LMFDB - Embedded newform 117.2.l.b.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(4,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("117.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.59035i q^{2} +(1.72707 - 0.131225i) q^{3} -4.70993 q^{4} +(1.18696 + 0.685292i) q^{5} +(-0.339918 - 4.47373i) q^{6} +(-3.20825 - 1.85228i) q^{7} +7.01967i q^{8} +(2.96556 - 0.453269i) q^{9} +(1.77515 - 3.07465i) q^{10} +0.487471i q^{11} +(-8.13439 + 0.618059i) q^{12} +(3.11904 + 1.80875i) q^{13} +(-4.79807 + 8.31050i) q^{14} +(2.13989 + 1.02779i) q^{15} +8.76356 q^{16} +(2.88951 + 5.00477i) q^{17} +(-1.17413 - 7.68185i) q^{18} +(-2.80767 + 1.62101i) q^{19} +(-5.59049 - 3.22767i) q^{20} +(-5.78395 - 2.77803i) q^{21} +1.26272 q^{22} +(-0.175893 - 0.304656i) q^{23} +(0.921153 + 12.1235i) q^{24} +(-1.56075 - 2.70330i) q^{25} +(4.68529 - 8.07942i) q^{26} +(5.06226 - 1.17198i) q^{27} +(15.1106 + 8.72412i) q^{28} +3.00808 q^{29} +(2.66234 - 5.54308i) q^{30} +(-3.62047 - 2.09028i) q^{31} -8.66137i q^{32} +(0.0639682 + 0.841898i) q^{33} +(12.9641 - 7.48484i) q^{34} +(-2.53871 - 4.39718i) q^{35} +(-13.9676 + 2.13486i) q^{36} +(-7.56549 - 4.36794i) q^{37} +(4.19899 + 7.27286i) q^{38} +(5.62417 + 2.71454i) q^{39} +(-4.81052 + 8.33206i) q^{40} +(1.44970 - 0.836982i) q^{41} +(-7.19607 + 14.9825i) q^{42} +(-5.78344 + 10.0172i) q^{43} -2.29595i q^{44} +(3.83062 + 1.49426i) q^{45} +(-0.789167 + 0.455626i) q^{46} +(3.26623 - 1.88576i) q^{47} +(15.1353 - 1.14999i) q^{48} +(3.36191 + 5.82301i) q^{49} +(-7.00250 + 4.04289i) q^{50} +(5.64714 + 8.26443i) q^{51} +(-14.6905 - 8.51907i) q^{52} -12.2232 q^{53} +(-3.03585 - 13.1130i) q^{54} +(-0.334060 + 0.578609i) q^{55} +(13.0024 - 22.5208i) q^{56} +(-4.63633 + 3.16804i) q^{57} -7.79200i q^{58} -5.70642i q^{59} +(-10.0787 - 4.84082i) q^{60} +(1.17729 - 2.03913i) q^{61} +(-5.41456 + 9.37829i) q^{62} +(-10.3538 - 4.03886i) q^{63} -4.90889 q^{64} +(2.46266 + 4.28437i) q^{65} +(2.18081 - 0.165700i) q^{66} +(0.0679883 - 0.0392530i) q^{67} +(-13.6094 - 23.5721i) q^{68} +(-0.343759 - 0.503082i) q^{69} +(-11.3902 + 6.57615i) q^{70} +(0.940139 - 0.542789i) q^{71} +(3.18180 + 20.8172i) q^{72} +2.49602i q^{73} +(-11.3145 + 19.5973i) q^{74} +(-3.05027 - 4.46399i) q^{75} +(13.2239 - 7.63484i) q^{76} +(0.902935 - 1.56393i) q^{77} +(7.03162 - 14.5686i) q^{78} +(-1.16667 - 2.02073i) q^{79} +(10.4020 + 6.00559i) q^{80} +(8.58909 - 2.68839i) q^{81} +(-2.16808 - 3.75522i) q^{82} +(-2.19957 + 1.26992i) q^{83} +(27.2420 + 13.0843i) q^{84} +7.92062i q^{85} +(25.9481 + 14.9812i) q^{86} +(5.19518 - 0.394735i) q^{87} -3.42189 q^{88} +(14.0114 + 8.08948i) q^{89} +(3.87066 - 9.92266i) q^{90} +(-6.65636 - 11.5803i) q^{91} +(0.828445 + 1.43491i) q^{92} +(-6.52711 - 3.13497i) q^{93} +(-4.88478 - 8.46068i) q^{94} -4.44346 q^{95} +(-1.13659 - 14.9588i) q^{96} +(-0.732699 - 0.423024i) q^{97} +(15.0836 - 8.70854i) q^{98} +(0.220956 + 1.44563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.59035i		−	1.83166i	−0.401571	−	0.915828i	$-0.631536\pi$
$2$		−	2.59035i		−	1.83166i	0.401571	−	0.915828i	$-0.368464\pi$
$3$	1.72707	−	0.131225i	0.997126	−	0.0757626i
$3$	1.72707	−	0.131225i	0.997126	−	0.0757626i
$4$	−4.70993			−2.35496
$5$	1.18696	+	0.685292i	0.530825	+	0.306472i	0.741352	−	0.671116i	$-0.234185\pi$
$5$	1.18696	+	0.685292i	0.530825	+	0.306472i	−0.210528	+	0.977588i	$0.567518\pi$
$6$	−0.339918	−	4.47373i	−0.138771	−	1.82639i
$7$	−3.20825	−	1.85228i	−1.21260	−	0.700098i	−0.249279	−	0.968432i	$-0.580194\pi$
$7$	−3.20825	−	1.85228i	−1.21260	−	0.700098i	−0.963326	+	0.268334i	$0.913527\pi$
$8$			7.01967i			2.48183i
$9$	2.96556	−	0.453269i	0.988520	−	0.151090i
$10$	1.77515	−	3.07465i	0.561351	−	0.972288i
$11$			0.487471i			0.146978i	0.997296	+	0.0734891i	$0.0234134\pi$
$11$			0.487471i			0.146978i	−0.997296	+	0.0734891i	$0.976587\pi$
$12$	−8.13439	+	0.618059i	−2.34819	+	0.178418i
$13$	3.11904	+	1.80875i	0.865067	+	0.501656i
$13$	3.11904	+	1.80875i	0.865067	+	0.501656i
$14$	−4.79807	+	8.31050i	−1.28234	+	2.22107i
$15$	2.13989	+	1.02779i	0.552518	+	0.265374i
$16$	8.76356			2.19089
$17$	2.88951	+	5.00477i	0.700808	+	1.21384i	0.968183	+	0.250243i	$0.0805104\pi$
$17$	2.88951	+	5.00477i	0.700808	+	1.21384i	−0.267375	+	0.963593i	$0.586156\pi$
$18$	−1.17413	−	7.68185i	−0.276744	−	1.81063i
$19$	−2.80767	+	1.62101i	−0.644124	+	0.371885i	−0.786201	−	0.617970i	$-0.787955\pi$
$19$	−2.80767	+	1.62101i	−0.644124	+	0.371885i	0.142077	+	0.989856i	$0.454622\pi$
$20$	−5.59049	−	3.22767i	−1.25007	−	0.721730i
$21$	−5.78395	−	2.77803i	−1.26216	−	0.606215i
$22$	1.26272			0.269213
$23$	−0.175893	−	0.304656i	−0.0366763	−	0.0635252i	0.847105	−	0.531426i	$-0.178344\pi$
$23$	−0.175893	−	0.304656i	−0.0366763	−	0.0635252i	−0.883781	+	0.467901i	$0.845010\pi$
$24$	0.921153	+	12.1235i	0.188030	+	2.47469i
$25$	−1.56075	−	2.70330i	−0.312150	−	0.540660i
$26$	4.68529	−	8.07942i	0.918861	−	1.58451i
$27$	5.06226	−	1.17198i	0.974232	−	0.225548i
$28$	15.1106	+	8.72412i	2.85564	+	1.64870i
$29$	3.00808			0.558587			0.279294	−	0.960206i	$-0.409900\pi$
$29$	3.00808			0.558587			0.279294	+	0.960206i	$0.409900\pi$
$30$	2.66234	−	5.54308i	0.486074	−	1.01202i
$31$	−3.62047	−	2.09028i	−0.650255	−	0.375425i	0.138299	−	0.990391i	$-0.455837\pi$
$31$	−3.62047	−	2.09028i	−0.650255	−	0.375425i	−0.788554	+	0.614965i	$0.789170\pi$
$32$		−	8.66137i		−	1.53113i
$33$	0.0639682	+	0.841898i	0.0111354	+	0.146556i
$34$	12.9641	−	7.48484i	2.22333	−	1.28364i
$35$	−2.53871	−	4.39718i	−0.429120	−	0.743258i
$36$	−13.9676	+	2.13486i	−2.32793	+	0.355811i
$37$	−7.56549	−	4.36794i	−1.24376	−	0.718084i	−0.273901	−	0.961758i	$-0.588314\pi$
$37$	−7.56549	−	4.36794i	−1.24376	−	0.718084i	−0.969857	+	0.243673i	$0.921648\pi$
$38$	4.19899	+	7.27286i	0.681165	+	1.17981i
$39$	5.62417	+	2.71454i	0.900588	+	0.434675i
$40$	−4.81052	+	8.33206i	−0.760610	+	1.31741i
$41$	1.44970	−	0.836982i	0.226404	−	0.130715i	−0.382508	−	0.923952i	$-0.624939\pi$
$41$	1.44970	−	0.836982i	0.226404	−	0.130715i	0.608912	+	0.793238i	$0.291606\pi$
$42$	−7.19607	+	14.9825i	−1.11038	+	2.31184i
$43$	−5.78344	+	10.0172i	−0.881967	+	1.52761i	−0.0328156	+	0.999461i	$0.510447\pi$
$43$	−5.78344	+	10.0172i	−0.881967	+	1.52761i	−0.849151	+	0.528150i	$0.822886\pi$
$44$		−	2.29595i		−	0.346128i
$45$	3.83062	+	1.49426i	0.571036	+	0.222751i
$46$	−0.789167	+	0.455626i	−0.116356	+	0.0671784i
$47$	3.26623	−	1.88576i	0.476428	−	0.275066i	−0.242499	−	0.970152i	$-0.577967\pi$
$47$	3.26623	−	1.88576i	0.476428	−	0.275066i	0.718927	+	0.695086i	$0.244634\pi$
$48$	15.1353	−	1.14999i	2.18459	−	0.165987i
$49$	3.36191	+	5.82301i	0.480273	+	0.831858i
$50$	−7.00250	+	4.04289i	−0.990303	+	0.571752i
$51$	5.64714	+	8.26443i	0.790757	+	1.15725i
$52$	−14.6905	−	8.51907i	−2.03720	−	1.18138i
$53$	−12.2232			−1.67898			−0.839492	−	0.543373i	$-0.817147\pi$
$53$	−12.2232			−1.67898			−0.839492	+	0.543373i	$0.817147\pi$
$54$	−3.03585	−	13.1130i	−0.413127	−	1.78446i
$55$	−0.334060	+	0.578609i	−0.0450446	+	0.0780196i
$56$	13.0024	−	22.5208i	1.73752	−	3.00947i
$57$	−4.63633	+	3.16804i	−0.614098	+	0.419617i
$58$		−	7.79200i		−	1.02314i
$59$		−	5.70642i		−	0.742912i	−0.928451	−	0.371456i	$-0.878859\pi$
$59$		−	5.70642i		−	0.742912i	0.928451	−	0.371456i	$-0.121141\pi$
$60$	−10.0787	−	4.84082i	−1.30116	−	0.624947i
$61$	1.17729	−	2.03913i	0.150737	−	0.261084i	−0.780762	−	0.624829i	$-0.785169\pi$
$61$	1.17729	−	2.03913i	0.150737	−	0.261084i	0.931499	+	0.363745i	$0.118502\pi$
$62$	−5.41456	+	9.37829i	−0.687650	+	1.19104i
$63$	−10.3538	−	4.03886i	−1.30446	−	0.508849i
$64$	−4.90889			−0.613611
$65$	2.46266	+	4.28437i	0.305456	+	0.531410i
$66$	2.18081	−	0.165700i	0.268440	−	0.0203963i
$67$	0.0679883	−	0.0392530i	0.00830609	−	0.00479552i	−0.495841	−	0.868413i	$-0.665140\pi$
$67$	0.0679883	−	0.0392530i	0.00830609	−	0.00479552i	0.504147	+	0.863618i	$0.331807\pi$
$68$	−13.6094	−	23.5721i	−1.65038	−	2.85854i
$69$	−0.343759	−	0.503082i	−0.0413837	−	0.0605639i
$70$	−11.3902	+	6.57615i	−1.36139	+	0.786001i
$71$	0.940139	−	0.542789i	0.111574	−	0.0644172i	−0.443175	−	0.896435i	$-0.646148\pi$
$71$	0.940139	−	0.542789i	0.111574	−	0.0644172i	0.554748	+	0.832018i	$0.312814\pi$
$72$	3.18180	+	20.8172i	0.374978	+	2.45334i
$73$			2.49602i			0.292137i	0.989274	+	0.146068i	$0.0466620\pi$
$73$			2.49602i			0.292137i	−0.989274	+	0.146068i	$0.953338\pi$
$74$	−11.3145	+	19.5973i	−1.31528	+	2.27814i
$75$	−3.05027	−	4.46399i	−0.352215	−	0.515457i
$76$	13.2239	−	7.63484i	1.51689	−	0.875776i
$77$	0.902935	−	1.56393i	0.102899	−	0.178226i
$78$	7.03162	−	14.5686i	0.796174	−	1.64957i
$79$	−1.16667	−	2.02073i	−0.131260	−	0.227350i	0.792902	−	0.609349i	$-0.208569\pi$
