LMFDB - Embedded newform 546.2.bn.f.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.f.173.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.23327 - 1.21616i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.567570 + 0.327687i) q^{5} +(-0.436593 - 1.67612i) q^{6} +(-2.19987 - 1.46989i) q^{7} -1.00000 q^{8} +(0.0419009 - 2.99971i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.23327 - 1.21616i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.567570 + 0.327687i) q^{5} +(-0.436593 - 1.67612i) q^{6} +(-2.19987 - 1.46989i) q^{7} -1.00000 q^{8} +(0.0419009 - 2.99971i) q^{9} +0.655374i q^{10} +3.09310 q^{11} +(-1.66986 - 0.459961i) q^{12} +(-3.50535 - 0.844105i) q^{13} +(-2.37289 + 1.17020i) q^{14} +(-0.301446 + 1.09438i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.51142 - 6.08195i) q^{17} +(-2.57687 - 1.53614i) q^{18} +6.51944 q^{19} +(0.567570 + 0.327687i) q^{20} +(-4.50065 + 0.862636i) q^{21} +(1.54655 - 2.67870i) q^{22} +(-1.24301 - 0.717651i) q^{23} +(-1.23327 + 1.21616i) q^{24} +(-2.28524 + 3.95816i) q^{25} +(-2.48369 + 2.61367i) q^{26} +(-3.59645 - 3.75040i) q^{27} +(-0.173023 + 2.64009i) q^{28} +(3.89073 - 2.24631i) q^{29} +(0.797041 + 0.808252i) q^{30} +(-2.26475 + 3.92266i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.81462 - 3.76171i) q^{33} -7.02284 q^{34} +(1.73024 + 0.113395i) q^{35} +(-2.61877 + 1.46357i) q^{36} +(2.56676 + 1.48192i) q^{37} +(3.25972 - 5.64600i) q^{38} +(-5.34961 + 3.22207i) q^{39} +(0.567570 - 0.327687i) q^{40} +(7.52039 - 4.34190i) q^{41} +(-1.50326 + 4.32900i) q^{42} +(-0.0380219 + 0.0658559i) q^{43} +(-1.54655 - 2.67870i) q^{44} +(0.959183 + 1.71628i) q^{45} +(-1.24301 + 0.717651i) q^{46} +(8.04448 - 4.64448i) q^{47} +(0.436593 + 1.67612i) q^{48} +(2.67887 + 6.46712i) q^{49} +(2.28524 + 3.95816i) q^{50} +(-11.7272 - 3.23023i) q^{51} +(1.02166 + 3.45778i) q^{52} +(9.68544 + 5.59189i) q^{53} +(-5.04617 + 1.23942i) q^{54} +(-1.75555 + 1.01357i) q^{55} +(2.19987 + 1.46989i) q^{56} +(8.04022 - 7.92869i) q^{57} -4.49263i q^{58} +(-6.13025 + 3.53930i) q^{59} +(1.09849 - 0.286132i) q^{60} +15.3529i q^{61} +(2.26475 + 3.92266i) q^{62} +(-4.50140 + 6.53738i) q^{63} +1.00000 q^{64} +(2.26614 - 0.669569i) q^{65} +(-1.35042 - 5.18441i) q^{66} -3.99636i q^{67} +(-3.51142 + 6.08195i) q^{68} +(-2.40574 + 0.626643i) q^{69} +(0.963325 - 1.44174i) q^{70} +(-0.469521 + 0.813235i) q^{71} +(-0.0419009 + 2.99971i) q^{72} +(5.44642 - 9.43348i) q^{73} +(2.56676 - 1.48192i) q^{74} +(1.99544 + 7.66069i) q^{75} +(-3.25972 - 5.64600i) q^{76} +(-6.80442 - 4.54650i) q^{77} +(0.115588 + 6.24393i) q^{78} +(-1.40194 - 2.42822i) q^{79} -0.655374i q^{80} +(-8.99649 - 0.251381i) q^{81} -8.68380i q^{82} -7.24087i q^{83} +(2.99739 + 3.46636i) q^{84} +(3.98595 + 2.30129i) q^{85} +(0.0380219 + 0.0658559i) q^{86} +(2.06643 - 7.50207i) q^{87} -3.09310 q^{88} +(-9.46532 - 5.46481i) q^{89} +(1.96593 + 0.0274608i) q^{90} +(6.47058 + 7.00939i) q^{91} +1.43530i q^{92} +(1.97755 + 7.59200i) q^{93} -9.28897i q^{94} +(-3.70024 + 2.13634i) q^{95} +(1.66986 + 0.459961i) q^{96} +(8.57395 - 14.8505i) q^{97} +(6.94013 + 0.913591i) q^{98} +(0.129604 - 9.27839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.23327	−	1.21616i	0.712028	−	0.702151i
$3$	1.23327	−	1.21616i	0.712028	−	0.702151i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.567570	+	0.327687i	−0.253825	+	0.146546i	−0.621515	−	0.783403i	$-0.713482\pi$
$5$	−0.567570	+	0.327687i	−0.253825	+	0.146546i	0.367689	+	0.929949i	$0.380149\pi$
$6$	−0.436593	−	1.67612i	−0.178238	−	0.684274i
$7$	−2.19987	−	1.46989i	−0.831473	−	0.555565i
$7$	−2.19987	−	1.46989i	−0.831473	−	0.555565i
$8$	−1.00000			−0.353553
$9$	0.0419009	−	2.99971i	0.0139670	−	0.999902i
$10$			0.655374i			0.207247i
$11$	3.09310			0.932604			0.466302	−	0.884626i	$-0.345586\pi$
$11$	3.09310			0.932604			0.466302	+	0.884626i	$0.345586\pi$
$12$	−1.66986	−	0.459961i	−0.482047	−	0.132779i
$13$	−3.50535	−	0.844105i	−0.972209	−	0.234113i
$13$	−3.50535	−	0.844105i	−0.972209	−	0.234113i
$14$	−2.37289	+	1.17020i	−0.634183	+	0.312750i
$15$	−0.301446	+	1.09438i	−0.0778331	+	0.282569i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.51142	−	6.08195i	−0.851644	−	1.47509i	−0.879724	−	0.475485i	$-0.842273\pi$
$17$	−3.51142	−	6.08195i	−0.851644	−	1.47509i	0.0280801	−	0.999606i	$-0.491061\pi$
$18$	−2.57687	−	1.53614i	−0.607375	−	0.362072i
$19$	6.51944			1.49566			0.747831	−	0.663889i	$-0.231095\pi$
$19$	6.51944			1.49566			0.747831	+	0.663889i	$0.231095\pi$
$20$	0.567570	+	0.327687i	0.126913	+	0.0732730i
$21$	−4.50065	+	0.862636i	−0.982123	+	0.188243i
$22$	1.54655	−	2.67870i	0.329725	−	0.571101i
$23$	−1.24301	−	0.717651i	−0.259185	−	0.149641i	0.364778	−	0.931095i	$-0.381145\pi$
$23$	−1.24301	−	0.717651i	−0.259185	−	0.149641i	−0.623963	+	0.781454i	$0.714478\pi$
$24$	−1.23327	+	1.21616i	−0.251740	+	0.248248i
$25$	−2.28524	+	3.95816i	−0.457049	+	0.791631i
$26$	−2.48369	+	2.61367i	−0.487092	+	0.512583i
$27$	−3.59645	−	3.75040i	−0.692138	−	0.721765i
$28$	−0.173023	+	2.64009i	−0.0326982	+	0.498930i
$29$	3.89073	−	2.24631i	0.722491	−	0.417130i	−0.0931780	−	0.995649i	$-0.529703\pi$
$29$	3.89073	−	2.24631i	0.722491	−	0.417130i	0.815669	+	0.578519i	$0.196369\pi$
$30$	0.797041	+	0.808252i	0.145519	+	0.147566i
$31$	−2.26475	+	3.92266i	−0.406761	+	0.704531i	−0.994525	−	0.104502i	$-0.966675\pi$
$31$	−2.26475	+	3.92266i	−0.406761	+	0.704531i	0.587763	+	0.809033i	$0.300009\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.81462	−	3.76171i	0.664040	−	0.654829i
$34$	−7.02284			−1.20441
$35$	1.73024	+	0.113395i	0.292465	+	0.0191672i
$36$	−2.61877	+	1.46357i	−0.436462	+	0.243928i
$37$	2.56676	+	1.48192i	0.421972	+	0.243626i	0.695921	−	0.718119i	$-0.254996\pi$
$37$	2.56676	+	1.48192i	0.421972	+	0.243626i	−0.273949	+	0.961744i	$0.588330\pi$
$38$	3.25972	−	5.64600i	0.528796	−	0.915902i
$39$	−5.34961	+	3.22207i	−0.856623	+	0.515944i
$40$	0.567570	−	0.327687i	0.0897408	−	0.0518119i
$41$	7.52039	−	4.34190i	1.17449	−	0.678091i	0.219755	−	0.975555i	$-0.429474\pi$
$41$	7.52039	−	4.34190i	1.17449	−	0.678091i	0.954733	+	0.297465i	$0.0961410\pi$
$42$	−1.50326	+	4.32900i	−0.231958	+	0.667979i
$43$	−0.0380219	+	0.0658559i	−0.00579829	+	0.0100429i	−0.868910	−	0.494970i	$-0.835179\pi$
$43$	−0.0380219	+	0.0658559i	−0.00579829	+	0.0100429i	0.863112	+	0.505013i	$0.168512\pi$
$44$	−1.54655	−	2.67870i	−0.233151	−	0.403829i
$45$	0.959183	+	1.71628i	0.142987	+	0.255847i
$46$	−1.24301	+	0.717651i	−0.183272	+	0.105812i
$47$	8.04448	−	4.64448i	1.17341	−	0.677468i	0.218928	−	0.975741i	$-0.429744\pi$
$47$	8.04448	−	4.64448i	1.17341	−	0.677468i	0.954480	+	0.298273i	$0.0964107\pi$
$48$	0.436593	+	1.67612i	0.0630168	+	0.241927i
$49$	2.67887	+	6.46712i	0.382696	+	0.923874i
$50$	2.28524	+	3.95816i	0.323182	+	0.559768i
$51$	−11.7272	−	3.23023i	−1.64213	−	0.452322i
$52$	1.02166	+	3.45778i	0.141679	+	0.479507i
$53$	9.68544	+	5.59189i	1.33040	+	0.768105i	0.985360	−	0.170484i	$-0.0545332\pi$
$53$	9.68544	+	5.59189i	1.33040	+	0.768105i	0.345037	+	0.938589i	$0.387867\pi$
$54$	−5.04617	+	1.23942i	−0.686697	+	0.168664i
$55$	−1.75555	+	1.01357i	−0.236718	+	0.136669i
$56$	2.19987	+	1.46989i	0.293970	+	0.196422i
$57$	8.04022	−	7.92869i	1.06495	−	1.05018i
$58$		−	4.49263i		−	0.589911i
$59$	−6.13025	+	3.53930i	−0.798091	+	0.460778i	−0.842803	−	0.538222i	$-0.819096\pi$
$59$	−6.13025	+	3.53930i	−0.798091	+	0.460778i	0.0447121	+	0.999000i	$0.485763\pi$
$60$	1.09849	−	0.286132i	0.141814	−	0.0369394i
$61$			15.3529i			1.96574i	0.184299	+	0.982870i	$0.440999\pi$
$61$			15.3529i			1.96574i	−0.184299	+	0.982870i	$0.559001\pi$
$62$	2.26475	+	3.92266i	0.287624	+	0.498179i
$63$	−4.50140	+	6.53738i	−0.567124	+	0.823633i
$64$	1.00000			0.125000
$65$	2.26614	−	0.669569i	0.281080	−	0.0830498i
$66$	−1.35042	−	5.18441i	−0.166226	−	0.638157i
$67$		−	3.99636i		−	0.488233i	−0.969746	−	0.244116i	$-0.921502\pi$
$67$		−	3.99636i		−	0.488233i	0.969746	−	0.244116i	$-0.0784979\pi$
$68$	−3.51142	+	6.08195i	−0.425822	+	0.737545i
$69$	−2.40574	+	0.626643i	−0.289617	+	0.0754389i
$70$	0.963325	−	1.44174i	0.115139	−	0.172321i
$71$	−0.469521	+	0.813235i	−0.0557219	+	0.0965132i	−0.892541	−	0.450967i	$-0.851079\pi$
$71$	−0.469521	+	0.813235i	−0.0557219	+	0.0965132i	0.836819	+	0.547480i	$0.184413\pi$
$72$	−0.0419009	+	2.99971i	−0.00493807	+	0.353519i
$73$	5.44642	−	9.43348i	0.637456	−	1.10411i	−0.348534	−	0.937296i	$-0.613320\pi$
$73$	5.44642	−	9.43348i	0.637456	−	1.10411i	0.985989	−	0.166809i	$-0.0533464\pi$
$74$	2.56676	−	1.48192i	0.298379	−	0.172269i
$75$	1.99544	+	7.66069i	0.230414	+	0.884581i
$76$	−3.25972	−	5.64600i	−0.373915	−	0.647641i
$77$	−6.80442	−	4.54650i	−0.775435	−	0.518122i
$78$	0.115588	+	6.24393i	0.0130878	+	0.706986i
$79$	−1.40194	−	2.42822i	−0.157730	−	0.273197i	0.776320	−	0.630339i	$-0.217084\pi$
