LMFDB - Embedded newform 299.2.i.a.231.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [299,2,Mod(231,299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(299, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("299.231");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 299 = 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	299.i (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:	$2.38752702044$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 22x^{16} + 193x^{14} + 865x^{12} + 2122x^{10} + 2860x^{8} + 1999x^{6} + 628x^{4} + 76x^{2} + 3 $ x^18 + 22x^16 + 193x^14 + 865x^12 + 2122x^10 + 2860x^8 + 1999x^6 + 628x^4 + 76x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			231.2
Root			$-1.37128i$ of defining polynomial
Character	$\chi$	$=$	299.231
Dual form			299.2.i.a.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18757 + 0.685642i) q^{2} +(0.476286 + 0.824952i) q^{3} +(-0.0597891 + 0.103558i) q^{4} -2.12469i q^{5} +(-1.13124 - 0.653124i) q^{6} +(-0.290894 - 0.167948i) q^{7} -2.90655i q^{8} +(1.04630 - 1.81225i) q^{9} +O(q^{10})$	\(q+(-1.18757 + 0.685642i) q^{2} +(0.476286 + 0.824952i) q^{3} +(-0.0597891 + 0.103558i) q^{4} -2.12469i q^{5} +(-1.13124 - 0.653124i) q^{6} +(-0.290894 - 0.167948i) q^{7} -2.90655i q^{8} +(1.04630 - 1.81225i) q^{9} +(1.45677 + 2.52321i) q^{10} +(3.56003 - 2.05538i) q^{11} -0.113907 q^{12} +(3.40414 + 1.18819i) q^{13} +0.460609 q^{14} +(1.75276 - 1.01196i) q^{15} +(1.87327 + 3.24460i) q^{16} +(-1.32577 + 2.29630i) q^{17} +2.86956i q^{18} +(-3.88041 - 2.24036i) q^{19} +(0.220028 + 0.127033i) q^{20} -0.319965i q^{21} +(-2.81852 + 4.88182i) q^{22} +(0.500000 + 0.866025i) q^{23} +(2.39776 - 1.38435i) q^{24} +0.485708 q^{25} +(-4.85733 + 0.922964i) q^{26} +4.85108 q^{27} +(0.0347846 - 0.0200829i) q^{28} +(-1.19594 - 2.07143i) q^{29} +(-1.38768 + 2.40354i) q^{30} +3.86285i q^{31} +(0.585010 + 0.337756i) q^{32} +(3.39119 + 1.95790i) q^{33} -3.63602i q^{34} +(-0.356837 + 0.618059i) q^{35} +(0.125115 + 0.216706i) q^{36} +(3.34267 - 1.92989i) q^{37} +6.14434 q^{38} +(0.641144 + 3.37418i) q^{39} -6.17550 q^{40} +(7.36700 - 4.25334i) q^{41} +(0.219382 + 0.379980i) q^{42} +(-3.17975 + 5.50748i) q^{43} +0.491559i q^{44} +(-3.85046 - 2.22306i) q^{45} +(-1.18757 - 0.685642i) q^{46} -7.81907i q^{47} +(-1.78443 + 3.09072i) q^{48} +(-3.44359 - 5.96447i) q^{49} +(-0.576811 + 0.333022i) q^{50} -2.52579 q^{51} +(-0.326577 + 0.281484i) q^{52} +7.28610 q^{53} +(-5.76098 + 3.32610i) q^{54} +(-4.36705 - 7.56395i) q^{55} +(-0.488148 + 0.845497i) q^{56} -4.26821i q^{57} +(2.84052 + 1.63997i) q^{58} +(2.48205 + 1.43301i) q^{59} +0.242017i q^{60} +(-2.71055 + 4.69480i) q^{61} +(-2.64854 - 4.58740i) q^{62} +(-0.608727 + 0.351449i) q^{63} -8.41941 q^{64} +(2.52454 - 7.23274i) q^{65} -5.36969 q^{66} +(-7.35946 + 4.24899i) q^{67} +(-0.158533 - 0.274588i) q^{68} +(-0.476286 + 0.824952i) q^{69} -0.978649i q^{70} +(0.710092 + 0.409972i) q^{71} +(-5.26738 - 3.04113i) q^{72} -9.32612i q^{73} +(-2.64643 + 4.58376i) q^{74} +(0.231336 + 0.400686i) q^{75} +(0.464013 - 0.267898i) q^{76} -1.38079 q^{77} +(-3.07488 - 3.56747i) q^{78} -13.1594 q^{79} +(6.89376 - 3.98012i) q^{80} +(-0.828405 - 1.43484i) q^{81} +(-5.83254 + 10.1023i) q^{82} +10.8510i q^{83} +(0.0331349 + 0.0191304i) q^{84} +(4.87893 + 2.81685i) q^{85} -8.72067i q^{86} +(1.13922 - 1.97319i) q^{87} +(-5.97407 - 10.3474i) q^{88} +(-1.95066 + 1.12622i) q^{89} +6.09691 q^{90} +(-0.790691 - 0.917358i) q^{91} -0.119578 q^{92} +(-3.18667 + 1.83982i) q^{93} +(5.36108 + 9.28567i) q^{94} +(-4.76006 + 8.24466i) q^{95} +0.643474i q^{96} +(1.81422 + 1.04744i) q^{97} +(8.17898 + 4.72214i) q^{98} -8.60222i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{3} + 4 q^{4} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 18 * q + 5 * q^3 + 4 * q^4 - 3 * q^7 - 6 * q^9	$ 18 q + 5 q^{3} + 4 q^{4} - 3 q^{7} - 6 q^{9} - 11 q^{10} + 2 q^{12} + 2 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 15 q^{17} + 6 q^{19} + 6 q^{20} - 8 q^{22} + 9 q^{23} + 24 q^{24} + 16 q^{25} + 18 q^{26} - 34 q^{27} - 24 q^{28} + 15 q^{29} + 4 q^{30} + 27 q^{32} - 18 q^{33} - 12 q^{35} - 20 q^{36} - 6 q^{37} - 30 q^{38} + 12 q^{39} - 52 q^{40} - 6 q^{41} + 12 q^{42} - 3 q^{43} + 12 q^{45} - 30 q^{48} - 18 q^{49} + 36 q^{50} + 24 q^{51} + 23 q^{52} - 18 q^{53} + 18 q^{54} + 16 q^{55} - 15 q^{56} + 6 q^{58} - 9 q^{59} + 10 q^{61} - 33 q^{62} + 63 q^{63} + 38 q^{64} + 60 q^{65} - 68 q^{66} - 18 q^{67} + 18 q^{68} - 5 q^{69} - 54 q^{71} + 27 q^{72} - 18 q^{74} + 8 q^{75} + 54 q^{76} + 12 q^{77} + 57 q^{78} - 56 q^{79} + 24 q^{80} + 15 q^{81} - 11 q^{82} + 15 q^{84} + 33 q^{85} + 5 q^{88} + 21 q^{89} - 38 q^{90} + 42 q^{91} + 8 q^{92} - 42 q^{93} - 14 q^{94} - 36 q^{95} - 30 q^{97} - 15 q^{98}+O(q^{100}) $ 18 * q + 5 * q^3 + 4 * q^4 - 3 * q^7 - 6 * q^9 - 11 * q^10 + 2 * q^12 + 2 * q^13 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 15 * q^17 + 6 * q^19 + 6 * q^20 - 8 * q^22 + 9 * q^23 + 24 * q^24 + 16 * q^25 + 18 * q^26 - 34 * q^27 - 24 * q^28 + 15 * q^29 + 4 * q^30 + 27 * q^32 - 18 * q^33 - 12 * q^35 - 20 * q^36 - 6 * q^37 - 30 * q^38 + 12 * q^39 - 52 * q^40 - 6 * q^41 + 12 * q^42 - 3 * q^43 + 12 * q^45 - 30 * q^48 - 18 * q^49 + 36 * q^50 + 24 * q^51 + 23 * q^52 - 18 * q^53 + 18 * q^54 + 16 * q^55 - 15 * q^56 + 6 * q^58 - 9 * q^59 + 10 * q^61 - 33 * q^62 + 63 * q^63 + 38 * q^64 + 60 * q^65 - 68 * q^66 - 18 * q^67 + 18 * q^68 - 5 * q^69 - 54 * q^71 + 27 * q^72 - 18 * q^74 + 8 * q^75 + 54 * q^76 + 12 * q^77 + 57 * q^78 - 56 * q^79 + 24 * q^80 + 15 * q^81 - 11 * q^82 + 15 * q^84 + 33 * q^85 + 5 * q^88 + 21 * q^89 - 38 * q^90 + 42 * q^91 + 8 * q^92 - 42 * q^93 - 14 * q^94 - 36 * q^95 - 30 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/299\mathbb{Z}\right)^\times$.

$n$	$93$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.18757	+	0.685642i	−0.839737	+	0.484822i	−0.857175	−	0.515026i	$-0.827782\pi$
$2$	−1.18757	+	0.685642i	−0.839737	+	0.484822i	0.0174378	+	0.999848i	$0.494449\pi$
$3$	0.476286	+	0.824952i	0.274984	+	0.476286i	0.970131	−	0.242581i	$-0.0779941\pi$
$3$	0.476286	+	0.824952i	0.274984	+	0.476286i	−0.695147	+	0.718868i	$0.744661\pi$
$4$	−0.0597891	+	0.103558i	−0.0298946	+	0.0517789i
$5$		−	2.12469i		−	0.950189i	−0.879935	−	0.475094i	$-0.842414\pi$
$5$		−	2.12469i		−	0.950189i	0.879935	−	0.475094i	$-0.157586\pi$
$6$	−1.13124	−	0.653124i	−0.461829	−	0.266637i
$7$	−0.290894	−	0.167948i	−0.109948	−	0.0634783i	0.444018	−	0.896018i	$-0.353553\pi$
$7$	−0.290894	−	0.167948i	−0.109948	−	0.0634783i	−0.553965	+	0.832540i	$0.686886\pi$
$8$		−	2.90655i		−	1.02762i
$9$	1.04630	−	1.81225i	0.348767	−	0.604083i
$10$	1.45677	+	2.52321i	0.460673	+	0.797909i
$11$	3.56003	−	2.05538i	1.07339	−	0.619722i	0.144284	−	0.989536i	$-0.453912\pi$
$11$	3.56003	−	2.05538i	1.07339	−	0.619722i	0.929106	+	0.369814i	$0.120579\pi$
$12$	−0.113907			−0.0328821
$13$	3.40414	+	1.18819i	0.944140	+	0.329546i
$13$	3.40414	+	1.18819i	0.944140	+	0.329546i
$14$	0.460609			0.123103
$15$	1.75276	−	1.01196i	0.452562	−	0.261287i
$16$	1.87327	+	3.24460i	0.468318	+	0.811151i
$17$	−1.32577	+	2.29630i	−0.321547	+	0.556936i	−0.980807	−	0.194979i	$-0.937536\pi$
$17$	−1.32577	+	2.29630i	−0.321547	+	0.556936i	0.659260	+	0.751915i	$0.270869\pi$
$18$			2.86956i			0.676361i
$19$	−3.88041	−	2.24036i	−0.890228	−	0.513973i	−0.0162108	−	0.999869i	$-0.505160\pi$
$19$	−3.88041	−	2.24036i	−0.890228	−	0.513973i	−0.874017	+	0.485895i	$0.838494\pi$
$20$	0.220028	+	0.127033i	0.0491997	+	0.0284055i
$21$		−	0.319965i		−	0.0698221i
$22$	−2.81852	+	4.88182i	−0.600910	+	1.04081i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	2.39776	−	1.38435i	0.489441	−	0.282579i
$25$	0.485708			0.0971415
$26$	−4.85733	+	0.922964i	−0.952600	+	0.181008i
$27$	4.85108			0.933590
$28$	0.0347846	−	0.0200829i	0.00657368	−	0.00379531i
$29$	−1.19594	−	2.07143i	−0.222080	−	0.384655i	0.733359	−	0.679841i	$-0.237951\pi$
$29$	−1.19594	−	2.07143i	−0.222080	−	0.384655i	−0.955440	+	0.295187i	$0.904618\pi$
$30$	−1.38768	+	2.40354i	−0.253355	+	0.438824i
$31$			3.86285i			0.693789i	0.937904	+	0.346894i	$0.112764\pi$
$31$			3.86285i			0.693789i	−0.937904	+	0.346894i	$0.887236\pi$
$32$	0.585010	+	0.337756i	0.103416	+	0.0597073i
$33$	3.39119	+	1.95790i	0.590330	+	0.340827i
$34$		−	3.63602i		−	0.623573i
$35$	−0.356837	+	0.618059i	−0.0603164	+	0.104471i
$36$	0.125115	+	0.216706i	0.0208525	+	0.0361176i
$37$	3.34267	−	1.92989i	0.549532	−	0.317273i	−0.199401	−	0.979918i	$-0.563900\pi$
$37$	3.34267	−	1.92989i	0.549532	−	0.317273i	0.748933	+	0.662645i	$0.230566\pi$
$38$	6.14434			0.996743
$39$	0.641144	+	3.37418i	0.102665	+	0.540301i
$40$	−6.17550			−0.976432
$41$	7.36700	−	4.25334i	1.15053	−	0.664260i	0.201516	−	0.979485i	$-0.435413\pi$
$41$	7.36700	−	4.25334i	1.15053	−	0.664260i	0.949017	+	0.315225i	$0.102080\pi$
$42$	0.219382	+	0.379980i	0.0338513	+	0.0586322i
