LMFDB - Embedded newform 209.2.f.b.58.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(20,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("209.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.4
Character	$\chi$	$=$	209.58
Dual form			209.2.f.b.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.161825 + 0.117573i) q^{2} +(0.378923 + 1.16621i) q^{3} +(-0.605670 + 1.86406i) q^{4} +(-0.0660344 - 0.0479768i) q^{5} +(-0.198433 - 0.144170i) q^{6} +(-0.276802 + 0.851908i) q^{7} +(-0.244773 - 0.753335i) q^{8} +(1.21060 - 0.879550i) q^{9} +0.0163268 q^{10} +(-0.976319 + 3.16967i) q^{11} -2.40338 q^{12} +(-3.76506 + 2.73547i) q^{13} +(-0.0553677 - 0.170404i) q^{14} +(0.0309289 - 0.0951892i) q^{15} +(-3.04315 - 2.21098i) q^{16} +(1.97795 + 1.43706i) q^{17} +(-0.0924937 + 0.284666i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(0.129427 - 0.0940340i) q^{20} -1.09839 q^{21} +(-0.214674 - 0.627720i) q^{22} +7.88800 q^{23} +(0.785793 - 0.570912i) q^{24} +(-1.54303 - 4.74895i) q^{25} +(0.287663 - 0.885336i) q^{26} +(4.46056 + 3.24079i) q^{27} +(-1.42036 - 1.03195i) q^{28} +(-1.56803 + 4.82589i) q^{29} +(0.00618659 + 0.0190404i) q^{30} +(6.31767 - 4.59005i) q^{31} +2.33661 q^{32} +(-4.06644 + 0.0624729i) q^{33} -0.489040 q^{34} +(0.0591502 - 0.0429752i) q^{35} +(0.906313 + 2.78934i) q^{36} +(0.444153 - 1.36696i) q^{37} +(0.161825 + 0.117573i) q^{38} +(-4.61680 - 3.35430i) q^{39} +(-0.0199791 + 0.0614894i) q^{40} +(-0.722756 - 2.22441i) q^{41} +(0.177746 - 0.129140i) q^{42} +6.94775 q^{43} +(-5.31713 - 3.73969i) q^{44} -0.122139 q^{45} +(-1.27648 + 0.927413i) q^{46} +(-1.53060 - 4.71069i) q^{47} +(1.42533 - 4.38673i) q^{48} +(5.01399 + 3.64288i) q^{49} +(0.808046 + 0.587080i) q^{50} +(-0.926420 + 2.85123i) q^{51} +(-2.81871 - 8.67509i) q^{52} +(7.87242 - 5.71965i) q^{53} -1.10286 q^{54} +(0.216541 - 0.162467i) q^{55} +0.709525 q^{56} +(0.992034 - 0.720755i) q^{57} +(-0.313647 - 0.965307i) q^{58} +(-2.47858 + 7.62828i) q^{59} +(0.158706 + 0.115307i) q^{60} +(-8.87344 - 6.44693i) q^{61} +(-0.482691 + 1.48557i) q^{62} +(0.414201 + 1.27478i) q^{63} +(5.70817 - 4.14723i) q^{64} +0.379863 q^{65} +(0.650706 - 0.488212i) q^{66} -13.3839 q^{67} +(-3.87675 + 2.81663i) q^{68} +(2.98895 + 9.19904i) q^{69} +(-0.00451928 + 0.0139089i) q^{70} +(-1.61590 - 1.17402i) q^{71} +(-0.958918 - 0.696694i) q^{72} +(-0.164937 + 0.507623i) q^{73} +(0.0888425 + 0.273429i) q^{74} +(4.95356 - 3.59897i) q^{75} +1.95999 q^{76} +(-2.43002 - 1.70910i) q^{77} +1.14149 q^{78} +(8.96326 - 6.51219i) q^{79} +(0.0948768 + 0.292001i) q^{80} +(-0.701995 + 2.16052i) q^{81} +(0.378490 + 0.274989i) q^{82} +(13.0874 + 9.50858i) q^{83} +(0.665260 - 2.04746i) q^{84} +(-0.0616668 - 0.189791i) q^{85} +(-1.12432 + 0.816866i) q^{86} -6.22215 q^{87} +(2.62680 - 0.0403557i) q^{88} -8.40759 q^{89} +(0.0197651 - 0.0143602i) q^{90} +(-1.28820 - 3.96467i) q^{91} +(-4.77753 + 14.7037i) q^{92} +(7.74686 + 5.62842i) q^{93} +(0.801537 + 0.582351i) q^{94} +(-0.0252229 + 0.0776281i) q^{95} +(0.885397 + 2.72497i) q^{96} +(0.0835782 - 0.0607231i) q^{97} -1.23969 q^{98} +(1.60595 + 4.69591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.161825	+	0.117573i	−0.114427	+	0.0831364i	−0.643527	−	0.765423i	$-0.722530\pi$
$2$	−0.161825	+	0.117573i	−0.114427	+	0.0831364i	0.529100	+	0.848560i	$0.322530\pi$
$3$	0.378923	+	1.16621i	0.218771	+	0.673309i	0.998864	+	0.0476456i	$0.0151718\pi$
$3$	0.378923	+	1.16621i	0.218771	+	0.673309i	−0.780093	+	0.625664i	$0.784828\pi$
$4$	−0.605670	+	1.86406i	−0.302835	+	0.932030i
$5$	−0.0660344	−	0.0479768i	−0.0295315	−	0.0214559i	0.572922	−	0.819610i	$-0.305810\pi$
$5$	−0.0660344	−	0.0479768i	−0.0295315	−	0.0214559i	−0.602453	+	0.798154i	$0.705810\pi$
$6$	−0.198433	−	0.144170i	−0.0810100	−	0.0588572i
$7$	−0.276802	+	0.851908i	−0.104621	+	0.321991i	−0.989641	−	0.143562i	$-0.954144\pi$
$7$	−0.276802	+	0.851908i	−0.104621	+	0.321991i	0.885020	+	0.465553i	$0.154144\pi$
$8$	−0.244773	−	0.753335i	−0.0865404	−	0.266344i
$9$	1.21060	−	0.879550i	0.403532	−	0.293183i
$10$	0.0163268			0.00516298
$11$	−0.976319	+	3.16967i	−0.294371	+	0.955691i
$11$	−0.976319	+	3.16967i	−0.294371	+	0.955691i
$12$	−2.40338			−0.693796
$13$	−3.76506	+	2.73547i	−1.04424	+	0.758684i	−0.971109	−	0.238638i	$-0.923299\pi$
$13$	−3.76506	+	2.73547i	−1.04424	+	0.758684i	−0.0731307	+	0.997322i	$0.523299\pi$
$14$	−0.0553677	−	0.170404i	−0.0147976	−	0.0455424i
$15$	0.0309289	−	0.0951892i	0.00798580	−	0.0245778i
$16$	−3.04315	−	2.21098i	−0.760787	−	0.552744i
$17$	1.97795	+	1.43706i	0.479722	+	0.348539i	0.801218	−	0.598372i	$-0.204186\pi$
$17$	1.97795	+	1.43706i	0.479722	+	0.348539i	−0.321496	+	0.946911i	$0.604186\pi$
$18$	−0.0924937	+	0.284666i	−0.0218010	+	0.0670965i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	0.129427	−	0.0940340i	0.0289407	−	0.0210266i
$21$	−1.09839			−0.239688
$22$	−0.214674	−	0.627720i	−0.0457686	−	0.133830i
$23$	7.88800			1.64476			0.822381	−	0.568937i	$-0.192645\pi$
$23$	7.88800			1.64476			0.822381	+	0.568937i	$0.192645\pi$
$24$	0.785793	−	0.570912i	0.160399	−	0.116537i
$25$	−1.54303	−	4.74895i	−0.308605	−	0.949789i
$26$	0.287663	−	0.885336i	0.0564154	−	0.173629i
$27$	4.46056	+	3.24079i	0.858436	+	0.623690i
$28$	−1.42036	−	1.03195i	−0.268422	−	0.195020i
$29$	−1.56803	+	4.82589i	−0.291175	+	0.896146i	0.693304	+	0.720645i	$0.256154\pi$
$29$	−1.56803	+	4.82589i	−0.291175	+	0.896146i	−0.984479	+	0.175500i	$0.943846\pi$
$30$	0.00618659	+	0.0190404i	0.00112951	+	0.00347628i
$31$	6.31767	−	4.59005i	1.13469	−	0.824398i	0.148316	−	0.988940i	$-0.452615\pi$
$31$	6.31767	−	4.59005i	1.13469	−	0.824398i	0.986370	+	0.164542i	$0.0526146\pi$
$32$	2.33661			0.413059
$33$	−4.06644	+	0.0624729i	−0.707876	+	0.0108751i
$34$	−0.489040			−0.0838696
$35$	0.0591502	−	0.0429752i	0.00999821	−	0.00726413i
$36$	0.906313	+	2.78934i	0.151052	+	0.464891i
$37$	0.444153	−	1.36696i	0.0730184	−	0.224727i	−0.907886	−	0.419216i	$-0.862305\pi$
$37$	0.444153	−	1.36696i	0.0730184	−	0.224727i	0.980905	+	0.194489i	$0.0623049\pi$
$38$	0.161825	+	0.117573i	0.0262515	+	0.0190728i
$39$	−4.61680	−	3.35430i	−0.739279	−	0.537118i
$40$	−0.0199791	+	0.0614894i	−0.00315898	+	0.00972233i
$41$	−0.722756	−	2.22441i	−0.112876	−	0.347395i	0.878622	−	0.477517i	$-0.158463\pi$
$41$	−0.722756	−	2.22441i	−0.112876	−	0.347395i	−0.991498	+	0.130122i	$0.958463\pi$
$42$	0.177746	−	0.129140i	0.0274268	−	0.0199268i
$43$	6.94775			1.05952			0.529761	−	0.848147i	$-0.322281\pi$
$43$	6.94775			1.05952			0.529761	+	0.848147i	$0.322281\pi$
$44$	−5.31713	−	3.73969i	−0.801587	−	0.563780i
$45$	−0.122139			−0.0182074
$46$	−1.27648	+	0.927413i	−0.188206	+	0.136740i
$47$	−1.53060	−	4.71069i	−0.223261	−	0.687125i	−0.998464	−	0.0554131i	$-0.982352\pi$
$47$	−1.53060	−	4.71069i	−0.223261	−	0.687125i	0.775203	−	0.631712i	$-0.217648\pi$
$48$	1.42533	−	4.38673i	0.205729	−	0.633170i
$49$	5.01399	+	3.64288i	0.716284	+	0.520411i
$50$	0.808046	+	0.587080i	0.114275	+	0.0830256i
$51$	−0.926420	+	2.85123i	−0.129725	+	0.399252i
$52$	−2.81871	−	8.67509i	−0.390885	−	1.20302i
$53$	7.87242	−	5.71965i	1.08136	−	0.785654i	0.103441	−	0.994636i	$-0.467015\pi$
$53$	7.87242	−	5.71965i	1.08136	−	0.785654i	0.977920	+	0.208981i	$0.0670148\pi$
$54$	−1.10286			−0.150080
$55$	0.216541	−	0.162467i	0.0291984	−	0.0219070i
$56$	0.709525			0.0948143
$57$	0.992034	−	0.720755i	0.131398	−	0.0954663i
$58$	−0.313647	−	0.965307i	−0.0411839	−	0.126751i
$59$	−2.47858	+	7.62828i	−0.322684	+	0.993118i	0.649792	+	0.760112i	$0.274856\pi$
$59$	−2.47858	+	7.62828i	−0.322684	+	0.993118i	−0.972475	+	0.233006i	$0.925144\pi$
$60$	0.158706	+	0.115307i	0.0204888	+	0.0148860i
$61$	−8.87344	−	6.44693i	−1.13613	−	0.825445i	−0.149552	−	0.988754i	$-0.547783\pi$
$61$	−8.87344	−	6.44693i	−1.13613	−	0.825445i	−0.986575	+	0.163309i	$0.947783\pi$
$62$	−0.482691	+	1.48557i	−0.0613018	+	0.188668i
$63$	0.414201	+	1.27478i	0.0521844	+	0.160607i
$64$	5.70817	−	4.14723i	0.713522	−	0.518404i
$65$	0.379863			0.0471162
$66$	0.650706	−	0.488212i	0.0800963	−	0.0600947i
$67$	−13.3839			−1.63511			−0.817554	−	0.575852i	$-0.804670\pi$
$67$	−13.3839			−1.63511			−0.817554	+	0.575852i	$0.804670\pi$
$68$	−3.87675	+	2.81663i	−0.470125	+	0.341566i
$69$	2.98895	+	9.19904i	0.359827	+	1.10743i
$70$	−0.00451928	+	0.0139089i	−0.000540157	+	0.00166243i
$71$	−1.61590	−	1.17402i	−0.191772	−	0.139331i	0.487756	−	0.872980i	$-0.337816\pi$
$71$	−1.61590	−	1.17402i	−0.191772	−	0.139331i	−0.679528	+	0.733649i	$0.737816\pi$
$72$	−0.958918	−	0.696694i	−0.113010	−	0.0821062i
$73$	−0.164937	+	0.507623i	−0.0193044	+	0.0594128i	−0.960245	−	0.279160i	$-0.909944\pi$
$73$	−0.164937	+	0.507623i	−0.0193044	+	0.0594128i	0.940940	+	0.338573i	$0.109944\pi$
$74$	0.0888425	+	0.273429i	0.0103277	+	0.0317855i
$75$	4.95356	−	3.59897i	0.571988	−	0.415574i
$76$	1.95999			0.224826
$77$	−2.43002	−	1.70910i	−0.276926	−	0.194770i
$78$	1.14149			0.129248
