948138i	0.880488	−	0.474069i	$-0.157215\pi$
$104$	−101.065	+	41.8624i	−0.971777	+	0.402523i
$105$	19.1519	−	5.76241i	0.182399	−	0.0548800i
$106$	175.625	−	175.625i	1.65684	−	1.65684i
$107$	26.4718	+	39.6179i	0.247400	+	0.370261i	0.934298	−	0.356494i	$-0.116028\pi$
$107$	26.4718	+	39.6179i	0.247400	+	0.370261i	−0.686897	+	0.726754i	$0.741028\pi$
$108$	73.5135	−	14.6228i	0.680681	−	0.135396i
$109$	80.3163	+	53.6656i	0.736847	+	0.492345i	0.866477	−	0.499217i	$-0.166379\pi$
$109$	80.3163	+	53.6656i	0.736847	+	0.492345i	−0.129630	+	0.991562i	$0.541379\pi$
$110$	−7.49027	−	77.8543i	−0.0680934	−	0.707766i
$111$	256.068	+	106.067i	2.30692	+	0.955556i
$112$	−4.44869	−	2.97252i	−0.0397204	−	0.0265404i
$113$	22.4635	+	112.931i	0.198792	+	0.999393i	0.943341	+	0.331826i	$0.107665\pi$
$113$	22.4635	+	112.931i	0.198792	+	0.999393i	−0.744549	+	0.667568i	$0.767335\pi$
$114$	−127.267	−	190.468i	−1.11638	−	1.67077i
$115$	−43.0594	−	13.1683i	−0.374429	−	0.114507i
$116$	54.5511	+	10.8509i	0.470268	+	0.0935421i
$117$	98.0531	−	40.6149i	0.838061	−	0.347136i
$118$	−300.780			−2.54899
$119$	17.7311	+	1.03736i	0.149001	+	0.00871733i
$120$	52.3979	+	98.5649i	0.436649	+	0.821374i
$121$	−88.8553	+	36.8051i	−0.734341	+	0.304174i
$122$	−18.5395	−	3.68774i	−0.151963	−	0.0302274i
$123$	−84.9248	−	84.9248i	−0.690445	−	0.690445i
$124$	130.787	−	87.3888i	1.05473	−	0.704749i
$125$	−11.4080	−	124.478i	−0.0912642	−	0.995827i
$126$	−15.4307	−	10.3104i	−0.122466	−	0.0818289i
$127$	187.019	+	77.4657i	1.47259	+	0.609966i	0.967448	−	0.253071i	$-0.0814407\pi$
$127$	187.019	+	77.4657i	1.47259	+	0.609966i	0.505140	+	0.863037i	$0.331441\pi$
$128$	63.7117	−	153.814i	0.497747	−	1.20167i
$129$	−82.0633	+	122.816i	−0.636149	+	0.952065i
$130$	−186.305	−	228.063i	−1.43312	−	1.75433i
$131$	73.7726	+	110.408i	0.563149	+	0.842813i	0.998344	−	0.0575237i	$-0.0183205\pi$
$131$	73.7726	+	110.408i	0.563149	+	0.842813i	−0.435195	+	0.900336i	$0.643320\pi$
$132$	−79.0040	+	79.0040i	−0.598515	+	0.598515i
$133$	3.88446	−	19.5285i	0.0292065	−	0.146831i
$134$	44.3473	+	107.064i	0.330950	+	0.798985i
$135$	30.0337	+	56.4959i	0.222472	+	0.418488i
$136$	13.6282	+	98.1915i	0.100207	+	0.721996i
$137$		−	117.031i		−	0.854241i	−0.904195	−	0.427121i	$-0.859528\pi$
$137$		−	117.031i		−	0.854241i	0.904195	−	0.427121i	$-0.140472\pi$
$138$	41.4249	+	100.009i	0.300181	+	0.724700i
$139$	−1.91522	+	9.62844i	−0.0137785	+	0.0692694i	−0.987063	−	0.160334i	$-0.948743\pi$
$139$	−1.91522	+	9.62844i	−0.0137785	+	0.0692694i	0.973284	+	0.229603i	$0.0737429\pi$
$140$	−8.94843	+	29.2607i	−0.0639174	+	0.209005i
$141$	−221.516	+	148.012i	−1.57103	+	1.04973i
$142$	221.103	−	43.9801i	1.55706	−	0.309719i
$143$	51.9265	−	77.7135i	0.363122	−	0.543451i
$144$	−11.0873	+	26.7671i	−0.0769951	+	0.185883i
$145$	4.54689	+	47.2606i	0.0313578	+	0.325935i
$146$	46.7644	−	69.9879i	0.320304	−	0.479369i
$147$	35.7831	+	179.894i	0.243423	+	1.22377i
$148$	−352.577	+	235.585i	−2.38228	+	1.59179i
$149$	107.462	+	107.462i	0.721220	+	0.721220i	0.968854	−	0.247633i	$-0.0796529\pi$
$149$	107.462	+	107.462i	0.721220	+	0.721220i	−0.247633	+	0.968854i	$0.579653\pi$
$150$	−213.447	+	211.525i	−1.42298	+	1.41017i
$151$	80.4585	+	194.244i	0.532838	+	1.28638i	0.929636	+	0.368479i	$0.120121\pi$
$151$	80.4585	+	194.244i	0.532838	+	1.28638i	−0.396798	+	0.917906i	$0.629879\pi$
$152$	111.131			0.731123
$153$	−13.2221	−	95.2654i	−0.0864188	−	0.622650i
$154$	−16.3434			−0.106126
$155$	103.601	+	85.4161i	0.668395	+	0.551072i
$156$	−82.0697	+	412.592i	−0.526088	+	2.64482i
$157$	−165.129	−	165.129i	−1.05178	−	1.05178i	−0.998584	−	0.0531931i	$-0.983060\pi$
$157$	−165.129	−	165.129i	−1.05178	−	1.05178i	−0.0531931	−	0.998584i	$-0.516940\pi$
$158$	196.049	+	293.408i	1.24082	+	1.85701i
$159$	−59.0866	−	297.048i	−0.371614	−	1.86823i
$160$	196.025	+	19.7544i	1.22515	+	0.123465i
$161$	−3.60065	+	8.69273i	−0.0223643	+	0.0539921i
$162$	120.041	−	289.804i	0.740992	−	1.78891i
$163$	91.3742	+	61.0543i	0.560578	+	0.374566i	0.803341	−	0.595520i	$-0.203054\pi$
$163$	91.3742	+	61.0543i	0.560578	+	0.374566i	−0.242763	+	0.970086i	$0.578054\pi$
$164$	180.215	−	35.8471i	1.09887	−	0.218580i
$165$	−84.0114	−	45.1495i	−0.509160	−	0.273634i
$166$	69.7530	+	69.7530i	0.420199	+	0.420199i
$167$	0.281532	−	1.41536i	0.00168582	−	0.00847519i	−0.979933	−	0.199326i	$-0.936125\pi$
$167$	0.281532	−	1.41536i	0.00168582	−	0.00847519i	0.981619	+	0.190851i	$0.0611247\pi$
$168$	21.5498	−	8.92623i	0.128273	−	0.0531323i
$169$		−	182.911i		−	1.08231i
$170$	−242.556	+	111.292i	−1.42680	+	0.654660i
$171$	−107.819			−0.630521
$172$	−86.4805	−	208.782i	−0.502794	−	1.21385i
$173$	68.4309	+	13.6118i	0.395554	+	0.0786807i	0.388860	−	0.921297i	$-0.372869\pi$
$173$	68.4309	+	13.6118i	0.395554	+	0.0786807i	0.00669459	+	0.999978i	$0.497869\pi$
$174$	80.7097	−	80.7097i	0.463849	−	0.463849i
$175$	−26.1195	−	0.118121i	−0.149254	−	0.000674976i
$176$	4.97767	+	25.0244i	0.0282822	+	0.142184i
$177$	−203.770	+	304.963i	−1.15124	+	1.72295i
$178$	5.65756	+	2.34344i	0.0317841	+	0.0131654i
$179$	−109.696	−	45.4378i	−0.612830	−	0.253842i	0.0546082	−	0.998508i	$-0.482609\pi$
$179$	−109.696	−	45.4378i	−0.612830	−	0.253842i	−0.667438	+	0.744666i	$0.732609\pi$
$180$	164.856	+	16.6134i	0.915867	+	0.0922965i
$181$	228.748	−	45.5009i	1.26380	−	0.251386i	0.482699	−	0.875786i	$-0.339657\pi$
$181$	228.748	−	45.5009i	1.26380	−	0.251386i	0.781104	+	0.624400i	$0.214657\pi$
$182$	−51.1648	+	34.1873i	−0.281125	+	0.187842i
$183$	−16.2990	+	16.2990i	−0.0890657	+	0.0890657i
$184$	−51.5055	−	10.2451i	−0.279921	−	0.0556798i
$185$	−279.290	−	230.267i	−1.50968	−	1.24468i
$186$		−	322.796i		−	1.73546i
$187$	−56.2916	−	63.2876i	−0.301024	−	0.338436i
$188$		−	407.593i		−	2.16805i
$189$	12.3520	−	5.11638i	0.0653547	−	0.0270708i
$190$	86.1964	+	286.482i	0.453665	+	1.50780i
$191$	100.280	−	100.280i	0.525027	−	0.525027i	−0.394058	−	0.919085i	$-0.628929\pi$
$191$	100.280	−	100.280i	0.525027	−	0.525027i	0.919085	+	0.394058i	$0.128929\pi$
$192$	−219.569	−	328.608i	−1.14359	−	1.71150i
$193$	62.4627	−	12.4246i	0.323641	−	0.0643762i	−0.0305963	−	0.999532i	$-0.509741\pi$
$193$	62.4627	−	12.4246i	0.323641	−	0.0643762i	0.354237	+	0.935156i	$0.384741\pi$
$194$	−56.5406	−	37.7792i	−0.291446	−	0.194738i
$195$	−357.451	+	34.3900i	−1.83308	+	0.176359i
$196$	−259.255	−	107.387i	−1.32273	−	0.547892i
$197$	−286.509	−	191.439i	−1.45436	−	0.971773i	−0.996574	−	0.0827116i	$-0.973642\pi$
$197$	−286.509	−	191.439i	−1.45436	−	0.971773i	−0.457788	−	0.889062i	$-0.651358\pi$
$198$	17.2655	+	86.7994i	0.0871994	+	0.438381i
$199$	−88.1240	−	131.887i	−0.442834	−	0.662748i	0.541166	−	0.840916i	$-0.317983\pi$
$199$	−88.1240	−	131.887i	−0.442834	−	0.662748i	−0.984000	+	0.178168i	$0.942983\pi$
$200$	−27.7940	−	143.109i	−0.138970	−	0.715547i
$201$	138.597	+	27.5686i	0.689536	+	0.137157i
$202$	88.9268	−	36.8347i	0.440232	−	0.182350i
$203$	9.92109			0.0488723
$204$	343.083	+	166.209i	1.68178	+	0.814752i
$205$	73.6263	+	138.497i	0.359153	+	0.675597i
$206$	283.272	−	117.335i	1.37511	−	0.569588i
$207$	49.9707	+	9.93979i	0.241404	+	0.0480183i
$208$	67.9294	+	67.9294i	0.326584	+	0.326584i
$209$	−78.9488	+	52.7519i	−0.377746	+	0.252402i
$210$	39.7255	+	48.6294i	0.189169	+	0.231569i
$211$	−166.378	−	111.170i	−0.788520	−	0.526872i	0.0948821	−	0.995489i	$-0.469753\pi$
$211$	−166.378	−	111.170i	−0.788520	−	0.526872i	−0.883402	+	0.468617i	$0.844753\pi$
$212$	428.092	+	177.321i	2.01930	+	0.836422i
$213$	105.199	−	253.973i	0.493892	−	1.19236i
$214$	−83.1120	+	124.386i	−0.388374	+	0.581243i
$215$	149.396	−	122.042i	0.694864	−	0.567636i
$216$	41.4573	+	62.0452i	0.191932	+	0.287246i
$217$	19.8395	−	19.8395i	0.0914264	−	0.0914264i
$218$	−59.1661	+	297.448i	−0.271404	+	1.36444i
$219$	−39.2796	−	94.8294i	−0.179359	−	0.433011i
$220$	128.842	−	68.4932i	0.585644	−	0.311333i
