LMFDB - Embedded newform 546.2.bi.f.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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			17.2
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.66986 - 0.459961i) q^{3} +1.00000 q^{4} +(0.567570 - 0.327687i) q^{5} +(-1.66986 - 0.459961i) q^{6} +(-2.37289 + 1.17020i) q^{7} +1.00000 q^{8} +(2.57687 + 1.53614i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.66986 - 0.459961i) q^{3} +1.00000 q^{4} +(0.567570 - 0.327687i) q^{5} +(-1.66986 - 0.459961i) q^{6} +(-2.37289 + 1.17020i) q^{7} +1.00000 q^{8} +(2.57687 + 1.53614i) q^{9} +(0.567570 - 0.327687i) q^{10} +(1.54655 + 2.67870i) q^{11} +(-1.66986 - 0.459961i) q^{12} +(3.50535 - 0.844105i) q^{13} +(-2.37289 + 1.17020i) q^{14} +(-1.09849 + 0.286132i) q^{15} +1.00000 q^{16} +7.02284 q^{17} +(2.57687 + 1.53614i) q^{18} +(3.25972 - 5.64600i) q^{19} +(0.567570 - 0.327687i) q^{20} +(4.50065 - 0.862636i) q^{21} +(1.54655 + 2.67870i) q^{22} +1.43530i q^{23} +(-1.66986 - 0.459961i) q^{24} +(-2.28524 + 3.95816i) q^{25} +(3.50535 - 0.844105i) q^{26} +(-3.59645 - 3.75040i) q^{27} +(-2.37289 + 1.17020i) q^{28} +(-3.89073 - 2.24631i) q^{29} +(-1.09849 + 0.286132i) q^{30} +(2.26475 - 3.92266i) q^{31} +1.00000 q^{32} +(-1.35042 - 5.18441i) q^{33} +7.02284 q^{34} +(-0.963325 + 1.44174i) q^{35} +(2.57687 + 1.53614i) q^{36} +2.96384i q^{37} +(3.25972 - 5.64600i) q^{38} +(-6.24170 - 0.202785i) q^{39} +(0.567570 - 0.327687i) q^{40} +(7.52039 + 4.34190i) q^{41} +(4.50065 - 0.862636i) q^{42} +(-0.0380219 - 0.0658559i) q^{43} +(1.54655 + 2.67870i) q^{44} +(1.96593 + 0.0274608i) q^{45} +1.43530i q^{46} +(-8.04448 + 4.64448i) q^{47} +(-1.66986 - 0.459961i) q^{48} +(4.26126 - 5.55353i) q^{49} +(-2.28524 + 3.95816i) q^{50} +(-11.7272 - 3.23023i) q^{51} +(3.50535 - 0.844105i) q^{52} +(9.68544 + 5.59189i) q^{53} +(-3.59645 - 3.75040i) q^{54} +(1.75555 + 1.01357i) q^{55} +(-2.37289 + 1.17020i) q^{56} +(-8.04022 + 7.92869i) q^{57} +(-3.89073 - 2.24631i) q^{58} +7.07861i q^{59} +(-1.09849 + 0.286132i) q^{60} +(-13.2960 - 7.67646i) q^{61} +(2.26475 - 3.92266i) q^{62} +(-7.91224 - 0.629640i) q^{63} +1.00000 q^{64} +(1.71293 - 1.62775i) q^{65} +(-1.35042 - 5.18441i) q^{66} +(3.46095 - 1.99818i) q^{67} +7.02284 q^{68} +(0.660182 - 2.39676i) q^{69} +(-0.963325 + 1.44174i) q^{70} +(0.469521 + 0.813235i) q^{71} +(2.57687 + 1.53614i) q^{72} +(-5.44642 + 9.43348i) q^{73} +2.96384i q^{74} +(5.63663 - 5.55845i) q^{75} +(3.25972 - 5.64600i) q^{76} +(-6.80442 - 4.54650i) q^{77} +(-6.24170 - 0.202785i) q^{78} +(-1.40194 - 2.42822i) q^{79} +(0.567570 - 0.327687i) q^{80} +(4.28054 + 7.91688i) q^{81} +(7.52039 + 4.34190i) q^{82} +7.24087i q^{83} +(4.50065 - 0.862636i) q^{84} +(3.98595 - 2.30129i) q^{85} +(-0.0380219 - 0.0658559i) q^{86} +(5.46376 + 5.54062i) q^{87} +(1.54655 + 2.67870i) q^{88} -10.9296i q^{89} +(1.96593 + 0.0274608i) q^{90} +(-7.33005 + 6.10494i) q^{91} +1.43530i q^{92} +(-5.58609 + 5.50861i) q^{93} +(-8.04448 + 4.64448i) q^{94} -4.27267i q^{95} +(-1.66986 - 0.459961i) q^{96} +(-8.57395 - 14.8505i) q^{97} +(4.26126 - 5.55353i) q^{98} +(-0.129604 + 9.27839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.66986	−	0.459961i	−0.964095	−	0.265558i
$3$	−1.66986	−	0.459961i	−0.964095	−	0.265558i
$4$	1.00000			0.500000
$5$	0.567570	−	0.327687i	0.253825	−	0.146546i	−0.367689	−	0.929949i	$-0.619851\pi$
$5$	0.567570	−	0.327687i	0.253825	−	0.146546i	0.621515	+	0.783403i	$0.286518\pi$
$6$	−1.66986	−	0.459961i	−0.681718	−	0.187778i
$7$	−2.37289	+	1.17020i	−0.896870	+	0.442295i
$7$	−2.37289	+	1.17020i	−0.896870	+	0.442295i
$8$	1.00000			0.353553
$9$	2.57687	+	1.53614i	0.858957	+	0.512047i
$10$	0.567570	−	0.327687i	0.179482	−	0.103624i
$11$	1.54655	+	2.67870i	0.466302	+	0.807659i	0.999259	−	0.0384835i	$-0.0122527\pi$
$11$	1.54655	+	2.67870i	0.466302	+	0.807659i	−0.532957	+	0.846142i	$0.678919\pi$
$12$	−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
$15$	−1.09849	+	0.286132i	−0.283628	+	0.0738789i
$16$	1.00000			0.250000
$17$	7.02284			1.70329			0.851644	−	0.524121i	$-0.175606\pi$
$17$	7.02284			1.70329			0.851644	+	0.524121i	$0.175606\pi$
$18$	2.57687	+	1.53614i	0.607375	+	0.362072i
$19$	3.25972	−	5.64600i	0.747831	−	1.29528i	−0.201029	−	0.979585i	$-0.564429\pi$
$19$	3.25972	−	5.64600i	0.747831	−	1.29528i	0.948860	−	0.315696i	$-0.102238\pi$
$20$	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
$23$			1.43530i			0.299281i	0.988740	+	0.149641i	$0.0478117\pi$
$23$			1.43530i			0.299281i	−0.988740	+	0.149641i	$0.952188\pi$
$24$	−1.66986	−	0.459961i	−0.340859	−	0.0938891i
$25$	−2.28524	+	3.95816i	−0.457049	+	0.791631i
$26$	3.50535	−	0.844105i	0.687456	−	0.165543i
$27$	−3.59645	−	3.75040i	−0.692138	−	0.721765i
$28$	−2.37289	+	1.17020i	−0.448435	+	0.221147i
$29$	−3.89073	−	2.24631i	−0.722491	−	0.417130i	0.0931780	−	0.995649i	$-0.470297\pi$
$29$	−3.89073	−	2.24631i	−0.722491	−	0.417130i	−0.815669	+	0.578519i	$0.803631\pi$
$30$	−1.09849	+	0.286132i	−0.200555	+	0.0522402i
$31$	2.26475	−	3.92266i	0.406761	−	0.704531i	−0.587763	−	0.809033i	$-0.699991\pi$
$31$	2.26475	−	3.92266i	0.406761	−	0.704531i	0.994525	+	0.104502i	$0.0333248\pi$
$32$	1.00000			0.176777
$33$	−1.35042	−	5.18441i	−0.235079	−	0.902490i
$34$	7.02284			1.20441
$35$	−0.963325	+	1.44174i	−0.162832	+	0.243698i
$36$	2.57687	+	1.53614i	0.429479	+	0.256023i
$37$			2.96384i			0.487252i	0.969869	+	0.243626i	$0.0783369\pi$
$37$			2.96384i			0.487252i	−0.969869	+	0.243626i	$0.921663\pi$
$38$	3.25972	−	5.64600i	0.528796	−	0.915902i
$39$	−6.24170	−	0.202785i	−0.999473	−	0.0324716i
$40$	0.567570	−	0.327687i	0.0897408	−	0.0518119i
$41$	7.52039	+	4.34190i	1.17449	+	0.678091i	0.954733	−	0.297465i	$-0.0961410\pi$
$41$	7.52039	+	4.34190i	1.17449	+	0.678091i	0.219755	+	0.975555i	$0.429474\pi$
$42$	4.50065	−	0.862636i	0.694466	−	0.133108i
$43$	−0.0380219	−	0.0658559i	−0.00579829	−	0.0100429i	0.863112	−	0.505013i	$-0.168512\pi$
$43$	−0.0380219	−	0.0658559i	−0.00579829	−	0.0100429i	−0.868910	+	0.494970i	$0.835179\pi$
$44$	1.54655	+	2.67870i	0.233151	+	0.403829i
$45$	1.96593	+	0.0274608i	0.293064	+	0.00409361i
$46$			1.43530i			0.211624i
$47$	−8.04448	+	4.64448i	−1.17341	+	0.677468i	−0.954480	−	0.298273i	$-0.903589\pi$
$47$	−8.04448	+	4.64448i	−1.17341	+	0.677468i	−0.218928	+	0.975741i	$0.570256\pi$
$48$	−1.66986	−	0.459961i	−0.241024	−	0.0663896i
$49$	4.26126	−	5.55353i	0.608751	−	0.793361i
$50$	−2.28524	+	3.95816i	−0.323182	+	0.559768i
$51$	−11.7272	−	3.23023i	−1.64213	−	0.452322i
$52$	3.50535	−	0.844105i	0.486105	−	0.117056i
$53$	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	$0.387867\pi$
$54$	−3.59645	−	3.75040i	−0.489415	−	0.510365i
$55$	1.75555	+	1.01357i	0.236718	+	0.136669i
$56$	−2.37289	+	1.17020i	−0.317091	+	0.156375i
$57$	−8.04022	+	7.92869i	−1.06495	+	1.05018i
$58$	−3.89073	−	2.24631i	−0.510878	−	0.294956i
$59$			7.07861i			0.921556i	0.887515	+	0.460778i	$0.152430\pi$
$59$			7.07861i			0.921556i	−0.887515	+	0.460778i	$0.847570\pi$
$60$	−1.09849	+	0.286132i	−0.141814	+	0.0369394i
$61$	−13.2960	−	7.67646i	−1.70238	−	0.982870i	−0.943340	−	0.331828i	$-0.892335\pi$
$61$	−13.2960	−	7.67646i	−1.70238	−	0.982870i	−0.759041	−	0.651043i	$-0.774332\pi$
$62$	2.26475	−	3.92266i	0.287624	−	0.498179i
$63$	−7.91224	−	0.629640i	−0.996849	−	0.0793271i
$64$	1.00000			0.125000
$65$	1.71293	−	1.62775i	0.212463	−	0.201897i
$66$	−1.35042	−	5.18441i	−0.166226	−	0.638157i
$67$	3.46095	−	1.99818i	0.422822	−	0.244116i	−0.273462	−	0.961883i	$-0.588169\pi$
$67$	3.46095	−	1.99818i	0.422822	−	0.244116i	0.696284	+	0.717766i	$0.254835\pi$
$68$	7.02284			0.851644
$69$	0.660182	−	2.39676i	0.0794766	−	0.288535i
$70$	−0.963325	+	1.44174i	−0.115139	+	0.172321i
$71$	0.469521	+	0.813235i	0.0557219	+	0.0965132i	0.892541	−	0.450967i	$-0.148921\pi$
$71$	0.469521	+	0.813235i	0.0557219	+	0.0965132i	−0.836819	+	0.547480i	$0.815587\pi$
$72$	2.57687	+	1.53614i	0.303687	+	0.181036i
$73$	−5.44642	+	9.43348i	−0.637456	+	1.10411i	0.348534	+	0.937296i	$0.386680\pi$
$73$	−5.44642	+	9.43348i	−0.637456	+	1.10411i	−0.985989	+	0.166809i	$0.946654\pi$
$74$			2.96384i			0.344539i
$75$	5.63663	−	5.55845i	0.650862	−	0.641834i
$76$	3.25972	−	5.64600i	0.373915	−	0.647641i
$77$	−6.80442	−	4.54650i	−0.775435	−	0.518122i
$78$	−6.24170	−	0.202785i	−0.706734	−	0.0229609i