$43$	−3.17975	+	5.50748i	−0.484907	+	0.839883i	−0.999850	−	0.0173414i	$-0.994480\pi$
$43$	−3.17975	+	5.50748i	−0.484907	+	0.839883i	0.514943	+	0.857224i	$0.327813\pi$
$44$			0.491559i			0.0741052i
$45$	−3.85046	−	2.22306i	−0.573993	−	0.331395i
$46$	−1.18757	−	0.685642i	−0.175097	−	0.101092i
$47$		−	7.81907i		−	1.14053i	−0.821461	−	0.570264i	$-0.806841\pi$
$47$		−	7.81907i		−	1.14053i	0.821461	−	0.570264i	$-0.193159\pi$
$48$	−1.78443	+	3.09072i	−0.257560	+	0.446107i
$49$	−3.44359	−	5.96447i	−0.491941	−	0.852067i
$50$	−0.576811	+	0.333022i	−0.0815733	+	0.0470964i
$51$	−2.52579			−0.353681
$52$	−0.326577	+	0.281484i	−0.0452881	+	0.0390349i
$53$	7.28610			1.00082			0.500412	−	0.865788i	$-0.333182\pi$
$53$	7.28610			1.00082			0.500412	+	0.865788i	$0.333182\pi$
$54$	−5.76098	+	3.32610i	−0.783970	+	0.452625i
$55$	−4.36705	−	7.56395i	−0.588853	−	1.01992i
$56$	−0.488148	+	0.845497i	−0.0652315	+	0.112984i
$57$		−	4.26821i		−	0.565338i
$58$	2.84052	+	1.63997i	0.372978	+	0.215339i
$59$	2.48205	+	1.43301i	0.323136	+	0.186562i	0.652789	−	0.757539i	$-0.273599\pi$
$59$	2.48205	+	1.43301i	0.323136	+	0.186562i	−0.329654	+	0.944102i	$0.606932\pi$
$60$			0.242017i			0.0312442i
$61$	−2.71055	+	4.69480i	−0.347050	+	0.601108i	−0.985724	−	0.168369i	$-0.946150\pi$
$61$	−2.71055	+	4.69480i	−0.347050	+	0.601108i	0.638674	+	0.769477i	$0.279483\pi$
$62$	−2.64854	−	4.58740i	−0.336364	−	0.582600i
$63$	−0.608727	+	0.351449i	−0.0766924	+	0.0442784i
$64$	−8.41941			−1.05243
$65$	2.52454	−	7.23274i	0.313131	−	0.897111i
$66$	−5.36969			−0.660963
$67$	−7.35946	+	4.24899i	−0.899101	+	0.519096i	−0.876909	−	0.480657i	$-0.840398\pi$
$67$	−7.35946	+	4.24899i	−0.899101	+	0.519096i	−0.0221929	+	0.999754i	$0.507065\pi$
$68$	−0.158533	−	0.274588i	−0.0192250	−	0.0332987i
$69$	−0.476286	+	0.824952i	−0.0573381	+	0.0993126i
$70$		−	0.978649i		−	0.116971i
$71$	0.710092	+	0.409972i	0.0842724	+	0.0486547i	0.541544	−	0.840672i	$-0.317840\pi$
$71$	0.710092	+	0.409972i	0.0842724	+	0.0486547i	−0.457272	+	0.889327i	$0.651173\pi$
$72$	−5.26738	−	3.04113i	−0.620767	−	0.358400i
$73$		−	9.32612i		−	1.09154i	−0.837935	−	0.545770i	$-0.816237\pi$
$73$		−	9.32612i		−	1.09154i	0.837935	−	0.545770i	$-0.183763\pi$
$74$	−2.64643	+	4.58376i	−0.307642	+	0.532851i
$75$	0.231336	+	0.400686i	0.0267124	+	0.0462672i
$76$	0.464013	−	0.267898i	0.0532259	−	0.0307300i
$77$	−1.38079			−0.157356
$78$	−3.07488	−	3.56747i	−0.348162	−	0.403936i
$79$	−13.1594			−1.48055			−0.740276	−	0.672303i	$-0.765305\pi$
$79$	−13.1594			−1.48055			−0.740276	+	0.672303i	$0.765305\pi$
$80$	6.89376	−	3.98012i	0.770746	−	0.444991i
$81$	−0.828405	−	1.43484i	−0.0920450	−	0.159427i
$82$	−5.83254	+	10.1023i	−0.644096	+	1.11561i
$83$			10.8510i			1.19105i	0.803337	+	0.595525i	$0.203056\pi$
$83$			10.8510i			1.19105i	−0.803337	+	0.595525i	$0.796944\pi$
$84$	0.0331349	+	0.0191304i	0.00361531	+	0.00208730i
$85$	4.87893	+	2.81685i	0.529194	+	0.305530i
$86$		−	8.72067i		−	0.940374i
$87$	1.13922	−	1.97319i	0.122137	−	0.211548i
$88$	−5.97407	−	10.3474i	−0.636838	−	1.10304i
$89$	−1.95066	+	1.12622i	−0.206770	+	0.119379i	−0.599809	−	0.800143i	$-0.704757\pi$
$89$	−1.95066	+	1.12622i	−0.206770	+	0.119379i	0.393039	+	0.919522i	$0.371424\pi$
$90$	6.09691			0.642671
$91$	−0.790691	−	0.917358i	−0.0828870	−	0.0961652i
$92$	−0.119578			−0.0124669
$93$	−3.18667	+	1.83982i	−0.330442	+	0.190781i
$94$	5.36108	+	9.28567i	0.552954	+	0.957744i
$95$	−4.76006	+	8.24466i	−0.488372	+	0.845884i
$96$			0.643474i			0.0656742i
$97$	1.81422	+	1.04744i	0.184206	+	0.106352i	0.589268	−	0.807938i	$-0.299416\pi$
$97$	1.81422	+	1.04744i	0.184206	+	0.106352i	−0.405061	+	0.914290i	$0.632750\pi$
$98$	8.17898	+	4.72214i	0.826202	+	0.477008i
$99$		−	8.60222i		−	0.864555i
$100$	−0.0290400	+	0.0502988i	−0.00290400	+	0.00502988i
$101$	−5.85022	−	10.1329i	−0.582119	−	1.00826i	−0.995228	−	0.0975780i	$-0.968890\pi$
$101$	−5.85022	−	10.1329i	−0.582119	−	1.00826i	0.413109	−	0.910682i	$-0.364443\pi$
$102$	2.99954	−	1.73179i	0.296999	−	0.171473i
$103$	−2.19893			−0.216667			−0.108333	−	0.994115i	$-0.534551\pi$
$103$	−2.19893			−0.216667			−0.108333	+	0.994115i	$0.534551\pi$
$104$	3.45354	−	9.89430i	0.338647	−	0.970216i
$105$	−0.679826			−0.0663442
$106$	−8.65274	+	4.99566i	−0.840428	+	0.485221i
$107$	3.12931	+	5.42013i	0.302522	+	0.523984i	0.976707	−	0.214579i	$-0.0688380\pi$
$107$	3.12931	+	5.42013i	0.302522	+	0.523984i	−0.674184	+	0.738563i	$0.735505\pi$
$108$	−0.290042	+	0.502367i	−0.0279093	+	0.0483403i
$109$			14.1692i			1.35717i	0.734523	+	0.678583i	$0.237406\pi$
$109$			14.1692i			1.35717i	−0.734523	+	0.678583i	$0.762594\pi$
$110$	10.3723	+	5.98847i	0.988963	+	0.570978i
$111$	3.18414	+	1.83836i	0.302225	+	0.174490i
$112$		−	1.25845i		−	0.118912i
$113$	−8.60624	+	14.9064i	−0.809607	+	1.40228i	0.103529	+	0.994626i	$0.466986\pi$
$113$	−8.60624	+	14.9064i	−0.809607	+	1.40228i	−0.913136	+	0.407654i	$0.866347\pi$
$114$	2.92646	+	5.06878i	0.274088	+	0.474735i
$115$	1.84003	−	1.06234i	0.171584	−	0.0990640i
$116$	0.286017			0.0265560
$117$	5.71507	−	4.92595i	0.528358	−	0.455404i
$118$	−3.93014			−0.361799
$119$	0.771319	−	0.445321i	0.0707067	−	0.0408225i
$120$	−2.94131	−	5.09449i	−0.268503	−	0.465061i
$121$	2.94921	−	5.10819i	0.268110	−	0.464381i
$122$		−	7.43386i		−	0.673030i
$123$	7.01761	+	4.05162i	0.632756	+	0.365322i
$124$	−0.400029	−	0.230957i	−0.0359236	−	0.0207405i
$125$		−	11.6554i		−	1.04249i
$126$	0.481936	−	0.834738i	0.0429343	−	0.0743644i
$127$	6.21613	+	10.7667i	0.551593	+	0.955387i	0.998160	+	0.0606365i	$0.0193130\pi$
$127$	6.21613	+	10.7667i	0.551593	+	0.955387i	−0.446567	+	0.894750i	$0.647354\pi$
$128$	8.82859	−	5.09719i	0.780345	−	0.450532i
$129$	−6.05788			−0.533367
$130$	1.96101	+	10.3203i	0.171992	+	0.905150i
$131$	4.64371			0.405723			0.202861	−	0.979207i	$-0.434976\pi$
$131$	4.64371			0.405723			0.202861	+	0.979207i	$0.434976\pi$
$132$	−0.405512	+	0.234123i	−0.0352953	+	0.0203778i
$133$	0.752527	+	1.30341i	0.0652523	+	0.113020i
$134$	5.82657	−	10.0919i	0.503339	−	0.871809i
$135$		−	10.3070i		−	0.887087i
$136$	6.67431	+	3.85342i	0.572318	+	0.330428i
$137$	5.53002	+	3.19276i	0.472461	+	0.272776i	0.717269	−	0.696796i	$-0.245392\pi$
$137$	5.53002	+	3.19276i	0.472461	+	0.272776i	−0.244808	+	0.969572i	$0.578725\pi$
$138$		−	1.30625i		−	0.111195i
$139$	8.14651	−	14.1102i	0.690978	−	1.19681i	−0.280540	−	0.959842i	$-0.590514\pi$
$139$	8.14651	−	14.1102i	0.690978	−	1.19681i	0.971518	−	0.236966i	$-0.0761532\pi$
$140$	−0.0426699	−	0.0739064i	−0.00360626	−	0.00624623i
$141$	6.45036	−	3.72412i	0.543218	−	0.313627i
$142$	−1.12438			−0.0943555
$143$	14.5611	−	2.76682i	1.21766	−	0.231373i
$144$	7.84004			0.653336
$145$	−4.40114	+	2.54100i	−0.365494	+	0.211018i
$146$	6.39438	+	11.0754i	0.529203	+	0.916606i
$147$	3.28027	−	5.68159i	0.270552	−	0.468610i
$148$			0.461547i			0.0379389i
$149$	−19.9902	−	11.5413i	−1.63766	−	0.945503i	−0.981636	−	0.190762i	$-0.938904\pi$
$149$	−19.9902	−	11.5413i	−1.63766	−	0.945503i	−0.656023	−	0.754741i	$-0.727763\pi$
$150$	−0.549454	−	0.317228i	−0.0448627	−	0.0259015i
$151$			23.4799i			1.91077i	0.295366	+	0.955384i	$0.404559\pi$
$151$			23.4799i			1.91077i	−0.295366	+	0.955384i	$0.595441\pi$
$152$	−6.51170	+	11.2786i	−0.528169	+	0.914815i
$153$	2.77432	+	4.80526i	0.224290	+	0.388482i
$154$	1.63978	−	0.946728i	0.132137	−	0.0762895i
$155$	8.20735			0.659230
$156$	−0.387756	−	0.135344i	−0.0310453	−	0.0108362i
$157$	−1.02613			−0.0818942			−0.0409471	−	0.999161i	$-0.513038\pi$
$157$	−1.02613			−0.0818942			−0.0409471	+	0.999161i	$0.513038\pi$
$158$	15.6277	−	9.02267i	1.24328	−	0.717805i
$159$	3.47027	+	6.01069i	0.275210	+	0.476679i
$160$	0.717625	−	1.24296i	0.0567332	−	0.0982648i
$161$		−	0.335896i		−	0.0264723i
$162$	1.96757	+	1.13598i	0.154587	+	0.0892510i
$163$	12.5975	+	7.27315i	0.986710	+	0.569677i	0.904289	−	0.426920i	$-0.140402\pi$
$163$	12.5975	+	7.27315i	0.986710	+	0.569677i	0.0824206	+	0.996598i	$0.473735\pi$
$164$			1.01721i			0.0794311i
$165$	4.15993	−	7.20521i	0.323850	−	0.560925i
$166$	−7.43989	−	12.8863i	−0.577447	−	1.00017i
$167$	−7.31373	+	4.22258i	−0.565953	+	0.326753i	−0.755531	−	0.655112i	$-0.772621\pi$
$167$	−7.31373	+	4.22258i	−0.565953	+	0.326753i	0.189578	+	0.981866i	$0.439288\pi$
$168$	−0.929993			−0.0717505
$169$	10.1764	+	8.08957i	0.782799	+	0.622274i
$170$	−7.72541			−0.592512
$171$	−8.12017	+	4.68818i	−0.620965	+	0.358514i
$172$	−0.380228	−	0.658575i	−0.0289921	−	0.0502159i
$173$	−8.22728	+	14.2501i	−0.625508	+	1.08341i	0.362934	+	0.931815i	$0.381775\pi$
$173$	−8.22728	+	14.2501i	−0.625508	+	1.08341i	−0.988442	+	0.151597i	$0.951558\pi$
$174$			3.12439i			0.236859i
$175$	−0.141290	−	0.0815736i	−0.0106805	−	0.00616638i
$176$	13.3378	+	7.70059i	1.00538	+	0.580454i
$177$			2.73010i			0.205207i
$178$	1.54436	−	2.67491i	0.115755	−	0.200493i
$179$	−1.56158	−	2.70473i	−0.116718	−	0.202161i	0.801747	−	0.597663i	$-0.203904\pi$
