LMFDB - Embedded newform 93.2.f.a.64.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [93,2,Mod(4,93)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("93.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(93, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	93.64
Dual form			93.2.f.a.16.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.169131 - 0.122881i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.604528 - 1.86055i) q^{4} +0.338261 q^{5} -0.209057 q^{6} +(-0.222562 - 0.684977i) q^{7} +(-0.255585 + 0.786610i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.0572103 - 0.0415657i) q^{10} +(1.39169 + 4.28319i) q^{11} +(-1.58268 - 1.14988i) q^{12} +(1.96086 - 1.42465i) q^{13} +(-0.0465282 + 0.143199i) q^{14} +(0.273659 - 0.198825i) q^{15} +(-3.02547 + 2.19813i) q^{16} +(-1.09618 + 3.37370i) q^{17} +(-0.169131 + 0.122881i) q^{18} +(0.226341 + 0.164446i) q^{19} +(-0.204489 - 0.629351i) q^{20} +(-0.582676 - 0.423339i) q^{21} +(0.290943 - 0.895431i) q^{22} +(-0.777438 + 2.39271i) q^{23} +(0.255585 + 0.786610i) q^{24} -4.88558 q^{25} -0.506704 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.13989 + 0.828176i) q^{28} +(-3.71878 - 2.70185i) q^{29} -0.0707158 q^{30} +(3.64679 + 4.20725i) q^{31} +2.43599 q^{32} +(3.64350 + 2.64716i) q^{33} +(0.599960 - 0.435897i) q^{34} +(-0.0752842 - 0.231701i) q^{35} -1.95630 q^{36} +6.73054 q^{37} +(-0.0180739 - 0.0556258i) q^{38} +(0.748983 - 2.30513i) q^{39} +(-0.0864545 + 0.266080i) q^{40} +(-7.27349 - 5.28450i) q^{41} +(0.0465282 + 0.143199i) q^{42} +(-1.68641 - 1.22525i) q^{43} +(7.12776 - 5.17862i) q^{44} +(0.104528 - 0.321706i) q^{45} +(0.425506 - 0.309148i) q^{46} +(5.21549 - 3.78928i) q^{47} +(-1.15563 + 3.55665i) q^{48} +(5.24346 - 3.80960i) q^{49} +(0.826301 + 0.600343i) q^{50} +(1.09618 + 3.37370i) q^{51} +(-3.83603 - 2.78704i) q^{52} +(3.59444 - 11.0625i) q^{53} +(-0.0646021 + 0.198825i) q^{54} +(0.470756 + 1.44884i) q^{55} +0.595693 q^{56} +0.279773 q^{57} +(0.296955 + 0.913933i) q^{58} +(-5.00234 + 3.63441i) q^{59} +(-0.535358 - 0.388960i) q^{60} -7.32624 q^{61} +(-0.0997949 - 1.15969i) q^{62} -0.720227 q^{63} +(5.63893 + 4.09692i) q^{64} +(0.663284 - 0.481904i) q^{65} +(-0.290943 - 0.895431i) q^{66} -6.47214 q^{67} +6.93960 q^{68} +(0.777438 + 2.39271i) q^{69} +(-0.0157387 + 0.0484387i) q^{70} +(-3.08639 + 9.49894i) q^{71} +(0.669131 + 0.486152i) q^{72} +(2.11143 + 6.49832i) q^{73} +(-1.13834 - 0.827053i) q^{74} +(-3.95252 + 2.87167i) q^{75} +(0.169131 - 0.520530i) q^{76} +(2.62415 - 1.90655i) q^{77} +(-0.409932 + 0.297833i) q^{78} +(-1.85886 + 5.72097i) q^{79} +(-1.02340 + 0.743542i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.580808 + 1.78754i) q^{82} +(-8.47670 - 6.15869i) q^{83} +(-0.435398 + 1.34002i) q^{84} +(-0.370796 + 1.14119i) q^{85} +(0.134665 + 0.414455i) q^{86} -4.59667 q^{87} -3.72490 q^{88} +(-1.86761 - 5.74790i) q^{89} +(-0.0572103 + 0.0415657i) q^{90} +(-1.41227 - 1.02607i) q^{91} +4.92173 q^{92} +(5.42327 + 1.26020i) q^{93} -1.34773 q^{94} +(0.0765624 + 0.0556258i) q^{95} +(1.97076 - 1.43184i) q^{96} +(-5.16565 - 15.8982i) q^{97} -1.35495 q^{98} +4.50361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9} - 11 q^{10} - 4 q^{11} - 2 q^{12} - 3 q^{13} - 6 q^{14} - 4 q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9 - 11 * q^10 - 4 * q^11 - 2 * q^12 - 3 * q^13 - 6 * q^14 - 4 * q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 + q^20 + 6 * q^21 + 6 * q^22 - 17 * q^23 + 4 * q^24 - 18 * q^25 + 12 * q^26 + 2 * q^27 - 9 * q^28 - 2 * q^29 - 4 * q^30 + 17 * q^31 - q^33 + 4 * q^34 - 3 * q^35 + 2 * q^36 + 8 * q^37 + 8 * q^38 + 3 * q^39 - 7 * q^40 - 5 * q^41 + 6 * q^42 - 19 * q^43 + 24 * q^44 - q^45 - 17 * q^46 - 4 * q^47 - 12 * q^48 + 11 * q^49 + 12 * q^50 - 9 * q^51 - 12 * q^52 + 2 * q^54 + 8 * q^55 - 12 * q^56 + 2 * q^57 + 33 * q^58 - 29 * q^59 - 6 * q^60 + 4 * q^61 + 47 * q^62 - 6 * q^63 + 16 * q^64 + 21 * q^65 - 6 * q^66 - 16 * q^67 + 6 * q^68 + 17 * q^69 - 3 * q^70 + 37 * q^71 + q^72 + 3 * q^73 - 2 * q^74 + 3 * q^75 - 3 * q^76 + 18 * q^77 - 27 * q^78 - 3 * q^79 - 24 * q^80 - 2 * q^81 + 35 * q^82 - 31 * q^83 - 6 * q^84 - 8 * q^85 - 44 * q^86 - 18 * q^87 - 8 * q^88 + 19 * q^89 - 11 * q^90 - 24 * q^91 + 2 * q^92 + 13 * q^93 - 94 * q^94 - 16 * q^95 + 20 * q^96 - 3 * q^97 - 34 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.169131	−	0.122881i	−0.119593	−	0.0868897i	0.526381	−	0.850249i	$-0.323549\pi$
$2$	−0.169131	−	0.122881i	−0.119593	−	0.0868897i	−0.645974	+	0.763359i	$0.723549\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.604528	−	1.86055i	−0.302264	−	0.930274i
$5$	0.338261			0.151275			0.0756375	−	0.997135i	$-0.475901\pi$
$5$	0.338261			0.151275			0.0756375	+	0.997135i	$0.475901\pi$
$6$	−0.209057			−0.0853471
$7$	−0.222562	−	0.684977i	−0.0841207	−	0.258897i	0.900145	−	0.435590i	$-0.143460\pi$
$7$	−0.222562	−	0.684977i	−0.0841207	−	0.258897i	−0.984266	+	0.176693i	$0.943460\pi$
$8$	−0.255585	+	0.786610i	−0.0903630	+	0.278109i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.0572103	−	0.0415657i	−0.0180915	−	0.0131442i
$11$	1.39169	+	4.28319i	0.419611	+	1.29143i	0.908061	+	0.418838i	$0.137563\pi$
$11$	1.39169	+	4.28319i	0.419611	+	1.29143i	−0.488450	+	0.872592i	$0.662437\pi$
$12$	−1.58268	−	1.14988i	−0.456879	−	0.331942i
$13$	1.96086	−	1.42465i	0.543846	−	0.395127i	−0.281666	−	0.959513i	$-0.590887\pi$
$13$	1.96086	−	1.42465i	0.543846	−	0.395127i	0.825511	+	0.564386i	$0.190887\pi$
$14$	−0.0465282	+	0.143199i	−0.0124352	+	0.0382716i
$15$	0.273659	−	0.198825i	0.0706585	−	0.0513364i
$16$	−3.02547	+	2.19813i	−0.756366	+	0.549532i
$17$	−1.09618	+	3.37370i	−0.265863	+	0.818242i	0.725630	+	0.688085i	$0.241548\pi$
$17$	−1.09618	+	3.37370i	−0.265863	+	0.818242i	−0.991493	+	0.130158i	$0.958452\pi$
$18$	−0.169131	+	0.122881i	−0.0398645	+	0.0289632i
$19$	0.226341	+	0.164446i	0.0519262	+	0.0377266i	0.613446	−	0.789737i	$-0.289783\pi$
$19$	0.226341	+	0.164446i	0.0519262	+	0.0377266i	−0.561519	+	0.827464i	$0.689783\pi$
$20$	−0.204489	−	0.629351i	−0.0457250	−	0.140727i
$21$	−0.582676	−	0.423339i	−0.127150	−	0.0923801i
$22$	0.290943	−	0.895431i	0.0620293	−	0.190906i
$23$	−0.777438	+	2.39271i	−0.162107	+	0.498914i	−0.998811	−	0.0487407i	$-0.984479\pi$
$23$	−0.777438	+	2.39271i	−0.162107	+	0.498914i	0.836705	+	0.547655i	$0.184479\pi$
$24$	0.255585	+	0.786610i	0.0521711	+	0.160566i
$25$	−4.88558			−0.977116
$26$	−0.506704			−0.0993728
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−1.13989	+	0.828176i	−0.215418	+	0.156511i
$29$	−3.71878	−	2.70185i	−0.690561	−	0.501722i	0.186284	−	0.982496i	$-0.440356\pi$
$29$	−3.71878	−	2.70185i	−0.690561	−	0.501722i	−0.876844	+	0.480774i	$0.840356\pi$
$30$	−0.0707158			−0.0129109
$31$	3.64679	+	4.20725i	0.654983	+	0.755644i
$31$	3.64679	+	4.20725i	0.654983	+	0.755644i
$32$	2.43599			0.430626
$33$	3.64350	+	2.64716i	0.634252	+	0.460811i
$34$	0.599960	−	0.435897i	0.102892	−	0.0747556i
$35$	−0.0752842	−	0.231701i	−0.0127254	−	0.0391646i
$36$	−1.95630			−0.326049
$37$	6.73054			1.10649			0.553247	−	0.833017i	$-0.313388\pi$
$37$	6.73054			1.10649			0.553247	+	0.833017i	$0.313388\pi$
$38$	−0.0180739	−	0.0556258i	−0.00293198	−	0.00902370i
$39$	0.748983	−	2.30513i	0.119933	−	0.369117i
$40$	−0.0864545	+	0.266080i	−0.0136697	+	0.0420709i
$41$	−7.27349	−	5.28450i	−1.13593	−	0.825301i	−0.149382	−	0.988780i	$-0.547728\pi$
$41$	−7.27349	−	5.28450i	−1.13593	−	0.825301i	−0.986547	+	0.163479i	$0.947728\pi$
$42$	0.0465282	+	0.143199i	0.00717946	+	0.0220961i
$43$	−1.68641	−	1.22525i	−0.257176	−	0.186849i	0.451725	−	0.892157i	$-0.350809\pi$
$43$	−1.68641	−	1.22525i	−0.257176	−	0.186849i	−0.708901	+	0.705308i	$0.750809\pi$
$44$	7.12776	−	5.17862i	1.07455	−	0.780707i
$45$	0.104528	−	0.321706i	0.0155822	−	0.0479570i
$46$	0.425506	−	0.309148i	0.0627374	−	0.0455814i
$47$	5.21549	−	3.78928i	0.760758	−	0.552723i	−0.138385	−	0.990379i	$-0.544191\pi$
$47$	5.21549	−	3.78928i	0.760758	−	0.552723i	0.899143	+	0.437656i	$0.144191\pi$
$48$	−1.15563	+	3.55665i	−0.166800	+	0.513358i
$49$	5.24346	−	3.80960i	0.749066	−	0.544228i
$50$	0.826301	+	0.600343i	0.116857	+	0.0849013i
$51$	1.09618	+	3.37370i	0.153496	+	0.472412i
$52$	−3.83603	−	2.78704i	−0.531961	−	0.386493i
$53$	3.59444	−	11.0625i	0.493734	−	1.51956i	−0.325187	−	0.945650i	$-0.605427\pi$
$53$	3.59444	−	11.0625i	0.493734	−	1.51956i	0.818921	−	0.573907i	$-0.194573\pi$
$54$	−0.0646021	+	0.198825i	−0.00879124	+	0.0270566i
$55$	0.470756	+	1.44884i	0.0634767	+	0.195361i
$56$	0.595693			0.0796029
$57$	0.279773			0.0370568
$58$	0.296955	+	0.913933i	0.0389921	+	0.120005i
$59$	−5.00234	+	3.63441i	−0.651249	+	0.473160i	−0.863696	−	0.504013i	$-0.831856\pi$
$59$	−5.00234	+	3.63441i	−0.651249	+	0.473160i	0.212448	+	0.977172i	$0.431856\pi$
$60$	−0.535358	−	0.388960i	−0.0691144	−	0.0502146i
$61$	−7.32624			−0.938029			−0.469014	−	0.883191i	$-0.655391\pi$
$61$	−7.32624			−0.938029			−0.469014	+	0.883191i	$0.655391\pi$
$62$	−0.0997949	−	1.15969i	−0.0126740	−	0.147281i
$63$	−0.720227			−0.0907401
$64$	5.63893	+	4.09692i	0.704866	+	0.512115i
$65$	0.663284	−	0.481904i	0.0822703	−	0.0597728i
$66$	−0.290943	−	0.895431i	−0.0358126	−	0.110220i
