LMFDB - Embedded newform 273.2.bz.a.73.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.9
Character	$\chi$	$=$	273.73
Dual form			273.2.bz.a.187.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.703128 - 2.62411i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-4.65951 - 2.69017i) q^{4} +(-1.03350 - 0.276925i) q^{5} +(1.92098 - 1.92098i) q^{6} +(-1.53729 - 2.15331i) q^{7} +(-6.49357 + 6.49357i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.703128 - 2.62411i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-4.65951 - 2.69017i) q^{4} +(-1.03350 - 0.276925i) q^{5} +(1.92098 - 1.92098i) q^{6} +(-1.53729 - 2.15331i) q^{7} +(-6.49357 + 6.49357i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.45336 + 2.51730i) q^{10} +(-1.12334 - 4.19238i) q^{11} +(-2.69017 - 4.65951i) q^{12} +(2.90196 + 2.13978i) q^{13} +(-6.73143 + 2.51996i) q^{14} +(-0.756573 - 0.756573i) q^{15} +(7.09368 + 12.2866i) q^{16} +(2.51619 - 4.35817i) q^{17} +(2.62411 - 0.703128i) q^{18} +(3.21660 + 0.861885i) q^{19} +(4.07062 + 4.07062i) q^{20} +(-0.254675 - 2.63347i) q^{21} -11.7911 q^{22} +(-2.25604 + 1.30252i) q^{23} +(-8.87037 + 2.37681i) q^{24} +(-3.33870 - 1.92760i) q^{25} +(7.65546 - 6.11051i) q^{26} +1.00000i q^{27} +(1.37024 + 14.1689i) q^{28} +8.78912 q^{29} +(-2.51730 + 1.45336i) q^{30} +(-0.156961 - 0.585786i) q^{31} +(19.4884 - 5.22191i) q^{32} +(1.12334 - 4.19238i) q^{33} +(-9.66712 - 9.66712i) q^{34} +(0.992479 + 2.65116i) q^{35} -5.38034i q^{36} +(6.15406 + 1.64898i) q^{37} +(4.52336 - 7.83469i) q^{38} +(1.44328 + 3.30408i) q^{39} +(8.50932 - 4.91286i) q^{40} +(2.51509 - 2.51509i) q^{41} +(-7.08957 - 1.18337i) q^{42} +5.67033i q^{43} +(-6.04398 + 22.5564i) q^{44} +(-0.276925 - 1.03350i) q^{45} +(1.83168 + 6.83592i) q^{46} +(2.04121 - 7.61792i) q^{47} +14.1874i q^{48} +(-2.27349 + 6.62052i) q^{49} +(-7.40575 + 7.40575i) q^{50} +(4.35817 - 2.51619i) q^{51} +(-7.76533 - 17.7771i) q^{52} +(-1.28035 + 2.21763i) q^{53} +(2.62411 + 0.703128i) q^{54} +4.64390i q^{55} +(23.9651 + 4.00018i) q^{56} +(2.35471 + 2.35471i) q^{57} +(6.17988 - 23.0636i) q^{58} +(0.531425 - 0.142395i) q^{59} +(1.48995 + 5.56057i) q^{60} +(-6.16432 + 3.55897i) q^{61} -1.64753 q^{62} +(1.09618 - 2.40799i) q^{63} -26.4367i q^{64} +(-2.40661 - 3.01508i) q^{65} +(-10.2114 - 5.89556i) q^{66} +(-6.69514 + 1.79396i) q^{67} +(-23.4485 + 13.5380i) q^{68} -2.60505 q^{69} +(7.65476 - 0.740272i) q^{70} +(-6.29265 - 6.29265i) q^{71} +(-8.87037 - 2.37681i) q^{72} +(-4.24525 + 1.13751i) q^{73} +(8.65418 - 14.9895i) q^{74} +(-1.92760 - 3.33870i) q^{75} +(-12.6692 - 12.6692i) q^{76} +(-7.30059 + 8.86381i) q^{77} +(9.68508 - 1.46413i) q^{78} +(4.13605 + 7.16384i) q^{79} +(-3.92883 - 14.6626i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.83144 - 8.36829i) q^{82} +(6.35771 - 6.35771i) q^{83} +(-5.89780 + 12.9558i) q^{84} +(-3.80737 + 3.80737i) q^{85} +(14.8796 + 3.98697i) q^{86} +(7.61160 + 4.39456i) q^{87} +(34.5180 + 19.9290i) q^{88} +(-0.934235 + 3.48661i) q^{89} -2.90673 q^{90} +(0.146462 - 9.53827i) q^{91} +14.0160 q^{92} +(0.156961 - 0.585786i) q^{93} +(-18.5550 - 10.7127i) q^{94} +(-3.08567 - 1.78151i) q^{95} +(19.4884 + 5.22191i) q^{96} +(10.0260 - 10.0260i) q^{97} +(15.7744 + 10.6210i) q^{98} +(3.06904 - 3.06904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q - 6 * q^7 + 18 * q^9	$ 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.703128	−	2.62411i	0.497187	−	1.85553i	−0.0202359	−	0.999795i	$-0.506442\pi$
$2$	0.703128	−	2.62411i	0.497187	−	1.85553i	0.517422	−	0.855730i	$-0.326892\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−4.65951	−	2.69017i	−2.32975	−	1.34508i
$5$	−1.03350	−	0.276925i	−0.462195	−	0.123845i	0.0202052	−	0.999796i	$-0.493568\pi$
$5$	−1.03350	−	0.276925i	−0.462195	−	0.123845i	−0.482400	+	0.875951i	$0.660235\pi$
$6$	1.92098	−	1.92098i	0.784237	−	0.784237i
$7$	−1.53729	−	2.15331i	−0.581040	−	0.813875i
$7$	−1.53729	−	2.15331i	−0.581040	−	0.813875i
$8$	−6.49357	+	6.49357i	−2.29582	+	2.29582i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.45336	+	2.51730i	−0.459594	+	0.796040i
$11$	−1.12334	−	4.19238i	−0.338701	−	1.26405i	−0.899800	−	0.436302i	$-0.856288\pi$
$11$	−1.12334	−	4.19238i	−0.338701	−	1.26405i	0.561099	−	0.827749i	$-0.310379\pi$
$12$	−2.69017	−	4.65951i	−0.776585	−	1.34508i
$13$	2.90196	+	2.13978i	0.804858	+	0.593468i
$13$	2.90196	+	2.13978i	0.804858	+	0.593468i
$14$	−6.73143	+	2.51996i	−1.79905	+	0.673487i
$15$	−0.756573	−	0.756573i	−0.195346	−	0.195346i
$16$	7.09368	+	12.2866i	1.77342	+	3.07165i
$17$	2.51619	−	4.35817i	0.610267	−	1.05701i	−0.380929	−	0.924604i	$-0.624396\pi$
$17$	2.51619	−	4.35817i	0.610267	−	1.05701i	0.991195	−	0.132408i	$-0.0422710\pi$
$18$	2.62411	−	0.703128i	0.618508	−	0.165729i
$19$	3.21660	+	0.861885i	0.737939	+	0.197730i	0.608162	−	0.793813i	$-0.291907\pi$
$19$	3.21660	+	0.861885i	0.737939	+	0.197730i	0.129777	+	0.991543i	$0.458574\pi$
$20$	4.07062	+	4.07062i	0.910218	+	0.910218i
$21$	−0.254675	−	2.63347i	−0.0555747	−	0.574669i
$22$	−11.7911			−2.51388
$23$	−2.25604	+	1.30252i	−0.470416	+	0.271595i	−0.716414	−	0.697676i	$-0.754218\pi$
$23$	−2.25604	+	1.30252i	−0.470416	+	0.271595i	0.245998	+	0.969270i	$0.420884\pi$
$24$	−8.87037	+	2.37681i	−1.81066	+	0.485164i
$25$	−3.33870	−	1.92760i	−0.667739	−	0.385519i
$26$	7.65546	−	6.11051i	1.50136	−	1.19837i
$27$			1.00000i			0.192450i
$28$	1.37024	+	14.1689i	0.258951	+	2.67768i
$29$	8.78912			1.63210			0.816050	−	0.577982i	$-0.196160\pi$
$29$	8.78912			1.63210			0.816050	+	0.577982i	$0.196160\pi$
$30$	−2.51730	+	1.45336i	−0.459594	+	0.265347i
$31$	−0.156961	−	0.585786i	−0.0281910	−	0.105210i	0.950397	−	0.311040i	$-0.100677\pi$
$31$	−0.156961	−	0.585786i	−0.0281910	−	0.105210i	−0.978588	+	0.205830i	$0.934011\pi$
$32$	19.4884	−	5.22191i	3.44510	−	0.923112i
$33$	1.12334	−	4.19238i	0.195549	−	0.729800i
$34$	−9.66712	−	9.66712i	−1.65790	−	1.65790i
$35$	0.992479	+	2.65116i	0.167760	+	0.448127i
$36$		−	5.38034i		−	0.896723i
$37$	6.15406	+	1.64898i	1.01172	+	0.271090i	0.726348	−	0.687327i	$-0.241216\pi$
$37$	6.15406	+	1.64898i	1.01172	+	0.271090i	0.285373	+	0.958417i	$0.407883\pi$
$38$	4.52336	−	7.83469i	0.733786	−	1.27096i
$39$	1.44328	+	3.30408i	0.231110	+	0.529076i
$40$	8.50932	−	4.91286i	1.34544	−	0.776791i
$41$	2.51509	−	2.51509i	0.392791	−	0.392791i	−0.482890	−	0.875681i	$-0.660413\pi$
$41$	2.51509	−	2.51509i	0.392791	−	0.392791i	0.875681	+	0.482890i	$0.160413\pi$
$42$	−7.08957	−	1.18337i	−1.09394	−	0.182597i
$43$			5.67033i			0.864718i	0.901702	+	0.432359i	$0.142319\pi$
$43$			5.67033i			0.864718i	−0.901702	+	0.432359i	$0.857681\pi$
$44$	−6.04398	+	22.5564i	−0.911164	+	3.40051i
$45$	−0.276925	−	1.03350i	−0.0412815	−	0.154065i
$46$	1.83168	+	6.83592i	0.270067	+	1.00790i
$47$	2.04121	−	7.61792i	0.297742	−	1.11119i	−0.641274	−	0.767312i	$-0.721594\pi$
$47$	2.04121	−	7.61792i	0.297742	−	1.11119i	0.939015	−	0.343875i	$-0.111740\pi$
$48$			14.1874i			2.04777i
$49$	−2.27349	+	6.62052i	−0.324784	+	0.945788i
$50$	−7.40575	+	7.40575i	−1.04733	+	1.04733i
$51$	4.35817	−	2.51619i	0.610267	−	0.352338i
$52$	−7.76533	−	17.7771i	−1.07686	−	2.46524i
$53$	−1.28035	+	2.21763i	−0.175869	+	0.304615i	−0.940462	−	0.339899i	$-0.889607\pi$
$53$	−1.28035	+	2.21763i	−0.175869	+	0.304615i	0.764592	+	0.644514i	$0.222940\pi$
$54$	2.62411	+	0.703128i	0.357096	+	0.0956836i
$55$			4.64390i			0.626183i
$56$	23.9651	+	4.00018i	3.20248	+	0.534546i
$57$	2.35471	+	2.35471i	0.311890	+	0.311890i
$58$	6.17988	−	23.0636i	0.811458	−	3.02840i
$59$	0.531425	−	0.142395i	0.0691857	−	0.0185383i	−0.224060	−	0.974575i	$-0.571931\pi$
$59$	0.531425	−	0.142395i	0.0691857	−	0.0185383i	0.293246	+	0.956037i	$0.405265\pi$
$60$	1.48995	+	5.56057i	0.192352	+	0.717867i
$61$	−6.16432	+	3.55897i	−0.789261	+	0.455680i	−0.839702	−	0.543047i	$-0.817270\pi$
$61$	−6.16432	+	3.55897i	−0.789261	+	0.455680i	0.0504415	+	0.998727i	$0.483937\pi$
$62$	−1.64753			−0.209237
$63$	1.09618	−	2.40799i	0.138105	−	0.303378i
$64$		−	26.4367i		−	3.30459i
$65$	−2.40661	−	3.01508i	−0.298503	−	0.373975i
$66$	−10.2114	−	5.89556i	−1.25694	−	0.725693i
$67$	−6.69514	+	1.79396i	−0.817941	+	0.219167i	−0.643446	−	0.765491i	$-0.722496\pi$
$67$	−6.69514	+	1.79396i	−0.817941	+	0.219167i	−0.174495	+	0.984658i	$0.555829\pi$
$68$	−23.4485	+	13.5380i	−2.84354	+	1.64172i
$69$	−2.60505			−0.313611
$70$	7.65476	−	0.740272i	0.914919	−	0.0884794i
$71$	−6.29265	−	6.29265i	−0.746800	−	0.746800i	0.227077	−	0.973877i	$-0.427083\pi$
$71$	−6.29265	−	6.29265i	−0.746800	−	0.746800i	−0.973877	+	0.227077i	$0.927083\pi$
$72$	−8.87037	−	2.37681i	−1.04538	−	0.280110i
$73$	−4.24525	+	1.13751i	−0.496869	+	0.133136i	−0.498547	−	0.866863i	$-0.666133\pi$
$73$	−4.24525	+	1.13751i	−0.496869	+	0.133136i	0.00167750	+	0.999999i	$0.499466\pi$
$74$	8.65418	−	14.9895i	1.00603	−	1.74249i
$75$	−1.92760	−	3.33870i	−0.222580	−	0.385519i
$76$	−12.6692	−	12.6692i	−1.45325	−	1.45325i
$77$	−7.30059	+	8.86381i	−0.831980	+	1.01012i
