LMFDB - Embedded newform 456.2.bk.a.253.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.13
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.873464 - 1.11223i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.474121 + 1.94299i) q^{4} +(-3.30436 + 0.582649i) q^{5} +(1.34390 - 0.440382i) q^{6} +(-1.96330 + 3.40053i) q^{7} +(2.57518 - 1.16980i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(3.53428 + 3.16630i) q^{10} +(2.32580 - 1.34280i) q^{11} +(-1.66365 - 1.11007i) q^{12} +(-1.43956 - 3.95517i) q^{13} +(5.49705 - 0.786598i) q^{14} +(0.582649 - 3.30436i) q^{15} +(-3.55042 - 1.84243i) q^{16} +(4.40701 - 3.69792i) q^{17} +(-0.0458169 + 1.41347i) q^{18} +(-3.87216 + 2.00160i) q^{19} +(0.434590 - 6.69659i) q^{20} +(-2.52397 - 3.00795i) q^{21} +(-3.52501 - 1.41394i) q^{22} +(0.958194 - 5.43419i) q^{23} +(0.218486 + 2.81998i) q^{24} +(5.88088 - 2.14047i) q^{25} +(-3.14166 + 5.05583i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-5.67636 - 5.42693i) q^{28} +(-0.439779 + 0.524109i) q^{29} +(-4.18414 + 2.23820i) q^{30} +(1.25037 - 2.16570i) q^{31} +(1.05196 + 5.55818i) q^{32} +(0.466350 + 2.64480i) q^{33} +(-7.96232 - 1.67162i) q^{34} +(4.50614 - 12.3805i) q^{35} +(1.61213 - 1.18366i) q^{36} +4.16521i q^{37} +(5.60843 + 2.55842i) q^{38} +4.20900 q^{39} +(-7.82777 + 5.36587i) q^{40} +(-10.3777 - 3.77718i) q^{41} +(-1.14094 + 5.43457i) q^{42} +(12.0055 - 2.11689i) q^{43} +(1.50634 + 5.15565i) q^{44} +(2.90581 + 1.67767i) q^{45} +(-6.88102 + 3.68083i) q^{46} +(4.55811 + 3.82471i) q^{47} +(2.94563 - 2.70615i) q^{48} +(-4.20907 - 7.29033i) q^{49} +(-7.51744 - 4.67129i) q^{50} +(1.96762 + 5.40600i) q^{51} +(8.36738 - 0.921827i) q^{52} +(-9.75666 - 1.72036i) q^{53} +(-1.31256 - 0.526489i) q^{54} +(-6.90290 + 5.79222i) q^{55} +(-1.07792 + 11.0537i) q^{56} +(-0.556531 - 4.32322i) q^{57} +(0.967062 + 0.0313468i) q^{58} +(-5.47945 - 6.53015i) q^{59} +(6.14410 + 2.69875i) q^{60} +(1.92854 + 0.340054i) q^{61} +(-3.50091 + 0.500962i) q^{62} +(3.68979 - 1.34297i) q^{63} +(5.26314 - 6.02489i) q^{64} +(7.06132 + 12.2306i) q^{65} +(2.53429 - 2.82883i) q^{66} +(-2.73629 + 3.26098i) q^{67} +(5.09557 + 10.3160i) q^{68} +(4.77874 + 2.75901i) q^{69} +(-17.7059 + 5.80206i) q^{70} +(-1.84959 - 10.4895i) q^{71} +(-2.72464 - 0.759179i) q^{72} +(-13.9260 - 5.06864i) q^{73} +(4.63269 - 3.63816i) q^{74} +6.25831i q^{75} +(-2.05321 - 8.47256i) q^{76} +10.5453i q^{77} +(-3.67641 - 4.68139i) q^{78} +(-3.82592 - 1.39252i) q^{79} +(12.8054 + 4.01940i) q^{80} +(0.173648 + 0.984808i) q^{81} +(4.86346 + 14.8417i) q^{82} +(-1.58055 - 0.912532i) q^{83} +(7.04108 - 3.47791i) q^{84} +(-12.4078 + 14.7870i) q^{85} +(-12.8408 - 11.5039i) q^{86} +(-0.342088 - 0.592513i) q^{87} +(4.41855 - 6.17867i) q^{88} +(-1.91937 + 0.698594i) q^{89} +(-0.672161 - 4.69732i) q^{90} +(16.2760 + 2.86989i) q^{91} +(10.1043 + 4.43822i) q^{92} +(1.60744 + 1.91567i) q^{93} +(0.272620 - 8.41043i) q^{94} +(11.6288 - 8.87012i) q^{95} +(-5.58277 - 0.912495i) q^{96} +(8.85598 - 7.43105i) q^{97} +(-4.43207 + 11.0493i) q^{98} +(-2.64480 - 0.466350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.873464	−	1.11223i	−0.617632	−	0.786467i
$2$	−0.873464	−	1.11223i	−0.617632	−	0.786467i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$4$	−0.474121	+	1.94299i	−0.237061	+	0.971495i
$5$	−3.30436	+	0.582649i	−1.47776	+	0.260568i	−0.853681	−	0.520796i	$-0.825635\pi$
$5$	−3.30436	+	0.582649i	−1.47776	+	0.260568i	−0.624075	+	0.781364i	$0.714524\pi$
$6$	1.34390	−	0.440382i	0.548644	−	0.179785i
$7$	−1.96330	+	3.40053i	−0.742057	+	1.28528i	0.209501	+	0.977809i	$0.432816\pi$
$7$	−1.96330	+	3.40053i	−0.742057	+	1.28528i	−0.951557	+	0.307471i	$0.900517\pi$
$8$	2.57518	−	1.16980i	0.910465	−	0.413586i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	3.53428	+	3.16630i	1.11764	+	1.00127i
$11$	2.32580	−	1.34280i	0.701254	−	0.404869i	−0.106560	−	0.994306i	$-0.533984\pi$
$11$	2.32580	−	1.34280i	0.701254	−	0.404869i	0.807814	+	0.589437i	$0.200650\pi$
$12$	−1.66365	−	1.11007i	−0.480256	−	0.320450i
$13$	−1.43956	−	3.95517i	−0.399263	−	1.09697i	−0.962644	−	0.270769i	$-0.912722\pi$
$13$	−1.43956	−	3.95517i	−0.399263	−	1.09697i	0.563381	−	0.826197i	$-0.309500\pi$
$14$	5.49705	−	0.786598i	1.46915	−	0.210227i
$15$	0.582649	−	3.30436i	0.150439	−	0.853183i
$16$	−3.55042	−	1.84243i	−0.887604	−	0.460606i
$17$	4.40701	−	3.69792i	1.06886	−	0.896878i	0.0739095	−	0.997265i	$-0.476452\pi$
$17$	4.40701	−	3.69792i	1.06886	−	0.896878i	0.994949	+	0.100387i	$0.0320079\pi$
$18$	−0.0458169	+	1.41347i	−0.0107992	+	0.333158i
$19$	−3.87216	+	2.00160i	−0.888334	+	0.459198i
$19$	−3.87216	+	2.00160i	−0.888334	+	0.459198i
$20$	0.434590	−	6.69659i	0.0971772	−	1.49740i
$21$	−2.52397	−	3.00795i	−0.550775	−	0.656388i
$22$	−3.52501	−	1.41394i	−0.751534	−	0.301453i
$23$	0.958194	−	5.43419i	0.199797	−	1.13311i	−0.705622	−	0.708588i	$-0.749332\pi$
$23$	0.958194	−	5.43419i	0.199797	−	1.13311i	0.905420	−	0.424518i	$-0.139556\pi$
$24$	0.218486	+	2.81998i	0.0445983	+	0.575625i
$25$	5.88088	−	2.14047i	1.17618	−	0.428093i
$26$	−3.14166	+	5.05583i	−0.616130	+	0.991529i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	−5.67636	−	5.42693i	−1.07273	−	1.02559i
$29$	−0.439779	+	0.524109i	−0.0816650	+	0.0973245i	−0.805330	−	0.592827i	$-0.798012\pi$
$29$	−0.439779	+	0.524109i	−0.0816650	+	0.0973245i	0.723665	+	0.690152i	$0.242456\pi$
$30$	−4.18414	+	2.23820i	−0.763917	+	0.408638i
$31$	1.25037	−	2.16570i	0.224573	−	0.388971i	−0.731619	−	0.681714i	$-0.761235\pi$
$31$	1.25037	−	2.16570i	0.224573	−	0.388971i	0.956191	+	0.292743i	$0.0945681\pi$
$32$	1.05196	+	5.55818i	0.185961	+	0.982557i
$33$	0.466350	+	2.64480i	0.0811810	+	0.460401i
$34$	−7.96232	−	1.67162i	−1.36553	−	0.286681i
$35$	4.50614	−	12.3805i	0.761676	−	2.09269i
$36$	1.61213	−	1.18366i	0.268688	−	0.197276i
$37$			4.16521i			0.684757i	0.939562	+	0.342379i	$0.111233\pi$
$37$			4.16521i			0.684757i	−0.939562	+	0.342379i	$0.888767\pi$
$38$	5.60843	+	2.55842i	0.909808	+	0.415030i
$39$	4.20900			0.673980
$40$	−7.82777	+	5.36587i	−1.23768	+	0.848418i
$41$	−10.3777	−	3.77718i	−1.62073	−	0.589897i	−0.637208	−	0.770692i	$-0.719911\pi$
$41$	−10.3777	−	3.77718i	−1.62073	−	0.589897i	−0.983521	+	0.180795i	$0.942133\pi$
$42$	−1.14094	+	5.43457i	−0.176051	+	0.838572i
$43$	12.0055	−	2.11689i	1.83082	−	0.322823i	0.851378	−	0.524553i	$-0.175767\pi$
$43$	12.0055	−	2.11689i	1.83082	−	0.322823i	0.979441	+	0.201730i	$0.0646563\pi$
$44$	1.50634	+	5.15565i	0.227089	+	0.777244i
$45$	2.90581	+	1.67767i	0.433173	+	0.250092i
$46$	−6.88102	+	3.68083i	−1.01455	+	0.542709i
$47$	4.55811	+	3.82471i	0.664869	+	0.557891i	0.911542	−	0.411207i	$-0.134893\pi$
$47$	4.55811	+	3.82471i	0.664869	+	0.557891i	−0.246673	+	0.969099i	$0.579337\pi$
$48$	2.94563	−	2.70615i	0.425165	−	0.390600i
$49$	−4.20907	−	7.29033i	−0.601296	−	1.04148i
$50$	−7.51744	−	4.67129i	−1.06313	−	0.660620i
$51$	1.96762	+	5.40600i	0.275523	+	0.756992i
$52$	8.36738	−	0.921827i	1.16035	−	0.127834i
$53$	−9.75666	−	1.72036i	−1.34018	−	0.236310i	−0.542838	−	0.839837i	$-0.682650\pi$
$53$	−9.75666	−	1.72036i	−1.34018	−	0.236310i	−0.797342	+	0.603527i	$0.793761\pi$
$54$	−1.31256	−	0.526489i	−0.178617	−	0.0716461i
$55$	−6.90290	+	5.79222i	−0.930787	+	0.781023i
$56$	−1.07792	+	11.0537i	−0.144043	+	1.47711i
$57$	−0.556531	−	4.32322i	−0.0737143	−	0.572625i
$58$	0.967062	+	0.0313468i	0.126981	+	0.00411604i
$59$	−5.47945	−	6.53015i	−0.713364	−	0.850154i	0.280604	−	0.959824i	$-0.409465\pi$
$59$	−5.47945	−	6.53015i	−0.713364	−	0.850154i	−0.993968	+	0.109670i	$0.965021\pi$
$60$	6.14410	+	2.69875i	0.793200	+	0.348407i
$61$	1.92854	+	0.340054i	0.246925	+	0.0435395i	0.295740	−	0.955268i	$-0.404434\pi$
$61$	1.92854	+	0.340054i	0.246925	+	0.0435395i	−0.0488159	+	0.998808i	$0.515545\pi$
$62$	−3.50091	+	0.500962i	−0.444616	+	0.0636222i
$63$	3.68979	−	1.34297i	0.464870	−	0.169199i
$64$	5.26314	−	6.02489i	0.657893	−	0.753111i
$65$	7.06132	+	12.2306i	0.875849	+	1.51701i
$66$	2.53429	−	2.82883i	0.311950	−	0.348204i
$67$	−2.73629	+	3.26098i	−0.334291	+	0.398393i	−0.906838	−	0.421479i	$-0.861511\pi$
$67$	−2.73629	+	3.26098i	−0.334291	+	0.398393i	0.572547	+	0.819872i	$0.305955\pi$
$68$	5.09557	+	10.3160i	0.617929	+	1.25100i
$69$	4.77874	+	2.75901i	0.575293	+	0.332146i
$70$	−17.7059	+	5.80206i	−2.11627	+	0.693478i
$71$	−1.84959	−	10.4895i	−0.219505	−	1.24488i	−0.872915	−	0.487872i	$-0.837773\pi$
$71$	−1.84959	−	10.4895i	−0.219505	−	1.24488i	0.653410	−	0.757005i	$-0.273338\pi$
$72$	−2.72464	−	0.759179i	−0.321102	−	0.0894701i
$73$	−13.9260	−	5.06864i	−1.62991	−	0.593239i	−0.644677	−	0.764455i	$-0.723008\pi$
$73$	−13.9260	−	5.06864i	−1.62991	−	0.593239i	−0.985234	+	0.171216i	$0.945230\pi$
$74$	4.63269	−	3.63816i	0.538539	−	0.422928i
$75$			6.25831i			0.722647i
$76$	−2.05321	−	8.47256i	−0.235519	−	0.971870i
$77$			10.5453i			1.20174i
$78$	−3.67641	−	4.68139i	−0.416272	−	0.530063i
$79$	−3.82592	−	1.39252i	−0.430450	−	0.156671i	0.117704	−	0.993049i	$-0.462447\pi$
$79$	−3.82592	−	1.39252i	−0.430450	−	0.156671i	−0.548153	+	0.836378i	$0.684669\pi$