$79$	−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	$0.883751\pi$
$80$	0.567570	−	0.327687i	0.0634563	−	0.0366365i
$81$	4.28054	+	7.91688i	0.475616	+	0.879653i
$82$	7.52039	+	4.34190i	0.830488	+	0.479483i
$83$			7.24087i			0.794789i	0.917648	+	0.397394i	$0.130085\pi$
$83$			7.24087i			0.794789i	−0.917648	+	0.397394i	$0.869915\pi$
$84$	4.50065	−	0.862636i	0.491061	−	0.0941213i
$85$	3.98595	−	2.30129i	0.432337	−	0.249610i
$86$	−0.0380219	−	0.0658559i	−0.00410001	−	0.00710143i
$87$	5.46376	+	5.54062i	0.585777	+	0.594017i
$88$	1.54655	+	2.67870i	0.164863	+	0.285550i
$89$		−	10.9296i		−	1.15854i	−0.815137	−	0.579268i	$-0.803338\pi$
$89$		−	10.9296i		−	1.15854i	0.815137	−	0.579268i	$-0.196662\pi$
$90$	1.96593	+	0.0274608i	0.207227	+	0.00289462i
$91$	−7.33005	+	6.10494i	−0.768399	+	0.639972i
$92$			1.43530i			0.149641i
$93$	−5.58609	+	5.50861i	−0.579251	+	0.571216i
$94$	−8.04448	+	4.64448i	−0.829725	+	0.479042i
$95$		−	4.27267i		−	0.438367i
$96$	−1.66986	−	0.459961i	−0.170429	−	0.0469445i
$97$	−8.57395	−	14.8505i	−0.870553	−	1.50784i	−0.861426	−	0.507883i	$-0.830428\pi$
$97$	−8.57395	−	14.8505i	−0.870553	−	1.50784i	−0.00912654	−	0.999958i	$-0.502905\pi$
$98$	4.26126	−	5.55353i	0.430452	−	0.560991i
$99$	−0.129604	+	9.27839i	−0.0130256	+	0.932513i
$100$	−2.28524	+	3.95816i	−0.228524	+	0.395816i
$101$	−3.72432	−	6.45070i	−0.370583	−	0.641869i	0.619072	−	0.785334i	$-0.287509\pi$
$101$	−3.72432	−	6.45070i	−0.370583	−	0.641869i	−0.989655	+	0.143465i	$0.954175\pi$
$102$	−11.7272	−	3.23023i	−1.16116	−	0.319840i
$103$	−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
$107$		−	17.5930i		−	1.70078i	−0.526155	−	0.850389i	$-0.676367\pi$
$107$		−	17.5930i		−	1.70078i	0.526155	−	0.850389i	$-0.323633\pi$
$108$	−3.59645	−	3.75040i	−0.346069	−	0.360883i
$109$	−8.31249	−	4.79922i	−0.796192	−	0.459682i	0.0459460	−	0.998944i	$-0.485370\pi$
$109$	−8.31249	−	4.79922i	−0.796192	−	0.459682i	−0.842138	+	0.539262i	$0.818703\pi$
$110$	1.75555	+	1.01357i	0.167385	+	0.0966399i
$111$	1.36325	−	4.94919i	0.129394	−	0.469757i
$112$	−2.37289	+	1.17020i	−0.224217	+	0.110574i
$113$	−2.25506	+	1.30196i	−0.212138	+	0.122478i	−0.602305	−	0.798266i	$-0.705751\pi$
$113$	−2.25506	+	1.30196i	−0.212138	+	0.122478i	0.390166	+	0.920744i	$0.372417\pi$
$114$	−8.04022	+	7.92869i	−0.753035	+	0.742590i
$115$	0.470330	+	0.814635i	0.0438585	+	0.0759651i
$116$	−3.89073	−	2.24631i	−0.361245	−	0.208565i
$117$	10.3295	+	3.20956i	0.954963	+	0.296724i
$118$			7.07861i			0.651639i
$119$	−16.6644	+	8.21813i	−1.52763	+	0.753355i
$120$	−1.09849	+	0.286132i	−0.100278	+	0.0261201i
$121$	0.716375	−	1.24080i	0.0651250	−	0.112800i
$122$	−13.2960	−	7.67646i	−1.20377	−	0.694994i
$123$	−10.5609	−	10.7095i	−0.952245	−	0.965639i
$124$	2.26475	−	3.92266i	0.203381	−	0.352266i
$125$			6.27225i			0.561007i
$126$	−7.91224	−	0.629640i	−0.704878	−	0.0560928i
$127$	−3.11947	+	5.40309i	−0.276808	+	0.479446i	−0.970590	−	0.240739i	$-0.922610\pi$
$127$	−3.11947	+	5.40309i	−0.276808	+	0.479446i	0.693781	+	0.720186i	$0.255943\pi$
$128$	1.00000			0.0883883
$129$	0.0332002	+	0.127459i	0.00292312	+	0.0112221i
$130$	1.71293	−	1.62775i	0.150234	−	0.142763i
$131$	−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	$0.885305\pi$
$132$	−1.35042	−	5.18441i	−0.117539	−	0.451245i
$133$	−1.12801	+	17.2119i	−0.0978110	+	1.49246i
$134$	3.46095	−	1.99818i	0.298980	−	0.172616i
$135$	−3.27020	−	0.950106i	−0.281454	−	0.0817721i
$136$	7.02284			0.602203
$137$	6.92624			0.591748			0.295874	−	0.955227i	$-0.404389\pi$
$137$	6.92624			0.591748			0.295874	+	0.955227i	$0.404389\pi$
$138$	0.660182	−	2.39676i	0.0561985	−	0.204025i
$139$	−2.27775	+	1.31506i	−0.193196	+	0.111542i	−0.593478	−	0.804850i	$-0.702246\pi$
$139$	−2.27775	+	1.31506i	−0.193196	+	0.111542i	0.400282	+	0.916392i	$0.368912\pi$
$140$	−0.963325	+	1.44174i	−0.0814158	+	0.121849i
$141$	15.5694	−	4.05550i	1.31118	−	0.341535i
$142$	0.469521	+	0.813235i	0.0394014	+	0.0682451i
$143$	7.68230	+	8.08434i	0.642426	+	0.676046i
$144$	2.57687	+	1.53614i	0.214739	+	0.128012i
$145$	−2.94435			−0.244515
$146$	−5.44642	+	9.43348i	−0.450749	+	0.780720i
$147$	−9.67011	+	7.31361i	−0.797577	+	0.603217i
$148$			2.96384i			0.243626i
$149$	3.03198	−	5.25155i	0.248390	−	0.430224i	−0.714689	−	0.699442i	$-0.753432\pi$
$149$	3.03198	−	5.25155i	0.248390	−	0.430224i	0.963079	+	0.269218i	$0.0867653\pi$
$150$	5.63663	−	5.55845i	0.460229	−	0.453845i
$151$	−0.715824	−	0.413281i	−0.0582530	−	0.0336324i	0.470591	−	0.882352i	$-0.344041\pi$
$151$	−0.715824	−	0.413281i	−0.0582530	−	0.0336324i	−0.528844	+	0.848719i	$0.677374\pi$
$152$	3.25972	−	5.64600i	0.264398	−	0.457951i
$153$	18.0969	+	10.7881i	1.46305	+	0.872163i
$154$	−6.80442	−	4.54650i	−0.548316	−	0.366367i
$155$		−	2.96852i		−	0.238437i
$156$	−6.24170	−	0.202785i	−0.499736	−	0.0162358i
$157$	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	$0.582114\pi$
$158$	−1.40194	−	2.42822i	−0.111532	−	0.193179i
$159$	−13.6013	−	13.7926i	−1.07865	−	1.09382i
$160$	0.567570	−	0.327687i	0.0448704	−	0.0259059i
$161$	−1.67959	−	3.40582i	−0.132370	−	0.268416i
$162$	4.28054	+	7.91688i	0.336311	+	0.622009i
$163$	3.86463	+	2.23125i	0.302701	+	0.174765i	0.643656	−	0.765315i	$-0.277417\pi$
$163$	3.86463	+	2.23125i	0.302701	+	0.174765i	−0.340955	+	0.940080i	$0.610750\pi$
$164$	7.52039	+	4.34190i	0.587244	+	0.339045i
$165$	−2.46532	−	2.50000i	−0.191925	−	0.194625i
$166$			7.24087i			0.562000i
$167$	−1.12359	−	0.648707i	−0.0869463	−	0.0501985i	0.455896	−	0.890033i	$-0.349319\pi$
$167$	−1.12359	−	0.648707i	−0.0869463	−	0.0501985i	−0.542843	+	0.839834i	$0.682652\pi$
$168$	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
$171$	17.0729	−	9.54163i	1.30560	−	0.729667i
$172$	−0.0380219	−	0.0658559i	−0.00289915	−	0.00502147i
$173$	6.33267	−	10.9685i	0.481464	−	0.833919i	−0.518310	−	0.855193i	$-0.673439\pi$
$173$	6.33267	−	10.9685i	0.481464	−	0.833919i	0.999774	+	0.0212733i	$0.00677201\pi$
$174$	5.46376	+	5.54062i	0.414207	+	0.420033i
$175$	0.790798	−	12.0665i	0.0597787	−	0.912140i
$176$	1.54655	+	2.67870i	0.116575	+	0.201915i
$177$	3.25588	−	11.8203i	0.244727	−	0.888468i
$178$		−	10.9296i		−	0.819209i
$179$	12.5760	−	7.26077i	0.939976	−	0.542696i	0.0500235	−	0.998748i	$-0.484070\pi$
$179$	12.5760	−	7.26077i	0.939976	−	0.542696i	0.889953	+	0.456052i	$0.150737\pi$
$180$	1.96593	+	0.0274608i	0.146532	+	0.00204680i
$181$		−	3.57257i		−	0.265547i	−0.991146	−	0.132773i	$-0.957612\pi$
$181$		−	3.57257i		−	0.265547i	0.991146	−	0.132773i	$-0.0423883\pi$
$182$	−7.33005	+	6.10494i	−0.543340	+	0.452528i
$183$	18.6716	+	18.9343i	1.38025	+	1.39966i
$184$			1.43530i			0.105812i
$185$	0.971210	+	1.68219i	0.0714048	+	0.123677i
$186$	−5.58609	+	5.50861i	−0.409592	+	0.403911i
$187$	10.8612	+	18.8121i	0.794246	+	1.37568i
$188$	−8.04448	+	4.64448i	−0.586704	+	0.338734i
$189$	12.9227	+	4.69073i	0.939991	+	0.341200i
$190$		−	4.27267i		−	0.309972i
$191$	5.22709	+	3.01786i	0.378219	+	0.218365i	0.677043	−	0.735943i	$-0.263261\pi$
$191$	5.22709	+	3.01786i	0.378219	+	0.218365i	−0.298824	+	0.954308i	$0.596594\pi$
$192$	−1.66986	−	0.459961i	−0.120512	−	0.0331948i
$193$	−20.2555	+	11.6945i	−1.45802	+	0.841791i	−0.998914	−	0.0465881i	$-0.985165\pi$
$193$	−20.2555	+	11.6945i	−1.45802	+	0.841791i	−0.459111	+	0.888379i	$0.651832\pi$
$194$	−8.57395	−	14.8505i	−0.615574	−	1.06620i
$195$	−3.60906	+	1.93023i	−0.258450	+	0.138227i
$196$	4.26126	−	5.55353i	0.304375	−	0.396681i
$197$	−7.90007	+	13.6833i	−0.562857	+	0.974896i	0.434389	+	0.900725i	$0.356964\pi$
$197$	−7.90007	+	13.6833i	−0.562857	+	0.974896i	−0.997246	+	0.0741708i	$0.976369\pi$
$198$	−0.129604	+	9.27839i	−0.00921052	+	0.659386i
$199$		−	24.5006i		−	1.73680i	−0.495863	−	0.868401i	$-0.665148\pi$
$199$		−	24.5006i		−	1.73680i	0.495863	−	0.868401i	$-0.334852\pi$
$200$	−2.28524	+	3.95816i	−0.161591	+	0.279884i
$201$	−6.69838	+	1.74478i	−0.472468	+	0.123067i
$202$	−3.72432	−	6.45070i	−0.262042	−	0.453870i
$203$	11.8609	+	0.777327i	0.832475	+	0.0545577i
$204$	−11.7272	−	3.23023i	−0.821065	−	0.226161i
$205$	5.69113			0.397486
$206$	−15.3456	+	8.85976i	−1.06918	+	0.617289i
$207$	−2.20483	+	3.69859i	−0.153246	+	0.257070i
$208$	3.50535	−	0.844105i	0.243052	−	0.0585282i
$209$	20.1653			1.39486
$210$	2.27176	−	1.96441i	0.156766	−	0.135557i
$211$	−5.93332	+	10.2768i	−0.408467	+	0.707485i	−0.994718	−	0.102644i	$-0.967270\pi$
