LMFDB - Embedded newform 546.2.bi.e.257.8

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			257.8
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.436593 - 1.67612i) q^{3} +1.00000 q^{4} +(-0.567570 - 0.327687i) q^{5} +(0.436593 + 1.67612i) q^{6} +(-2.37289 - 1.17020i) q^{7} -1.00000 q^{8} +(-2.61877 + 1.46357i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.436593 - 1.67612i) q^{3} +1.00000 q^{4} +(-0.567570 - 0.327687i) q^{5} +(0.436593 + 1.67612i) q^{6} +(-2.37289 - 1.17020i) q^{7} -1.00000 q^{8} +(-2.61877 + 1.46357i) q^{9} +(0.567570 + 0.327687i) q^{10} +(-1.54655 + 2.67870i) q^{11} +(-0.436593 - 1.67612i) q^{12} +(3.50535 + 0.844105i) q^{13} +(2.37289 + 1.17020i) q^{14} +(-0.301446 + 1.09438i) q^{15} +1.00000 q^{16} -7.02284 q^{17} +(2.61877 - 1.46357i) q^{18} +(3.25972 + 5.64600i) q^{19} +(-0.567570 - 0.327687i) q^{20} +(-0.925413 + 4.48816i) q^{21} +(1.54655 - 2.67870i) q^{22} +1.43530i q^{23} +(0.436593 + 1.67612i) 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} +(0.301446 - 1.09438i) q^{30} +(2.26475 + 3.92266i) q^{31} -1.00000 q^{32} +(5.16504 + 1.42270i) q^{33} +7.02284 q^{34} +(0.963325 + 1.44174i) q^{35} +(-2.61877 + 1.46357i) q^{36} -2.96384i q^{37} +(-3.25972 - 5.64600i) q^{38} +(-0.115588 - 6.24393i) q^{39} +(0.567570 + 0.327687i) q^{40} +(-7.52039 + 4.34190i) q^{41} +(0.925413 - 4.48816i) 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} +(-0.436593 - 1.67612i) q^{48} +(4.26126 + 5.55353i) q^{49} +(2.28524 + 3.95816i) q^{50} +(3.06612 + 11.7711i) 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} +(-0.301446 + 1.09438i) q^{60} +(-13.2960 + 7.67646i) q^{61} +(-2.26475 - 3.92266i) q^{62} +(7.92674 - 0.408396i) q^{63} +1.00000 q^{64} +(-1.71293 - 1.62775i) q^{65} +(-5.16504 - 1.42270i) q^{66} +(3.46095 + 1.99818i) q^{67} -7.02284 q^{68} +(2.40574 - 0.626643i) q^{69} +(-0.963325 - 1.44174i) q^{70} +(-0.469521 + 0.813235i) q^{71} +(2.61877 - 1.46357i) 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} +(0.115588 + 6.24393i) q^{78} +(-1.40194 + 2.42822i) q^{79} +(-0.567570 - 0.327687i) q^{80} +(4.71595 - 7.66550i) q^{81} +(7.52039 - 4.34190i) q^{82} +7.24087i q^{83} +(-0.925413 + 4.48816i) 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} +(0.436593 + 1.67612i) 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} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.436593	−	1.67612i	−0.252067	−	0.967710i
$3$	−0.436593	−	1.67612i	−0.252067	−	0.967710i
$4$	1.00000			0.500000
$5$	−0.567570	−	0.327687i	−0.253825	−	0.146546i	0.367689	−	0.929949i	$-0.380149\pi$
$5$	−0.567570	−	0.327687i	−0.253825	−	0.146546i	−0.621515	+	0.783403i	$0.713482\pi$
$6$	0.436593	+	1.67612i	0.178238	+	0.684274i
$7$	−2.37289	−	1.17020i	−0.896870	−	0.442295i
$7$	−2.37289	−	1.17020i	−0.896870	−	0.442295i
$8$	−1.00000			−0.353553
$9$	−2.61877	+	1.46357i	−0.872924	+	0.487855i
$10$	0.567570	+	0.327687i	0.179482	+	0.103624i
$11$	−1.54655	+	2.67870i	−0.466302	+	0.807659i	−0.999259	−	0.0384835i	$-0.987747\pi$
$11$	−1.54655	+	2.67870i	−0.466302	+	0.807659i	0.532957	+	0.846142i	$0.321081\pi$
$12$	−0.436593	−	1.67612i	−0.126034	−	0.483855i
$13$	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
$16$	1.00000			0.250000
$17$	−7.02284			−1.70329			−0.851644	−	0.524121i	$-0.824394\pi$
$17$	−7.02284			−1.70329			−0.851644	+	0.524121i	$0.824394\pi$
$18$	2.61877	−	1.46357i	0.617251	−	0.344966i
$19$	3.25972	+	5.64600i	0.747831	+	1.29528i	0.948860	+	0.315696i	$0.102238\pi$
$19$	3.25972	+	5.64600i	0.747831	+	1.29528i	−0.201029	+	0.979585i	$0.564429\pi$
$20$	−0.567570	−	0.327687i	−0.126913	−	0.0732730i
$21$	−0.925413	+	4.48816i	−0.201942	+	0.979398i
$22$	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	$0.952188\pi$
$24$	0.436593	+	1.67612i	0.0891192	+	0.342137i
$25$	−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	$-0.529703\pi$
$29$	3.89073	−	2.24631i	0.722491	−	0.417130i	0.815669	+	0.578519i	$0.196369\pi$
$30$	0.301446	−	1.09438i	0.0550363	−	0.199806i
$31$	2.26475	+	3.92266i	0.406761	+	0.704531i	0.994525	−	0.104502i	$-0.0333248\pi$
$31$	2.26475	+	3.92266i	0.406761	+	0.704531i	−0.587763	+	0.809033i	$0.699991\pi$
$32$	−1.00000			−0.176777
$33$	5.16504	+	1.42270i	0.899119	+	0.247661i
$34$	7.02284			1.20441
$35$	0.963325	+	1.44174i	0.162832	+	0.243698i
$36$	−2.61877	+	1.46357i	−0.436462	+	0.243928i
$37$		−	2.96384i		−	0.487252i	−0.969869	−	0.243626i	$-0.921663\pi$
$37$		−	2.96384i		−	0.487252i	0.969869	−	0.243626i	$-0.0783369\pi$
$38$	−3.25972	−	5.64600i	−0.528796	−	0.915902i
$39$	−0.115588	−	6.24393i	−0.0185089	−	0.999829i
$40$	0.567570	+	0.327687i	0.0897408	+	0.0518119i
$41$	−7.52039	+	4.34190i	−1.17449	+	0.678091i	−0.954733	−	0.297465i	$-0.903859\pi$
$41$	−7.52039	+	4.34190i	−1.17449	+	0.678091i	−0.219755	+	0.975555i	$0.570526\pi$
$42$	0.925413	−	4.48816i	0.142794	−	0.692539i
$43$	−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
$45$	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	$-0.0964107\pi$
$47$	8.04448	+	4.64448i	1.17341	+	0.677468i	0.218928	+	0.975741i	$0.429744\pi$
$48$	−0.436593	−	1.67612i	−0.0630168	−	0.241927i
$49$	4.26126	+	5.55353i	0.608751	+	0.793361i
$50$	2.28524	+	3.95816i	0.323182	+	0.559768i
$51$	3.06612	+	11.7711i	0.429343	+	1.64829i
$52$	3.50535	+	0.844105i	0.486105	+	0.117056i
$53$	−9.68544	+	5.59189i	−1.33040	+	0.768105i	−0.985360	−	0.170484i	$-0.945467\pi$
$53$	−9.68544	+	5.59189i	−1.33040	+	0.768105i	−0.345037	+	0.938589i	$0.612133\pi$
$54$	−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	$0.847570\pi$
$60$	−0.301446	+	1.09438i	−0.0389165	+	0.141284i
$61$	−13.2960	+	7.67646i	−1.70238	+	0.982870i	−0.759041	+	0.651043i	$0.774332\pi$
$61$	−13.2960	+	7.67646i	−1.70238	+	0.982870i	−0.943340	+	0.331828i	$0.892335\pi$
$62$	−2.26475	−	3.92266i	−0.287624	−	0.498179i
$63$	7.92674	−	0.408396i	0.998675	−	0.0514530i
$64$	1.00000			0.125000
$65$	−1.71293	−	1.62775i	−0.212463	−	0.201897i
$66$	−5.16504	−	1.42270i	−0.635773	−	0.175123i
$67$	3.46095	+	1.99818i	0.422822	+	0.244116i	0.696284	−	0.717766i	$-0.254835\pi$
$67$	3.46095	+	1.99818i	0.422822	+	0.244116i	−0.273462	+	0.961883i	$0.588169\pi$
$68$	−7.02284			−0.851644
$69$	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	$0.184413\pi$
$72$	2.61877	−	1.46357i	0.308625	−	0.172483i
$73$	−5.44642	−	9.43348i	−0.637456	−	1.10411i	−0.985989	−	0.166809i	$-0.946654\pi$
$73$	−5.44642	−	9.43348i	−0.637456	−	1.10411i	0.348534	−	0.937296i	$-0.386680\pi$
$74$			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
$78$	0.115588	+	6.24393i	0.0130878	+	0.706986i