$79$	−1.40194	−	2.42822i	−0.157730	−	0.273197i	−0.934050	+	0.357143i	$0.883751\pi$
$80$		−	0.655374i		−	0.0732730i
$81$	−8.99649	−	0.251381i	−0.999610	−	0.0279312i
$82$		−	8.68380i		−	0.958965i
$83$		−	7.24087i		−	0.794789i	−0.917648	−	0.397394i	$-0.869915\pi$
$83$		−	7.24087i		−	0.794789i	0.917648	−	0.397394i	$-0.130085\pi$
$84$	2.99739	+	3.46636i	0.327042	+	0.378211i
$85$	3.98595	+	2.30129i	0.432337	+	0.249610i
$86$	0.0380219	+	0.0658559i	0.00410001	+	0.00710143i
$87$	2.06643	−	7.50207i	0.221545	−	0.804306i
$88$	−3.09310			−0.329725
$89$	−9.46532	−	5.46481i	−1.00332	−	0.579268i	−0.0940927	−	0.995563i	$-0.529995\pi$
$89$	−9.46532	−	5.46481i	−1.00332	−	0.579268i	−0.909230	+	0.416295i	$0.863328\pi$
$90$	1.96593	+	0.0274608i	0.207227	+	0.00289462i
$91$	6.47058	+	7.00939i	0.678302	+	0.734784i
$92$			1.43530i			0.149641i
$93$	1.97755	+	7.59200i	0.205062	+	0.787254i
$94$		−	9.28897i		−	0.958084i
$95$	−3.70024	+	2.13634i	−0.379637	+	0.219183i
$96$	1.66986	+	0.459961i	0.170429	+	0.0469445i
$97$	8.57395	−	14.8505i	0.870553	−	1.50784i	0.00912654	−	0.999958i	$-0.497095\pi$
$97$	8.57395	−	14.8505i	0.870553	−	1.50784i	0.861426	−	0.507883i	$-0.169572\pi$
$98$	6.94013	+	0.913591i	0.701059	+	0.0922866i
$99$	0.129604	−	9.27839i	0.0130256	−	0.932513i
$100$	4.57049			0.457049
$101$	7.44863			0.741166			0.370583	−	0.928799i	$-0.379158\pi$
$101$	7.44863			0.741166			0.370583	+	0.928799i	$0.379158\pi$
$102$	−8.66104	+	8.54090i	−0.857571	+	0.845675i
$103$	−15.3456	+	8.85976i	−1.51204	+	0.872978i	−0.512141	+	0.858901i	$0.671148\pi$
$103$	−15.3456	+	8.85976i	−1.51204	+	0.872978i	−0.999901	+	0.0140769i	$0.995519\pi$
$104$	3.50535	+	0.844105i	0.343728	+	0.0827713i
$105$	2.27176	−	1.96441i	0.221701	−	0.191707i
$106$	9.68544	−	5.59189i	0.940733	−	0.543132i
$107$	15.2360	+	8.79649i	1.47292	+	0.850389i	0.999536	−	0.0304688i	$-0.00970002\pi$
$107$	15.2360	+	8.79649i	1.47292	+	0.850389i	0.473381	+	0.880858i	$0.343033\pi$
$108$	−1.44972	+	4.98982i	−0.139499	+	0.480146i
$109$	8.31249	+	4.79922i	0.796192	+	0.459682i	0.842138	−	0.539262i	$-0.181297\pi$
$109$	8.31249	+	4.79922i	0.796192	+	0.459682i	−0.0459460	+	0.998944i	$0.514630\pi$
$110$			2.02714i			0.193280i
$111$	4.96775	−	1.29399i	0.471518	−	0.122820i
$112$	2.37289	−	1.17020i	0.224217	−	0.110574i
$113$	2.25506	+	1.30196i	0.212138	+	0.122478i	0.602305	−	0.798266i	$-0.294249\pi$
$113$	2.25506	+	1.30196i	0.212138	+	0.122478i	−0.390166	+	0.920744i	$0.627583\pi$
$114$	−2.84634	−	10.9274i	−0.266584	−	1.02344i
$115$	0.940659			0.0877169
$116$	−3.89073	−	2.24631i	−0.361245	−	0.208565i
$117$	−2.67895	+	10.4797i	−0.247669	+	0.968845i
$118$			7.07861i			0.651639i
$119$	−1.21511	+	18.5409i	−0.111389	+	1.69964i
$120$	0.301446	−	1.09438i	0.0275181	−	0.0999031i
$121$	−1.43275			−0.130250
$122$	13.2960	+	7.67646i	1.20377	+	0.694994i
$123$	3.99421	−	14.5007i	0.360145	−	1.30749i
$124$	4.52950			0.406761
$125$		−	6.27225i		−	0.561007i
$126$	3.41084	+	7.16702i	0.303861	+	0.638489i
$127$	−3.11947	−	5.40309i	−0.276808	−	0.479446i	0.693781	−	0.720186i	$-0.255943\pi$
$127$	−3.11947	−	5.40309i	−0.276808	−	0.479446i	−0.970590	+	0.240739i	$0.922610\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.0332002	+	0.127459i	0.00292312	+	0.0112221i
$130$	0.553204	−	2.29732i	0.0485192	−	0.201488i
$131$	−1.86046	−	3.22241i	−0.162549	−	0.281543i	0.773233	−	0.634122i	$-0.218638\pi$
$131$	−1.86046	−	3.22241i	−0.162549	−	0.281543i	−0.935782	+	0.352579i	$0.885305\pi$
$132$	−5.16504	−	1.42270i	−0.449559	−	0.123830i
$133$	−14.3419	−	9.58283i	−1.24360	−	0.830937i
$134$	−3.46095	−	1.99818i	−0.298980	−	0.172616i
$135$	3.27020	+	0.950106i	0.281454	+	0.0817721i
$136$	3.51142	+	6.08195i	0.301102	+	0.521523i
$137$	3.46312	+	5.99830i	0.295874	+	0.512469i	0.975188	−	0.221379i	$-0.0710558\pi$
$137$	3.46312	+	5.99830i	0.295874	+	0.512469i	−0.679314	+	0.733848i	$0.737722\pi$
$138$	−0.660182	+	2.39676i	−0.0561985	+	0.204025i
$139$	2.27775	+	1.31506i	0.193196	+	0.111542i	0.593478	−	0.804850i	$-0.297754\pi$
$139$	2.27775	+	1.31506i	0.193196	+	0.111542i	−0.400282	+	0.916392i	$0.631088\pi$
$140$	−0.766920	−	1.55513i	−0.0648165	−	0.131433i
$141$	4.27256	−	15.5113i	0.359814	−	1.30629i
$142$	0.469521	+	0.813235i	0.0394014	+	0.0682451i
$143$	−10.8424	−	2.61090i	−0.906686	−	0.218334i
$144$	2.57687	+	1.53614i	0.214739	+	0.128012i
$145$	−1.47218	+	2.54988i	−0.122258	+	0.211756i
$146$	−5.44642	−	9.43348i	−0.450749	−	0.780720i
$147$	11.1688	+	4.71775i	0.921190	+	0.389114i
$148$		−	2.96384i		−	0.243626i
$149$	6.06396			0.496779			0.248390	−	0.968660i	$-0.420099\pi$
$149$	6.06396			0.496779			0.248390	+	0.968660i	$0.420099\pi$
$150$	7.63208	+	2.10224i	0.623156	+	0.171647i
$151$	0.715824	+	0.413281i	0.0582530	+	0.0336324i	0.528844	−	0.848719i	$-0.322626\pi$
$151$	0.715824	+	0.413281i	0.0582530	+	0.0336324i	−0.470591	+	0.882352i	$0.655959\pi$
$152$	−6.51944			−0.528796
$153$	−18.3912	+	10.2784i	−1.48684	+	0.830958i
$154$	−7.33959	+	3.61955i	−0.591441	+	0.291671i
$155$		−	2.96852i		−	0.238437i
$156$	5.46519	+	3.02186i	0.437566	+	0.241943i
$157$	5.69728	+	3.28932i	0.454692	+	0.262517i	0.709810	−	0.704393i	$-0.248781\pi$
$157$	5.69728	+	3.28932i	0.454692	+	0.262517i	−0.255118	+	0.966910i	$0.582114\pi$
$158$	−2.80387			−0.223064
$159$	18.7454	−	4.88276i	1.48661	−	0.387228i
$160$	−0.567570	−	0.327687i	−0.0448704	−	0.0259059i
$161$	1.67959	+	3.40582i	0.132370	+	0.268416i
$162$	−4.71595	+	7.66550i	−0.370520	+	0.602258i
$163$			4.46249i			0.349529i	0.984610	+	0.174765i	$0.0559165\pi$
$163$			4.46249i			0.349529i	−0.984610	+	0.174765i	$0.944084\pi$
$164$	−7.52039	−	4.34190i	−0.587244	−	0.339045i
$165$	−0.932402	+	3.38503i	−0.0725874	+	0.263525i
$166$	−6.27078	−	3.62043i	−0.486707	−	0.281000i
$167$	−1.12359	+	0.648707i	−0.0869463	+	0.0501985i	−0.542843	−	0.839834i	$-0.682652\pi$
$167$	−1.12359	+	0.648707i	−0.0869463	+	0.0501985i	0.455896	+	0.890033i	$0.349319\pi$
$168$	4.50065	−	0.862636i	0.347233	−	0.0665538i
$169$	11.5750	+	5.91777i	0.890383	+	0.455213i
$170$	3.98595	−	2.30129i	0.305709	−	0.176501i
$171$	0.273170	−	19.5564i	0.0208899	−	1.49552i
$172$	0.0760439			0.00579829
$173$	−12.6653			−0.962927			−0.481464	−	0.876466i	$-0.659895\pi$
$173$	−12.6653			−0.962927			−0.481464	+	0.876466i	$0.659895\pi$
$174$	−5.46376	−	5.54062i	−0.414207	−	0.420033i
$175$	10.8453	−	5.34839i	0.819826	−	0.404300i
$176$	−1.54655	+	2.67870i	−0.116575	+	0.201915i
$177$	−3.25588	+	11.8203i	−0.244727	+	0.888468i
$178$	−9.46532	+	5.46481i	−0.709456	+	0.409605i
$179$			14.5215i			1.08539i	0.839929	+	0.542696i	$0.182596\pi$
$179$			14.5215i			1.08539i	−0.839929	+	0.542696i	$0.817404\pi$
$180$	1.00675	−	1.68881i	0.0750385	−	0.125877i
$181$		−	3.57257i		−	0.265547i	−0.991146	−	0.132773i	$-0.957612\pi$
$181$		−	3.57257i		−	0.265547i	0.991146	−	0.132773i	$-0.0423883\pi$
$182$	9.30560	−	2.09900i	0.689777	−	0.155588i
$183$	18.6716	+	18.9343i	1.38025	+	1.39966i
$184$	1.24301	+	0.717651i	0.0916358	+	0.0529059i
$185$	−1.94242			−0.142810
$186$	7.56364	+	2.08339i	0.554593	+	0.152762i
$187$	−10.8612	−	18.8121i	−0.794246	−	1.37568i
$188$	−8.04448	−	4.64448i	−0.586704	−	0.338734i
$189$	2.39908	+	13.5368i	0.174507	+	0.984656i
$190$			4.27267i			0.309972i
$191$		−	6.03573i		−	0.436730i	−0.975867	−	0.218365i	$-0.929928\pi$
$191$		−	6.03573i		−	0.436730i	0.975867	−	0.218365i	$-0.0700723\pi$
$192$	1.23327	−	1.21616i	0.0890035	−	0.0877689i
$193$			23.3891i			1.68358i	0.539804	+	0.841791i	$0.318499\pi$
$193$			23.3891i			1.68358i	−0.539804	+	0.841791i	$0.681501\pi$
$194$	−8.57395	−	14.8505i	−0.615574	−	1.06620i
$195$	1.98045	−	3.58175i	0.141823	−	0.256494i
$196$	4.26126	−	5.55353i	0.304375	−	0.396681i
$197$	7.90007	+	13.6833i	0.562857	+	0.974896i	0.997246	+	0.0741708i	$0.0236310\pi$
$197$	7.90007	+	13.6833i	0.562857	+	0.974896i	−0.434389	+	0.900725i	$0.643036\pi$
$198$	−7.97052	−	4.75143i	−0.566440	−	0.337670i
$199$	−21.2181	+	12.2503i	−1.50411	+	0.868401i	−0.504125	+	0.863630i	$0.668185\pi$
$199$	−21.2181	+	12.2503i	−1.50411	+	0.868401i	−0.999989	+	0.00477013i	$0.998482\pi$
$200$	2.28524	−	3.95816i	0.161591	−	0.279884i
$201$	−4.86022	−	4.92858i	−0.342813	−	0.347635i
$202$	3.72432	−	6.45070i	0.262042	−	0.453870i
$203$	−11.8609	−	0.777327i	−0.832475	−	0.0545577i
$204$	3.06612	+	11.7711i	0.214671	+	0.824144i
$205$	−2.84557	+	4.92867i	−0.198743	+	0.344233i
$206$			17.7195i			1.23458i
$207$	−2.20483	+	3.69859i	−0.153246	+	0.257070i
$208$	2.48369	−	2.61367i	0.172213	−	0.181225i
$209$	20.1653			1.39486
$210$	−0.565349	−	2.94961i	−0.0390128	−	0.203542i
$211$	−5.93332	−	10.2768i	−0.408467	−	0.707485i	0.586251	−	0.810129i	$-0.300603\pi$
$211$	−5.93332	−	10.2768i	−0.408467	−	0.707485i	−0.994718	+	0.102644i	$0.967270\pi$
$212$		−	11.1838i		−	0.768105i
$213$	0.409979	+	1.57395i	0.0280913	+	0.107845i
$214$	15.2360	−	8.79649i	1.04151	−	0.601316i