$211$	−5.93332	+	10.2768i	−0.408467	+	0.707485i	0.586251	+	0.810129i	$0.300603\pi$
$212$	9.68544	+	5.59189i	0.665198	+	0.384053i
$213$	−0.409979	−	1.57395i	−0.0280913	−	0.107845i
$214$		−	17.5930i		−	1.20263i
$215$	−0.0431603	−	0.0249186i	−0.00294351	−	0.00169943i
$216$	−3.59645	−	3.75040i	−0.244708	−	0.255183i
$217$	−0.783707	+	11.9583i	−0.0532015	+	0.811781i
$218$	−8.31249	−	4.79922i	−0.562993	−	0.325044i
$219$	13.4338	−	13.2475i	0.907772	−	0.895181i
$220$	1.75555	+	1.01357i	0.118359	+	0.0683347i
$221$	24.6175	−	5.92801i	1.65595	−	0.398761i
$222$	1.36325	−	4.94919i	0.0914952	−	0.332168i
$223$	11.4114	−	19.7652i	0.764166	−	1.32358i	−0.176520	−	0.984297i	$-0.556484\pi$
$223$	11.4114	−	19.7652i	0.764166	−	1.32358i	0.940686	−	0.339278i	$-0.110183\pi$
$224$	−2.37289	+	1.17020i	−0.158546	+	0.0781874i
$225$	−11.9691	+	6.68921i	−0.797938	+	0.445947i
$226$	−2.25506	+	1.30196i	−0.150005	+	0.0866052i
$227$			10.6843i			0.709140i	0.935029	+	0.354570i	$0.115373\pi$
$227$			10.6843i			0.709140i	−0.935029	+	0.354570i	$0.884627\pi$
$228$	−8.04022	+	7.92869i	−0.532476	+	0.525091i
$229$	1.86852	+	3.23637i	0.123475	+	0.213865i	0.921136	−	0.389241i	$-0.127263\pi$
$229$	1.86852	+	3.23637i	0.123475	+	0.213865i	−0.797661	+	0.603106i	$0.793929\pi$
$230$	0.470330	+	0.814635i	0.0310126	+	0.0537154i
$231$	9.27122	+	10.7218i	0.610001	+	0.705442i
$232$	−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	$0.427788\pi$
$234$	10.3295	+	3.20956i	0.675261	+	0.209816i
$235$	−3.04387	+	5.27214i	−0.198560	+	0.343917i
$236$			7.07861i			0.460778i
$237$	1.22415	+	4.69963i	0.0795171	+	0.305274i
$238$	−16.6644	+	8.21813i	−1.08020	+	0.532702i
$239$	2.27619			0.147234			0.0736172	−	0.997287i	$-0.476546\pi$
$239$	2.27619			0.147234			0.0736172	+	0.997287i	$0.476546\pi$
$240$	−1.09849	+	0.286132i	−0.0709070	+	0.0184697i
$241$	−4.13240			−0.266191			−0.133096	−	0.991103i	$-0.542492\pi$
$241$	−4.13240			−0.266191			−0.133096	+	0.991103i	$0.542492\pi$
$242$	0.716375	−	1.24080i	0.0460503	−	0.0797615i
$243$	−3.50646	−	15.1890i	−0.224939	−	0.974373i
$244$	−13.2960	−	7.67646i	−0.851191	−	0.491435i
$245$	0.598743	−	4.54838i	0.0382523	−	0.290585i
$246$	−10.5609	−	10.7095i	−0.673339	−	0.682810i
$247$	6.66064	−	22.5428i	0.423807	−	1.43436i
$248$	2.26475	−	3.92266i	0.143812	−	0.249089i
$249$	3.33051	−	12.0912i	0.211063	−	0.766251i
$250$			6.27225i			0.396692i
$251$	3.75716	+	6.50759i	0.237150	+	0.410756i	0.959895	−	0.280359i	$-0.0904534\pi$
$251$	3.75716	+	6.50759i	0.237150	+	0.410756i	−0.722745	+	0.691114i	$0.757120\pi$
$252$	−7.91224	−	0.629640i	−0.498424	−	0.0396636i
$253$	−3.84474	+	2.21976i	−0.241717	+	0.139555i
$254$	−3.11947	+	5.40309i	−0.195733	+	0.339020i
$255$	−7.71449	+	2.00946i	−0.483100	+	0.125837i
$256$	1.00000			0.0625000
$257$	−25.2022			−1.57207			−0.786034	−	0.618184i	$-0.787869\pi$
$257$	−25.2022			−1.57207			−0.786034	+	0.618184i	$0.787869\pi$
$258$	0.0332002	+	0.127459i	0.00206696	+	0.00793524i
$259$	−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
$262$	−1.86046	−	3.22241i	−0.114940	−	0.199081i
$263$	−17.2636	+	9.96713i	−1.06452	+	0.614600i	−0.926679	−	0.375855i	$-0.877349\pi$
$263$	−17.2636	+	9.96713i	−1.06452	+	0.614600i	−0.137839	+	0.990455i	$0.544016\pi$
$264$	−1.35042	−	5.18441i	−0.0831129	−	0.319078i
$265$	7.32956			0.450251
$266$	−1.12801	+	17.2119i	−0.0691628	+	1.05533i
$267$	−5.02719	+	18.2509i	−0.307659	+	1.11694i
$268$	3.46095	−	1.99818i	0.211411	−	0.122058i
$269$	20.2140			1.23247			0.616235	−	0.787562i	$-0.288657\pi$
$269$	20.2140			1.23247			0.616235	+	0.787562i	$0.288657\pi$
$270$	−3.27020	−	0.950106i	−0.199018	−	0.0578216i
$271$	−26.4526			−1.60688			−0.803442	−	0.595383i	$-0.797000\pi$
$271$	−26.4526			−1.60688			−0.803442	+	0.595383i	$0.797000\pi$
$272$	7.02284			0.425822
$273$	15.0482	−	6.82287i	0.910759	−	0.412939i
$274$	6.92624			0.418429
$275$	−14.1370			−0.852490
$276$	0.660182	−	2.39676i	0.0397383	−	0.144268i
$277$	3.36980			0.202472			0.101236	−	0.994862i	$-0.467720\pi$
$277$	3.36980			0.202472			0.101236	+	0.994862i	$0.467720\pi$
$278$	−2.27775	+	1.31506i	−0.136610	+	0.0788719i
$279$	11.8617	−	6.62923i	0.710144	−	0.396881i
$280$	−0.963325	+	1.44174i	−0.0575697	+	0.0861604i
$281$	−20.1579			−1.20252			−0.601259	−	0.799055i	$-0.705334\pi$
$281$	−20.1579			−1.20252			−0.601259	+	0.799055i	$0.705334\pi$
$282$	15.5694	−	4.05550i	0.927147	−	0.241501i
$283$	5.52469	−	3.18968i	0.328409	−	0.189607i	−0.326726	−	0.945119i	$-0.605945\pi$
$283$	5.52469	−	3.18968i	0.328409	−	0.189607i	0.655134	+	0.755512i	$0.272612\pi$
$284$	0.469521	+	0.813235i	0.0278610	+	0.0482566i
$285$	−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
$288$	2.57687	+	1.53614i	0.151844	+	0.0905180i
$289$	32.3202			1.90119
$290$	−2.94435			−0.172898
$291$	7.48665	+	28.7420i	0.438875	+	1.68488i
$292$	−5.44642	+	9.43348i	−0.318728	+	0.552053i
$293$	−5.30689	+	3.06394i	−0.310032	+	0.178997i	−0.646941	−	0.762540i	$-0.723952\pi$
$293$	−5.30689	+	3.06394i	−0.310032	+	0.178997i	0.336909	+	0.941537i	$0.390619\pi$
$294$	−9.67011	+	7.31361i	−0.563972	+	0.426539i
$295$	2.31957	+	4.01761i	0.135050	+	0.233914i
$296$			2.96384i			0.172269i
$297$	4.48411	−	15.4340i	0.260195	−	0.895572i
$298$	3.03198	−	5.25155i	0.175638	−	0.304214i
$299$	1.21155	+	5.03124i	0.0700655	+	0.290964i
$300$	5.63663	−	5.55845i	0.325431	−	0.320917i
$301$	0.167287	+	0.111776i	0.00964225	+	0.00644265i
$302$	−0.715824	−	0.413281i	−0.0411911	−	0.0237817i
$303$	3.25202	+	12.4848i	0.186824	+	0.717234i
$304$	3.25972	−	5.64600i	0.186958	−	0.323820i
$305$	−10.0619			−0.576143
$306$	18.0969	+	10.7881i	1.03453	+	0.616713i
$307$	5.38161			0.307145			0.153572	−	0.988137i	$-0.450922\pi$
$307$	5.38161			0.307145			0.153572	+	0.988137i	$0.450922\pi$
$308$	−6.80442	−	4.54650i	−0.387718	−	0.259061i
$309$	29.7001	−	7.73622i	1.68958	−	0.440098i
$310$		−	2.96852i		−	0.168600i
$311$	−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	$0.223844\pi$
$312$	−6.24170	−	0.202785i	−0.353367	−	0.0114805i
$313$	−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
$315$	−4.69708	+	2.23537i	−0.264650	+	0.125949i
$316$	−1.40194	−	2.42822i	−0.0788651	−	0.136598i
$317$	−0.443737	−	0.768575i	−0.0249227	−	0.0431674i	0.853295	−	0.521428i	$-0.174601\pi$
$317$	−0.443737	−	0.768575i	−0.0249227	−	0.0431674i	−0.878218	+	0.478261i	$0.841267\pi$
$318$	−13.6013	−	13.7926i	−0.762722	−	0.773451i
$319$		−	13.8961i		−	0.778035i
$320$	0.567570	−	0.327687i	0.0317282	−	0.0183183i
$321$	−8.09208	+	29.3778i	−0.451656	+	1.63971i
$322$	−1.67959	−	3.40582i	−0.0936001	−	0.189799i
$323$	22.8925	−	39.6509i	1.27377	−	2.20624i
$324$	4.28054	+	7.91688i	0.237808	+	0.439827i
$325$	−4.66948	+	15.8037i	−0.259016	+	0.876632i
$326$	3.86463	+	2.23125i	0.214042	+	0.123577i
$327$	11.6732	+	11.8374i	0.645532	+	0.654612i
$328$	7.52039	+	4.34190i	0.415244	+	0.239741i
$329$	13.6537	−	20.4345i	0.752754	−	1.12659i
$330$	−2.46532	−	2.50000i	−0.135712	−	0.137621i
$331$	16.7252	+	9.65631i	0.919301	+	0.530759i	0.883412	−	0.468597i	$-0.155240\pi$
$331$	16.7252	+	9.65631i	0.919301	+	0.530759i	0.0358889	+	0.999356i	$0.488574\pi$
$332$			7.24087i			0.397394i
$333$	−4.55287	+	7.63743i	−0.249496	+	0.418528i
$334$	−1.12359	−	0.648707i	−0.0614803	−	0.0354957i
$335$	1.30955	−	2.26821i	0.0715486	−	0.123926i
$336$	4.50065	−	0.862636i	0.245531	−	0.0470607i
$337$	−1.76473			−0.0961307			−0.0480654	−	0.998844i	$-0.515306\pi$
$337$	−1.76473			−0.0961307			−0.0480654	+	0.998844i	$0.515306\pi$
$338$	11.5750	−	5.91777i	0.629596	−	0.321884i
$339$	4.36449	−	1.13685i	0.237047	−	0.0617454i
$340$	3.98595	−	2.30129i	0.216169	−	0.124805i
$341$	14.0102			0.758694
$342$	17.0729	−	9.54163i	0.923198	−	0.515952i
$343$	−3.61276	+	18.1645i	−0.195071	+	0.980789i
$344$	−0.0380219	−	0.0658559i	−0.00205001	−	0.00355071i
$345$	−0.410685	−	1.57666i	−0.0221106	−	0.0848845i
$346$	6.33267	−	10.9685i	0.340446	−	0.589670i
$347$		−	22.7100i		−	1.21914i	−0.792733	−	0.609569i	$-0.791343\pi$
$347$		−	22.7100i		−	1.21914i	0.792733	−	0.609569i	$-0.208657\pi$
$348$	5.46376	+	5.54062i	0.292889	+	0.297008i
$349$	−0.756268	+	1.30990i	−0.0404821	+	0.0701171i	−0.885557	−	0.464532i	$-0.846223\pi$
$349$	−0.756268	+	1.30990i	−0.0404821	+	0.0701171i	0.845074	+	0.534649i	$0.179556\pi$
$350$	0.790798	−	12.0665i	0.0422699	−	0.644981i
