LMFDB - Embedded newform 315.2.l.c.121.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.8
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.390993 q^{2} +(0.919343 + 1.46793i) q^{3} -1.84712 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.359457 - 0.573950i) q^{6} +(2.26118 + 1.37370i) q^{7} +1.50420 q^{8} +(-1.30962 + 2.69906i) q^{9} +O(q^{10})$	\(q-0.390993 q^{2} +(0.919343 + 1.46793i) q^{3} -1.84712 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.359457 - 0.573950i) q^{6} +(2.26118 + 1.37370i) q^{7} +1.50420 q^{8} +(-1.30962 + 2.69906i) q^{9} +(0.195497 + 0.338610i) q^{10} +(-1.55757 + 2.69779i) q^{11} +(-1.69814 - 2.71144i) q^{12} +(-1.07656 + 1.86466i) q^{13} +(-0.884107 - 0.537109i) q^{14} +(0.811590 - 1.53014i) q^{15} +3.10612 q^{16} +(-0.0261799 - 0.0453449i) q^{17} +(0.512052 - 1.05531i) q^{18} +(-3.73155 + 6.46324i) q^{19} +(0.923562 + 1.59966i) q^{20} +(0.0623031 + 4.58215i) q^{21} +(0.609001 - 1.05482i) q^{22} +(0.0525164 + 0.0909611i) q^{23} +(1.38288 + 2.20806i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.420929 - 0.729070i) q^{26} +(-5.16600 + 0.558937i) q^{27} +(-4.17668 - 2.53740i) q^{28} +(-2.27483 - 3.94011i) q^{29} +(-0.317326 + 0.598274i) q^{30} +6.44711 q^{31} -4.22287 q^{32} +(-5.39211 + 0.193797i) q^{33} +(0.0102362 + 0.0177296i) q^{34} +(0.0590728 - 2.64509i) q^{35} +(2.41902 - 4.98549i) q^{36} +(-0.298590 + 0.517173i) q^{37} +(1.45901 - 2.52708i) q^{38} +(-3.72692 + 0.133948i) q^{39} +(-0.752100 - 1.30268i) q^{40} +(4.88281 - 8.45728i) q^{41} +(-0.0243601 - 1.79159i) q^{42} +(3.29411 + 5.70556i) q^{43} +(2.87703 - 4.98316i) q^{44} +(2.99226 - 0.215367i) q^{45} +(-0.0205336 - 0.0355652i) q^{46} +7.27408 q^{47} +(2.85559 + 4.55955i) q^{48} +(3.22587 + 6.21239i) q^{49} +(0.195497 - 0.338610i) q^{50} +(0.0424947 - 0.0801177i) q^{51} +(1.98855 - 3.44426i) q^{52} +(-2.39011 - 4.13979i) q^{53} +(2.01987 - 0.218541i) q^{54} +3.11514 q^{55} +(3.40127 + 2.06633i) q^{56} +(-12.9181 + 0.464288i) q^{57} +(0.889442 + 1.54056i) q^{58} +1.25107 q^{59} +(-1.49911 + 2.82635i) q^{60} +6.68007 q^{61} -2.52078 q^{62} +(-6.66898 + 4.30403i) q^{63} -4.56112 q^{64} +2.15313 q^{65} +(2.10828 - 0.0757732i) q^{66} +2.84690 q^{67} +(0.0483575 + 0.0837576i) q^{68} +(-0.0852436 + 0.160715i) q^{69} +(-0.0230971 + 1.03421i) q^{70} +6.22208 q^{71} +(-1.96993 + 4.05992i) q^{72} +(-2.38580 - 4.13233i) q^{73} +(0.116747 - 0.202211i) q^{74} +(-1.73093 + 0.0622111i) q^{75} +(6.89264 - 11.9384i) q^{76} +(-7.22792 + 3.96056i) q^{77} +(1.45720 - 0.0523729i) q^{78} +12.0168 q^{79} +(-1.55306 - 2.68998i) q^{80} +(-5.56981 - 7.06946i) q^{81} +(-1.90915 + 3.30674i) q^{82} +(-7.38093 - 12.7842i) q^{83} +(-0.115081 - 8.46380i) q^{84} +(-0.0261799 + 0.0453449i) q^{85} +(-1.28797 - 2.23084i) q^{86} +(3.69245 - 6.96159i) q^{87} +(-2.34290 + 4.05802i) q^{88} +(4.22085 - 7.31072i) q^{89} +(-1.16995 + 0.0842069i) q^{90} +(-4.99580 + 2.73746i) q^{91} +(-0.0970043 - 0.168016i) q^{92} +(5.92711 + 9.46389i) q^{93} -2.84412 q^{94} +7.46310 q^{95} +(-3.88227 - 6.19886i) q^{96} +(0.575428 + 0.996671i) q^{97} +(-1.26129 - 2.42900i) q^{98} +(-5.24168 - 7.73705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.390993			−0.276474			−0.138237	−	0.990399i	$-0.544144\pi$
$2$	−0.390993			−0.276474			−0.138237	+	0.990399i	$0.544144\pi$
$3$	0.919343	+	1.46793i	0.530783	+	0.847508i
$3$	0.919343	+	1.46793i	0.530783	+	0.847508i
$4$	−1.84712			−0.923562
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.359457	−	0.573950i	−0.146748	−	0.234314i
$7$	2.26118	+	1.37370i	0.854646	+	0.519211i
$7$	2.26118	+	1.37370i	0.854646	+	0.519211i
$8$	1.50420			0.531815
$9$	−1.30962	+	2.69906i	−0.436539	+	0.899685i
$10$	0.195497	+	0.338610i	0.0618215	+	0.107078i
$11$	−1.55757	+	2.69779i	−0.469626	+	0.813416i	−0.999397	−	0.0347249i	$-0.988944\pi$
$11$	−1.55757	+	2.69779i	−0.469626	+	0.813416i	0.529771	+	0.848141i	$0.322278\pi$
$12$	−1.69814	−	2.71144i	−0.490211	−	0.782726i
$13$	−1.07656	+	1.86466i	−0.298585	+	0.517164i	−0.975812	−	0.218610i	$-0.929848\pi$
$13$	−1.07656	+	1.86466i	−0.298585	+	0.517164i	0.677228	+	0.735774i	$0.263181\pi$
$14$	−0.884107	−	0.537109i	−0.236287	−	0.143549i
$15$	0.811590	−	1.53014i	0.209552	−	0.395080i
$16$	3.10612			0.776529
$17$	−0.0261799	−	0.0453449i	−0.00634955	−	0.0109978i	0.862833	−	0.505489i	$-0.168688\pi$
$17$	−0.0261799	−	0.0453449i	−0.00634955	−	0.0109978i	−0.869183	+	0.494491i	$0.835354\pi$
$18$	0.512052	−	1.05531i	0.120692	−	0.248740i
$19$	−3.73155	+	6.46324i	−0.856077	+	1.48277i	0.0195660	+	0.999809i	$0.493772\pi$
$19$	−3.73155	+	6.46324i	−0.856077	+	1.48277i	−0.875643	+	0.482960i	$0.839562\pi$
$20$	0.923562	+	1.59966i	0.206515	+	0.357694i
$21$	0.0623031	+	4.58215i	0.0135956	+	0.999908i
$22$	0.609001	−	1.05482i	0.129839	−	0.224888i
$23$	0.0525164	+	0.0909611i	0.0109504	+	0.0189667i	0.871449	−	0.490487i	$-0.163181\pi$
$23$	0.0525164	+	0.0909611i	0.0109504	+	0.0189667i	−0.860498	+	0.509453i	$0.829848\pi$
$24$	1.38288	+	2.20806i	0.282278	+	0.450717i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.420929	−	0.729070i	0.0825510	−	0.142982i
$27$	−5.16600	+	0.558937i	−0.994198	+	0.107568i
$28$	−4.17668	−	2.53740i	−0.789318	−	0.479524i
$29$	−2.27483	−	3.94011i	−0.422424	−	0.731661i	0.573752	−	0.819029i	$-0.305487\pi$
$29$	−2.27483	−	3.94011i	−0.422424	−	0.731661i	−0.996176	+	0.0873688i	$0.972154\pi$
$30$	−0.317326	+	0.598274i	−0.0579356	+	0.109229i
$31$	6.44711			1.15794			0.578968	−	0.815350i	$-0.303456\pi$
$31$	6.44711			1.15794			0.578968	+	0.815350i	$0.303456\pi$
$32$	−4.22287			−0.746505
$33$	−5.39211	+	0.193797i	−0.938645	+	0.0337357i
$34$	0.0102362	+	0.0177296i	0.00175549	+	0.00304059i
$35$	0.0590728	−	2.64509i	0.00998513	−	0.447102i
$36$	2.41902	−	4.98549i	0.403171	−	0.830915i
$37$	−0.298590	+	0.517173i	−0.0490879	+	0.0850227i	−0.889525	−	0.456886i	$-0.848965\pi$
$37$	−0.298590	+	0.517173i	−0.0490879	+	0.0850227i	0.840437	+	0.541909i	$0.182298\pi$
$38$	1.45901	−	2.52708i	0.236683	−	0.409947i
$39$	−3.72692	+	0.133948i	−0.596784	+	0.0214489i
$40$	−0.752100	−	1.30268i	−0.118917	−	0.205971i
$41$	4.88281	−	8.45728i	0.762567	−	1.32081i	−0.178956	−	0.983857i	$-0.557272\pi$
$41$	4.88281	−	8.45728i	0.762567	−	1.32081i	0.941523	−	0.336948i	$-0.109395\pi$
$42$	−0.0243601	−	1.79159i	−0.00375884	−	0.276449i
$43$	3.29411	+	5.70556i	0.502347	+	0.870090i	0.999996	+	0.00271165i	$0.000863146\pi$
$43$	3.29411	+	5.70556i	0.502347	+	0.870090i	−0.497650	+	0.867378i	$0.665804\pi$
$44$	2.87703	−	4.98316i	0.433729	−	0.751240i
$45$	2.99226	−	0.215367i	0.446060	−	0.0321050i
$46$	−0.0205336	−	0.0355652i	−0.00302751	−	0.00524380i
$47$	7.27408			1.06103			0.530516	−	0.847675i	$-0.321998\pi$
$47$	7.27408			1.06103			0.530516	+	0.847675i	$0.321998\pi$
$48$	2.85559	+	4.55955i	0.412168	+	0.658114i
$49$	3.22587	+	6.21239i	0.460839	+	0.887484i
$50$	0.195497	−	0.338610i	0.0276474	−	0.0478867i
$51$	0.0424947	−	0.0801177i	0.00595044	−	0.0112187i
$52$	1.98855	−	3.44426i	0.275762	−	0.477633i
$53$	−2.39011	−	4.13979i	−0.328307	−	0.568644i	0.653869	−	0.756607i	$-0.273145\pi$
$53$	−2.39011	−	4.13979i	−0.328307	−	0.568644i	−0.982176	+	0.187964i	$0.939811\pi$
$54$	2.01987	−	0.218541i	0.274870	−	0.0297396i
$55$	3.11514			0.420046
$56$	3.40127	+	2.06633i	0.454514	+	0.276124i
$57$	−12.9181	+	0.464288i	−1.71105	+	0.0614965i
$58$	0.889442	+	1.54056i	0.116789	+	0.202285i
$59$	1.25107			0.162875			0.0814374	−	0.996678i	$-0.474049\pi$
$59$	1.25107			0.162875			0.0814374	+	0.996678i	$0.474049\pi$
$60$	−1.49911	+	2.82635i	−0.193534	+	0.364881i
$61$	6.68007			0.855296			0.427648	−	0.903945i	$-0.359342\pi$
$61$	6.68007			0.855296			0.427648	+	0.903945i	$0.359342\pi$
$62$	−2.52078			−0.320139
$63$	−6.66898	+	4.30403i	−0.840213	+	0.542256i
$64$	−4.56112			−0.570140
$65$	2.15313			0.267062
$66$	2.10828	−	0.0757732i	0.259511	−	0.00932704i
$67$	2.84690			0.347804			0.173902	−	0.984763i	$-0.444362\pi$
$67$	2.84690			0.347804			0.173902	+	0.984763i	$0.444362\pi$
$68$	0.0483575	+	0.0837576i	0.00586421	+	0.0101571i
$69$	−0.0852436	+	0.160715i	−0.0102621	+	0.0193478i
$70$	−0.0230971	+	1.03421i	−0.00276063	+	0.123612i
$71$	6.22208			0.738425			0.369212	−	0.929345i	$-0.379628\pi$
$71$	6.22208			0.738425			0.369212	+	0.929345i	$0.379628\pi$
$72$	−1.96993	+	4.05992i	−0.232158	+	0.478466i
$73$	−2.38580	−	4.13233i	−0.279237	−	0.483653i	0.691958	−	0.721938i	$-0.256748\pi$
$73$	−2.38580	−	4.13233i	−0.279237	−	0.483653i	−0.971195	+	0.238285i	$0.923415\pi$
$74$	0.116747	−	0.202211i	0.0135715	−	0.0235066i
$75$	−1.73093	+	0.0622111i	−0.199871	+	0.00718352i
$76$	6.89264	−	11.9384i	0.790640	−	1.36943i
$77$	−7.22792	+	3.96056i	−0.823698	+	0.451347i
$78$	1.45720	−	0.0523729i	0.164995	−	0.00593007i
$79$	12.0168			1.35199			0.675996	−	0.736906i	$-0.263714\pi$
$79$	12.0168			1.35199			0.675996	+	0.736906i	$0.263714\pi$