$78$	9.68508	−	1.46413i	1.09662	−	0.165780i
$79$	4.13605	+	7.16384i	0.465342	+	0.805995i	0.999217	−	0.0395680i	$-0.0125982\pi$
$79$	4.13605	+	7.16384i	0.465342	+	0.805995i	−0.533875	+	0.845563i	$0.679265\pi$
$80$	−3.92883	−	14.6626i	−0.439257	−	1.63933i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.83144	−	8.36829i	−0.533543	−	0.924123i
$83$	6.35771	−	6.35771i	0.697850	−	0.697850i	−0.266097	−	0.963946i	$-0.585734\pi$
$83$	6.35771	−	6.35771i	0.697850	−	0.697850i	0.963946	+	0.266097i	$0.0857340\pi$
$84$	−5.89780	+	12.9558i	−0.643503	+	1.41359i
$85$	−3.80737	+	3.80737i	−0.412967	+	0.412967i
$86$	14.8796	+	3.98697i	1.60451	+	0.429926i
$87$	7.61160	+	4.39456i	0.816050	+	0.471146i
$88$	34.5180	+	19.9290i	3.67963	+	2.12444i
$89$	−0.934235	+	3.48661i	−0.0990287	+	0.369580i	−0.997599	−	0.0692485i	$-0.977940\pi$
$89$	−0.934235	+	3.48661i	−0.0990287	+	0.369580i	0.898571	+	0.438829i	$0.144607\pi$
$90$	−2.90673			−0.306396
$91$	0.146462	−	9.53827i	0.0153534	−	0.999882i
$92$	14.0160			1.46127
$93$	0.156961	−	0.585786i	0.0162761	−	0.0607432i
$94$	−18.5550	−	10.7127i	−1.91380	−	1.10493i
$95$	−3.08567	−	1.78151i	−0.316583	−	0.182780i
$96$	19.4884	+	5.22191i	1.98903	+	0.532959i
$97$	10.0260	−	10.0260i	1.01798	−	1.01798i	0.0181484	−	0.999835i	$-0.494223\pi$
$97$	10.0260	−	10.0260i	1.01798	−	1.01798i	0.999835	−	0.0181484i	$-0.00577715\pi$
$98$	15.7744	+	10.6210i	1.59346	+	1.07288i
$99$	3.06904	−	3.06904i	0.308450	−	0.308450i
$100$	10.3711	+	17.9633i	1.03711	+	1.79633i
$101$	−5.78716	+	10.0236i	−0.575844	+	0.997390i	0.420106	+	0.907475i	$0.361993\pi$
$101$	−5.78716	+	10.0236i	−0.575844	+	0.997390i	−0.995949	+	0.0899152i	$0.971340\pi$
$102$	−3.53841	−	13.2055i	−0.350355	−	1.30754i
$103$	8.14974	+	14.1158i	0.803018	+	1.39087i	0.917621	+	0.397457i	$0.130107\pi$
$103$	8.14974	+	14.1158i	0.803018	+	1.39087i	−0.114603	+	0.993411i	$0.536560\pi$
$104$	−32.7388	+	4.94926i	−3.21031	+	0.485315i
$105$	−0.466066	+	2.79221i	−0.0454834	+	0.272492i
$106$	4.91905	+	4.91905i	0.477781	+	0.477781i
$107$	−3.84485	−	6.65947i	−0.371695	−	0.643795i	0.618131	−	0.786075i	$-0.287890\pi$
$107$	−3.84485	−	6.65947i	−0.371695	−	0.643795i	−0.989826	+	0.142280i	$0.954557\pi$
$108$	2.69017	−	4.65951i	0.258862	−	0.448361i
$109$	1.39028	−	0.372523i	0.133164	−	0.0356812i	−0.191621	−	0.981469i	$-0.561375\pi$
$109$	1.39028	−	0.372523i	0.133164	−	0.0356812i	0.324786	+	0.945788i	$0.394708\pi$
$110$	12.1861	+	3.26526i	1.16190	+	0.311330i
$111$	4.50508	+	4.50508i	0.427604	+	0.427604i
$112$	15.5519	−	34.1630i	1.46951	−	3.22810i
$113$	−3.28419			−0.308951			−0.154475	−	0.987997i	$-0.549369\pi$
$113$	−3.28419			−0.308951			−0.154475	+	0.987997i	$0.549369\pi$
$114$	7.83469	−	4.52336i	0.733786	−	0.423652i
$115$	2.69231	−	0.721402i	0.251059	−	0.0672711i
$116$	−40.9530	−	23.6442i	−3.80239	−	2.19531i
$117$	−0.402124	+	3.58306i	−0.0371763	+	0.331254i
$118$		−	1.49464i		−	0.137593i
$119$	−13.2526	+	1.28163i	−1.21487	+	0.117486i
$120$	9.82572			0.896961
$121$	−6.78787	+	3.91898i	−0.617079	+	0.356271i
$122$	5.00483	+	18.6783i	0.453116	+	1.69105i
$123$	3.43567	−	0.920586i	0.309784	−	0.0830064i
$124$	−0.844503	+	3.15173i	−0.0758386	+	0.283033i
$125$	6.69960	+	6.69960i	0.599231	+	0.599231i
$126$	−5.54806	−	4.56961i	−0.494261	−	0.407093i
$127$			8.69942i			0.771949i	0.922510	+	0.385974i	$0.126135\pi$
$127$			8.69942i			0.771949i	−0.922510	+	0.385974i	$0.873865\pi$
$128$	−30.3960	−	8.14457i	−2.68665	−	0.719885i
$129$	−2.83517	+	4.91065i	−0.249623	+	0.432359i
$130$	−9.60406	+	4.19522i	−0.842331	+	0.367945i
$131$	0.237690	−	0.137230i	0.0207671	−	0.0119899i	−0.489581	−	0.871958i	$-0.662850\pi$
$131$	0.237690	−	0.137230i	0.0207671	−	0.0119899i	0.510348	+	0.859968i	$0.329517\pi$
$132$	−16.5124	+	16.5124i	−1.43722	+	1.43722i
$133$	−3.08893	−	8.25130i	−0.267845	−	0.715479i
$134$			18.8302i			1.62668i
$135$	0.276925	−	1.03350i	0.0238339	−	0.0889494i
$136$	11.9610	+	44.6392i	1.02565	+	3.82778i
$137$	3.48719	+	13.0144i	0.297930	+	1.11189i	0.938862	+	0.344293i	$0.111881\pi$
$137$	3.48719	+	13.0144i	0.297930	+	1.11189i	−0.640932	+	0.767598i	$0.721452\pi$
$138$	−1.83168	+	6.83592i	−0.155923	+	0.581912i
$139$		−	10.7556i		−	0.912281i	−0.889908	−	0.456140i	$-0.849231\pi$
$139$		−	10.7556i		−	0.912281i	0.889908	−	0.456140i	$-0.150769\pi$
$140$	2.50759	−	15.0230i	0.211930	−	1.26968i
$141$	5.57670	−	5.57670i	0.469643	−	0.469643i
$142$	−20.9371	+	12.0881i	−1.75701	+	1.01441i
$143$	5.71086	−	14.5698i	0.477566	−	1.21839i
$144$	−7.09368	+	12.2866i	−0.591140	+	1.02388i
$145$	−9.08355	−	2.43393i	−0.754347	−	0.202127i
$146$			11.9398i			0.988146i
$147$	−5.27916	+	4.59679i	−0.435418	+	0.379137i
$148$	−24.2389	−	24.2389i	−1.99242	−	1.99242i
$149$	2.00830	−	7.49506i	0.164526	−	0.614019i	−0.833574	−	0.552408i	$-0.813709\pi$
$149$	2.00830	−	7.49506i	0.164526	−	0.614019i	0.998100	−	0.0616119i	$-0.0196241\pi$
$150$	−10.1164	+	2.71069i	−0.826005	+	0.221327i
$151$	2.58654	+	9.65308i	0.210489	+	0.785557i	0.987706	+	0.156324i	$0.0499643\pi$
$151$	2.58654	+	9.65308i	0.210489	+	0.785557i	−0.777217	+	0.629233i	$0.783369\pi$
$152$	−26.4839	+	15.2905i	−2.14813	+	1.24022i
$153$	5.03239			0.406844
$154$	18.1263	+	25.3899i	1.46066	+	2.04598i
$155$			0.648875i			0.0521189i
$156$	2.16356	−	19.2781i	0.173223	−	1.54348i
$157$	10.9016	+	6.29402i	0.870040	+	0.502318i	0.867362	−	0.497679i	$-0.165814\pi$
$157$	10.9016	+	6.29402i	0.870040	+	0.502318i	0.00267852	+	0.999996i	$0.499147\pi$
$158$	21.7069	−	5.81634i	1.72691	−	0.462723i
$159$	−2.21763	+	1.28035i	−0.175869	+	0.101538i
$160$	−21.5873			−1.70663
$161$	6.27291	+	2.85559i	0.494375	+	0.225052i
$162$	1.92098	+	1.92098i	0.150927	+	0.150927i
$163$	−19.0351	−	5.10043i	−1.49094	−	0.399496i	−0.580886	−	0.813985i	$-0.697294\pi$
$163$	−19.0351	−	5.10043i	−1.49094	−	0.399496i	−0.910055	+	0.414489i	$0.863960\pi$
$164$	−18.4851	+	4.95306i	−1.44344	+	0.386769i
$165$	−2.32195	+	4.02174i	−0.180764	+	0.313092i
$166$	−12.2130	−	21.1536i	−0.947916	−	1.64184i
$167$	12.5710	+	12.5710i	0.972775	+	0.972775i	0.999639	−	0.0268642i	$-0.00855218\pi$
$167$	12.5710	+	12.5710i	0.972775	+	0.972775i	−0.0268642	+	0.999639i	$0.508552\pi$
$168$	18.7543	+	15.4468i	1.44693	+	1.19175i
$169$	3.84270	+	12.4191i	0.295593	+	0.955314i
$170$	7.31389	+	12.6680i	0.560949	+	0.971593i
$171$	0.861885	+	3.21660i	0.0659100	+	0.245980i
$172$	15.2542	−	26.4210i	1.16312	−	2.01458i
$173$	6.28575	+	10.8872i	0.477897	+	0.827742i	0.999679	−	0.0253370i	$-0.00806588\pi$
$173$	6.28575	+	10.8872i	0.477897	+	0.827742i	−0.521782	+	0.853079i	$0.674733\pi$
$174$	16.8837	−	16.8837i	1.27995	−	1.27995i
$175$	0.981823	+	10.1525i	0.0742189	+	0.767458i
$176$	43.5415	−	43.5415i	3.28206	−	3.28206i
$177$	0.531425	+	0.142395i	0.0399444	+	0.0107031i
$178$	8.49237	+	4.90307i	0.636530	+	0.367501i
$179$	−8.55401	−	4.93866i	−0.639357	−	0.369133i	0.145010	−	0.989430i	$-0.453679\pi$
$179$	−8.55401	−	4.93866i	−0.639357	−	0.369133i	−0.784367	+	0.620297i	$0.787012\pi$
$180$	−1.48995	+	5.56057i	−0.111054	+	0.414460i
$181$	13.4786			1.00186			0.500928	−	0.865489i	$-0.332992\pi$
$181$	13.4786			1.00186			0.500928	+	0.865489i	$0.332992\pi$
$182$	−24.9265	−	7.09095i	−1.84767	−	0.525616i
$183$	−7.11795			−0.526174
$184$	6.19170	−	23.1077i	0.456458	−	1.70352i
$185$	−5.90357	−	3.40843i	−0.434039	−	0.250593i
$186$	−1.42680	−	0.823765i	−0.104618	−	0.0604014i
$187$	−21.0977	−	5.65311i	−1.54282	−	0.413396i
$188$	−30.0045	+	30.0045i	−2.18831	+	2.18831i
$189$	2.15331	−	1.53729i	0.156630	−	0.111821i
$190$	−6.84451	+	6.84451i	−0.496553	+	0.496553i
$191$	−11.7254	−	20.3089i	−0.848417	−	1.46950i	−0.882620	−	0.470087i	$-0.844222\pi$
$191$	−11.7254	−	20.3089i	−0.848417	−	1.46950i	0.0342025	−	0.999415i	$-0.489111\pi$
$192$	13.2184	−	22.8949i	0.953953	−	1.65229i
$193$	0.699244	+	2.60961i	0.0503327	+	0.187844i	0.986515	−	0.163671i	$-0.0523334\pi$
$193$	0.699244	+	2.60961i	0.0503327	+	0.187844i	−0.936182	+	0.351515i	$0.885667\pi$
$194$	−19.2597	−	33.3588i	−1.38277	−	2.39502i
$195$	−0.576644	−	3.81444i	−0.0412943	−	0.273158i
$196$	28.4037	−	24.7323i	2.02883	−	1.76659i
$197$	14.0722	+	14.0722i	1.00260	+	1.00260i	0.999997	+	0.00260349i	$0.000828719\pi$
$197$	14.0722	+	14.0722i	1.00260	+	1.00260i	0.00260349	+	0.999997i	$0.499171\pi$
$198$	−5.89556	−	10.2114i	−0.418979	−	0.725693i
$199$	12.1733	−	21.0848i	0.862944	−	1.49466i	−0.00612967	−	0.999981i	$-0.501951\pi$
$199$	12.1733	−	21.0848i	0.862944	−	1.49466i	0.869074	−	0.494682i	$-0.164716\pi$
$200$	34.1970	−	9.16306i	2.41809	−	0.647926i
$201$	−6.69514	−	1.79396i	−0.472239	−	0.126536i
$202$	22.2340	+	22.2340i	1.56438	+	1.56438i
$203$	−13.5114	−	18.9257i	−0.948316	−	1.32832i
$204$	−27.0759			−1.89570
$205$	−3.29583	+	1.90285i	−0.230191	+	0.132901i
$206$	42.7716	−	11.4606i	2.98004	−	0.798500i
$207$	−2.25604	−	1.30252i	−0.156805	−	0.0905316i
$208$	−5.70507	+	50.8341i	−0.395575	+	3.52471i
$209$		−	14.4534i		−	0.999763i
$210$	6.99936	+	3.18629i	0.483001	+	0.219875i
$211$	3.62662			0.249667			0.124833	−	0.992178i	$-0.460160\pi$