$179$	−1.56158	−	2.70473i	−0.116718	−	0.202161i	−0.918465	+	0.395502i	$0.870571\pi$
$180$	0.460431	−	0.265830i	0.0343185	−	0.0198138i
$181$	0.855479			0.0635873			0.0317936	−	0.999494i	$-0.489878\pi$
$181$	0.855479			0.0635873			0.0317936	+	0.999494i	$0.489878\pi$
$182$	1.56798	+	0.547293i	0.116226	+	0.0405680i
$183$	−5.16398			−0.381733
$184$	2.51714	−	1.45327i	0.185566	−	0.107137i
$185$	−4.10042	−	7.10213i	−0.301469	−	0.522159i
$186$	2.52292	−	4.36983i	0.184990	−	0.320412i
$187$			10.8999i			0.797079i
$188$	0.809725	+	0.467495i	0.0590553	+	0.0340956i
$189$	−1.41115	−	0.814728i	−0.102646	−	0.0592628i
$190$		−	13.0548i		−	0.947094i
$191$	−2.19687	+	3.80510i	−0.158960	+	0.275327i	−0.934494	−	0.355979i	$-0.884147\pi$
$191$	−2.19687	+	3.80510i	−0.158960	+	0.275327i	0.775534	+	0.631306i	$0.217481\pi$
$192$	−4.01005	−	6.94561i	−0.289400	−	0.501256i
$193$	14.7615	−	8.52257i	1.06256	−	0.613468i	0.136419	−	0.990651i	$-0.456441\pi$
$193$	14.7615	−	8.52257i	1.06256	−	0.613468i	0.926139	+	0.377183i	$0.123107\pi$
$194$	−2.87268			−0.206247
$195$	7.16907	−	1.36223i	0.513388	−	0.0975513i
$196$	0.823556			0.0588254
$197$	−16.0334	+	9.25688i	−1.14233	+	0.659526i	−0.947007	−	0.321213i	$-0.895910\pi$
$197$	−16.0334	+	9.25688i	−1.14233	+	0.659526i	−0.195325	+	0.980739i	$0.562576\pi$
$198$	5.89804	+	10.2157i	0.419156	+	0.725999i
$199$	−9.91466	+	17.1727i	−0.702832	+	1.21734i	0.264637	+	0.964348i	$0.414748\pi$
$199$	−9.91466	+	17.1727i	−0.702832	+	1.21734i	−0.967468	+	0.252992i	$0.918585\pi$
$200$		−	1.41173i		−	0.0998245i
$201$	−7.01042	−	4.04747i	−0.494477	−	0.285487i
$202$	13.8951	+	8.02232i	0.977654	+	0.564449i
$203$			0.803422i			0.0563892i
$204$	0.151015	−	0.261565i	0.0105731	−	0.0183132i
$205$	−9.03702	−	15.6526i	−0.631173	−	1.09322i
$206$	2.61137	−	1.50768i	0.181943	−	0.105045i
$207$	2.09260			0.145446
$208$	2.52167	+	13.2709i	0.174846	+	0.920172i
$209$	−18.4192			−1.27408
$210$	0.807339	−	0.466117i	0.0557117	−	0.0321651i
$211$	−4.77713	−	8.27424i	−0.328871	−	0.569622i	0.653417	−	0.756998i	$-0.273335\pi$
$211$	−4.77713	−	8.27424i	−0.328871	−	0.569622i	−0.982288	+	0.187376i	$0.940002\pi$
$212$	−0.435630	+	0.754533i	−0.0299192	+	0.0518215i
$213$			0.781056i			0.0535171i
$214$	−7.43254	−	4.29118i	−0.508078	−	0.293339i
$215$	11.7017	+	6.75596i	0.798047	+	0.460753i
$216$		−	14.0999i		−	0.959375i
$217$	0.648758	−	1.12368i	0.0440406	−	0.0762805i
$218$	−9.71503	−	16.8269i	−0.657985	−	1.13966i
$219$	7.69360	−	4.44190i	0.519886	−	0.300156i
$220$	1.04441			0.0704140
$221$	−7.24157	+	6.24168i	−0.487121	+	0.419861i
$222$	−5.04184			−0.338386
$223$	−4.94063	+	2.85247i	−0.330849	+	0.191016i	−0.656218	−	0.754571i	$-0.727845\pi$
$223$	−4.94063	+	2.85247i	−0.330849	+	0.191016i	0.325369	+	0.945587i	$0.394511\pi$
$224$	−0.113451	−	0.196502i	−0.00758024	−	0.0131294i
$225$	0.508197	−	0.880223i	0.0338798	−	0.0586816i
$226$		−	23.6032i		−	1.57006i
$227$	−13.8896	−	8.01918i	−0.921887	−	0.532252i	−0.0376505	−	0.999291i	$-0.511987\pi$
$227$	−13.8896	−	8.01918i	−0.921887	−	0.532252i	−0.884237	+	0.467039i	$0.845321\pi$
$228$	0.442006	+	0.255192i	0.0292726	+	0.0169005i
$229$		−	1.92324i		−	0.127091i	−0.997979	−	0.0635456i	$-0.979759\pi$
$229$		−	1.92324i		−	0.127091i	0.997979	−	0.0635456i	$-0.0202408\pi$
$230$	−1.45677	+	2.52321i	−0.0960569	+	0.166375i
$231$	−0.657652	−	1.13909i	−0.0432703	−	0.0749464i
$232$	−6.02070	+	3.47605i	−0.395278	+	0.228214i
$233$	20.2683			1.32782			0.663909	−	0.747813i	$-0.268896\pi$
$233$	20.2683			1.32782			0.663909	+	0.747813i	$0.268896\pi$
$234$	−3.40959	+	9.76839i	−0.222892	+	0.638579i
$235$	−16.6131			−1.08372
$236$	−0.296799	+	0.171357i	−0.0193200	+	0.0111544i
$237$	−6.26766	−	10.8559i	−0.407129	−	0.705167i
$238$	−0.610662	+	1.05770i	−0.0395833	+	0.0685604i
$239$		−	28.1199i		−	1.81893i	−0.415783	−	0.909464i	$-0.636492\pi$
$239$		−	28.1199i		−	1.81893i	0.415783	−	0.909464i	$-0.363508\pi$
$240$	6.56681	+	3.79135i	0.423886	+	0.244731i
$241$	−13.1877	−	7.61394i	−0.849496	−	0.490457i	0.0109847	−	0.999940i	$-0.496503\pi$
$241$	−13.1877	−	7.61394i	−0.849496	−	0.490457i	−0.860481	+	0.509483i	$0.829837\pi$
$242$			8.08842i			0.519944i
$243$	8.06573	−	13.9703i	0.517417	−	0.896192i
$244$	−0.324122	−	0.561396i	−0.0207498	−	0.0359397i
$245$	−12.6726	+	7.31654i	−0.809624	+	0.467437i
$246$	−11.1118			−0.708465
$247$	−10.5475	−	12.2372i	−0.671122	−	0.778633i
$248$	11.2276			0.712951
$249$	−8.95154	+	5.16817i	−0.567281	+	0.327520i
$250$	7.99144	+	13.8416i	0.505423	+	0.875419i
$251$	−2.37220	+	4.10877i	−0.149732	+	0.259343i	−0.931128	−	0.364692i	$-0.881174\pi$
$251$	−2.37220	+	4.10877i	−0.149732	+	0.259343i	0.781396	+	0.624035i	$0.214508\pi$
$252$		−	0.0840512i		−	0.00529473i
$253$	3.56003	+	2.05538i	0.223817	+	0.129221i
$254$	−14.7642	−	8.52409i	−0.926386	−	0.534849i
$255$			5.36651i			0.336064i
$256$	1.42971	−	2.47633i	0.0893567	−	0.154770i
$257$	−1.74340	−	3.01966i	−0.108750	−	0.188361i	0.806514	−	0.591215i	$-0.201352\pi$
$257$	−1.74340	−	3.01966i	−0.108750	−	0.188361i	−0.915264	+	0.402854i	$0.868018\pi$
$258$	7.19414	−	4.15354i	0.447888	−	0.258588i
$259$	−1.29649			−0.0805597
$260$	0.598066	+	0.693875i	0.0370905	+	0.0430323i
$261$	−5.00526			−0.309818
$262$	−5.51472	+	3.18392i	−0.340700	+	0.196703i
$263$	10.8073	+	18.7187i	0.666405	+	1.15425i	0.978902	+	0.204329i	$0.0655012\pi$
$263$	10.8073	+	18.7187i	0.666405	+	1.15425i	−0.312497	+	0.949919i	$0.601165\pi$
$264$	5.69074	−	9.85664i	0.350241	−	0.606634i
$265$		−	15.4807i		−	0.950971i
$266$	−1.78735	−	1.03193i	−0.109590	−	0.0632716i
$267$	−1.85815	−	1.07280i	−0.113717	−	0.0656545i
$268$		−	1.01617i		−	0.0620726i
$269$	−5.66448	+	9.81117i	−0.345370	+	0.598198i	−0.985421	−	0.170135i	$-0.945580\pi$
$269$	−5.66448	+	9.81117i	−0.345370	+	0.598198i	0.640051	+	0.768332i	$0.278913\pi$
$270$	7.06693	+	12.2403i	0.430080	+	0.744920i
$271$	−11.9589	+	6.90448i	−0.726452	+	0.419417i	−0.817123	−	0.576464i	$-0.804432\pi$
$271$	−11.9589	+	6.90448i	−0.726452	+	0.419417i	0.0906710	+	0.995881i	$0.471099\pi$
$272$	−9.93413			−0.602345
$273$	0.380181	−	1.08921i	0.0230096	−	0.0659218i
$274$	−8.75636			−0.528991
$275$	1.72913	−	0.998316i	0.104271	−	0.0602007i
$276$	−0.0569535	−	0.0986463i	−0.00342820	−	0.00593781i
$277$	−11.0350	+	19.1132i	−0.663028	+	1.14840i	0.316788	+	0.948496i	$0.397396\pi$
$277$	−11.0350	+	19.1132i	−0.663028	+	1.14840i	−0.979816	+	0.199902i	$0.935938\pi$
$278$			22.3424i			1.34001i
$279$	7.00045	+	4.04171i	0.419106	+	0.241971i
$280$	1.79642	+	1.03716i	0.107356	+	0.0619823i
$281$		−	17.5223i		−	1.04529i	−0.852550	−	0.522646i	$-0.824945\pi$
$281$		−	17.5223i		−	1.04529i	0.852550	−	0.522646i	$-0.175055\pi$
$282$	−5.10682	+	8.84528i	−0.304107	+	0.526729i
$283$	14.0605	+	24.3535i	0.835809	+	1.44766i	0.893370	+	0.449321i	$0.148334\pi$
$283$	14.0605	+	24.3535i	0.835809	+	1.44766i	−0.0575616	+	0.998342i	$0.518333\pi$
$284$	−0.0849115	+	0.0490237i	−0.00503857	+	0.00290902i
$285$	−9.06860			−0.537178
$286$	−15.3952	+	13.2695i	−0.910336	+	0.784639i
$287$	−2.85736			−0.168665
$288$	1.22419	−	0.706789i	0.0721363	−	0.0416479i
$289$	4.98466	+	8.63368i	0.293215	+	0.507864i
$290$	3.48443	−	6.03521i	0.204613	−	0.354400i
$291$			1.99553i			0.116980i
$292$	0.965792	+	0.557601i	0.0565187	+	0.0326311i
$293$	−8.44917	−	4.87813i	−0.493606	−	0.284984i	0.232463	−	0.972605i	$-0.425321\pi$
$293$	−8.44917	−	4.87813i	−0.493606	−	0.284984i	−0.726069	+	0.687622i	$0.758655\pi$
$294$			8.99636i			0.524678i
$295$	3.04470	−	5.27358i	0.177270	−	0.307040i
$296$	−5.60932	−	9.71563i	−0.326035	−	0.564710i
$297$	17.2700	−	9.97083i	1.00211	−	0.578566i
$298$	31.6529			1.83360
$299$	0.673066	+	3.54217i	0.0389244	+	0.204849i
$300$	−0.0553255			−0.00319422
$301$	1.84994	−	1.06806i	0.106629	−	0.0615621i
$302$	−16.0988	−	27.8840i	−0.926383	−	1.60454i
$303$	5.57276	−	9.65231i	0.320147	−	0.554511i
$304$		−	16.7872i		−	0.962812i
$305$	9.97498	+	5.75906i	0.571166	+	0.329763i
$306$	−6.58938	−	3.80438i	−0.376690	−	0.217482i
$307$		−	1.63434i		−	0.0932769i	−0.998912	−	0.0466384i	$-0.985149\pi$
$307$		−	1.63434i		−	0.0932769i	0.998912	−	0.0466384i	$-0.0148509\pi$
$308$	0.0825562	−	0.142992i	0.00470408	−	0.00814770i
$309$	−1.04732	−	1.81401i	−0.0595799	−	0.103195i
$310$	−9.74678	+	5.62731i	−0.553580	+	0.319610i
$311$	−8.62476			−0.489065			−0.244532	−	0.969641i	$-0.578634\pi$
$311$	−8.62476			−0.489065			−0.244532	+	0.969641i	$0.578634\pi$
$312$	9.80720	−	1.86351i	0.555223	−	0.105501i
$313$	32.2266			1.82156			0.910779	−	0.412894i	$-0.135482\pi$
$313$	32.2266			1.82156			0.910779	+	0.412894i	$0.135482\pi$
$314$	1.21860	−	0.703559i	0.0687696	−	0.0397041i
$315$	0.746718	+	1.29335i	0.0420728	+	0.0728722i
$316$	0.786791	−	1.36276i	0.0442605	−	0.0766614i
$317$		−	16.9210i		−	0.950378i	−0.879884	−	0.475189i	$-0.842380\pi$
$317$		−	16.9210i		−	0.950378i	0.879884	−	0.475189i	$-0.157620\pi$
$318$	−8.24236	−	4.75873i	−0.462209	−	0.266856i
$319$	−8.51517	−	4.91623i	−0.476758	−	0.275256i