$351$	−15.7726	−	10.1107i	−0.841877	−	0.539669i
$352$	1.54655	+	2.67870i	0.0824313	+	0.142775i
$353$	−28.2367	+	16.3025i	−1.50289	+	0.867692i	−0.502892	+	0.864349i	$0.667731\pi$
$353$	−28.2367	+	16.3025i	−1.50289	+	0.867692i	−0.999994	+	0.00334317i	$0.998936\pi$
$354$	3.25588	−	11.8203i	0.173048	−	0.628241i
$355$	0.532973	+	0.307712i	0.0282873	+	0.0163317i
$356$		−	10.9296i		−	0.579268i
$357$	31.6073	−	6.05815i	1.67284	−	0.320631i
$358$	12.5760	−	7.26077i	0.664664	−	0.383744i
$359$	3.19150	+	5.52784i	0.168441	+	0.291748i	0.937872	−	0.346982i	$-0.112793\pi$
$359$	3.19150	+	5.52784i	0.168441	+	0.291748i	−0.769431	+	0.638730i	$0.779460\pi$
$360$	1.96593	+	0.0274608i	0.103614	+	0.00144731i
$361$	−11.7515	−	20.3543i	−0.618502	−	1.07128i
$362$		−	3.57257i		−	0.187770i
$363$	−1.76696	+	1.74246i	−0.0927416	+	0.0914552i
$364$	−7.33005	+	6.10494i	−0.384199	+	0.319986i
$365$			7.13889i			0.373666i
$366$	18.6716	+	18.9343i	0.975982	+	0.989710i
$367$	−10.4124	+	6.01163i	−0.543525	+	0.313804i	−0.746506	−	0.665378i	$-0.768270\pi$
$367$	−10.4124	+	6.01163i	−0.543525	+	0.313804i	0.202981	+	0.979183i	$0.434937\pi$
$368$			1.43530i			0.0748203i
$369$	12.7093	+	22.7409i	0.661620	+	1.18384i
$370$	0.971210	+	1.68219i	0.0504908	+	0.0874527i
$371$	−29.5262	−	1.93505i	−1.53292	−	0.100463i
$372$	−5.58609	+	5.50861i	−0.289625	+	0.285608i
$373$	10.8556	−	18.8024i	0.562081	−	0.973553i	−0.435234	−	0.900317i	$-0.643334\pi$
$373$	10.8556	−	18.8024i	0.562081	−	0.973553i	0.997315	−	0.0732353i	$-0.0233324\pi$
$374$	10.8612	+	18.8121i	0.561617	+	0.972749i
$375$	2.88499	−	10.4738i	0.148980	−	0.540864i
$376$	−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	0.433281	−	0.901259i	$-0.357356\pi$
$379$	−2.54234	−	1.46782i	−0.130591	−	0.0753970i	−0.563873	+	0.825862i	$0.690689\pi$
$380$		−	4.27267i		−	0.219183i
$381$	7.69429	−	7.58757i	0.394191	−	0.388723i
$382$	5.22709	+	3.01786i	0.267441	+	0.154407i
$383$	26.1275	+	15.0847i	1.33505	+	0.770793i	0.986069	−	0.166335i	$-0.0531934\pi$
$383$	26.1275	+	15.0847i	1.33505	+	0.770793i	0.348984	+	0.937129i	$0.386527\pi$
$384$	−1.66986	−	0.459961i	−0.0852147	−	0.0234723i
$385$	−5.35181	−	0.350741i	−0.272754	−	0.0178754i
$386$	−20.2555	+	11.6945i	−1.03098	+	0.595236i
$387$	0.00318631	−	0.228109i	0.000161969	−	0.0115955i
$388$	−8.57395	−	14.8505i	−0.435276	−	0.753921i
$389$	−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	$0.856223\pi$
$390$	−3.60906	+	1.93023i	−0.182752	+	0.0977410i
$391$			10.0799i			0.509762i
$392$	4.26126	−	5.55353i	0.215226	−	0.280496i
$393$	1.62453	+	6.23671i	0.0819465	+	0.314601i
$394$	−7.90007	+	13.6833i	−0.398000	+	0.689356i
$395$	−1.59139	−	0.918792i	−0.0800718	−	0.0462295i
$396$	−0.129604	+	9.27839i	−0.00651282	+	0.466256i
$397$	6.54053	−	11.3285i	0.328260	−	0.568562i	−0.653907	−	0.756575i	$-0.726871\pi$
$397$	6.54053	−	11.3285i	0.328260	−	0.568562i	0.982167	+	0.188013i	$0.0602046\pi$
$398$		−	24.5006i		−	1.22810i
$399$	9.80042	−	28.2226i	0.490634	−	1.41290i
$400$	−2.28524	+	3.95816i	−0.114262	+	0.197908i
$401$	−6.92658			−0.345897			−0.172948	−	0.984931i	$-0.555329\pi$
$401$	−6.92658			−0.345897			−0.172948	+	0.984931i	$0.555329\pi$
$402$	−6.69838	+	1.74478i	−0.334085	+	0.0870218i
$403$	4.62761	−	15.6620i	0.230517	−	0.780180i
$404$	−3.72432	−	6.45070i	−0.185292	−	0.320934i
$405$	5.02377	+	3.09071i	0.249633	+	0.153579i
$406$	11.8609	+	0.777327i	0.588648	+	0.0385781i
$407$	−7.93923	+	4.58372i	−0.393533	+	0.227206i
$408$	−11.7272	−	3.23023i	−0.580581	−	0.159920i
$409$	32.6793			1.61589			0.807944	−	0.589260i	$-0.200580\pi$
$409$	32.6793			1.61589			0.807944	+	0.589260i	$0.200580\pi$
$410$	5.69113			0.281065
$411$	−11.5659	−	3.18580i	−0.570501	−	0.157144i
$412$	−15.3456	+	8.85976i	−0.756021	+	0.436489i
$413$	−8.28340	−	16.7968i	−0.407599	−	0.826516i
$414$	−2.20483	+	3.69859i	−0.108361	+	0.181776i
$415$	2.37274	+	4.10970i	0.116473	+	0.201737i
$416$	3.50535	−	0.844105i	0.171864	−	0.0413857i
$417$	4.40839	−	1.14829i	0.215880	−	0.0562319i
$418$	20.1653			0.986315
$419$	−3.98319	+	6.89908i	−0.194591	+	0.337042i	−0.946766	−	0.321921i	$-0.895671\pi$
$419$	−3.98319	+	6.89908i	−0.194591	+	0.337042i	0.752175	+	0.658963i	$0.229005\pi$
$420$	2.27176	−	1.96441i	0.110851	−	0.0958535i
$421$			14.1689i			0.690552i	0.938501	+	0.345276i	$0.112215\pi$
$421$			14.1689i			0.690552i	−0.938501	+	0.345276i	$0.887785\pi$
$422$	−5.93332	+	10.2768i	−0.288830	+	0.500268i
$423$	−27.8642	−	0.389216i	−1.35480	−	0.0189243i
$424$	9.68544	+	5.59189i	0.470366	+	0.271566i
$425$	−16.0489	+	27.7975i	−0.778485	+	1.34838i
$426$	−0.409979	−	1.57395i	−0.0198636	−	0.0762582i
$427$	40.5331	+	2.65641i	1.96153	+	0.128552i
$428$		−	17.5930i		−	0.850389i
$429$	−9.10990	−	17.0333i	−0.439830	−	0.822374i
$430$	−0.0431603	−	0.0249186i	−0.00208137	−	0.00120168i
$431$	12.9721	+	22.4684i	0.624845	+	1.08226i	0.988571	+	0.150758i	$0.0481713\pi$
$431$	12.9721	+	22.4684i	0.624845	+	1.08226i	−0.363725	+	0.931506i	$0.618495\pi$
$432$	−3.59645	−	3.75040i	−0.173034	−	0.180441i
$433$	−14.7383	+	8.50919i	−0.708280	+	0.408925i	−0.810424	−	0.585844i	$-0.800763\pi$
$433$	−14.7383	+	8.50919i	−0.708280	+	0.408925i	0.102144	+	0.994770i	$0.467430\pi$
$434$	−0.783707	+	11.9583i	−0.0376191	+	0.574016i
$435$	4.91666	+	1.35429i	0.235736	+	0.0649331i
$436$	−8.31249	−	4.79922i	−0.398096	−	0.229841i
$437$	8.10372	+	4.67868i	0.387653	+	0.223812i
$438$	13.4338	−	13.2475i	0.641892	−	0.632988i
$439$		−	29.6229i		−	1.41382i	−0.707301	−	0.706912i	$-0.750087\pi$
$439$		−	29.6229i		−	1.41382i	0.707301	−	0.706912i	$-0.249913\pi$
$440$	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	$0.194546\pi$
$444$	1.36325	−	4.94919i	0.0646969	−	0.234878i
$445$	−3.58149	−	6.20333i	−0.169779	−	0.294066i
$446$	11.4114	−	19.7652i	0.540347	−	0.935909i
$447$	−7.47850	+	7.37476i	−0.353721	+	0.348814i
$448$	−2.37289	+	1.17020i	−0.112109	+	0.0552868i
$449$	−11.2383	−	19.4653i	−0.530369	−	0.918626i	−0.999372	−	0.0354297i	$-0.988720\pi$
$449$	−11.2383	−	19.4653i	−0.530369	−	0.918626i	0.469003	−	0.883197i	$-0.344613\pi$
$450$	−11.9691	+	6.68921i	−0.564227	+	0.315332i
$451$			26.8598i			1.26478i
$452$	−2.25506	+	1.30196i	−0.106069	+	0.0612391i
$453$	1.00523	+	1.01937i	0.0472300	+	0.0478943i
$454$			10.6843i			0.501438i
$455$	−2.15981	+	5.86695i	−0.101254	+	0.275047i
$456$	−8.04022	+	7.92869i	−0.376518	+	0.371295i
$457$			26.4676i			1.23810i	0.785350	+	0.619051i	$0.212483\pi$
$457$			26.4676i			1.23810i	−0.785350	+	0.619051i	$0.787517\pi$
$458$	1.86852	+	3.23637i	0.0873101	+	0.151226i
$459$	−25.2573	−	26.3385i	−1.17891	−	1.22937i
$460$	0.470330	+	0.814635i	0.0219292	+	0.0379826i
$461$	6.02929	−	3.48101i	0.280812	−	0.162127i	−0.352979	−	0.935631i	$-0.614831\pi$
$461$	6.02929	−	3.48101i	0.280812	−	0.162127i	0.633791	+	0.773504i	$0.281498\pi$
$462$	9.27122	+	10.7218i	0.431336	+	0.498823i
$463$		−	10.3837i		−	0.482572i	−0.970454	−	0.241286i	$-0.922431\pi$
$463$		−	10.3837i		−	0.482572i	0.970454	−	0.241286i	$-0.0775692\pi$
$464$	−3.89073	−	2.24631i	−0.180623	−	0.104283i
$465$	−1.36540	+	4.95701i	−0.0633190	+	0.229876i
$466$	−7.73067	+	4.46331i	−0.358117	+	0.206759i
$467$	−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	$-0.349589\pi$
$468$	10.3295	+	3.20956i	0.477482	+	0.148362i
$469$	−5.87419	+	8.79147i	−0.271245	+	0.405953i
$470$	−3.04387	+	5.27214i	−0.140403	+	0.243186i
$471$	−8.00070	−	8.11324i	−0.368653	−	0.373838i
$472$			7.07861i			0.325819i
$473$	0.117606	−	0.203699i	0.00540751	−	0.00936608i
$474$	1.22415	+	4.69963i	0.0562271	+	0.215861i
$475$	14.8985	+	25.8050i	0.683590	+	1.18401i
$476$	−16.6644	+	8.21813i	−0.763814	+	0.376678i
$477$	16.3682	+	29.2878i	0.749449	+	1.34100i
$478$	2.27619			0.104110
$479$	−7.41327	+	4.28005i	−0.338721	+	0.195561i	−0.659706	−	0.751524i	$-0.729319\pi$
$479$	−7.41327	+	4.28005i	−0.338721	+	0.195561i	0.320985	+	0.947084i	$0.395986\pi$
$480$	−1.09849	+	0.286132i	−0.0501388	+	0.0130601i
$481$	2.50179	+	10.3893i	0.114072	+	0.473711i
$482$	−4.13240			−0.188226
$483$	1.23814	+	6.45979i	0.0563375	+	0.293931i
$484$	0.716375	−	1.24080i	0.0325625	−	0.0563999i
$485$	−9.73264	−	5.61914i	−0.441936	−	0.255152i
$486$	−3.50646	−	15.1890i	−0.159056	−	0.688986i
$487$			17.5739i			0.796348i	0.917310	+	0.398174i	$0.130356\pi$
$487$			17.5739i			0.796348i	−0.917310	+	0.398174i	$0.869644\pi$