$80$	−1.55306	−	2.68998i	−0.173637	−	0.300748i
$81$	−5.56981	−	7.06946i	−0.618868	−	0.785495i
$82$	−1.90915	+	3.30674i	−0.210830	+	0.365169i
$83$	−7.38093	−	12.7842i	−0.810163	−	1.40324i	−0.912750	−	0.408519i	$-0.866045\pi$
$83$	−7.38093	−	12.7842i	−0.810163	−	1.40324i	0.102587	−	0.994724i	$-0.467288\pi$
$84$	−0.115081	−	8.46380i	−0.0125564	−	0.923477i
$85$	−0.0261799	+	0.0453449i	−0.00283961	+	0.00491834i
$86$	−1.28797	−	2.23084i	−0.138886	−	0.240557i
$87$	3.69245	−	6.96159i	0.395872	−	0.746361i
$88$	−2.34290	+	4.05802i	−0.249754	+	0.432587i
$89$	4.22085	−	7.31072i	0.447409	−	0.774935i	−0.550807	−	0.834632i	$-0.685680\pi$
$89$	4.22085	−	7.31072i	0.447409	−	0.774935i	0.998217	+	0.0596971i	$0.0190135\pi$
$90$	−1.16995	+	0.0842069i	−0.123324	+	0.00887619i
$91$	−4.99580	+	2.73746i	−0.523702	+	0.286963i
$92$	−0.0970043	−	0.168016i	−0.0101134	−	0.0175169i
$93$	5.92711	+	9.46389i	0.614612	+	0.981359i
$94$	−2.84412			−0.293348
$95$	7.46310			0.765698
$96$	−3.88227	−	6.19886i	−0.396232	−	0.632669i
$97$	0.575428	+	0.996671i	0.0584259	+	0.101197i	0.893759	−	0.448548i	$-0.148059\pi$
$97$	0.575428	+	0.996671i	0.0584259	+	0.101197i	−0.835333	+	0.549744i	$0.814725\pi$
$98$	−1.26129	−	2.42900i	−0.127410	−	0.245366i
$99$	−5.24168	−	7.73705i	−0.526808	−	0.777603i
$100$	0.923562	−	1.59966i	0.0923562	−	0.159966i
$101$	−7.32207	+	12.6822i	−0.728573	+	1.26193i	0.228914	+	0.973447i	$0.426483\pi$
$101$	−7.32207	+	12.6822i	−0.728573	+	1.26193i	−0.957486	+	0.288478i	$0.906851\pi$
$102$	−0.0166151	+	0.0313255i	−0.00164514	+	0.00310168i
$103$	−6.31934	−	10.9454i	−0.622663	−	1.07848i	−0.988988	−	0.147997i	$-0.952717\pi$
$103$	−6.31934	−	10.9454i	−0.622663	−	1.07848i	0.366325	−	0.930487i	$-0.380616\pi$
$104$	−1.61937	+	2.80482i	−0.158792	+	0.275036i
$105$	3.93711	−	2.34503i	0.384222	−	0.228852i
$106$	0.934516	+	1.61863i	0.0907683	+	0.157215i
$107$	−6.58404	+	11.4039i	−0.636503	+	1.10246i	0.349692	+	0.936865i	$0.386286\pi$
$107$	−6.58404	+	11.4039i	−0.636503	+	1.10246i	−0.986195	+	0.165591i	$0.947047\pi$
$108$	9.54225	−	1.03243i	0.918203	−	0.0993453i
$109$	−7.27924	−	12.6080i	−0.697225	−	1.20763i	−0.969425	−	0.245388i	$-0.921084\pi$
$109$	−7.27924	−	12.6080i	−0.697225	−	1.20763i	0.272200	−	0.962241i	$-0.412249\pi$
$110$	−1.21800			−0.116132
$111$	−1.03368	+	0.0371512i	−0.0981124	+	0.00352624i
$112$	7.02349	+	4.26689i	0.663657	+	0.403183i
$113$	2.05008	−	3.55084i	0.192855	−	0.334034i	−0.753340	−	0.657631i	$-0.771559\pi$
$113$	2.05008	−	3.55084i	0.192855	−	0.334034i	0.946195	+	0.323596i	$0.104892\pi$
$114$	5.05090	−	0.181534i	0.473061	−	0.0170022i
$115$	0.0525164	−	0.0909611i	0.00489718	−	0.00848216i
$116$	4.20188	+	7.27788i	0.390135	+	0.675734i
$117$	−3.62294	−	5.34770i	−0.334941	−	0.494395i
$118$	−0.489158			−0.0450307
$119$	0.00309304	−	0.138496i	0.000283538	−	0.0126959i
$120$	1.22079	−	2.30163i	0.111443	−	0.210109i
$121$	0.647936	+	1.12226i	0.0589033	+	0.102023i
$122$	−2.61186			−0.236467
$123$	16.9037	−	0.607531i	1.52415	−	0.0547792i
$124$	−11.9086			−1.06943
$125$	1.00000			0.0894427
$126$	2.60753	−	1.68285i	0.232297	−	0.149920i
$127$	−8.15310			−0.723470			−0.361735	−	0.932281i	$-0.617816\pi$
$127$	−8.15310			−0.723470			−0.361735	+	0.932281i	$0.617816\pi$
$128$	10.2291			0.904134
$129$	−5.34693	+	10.0809i	−0.470771	+	0.887571i
$130$	−0.841858			−0.0738358
$131$	3.31890	+	5.74850i	0.289973	+	0.502249i	0.973803	−	0.227393i	$-0.0730202\pi$
$131$	3.31890	+	5.74850i	0.289973	+	0.502249i	−0.683830	+	0.729642i	$0.739687\pi$
$132$	9.95989	−	0.357967i	0.866897	−	0.0311570i
$133$	−17.3163	+	9.48849i	−1.50151	+	0.822757i
$134$	−1.11312			−0.0961588
$135$	3.06706	+	4.19442i	0.263970	+	0.360998i
$136$	−0.0393798	−	0.0682078i	−0.00337679	−	0.00584877i
$137$	−10.0539	+	17.4139i	−0.858964	+	1.48777i	0.0139534	+	0.999903i	$0.495558\pi$
$137$	−10.0539	+	17.4139i	−0.858964	+	1.48777i	−0.872918	+	0.487867i	$0.837775\pi$
$138$	0.0333297	−	0.0628384i	0.00283721	−	0.00534916i
$139$	8.86312	−	15.3514i	0.751760	−	1.30209i	−0.195209	−	0.980762i	$-0.562539\pi$
$139$	8.86312	−	15.3514i	0.751760	−	1.30209i	0.946969	−	0.321325i	$-0.104128\pi$
$140$	−0.109115	+	4.88581i	−0.00922189	+	0.412927i
$141$	6.68737	+	10.6778i	0.563178	+	0.899234i
$142$	−2.43279			−0.204155
$143$	−3.35365	−	5.80869i	−0.280446	−	0.485747i
$144$	−4.06782	+	8.38358i	−0.338985	+	0.698632i
$145$	−2.27483	+	3.94011i	−0.188914	+	0.327209i
$146$	0.932834	+	1.61572i	0.0772019	+	0.133718i
$147$	−6.15364	+	10.4467i	−0.507544	+	0.861626i
$148$	0.551532	−	0.955282i	0.0453357	−	0.0785237i
$149$	9.05624	+	15.6859i	0.741916	+	1.28504i	0.951622	+	0.307272i	$0.0994162\pi$
$149$	9.05624	+	15.6859i	0.741916	+	1.28504i	−0.209705	+	0.977765i	$0.567250\pi$
$150$	0.676783	−	0.0243241i	0.0552591	−	0.00198606i
$151$	−4.52174	+	7.83189i	−0.367974	+	0.637350i	−0.989249	−	0.146243i	$-0.953282\pi$
$151$	−4.52174	+	7.83189i	−0.367974	+	0.637350i	0.621274	+	0.783593i	$0.286615\pi$
$152$	−5.61300	+	9.72200i	−0.455274	+	0.788558i
$153$	0.156674	−	0.0112765i	0.0126663	−	0.000911655i
$154$	2.82607	−	1.54855i	0.227731	−	0.124786i
$155$	−3.22356	−	5.58336i	−0.258922	−	0.448467i
$156$	6.88408	−	0.247419i	0.551167	−	0.0198094i
$157$	−3.28870			−0.262467			−0.131233	−	0.991352i	$-0.541894\pi$
$157$	−3.28870			−0.262467			−0.131233	+	0.991352i	$0.541894\pi$
$158$	−4.69847			−0.373790
$159$	3.87958	−	7.31439i	0.307670	−	0.580069i
$160$	2.11144	+	3.65711i	0.166924	+	0.289120i
$161$	−0.00620458	+	0.277821i	−0.000488990	+	0.0218954i
$162$	2.17776	+	2.76411i	0.171101	+	0.217169i
$163$	3.72039	−	6.44390i	0.291403	−	0.504725i	−0.682739	−	0.730663i	$-0.739211\pi$
$163$	3.72039	−	6.44390i	0.291403	−	0.504725i	0.974142	+	0.225938i	$0.0725445\pi$
$164$	−9.01916	+	15.6217i	−0.704278	+	1.21985i
$165$	2.86389	+	4.57280i	0.222953	+	0.355992i
$166$	2.88590	+	4.99852i	0.223989	+	0.387960i
$167$	8.51412	−	14.7469i	0.658842	−	1.14115i	−0.322074	−	0.946715i	$-0.604380\pi$
$167$	8.51412	−	14.7469i	0.658842	−	1.14115i	0.980916	−	0.194433i	$-0.0622868\pi$
$168$	0.0937163	+	6.89247i	0.00723037	+	0.531766i
$169$	4.18203	+	7.24348i	0.321694	+	0.557191i
$170$	0.0102362	−	0.0177296i	0.000785078	−	0.00135979i
$171$	−12.5577	−	18.5360i	−0.960314	−	1.41749i
$172$	−6.08462	−	10.5389i	−0.463948	−	0.803582i
$173$	19.4110			1.47579			0.737896	−	0.674914i	$-0.235819\pi$
$173$	19.4110			1.47579			0.737896	+	0.674914i	$0.235819\pi$
$174$	−1.44372	+	2.72194i	−0.109448	+	0.206349i
$175$	−2.32025	+	1.27139i	−0.175395	+	0.0961078i
$176$	−4.83800	+	8.37966i	−0.364678	+	0.631641i
$177$	1.15016	+	1.83647i	0.0864512	+	0.138038i
$178$	−1.65032	+	2.85845i	−0.123697	+	0.214250i
$179$	10.8440	+	18.7824i	0.810522	+	1.40387i	0.912499	+	0.409078i	$0.134150\pi$
$179$	10.8440	+	18.7824i	0.810522	+	1.40387i	−0.101977	+	0.994787i	$0.532517\pi$
$180$	−5.52707	+	0.397809i	−0.411964	+	0.0296509i
$181$	15.4159			1.14586			0.572928	−	0.819606i	$-0.305808\pi$
$181$	15.4159			1.14586			0.572928	+	0.819606i	$0.305808\pi$
$182$	1.95332	−	1.07033i	0.144790	−	0.0793379i
$183$	6.14128	+	9.80585i	0.453976	+	0.724870i
$184$	0.0789952	+	0.136824i	0.00582360	+	0.0100868i
$185$	0.597180			0.0439055
$186$	−2.31746	−	3.70032i	−0.169924	−	0.271320i
$187$	0.163108			0.0119277
$188$	−13.4361			−0.979930
$189$	−12.4491	−	5.83270i	−0.905537	−	0.424267i
$190$	−2.91802			−0.211696
$191$	−20.8471			−1.50844			−0.754220	−	0.656621i	$-0.771985\pi$
$191$	−20.8471			−1.50844			−0.754220	+	0.656621i	$0.771985\pi$
$192$	−4.19323	−	6.69539i	−0.302620	−	0.483198i
$193$	−20.9059			−1.50484			−0.752420	−	0.658684i	$-0.771113\pi$
$193$	−20.9059			−1.50484			−0.752420	+	0.658684i	$0.771113\pi$
$194$	−0.224989	−	0.389692i	−0.0161532	−	0.0279782i
$195$	1.97946	+	3.16063i	0.141752	+	0.226337i
$196$	−5.95859	−	11.4750i	−0.425613	−	0.819646i
$197$	6.57881			0.468721			0.234360	−	0.972150i	$-0.424700\pi$
$197$	6.57881			0.468721			0.234360	+	0.972150i	$0.424700\pi$
$198$	2.04946	+	3.02514i	0.145649	+	0.214987i
$199$	9.73940	+	16.8691i	0.690408	+	1.19582i	0.971704	+	0.236201i	$0.0759023\pi$
$199$	9.73940	+	16.8691i	0.690408	+	1.19582i	−0.281296	+	0.959621i	$0.590764\pi$
$200$	−0.752100	+	1.30268i	−0.0531815	+	0.0921131i
$201$	2.61728	+	4.17904i	0.184608	+	0.294767i
$202$	2.86288	−	4.95865i	0.201432	−	0.348890i
$203$	0.268761	−	12.0342i	0.0188633	−	0.844638i
$204$	−0.0784929	+	0.147987i	−0.00549561	+	0.0103612i
$205$	−9.76563			−0.682061
$206$	2.47082	+	4.27958i	0.172150	+	0.298173i
$207$	−0.314285	+	0.0226206i	−0.0218443	+	0.00157224i
$208$	−3.34393	+	5.79185i	−0.231860	+	0.401593i
$209$	−11.6243	−	20.1339i	−0.804071	−	1.39269i
$210$	−1.53938	+	0.916892i	−0.106228	+	0.0632716i
$211$	6.82067	−	11.8137i	0.469554	−	0.813291i	−0.529840	−	0.848098i	$-0.677748\pi$
$211$	6.82067	−	11.8137i	0.469554	−	0.813291i	0.999394	+	0.0348062i	$0.0110814\pi$
$212$	4.41483	+	7.64670i	0.303211	+	0.525178i