$221$	−308.613	−	80.3777i	−1.39644	−	0.363700i
$222$			870.200i			3.91982i
$223$	117.622	+	283.965i	0.527454	+	1.27339i	0.933186	+	0.359395i	$0.117017\pi$
$223$	117.622	+	283.965i	0.527454	+	1.27339i	−0.405731	+	0.913992i	$0.632983\pi$
$224$	8.03156	−	40.3774i	0.0358552	−	0.180256i
$225$	26.9658	+	138.845i	0.119848	+	0.617088i
$226$	−300.585	+	200.844i	−1.33002	+	0.888692i
$227$	159.541	−	31.7347i	0.702825	−	0.139801i	0.169275	−	0.985569i	$-0.445857\pi$
$227$	159.541	−	31.7347i	0.702825	−	0.139801i	0.533550	+	0.845768i	$0.320857\pi$
$228$	237.430	−	355.339i	1.04136	−	1.55850i
$229$	−75.6844	+	182.718i	−0.330500	+	0.797897i	0.668053	+	0.744114i	$0.267128\pi$
$229$	−75.6844	+	182.718i	−0.330500	+	0.797897i	−0.998553	+	0.0537829i	$0.982872\pi$
$230$	−13.5387	−	140.722i	−0.0588637	−	0.611833i
$231$	−11.0722	+	16.5707i	−0.0479315	+	0.0717345i
$232$	10.8027	+	54.3090i	0.0465635	+	0.234091i
$233$	24.7396	−	16.5304i	0.106178	−	0.0709461i	−0.501347	−	0.865246i	$-0.667162\pi$
$233$	24.7396	−	16.5304i	0.106178	−	0.0709461i	0.607526	+	0.794300i	$0.292162\pi$
$234$	235.619	+	235.619i	1.00692	+	1.00692i
$235$	333.180	−	100.247i	1.41779	−	0.426582i
$236$	−214.738	−	518.423i	−0.909907	−	2.19671i
$237$	430.306			1.81564
$238$	18.2947	+	52.6781i	0.0768685	+	0.221337i
$239$	−415.551			−1.73871			−0.869354	−	0.494190i	$-0.835465\pi$
$239$	−415.551			−1.73871			−0.869354	+	0.494190i	$0.835465\pi$
$240$	62.3605	−	75.6371i	0.259836	−	0.315155i
$241$	26.4472	−	132.959i	0.109739	−	0.551697i	−0.886325	−	0.463064i	$-0.846750\pi$
$241$	26.4472	−	132.959i	0.109739	−	0.551697i	0.996064	−	0.0886333i	$-0.0282499\pi$
$242$	−213.517	−	213.517i	−0.882302	−	0.882302i
$243$	−148.525	−	222.284i	−0.611215	−	0.914748i
$244$	−6.87988	−	34.5875i	−0.0281962	−	0.141752i
$245$	24.0182	−	238.335i	0.0980335	−	0.972796i
$246$	144.301	−	348.373i	0.586589	−	1.41615i
$247$	−136.811	+	330.292i	−0.553892	+	1.33721i
$248$	130.206	+	87.0011i	0.525025	+	0.350811i
$249$	117.979	−	23.4674i	0.473810	−	0.0942466i
$250$	347.361	−	182.650i	1.38944	−	0.730599i
$251$	21.3651	+	21.3651i	0.0851199	+	0.0851199i	0.748385	−	0.663265i	$-0.230830\pi$
$251$	21.3651	+	21.3651i	0.0851199	+	0.0851199i	−0.663265	+	0.748385i	$0.730830\pi$
$252$	6.75451	−	33.9572i	0.0268036	−	0.134751i
$253$	41.4534	−	17.1706i	0.163848	−	0.0678679i
$254$			635.549i			2.50216i
$255$	−51.4844	+	321.326i	−0.201900	+	1.26010i
$256$	109.793			0.428880
$257$	23.0235	+	55.5836i	0.0895855	+	0.216279i	0.962322	−	0.271914i	$-0.0876565\pi$
$257$	23.0235	+	55.5836i	0.0895855	+	0.216279i	−0.872736	+	0.488192i	$0.837657\pi$
$258$	−454.845	−	90.4743i	−1.76297	−	0.350676i
$259$	−53.4838	+	53.4838i	−0.206501	+	0.206501i
$260$	260.079	−	483.938i	1.00030	−	1.86130i
$261$	−10.4808	−	52.6906i	−0.0401564	−	0.201880i
$262$	−231.619	+	346.643i	−0.884043	+	1.32306i
$263$	−300.430	−	124.442i	−1.14232	−	0.473164i	−0.270368	−	0.962757i	$-0.587145\pi$
$263$	−300.430	−	124.442i	−1.14232	−	0.473164i	−0.871951	+	0.489593i	$0.837145\pi$
$264$	−102.766	−	42.5669i	−0.389264	−	0.161238i
$265$	−39.6598	+	393.548i	−0.149660	+	1.48509i
$266$	61.3124	−	12.1958i	0.230498	−	0.0458489i
$267$	6.20886	−	4.14863i	0.0232541	−	0.0155379i
$268$	−152.874	+	152.874i	−0.570424	+	0.570424i
$269$	−53.6514	−	10.6719i	−0.199448	−	0.0396726i	0.0943555	−	0.995539i	$-0.469921\pi$
$269$	−53.6514	−	10.6719i	−0.199448	−	0.0396726i	−0.293803	+	0.955866i	$0.594921\pi$
$270$	−127.790	+	154.996i	−0.473295	+	0.574060i
$271$		−	26.2090i		−	0.0967123i	−0.998830	−	0.0483562i	$-0.984602\pi$
$271$		−	26.2090i		−	0.0967123i	0.998830	−	0.0483562i	$-0.0153983\pi$
$272$	75.0868	−	44.0562i	0.276055	−	0.161971i
$273$			75.0372i			0.274861i
$274$	339.466	−	140.611i	1.23893	−	0.513180i
$275$	87.6770	+	88.4736i	0.318825	+	0.321722i
$276$	−142.800	+	142.800i	−0.517390	+	0.517390i
$277$	−136.208	−	203.850i	−0.491727	−	0.735921i	0.499755	−	0.866167i	$-0.333423\pi$
$277$	−136.208	−	203.850i	−0.491727	−	0.735921i	−0.991482	+	0.130246i	$0.958423\pi$
$278$	−30.2298	+	6.01309i	−0.108740	+	0.0216298i
$279$	−126.326	−	84.4084i	−0.452782	−	0.302539i
$280$	−30.3226	+	2.91730i	−0.108295	+	0.0104189i
$281$	164.221	+	68.0225i	0.584416	+	0.242073i	0.655246	−	0.755415i	$-0.272565\pi$
$281$	164.221	+	68.0225i	0.584416	+	0.242073i	−0.0708304	+	0.997488i	$0.522565\pi$
$282$	−695.479	−	464.704i	−2.46624	−	1.64789i
$283$	−76.8491	−	386.347i	−0.271552	−	1.36518i	−0.840055	−	0.542501i	$-0.817477\pi$
$283$	−76.8491	−	386.347i	−0.271552	−	1.36518i	0.568503	−	0.822681i	$-0.307523\pi$
$284$	233.657	+	349.693i	0.822737	+	1.23131i
$285$	348.861	+	106.688i	1.22407	+	0.374343i
$286$	287.808	+	57.2487i	1.00632	+	0.200170i
$287$	30.2805	−	12.5426i	0.105507	−	0.0437024i
$288$	−222.928			−0.774055
$289$	−140.976	+	252.283i	−0.487807	+	0.872951i
$290$	−131.623	+	69.9719i	−0.453874	+	0.241283i
$291$	−76.6091	+	31.7325i	−0.263262	+	0.109047i
$292$	154.018	+	30.6360i	0.527458	+	0.104918i
$293$	13.5860	+	13.5860i	0.0463687	+	0.0463687i	0.729911	−	0.683542i	$-0.239562\pi$
$293$	13.5860	+	13.5860i	0.0463687	+	0.0463687i	−0.683542	+	0.729911i	$0.739562\pi$
$294$	−478.816	+	319.935i	−1.62863	+	1.08821i
$295$	370.962	−	303.039i	1.25750	−	1.02725i
$296$	−351.013	−	234.539i	−1.18585	−	0.792362i
$297$	−58.9037	−	24.3987i	−0.198329	−	0.0821506i
$298$	−182.595	+	440.823i	−0.612734	+	1.47927i
$299$	93.8571	−	140.467i	0.313903	−	0.469790i
$300$	−516.972	−	216.881i	−1.72324	−	0.722937i
$301$	−22.3948	−	33.5162i	−0.0744013	−	0.111349i
$302$	−466.764	+	466.764i	−1.54558	+	1.54558i
$303$	22.8984	−	115.118i	0.0755722	−	0.379927i
$304$	−37.3475	−	90.1649i	−0.122854	−	0.296595i
$305$	26.5808	−	14.1306i	0.0871503	−	0.0463298i
$306$	260.445	−	152.813i	0.851128	−	0.499388i
$307$		−	59.3971i		−	0.193476i	−0.995310	−	0.0967379i	$-0.969159\pi$
$307$		−	59.3971i		−	0.193476i	0.995310	−	0.0967379i	$-0.0308409\pi$
$308$	−11.6681	−	28.1694i	−0.0378836	−	0.0914591i
$309$	72.9417	−	366.702i	0.236057	−	1.18674i
$310$	−123.286	+	403.137i	−0.397698	+	1.30044i
$311$	381.722	−	255.059i	1.22740	−	0.820124i	0.238858	−	0.971054i	$-0.423227\pi$
$311$	381.722	−	255.059i	1.22740	−	0.820124i	0.988544	+	0.150930i	$0.0482269\pi$
$312$	−410.761	+	81.7055i	−1.31654	+	0.261877i
$313$	−142.386	+	213.095i	−0.454906	+	0.680815i	−0.986047	−	0.166469i	$-0.946764\pi$
$313$	−142.386	+	213.095i	−0.454906	+	0.680815i	0.531141	+	0.847284i	$0.321764\pi$
$314$	280.581	−	677.382i	0.893569	−	2.15727i
$315$	29.4190	−	2.83037i	0.0933937	−	0.00898530i
$316$	−365.751	+	547.384i	−1.15744	+	1.73223i
$317$	57.9173	+	291.170i	0.182704	+	0.918517i	0.957967	+	0.286878i	$0.0926174\pi$
$317$	57.9173	+	291.170i	0.182704	+	0.918517i	−0.775263	+	0.631639i	$0.782383\pi$
$318$	790.640	−	528.289i	2.48629	−	1.66129i
$319$	−33.4540	−	33.4540i	−0.104872	−	0.104872i
$320$	148.711	+	494.256i	0.464723	+	1.54455i
$321$	69.8097	+	168.536i	0.217476	+	0.525033i
$322$	−29.5407			−0.0917413
$323$	258.405	+	195.418i	0.800016	+	0.605009i
$324$	585.206			1.80619
$325$	459.552	+	93.5731i	1.41401	+	0.287917i
$326$	−67.3120	+	338.400i	−0.206478	+	1.03804i
$327$	261.501	+	261.501i	0.799697	+	0.799697i
$328$	101.631	+	152.101i	0.309850	+	0.463724i
$329$	−14.1838	−	71.3066i	−0.0431118	−	0.216738i
$330$	30.0243	−	297.934i	0.0909827	−	0.902830i
$331$	−153.858	+	371.447i	−0.464828	+	1.12220i	0.501563	+	0.865121i	$0.332758\pi$
$331$	−153.858	+	371.447i	−0.464828	+	1.12220i	−0.966392	+	0.257074i	$0.917242\pi$
$332$	−70.4267	+	170.025i	−0.212129	+	0.512124i
$333$	340.553	+	227.550i	1.02268	+	0.683333i
$334$	4.44371	−	0.883909i	0.0133045	−	0.00264643i
$335$	−162.563	−	87.3649i	−0.485263	−	0.260791i
$336$	−14.4844	−	14.4844i	−0.0431084	−	0.0431084i
$337$	116.538	−	585.877i	0.345810	−	1.73851i	−0.281340	−	0.959608i	$-0.590779\pi$
$337$	116.538	−	585.877i	0.345810	−	1.73851i	0.627150	−	0.778898i	$-0.284221\pi$
