LMFDB - Embedded newform 315.2.be.c.236.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.1
Character	$\chi$	$=$	315.236
Dual form			315.2.be.c.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27381 + 1.31279i) q^{2} +(-0.933716 + 1.45883i) q^{3} +(2.44681 - 4.23800i) q^{4} -1.00000 q^{5} +(0.207969 - 4.54286i) q^{6} +(-2.64220 - 0.136993i) q^{7} +7.59741i q^{8} +(-1.25635 - 2.72426i) q^{9} +O(q^{10})$	\(q+(-2.27381 + 1.31279i) q^{2} +(-0.933716 + 1.45883i) q^{3} +(2.44681 - 4.23800i) q^{4} -1.00000 q^{5} +(0.207969 - 4.54286i) q^{6} +(-2.64220 - 0.136993i) q^{7} +7.59741i q^{8} +(-1.25635 - 2.72426i) q^{9} +(2.27381 - 1.31279i) q^{10} +0.107931i q^{11} +(3.89788 + 7.52656i) q^{12} +(5.35335 - 3.09076i) q^{13} +(6.18771 - 3.15715i) q^{14} +(0.933716 - 1.45883i) q^{15} +(-5.08015 - 8.79908i) q^{16} +(-0.643963 - 1.11538i) q^{17} +(6.43307 + 4.54514i) q^{18} +(-2.22804 - 1.28636i) q^{19} +(-2.44681 + 4.23800i) q^{20} +(2.66692 - 3.72660i) q^{21} +(-0.141691 - 0.245416i) q^{22} -0.764400i q^{23} +(-11.0833 - 7.09383i) q^{24} +1.00000 q^{25} +(-8.11501 + 14.0556i) q^{26} +(5.14729 + 0.710892i) q^{27} +(-7.04555 + 10.8625i) q^{28} +(8.71958 + 5.03425i) q^{29} +(-0.207969 + 4.54286i) q^{30} +(4.65132 + 2.68544i) q^{31} +(9.94350 + 5.74088i) q^{32} +(-0.157453 - 0.100777i) q^{33} +(2.92850 + 1.69077i) q^{34} +(2.64220 + 0.136993i) q^{35} +(-14.6195 - 1.34135i) q^{36} +(-0.952679 + 1.65009i) q^{37} +6.75486 q^{38} +(-0.489632 + 10.6955i) q^{39} -7.59741i q^{40} +(-3.87282 - 6.70793i) q^{41} +(-1.17184 + 11.9747i) q^{42} +(-3.74174 + 6.48088i) q^{43} +(0.457414 + 0.264088i) q^{44} +(1.25635 + 2.72426i) q^{45} +(1.00349 + 1.73810i) q^{46} +(-3.85718 - 6.68083i) q^{47} +(17.5797 + 0.804786i) q^{48} +(6.96247 + 0.723928i) q^{49} +(-2.27381 + 1.31279i) q^{50} +(2.22842 + 0.102015i) q^{51} -30.2500i q^{52} +(4.83694 - 2.79261i) q^{53} +(-12.6372 + 5.14086i) q^{54} -0.107931i q^{55} +(1.04080 - 20.0739i) q^{56} +(3.95694 - 2.04923i) q^{57} -26.4356 q^{58} +(1.18518 - 2.05280i) q^{59} +(-3.89788 - 7.52656i) q^{60} +(7.25479 - 4.18855i) q^{61} -14.1016 q^{62} +(2.94632 + 7.37016i) q^{63} -9.82559 q^{64} +(-5.35335 + 3.09076i) q^{65} +(0.490318 + 0.0224463i) q^{66} +(4.21881 - 7.30720i) q^{67} -6.30262 q^{68} +(1.11513 + 0.713733i) q^{69} +(-6.18771 + 3.15715i) q^{70} -10.2356i q^{71} +(20.6973 - 9.54499i) q^{72} +(9.71863 - 5.61106i) q^{73} -5.00265i q^{74} +(-0.933716 + 1.45883i) q^{75} +(-10.9032 + 6.29496i) q^{76} +(0.0147859 - 0.285177i) q^{77} +(-12.9276 - 24.9623i) q^{78} +(5.09156 + 8.81884i) q^{79} +(5.08015 + 8.79908i) q^{80} +(-5.84318 + 6.84524i) q^{81} +(17.6121 + 10.1684i) q^{82} +(7.13623 - 12.3603i) q^{83} +(-9.26790 - 20.4207i) q^{84} +(0.643963 + 1.11538i) q^{85} -19.6484i q^{86} +(-15.4857 + 8.01979i) q^{87} -0.819999 q^{88} +(0.334543 - 0.579445i) q^{89} +(-6.43307 - 4.54514i) q^{90} +(-14.5681 + 7.43304i) q^{91} +(-3.23953 - 1.87034i) q^{92} +(-8.26061 + 4.27803i) q^{93} +(17.5410 + 10.1273i) q^{94} +(2.22804 + 1.28636i) q^{95} +(-17.6594 + 9.14548i) q^{96} +(-7.16437 - 4.13635i) q^{97} +(-16.7817 + 7.49415i) q^{98} +(0.294033 - 0.135599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.27381	+	1.31279i	−1.60783	+	0.928280i	−0.617972	+	0.786200i	$0.712046\pi$
$2$	−2.27381	+	1.31279i	−1.60783	+	0.928280i	−0.989855	+	0.142079i	$0.954621\pi$
$3$	−0.933716	+	1.45883i	−0.539081	+	0.842254i
$3$	−0.933716	+	1.45883i	−0.539081	+	0.842254i
$4$	2.44681	−	4.23800i	1.22341	−	2.11900i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.207969	−	4.54286i	0.0849028	−	1.85462i
$7$	−2.64220	−	0.136993i	−0.998659	−	0.0517786i
$7$	−2.64220	−	0.136993i	−0.998659	−	0.0517786i
$8$			7.59741i			2.68609i
$9$	−1.25635	−	2.72426i	−0.418783	−	0.908087i
$10$	2.27381	−	1.31279i	0.719042	−	0.415139i
$11$			0.107931i			0.0325425i	0.999868	+	0.0162713i	$0.00517954\pi$
$11$			0.107931i			0.0325425i	−0.999868	+	0.0162713i	$0.994820\pi$
$12$	3.89788	+	7.52656i	1.12522	+	2.17273i
$13$	5.35335	−	3.09076i	1.48475	−	0.857223i	0.484904	−	0.874568i	$-0.338855\pi$
$13$	5.35335	−	3.09076i	1.48475	−	0.857223i	0.999850	+	0.0173448i	$0.00552131\pi$
$14$	6.18771	−	3.15715i	1.65374	−	0.843783i
$15$	0.933716	−	1.45883i	0.241085	−	0.376667i
$16$	−5.08015	−	8.79908i	−1.27004	−	2.19977i
$17$	−0.643963	−	1.11538i	−0.156184	−	0.270519i	0.777306	−	0.629123i	$-0.216586\pi$
$17$	−0.643963	−	1.11538i	−0.156184	−	0.270519i	−0.933490	+	0.358605i	$0.883253\pi$
$18$	6.43307	+	4.54514i	1.51629	+	1.07130i
$19$	−2.22804	−	1.28636i	−0.511148	−	0.295111i	0.222158	−	0.975011i	$-0.428690\pi$
$19$	−2.22804	−	1.28636i	−0.511148	−	0.295111i	−0.733305	+	0.679899i	$0.762023\pi$
$20$	−2.44681	+	4.23800i	−0.547124	+	0.947646i
$21$	2.66692	−	3.72660i	0.581969	−	0.813211i
$22$	−0.141691	−	0.245416i	−0.0302086	−	0.0523228i
$23$		−	0.764400i		−	0.159388i	−0.996819	−	0.0796942i	$-0.974606\pi$
$23$		−	0.764400i		−	0.159388i	0.996819	−	0.0796942i	$-0.0253944\pi$
$24$	−11.0833	−	7.09383i	−2.26237	−	1.44802i
$25$	1.00000			0.200000
$26$	−8.11501	+	14.0556i	−1.59148	+	2.75653i
$27$	5.14729	+	0.710892i	0.990597	+	0.136811i
$28$	−7.04555	+	10.8625i	−1.33148	+	2.05281i
$29$	8.71958	+	5.03425i	1.61919	+	0.934838i	0.987131	+	0.159914i	$0.0511217\pi$
$29$	8.71958	+	5.03425i	1.61919	+	0.934838i	0.632055	+	0.774923i	$0.282212\pi$
$30$	−0.207969	+	4.54286i	−0.0379697	+	0.829410i
$31$	4.65132	+	2.68544i	0.835402	+	0.482320i	0.855699	−	0.517474i	$-0.173128\pi$
$31$	4.65132	+	2.68544i	0.835402	+	0.482320i	−0.0202966	+	0.999794i	$0.506461\pi$
$32$	9.94350	+	5.74088i	1.75778	+	1.01485i
$33$	−0.157453	−	0.100777i	−0.0274091	−	0.0175431i
$34$	2.92850	+	1.69077i	0.502234	+	0.289965i
$35$	2.64220	+	0.136993i	0.446614	+	0.0231561i
$36$	−14.6195	−	1.34135i	−2.43658	−	0.223558i
$37$	−0.952679	+	1.65009i	−0.156619	+	0.271273i	−0.933648	−	0.358193i	$-0.883393\pi$
$37$	−0.952679	+	1.65009i	−0.156619	+	0.271273i	0.777028	+	0.629466i	$0.216726\pi$
$38$	6.75486			1.09578
$39$	−0.489632	+	10.6955i	−0.0784038	+	1.71265i
$40$		−	7.59741i		−	1.20126i
$41$	−3.87282	−	6.70793i	−0.604834	−	1.04760i	−0.992078	−	0.125625i	$-0.959906\pi$
$41$	−3.87282	−	6.70793i	−0.604834	−	1.04760i	0.387244	−	0.921977i	$-0.373427\pi$
$42$	−1.17184	+	11.9747i	−0.180818	+	1.84773i
$43$	−3.74174	+	6.48088i	−0.570610	+	0.988325i	0.425894	+	0.904773i	$0.359960\pi$
$43$	−3.74174	+	6.48088i	−0.570610	+	0.988325i	−0.996503	+	0.0835517i	$0.973374\pi$
$44$	0.457414	+	0.264088i	0.0689577	+	0.0398127i
$45$	1.25635	+	2.72426i	0.187285	+	0.406109i
$46$	1.00349	+	1.73810i	0.147957	+	0.256269i
$47$	−3.85718	−	6.68083i	−0.562627	−	0.974499i	−0.997266	−	0.0738943i	$-0.976457\pi$
$47$	−3.85718	−	6.68083i	−0.562627	−	0.974499i	0.434639	−	0.900605i	$-0.356876\pi$
$48$	17.5797	+	0.804786i	2.53742	+	0.116161i
$49$	6.96247	+	0.723928i	0.994638	+	0.103418i
$50$	−2.27381	+	1.31279i	−0.321565	+	0.185656i
$51$	2.22842	+	0.102015i	0.312041	+	0.0142850i
$52$		−	30.2500i		−	4.19492i
$53$	4.83694	−	2.79261i	0.664405	−	0.383595i	−0.129548	−	0.991573i	$-0.541353\pi$
$53$	4.83694	−	2.79261i	0.664405	−	0.383595i	0.793953	+	0.607979i	$0.208019\pi$
$54$	−12.6372	+	5.14086i	−1.71971	+	0.699582i
$55$		−	0.107931i		−	0.0145535i
$56$	1.04080	−	20.0739i	0.139082	−	2.68249i
$57$	3.95694	−	2.04923i	0.524109	−	0.271427i
$58$	−26.4356			−3.47116
$59$	1.18518	−	2.05280i	0.154298	−	0.267252i	−0.778505	−	0.627638i	$-0.784022\pi$
$59$	1.18518	−	2.05280i	0.154298	−	0.267252i	0.932803	+	0.360386i	$0.117355\pi$
$60$	−3.89788	−	7.52656i	−0.503214	−	0.971675i
$61$	7.25479	−	4.18855i	0.928880	−	0.536289i	0.0424229	−	0.999100i	$-0.486492\pi$
$61$	7.25479	−	4.18855i	0.928880	−	0.536289i	0.886457	+	0.462811i	$0.153159\pi$
$62$	−14.1016			−1.79091
$63$	2.94632	+	7.37016i	0.371201	+	0.928552i
$64$	−9.82559			−1.22820
$65$	−5.35335	+	3.09076i	−0.664002	+	0.383362i
$66$	0.490318	+	0.0224463i	0.0603539	+	0.00276295i
$67$	4.21881	−	7.30720i	0.515410	−	0.892717i	−0.484430	−	0.874830i	$-0.660973\pi$
$67$	4.21881	−	7.30720i	0.515410	−	0.892717i	0.999840	−	0.0178865i	$-0.00569374\pi$
$68$	−6.30262			−0.764305
$69$	1.11513	+	0.713733i	0.134245	+	0.0859233i
$70$	−6.18771	+	3.15715i	−0.739573	+	0.377351i
$71$		−	10.2356i		−	1.21474i	−0.794420	−	0.607368i	$-0.792225\pi$
$71$		−	10.2356i		−	1.21474i	0.794420	−	0.607368i	$-0.207775\pi$
$72$	20.6973	−	9.54499i	2.43920	−	1.12489i
$73$	9.71863	−	5.61106i	1.13748	−	0.656724i	0.191675	−	0.981459i	$-0.438608\pi$
$73$	9.71863	−	5.61106i	1.13748	−	0.656724i	0.945805	+	0.324734i	$0.105275\pi$
$74$		−	5.00265i		−	0.581547i
$75$	−0.933716	+	1.45883i	−0.107816	+	0.168451i
$76$	−10.9032	+	6.29496i	−1.25068	+	0.722082i
$77$	0.0147859	−	0.285177i	0.00168501	−	0.0324989i
$78$	−12.9276	−	24.9623i	−1.46376	−	2.82643i