$67$	−6.47214			−0.790697			−0.395349	−	0.918531i	$-0.629376\pi$
$67$	−6.47214			−0.790697			−0.395349	+	0.918531i	$0.629376\pi$
$68$	6.93960			0.841550
$69$	0.777438	+	2.39271i	0.0935925	+	0.288048i
$70$	−0.0157387	+	0.0484387i	−0.00188113	+	0.00578953i
$71$	−3.08639	+	9.49894i	−0.366287	+	1.12732i	0.582884	+	0.812556i	$0.301924\pi$
$71$	−3.08639	+	9.49894i	−0.366287	+	1.12732i	−0.949171	+	0.314761i	$0.898076\pi$
$72$	0.669131	+	0.486152i	0.0788578	+	0.0572935i
$73$	2.11143	+	6.49832i	0.247124	+	0.760571i	0.995280	+	0.0970472i	$0.0309398\pi$
$73$	2.11143	+	6.49832i	0.247124	+	0.760571i	−0.748155	+	0.663524i	$0.769060\pi$
$74$	−1.13834	−	0.827053i	−0.132329	−	0.0961430i
$75$	−3.95252	+	2.87167i	−0.456397	+	0.331592i
$76$	0.169131	−	0.520530i	0.0194006	−	0.0597089i
$77$	2.62415	−	1.90655i	0.299049	−	0.217272i
$78$	−0.409932	+	0.297833i	−0.0464157	+	0.0337230i
$79$	−1.85886	+	5.72097i	−0.209138	+	0.643660i	0.790380	+	0.612616i	$0.209883\pi$
$79$	−1.85886	+	5.72097i	−0.209138	+	0.643660i	−0.999518	+	0.0310433i	$0.990117\pi$
$80$	−1.02340	+	0.743542i	−0.114419	+	0.0831305i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.580808	+	1.78754i	0.0641395	+	0.197401i
$83$	−8.47670	−	6.15869i	−0.930439	−	0.676004i	0.0156611	−	0.999877i	$-0.495015\pi$
$83$	−8.47670	−	6.15869i	−0.930439	−	0.676004i	−0.946100	+	0.323874i	$0.895015\pi$
$84$	−0.435398	+	1.34002i	−0.0475058	+	0.146208i
$85$	−0.370796	+	1.14119i	−0.0402184	+	0.123780i
$86$	0.134665	+	0.414455i	0.0145213	+	0.0446919i
$87$	−4.59667			−0.492815
$88$	−3.72490			−0.397075
$89$	−1.86761	−	5.74790i	−0.197966	−	0.609277i	−0.999929	−	0.0119032i	$-0.996211\pi$
$89$	−1.86761	−	5.74790i	−0.197966	−	0.609277i	0.801963	−	0.597373i	$-0.203789\pi$
$90$	−0.0572103	+	0.0415657i	−0.00603050	+	0.00438141i
$91$	−1.41227	−	1.02607i	−0.148046	−	0.107562i
$92$	4.92173			0.513126
$93$	5.42327	+	1.26020i	0.562367	+	0.130677i
$94$	−1.34773			−0.139008
$95$	0.0765624	+	0.0556258i	0.00785513	+	0.00570709i
$96$	1.97076	−	1.43184i	0.201139	−	0.146136i
$97$	−5.16565	−	15.8982i	−0.524493	−	1.61422i	−0.765317	−	0.643654i	$-0.777418\pi$
$97$	−5.16565	−	15.8982i	−0.524493	−	1.61422i	0.240824	−	0.970569i	$-0.422582\pi$
$98$	−1.35495			−0.136871
$99$	4.50361			0.452630
$100$	2.95347	+	9.08985i	0.295347	+	0.908985i
$101$	−5.69147	+	17.5165i	−0.566323	+	1.74296i	0.0976664	+	0.995219i	$0.468862\pi$
$101$	−5.69147	+	17.5165i	−0.566323	+	1.74296i	−0.663989	+	0.747742i	$0.731138\pi$
$102$	0.229164	−	0.705295i	0.0226907	−	0.0698346i
$103$	4.75999	+	3.45833i	0.469016	+	0.340760i	0.797058	−	0.603903i	$-0.206389\pi$
$103$	4.75999	+	3.45833i	0.469016	+	0.340760i	−0.328042	+	0.944663i	$0.606389\pi$
$104$	0.619477	+	1.90655i	0.0607447	+	0.186953i
$105$	−0.197097	−	0.143199i	−0.0192347	−	0.0139748i
$106$	−1.96730	+	1.42933i	−0.191081	+	0.138829i
$107$	−2.32853	+	7.16649i	−0.225108	+	0.692811i	0.773173	+	0.634195i	$0.218669\pi$
$107$	−2.32853	+	7.16649i	−0.225108	+	0.692811i	−0.998281	+	0.0586154i	$0.981331\pi$
$108$	−1.58268	+	1.14988i	−0.152293	+	0.110647i
$109$	5.98203	−	4.34620i	0.572974	−	0.416290i	−0.263210	−	0.964739i	$-0.584781\pi$
$109$	5.98203	−	4.34620i	0.572974	−	0.416290i	0.836184	+	0.548448i	$0.184781\pi$
$110$	0.0984148	−	0.302889i	0.00938348	−	0.0288794i
$111$	5.44512	−	3.95611i	0.516828	−	0.375498i
$112$	2.17902	+	1.58315i	0.205898	+	0.149594i
$113$	−5.73133	−	17.6392i	−0.539159	−	1.65936i	−0.734488	−	0.678622i	$-0.762578\pi$
$113$	−5.73133	−	17.6392i	−0.539159	−	1.65936i	0.195329	−	0.980738i	$-0.437422\pi$
$114$	−0.0473181	−	0.0343786i	−0.00443175	−	0.00321985i
$115$	−0.262977	+	0.809360i	−0.0245227	+	0.0754732i
$116$	−2.77882	+	8.55232i	−0.258007	+	0.794063i
$117$	−0.748983	−	2.30513i	−0.0692435	−	0.213110i
$118$	1.29265			0.118998
$119$	2.55488			0.234205
$120$	0.0864545	+	0.266080i	0.00789218	+	0.0242896i
$121$	−7.50973	+	5.45614i	−0.682702	+	0.496012i
$122$	1.23909	+	0.900252i	0.112182	+	0.0815050i
$123$	−8.99053			−0.810649
$124$	5.62319	−	9.32843i	0.504978	−	0.837717i
$125$	−3.34391			−0.299088
$126$	0.121812	+	0.0885019i	0.0108519	+	0.00788438i
$127$	14.5411	−	10.5648i	1.29032	−	0.937471i	0.290506	−	0.956873i	$-0.406176\pi$
$127$	14.5411	−	10.5648i	1.29032	−	0.937471i	0.999812	+	0.0194026i	$0.00617641\pi$
$128$	−1.95581	−	6.01936i	−0.172871	−	0.532041i
$129$	−2.08452			−0.183532
$130$	−0.171398			−0.0150326
$131$	5.70120	+	17.5465i	0.498116	+	1.53304i	0.812044	+	0.583597i	$0.198355\pi$
$131$	5.70120	+	17.5465i	0.498116	+	1.53304i	−0.313928	+	0.949447i	$0.601645\pi$
$132$	2.72256	−	8.37919i	0.236969	−	0.729314i
$133$	0.0622669	−	0.191638i	0.00539923	−	0.0166171i
$134$	1.09464	+	0.795300i	0.0945622	+	0.0687034i
$135$	−0.104528	−	0.321706i	−0.00899638	−	0.0276880i
$136$	−2.37362	−	1.72454i	−0.203536	−	0.147878i
$137$	14.1658	−	10.2920i	1.21026	−	0.879308i	0.215009	−	0.976612i	$-0.431022\pi$
$137$	14.1658	−	10.2920i	1.21026	−	0.879308i	0.995255	+	0.0973037i	$0.0310218\pi$
$138$	0.162529	−	0.500212i	0.0138354	−	0.0425809i
$139$	−5.95836	+	4.32900i	−0.505382	+	0.367181i	−0.811069	−	0.584951i	$-0.801114\pi$
$139$	−5.95836	+	4.32900i	−0.505382	+	0.367181i	0.305687	+	0.952132i	$0.401114\pi$
$140$	−0.385579	+	0.280140i	−0.0325874	+	0.0236761i
$141$	1.99214	−	6.13118i	0.167769	−	0.516339i
$142$	1.68924	−	1.22730i	0.141758	−	0.102993i
$143$	8.83097	+	6.41608i	0.738483	+	0.536539i
$144$	1.15563	+	3.55665i	0.0963021	+	0.296387i
$145$	−1.25792	−	0.913933i	−0.104465	−	0.0758980i
$146$	0.441410	−	1.35852i	0.0365313	−	0.112432i
$147$	2.00282	−	6.16406i	0.165190	−	0.508403i
$148$	−4.06881	−	12.5225i	−0.334454	−	1.02934i
$149$	−1.55606			−0.127477			−0.0637385	−	0.997967i	$-0.520302\pi$
$149$	−1.55606			−0.127477			−0.0637385	+	0.997967i	$0.520302\pi$
$150$	1.02136			0.0833940
$151$	−5.44785	−	16.7667i	−0.443339	−	1.36446i	−0.884295	−	0.466929i	$-0.845360\pi$
$151$	−5.44785	−	16.7667i	−0.443339	−	1.36446i	0.440955	−	0.897529i	$-0.354640\pi$
$152$	−0.187205	+	0.136012i	−0.0151843	+	0.0110320i
$153$	2.86984	+	2.08506i	0.232013	+	0.168567i
$154$	−0.678102			−0.0546430
$155$	1.23357	+	1.42315i	0.0990825	+	0.114310i
$156$	−4.74159			−0.379631
$157$	7.70081	+	5.59497i	0.614592	+	0.446527i	0.851028	−	0.525120i	$-0.175980\pi$
$157$	7.70081	+	5.59497i	0.614592	+	0.446527i	−0.236437	+	0.971647i	$0.575980\pi$
$158$	1.01739	−	0.739174i	0.0809389	−	0.0588055i
$159$	−3.59444	−	11.0625i	−0.285057	−	0.877316i
$160$	0.824000			0.0651429
$161$	1.81198			0.142804
$162$	0.0646021	+	0.198825i	0.00507562	+	0.0156212i
$163$	1.59949	−	4.92273i	0.125282	−	0.385578i	−0.868670	−	0.495391i	$-0.835025\pi$
$163$	1.59949	−	4.92273i	0.125282	−	0.385578i	0.993952	+	0.109812i	$0.0350250\pi$
$164$	−5.43503	+	16.7273i	−0.424405	+	1.30618i
$165$	1.23245	+	0.895431i	0.0959465	+	0.0697092i
$166$	0.676887	+	2.08324i	0.0525366	+	0.161691i
$167$	18.1132	+	13.1600i	1.40164	+	1.01835i	0.994472	+	0.105003i	$0.0334852\pi$
$167$	18.1132	+	13.1600i	1.40164	+	1.01835i	0.407172	+	0.913351i	$0.366515\pi$
$168$	0.481926	−	0.350140i	0.0371814	−	0.0270139i
$169$	−2.20186	+	6.77664i	−0.169374	+	0.521280i
$170$	0.202943	−	0.147447i	0.0155650	−	0.0113087i
$171$	0.226341	−	0.164446i	0.0173087	−	0.0125755i
$172$	−1.26015	+	3.87835i	−0.0960858	+	0.295722i
$173$	−7.39202	+	5.37061i	−0.562005	+	0.408320i	−0.832192	−	0.554488i	$-0.812914\pi$
$173$	−7.39202	+	5.37061i	−0.562005	+	0.408320i	0.270187	+	0.962808i	$0.412914\pi$
$174$	0.777438	+	0.564841i	0.0589374	+	0.0428205i
$175$	1.08735	+	3.34651i	0.0821957	+	0.252972i
$176$	−13.6255	−	9.89953i	−1.02706	−	0.746205i
$177$	−1.91072	+	5.88060i	−0.143619	+	0.442013i
$178$	−0.390436	+	1.20164i	−0.0292644	+	0.0900667i
$179$	0.0778059	+	0.239462i	0.00581549	+	0.0178982i	0.953922	−	0.300054i	$-0.0970048\pi$
$179$	0.0778059	+	0.239462i	0.00581549	+	0.0178982i	−0.948107	+	0.317952i	$0.897005\pi$
$180$	−0.661739			−0.0493231
$181$	15.5043			1.15242			0.576211	−	0.817301i	$-0.304531\pi$
$181$	15.5043			1.15242			0.576211	+	0.817301i	$0.304531\pi$
$182$	0.112773	+	0.347080i	0.00835931	+	0.0257273i
$183$	−5.92705	+	4.30625i	−0.438140	+	0.318328i
$184$	−1.68343	−	1.22308i	−0.124104	−	0.0901667i
$185$	2.27668			0.167385
$186$	−0.762387	−	0.879554i	−0.0559009	−	0.0644920i
$187$	−15.9757			−1.16826
$188$	−10.2030	−	7.41295i	−0.744134	−	0.540645i
$189$	−0.582676	+	0.423339i	−0.0423834	+	0.0307934i
$190$	−0.00611371	−	0.0188161i	−0.000443535	−	0.00136506i
$191$	−7.57722			−0.548268			−0.274134	−	0.961691i	$-0.588391\pi$
$191$	−7.57722			−0.548268			−0.274134	+	0.961691i	$0.588391\pi$
$192$	6.97010			0.503024
$193$	6.35574	+	19.5610i	0.457497	+	1.40803i	0.868179	+	0.496251i	$0.165290\pi$
$193$	6.35574	+	19.5610i	0.457497	+	1.40803i	−0.410683	+	0.911778i	$0.634710\pi$
$194$	−1.07992	+	3.32364i	−0.0775334	+	0.238623i
$195$	0.253352	−	0.779737i	0.0181429	−	0.0558381i
$196$	−10.2578	−	7.45270i	−0.732697	−	0.532335i
$197$	−1.71556	−	5.27994i	−0.122228	−	0.376180i	0.871158	−	0.491004i	$-0.163370\pi$
$197$	−1.71556	−	5.27994i	−0.122228	−	0.376180i	−0.993386	+	0.114823i	$0.963370\pi$
$198$	−0.761699	−	0.553407i	−0.0541316	−	0.0393289i
$199$	−4.48203	+	3.25638i	−0.317723	+	0.230839i	−0.735203	−	0.677847i	$-0.762913\pi$
