LMFDB - Embedded newform 390.2.bd.c.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	390.37
Dual form			390.2.bd.c.253.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.900968 - 2.04652i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.0298867 - 0.0517653i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.900968 - 2.04652i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.0298867 - 0.0517653i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.80352 - 1.32186i) q^{10} +(2.65266 + 0.710778i) q^{11} +(0.707107 - 0.707107i) q^{12} +(0.914264 - 3.48771i) q^{13} -0.0597735i q^{14} +(-0.340590 - 2.20998i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.22446 + 4.56975i) q^{17} +1.00000 q^{18} +(-2.19449 - 8.18996i) q^{19} +(-2.22283 - 0.243000i) q^{20} +(0.0422662 - 0.0422662i) q^{21} +(2.65266 - 0.710778i) q^{22} +(-0.837992 + 3.12743i) q^{23} +(0.258819 - 0.965926i) q^{24} +(-3.37651 + 3.68770i) q^{25} +(-0.952079 - 3.47758i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.0298867 - 0.0517653i) q^{28} +(-3.06351 + 1.76872i) q^{29} +(-1.39995 - 1.74360i) q^{30} +(5.45532 + 5.45532i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.37831 + 1.37312i) q^{33} +(3.34529 + 3.34529i) q^{34} +(-0.132866 - 0.0145249i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.224405 + 0.388680i) q^{37} +(-5.99546 - 5.99546i) q^{38} +(1.78580 - 3.13224i) q^{39} +(-2.04652 + 0.900968i) q^{40} +(-2.07938 + 7.76037i) q^{41} +(0.0154705 - 0.0577367i) q^{42} +(-3.94997 + 1.05839i) q^{43} +(1.94188 - 1.94188i) q^{44} +(0.243000 - 2.22283i) q^{45} +(0.837992 + 3.12743i) q^{46} +8.10752 q^{47} +(-0.258819 - 0.965926i) q^{48} +(3.49821 + 6.05908i) q^{49} +(-1.08029 + 4.88190i) q^{50} +4.73095i q^{51} +(-2.56331 - 2.53563i) q^{52} +(-3.62218 + 3.62218i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-0.935339 - 6.06912i) q^{55} +(-0.0517653 - 0.0298867i) q^{56} -8.47887i q^{57} +(-1.76872 + 3.06351i) q^{58} +(-8.24745 + 2.20990i) q^{59} +(-2.08419 - 0.810029i) q^{60} +(5.07861 - 8.79641i) q^{61} +(7.45211 + 1.99679i) q^{62} +(0.0517653 - 0.0298867i) q^{63} -1.00000 q^{64} +(-7.96140 + 1.27125i) q^{65} +2.74624 q^{66} +(-8.49129 + 4.90245i) q^{67} +(4.56975 + 1.22446i) q^{68} +(-1.61888 + 2.80397i) q^{69} +(-0.122328 + 0.0538540i) q^{70} +(-1.76948 + 0.474132i) q^{71} +(0.500000 - 0.866025i) q^{72} +11.0595i q^{73} +(0.388680 + 0.224405i) q^{74} +(-4.21591 + 2.68814i) q^{75} +(-8.18996 - 2.19449i) q^{76} +(0.116073 - 0.116073i) q^{77} +(-0.0195744 - 3.60550i) q^{78} -12.6945i q^{79} +(-1.32186 + 1.80352i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.07938 + 7.76037i) q^{82} +0.810683 q^{83} +(-0.0154705 - 0.0577367i) q^{84} +(8.24889 - 6.62308i) q^{85} +(-2.89158 + 2.89158i) q^{86} +(-3.41690 + 0.915555i) q^{87} +(0.710778 - 2.65266i) q^{88} +(3.49929 - 13.0595i) q^{89} +(-0.900968 - 2.04652i) q^{90} +(-0.153218 - 0.151563i) q^{91} +(2.28944 + 2.28944i) q^{92} +(3.85749 + 6.68138i) q^{93} +(7.02131 - 4.05376i) q^{94} +(-14.7838 + 11.8700i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(9.22020 + 5.32328i) q^{97} +(6.05908 + 3.49821i) q^{98} +(1.94188 + 1.94188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 4 q^{11} + 20 q^{13} + 4 q^{15} - 16 q^{16} - 20 q^{17} + 32 q^{18} - 20 q^{19} + 8 q^{21} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{26} - 24 q^{29} + 4 q^{30} + 12 q^{31} - 12 q^{33} + 16 q^{34} + 12 q^{35} + 20 q^{37} + 4 q^{38} + 20 q^{39} - 28 q^{41} + 8 q^{42} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} + 28 q^{50} + 16 q^{52} - 4 q^{53} - 40 q^{55} - 12 q^{56} - 36 q^{59} - 4 q^{60} - 28 q^{61} - 36 q^{62} + 12 q^{63} - 32 q^{64} - 32 q^{65} - 36 q^{67} - 4 q^{68} + 20 q^{69} - 24 q^{70} - 4 q^{71} + 16 q^{72} - 24 q^{74} - 16 q^{76} - 20 q^{77} - 16 q^{78} + 16 q^{81} + 28 q^{82} - 40 q^{83} - 8 q^{84} + 88 q^{85} - 8 q^{86} - 16 q^{87} - 8 q^{88} + 16 q^{89} - 40 q^{91} + 20 q^{92} + 24 q^{94} - 8 q^{95} + 72 q^{97} + 72 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 4 * q^11 + 20 * q^13 + 4 * q^15 - 16 * q^16 - 20 * q^17 + 32 * q^18 - 20 * q^19 + 8 * q^21 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^26 - 24 * q^29 + 4 * q^30 + 12 * q^31 - 12 * q^33 + 16 * q^34 + 12 * q^35 + 20 * q^37 + 4 * q^38 + 20 * q^39 - 28 * q^41 + 8 * q^42 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 + 28 * q^50 + 16 * q^52 - 4 * q^53 - 40 * q^55 - 12 * q^56 - 36 * q^59 - 4 * q^60 - 28 * q^61 - 36 * q^62 + 12 * q^63 - 32 * q^64 - 32 * q^65 - 36 * q^67 - 4 * q^68 + 20 * q^69 - 24 * q^70 - 4 * q^71 + 16 * q^72 - 24 * q^74 - 16 * q^76 - 20 * q^77 - 16 * q^78 + 16 * q^81 + 28 * q^82 - 40 * q^83 - 8 * q^84 + 88 * q^85 - 8 * q^86 - 16 * q^87 - 8 * q^88 + 16 * q^89 - 40 * q^91 + 20 * q^92 + 24 * q^94 - 8 * q^95 + 72 * q^97 + 72 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.900968	−	2.04652i	−0.402925	−	0.915233i
$5$	−0.900968	−	2.04652i	−0.402925	−	0.915233i
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	0.0298867	−	0.0517653i	0.0112961	−	0.0195655i	−0.860322	−	0.509751i	$-0.829738\pi$
$7$	0.0298867	−	0.0517653i	0.0112961	−	0.0195655i	0.871618	+	0.490185i	$0.163071\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−1.80352	−	1.32186i	−0.570324	−	0.418008i
$11$	2.65266	+	0.710778i	0.799807	+	0.214308i	0.635499	−	0.772101i	$-0.280794\pi$
$11$	2.65266	+	0.710778i	0.799807	+	0.214308i	0.164308	+	0.986409i	$0.447461\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	0.914264	−	3.48771i	0.253571	−	0.967317i
$13$	0.914264	−	3.48771i	0.253571	−	0.967317i
$14$		−	0.0597735i		−	0.0159751i
$15$	−0.340590	−	2.20998i	−0.0879398	−	0.570614i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.22446	+	4.56975i	0.296975	+	1.10833i	0.939636	+	0.342176i	$0.111164\pi$
$17$	1.22446	+	4.56975i	0.296975	+	1.10833i	−0.642661	+	0.766151i	$0.722170\pi$
$18$	1.00000			0.235702
$19$	−2.19449	−	8.18996i	−0.503451	−	1.87890i	−0.476318	−	0.879273i	$-0.658029\pi$
$19$	−2.19449	−	8.18996i	−0.503451	−	1.87890i	−0.0271328	−	0.999632i	$-0.508638\pi$
$20$	−2.22283	−	0.243000i	−0.497039	−	0.0543364i
$21$	0.0422662	−	0.0422662i	0.00922324	−	0.00922324i
$22$	2.65266	−	0.710778i	0.565549	−	0.151538i
$23$	−0.837992	+	3.12743i	−0.174733	+	0.652114i	0.821864	+	0.569684i	$0.192935\pi$
$23$	−0.837992	+	3.12743i	−0.174733	+	0.652114i	−0.996597	+	0.0824293i	$0.973732\pi$
$24$	0.258819	−	0.965926i	0.0528312	−	0.197169i
$25$	−3.37651	+	3.68770i	−0.675302	+	0.737541i
$26$	−0.952079	−	3.47758i	−0.186718	−	0.682009i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.0298867	−	0.0517653i	−0.00564806	−	0.00978273i
$29$	−3.06351	+	1.76872i	−0.568879	+	0.328442i	−0.756701	−	0.653761i	$-0.773190\pi$
$29$	−3.06351	+	1.76872i	−0.568879	+	0.328442i	0.187823	+	0.982203i	$0.439857\pi$
$30$	−1.39995	−	1.74360i	−0.255594	−	0.318337i
$31$	5.45532	+	5.45532i	0.979804	+	0.979804i	0.999800	−	0.0199957i	$-0.00636524\pi$
$31$	5.45532	+	5.45532i	0.979804	+	0.979804i	−0.0199957	+	0.999800i	$0.506365\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.37831	+	1.37312i	0.414011	+	0.239029i
$34$	3.34529	+	3.34529i	0.573712	+	0.573712i
$35$	−0.132866	−	0.0145249i	−0.0224584	−	0.00245516i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	0.224405	+	0.388680i	0.0368919	+	0.0638987i	0.883882	−	0.467710i	$-0.154921\pi$
$37$	0.224405	+	0.388680i	0.0368919	+	0.0638987i	−0.846990	+	0.531609i	$0.821588\pi$
$38$	−5.99546	−	5.99546i	−0.972593	−	0.972593i
$39$	1.78580	−	3.13224i	0.285956	−	0.501560i
$40$	−2.04652	+	0.900968i	−0.323584	+	0.142456i
$41$	−2.07938	+	7.76037i	−0.324745	+	1.21197i	0.589823	+	0.807533i	$0.299198\pi$
$41$	−2.07938	+	7.76037i	−0.324745	+	1.21197i	−0.914568	+	0.404433i	$0.867469\pi$
$42$	0.0154705	−	0.0577367i	0.00238715	−	0.00890897i
$43$	−3.94997	+	1.05839i	−0.602365	+	0.161403i	−0.547098	−	0.837068i	$-0.684268\pi$
$43$	−3.94997	+	1.05839i	−0.602365	+	0.161403i	−0.0552666	+	0.998472i	$0.517601\pi$
$44$	1.94188	−	1.94188i	0.292750	−	0.292750i
$45$	0.243000	−	2.22283i	0.0362243	−	0.331359i
$46$	0.837992	+	3.12743i	0.123555	+	0.461114i
$47$	8.10752			1.18260			0.591301	−	0.806451i	$-0.298614\pi$
$47$	8.10752			1.18260			0.591301	+	0.806451i	$0.298614\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	3.49821	+	6.05908i	0.499745	+	0.865583i
$50$	−1.08029	+	4.88190i	−0.152776	+	0.690405i
$51$			4.73095i			0.662465i
$52$	−2.56331	−	2.53563i	−0.355468	−	0.351629i
$53$	−3.62218	+	3.62218i	−0.497544	+	0.497544i	−0.910673	−	0.413128i	$-0.864436\pi$
$53$	−3.62218	+	3.62218i	−0.497544	+	0.497544i	0.413128	+	0.910673i	$0.364436\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	−0.935339	−	6.06912i	−0.126121	−	0.818360i
$56$	−0.0517653	−	0.0298867i	−0.00691743	−	0.00399378i
$57$		−	8.47887i		−	1.12305i
$58$	−1.76872	+	3.06351i	−0.232244	+	0.402258i
$59$	−8.24745	+	2.20990i	−1.07373	+	0.287704i	−0.752023	−	0.659137i	$-0.770922\pi$
$59$	−8.24745	+	2.20990i	−1.07373	+	0.287704i	−0.321703	+	0.946841i	$0.604255\pi$
$60$	−2.08419	−	0.810029i	−0.269068	−	0.104574i
$61$	5.07861	−	8.79641i	0.650250	−	1.12627i	−0.332813	−	0.942993i	$-0.607998\pi$
$61$	5.07861	−	8.79641i	0.650250	−	1.12627i	0.983062	−	0.183272i	$-0.0586690\pi$
$62$	7.45211	+	1.99679i	0.946418	+	0.253592i
$63$	0.0517653	−	0.0298867i	0.00652182	−	0.00376537i
$64$	−1.00000			−0.125000
$65$	−7.96140	+	1.27125i	−0.987490	+	0.157680i
$66$	2.74624			0.338038