$79$	−1.40194	+	2.42822i	−0.157730	+	0.273197i	−0.934050	−	0.357143i	$-0.883751\pi$
$79$	−1.40194	+	2.42822i	−0.157730	+	0.273197i	0.776320	+	0.630339i	$0.217084\pi$
$80$	−0.567570	−	0.327687i	−0.0634563	−	0.0366365i
$81$	4.71595	−	7.66550i	0.523994	−	0.851722i
$82$	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	$0.869915\pi$
$84$	−0.925413	+	4.48816i	−0.100971	+	0.489699i
$85$	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
$96$	0.436593	+	1.67612i	0.0445596	+	0.171069i
$97$	−8.57395	+	14.8505i	−0.870553	+	1.50784i	−0.00912654	+	0.999958i	$0.502905\pi$
$97$	−8.57395	+	14.8505i	−0.870553	+	1.50784i	−0.861426	+	0.507883i	$0.830428\pi$
$98$	−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	$-0.712491\pi$
$101$	3.72432	−	6.45070i	0.370583	−	0.641869i	0.989655	+	0.143465i	$0.0458245\pi$
$102$	−3.06612	−	11.7711i	−0.303591	−	1.16552i
$103$	−15.3456	−	8.85976i	−1.51204	−	0.872978i	−0.999901	−	0.0140769i	$-0.995519\pi$
$103$	−15.3456	−	8.85976i	−1.51204	−	0.872978i	−0.512141	−	0.858901i	$-0.671148\pi$
$104$	−3.50535	−	0.844105i	−0.343728	−	0.0827713i
$105$	1.99595	−	2.24410i	0.194785	−	0.219002i
$106$	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	−0.842138	−	0.539262i	$-0.818703\pi$
$109$	−8.31249	+	4.79922i	−0.796192	+	0.459682i	0.0459460	+	0.998944i	$0.485370\pi$
$110$	−1.75555	+	1.01357i	−0.167385	+	0.0966399i
$111$	−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	$0.627583\pi$
$114$	−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
$117$	−10.4151	+	2.91979i	−0.962879	+	0.269935i
$118$		−	7.07861i		−	0.651639i
$119$	16.6644	+	8.21813i	1.52763	+	0.753355i
$120$	0.301446	−	1.09438i	0.0275181	−	0.0999031i
$121$	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
$126$	−7.92674	+	0.408396i	−0.706170	+	0.0363828i
$127$	−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	$0.922610\pi$
$128$	−1.00000			−0.0883883
$129$	0.126983	+	0.0349772i	0.0111802	+	0.00307957i
$130$	1.71293	+	1.62775i	0.150234	+	0.142763i
$131$	1.86046	−	3.22241i	0.162549	−	0.281543i	−0.773233	−	0.634122i	$-0.781362\pi$
$131$	1.86046	−	3.22241i	0.162549	−	0.281543i	0.935782	+	0.352579i	$0.114695\pi$
$132$	5.16504	+	1.42270i	0.449559	+	0.123830i
$133$	−1.12801	−	17.2119i	−0.0978110	−	1.49246i
$134$	−3.46095	−	1.99818i	−0.298980	−	0.172616i
$135$	−0.812284	−	3.30713i	−0.0699102	−	0.284632i
$136$	7.02284			0.602203
$137$	−6.92624			−0.591748			−0.295874	−	0.955227i	$-0.595611\pi$
$137$	−6.92624			−0.591748			−0.295874	+	0.955227i	$0.595611\pi$
$138$	−2.40574	+	0.626643i	−0.204790	+	0.0533434i
$139$	−2.27775	−	1.31506i	−0.193196	−	0.111542i	0.400282	−	0.916392i	$-0.368912\pi$
$139$	−2.27775	−	1.31506i	−0.193196	−	0.111542i	−0.593478	+	0.804850i	$0.702246\pi$
$140$	0.963325	+	1.44174i	0.0814158	+	0.121849i
$141$	4.27256	−	15.5113i	0.359814	−	1.30629i
$142$	0.469521	−	0.813235i	0.0394014	−	0.0682451i
$143$	−7.68230	+	8.08434i	−0.642426	+	0.676046i
$144$	−2.61877	+	1.46357i	−0.218231	+	0.121964i
$145$	−2.94435			−0.244515
$146$	5.44642	+	9.43348i	0.450749	+	0.780720i
$147$	7.44796	−	9.56702i	0.614298	−	0.789074i
$148$		−	2.96384i		−	0.243626i
$149$	−3.03198	−	5.25155i	−0.248390	−	0.430224i	0.714689	−	0.699442i	$-0.246568\pi$
$149$	−3.03198	−	5.25155i	−0.248390	−	0.430224i	−0.963079	+	0.269218i	$0.913235\pi$
$150$	5.63663	−	5.55845i	0.460229	−	0.453845i
$151$	−0.715824	+	0.413281i	−0.0582530	+	0.0336324i	−0.528844	−	0.848719i	$-0.677374\pi$
$151$	−0.715824	+	0.413281i	−0.0582530	+	0.0336324i	0.470591	+	0.882352i	$0.344041\pi$
$152$	−3.25972	−	5.64600i	−0.264398	−	0.457951i
$153$	18.3912	−	10.2784i	1.48684	−	0.830958i
$154$	−6.80442	+	4.54650i	−0.548316	+	0.366367i
$155$		−	2.96852i		−	0.238437i
$156$	−0.115588	−	6.24393i	−0.00925444	−	0.499914i
$157$	5.69728	−	3.28932i	0.454692	−	0.262517i	−0.255118	−	0.966910i	$-0.582114\pi$
$157$	5.69728	−	3.28932i	0.454692	−	0.262517i	0.709810	+	0.704393i	$0.248781\pi$
$158$	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
$162$	−4.71595	+	7.66550i	−0.370520	+	0.602258i
$163$	3.86463	−	2.23125i	0.302701	−	0.174765i	−0.340955	−	0.940080i	$-0.610750\pi$
$163$	3.86463	−	2.23125i	0.302701	−	0.174765i	0.643656	+	0.765315i	$0.277417\pi$
$164$	−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	$-0.650681\pi$
$167$	1.12359	−	0.648707i	0.0869463	−	0.0501985i	0.542843	+	0.839834i	$0.317348\pi$
$168$	0.925413	−	4.48816i	0.0713971	−	0.346269i
$169$	11.5750	+	5.91777i	0.890383	+	0.455213i
$170$	−3.98595	−	2.30129i	−0.305709	−	0.176501i
$171$	−16.7998	−	10.0148i	−1.28471	−	0.765849i
$172$	−0.0380219	+	0.0658559i	−0.00289915	+	0.00502147i
$173$	−6.33267	−	10.9685i	−0.481464	−	0.833919i	0.518310	−	0.855193i	$-0.326561\pi$
$173$	−6.33267	−	10.9685i	−0.481464	−	0.833919i	−0.999774	+	0.0212733i	$0.993228\pi$
$174$	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
$177$	11.8646	−	3.09047i	0.891799	−	0.232294i
$178$			10.9296i			0.819209i
$179$	−12.5760	−	7.26077i	−0.939976	−	0.542696i	−0.0500235	−	0.998748i	$-0.515930\pi$
$179$	−12.5760	−	7.26077i	−0.939976	−	0.542696i	−0.889953	+	0.456052i	$0.849263\pi$
$180$	1.96593	+	0.0274608i	0.146532	+	0.00204680i
$181$			3.57257i			0.265547i	0.991146	+	0.132773i	$0.0423883\pi$
$181$			3.57257i			0.265547i	−0.991146	+	0.132773i	$0.957612\pi$
$182$	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
$189$	−4.14528	−	13.1079i	−0.301525	−	0.953458i
$190$			4.27267i			0.309972i
$191$	−5.22709	+	3.01786i	−0.378219	+	0.218365i	−0.677043	−	0.735943i	$-0.736739\pi$
$191$	−5.22709	+	3.01786i	−0.378219	+	0.218365i	0.298824	+	0.954308i	$0.403406\pi$
$192$	−0.436593	−	1.67612i	−0.0315084	−	0.120964i
$193$	−20.2555	−	11.6945i	−1.45802	−	0.841791i	−0.459111	−	0.888379i	$-0.651832\pi$
$193$	−20.2555	−	11.6945i	−1.45802	−	0.841791i	−0.998914	+	0.0465881i	$0.985165\pi$
$194$	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	$0.643036\pi$
$198$	−0.129604	+	9.27839i	−0.00921052	+	0.659386i
$199$			24.5006i			1.73680i	0.495863	+	0.868401i	$0.334852\pi$
$199$			24.5006i			1.73680i	−0.495863	+	0.868401i	$0.665148\pi$
$200$	2.28524	+	3.95816i	0.161591	+	0.279884i
$201$	1.83817	−	6.67336i	0.129654	−	0.470703i
$202$	−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
$205$	5.69113			0.397486
$206$	15.3456	+	8.85976i	1.06918	+	0.617289i
$207$	−2.10066	−	3.75873i	−0.146006	−	0.261250i
$208$	3.50535	+	0.844105i	0.243052	+	0.0585282i
$209$	−20.1653			−1.39486
$210$	−1.99595	+	2.24410i	−0.137734	+	0.154858i
$211$	−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	$0.967270\pi$
$212$	−9.68544	+	5.59189i	−0.665198	+	0.384053i