$213$	5.72022	+	9.13355i	0.391943	+	0.625821i
$214$	2.57432	−	4.45885i	0.175977	−	0.304800i
$215$	3.29411	−	5.70556i	0.224656	−	0.389116i
$216$	−7.77070	+	0.840753i	−0.528729	+	0.0572060i
$217$	14.5781	+	8.85643i	0.989625	+	0.601213i
$218$	2.84614	+	4.92965i	0.192765	+	0.333878i
$219$	3.87259	−	7.30122i	0.261685	−	0.493371i
$220$	−5.75406			−0.387939
$221$	0.112737			0.00758352
$222$	0.404161	−	0.0145259i	0.0271255	−	0.000974913i
$223$	3.76397	+	6.51939i	0.252054	+	0.436570i	0.964091	−	0.265571i	$-0.0855606\pi$
$223$	3.76397	+	6.51939i	0.252054	+	0.436570i	−0.712037	+	0.702142i	$0.752227\pi$
$224$	−9.54867	−	5.80098i	−0.637998	−	0.387594i
$225$	−1.68264	−	2.48369i	−0.112176	−	0.165579i
$226$	−0.801566	+	1.38835i	−0.0533194	+	0.0923519i
$227$	13.7546	−	23.8237i	0.912927	−	1.58124i	0.103018	−	0.994679i	$-0.467150\pi$
$227$	13.7546	−	23.8237i	0.912927	−	1.58124i	0.809909	−	0.586556i	$-0.199517\pi$
$228$	23.8614	−	0.857598i	1.58026	−	0.0567958i
$229$	−0.667716	−	1.15652i	−0.0441239	−	0.0764248i	0.843120	−	0.537725i	$-0.180716\pi$
$229$	−0.667716	−	1.15652i	−0.0441239	−	0.0764248i	−0.887244	+	0.461301i	$0.847383\pi$
$230$	−0.0205336	+	0.0355652i	−0.00135394	+	0.00234510i
$231$	−12.4587	−	6.96895i	−0.819725	−	0.458523i
$232$	−3.42179	−	5.92672i	−0.224652	−	0.389108i
$233$	−8.28264	+	14.3460i	−0.542614	+	0.939835i	0.456139	+	0.889908i	$0.349232\pi$
$233$	−8.28264	+	14.3460i	−0.542614	+	0.939835i	−0.998753	+	0.0499262i	$0.984101\pi$
$234$	1.41655	+	2.09091i	0.0926025	+	0.136687i
$235$	−3.63704	−	6.29953i	−0.237254	−	0.410936i
$236$	−2.31087			−0.150425
$237$	11.0475	+	17.6397i	0.717614	+	1.14582i
$238$	−0.00120936	+	0.0541512i	−7.83910e−5	+	0.00351010i
$239$	−7.99809	+	13.8531i	−0.517354	+	0.896083i	0.482443	+	0.875927i	$0.339749\pi$
$239$	−7.99809	+	13.8531i	−0.517354	+	0.896083i	−0.999797	+	0.0201556i	$0.993584\pi$
$240$	2.52089	−	4.75279i	0.162723	−	0.306791i
$241$	10.7590	−	18.6351i	0.693046	−	1.20039i	−0.277788	−	0.960642i	$-0.589601\pi$
$241$	10.7590	−	18.6351i	0.693046	−	1.20039i	0.970835	−	0.239749i	$-0.0770652\pi$
$242$	−0.253339	−	0.438796i	−0.0162852	−	0.0282068i
$243$	5.25688	−	14.6753i	0.337229	−	0.941423i
$244$	−12.3389			−0.789919
$245$	3.76715	−	5.89988i	0.240674	−	0.376930i
$246$	−6.60922	+	0.237541i	−0.421388	+	0.0151450i
$247$	−8.03450	−	13.9162i	−0.511223	−	0.885464i
$248$	9.69775			0.615808
$249$	11.9806	−	22.5877i	0.759239	−	1.43144i
$250$	−0.390993			−0.0247286
$251$	−27.6344			−1.74427			−0.872133	−	0.489269i	$-0.837264\pi$
$251$	−27.6344			−1.74427			−0.872133	+	0.489269i	$0.837264\pi$
$252$	12.3184	−	7.95007i	0.775989	−	0.500807i
$253$	−0.327192			−0.0205704
$254$	3.18781			0.200021
$255$	−0.0906313	+	0.00325736i	−0.00567555	+	0.000203984i
$256$	5.12272			0.320170
$257$	−6.27298	−	10.8651i	−0.391298	−	0.677748i	0.601323	−	0.799006i	$-0.294640\pi$
$257$	−6.27298	−	10.8651i	−0.391298	−	0.677748i	−0.992621	+	0.121258i	$0.961307\pi$
$258$	2.09061	−	3.94155i	0.130156	−	0.245390i
$259$	−1.38561	+	0.759246i	−0.0860975	+	0.0471773i
$260$	−3.97709			−0.246649
$261$	13.6137	−	0.979843i	0.842669	−	0.0606508i
$262$	−1.29767	−	2.24763i	−0.0801701	−	0.138859i
$263$	10.3338	−	17.8987i	0.637211	−	1.10368i	−0.348831	−	0.937186i	$-0.613421\pi$
$263$	10.3338	−	17.8987i	0.637211	−	1.10368i	0.986042	−	0.166496i	$-0.0532454\pi$
$264$	−8.11081	+	0.291509i	−0.499186	+	0.0179411i
$265$	−2.39011	+	4.13979i	−0.146823	+	0.254305i
$266$	6.77055	−	3.70994i	0.415129	−	0.227471i
$267$	14.6120	−	0.525168i	0.894241	−	0.0321397i
$268$	−5.25857			−0.321219
$269$	1.78066	+	3.08420i	0.108569	+	0.188047i	0.915191	−	0.403021i	$-0.132040\pi$
$269$	1.78066	+	3.08420i	0.108569	+	0.188047i	−0.806622	+	0.591068i	$0.798707\pi$
$270$	−1.19920	−	1.63999i	−0.0729809	−	0.0998067i
$271$	−4.79811	+	8.31057i	−0.291464	+	0.504831i	−0.974156	−	0.225875i	$-0.927476\pi$
$271$	−4.79811	+	8.31057i	−0.291464	+	0.504831i	0.682692	+	0.730706i	$0.260809\pi$
$272$	−0.0813178	−	0.140846i	−0.00493061	−	0.00854007i
$273$	−8.61124	−	4.81680i	−0.521176	−	0.291526i
$274$	3.93102	−	6.80872i	0.237481	−	0.411330i
$275$	−1.55757	−	2.69779i	−0.0939252	−	0.162683i
$276$	0.157455	−	0.296860i	0.00947771	−	0.0178689i
$277$	−2.54473	+	4.40760i	−0.152898	+	0.264827i	−0.932292	−	0.361707i	$-0.882194\pi$
$277$	−2.54473	+	4.40760i	−0.152898	+	0.264827i	0.779394	+	0.626535i	$0.215527\pi$
$278$	−3.46542	+	6.00228i	−0.207842	+	0.359993i
$279$	−8.44325	+	17.4011i	−0.505484	+	1.04178i
$280$	0.0888574	−	3.97875i	0.00531024	−	0.237776i
$281$	13.4769	+	23.3427i	0.803967	+	1.39251i	0.916986	+	0.398919i	$0.130614\pi$
$281$	13.4769	+	23.3427i	0.803967	+	1.39251i	−0.113019	+	0.993593i	$0.536052\pi$
$282$	−2.61472	−	4.17495i	−0.155704	−	0.248615i
$283$	−12.7060			−0.755291			−0.377645	−	0.925950i	$-0.623266\pi$
$283$	−12.7060			−0.755291			−0.377645	+	0.925950i	$0.623266\pi$
$284$	−11.4929			−0.681981
$285$	6.86115	+	10.9553i	0.406420	+	0.648935i
$286$	1.31125	+	2.27116i	0.0775361	+	0.134296i
$287$	22.6587	−	12.4159i	1.33750	−	0.732887i
$288$	5.53034	−	11.3978i	0.325879	−	0.671620i
$289$	8.49863	−	14.7201i	0.499919	−	0.865886i
$290$	0.889442	−	1.54056i	0.0522298	−	0.0904647i
$291$	−0.934024	+	1.76097i	−0.0547535	+	0.103230i
$292$	4.40688	+	7.63293i	0.257893	+	0.446684i
$293$	−8.79850	+	15.2394i	−0.514014	+	0.890298i	0.485854	+	0.874040i	$0.338509\pi$
$293$	−8.79850	+	15.2394i	−0.514014	+	0.890298i	−0.999868	+	0.0162581i	$0.994825\pi$
$294$	2.40603	−	4.08457i	0.140323	−	0.238217i
$295$	−0.625533	−	1.08345i	−0.0364199	−	0.0630811i
$296$	−0.449139	+	0.777931i	−0.0261057	+	0.0452163i
$297$	6.53853	−	14.8074i	0.379404	−	0.859213i
$298$	−3.54093	−	6.13307i	−0.205121	−	0.355279i
$299$	−0.226149			−0.0130785
$300$	3.19725	−	0.114912i	0.184593	−	0.00663443i
$301$	−0.389184	+	17.4264i	−0.0224322	+	1.00444i
$302$	1.76797	−	3.06222i	0.101735	−	0.176211i
$303$	−25.3480	+	0.911028i	−1.45621	+	0.0523372i
$304$	−11.5906	+	20.0756i	−0.664768	+	1.15141i
$305$	−3.34004	−	5.78511i	−0.191250	−	0.331255i
$306$	−0.0612585	+	0.00440906i	−0.00350192	+	0.000252049i
$307$	7.58317			0.432795			0.216397	−	0.976305i	$-0.430569\pi$
$307$	7.58317			0.432795			0.216397	+	0.976305i	$0.430569\pi$
$308$	13.3509	−	7.31564i	0.760737	−	0.416847i
$309$	10.2574	−	19.3389i	0.583525	−	1.10015i
$310$	1.26039	+	2.18306i	0.0715853	+	0.123989i
$311$	−5.07617			−0.287843			−0.143922	−	0.989589i	$-0.545971\pi$
$311$	−5.07617			−0.287843			−0.143922	+	0.989589i	$0.545971\pi$
$312$	−5.60603	+	0.201485i	−0.317379	+	0.0114069i
$313$	30.1969			1.70683			0.853416	−	0.521231i	$-0.174527\pi$
$313$	30.1969			1.70683			0.853416	+	0.521231i	$0.174527\pi$
$314$	1.28586			0.0725653
$315$	7.06189	+	3.62350i	0.397892	+	0.204161i
$316$	−22.1964			−1.24865
$317$	−19.5191			−1.09630			−0.548151	−	0.836380i	$-0.684668\pi$
$317$	−19.5191			−1.09630			−0.548151	+	0.836380i	$0.684668\pi$
$318$	−1.51689	+	2.85988i	−0.0850629	+	0.160374i
$319$	14.1728			0.793526
$320$	2.28056	+	3.95004i	0.127487	+	0.220814i
$321$	−22.7931	+	0.819201i	−1.27218	+	0.0457233i
$322$	0.00242595	−	0.108626i	0.000135193	−	0.00605351i
$323$	0.390766			0.0217428
$324$	10.2881	+	13.0582i	0.571563	+	0.725454i
$325$	−1.07656	−	1.86466i	−0.0597170	−	0.103433i
$326$	−1.45465	+	2.51952i	−0.0805654	+	0.139543i
$327$	11.8155	−	22.2765i	0.653400	−	1.23189i
$328$	7.34473	−	12.7214i	0.405545	−	0.702424i
$329$	16.4480	+	9.99243i	0.906807	+	0.550900i
$330$	−1.11976	−	1.78794i	−0.0616408	−	0.0984226i
$331$	−0.122408			−0.00672816			−0.00336408	−	0.999994i	$-0.501071\pi$
$331$	−0.122408			−0.00672816			−0.00336408	+	0.999994i	$0.501071\pi$
$332$	13.6335	+	23.6139i	0.748236	+	1.29598i
$333$	−1.00484	−	1.48321i	−0.0550649	−	0.0812793i
$334$	−3.32896	+	5.76593i	−0.182153	+	0.315498i
$335$	−1.42345	−	2.46549i	−0.0777713	−	0.134704i
$336$	0.193521	+	14.2327i	0.0105574	+	0.776457i
$337$	−3.14954	+	5.45516i	−0.171566	+	0.297161i	−0.938968	−	0.344006i	$-0.888216\pi$
$337$	−3.14954	+	5.45516i	−0.171566	+	0.297161i	0.767401	+	0.641167i	$0.221549\pi$
$338$	−1.63514	−	2.83215i	−0.0889401	−	0.154049i
$339$	7.09709	−	0.255075i	0.385461	−	0.0138538i
$340$	0.0483575	−	0.0837576i	0.00262255	−	0.00454240i
$341$	−10.0418	+	17.3930i	−0.543796	+	0.941883i
$342$	4.90999	+	7.24747i	0.265502	+	0.391898i
$343$	−1.23970	+	18.4787i	−0.0669378	+	0.997757i
$344$	4.95500	+	8.58230i	0.267155	+	0.462727i
$345$	0.181805	−	0.00653421i	0.00978804	−	0.000351790i
$346$	−7.58958			−0.408018
$347$	−5.60174			−0.300717			−0.150359	−	0.988632i	$-0.548043\pi$
$347$	−5.60174			−0.300717			−0.150359	+	0.988632i	$0.548043\pi$
$348$	−6.82042	+	12.8589i	−0.365613	+	0.689311i
$349$	−1.32460	−	2.29428i	−0.0709043	−	0.122810i	0.828394	−	0.560146i	$-0.189255\pi$
$349$	−1.32460	−	2.29428i	−0.0709043	−	0.122810i	−0.899298	+	0.437337i	$0.855922\pi$