$67$	−8.49129	+	4.90245i	−1.03738	+	0.598930i	−0.919089	−	0.394050i	$-0.871074\pi$
$67$	−8.49129	+	4.90245i	−1.03738	+	0.598930i	−0.118288	+	0.992979i	$0.537740\pi$
$68$	4.56975	+	1.22446i	0.554163	+	0.148488i
$69$	−1.61888	+	2.80397i	−0.194890	+	0.337559i
$70$	−0.122328	+	0.0538540i	−0.0146210	+	0.00643678i
$71$	−1.76948	+	0.474132i	−0.209999	+	0.0562691i	−0.362285	−	0.932067i	$-0.618003\pi$
$71$	−1.76948	+	0.474132i	−0.209999	+	0.0562691i	0.152286	+	0.988336i	$0.451337\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$			11.0595i			1.29442i	0.762314	+	0.647208i	$0.224063\pi$
$73$			11.0595i			1.29442i	−0.762314	+	0.647208i	$0.775937\pi$
$74$	0.388680	+	0.224405i	0.0451832	+	0.0260865i
$75$	−4.21591	+	2.68814i	−0.486811	+	0.310400i
$76$	−8.18996	−	2.19449i	−0.939452	−	0.251726i
$77$	0.116073	−	0.116073i	0.0132278	−	0.0132278i
$78$	−0.0195744	−	3.60550i	−0.00221636	−	0.408242i
$79$		−	12.6945i		−	1.42824i	−0.700023	−	0.714120i	$-0.746827\pi$
$79$		−	12.6945i		−	1.42824i	0.700023	−	0.714120i	$-0.253173\pi$
$80$	−1.32186	+	1.80352i	−0.147788	+	0.201640i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.07938	+	7.76037i	0.229630	+	0.856989i
$83$	0.810683			0.0889840			0.0444920	−	0.999010i	$-0.485833\pi$
$83$	0.810683			0.0889840			0.0444920	+	0.999010i	$0.485833\pi$
$84$	−0.0154705	−	0.0577367i	−0.00168797	−	0.00629959i
$85$	8.24889	−	6.62308i	0.894718	−	0.718374i
$86$	−2.89158	+	2.89158i	−0.311807	+	0.311807i
$87$	−3.41690	+	0.915555i	−0.366330	+	0.0981578i
$88$	0.710778	−	2.65266i	0.0757692	−	0.282775i
$89$	3.49929	−	13.0595i	0.370924	−	1.38431i	−0.488287	−	0.872683i	$-0.662378\pi$
$89$	3.49929	−	13.0595i	0.370924	−	1.38431i	0.859210	−	0.511623i	$-0.170955\pi$
$90$	−0.900968	−	2.04652i	−0.0949704	−	0.215722i
$91$	−0.153218	−	0.151563i	−0.0160616	−	0.0158882i
$92$	2.28944	+	2.28944i	0.238690	+	0.238690i
$93$	3.85749	+	6.68138i	0.400003	+	0.692826i
$94$	7.02131	−	4.05376i	0.724193	−	0.418113i
$95$	−14.7838	+	11.8700i	−1.51678	+	1.21783i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	9.22020	+	5.32328i	0.936169	+	0.540497i	0.888757	−	0.458378i	$-0.151569\pi$
$97$	9.22020	+	5.32328i	0.936169	+	0.540497i	0.0474117	+	0.998875i	$0.484903\pi$
$98$	6.05908	+	3.49821i	0.612060	+	0.353373i
$99$	1.94188	+	1.94188i	0.195167	+	0.195167i
$100$	1.50539	+	4.76800i	0.150539	+	0.476800i
$101$	−5.01449	+	2.89512i	−0.498960	+	0.288075i	−0.728284	−	0.685275i	$-0.759682\pi$
$101$	−5.01449	+	2.89512i	−0.498960	+	0.288075i	0.229324	+	0.973350i	$0.426348\pi$
$102$	2.36547	+	4.09712i	0.234217	+	0.405676i
$103$	−5.80890	−	5.80890i	−0.572368	−	0.572368i	0.360422	−	0.932790i	$-0.382633\pi$
$103$	−5.80890	−	5.80890i	−0.572368	−	0.572368i	−0.932790	+	0.360422i	$0.882633\pi$
$104$	−3.48771	−	0.914264i	−0.341998	−	0.0896510i
$105$	−0.124579	−	0.0484183i	−0.0121577	−	0.00472514i
$106$	−1.32581	+	4.94799i	−0.128774	+	0.480591i
$107$	−2.06732	+	7.71536i	−0.199856	+	0.745872i	0.791100	+	0.611686i	$0.209508\pi$
$107$	−2.06732	+	7.71536i	−0.199856	+	0.745872i	−0.990956	+	0.134186i	$0.957158\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	8.01003	−	8.01003i	0.767222	−	0.767222i	−0.210394	−	0.977617i	$-0.567475\pi$
$109$	8.01003	−	8.01003i	0.767222	−	0.767222i	0.977617	+	0.210394i	$0.0674748\pi$
$110$	−3.84459	−	4.78834i	−0.366567	−	0.456551i
$111$	0.116160	+	0.433517i	0.0110255	+	0.0411476i
$112$	−0.0597735			−0.00564806
$113$	3.02824	+	11.3016i	0.284873	+	1.06316i	0.948932	+	0.315481i	$0.102166\pi$
$113$	3.02824	+	11.3016i	0.284873	+	1.06316i	−0.664059	+	0.747680i	$0.731168\pi$
$114$	−4.23943	−	7.34291i	−0.397059	−	0.687727i
$115$	7.15536	−	1.10274i	0.667240	−	0.102831i
$116$			3.53743i			0.328442i
$117$	2.53563	−	2.56331i	0.234419	−	0.236978i
$118$	−6.03755	+	6.03755i	−0.555802	+	0.555802i
$119$	0.273150	+	0.0731902i	0.0250396	+	0.00670933i
$120$	−2.20998	+	0.340590i	−0.201742	+	0.0310914i
$121$	−2.99487	−	1.72909i	−0.272261	−	0.157190i
$122$		−	10.1572i		−	0.919592i
$123$	−4.01706	+	6.95775i	−0.362206	+	0.627360i
$124$	7.45211	−	1.99679i	0.669219	−	0.179317i
$125$	10.5891	+	3.58760i	0.947118	+	0.320885i
$126$	0.0298867	−	0.0517653i	0.00266252	−	0.00461162i
$127$	−14.9266	−	3.99958i	−1.32452	−	0.354905i	−0.473853	−	0.880604i	$-0.657137\pi$
$127$	−14.9266	−	3.99958i	−1.32452	−	0.354905i	−0.850671	+	0.525699i	$0.823804\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−4.08931			−0.360044
$130$	−6.25915	+	5.08164i	−0.548964	+	0.445689i
$131$	3.52073			0.307608			0.153804	−	0.988101i	$-0.450848\pi$
$131$	3.52073			0.307608			0.153804	+	0.988101i	$0.450848\pi$
$132$	2.37831	−	1.37312i	0.207005	−	0.119515i
$133$	−0.489542	−	0.131172i	−0.0424487	−	0.0113741i
$134$	−4.90245	+	8.49129i	−0.423507	+	0.733536i
$135$	0.810029	−	2.08419i	0.0697162	−	0.179379i
$136$	4.56975	−	1.22446i	0.391853	−	0.104997i
$137$	−1.44166	+	2.49703i	−0.123170	+	0.213336i	−0.921016	−	0.389525i	$-0.872639\pi$
$137$	−1.44166	+	2.49703i	−0.123170	+	0.213336i	0.797846	+	0.602861i	$0.205973\pi$
$138$			3.23775i			0.275616i
$139$	8.92480	+	5.15274i	0.756992	+	0.437049i	0.828215	−	0.560411i	$-0.189357\pi$
$139$	8.92480	+	5.15274i	0.756992	+	0.437049i	−0.0712230	+	0.997460i	$0.522690\pi$
$140$	−0.0790119	+	0.107803i	−0.00667773	+	0.00911100i
$141$	7.83126	+	2.09838i	0.659511	+	0.176715i
$142$	−1.29535	+	1.29535i	−0.108703	+	0.108703i
$143$	4.90422	−	8.60187i	0.410112	−	0.719325i
$144$		−	1.00000i		−	0.0833333i
$145$	6.37984	+	4.67598i	0.529817	+	0.388319i
$146$	5.52975	+	9.57780i	0.457645	+	0.792665i
$147$	1.81081	+	6.75803i	0.149353	+	0.557393i
$148$	0.448809			0.0368919
$149$	−1.66453	−	6.21211i	−0.136364	−	0.508916i	−0.999989	−	0.00478120i	$-0.998478\pi$
$149$	−1.66453	−	6.21211i	−0.136364	−	0.508916i	0.863625	−	0.504135i	$-0.168189\pi$
$150$	−2.30701	+	4.43595i	−0.188367	+	0.362194i
$151$	14.2507	−	14.2507i	1.15971	−	1.15971i	0.175167	−	0.984539i	$-0.443953\pi$
$151$	14.2507	−	14.2507i	1.15971	−	1.15971i	0.984539	−	0.175167i	$-0.0560467\pi$
$152$	−8.18996	+	2.19449i	−0.664293	+	0.177997i
$153$	−1.22446	+	4.56975i	−0.0989917	+	0.369442i
$154$	0.0424857	−	0.158559i	0.00342359	−	0.0127770i
$155$	6.24937	−	16.0795i	0.501961	−	1.29154i
$156$	−1.81970	−	3.11267i	−0.145693	−	0.249213i
$157$	8.02272	+	8.02272i	0.640283	+	0.640283i	0.950625	−	0.310342i	$-0.100444\pi$
$157$	8.02272	+	8.02272i	0.640283	+	0.640283i	−0.310342	+	0.950625i	$0.600444\pi$
$158$	−6.34724	−	10.9937i	−0.504959	−	0.874615i
$159$	−4.43624	+	2.56127i	−0.351817	+	0.203122i
$160$	−0.243000	+	2.22283i	−0.0192108	+	0.175730i
$161$	0.136847	+	0.136847i	0.0107851	+	0.0107851i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−16.3042	−	9.41324i	−1.27704	−	0.737302i	−0.300740	−	0.953706i	$-0.597234\pi$
$163$	−16.3042	−	9.41324i	−1.27704	−	0.737302i	−0.976304	+	0.216405i	$0.930567\pi$
$164$	5.68098	+	5.68098i	0.443610	+	0.443610i
$165$	0.667335	−	6.10440i	0.0519520	−	0.475227i
$166$	0.702072	−	0.405341i	0.0544913	−	0.0314606i
$167$	−5.92423	−	10.2611i	−0.458430	−	0.794025i	0.540448	−	0.841378i	$-0.318255\pi$
$167$	−5.92423	−	10.2611i	−0.458430	−	0.794025i	−0.998878	+	0.0473527i	$0.984922\pi$
$168$	−0.0422662	−	0.0422662i	−0.00326091	−	0.00326091i
$169$	−11.3282	−	6.37738i	−0.871403	−	0.490567i
$170$	3.83221	−	9.86020i	0.293917	−	0.756243i
$171$	2.19449	−	8.18996i	0.167817	−	0.626302i
$172$	−1.05839	+	3.94997i	−0.0807016	+	0.301182i
$173$	−8.27528	+	2.21736i	−0.629158	+	0.168582i	−0.559288	−	0.828974i	$-0.688925\pi$
$173$	−8.27528	+	2.21736i	−0.629158	+	0.168582i	−0.0698704	+	0.997556i	$0.522259\pi$
$174$	−2.50134	+	2.50134i	−0.189626	+	0.189626i
$175$	0.0899824	+	0.285000i	0.00680203	+	0.0215440i
$176$	−0.710778	−	2.65266i	−0.0535769	−	0.199952i
$177$	−8.53839			−0.641784
$178$	−3.49929	−	13.0595i	−0.262283	−	0.978852i
$179$	−10.0352	−	17.3814i	−0.750063	−	1.29915i	−0.947792	−	0.318890i	$-0.896690\pi$
$179$	−10.0352	−	17.3814i	−0.750063	−	1.29915i	0.197729	−	0.980257i	$-0.436644\pi$
$180$	−1.80352	−	1.32186i	−0.134427	−	0.0985254i
$181$		−	13.3312i		−	0.990901i	−0.868636	−	0.495451i	$-0.835003\pi$
$181$		−	13.3312i		−	0.990901i	0.868636	−	0.495451i	$-0.164997\pi$
$182$	−0.208472	−	0.0546487i	−0.0154530	−	0.00405083i
$183$	7.18224	−	7.18224i	0.530927	−	0.530927i
$184$	3.12743	+	0.837992i	0.230557	+	0.0617776i
$185$	0.593262	−	0.809438i	0.0436175	−	0.0595111i
$186$	6.68138	+	3.85749i	0.489902	+	0.282845i
$187$			12.9923i			0.950092i
$188$	4.05376	−	7.02131i	0.295651	−	0.512082i
$189$	0.0577367	−	0.0154705i	0.00419973	−	0.00112531i
$190$	−6.86813	+	17.6716i	−0.498267	+	1.28203i
$191$	1.12684	−	1.95175i	0.0815356	−	0.141224i	−0.822374	−	0.568947i	$-0.807351\pi$
$191$	1.12684	−	1.95175i	0.0815356	−	0.141224i	0.903910	+	0.427723i	$0.140684\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	7.39614	−	4.27016i	0.532386	−	0.307373i	−0.209602	−	0.977787i	$-0.567217\pi$
$193$	7.39614	−	4.27016i	0.532386	−	0.307373i	0.741987	+	0.670414i	$0.233883\pi$
$194$	10.6466			0.764379
$195$	−8.01915	−	0.832625i	−0.574263	−	0.0596255i
$196$	6.99643			0.499745
$197$	9.53494	−	5.50500i	0.679336	−	0.392215i	−0.120269	−	0.992741i	$-0.538376\pi$
$197$	9.53494	−	5.50500i	0.679336	−	0.392215i	0.799605	+	0.600526i	$0.205042\pi$
$198$	2.65266	+	0.710778i	0.188516	+	0.0505128i
$199$	−9.23263	+	15.9914i	−0.654484	+	1.13360i	0.327539	+	0.944838i	$0.393781\pi$
$199$	−9.23263	+	15.9914i	−0.654484	+	1.13360i	−0.982023	+	0.188762i	$0.939553\pi$
$200$	3.68770	+	3.37651i	0.260760	+	0.238755i