$215$		−	0.0498372i		−	0.00339887i
$216$	3.59645	+	3.75040i	0.244708	+	0.255183i
$217$	10.7480	−	5.30043i	0.729624	−	0.359817i
$218$	8.31249	−	4.79922i	0.562993	−	0.325044i
$219$	−4.75574	−	18.2577i	−0.321363	−	1.23374i
$220$	1.75555	+	1.01357i	0.118359	+	0.0683347i
$221$	7.17494	+	24.2834i	0.482639	+	1.63348i
$222$	1.36325	−	4.94919i	0.0914952	−	0.332168i
$223$	−11.4114	−	19.7652i	−0.764166	−	1.32358i	−0.940686	−	0.339278i	$-0.889817\pi$
$223$	−11.4114	−	19.7652i	−0.764166	−	1.32358i	0.176520	−	0.984297i	$-0.443516\pi$
$224$	0.173023	−	2.64009i	0.0115606	−	0.176398i
$225$	11.7776	+	7.02091i	0.785170	+	0.468061i
$226$	2.25506	−	1.30196i	0.150005	−	0.0866052i
$227$	−9.25285	+	5.34214i	−0.614134	+	0.354570i	−0.774581	−	0.632474i	$-0.782039\pi$
$227$	−9.25285	+	5.34214i	−0.614134	+	0.354570i	0.160448	+	0.987044i	$0.448706\pi$
$228$	−10.8866	−	2.99869i	−0.720980	−	0.198593i
$229$	−1.86852	−	3.23637i	−0.123475	−	0.213865i	0.797661	−	0.603106i	$-0.206071\pi$
$229$	−1.86852	−	3.23637i	−0.123475	−	0.213865i	−0.921136	+	0.389241i	$0.872737\pi$
$230$	0.470330	−	0.814635i	0.0310126	−	0.0537154i
$231$	−13.9210	+	2.66822i	−0.915931	+	0.175556i
$232$	−3.89073	+	2.24631i	−0.255439	+	0.147478i
$233$	−7.73067	+	4.46331i	−0.506453	+	0.292401i	−0.731375	−	0.681976i	$-0.761121\pi$
$233$	−7.73067	+	4.46331i	−0.506453	+	0.292401i	0.224921	+	0.974377i	$0.427788\pi$
$234$	7.73618	+	7.55986i	0.505730	+	0.494204i
$235$	−3.04387	+	5.27214i	−0.198560	+	0.343917i
$236$	6.13025	+	3.53930i	0.399046	+	0.230389i
$237$	−4.68208	−	1.28967i	−0.304134	−	0.0837731i
$238$	15.4493	+	10.3228i	1.00143	+	0.669126i
$239$	−2.27619			−0.147234			−0.0736172	−	0.997287i	$-0.523454\pi$
$239$	−2.27619			−0.147234			−0.0736172	+	0.997287i	$0.523454\pi$
$240$	−0.797041	−	0.808252i	−0.0514488	−	0.0521724i
$241$	−2.06620	−	3.57876i	−0.133096	−	0.230528i	0.791773	−	0.610816i	$-0.209158\pi$
$241$	−2.06620	−	3.57876i	−0.133096	−	0.230528i	−0.924868	+	0.380287i	$0.875825\pi$
$242$	−0.716375	+	1.24080i	−0.0460503	+	0.0797615i
$243$	−11.4008	+	10.6312i	−0.731362	+	0.681990i
$244$	13.2960	−	7.67646i	0.851191	−	0.491435i
$245$	−3.63964	−	2.79272i	−0.232528	−	0.178420i
$246$	−10.5609	−	10.7095i	−0.673339	−	0.682810i
$247$	−22.8529	−	5.50309i	−1.45410	−	0.350153i
$248$	2.26475	−	3.92266i	0.143812	−	0.249089i
$249$	−8.80607	−	8.92993i	−0.558062	−	0.565911i
$250$	−5.43192	−	3.13612i	−0.343545	−	0.198346i
$251$	3.75716	−	6.50759i	0.237150	−	0.410756i	−0.722745	−	0.691114i	$-0.757120\pi$
$251$	3.75716	−	6.50759i	0.237150	−	0.410756i	0.959895	+	0.280359i	$0.0904534\pi$
$252$	7.91224	+	0.629640i	0.498424	+	0.0396636i
$253$	−3.84474	−	2.21976i	−0.241717	−	0.139555i
$254$	−6.23895			−0.391466
$255$	7.71449	−	2.00946i	0.483100	−	0.125837i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.6011	−	21.8257i	0.786034	−	1.36145i	−0.142346	−	0.989817i	$-0.545465\pi$
$257$	12.6011	−	21.8257i	0.786034	−	1.36145i	0.928380	−	0.371633i	$-0.121202\pi$
$258$	0.126983	+	0.0349772i	0.00790560	+	0.00217759i
$259$	−3.46829	−	7.03287i	−0.215509	−	0.437001i
$260$	−1.71293	−	1.62775i	−0.106231	−	0.100949i
$261$	−6.57526	−	11.7652i	−0.406999	−	0.728246i
$262$	−3.72092			−0.229879
$263$		−	19.9343i		−	1.22920i	−0.788839	−	0.614600i	$-0.789318\pi$
$263$		−	19.9343i		−	1.22920i	0.788839	−	0.614600i	$-0.210682\pi$
$264$	−3.81462	+	3.76171i	−0.234774	+	0.231517i
$265$	−7.32956			−0.450251
$266$	−15.4699	+	7.62906i	−0.948523	+	0.467768i
$267$	−18.3194	+	4.77179i	−1.12113	+	0.292029i
$268$	−3.46095	+	1.99818i	−0.211411	+	0.122058i
$269$	−10.1070	−	17.5059i	−0.616235	−	1.06735i	−0.990166	−	0.139894i	$-0.955324\pi$
$269$	−10.1070	−	17.5059i	−0.616235	−	1.06735i	0.373931	−	0.927456i	$-0.378010\pi$
$270$	2.45792	−	2.35702i	0.149584	−	0.143444i
$271$	−13.2263	+	22.9087i	−0.803442	+	1.39160i	0.113896	+	0.993493i	$0.463667\pi$
$271$	−13.2263	+	22.9087i	−0.803442	+	1.39160i	−0.917338	+	0.398109i	$0.869667\pi$
$272$	7.02284			0.425822
$273$	16.5045	+	0.775180i	0.998899	+	0.0469160i
$274$	6.92624			0.418429
$275$	−7.06848	+	12.2430i	−0.426245	+	0.738278i
$276$	1.74556	+	1.77011i	0.105070	+	0.106548i
$277$	−1.68490	−	2.91833i	−0.101236	−	0.175346i	0.810958	−	0.585104i	$-0.198946\pi$
$277$	−1.68490	−	2.91833i	−0.101236	−	0.175346i	−0.912194	+	0.409758i	$0.865613\pi$
$278$	2.27775	−	1.31506i	0.136610	−	0.0788719i
$279$	11.6719	+	6.95795i	0.698781	+	0.416562i
$280$	−1.73024	−	0.113395i	−0.103402	−	0.00677662i
$281$	20.1579			1.20252			0.601259	−	0.799055i	$-0.294666\pi$
$281$	20.1579			1.20252			0.601259	+	0.799055i	$0.294666\pi$
$282$	−11.2969	−	11.4558i	−0.672720	−	0.682182i
$283$			6.37936i			0.379214i	0.981860	+	0.189607i	$0.0607214\pi$
$283$			6.37936i			0.379214i	−0.981860	+	0.189607i	$0.939279\pi$
$284$	0.939043			0.0557219
$285$	−1.96526	+	7.13477i	−0.116412	+	0.422627i
$286$	−7.68230	+	8.08434i	−0.454264	+	0.478037i
$287$	−22.9260	−	1.50249i	−1.35328	−	0.0886895i
$288$	2.61877	−	1.46357i	0.154313	−	0.0862415i
$289$	−16.1601	+	27.9901i	−0.950594	+	1.64648i
$290$	1.47218	+	2.54988i	0.0864492	+	0.149734i
$291$	−7.48665	−	28.7420i	−0.438875	−	1.68488i
$292$	−10.8928			−0.637456
$293$	−5.30689	−	3.06394i	−0.310032	−	0.178997i	0.336909	−	0.941537i	$-0.390619\pi$
$293$	−5.30689	−	3.06394i	−0.310032	−	0.178997i	−0.646941	+	0.762540i	$0.723952\pi$
$294$	9.67011	−	7.31361i	0.563972	−	0.426539i
$295$	2.31957	−	4.01761i	0.135050	−	0.233914i
$296$	−2.56676	−	1.48192i	−0.149190	−	0.0861347i
$297$	−11.1242	−	11.6004i	−0.645491	−	0.673121i
$298$	3.03198	−	5.25155i	0.175638	−	0.304214i
$299$	3.75141	+	3.56485i	0.216949	+	0.206160i
$300$	5.63663	−	5.55845i	0.325431	−	0.320917i
$301$	0.180444	−	0.0889867i	0.0104006	−	0.00512911i
$302$	0.715824	−	0.413281i	0.0411911	−	0.0237817i
$303$	9.18616	−	9.05874i	0.527731	−	0.520411i
$304$	−3.25972	+	5.64600i	−0.186958	+	0.323820i
$305$	−5.03095	−	8.71387i	−0.288072	−	0.498955i
$306$	−0.294263	+	21.0665i	−0.0168219	+	1.20429i
$307$	−5.38161			−0.307145			−0.153572	−	0.988137i	$-0.549078\pi$
$307$	−5.38161			−0.307145			−0.153572	+	0.988137i	$0.549078\pi$
$308$	−0.535176	+	8.16605i	−0.0304945	+	0.465304i
$309$	−8.15028	+	29.5891i	−0.463653	+	1.68327i
$310$	−2.57081	−	1.48426i	−0.146012	−	0.0843002i
$311$	−3.15077	+	5.45729i	−0.178664	+	0.309454i	−0.941423	−	0.337228i	$-0.890511\pi$
$311$	−3.15077	+	5.45729i	−0.178664	+	0.309454i	0.762759	+	0.646682i	$0.223844\pi$
$312$	5.34961	−	3.22207i	0.302862	−	0.182414i
$313$	−9.08951	+	5.24783i	−0.513770	+	0.296625i	−0.734382	−	0.678737i	$-0.762528\pi$
$313$	−9.08951	+	5.24783i	−0.513770	+	0.296625i	0.220612	+	0.975362i	$0.429194\pi$
$314$	5.69728	−	3.28932i	0.321516	−	0.185627i
$315$	0.412649	−	5.18548i	0.0232502	−	0.292168i
$316$	−1.40194	+	2.42822i	−0.0788651	+	0.136598i
$317$	0.443737	+	0.768575i	0.0249227	+	0.0431674i	0.878218	−	0.478261i	$-0.158733\pi$
$317$	0.443737	+	0.768575i	0.0249227	+	0.0431674i	−0.853295	+	0.521428i	$0.825399\pi$
$318$	5.14410	−	18.6754i	0.288467	−	1.04726i
$319$	12.0344	−	6.94807i	0.673798	−	0.389017i
$320$	−0.567570	+	0.327687i	−0.0317282	+	0.0183183i
$321$	29.4880	−	7.68097i	1.64586	−	0.428710i
$322$	3.78932	+	0.248340i	0.211171	+	0.0138394i
$323$	−22.8925	−	39.6509i	−1.27377	−	2.20624i
$324$	4.28054	+	7.91688i	0.237808	+	0.439827i
$325$	11.3517	−	11.9457i	0.629678	−	0.662631i
$326$	3.86463	+	2.23125i	0.214042	+	0.123577i
$327$	16.0882	−	4.19061i	0.889677	−	0.231741i
$328$	−7.52039	+	4.34190i	−0.415244	+	0.239741i
$329$	−24.5237	−	1.60720i	−1.35203	−	0.0886080i
$330$	2.46532	+	2.50000i	0.135712	+	0.137621i
$331$			19.3126i			1.06152i	0.847523	+	0.530759i	$0.178093\pi$
$331$			19.3126i			1.06152i	−0.847523	+	0.530759i	$0.821907\pi$
$332$	−6.27078	+	3.62043i	−0.344154	+	0.198697i
$333$	4.55287	−	7.63743i	0.249496	−	0.418528i
$334$			1.29741i			0.0709914i
$335$	1.30955	+	2.26821i	0.0715486	+	0.123926i
$336$	1.50326	−	4.32900i	0.0820096	−	0.236166i
$337$	−1.76473			−0.0961307			−0.0480654	−	0.998844i	$-0.515306\pi$
$337$	−1.76473			−0.0961307			−0.0480654	+	0.998844i	$0.515306\pi$
$338$	10.9124	−	7.06534i	0.593558	−	0.384304i
$339$	4.36449	−	1.13685i	0.237047	−	0.0617454i
$340$		−	4.60258i		−	0.249610i
$341$	−7.00509	+	12.1332i	−0.379347	+	0.657048i
$342$	−16.7998	−	10.0148i	−0.908427	−	0.541537i
$343$	3.61276	−	18.1645i	0.195071	−	0.980789i
$344$	0.0380219	−	0.0658559i	0.00205001	−	0.00355071i
$345$	1.16009	−	1.14399i	0.0624569	−	0.0615906i
$346$	−6.33267	+	10.9685i	−0.340446	+	0.589670i
$347$	−19.6675	+	11.3550i	−1.05580	+	0.609569i	−0.924269	−	0.381742i	$-0.875324\pi$
$347$	−19.6675	+	11.3550i	−1.05580	+	0.609569i	−0.131536	+	0.991311i	$0.541991\pi$
$348$	−7.53020	+	1.96145i	−0.403661	+	0.105145i
$349$	0.756268	+	1.30990i	0.0404821	+	0.0701171i	0.885557	−	0.464532i	$-0.153777\pi$
$349$	0.756268	+	1.30990i	0.0404821	+	0.0701171i	−0.845074	+	0.534649i	$0.820444\pi$