$350$	0.907204	−	0.497104i	0.0484921	−	0.0265713i
$351$	4.51930	−	10.2346i	0.241222	−	0.546281i
$352$	6.57743	−	11.3924i	0.350578	−	0.607219i
$353$	−1.80918	+	3.13359i	−0.0962929	+	0.166784i	−0.910147	−	0.414284i	$-0.864032\pi$
$353$	−1.80918	+	3.13359i	−0.0962929	+	0.166784i	0.813855	+	0.581069i	$0.197365\pi$
$354$	−0.449704	−	0.718048i	−0.0239015	−	0.0381638i
$355$	−3.11104	−	5.38848i	−0.165117	−	0.285991i
$356$	−7.79643	+	13.5038i	−0.413210	+	0.715701i
$357$	0.206146	−	0.122785i	0.0109104	−	0.00649849i
$358$	−4.23995	−	7.34381i	−0.224088	−	0.388132i
$359$	14.7465	−	25.5417i	0.778291	−	1.34804i	−0.154634	−	0.987972i	$-0.549420\pi$
$359$	14.7465	−	25.5417i	0.778291	−	1.34804i	0.932926	−	0.360068i	$-0.117247\pi$
$360$	4.50096	−	0.323955i	0.237221	−	0.0170739i
$361$	−18.3490	−	31.7813i	−0.965734	−	1.67270i
$362$	−6.02752			−0.316799
$363$	−1.05172	+	1.98286i	−0.0552008	+	0.104073i
$364$	9.22786	−	5.05642i	0.483671	−	0.265029i
$365$	−2.38580	+	4.13233i	−0.124879	+	0.216296i
$366$	−2.40120	−	3.83402i	−0.125513	−	0.200408i
$367$	15.5622	−	26.9546i	0.812343	−	1.40702i	−0.0988775	−	0.995100i	$-0.531525\pi$
$367$	15.5622	−	26.9546i	0.812343	−	1.40702i	0.911220	−	0.411919i	$-0.135141\pi$
$368$	0.163122	+	0.282536i	0.00850332	+	0.0147282i
$369$	16.4321	+	24.2548i	0.855419	+	1.26265i
$370$	−0.233493			−0.0121387
$371$	0.282381	−	12.6441i	0.0146605	−	0.656449i
$372$	−10.9481	−	17.4810i	−0.567633	−	0.906346i
$373$	−12.0685	−	20.9033i	−0.624885	−	1.08233i	−0.988563	−	0.150807i	$-0.951813\pi$
$373$	−12.0685	−	20.9033i	−0.624885	−	1.08233i	0.363679	−	0.931525i	$-0.381521\pi$
$374$	−0.0637743			−0.00329769
$375$	0.919343	+	1.46793i	0.0474747	+	0.0758034i
$376$	10.9417			0.564273
$377$	9.79597			0.504518
$378$	4.86751	+	2.28055i	0.250358	+	0.117299i
$379$	15.5639			0.799462			0.399731	−	0.916633i	$-0.369104\pi$
$379$	15.5639			0.799462			0.399731	+	0.916633i	$0.369104\pi$
$380$	−13.7853			−0.707170
$381$	−7.49549	−	11.9681i	−0.384006	−	0.613147i
$382$	8.15106			0.417045
$383$	−10.0220	−	17.3586i	−0.512101	−	0.886985i	−0.999902	−	0.0140301i	$-0.995534\pi$
$383$	−10.0220	−	17.3586i	−0.512101	−	0.886985i	0.487800	−	0.872955i	$-0.337799\pi$
$384$	9.40406	+	15.0156i	0.479899	+	0.766261i
$385$	7.04390	+	4.27929i	0.358991	+	0.218093i
$386$	8.17407			0.416049
$387$	−19.7136	+	1.41888i	−1.00210	+	0.0721258i
$388$	−1.06289	−	1.84098i	−0.0539599	−	0.0934614i
$389$	−5.99706	+	10.3872i	−0.304063	+	0.526653i	−0.977052	−	0.213000i	$-0.931677\pi$
$389$	−5.99706	+	10.3872i	−0.304063	+	0.526653i	0.672989	+	0.739652i	$0.265010\pi$
$390$	−0.773956	−	1.23579i	−0.0391908	−	0.0625764i
$391$	0.00274975	−	0.00476270i	0.000139061	−	0.000240860i
$392$	4.85236	+	9.34467i	0.245081	+	0.471977i
$393$	−5.38717	+	10.1567i	−0.271747	+	0.512340i
$394$	−2.57227			−0.129589
$395$	−6.00838	−	10.4068i	−0.302314	−	0.523624i
$396$	9.68203	+	14.2913i	0.486540	+	0.718165i
$397$	−9.35248	+	16.1990i	−0.469387	+	0.813003i	−0.999387	−	0.0349949i	$-0.988859\pi$
$397$	−9.35248	+	16.1990i	−0.469387	+	0.813003i	0.530000	+	0.847998i	$0.322192\pi$
$398$	−3.80804	−	6.59572i	−0.190880	−	0.330614i
$399$	−29.8480	−	16.6959i	−1.49427	−	0.835838i
$400$	−1.55306	+	2.68998i	−0.0776529	+	0.134499i
$401$	−11.4967	−	19.9128i	−0.574116	−	0.994398i	−0.996137	−	0.0878118i	$-0.972013\pi$
$401$	−11.4967	−	19.9128i	−0.574116	−	0.994398i	0.422021	−	0.906586i	$-0.361321\pi$
$402$	−1.02334	−	1.63398i	−0.0510394	−	0.0814953i
$403$	−6.94072	+	12.0217i	−0.345742	+	0.598843i
$404$	13.5248	−	23.4256i	0.672882	−	1.16547i
$405$	−3.33743	+	8.35832i	−0.165838	+	0.415328i
$406$	−0.105084	+	4.70531i	−0.00521521	+	0.233521i
$407$	−0.930150	−	1.61107i	−0.0461058	−	0.0798577i
$408$	0.0639205	−	0.120513i	0.00316454	−	0.00596628i
$409$	−11.3530			−0.561371			−0.280686	−	0.959800i	$-0.590562\pi$
$409$	−11.3530			−0.561371			−0.280686	+	0.959800i	$0.590562\pi$
$410$	3.81830			0.188572
$411$	−34.8053	+	1.25093i	−1.71682	+	0.0617039i
$412$	11.6726	+	20.2175i	0.575068	+	0.996047i
$413$	2.82888	+	1.71859i	0.139200	+	0.0845665i
$414$	0.122884	−	0.00884449i	0.00603940	−	0.000434683i
$415$	−7.38093	+	12.7842i	−0.362316	+	0.627549i
$416$	4.54619	−	7.87422i	0.222895	−	0.386066i
$417$	30.6829	−	1.10277i	1.50255	−	0.0540028i
$418$	4.54503	+	7.87223i	0.222305	+	0.385043i
$419$	10.7473	−	18.6148i	0.525038	−	0.909393i	−0.474537	−	0.880236i	$-0.657384\pi$
$419$	10.7473	−	18.6148i	0.525038	−	0.909393i	0.999575	−	0.0291571i	$-0.00928232\pi$
$420$	−7.27233	+	4.33157i	−0.354853	+	0.211359i
$421$	−5.82015	−	10.0808i	−0.283657	−	0.491308i	0.688626	−	0.725117i	$-0.258214\pi$
$421$	−5.82015	−	10.0808i	−0.283657	−	0.491308i	−0.972283	+	0.233809i	$0.924881\pi$
$422$	−2.66684	+	4.61909i	−0.129820	+	0.224854i
$423$	−9.52625	+	19.6331i	−0.463182	+	0.954596i
$424$	−3.59520	−	6.22707i	−0.174598	−	0.302413i
$425$	0.0523598			0.00253982
$426$	−2.23657	−	3.57116i	−0.108362	−	0.173023i
$427$	15.1048	+	9.17644i	0.730975	+	0.444079i
$428$	12.1615	−	21.0644i	0.587850	−	1.01819i
$429$	5.44358	−	10.2631i	0.262818	−	0.495507i
$430$	−1.28797	+	2.23084i	−0.0621116	+	0.107580i
$431$	3.29836	+	5.71293i	0.158876	+	0.275182i	0.934464	−	0.356058i	$-0.115880\pi$
$431$	3.29836	+	5.71293i	0.158876	+	0.275182i	−0.775587	+	0.631240i	$0.782546\pi$
$432$	−16.0462	+	1.73612i	−0.772023	+	0.0835293i
$433$	10.1227			0.486468			0.243234	−	0.969968i	$-0.421792\pi$
$433$	10.1227			0.486468			0.243234	+	0.969968i	$0.421792\pi$
$434$	−5.69993	−	3.46280i	−0.273606	−	0.166220i
$435$	−7.87514	+	0.283039i	−0.377584	+	0.0135707i
$436$	13.4457	+	23.2886i	0.643931	+	1.11532i
$437$	−0.783871			−0.0374976
$438$	−1.51416	+	2.85473i	−0.0723492	+	0.136404i
$439$	20.4939			0.978121			0.489060	−	0.872250i	$-0.337340\pi$
$439$	20.4939			0.978121			0.489060	+	0.872250i	$0.337340\pi$
$440$	4.68580			0.223387
$441$	−20.9922	+	0.570964i	−0.999630	+	0.0271888i
$442$	−0.0440795			−0.00209665
$443$	8.62333			0.409707			0.204853	−	0.978793i	$-0.434328\pi$
$443$	8.62333			0.409707			0.204853	+	0.978793i	$0.434328\pi$
$444$	1.90933	−	0.0686229i	0.0906129	−	0.00325670i
$445$	−8.44170			−0.400175
$446$	−1.47169	−	2.54904i	−0.0696864	−	0.120700i
$447$	−14.6999	+	27.7146i	−0.695282	+	1.31086i
$448$	−10.3135	−	6.26563i	−0.487267	−	0.296023i
$449$	−0.0789673			−0.00372670			−0.00186335	−	0.999998i	$-0.500593\pi$
$449$	−0.0789673			−0.00372670			−0.00186335	+	0.999998i	$0.500593\pi$
$450$	0.657902	+	0.971106i	0.0310138	+	0.0457784i
$451$	15.2107	+	26.3457i	0.716243	+	1.24057i
$452$	−3.78674	+	6.55883i	−0.178113	+	0.308502i
$453$	−15.6537	+	0.562606i	−0.735474	+	0.0264335i
$454$	−5.37797	+	9.31491i	−0.252401	+	0.437171i
$455$	4.86860	+	2.95776i	0.228244	+	0.138662i
$456$	−19.4315	+	0.698382i	−0.909961	+	0.0327047i
$457$	−22.9165			−1.07199			−0.535994	−	0.844222i	$-0.680063\pi$
$457$	−22.9165			−1.07199			−0.535994	+	0.844222i	$0.680063\pi$
$458$	0.261072	+	0.452191i	0.0121991	+	0.0211295i
$459$	0.160590	+	0.219619i	0.00749571	+	0.0102509i
$460$	−0.0970043	+	0.168016i	−0.00452285	+	0.00783380i
$461$	12.2509	+	21.2191i	0.570579	+	0.988272i	0.996507	+	0.0835150i	$0.0266147\pi$
$461$	12.2509	+	21.2191i	0.570579	+	0.988272i	−0.425927	+	0.904757i	$0.640052\pi$
$462$	4.87129	+	2.72481i	0.226633	+	0.126770i
$463$	−20.3034	+	35.1666i	−0.943581	+	1.63433i	−0.185013	+	0.982736i	$0.559233\pi$
$463$	−20.3034	+	35.1666i	−0.943581	+	1.63433i	−0.758568	+	0.651594i	$0.774101\pi$
$464$	−7.06587	−	12.2384i	−0.328025	−	0.568156i
$465$	5.23241	−	9.86497i	0.242647	−	0.457477i
$466$	3.23846	−	5.60917i	0.150019	−	0.259840i
$467$	18.1554	−	31.4460i	0.840130	−	1.45515i	−0.0496542	−	0.998766i	$-0.515812\pi$
$467$	18.1554	−	31.4460i	0.840130	−	1.45515i	0.889784	−	0.456381i	$-0.150855\pi$
$468$	6.69202	+	9.87786i	0.309339	+	0.456604i
$469$	6.43735	+	3.91080i	0.297249	+	0.180584i
$470$	1.42206	+	2.46308i	0.0655946	+	0.113613i
$471$	−3.02344	−	4.82757i	−0.139313	−	0.222443i
$472$	1.88185			0.0866193
$473$	−20.5232			−0.943659
$474$	−4.31951	−	6.89701i	−0.198402	−	0.316790i
$475$	−3.73155	−	6.46324i	−0.171215	−	0.296554i
$476$	−0.00571323	+	0.255820i	−0.000261865	+	0.0117255i
$477$	14.3036	−	1.02950i	0.654919	−	0.0471375i
$478$	3.12720	−	5.41647i	0.143035	−	0.247744i
$479$	−8.60799	+	14.9095i	−0.393309	+	0.681231i	−0.992884	−	0.119087i	$-0.962003\pi$
$479$	−8.60799	+	14.9095i	−0.393309	+	0.681231i	0.599575	+	0.800319i	$0.295336\pi$
$480$	−3.42724	+	6.46157i	−0.156431	+	0.294929i
$481$	−0.642901	−	1.11354i	−0.0293138	−	0.0507729i
$482$	−4.20669	+	7.28620i	−0.191609	+	0.331877i
$483$	−0.413526	+	0.246305i	−0.0188161	+	0.0112073i
$484$	−1.19682	−	2.07295i	−0.0544008	−	0.0942250i
$485$	0.575428	−	0.996671i	0.0261289	−	0.0452565i
$486$	−2.05541	+	5.73796i	−0.0932351	+	0.260279i
$487$	17.9352	+	31.0647i	0.812723	+	1.40768i	0.910951	+	0.412514i	$0.135349\pi$
$487$	17.9352	+	31.0647i	0.812723	+	1.40768i	−0.0982285	+	0.995164i	$0.531318\pi$