$201$	−9.47081	+	2.53770i	−0.668019	+	0.178995i
$202$	−2.89512	+	5.01449i	−0.203700	+	0.352818i
$203$			0.211445i			0.0148405i
$204$	4.09712	+	2.36547i	0.286856	+	0.165616i
$205$	17.7552	−	2.73634i	1.24008	−	0.191114i
$206$	−7.93511	−	2.12621i	−0.552865	−	0.148140i
$207$	−2.28944	+	2.28944i	−0.159127	+	0.159127i
$208$	−3.47758	+	0.952079i	−0.241127	+	0.0660148i
$209$		−	23.2850i		−	1.61066i
$210$	−0.132098	+	0.0203582i	−0.00911563	+	0.00140485i
$211$	−9.82300	−	17.0139i	−0.676243	−	1.17129i	−0.976104	−	0.217305i	$-0.930273\pi$
$211$	−9.82300	−	17.0139i	−0.676243	−	1.17129i	0.299860	−	0.953983i	$-0.403060\pi$
$212$	1.32581	+	4.94799i	0.0910569	+	0.339829i
$213$	−1.83190			−0.125520
$214$	2.06732	+	7.71536i	0.141319	+	0.527411i
$215$	5.72482	+	7.13013i	0.390429	+	0.486271i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	0.445438	−	0.119355i	0.0302383	−	0.00810233i
$218$	2.93188	−	10.9419i	0.198572	−	0.741080i
$219$	−2.86241	+	10.6827i	−0.193424	+	0.721867i
$220$	−5.72368	−	2.22453i	−0.385891	−	0.149978i
$221$	17.0574	−	0.0926054i	1.14741	−	0.00622932i
$222$	0.317356	+	0.317356i	0.0212996	+	0.0212996i
$223$	0.708412	+	1.22701i	0.0474388	+	0.0821663i	0.888770	−	0.458354i	$-0.151561\pi$
$223$	0.708412	+	1.22701i	0.0474388	+	0.0821663i	−0.841331	+	0.540520i	$0.818227\pi$
$224$	−0.0517653	+	0.0298867i	−0.00345872	+	0.00199689i
$225$	−4.76800	+	1.50539i	−0.317867	+	0.100359i
$226$	8.27332	+	8.27332i	0.550333	+	0.550333i
$227$	1.37971	+	0.796577i	0.0915747	+	0.0528707i	0.545088	−	0.838379i	$-0.316496\pi$
$227$	1.37971	+	0.796577i	0.0915747	+	0.0528707i	−0.453513	+	0.891249i	$0.649830\pi$
$228$	−7.34291	−	4.23943i	−0.486296	−	0.280763i
$229$	5.31411	+	5.31411i	0.351166	+	0.351166i	0.860543	−	0.509377i	$-0.170124\pi$
$229$	5.31411	+	5.31411i	0.351166	+	0.351166i	−0.509377	+	0.860543i	$0.670124\pi$
$230$	5.64535	−	4.53268i	0.372243	−	0.298876i
$231$	0.142160	−	0.0820760i	0.00935343	−	0.00540021i
$232$	1.76872	+	3.06351i	0.116122	+	0.201129i
$233$	13.2710	+	13.2710i	0.869414	+	0.869414i	0.992408	−	0.122993i	$-0.0392494\pi$
$233$	13.2710	+	13.2710i	0.869414	+	0.869414i	−0.122993	+	0.992408i	$0.539249\pi$
$234$	0.914264	−	3.48771i	0.0597673	−	0.227999i
$235$	−7.30462	−	16.5922i	−0.476501	−	1.08236i
$236$	−2.20990	+	8.24745i	−0.143852	+	0.536863i
$237$	3.28557	−	12.2619i	0.213421	−	0.796498i
$238$	0.273150	−	0.0731902i	0.0177057	−	0.00474422i
$239$	7.55627	−	7.55627i	0.488775	−	0.488775i	−0.419145	−	0.907919i	$-0.637670\pi$
$239$	7.55627	−	7.55627i	0.488775	−	0.488775i	0.907919	+	0.419145i	$0.137670\pi$
$240$	−1.74360	+	1.39995i	−0.112549	+	0.0903662i
$241$	−2.00717	−	7.49086i	−0.129293	−	0.482529i	0.870663	−	0.491880i	$-0.163690\pi$
$241$	−2.00717	−	7.49086i	−0.129293	−	0.482529i	−0.999956	+	0.00935118i	$0.997023\pi$
$242$	−3.45818			−0.222300
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−5.07861	−	8.79641i	−0.325125	−	0.563133i
$245$	9.24827	−	12.6182i	0.590851	−	0.806148i
$246$			8.03412i			0.512237i
$247$	−30.5705	+	0.165969i	−1.94516	+	0.0105603i
$248$	5.45532	−	5.45532i	0.346413	−	0.346413i
$249$	0.783059	+	0.209820i	0.0496244	+	0.0132968i
$250$	10.9642	−	2.18760i	0.693439	−	0.138356i
$251$	−3.97075	−	2.29252i	−0.250632	−	0.144702i	0.369422	−	0.929262i	$-0.379556\pi$
$251$	−3.97075	−	2.29252i	−0.250632	−	0.144702i	−0.620053	+	0.784560i	$0.712889\pi$
$252$		−	0.0597735i		−	0.00376537i
$253$	−4.44582	+	7.70038i	−0.279506	+	0.484119i
$254$	−14.9266	+	3.99958i	−0.936580	+	0.250956i
$255$	9.68200	−	4.26244i	0.606310	−	0.266924i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.06269	+	1.62449i	0.378180	+	0.101333i	0.442901	−	0.896570i	$-0.353949\pi$
$257$	6.06269	+	1.62449i	0.378180	+	0.101333i	−0.0647212	+	0.997903i	$0.520616\pi$
$258$	−3.54145	+	2.04465i	−0.220481	+	0.127295i
$259$	0.0268269			0.00166694
$260$	−2.87976	+	7.53040i	−0.178595	+	0.467016i
$261$	−3.53743			−0.218962
$262$	3.04904	−	1.76037i	0.188371	−	0.108756i
$263$	2.94738	+	0.789749i	0.181743	+	0.0486980i	0.348543	−	0.937293i	$-0.386677\pi$
$263$	2.94738	+	0.789749i	0.181743	+	0.0486980i	−0.166799	+	0.985991i	$0.553343\pi$
$264$	1.37312	−	2.37831i	0.0845096	−	0.146375i
$265$	10.6763	+	4.14940i	0.655842	+	0.254896i
$266$	−0.489542	+	0.131172i	−0.0300157	+	0.00804269i
$267$	6.76010	−	11.7088i	0.413712	−	0.716569i
$268$			9.80490i			0.598930i
$269$	18.0748	+	10.4355i	1.10204	+	0.636262i	0.936756	−	0.349984i	$-0.113813\pi$
$269$	18.0748	+	10.4355i	1.10204	+	0.636262i	0.165283	+	0.986246i	$0.447146\pi$
$270$	−0.340590	−	2.20998i	−0.0207276	−	0.134495i
$271$	−8.49595	−	2.27648i	−0.516093	−	0.138287i	−0.00863393	−	0.999963i	$-0.502748\pi$
$271$	−8.49595	−	2.27648i	−0.516093	−	0.138287i	−0.507459	+	0.861676i	$0.669415\pi$
$272$	3.34529	−	3.34529i	0.202838	−	0.202838i
$273$	−0.108770	−	0.186055i	−0.00658305	−	0.0112605i
$274$			2.88333i			0.174188i
$275$	−11.5779	+	7.38228i	−0.698173	+	0.445168i
$276$	1.61888	+	2.80397i	0.0974448	+	0.168779i
$277$	4.77337	+	17.8145i	0.286804	+	1.07037i	0.947511	+	0.319723i	$0.103590\pi$
$277$	4.77337	+	17.8145i	0.286804	+	1.07037i	−0.660707	+	0.750644i	$0.729743\pi$
$278$	10.3055			0.618081
$279$	1.99679	+	7.45211i	0.119544	+	0.446146i
$280$	−0.0145249	+	0.132866i	−0.000868032	+	0.00794026i
$281$	6.35313	−	6.35313i	0.378996	−	0.378996i	−0.491744	−	0.870740i	$-0.663640\pi$
$281$	6.35313	−	6.35313i	0.378996	−	0.378996i	0.870740	+	0.491744i	$0.163640\pi$
$282$	7.83126	−	2.09838i	0.466345	−	0.124957i
$283$	−0.0862084	+	0.321734i	−0.00512456	+	0.0191251i	−0.968441	−	0.249244i	$-0.919818\pi$
$283$	−0.0862084	+	0.321734i	−0.00512456	+	0.0191251i	0.963316	+	0.268369i	$0.0864846\pi$
$284$	−0.474132	+	1.76948i	−0.0281345	+	0.105000i
$285$	−17.3522	+	7.63919i	−1.02786	+	0.452507i
$286$	−0.0537559	−	9.90155i	−0.00317865	−	0.585491i
$287$	0.339572	+	0.339572i	0.0200443	+	0.0200443i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−4.66085	+	2.69094i	−0.274168	+	0.158291i
$290$	7.86309	+	0.859596i	0.461737	+	0.0504772i
$291$	7.52826	+	7.52826i	0.441314	+	0.441314i
$292$	9.57780	+	5.52975i	0.560498	+	0.323604i
$293$	−17.4725	−	10.0877i	−1.02075	−	0.589333i	−0.106432	−	0.994320i	$-0.533943\pi$
$293$	−17.4725	−	10.0877i	−1.02075	−	0.589333i	−0.914322	+	0.404987i	$0.867276\pi$
$294$	4.94722	+	4.94722i	0.288528	+	0.288528i
$295$	11.9533	+	14.8875i	0.695948	+	0.866786i
$296$	0.388680	−	0.224405i	0.0225916	−	0.0130433i
$297$	1.37312	+	2.37831i	0.0796764	+	0.138004i
$298$	−4.54758	−	4.54758i	−0.263434	−	0.263434i
$299$	10.1414	+	5.78197i	0.586493	+	0.334380i
$300$	0.220047	+	4.99516i	0.0127044	+	0.288395i
$301$	−0.0632637	+	0.236103i	−0.00364646	+	0.0136088i
$302$	5.21612	−	19.4668i	0.300154	−	1.12019i
$303$	−5.59293	+	1.49862i	−0.321306	+	0.0860936i
$304$	−5.99546	+	5.99546i	−0.343863	+	0.343863i
$305$	−22.5777	−	2.46820i	−1.29280	−	0.141329i
$306$	1.22446	+	4.56975i	0.0699977	+	0.261235i
$307$	−30.3433			−1.73178			−0.865891	−	0.500232i	$-0.833248\pi$
$307$	−30.3433			−1.73178			−0.865891	+	0.500232i	$0.833248\pi$
$308$	−0.0424857	−	0.158559i	−0.00242085	−	0.00903472i
$309$	−4.10751	−	7.11442i	−0.233668	−	0.404725i
$310$	−2.62764	−	17.0499i	−0.149240	−	0.968372i
$311$		−	3.98354i		−	0.225886i	−0.993601	−	0.112943i	$-0.963972\pi$
$311$		−	3.98354i		−	0.225886i	0.993601	−	0.112943i	$-0.0360277\pi$
$312$	−3.13224	−	1.78580i	−0.177328	−	0.101101i
$313$	2.19346	−	2.19346i	0.123982	−	0.123982i	−0.642393	−	0.766375i	$-0.722058\pi$
$313$	2.19346	−	2.19346i	0.123982	−	0.123982i	0.766375	+	0.642393i	$0.222058\pi$
$314$	10.9592	+	2.93652i	0.618466	+	0.165717i
$315$	−0.107803	−	0.0790119i	−0.00607400	−	0.00445182i
$316$	−10.9937	−	6.34724i	−0.618446	−	0.357060i
$317$		−	28.6926i		−	1.61154i	−0.592230	−	0.805769i	$-0.701752\pi$
$317$		−	28.6926i		−	1.61154i	0.592230	−	0.805769i	$-0.298248\pi$
$318$	−2.56127	+	4.43624i	−0.143629	+	0.248772i
$319$	−9.38361	+	2.51433i	−0.525381	+	0.140775i
$320$	0.900968	+	2.04652i	0.0503657	+	0.114404i
$321$	−3.99376	+	6.91740i	−0.222910	+	0.386092i
$322$	0.186937	+	0.0500897i	0.0104176	+	0.00279139i
$323$	34.7390	−	20.0565i	1.93293	−	1.11598i
$324$	1.00000			0.0555556
$325$	9.77462	+	15.1478i	0.542198	+	0.840250i
$326$	−18.8265			−1.04270
$327$	9.81025	−	5.66395i	0.542508	−	0.313217i
$328$	7.76037	+	2.07938i	0.428495	+	0.114815i
$329$	0.242307	−	0.419688i	0.0133588	−	0.0231382i
$330$	−2.47427	−	5.62024i	−0.136204	−	0.309384i
$331$	13.7595	−	3.68686i	0.756292	−	0.202648i	0.139985	−	0.990154i	$-0.455295\pi$
$331$	13.7595	−	3.68686i	0.756292	−	0.202648i	0.616307	+	0.787506i	$0.288628\pi$
$332$	0.405341	−	0.702072i	0.0222460	−	0.0385312i
$333$			0.448809i			0.0245946i
$334$	−10.2611	−	5.92423i	−0.561460	−	0.324159i
$335$	17.6834	+	12.9607i	0.966146	+	0.708117i
$336$	−0.0577367	−	0.0154705i	−0.00314980	−	0.000843985i
$337$	−11.4486	+	11.4486i	−0.623643	+	0.623643i	−0.946461	−	0.322818i	$-0.895370\pi$
$337$	−11.4486	+	11.4486i	−0.623643	+	0.623643i	0.322818	+	0.946461i	$0.395370\pi$
$338$	−12.9992	+	0.141151i	−0.707065	+	0.00767759i
$339$			11.7002i			0.635470i
$340$	−1.61131	−	10.4553i	−0.0873857	−	0.567018i
$341$	10.5936	+	18.3486i	0.573675	+	0.993634i
$342$	−2.19449	−	8.18996i	−0.118665	−	0.442862i
$343$	0.836615			0.0451730
$344$	1.05839	+	3.94997i	0.0570646	+	0.212968i
$345$	7.19695	+	0.786773i	0.387471	+	0.0423584i
$346$	−6.05793	+	6.05793i	−0.325676	+	0.325676i
$347$	−18.7437	+	5.02236i	−1.00621	+	0.269614i	−0.724047	−	0.689751i	$-0.757720\pi$