$199$	−4.48203	+	3.25638i	−0.317723	+	0.230839i	0.417481	+	0.908686i	$0.362913\pi$
$200$	1.24868	−	3.84305i	0.0882951	−	0.271744i
$201$	−5.23607	+	3.80423i	−0.369324	+	0.268329i
$202$	3.11505	−	2.26321i	0.219174	−	0.159239i
$203$	−1.02305	+	3.14861i	−0.0718038	+	0.220989i
$204$	5.61426	−	4.07900i	0.393077	−	0.285587i
$205$	−2.46034	−	1.78754i	−0.171838	−	0.124847i
$206$	−0.380098	−	1.16982i	−0.0264827	−	0.0815052i
$207$	2.03536	+	1.47877i	0.141467	+	0.102782i
$208$	−2.80096	+	8.62046i	−0.194212	+	0.597722i
$209$	−0.389358	+	1.19832i	−0.0269324	+	0.0828895i
$210$	0.0157387	+	0.0484387i	0.00108607	+	0.00334259i
$211$	−7.98391			−0.549635			−0.274818	−	0.961496i	$-0.588617\pi$
$211$	−7.98391			−0.549635			−0.274818	+	0.961496i	$0.588617\pi$
$212$	−22.7553			−1.56284
$213$	3.08639	+	9.49894i	0.211476	+	0.650856i
$214$	1.27445	−	0.925941i	0.0871195	−	0.0632961i
$215$	−0.570449	−	0.414455i	−0.0389043	−	0.0282656i
$216$	0.827091			0.0562764
$217$	2.07023	−	3.43434i	0.140536	−	0.233138i
$218$	−1.54581			−0.104695
$219$	5.52780	+	4.01618i	0.373534	+	0.271388i
$220$	2.41105	−	1.75173i	0.162553	−	0.118101i
$221$	2.65688	+	8.17704i	0.178721	+	0.550047i
$222$	−1.40707			−0.0944362
$223$	5.49988			0.368299			0.184149	−	0.982898i	$-0.441047\pi$
$223$	5.49988			0.368299			0.184149	+	0.982898i	$0.441047\pi$
$224$	−0.542159	−	1.66860i	−0.0362246	−	0.111488i
$225$	−1.50973	+	4.64646i	−0.100648	+	0.309764i
$226$	−1.19818	+	3.68760i	−0.0797014	+	0.245296i
$227$	1.23012	+	0.893734i	0.0816459	+	0.0593192i	0.627859	−	0.778327i	$-0.283931\pi$
$227$	1.23012	+	0.893734i	0.0816459	+	0.0593192i	−0.546214	+	0.837646i	$0.683931\pi$
$228$	−0.169131	−	0.520530i	−0.0112009	−	0.0344730i
$229$	−6.37878	−	4.63445i	−0.421522	−	0.306253i	0.356728	−	0.934208i	$-0.383892\pi$
$229$	−6.37878	−	4.63445i	−0.421522	−	0.306253i	−0.778250	+	0.627955i	$0.783892\pi$
$230$	0.143932	−	0.104573i	0.00949060	−	0.00689532i
$231$	1.00234	−	3.08487i	0.0659488	−	0.202970i
$232$	3.07577	−	2.23468i	0.201934	−	0.146714i
$233$	13.2225	−	9.60671i	0.866235	−	0.629356i	−0.0633392	−	0.997992i	$-0.520175\pi$
$233$	13.2225	−	9.60671i	0.866235	−	0.629356i	0.929574	+	0.368636i	$0.120175\pi$
$234$	−0.156580	+	0.481904i	−0.0102360	+	0.0315031i
$235$	1.76420	−	1.28177i	0.115084	−	0.0836132i
$236$	9.78604	+	7.10998i	0.637017	+	0.462820i
$237$	1.85886	+	5.72097i	0.120746	+	0.371617i
$238$	−0.432108	−	0.313945i	−0.0280094	−	0.0203500i
$239$	9.16302	−	28.2009i	0.592706	−	1.82416i	0.0268789	−	0.999639i	$-0.491443\pi$
$239$	9.16302	−	28.2009i	0.592706	−	1.82416i	0.565827	−	0.824524i	$-0.308557\pi$
$240$	−0.390903	+	1.20308i	−0.0252327	+	0.0776582i
$241$	7.13137	+	21.9481i	0.459372	+	1.41380i	0.865924	+	0.500175i	$0.166731\pi$
$241$	7.13137	+	21.9481i	0.459372	+	1.41380i	−0.406552	+	0.913628i	$0.633269\pi$
$242$	1.94058			0.124745
$243$	−1.00000			−0.0641500
$244$	4.42892	+	13.6308i	0.283533	+	0.872623i
$245$	1.77366	−	1.28864i	0.113315	−	0.0823281i
$246$	1.52057	+	1.10476i	0.0969483	+	0.0704370i
$247$	0.678102			0.0431466
$248$	−4.24153	+	1.79329i	−0.269337	+	0.113874i
$249$	−10.4778			−0.664003
$250$	0.565557	+	0.410901i	0.0357690	+	0.0259877i
$251$	12.5630	−	9.12755i	0.792969	−	0.576126i	−0.115874	−	0.993264i	$-0.536967\pi$
$251$	12.5630	−	9.12755i	0.792969	−	0.576126i	0.908843	+	0.417138i	$0.136967\pi$
$252$	0.435398	+	1.34002i	0.0274275	+	0.0844131i
$253$	−11.3304			−0.712335
$254$	−3.75756			−0.235770
$255$	0.370796	+	1.14119i	0.0232201	+	0.0714642i
$256$	3.89889	−	11.9995i	0.243680	−	0.749971i
$257$	−3.52041	+	10.8347i	−0.219597	+	0.675850i	0.779198	+	0.626778i	$0.215627\pi$
$257$	−3.52041	+	10.8347i	−0.219597	+	0.675850i	−0.998795	+	0.0490726i	$0.984373\pi$
$258$	0.352557	+	0.256147i	0.0219492	+	0.0159470i
$259$	−1.49797	−	4.61027i	−0.0930791	−	0.286468i
$260$	−1.29758	−	0.942747i	−0.0804725	−	0.0584667i
$261$	−3.71878	+	2.70185i	−0.230187	+	0.167241i
$262$	1.19187	−	3.66821i	0.0736343	−	0.226623i
$263$	21.7544	−	15.8055i	1.34143	−	0.974609i	0.342044	−	0.939684i	$-0.388881\pi$
$263$	21.7544	−	15.8055i	1.34143	−	0.974609i	0.999390	−	0.0349248i	$-0.0111192\pi$
$264$	−3.01351	+	2.18944i	−0.185468	+	0.134751i
$265$	1.21586	−	3.74203i	0.0746896	−	0.229871i
$266$	−0.0340798	+	0.0247604i	−0.00208957	+	0.00151816i
$267$	−4.88946	−	3.55240i	−0.299230	−	0.217403i
$268$	3.91259	+	12.0417i	0.238999	+	0.735565i
$269$	−9.33603	−	6.78302i	−0.569228	−	0.413568i	0.265597	−	0.964084i	$-0.414431\pi$
$269$	−9.33603	−	6.78302i	−0.569228	−	0.413568i	−0.834825	+	0.550516i	$0.814431\pi$
$270$	−0.0218524	+	0.0672548i	−0.00132989	+	0.00409299i
$271$	4.20004	−	12.9264i	0.255134	−	0.785223i	−0.738669	−	0.674069i	$-0.764545\pi$
$271$	4.20004	−	12.9264i	0.255134	−	0.785223i	0.993803	−	0.111154i	$-0.0354548\pi$
$272$	−4.09937	−	12.6166i	−0.248561	−	0.764991i
$273$	−1.74566			−0.105652
$274$	−3.66056			−0.221142
$275$	−6.79923	−	20.9259i	−0.410009	−	1.26188i
$276$	3.98176	−	2.89292i	0.239674	−	0.174133i
$277$	1.75414	+	1.27446i	0.105396	+	0.0765748i	0.639235	−	0.769011i	$-0.279251\pi$
$277$	1.75414	+	1.27446i	0.105396	+	0.0765748i	−0.533839	+	0.845586i	$0.679251\pi$
$278$	1.53969			0.0923446
$279$	5.12825	−	2.16819i	0.307020	−	0.129806i
$280$	0.201500			0.0120419
$281$	−7.92865	−	5.76050i	−0.472984	−	0.343643i	0.325619	−	0.945501i	$-0.394427\pi$
$281$	−7.92865	−	5.76050i	−0.472984	−	0.343643i	−0.798603	+	0.601858i	$0.794427\pi$
$282$	−1.09034	+	0.792175i	−0.0649285	+	0.0471733i
$283$	−1.00089	−	3.08043i	−0.0594969	−	0.183112i	0.916891	−	0.399138i	$-0.130691\pi$
$283$	−1.00089	−	3.08043i	−0.0594969	−	0.183112i	−0.976388	+	0.216026i	$0.930691\pi$
$284$	19.5390			1.15943
$285$	0.0946363			0.00560577
$286$	−0.705176	−	2.17031i	−0.0416980	−	0.128333i
$287$	−2.00096	+	6.15831i	−0.118113	+	0.363513i
$288$	0.752762	−	2.31676i	0.0443569	−	0.136517i
$289$	3.57305	+	2.59597i	0.210179	+	0.152704i
$290$	0.100448	+	0.309148i	0.00589853	+	0.0181538i
$291$	−13.5239	−	9.82566i	−0.792783	−	0.575990i
$292$	10.8140	−	7.85684i	0.632842	−	0.459787i
$293$	1.52931	−	4.70672i	0.0893431	−	0.274970i	−0.896395	−	0.443256i	$-0.853823\pi$
$293$	1.52931	−	4.70672i	0.0893431	−	0.274970i	0.985738	+	0.168286i	$0.0538233\pi$
$294$	−1.09618	+	0.796423i	−0.0639306	+	0.0464483i
$295$	−1.69210	+	1.22938i	−0.0985176	+	0.0715773i
$296$	−1.72023	+	5.29432i	−0.0999862	+	0.307726i
$297$	3.64350	−	2.64716i	0.211417	−	0.153604i
$298$	0.263177	+	0.191209i	0.0152454	+	0.0110764i
$299$	1.88432	+	5.79935i	0.108973	+	0.335385i
$300$	7.73229	+	5.61784i	0.446424	+	0.324346i
$301$	−0.463937	+	1.42785i	−0.0267409	+	0.0822999i
$302$	−1.13891	+	3.50520i	−0.0655369	+	0.201702i
$303$	5.69147	+	17.5165i	0.326966	+	1.00630i
$304$	−1.04626			−0.0600072
$305$	−2.47818			−0.141900
$306$	−0.229164	−	0.705295i	−0.0131005	−	0.0403191i
$307$	−18.1144	+	13.1609i	−1.03384	+	0.751132i	−0.969074	−	0.246768i	$-0.920631\pi$
$307$	−18.1144	+	13.1609i	−1.03384	+	0.751132i	−0.0647697	+	0.997900i	$0.520631\pi$
$308$	−5.13361	−	3.72978i	−0.292514	−	0.212524i
$309$	5.88367			0.334710
$310$	−0.0337568	−	0.392279i	−0.00191725	−	0.0222800i
$311$	29.9230			1.69678			0.848388	−	0.529375i	$-0.177573\pi$
$311$	29.9230			1.69678			0.848388	+	0.529375i	$0.177573\pi$
$312$	1.62181	+	1.17832i	0.0918171	+	0.0667090i
$313$	−14.0584	+	10.2140i	−0.794629	+	0.577332i	−0.909334	−	0.416068i	$-0.863408\pi$
$313$	−14.0584	+	10.2140i	−0.794629	+	0.577332i	0.114704	+	0.993400i	$0.463408\pi$
$314$	−0.614930	−	1.89256i	−0.0347025	−	0.106803i
$315$	−0.243625			−0.0137267
$316$	11.7679			0.661995
$317$	−6.79389	−	20.9094i	−0.381583	−	1.17439i	−0.938929	−	0.344111i	$-0.888180\pi$
$317$	−6.79389	−	20.9094i	−0.381583	−	1.17439i	0.557346	−	0.830280i	$-0.311820\pi$
$318$	−0.751442	+	2.31270i	−0.0421388	+	0.129690i
$319$	6.39715	−	19.6884i	0.358172	−	1.10234i
$320$	1.90743	+	1.38583i	0.106629	+	0.0774703i
$321$	2.32853	+	7.16649i	0.129966	+	0.399995i
$322$	−0.306461	−	0.222657i	−0.0170784	−	0.0124082i
$323$	−0.802903	+	0.583343i	−0.0446747	+	0.0324581i
$324$	−0.604528	+	1.86055i	−0.0335849	+	0.103364i
$325$	−9.57995	+	6.96024i	−0.531400	+	0.386085i
$326$	−0.875432	+	0.636038i	−0.0484857	+	0.0352269i
$327$	2.28493	−	7.03230i	0.126357	−	0.388887i
$328$	6.01584	−	4.37076i	0.332169	−	0.241335i
$329$	−3.75634	−	2.72914i	−0.207094	−	0.150462i
$330$	−0.0984148	−	0.302889i	−0.00541755	−	0.0166735i
$331$	18.1802	+	13.2087i	0.999276	+	0.726017i	0.961933	−	0.273286i	$-0.0881105\pi$
$331$	18.1802	+	13.2087i	0.999276	+	0.726017i	0.0373434	+	0.999302i	$0.488110\pi$
$332$	−6.33412	+	19.4944i	−0.347630	+	1.06989i
$333$	2.07985	−	6.40113i	0.113975	−	0.350780i
$334$	−1.44639	−	4.45153i	−0.0791429	−	0.243577i
$335$	−2.18927			−0.119613
$336$	2.69342			0.146938
$337$	4.88558	+	15.0363i	0.266134	+	0.819078i	0.991430	+	0.130640i	$0.0417032\pi$
$337$	4.88558	+	15.0363i	0.266134	+	0.819078i	−0.725295	+	0.688438i	$0.758297\pi$
$338$	1.20512	−	0.875571i	0.0655499	−	0.0476248i
$339$	−15.0048	−	10.9016i	−0.814950	−	0.592096i
$340$	2.34740			0.127306
$341$	−12.9452	+	21.4751i	−0.701023	+	1.16294i
$342$	−0.0584884			−0.00316269
$343$	−7.85521	−	5.70715i	−0.424142	−	0.308157i