$211$	3.62662			0.249667			0.124833	+	0.992178i	$0.460160\pi$
$212$	11.9316	−	6.88871i	0.819465	−	0.473119i
$213$	−2.30327	−	8.59592i	−0.157817	−	0.588983i
$214$	−20.1786	+	5.40684i	−1.37938	+	0.369604i
$215$	1.57026	−	5.86028i	0.107091	−	0.399668i
$216$	−6.49357	−	6.49357i	−0.441831	−	0.441831i
$217$	−1.02009	+	1.23851i	−0.0692479	+	0.0840754i
$218$		−	3.91017i		−	0.264830i
$219$	−4.24525	−	1.13751i	−0.286867	−	0.0768659i
$220$	12.4929	−	21.6383i	0.842270	−	1.45885i
$221$	16.6274	−	7.26314i	1.11848	−	0.488572i
$222$	14.9895	−	8.65418i	1.00603	−	0.580831i
$223$	−14.9253	+	14.9253i	−0.999470	+	0.999470i	−1.00000		0.000529583i	$-0.999831\pi$
$223$	−14.9253	+	14.9253i	−0.999470	+	0.999470i	0.000529583		1.00000i	$0.499831\pi$
$224$	−41.2037	−	33.9370i	−2.75304	−	2.26751i
$225$		−	3.85519i		−	0.257013i
$226$	−2.30921	+	8.61807i	−0.153606	+	0.573266i
$227$	−0.0674245	−	0.251632i	−0.00447512	−	0.0167014i	0.963652	−	0.267160i	$-0.0860852\pi$
$227$	−0.0674245	−	0.251632i	−0.00447512	−	0.0167014i	−0.968127	+	0.250459i	$0.919419\pi$
$228$	−4.63723	−	17.3064i	−0.307108	−	1.14614i
$229$	2.88832	−	10.7794i	0.190866	−	0.712321i	−0.802433	−	0.596743i	$-0.796461\pi$
$229$	2.88832	−	10.7794i	0.190866	−	0.712321i	0.993298	−	0.115578i	$-0.0368721\pi$
$230$		−	7.57215i		−	0.499293i
$231$	−10.7544	+	4.02599i	−0.707588	+	0.264890i
$232$	−57.0727	+	57.0727i	−3.74701	+	3.74701i
$233$	0.550848	−	0.318032i	0.0360872	−	0.0208350i	−0.481848	−	0.876255i	$-0.660034\pi$
$233$	0.550848	−	0.318032i	0.0360872	−	0.0208350i	0.517935	+	0.855420i	$0.326701\pi$
$234$	9.11959	+	3.57456i	0.596166	+	0.233677i
$235$	−4.21918	+	7.30784i	−0.275229	+	0.476711i
$236$	−2.85925	−	0.766133i	−0.186121	−	0.0498710i
$237$			8.27209i			0.537330i
$238$	−5.95516	+	35.6775i	−0.386016	+	2.31263i
$239$	−12.2533	−	12.2533i	−0.792601	−	0.792601i	0.189316	−	0.981916i	$-0.439373\pi$
$239$	−12.2533	−	12.2533i	−0.792601	−	0.792601i	−0.981916	+	0.189316i	$0.939373\pi$
$240$	3.92883	−	14.6626i	0.253605	−	0.946467i
$241$	12.4088	−	3.32492i	0.799319	−	0.214177i	0.164034	−	0.986455i	$-0.447549\pi$
$241$	12.4088	−	3.32492i	0.799319	−	0.214177i	0.635285	+	0.772278i	$0.280883\pi$
$242$	5.51109	+	20.5677i	0.354266	+	1.32214i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	38.2970			2.45171
$245$	4.18304	−	6.21271i	0.267244	−	0.396915i
$246$		−	9.66287i		−	0.616082i
$247$	7.49019	+	9.38396i	0.476589	+	0.597087i
$248$	4.82308	+	2.78460i	0.306266	+	0.176823i
$249$	8.68480	−	2.32708i	0.550377	−	0.147473i
$250$	22.2912	−	12.8698i	1.40982	−	0.813958i
$251$	0.197154			0.0124442			0.00622212	−	0.999981i	$-0.498019\pi$
$251$	0.197154			0.0124442			0.00622212	+	0.999981i	$0.498019\pi$
$252$	−11.5855	+	8.27113i	−0.729820	+	0.521032i
$253$	7.99498	+	7.99498i	0.502640	+	0.502640i
$254$	22.8282	+	6.11681i	1.43237	+	0.383802i
$255$	−5.20096	+	1.39359i	−0.325697	+	0.0872702i
$256$	−16.3078	+	28.2459i	−1.01924	+	1.76537i
$257$	−3.83836	−	6.64823i	−0.239430	−	0.414705i	0.721121	−	0.692809i	$-0.243627\pi$
$257$	−3.83836	−	6.64823i	−0.239430	−	0.414705i	−0.960551	+	0.278104i	$0.910294\pi$
$258$	10.8926	+	10.8926i	0.678144	+	0.678144i
$259$	−5.90981	−	15.7866i	−0.367218	−	0.980928i
$260$	3.10254	+	20.5230i	0.192411	+	1.27278i
$261$	4.39456	+	7.61160i	0.272017	+	0.471146i
$262$	−0.192981	−	0.720215i	−0.0119224	−	0.0444950i
$263$	−4.03084	+	6.98162i	−0.248552	+	0.430505i	−0.963124	−	0.269057i	$-0.913288\pi$
$263$	−4.03084	+	6.98162i	−0.248552	+	0.430505i	0.714572	+	0.699562i	$0.246621\pi$
$264$	19.9290	+	34.5180i	1.22654	+	2.12444i
$265$	1.93736	−	1.93736i	0.119011	−	0.119011i
$266$	−23.8242	+	2.30398i	−1.46076	+	0.141266i
$267$	−2.55238	+	2.55238i	−0.156203	+	0.156203i
$268$	36.0221	+	9.65209i	2.20040	+	0.589595i
$269$	−9.53401	−	5.50447i	−0.581299	−	0.335613i	0.180350	−	0.983602i	$-0.442277\pi$
$269$	−9.53401	−	5.50447i	−0.581299	−	0.335613i	−0.761649	+	0.647989i	$0.775610\pi$
$270$	−2.51730	−	1.45336i	−0.153198	−	0.0884489i
$271$	3.62785	−	13.5393i	0.220376	−	0.822456i	−0.763828	−	0.645420i	$-0.776682\pi$
$271$	3.62785	−	13.5393i	0.220376	−	0.822456i	0.984204	−	0.177036i	$-0.0566510\pi$
$272$	71.3963			4.32903
$273$	4.89597	−	8.18715i	0.296318	−	0.495509i
$274$	36.6030			2.21127
$275$	−4.33071	+	16.1624i	−0.261152	+	0.974632i
$276$	12.1382	+	7.00801i	0.730636	+	0.421833i
$277$	−20.7517	−	11.9810i	−1.24685	−	0.719867i	−0.276367	−	0.961052i	$-0.589131\pi$
$277$	−20.7517	−	11.9810i	−1.24685	−	0.719867i	−0.970479	+	0.241185i	$0.922464\pi$
$278$	−28.2239	−	7.56258i	−1.69276	−	0.453574i
$279$	0.428825	−	0.428825i	0.0256731	−	0.0256731i
$280$	−23.6602	−	10.7707i	−1.41397	−	0.643674i
$281$	−18.0236	+	18.0236i	−1.07520	+	1.07520i	−0.0782650	+	0.996933i	$0.524938\pi$
$281$	−18.0236	+	18.0236i	−1.07520	+	1.07520i	−0.996933	+	0.0782650i	$0.975062\pi$
$282$	−10.7127	−	18.5550i	−0.637934	−	1.10493i
$283$	5.63335	−	9.75724i	0.334868	−	0.580008i	−0.648592	−	0.761136i	$-0.724642\pi$
$283$	5.63335	−	9.75724i	0.334868	−	0.580008i	0.983459	+	0.181129i	$0.0579751\pi$
$284$	12.3924	+	46.2490i	0.735352	+	2.74437i
$285$	−1.78151	−	3.08567i	−0.105528	−	0.182780i
$286$	−34.2173	−	25.2304i	−2.02331	−	1.49190i
$287$	−9.28218	−	1.54935i	−0.547910	−	0.0914552i
$288$	14.2665	+	14.2665i	0.840663	+	0.840663i
$289$	−4.16246	−	7.20959i	−0.244851	−	0.424094i
$290$	−12.7738	+	22.1249i	−0.750103	+	1.29922i
$291$	13.6957	−	3.66976i	0.802858	−	0.215125i
$292$	22.8409	+	6.12020i	1.33666	+	0.358157i
$293$	−10.6692	−	10.6692i	−0.623304	−	0.623304i	0.323071	−	0.946375i	$-0.395285\pi$
$293$	−10.6692	−	10.6692i	−0.623304	−	0.623304i	−0.946375	+	0.323071i	$0.895285\pi$
$294$	8.35056	+	17.0852i	0.487014	+	0.996430i
$295$	−0.588660			−0.0342731
$296$	−50.6695	+	29.2541i	−2.94511	+	1.70036i
$297$	4.19238	−	1.12334i	0.243267	−	0.0651831i
$298$	−18.2558	−	10.5400i	−1.05753	−	0.610564i
$299$	−9.33403	−	1.04755i	−0.539801	−	0.0605814i
$300$			20.7422i			1.19755i
$301$	12.2100	−	8.71694i	0.703772	−	0.502436i
$302$	27.1494			1.56227
$303$	−10.0236	+	5.78716i	−0.575844	+	0.332463i
$304$	12.2279	+	45.6351i	0.701317	+	2.61735i
$305$	7.35639	−	1.97114i	0.421226	−	0.112867i
$306$	3.53841	−	13.2055i	0.202278	−	0.754910i
$307$	−15.1449	−	15.1449i	−0.864367	−	0.864367i	0.127475	−	0.991842i	$-0.459313\pi$
$307$	−15.1449	−	15.1449i	−0.864367	−	0.864367i	−0.991842	+	0.127475i	$0.959313\pi$
$308$	57.8623	−	21.6612i	3.29701	−	1.23426i
$309$			16.2995i			0.927245i
$310$	1.70272	+	0.456242i	0.0967080	+	0.0259128i
$311$	−11.2329	+	19.4559i	−0.636958	+	1.10324i	0.349139	+	0.937071i	$0.386474\pi$
$311$	−11.2329	+	19.4559i	−0.636958	+	1.10324i	−0.986097	+	0.166172i	$0.946859\pi$
$312$	−30.8273	−	12.0832i	−1.74525	−	0.684078i
$313$	−12.7951	+	7.38725i	−0.723222	+	0.417552i	−0.815937	−	0.578140i	$-0.803779\pi$
$313$	−12.7951	+	7.38725i	−0.723222	+	0.417552i	0.0927156	+	0.995693i	$0.470445\pi$
$314$	24.1814	−	24.1814i	1.36464	−	1.36464i
$315$	−1.79973	+	2.18509i	−0.101403	+	0.123116i
$316$		−	44.5067i		−	2.50369i
$317$	−1.88463	+	7.03352i	−0.105851	+	0.395042i	−0.998440	−	0.0558290i	$-0.982220\pi$
$317$	−1.88463	+	7.03352i	−0.105851	+	0.395042i	0.892589	+	0.450871i	$0.148886\pi$
$318$	1.80050	+	6.71955i	0.100967	+	0.376814i
$319$	−9.87322	−	36.8474i	−0.552794	−	2.06306i
$320$	−7.32099	+	27.3223i	−0.409256	+	1.52736i
$321$		−	7.68969i		−	0.429197i
$322$	11.9040	−	14.4530i	0.663386	−	0.805432i
$323$	11.8498	−	11.8498i	0.659343	−	0.659343i
$324$	4.65951	−	2.69017i	0.258862	−	0.149454i
$325$	−5.56412	−	12.7379i	−0.308642	−	0.706570i
$326$	−26.7682	+	46.3638i	−1.48255	+	2.56785i
$327$	1.39028	+	0.372523i	0.0768824	+	0.0206006i
$328$			32.6638i			1.80355i
$329$	−19.5417	+	7.31557i	−1.07737	+	0.403320i
$330$	8.92085	+	8.92085i	0.491076	+	0.491076i
$331$	6.40593	−	23.9073i	0.352102	−	1.31406i	−0.531991	−	0.846750i	$-0.678556\pi$
$331$	6.40593	−	23.9073i	0.352102	−	1.31406i	0.884093	−	0.467312i	$-0.154777\pi$
$332$	−46.7271	+	12.5205i	−2.56449	+	0.687152i
$333$	1.64898	+	6.15406i	0.0903633	+	0.337240i
$334$	41.8268	−	24.1487i	2.28866	−	1.32136i
$335$	7.41621			0.405191
$336$	30.5498	−	21.8101i	1.66663	−	1.18984i
$337$		−	1.12148i		−	0.0610910i	−0.999533	−	0.0305455i	$-0.990276\pi$
$337$		−	1.12148i		−	0.0610910i	0.999533	−	0.0305455i	$-0.00972445\pi$
$338$	35.2909	−	1.35147i	1.91957	−	0.0735102i
$339$	−2.84419	−	1.64209i	−0.154475	−	0.0891863i
$340$	27.9829	−	7.49801i	1.51759	−	0.406636i
$341$	−2.27952	+	1.31608i	−0.123443	+	0.0712697i
$342$	9.04673			0.489191
$343$	17.7510	−	5.28211i	0.958466	−	0.285207i
$344$	−36.8207	−	36.8207i	−1.98524	−	1.98524i
$345$	2.69231	+	0.721402i	0.144949	+	0.0388390i
$346$	32.9890	−	8.83938i	1.77350	−	0.475208i
$347$	2.22109	−	3.84704i	0.119234	−	0.206520i	−0.800230	−	0.599693i	$-0.795289\pi$
$347$	2.22109	−	3.84704i	0.119234	−	0.206520i	0.919464	+	0.393173i	$0.128623\pi$
$348$	−23.6442	−	40.9530i	−1.26746	−	2.19531i
$349$	18.9017	+	18.9017i	1.01179	+	1.01179i	0.999930	+	0.0118569i	$0.00377427\pi$
$349$	18.9017	+	18.9017i	1.01179	+	1.01179i	0.0118569	+	0.999930i	$0.496226\pi$