$79$	5.09156	+	8.81884i	0.572845	+	0.992197i	0.996272	+	0.0862667i	$0.0274937\pi$
$79$	5.09156	+	8.81884i	0.572845	+	0.992197i	−0.423427	+	0.905930i	$0.639173\pi$
$80$	5.08015	+	8.79908i	0.567978	+	0.983767i
$81$	−5.84318	+	6.84524i	−0.649242	+	0.760582i
$82$	17.6121	+	10.1684i	1.94494	+	1.12291i
$83$	7.13623	−	12.3603i	0.783302	−	1.35672i	−0.146705	−	0.989180i	$-0.546867\pi$
$83$	7.13623	−	12.3603i	0.783302	−	1.35672i	0.930008	−	0.367539i	$-0.119800\pi$
$84$	−9.26790	−	20.4207i	−1.01121	−	2.22808i
$85$	0.643963	+	1.11538i	0.0698476	+	0.120980i
$86$		−	19.6484i		−	2.11874i
$87$	−15.4857	+	8.01979i	−1.66024	+	0.859812i
$88$	−0.819999			−0.0874122
$89$	0.334543	−	0.579445i	0.0354615	−	0.0614211i	−0.847750	−	0.530396i	$-0.822043\pi$
$89$	0.334543	−	0.579445i	0.0354615	−	0.0614211i	0.883211	+	0.468975i	$0.155377\pi$
$90$	−6.43307	−	4.54514i	−0.678105	−	0.479099i
$91$	−14.5681	+	7.43304i	−1.52715	+	0.779194i
$92$	−3.23953	−	1.87034i	−0.337744	−	0.194997i
$93$	−8.26061	+	4.27803i	−0.856585	+	0.443611i
$94$	17.5410	+	10.1273i	1.80922	+	1.04455i
$95$	2.22804	+	1.28636i	0.228592	+	0.131978i
$96$	−17.6594	+	9.14548i	−1.80235	+	0.933407i
$97$	−7.16437	−	4.13635i	−0.727431	−	0.419983i	0.0900505	−	0.995937i	$-0.471297\pi$
$97$	−7.16437	−	4.13635i	−0.727431	−	0.419983i	−0.817482	+	0.575955i	$0.804630\pi$
$98$	−16.7817	+	7.49415i	−1.69521	+	0.757023i
$99$	0.294033	−	0.135599i	0.0295514	−	0.0136283i
$100$	2.44681	−	4.23800i	0.244681	−	0.423800i
$101$	−11.1892			−1.11337			−0.556685	−	0.830724i	$-0.687927\pi$
$101$	−11.1892			−1.11337			−0.556685	+	0.830724i	$0.687927\pi$
$102$	−5.20093	+	2.69347i	−0.514969	+	0.266694i
$103$		−	2.55531i		−	0.251782i	−0.992044	−	0.125891i	$-0.959821\pi$
$103$		−	2.55531i		−	0.251782i	0.992044	−	0.125891i	$-0.0401790\pi$
$104$	23.4818	+	40.6716i	2.30258	+	3.98818i
$105$	−2.66692	+	3.72660i	−0.260264	+	0.363679i
$106$	−7.33220	+	12.6997i	−0.712166	+	1.23351i
$107$	6.29942	+	3.63697i	0.608988	+	0.351599i	0.772569	−	0.634931i	$-0.218971\pi$
$107$	6.29942	+	3.63697i	0.608988	+	0.351599i	−0.163581	+	0.986530i	$0.552305\pi$
$108$	15.6072	−	20.0748i	1.50181	−	1.93170i
$109$	−5.61363	−	9.72309i	−0.537688	−	0.931303i	−0.999028	−	0.0440795i	$-0.985965\pi$
$109$	−5.61363	−	9.72309i	−0.537688	−	0.931303i	0.461340	−	0.887223i	$-0.347369\pi$
$110$	0.141691	+	0.245416i	0.0135097	+	0.0233995i
$111$	−1.51766	−	2.93051i	−0.144050	−	0.278151i
$112$	12.2174	+	23.9449i	1.15443	+	2.26258i
$113$	12.2520	−	7.07371i	1.15257	−	0.665438i	0.203060	−	0.979166i	$-0.434911\pi$
$113$	12.2520	−	7.07371i	1.15257	−	0.665438i	0.949513	+	0.313728i	$0.101578\pi$
$114$	−6.30712	+	9.85417i	−0.590716	+	0.922928i
$115$			0.764400i			0.0712807i
$116$	42.6704	−	24.6357i	3.96184	−	2.28737i
$117$	−15.1457	−	10.7009i	−1.40022	−	0.989294i
$118$			6.22357i			0.572926i
$119$	1.54868	+	3.03527i	0.141967	+	0.278243i
$120$	11.0833	+	7.09383i	1.01176	+	0.647575i
$121$	10.9884			0.998941
$122$	−10.9973	+	19.0480i	−0.995653	+	1.72452i
$123$	13.4018	+	0.613524i	1.20840	+	0.0553196i
$124$	22.7618	−	13.1415i	2.04407	−	1.18015i
$125$	−1.00000			−0.0894427
$126$	−16.3748	−	12.8905i	−1.45878	−	1.14837i
$127$	−4.51354			−0.400512			−0.200256	−	0.979744i	$-0.564177\pi$
$127$	−4.51354			−0.400512			−0.200256	+	0.979744i	$0.564177\pi$
$128$	2.45453	−	1.41712i	0.216952	−	0.125257i
$129$	−5.96076	−	11.5098i	−0.524815	−	1.01339i
$130$	8.11501	−	14.0556i	0.711734	−	1.23276i
$131$	2.28491			0.199634			0.0998169	−	0.995006i	$-0.468174\pi$
$131$	2.28491			0.199634			0.0998169	+	0.995006i	$0.468174\pi$
$132$	−0.812353	+	0.420704i	−0.0707062	+	0.0366176i
$133$	5.71071	+	3.70405i	0.495182	+	0.321182i
$134$			22.1536i			1.91378i
$135$	−5.14729	−	0.710892i	−0.443009	−	0.0611839i
$136$	8.47398	−	4.89245i	0.726637	−	0.419524i
$137$			13.6642i			1.16741i	0.811964	+	0.583707i	$0.198398\pi$
$137$			13.6642i			1.16741i	−0.811964	+	0.583707i	$0.801602\pi$
$138$	−3.47257	−	0.158971i	−0.295604	−	0.0135325i
$139$	−14.1970	+	8.19662i	−1.20417	+	0.695229i	−0.961480	−	0.274875i	$-0.911363\pi$
$139$	−14.1970	+	8.19662i	−1.20417	+	0.695229i	−0.242691	+	0.970104i	$0.578030\pi$
$140$	7.04555	−	10.8625i	0.595458	−	0.918046i
$141$	13.3477	+	0.611046i	1.12408	+	0.0514593i
$142$	13.4371	+	23.2737i	1.12762	+	1.95309i
$143$	0.333590	+	0.577795i	0.0278962	+	0.0483177i
$144$	−17.5885	+	24.8944i	−1.46571	+	2.07453i
$145$	−8.71958	−	5.03425i	−0.724122	−	0.418072i
$146$	−14.7322	+	25.5170i	−1.21925	+	2.11180i
$147$	−7.55705	+	9.48108i	−0.623295	+	0.781987i
$148$	4.66205	+	8.07491i	0.383218	+	0.663754i
$149$		−	5.36768i		−	0.439738i	−0.975529	−	0.219869i	$-0.929437\pi$
$149$		−	5.36768i		−	0.439738i	0.975529	−	0.219869i	$-0.0705630\pi$
$150$	0.207969	−	4.54286i	0.0169806	−	0.370923i
$151$	−2.24506			−0.182700			−0.0913501	−	0.995819i	$-0.529118\pi$
$151$	−2.24506			−0.182700			−0.0913501	+	0.995819i	$0.529118\pi$
$152$	9.77301	−	16.9274i	0.792696	−	1.37299i
$153$	−2.22953	+	3.15562i	−0.180247	+	0.255117i
$154$	0.340755	+	0.667848i	0.0274589	+	0.0538168i
$155$	−4.65132	−	2.68544i	−0.373603	−	0.215700i
$156$	44.1295	+	28.2449i	3.53319	+	2.26141i
$157$	−13.6999	−	7.90965i	−1.09337	−	0.631259i	−0.158900	−	0.987295i	$-0.550795\pi$
$157$	−13.6999	−	7.90965i	−1.09337	−	0.631259i	−0.934472	+	0.356036i	$0.884128\pi$
$158$	−23.1545	−	13.3683i	−1.84207	−	1.06352i
$159$	−0.442399	+	9.66377i	−0.0350846	+	0.766387i
$160$	−9.94350	−	5.74088i	−0.786103	−	0.453857i
$161$	−0.104718	+	2.01970i	−0.00825291	+	0.159175i
$162$	4.29996	−	23.2356i	0.337837	−	1.82556i
$163$	4.56650	−	7.90941i	0.357676	−	0.619513i	−0.629896	−	0.776679i	$-0.716903\pi$
$163$	4.56650	−	7.90941i	0.357676	−	0.619513i	0.987572	+	0.157167i	$0.0502360\pi$
$164$	−37.9043			−2.95983
$165$	0.157453	+	0.100777i	0.0122577	+	0.00784550i
$166$			37.4733i			2.90849i
$167$	1.79055	+	3.10133i	0.138557	+	0.239988i	0.926951	−	0.375183i	$-0.122420\pi$
$167$	1.79055	+	3.10133i	0.138557	+	0.239988i	−0.788394	+	0.615171i	$0.789087\pi$
$168$	28.3125	+	20.2617i	2.18436	+	1.56322i
$169$	12.6056	−	21.8335i	0.969662	−	1.67950i
$170$	−2.92850	−	1.69077i	−0.224606	−	0.129676i
$171$	−0.705185	+	7.68588i	−0.0539268	+	0.587754i
$172$	18.3107	+	31.7150i	1.39617	+	2.41824i
$173$	−0.0553457	−	0.0958615i	−0.00420785	−	0.00728821i	0.863914	−	0.503640i	$-0.168006\pi$
$173$	−0.0553457	−	0.0958615i	−0.00420785	−	0.00728821i	−0.868122	+	0.496351i	$0.834673\pi$
$174$	24.6833	−	38.5649i	1.87124	−	2.92360i
$175$	−2.64220	−	0.136993i	−0.199732	−	0.0103557i
$176$	0.949697	−	0.548308i	0.0715861	−	0.0413303i
$177$	1.88805	+	3.64571i	0.141915	+	0.274028i
$178$			1.75673i			0.131673i
$179$	0.238794	−	0.137868i	0.0178483	−	0.0103047i	−0.491049	−	0.871132i	$-0.663387\pi$
$179$	0.238794	−	0.137868i	0.0178483	−	0.0103047i	0.508898	+	0.860827i	$0.330053\pi$
$180$	14.6195	+	1.34135i	1.08967	+	0.0999780i
$181$		−	9.56064i		−	0.710637i	−0.934745	−	0.355319i	$-0.884372\pi$
$181$		−	9.56064i		−	0.710637i	0.934745	−	0.355319i	$-0.115628\pi$
$182$	23.3670	−	36.0261i	1.73208	−	2.67043i
$183$	−0.663541	+	14.4944i	−0.0490504	+	1.07146i
$184$	5.80746			0.428132
$185$	0.952679	−	1.65009i	0.0700424	−	0.121317i
$186$	13.1669	−	20.5718i	0.965446	−	1.50840i
$187$	0.120384	−	0.0695038i	0.00880336	−	0.00508262i
$188$	−37.7512			−2.75329
$189$	−13.5028	−	2.58347i	−0.982184	−	0.187920i
$190$	−6.75486			−0.490049
$191$	−11.5530	+	6.67014i	−0.835947	+	0.482634i	−0.855884	−	0.517167i	$-0.826987\pi$
$191$	−11.5530	+	6.67014i	−0.835947	+	0.482634i	0.0199377	+	0.999801i	$0.493653\pi$
$192$	9.17431	−	14.3338i	0.662099	−	1.03445i
$193$	−7.69329	+	13.3252i	−0.553775	+	0.959167i	0.444223	+	0.895916i	$0.353480\pi$
$193$	−7.69329	+	13.3252i	−0.553775	+	0.959167i	−0.997998	+	0.0632503i	$0.979853\pi$
$194$	21.7206			1.55944
$195$	0.489632	−	10.6955i	0.0350632	−	0.765921i
$196$	20.1039	−	27.7356i	1.43599	−	1.98112i
$197$		−	12.1119i		−	0.862940i	−0.902127	−	0.431470i	$-0.857995\pi$
$197$		−	12.1119i		−	0.862940i	0.902127	−	0.431470i	$-0.142005\pi$
$198$	−0.490563	+	0.694330i	−0.0348628	+	0.0493439i
$199$	0.805586	−	0.465105i	0.0571065	−	0.0329704i	−0.471175	−	0.882040i	$-0.656170\pi$
$199$	0.805586	−	0.465105i	0.0571065	−	0.0329704i	0.528281	+	0.849069i	$0.322837\pi$
$200$			7.59741i			0.537218i
$201$	6.72076	+	12.9774i	0.474046	+	0.915353i
$202$	25.4422	−	14.6891i	1.79011	−	1.03352i
$203$	−22.3492	−	14.4960i	−1.56861	−	1.01742i
$204$	5.88486	−	9.19443i	0.412023	−	0.643739i
$205$	3.87282	+	6.70793i	0.270490	+	0.468502i
$206$	3.35458	+	5.81030i	0.233724	+	0.404823i
$207$	−2.08242	+	0.960352i	−0.144738	+	0.0667491i
$208$	−54.3917	−	31.4031i	−3.77138	−	2.17741i
$209$	0.138839	−	0.240476i	0.00960367	−	0.0166341i
$210$	1.17184	−	11.9747i	0.0808645	−	0.826331i
$211$	4.55602	+	7.89127i	0.313650	+	0.543257i	0.979150	−	0.203141i	$-0.0651149\pi$