$213$	1.56807	+	0.431923i	0.107442	+	0.0295949i
$214$			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
$222$	4.96775	−	1.29399i	0.333414	−	0.0868469i
$223$	11.4114	+	19.7652i	0.764166	+	1.32358i	0.940686	+	0.339278i	$0.110183\pi$
$223$	11.4114	+	19.7652i	0.764166	+	1.32358i	−0.176520	+	0.984297i	$0.556484\pi$
$224$	2.37289	+	1.17020i	0.158546	+	0.0781874i
$225$	11.7776	+	7.02091i	0.785170	+	0.468061i
$226$	−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	−0.797661	−	0.603106i	$-0.793929\pi$
$229$	1.86852	−	3.23637i	0.123475	−	0.213865i	0.921136	+	0.389241i	$0.127263\pi$
$230$	−0.470330	+	0.814635i	−0.0310126	+	0.0537154i
$231$	−10.5913	−	9.42007i	−0.696853	−	0.619795i
$232$	−3.89073	+	2.24631i	−0.255439	+	0.147478i
$233$	7.73067	+	4.46331i	0.506453	+	0.292401i	0.731375	−	0.681976i	$-0.238879\pi$
$233$	7.73067	+	4.46331i	0.506453	+	0.292401i	−0.224921	+	0.974377i	$0.572212\pi$
$234$	10.4151	−	2.91979i	0.680858	−	0.190873i
$235$	−3.04387	−	5.27214i	−0.198560	−	0.343917i
$236$			7.07861i			0.460778i
$237$	4.68208	+	1.28967i	0.304134	+	0.0837731i
$238$	−16.6644	−	8.21813i	−1.08020	−	0.532702i
$239$	−2.27619			−0.147234			−0.0736172	−	0.997287i	$-0.523454\pi$
$239$	−2.27619			−0.147234			−0.0736172	+	0.997287i	$0.523454\pi$
$240$	−0.301446	+	1.09438i	−0.0194583	+	0.0706421i
$241$	−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
$243$	−14.9073	−	4.55780i	−0.956301	−	0.292383i
$244$	−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
$249$	12.1366	−	3.16131i	0.769125	−	0.200340i
$250$		−	6.27225i		−	0.396692i
$251$	−3.75716	+	6.50759i	−0.237150	+	0.410756i	−0.959895	−	0.280359i	$-0.909547\pi$
$251$	−3.75716	+	6.50759i	−0.237150	+	0.410756i	0.722745	+	0.691114i	$0.242880\pi$
$252$	7.92674	−	0.408396i	0.499338	−	0.0257265i
$253$	−3.84474	−	2.21976i	−0.241717	−	0.139555i
$254$	3.11947	+	5.40309i	0.195733	+	0.339020i
$255$	2.11701	−	7.68567i	0.132572	−	0.481296i
$256$	1.00000			0.0625000
$257$	25.2022			1.57207			0.786034	−	0.618184i	$-0.212131\pi$
$257$	25.2022			1.57207			0.786034	+	0.618184i	$0.212131\pi$
$258$	−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
$261$	−6.90131	+	11.5769i	−0.427181	+	0.716594i
$262$	−1.86046	+	3.22241i	−0.114940	+	0.199081i
$263$	17.2636	+	9.96713i	1.06452	+	0.614600i	0.926679	−	0.375855i	$-0.122651\pi$
$263$	17.2636	+	9.96713i	1.06452	+	0.614600i	0.137839	+	0.990455i	$0.455984\pi$
$264$	−5.16504	−	1.42270i	−0.317886	−	0.0875613i
$265$	7.32956			0.450251
$266$	1.12801	+	17.2119i	0.0691628	+	1.05533i
$267$	−18.3194	+	4.77179i	−1.12113	+	0.292029i
$268$	3.46095	+	1.99818i	0.211411	+	0.122058i
$269$	−20.2140			−1.23247			−0.616235	−	0.787562i	$-0.711343\pi$
$269$	−20.2140			−1.23247			−0.616235	+	0.787562i	$0.711343\pi$
$270$	0.812284	+	3.30713i	0.0494340	+	0.201265i
$271$	−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
$273$	−7.03238	+	14.9514i	−0.425619	+	0.904903i
$274$	6.92624			0.418429
$275$	14.1370			0.852490
$276$	2.40574	−	0.626643i	0.144809	−	0.0377195i
$277$	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
$279$	−11.6719	−	6.95795i	−0.698781	−	0.416562i
$280$	−0.963325	−	1.44174i	−0.0575697	−	0.0861604i
$281$	20.1579			1.20252			0.601259	−	0.799055i	$-0.294666\pi$
$281$	20.1579			1.20252			0.601259	+	0.799055i	$0.294666\pi$
$282$	−4.27256	+	15.5113i	−0.254427	+	0.923684i
$283$	5.52469	+	3.18968i	0.328409	+	0.189607i	0.655134	−	0.755512i	$-0.272612\pi$
$283$	5.52469	+	3.18968i	0.328409	+	0.189607i	−0.326726	+	0.945119i	$0.605945\pi$
$284$	−0.469521	+	0.813235i	−0.0278610	+	0.0482566i
$285$	−7.16152	+	1.86542i	−0.424212	+	0.110498i
$286$	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
$289$	32.3202			1.90119
$290$	2.94435			0.172898
$291$	28.6346	+	7.88736i	1.67859	+	0.462365i
$292$	−5.44642	−	9.43348i	−0.318728	−	0.552053i
$293$	5.30689	+	3.06394i	0.310032	+	0.178997i	0.646941	−	0.762540i	$-0.276048\pi$
$293$	5.30689	+	3.06394i	0.310032	+	0.178997i	−0.336909	+	0.941537i	$0.609381\pi$
$294$	−7.44796	+	9.56702i	−0.434374	+	0.557960i
$295$	2.31957	−	4.01761i	0.135050	−	0.233914i
$296$			2.96384i			0.172269i
$297$	−15.6083	+	3.83365i	−0.905685	+	0.222451i
$298$	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
$303$	−12.4382	−	3.42608i	−0.714555	−	0.196823i
$304$	3.25972	+	5.64600i	0.186958	+	0.323820i
$305$	10.0619			0.576143
$306$	−18.3912	+	10.2784i	−1.05136	+	0.587576i
$307$	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
$309$	−8.15028	+	29.5891i	−0.463653	+	1.68327i
$310$			2.96852i			0.168600i
$311$	3.15077	+	5.45729i	0.178664	+	0.309454i	0.941423	−	0.337228i	$-0.109489\pi$
$311$	3.15077	+	5.45729i	0.178664	+	0.309454i	−0.762759	+	0.646682i	$0.776156\pi$
$312$	0.115588	+	6.24393i	0.00654388	+	0.353493i
$313$	−9.08951	−	5.24783i	−0.513770	−	0.296625i	0.220612	−	0.975362i	$-0.429194\pi$
$313$	−9.08951	−	5.24783i	−0.513770	−	0.296625i	−0.734382	+	0.678737i	$0.762528\pi$
$314$	−5.69728	+	3.28932i	−0.321516	+	0.185627i
$315$	−4.63281	−	2.36570i	−0.261029	−	0.133292i
$316$	−1.40194	+	2.42822i	−0.0788651	+	0.136598i
$317$	0.443737	−	0.768575i	0.0249227	−	0.0431674i	−0.853295	−	0.521428i	$-0.825399\pi$
$317$	0.443737	−	0.768575i	0.0249227	−	0.0431674i	0.878218	+	0.478261i	$0.158733\pi$
$318$	−13.6013	−	13.7926i	−0.762722	−	0.773451i
$319$			13.8961i			0.778035i
$320$	−0.567570	−	0.327687i	−0.0317282	−	0.0183183i
$321$	−29.4880	+	7.68097i	−1.64586	+	0.428710i
$322$	−1.67959	+	3.40582i	−0.0936001	+	0.189799i
$323$	−22.8925	−	39.6509i	−1.27377	−	2.20624i
$324$	4.71595	−	7.66550i	0.261997	−	0.425861i
$325$	−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	0.0358889	−	0.999356i	$-0.488574\pi$
$331$	16.7252	−	9.65631i	0.919301	−	0.530759i	0.883412	+	0.468597i	$0.155240\pi$
$332$			7.24087i			0.397394i
$333$	4.33777	+	7.76161i	0.237708	+	0.425334i
$334$	−1.12359	+	0.648707i	−0.0614803	+	0.0354957i
$335$	−1.30955	−	2.26821i	−0.0715486	−	0.123926i
$336$	−0.925413	+	4.48816i	−0.0504854	+	0.244849i
$337$	−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
$339$	1.19770	−	4.34819i	0.0650502	−	0.236161i
$340$	3.98595	+	2.30129i	0.216169	+	0.124805i
$341$	−14.0102			−0.758694
$342$	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
$345$	−1.57077	−	0.432666i	−0.0845675	−	0.0232940i
$346$	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	0.845074	−	0.534649i	$-0.179556\pi$
$349$	−0.756268	−	1.30990i	−0.0404821	−	0.0701171i	−0.885557	+	0.464532i	$0.846223\pi$
$350$	−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
$353$	28.2367	+	16.3025i	1.50289	+	0.867692i	0.999994	+	0.00334317i	$0.00106416\pi$