$344$	1.39482	−	1.01339i	0.0752036	−	0.0546386i
$345$	0.262977	+	0.809360i	0.0141582	+	0.0435745i
$346$	1.91016			0.102691
$347$	−26.2231			−1.40773			−0.703865	−	0.710334i	$-0.748544\pi$
$347$	−26.2231			−1.40773			−0.703865	+	0.710334i	$0.748544\pi$
$348$	2.77882	+	8.55232i	0.148960	+	0.458453i
$349$	−2.81303	+	8.65763i	−0.150578	+	0.463432i	−0.997686	−	0.0679888i	$-0.978342\pi$
$349$	−2.81303	+	8.65763i	−0.150578	+	0.463432i	0.847108	+	0.531421i	$0.178342\pi$
$350$	0.227317	−	0.699611i	0.0121506	−	0.0373958i
$351$	−1.96086	−	1.42465i	−0.104663	−	0.0760422i
$352$	3.39015	+	10.4338i	0.180695	+	0.556124i
$353$	19.3945	+	14.0909i	1.03226	+	0.749983i	0.968760	−	0.247999i	$-0.0797730\pi$
$353$	19.3945	+	14.0909i	1.03226	+	0.749983i	0.0635023	+	0.997982i	$0.479773\pi$
$354$	1.04577	−	0.759798i	0.0555822	−	0.0403828i
$355$	−1.04401	+	3.21312i	−0.0554101	+	0.170535i
$356$	−9.56523	+	6.94954i	−0.506956	+	0.368325i
$357$	2.06694	−	1.50172i	0.109394	−	0.0794793i
$358$	0.0162659	−	0.0500612i	0.000859678	−	0.00264582i
$359$	−18.0922	+	13.1448i	−0.954872	+	0.693755i	−0.951954	−	0.306241i	$-0.900929\pi$
$359$	−18.0922	+	13.1448i	−0.954872	+	0.693755i	−0.00291771	+	0.999996i	$0.500929\pi$
$360$	0.226341	+	0.164446i	0.0119292	+	0.00866708i
$361$	−5.84714	−	17.9956i	−0.307744	−	0.947139i
$362$	−2.62224	−	1.90517i	−0.137822	−	0.100134i
$363$	−2.86846	+	8.82821i	−0.150555	+	0.463361i
$364$	−1.05530	+	3.24788i	−0.0553128	+	0.170235i
$365$	0.714216	+	2.19813i	0.0373838	+	0.115055i
$366$	1.53160			0.0800581
$367$	−0.534114			−0.0278805			−0.0139403	−	0.999903i	$-0.504437\pi$
$367$	−0.534114			−0.0278805			−0.0139403	+	0.999903i	$0.504437\pi$
$368$	−2.90737	−	8.94796i	−0.151557	−	0.466445i
$369$	−7.27349	+	5.28450i	−0.378643	+	0.275100i
$370$	−0.385057	−	0.279760i	−0.0200181	−	0.0145440i
$371$	−8.37757			−0.434942
$372$	−0.933853	−	10.8521i	−0.0484180	−	0.562654i
$373$	3.31092			0.171433			0.0857165	−	0.996320i	$-0.472682\pi$
$373$	3.31092			0.171433			0.0857165	+	0.996320i	$0.472682\pi$
$374$	2.70199	+	1.96311i	0.139716	+	0.101510i
$375$	−2.70528	+	1.96550i	−0.139700	+	0.101498i
$376$	1.64768	+	5.07104i	0.0849727	+	0.261519i
$377$	−11.1412			−0.573802
$378$	0.150568			0.00774441
$379$	−10.2570	−	31.5677i	−0.526865	−	1.62152i	−0.760598	−	0.649223i	$-0.775094\pi$
$379$	−10.2570	−	31.5677i	−0.526865	−	1.62152i	0.233733	−	0.972301i	$-0.424906\pi$
$380$	0.0572103	−	0.176075i	0.00293483	−	0.00903247i
$381$	5.55422	−	17.0941i	0.284551	−	0.875759i
$382$	1.28154	+	0.931093i	0.0655692	+	0.0476388i
$383$	−1.49628	−	4.60509i	−0.0764566	−	0.235309i	0.905523	−	0.424298i	$-0.139479\pi$
$383$	−1.49628	−	4.60509i	−0.0764566	−	0.235309i	−0.981979	+	0.188989i	$0.939479\pi$
$384$	−5.12037	−	3.72017i	−0.261298	−	0.189844i
$385$	0.887647	−	0.644914i	0.0452387	−	0.0328678i
$386$	1.32871	−	4.08936i	0.0676297	−	0.208143i
$387$	−1.68641	+	1.22525i	−0.0857253	+	0.0622831i
$388$	−26.4567	+	19.2219i	−1.34313	+	0.975843i
$389$	−10.0725	+	31.0000i	−0.510697	+	1.57176i	0.280280	+	0.959918i	$0.409573\pi$
$389$	−10.0725	+	31.0000i	−0.510697	+	1.57176i	−0.790977	+	0.611846i	$0.790427\pi$
$390$	−0.138664	+	0.100745i	−0.00702153	+	0.00510144i
$391$	−7.22006	−	5.24568i	−0.365134	−	0.265286i
$392$	1.65652	+	5.09824i	0.0836667	+	0.257500i
$393$	14.9259	+	10.8443i	0.752914	+	0.547024i
$394$	−0.358649	+	1.10381i	−0.0180685	+	0.0556091i
$395$	−0.628779	+	1.93518i	−0.0316373	+	0.0973696i
$396$	−2.72256	−	8.37919i	−0.136814	−	0.421070i
$397$	−15.5216			−0.779005			−0.389502	−	0.921025i	$-0.627353\pi$
$397$	−15.5216			−0.779005			−0.389502	+	0.921025i	$0.627353\pi$
$398$	1.15819			0.0580550
$399$	−0.0622669	−	0.191638i	−0.00311724	−	0.00959389i
$400$	14.7812	−	10.7391i	0.739058	−	0.536957i
$401$	13.2031	+	9.59265i	0.659334	+	0.479034i	0.866438	−	0.499285i	$-0.166404\pi$
$401$	13.2031	+	9.59265i	0.659334	+	0.479034i	−0.207104	+	0.978319i	$0.566404\pi$
$402$	1.35304			0.0674837
$403$	13.1447	+	3.05443i	0.654785	+	0.152152i
$404$	36.0310			1.79261
$405$	−0.273659	−	0.198825i	−0.0135982	−	0.00987969i
$406$	0.559932	−	0.406814i	0.0277889	−	0.0201898i
$407$	9.36685	+	28.8282i	0.464298	+	1.42896i
$408$	−2.93395			−0.145252
$409$	−15.9103			−0.786713			−0.393356	−	0.919386i	$-0.628686\pi$
$409$	−15.9103			−0.786713			−0.393356	+	0.919386i	$0.628686\pi$
$410$	0.196465	+	0.604656i	0.00970270	+	0.0298618i
$411$	5.41085	−	16.6529i	0.266897	−	0.821425i
$412$	3.55685	−	10.9468i	0.175233	−	0.539312i
$413$	3.60282	+	2.61760i	0.177283	+	0.128804i
$414$	−0.162529	−	0.500212i	−0.00798785	−	0.0245841i
$415$	−2.86734	−	2.08324i	−0.140752	−	0.102262i
$416$	4.77664	−	3.47043i	0.234194	−	0.170152i
$417$	−2.27589	+	7.00448i	−0.111451	+	0.343011i
$418$	0.213103	−	0.154828i	0.0104232	−	0.00757289i
$419$	−16.2198	+	11.7844i	−0.792391	+	0.575706i	−0.908672	−	0.417511i	$-0.862903\pi$
$419$	−16.2198	+	11.7844i	−0.792391	+	0.575706i	0.116281	+	0.993216i	$0.462903\pi$
$420$	−0.147278	+	0.453276i	−0.00718644	+	0.0221176i
$421$	19.0718	−	13.8564i	0.929501	−	0.675322i	−0.0163696	−	0.999866i	$-0.505211\pi$
$421$	19.0718	−	13.8564i	0.929501	−	0.675322i	0.945871	+	0.324544i	$0.105211\pi$
$422$	1.35032	+	0.981067i	0.0657327	+	0.0477576i
$423$	−1.99214	−	6.13118i	−0.0968612	−	0.298108i
$424$	7.78322	+	5.65484i	0.377987	+	0.274623i
$425$	5.35548	−	16.4825i	0.259779	−	0.799518i
$426$	0.645232	−	1.98582i	0.0312616	−	0.0962132i
$427$	1.63055	+	5.01830i	0.0789076	+	0.242853i
$428$	14.7413			0.712546
$429$	10.9157			0.527014
$430$	0.0455518	+	0.140194i	0.00219670	+	0.00676076i
$431$	8.96576	−	6.51400i	0.431865	−	0.313768i	−0.350529	−	0.936552i	$-0.613998\pi$
$431$	8.96576	−	6.51400i	0.431865	−	0.313768i	0.782394	+	0.622783i	$0.213998\pi$
$432$	3.02547	+	2.19813i	0.145563	+	0.105758i
$433$	−2.84260			−0.136607			−0.0683034	−	0.997665i	$-0.521759\pi$
$433$	−2.84260			−0.136607			−0.0683034	+	0.997665i	$0.521759\pi$
$434$	−0.772153	+	0.326462i	−0.0370645	+	0.0156707i
$435$	−1.55488			−0.0745506
$436$	−11.7026	−	8.50245i	−0.560454	−	0.407193i
$437$	−0.569438	+	0.413721i	−0.0272399	+	0.0197909i
$438$	−0.441410	−	1.35852i	−0.0210914	−	0.0649125i
$439$	18.0543			0.861684			0.430842	−	0.902427i	$-0.358217\pi$
$439$	18.0543			0.861684			0.430842	+	0.902427i	$0.358217\pi$
$440$	−1.25999			−0.0600676
$441$	−2.00282	−	6.16406i	−0.0953725	−	0.293527i
$442$	0.555440	−	1.70947i	0.0264196	−	0.0813111i
$443$	3.23229	−	9.94796i	0.153571	−	0.472642i	−0.844443	−	0.535646i	$-0.820068\pi$
$443$	3.23229	−	9.94796i	0.153571	−	0.472642i	0.998013	+	0.0630041i	$0.0200681\pi$
$444$	−10.6523	−	7.73933i	−0.505534	−	0.367292i
$445$	−0.631739	−	1.94429i	−0.0299473	−	0.0921683i
$446$	−0.930197	−	0.675828i	−0.0440461	−	0.0320014i
$447$	−1.25888	+	0.914627i	−0.0595428	+	0.0432604i
$448$	1.55128	−	4.77436i	0.0732912	−	0.225567i
$449$	11.9699	−	8.69664i	0.564895	−	0.410420i	−0.268352	−	0.963321i	$-0.586479\pi$
$449$	11.9699	−	8.69664i	0.564895	−	0.410420i	0.833247	+	0.552901i	$0.186479\pi$
$450$	0.826301	−	0.600343i	0.0389522	−	0.0283004i
$451$	12.5121	−	38.5082i	0.589170	−	1.81328i
$452$	−29.3539	+	21.3268i	−1.38069	+	1.00313i
$453$	−14.2626	−	10.3624i	−0.670118	−	0.486869i
$454$	−0.0982283	−	0.302316i	−0.00461008	−	0.0141884i
$455$	−0.477715	−	0.347080i	−0.0223956	−	0.0162714i
$456$	−0.0715058	+	0.220072i	−0.00334856	+	0.0103058i
$457$	−0.821079	+	2.52702i	−0.0384085	+	0.118209i	−0.968422	−	0.249315i	$-0.919795\pi$
$457$	−0.821079	+	2.52702i	−0.0384085	+	0.118209i	0.930014	+	0.367524i	$0.119795\pi$
$458$	0.509362	+	1.56766i	0.0238009	+	0.0732517i
$459$	3.54732			0.165575
$460$	1.66483			0.0776231
$461$	−0.592466	−	1.82342i	−0.0275939	−	0.0849253i	0.936311	−	0.351171i	$-0.114217\pi$
$461$	−0.592466	−	1.82342i	−0.0275939	−	0.0849253i	−0.963905	+	0.266246i	$0.914217\pi$
$462$	−0.548596	+	0.398579i	−0.0255230	+	0.0185436i
$463$	4.72591	+	3.43357i	0.219632	+	0.159572i	0.692161	−	0.721743i	$-0.256659\pi$
$463$	4.72591	+	3.43357i	0.219632	+	0.159572i	−0.472529	+	0.881315i	$0.656659\pi$
$464$	17.1901			0.798029
$465$	1.83448	+	0.426278i	0.0850721	+	0.0197682i
$466$	−3.41681			−0.158281
$467$	0.377130	+	0.274001i	0.0174515	+	0.0126793i	0.596477	−	0.802630i	$-0.296567\pi$
$467$	0.377130	+	0.274001i	0.0174515	+	0.0126793i	−0.579025	+	0.815310i	$0.696567\pi$
$468$	−3.83603	+	2.78704i	−0.177320	+	0.128831i
$469$	1.44045	+	4.43326i	0.0665140	+	0.204709i
$470$	−0.455884			−0.0210284
$471$	9.51873			0.438600
$472$	−1.58034	−	4.86379i	−0.0727411	−	0.223874i
$473$	2.90102	−	8.92841i	0.133389	−	0.410529i
$474$	0.388607	−	1.19601i	0.0178493	−	0.0549345i
$475$	−1.10581	−	0.803416i	−0.0507379	−	0.0368632i
$476$	−1.54449	−	4.75347i	−0.0707918	−	0.217875i
$477$	−9.41036	−	6.83702i	−0.430871	−	0.313046i
$478$	−5.01509	+	3.64367i	−0.229385	+	0.166658i
$479$	−4.71458	+	14.5100i	−0.215415	+	0.662978i	0.783709	+	0.621128i	$0.213325\pi$
$479$	−4.71458	+	14.5100i	−0.215415	+	0.662978i	−0.999124	+	0.0418503i	$0.986675\pi$
$480$	0.666630	−	0.484335i	0.0304274	−	0.0221068i
$481$	13.1977	−	9.58868i	0.601762	−	0.437206i
$482$	1.49086	−	4.58841i	0.0679070	−	0.208996i
$483$	1.46592	−	1.06505i	0.0667017	−	0.0484616i
$484$	14.6912	+	10.6738i	0.667784	+	0.485173i