$211$	4.55602	+	7.89127i	0.313650	+	0.543257i	−0.665500	+	0.746398i	$0.731782\pi$
$212$		−	27.3320i		−	1.87717i
$213$	14.9319	+	9.55710i	1.02312	+	0.654842i
$214$	−19.0983			−1.30553
$215$	3.74174	−	6.48088i	0.255184	−	0.441992i
$216$	−5.40094	+	39.1061i	−0.367488	+	2.66083i
$217$	−11.9218	−	7.73268i	−0.809308	−	0.524929i
$218$	25.5287	+	14.7390i	1.72902	+	0.998249i
$219$	−0.888891	+	19.4169i	−0.0600657	+	1.31207i
$220$	−0.457414	−	0.264088i	−0.0308388	−	0.0178048i
$221$	−6.89472	−	3.98067i	−0.463789	−	0.267769i
$222$	7.29800	+	4.67106i	0.489810	+	0.313501i
$223$	−5.56608	−	3.21358i	−0.372732	−	0.215197i	0.301919	−	0.953333i	$-0.402373\pi$
$223$	−5.56608	−	3.21358i	−0.372732	−	0.215197i	−0.674651	+	0.738137i	$0.735706\pi$
$224$	−25.4863	−	16.5308i	−1.70287	−	1.10451i
$225$	−1.25635	−	2.72426i	−0.0837565	−	0.181617i
$226$	−18.5725	+	32.1686i	−1.23543	+	2.13982i
$227$	19.4261			1.28935			0.644677	−	0.764455i	$-0.276992\pi$
$227$	19.4261			1.28935			0.644677	+	0.764455i	$0.276992\pi$
$228$	0.997234	−	21.7836i	0.0660435	−	1.44265i
$229$		−	0.0783397i		−	0.00517684i	−0.999997	−	0.00258842i	$-0.999176\pi$
$229$		−	0.0783397i		−	0.00517684i	0.999997	−	0.00258842i	$-0.000823920\pi$
$230$	−1.00349	−	1.73810i	−0.0661684	−	0.114607i
$231$	0.402217	+	0.287844i	0.0264640	+	0.0189388i
$232$	−38.2473	+	66.2463i	−2.51106	+	4.34928i
$233$	13.4942	+	7.79085i	0.884031	+	0.510396i	0.871985	−	0.489532i	$-0.162832\pi$
$233$	13.4942	+	7.79085i	0.884031	+	0.510396i	0.0120459	+	0.999927i	$0.496166\pi$
$234$	48.4864	+	4.44866i	3.16966	+	0.290818i
$235$	3.85718	+	6.68083i	0.251615	+	0.435809i
$236$	−5.79985	−	10.0456i	−0.377538	−	0.653915i
$237$	−17.6192	−	0.806594i	−1.14449	−	0.0523939i
$238$	−7.50607	−	4.86854i	−0.486546	−	0.315581i
$239$	−9.50772	+	5.48929i	−0.615003	+	0.355072i	−0.774921	−	0.632058i	$-0.782210\pi$
$239$	−9.50772	+	5.48929i	−0.615003	+	0.355072i	0.159918	+	0.987130i	$0.448877\pi$
$240$	−17.5797	−	0.804786i	−1.13477	−	0.0519487i
$241$			23.6574i			1.52391i	0.647632	+	0.761954i	$0.275760\pi$
$241$			23.6574i			1.52391i	−0.647632	+	0.761954i	$0.724240\pi$
$242$	−24.9854	+	14.4253i	−1.60612	+	0.927296i
$243$	−4.53014	−	14.9157i	−0.290608	−	0.956842i
$244$		−	40.9944i		−	2.62440i
$245$	−6.96247	−	0.723928i	−0.444816	−	0.0462501i
$246$	−31.2786	+	16.1987i	−1.99425	+	1.03279i
$247$	−15.9033			−1.01190
$248$	−20.4024	+	35.3380i	−1.29555	+	2.24397i
$249$	11.3683	+	21.9515i	0.720438	+	1.39112i
$250$	2.27381	−	1.31279i	0.143808	−	0.0830278i
$251$	10.0851			0.636567			0.318283	−	0.947996i	$-0.396894\pi$
$251$	10.0851			0.636567			0.318283	+	0.947996i	$0.396894\pi$
$252$	38.4438	+	5.54687i	2.42173	+	0.349420i
$253$	0.0825028			0.00518690
$254$	10.2629	−	5.92531i	0.643954	−	0.371787i
$255$	−2.22842	−	0.102015i	−0.139549	−	0.00638844i
$256$	6.10483	−	10.5739i	0.381552	−	0.660867i
$257$	1.88604			0.117648			0.0588240	−	0.998268i	$-0.481265\pi$
$257$	1.88604			0.117648			0.0588240	+	0.998268i	$0.481265\pi$
$258$	28.6636	+	18.3460i	1.78452	+	1.14217i
$259$	2.74322	−	4.22936i	0.170456	−	0.262799i
$260$			30.2500i			1.87603i
$261$	2.75978	−	30.0792i	0.170826	−	1.86185i
$262$	−5.19546	+	2.99960i	−0.320977	+	0.185316i
$263$			28.6816i			1.76858i	0.466937	+	0.884291i	$0.345358\pi$
$263$			28.6816i			1.76858i	−0.466937	+	0.884291i	$0.654642\pi$
$264$	0.765647	−	1.19624i	0.0471223	−	0.0736233i
$265$	−4.83694	+	2.79261i	−0.297131	+	0.171549i
$266$	−17.8477	−	0.925371i	−1.09431	−	0.0567381i
$267$	0.532942	+	1.02908i	0.0326155	+	0.0629785i
$268$	−20.6453	−	35.7587i	−1.26111	−	2.18431i
$269$	−15.5910	−	27.0044i	−0.950601	−	1.64649i	−0.744129	−	0.668036i	$-0.767135\pi$
$269$	−15.5910	−	27.0044i	−0.950601	−	1.64649i	−0.206472	−	0.978452i	$-0.566198\pi$
$270$	12.6372	−	5.14086i	0.769077	−	0.312863i
$271$	9.11994	+	5.26540i	0.553997	+	0.319850i	0.750733	−	0.660606i	$-0.229701\pi$
$271$	9.11994	+	5.26540i	0.553997	+	0.319850i	−0.196736	+	0.980457i	$0.563034\pi$
$272$	−6.54286	+	11.3326i	−0.396719	+	0.687137i
$273$	2.75892	−	28.1926i	0.166977	−	1.70629i
$274$	−17.9382	−	31.0699i	−1.08369	−	1.87700i
$275$			0.107931i			0.00650851i
$276$	5.75331	−	2.97954i	0.346308	−	0.179347i
$277$	−21.4605			−1.28944			−0.644718	−	0.764420i	$-0.723025\pi$
$277$	−21.4605			−1.28944			−0.644718	+	0.764420i	$0.723025\pi$
$278$	21.5208	−	37.2751i	1.29073	−	2.23561i
$279$	1.47216	−	16.0453i	0.0881361	−	0.960604i
$280$	−1.04080	+	20.0739i	−0.0621994	+	1.19965i
$281$	7.44154	+	4.29637i	0.443925	+	0.256300i	0.705261	−	0.708948i	$-0.250830\pi$
$281$	7.44154	+	4.29637i	0.443925	+	0.256300i	−0.261336	+	0.965248i	$0.584163\pi$
$282$	−31.1523	+	16.1332i	−1.85509	+	0.960720i
$283$	3.96638	+	2.28999i	0.235777	+	0.136126i	0.613234	−	0.789901i	$-0.289868\pi$
$283$	3.96638	+	2.28999i	0.235777	+	0.136126i	−0.377457	+	0.926027i	$0.623202\pi$
$284$	−43.3783	−	25.0445i	−2.57403	−	1.48612i
$285$	−3.95694	+	2.04923i	−0.234389	+	0.121386i
$286$	−1.51704	−	0.875865i	−0.0897046	−	0.0517910i
$287$	9.31384	+	18.2543i	0.549779	+	1.07751i
$288$	3.14716	−	34.3012i	0.185448	−	2.02122i
$289$	7.67062	−	13.2859i	0.451213	−	0.781524i
$290$	26.4356			1.55235
$291$	12.7237	−	6.58939i	0.745876	−	0.386277i
$292$		−	54.9168i		−	3.21376i
$293$	3.19302	+	5.53047i	0.186538	+	0.323094i	0.944094	−	0.329677i	$-0.106940\pi$
$293$	3.19302	+	5.53047i	0.186538	+	0.323094i	−0.757556	+	0.652771i	$0.773607\pi$
$294$	4.73668	−	31.4790i	0.276249	−	1.83589i
$295$	−1.18518	+	2.05280i	−0.0690041	+	0.119519i
$296$	−12.5364	−	7.23790i	−0.728664	−	0.420694i
$297$	−0.0767276	+	0.555555i	−0.00445219	+	0.0322366i
$298$	7.04662	+	12.2051i	0.408200	+	0.707023i
$299$	−2.36258	−	4.09210i	−0.136631	−	0.236652i
$300$	3.89788	+	7.52656i	0.225044	+	0.434546i
$301$	10.7743	−	16.6112i	0.621018	−	0.957454i
$302$	5.10484	−	2.94728i	0.293750	−	0.169597i
$303$	10.4476	−	16.3231i	0.600197	−	0.937740i
$304$			26.1396i			1.49921i
$305$	−7.25479	+	4.18855i	−0.415408	+	0.239836i
$306$	0.926883	−	10.1022i	0.0529863	−	0.577504i
$307$			8.86419i			0.505906i	0.967479	+	0.252953i	$0.0814018\pi$
$307$			8.86419i			0.505906i	−0.967479	+	0.252953i	$0.918598\pi$
$308$	−1.17240	−	0.760436i	−0.0668037	−	0.0433299i
$309$	3.72776	+	2.38594i	0.212065	+	0.135731i
$310$	14.1016			0.800919
$311$	−3.40803	+	5.90288i	−0.193252	+	0.334721i	−0.946326	−	0.323214i	$-0.895237\pi$
$311$	−3.40803	+	5.90288i	−0.193252	+	0.334721i	0.753074	+	0.657935i	$0.228570\pi$
$312$	−81.2582	−	3.71993i	−4.60034	−	0.210600i
$313$	10.4831	−	6.05239i	0.592537	−	0.342101i	−0.173563	−	0.984823i	$-0.555528\pi$
$313$	10.4831	−	6.05239i	0.592537	−	0.342101i	0.766100	+	0.642721i	$0.222195\pi$
$314$	41.5347			2.34394
$315$	−2.94632	−	7.37016i	−0.166006	−	0.415261i
$316$	49.8323			2.80329
$317$	9.38015	−	5.41563i	0.526842	−	0.304172i	−0.212888	−	0.977077i	$-0.568287\pi$
$317$	9.38015	−	5.41563i	0.526842	−	0.304172i	0.739729	+	0.672904i	$0.234953\pi$
$318$	−11.6805	−	22.5544i	−0.655011	−	1.26479i
$319$	−0.543354	+	0.941117i	−0.0304220	+	0.0526924i
$320$	9.82559			0.549267
$321$	−11.1876	+	5.79386i	−0.624430	+	0.323382i
$322$	−2.41332	−	4.72989i	−0.134489	−	0.263586i
$323$			3.31347i			0.184367i
$324$	14.7130	+	41.5124i	0.817387	+	2.30624i
$325$	5.35335	−	3.09076i	0.296951	−	0.171445i
$326$			23.9793i			1.32809i
$327$	19.4258	+	0.889299i	1.07425	+	0.0491783i
$328$	50.9629	−	29.4234i	2.81396	−	1.62464i
$329$	9.27622	+	18.1805i	0.511414	+	1.00232i
$330$	−0.490318	−	0.0224463i	−0.0269911	−	0.00123563i
$331$	−8.07381	−	13.9842i	−0.443777	−	0.768644i	0.554189	−	0.832391i	$-0.313028\pi$
$331$	−8.07381	−	13.9842i	−0.443777	−	0.768644i	−0.997966	+	0.0637468i	$0.979695\pi$
$332$	−34.9220	−	60.4867i	−1.91659	−	3.31964i
$333$	5.69217	+	0.522260i	0.311929	+	0.0286197i
$334$	−8.14275	−	4.70122i	−0.445552	−	0.257239i
$335$	−4.21881	+	7.30720i	−0.230498	+	0.399235i
$336$	−46.3390	−	4.53472i	−2.52800	−	0.247389i
$337$	11.4187	+	19.7777i	0.622015	+	1.07736i	0.989110	+	0.147178i	$0.0470189\pi$
$337$	11.4187	+	19.7777i	0.622015	+	1.07736i	−0.367096	+	0.930183i	$0.619648\pi$
$338$			66.1938i			3.60047i
$339$	−1.12060	+	24.4784i	−0.0608627	+	1.32948i
$340$	6.30262			0.341808
$341$	−0.289844	+	0.502024i	−0.0156959	+	0.0271861i
$342$	−8.48646	−	18.4020i	−0.458895	−	0.995066i
$343$	−18.2971	−	2.86658i	−0.987949	−	0.154781i
$344$	−49.2379	−	28.4275i	−2.65473	−	1.53271i
$345$	−1.11513	−	0.713733i	−0.0600364	−	0.0384261i
$346$	0.251691	+	0.145314i	0.0135310	+	0.00781213i
$347$	−0.0935690	−	0.0540221i	−0.00502305	−	0.00290006i	0.497486	−	0.867472i	$-0.334256\pi$
$347$	−0.0935690	−	0.0540221i	−0.00502305	−	0.00290006i	−0.502509	+	0.864572i	$0.667590\pi$
$348$	−3.90274	+	85.2514i	−0.209209	+	4.56996i
$349$	−19.0311	−	10.9876i	−1.01871	−	0.588153i	−0.104981	−	0.994474i	$-0.533478\pi$