$338$	530.560	−	219.765i	1.56970	−	0.650193i
$339$			440.831i			1.30039i
$340$	−364.992	−	338.612i	−1.07351	−	0.995918i
$341$	−133.798			−0.392371
$342$	−129.543	−	312.745i	−0.378781	−	0.914459i
$343$	−99.3035	−	19.7527i	−0.289515	−	0.0575880i
$344$	159.086	−	159.086i	0.462460	−	0.462460i
$345$	−151.850	−	81.6078i	−0.440146	−	0.236544i
$346$	42.7360	+	214.848i	0.123514	+	0.620949i
$347$	54.7921	−	82.0022i	0.157902	−	0.236318i	−0.744080	−	0.668091i	$-0.767112\pi$
$347$	54.7921	−	82.0022i	0.157902	−	0.236318i	0.901982	+	0.431773i	$0.142112\pi$
$348$	196.732	+	81.4892i	0.565323	+	0.234164i
$349$	288.155	+	119.358i	0.825659	+	0.341999i	0.755183	−	0.655514i	$-0.227548\pi$
$349$	288.155	+	119.358i	0.825659	+	0.341999i	0.0704764	+	0.997513i	$0.477548\pi$
$350$	−31.0396	−	75.9054i	−0.0886846	−	0.216872i
$351$	−235.442	+	46.8324i	−0.670775	+	0.133426i
$352$	−163.236	+	109.071i	−0.463737	+	0.309859i
$353$	182.112	−	182.112i	0.515898	−	0.515898i	−0.400429	−	0.916328i	$-0.631139\pi$
$353$	182.112	−	182.112i	0.515898	−	0.515898i	0.916328	+	0.400429i	$0.131139\pi$
$354$	−1129.42	−	224.655i	−3.19044	−	0.634618i
$355$	−228.383	+	277.006i	−0.643332	+	0.780297i
$356$			11.4244i			0.0320910i
$357$	65.8048	+	17.1388i	0.184327	+	0.0480077i
$358$		−	372.784i		−	1.04130i
$359$	218.420	−	90.4725i	0.608412	−	0.252013i	−0.0571373	−	0.998366i	$-0.518197\pi$
$359$	218.420	−	90.4725i	0.608412	−	0.252013i	0.665549	+	0.746354i	$0.268197\pi$
$360$	47.5271	+	157.961i	0.132020	+	0.438780i
$361$	1.54723	−	1.54723i	0.00428596	−	0.00428596i
$362$	406.820	+	608.850i	1.12381	+	1.68191i
$363$	−361.138	+	71.8347i	−0.994870	+	0.197892i
$364$	−95.4534	−	63.7799i	−0.262235	−	0.175220i
$365$	12.8375	+	133.434i	0.0351713	+	0.365572i
$366$	−66.8608	−	27.6946i	−0.182680	−	0.0756684i
$367$	−194.644	−	130.057i	−0.530366	−	0.354379i	0.261374	−	0.965238i	$-0.415824\pi$
$367$	−194.644	−	130.057i	−0.530366	−	0.354379i	−0.791740	+	0.610858i	$0.790824\pi$
$368$	8.99713	+	45.2316i	0.0244487	+	0.122912i
$369$	−98.6023	−	147.569i	−0.267215	−	0.399915i
$370$	332.358	−	1086.79i	0.898265	−	2.93726i
$371$	81.0635	+	16.1245i	0.218500	+	0.0434623i
$372$	556.369	−	230.456i	1.49562	−	0.619505i
$373$	−258.982			−0.694321			−0.347160	−	0.937806i	$-0.612854\pi$
$373$	−258.982			−0.694321			−0.347160	+	0.937806i	$0.612854\pi$
$374$	115.941	−	239.321i	0.310004	−	0.639896i
$375$	50.1372	−	475.931i	0.133699	−	1.26915i
$376$	374.896	−	155.287i	0.997063	−	0.412997i
$377$	−174.711	−	34.7522i	−0.463424	−	0.0921809i
$378$	29.6816	+	29.6816i	0.0785228	+	0.0785228i
$379$	−499.058	+	333.460i	−1.31678	+	0.879842i	−0.997693	−	0.0678848i	$-0.978375\pi$
$379$	−499.058	+	333.460i	−1.31678	+	0.879842i	−0.319083	+	0.947727i	$0.603375\pi$
$380$	−432.240	+	353.097i	−1.13747	+	0.929204i
$381$	644.387	+	430.566i	1.69131	+	1.13009i
$382$	411.363	+	170.392i	1.07687	+	0.446052i
$383$	56.9029	−	137.376i	0.148572	−	0.358683i	−0.832020	−	0.554746i	$-0.812816\pi$
$383$	56.9029	−	137.376i	0.148572	−	0.358683i	0.980591	+	0.196062i	$0.0628155\pi$
$384$	354.119	−	529.977i	0.922185	−	1.38015i
$385$	20.1568	−	16.4661i	0.0523554	−	0.0427692i
$386$	111.087	+	166.254i	0.287791	+	0.430710i
$387$	−154.345	+	154.345i	−0.398825	+	0.398825i
$388$	24.7497	−	124.425i	0.0637878	−	0.320683i
$389$	−119.943	−	289.569i	−0.308338	−	0.744394i	−0.999759	−	0.0219418i	$-0.993015\pi$
$389$	−119.943	−	289.569i	−0.308338	−	0.744394i	0.691421	−	0.722452i	$-0.256985\pi$
$390$	−529.226	−	995.521i	−1.35699	−	2.55262i
$391$	−101.747	−	114.392i	−0.260222	−	0.292563i
$392$		−	279.370i		−	0.712679i
$393$	194.548	+	469.680i	0.495033	+	1.19511i
$394$	211.061	−	1061.07i	0.535687	−	2.69308i
$395$	−537.406	−	164.348i	−1.36052	−	0.416071i
$396$	−137.281	+	91.7279i	−0.346668	+	0.231636i
$397$	−772.130	+	153.586i	−1.94491	+	0.386867i	−0.947085	+	0.320984i	$0.895986\pi$
$397$	−772.130	+	153.586i	−1.94491	+	0.386867i	−0.997827	+	0.0658832i	$0.979014\pi$
$398$	276.678	−	414.077i	0.695170	−	1.04039i
$399$	29.1720	−	70.4273i	0.0731127	−	0.176510i
$400$	−106.770	+	70.6450i	−0.266925	+	0.176613i
$401$	236.884	−	354.522i	0.590734	−	0.884096i	−0.408860	−	0.912597i	$-0.634074\pi$
$401$	236.884	−	354.522i	0.590734	−	0.884096i	0.999594	+	0.0285015i	$0.00907354\pi$
$402$	86.5555	+	435.144i	0.215312	+	1.08245i
$403$	−418.871	+	279.881i	−1.03938	+	0.694493i
$404$	126.976	+	126.976i	0.314298	+	0.314298i
$405$	143.930	+	478.366i	0.355384	+	1.18115i
$406$	11.9201	+	28.7776i	0.0293598	+	0.0708807i
$407$	360.697			0.886232
$408$	−22.1667	+	378.884i	−0.0543301	+	0.928637i
$409$	446.077			1.09065			0.545326	−	0.838224i	$-0.316406\pi$
$409$	446.077			1.09065			0.545326	+	0.838224i	$0.316406\pi$
$410$	−313.271	+	379.967i	−0.764076	+	0.926749i
$411$	87.4114	−	439.447i	0.212680	−	1.06921i
$412$	404.477	+	404.477i	0.981740	+	0.981740i
$413$	−55.6081	−	83.2234i	−0.134644	−	0.201509i
$414$	31.2073	+	156.890i	0.0753800	+	0.378961i
$415$	−156.305	−	15.7517i	−0.376640	−	0.0379559i
$416$	−282.873	+	682.915i	−0.679982	+	1.64162i
$417$	−14.3831	+	34.7239i	−0.0344919	+	0.0832707i
$418$	−247.871	−	165.622i	−0.592992	−	0.396225i
$419$	−276.806	+	55.0601i	−0.660635	+	0.131408i	−0.514011	−	0.857784i	$-0.671841\pi$
$419$	−276.806	+	55.0601i	−0.660635	+	0.131408i	−0.146624	+	0.989192i	$0.546841\pi$
$420$	−55.4560	+	103.189i	−0.132038	+	0.245688i
$421$	−234.445	−	234.445i	−0.556877	−	0.556877i	0.371540	−	0.928417i	$-0.378830\pi$
$421$	−234.445	−	234.445i	−0.556877	−	0.556877i	−0.928417	+	0.371540i	$0.878830\pi$
$422$	122.564	−	616.172i	0.290437	−	1.46012i
$423$	−363.724	+	150.659i	−0.859867	+	0.356169i
$424$			461.307i			1.08799i
$425$	187.023	−	381.638i	0.440055	−	0.897971i
$426$	863.081			2.02601
$427$	−2.40721	−	5.81152i	−0.00563750	−	0.0136101i
$428$	−273.728	−	54.4478i	−0.639551	−	0.127215i
$429$	253.026	−	253.026i	0.589805	−	0.589805i
$430$	533.497	+	286.713i	1.24069	+	0.666774i
$431$	41.0749	+	206.498i	0.0953015	+	0.479113i	0.998730	+	0.0503750i	$0.0160416\pi$
$431$	41.0749	+	206.498i	0.0953015	+	0.479113i	−0.903429	+	0.428738i	$0.858958\pi$
$432$	36.4074	−	54.4875i	0.0842763	−	0.126128i
$433$	−256.565	−	106.273i	−0.592528	−	0.245433i	0.0662097	−	0.997806i	$-0.478909\pi$
$433$	−256.565	−	106.273i	−0.592528	−	0.245433i	−0.658738	+	0.752373i	$0.728909\pi$
$434$	81.3845	+	33.7106i	0.187522	+	0.0776741i
$435$	−18.2259	+	180.858i	−0.0418987	+	0.415765i
$436$	−554.920	+	110.381i	−1.27275	+	0.253166i
$437$	−142.700	+	95.3491i	−0.326545	+	0.218190i
$438$	227.873	−	227.873i	0.520257	−	0.520257i
$439$	141.565	+	28.1591i	0.322473	+	0.0641438i	0.353672	−	0.935369i	$-0.384933\pi$
$439$	141.565	+	28.1591i	0.322473	+	0.0641438i	−0.0311997	+	0.999513i	$0.509933\pi$
$440$	112.085	+	92.4111i	0.254740	+	0.210025i
$441$			271.045i			0.614614i
$442$	−137.647	−	991.749i	−0.311418	−	2.24378i
$443$		−	438.344i		−	0.989490i	−0.869038	−	0.494745i	$-0.835261\pi$
$443$		−	438.344i		−	0.989490i	0.869038	−	0.494745i	$-0.164739\pi$
$444$	−1499.87	+	621.267i	−3.37809	+	1.39925i
$445$	−9.33869	+	2.80982i	−0.0209858	+	0.00631419i
$446$	−682.362	+	682.362i	−1.52996	+	1.52996i
$447$	323.250	+	483.778i	0.723155	+	1.08228i
$448$	105.780	−	21.0409i	0.236116	−	0.0469664i
$449$	188.867	+	126.197i	0.420640	+	0.281063i	0.747823	−	0.663898i	$-0.231099\pi$
$449$	188.867	+	126.197i	0.420640	+	0.281063i	−0.327183	+	0.944961i	$0.606099\pi$
$450$	−370.341	+	245.039i	−0.822979	+	0.544530i
$451$	−144.400	−	59.8125i	−0.320178	−	0.132622i
$452$	−560.773	−	374.696i	−1.24065	−	0.828974i
$453$	157.036	+	789.473i	0.346658	+	1.74277i
$454$	283.738	+	424.644i	0.624974	+	0.935340i
$455$	28.6592	−	93.7133i	0.0629872	−	0.205963i
$456$	417.291	+	83.0043i	0.915112	+	0.182027i
$457$	291.671	−	120.814i	0.638230	−	0.264364i	−0.0400151	−	0.999199i	$-0.512741\pi$