$79$	8.96326	−	6.51219i	1.00845	−	0.732679i	0.0445632	−	0.999007i	$-0.485810\pi$
$79$	8.96326	−	6.51219i	1.00845	−	0.732679i	0.963882	+	0.266328i	$0.0858104\pi$
$80$	0.0948768	+	0.292001i	0.0106076	+	0.0326467i
$81$	−0.701995	+	2.16052i	−0.0779995	+	0.240058i
$82$	0.378490	+	0.274989i	0.0417972	+	0.0303675i
$83$	13.0874	+	9.50858i	1.43653	+	1.04370i	0.988753	+	0.149559i	$0.0477855\pi$
$83$	13.0874	+	9.50858i	1.43653	+	1.04370i	0.447781	+	0.894143i	$0.352215\pi$
$84$	0.665260	−	2.04746i	0.0725858	−	0.223396i
$85$	−0.0616668	−	0.189791i	−0.00668871	−	0.0205857i
$86$	−1.12432	+	0.816866i	−0.121238	+	0.0880849i
$87$	−6.22215			−0.667084
$88$	2.62680	−	0.0403557i	0.280018	−	0.00430193i
$89$	−8.40759			−0.891203			−0.445602	−	0.895231i	$-0.647010\pi$
$89$	−8.40759			−0.891203			−0.445602	+	0.895231i	$0.647010\pi$
$90$	0.0197651	−	0.0143602i	0.00208343	−	0.00151370i
$91$	−1.28820	−	3.96467i	−0.135040	−	0.415610i
$92$	−4.77753	+	14.7037i	−0.498092	+	1.53297i
$93$	7.74686	+	5.62842i	0.803312	+	0.583640i
$94$	0.801537	+	0.582351i	0.0826723	+	0.0600649i
$95$	−0.0252229	+	0.0776281i	−0.00258781	+	0.00796447i
$96$	0.885397	+	2.72497i	0.0903655	+	0.278116i
$97$	0.0835782	−	0.0607231i	0.00848608	−	0.00616550i	−0.583534	−	0.812089i	$-0.698331\pi$
$97$	0.0835782	−	0.0607231i	0.00848608	−	0.00616550i	0.592020	+	0.805923i	$0.298331\pi$
$98$	−1.23969			−0.125228
$99$	1.60595	+	4.69591i	0.161405	+	0.471957i
$100$	9.78689			0.978689
$101$	−8.39671	+	6.10057i	−0.835504	+	0.607029i	−0.921111	−	0.389300i	$-0.872717\pi$
$101$	−8.39671	+	6.10057i	−0.835504	+	0.607029i	0.0856073	+	0.996329i	$0.472717\pi$
$102$	−0.185309	−	0.570321i	−0.0183483	−	0.0564702i
$103$	−1.07701	+	3.31470i	−0.106121	+	0.326607i	−0.989992	−	0.141124i	$-0.954928\pi$
$103$	−1.07701	+	3.31470i	−0.106121	+	0.326607i	0.883871	+	0.467731i	$0.154928\pi$
$104$	2.98231	+	2.16678i	0.292440	+	0.212470i
$105$	0.0725313	+	0.0526971i	0.00707833	+	0.00514271i
$106$	−0.601479	+	1.85116i	−0.0584208	+	0.179801i
$107$	−2.34068	−	7.20388i	−0.226282	−	0.696425i	−0.998159	−	0.0606528i	$-0.980682\pi$
$107$	−2.34068	−	7.20388i	−0.226282	−	0.696425i	0.771877	−	0.635772i	$-0.219318\pi$
$108$	−8.74266	+	6.35191i	−0.841262	+	0.611213i
$109$	−14.3006			−1.36975			−0.684875	−	0.728661i	$-0.740143\pi$
$109$	−14.3006			−1.36975			−0.684875	+	0.728661i	$0.740143\pi$
$110$	−0.0159401	+	0.0517504i	−0.00151983	+	0.00493421i
$111$	1.76246			0.167285
$112$	2.72590	−	1.98048i	0.257573	−	0.187138i
$113$	4.49289	+	13.8277i	0.422655	+	1.30080i	0.905222	+	0.424940i	$0.139705\pi$
$113$	4.49289	+	13.8277i	0.422655	+	1.30080i	−0.482567	+	0.875859i	$0.660295\pi$
$114$	−0.0757947	+	0.233272i	−0.00709883	+	0.0218479i
$115$	−0.520879	−	0.378441i	−0.0485723	−	0.0352898i
$116$	−8.04605	−	5.84580i	−0.747057	−	0.542769i
$117$	−2.15198	+	6.62312i	−0.198951	+	0.612307i
$118$	−0.495782	−	1.52586i	−0.0456404	−	0.140467i
$119$	−1.77174	+	1.28725i	−0.162415	+	0.118002i
$120$	−0.0792799			−0.00723723
$121$	−9.09360	−	6.18921i	−0.826691	−	0.562656i
$122$	2.19393			0.198629
$123$	2.32026	−	1.68576i	0.209210	−	0.152000i
$124$	4.72972	+	14.5566i	0.424741	+	1.30722i
$125$	−0.252061	+	0.775764i	−0.0225450	+	0.0693864i
$126$	−0.216907	−	0.157592i	−0.0193236	−	0.0140394i
$127$	−15.9333	−	11.5762i	−1.41386	−	1.02723i	−0.992748	−	0.120215i	$-0.961642\pi$
$127$	−15.9333	−	11.5762i	−1.41386	−	1.02723i	−0.421107	−	0.907011i	$-0.638358\pi$
$128$	−1.88023	+	5.78675i	−0.166190	+	0.511481i
$129$	2.63267	+	8.10251i	0.231793	+	0.713387i
$130$	−0.0614712	+	0.0446615i	−0.00539138	+	0.00391707i
$131$	14.6793			1.28253			0.641267	−	0.767318i	$-0.278409\pi$
$131$	14.6793			1.28253			0.641267	+	0.767318i	$0.278409\pi$
$132$	2.34647	−	7.61792i	0.204234	−	0.663055i
$133$	0.895749			0.0776713
$134$	2.16585	−	1.57358i	0.187101	−	0.135937i
$135$	−0.139068	−	0.428007i	−0.0119691	−	0.0368370i
$136$	0.598440	−	1.84181i	0.0513158	−	0.157934i
$137$	10.1264	+	7.35724i	0.865154	+	0.628571i	0.929282	−	0.369370i	$-0.120427\pi$
$137$	10.1264	+	7.35724i	0.865154	+	0.628571i	−0.0641282	+	0.997942i	$0.520427\pi$
$138$	−1.56524	−	1.13721i	−0.133242	−	0.0968061i
$139$	2.13441	−	6.56905i	0.181039	−	0.557179i	−0.818819	−	0.574052i	$-0.805371\pi$
$139$	2.13441	−	6.56905i	0.181039	−	0.557179i	0.999858	+	0.0168722i	$0.00537084\pi$
$140$	0.0442828	+	0.136288i	0.00374258	+	0.0115185i
$141$	4.91366	−	3.56998i	0.413805	−	0.300647i
$142$	0.399526			0.0335275
$143$	−4.99465	−	14.6047i	−0.417674	−	1.22131i
$144$	−5.62869			−0.469058
$145$	0.335075	−	0.243446i	0.0278264	−	0.0202171i
$146$	−0.0329917	−	0.101538i	−0.00273042	−	0.00840336i
$147$	−2.34843	+	7.22772i	−0.193695	+	0.596132i
$148$	2.27909	+	1.65586i	0.187340	+	0.136111i
$149$	−12.3329	−	8.96041i	−1.01035	−	0.734065i	−0.0460707	−	0.998938i	$-0.514670\pi$
$149$	−12.3329	−	8.96041i	−1.01035	−	0.734065i	−0.964283	+	0.264873i	$0.914670\pi$
$150$	−0.378469	+	1.16481i	−0.0309018	+	0.0951061i
$151$	1.89686	+	5.83795i	0.154365	+	0.475086i	0.998096	−	0.0616802i	$-0.0196459\pi$
$151$	1.89686	+	5.83795i	0.154365	+	0.475086i	−0.843731	+	0.536766i	$0.819646\pi$
$152$	−0.640825	+	0.465586i	−0.0519778	+	0.0377640i
$153$	3.65846			0.295769
$154$	0.594181	−	0.00912844i	0.0478805	−	0.000735591i
$155$	−0.637399			−0.0511971
$156$	9.04887	−	6.57439i	0.724490	−	0.526372i
$157$	−1.27799	−	3.93326i	−0.101995	−	0.313908i	0.887018	−	0.461734i	$-0.152773\pi$
$157$	−1.27799	−	3.93326i	−0.101995	−	0.313908i	−0.989013	+	0.147826i	$0.952773\pi$
$158$	−0.684823	+	2.10767i	−0.0544816	+	0.167677i
$159$	9.65333	+	7.01356i	0.765559	+	0.556211i
$160$	−0.154297	−	0.112103i	−0.0121982	−	0.00886254i
$161$	−2.18341	+	6.71985i	−0.172077	+	0.529599i
$162$	−0.140418	−	0.432161i	−0.0110323	−	0.0339538i
$163$	12.8900	−	9.36515i	1.00962	−	0.733535i	0.0454941	−	0.998965i	$-0.485514\pi$
$163$	12.8900	−	9.36515i	1.00962	−	0.733535i	0.964130	+	0.265430i	$0.0855138\pi$
$164$	4.58419			0.357965
$165$	0.271522	+	0.190969i	0.0211380	+	0.0148669i
$166$	−3.23582			−0.251149
$167$	−1.18148	+	0.858395i	−0.0914256	+	0.0664246i	−0.632559	−	0.774512i	$-0.717995\pi$
$167$	−1.18148	+	0.858395i	−0.0914256	+	0.0664246i	0.541133	+	0.840937i	$0.317995\pi$
$168$	0.268856	+	0.827453i	0.0207427	+	0.0638394i
$169$	2.67562	−	8.23471i	0.205817	−	0.633439i
$170$	0.0322934	+	0.0234626i	0.00247679	+	0.00179950i
$171$	−1.21060	−	0.879550i	−0.0925767	−	0.0672609i
$172$	−4.20805	+	12.9510i	−0.320861	+	0.987507i
$173$	−4.52395	−	13.9233i	−0.343950	−	1.05857i	−0.962144	−	0.272543i	$-0.912135\pi$
$173$	−4.52395	−	13.9233i	−0.343950	−	1.05857i	0.618194	−	0.786026i	$-0.287865\pi$
$174$	1.00690	−	0.731554i	0.0763328	−	0.0554590i
$175$	4.47278			0.338110
$176$	9.97914	−	7.48715i	0.752206	−	0.564365i
$177$	−9.83534			−0.739270
$178$	1.36056	−	0.988503i	0.101978	−	0.0740914i
$179$	−4.30475	−	13.2487i	−0.321752	−	0.990251i	−0.972885	−	0.231287i	$-0.925706\pi$
$179$	−4.30475	−	13.2487i	−0.321752	−	0.990251i	0.651134	−	0.758963i	$-0.274294\pi$
$180$	0.0739760	−	0.227675i	0.00551384	−	0.0169699i
$181$	−14.9569	−	10.8668i	−1.11173	−	0.807722i	−0.128799	−	0.991671i	$-0.541112\pi$
$181$	−14.9569	−	10.8668i	−1.11173	−	0.807722i	−0.982936	+	0.183948i	$0.941112\pi$
$182$	0.674599	+	0.490125i	0.0500046	+	0.0363305i
$183$	4.15610	−	12.7912i	0.307228	−	0.945549i
$184$	−1.93077	−	5.94231i	−0.142338	−	0.438073i
$185$	−0.0949119	+	0.0689575i	−0.00697806	+	0.00506986i
$186$	−1.91538			−0.140443
$187$	−6.48611	+	4.86640i	−0.474312	+	0.355867i
$188$	9.70806			0.708033
$189$	−3.99554	+	2.90293i	−0.290633	+	0.211157i
$190$	−0.00504525	−	0.0155277i	−0.000366021	−	0.00112650i
$191$	−1.34903	+	4.15190i	−0.0976126	+	0.300421i	−0.987926	−	0.154928i	$-0.950485\pi$
$191$	−1.34903	+	4.15190i	−0.0976126	+	0.300421i	0.890313	+	0.455349i	$0.150485\pi$
$192$	6.99949	+	5.08542i	0.505144	+	0.367009i
$193$	5.50955	+	4.00293i	0.396586	+	0.288137i	0.768149	−	0.640271i	$-0.221178\pi$
$193$	5.50955	+	4.00293i	0.396586	+	0.288137i	−0.371563	+	0.928408i	$0.621178\pi$
$194$	−0.00638565	+	0.0196530i	−0.000458463	+	0.00141100i
$195$	0.143939	+	0.442998i	0.0103077	+	0.0317238i
$196$	−9.82737	+	7.14000i	−0.701955	+	0.510000i
$197$	10.5905			0.754542			0.377271	−	0.926103i	$-0.376863\pi$
$197$	10.5905			0.754542			0.377271	+	0.926103i	$0.376863\pi$
$198$	−0.811994	−	0.571099i	−0.0577059	−	0.0405863i
$199$	2.81828			0.199782			0.0998911	−	0.994998i	$-0.468151\pi$
$199$	2.81828			0.199782			0.0998911	+	0.994998i	$0.468151\pi$
$200$	−3.19985	+	2.32483i	−0.226264	+	0.164390i
$201$	−5.07148	−	15.6084i	−0.357715	−	1.10093i
$202$	0.641537	−	1.97445i	0.0451384	−	0.138922i
$203$	−3.67718	−	2.67163i	−0.258088	−	0.187512i
$204$	−4.75376	−	3.45381i	−0.332830	−	0.241815i
$205$	−0.0589935	+	0.181563i	−0.00412029	+	0.0126809i
$206$	−0.215431	−	0.663028i	−0.0150098	−	0.0461954i
$207$	9.54919	−	6.93790i	0.663715	−	0.482217i
$208$	17.5057			1.21380
$209$	3.31623	−	0.0509475i	0.229389	−	0.00352411i