$350$	27.3317	+	4.56211i	1.46094	+	0.243855i
$351$	−2.13978	+	2.90196i	−0.114213	+	0.154895i
$352$	−43.7844	−	75.8369i	−2.33372	−	4.04212i
$353$	2.29856	+	8.57834i	0.122340	+	0.456579i	0.999731	−	0.0231970i	$-0.00738451\pi$
$353$	2.29856	+	8.57834i	0.122340	+	0.456579i	−0.877391	+	0.479776i	$0.840718\pi$
$354$	0.747320	−	1.29440i	0.0397196	−	0.0687964i
$355$	4.76085	+	8.24604i	0.252680	+	0.437654i
$356$	13.7327	−	13.7327i	0.727829	−	0.727829i
$357$	−12.1179	−	5.51639i	−0.641348	−	0.291958i
$358$	−18.9741	+	18.9741i	−1.00281	+	1.00281i
$359$	21.4910	+	5.75851i	1.13425	+	0.303922i	0.776638	−	0.629947i	$-0.216923\pi$
$359$	21.4910	+	5.75851i	1.13425	+	0.303922i	0.357615	+	0.933869i	$0.383590\pi$
$360$	8.50932	+	4.91286i	0.448481	+	0.258930i
$361$	−6.85081	−	3.95532i	−0.360569	−	0.208175i
$362$	9.47717	−	35.3693i	0.498109	−	1.85897i
$363$	−7.83796			−0.411386
$364$	−26.3420	+	44.0496i	−1.38070	+	2.30883i
$365$	4.70247			0.246138
$366$	−5.00483	+	18.6783i	−0.261607	+	0.976329i
$367$	19.0891	+	11.0211i	0.996444	+	0.575297i	0.907194	−	0.420712i	$-0.138220\pi$
$367$	19.0891	+	11.0211i	0.996444	+	0.575297i	0.0892495	+	0.996009i	$0.471553\pi$
$368$	−32.0072	−	18.4794i	−1.66849	−	0.963303i
$369$	3.43567	+	0.920586i	0.178854	+	0.0479238i
$370$	−13.0950	+	13.0950i	−0.680779	+	0.680779i
$371$	6.74351	−	0.652147i	0.350106	−	0.0338578i
$372$	−2.30722	+	2.30722i	−0.119624	+	0.119624i
$373$	1.61112	+	2.79055i	0.0834209	+	0.144489i	0.904717	−	0.426013i	$-0.140082\pi$
$373$	1.61112	+	2.79055i	0.0834209	+	0.144489i	−0.821296	+	0.570502i	$0.806749\pi$
$374$	−29.6687	+	51.3878i	−1.53413	+	2.65720i
$375$	2.45222	+	9.15183i	0.126632	+	0.472598i
$376$	36.2127	+	62.7222i	1.86753	+	3.23465i
$377$	25.5057	+	18.8068i	1.31361	+	0.968598i
$378$	−2.51996	−	6.73143i	−0.129613	−	0.346227i
$379$	5.32866	+	5.32866i	0.273715	+	0.273715i	0.830594	−	0.556879i	$-0.188001\pi$
$379$	5.32866	+	5.32866i	0.273715	+	0.273715i	−0.556879	+	0.830594i	$0.688001\pi$
$380$	9.58515	+	16.6020i	0.491708	+	0.851663i
$381$	−4.34971	+	7.53392i	−0.222842	+	0.385974i
$382$	−61.5373	+	16.4889i	−3.14852	+	0.843643i
$383$	−6.80116	−	1.82237i	−0.347523	−	0.0931185i	0.0808353	−	0.996727i	$-0.474241\pi$
$383$	−6.80116	−	1.82237i	−0.347523	−	0.0931185i	−0.428358	+	0.903609i	$0.640908\pi$
$384$	−22.2514	−	22.2514i	−1.13551	−	1.13551i
$385$	9.99976	−	7.13901i	0.509635	−	0.363838i
$386$	7.33957			0.373574
$387$	−4.91065	+	2.83517i	−0.249623	+	0.144120i
$388$	−73.6877	+	19.7446i	−3.74093	+	1.00238i
$389$	24.4885	+	14.1384i	1.24162	+	0.716847i	0.969423	−	0.245395i	$-0.0789178\pi$
$389$	24.4885	+	14.1384i	1.24162	+	0.716847i	0.272193	+	0.962243i	$0.412251\pi$
$390$	−10.4150	−	1.16886i	−0.527382	−	0.0591877i
$391$			13.1096i			0.662981i
$392$	−28.2277	−	57.7538i	−1.42571	−	2.91701i
$393$	0.274461			0.0138447
$394$	46.8214	−	27.0324i	2.35883	−	1.36187i
$395$	−2.29075	−	8.54919i	−0.115260	−	0.430157i
$396$	−22.5564	+	6.04398i	−1.13350	+	0.303721i
$397$	−0.456998	+	1.70554i	−0.0229361	+	0.0855986i	−0.976445	−	0.215766i	$-0.930775\pi$
$397$	−0.456998	+	1.70554i	−0.0229361	+	0.0855986i	0.953509	+	0.301364i	$0.0974420\pi$
$398$	−46.7695	−	46.7695i	−2.34434	−	2.34434i
$399$	1.45056	−	8.69031i	0.0726186	−	0.435060i
$400$		−	54.6950i		−	2.73475i
$401$	−33.1845	−	8.89176i	−1.65715	−	0.444033i	−0.695551	−	0.718477i	$-0.744840\pi$
$401$	−33.1845	−	8.89176i	−1.65715	−	0.444033i	−0.961603	+	0.274443i	$0.911506\pi$
$402$	−9.41508	+	16.3074i	−0.469581	+	0.813339i
$403$	0.797958	−	2.03579i	0.0397491	−	0.101410i
$404$	53.9306	−	31.1369i	2.68315	−	1.54912i
$405$	0.756573	−	0.756573i	0.0375944	−	0.0375944i
$406$	−59.1634	+	22.1482i	−2.93623	+	1.09920i
$407$		−	27.6525i		−	1.37068i
$408$	−11.9610	+	44.6392i	−0.592159	+	2.20997i
$409$	−8.03771	−	29.9971i	−0.397439	−	1.48326i	−0.817586	−	0.575807i	$-0.804688\pi$
$409$	−8.03771	−	29.9971i	−0.397439	−	1.48326i	0.420147	−	0.907456i	$-0.361979\pi$
$410$	2.67589	+	9.98656i	0.132153	+	0.493201i
$411$	−3.48719	+	13.0144i	−0.172010	+	0.641951i
$412$		−	87.6967i		−	4.32051i
$413$	−1.12357	−	0.925422i	−0.0552875	−	0.0455370i
$414$	−5.00424	+	5.00424i	−0.245945	+	0.245945i
$415$	−8.33130	+	4.81008i	−0.408967	+	0.236117i
$416$	67.7283	+	26.5471i	3.32065	+	1.30158i
$417$	5.37782	−	9.31465i	0.263353	−	0.456140i
$418$	−37.9273	−	10.1626i	−1.85509	−	0.497069i
$419$			1.03283i			0.0504572i	0.999682	+	0.0252286i	$0.00803136\pi$
$419$			1.03283i			0.0504572i	−0.999682	+	0.0252286i	$0.991969\pi$
$420$	9.68315	−	11.7565i	0.472489	−	0.573660i
$421$	10.8179	+	10.8179i	0.527234	+	0.527234i	0.919746	−	0.392513i	$-0.128394\pi$
$421$	10.8179	+	10.8179i	0.527234	+	0.527234i	−0.392513	+	0.919746i	$0.628394\pi$
$422$	2.54998	−	9.51665i	0.124131	−	0.463263i
$423$	7.61792	−	2.04121i	0.370396	−	0.0992473i
$424$	−6.08629	−	22.7143i	−0.295576	−	1.10311i
$425$	−16.8016	+	9.70041i	−0.814998	+	0.470539i
$426$	−24.1761			−1.17134
$427$	17.1399	+	7.80253i	0.829459	+	0.377591i
$428$			41.3731i			1.99985i
$429$	12.2307	−	9.76240i	0.590502	−	0.471333i
$430$	−14.2739	−	8.24105i	−0.688350	−	0.397419i
$431$	−28.3454	+	7.59512i	−1.36535	+	0.365844i	−0.865778	−	0.500429i	$-0.833176\pi$
$431$	−28.3454	+	7.59512i	−1.36535	+	0.365844i	−0.499571	+	0.866273i	$0.666509\pi$
$432$	−12.2866	+	7.09368i	−0.591140	+	0.341295i
$433$	18.2027			0.874764			0.437382	−	0.899276i	$-0.355906\pi$
$433$	18.2027			0.874764			0.437382	+	0.899276i	$0.355906\pi$
$434$	2.53273	+	3.54764i	0.121575	+	0.170292i
$435$	−6.64962	−	6.64962i	−0.318825	−	0.318825i
$436$	−7.48015	−	2.00430i	−0.358234	−	0.0959886i
$437$	−8.37939	+	2.24525i	−0.400841	+	0.107405i
$438$	−5.96991	+	10.3402i	−0.285253	+	0.494073i
$439$	16.0458	+	27.7921i	0.765823	+	1.32644i	0.939810	+	0.341697i	$0.111002\pi$
$439$	16.0458	+	27.7921i	0.765823	+	1.32644i	−0.173987	+	0.984748i	$0.555665\pi$
$440$	−30.1555	−	30.1555i	−1.43761	−	1.43761i
$441$	−6.87028	+	1.34136i	−0.327156	+	0.0638742i
$442$	−7.36808	−	48.7391i	−0.350464	−	2.31828i
$443$	−7.30344	−	12.6499i	−0.346997	−	0.601016i	0.638718	−	0.769441i	$-0.279465\pi$
$443$	−7.30344	−	12.6499i	−0.346997	−	0.601016i	−0.985714	+	0.168425i	$0.946132\pi$
$444$	−8.87204	−	33.1109i	−0.421049	−	1.57137i
$445$	1.93106	−	3.34470i	0.0915411	−	0.158554i
$446$	28.6712	+	49.6599i	1.35762	+	2.35147i
$447$	5.48677	−	5.48677i	0.259515	−	0.259515i
$448$	−56.9264	+	40.6408i	−2.68952	+	1.92010i
$449$	7.00187	−	7.00187i	0.330439	−	0.330439i	−0.522314	−	0.852753i	$-0.674931\pi$
$449$	7.00187	−	7.00187i	0.330439	−	0.330439i	0.852753	+	0.522314i	$0.174931\pi$
$450$	−10.1164	−	2.71069i	−0.476894	−	0.127783i
$451$	−13.3695	−	7.71889i	−0.629546	−	0.363468i
$452$	15.3027	+	8.83502i	0.719779	+	0.415565i
$453$	−2.58654	+	9.65308i	−0.121526	+	0.453541i
$454$	−0.707717			−0.0332148
$455$	−2.79275	+	9.81723i	−0.130926	+	0.460239i
$456$	−30.5810			−1.43209
$457$	−5.48279	+	20.4621i	−0.256474	+	0.957175i	0.710790	+	0.703404i	$0.248338\pi$
$457$	−5.48279	+	20.4621i	−0.256474	+	0.957175i	−0.967264	+	0.253771i	$0.918329\pi$
$458$	−26.2554	−	15.1586i	−1.22683	−	0.708313i
$459$	4.35817	+	2.51619i	0.203422	+	0.117446i
$460$	−14.4855	−	3.88139i	−0.675392	−	0.180971i
$461$	−11.7492	+	11.7492i	−0.547216	+	0.547216i	−0.925634	−	0.378419i	$-0.876468\pi$
$461$	−11.7492	+	11.7492i	−0.547216	+	0.547216i	0.378419	+	0.925634i	$0.376468\pi$
$462$	3.00291	+	31.0515i	0.139708	+	1.44465i
$463$	−9.47620	+	9.47620i	−0.440396	+	0.440396i	−0.892145	−	0.451749i	$-0.850800\pi$
$463$	−9.47620	+	9.47620i	−0.440396	+	0.440396i	0.451749	+	0.892145i	$0.350800\pi$
$464$	62.3472	+	107.989i	2.89440	+	5.01324i
$465$	−0.324438	+	0.561943i	−0.0150454	+	0.0260595i
$466$	−0.447234	−	1.66910i	−0.0207177	−	0.0773196i
$467$	6.58282	+	11.4018i	0.304616	+	0.527611i	0.977176	−	0.212432i	$-0.0681384\pi$
$467$	6.58282	+	11.4018i	0.304616	+	0.527611i	−0.672559	+	0.740043i	$0.734805\pi$
$468$	11.5127	−	15.6135i	0.532176	−	0.721735i
$469$	14.1553	+	11.6589i	0.653631	+	0.538357i
$470$	16.2099	+	16.2099i	0.747709	+	0.747709i
$471$	6.29402	+	10.9016i	0.290013	+	0.502318i
$472$	−2.52619	+	4.37550i	−0.116278	+	0.201399i
$473$	23.7722	−	6.36974i	1.09305	−	0.292881i
$474$	21.7069	+	5.81634i	0.997030	+	0.267153i
$475$	−9.07788	−	9.07788i	−0.416522	−	0.416522i
$476$	65.1985	+	29.6800i	2.98837	+	1.36038i
$477$	−2.56070			−0.117246
$478$	−40.7697	+	23.5384i	−1.86476	+	1.07662i
$479$	6.85761	−	1.83749i	0.313332	−	0.0839571i	−0.0987259	−	0.995115i	$-0.531477\pi$
$479$	6.85761	−	1.83749i	0.313332	−	0.0839571i	0.412058	+	0.911158i	$0.364810\pi$
$480$	−18.6952	−	10.7937i	−0.853314	−	0.492661i
$481$	14.3304	+	17.9536i	0.653409	+	0.818613i
$482$		−	34.8998i		−	1.58964i
$483$	4.00471	+	5.60947i	0.182220	+	0.255240i
$484$	42.1709			1.91686
$485$	−13.1383	+	7.58539i	−0.596578	+	0.344435i
$486$	0.703128	+	2.62411i	0.0318945	+	0.119032i
$487$	−10.8121	+	2.89709i	−0.489943	+	0.131280i	−0.495329	−	0.868706i	$-0.664952\pi$