$349$	−19.0311	−	10.9876i	−1.01871	−	0.588153i	−0.913730	+	0.406321i	$0.866811\pi$
$350$	6.18771	−	3.15715i	0.330747	−	0.168757i
$351$	29.7525	−	12.1034i	1.58807	−	0.646031i
$352$	−0.619622	+	1.07322i	−0.0330259	+	0.0572026i
$353$	−17.1796			−0.914376			−0.457188	−	0.889370i	$-0.651143\pi$
$353$	−17.1796			−0.914376			−0.457188	+	0.889370i	$0.651143\pi$
$354$	−9.07911	−	5.81105i	−0.482549	−	0.308854i
$355$			10.2356i			0.543247i
$356$	−1.63713	−	2.83559i	−0.0867675	−	0.150286i
$357$	−5.87396	−	0.574823i	−0.310883	−	0.0304229i
$358$	−0.361982	+	0.626970i	−0.0191313	+	0.0331364i
$359$	14.1707	+	8.18146i	0.747901	+	0.431801i	0.824935	−	0.565228i	$-0.191212\pi$
$359$	14.1707	+	8.18146i	0.747901	+	0.431801i	−0.0770340	+	0.997028i	$0.524545\pi$
$360$	−20.6973	+	9.54499i	−1.09084	+	0.503065i
$361$	−6.19055	−	10.7224i	−0.325819	−	0.564334i
$362$	12.5511	+	21.7391i	0.659670	+	1.14258i
$363$	−10.2600	+	16.0301i	−0.538510	+	0.841362i
$364$	−4.14405	+	79.9267i	−0.217207	+	4.18930i
$365$	−9.71863	+	5.61106i	−0.508697	+	0.293696i
$366$	−17.5193	−	33.8286i	−0.915746	−	1.76825i
$367$		−	14.8575i		−	0.775556i	−0.921753	−	0.387778i	$-0.873243\pi$
$367$		−	14.8575i		−	0.775556i	0.921753	−	0.387778i	$-0.126757\pi$
$368$	−6.72602	+	3.88327i	−0.350618	+	0.202429i
$369$	−13.4085	+	18.9781i	−0.698020	+	0.987959i
$370$			5.00265i			0.260076i
$371$	−13.1628	+	6.71601i	−0.683376	+	0.348678i
$372$	−2.08185	+	45.4760i	−0.107939	+	2.35782i
$373$	−2.53984			−0.131508			−0.0657541	−	0.997836i	$-0.520945\pi$
$373$	−2.53984			−0.131508			−0.0657541	+	0.997836i	$0.520945\pi$
$374$	−0.182487	+	0.316077i	−0.00943619	+	0.0163440i
$375$	0.933716	−	1.45883i	0.0482169	−	0.0753335i
$376$	50.7570	−	29.3046i	2.61759	−	1.51127i
$377$	62.2387			3.20546
$378$	34.0944	−	11.8520i	1.75362	−	0.609600i
$379$	−9.92334			−0.509728			−0.254864	−	0.966977i	$-0.582031\pi$
$379$	−9.92334			−0.509728			−0.254864	+	0.966977i	$0.582031\pi$
$380$	10.9032	−	6.29496i	0.559322	−	0.322925i
$381$	4.21437	−	6.58447i	0.215909	−	0.337333i
$382$	17.5129	−	30.3333i	0.896039	−	1.55198i
$383$	15.9699			0.816024			0.408012	−	0.912976i	$-0.366222\pi$
$383$	15.9699			0.816024			0.408012	+	0.912976i	$0.366222\pi$
$384$	−0.224498	+	4.90393i	−0.0114564	+	0.250252i
$385$	−0.0147859	+	0.285177i	−0.000753559	+	0.0145339i
$386$		−	40.3986i		−	2.05623i
$387$	22.3565	+	2.05123i	1.13645	+	0.104270i
$388$	−35.0597	+	20.2417i	−1.77989	+	1.02762i
$389$			21.2886i			1.07938i	0.841865	+	0.539688i	$0.181458\pi$
$389$			21.2886i			1.07938i	−0.841865	+	0.539688i	$0.818542\pi$
$390$	12.9276	+	24.9623i	0.654613	+	1.26402i
$391$	−0.852594	+	0.492245i	−0.0431175	+	0.0248939i
$392$	−5.49998	+	52.8967i	−0.277791	+	2.67169i
$393$	−2.13346	+	3.33329i	−0.107619	+	0.168142i
$394$	15.9004	+	27.5403i	0.801049	+	1.38746i
$395$	−5.09156	−	8.81884i	−0.256184	−	0.443724i
$396$	0.144773	−	1.57790i	0.00727513	−	0.0792924i
$397$	7.42803	+	4.28857i	0.372802	+	0.215237i	0.674682	−	0.738109i	$-0.264281\pi$
$397$	7.42803	+	4.28857i	0.372802	+	0.215237i	−0.301880	+	0.953346i	$0.597614\pi$
$398$	−1.22117	+	2.11512i	−0.0612115	+	0.106022i
$399$	−10.7358	+	4.87241i	−0.537460	+	0.243925i
$400$	−5.08015	−	8.79908i	−0.254008	−	0.439954i
$401$			21.2268i			1.06001i	0.847993	+	0.530007i	$0.177811\pi$
$401$			21.2268i			1.06001i	−0.847993	+	0.530007i	$0.822189\pi$
$402$	−32.3182	−	20.6852i	−1.61189	−	1.03168i
$403$	33.2002			1.65382
$404$	−27.3779	+	47.4200i	−1.36210	+	2.35923i
$405$	5.84318	−	6.84524i	0.290350	−	0.340142i
$406$	69.8482	+	3.62150i	3.46651	+	0.179732i
$407$	−0.178096	−	0.102824i	−0.00882791	−	0.00509680i
$408$	−0.775052	+	16.9302i	−0.0383708	+	0.838171i
$409$	3.04788	+	1.75969i	0.150708	+	0.0870112i	0.573458	−	0.819235i	$-0.305602\pi$
$409$	3.04788	+	1.75969i	0.150708	+	0.0870112i	−0.422750	+	0.906246i	$0.638935\pi$
$410$	−17.6121	−	10.1684i	−0.869802	−	0.502180i
$411$	−19.9337	−	12.7585i	−0.983259	−	0.629331i
$412$	−10.8294	−	6.25237i	−0.533527	−	0.308032i
$413$	−3.41272	+	5.26155i	−0.167929	+	0.258904i
$414$	3.47430	−	4.91744i	0.170753	−	0.241679i
$415$	−7.13623	+	12.3603i	−0.350304	+	0.606743i
$416$	70.9748			3.47982
$417$	1.29849	−	28.3642i	0.0635874	−	1.38900i
$418$			0.729062i			0.0356596i
$419$	−10.2456	−	17.7459i	−0.500529	−	0.866942i	−1.00000		0.000610964i	$-0.999806\pi$
$419$	−10.2456	−	17.7459i	−0.500529	−	0.866942i	0.499471	−	0.866331i	$-0.333528\pi$
$420$	9.26790	+	20.4207i	0.452227	+	0.996428i
$421$	−13.7370	+	23.7931i	−0.669499	+	1.15961i	0.308546	+	0.951210i	$0.400158\pi$
$421$	−13.7370	+	23.7931i	−0.669499	+	1.15961i	−0.978044	+	0.208396i	$0.933176\pi$
$422$	−20.7191	−	11.9622i	−1.00859	−	0.582309i
$423$	−13.3544	+	18.9014i	−0.649311	+	0.919018i
$424$	21.2166	+	36.7483i	1.03037	+	1.78465i
$425$	−0.643963	−	1.11538i	−0.0312368	−	0.0541037i
$426$	−46.4987	−	2.12867i	−2.25287	−	0.103135i
$427$	−19.7424	+	10.0731i	−0.955402	+	0.487474i
$428$	30.8270	−	17.7980i	1.49008	−	0.860297i
$429$	−1.15438	−	0.0528466i	−0.0557340	−	0.00255146i
$430$			19.6484i			0.947530i
$431$	−1.34674	+	0.777543i	−0.0648704	+	0.0374529i	−0.532084	−	0.846691i	$-0.678591\pi$
$431$	−1.34674	+	0.777543i	−0.0648704	+	0.0374529i	0.467214	+	0.884144i	$0.345258\pi$
$432$	−19.8938	−	48.9029i	−0.957142	−	2.35284i
$433$		−	8.27463i		−	0.397653i	−0.980035	−	0.198827i	$-0.936287\pi$
$433$		−	8.27463i		−	0.397653i	0.980035	−	0.198827i	$-0.0637131\pi$
$434$	37.2594	+	1.93183i	1.78851	+	0.0927308i
$435$	15.4857	−	8.01979i	0.742483	−	0.384520i
$436$	−54.9420			−2.63124
$437$	−0.983294	+	1.70312i	−0.0470373	+	0.0814710i
$438$	−23.4691	−	45.3174i	−1.12140	−	2.16535i
$439$	−3.09254	+	1.78548i	−0.147599	+	0.0852164i	−0.571981	−	0.820267i	$-0.693825\pi$
$439$	−3.09254	+	1.78548i	−0.147599	+	0.0852164i	0.424382	+	0.905483i	$0.360491\pi$
$440$	0.819999			0.0390919
$441$	−6.77511	−	19.8771i	−0.322624	−	0.946527i
$442$	20.9031			0.994257
$443$	29.0928	−	16.7967i	1.38224	−	0.798037i	0.389817	−	0.920893i	$-0.372538\pi$
$443$	29.0928	−	16.7967i	1.38224	−	0.798037i	0.992425	+	0.122855i	$0.0392051\pi$
$444$	−16.1329	−	0.738552i	−0.765635	−	0.0350501i
$445$	−0.334543	+	0.579445i	−0.0158589	+	0.0274683i
$446$	16.8749			0.799052
$447$	7.83052	+	5.01189i	0.370371	+	0.237054i
$448$	25.9612	+	1.34604i	1.22655	+	0.0635944i
$449$			7.96280i			0.375788i	0.982189	+	0.187894i	$0.0601661\pi$
$449$			7.96280i			0.375788i	−0.982189	+	0.187894i	$0.939834\pi$
$450$	6.43307	+	4.54514i	0.303258	+	0.214260i
$451$	0.723996	−	0.417999i	0.0340917	−	0.0196828i
$452$		−	69.2321i		−	3.25640i
$453$	2.09625	−	3.27515i	0.0984902	−	0.153880i
$454$	−44.1712	+	25.5023i	−2.07306	+	1.19688i
$455$	14.5681	−	7.43304i	0.682961	−	0.348466i
$456$	15.5688	+	30.0625i	0.729078	+	1.40780i
$457$	−18.3495	−	31.7823i	−0.858356	−	1.48672i	−0.873497	−	0.486830i	$-0.838153\pi$
$457$	−18.3495	−	31.7823i	−0.858356	−	1.48672i	0.0151411	−	0.999885i	$-0.495180\pi$
$458$	0.102843	+	0.178130i	0.00480555	+	0.00832346i
$459$	−2.52175	−	6.19896i	−0.117705	−	0.289343i
$460$	3.23953	+	1.87034i	0.151044	+	0.0872052i
$461$	3.34188	−	5.78830i	0.155647	−	0.269588i	−0.777648	−	0.628700i	$-0.783587\pi$
$461$	3.34188	−	5.78830i	0.155647	−	0.269588i	0.933294	+	0.359112i	$0.116921\pi$
$462$	−1.29244	−	0.126478i	−0.0601299	−	0.00588429i
$463$	3.45184	+	5.97877i	0.160421	+	0.277857i	0.935020	−	0.354596i	$-0.115382\pi$
$463$	3.45184	+	5.97877i	0.160421	+	0.277857i	−0.774599	+	0.632453i	$0.782048\pi$
$464$		−	102.299i		−	4.74912i
$465$	8.26061	−	4.27803i	0.383077	−	0.198389i
$466$	−40.9109			−1.89516
$467$	−3.63751	+	6.30035i	−0.168324	+	0.291545i	−0.937831	−	0.347093i	$-0.887169\pi$
$467$	−3.63751	+	6.30035i	−0.168324	+	0.291545i	0.769507	+	0.638639i	$0.220502\pi$
$468$	−82.4089	+	38.0046i	−3.80935	+	1.75676i
$469$	−12.1480	+	18.7292i	−0.560942	+	0.864832i
$470$	−17.5410	−	10.1273i	−0.809106	−	0.467137i
$471$	24.3306	−	12.6004i	1.12110	−	0.580597i
$472$	15.5960	+	9.00434i	0.717863	+	0.414458i
$473$	−0.699491	−	0.403851i	−0.0321626	−	0.0185691i
$474$	41.1217	−	21.2962i	1.88878	−	0.978168i
$475$	−2.22804	−	1.28636i	−0.102230	−	0.0590223i
$476$	16.6528	+	0.863418i	0.763280	+	0.0395747i
$477$	−13.6847	−	9.66860i	−0.626578	−	0.442695i
$478$	14.4125	−	24.9632i	0.659213	−	1.14179i
$479$	15.7473			0.719511			0.359755	−	0.933047i	$-0.382860\pi$
$479$	15.7473			0.719511			0.359755	+	0.933047i	$0.382860\pi$
$480$	17.6594	−	9.14548i	0.806036	−	0.417432i
$481$			11.7780i			0.537031i
$482$	−31.0571	−	53.7925i	−1.41461	−	2.45018i
$483$	−2.84861	−	2.03859i	−0.129616	−	0.0927591i
$484$	26.8864	−	46.5687i	1.22211	−	2.11676i
$485$	7.16437	+	4.13635i	0.325317	+	0.187822i
$486$	29.8818	+	27.9684i	1.35546	+	1.26867i
$487$	7.41905	+	12.8502i	0.336189	+	0.582297i	0.983713	−	0.179749i	$-0.0575285\pi$