$350$	0.790798	−	12.0665i	0.0422699	−	0.644981i
$351$	9.44110	+	16.1823i	0.503929	+	0.863745i
$352$	1.54655	+	2.67870i	0.0824313	+	0.142775i
$353$			32.6049i			1.73538i	0.497102	+	0.867692i	$0.334397\pi$
$353$			32.6049i			1.73538i	−0.497102	+	0.867692i	$0.665603\pi$
$354$	8.60873	+	8.72982i	0.457549	+	0.463985i
$355$		−	0.615424i		−	0.0326633i
$356$			10.9296i			0.579268i
$357$	21.0502	+	24.3437i	1.11409	+	1.28840i
$358$	12.5760	+	7.26077i	0.664664	+	0.383744i
$359$	−3.19150	−	5.52784i	−0.168441	−	0.291748i	0.769431	−	0.638730i	$-0.220540\pi$
$359$	−3.19150	−	5.52784i	−0.168441	−	0.291748i	−0.937872	+	0.346982i	$0.887207\pi$
$360$	−0.959183	−	1.71628i	−0.0505534	−	0.0904557i
$361$	23.5031			1.23700
$362$	−3.09394	−	1.78628i	−0.162614	−	0.0938850i
$363$	−1.76696	+	1.74246i	−0.0927416	+	0.0914552i
$364$	2.83502	−	9.10839i	0.148595	−	0.477409i
$365$			7.13889i			0.373666i
$366$	25.7334	−	6.70298i	1.34511	−	0.350370i
$367$		−	12.0233i		−	0.627609i	−0.949488	−	0.313804i	$-0.898396\pi$
$367$		−	12.0233i		−	0.627609i	0.949488	−	0.313804i	$-0.101604\pi$
$368$	1.24301	−	0.717651i	0.0647963	−	0.0374101i
$369$	−12.7093	−	22.7409i	−0.661620	−	1.18384i
$370$	−0.971210	+	1.68219i	−0.0504908	+	0.0874527i
$371$	−13.0873	−	26.5379i	−0.679458	−	1.37778i
$372$	5.58609	−	5.50861i	0.289625	−	0.285608i
$373$	−21.7112			−1.12416			−0.562081	−	0.827082i	$-0.689999\pi$
$373$	−21.7112			−1.12416			−0.562081	+	0.827082i	$0.689999\pi$
$374$	−21.7223			−1.12323
$375$	−7.62807	−	7.73536i	−0.393912	−	0.399452i
$376$	−8.04448	+	4.64448i	−0.414863	+	0.239521i
$377$	−15.5345	+	4.58994i	−0.800068	+	0.236394i
$378$	12.9227	+	4.69073i	0.664674	+	0.241265i
$379$	−2.54234	+	1.46782i	−0.130591	+	0.0753970i	−0.563873	−	0.825862i	$-0.690689\pi$
$379$	−2.54234	+	1.46782i	−0.130591	+	0.0753970i	0.433281	+	0.901259i	$0.357356\pi$
$380$	3.70024	+	2.13634i	0.189818	+	0.109592i
$381$	−10.4182	−	2.86967i	−0.533739	−	0.147018i
$382$	−5.22709	−	3.01786i	−0.267441	−	0.154407i
$383$			30.1694i			1.54159i	0.637085	+	0.770793i	$0.280140\pi$
$383$			30.1694i			1.54159i	−0.637085	+	0.770793i	$0.719860\pi$
$384$	−0.436593	−	1.67612i	−0.0222798	−	0.0855343i
$385$	5.35181	+	0.350741i	0.272754	+	0.0178754i
$386$	20.2555	+	11.6945i	1.03098	+	0.595236i
$387$	0.195955	+	0.116814i	0.00996097	+	0.00593800i
$388$	−17.1479			−0.870553
$389$	−19.1621	−	11.0633i	−0.971559	−	0.560930i	−0.0718481	−	0.997416i	$-0.522890\pi$
$389$	−19.1621	−	11.0633i	−0.971559	−	0.560930i	−0.899711	+	0.436485i	$0.856223\pi$
$390$	−2.11166	−	3.50599i	−0.106928	−	0.177533i
$391$			10.0799i			0.509762i
$392$	−2.67887	−	6.46712i	−0.135303	−	0.326639i
$393$	−6.21342	−	1.71148i	−0.313425	−	0.0863325i
$394$	15.8001			0.795999
$395$	1.59139	+	0.918792i	0.0800718	+	0.0462295i
$396$	−8.10012	+	4.52695i	−0.407046	+	0.227488i
$397$	13.0811			0.656519			0.328260	−	0.944588i	$-0.393538\pi$
$397$	13.0811			0.656519			0.328260	+	0.944588i	$0.393538\pi$
$398$			24.5006i			1.22810i
$399$	−29.3417	+	5.62390i	−1.46892	+	0.281547i
$400$	−2.28524	−	3.95816i	−0.114262	−	0.197908i
$401$	−3.46329	+	5.99859i	−0.172948	+	0.299555i	−0.939449	−	0.342688i	$-0.888663\pi$
$401$	−3.46329	+	5.99859i	−0.172948	+	0.299555i	0.766501	+	0.642243i	$0.221996\pi$
$402$	−6.69838	+	1.74478i	−0.334085	+	0.0870218i
$403$	11.2499	−	11.8386i	0.560397	−	0.589724i
$404$	−3.72432	−	6.45070i	−0.185292	−	0.320934i
$405$	5.18852	−	2.80536i	0.257819	−	0.139399i
$406$	−6.60365	+	9.88321i	−0.327734	+	0.490495i
$407$	7.93923	+	4.58372i	0.393533	+	0.227206i
$408$	11.7272	+	3.23023i	0.580581	+	0.159920i
$409$	16.3397	+	28.3011i	0.807944	+	1.39940i	0.914286	+	0.405070i	$0.132753\pi$
$409$	16.3397	+	28.3011i	0.807944	+	1.39940i	−0.106342	+	0.994330i	$0.533914\pi$
$410$	2.84557	+	4.92867i	0.140533	+	0.243410i
$411$	11.5659	+	3.18580i	0.570501	+	0.157144i
$412$	15.3456	+	8.85976i	0.756021	+	0.436489i
$413$	18.6881	+	1.22476i	0.919584	+	0.0602665i
$414$	2.10066	+	3.75873i	0.103242	+	0.184732i
$415$	2.37274	+	4.10970i	0.116473	+	0.201737i
$416$	−1.02166	−	3.45778i	−0.0500910	−	0.169531i
$417$	4.40839	−	1.14829i	0.215880	−	0.0562319i
$418$	10.0826	−	17.4636i	0.493158	−	0.854174i
$419$	−3.98319	−	6.89908i	−0.194591	−	0.337042i	0.752175	−	0.658963i	$-0.229005\pi$
$419$	−3.98319	−	6.89908i	−0.194591	−	0.337042i	−0.946766	+	0.321921i	$0.895671\pi$
$420$	−2.83711	−	0.985198i	−0.138437	−	0.0480727i
$421$		−	14.1689i		−	0.690552i	−0.938501	−	0.345276i	$-0.887785\pi$
$421$		−	14.1689i		−	0.690552i	0.938501	−	0.345276i	$-0.112215\pi$
$422$	−11.8666			−0.577659
$423$	−13.5950	−	24.3257i	−0.661013	−	1.18276i
$424$	−9.68544	−	5.59189i	−0.470366	−	0.271566i
$425$	32.0978			1.55697
$426$	1.56807	+	0.431923i	0.0759733	+	0.0209267i
$427$	22.5670	−	33.7745i	1.09210	−	1.63446i
$428$		−	17.5930i		−	0.850389i
$429$	−16.5469	+	9.96616i	−0.798890	+	0.481171i
$430$	−0.0431603	−	0.0249186i	−0.00208137	−	0.00120168i
$431$	25.9443			1.24969			0.624845	−	0.780749i	$-0.285162\pi$
$431$	25.9443			1.24969			0.624845	+	0.780749i	$0.285162\pi$
$432$	5.04617	−	1.23942i	0.242784	−	0.0596316i
$433$	14.7383	+	8.50919i	0.708280	+	0.408925i	0.810424	−	0.585844i	$-0.199237\pi$
$433$	14.7383	+	8.50919i	0.708280	+	0.408925i	−0.102144	+	0.994770i	$0.532570\pi$
$434$	0.783707	−	11.9583i	0.0376191	−	0.574016i
$435$	1.28548	+	4.93510i	0.0616342	+	0.236620i
$436$		−	9.59843i		−	0.459682i
$437$	−8.10372	−	4.67868i	−0.387653	−	0.223812i
$438$	−18.1895	−	5.01028i	−0.869130	−	0.239400i
$439$	25.6542	+	14.8115i	1.22441	+	0.706912i	0.965855	−	0.259084i	$-0.0834208\pi$
$439$	25.6542	+	14.8115i	1.22441	+	0.706912i	0.258554	+	0.965997i	$0.416754\pi$
$440$	1.75555	−	1.01357i	0.0836926	−	0.0483199i
$441$	19.5117	−	7.76485i	0.929129	−	0.369755i
$442$	24.6175	+	5.92801i	1.17094	+	0.281967i
$443$	15.3962	−	8.88898i	0.731494	−	0.422328i	−0.0874748	−	0.996167i	$-0.527880\pi$
$443$	15.3962	−	8.88898i	0.731494	−	0.422328i	0.818968	+	0.573839i	$0.194546\pi$
$444$	−3.60450	−	3.65520i	−0.171062	−	0.173468i
$445$	7.16298			0.339558
$446$	−22.8229			−1.08069
$447$	7.47850	−	7.37476i	0.353721	−	0.348814i
$448$	−2.19987	−	1.46989i	−0.103934	−	0.0694456i
$449$	11.2383	−	19.4653i	0.530369	−	0.918626i	−0.469003	−	0.883197i	$-0.655387\pi$
$449$	11.2383	−	19.4653i	0.530369	−	0.918626i	0.999372	−	0.0354297i	$-0.0112800\pi$
$450$	11.9691	−	6.68921i	0.564227	−	0.315332i
$451$	23.2613	−	13.4299i	1.09533	−	0.632390i
$452$		−	2.60392i		−	0.122478i
$453$	1.38542	−	0.360871i	0.0650927	−	0.0169552i
$454$			10.6843i			0.501438i
$455$	−5.96940	−	1.85800i	−0.279850	−	0.0871042i
$456$	−8.04022	+	7.92869i	−0.376518	+	0.371295i
$457$	22.9216	+	13.2338i	1.07223	+	0.619051i	0.928790	−	0.370608i	$-0.120851\pi$
$457$	22.9216	+	13.2338i	1.07223	+	0.619051i	0.143439	+	0.989659i	$0.454184\pi$
$458$	−3.73704			−0.174620
$459$	−10.1811	+	35.0427i	−0.475214	+	1.63565i
$460$	−0.470330	−	0.814635i	−0.0219292	−	0.0379826i
$461$	6.02929	+	3.48101i	0.280812	+	0.162127i	0.633791	−	0.773504i	$-0.281498\pi$
$461$	6.02929	+	3.48101i	0.280812	+	0.162127i	−0.352979	+	0.935631i	$0.614831\pi$
$462$	−4.64973	+	13.3900i	−0.216325	+	0.622959i
$463$			10.3837i			0.482572i	0.970454	+	0.241286i	$0.0775692\pi$
$463$			10.3837i			0.482572i	−0.970454	+	0.241286i	$0.922431\pi$
$464$			4.49263i			0.208565i
$465$	−3.61020	−	3.66098i	−0.167419	−	0.169774i
$466$			8.92661i			0.413517i
$467$	−11.7463	−	20.3453i	−0.543556	−	0.941467i	−0.998696	−	0.0510470i	$-0.983744\pi$
$467$	−11.7463	−	20.3453i	−0.543556	−	0.941467i	0.455140	−	0.890420i	$-0.349589\pi$
$468$	10.4151	−	2.91979i	0.481439	−	0.134968i
$469$	−5.87419	+	8.79147i	−0.271245	+	0.405953i
$470$	3.04387	+	5.27214i	0.140403	+	0.243186i
$471$	11.0266	−	2.87219i	0.508080	−	0.132344i
$472$	6.13025	−	3.53930i	0.282168	−	0.162910i
$473$	−0.117606	+	0.203699i	−0.00540751	+	0.00936608i
$474$	−3.45793	+	3.40996i	−0.158828	+	0.156625i
$475$	−14.8985	+	25.8050i	−0.683590	+	1.18401i
$476$	16.6644	−	8.21813i	0.763814	−	0.376678i
$477$	17.1799	−	28.8192i	0.786612	−	1.31954i
$478$	−1.13809	+	1.97124i	−0.0520552	+	0.0901623i
$479$			8.56011i			0.391121i	0.980692	+	0.195561i	$0.0626527\pi$
$479$			8.56011i			0.391121i	−0.980692	+	0.195561i	$0.937347\pi$
$480$	−1.09849	+	0.286132i	−0.0501388	+	0.0130601i
$481$	−7.74649	−	7.36126i	−0.353210	−	0.335644i
$482$	−4.13240			−0.188226
$483$	6.21342	+	2.15763i	0.282720	+	0.0981757i
$484$	0.716375	+	1.24080i	0.0325625	+	0.0563999i
$485$			11.2383i			0.510304i
$486$	3.50646	+	15.1890i	0.159056	+	0.688986i
$487$	−15.2194	+	8.78693i	−0.689657	+	0.398174i	−0.803484	−	0.595327i	$-0.797023\pi$
$487$	−15.2194	+	8.78693i	−0.689657	+	0.398174i	0.113826	+	0.993501i	$0.463689\pi$
$488$		−	15.3529i		−	0.694994i
$489$	5.42711	+	5.50345i	0.245422	+	0.248875i
$490$	−4.23838	+	1.75566i	−0.191471	+	0.0793127i