$80$	12.8054	+	4.01940i	1.43168	+	0.449383i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	4.86346	+	14.8417i	0.537080	+	1.63899i
$83$	−1.58055	−	0.912532i	−0.173488	−	0.100163i	0.410741	−	0.911752i	$-0.365270\pi$
$83$	−1.58055	−	0.912532i	−0.173488	−	0.100163i	−0.584230	+	0.811588i	$0.698603\pi$
$84$	7.04108	−	3.47791i	0.768244	−	0.379471i
$85$	−12.4078	+	14.7870i	−1.34581	+	1.60388i
$86$	−12.8408	−	11.5039i	−1.38466	−	1.24049i
$87$	−0.342088	−	0.592513i	−0.0366756	−	0.0635241i
$88$	4.41855	−	6.17867i	0.471019	−	0.658649i
$89$	−1.91937	+	0.698594i	−0.203453	+	0.0740508i	−0.441737	−	0.897145i	$-0.645637\pi$
$89$	−1.91937	+	0.698594i	−0.203453	+	0.0740508i	0.238284	+	0.971196i	$0.423415\pi$
$90$	−0.672161	−	4.69732i	−0.0708520	−	0.495141i
$91$	16.2760	+	2.86989i	1.70618	+	0.300846i
$92$	10.1043	+	4.43822i	1.05344	+	0.462717i
$93$	1.60744	+	1.91567i	0.166684	+	0.198646i
$94$	0.272620	−	8.41043i	0.0281186	−	0.867469i
$95$	11.6288	−	8.87012i	1.19309	−	0.910055i
$96$	−5.58277	−	0.912495i	−0.569789	−	0.0931311i
$97$	8.85598	−	7.43105i	0.899189	−	0.754509i	−0.0708427	−	0.997487i	$-0.522569\pi$
$97$	8.85598	−	7.43105i	0.899189	−	0.754509i	0.970032	+	0.242978i	$0.0781244\pi$
$98$	−4.43207	+	11.0493i	−0.447706	+	1.11615i
$99$	−2.64480	−	0.466350i	−0.265812	−	0.0468699i
$100$	1.37065	+	12.4413i	0.137065	+	1.24413i
$101$	−4.93980	−	13.5720i	−0.491528	−	1.35046i	−0.899281	−	0.437371i	$-0.855910\pi$
$101$	−4.93980	−	13.5720i	−0.491528	−	1.35046i	0.407753	−	0.913092i	$-0.366313\pi$
$102$	4.29408	−	6.91041i	0.425178	−	0.684232i
$103$	1.20422	+	2.08577i	0.118655	+	0.205517i	0.919235	−	0.393709i	$-0.128808\pi$
$103$	1.20422	+	2.08577i	0.118655	+	0.205517i	−0.800580	+	0.599226i	$0.795475\pi$
$104$	−8.33389	−	8.50129i	−0.817205	−	0.833620i
$105$	10.0927	+	8.46877i	0.984945	+	0.826467i
$106$	6.60865	+	12.3544i	0.641889	+	1.19996i
$107$	10.3252	+	5.96125i	0.998174	+	0.576296i	0.907708	−	0.419603i	$-0.137831\pi$
$107$	10.3252	+	5.96125i	0.998174	+	0.576296i	0.0904668	+	0.995899i	$0.471164\pi$
$108$	0.560894	+	1.91974i	0.0539720	+	0.184727i
$109$	3.53768	−	0.623789i	0.338849	−	0.0597482i	−0.00163482	−	0.999999i	$-0.500520\pi$
$109$	3.53768	−	0.623789i	0.338849	−	0.0597482i	0.340483	+	0.940251i	$0.389409\pi$
$110$	12.4717	+	2.61833i	1.18913	+	0.249648i
$111$	−3.91402	−	1.42459i	−0.371502	−	0.135216i
$112$	13.2358	−	8.45608i	1.25066	−	0.799024i
$113$	3.04887			0.286813			0.143407	−	0.989664i	$-0.454194\pi$
$113$	3.04887			0.286813			0.143407	+	0.989664i	$0.454194\pi$
$114$	−4.32232	+	4.39517i	−0.404822	+	0.411646i
$115$			18.5148i			1.72652i
$116$	−0.809829	−	1.10298i	−0.0751907	−	0.102409i
$117$	−1.43956	+	3.95517i	−0.133088	+	0.365655i
$118$	−2.47695	+	11.7983i	−0.228021	+	1.08612i
$119$	3.92263	+	22.2463i	0.359587	+	2.03932i
$120$	−2.36501	−	9.19093i	−0.215895	−	0.839013i
$121$	−1.89378	+	3.28012i	−0.172161	+	0.298192i
$122$	−1.30629	−	2.44201i	−0.118266	−	0.221089i
$123$	7.09878	−	8.46000i	0.640076	−	0.762812i
$124$	3.61511	+	3.45626i	0.324646	+	0.310381i
$125$	−3.65640	+	2.11102i	−0.327038	+	0.188815i
$126$	−4.71660	−	2.93087i	−0.420188	−	0.261102i
$127$	12.5136	−	4.55459i	1.11040	−	0.404154i	0.279263	−	0.960215i	$-0.409910\pi$
$127$	12.5136	−	4.55459i	1.11040	−	0.404154i	0.831142	+	0.556060i	$0.187688\pi$
$128$	−11.2982	−	0.591313i	−0.998633	−	0.0522651i
$129$	−2.11689	+	12.0055i	−0.186382	+	1.05702i
$130$	7.43542	−	18.5368i	0.652129	−	1.62578i
$131$	−2.74268	−	3.26859i	−0.239629	−	0.285578i	0.632805	−	0.774311i	$-0.281904\pi$
$131$	−2.74268	−	3.26859i	−0.239629	−	0.285578i	−0.872433	+	0.488733i	$0.837459\pi$
$132$	−5.35992	−	0.347844i	−0.466522	−	0.0302759i
$133$	0.795702	−	17.0971i	0.0689961	−	1.48251i
$134$	6.01702	+	0.195039i	0.519791	+	0.0168488i
$135$	−2.57034	+	2.15677i	−0.221220	+	0.185625i
$136$	7.02305	−	14.6782i	0.602221	−	1.25864i
$137$	−1.50846	+	8.55490i	−0.128876	+	0.730894i	0.850053	+	0.526697i	$0.176570\pi$
$137$	−1.50846	+	8.55490i	−0.128876	+	0.730894i	−0.978930	+	0.204198i	$0.934541\pi$
$138$	−1.10540	−	7.72497i	−0.0940980	−	0.657593i
$139$	−3.05374	−	8.39008i	−0.259015	−	0.711638i	−0.999229	−	0.0392662i	$-0.987498\pi$
$139$	−3.05374	−	8.39008i	−0.259015	−	0.711638i	0.740214	−	0.672372i	$-0.234724\pi$
$140$	21.9187	+	14.6252i	1.85247	+	1.23606i
$141$	−5.15302	+	2.97510i	−0.433963	+	0.250548i
$142$	−10.0512	+	11.2194i	−0.843481	+	0.941510i
$143$	−8.65913	−	7.26588i	−0.724113	−	0.607603i
$144$	1.53549	+	3.69354i	0.127957	+	0.307795i
$145$	1.14782	−	1.98808i	0.0953213	−	0.165101i
$146$	6.52633	+	19.9162i	0.540123	+	1.64827i
$147$	8.29026	−	1.46180i	0.683769	−	0.120567i
$148$	−8.09297	−	1.97482i	−0.665238	−	0.162329i
$149$	0.906991	−	2.49194i	0.0743036	−	0.204147i	−0.896981	−	0.442070i	$-0.854244\pi$
$149$	0.906991	−	2.49194i	0.0743036	−	0.204147i	0.971284	+	0.237923i	$0.0764665\pi$
$150$	6.96069	−	5.46640i	0.568338	−	0.446330i
$151$	−10.4436			−0.849887			−0.424943	−	0.905220i	$-0.639706\pi$
$151$	−10.4436			−0.849887			−0.424943	+	0.905220i	$0.639706\pi$
$152$	−7.63005	+	9.68413i	−0.618879	+	0.785486i
$153$	−5.75295			−0.465098
$154$	11.7288	−	9.21091i	0.945132	−	0.742236i
$155$	−2.86983	+	7.88479i	−0.230510	+	0.633321i
$156$	−1.99558	+	8.17805i	−0.159774	+	0.654768i
$157$	−10.0499	+	1.77207i	−0.802069	+	0.141426i	−0.559632	−	0.828741i	$-0.689058\pi$
$157$	−10.0499	+	1.77207i	−0.802069	+	0.141426i	−0.242436	+	0.970167i	$0.577947\pi$
$158$	1.79300	+	5.47163i	0.142643	+	0.435299i
$159$	4.95359	−	8.57987i	0.392845	−	0.680428i
$160$	−6.71451	−	17.7533i	−0.530829	−	1.40352i
$161$	16.5979	+	13.9273i	1.30810	+	1.09762i
$162$	0.943660	−	1.05333i	0.0741409	−	0.0827575i
$163$	8.63177	−	4.98356i	0.676093	−	0.390342i	−0.122289	−	0.992495i	$-0.539023\pi$
$163$	8.63177	−	4.98356i	0.676093	−	0.390342i	0.798381	+	0.602152i	$0.205690\pi$
$164$	12.2593	−	18.3730i	0.957293	−	1.43469i
$165$	−3.08198	−	8.46766i	−0.239932	−	0.659207i
$166$	0.365607	+	2.55500i	0.0283766	+	0.198307i
$167$	0.969007	−	5.49551i	0.0749840	−	0.425255i	−0.924088	−	0.382180i	$-0.875173\pi$
$167$	0.969007	−	5.49551i	0.0749840	−	0.425255i	0.999072	−	0.0430753i	$-0.0137155\pi$
$168$	−10.0184	−	4.79348i	−0.772934	−	0.369825i
$169$	−3.61244	+	3.03120i	−0.277880	+	0.233169i
$170$	27.2844	+	0.884409i	2.09262	+	0.0678310i
$171$	4.25285	+	0.955662i	0.325223	+	0.0730813i
$172$	−1.57896	+	24.3302i	−0.120395	+	1.85516i
$173$	−7.67404	−	9.14556i	−0.583446	−	0.695324i	0.390886	−	0.920439i	$-0.372169\pi$
$173$	−7.67404	−	9.14556i	−0.583446	−	0.695324i	−0.974332	+	0.225115i	$0.927724\pi$
$174$	−0.360211	+	0.898020i	−0.0273075	+	0.0680787i
$175$	−4.26720	+	24.2005i	−0.322570	+	1.82939i
$176$	−10.7316	+	0.482391i	−0.808922	+	0.0363616i
$177$	8.01042	−	2.91555i	0.602100	−	0.219147i
$178$	2.45350	+	1.52459i	0.183898	+	0.114273i
$179$	−12.7477	+	7.35988i	−0.952806	+	0.550103i	−0.893952	−	0.448163i	$-0.852078\pi$
$179$	−12.7477	+	7.35988i	−0.952806	+	0.550103i	−0.0588548	+	0.998267i	$0.518745\pi$
$180$	−4.63740	+	4.85054i	−0.345652	+	0.361538i
$181$	−8.94214	+	10.6568i	−0.664664	+	0.792116i	−0.988047	−	0.154153i	$-0.950735\pi$
$181$	−8.94214	+	10.6568i	−0.664664	+	0.792116i	0.323383	+	0.946268i	$0.395180\pi$
$182$	−11.0245	−	20.6094i	−0.817189	−	1.52767i
$183$	−0.979147	+	1.69593i	−0.0723806	+	0.125367i
$184$	−3.88938	−	15.1149i	−0.286729	−	1.11429i
$185$	−2.42686	−	13.7634i	−0.178426	−	1.01190i
$186$	0.726632	−	3.46112i	0.0532793	−	0.253782i
$187$	5.28425	−	14.5184i	0.386423	−	1.06169i
$188$	−9.59247	+	7.04299i	−0.699603	+	0.513663i
$189$			3.92659i			0.285618i
$190$	−20.0230	−	5.18619i	−1.45262	−	0.376246i
$191$	−24.0046			−1.73691			−0.868456	−	0.495766i	$-0.834887\pi$
$191$	−24.0046			−1.73691			−0.868456	+	0.495766i	$0.834887\pi$
$192$	3.86145	+	7.00637i	0.278676	+	0.505641i
$193$	−16.5357	−	6.01851i	−1.19027	−	0.433222i	−0.330450	−	0.943824i	$-0.607200\pi$
$193$	−16.5357	−	6.01851i	−1.19027	−	0.433222i	−0.859817	+	0.510602i	$0.829423\pi$
$194$	−16.0004	−	3.35915i	−1.14876	−	0.241173i
$195$	−13.9081	+	2.45237i	−0.995978	+	0.175618i
$196$	16.1606	−	4.72169i	1.15433	−	0.337263i
$197$	1.97709	+	1.14147i	0.140862	+	0.0813266i	0.568775	−	0.822493i	$-0.307418\pi$
$197$	1.97709	+	1.14147i	0.140862	+	0.0813266i	−0.427913	+	0.903820i	$0.640751\pi$
$198$	1.79145	+	3.34897i	0.127313	+	0.238001i
$199$	−1.54567	−	1.29697i	−0.109570	−	0.0919398i	0.586357	−	0.810053i	$-0.300562\pi$
$199$	−1.54567	−	1.29697i	−0.109570	−	0.0919398i	−0.695926	+	0.718113i	$0.745006\pi$
$200$	12.6404	−	12.3915i	0.893814	−	0.876214i
$201$	−2.12846	−	3.68659i	−0.150130	−	0.260032i
$202$	−10.7805	+	17.3488i	−0.758511	+	1.22066i
$203$	−0.918830	−	2.52446i	−0.0644892	−	0.177183i
$204$	−11.4367	+	1.25997i	−0.800729	+	0.0882157i
$205$	36.4926	+	6.43462i	2.54875	+	0.449414i
$206$	1.26802	−	3.16122i	0.0883470	−	0.220252i
$207$	−4.22705	+	3.54691i	−0.293800	+	0.246527i
$208$	−2.17605	+	16.6948i	−0.150882	+	1.15758i
$209$	−6.31811	+	9.85485i	−0.437033	+	0.681674i
$210$	0.603641	−	18.6226i	0.0416552	−	1.28508i
$211$	−5.93930	−	7.07818i	−0.408878	−	0.487282i	0.521828	−	0.853051i	$-0.325250\pi$
$211$	−5.93930	−	7.07818i	−0.408878	−	0.487282i	−0.930706	+	0.365769i	$0.880806\pi$
$212$	7.96849	−	18.1414i	0.547278	−	1.24596i