$210$	−0.0179331			−0.00123750
$211$	−8.68780	+	6.31206i	−0.598093	+	0.434540i	−0.845201	−	0.534448i	$-0.820520\pi$
$211$	−8.68780	+	6.31206i	−0.598093	+	0.434540i	0.247109	+	0.968988i	$0.420520\pi$
$212$	5.89368	+	18.1389i	0.404780	+	1.24578i
$213$	0.756848	−	2.32934i	0.0518584	−	0.159604i
$214$	1.22576	+	0.890566i	0.0837912	+	0.0608779i
$215$	−0.458791	−	0.333331i	−0.0312893	−	0.0227330i
$216$	1.34957	−	4.15356i	0.0918267	−	0.282614i
$217$	2.16156	+	6.65260i	0.146736	+	0.451608i
$218$	2.31419	−	1.68136i	0.156737	−	0.113876i
$219$	−0.654492			−0.0442265
$220$	0.171695	+	0.502047i	0.0115757	+	0.0338480i
$221$	−11.3781			−0.765376
$222$	−0.285210	+	0.207217i	−0.0191420	+	0.0139075i
$223$	1.23532	+	3.80193i	0.0827233	+	0.254596i	0.983860	−	0.178938i	$-0.0572662\pi$
$223$	1.23532	+	3.80193i	0.0827233	+	0.254596i	−0.901137	+	0.433534i	$0.857266\pi$
$224$	−0.646778	+	1.99058i	−0.0432147	+	0.133001i
$225$	−6.04492	−	4.39189i	−0.402995	−	0.292793i
$226$	−2.35282	−	1.70942i	−0.156507	−	0.113709i
$227$	6.63347	−	20.4157i	0.440279	−	1.35504i	−0.447300	−	0.894384i	$-0.647614\pi$
$227$	6.63347	−	20.4157i	0.440279	−	1.35504i	0.887579	−	0.460656i	$-0.152386\pi$
$228$	0.742686	+	2.28575i	0.0491856	+	0.151378i
$229$	−4.04280	+	2.93727i	−0.267156	+	0.194100i	−0.713296	−	0.700863i	$-0.752798\pi$
$229$	−4.04280	+	2.93727i	−0.267156	+	0.194100i	0.446140	+	0.894963i	$0.352798\pi$
$230$	0.128786			0.00849187
$231$	1.07238	−	3.48152i	0.0705571	−	0.229067i
$232$	4.01932			0.263882
$233$	10.8158	−	7.85817i	0.708570	−	0.514806i	−0.174142	−	0.984721i	$-0.555715\pi$
$233$	10.8158	−	7.85817i	0.708570	−	0.514806i	0.882712	+	0.469914i	$0.155715\pi$
$234$	−0.430453	−	1.32480i	−0.0281396	−	0.0866048i
$235$	−0.124932	+	0.384501i	−0.00814966	+	0.0250821i
$236$	−12.7184	−	9.24044i	−0.827896	−	0.601502i
$237$	10.9909	+	7.98539i	0.713939	+	0.518707i
$238$	0.135367	−	0.416617i	0.00877454	−	0.0270053i
$239$	−3.73232	−	11.4869i	−0.241424	−	0.743026i	−0.996204	−	0.0870482i	$-0.972257\pi$
$239$	−3.73232	−	11.4869i	−0.241424	−	0.743026i	0.754780	−	0.655978i	$-0.227743\pi$
$240$	−0.304582	+	0.221292i	−0.0196607	+	0.0142843i
$241$	−22.7610			−1.46617			−0.733083	−	0.680139i	$-0.761920\pi$
$241$	−22.7610			−1.46617			−0.733083	+	0.680139i	$0.761920\pi$
$242$	2.19925	−	0.0675905i	0.141373	−	0.00434488i
$243$	13.7551			0.882388
$244$	17.3918	−	12.6359i	1.11340	−	0.808932i
$245$	−0.156322	−	0.481110i	−0.00998706	−	0.0307370i
$246$	−0.177275	+	0.545597i	−0.0113027	+	0.0347860i
$247$	3.76506	+	2.73547i	0.239565	+	0.174054i
$248$	−5.00424	−	3.63580i	−0.317770	−	0.230873i
$249$	−6.12983	+	18.8657i	−0.388462	+	1.19556i
$250$	−0.0504189	−	0.155173i	−0.00318877	−	0.00981402i
$251$	−11.5925	+	8.42247i	−0.731714	+	0.531622i	−0.890105	−	0.455755i	$-0.849369\pi$
$251$	−11.5925	+	8.42247i	−0.731714	+	0.531622i	0.158391	+	0.987376i	$0.449369\pi$
$252$	−2.62713			−0.165494
$253$	−7.70120	+	25.0024i	−0.484171	+	1.57188i
$254$	3.93946			0.247184
$255$	0.197968	−	0.143832i	0.0123973	−	0.00900714i
$256$	3.98456	+	12.2632i	0.249035	+	0.766451i
$257$	−1.40416	+	4.32157i	−0.0875892	+	0.269572i	−0.985252	−	0.171112i	$-0.945264\pi$
$257$	−1.40416	+	4.32157i	−0.0875892	+	0.269572i	0.897662	+	0.440684i	$0.145264\pi$
$258$	−1.37866	−	1.00166i	−0.0858319	−	0.0623605i
$259$	1.04158	+	0.756755i	0.0647209	+	0.0470225i
$260$	−0.230071	+	0.708087i	−0.0142684	+	0.0439137i
$261$	2.34637	+	7.22137i	0.145236	+	0.446992i
$262$	−2.37547	+	1.72588i	−0.146757	+	0.106625i
$263$	7.21456			0.444869			0.222434	−	0.974948i	$-0.428600\pi$
$263$	7.21456			0.444869			0.222434	+	0.974948i	$0.428600\pi$
$264$	1.04242	+	3.04810i	0.0641564	+	0.187597i
$265$	−0.794261			−0.0487911
$266$	−0.144954	+	0.105316i	−0.00888773	+	0.00645731i
$267$	−3.18583	−	9.80499i	−0.194970	−	0.600056i
$268$	8.10625	−	24.9485i	0.495168	−	1.52397i
$269$	−7.86317	−	5.71293i	−0.479426	−	0.348323i	0.321677	−	0.946849i	$-0.395753\pi$
$269$	−7.86317	−	5.71293i	−0.479426	−	0.348323i	−0.801103	+	0.598526i	$0.795753\pi$
$270$	0.0728266	+	0.0529116i	0.00443208	+	0.00322010i
$271$	−5.43485	+	16.7267i	−0.330144	+	1.01608i	0.638922	+	0.769272i	$0.279381\pi$
$271$	−5.43485	+	16.7267i	−0.330144	+	1.01608i	−0.969065	+	0.246805i	$0.920619\pi$
$272$	−2.84187	−	8.74638i	−0.172314	−	0.530327i
$273$	4.13549	−	3.00461i	0.250291	−	0.181847i
$274$	−2.50371			−0.151255
$275$	16.5591	−	0.254398i	0.998550	−	0.0153408i
$276$	−18.9579			−1.14113
$277$	−0.805408	+	0.585163i	−0.0483923	+	0.0351590i	−0.611718	−	0.791076i	$-0.709521\pi$
$277$	−0.805408	+	0.585163i	−0.0483923	+	0.0351590i	0.563326	+	0.826235i	$0.309521\pi$
$278$	0.426939	+	1.31398i	0.0256061	+	0.0788075i
$279$	3.61097	−	11.1134i	0.216183	−	0.665343i
$280$	−0.0468531	−	0.0340408i	−0.00280001	−	0.00203432i
$281$	11.9116	+	8.65428i	0.710586	+	0.516271i	0.883363	−	0.468690i	$-0.155274\pi$
$281$	11.9116	+	8.65428i	0.710586	+	0.516271i	−0.172776	+	0.984961i	$0.555274\pi$
$282$	−0.375420	+	1.15542i	−0.0223559	+	0.0688045i
$283$	1.55763	+	4.79389i	0.0925915	+	0.284967i	0.986619	−	0.163046i	$-0.0521318\pi$
$283$	1.55763	+	4.79389i	0.0925915	+	0.284967i	−0.894027	+	0.448013i	$0.852132\pi$
$284$	3.16715	−	2.30107i	0.187936	−	0.136543i
$285$	−0.100088			−0.00592869
$286$	2.52537	+	1.77617i	0.149328	+	0.105027i
$287$	2.09506			0.123667
$288$	2.82870	−	2.05517i	0.166683	−	0.121102i
$289$	−3.40617	−	10.4831i	−0.200363	−	0.616653i
$290$	−0.0256008	+	0.0787912i	−0.00150333	+	0.00462678i
$291$	0.102485	+	0.0744600i	0.00600780	+	0.00436492i
$292$	−0.846343	−	0.614904i	−0.0495285	−	0.0359846i
$293$	−4.50168	+	13.8547i	−0.262991	+	0.809402i	0.729159	+	0.684345i	$0.239912\pi$
$293$	−4.50168	+	13.8547i	−0.262991	+	0.809402i	−0.992149	+	0.125058i	$0.960088\pi$
$294$	−0.469748	−	1.44574i	−0.0273963	−	0.0843170i
$295$	0.529652	−	0.384815i	0.0308375	−	0.0224048i
$296$	−1.13850			−0.0661738
$297$	−14.6272	+	10.9745i	−0.848754	+	0.636803i
$298$	3.04928			0.176640
$299$	−29.6988	+	21.5774i	−1.71753	+	1.24786i
$300$	3.70848	+	11.4135i	0.214109	+	0.658960i
$301$	−1.92315	+	5.91885i	−0.110849	+	0.341157i
$302$	−0.993343	−	0.721706i	−0.0571605	−	0.0415295i
$303$	−10.2962	−	7.48065i	−0.591503	−	0.429752i
$304$	−1.16238	+	3.57743i	−0.0666670	+	0.205180i
$305$	0.276649	+	0.851438i	0.0158409	+	0.0487532i
$306$	−0.592030	+	0.430135i	−0.0338441	+	0.0245892i
$307$	−4.11852			−0.235056			−0.117528	−	0.993070i	$-0.537497\pi$
$307$	−4.11852			−0.235056			−0.117528	+	0.993070i	$0.537497\pi$
$308$	4.65766	−	3.49455i	0.265395	−	0.199121i
$309$	−4.27373			−0.243124
$310$	0.103147	−	0.0749407i	0.00585836	−	0.00425635i
$311$	0.828478	+	2.54979i	0.0469787	+	0.144586i	0.971794	−	0.235830i	$-0.0757809\pi$
$311$	0.828478	+	2.54979i	0.0469787	+	0.144586i	−0.924816	+	0.380416i	$0.875781\pi$
$312$	−1.39684	+	4.29904i	−0.0790806	+	0.243385i
$313$	3.80231	+	2.76254i	0.214919	+	0.156148i	0.690037	−	0.723774i	$-0.257594\pi$
$313$	3.80231	+	2.76254i	0.214919	+	0.156148i	−0.475117	+	0.879922i	$0.657594\pi$
$314$	0.669255	+	0.486242i	0.0377682	+	0.0274402i
$315$	0.0338083	−	0.104051i	0.00190488	−	0.00586262i
$316$	6.71034	+	20.6523i	0.377486	+	1.16178i
$317$	1.43948	−	1.04584i	0.0808490	−	0.0587402i	−0.546627	−	0.837377i	$-0.684088\pi$
$317$	1.43948	−	1.04584i	0.0808490	−	0.0587402i	0.627476	+	0.778636i	$0.284088\pi$
$318$	−2.38675			−0.133842
$319$	−13.7656	−	9.68174i	−0.770725	−	0.542073i
$320$	−0.575907			−0.0321942
$321$	7.51427	−	5.45943i	0.419405	−	0.304716i
$322$	−0.436740	−	1.34415i	−0.0243386	−	0.0749065i
$323$	0.755508	−	2.32521i	0.0420376	−	0.129378i
$324$	−3.60216	−	2.61712i	−0.200120	−	0.145396i
$325$	18.8002	+	13.6592i	1.04285	+	0.757673i
$326$	−0.984841	+	3.03103i	−0.0545453	+	0.167873i
$327$	−5.41883	−	16.6774i	−0.299662	−	0.922265i
$328$	−1.49882	+	1.08895i	−0.0827583	+	0.0601274i
$329$	4.43675			0.244606
$330$	−0.0663918	+	0.00101998i	−0.00365475	+	5.61481e-5i
$331$	18.2118			1.00101			0.500505	−	0.865734i	$-0.333148\pi$
$331$	18.2118			1.00101			0.500505	+	0.865734i	$0.333148\pi$
$332$	−25.6512	+	18.6367i	−1.40780	+	1.02282i
$333$	−0.664622	−	2.04550i	−0.0364211	−	0.112093i
$334$	0.0902690	−	0.277819i	0.00493930	−	0.0152016i
$335$	0.883800	+	0.642118i	0.0482871	+	0.0350827i
$336$	3.34255	+	2.42851i	0.182351	+	0.132486i
$337$	0.544893	−	1.67701i	0.0296822	−	0.0913525i	−0.935118	−	0.354337i	$-0.884707\pi$
$337$	0.544893	−	1.67701i	0.0296822	−	0.0913525i	0.964800	+	0.262984i	$0.0847067\pi$
$338$	0.535195	+	1.64716i	0.0291108	+	0.0895937i
$339$	−14.4235	+	10.4793i	−0.783375	+	0.569155i
$340$	0.391132			0.0212121
$341$	8.38090	+	24.5063i	0.453851	+	1.32709i
$342$	0.299316			0.0161851
$343$	−9.56401	+	6.94866i	−0.516408	+	0.375192i
$344$	−1.70062	−	5.23398i	−0.0916915	−	0.282198i
$345$	0.243967	−	0.750853i	0.0131347	−	0.0404246i
$346$	2.36909	+	1.72124i	0.127363	+	0.0925346i
$347$	27.7116	+	20.1336i	1.48763	+	1.08083i	0.974995	+	0.222225i	$0.0713320\pi$