$491$	−7.73222	+	4.46420i	−0.348950	+	0.201467i	−0.664223	−	0.747535i	$-0.731237\pi$
$491$	−7.73222	+	4.46420i	−0.348950	+	0.201467i	0.315273	+	0.949001i	$0.397904\pi$
$492$	−14.5551	+	3.79128i	−0.656195	+	0.170924i
$493$	−27.3240	−	15.7755i	−1.23061	−	0.710493i
$494$	−16.1923	+	17.0397i	−0.728525	+	0.766651i
$495$	2.96685	+	5.30861i	0.133350	+	0.238604i
$496$	−2.26475	−	3.92266i	−0.101690	−	0.176133i
$497$	2.22825	−	1.09887i	0.0999506	−	0.0492910i
$498$	−12.1366	+	3.16131i	−0.543853	+	0.141662i
$499$	8.26926	−	4.77426i	0.370183	−	0.213725i	−0.303355	−	0.952877i	$-0.598107\pi$
$499$	8.26926	−	4.77426i	0.370183	−	0.213725i	0.673538	+	0.739152i	$0.264774\pi$
$500$	−5.43192	+	3.13612i	−0.242923	+	0.140252i
$501$	−0.596760	+	2.16650i	−0.0266613	+	0.0967922i
$502$	−3.75716	−	6.50759i	−0.167690	−	0.290448i
$503$	−12.4146	+	21.5027i	−0.553539	+	0.958757i	0.444477	+	0.895790i	$0.353390\pi$
$503$	−12.4146	+	21.5027i	−0.553539	+	0.958757i	−0.998016	+	0.0629667i	$0.979944\pi$
$504$	4.50140	−	6.53738i	0.200508	−	0.291198i
$505$	−4.22762	+	2.44082i	−0.188127	+	0.108615i
$506$	−3.84474	+	2.21976i	−0.170920	+	0.0986806i
$507$	21.4720	−	6.77884i	0.953606	−	0.301059i
$508$	−3.11947	+	5.40309i	−0.138404	+	0.239723i
$509$	−12.5079	−	7.22142i	−0.554402	−	0.320084i	0.196494	−	0.980505i	$-0.437044\pi$
$509$	−12.5079	−	7.22142i	−0.554402	−	0.320084i	−0.750895	+	0.660421i	$0.770378\pi$
$510$	2.11701	−	7.68567i	0.0937427	−	0.340327i
$511$	−25.8476	+	12.7468i	−1.14343	+	0.563886i
$512$	−1.00000			−0.0441942
$513$	−23.4469	−	24.4505i	−1.03520	−	1.07952i
$514$	−12.6011	−	21.8257i	−0.555810	−	0.962691i
$515$	5.80646	−	10.0571i	0.255863	−	0.443168i
$516$	0.0937825	−	0.0924817i	0.00412854	−	0.00407128i
$517$	24.8824	−	14.3658i	1.09433	−	0.631809i
$518$	−7.82479	−	0.512811i	−0.343801	−	0.0225316i
$519$	−15.6197	+	15.4031i	−0.685631	+	0.676121i
$520$	−2.26614	+	0.669569i	−0.0993766	+	0.0293625i
$521$	−15.0954	+	26.1460i	−0.661341	+	1.14548i	0.318923	+	0.947781i	$0.396679\pi$
$521$	−15.0954	+	26.1460i	−0.661341	+	1.14548i	−0.980264	+	0.197695i	$0.936654\pi$
$522$	−13.4766	−	0.188245i	−0.589854	−	0.00823927i
$523$	13.5050	+	7.79711i	0.590532	+	0.340944i	0.765308	−	0.643665i	$-0.222587\pi$
$523$	13.5050	+	7.79711i	0.590532	+	0.340944i	−0.174776	+	0.984608i	$0.555920\pi$
$524$	−1.86046	+	3.22241i	−0.0812745	+	0.140772i
$525$	6.87063	−	19.7856i	0.299859	−	0.863515i
$526$	−17.2636	−	9.96713i	−0.752728	−	0.434588i
$527$	31.8099			1.38566
$528$	1.35042	+	5.18441i	0.0587697	+	0.225622i
$529$	−10.4700	−	18.1345i	−0.455215	−	0.788456i
$530$	−3.66478	+	6.34758i	−0.159188	+	0.275721i
$531$	10.3600	+	18.5373i	0.449586	+	0.804449i
$532$	−1.12801	+	17.2119i	−0.0489055	+	0.746230i
$533$	−30.0266	+	8.87188i	−1.30060	+	0.384284i
$534$	−5.02719	+	18.2509i	−0.217548	+	0.789795i
$535$	−11.5300			−0.498485
$536$			3.99636i			0.172616i
$537$	17.6605	+	17.9090i	0.762109	+	0.772829i
$538$	−20.2140			−0.871488
$539$	8.28601	+	20.0034i	0.356904	+	0.861609i
$540$	−0.812284	−	3.30713i	−0.0349551	−	0.142316i
$541$	36.0971	−	20.8407i	1.55194	−	0.896011i	0.553953	−	0.832548i	$-0.313119\pi$
$541$	36.0971	−	20.8407i	1.55194	−	0.896011i	0.997984	−	0.0634632i	$-0.0202145\pi$
$542$	13.2263	+	22.9087i	0.568119	+	0.984011i
$543$	−4.34482	−	4.40594i	−0.186454	−	0.189077i
$544$	3.51142	−	6.08195i	0.150551	−	0.260762i
$545$	−6.29056			−0.269458
$546$	8.92358	−	13.9057i	0.381894	−	0.595111i
$547$	−0.933149			−0.0398986			−0.0199493	−	0.999801i	$-0.506350\pi$
$547$	−0.933149			−0.0398986			−0.0199493	+	0.999801i	$0.506350\pi$
$548$	3.46312	−	5.99830i	0.147937	−	0.256235i
$549$	46.0543	+	0.643301i	1.96555	+	0.0274554i
$550$	7.06848	+	12.2430i	0.301401	+	0.522042i
$551$	25.3654	−	14.6447i	1.08060	−	0.623886i
$552$	2.40574	−	0.626643i	0.102395	−	0.0266717i
$553$	−0.485134	+	7.40247i	−0.0206300	+	0.314785i
$554$	−3.36980			−0.143169
$555$	−2.39553	+	2.36230i	−0.101684	+	0.100274i
$556$		−	2.63011i		−	0.111542i
$557$	33.5205			1.42031			0.710155	−	0.704045i	$-0.248625\pi$
$557$	33.5205			1.42031			0.710155	+	0.704045i	$0.248625\pi$
$558$	11.8617	−	6.62923i	0.502147	−	0.280638i
$559$	0.188870	−	0.198754i	0.00798833	−	0.00840638i
$560$	−0.963325	+	1.44174i	−0.0407079	+	0.0609246i
$561$	−36.2732	−	9.99141i	−1.53146	−	0.421838i
$562$	10.0789	−	17.4572i	0.425154	−	0.736388i
$563$	1.93176	+	3.34590i	0.0814138	+	0.141013i	0.903857	−	0.427834i	$-0.140723\pi$
$563$	1.93176	+	3.34590i	0.0814138	+	0.141013i	−0.822444	+	0.568847i	$0.807390\pi$
$564$	−15.5694	+	4.05550i	−0.655592	+	0.170767i
$565$	−1.70654			−0.0717948
$566$	5.52469	+	3.18968i	0.232220	+	0.134072i
$567$	19.4216	+	13.7768i	0.815631	+	0.578572i
$568$	0.469521	−	0.813235i	0.0197007	−	0.0341226i
$569$	23.3163	+	13.4617i	0.977469	+	0.564342i	0.901505	−	0.432769i	$-0.142463\pi$
$569$	23.3163	+	13.4617i	0.977469	+	0.564342i	0.0759636	+	0.997111i	$0.475797\pi$
$570$	5.19626	+	5.26935i	0.217647	+	0.220709i
$571$	5.20460	−	9.01463i	0.217806	−	0.377250i	−0.736331	−	0.676621i	$-0.763443\pi$
$571$	5.20460	−	9.01463i	0.217806	−	0.377250i	0.954137	+	0.299371i	$0.0967768\pi$
$572$	3.16009	+	10.6952i	0.132130	+	0.447190i
$573$	−7.34042	−	7.44367i	−0.306651	−	0.310964i
$574$	−12.7642	+	19.1032i	−0.532767	+	0.797354i
$575$	5.68115	−	3.28001i	0.236920	−	0.136786i
$576$	0.0419009	−	2.99971i	0.00174587	−	0.124988i
$577$	10.2980	−	17.8366i	0.428711	−	0.742549i	−0.568048	−	0.822995i	$-0.692301\pi$
$577$	10.2980	−	17.8366i	0.428711	−	0.742549i	0.996759	+	0.0804462i	$0.0256345\pi$
$578$	16.1601	+	27.9901i	0.672172	+	1.16424i
$579$	28.4449	+	28.8450i	1.18213	+	1.19876i
$580$	2.94435			0.122258
$581$	−10.6433	+	15.9290i	−0.441556	+	0.660845i
$582$	−28.6346	−	7.88736i	−1.18694	−	0.326942i
$583$	29.9580	+	17.2963i	1.24073	+	0.716338i
$584$	−5.44642	+	9.43348i	−0.225375	+	0.390360i
$585$	−1.91356	−	6.82580i	−0.0791158	−	0.282212i
$586$	−5.30689	+	3.06394i	−0.219226	+	0.126570i
$587$	23.7246	−	13.6974i	0.979217	−	0.565351i	0.0771834	−	0.997017i	$-0.475407\pi$
$587$	23.7246	−	13.6974i	0.979217	−	0.565351i	0.902034	+	0.431666i	$0.142074\pi$
$588$	−1.49872	−	12.0314i	−0.0618062	−	0.496165i
$589$	−14.7649	+	25.5736i	−0.608377	+	1.05374i
$590$	−2.31957	−	4.01761i	−0.0954951	−	0.165402i
$591$	26.3840	+	7.26744i	1.08529	+	0.298943i
$592$	−2.56676	+	1.48192i	−0.105493	+	0.0609065i
$593$	−11.0590	+	6.38494i	−0.454141	+	0.262198i	−0.709577	−	0.704628i	$-0.751114\pi$
$593$	−11.0590	+	6.38494i	−0.454141	+	0.262198i	0.255437	+	0.966826i	$0.417781\pi$
$594$	−15.6083	+	3.83365i	−0.640416	+	0.157296i
$595$	−5.38595	−	10.9214i	−0.220802	−	0.447736i
$596$	−3.03198	−	5.25155i	−0.124195	−	0.215112i
$597$	−11.2693	+	40.9126i	−0.461222	+	1.67444i
$598$	4.96295	−	1.46639i	0.202950	−	0.0599651i
$599$	−29.5140	−	17.0399i	−1.20591	−	0.696231i	−0.244045	−	0.969764i	$-0.578475\pi$
$599$	−29.5140	−	17.0399i	−1.20591	−	0.696231i	−0.961863	+	0.273533i	$0.911808\pi$
$600$	−1.99544	−	7.66069i	−0.0814636	−	0.312746i
$601$	33.7422	−	19.4811i	1.37637	−	0.794649i	0.384652	−	0.923062i	$-0.374322\pi$
$601$	33.7422	−	19.4811i	1.37637	−	0.794649i	0.991721	+	0.128413i	$0.0409882\pi$
$602$	0.0131573	−	0.200763i	0.000536252	−	0.00818247i
$603$	−11.9879	−	0.167451i	−0.488185	−	0.00681913i
$604$		−	0.826563i		−	0.0336324i
$605$	0.813186	−	0.469493i	0.0330607	−	0.0190876i
$606$	−3.25202	−	12.4848i	−0.132104	−	0.507161i
$607$			0.976706i			0.0396433i	0.999804	+	0.0198216i	$0.00630983\pi$
$607$			0.976706i			0.0396433i	−0.999804	+	0.0198216i	$0.993690\pi$
$608$	3.25972	+	5.64600i	0.132199	+	0.228976i
$609$	−15.5731	+	13.4662i	−0.631053	+	0.545677i
$610$	−10.0619			−0.407395
$611$	−32.1192	+	9.49016i	−1.29940	+	0.383931i
$612$	18.0969	+	10.7881i	0.731526	+	0.436082i
$613$		−	5.82682i		−	0.235343i	−0.993053	−	0.117672i	$-0.962457\pi$
$613$		−	5.82682i		−	0.235343i	0.993053	−	0.117672i	$-0.0375430\pi$
$614$	−2.69080	+	4.66061i	−0.108592	+	0.188087i
$615$	2.48471	+	9.53904i	0.100193	+	0.384651i
$616$	6.80442	+	4.54650i	0.274158	+	0.183184i
$617$	10.4203	−	18.0485i	0.419506	−	0.726606i	−0.576384	−	0.817179i	$-0.695537\pi$
$617$	10.4203	−	18.0485i	0.419506	−	0.726606i	0.995890	+	0.0905731i	$0.0288699\pi$
$618$	21.5498	+	21.8529i	0.866860	+	0.879053i
$619$	3.21016	−	5.56015i	0.129027	−	0.223481i	−0.794273	−	0.607561i	$-0.792148\pi$
$619$	3.21016	−	5.56015i	0.129027	−	0.223481i	0.923300	+	0.384080i	$0.125481\pi$
$620$	−2.57081	+	1.48426i	−0.103246	+	0.0596093i
$621$	1.77894	+	7.24278i	0.0713865	+	0.290643i
$622$	3.15077	+	5.45729i	0.126334	+	0.218817i
$623$	12.7899	+	25.9348i	0.512415	+	1.03906i
$624$	−0.115588	−	6.24393i	−0.00462722	−	0.249957i
$625$	−9.37088	−	16.2308i	−0.374835	−	0.649234i
$626$			10.4957i			0.419491i
$627$	24.8692	−	24.5242i	0.993179	−	0.979403i
$628$		−	6.57865i		−	0.262517i
$629$		−	20.8145i		−	0.829930i
$630$	−4.28443	−	2.95010i	−0.170696	−	0.117535i