$485$	−1.74734	−	5.37776i	−0.0793426	−	0.244192i
$486$	0.169131	+	0.122881i	0.00767192	+	0.00557398i
$487$	1.35634	−	4.17437i	0.0614614	−	0.189159i	−0.915611	−	0.402065i	$-0.868293\pi$
$487$	1.35634	−	4.17437i	0.0614614	−	0.189159i	0.977073	+	0.212906i	$0.0682927\pi$
$488$	1.87248	−	5.76289i	0.0847631	−	0.260874i
$489$	−1.59949	−	4.92273i	−0.0723316	−	0.222614i
$490$	−0.458329			−0.0207052
$491$	−7.45678			−0.336520			−0.168260	−	0.985743i	$-0.553815\pi$
$491$	−7.45678			−0.336520			−0.168260	+	0.985743i	$0.553815\pi$
$492$	5.43503	+	16.7273i	0.245030	+	0.754125i
$493$	13.1917	−	9.58434i	0.594125	−	0.431657i
$494$	−0.114688	−	0.0833256i	−0.00516005	−	0.00374900i
$495$	1.52340			0.0684716
$496$	−20.2813	−	4.71276i	−0.910658	−	0.211609i
$497$	7.19347			0.322671
$498$	1.77211	+	1.28752i	0.0794103	+	0.0576950i
$499$	−25.8687	+	18.7947i	−1.15804	+	0.841365i	−0.989529	−	0.144334i	$-0.953896\pi$
$499$	−25.8687	+	18.7947i	−1.15804	+	0.841365i	−0.168511	+	0.985700i	$0.553896\pi$
$500$	2.02149	+	6.22150i	0.0904037	+	0.278234i
$501$	22.3892			1.00028
$502$	−3.24639			−0.144893
$503$	−10.7308	−	33.0259i	−0.478461	−	1.47255i	−0.841232	−	0.540674i	$-0.818169\pi$
$503$	−10.7308	−	33.0259i	−0.478461	−	1.47255i	0.362771	−	0.931878i	$-0.381831\pi$
$504$	0.184079	−	0.566538i	0.00819955	−	0.0252356i
$505$	−1.92520	+	5.92517i	−0.0856705	+	0.263667i
$506$	1.91631	+	1.39228i	0.0851905	+	0.0618945i
$507$	2.20186	+	6.77664i	0.0977882	+	0.300961i
$508$	−28.4468	−	20.6678i	−1.26212	−	0.916985i
$509$	−25.7010	+	18.6729i	−1.13918	+	0.827661i	−0.987005	−	0.160693i	$-0.948627\pi$
$509$	−25.7010	+	18.6729i	−1.13918	+	0.827661i	−0.152173	+	0.988354i	$0.548627\pi$
$510$	0.0775174	−	0.238574i	0.00343253	−	0.0105642i
$511$	3.98127	−	2.89256i	0.176121	−	0.127959i
$512$	−12.3747	+	8.99072i	−0.546888	+	0.397338i
$513$	0.0864545	−	0.266080i	0.00381706	−	0.0117477i
$514$	1.92678	−	1.39989i	0.0849868	−	0.0617465i
$515$	1.61012	+	1.16982i	0.0709503	+	0.0515484i
$516$	1.26015	+	3.87835i	0.0554752	+	0.170735i
$517$	23.4886	+	17.0654i	1.03303	+	0.750537i
$518$	−0.313160	+	0.963808i	−0.0137595	+	0.0423473i
$519$	−2.82350	+	8.68984i	−0.123938	+	0.381441i
$520$	0.209545	+	0.644914i	0.00918916	+	0.0282813i
$521$	16.8542			0.738397			0.369199	−	0.929351i	$-0.379632\pi$
$521$	16.8542			0.738397			0.369199	+	0.929351i	$0.379632\pi$
$522$	0.960966			0.0420603
$523$	10.7973	+	33.2305i	0.472131	+	1.45307i	0.849788	+	0.527124i	$0.176730\pi$
$523$	10.7973	+	33.2305i	0.472131	+	1.45307i	−0.377657	+	0.925945i	$0.623270\pi$
$524$	29.1995	−	21.2147i	1.27559	−	0.926768i
$525$	2.84671	+	2.06826i	0.124241	+	0.0902661i
$526$	−5.62152			−0.245110
$527$	−18.1915	+	7.69127i	−0.792436	+	0.335037i
$528$	−16.8421			−0.732957
$529$	13.4868	+	9.79870i	0.586381	+	0.426030i
$530$	−0.665461	+	0.483486i	−0.0289058	+	0.0210013i
$531$	1.91072	+	5.88060i	0.0829183	+	0.255196i
$532$	−0.394193			−0.0170905
$533$	−21.7909			−0.943869
$534$	0.390436	+	1.20164i	0.0168958	+	0.0520000i
$535$	−0.787653	+	2.42415i	−0.0340532	+	0.104805i
$536$	1.65418	−	5.09105i	0.0714498	−	0.219900i
$537$	0.203699	+	0.147996i	0.00879024	+	0.00638649i
$538$	0.745506	+	2.29443i	0.0321411	+	0.0989200i
$539$	23.6145	+	17.1569i	1.01715	+	0.739002i
$540$	−0.535358	+	0.388960i	−0.0230381	+	0.0167382i
$541$	5.39939	−	16.6176i	0.232138	−	0.714447i	−0.765350	−	0.643614i	$-0.777434\pi$
$541$	5.39939	−	16.6176i	0.232138	−	0.714447i	0.997488	−	0.0708328i	$-0.0225657\pi$
$542$	−2.29876	+	1.67015i	−0.0987402	+	0.0717390i
$543$	12.5432	−	9.11318i	0.538281	−	0.391084i
$544$	−2.67029	+	8.21829i	−0.114488	+	0.352356i
$545$	2.02349	−	1.47015i	0.0866767	−	0.0629743i
$546$	0.295244	+	0.214508i	0.0126353	+	0.00918007i
$547$	7.23174	+	22.2570i	0.309207	+	0.951641i	0.978074	+	0.208259i	$0.0667796\pi$
$547$	7.23174	+	22.2570i	0.309207	+	0.951641i	−0.668867	+	0.743382i	$0.733220\pi$
$548$	−27.7124	−	20.1343i	−1.18382	−	0.860093i
$549$	−2.26393	+	6.96767i	−0.0966223	+	0.297373i
$550$	−1.42143	+	4.37470i	−0.0606098	+	0.186538i
$551$	−0.397403	−	1.22308i	−0.0169299	−	0.0521050i
$552$	−2.08083			−0.0885660
$553$	4.33245			0.184234
$554$	−0.140073	−	0.431100i	−0.00595113	−	0.0183157i
$555$	1.84187	−	1.33820i	0.0781832	−	0.0568034i
$556$	11.6563	+	8.46881i	0.494338	+	0.359158i
$557$	−2.04586			−0.0866859			−0.0433430	−	0.999060i	$-0.513801\pi$
$557$	−2.04586			−0.0866859			−0.0433430	+	0.999060i	$0.513801\pi$
$558$	−1.13377	−	0.263454i	−0.0479964	−	0.0111529i
$559$	−5.05239			−0.213693
$560$	0.737079	+	0.535519i	0.0311473	+	0.0226298i
$561$	−12.9247	+	9.39031i	−0.545679	+	0.396459i
$562$	0.633124	+	1.94855i	0.0267067	+	0.0821948i
$563$	−13.2675			−0.559159			−0.279579	−	0.960123i	$-0.590195\pi$
$563$	−13.2675			−0.559159			−0.279579	+	0.960123i	$0.590195\pi$
$564$	−12.6117			−0.531047
$565$	−1.93869	−	5.96667i	−0.0815612	−	0.251020i
$566$	−0.209243	+	0.643985i	−0.00879516	+	0.0270687i
$567$	−0.222562	+	0.684977i	−0.00934674	+	0.0287663i
$568$	−6.68312	−	4.85557i	−0.280418	−	0.203735i
$569$	−12.6831	−	39.0346i	−0.531704	−	1.63642i	−0.750665	−	0.660684i	$-0.770267\pi$
$569$	−12.6831	−	39.0346i	−0.531704	−	1.63642i	0.218960	−	0.975734i	$-0.429733\pi$
$570$	−0.0160059	−	0.0116290i	−0.000670413	−	0.000487084i
$571$	−36.3259	+	26.3923i	−1.52019	+	1.10448i	−0.558800	+	0.829303i	$0.688738\pi$
$571$	−36.3259	+	26.3923i	−1.52019	+	1.10448i	−0.961392	+	0.275181i	$0.911262\pi$
$572$	6.59884	−	20.3091i	0.275911	−	0.849168i
$573$	−6.13010	+	4.45378i	−0.256088	+	0.186059i
$574$	1.09516	−	0.795680i	0.0457111	−	0.0332110i
$575$	3.79823	−	11.6898i	0.158397	−	0.487497i
$576$	5.63893	−	4.09692i	0.234955	−	0.170705i
$577$	−33.7114	−	24.4928i	−1.40343	−	1.01965i	−0.994238	−	0.107198i	$-0.965812\pi$
$577$	−33.7114	−	24.4928i	−1.40343	−	1.01965i	−0.409188	−	0.912450i	$-0.634188\pi$
$578$	−0.285318	−	0.878117i	−0.0118676	−	0.0365249i
$579$	16.6396	+	12.0893i	0.691516	+	0.502416i
$580$	−0.939966	+	2.89292i	−0.0390300	+	0.120122i
$581$	−2.33196	+	7.17704i	−0.0967460	+	0.297754i
$582$	1.07992	+	3.32364i	0.0447639	+	0.137769i
$583$	52.3853			2.16958
$584$	−5.65130			−0.233852
$585$	−0.253352	−	0.779737i	−0.0104748	−	0.0322382i
$586$	−0.837018	+	0.608129i	−0.0345769	+	0.0251216i
$587$	−0.701665	−	0.509790i	−0.0289608	−	0.0210413i	0.573211	−	0.819408i	$-0.305698\pi$
$587$	−0.701665	−	0.509790i	−0.0289608	−	0.0210413i	−0.602172	+	0.798367i	$0.705698\pi$
$588$	−12.6793			−0.522885
$589$	0.133552	+	1.55197i	0.00550290	+	0.0639479i
$590$	0.437252			0.0180014
$591$	−4.49139	−	3.26318i	−0.184751	−	0.134229i
$592$	−20.3630	+	14.7946i	−0.836915	+	0.608055i
$593$	8.28104	+	25.4864i	0.340061	+	1.04660i	0.964175	+	0.265268i	$0.0854603\pi$
$593$	8.28104	+	25.4864i	0.340061	+	1.04660i	−0.624113	+	0.781334i	$0.714540\pi$
$594$	−0.941512			−0.0386307
$595$	0.864215			0.0354294
$596$	0.940680	+	2.89512i	0.0385318	+	0.118589i
$597$	−1.71198	+	5.26894i	−0.0700668	+	0.215643i
$598$	0.393931	−	1.21239i	0.0161090	−	0.0495785i
$599$	11.4761	+	8.33785i	0.468900	+	0.340676i	0.797012	−	0.603963i	$-0.206413\pi$
$599$	11.4761	+	8.33785i	0.468900	+	0.340676i	−0.328113	+	0.944639i	$0.606413\pi$
$600$	−1.24868	−	3.84305i	−0.0509772	−	0.156892i
$601$	15.8143	+	11.4898i	0.645080	+	0.468678i	0.861592	−	0.507602i	$-0.169468\pi$
$601$	15.8143	+	11.4898i	0.645080	+	0.468678i	−0.216512	+	0.976280i	$0.569468\pi$
$602$	0.253921	−	0.184484i	0.0103490	−	0.00751902i
$603$	−2.00000	+	6.15537i	−0.0814463	+	0.250666i
$604$	−27.9019	+	20.2720i	−1.13531	+	0.824854i
$605$	−2.54025	+	1.84560i	−0.103276	+	0.0750343i
$606$	1.18984	−	3.66196i	0.0483340	−	0.148757i
$607$	−35.6549	+	25.9048i	−1.44719	+	1.05144i	−0.460708	+	0.887552i	$0.652404\pi$
$607$	−35.6549	+	25.9048i	−1.44719	+	1.05144i	−0.986479	+	0.163891i	$0.947596\pi$
$608$	0.551364	+	0.400589i	0.0223608	+	0.0162460i
$609$	1.02305	+	3.14861i	0.0414559	+	0.127588i
$610$	0.419136	+	0.304520i	0.0169703	+	0.0123297i
$611$	4.82847	−	14.8605i	0.195339	−	0.601192i
$612$	2.14445	−	6.59995i	0.0866844	−	0.266787i
$613$	−4.15761	−	12.7958i	−0.167924	−	0.516818i	0.831316	−	0.555801i	$-0.187588\pi$
$613$	−4.15761	−	12.7958i	−0.167924	−	0.516818i	−0.999240	+	0.0389829i	$0.987588\pi$
$614$	4.68092			0.188907
$615$	−3.04115			−0.122631
$616$	0.829022	+	2.55147i	0.0334023	+	0.102802i
$617$	22.7831	−	16.5529i	0.917214	−	0.666395i	−0.0256150	−	0.999672i	$-0.508154\pi$
$617$	22.7831	−	16.5529i	0.917214	−	0.666395i	0.942829	+	0.333277i	$0.108154\pi$
$618$	−0.995109	−	0.722989i	−0.0400291	−	0.0290829i
$619$	13.5207			0.543443			0.271722	−	0.962376i	$-0.412407\pi$
$619$	13.5207			0.543443			0.271722	+	0.962376i	$0.412407\pi$
$620$	1.90211	−	3.15544i	0.0763905	−	0.126726i
$621$	2.51584			0.100957
$622$	−5.06089	−	3.67695i	−0.202923	−	0.147432i
$623$	−3.52152	+	2.55854i	−0.141087	+	0.102506i
$624$	2.80096	+	8.62046i	0.112128	+	0.345095i
$625$	23.2968			0.931871
$626$	3.63282			0.145197
$627$	0.389358	+	1.19832i	0.0155495	+	0.0478563i
$628$	5.75434	−	17.7100i	0.229623	−	0.706708i
$629$	−7.37790	+	22.7068i	−0.294176	+	0.905381i
$630$	0.0412044	+	0.0299368i	0.00164162	+	0.00119271i
$631$	−1.54120	−	4.74334i	−0.0613544	−	0.188829i	0.915681	−	0.401905i	$-0.131652\pi$