$457$	291.671	−	120.814i	0.638230	−	0.264364i	0.678246	+	0.734835i	$0.262741\pi$
$458$	−620.935			−1.35575
$459$	−12.7056	+	217.170i	−0.0276810	+	0.473138i
$460$	232.881	−	123.801i	0.506264	−	0.269134i
$461$	−639.723	+	264.982i	−1.38769	+	0.574798i	−0.946525	−	0.322630i	$-0.895433\pi$
$461$	−639.723	+	264.982i	−1.38769	+	0.574798i	−0.441161	+	0.897428i	$0.645433\pi$
$462$	−61.3687	−	12.2070i	−0.132833	−	0.0264221i
$463$	320.915	+	320.915i	0.693122	+	0.693122i	0.962918	−	0.269796i	$-0.0869563\pi$
$463$	320.915	+	320.915i	0.693122	+	0.693122i	−0.269796	+	0.962918i	$0.586956\pi$
$464$	40.4327	−	27.0163i	0.0871395	−	0.0582247i
$465$	325.220	+	398.114i	0.699398	+	0.856160i
$466$	77.6732	+	51.8996i	0.166681	+	0.111373i
$467$	−78.5327	−	32.5293i	−0.168164	−	0.0696559i	0.297013	−	0.954873i	$-0.404009\pi$
$467$	−78.5327	−	32.5293i	−0.168164	−	0.0696559i	−0.465177	+	0.885217i	$0.654009\pi$
$468$	−237.895	+	574.329i	−0.508322	+	1.22720i
$469$	−21.4248	+	32.0645i	−0.0456818	+	0.0683677i
$470$	691.092	+	845.991i	1.47041	+	1.79998i
$471$	−496.716	−	743.388i	−1.05460	−	1.57832i
$472$	395.023	−	395.023i	0.836914	−	0.836914i
$473$	−37.5015	+	188.533i	−0.0792843	+	0.398589i
$474$	517.007	+	1248.17i	1.09073	+	2.63326i
$475$	−394.942	−	266.483i	−0.831457	−	0.561017i
$476$	−77.7345	+	69.1415i	−0.163308	+	0.145255i
$477$		−	447.560i		−	0.938282i
$478$	−499.279	−	1205.37i	−1.04452	−	2.52169i
$479$	−50.1882	+	252.313i	−0.104777	+	0.526749i	0.892373	+	0.451299i	$0.149039\pi$
$479$	−50.1882	+	252.313i	−0.104777	+	0.526749i	−0.997150	+	0.0754500i	$0.975961\pi$
$480$	721.309	+	220.589i	1.50273	+	0.459561i
$481$	1129.20	−	754.508i	2.34761	−	1.56862i
$482$	417.443	−	83.0346i	0.866065	−	0.172271i
$483$	−20.0129	+	29.9515i	−0.0414347	+	0.0620113i
$484$	215.579	−	520.455i	0.445412	−	1.07532i
$485$	107.796	−	10.3710i	0.222260	−	0.0213834i
$486$	466.316	−	697.891i	0.959497	−	1.43599i
$487$	−57.7733	−	290.446i	−0.118631	−	0.596398i	−0.993669	−	0.112344i	$-0.964164\pi$
$487$	−57.7733	−	290.446i	−0.118631	−	0.596398i	0.875038	−	0.484053i	$-0.160836\pi$
$488$	29.1917	−	19.5053i	0.0598192	−	0.0399699i
$489$	297.504	+	297.504i	0.608393	+	0.608393i
$490$	720.183	−	216.688i	1.46976	−	0.442221i
$491$	192.066	+	463.688i	0.391173	+	0.944375i	0.989685	+	0.143261i	$0.0457589\pi$
$491$	192.066	+	463.688i	0.391173	+	0.944375i	−0.598512	+	0.801114i	$0.704241\pi$
$492$	703.476			1.42983
$493$	−70.3809	+	145.277i	−0.142761	+	0.294680i
$494$	−1122.44			−2.27214
$495$	−108.745	−	89.6573i	−0.219688	−	0.181126i
$496$	26.8293	−	134.880i	0.0540914	−	0.271936i
$497$	53.0463	+	53.0463i	0.106733	+	0.106733i
$498$	209.820	+	314.019i	0.421326	+	0.630559i
$499$	−98.3433	−	494.405i	−0.197081	−	0.990792i	−0.945017	−	0.327021i	$-0.893955\pi$
$499$	−98.3433	−	494.405i	−0.197081	−	0.990792i	0.747936	−	0.663771i	$-0.231045\pi$
$500$	562.808	+	468.310i	1.12562	+	0.936619i
$501$	2.11428	−	5.10433i	0.00422012	−	0.0101883i
$502$	−36.3027	+	87.6425i	−0.0723162	+	0.174587i
$503$	504.248	+	336.928i	1.00248	+	0.669836i	0.944510	−	0.328482i	$-0.106537\pi$
$503$	504.248	+	336.928i	1.00248	+	0.669836i	0.0579708	+	0.998318i	$0.481537\pi$
$504$	33.8066	−	6.72454i	0.0670765	−	0.0133423i
$505$	−72.5649	+	135.024i	−0.143693	+	0.267375i
$506$	99.6116	+	99.6116i	0.196861	+	0.196861i
$507$	136.618	−	686.823i	0.269463	−	1.35468i
$508$	−1095.43	+	453.742i	−2.15636	+	0.893193i
$509$			586.035i			1.15135i	0.817680	+	0.575673i	$0.195260\pi$
$509$			586.035i			1.15135i	−0.817680	+	0.575673i	$0.804740\pi$
$510$	−993.911	+	236.731i	−1.94884	+	0.464178i
$511$	28.0108			0.0548157
$512$	−122.932	−	296.783i	−0.240101	−	0.579655i
$513$	239.185	+	47.5768i	0.466247	+	0.0927423i
$514$	−133.566	+	133.566i	−0.259856	+	0.259856i
$515$	−231.152	+	430.113i	−0.448839	+	0.835171i
$516$	−168.789	−	848.562i	−0.327111	−	1.64450i
$517$	−192.619	+	288.275i	−0.372571	+	0.557592i
$518$	−219.398	−	90.8776i	−0.423548	−	0.175439i
$519$	246.788	+	102.223i	0.475507	+	0.196962i
$520$	544.202	+	54.8420i	1.04654	+	0.105465i
$521$	66.5951	−	13.2466i	0.127822	−	0.0254253i	−0.130765	−	0.991413i	$-0.541743\pi$
$521$	66.5951	−	13.2466i	0.127822	−	0.0254253i	0.258587	+	0.965988i	$0.416743\pi$
$522$	140.244	−	93.7083i	0.268667	−	0.179518i
$523$	354.673	−	354.673i	0.678152	−	0.678152i	−0.281430	−	0.959582i	$-0.590809\pi$
$523$	354.673	−	354.673i	0.678152	−	0.678152i	0.959582	+	0.281430i	$0.0908087\pi$
$524$	−762.833	−	151.737i	−1.45579	−	0.289574i
$525$	−97.9893	−	19.9524i	−0.186646	−	0.0380045i
$526$		−	1020.96i		−	1.94098i
$527$	149.773	+	431.259i	0.284199	+	0.818329i
$528$			97.6835i			0.185007i
$529$	−413.805	+	171.404i	−0.782240	+	0.324015i
$530$	−1189.20	+	357.804i	−2.24377	+	0.675102i
$531$	−383.252	+	383.252i	−0.721755	+	0.721755i
$532$	64.7938	+	96.9708i	0.121793	+	0.182276i
$533$	−577.177	+	114.808i	−1.08288	+	0.215399i
$534$	19.4936	+	13.0252i	0.0365048	+	0.0243917i
$535$	−22.8155	−	237.145i	−0.0426457	−	0.443262i
$536$	−198.853	−	82.3676i	−0.370994	−	0.153671i
$537$	−377.968	−	252.550i	−0.703850	−	0.470298i
$538$	−33.5060	−	168.446i	−0.0622788	−	0.313097i
$539$	132.612	+	198.469i	0.246034	+	0.368216i
$540$	−358.384	−	109.600i	−0.663675	−	0.202963i
$541$	−941.924	−	187.360i	−1.74108	−	0.346322i	−0.780677	−	0.624935i	$-0.785125\pi$
$541$	−941.924	−	187.360i	−1.74108	−	0.346322i	−0.960404	+	0.278613i	$0.910125\pi$
$542$	76.0232	−	31.4898i	0.140264	−	0.0580993i
$543$	892.925			1.64443
$544$	534.281	+	404.049i	0.982135	+	0.742736i
$545$	−226.710	−	426.462i	−0.415983	−	0.782499i
$546$	−217.656	+	90.1562i	−0.398638	+	0.165121i
$547$	407.466	+	81.0501i	0.744911	+	0.148172i	0.552931	−	0.833227i	$-0.313509\pi$
$547$	407.466	+	81.0501i	0.744911	+	0.148172i	0.191980	+	0.981399i	$0.438509\pi$
$548$	484.714	+	484.714i	0.884515	+	0.884515i
$549$	−28.3218	+	18.9240i	−0.0515880	+	0.0344700i
$550$	−151.288	+	360.620i	−0.275069	+	0.655673i
$551$	150.467	+	100.539i	0.273080	+	0.182467i
$552$	−185.749	−	76.9397i	−0.336502	−	0.139384i
$553$	−44.9382	+	108.490i	−0.0812625	+	0.196185i
$554$	427.645	−	640.015i	0.771922	−	1.15526i
$555$	−876.735	−	1073.24i	−1.57970	−	1.93377i
$556$	−31.9463	−	47.8110i	−0.0574574	−	0.0859910i
$557$	36.0281	−	36.0281i	0.0646824	−	0.0646824i	−0.674026	−	0.738708i	$-0.735436\pi$
$557$	36.0281	−	36.0281i	0.0646824	−	0.0646824i	0.738708	+	0.674026i	$0.235436\pi$
$558$	93.0598	−	467.843i	0.166774	−	0.838429i
$559$	276.971	+	668.668i	0.495477	+	1.19619i
$560$	12.5574	+	23.6216i	0.0224239	+	0.0421814i
$561$	−164.102	−	279.687i	−0.292518	−	0.498550i
$562$			558.075i			0.993016i
$563$	−0.0280950	−	0.0678273i	−4.99023e−5	−	0.000120475i	0.923855	−	0.382744i	$-0.125021\pi$
$563$	−0.0280950	−	0.0678273i	−4.99023e−5	−	0.000120475i	−0.923904	+	0.382623i	$0.875021\pi$
$564$	304.434	−	1530.49i	0.539776	−	2.71364i
$565$	168.368	−	550.550i	0.297996	−	0.974425i
$566$	1028.32	−	687.103i	1.81682	−	1.21396i
$567$	102.379	−	20.3645i	0.180563	−	0.0359163i
$568$	−232.621	+	348.141i	−0.409543	+	0.612925i
$569$	246.037	−	593.986i	0.432403	−	1.04391i	−0.546108	−	0.837715i	$-0.683891\pi$
$569$	246.037	−	593.986i	0.432403	−	1.04391i	0.978510	−	0.206198i	$-0.0661089\pi$
$570$	109.688	+	1140.11i	0.192436	+	2.00019i
$571$	−75.2274	+	112.586i	−0.131747	+	0.197173i	−0.891478	−	0.453065i	$-0.850331\pi$
$571$	−75.2274	+	112.586i	−0.131747	+	0.197173i	0.759731	+	0.650238i	$0.225331\pi$
$572$	106.803	+	536.937i	0.186719	+	0.938701i
$573$	451.448	−	301.648i	0.787867	−	0.526436i
$574$	72.7633	+	72.7633i	0.126765	+	0.126765i
$575$	158.476	+	159.916i	0.275611	+	0.278115i
$576$	−223.496	−	539.567i	−0.388014	−	0.936748i
$577$	0.694820			0.00120419			0.000602097	−	1.00000i	$-0.499808\pi$
$577$	0.694820			0.00120419			0.000602097		1.00000i	$0.499808\pi$
$578$	−901.165	−	105.808i	−1.55911	−	0.183059i
$579$	243.825			0.421113
$580$	−214.574	−	176.910i	−0.369955	−	0.305017i