$79$	−1.16667	−	2.02073i	−0.131260	−	0.227350i	−0.924163	+	0.381999i	$0.875236\pi$
$80$	10.4020	+	6.00559i	1.16298	+	0.671446i
$81$	8.58909	−	2.68839i	0.954344	−	0.298710i
$82$	−2.16808	−	3.75522i	−0.239424	−	0.414695i
$83$	−2.19957	+	1.26992i	−0.241434	+	0.139392i	−0.615836	−	0.787875i	$-0.711182\pi$
$83$	−2.19957	+	1.26992i	−0.241434	+	0.139392i	0.374401	+	0.927267i	$0.377848\pi$
$84$	27.2420	+	13.0843i	2.97234	+	1.42762i
$85$			7.92062i			0.859112i
$86$	25.9481	+	14.9812i	2.79806	+	1.61546i
$87$	5.19518	−	0.394735i	0.556982	−	0.0423200i
$88$	−3.42189			−0.364774
$89$	14.0114	+	8.08948i	1.48520	+	0.857483i	0.999858	−	0.0168392i	$-0.00536032\pi$
$89$	14.0114	+	8.08948i	1.48520	+	0.857483i	0.485346	+	0.874322i	$0.338694\pi$
$90$	3.87066	−	9.92266i	0.408004	−	1.04594i
$91$	−6.65636	−	11.5803i	−0.697776	−	1.21394i
$92$	0.828445	+	1.43491i	0.0863713	+	0.149600i
$93$	−6.52711	−	3.13497i	−0.676830	−	0.325081i
$94$	−4.88478	−	8.46068i	−0.503826	−	0.872652i
$95$	−4.44346			−0.455889
$96$	−1.13659	−	14.9588i	−0.116002	−	1.52673i
$97$	−0.732699	−	0.423024i	−0.0743943	−	0.0429516i	0.462341	−	0.886702i	$-0.347009\pi$
$97$	−0.732699	−	0.423024i	−0.0743943	−	0.0429516i	−0.536736	+	0.843750i	$0.680343\pi$
$98$	15.0836	−	8.70854i	1.52368	−	0.879696i
$99$	0.220956	+	1.44563i	0.0222069	+	0.145291i
$100$	7.35102	+	12.7323i	0.735102	+	1.27323i
$101$	−3.02905			−0.301401			−0.150701	−	0.988579i	$-0.548153\pi$
$101$	−3.02905			−0.301401			−0.150701	+	0.988579i	$0.548153\pi$
$102$	21.4078	−	14.6281i	2.11969	−	1.44840i
$103$	2.74723	−	4.75835i	0.270693	−	0.468854i	−0.698347	−	0.715760i	$-0.746081\pi$
$103$	2.74723	−	4.75835i	0.270693	−	0.468854i	0.969039	+	0.246906i	$0.0794139\pi$
$104$	−12.6968	+	21.8946i	−1.24502	+	2.14695i
$105$	−4.96155	−	7.26110i	−0.484198	−	0.708611i
$106$			31.6624i			3.07532i
$107$	−2.78934	+	4.83127i	−0.269655	+	0.467057i	−0.968773	−	0.247950i	$-0.920243\pi$
$107$	−2.78934	+	4.83127i	−0.269655	+	0.467057i	0.699118	+	0.715007i	$0.253576\pi$
$108$	−23.8429	+	5.51995i	−2.29428	+	0.531158i
$109$		−	0.977746i		−	0.0936511i	−0.998903	−	0.0468256i	$-0.985090\pi$
$109$		−	0.977746i		−	0.0936511i	0.998903	−	0.0468256i	$-0.0149105\pi$
$110$	1.49880	+	0.865333i	0.142905	+	0.0825063i
$111$	−13.6393	−	6.55097i	−1.29459	−	0.621790i
$112$	−28.1157	−	16.2326i	−2.65668	−	1.53384i
$113$	−1.66014			−0.156173			−0.0780866	−	0.996947i	$-0.524881\pi$
$113$	−1.66014			−0.156173			−0.0780866	+	0.996947i	$0.524881\pi$
$114$	8.20633	+	12.0097i	0.768593	+	1.12482i
$115$		−	0.482153i		−	0.0449610i
$116$	−14.1679			−1.31545
$117$	10.0696	+	3.95018i	0.930931	+	0.365194i
$118$	−14.7816			−1.36076
$119$		−	21.4087i		−	1.96254i
$120$	−7.21474	+	15.0213i	−0.658613	+	1.37125i
$121$	10.7624			0.978397
$122$	−5.28207	−	3.04961i	−0.478216	−	0.276098i
$123$	2.39390	−	1.63576i	0.215850	−	0.147492i
$124$	17.0521	+	9.84506i	1.53133	+	0.884112i
$125$		−	11.1312i		−	0.995604i
$126$	−10.4621	+	26.8201i	−0.932035	+	2.38932i
$127$	8.91305	−	15.4379i	0.790905	−	1.36989i	−0.134502	−	0.990913i	$-0.542943\pi$
$127$	8.91305	−	15.4379i	0.790905	−	1.36989i	0.925407	−	0.378975i	$-0.123723\pi$
$128$		−	4.60699i		−	0.407204i
$129$	−8.67392	+	18.0594i	−0.763696	+	1.59004i
$130$	11.0980	−	6.37916i	0.973360	−	0.559489i
$131$	8.49796	−	14.7189i	0.742470	−	1.28600i	−0.208898	−	0.977937i	$-0.566988\pi$
$131$	8.49796	−	14.7189i	0.742470	−	1.28600i	0.951368	−	0.308058i	$-0.0996791\pi$
$132$	−0.301286	−	3.96528i	−0.0262236	−	0.345133i
$133$	12.0103			1.04142
$134$	−0.101679	−	0.176114i	−0.00878375	−	0.0152139i
$135$	6.81185	+	2.07803i	0.586271	+	0.178848i
$136$	−35.1318	+	20.2834i	−3.01253	+	1.73928i
$137$	−1.87952	−	1.08514i	−0.160579	−	0.0927101i	0.417557	−	0.908651i	$-0.362886\pi$
$137$	−1.87952	−	1.08514i	−0.160579	−	0.0927101i	−0.578136	+	0.815941i	$0.696220\pi$
$138$	−1.30316	+	0.890457i	−0.110932	+	0.0758007i
$139$	−9.19253			−0.779700			−0.389850	−	0.920878i	$-0.627473\pi$
$139$	−9.19253			−0.779700			−0.389850	+	0.920878i	$0.627473\pi$
$140$	11.9571	+	20.7104i	1.01056	+	1.75035i
$141$	5.39355	−	3.68545i	0.454219	−	0.310371i
$142$	−1.40602	−	2.43529i	−0.117990	−	0.204365i
$143$	−0.881712	+	1.52044i	−0.0737325	+	0.127146i
$144$	25.9889	−	3.97225i	2.16574	−	0.331021i
$145$	3.57048	+	2.06141i	0.296512	+	0.171191i
$146$	6.46557			0.535094
$147$	6.57039	+	9.61559i	0.541917	+	0.793080i
$148$	35.6329	+	20.5727i	2.92901	+	1.69106i
$149$		−	5.79717i		−	0.474923i	−0.971397	−	0.237461i	$-0.923685\pi$
$149$		−	5.79717i		−	0.474923i	0.971397	−	0.237461i	$-0.0763153\pi$
$150$	−11.5633	+	7.90127i	−0.944139	+	0.645136i
$151$	−12.1366	+	7.00709i	−0.987666	+	0.570229i	−0.904576	−	0.426313i	$-0.859812\pi$
$151$	−12.1366	+	7.00709i	−0.987666	+	0.570229i	−0.0830899	+	0.996542i	$0.526479\pi$
$152$	−11.3789	−	19.7089i	−0.922954	−	1.59860i
$153$	10.8375	+	13.5322i	0.876161	+	1.09402i
$154$	−4.05113	−	2.33892i	−0.326449	−	0.188476i
$155$	−2.86490	−	4.96215i	−0.230114	−	0.398570i
$156$	−26.4894	−	12.7853i	−2.12085	−	1.02364i
$157$	2.77149	−	4.80037i	0.221189	−	0.383111i	−0.733980	−	0.679171i	$-0.762339\pi$
$157$	2.77149	−	4.80037i	0.221189	−	0.383111i	0.955169	+	0.296060i	$0.0956728\pi$
$158$	−5.23440	+	3.02208i	−0.416426	+	0.240424i
$159$	−21.1103	+	1.60398i	−1.67416	+	0.127204i
$160$	5.93556	−	10.2807i	0.469248	−	0.812761i
$161$			1.30322i			0.102708i
$162$	−6.96389	−	22.2488i	−0.547135	−	1.74803i
$163$	−0.109427	+	0.0631777i	−0.00857098	+	0.00494846i	−0.504279	−	0.863541i	$-0.668242\pi$
$163$	−0.109427	+	0.0631777i	−0.00857098	+	0.00494846i	0.495708	+	0.868489i	$0.334908\pi$
$164$	−6.82796	+	3.94212i	−0.533174	+	0.307828i
$165$	−0.501018	+	1.04314i	−0.0390042	+	0.0812081i
$166$	3.28955	+	5.69767i	0.255319	+	0.442225i
$167$	−7.99623	+	4.61663i	−0.618767	+	0.357245i	−0.776389	−	0.630254i	$-0.782951\pi$
$167$	−7.99623	+	4.61663i	−0.618767	+	0.357245i	0.157622	+	0.987500i	$0.449617\pi$
$168$	19.5008	−	40.6014i	1.50452	−	3.13246i
$169$	6.45687	+	11.2831i	0.496682	+	0.867932i
$170$	20.5172			1.57360
$171$	−7.59156	+	6.07983i	−0.580541	+	0.464936i
$172$	27.2396	−	47.1804i	2.07700	−	3.59747i
$173$	−8.08378	+	14.0015i	−0.614599	+	1.06452i	0.375856	+	0.926678i	$0.377349\pi$
$173$	−8.08378	+	14.0015i	−0.614599	+	1.06452i	−0.990455	+	0.137838i	$0.955985\pi$
$174$	−1.02250	−	13.4573i	−0.0775157	−	1.02020i
$175$			11.5638i			0.874142i
$176$			4.27198i			0.322013i
$177$	−0.748822	−	9.85539i	−0.0562849	−	0.740777i
$178$	20.9546	−	36.2944i	1.57061	−	2.72038i
$179$	4.88798	−	8.46622i	0.365345	−	0.632795i	−0.623487	−	0.781834i	$-0.714285\pi$
$179$	4.88798	−	8.46622i	0.365345	−	0.632795i	0.988831	+	0.149039i	$0.0476179\pi$
$180$	−18.0420	−	7.03786i	−1.34477	−	0.524571i
$181$	10.9633			0.814896			0.407448	−	0.913229i	$-0.366419\pi$
$181$	10.9633			0.814896			0.407448	+	0.913229i	$0.366419\pi$
$182$	−29.9970	+	17.2423i	−2.22352	+	1.27809i
$183$	1.76569	−	3.67622i	0.130523	−	0.271754i
$184$	2.13858	−	1.23471i	0.157659	−	0.0910242i
$185$	−5.98662	−	10.3691i	−0.440145	−	0.762354i
$186$	−8.12067	+	16.9075i	−0.595437	+	1.23972i
$187$	−2.43968	+	1.40855i	−0.178407	+	0.103003i
$188$	−15.3837	+	8.88178i	−1.12197	+	0.647770i
$189$	−18.4118	−	5.61673i	−1.33926	−	0.408557i
$190$			11.5101i			0.835032i
$191$	1.09288	−	1.89292i	0.0790778	−	0.136967i	−0.823775	−	0.566918i	$-0.808136\pi$
$191$	1.09288	−	1.89292i	0.0790778	−	0.136967i	0.902852	+	0.429951i	$0.141469\pi$
$192$	−8.47801	+	0.644167i	−0.611847	+	0.0464888i
$193$	2.64074	−	1.52463i	0.190085	−	0.109746i	−0.401937	−	0.915667i	$-0.631663\pi$
$193$	2.64074	−	1.52463i	0.190085	−	0.109746i	0.592022	+	0.805922i	$0.298330\pi$
$194$	−1.09578	+	1.89795i	−0.0786725	+	0.136265i
$195$	4.81541	+	7.07625i	0.344839	+	0.506741i
$196$	−15.8344	−	27.4259i	−1.13103	−	1.95900i
$197$	8.84639	+	5.10747i	0.630279	+	0.363892i	0.780860	−	0.624706i	$-0.214781\pi$
$197$	8.84639	+	5.10747i	0.630279	+	0.363892i	−0.150581	+	0.988598i	$0.548114\pi$
$198$	3.74468	−	0.572353i	0.266123	−	0.0406754i
$199$	−3.41850	−	5.92102i	−0.242331	−	0.419730i	0.719047	−	0.694962i	$-0.244579\pi$
$199$	−3.41850	−	5.92102i	−0.242331	−	0.419730i	−0.961378	+	0.275232i	$0.911245\pi$
$200$	18.9763	−	10.9559i	1.34182	−	0.774702i
$201$	0.112270	−	0.0767146i	0.00791889	−	0.00541103i
$202$			7.84630i			0.552064i
$203$	−9.65069	−	5.57183i	−0.677345	−	0.391066i
$204$	−26.5976	−	38.9249i	−1.86220	−	2.72528i
$205$	2.29431			0.160241
$206$	−12.3258	−	7.11630i	−0.858779	−	0.495816i
$207$	−0.659714	−	0.823749i	−0.0458533	−	0.0572545i
$208$	27.3339	+	15.8511i	1.89527	+	1.09907i
$209$	−0.790195	−	1.36866i	−0.0546590	−	0.0946721i
$210$	−18.8088	+	12.8522i	−1.29793	+	0.886884i