$488$	−13.2960	−	7.67646i	−0.601883	−	0.347497i
$489$	−5.42711	−	5.50345i	−0.245422	−	0.248875i
$490$	0.598743	−	4.54838i	0.0270485	−	0.205475i
$491$	7.73222	+	4.46420i	0.348950	+	0.201467i	0.664223	−	0.747535i	$-0.268763\pi$
$491$	7.73222	+	4.46420i	0.348950	+	0.201467i	−0.315273	+	0.949001i	$0.602096\pi$
$492$	−10.5609	−	10.7095i	−0.476122	−	0.482819i
$493$	−27.3240	−	15.7755i	−1.23061	−	0.710493i
$494$	6.66064	−	22.5428i	0.299677	−	1.01425i
$495$	2.96685	+	5.30861i	0.133350	+	0.238604i
$496$	2.26475	−	3.92266i	0.101690	−	0.176133i
$497$	−2.06577	−	1.38029i	−0.0926626	−	0.0619143i
$498$	3.33051	−	12.0912i	0.149244	−	0.541822i
$499$	−8.26926	+	4.77426i	−0.370183	+	0.213725i	−0.673538	−	0.739152i	$-0.735226\pi$
$499$	−8.26926	+	4.77426i	−0.370183	+	0.213725i	0.303355	+	0.952877i	$0.401893\pi$
$500$			6.27225i			0.280503i
$501$	1.57787	+	1.60006i	0.0704938	+	0.0714854i
$502$	3.75716	+	6.50759i	0.167690	+	0.290448i
$503$	−12.4146	−	21.5027i	−0.553539	−	0.958757i	−0.998016	−	0.0629667i	$-0.979944\pi$
$503$	−12.4146	−	21.5027i	−0.553539	−	0.958757i	0.444477	−	0.895790i	$-0.353390\pi$
$504$	−7.91224	−	0.629640i	−0.352439	−	0.0280464i
$505$	−4.22762	−	2.44082i	−0.188127	−	0.108615i
$506$	−3.84474	+	2.21976i	−0.170920	+	0.0986806i
$507$	−22.0505	+	4.55782i	−0.979299	+	0.202420i
$508$	−3.11947	+	5.40309i	−0.138404	+	0.239723i
$509$		−	14.4428i		−	0.640168i	−0.947389	−	0.320084i	$-0.896289\pi$
$509$		−	14.4428i		−	0.640168i	0.947389	−	0.320084i	$-0.103711\pi$
$510$	−7.71449	+	2.00946i	−0.341603	+	0.0889802i
$511$	1.88471	−	28.7581i	0.0833747	−	1.27218i
$512$	1.00000			0.0441942
$513$	−32.8982	+	8.08032i	−1.45249	+	0.356755i
$514$	−25.2022			−1.11162
$515$	−5.80646	+	10.0571i	−0.255863	+	0.443168i
$516$	0.0332002	+	0.127459i	0.00146156	+	0.00561106i
$517$	−24.8824	−	14.3658i	−1.09433	−	0.631809i
$518$	−3.46829	−	7.03287i	−0.152388	−	0.309007i
$519$	−15.6197	+	15.4031i	−0.685631	+	0.676121i
$520$	1.71293	−	1.62775i	0.0751170	−	0.0713814i
$521$	−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	$0.936654\pi$
$522$	−6.57526	−	11.7652i	−0.287791	−	0.514948i
$523$		−	15.5942i		−	0.681887i	−0.940084	−	0.340944i	$-0.889253\pi$
$523$		−	15.5942i		−	0.681887i	0.940084	−	0.340944i	$-0.110747\pi$
$524$	−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
$527$	15.9050	−	27.5482i	0.692831	−	1.20002i
$528$	−1.35042	−	5.18441i	−0.0587697	−	0.225622i
$529$	20.9399			0.910431
$530$	7.32956			0.318376
$531$	−10.8737	+	18.2407i	−0.471880	+	0.791578i
$532$	−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
$535$	−5.76499	−	9.98526i	−0.249242	−	0.431700i
$536$	3.46095	−	1.99818i	0.149490	−	0.0863082i
$537$	−24.3399	+	6.34000i	−1.05034	+	0.273591i
$538$	20.2140			0.871488
$539$	21.4665	+	2.82582i	0.924627	+	0.121717i
$540$	−3.27020	−	0.950106i	−0.140727	−	0.0408861i
$541$	−36.0971	+	20.8407i	−1.55194	+	0.896011i	−0.553953	+	0.832548i	$0.686881\pi$
$541$	−36.0971	+	20.8407i	−1.55194	+	0.896011i	−0.997984	+	0.0634632i	$0.979785\pi$
$542$	−26.4526			−1.13624
$543$	−1.64324	+	5.96569i	−0.0705182	+	0.256012i
$544$	7.02284			0.301102
$545$	−6.29056			−0.269458
$546$	15.0482	−	6.82287i	0.644004	−	0.291992i
$547$	−0.933149			−0.0398986			−0.0199493	−	0.999801i	$-0.506350\pi$
$547$	−0.933149			−0.0398986			−0.0199493	+	0.999801i	$0.506350\pi$
$548$	6.92624			0.295874
$549$	−22.4700	−	40.2058i	−0.958997	−	1.71594i
$550$	−14.1370			−0.602802
$551$	−25.3654	+	14.6447i	−1.08060	+	0.623886i
$552$	0.660182	−	2.39676i	0.0280992	−	0.102013i
$553$	6.16816	+	4.12137i	0.262297	+	0.175259i
$554$	3.36980			0.143169
$555$	−0.848047	−	3.25574i	−0.0359976	−	0.138198i
$556$	−2.27775	+	1.31506i	−0.0965979	+	0.0557708i
$557$	16.7603	+	29.0296i	0.710155	+	1.23002i	0.964799	+	0.262990i	$0.0847085\pi$
$557$	16.7603	+	29.0296i	0.710155	+	1.23002i	−0.254644	+	0.967035i	$0.581958\pi$
$558$	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
$561$	−9.48381	−	36.4093i	−0.400407	−	1.53720i
$562$	−20.1579			−0.850308
$563$	−3.86351			−0.162828			−0.0814138	−	0.996680i	$-0.525944\pi$
$563$	−3.86351			−0.162828			−0.0814138	+	0.996680i	$0.525944\pi$
$564$	15.5694	−	4.05550i	0.655592	−	0.170767i
$565$	−0.853271	+	1.47791i	−0.0358974	+	0.0621761i
$566$	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
$569$		−	26.9233i		−	1.12868i	−0.825541	−	0.564342i	$-0.809130\pi$
$569$		−	26.9233i		−	1.12868i	0.825541	−	0.564342i	$-0.190870\pi$
$570$	−1.96526	+	7.13477i	−0.0823157	+	0.298842i
$571$	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	$0.0967768\pi$
$572$	7.68230	+	8.08434i	0.321213	+	0.338023i
$573$	−7.34042	−	7.44367i	−0.306651	−	0.310964i
$574$	−22.9260	−	1.50249i	−0.956912	−	0.0627129i
$575$	−5.68115	−	3.28001i	−0.236920	−	0.136786i
$576$	2.57687	+	1.53614i	0.107370	+	0.0640059i
$577$	−10.2980	+	17.8366i	−0.428711	+	0.742549i	−0.996759	−	0.0804462i	$-0.974365\pi$
$577$	−10.2980	+	17.8366i	−0.428711	+	0.742549i	0.568048	+	0.822995i	$0.307699\pi$
$578$	32.3202			1.34434
$579$	39.2029	−	10.2115i	1.62922	−	0.424376i
$580$	−2.94435			−0.122258
$581$	−8.47328	−	17.1818i	−0.351531	−	0.712822i
$582$	7.48665	+	28.7420i	0.310332	+	1.19139i
$583$			34.5925i			1.43268i
$584$	−5.44642	+	9.43348i	−0.225375	+	0.390360i
$585$	6.91445	−	1.56319i	0.285878	−	0.0646300i
$586$	−5.30689	+	3.06394i	−0.219226	+	0.126570i
$587$	23.7246	+	13.6974i	0.979217	+	0.565351i	0.902034	−	0.431666i	$-0.142074\pi$
$587$	23.7246	+	13.6974i	0.979217	+	0.565351i	0.0771834	+	0.997017i	$0.475407\pi$
$588$	−9.67011	+	7.31361i	−0.398789	+	0.301608i
$589$	−14.7649	−	25.5736i	−0.608377	−	1.05374i
$590$	2.31957	+	4.01761i	0.0954951	+	0.165402i
$591$	19.4858	−	19.2155i	0.801539	−	0.790421i
$592$			2.96384i			0.121813i
$593$	11.0590	−	6.38494i	0.454141	−	0.262198i	−0.255437	−	0.966826i	$-0.582219\pi$
$593$	11.0590	−	6.38494i	0.454141	−	0.262198i	0.709577	+	0.704628i	$0.248886\pi$
$594$	4.48411	−	15.4340i	0.183985	−	0.633265i
$595$	−6.76527	+	10.1251i	−0.277349	+	0.415088i
$596$	3.03198	−	5.25155i	0.124195	−	0.215112i
$597$	−11.2693	+	40.9126i	−0.461222	+	1.67444i
$598$	1.21155	+	5.03124i	0.0495438	+	0.205743i
$599$	−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	$0.911808\pi$
$600$	5.63663	−	5.55845i	0.230115	−	0.226923i
$601$	−33.7422	−	19.4811i	−1.37637	−	0.794649i	−0.384652	−	0.923062i	$-0.625678\pi$
$601$	−33.7422	−	19.4811i	−1.37637	−	0.794649i	−0.991721	+	0.128413i	$0.959012\pi$
$602$	0.167287	+	0.111776i	0.00681810	+	0.00455564i
$603$	11.9879	+	0.167451i	0.488185	+	0.00681913i
$604$	−0.715824	−	0.413281i	−0.0291265	−	0.0168162i
$605$		−	0.938987i		−	0.0381752i
$606$	3.25202	+	12.4848i	0.132104	+	0.507161i
$607$	−0.845852	−	0.488353i	−0.0343321	−	0.0198216i	0.482736	−	0.875766i	$-0.339643\pi$
$607$	−0.845852	−	0.488353i	−0.0343321	−	0.0198216i	−0.517068	+	0.855944i	$0.672976\pi$
$608$	3.25972	−	5.64600i	0.132199	−	0.228976i
$609$	−19.4486	−	6.75359i	−0.788096	−	0.273669i
$610$	−10.0619			−0.407395
$611$	−24.2783	+	23.0709i	−0.982195	+	0.933350i
$612$	18.0969	+	10.7881i	0.731526	+	0.436082i
$613$	5.04618	−	2.91341i	0.203813	−	0.117672i	−0.394620	−	0.918845i	$-0.629124\pi$
$613$	5.04618	−	2.91341i	0.203813	−	0.117672i	0.598433	+	0.801173i	$0.295790\pi$
$614$	5.38161			0.217184
$615$	−9.50340	−	2.61770i	−0.383214	−	0.105556i
$616$	−6.80442	−	4.54650i	−0.274158	−	0.183184i
$617$	−10.4203	−	18.0485i	−0.419506	−	0.726606i	0.576384	−	0.817179i	$-0.304463\pi$
$617$	−10.4203	−	18.0485i	−0.419506	−	0.726606i	−0.995890	+	0.0905731i	$0.971130\pi$
$618$	29.7001	−	7.73622i	1.19471	−	0.311196i
$619$	−3.21016	+	5.56015i	−0.129027	+	0.223481i	−0.923300	−	0.384080i	$-0.874519\pi$
$619$	−3.21016	+	5.56015i	−0.129027	+	0.223481i	0.794273	+	0.607561i	$0.207852\pi$
$620$		−	2.96852i		−	0.119219i
$621$	5.38296	−	5.16200i	0.216011	−	0.207144i
$622$	−3.15077	+	5.45729i	−0.126334	+	0.218817i
$623$	12.7899	+	25.9348i	0.512415	+	1.03906i
$624$	−6.24170	−	0.202785i	−0.249868	−	0.00811791i
$625$	−9.37088	−	16.2308i	−0.374835	−	0.649234i
$626$	−9.08951	+	5.24783i	−0.363290	+	0.209746i
$627$	−33.6732	−	9.27523i	−1.34478	−	0.370417i
$628$	5.69728	+	3.28932i	0.227346	+	0.131258i
$629$			20.8145i			0.829930i
$630$	−4.69708	+	2.23537i	−0.187136	+	0.0890594i
$631$	−14.8774	+	8.58945i	−0.592258	+	0.341941i	−0.765990	−	0.642852i	$-0.777751\pi$
$631$	−14.8774	+	8.58945i	−0.592258	+	0.341941i	0.173732	+	0.984793i	$0.444418\pi$