$487$	7.41905	+	12.8502i	0.336189	+	0.582297i	−0.647523	+	0.762046i	$0.724195\pi$
$488$	31.8222	+	55.1176i	1.44052	+	2.49506i
$489$	7.27464	+	14.0469i	0.328970	+	0.635221i
$490$	16.7817	−	7.49415i	0.758120	−	0.338551i
$491$	28.9366	−	16.7066i	1.30589	−	0.753956i	0.324483	−	0.945891i	$-0.394810\pi$
$491$	28.9366	−	16.7066i	1.30589	−	0.753956i	0.981408	+	0.191935i	$0.0614763\pi$
$492$	35.3919	−	55.2958i	1.59559	−	2.49293i
$493$		−	12.9675i		−	0.584026i
$494$	36.1612	−	20.8777i	1.62697	−	0.939330i
$495$	−0.294033	+	0.135599i	−0.0132158	+	0.00609474i
$496$		−	54.5698i		−	2.45026i
$497$	−1.40220	+	27.0444i	−0.0628974	+	1.21311i
$498$	−54.6671	−	34.9895i	−2.44969	−	1.56792i
$499$	−10.6896			−0.478534			−0.239267	−	0.970954i	$-0.576907\pi$
$499$	−10.6896			−0.478534			−0.239267	+	0.970954i	$0.576907\pi$
$500$	−2.44681	+	4.23800i	−0.109425	+	0.189529i
$501$	−6.19616	−	0.283655i	−0.276824	−	0.0126728i
$502$	−22.9316	+	13.2396i	−1.02349	+	0.590912i
$503$	2.28280			0.101785			0.0508925	−	0.998704i	$-0.483793\pi$
$503$	2.28280			0.101785			0.0508925	+	0.998704i	$0.483793\pi$
$504$	−55.9941	+	22.3844i	−2.49418	+	0.997081i
$505$	11.1892			0.497914
$506$	−0.187596	+	0.108308i	−0.00833965	+	0.00481490i
$507$	20.0813	+	38.7757i	0.891841	+	1.72209i
$508$	−11.0438	+	19.1284i	−0.489989	+	0.848685i
$509$	−23.1092			−1.02430			−0.512149	−	0.858897i	$-0.671150\pi$
$509$	−23.1092			−1.02430			−0.512149	+	0.858897i	$0.671150\pi$
$510$	5.20093	−	2.69347i	0.230301	−	0.119269i
$511$	−26.4473	+	13.4942i	−1.16996	+	0.596946i
$512$			37.7258i			1.66726i
$513$	−10.5539	−	8.20517i	−0.465967	−	0.362267i
$514$	−4.28850	+	2.47597i	−0.189158	+	0.109210i
$515$			2.55531i			0.112601i
$516$	−63.3636	−	2.90073i	−2.78943	−	0.127698i
$517$	0.721071	−	0.416311i	0.0317127	−	0.0183093i
$518$	−0.685330	+	13.2180i	−0.0301117	+	0.580766i
$519$	0.191522	+	0.00876774i	0.00840690	+	0.000384861i
$520$	−23.4818	−	40.6716i	−1.02974	−	1.78357i
$521$	−7.37414	−	12.7724i	−0.323067	−	0.559569i	0.658052	−	0.752972i	$-0.271381\pi$
$521$	−7.37414	−	12.7724i	−0.323067	−	0.559569i	−0.981119	+	0.193404i	$0.938047\pi$
$522$	33.2123	+	72.0174i	1.45366	+	3.15212i
$523$	−22.9326	−	13.2401i	−1.00277	−	0.578950i	−0.0937044	−	0.995600i	$-0.529871\pi$
$523$	−22.9326	−	13.2401i	−1.00277	−	0.578950i	−0.909067	+	0.416650i	$0.863204\pi$
$524$	5.59075	−	9.68346i	0.244233	−	0.423024i
$525$	2.66692	−	3.72660i	0.116394	−	0.162642i
$526$	−37.6528	−	65.2165i	−1.64174	−	2.84357i
$527$		−	6.91730i		−	0.301322i
$528$	−0.0868617	+	1.89741i	−0.00378017	+	0.0825740i
$529$	22.4157			0.974595
$530$	7.33220	−	12.6997i	0.318490	−	0.551641i
$531$	−7.08136	−	0.649720i	−0.307305	−	0.0281954i
$532$	29.6708	−	15.1389i	1.28639	−	0.656355i
$533$	−41.4652	−	23.9399i	−1.79606	−	1.03695i
$534$	−2.56277	−	1.64029i	−0.110902	−	0.0709823i
$535$	−6.29942	−	3.63697i	−0.272348	−	0.157240i
$536$	55.5158	+	32.0521i	2.39792	+	1.38444i
$537$	−0.0218407	+	0.477088i	−0.000942496	+	0.0205879i
$538$	70.9020	+	40.9353i	3.05680	+	1.76485i
$539$	−0.0781346	+	0.751469i	−0.00336550	+	0.0323681i
$540$	−15.6072	+	20.0748i	−0.671628	+	0.863883i
$541$	−18.8183	+	32.5943i	−0.809062	+	1.40134i	0.104452	+	0.994530i	$0.466691\pi$
$541$	−18.8183	+	32.5943i	−0.809062	+	1.40134i	−0.913514	+	0.406807i	$0.866642\pi$
$542$	−27.6494			−1.18764
$543$	13.9473	+	8.92693i	0.598537	+	0.383091i
$544$		−	14.7877i		−	0.634016i
$545$	5.61363	+	9.72309i	0.240461	+	0.416491i
$546$	30.7376	+	67.7266i	1.31545	+	2.89843i
$547$	15.4329	−	26.7305i	0.659862	−	1.14292i	−0.320788	−	0.947151i	$-0.603948\pi$
$547$	15.4329	−	26.7305i	0.659862	−	1.14292i	0.980651	−	0.195764i	$-0.0627188\pi$
$548$	57.9091	+	33.4338i	2.47375	+	1.42822i
$549$	−20.5252	−	14.5016i	−0.875996	−	0.618915i
$550$	−0.141691	−	0.245416i	−0.00604172	−	0.0104646i
$551$	−12.9517	−	22.4331i	−0.551762	−	0.955680i
$552$	−5.42252	+	8.47208i	−0.230798	+	0.360596i
$553$	−12.2448	−	23.9987i	−0.520702	−	1.02053i
$554$	48.7971	−	28.1730i	2.07319	−	1.19696i
$555$	1.51766	+	2.93051i	0.0644211	+	0.124393i
$556$			80.2224i			3.40219i
$557$	−0.431897	+	0.249356i	−0.0183001	+	0.0105655i	−0.509122	−	0.860694i	$-0.670030\pi$
$557$	−0.431897	+	0.249356i	−0.0183001	+	0.0105655i	0.490822	+	0.871260i	$0.336697\pi$
$558$	17.7166	+	38.4165i	0.750002	+	1.62630i
$559$			46.2593i			1.95656i
$560$	−12.2174	−	23.9449i	−0.516278	−	1.01186i
$561$	−0.0110106	+	0.240516i	−0.000464870	+	0.0101546i
$562$	−22.5609			−0.951673
$563$	−2.41559	+	4.18392i	−0.101805	+	0.176331i	−0.912428	−	0.409237i	$-0.865795\pi$
$563$	−2.41559	+	4.18392i	−0.101805	+	0.176331i	0.810623	+	0.585568i	$0.199128\pi$
$564$	35.2489	−	55.0724i	1.48425	−	2.31897i
$565$	−12.2520	+	7.07371i	−0.515446	+	0.297593i
$566$	−12.0251			−0.505451
$567$	16.3766	−	17.2860i	0.687753	−	0.725945i
$568$	77.7637			3.26289
$569$	3.18125	−	1.83670i	0.133365	−	0.0769983i	−0.431833	−	0.901954i	$-0.642133\pi$
$569$	3.18125	−	1.83670i	0.133365	−	0.0769983i	0.565198	+	0.824955i	$0.308800\pi$
$570$	6.30712	−	9.85417i	0.264176	−	0.412746i
$571$	12.1396	−	21.0264i	0.508025	−	0.879926i	−0.491932	−	0.870634i	$-0.663709\pi$
$571$	12.1396	−	21.0264i	0.508025	−	0.879926i	0.999957	−	0.00929175i	$-0.00295770\pi$
$572$	3.26493			0.136514
$573$	1.05667	−	23.0819i	0.0441430	−	0.964258i
$574$	−45.1418	−	29.2797i	−1.88418	−	1.22211i
$575$		−	0.764400i		−	0.0318777i
$576$	12.3444	+	26.7675i	0.514348	+	1.11531i
$577$	25.8066	−	14.8995i	1.07434	−	0.620273i	0.144979	−	0.989435i	$-0.453689\pi$
$577$	25.8066	−	14.8995i	1.07434	−	0.620273i	0.929365	+	0.369162i	$0.120355\pi$
$578$			40.2795i			1.67541i
$579$	−12.2558	−	23.6651i	−0.509332	−	0.983488i
$580$	−42.6704	+	24.6357i	−1.77179	+	1.02294i
$581$	−20.5486	+	31.6808i	−0.852501	+	1.31434i
$582$	−20.2808	+	31.6865i	−0.840668	+	1.31345i
$583$	0.301410	+	0.522058i	0.0124831	+	0.0216214i
$584$	42.6295	+	73.8365i	1.76402	+	3.05537i
$585$	15.1457	+	10.7009i	0.626198	+	0.442426i
$586$	−14.5206	−	8.38350i	−0.599842	−	0.346319i
$587$	−10.5048	+	18.1948i	−0.433579	+	0.750981i	−0.997178	−	0.0750669i	$-0.976083\pi$
$587$	−10.5048	+	18.1948i	−0.433579	+	0.750981i	0.563599	+	0.826048i	$0.309416\pi$
$588$	21.6902	+	55.2252i	0.894487	+	2.27745i
$589$	−6.90889	−	11.9666i	−0.284676	−	0.493073i
$590$		−	6.22357i		−	0.256220i
$591$	17.6692	+	11.3091i	0.726814	+	0.465195i
$592$	19.3590			0.795650
$593$	−0.141047	+	0.244300i	−0.00579210	+	0.0100322i	−0.868907	−	0.494976i	$-0.835177\pi$
$593$	−0.141047	+	0.244300i	−0.00579210	+	0.0100322i	0.863115	+	0.505008i	$0.168510\pi$
$594$	−0.554860	−	1.36395i	−0.0227662	−	0.0559637i
$595$	−1.54868	−	3.03527i	−0.0634897	−	0.124434i
$596$	−22.7483	−	13.1337i	−0.931805	−	0.537978i
$597$	−0.0736809	+	1.60949i	−0.00301556	+	0.0658719i
$598$	10.7441	+	6.20311i	0.439359	+	0.253664i
$599$	−39.9757	−	23.0800i	−1.63336	−	0.943022i	−0.983046	−	0.183359i	$-0.941303\pi$
$599$	−39.9757	−	23.0800i	−1.63336	−	0.943022i	−0.650317	−	0.759663i	$-0.725364\pi$
$600$	−11.0833	−	7.09383i	−0.452474	−	0.289604i
$601$	33.5229	+	19.3544i	1.36743	+	0.789484i	0.990599	−	0.136800i	$-0.0436818\pi$
$601$	33.5229	+	19.3544i	1.36743	+	0.789484i	0.376827	+	0.926284i	$0.377015\pi$
$602$	−2.69170	+	51.9150i	−0.109705	+	2.11590i
$603$	−25.2070	−	2.31276i	−1.02651	−	0.0941828i
$604$	−5.49323	+	9.51456i	−0.223516	+	0.387142i
$605$	−10.9884			−0.446740
$606$	−2.32701	+	50.8312i	−0.0945283	+	2.06487i
$607$			2.88257i			0.117000i	0.998287	+	0.0585000i	$0.0186318\pi$
$607$			2.88257i			0.117000i	−0.998287	+	0.0585000i	$0.981368\pi$
$608$	−14.7697	−	25.5819i	−0.598990	−	1.03748i
$609$	42.0151	−	19.0685i	1.70254	−	0.772694i
$610$	10.9973	−	19.0480i	0.445269	−	0.771229i
$611$	−41.2977	−	23.8432i	−1.67073	−	0.964594i
$612$	7.91829	+	17.1700i	0.320078	+	0.694055i
$613$	−4.23686	−	7.33845i	−0.171125	−	0.296397i	0.767688	−	0.640823i	$-0.221407\pi$
$613$	−4.23686	−	7.33845i	−0.171125	−	0.296397i	−0.938813	+	0.344426i	$0.888074\pi$
$614$	−11.6368	−	20.1555i	−0.469622	−	0.813409i
$615$	−13.4018	−	0.613524i	−0.540414	−	0.0247397i
$616$	2.16660	+	0.112334i	0.0872950	+	0.00452609i
$617$	−13.3572	+	7.71176i	−0.537739	+	0.310464i	−0.744162	−	0.667999i	$-0.767151\pi$
$617$	−13.3572	+	7.71176i	−0.537739	+	0.310464i	0.206423	+	0.978463i	$0.433818\pi$
$618$	−11.6084	−	0.531425i	−0.466960	−	0.0213770i
$619$		−	28.3024i		−	1.13757i	−0.822487	−	0.568784i	$-0.807414\pi$
$619$		−	28.3024i		−	1.13757i	0.822487	−	0.568784i	$-0.192586\pi$
$620$	−22.7618	+	13.1415i	−0.914137	+	0.527777i
$621$	0.543406	−	3.93459i	0.0218061	−	0.157890i
$622$		−	17.8960i		−	0.717566i
$623$	−0.963310	+	1.48518i	−0.0385942	+	0.0595025i
$624$	96.5980	−	50.0265i	3.86701	−	2.00266i
$625$	1.00000			0.0400000
$626$	−15.8910	+	27.5240i	−0.635131	+	1.10008i
$627$	0.221176	+	0.427078i	0.00883293	+	0.0170558i
$628$	−67.0422	+	38.7069i	−2.67528	+	1.54457i