$211$	11.5354	+	19.9799i	0.794128	+	1.37547i	0.923391	+	0.383860i	$0.125405\pi$
$211$	11.5354	+	19.9799i	0.794128	+	1.37547i	−0.129264	+	0.991610i	$0.541261\pi$
$212$	57.5703			3.95394
$213$	1.55246	−	1.06081i	0.106373	−	0.0726852i
$214$	12.5147	+	7.22536i	0.855487	+	0.493916i
$215$	−13.7294	+	7.92669i	−0.936339	+	0.540596i
$216$	8.22693	+	35.5354i	0.559772	+	2.41787i
$217$	7.74358	+	13.4123i	0.525669	+	0.910485i
$218$	−2.53271			−0.171537
$219$	0.327539	+	4.31080i	0.0221330	+	0.291297i
$220$	1.57340	−	2.72521i	0.106078	−	0.183733i
$221$	−0.0398687	+	20.8365i	−0.00268186	+	1.40161i
$222$	−16.9693	+	35.3307i	−1.13891	+	2.37124i
$223$		−	9.67359i		−	0.647791i	−0.946093	−	0.323896i	$-0.895007\pi$
$223$		−	9.67359i		−	0.647791i	0.946093	−	0.323896i	$-0.104993\pi$
$224$	−16.0433	+	27.7878i	−1.07194	+	1.85665i
$225$	−5.85382	−	7.30936i	−0.390255	−	0.487290i
$226$			4.30036i			0.286055i
$227$	23.1988	+	13.3938i	1.53976	+	0.888978i	0.998852	+	0.0478937i	$0.0152509\pi$
$227$	23.1988	+	13.3938i	1.53976	+	0.888978i	0.540903	+	0.841085i	$0.318082\pi$
$228$	21.8368	−	14.9212i	1.44618	−	0.988182i
$229$	−5.55568	−	3.20757i	−0.367129	−	0.211962i	0.305074	−	0.952329i	$-0.401319\pi$
$229$	−5.55568	−	3.20757i	−0.367129	−	0.211962i	−0.672204	+	0.740366i	$0.734652\pi$
$230$	−1.24895			−0.0823531
$231$	1.35421	−	2.81951i	0.0891004	−	0.185510i
$232$			21.1157i			1.38632i
$233$	−21.9858			−1.44034			−0.720170	−	0.693798i	$-0.755936\pi$
$233$	−21.9858			−1.44034			−0.720170	+	0.693798i	$0.755936\pi$
$234$	10.2324	−	26.0837i	0.668911	−	1.70515i
$235$	5.16917			0.337200
$236$			26.8768i			1.74953i
$237$	−2.28009	−	3.33685i	−0.148108	−	0.216752i
$238$	−55.4562			−3.59469
$239$	9.86048	+	5.69295i	0.637821	+	0.368246i	0.783775	−	0.621045i	$-0.213292\pi$
$239$	9.86048	+	5.69295i	0.637821	+	0.368246i	−0.145954	+	0.989291i	$0.546625\pi$
$240$	18.7531	+	9.00710i	1.21051	+	0.581406i
$241$	−17.4620	−	10.0817i	−1.12483	−	0.649419i	−0.182198	−	0.983262i	$-0.558321\pi$
$241$	−17.4620	−	10.0817i	−1.12483	−	0.649419i	−0.942629	+	0.333843i	$0.891655\pi$
$242$		−	27.8783i		−	1.79209i
$243$	14.4812	−	5.77015i	0.928970	−	0.370155i
$244$	−5.54497	+	9.60416i	−0.354980	+	0.614844i
$245$			9.21557i			0.588761i
$246$	−4.23721	−	6.20104i	−0.270154	−	0.395364i
$247$	−11.6892	−	0.0223663i	−0.743769	−	0.00142313i
$248$	14.6731	−	25.4145i	0.931740	−	1.61382i
$249$	−3.63217	+	2.48189i	−0.230180	+	0.157283i
$250$	−28.8337			−1.82360
$251$	5.96356	+	10.3292i	0.376417	+	0.651973i	0.990538	−	0.137239i	$-0.0438227\pi$
$251$	5.96356	+	10.3292i	0.376417	+	0.651973i	−0.614121	+	0.789212i	$0.710489\pi$
$252$	48.7658	+	19.0227i	3.07196	+	1.19832i
$253$	0.148511	−	0.0857430i	0.00933682	−	0.00539061i
$254$	−39.9895	−	23.0879i	−2.50916	−	1.44867i
$255$	1.03938	+	13.6795i	0.0650885	+	0.856642i
$256$	−21.7515			−1.35947
$257$	−8.18195	−	14.1716i	−0.510376	−	0.883997i	−0.999928	−	0.0120231i	$-0.996173\pi$
$257$	−8.18195	−	14.1716i	−0.510376	−	0.883997i	0.489552	−	0.871974i	$-0.337161\pi$
$258$	46.7802	+	22.4685i	2.91241	+	1.39883i
$259$	16.1813	+	28.0269i	1.00546	+	1.74151i
$260$	−11.5990	−	20.1790i	−0.719337	−	1.25145i
$261$	8.92065	−	1.36347i	0.552175	−	0.0843968i
$262$	−38.1271	−	22.0127i	−2.35550	−	1.35995i
$263$	14.7168			0.907476			0.453738	−	0.891135i	$-0.350090\pi$
$263$	14.7168			0.907476			0.453738	+	0.891135i	$0.350090\pi$
$264$	−5.90984	+	0.449036i	−0.363726	+	0.0276362i
$265$	−14.5084	−	8.37645i	−0.891246	−	0.514561i
$266$		−	31.1109i		−	1.90753i
$267$	25.2602	+	12.1325i	1.54590	+	0.742496i
$268$	−0.320220	+	0.184879i	−0.0195605	+	0.0112933i
$269$	13.6669	+	23.6718i	0.833288	+	1.44330i	0.895416	+	0.445230i	$0.146878\pi$
$269$	13.6669	+	23.6718i	0.833288	+	1.44330i	−0.0621279	+	0.998068i	$0.519789\pi$
$270$	5.38282	−	17.6451i	0.327588	−	1.07385i
$271$	10.2655	+	5.92679i	0.623585	+	0.360027i	0.778263	−	0.627938i	$-0.216101\pi$
$271$	10.2655	+	5.92679i	0.623585	+	0.360027i	−0.154678	+	0.987965i	$0.549434\pi$
$272$	25.3223	+	43.8596i	1.53539	+	2.65938i
$273$	−13.0156	−	19.1265i	−0.787742	−	1.15759i
$274$	−2.81090	+	4.86863i	−0.169813	+	0.294125i
$275$	1.31778	−	0.760821i	0.0794652	−	0.0458792i
$276$	1.61908	+	2.36948i	0.0974572	+	0.142626i
$277$	7.14586	−	12.3770i	0.429353	−	0.743661i	−0.567463	−	0.823399i	$-0.692075\pi$
$277$	7.14586	−	12.3770i	0.429353	−	0.743661i	0.996816	+	0.0797377i	$0.0254083\pi$
$278$			23.8119i			1.42814i
$279$	−11.6842	−	4.55780i	−0.699513	−	0.272868i
$280$	30.8667	−	17.8209i	1.84464	−	1.06500i
$281$	20.3164	−	11.7297i	1.21198	−	0.699735i	0.248787	−	0.968558i	$-0.419968\pi$
$281$	20.3164	−	11.7297i	1.21198	−	0.699735i	0.963190	+	0.268823i	$0.0866346\pi$
$282$	−9.54661	−	13.9712i	−0.568493	−	0.831973i
$283$	−13.6592	−	23.6584i	−0.811953	−	1.40634i	−0.911496	−	0.411310i	$-0.865071\pi$
$283$	−13.6592	−	23.6584i	−0.811953	−	1.40634i	0.0995428	−	0.995033i	$-0.468262\pi$
$284$	−4.42798	+	2.55650i	−0.262753	+	0.151700i
$285$	−7.67417	+	0.583091i	−0.454579	+	0.0345393i
$286$	3.93849	+	2.28395i	0.232888	+	0.135053i
$287$	−6.20132			−0.366052
$288$	−3.92593	−	25.6858i	−0.231338	−	1.51355i
$289$	−8.19849	+	14.2002i	−0.482264	+	0.835306i
$290$	5.33979	−	9.24879i	0.313563	−	0.543108i
$291$	−1.32094	−	0.634445i	−0.0774346	−	0.0371918i
$292$		−	11.7561i		−	0.687972i
$293$			27.8967i			1.62974i	0.579642	+	0.814871i	$0.303192\pi$
$293$			27.8967i			1.62974i	−0.579642	+	0.814871i	$0.696808\pi$
$294$	24.9078	−	17.0196i	1.45265	−	0.992605i
$295$	3.91056	−	6.77329i	0.227682	−	0.394356i
$296$	30.6615	−	53.1072i	1.78216	−	3.08679i
$297$	0.571308	+	2.46771i	0.0331507	+	0.143191i
$298$	−15.0167			−0.869895
$299$	0.00242694	−	1.26838i	0.000140353	−	0.0733525i
$300$	14.3665	+	21.0250i	0.829453	+	1.21388i
$301$	37.1095	−	21.4252i	2.13895	−	1.23493i
$302$	18.1508	+	31.4382i	1.04446	+	1.80906i
$303$	−5.23138	+	0.397485i	−0.300535	+	0.0228349i
$304$	−24.6052	+	14.2058i	−1.41120	+	0.814759i
$305$	2.79480	−	1.61358i	0.160030	−	0.0923933i
$306$	35.0532	−	28.0730i	2.00386	−	1.60483i
$307$			28.7426i			1.64043i	0.572059	+	0.820213i	$0.306145\pi$
$307$			28.7426i			1.64043i	−0.572059	+	0.820213i	$0.693855\pi$
$308$	−4.25276	+	7.36600i	−0.242323	+	0.419717i
$309$	4.12026	−	8.57851i	0.234393	−	0.488015i
$310$	−12.8537	+	7.42110i	−0.730043	+	0.421490i
$311$	6.83305	−	11.8352i	0.387467	−	0.671112i	−0.604641	−	0.796498i	$-0.706684\pi$
$311$	6.83305	−	11.8352i	0.387467	−	0.671112i	0.992108	+	0.125386i	$0.0400169\pi$
$312$	−19.0552	+	39.4798i	−1.07879	+	2.23510i
$313$	−5.90331	−	10.2248i	−0.333675	−	0.577942i	0.649554	−	0.760315i	$-0.274955\pi$
$313$	−5.90331	−	10.2248i	−0.333675	−	0.577942i	−0.983229	+	0.182373i	$0.941622\pi$
$314$	−12.4346	−	7.17915i	−0.701728	−	0.405143i
$315$	−9.52180	−	11.8894i	−0.536493	−	0.669890i
$316$	5.49492	+	9.51748i	0.309113	+	0.535400i
$317$	−26.0847	+	15.0600i	−1.46506	+	0.845854i	−0.999238	−	0.0390236i	$-0.987575\pi$
$317$	−26.0847	+	15.0600i	−1.46506	+	0.845854i	−0.465824	+	0.884878i	$0.654242\pi$
$318$	4.15488	+	54.6832i	0.232994	+	3.06648i
$319$			1.46635i			0.0821001i
$320$	−5.82665	−	3.36402i	−0.325720	−	0.188054i
$321$	−4.18340	+	8.70999i	−0.233495	+	0.486144i
$322$	3.37579			0.188126
$323$	−16.2256	−	9.36783i	−0.902814	−	0.521240i
$324$	−40.4540	+	12.6621i	−2.24744	+	0.703452i
$325$	0.0215349	−	11.2547i	0.00119454	−	0.624299i
$326$	0.163653	+	0.283454i	0.00906388	+	0.0156991i
$327$	−0.128304	−	1.68864i	−0.00709525	−	0.0933820i
$328$	5.87533	+	10.1764i	0.324411	+	0.561896i
$329$	−13.9718			−0.770292
$330$	2.70209	+	1.29781i	0.148745	+	0.0714423i
$331$	8.20768	+	4.73870i	0.451135	+	0.260463i	0.708309	−	0.705902i	$-0.249458\pi$
$331$	8.20768	+	4.73870i	0.451135	+	0.260463i	−0.257175	+	0.966365i	$0.582792\pi$
$332$	10.3598	−	5.98125i	0.568569	−	0.328263i
$333$	−24.4158	−	9.52418i	−1.33798	−	0.521922i
$334$	11.9587	+	20.7131i	0.654350	+	1.13337i
$335$	0.107599			0.00587877
$336$	−50.6879	−	24.3454i	−2.76525	−	1.32815i
$337$	8.14215	−	14.1026i	0.443531	−	0.768218i	−0.554417	−	0.832239i	$-0.687059\pi$
$337$	8.14215	−	14.1026i	0.443531	−	0.768218i	0.997949	+	0.0640203i	$0.0203922\pi$
$338$	29.2273	−	16.7256i	1.58975	−	0.909751i
$339$	−2.86719	+	0.217852i	−0.155724	+	0.0118321i
$340$		−	37.3055i		−	2.02318i
$341$	1.01895	−	1.76487i	0.0551793	−	0.0955733i
$342$	15.7489	+	19.6648i	0.851603	+	1.06335i
$343$			1.02310i			0.0552420i
$344$	−70.3175	−	40.5978i	−3.79127	−	2.18889i
$345$	−0.0632704	−	0.832713i	−0.00340636	−	0.0448318i
$346$	36.2689	+	20.9399i	1.94983	+	1.12573i
$347$	3.27692			0.175914			0.0879571	−	0.996124i	$-0.471966\pi$
$347$	3.27692			0.175914			0.0879571	+	0.996124i	$0.471966\pi$
$348$	−24.4689	+	1.85917i	−1.31167	+	0.0996621i