$347$	27.7116	+	20.1336i	1.48763	+	1.08083i	0.512639	+	0.858604i	$0.328668\pi$
$348$	3.76857	−	11.5985i	0.202016	−	0.621743i
$349$	7.10856	+	21.8779i	0.380512	+	1.17110i	0.939684	+	0.342045i	$0.111119\pi$
$349$	7.10856	+	21.8779i	0.380512	+	1.17110i	−0.559171	+	0.829052i	$0.688881\pi$
$350$	−0.723807	+	0.525876i	−0.0386891	+	0.0281093i
$351$	−25.6594			−1.36960
$352$	−2.28128	+	7.40629i	−0.121593	+	0.394757i
$353$	7.46659			0.397407			0.198703	−	0.980060i	$-0.436327\pi$
$353$	7.46659			0.397407			0.198703	+	0.980060i	$0.436327\pi$
$354$	1.59160	−	1.15637i	0.0845927	−	0.0614602i
$355$	0.0503793	+	0.155052i	0.00267386	+	0.00822929i
$356$	5.09223	−	15.6723i	0.269888	−	0.830628i
$357$	−2.17255	−	1.57845i	−0.114983	−	0.0835404i
$358$	2.25429	+	1.63784i	0.119143	+	0.0865626i
$359$	10.6738	−	32.8505i	0.563340	−	1.73378i	−0.109493	−	0.993988i	$-0.534923\pi$
$359$	10.6738	−	32.8505i	0.563340	−	1.73378i	0.672833	−	0.739794i	$-0.265077\pi$
$360$	0.0298964	+	0.0920116i	0.00157568	+	0.00484944i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	3.69803			0.194364
$363$	3.77212	−	12.9503i	0.197985	−	0.679712i
$364$	8.17060			0.428256
$365$	0.0352456	−	0.0256075i	0.00184484	−	0.00134036i
$366$	0.831330	+	2.55857i	0.0434543	+	0.133739i
$367$	−2.69914	+	8.30710i	−0.140894	+	0.433627i	−0.996460	−	0.0840665i	$-0.973209\pi$
$367$	−2.69914	+	8.30710i	−0.140894	+	0.433627i	0.855566	+	0.517693i	$0.173209\pi$
$368$	−24.0044	−	17.4402i	−1.25131	−	0.909133i
$369$	−2.83145	−	2.05717i	−0.147399	−	0.107092i
$370$	0.00725159	−	0.0223181i	0.000376992	−	0.00116026i
$371$	2.69351	+	8.28979i	0.139840	+	0.430384i
$372$	−15.1838	+	11.0317i	−0.787242	+	0.571964i
$373$	29.9452			1.55050			0.775251	−	0.631654i	$-0.217624\pi$
$373$	29.9452			1.55050			0.775251	+	0.631654i	$0.217624\pi$
$374$	0.477459	−	1.55009i	0.0246888	−	0.0801535i
$375$	−1.00021			−0.0516507
$376$	−3.17408	+	2.30610i	−0.163691	+	0.118928i
$377$	−7.29739	−	22.4591i	−0.375835	−	1.15670i
$378$	0.305273	−	0.939534i	0.0157015	−	0.0483244i
$379$	6.06315	+	4.40513i	0.311443	+	0.226277i	0.732515	−	0.680750i	$-0.238346\pi$
$379$	6.06315	+	4.40513i	0.311443	+	0.226277i	−0.421072	+	0.907027i	$0.638346\pi$
$380$	−0.129427	−	0.0940340i	−0.00663945	−	0.00482384i
$381$	7.46278	−	22.9681i	0.382330	−	1.17669i
$382$	−0.269842	−	0.830490i	−0.0138063	−	0.0424915i
$383$	−3.24539	+	2.35791i	−0.165831	+	0.120484i	−0.667606	−	0.744515i	$-0.732681\pi$
$383$	−3.24539	+	2.35791i	−0.165831	+	0.120484i	0.501774	+	0.864999i	$0.332681\pi$
$384$	−7.46101			−0.380743
$385$	0.0784676	+	0.229444i	0.00399908	+	0.0116936i
$386$	−1.36222			−0.0693350
$387$	8.41093	−	6.11090i	0.427552	−	0.310634i
$388$	0.0625708	+	0.192573i	0.00317655	+	0.00977641i
$389$	9.48540	−	29.1931i	0.480929	−	1.48015i	−0.356863	−	0.934157i	$-0.616154\pi$
$389$	9.48540	−	29.1931i	0.480929	−	1.48015i	0.837792	−	0.545990i	$-0.183846\pi$
$390$	−0.0753773	−	0.0547648i	−0.00381688	−	0.00277313i
$391$	15.6020	+	11.3355i	0.789029	+	0.573263i
$392$	1.51702	−	4.66889i	0.0766208	−	0.235815i
$393$	5.56232	+	17.1191i	0.280582	+	0.863543i
$394$	−1.71381	+	1.24515i	−0.0863403	+	0.0627299i
$395$	−0.904318			−0.0455012
$396$	−9.72615	+	0.149423i	−0.488757	+	0.00750881i
$397$	−1.79554			−0.0901158			−0.0450579	−	0.998984i	$-0.514347\pi$
$397$	−1.79554			−0.0901158			−0.0450579	+	0.998984i	$0.514347\pi$
$398$	−0.456067	+	0.331352i	−0.0228606	+	0.0166092i
$399$	0.339420	+	1.04463i	0.0169923	+	0.0522968i
$400$	−5.80415	+	17.8633i	−0.290208	+	0.893167i
$401$	5.19406	+	3.77370i	0.259379	+	0.188450i	0.709873	−	0.704330i	$-0.248752\pi$
$401$	5.19406	+	3.77370i	0.259379	+	0.188450i	−0.450494	+	0.892779i	$0.648752\pi$
$402$	2.65582	+	1.92956i	0.132460	+	0.0962379i
$403$	−11.2304	+	34.5636i	−0.559426	+	1.72174i
$404$	−6.28619	−	19.3469i	−0.312750	−	0.962544i
$405$	0.150011	−	0.108989i	0.00745409	−	0.00541571i
$406$	0.909170			0.0451214
$407$	3.89919	+	2.74241i	0.193276	+	0.135936i
$408$	2.37469			0.117565
$409$	3.46690	−	2.51885i	0.171427	−	0.124549i	−0.498763	−	0.866738i	$-0.666212\pi$
$409$	3.46690	−	2.51885i	0.171427	−	0.124549i	0.670191	+	0.742189i	$0.266212\pi$
$410$	−0.0118003	−	0.0363175i	−0.000582774	−	0.00179359i
$411$	−4.74294	+	14.5973i	−0.233952	+	0.720030i
$412$	−5.52649	−	4.01523i	−0.272271	−	0.197816i
$413$	−5.81252	−	4.22304i	−0.286015	−	0.207802i
$414$	−0.729590	+	2.24545i	−0.0358574	+	0.110358i
$415$	−0.408030	−	1.25579i	−0.0200294	−	0.0616442i
$416$	−8.79748	+	6.39175i	−0.431332	+	0.313381i
$417$	8.46964			0.414760
$418$	−0.530659	+	0.398143i	−0.0259554	+	0.0194738i
$419$	17.0735			0.834094			0.417047	−	0.908885i	$-0.363065\pi$
$419$	17.0735			0.834094			0.417047	+	0.908885i	$0.363065\pi$
$420$	−0.142161	+	0.103286i	−0.00693673	+	0.00503983i
$421$	−10.7605	−	33.1175i	−0.524437	−	1.61405i	−0.765427	−	0.643523i	$-0.777472\pi$
$421$	−10.7605	−	33.1175i	−0.524437	−	1.61405i	0.240990	−	0.970528i	$-0.422528\pi$
$422$	0.663777	−	2.04290i	0.0323122	−	0.0994466i
$423$	−5.99623	−	4.35652i	−0.291547	−	0.211821i
$424$	−6.23577	−	4.53055i	−0.302836	−	0.220023i
$425$	3.77251	−	11.6106i	0.182993	−	0.563196i
$426$	0.151390	+	0.465930i	0.00733486	+	0.0225744i
$427$	7.94837	−	5.77483i	0.384649	−	0.279464i
$428$	14.8461			0.717615
$429$	15.1395	−	11.3589i	0.730941	−	0.548411i
$430$	0.113434			0.00547029
$431$	−3.88307	+	2.82121i	−0.187041	+	0.135893i	−0.677365	−	0.735647i	$-0.736878\pi$
$431$	−3.88307	+	2.82121i	−0.187041	+	0.135893i	0.490324	+	0.871540i	$0.336878\pi$
$432$	−6.40884	−	19.7244i	−0.308346	−	0.948990i
$433$	8.74051	−	26.9005i	0.420042	−	1.29276i	−0.487620	−	0.873056i	$-0.662135\pi$
$433$	8.74051	−	26.9005i	0.420042	−	1.29276i	0.907663	−	0.419701i	$-0.137865\pi$
$434$	−1.13196	−	0.822416i	−0.0543358	−	0.0394772i
$435$	0.410876	+	0.298519i	0.0197000	+	0.0143129i
$436$	8.66144	−	26.6572i	0.414808	−	1.27665i
$437$	−2.43753	−	7.50194i	−0.116603	−	0.358866i
$438$	0.105913	−	0.0769503i	0.00506072	−	0.00367683i
$439$	−29.2851			−1.39770			−0.698850	−	0.715268i	$-0.746304\pi$
$439$	−29.2851			−1.39770			−0.698850	+	0.715268i	$0.746304\pi$
$440$	−0.175395	−	0.123360i	−0.00836164	−	0.00588098i
$441$	9.27402			0.441620
$442$	1.84126	−	1.33776i	0.0875800	−	0.0636306i
$443$	3.04934	+	9.38489i	0.144878	+	0.445890i	0.996995	−	0.0774617i	$-0.0246816\pi$
$443$	3.04934	+	9.38489i	0.144878	+	0.445890i	−0.852117	+	0.523351i	$0.824682\pi$
$444$	−1.06747	+	3.28533i	−0.0506599	+	0.155915i
$445$	0.555190	+	0.403369i	0.0263185	+	0.0191215i
$446$	−0.646909	−	0.470007i	−0.0306320	−	0.0222555i
$447$	5.77644	−	17.7781i	0.273216	−	0.840873i
$448$	1.95303	+	6.01080i	0.0922718	+	0.283983i
$449$	−3.81030	+	2.76835i	−0.179819	+	0.130646i	−0.674054	−	0.738682i	$-0.735448\pi$
$449$	−3.81030	+	2.76835i	−0.179819	+	0.130646i	0.494234	+	0.869329i	$0.335448\pi$
$450$	1.49458			0.0704554
$451$	7.75630	−	0.119160i	0.365230	−	0.00561105i
$452$	−28.4968			−1.34038
$453$	−6.08949	+	4.42427i	−0.286109	+	0.207870i
$454$	1.32687	+	4.08369i	0.0622731	+	0.191657i
$455$	−0.105147	+	0.323608i	−0.00492935	+	0.0151710i
$456$	−0.785793	−	0.570912i	−0.0367981	−	0.0267354i
$457$	−0.934568	−	0.679003i	−0.0437172	−	0.0317624i	0.565712	−	0.824603i	$-0.308601\pi$
$457$	−0.934568	−	0.679003i	−0.0437172	−	0.0317624i	−0.609429	+	0.792840i	$0.708601\pi$
$458$	0.308883	−	0.950645i	0.0144332	−	0.0444207i
$459$	4.16554	+	12.8202i	0.194431	+	0.598396i
$460$	1.02092	−	0.741741i	0.0476006	−	0.0345838i
$461$	−41.3195			−1.92444			−0.962221	−	0.272271i	$-0.912225\pi$
$461$	−41.3195			−1.92444			−0.962221	+	0.272271i	$0.912225\pi$
$462$	0.235795	+	0.689479i	0.0109702	+	0.0320775i
$463$	−8.31946			−0.386638			−0.193319	−	0.981136i	$-0.561925\pi$
$463$	−8.31946			−0.386638			−0.193319	+	0.981136i	$0.561925\pi$
$464$	15.4417	−	11.2190i	0.716862	−	0.520830i
$465$	−0.241525	−	0.743339i	−0.0112005	−	0.0344715i
$466$	−0.826367	+	2.54330i	−0.0382807	+	0.117816i
$467$	−5.75647	−	4.18232i	−0.266378	−	0.193535i	0.446576	−	0.894746i	$-0.352643\pi$
$467$	−5.75647	−	4.18232i	−0.266378	−	0.193535i	−0.712954	+	0.701211i	$0.752643\pi$
$468$	−11.0425	−	8.02285i	−0.510440	−	0.370856i
$469$	3.70469	−	11.4019i	0.171067	−	0.526490i
$470$	−0.0249897	−	0.0769104i	−0.00115269	−	0.00354761i
$471$	4.10273	−	2.98081i	0.189044	−	0.137348i
$472$	6.35334			0.292436
$473$	−6.78322	+	22.0221i	−0.311893	+	1.01258i
$474$	−2.71747			−0.124818
$475$	−4.03970	+	2.93501i	−0.185354	+	0.134668i
$476$	−1.32641	−	4.08228i	−0.0607961	−	0.187111i
$477$	4.49961	−	13.8484i	0.206023	−	0.634074i
$478$	1.95453	+	1.42005i	0.0893980	+	0.0649514i
$479$	16.9021	+	12.2801i	0.772278	+	0.561093i	0.902652	−	0.430372i	$-0.141618\pi$
$479$	16.9021	+	12.2801i	0.772278	+	0.561093i	−0.130374	+	0.991465i	$0.541618\pi$
$480$	0.0722688	−	0.222420i	0.00329860	−	0.0101521i
$481$	2.06703	+	6.36167i	0.0942485	+	0.290067i
$482$	3.68330	−	2.67607i	0.167770	−	0.121892i
$483$	−8.66408			−0.394229
$484$	17.0448	−	13.2024i	0.774763	−	0.600109i