$320$			17.8886i			1.00000i
$321$	−2.98090	+	5.16307i	−0.166378	+	0.288175i
$322$	0.230304	+	0.398899i	0.0128344	+	0.0222298i
$323$	10.2891	−	5.94041i	0.572500	−	0.330533i
$324$	0.198118			0.0110066
$325$	1.65342	+	0.577115i	0.0917152	+	0.0320126i
$326$	−19.9471			−1.10477
$327$	−11.6889	+	6.74862i	−0.646400	+	0.373199i
$328$	−12.3625	−	21.4125i	−0.682606	−	1.18231i
$329$	−1.31320	+	2.27452i	−0.0723988	+	0.125398i
$330$			11.4089i			0.628039i
$331$	25.4353	+	14.6851i	1.39805	+	0.807166i	0.994188	−	0.107654i	$-0.0343338\pi$
$331$	25.4353	+	14.6851i	1.39805	+	0.807166i	0.403863	+	0.914819i	$0.367667\pi$
$332$	−1.12370	−	0.648770i	−0.0616712	−	0.0356059i
$333$		−	8.07701i		−	0.442617i
$334$	5.79036	−	10.0292i	0.316835	−	0.548774i
$335$	9.02777	+	15.6365i	0.493240	+	0.854316i
$336$	1.03816	−	0.599382i	0.0566363	−	0.0326990i
$337$	24.0090			1.30785			0.653926	−	0.756559i	$-0.273121\pi$
$337$	24.0090			1.30785			0.653926	+	0.756559i	$0.273121\pi$
$338$	−17.6317	−	2.62954i	−0.959038	−	0.143028i
$339$	−16.3961			−0.890516
$340$	−0.583413	+	0.336834i	−0.0316400	+	0.0182674i
$341$	7.93965	+	13.7519i	0.429956	+	0.744706i
$342$	6.42883	−	11.1351i	0.347632	−	0.602116i
$343$			4.66464i			0.251867i
$344$	16.0077	+	9.24208i	0.863080	+	0.498299i
$345$	1.75276	+	1.01196i	0.0943657	+	0.0544821i
$346$		−	22.5639i		−	1.21304i
$347$	−6.95256	+	12.0422i	−0.373233	+	0.646458i	−0.990061	−	0.140640i	$-0.955084\pi$
$347$	−6.95256	+	12.0422i	−0.373233	+	0.646458i	0.616828	+	0.787098i	$0.288417\pi$
$348$	0.136226	+	0.235950i	0.00730247	+	0.0126483i
$349$	−19.8694	+	11.4716i	−1.06358	+	0.614060i	−0.926421	−	0.376488i	$-0.877132\pi$
$349$	−19.8694	+	11.4716i	−1.06358	+	0.614060i	−0.137162	+	0.990549i	$0.543798\pi$
$350$	0.223721			0.0119584
$351$	16.5138	+	5.76402i	0.881440	+	0.307661i
$352$	2.77687			0.148008
$353$	−12.6732	+	7.31690i	−0.674529	+	0.389439i	−0.797790	−	0.602935i	$-0.793998\pi$
$353$	−12.6732	+	7.31690i	−0.674529	+	0.389439i	0.123262	+	0.992374i	$0.460665\pi$
$354$	−1.87187	−	3.24218i	−0.0994889	−	0.172320i
$355$	0.871061	−	1.50872i	0.0462311	−	0.0800747i
$356$		−	0.269342i		−	0.0142751i
$357$	0.734737	+	0.424201i	0.0388864	+	0.0224511i
$358$	3.70895	+	2.14137i	0.196024	+	0.113175i
$359$			20.9420i			1.10528i	0.833421	+	0.552639i	$0.186379\pi$
$359$			20.9420i			1.10528i	−0.833421	+	0.552639i	$0.813621\pi$
$360$	−6.46144	+	11.1915i	−0.340548	+	0.589846i
$361$	0.538405	+	0.932544i	0.0283371	+	0.0490813i
$362$	−1.01594	+	0.586553i	−0.0533966	+	0.0308285i
$363$	5.61868			0.294904
$364$	0.142274	−	0.0270342i	0.00745720	−	0.00141698i
$365$	−19.8151			−1.03717
$366$	6.13258	−	3.54065i	0.320555	−	0.185073i
$367$	4.20961	+	7.29125i	0.219740	+	0.380600i	0.954728	−	0.297479i	$-0.0961459\pi$
$367$	4.20961	+	7.29125i	0.219740	+	0.380600i	−0.734989	+	0.678079i	$0.762813\pi$
$368$	−1.87327	+	3.24460i	−0.0976511	+	0.169137i
$369$		−	17.8011i		−	0.926689i
$370$	9.73905	+	5.62284i	0.506309	+	0.292318i
$371$	−2.11949	−	1.22369i	−0.110038	−	0.0635306i
$372$		−	0.440006i		−	0.0228132i
$373$	10.1668	−	17.6094i	0.526418	−	0.911782i	−0.473109	−	0.881004i	$-0.656868\pi$
$373$	10.1668	−	17.6094i	0.526418	−	0.911782i	0.999526	−	0.0307779i	$-0.00979846\pi$
$374$	−7.47342	−	12.9443i	−0.386442	−	0.669336i
$375$	9.61516	−	5.55131i	0.496525	−	0.286669i
$376$	−22.7265			−1.17203
$377$	−1.60989	−	8.47245i	−0.0829136	−	0.436353i
$378$	2.23445			0.114928
$379$	3.47805	−	2.00805i	0.178655	−	0.103147i	−0.408005	−	0.912979i	$-0.633776\pi$
$379$	3.47805	−	2.00805i	0.178655	−	0.103147i	0.586661	+	0.809833i	$0.300442\pi$
$380$	−0.569199	−	0.985882i	−0.0291993	−	0.0505747i
$381$	−5.92132	+	10.2560i	−0.303358	+	0.525432i
$382$		−	6.02508i		−	0.308270i
$383$	−3.40895	−	1.96816i	−0.174189	−	0.100568i	0.410370	−	0.911919i	$-0.365399\pi$
$383$	−3.40895	−	1.96816i	−0.174189	−	0.100568i	−0.584560	+	0.811351i	$0.698733\pi$
$384$	8.40988	+	4.85545i	0.429165	+	0.247778i
$385$			2.93375i			0.149518i
$386$	−11.6869	+	20.2423i	−0.594846	+	1.03030i
$387$	6.65395	+	11.5250i	0.338239	+	0.585848i
$388$	−0.216942	+	0.125251i	−0.0110135	+	0.00635867i
$389$	30.4119			1.54195			0.770973	−	0.636868i	$-0.219770\pi$
$389$	30.4119			1.54195			0.770973	+	0.636868i	$0.219770\pi$
$390$	−7.57975	+	6.53316i	−0.383815	+	0.330819i
$391$	−2.65154			−0.134094
$392$	−17.3360	+	10.0089i	−0.875600	+	0.505528i
$393$	2.21173	+	3.83084i	0.111567	+	0.193240i
$394$	12.6938	−	21.9863i	0.639506	−	1.10766i
$395$			27.9597i			1.40680i
$396$	0.890827	+	0.514319i	0.0447657	+	0.0258455i
$397$	−25.2473	−	14.5766i	−1.26713	−	0.731576i	−0.292684	−	0.956209i	$-0.594548\pi$
$397$	−25.2473	−	14.5766i	−1.26713	−	0.731576i	−0.974443	+	0.224633i	$0.927882\pi$
$398$		−	27.1916i		−	1.36299i
$399$	−0.716836	+	1.24160i	−0.0358867	+	0.0621576i
$400$	0.909863	+	1.57593i	0.0454931	+	0.0787964i
$401$	9.96437	−	5.75293i	0.497597	−	0.287288i	−0.230124	−	0.973161i	$-0.573913\pi$
$401$	9.96437	−	5.75293i	0.497597	−	0.287288i	0.727721	+	0.685874i	$0.240580\pi$
$402$	11.1005			0.553641
$403$	−4.58982	+	13.1497i	−0.228635	+	0.655034i
$404$	1.39912			0.0696088
$405$	−3.04859	+	1.76010i	−0.151485	+	0.0874601i
$406$	−0.550860	−	0.954118i	−0.0273387	−	0.0473521i
$407$	7.93335	−	13.7410i	0.393242	−	0.681114i
$408$			7.34132i			0.363449i
$409$	−5.21329	−	3.00989i	−0.257781	−	0.148830i	0.365541	−	0.930795i	$-0.380884\pi$
$409$	−5.21329	−	3.00989i	−0.257781	−	0.148830i	−0.623322	+	0.781966i	$0.714217\pi$
$410$	21.4641	+	12.3923i	1.06004	+	0.612013i
$411$			6.08267i			0.300036i
$412$	0.131472	−	0.227716i	0.00647716	−	0.0112188i
$413$	−0.481343	−	0.833711i	−0.0236854	−	0.0410242i
$414$	−2.48511	+	1.43478i	−0.122136	+	0.0705155i
$415$	23.0549			1.13172
$416$	1.59014	+	1.84487i	0.0779629	+	0.0904524i
$417$	15.5203			0.760032
$418$	21.8740	−	12.6290i	1.06989	−	0.617703i
$419$	−15.7747	−	27.3225i	−0.770642	−	1.33479i	−0.937211	−	0.348762i	$-0.886602\pi$
$419$	−15.7747	−	27.3225i	−0.770642	−	1.33479i	0.166569	−	0.986030i	$-0.446731\pi$
$420$	0.0406462	−	0.0704012i	0.00198333	−	0.00343523i
$421$			3.16597i			0.154300i	0.997020	+	0.0771499i	$0.0245820\pi$
$421$			3.16597i			0.154300i	−0.997020	+	0.0771499i	$0.975418\pi$
$422$	11.3463	+	6.55081i	0.552331	+	0.318888i
$423$	−14.1701	−	8.18111i	−0.688974	−	0.397779i
$424$		−	21.1774i		−	1.02846i
$425$	−0.643938	+	1.11533i	−0.0312356	+	0.0541016i
$426$	−0.535525	−	0.927556i	−0.0259463	−	0.0449402i
$427$	1.57696	−	0.910461i	0.0763147	−	0.0440603i
$428$	−0.748396			−0.0361751
$429$	9.21772	+	10.6944i	0.445036	+	0.516329i
$430$	−18.5287			−0.893533
$431$	−1.52650	+	0.881328i	−0.0735291	+	0.0424521i	−0.536314	−	0.844019i	$-0.680184\pi$
$431$	−1.52650	+	0.881328i	−0.0735291	+	0.0424521i	0.462785	+	0.886471i	$0.346850\pi$
$432$	9.08739	+	15.7398i	0.437217	+	0.757282i
$433$	9.14637	−	15.8420i	0.439546	−	0.761317i	−0.558108	−	0.829768i	$-0.688473\pi$
$433$	9.14637	−	15.8420i	0.439546	−	0.761317i	0.997654	+	0.0684516i	$0.0218059\pi$
$434$			1.77926i			0.0854074i
$435$	−4.19240	−	2.42048i	−0.201010	−	0.116053i
$436$	−1.46733	−	0.847166i	−0.0702726	−	0.0405719i
$437$		−	4.48072i		−	0.214342i
$438$	−6.09112	+	10.5501i	−0.291045	+	0.504104i
$439$	16.2272	+	28.1063i	0.774481	+	1.34144i	0.935086	+	0.354422i	$0.115322\pi$
$439$	16.2272	+	28.1063i	0.774481	+	1.34144i	−0.160604	+	0.987019i	$0.551344\pi$
$440$	−21.9850	+	12.6930i	−1.04809	+	0.605116i
$441$	−14.4121			−0.686292
$442$	4.32030	−	12.3775i	0.205496	−	0.588740i
$443$	2.26572			0.107648			0.0538239	−	0.998550i	$-0.482859\pi$
$443$	2.26572			0.107648			0.0538239	+	0.998550i	$0.482859\pi$
$444$	−0.380754	+	0.219828i	−0.0180698	+	0.0104326i
$445$	2.39286	+	4.14455i	0.113432	+	0.196470i
$446$	3.91155	−	6.77501i	0.185217	−	0.320806i
$447$		−	21.9879i		−	1.03999i
$448$	2.44916	+	1.41402i	0.115712	+	0.0668062i
$449$	−25.2354	−	14.5697i	−1.19093	−	0.687586i	−0.232416	−	0.972617i	$-0.574663\pi$
$449$	−25.2354	−	14.5697i	−1.19093	−	0.687586i	−0.958519	+	0.285030i	$0.907996\pi$
$450$			1.39377i			0.0657028i
$451$	17.4845	−	30.2840i	0.823313	−	1.42602i
$452$	−1.02912	−	1.78249i	−0.0484057	−	0.0838411i
$453$	−19.3698	+	11.1832i	−0.910073	+	0.525431i
$454$	21.9932			1.03219
$455$	−1.94910	+	1.67997i	−0.0913751	+	0.0787583i
$456$	−12.4057			−0.580952
$457$	3.82050	−	2.20576i	0.178715	−	0.103181i	−0.407974	−	0.912994i	$-0.633764\pi$
$457$	3.82050	−	2.20576i	0.178715	−	0.103181i	0.586689	+	0.809812i	$0.300431\pi$
$458$	1.31865	+	2.28398i	0.0616167	+	0.106723i
$459$	−6.43142	+	11.1395i	−0.300193	+	0.519950i
$460$			0.254066i			0.0118459i
$461$	−16.3443	−	9.43638i	−0.761230	−	0.439496i	0.0685074	−	0.997651i	$-0.478176\pi$
$461$	−16.3443	−	9.43638i	−0.761230	−	0.439496i	−0.829737	+	0.558154i	$0.811510\pi$
$462$	1.56201	+	0.901828i	0.0726713	+	0.0419568i
$463$			5.42980i			0.252344i	0.992008	+	0.126172i	$0.0402691\pi$
$463$			5.42980i			0.252344i	−0.992008	+	0.126172i	$0.959731\pi$