$349$		−	23.3467i		−	1.24972i	−0.780736	−	0.624861i	$-0.785156\pi$
$349$		−	23.3467i		−	1.24972i	0.780736	−	0.624861i	$-0.214844\pi$
$350$	29.9544			1.60113
$351$	17.9092	+	5.50088i	0.955924	+	0.293615i
$352$	4.22217			0.225042
$353$			1.48233i			0.0788963i	0.999222	+	0.0394482i	$0.0125600\pi$
$353$			1.48233i			0.0788963i	−0.999222	+	0.0394482i	$0.987440\pi$
$354$	−25.5289	+	1.93971i	−1.35685	+	0.103095i
$355$	1.48788			0.0789683
$356$	−65.9926	−	38.1009i	−3.49760	−	2.01934i
$357$	−2.80936	−	36.9745i	−0.148687	−	1.95690i
$358$	−21.9305	−	12.6616i	−1.15906	−	0.669185i
$359$		−	5.04499i		−	0.266264i	−0.991098	−	0.133132i	$-0.957497\pi$
$359$		−	5.04499i		−	0.266264i	0.991098	−	0.133132i	$-0.0425035\pi$
$360$	−10.4892	+	26.8897i	−0.552830	+	1.41721i
$361$	−4.24466	+	7.35196i	−0.223403	+	0.386945i
$362$		−	28.3988i		−	1.49261i
$363$	18.5874	−	1.41229i	0.975585	−	0.0741259i
$364$	31.3510	+	54.5422i	1.64324	+	2.85879i
$365$	−1.71050	+	2.96267i	−0.0895317	+	0.155073i
$366$	−9.52271	−	4.57375i	−0.497760	−	0.239074i
$367$	−4.19706			−0.219085			−0.109542	−	0.993982i	$-0.534939\pi$
$367$	−4.19706			−0.219085			−0.109542	+	0.993982i	$0.534939\pi$
$368$	−1.54145	−	2.66987i	−0.0803537	−	0.139177i
$369$	3.91978	−	3.13922i	0.204056	−	0.163421i
$370$	−26.8597	+	15.5075i	−1.39637	+	0.806195i
$371$	39.2150	+	22.6408i	2.03594	+	1.17545i
$372$	30.7422	+	14.7655i	1.59391	+	0.765554i
$373$	−27.2515			−1.41103			−0.705515	−	0.708695i	$-0.749284\pi$
$373$	−27.2515			−1.41103			−0.705515	+	0.708695i	$0.749284\pi$
$374$	3.64864	+	6.31964i	0.188667	+	0.326781i
$375$	−1.46069	−	19.2244i	−0.0754296	−	0.992743i
$376$	13.2374	+	22.9278i	0.682666	+	1.18241i
$377$	9.38235	+	5.44086i	0.483215	+	0.280219i
$378$	−14.5493	+	47.6932i	−0.748335	+	2.45307i
$379$	−3.91133	−	2.25821i	−0.200912	−	0.115996i	0.396169	−	0.918178i	$-0.370339\pi$
$379$	−3.91133	−	2.25821i	−0.200912	−	0.115996i	−0.597081	+	0.802181i	$0.703673\pi$
$380$	20.9284			1.07360
$381$	13.3677	−	27.8319i	0.684846	−	1.42587i
$382$	−4.90332	−	2.83093i	−0.250876	−	0.144843i
$383$			19.2761i			0.984961i	0.870324	+	0.492480i	$0.163910\pi$
$383$			19.2761i			0.984961i	−0.870324	+	0.492480i	$0.836090\pi$
$384$	−0.604550	−	7.95660i	−0.0308508	−	0.406034i
$385$	2.14350	−	1.23755i	0.109243	−	0.0630713i
$386$	−3.94934	−	6.84045i	−0.201016	−	0.348170i
$387$	−12.6107	+	32.3281i	−0.641036	+	1.64333i
$388$	3.45096	+	1.99241i	0.175196	+	0.101149i
$389$	−2.21704	−	3.84003i	−0.112409	−	0.194697i	0.804332	−	0.594180i	$-0.202523\pi$
$389$	−2.21704	−	3.84003i	−0.112409	−	0.194697i	−0.916741	+	0.399482i	$0.869190\pi$
$390$	18.3300	−	12.4736i	0.928175	−	0.631626i
$391$	1.01649	−	1.76061i	0.0514061	−	0.0890380i
$392$	−40.8756	+	23.5995i	−2.06453	+	1.19196i
$393$	12.7451	−	26.5357i	0.642906	−	1.33855i
$394$	13.2301	−	22.9153i	0.666525	−	1.15445i
$395$		−	3.19803i		−	0.160910i
$396$	−1.04068	−	6.80879i	−0.0522964	−	0.342155i
$397$	5.79822	−	3.34760i	0.291004	−	0.168011i	−0.347390	−	0.937721i	$-0.612932\pi$
$397$	5.79822	−	3.34760i	0.291004	−	0.168011i	0.638395	+	0.769709i	$0.279599\pi$
$398$	−15.3375	+	8.85513i	−0.768801	+	0.443867i
$399$	20.7426	−	1.57604i	1.03843	−	0.0789009i
$400$	−13.6777	−	23.6905i	−0.683886	−	1.18453i
$401$	−12.6939	+	7.32884i	−0.633905	+	0.365985i	−0.782263	−	0.622949i	$-0.785935\pi$
$401$	−12.6939	+	7.32884i	−0.633905	+	0.365985i	0.148358	+	0.988934i	$0.452601\pi$
$402$	−0.198718	−	0.290818i	−0.00991114	−	0.0145047i
$403$	−7.51162	−	13.0682i	−0.374180	−	0.650973i
$404$	14.2666			0.709789
$405$	12.0372	+	2.69502i	0.598136	+	0.133917i
$406$	−14.4330	+	24.9987i	−0.716298	+	1.24066i
$407$	2.12924	−	3.68796i	0.105543	−	0.182805i
$408$	−58.0135	+	39.6410i	−2.87210	+	1.96252i
$409$			14.9121i			0.737358i	0.929557	+	0.368679i	$0.120190\pi$
$409$			14.9121i			0.737358i	−0.929557	+	0.368679i	$0.879810\pi$
$410$		−	5.94307i		−	0.293507i
$411$	−3.38847	−	1.62748i	−0.167141	−	0.0802778i
$412$	−12.9393	+	22.4115i	−0.637472	+	1.10413i
$413$	−10.5699	+	18.3076i	−0.520111	+	0.900859i
$414$	−2.13380	+	1.70889i	−0.104871	+	0.0839874i
$415$	−3.48107			−0.170879
$416$	15.6662	−	27.0152i	0.768100	−	1.32453i
$417$	−15.8762	+	1.20629i	−0.777459	+	0.0590721i
$418$	−3.54531	+	2.04688i	−0.173407	+	0.100116i
$419$	6.36693	+	11.0278i	0.311045	+	0.538745i	0.978589	−	0.205825i	$-0.0659877\pi$
$419$	6.36693	+	11.0278i	0.311045	+	0.538745i	−0.667544	+	0.744570i	$0.732654\pi$
$420$	23.3686	+	34.1992i	1.14027	+	1.66875i
$421$	11.8508	−	6.84207i	0.577573	−	0.333462i	−0.182595	−	0.983188i	$-0.558450\pi$
$421$	11.8508	−	6.84207i	0.577573	−	0.333462i	0.760168	+	0.649726i	$0.225116\pi$
$422$	51.7549	−	29.8807i	2.51939	−	1.45457i
$423$	8.83144	−	7.07281i	0.429399	−	0.343892i
$424$		−	85.8027i		−	4.16695i
$425$	9.01960	−	15.6224i	0.437515	−	0.757798i
$426$	−2.74786	−	4.02142i	−0.133134	−	0.194838i
$427$	−7.55411	+	4.36136i	−0.365569	+	0.211061i
$428$	13.1376	−	22.7549i	0.635028	−	1.09990i
$429$	−1.32326	+	2.74162i	−0.0638877	+	0.132367i
$430$	20.5329	+	35.5641i	0.990186	+	1.71505i
$431$	−19.8288	−	11.4482i	−0.955120	−	0.551439i	−0.0604526	−	0.998171i	$-0.519254\pi$
$431$	−19.8288	−	11.4482i	−0.955120	−	0.551439i	−0.894668	+	0.446732i	$0.852588\pi$
$432$	44.3634	−	10.2707i	2.13443	−	0.494151i
$433$	−7.61501	−	13.1896i	−0.365954	−	0.633851i	0.622975	−	0.782242i	$-0.285924\pi$
$433$	−7.61501	−	13.1896i	−0.365954	−	0.633851i	−0.988929	+	0.148391i	$0.952591\pi$
$434$	34.7425	−	20.0586i	1.66769	−	0.962844i
$435$	6.43698	+	3.09168i	0.308630	+	0.148235i
$436$			4.60511i			0.220545i
$437$	0.987701	+	0.570250i	0.0472482	+	0.0272787i
$438$	11.1665	−	0.848442i	0.533556	−	0.0405401i
$439$	−27.3214			−1.30398			−0.651991	−	0.758227i	$-0.726066\pi$
$439$	−27.3214			−1.30398			−0.651991	+	0.758227i	$0.726066\pi$
$440$	−4.06164	−	2.34499i	−0.193631	−	0.111793i
$441$	12.6093	+	15.7446i	0.600445	+	0.749744i
$442$	53.9738	+	0.103274i	2.56727	+	0.00491225i
$443$	−0.234040	−	0.405370i	−0.0111196	−	0.0192597i	0.860412	−	0.509599i	$-0.170206\pi$
$443$	−0.234040	−	0.405370i	−0.0111196	−	0.0192597i	−0.871532	+	0.490339i	$0.836873\pi$
$444$	64.2402	+	30.8546i	3.04871	+	1.46429i
$445$	11.0873	+	19.2038i	0.525589	+	0.910346i
$446$	−25.0580			−1.18653
$447$	−0.760732	−	10.0121i	−0.0359814	−	0.473558i
$448$	15.7489	+	9.09266i	0.744068	+	0.429588i
$449$	32.6429	−	18.8464i	1.54051	−	0.889416i	0.541708	−	0.840567i	$-0.317778\pi$
$449$	32.6429	−	18.8464i	1.54051	−	0.889416i	0.998806	−	0.0488494i	$-0.0155554\pi$
$450$	−18.9338	+	15.1635i	−0.892548	+	0.714812i
$451$	0.408005	+	0.706685i	0.0192122	+	0.0332765i
$452$	7.81915			0.367782
$453$	−20.0414	+	13.6944i	−0.941625	+	0.643418i
$454$	34.6947	−	60.0930i	1.62830	−	2.82030i
$455$	0.0350285	−	18.3069i	0.00164216	−	0.858239i
$456$	−22.2386	−	32.5455i	−1.04142	−	1.52408i
$457$			30.8944i			1.44518i	0.691277	+	0.722590i	$0.257049\pi$
$457$			30.8944i			1.44518i	−0.691277	+	0.722590i	$0.742951\pi$
$458$	−8.30874	+	14.3912i	−0.388242	+	0.672455i
$459$	20.4929	+	21.9490i	0.956528	+	1.02449i
$460$			2.27091i			0.105882i
$461$	−34.6487	−	20.0045i	−1.61375	−	0.931700i	−0.988490	−	0.151285i	$-0.951659\pi$
$461$	−34.6487	−	20.0045i	−1.61375	−	0.931700i	−0.625262	−	0.780415i	$-0.715008\pi$
$462$	−7.30352	−	3.50788i	−0.339790	−	0.163201i
$463$	−12.0417	−	6.95225i	−0.559623	−	0.323099i	0.193371	−	0.981126i	$-0.438058\pi$
$463$	−12.0417	−	6.95225i	−0.559623	−	0.323099i	−0.752994	+	0.658027i	$0.771391\pi$
$464$	26.3615			1.22380
$465$	−5.59905	−	8.19406i	−0.259650	−	0.379990i
$466$			56.9511i			2.63821i
$467$	−36.5921			−1.69328			−0.846640	−	0.532166i	$-0.821378\pi$
$467$	−36.5921			−1.69328			−0.846640	+	0.532166i	$0.821378\pi$
$468$	−47.4269	−	18.6051i	−2.19231	−	0.860020i
$469$	−0.290831			−0.0134293
$470$		−	13.3900i		−	0.617634i
$471$	4.15664	−	8.65427i	0.191528	−	0.398768i
$472$	40.0571			1.84378
$473$	−4.88311	−	2.81926i	−0.224525	−	0.129630i
$474$	−8.64361	+	5.90623i	−0.397014	+	0.271282i
$475$	8.76415	+	5.05998i	0.402127	+	0.232168i
$476$			100.834i			4.62170i
$477$	−36.2486	+	5.54039i	−1.65971	+	0.253677i
$478$	14.7467	−	25.5421i	0.674500	−	1.16827i
$479$			31.7921i			1.45262i	0.687368	+	0.726309i	$0.258766\pi$
$479$			31.7921i			1.45262i	−0.687368	+	0.726309i	$0.741234\pi$
$480$	8.90207	−	18.5344i	0.406322	−	0.845976i
$481$	−15.6966	−	27.3078i	−0.715703	−	1.24513i
$482$	−26.1151	+	45.2328i	−1.18951	+	2.06030i
$483$	0.171014	+	2.25075i	0.00778142	+	0.102413i
$484$	−50.6900			−2.30409
$485$	−0.579790	−	1.00423i	−0.0263269	−	0.0455995i
$486$	−14.9467	−	37.5114i	−0.677997	−	1.70155i
$487$	−1.10889	+	0.640220i	−0.0502488	+	0.0290111i	−0.524914	−	0.851155i	$-0.675902\pi$