$213$	10.4895	+	1.84959i	0.718730	+	0.126731i
$214$	−2.38839	−	16.6910i	−0.163267	−	1.14097i
$215$	−38.4371	+	13.9900i	−2.62139	+	0.954107i
$216$	1.64528	−	2.30067i	0.111947	−	0.156541i
$217$	4.90969	+	8.50383i	0.333291	+	0.577277i
$218$	−3.78384	−	3.38987i	−0.256274	−	0.229591i
$219$	9.52592	−	11.3525i	0.643702	−	0.767134i
$220$	−7.98142	−	16.1585i	−0.538107	−	1.08941i
$221$	−20.9701	−	12.1071i	−1.41060	−	0.814411i
$222$	1.83428	+	5.59763i	0.123109	+	0.375688i
$223$	0.0241630	+	0.137035i	0.00161807	+	0.00917655i	0.985606	−	0.169058i	$-0.0540725\pi$
$223$	0.0241630	+	0.137035i	0.00161807	+	0.00917655i	−0.983988	+	0.178235i	$0.942961\pi$
$224$	−20.9661	−	7.33515i	−1.40085	−	0.490101i
$225$	−5.88088	−	2.14047i	−0.392059	−	0.142698i
$226$	−2.66307	−	3.39105i	−0.177145	−	0.225569i
$227$			8.55037i			0.567508i	0.958897	+	0.283754i	$0.0915799\pi$
$227$			8.55037i			0.567508i	−0.958897	+	0.283754i	$0.908420\pi$
$228$	8.66384	+	0.968400i	0.573777	+	0.0641338i
$229$			2.88099i			0.190381i	0.995459	+	0.0951907i	$0.0303461\pi$
$229$			2.88099i			0.190381i	−0.995459	+	0.0951907i	$0.969654\pi$
$230$	20.5928	−	16.1720i	1.35785	−	1.06635i
$231$	−9.90931	−	3.60669i	−0.651984	−	0.237303i
$232$	−0.519411	+	1.86413i	−0.0341010	+	0.122386i
$233$	1.35989	+	7.71234i	0.0890896	+	0.505252i	0.996399	+	0.0847884i	$0.0270214\pi$
$233$	1.35989	+	7.71234i	0.0890896	+	0.505252i	−0.907309	+	0.420464i	$0.861867\pi$
$234$	5.65647	−	1.85357i	0.369775	−	0.121172i
$235$	−17.2901	−	9.98246i	−1.12788	−	0.651184i
$236$	15.2859	−	7.55043i	0.995030	−	0.491491i
$237$	2.61708	−	3.11892i	0.169998	−	0.202595i
$238$	21.3168	−	23.7942i	1.38176	−	1.54235i
$239$	0.623181	+	1.07938i	0.0403102	+	0.0698194i	0.885477	−	0.464684i	$-0.153832\pi$
$239$	0.623181	+	1.07938i	0.0403102	+	0.0698194i	−0.845166	+	0.534503i	$0.820499\pi$
$240$	−8.15669	+	10.6584i	−0.526512	+	0.687996i
$241$	−0.0959959	+	0.0349397i	−0.00618364	+	0.00225066i	−0.345110	−	0.938562i	$-0.612158\pi$
$241$	−0.0959959	+	0.0349397i	−0.00618364	+	0.00225066i	0.338926	+	0.940813i	$0.389936\pi$
$242$	5.30240	−	0.758745i	0.340851	−	0.0487740i
$243$	−0.984808	−	0.173648i	−0.0631754	−	0.0111395i
$244$	−1.57508	+	3.58591i	−0.100834	+	0.229564i
$245$	18.1560	+	21.6375i	1.15995	+	1.38237i
$246$	−15.6100	−	0.505990i	−0.995258	−	0.0322608i
$247$	13.4909	+	12.4336i	0.858404	+	0.791132i
$248$	0.686494	−	7.03975i	0.0435924	−	0.447025i
$249$	1.39808	−	1.17313i	0.0885997	−	0.0743440i
$250$	5.54168	+	2.22286i	0.350486	+	0.140586i
$251$	−14.3889	−	2.53715i	−0.908220	−	0.160144i	−0.300025	−	0.953931i	$-0.596995\pi$
$251$	−14.3889	−	2.53715i	−0.908220	−	0.160144i	−0.608195	+	0.793788i	$0.708106\pi$
$252$	0.859976	+	7.80596i	0.0541734	+	0.491729i
$253$	−5.06846	−	13.9255i	−0.318651	−	0.875487i
$254$	−15.9960	−	9.93979i	−1.00368	−	0.623678i
$255$	−9.65155	−	16.7170i	−0.604403	−	1.04686i
$256$	9.21093	+	13.0828i	0.575683	+	0.817673i
$257$	−14.8341	−	12.4473i	−0.925326	−	0.776440i	0.0496467	−	0.998767i	$-0.484190\pi$
$257$	−14.8341	−	12.4473i	−0.925326	−	0.776440i	−0.974972	+	0.222326i	$0.928635\pi$
$258$	15.2019	−	8.13188i	0.946430	−	0.506269i
$259$	−14.1639	−	8.17755i	−0.880104	−	0.508129i
$260$	−27.1118	+	7.92130i	−1.68140	+	0.491258i
$261$	0.673781	−	0.118806i	0.0417060	−	0.00735389i
$262$	−1.23981	+	5.90549i	−0.0765955	+	0.364842i
$263$	16.7925	+	6.11196i	1.03547	+	0.376880i	0.803160	−	0.595763i	$-0.203150\pi$
$263$	16.7925	+	6.11196i	1.03547	+	0.376880i	0.232308	+	0.972642i	$0.425372\pi$
$264$	4.29482	+	6.26531i	0.264328	+	0.385603i
$265$	33.2419			2.04204
$266$	−19.7110	+	14.0487i	−1.20856	+	0.861382i
$267$		−	2.04255i		−	0.125002i
$268$	−5.03872	−	6.86268i	−0.307789	−	0.419205i
$269$	6.93701	−	19.0593i	0.422957	−	1.16206i	−0.527050	−	0.849834i	$-0.676702\pi$
$269$	6.93701	−	19.0593i	0.422957	−	1.16206i	0.950007	−	0.312230i	$-0.101076\pi$
$270$	4.64393	+	0.974953i	0.282621	+	0.0593337i
$271$	4.40266	+	24.9687i	0.267442	+	1.51674i	0.761989	+	0.647590i	$0.224223\pi$
$271$	4.40266	+	24.9687i	0.267442	+	1.51674i	−0.494547	+	0.869151i	$0.664666\pi$
$272$	−22.4599	+	5.00958i	−1.36183	+	0.303750i
$273$	−8.26352	+	14.3128i	−0.500131	+	0.866253i
$274$	10.8326	−	5.79464i	0.654423	−	0.350067i
$275$	10.8035	−	12.8751i	0.651477	−	0.776400i
$276$	−7.62643	+	7.97694i	−0.459057	+	0.480156i
$277$	27.7246	−	16.0068i	1.66581	−	0.961757i	0.695953	−	0.718087i	$-0.254982\pi$
$277$	27.7246	−	16.0068i	1.66581	−	0.961757i	0.969858	−	0.243669i	$-0.0783511\pi$
$278$	−6.66439	+	10.7249i	−0.399704	+	0.643237i
$279$	−2.34992	+	0.855302i	−0.140686	+	0.0512056i
$280$	−2.87857	−	37.1534i	−0.172027	−	2.22034i
$281$	−1.87004	+	10.6055i	−0.111558	+	0.632674i	0.876840	+	0.480783i	$0.159647\pi$
$281$	−1.87004	+	10.6055i	−0.111558	+	0.632674i	−0.988397	+	0.151891i	$0.951464\pi$
$282$	7.80998	+	3.13271i	0.465077	+	0.186550i
$283$	11.8919	+	14.1723i	0.706903	+	0.842454i	0.993289	−	0.115661i	$-0.0368985\pi$
$283$	11.8919	+	14.1723i	0.706903	+	0.842454i	−0.286386	+	0.958114i	$0.592454\pi$
$284$	21.2580	+	1.37958i	1.26143	+	0.0818630i
$285$	4.35790	+	13.9612i	0.258140	+	0.826993i
$286$	−0.517901	+	15.9775i	−0.0306241	+	0.944766i
$287$	33.2190	−	27.8740i	1.96086	−	1.64535i
$288$	2.76689	−	4.93400i	0.163040	−	0.290739i
$289$	2.79511	−	15.8519i	0.164419	−	0.932464i
$290$	−3.21379	+	0.459876i	−0.188720	+	0.0270048i
$291$	3.95398	+	10.8635i	0.231786	+	0.636828i
$292$	16.4509	−	24.6549i	0.962716	−	1.44282i
$293$	7.67346	−	4.43027i	0.448288	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$293$	7.67346	−	4.43027i	0.448288	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$294$	−8.86710	−	7.94387i	−0.517140	−	0.463296i
$295$	21.9109	+	18.3854i	1.27570	+	1.07044i
$296$	4.87246	+	10.7262i	0.283206	+	0.623447i
$297$	1.34280	−	2.32580i	0.0779172	−	0.134956i
$298$	−3.56384	+	1.16783i	−0.206448	+	0.0676507i
$299$	−22.8725	+	4.03304i	−1.32275	+	0.233237i
$300$	−12.1598	−	2.96720i	−0.702048	−	0.171311i
$301$	−16.3718	+	44.9811i	−0.943654	+	2.59267i
$302$	9.12210	+	11.6157i	0.524918	+	0.668408i
$303$	14.4430			0.829729
$304$	17.4356	+	0.0276548i	0.999999	+	0.00158611i
$305$	−6.57074			−0.376239
$306$	5.02499	+	6.39862i	0.287260	+	0.365785i
$307$	−1.16967	+	3.21365i	−0.0667568	+	0.183413i	−0.968585	−	0.248681i	$-0.920003\pi$
$307$	−1.16967	+	3.21365i	−0.0667568	+	0.183413i	0.901829	+	0.432094i	$0.142225\pi$
$308$	−20.4893	−	4.99973i	−1.16749	−	0.284886i
$309$	−2.37185	+	0.418221i	−0.134930	+	0.0237918i
$310$	11.2764	−	3.69516i	0.640457	−	0.209871i
$311$	3.11432	−	5.39416i	0.176597	−	0.305875i	−0.764116	−	0.645079i	$-0.776824\pi$
$311$	3.11432	−	5.39416i	0.176597	−	0.305875i	0.940713	+	0.339204i	$0.110158\pi$
$312$	10.8390	−	4.92368i	0.613635	−	0.278749i
$313$	7.63289	+	6.40476i	0.431436	+	0.362018i	0.832493	−	0.554035i	$-0.186913\pi$
$313$	7.63289	+	6.40476i	0.431436	+	0.362018i	−0.401057	+	0.916053i	$0.631357\pi$
$314$	10.7492	+	9.62998i	0.606611	+	0.543451i
$315$	−11.4099	+	6.58753i	−0.642877	+	0.371165i
$316$	4.51960	−	6.77350i	0.254248	−	0.381039i
$317$	−5.91982	−	16.2646i	−0.332490	−	0.913509i	−0.987462	−	0.157856i	$-0.949542\pi$
$317$	−5.91982	−	16.2646i	−0.332490	−	0.913509i	0.654972	−	0.755653i	$-0.272680\pi$
$318$	−13.8696	+	1.98466i	−0.777768	+	0.111294i
$319$	−0.319065	+	1.80951i	−0.0178642	+	0.101313i
$320$	−13.8810	+	22.9750i	−0.775969	+	1.28434i
$321$	−9.13317	+	7.66364i	−0.509764	+	0.427743i
$322$	0.992716	−	30.6257i	0.0553219	−	1.70670i
$323$	−9.66290	+	23.1400i	−0.537658	+	1.28755i
$324$	−1.99580	−	0.129522i	−0.110878	−	0.00719566i
$325$	−16.9318	−	20.1785i	−0.939208	−	1.11930i
$326$	−13.0824	−	5.24758i	−0.724568	−	0.290637i
$327$	−0.623789	+	3.53768i	−0.0344956	+	0.195634i
$328$	−31.1431	+	2.41291i	−1.71959	+	0.133230i
$329$	−21.9550	+	7.99096i	−1.21042	+	0.440556i
$330$	−6.72601	+	10.8241i	−0.370255	+	0.595846i
$331$	−9.98839	+	5.76680i	−0.549011	+	0.316972i	−0.748723	−	0.662883i	$-0.769333\pi$
$331$	−9.98839	+	5.76680i	−0.549011	+	0.316972i	0.199712	+	0.979855i	$0.435999\pi$
$332$	2.52241	−	2.63834i	0.138435	−	0.144798i
$333$	2.67735	−	3.19074i	0.146718	−	0.174851i
$334$	−6.95868	+	3.72237i	−0.380762	+	0.203679i
$335$	7.14169	−	12.3698i	0.390192	−	0.675833i
$336$	3.41922	+	15.3297i	0.186534	+	0.836303i
$337$	−2.93176	−	16.6269i	−0.159703	−	0.905723i	−0.954359	−	0.298662i	$-0.903460\pi$
$337$	−2.93176	−	16.6269i	−0.159703	−	0.905723i	0.794656	−	0.607061i	$-0.207651\pi$
$338$	6.52673	+	1.37023i	0.355007	+	0.0745307i
$339$	−1.04277	+	2.86500i	−0.0566357	+	0.155605i
$340$	−22.8483	−	31.1191i	−1.23912	−	1.68767i
$341$		−	6.71597i		−	0.363690i
$342$	−2.65179	−	5.56489i	−0.143392	−	0.300915i
$343$	5.56849			0.300670
$344$	28.4400	−	19.4954i	1.53338	−	1.05112i
$345$	−17.3982	−	6.33244i	−0.936690	−	0.340927i
$346$	−3.46900	+	16.5236i	−0.186494	+	0.888316i
$347$	1.58502	−	0.279482i	0.0850884	−	0.0150034i	−0.130942	−	0.991390i	$-0.541800\pi$
$347$	1.58502	−	0.279482i	0.0850884	−	0.0150034i	0.216030	+	0.976387i	$0.430689\pi$
$348$	1.31344	−	0.383749i	0.0704077	−	0.0205711i
$349$	13.3259	+	7.69374i	0.713322	+	0.411836i	0.812290	−	0.583254i	$-0.198221\pi$