$488$	10.0482			0.454859
$489$	12.8795	−	0.462899i	0.582430	−	0.0209330i
$490$	−1.47293	+	2.30681i	−0.0665402	+	0.104211i
$491$	−1.19611	+	2.07173i	−0.0539798	+	0.0934958i	−0.891753	−	0.452523i	$-0.850524\pi$
$491$	−1.19611	+	2.07173i	−0.0539798	+	0.0934958i	0.837773	+	0.546019i	$0.183857\pi$
$492$	−31.2231	+	1.12218i	−1.40765	+	0.0505920i
$493$	−0.119109	+	0.206303i	−0.00536441	+	0.00929144i
$494$	3.14144	+	5.44113i	0.141340	+	0.244808i
$495$	−4.07965	+	8.40795i	−0.183366	+	0.377909i
$496$	20.0255			0.899171
$497$	14.0692	+	8.54729i	0.631091	+	0.383399i
$498$	−4.68433	+	8.83164i	−0.209910	+	0.395755i
$499$	−4.59985	−	7.96717i	−0.205917	−	0.356659i	0.744507	−	0.667614i	$-0.232685\pi$
$499$	−4.59985	−	7.96717i	−0.205917	−	0.356659i	−0.950425	+	0.310955i	$0.899351\pi$
$500$	−1.84712			−0.0826059
$501$	29.4747	−	1.05935i	1.31683	−	0.0473281i
$502$	10.8049			0.482244
$503$	−2.85710			−0.127392			−0.0636959	−	0.997969i	$-0.520289\pi$
$503$	−2.85710			−0.127392			−0.0636959	+	0.997969i	$0.520289\pi$
$504$	−10.0315	+	6.47412i	−0.446838	+	0.288380i
$505$	14.6441			0.651655
$506$	0.127930			0.00568718
$507$	−6.78818	+	12.7981i	−0.301474	+	0.568386i
$508$	15.0598			0.668170
$509$	3.91208	+	6.77593i	0.173400	+	0.300338i	0.939606	−	0.342257i	$-0.111191\pi$
$509$	3.91208	+	6.77593i	0.173400	+	0.300338i	−0.766206	+	0.642595i	$0.777858\pi$
$510$	0.0354362	−	0.00127361i	0.00156914	−	5.63963e-5i
$511$	0.281872	−	12.6213i	0.0124693	−	0.558335i
$512$	−22.4612			−0.992653
$513$	15.6647	−	35.4748i	0.691612	−	1.56625i
$514$	2.45270	+	4.24819i	0.108184	+	0.187380i
$515$	−6.31934	+	10.9454i	−0.278463	+	0.482313i
$516$	9.87644	−	18.6206i	0.434786	−	0.819727i
$517$	−11.3299	+	19.6240i	−0.498288	+	0.863061i
$518$	0.541763	−	0.296860i	0.0238037	−	0.0130433i
$519$	17.8454	+	28.4939i	0.783325	+	1.25075i
$520$	3.23873			0.142028
$521$	−4.04697	−	7.00956i	−0.177301	−	0.307094i	0.763654	−	0.645626i	$-0.223403\pi$
$521$	−4.04697	−	7.00956i	−0.177301	−	0.307094i	−0.940955	+	0.338531i	$0.890070\pi$
$522$	−5.32288	+	0.383112i	−0.232976	+	0.0167684i
$523$	−6.30363	+	10.9182i	−0.275638	+	0.477420i	−0.970296	−	0.241921i	$-0.922223\pi$
$523$	−6.30363	+	10.9182i	−0.275638	+	0.477420i	0.694658	+	0.719341i	$0.255556\pi$
$524$	−6.13042	−	10.6182i	−0.267808	−	0.463858i
$525$	−3.99941	−	2.23712i	−0.174549	−	0.0976359i
$526$	−4.04046	+	6.99828i	−0.176172	+	0.305139i
$527$	−0.168785	−	0.292344i	−0.00735238	−	0.0127347i
$528$	−16.7485	+	0.601955i	−0.728885	+	0.0261967i
$529$	11.4945	−	19.9090i	0.499760	−	0.865610i
$530$	0.934516	−	1.61863i	0.0405928	−	0.0703088i
$531$	−1.63842	+	3.37670i	−0.0711012	+	0.146536i
$532$	31.9853	−	17.5264i	1.38674	−	0.759867i
$533$	10.5133	+	18.2096i	0.455382	+	0.788745i
$534$	−5.71320	+	0.205337i	−0.247234	+	0.00888581i
$535$	13.1681			0.569306
$536$	4.28230			0.184967
$537$	−17.6018	+	33.1858i	−0.759575	+	1.43207i
$538$	−0.696227	−	1.20590i	−0.0300165	−	0.0519901i
$539$	−21.7843	−	0.973502i	−0.938315	−	0.0419317i
$540$	−5.66523	−	7.74762i	−0.243793	−	0.333404i
$541$	−8.97424	+	15.5438i	−0.385833	+	0.668282i	−0.991884	−	0.127143i	$-0.959419\pi$
$541$	−8.97424	+	15.5438i	−0.385833	+	0.668282i	0.606052	+	0.795425i	$0.292753\pi$
$542$	1.87603	−	3.24938i	0.0805824	−	0.139573i
$543$	14.1725	+	22.6294i	0.608200	+	0.971121i
$544$	0.110554	+	0.191486i	0.00473998	+	0.00820988i
$545$	−7.27924	+	12.6080i	−0.311809	+	0.540068i
$546$	3.36694	+	1.88334i	0.144092	+	0.0805994i
$547$	−12.3751	−	21.4343i	−0.529121	−	0.916465i	−0.999423	−	0.0339594i	$-0.989188\pi$
$547$	−12.3751	−	21.4343i	−0.529121	−	0.916465i	0.470302	−	0.882506i	$-0.344145\pi$
$548$	18.5708	−	32.1656i	0.793307	−	1.37405i
$549$	−8.74833	+	18.0299i	−0.373370	+	0.769497i
$550$	0.609001	+	1.05482i	0.0259679	+	0.0449777i
$551$	33.9545			1.44651
$552$	−0.128223	+	0.241747i	−0.00545755	+	0.0102894i
$553$	27.1721	+	16.5075i	1.15547	+	0.701969i
$554$	0.994973	−	1.72334i	0.0422723	−	0.0732178i
$555$	0.549013	+	0.876616i	0.0233043	+	0.0372103i
$556$	−16.3713	+	28.3559i	−0.694297	+	1.20256i
$557$	6.53043	+	11.3110i	0.276703	+	0.479264i	0.970563	−	0.240846i	$-0.0774247\pi$
$557$	6.53043	+	11.3110i	0.276703	+	0.479264i	−0.693860	+	0.720110i	$0.744091\pi$
$558$	3.30125	−	6.80372i	0.139753	−	0.288025i
$559$	−14.1852			−0.599972
$560$	0.183487	−	8.21596i	0.00775374	−	0.347188i
$561$	0.149952	+	0.239431i	0.00633100	+	0.0101088i
$562$	−5.26940	−	9.12686i	−0.222276	−	0.384993i
$563$	−13.2978			−0.560435			−0.280217	−	0.959937i	$-0.590407\pi$
$563$	−13.2978			−0.560435			−0.280217	+	0.959937i	$0.590407\pi$
$564$	−12.3524	−	19.7232i	−0.520130	−	0.830498i
$565$	−4.10015			−0.172495
$566$	4.96794			0.208818
$567$	−2.88299	−	23.6366i	−0.121074	−	0.992643i
$568$	9.35925			0.392705
$569$	−28.2599			−1.18472			−0.592358	−	0.805675i	$-0.701803\pi$
$569$	−28.2599			−1.18472			−0.592358	+	0.805675i	$0.701803\pi$
$570$	−2.68267	−	4.28345i	−0.112364	−	0.179414i
$571$	7.16732			0.299943			0.149972	−	0.988690i	$-0.452082\pi$
$571$	7.16732			0.299943			0.149972	+	0.988690i	$0.452082\pi$
$572$	6.19461	+	10.7294i	0.259009	+	0.448618i
$573$	−19.1656	−	30.6020i	−0.800655	−	1.27842i
$574$	−8.85941	+	4.85453i	−0.369785	+	0.202624i
$575$	−0.105033			−0.00438017
$576$	5.97332	−	12.3107i	0.248888	−	0.512946i
$577$	−10.3406	−	17.9104i	−0.430484	−	0.745620i	0.566431	−	0.824109i	$-0.308324\pi$
$577$	−10.3406	−	17.9104i	−0.430484	−	0.745620i	−0.996915	+	0.0784890i	$0.974990\pi$
$578$	−3.32291	+	5.75545i	−0.138215	+	0.239395i
$579$	−19.2197	−	30.6883i	−0.798743	−	1.27536i
$580$	4.20188	−	7.27788i	0.174474	−	0.302197i
$581$	0.872025	−	39.0465i	0.0361777	−	1.61992i
$582$	0.365197	−	0.688527i	0.0151379	−	0.0285404i
$583$	14.8911			0.616725
$584$	−3.58873	−	6.21586i	−0.148503	−	0.257214i
$585$	−2.81977	+	5.81141i	−0.116583	+	0.240272i
$586$	3.44016	−	5.95852i	0.142112	−	0.246144i
$587$	7.32156	+	12.6813i	0.302193	+	0.523414i	0.976632	−	0.214916i	$-0.0689479\pi$
$587$	7.32156	+	12.6813i	0.302193	+	0.523414i	−0.674439	+	0.738330i	$0.735615\pi$
$588$	11.3665	−	19.2963i	0.468748	−	0.795765i
$589$	−24.0577	+	41.6692i	−0.991282	+	1.71695i
$590$	0.244579	+	0.423623i	0.0100692	+	0.0174403i
$591$	6.04818	+	9.65721i	0.248789	+	0.397245i
$592$	−0.927454	+	1.60640i	−0.0381181	+	0.0660226i
$593$	−13.5984	+	23.5532i	−0.558421	+	0.967214i	0.439207	+	0.898386i	$0.355259\pi$
$593$	−13.5984	+	23.5532i	−0.558421	+	0.967214i	−0.997629	+	0.0688282i	$0.978074\pi$
$594$	−2.55652	+	5.78960i	−0.104895	+	0.237550i
$595$	−0.121488	+	0.0665695i	−0.00498052	+	0.00272909i
$596$	−16.7280	−	28.9738i	−0.685206	−	1.18681i
$597$	−15.8088	+	29.8053i	−0.647011	+	1.21985i
$598$	0.0884227			0.00361587
$599$	28.9630			1.18340			0.591699	−	0.806159i	$-0.298457\pi$
$599$	28.9630			1.18340			0.591699	+	0.806159i	$0.298457\pi$
$600$	−2.60367	+	0.0935780i	−0.106294	+	0.00382031i
$601$	3.09150	+	5.35463i	0.126105	+	0.218420i	0.922164	−	0.386798i	$-0.126419\pi$
$601$	3.09150	+	5.35463i	0.126105	+	0.218420i	−0.796059	+	0.605218i	$0.793086\pi$
$602$	0.152169	−	6.81362i	0.00620193	−	0.277702i
$603$	−3.72835	+	7.68394i	−0.151830	+	0.312914i
$604$	8.35222	−	14.4665i	0.339847	−	0.588632i
$605$	0.647936	−	1.12226i	0.0263423	−	0.0456263i
$606$	9.91091	−	0.356206i	0.402603	−	0.0144699i
$607$	1.12891	+	1.95533i	0.0458211	+	0.0793646i	0.888026	−	0.459793i	$-0.152076\pi$
$607$	1.12891	+	1.95533i	0.0458211	+	0.0793646i	−0.842205	+	0.539157i	$0.818743\pi$
$608$	15.7579	−	27.2934i	0.639066	−	1.10689i
$609$	17.9125	−	10.6691i	0.725850	−	0.432333i
$610$	1.30593	+	2.26194i	0.0528756	+	0.0915833i
$611$	−7.83100	+	13.5637i	−0.316808	+	0.548728i
$612$	−0.289396	+	0.0208292i	−0.0116982	+	0.000841970i
$613$	−4.84795	−	8.39689i	−0.195807	−	0.339147i	0.751358	−	0.659895i	$-0.229399\pi$
$613$	−4.84795	−	8.39689i	−0.195807	−	0.339147i	−0.947165	+	0.320748i	$0.896066\pi$
$614$	−2.96497			−0.119656
$615$	−8.97796	−	14.3352i	−0.362026	−	0.578052i
$616$	−10.8722	+	5.95747i	−0.438055	+	0.240033i
$617$	3.01551	−	5.22302i	0.121400	−	0.210271i	−0.798920	−	0.601437i	$-0.794595\pi$
$617$	3.01551	−	5.22302i	0.121400	−	0.210271i	0.920320	+	0.391166i	$0.127928\pi$
$618$	−4.01059	+	7.56139i	−0.161329	+	0.304164i
$619$	13.4854	−	23.3575i	0.542026	−	0.938816i	−0.456762	−	0.889589i	$-0.650991\pi$
$619$	13.4854	−	23.3575i	0.542026	−	0.938816i	0.998788	−	0.0492272i	$-0.0156758\pi$
$620$	5.95431	+	10.3132i	0.239131	+	0.414187i
$621$	−0.322141	−	0.440552i	−0.0129271	−	0.0176787i
$622$	1.98475			0.0795812
$623$	19.5869	−	10.7327i	0.784732	−	0.429995i
$624$	−11.5762	+	0.416059i	−0.463420	+	0.0166557i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.8068			−0.471895
$627$	18.8684	−	35.5736i	0.753530	−	1.42067i
$628$	6.07464			0.242404
$629$	0.0312682			0.00124674
$630$	−2.76115	−	1.41676i	−0.110007	−	0.0564452i