$487$	−1.10889	+	0.640220i	−0.0502488	+	0.0290111i	0.474665	+	0.880166i	$0.342569\pi$
$488$	14.3140	+	8.26421i	0.647966	+	0.374103i
$489$	−0.180698	+	0.123472i	−0.00817144	+	0.00558360i
$490$	23.8716			1.07841
$491$	10.8321	+	18.7618i	0.488846	+	0.846706i	0.999918	−	0.0128321i	$-0.00408468\pi$
$491$	10.8321	+	18.7618i	0.488846	+	0.846706i	−0.511072	+	0.859538i	$0.670751\pi$
$492$	−11.2751	+	7.70433i	−0.508320	+	0.347338i
$493$	8.69188	+	15.0548i	0.391462	+	0.678033i
$494$	−0.0579366	+	30.2793i	−0.00260669	+	1.36233i
$495$	−0.728410	+	1.86732i	−0.0327396	+	0.0839297i
$496$	−31.7282	−	18.3183i	−1.42464	−	0.822515i
$497$	−4.02160			−0.180393
$498$	6.42896	+	9.40861i	0.288089	+	0.421610i
$499$	−8.28148	−	4.78131i	−0.370730	−	0.214041i	0.303047	−	0.952975i	$-0.401996\pi$
$499$	−8.28148	−	4.78131i	−0.370730	−	0.214041i	−0.673777	+	0.738935i	$0.735329\pi$
$500$			52.4271i			2.34461i
$501$	−13.2043	+	9.02255i	−0.589923	+	0.403098i
$502$	26.7563	−	15.4477i	1.19419	−	0.689466i
$503$	−12.2128	−	21.1531i	−0.544540	−	0.943171i	−0.998636	−	0.0522178i	$-0.983371\pi$
$503$	−12.2128	−	21.1531i	−0.544540	−	0.943171i	0.454096	−	0.890953i	$-0.349962\pi$
$504$	28.3514	−	72.6805i	1.26287	−	3.23745i
$505$	−3.59536	−	2.07578i	−0.159991	−	0.0923710i
$506$	−0.222104	−	0.384696i	−0.00987375	−	0.0171018i
$507$	12.6321	+	18.6395i	0.561012	+	0.827808i
$508$	−41.9798	+	72.7112i	−1.86255	+	3.22604i
$509$	−12.9810	+	7.49461i	−0.575375	+	0.332193i	−0.759293	−	0.650749i	$-0.774455\pi$
$509$	−12.9810	+	7.49461i	−0.575375	+	0.332193i	0.183919	+	0.982941i	$0.441122\pi$
$510$	35.4347	−	2.69236i	1.56907	−	0.119220i
$511$	4.62334	−	8.00785i	0.204524	−	0.354246i
$512$			47.1301i			2.08287i
$513$	−12.3134	+	11.4965i	−0.543648	+	0.507583i
$514$	−36.7093	+	21.1941i	−1.61918	+	0.934834i
$515$	6.52171	−	3.76531i	0.287381	−	0.165919i
$516$	40.8535	−	85.0584i	1.79848	−	3.74449i
$517$	0.919252	+	1.59219i	0.0404287	+	0.0700245i
$518$	72.5995	−	41.9153i	3.18984	−	1.84165i
$519$	−12.1239	+	25.2424i	−0.532182	+	1.10802i
$520$	−30.0748	+	17.2871i	−1.31887	+	0.758088i
$521$	13.1757			0.577239			0.288619	−	0.957444i	$-0.406804\pi$
$521$	13.1757			0.577239			0.288619	+	0.957444i	$0.406804\pi$
$522$	−3.53187	−	23.1076i	−0.154586	−	1.01139i
$523$	−4.56640	+	7.90924i	−0.199675	+	0.345847i	−0.948423	−	0.317008i	$-0.897322\pi$
$523$	−4.56640	+	7.90924i	−0.199675	+	0.345847i	0.748748	+	0.662854i	$0.230655\pi$
$524$	−40.0247	+	69.3249i	−1.74849	+	3.02847i
$525$	1.51746	+	19.9715i	0.0662273	+	0.871630i
$526$		−	38.1217i		−	1.66218i
$527$		−	24.1595i		−	1.05240i
$528$	0.560589	+	7.37802i	0.0243965	+	0.321087i
$529$	11.4381	−	19.8114i	0.497310	−	0.861366i
$530$	−21.6979	+	37.5820i	−0.942499	+	1.63246i
$531$	−2.58654	−	16.9227i	−0.112246	−	0.734383i
$532$	−56.5675			−2.45251
$533$	6.03555	+	0.0115485i	0.261429	+	0.000500220i
$534$	31.4274	−	65.4329i	1.36000	−	2.83156i
$535$	−6.62166	+	3.82302i	−0.286279	+	0.165283i
$536$	0.275543	+	0.477255i	0.0119017	+	0.0206143i
$537$	7.33091	−	15.2632i	0.316352	−	0.658656i
$538$	61.3184	−	35.4022i	2.64363	−	1.52630i
$539$	−2.83855	+	1.63884i	−0.122265	+	0.0705897i
$540$	−32.0833	−	9.78735i	−1.38065	−	0.421181i
$541$		−	1.26741i		−	0.0544903i	−0.999629	−	0.0272451i	$-0.991327\pi$
$541$		−	1.26741i		−	0.0544903i	0.999629	−	0.0272451i	$-0.00867347\pi$
$542$	15.3525	−	26.5913i	0.659445	−	1.14219i
$543$	18.9344	−	1.43865i	0.812553	−	0.0617386i
$544$	43.3482	−	25.0271i	1.85854	−	1.07303i
$545$	0.670041	−	1.16055i	0.0287014	−	0.0497123i
$546$	−49.5443	+	33.7151i	−2.12030	+	1.44287i
$547$	16.8274	+	29.1459i	0.719487	+	1.24619i	0.961203	+	0.275840i	$0.0889561\pi$
$547$	16.8274	+	29.1459i	0.719487	+	1.24619i	−0.241717	+	0.970347i	$0.577711\pi$
$548$	8.85242	+	5.11095i	0.378157	+	0.218329i
$549$	2.56706	−	6.58080i	0.109559	−	0.280862i
$550$	−1.97079	−	3.41352i	−0.0840350	−	0.145553i
$551$	−8.44571	+	4.87613i	−0.359799	+	0.207730i
$552$	3.53147	−	2.41307i	0.150309	−	0.102707i
$553$			8.64400i			0.367580i
$554$	−32.0608	−	18.5103i	−1.36213	−	0.786427i
$555$	−11.7000	−	17.1227i	−0.496638	−	0.726816i
$556$	43.2961			1.83617
$557$	36.9465	+	21.3311i	1.56547	+	0.903826i	0.996686	+	0.0813415i	$0.0259205\pi$
$557$	36.9465	+	21.3311i	1.56547	+	0.903826i	0.568787	+	0.822485i	$0.307413\pi$
$558$	−11.8063	+	30.2661i	−0.499801	+	1.28127i
$559$	−36.1574	+	20.7834i	−1.52930	+	0.879042i
$560$	−22.2481	−	38.5349i	−0.940155	−	1.62840i
$561$	−4.02867	+	2.75282i	−0.170091	+	0.116224i
$562$	−30.3841	−	52.6267i	−1.28167	−	2.21993i
$563$	4.71871			0.198870			0.0994349	−	0.995044i	$-0.468297\pi$
$563$	4.71871			0.198870			0.0994349	+	0.995044i	$0.468297\pi$
$564$	−25.4032	+	17.3582i	−1.06967	+	0.730912i
$565$	−1.97052	−	1.13768i	−0.0829006	−	0.0478627i
$566$	−61.2835	+	35.3820i	−2.57594	+	1.48722i
$567$	−32.5356	−	7.28441i	−1.36637	−	0.305916i
$568$	3.81020	+	6.59946i	0.159872	+	0.276907i
$569$	−24.0375			−1.00770			−0.503851	−	0.863790i	$-0.668084\pi$
$569$	−24.0375			−1.00770			−0.503851	+	0.863790i	$0.668084\pi$
$570$	1.51041	+	19.8788i	0.0632642	+	0.832632i
$571$	5.86175	−	10.1528i	0.245306	−	0.424883i	−0.716911	−	0.697164i	$-0.754445\pi$
$571$	5.86175	−	10.1528i	0.245306	−	0.424883i	0.962218	+	0.272281i	$0.0877781\pi$
$572$	4.15280	−	7.16118i	0.173637	−	0.299424i
$573$	1.63908	−	3.41262i	0.0684735	−	0.142564i
$574$			16.0636i			0.670481i
$575$	−0.549051	+	0.950985i	−0.0228970	+	0.0396588i
$576$	−14.5576	+	2.22505i	−0.606567	+	0.0927103i
$577$		−	6.65490i		−	0.277047i	−0.990359	−	0.138523i	$-0.955764\pi$
$577$		−	6.65490i		−	0.277047i	0.990359	−	0.138523i	$-0.0442356\pi$
$578$	36.7835	+	21.2370i	1.52999	+	0.883342i
$579$	4.36069	−	2.97968i	0.181224	−	0.123831i
$580$	−16.8167	−	9.70911i	−0.698275	−	0.403149i
$581$	9.40904			0.390353
$582$	−1.64344	+	3.42169i	−0.0681226	+	0.141834i
$583$		−	5.95845i		−	0.246774i
$584$	−17.5212			−0.725033
$585$	9.24514	+	11.5893i	0.382240	+	0.479158i
$586$	72.2623			2.98513
$587$			21.5477i			0.889367i	0.895688	+	0.444684i	$0.146684\pi$
$587$			21.5477i			0.889367i	−0.895688	+	0.444684i	$0.853316\pi$
$588$	−30.9461	−	45.2887i	−1.27619	−	1.86768i
$589$	13.5534			0.558460
$590$	−17.5452	−	10.1297i	−0.722325	−	0.417034i
$591$	15.9486	+	7.66010i	0.656037	+	0.315094i
$592$	−66.3006	−	38.2787i	−2.72494	−	1.57324i
$593$			0.0314626i			0.00129201i	1.00000		0.000646006i	$0.000205630\pi$
$593$			0.0314626i			0.00129201i	−1.00000		0.000646006i	$0.999794\pi$
$594$	6.39223	−	1.47989i	0.262276	−	0.0607206i
$595$	14.6712	−	25.4113i	0.601462	−	1.04176i
$596$			27.3042i			1.11843i
$597$	−6.68099	−	9.77744i	−0.273435	−	0.400164i
$598$	−3.28556	−	0.00628662i	−0.134356	−	0.000257079i
$599$	14.1320	−	24.4773i	0.577416	−	1.00011i	−0.418358	−	0.908282i	$-0.637394\pi$
$599$	14.1320	−	24.4773i	0.577416	−	1.00011i	0.995774	−	0.0918325i	$-0.0292724\pi$
$600$	31.3357	−	21.4119i	1.27927	−	0.874136i
$601$	−26.3337			−1.07417			−0.537087	−	0.843527i	$-0.680475\pi$
$601$	−26.3337			−1.07417			−0.537087	+	0.843527i	$0.680475\pi$
$602$	−55.4987	−	96.1266i	−2.26196	−	3.91783i
$603$	0.183831	−	0.147224i	0.00748618	−	0.00599543i
$604$	57.1627	−	33.0029i	2.32592	−	1.34287i
$605$	12.7745	+	7.37536i	0.519358	+	0.299851i
$606$	1.02963	+	13.5511i	0.0418258	+	0.550477i
$607$	8.05575			0.326973			0.163486	−	0.986546i	$-0.447726\pi$
$607$	8.05575			0.326973			0.163486	+	0.986546i	$0.447726\pi$
$608$	14.0402	+	24.3183i	0.569404	+	0.986236i
$609$	−17.3986	−	8.35654i	−0.705027	−	0.338624i
$610$	−4.17974	−	7.23952i	−0.169233	−	0.293120i
$611$	13.5984	+	0.0260192i	0.550131	+	0.00105263i
$612$	−51.0439	−	63.7358i	−2.06333	−	2.57637i
$613$	31.5638	+	18.2234i	1.27485	+	0.736036i	0.975897	−	0.218232i	$-0.0700289\pi$
$613$	31.5638	+	18.2234i	1.27485	+	0.736036i	0.298954	+	0.954267i	$0.403362\pi$
$614$	74.4534			3.00469
$615$	3.96244	−	0.301070i	0.159781	−	0.0121403i
$616$	10.9783	+	6.33830i	0.442327	+	0.255378i
$617$		−	11.4369i		−	0.460432i	−0.973140	−	0.230216i	$-0.926057\pi$
$617$		−	11.4369i		−	0.460432i	0.973140	−	0.230216i	$-0.0739433\pi$
$618$	−22.2214	−	10.6729i	−0.893875	−	0.429328i
$619$	32.5739	−	18.8065i	1.30925	−	0.755899i	0.327283	−	0.944926i	$-0.393867\pi$
$619$	32.5739	−	18.8065i	1.30925	−	0.755899i	0.981972	+	0.189028i	$0.0605336\pi$
$620$	13.4935	+	23.3714i	0.541911	+	0.938617i
$621$	−1.24747	−	1.33610i	−0.0500592	−	0.0536160i
$622$	−30.6573	−	17.7000i	−1.22925	−	0.709705i
$623$	−29.9680	−	51.9061i	−1.20064	−	2.07958i
$624$	49.2877	+	23.7890i	1.97309	+	0.952324i
$625$	−0.175637	+	0.304212i	−0.00702548	+	0.0121685i
$626$	−26.4859	+	15.2917i	−1.05859	+	0.611178i
$627$	−1.54433	−	2.26008i	−0.0616745	−	0.0902589i
$628$	−13.0535	+	22.6094i	−0.520893	+	0.902213i