$581$	−6.40418	+	32.1960i	−0.0110227	+	0.0554148i
$582$	−184.090	−	184.090i	−0.316306	−	0.316306i
$583$	−218.975	−	327.719i	−0.375600	−	0.562126i
$584$	30.5001	+	153.334i	0.0522261	+	0.262559i
$585$	−527.985	−	53.2077i	−0.902539	−	0.0909534i
$586$	−23.0848	+	55.7317i	−0.0393939	+	0.0951053i
$587$	−181.654	+	438.552i	−0.309462	+	0.747108i	0.690260	+	0.723561i	$0.257496\pi$
$587$	−181.654	+	438.552i	−0.309462	+	0.747108i	−0.999723	+	0.0235471i	$0.992504\pi$
$588$	−893.282	−	596.872i	−1.51919	−	1.01509i
$589$	501.946	−	99.8433i	0.852201	−	0.169513i
$590$	1324.72	+	711.931i	2.24528	+	1.20666i
$591$	−932.842	−	932.842i	−1.57841	−	1.57841i
$592$	−72.3270	+	363.613i	−0.122174	+	0.614210i
$593$	908.273	−	376.219i	1.53166	−	0.634433i	0.551772	−	0.833995i	$-0.313952\pi$
$593$	908.273	−	376.219i	1.53166	−	0.634433i	0.979885	+	0.199561i	$0.0639517\pi$
$594$		−	200.174i		−	0.336993i
$595$	−75.6372	−	46.5375i	−0.127121	−	0.0782142i
$596$	−890.161			−1.49356
$597$	−232.395	−	561.050i	−0.389271	−	0.939782i
$598$	520.214	+	103.477i	0.869922	+	0.173038i
$599$	615.686	−	615.686i	1.02786	−	1.02786i	0.0282550	−	0.999601i	$-0.491005\pi$
$599$	615.686	−	615.686i	1.02786	−	1.02786i	0.999601	−	0.0282550i	$-0.00899505\pi$
$600$	2.52404	−	558.129i	0.00420673	−	0.930215i
$601$	12.9998	+	65.3544i	0.0216303	+	0.108743i	0.990092	−	0.140419i	$-0.0448449\pi$
$601$	12.9998	+	65.3544i	0.0216303	+	0.108743i	−0.968462	+	0.249162i	$0.919845\pi$
$602$	70.3116	−	105.229i	0.116797	−	0.174799i
$603$	192.927	+	79.9130i	0.319945	+	0.132526i
$604$	−1137.75	−	471.272i	−1.88369	−	0.780252i
$605$	478.458	+	48.2166i	0.790840	+	0.0796969i
$606$	361.428	−	71.8926i	0.596417	−	0.118635i
$607$	982.189	−	656.278i	1.61810	−	1.08118i	0.680915	−	0.732363i	$-0.261582\pi$
$607$	982.189	−	656.278i	1.61810	−	1.08118i	0.937190	−	0.348820i	$-0.113418\pi$
$608$	530.989	−	530.989i	0.873337	−	0.873337i
$609$	37.2532	+	7.41013i	0.0611712	+	0.0121677i
$610$	72.9244	+	60.1240i	0.119548	+	0.0985639i
$611$			1305.40i			2.13650i
$612$	449.329	+	339.804i	0.734197	+	0.555235i
$613$			891.537i			1.45438i	0.686434	+	0.727192i	$0.259175\pi$
$613$			891.537i			1.45438i	−0.686434	+	0.727192i	$0.740825\pi$
$614$	172.290	−	71.3649i	0.280603	−	0.116229i
$615$	173.019	+	575.044i	0.281331	+	0.935031i
$616$	21.4643	−	21.4643i	0.0348446	−	0.0348446i
$617$	−564.833	−	845.333i	−0.915451	−	1.37007i	−0.928968	−	0.370161i	$-0.879303\pi$
$617$	−564.833	−	845.333i	−0.915451	−	1.37007i	0.0135164	−	0.999909i	$-0.495697\pi$
$618$	1151.31	−	229.010i	1.86297	−	0.370567i
$619$	−41.0817	−	27.4499i	−0.0663679	−	0.0443456i	0.521944	−	0.852980i	$-0.325207\pi$
$619$	−41.0817	−	27.4499i	−0.0663679	−	0.0443456i	−0.588312	+	0.808634i	$0.700207\pi$
$620$	−782.864	+	75.3184i	−1.26268	+	0.121481i
$621$	−106.468	−	44.1007i	−0.171447	−	0.0710156i
$622$	1198.47	+	800.792i	1.92680	+	1.28745i
$623$	0.397557	+	1.99865i	0.000638133	+	0.00320811i
$624$	204.335	+	305.809i	0.327460	+	0.490078i
$625$	−244.390	+	575.238i	−0.391024	+	0.920381i
$626$	−789.188	−	156.979i	−1.26068	−	0.250766i
$627$	−335.850	+	139.114i	−0.535646	+	0.221872i
$628$	1367.85			2.17810
$629$	−403.761	−	1162.60i	−0.641910	−	1.84833i
$630$	43.5565	+	81.9335i	0.0691373	+	0.130053i
$631$	476.068	−	197.194i	0.754466	−	0.312510i	0.0279037	−	0.999611i	$-0.491117\pi$
$631$	476.068	−	197.194i	0.754466	−	0.312510i	0.726562	+	0.687101i	$0.241117\pi$
$632$	−642.819	−	127.865i	−1.01712	−	0.202317i
$633$	−541.707	−	541.707i	−0.855777	−	0.855777i
$634$	−774.994	+	517.835i	−1.22239	+	0.816774i
$635$	−640.323	−	783.843i	−1.00838	−	1.23440i
$636$	1475.02	+	985.579i	2.31922	+	1.54965i
$637$	830.316	+	343.928i	1.30348	+	0.539919i
$638$	56.8438	−	137.233i	0.0890968	−	0.215099i
$639$	225.688	−	337.767i	0.353190	−	0.528586i
$640$	−644.672	+	526.634i	−1.00730	+	0.822865i
$641$	537.731	+	804.772i	0.838894	+	1.25549i	0.964677	+	0.263436i	$0.0848559\pi$
$641$	537.731	+	804.772i	0.838894	+	1.25549i	−0.125782	+	0.992058i	$0.540144\pi$
$642$	−404.987	+	404.987i	−0.630820	+	0.630820i
$643$	−150.230	+	755.257i	−0.233639	+	1.17458i	0.668692	+	0.743540i	$0.266855\pi$
$643$	−150.230	+	755.257i	−0.233639	+	1.17458i	−0.902331	+	0.431044i	$0.858145\pi$
$644$	−21.0902	−	50.9162i	−0.0327487	−	0.0790624i
$645$	652.129	−	346.676i	1.01105	−	0.537483i
$646$	−256.368	+	984.334i	−0.396855	+	1.52374i
$647$		−	209.835i		−	0.324320i	−0.986765	−	0.162160i	$-0.948154\pi$
$647$		−	209.835i		−	0.324320i	0.986765	−	0.162160i	$-0.0518460\pi$
$648$	222.955	+	538.261i	0.344066	+	0.830649i
$649$	−93.1191	+	468.142i	−0.143481	+	0.721328i
$650$	280.724	+	1445.43i	0.431883	+	2.22373i
$651$	89.3149	−	59.6783i	0.137196	−	0.0916717i
$652$	−631.321	+	125.578i	−0.968284	+	0.192604i
$653$	−489.100	+	731.990i	−0.749005	+	1.12097i	0.239664	+	0.970856i	$0.422963\pi$
$653$	−489.100	+	731.990i	−0.749005	+	1.12097i	−0.988669	+	0.150110i	$0.952037\pi$
$654$	−444.332	+	1072.71i	−0.679407	+	1.64023i
$655$	−63.5829	−	660.884i	−0.0970731	−	1.00898i
$656$	89.2512	−	133.574i	0.136054	−	0.203619i
$657$	−29.5912	−	148.765i	−0.0450398	−	0.226431i
$658$	189.794	−	126.816i	0.288440	−	0.192730i
$659$	209.585	+	209.585i	0.318035	+	0.318035i	0.848012	−	0.529977i	$-0.177800\pi$
$659$	209.585	+	209.585i	0.318035	+	0.318035i	−0.529977	+	0.848012i	$0.677800\pi$
$660$	534.953	−	160.956i	0.810535	−	0.243873i
$661$	−230.404	−	556.245i	−0.348569	−	0.841520i	−0.996789	−	0.0800675i	$-0.974486\pi$
$661$	−230.404	−	556.245i	−0.348569	−	0.841520i	0.648220	−	0.761453i	$-0.275514\pi$
$662$	−1262.29			−1.90679
$663$	−1098.79	−	532.320i	−1.65730	−	0.802895i
$664$	−183.217			−0.275930
$665$	−63.3312	+	76.8144i	−0.0952348	+	0.115510i
$666$	−250.873	+	1261.22i	−0.376686	+	1.89373i
$667$	−60.4682	−	60.4682i	−0.0906569	−	0.0906569i
$668$	4.69603	+	7.02810i	0.00702998	+	0.0105211i
$669$	229.571	+	1154.13i	0.343155	+	1.72516i
$670$	58.0974	−	576.506i	0.0867125	−	0.860457i
$671$	−11.4794	+	27.7137i	−0.0171079	+	0.0413021i
$672$	60.3163	−	145.616i	0.0897564	−	0.216691i
$673$	−74.5569	−	49.8174i	−0.110783	−	0.0740228i	0.498945	−	0.866634i	$-0.333721\pi$
$673$	−74.5569	−	49.8174i	−0.110783	−	0.0740228i	−0.609728	+	0.792611i	$0.708721\pi$
$674$	1839.44	−	365.888i	2.72914	−	0.542860i
$675$	1.44674	−	319.911i	0.00214332	−	0.473943i
$676$	757.573	+	757.573i	1.12067	+	1.12067i
$677$	63.4917	−	319.194i	0.0937838	−	0.471483i	−0.905140	−	0.425113i	$-0.860234\pi$
$677$	63.4917	−	319.194i	0.0937838	−	0.471483i	0.998924	−	0.0463706i	$-0.0147655\pi$
$678$	−1278.69	+	529.653i	−1.88598	+	0.781199i
$679$		−	22.6289i		−	0.0333268i
$680$	172.392	−	464.719i	0.253518	−	0.683410i
$681$	622.773			0.914498
$682$	−160.757	−	388.102i	−0.235714	−	0.569065i
$683$	527.992	+	105.024i	0.773049	+	0.153769i	0.565826	−	0.824525i	$-0.308557\pi$
$683$	527.992	+	105.024i	0.773049	+	0.153769i	0.207223	+	0.978294i	$0.433557\pi$
$684$	446.560	−	446.560i	0.652866	−	0.652866i
$685$	−277.007	+	515.436i	−0.404389	+	0.752461i
$686$	−62.0163	−	311.777i	−0.0904028	−	0.454486i
$687$	−420.665	+	629.570i	−0.612322	+	0.916405i
$688$	−182.537	−	75.6093i	−0.265315	−	0.109897i
$689$	−1371.05	−	567.908i	−1.98992	−	0.824250i
$690$	54.2689	−	538.515i	0.0786506	−	0.780457i
$691$	−1212.42	+	241.166i	−1.75459	+	0.349010i	−0.964521	−	0.264006i	$-0.914956\pi$
$691$	−1212.42	+	241.166i	−1.75459	+	0.349010i	−0.790070	+	0.613016i	$0.789956\pi$
$692$	−339.801	+	227.048i	−0.491042	+	0.328103i
$693$	−20.8246	+	20.8246i	−0.0300500	+	0.0300500i
$694$	303.691	+	60.4080i	0.437596	+	0.0870432i
$695$	31.2251	−	37.8730i	0.0449283	−	0.0544935i
$696$			211.997i			0.304593i
$697$	−31.1473	+	532.385i	−0.0446876	+	0.763823i
$698$			979.243i			1.40293i
$699$	105.243	−	43.5929i	0.150562	−	0.0623647i
$700$	108.670	−	107.691i	0.155243	−	0.153845i
$701$	29.3444	−	29.3444i	0.0418608	−	0.0418608i	−0.685867	−	0.727727i	$-0.740577\pi$