$347$	−18.7437	+	5.02236i	−1.00621	+	0.269614i	−0.282167	+	0.959365i	$0.591053\pi$
$348$	−0.915555	+	3.41690i	−0.0490789	+	0.183165i
$349$	−7.44233	+	27.7752i	−0.398379	+	1.48677i	0.417569	+	0.908645i	$0.362882\pi$
$349$	−7.44233	+	27.7752i	−0.398379	+	1.48677i	−0.815948	+	0.578126i	$0.803784\pi$
$350$	0.220427	+	0.201826i	0.0117823	+	0.0107880i
$351$	3.11267	−	1.81970i	0.166142	−	0.0971285i
$352$	−1.94188	−	1.94188i	−0.103503	−	0.103503i
$353$	9.91387	+	17.1713i	0.527662	+	0.913938i	0.999480	+	0.0322417i	$0.0102646\pi$
$353$	9.91387	+	17.1713i	0.527662	+	0.913938i	−0.471818	+	0.881696i	$0.656402\pi$
$354$	−7.39446	+	4.26919i	−0.393011	+	0.226905i
$355$	2.56457	+	3.19411i	0.136113	+	0.169526i
$356$	−9.56023	−	9.56023i	−0.506691	−	0.506691i
$357$	0.244899	+	0.141393i	0.0129614	+	0.00748329i
$358$	−17.3814	−	10.0352i	−0.918636	−	0.530375i
$359$	17.9231	+	17.9231i	0.945945	+	0.945945i	0.998612	−	0.0526669i	$-0.0167722\pi$
$359$	17.9231	+	17.9231i	0.945945	+	0.945945i	−0.0526669	+	0.998612i	$0.516772\pi$
$360$	−2.22283	−	0.243000i	−0.117153	−	0.0128072i
$361$	−45.8051	+	26.4456i	−2.41079	+	1.39187i
$362$	−6.66561	−	11.5452i	−0.350336	−	0.606801i
$363$	−2.44531	−	2.44531i	−0.128345	−	0.128345i
$364$	−0.207867	+	0.0569091i	−0.0108952	+	0.00298284i
$365$	22.6335	−	9.96425i	1.18469	−	0.521553i
$366$	2.62888	−	9.81113i	0.137414	−	0.512836i
$367$	6.21836	−	23.2072i	0.324596	−	1.21141i	−0.590122	−	0.807314i	$-0.700920\pi$
$367$	6.21836	−	23.2072i	0.324596	−	1.21141i	0.914717	−	0.404094i	$-0.132413\pi$
$368$	3.12743	−	0.837992i	0.163028	−	0.0436833i
$369$	−5.68098	+	5.68098i	−0.295740	+	0.295740i
$370$	0.109061	−	0.997625i	0.00566979	−	0.0518640i
$371$	0.0792482	+	0.295758i	0.00411436	+	0.0153550i
$372$	7.71499			0.400003
$373$	2.66221	+	9.93549i	0.137844	+	0.514440i	0.999970	+	0.00774660i	$0.00246584\pi$
$373$	2.66221	+	9.93549i	0.137844	+	0.514440i	−0.862126	+	0.506694i	$0.830867\pi$
$374$	6.49615	+	11.2517i	0.335908	+	0.581810i
$375$	9.29975	+	6.20602i	0.480237	+	0.320478i
$376$		−	8.10752i		−	0.418113i
$377$	3.36791	+	12.3017i	0.173456	+	0.633570i
$378$	0.0422662	−	0.0422662i	0.00217394	−	0.00217394i
$379$	31.0601	+	8.32254i	1.59545	+	0.427500i	0.943665	−	0.330902i	$-0.107353\pi$
$379$	31.0601	+	8.32254i	1.59545	+	0.427500i	0.651787	+	0.758402i	$0.274020\pi$
$380$	2.88781	+	18.7381i	0.148142	+	0.961244i
$381$	−13.3829	−	7.72659i	−0.685624	−	0.395845i
$382$		−	2.25369i		−	0.115309i
$383$	−7.32594	+	12.6889i	−0.374338	+	0.648373i	−0.990228	−	0.139460i	$-0.955463\pi$
$383$	−7.32594	+	12.6889i	−0.374338	+	0.648373i	0.615890	+	0.787832i	$0.288797\pi$
$384$	−0.965926	+	0.258819i	−0.0492922	+	0.0132078i
$385$	−0.342124	−	0.132968i	−0.0174363	−	0.00677668i
$386$	4.27016	−	7.39614i	0.217345	−	0.376453i
$387$	−3.94997	−	1.05839i	−0.200788	−	0.0538010i
$388$	9.22020	−	5.32328i	0.468085	−	0.270249i
$389$	−32.7289			−1.65942			−0.829711	−	0.558194i	$-0.811495\pi$
$389$	−32.7289			−1.65942			−0.829711	+	0.558194i	$0.811495\pi$
$390$	−7.36110	+	3.28850i	−0.372744	+	0.166520i
$391$	−15.3176			−0.774646
$392$	6.05908	−	3.49821i	0.306030	−	0.176686i
$393$	3.40077	+	0.911233i	0.171546	+	0.0459656i
$394$	5.50500	−	9.53494i	0.277338	−	0.480363i
$395$	−25.9795	+	11.4373i	−1.30717	+	0.575474i
$396$	2.65266	−	0.710778i	0.133301	−	0.0357180i
$397$	−8.11811	+	14.0610i	−0.407436	+	0.705700i	−0.994602	−	0.103767i	$-0.966910\pi$
$397$	−8.11811	+	14.0610i	−0.407436	+	0.705700i	0.587166	+	0.809467i	$0.300244\pi$
$398$			18.4653i			0.925580i
$399$	−0.438911	−	0.253406i	−0.0219731	−	0.0126861i
$400$	4.88190	+	1.08029i	0.244095	+	0.0540146i
$401$	−34.3382	−	9.20088i	−1.71477	−	0.459470i	−0.738181	−	0.674602i	$-0.764315\pi$
$401$	−34.3382	−	9.20088i	−1.71477	−	0.459470i	−0.976585	+	0.215132i	$0.930982\pi$
$402$	−6.93311	+	6.93311i	−0.345792	+	0.345792i
$403$	24.0142	−	14.0390i	1.19623	−	0.699331i
$404$			5.79023i			0.288075i
$405$	1.32186	−	1.80352i	0.0656836	−	0.0896178i
$406$	0.105722	+	0.183116i	0.00524691	+	0.00908791i
$407$	0.319004	+	1.19054i	0.0158124	+	0.0590128i
$408$	4.73095			0.234217
$409$	6.01537	+	22.4497i	0.297441	+	1.11006i	0.939259	+	0.343208i	$0.111514\pi$
$409$	6.01537	+	22.4497i	0.297441	+	1.11006i	−0.641818	+	0.766857i	$0.721820\pi$
$410$	14.0083	−	11.2474i	0.691821	−	0.555467i
$411$	−2.03882	+	2.03882i	−0.100568	+	0.100568i
$412$	−7.93511	+	2.12621i	−0.390935	+	0.104751i
$413$	−0.132093	+	0.492978i	−0.00649988	+	0.0242579i
$414$	−0.837992	+	3.12743i	−0.0411850	+	0.153705i
$415$	−0.730399	−	1.65908i	−0.0358539	−	0.0814411i
$416$	−2.53563	+	2.56331i	−0.124320	+	0.125677i
$417$	7.28707	+	7.28707i	0.356849	+	0.356849i
$418$	−11.6425	−	20.1654i	−0.569453	−	0.986321i
$419$	−19.9734	+	11.5317i	−0.975765	+	0.563358i	−0.900989	−	0.433842i	$-0.857158\pi$
$419$	−19.9734	+	11.5317i	−0.975765	+	0.563358i	−0.0747763	+	0.997200i	$0.523824\pi$
$420$	−0.104221	+	0.0836797i	−0.00508547	+	0.00408315i
$421$	−2.82066	−	2.82066i	−0.137470	−	0.137470i	0.635023	−	0.772493i	$-0.280991\pi$
$421$	−2.82066	−	2.82066i	−0.137470	−	0.137470i	−0.772493	+	0.635023i	$0.780991\pi$
$422$	−17.0139	−	9.82300i	−0.828226	−	0.478176i
$423$	7.02131	+	4.05376i	0.341388	+	0.197100i
$424$	3.62218	+	3.62218i	0.175909	+	0.175909i
$425$	−20.9863	−	10.9144i	−1.01798	−	0.529424i
$426$	−1.58648	+	0.915952i	−0.0768650	+	0.0443780i
$427$	−0.303566	−	0.525792i	−0.0146906	−	0.0254449i
$428$	5.64803	+	5.64803i	0.273008	+	0.273008i
$429$	6.96344	−	7.03947i	0.336198	−	0.339869i
$430$	8.52290	+	3.31246i	0.411011	+	0.159741i
$431$	−5.99669	+	22.3799i	−0.288850	+	1.07800i	0.657130	+	0.753778i	$0.271770\pi$
$431$	−5.99669	+	22.3799i	−0.288850	+	1.07800i	−0.945980	+	0.324226i	$0.894896\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	−2.45624	+	0.658147i	−0.118039	+	0.0316285i	−0.317355	−	0.948307i	$-0.602795\pi$
$433$	−2.45624	+	0.658147i	−0.118039	+	0.0316285i	0.199316	+	0.979935i	$0.436128\pi$
$434$	0.326083	−	0.326083i	0.0156525	−	0.0156525i
$435$	4.95222	+	6.16787i	0.237441	+	0.295727i
$436$	−2.93188	−	10.9419i	−0.140411	−	0.524022i
$437$	27.4525			1.31323
$438$	2.86241	+	10.6827i	0.136771	+	0.510437i
$439$	−6.91442	−	11.9761i	−0.330007	−	0.571589i	0.652506	−	0.757784i	$-0.273718\pi$
$439$	−6.91442	−	11.9761i	−0.330007	−	0.571589i	−0.982513	+	0.186195i	$0.940384\pi$
$440$	−6.06912	+	0.935339i	−0.289334	+	0.0445906i
$441$			6.99643i			0.333163i
$442$	14.7259	−	8.60891i	0.700438	−	0.409484i
$443$	−17.6040	+	17.6040i	−0.836390	+	0.836390i	−0.988382	−	0.151992i	$-0.951431\pi$
$443$	−17.6040	+	17.6040i	−0.836390	+	0.836390i	0.151992	+	0.988382i	$0.451431\pi$
$444$	0.433517	+	0.116160i	0.0205738	+	0.00551273i
$445$	−29.8793	+	4.60484i	−1.41642	+	0.218290i
$446$	1.22701	+	0.708412i	0.0581004	+	0.0335443i
$447$		−	6.43125i		−	0.304188i
$448$	−0.0298867	+	0.0517653i	−0.00141202	+	0.00244568i
$449$	−27.0137	+	7.23830i	−1.27486	+	0.341597i	−0.831889	−	0.554942i	$-0.812741\pi$
$449$	−27.0137	+	7.23830i	−1.27486	+	0.341597i	−0.442967	+	0.896538i	$0.646074\pi$
$450$	−3.37651	+	3.68770i	−0.159170	+	0.173840i
$451$	−11.0318	+	19.1076i	−0.519467	+	0.899744i
$452$	11.3016	+	3.02824i	0.531581	+	0.142437i
$453$	17.4535	−	10.0768i	0.820036	−	0.473448i
$454$	1.59315			0.0747704
$455$	−0.172133	+	0.450118i	−0.00806974	+	0.0211019i
$456$	−8.47887			−0.397059
$457$	21.2291	−	12.2566i	0.993053	−	0.573340i	0.0868678	−	0.996220i	$-0.472314\pi$
$457$	21.2291	−	12.2566i	0.993053	−	0.573340i	0.906186	+	0.422880i	$0.138981\pi$
$458$	7.25920	+	1.94510i	0.339200	+	0.0908884i
$459$	−2.36547	+	4.09712i	−0.110411	+	0.191237i
$460$	2.62267	−	6.74809i	0.122283	−	0.314631i
$461$	1.77089	−	0.474508i	0.0824784	−	0.0221000i	−0.217344	−	0.976095i	$-0.569739\pi$
$461$	1.77089	−	0.474508i	0.0824784	−	0.0221000i	0.299822	+	0.953995i	$0.403073\pi$
$462$	0.0820760	−	0.142160i	0.00381852	−	0.00661388i
$463$			1.73101i			0.0804467i	0.999191	+	0.0402234i	$0.0128070\pi$
$463$			1.73101i			0.0804467i	−0.999191	+	0.0402234i	$0.987193\pi$
$464$	3.06351	+	1.76872i	0.142220	+	0.0821106i
$465$	10.1981	−	13.9142i	0.472926	−	0.645254i
$466$	18.1286	+	4.85754i	0.839790	+	0.225021i
$467$	18.5723	−	18.5723i	0.859425	−	0.859425i	−0.131845	−	0.991270i	$-0.542090\pi$
$467$	18.5723	−	18.5723i	0.859425	−	0.859425i	0.991270	+	0.131845i	$0.0420901\pi$
$468$	−0.952079	−	3.47758i	−0.0440099	−	0.160751i
$469$			0.586073i			0.0270623i
$470$	−14.6221	−	10.7170i	−0.674467	−	0.494337i
$471$	5.67292	+	9.82579i	0.261394	+	0.452748i
$472$	2.20990	+	8.24745i	0.101719	+	0.379620i
$473$	−11.2302			−0.516366
$474$	−3.28557	−	12.2619i	−0.150911	−	0.563209i
$475$	37.6119	+	19.5608i	1.72575	+	0.897513i
$476$	0.199959	−	0.199959i	0.00916512	−	0.00916512i
$477$	−4.94799	+	1.32581i	−0.226553	+	0.0607046i
$478$	2.76579	−	10.3221i	0.126504	−	0.472120i
$479$	7.29554	−	27.2273i	0.333342	−	1.24405i	−0.572314	−	0.820034i	$-0.693954\pi$
$479$	7.29554	−	27.2273i	0.333342	−	1.24405i	0.905656	−	0.424013i	$-0.139379\pi$
$480$	−0.810029	+	2.08419i	−0.0369726	+	0.0951299i
$481$	1.56077	−	0.427302i	0.0711650	−	0.0194833i
$482$	−5.48369	−	5.48369i	−0.249775	−	0.249775i
$483$	0.0967658	+	0.167603i	0.00440300	+	0.00762621i
$484$	−2.99487	+	1.72909i	−0.136131	+	0.0785951i
$485$	2.58711	−	23.6655i	0.117475	−	1.07459i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−6.95941	−	4.01802i	−0.315361	−	0.182074i	0.333962	−	0.942587i	$-0.391614\pi$