$629$		−	50.4847i		−	2.01296i
$630$	−30.7977	+	24.6648i	−1.22701	+	0.982670i
$631$	−22.9975	+	13.2776i	−0.915516	+	0.528573i	−0.882202	−	0.470872i	$-0.843939\pi$
$631$	−22.9975	+	13.2776i	−0.915516	+	0.528573i	−0.0333140	+	0.999445i	$0.510606\pi$
$632$	14.1848	−	8.18962i	0.564242	−	0.325765i
$633$	22.5443	+	32.9929i	0.896055	+	1.31135i
$634$	39.0107	+	67.5685i	1.54931	+	2.68349i
$635$	21.1589	−	12.2161i	0.839664	−	0.484780i
$636$	99.4281	−	7.55464i	3.94258	−	0.299561i
$637$	−0.0463869	+	24.2431i	−0.00183792	+	0.960545i
$638$	3.79838			0.150379
$639$	2.54201	−	2.03581i	0.100560	−	0.0805354i
$640$	3.15713	−	5.46831i	0.124797	−	0.216154i
$641$	8.30243	−	14.3802i	0.327926	−	0.567985i	−0.654174	−	0.756344i	$-0.726984\pi$
$641$	8.30243	−	14.3802i	0.327926	−	0.567985i	0.982100	+	0.188359i	$0.0603169\pi$
$642$	22.5619	+	10.8365i	0.890449	+	0.427682i
$643$		−	3.67108i		−	0.144773i	−0.997377	−	0.0723866i	$-0.976938\pi$
$643$		−	3.67108i		−	0.144773i	0.997377	−	0.0723866i	$-0.0230615\pi$
$644$		−	6.13806i		−	0.241873i
$645$	−22.6715	+	15.4916i	−0.892691	+	0.609982i
$646$	−24.2660	+	42.0299i	−0.954733	+	1.65365i
$647$	−3.97129	+	6.87848i	−0.156128	+	0.270421i	−0.933469	−	0.358658i	$-0.883234\pi$
$647$	−3.97129	+	6.87848i	−0.156128	+	0.270421i	0.777341	+	0.629079i	$0.216568\pi$
$648$	18.8716	+	60.2926i	0.741347	+	2.36852i
$649$	2.78171			0.109192
$650$	−29.1537	−	0.0557829i	−1.14350	−	0.00218799i
$651$	15.1337	+	22.1478i	0.593138	+	0.868042i
$652$	0.515393	−	0.297562i	0.0201844	−	0.0116534i
$653$	17.9235	+	31.0443i	0.701399	+	1.21486i	0.967975	+	0.251045i	$0.0807743\pi$
$653$	17.9235	+	31.0443i	0.701399	+	1.21486i	−0.266576	+	0.963814i	$0.585892\pi$
$654$	−4.37417	+	0.332354i	−0.171044	+	0.0129961i
$655$	20.1735	−	11.6472i	0.788243	−	0.455092i
$656$	12.7045	−	7.33494i	0.496027	−	0.286381i
$657$	1.13137	+	7.40209i	0.0441389	+	0.288783i
$658$			36.1920i			1.41091i
$659$	−9.36059	+	16.2130i	−0.364637	+	0.631570i	−0.988718	−	0.149790i	$-0.952140\pi$
$659$	−9.36059	+	16.2130i	−0.364637	+	0.631570i	0.624081	+	0.781360i	$0.285474\pi$
$660$	2.35976	−	4.91310i	0.0918535	−	0.191242i
$661$	−25.3674	+	14.6459i	−0.986679	+	0.569659i	−0.904280	−	0.426940i	$-0.859591\pi$
$661$	−25.3674	+	14.6459i	−0.986679	+	0.569659i	−0.0823989	+	0.996599i	$0.526258\pi$
$662$	12.2749	−	21.2608i	0.477078	−	0.826323i
$663$	2.66540	+	35.9914i	0.103516	+	1.39779i
$664$	−8.91444	−	15.4403i	−0.345947	−	0.599198i
$665$	14.2557	+	8.23055i	0.552813	+	0.319167i
$666$	−24.6710	+	63.2454i	−0.955981	+	2.45071i
$667$	−0.529102	−	0.916431i	−0.0204869	−	0.0354844i
$668$	37.6617	−	21.7440i	1.45717	−	0.841300i
$669$	−1.26941	−	16.7070i	−0.0490783	−	0.645929i
$670$		−	0.278720i		−	0.0107679i
$671$	0.994018	+	0.573897i	0.0383737	+	0.0221550i
$672$	−24.0615	+	50.0969i	−0.928194	+	1.93253i
$673$	−9.27930			−0.357691			−0.178845	−	0.983877i	$-0.557236\pi$
$673$	−9.27930			−0.357691			−0.178845	+	0.983877i	$0.557236\pi$
$674$	−36.5307	−	21.0910i	−1.40711	−	0.812396i
$675$	−11.0691	−	11.8556i	−0.426052	−	0.456323i
$676$	−30.4114	−	53.1427i	−1.16967	−	2.04395i
$677$	−21.0550	−	36.4684i	−0.809210	−	1.40159i	−0.913412	−	0.407037i	$-0.866562\pi$
$677$	−21.0550	−	36.4684i	−0.809210	−	1.40159i	0.104202	−	0.994556i	$-0.466771\pi$
$678$	0.564313	+	7.42703i	0.0216723	+	0.285233i
$679$	1.56712	+	2.71433i	0.0601406	+	0.104167i
$680$	−55.6001			−2.13217
$681$	41.8235	+	20.0878i	1.60268	+	0.769768i
$682$	−4.57165	−	2.63944i	−0.175057	−	0.101069i
$683$	28.6729	−	16.5543i	1.09714	−	0.633434i	0.161671	−	0.986845i	$-0.448312\pi$
$683$	28.6729	−	16.5543i	1.09714	−	0.633434i	0.935468	+	0.353411i	$0.114978\pi$
$684$	35.7557	−	28.6356i	1.36715	−	1.09491i
$685$	−1.48728	−	2.57604i	−0.0568260	−	0.0984256i
$686$	2.65018			0.101184
$687$	−10.0160	−	4.81067i	−0.382133	−	0.183538i
$688$	−50.6835	+	87.7864i	−1.93229	+	3.34683i
$689$	−38.1246	−	22.1086i	−1.45243	−	0.842272i
$690$	−2.15702	+	0.163893i	−0.0821164	+	0.00623928i
$691$		−	24.4135i		−	0.928733i	−0.885643	−	0.464366i	$-0.846282\pi$
$691$		−	24.4135i		−	0.928733i	0.885643	−	0.464366i	$-0.153718\pi$
$692$	38.0740	−	65.9462i	1.44736	−	2.50690i
$693$	1.96883	−	5.04720i	0.0747896	−	0.191727i
$694$		−	8.48837i		−	0.322214i
$695$	−10.9112	−	6.29957i	−0.413884	−	0.238956i
$696$	2.77091	+	36.4684i	0.105031	+	1.38233i
$697$	8.37781	+	4.83693i	0.317332	+	0.183212i
$698$	−60.4763			−2.28906
$699$	−37.9711	+	2.88508i	−1.43620	+	0.109124i
$700$		−	54.4647i		−	2.05857i
$701$	14.3928			0.543607			0.271803	−	0.962353i	$-0.412380\pi$
$701$	14.3928			0.543607			0.271803	+	0.962353i	$0.412380\pi$
$702$	14.2492	−	46.3912i	0.537802	−	1.75092i
$703$	28.3219			1.06818
$704$		−	2.39294i		−	0.0901874i
$705$	8.92754	−	0.678323i	0.336231	−	0.0255471i
$706$	3.83975			0.144511
$707$	9.71794	+	5.61065i	0.365481	+	0.211010i
$708$	3.52690	+	46.4182i	0.132549	+	1.74450i
$709$	29.2083	+	16.8634i	1.09694	+	0.633320i	0.935416	−	0.353548i	$-0.115025\pi$
$709$	29.2083	+	16.8634i	1.09694	+	0.633320i	0.161526	+	0.986868i	$0.448358\pi$
$710$		−	3.85412i		−	0.144643i
$711$	−4.37576	−	5.46378i	−0.164104	−	0.204908i
$712$	−56.7854	+	98.3553i	−2.12812	+	3.68602i
$713$			1.47066i			0.0550768i
$714$	−95.7769	+	7.27722i	−3.58436	+	0.272343i
$715$	−2.08850	+	1.20048i	−0.0781057	+	0.0448953i
$716$	−23.0220	+	39.8753i	−0.860373	+	1.49021i
$717$	17.7768	+	8.53820i	0.663887	+	0.318865i
$718$	−13.0683			−0.487704
$719$	17.3402	+	30.0341i	0.646679	+	1.12008i	0.983911	+	0.178659i	$0.0571760\pi$
$719$	17.3402	+	30.0341i	0.646679	+	1.12008i	−0.337232	+	0.941422i	$0.609491\pi$
$720$	33.5699	+	13.0950i	1.25108	+	0.488024i
$721$	−17.6276	+	10.1773i	−0.656487	+	0.379023i
$722$	19.0442	+	10.9952i	0.708751	+	0.409197i
$723$	−31.4811	−	15.1204i	−1.17080	−	0.562333i
$724$	−51.6363			−1.91905
$725$	−4.69487	−	8.13175i	−0.174363	−	0.302006i
$726$	−3.65833	−	48.1479i	−0.135773	−	1.78694i
$727$	−2.57894	−	4.46685i	−0.0956474	−	0.165666i	0.814231	−	0.580541i	$-0.197159\pi$
$727$	−2.57894	−	4.46685i	−0.0956474	−	0.165666i	−0.909879	+	0.414875i	$0.863825\pi$
$728$	81.2896	−	46.7254i	3.01279	−	1.73176i
$729$	24.2529	−	11.8658i	0.898256	−	0.439473i
$730$	7.67437	+	4.43080i	0.284041	+	0.163991i
$731$	−66.8452			−2.47236
$732$	−8.31626	+	17.3147i	−0.307378	+	0.639971i
$733$	15.9989	+	9.23695i	0.590931	+	0.341174i	0.765466	−	0.643477i	$-0.222509\pi$
$733$	15.9989	+	9.23695i	0.590931	+	0.341174i	−0.174534	+	0.984651i	$0.555842\pi$
$734$			10.8719i			0.401288i
$735$	1.20931	+	15.9160i	0.0446061	+	0.587069i
$736$	−2.63874	+	1.52348i	−0.0972653	+	0.0561561i
$737$	0.0191347	+	0.0331423i	0.000704837	+	0.00122081i
$738$	−8.13169	−	10.1536i	−0.299332	−	0.373760i
$739$	40.0149	+	23.1026i	1.47197	+	0.849844i	0.999504	−	0.0315024i	$-0.0100292\pi$
$739$	40.0149	+	23.1026i	1.47197	+	0.849844i	0.472470	+	0.881347i	$0.343363\pi$
$740$	28.1966	+	48.8379i	1.03653	+	1.79532i
$741$	−20.1911	+	1.49529i	−0.741739	+	0.0549308i
$742$	58.6477	−	101.581i	2.15302	−	3.72915i
$743$	21.0503	−	12.1534i	0.772260	−	0.445865i	−0.0614202	−	0.998112i	$-0.519563\pi$
$743$	21.0503	−	12.1534i	0.772260	−	0.445865i	0.833680	+	0.552247i	$0.186230\pi$
$744$	22.0064	−	45.8181i	0.806795	−	1.67977i
$745$	3.97275	−	6.88101i	0.145550	−	0.252101i
$746$			70.5910i			2.58452i
$747$	−5.94735	+	4.76303i	−0.217602	+	0.174270i
$748$	11.4907	−	6.63417i	0.420142	−	0.242569i
$749$	17.8978	−	10.3333i	0.653971	−	0.377570i
$750$	−49.7979	+	3.78369i	−1.81836	+	0.138161i
$751$	15.8328	+	27.4232i	0.577746	+	1.00069i	0.995737	+	0.0922350i	$0.0294011\pi$
$751$	15.8328	+	27.4232i	0.577746	+	1.00069i	−0.417991	+	0.908451i	$0.637266\pi$
$752$	28.6238	−	16.5259i	1.04380	−	0.602639i
$753$	11.6550	+	17.0567i	0.424730	+	0.621581i
$754$	14.0938	−	24.3036i	0.513264	−	0.885084i
$755$	−19.2076			−0.699036
$756$	86.7184	+	26.4544i	3.15392	+	0.962136i
$757$	−10.5340	+	18.2454i	−0.382863	+	0.663139i	−0.991470	−	0.130333i	$-0.958395\pi$
$757$	−10.5340	+	18.2454i	−0.382863	+	0.663139i	0.608607	+	0.793472i	$0.291729\pi$
$758$	−5.84955	+	10.1317i	−0.212465	+	0.368001i
$759$	0.245238	−	0.167573i	0.00890157	−	0.00608250i
$760$		−	31.1916i		−	1.13144i
$761$		−	11.8420i		−	0.429272i	−0.976694	−	0.214636i	$-0.931143\pi$
$761$		−	11.8420i		−	0.429272i	0.976694	−	0.214636i	$-0.0688566\pi$
$762$	−72.0945	−	34.6270i	−2.61171	−	1.25440i
$763$	−1.81106	+	3.13686i	−0.0655649	+	0.113562i
$764$	−5.14737	+	8.91550i	−0.186225	+	0.322552i
$765$	3.59017	+	23.4891i	0.129803	+	0.849249i
$766$	49.9318			1.80411
$767$	10.3215	−	17.7986i	0.372686	−	0.642669i
$768$	−37.5664	+	2.85433i	−1.35556	+	0.102997i
$769$	−23.3468	+	13.4793i	−0.841906	+	0.486075i	−0.857912	−	0.513797i	$-0.828238\pi$