$464$	4.48064	−	7.76070i	0.208009	−	0.360281i
$465$	3.90905	+	6.77067i	0.181278	+	0.313982i
$466$	−24.0699	+	13.8968i	−1.11502	+	0.643756i
$467$	−0.115817			−0.00535936			−0.00267968	−	0.999996i	$-0.500853\pi$
$467$	−0.115817			−0.00535936			−0.00267968	+	0.999996i	$0.500853\pi$
$468$	0.168421	+	0.886358i	0.00778527	+	0.0409719i
$469$	2.85443			0.131806
$470$	19.7291	−	11.3906i	0.910037	−	0.525410i
$471$	−0.488732	−	0.846509i	−0.0225196	−	0.0390051i
$472$	4.16512	−	7.21420i	0.191715	−	0.332060i
$473$			26.1424i			1.20203i
$474$	14.8865	+	8.59475i	0.683762	+	0.394770i
$475$	−1.88475	−	1.08816i	−0.0864781	−	0.0499282i
$476$			0.106501i			0.00488149i
$477$	7.62347	−	13.2042i	0.349055	−	0.604580i
$478$	19.2802	+	33.3943i	0.881857	+	1.52742i
$479$	−2.77989	+	1.60497i	−0.127016	+	0.0733329i	−0.562162	−	0.827027i	$-0.690030\pi$
$479$	−2.77989	+	1.60497i	−0.127016	+	0.0733329i	0.435146	+	0.900360i	$0.356697\pi$
$480$	1.36718			0.0624029
$481$	13.6720	−	2.59789i	0.623391	−	0.118454i
$482$	20.8818			0.951138
$483$	0.277098	−	0.159983i	0.0126084	−	0.00727946i
$484$	0.352662	+	0.610828i	0.0160301	+	0.0277649i
$485$	2.22549	−	3.85466i	0.101054	−	0.175031i
$486$			22.1208i			1.00342i
$487$	15.1392	+	8.74063i	0.686024	+	0.396076i	0.802121	−	0.597162i	$-0.203705\pi$
$487$	15.1392	+	8.74063i	0.686024	+	0.396076i	−0.116097	+	0.993238i	$0.537038\pi$
$488$	13.6457	+	7.87832i	0.617710	+	0.356635i
$489$			13.8564i			0.626609i
$490$	10.0331	−	17.3778i	0.453248	−	0.785048i
$491$	−7.49182	−	12.9762i	−0.338101	−	0.585609i	0.645974	−	0.763359i	$-0.276451\pi$
$491$	−7.49182	−	12.9762i	−0.338101	−	0.585609i	−0.984076	+	0.177751i	$0.943118\pi$
$492$	−0.839153	+	0.484485i	−0.0378319	+	0.0218423i
$493$	6.34217			0.285637
$494$	20.9162	+	7.30066i	0.941065	+	0.328472i
$495$	−18.2770			−0.821491
$496$	−12.5334	+	7.23618i	−0.562767	+	0.324914i
$497$	−0.137708	−	0.238517i	−0.00617704	−	0.0106989i
$498$	7.08704	−	12.2751i	0.317578	−	0.550061i
$499$		−	32.9561i		−	1.47532i	−0.675173	−	0.737659i	$-0.735931\pi$
$499$		−	32.9561i		−	1.47532i	0.675173	−	0.737659i	$-0.264069\pi$
$500$	1.20701	+	0.696867i	0.0539790	+	0.0311648i
$501$	−6.96686	−	4.02232i	−0.311256	−	0.179704i
$502$		−	6.50592i		−	0.290373i
$503$	9.49476	−	16.4454i	0.423351	−	0.733265i	−0.572914	−	0.819615i	$-0.694187\pi$
$503$	9.49476	−	16.4454i	0.423351	−	0.733265i	0.996265	+	0.0863505i	$0.0275205\pi$
$504$	1.02150	+	1.76929i	0.0455013	+	0.0788105i
$505$	−21.5292	+	12.4299i	−0.958037	+	0.553123i
$506$	−5.63704			−0.250597
$507$	−1.82663	+	12.2480i	−0.0811235	+	0.543952i
$508$	−1.48663			−0.0659585
$509$	22.1620	−	12.7952i	0.982312	−	0.567138i	0.0793443	−	0.996847i	$-0.474717\pi$
$509$	22.1620	−	12.7952i	0.982312	−	0.567138i	0.902967	+	0.429709i	$0.141384\pi$
$510$	−3.67951	−	6.37309i	−0.162931	−	0.282205i
$511$	−1.56630	+	2.71292i	−0.0692891	+	0.120012i
$512$			24.3098i			1.07435i
$513$	−18.8242	−	10.8681i	−0.831108	−	0.479840i
$514$	4.14081	+	2.39070i	0.182643	+	0.105449i
$515$			4.67203i			0.205874i
$516$	0.362195	−	0.627341i	0.0159448	−	0.0276171i
$517$	−16.0712	−	27.8361i	−0.706810	−	1.22423i
$518$	1.53967	−	0.888926i	0.0676490	−	0.0390572i
$519$	−15.6742			−0.688019
$520$	−21.0223	−	7.33769i	−0.921888	−	0.321779i
$521$	37.6462			1.64931			0.824654	−	0.565637i	$-0.191370\pi$
$521$	37.6462			1.64931			0.824654	+	0.565637i	$0.191370\pi$
$522$	5.94408	−	3.43182i	0.260165	−	0.150207i
$523$	−18.6421	−	32.2891i	−0.815164	−	1.41190i	−0.909210	−	0.416337i	$-0.863314\pi$
$523$	−18.6421	−	32.2891i	−0.815164	−	1.41190i	0.0940469	−	0.995568i	$-0.470020\pi$
$524$	−0.277643	+	0.480892i	−0.0121289	+	0.0210079i
$525$		−	0.155410i		−	0.00678263i
$526$	−25.6687	−	14.8199i	−1.11921	−	0.646176i
$527$	−8.87029	−	5.12126i	−0.386396	−	0.223086i
$528$			14.6707i			0.638462i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	10.6142	+	18.3844i	0.461052	+	0.798565i
$531$	5.19396	−	2.99873i	0.225398	−	0.130134i
$532$	−0.179972			−0.00780276
$533$	30.1321	−	5.72555i	1.30517	−	0.248001i
$534$	2.94224			0.127323
$535$	11.5161	−	6.64881i	0.497884	−	0.287453i
$536$	12.3499	+	21.3906i	0.533433	+	0.923934i
$537$	1.48751	−	2.57645i	0.0641910	−	0.111182i
$538$		−	15.5352i		−	0.669771i
$539$	−24.5186	−	14.1558i	−1.05609	−	0.609733i
$540$	1.06737	+	0.616247i	0.0459324	+	0.0265191i
$541$			22.3311i			0.960090i	0.877244	+	0.480045i	$0.159380\pi$
$541$			22.3311i			0.960090i	−0.877244	+	0.480045i	$0.840620\pi$
$542$	9.46800	−	16.3991i	0.406686	−	0.704400i
$543$	0.407453	+	0.705729i	0.0174855	+	0.0302857i
$544$	−1.55118	+	0.895574i	−0.0665063	+	0.0383974i
$545$	30.1052			1.28956
$546$	0.295317	+	1.55418i	0.0126384	+	0.0665126i
$547$	−0.265048			−0.0113326			−0.00566631	−	0.999984i	$-0.501804\pi$
$547$	−0.265048			−0.0113326			−0.00566631	+	0.999984i	$0.501804\pi$
$548$	−0.661270	+	0.381784i	−0.0282480	+	0.0163090i
$549$	5.67210	+	9.82437i	0.242079	+	0.419294i
$550$	−1.36898	+	2.37114i	−0.0583733	+	0.101106i
$551$			10.7173i			0.456574i
$552$	2.39776	+	1.38435i	0.102055	+	0.0589218i
$553$	3.82801	+	2.21010i	0.162783	+	0.0939830i
$554$		−	30.2642i		−	1.28580i
$555$	3.90595	−	6.76530i	0.165798	−	0.287171i
$556$	0.974145	+	1.68727i	0.0413130	+	0.0715561i
$557$	−21.7576	+	12.5618i	−0.921901	+	0.532260i	−0.884241	−	0.467031i	$-0.845324\pi$
$557$	−21.7576	+	12.5618i	−0.921901	+	0.532260i	−0.0376597	+	0.999291i	$0.511990\pi$
$558$	−11.0847			−0.469252
$559$	−17.3683	+	14.9701i	−0.734600	+	0.633168i
$560$	−2.67381			−0.112989
$561$	−8.99189	+	5.19147i	−0.379638	+	0.219184i
$562$	12.0140	+	20.8089i	0.506781	+	0.877770i
$563$	−17.0479	+	29.5279i	−0.718485	+	1.24445i	0.243116	+	0.969997i	$0.421831\pi$
$563$	−17.0479	+	29.5279i	−0.718485	+	1.24445i	−0.961600	+	0.274454i	$0.911503\pi$
$564$			0.890646i			0.0375030i
$565$	31.6715	+	18.2856i	1.33243	+	0.769280i
$566$	−33.3955	−	19.2809i	−1.40372	−	0.810437i
$567$			0.556516i			0.0233715i
$568$	1.19160	−	2.06391i	0.0499985	−	0.0865999i
$569$	0.701647	+	1.21529i	0.0294146	+	0.0509476i	0.880358	−	0.474310i	$-0.157302\pi$
$569$	0.701647	+	1.21529i	0.0294146	+	0.0509476i	−0.850943	+	0.525257i	$0.823969\pi$
$570$	10.7696	−	6.21782i	0.451088	−	0.260436i
$571$	−14.8406			−0.621059			−0.310529	−	0.950564i	$-0.600506\pi$
$571$	−14.8406			−0.621059			−0.310529	+	0.950564i	$0.600506\pi$
$572$	−0.584067	+	1.67334i	−0.0244211	+	0.0699657i
$573$	−4.18536			−0.174846
$574$	3.39331	−	1.95913i	0.141634	−	0.0817723i
$575$	0.242854	+	0.420635i	0.0101277	+	0.0175417i
$576$	−8.80925	+	15.2581i	−0.367052	+	0.635753i
$577$		−	16.3865i		−	0.682180i	−0.940031	−	0.341090i	$-0.889204\pi$
$577$		−	16.3865i		−	0.682180i	0.940031	−	0.341090i	$-0.110796\pi$
$578$	−11.8392	−	6.83538i	−0.492447	−	0.284315i
$579$	14.0614	+	8.11837i	0.584373	+	0.337388i
$580$		−	0.607696i		−	0.0252332i
$581$	1.82240	−	3.15649i	0.0756058	−	0.130953i
$582$	−1.36822	−	2.36983i	−0.0567146	−	0.0982325i
$583$	25.9388	−	14.9757i	1.07427	−	0.620232i
$584$	−27.1068			−1.12169
$585$	−10.4661	−	12.1427i	−0.432720	−	0.502040i
$586$	13.3786			0.552666
$587$	12.8950	−	7.44494i	0.532234	−	0.307286i	−0.209691	−	0.977768i	$-0.567246\pi$
$587$	12.8950	−	7.44494i	0.532234	−	0.307286i	0.741926	+	0.670482i	$0.233913\pi$
$588$	0.392249	+	0.679394i	0.0161761	+	0.0280178i
$589$	8.65417	−	14.9895i	0.356589	−	0.617630i
$590$			8.35031i			0.343777i
$591$	−15.2730	−	8.81786i	−0.628246	−	0.362718i
$592$	12.5235	+	7.23043i	0.514712	+	0.297169i
$593$			36.2355i			1.48801i	0.668172	+	0.744007i	$0.267077\pi$
$593$			36.2355i			1.48801i	−0.668172	+	0.744007i	$0.732923\pi$
$594$	−13.6728	+	23.6821i	−0.561004	+	0.971687i
$595$	−0.946168	−	1.63881i	−0.0387891	−	0.0671847i
$596$	2.39039	−	1.38009i	0.0979142	−	0.0565308i
$597$	−18.8889			−0.773070
$598$	−3.22797	−	3.74509i	−0.132002	−	0.153148i
$599$	28.1545			1.15036			0.575180	−	0.818027i	$-0.304932\pi$
$599$	28.1545			1.15036			0.575180	+	0.818027i	$0.304932\pi$
$600$	1.16461	−	0.672389i	0.0475450	−	0.0274501i
$601$	6.40382	+	11.0917i	0.261217	+	0.452441i	0.966566	−	0.256419i	$-0.0825428\pi$
$601$	6.40382	+	11.0917i	0.261217	+	0.452441i	−0.705349	+	0.708861i	$0.749209\pi$
$602$	−1.46462	+	2.53679i	−0.0596934	+	0.103392i
$603$			17.7829i			0.724176i
$604$	−2.43153	−	1.40384i	−0.0989375	−	0.0571216i
$605$	−10.8533	−	6.26615i	−0.441249	−	0.254755i
$606$			15.2837i			0.620858i
$607$	−13.0475	+	22.5990i	−0.529583	+	0.917265i	0.469821	+	0.882761i	$0.344318\pi$
$607$	−13.0475	+	22.5990i	−0.529583	+	0.917265i	−0.999405	+	0.0345034i	$0.989015\pi$
$608$	−1.51339	−	2.62126i	−0.0613759	−	0.106306i
$609$	−0.662785	+	0.382659i	−0.0268574	+	0.0155061i
$610$	−15.7946			−0.639505
$611$	9.29057	−	26.6172i	0.375856	−	1.07682i
$612$	−0.663496			−0.0268202
$613$	−20.3438	+	11.7455i	−0.821680	+	0.474397i	−0.850995	−	0.525173i	$-0.824001\pi$
$613$	−20.3438	+	11.7455i	−0.821680	+	0.474397i	0.0293154	+	0.999570i	$0.490667\pi$
$614$	1.12057	+	1.94089i	0.0452227	+	0.0783281i