$629$	2.45396			0.0978458
$630$	16.3748	+	12.8905i	0.652388	+	0.513568i
$631$	−10.3968			−0.413890			−0.206945	−	0.978353i	$-0.566352\pi$
$631$	−10.3968			−0.413890			−0.206945	+	0.978353i	$0.566352\pi$
$632$	−67.0004	+	38.6827i	−2.66513	+	1.53871i
$633$	−15.7660	−	0.721755i	−0.626643	−	0.0286872i
$634$	−14.2191	+	24.6283i	−0.564714	+	0.978113i
$635$	4.51354			0.179114
$636$	39.8726	+	25.5203i	1.58105	+	1.01195i
$637$	39.5100	−	17.6439i	1.56544	−	0.699076i
$638$		−	2.85323i		−	0.112960i
$639$	−27.8843	+	12.8594i	−1.10309	+	0.508711i
$640$	−2.45453	+	1.41712i	−0.0970238	+	0.0560167i
$641$			15.2686i			0.603075i	0.953454	+	0.301538i	$0.0974999\pi$
$641$			15.2686i			0.603075i	−0.953454	+	0.301538i	$0.902500\pi$
$642$	17.8324	−	27.8610i	0.703787	−	1.09959i
$643$	−26.0206	+	15.0230i	−1.02615	+	0.592450i	−0.915880	−	0.401452i	$-0.868506\pi$
$643$	−26.0206	+	15.0230i	−1.02615	+	0.592450i	−0.110273	+	0.993901i	$0.535172\pi$
$644$	8.30327	+	5.38562i	0.327194	+	0.212223i
$645$	5.96076	+	11.5098i	0.234705	+	0.453200i
$646$	−4.34988	−	7.53421i	−0.171144	−	0.296430i
$647$	−1.09203	−	1.89146i	−0.0429323	−	0.0743608i	0.843761	−	0.536719i	$-0.180337\pi$
$647$	−1.09203	−	1.89146i	−0.0429323	−	0.0743608i	−0.886693	+	0.462359i	$0.847003\pi$
$648$	−52.0061	−	44.3931i	−2.04299	−	1.74392i
$649$	0.221562	+	0.127919i	0.00869705	+	0.00502125i
$650$	−8.11501	+	14.0556i	−0.318297	+	0.551306i
$651$	22.4123	−	10.1718i	0.878406	−	0.398663i
$652$	−22.3467	−	38.7057i	−0.875165	−	1.51583i
$653$		−	3.01533i		−	0.117999i	−0.998258	−	0.0589995i	$-0.981209\pi$
$653$		−	3.01533i		−	0.117999i	0.998258	−	0.0589995i	$-0.0187910\pi$
$654$	−45.3381	+	23.4799i	−1.77286	+	0.918135i
$655$	−2.28491			−0.0892789
$656$	−39.3491	+	68.1546i	−1.53632	+	2.66099i
$657$	−27.4960	−	19.4266i	−1.07272	−	0.757906i
$658$	−44.9595	−	29.1614i	−1.75270	−	1.13683i
$659$	−17.4300	−	10.0632i	−0.678978	−	0.392008i	0.120492	−	0.992714i	$-0.461553\pi$
$659$	−17.4300	−	10.0632i	−0.678978	−	0.392008i	−0.799470	+	0.600706i	$0.794886\pi$
$660$	0.812353	−	0.420704i	0.0316208	−	0.0163759i
$661$	23.8655	+	13.7788i	0.928261	+	0.535932i	0.886261	−	0.463186i	$-0.153294\pi$
$661$	23.8655	+	13.7788i	0.928261	+	0.535932i	0.0420000	+	0.999118i	$0.486627\pi$
$662$	36.7166	+	21.1984i	1.42703	+	0.823898i
$663$	12.2448	−	6.34139i	0.475549	−	0.246279i
$664$	93.9063	+	54.2168i	3.64427	+	2.10402i
$665$	−5.71071	−	3.70405i	−0.221452	−	0.143637i
$666$	−13.6285	+	6.28507i	−0.528095	+	0.243542i
$667$	3.84818	−	6.66525i	0.149002	−	0.258080i
$668$	17.5246			0.678046
$669$	9.88518	−	5.11937i	0.382183	−	0.197926i
$670$		−	22.1536i		−	0.855868i
$671$	0.452076	+	0.783019i	0.0174522	+	0.0302281i
$672$	47.9125	−	21.7450i	1.84826	−	0.838832i
$673$	−4.21453	+	7.29978i	−0.162458	+	0.281386i	−0.935750	−	0.352665i	$-0.885276\pi$
$673$	−4.21453	+	7.29978i	−0.162458	+	0.281386i	0.773292	+	0.634051i	$0.218609\pi$
$674$	−51.9278	−	29.9805i	−2.00018	−	1.15481i
$675$	5.14729	+	0.710892i	0.198119	+	0.0273623i
$676$	−61.6871	−	106.845i	−2.37258	−	4.10943i
$677$	2.84727	+	4.93161i	0.109429	+	0.189537i	0.915539	−	0.402229i	$-0.131764\pi$
$677$	2.84727	+	4.93161i	0.109429	+	0.189537i	−0.806110	+	0.591766i	$0.798431\pi$
$678$	−29.5869	−	57.1304i	−1.13628	−	2.19408i
$679$	18.3631	+	11.9105i	0.704709	+	0.457085i
$680$	−8.47398	+	4.89245i	−0.324962	+	0.187617i
$681$	−18.1384	+	28.3393i	−0.695066	+	1.08596i
$682$		−	1.52201i		−	0.0582808i
$683$	3.57383	−	2.06335i	0.136749	−	0.0789519i	−0.430065	−	0.902798i	$-0.641509\pi$
$683$	3.57383	−	2.06335i	0.136749	−	0.0789519i	0.566814	+	0.823846i	$0.308176\pi$
$684$	30.8473	+	21.7945i	1.17948	+	0.833333i
$685$		−	13.6642i		−	0.522084i
$686$	45.3673	−	17.5021i	1.73213	−	0.668232i
$687$	0.114284	+	0.0731471i	0.00436021	+	0.00279074i
$688$	76.0344			2.89878
$689$	17.2626	−	29.8997i	0.657652	−	1.13909i
$690$	3.47257	+	0.158971i	0.132198	+	0.00605193i
$691$	28.4622	−	16.4327i	1.08275	−	0.625128i	0.151115	−	0.988516i	$-0.451714\pi$
$691$	28.4622	−	16.4327i	1.08275	−	0.625128i	0.931638	+	0.363389i	$0.118380\pi$
$692$	−0.541682			−0.0205916
$693$	−0.795471	+	0.318000i	−0.0302175	+	0.0120798i
$694$	0.283678			0.0107683
$695$	14.1970	−	8.19662i	0.538522	−	0.310916i
$696$	−60.9297	−	117.651i	−2.30953	−	4.45956i
$697$	−4.98791	+	8.63932i	−0.188931	+	0.327237i
$698$	57.6975			2.18388
$699$	−23.9652	+	12.4112i	−0.906448	+	0.469434i
$700$	−7.04555	+	10.8625i	−0.266297	+	0.410562i
$701$			14.8571i			0.561143i	0.959833	+	0.280572i	$0.0905240\pi$
$701$			14.8571i			0.561143i	−0.959833	+	0.280572i	$0.909476\pi$
$702$	−51.7624	+	66.5795i	−1.95364	+	2.51288i
$703$	4.24522	−	2.45098i	0.160111	−	0.0924404i
$704$		−	1.06049i		−	0.0399687i
$705$	−13.3477	−	0.611046i	−0.502703	−	0.0230133i
$706$	39.0631	−	22.5531i	1.47016	−	0.848796i
$707$	29.5642	+	1.53285i	1.11188	+	0.0576488i
$708$	20.0702	+	0.918799i	0.754286	+	0.0345306i
$709$	23.3828	+	40.5002i	0.878161	+	1.52102i	0.853357	+	0.521326i	$0.174563\pi$
$709$	23.3828	+	40.5002i	0.878161	+	1.52102i	0.0248031	+	0.999692i	$0.492104\pi$
$710$	−13.4371	−	23.2737i	−0.504285	−	0.873447i
$711$	17.6280	−	24.9503i	0.661103	−	0.935708i
$712$	4.40228	+	2.54166i	0.164983	+	0.0952527i
$713$	2.05275	−	3.55547i	0.0768762	−	0.133153i
$714$	14.1109	−	6.40421i	0.528087	−	0.239671i
$715$	−0.333590	−	0.577795i	−0.0124756	−	0.0216083i
$716$		−	1.34935i		−	0.0504274i
$717$	0.869601	−	18.9956i	0.0324758	−	0.709402i
$718$	−42.9620			−1.60333
$719$	−10.5490	+	18.2715i	−0.393413	+	0.681410i	−0.992897	−	0.118976i	$-0.962039\pi$
$719$	−10.5490	+	18.2715i	−0.393413	+	0.681410i	0.599485	+	0.800386i	$0.295372\pi$
$720$	17.5885	−	24.8944i	0.655486	−	0.927758i
$721$	−0.350061	+	6.75165i	−0.0130369	+	0.251445i
$722$	28.1523	+	16.2537i	1.04772	+	0.604901i
$723$	−34.5120	−	22.0893i	−1.28352	−	0.821510i
$724$	−40.5180	−	23.3931i	−1.50584	−	0.869397i
$725$	8.71958	+	5.03425i	0.323837	+	0.186968i
$726$	2.28523	−	49.9186i	0.0848129	−	1.85265i
$727$	−19.2054	−	11.0883i	−0.712290	−	0.411241i	0.0996181	−	0.995026i	$-0.468238\pi$
$727$	−19.2054	−	11.0883i	−0.712290	−	0.411241i	−0.811908	+	0.583785i	$0.801571\pi$
$728$	−56.4719	−	110.680i	−2.09299	−	4.10206i
$729$	25.9893	+	7.31834i	0.962565	+	0.271050i
$730$	14.7322	−	25.5170i	0.545264	−	0.944425i
$731$	9.63816			0.356480
$732$	59.8037	+	38.2771i	2.21041	+	1.41476i
$733$			17.2139i			0.635810i	0.948123	+	0.317905i	$0.102979\pi$
$733$			17.2139i			0.635810i	−0.948123	+	0.317905i	$0.897021\pi$
$734$	19.5047	+	33.7832i	0.719933	+	1.24696i
$735$	7.55705	−	9.48108i	0.278746	−	0.349715i
$736$	4.38833	−	7.60081i	0.161756	−	0.280170i
$737$	0.788676	+	0.455343i	0.0290513	+	0.0167728i
$738$	5.57432	−	60.7551i	0.205193	−	2.23642i
$739$	−23.2171	−	40.2133i	−0.854057	−	1.47927i	−0.877517	−	0.479545i	$-0.840802\pi$
$739$	−23.2171	−	40.2133i	−0.854057	−	1.47927i	0.0234608	−	0.999725i	$-0.492532\pi$
$740$	−4.66205	−	8.07491i	−0.171380	−	0.296840i
$741$	14.8492	−	23.2002i	0.545499	−	0.852280i
$742$	21.1129	−	32.5508i	0.775080	−	1.19498i
$743$	−13.0366	+	7.52670i	−0.478267	+	0.276128i	−0.719694	−	0.694291i	$-0.755718\pi$
$743$	−13.0366	+	7.52670i	−0.478267	+	0.276128i	0.241427	+	0.970419i	$0.422385\pi$
$744$	−32.5020	−	62.7593i	−1.19158	−	2.30087i
$745$			5.36768i			0.196657i
$746$	5.77513	−	3.33427i	0.211442	−	0.122076i
$747$	−42.6383	−	3.91209i	−1.56005	−	0.143136i
$748$		−	0.680251i		−	0.0248724i
$749$	−16.1461	−	10.4726i	−0.589966	−	0.382660i
$750$	−0.207969	+	4.54286i	−0.00759394	+	0.165882i
$751$	26.5121			0.967440			0.483720	−	0.875223i	$-0.339285\pi$
$751$	26.5121			0.967440			0.483720	+	0.875223i	$0.339285\pi$
$752$	−39.1901	+	67.8792i	−1.42912	+	2.47530i
$753$	−9.41663	+	14.7124i	−0.343161	+	0.536151i
$754$	−141.519	+	81.7061i	−5.15382	+	2.97556i
$755$	2.24506			0.0817060
$756$	−43.9876	+	50.9037i	−1.59981	+	1.85135i
$757$	0.366541			0.0133222			0.00666108	−	0.999978i	$-0.497880\pi$
$757$	0.366541			0.0133222			0.00666108	+	0.999978i	$0.497880\pi$
$758$	22.5638	−	13.0272i	0.819554	−	0.473170i
$759$	−0.0770342	+	0.120357i	−0.00279616	+	0.00436869i
$760$	−9.77301	+	16.9274i	−0.354504	+	0.614020i
$761$	14.3679			0.520835			0.260418	−	0.965496i	$-0.416140\pi$
$761$	14.3679			0.520835			0.260418	+	0.965496i	$0.416140\pi$
$762$	−0.938675	+	20.5044i	−0.0340046	+	0.742796i
$763$	13.5003	+	26.4594i	0.488745	+	0.957894i
$764$			65.2823i			2.36183i
$765$	2.22953	−	3.15562i	0.0806090	−	0.114092i
$766$	−36.3126	+	20.9651i	−1.31203	+	0.757499i
$767$		−	14.6525i		−	0.529071i
$768$	9.72526	+	18.7789i	0.350930	+	0.677624i
$769$	−16.6324	+	9.60274i	−0.599781	+	0.346284i	−0.768955	−	0.639302i	$-0.779223\pi$
$769$	−16.6324	+	9.60274i	−0.599781	+	0.346284i	0.169174	+	0.985586i	$0.445890\pi$
$770$	−0.340755	−	0.667848i	−0.0122800	−	0.0240676i