$631$	−14.8774	−	8.58945i	−0.592258	−	0.341941i	0.173732	−	0.984793i	$-0.444418\pi$
$631$	−14.8774	−	8.58945i	−0.592258	−	0.341941i	−0.765990	+	0.642852i	$0.777751\pi$
$632$	1.40194	+	2.42822i	0.0557660	+	0.0965896i
$633$	−19.8157	−	5.45819i	−0.787602	−	0.216944i
$634$	0.887473			0.0352461
$635$	3.54104	+	2.04442i	0.140522	+	0.0811304i
$636$	−13.6013	−	13.7926i	−0.539326	−	0.546912i
$637$	−3.93145	−	24.9308i	−0.155770	−	0.987793i
$638$		−	13.8961i		−	0.550153i
$639$	2.41979	+	1.44250i	0.0957255	+	0.0570645i
$640$			0.655374i			0.0259059i
$641$	18.9400	−	10.9350i	0.748085	−	0.431907i	−0.0769168	−	0.997038i	$-0.524508\pi$
$641$	18.9400	−	10.9350i	0.748085	−	0.431907i	0.825001	+	0.565131i	$0.191174\pi$
$642$	8.09208	−	29.3778i	0.319369	−	1.15945i
$643$	−4.78089	+	8.28074i	−0.188540	+	0.326561i	−0.944764	−	0.327753i	$-0.893709\pi$
$643$	−4.78089	+	8.28074i	−0.188540	+	0.326561i	0.756224	+	0.654313i	$0.227042\pi$
$644$	2.10973	−	3.15748i	0.0831350	−	0.124422i
$645$	−0.0606101	−	0.0614626i	−0.00238652	−	0.00242009i
$646$	−45.7849			−1.80138
$647$	32.6527			1.28371			0.641854	−	0.766827i	$-0.278165\pi$
$647$	32.6527			1.28371			0.641854	+	0.766827i	$0.278165\pi$
$648$	8.99649	+	0.251381i	0.353415	+	0.00987517i
$649$	−18.9615	+	10.9474i	−0.744303	+	0.429724i
$650$	−4.66948	−	15.8037i	−0.183152	−	0.619873i
$651$	6.80902	−	19.6082i	0.266867	−	0.768506i
$652$	3.86463	−	2.23125i	0.151351	−	0.0873823i
$653$	−33.1532	−	19.1410i	−1.29738	−	0.749045i	−0.317433	−	0.948281i	$-0.602821\pi$
$653$	−33.1532	−	19.1410i	−1.29738	−	0.749045i	−0.979952	+	0.199236i	$0.936154\pi$
$654$	4.41490	−	16.0281i	0.172636	−	0.626746i
$655$	2.11188	+	1.21930i	0.0825181	+	0.0476418i
$656$			8.68380i			0.339045i
$657$	−28.0695	−	16.7329i	−1.09509	−	0.652814i
$658$	−13.6537	+	20.4345i	−0.532278	+	0.796621i
$659$	4.16940	+	2.40720i	0.162417	+	0.0937713i	0.579005	−	0.815324i	$-0.303441\pi$
$659$	4.16940	+	2.40720i	0.162417	+	0.0937713i	−0.416589	+	0.909095i	$0.636774\pi$
$660$	3.39773	−	0.885033i	0.132256	−	0.0344499i
$661$	12.7902			0.497480			0.248740	−	0.968570i	$-0.419984\pi$
$661$	12.7902			0.497480			0.248740	+	0.968570i	$0.419984\pi$
$662$	16.7252	+	9.65631i	0.650044	+	0.375303i
$663$	38.3812	+	21.2220i	1.49060	+	0.824196i
$664$			7.24087i			0.281000i
$665$	11.2802	+	0.739269i	0.437428	+	0.0286676i
$666$	−4.33777	−	7.76161i	−0.168085	−	0.300756i
$667$	−6.44828			−0.249678
$668$	1.12359	+	0.648707i	0.0434732	+	0.0250992i
$669$	−38.1110	−	10.4976i	−1.47346	−	0.405862i
$670$	2.61911			0.101185
$671$			47.4881i			1.83326i
$672$	−2.99739	−	3.46636i	−0.115627	−	0.133718i
$673$	20.4148	+	35.3595i	0.786934	+	1.36301i	0.927837	+	0.372986i	$0.121666\pi$
$673$	20.4148	+	35.3595i	0.786934	+	1.36301i	−0.140903	+	0.990023i	$0.545000\pi$
$674$	−0.882363	+	1.52830i	−0.0339873	+	0.0588678i
$675$	23.0634	−	5.66475i	0.887713	−	0.218036i
$676$	−0.662548	−	12.9831i	−0.0254826	−	0.499350i
$677$	1.70470	+	2.95263i	0.0655169	+	0.113479i	0.896923	−	0.442186i	$-0.145797\pi$
$677$	1.70470	+	2.95263i	0.0655169	+	0.113479i	−0.831406	+	0.555665i	$0.812464\pi$
$678$	1.19770	−	4.34819i	0.0459975	−	0.166991i
$679$	−40.6902	+	20.0665i	−1.56154	+	0.770082i
$680$	−3.98595	−	2.30129i	−0.152854	−	0.0882505i
$681$	−4.91435	+	17.8413i	−0.188318	+	0.683678i
$682$	7.00509	+	12.1332i	0.268239	+	0.464603i
$683$	3.30894	+	5.73125i	0.126613	+	0.219300i	0.922362	−	0.386326i	$-0.126256\pi$
$683$	3.30894	+	5.73125i	0.126613	+	0.219300i	−0.795749	+	0.605626i	$0.792923\pi$
$684$	−17.0729	+	9.54163i	−0.652800	+	0.364833i
$685$	−3.93113	−	2.26964i	−0.150201	−	0.0867184i
$686$	−13.9245	−	12.2110i	−0.531640	−	0.466217i
$687$	−6.24033	−	1.71889i	−0.238084	−	0.0655797i
$688$	−0.0380219	−	0.0658559i	−0.00144957	−	0.00251073i
$689$	−29.2307	−	27.7771i	−1.11360	−	1.05822i
$690$	−0.410685	−	1.57666i	−0.0156345	−	0.0600224i
$691$	24.0607	−	41.6744i	0.915313	−	1.58537i	0.108872	−	0.994056i	$-0.465276\pi$
$691$	24.0607	−	41.6744i	0.915313	−	1.58537i	0.806442	−	0.591314i	$-0.201390\pi$
$692$	6.33267	+	10.9685i	0.240732	+	0.416960i
$693$	−13.9233	+	20.2208i	−0.528902	+	0.768123i
$694$			22.7100i			0.862061i
$695$	−1.72371			−0.0653840
$696$	−2.06643	+	7.50207i	−0.0783279	+	0.284365i
$697$	−52.8145	−	30.4924i	−2.00049	−	1.15498i
$698$	1.51254			0.0572504
$699$	−4.10589	+	14.9062i	−0.155299	+	0.563805i
$700$	−10.0545	−	6.71809i	−0.380024	−	0.253920i
$701$		−	37.9458i		−	1.43319i	−0.697487	−	0.716597i	$-0.745699\pi$
$701$		−	37.9458i		−	1.43319i	0.697487	−	0.716597i	$-0.254301\pi$
$702$	18.7348	−	0.0851037i	0.707099	−	0.00321203i
$703$	16.7338	+	9.66127i	0.631128	+	0.364382i
$704$	3.09310			0.116575
$705$	2.65787	+	10.2038i	0.100101	+	0.384298i
$706$	28.2367	+	16.3025i	1.06270	+	0.613551i
$707$	−16.3860	−	10.9486i	−0.616260	−	0.411766i
$708$	11.8646	−	3.09047i	0.445900	−	0.116147i
$709$		−	12.8786i		−	0.483666i	−0.970318	−	0.241833i	$-0.922251\pi$
$709$		−	12.8786i		−	0.483666i	0.970318	−	0.241833i	$-0.0777485\pi$
$710$	−0.532973	−	0.307712i	−0.0200021	−	0.0115482i
$711$	−7.34270	+	4.10365i	−0.275373	+	0.153899i
$712$	9.46532	+	5.46481i	0.354728	+	0.204802i
$713$	5.63021	−	3.25060i	0.210853	−	0.121736i
$714$	31.6073	−	6.05815i	1.18287	−	0.226721i
$715$	7.00938	−	2.07104i	0.262136	−	0.0774525i
$716$	12.5760	−	7.26077i	0.469988	−	0.271348i
$717$	−2.80715	+	2.76821i	−0.104835	+	0.103381i
$718$	−6.38300			−0.238211
$719$	33.3356			1.24321			0.621603	−	0.783332i	$-0.286482\pi$
$719$	33.3356			1.24321			0.621603	+	0.783332i	$0.286482\pi$
$720$	−1.96593	−	0.0274608i	−0.0732659	−	0.00102340i
$721$	46.7811	+	3.06588i	1.74222	+	0.114179i
$722$	11.7515	−	20.3543i	0.437347	−	0.757508i
$723$	−6.90053	−	1.90074i	−0.256633	−	0.0706893i
$724$	−3.09394	+	1.78628i	−0.114985	+	0.0663867i
$725$			20.5335i			0.762595i
$726$	0.625528	+	2.40146i	0.0232155	+	0.0891267i
$727$		−	3.84364i		−	0.142553i	−0.997457	−	0.0712764i	$-0.977293\pi$
$727$		−	3.84364i		−	0.142553i	0.997457	−	0.0712764i	$-0.0227072\pi$
$728$	−6.47058	−	7.00939i	−0.239816	−	0.259785i
$729$	−1.13103	+	26.9763i	−0.0418900	+	0.999122i
$730$	6.18246	+	3.56944i	0.228823	+	0.132111i
$731$	0.534044			0.0197523
$732$	7.06174	−	25.6373i	0.261009	−	0.947580i
$733$	21.0661	+	36.4875i	0.778093	+	1.34770i	0.933040	+	0.359773i	$0.117146\pi$
$733$	21.0661	+	36.4875i	0.778093	+	1.34770i	−0.154947	+	0.987923i	$0.549521\pi$
$734$	−10.4124	−	6.01163i	−0.384330	−	0.221893i
$735$	−7.88505	+	0.982222i	−0.290844	+	0.0362298i
$736$		−	1.43530i		−	0.0529059i
$737$		−	12.3611i		−	0.455328i
$738$	−26.0489	−	0.363859i	−0.958871	−	0.0133938i
$739$			17.9699i			0.661033i	0.943800	+	0.330517i	$0.107223\pi$
$739$			17.9699i			0.661033i	−0.943800	+	0.330517i	$0.892777\pi$
$740$	0.971210	+	1.68219i	0.0357024	+	0.0618384i
$741$	−34.8764	+	21.0061i	−1.28122	+	0.771677i
$742$	−29.5262	−	1.93505i	−1.08394	−	0.0710379i
$743$	3.17479	+	5.49889i	0.116472	+	0.201735i	0.918367	−	0.395730i	$-0.129508\pi$
$743$	3.17479	+	5.49889i	0.116472	+	0.201735i	−0.801895	+	0.597464i	$0.796175\pi$
$744$	−1.97755	−	7.59200i	−0.0725004	−	0.278336i
$745$	−3.44173	+	1.98708i	−0.126095	+	0.0728011i
$746$	−10.8556	+	18.8024i	−0.397451	+	0.688406i
$747$	−21.7205	−	0.303399i	−0.794711	−	0.0111008i
$748$	−10.8612	+	18.8121i	−0.397123	+	0.687838i
$749$	−20.5873	−	41.7463i	−0.752245	−	1.52538i
$750$	−10.5131	+	2.73842i	−0.383882	+	0.0999929i
$751$	−15.7354	+	27.2544i	−0.574191	+	0.994529i	0.421938	+	0.906625i	$0.361350\pi$
$751$	−15.7354	+	27.2544i	−0.574191	+	0.994529i	−0.996129	+	0.0879037i	$0.971983\pi$
$752$			9.28897i			0.338734i
$753$	−3.28070	−	12.5949i	−0.119555	−	0.458985i
$754$	−3.79225	+	15.7482i	−0.138106	+	0.573517i
$755$	−0.541708			−0.0197148
$756$	10.5237	−	8.84605i	0.382742	−	0.321728i
$757$	−2.57146	−	4.45391i	−0.0934614	−	0.161880i	0.815504	−	0.578751i	$-0.196460\pi$
$757$	−2.57146	−	4.45391i	−0.0934614	−	0.161880i	−0.908965	+	0.416871i	$0.863127\pi$
$758$			2.93565i			0.106627i
$759$	−7.44119	+	1.93827i	−0.270098	+	0.0703546i
$760$	3.70024	−	2.13634i	0.134222	−	0.0774930i
$761$			7.50899i			0.272201i	0.990695	+	0.136100i	$0.0434570\pi$
$761$			7.50899i			0.272201i	−0.990695	+	0.136100i	$0.956543\pi$
$762$	−7.69429	+	7.58757i	−0.278735	+	0.274869i
$763$	−11.2321	−	22.7761i	−0.406629	−	0.824549i
$764$	−5.22709	+	3.01786i	−0.189110	+	0.109183i
$765$	7.07022	−	11.8603i	0.255624	−	0.428809i
$766$	26.1275	+	15.0847i	0.944025	+	0.545033i
$767$	24.4762	−	7.23192i	0.883786	−	0.261130i
$768$	−1.66986	−	0.459961i	−0.0602559	−	0.0165974i
$769$	−12.5070	−	21.6627i	−0.451013	−	0.781177i	0.547437	−	0.836847i	$-0.315604\pi$
$769$	−12.5070	−	21.6627i	−0.451013	−	0.781177i	−0.998449	+	0.0556704i	$0.982270\pi$
$770$	2.97966	−	4.45944i	0.107379	−	0.160707i
$771$	−11.0031	−	42.2419i	−0.396266	−	1.52130i
$772$	20.2555	−	11.6945i	0.729012	−	0.420896i