$485$	−0.00843234			−0.000382893
$486$	−2.22591	+	1.61722i	−0.100969	+	0.0733586i
$487$	0.345327	+	1.06281i	0.0156482	+	0.0481604i	0.958576	−	0.284838i	$-0.0919397\pi$
$487$	0.345327	+	1.06281i	0.0156482	+	0.0481604i	−0.942927	+	0.332998i	$0.891940\pi$
$488$	−2.68472	+	8.26271i	−0.121531	+	0.374035i
$489$	15.8060	+	11.4837i	0.714773	+	0.519313i
$490$	0.0818623	+	0.0594764i	0.00369816	+	0.00268687i
$491$	8.99131	−	27.6724i	0.405772	−	1.24884i	−0.514477	−	0.857504i	$-0.672014\pi$
$491$	8.99131	−	27.6724i	0.405772	−	1.24884i	0.920249	−	0.391334i	$-0.127986\pi$
$492$	1.73706	+	5.34612i	0.0783126	+	0.241022i
$493$	−10.0366	+	7.29200i	−0.452025	+	0.328415i
$494$	−0.930897			−0.0418830
$495$	0.119247	−	0.387140i	0.00535974	−	0.0174007i
$496$	−29.3741			−1.31894
$497$	1.44744	−	1.05163i	0.0649267	−	0.0471720i
$498$	−1.22613	−	3.77364i	−0.0549442	−	0.169101i
$499$	−0.913859	+	2.81257i	−0.0409100	+	0.125908i	−0.969426	−	0.245385i	$-0.921086\pi$
$499$	−0.913859	+	2.81257i	−0.0409100	+	0.125908i	0.928516	+	0.371293i	$0.121086\pi$
$500$	−1.29340	−	0.939714i	−0.0578428	−	0.0420253i
$501$	−1.44876	−	1.05258i	−0.0647256	−	0.0470259i
$502$	0.885708	−	2.72593i	0.0395311	−	0.121664i
$503$	−7.39279	−	22.7527i	−0.329628	−	1.01449i	−0.969308	−	0.245850i	$-0.920933\pi$
$503$	−7.39279	−	22.7527i	−0.329628	−	1.01449i	0.639680	−	0.768642i	$-0.279067\pi$
$504$	0.858949	−	0.624063i	0.0382606	−	0.0277980i
$505$	0.847157			0.0376980
$506$	−1.69335	−	4.95145i	−0.0752785	−	0.220119i
$507$	10.6172			0.471528
$508$	31.2292	−	22.6893i	1.38557	−	1.00668i
$509$	3.04321	+	9.36605i	0.134888	+	0.415143i	0.995573	−	0.0939958i	$-0.0299640\pi$
$509$	3.04321	+	9.36605i	0.134888	+	0.415143i	−0.860684	+	0.509139i	$0.829964\pi$
$510$	−0.0151254	+	0.0465513i	−0.000669766	+	0.00206133i
$511$	−0.386794	−	0.281022i	−0.0171107	−	0.0124317i
$512$	−11.9316	−	8.66884i	−0.527309	−	0.383112i
$513$	1.70378	−	5.24371i	0.0752239	−	0.231515i
$514$	−0.280870	−	0.864428i	−0.0123886	−	0.0381283i
$515$	0.230149	−	0.167213i	0.0101416	−	0.00736827i
$516$	−16.6981			−0.735093
$517$	16.4257	−	0.252349i	0.722401	−	0.0110983i
$518$	−0.257528			−0.0113151
$519$	14.5232	−	10.5517i	0.637498	−	0.463169i
$520$	−0.0929802	−	0.286164i	−0.00407745	−	0.0125491i
$521$	−7.58209	+	23.3353i	−0.332177	+	1.02234i	0.635919	+	0.771756i	$0.280621\pi$
$521$	−7.58209	+	23.3353i	−0.332177	+	1.02234i	−0.968096	+	0.250580i	$0.919379\pi$
$522$	−1.22874	−	0.892729i	−0.0537803	−	0.0390737i
$523$	35.7180	+	25.9507i	1.56184	+	1.13474i	0.934481	+	0.356013i	$0.115864\pi$
$523$	35.7180	+	25.9507i	1.56184	+	1.13474i	0.627359	+	0.778730i	$0.284136\pi$
$524$	−8.89080	+	27.3631i	−0.388396	+	1.19536i
$525$	1.69484	+	5.21618i	0.0739689	+	0.227653i
$526$	−1.16750	+	0.848235i	−0.0509052	+	0.0369848i
$527$	19.0922			0.831669
$528$	12.5129	+	8.80068i	0.544554	+	0.383001i
$529$	39.2206			1.70524
$530$	0.128531	−	0.0933834i	0.00558304	−	0.00405631i
$531$	3.70890	+	11.4148i	0.160952	+	0.495361i
$532$	−0.542528	+	1.66973i	−0.0235216	+	0.0723920i
$533$	8.80605	+	6.39797i	0.381432	+	0.277127i
$534$	1.66835	+	1.21212i	0.0721964	+	0.0524537i
$535$	−0.191053	+	0.588002i	−0.00825996	+	0.0254215i
$536$	3.27603	+	10.0826i	0.141503	+	0.435501i
$537$	13.8195	−	10.0404i	0.596355	−	0.433277i
$538$	1.94414			0.0838178
$539$	−16.4420	+	12.3361i	−0.708206	+	0.531353i
$540$	0.882060			0.0379578
$541$	4.38266	−	3.18419i	0.188425	−	0.136899i	−0.489573	−	0.871962i	$-0.662848\pi$
$541$	4.38266	−	3.18419i	0.188425	−	0.136899i	0.677999	+	0.735063i	$0.262848\pi$
$542$	−1.08711	−	3.34579i	−0.0466955	−	0.143714i
$543$	7.00542	−	21.5605i	0.300631	−	0.925248i
$544$	4.62169	+	3.35786i	0.198153	+	0.143967i
$545$	0.944331	+	0.686097i	0.0404507	+	0.0293892i
$546$	−0.315965	+	0.972441i	−0.0135221	+	0.0416166i
$547$	−0.373577	−	1.14975i	−0.0159730	−	0.0491598i	0.942752	−	0.333494i	$-0.108228\pi$
$547$	−0.373577	−	1.14975i	−0.0159730	−	0.0491598i	−0.958725	+	0.284334i	$0.908228\pi$
$548$	−19.8476	+	14.4201i	−0.847846	+	0.615996i
$549$	−16.4126			−0.700471
$550$	−2.64976	+	1.98806i	−0.112986	+	0.0847713i
$551$	5.07424			0.216170
$552$	6.19834	−	4.50336i	0.263819	−	0.191676i
$553$	3.06674	+	9.43846i	0.130411	+	0.401364i
$554$	0.0615359	−	0.189388i	0.00261441	−	0.00804632i
$555$	−0.116383	−	0.0845572i	−0.00494019	−	0.00358925i
$556$	10.9524	+	7.95735i	0.464483	+	0.337467i
$557$	8.78129	−	27.0260i	0.372075	−	1.14513i	−0.573356	−	0.819307i	$-0.694359\pi$
$557$	8.78129	−	27.0260i	0.372075	−	1.14513i	0.945431	−	0.325823i	$-0.105641\pi$
$558$	0.722289	+	2.22298i	0.0305769	+	0.0941061i
$559$	−26.1587	+	19.0054i	−1.10640	+	0.803843i
$560$	−0.275020			−0.0116217
$561$	−8.13297	−	5.72015i	−0.343374	−	0.241505i
$562$	−2.94510			−0.124232
$563$	−20.4627	+	14.8671i	−0.862402	+	0.626571i	−0.928537	−	0.371239i	$-0.878933\pi$
$563$	−20.4627	+	14.8671i	−0.862402	+	0.626571i	0.0661356	+	0.997811i	$0.478933\pi$
$564$	3.67861	+	11.3216i	0.154897	+	0.476725i
$565$	0.366723	−	1.12866i	0.0154281	−	0.0474829i
$566$	−0.815694	−	0.592636i	−0.0342862	−	0.0249104i
$567$	−1.64625	−	1.19607i	−0.0691360	−	0.0502303i
$568$	−0.488902	+	1.50468i	−0.0205139	+	0.0631352i
$569$	2.72525	+	8.38746i	0.114248	+	0.351620i	0.991790	−	0.127881i	$-0.0408175\pi$
$569$	2.72525	+	8.38746i	0.114248	+	0.351620i	−0.877541	+	0.479501i	$0.840818\pi$
$570$	0.0161967	−	0.0117676i	0.000678406	−	0.000492890i
$571$	−28.4197			−1.18933			−0.594663	−	0.803975i	$-0.702715\pi$
$571$	−28.4197			−1.18933			−0.594663	+	0.803975i	$0.702715\pi$
$572$	30.2491	−	0.464719i	1.26478	−	0.0194309i
$573$	−5.35315			−0.223631
$574$	−0.339032	+	0.246321i	−0.0141509	+	0.0102813i
$575$	−12.1714	−	37.4597i	−0.507582	−	1.56218i
$576$	3.26260	−	10.0412i	0.135942	−	0.418385i
$577$	−22.8649	−	16.6124i	−0.951880	−	0.691581i	−0.000629273	−	1.00000i	$-0.500200\pi$
$577$	−22.8649	−	16.6124i	−0.951880	−	0.691581i	−0.951251	+	0.308418i	$0.900200\pi$
$578$	1.78373	+	1.29595i	0.0741933	+	0.0539046i
$579$	−2.58054	+	7.94208i	−0.107243	+	0.330062i
$580$	0.250853	+	0.772047i	0.0104161	+	0.0320575i
$581$	−11.7231	+	8.51730i	−0.486355	+	0.353357i
$582$	−0.0253391			−0.00105034
$583$	10.4434	+	30.5372i	0.432522	+	1.26472i
$584$	0.422782			0.0174949
$585$	0.459861	−	0.334108i	0.0190129	−	0.0138137i
$586$	−0.900455	−	2.77131i	−0.0371974	−	0.114482i
$587$	−10.5887	+	32.5887i	−0.437043	+	1.34508i	0.453935	+	0.891035i	$0.350020\pi$
$587$	−10.5887	+	32.5887i	−0.437043	+	1.34508i	−0.890978	+	0.454046i	$0.849980\pi$
$588$	−12.0505	−	8.75523i	−0.496956	−	0.361059i
$589$	−6.31767	−	4.59005i	−0.260315	−	0.189130i
$590$	−0.0404672	+	0.124545i	−0.00166601	+	0.00512744i
$591$	4.01299	+	12.3507i	0.165072	+	0.508040i
$592$	−4.37395	+	3.17786i	−0.179768	+	0.130609i
$593$	−25.9391			−1.06519			−0.532595	−	0.846370i	$-0.678783\pi$
$593$	−25.9391			−1.06519			−0.532595	+	0.846370i	$0.678783\pi$
$594$	1.07674	−	3.49570i	0.0441792	−	0.143430i
$595$	0.178754			0.00732819
$596$	24.1724	−	17.5623i	0.990142	−	0.719380i
$597$	1.06791	+	3.28669i	0.0437067	+	0.134515i
$598$	2.26909	−	6.98353i	0.0927899	−	0.285578i
$599$	−9.67780	−	7.03133i	−0.395424	−	0.287292i	0.372250	−	0.928132i	$-0.378586\pi$
$599$	−9.67780	−	7.03133i	−0.395424	−	0.287292i	−0.767675	+	0.640840i	$0.778586\pi$
$600$	−3.92373	−	2.85076i	−0.160186	−	0.116382i
$601$	14.8035	−	45.5604i	0.603846	−	1.85845i	0.0993129	−	0.995056i	$-0.468336\pi$
$601$	14.8035	−	45.5604i	0.603846	−	1.85845i	0.504534	−	0.863392i	$-0.331664\pi$
$602$	−0.384681	−	1.18393i	−0.0156784	−	0.0482532i
$603$	−16.2026	+	11.7718i	−0.659819	+	0.479386i
$604$	−12.0312			−0.489541
$605$	0.303552	+	0.844983i	0.0123411	+	0.0343534i
$606$	2.54570			0.103412
$607$	−30.4546	+	22.1266i	−1.23612	+	0.898090i	−0.997333	−	0.0729827i	$-0.976748\pi$
$607$	−30.4546	+	22.1266i	−1.23612	+	0.898090i	−0.238782	+	0.971073i	$0.576748\pi$
$608$	−0.722053	−	2.22225i	−0.0292831	−	0.0901242i
$609$	1.72230	−	5.30070i	0.0697912	−	0.214795i
$610$	−0.144875	−	0.105258i	−0.00586580	−	0.00426175i
$611$	18.6488	+	13.5491i	0.754449	+	0.548139i
$612$	−2.21582	+	6.81960i	−0.0895693	+	0.275666i
$613$	9.18773	+	28.2769i	0.371089	+	1.14209i	0.946079	+	0.323935i	$0.105006\pi$
$613$	9.18773	+	28.2769i	0.371089	+	1.14209i	−0.574990	+	0.818160i	$0.694994\pi$
$614$	0.666479	−	0.484225i	0.0268969	−	0.0195417i
$615$	−0.234094			−0.00943959
$616$	−0.692723	+	2.24896i	−0.0279106	+	0.0906132i
$617$	−31.2183			−1.25680			−0.628401	−	0.777890i	$-0.716290\pi$
$617$	−31.2183			−1.25680			−0.628401	+	0.777890i	$0.716290\pi$
$618$	0.691596	−	0.502474i	0.0278201	−	0.0202125i
$619$	8.32140	+	25.6106i	0.334465	+	1.02938i	0.966985	+	0.254834i	$0.0820208\pi$
$619$	8.32140	+	25.6106i	0.334465	+	1.02938i	−0.632520	+	0.774544i	$0.717979\pi$
$620$	0.386054	−	1.18815i	0.0155043	−	0.0477173i
$621$	35.1849	+	25.5634i	1.41192	+	1.02582i
$622$	−0.433855	−	0.315214i	−0.0173960	−	0.0126389i
$623$	2.32724	−	7.16250i	0.0932387	−	0.286959i