$487$	−6.95941	−	4.01802i	−0.315361	−	0.182074i	−0.649323	+	0.760513i	$0.724948\pi$
$488$	−8.79641	−	5.07861i	−0.398195	−	0.229898i
$489$	−13.3123	−	13.3123i	−0.602004	−	0.602004i
$490$	1.70013	−	15.5518i	0.0768041	−	0.702560i
$491$	20.8782	−	12.0541i	0.942221	−	0.543992i	0.0515655	−	0.998670i	$-0.483579\pi$
$491$	20.8782	−	12.0541i	0.942221	−	0.543992i	0.890656	+	0.454678i	$0.150246\pi$
$492$	4.01706	+	6.95775i	0.181103	+	0.313680i
$493$	−11.8337	−	11.8337i	−0.532964	−	0.532964i
$494$	−26.3919	+	15.4290i	−1.18743	+	0.694184i
$495$	2.22453	−	5.72368i	0.0999853	−	0.257260i
$496$	1.99679	−	7.45211i	0.0896583	−	0.334609i
$497$	−0.0283405	+	0.105768i	−0.00127124	+	0.00474435i
$498$	0.783059	−	0.209820i	0.0350897	−	0.00940226i
$499$	−2.44387	+	2.44387i	−0.109403	+	0.109403i	−0.759689	−	0.650286i	$-0.774649\pi$
$499$	−2.44387	+	2.44387i	−0.109403	+	0.109403i	0.650286	+	0.759689i	$0.274649\pi$
$500$	8.40151	−	7.37663i	0.375727	−	0.329893i
$501$	−3.06661	−	11.4447i	−0.137006	−	0.511313i
$502$	−4.58503			−0.204640
$503$	−2.45857	−	9.17550i	−0.109622	−	0.409115i	0.889206	−	0.457506i	$-0.151257\pi$
$503$	−2.45857	−	9.17550i	−0.109622	−	0.409115i	−0.998828	+	0.0483911i	$0.984591\pi$
$504$	−0.0298867	−	0.0517653i	−0.00133126	−	0.00230581i
$505$	10.4428	+	7.65385i	0.464699	+	0.340592i
$506$			8.89163i			0.395281i
$507$	−9.29166	−	9.09204i	−0.412657	−	0.403792i
$508$	−10.9271	+	10.9271i	−0.484810	+	0.484810i
$509$	−35.5002	−	9.51225i	−1.57352	−	0.421623i	−0.636607	−	0.771189i	$-0.719663\pi$
$509$	−35.5002	−	9.51225i	−1.57352	−	0.421623i	−0.936912	+	0.349565i	$0.886329\pi$
$510$	6.25364	−	8.53238i	0.276916	−	0.377820i
$511$	0.572498	+	0.330532i	0.0253258	+	0.0146219i
$512$			1.00000i			0.0441942i
$513$	4.23943	−	7.34291i	0.187176	−	0.324198i
$514$	6.06269	−	1.62449i	0.267414	−	0.0716533i
$515$	−6.65441	+	17.1217i	−0.293228	+	0.754472i
$516$	−2.04465	+	3.54145i	−0.0900109	+	0.155903i
$517$	21.5065	+	5.76265i	0.945854	+	0.253441i
$518$	0.0232328	−	0.0134134i	0.00102079	−	0.000589353i
$519$	−8.56720			−0.376058
$520$	1.27125	+	7.96140i	0.0557482	+	0.349131i
$521$	21.4660			0.940442			0.470221	−	0.882549i	$-0.344174\pi$
$521$	21.4660			0.940442			0.470221	+	0.882549i	$0.344174\pi$
$522$	−3.06351	+	1.76872i	−0.134086	+	0.0774146i
$523$	11.2954	+	3.02659i	0.493913	+	0.132344i	0.497174	−	0.867651i	$-0.334371\pi$
$523$	11.2954	+	3.02659i	0.493913	+	0.132344i	−0.00326058	+	0.999995i	$0.501038\pi$
$524$	1.76037	−	3.04904i	0.0769020	−	0.133198i
$525$	0.0131529	+	0.298578i	0.000574042	+	0.0130310i
$526$	2.94738	−	0.789749i	0.128512	−	0.0344347i
$527$	−18.2496	+	31.6092i	−0.794965	+	1.37692i
$528$		−	2.74624i		−	0.119515i
$529$	10.8400	+	6.25848i	0.471305	+	0.272108i
$530$	11.3207	−	1.74468i	0.491739	−	0.0757841i
$531$	−8.24745	−	2.20990i	−0.357909	−	0.0959014i
$532$	−0.358370	+	0.358370i	−0.0155373	+	0.0155373i
$533$	25.1648	+	14.3473i	1.09001	+	0.621451i
$534$		−	13.5202i		−	0.585077i
$535$	17.6522	−	2.72047i	0.763173	−	0.117616i
$536$	4.90245	+	8.49129i	0.211754	+	0.366768i
$537$	−5.19458	−	19.3864i	−0.224163	−	0.836587i
$538$	20.8710			0.899811
$539$	4.97291	+	18.5591i	0.214198	+	0.799399i
$540$	−1.39995	−	1.74360i	−0.0602442	−	0.0750327i
$541$	8.37451	−	8.37451i	0.360048	−	0.360048i	−0.503782	−	0.863831i	$-0.668059\pi$
$541$	8.37451	−	8.37451i	0.360048	−	0.360048i	0.863831	+	0.503782i	$0.168059\pi$
$542$	−8.49595	+	2.27648i	−0.364933	+	0.0977834i
$543$	3.45037	−	12.8770i	0.148070	−	0.552603i
$544$	1.22446	−	4.56975i	0.0524983	−	0.195926i
$545$	−23.6095	−	9.17593i	−1.01132	−	0.393054i
$546$	−0.187225	−	0.106743i	−0.00801248	−	0.00456819i
$547$	2.65601	+	2.65601i	0.113563	+	0.113563i	0.761605	−	0.648042i	$-0.224412\pi$
$547$	2.65601	+	2.65601i	0.113563	+	0.113563i	−0.648042	+	0.761605i	$0.724412\pi$
$548$	1.44166	+	2.49703i	0.0615848	+	0.106668i
$549$	8.79641	−	5.07861i	0.375422	−	0.216750i
$550$	−6.33560	+	12.1822i	−0.270151	+	0.519450i
$551$	21.2085	+	21.2085i	0.903515	+	0.903515i
$552$	2.80397	+	1.61888i	0.119345	+	0.0689039i
$553$	−0.657134	−	0.379397i	−0.0279442	−	0.0161336i
$554$	13.0411	+	13.0411i	0.554063	+	0.554063i
$555$	0.782545	−	0.628310i	0.0332172	−	0.0266703i
$556$	8.92480	−	5.15274i	0.378496	−	0.218525i
$557$	−16.3471	−	28.3139i	−0.692647	−	1.19970i	−0.970967	−	0.239212i	$-0.923111\pi$
$557$	−16.3471	−	28.3139i	−0.692647	−	1.19970i	0.278320	−	0.960488i	$-0.410222\pi$
$558$	5.45532	+	5.45532i	0.230942	+	0.230942i
$559$	0.0800457	+	14.7440i	0.00338557	+	0.623605i
$560$	0.0538540	+	0.122328i	0.00227575	+	0.00516929i
$561$	−3.36266	+	12.5496i	−0.141971	+	0.529845i
$562$	2.32541	−	8.67854i	0.0980914	−	0.366082i
$563$	3.02146	−	0.809599i	0.127339	−	0.0341205i	−0.194586	−	0.980885i	$-0.562336\pi$
$563$	3.02146	−	0.809599i	0.127339	−	0.0341205i	0.321926	+	0.946765i	$0.395670\pi$
$564$	5.73288	−	5.73288i	0.241398	−	0.241398i
$565$	20.4005	−	16.3797i	0.858257	−	0.689100i
$566$	0.0862084	+	0.321734i	0.00362361	+	0.0135235i
$567$	0.0597735			0.00251025
$568$	0.474132	+	1.76948i	0.0198941	+	0.0742459i
$569$	18.4196	+	31.9037i	0.772190	+	1.33747i	0.936360	+	0.351041i	$0.114172\pi$
$569$	18.4196	+	31.9037i	0.772190	+	1.33747i	−0.164170	+	0.986432i	$0.552494\pi$
$570$	−11.2078	+	15.2918i	−0.469445	+	0.640504i
$571$			18.0545i			0.755555i	0.925896	+	0.377778i	$0.123312\pi$
$571$			18.0545i			0.755555i	−0.925896	+	0.377778i	$0.876688\pi$
$572$	−4.99733	−	8.54812i	−0.208949	−	0.357415i
$573$	1.59360	−	1.59360i	0.0665735	−	0.0665735i
$574$	0.463864	+	0.124292i	0.0193613	+	0.00518785i
$575$	−8.70354	−	13.6501i	−0.362963	−	0.569247i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$		−	33.4643i		−	1.39314i	−0.717491	−	0.696568i	$-0.754710\pi$
$577$		−	33.4643i		−	1.39314i	0.717491	−	0.696568i	$-0.245290\pi$
$578$	−2.69094	+	4.66085i	−0.111928	+	0.193866i
$579$	8.24932	−	2.21040i	0.342830	−	0.0918610i
$580$	7.23944	−	3.18711i	0.300601	−	0.132338i
$581$	0.0242287	−	0.0419653i	0.00100517	−	0.00174101i
$582$	10.2838	+	2.75553i	0.426277	+	0.114221i
$583$	−12.1830	+	7.03384i	−0.504567	+	0.291312i
$584$	11.0595			0.457645
$585$	−7.53040	−	2.87976i	−0.311344	−	0.119064i
$586$	−20.1755			−0.833442
$587$	3.75690	−	2.16905i	0.155064	−	0.0895261i	−0.420460	−	0.907311i	$-0.638131\pi$
$587$	3.75690	−	2.16905i	0.155064	−	0.0895261i	0.575524	+	0.817785i	$0.304798\pi$
$588$	6.75803	+	1.81081i	0.278696	+	0.0746765i
$589$	32.7072	−	56.6505i	1.34768	−	2.33424i
$590$	17.7956	+	6.91634i	0.732634	+	0.284741i
$591$	10.6348	−	2.84960i	0.437459	−	0.117217i
$592$	0.224405	−	0.388680i	0.00922298	−	0.0159747i
$593$		−	46.7207i		−	1.91859i	−0.282404	−	0.959296i	$-0.591132\pi$
$593$		−	46.7207i		−	1.91859i	0.282404	−	0.959296i	$-0.408868\pi$
$594$	2.37831	+	1.37312i	0.0975833	+	0.0563397i
$595$	−0.0963137	−	0.624949i	−0.00394848	−	0.0256204i
$596$	−6.21211	−	1.66453i	−0.254458	−	0.0681818i
$597$	−13.0569	+	13.0569i	−0.534384	+	0.534384i
$598$	11.6737	−	0.0633770i	0.477373	−	0.00259168i
$599$		−	27.4403i		−	1.12118i	−0.828093	−	0.560591i	$-0.810574\pi$
$599$		−	27.4403i		−	1.12118i	0.828093	−	0.560591i	$-0.189426\pi$
$600$	2.68814	+	4.21591i	0.109743	+	0.172114i
$601$	−5.16355	−	8.94352i	−0.210625	−	0.364814i	0.741285	−	0.671190i	$-0.234217\pi$
$601$	−5.16355	−	8.94352i	−0.210625	−	0.364814i	−0.951910	+	0.306376i	$0.900883\pi$
$602$	0.0632637	+	0.236103i	0.00257844	+	0.00962285i
$603$	−9.80490			−0.399286
$604$	−5.21612	−	19.4668i	−0.212241	−	0.792094i
$605$	−0.840338	+	7.68694i	−0.0341646	+	0.312518i
$606$	−4.09431	+	4.09431i	−0.166320	+	0.166320i
$607$	−10.5917	+	2.83804i	−0.429905	+	0.115193i	−0.467281	−	0.884109i	$-0.654767\pi$
$607$	−10.5917	+	2.83804i	−0.429905	+	0.115193i	0.0373767	+	0.999301i	$0.488100\pi$
$608$	−2.19449	+	8.18996i	−0.0889984	+	0.332147i
$609$	−0.0547259	+	0.204240i	−0.00221760	+	0.00827621i
$610$	−20.7870	+	9.15134i	−0.841641	+	0.370527i
$611$	7.41241	−	28.2767i	0.299874	−	1.14395i
$612$	3.34529	+	3.34529i	0.135225	+	0.135225i
$613$	15.9337	+	27.5980i	0.643556	+	1.11467i	0.984633	+	0.174636i	$0.0558749\pi$
$613$	15.9337	+	27.5980i	0.643556	+	1.11467i	−0.341077	+	0.940035i	$0.610792\pi$
$614$	−26.2781	+	15.1716i	−1.06050	+	0.612278i
$615$	17.8584	+	1.95229i	0.720122	+	0.0787240i
$616$	−0.116073	−	0.116073i	−0.00467672	−	0.00467672i
$617$	−13.3982	−	7.73547i	−0.539393	−	0.311418i	0.205440	−	0.978670i	$-0.434137\pi$
$617$	−13.3982	−	7.73547i	−0.539393	−	0.311418i	−0.744833	+	0.667251i	$0.767471\pi$
$618$	−7.11442	−	4.10751i	−0.286184	−	0.165228i
$619$	−4.41938	−	4.41938i	−0.177630	−	0.177630i	0.612692	−	0.790322i	$-0.290087\pi$
$619$	−4.41938	−	4.41938i	−0.177630	−	0.177630i	−0.790322	+	0.612692i	$0.790087\pi$
$620$	−10.8006	−	13.4519i	−0.433762	−	0.540240i
$621$	−2.80397	+	1.61888i	−0.112520	+	0.0649632i
$622$	−1.99177	−	3.44984i	−0.0798626	−	0.138326i
$623$	−0.571448	−	0.571448i	−0.0228946	−	0.0228946i
$624$	−3.60550	+	0.0195744i	−0.144335	+	0.000783603i
$625$	−2.19833	−	24.9032i	−0.0879334	−	0.996126i
$626$	0.802862	−	2.99632i	0.0320888	−	0.119757i
$627$	6.02659	−	22.4916i	0.240679	−	0.898226i
$628$	10.9592	−	2.93652i	0.437321	−	0.117180i
$629$	−1.50140	+	1.50140i	−0.0598646	+	0.0598646i
$630$	−0.132866	−	0.0145249i	−0.00529351	−	0.000578688i
$631$	−6.31012	−	23.5497i	−0.251202	−	0.937499i	−0.970164	−	0.242449i	$-0.922049\pi$
$631$	−6.31012	−	23.5497i	−0.251202	−	0.937499i	0.718962	−	0.695049i	$-0.244618\pi$
$632$	−12.6945			−0.504959
$633$	−5.08476	−	18.9766i	−0.202101	−	0.754251i