$349$	13.3259	+	7.69374i	0.713322	+	0.411836i	−0.0989681	+	0.995091i	$0.531554\pi$
$350$	30.6438	−	16.3921i	1.63798	−	0.876197i
$351$	−3.22428	−	2.70549i	−0.172100	−	0.144409i
$352$	9.91016	+	11.5146i	0.528214	+	0.613732i
$353$	−4.72335	−	8.18108i	−0.251398	−	0.435435i	0.712513	−	0.701659i	$-0.247557\pi$
$353$	−4.72335	−	8.18108i	−0.251398	−	0.435435i	−0.963911	+	0.266224i	$0.914224\pi$
$354$	−10.2396	−	6.36282i	−0.544228	−	0.338180i
$355$	12.2234	+	33.5835i	0.648751	+	1.78243i
$356$	−0.447346	−	4.06054i	−0.0237093	−	0.215208i
$357$	−22.2463	−	3.92263i	−1.17740	−	0.207607i
$358$	19.3205	+	7.74980i	1.02112	+	0.409589i
$359$	5.65631	−	4.74621i	0.298529	−	0.250495i	−0.481203	−	0.876609i	$-0.659800\pi$
$359$	5.65631	−	4.74621i	0.298529	−	0.250495i	0.779732	+	0.626114i	$0.215355\pi$
$360$	9.44553	+	0.921097i	0.497823	+	0.0485461i
$361$	10.9872	−	15.5010i	0.578274	−	0.815842i
$362$	19.6635	+	0.637382i	1.03349	+	0.0335001i
$363$	−2.43459	−	2.90143i	−0.127783	−	0.152286i
$364$	−13.2930	+	30.2634i	−0.696740	+	1.58623i
$365$	48.9697	+	8.63468i	2.56319	+	0.451960i
$366$	2.74152	−	0.392297i	0.143302	−	0.0205057i
$367$	−3.62034	+	1.31769i	−0.188980	+	0.0687831i	−0.434777	−	0.900538i	$-0.643173\pi$
$367$	−3.62034	+	1.31769i	−0.188980	+	0.0687831i	0.245797	+	0.969321i	$0.420950\pi$
$368$	−13.4141	+	17.5282i	−0.699257	+	0.913722i
$369$	5.52187	+	9.56416i	0.287457	+	0.497890i
$370$	−13.1883	+	14.7211i	−0.685628	+	0.765311i
$371$	25.0054	−	29.8003i	1.29821	−	1.54715i
$372$	−4.48426	+	2.21498i	−0.232498	+	0.114841i
$373$	−2.03091	−	1.17254i	−0.105156	−	0.0607121i	0.446499	−	0.894784i	$-0.352670\pi$
$373$	−2.03091	−	1.17254i	−0.105156	−	0.0607121i	−0.551656	+	0.834072i	$0.686004\pi$
$374$	−20.7634	+	6.80395i	−1.07365	+	0.351824i
$375$	−0.733150	−	4.15790i	−0.0378597	−	0.214713i
$376$	16.2121	+	4.51726i	0.836076	+	0.232960i
$377$	2.70603	+	0.984914i	0.139368	+	0.0507256i
$378$	4.36729	−	3.42974i	0.224629	−	0.176407i
$379$		−	22.6000i		−	1.16088i	−0.814302	−	0.580442i	$-0.802880\pi$
$379$		−	22.6000i		−	1.16088i	0.814302	−	0.580442i	$-0.197120\pi$
$380$	11.7211	+	26.8001i	0.601279	+	1.37482i
$381$			13.3167i			0.682236i
$382$	20.9672	+	26.6987i	1.07277	+	1.36602i
$383$	8.67901	+	3.15890i	0.443477	+	0.161412i	0.554100	−	0.832450i	$-0.313063\pi$
$383$	8.67901	+	3.15890i	0.443477	+	0.161412i	−0.110623	+	0.993862i	$0.535285\pi$
$384$	4.41988	−	10.4146i	0.225551	−	0.531470i
$385$	−6.14418	−	34.8454i	−0.313137	−	1.77589i
$386$	7.74937	+	23.6485i	0.394433	+	1.20368i
$387$	−10.5574	−	6.09534i	−0.536665	−	0.309844i
$388$	10.2396	+	20.7303i	0.519839	+	1.05242i
$389$	9.28178	−	11.0616i	0.470605	−	0.560845i	−0.477570	−	0.878594i	$-0.658482\pi$
$389$	9.28178	−	11.0616i	0.470605	−	0.560845i	0.948175	+	0.317749i	$0.102927\pi$
$390$	14.8758	+	13.3270i	0.753266	+	0.674837i
$391$	−15.8724	−	27.4919i	−0.802704	−	1.39032i
$392$	−19.3674	−	13.8502i	−0.978199	−	0.699539i
$393$	4.00952	−	1.45935i	0.202254	−	0.0736143i
$394$	−0.457333	−	3.19602i	−0.0230401	−	0.161013i
$395$	13.4536	+	2.37223i	0.676923	+	0.119360i
$396$	2.16007	−	4.91771i	0.108548	−	0.247124i
$397$	−10.7527	−	12.8146i	−0.539662	−	0.643144i	0.425450	−	0.904982i	$-0.360116\pi$
$397$	−10.7527	−	12.8146i	−0.539662	−	0.643144i	−0.965112	+	0.261838i	$0.915671\pi$
$398$	−0.0924461	+	2.85200i	−0.00463390	+	0.142958i
$399$	15.7939	+	6.59528i	0.790684	+	0.330177i
$400$	−24.8232	−	3.23554i	−1.24116	−	0.161777i
$401$	−26.3826	+	22.1376i	−1.31748	+	1.10550i	−0.330652	+	0.943753i	$0.607269\pi$
$401$	−26.3826	+	22.1376i	−1.31748	+	1.10550i	−0.986832	+	0.161748i	$0.948287\pi$
$402$	−2.24122	+	5.58744i	−0.111782	+	0.278676i
$403$	−10.3657	−	1.82775i	−0.516352	−	0.0910468i
$404$	28.7123	−	3.16321i	1.42849	−	0.157376i
$405$	−1.14759	−	3.15299i	−0.0570244	−	0.156673i
$406$	−2.00523	+	3.22698i	−0.0995177	+	0.160152i
$407$	5.59305	+	9.68745i	0.277237	+	0.480189i
$408$	11.3909	+	11.6197i	0.563935	+	0.575262i
$409$	14.4081	+	12.0899i	0.712437	+	0.597806i	0.925282	−	0.379280i	$-0.123828\pi$
$409$	14.4081	+	12.0899i	0.712437	+	0.597806i	−0.212845	+	0.977086i	$0.568273\pi$
$410$	−24.7181	−	46.2086i	−1.22074	−	2.28208i
$411$	−7.52305	−	4.34344i	−0.371085	−	0.214246i
$412$	−4.62357	+	1.35088i	−0.227787	+	0.0665530i
$413$	32.9638	−	5.81240i	1.62204	−	0.286010i
$414$	7.63716	+	1.60336i	0.375346	+	0.0788007i
$415$	5.75440	+	2.09443i	0.282473	+	0.102812i
$416$	20.4692	−	12.1620i	1.00358	−	0.596292i
$417$	8.92854			0.437233
$418$	16.4795	−	1.58065i	0.806040	−	0.0773119i
$419$			3.15366i			0.154066i	0.997029	+	0.0770331i	$0.0245447\pi$
$419$			3.15366i			0.154066i	−0.997029	+	0.0770331i	$0.975455\pi$
$420$	−21.2399	+	15.5948i	−1.03640	+	0.760946i
$421$	2.10816	−	5.79211i	0.102745	−	0.282290i	−0.877659	−	0.479285i	$-0.840896\pi$
$421$	2.10816	−	5.79211i	0.102745	−	0.282290i	0.980405	+	0.196995i	$0.0631182\pi$
$422$	−2.68482	+	12.7884i	−0.130695	+	0.622530i
$423$	−1.03324	−	5.85980i	−0.0502379	−	0.284913i
$424$	−27.1377	+	6.98308i	−1.31792	+	0.339128i
$425$	18.0019	−	31.1801i	0.873218	−	1.51246i
$426$	−7.10505	−	13.2823i	−0.344241	−	0.643531i
$427$	−4.94267	+	5.89044i	−0.239192	+	0.285058i
$428$	−16.4781	+	17.2354i	−0.796497	+	0.833104i
$429$	9.78929	−	5.65185i	0.472631	−	0.272874i
$430$	49.1335	+	30.5313i	2.36943	+	1.47235i
$431$	25.1995	−	9.17186i	1.21382	−	0.441793i	0.345791	−	0.938312i	$-0.387611\pi$
$431$	25.1995	−	9.17186i	1.21382	−	0.441793i	0.868026	+	0.496518i	$0.165389\pi$
$432$	−3.99596	+	0.179621i	−0.192256	+	0.00864203i
$433$	4.96039	−	28.1318i	0.238381	−	1.35193i	−0.596994	−	0.802246i	$-0.703638\pi$
$433$	4.96039	−	28.1318i	0.238381	−	1.35193i	0.835375	−	0.549680i	$-0.185250\pi$
$434$	5.16980	−	12.8885i	0.248158	−	0.618668i
$435$	1.47561	+	1.75856i	0.0707500	+	0.0843166i
$436$	−0.465276	+	7.16943i	−0.0222827	+	0.343354i
$437$	7.16678	+	22.9599i	0.342834	+	1.09832i
$438$	−20.9472	−	0.678993i	−1.00090	−	0.0324435i
$439$	−26.0061	+	21.8217i	−1.24120	+	1.04149i	−0.243773	+	0.969832i	$0.578385\pi$
$439$	−26.0061	+	21.8217i	−1.24120	+	1.04149i	−0.997429	+	0.0716602i	$0.977170\pi$
$440$	−11.0005	+	22.9910i	−0.524429	+	1.09606i
$441$	−1.46180	+	8.29026i	−0.0696093	+	0.394774i
$442$	4.85073	+	33.8987i	0.230725	+	1.61240i
$443$	4.79305	+	13.1688i	0.227725	+	0.625669i	0.999953	−	0.00967641i	$-0.00308014\pi$
$443$	4.79305	+	13.1688i	0.227725	+	0.625669i	−0.772228	+	0.635345i	$0.780858\pi$
$444$	4.62368	−	6.92948i	0.219430	−	0.328858i
$445$	5.93527	−	3.42673i	0.281359	−	0.162443i
$446$	0.131309	−	0.146570i	0.00621768	−	0.00694030i
$447$	2.03145	+	1.70459i	0.0960841	+	0.0806241i
$448$	10.1547	+	29.7261i	0.479765	+	1.40443i
$449$	−3.35431	+	5.80984i	−0.158300	+	0.274183i	−0.934256	−	0.356604i	$-0.883935\pi$
$449$	−3.35431	+	5.80984i	−0.158300	+	0.274183i	0.775956	+	0.630787i	$0.217268\pi$
$450$	2.75604	+	8.41053i	0.129921	+	0.396476i
$451$	−29.2085	+	5.15025i	−1.37537	+	0.242516i
$452$	−1.44553	+	5.92391i	−0.0679921	+	0.278637i
$453$	3.57192	−	9.81376i	0.167823	−	0.461091i
$454$	9.51000	−	7.46844i	0.446326	−	0.350511i
$455$	−55.4539			−2.59972
$456$	−6.49047	−	10.4821i	−0.303944	−	0.490868i
$457$	−37.7360			−1.76521			−0.882607	−	0.470111i	$-0.844214\pi$
$457$	−37.7360			−1.76521			−0.882607	+	0.470111i	$0.844214\pi$
$458$	3.20433	−	2.51644i	0.149729	−	0.117586i
$459$	1.96762	−	5.40600i	0.0918408	−	0.252331i
$460$	−35.9741	−	8.77827i	−1.67730	−	0.409289i
$461$	0.871615	−	0.153689i	0.0405951	−	0.00715802i	−0.153314	−	0.988178i	$-0.548995\pi$
$461$	0.871615	−	0.153689i	0.0405951	−	0.00715802i	0.193909	+	0.981020i	$0.437883\pi$
$462$	4.64394	+	14.1718i	0.216056	+	0.659330i
$463$	5.04121	−	8.73163i	0.234285	−	0.405793i	−0.724780	−	0.688981i	$-0.758058\pi$
$463$	5.04121	−	8.73163i	0.234285	−	0.405793i	0.959065	+	0.283187i	$0.0913918\pi$
$464$	2.52703	−	1.05054i	0.117314	−	0.0487703i
$465$	−6.42774	−	5.39351i	−0.298079	−	0.250118i
$466$	7.39009	−	8.24897i	0.342339	−	0.382126i
$467$	9.14004	−	5.27700i	0.422951	−	0.244191i	−0.273388	−	0.961904i	$-0.588144\pi$
$467$	9.14004	−	5.27700i	0.422951	−	0.244191i	0.696339	+	0.717713i	$0.254811\pi$
$468$	−7.00232	−	4.67229i	−0.323683	−	0.215977i
$469$	−5.71692	−	15.7071i	−0.263983	−	0.725287i
$470$	3.99949	+	27.9500i	0.184483	+	1.28924i
$471$	1.77207	−	10.0499i	0.0816525	−	0.463075i
$472$	−21.7496	−	10.4065i	−1.00110	−	0.478998i
$473$	25.0798	−	21.0444i	1.15317	−	0.967624i
$474$	−5.75489	−	0.186542i	−0.264331	−	0.00856814i
$475$	−18.4874	+	20.0594i	−0.848258	+	0.920388i
$476$	−45.0842	−	2.92583i	−2.06643	−	0.134105i
$477$	6.36821	+	7.58934i	0.291580	+	0.347492i
$478$	0.656196	−	1.63592i	0.0300137	−	0.0748254i
$479$	−3.25649	+	18.4684i	−0.148793	+	0.843845i	0.815451	+	0.578826i	$0.196489\pi$
$479$	−3.25649	+	18.4684i	−0.148793	+	0.843845i	−0.964243	+	0.265018i	$0.914622\pi$
$480$	18.9792	−	0.237580i	0.866277	−	0.0108440i
$481$	16.4741	−	5.99609i	0.751155	−	0.273398i
$482$	0.122710	+	0.0762513i	0.00558929	+	0.00347315i
$483$	−18.7642	+	10.8335i	−0.853800	+	0.492942i
$484$	−5.47535	−	5.23476i	−0.248880	−	0.237944i
$485$	−24.9337	+	29.7148i	−1.13218	+	1.34928i
$486$	0.667057	+	1.24701i	0.0302583	+	0.0565655i