$353$	28.2367	+	16.3025i	1.50289	+	0.867692i	0.502892	+	0.864349i	$0.332269\pi$
$354$	−11.8646	+	3.09047i	−0.630597	+	0.164257i
$355$	0.532973	−	0.307712i	0.0282873	−	0.0163317i
$356$		−	10.9296i		−	0.579268i
$357$	6.49902	−	31.5196i	0.343965	−	1.66820i
$358$	12.5760	+	7.26077i	0.664664	+	0.383744i
$359$	−3.19150	+	5.52784i	−0.168441	+	0.291748i	−0.937872	−	0.346982i	$-0.887207\pi$
$359$	−3.19150	+	5.52784i	−0.168441	+	0.291748i	0.769431	+	0.638730i	$0.220540\pi$
$360$	−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	0.202981	−	0.979183i	$-0.434937\pi$
$367$	−10.4124	−	6.01163i	−0.543525	−	0.313804i	−0.746506	+	0.665378i	$0.768270\pi$
$368$			1.43530i			0.0748203i
$369$	13.3395	−	22.3770i	0.694429	−	1.16490i
$370$	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	0.997315	+	0.0732353i	$0.0233324\pi$
$373$	10.8556	+	18.8024i	0.562081	+	0.973553i	−0.435234	+	0.900317i	$0.643334\pi$
$374$	−10.8612	+	18.8121i	−0.561617	+	0.972749i
$375$	10.5131	−	2.73842i	0.542892	−	0.141411i
$376$	−8.04448	−	4.64448i	−0.414863	−	0.239521i
$377$	15.5345	−	4.58994i	0.800068	−	0.236394i
$378$	4.14528	+	13.1079i	0.213210	+	0.674197i
$379$	−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	$0.357356\pi$
$380$		−	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	$-0.946807\pi$
$383$	−26.1275	+	15.0847i	−1.33505	+	0.770793i	−0.348984	+	0.937129i	$0.613473\pi$
$384$	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
$387$	0.00318631	−	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	$-0.477110\pi$
$389$	19.1621	−	11.0633i	0.971559	−	0.560930i	0.899711	+	0.436485i	$0.143777\pi$
$390$	1.98045	−	3.58175i	0.100284	−	0.181369i
$391$		−	10.0799i		−	0.509762i
$392$	−4.26126	−	5.55353i	−0.215226	−	0.280496i
$393$	−6.21342	−	1.71148i	−0.313425	−	0.0863325i
$394$	−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	0.982167	−	0.188013i	$-0.0602046\pi$
$397$	6.54053	+	11.3285i	0.328260	+	0.568562i	−0.653907	+	0.756575i	$0.726871\pi$
$398$		−	24.5006i		−	1.22810i
$399$	−28.3568	+	9.40528i	−1.41961	+	0.470853i
$400$	−2.28524	−	3.95816i	−0.114262	−	0.197908i
$401$	6.92658			0.345897			0.172948	−	0.984931i	$-0.444671\pi$
$401$	6.92658			0.345897			0.172948	+	0.984931i	$0.444671\pi$
$402$	−1.83817	+	6.67336i	−0.0916795	+	0.332837i
$403$	4.62761	+	15.6620i	0.230517	+	0.780180i
$404$	3.72432	−	6.45070i	0.185292	−	0.320934i
$405$	−5.18852	+	2.80536i	−0.257819	+	0.139399i
$406$	11.8609	−	0.777327i	0.588648	−	0.0385781i
$407$	7.93923	+	4.58372i	0.393533	+	0.227206i
$408$	−3.06612	−	11.7711i	−0.151796	−	0.582758i
$409$	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
$411$	3.02395	+	11.6092i	0.149160	+	0.572641i
$412$	−15.3456	−	8.85976i	−0.756021	−	0.436489i
$413$	8.28340	−	16.7968i	0.407599	−	0.826516i
$414$	2.10066	+	3.75873i	0.103242	+	0.184732i
$415$	2.37274	−	4.10970i	0.116473	−	0.201737i
$416$	−3.50535	−	0.844105i	−0.171864	−	0.0413857i
$417$	−1.20975	+	4.39192i	−0.0592417	+	0.215073i
$418$	20.1653			0.986315
$419$	3.98319	+	6.89908i	0.194591	+	0.337042i	0.946766	−	0.321921i	$-0.104329\pi$
$419$	3.98319	+	6.89908i	0.194591	+	0.337042i	−0.752175	+	0.658963i	$0.770995\pi$
$420$	1.99595	−	2.24410i	0.0973924	−	0.109501i
$421$		−	14.1689i		−	0.690552i	−0.938501	−	0.345276i	$-0.887785\pi$
$421$		−	14.1689i		−	0.690552i	0.938501	−	0.345276i	$-0.112215\pi$
$422$	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
$426$	−1.56807	−	0.431923i	−0.0759733	−	0.0209267i
$427$	40.5331	−	2.65641i	1.96153	−	0.128552i
$428$		−	17.5930i		−	0.850389i
$429$	16.9044	+	9.34691i	0.816151	+	0.451273i
$430$	−0.0431603	+	0.0249186i	−0.00208137	+	0.00120168i
$431$	−12.9721	+	22.4684i	−0.624845	+	1.08226i	0.363725	+	0.931506i	$0.381505\pi$
$431$	−12.9721	+	22.4684i	−0.624845	+	1.08226i	−0.988571	+	0.150758i	$0.951829\pi$
$432$	3.59645	+	3.75040i	0.173034	+	0.180441i
$433$	−14.7383	−	8.50919i	−0.708280	−	0.408925i	0.102144	−	0.994770i	$-0.467430\pi$
$433$	−14.7383	−	8.50919i	−0.708280	−	0.408925i	−0.810424	+	0.585844i	$0.800763\pi$
$434$	0.783707	+	11.9583i	0.0376191	+	0.574016i
$435$	1.28548	+	4.93510i	0.0616342	+	0.236620i
$436$	−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	$0.249913\pi$
$439$			29.6229i			1.41382i	−0.707301	+	0.706912i	$0.750087\pi$
$440$	−1.75555	+	1.01357i	−0.0836926	+	0.0483199i
$441$	−19.2872	−	8.30681i	−0.918439	−	0.395562i
$442$	24.6175	+	5.92801i	1.17094	+	0.281967i
$443$	−15.3962	−	8.88898i	−0.731494	−	0.422328i	0.0874748	−	0.996167i	$-0.472120\pi$
$443$	−15.3962	−	8.88898i	−0.731494	−	0.422328i	−0.818968	+	0.573839i	$0.805454\pi$
$444$	−4.96775	+	1.29399i	−0.235759	+	0.0614100i
$445$	−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	−0.469003	−	0.883197i	$-0.655387\pi$
$449$	11.2383	−	19.4653i	0.530369	−	0.918626i	0.999372	−	0.0354297i	$-0.0112800\pi$
$450$	−11.7776	−	7.02091i	−0.555199	−	0.330969i
$451$		−	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	$-0.787517\pi$
$457$		−	26.4676i		−	1.23810i	0.785350	−	0.619051i	$-0.212483\pi$
$458$	−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	$-0.385169\pi$
$461$	−6.02929	−	3.48101i	−0.280812	−	0.162127i	−0.633791	+	0.773504i	$0.718502\pi$
$462$	10.5913	+	9.42007i	0.492750	+	0.438261i
$463$			10.3837i			0.482572i	0.970454	+	0.241286i	$0.0775692\pi$
$463$			10.3837i			0.482572i	−0.970454	+	0.241286i	$0.922431\pi$
$464$	3.89073	−	2.24631i	0.180623	−	0.104283i
$465$	−4.97560	+	1.29603i	−0.230738	+	0.0601021i
$466$	−7.73067	−	4.46331i	−0.358117	−	0.206759i
$467$	11.7463	−	20.3453i	0.543556	−	0.941467i	−0.455140	−	0.890420i	$-0.650411\pi$
$467$	11.7463	−	20.3453i	0.543556	−	0.941467i	0.998696	−	0.0510470i	$-0.0162558\pi$
$468$	−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
$471$	−8.00070	−	8.11324i	−0.368653	−	0.373838i
$472$		−	7.07861i		−	0.325819i
$473$	−0.117606	−	0.203699i	−0.00540751	−	0.00936608i
$474$	−4.68208	−	1.28967i	−0.215055	−	0.0592365i
$475$	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
$478$	2.27619			0.104110
$479$	7.41327	+	4.28005i	0.338721	+	0.195561i	0.659706	−	0.751524i	$-0.270681\pi$
$479$	7.41327	+	4.28005i	0.338721	+	0.195561i	−0.320985	+	0.947084i	$0.604014\pi$
$480$	0.301446	−	1.09438i	0.0137591	−	0.0499515i
$481$	2.50179	−	10.3893i	0.114072	−	0.473711i
$482$	4.13240			0.188226
$483$	−6.44187	−	1.32825i	−0.293115	−	0.0604373i
$484$	0.716375	+	1.24080i	0.0325625	+	0.0563999i
$485$	9.73264	−	5.61914i	0.441936	−	0.255152i
$486$	14.9073	+	4.55780i	0.676207	+	0.206746i
$487$		−	17.5739i		−	0.796348i	−0.917310	−	0.398174i	$-0.869644\pi$