$701$	29.3444	−	29.3444i	0.0418608	−	0.0418608i	0.727727	+	0.685867i	$0.240577\pi$
$702$	−418.725	−	626.666i	−0.596474	−	0.892687i
$703$	−1353.16	+	269.160i	−1.92483	+	0.382873i
$704$	−427.642	−	285.741i	−0.607446	−	0.405882i
$705$	1325.95	−	127.568i	1.88078	−	0.180948i
$706$	747.048	+	309.438i	1.05814	+	0.438297i
$707$	26.6326	+	17.7953i	0.0376699	+	0.0251702i
$708$	−419.118	−	2107.05i	−0.591974	−	2.97605i
$709$	−263.526	−	394.394i	−0.371686	−	0.556268i	0.597728	−	0.801699i	$-0.296070\pi$
$709$	−263.526	−	394.394i	−0.371686	−	0.556268i	−0.969414	+	0.245431i	$0.921070\pi$
$710$	−1077.89	−	329.639i	−1.51816	−	0.464280i
$711$	623.663	+	124.054i	0.877163	+	0.174479i
$712$	−10.5079	+	4.35253i	−0.0147584	+	0.00611311i
$713$	−241.841			−0.339187
$714$	29.3501	+	211.468i	0.0411066	+	0.296174i
$715$	−412.642	+	219.363i	−0.577121	+	0.306802i
$716$	642.528	−	266.144i	0.897386	−	0.371709i
$717$	−1560.38	−	310.378i	−2.17626	−	0.432884i
$718$	524.858	+	524.858i	0.731000	+	0.731000i
$719$	104.397	−	69.7559i	0.145198	−	0.0970179i	−0.480850	−	0.876803i	$-0.659672\pi$
$719$	104.397	−	69.7559i	0.145198	−	0.0970179i	0.626047	+	0.779785i	$0.284672\pi$
$720$	112.188	−	91.6464i	0.155816	−	0.127287i
$721$	84.8369	+	56.6862i	0.117666	+	0.0786216i
$722$	6.34695	+	2.62899i	0.00879079	+	0.00364126i
$723$	198.616	−	479.502i	0.274711	−	0.663211i
$724$	−758.967	+	1135.87i	−1.04830	+	1.56889i
$725$	91.8377	−	218.911i	0.126673	−	0.301946i
$726$	−642.270	−	961.224i	−0.884669	−	1.32400i
$727$	445.987	−	445.987i	0.613462	−	0.613462i	−0.330384	−	0.943846i	$-0.607178\pi$
$727$	445.987	−	445.987i	0.613462	−	0.613462i	0.943846	+	0.330384i	$0.107178\pi$
$728$	22.2972	−	112.095i	0.0306280	−	0.153977i
$729$	−47.5752	−	114.857i	−0.0652609	−	0.157554i
$730$	−371.621	+	197.556i	−0.509069	+	0.270625i
$731$	649.658	−	90.1673i	0.888725	−	0.123348i
$732$		−	135.013i		−	0.184444i
$733$	−23.4312	−	56.5678i	−0.0319661	−	0.0771730i	0.907090	−	0.420936i	$-0.138298\pi$
$733$	−23.4312	−	56.5678i	−0.0319661	−	0.0771730i	−0.939056	+	0.343763i	$0.888298\pi$
$734$	143.387	−	720.857i	0.195351	−	0.982093i
$735$	268.201	−	876.998i	0.364900	−	1.19319i
$736$	−295.048	+	197.145i	−0.400881	+	0.267860i
$737$	180.366	−	35.8771i	0.244731	−	0.0486799i
$738$	309.576	−	463.313i	0.419479	−	0.627795i
$739$	−49.4883	+	119.475i	−0.0669665	+	0.161672i	−0.953820	−	0.300380i	$-0.902886\pi$
$739$	−49.4883	+	119.475i	−0.0669665	+	0.161672i	0.886853	+	0.462052i	$0.152886\pi$
$740$	2110.46	−	203.045i	2.85197	−	0.274385i
$741$	−760.418	+	1138.05i	−1.02620	+	1.53582i
$742$	50.6252	+	254.510i	0.0682280	+	0.343005i
$743$	−782.654	+	522.953i	−1.05337	+	0.703839i	−0.956581	−	0.291466i	$-0.905857\pi$
$743$	−782.654	+	522.953i	−1.05337	+	0.703839i	−0.0967887	+	0.995305i	$0.530857\pi$
$744$	423.937	+	423.937i	0.569808	+	0.569808i
$745$	−218.934	−	727.647i	−0.293871	−	0.976707i
$746$	−311.163	−	751.214i	−0.417109	−	1.00699i
$747$	177.758			0.237962
$748$	495.268	+	28.9757i	0.662123	+	0.0387376i
$749$	−49.7822			−0.0664650
$750$	1440.75	−	426.395i	1.92100	−	0.568527i
$751$	−24.6690	+	124.020i	−0.0328482	+	0.165139i	−0.993728	−	0.111828i	$-0.964329\pi$
$751$	−24.6690	+	124.020i	−0.0328482	+	0.165139i	0.960879	+	0.276967i	$0.0893294\pi$
$752$	−251.981	−	251.981i	−0.335082	−	0.335082i
$753$	64.2672	+	96.1827i	0.0853483	+	0.127733i
$754$	−109.109	−	548.529i	−0.144707	−	0.727493i
$755$	105.405	−	1045.94i	0.139609	−	1.38536i
$756$	−29.9683	+	72.3499i	−0.0396406	+	0.0957009i
$757$	0.178855	−	0.431793i	0.000236268	−	0.000570401i	−0.923761	−	0.382969i	$-0.874902\pi$
$757$	0.178855	−	0.431793i	0.000236268	−	0.000570401i	0.923998	+	0.382398i	$0.124902\pi$
$758$	−1566.86	−	1046.94i	−2.06710	−	1.38119i
$759$	168.481	−	33.5129i	0.221977	−	0.0441540i
$760$	−489.449	−	263.041i	−0.644012	−	0.346106i
$761$	964.333	+	964.333i	1.26719	+	1.26719i	0.947533	+	0.319659i	$0.103568\pi$
$761$	964.333	+	964.333i	1.26719	+	1.26719i	0.319659	+	0.947533i	$0.396432\pi$
$762$	−474.696	+	2386.46i	−0.622961	+	3.13184i
$763$	−93.2399	+	38.6212i	−0.122202	+	0.0506176i
$764$			830.672i			1.08727i
$765$	−167.255	+	450.870i	−0.218634	+	0.589373i
$766$	466.847			0.609460
$767$	687.742	+	1660.36i	0.896665	+	2.16474i
$768$	412.268	+	82.0053i	0.536808	+	0.106778i
$769$	−88.1092	+	88.1092i	−0.114576	+	0.114576i	−0.762070	−	0.647494i	$-0.775817\pi$
$769$	−88.1092	+	88.1092i	−0.114576	+	0.114576i	0.647494	+	0.762070i	$0.275817\pi$
$770$	71.9807	+	38.6840i	0.0934814	+	0.0502389i
$771$	44.9364	+	225.910i	0.0582832	+	0.293010i
$772$	−207.245	+	310.165i	−0.268453	+	0.401768i
$773$	437.142	+	181.070i	0.565514	+	0.234244i	0.647077	−	0.762425i	$-0.275991\pi$
$773$	437.142	+	181.070i	0.565514	+	0.234244i	−0.0815630	+	0.996668i	$0.525991\pi$
$774$	−633.145	−	262.257i	−0.818017	−	0.338834i
$775$	−254.112	−	621.414i	−0.327886	−	0.801825i
$776$	123.873	−	24.6399i	0.159630	−	0.0317524i
$777$	−240.777	+	160.882i	−0.309880	+	0.207055i
$778$	695.827	−	695.827i	0.894380	−	0.894380i
$779$	586.352	+	116.633i	0.752698	+	0.149721i
$780$	1338.04	−	1622.91i	1.71544	−	2.08065i
$781$		−	357.746i		−	0.458061i
$782$	209.564	−	432.573i	0.267984	−	0.553162i
$783$			121.513i			0.155189i
$784$	−226.665	+	93.8875i	−0.289113	+	0.119755i
$785$	336.420	+	1118.12i	0.428561	+	1.42436i
$786$	−1128.63	+	1128.63i	−1.43592	+	1.43592i
$787$	813.939	+	1218.15i	1.03423	+	1.54783i	0.821079	+	0.570814i	$0.193372\pi$
$787$	813.939	+	1218.15i	1.03423	+	1.54783i	0.213150	+	0.977019i	$0.431628\pi$
$788$	1979.55	−	393.756i	2.51211	−	0.499691i
$789$	−1035.15	−	691.668i	−1.31198	−	0.876639i
$790$	−168.970	−	1756.29i	−0.213886	−	2.22315i
$791$	−111.144	−	46.0373i	−0.140511	−	0.0582014i
$792$	−136.671	−	91.3209i	−0.172565	−	0.115304i
$793$	22.0342	+	110.773i	0.0277859	+	0.139689i
$794$	−1373.20	−	2055.15i	−1.72948	−	2.58834i
$795$	−442.865	+	1448.13i	−0.557063	+	1.82155i
$796$	911.232	+	181.255i	1.14476	+	0.227708i
$797$	−185.650	+	76.8989i	−0.232937	+	0.0964855i	−0.496099	−	0.868266i	$-0.665235\pi$
$797$	−185.650	+	76.8989i	−0.232937	+	0.0964855i	0.263162	+	0.964752i	$0.415235\pi$
$798$	239.335			0.299918
$799$	1144.79	+	298.158i	1.43277	+	0.373163i
$800$	−816.587	−	550.984i	−1.02073	−	0.688730i
$801$	10.1948	−	4.22283i	0.0127276	−	0.00527195i
$802$	1312.96	+	261.164i	1.63710	+	0.325640i
$803$	−94.4529	−	94.4529i	−0.117625	−	0.117625i
$804$	−688.217	+	459.852i	−0.855991	+	0.571955i
$805$	36.4335	−	29.7626i	0.0452590	−	0.0369721i
$806$	−1315.10	−	878.724i	−1.63164	−	1.09023i
$807$	−193.488	−	80.1452i	−0.239762	−	0.0993125i
$808$	−68.4141	+	165.166i	−0.0846710	+	0.204414i
$809$	−769.532	+	1151.69i	−0.951214	+	1.42359i	−0.0458543	+	0.998948i	$0.514601\pi$
$809$	−769.532	+	1151.69i	−0.951214	+	1.42359i	−0.905360	+	0.424645i	$0.860399\pi$
$810$	−1214.64	+	992.243i	−1.49956	+	1.22499i
$811$	115.781	+	173.278i	0.142763	+	0.213660i	0.895960	−	0.444136i	$-0.146489\pi$
$811$	115.781	+	173.278i	0.142763	+	0.213660i	−0.753197	+	0.657795i	$0.771489\pi$
$812$	−41.0907	+	41.0907i	−0.0506043	+	0.0506043i
$813$	19.5757	−	98.4138i	0.0240784	−	0.121050i
$814$	433.372	+	1046.25i	0.532398	+	1.28532i
$815$	−257.924	−	485.177i	−0.316471	−	0.595309i
$816$	314.854	−	109.346i	0.385850	−	0.134003i
$817$		−	735.267i		−	0.899959i
$818$	535.955	+	1293.91i	0.655202	+	1.58180i
$819$	−21.6327	+	108.755i	−0.0264136	+	0.132790i
$820$	−878.565	−	268.681i	−1.07142	−	0.327659i
$821$	119.759	−	80.0205i	0.145870	−	0.0974671i	−0.480494	−	0.876998i	$-0.659543\pi$
$821$	119.759	−	80.0205i	0.145870	−	0.0974671i	0.626364	+	0.779531i	$0.284543\pi$
$822$	1379.70	−	274.440i	1.67847	−	0.333869i
$823$	536.222	−	802.512i	0.651545	−	0.975106i	−0.347751	−	0.937587i	$-0.613055\pi$
$823$	536.222	−	802.512i	0.651545	−	0.975106i	0.999296	−	0.0375190i	$-0.0119455\pi$
$824$	−217.930	+	526.129i	−0.264478	+	0.638506i