$487$	−8.28900	+	14.3570i	−0.375610	+	0.650576i	−0.990418	−	0.138101i	$-0.955900\pi$
$487$	−8.28900	+	14.3570i	−0.375610	+	0.650576i	0.614808	+	0.788677i	$0.289234\pi$
$488$	5.36415	−	1.38030i	0.242823	−	0.0624834i
$489$	1.73077	+	9.81569i	0.0782682	+	0.443881i
$490$	8.20730	−	39.0933i	0.370768	−	1.76605i
$491$	−13.7826	+	37.8674i	−0.622000	+	1.70893i	0.0800381	+	0.996792i	$0.474496\pi$
$491$	−13.7826	+	37.8674i	−0.622000	+	1.70893i	−0.702038	+	0.712139i	$0.747726\pi$
$492$	13.0720	+	17.8039i	0.589332	+	0.802663i
$493$			3.93602i			0.177270i
$494$	2.04527	−	25.8653i	0.0920210	−	1.16373i
$495$	9.01110			0.405019
$496$	−8.42947	+	5.38543i	−0.378494	+	0.241813i
$497$	39.3012	+	14.3045i	1.76290	+	0.641643i
$498$	−2.52596	−	0.530304i	−0.113191	−	0.0237635i
$499$	34.0851	−	6.01012i	1.52586	−	0.269050i	0.653127	−	0.757249i	$-0.273457\pi$
$499$	34.0851	−	6.01012i	1.52586	−	0.269050i	0.872733	+	0.488199i	$0.162346\pi$
$500$	−2.36812	−	8.10522i	−0.105905	−	0.362476i
$501$	4.83267	+	2.79014i	0.215908	+	0.124654i
$502$	9.74629	+	18.2199i	0.434998	+	0.813195i
$503$	−8.18395	−	6.86715i	−0.364904	−	0.306191i	0.441837	−	0.897095i	$-0.354327\pi$
$503$	−8.18395	−	6.86715i	−0.364904	−	0.306191i	−0.806742	+	0.590904i	$0.798771\pi$
$504$	7.93088	−	7.77472i	0.353270	−	0.346314i
$505$	24.2306	+	41.9686i	1.07825	+	1.86758i
$506$	−11.0613	+	17.8007i	−0.491733	+	0.791338i
$507$	−1.61287	−	4.43131i	−0.0716299	−	0.196801i
$508$	2.91654	+	26.4733i	0.129400	+	1.17456i
$509$	−33.2370	−	5.86057i	−1.47320	−	0.259765i	−0.621344	−	0.783538i	$-0.713413\pi$
$509$	−33.2370	−	5.86057i	−1.47320	−	0.259765i	−0.851858	+	0.523773i	$0.824524\pi$
$510$	−10.1629	+	25.3364i	−0.450020	+	1.12192i
$511$	44.5769	−	37.4044i	1.97196	−	1.65467i
$512$	6.50565	−	21.6720i	0.287512	−	0.957777i
$513$	−2.35259	+	3.66951i	−0.103869	+	0.162013i
$514$	−0.887224	+	27.3712i	−0.0391338	+	1.20729i
$515$	−5.19445	−	6.19050i	−0.228895	−	0.272786i
$516$	−22.3229	−	9.80515i	−0.982710	−	0.431648i
$517$	15.7371	+	2.77487i	0.692116	+	0.122039i
$518$	3.27635	+	22.8964i	0.143955	+	1.00601i
$519$	11.2187	−	4.08327i	0.492446	−	0.179236i
$520$	32.4915	+	23.2356i	1.42485	+	1.01895i
$521$	−2.74892	−	4.76127i	−0.120432	−	0.208595i	0.799506	−	0.600658i	$-0.205095\pi$
$521$	−2.74892	−	4.76127i	−0.120432	−	0.208595i	−0.919938	+	0.392063i	$0.871761\pi$
$522$	−0.720663	−	0.645628i	−0.0315426	−	0.0282584i
$523$	−19.1994	+	22.8809i	−0.839531	+	1.00051i	0.160379	+	0.987056i	$0.448728\pi$
$523$	−19.1994	+	22.8809i	−0.839531	+	1.00051i	−0.999909	+	0.0134581i	$0.995716\pi$
$524$	7.65120	−	3.77928i	0.334244	−	0.165099i
$525$	−21.2816	−	12.2869i	−0.928803	−	0.536245i
$526$	−7.86970	−	24.0157i	−0.343135	−	1.04713i
$527$	−2.49821	−	14.1680i	−0.108824	−	0.617169i
$528$	3.21711	−	10.2494i	0.140007	−	0.446046i
$529$	−6.99931	−	2.54754i	−0.304318	−	0.110763i
$530$	−29.0356	−	36.9728i	−1.26123	−	1.60599i
$531$			8.52451i			0.369932i
$532$	32.8423	+	9.65215i	1.42389	+	0.418474i
$533$			46.4832i			2.01341i
$534$	−2.27179	+	1.78410i	−0.0983101	+	0.0772054i
$535$	−37.5915	−	13.6822i	−1.62522	−	0.591533i
$536$	−3.23176	+	11.5985i	−0.139591	+	0.500981i
$537$	−2.55606	−	14.4961i	−0.110302	−	0.625554i
$538$	−27.2576	+	8.93202i	−1.17516	+	0.385087i
$539$	−19.5789	−	11.3039i	−0.843323	−	0.486893i
$540$	−2.97193	−	6.01671i	−0.127892	−	0.258918i
$541$	21.1941	−	25.2581i	0.911205	−	1.08593i	−0.0847789	−	0.996400i	$-0.527018\pi$
$541$	21.1941	−	25.2581i	0.911205	−	1.08593i	0.995984	−	0.0895321i	$-0.0285372\pi$
$542$	23.9254	−	26.7060i	1.02769	−	1.14712i
$543$	−6.95575	−	12.0477i	−0.298500	−	0.517017i
$544$	25.1897	+	20.6049i	1.08000	+	0.883429i
$545$	−11.3263	+	4.12245i	−0.485167	+	0.176586i
$546$	23.1371	−	3.31079i	0.990176	−	0.141689i
$547$	9.54968	+	1.68387i	0.408315	+	0.0719969i	0.374033	−	0.927415i	$-0.377975\pi$
$547$	9.54968	+	1.68387i	0.408315	+	0.0719969i	0.0342816	+	0.999412i	$0.489086\pi$
$548$	−15.9069	−	6.98698i	−0.679509	−	0.298469i
$549$	−1.25877	−	1.50014i	−0.0537229	−	0.0640244i
$550$	−23.7566	−	0.770059i	−1.01299	−	0.0328354i
$551$	0.653840	−	2.90969i	0.0278545	−	0.123957i
$552$	15.5336	+	1.51479i	0.661155	+	0.0644737i
$553$	12.2467	−	10.2762i	0.520784	−	0.436990i
$554$	−42.0198	−	16.8548i	−1.78525	−	0.716094i
$555$	13.7634	+	2.42686i	0.584223	+	0.103014i
$556$	17.7497	−	1.95547i	0.752755	−	0.0829303i
$557$	13.2236	+	36.3314i	0.560300	+	1.53941i	0.819200	+	0.573509i	$0.194418\pi$
$557$	13.2236	+	36.3314i	0.560300	+	1.53941i	−0.258899	+	0.965904i	$0.583360\pi$
$558$	3.00387	+	1.86658i	0.127164	+	0.0790188i
$559$	−25.6553	−	44.4363i	−1.08510	−	1.87946i
$560$	−38.8088	+	35.6538i	−1.63997	+	1.50665i
$561$	11.8355	+	9.93115i	0.499694	+	0.419293i
$562$	13.4293	−	7.18364i	0.566479	−	0.303024i
$563$	−19.1200	−	11.0390i	−0.805813	−	0.465237i	0.0396864	−	0.999212i	$-0.487364\pi$
$563$	−19.1200	−	11.0390i	−0.805813	−	0.465237i	−0.845500	+	0.533976i	$0.820697\pi$
$564$	−3.33743	−	11.4228i	−0.140531	−	0.480988i
$565$	−10.0746	+	1.77642i	−0.423840	+	0.0747344i
$566$	5.37567	−	25.6056i	0.225956	−	1.07628i
$567$	−3.68979	−	1.34297i	−0.154957	−	0.0563996i
$568$	−17.0336	−	24.8488i	−0.714716	−	1.04263i
$569$	46.8208			1.96283			0.981415	−	0.191900i	$-0.0614648\pi$
$569$	46.8208			1.96283			0.981415	+	0.191900i	$0.0614648\pi$
$570$	11.7217	−	17.0416i	0.490967	−	0.713796i
$571$		−	17.1255i		−	0.716682i	−0.933591	−	0.358341i	$-0.883343\pi$
$571$		−	17.1255i		−	0.716682i	0.933591	−	0.358341i	$-0.116657\pi$
$572$	18.2230	−	13.3797i	0.761942	−	0.559433i
$573$	8.21006	−	22.5569i	0.342980	−	0.942330i
$574$	−60.0180	−	12.6003i	−2.50510	−	0.525925i
$575$	−5.99667	−	34.0088i	−0.250078	−	1.41826i
$576$	−7.90453	+	1.23225i	−0.329355	+	0.0513438i
$577$	−11.7435	+	20.3404i	−0.488890	+	0.846782i	−0.999918	−	0.0127818i	$-0.995931\pi$
$577$	−11.7435	+	20.3404i	−0.488890	+	0.846782i	0.511029	+	0.859564i	$0.329265\pi$
$578$	−20.0724	+	10.7372i	−0.834902	+	0.446610i
$579$	11.3111	−	13.4800i	0.470073	−	0.560211i
$580$	3.31862	+	3.17279i	0.137798	+	0.131743i
$581$	6.20619	−	3.58314i	0.257476	−	0.148654i
$582$	8.62905	−	13.8866i	0.357685	−	0.575618i
$583$	−25.0021	+	9.10003i	−1.03548	+	0.376885i
$584$	−41.7912	+	3.23790i	−1.72933	+	0.133985i
$585$	2.45237	−	13.9081i	0.101393	−	0.575028i
$586$	−11.6300	−	4.66498i	−0.480430	−	0.192709i
$587$	18.3963	+	21.9238i	0.759295	+	0.904893i	0.997803	−	0.0662476i	$-0.0211027\pi$
$587$	18.3963	+	21.9238i	0.759295	+	0.904893i	−0.238508	+	0.971141i	$0.576658\pi$
$588$	−1.09033	+	16.8010i	−0.0449646	+	0.692860i
$589$	−0.506759	+	10.8887i	−0.0208807	+	0.448660i
$590$	1.31048	−	40.4290i	0.0539518	−	1.66444i
$591$	−1.74884	+	1.46745i	−0.0719376	+	0.0603628i
$592$	7.67410	−	14.7883i	0.315404	−	0.607793i
$593$	1.43245	−	8.12384i	0.0588238	−	0.333606i	−0.941167	−	0.337942i	$-0.890269\pi$
$593$	1.43245	−	8.12384i	0.0588238	−	0.333606i	0.999991	+	0.00433617i	$0.00138025\pi$
$594$	−3.75971	+	0.537995i	−0.154263	+	0.0220742i
$595$	−25.9236	−	71.2244i	−1.06276	−	2.91992i
$596$	4.41178	+	2.94376i	0.180714	+	0.120581i
$597$	1.74740	−	1.00886i	0.0715165	−	0.0412900i
$598$	24.4640	+	21.9168i	1.00041	+	0.896246i
$599$	19.0326	+	15.9703i	0.777651	+	0.652527i	0.942656	−	0.333766i	$-0.108320\pi$
$599$	19.0326	+	15.9703i	0.777651	+	0.652527i	−0.165005	+	0.986293i	$0.552764\pi$
$600$	7.32096	+	16.1163i	0.298877	+	0.657945i
$601$	13.0666	−	22.6320i	0.532998	−	0.923180i	−0.466259	−	0.884648i	$-0.654398\pi$
$601$	13.0666	−	22.6320i	0.532998	−	0.923180i	0.999257	−	0.0385321i	$-0.0122682\pi$
$602$	64.3296	−	21.0801i	2.62188	−	0.859163i
$603$	4.19224	−	0.739205i	0.170721	−	0.0301028i
$604$	4.95153	−	20.2918i	0.201475	−	0.825661i
$605$	4.34657	−	11.9421i	0.176713	−	0.485516i
$606$	−12.6154	−	16.0640i	−0.512467	−	0.652555i
$607$	25.4042			1.03112			0.515562	−	0.856853i	$-0.327583\pi$
$607$	25.4042			1.03112			0.515562	+	0.856853i	$0.327583\pi$
$608$	−15.1986	−	19.4166i	−0.616384	−	0.787446i
$609$	2.68648			0.108862
$610$	5.73930	+	7.30819i	0.232378	+	0.295900i
$611$	8.56568	−	23.5340i	0.346530	−	0.952085i
$612$	2.72760	−	11.1779i	0.110257	−	0.451841i
$613$	12.8156	−	2.25974i	0.517619	−	0.0912702i	0.0912652	−	0.995827i	$-0.470909\pi$
$613$	12.8156	−	2.25974i	0.517619	−	0.0912702i	0.426354	+	0.904556i	$0.359798\pi$
$614$	4.59600	−	1.50606i	0.185479	−	0.0607797i
$615$	−18.5278	+	32.0910i	−0.747111	+	1.29403i
$616$	12.3358	+	27.1560i	0.497025	+	1.09415i
$617$	−16.1716	−	13.5696i	−0.651044	−	0.546291i	0.256344	−	0.966586i	$-0.417482\pi$
$617$	−16.1716	−	13.5696i	−0.651044	−	0.546291i	−0.907388	+	0.420295i	$0.861927\pi$
$618$	2.53688	+	2.27275i	0.102048	+	0.0914232i
$619$	−30.9165	+	17.8497i	−1.24264	+	0.717439i	−0.969631	−	0.244573i	$-0.921352\pi$
$619$	−30.9165	+	17.8497i	−1.24264	+	0.717439i	−0.273009	+	0.962011i	$0.588019\pi$
$620$	−13.9594	−	9.31439i	−0.560624	−	0.374075i
$621$	−1.88727	−	5.18524i	−0.0757337	−	0.208077i
$622$	−8.71981	+	1.24776i	−0.349632	+	0.0500305i
$623$	1.39271	−	7.89843i	0.0557976	−	0.316444i
$624$	−14.9437	−	7.75478i	−0.598228	−	0.310439i
$625$	−13.1186	+	11.0078i	−0.524745	+	0.440313i
$626$	0.456521	−	14.0839i	0.0182463	−	0.562905i
$627$	−7.09960	−	9.30764i	−0.283531	−	0.371711i