$771$	−1.76103	+	2.75140i	−0.0634218	+	0.0990894i
$772$	37.6481	+	65.2084i	1.35498	+	2.34690i
$773$	8.19251	+	14.1898i	0.294664	+	0.510373i	0.974907	−	0.222614i	$-0.0714589\pi$
$773$	8.19251	+	14.1898i	0.294664	+	0.510373i	−0.680243	+	0.732987i	$0.738126\pi$
$774$	−53.5273	+	24.6852i	−1.92400	+	0.887292i
$775$	4.65132	+	2.68544i	0.167080	+	0.0964639i
$776$	31.4255	−	54.4306i	1.12811	−	1.95395i
$777$	3.60851	+	7.95090i	0.129454	+	0.285237i
$778$	−27.9474	−	48.4063i	−1.00196	−	1.73545i
$779$			19.9274i			0.713973i
$780$	−44.1295	−	28.2449i	−1.58009	−	1.01133i
$781$	1.10474			0.0395306
$782$	1.29242	−	2.23855i	0.0462170	−	0.0800502i
$783$	41.3034	+	32.1115i	1.47606	+	1.14757i
$784$	−29.0005	−	64.9409i	−1.03573	−	2.31932i
$785$	13.6999	+	7.90965i	0.488971	+	0.282308i
$786$	0.475190	−	10.3800i	0.0169495	−	0.370244i
$787$	20.3684	+	11.7597i	0.726055	+	0.419188i	0.816977	−	0.576670i	$-0.195648\pi$
$787$	20.3684	+	11.7597i	0.726055	+	0.419188i	−0.0909221	+	0.995858i	$0.528981\pi$
$788$	−51.3304	−	29.6356i	−1.82857	−	1.05573i
$789$	−41.8414	−	26.7805i	−1.48959	−	0.953409i
$790$	23.1545	+	13.3683i	0.823800	+	0.475621i
$791$	−33.3414	+	17.0117i	−1.18548	+	0.604867i
$792$	1.03020	+	2.23389i	0.0366067	+	0.0793779i
$793$	25.8916	−	44.8456i	0.919439	−	1.59251i
$794$	−22.5199			−0.799202
$795$	0.442399	−	9.66377i	0.0156903	−	0.342738i
$796$		−	4.55210i		−	0.161345i
$797$	7.30322	+	12.6495i	0.258693	+	0.448070i	0.965892	−	0.258945i	$-0.0833748\pi$
$797$	7.30322	+	12.6495i	0.258693	+	0.448070i	−0.707199	+	0.707015i	$0.750041\pi$
$798$	18.0147	−	25.1727i	0.637712	−	0.891103i
$799$	−4.96776	+	8.60441i	−0.175747	+	0.304402i
$800$	9.94350	+	5.74088i	0.351556	+	0.202971i
$801$	−1.99886	−	0.183397i	−0.0706263	−	0.00648001i
$802$	−27.8662	−	48.2657i	−0.983990	−	1.70432i
$803$	0.605609	+	1.04895i	0.0213715	+	0.0370165i
$804$	71.4425	+	3.27058i	2.51958	+	0.115345i
$805$	0.104718	−	2.01970i	0.00369081	−	0.0711851i
$806$	−75.4911	+	43.5848i	−2.65906	+	1.53521i
$807$	53.9523	+	2.46989i	1.89921	+	0.0869444i
$808$		−	85.0092i		−	2.99061i
$809$	−29.0893	+	16.7947i	−1.02272	+	0.590471i	−0.914892	−	0.403699i	$-0.867724\pi$
$809$	−29.0893	+	16.7947i	−1.02272	+	0.590471i	−0.107833	+	0.994169i	$0.534391\pi$
$810$	−4.29996	+	23.2356i	−0.151085	+	0.816416i
$811$			39.1986i			1.37645i	0.725499	+	0.688224i	$0.241609\pi$
$811$			39.1986i			1.37645i	−0.725499	+	0.688224i	$0.758391\pi$
$812$	−116.119	+	59.2471i	−4.07497	+	2.07916i
$813$	−16.1967	+	8.38802i	−0.568045	+	0.294181i
$814$	0.539943			0.0189250
$815$	−4.56650	+	7.90941i	−0.159957	+	0.277054i
$816$	−10.4231	−	20.1263i	−0.364880	−	0.704561i
$817$	16.6735	−	9.62645i	0.583332	−	0.336787i
$818$	−9.24039			−0.323083
$819$	38.5521	+	30.3487i	1.34712	+	1.06047i
$820$	37.9043			1.32368
$821$	17.6061	−	10.1649i	0.614458	−	0.354758i	−0.160250	−	0.987076i	$-0.551230\pi$
$821$	17.6061	−	10.1649i	0.614458	−	0.354758i	0.774708	+	0.632319i	$0.217897\pi$
$822$	62.0748	+	2.84173i	2.16511	+	0.0991168i
$823$	12.6928	−	21.9846i	0.442443	−	0.766334i	−0.555427	−	0.831565i	$-0.687445\pi$
$823$	12.6928	−	21.9846i	0.442443	−	0.766334i	0.997870	+	0.0652312i	$0.0207785\pi$
$824$	19.4138			0.676311
$825$	−0.157453	−	0.100777i	−0.00548182	−	0.00350862i
$826$	0.852588	−	16.4439i	0.0296653	−	0.572158i
$827$		−	2.03073i		−	0.0706153i	−0.999376	−	0.0353076i	$-0.988759\pi$
$827$		−	2.03073i		−	0.0706153i	0.999376	−	0.0353076i	$-0.0112411\pi$
$828$	−1.02532	+	11.1751i	−0.0356325	+	0.388362i
$829$	31.5729	−	18.2286i	1.09657	−	0.633107i	0.161255	−	0.986913i	$-0.448446\pi$
$829$	31.5729	−	18.2286i	1.09657	−	0.633107i	0.935319	+	0.353806i	$0.115113\pi$
$830$		−	37.4733i		−	1.30072i
$831$	20.0380	−	31.3071i	0.695111	−	1.08603i
$832$	−52.5998	+	30.3685i	−1.82357	+	1.05284i
$833$	−3.67612	−	8.23195i	−0.127370	−	0.285220i
$834$	34.2836	+	66.1995i	1.18714	+	2.29230i
$835$	−1.79055	−	3.10133i	−0.0619646	−	0.107326i
$836$	−0.679424	−	1.17680i	−0.0234984	−	0.0407004i
$837$	22.0327	+	17.1293i	0.761560	+	0.592077i
$838$	46.5930	+	26.9005i	1.60953	+	0.929262i
$839$	25.1634	−	43.5842i	0.868735	−	1.50469i	0.00544570	−	0.999985i	$-0.498267\pi$
$839$	25.1634	−	43.5842i	0.868735	−	1.50469i	0.863290	−	0.504709i	$-0.168400\pi$
$840$	−28.3125	−	20.2617i	−0.976875	−	0.699094i
$841$	36.1874	+	62.6785i	1.24784	+	2.16133i
$842$		−	72.1348i		−	2.48593i
$843$	−13.2160	+	6.84432i	−0.455182	+	0.235731i
$844$	44.5909			1.53488
$845$	−12.6056	+	21.8335i	−0.433646	+	0.751097i
$846$	5.55180	−	60.5096i	0.190875	−	2.08036i
$847$	−29.0334	−	1.50533i	−0.997601	−	0.0517238i
$848$	−49.1448	−	28.3738i	−1.68764	−	0.974359i
$849$	−7.04417	+	3.64806i	−0.241755	+	0.125201i
$850$	2.92850	+	1.69077i	0.100447	+	0.0579929i
$851$	1.26133	+	0.728228i	0.0432378	+	0.0249633i
$852$	77.0386	−	39.8970i	2.63930	−	1.36685i
$853$	31.9795	+	18.4634i	1.09496	+	0.632175i	0.934892	−	0.354932i	$-0.115496\pi$
$853$	31.9795	+	18.4634i	1.09496	+	0.632175i	0.160066	+	0.987106i	$0.448829\pi$
$854$	31.6666	−	48.8220i	1.08361	−	1.67065i
$855$	0.705185	−	7.68588i	0.0241168	−	0.262852i
$856$	−27.6316	+	47.8593i	−0.944428	+	1.63580i
$857$	39.7259			1.35701			0.678505	−	0.734596i	$-0.262628\pi$
$857$	39.7259			1.35701			0.678505	+	0.734596i	$0.262628\pi$
$858$	2.69422	−	1.39529i	0.0919792	−	0.0476345i
$859$		−	40.2393i		−	1.37295i	−0.727155	−	0.686474i	$-0.759158\pi$
$859$		−	40.2393i		−	1.37295i	0.727155	−	0.686474i	$-0.240842\pi$
$860$	−18.3107	−	31.7150i	−0.624388	−	1.08147i
$861$	−35.3263	−	3.45702i	−1.20392	−	0.117815i
$862$	2.04150	−	3.53597i	0.0695336	−	0.120436i
$863$	−38.0305	−	21.9569i	−1.29457	−	0.747422i	−0.315112	−	0.949054i	$-0.602042\pi$
$863$	−38.0305	−	21.9569i	−1.29457	−	0.747422i	−0.979461	+	0.201632i	$0.935376\pi$
$864$	47.1010	+	36.6188i	1.60241	+	1.24580i
$865$	0.0553457	+	0.0958615i	0.00188181	+	0.00325939i
$866$	10.8628	+	18.8149i	0.369133	+	0.639358i
$867$	12.2196	+	23.5954i	0.415001	+	0.801341i
$868$	−61.9416	+	31.6044i	−2.10244	+	1.07272i
$869$	−0.951830	+	0.549539i	−0.0322886	+	0.0186418i
$870$	−24.6833	+	38.5649i	−0.836843	+	1.30747i
$871$		−	52.1574i		−	1.76729i
$872$	73.8703	−	42.6490i	2.50156	−	1.44428i
$873$	−2.26755	+	24.7143i	−0.0767450	+	0.836452i
$874$		−	5.16342i		−	0.174655i
$875$	2.64220	+	0.136993i	0.0893227	+	0.00463122i
$876$	80.1140	+	51.2767i	2.70680	+	1.73248i
$877$	−12.5212			−0.422811			−0.211406	−	0.977398i	$-0.567804\pi$
$877$	−12.5212			−0.422811			−0.211406	+	0.977398i	$0.567804\pi$
$878$	4.68791	−	8.11969i	0.158209	−	0.274026i
$879$	−11.0494	−	0.505831i	−0.372686	−	0.0170613i
$880$	−0.949697	+	0.548308i	−0.0320143	+	0.0184835i
$881$	5.13011			0.172838			0.0864189	−	0.996259i	$-0.472458\pi$
$881$	5.13011			0.172838			0.0864189	+	0.996259i	$0.472458\pi$
$882$	41.4996	+	36.3024i	1.39737	+	1.22237i
$883$	10.5436			0.354820			0.177410	−	0.984137i	$-0.443228\pi$
$883$	10.5436			0.354820			0.177410	+	0.984137i	$0.443228\pi$
$884$	−33.7402	+	19.4799i	−1.13480	+	0.655180i
$885$	−1.88805	−	3.64571i	−0.0634662	−	0.122549i
$886$	−44.1010	+	76.3852i	−1.48160	+	2.56621i
$887$	13.3651			0.448757			0.224379	−	0.974502i	$-0.427965\pi$
$887$	13.3651			0.448757			0.224379	+	0.974502i	$0.427965\pi$
$888$	22.2643	−	11.5303i	0.747140	−	0.386931i
$889$	11.9257	+	0.618325i	0.399975	+	0.0207380i
$890$		−	1.75673i		−	0.0588858i
$891$	−0.738816	−	0.630663i	−0.0247513	−	0.0211280i
$892$	−27.2383	+	15.7260i	−0.912005	+	0.526546i
$893$			19.8469i			0.664151i
$894$	−24.3847	−	1.11631i	−0.815545	−	0.0373350i
$895$	−0.238794	+	0.137868i	−0.00798200	+	0.00460841i
$896$	−6.67950	+	3.40807i	−0.223147	+	0.113856i
$897$	8.17565	+	0.374274i	0.272977	+	0.0124967i
$898$	−10.4535	−	18.1059i	−0.348836	−	0.604202i
$899$	27.0384	+	46.8319i	0.901781	+	1.56193i
$900$	−14.6195	−	1.34135i	−0.487315	−	0.0447115i
$901$	−6.22963	−	3.59668i	−0.207539	−	0.119823i
$902$	−1.09749	+	1.90090i	−0.0365423	+	0.0632932i
$903$	14.1728	+	31.2279i	0.471640	+	1.03920i
$904$	53.7419	+	93.0837i	1.78743	+	3.09592i
$905$			9.56064i			0.317807i
$906$	−0.466901	+	10.1990i	−0.0155118	+	0.338839i
$907$	−58.5432			−1.94389			−0.971947	−	0.235201i	$-0.924425\pi$
$907$	−58.5432			−1.94389			−0.971947	+	0.235201i	$0.924425\pi$
$908$	47.5319	−	82.3277i	1.57740	−	2.73214i
$909$	14.0576	+	30.4824i	0.466260	+	1.01104i
$910$	−23.3670	+	36.0261i	−0.774609	+	1.19425i
$911$	−42.7733	−	24.6952i	−1.41714	−	0.818188i	−0.421097	−	0.907016i	$-0.638355\pi$
$911$	−42.7733	−	24.6952i	−1.41714	−	0.818188i	−0.996047	+	0.0888275i	$0.971688\pi$
$912$	−38.1332	−	24.4070i	−1.26272	−	0.808196i
$913$	1.33407	+	0.770223i	0.0441511	+	0.0254907i
$914$	83.4468	+	48.1780i	2.76018	+	1.59359i
$915$	0.663541	−	14.4944i	0.0219360	−	0.479170i
$916$	−0.332004	−	0.191683i	−0.0109697	−	0.00633337i
$917$	−6.03720	−	0.313018i	−0.199366	−	0.0103368i