$487$	−10.8121	+	2.89709i	−0.489943	+	0.131280i	0.00538562	+	0.999985i	$0.498286\pi$
$488$	16.9180	−	63.1389i	0.765842	−	2.85816i
$489$	−13.9346	−	13.9346i	−0.630146	−	0.630146i
$490$	−13.3616	−	15.3451i	−0.603616	−	0.693220i
$491$		−	20.3928i		−	0.920314i	−0.887838	−	0.460157i	$-0.847793\pi$
$491$		−	20.3928i		−	0.920314i	0.887838	−	0.460157i	$-0.152207\pi$
$492$	−18.4851	−	4.95306i	−0.833372	−	0.223301i
$493$	22.1151	−	38.3045i	0.996016	−	1.72515i
$494$	29.8911	−	13.0570i	1.34486	−	0.587460i
$495$	−4.02174	+	2.32195i	−0.180764	+	0.104364i
$496$	6.08390	−	6.08390i	0.273175	−	0.273175i
$497$	−3.87641	+	23.2236i	−0.173881	+	1.04172i
$498$		−	24.4261i		−	1.09456i
$499$	−1.51706	+	5.66176i	−0.0679131	+	0.253455i	−0.991533	−	0.129854i	$-0.958549\pi$
$499$	−1.51706	+	5.66176i	−0.0679131	+	0.253455i	0.923620	+	0.383309i	$0.125216\pi$
$500$	−13.1938	−	49.2399i	−0.590045	−	2.20208i
$501$	4.60131	+	17.1723i	0.205572	+	0.767203i
$502$	0.138624	−	0.517353i	0.00618711	−	0.0230906i
$503$			41.4902i			1.84996i	0.380018	+	0.924979i	$0.375918\pi$
$503$			41.4902i			1.84996i	−0.380018	+	0.924979i	$0.624082\pi$
$504$	8.51831	+	22.7545i	0.379436	+	1.01357i
$505$	8.75682	−	8.75682i	0.389673	−	0.389673i
$506$	26.6012	−	15.3582i	1.18257	−	0.682755i
$507$	−2.88166	+	12.6766i	−0.127979	+	0.562987i
$508$	23.4029	−	40.5350i	1.03834	−	1.79845i
$509$	−5.13441	−	1.37576i	−0.227579	−	0.0609795i	0.143228	−	0.989690i	$-0.454252\pi$
$509$	−5.13441	−	1.37576i	−0.227579	−	0.0609795i	−0.370806	+	0.928710i	$0.620919\pi$
$510$			14.6278i			0.647729i
$511$	8.97559	+	7.39266i	0.397057	+	0.327032i
$512$	18.1511	+	18.1511i	0.802174	+	0.802174i
$513$	−0.861885	+	3.21660i	−0.0380532	+	0.142016i
$514$	−20.1445	+	5.39771i	−0.888537	+	0.238083i
$515$	−4.51374	−	16.8455i	−0.198899	−	0.742301i
$516$	26.4210	−	15.2542i	1.16312	−	0.671527i
$517$	−34.2302			−1.50544
$518$	−45.5810	+	4.40802i	−2.00271	+	0.193677i
$519$			12.5715i			0.551828i
$520$	35.2061	+	3.95115i	1.54389	+	0.173269i
$521$	38.6249	+	22.3001i	1.69219	+	0.976986i	0.952746	+	0.303767i	$0.0982445\pi$
$521$	38.6249	+	22.3001i	1.69219	+	0.976986i	0.739443	+	0.673219i	$0.235089\pi$
$522$	23.0636	−	6.17988i	1.00947	−	0.270486i
$523$	36.8046	−	21.2492i	1.60935	−	0.929160i	0.619838	−	0.784730i	$-0.287198\pi$
$523$	36.8046	−	21.2492i	1.60935	−	0.929160i	0.989515	−	0.144431i	$-0.0461352\pi$
$524$	−1.47669			−0.0645095
$525$	−4.22598	+	9.28325i	−0.184437	+	0.405154i
$526$	15.4863	+	15.4863i	0.675236	+	0.675236i
$527$	−2.94790	−	0.789888i	−0.128413	−	0.0344081i
$528$	59.4788	−	15.9373i	2.58848	−	0.693582i
$529$	−8.10687	+	14.0415i	−0.352473	+	0.610500i
$530$	−3.72162	−	6.44604i	−0.161657	−	0.279998i
$531$	0.389030	+	0.389030i	0.0168825	+	0.0168825i
$532$	−7.80448	+	46.7568i	−0.338367	+	2.02716i
$533$	12.6804	−	1.91695i	0.549249	−	0.0830322i
$534$	4.90307	+	8.49237i	0.212177	+	0.367501i
$535$	2.12947	+	7.94728i	0.0920649	+	0.343591i
$536$	31.8261	−	55.1245i	1.37468	−	2.38102i
$537$	−4.93866	−	8.55401i	−0.213119	−	0.369133i
$538$	−21.1480	+	21.1480i	−0.911753	+	0.911753i
$539$	30.3096	+	2.09421i	1.30553	+	0.0902041i
$540$	−4.07062	+	4.07062i	−0.175172	+	0.175172i
$541$	−25.1788	−	6.74664i	−1.08252	−	0.290061i	−0.326893	−	0.945061i	$-0.606002\pi$
$541$	−25.1788	−	6.74664i	−1.08252	−	0.290061i	−0.755628	+	0.655001i	$0.772668\pi$
$542$	−32.9779	−	19.0398i	−1.41652	−	0.817828i
$543$	11.6728	+	6.73929i	0.500928	+	0.289211i
$544$	26.2787	−	98.0733i	1.12669	−	4.20486i
$545$	−1.54001			−0.0659667
$546$	−18.0415	−	18.6042i	−0.772104	−	0.796186i
$547$	−26.5968			−1.13720			−0.568599	−	0.822615i	$-0.692514\pi$
$547$	−26.5968			−1.13720			−0.568599	+	0.822615i	$0.692514\pi$
$548$	18.7622	−	70.0216i	0.801483	−	2.99118i
$549$	−6.16432	−	3.55897i	−0.263087	−	0.151893i
$550$	39.3670	+	22.7285i	1.67861	+	0.969148i
$551$	28.2711	+	7.57522i	1.20439	+	0.322715i
$552$	16.9160	−	16.9160i	0.719994	−	0.719994i
$553$	9.06768	−	19.9191i	0.385597	−	0.847045i
$554$	−46.0304	+	46.0304i	−1.95565	+	1.95565i
$555$	−3.40843	−	5.90357i	−0.144680	−	0.250593i
$556$	−28.9345	+	50.1160i	−1.22709	+	2.12539i
$557$	7.55425	+	28.1928i	0.320084	+	1.19457i	0.919162	+	0.393879i	$0.128867\pi$
$557$	7.55425	+	28.1928i	0.320084	+	1.19457i	−0.599079	+	0.800690i	$0.704466\pi$
$558$	−0.823765	−	1.42680i	−0.0348728	−	0.0604014i
$559$	−12.1333	+	16.4551i	−0.513182	+	0.695975i
$560$	−25.5334	+	31.0007i	−1.07898	+	1.31002i
$561$	−15.4446	−	15.4446i	−0.652070	−	0.652070i
$562$	34.6230	+	59.9688i	1.46048	+	2.52963i
$563$	−2.18467	+	3.78395i	−0.0920727	+	0.159475i	−0.908383	−	0.418139i	$-0.862683\pi$
$563$	−2.18467	+	3.78395i	−0.0920727	+	0.159475i	0.816310	+	0.577613i	$0.196016\pi$
$564$	−40.9870	+	10.9824i	−1.72586	+	0.462444i
$565$	3.39420	+	0.909474i	0.142795	+	0.0382619i
$566$	−21.6431	−	21.6431i	−0.909727	−	0.909727i
$567$	2.63347	−	0.254675i	0.110595	−	0.0106954i
$568$	81.7235			3.42904
$569$	−6.16368	+	3.55860i	−0.258395	+	0.149184i	−0.623602	−	0.781742i	$-0.714331\pi$
$569$	−6.16368	+	3.55860i	−0.258395	+	0.149184i	0.365207	+	0.930926i	$0.380998\pi$
$570$	−9.34978	+	2.50527i	−0.391619	+	0.104934i
$571$	22.9971	+	13.2774i	0.962400	+	0.555642i	0.896911	−	0.442211i	$-0.145806\pi$
$571$	22.9971	+	13.2774i	0.962400	+	0.555642i	0.0654891	+	0.997853i	$0.479139\pi$
$572$	−65.8051	+	52.5250i	−2.75145	+	2.19618i
$573$		−	23.4507i		−	0.979668i
$574$	−10.5922	+	23.2681i	−0.442111	+	0.971190i
$575$	10.0430			0.418820
$576$	22.8949	−	13.2184i	0.953953	−	0.550765i
$577$	1.51893	+	5.66871i	0.0632337	+	0.235991i	0.990309	−	0.138885i	$-0.0443518\pi$
$577$	1.51893	+	5.66871i	0.0632337	+	0.235991i	−0.927075	+	0.374876i	$0.877685\pi$
$578$	−21.8455	+	5.85348i	−0.908653	+	0.243473i
$579$	−0.699244	+	2.60961i	−0.0290596	+	0.108452i
$580$	35.7772	+	35.7772i	1.48557	+	1.48557i
$581$	−23.4638	−	3.91649i	−0.973441	−	0.162483i
$582$		−	38.5194i		−	1.59668i
$583$	10.7354	+	2.87655i	0.444616	+	0.119134i
$584$	20.1803	−	34.9533i	0.835067	−	1.44638i
$585$	1.40783	−	3.59173i	0.0582067	−	0.148500i
$586$	−35.4991	+	20.4954i	−1.46645	+	0.846658i
$587$	−19.6023	+	19.6023i	−0.809073	+	0.809073i	−0.984494	−	0.175421i	$-0.943871\pi$
$587$	−19.6023	+	19.6023i	−0.809073	+	0.809073i	0.175421	+	0.984494i	$0.443871\pi$
$588$	36.9644	−	7.21696i	1.52439	−	0.297622i
$589$		−	2.01952i		−	0.0832130i
$590$	−0.413903	+	1.54471i	−0.0170401	+	0.0635946i
$591$	5.15077	+	19.2229i	0.211874	+	0.790726i
$592$	23.3946	+	87.3098i	0.961512	+	3.58841i
$593$	−2.81437	+	10.5034i	−0.115572	+	0.431322i	−0.999329	−	0.0366247i	$-0.988339\pi$
$593$	−2.81437	+	10.5034i	−0.115572	+	0.431322i	0.883757	+	0.467947i	$0.155006\pi$
$594$		−	11.7911i		−	0.483795i
$595$	14.0515	+	2.34542i	0.576054	+	0.0961530i
$596$	−29.5207	+	29.5207i	−1.20921	+	1.20921i
$597$	21.0848	−	12.1733i	0.862944	−	0.498221i
$598$	−9.31190	+	23.7569i	−0.380792	+	0.971494i
$599$	7.94959	−	13.7691i	0.324811	−	0.562590i	−0.656663	−	0.754184i	$-0.728032\pi$
$599$	7.94959	−	13.7691i	0.324811	−	0.562590i	0.981474	+	0.191594i	$0.0613658\pi$
$600$	34.1970	+	9.16306i	1.39609	+	0.374080i
$601$		−	24.0530i		−	0.981144i	−0.871401	−	0.490572i	$-0.836788\pi$
$601$		−	24.0530i		−	0.981144i	0.871401	−	0.490572i	$-0.163212\pi$
$602$	−14.2890	−	38.1695i	−0.582377	−	1.55567i
$603$	−4.90118	−	4.90118i	−0.199592	−	0.199592i
$604$	13.9164	−	51.9368i	0.566252	−	2.11328i
$605$	8.10052	−	2.17053i	0.329333	−	0.0882445i
$606$	8.13822	+	30.3723i	0.330593	+	1.23379i
$607$	−28.0098	+	16.1715i	−1.13688	+	0.656380i	−0.945657	−	0.325167i	$-0.894580\pi$
$607$	−28.0098	+	16.1715i	−1.13688	+	0.656380i	−0.191226	+	0.981546i	$0.561246\pi$
$608$	67.1872			2.72480
$609$	−2.23837	−	23.1459i	−0.0907035	−	0.937917i
$610$		−	20.6899i		−	0.837711i
$611$	22.2242	−	17.7391i	0.899094	−	0.717648i
$612$	−23.4485	−	13.5380i	−0.947848	−	0.547240i
$613$	−20.1571	+	5.40108i	−0.814138	+	0.218148i	−0.641782	−	0.766887i	$-0.721805\pi$
$613$	−20.1571	+	5.40108i	−0.814138	+	0.218148i	−0.172356	+	0.985035i	$0.555138\pi$
$614$	−50.3908	+	29.0931i	−2.03361	+	1.17410i
$615$	−3.80570			−0.153460
$616$	−10.1508	−	104.965i	−0.408989	−	4.22914i
$617$	20.2243	+	20.2243i	0.814202	+	0.814202i	0.985261	−	0.171059i	$-0.0547189\pi$
$617$	20.2243	+	20.2243i	0.814202	+	0.814202i	−0.171059	+	0.985261i	$0.554719\pi$
$618$	42.7716	+	11.4606i	1.72053	+	0.461014i
$619$	−7.64745	+	2.04913i	−0.307377	+	0.0823614i	−0.409210	−	0.912440i	$-0.634196\pi$
$619$	−7.64745	+	2.04913i	−0.307377	+	0.0823614i	0.101833	+	0.994801i	$0.467529\pi$
$620$	1.74558	−	3.02344i	0.0701044	−	0.121424i
$621$	−1.30252	−	2.25604i	−0.0522684	−	0.0905316i
$622$	43.1563	+	43.1563i	1.73041	+	1.73041i
$623$	8.94395	−	3.34823i	0.358332	−	0.134144i
$624$	−30.3578	+	41.1711i	−1.21528	+	1.64816i
$625$	4.56924	+	7.91416i	0.182770	+	0.316566i
$626$	10.3884	+	38.7699i	0.415203	+	1.54956i
$627$	7.22670	−	12.5170i	0.288607	−	0.499882i
$628$	−33.8640	−	58.6541i	−1.35132	−	2.34055i
$629$	22.6713	−	22.6713i	0.903965	−	0.903965i
$630$	4.46848	+	6.25908i	0.178028	+	0.249368i