$615$	8.60842	−	14.9102i	0.347125	−	0.601238i
$616$			4.01333i			0.161702i
$617$	16.9397	+	9.78015i	0.681967	+	0.393734i	0.800596	−	0.599205i	$-0.204516\pi$
$617$	16.9397	+	9.78015i	0.681967	+	0.393734i	−0.118628	+	0.992939i	$0.537850\pi$
$618$	2.48752	+	1.43617i	0.100063	+	0.0577713i
$619$			20.9950i			0.843862i	0.906628	+	0.421931i	$0.138648\pi$
$619$			20.9950i			0.843862i	−0.906628	+	0.421931i	$0.861352\pi$
$620$	−0.490710	+	0.849935i	−0.0197074	+	0.0341342i
$621$	2.42554	+	4.20116i	0.0973335	+	0.168587i
$622$	10.2425	−	5.91350i	0.410686	−	0.237110i
$623$	0.756582			0.0303118
$624$	−9.74683	+	8.40101i	−0.390185	+	0.336310i
$625$	−22.3355			−0.893422
$626$	−38.2713	+	22.0960i	−1.52963	+	0.883132i
$627$	−8.77281	−	15.1950i	−0.350352	−	0.606828i
$628$	0.0613515	−	0.106264i	0.00244819	−	0.00424039i
$629$			10.2344i			0.408072i
$630$	−1.77356	−	1.02396i	−0.0706602	−	0.0407957i
$631$	7.08017	+	4.08774i	0.281857	+	0.162730i	0.634264	−	0.773117i	$-0.281303\pi$
$631$	7.08017	+	4.08774i	0.281857	+	0.162730i	−0.352407	+	0.935847i	$0.614637\pi$
$632$			38.2485i			1.52144i
$633$	4.55057	−	7.88181i	0.180869	−	0.313274i
$634$	11.6018	+	20.0948i	0.460765	+	0.798068i
$635$	22.8758	−	13.2073i	0.907797	−	0.524117i
$636$	−0.829938			−0.0329092
$637$	−4.63552	−	24.3956i	−0.183666	−	0.966587i
$638$	13.4831			0.533801
$639$	1.48594	−	0.857909i	0.0587829	−	0.0339383i
$640$	−10.8299	−	18.7580i	−0.428091	−	0.741475i
$641$	14.1595	−	24.5250i	0.559268	−	0.968680i	−0.438290	−	0.898834i	$-0.644416\pi$
$641$	14.1595	−	24.5250i	0.559268	−	0.968680i	0.997558	−	0.0698464i	$-0.0222509\pi$
$642$		−	8.17533i		−	0.322654i
$643$	−36.5058	−	21.0766i	−1.43965	−	0.831180i	−0.441822	−	0.897103i	$-0.645668\pi$
$643$	−36.5058	−	21.0766i	−1.43965	−	0.831180i	−0.997825	+	0.0659225i	$0.979001\pi$
$644$	0.0347846	+	0.0200829i	0.00137071	+	0.000791378i
$645$			12.8711i			0.506799i
$646$	−8.14599	+	14.1093i	−0.320500	+	0.555122i
$647$	−3.98450	−	6.90136i	−0.156647	−	0.271321i	0.777011	−	0.629488i	$-0.216735\pi$
$647$	−3.98450	−	6.90136i	−0.156647	−	0.271321i	−0.933658	+	0.358167i	$0.883402\pi$
$648$	−4.17043	+	2.40780i	−0.163830	+	0.0945872i
$649$	11.7816			0.462467
$650$	−2.35924	+	0.448291i	−0.0925370	+	0.0175834i
$651$	1.23598			0.0484418
$652$	−1.50638	+	0.869711i	−0.0589945	+	0.0340605i
$653$	0.140438	+	0.243246i	0.00549577	+	0.00951894i	0.868760	−	0.495233i	$-0.164917\pi$
$653$	0.140438	+	0.243246i	0.00549577	+	0.00951894i	−0.863264	+	0.504752i	$0.831584\pi$
$654$	9.25427	−	16.0289i	0.361871	−	0.626778i
$655$		−	9.86642i		−	0.385513i
$656$	27.6008	+	15.9353i	1.07763	+	0.622170i
$657$	−16.9013	−	9.75794i	−0.659381	−	0.380694i
$658$		−	3.60153i		−	0.140402i
$659$	−16.4608	+	28.5109i	−0.641221	+	1.11063i	0.343940	+	0.938992i	$0.388238\pi$
$659$	−16.4608	+	28.5109i	−0.641221	+	1.11063i	−0.985161	+	0.171635i	$0.945095\pi$
$660$	0.497437	+	0.861587i	0.0193627	+	0.0335372i
$661$	12.2451	−	7.06970i	0.476279	−	0.274980i	−0.242586	−	0.970130i	$-0.577996\pi$
$661$	12.2451	−	7.06970i	0.476279	−	0.274980i	0.718864	+	0.695150i	$0.244662\pi$
$662$	−40.2749			−1.56533
$663$	−8.59815	−	3.00113i	−0.333924	−	0.116554i
$664$	31.5389			1.22394
$665$	2.76935	−	1.59888i	0.107391	−	0.0620020i
$666$	5.53794	+	9.59200i	0.214591	+	0.371682i
$667$	1.19594	−	2.07143i	0.0463070	−	0.0802060i
$668$		−	1.00986i		−	0.0390726i
$669$	−4.70631	−	2.71719i	−0.181956	−	0.105053i
$670$	−21.4422	−	12.3796i	−0.828383	−	0.478267i
$671$			22.2849i			0.860297i
$672$	0.108070	−	0.187183i	0.00416889	−	0.00722073i
$673$	−1.16187	−	2.01242i	−0.0447869	−	0.0775732i	0.842763	−	0.538285i	$-0.180928\pi$
$673$	−1.16187	−	2.01242i	−0.0447869	−	0.0775732i	−0.887550	+	0.460712i	$0.847594\pi$
$674$	−28.5123	+	16.4616i	−1.09825	+	0.634076i
$675$	2.35621			0.0906904
$676$	−1.44617	+	0.570176i	−0.0556221	+	0.0219299i
$677$	−40.4972			−1.55643			−0.778216	−	0.627997i	$-0.783875\pi$
$677$	−40.4972			−1.55643			−0.778216	+	0.627997i	$0.783875\pi$
$678$	19.4715	−	11.2419i	0.747799	−	0.431742i
$679$	−0.351831	−	0.609390i	−0.0135021	−	0.0233862i
$680$	8.18730	−	14.1808i	0.313969	−	0.543810i
$681$		−	15.2777i		−	0.585443i
$682$	−18.8577	−	10.8875i	−0.722100	−	0.416905i
$683$	−24.7921	−	14.3137i	−0.948643	−	0.547699i	−0.0559840	−	0.998432i	$-0.517830\pi$
$683$	−24.7921	−	14.3137i	−0.948643	−	0.547699i	−0.892659	+	0.450732i	$0.851163\pi$
$684$		−	1.12121i		−	0.0428705i
$685$	6.78361	−	11.7496i	0.259188	−	0.448927i
$686$	−3.19828	−	5.53958i	−0.122111	−	0.211502i
$687$	1.58658	−	0.916013i	0.0605319	−	0.0349481i
$688$	−23.8261			−0.908362
$689$	24.8029	+	8.65730i	0.944917	+	0.329817i
$690$	−2.77537			−0.105656
$691$	−13.9244	+	8.03923i	−0.529708	+	0.305827i	−0.740897	−	0.671618i	$-0.765600\pi$
$691$	−13.9244	+	8.03923i	−0.529708	+	0.305827i	0.211190	+	0.977445i	$0.432266\pi$
$692$	−0.983803	−	1.70400i	−0.0373986	−	0.0647762i
$693$	−1.44472	+	2.50234i	−0.0548805	+	0.0950559i
$694$		−	19.0679i		−	0.723807i
$695$	−29.9797	−	17.3088i	−1.13719	−	0.656559i
$696$	−5.73516	−	3.31119i	−0.217391	−	0.125510i
$697$			22.5558i			0.854363i
$698$	15.7308	−	27.2466i	0.595420	−	1.03130i
$699$	9.65350	+	16.7203i	0.365129	+	0.632422i
$700$	0.0168952	−	0.00975442i	0.000638577	−	0.000368683i
$701$	−14.0412			−0.530330			−0.265165	−	0.964203i	$-0.585426\pi$
$701$	−14.0412			−0.530330			−0.265165	+	0.964203i	$0.585426\pi$
$702$	−23.5633	+	4.47737i	−0.889338	+	0.168988i
$703$	−17.2946			−0.652279
$704$	−29.9734	+	17.3051i	−1.12966	+	0.652211i
$705$	−7.91258	−	13.7050i	−0.298005	−	0.516160i
$706$	10.0336	−	17.3786i	0.377618	−	0.654053i
$707$			3.93013i			0.147808i
$708$	−0.282723	−	0.163230i	−0.0106254	−	0.00613457i
$709$	13.5726	+	7.83615i	0.509730	+	0.294293i	0.732723	−	0.680527i	$-0.238249\pi$
$709$	13.5726	+	7.83615i	0.509730	+	0.294293i	−0.222993	+	0.974820i	$0.571583\pi$
$710$			2.38895i			0.0896555i
$711$	−13.7688	+	23.8482i	−0.516369	+	0.894377i
$712$	3.27340	+	5.66969i	0.122676	+	0.212481i
$713$	−3.34533	+	1.93143i	−0.125284	+	0.0723325i
$714$	−1.16340			−0.0435392
$715$	−5.87862	−	30.9377i	−0.219848	−	1.15700i
$716$	0.373461			0.0139569
$717$	23.1976	−	13.3931i	0.866331	−	0.500176i
$718$	−14.3587	−	24.8701i	−0.535863	−	0.928142i
$719$	16.6108	−	28.7707i	0.619478	−	1.07297i	−0.370104	−	0.928990i	$-0.620678\pi$
$719$	16.6108	−	28.7707i	0.619478	−	1.07297i	0.989581	−	0.143976i	$-0.0459889\pi$
$720$		−	16.6576i		−	0.620793i
$721$	0.639655	+	0.369305i	0.0238220	+	0.0137536i
$722$	−1.27878	−	0.738306i	−0.0475914	−	0.0274769i
$723$		−	14.5057i		−	0.539471i
$724$	−0.0511483	+	0.0885915i	−0.00190091	+	0.00329248i
$725$	−0.580877	−	1.00611i	−0.0215732	−	0.0373659i
$726$	−6.67256	+	3.85241i	−0.247642	+	0.142976i
$727$	19.6017			0.726986			0.363493	−	0.931597i	$-0.381584\pi$
$727$	19.6017			0.726986			0.363493	+	0.931597i	$0.381584\pi$
$728$	−2.66634	+	2.29818i	−0.0988212	+	0.0851762i
$729$	10.3960			0.385036
$730$	23.5317	−	13.5861i	0.870949	−	0.502843i
$731$	−8.43124	−	14.6033i	−0.311841	−	0.540124i
$732$	0.308750	−	0.534771i	0.0114117	−	0.0197657i
$733$		−	18.6636i		−	0.689357i	−0.938721	−	0.344678i	$-0.887988\pi$
$733$		−	18.6636i		−	0.689357i	0.938721	−	0.344678i	$-0.112012\pi$
$734$	−9.99839	−	5.77257i	−0.369047	−	0.213069i
$735$	−12.0716	−	6.96954i	−0.445268	−	0.257075i
$736$			0.675511i			0.0248997i
$737$	−17.4666	+	30.2531i	−0.643391	+	1.11439i
$738$	12.2052	+	21.1400i	0.449280	+	0.778175i
$739$	7.24432	−	4.18251i	0.266487	−	0.153856i	−0.360803	−	0.932642i	$-0.617497\pi$
$739$	7.24432	−	4.18251i	0.266487	−	0.153856i	0.627290	+	0.778786i	$0.284164\pi$
$740$	0.980642			0.0360491
$741$	5.07146	−	14.5296i	0.186305	−	0.533758i
$742$	3.35604			0.123204
$743$	40.8101	−	23.5617i	1.49718	−	0.864395i	0.497181	−	0.867647i	$-0.334368\pi$
$743$	40.8101	−	23.5617i	1.49718	−	0.864395i	0.999995	+	0.00325192i	$0.00103512\pi$
$744$	5.34753	+	9.26220i	0.196050	+	0.339569i
$745$	−24.5217	+	42.4729i	−0.898406	+	1.55609i
$746$			27.8832i			1.02088i
$747$	19.6647	+	11.3534i	0.719493	+	0.415399i
$748$	−1.12877	−	0.651695i	−0.0412718	−	0.0238283i
$749$		−	2.10225i		−	0.0768144i
$750$	−7.61243	+	13.1851i	−0.277967	+	0.481452i
$751$	−22.6469	−	39.2255i	−0.826395	−	1.43136i	−0.900848	−	0.434134i	$-0.857054\pi$
$751$	−22.6469	−	39.2255i	−0.826395	−	1.43136i	0.0744529	−	0.997225i	$-0.476279\pi$
$752$	25.3698	−	14.6472i	0.925140	−	0.534130i
$753$	−4.51938			−0.164695
$754$	7.72092	+	8.95779i	0.281180	+	0.326224i
$755$	49.8875			1.81559
$756$	0.168743	−	0.0974237i	0.00613712	−	0.00354327i
$757$	6.28908	+	10.8930i	0.228580	+	0.395913i	0.957388	−	0.288806i	$-0.0932583\pi$
$757$	6.28908	+	10.8930i	0.228580	+	0.395913i	−0.728807	+	0.684719i	$0.759925\pi$
$758$	−2.75361	+	4.76939i	−0.100016	+	0.173232i
$759$			3.91581i			0.142135i
$760$	23.9635	+	13.8353i	0.869247	+	0.501860i
$761$	29.4031	+	16.9759i	1.06586	+	0.615376i	0.927048	−	0.374942i	$-0.122337\pi$
$761$	29.4031	+	16.9759i	1.06586	+	0.615376i	0.138815	+	0.990318i	$0.455671\pi$