$487$		−	17.5739i		−	0.796348i	0.917310	−	0.398174i	$-0.130356\pi$
$488$	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	$-0.731237\pi$
$491$	−7.73222	+	4.46420i	−0.348950	+	0.201467i	0.315273	+	0.949001i	$0.397904\pi$
$492$	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
$495$	−3.11397	+	5.22367i	−0.139962	+	0.234786i
$496$	2.26475	+	3.92266i	0.101690	+	0.176133i
$497$	2.06577	−	1.38029i	0.0926626	−	0.0619143i
$498$	−12.1366	+	3.16131i	−0.543853	+	0.141662i
$499$	−8.26926	−	4.77426i	−0.370183	−	0.213725i	0.303355	−	0.952877i	$-0.401893\pi$
$499$	−8.26926	−	4.77426i	−0.370183	−	0.213725i	−0.673538	+	0.739152i	$0.735226\pi$
$500$			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	−0.444477	−	0.895790i	$-0.646610\pi$
$503$	12.4146	−	21.5027i	0.553539	−	0.958757i	0.998016	−	0.0629667i	$-0.0200562\pi$
$504$	−7.92674	+	0.408396i	−0.353085	+	0.0181914i
$505$	−4.22762	+	2.44082i	−0.188127	+	0.108615i
$506$	3.84474	+	2.21976i	0.170920	+	0.0986806i
$507$	4.86536	−	21.9847i	0.216078	−	0.976376i
$508$	−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	$-0.103711\pi$
$510$	−2.11701	+	7.68567i	−0.0937427	+	0.340327i
$511$	1.88471	+	28.7581i	0.0833747	+	1.27218i
$512$	−1.00000			−0.0441942
$513$	−9.45134	+	32.5308i	−0.417287	+	1.43627i
$514$	−25.2022			−1.11162
$515$	5.80646	+	10.0571i	0.255863	+	0.443168i
$516$	0.126983	+	0.0349772i	0.00559010	+	0.00153979i
$517$	−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	0.980264	+	0.197695i	$0.0633456\pi$
$521$	15.0954	+	26.1460i	0.661341	+	1.14548i	−0.318923	+	0.947781i	$0.603321\pi$
$522$	6.90131	−	11.5769i	0.302062	−	0.506709i
$523$			15.5942i			0.681887i	0.940084	+	0.340944i	$0.110747\pi$
$523$			15.5942i			0.681887i	−0.940084	+	0.340944i	$0.889253\pi$
$524$	1.86046	−	3.22241i	0.0812745	−	0.140772i
$525$	19.8796	−	6.59361i	0.867619	−	0.287769i
$526$	−17.2636	−	9.96713i	−0.752728	−	0.434588i
$527$	−15.9050	−	27.5482i	−0.692831	−	1.20002i
$528$	5.16504	+	1.42270i	0.224780	+	0.0619152i
$529$	20.9399			0.910431
$530$	−7.32956			−0.318376
$531$	−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
$534$	18.3194	−	4.77179i	0.792757	−	0.206496i
$535$	−5.76499	+	9.98526i	−0.249242	+	0.431700i
$536$	−3.46095	−	1.99818i	−0.149490	−	0.0863082i
$537$	−6.67934	+	24.2490i	−0.288235	+	1.04642i
$538$	20.2140			0.871488
$539$	−21.4665	+	2.82582i	−0.924627	+	0.121717i
$540$	−0.812284	−	3.30713i	−0.0349551	−	0.142316i
$541$	−36.0971	−	20.8407i	−1.55194	−	0.896011i	−0.997984	−	0.0634632i	$-0.979785\pi$
$541$	−36.0971	−	20.8407i	−1.55194	−	0.896011i	−0.553953	−	0.832548i	$-0.686881\pi$
$542$	26.4526			1.13624
$543$	5.98806	−	1.55976i	0.256972	−	0.0669356i
$544$	7.02284			0.301102
$545$	6.29056			0.269458
$546$	7.03238	−	14.9514i	0.300958	−	0.639863i
$547$	−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
$549$	23.5843	−	39.5625i	1.00655	−	1.68849i
$550$	−14.1370			−0.602802
$551$	25.3654	+	14.6447i	1.08060	+	0.623886i
$552$	−2.40574	+	0.626643i	−0.102395	+	0.0266717i
$553$	6.16816	−	4.12137i	0.262297	−	0.175259i
$554$	−3.36980			−0.143169
$555$	3.24357	+	0.893437i	0.137682	+	0.0379243i
$556$	−2.27775	−	1.31506i	−0.0965979	−	0.0557708i
$557$	−16.7603	+	29.0296i	−0.710155	+	1.23002i	0.254644	+	0.967035i	$0.418042\pi$
$557$	−16.7603	+	29.0296i	−0.710155	+	1.23002i	−0.964799	+	0.262990i	$0.915292\pi$
$558$	11.6719	+	6.95795i	0.494113	+	0.294554i
$559$	−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
$562$	−20.1579			−0.850308
$563$	3.86351			0.162828			0.0814138	−	0.996680i	$-0.474056\pi$
$563$	3.86351			0.162828			0.0814138	+	0.996680i	$0.474056\pi$
$564$	4.27256	−	15.5113i	0.179907	−	0.653143i
$565$	−0.853271	−	1.47791i	−0.0358974	−	0.0621761i
$566$	−5.52469	−	3.18968i	−0.232220	−	0.134072i
$567$	−20.1606	+	12.6708i	−0.846667	+	0.532124i
$568$	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	$-0.190870\pi$
$570$	7.16152	−	1.86542i	0.299963	−	0.0781337i
$571$	5.20460	+	9.01463i	0.217806	+	0.377250i	0.954137	−	0.299371i	$-0.0967768\pi$
$571$	5.20460	+	9.01463i	0.217806	+	0.377250i	−0.736331	+	0.676621i	$0.763443\pi$
$572$	−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
$576$	−2.61877	+	1.46357i	−0.109116	+	0.0609819i
$577$	−10.2980	−	17.8366i	−0.428711	−	0.742549i	0.568048	−	0.822995i	$-0.307699\pi$
$577$	−10.2980	−	17.8366i	−0.428711	−	0.742549i	−0.996759	+	0.0804462i	$0.974365\pi$
$578$	−32.3202			−1.34434
$579$	−10.7581	+	39.0565i	−0.447089	+	1.62313i
$580$	−2.94435			−0.122258
$581$	8.47328	−	17.1818i	0.351531	−	0.712822i
$582$	−28.6346	−	7.88736i	−1.18694	−	0.326942i
$583$		−	34.5925i		−	1.43268i
$584$	5.44642	+	9.43348i	0.225375	+	0.390360i
$585$	6.86809	+	1.75571i	0.283961	+	0.0725897i
$586$	−5.30689	−	3.06394i	−0.219226	−	0.126570i
$587$	−23.7246	+	13.6974i	−0.979217	+	0.565351i	−0.902034	−	0.431666i	$-0.857926\pi$
$587$	−23.7246	+	13.6974i	−0.979217	+	0.565351i	−0.0771834	+	0.997017i	$0.524593\pi$
$588$	7.44796	−	9.56702i	0.307149	−	0.394537i
$589$	−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	$-0.417781\pi$
$593$	−11.0590	−	6.38494i	−0.454141	−	0.262198i	−0.709577	+	0.704628i	$0.751114\pi$
$594$	15.6083	−	3.83365i	0.640416	−	0.157296i
$595$	−6.76527	−	10.1251i	−0.277349	−	0.415088i
$596$	−3.03198	−	5.25155i	−0.124195	−	0.215112i
$597$	41.0660	−	10.6968i	1.68072	−	0.437790i
$598$	1.21155	−	5.03124i	0.0495438	−	0.205743i
$599$	29.5140	−	17.0399i	1.20591	−	0.696231i	0.244045	−	0.969764i	$-0.421525\pi$
$599$	29.5140	−	17.0399i	1.20591	−	0.696231i	0.961863	+	0.273533i	$0.0881921\pi$
$600$	5.63663	−	5.55845i	0.230115	−	0.226923i
$601$	−33.7422	+	19.4811i	−1.37637	+	0.794649i	−0.991721	−	0.128413i	$-0.959012\pi$
$601$	−33.7422	+	19.4811i	−1.37637	+	0.794649i	−0.384652	+	0.923062i	$0.625678\pi$
$602$	−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
$606$	12.4382	+	3.42608i	0.505266	+	0.139175i
$607$	−0.845852	+	0.488353i	−0.0343321	+	0.0198216i	−0.517068	−	0.855944i	$-0.672976\pi$
$607$	−0.845852	+	0.488353i	−0.0343321	+	0.0198216i	0.482736	+	0.875766i	$0.339643\pi$
$608$	−3.25972	−	5.64600i	−0.132199	−	0.228976i
$609$	6.48130	+	19.5410i	0.262635	+	0.791842i
$610$	−10.0619			−0.407395
$611$	24.2783	+	23.0709i	0.982195	+	0.933350i
$612$	18.3912	−	10.2784i	0.743421	−	0.415479i
$613$	5.04618	+	2.91341i	0.203813	+	0.117672i	0.598433	−	0.801173i	$-0.295790\pi$
$613$	5.04618	+	2.91341i	0.203813	+	0.117672i	−0.394620	+	0.918845i	$0.629124\pi$
$614$	−5.38161			−0.217184
$615$	−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	$0.0288699\pi$
$618$	8.15028	−	29.5891i	0.327852	−	1.19025i