$631$	−0.193755	+	0.193755i	−0.00771326	+	0.00771326i	−0.710953	−	0.703240i	$-0.751736\pi$
$631$	−0.193755	+	0.193755i	−0.00771326	+	0.00771326i	0.703240	+	0.710953i	$0.251736\pi$
$632$	−73.3766	−	19.6612i	−2.91876	−	0.782080i
$633$	3.14075	+	1.81331i	0.124833	+	0.0720726i
$634$	17.1316	+	9.89093i	0.680382	+	0.392819i
$635$	2.40909	−	8.99084i	0.0956017	−	0.356790i
$636$	13.7774			0.546310
$637$	−20.7640	+	14.3477i	−0.822700	+	0.568476i
$638$	−103.634			−4.10289
$639$	2.30327	−	8.59592i	0.0911160	−	0.340049i
$640$	29.1587	+	16.8348i	1.15260	+	0.665454i
$641$	−22.3947	−	12.9296i	−0.884536	−	0.510687i	−0.0123844	−	0.999923i	$-0.503942\pi$
$641$	−22.3947	−	12.9296i	−0.884536	−	0.510687i	−0.872151	+	0.489236i	$0.837276\pi$
$642$	−20.1786	−	5.40684i	−0.796385	−	0.213391i
$643$	3.84550	−	3.84550i	0.151652	−	0.151652i	−0.627204	−	0.778855i	$-0.715801\pi$
$643$	3.84550	−	3.84550i	0.151652	−	0.151652i	0.778855	+	0.627204i	$0.215801\pi$
$644$	−21.5467	−	30.1808i	−0.849058	−	1.18929i
$645$	4.29002	−	4.29002i	0.168919	−	0.168919i
$646$	−22.7633	−	39.4272i	−0.895611	−	1.55124i
$647$	2.48520	−	4.30449i	0.0977031	−	0.169227i	−0.813030	−	0.582221i	$-0.802184\pi$
$647$	2.48520	−	4.30449i	0.0977031	−	0.169227i	0.910734	+	0.412994i	$0.135517\pi$
$648$	−2.37681	−	8.87037i	−0.0933699	−	0.348461i
$649$	−1.19395	−	2.06798i	−0.0468666	−	0.0811753i
$650$	−37.3378	+	5.64451i	−1.46451	+	0.221396i
$651$	−1.50267	+	0.562537i	−0.0588944	+	0.0220475i
$652$	74.9730	+	74.9730i	2.93617	+	2.93617i
$653$	3.05534	+	5.29201i	0.119565	+	0.207092i	0.919595	−	0.392867i	$-0.128517\pi$
$653$	3.05534	+	5.29201i	0.119565	+	0.207092i	−0.800030	+	0.599959i	$0.795183\pi$
$654$	1.95508	−	3.38630i	0.0764498	−	0.132415i
$655$	−0.283655	+	0.0760050i	−0.0110833	+	0.00296976i
$656$	48.7431	+	13.0607i	1.90310	+	0.509934i
$657$	−3.10774	−	3.10774i	−0.121244	−	0.121244i
$658$	5.45655	+	56.4233i	0.212718	+	2.19961i
$659$	−10.6270			−0.413968			−0.206984	−	0.978344i	$-0.566365\pi$
$659$	−10.6270			−0.413968			−0.206984	+	0.978344i	$0.566365\pi$
$660$	21.6383	−	12.4929i	0.842270	−	0.486285i
$661$	2.39740	−	0.642383i	0.0932482	−	0.0249858i	−0.211893	−	0.977293i	$-0.567963\pi$
$661$	2.39740	−	0.642383i	0.0932482	−	0.0249858i	0.305141	+	0.952307i	$0.401296\pi$
$662$	−58.2311	−	33.6197i	−2.26321	−	1.30667i
$663$	18.0313	+	2.02364i	0.700279	+	0.0785917i
$664$			82.5685i			3.20428i
$665$	0.907416	+	9.38311i	0.0351881	+	0.363862i
$666$	17.3084			0.670686
$667$	−19.8286	+	11.4480i	−0.767766	+	0.443270i
$668$	−24.7566	−	92.3930i	−0.957862	−	3.57479i
$669$	−20.3883	+	5.46303i	−0.788257	+	0.211213i
$670$	5.21454	−	19.4609i	0.201455	−	0.751842i
$671$	21.8452	+	21.8452i	0.843326	+	0.843326i
$672$	−18.7149	−	49.9922i	−0.721944	−	1.92849i
$673$			19.4334i			0.749101i	0.927206	+	0.374551i	$0.122203\pi$
$673$			19.4334i			0.749101i	−0.927206	+	0.374551i	$0.877797\pi$
$674$	−2.94289	−	0.788545i	−0.113356	−	0.0303736i
$675$	1.92760	−	3.33870i	0.0741932	−	0.128506i
$676$	15.5043	−	68.2044i	0.596320	−	2.62324i
$677$	19.5099	−	11.2640i	0.749826	−	0.432912i	−0.0758049	−	0.997123i	$-0.524153\pi$
$677$	19.5099	−	11.2640i	0.749826	−	0.432912i	0.825631	+	0.564210i	$0.190819\pi$
$678$	−6.30887	+	6.30887i	−0.242291	+	0.242291i
$679$	−37.0019	−	6.17622i	−1.42000	−	0.237022i
$680$		−	49.4468i		−	1.89620i
$681$	0.0674245	−	0.251632i	0.00258371	−	0.00964254i
$682$	1.85074	+	6.90707i	0.0708687	+	0.264486i
$683$	3.53426	+	13.1900i	0.135235	+	0.504703i	0.999997	+	0.00252119i	$0.000802520\pi$
$683$	3.53426	+	13.1900i	0.135235	+	0.504703i	−0.864762	+	0.502182i	$0.832531\pi$
$684$	4.63723	−	17.3064i	0.177309	−	0.661727i
$685$		−	14.4160i		−	0.550807i
$686$	−1.37959	−	50.2947i	−0.0526730	−	1.92026i
$687$	7.89105	−	7.89105i	0.301062	−	0.301062i
$688$	−69.6692	+	40.2235i	−2.65611	+	1.53351i
$689$	−8.46075	+	3.69580i	−0.322329	+	0.140799i
$690$	3.78608	−	6.55768i	0.144133	−	0.249647i
$691$	45.0162	+	12.0621i	1.71250	+	0.458862i	0.976034	−	0.217616i	$-0.0698281\pi$
$691$	45.0162	+	12.0621i	1.71250	+	0.458862i	0.736463	+	0.676478i	$0.236495\pi$
$692$		−	67.6390i		−	2.57125i
$693$	−11.3266	−	1.89059i	−0.430261	−	0.0718177i
$694$	−8.53334	−	8.53334i	−0.323921	−	0.323921i
$695$	−2.97850	+	11.1159i	−0.112981	+	0.421651i
$696$	−77.9628	+	20.8901i	−2.95517	+	0.791836i
$697$	−4.63274	−	17.2896i	−0.175478	−	0.654892i
$698$	62.8906	−	36.3099i	2.38044	−	1.37435i
$699$	0.636064			0.0240582
$700$	22.7372	−	49.9470i	0.859384	−	1.88782i
$701$		−	43.0033i		−	1.62421i	−0.583510	−	0.812106i	$-0.698321\pi$
$701$		−	43.0033i		−	1.62421i	0.583510	−	0.812106i	$-0.301679\pi$
$702$	6.11051	+	7.65546i	0.230626	+	0.288937i
$703$	18.3739	+	10.6082i	0.692986	+	0.400095i
$704$	−110.833	+	29.6975i	−4.17717	+	1.11927i
$705$	−7.30784	+	4.21918i	−0.275229	+	0.158904i
$706$	24.1267			0.908020
$707$	30.4806	−	2.94769i	1.14634	−	0.110859i
$708$	−2.09311	−	2.09311i	−0.0786641	−	0.0786641i
$709$	5.38572	+	1.44310i	0.202265	+	0.0541968i	0.358529	−	0.933519i	$-0.383278\pi$
$709$	5.38572	+	1.44310i	0.202265	+	0.0541968i	−0.156264	+	0.987715i	$0.549945\pi$
$710$	24.9860	−	6.69498i	0.937707	−	0.251258i
$711$	−4.13605	+	7.16384i	−0.155114	+	0.268665i
$712$	−16.5740	−	28.7071i	−0.621138	−	1.07584i
$713$	1.11711	+	1.11711i	0.0418361	+	0.0418361i
$714$	−22.9961	+	27.9200i	−0.860606	+	1.04488i
$715$	−9.93692	+	13.4764i	−0.371620	+	0.503989i
$716$	26.5717	+	46.0235i	0.993030	+	1.71998i
$717$	−4.48502	−	16.7383i	−0.167496	−	0.625104i
$718$	30.2219	−	52.3459i	1.12787	−	1.95353i
$719$	−5.49906	−	9.52465i	−0.205080	−	0.355210i	0.745078	−	0.666977i	$-0.232412\pi$
$719$	−5.49906	−	9.52465i	−0.205080	−	0.355210i	−0.950158	+	0.311768i	$0.899079\pi$
$720$	10.7338	−	10.7338i	0.400024	−	0.400024i
$721$	17.8671	−	39.2489i	0.665407	−	1.46171i
$722$	−15.1962	+	15.1962i	−0.565543	+	0.565543i
$723$	12.4088	+	3.32492i	0.461487	+	0.123655i
$724$	−62.8036	−	36.2597i	−2.33408	−	1.34758i
$725$	−29.3442	−	16.9419i	−1.08982	−	0.629206i
$726$	−5.51109	+	20.5677i	−0.204536	+	0.763337i
$727$	−37.1962			−1.37953			−0.689765	−	0.724034i	$-0.742286\pi$
$727$	−37.1962			−1.37953			−0.689765	+	0.724034i	$0.742286\pi$
$728$	60.9863	+	62.8884i	2.26030	+	2.33080i
$729$	−1.00000			−0.0370370
$730$	3.30643	−	12.3398i	0.122377	−	0.456716i
$731$	24.7123	+	14.2677i	0.914018	+	0.527708i
$732$	33.1661	+	19.1485i	1.22586	+	0.707748i
$733$	−20.2144	−	5.41643i	−0.746635	−	0.200060i	−0.134610	−	0.990899i	$-0.542978\pi$
$733$	−20.2144	−	5.41643i	−0.746635	−	0.200060i	−0.612025	+	0.790838i	$0.709645\pi$
$734$	42.3427	−	42.3427i	1.56290	−	1.56290i
$735$	6.72897	−	3.28884i	0.248202	−	0.121311i
$736$	−37.1649	+	37.1649i	−1.36992	+	1.36992i
$737$	15.0419	+	26.0533i	0.554076	+	0.959687i
$738$	4.83144	−	8.36829i	0.177848	−	0.308041i
$739$	−6.93552	−	25.8837i	−0.255127	−	0.952147i	−0.968020	−	0.250874i	$-0.919282\pi$
$739$	−6.93552	−	25.8837i	−0.255127	−	0.952147i	0.712893	−	0.701273i	$-0.247385\pi$
$740$	18.3385	+	31.7632i	0.674136	+	1.16764i
$741$	1.79471	+	11.8718i	0.0659305	+	0.436123i
$742$	3.03024	−	18.1542i	0.111244	−	0.666463i
$743$	−28.9424	−	28.9424i	−1.06179	−	1.06179i	−0.997961	−	0.0638329i	$-0.979668\pi$
$743$	−28.9424	−	28.9424i	−1.06179	−	1.06179i	−0.0638329	−	0.997961i	$-0.520332\pi$
$744$	2.78460	+	4.82308i	0.102089	+	0.176823i
$745$	−4.15114	+	7.18999i	−0.152086	+	0.263421i
$746$	8.45553	−	2.26565i	0.309579	−	0.0829515i
$747$	8.68480	+	2.32708i	0.317760	+	0.0851436i
$748$	83.0970	+	83.0970i	3.03833	+	3.03833i
$749$	−8.42926	+	18.5167i	−0.307999	+	0.676584i
$750$	25.7396			0.939878
$751$	10.2089	−	5.89412i	0.372529	−	0.215080i	−0.302034	−	0.953297i	$-0.597666\pi$
$751$	10.2089	−	5.89412i	0.372529	−	0.215080i	0.674563	+	0.738218i	$0.264332\pi$
$752$	108.078	−	28.9594i	3.94120	−	1.05604i
$753$	0.170740	+	0.0985769i	0.00622212	+	0.00359234i
$754$	67.2848	−	53.7061i	2.45037	−	1.95586i
$755$		−	10.6927i		−	0.389148i
$756$	−14.1689	+	1.37024i	−0.515319	+	0.0498352i
$757$	−8.01916			−0.291461			−0.145731	−	0.989324i	$-0.546553\pi$
$757$	−8.01916			−0.291461			−0.145731	+	0.989324i	$0.546553\pi$
$758$	17.7297	−	10.2363i	0.643973	−	0.371798i
$759$	2.92636	+	10.9213i	0.106220	+	0.396420i
$760$	31.6054	−	8.46864i	1.14645	−	0.307190i
$761$	−6.05831	+	22.6099i	−0.219614	+	0.819609i	0.764878	+	0.644176i	$0.222799\pi$
$761$	−6.05831	+	22.6099i	−0.219614	+	0.819609i	−0.984491	+	0.175434i	$0.943867\pi$
$762$	16.7114	+	16.7114i	0.605391	+	0.605391i
$763$	−2.93941	−	2.42102i	−0.106414	−	0.0876468i
$764$			126.173i			4.56477i
$765$	−5.20096	−	1.39359i	−0.188041	−	0.0503855i
$766$	−9.56417	+	16.5656i	−0.345568	+	0.598541i
$767$	1.84687	+	0.723908i	0.0666865	+	0.0261388i
$768$	−28.2459	+	16.3078i	−1.01924	+	0.588456i
$769$	−5.68664	+	5.68664i	−0.205066	+	0.205066i	−0.802166	−	0.597101i	$-0.796319\pi$
$769$	−5.68664	+	5.68664i	−0.205066	+	0.205066i	0.597101	+	0.802166i	$0.296319\pi$
$770$	−11.7024	−	31.2601i	−0.421727	−	1.12654i
$771$		−	7.67671i		−	0.276470i
$772$	3.76217	−	14.0406i	0.135403	−	0.505333i