$634$	−14.3463	−	24.8485i	−0.569765	−	0.986862i
$635$	5.26319	+	34.1512i	0.208863	+	1.35525i
$636$			5.12253i			0.203122i
$637$	24.3306	−	6.66115i	0.964014	−	0.263924i
$638$	−6.86928	+	6.86928i	−0.271957	+	0.271957i
$639$	−1.76948	−	0.474132i	−0.0699997	−	0.0187564i
$640$	1.80352	+	1.32186i	0.0712905	+	0.0522510i
$641$	−24.6489	−	14.2311i	−0.973575	−	0.562094i	−0.0732504	−	0.997314i	$-0.523337\pi$
$641$	−24.6489	−	14.2311i	−0.973575	−	0.562094i	−0.900324	+	0.435220i	$0.856671\pi$
$642$			7.98753i			0.315242i
$643$	13.6970	−	23.7239i	0.540158	−	0.935581i	−0.458737	−	0.888572i	$-0.651698\pi$
$643$	13.6970	−	23.7239i	0.540158	−	0.935581i	0.998894	−	0.0470085i	$-0.0149688\pi$
$644$	0.186937	−	0.0500897i	0.00736636	−	0.00197381i
$645$	3.68434	+	8.36887i	0.145071	+	0.329524i
$646$	20.0565	−	34.7390i	0.789114	−	1.36679i
$647$	26.6819	+	7.14940i	1.04897	+	0.281072i	0.741828	−	0.670590i	$-0.233959\pi$
$647$	26.6819	+	7.14940i	1.04897	+	0.281072i	0.307147	+	0.951662i	$0.400626\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−23.4484			−0.920431
$650$	16.0390	+	8.23110i	0.629101	+	0.322850i
$651$	0.461151			0.0180740
$652$	−16.3042	+	9.41324i	−0.638522	+	0.368651i
$653$	−33.4174	−	8.95417i	−1.30772	−	0.350404i	−0.463359	−	0.886171i	$-0.653356\pi$
$653$	−33.4174	−	8.95417i	−1.30772	−	0.350404i	−0.844366	+	0.535767i	$0.820023\pi$
$654$	5.66395	−	9.81025i	0.221478	−	0.383611i
$655$	−3.17207	−	7.20526i	−0.123943	−	0.281533i
$656$	7.76037	−	2.07938i	0.302991	−	0.0811863i
$657$	−5.52975	+	9.57780i	−0.215736	+	0.373666i
$658$		−	0.484614i		−	0.0188922i
$659$	7.95962	+	4.59549i	0.310063	+	0.179015i	0.646955	−	0.762529i	$-0.276042\pi$
$659$	7.95962	+	4.59549i	0.310063	+	0.179015i	−0.336892	+	0.941543i	$0.609376\pi$
$660$	−4.95290	−	3.63013i	−0.192791	−	0.141303i
$661$	33.9933	+	9.10847i	1.32219	+	0.354278i	0.849796	−	0.527112i	$-0.176725\pi$
$661$	33.9933	+	9.10847i	1.32219	+	0.354278i	0.472389	+	0.881390i	$0.343392\pi$
$662$	10.0727	−	10.0727i	0.391486	−	0.391486i
$663$	16.5002	+	4.32534i	0.640814	+	0.167982i
$664$		−	0.810683i		−	0.0314606i
$665$	0.172615	+	1.12004i	0.00669371	+	0.0434333i
$666$	0.224405	+	0.388680i	0.00869551	+	0.0150611i
$667$	−2.96434	−	11.0631i	−0.114780	−	0.428363i
$668$	−11.8485			−0.458430
$669$	0.366701	+	1.36855i	0.0141775	+	0.0529111i
$670$	21.7946	+	2.38259i	0.841998	+	0.0920475i
$671$	19.7241	−	19.7241i	0.761442	−	0.761442i
$672$	−0.0577367	+	0.0154705i	−0.00222724	+	0.000596788i
$673$	−1.65990	+	6.19481i	−0.0639843	+	0.238793i	−0.990510	−	0.137438i	$-0.956113\pi$
$673$	−1.65990	+	6.19481i	−0.0639843	+	0.238793i	0.926526	+	0.376230i	$0.122780\pi$
$674$	−4.19046	+	15.6390i	−0.161411	+	0.602393i
$675$	−4.99516	+	0.220047i	−0.192264	+	0.00846960i
$676$	−11.1871	+	6.62186i	−0.430273	+	0.254687i
$677$	29.2524	+	29.2524i	1.12426	+	1.12426i	0.991094	+	0.133166i	$0.0425142\pi$
$677$	29.2524	+	29.2524i	1.12426	+	1.12426i	0.133166	+	0.991094i	$0.457486\pi$
$678$	5.85012	+	10.1327i	0.224672	+	0.389144i
$679$	0.551123	−	0.318191i	0.0211502	−	0.0122111i
$680$	−6.62308	−	8.24889i	−0.253984	−	0.316331i
$681$	1.12653	+	1.12653i	0.0431687	+	0.0431687i
$682$	18.3486	+	10.5936i	0.702606	+	0.405650i
$683$	10.5986	+	6.11911i	0.405544	+	0.234141i	0.688873	−	0.724882i	$-0.258106\pi$
$683$	10.5986	+	6.11911i	0.405544	+	0.234141i	−0.283329	+	0.959023i	$0.591439\pi$
$684$	−5.99546	−	5.99546i	−0.229242	−	0.229242i
$685$	6.40913	+	0.700648i	0.244880	+	0.0267704i
$686$	0.724530	−	0.418307i	0.0276627	−	0.0159711i
$687$	3.75764	+	6.50842i	0.143363	+	0.248312i
$688$	2.89158	+	2.89158i	0.110240	+	0.110240i
$689$	9.32148	+	15.9447i	0.355120	+	0.607446i
$690$	6.62613	−	2.91711i	0.252252	−	0.111053i
$691$	0.165414	−	0.617335i	0.00629266	−	0.0234845i	−0.962708	−	0.270542i	$-0.912797\pi$
$691$	0.165414	−	0.617335i	0.00629266	−	0.0234845i	0.969001	+	0.247058i	$0.0794637\pi$
$692$	−2.21736	+	8.27528i	−0.0842912	+	0.314579i
$693$	0.158559	−	0.0424857i	0.00602315	−	0.00161390i
$694$	−13.7213	+	13.7213i	−0.520855	+	0.520855i
$695$	2.50423	−	22.9073i	0.0949908	−	0.868922i
$696$	0.915555	+	3.41690i	0.0347040	+	0.129517i
$697$	−38.0090			−1.43969
$698$	7.44233	+	27.7752i	0.281697	+	1.05131i
$699$	9.38404	+	16.2536i	0.354937	+	0.614769i
$700$	0.291808	+	0.0645728i	0.0110293	+	0.00244062i
$701$			8.15376i			0.307963i	0.988074	+	0.153982i	$0.0492097\pi$
$701$			8.15376i			0.307963i	−0.988074	+	0.153982i	$0.950790\pi$
$702$	1.78580	−	3.13224i	0.0674006	−	0.118219i
$703$	2.69082	−	2.69082i	0.101486	−	0.101486i
$704$	−2.65266	−	0.710778i	−0.0999759	−	0.0267885i
$705$	−2.76133	−	17.9174i	−0.103998	−	0.674809i
$706$	17.1713	+	9.91387i	0.646252	+	0.373114i
$707$			0.346102i			0.0130165i
$708$	−4.26919	+	7.39446i	−0.160446	+	0.277901i
$709$	−23.1506	+	6.20318i	−0.869438	+	0.232965i	−0.665845	−	0.746090i	$-0.731929\pi$
$709$	−23.1506	+	6.20318i	−0.869438	+	0.232965i	−0.203593	+	0.979056i	$0.565262\pi$
$710$	3.81804	+	1.48390i	0.143288	+	0.0556896i
$711$	6.34724	−	10.9937i	0.238040	−	0.412298i
$712$	−13.0595	−	3.49929i	−0.489426	−	0.131141i
$713$	−21.6326	+	12.4896i	−0.810148	+	0.467739i
$714$	0.282785			0.0105830
$715$	−22.0225	−	2.28659i	−0.823594	−	0.0855135i
$716$	−20.0703			−0.750063
$717$	9.25450	−	5.34309i	0.345616	−	0.199541i
$718$	24.4834	+	6.56031i	0.913713	+	0.244829i
$719$	−17.5179	+	30.3418i	−0.653306	+	1.13156i	0.329010	+	0.944327i	$0.393285\pi$
$719$	−17.5179	+	30.3418i	−0.653306	+	1.13156i	−0.982316	+	0.187232i	$0.940048\pi$
$720$	−2.04652	+	0.900968i	−0.0762694	+	0.0335771i
$721$	−0.474309	+	0.127091i	−0.0176642	+	0.00473310i
$722$	−26.4456	+	45.8051i	−0.984203	+	1.70469i
$723$		−	7.75511i		−	0.288416i
$724$	−11.5452	−	6.66561i	−0.429073	−	0.247725i
$725$	3.82146	−	17.2694i	0.141926	−	0.641369i
$726$	−3.34035	−	0.895044i	−0.123972	−	0.0332182i
$727$	36.3067	−	36.3067i	1.34654	−	1.34654i	0.457150	−	0.889389i	$-0.348870\pi$
$727$	36.3067	−	36.3067i	1.34654	−	1.34654i	0.889389	−	0.457150i	$-0.151130\pi$
$728$	−0.151563	+	0.153218i	−0.00561731	+	0.00567864i
$729$			1.00000i			0.0370370i
$730$	14.6191	−	19.9461i	0.541076	−	0.738236i
$731$	−9.67316	−	16.7544i	−0.357775	−	0.619684i
$732$	−2.62888	−	9.81113i	−0.0971663	−	0.362630i
$733$	−31.5778			−1.16635			−0.583176	−	0.812346i	$-0.698190\pi$
$733$	−31.5778			−1.16635			−0.583176	+	0.812346i	$0.698190\pi$
$734$	−6.21836	−	23.2072i	−0.229524	−	0.856595i
$735$	12.1990	−	9.79463i	0.449966	−	0.361280i
$736$	2.28944	−	2.28944i	0.0843897	−	0.0843897i
$737$	−26.0091	+	6.96911i	−0.958057	+	0.256711i
$738$	−2.07938	+	7.76037i	−0.0765432	+	0.285663i
$739$	−2.98484	+	11.1396i	−0.109799	+	0.409775i	−0.998845	−	0.0480419i	$-0.984702\pi$
$739$	−2.98484	+	11.1396i	−0.109799	+	0.409775i	0.889046	+	0.457817i	$0.151369\pi$
$740$	−0.404363	−	0.918499i	−0.0148647	−	0.0337647i
$741$	−29.5718	−	7.75192i	−1.08635	−	0.284774i
$742$	0.216510	+	0.216510i	0.00794834	+	0.00794834i
$743$	−9.17935	−	15.8991i	−0.336758	−	0.583282i	0.647063	−	0.762436i	$-0.275997\pi$
$743$	−9.17935	−	15.8991i	−0.336758	−	0.583282i	−0.983821	+	0.179155i	$0.942664\pi$
$744$	6.68138	−	3.85749i	0.244951	−	0.141423i
$745$	−11.2135	+	9.00342i	−0.410832	+	0.329860i
$746$	7.27329	+	7.27329i	0.266294	+	0.266294i
$747$	0.702072	+	0.405341i	0.0256875	+	0.0148307i
$748$	11.2517	+	6.49615i	0.411402	+	0.237523i
$749$	0.337603	+	0.337603i	0.0123357	+	0.0123357i
$750$	11.1568	+	0.724697i	0.407390	+	0.0264622i
$751$	−43.8619	+	25.3237i	−1.60054	+	0.924074i	−0.609164	+	0.793044i	$0.708495\pi$
$751$	−43.8619	+	25.3237i	−1.60054	+	0.924074i	−0.991378	+	0.131030i	$0.958172\pi$
$752$	−4.05376	−	7.02131i	−0.147825	−	0.256041i
$753$	−3.24211	−	3.24211i	−0.118149	−	0.118149i
$754$	9.06755	+	8.96962i	0.330221	+	0.326654i
$755$	−42.0038	−	16.3250i	−1.52868	−	0.594126i
$756$	0.0154705	−	0.0577367i	0.000562657	−	0.00209986i
$757$	−2.22914	+	8.31926i	−0.0810194	+	0.302369i	−0.994531	−	0.104445i	$-0.966693\pi$
$757$	−2.22914	+	8.31926i	−0.0810194	+	0.302369i	0.913511	+	0.406813i	$0.133360\pi$
$758$	31.0601	−	8.32254i	1.12815	−	0.302288i
$759$	−6.28733	+	6.28733i	−0.228216	+	0.228216i
$760$	11.8700	+	14.7838i	0.430569	+	0.536264i
$761$	11.1159	+	41.4849i	0.402949	+	1.50383i	0.807807	+	0.589447i	$0.200654\pi$
$761$	11.1159	+	41.4849i	0.402949	+	1.50383i	−0.404858	+	0.914380i	$0.632679\pi$
$762$	−15.4532			−0.559810
$763$	−0.175248	−	0.654036i	−0.00634442	−	0.0236777i
$764$	−1.12684	−	1.95175i	−0.0407678	−	0.0706119i
$765$	10.4553	−	1.61131i	0.378012	−	0.0582571i
$766$			14.6519i			0.529394i
$767$	0.167134	+	30.7851i	0.00603485	+	1.11159i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−3.61036	−	0.967392i	−0.130193	−	0.0348851i	0.193134	−	0.981172i	$-0.438135\pi$
$769$	−3.61036	−	0.967392i	−0.130193	−	0.0348851i	−0.323327	+	0.946287i	$0.604801\pi$
$770$	−0.362772	+	0.0559085i	−0.0130734	+	0.00201480i
$771$	5.43566	+	3.13828i	0.195760	+	0.113022i
$772$		−	8.54032i		−	0.307373i
$773$	−16.8322	+	29.1543i	−0.605413	+	1.04861i	0.386573	+	0.922259i	$0.373659\pi$
$773$	−16.8322	+	29.1543i	−0.605413	+	1.04861i	−0.991986	+	0.126347i	$0.959675\pi$
$774$	−3.94997	+	1.05839i	−0.141979	+	0.0380431i
$775$	−38.5376	+	1.69766i	−1.38431	+	0.0609816i
$776$	5.32328	−	9.22020i	0.191095	−	0.330986i
$777$	0.0259128	+	0.00694331i	0.000929616	+	0.000249090i
$778$	−28.3441	+	16.3645i	−1.01618	+	0.586694i
$779$	68.1202			2.44066
$780$	−4.73065	+	6.52847i	−0.169384	+	0.233757i
$781$	−5.03084			−0.180018