$632$	−1.40194	−	2.42822i	−0.0557660	−	0.0965896i
$633$	14.6348	−	14.4318i	0.581679	−	0.573611i
$634$	−0.443737	−	0.768575i	−0.0176230	−	0.0305240i
$635$			4.08884i			0.162261i
$636$	−13.6013	−	13.7926i	−0.539326	−	0.546912i
$637$	10.2494	−	23.0640i	0.406097	−	0.913830i
$638$		−	13.8961i		−	0.550153i
$639$	−0.0393467	+	2.81685i	−0.00155653	+	0.111433i
$640$	0.567570	−	0.327687i	0.0224352	−	0.0129530i
$641$			21.8700i			0.863814i	0.901918	+	0.431907i	$0.142159\pi$
$641$			21.8700i			0.863814i	−0.901918	+	0.431907i	$0.857841\pi$
$642$	−8.09208	+	29.3778i	−0.319369	+	1.15945i
$643$	4.78089	+	8.28074i	0.188540	+	0.326561i	0.944764	−	0.327753i	$-0.106291\pi$
$643$	4.78089	+	8.28074i	0.188540	+	0.326561i	−0.756224	+	0.654313i	$0.772958\pi$
$644$	−1.67959	−	3.40582i	−0.0661852	−	0.134208i
$645$	0.0606101	+	0.0614626i	0.00238652	+	0.00242009i
$646$	22.8925	−	39.6509i	0.900692	−	1.56004i
$647$	−16.3263	−	28.2780i	−0.641854	−	1.11172i	−0.985018	−	0.172449i	$-0.944832\pi$
$647$	−16.3263	−	28.2780i	−0.641854	−	1.11172i	0.343164	−	0.939275i	$-0.388501\pi$
$648$	4.28054	+	7.91688i	0.168156	+	0.311004i
$649$	−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
$653$			38.2820i			1.49809i	0.662519	+	0.749045i	$0.269487\pi$
$653$			38.2820i			1.49809i	−0.662519	+	0.749045i	$0.730513\pi$
$654$	11.6732	+	11.8374i	0.456460	+	0.462881i
$655$	−2.11188	−	1.21930i	−0.0825181	−	0.0476418i
$656$	7.52039	+	4.34190i	0.293622	+	0.169523i
$657$	−28.5259	+	15.9424i	−1.11290	+	0.621972i
$658$	13.6537	−	20.4345i	0.532278	−	0.796621i
$659$	−4.16940	+	2.40720i	−0.162417	+	0.0937713i	−0.579005	−	0.815324i	$-0.696559\pi$
$659$	−4.16940	+	2.40720i	−0.162417	+	0.0937713i	0.416589	+	0.909095i	$0.363226\pi$
$660$	−2.46532	−	2.50000i	−0.0959626	−	0.0973124i
$661$	6.39508	+	11.0766i	0.248740	+	0.430830i	0.963176	−	0.268870i	$-0.0866502\pi$
$661$	6.39508	+	11.0766i	0.248740	+	0.430830i	−0.714437	+	0.699700i	$0.753317\pi$
$662$	16.7252	+	9.65631i	0.650044	+	0.375303i
$663$	−43.8345	−	1.42413i	−1.70239	−	0.0553085i
$664$			7.24087i			0.281000i
$665$	4.99989	+	10.1386i	0.193887	+	0.393158i
$666$	−4.55287	+	7.63743i	−0.176420	+	0.295944i
$667$	3.22414	−	5.58437i	0.124839	−	0.216228i
$668$	−1.12359	−	0.648707i	−0.0434732	−	0.0250992i
$669$	−28.1467	+	27.7563i	−1.08822	+	1.07312i
$670$	1.30955	−	2.26821i	0.0505925	−	0.0876288i
$671$		−	47.4881i		−	1.83326i
$672$	4.50065	−	0.862636i	0.173616	−	0.0332769i
$673$	20.4148	−	35.3595i	0.786934	−	1.36301i	−0.140903	−	0.990023i	$-0.545000\pi$
$673$	20.4148	−	35.3595i	0.786934	−	1.36301i	0.927837	−	0.372986i	$-0.121666\pi$
$674$	−1.76473			−0.0679747
$675$	23.0634	−	5.66475i	0.887713	−	0.218036i
$676$	11.5750	−	5.91777i	0.445191	−	0.227607i
$677$	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	$0.812464\pi$
$678$	4.36449	−	1.13685i	0.167617	−	0.0436606i
$679$	37.7232	+	25.2055i	1.44768	+	0.967297i
$680$	3.98595	−	2.30129i	0.152854	−	0.0882505i
$681$	4.91435	−	17.8413i	0.188318	−	0.683678i
$682$	14.0102			0.536478
$683$	6.61788			0.253226			0.126613	−	0.991952i	$-0.459589\pi$
$683$	6.61788			0.253226			0.126613	+	0.991952i	$0.459589\pi$
$684$	17.0729	−	9.54163i	0.652800	−	0.364833i
$685$	3.93113	−	2.26964i	0.150201	−	0.0867184i
$686$	−3.61276	+	18.1645i	−0.137936	+	0.693523i
$687$	−1.63156	−	6.26373i	−0.0622480	−	0.238976i
$688$	−0.0380219	−	0.0658559i	−0.00144957	−	0.00251073i
$689$	38.6710	+	11.4260i	1.47325	+	0.435296i
$690$	−0.410685	−	1.57666i	−0.0156345	−	0.0600224i
$691$	48.1215			1.83063			0.915313	−	0.402742i	$-0.131943\pi$
$691$	48.1215			1.83063			0.915313	+	0.402742i	$0.131943\pi$
$692$	6.33267	−	10.9685i	0.240732	−	0.416960i
$693$	−10.5500	−	22.1683i	−0.400763	−	0.842104i
$694$		−	22.7100i		−	0.862061i
$695$	−0.861854	+	1.49277i	−0.0326920	+	0.0566242i
$696$	5.46376	+	5.54062i	0.207103	+	0.210017i
$697$	52.8145	+	30.4924i	2.00049	+	1.15498i
$698$	−0.756268	+	1.30990i	−0.0286252	+	0.0495803i
$699$	14.9621	−	3.89730i	0.565919	−	0.147409i
$700$	0.790798	−	12.0665i	0.0298894	−	0.456070i
$701$		−	37.9458i		−	1.43319i	−0.697487	−	0.716597i	$-0.745699\pi$
$701$		−	37.9458i		−	1.43319i	0.697487	−	0.716597i	$-0.254301\pi$
$702$	−15.7726	−	10.1107i	−0.595297	−	0.381603i
$703$	16.7338	+	9.66127i	0.631128	+	0.364382i
$704$	1.54655	+	2.67870i	0.0582877	+	0.100957i
$705$	7.50783	−	7.40369i	0.282761	−	0.278839i
$706$	−28.2367	+	16.3025i	−1.06270	+	0.613551i
$707$	16.3860	+	10.9486i	0.616260	+	0.411766i
$708$	3.25588	−	11.8203i	0.122364	−	0.444234i
$709$	−11.1532	−	6.43929i	−0.418867	−	0.241833i	0.275726	−	0.961236i	$-0.411082\pi$
$709$	−11.1532	−	6.43929i	−0.418867	−	0.241833i	−0.694592	+	0.719404i	$0.744415\pi$
$710$	0.532973	+	0.307712i	0.0200021	+	0.0115482i
$711$	0.117485	−	8.41080i	0.00440602	−	0.315429i
$712$		−	10.9296i		−	0.409605i
$713$	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
$717$	−3.80092	−	1.04696i	−0.141948	−	0.0390993i
$718$	3.19150	+	5.52784i	0.119106	+	0.206297i
$719$	−16.6678	+	28.8694i	−0.621603	+	1.07665i	0.367584	+	0.929990i	$0.380185\pi$
$719$	−16.6678	+	28.8694i	−0.621603	+	1.07665i	−0.989187	+	0.146658i	$0.953148\pi$
$720$	1.96593	+	0.0274608i	0.0732659	+	0.00102340i
$721$	26.0457	−	38.9807i	0.969992	−	1.45172i
$722$	−11.7515	−	20.3543i	−0.437347	−	0.757508i
$723$	6.90053	+	1.90074i	0.256633	+	0.0706893i
$724$		−	3.57257i		−	0.132773i
$725$	17.7825	−	10.2667i	0.660427	−	0.381297i
$726$	−1.76696	+	1.74246i	−0.0655782	+	0.0646686i
$727$		−	3.84364i		−	0.142553i	−0.997457	−	0.0712764i	$-0.977293\pi$
$727$		−	3.84364i		−	0.142553i	0.997457	−	0.0712764i	$-0.0227072\pi$
$728$	−7.33005	+	6.10494i	−0.271670	+	0.226264i
$729$	−1.13103	+	26.9763i	−0.0418900	+	0.999122i
$730$			7.13889i			0.264222i
$731$	−0.267022	−	0.462495i	−0.00987616	−	0.0171060i
$732$	18.6716	+	18.9343i	0.690124	+	0.699831i
$733$	−21.0661	−	36.4875i	−0.778093	−	1.34770i	−0.933040	−	0.359773i	$-0.882854\pi$
$733$	−21.0661	−	36.4875i	−0.778093	−	1.34770i	0.154947	−	0.987923i	$-0.450479\pi$
$734$	−10.4124	+	6.01163i	−0.384330	+	0.221893i
$735$	−3.09189	+	7.31976i	−0.114046	+	0.269993i
$736$			1.43530i			0.0529059i
$737$	10.7050	+	6.18056i	0.394325	+	0.227664i
$738$	12.7093	+	22.7409i	0.467836	+	0.837104i
$739$	−15.5624	+	8.98495i	−0.572471	+	0.330517i	−0.758136	−	0.652097i	$-0.773890\pi$
$739$	−15.5624	+	8.98495i	−0.572471	+	0.330517i	0.185664	+	0.982613i	$0.440556\pi$
$740$	0.971210	+	1.68219i	0.0357024	+	0.0618384i
$741$	−21.4911	+	34.5796i	−0.789497	+	1.27031i
$742$	−29.5262	−	1.93505i	−1.08394	−	0.0710379i
$743$	−3.17479	+	5.49889i	−0.116472	+	0.201735i	−0.918367	−	0.395730i	$-0.870492\pi$
$743$	−3.17479	+	5.49889i	−0.116472	+	0.201735i	0.801895	+	0.597464i	$0.203825\pi$
$744$	−5.58609	+	5.50861i	−0.204796	+	0.201955i
$745$		−	3.97416i		−	0.145602i
$746$	10.8556	−	18.8024i	0.397451	−	0.688406i
$747$	−11.1230	+	18.6588i	−0.406969	+	0.682690i
$748$	10.8612	+	18.8121i	0.397123	+	0.687838i
$749$	20.5873	+	41.7463i	0.752245	+	1.52538i
$750$	2.88499	−	10.4738i	0.105345	−	0.382448i
$751$	31.4707			1.14838			0.574191	−	0.818721i	$-0.305317\pi$
$751$	31.4707			1.14838			0.574191	+	0.818721i	$0.305317\pi$
$752$	−8.04448	+	4.64448i	−0.293352	+	0.169367i
$753$	−3.28070	−	12.5949i	−0.119555	−	0.458985i
$754$	−15.5345	−	4.58994i	−0.565733	−	0.167156i
$755$	−0.541708			−0.0197148
$756$	12.9227	+	4.69073i	0.469995	+	0.170600i
$757$	−2.57146	+	4.45391i	−0.0934614	+	0.161880i	−0.908965	−	0.416871i	$-0.863127\pi$
$757$	−2.57146	+	4.45391i	−0.0934614	+	0.161880i	0.815504	+	0.578751i	$0.196460\pi$
$758$	−2.54234	−	1.46782i	−0.0923421	−	0.0533137i
$759$	7.44119	−	1.93827i	0.270098	−	0.0703546i
$760$		−	4.27267i		−	0.154986i
$761$	6.50298	+	3.75450i	0.235733	+	0.136100i	0.613214	−	0.789917i	$-0.289876\pi$
$761$	6.50298	+	3.75450i	0.235733	+	0.136100i	−0.377481	+	0.926017i	$0.623210\pi$
$762$	7.69429	−	7.58757i	0.278735	−	0.274869i
$763$	25.3407	+	1.66075i	0.917395	+	0.0601231i
$764$	5.22709	+	3.01786i	0.189110	+	0.109183i
$765$	13.8064	+	0.192852i	0.499171	+	0.00697259i
$766$	26.1275	+	15.0847i	0.944025	+	0.545033i
$767$	5.97509	+	24.8130i	0.215748	+	0.895946i
$768$	−1.66986	−	0.459961i	−0.0602559	−	0.0165974i
$769$	12.5070	−	21.6627i	0.451013	−	0.781177i	−0.547437	−	0.836847i	$-0.684396\pi$
$769$	12.5070	−	21.6627i	0.451013	−	0.781177i	0.998449	+	0.0556704i	$0.0177296\pi$