$619$	−3.21016	−	5.56015i	−0.129027	−	0.223481i	0.794273	−	0.607561i	$-0.207852\pi$
$619$	−3.21016	−	5.56015i	−0.129027	−	0.223481i	−0.923300	+	0.384080i	$0.874519\pi$
$620$		−	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
$624$	−0.115588	−	6.24393i	−0.00462722	−	0.249957i
$625$	−9.37088	+	16.2308i	−0.374835	+	0.649234i
$626$	9.08951	+	5.24783i	0.363290	+	0.209746i
$627$	8.80401	+	33.7994i	0.351598	+	1.34982i
$628$	5.69728	−	3.28932i	0.227346	−	0.131258i
$629$			20.8145i			0.829930i
$630$	4.63281	+	2.36570i	0.184576	+	0.0942516i
$631$	−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
$633$	−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	$0.857841\pi$
$642$	29.4880	−	7.68097i	1.16380	−	0.303144i
$643$	4.78089	−	8.28074i	0.188540	−	0.326561i	−0.756224	−	0.654313i	$-0.772958\pi$
$643$	4.78089	−	8.28074i	0.188540	−	0.326561i	0.944764	+	0.327753i	$0.106291\pi$
$644$	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	−0.343164	−	0.939275i	$-0.611499\pi$
$647$	16.3263	−	28.2780i	0.641854	−	1.11172i	0.985018	−	0.172449i	$-0.0551680\pi$
$648$	−4.71595	+	7.66550i	−0.185260	+	0.301129i
$649$	−18.9615	−	10.9474i	−0.744303	−	0.429724i
$650$	4.66948	+	15.8037i	0.183152	+	0.619873i
$651$	−19.7014	+	6.53449i	−0.772158	+	0.256107i
$652$	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
$657$	28.0695	+	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	$0.636774\pi$
$660$	−2.46532	−	2.50000i	−0.0959626	−	0.0973124i
$661$	6.39508	−	11.0766i	0.248740	−	0.430830i	−0.714437	−	0.699700i	$-0.753317\pi$
$661$	6.39508	−	11.0766i	0.248740	−	0.430830i	0.963176	+	0.268870i	$0.0866502\pi$
$662$	−16.7252	+	9.65631i	−0.650044	+	0.375303i
$663$	0.811755	+	43.8501i	0.0315259	+	1.70300i
$664$		−	7.24087i		−	0.281000i
$665$	−4.99989	+	10.1386i	−0.193887	+	0.393158i
$666$	−4.33777	−	7.76161i	−0.168085	−	0.300756i
$667$	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
$672$	0.925413	−	4.48816i	0.0356986	−	0.173135i
$673$	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	$0.545000\pi$
$674$	1.76473			0.0679747
$675$	6.62591	−	22.8059i	0.255031	−	0.877800i
$676$	11.5750	+	5.91777i	0.445191	+	0.227607i
$677$	−1.70470	+	2.95263i	−0.0655169	+	0.113479i	−0.896923	−	0.442186i	$-0.854203\pi$
$677$	−1.70470	+	2.95263i	−0.0655169	+	0.113479i	0.831406	+	0.555665i	$0.187536\pi$
$678$	−1.19770	+	4.34819i	−0.0459975	+	0.166991i
$679$	37.7232	−	25.2055i	1.44768	−	0.967297i
$680$	−3.98595	−	2.30129i	−0.152854	−	0.0882505i
$681$	17.9082	−	4.66468i	0.686242	−	0.178751i
$682$	14.0102			0.536478
$683$	−6.61788			−0.253226			−0.126613	−	0.991952i	$-0.540411\pi$
$683$	−6.61788			−0.253226			−0.126613	+	0.991952i	$0.540411\pi$
$684$	−16.7998	−	10.0148i	−0.642355	−	0.382925i
$685$	3.93113	+	2.26964i	0.150201	+	0.0867184i
$686$	3.61276	+	18.1645i	0.137936	+	0.693523i
$687$	−6.24033	−	1.71889i	−0.238084	−	0.0655797i
$688$	−0.0380219	+	0.0658559i	−0.00144957	+	0.00251073i
$689$	−38.6710	+	11.4260i	−1.47325	+	0.435296i
$690$	1.57077	+	0.432666i	0.0597982	+	0.0164713i
$691$	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
$693$	−11.1651	+	21.8650i	−0.424128	+	0.830582i
$694$			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
$699$	4.10589	−	14.9062i	0.155299	−	0.563805i
$700$	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	$-0.254301\pi$
$702$	−9.44110	−	16.1823i	−0.356331	−	0.610760i
$703$	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
$708$	11.8646	−	3.09047i	0.445900	−	0.116147i
$709$	−11.1532	+	6.43929i	−0.418867	+	0.241833i	−0.694592	−	0.719404i	$-0.744415\pi$
$709$	−11.1532	+	6.43929i	−0.418867	+	0.241833i	0.275726	+	0.961236i	$0.411082\pi$
$710$	−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
$714$	−6.49902	+	31.5196i	−0.243220	+	1.17959i
$715$	7.00938	−	2.07104i	0.262136	−	0.0774525i
$716$	−12.5760	−	7.26077i	−0.469988	−	0.271348i
$717$	0.993768	+	3.81517i	0.0371129	+	0.142480i
$718$	3.19150	−	5.52784i	0.119106	−	0.206297i
$719$	16.6678	+	28.8694i	0.621603	+	1.07665i	0.989187	+	0.146658i	$0.0468517\pi$
$719$	16.6678	+	28.8694i	0.621603	+	1.07665i	−0.367584	+	0.929990i	$0.619815\pi$
$720$	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
$723$	1.80418	+	6.92640i	0.0670980	+	0.257596i
$724$			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	$0.0227072\pi$
$727$			3.84364i			0.142553i	−0.997457	+	0.0712764i	$0.977293\pi$
$728$	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	0.154947	+	0.987923i	$0.450479\pi$
$733$	−21.0661	+	36.4875i	−0.778093	+	1.34770i	−0.933040	+	0.359773i	$0.882854\pi$
$734$	10.4124	+	6.01163i	0.384330	+	0.221893i
$735$	−7.36223	+	2.98936i	−0.271560	+	0.110264i
$736$		−	1.43530i		−	0.0529059i
$737$	−10.7050	+	6.18056i	−0.394325	+	0.227664i
$738$	−13.3395	+	22.3770i	−0.491035	+	0.823710i
$739$	−15.5624	−	8.98495i	−0.572471	−	0.330517i	0.185664	−	0.982613i	$-0.440556\pi$
$739$	−15.5624	−	8.98495i	−0.572471	−	0.330517i	−0.758136	+	0.652097i	$0.773890\pi$
$740$	−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	$0.796175\pi$
$744$	−5.58609	+	5.50861i	−0.204796	+	0.201955i
$745$			3.97416i			0.145602i
$746$	−10.8556	−	18.8024i	−0.397451	−	0.688406i
$747$	−10.5975	−	18.9622i	−0.387742	−	0.693790i
$748$	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
$751$	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
$753$	12.5479	+	3.45629i	0.457270	+	0.125954i
$754$	−15.5345	+	4.58994i	−0.565733	+	0.167156i
$755$	0.541708			0.0197148
$756$	−4.14528	−	13.1079i	−0.150762	−	0.476729i
$757$	−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	$0.863127\pi$
$758$	2.54234	−	1.46782i	0.0923421	−	0.0533137i
$759$	−2.04201	+	7.41340i	−0.0741202	+	0.269089i
$760$			4.27267i			0.154986i
$761$	−6.50298	+	3.75450i	−0.235733	+	0.136100i	−0.613214	−	0.789917i	$-0.710124\pi$
$761$	−6.50298	+	3.75450i	−0.235733	+	0.136100i	0.377481	+	0.926017i	$0.376790\pi$
$762$	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
$768$	−0.436593	−	1.67612i	−0.0157542	−	0.0604819i
$769$	12.5070	+	21.6627i	0.451013	+	0.781177i	0.998449	−	0.0556704i	$-0.0177296\pi$
$769$	12.5070	+	21.6627i	0.451013	+	0.781177i	−0.547437	+	0.836847i	$0.684396\pi$
$770$	5.35181	−	0.350741i	0.192866	−	0.0126398i
$771$	−11.0031	−	42.2419i	−0.396266	−	1.52130i
$772$	−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
$777$	13.3022	+	2.74277i	0.477213	+	0.0983964i
$778$	−19.1621	+	11.0633i	−0.686996	+	0.396637i
$779$	−49.0287	−	28.3067i	−1.75664	−	1.01419i
$780$	−1.98045	+	3.58175i	−0.0709115	+	0.128247i
$781$	−1.45228	−	2.51541i	−0.0519665	−	0.0900086i
$782$			10.0799i			0.360456i