$825$	263.142	+	397.701i	0.318960	+	0.482062i
$826$	174.589	−	261.291i	0.211367	−	0.316333i
$827$	49.1297	+	246.992i	0.0594071	+	0.298660i	0.999054	−	0.0434859i	$-0.0138464\pi$
$827$	49.1297	+	246.992i	0.0594071	+	0.298660i	−0.939647	+	0.342146i	$0.888846\pi$
$828$	−248.135	+	165.798i	−0.299679	+	0.200239i
$829$	423.764	+	423.764i	0.511175	+	0.511175i	0.914886	−	0.403712i	$-0.132280\pi$
$829$	423.764	+	423.764i	0.511175	+	0.511175i	−0.403712	+	0.914886i	$0.632280\pi$
$830$	−142.109	−	472.313i	−0.171216	−	0.569051i
$831$	−359.199	−	867.183i	−0.432249	−	1.04354i
$832$	−1936.50			−2.32752
$833$	491.259	−	649.601i	0.589747	−	0.779834i
$834$	−118.003			−0.141490
$835$	−4.59002	+	5.56724i	−0.00549703	+	0.00666735i
$836$	108.501	−	545.473i	0.129786	−	0.652479i
$837$	242.994	+	242.994i	0.290316	+	0.290316i
$838$	−492.289	−	736.762i	−0.587457	−	0.879191i
$839$	39.9197	+	200.690i	0.0475800	+	0.239201i	0.997256	−	0.0740339i	$-0.0235873\pi$
$839$	39.9197	+	200.690i	0.0475800	+	0.239201i	−0.949676	+	0.313235i	$0.898587\pi$
$840$	−116.039	−	11.6938i	−0.138142	−	0.0139212i
$841$	287.330	−	693.677i	0.341653	−	0.824824i
$842$	398.360	−	961.726i	0.473111	−	1.14219i
$843$	565.835	+	378.079i	0.671216	+	0.448492i
$844$	1149.53	−	228.657i	1.36201	−	0.270920i
$845$	−432.941	+	805.589i	−0.512356	+	0.953359i
$846$	−874.019	−	874.019i	−1.03312	−	1.03312i
$847$	19.6035	−	98.5533i	0.0231446	−	0.116356i
$848$	374.278	−	155.031i	0.441365	−	0.182819i
$849$		−	1508.11i		−	1.77634i
$850$	1331.70	+	83.9561i	1.56671	+	0.0987719i
$851$	651.959			0.766109
$852$	616.185	+	1487.60i	0.723222	+	1.74601i
$853$	607.542	+	120.848i	0.712241	+	0.141674i	0.537896	−	0.843011i	$-0.319219\pi$
$853$	607.542	+	120.848i	0.712241	+	0.141674i	0.174345	+	0.984685i	$0.444219\pi$
$854$	13.9649	−	13.9649i	0.0163524	−	0.0163524i
$855$	474.864	+	255.202i	0.555396	+	0.298482i
$856$	−54.2062	−	272.513i	−0.0633250	−	0.318356i
$857$	576.776	−	863.206i	0.673018	−	1.00724i	−0.325086	−	0.945684i	$-0.605393\pi$
$857$	576.776	−	863.206i	0.673018	−	1.00724i	0.998104	−	0.0615575i	$-0.0196068\pi$
$858$	1037.95	+	429.932i	1.20973	+	0.501087i
$859$	−188.451	−	78.0591i	−0.219385	−	0.0908721i	0.270284	−	0.962781i	$-0.412882\pi$
$859$	−188.451	−	78.0591i	−0.219385	−	0.0908721i	−0.489669	+	0.871908i	$0.662882\pi$
$860$	−113.294	+	1124.23i	−0.131737	+	1.30724i
$861$	123.070	−	24.4802i	0.142939	−	0.0284323i
$862$	−549.626	+	367.248i	−0.637617	+	0.426042i
$863$	−1026.13	+	1026.13i	−1.18902	+	1.18902i	−0.211684	+	0.977338i	$0.567895\pi$
$863$	−1026.13	+	1026.13i	−1.18902	+	1.18902i	−0.977338	+	0.211684i	$0.932105\pi$
$864$	494.541	+	98.3704i	0.572386	+	0.113855i
$865$	−269.170	−	221.922i	−0.311179	−	0.256558i
$866$		−	871.889i		−	1.00680i
$867$	−717.792	+	842.015i	−0.827903	+	0.971182i
$868$			164.341i			0.189333i
$869$	517.363	−	214.299i	0.595354	−	0.246604i
$870$	−546.502	+	164.431i	−0.628164	+	0.189001i
$871$	489.609	−	489.609i	0.562123	−	0.562123i
$872$	−312.942	−	468.351i	−0.358879	−	0.537100i
$873$	−120.182	+	23.9056i	−0.137665	+	0.0273833i
$874$	−448.026	−	299.362i	−0.512616	−	0.342519i
$875$	114.758	+	62.3437i	0.131152	+	0.0712500i
$876$	555.447	+	230.074i	0.634072	+	0.262641i
$877$	−552.307	−	369.040i	−0.629768	−	0.420798i	0.199305	−	0.979937i	$-0.436131\pi$
$877$	−552.307	−	369.040i	−0.629768	−	0.420798i	−0.829073	+	0.559140i	$0.811131\pi$
$878$	88.4095	+	444.464i	0.100694	+	0.506224i
$879$	40.8674	+	61.1624i	0.0464931	+	0.0695818i
$880$	37.3085	−	121.996i	0.0423961	−	0.138632i
$881$	−611.125	−	121.560i	−0.693672	−	0.137980i	−0.164352	−	0.986402i	$-0.552553\pi$
$881$	−611.125	−	121.560i	−0.693672	−	0.137980i	−0.529321	+	0.848422i	$0.677553\pi$
$882$	−786.206	+	325.657i	−0.891390	+	0.369226i
$883$	464.251			0.525765			0.262883	−	0.964828i	$-0.415327\pi$
$883$	464.251			0.525765			0.262883	+	0.964828i	$0.415327\pi$
$884$	1611.10	−	945.293i	1.82251	−	1.06934i
$885$	1619.29	−	860.825i	1.82970	−	0.972684i
$886$	1271.48	−	526.665i	1.43508	−	0.594430i
$887$	−728.743	−	144.956i	−0.821582	−	0.163423i	−0.233637	−	0.972324i	$-0.575063\pi$
$887$	−728.743	−	144.956i	−0.821582	−	0.163423i	−0.587945	+	0.808901i	$0.700063\pi$
$888$	−1142.86	−	1142.86i	−1.28700	−	1.28700i
$889$	−175.851	+	117.500i	−0.197808	+	0.132171i
$890$	−19.3706	−	23.7123i	−0.0217647	−	0.0266430i
$891$	−413.894	−	276.555i	−0.464527	−	0.310387i
$892$	−1663.28	−	688.952i	−1.86466	−	0.772368i
$893$	507.496	−	1225.20i	0.568304	−	1.37201i
$894$	−1014.89	+	1518.89i	−1.13522	+	1.69898i
$895$	375.584	+	459.766i	0.419647	+	0.513705i
$896$	96.6379	+	144.629i	0.107855	+	0.161416i
$897$	457.345	−	457.345i	0.509861	−	0.509861i
$898$	−139.132	+	699.462i	−0.154935	+	0.778911i
$899$	97.5859	+	235.593i	0.108549	+	0.262061i
$900$	−686.747	−	463.376i	−0.763052	−	0.514862i
$901$	−811.187	+	1072.65i	−0.900318	+	1.19051i
$902$		−	490.718i		−	0.544033i
$903$	−59.0580	−	142.579i	−0.0654020	−	0.157894i
$904$	130.992	−	658.541i	0.144903	−	0.728475i
$905$	−1115.17	−	341.038i	−1.23223	−	0.376837i
$906$	−2101.31	+	1404.05i	−2.31932	+	1.54972i
$907$	−779.172	+	154.987i	−0.859065	+	0.170879i	−0.604919	−	0.796287i	$-0.706794\pi$
$907$	−779.172	+	154.987i	−0.859065	+	0.170879i	−0.254146	+	0.967166i	$0.581794\pi$
$908$	−529.344	+	792.219i	−0.582978	+	0.872488i
$909$	66.3754	−	160.244i	0.0730202	−	0.176286i
$910$	306.263	−	29.4652i	0.336553	−	0.0323793i
$911$	461.042	−	689.998i	0.506084	−	0.757408i	−0.487178	−	0.873303i	$-0.661974\pi$
$911$	461.042	−	689.998i	0.506084	−	0.757408i	0.993261	+	0.115895i	$0.0369736\pi$
$912$	−72.8935	−	366.461i	−0.0799271	−	0.401821i
$913$	130.160	−	86.9703i	0.142563	−	0.0952577i
$914$	700.879	+	700.879i	0.766826	+	0.766826i
$915$	110.364	−	33.2063i	0.120617	−	0.0362910i
$916$	−443.308	−	1070.24i	−0.483961	−	1.16839i
$917$	−138.735			−0.151292
$918$	−645.201	+	224.073i	−0.702833	+	0.244088i
$919$	470.363			0.511821			0.255910	−	0.966700i	$-0.417625\pi$
$919$	470.363			0.511821			0.255910	+	0.966700i	$0.417625\pi$
$920$	202.594	+	167.033i	0.220211	+	0.181558i
$921$	44.3641	−	223.033i	0.0481695	−	0.242164i
$922$	−1537.24	−	1537.24i	−1.66729	−	1.66729i
$923$	−748.335	−	1119.96i	−0.810764	−	1.21339i
$924$	−22.7735	−	114.490i	−0.0246466	−	0.123907i
$925$	685.040	+	1675.22i	0.740584	+	1.81105i
$926$	−545.286	+	1316.44i	−0.588862	+	1.42164i
$927$	211.436	−	510.451i	0.228086	−	0.550648i
$928$	311.108	+	207.876i	0.335246	+	0.224004i
$929$	−934.799	+	185.943i	−1.00624	+	0.200154i	−0.670587	−	0.741831i	$-0.733958\pi$
$929$	−934.799	+	185.943i	−1.00624	+	0.200154i	−0.335655	+	0.941985i	$0.608958\pi$
$930$	−764.041	+	1421.68i	−0.821549	+	1.52869i
$931$	−645.599	−	645.599i	−0.693446	−	0.693446i
$932$	−34.0001	+	170.930i	−0.0364808	+	0.183402i
$933$	1623.86	−	672.623i	1.74047	−	0.720925i
$934$		−	266.879i		−	0.285738i
$935$	98.1246	+	411.975i	0.104946	+	0.440615i
$936$	−618.891			−0.661208
$937$	−187.442	−	452.524i	−0.200044	−	0.482950i	0.791742	−	0.610856i	$-0.209174\pi$
$937$	−187.442	−	452.524i	−0.200044	−	0.482950i	−0.991786	+	0.127906i	$0.959174\pi$
$938$	−118.749	−	23.6207i	−0.126598	−	0.0251820i
$939$	−693.814	+	693.814i	−0.738886	+	0.738886i
$940$	−964.751	+	1795.15i	−1.02633	+	1.90973i
$941$	30.6525	+	154.100i	0.0325743	+	0.163762i	0.993649	−	0.112528i	$-0.0358948\pi$
$941$	30.6525	+	154.100i	0.0325743	+	0.163762i	−0.961074	+	0.276290i	$0.910895\pi$
$942$	1559.51	−	2333.97i	1.65553	−	2.47768i
$943$	−261.003	−	108.111i	−0.276780	−	0.114646i
$944$	−453.254	−	187.744i	−0.480142	−	0.198881i
$945$	−66.5118	−	6.70273i	−0.0703829	−	0.00709284i
$946$	−591.924	+	117.741i	−0.625713	+	0.124462i
$947$	−985.208	+	658.295i	−1.04035	+	0.695137i	−0.953595	−	0.301093i	$-0.902649\pi$
$947$	−985.208	+	658.295i	−1.04035	+	0.695137i	−0.0867515	+	0.996230i	$0.527649\pi$
$948$	−1782.22	+	1782.22i	−1.87998	+	1.87998i