$770$	−5.35181	−	0.350741i	−0.192866	−	0.0126398i
$771$	42.0841	+	11.5920i	1.51562	+	0.417476i
$772$	−20.2555	+	11.6945i	−0.729012	+	0.420896i
$773$			13.2394i			0.476187i	0.971242	+	0.238093i	$0.0765224\pi$
$773$			13.2394i			0.476187i	−0.971242	+	0.238093i	$0.923478\pi$
$774$	0.00318631	−	0.228109i	0.000114529	−	0.00819922i
$775$	10.3510	+	17.9285i	0.371819	+	0.644010i
$776$	−8.57395	−	14.8505i	−0.307787	−	0.533102i
$777$	2.55671	+	13.3392i	0.0917215	+	0.478541i
$778$	−19.1621	−	11.0633i	−0.686996	−	0.396637i
$779$	49.0287	−	28.3067i	1.75664	−	1.01419i
$780$	−3.60906	+	1.93023i	−0.129225	+	0.0691133i
$781$	−1.45228	+	2.51541i	−0.0519665	+	0.0900086i
$782$			10.0799i			0.360456i
$783$	5.56826	+	22.6706i	0.198993	+	0.810180i
$784$	4.26126	−	5.55353i	0.152188	−	0.198340i
$785$	4.31148			0.153883
$786$	1.62453	+	6.23671i	0.0579449	+	0.222456i
$787$	16.2500			0.579250			0.289625	−	0.957140i	$-0.406469\pi$
$787$	16.2500			0.579250			0.289625	+	0.957140i	$0.406469\pi$
$788$	−7.90007	+	13.6833i	−0.281428	+	0.487448i
$789$	33.4123	−	8.70316i	1.18951	−	0.309841i
$790$	−1.59139	−	0.918792i	−0.0566193	−	0.0326892i
$791$	3.82747	−	5.72830i	0.136089	−	0.203675i
$792$	−0.129604	+	9.27839i	−0.00460526	+	0.329693i
$793$	−53.0870	−	15.6855i	−1.88517	−	0.557007i
$794$	6.54053	−	11.3285i	0.232115	−	0.402034i
$795$	−12.2393	−	3.37131i	−0.434085	−	0.119568i
$796$		−	24.5006i		−	0.868401i
$797$	−6.45285	−	11.1767i	−0.228572	−	0.395898i	0.728813	−	0.684712i	$-0.240072\pi$
$797$	−6.45285	−	11.1767i	−0.228572	−	0.395898i	−0.957385	+	0.288815i	$0.906739\pi$
$798$	9.80042	−	28.2226i	0.346931	−	0.999070i
$799$	−56.4951	+	32.6174i	−1.99865	+	1.15392i
$800$	−2.28524	+	3.95816i	−0.0807955	+	0.139942i
$801$	16.7894	−	28.1642i	0.593225	−	0.995134i
$802$	−6.92658			−0.244586
$803$	−33.6926			−1.18899
$804$	−6.69838	+	1.74478i	−0.236234	+	0.0615337i
$805$	−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
$808$	−3.72432	−	6.45070i	−0.131021	−	0.226935i
$809$	30.9586	−	17.8740i	1.08845	−	0.628415i	0.155285	−	0.987870i	$-0.450371\pi$
$809$	30.9586	−	17.8740i	1.08845	−	0.628415i	0.933163	+	0.359454i	$0.117037\pi$
$810$	5.02377	+	3.09071i	0.176517	+	0.108596i
$811$	19.1592			0.672770			0.336385	−	0.941724i	$-0.390796\pi$
$811$	19.1592			0.672770			0.336385	+	0.941724i	$0.390796\pi$
$812$	11.8609	+	0.777327i	0.416237	+	0.0272788i
$813$	44.1722	+	12.1672i	1.54919	+	0.426721i
$814$	−7.93923	+	4.58372i	−0.278270	+	0.160659i
$815$	2.92460			0.102444
$816$	−11.7272	−	3.23023i	−0.410533	−	0.113081i
$817$	−0.495763			−0.0173446
$818$	32.6793			1.14260
$819$	−28.2667	+	4.47165i	−0.987717	+	0.156252i
$820$	5.69113			0.198743
$821$	−25.3341			−0.884165			−0.442083	−	0.896974i	$-0.645760\pi$
$821$	−25.3341			−0.884165			−0.442083	+	0.896974i	$0.645760\pi$
$822$	−11.5659	−	3.18580i	−0.403405	−	0.111117i
$823$	−3.93776			−0.137262			−0.0686309	−	0.997642i	$-0.521863\pi$
$823$	−3.93776			−0.137262			−0.0686309	+	0.997642i	$0.521863\pi$
$824$	−15.3456	+	8.85976i	−0.534588	+	0.308644i
$825$	23.6068	+	6.50244i	0.821882	+	0.226386i
$826$	−8.28340	−	16.7968i	−0.288216	−	0.584435i
$827$	43.3874			1.50873			0.754363	−	0.656458i	$-0.227946\pi$
$827$	43.3874			1.50873			0.754363	+	0.656458i	$0.227946\pi$
$828$	−2.20483	+	3.69859i	−0.0766230	+	0.128535i
$829$	−12.2260	+	7.05866i	−0.424625	+	0.245157i	−0.697054	−	0.717018i	$-0.745506\pi$
$829$	−12.2260	+	7.05866i	−0.424625	+	0.245157i	0.272429	+	0.962176i	$0.412173\pi$
$830$	2.37274	+	4.10970i	0.0823589	+	0.142650i
$831$	−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
$834$	4.40839	−	1.14829i	0.152650	−	0.0397620i
$835$	−0.850292			−0.0294256
$836$	20.1653			0.697430
$837$	−22.8566	+	5.61395i	−0.790041	+	0.194047i
$838$	−3.98319	+	6.89908i	−0.137597	+	0.238325i
$839$	−6.87396	+	3.96868i	−0.237315	+	0.137014i	−0.613942	−	0.789351i	$-0.710417\pi$
$839$	−6.87396	+	3.96868i	−0.237315	+	0.137014i	0.376627	+	0.926365i	$0.377084\pi$
$840$	2.27176	−	1.96441i	0.0783832	−	0.0677786i
$841$	−4.40814	−	7.63512i	−0.152005	−	0.263280i
$842$			14.1689i			0.488294i
$843$	33.6608	+	9.27182i	1.15934	+	0.319339i
$844$	−5.93332	+	10.2768i	−0.204233	+	0.353743i
$845$	4.63044	−	7.15172i	0.159292	−	0.246027i
$846$	−27.8642	−	0.389216i	−0.957990	−	0.0133815i
$847$	−0.247898	+	3.78258i	−0.00851789	+	0.129971i
$848$	9.68544	+	5.59189i	0.332599	+	0.192026i
$849$	−10.6926	+	2.78519i	−0.366969	+	0.0955873i
$850$	−16.0489	+	27.7975i	−0.550472	+	0.953446i
$851$	−4.25400			−0.145825
$852$	−0.409979	−	1.57395i	−0.0140457	−	0.0539227i
$853$	−27.9388			−0.956605			−0.478302	−	0.878195i	$-0.658748\pi$
$853$	−27.9388			−0.956605			−0.478302	+	0.878195i	$0.658748\pi$
$854$	40.5331	+	2.65641i	1.38701	+	0.0909003i
$855$	6.56342	−	11.0101i	0.224464	−	0.376538i
$856$		−	17.5930i		−	0.601316i
$857$	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	$0.153632\pi$
$858$	−9.10990	−	17.0333i	−0.311007	−	0.581506i
$859$	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
$861$	37.5921	+	13.0540i	1.28114	+	0.444879i
$862$	12.9721	+	22.4684i	0.441832	+	0.765276i
$863$	−0.0710829	−	0.123119i	−0.00241969	−	0.00419102i	0.864813	−	0.502094i	$-0.167437\pi$
$863$	−0.0710829	−	0.123119i	−0.00241969	−	0.00419102i	−0.867233	+	0.497903i	$0.834104\pi$
$864$	−3.59645	−	3.75040i	−0.122354	−	0.127591i
$865$		−	8.30053i		−	0.282226i
$866$	−14.7383	+	8.50919i	−0.500829	+	0.289154i
$867$	−53.9703	−	14.8660i	−1.83293	−	0.504877i
$868$	−0.783707	+	11.9583i	−0.0266007	+	0.405890i
$869$	4.33632	−	7.51073i	0.147100	−	0.254784i
$870$	4.91666	+	1.35429i	0.166690	+	0.0459146i
$871$	10.4452	−	9.92572i	0.353921	−	0.336320i
$872$	−8.31249	−	4.79922i	−0.281496	−	0.162522i
$873$	0.718512	−	51.4387i	0.0243180	−	1.74094i
$874$	8.10372	+	4.67868i	0.274112	+	0.158259i
$875$	−7.33979	−	14.8834i	−0.248130	−	0.503150i
$876$	13.4338	−	13.2475i	0.453886	−	0.447590i
$877$	−9.84863	−	5.68611i	−0.332564	−	0.192006i	0.324415	−	0.945915i	$-0.394833\pi$
$877$	−9.84863	−	5.68611i	−0.332564	−	0.192006i	−0.656979	+	0.753909i	$0.728166\pi$
$878$		−	29.6229i		−	0.999725i
$879$	10.2711	−	2.67539i	0.346434	−	0.0902385i
$880$	1.75555	+	1.01357i	0.0591796	+	0.0341674i
$881$	−15.4774	+	26.8077i	−0.521448	+	0.903174i	0.478241	+	0.878229i	$0.341275\pi$
$881$	−15.4774	+	26.8077i	−0.521448	+	0.903174i	−0.999689	+	0.0249457i	$0.992059\pi$
$882$	19.5117	−	7.76485i	0.656994	−	0.261456i
$883$	−29.8101			−1.00319			−0.501594	−	0.865103i	$-0.667253\pi$
$883$	−29.8101			−1.00319			−0.501594	+	0.865103i	$0.667253\pi$
$884$	24.6175	−	5.92801i	0.827976	−	0.199381i
$885$	−2.02541	−	7.77576i	−0.0680835	−	0.261379i
$886$	15.3962	−	8.88898i	0.517244	−	0.298631i
$887$	−0.410274			−0.0137757			−0.00688783	−	0.999976i	$-0.502192\pi$
$887$	−0.410274			−0.0137757			−0.00688783	+	0.999976i	$0.502192\pi$
$888$	1.36325	−	4.94919i	0.0457476	−	0.166084i
$889$	1.07948	−	16.4714i	0.0362046	−	0.552432i
$890$	−3.58149	−	6.20333i	−0.120052	−	0.207936i
$891$	−14.5869	+	23.7101i	−0.488679	+	0.794319i
$892$	11.4114	−	19.7652i	0.382083	−	0.661788i
$893$			60.5589i			2.02653i
$894$	−7.47850	+	7.37476i	−0.250118	+	0.246649i
$895$	4.75852	−	8.24200i	0.159060	−	0.275500i
$896$	−2.37289	+	1.17020i	−0.0792728	+	0.0390937i
$897$	0.291058	−	8.95873i	0.00971815	−	0.299123i
$898$	−11.2383	−	19.4653i	−0.375028	−	0.649567i
$899$	−17.6231	+	10.1747i	−0.587762	+	0.339345i
$900$	−11.9691	+	6.68921i	−0.398969	+	0.222974i
$901$	68.0192	+	39.2709i	2.26605	+	1.30830i
$902$			26.8598i			0.894335i
$903$	−0.227933	−	0.263595i	−0.00758514	−	0.00877191i
$904$	−2.25506	+	1.30196i	−0.0750023	+	0.0433026i
$905$	−1.17068	−	2.02768i	−0.0389149	−	0.0674025i
$906$	1.00523	+	1.01937i	0.0333967	+	0.0338664i
$907$	24.9010	+	43.1298i	0.826825	+	1.43210i	0.900516	+	0.434822i	$0.143189\pi$
$907$	24.9010	+	43.1298i	0.826825	+	1.43210i	−0.0736914	+	0.997281i	$0.523478\pi$
$908$			10.6843i			0.354570i
$909$	0.312104	−	22.3437i	0.0103518	−	0.741094i
$910$	−2.15981	+	5.86695i	−0.0715971	+	0.194487i
$911$			12.8444i			0.425553i	0.977101	+	0.212776i	$0.0682506\pi$
$911$			12.8444i			0.425553i	−0.977101	+	0.212776i	$0.931749\pi$
$912$	−8.04022	+	7.92869i	−0.266238	+	0.262545i
$913$	−19.3961	+	11.1984i	−0.641918	+	0.370611i
$914$			26.4676i			0.875471i
$915$	16.8020	+	4.62808i	0.555456	+	0.153000i