$782$	−13.2655	+	7.65882i	−0.474372	+	0.273879i
$783$	−3.41690	−	0.915555i	−0.122110	−	0.0327193i
$784$	3.49821	−	6.05908i	0.124936	−	0.216396i
$785$	9.19047	−	23.6469i	0.328022	−	0.843994i
$786$	3.40077	−	0.911233i	0.121301	−	0.0325026i
$787$	15.5130	−	26.8693i	0.552978	−	0.957787i	−0.445079	−	0.895491i	$-0.646825\pi$
$787$	15.5130	−	26.8693i	0.552978	−	0.957787i	0.998058	−	0.0622956i	$-0.0198421\pi$
$788$		−	11.0100i		−	0.392215i
$789$	2.64255	+	1.52568i	0.0940773	+	0.0543156i
$790$	−16.7803	+	22.8948i	−0.597016	+	0.814560i
$791$	0.675533	+	0.181009i	0.0240192	+	0.00643592i
$792$	1.94188	−	1.94188i	0.0690018	−	0.0690018i
$793$	−26.0361	−	25.7550i	−0.924571	−	0.914586i
$794$			16.2362i			0.576202i
$795$	9.23861	+	6.77125i	0.327660	+	0.240152i
$796$	9.23263	+	15.9914i	0.327242	+	0.566800i
$797$	5.95563	+	22.2267i	0.210959	+	0.787311i	0.987550	+	0.157305i	$0.0502807\pi$
$797$	5.95563	+	22.2267i	0.210959	+	0.787311i	−0.776591	+	0.630005i	$0.783053\pi$
$798$	−0.506811			−0.0179409
$799$	9.92733	+	37.0493i	0.351204	+	1.31071i
$800$	4.76800	−	1.50539i	0.168574	−	0.0532236i
$801$	9.56023	−	9.56023i	0.337794	−	0.337794i
$802$	−34.3382	+	9.20088i	−1.21252	+	0.324895i
$803$	−7.86085	+	29.3371i	−0.277403	+	1.03528i
$804$	−2.53770	+	9.47081i	−0.0894976	+	0.334010i
$805$	0.156766	−	0.403357i	0.00552528	−	0.0142165i
$806$	13.7774	−	24.1652i	0.485288	−	0.851183i
$807$	14.7580	+	14.7580i	0.519506	+	0.519506i
$808$	2.89512	+	5.01449i	0.101850	+	0.176409i
$809$	−2.05790	+	1.18813i	−0.0723519	+	0.0417724i	−0.535740	−	0.844383i	$-0.679967\pi$
$809$	−2.05790	+	1.18813i	−0.0723519	+	0.0417724i	0.463388	+	0.886156i	$0.346634\pi$
$810$	0.243000	−	2.22283i	0.00853815	−	0.0781021i
$811$	16.8751	+	16.8751i	0.592564	+	0.592564i	0.938323	−	0.345759i	$-0.112379\pi$
$811$	16.8751	+	16.8751i	0.592564	+	0.592564i	−0.345759	+	0.938323i	$0.612379\pi$
$812$	0.183116	+	0.105722i	0.00642612	+	0.00371012i
$813$	−7.61726	−	4.39783i	−0.267149	−	0.154239i
$814$	0.871535	+	0.871535i	0.0305473	+	0.0305473i
$815$	−4.57483	+	41.8480i	−0.160249	+	1.46587i
$816$	4.09712	−	2.36547i	0.143428	−	0.0828082i
$817$	17.3364	+	30.0274i	0.606522	+	1.05053i
$818$	16.4343	+	16.4343i	0.574612	+	0.574612i
$819$	−0.0569091	−	0.207867i	−0.00198856	−	0.00726346i
$820$	6.50787	−	16.7446i	0.227265	−	0.584748i
$821$	9.48774	−	35.4087i	0.331124	−	1.23577i	−0.576886	−	0.816825i	$-0.695732\pi$
$821$	9.48774	−	35.4087i	0.331124	−	1.23577i	0.908010	−	0.418948i	$-0.137601\pi$
$822$	−0.746260	+	2.78508i	−0.0260288	+	0.0971408i
$823$	−1.97965	+	0.530446i	−0.0690063	+	0.0184902i	−0.293157	−	0.956064i	$-0.594706\pi$
$823$	−1.97965	+	0.530446i	−0.0690063	+	0.0184902i	0.224151	+	0.974554i	$0.428039\pi$
$824$	−5.80890	+	5.80890i	−0.202363	+	0.202363i
$825$	−13.0941	+	4.13416i	−0.455876	+	0.143933i
$826$	0.132093	+	0.492978i	0.00459611	+	0.0171529i
$827$	−25.6576			−0.892202			−0.446101	−	0.894983i	$-0.647188\pi$
$827$	−25.6576			−0.892202			−0.446101	+	0.894983i	$0.647188\pi$
$828$	0.837992	+	3.12743i	0.0291222	+	0.108686i
$829$	−12.5720	−	21.7753i	−0.436643	−	0.756288i	0.560785	−	0.827962i	$-0.310499\pi$
$829$	−12.5720	−	21.7753i	−0.436643	−	0.756288i	−0.997428	+	0.0716731i	$0.977166\pi$
$830$	−1.46208	−	1.07161i	−0.0507497	−	0.0371960i
$831$			18.4429i			0.639777i
$832$	−0.914264	+	3.48771i	−0.0316964	+	0.120915i
$833$	−23.4051	+	23.4051i	−0.810937	+	0.810937i
$834$	9.95432	+	2.66725i	0.344690	+	0.0923594i
$835$	−15.6620	+	21.3690i	−0.542004	+	0.739503i
$836$	−20.1654	−	11.6425i	−0.697434	−	0.402664i
$837$			7.71499i			0.266669i
$838$	−11.5317	+	19.9734i	−0.398354	+	0.689970i
$839$	51.4970	−	13.7986i	1.77787	−	0.476380i	0.787680	−	0.616085i	$-0.211282\pi$
$839$	51.4970	−	13.7986i	1.77787	−	0.476380i	0.990193	+	0.139705i	$0.0446156\pi$
$840$	−0.0484183	+	0.124579i	−0.00167059	+	0.00429839i
$841$	−8.24329	+	14.2778i	−0.284251	+	0.492338i
$842$	−3.85309	−	1.03243i	−0.132786	−	0.0355800i
$843$	7.78097	−	4.49234i	0.267991	−	0.154725i
$844$	−19.6460			−0.676243
$845$	−2.84506	+	28.9293i	−0.0978730	+	0.995199i
$846$	8.10752			0.278742
$847$	−0.179014	+	0.103354i	−0.00615099	+	0.00355128i
$848$	4.94799	+	1.32581i	0.169915	+	0.0455285i
$849$	−0.166542	+	0.288459i	−0.00571570	+	0.00989988i
$850$	−23.6318	+	1.04103i	−0.810565	+	0.0357070i
$851$	−1.40362	+	0.376099i	−0.0481154	+	0.0128925i
$852$	−0.915952	+	1.58648i	−0.0313800	+	0.0543517i
$853$		−	14.4381i		−	0.494351i	−0.968971	−	0.247176i	$-0.920498\pi$
$853$		−	14.4381i		−	0.494351i	0.968971	−	0.247176i	$-0.0795025\pi$
$854$	−0.525792	−	0.303566i	−0.0179922	−	0.0103878i
$855$	−18.7381	+	2.88781i	−0.640830	+	0.0987611i
$856$	7.71536	+	2.06732i	0.263705	+	0.0706597i
$857$	27.7097	−	27.7097i	0.946544	−	0.946544i	−0.0520979	−	0.998642i	$-0.516591\pi$
$857$	27.7097	−	27.7097i	0.946544	−	0.946544i	0.998642	+	0.0520979i	$0.0165908\pi$
$858$	2.51079	−	9.57808i	0.0857168	−	0.326990i
$859$		−	20.1695i		−	0.688176i	−0.938937	−	0.344088i	$-0.888188\pi$
$859$		−	20.1695i		−	0.688176i	0.938937	−	0.344088i	$-0.111812\pi$
$860$	9.03728	−	1.39278i	0.308169	−	0.0474933i
$861$	0.240114	+	0.415889i	0.00818305	+	0.0141735i
$862$	5.99669	+	22.3799i	0.204248	+	0.762264i
$863$	−24.8056			−0.844391			−0.422196	−	0.906505i	$-0.638740\pi$
$863$	−24.8056			−0.844391			−0.422196	+	0.906505i	$0.638740\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	11.9936	+	14.9378i	0.407796	+	0.507900i
$866$	−1.79809	+	1.79809i	−0.0611016	+	0.0611016i
$867$	−5.19850	+	1.39293i	−0.176550	+	0.0473065i
$868$	0.119355	−	0.445438i	0.00405117	−	0.0151192i
$869$	9.02296	−	33.6742i	0.306083	−	1.14232i
$870$	7.37268	+	2.86542i	0.249957	+	0.0971470i
$871$	9.33504	+	34.0973i	0.316306	+	1.15534i
$872$	−8.01003	−	8.01003i	−0.271254	−	0.271254i
$873$	5.32328	+	9.22020i	0.180166	+	0.312056i
$874$	23.7745	−	13.7262i	0.804185	−	0.464297i
$875$	0.502187	−	0.440927i	0.0169770	−	0.0149060i
$876$	7.82024	+	7.82024i	0.264222	+	0.264222i
$877$	−13.8854	−	8.01676i	−0.468878	−	0.270707i	0.246892	−	0.969043i	$-0.420591\pi$
$877$	−13.8854	−	8.01676i	−0.468878	−	0.270707i	−0.715770	+	0.698336i	$0.753924\pi$
$878$	−11.9761	−	6.91442i	−0.404174	−	0.233350i
$879$	−14.2662	−	14.2662i	−0.481188	−	0.481188i
$880$	−4.78834	+	3.84459i	−0.161415	+	0.129601i
$881$	−9.72728	+	5.61605i	−0.327720	+	0.189209i	−0.654829	−	0.755777i	$-0.727259\pi$
$881$	−9.72728	+	5.61605i	−0.327720	+	0.189209i	0.327108	+	0.944987i	$0.393926\pi$
$882$	3.49821	+	6.05908i	0.117791	+	0.204020i
$883$	23.5398	+	23.5398i	0.792177	+	0.792177i	0.981848	−	0.189671i	$-0.0607421\pi$
$883$	23.5398	+	23.5398i	0.792177	+	0.792177i	−0.189671	+	0.981848i	$0.560742\pi$
$884$	8.44852	−	14.8185i	0.284154	−	0.498399i
$885$	7.69282	+	17.4740i	0.258591	+	0.587382i
$886$	−6.44350	+	24.0475i	−0.216474	+	0.807890i
$887$	2.77413	−	10.3532i	0.0931461	−	0.347626i	−0.903586	−	0.428407i	$-0.859075\pi$
$887$	2.77413	−	10.3532i	0.0931461	−	0.347626i	0.996732	+	0.0807814i	$0.0257416\pi$
$888$	0.433517	−	0.116160i	0.0145479	−	0.00389809i
$889$	−0.653148	+	0.653148i	−0.0219059	+	0.0219059i
$890$	−23.5739	+	18.9276i	−0.790197	+	0.634454i
$891$	0.710778	+	2.65266i	0.0238120	+	0.0888675i
$892$	1.41682			0.0474388
$893$	−17.7919	−	66.4002i	−0.595383	−	2.22200i
$894$	−3.21563	−	5.56963i	−0.107547	−	0.186276i
$895$	−26.5301	+	36.1973i	−0.886803	+	1.20994i
$896$			0.0597735i			0.00199689i
$897$	8.29937	+	8.20974i	0.277108	+	0.274115i
$898$	−19.7754	+	19.7754i	−0.659914	+	0.659914i
$899$	−26.3613	−	7.06349i	−0.879199	−	0.235581i
$900$	−1.08029	+	4.88190i	−0.0360098	+	0.162730i
$901$	−20.9876	−	12.1172i	−0.699200	−	0.403683i
$902$			22.0636i			0.734638i
$903$	−0.122216	+	0.211684i	−0.00406710	+	0.00704442i
$904$	11.3016	−	3.02824i	0.375884	−	0.100718i
$905$	−27.2826	+	12.0110i	−0.906905	+	0.399259i
$906$	10.0768	−	17.4535i	0.334778	−	0.579853i
$907$	13.4904	+	3.61474i	0.447941	+	0.120025i	0.475736	−	0.879588i	$-0.342182\pi$
$907$	13.4904	+	3.61474i	0.447941	+	0.120025i	−0.0277950	+	0.999614i	$0.508849\pi$
$908$	1.37971	−	0.796577i	0.0457874	−	0.0264353i
$909$	−5.79023			−0.192050
$910$	0.0759872	+	0.475881i	0.00251895	+	0.0157753i
$911$	−23.8021			−0.788598			−0.394299	−	0.918982i	$-0.629013\pi$
$911$	−23.8021			−0.788598			−0.394299	+	0.918982i	$0.629013\pi$
$912$	−7.34291	+	4.23943i	−0.243148	+	0.140382i
$913$	2.15047	+	0.576216i	0.0711700	+	0.0190700i
$914$	12.2566	−	21.2291i	0.405412	−	0.702195i
$915$	−21.1696	−	8.22765i	−0.699845	−	0.271998i
$916$	7.25920	−	1.94510i	0.239851	−	0.0642678i
$917$	0.105223	−	0.182252i	0.00347478	−	0.00601849i
$918$			4.73095i			0.156145i
$919$	21.3060	+	12.3010i	0.702821	+	0.405774i	0.808397	−	0.588637i	$-0.200335\pi$
$919$	21.3060	+	12.3010i	0.702821	+	0.405774i	−0.105576	+	0.994411i	$0.533669\pi$
$920$	−1.10274	−	7.15536i	−0.0363564	−	0.235905i
$921$	−29.3094	−	7.85342i	−0.965776	−	0.258779i
$922$	1.29638	−	1.29638i	0.0426940	−	0.0426940i
$923$	0.0358584	+	6.60493i	0.00118029	+	0.217404i
$924$		−	0.164152i		−	0.00540021i
$925$	−2.19104	−	0.484846i	−0.0720411	−	0.0159416i
$926$	0.865504	+	1.49910i	0.0284422	+	0.0492634i
$927$	−2.12621	−	7.93511i	−0.0698337	−	0.260623i
$928$	3.53743			0.116122
$929$	−9.98656	−	37.2704i	−0.327649	−	1.22280i	−0.911622	−	0.411029i	$-0.865170\pi$
$929$	−9.98656	−	37.2704i	−0.327649	−	1.22280i	0.583974	−	0.811772i	$-0.301497\pi$
$930$	1.87474	−	17.1491i	0.0614752	−	0.562340i
$931$	41.9468	−	41.9468i	1.37475	−	1.37475i
$932$	18.1286	−	4.85754i	0.593821	−	0.159114i