$769$	−23.3468	+	13.4793i	−0.841906	+	0.486075i	0.0160056	+	0.999872i	$0.494905\pi$
$770$	−3.20569	−	5.55241i	−0.115525	−	0.200095i
$771$	−15.9905	−	23.4016i	−0.575883	−	0.842789i
$772$	−12.4377	+	7.18091i	−0.447643	+	0.258447i
$773$	−30.2027	+	17.4375i	−1.08631	+	0.627184i	−0.932593	−	0.360930i	$-0.882459\pi$
$773$	−30.2027	+	17.4375i	−1.08631	+	0.627184i	−0.153722	+	0.988114i	$0.549126\pi$
$774$	83.7412	+	32.6660i	3.01002	+	1.17416i
$775$			13.0496i			0.468756i
$776$	2.96949	−	5.14330i	0.106598	−	0.184634i
$777$	31.6241	+	46.2811i	1.13451	+	1.66032i
$778$	−9.94703	+	5.74292i	−0.356618	+	0.205894i
$779$	−2.71351	+	4.69994i	−0.0972216	+	0.168393i
$780$	−22.6802	−	33.3286i	−0.812082	−	1.19336i
$781$	0.264594	+	0.458291i	0.00946792	+	0.0163989i
$782$	−4.56061	−	2.63307i	−0.163087	−	0.0941583i
$783$	15.2277	−	3.52542i	0.544193	−	0.125988i
$784$	29.4623	+	51.0302i	1.05223	+	1.82251i
$785$	6.57931	−	3.79856i	0.234825	−	0.135577i
$786$	−68.7369	−	33.0143i	−2.45176	−	1.17758i
$787$		−	33.3246i		−	1.18789i	−0.804504	−	0.593947i	$-0.797569\pi$
$787$		−	33.3246i		−	1.18789i	0.804504	−	0.593947i	$-0.202431\pi$
$788$	−41.6658	−	24.0558i	−1.48428	−	0.856952i
$789$	25.4170	−	1.93120i	0.904868	−	0.0687527i
$790$	−8.28403			−0.294732
$791$	5.32616	+	3.07506i	0.189376	+	0.109336i
$792$	−10.1478	+	1.55103i	−0.360587	+	0.0551136i
$793$	7.36030	−	4.23072i	0.261372	−	0.150237i
$794$	−8.67147	−	15.0194i	−0.307739	−	0.533019i
$795$	−26.1563	−	12.5629i	−0.927669	−	0.445559i
$796$	16.1009	+	27.8876i	0.570681	+	0.988449i
$797$	38.5783			1.36651			0.683257	−	0.730178i	$-0.260563\pi$
$797$	38.5783			1.36651			0.683257	+	0.730178i	$0.260563\pi$
$798$	−4.08251	−	53.7307i	−0.144519	−	1.90205i
$799$	18.8756	+	10.8978i	0.667769	+	0.385537i
$800$	−23.4143	+	13.5182i	−0.827820	+	0.477942i
$801$	45.2183	+	17.6389i	1.59771	+	0.623240i
$802$	18.9843	+	32.8818i	0.670359	+	1.16110i
$803$	−1.21674			−0.0429377
$804$	−0.528782	+	0.361320i	−0.0186487	+	0.0127428i
$805$	−0.893085	+	1.54687i	−0.0314771	+	0.0545199i
$806$	−33.8512	+	19.4577i	−1.19236	+	0.685369i
$807$	26.7101	+	39.0896i	0.940241	+	1.37602i
$808$		−	21.2629i		−	0.748026i
$809$	17.9720	−	31.1284i	0.631862	−	1.09442i	−0.355309	−	0.934749i	$-0.615624\pi$
$809$	17.9720	−	31.1284i	0.631862	−	1.09442i	0.987171	−	0.159668i	$-0.0510422\pi$
$810$	6.98105	−	31.1807i	0.245289	−	1.09558i
$811$		−	27.4003i		−	0.962156i	−0.876678	−	0.481078i	$-0.840245\pi$
$811$		−	27.4003i		−	0.962156i	0.876678	−	0.481078i	$-0.159755\pi$
$812$	45.4540	+	26.2429i	1.59512	+	0.920945i
$813$	18.5070	+	8.88891i	0.649069	+	0.311748i
$814$	−9.55311	−	5.51549i	−0.334836	−	0.193318i
$815$	−0.173181			−0.00606625
$816$	49.4890	+	72.4258i	1.73246	+	2.53541i
$817$		−	37.5001i		−	1.31196i
$818$	38.6277			1.35059
$819$	−24.9888	−	31.3249i	−0.873180	−	1.09458i
$820$	−10.8060			−0.377363
$821$		−	37.1277i		−	1.29576i	−0.761741	−	0.647882i	$-0.775655\pi$
$821$		−	37.1277i		−	1.29576i	0.761741	−	0.647882i	$-0.224345\pi$
$822$	−4.21575	+	8.77734i	−0.147041	+	0.306145i
$823$	−14.0029			−0.488111			−0.244056	−	0.969761i	$-0.578478\pi$
$823$	−14.0029			−0.488111			−0.244056	+	0.969761i	$0.578478\pi$
$824$	33.4020	+	19.2847i	1.16361	+	0.671813i
$825$	2.17606	−	1.48692i	0.0757608	−	0.0517679i
$826$	47.4232	+	27.3798i	1.65006	+	0.952664i
$827$		−	16.4147i		−	0.570796i	−0.958409	−	0.285398i	$-0.907874\pi$
$827$		−	16.4147i		−	0.570796i	0.958409	−	0.285398i	$-0.0921258\pi$
$828$	3.10720	+	3.87980i	0.107983	+	0.134832i
$829$	18.1805	−	31.4895i	0.631435	−	1.09368i	−0.355824	−	0.934553i	$-0.615800\pi$
$829$	18.1805	−	31.4895i	0.631435	−	1.09368i	0.987259	−	0.159124i	$-0.0508669\pi$
$830$			9.01720i			0.312992i
$831$	10.7173	−	22.3137i	0.371777	−	0.774053i
$832$	−15.3110	−	8.87894i	−0.530815	−	0.307822i
$833$	−19.4285	+	33.6512i	−0.673159	+	1.16595i
$834$	3.12471	+	41.1249i	0.108200	+	1.42404i
$835$	−12.6549			−0.437942
$836$	3.72176	+	6.44628i	0.128720	+	0.222949i
$837$	−20.7775	−	6.33840i	−0.718176	−	0.219087i
$838$	28.5660	−	16.4926i	0.986796	−	0.569727i
$839$	26.3679	+	15.2235i	0.910321	+	0.525574i	0.880534	−	0.473982i	$-0.157184\pi$
$839$	26.3679	+	15.2235i	0.910321	+	0.525574i	0.0297863	+	0.999556i	$0.490517\pi$
$840$	50.9705	−	34.8285i	1.75865	−	1.20170i
$841$	−19.9514			−0.687980
$842$	−17.7234	−	30.6978i	−0.610788	−	1.05792i
$843$	33.5487	−	22.9241i	1.15548	−	0.789547i
$844$	−54.3308	−	94.1037i	−1.87014	−	3.23918i
$845$	−0.0681844	+	17.8175i	−0.00234561	+	0.612939i
$846$	−18.3211	−	22.8765i	−0.629891	−	0.786512i
$847$	−34.5284	−	19.9350i	−1.18641	−	0.684974i
$848$	−107.119			−3.67847
$849$	−26.6949	−	39.0673i	−0.916167	−	1.34079i
$850$	−40.4675	−	23.3639i	−1.38802	−	0.801376i
$851$			3.07316i			0.105347i
$852$	−7.31197	+	4.99632i	−0.250504	+	0.171171i
$853$	−9.06197	+	5.23193i	−0.310276	+	0.179138i	−0.647050	−	0.762448i	$-0.723998\pi$
$853$	−9.06197	+	5.23193i	−0.310276	+	0.179138i	0.336774	+	0.941586i	$0.390664\pi$
$854$	11.2975	+	19.5678i	0.386592	+	0.669596i
$855$	−13.1773	+	2.01408i	−0.450656	+	0.0688801i
$856$	−33.9139	−	19.5802i	−1.15915	−	0.669238i
$857$	3.72589	+	6.45343i	0.127274	+	0.220445i	0.922620	−	0.385711i	$-0.126044\pi$
$857$	3.72589	+	6.45343i	0.127274	+	0.220445i	−0.795346	+	0.606156i	$0.792711\pi$
$858$	7.10176	+	3.42771i	0.242450	+	0.117020i
$859$	−19.7941	+	34.2843i	−0.675365	+	1.16977i	0.300997	+	0.953625i	$0.402681\pi$
$859$	−19.7941	+	34.2843i	−0.675365	+	1.16977i	−0.976362	+	0.216141i	$0.930653\pi$
$860$	64.6646	−	37.3341i	2.20505	−	1.27308i
$861$	−10.7101	+	0.813765i	−0.365000	+	0.0277331i
$862$	−29.6548	+	51.3636i	−1.01005	+	1.74945i
$863$			39.0451i			1.32911i	0.747240	+	0.664555i	$0.231379\pi$
$863$			39.0451i			1.32911i	−0.747240	+	0.664555i	$0.768621\pi$
$864$	−10.1510	−	43.8461i	−0.345343	−	1.49167i
$865$	−19.1903	+	11.0795i	−0.652488	+	0.376714i
$866$	−34.1657	+	19.7256i	−1.16100	+	0.670302i
$867$	−12.2960	+	25.6006i	−0.417593	+	0.869442i
$868$	−36.4717	−	63.1708i	−1.23793	−	2.14416i
$869$	0.985047	−	0.568717i	0.0334154	−	0.0192924i
$870$	8.00854	−	16.6740i	0.271515	−	0.565303i
$871$	0.283057		0.000541604i	0.00959103		1.83516e-5i
$872$	6.86345			0.232426
$873$	−2.36461	−	0.922393i	−0.0800298	−	0.0312183i
$874$	1.47715	−	2.55849i	0.0499653	−	0.0865424i
$875$	−20.6181	+	35.7117i	−0.697020	+	1.20727i
$876$	−1.54269	−	20.3036i	−0.0521225	−	0.685994i
$877$			25.3962i			0.857567i	0.903407	+	0.428784i	$0.141058\pi$
$877$			25.3962i			0.857567i	−0.903407	+	0.428784i	$0.858942\pi$
$878$			70.7722i			2.38844i
$879$	3.66074	+	48.1796i	0.123474	+	1.62506i
$880$	−2.92755	+	5.07067i	−0.0986878	+	0.170932i
$881$	20.1610	−	34.9200i	0.679243	−	1.17648i	−0.295966	−	0.955198i	$-0.595642\pi$
$881$	20.1610	−	34.9200i	0.679243	−	1.17648i	0.975209	−	0.221285i	$-0.0710251\pi$
$882$	40.7841	−	32.6627i	1.37327	−	1.09981i
$883$	2.60260			0.0875845			0.0437923	−	0.999041i	$-0.486056\pi$
$883$	2.60260			0.0875845			0.0437923	+	0.999041i	$0.486056\pi$
$884$	0.187779	−	98.1383i	0.00631568	−	3.30075i
$885$	5.86500	−	12.2111i	0.197150	−	0.410472i
$886$	−1.05005	+	0.606247i	−0.0352772	+	0.0203673i
$887$	−13.8663	−	24.0172i	−0.465585	−	0.806418i	0.533642	−	0.845710i	$-0.320823\pi$
$887$	−13.8663	−	24.0172i	−0.465585	−	0.806418i	−0.999228	+	0.0392926i	$0.987490\pi$
$888$	45.9856	−	95.7435i	1.54318	−	3.21294i
$889$	−57.1906	+	33.0190i	−1.91811	+	1.10742i
$890$	49.7446	−	28.7200i	1.66744	−	0.962698i
$891$	1.31051	+	4.18694i	0.0439039	+	0.140268i
$892$			45.5619i			1.52552i
$893$	−6.11366	+	10.5892i	−0.204586	+	0.354353i
$894$	−25.9350	+	1.97056i	−0.867395	+	0.0659055i
$895$	11.6037	−	6.69938i	0.387868	−	0.223936i
$896$	−8.53345	+	14.7804i	−0.285083	+	0.493777i
$897$	−0.162252	−	2.19091i	−0.00541742	−	0.0731523i
$898$	−48.8188	−	84.5566i	−1.62910	−	2.82169i
$899$	−10.8907	−	6.28773i	−0.363224	−	0.209708i
$900$	27.5711	+	34.4265i	0.919036	+	1.14755i
$901$	−35.3190	−	61.1742i	−1.17665	−	2.03801i
$902$	1.83056	−	1.05688i	0.0609511	−	0.0351901i
$903$	61.2792	−	41.8725i	2.03925	−	1.39343i
$904$		−	11.6537i		−	0.387595i
$905$	13.0130	+	7.51306i	0.432567	+	0.249742i
$906$	35.4733	+	51.9142i	1.17852	+	1.72473i
$907$	−57.1851			−1.89880			−0.949400	−	0.314068i	$-0.898308\pi$
$907$	−57.1851			−1.89880			−0.949400	+	0.314068i	$0.898308\pi$
$908$	−109.264	−	63.0839i	−3.62607	−	2.09351i
$909$	−8.98282	+	1.37297i	−0.297941	+	0.0455386i
$910$	−47.4212	−	0.0907362i	−1.57200	−	0.00300788i
$911$	19.8268	+	34.3411i	0.656893	+	1.13777i	0.981416	+	0.191894i	$0.0614629\pi$
$911$	19.8268	+	34.3411i	0.656893	+	1.13777i	−0.324523	+	0.945878i	$0.605204\pi$
$912$	−40.6308	+	27.7633i	−1.34542	+	0.919334i
$913$	−0.619051	−	1.07223i	−0.0204876	−	0.0354856i