$783$	22.4174	+	6.51304i	0.801133	+	0.232757i
$784$	4.26126	+	5.55353i	0.152188	+	0.198340i
$785$	−4.31148			−0.153883
$786$	6.21342	+	1.71148i	0.221625	+	0.0610463i
$787$	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
$789$	9.16898	−	33.2875i	0.326424	−	1.18506i
$790$	−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
$795$	−3.20003	−	12.2852i	−0.113493	−	0.435712i
$796$			24.5006i			0.868401i
$797$	6.45285	−	11.1767i	0.228572	−	0.395898i	−0.728813	−	0.684712i	$-0.759928\pi$
$797$	6.45285	−	11.1767i	0.228572	−	0.395898i	0.957385	+	0.288815i	$0.0932612\pi$
$798$	28.3568	−	9.40528i	1.00382	−	0.332943i
$799$	−56.4951	−	32.6174i	−1.99865	−	1.15392i
$800$	2.28524	+	3.95816i	0.0807955	+	0.139942i
$801$	15.9962	+	28.6222i	0.565199	+	1.01132i
$802$	−6.92658			−0.244586
$803$	33.6926			1.18899
$804$	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
$807$	8.82530	+	33.8812i	0.310665	+	1.19267i
$808$	−3.72432	+	6.45070i	−0.131021	+	0.226935i
$809$	−30.9586	−	17.8740i	−1.08845	−	0.628415i	−0.155285	−	0.987870i	$-0.549629\pi$
$809$	−30.9586	−	17.8740i	−1.08845	−	0.628415i	−0.933163	+	0.359454i	$0.882963\pi$
$810$	5.18852	−	2.80536i	0.182306	−	0.0985701i
$811$	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
$813$	11.5490	+	44.3379i	0.405042	+	1.55500i
$814$	−7.93923	−	4.58372i	−0.278270	−	0.160659i
$815$	−2.92460			−0.102444
$816$	3.06612	+	11.7711i	0.107336	+	0.412072i
$817$	−0.495763			−0.0173446
$818$	−32.6793			−1.14260
$819$	28.1307	+	5.25943i	0.982968	+	0.183779i
$820$	5.69113			0.198743
$821$	25.3341			0.884165			0.442083	−	0.896974i	$-0.354240\pi$
$821$	25.3341			0.884165			0.442083	+	0.896974i	$0.354240\pi$
$822$	−3.02395	−	11.6092i	−0.105472	−	0.404918i
$823$	−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
$825$	−6.17209	−	23.6953i	−0.214885	−	0.824963i
$826$	−8.28340	+	16.7968i	−0.288216	+	0.584435i
$827$	−43.3874			−1.50873			−0.754363	−	0.656458i	$-0.772054\pi$
$827$	−43.3874			−1.50873			−0.754363	+	0.656458i	$0.772054\pi$
$828$	−2.10066	−	3.75873i	−0.0730030	−	0.130625i
$829$	−12.2260	−	7.05866i	−0.424625	−	0.245157i	0.272429	−	0.962176i	$-0.412173\pi$
$829$	−12.2260	−	7.05866i	−0.424625	−	0.245157i	−0.697054	+	0.717018i	$0.745506\pi$
$830$	−2.37274	+	4.10970i	−0.0823589	+	0.142650i
$831$	−1.47123	−	5.64820i	−0.0510364	−	0.195934i
$832$	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
$835$	−0.850292			−0.0294256
$836$	−20.1653			−0.697430
$837$	−6.56649	+	22.6014i	−0.226971	+	0.781219i
$838$	−3.98319	−	6.89908i	−0.137597	−	0.238325i
$839$	6.87396	+	3.96868i	0.237315	+	0.137014i	0.613942	−	0.789351i	$-0.289583\pi$
$839$	6.87396	+	3.96868i	0.237315	+	0.137014i	−0.376627	+	0.926365i	$0.622916\pi$
$840$	−1.99595	+	2.24410i	−0.0688668	+	0.0774289i
$841$	−4.40814	+	7.63512i	−0.152005	+	0.263280i
$842$			14.1689i			0.488294i
$843$	−8.80078	−	33.7870i	−0.303115	−	1.16369i
$844$	−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
$849$	2.93426	−	10.6527i	0.100703	−	0.365598i
$850$	−16.0489	−	27.7975i	−0.550472	−	0.953446i
$851$	4.25400			0.145825
$852$	1.56807	+	0.431923i	0.0537212	+	0.0147974i
$853$	−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
$855$	6.25334	+	11.1892i	0.213860	+	0.382661i
$856$			17.5930i			0.601316i
$857$	−1.19842	−	2.07572i	−0.0409372	−	0.0709054i	0.844831	−	0.535034i	$-0.179701\pi$
$857$	−1.19842	−	2.07572i	−0.0409372	−	0.0709054i	−0.885768	+	0.464128i	$0.846368\pi$
$858$	−16.9044	−	9.34691i	−0.577106	−	0.319098i
$859$	9.45554	+	5.45916i	0.322619	+	0.186264i	0.652559	−	0.757738i	$-0.273695\pi$
$859$	9.45554	+	5.45916i	0.322619	+	0.186264i	−0.329940	+	0.944002i	$0.607029\pi$
$860$	0.0431603	−	0.0249186i	0.00147175	−	0.000849717i
$861$	−12.5277	−	37.7708i	−0.426942	−	1.28722i
$862$	12.9721	−	22.4684i	0.441832	−	0.765276i
$863$	0.0710829	−	0.123119i	0.00241969	−	0.00419102i	−0.864813	−	0.502094i	$-0.832563\pi$
$863$	0.0710829	−	0.123119i	0.00241969	−	0.00419102i	0.867233	+	0.497903i	$0.165896\pi$
$864$	−3.59645	−	3.75040i	−0.122354	−	0.127591i
$865$			8.30053i			0.282226i
$866$	14.7383	+	8.50919i	0.500829	+	0.289154i
$867$	−14.1108	−	54.1726i	−0.479227	−	1.83980i
$868$	−0.783707	−	11.9583i	−0.0266007	−	0.405890i
$869$	−4.33632	−	7.51073i	−0.147100	−	0.254784i
$870$	−1.28548	−	4.93510i	−0.0435820	−	0.167315i
$871$	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	−0.656979	−	0.753909i	$-0.728166\pi$
$877$	−9.84863	+	5.68611i	−0.332564	+	0.192006i	0.324415	+	0.945915i	$0.394833\pi$
$878$		−	29.6229i		−	0.999725i
$879$	2.81858	−	10.2327i	0.0950683	−	0.345140i
$880$	1.75555	−	1.01357i	0.0591796	−	0.0341674i
$881$	15.4774	+	26.8077i	0.521448	+	0.903174i	0.999689	+	0.0249457i	$0.00794128\pi$
$881$	15.4774	+	26.8077i	0.521448	+	0.903174i	−0.478241	+	0.878229i	$0.658725\pi$
$882$	19.2872	+	8.30681i	0.649435	+	0.279705i
$883$	−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
$885$	−7.74671	−	2.13382i	−0.260403	−	0.0717276i
$886$	15.3962	+	8.88898i	0.517244	+	0.298631i
$887$	0.410274			0.0137757			0.00688783	−	0.999976i	$-0.497808\pi$
$887$	0.410274			0.0137757			0.00688783	+	0.999976i	$0.497808\pi$
$888$	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
$891$	13.2401	+	24.4877i	0.443561	+	0.820368i
$892$	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
$897$	8.96192	−	0.165904i	0.299230	−	0.00553936i
$898$	−11.2383	+	19.4653i	−0.375028	+	0.649567i
$899$	17.6231	+	10.1747i	0.587762	+	0.339345i
$900$	11.7776	+	7.02091i	0.392585	+	0.234030i
$901$	68.0192	−	39.2709i	2.26605	−	1.30830i
$902$			26.8598i			0.894335i
$903$	−0.260386	−	0.231593i	−0.00866511	−	0.00770692i
$904$	−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	−0.0736914	−	0.997281i	$-0.523478\pi$
$907$	24.9010	−	43.1298i	0.826825	−	1.43210i	0.900516	−	0.434822i	$-0.143189\pi$
$908$			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
$915$	−4.39296	−	16.8650i	−0.145227	−	0.557539i
$916$	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	0.973593	+	0.228292i	$0.0733142\pi$
$919$	20.7507	+	35.9413i	0.684503	+	1.18559i	−0.289089	+	0.957302i	$0.593352\pi$
$920$	−0.470330	+	0.814635i	−0.0155063	+	0.0268577i
$921$	−2.34957	−	9.02023i	−0.0774210	−	0.297227i
$922$	6.02929	+	3.48101i	0.198564	+	0.114641i
$923$	−2.33229	+	2.45435i	−0.0767684	+	0.0807859i
$924$	−10.5913	−	9.42007i	−0.348427	−	0.309897i
$925$	−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	$-0.645260\pi$
$929$	3.54765	−	2.04824i	0.116395	−	0.0672005i	0.557067	+	0.830467i	$0.311927\pi$
$930$	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