$628$	1.32176	−	20.3670i	0.0527440	−	0.812732i
$629$	15.4026	+	18.3562i	0.614144	+	0.731908i
$630$	17.2930	+	6.93653i	0.688971	+	0.276358i
$631$	−7.18915	+	40.7717i	−0.286196	+	1.62310i	0.414788	+	0.909918i	$0.363856\pi$
$631$	−7.18915	+	40.7717i	−0.286196	+	1.62310i	−0.700983	+	0.713178i	$0.747255\pi$
$632$	−11.4814	+	0.889557i	−0.456706	+	0.0353847i
$633$	8.68267	−	3.16023i	0.345105	−	0.125608i
$634$	−12.9192	+	20.7907i	−0.513088	+	0.825705i
$635$	−38.6959	+	22.3411i	−1.53560	+	0.886578i
$636$	14.3220	+	13.6927i	0.567904	+	0.542950i
$637$	−22.7753	+	27.1425i	−0.902389	+	1.07542i
$638$	2.29128	−	1.22566i	0.0907127	−	0.0485245i
$639$	−5.32567	+	9.22433i	−0.210680	+	0.364909i
$640$	37.6781	−	4.62900i	1.48936	−	0.182977i
$641$	−7.08963	−	40.2073i	−0.280024	−	1.58809i	−0.722537	−	0.691332i	$-0.757024\pi$
$641$	−7.08963	−	40.2073i	−0.280024	−	1.58809i	0.442514	−	0.896762i	$-0.354087\pi$
$642$	16.5012	+	3.46429i	0.651252	+	0.136725i
$643$	14.5677	−	40.0246i	0.574496	−	1.57841i	−0.222825	−	0.974859i	$-0.571528\pi$
$643$	14.5677	−	40.0246i	0.574496	−	1.57841i	0.797321	−	0.603556i	$-0.206250\pi$
$644$	−34.9300	+	25.6463i	−1.37643	+	1.01061i
$645$		−	40.9039i		−	1.61059i
$646$	34.1773	−	9.46458i	1.34469	−	0.372379i
$647$	−9.54743			−0.375348			−0.187674	−	0.982231i	$-0.560095\pi$
$647$	−9.54743			−0.375348			−0.187674	+	0.982231i	$0.560095\pi$
$648$	1.59920	+	2.33293i	0.0628226	+	0.0916461i
$649$	−21.5128	−	7.83001i	−0.844451	−	0.307355i
$650$	−7.65391	+	36.4573i	−0.300211	+	1.42997i
$651$	−9.67019	+	1.70512i	−0.379005	+	0.0668288i
$652$	5.59049	+	19.1343i	0.218941	+	0.749355i
$653$	−3.53609	−	2.04156i	−0.138378	−	0.0798926i	0.429213	−	0.903203i	$-0.358791\pi$
$653$	−3.53609	−	2.04156i	−0.138378	−	0.0798926i	−0.567591	+	0.823311i	$0.692124\pi$
$654$	4.47958	−	2.39624i	0.175166	−	0.0937004i
$655$	10.9672	+	9.20261i	0.428526	+	0.359576i
$656$	29.8861	+	32.5308i	1.16686	+	1.27011i
$657$	7.40985	+	12.8342i	0.289086	+	0.500711i
$658$	28.0647	+	17.4392i	1.09408	+	0.679852i
$659$	3.58781	+	9.85743i	0.139761	+	0.383991i	0.989750	−	0.142810i	$-0.0456137\pi$
$659$	3.58781	+	9.85743i	0.139761	+	0.383991i	−0.849989	+	0.526801i	$0.823391\pi$
$660$	17.9138	−	1.97355i	0.697294	−	0.0768203i
$661$	38.6472	+	6.81455i	1.50320	+	0.265055i	0.863807	−	0.503822i	$-0.168073\pi$
$661$	38.6472	+	6.81455i	1.50320	+	0.265055i	0.639396	+	0.768877i	$0.279184\pi$
$662$	15.1385	+	6.07232i	0.588375	+	0.236007i
$663$	18.5491	−	15.5646i	0.720389	−	0.604478i
$664$	−5.13769	−	0.501011i	−0.199381	−	0.0194430i
$665$	7.33233	+	56.9587i	0.284335	+	2.20877i
$666$	−5.88741	−	0.190837i	−0.228133	−	0.00739480i
$667$	2.42671	+	2.89204i	0.0939626	+	0.111980i
$668$	10.2183	+	4.48831i	0.395358	+	0.173658i
$669$	−0.137035	−	0.0241630i	−0.00529808	−	0.000934195i
$670$	−19.9961	+	2.86133i	−0.772516	+	0.110543i
$671$	4.94202	−	1.79875i	0.190785	−	0.0694400i
$672$	14.0636	−	17.1929i	0.542516	−	0.663230i
$673$	2.17339	+	3.76442i	0.0837780	+	0.145108i	0.904870	−	0.425688i	$-0.139968\pi$
$673$	2.17339	+	3.76442i	0.0837780	+	0.145108i	−0.821092	+	0.570796i	$0.806635\pi$
$674$	−15.9321	+	17.7838i	−0.613683	+	0.685005i
$675$	4.02276	−	4.79414i	0.154836	−	0.184527i
$676$	−4.17685	−	8.45609i	−0.160648	−	0.325234i
$677$	12.5037	+	7.21903i	0.480557	+	0.277450i	0.720649	−	0.693300i	$-0.243844\pi$
$677$	12.5037	+	7.21903i	0.480557	+	0.277450i	−0.240091	+	0.970750i	$0.577177\pi$
$678$	4.09737	−	1.34266i	0.157358	−	0.0515647i
$679$	7.88260	+	44.7044i	0.302506	+	1.71560i
$680$	−14.6545	+	52.5939i	−0.561975	+	2.01689i
$681$	−8.03472	−	2.92440i	−0.307891	−	0.112063i
$682$	−7.46972	+	5.86616i	−0.286030	+	0.224627i
$683$			3.35870i			0.128517i	0.997933	+	0.0642585i	$0.0204682\pi$
$683$			3.35870i			0.128517i	−0.997933	+	0.0642585i	$0.979532\pi$
$684$	−3.87321	+	7.81014i	−0.148096	+	0.298628i
$685$		−	29.1474i		−	1.11367i
$686$	−4.86388	−	6.19346i	−0.185704	−	0.236467i
$687$	−2.70725	−	0.985357i	−0.103288	−	0.0375937i
$688$	−46.5247	−	14.6034i	−1.77374	−	0.556748i
$689$	7.24101	+	41.0658i	0.275861	+	1.56448i
$690$	8.15359	+	24.8820i	0.310402	+	0.947243i
$691$	27.8912	+	16.1030i	1.06103	+	0.612586i	0.925717	−	0.378217i	$-0.123463\pi$
$691$	27.8912	+	16.1030i	1.06103	+	0.612586i	0.135313	+	0.990803i	$0.456796\pi$
$692$	21.4082	−	10.5745i	0.813816	−	0.401981i
$693$	6.77836	−	8.07814i	0.257489	−	0.306863i
$694$	−1.69531	−	1.51879i	−0.0643530	−	0.0576526i
$695$	14.9791	+	25.9446i	0.568191	+	0.984136i
$696$	−1.57406	−	1.12566i	−0.0596646	−	0.0426679i
$697$	−59.7025	+	21.7299i	−2.26139	+	0.823080i
$698$	−3.08251	−	21.5418i	−0.116675	−	0.815367i
$699$	−7.71234	−	1.35989i	−0.291707	−	0.0514359i
$700$	−44.9981	−	19.7651i	−1.70077	−	0.747051i
$701$	−27.4511	−	32.7149i	−1.03681	−	1.23563i	−0.971321	−	0.237773i	$-0.923583\pi$
$701$	−27.4511	−	32.7149i	−1.03681	−	1.23563i	−0.0654921	−	0.997853i	$-0.520862\pi$
$702$	−0.192844	+	5.94930i	−0.00727841	+	0.224542i
$703$	−8.33708	−	16.1284i	−0.314439	−	0.608293i
$704$	4.15078	−	21.0800i	0.156439	−	0.794483i
$705$	15.2940	−	12.8332i	0.576006	−	0.483326i
$706$	−4.97359	+	12.3993i	−0.187183	+	0.466655i
$707$	55.8503	+	9.84791i	2.10047	+	0.370369i
$708$	1.86698	+	16.9465i	0.0701654	+	0.636888i
$709$	−16.6710	−	45.8032i	−0.626092	−	1.72017i	−0.691560	−	0.722319i	$-0.743076\pi$
$709$	−16.6710	−	45.8032i	−0.626092	−	1.72017i	0.0654678	−	0.997855i	$-0.479146\pi$
$710$	26.6760	−	42.9293i	1.00113	−	1.61111i
$711$	2.03573	+	3.52599i	0.0763458	+	0.132235i
$712$	−4.12552	+	4.04429i	−0.154610	+	0.151566i
$713$	−10.5707	−	8.86989i	−0.395877	−	0.332180i
$714$	15.0685	+	28.1693i	0.563924	+	1.05421i
$715$	32.8464	+	18.9639i	1.22839	+	0.709209i
$716$	−8.25622	−	28.2581i	−0.308549	−	1.05605i
$717$	−1.22743	+	0.216429i	−0.0458391	+	0.00808267i
$718$	−10.2195	−	2.14549i	−0.381387	−	0.0800690i
$719$	48.6000	+	17.6890i	1.81247	+	0.659687i	0.996687	+	0.0813346i	$0.0259182\pi$
$719$	48.6000	+	17.6890i	1.81247	+	0.659687i	0.815787	+	0.578352i	$0.196304\pi$
$720$	−7.22586	−	11.3102i	−0.269292	−	0.421505i
$721$	−9.45696			−0.352196
$722$	−26.8377	+	1.31924i	−0.998794	+	0.0490970i
$723$		−	0.102157i		−	0.00379925i
$724$	−16.4664	−	22.4271i	−0.611971	−	0.833497i
$725$	−1.46445	+	4.02355i	−0.0543885	+	0.149431i
$726$	−1.10054	+	5.24213i	−0.0408449	+	0.194554i
$727$	−5.86279	−	33.2496i	−0.217439	−	1.23316i	−0.876624	−	0.481177i	$-0.840210\pi$
$727$	−5.86279	−	33.2496i	−0.217439	−	1.23316i	0.659185	−	0.751981i	$-0.270902\pi$
$728$	45.2708	−	11.6491i	1.67785	−	0.431744i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−33.1695	−	62.0078i	−1.22766	−	2.29501i
$731$	45.0802	−	53.7245i	1.66735	−	1.98707i
$732$	−2.83094	−	2.70655i	−0.104635	−	0.100037i
$733$	−18.8833	+	10.9023i	−0.697472	+	0.402686i	−0.806405	−	0.591363i	$-0.798590\pi$
$733$	−18.8833	+	10.9023i	−0.697472	+	0.402686i	0.108933	+	0.994049i	$0.465257\pi$
$734$	4.62781	+	2.87570i	0.170816	+	0.106144i
$735$	−26.5423	+	9.66061i	−0.979028	+	0.356337i
$736$	31.2122	−	0.390712i	1.15050	−	0.0144018i
$737$	−1.98521	+	11.2587i	−0.0731261	+	0.414719i
$738$	5.81442	−	14.4956i	0.214032	−	0.533589i
$739$	4.10736	+	4.89496i	0.151092	+	0.180064i	0.836281	−	0.548301i	$-0.184725\pi$
$739$	4.10736	+	4.89496i	0.151092	+	0.180064i	−0.685190	+	0.728365i	$0.740281\pi$
$740$	27.8927	+	1.81016i	1.02536	+	0.0665428i
$741$	−16.2979	+	8.42473i	−0.598719	+	0.309490i
$742$	−54.9861	−	1.78235i	−2.01860	−	0.0654320i
$743$	19.1037	−	16.0299i	0.700847	−	0.588080i	−0.221168	−	0.975236i	$-0.570987\pi$
$743$	19.1037	−	16.0299i	0.700847	−	0.588080i	0.922014	+	0.387156i	$0.126542\pi$
$744$	6.38041	+	3.05283i	0.233917	+	0.111922i
$745$	−1.54511	+	8.76273i	−0.0566083	+	0.321041i
$746$	0.469782	+	3.28302i	0.0171999	+	0.120200i
$747$	0.624209	+	1.71500i	0.0228386	+	0.0627485i
$748$	25.7037	+	17.1507i	0.939819	+	0.627092i
$749$	−40.5429	+	23.4074i	−1.48140	+	0.855289i
$750$	−3.98417	+	4.44721i	−0.145481	+	0.162389i
$751$	−24.3713	−	20.4499i	−0.889321	−	0.746229i	0.0787530	−	0.996894i	$-0.474906\pi$
$751$	−24.3713	−	20.4499i	−0.889321	−	0.746229i	−0.968074	+	0.250665i	$0.919351\pi$
$752$	−9.13646	−	21.9773i	−0.333172	−	0.801430i
$753$	7.30544	−	12.6534i	0.266225	−	0.461115i
$754$	−1.26817	−	3.87002i	−0.0461839	−	0.140938i
$755$	34.5094	−	6.08494i	1.25593	−	0.221454i
$756$	−7.62933	−	1.86168i	−0.277476	−	0.0677087i
$757$	2.52743	−	6.94406i	0.0918610	−	0.252386i	−0.885250	−	0.465115i	$-0.846013\pi$
$757$	2.52743	−	6.94406i	0.0918610	−	0.252386i	0.977111	+	0.212729i	$0.0682351\pi$
$758$	−25.1364	+	19.7403i	−0.912996	+	0.716999i
$759$	14.8192			0.537902
$760$	19.5700	−	36.4455i	0.709880	−	1.32202i
$761$	−20.7690			−0.752875			−0.376437	−	0.926442i	$-0.622851\pi$
$761$	−20.7690			−0.752875			−0.376437	+	0.926442i	$0.622851\pi$
$762$	14.8113	−	11.6317i	0.536556	−	0.421371i
$763$	−4.82431	+	13.2547i	−0.174652	+	0.479852i
$764$	11.3811	−	46.6407i	0.411754	−	1.68740i
$765$	19.0098	−	3.35195i	0.687302	−	0.121190i
$766$	−4.06737	−	12.4123i	−0.146960	−	0.448473i
$767$	−17.9398	+	31.0727i	−0.647770	+	1.12197i
$768$	−15.4441	+	4.18088i	−0.557291	+	0.150864i
$769$	1.18409	+	0.993567i	0.0426993	+	0.0358289i	0.663888	−	0.747832i	$-0.268905\pi$