$631$	−1.54120	−	4.74334i	−0.0613544	−	0.188829i	−0.977036	+	0.213076i	$0.931652\pi$
$632$	−4.02508	−	2.92439i	−0.160109	−	0.116326i
$633$	−6.45912	+	4.69282i	−0.256727	+	0.186523i
$634$	−1.42031	+	4.37126i	−0.0564077	+	0.173605i
$635$	4.91870	−	3.57365i	0.195193	−	0.141816i
$636$	−18.4094	+	13.3752i	−0.729982	+	0.530363i
$637$	4.85436	−	14.9402i	0.192337	−	0.591952i
$638$	−3.50128	+	2.54383i	−0.138617	+	0.100711i
$639$	8.08028	+	5.87067i	0.319651	+	0.232240i
$640$	−0.661574	−	2.03611i	−0.0261510	−	0.0804845i
$641$	3.66562	+	2.66323i	0.144783	+	0.105191i	0.657819	−	0.753176i	$-0.271479\pi$
$641$	3.66562	+	2.66323i	0.144783	+	0.105191i	−0.513036	+	0.858367i	$0.671479\pi$
$642$	0.486796	−	1.49820i	0.0192123	−	0.0591294i
$643$	2.36462	−	7.27755i	0.0932515	−	0.286999i	−0.893543	−	0.448978i	$-0.851788\pi$
$643$	2.36462	−	7.27755i	0.0932515	−	0.286999i	0.986794	+	0.161980i	$0.0517880\pi$
$644$	−1.09539	−	3.37127i	−0.0431645	−	0.132847i
$645$	−0.705113			−0.0277638
$646$	0.207477			0.00816308
$647$	0.890050	+	2.73929i	0.0349915	+	0.107693i	0.967027	−	0.254675i	$-0.0819685\pi$
$647$	0.890050	+	2.73929i	0.0349915	+	0.107693i	−0.932035	+	0.362368i	$0.881968\pi$
$648$	0.669131	−	0.486152i	0.0262859	−	0.0190978i
$649$	−22.5286	−	16.3680i	−0.884324	−	0.642499i
$650$	2.47554			0.0970988
$651$	−0.343806	−	3.99529i	−0.0134748	−	0.156588i
$652$	−10.1259			−0.396562
$653$	−6.40056	−	4.65028i	−0.250473	−	0.181980i	0.455463	−	0.890255i	$-0.349474\pi$
$653$	−6.40056	−	4.65028i	−0.250473	−	0.181980i	−0.705937	+	0.708275i	$0.749474\pi$
$654$	−1.25058	+	0.908603i	−0.0489017	+	0.0355292i
$655$	1.92849	+	5.93529i	0.0753525	+	0.231911i
$656$	33.6217			1.31271
$657$	6.83274			0.266570
$658$	0.299954	+	0.923163i	0.0116934	+	0.0359886i
$659$	−0.496833	+	1.52910i	−0.0193539	+	0.0595651i	−0.960267	−	0.279083i	$-0.909970\pi$
$659$	−0.496833	+	1.52910i	−0.0193539	+	0.0595651i	0.940913	+	0.338648i	$0.109970\pi$
$660$	0.920937	−	2.83435i	0.0358474	−	0.110327i
$661$	15.7590	+	11.4496i	0.612953	+	0.445337i	0.850453	−	0.526051i	$-0.176328\pi$
$661$	15.7590	+	11.4496i	0.612953	+	0.445337i	−0.237500	+	0.971388i	$0.576328\pi$
$662$	−1.45174	−	4.46800i	−0.0564235	−	0.173654i
$663$	6.95581	+	5.05369i	0.270141	+	0.196269i
$664$	7.01101	−	5.09379i	0.272080	−	0.197678i
$665$	0.0210625	−	0.0648237i	0.000816768	−	0.00251375i
$666$	−1.13834	+	0.827053i	−0.0441098	+	0.0320477i
$667$	9.35587	−	6.79744i	0.362261	−	0.263198i
$668$	13.5349	−	41.6562i	0.523681	−	1.61172i
$669$	4.44949	−	3.23275i	0.172027	−	0.124985i
$670$	0.370273	+	0.269019i	0.0143049	+	0.0103931i
$671$	−10.1959	−	31.3797i	−0.393607	−	1.21140i
$672$	−1.41939	−	1.03125i	−0.0547542	−	0.0397813i
$673$	−15.7021	+	48.3261i	−0.605272	+	1.86283i	−0.110359	+	0.993892i	$0.535200\pi$
$673$	−15.7021	+	48.3261i	−0.605272	+	1.86283i	−0.494913	+	0.868943i	$0.664800\pi$
$674$	1.02136	−	3.14344i	0.0393415	−	0.121081i
$675$	1.50973	+	4.64646i	0.0581094	+	0.178842i
$676$	13.9394			0.536129
$677$	23.5935			0.906770			0.453385	−	0.891315i	$-0.350216\pi$
$677$	23.5935			0.906770			0.453385	+	0.891315i	$0.350216\pi$
$678$	1.19818	+	3.68760i	0.0460156	+	0.141622i
$679$	−9.74025	+	7.07671i	−0.373796	+	0.271579i
$680$	−0.802903	−	0.583343i	−0.0307899	−	0.0223702i
$681$	1.52051			0.0582661
$682$	4.82831	−	2.04138i	0.184885	−	0.0781684i
$683$	−10.3947			−0.397743			−0.198871	−	0.980026i	$-0.563728\pi$
$683$	−10.3947			−0.397743			−0.198871	+	0.980026i	$0.563728\pi$
$684$	−0.442790	−	0.321706i	−0.0169305	−	0.0123007i
$685$	4.79173	−	3.48140i	0.183083	−	0.133017i
$686$	0.627260	+	1.93051i	0.0239489	+	0.0737071i
$687$	−7.88460			−0.300816
$688$	7.79545			0.297199
$689$	−8.71205	−	26.8129i	−0.331903	−	1.02149i
$690$	0.0549772	−	0.169202i	0.00209294	−	0.00644142i
$691$	14.9942	−	46.1476i	0.570408	−	1.75554i	−0.0809000	−	0.996722i	$-0.525779\pi$
$691$	14.9942	−	46.1476i	0.570408	−	1.75554i	0.651308	−	0.758813i	$-0.274221\pi$
$692$	14.4610	+	10.5065i	0.549723	+	0.399397i
$693$	−1.00234	−	3.08487i	−0.0380756	−	0.117185i
$694$	4.43513	+	3.22231i	0.168355	+	0.122317i
$695$	−2.01548	+	1.46433i	−0.0764516	+	0.0555454i
$696$	1.17484	−	3.61579i	0.0445322	−	0.137056i
$697$	25.8014	−	18.7458i	0.977298	−	0.710048i
$698$	1.53962	−	1.11860i	0.0582757	−	0.0423397i
$699$	5.05055	−	15.5440i	0.191029	−	0.587927i
$700$	5.56901	−	4.04612i	0.210489	−	0.152929i
$701$	−19.1492	−	13.9127i	−0.723256	−	0.525476i	0.164167	−	0.986433i	$-0.447507\pi$
$701$	−19.1492	−	13.9127i	−0.723256	−	0.525476i	−0.887423	+	0.460956i	$0.847507\pi$
$702$	0.156580	+	0.481904i	0.00590974	+	0.0181883i
$703$	1.52340	+	1.10681i	0.0574560	+	0.0417443i
$704$	−9.70024	+	29.8543i	−0.365592	+	1.12518i
$705$	0.673864	−	2.07394i	0.0253792	−	0.0781091i
$706$	−1.54870	−	4.76640i	−0.0582860	−	0.179386i
$707$	13.2651			0.498887
$708$	12.0962			0.454604
$709$	−8.62924	−	26.5581i	−0.324078	−	0.997409i	−0.971855	−	0.235579i	$-0.924301\pi$
$709$	−8.62924	−	26.5581i	−0.324078	−	0.997409i	0.647777	−	0.761830i	$-0.275699\pi$
$710$	0.571404	−	0.415149i	0.0214444	−	0.0155803i
$711$	4.86655	+	3.53576i	0.182510	+	0.132601i
$712$	4.99869			0.187334
$713$	−12.9019	+	5.45483i	−0.483178	+	0.204285i
$714$	−0.534114			−0.0199887
$715$	2.98718	+	2.17031i	0.111714	+	0.0811650i
$716$	0.398495	−	0.289523i	0.0148924	−	0.0108200i
$717$	−9.16302	−	28.2009i	−0.342199	−	1.05318i
$718$	4.67519			0.174477
$719$	−43.2306			−1.61223			−0.806114	−	0.591760i	$-0.798433\pi$
$719$	−43.2306			−1.61223			−0.806114	+	0.591760i	$0.798433\pi$
$720$	0.390903	+	1.20308i	0.0145681	+	0.0448360i
$721$	1.30948	−	4.03018i	0.0487677	−	0.150092i
$722$	−1.22238	+	3.76211i	−0.0454924	+	0.140011i
$723$	18.6702	+	13.5647i	0.694351	+	0.504476i
$724$	−9.37277	−	28.8464i	−0.348336	−	1.07207i
$725$	18.1684	+	13.2001i	0.674758	+	0.490240i
$726$	1.56996	−	1.14064i	0.0582667	−	0.0423332i
$727$	−9.03429	+	27.8047i	−0.335063	+	1.03122i	0.631628	+	0.775272i	$0.282387\pi$
$727$	−9.03429	+	27.8047i	−0.335063	+	1.03122i	−0.966691	+	0.255947i	$0.917613\pi$
$728$	1.16807	−	0.848655i	0.0432917	−	0.0314532i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	0.149312	−	0.459534i	0.00552627	−	0.0170081i
$731$	5.98225	−	4.34636i	0.221261	−	0.160756i
$732$	11.5951	+	8.42431i	0.428566	+	0.311371i
$733$	−6.61028	−	20.3443i	−0.244156	−	0.751435i	−0.995774	−	0.0918367i	$-0.970726\pi$
$733$	−6.61028	−	20.3443i	−0.244156	−	0.751435i	0.751618	−	0.659599i	$-0.229274\pi$
$734$	0.0903351	+	0.0656323i	0.00333433	+	0.00242253i
$735$	0.677477	−	2.08506i	0.0249891	−	0.0769086i
$736$	−1.89383	+	5.82861i	−0.0698074	+	0.214845i
$737$	−9.00723	−	27.7214i	−0.331785	−	1.02113i
$738$	1.87953			0.0691866
$739$	20.7645			0.763834			0.381917	−	0.924197i	$-0.375264\pi$
$739$	20.7645			0.763834			0.381917	+	0.924197i	$0.375264\pi$
$740$	−1.37632	−	4.23587i	−0.0505945	−	0.155714i
$741$	0.548596	−	0.398579i	0.0201532	−	0.0146421i
$742$	1.41690	+	1.02944i	0.0520162	+	0.0377919i
$743$	−3.76121			−0.137986			−0.0689928	−	0.997617i	$-0.521979\pi$
$743$	−3.76121			−0.137986			−0.0689928	+	0.997617i	$0.521979\pi$
$744$	−2.37740	+	3.94391i	−0.0871596	+	0.144591i
$745$	−0.526353			−0.0192841
$746$	−0.559978	−	0.406848i	−0.0205022	−	0.0148958i
$747$	−8.47670	+	6.15869i	−0.310146	+	0.225335i
$748$	9.65780	+	29.7236i	0.353124	+	1.08680i
$749$	5.42712			0.198303
$750$	0.699067			0.0255263
$751$	4.89296	+	15.0590i	0.178547	+	0.549510i	0.999778	−	0.0210859i	$-0.00671234\pi$
$751$	4.89296	+	15.0590i	0.178547	+	0.549510i	−0.821231	+	0.570596i	$0.806712\pi$
$752$	−7.44997	+	22.9287i	−0.271673	+	0.836122i
$753$	4.79864	−	14.7687i	0.174872	−	0.538201i
$754$	1.88432	+	1.36904i	0.0686230	+	0.0498575i
$755$	−1.84280	−	5.67154i	−0.0670662	−	0.206408i
$756$	1.13989	+	0.828176i	0.0414573	+	0.0301205i
$757$	−14.6691	+	10.6577i	−0.533158	+	0.387362i	−0.821538	−	0.570154i	$-0.806884\pi$
$757$	−14.6691	+	10.6577i	−0.533158	+	0.387362i	0.288379	+	0.957516i	$0.406884\pi$
$758$	−2.14429	+	6.59944i	−0.0778841	+	0.239703i
$759$	−9.16647	+	6.65983i	−0.332722	+	0.241736i
$760$	−0.0633240	+	0.0460076i	−0.00229700	+	0.00166887i
$761$	−7.60197	+	23.3964i	−0.275571	+	0.848120i	0.713497	+	0.700659i	$0.247110\pi$
$761$	−7.60197	+	23.3964i	−0.275571	+	0.848120i	−0.989068	+	0.147462i	$0.952890\pi$
$762$	−3.03993	+	2.20864i	−0.110125	+	0.0800104i
$763$	−4.30842	−	3.13025i	−0.155975	−	0.113323i
$764$	4.58064	+	14.0978i	0.165722	+	0.510039i
$765$	0.970756	+	0.705295i	0.0350977	+	0.0255000i
$766$	−0.312809	+	0.962726i	−0.0113022	+	0.0347847i
$767$	−4.63113	+	14.2532i	−0.167221	+	0.514652i
$768$	−3.89889	−	11.9995i	−0.140689	−	0.432996i
$769$	−22.6533			−0.816900			−0.408450	−	0.912781i	$-0.633931\pi$
$769$	−22.6533			−0.816900			−0.408450	+	0.912781i	$0.633931\pi$
$770$	−0.229376			−0.00826613
$771$	3.52041	+	10.8347i	0.126784	+	0.390202i
$772$	32.5519	−	23.6503i	1.17157	−	0.851194i
$773$	35.6378	+	25.8924i	1.28180	+	0.931284i	0.999606	−	0.0280723i	$-0.00893688\pi$
$773$	35.6378	+	25.8924i	1.28180	+	0.931284i	0.282197	+	0.959357i	$0.408937\pi$
$774$	0.435784			0.0156639
$775$	−17.8167	−	20.5548i	−0.639994	−	0.738352i
$776$	13.8260			0.496324