$933$	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
$936$	10.4151	−	2.91979i	0.340429	−	0.0954365i
$937$		−	26.3778i		−	0.861725i	−0.902418	−	0.430862i	$-0.858209\pi$
$937$		−	26.3778i		−	0.861725i	0.902418	−	0.430862i	$-0.141791\pi$
$938$	5.87419	+	8.79147i	0.191799	+	0.287052i
$939$	−4.82759	+	17.5263i	−0.157543	+	0.571949i
$940$	−3.04387	−	5.27214i	−0.0992802	−	0.171958i
$941$	−31.1389	+	17.9781i	−1.01510	+	0.586068i	−0.912681	−	0.408673i	$-0.865992\pi$
$941$	−31.1389	+	17.9781i	−1.01510	+	0.586068i	−0.102419	+	0.994741i	$0.532658\pi$
$942$	8.00070	+	8.11324i	0.260677	+	0.264344i
$943$	−6.23194	−	10.7940i	−0.202940	−	0.351502i
$944$			7.07861i			0.230389i
$945$	−1.94254	+	8.79800i	−0.0631910	+	0.286199i
$946$	0.117606	+	0.203699i	0.00382369	+	0.00662282i
$947$	6.19253			0.201230			0.100615	−	0.994925i	$-0.467919\pi$
$947$	6.19253			0.201230			0.100615	+	0.994925i	$0.467919\pi$
$948$	4.68208	+	1.28967i	0.152067	+	0.0418866i
$949$	−11.1288	−	37.6650i	−0.361255	−	1.22266i
$950$	−14.8985	+	25.8050i	−0.483371	+	0.837223i
$951$	−1.48196	−	0.408203i	−0.0480558	−	0.0132369i
$952$	−16.6644	−	8.21813i	−0.540098	−	0.266351i
$953$	−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	$0.804724\pi$
$954$	−17.1799	+	28.8192i	−0.556219	+	0.933055i
$955$	3.95566			0.128002
$956$	−2.27619			−0.0736172
$957$	23.2916	−	6.06696i	0.752912	−	0.196117i
$958$	−7.41327	−	4.28005i	−0.239512	−	0.138282i
$959$	16.4352	+	8.10509i	0.530721	+	0.261727i
$960$	−0.301446	+	1.09438i	−0.00972914	+	0.0353211i
$961$	5.24181	−	9.07908i	0.169091	−	0.292874i
$962$	−2.50179	+	10.3893i	−0.0806609	+	0.334964i
$963$	25.7485	+	46.0720i	0.829734	+	1.48465i
$964$	−4.13240			−0.133096
$965$	7.66429	+	13.2749i	0.246722	+	0.427336i
$966$	6.44187	+	1.32825i	0.207264	+	0.0427356i
$967$			27.4624i			0.883132i	0.897229	+	0.441566i	$0.145577\pi$
$967$			27.4624i			0.883132i	−0.897229	+	0.441566i	$0.854423\pi$
$968$	−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	$-0.137063\pi$
$971$	2.89389	+	5.01236i	0.0928692	+	0.160854i	−0.815848	+	0.578266i	$0.803729\pi$
$972$	−14.9073	−	4.55780i	−0.478151	−	0.146192i
$973$	3.86597	+	5.78591i	0.123937	+	0.185488i
$974$			17.5739i			0.563103i
$975$	−24.4503	+	14.7264i	−0.783036	+	0.471622i
$976$	−13.2960	+	7.67646i	−0.425595	+	0.245718i
$977$	−22.5457	+	39.0503i	−0.721301	+	1.24933i	0.239178	+	0.970976i	$0.423122\pi$
$977$	−22.5457	+	39.0503i	−0.721301	+	1.24933i	−0.960479	+	0.278354i	$0.910211\pi$
$978$	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
$981$	14.7445	−	24.7339i	0.470757	−	0.789694i
$982$	7.73222	−	4.46420i	0.246745	−	0.142458i
$983$	−3.66890	+	2.11824i	−0.117020	+	0.0675613i	−0.557367	−	0.830266i	$-0.688189\pi$
$983$	−3.66890	+	2.11824i	−0.117020	+	0.0675613i	0.440348	+	0.897827i	$0.354855\pi$
$984$	−10.5609	−	10.7095i	−0.336669	−	0.341405i
$985$		−	10.3550i		−	0.329938i
$986$	27.3240	−	15.7755i	0.870172	−	0.502394i
$987$	−28.2897	+	31.8069i	−0.900470	+	1.01242i
$988$	6.66064	+	22.5428i	0.211903	+	0.717181i
$989$	−0.0945232	−	0.0545730i	−0.00300566	−	0.00173532i
$990$	3.11397	−	5.22367i	0.0989683	−	0.166019i
$991$	−14.7891	+	25.6154i	−0.469791	+	0.813701i	−0.999403	−	0.0345382i	$-0.989004\pi$
$991$	−14.7891	+	25.6154i	−0.469791	+	0.813701i	0.529613	+	0.848240i	$0.322337\pi$
$992$	−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
$996$	12.1366	−	3.16131i	0.384562	−	0.100170i
$997$		−	28.6016i		−	0.905821i	−0.891556	−	0.452910i	$-0.850386\pi$
$997$		−	28.6016i		−	0.905821i	0.891556	−	0.452910i	$-0.149614\pi$
$998$	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.e.257.8	yes	34
3.2	odd	2		546.2.bi.f.257.2	yes	34
7.3	odd	6		546.2.bn.f.101.14	yes	34
13.4	even	6		546.2.bn.e.173.4	yes	34
21.17	even	6		546.2.bn.e.101.4	yes	34
39.17	odd	6		546.2.bn.f.173.14	yes	34
91.17	odd	6		546.2.bi.f.17.2	yes	34
273.17	even	6	inner	546.2.bi.e.17.8	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.8	✓	34	273.17	even	6	inner
546.2.bi.e.257.8	yes	34	1.1	even	1	trivial
546.2.bi.f.17.2	yes	34	91.17	odd	6
546.2.bi.f.257.2	yes	34	3.2	odd	2
546.2.bn.e.101.4	yes	34	21.17	even	6
546.2.bn.e.173.4	yes	34	13.4	even	6
546.2.bn.f.101.14	yes	34	7.3	odd	6
546.2.bn.f.173.14	yes	34	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.436593 - 1.67612i) q^{3} +1.00000 q^{4} +(-0.567570 - 0.327687i) q^{5} +(0.436593 + 1.67612i) q^{6} +(-2.37289 - 1.17020i) q^{7} -1.00000 q^{8} +(-2.61877 + 1.46357i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.436593 - 1.67612i) q^{3} +1.00000 q^{4} +(-0.567570 - 0.327687i) q^{5} +(0.436593 + 1.67612i) q^{6} +(-2.37289 - 1.17020i) q^{7} -1.00000 q^{8} +(-2.61877 + 1.46357i) q^{9} +(0.567570 + 0.327687i) q^{10} +(-1.54655 + 2.67870i) q^{11} +(-0.436593 - 1.67612i) q^{12} +(3.50535 + 0.844105i) q^{13} +(2.37289 + 1.17020i) q^{14} +(-0.301446 + 1.09438i) q^{15} +1.00000 q^{16} -7.02284 q^{17} +(2.61877 - 1.46357i) q^{18} +(3.25972 + 5.64600i) q^{19} +(-0.567570 - 0.327687i) q^{20} +(-0.925413 + 4.48816i) q^{21} +(1.54655 - 2.67870i) q^{22} +1.43530i q^{23} +(0.436593 + 1.67612i) 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} +(0.301446 - 1.09438i) q^{30} +(2.26475 + 3.92266i) q^{31} -1.00000 q^{32} +(5.16504 + 1.42270i) q^{33} +7.02284 q^{34} +(0.963325 + 1.44174i) q^{35} +(-2.61877 + 1.46357i) q^{36} -2.96384i q^{37} +(-3.25972 - 5.64600i) q^{38} +(-0.115588 - 6.24393i) q^{39} +(0.567570 + 0.327687i) q^{40} +(-7.52039 + 4.34190i) q^{41} +(0.925413 - 4.48816i) 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} +(-0.436593 - 1.67612i) q^{48} +(4.26126 + 5.55353i) q^{49} +(2.28524 + 3.95816i) q^{50} +(3.06612 + 11.7711i) 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} +(-0.301446 + 1.09438i) q^{60} +(-13.2960 + 7.67646i) q^{61} +(-2.26475 - 3.92266i) q^{62} +(7.92674 - 0.408396i) q^{63} +1.00000 q^{64} +(-1.71293 - 1.62775i) q^{65} +(-5.16504 - 1.42270i) q^{66} +(3.46095 + 1.99818i) q^{67} -7.02284 q^{68} +(2.40574 - 0.626643i) q^{69} +(-0.963325 - 1.44174i) q^{70} +(-0.469521 + 0.813235i) q^{71} +(2.61877 - 1.46357i) 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} +(0.115588 + 6.24393i) q^{78} +(-1.40194 + 2.42822i) q^{79} +(-0.567570 - 0.327687i) q^{80} +(4.71595 - 7.66550i) q^{81} +(7.52039 - 4.34190i) q^{82} +7.24087i q^{83} +(-0.925413 + 4.48816i) 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} +(0.436593 + 1.67612i) q^{96} +(-8.57395 + 14.8505i) q^{97} +(-4.26126 - 5.55353i) q^{98} +(0.129604 - 9.27839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * 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