$769$	1.18409	+	0.993567i	0.0426993	+	0.0358289i	−0.621188	+	0.783661i	$0.713350\pi$
$770$	−33.3895	+	37.2700i	−1.20327	+	1.34312i
$771$	16.7702	−	9.68227i	0.603963	−	0.348698i
$772$	19.5338	−	29.2752i	0.703038	−	1.05364i
$773$	1.17978	+	3.24141i	0.0424336	+	0.116585i	0.959100	−	0.283069i	$-0.0913525\pi$
$773$	1.17978	+	3.24141i	0.0424336	+	0.116585i	−0.916666	+	0.399654i	$0.869130\pi$
$774$	2.44211	+	17.0664i	0.0877798	+	0.613439i
$775$	2.71766	−	15.4126i	0.0976211	−	0.553637i
$776$	14.1130	−	29.4960i	0.506626	−	1.05885i
$777$	12.5287	−	10.5129i	0.449466	−	0.377147i
$778$	−20.4104	−	0.661591i	−0.731747	−	0.0237192i
$779$	47.7446	−	6.14619i	1.71063	−	0.220210i
$780$	1.82919	−	28.1860i	0.0654955	−	1.00922i
$781$	−18.3871	−	21.9129i	−0.657942	−	0.784104i
$782$	−16.7133	+	41.6670i	−0.597668	+	1.49001i
$783$	−0.118806	+	0.673781i	−0.00424577	+	0.0240790i
$784$	1.51208	+	33.6386i	0.0540028	+	1.20138i
$785$	32.1760	−	11.7111i	1.14841	−	0.417988i
$786$	−5.12531	−	3.18483i	−0.182814	−	0.113599i
$787$	−10.2117	+	5.89571i	−0.364007	+	0.210160i	−0.670837	−	0.741605i	$-0.734065\pi$
$787$	−10.2117	+	5.89571i	−0.364007	+	0.210160i	0.306830	+	0.951764i	$0.400732\pi$
$788$	−3.15525	+	3.30027i	−0.112401	+	0.117567i
$789$	−11.4867	+	13.6893i	−0.408938	+	0.487354i
$790$	−9.11275	−	17.0356i	−0.324217	−	0.606098i
$791$	−5.98583	+	10.3678i	−0.212832	+	0.368635i
$792$	−7.35638	+	1.89295i	−0.261398	+	0.0672629i
$793$	−1.43129	−	8.11724i	−0.0508265	−	0.288252i
$794$	−4.86068	+	23.1525i	−0.172499	+	0.821653i
$795$	−11.3694	+	31.2372i	−0.403232	+	1.10787i
$796$	3.25283	−	2.38830i	0.115294	−	0.0846510i
$797$		−	5.04623i		−	0.178747i	−0.995998	−	0.0893733i	$-0.971514\pi$
$797$		−	5.04623i		−	0.178747i	0.995998	−	0.0893733i	$-0.0284864\pi$
$798$	−6.45992	−	23.3272i	−0.228679	−	0.825775i
$799$	34.2312			1.21101
$800$	18.0835	+	30.4353i	0.639350	+	1.07605i
$801$	1.91937	+	0.698594i	0.0678177	+	0.0246836i
$802$	47.6664	+	10.0072i	1.68316	+	0.353365i
$803$	−39.1951	+	6.91116i	−1.38317	+	0.243890i
$804$	8.17216	−	2.38767i	0.288210	−	0.0842068i
$805$	−62.9602	−	36.3501i	−2.21906	−	1.28117i
$806$	7.02117	+	13.1255i	0.247310	+	0.462327i
$807$	15.5373	+	13.0373i	0.546938	+	0.458935i
$808$	−28.5974	−	29.1718i	−1.00605	−	1.02626i
$809$	−14.5521	−	25.2050i	−0.511626	−	0.886162i	−0.999909	−	0.0134765i	$-0.995710\pi$
$809$	−14.5521	−	25.2050i	−0.511626	−	0.886162i	0.488284	−	0.872685i	$-0.337623\pi$
$810$	−2.50447	+	4.03041i	−0.0879982	+	0.141614i
$811$	−15.7759	−	43.3441i	−0.553968	−	1.52202i	−0.828246	−	0.560365i	$-0.810661\pi$
$811$	−15.7759	−	43.3441i	−0.553968	−	1.52202i	0.274277	−	0.961651i	$-0.411561\pi$
$812$	5.34064	−	0.588374i	0.187420	−	0.0206479i
$813$	−24.9687	−	4.40266i	−0.875691	−	0.154408i
$814$	5.88936	−	14.6824i	0.206422	−	0.514618i
$815$	−25.6189	+	21.4968i	−0.897390	+	0.752999i
$816$	2.97427	−	22.8188i	0.104120	−	0.798817i
$817$	−42.2500	+	32.2271i	−1.47814	+	1.12748i
$818$	0.861748	−	26.5853i	0.0301303	−	0.929532i
$819$	−10.6234	−	12.6605i	−0.371211	−	0.442392i
$820$	−29.8043	+	67.8539i	−1.04081	+	2.36956i
$821$	−0.208800	−	0.0368171i	−0.00728718	−	0.00128493i	0.170003	−	0.985443i	$-0.445622\pi$
$821$	−0.208800	−	0.0368171i	−0.00728718	−	0.00128493i	−0.177291	+	0.984159i	$0.556733\pi$
$822$	1.74021	+	12.1612i	0.0606966	+	0.424171i
$823$	38.3979	−	13.9757i	1.33847	−	0.487163i	0.429138	−	0.903239i	$-0.358817\pi$
$823$	38.3979	−	13.9757i	1.33847	−	0.487163i	0.909330	+	0.416076i	$0.136595\pi$
$824$	5.54101	+	3.96254i	0.193030	+	0.138042i
$825$	8.40365	+	14.5556i	0.292578	+	0.506759i
$826$	−35.2574	−	31.5865i	−1.22676	−	1.09903i
$827$	−12.7163	+	15.1547i	−0.442190	+	0.526982i	−0.940398	−	0.340076i	$-0.889547\pi$
$827$	−12.7163	+	15.1547i	−0.442190	+	0.526982i	0.498208	+	0.867058i	$0.333992\pi$
$828$	−4.88748	−	9.89477i	−0.169852	−	0.343867i
$829$	20.4848	+	11.8269i	0.711465	+	0.410764i	0.811603	−	0.584209i	$-0.198595\pi$
$829$	20.4848	+	11.8269i	0.711465	+	0.410764i	−0.100138	+	0.994974i	$0.531929\pi$
$830$	−2.69677	−	8.22964i	−0.0936062	−	0.285655i
$831$	5.55911	+	31.5273i	0.192843	+	1.09367i
$832$	−31.4061	−	12.1434i	−1.08881	−	0.420997i
$833$	−45.5085	−	16.5638i	−1.57678	−	0.573900i
$834$	−7.79876	−	9.93061i	−0.270049	−	0.343869i
$835$			18.7238i			0.647963i
$836$	−16.1523	−	16.9484i	−0.558639	−	0.586173i
$837$		−	2.50073i		−	0.0864380i
$838$	3.50760	−	2.75461i	0.121168	−	0.0951563i
$839$	−9.38141	−	3.41455i	−0.323882	−	0.117883i	0.174962	−	0.984575i	$-0.444020\pi$
$839$	−9.38141	−	3.41455i	−0.323882	−	0.117883i	−0.498844	+	0.866692i	$0.666242\pi$
$840$	35.8973	+	10.0022i	1.23857	+	0.345110i
$841$	4.95451	+	28.0984i	0.170845	+	0.968912i
$842$	−8.28357	+	2.71444i	−0.285471	+	0.0935458i
$843$	−9.32636	−	5.38458i	−0.321217	−	0.185455i
$844$	16.5688	−	8.18408i	0.570321	−	0.281707i
$845$	10.1707	−	12.1210i	0.349882	−	0.416974i
$846$	−5.61496	+	6.26753i	−0.193046	+	0.215482i
$847$	−7.43609	−	12.8797i	−0.255507	−	0.442551i
$848$	31.4706	+	24.0839i	1.08070	+	0.827046i
$849$	−17.3849	+	6.32757i	−0.596647	+	0.217162i
$850$	−50.4035	+	7.21247i	−1.72883	+	0.247386i
$851$	22.6346	+	3.99108i	0.775902	+	0.136813i
$852$	−8.56703	+	19.5041i	−0.293502	+	0.668199i
$853$	9.43067	+	11.2390i	0.322900	+	0.384817i	0.902937	−	0.429773i	$-0.141406\pi$
$853$	9.43067	+	11.2390i	0.322900	+	0.384817i	−0.580037	+	0.814590i	$0.696962\pi$
$854$	10.8688	+	0.352306i	0.371922	+	0.0120557i
$855$	−14.6098	−	0.679940i	−0.499644	−	0.0232535i
$856$	33.5627	+	3.27293i	1.14715	+	0.111866i
$857$	−33.6219	+	28.2121i	−1.14850	+	0.963707i	−0.999684	−	0.0251574i	$-0.991991\pi$
$857$	−33.6219	+	28.2121i	−1.14850	+	0.963707i	−0.148818	+	0.988865i	$0.547547\pi$
$858$	−14.8368	−	5.95128i	−0.506519	−	0.203173i
$859$	12.7107	+	2.24124i	0.433683	+	0.0764700i	0.386228	−	0.922403i	$-0.373778\pi$
$859$	12.7107	+	2.24124i	0.433683	+	0.0764700i	0.0474551	+	0.998873i	$0.484889\pi$
$860$	−8.95850	−	81.3158i	−0.305482	−	2.77285i
$861$	14.8315	+	40.7491i	0.505455	+	1.38873i
$862$	−32.2121	−	20.0164i	−1.09715	−	0.681761i
$863$	−6.55360	−	11.3512i	−0.223087	−	0.386398i	0.732657	−	0.680598i	$-0.238280\pi$
$863$	−6.55360	−	11.3512i	−0.223087	−	0.386398i	−0.955744	+	0.294200i	$0.904947\pi$
$864$	3.69011	+	4.28755i	0.125540	+	0.145865i
$865$	30.6865	+	25.7490i	1.04337	+	0.875493i
$866$	−35.6218	+	19.0550i	−1.21048	+	0.647514i
$867$	13.9399	+	8.04821i	0.473424	+	0.273332i
$868$	−18.8506	+	5.50762i	−0.639832	+	0.186941i
$869$	−10.7682	+	1.89872i	−0.365286	+	0.0644098i
$870$	0.667038	−	3.17726i	0.0226147	−	0.107719i
$871$	16.8368	+	6.12810i	0.570493	+	0.207643i
$872$	8.38048	−	5.74475i	0.283799	−	0.194542i
$873$	−11.5607			−0.391269
$874$	19.2769	−	28.0258i	0.652050	−	0.947987i
$875$		−	16.5782i		−	0.560447i
$876$	17.5414	+	23.8912i	0.592670	+	0.807210i
$877$	−14.0533	+	38.6112i	−0.474547	+	1.30381i	0.439515	+	0.898235i	$0.355150\pi$
$877$	−14.0533	+	38.6112i	−0.474547	+	1.30381i	−0.914063	+	0.405573i	$0.867072\pi$
$878$	46.9862	+	9.86434i	1.58571	+	0.332905i
$879$	1.53862	+	8.72594i	0.0518963	+	0.294318i
$880$	35.1799	−	7.84673i	1.18592	−	0.264513i
$881$	11.4126	−	19.7671i	0.384499	−	0.665972i	−0.607201	−	0.794548i	$-0.707708\pi$
$881$	11.4126	−	19.7671i	0.384499	−	0.665972i	0.991700	+	0.128577i	$0.0410409\pi$
$882$	10.4975	−	5.61538i	0.353470	−	0.189080i
$883$	−15.1560	+	18.0622i	−0.510041	+	0.607843i	−0.958196	−	0.286113i	$-0.907637\pi$
$883$	−15.1560	+	18.0622i	−0.510041	+	0.607843i	0.448155	+	0.893956i	$0.352081\pi$
$884$	33.4663	−	35.0044i	1.12559	−	1.17733i
$885$	−24.7706	+	14.3013i	−0.832655	+	0.480734i
$886$	10.4602	−	16.8335i	0.351418	−	0.565531i
$887$	−17.4520	+	6.35201i	−0.585981	+	0.213280i	−0.617961	−	0.786209i	$-0.712041\pi$
$887$	−17.4520	+	6.35201i	−0.585981	+	0.213280i	0.0319798	+	0.999489i	$0.489819\pi$
$888$	−11.7458	+	0.910042i	−0.394163	+	0.0305390i
$889$	−9.07995	+	51.4950i	−0.304532	+	1.72709i
$890$	−8.99556	−	3.60827i	−0.301532	−	0.120950i
$891$	1.72627	+	2.05729i	0.0578322	+	0.0689218i
$892$	−0.277714	−	0.0180228i	−0.00929855	−	0.000603450i
$893$	−25.3053	−	5.68637i	−0.846808	−	0.190287i
$894$	0.121500	−	3.74833i	0.00406358	−	0.125363i
$895$	37.8348	−	31.7471i	1.26468	−	1.06119i
$896$	24.1926	−	37.2591i	0.808218	−	1.24474i
$897$	4.03304	−	22.8725i	0.134659	−	0.763691i
$898$	9.39176	−	1.34391i	0.313407	−	0.0448469i
$899$	0.585176	+	1.60776i	0.0195167	+	0.0536217i
$900$	6.94716	−	10.4117i	0.231572	−	0.347055i
$901$	−49.3595	+	28.4977i	−1.64440	+	0.949397i
$902$	31.2408	+	27.9881i	1.04021	+	0.931901i
$903$	−36.6689	−	30.7689i	−1.22027	−	1.02392i
$904$	7.85139	−	3.56656i	0.261133	−	0.118622i
$905$	23.3389	−	40.4242i	0.775811	−	1.34374i
$906$	−14.0351	+	4.59917i	−0.466286	+	0.152797i
$907$	−2.09717	+	0.369787i	−0.0696353	+	0.0122786i	−0.208357	−	0.978053i	$-0.566812\pi$
$907$	−2.09717	+	0.369787i	−0.0696353	+	0.0122786i	0.138722	+	0.990331i	$0.455701\pi$
$908$	−16.6133	−	4.05391i	−0.551331	−	0.134534i
$909$	−4.93980	+	13.5720i	−0.163843	+	0.450154i
$910$	48.4370	+	61.6776i	1.60567	+	2.04459i
$911$	−30.4406			−1.00854			−0.504270	−	0.863546i	$-0.668239\pi$