$631$	29.4422			1.17208			0.586038	−	0.810283i	$-0.300687\pi$
$631$	29.4422			1.17208			0.586038	+	0.810283i	$0.300687\pi$
$632$	18.0756			0.719009
$633$	23.6122	−	0.848643i	0.938502	−	0.0337305i
$634$	7.63183			0.303099
$635$	4.07655	+	7.06079i	0.161773	+	0.280199i
$636$	−7.16606	+	13.5106i	−0.284153	+	0.535729i
$637$	−15.0569	−	0.672865i	−0.596574	−	0.0266599i
$638$	−5.54148			−0.219389
$639$	−8.14854	+	16.7937i	−0.322351	+	0.664350i
$640$	−5.11455	−	8.85867i	−0.202171	−	0.350170i
$641$	19.4925	−	33.7620i	0.769908	−	1.33352i	−0.167705	−	0.985837i	$-0.553636\pi$
$641$	19.4925	−	33.7620i	0.769908	−	1.33352i	0.937613	−	0.347682i	$-0.113031\pi$
$642$	8.91194	−	0.320302i	0.351726	−	0.0126413i
$643$	−4.12119	+	7.13810i	−0.162524	+	0.281499i	−0.935773	−	0.352603i	$-0.885297\pi$
$643$	−4.12119	+	7.13810i	−0.162524	+	0.281499i	0.773249	+	0.634102i	$0.218630\pi$
$644$	0.0114606	−	0.513171i	0.000451612	−	0.0202218i
$645$	11.4038	−	0.409860i	0.449022	−	0.0161382i
$646$	−0.152787			−0.00601133
$647$	−19.8309	−	34.3481i	−0.779633	−	1.35036i	−0.932153	−	0.362064i	$-0.882072\pi$
$647$	−19.8309	−	34.3481i	−0.779633	−	1.35036i	0.152520	−	0.988300i	$-0.451261\pi$
$648$	−8.37811	−	10.6339i	−0.329123	−	0.417738i
$649$	−1.94862	+	3.37512i	−0.0764902	+	0.132485i
$650$	0.420929	+	0.729070i	0.0165102	+	0.0285965i
$651$	0.401675	+	29.5416i	0.0157429	+	1.15783i
$652$	−6.87202	+	11.9027i	−0.269129	+	0.466145i
$653$	4.92214	+	8.52540i	0.192618	+	0.333625i	0.946117	−	0.323824i	$-0.104969\pi$
$653$	4.92214	+	8.52540i	0.192618	+	0.333625i	−0.753499	+	0.657449i	$0.771635\pi$
$654$	−4.61979	+	8.70996i	−0.180648	+	0.340586i
$655$	3.31890	−	5.74850i	0.129680	−	0.224612i
$656$	15.1666	−	26.2693i	0.592156	−	1.02564i
$657$	14.2779	−	1.02765i	0.557034	−	0.0400923i
$658$	−6.43106	−	3.90697i	−0.250709	−	0.152310i
$659$	−6.44285	−	11.1593i	−0.250978	−	0.434706i	0.712817	−	0.701350i	$-0.247419\pi$
$659$	−6.44285	−	11.1593i	−0.250978	−	0.434706i	−0.963795	+	0.266643i	$0.914085\pi$
$660$	−5.28995	−	8.44654i	−0.205911	−	0.328781i
$661$	−17.0159			−0.661840			−0.330920	−	0.943659i	$-0.607359\pi$
$661$	−17.0159			−0.661840			−0.330920	+	0.943659i	$0.607359\pi$
$662$	0.0478608			0.00186016
$663$	0.103644	+	0.165490i	0.00402520	+	0.00642709i
$664$	−11.1024	−	19.2299i	−0.430857	−	0.746266i
$665$	16.8754	+	10.2521i	0.654401	+	0.397559i
$666$	0.392886	+	0.579925i	0.0152240	+	0.0224716i
$667$	0.238931	−	0.413841i	0.00925145	−	0.0160240i
$668$	−15.7266	+	27.2393i	−0.608482	+	1.05392i
$669$	−6.10960	+	11.5188i	−0.236211	+	0.445342i
$670$	0.556559	+	0.963989i	0.0215018	+	0.0372421i
$671$	−10.4047	+	18.0215i	−0.401669	+	0.695711i
$672$	−0.263098	−	19.3498i	−0.0101492	−	0.746436i
$673$	−18.2152	−	31.5496i	−0.702144	−	1.21615i	−0.967713	−	0.252057i	$-0.918893\pi$
$673$	−18.2152	−	31.5496i	−0.702144	−	1.21615i	0.265569	−	0.964092i	$-0.414440\pi$
$674$	1.23145	−	2.13293i	0.0474336	−	0.0821574i
$675$	2.09895	−	4.75336i	0.0807885	−	0.182957i
$676$	−7.72472	−	13.3796i	−0.297105	−	0.514600i
$677$	−39.6052			−1.52215			−0.761075	−	0.648664i	$-0.775328\pi$
$677$	−39.6052			−1.52215			−0.761075	+	0.648664i	$0.775328\pi$
$678$	−2.77491	+	0.0997327i	−0.106570	+	0.00383021i
$679$	−0.0679844	+	3.04412i	−0.00260900	+	0.116823i
$680$	−0.0393798	+	0.0682078i	−0.00151015	+	0.00261565i
$681$	47.6167	−	1.71138i	1.82468	−	0.0655803i
$682$	3.92629	−	6.80054i	0.150346	−	0.260406i
$683$	0.225341	+	0.390303i	0.00862245	+	0.0149345i	0.870304	−	0.492514i	$-0.163922\pi$
$683$	0.225341	+	0.390303i	0.00862245	+	0.0149345i	−0.861682	+	0.507449i	$0.830589\pi$
$684$	23.1957	+	34.2383i	0.886910	+	1.30914i
$685$	20.1078			0.768281
$686$	0.484716	−	7.22506i	0.0185066	−	0.275854i
$687$	1.08382	−	2.04339i	0.0413504	−	0.0779603i
$688$	10.2319	+	17.7221i	0.390087	+	0.675650i
$689$	10.2924			0.392109
$690$	−0.0710845	+	0.00255483i	−0.00270614	+	9.72608e-5i
$691$	−24.7707			−0.942320			−0.471160	−	0.882048i	$-0.656165\pi$
$691$	−24.7707			−0.942320			−0.471160	+	0.882048i	$0.656165\pi$
$692$	−35.8546			−1.36299
$693$	−1.22395	−	24.6954i	−0.0464941	−	0.938100i
$694$	2.19024			0.0831406
$695$	−17.7262			−0.672394
$696$	5.55419	−	10.4716i	0.210531	−	0.396926i
$697$	−0.511326			−0.0193679
$698$	0.517910	+	0.897047i	0.0196032	+	0.0339537i
$699$	−28.6734	+	1.03055i	−1.08453	+	0.0389788i
$700$	4.28580	−	2.34841i	0.161988	−	0.0887616i
$701$	3.03950			0.114800			0.0574001	−	0.998351i	$-0.481719\pi$
$701$	3.03950			0.114800			0.0574001	+	0.998351i	$0.481719\pi$
$702$	−1.76702	+	4.00165i	−0.0666917	+	0.151033i
$703$	−2.22841	−	3.85971i	−0.0840459	−	0.145572i
$704$	7.10427	−	12.3050i	0.267752	−	0.463761i
$705$	5.90357	−	11.1303i	0.222341	−	0.419193i
$706$	0.707377	−	1.22521i	0.0266225	−	0.0461115i
$707$	−33.9781	+	18.6184i	−1.27788	+	0.700216i
$708$	−2.12448	−	3.39219i	−0.0798430	−	0.127486i
$709$	−2.39313			−0.0898758			−0.0449379	−	0.998990i	$-0.514309\pi$
$709$	−2.39313			−0.0898758			−0.0449379	+	0.998990i	$0.514309\pi$
$710$	1.21640	+	2.10686i	0.0456505	+	0.0790690i
$711$	−15.7373	+	32.4339i	−0.590197	+	1.21637i
$712$	6.34900	−	10.9968i	0.237939	−	0.412122i
$713$	0.338579	+	0.586436i	0.0126799	+	0.0219622i
$714$	−0.0806018	+	0.0480083i	−0.00301645	+	0.00179666i
$715$	−3.35365	+	5.80869i	−0.125419	+	0.217233i
$716$	−20.0303	−	34.6935i	−0.748567	−	1.29656i
$717$	−27.6883	+	0.995141i	−1.03404	+	0.0371642i
$718$	−5.76579	+	9.98664i	−0.215177	+	0.372698i
$719$	−4.59698	+	7.96220i	−0.171438	+	0.296940i	−0.938923	−	0.344127i	$-0.888175\pi$
$719$	−4.59698	+	7.96220i	−0.171438	+	0.296940i	0.767485	+	0.641067i	$0.221508\pi$
$720$	9.29431	−	0.668954i	0.346378	−	0.0249304i
$721$	0.746602	−	33.4305i	0.0278049	−	1.24502i
$722$	7.17432	+	12.4263i	0.267001	+	0.462459i
$723$	37.2461	−	1.33866i	1.38520	−	0.0497852i
$724$	−28.4751			−1.05827
$725$	4.54965			0.168970
$726$	0.411214	−	0.775286i	0.0152616	−	0.0287736i
$727$	3.53523	+	6.12320i	0.131114	+	0.227097i	0.924106	−	0.382135i	$-0.124811\pi$
$727$	3.53523	+	6.12320i	0.131114	+	0.227097i	−0.792992	+	0.609232i	$0.791478\pi$
$728$	−7.51468	+	4.11768i	−0.278512	+	0.152611i
$729$	26.3752	−	5.77494i	0.976858	−	0.213887i
$730$	0.932834	−	1.61572i	0.0345257	−	0.0598003i
$731$	0.172479	−	0.298742i	0.00637935	−	0.0110494i
$732$	−11.3437	−	18.1126i	−0.419275	−	0.669462i
$733$	−3.12567	−	5.41383i	−0.115449	−	0.199964i	0.802510	−	0.596639i	$-0.203497\pi$
$733$	−3.12567	−	5.41383i	−0.115449	−	0.199964i	−0.917959	+	0.396675i	$0.870164\pi$
$734$	−6.08474	+	10.5391i	−0.224592	+	0.389004i
$735$	12.1239	+	0.105883i	0.447197	+	0.00390557i
$736$	−0.221770	−	0.384117i	−0.00817455	−	0.0141587i
$737$	−4.43425	+	7.68035i	−0.163338	+	0.282909i
$738$	−6.42483	−	9.48346i	−0.236501	−	0.349091i
$739$	−6.69473	−	11.5956i	−0.246269	−	0.426551i	0.716218	−	0.697876i	$-0.245871\pi$
$739$	−6.69473	−	11.5956i	−0.246269	−	0.426551i	−0.962488	+	0.271325i	$0.912538\pi$
$740$	−1.10306			−0.0405495
$741$	13.0414	−	24.5878i	0.479089	−	0.903255i
$742$	−0.110409	+	4.94376i	−0.00405324	+	0.181491i
$743$	4.39039	−	7.60438i	0.161068	−	0.278978i	−0.774184	−	0.632961i	$-0.781840\pi$
$743$	4.39039	−	7.60438i	0.161068	−	0.278978i	0.935252	+	0.353983i	$0.115173\pi$
$744$	8.91556	+	14.2356i	0.326860	+	0.521902i
$745$	9.05624	−	15.6859i	0.331795	−	0.574686i
$746$	4.71871	+	8.17305i	0.172764	+	0.299237i
$747$	44.1713	−	3.17921i	1.61614	−	0.116321i
$748$	−0.301281			−0.0110159
$749$	−30.5533	+	16.7417i	−1.11639	+	0.611729i
$750$	−0.359457	−	0.573950i	−0.0131255	−	0.0209577i
$751$	−2.28972	−	3.96591i	−0.0835531	−	0.144718i	0.821221	−	0.570611i	$-0.193293\pi$
$751$	−2.28972	−	3.96591i	−0.0835531	−	0.144718i	−0.904774	+	0.425893i	$0.859960\pi$
$752$	22.5941			0.823923
$753$	−25.4055	−	40.5652i	−0.925826	−	1.47828i
$754$	−3.83016			−0.139486
$755$	9.04349			0.329126
$756$	22.9950	+	10.7737i	0.836320	+	0.391837i
$757$	−8.40020			−0.305310			−0.152655	−	0.988280i	$-0.548782\pi$
$757$	−8.40020			−0.305310			−0.152655	+	0.988280i	$0.548782\pi$
$758$	−6.08537			−0.221030
$759$	−0.300802	−	0.480294i	−0.0109184	−	0.0174336i
$760$	11.2260			0.407210
$761$	20.9233	+	36.2403i	0.758471	+	1.31371i	0.943630	+	0.331001i	$0.107386\pi$
$761$	20.9233	+	36.2403i	0.758471	+	1.31371i	−0.185160	+	0.982708i	$0.559280\pi$
$762$	2.93069	+	4.67947i	0.106168	+	0.169519i
$763$	0.860011	−	38.5085i	0.0311345	−	1.39410i
$764$	38.5071			1.39314
$765$	−0.0881028	−	0.130045i	−0.00318536	−	0.00470180i
$766$	3.91854	+	6.78712i	0.141583	+	0.245228i
$767$	−1.34685	+	2.33281i	−0.0486319	+	0.0842330i
$768$	4.70954	+	7.51978i	0.169941	+	0.271347i
$769$	−1.25915	+	2.18091i	−0.0454061	+	0.0786457i	−0.887835	−	0.460161i	$-0.847792\pi$
$769$	−1.25915	+	2.18091i	−0.0454061	+	0.0786457i	0.842429	+	0.538807i	$0.181125\pi$
$770$	−2.75412	−	1.67317i	−0.0992516	−	0.0602970i
$771$	10.1822	−	19.1971i	0.366702	−	0.691365i
$772$	38.6158			1.38981