$914$	80.0275			2.64707
$915$	4.61508	−	3.15352i	0.152570	−	0.104252i
$916$	26.1668	+	15.1074i	0.864576	+	0.499163i
$917$	−54.5271	+	31.4813i	−1.80064	+	1.03960i
$918$	56.8556	−	53.0839i	1.87652	−	1.75203i
$919$	−2.93836	−	5.08939i	−0.0969276	−	0.167884i	0.813484	−	0.581587i	$-0.197568\pi$
$919$	−2.93836	−	5.08939i	−0.0969276	−	0.167884i	−0.910411	+	0.413704i	$0.864235\pi$
$920$	3.38455			0.111585
$921$	3.77173	+	49.6405i	0.124283	+	1.63571i
$922$	−51.8186	+	89.7524i	−1.70655	+	2.95584i
$923$	3.91410	+	0.00748928i	0.128834	+	0.000246513i
$924$	−6.37822	+	13.2797i	−0.209828	+	0.436869i
$925$			27.2690i			0.896601i
$926$	−18.0088	+	31.1921i	−0.591805	+	1.02504i
$927$	5.99027	−	15.3564i	0.196746	−	0.504370i
$928$		−	26.0541i		−	0.855269i
$929$	−5.62125	−	3.24543i	−0.184427	−	0.106479i	0.404944	−	0.914342i	$-0.367291\pi$
$929$	−5.62125	−	3.24543i	−0.184427	−	0.106479i	−0.589371	+	0.807862i	$0.700624\pi$
$930$	−21.2255	+	14.5035i	−0.696011	+	0.475589i
$931$	−18.8783	−	10.8994i	−0.618711	−	0.357213i
$932$	103.552			3.39195
$933$	10.2481	−	21.3369i	0.335508	−	0.698538i
$934$			94.7864i			3.10151i
$935$	−3.86107			−0.126271
$936$	−27.7290	+	70.6850i	−0.906349	+	2.31041i
$937$	−34.5116			−1.12744			−0.563722	−	0.825964i	$-0.690631\pi$
$937$	−34.5116			−1.12744			−0.563722	+	0.825964i	$0.690631\pi$
$938$			0.753355i			0.0245979i
$939$	−11.5372	−	16.8844i	−0.376502	−	0.551001i
$940$	−24.3464			−0.794093
$941$	16.5489	+	9.55449i	0.539477	+	0.311467i	0.744867	−	0.667213i	$-0.232513\pi$
$941$	16.5489	+	9.55449i	0.539477	+	0.311467i	−0.205390	+	0.978680i	$0.565846\pi$
$942$	−22.4176	−	10.7672i	−0.730406	−	0.350814i
$943$	−0.509984	−	0.294439i	−0.0166074	−	0.00958826i
$944$		−	50.0085i		−	1.62764i
$945$	−18.0050	−	19.2843i	−0.585703	−	0.627319i
$946$	−7.30288	+	12.6490i	−0.237437	+	0.411253i
$947$			48.1442i			1.56448i	0.622980	+	0.782238i	$0.285922\pi$
$947$			48.1442i			1.56448i	−0.622980	+	0.782238i	$0.714078\pi$
$948$	10.7391	+	15.7163i	0.348788	+	0.510442i
$949$	−4.51467	+	7.78519i	−0.146552	+	0.252718i
$950$	13.1071	−	22.7022i	0.425252	−	0.736558i
$951$	−43.0739	+	29.4327i	−1.39677	+	0.954420i
$952$	150.282			4.87068
$953$	−14.5624	−	25.2228i	−0.471721	−	0.817045i	0.527755	−	0.849396i	$-0.323034\pi$
$953$	−14.5624	−	25.2228i	−0.471721	−	0.817045i	−0.999477	+	0.0323512i	$0.989700\pi$
$954$	14.3516	+	93.8966i	0.464649	+	3.04002i
$955$	2.59440	−	1.49788i	0.0839528	−	0.0484702i
$956$	−46.4421	−	26.8134i	−1.50205	−	0.867206i
$957$	0.192422	+	2.53250i	0.00622012	+	0.0818641i
$958$	82.3527			2.66070
$959$	4.01999	+	6.96282i	0.129812	+	0.224841i
$960$	−10.5045	−	5.04531i	−0.339031	−	0.162837i
$961$	−6.76147	−	11.7112i	−0.218112	−	0.377781i
$962$	−70.7369	+	40.6597i	−2.28065	+	1.31092i
$963$	−6.08208	+	15.5917i	−0.195992	+	0.502437i
$964$	82.2448	+	47.4841i	2.64893	+	1.52936i
$965$	4.17927			0.134536
$966$	5.83024	−	0.442987i	0.187585	−	0.0142529i
$967$	36.5969	+	21.1292i	1.17688	+	0.679469i	0.955290	−	0.295671i	$-0.0955433\pi$
$967$	36.5969	+	21.1292i	1.17688	+	0.679469i	0.221586	+	0.975141i	$0.428877\pi$
$968$			75.5483i			2.42821i
$969$	−29.2520	−	14.0497i	−0.939710	−	0.451342i
$970$	−2.60130	+	1.50186i	−0.0835226	+	0.0482218i
$971$	−13.7985	−	23.8997i	−0.442816	−	0.766979i	0.555082	−	0.831796i	$-0.312687\pi$
$971$	−13.7985	−	23.8997i	−0.442816	−	0.766979i	−0.997897	+	0.0648168i	$0.979354\pi$
$972$	−68.2054	+	27.1770i	−2.18769	+	0.871702i
$973$	29.4919	+	17.0272i	0.945468	+	0.545866i
$974$	1.65840	+	2.87243i	0.0531384	+	0.0920385i
$975$	−1.43970	−	19.4405i	−0.0461074	−	0.622595i
$976$	10.3173	−	17.8701i	0.330248	−	0.572006i
$977$	−34.5310	+	19.9365i	−1.10475	+	0.637825i	−0.937463	−	0.348084i	$-0.886832\pi$
$977$	−34.5310	+	19.9365i	−1.10475	+	0.637825i	−0.167282	+	0.985909i	$0.553499\pi$
$978$	0.319836	+	0.468071i	0.0102272	+	0.0149673i
$979$	−3.94339	+	6.83015i	−0.126031	+	0.218293i
$980$		−	43.4046i		−	1.38651i
$981$	−0.443182	−	2.89957i	−0.0141497	−	0.0925760i
$982$	48.5996	−	28.0590i	1.55087	−	0.895398i
$983$	−7.38449	+	4.26344i	−0.235529	+	0.135983i	−0.613120	−	0.789990i	$-0.710086\pi$
$983$	−7.38449	+	4.26344i	−0.235529	+	0.135983i	0.377591	+	0.925972i	$0.376752\pi$
$984$	11.4825	+	16.8044i	0.366049	+	0.535703i
$985$	7.00021	+	12.1247i	0.223045	+	0.386326i
$986$	38.9972	−	22.5150i	1.24192	−	0.717024i
$987$	−24.1304	+	1.83345i	−0.768078	+	0.0583593i
$988$	55.0555	+	0.105344i	1.75155	+	0.00335143i
$989$	4.06908			0.129389
$990$	4.83701	+	1.88684i	0.153730	+	0.0599676i
$991$	26.2767	−	45.5127i	0.834708	−	1.44576i	−0.0595594	−	0.998225i	$-0.518970\pi$
$991$	26.2767	−	45.5127i	0.834708	−	1.44576i	0.894268	−	0.447532i	$-0.147697\pi$
$992$	−18.1047	+	31.3582i	−0.574824	+	0.995624i
$993$	14.7971	+	7.10704i	0.469571	+	0.225535i
$994$			10.4174i			0.330419i
$995$		−	9.37068i		−	0.297071i
$996$	17.1073	−	11.6895i	0.542065	−	0.370396i
$997$	2.25570	−	3.90698i	0.0714387	−	0.123735i	−0.828093	−	0.560590i	$-0.810574\pi$
$997$	2.25570	−	3.90698i	0.0714387	−	0.123735i	0.899532	+	0.436855i	$0.143908\pi$
$998$	−12.3853	+	21.4519i	−0.392049	+	0.679049i
$999$	−43.4176	−	13.2450i	−1.37367	−	0.419053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.4.1	✓	22
3.2	odd	2		351.2.l.b.199.11		22
9.2	odd	6		351.2.r.b.316.11		22
9.7	even	3		117.2.r.b.43.1	yes	22
13.10	even	6		117.2.r.b.49.1	yes	22
39.23	odd	6		351.2.r.b.10.11		22
117.88	even	6	inner	117.2.l.b.88.11	yes	22
117.101	odd	6		351.2.l.b.127.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.1	✓	22	1.1	even	1	trivial
117.2.l.b.88.11	yes	22	117.88	even	6	inner
117.2.r.b.43.1	yes	22	9.7	even	3
117.2.r.b.49.1	yes	22	13.10	even	6
351.2.l.b.127.1		22	117.101	odd	6
351.2.l.b.199.11		22	3.2	odd	2
351.2.r.b.10.11		22	39.23	odd	6
351.2.r.b.316.11		22	9.2	odd	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.59035i q^{2} +(1.72707 - 0.131225i) q^{3} -4.70993 q^{4} +(1.18696 + 0.685292i) q^{5} +(-0.339918 - 4.47373i) q^{6} +(-3.20825 - 1.85228i) q^{7} +7.01967i q^{8} +(2.96556 - 0.453269i) q^{9} +(1.77515 - 3.07465i) q^{10} +0.487471i q^{11} +(-8.13439 + 0.618059i) q^{12} +(3.11904 + 1.80875i) q^{13} +(-4.79807 + 8.31050i) q^{14} +(2.13989 + 1.02779i) q^{15} +8.76356 q^{16} +(2.88951 + 5.00477i) q^{17} +(-1.17413 - 7.68185i) q^{18} +(-2.80767 + 1.62101i) q^{19} +(-5.59049 - 3.22767i) q^{20} +(-5.78395 - 2.77803i) q^{21} +1.26272 q^{22} +(-0.175893 - 0.304656i) q^{23} +(0.921153 + 12.1235i) q^{24} +(-1.56075 - 2.70330i) q^{25} +(4.68529 - 8.07942i) q^{26} +(5.06226 - 1.17198i) q^{27} +(15.1106 + 8.72412i) q^{28} +3.00808 q^{29} +(2.66234 - 5.54308i) q^{30} +(-3.62047 - 2.09028i) q^{31} -8.66137i q^{32} +(0.0639682 + 0.841898i) q^{33} +(12.9641 - 7.48484i) q^{34} +(-2.53871 - 4.39718i) q^{35} +(-13.9676 + 2.13486i) q^{36} +(-7.56549 - 4.36794i) q^{37} +(4.19899 + 7.27286i) q^{38} +(5.62417 + 2.71454i) q^{39} +(-4.81052 + 8.33206i) q^{40} +(1.44970 - 0.836982i) q^{41} +(-7.19607 + 14.9825i) q^{42} +(-5.78344 + 10.0172i) q^{43} -2.29595i q^{44} +(3.83062 + 1.49426i) q^{45} +(-0.789167 + 0.455626i) q^{46} +(3.26623 - 1.88576i) q^{47} +(15.1353 - 1.14999i) q^{48} +(3.36191 + 5.82301i) q^{49} +(-7.00250 + 4.04289i) q^{50} +(5.64714 + 8.26443i) q^{51} +(-14.6905 - 8.51907i) q^{52} -12.2232 q^{53} +(-3.03585 - 13.1130i) q^{54} +(-0.334060 + 0.578609i) q^{55} +(13.0024 - 22.5208i) q^{56} +(-4.63633 + 3.16804i) q^{57} -7.79200i q^{58} -5.70642i q^{59} +(-10.0787 - 4.84082i) q^{60} +(1.17729 - 2.03913i) q^{61} +(-5.41456 + 9.37829i) q^{62} +(-10.3538 - 4.03886i) q^{63} -4.90889 q^{64} +(2.46266 + 4.28437i) q^{65} +(2.18081 - 0.165700i) q^{66} +(0.0679883 - 0.0392530i) q^{67} +(-13.6094 - 23.5721i) q^{68} +(-0.343759 - 0.503082i) q^{69} +(-11.3902 + 6.57615i) q^{70} +(0.940139 - 0.542789i) q^{71} +(3.18180 + 20.8172i) q^{72} +2.49602i q^{73} +(-11.3145 + 19.5973i) q^{74} +(-3.05027 - 4.46399i) q^{75} +(13.2239 - 7.63484i) q^{76} +(0.902935 - 1.56393i) q^{77} +(7.03162 - 14.5686i) q^{78} +(-1.16667 - 2.02073i) q^{79} +(10.4020 + 6.00559i) q^{80} +(8.58909 - 2.68839i) q^{81} +(-2.16808 - 3.75522i) q^{82} +(-2.19957 + 1.26992i) q^{83} +(27.2420 + 13.0843i) q^{84} +7.92062i q^{85} +(25.9481 + 14.9812i) q^{86} +(5.19518 - 0.394735i) q^{87} -3.42189 q^{88} +(14.0114 + 8.08948i) q^{89} +(3.87066 - 9.92266i) q^{90} +(-6.65636 - 11.5803i) q^{91} +(0.828445 + 1.43491i) q^{92} +(-6.52711 - 3.13497i) q^{93} +(-4.88478 - 8.46068i) q^{94} -4.44346 q^{95} +(-1.13659 - 14.9588i) q^{96} +(-0.732699 - 0.423024i) q^{97} +(15.0836 - 8.70854i) q^{98} +(0.220956 + 1.44563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

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