$773$	−11.4656	+	6.61968i	−0.412390	+	0.238093i	−0.691816	−	0.722074i	$-0.743189\pi$
$773$	−11.4656	+	6.61968i	−0.412390	+	0.238093i	0.279426	+	0.960167i	$0.409856\pi$
$774$	0.199142	−	0.111295i	0.00715800	−	0.00400043i
$775$	−10.3510	−	17.9285i	−0.371819	−	0.644010i
$776$	−8.57395	+	14.8505i	−0.307787	+	0.533102i
$777$	−12.8304	−	4.45542i	−0.460289	−	0.159837i
$778$	−19.1621	+	11.0633i	−0.686996	+	0.396637i
$779$	49.0287	−	28.3067i	1.75664	−	1.01419i
$780$	−4.09211	+	0.0757533i	−0.146521	+	0.00271240i
$781$	−1.45228	+	2.51541i	−0.0519665	+	0.0900086i
$782$	8.72944	+	5.03994i	0.312164	+	0.180228i
$783$	−22.4174	−	6.51304i	−0.801133	−	0.232757i
$784$	−6.94013	−	0.913591i	−0.247862	−	0.0326282i
$785$	−4.31148			−0.153883
$786$	−4.58889	+	4.52524i	−0.163680	+	0.161410i
$787$	8.12500	+	14.0729i	0.289625	+	0.501645i	0.973720	−	0.227747i	$-0.0731360\pi$
$787$	8.12500	+	14.0729i	0.289625	+	0.501645i	−0.684095	+	0.729393i	$0.739803\pi$
$788$	7.90007	−	13.6833i	0.281428	−	0.487448i
$789$	−24.2433	−	24.5843i	−0.863084	−	0.875224i
$790$	1.59139	−	0.918792i	0.0566193	−	0.0326892i
$791$	−3.04711	−	6.17883i	−0.108343	−	0.219694i
$792$	−0.129604	+	9.27839i	−0.00460526	+	0.329693i
$793$	12.9595	−	53.8174i	0.460205	−	1.91111i
$794$	6.54053	−	11.3285i	0.232115	−	0.402034i
$795$	−9.03931	+	8.91393i	−0.320591	+	0.316144i
$796$	21.2181	+	12.2503i	0.752057	+	0.434200i
$797$	−6.45285	+	11.1767i	−0.228572	+	0.395898i	−0.957385	−	0.288815i	$-0.906739\pi$
$797$	−6.45285	+	11.1767i	−0.228572	+	0.395898i	0.728813	+	0.684712i	$0.240072\pi$
$798$	−9.80042	+	28.2226i	−0.346931	+	0.999070i
$799$	−56.4951	−	32.6174i	−1.99865	−	1.15392i
$800$	−4.57049			−0.161591
$801$	−16.7894	+	28.1642i	−0.593225	+	0.995134i
$802$	3.46329	+	5.99859i	0.122293	+	0.211818i
$803$	16.8463	−	29.1787i	0.594494	−	1.02969i
$804$	−1.83817	+	6.67336i	−0.0648272	+	0.235351i
$805$	−2.06933	−	1.38266i	−0.0729343	−	0.0487324i
$806$	−4.62761	−	15.6620i	−0.163000	−	0.551670i
$807$	−33.7546	−	9.29765i	−1.18822	−	0.327293i
$808$	−7.44863			−0.262042
$809$			35.7479i			1.25683i	0.777878	+	0.628415i	$0.216296\pi$
$809$			35.7479i			1.25683i	−0.777878	+	0.628415i	$0.783704\pi$
$810$	0.164748	−	5.89606i	0.00578867	−	0.207167i
$811$	−19.1592			−0.672770			−0.336385	−	0.941724i	$-0.609204\pi$
$811$	−19.1592			−0.672770			−0.336385	+	0.941724i	$0.609204\pi$
$812$	5.25728	+	10.6605i	0.184494	+	0.374111i
$813$	11.5490	+	44.3379i	0.405042	+	1.55500i
$814$	7.93923	−	4.58372i	0.278270	−	0.160659i
$815$	−1.46230	−	2.53278i	−0.0512221	−	0.0887193i
$816$	8.66104	−	8.54090i	0.303197	−	0.298991i
$817$	−0.247882	+	0.429344i	−0.00867228	+	0.0150208i
$818$	32.6793			1.14260
$819$	21.2972	−	19.1162i	0.744186	−	0.667973i
$820$	5.69113			0.198743
$821$	−12.6670	+	21.9400i	−0.442083	+	0.765710i	−0.997844	−	0.0656323i	$-0.979094\pi$
$821$	−12.6670	+	21.9400i	−0.442083	+	0.765710i	0.555761	+	0.831342i	$0.312427\pi$
$822$	8.54191	−	8.42342i	0.297933	−	0.293801i
$823$	1.96888	+	3.41020i	0.0686309	+	0.118872i	0.898299	−	0.439385i	$-0.144804\pi$
$823$	1.96888	+	3.41020i	0.0686309	+	0.118872i	−0.829668	+	0.558257i	$0.811470\pi$
$824$	15.3456	−	8.85976i	0.534588	−	0.308644i
$825$	6.17209	+	23.6953i	0.214885	+	0.824963i
$826$	10.4047	−	15.5720i	0.362027	−	0.541820i
$827$	−43.3874			−1.50873			−0.754363	−	0.656458i	$-0.772054\pi$
$827$	−43.3874			−1.50873			−0.754363	+	0.656458i	$0.772054\pi$
$828$	4.30549	+	0.0601404i	0.149626	+	0.00209002i
$829$		−	14.1173i		−	0.490315i	−0.969483	−	0.245157i	$-0.921160\pi$
$829$		−	14.1173i		−	0.490315i	0.969483	−	0.245157i	$-0.0788397\pi$
$830$	4.74548			0.164718
$831$	−5.62710	−	1.54998i	−0.195202	−	0.0537681i
$832$	−3.50535	−	0.844105i	−0.121526	−	0.0292641i
$833$	29.9261	−	39.0015i	1.03688	−	1.35132i
$834$	1.20975	−	4.39192i	0.0418902	−	0.152080i
$835$	0.425146	−	0.736374i	0.0147128	−	0.0254833i
$836$	−10.0826	−	17.4636i	−0.348715	−	0.603992i
$837$	22.8566	−	5.61395i	0.790041	−	0.194047i
$838$	−7.96637			−0.275194
$839$	−6.87396	−	3.96868i	−0.237315	−	0.137014i	0.376627	−	0.926365i	$-0.377084\pi$
$839$	−6.87396	−	3.96868i	−0.237315	−	0.137014i	−0.613942	+	0.789351i	$0.710417\pi$
$840$	−2.27176	+	1.96441i	−0.0783832	+	0.0677786i
$841$	−4.40814	+	7.63512i	−0.152005	+	0.263280i
$842$	−12.2707	−	7.08447i	−0.422875	−	0.244147i
$843$	24.8600	−	24.5152i	0.856226	−	0.844349i
$844$	−5.93332	+	10.2768i	−0.204233	+	0.353743i
$845$	−8.50879	+	0.434216i	−0.292711	+	0.0149375i
$846$	−27.8642	−	0.389216i	−0.957990	−	0.0133815i
$847$	3.15186	+	2.10598i	0.108299	+	0.0723623i
$848$	−9.68544	+	5.59189i	−0.332599	+	0.192026i
$849$	7.75834	+	7.86747i	0.266265	+	0.270011i
$850$	16.0489	−	27.7975i	0.550472	−	0.953446i
$851$	−2.12700	−	3.68407i	−0.0729126	−	0.126288i
$852$	1.15809	−	1.14203i	0.0396756	−	0.0391252i
$853$	27.9388			0.956605			0.478302	−	0.878195i	$-0.341252\pi$
$853$	27.9388			0.956605			0.478302	+	0.878195i	$0.341252\pi$
$854$	−17.9660	−	36.4309i	−0.614784	−	1.24664i
$855$	6.25334	+	11.1892i	0.213860	+	0.382661i
$856$	−15.2360	−	8.79649i	−0.520755	−	0.300658i
$857$	1.19842	−	2.07572i	0.0409372	−	0.0709054i	−0.844831	−	0.535034i	$-0.820299\pi$
$857$	1.19842	−	2.07572i	0.0409372	−	0.0709054i	0.885768	+	0.464128i	$0.153632\pi$
$858$	0.357525	+	19.3131i	0.0122057	+	0.659338i
$859$	9.45554	−	5.45916i	0.322619	−	0.186264i	−0.329940	−	0.944002i	$-0.607029\pi$
$859$	9.45554	−	5.45916i	0.322619	−	0.186264i	0.652559	+	0.757738i	$0.273695\pi$
$860$	−0.0431603	+	0.0249186i	−0.00147175	+	0.000849717i
$861$	−30.1012	+	26.0287i	−1.02585	+	0.887057i
$862$	12.9721	−	22.4684i	0.441832	−	0.765276i
$863$	0.0710829	+	0.123119i	0.00241969	+	0.00419102i	0.867233	−	0.497903i	$-0.165896\pi$
$863$	0.0710829	+	0.123119i	0.00241969	+	0.00419102i	−0.864813	+	0.502094i	$0.832563\pi$
$864$	1.44972	−	4.98982i	0.0493203	−	0.169757i
$865$	7.18847	−	4.15026i	0.244415	−	0.141113i
$866$	14.7383	−	8.50919i	0.500829	−	0.289154i
$867$	14.1108	+	54.1726i	0.479227	+	1.83980i
$868$	−9.96432	−	6.65785i	−0.338211	−	0.225982i
$869$	−4.33632	−	7.51073i	−0.147100	−	0.254784i
$870$	4.91666	+	1.35429i	0.166690	+	0.0459146i
$871$	−3.37335	+	14.0086i	−0.114301	+	0.474665i
$872$	−8.31249	−	4.79922i	−0.281496	−	0.162522i
$873$	−44.1879	−	26.3416i	−1.49554	−	0.891528i
$874$	−8.10372	+	4.67868i	−0.274112	+	0.158259i
$875$	−9.21949	+	13.7981i	−0.311676	+	0.466462i
$876$	−13.4338	+	13.2475i	−0.453886	+	0.447590i
$877$		−	11.3722i		−	0.384012i	−0.981394	−	0.192006i	$-0.938501\pi$
$877$		−	11.3722i		−	0.384012i	0.981394	−	0.192006i	$-0.0614994\pi$
$878$	25.6542	−	14.8115i	0.865787	−	0.499863i
$879$	−10.2711	+	2.67539i	−0.346434	+	0.0902385i
$880$		−	2.02714i		−	0.0683347i
$881$	−15.4774	−	26.8077i	−0.521448	−	0.903174i	−0.999689	−	0.0249457i	$-0.992059\pi$
$881$	−15.4774	−	26.8077i	−0.521448	−	0.903174i	0.478241	−	0.878229i	$-0.341275\pi$
$882$	3.03130	−	20.7801i	0.102069	−	0.699701i
$883$	−29.8101			−1.00319			−0.501594	−	0.865103i	$-0.667253\pi$
$883$	−29.8101			−1.00319			−0.501594	+	0.865103i	$0.667253\pi$
$884$	17.4426	−	18.3554i	0.586657	−	0.617358i
$885$	−2.02541	−	7.77576i	−0.0680835	−	0.261379i
$886$		−	17.7780i		−	0.597262i
$887$	0.205137	−	0.355308i	0.00688783	−	0.0119301i	−0.862561	−	0.505953i	$-0.831141\pi$
$887$	0.205137	−	0.355308i	0.00688783	−	0.0119301i	0.869449	+	0.494023i	$0.164474\pi$
$888$	−4.96775	+	1.29399i	−0.166707	+	0.0434235i
$889$	−1.07948	+	16.4714i	−0.0362046	+	0.552432i
$890$	3.58149	−	6.20333i	0.120052	−	0.207936i
$891$	−27.8270	−	0.777545i	−0.932240	−	0.0260487i
$892$	−11.4114	+	19.7652i	−0.382083	+	0.661788i
$893$	52.4455	−	30.2794i	1.75502	−	1.01326i
$894$	−2.64748	−	10.1639i	−0.0885451	−	0.339933i
$895$	−4.75852	−	8.24200i	−0.159060	−	0.275500i
$896$	−2.37289	+	1.17020i	−0.0792728	+	0.0390937i
$897$	8.96192	−	0.165904i	0.299230	−	0.00553936i
$898$	−11.2383	−	19.4653i	−0.375028	−	0.649567i
$899$			20.3494i			0.678690i
$900$	0.191507	−	13.7101i	0.00638358	−	0.457004i
$901$		−	78.5418i		−	2.61661i
$902$		−	26.8598i		−	0.894335i
$903$	0.114314	−	0.329194i	0.00380412	−	0.0109549i
$904$	−2.25506	−	1.30196i	−0.0750023	−	0.0433026i
$905$	1.17068	+	2.02768i	0.0389149	+	0.0674025i
$906$	0.380186	−	1.38025i	0.0126308	−	0.0458556i
$907$	−49.8021			−1.65365			−0.826825	−	0.562459i	$-0.809855\pi$
$907$	−49.8021			−1.65365			−0.826825	+	0.562459i	$0.809855\pi$
$908$	9.25285	+	5.34214i	0.307067	+	0.177285i
$909$	0.312104	−	22.3437i	0.0103518	−	0.741094i
$910$	−4.59377	+	4.24065i	−0.152282	+	0.140576i
$911$			12.8444i			0.425553i	0.977101	+	0.212776i	$0.0682506\pi$
$911$			12.8444i			0.425553i	−0.977101	+	0.212776i	$0.931749\pi$
$912$	2.84634	+	10.9274i	0.0942518	+	0.361842i
$913$		−	22.3967i		−	0.741223i
$914$	22.9216	−	13.2338i	0.758180	−	0.437736i
$915$	−16.8020	−	4.62808i	−0.555456	−	0.153000i
$916$	−1.86852	+	3.23637i	−0.0617376	+	0.106933i