$773$	17.6807	+	30.6238i	0.635929	+	1.10146i	0.986317	+	0.164857i	$0.0527163\pi$
$773$	17.6807	+	30.6238i	0.635929	+	1.10146i	−0.350388	+	0.936604i	$0.613950\pi$
$774$	7.70790	−	0.554773i	0.277055	−	0.0199409i
$775$	−3.22356	+	5.58336i	−0.115794	+	0.200560i
$776$	0.865559	+	1.49919i	0.0310718	+	0.0538179i
$777$	−2.38837	−	1.33596i	−0.0856822	−	0.0479274i
$778$	2.34481	−	4.06133i	0.0840656	−	0.145606i
$779$	36.4409	+	63.1176i	1.30563	+	2.26142i
$780$	−3.65631	−	5.83808i	−0.130917	−	0.209037i
$781$	−9.69133	+	16.7859i	−0.346783	+	0.600646i
$782$	−0.00107513	+	0.00186218i	−3.84467e−5	+	6.65916e-5i
$783$	13.9540	+	19.0831i	0.498676	+	0.681976i
$784$	10.0199	+	19.2964i	0.357855	+	0.689157i
$785$	1.64435	+	2.84810i	0.0586894	+	0.101653i
$786$	2.10635	−	3.97122i	0.0751309	−	0.141649i
$787$	−29.4578			−1.05006			−0.525029	−	0.851084i	$-0.675946\pi$
$787$	−29.4578			−1.05006			−0.525029	+	0.851084i	$0.675946\pi$
$788$	−12.1519			−0.432893
$789$	35.7743	−	1.28576i	1.27360	−	0.0457742i
$790$	2.34924	+	4.06900i	0.0835821	+	0.144768i
$791$	9.51339	−	5.21288i	0.338257	−	0.185349i
$792$	−7.88453	−	11.6381i	−0.280165	−	0.413541i
$793$	−7.19152	+	12.4561i	−0.255378	+	0.442328i
$794$	3.65676	−	6.33369i	0.129773	−	0.224774i
$795$	−8.27423	+	0.297383i	−0.293457	+	0.0105471i
$796$	−17.9899	−	31.1594i	−0.637635	−	1.10442i
$797$	17.5902	−	30.4671i	0.623076	−	1.07920i	−0.365833	−	0.930680i	$-0.619216\pi$
$797$	17.5902	−	30.4671i	0.623076	−	1.07920i	0.988909	−	0.148519i	$-0.0474508\pi$
$798$	11.6704	+	6.52797i	0.413127	+	0.231088i
$799$	−0.190434	−	0.329842i	−0.00673709	−	0.0116690i
$800$	2.11144	−	3.65711i	0.0746505	−	0.129298i
$801$	14.2044	+	20.9666i	0.501886	+	0.740817i
$802$	4.49512	+	7.78577i	0.158728	+	0.274925i
$803$	14.8643			0.524548
$804$	−4.83443	−	7.71920i	−0.170497	−	0.272235i
$805$	0.243703	−	0.133537i	0.00858939	−	0.00470657i
$806$	2.71378	−	4.70040i	0.0955887	−	0.165564i
$807$	−2.89034	+	5.44932i	−0.101745	+	0.191825i
$808$	−11.0139	+	19.0766i	−0.387466	+	0.671111i
$809$	−11.4989	−	19.9166i	−0.404278	−	0.700231i	0.589959	−	0.807433i	$-0.299144\pi$
$809$	−11.4989	−	19.9166i	−0.404278	−	0.700231i	−0.994237	+	0.107203i	$0.965811\pi$
$810$	1.30491	−	3.26805i	0.0458499	−	0.114828i
$811$	20.3449			0.714405			0.357203	−	0.934027i	$-0.383731\pi$
$811$	20.3449			0.714405			0.357203	+	0.934027i	$0.383731\pi$
$812$	−0.496434	+	22.2287i	−0.0174214	+	0.780076i
$813$	−16.6104	+	0.596992i	−0.582553	+	0.0209374i
$814$	0.363683	+	0.629917i	0.0127471	+	0.0220786i
$815$	−7.44077			−0.260639
$816$	0.131993	−	0.248855i	0.00462069	−	0.00871166i
$817$	−49.1685			−1.72019
$818$	4.43896			0.155205
$819$	−0.845970	−	17.0690i	−0.0295606	−	0.596437i
$820$	18.0383			0.629926
$821$	10.7873			0.376479			0.188240	−	0.982123i	$-0.439722\pi$
$821$	10.7873			0.376479			0.188240	+	0.982123i	$0.439722\pi$
$822$	13.6087	−	0.489106i	0.474656	−	0.0170595i
$823$	38.1356			1.32932			0.664661	−	0.747145i	$-0.268576\pi$
$823$	38.1356			1.32932			0.664661	+	0.747145i	$0.268576\pi$
$824$	−9.50555	−	16.4641i	−0.331141	−	0.573554i
$825$	2.52822	−	4.76660i	0.0880214	−	0.165952i
$826$	−1.10608	−	0.671959i	−0.0384853	−	0.0233804i
$827$	−40.2684			−1.40027			−0.700135	−	0.714011i	$-0.746877\pi$
$827$	−40.2684			−1.40027			−0.700135	+	0.714011i	$0.746877\pi$
$828$	0.580524	−	0.0417830i	0.0201746	−	0.00145206i
$829$	−6.36099	−	11.0175i	−0.220926	−	0.382655i	0.734163	−	0.678973i	$-0.237575\pi$
$829$	−6.36099	−	11.0175i	−0.220926	−	0.382655i	−0.955089	+	0.296318i	$0.904241\pi$
$830$	2.88590	−	4.99852i	0.100171	−	0.173501i
$831$	−8.80952	+	0.316621i	−0.305599	+	0.0109835i
$832$	4.91033	−	8.50494i	0.170235	−	0.294856i
$833$	0.197247	−	0.308916i	0.00683420	−	0.0107033i
$834$	−11.9968	+	0.431175i	−0.415416	+	0.0149304i
$835$	−17.0282			−0.589286
$836$	21.4716	+	37.1898i	0.742610	+	1.28624i
$837$	−33.3058	+	3.60353i	−1.15122	+	0.124556i
$838$	−4.20211	+	7.27827i	−0.145159	+	0.251424i
$839$	−6.43901	−	11.1527i	−0.222299	−	0.385034i	0.733206	−	0.680006i	$-0.238023\pi$
$839$	−6.43901	−	11.1527i	−0.222299	−	0.385034i	−0.955506	+	0.294972i	$0.904690\pi$
$840$	5.92220	−	3.52740i	0.204335	−	0.121707i
$841$	4.15034	−	7.18860i	0.143115	−	0.247883i
$842$	2.27564	+	3.94152i	0.0784237	+	0.135834i
$843$	−21.8755	+	41.2432i	−0.753432	+	1.42049i
$844$	−12.5986	+	21.8214i	−0.433662	+	0.751125i
$845$	4.18203	−	7.24348i	0.143866	−	0.249183i
$846$	3.72470	−	7.67643i	0.128058	−	0.263921i
$847$	−0.0765508	+	3.42770i	−0.00263032	+	0.117777i
$848$	−7.42395	−	12.8587i	−0.254940	−	0.441568i
$849$	−11.6811	−	18.6514i	−0.400895	−	0.640115i
$850$	−0.0204723			−0.000702195
$851$	−0.0627234			−0.00215013
$852$	−10.5660	−	16.8708i	−0.361984	−	0.577984i
$853$	−10.1609	−	17.5992i	−0.347903	−	0.602585i	0.637974	−	0.770058i	$-0.279773\pi$
$853$	−10.1609	−	17.5992i	−0.347903	−	0.602585i	−0.985877	+	0.167473i	$0.946439\pi$
$854$	−5.90590	−	3.58793i	−0.202096	−	0.122776i
$855$	−9.77381	+	20.1433i	−0.334257	+	0.688887i
$856$	−9.90371	+	17.1537i	−0.338502	+	0.586302i
$857$	17.9192	−	31.0370i	0.612109	−	1.06020i	−0.378775	−	0.925489i	$-0.623655\pi$
$857$	17.9192	−	31.0370i	0.612109	−	1.06020i	0.990884	−	0.134716i	$-0.0430121\pi$
$858$	−2.12840	+	4.01280i	−0.0726625	+	0.136995i
$859$	−3.38655	−	5.86568i	−0.115548	−	0.200135i	0.802451	−	0.596718i	$-0.203529\pi$
$859$	−3.38655	−	5.86568i	−0.115548	−	0.200135i	−0.917999	+	0.396584i	$0.870196\pi$
$860$	−6.08462	+	10.5389i	−0.207484	+	0.359373i
$861$	39.0568	+	21.8469i	1.33105	+	0.744540i
$862$	−1.28964	−	2.23372i	−0.0439252	−	0.0760807i
$863$	−22.8677	+	39.6081i	−0.778427	+	1.34828i	0.154421	+	0.988005i	$0.450649\pi$
$863$	−22.8677	+	39.6081i	−0.778427	+	1.34828i	−0.932848	+	0.360270i	$0.882685\pi$
$864$	21.8154	−	2.36032i	0.742174	−	0.0802997i
$865$	−9.70551	−	16.8104i	−0.329997	−	0.571572i
$866$	−3.95793			−0.134496
$867$	29.4211	−	1.05742i	0.999194	−	0.0359118i
$868$	−26.9275	−	16.3589i	−0.913980	−	0.555258i
$869$	−18.7170	+	32.4187i	−0.634930	+	1.09973i
$870$	3.07913	−	0.110666i	0.104392	−	0.00375194i
$871$	−3.06486	+	5.30850i	−0.103849	+	0.179872i
$872$	−10.9494	−	18.9650i	−0.370795	−	0.642235i
$873$	−3.44366	+	0.247856i	−0.116550	+	0.00838866i
$874$	0.306488			0.0103671
$875$	2.26118	+	1.37370i	0.0764418	+	0.0464397i
$876$	−7.15316	+	13.4863i	−0.241683	+	0.455658i
$877$	−15.8336	−	27.4246i	−0.534662	−	0.926062i	−0.999180	−	0.0404979i	$-0.987106\pi$
$877$	−15.8336	−	27.4246i	−0.534662	−	0.926062i	0.464518	−	0.885564i	$-0.346228\pi$
$878$	−8.01298			−0.270425
$879$	−30.4592	+	1.09473i	−1.02736	+	0.0369243i
$880$	9.67600			0.326178
$881$	−17.1461			−0.577667			−0.288833	−	0.957379i	$-0.593267\pi$
$881$	−17.1461			−0.577667			−0.288833	+	0.957379i	$0.593267\pi$
$882$	8.20783	−	0.223243i	0.276372	−	0.00751699i
$883$	29.3139			0.986490			0.493245	−	0.869890i	$-0.335811\pi$
$883$	29.3139			0.986490			0.493245	+	0.869890i	$0.335811\pi$
$884$	−0.208240			−0.00700385
$885$	1.01535	−	1.91430i	0.0341307	−	0.0643486i
$886$	−3.37167			−0.113273
$887$	17.7727	+	30.7832i	0.596748	+	1.03360i	0.993298	+	0.115584i	$0.0368741\pi$
$887$	17.7727	+	30.7832i	0.596748	+	1.03360i	−0.396550	+	0.918013i	$0.629793\pi$
$888$	−1.55486	+	0.0558829i	−0.0521776	+	0.00187531i
$889$	−18.4356	−	11.1999i	−0.618311	−	0.375634i
$890$	3.30065			0.110638
$891$	27.7473	−	4.01500i	0.929570	−	0.134508i
$892$	−6.95252	−	12.0421i	−0.232788	−	0.403200i
$893$	−27.1436	+	47.0141i	−0.908325	+	1.57327i
$894$	5.74757	−	10.8362i	0.192228	−	0.362418i
$895$	10.8440	−	18.7824i	0.362476	−	0.627828i
$896$	23.1299	+	14.0518i	0.772714	+	0.469437i
$897$	−0.207908	−	0.331970i	−0.00694186	−	0.0110841i
$898$	0.0308757			0.00103034
$899$	−14.6661	−	25.4023i	−0.489140	−	0.847216i
$900$	3.10805	+	4.58768i	0.103602	+	0.152923i
$901$	−0.125145	+	0.216758i	−0.00416920	+	0.00722127i
$902$	−5.94727	−	10.3010i	−0.198023	−	0.342985i
$903$	−25.9385	+	15.4496i	−0.863180	+	0.514130i
$904$	3.08372	−	5.34117i	0.102563	−	0.177645i
$905$	−7.70795	−	13.3506i	−0.256221	−	0.443788i
$906$	6.12048	−	0.219975i	0.203339	−	0.00730818i
$907$	−28.6781	+	49.6719i	−0.952240	+	1.64933i	−0.211677	+	0.977340i	$0.567893\pi$
$907$	−28.6781	+	49.6719i	−0.952240	+	1.64933i	−0.740562	+	0.671988i	$0.765441\pi$
$908$	−25.4065	+	44.0054i	−0.843144	+	1.46037i
$909$	−24.6408	−	36.3715i	−0.817285	−	1.20637i
$910$	−1.90359	−	1.15646i	−0.0631035	−	0.0383364i
$911$	0.121453	+	0.210362i	0.00402390	+	0.00696961i	0.868030	−	0.496511i	$-0.165386\pi$
$911$	0.121453	+	0.210362i	0.00402390	+	0.00696961i	−0.864006	+	0.503481i	$0.832052\pi$
$912$	−40.1252	+	1.44213i	−1.32868	+	0.0477538i
$913$	45.9854			1.52189
$914$	8.96020			0.296377
$915$	5.42148	−	10.2214i	0.179229	−	0.337910i
$916$	1.23335	+	2.13623i	0.0407512	+	0.0705831i
$917$	−0.392113	+	17.5576i	−0.0129487	+	0.579802i
$918$	−0.0627898	−	0.0858696i	−0.00207237	−	0.00283412i