$773$	5.84826	+	21.8260i	0.210347	+	0.785027i	0.987753	+	0.156027i	$0.0498687\pi$
$773$	5.84826	+	21.8260i	0.210347	+	0.785027i	−0.777406	+	0.629000i	$0.783465\pi$
$774$	3.98697	+	14.8796i	0.143309	+	0.534835i
$775$	−0.605115	+	2.25832i	−0.0217364	+	0.0811212i
$776$			130.209i			4.67422i
$777$	2.77523	−	16.6265i	0.0995609	−	0.596471i
$778$	54.3193	−	54.3193i	1.94744	−	1.94744i
$779$	10.2577	−	5.92231i	0.367522	−	0.212189i
$780$	−7.57461	+	19.3247i	−0.271215	+	0.691935i
$781$	−19.3124	+	33.4500i	−0.691051	+	1.19694i
$782$	34.4010	+	9.21772i	1.23018	+	0.329625i
$783$			8.78912i			0.314098i
$784$	−97.4711	+	19.0303i	−3.48111	+	0.679655i
$785$	−9.52378	−	9.52378i	−0.339918	−	0.339918i
$786$	0.192981	−	0.720215i	0.00688340	−	0.0256892i
$787$	−16.3828	+	4.38975i	−0.583982	+	0.156478i	−0.538702	−	0.842497i	$-0.681085\pi$
$787$	−16.3828	+	4.38975i	−0.583982	+	0.156478i	−0.0452809	+	0.998974i	$0.514418\pi$
$788$	−27.7129	−	103.426i	−0.987230	−	3.68439i
$789$	−6.98162	+	4.03084i	−0.248552	+	0.143502i
$790$	−24.0447			−0.855472
$791$	5.04875	+	7.07188i	0.179513	+	0.251447i
$792$			39.8580i			1.41629i
$793$	−25.5040	−	2.86229i	−0.905674	−	0.101643i
$794$	4.15419	+	2.39842i	0.147427	+	0.0851169i
$795$	2.64648	−	0.709121i	0.0938609	−	0.0251499i
$796$	−113.443	+	65.4966i	−4.02090	+	2.32147i
$797$	−42.7984			−1.51600			−0.757998	−	0.652257i	$-0.773822\pi$
$797$	−42.7984			−1.51600			−0.757998	+	0.652257i	$0.773822\pi$
$798$	−21.7844	−	9.91682i	−0.771159	−	0.351051i
$799$	−28.0641	−	28.0641i	−0.992837	−	0.992837i
$800$	−75.1317	−	20.1315i	−2.65631	−	0.711755i
$801$	−3.48661	+	0.934235i	−0.123193	+	0.0330096i
$802$	−46.6659	+	80.8277i	−1.64783	+	2.85412i
$803$	9.53776	+	16.5199i	0.336580	+	0.582974i
$804$	26.3700	+	26.3700i	0.929999	+	0.929999i
$805$	−5.69226	−	4.68838i	−0.200626	−	0.165244i
$806$	−4.78106	−	3.52535i	−0.168406	−	0.124175i
$807$	−5.50447	−	9.53401i	−0.193766	−	0.335613i
$808$	−27.5099	−	102.668i	−0.967796	−	3.61186i
$809$	16.0864	−	27.8625i	0.565569	−	0.979594i	−0.431428	−	0.902147i	$-0.641990\pi$
$809$	16.0864	−	27.8625i	0.565569	−	0.979594i	0.996997	−	0.0774461i	$-0.0246766\pi$
$810$	−1.45336	−	2.51730i	−0.0510660	−	0.0884489i
$811$	−4.05760	+	4.05760i	−0.142481	+	0.142481i	−0.774750	−	0.632268i	$-0.782124\pi$
$811$	−4.05760	+	4.05760i	−0.142481	+	0.142481i	0.632268	+	0.774750i	$0.282124\pi$
$812$	12.0432	+	124.533i	0.422634	+	4.37023i
$813$	9.91148	−	9.91148i	0.347611	−	0.347611i
$814$	−72.5633	−	19.4433i	−2.54334	−	0.681486i
$815$	18.2603	+	10.5426i	0.639629	+	0.369290i
$816$	61.8310	+	35.6981i	2.16452	+	1.24968i
$817$	−4.88718	+	18.2392i	−0.170981	+	0.638109i
$818$	−84.3673			−2.94983
$819$	8.33361	−	4.64229i	0.291200	−	0.162215i
$820$	20.4759			0.715050
$821$	7.81596	−	29.1696i	0.272779	−	1.01802i	−0.684536	−	0.728979i	$-0.739995\pi$
$821$	7.81596	−	29.1696i	0.272779	−	1.01802i	0.957315	−	0.289046i	$-0.0933381\pi$
$822$	31.6991	+	18.3015i	1.10563	+	0.638338i
$823$	43.7643	+	25.2673i	1.52553	+	0.880763i	0.999542	+	0.0302686i	$0.00963628\pi$
$823$	43.7643	+	25.2673i	1.52553	+	0.880763i	0.525984	+	0.850494i	$0.323697\pi$
$824$	−144.583	−	38.7408i	−5.03677	−	1.34960i
$825$	−11.8317	+	11.8317i	−0.411928	+	0.411928i
$826$	−3.21842	+	2.29769i	−0.111983	+	0.0799469i
$827$	28.0479	−	28.0479i	0.975322	−	0.975322i	−0.0243810	−	0.999703i	$-0.507761\pi$
$827$	28.0479	−	28.0479i	0.975322	−	0.975322i	0.999703	+	0.0243810i	$0.00776149\pi$
$828$	7.00801	+	12.1382i	0.243545	+	0.421833i
$829$	15.2364	−	26.3902i	0.529181	−	0.916568i	−0.470240	−	0.882539i	$-0.655833\pi$
$829$	15.2364	−	26.3902i	0.529181	−	0.916568i	0.999421	−	0.0340297i	$-0.0108341\pi$
$830$	6.76420	+	25.2443i	0.234789	+	0.876243i
$831$	−11.9810	−	20.7517i	−0.415615	−	0.719867i
$832$	56.5687	−	76.7182i	1.96117	−	2.65972i
$833$	23.1328	+	26.5668i	0.801505	+	0.920484i
$834$	−20.6614	−	20.6614i	−0.715445	−	0.715445i
$835$	−9.51090	−	16.4734i	−0.329138	−	0.570084i
$836$	−38.8821	+	67.3458i	−1.34477	+	2.32920i
$837$	0.585786	−	0.156961i	0.0202477	−	0.00542536i
$838$	2.71027	+	0.726213i	0.0936246	+	0.0250866i
$839$	−4.53265	−	4.53265i	−0.156485	−	0.156485i	0.624522	−	0.781007i	$-0.285294\pi$
$839$	−4.53265	−	4.53265i	−0.156485	−	0.156485i	−0.781007	+	0.624522i	$0.785294\pi$
$840$	−15.1050	−	21.1578i	−0.521171	−	0.730014i
$841$	48.2487			1.66375
$842$	35.9938	−	20.7810i	1.24043	−	0.716162i
$843$	−24.6207	+	6.59709i	−0.847982	+	0.227216i
$844$	−16.8983	−	9.75622i	−0.581663	−	0.335823i
$845$	−0.532272	−	13.8992i	−0.0183107	−	0.478149i
$846$		−	21.4255i		−	0.736623i
$847$	18.8737	+	8.59179i	0.648508	+	0.295217i
$848$	−36.3295			−1.24756
$849$	9.75724	−	5.63335i	0.334868	−	0.193336i
$850$	13.6413	+	50.9099i	0.467891	+	1.74619i
$851$	−16.0316	+	4.29566i	−0.549556	+	0.147253i
$852$	−12.3924	+	46.2490i	−0.424556	+	1.58446i
$853$	−19.9644	−	19.9644i	−0.683568	−	0.683568i	0.277234	−	0.960802i	$-0.410582\pi$
$853$	−19.9644	−	19.9644i	−0.683568	−	0.683568i	−0.960802	+	0.277234i	$0.910582\pi$
$854$	32.5263	−	39.4908i	1.11303	−	1.35135i
$855$		−	3.56303i		−	0.121853i
$856$	68.2104	+	18.2769i	2.33138	+	0.624693i
$857$	−13.8418	+	23.9747i	−0.472828	+	0.818961i	−0.999516	−	0.0310968i	$-0.990100\pi$
$857$	−13.8418	+	23.9747i	−0.472828	+	0.818961i	0.526689	+	0.850058i	$0.323433\pi$
$858$	−17.0179	−	38.9588i	−0.580981	−	1.33003i
$859$	7.21915	−	4.16798i	0.246314	−	0.142210i	−0.371761	−	0.928328i	$-0.621246\pi$
$859$	7.21915	−	4.16798i	0.246314	−	0.142210i	0.618075	+	0.786119i	$0.287913\pi$
$860$	−23.0818	+	23.0818i	−0.787082	+	0.787082i
$861$	−7.26393	−	5.98286i	−0.247554	−	0.203895i
$862$			79.7217i			2.71533i
$863$	−7.26831	+	27.1257i	−0.247416	+	0.923369i	0.724738	+	0.689025i	$0.241961\pi$
$863$	−7.26831	+	27.1257i	−0.247416	+	0.923369i	−0.972154	+	0.234344i	$0.924706\pi$
$864$	5.22191	+	19.4884i	0.177653	+	0.663010i
$865$	−3.48137	−	12.9926i	−0.118370	−	0.441763i
$866$	12.7988	−	47.7657i	0.434921	−	1.62315i
$867$		−	8.32492i		−	0.282729i
$868$	8.08489	−	3.02664i	0.274419	−	0.102731i
$869$	25.3873	−	25.3873i	0.861207	−	0.861207i
$870$	−22.1249	+	12.7738i	−0.750103	+	0.433072i
$871$	−23.2677	−	9.12012i	−0.788395	−	0.309024i
$872$	−6.60884	+	11.4468i	−0.223804	+	0.387639i
$873$	13.6957	+	3.66976i	0.463531	+	0.124203i
$874$			23.5671i			0.797170i
$875$	4.12710	−	24.7255i	0.139522	−	0.835876i
$876$	16.7207	+	16.7207i	0.564940	+	0.564940i
$877$	−3.96440	+	14.7953i	−0.133868	+	0.499603i	−1.00000		0.000212721i	$-0.999932\pi$
$877$	−3.96440	+	14.7953i	−0.133868	+	0.499603i	0.866132	+	0.499816i	$0.166599\pi$
$878$	84.2117	−	22.5645i	2.84201	−	0.761514i
$879$	−3.90521	−	14.5745i	−0.131720	−	0.491584i
$880$	−57.0578	+	32.9423i	−1.92342	+	1.11049i
$881$	44.0182			1.48301			0.741506	−	0.670946i	$-0.234112\pi$
$881$	44.0182			1.48301			0.741506	+	0.670946i	$0.234112\pi$
$882$	−1.31082	+	18.9715i	−0.0441375	+	0.638804i
$883$			25.4100i			0.855115i	0.903988	+	0.427558i	$0.140626\pi$
$883$			25.4100i			0.855115i	−0.903988	+	0.427558i	$0.859374\pi$
$884$	−97.0146	−	10.8879i	−3.26296	−	0.366199i
$885$	−0.509795	−	0.294330i	−0.0171366	−	0.00989379i
$886$	−38.3300	+	10.2705i	−1.28772	+	0.345044i
$887$	9.08684	−	5.24629i	0.305106	−	0.176153i	−0.339628	−	0.940560i	$-0.610301\pi$
$887$	9.08684	−	5.24629i	0.305106	−	0.176153i	0.644735	+	0.764407i	$0.276968\pi$
$888$	−58.5081			−1.96340
$889$	18.7326	−	13.3735i	0.628270	−	0.448533i
$890$	−7.41906	−	7.41906i	−0.248688	−	0.248688i
$891$	4.19238	+	1.12334i	0.140450	+	0.0376335i
$892$	109.696	−	29.3929i	3.67289	−	0.984149i
$893$	13.1315	−	22.7445i	0.439430	−	0.761116i
$894$	−10.5400	−	18.2558i	−0.352510	−	0.610564i
$895$	7.47292	+	7.47292i	0.249792	+	0.249792i
$896$	29.1896	+	77.9725i	0.975155	+	2.60488i
$897$	−7.55973	−	5.57422i	−0.252412	−	0.186118i
$898$	−13.4505	−	23.2969i	−0.448848	−	0.777427i
$899$	−1.37955	−	5.14855i	−0.0460105	−	0.171714i
$900$	−10.3711	+	17.9633i	−0.345704	+	0.598777i
$901$	6.44321	+	11.1600i	0.214654	+	0.371792i
$902$	−29.6557	+	29.6557i	−0.987427	+	0.987427i
$903$	14.9326	−	1.44409i	0.496927	−	0.0480565i
$904$	21.3261	−	21.3261i	0.709295	−	0.709295i
$905$	−13.9301	−	3.73256i	−0.463052	−	0.124074i
$906$	23.5121	+	13.5747i	0.781137	+	0.450989i
$907$	21.7808	+	12.5751i	0.723219	+	0.417551i	0.815936	−	0.578142i	$-0.196222\pi$
$907$	21.7808	+	12.5751i	0.723219	+	0.417551i	−0.0927170	+	0.995693i	$0.529555\pi$
$908$	−0.362766	+	1.35386i	−0.0120388	+	0.0449295i
$909$	−11.5743			−0.383896
$910$	23.7978	+	14.2313i	0.788890	+	0.471761i
$911$	8.58064			0.284289			0.142145	−	0.989846i	$-0.454600\pi$
$911$	8.58064			0.284289			0.142145	+	0.989846i	$0.454600\pi$
$912$	−12.2279	+	45.6351i	−0.404905	+	1.51113i
$913$	−33.7959	−	19.5120i	−1.11848	−	0.645755i
$914$	49.8396	+	28.7749i	1.64855	+	0.951789i
$915$	7.35639	+	1.97114i	0.243195	+	0.0651638i
$916$	−42.4565	+	42.4565i	−1.40280	+	1.40280i
$917$	−0.660897	−	0.300857i	−0.0218247	−	0.00993519i
$918$	9.66712	−	9.66712i	0.319063	−	0.319063i
$919$	−8.57833	−	14.8581i	−0.282973	−	0.490123i	0.689143	−	0.724626i	$-0.257987\pi$