$762$		−	16.2396i		−	0.588300i
$763$	2.37969	−	4.12175i	0.0861507	−	0.149217i
$764$	−0.262698	−	0.455007i	−0.00950409	−	0.0164616i
$765$	10.2097	−	5.89455i	0.369131	−	0.213118i
$766$	5.39782			0.195031
$767$	6.74656	+	7.82734i	0.243604	+	0.282629i
$768$	2.72380			0.0982867
$769$	16.4579	−	9.50197i	0.593487	−	0.342650i	−0.172988	−	0.984924i	$-0.555342\pi$
$769$	16.4579	−	9.50197i	0.593487	−	0.342650i	0.766475	+	0.642274i	$0.222009\pi$
$770$	−2.01150	−	3.48402i	−0.0724894	−	0.125555i
$771$	1.66072	−	2.87644i	0.0598092	−	0.103593i
$772$			2.03823i			0.0733575i
$773$	−33.2170	−	19.1778i	−1.19473	−	0.689778i	−0.235355	−	0.971909i	$-0.575625\pi$
$773$	−33.2170	−	19.1778i	−1.19473	−	0.689778i	−0.959376	+	0.282131i	$0.908959\pi$
$774$	−15.8040	−	9.12446i	−0.568064	−	0.327972i
$775$			1.87622i			0.0673957i
$776$	3.04444	−	5.27312i	0.109289	−	0.189294i
$777$	−0.617499	−	1.06954i	−0.0221526	−	0.0383695i
$778$	−36.1162	+	20.8517i	−1.29483	+	0.747570i
$779$	−38.1160			−1.36565
$780$	−0.287563	+	0.823859i	−0.0102964	+	0.0294989i
$781$	3.37060			0.120609
$782$	3.14889	−	1.81801i	0.112604	−	0.0650119i
$783$	−5.80160	−	10.0487i	−0.207332	−	0.359110i
$784$	12.9016	−	22.3461i	0.460770	−	0.798077i
$785$			2.18021i			0.0778149i
$786$	−5.25317	−	3.03292i	−0.187374	−	0.108181i
$787$	0.197334	+	0.113931i	0.00703421	+	0.00406120i	0.503513	−	0.863988i	$-0.332041\pi$
$787$	0.197334	+	0.113931i	0.00703421	+	0.00406120i	−0.496479	+	0.868049i	$0.665374\pi$
$788$		−	2.21384i		−	0.0788649i
$789$	−10.2947	+	17.8310i	−0.366502	+	0.634799i
$790$	−19.1703	−	33.2040i	−0.682050	−	1.18135i
$791$	5.00701	−	2.89080i	0.178029	−	0.102785i
$792$	−25.0027			−0.888433
$793$	−14.8054	+	12.7611i	−0.525756	+	0.453161i
$794$	39.9772			1.41874
$795$	12.7708	−	7.37324i	0.452935	−	0.261502i
$796$	−1.18558	−	2.05348i	−0.0420217	−	0.0727837i
$797$	5.88524	−	10.1935i	0.208466	−	0.361074i	−0.742765	−	0.669552i	$-0.766486\pi$
$797$	5.88524	−	10.1935i	0.208466	−	0.361074i	0.951232	+	0.308478i	$0.0998196\pi$
$798$		−	1.96597i		−	0.0695947i
$799$	17.9550	+	10.3663i	0.635201	+	0.366733i
$800$	0.284144	+	0.164050i	0.0100460	+	0.00580006i
$801$			4.71345i			0.166542i
$802$	−7.88891	+	13.6640i	−0.278567	+	0.482492i
$803$	−19.1688	−	33.2013i	−0.676451	−	1.17165i
$804$	0.838294	−	0.483989i	0.0295644	−	0.0170690i
$805$	−0.713673			−0.0251537
$806$	−3.56528	−	18.7631i	−0.125582	−	0.660903i
$807$	−10.7917			−0.379885
$808$	−29.4517	+	17.0039i	−1.03611	+	0.598196i
$809$	20.9824	+	36.3426i	0.737701	+	1.27774i	0.953528	+	0.301304i	$0.0974220\pi$
$809$	20.9824	+	36.3426i	0.737701	+	1.27774i	−0.215827	+	0.976432i	$0.569245\pi$
$810$	2.41360	−	4.18048i	0.0848053	−	0.146887i
$811$			28.4230i			0.998068i	0.866583	+	0.499034i	$0.166312\pi$
$811$			28.4230i			0.998068i	−0.866583	+	0.499034i	$0.833688\pi$
$812$	−0.0832006	−	0.0480359i	−0.00291977	−	0.00168573i
$813$	−11.3917	−	6.57702i	−0.399525	−	0.230666i
$814$			21.7578i			0.762609i
$815$	15.4532	−	26.7657i	0.541301	−	0.937560i
$816$	−4.73149	−	8.19518i	−0.165635	−	0.286889i
$817$	24.6775	−	14.2475i	0.863355	−	0.498458i
$818$	8.25484			0.288624
$819$	−2.48978	+	0.473096i	−0.0870000	+	0.0165313i
$820$	2.16126			0.0754745
$821$	38.0102	−	21.9452i	1.32656	−	0.765892i	0.341797	−	0.939774i	$-0.388964\pi$
$821$	38.0102	−	21.9452i	1.32656	−	0.765892i	0.984767	+	0.173882i	$0.0556310\pi$
$822$	−4.17053	−	7.22358i	−0.145464	−	0.251951i
$823$	−13.3423	+	23.1095i	−0.465083	+	0.805547i	−0.999205	−	0.0398601i	$-0.987309\pi$
$823$	−13.3423	+	23.1095i	−0.465083	+	0.805547i	0.534123	+	0.845407i	$0.320642\pi$
$824$			6.39128i			0.222651i
$825$	1.64713	+	0.950969i	0.0573456	+	0.0331085i
$826$	1.14326	+	0.660059i	0.0397789	+	0.0229664i
$827$			6.19364i			0.215374i	0.994185	+	0.107687i	$0.0343444\pi$
$827$			6.19364i			0.215374i	−0.994185	+	0.107687i	$0.965656\pi$
$828$	−0.125115	+	0.216706i	−0.00434805	+	0.00753104i
$829$	15.8724	+	27.4918i	0.551271	+	0.954829i	0.998183	+	0.0602510i	$0.0191901\pi$
$829$	15.8724	+	27.4918i	0.551271	+	0.954829i	−0.446913	+	0.894578i	$0.647477\pi$
$830$	−27.3793	+	15.8074i	−0.950348	+	0.548684i
$831$	−21.0233			−0.729289
$832$	−28.6609	−	10.0039i	−0.993637	−	0.346823i
$833$	18.2616			0.632728
$834$	−18.4314	+	10.6414i	−0.638227	+	0.368480i
$835$	8.97166	+	15.5394i	0.310477	+	0.537762i
$836$	1.10127	−	1.90745i	0.0380881	−	0.0659705i
$837$			18.7390i			0.647715i
$838$	37.4669	+	21.6315i	1.29427	+	0.747249i
$839$	−6.31618	−	3.64665i	−0.218059	−	0.125896i	0.386992	−	0.922083i	$-0.373514\pi$
$839$	−6.31618	−	3.64665i	−0.218059	−	0.125896i	−0.605051	+	0.796187i	$0.706847\pi$
$840$			1.97594i			0.0681765i
$841$	11.6395	−	20.1601i	0.401361	−	0.695177i
$842$	−2.17072	−	3.75980i	−0.0748080	−	0.129571i
$843$	14.4551	−	8.34563i	0.497858	−	0.287439i
$844$	1.14248			0.0393259
$845$	17.1878	−	21.6216i	0.591278	−	0.743807i
$846$	22.4373			0.771409
$847$	−1.71582	+	0.990628i	−0.0589562	+	0.0340384i
$848$	13.6489	+	23.6405i	0.468704	+	0.811818i
$849$	−13.3936	+	23.1984i	−0.459668	+	0.796169i
$850$		−	1.76604i		−	0.0605748i
$851$	3.34267	+	1.92989i	0.114585	+	0.0661559i
$852$	−0.0808844	−	0.0466986i	−0.00277105	−	0.00159987i
$853$			22.5693i			0.772756i	0.922340	+	0.386378i	$0.126274\pi$
$853$			22.5693i			0.772756i	−0.922340	+	0.386378i	$0.873726\pi$
$854$	−1.24850	+	2.16247i	−0.0427228	+	0.0739981i
$855$	9.96092	+	17.2528i	0.340656	+	0.590034i
$856$	15.7539	−	9.09550i	0.538456	−	0.310878i
$857$	42.3246			1.44578			0.722890	−	0.690963i	$-0.242813\pi$
$857$	42.3246			1.44578			0.722890	+	0.690963i	$0.242813\pi$
$858$	−18.2792	−	6.38023i	−0.624041	−	0.217817i
$859$	23.4627			0.800538			0.400269	−	0.916398i	$-0.368917\pi$
$859$	23.4627			0.800538			0.400269	+	0.916398i	$0.368917\pi$
$860$	−1.39927	+	0.807866i	−0.0477145	+	0.0275480i
$861$	−1.36092	−	2.35718i	−0.0463801	−	0.0803326i
$862$	1.20855	−	2.09327i	0.0411634	−	0.0712971i
$863$			17.4773i			0.594933i	0.954732	+	0.297467i	$0.0961417\pi$
$863$			17.4773i			0.594933i	−0.954732	+	0.297467i	$0.903858\pi$
$864$	2.83793	+	1.63848i	0.0965483	+	0.0557422i
$865$	30.2769	+	17.4804i	1.02945	+	0.594351i
$866$			25.0846i			0.852408i
$867$	−4.74825	+	8.22421i	−0.161259	+	0.279309i
$868$	0.0775773	+	0.134368i	0.00263315	+	0.00456074i
$869$	−46.8480	+	27.0477i	−1.58921	+	0.917531i
$870$	6.63835			0.225061
$871$	−30.1013	+	5.71969i	−1.01994	+	0.193804i
$872$	41.1835			1.39465
$873$	3.79645	−	2.19188i	0.128490	−	0.0741840i
$874$	3.07217	+	5.32115i	0.103918	+	0.179991i
$875$	−1.95750	+	3.39049i	−0.0661756	+	0.114620i
$876$			1.06231i			0.0358921i
$877$	30.8863	+	17.8322i	1.04296	+	0.602151i	0.920669	−	0.390344i	$-0.127644\pi$
$877$	30.8863	+	17.8322i	1.04296	+	0.602151i	0.122286	+	0.992495i	$0.460977\pi$
$878$	−38.5417	−	22.2521i	−1.30072	−	0.750972i
$879$		−	9.29355i		−	0.313464i
$880$	16.3613	−	28.3387i	0.551541	−	0.955296i
$881$	6.81581	+	11.8053i	0.229630	+	0.397731i	0.957699	−	0.287773i	$-0.0929150\pi$
$881$	6.81581	+	11.8053i	0.229630	+	0.397731i	−0.728068	+	0.685505i	$0.759582\pi$
$882$	17.1154	−	9.88157i	0.576305	−	0.332730i
$883$	−6.36388			−0.214162			−0.107081	−	0.994250i	$-0.534150\pi$
$883$	−6.36388			−0.214162			−0.107081	+	0.994250i	$0.534150\pi$
$884$	−0.213407	−	1.12311i	−0.00717765	−	0.0377741i
$885$	5.80061			0.194985
$886$	−2.69070	+	1.55348i	−0.0903958	+	0.0521900i
$887$	−22.8492	−	39.5759i	−0.767200	−	1.32883i	−0.939076	−	0.343711i	$-0.888316\pi$
$887$	−22.8492	−	39.5759i	−0.767200	−	1.32883i	0.171876	−	0.985119i	$-0.445017\pi$
$888$	5.34329	−	9.25485i	0.179309	−	0.310572i
$889$		−	4.17595i		−	0.140057i
$890$	−5.68336	−	3.28129i	−0.190507	−	0.109989i
$891$	−5.89830	−	3.40538i	−0.197600	−	0.114085i
$892$		−	0.682187i		−	0.0228413i
$893$	−17.5175	+	30.3412i	−0.586201	+	1.01533i
$894$	15.0759	+	26.1121i	0.504212	+	0.873321i
$895$	−5.74670	+	3.31786i	−0.192091	+	0.110904i
$896$	−3.42425			−0.114396
$897$	−2.60155	+	2.24234i	−0.0868633	+	0.0748694i
$898$	39.9584			1.33343
$899$	8.00162	−	4.61974i	0.266869	−	0.154077i
$900$	0.0607693	+	0.105256i	0.00202564	+	0.00350852i
$901$	−9.65971	+	16.7311i	−0.321812	+	0.557394i
$902$			47.9525i			1.59664i
$903$	1.76220	+	1.01741i	0.0586424	+	0.0338572i
$904$	43.3263	+	25.0144i	1.44101	+	0.831968i
$905$		−	1.81762i		−	0.0604199i
$906$	15.3353	−	26.5615i	0.509481	−	0.882448i
$907$	11.4148	+	19.7711i	0.379023	+	0.656488i	0.990920	−	0.134450i	$-0.0429267\pi$
$907$	11.4148	+	19.7711i	0.379023	+	0.656488i	−0.611897	+	0.790937i	$0.709593\pi$
$908$	1.66090	−	0.958920i	0.0551188	−	0.0318229i
$909$	−24.4844			−0.812097
$910$	1.16283	−	3.33146i	0.0385473	−	0.110437i
$911$	22.8170			0.755961			0.377981	−	0.925813i	$-0.376619\pi$
$911$	22.8170			0.755961			0.377981	+	0.925813i	$0.376619\pi$
$912$	13.8486	−	7.99552i	0.458574	−	0.264758i
$913$	22.3029	+	38.6298i	0.738119	+	1.27846i
$914$	−3.02473	+	5.23899i	−0.100049	+	0.173290i
$915$			10.9718i			0.362718i