$911$	−30.4406			−1.00854			−0.504270	+	0.863546i	$0.668239\pi$
$912$	−5.98930	+	16.3746i	−0.198326	+	0.542218i
$913$	−4.90139			−0.162212
$914$	32.9610	+	41.9712i	1.09025	+	1.38828i
$915$	2.24733	−	6.17448i	0.0742943	−	0.204122i
$916$	−5.59774	−	1.36594i	−0.184954	−	0.0451319i
$917$	16.4996	−	2.90933i	0.544866	−	0.0960746i
$918$	−7.73138	+	2.53349i	−0.255174	+	0.0836178i
$919$	−13.8182	+	23.9339i	−0.455821	+	0.789505i	−0.998735	−	0.0502829i	$-0.983988\pi$
$919$	−13.8182	+	23.9339i	−0.455821	+	0.789505i	0.542914	+	0.839788i	$0.317321\pi$
$920$	21.6586	+	47.6791i	0.714063	+	1.57193i
$921$	−2.61979	−	2.19827i	−0.0863252	−	0.0724354i
$922$	−0.932262	−	0.835196i	−0.0307024	−	0.0275057i
$923$	−38.8252	+	22.4158i	−1.27795	+	0.737823i
$924$	11.7060	−	17.5437i	0.385098	−	0.577144i
$925$	8.91550	+	24.4951i	0.293140	+	0.805395i
$926$	−14.1149	+	2.01977i	−0.463845	+	0.0663737i
$927$	0.418221	−	2.37185i	0.0137362	−	0.0779017i
$928$	−3.37572	−	1.89303i	−0.110813	−	0.0621419i
$929$	3.70922	−	3.11241i	0.121696	−	0.102115i	−0.579909	−	0.814681i	$-0.696912\pi$
$929$	3.70922	−	3.11241i	0.121696	−	0.102115i	0.701604	+	0.712567i	$0.252467\pi$
$930$	−0.384441	+	11.8602i	−0.0126063	+	0.388910i
$931$	30.8905	+	19.8044i	1.01240	+	0.649064i
$932$	−15.6297	−	1.01433i	−0.511969	−	0.0332253i
$933$	4.00369	+	4.77142i	0.131075	+	0.156209i
$934$	−13.8527	−	5.55657i	−0.453276	−	0.181817i
$935$	−9.00199	+	51.0528i	−0.294397	+	1.66961i
$936$	0.919609	+	11.8693i	0.0300584	+	0.387960i
$937$	−37.1284	+	13.5136i	−1.21293	+	0.441471i	−0.867720	−	0.497053i	$-0.834415\pi$
$937$	−37.1284	+	13.5136i	−1.21293	+	0.441471i	−0.345213	+	0.938525i	$0.612193\pi$
$938$	−12.4764	+	20.0781i	−0.407370	+	0.655575i
$939$	−8.62910	+	4.98202i	−0.281600	+	0.162582i
$940$	27.5934	−	28.8616i	0.899999	−	0.941363i
$941$	−6.28939	+	7.49540i	−0.205028	+	0.244343i	−0.858754	−	0.512389i	$-0.828761\pi$
$941$	−6.28939	+	7.49540i	−0.205028	+	0.244343i	0.653725	+	0.756732i	$0.273205\pi$
$942$	−12.7257	+	6.80727i	−0.414624	+	0.221793i
$943$	−30.4698	+	52.7752i	−0.992233	+	1.71860i
$944$	7.42301	+	33.2803i	0.241598	+	1.08318i
$945$	−2.28783	−	12.9749i	−0.0744230	−	0.422074i
$946$	−45.3126	−	9.51298i	−1.47324	−	0.309294i
$947$	−9.95349	+	27.3470i	−0.323445	+	0.888657i	0.666284	+	0.745698i	$0.267884\pi$
$947$	−9.95349	+	27.3470i	−0.323445	+	0.888657i	−0.989729	+	0.142959i	$0.954338\pi$
$948$	4.81921	+	6.56371i	0.156521	+	0.213179i
$949$			62.3762i			2.02482i
$950$	38.4587	+	3.04108i	1.24777	+	0.0986657i
$951$	17.3084			0.561263
$952$	36.1252	+	52.6997i	1.17082	+	1.70801i
$953$	48.3929	+	17.6136i	1.56760	+	0.570559i	0.972461	−	0.233065i	$-0.0748755\pi$
$953$	48.3929	+	17.6136i	1.56760	+	0.570559i	0.595137	+	0.803624i	$0.297098\pi$
$954$	2.87870	−	13.7119i	0.0932015	−	0.443940i
$955$	79.3200	−	13.9862i	2.56673	−	0.452584i
$956$	−2.39269	+	0.699077i	−0.0773851	+	0.0226098i
$957$	−1.59125	−	0.918710i	−0.0514379	−	0.0296977i
$958$	23.3856	−	12.5096i	0.755555	−	0.404165i
$959$	−26.1296	−	21.9254i	−0.843770	−	0.708007i
$960$	−16.8419	−	20.9017i	−0.543569	−	0.674601i
$961$	12.3732	+	21.4309i	0.399134	+	0.691321i
$962$	−21.0586	−	13.0857i	−0.678957	−	0.421899i
$963$	−4.07774	−	11.2035i	−0.131403	−	0.361028i
$964$	−0.0223737	−	0.203085i	−0.000720608	−	0.00654092i
$965$	58.1467	+	10.2528i	1.87181	+	0.330050i
$966$	28.4392	+	11.4075i	0.915017	+	0.367029i
$967$	−21.0088	+	17.6284i	−0.675596	+	0.566892i	−0.914716	−	0.404098i	$-0.867586\pi$
$967$	−21.0088	+	17.6284i	−0.675596	+	0.566892i	0.239120	+	0.970990i	$0.423141\pi$
$968$	−1.03975	+	10.6622i	−0.0334187	+	0.342697i
$969$	−18.4396	−	16.9945i	−0.592365	−	0.545942i
$970$	54.8285	+	1.77724i	1.76044	+	0.0570636i
$971$	−10.7243	−	12.7807i	−0.344158	−	0.410151i	0.566005	−	0.824402i	$-0.308488\pi$
$971$	−10.7243	−	12.7807i	−0.344158	−	0.410151i	−0.910163	+	0.414251i	$0.864044\pi$
$972$	0.804315	−	1.83114i	0.0257984	−	0.0587339i
$973$	34.5261	+	6.08789i	1.10686	+	0.195169i
$974$	23.2084	−	3.32100i	0.743646	−	0.106412i
$975$	24.7527	−	9.00923i	0.792719	−	0.288526i
$976$	−6.22061	−	4.76053i	−0.199117	−	0.152381i
$977$	−10.9005	−	18.8803i	−0.348739	−	0.604034i	0.637287	−	0.770627i	$-0.280057\pi$
$977$	−10.9005	−	18.8803i	−0.348739	−	0.604034i	−0.986026	+	0.166593i	$0.946723\pi$
$978$	9.40556	−	10.4987i	0.300757	−	0.335711i
$979$	−3.52600	+	4.20212i	−0.112691	+	0.134300i
$980$	−50.6496	+	25.0182i	−1.61794	+	0.799176i
$981$	−3.11099	−	1.79613i	−0.0993262	−	0.0573460i
$982$	54.1559	−	17.7463i	1.72819	−	0.566309i
$983$	−1.55555	−	8.82199i	−0.0496145	−	0.281378i	0.949899	−	0.312556i	$-0.101185\pi$
$983$	−1.55555	−	8.82199i	−0.0496145	−	0.281378i	−0.999514	+	0.0311782i	$0.990074\pi$
$984$	8.38418	−	30.0902i	0.267278	−	0.959240i
$985$	−7.19811	−	2.61990i	−0.229351	−	0.0834768i
$986$	4.37777	−	3.43798i	0.139417	−	0.109487i
$987$		−	23.3640i		−	0.743684i
$988$	−30.5547	+	20.3176i	−0.972074	+	0.646389i
$989$		−	67.2684i		−	2.13901i
$990$	−7.87087	−	10.0224i	−0.250153	−	0.318534i
$991$	20.8997	+	7.60687i	0.663901	+	0.241640i	0.651920	−	0.758288i	$-0.273964\pi$
$991$	20.8997	+	7.60687i	0.663901	+	0.241640i	0.0119811	+	0.999928i	$0.496186\pi$
$992$	13.3527	+	4.67155i	0.423948	+	0.148322i
$993$	−2.00279	−	11.3584i	−0.0635566	−	0.360447i
$994$	−18.4183	−	56.2065i	−0.584193	−	1.78276i
$995$	5.86313	+	3.38508i	0.185874	+	0.107314i
$996$	1.61652	+	3.27266i	0.0512213	+	0.103698i
$997$	−18.5043	+	22.0526i	−0.586038	+	0.698413i	−0.974839	−	0.222909i	$-0.928445\pi$
$997$	−18.5043	+	22.0526i	−0.586038	+	0.698413i	0.388801	+	0.921322i	$0.372889\pi$
$998$	−36.4568	−	32.6609i	−1.15402	−	1.03386i
$999$	2.08261	+	3.60718i	0.0658908	+	0.114126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.13	✓	240
8.5	even	2	inner	456.2.bk.a.253.30	yes	240
19.16	even	9	inner	456.2.bk.a.301.30	yes	240
152.149	even	18	inner	456.2.bk.a.301.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.13	✓	240	1.1	even	1	trivial
456.2.bk.a.253.30	yes	240	8.5	even	2	inner
456.2.bk.a.301.13	yes	240	152.149	even	18	inner
456.2.bk.a.301.30	yes	240	19.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.873464 - 1.11223i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.474121 + 1.94299i) q^{4} +(-3.30436 + 0.582649i) q^{5} +(1.34390 - 0.440382i) q^{6} +(-1.96330 + 3.40053i) q^{7} +(2.57518 - 1.16980i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(3.53428 + 3.16630i) q^{10} +(2.32580 - 1.34280i) q^{11} +(-1.66365 - 1.11007i) q^{12} +(-1.43956 - 3.95517i) q^{13} +(5.49705 - 0.786598i) q^{14} +(0.582649 - 3.30436i) q^{15} +(-3.55042 - 1.84243i) q^{16} +(4.40701 - 3.69792i) q^{17} +(-0.0458169 + 1.41347i) q^{18} +(-3.87216 + 2.00160i) q^{19} +(0.434590 - 6.69659i) q^{20} +(-2.52397 - 3.00795i) q^{21} +(-3.52501 - 1.41394i) q^{22} +(0.958194 - 5.43419i) q^{23} +(0.218486 + 2.81998i) q^{24} +(5.88088 - 2.14047i) q^{25} +(-3.14166 + 5.05583i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-5.67636 - 5.42693i) q^{28} +(-0.439779 + 0.524109i) q^{29} +(-4.18414 + 2.23820i) q^{30} +(1.25037 - 2.16570i) q^{31} +(1.05196 + 5.55818i) q^{32} +(0.466350 + 2.64480i) q^{33} +(-7.96232 - 1.67162i) q^{34} +(4.50614 - 12.3805i) q^{35} +(1.61213 - 1.18366i) q^{36} +4.16521i q^{37} +(5.60843 + 2.55842i) q^{38} +4.20900 q^{39} +(-7.82777 + 5.36587i) q^{40} +(-10.3777 - 3.77718i) q^{41} +(-1.14094 + 5.43457i) q^{42} +(12.0055 - 2.11689i) q^{43} +(1.50634 + 5.15565i) q^{44} +(2.90581 + 1.67767i) q^{45} +(-6.88102 + 3.68083i) q^{46} +(4.55811 + 3.82471i) q^{47} +(2.94563 - 2.70615i) q^{48} +(-4.20907 - 7.29033i) q^{49} +(-7.51744 - 4.67129i) q^{50} +(1.96762 + 5.40600i) q^{51} +(8.36738 - 0.921827i) q^{52} +(-9.75666 - 1.72036i) q^{53} +(-1.31256 - 0.526489i) q^{54} +(-6.90290 + 5.79222i) q^{55} +(-1.07792 + 11.0537i) q^{56} +(-0.556531 - 4.32322i) q^{57} +(0.967062 + 0.0313468i) q^{58} +(-5.47945 - 6.53015i) q^{59} +(6.14410 + 2.69875i) q^{60} +(1.92854 + 0.340054i) q^{61} +(-3.50091 + 0.500962i) q^{62} +(3.68979 - 1.34297i) q^{63} +(5.26314 - 6.02489i) q^{64} +(7.06132 + 12.2306i) q^{65} +(2.53429 - 2.82883i) q^{66} +(-2.73629 + 3.26098i) q^{67} +(5.09557 + 10.3160i) q^{68} +(4.77874 + 2.75901i) q^{69} +(-17.7059 + 5.80206i) q^{70} +(-1.84959 - 10.4895i) q^{71} +(-2.72464 - 0.759179i) q^{72} +(-13.9260 - 5.06864i) q^{73} +(4.63269 - 3.63816i) q^{74} +6.25831i q^{75} +(-2.05321 - 8.47256i) q^{76} +10.5453i q^{77} +(-3.67641 - 4.68139i) q^{78} +(-3.82592 - 1.39252i) q^{79} +(12.8054 + 4.01940i) q^{80} +(0.173648 + 0.984808i) q^{81} +(4.86346 + 14.8417i) q^{82} +(-1.58055 - 0.912532i) q^{83} +(7.04108 - 3.47791i) q^{84} +(-12.4078 + 14.7870i) q^{85} +(-12.8408 - 11.5039i) q^{86} +(-0.342088 - 0.592513i) q^{87} +(4.41855 - 6.17867i) q^{88} +(-1.91937 + 0.698594i) q^{89} +(-0.672161 - 4.69732i) q^{90} +(16.2760 + 2.86989i) q^{91} +(10.1043 + 4.43822i) q^{92} +(1.60744 + 1.91567i) q^{93} +(0.272620 - 8.41043i) q^{94} +(11.6288 - 8.87012i) q^{95} +(-5.58277 - 0.912495i) q^{96} +(8.85598 - 7.43105i) q^{97} +(-4.43207 + 11.0493i) q^{98} +(-2.64480 - 0.466350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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