$917$	−0.643803	+	9.82355i	−0.0212603	+	0.324402i
$918$	25.2573	+	26.3385i	0.833615	+	0.869299i
$919$	−41.5015			−1.36901			−0.684503	−	0.729010i	$-0.739981\pi$
$919$	−41.5015			−1.36901			−0.684503	+	0.729010i	$0.739981\pi$
$920$	−0.940659			−0.0310126
$921$	−6.63697	+	6.54491i	−0.218695	+	0.215662i
$922$	6.02929	−	3.48101i	0.198564	−	0.114641i
$923$	2.33229	−	2.45435i	0.0767684	−	0.0807859i
$924$	9.27122	+	10.7218i	0.305001	+	0.352721i
$925$	−11.7313	+	6.77308i	−0.385724	+	0.222698i
$926$	8.99256	+	5.19186i	0.295514	+	0.170615i
$927$	25.9337	+	46.4034i	0.851774	+	1.52409i
$928$	3.89073	+	2.24631i	0.127720	+	0.0737389i
$929$		−	4.09648i		−	0.134401i	−0.997739	−	0.0672005i	$-0.978593\pi$
$929$		−	4.09648i		−	0.134401i	0.997739	−	0.0672005i	$-0.0214067\pi$
$930$	−4.97560	+	1.29603i	−0.163156	+	0.0424986i
$931$	17.4647	+	42.1620i	0.572384	+	1.38180i
$932$	7.73067	+	4.46331i	0.253227	+	0.146200i
$933$	2.75120	+	10.5621i	0.0900704	+	0.345789i
$934$	−23.4927			−0.768704
$935$	12.3289	+	7.11812i	0.403200	+	0.232787i
$936$	2.67895	−	10.4797i	0.0875641	−	0.342538i
$937$			26.3778i			0.861725i	0.902418	+	0.430862i	$0.141791\pi$
$937$			26.3778i			0.861725i	−0.902418	+	0.430862i	$0.858209\pi$
$938$	4.67654	+	9.48293i	0.152695	+	0.309629i
$939$	−4.82759	+	17.5263i	−0.157543	+	0.571949i
$940$	6.08775			0.198560
$941$	−31.1389	−	17.9781i	−1.01510	−	0.586068i	−0.102419	−	0.994741i	$-0.532658\pi$
$941$	−31.1389	−	17.9781i	−1.01510	−	0.586068i	−0.912681	+	0.408673i	$0.865992\pi$
$942$	3.02592	−	10.9854i	0.0985898	−	0.357925i
$943$	−12.4639			−0.405880
$944$		−	7.07861i		−	0.230389i
$945$	−5.79747	−	6.89693i	−0.188592	−	0.224357i
$946$	0.117606	+	0.203699i	0.00382369	+	0.00662282i
$947$	−3.09627	+	5.36289i	−0.100615	+	0.174271i	−0.911938	−	0.410327i	$-0.865414\pi$
$947$	−3.09627	+	5.36289i	−0.100615	+	0.174271i	0.811323	+	0.584598i	$0.198748\pi$
$948$	1.22415	+	4.69963i	0.0397586	+	0.152637i
$949$	−27.0545	+	28.4703i	−0.878225	+	0.924185i
$950$	14.8985	+	25.8050i	0.483371	+	0.837223i
$951$	1.48196	+	0.408203i	0.0480558	+	0.0132369i
$952$	1.21511	−	18.5409i	0.0393820	−	0.600914i
$953$	−22.4705	−	12.9734i	−0.727891	−	0.420248i	0.0897592	−	0.995964i	$-0.471390\pi$
$953$	−22.4705	−	12.9734i	−0.727891	−	0.420248i	−0.817650	+	0.575715i	$0.804724\pi$
$954$	−16.3682	−	29.2878i	−0.529940	−	0.948227i
$955$	1.97783	+	3.42570i	0.0640011	+	0.110853i
$956$	1.13809	+	1.97124i	0.0368086	+	0.0637544i
$957$	6.39168	−	23.2046i	0.206614	−	0.750099i
$958$	7.41327	+	4.28005i	0.239512	+	0.138282i
$959$	1.19840	−	18.2859i	0.0386982	−	0.590482i
$960$	−0.301446	+	1.09438i	−0.00972914	+	0.0353211i
$961$	5.24181	+	9.07908i	0.169091	+	0.292874i
$962$	−10.2483	+	3.02803i	−0.330418	+	0.0976276i
$963$	27.0253	−	45.3349i	0.870878	−	1.46090i
$964$	−2.06620	+	3.57876i	−0.0665478	+	0.115264i
$965$	−7.66429	−	13.2749i	−0.246722	−	0.427336i
$966$	4.97527	−	4.30216i	0.160077	−	0.138420i
$967$			27.4624i			0.883132i	0.897229	+	0.441566i	$0.145577\pi$
$967$			27.4624i			0.883132i	−0.897229	+	0.441566i	$0.854423\pi$
$968$	1.43275			0.0460503
$969$	−76.4545	−	21.0593i	−2.45607	−	0.676521i
$970$	9.73264	+	5.61914i	0.312496	+	0.180420i
$971$	5.78777			0.185738			0.0928692	−	0.995678i	$-0.470396\pi$
$971$	5.78777			0.185738			0.0928692	+	0.995678i	$0.470396\pi$
$972$	14.9073	+	4.55780i	0.478151	+	0.146192i
$973$	−3.07776	−	6.24098i	−0.0986686	−	0.200077i
$974$			17.5739i			0.563103i
$975$	−0.528293	−	28.5378i	−0.0169189	−	0.913940i
$976$	−13.2960	−	7.67646i	−0.425595	−	0.245718i
$977$	45.0914			1.44260			0.721301	−	0.692622i	$-0.243545\pi$
$977$	45.0914			1.44260			0.721301	+	0.692622i	$0.243545\pi$
$978$	7.47968	−	1.94829i	0.239174	−	0.0622995i
$979$	−29.2772	−	16.9032i	−0.935702	−	0.540228i
$980$	−0.598743	+	4.54838i	−0.0191262	+	0.145293i
$981$	14.7445	−	24.7339i	0.470757	−	0.789694i
$982$			8.92840i			0.284917i
$983$	−3.66890	−	2.11824i	−0.117020	−	0.0675613i	0.440348	−	0.897827i	$-0.354855\pi$
$983$	−3.66890	−	2.11824i	−0.117020	−	0.0675613i	−0.557367	+	0.830266i	$0.688189\pi$
$984$	−3.99421	+	14.5007i	−0.127331	+	0.462267i
$985$	−8.96769	−	5.17750i	−0.285734	−	0.164969i
$986$	−27.3240	+	15.7755i	−0.870172	+	0.502394i
$987$	−32.1989	+	27.8427i	−1.02490	+	0.886242i
$988$	6.66064	+	22.5428i	0.211903	+	0.717181i
$989$	0.0945232	−	0.0545730i	0.00300566	−	0.00173532i
$990$	6.08081	+	0.0849388i	0.193261	+	0.00269953i
$991$	29.5782			0.939581			0.469791	−	0.882778i	$-0.344329\pi$
$991$	29.5782			0.939581			0.469791	+	0.882778i	$0.344329\pi$
$992$	−4.52950			−0.143812
$993$	23.4873	+	23.8176i	0.745346	+	0.755830i
$994$	0.162476	−	2.47915i	0.00515342	−	0.0786340i
$995$	8.02853	−	13.9058i	0.254521	−	0.440844i
$996$	−3.33051	+	12.0912i	−0.105531	+	0.383126i
$997$	24.7697	−	14.3008i	0.784464	−	0.452910i	−0.0535463	−	0.998565i	$-0.517052\pi$
$997$	24.7697	−	14.3008i	0.784464	−	0.452910i	0.838010	+	0.545655i	$0.183719\pi$
$998$		−	9.54852i		−	0.302253i
$999$	−3.67344	−	14.9560i	−0.116222	−	0.473188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.f.101.14	yes	34
3.2	odd	2		546.2.bn.e.101.4	yes	34
7.5	odd	6		546.2.bi.e.257.8	yes	34
13.4	even	6		546.2.bi.f.17.2	yes	34
21.5	even	6		546.2.bi.f.257.2	yes	34
39.17	odd	6		546.2.bi.e.17.8	✓	34
91.82	odd	6		546.2.bn.e.173.4	yes	34
273.173	even	6	inner	546.2.bn.f.173.14	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.8	✓	34	39.17	odd	6
546.2.bi.e.257.8	yes	34	7.5	odd	6
546.2.bi.f.17.2	yes	34	13.4	even	6
546.2.bi.f.257.2	yes	34	21.5	even	6
546.2.bn.e.101.4	yes	34	3.2	odd	2
546.2.bn.e.173.4	yes	34	91.82	odd	6
546.2.bn.f.101.14	yes	34	1.1	even	1	trivial
546.2.bn.f.173.14	yes	34	273.173	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.23327 - 1.21616i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.567570 + 0.327687i) q^{5} +(-0.436593 - 1.67612i) q^{6} +(-2.19987 - 1.46989i) q^{7} -1.00000 q^{8} +(0.0419009 - 2.99971i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.23327 - 1.21616i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.567570 + 0.327687i) q^{5} +(-0.436593 - 1.67612i) q^{6} +(-2.19987 - 1.46989i) q^{7} -1.00000 q^{8} +(0.0419009 - 2.99971i) q^{9} +0.655374i q^{10} +3.09310 q^{11} +(-1.66986 - 0.459961i) q^{12} +(-3.50535 - 0.844105i) q^{13} +(-2.37289 + 1.17020i) q^{14} +(-0.301446 + 1.09438i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.51142 - 6.08195i) q^{17} +(-2.57687 - 1.53614i) q^{18} +6.51944 q^{19} +(0.567570 + 0.327687i) q^{20} +(-4.50065 + 0.862636i) q^{21} +(1.54655 - 2.67870i) q^{22} +(-1.24301 - 0.717651i) q^{23} +(-1.23327 + 1.21616i) q^{24} +(-2.28524 + 3.95816i) q^{25} +(-2.48369 + 2.61367i) q^{26} +(-3.59645 - 3.75040i) q^{27} +(-0.173023 + 2.64009i) q^{28} +(3.89073 - 2.24631i) q^{29} +(0.797041 + 0.808252i) q^{30} +(-2.26475 + 3.92266i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.81462 - 3.76171i) q^{33} -7.02284 q^{34} +(1.73024 + 0.113395i) q^{35} +(-2.61877 + 1.46357i) q^{36} +(2.56676 + 1.48192i) q^{37} +(3.25972 - 5.64600i) q^{38} +(-5.34961 + 3.22207i) q^{39} +(0.567570 - 0.327687i) q^{40} +(7.52039 - 4.34190i) q^{41} +(-1.50326 + 4.32900i) q^{42} +(-0.0380219 + 0.0658559i) q^{43} +(-1.54655 - 2.67870i) q^{44} +(0.959183 + 1.71628i) q^{45} +(-1.24301 + 0.717651i) q^{46} +(8.04448 - 4.64448i) q^{47} +(0.436593 + 1.67612i) q^{48} +(2.67887 + 6.46712i) q^{49} +(2.28524 + 3.95816i) q^{50} +(-11.7272 - 3.23023i) q^{51} +(1.02166 + 3.45778i) q^{52} +(9.68544 + 5.59189i) q^{53} +(-5.04617 + 1.23942i) q^{54} +(-1.75555 + 1.01357i) q^{55} +(2.19987 + 1.46989i) q^{56} +(8.04022 - 7.92869i) q^{57} -4.49263i q^{58} +(-6.13025 + 3.53930i) q^{59} +(1.09849 - 0.286132i) q^{60} +15.3529i q^{61} +(2.26475 + 3.92266i) q^{62} +(-4.50140 + 6.53738i) q^{63} +1.00000 q^{64} +(2.26614 - 0.669569i) q^{65} +(-1.35042 - 5.18441i) q^{66} -3.99636i q^{67} +(-3.51142 + 6.08195i) q^{68} +(-2.40574 + 0.626643i) q^{69} +(0.963325 - 1.44174i) q^{70} +(-0.469521 + 0.813235i) q^{71} +(-0.0419009 + 2.99971i) q^{72} +(5.44642 - 9.43348i) q^{73} +(2.56676 - 1.48192i) q^{74} +(1.99544 + 7.66069i) q^{75} +(-3.25972 - 5.64600i) q^{76} +(-6.80442 - 4.54650i) q^{77} +(0.115588 + 6.24393i) q^{78} +(-1.40194 - 2.42822i) q^{79} -0.655374i q^{80} +(-8.99649 - 0.251381i) q^{81} -8.68380i q^{82} -7.24087i q^{83} +(2.99739 + 3.46636i) q^{84} +(3.98595 + 2.30129i) q^{85} +(0.0380219 + 0.0658559i) q^{86} +(2.06643 - 7.50207i) q^{87} -3.09310 q^{88} +(-9.46532 - 5.46481i) q^{89} +(1.96593 + 0.0274608i) q^{90} +(6.47058 + 7.00939i) q^{91} +1.43530i q^{92} +(1.97755 + 7.59200i) q^{93} -9.28897i q^{94} +(-3.70024 + 2.13634i) q^{95} +(1.66986 + 0.459961i) q^{96} +(8.57395 - 14.8505i) q^{97} +(6.94013 + 0.913591i) q^{98} +(0.129604 - 9.27839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

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