$624$	6.63332	+	20.4153i	0.265545	+	0.817264i
$625$	−20.1446	+	14.6359i	−0.805784	+	0.585437i
$626$	−0.940108			−0.0375743
$627$	1.31601	+	3.84811i	0.0525565	+	0.153679i
$628$	8.10587			0.323460
$629$	2.84292	−	2.06550i	0.113355	−	0.0823570i
$630$	0.00676255	+	0.0208130i	0.000269427	+	0.000829210i
$631$	6.00314	−	18.4758i	0.238981	−	0.735509i	−0.757587	−	0.652734i	$-0.773622\pi$
$631$	6.00314	−	18.4758i	0.238981	−	0.735509i	0.996568	−	0.0827746i	$-0.0263782\pi$
$632$	−7.09983	−	5.15833i	−0.282416	−	0.205187i
$633$	−10.6532	−	7.73998i	−0.423426	−	0.307637i
$634$	−0.109981	+	0.338486i	−0.00436789	+	0.0134430i
$635$	0.496757	+	1.52886i	0.0197132	+	0.0606710i
$636$	−18.9204	+	13.7465i	−0.750244	+	0.545084i
$637$	−28.8430			−1.14280
$638$	3.36592	−	0.0517109i	0.133258	−	0.00204725i
$639$	−2.98882			−0.118236
$640$	0.401790	−	0.291917i	0.0158821	−	0.0115390i
$641$	−1.04573	−	3.21841i	−0.0413037	−	0.127120i	0.928278	−	0.371886i	$-0.121289\pi$
$641$	−1.04573	−	3.21841i	−0.0413037	−	0.127120i	−0.969582	+	0.244766i	$0.921289\pi$
$642$	−0.574115	+	1.76694i	−0.0226585	+	0.0697357i
$643$	−16.4102	−	11.9227i	−0.647154	−	0.470185i	0.215147	−	0.976582i	$-0.430977\pi$
$643$	−16.4102	−	11.9227i	−0.647154	−	0.470185i	−0.862300	+	0.506397i	$0.830977\pi$
$644$	−11.2038	−	8.14003i	−0.441491	−	0.320762i
$645$	0.214886	−	0.661351i	0.00846113	−	0.0260407i
$646$	0.151122	+	0.465105i	0.00594580	+	0.0182993i
$647$	−2.79440	+	2.03025i	−0.109859	+	0.0798173i	−0.641358	−	0.767241i	$-0.721629\pi$
$647$	−2.79440	+	2.03025i	−0.109859	+	0.0798173i	0.531499	+	0.847059i	$0.321629\pi$
$648$	1.79942			0.0706881
$649$	−21.7592	−	15.3039i	−0.854125	−	0.600731i
$650$	−4.64828			−0.182321
$651$	−6.93924	+	5.04165i	−0.271970	+	0.197598i
$652$	9.65011	+	29.7000i	0.377927	+	1.16314i
$653$	−8.01052	+	24.6538i	−0.313476	+	0.964780i	0.662901	+	0.748707i	$0.269325\pi$
$653$	−8.01052	+	24.6538i	−0.313476	+	0.964780i	−0.976377	+	0.216073i	$0.930675\pi$
$654$	2.83771	+	2.06172i	0.110963	+	0.0806196i
$655$	−0.969337	−	0.704265i	−0.0378751	−	0.0275179i
$656$	−2.71867	+	8.36722i	−0.106146	+	0.326685i
$657$	0.246808	+	0.759598i	0.00962890	+	0.0296347i
$658$	−0.717976	+	0.521640i	−0.0279896	+	0.0203357i
$659$	39.0302			1.52040			0.760201	−	0.649688i	$-0.225101\pi$
$659$	39.0302			1.52040			0.760201	+	0.649688i	$0.225101\pi$
$660$	−0.520431	+	0.390469i	−0.0202577	+	0.0151990i
$661$	−12.0694			−0.469444			−0.234722	−	0.972063i	$-0.575418\pi$
$661$	−12.0694			−0.469444			−0.234722	+	0.972063i	$0.575418\pi$
$662$	−2.94712	+	2.14121i	−0.114543	+	0.0832203i
$663$	−4.31144	−	13.2692i	−0.167442	−	0.515335i
$664$	3.95969	−	12.1867i	0.153666	−	0.472935i
$665$	−0.0591502	−	0.0429752i	−0.00229375	−	0.00166651i
$666$	0.348047	+	0.252871i	0.0134865	+	0.00979855i
$667$	−12.3686	+	38.0667i	−0.478914	+	1.47395i
$668$	−0.884514	−	2.72225i	−0.0342229	−	0.105327i
$669$	−3.96574	+	2.88128i	−0.153325	+	0.111397i
$670$	−0.218516			−0.00844202
$671$	29.0979	−	21.8316i	1.12331	−	0.842800i
$672$	−2.56651			−0.0990051
$673$	28.4932	−	20.7016i	1.09833	−	0.797986i	0.117547	−	0.993067i	$-0.462497\pi$
$673$	28.4932	−	20.7016i	1.09833	−	0.797986i	0.980787	+	0.195081i	$0.0624970\pi$
$674$	0.108993	+	0.335446i	0.00419826	+	0.0129209i
$675$	8.50757	−	26.1836i	0.327456	−	1.00781i
$676$	13.7295	+	9.97503i	0.528056	+	0.383655i
$677$	12.0067	+	8.72340i	0.461456	+	0.335267i	0.794102	−	0.607784i	$-0.207941\pi$
$677$	12.0067	+	8.72340i	0.461456	+	0.335267i	−0.332646	+	0.943052i	$0.607941\pi$
$678$	1.10200	−	3.39161i	0.0423221	−	0.130254i
$679$	0.0285959	+	0.0880092i	0.00109741	+	0.00337748i
$680$	−0.127882	+	0.0929115i	−0.00490404	+	0.00356299i
$681$	26.3225			1.00868
$682$	−4.23750	−	2.98036i	−0.162262	−	0.114124i
$683$	−31.1026			−1.19011			−0.595054	−	0.803686i	$-0.702869\pi$
$683$	−31.1026			−1.19011			−0.595054	+	0.803686i	$0.702869\pi$
$684$	2.37276	−	1.72391i	0.0907246	−	0.0659153i
$685$	−0.315712	−	0.971661i	−0.0120627	−	0.0371253i
$686$	0.730722	−	2.24893i	0.0278991	−	0.0858646i
$687$	−4.95737	−	3.60174i	−0.189135	−	0.137415i
$688$	−21.1430	−	15.3613i	−0.806071	−	0.585645i
$689$	−13.9942	+	43.0696i	−0.533135	+	1.64082i
$690$	0.0487999	+	0.150191i	0.00185778	+	0.00571766i
$691$	−39.3391	+	28.5815i	−1.49653	+	1.08729i	−0.524792	+	0.851230i	$0.675857\pi$
$691$	−39.3391	+	28.5815i	−1.49653	+	1.08729i	−0.971738	+	0.236063i	$0.924143\pi$
$692$	28.6939			1.09078
$693$	−4.44502	+	0.0682891i	−0.168852	+	0.00259409i
$694$	−6.85158			−0.260082
$695$	−0.456107	+	0.331381i	−0.0173011	+	0.0125700i
$696$	1.52302	+	4.68736i	0.0577298	+	0.177674i
$697$	1.76705	−	5.43841i	0.0669317	−	0.205995i
$698$	−3.72258	−	2.70461i	−0.140902	−	0.102371i
$699$	13.2626	+	9.63586i	0.501639	+	0.364462i
$700$	−2.70903	+	8.33753i	−0.102392	+	0.315129i
$701$	−5.35692	−	16.4869i	−0.202328	−	0.622701i	−0.999813	−	0.0193621i	$-0.993836\pi$
$701$	−5.35692	−	16.4869i	−0.202328	−	0.622701i	0.797485	−	0.603339i	$-0.206164\pi$
$702$	4.15233	−	3.01684i	0.156719	−	0.113863i
$703$	−1.43731			−0.0542092
$704$	7.57235	+	22.1420i	0.285394	+	0.834509i
$705$	−0.495747			−0.0186709
$706$	−1.20828	+	0.877867i	−0.0454742	+	0.0330390i
$707$	−2.87290	−	8.84187i	−0.108046	−	0.332533i
$708$	5.95697	−	18.3337i	0.223877	−	0.689022i
$709$	−14.3904	−	10.4552i	−0.540443	−	0.392655i	0.283806	−	0.958882i	$-0.408403\pi$
$709$	−14.3904	−	10.4552i	−0.540443	−	0.392655i	−0.824250	+	0.566227i	$0.808403\pi$
$710$	−0.0263825	−	0.0191680i	−0.000990116	−	0.000719361i
$711$	5.12310	−	15.7673i	0.192131	−	0.591319i
$712$	2.05795	+	6.33373i	0.0771251	+	0.237367i
$713$	49.8338	−	36.2064i	1.86629	−	1.35594i
$714$	0.537155			0.0201025
$715$	−0.370867	+	1.20404i	−0.0138696	+	0.0450285i
$716$	27.3035			1.02038
$717$	11.9818	−	8.70531i	0.447470	−	0.325106i
$718$	2.13504	+	6.57097i	0.0796789	+	0.245226i
$719$	−15.0763	+	46.4001i	−0.562252	+	1.73043i	0.113727	+	0.993512i	$0.463721\pi$
$719$	−15.0763	+	46.4001i	−0.562252	+	1.73043i	−0.675979	+	0.736921i	$0.736279\pi$
$720$	0.371687	+	0.270046i	0.0138520	+	0.0100640i
$721$	−2.52570	−	1.83503i	−0.0940621	−	0.0683401i
$722$	0.0618116	−	0.190237i	0.00230039	−	0.00707987i
$723$	−8.62469	−	26.5441i	−0.320756	−	0.987184i
$724$	29.3153	−	21.2988i	1.08949	−	0.791564i
$725$	25.3374			0.941008
$726$	0.912173	+	2.53917i	0.0338539	+	0.0942375i
$727$	−11.3288			−0.420162			−0.210081	−	0.977684i	$-0.567373\pi$
$727$	−11.3288			−0.420162			−0.210081	+	0.977684i	$0.567373\pi$
$728$	−2.67140	+	1.94089i	−0.0990088	+	0.0719341i
$729$	7.31810	+	22.5228i	0.271041	+	0.834178i
$730$	−0.00269288	+	0.00828785i	−9.96681e−5	+	0.000306747i
$731$	13.7423	+	9.98435i	0.508277	+	0.369285i
$732$	21.3263	+	15.4944i	0.788241	+	0.572691i
$733$	4.42597	−	13.6217i	0.163477	−	0.503131i	−0.835444	−	0.549576i	$-0.814789\pi$
$733$	4.42597	−	13.6217i	0.163477	−	0.503131i	0.998921	+	0.0464453i	$0.0147893\pi$
$734$	−0.539899	−	1.66164i	−0.0199281	−	0.0613322i
$735$	0.501840	−	0.364608i	0.0185106	−	0.0134488i
$736$	18.4312			0.679383
$737$	13.0670	−	42.4226i	0.481328	−	1.56266i
$738$	0.700066			0.0257698
$739$	−34.4641	+	25.0396i	−1.26778	+	0.921097i	−0.999112	−	0.0421353i	$-0.986584\pi$
$739$	−34.4641	+	25.0396i	−1.26778	+	0.921097i	−0.268669	+	0.963232i	$0.586584\pi$
$740$	−0.0710557	−	0.218687i	−0.00261206	−	0.00803910i
$741$	−1.76346	+	5.42737i	−0.0647823	+	0.199379i
$742$	−1.41053	−	1.02481i	−0.0517822	−	0.0376220i
$743$	20.6733	+	15.0200i	0.758430	+	0.551031i	0.898428	−	0.439120i	$-0.144710\pi$
$743$	20.6733	+	15.0200i	0.758430	+	0.551031i	−0.139999	+	0.990152i	$0.544710\pi$
$744$	2.34386	−	7.21367i	0.0859302	−	0.264466i
$745$	0.384507	+	1.18339i	0.0140872	+	0.0433561i
$746$	−4.84587	+	3.52073i	−0.177420	+	0.128903i
$747$	24.2069			0.885684
$748$	−5.14282	−	15.0379i	−0.188040	−	0.549842i
$749$	6.78494			0.247916
$750$	0.161859	−	0.117598i	0.00591026	−	0.00429406i
$751$	13.2318	+	40.7234i	0.482837	+	1.48602i	0.835090	+	0.550113i	$0.185416\pi$
$751$	13.2318	+	40.7234i	0.482837	+	1.48602i	−0.352253	+	0.935905i	$0.614584\pi$
$752$	−5.75740	+	17.7195i	−0.209951	+	0.646162i
$753$	−14.2150	−	10.3278i	−0.518024	−	0.376366i
$754$	3.82147	+	2.77646i	0.139170	+	0.101113i
$755$	0.154828	−	0.476511i	0.00563476	−	0.0173420i
$756$	−2.99126	−	9.20616i	−0.108791	−	0.334825i
$757$	25.4974	−	18.5250i	0.926720	−	0.673301i	−0.0184677	−	0.999829i	$-0.505879\pi$
$757$	25.4974	−	18.5250i	0.926720	−	0.673301i	0.945187	+	0.326528i	$0.105879\pi$
$758$	−1.49909			−0.0544494
$759$	−32.0761	+	0.492787i	−1.16429	+	0.0178870i
$760$	0.0646538			0.00234524
$761$	28.4906	−	20.6996i	1.03278	−	0.750362i	0.0639201	−	0.997955i	$-0.479640\pi$
$761$	28.4906	−	20.6996i	1.03278	−	0.750362i	0.968864	+	0.247593i	$0.0796397\pi$
$762$	1.49275	+	4.59422i	0.0540768	+	0.166431i
$763$	3.95843	−	12.1828i	0.143305	−	0.441047i
$764$	−6.92232	−	5.02936i	−0.250441	−	0.181956i
$765$	−0.241584	−	0.175521i	−0.00873450	−	0.00634599i