$919$	−2.48697	+	4.30756i	−0.0820376	+	0.142093i	−0.904125	−	0.427268i	$-0.859476\pi$
$919$	−2.48697	+	4.30756i	−0.0820376	+	0.142093i	0.822087	+	0.569361i	$0.192809\pi$
$920$	0.0789952	−	0.136824i	0.00260439	−	0.00451094i
$921$	6.97154	+	11.1315i	0.229720	+	0.366797i
$922$	−4.79000	−	8.29653i	−0.157750	−	0.273232i
$923$	−6.69846	+	11.6021i	−0.220482	+	0.381887i
$924$	23.0129	+	12.8725i	0.757067	+	0.423475i
$925$	−0.298590	−	0.517173i	−0.00981757	−	0.0170045i
$926$	7.93851	−	13.7499i	0.260876	−	0.451850i
$927$	37.8182	−	2.72195i	1.24211	−	0.0894005i
$928$	9.60629	+	16.6386i	0.315342	+	0.546188i
$929$	−3.32823			−0.109196			−0.0545979	−	0.998508i	$-0.517388\pi$
$929$	−3.32823			−0.109196			−0.0545979	+	0.998508i	$0.517388\pi$
$930$	−2.04584	+	3.85714i	−0.0670857	+	0.126481i
$931$	−52.1896	−	2.33227i	−1.71045	−	0.0764369i
$932$	15.2991	−	26.4988i	0.501138	−	0.867996i
$933$	−4.66674	−	7.45144i	−0.152782	−	0.243949i
$934$	−7.09863	+	12.2952i	−0.232274	+	0.402311i
$935$	−0.0815541	−	0.141256i	−0.00266711	−	0.00461956i
$936$	−5.44963	−	8.04400i	−0.178127	−	0.262926i
$937$	−57.6442			−1.88315			−0.941577	−	0.336797i	$-0.890656\pi$
$937$	−57.6442			−1.88315			−0.941577	+	0.336797i	$0.890656\pi$
$938$	−2.51696	−	1.52910i	−0.0821817	−	0.0499267i
$939$	27.7613	+	44.3269i	0.905957	+	1.44655i
$940$	6.71806	+	11.6360i	0.219119	+	0.379525i
$941$	−0.00945927			−0.000308363			−0.000154182	−	1.00000i	$-0.500049\pi$
$941$	−0.00945927			−0.000308363			−0.000154182		1.00000i	$0.500049\pi$
$942$	1.18215	+	1.88755i	0.0385164	+	0.0614996i
$943$	1.02571			0.0334018
$944$	3.88595			0.126477
$945$	1.17327	+	13.6976i	0.0381665	+	0.445582i
$946$	8.02445			0.260897
$947$	44.5604			1.44802			0.724010	−	0.689790i	$-0.242297\pi$
$947$	44.5604			1.44802			0.724010	+	0.689790i	$0.242297\pi$
$948$	−20.4061	−	32.5828i	−0.662761	−	1.05824i
$949$	10.2739			0.333504
$950$	1.45901	+	2.52708i	0.0473366	+	0.0819894i
$951$	−17.9447	−	28.6526i	−0.581898	−	0.929124i
$952$	0.00465255	−	0.208326i	0.000150790	−	0.00675189i
$953$	−5.51961			−0.178798			−0.0893988	−	0.995996i	$-0.528495\pi$
$953$	−5.51961			−0.178798			−0.0893988	+	0.995996i	$0.528495\pi$
$954$	−5.59263	+	0.402527i	−0.181068	+	0.0130323i
$955$	10.4235	+	18.0541i	0.337298	+	0.584217i
$956$	14.7735	−	25.5884i	0.477808	−	0.827588i
$957$	13.0297	+	20.8047i	0.421190	+	0.672519i
$958$	3.36567	−	5.82951i	0.108740	−	0.188343i
$959$	−46.6553	+	25.5649i	−1.50658	+	0.825532i
$960$	−3.70176	+	6.97914i	−0.119474	+	0.225251i
$961$	10.5653			0.340815
$962$	0.251370	+	0.435386i	0.00810450	+	0.0140374i
$963$	−22.1572	−	32.7054i	−0.714005	−	1.05392i
$964$	−19.8732	+	34.4213i	−0.640071	+	1.10864i
$965$	10.4529	+	18.1050i	0.336492	+	0.582822i
$966$	0.161686	−	0.0963037i	0.00520215	−	0.00309852i
$967$	−3.99665	+	6.92240i	−0.128524	+	0.222609i	−0.923105	−	0.384549i	$-0.874357\pi$
$967$	−3.99665	+	6.92240i	−0.128524	+	0.222609i	0.794581	+	0.607158i	$0.207690\pi$
$968$	0.974626	+	1.68810i	0.0313257	+	0.0542576i
$969$	0.359248	+	0.573616i	0.0115407	+	0.0184272i
$970$	−0.224989	+	0.389692i	−0.00722395	+	0.0125123i
$971$	−10.4759	+	18.1447i	−0.336187	+	0.582292i	−0.983712	−	0.179752i	$-0.942471\pi$
$971$	−10.4759	+	18.1447i	−0.336187	+	0.582292i	0.647526	+	0.762044i	$0.275804\pi$
$972$	−9.71011	+	27.1071i	−0.311452	+	0.869462i
$973$	41.1293	−	22.5369i	1.31855	−	0.722500i
$974$	−7.01256	−	12.1461i	−0.224697	−	0.389186i
$975$	1.74746	−	3.29458i	0.0559634	−	0.105511i
$976$	20.7491			0.664162
$977$	−18.7221			−0.598973			−0.299487	−	0.954100i	$-0.596815\pi$
$977$	−18.7221			−0.598973			−0.299487	+	0.954100i	$0.596815\pi$
$978$	−5.03579	+	0.180990i	−0.161027	+	0.00578744i
$979$	13.1486	+	22.7740i	0.420230	+	0.727859i
$980$	−6.95839	+	10.8978i	−0.222278	+	0.348118i
$981$	43.5628	−	3.13541i	1.39085	−	0.100106i
$982$	0.467672	−	0.810032i	0.0149240	−	0.0258492i
$983$	−9.63843	+	16.6943i	−0.307418	+	0.532464i	−0.977797	−	0.209555i	$-0.932798\pi$
$983$	−9.63843	+	16.6943i	−0.307418	+	0.532464i	0.670379	+	0.742019i	$0.266132\pi$
$984$	25.4265	−	0.913848i	0.810566	−	0.0291324i
$985$	−3.28941	−	5.69742i	−0.104809	−	0.181535i
$986$	0.0465710	−	0.0806633i	0.00148312	−	0.00256884i
$987$	0.453197	+	33.3309i	0.0144254	+	1.06093i
$988$	14.8407	+	25.7049i	0.472146	+	0.817781i
$989$	−0.345989	+	0.599271i	−0.0110018	+	0.0190557i
$990$	1.59511	−	3.28745i	0.0506961	−	0.104482i
$991$	−6.22762	−	10.7866i	−0.197827	−	0.342646i	0.749997	−	0.661442i	$-0.230055\pi$
$991$	−6.22762	−	10.7866i	−0.197827	−	0.342646i	−0.947824	+	0.318795i	$0.896722\pi$
$992$	−27.2253			−0.864405
$993$	−0.112535	−	0.179686i	−0.00357119	−	0.00570217i
$994$	−5.50098	−	3.34194i	−0.174480	−	0.106000i
$995$	9.73940	−	16.8691i	0.308760	−	0.534788i
$996$	−22.1296	+	41.7223i	−0.701204	+	1.32202i
$997$	6.19315	−	10.7269i	0.196139	−	0.339723i	−0.751134	−	0.660150i	$-0.770493\pi$
$997$	6.19315	−	10.7269i	0.196139	−	0.339723i	0.947273	+	0.320427i	$0.103826\pi$
$998$	1.79851	+	3.11511i	0.0569308	+	0.0986071i
$999$	1.25345	−	2.83861i	0.0396574	−	0.0898096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.8	yes	36
3.2	odd	2		945.2.l.c.226.11		36
7.4	even	3		315.2.k.c.256.11	yes	36
9.2	odd	6		945.2.k.c.856.8		36
9.7	even	3		315.2.k.c.16.11	✓	36
21.11	odd	6		945.2.k.c.361.8		36
63.11	odd	6		945.2.l.c.46.11		36
63.25	even	3	inner	315.2.l.c.151.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.11	✓	36	9.7	even	3
315.2.k.c.256.11	yes	36	7.4	even	3
315.2.l.c.121.8	yes	36	1.1	even	1	trivial
315.2.l.c.151.8	yes	36	63.25	even	3	inner
945.2.k.c.361.8		36	21.11	odd	6
945.2.k.c.856.8		36	9.2	odd	6
945.2.l.c.46.11		36	63.11	odd	6
945.2.l.c.226.11		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.390993 q^{2} +(0.919343 + 1.46793i) q^{3} -1.84712 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.359457 - 0.573950i) q^{6} +(2.26118 + 1.37370i) q^{7} +1.50420 q^{8} +(-1.30962 + 2.69906i) q^{9} +O(q^{10})\)	\(q-0.390993 q^{2} +(0.919343 + 1.46793i) q^{3} -1.84712 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.359457 - 0.573950i) q^{6} +(2.26118 + 1.37370i) q^{7} +1.50420 q^{8} +(-1.30962 + 2.69906i) q^{9} +(0.195497 + 0.338610i) q^{10} +(-1.55757 + 2.69779i) q^{11} +(-1.69814 - 2.71144i) q^{12} +(-1.07656 + 1.86466i) q^{13} +(-0.884107 - 0.537109i) q^{14} +(0.811590 - 1.53014i) q^{15} +3.10612 q^{16} +(-0.0261799 - 0.0453449i) q^{17} +(0.512052 - 1.05531i) q^{18} +(-3.73155 + 6.46324i) q^{19} +(0.923562 + 1.59966i) q^{20} +(0.0623031 + 4.58215i) q^{21} +(0.609001 - 1.05482i) q^{22} +(0.0525164 + 0.0909611i) q^{23} +(1.38288 + 2.20806i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.420929 - 0.729070i) q^{26} +(-5.16600 + 0.558937i) q^{27} +(-4.17668 - 2.53740i) q^{28} +(-2.27483 - 3.94011i) q^{29} +(-0.317326 + 0.598274i) q^{30} +6.44711 q^{31} -4.22287 q^{32} +(-5.39211 + 0.193797i) q^{33} +(0.0102362 + 0.0177296i) q^{34} +(0.0590728 - 2.64509i) q^{35} +(2.41902 - 4.98549i) q^{36} +(-0.298590 + 0.517173i) q^{37} +(1.45901 - 2.52708i) q^{38} +(-3.72692 + 0.133948i) q^{39} +(-0.752100 - 1.30268i) q^{40} +(4.88281 - 8.45728i) q^{41} +(-0.0243601 - 1.79159i) q^{42} +(3.29411 + 5.70556i) q^{43} +(2.87703 - 4.98316i) q^{44} +(2.99226 - 0.215367i) q^{45} +(-0.0205336 - 0.0355652i) q^{46} +7.27408 q^{47} +(2.85559 + 4.55955i) q^{48} +(3.22587 + 6.21239i) q^{49} +(0.195497 - 0.338610i) q^{50} +(0.0424947 - 0.0801177i) q^{51} +(1.98855 - 3.44426i) q^{52} +(-2.39011 - 4.13979i) q^{53} +(2.01987 - 0.218541i) q^{54} +3.11514 q^{55} +(3.40127 + 2.06633i) q^{56} +(-12.9181 + 0.464288i) q^{57} +(0.889442 + 1.54056i) q^{58} +1.25107 q^{59} +(-1.49911 + 2.82635i) q^{60} +6.68007 q^{61} -2.52078 q^{62} +(-6.66898 + 4.30403i) q^{63} -4.56112 q^{64} +2.15313 q^{65} +(2.10828 - 0.0757732i) q^{66} +2.84690 q^{67} +(0.0483575 + 0.0837576i) q^{68} +(-0.0852436 + 0.160715i) q^{69} +(-0.0230971 + 1.03421i) q^{70} +6.22208 q^{71} +(-1.96993 + 4.05992i) q^{72} +(-2.38580 - 4.13233i) q^{73} +(0.116747 - 0.202211i) q^{74} +(-1.73093 + 0.0622111i) q^{75} +(6.89264 - 11.9384i) q^{76} +(-7.22792 + 3.96056i) q^{77} +(1.45720 - 0.0523729i) q^{78} +12.0168 q^{79} +(-1.55306 - 2.68998i) q^{80} +(-5.56981 - 7.06946i) q^{81} +(-1.90915 + 3.30674i) q^{82} +(-7.38093 - 12.7842i) q^{83} +(-0.115081 - 8.46380i) q^{84} +(-0.0261799 + 0.0453449i) q^{85} +(-1.28797 - 2.23084i) q^{86} +(3.69245 - 6.96159i) q^{87} +(-2.34290 + 4.05802i) q^{88} +(4.22085 - 7.31072i) q^{89} +(-1.16995 + 0.0842069i) q^{90} +(-4.99580 + 2.73746i) q^{91} +(-0.0970043 - 0.168016i) q^{92} +(5.92711 + 9.46389i) q^{93} -2.84412 q^{94} +7.46310 q^{95} +(-3.88227 - 6.19886i) q^{96} +(0.575428 + 0.996671i) q^{97} +(-1.26129 - 2.42900i) q^{98} +(-5.24168 - 7.73705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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