$916$	1.86852	+	3.23637i	0.0617376	+	0.106933i
$917$	8.18554	+	5.46932i	0.270310	+	0.180613i
$918$	−25.2573	−	26.3385i	−0.833615	−	0.869299i
$919$	20.7507	−	35.9413i	0.684503	−	1.18559i	−0.289089	−	0.957302i	$-0.593352\pi$
$919$	20.7507	−	35.9413i	0.684503	−	1.18559i	0.973593	−	0.228292i	$-0.0733142\pi$
$920$	0.470330	+	0.814635i	0.0155063	+	0.0268577i
$921$	−8.98654	−	2.47533i	−0.296117	−	0.0815648i
$922$	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
$926$		−	10.3837i		−	0.341230i
$927$	−53.1534	−	0.742464i	−1.74579	−	0.0243857i
$928$	−3.89073	−	2.24631i	−0.127720	−	0.0737389i
$929$	−3.54765	−	2.04824i	−0.116395	−	0.0672005i	0.440672	−	0.897668i	$-0.354740\pi$
$929$	−3.54765	−	2.04824i	−0.116395	−	0.0672005i	−0.557067	+	0.830467i	$0.688073\pi$
$930$	−1.36540	+	4.95701i	−0.0447733	+	0.162547i
$931$	−17.4647	−	42.1620i	−0.572384	−	1.38180i
$932$	−7.73067	+	4.46331i	−0.253227	+	0.146200i
$933$	7.77148	−	7.66368i	0.254427	−	0.250898i
$934$	−11.7463	−	20.3453i	−0.384352	−	0.665718i
$935$	12.3289	+	7.11812i	0.403200	+	0.232787i
$936$	10.3295	+	3.20956i	0.337630	+	0.104908i
$937$			26.3778i			0.861725i	0.902418	+	0.430862i	$0.141791\pi$
$937$			26.3778i			0.861725i	−0.902418	+	0.430862i	$0.858209\pi$
$938$	−5.87419	+	8.79147i	−0.191799	+	0.287052i
$939$	17.5920	−	4.58233i	0.574094	−	0.149539i
$940$	−3.04387	+	5.27214i	−0.0992802	+	0.171958i
$941$	31.1389	+	17.9781i	1.01510	+	0.586068i	0.912681	−	0.408673i	$-0.134008\pi$
$941$	31.1389	+	17.9781i	1.01510	+	0.586068i	0.102419	+	0.994741i	$0.467342\pi$
$942$	−8.00070	−	8.11324i	−0.260677	−	0.264344i
$943$	−6.23194	+	10.7940i	−0.202940	+	0.351502i
$944$			7.07861i			0.230389i
$945$	8.87165	−	1.57229i	0.288595	−	0.0511466i
$946$	0.117606	−	0.203699i	0.00382369	−	0.00662282i
$947$	−6.19253			−0.201230			−0.100615	−	0.994925i	$-0.532081\pi$
$947$	−6.19253			−0.201230			−0.100615	+	0.994925i	$0.532081\pi$
$948$	1.22415	+	4.69963i	0.0397586	+	0.152637i
$949$	−11.1288	+	37.6650i	−0.361255	+	1.22266i
$950$	14.8985	+	25.8050i	0.483371	+	0.837223i
$951$	0.387465	+	1.48751i	0.0125644	+	0.0482360i
$952$	−16.6644	+	8.21813i	−0.540098	+	0.266351i
$953$	22.4705	−	12.9734i	0.727891	−	0.420248i	−0.0897592	−	0.995964i	$-0.528610\pi$
$953$	22.4705	−	12.9734i	0.727891	−	0.420248i	0.817650	+	0.575715i	$0.195276\pi$
$954$	16.3682	+	29.2878i	0.529940	+	0.948227i
$955$	3.95566			0.128002
$956$	2.27619			0.0736172
$957$	−6.39168	+	23.2046i	−0.206614	+	0.750099i
$958$	−7.41327	+	4.28005i	−0.239512	+	0.138282i
$959$	−16.4352	+	8.10509i	−0.530721	+	0.261727i
$960$	−1.09849	+	0.286132i	−0.0354535	+	0.00923486i
$961$	5.24181	+	9.07908i	0.169091	+	0.292874i
$962$	2.50179	+	10.3893i	0.0806609	+	0.334964i
$963$	27.0253	−	45.3349i	0.870878	−	1.46090i
$964$	−4.13240			−0.133096
$965$	−7.66429	+	13.2749i	−0.246722	+	0.427336i
$966$	1.23814	+	6.45979i	0.0398366	+	0.207840i
$967$		−	27.4624i		−	0.883132i	−0.897229	−	0.441566i	$-0.854423\pi$
$967$		−	27.4624i		−	0.883132i	0.897229	−	0.441566i	$-0.145577\pi$
$968$	0.716375	−	1.24080i	0.0230252	−	0.0398807i
$969$	−56.4651	+	55.6819i	−1.81392	+	1.78876i
$970$	−9.73264	−	5.61914i	−0.312496	−	0.180420i
$971$	−2.89389	+	5.01236i	−0.0928692	+	0.160854i	−0.908717	−	0.417412i	$-0.862937\pi$
$971$	−2.89389	+	5.01236i	−0.0928692	+	0.160854i	0.815848	+	0.578266i	$0.196271\pi$
$972$	−3.50646	−	15.1890i	−0.112470	−	0.487186i
$973$	3.86597	−	5.78591i	0.123937	−	0.185488i
$974$			17.5739i			0.563103i
$975$	15.0665	−	24.2422i	0.482513	−	0.776373i
$976$	−13.2960	−	7.67646i	−0.425595	−	0.245718i
$977$	22.5457	+	39.0503i	0.721301	+	1.24933i	0.960479	+	0.278354i	$0.0897887\pi$
$977$	22.5457	+	39.0503i	0.721301	+	1.24933i	−0.239178	+	0.970976i	$0.576878\pi$
$978$	−5.42711	−	5.50345i	−0.173540	−	0.175981i
$979$	29.2772	−	16.9032i	0.935702	−	0.540228i
$980$	0.598743	−	4.54838i	0.0191262	−	0.145293i
$981$	−14.0479	−	25.1361i	−0.448516	−	0.802535i
$982$	7.73222	+	4.46420i	0.246745	+	0.142458i
$983$	3.66890	+	2.11824i	0.117020	+	0.0675613i	0.557367	−	0.830266i	$-0.311811\pi$
$983$	3.66890	+	2.11824i	0.117020	+	0.0675613i	−0.440348	+	0.897827i	$0.645145\pi$
$984$	−10.5609	−	10.7095i	−0.336669	−	0.341405i
$985$			10.3550i			0.329938i
$986$	−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
$990$	2.96685	+	5.30861i	0.0942926	+	0.168719i
$991$	−14.7891	−	25.6154i	−0.469791	−	0.813701i	0.529613	−	0.848240i	$-0.322337\pi$
$991$	−14.7891	−	25.6154i	−0.469791	−	0.813701i	−0.999403	+	0.0345382i	$0.989004\pi$
$992$	2.26475	−	3.92266i	0.0719059	−	0.124545i
$993$	−23.4873	−	23.8176i	−0.745346	−	0.755830i
$994$	−2.06577	−	1.38029i	−0.0655223	−	0.0437800i
$995$	−8.02853	−	13.9058i	−0.254521	−	0.440844i
$996$	3.33051	−	12.0912i	0.105531	−	0.383126i
$997$			28.6016i			0.905821i	0.891556	+	0.452910i	$0.149614\pi$
$997$			28.6016i			0.905821i	−0.891556	+	0.452910i	$0.850386\pi$
$998$	−8.26926	+	4.77426i	−0.261759	+	0.151127i
$999$	11.1156	−	10.6593i	0.351681	−	0.337245i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.8	✓	34	3.2	odd	2
546.2.bi.e.257.8	yes	34	91.75	odd	6
546.2.bi.f.17.2	yes	34	1.1	even	1	trivial
546.2.bi.f.257.2	yes	34	273.257	even	6	inner
546.2.bn.e.101.4	yes	34	39.23	odd	6
546.2.bn.e.173.4	yes	34	7.5	odd	6
546.2.bn.f.101.14	yes	34	13.10	even	6
546.2.bn.f.173.14	yes	34	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.66986 - 0.459961i) q^{3} +1.00000 q^{4} +(0.567570 - 0.327687i) q^{5} +(-1.66986 - 0.459961i) q^{6} +(-2.37289 + 1.17020i) q^{7} +1.00000 q^{8} +(2.57687 + 1.53614i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.66986 - 0.459961i) q^{3} +1.00000 q^{4} +(0.567570 - 0.327687i) q^{5} +(-1.66986 - 0.459961i) q^{6} +(-2.37289 + 1.17020i) q^{7} +1.00000 q^{8} +(2.57687 + 1.53614i) q^{9} +(0.567570 - 0.327687i) q^{10} +(1.54655 + 2.67870i) q^{11} +(-1.66986 - 0.459961i) q^{12} +(3.50535 - 0.844105i) q^{13} +(-2.37289 + 1.17020i) q^{14} +(-1.09849 + 0.286132i) q^{15} +1.00000 q^{16} +7.02284 q^{17} +(2.57687 + 1.53614i) q^{18} +(3.25972 - 5.64600i) q^{19} +(0.567570 - 0.327687i) q^{20} +(4.50065 - 0.862636i) q^{21} +(1.54655 + 2.67870i) q^{22} +1.43530i q^{23} +(-1.66986 - 0.459961i) q^{24} +(-2.28524 + 3.95816i) q^{25} +(3.50535 - 0.844105i) q^{26} +(-3.59645 - 3.75040i) q^{27} +(-2.37289 + 1.17020i) q^{28} +(-3.89073 - 2.24631i) q^{29} +(-1.09849 + 0.286132i) q^{30} +(2.26475 - 3.92266i) q^{31} +1.00000 q^{32} +(-1.35042 - 5.18441i) q^{33} +7.02284 q^{34} +(-0.963325 + 1.44174i) q^{35} +(2.57687 + 1.53614i) q^{36} +2.96384i q^{37} +(3.25972 - 5.64600i) q^{38} +(-6.24170 - 0.202785i) q^{39} +(0.567570 - 0.327687i) q^{40} +(7.52039 + 4.34190i) q^{41} +(4.50065 - 0.862636i) q^{42} +(-0.0380219 - 0.0658559i) q^{43} +(1.54655 + 2.67870i) q^{44} +(1.96593 + 0.0274608i) q^{45} +1.43530i q^{46} +(-8.04448 + 4.64448i) q^{47} +(-1.66986 - 0.459961i) q^{48} +(4.26126 - 5.55353i) q^{49} +(-2.28524 + 3.95816i) q^{50} +(-11.7272 - 3.23023i) q^{51} +(3.50535 - 0.844105i) q^{52} +(9.68544 + 5.59189i) q^{53} +(-3.59645 - 3.75040i) q^{54} +(1.75555 + 1.01357i) q^{55} +(-2.37289 + 1.17020i) q^{56} +(-8.04022 + 7.92869i) q^{57} +(-3.89073 - 2.24631i) q^{58} +7.07861i q^{59} +(-1.09849 + 0.286132i) q^{60} +(-13.2960 - 7.67646i) q^{61} +(2.26475 - 3.92266i) q^{62} +(-7.91224 - 0.629640i) q^{63} +1.00000 q^{64} +(1.71293 - 1.62775i) q^{65} +(-1.35042 - 5.18441i) q^{66} +(3.46095 - 1.99818i) q^{67} +7.02284 q^{68} +(0.660182 - 2.39676i) q^{69} +(-0.963325 + 1.44174i) q^{70} +(0.469521 + 0.813235i) q^{71} +(2.57687 + 1.53614i) q^{72} +(-5.44642 + 9.43348i) q^{73} +2.96384i q^{74} +(5.63663 - 5.55845i) q^{75} +(3.25972 - 5.64600i) q^{76} +(-6.80442 - 4.54650i) q^{77} +(-6.24170 - 0.202785i) q^{78} +(-1.40194 - 2.42822i) q^{79} +(0.567570 - 0.327687i) q^{80} +(4.28054 + 7.91688i) q^{81} +(7.52039 + 4.34190i) q^{82} +7.24087i q^{83} +(4.50065 - 0.862636i) q^{84} +(3.98595 - 2.30129i) q^{85} +(-0.0380219 - 0.0658559i) q^{86} +(5.46376 + 5.54062i) q^{87} +(1.54655 + 2.67870i) q^{88} -10.9296i q^{89} +(1.96593 + 0.0274608i) q^{90} +(-7.33005 + 6.10494i) q^{91} +1.43530i q^{92} +(-5.58609 + 5.50861i) q^{93} +(-8.04448 + 4.64448i) q^{94} -4.27267i q^{95} +(-1.66986 - 0.459961i) q^{96} +(-8.57395 - 14.8505i) q^{97} +(4.26126 - 5.55353i) q^{98} +(-0.129604 + 9.27839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more