$933$	1.03102	−	3.84780i	0.0337539	−	0.125971i
$934$	6.79795	−	25.3703i	0.222436	−	0.830141i
$935$	26.5891	−	11.7057i	0.869555	−	0.382816i
$936$	−2.56331	−	2.53563i	−0.0837845	−	0.0828797i
$937$	41.3567	+	41.3567i	1.35106	+	1.35106i	0.884473	+	0.466590i	$0.154518\pi$
$937$	41.3567	+	41.3567i	1.35106	+	1.35106i	0.466590	+	0.884473i	$0.345482\pi$
$938$	0.293036	+	0.507554i	0.00956798	+	0.0165722i
$939$	2.68643	−	1.55101i	0.0876683	−	0.0506153i
$940$	−18.0216	−	1.97013i	−0.587799	−	0.0642584i
$941$	34.1176	+	34.1176i	1.11220	+	1.11220i	0.992852	+	0.119350i	$0.0380812\pi$
$941$	34.1176	+	34.1176i	1.11220	+	1.11220i	0.119350	+	0.992852i	$0.461919\pi$
$942$	9.82579	+	5.67292i	0.320141	+	0.184834i
$943$	−22.5275	−	13.0062i	−0.733595	−	0.423542i
$944$	6.03755	+	6.03755i	0.196506	+	0.196506i
$945$	−0.0836797	−	0.104221i	−0.00272210	−	0.00339031i
$946$	−9.72565	+	5.61511i	−0.316208	+	0.182563i
$947$	−17.0920	−	29.6042i	−0.555415	−	0.962007i	−0.997871	−	0.0652169i	$-0.979226\pi$
$947$	−17.0920	−	29.6042i	−0.555415	−	0.962007i	0.442456	−	0.896790i	$-0.354107\pi$
$948$	−8.97635	−	8.97635i	−0.291538	−	0.291538i
$949$	38.5723	+	10.1113i	1.25211	+	0.328227i
$950$	42.3533	−	1.86575i	1.37412	−	0.0605328i
$951$	7.42620	−	27.7149i	0.240811	−	0.898719i
$952$	0.0731902	−	0.273150i	0.00237211	−	0.00885283i
$953$	31.8846	−	8.54345i	1.03284	−	0.276750i	0.297699	−	0.954660i	$-0.403781\pi$
$953$	31.8846	−	8.54345i	1.03284	−	0.276750i	0.735145	+	0.677910i	$0.237114\pi$
$954$	−3.62218	+	3.62218i	−0.117272	+	0.117272i
$955$	−5.00956	−	0.547646i	−0.162105	−	0.0177214i
$956$	−2.76579	−	10.3221i	−0.0894519	−	0.333839i
$957$	−9.71463			−0.314029
$958$	−7.29554	−	27.2273i	−0.235708	−	0.879675i
$959$	0.0861732	+	0.149256i	0.00278268	+	0.00481974i
$960$	0.340590	+	2.20998i	0.0109925	+	0.0713267i
$961$			28.5210i			0.920033i
$962$	1.13802	−	1.15044i	0.0366911	−	0.0370917i
$963$	−5.64803	+	5.64803i	−0.182005	+	0.182005i
$964$	−7.49086	−	2.00717i	−0.241264	−	0.0646466i
$965$	−15.4027	−	11.2891i	−0.495829	−	0.363408i
$966$	0.167603	+	0.0967658i	0.00539255	+	0.00311339i
$967$			9.57982i			0.308066i	0.988066	+	0.154033i	$0.0492262\pi$
$967$			9.57982i			0.308066i	−0.988066	+	0.154033i	$0.950774\pi$
$968$	−1.72909	+	2.99487i	−0.0555751	+	0.0962589i
$969$	38.7463	−	10.3820i	1.24471	−	0.333519i
$970$	−9.59222	−	21.7884i	−0.307988	−	0.699585i
$971$	15.4536	−	26.7664i	0.495930	−	0.858976i	−0.504059	−	0.863669i	$-0.668161\pi$
$971$	15.4536	−	26.7664i	0.495930	−	0.858976i	0.999989	+	0.00469356i	$0.00149401\pi$
$972$	0.965926	+	0.258819i	0.0309821	+	0.00830162i
$973$	0.533466	−	0.307997i	0.0171021	−	0.00987392i
$974$	−8.03604			−0.257491
$975$	5.52101	+	17.1615i	0.176814	+	0.549609i
$976$	−10.1572			−0.325125
$977$	−39.2238	+	22.6459i	−1.25488	+	0.724506i	−0.972075	−	0.234671i	$-0.924599\pi$
$977$	−39.2238	+	22.6459i	−1.25488	+	0.724506i	−0.282806	+	0.959177i	$0.591265\pi$
$978$	−18.1850	−	4.87265i	−0.581491	−	0.155810i
$979$	18.5648	−	32.1553i	0.593335	−	1.02769i
$980$	−6.30356	−	14.3183i	−0.201360	−	0.457383i
$981$	10.9419	−	2.93188i	0.349348	−	0.0936076i
$982$	12.0541	−	20.8782i	0.384660	−	0.666251i
$983$		−	33.1084i		−	1.05599i	−0.849246	−	0.527997i	$-0.822943\pi$
$983$		−	33.1084i		−	1.05599i	0.849246	−	0.527997i	$-0.177057\pi$
$984$	6.95775	+	4.01706i	0.221805	+	0.128059i
$985$	−19.8568	−	14.5536i	−0.632690	−	0.463718i
$986$	−16.1652	−	4.33144i	−0.514804	−	0.137941i
$987$	0.342674	−	0.342674i	0.0109074	−	0.0109074i
$988$	−15.1415	+	26.5578i	−0.481716	+	0.844918i
$989$		−	13.2402i		−	0.421013i
$990$	−0.935339	−	6.06912i	−0.0297270	−	0.192889i
$991$	1.03126	+	1.78620i	0.0327591	+	0.0567404i	0.881940	−	0.471361i	$-0.156237\pi$
$991$	1.03126	+	1.78620i	0.0327591	+	0.0567404i	−0.849181	+	0.528102i	$0.822904\pi$
$992$	−1.99679	−	7.45211i	−0.0633980	−	0.236605i
$993$	14.2449			0.452049
$994$	0.0283405	+	0.105768i	0.000898906	+	0.00335476i
$995$	41.0451	+	4.48706i	1.30122	+	0.142249i
$996$	0.573239	−	0.573239i	0.0181638	−	0.0181638i
$997$	2.25541	−	0.604334i	0.0714294	−	0.0191395i	−0.222927	−	0.974835i	$-0.571561\pi$
$997$	2.25541	−	0.604334i	0.0714294	−	0.0191395i	0.294357	+	0.955696i	$0.404895\pi$
$998$	−0.894519	+	3.33839i	−0.0283155	+	0.105675i
$999$	−0.116160	+	0.433517i	−0.00367515	+	0.0137159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.c.37.6	✓	32
5.3	odd	4		390.2.bn.c.193.1	yes	32
13.6	odd	12		390.2.bn.c.97.1	yes	32
65.58	even	12	inner	390.2.bd.c.253.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.37.6	✓	32	1.1	even	1	trivial
390.2.bd.c.253.6	yes	32	65.58	even	12	inner
390.2.bn.c.97.1	yes	32	13.6	odd	12
390.2.bn.c.193.1	yes	32	5.3	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.900968 - 2.04652i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.0298867 - 0.0517653i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.900968 - 2.04652i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.0298867 - 0.0517653i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.80352 - 1.32186i) q^{10} +(2.65266 + 0.710778i) q^{11} +(0.707107 - 0.707107i) q^{12} +(0.914264 - 3.48771i) q^{13} -0.0597735i q^{14} +(-0.340590 - 2.20998i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.22446 + 4.56975i) q^{17} +1.00000 q^{18} +(-2.19449 - 8.18996i) q^{19} +(-2.22283 - 0.243000i) q^{20} +(0.0422662 - 0.0422662i) q^{21} +(2.65266 - 0.710778i) q^{22} +(-0.837992 + 3.12743i) q^{23} +(0.258819 - 0.965926i) q^{24} +(-3.37651 + 3.68770i) q^{25} +(-0.952079 - 3.47758i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.0298867 - 0.0517653i) q^{28} +(-3.06351 + 1.76872i) q^{29} +(-1.39995 - 1.74360i) q^{30} +(5.45532 + 5.45532i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.37831 + 1.37312i) q^{33} +(3.34529 + 3.34529i) q^{34} +(-0.132866 - 0.0145249i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.224405 + 0.388680i) q^{37} +(-5.99546 - 5.99546i) q^{38} +(1.78580 - 3.13224i) q^{39} +(-2.04652 + 0.900968i) q^{40} +(-2.07938 + 7.76037i) q^{41} +(0.0154705 - 0.0577367i) q^{42} +(-3.94997 + 1.05839i) q^{43} +(1.94188 - 1.94188i) q^{44} +(0.243000 - 2.22283i) q^{45} +(0.837992 + 3.12743i) q^{46} +8.10752 q^{47} +(-0.258819 - 0.965926i) q^{48} +(3.49821 + 6.05908i) q^{49} +(-1.08029 + 4.88190i) q^{50} +4.73095i q^{51} +(-2.56331 - 2.53563i) q^{52} +(-3.62218 + 3.62218i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-0.935339 - 6.06912i) q^{55} +(-0.0517653 - 0.0298867i) q^{56} -8.47887i q^{57} +(-1.76872 + 3.06351i) q^{58} +(-8.24745 + 2.20990i) q^{59} +(-2.08419 - 0.810029i) q^{60} +(5.07861 - 8.79641i) q^{61} +(7.45211 + 1.99679i) q^{62} +(0.0517653 - 0.0298867i) q^{63} -1.00000 q^{64} +(-7.96140 + 1.27125i) q^{65} +2.74624 q^{66} +(-8.49129 + 4.90245i) q^{67} +(4.56975 + 1.22446i) q^{68} +(-1.61888 + 2.80397i) q^{69} +(-0.122328 + 0.0538540i) q^{70} +(-1.76948 + 0.474132i) q^{71} +(0.500000 - 0.866025i) q^{72} +11.0595i q^{73} +(0.388680 + 0.224405i) q^{74} +(-4.21591 + 2.68814i) q^{75} +(-8.18996 - 2.19449i) q^{76} +(0.116073 - 0.116073i) q^{77} +(-0.0195744 - 3.60550i) q^{78} -12.6945i q^{79} +(-1.32186 + 1.80352i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.07938 + 7.76037i) q^{82} +0.810683 q^{83} +(-0.0154705 - 0.0577367i) q^{84} +(8.24889 - 6.62308i) q^{85} +(-2.89158 + 2.89158i) q^{86} +(-3.41690 + 0.915555i) q^{87} +(0.710778 - 2.65266i) q^{88} +(3.49929 - 13.0595i) q^{89} +(-0.900968 - 2.04652i) q^{90} +(-0.153218 - 0.151563i) q^{91} +(2.28944 + 2.28944i) q^{92} +(3.85749 + 6.68138i) q^{93} +(7.02131 - 4.05376i) q^{94} +(-14.7838 + 11.8700i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(9.22020 + 5.32328i) q^{97} +(6.05908 + 3.49821i) q^{98} +(1.94188 + 1.94188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 4 q^{11} + 20 q^{13} + 4 q^{15} - 16 q^{16} - 20 q^{17} + 32 q^{18} - 20 q^{19} + 8 q^{21} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{26} - 24 q^{29} + 4 q^{30} + 12 q^{31} - 12 q^{33} + 16 q^{34} + 12 q^{35} + 20 q^{37} + 4 q^{38} + 20 q^{39} - 28 q^{41} + 8 q^{42} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} + 28 q^{50} + 16 q^{52} - 4 q^{53} - 40 q^{55} - 12 q^{56} - 36 q^{59} - 4 q^{60} - 28 q^{61} - 36 q^{62} + 12 q^{63} - 32 q^{64} - 32 q^{65} - 36 q^{67} - 4 q^{68} + 20 q^{69} - 24 q^{70} - 4 q^{71} + 16 q^{72} - 24 q^{74} - 16 q^{76} - 20 q^{77} - 16 q^{78} + 16 q^{81} + 28 q^{82} - 40 q^{83} - 8 q^{84} + 88 q^{85} - 8 q^{86} - 16 q^{87} - 8 q^{88} + 16 q^{89} - 40 q^{91} + 20 q^{92} + 24 q^{94} - 8 q^{95} + 72 q^{97} + 72 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 4 * q^11 + 20 * q^13 + 4 * q^15 - 16 * q^16 - 20 * q^17 + 32 * q^18 - 20 * q^19 + 8 * q^21 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^26 - 24 * q^29 + 4 * q^30 + 12 * q^31 - 12 * q^33 + 16 * q^34 + 12 * q^35 + 20 * q^37 + 4 * q^38 + 20 * q^39 - 28 * q^41 + 8 * q^42 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 + 28 * q^50 + 16 * q^52 - 4 * q^53 - 40 * q^55 - 12 * q^56 - 36 * q^59 - 4 * q^60 - 28 * q^61 - 36 * q^62 + 12 * q^63 - 32 * q^64 - 32 * q^65 - 36 * q^67 - 4 * q^68 + 20 * q^69 - 24 * q^70 - 4 * q^71 + 16 * q^72 - 24 * q^74 - 16 * q^76 - 20 * q^77 - 16 * q^78 + 16 * q^81 + 28 * q^82 - 40 * q^83 - 8 * q^84 + 88 * q^85 - 8 * q^86 - 16 * q^87 - 8 * q^88 + 16 * q^89 - 40 * q^91 + 20 * q^92 + 24 * q^94 - 8 * q^95 + 72 * q^97 + 72 * q^98 + 4 * q^99

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