$949$	−493.273	−	98.1181i	−0.519782	−	0.103391i
$950$	298.456	−	1465.76i	0.314164	−	1.54291i
$951$			1136.59i			1.19515i
$952$	−93.2107	−	45.1567i	−0.0979104	−	0.0474335i
$953$			1593.67i			1.67227i	0.548526	+	0.836134i	$0.315189\pi$
$953$			1593.67i			1.67227i	−0.548526	+	0.836134i	$0.684811\pi$
$954$	1298.22	−	537.738i	1.36081	−	0.563667i
$955$	−679.018	+	204.302i	−0.711014	+	0.213929i
$956$	1721.11	−	1721.11i	1.80033	−	1.80033i
$957$	−100.631	−	150.606i	−0.105153	−	0.157373i
$958$	−792.171	+	157.573i	−0.826901	+	0.164481i
$959$	101.666	+	67.9312i	0.106013	+	0.0708355i
$960$	189.241	+	1966.98i	0.197126	+	2.04894i
$961$	−221.579	−	91.7808i	−0.230571	−	0.0955055i
$962$	3545.28	+	2368.88i	3.68532	+	2.46245i
$963$	52.5909	+	264.392i	0.0546115	+	0.274551i
$964$	441.146	+	660.222i	0.457620	+	0.684877i
$965$	−304.511	−	93.1247i	−0.315555	−	0.0965023i
$966$	−110.924	−	22.0641i	−0.114828	−	0.0228407i
$967$	609.471	−	252.451i	0.630270	−	0.261066i	−0.0445979	−	0.999005i	$-0.514201\pi$
$967$	609.471	−	252.451i	0.630270	−	0.261066i	0.674868	+	0.737939i	$0.264201\pi$
$968$	560.836			0.579376
$969$	824.340	+	926.791i	0.850713	+	0.956440i
$970$	159.598	+	300.218i	0.164534	+	0.309503i
$971$	405.286	−	167.875i	0.417390	−	0.172889i	−0.164097	−	0.986444i	$-0.552471\pi$
$971$	405.286	−	167.875i	0.417390	−	0.172889i	0.581487	+	0.813556i	$0.302471\pi$
$972$	1535.80	+	305.490i	1.58004	+	0.314290i
$973$	−7.25264	−	7.25264i	−0.00745390	−	0.00745390i
$974$	773.067	−	516.547i	0.793703	−	0.530336i
$975$	1655.71	+	694.606i	1.69816	+	0.712416i
$976$	−25.6359	−	17.1294i	−0.0262663	−	0.0175506i
$977$	−189.595	−	78.5328i	−0.194058	−	0.0803816i	0.283538	−	0.958961i	$-0.408492\pi$
$977$	−189.595	−	78.5328i	−0.194058	−	0.0803816i	−0.477596	+	0.878579i	$0.658492\pi$
$978$	−505.507	+	1220.40i	−0.516878	+	1.24785i
$979$	5.39892	−	8.08005i	0.00551473	−	0.00825337i
$980$	887.648	+	1086.60i	0.905763	+	1.10878i
$981$	303.617	+	454.395i	0.309497	+	0.463195i
$982$	−1114.23	+	1114.23i	−1.13465	+	1.13465i
$983$	114.447	−	575.365i	0.116426	−	0.585315i	−0.877891	−	0.478860i	$-0.841050\pi$
$983$	114.447	−	575.365i	0.116426	−	0.585315i	0.994318	−	0.106455i	$-0.0339499\pi$
$984$	268.014	+	647.043i	0.272372	+	0.657564i
$985$	808.736	+	1521.30i	0.821051	+	1.54447i
$986$	−505.960	−	29.6013i	−0.513144	−	0.0300216i
$987$		−	278.347i		−	0.282013i
$988$	−801.349	−	1934.63i	−0.811081	−	1.95812i
$989$	−67.7839	+	340.773i	−0.0685378	+	0.344563i
$990$	129.408	−	423.154i	0.130715	−	0.427428i
$991$	−230.345	+	153.912i	−0.232437	+	0.155310i	−0.666335	−	0.745652i	$-0.732138\pi$
$991$	−230.345	+	153.912i	−0.232437	+	0.155310i	0.433898	+	0.900962i	$0.357138\pi$
$992$	1037.83	−	206.437i	1.04620	−	0.208102i
$993$	−855.167	+	1279.85i	−0.861195	+	1.28887i
$994$	−90.1341	+	217.603i	−0.0906782	+	0.218917i
$995$	75.9521	+	789.450i	0.0763337	+	0.793417i
$996$	−391.442	+	585.835i	−0.393014	+	0.588188i
$997$	−44.2058	−	222.237i	−0.0443388	−	0.222906i	0.952263	−	0.305280i	$-0.0987500\pi$
$997$	−44.2058	−	222.237i	−0.0443388	−	0.222906i	−0.996602	+	0.0823735i	$0.973750\pi$
$998$	1315.94	−	879.281i	1.31857	−	0.881043i
$999$	−655.069	−	655.069i	−0.655725	−	0.655725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.3.p.a.14.14	yes	128
5.2	odd	4		425.3.u.f.201.3		128
5.3	odd	4		425.3.u.f.201.14		128
5.4	even	2	inner	85.3.p.a.14.3	✓	128
17.11	odd	16	inner	85.3.p.a.79.3	yes	128
85.28	even	16		425.3.u.f.351.14		128
85.62	even	16		425.3.u.f.351.3		128
85.79	odd	16	inner	85.3.p.a.79.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.p.a.14.3	✓	128	5.4	even	2	inner
85.3.p.a.14.14	yes	128	1.1	even	1	trivial
85.3.p.a.79.3	yes	128	17.11	odd	16	inner
85.3.p.a.79.14	yes	128	85.79	odd	16	inner
425.3.u.f.201.3		128	5.2	odd	4
425.3.u.f.201.14		128	5.3	odd	4
425.3.u.f.351.3		128	85.62	even	16
425.3.u.f.351.14		128	85.28	even	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	85.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20149 + 2.90065i) q^{2} +(3.75496 + 0.746907i) q^{3} +(-4.14176 + 4.14176i) q^{4} +(-4.40427 - 2.36695i) q^{5} +(2.34502 + 11.7892i) q^{6} +(-0.580455 + 0.868712i) q^{7} +(-5.38745 - 2.23156i) q^{8} +(5.22691 + 2.16506i) q^{9} +(1.57401 - 15.6191i) q^{10} +(4.88661 - 0.972007i) q^{11} +(-18.6456 + 12.4586i) q^{12} +(13.2648 - 13.2648i) q^{13} +(-3.21723 - 0.639948i) q^{14} +(-14.7699 - 12.1774i) q^{15} +5.12102i q^{16} +(-8.60301 - 14.6625i) q^{17} +17.7627i q^{18} +(-17.6068 + 7.29299i) q^{19} +(28.0447 - 8.43807i) q^{20} +(-2.82843 + 2.82843i) q^{21} +(8.69065 + 13.0065i) q^{22} +(8.83254 - 1.75690i) q^{23} +(-18.5629 - 12.4033i) q^{24} +(13.7951 + 20.8493i) q^{25} +(54.4141 + 22.5391i) q^{26} +(-10.6400 - 7.10940i) q^{27} +(-1.19389 - 6.00209i) q^{28} +(-5.27556 - 7.89544i) q^{29} +(17.5764 - 57.4733i) q^{30} +(-26.3385 - 5.23906i) q^{31} +(-36.4041 + 15.0791i) q^{32} +19.0750 q^{33} +(32.1943 - 42.5711i) q^{34} +(4.61267 - 2.45213i) q^{35} +(-30.6157 + 12.6814i) q^{36} +(71.0039 + 14.1236i) q^{37} +(-42.3088 - 42.3088i) q^{38} +(59.7164 - 39.9012i) q^{39} +(18.4458 + 22.5802i) q^{40} +(-26.0834 - 17.4284i) q^{41} +(-11.6026 - 4.80595i) q^{42} +(-14.7645 + 35.6447i) q^{43} +(-16.2133 + 24.2650i) q^{44} +(-17.8961 - 21.9073i) q^{45} +(15.7083 + 23.5092i) q^{46} +(-49.2053 + 49.2053i) q^{47} +(-3.82493 + 19.2292i) q^{48} +(18.3338 + 44.2616i) q^{49} +(-43.9019 + 65.0650i) q^{50} +(-21.3524 - 61.4826i) q^{51} +109.879i q^{52} +(-30.2734 - 73.0866i) q^{53} +(7.83807 - 39.4046i) q^{54} +(-23.8226 - 7.28537i) q^{55} +(5.06575 - 3.38483i) q^{56} +(-71.5601 + 14.2342i) q^{57} +(16.5634 - 24.7888i) q^{58} +(-36.6614 + 88.5085i) q^{59} +(111.609 - 10.7378i) q^{60} +(-3.34491 + 5.00601i) q^{61} +(-16.4487 - 82.6934i) q^{62} +(-4.91479 + 3.28396i) q^{63} +(-72.9937 - 72.9937i) q^{64} +(-89.8189 + 27.0246i) q^{65} +(22.9184 + 55.3298i) q^{66} +36.9104 q^{67} +(96.3600 + 25.0968i) q^{68} +34.4780 q^{69} +(12.6548 + 10.4335i) q^{70} +(14.0080 - 70.4230i) q^{71} +(-23.3283 - 23.3283i) q^{72} +(-14.8948 - 22.2917i) q^{73} +(44.3429 + 222.927i) q^{74} +(36.2275 + 88.5920i) q^{75} +(42.7174 - 103.129i) q^{76} +(-1.99206 + 4.80926i) q^{77} +(187.488 + 125.275i) q^{78} +(110.235 - 21.9271i) q^{79} +(12.1212 - 22.5543i) q^{80} +(-70.6471 - 70.6471i) q^{81} +(19.2147 - 96.5989i) q^{82} +(29.0278 - 12.0237i) q^{83} -23.4293i q^{84} +(3.18463 + 84.9403i) q^{85} -121.132 q^{86} +(-13.9124 - 33.5874i) q^{87} +(-28.4955 - 5.66810i) q^{88} +(1.37917 - 1.37917i) q^{89} +(42.0434 - 78.2317i) q^{90} +(3.82368 + 19.2229i) q^{91} +(-29.3056 + 43.8589i) q^{92} +(-94.9869 - 39.3449i) q^{93} +(-201.847 - 83.6077i) q^{94} +(94.8073 + 9.55420i) q^{95} +(-147.958 + 29.4308i) q^{96} +(-18.0086 + 12.0330i) q^{97} +(-106.360 + 106.360i) q^{98} +(27.6463 + 5.49919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{4} - 8 q^{5} - 16 q^{6} - 16 q^{9} + 16 q^{10} - 96 q^{11} - 16 q^{14} + 16 q^{15} - 16 q^{19} - 120 q^{20} + 224 q^{21} - 160 q^{24} - 240 q^{25} + 288 q^{26} - 176 q^{29} - 200 q^{30} + 48 q^{31}+ \cdots - 1664 q^{99}+O(q^{100}) \) 128 * q - 16 * q^4 - 8 * q^5 - 16 * q^6 - 16 * q^9 + 16 * q^10 - 96 * q^11 - 16 * q^14 + 16 * q^15 - 16 * q^19 - 120 * q^20 + 224 * q^21 - 160 * q^24 - 240 * q^25 + 288 * q^26 - 176 * q^29 - 200 * q^30 + 48 * q^31 + 48 * q^34 + 48 * q^35 - 144 * q^36 + 440 * q^40 - 336 * q^41 - 48 * q^44 + 232 * q^45 - 224 * q^46 - 48 * q^49 - 16 * q^51 + 512 * q^54 - 392 * q^55 - 16 * q^56 + 272 * q^59 - 736 * q^60 - 16 * q^61 + 688 * q^64 - 128 * q^65 - 80 * q^66 + 448 * q^69 + 736 * q^70 + 192 * q^71 + 704 * q^74 + 1048 * q^75 + 496 * q^76 + 304 * q^79 + 1240 * q^80 + 128 * q^81 + 672 * q^85 - 2496 * q^86 - 256 * q^89 + 1104 * q^90 - 1632 * q^91 - 1296 * q^94 + 120 * q^95 - 1728 * q^96 - 1664 * q^99

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