$766$	0.247958	−	0.763137i	0.00895910	−	0.0275733i
$767$	−11.5350	−	35.5010i	−0.416504	−	1.28187i
$768$	−12.7916	+	9.29364i	−0.461577	+	0.335355i
$769$	9.89036			0.356655			0.178328	−	0.983971i	$-0.442931\pi$
$769$	9.89036			0.356655			0.178328	+	0.983971i	$0.442931\pi$
$770$	−0.0396744	−	0.0279041i	−0.00142976	−	0.00100559i
$771$	−5.57191			−0.200667
$772$	−10.7987	+	7.84569i	−0.388653	+	0.282373i
$773$	−10.1492	−	31.2359i	−0.365040	−	1.12348i	−0.949956	−	0.312384i	$-0.898872\pi$
$773$	−10.1492	−	31.2359i	−0.365040	−	1.12348i	0.584915	−	0.811094i	$-0.301128\pi$
$774$	−0.642623	+	1.97779i	−0.0230986	+	0.0710902i
$775$	−31.5462	−	22.9197i	−1.13317	−	0.823300i
$776$	−0.0662025	−	0.0480990i	−0.00237653	−	0.00172665i
$777$	−0.487852	+	1.50145i	−0.0175016	+	0.0538644i
$778$	1.89733	+	5.83939i	0.0680226	+	0.209352i
$779$	−1.89220	+	1.37476i	−0.0677951	+	0.0492560i
$780$	−0.912955			−0.0326890
$781$	5.29890	−	3.97566i	0.189609	−	0.142260i
$782$	−3.85755			−0.137946
$783$	−22.6340	+	16.4446i	−0.808873	+	0.587680i
$784$	−7.20400	−	22.1716i	−0.257286	−	0.791844i
$785$	−0.104314	+	0.321044i	−0.00372311	+	0.0114586i
$786$	−2.91286	−	2.11631i	−0.103898	−	0.0754864i
$787$	−42.3741	−	30.7866i	−1.51047	−	1.09742i	−0.965967	−	0.258666i	$-0.916717\pi$
$787$	−42.3741	−	30.7866i	−1.51047	−	1.09742i	−0.544506	−	0.838757i	$-0.683283\pi$
$788$	−6.41435	+	19.7413i	−0.228502	+	0.703256i
$789$	2.73377	+	8.41367i	0.0973246	+	0.299534i
$790$	0.146341	−	0.106323i	0.00520658	−	0.00378280i
$791$	−13.0235			−0.463064
$792$	3.14450	−	2.35926i	0.111735	−	0.0838325i
$793$	51.0444			1.81264
$794$	0.290564	−	0.211107i	0.0103117	−	0.00749191i
$795$	−0.300964	−	0.926272i	−0.0106741	−	0.0328515i
$796$	−1.70694	+	5.25344i	−0.0605011	+	0.186203i
$797$	14.3930	+	10.4572i	0.509827	+	0.370411i	0.812758	−	0.582601i	$-0.197965\pi$
$797$	14.3930	+	10.4572i	0.509827	+	0.370411i	−0.302931	+	0.953013i	$0.597965\pi$
$798$	−0.177746	−	0.129140i	−0.00629215	−	0.00457152i
$799$	3.74212	−	11.5171i	0.132387	−	0.407444i
$800$	−3.60546	−	11.0965i	−0.127472	−	0.392319i
$801$	−10.1782	+	7.39490i	−0.359629	+	0.261286i
$802$	−1.28421			−0.0453471
$803$	−1.44797	−	1.01840i	−0.0510976	−	0.0359385i
$804$	32.1667			1.13443
$805$	0.466577	−	0.338988i	0.0164447	−	0.0119478i
$806$	−2.24638	−	6.91365i	−0.0791253	−	0.243523i
$807$	3.68291	−	11.3348i	0.129645	−	0.399005i
$808$	6.65106	+	4.83228i	0.233983	+	0.169999i
$809$	−29.7156	−	21.5896i	−1.04474	−	0.759051i	−0.0735382	−	0.997292i	$-0.523429\pi$
$809$	−29.7156	−	21.5896i	−1.04474	−	0.759051i	−0.971206	+	0.238241i	$0.923429\pi$
$810$	−0.0114613	+	0.0352743i	−0.000402710	+	0.00123941i
$811$	−11.9122	−	36.6618i	−0.418292	−	1.28737i	−0.909273	−	0.416201i	$-0.863361\pi$
$811$	−11.9122	−	36.6618i	−0.418292	−	1.28737i	0.490981	−	0.871171i	$-0.336639\pi$
$812$	7.20724	−	5.23637i	0.252925	−	0.183760i
$813$	−21.5662			−0.756360
$814$	−0.953418	+	0.0146474i	−0.0334173	+	0.000513392i
$815$	−1.30049			−0.0455543
$816$	9.12323	−	6.62841i	0.319377	−	0.232041i
$817$	−2.14697	−	6.60771i	−0.0751131	−	0.231174i
$818$	−0.264883	+	0.815226i	−0.00926141	+	0.0285037i
$819$	−5.04661	−	3.66658i	−0.176343	−	0.128121i
$820$	−0.302714	−	0.219935i	−0.0105712	−	0.00768046i
$821$	7.98377	−	24.5715i	0.278636	−	0.857552i	−0.709599	−	0.704606i	$-0.751124\pi$
$821$	7.98377	−	24.5715i	0.278636	−	0.857552i	0.988235	−	0.152946i	$-0.0488761\pi$
$822$	−0.948714	−	2.91984i	−0.0330902	−	0.101841i
$823$	17.2510	−	12.5336i	0.601333	−	0.436894i	−0.245019	−	0.969518i	$-0.578794\pi$
$823$	17.2510	−	12.5336i	0.601333	−	0.436894i	0.846352	+	0.532624i	$0.178794\pi$
$824$	2.76070			0.0961737
$825$	6.57130	+	19.2149i	0.228783	+	0.668977i
$826$	1.43712			0.0500040
$827$	−9.87124	+	7.17188i	−0.343257	+	0.249391i	−0.746035	−	0.665907i	$-0.768045\pi$
$827$	−9.87124	+	7.17188i	−0.343257	+	0.249391i	0.402778	+	0.915298i	$0.368045\pi$
$828$	7.14900	+	22.0024i	0.248445	+	0.764635i
$829$	16.4649	−	50.6737i	0.571849	−	1.75997i	−0.0748191	−	0.997197i	$-0.523838\pi$
$829$	16.4649	−	50.6737i	0.571849	−	1.75997i	0.646668	−	0.762772i	$-0.276162\pi$
$830$	0.213676	+	0.155244i	0.00741679	+	0.00538861i
$831$	−0.987609	−	0.717540i	−0.0342598	−	0.0248912i
$832$	−10.1470	+	31.2291i	−0.351782	+	1.08268i
$833$	4.68236	+	14.4108i	0.162234	+	0.499306i
$834$	−1.37060	+	0.995799i	−0.0474600	+	0.0344817i
$835$	0.119201			0.00412513
$836$	−1.91357	+	6.21252i	−0.0661823	+	0.214864i
$837$	43.0557			1.48822
$838$	−2.76291	+	2.00737i	−0.0954433	+	0.0693436i
$839$	−2.59553	−	7.98822i	−0.0896077	−	0.275784i	0.896203	−	0.443644i	$-0.146314\pi$
$839$	−2.59553	−	7.98822i	−0.0896077	−	0.275784i	−0.985811	+	0.167860i	$0.946314\pi$
$840$	0.0219448	−	0.0675392i	0.000757168	−	0.00233032i
$841$	2.63096	+	1.91151i	0.0907228	+	0.0659140i
$842$	5.63504	+	4.09410i	0.194196	+	0.141092i
$843$	−5.57909	+	17.1707i	−0.192154	+	0.591390i
$844$	−6.50412	−	20.0176i	−0.223881	−	0.689035i
$845$	−0.571758	+	0.415406i	−0.0196691	+	0.0142904i
$846$	1.48255			0.0509710
$847$	7.78976	−	6.03373i	0.267659	−	0.207321i
$848$	−36.6029			−1.25695
$849$	−5.00044	+	3.63304i	−0.171615	+	0.124685i
$850$	0.754601	+	2.32242i	0.0258826	+	0.0796585i
$851$	3.50348	−	10.7826i	0.120098	−	0.369623i
$852$	3.88363	+	2.82162i	0.133051	+	0.0966672i
$853$	−43.2626	−	31.4321i	−1.48128	−	1.07622i	−0.977140	−	0.212596i	$-0.931808\pi$
$853$	−43.2626	−	31.4321i	−1.48128	−	1.07622i	−0.504144	−	0.863620i	$-0.668192\pi$
$854$	−0.607282	+	1.86902i	−0.0207808	+	0.0639566i
$855$	0.0377430	+	0.116161i	0.00129078	+	0.00397263i
$856$	−4.85399	+	3.52663i	−0.165906	+	0.120538i
$857$	−26.7668			−0.914335			−0.457168	−	0.889381i	$-0.651136\pi$
$857$	−26.7668			−0.914335			−0.457168	+	0.889381i	$0.651136\pi$
$858$	−1.11445	+	3.61813i	−0.0380468	+	0.123521i
$859$	20.6673			0.705158			0.352579	−	0.935782i	$-0.385305\pi$
$859$	20.6673			0.705158			0.352579	+	0.935782i	$0.385305\pi$
$860$	0.899225	−	0.653325i	0.0306633	−	0.0222782i
$861$	0.793866	+	2.44327i	0.0270549	+	0.0832663i
$862$	0.296679	−	0.913085i	0.0101049	−	0.0310998i
$863$	−30.6766	−	22.2879i	−1.04424	−	0.758688i	−0.0731351	−	0.997322i	$-0.523300\pi$
$863$	−30.6766	−	22.2879i	−1.04424	−	0.758688i	−0.971110	+	0.238634i	$0.923300\pi$
$864$	10.4226	+	7.57247i	0.354584	+	0.257621i
$865$	−0.369259	+	1.13646i	−0.0125552	+	0.0386408i
$866$	1.74833	+	5.38082i	0.0594108	+	0.182848i
$867$	10.9348	−	7.94458i	0.371365	−	0.269812i
$868$	−13.7101			−0.465349
$869$	11.8905	+	34.7685i	0.403357	+	1.17944i
$870$	−0.101588			−0.00344414
$871$	50.3913	−	36.6114i	1.70744	−	1.24053i
$872$	3.50040	+	10.7731i	0.118539	+	0.364824i
$873$	0.0477705	−	0.147022i	0.00161679	−	0.00497596i
$874$	1.27648	+	0.927413i	0.0431774	+	0.0313702i
$875$	−0.591108	−	0.429465i	−0.0199831	−	0.0145186i
$876$	0.396406	−	1.22001i	0.0133933	−	0.0412204i
$877$	−0.225418	−	0.693765i	−0.00761182	−	0.0234268i	0.947178	−	0.320707i	$-0.103920\pi$
$877$	−0.225418	−	0.693765i	−0.00761182	−	0.0234268i	−0.954790	+	0.297280i	$0.903920\pi$
$878$	4.73905	−	3.44312i	0.159935	−	0.116200i
$879$	−17.8633			−0.602513
$880$	−1.01818	+	0.0156423i	−0.0343227	+	0.000527302i
$881$	−42.5972			−1.43514			−0.717569	−	0.696488i	$-0.754745\pi$
$881$	−42.5972			−1.43514			−0.717569	+	0.696488i	$0.754745\pi$
$882$	−1.50077	+	1.09037i	−0.0505334	+	0.0367147i
$883$	0.422755	+	1.30111i	0.0142268	+	0.0437857i	0.957918	−	0.287042i	$-0.0926720\pi$
$883$	0.422755	+	1.30111i	0.0142268	+	0.0437857i	−0.943691	+	0.330828i	$0.892672\pi$
$884$	6.89139	−	21.2095i	0.231783	−	0.713353i
$885$	0.649471	+	0.471868i	0.0218317	+	0.0158617i
$886$	−1.59686	−	1.16019i	−0.0536477	−	0.0389773i
$887$	6.96654	−	21.4408i	0.233913	−	0.719911i	−0.763350	−	0.645985i	$-0.776447\pi$
$887$	6.96654	−	21.4408i	0.233913	−	0.719911i	0.997264	−	0.0739266i	$-0.0235530\pi$
$888$	−0.431403	−	1.32772i	−0.0144770	−	0.0445555i
$889$	14.2723	−	10.3694i	0.478677	−	0.347779i
$890$	−0.137269			−0.00460126
$891$	−6.16276	−	4.33445i	−0.206460	−	0.145210i
$892$	−7.83523			−0.262343
$893$	−4.00716	+	2.91137i	−0.134094	+	0.0974252i
$894$	1.15544	+	3.55608i	0.0386438	+	0.118933i
$895$	−0.351366	+	1.08139i	−0.0117449	+	0.0361470i
$896$	−4.40933	−	3.20357i	−0.147305	−	0.107024i
$897$	−36.4173	−	26.4587i	−1.21594	−	0.883431i
$898$	0.291120	−	0.895975i	0.00971480	−	0.0298991i
$899$	12.2448	+	37.6857i	0.408388	+	1.25689i
$900$	11.8480	−	8.60806i	0.394933	−	0.286935i
$901$	23.7907			0.792583
$902$	−1.24115	+	0.931211i	−0.0413258	+	0.0310059i
$903$	−7.63132			−0.253954
$904$	9.31713	−	6.76929i	0.309883	−	0.225143i
$905$	0.466313	+	1.43516i	0.0155008	+	0.0477065i
$906$	0.465257	−	1.43191i	0.0154571	−	0.0475722i
$907$	17.9005	+	13.0055i	0.594378	+	0.431841i	0.843879	−	0.536534i	$-0.180267\pi$
$907$	17.9005	+	13.0055i	0.594378	+	0.431841i	−0.249501	+	0.968375i	$0.580267\pi$
$908$	34.0385	+	24.7304i	1.12961	+	0.820707i
$909$	−4.79928	+	14.7707i	−0.159182	+	0.489912i