$777$	−3.92173	−	2.84930i	−0.140691	−	0.102218i
$778$	5.51287	−	4.00534i	0.197646	−	0.143598i
$779$	−0.777272	−	2.39220i	−0.0278487	−	0.0857094i
$780$	−1.60390			−0.0574287
$781$	−44.9811			−1.60955
$782$	0.576541	+	1.77441i	0.0206171	+	0.0634528i
$783$	−1.42045	+	4.37169i	−0.0507627	+	0.156232i
$784$	−7.48992	+	23.0516i	−0.267497	+	0.823272i
$785$	2.60489	+	1.89256i	0.0929724	+	0.0675484i
$786$	−1.19187	−	3.66821i	−0.0425128	−	0.130841i
$787$	−2.67199	−	1.94131i	−0.0952461	−	0.0692003i	0.539143	−	0.842214i	$-0.318748\pi$
$787$	−2.67199	−	1.94131i	−0.0952461	−	0.0692003i	−0.634389	+	0.773014i	$0.718748\pi$
$788$	−8.78648	+	6.38375i	−0.313005	+	0.227412i
$789$	8.30944	−	25.5738i	0.295824	−	0.910453i
$790$	0.344142	−	0.250034i	0.0122440	−	0.00889581i
$791$	−10.8069	+	7.85166i	−0.384249	+	0.279173i
$792$	−1.15106	+	3.54259i	−0.0409010	+	0.125880i
$793$	−14.3658	+	10.4373i	−0.510143	+	0.370640i
$794$	2.62517	+	1.90730i	0.0931638	+	0.0676875i
$795$	−1.21586	−	3.74203i	−0.0431221	−	0.132716i
$796$	8.76817	+	6.37045i	0.310780	+	0.225795i
$797$	−3.71267	+	11.4264i	−0.131510	+	0.404745i	−0.995031	−	0.0995677i	$-0.968254\pi$
$797$	−3.71267	+	11.4264i	−0.131510	+	0.404745i	0.863521	+	0.504312i	$0.168254\pi$
$798$	−0.0130173	+	0.0400632i	−0.000460808	+	0.00141822i
$799$	7.06676	+	21.7492i	0.250004	+	0.769433i
$800$	−11.9012			−0.420771
$801$	−6.04370			−0.213544
$802$	−1.05431	−	3.24482i	−0.0372288	−	0.114579i
$803$	−24.8951	+	18.0873i	−0.878528	+	0.638288i
$804$	10.2433	+	7.44219i	0.361253	+	0.262466i
$805$	0.612922			0.0216026
$806$	−1.84784	−	2.13183i	−0.0650875	−	0.0750905i
$807$	−11.5400			−0.406226
$808$	−12.3240	−	8.95394i	−0.433558	−	0.314998i
$809$	−14.7819	+	10.7397i	−0.519705	+	0.377588i	−0.816493	−	0.577355i	$-0.804085\pi$
$809$	−14.7819	+	10.7397i	−0.519705	+	0.377588i	0.296787	+	0.954944i	$0.404085\pi$
$810$	0.0218524	+	0.0672548i	0.000767815	+	0.00236309i
$811$	−9.96726			−0.349998			−0.174999	−	0.984569i	$-0.555992\pi$
$811$	−9.96726			−0.349998			−0.174999	+	0.984569i	$0.555992\pi$
$812$	6.47660			0.227284
$813$	−4.20004	−	12.9264i	−0.147302	−	0.453349i
$814$	1.95821	−	6.02674i	0.0686351	−	0.211237i
$815$	0.541047	−	1.66517i	0.0189520	−	0.0583284i
$816$	−10.7323	−	7.79746i	−0.375705	−	0.272966i
$817$	−0.180216	−	0.554649i	−0.00630498	−	0.0194047i
$818$	2.69092	+	1.95506i	0.0940857	+	0.0683572i
$819$	−1.41227	+	1.02607i	−0.0493486	+	0.0358539i
$820$	−1.83846	+	5.65820i	−0.0642018	+	0.197593i
$821$	0.882103	−	0.640885i	0.0307856	−	0.0223670i	−0.572286	−	0.820054i	$-0.693943\pi$
$821$	0.882103	−	0.640885i	0.0307856	−	0.0223670i	0.603072	+	0.797687i	$0.293943\pi$
$822$	−2.96145	+	2.15162i	−0.103293	+	0.0750464i
$823$	−2.94985	+	9.07872i	−0.102825	+	0.316464i	−0.989214	−	0.146478i	$-0.953206\pi$
$823$	−2.94985	+	9.07872i	−0.102825	+	0.316464i	0.886388	+	0.462942i	$0.153206\pi$
$824$	−3.93694	+	2.86036i	−0.137150	+	0.0996452i
$825$	−17.8006	−	12.9329i	−0.619738	−	0.450266i
$826$	−0.287695	−	0.885433i	−0.0100102	−	0.0308081i
$827$	35.9494	+	26.1188i	1.25008	+	0.908239i	0.998227	−	0.0595260i	$-0.0189589\pi$
$827$	35.9494	+	26.1188i	1.25008	+	0.908239i	0.251856	+	0.967765i	$0.418959\pi$
$828$	1.52090	−	4.68084i	0.0528548	−	0.162670i
$829$	13.1912	−	40.5985i	0.458151	−	1.41004i	−0.409245	−	0.912424i	$-0.634208\pi$
$829$	13.1912	−	40.5985i	0.458151	−	1.41004i	0.867396	−	0.497619i	$-0.165792\pi$
$830$	0.228965	+	0.704681i	0.00794748	+	0.0244598i
$831$	2.16824			0.0752154
$832$	16.8939			0.585689
$833$	7.10465	+	21.8659i	0.246162	+	0.757607i
$834$	1.24564	−	0.905008i	0.0431329	−	0.0313379i
$835$	6.12701	+	4.45153i	0.212034	+	0.154052i
$836$	2.46491			0.0852507
$837$	2.87441	−	4.76841i	0.0993541	−	0.164821i
$838$	4.19134			0.144788
$839$	−35.0361	−	25.4552i	−1.20958	−	0.878813i	−0.214389	−	0.976748i	$-0.568776\pi$
$839$	−35.0361	−	25.4552i	−1.20958	−	0.878813i	−0.995193	+	0.0979355i	$0.968776\pi$
$840$	0.163017	−	0.118439i	0.00562462	−	0.00408652i
$841$	−2.43216	−	7.48541i	−0.0838675	−	0.258118i
$842$	−4.92831			−0.169841
$843$	−9.80035			−0.337542
$844$	4.82650	+	14.8544i	0.166135	+	0.511311i
$845$	−0.744805	+	2.29228i	−0.0256221	+	0.0788567i
$846$	−0.416471	+	1.28177i	−0.0143186	+	0.0440680i
$847$	5.40871	+	3.92966i	0.185845	+	0.135025i
$848$	13.4420	+	41.3704i	0.461602	+	1.42066i
$849$	−2.62037	−	1.90381i	−0.0899308	−	0.0653386i
$850$	−2.93115	+	2.12961i	−0.100538	+	0.0730449i
$851$	−5.23258	+	16.1042i	−0.179370	+	0.552046i
$852$	15.8074	−	11.4848i	0.541553	−	0.393461i
$853$	2.37970	−	1.72895i	0.0814793	−	0.0591982i	−0.546300	−	0.837590i	$-0.683964\pi$
$853$	2.37970	−	1.72895i	0.0814793	−	0.0591982i	0.627779	+	0.778391i	$0.283964\pi$
$854$	0.340877	−	1.04911i	0.0116646	−	0.0358998i
$855$	0.0765624	−	0.0556258i	0.00261838	−	0.00190236i
$856$	−5.04210	−	3.66330i	−0.172335	−	0.125209i
$857$	1.71891	+	5.29026i	0.0587169	+	0.180712i	0.976113	−	0.217263i	$-0.0697130\pi$
$857$	1.71891	+	5.29026i	0.0587169	+	0.180712i	−0.917396	+	0.397975i	$0.869713\pi$
$858$	−1.84618	−	1.34133i	−0.0630274	−	0.0457921i
$859$	5.36355	−	16.5073i	0.183002	−	0.563222i	−0.816906	−	0.576770i	$-0.804313\pi$
$859$	5.36355	−	16.5073i	0.183002	−	0.563222i	0.999908	+	0.0135484i	$0.00431273\pi$
$860$	−0.426261	+	1.31190i	−0.0145354	+	0.0447353i
$861$	2.00096	+	6.15831i	0.0681924	+	0.209875i
$862$	−2.31683			−0.0789115
$863$	14.5198			0.494260			0.247130	−	0.968982i	$-0.420513\pi$
$863$	14.5198			0.494260			0.247130	+	0.968982i	$0.420513\pi$
$864$	−0.752762	−	2.31676i	−0.0256095	−	0.0788179i
$865$	−2.50043	+	1.81667i	−0.0850172	+	0.0617686i
$866$	0.480771	+	0.349301i	0.0163373	+	0.0118697i
$867$	4.41653			0.149993
$868$	−7.64127	−	1.77560i	−0.259361	−	0.0602678i
$869$	−27.0910			−0.918998
$870$	0.262977	+	0.191064i	0.00891575	+	0.00647767i
$871$	−12.6910	+	9.22053i	−0.430017	+	0.312426i
$872$	1.88985	+	5.81635i	0.0639983	+	0.196966i
$873$	−16.7164			−0.565765
$874$	0.147148			0.00497734
$875$	0.744228	+	2.29050i	0.0251595	+	0.0774330i
$876$	4.13058	−	12.7126i	0.139560	−	0.429520i
$877$	2.86408	−	8.81473i	0.0967131	−	0.297652i	−0.890983	−	0.454036i	$-0.849984\pi$
$877$	2.86408	−	8.81473i	0.0967131	−	0.297652i	0.987696	+	0.156384i	$0.0499837\pi$
$878$	−3.05353	−	2.21852i	−0.103052	−	0.0748715i
$879$	−1.52931	−	4.70672i	−0.0515823	−	0.158754i
$880$	−4.60899	−	3.34863i	−0.155369	−	0.112882i
$881$	3.22811	−	2.34536i	0.108758	−	0.0790171i	−0.532077	−	0.846696i	$-0.678588\pi$
$881$	3.22811	−	2.34536i	0.108758	−	0.0790171i	0.640835	+	0.767679i	$0.278588\pi$
$882$	−0.418704	+	1.28864i	−0.0140985	+	0.0433907i
$883$	−20.6783	+	15.0237i	−0.695880	+	0.505587i	−0.878588	−	0.477581i	$-0.841514\pi$
$883$	−20.6783	+	15.0237i	−0.695880	+	0.505587i	0.182708	+	0.983167i	$0.441514\pi$
$884$	13.6076	−	9.88651i	0.457674	−	0.332519i
$885$	−0.646323	+	1.98918i	−0.0217259	+	0.0668655i
$886$	−1.76909	+	1.28532i	−0.0594338	+	0.0431812i
$887$	25.6014	+	18.6005i	0.859610	+	0.624543i	0.927779	−	0.373131i	$-0.121716\pi$
$887$	25.6014	+	18.6005i	0.859610	+	0.624543i	−0.0681690	+	0.997674i	$0.521716\pi$
$888$	1.72023	+	5.29432i	0.0577270	+	0.177666i
$889$	−10.4729	−	7.60903i	−0.351251	−	0.255199i
$890$	−0.132069	+	0.406468i	−0.00442698	+	0.0136248i
$891$	1.39169	−	4.28319i	0.0466235	−	0.143492i
$892$	−3.32483	−	10.2328i	−0.111324	−	0.342619i
$893$	1.80361			0.0603556
$894$	0.325304			0.0108798
$895$	0.0263187	+	0.0810007i	0.000879738	+	0.00270756i
$896$	−3.68783	+	2.67936i	−0.123202	+	0.0895113i
$897$	4.93322	+	3.58419i	0.164715	+	0.119673i
$898$	−3.09313			−0.103219
$899$	−2.19426	−	25.4989i	−0.0731825	−	0.850437i
$900$	9.55764			0.318588
$901$	33.3815	+	24.2531i	1.11210	+	0.807988i
$902$	−6.84808	+	4.97542i	−0.228016	+	0.165663i
$903$	0.463937	+	1.42785i	0.0154388	+	0.0475159i
$904$	15.3400			0.510202
$905$	5.24449			0.174333
$906$	1.13891	+	3.50520i	0.0378378	+	0.116453i
$907$	−2.50061	+	7.69609i	−0.0830314	+	0.255545i	−0.983950	−	0.178443i	$-0.942894\pi$
$907$	−2.50061	+	7.69609i	−0.0830314	+	0.255545i	0.900919	+	0.433988i	$0.142894\pi$
$908$	0.919192	−	2.82898i	0.0305045	−	0.0938831i
$909$	14.9005	+	10.8258i	0.494217	+	0.359070i
$910$	0.0381468	+	0.117404i	0.00126455	+	0.00389190i
$911$	3.23820	+	2.35269i	0.107286	+	0.0779482i	0.640135	−	0.768262i	$-0.278878\pi$
$911$	3.23820	+	2.35269i	0.107286	+	0.0779482i	−0.532848	+	0.846211i	$0.678878\pi$
$912$	−0.846443	+	0.614977i	−0.0280285	+	0.0203639i
$913$	14.5819	−	44.8783i	0.482589	−	1.48526i
$914$	0.449392	−	0.326502i	0.0148646	−	0.0107997i
$915$	−2.00489	+	1.45664i	−0.0662797	+	0.0481550i
$916$	−4.76647	+	14.6697i	−0.157488	+	0.484700i
$917$	10.7501	−	7.81038i	0.354998	−	0.257921i
$918$	−0.599960	−	0.435897i	−0.0198016	−	0.0143867i
$919$	8.08184	+	24.8734i	0.266595	+	0.820496i	0.991322	+	0.131459i	$0.0419663\pi$
$919$	8.08184	+	24.8734i	0.266595	+	0.820496i	−0.724726	+	0.689037i	$0.758034\pi$
$920$	−0.569438	−	0.413721i	−0.0187738	−	0.0136400i
$921$	−6.91909	+	21.2948i	−0.227992	+	0.701687i
$922$	−0.123859	+	0.381199i	−0.00407908	+	0.0125541i
$923$	7.48067	+	23.0231i	0.246229	+	0.757816i
$924$	−6.34549			−0.208751
$925$	−32.8826			−1.08117
$926$	−0.377376	−	1.16144i	−0.0124014	−	0.0381674i