$919$	−8.57833	−	14.8581i	−0.282973	−	0.490123i	−0.972116	+	0.234502i	$0.924654\pi$
$920$	−12.7982	+	22.1672i	−0.421945	+	0.730830i
$921$	−5.54343	−	20.6884i	−0.182662	−	0.681704i
$922$	22.5700	+	39.0924i	0.743304	+	1.28744i
$923$	−4.79613	−	31.7259i	−0.157866	−	1.04427i
$924$	60.9408	+	10.1720i	2.00481	+	0.334635i
$925$	−17.3680	−	17.3680i	−0.571055	−	0.571055i
$926$	18.2036	+	31.5296i	0.598207	+	1.03613i
$927$	−8.14974	+	14.1158i	−0.267673	+	0.463623i
$928$	171.286	−	45.8960i	5.62274	−	1.50661i
$929$	−36.9354	−	9.89680i	−1.21181	−	0.324704i	−0.404338	−	0.914609i	$-0.632498\pi$
$929$	−36.9354	−	9.89680i	−1.21181	−	0.324704i	−0.807472	+	0.589906i	$0.799165\pi$
$930$	1.24648	+	1.24648i	0.0408736	+	0.0408736i
$931$	−13.0190	+	19.3361i	−0.426682	+	0.633714i
$932$	−3.42224			−0.112099
$933$	−19.4559	+	11.2329i	−0.636958	+	0.367748i
$934$	34.5481	−	9.25712i	1.13045	−	0.302902i
$935$	20.2389	+	11.6850i	0.661884	+	0.382139i
$936$	−20.6556	−	25.8780i	−0.675149	−	0.845850i
$937$			29.1777i			0.953192i	0.879122	+	0.476596i	$0.158130\pi$
$937$			29.1777i			0.953192i	−0.879122	+	0.476596i	$0.841870\pi$
$938$	40.5472	−	28.9474i	1.32391	−	0.945165i
$939$	−14.7745			−0.482148
$940$	39.3187	−	22.7006i	1.28243	−	0.740413i
$941$	−5.17882	−	19.3276i	−0.168825	−	0.630062i	−0.997521	−	0.0703641i	$-0.977584\pi$
$941$	−5.17882	−	19.3276i	−0.168825	−	0.630062i	0.828697	−	0.559698i	$-0.189083\pi$
$942$	33.0324	−	8.85101i	1.07625	−	0.288381i
$943$	−2.39817	+	8.95008i	−0.0780951	+	0.291455i
$944$	5.51931	+	5.51931i	0.179638	+	0.179638i
$945$	−2.65116	+	0.992479i	−0.0862421	+	0.0322854i
$946$		−	66.8596i		−	2.17379i
$947$	−44.9812	−	12.0527i	−1.46169	−	0.391660i	−0.561619	−	0.827396i	$-0.689821\pi$
$947$	−44.9812	−	12.0527i	−1.46169	−	0.391660i	−0.900074	+	0.435736i	$0.856488\pi$
$948$	22.2533	−	38.5439i	0.722754	−	1.25185i
$949$	−14.7536	−	5.78288i	−0.478921	−	0.187720i
$950$	−30.2043	+	17.4384i	−0.979956	+	0.565778i
$951$	−5.14889	+	5.14889i	−0.166964	+	0.166964i
$952$	77.7344	−	94.3791i	2.51939	−	3.05884i
$953$		−	29.0930i		−	0.942415i	−0.882022	−	0.471207i	$-0.843818\pi$
$953$		−	29.0930i		−	0.942415i	0.882022	−	0.471207i	$-0.156182\pi$
$954$	−1.80050	+	6.71955i	−0.0582933	+	0.217553i
$955$	6.49409	+	24.2363i	0.210144	+	0.784268i
$956$	24.1309	+	90.0579i	0.780450	+	2.91268i
$957$	9.87322	−	36.8474i	0.319156	−	1.19111i
$958$		−	19.2871i		−	0.623138i
$959$	22.6631	−	27.5158i	0.731831	−	0.888532i
$960$	−20.0013	+	20.0013i	−0.645539	+	0.645539i
$961$	26.5283	−	15.3161i	0.855751	−	0.494068i
$962$	57.1882	−	24.9808i	1.84382	−	0.805413i
$963$	3.84485	−	6.65947i	0.123898	−	0.214598i
$964$	−66.7634	−	17.8892i	−2.15030	−	0.576172i
$965$		−	2.89067i		−	0.0930540i
$966$	17.5357	−	6.56461i	0.564201	−	0.211213i
$967$	−14.5879	−	14.5879i	−0.469116	−	0.469116i	0.432512	−	0.901628i	$-0.357627\pi$
$967$	−14.5879	−	14.5879i	−0.469116	−	0.469116i	−0.901628	+	0.432512i	$0.857627\pi$
$968$	18.6293	−	69.5256i	0.598770	−	2.23464i
$969$	16.1872	−	4.33734i	0.520007	−	0.139335i
$970$	10.6670	+	39.8098i	0.342497	+	1.27821i
$971$	−9.77670	+	5.64458i	−0.313749	+	0.181143i	−0.648603	−	0.761127i	$-0.724646\pi$
$971$	−9.77670	+	5.64458i	−0.313749	+	0.181143i	0.334854	+	0.942270i	$0.391313\pi$
$972$	5.38034			0.172574
$973$	−23.1602	+	16.5345i	−0.742482	+	0.530072i
$974$			30.4092i			0.974372i
$975$	1.55026	−	13.8134i	0.0496482	−	0.442382i
$976$	−87.4555	−	50.4924i	−2.79938	−	1.61622i
$977$	−7.33971	+	1.96667i	−0.234818	+	0.0629194i	−0.374309	−	0.927304i	$-0.622120\pi$
$977$	−7.33971	+	1.96667i	−0.234818	+	0.0629194i	0.139491	+	0.990223i	$0.455453\pi$
$978$	−46.3638	+	26.7682i	−1.48255	+	0.855951i
$979$	15.6667			0.500709
$980$	−36.2041	+	17.6951i	−1.15650	+	0.565249i
$981$	1.01775	+	1.01775i	0.0324943	+	0.0324943i
$982$	−53.5129	−	14.3387i	−1.70767	−	0.457567i
$983$	1.30291	−	0.349113i	0.0415563	−	0.0111350i	−0.237981	−	0.971270i	$-0.576486\pi$
$983$	1.30291	−	0.349113i	0.0415563	−	0.0111350i	0.279537	+	0.960135i	$0.409819\pi$
$984$	−16.3319	+	28.2877i	−0.520641	+	0.901777i
$985$	−10.6466	−	18.4405i	−0.339230	−	0.587563i
$986$	−84.9655	−	84.9655i	−2.70585	−	2.70585i
$987$	−20.5814	−	3.43537i	−0.655112	−	0.109349i
$988$	−9.65617	−	63.8745i	−0.307204	−	2.03212i
$989$	−7.38574	−	12.7925i	−0.234853	−	0.406777i
$990$	3.26526	+	12.1861i	0.103777	+	0.387300i
$991$	8.96512	−	15.5280i	0.284787	−	0.493265i	−0.687771	−	0.725928i	$-0.741411\pi$
$991$	8.96512	−	15.5280i	0.284787	−	0.493265i	0.972557	+	0.232663i	$0.0747440\pi$
$992$	−6.11784	−	10.5964i	−0.194242	−	0.336436i
$993$	17.5013	−	17.5013i	0.555388	−	0.555388i
$994$	58.2158	+	26.5013i	1.84649	+	0.840571i
$995$	−18.4200	+	18.4200i	−0.583954	+	0.583954i
$996$	−46.7271	−	12.5205i	−1.48061	−	0.396727i
$997$	21.8663	+	12.6245i	0.692512	+	0.399822i	0.804553	−	0.593881i	$-0.202405\pi$
$997$	21.8663	+	12.6245i	0.692512	+	0.399822i	−0.112040	+	0.993704i	$0.535739\pi$
$998$	13.7904	+	7.96188i	0.436527	+	0.252029i
$999$	−1.64898	+	6.15406i	−0.0521713	+	0.194706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.a.73.9	✓	36
3.2	odd	2		819.2.fn.f.73.1		36
7.5	odd	6		273.2.bz.b.229.1	yes	36
13.5	odd	4		273.2.bz.b.31.1	yes	36
21.5	even	6		819.2.fn.g.775.9		36
39.5	even	4		819.2.fn.g.577.9		36
91.5	even	12	inner	273.2.bz.a.187.9	yes	36
273.5	odd	12		819.2.fn.f.460.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.9	✓	36	1.1	even	1	trivial
273.2.bz.a.187.9	yes	36	91.5	even	12	inner
273.2.bz.b.31.1	yes	36	13.5	odd	4
273.2.bz.b.229.1	yes	36	7.5	odd	6
819.2.fn.f.73.1		36	3.2	odd	2
819.2.fn.f.460.1		36	273.5	odd	12
819.2.fn.g.577.9		36	39.5	even	4
819.2.fn.g.775.9		36	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.703128 - 2.62411i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-4.65951 - 2.69017i) q^{4} +(-1.03350 - 0.276925i) q^{5} +(1.92098 - 1.92098i) q^{6} +(-1.53729 - 2.15331i) q^{7} +(-6.49357 + 6.49357i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.703128 - 2.62411i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-4.65951 - 2.69017i) q^{4} +(-1.03350 - 0.276925i) q^{5} +(1.92098 - 1.92098i) q^{6} +(-1.53729 - 2.15331i) q^{7} +(-6.49357 + 6.49357i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.45336 + 2.51730i) q^{10} +(-1.12334 - 4.19238i) q^{11} +(-2.69017 - 4.65951i) q^{12} +(2.90196 + 2.13978i) q^{13} +(-6.73143 + 2.51996i) q^{14} +(-0.756573 - 0.756573i) q^{15} +(7.09368 + 12.2866i) q^{16} +(2.51619 - 4.35817i) q^{17} +(2.62411 - 0.703128i) q^{18} +(3.21660 + 0.861885i) q^{19} +(4.07062 + 4.07062i) q^{20} +(-0.254675 - 2.63347i) q^{21} -11.7911 q^{22} +(-2.25604 + 1.30252i) q^{23} +(-8.87037 + 2.37681i) q^{24} +(-3.33870 - 1.92760i) q^{25} +(7.65546 - 6.11051i) q^{26} +1.00000i q^{27} +(1.37024 + 14.1689i) q^{28} +8.78912 q^{29} +(-2.51730 + 1.45336i) q^{30} +(-0.156961 - 0.585786i) q^{31} +(19.4884 - 5.22191i) q^{32} +(1.12334 - 4.19238i) q^{33} +(-9.66712 - 9.66712i) q^{34} +(0.992479 + 2.65116i) q^{35} -5.38034i q^{36} +(6.15406 + 1.64898i) q^{37} +(4.52336 - 7.83469i) q^{38} +(1.44328 + 3.30408i) q^{39} +(8.50932 - 4.91286i) q^{40} +(2.51509 - 2.51509i) q^{41} +(-7.08957 - 1.18337i) q^{42} +5.67033i q^{43} +(-6.04398 + 22.5564i) q^{44} +(-0.276925 - 1.03350i) q^{45} +(1.83168 + 6.83592i) q^{46} +(2.04121 - 7.61792i) q^{47} +14.1874i q^{48} +(-2.27349 + 6.62052i) q^{49} +(-7.40575 + 7.40575i) q^{50} +(4.35817 - 2.51619i) q^{51} +(-7.76533 - 17.7771i) q^{52} +(-1.28035 + 2.21763i) q^{53} +(2.62411 + 0.703128i) q^{54} +4.64390i q^{55} +(23.9651 + 4.00018i) q^{56} +(2.35471 + 2.35471i) q^{57} +(6.17988 - 23.0636i) q^{58} +(0.531425 - 0.142395i) q^{59} +(1.48995 + 5.56057i) q^{60} +(-6.16432 + 3.55897i) q^{61} -1.64753 q^{62} +(1.09618 - 2.40799i) q^{63} -26.4367i q^{64} +(-2.40661 - 3.01508i) q^{65} +(-10.2114 - 5.89556i) q^{66} +(-6.69514 + 1.79396i) q^{67} +(-23.4485 + 13.5380i) q^{68} -2.60505 q^{69} +(7.65476 - 0.740272i) q^{70} +(-6.29265 - 6.29265i) q^{71} +(-8.87037 - 2.37681i) q^{72} +(-4.24525 + 1.13751i) q^{73} +(8.65418 - 14.9895i) q^{74} +(-1.92760 - 3.33870i) q^{75} +(-12.6692 - 12.6692i) q^{76} +(-7.30059 + 8.86381i) q^{77} +(9.68508 - 1.46413i) q^{78} +(4.13605 + 7.16384i) q^{79} +(-3.92883 - 14.6626i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.83144 - 8.36829i) q^{82} +(6.35771 - 6.35771i) q^{83} +(-5.89780 + 12.9558i) q^{84} +(-3.80737 + 3.80737i) q^{85} +(14.8796 + 3.98697i) q^{86} +(7.61160 + 4.39456i) q^{87} +(34.5180 + 19.9290i) q^{88} +(-0.934235 + 3.48661i) q^{89} -2.90673 q^{90} +(0.146462 - 9.53827i) q^{91} +14.0160 q^{92} +(0.156961 - 0.585786i) q^{93} +(-18.5550 - 10.7127i) q^{94} +(-3.08567 - 1.78151i) q^{95} +(19.4884 + 5.22191i) q^{96} +(10.0260 - 10.0260i) q^{97} +(15.7744 + 10.6210i) q^{98} +(3.06904 - 3.06904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q - 6 * q^7 + 18 * q^9	\( 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

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