$918$	13.8719	+	10.7847i	0.457841	+	0.355949i
$919$	−14.0820	+	24.3908i	−0.464523	+	0.804577i	−0.999180	−	0.0404918i	$-0.987108\pi$
$919$	−14.0820	+	24.3908i	−0.464523	+	0.804577i	0.534657	+	0.845069i	$0.320441\pi$
$920$	−5.80746			−0.191466
$921$	−12.9313	−	8.27663i	−0.426101	−	0.272724i
$922$			17.5487i			0.577935i
$923$	−31.6356	−	54.7945i	−1.04130	−	1.80358i
$924$	2.20403	−	1.00030i	0.0725074	−	0.0329074i
$925$	−0.952679	+	1.65009i	−0.0313239	+	0.0542546i
$926$	−15.6977	−	9.06306i	−0.515858	−	0.297831i
$927$	−6.96134	+	3.21036i	−0.228640	+	0.105442i
$928$	57.8021	+	100.116i	1.89745	+	3.28648i
$929$	−12.1384	−	21.0243i	−0.398248	−	0.689785i	0.595262	−	0.803532i	$-0.297048\pi$
$929$	−12.1384	−	21.0243i	−0.398248	−	0.689785i	−0.993510	+	0.113746i	$0.963715\pi$
$930$	−13.1669	+	20.5718i	−0.431761	+	0.674577i
$931$	−14.5814	−	10.5692i	−0.477887	−	0.346391i
$932$	66.0353	−	38.1255i	2.16306	−	1.24884i
$933$	−5.42914	−	10.4833i	−0.177742	−	0.343209i
$934$		−	19.1011i		−	0.625006i
$935$	−0.120384	+	0.0695038i	−0.00393698	+	0.00227302i
$936$	81.2988	−	115.068i	2.65734	−	3.76112i
$937$			40.1097i			1.31033i	0.755487	+	0.655163i	$0.227400\pi$
$937$			40.1097i			1.31033i	−0.755487	+	0.655163i	$0.772600\pi$
$938$	3.03489	−	58.5343i	0.0990928	−	1.91121i
$939$	−0.958807	+	20.9442i	−0.0312895	+	0.683487i
$940$	37.7512			1.23131
$941$	7.28495	−	12.6179i	0.237482	−	0.411332i	−0.722509	−	0.691362i	$-0.757011\pi$
$941$	7.28495	−	12.6179i	0.237482	−	0.411332i	0.959991	+	0.280030i	$0.0903444\pi$
$942$	−38.7816	+	60.5919i	−1.26357	+	1.97419i
$943$	−5.12754	+	2.96039i	−0.166976	+	0.0964035i
$944$	−24.0837			−0.783856
$945$	13.5028	+	2.58347i	0.439246	+	0.0840402i
$946$	2.12068			0.0689492
$947$	44.2920	−	25.5720i	1.43930	−	0.830978i	0.441495	−	0.897264i	$-0.354448\pi$
$947$	44.2920	−	25.5720i	1.43930	−	0.830978i	0.997801	+	0.0662863i	$0.0211151\pi$
$948$	−46.5293	+	72.6967i	−1.51120	+	2.36108i
$949$	34.6849	−	60.0759i	1.12592	−	1.95015i
$950$	6.75486			0.219157
$951$	−0.857933	+	18.7407i	−0.0278204	+	0.607708i
$952$	−23.0602	+	11.7660i	−0.747385	+	0.381337i
$953$			11.2676i			0.364992i	0.983207	+	0.182496i	$0.0584177\pi$
$953$			11.2676i			0.364992i	−0.983207	+	0.182496i	$0.941582\pi$
$954$	43.8092	+	4.01952i	1.41837	+	0.130137i
$955$	11.5530	−	6.67014i	0.373847	−	0.215841i
$956$			53.7250i			1.73759i
$957$	−0.865588	−	1.67140i	−0.0279805	−	0.0540285i
$958$	−35.8063	+	20.6728i	−1.15685	+	0.667907i
$959$	1.87191	−	36.1037i	0.0604471	−	1.16585i
$960$	−9.17431	+	14.3338i	−0.296100	+	0.462622i
$961$	−1.07680	−	1.86508i	−0.0347355	−	0.0601637i
$962$	−15.4620	−	26.7810i	−0.498515	−	0.863453i
$963$	1.99379	−	21.7306i	0.0642491	−	0.700257i
$964$	100.260	+	57.8852i	3.22916	+	1.86436i
$965$	7.69329	−	13.3252i	0.247656	−	0.428952i
$966$	9.15344	+	0.895753i	0.294507	+	0.0288204i
$967$	18.2443	+	31.6001i	0.586697	+	1.01619i	0.994661	+	0.103192i	$0.0329055\pi$
$967$	18.2443	+	31.6001i	0.586697	+	1.01619i	−0.407964	+	0.912998i	$0.633761\pi$
$968$			83.4830i			2.68325i
$969$	−4.83378	−	3.09384i	−0.155283	−	0.0993886i
$970$	−21.7206			−0.697405
$971$	−15.7734	+	27.3203i	−0.506193	+	0.876752i	0.493781	+	0.869586i	$0.335614\pi$
$971$	−15.7734	+	27.3203i	−0.506193	+	0.876752i	−0.999974	+	0.00716569i	$0.997719\pi$
$972$	−74.2971	−	17.2972i	−2.38308	−	0.554807i
$973$	38.6341	−	19.7122i	1.23855	−	0.631946i
$974$	−33.7390	−	19.4792i	−1.08107	−	0.624155i
$975$	−0.489632	+	10.6955i	−0.0156808	+	0.342530i
$976$	−73.7108	−	42.5570i	−2.35943	−	1.36221i
$977$	−25.9666	−	14.9918i	−0.830744	−	0.479630i	0.0233634	−	0.999727i	$-0.492563\pi$
$977$	−25.9666	−	14.9918i	−0.830744	−	0.479630i	−0.854107	+	0.520097i	$0.825896\pi$
$978$	−34.9817	−	22.3899i	−1.11859	−	0.715950i
$979$	0.0625403	+	0.0361077i	0.00199880	+	0.00115401i
$980$	−20.1039	+	27.7356i	−0.642194	+	0.885982i
$981$	−19.4355	+	27.5086i	−0.620529	+	0.878281i
$982$	−43.8643	+	75.9751i	−1.39976	+	2.42446i
$983$	1.24727			0.0397819			0.0198909	−	0.999802i	$-0.493668\pi$
$983$	1.24727			0.0397819			0.0198909	+	0.999802i	$0.493668\pi$
$984$	−4.66120	+	101.819i	−0.148594	+	3.24588i
$985$			12.1119i			0.385918i
$986$	17.0235	+	29.4856i	0.542140	+	0.939014i
$987$	−35.1836	−	3.44305i	−1.11991	−	0.109594i
$988$	−38.9124	+	67.3983i	−1.23797	+	2.14423i
$989$	4.95398	+	2.86018i	0.157528	+	0.0909486i
$990$	0.490563	−	0.694330i	0.0155911	−	0.0220673i
$991$	3.10232	+	5.37338i	0.0985485	+	0.170691i	0.911084	−	0.412221i	$-0.135247\pi$
$991$	3.10232	+	5.37338i	0.0985485	+	0.170691i	−0.812536	+	0.582912i	$0.801913\pi$
$992$	30.8336	+	53.4054i	0.978968	+	1.69562i
$993$	27.9392	+	1.27904i	0.886625	+	0.0405890i
$994$	−32.3152	−	63.3347i	−1.02497	−	2.00885i
$995$	−0.805586	+	0.465105i	−0.0255388	+	0.0147448i
$996$	120.847	+	5.53227i	3.82918	+	0.175297i
$997$			53.3709i			1.69027i	0.534551	+	0.845137i	$0.320481\pi$
$997$			53.3709i			1.69027i	−0.534551	+	0.845137i	$0.679519\pi$
$998$	24.3062	−	14.0332i	0.769400	−	0.444213i
$999$	−6.07675	+	7.81624i	−0.192260	+	0.247295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.236.1	yes	32
3.2	odd	2		945.2.be.c.656.16		32
7.3	odd	6		315.2.t.c.101.1	✓	32
9.4	even	3		945.2.t.c.341.1		32
9.5	odd	6		315.2.t.c.131.16	yes	32
21.17	even	6		945.2.t.c.521.16		32
63.31	odd	6		945.2.be.c.206.16		32
63.59	even	6	inner	315.2.be.c.311.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.1	✓	32	7.3	odd	6
315.2.t.c.131.16	yes	32	9.5	odd	6
315.2.be.c.236.1	yes	32	1.1	even	1	trivial
315.2.be.c.311.1	yes	32	63.59	even	6	inner
945.2.t.c.341.1		32	9.4	even	3
945.2.t.c.521.16		32	21.17	even	6
945.2.be.c.206.16		32	63.31	odd	6
945.2.be.c.656.16		32	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27381 + 1.31279i) q^{2} +(-0.933716 + 1.45883i) q^{3} +(2.44681 - 4.23800i) q^{4} -1.00000 q^{5} +(0.207969 - 4.54286i) q^{6} +(-2.64220 - 0.136993i) q^{7} +7.59741i q^{8} +(-1.25635 - 2.72426i) q^{9} +O(q^{10})\)	\(q+(-2.27381 + 1.31279i) q^{2} +(-0.933716 + 1.45883i) q^{3} +(2.44681 - 4.23800i) q^{4} -1.00000 q^{5} +(0.207969 - 4.54286i) q^{6} +(-2.64220 - 0.136993i) q^{7} +7.59741i q^{8} +(-1.25635 - 2.72426i) q^{9} +(2.27381 - 1.31279i) q^{10} +0.107931i q^{11} +(3.89788 + 7.52656i) q^{12} +(5.35335 - 3.09076i) q^{13} +(6.18771 - 3.15715i) q^{14} +(0.933716 - 1.45883i) q^{15} +(-5.08015 - 8.79908i) q^{16} +(-0.643963 - 1.11538i) q^{17} +(6.43307 + 4.54514i) q^{18} +(-2.22804 - 1.28636i) q^{19} +(-2.44681 + 4.23800i) q^{20} +(2.66692 - 3.72660i) q^{21} +(-0.141691 - 0.245416i) q^{22} -0.764400i q^{23} +(-11.0833 - 7.09383i) q^{24} +1.00000 q^{25} +(-8.11501 + 14.0556i) q^{26} +(5.14729 + 0.710892i) q^{27} +(-7.04555 + 10.8625i) q^{28} +(8.71958 + 5.03425i) q^{29} +(-0.207969 + 4.54286i) q^{30} +(4.65132 + 2.68544i) q^{31} +(9.94350 + 5.74088i) q^{32} +(-0.157453 - 0.100777i) q^{33} +(2.92850 + 1.69077i) q^{34} +(2.64220 + 0.136993i) q^{35} +(-14.6195 - 1.34135i) q^{36} +(-0.952679 + 1.65009i) q^{37} +6.75486 q^{38} +(-0.489632 + 10.6955i) q^{39} -7.59741i q^{40} +(-3.87282 - 6.70793i) q^{41} +(-1.17184 + 11.9747i) q^{42} +(-3.74174 + 6.48088i) q^{43} +(0.457414 + 0.264088i) q^{44} +(1.25635 + 2.72426i) q^{45} +(1.00349 + 1.73810i) q^{46} +(-3.85718 - 6.68083i) q^{47} +(17.5797 + 0.804786i) q^{48} +(6.96247 + 0.723928i) q^{49} +(-2.27381 + 1.31279i) q^{50} +(2.22842 + 0.102015i) q^{51} -30.2500i q^{52} +(4.83694 - 2.79261i) q^{53} +(-12.6372 + 5.14086i) q^{54} -0.107931i q^{55} +(1.04080 - 20.0739i) q^{56} +(3.95694 - 2.04923i) q^{57} -26.4356 q^{58} +(1.18518 - 2.05280i) q^{59} +(-3.89788 - 7.52656i) q^{60} +(7.25479 - 4.18855i) q^{61} -14.1016 q^{62} +(2.94632 + 7.37016i) q^{63} -9.82559 q^{64} +(-5.35335 + 3.09076i) q^{65} +(0.490318 + 0.0224463i) q^{66} +(4.21881 - 7.30720i) q^{67} -6.30262 q^{68} +(1.11513 + 0.713733i) q^{69} +(-6.18771 + 3.15715i) q^{70} -10.2356i q^{71} +(20.6973 - 9.54499i) q^{72} +(9.71863 - 5.61106i) q^{73} -5.00265i q^{74} +(-0.933716 + 1.45883i) q^{75} +(-10.9032 + 6.29496i) q^{76} +(0.0147859 - 0.285177i) q^{77} +(-12.9276 - 24.9623i) q^{78} +(5.09156 + 8.81884i) q^{79} +(5.08015 + 8.79908i) q^{80} +(-5.84318 + 6.84524i) q^{81} +(17.6121 + 10.1684i) q^{82} +(7.13623 - 12.3603i) q^{83} +(-9.26790 - 20.4207i) q^{84} +(0.643963 + 1.11538i) q^{85} -19.6484i q^{86} +(-15.4857 + 8.01979i) q^{87} -0.819999 q^{88} +(0.334543 - 0.579445i) q^{89} +(-6.43307 - 4.54514i) q^{90} +(-14.5681 + 7.43304i) q^{91} +(-3.23953 - 1.87034i) q^{92} +(-8.26061 + 4.27803i) q^{93} +(17.5410 + 10.1273i) q^{94} +(2.22804 + 1.28636i) q^{95} +(-17.6594 + 9.14548i) q^{96} +(-7.16437 - 4.13635i) q^{97} +(-16.7817 + 7.49415i) q^{98} +(0.294033 - 0.135599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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