$927$	4.75999	−	3.45833i	0.156339	−	0.113587i
$928$	−9.05891	−	6.58169i	−0.297373	−	0.216054i
$929$	24.8746			0.816108			0.408054	−	0.912958i	$-0.366207\pi$
$929$	24.8746			0.816108			0.408054	+	0.912958i	$0.366207\pi$
$930$	−0.257886	−	0.297519i	−0.00845641	−	0.00975603i
$931$	1.81328			0.0594280
$932$	−25.8671	−	18.7936i	−0.847305	−	0.615603i
$933$	24.2082	−	17.5883i	0.792541	−	0.575815i
$934$	−0.0301149	−	0.0926840i	−0.000985388	−	0.00303271i
$935$	−5.40398			−0.176729
$936$	2.00467			0.0655247
$937$	−13.8591	−	42.6539i	−0.452757	−	1.39344i	−0.873749	−	0.486377i	$-0.838318\pi$
$937$	−13.8591	−	42.6539i	−0.452757	−	1.39344i	0.420992	−	0.907064i	$-0.361682\pi$
$938$	0.301137	−	0.926804i	0.00983247	−	0.0302612i
$939$	−5.36984	+	16.5267i	−0.175238	+	0.539327i
$940$	−3.45129	−	2.50751i	−0.112569	−	0.0817860i
$941$	−0.158614	−	0.488163i	−0.00517066	−	0.0159136i	0.948438	−	0.316963i	$-0.102663\pi$
$941$	−0.158614	−	0.488163i	−0.00517066	−	0.0159136i	−0.953609	+	0.301049i	$0.902663\pi$
$942$	−1.60991	−	1.16967i	−0.0524536	−	0.0381098i
$943$	18.2990	−	13.2950i	0.595896	−	0.432944i
$944$	7.14549	−	21.9916i	0.232566	−	0.715764i
$945$	−0.197097	+	0.143199i	−0.00641156	+	0.00465827i
$946$	−1.58778	+	1.15359i	−0.0516231	+	0.0375064i
$947$	4.03005	−	12.4032i	0.130959	−	0.403050i	−0.863981	−	0.503525i	$-0.832036\pi$
$947$	4.03005	−	12.4032i	0.130959	−	0.403050i	0.994940	+	0.100475i	$0.0320362\pi$
$948$	9.52041	−	6.91698i	0.309209	−	0.224653i
$949$	13.3981	+	9.73427i	0.434920	+	0.315988i
$950$	0.0883016	+	0.271764i	0.00286488	+	0.00881720i
$951$	−17.7866	−	12.9227i	−0.576771	−	0.419049i
$952$	−0.652988	+	2.00969i	−0.0211635	+	0.0651345i
$953$	6.76088	−	20.8079i	0.219006	−	0.674032i	−0.779838	−	0.625981i	$-0.784699\pi$
$953$	6.76088	−	20.8079i	0.219006	−	0.674032i	0.998845	−	0.0480516i	$-0.0153012\pi$
$954$	0.751442	+	2.31270i	0.0243288	+	0.0748764i
$955$	−2.56308			−0.0829393
$956$	−58.0084			−1.87612
$957$	−6.39715	−	19.6884i	−0.206791	−	0.636436i
$958$	2.58038	−	1.87475i	0.0833681	−	0.0605705i
$959$	−10.2026	−	7.41261i	−0.329458	−	0.239366i
$960$	2.35772			0.0760949
$961$	−4.40185	+	30.6859i	−0.141995	+	0.989867i
$962$	−3.41039			−0.109956
$963$	6.09618	+	4.42914i	0.196447	+	0.142727i
$964$	36.5244	−	26.5365i	1.17637	−	0.854684i
$965$	2.14990	+	6.61672i	0.0692078	+	0.213000i
$966$	−0.378806			−0.0121879
$967$	23.4563			0.754303			0.377152	−	0.926152i	$-0.376904\pi$
$967$	23.4563			0.754303			0.377152	+	0.926152i	$0.376904\pi$
$968$	−2.37248	−	7.30174i	−0.0762543	−	0.234687i
$969$	−0.306682	+	0.943869i	−0.00985204	+	0.0303215i
$970$	−0.365294	+	1.12426i	−0.0117289	+	0.0360978i
$971$	−35.6422	−	25.8956i	−1.14381	−	0.831028i	−0.156166	−	0.987731i	$-0.549914\pi$
$971$	−35.6422	−	25.8956i	−1.14381	−	0.831028i	−0.987646	+	0.156703i	$0.949914\pi$
$972$	0.604528	+	1.86055i	0.0193903	+	0.0596771i
$973$	4.29138	+	3.11787i	0.137575	+	0.0999542i
$974$	−0.742347	+	0.539347i	−0.0237863	+	0.0172818i
$975$	−3.65922	+	11.2619i	−0.117189	+	0.360670i
$976$	22.1653	−	16.1040i	0.709493	−	0.515477i
$977$	30.9390	−	22.4785i	0.989828	−	0.719152i	0.0299443	−	0.999552i	$-0.490467\pi$
$977$	30.9390	−	22.4785i	0.989828	−	0.719152i	0.959883	+	0.280400i	$0.0904670\pi$
$978$	−0.334385	+	1.02913i	−0.0106925	+	0.0329080i
$979$	22.0202	−	15.9986i	0.703770	−	0.511319i
$980$	−3.46980	−	2.52096i	−0.110839	−	0.0805290i
$981$	−2.28493	−	7.03230i	−0.0729522	−	0.224524i
$982$	1.26117	+	0.916293i	0.0402455	+	0.0292401i
$983$	8.30309	−	25.5543i	0.264827	−	0.815055i	−0.726906	−	0.686737i	$-0.759042\pi$
$983$	8.30309	−	25.5543i	0.264827	−	0.815055i	0.991733	−	0.128318i	$-0.0409577\pi$
$984$	2.29785	−	7.07204i	0.0732527	−	0.225449i
$985$	−0.580306	−	1.78600i	−0.0184901	−	0.0569067i
$986$	−3.40885			−0.108560
$987$	−4.64309			−0.147791
$988$	−0.409932	−	1.26164i	−0.0130417	−	0.0401382i
$989$	4.24275	−	3.08254i	0.134912	−	0.0980190i
$990$	−0.257653	−	0.187196i	−0.00818876	−	0.00594948i
$991$	35.4899			1.12737			0.563686	−	0.825989i	$-0.309383\pi$
$991$	35.4899			1.12737			0.563686	+	0.825989i	$0.309383\pi$
$992$	8.88354	+	10.2488i	0.282053	+	0.325400i
$993$	22.4720			0.713128
$994$	−1.21664	−	0.883937i	−0.0385893	−	0.0280368i
$995$	−1.51610	+	1.10151i	−0.0480635	+	0.0349202i
$996$	6.33412	+	19.4944i	0.200704	+	0.617704i
$997$	−38.4715			−1.21841			−0.609203	−	0.793014i	$-0.708511\pi$
$997$	−38.4715			−1.21841			−0.609203	+	0.793014i	$0.708511\pi$
$998$	6.68468			0.211600
$999$	−2.07985	−	6.40113i	−0.0658036	−	0.202523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.f.a.64.1	yes	8
3.2	odd	2		279.2.i.b.64.2		8
31.4	even	5		2883.2.a.k.1.3		4
31.16	even	5	inner	93.2.f.a.16.1	✓	8
31.27	odd	10		2883.2.a.l.1.3		4
93.35	odd	10		8649.2.a.w.1.2		4
93.47	odd	10		279.2.i.b.109.2		8
93.89	even	10		8649.2.a.x.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.f.a.16.1	✓	8	31.16	even	5	inner
93.2.f.a.64.1	yes	8	1.1	even	1	trivial
279.2.i.b.64.2		8	3.2	odd	2
279.2.i.b.109.2		8	93.47	odd	10
2883.2.a.k.1.3		4	31.4	even	5
2883.2.a.l.1.3		4	31.27	odd	10
8649.2.a.w.1.2		4	93.35	odd	10
8649.2.a.x.1.2		4	93.89	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.169131 - 0.122881i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.604528 - 1.86055i) q^{4} +0.338261 q^{5} -0.209057 q^{6} +(-0.222562 - 0.684977i) q^{7} +(-0.255585 + 0.786610i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.0572103 - 0.0415657i) q^{10} +(1.39169 + 4.28319i) q^{11} +(-1.58268 - 1.14988i) q^{12} +(1.96086 - 1.42465i) q^{13} +(-0.0465282 + 0.143199i) q^{14} +(0.273659 - 0.198825i) q^{15} +(-3.02547 + 2.19813i) q^{16} +(-1.09618 + 3.37370i) q^{17} +(-0.169131 + 0.122881i) q^{18} +(0.226341 + 0.164446i) q^{19} +(-0.204489 - 0.629351i) q^{20} +(-0.582676 - 0.423339i) q^{21} +(0.290943 - 0.895431i) q^{22} +(-0.777438 + 2.39271i) q^{23} +(0.255585 + 0.786610i) q^{24} -4.88558 q^{25} -0.506704 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.13989 + 0.828176i) q^{28} +(-3.71878 - 2.70185i) q^{29} -0.0707158 q^{30} +(3.64679 + 4.20725i) q^{31} +2.43599 q^{32} +(3.64350 + 2.64716i) q^{33} +(0.599960 - 0.435897i) q^{34} +(-0.0752842 - 0.231701i) q^{35} -1.95630 q^{36} +6.73054 q^{37} +(-0.0180739 - 0.0556258i) q^{38} +(0.748983 - 2.30513i) q^{39} +(-0.0864545 + 0.266080i) q^{40} +(-7.27349 - 5.28450i) q^{41} +(0.0465282 + 0.143199i) q^{42} +(-1.68641 - 1.22525i) q^{43} +(7.12776 - 5.17862i) q^{44} +(0.104528 - 0.321706i) q^{45} +(0.425506 - 0.309148i) q^{46} +(5.21549 - 3.78928i) q^{47} +(-1.15563 + 3.55665i) q^{48} +(5.24346 - 3.80960i) q^{49} +(0.826301 + 0.600343i) q^{50} +(1.09618 + 3.37370i) q^{51} +(-3.83603 - 2.78704i) q^{52} +(3.59444 - 11.0625i) q^{53} +(-0.0646021 + 0.198825i) q^{54} +(0.470756 + 1.44884i) q^{55} +0.595693 q^{56} +0.279773 q^{57} +(0.296955 + 0.913933i) q^{58} +(-5.00234 + 3.63441i) q^{59} +(-0.535358 - 0.388960i) q^{60} -7.32624 q^{61} +(-0.0997949 - 1.15969i) q^{62} -0.720227 q^{63} +(5.63893 + 4.09692i) q^{64} +(0.663284 - 0.481904i) q^{65} +(-0.290943 - 0.895431i) q^{66} -6.47214 q^{67} +6.93960 q^{68} +(0.777438 + 2.39271i) q^{69} +(-0.0157387 + 0.0484387i) q^{70} +(-3.08639 + 9.49894i) q^{71} +(0.669131 + 0.486152i) q^{72} +(2.11143 + 6.49832i) q^{73} +(-1.13834 - 0.827053i) q^{74} +(-3.95252 + 2.87167i) q^{75} +(0.169131 - 0.520530i) q^{76} +(2.62415 - 1.90655i) q^{77} +(-0.409932 + 0.297833i) q^{78} +(-1.85886 + 5.72097i) q^{79} +(-1.02340 + 0.743542i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.580808 + 1.78754i) q^{82} +(-8.47670 - 6.15869i) q^{83} +(-0.435398 + 1.34002i) q^{84} +(-0.370796 + 1.14119i) q^{85} +(0.134665 + 0.414455i) q^{86} -4.59667 q^{87} -3.72490 q^{88} +(-1.86761 - 5.74790i) q^{89} +(-0.0572103 + 0.0415657i) q^{90} +(-1.41227 - 1.02607i) q^{91} +4.92173 q^{92} +(5.42327 + 1.26020i) q^{93} -1.34773 q^{94} +(0.0765624 + 0.0556258i) q^{95} +(1.97076 - 1.43184i) q^{96} +(-5.16565 - 15.8982i) q^{97} -1.35495 q^{98} +4.50361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9} - 11 q^{10} - 4 q^{11} - 2 q^{12} - 3 q^{13} - 6 q^{14} - 4 q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9 - 11 * q^10 - 4 * q^11 - 2 * q^12 - 3 * q^13 - 6 * q^14 - 4 * q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 + q^20 + 6 * q^21 + 6 * q^22 - 17 * q^23 + 4 * q^24 - 18 * q^25 + 12 * q^26 + 2 * q^27 - 9 * q^28 - 2 * q^29 - 4 * q^30 + 17 * q^31 - q^33 + 4 * q^34 - 3 * q^35 + 2 * q^36 + 8 * q^37 + 8 * q^38 + 3 * q^39 - 7 * q^40 - 5 * q^41 + 6 * q^42 - 19 * q^43 + 24 * q^44 - q^45 - 17 * q^46 - 4 * q^47 - 12 * q^48 + 11 * q^49 + 12 * q^50 - 9 * q^51 - 12 * q^52 + 2 * q^54 + 8 * q^55 - 12 * q^56 + 2 * q^57 + 33 * q^58 - 29 * q^59 - 6 * q^60 + 4 * q^61 + 47 * q^62 - 6 * q^63 + 16 * q^64 + 21 * q^65 - 6 * q^66 - 16 * q^67 + 6 * q^68 + 17 * q^69 - 3 * q^70 + 37 * q^71 + q^72 + 3 * q^73 - 2 * q^74 + 3 * q^75 - 3 * q^76 + 18 * q^77 - 27 * q^78 - 3 * q^79 - 24 * q^80 - 2 * q^81 + 35 * q^82 - 31 * q^83 - 6 * q^84 - 8 * q^85 - 44 * q^86 - 18 * q^87 - 8 * q^88 + 19 * q^89 - 11 * q^90 - 24 * q^91 + 2 * q^92 + 13 * q^93 - 94 * q^94 - 16 * q^95 + 20 * q^96 - 3 * q^97 - 34 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more