$910$	−0.0210321	−	0.0647302i	−0.000697208	−	0.00214578i
$911$	−11.1991	+	8.13659i	−0.371041	+	0.269577i	−0.757643	−	0.652670i	$-0.773649\pi$
$911$	−11.1991	+	8.13659i	−0.371041	+	0.269577i	0.386601	+	0.922247i	$0.373649\pi$
$912$	−4.61248			−0.152734
$913$	−42.9166	+	32.1995i	−1.42033	+	1.06565i
$914$	0.231068			0.00764307
$915$	−0.888124	+	0.645260i	−0.0293605	+	0.0213316i
$916$	−3.02664	−	9.31504i	−0.100003	−	0.307777i
$917$	−4.06325	+	12.5054i	−0.134180	+	0.412964i
$918$	−2.18139	−	1.58487i	−0.0719967	−	0.0523087i
$919$	11.6444	+	8.46019i	0.384115	+	0.279076i	0.763040	−	0.646352i	$-0.223706\pi$
$919$	11.6444	+	8.46019i	0.384115	+	0.279076i	−0.378925	+	0.925427i	$0.623706\pi$
$920$	−0.157595	+	0.485029i	−0.00519577	+	0.0159909i
$921$	−1.56060	−	4.80304i	−0.0514236	−	0.158266i
$922$	6.68652	−	4.85804i	0.220209	−	0.159991i
$923$	9.29547			0.305964
$924$	5.84026	+	4.10763i	0.192131	+	0.135131i
$925$	−7.17698			−0.235978
$926$	1.34629	−	0.978140i	0.0442420	−	0.0321437i
$927$	1.61162	+	4.96005i	0.0529325	+	0.162910i
$928$	−3.66387	+	11.2762i	−0.120273	+	0.370161i
$929$	−18.7115	−	13.5947i	−0.613904	−	0.446027i	0.236883	−	0.971538i	$-0.423874\pi$
$929$	−18.7115	−	13.5947i	−0.613904	−	0.446027i	−0.850787	+	0.525511i	$0.823874\pi$
$930$	0.126481	+	0.0918940i	0.00414748	+	0.00301332i
$931$	1.91517	−	5.89430i	0.0627673	−	0.193178i
$932$	8.09728	+	24.9209i	0.265235	+	0.816310i
$933$	−2.65966	+	1.93235i	−0.0870732	+	0.0632624i
$934$	1.42327			0.0465707
$935$	0.661781	−	0.0101670i	0.0216426	−	0.000332496i
$936$	5.51617			0.180302
$937$	4.04113	−	2.93605i	0.132018	−	0.0959167i	−0.519817	−	0.854278i	$-0.674000\pi$
$937$	4.04113	−	2.93605i	0.132018	−	0.0959167i	0.651834	+	0.758361i	$0.274000\pi$
$938$	0.741037	+	2.28068i	0.0241957	+	0.0744668i
$939$	−1.78091	+	5.48107i	−0.0581177	+	0.178868i
$940$	−0.641066	−	0.465761i	−0.0209093	−	0.0151915i
$941$	46.5415	+	33.8144i	1.51721	+	1.10232i	0.962848	+	0.270042i	$0.0870377\pi$
$941$	46.5415	+	33.8144i	1.51721	+	1.10232i	0.554362	+	0.832276i	$0.312962\pi$
$942$	−0.313462	+	0.964737i	−0.0102131	+	0.0314328i
$943$	−5.70110	−	17.5462i	−0.185653	−	0.571382i
$944$	24.4086	−	17.7339i	0.794433	−	0.577190i
$945$	0.403117			0.0131134
$946$	−1.49150	−	4.36124i	−0.0484929	−	0.141796i
$947$	26.9892			0.877032			0.438516	−	0.898723i	$-0.355504\pi$
$947$	26.9892			0.877032			0.438516	+	0.898723i	$0.355504\pi$
$948$	−21.5421	+	15.6513i	−0.699656	+	0.508330i
$949$	−0.767594	−	2.36241i	−0.0249172	−	0.0766871i
$950$	0.308646	−	0.949915i	0.0100138	−	0.0308193i
$951$	1.76512	+	1.28243i	0.0572378	+	0.0415857i
$952$	1.40340	+	1.01963i	0.0454845	+	0.0330464i
$953$	−13.8266	+	42.5540i	−0.447889	+	1.37846i	0.431396	+	0.902163i	$0.358021\pi$
$953$	−13.8266	+	42.5540i	−0.447889	+	1.37846i	−0.879285	+	0.476297i	$0.841979\pi$
$954$	0.900042	+	2.77004i	0.0291399	+	0.0896835i
$955$	0.288277	−	0.209446i	0.00932843	−	0.00677750i
$956$	23.6728			0.765634
$957$	6.07480	−	19.7222i	0.196370	−	0.637527i
$958$	−4.17899			−0.135017
$959$	−9.07068	+	6.59024i	−0.292908	+	0.212810i
$960$	−0.218224	−	0.671626i	−0.00704316	−	0.0216766i
$961$	9.26480	−	28.5141i	0.298864	−	0.919810i
$962$	−1.08246	−	0.786450i	−0.0348998	−	0.0253562i
$963$	−9.16979	−	6.66225i	−0.295492	−	0.214688i
$964$	13.7857	−	42.4279i	0.444007	−	1.36651i
$965$	−0.171773	−	0.528662i	−0.00552955	−	0.0170182i
$966$	1.40206	−	1.01866i	0.0451106	−	0.0327748i
$967$	15.9104			0.511644			0.255822	−	0.966724i	$-0.417654\pi$
$967$	15.9104			0.511644			0.255822	+	0.966724i	$0.417654\pi$
$968$	−2.43668	+	8.36548i	−0.0783178	+	0.268877i
$969$	2.99796			0.0963083
$970$	0.00136456		0.000991412i	4.38134e−5		3.18323e-5i
$971$	9.67376	+	29.7728i	0.310446	+	0.955454i	0.977589	+	0.210524i	$0.0675171\pi$
$971$	9.67376	+	29.7728i	0.310446	+	0.955454i	−0.667143	+	0.744930i	$0.732483\pi$
$972$	−8.33103	+	25.6403i	−0.267218	+	0.822412i
$973$	5.00542	+	3.63665i	0.160466	+	0.116586i
$974$	−0.180839	−	0.131388i	−0.00579447	−	0.00420993i
$975$	−8.80555	+	27.1007i	−0.282003	+	0.867917i
$976$	12.7492	+	39.2379i	0.408091	+	1.25598i
$977$	−13.3427	+	9.69406i	−0.426872	+	0.310141i	−0.780397	−	0.625285i	$-0.784983\pi$
$977$	−13.3427	+	9.69406i	−0.426872	+	0.310141i	0.353525	+	0.935425i	$0.384983\pi$
$978$	−3.90798			−0.124964
$979$	8.20849	−	26.6493i	0.262344	−	0.851715i
$980$	0.991499			0.0316723
$981$	−17.3123	+	12.5781i	−0.552738	+	0.401588i
$982$	1.79850	+	5.53521i	0.0573924	+	0.176636i
$983$	−8.56967	+	26.3747i	−0.273330	+	0.841223i	0.716327	+	0.697765i	$0.245822\pi$
$983$	−8.56967	+	26.3747i	−0.273330	+	0.841223i	−0.989656	+	0.143458i	$0.954178\pi$
$984$	−1.83788	−	1.33530i	−0.0585895	−	0.0425678i
$985$	−0.699337	−	0.508098i	−0.0222827	−	0.0161893i
$986$	0.766828	−	2.36005i	0.0244208	−	0.0751594i
$987$	1.68119	+	5.17416i	0.0535128	+	0.164695i
$988$	−7.37947	+	5.36150i	−0.234772	+	0.170572i
$989$	54.8039			1.74266
$990$	0.0262200	+	0.0766691i	0.000833328	+	0.00243670i
$991$	36.0016			1.14363			0.571815	−	0.820383i	$-0.306240\pi$
$991$	36.0016			1.14363			0.571815	+	0.820383i	$0.306240\pi$
$992$	14.7619	−	10.7252i	0.468692	−	0.340525i
$993$	6.90086	+	21.2387i	0.218992	+	0.673989i
$994$	−0.110589	+	0.340359i	−0.00350768	+	0.0107955i
$995$	−0.186103	−	0.135212i	−0.00589986	−	0.00428650i
$996$	−31.4541	−	22.8528i	−0.996662	−	0.724117i
$997$	−8.37486	+	25.7752i	−0.265234	+	0.816308i	0.726405	+	0.687267i	$0.241190\pi$
$997$	−8.37486	+	25.7752i	−0.265234	+	0.816308i	−0.991639	+	0.129041i	$0.958810\pi$
$998$	−0.182796	−	0.562589i	−0.00578631	−	0.0178084i
$999$	6.41121	−	4.65802i	0.202842	−	0.147373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.b.58.4	✓	28
11.2	odd	10		2299.2.a.u.1.7		14
11.4	even	5	inner	209.2.f.b.191.4	yes	28
11.9	even	5		2299.2.a.t.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.b.58.4	✓	28	1.1	even	1	trivial
209.2.f.b.191.4	yes	28	11.4	even	5	inner
2299.2.a.t.1.8		14	11.9	even	5
2299.2.a.u.1.7		14	11.2	odd	10

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.161825 + 0.117573i) q^{2} +(0.378923 + 1.16621i) q^{3} +(-0.605670 + 1.86406i) q^{4} +(-0.0660344 - 0.0479768i) q^{5} +(-0.198433 - 0.144170i) q^{6} +(-0.276802 + 0.851908i) q^{7} +(-0.244773 - 0.753335i) q^{8} +(1.21060 - 0.879550i) q^{9} +0.0163268 q^{10} +(-0.976319 + 3.16967i) q^{11} -2.40338 q^{12} +(-3.76506 + 2.73547i) q^{13} +(-0.0553677 - 0.170404i) q^{14} +(0.0309289 - 0.0951892i) q^{15} +(-3.04315 - 2.21098i) q^{16} +(1.97795 + 1.43706i) q^{17} +(-0.0924937 + 0.284666i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(0.129427 - 0.0940340i) q^{20} -1.09839 q^{21} +(-0.214674 - 0.627720i) q^{22} +7.88800 q^{23} +(0.785793 - 0.570912i) q^{24} +(-1.54303 - 4.74895i) q^{25} +(0.287663 - 0.885336i) q^{26} +(4.46056 + 3.24079i) q^{27} +(-1.42036 - 1.03195i) q^{28} +(-1.56803 + 4.82589i) q^{29} +(0.00618659 + 0.0190404i) q^{30} +(6.31767 - 4.59005i) q^{31} +2.33661 q^{32} +(-4.06644 + 0.0624729i) q^{33} -0.489040 q^{34} +(0.0591502 - 0.0429752i) q^{35} +(0.906313 + 2.78934i) q^{36} +(0.444153 - 1.36696i) q^{37} +(0.161825 + 0.117573i) q^{38} +(-4.61680 - 3.35430i) q^{39} +(-0.0199791 + 0.0614894i) q^{40} +(-0.722756 - 2.22441i) q^{41} +(0.177746 - 0.129140i) q^{42} +6.94775 q^{43} +(-5.31713 - 3.73969i) q^{44} -0.122139 q^{45} +(-1.27648 + 0.927413i) q^{46} +(-1.53060 - 4.71069i) q^{47} +(1.42533 - 4.38673i) q^{48} +(5.01399 + 3.64288i) q^{49} +(0.808046 + 0.587080i) q^{50} +(-0.926420 + 2.85123i) q^{51} +(-2.81871 - 8.67509i) q^{52} +(7.87242 - 5.71965i) q^{53} -1.10286 q^{54} +(0.216541 - 0.162467i) q^{55} +0.709525 q^{56} +(0.992034 - 0.720755i) q^{57} +(-0.313647 - 0.965307i) q^{58} +(-2.47858 + 7.62828i) q^{59} +(0.158706 + 0.115307i) q^{60} +(-8.87344 - 6.44693i) q^{61} +(-0.482691 + 1.48557i) q^{62} +(0.414201 + 1.27478i) q^{63} +(5.70817 - 4.14723i) q^{64} +0.379863 q^{65} +(0.650706 - 0.488212i) q^{66} -13.3839 q^{67} +(-3.87675 + 2.81663i) q^{68} +(2.98895 + 9.19904i) q^{69} +(-0.00451928 + 0.0139089i) q^{70} +(-1.61590 - 1.17402i) q^{71} +(-0.958918 - 0.696694i) q^{72} +(-0.164937 + 0.507623i) q^{73} +(0.0888425 + 0.273429i) q^{74} +(4.95356 - 3.59897i) q^{75} +1.95999 q^{76} +(-2.43002 - 1.70910i) q^{77} +1.14149 q^{78} +(8.96326 - 6.51219i) q^{79} +(0.0948768 + 0.292001i) q^{80} +(-0.701995 + 2.16052i) q^{81} +(0.378490 + 0.274989i) q^{82} +(13.0874 + 9.50858i) q^{83} +(0.665260 - 2.04746i) q^{84} +(-0.0616668 - 0.189791i) q^{85} +(-1.12432 + 0.816866i) q^{86} -6.22215 q^{87} +(2.62680 - 0.0403557i) q^{88} -8.40759 q^{89} +(0.0197651 - 0.0143602i) q^{90} +(-1.28820 - 3.96467i) q^{91} +(-4.77753 + 14.7037i) q^{92} +(7.74686 + 5.62842i) q^{93} +(0.801537 + 0.582351i) q^{94} +(-0.0252229 + 0.0776281i) q^{95} +(0.885397 + 2.72497i) q^{96} +(0.0835782 - 0.0607231i) q^{97} -1.23969 q^{98} +(1.60595 + 4.69591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

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