$916$	0.199166	+	0.114989i	0.00658065	+	0.00379934i
$917$	−1.35083	−	0.779901i	−0.0446083	−	0.0257546i
$918$		−	17.6386i		−	0.582161i
$919$	17.1231	−	29.6580i	0.564838	−	0.978327i	−0.432227	−	0.901765i	$-0.642272\pi$
$919$	17.1231	−	29.6580i	0.564838	−	0.978327i	0.997065	−	0.0765625i	$-0.0243945\pi$
$920$	−3.08775	−	5.34814i	−0.101800	−	0.176323i
$921$	1.34826	−	0.778416i	0.0444265	−	0.0256497i
$922$	25.8799			0.852310
$923$	1.93013	+	2.23933i	0.0635309	+	0.0737084i
$924$	0.157282			0.00517419
$925$	1.62356	−	0.937364i	0.0533824	−	0.0308204i
$926$	−3.72290	−	6.44825i	−0.122342	−	0.211903i
$927$	−2.30074	+	3.98500i	−0.0755663	+	0.130885i
$928$		−	1.61574i		−	0.0530393i
$929$	3.57668	+	2.06500i	0.117347	+	0.0677503i	0.557525	−	0.830160i	$-0.311751\pi$
$929$	3.57668	+	2.06500i	0.117347	+	0.0677503i	−0.440178	+	0.897911i	$0.645085\pi$
$930$	−9.28452	−	5.36042i	−0.304451	−	0.175775i
$931$			30.8595i			1.01138i
$932$	−1.21182	+	2.09894i	−0.0396945	+	0.0687529i
$933$	−4.10785	−	7.11501i	−0.134485	−	0.232935i
$934$	0.137540	−	0.0794088i	0.00450045	−	0.00259834i
$935$	23.1588			0.757375
$936$	−14.3175	−	16.6111i	−0.467982	−	0.542951i
$937$	−46.3833			−1.51528			−0.757638	−	0.652675i	$-0.773647\pi$
$937$	−46.3833			−1.51528			−0.757638	+	0.652675i	$0.773647\pi$
$938$	−3.38983	+	1.95712i	−0.110682	+	0.0639023i
$939$	15.3491	+	26.5854i	0.500899	+	0.867583i
$940$	0.993281	−	1.72041i	0.0323972	−	0.0561137i
$941$		−	55.5574i		−	1.81112i	−0.424219	−	0.905560i	$-0.639451\pi$
$941$		−	55.5574i		−	1.81112i	0.424219	−	0.905560i	$-0.360549\pi$
$942$	1.16081	+	0.670191i	0.0378211	+	0.0218360i
$943$	7.36700	+	4.25334i	0.239903	+	0.138508i
$944$			10.7377i			0.349482i
$945$	−1.73104	+	2.99825i	−0.0563108	+	0.0975332i
$946$	−17.9243	−	31.0459i	−0.582771	−	1.00939i
$947$	−8.76651	+	5.06135i	−0.284873	+	0.164472i	−0.635628	−	0.771996i	$-0.719259\pi$
$947$	−8.76651	+	5.06135i	−0.284873	+	0.164472i	0.350754	+	0.936468i	$0.385925\pi$
$948$	1.49895			0.0486837
$949$	11.0812	−	31.7475i	0.359712	−	1.03057i
$950$	2.98435			0.0968252
$951$	13.9590	−	8.05925i	0.452652	−	0.261339i
$952$	−1.29435	−	2.24187i	−0.0419500	−	0.0726595i
$953$	−7.35067	+	12.7317i	−0.238111	+	0.412421i	−0.960172	−	0.279408i	$-0.909862\pi$
$953$	−7.35067	+	12.7317i	−0.238111	+	0.412421i	0.722061	+	0.691829i	$0.243195\pi$
$954$			20.9079i			0.676918i
$955$	8.08463	+	4.66767i	0.261613	+	0.151042i
$956$	2.91204	+	1.68127i	0.0941821	+	0.0543760i
$957$		−	9.36614i		−	0.302764i
$958$	2.20087	−	3.81202i	0.0711069	−	0.123161i
$959$	−1.07243	−	1.85751i	−0.0346307	−	0.0599821i
$960$	−14.7572	+	8.52010i	−0.476288	+	0.274985i
$961$	16.0784			0.518657
$962$	−14.4552	+	12.4593i	−0.466056	+	0.401704i
$963$	13.0968			0.422040
$964$	1.57696	−	0.910461i	0.0507906	−	0.0293240i
$965$	−18.1078	−	31.3636i	−0.582911	−	1.00963i
$966$	−0.219382	+	0.379980i	−0.00705849	+	0.0122257i
$967$		−	47.3238i		−	1.52183i	−0.648851	−	0.760916i	$-0.724750\pi$
$967$		−	47.3238i		−	1.52183i	0.648851	−	0.760916i	$-0.275250\pi$
$968$	−14.8472	−	8.57202i	−0.477206	−	0.275515i
$969$	9.80110	+	5.65867i	0.314857	+	0.181783i
$970$			6.10355i			0.195973i
$971$	15.4795	−	26.8114i	0.496762	−	0.860417i	−0.503231	−	0.864152i	$-0.667855\pi$
$971$	15.4795	−	26.8114i	0.496762	−	0.860417i	0.999993	+	0.00373458i	$0.00118876\pi$
$972$	0.964486	+	1.67054i	0.0309359	+	0.0535826i
$973$	−4.73955	+	2.73638i	−0.151943	+	0.0877243i
$974$	−23.9718			−0.768106
$975$	0.311409	+	1.63886i	0.00997306	+	0.0524856i
$976$	−20.3104			−0.650119
$977$	25.1099	−	14.4972i	0.803336	−	0.463806i	−0.0413002	−	0.999147i	$-0.513150\pi$
$977$	25.1099	−	14.4972i	0.803336	−	0.463806i	0.844636	+	0.535340i	$0.179817\pi$
$978$	−9.50054	−	16.4554i	−0.303794	−	0.526186i
$979$	−4.62961	+	8.01873i	−0.147963	+	0.256280i
$980$		−	1.74980i		−	0.0558953i
$981$	25.6782	+	14.8253i	0.819841	+	0.473336i
$982$	17.7941	+	10.2734i	0.567832	+	0.327838i
$983$		−	26.4807i		−	0.844605i	−0.906455	−	0.422302i	$-0.861222\pi$
$983$		−	26.4807i		−	0.844605i	0.906455	−	0.422302i	$-0.138778\pi$
$984$	11.7762	−	20.3970i	0.375412	−	0.650232i
$985$	19.6680	+	34.0659i	0.626674	+	1.08543i
$986$	−7.53176	+	4.34846i	−0.239860	+	0.138483i
$987$	−2.50183			−0.0796341
$988$	1.89788	−	0.360626i	0.0603797	−	0.0114730i
$989$	−6.35949			−0.202220
$990$	21.7052	−	12.5315i	0.689836	−	0.398277i
$991$	−27.5905	−	47.7881i	−0.876440	−	1.51804i	−0.855221	−	0.518263i	$-0.826579\pi$
$991$	−27.5905	−	47.7881i	−0.876440	−	1.51804i	−0.0212186	−	0.999775i	$-0.506755\pi$
$992$	−1.30470	+	2.25981i	−0.0414243	+	0.0717489i
$993$			27.9772i			0.887831i
$994$	0.327074	+	0.188837i	0.0103742	+	0.00598953i
$995$	36.4866	+	21.0655i	1.15670	+	0.667823i
$996$		−	1.23600i		−	0.0391642i
$997$	12.2622	−	21.2388i	0.388349	−	0.672640i	−0.603879	−	0.797076i	$-0.706379\pi$
$997$	12.2622	−	21.2388i	0.388349	−	0.672640i	0.992228	+	0.124436i	$0.0397122\pi$
$998$	22.5961	+	39.1376i	0.715267	+	1.23888i
$999$	16.2156	−	9.36206i	0.513038	−	0.296203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	299.2.i.a.231.2	✓	18
13.2	odd	12		3887.2.a.t.1.4		18
13.4	even	6	inner	299.2.i.a.277.2	yes	18
13.11	odd	12		3887.2.a.t.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.i.a.231.2	✓	18	1.1	even	1	trivial
299.2.i.a.277.2	yes	18	13.4	even	6	inner
3887.2.a.t.1.4		18	13.2	odd	12
3887.2.a.t.1.15		18	13.11	odd	12

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:	\( N \)	\(=\)	\( 299 = 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	299.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18757 + 0.685642i) q^{2} +(0.476286 + 0.824952i) q^{3} +(-0.0597891 + 0.103558i) q^{4} -2.12469i q^{5} +(-1.13124 - 0.653124i) q^{6} +(-0.290894 - 0.167948i) q^{7} -2.90655i q^{8} +(1.04630 - 1.81225i) q^{9} +O(q^{10})\)	\(q+(-1.18757 + 0.685642i) q^{2} +(0.476286 + 0.824952i) q^{3} +(-0.0597891 + 0.103558i) q^{4} -2.12469i q^{5} +(-1.13124 - 0.653124i) q^{6} +(-0.290894 - 0.167948i) q^{7} -2.90655i q^{8} +(1.04630 - 1.81225i) q^{9} +(1.45677 + 2.52321i) q^{10} +(3.56003 - 2.05538i) q^{11} -0.113907 q^{12} +(3.40414 + 1.18819i) q^{13} +0.460609 q^{14} +(1.75276 - 1.01196i) q^{15} +(1.87327 + 3.24460i) q^{16} +(-1.32577 + 2.29630i) q^{17} +2.86956i q^{18} +(-3.88041 - 2.24036i) q^{19} +(0.220028 + 0.127033i) q^{20} -0.319965i q^{21} +(-2.81852 + 4.88182i) q^{22} +(0.500000 + 0.866025i) q^{23} +(2.39776 - 1.38435i) q^{24} +0.485708 q^{25} +(-4.85733 + 0.922964i) q^{26} +4.85108 q^{27} +(0.0347846 - 0.0200829i) q^{28} +(-1.19594 - 2.07143i) q^{29} +(-1.38768 + 2.40354i) q^{30} +3.86285i q^{31} +(0.585010 + 0.337756i) q^{32} +(3.39119 + 1.95790i) q^{33} -3.63602i q^{34} +(-0.356837 + 0.618059i) q^{35} +(0.125115 + 0.216706i) q^{36} +(3.34267 - 1.92989i) q^{37} +6.14434 q^{38} +(0.641144 + 3.37418i) q^{39} -6.17550 q^{40} +(7.36700 - 4.25334i) q^{41} +(0.219382 + 0.379980i) q^{42} +(-3.17975 + 5.50748i) q^{43} +0.491559i q^{44} +(-3.85046 - 2.22306i) q^{45} +(-1.18757 - 0.685642i) q^{46} -7.81907i q^{47} +(-1.78443 + 3.09072i) q^{48} +(-3.44359 - 5.96447i) q^{49} +(-0.576811 + 0.333022i) q^{50} -2.52579 q^{51} +(-0.326577 + 0.281484i) q^{52} +7.28610 q^{53} +(-5.76098 + 3.32610i) q^{54} +(-4.36705 - 7.56395i) q^{55} +(-0.488148 + 0.845497i) q^{56} -4.26821i q^{57} +(2.84052 + 1.63997i) q^{58} +(2.48205 + 1.43301i) q^{59} +0.242017i q^{60} +(-2.71055 + 4.69480i) q^{61} +(-2.64854 - 4.58740i) q^{62} +(-0.608727 + 0.351449i) q^{63} -8.41941 q^{64} +(2.52454 - 7.23274i) q^{65} -5.36969 q^{66} +(-7.35946 + 4.24899i) q^{67} +(-0.158533 - 0.274588i) q^{68} +(-0.476286 + 0.824952i) q^{69} -0.978649i q^{70} +(0.710092 + 0.409972i) q^{71} +(-5.26738 - 3.04113i) q^{72} -9.32612i q^{73} +(-2.64643 + 4.58376i) q^{74} +(0.231336 + 0.400686i) q^{75} +(0.464013 - 0.267898i) q^{76} -1.38079 q^{77} +(-3.07488 - 3.56747i) q^{78} -13.1594 q^{79} +(6.89376 - 3.98012i) q^{80} +(-0.828405 - 1.43484i) q^{81} +(-5.83254 + 10.1023i) q^{82} +10.8510i q^{83} +(0.0331349 + 0.0191304i) q^{84} +(4.87893 + 2.81685i) q^{85} -8.72067i q^{86} +(1.13922 - 1.97319i) q^{87} +(-5.97407 - 10.3474i) q^{88} +(-1.95066 + 1.12622i) q^{89} +6.09691 q^{90} +(-0.790691 - 0.917358i) q^{91} -0.119578 q^{92} +(-3.18667 + 1.83982i) q^{93} +(5.36108 + 9.28567i) q^{94} +(-4.76006 + 8.24466i) q^{95} +0.643474i q^{96} +(1.81422 + 1.04744i) q^{97} +(8.17898 + 4.72214i) q^{98} -8.60222i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{3} + 4 q^{4} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 18 * q + 5 * q^3 + 4 * q^4 - 3 * q^7 - 6 * q^9	\( 18 q + 5 q^{3} + 4 q^{4} - 3 q^{7} - 6 q^{9} - 11 q^{10} + 2 q^{12} + 2 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 15 q^{17} + 6 q^{19} + 6 q^{20} - 8 q^{22} + 9 q^{23} + 24 q^{24} + 16 q^{25} + 18 q^{26} - 34 q^{27} - 24 q^{28} + 15 q^{29} + 4 q^{30} + 27 q^{32} - 18 q^{33} - 12 q^{35} - 20 q^{36} - 6 q^{37} - 30 q^{38} + 12 q^{39} - 52 q^{40} - 6 q^{41} + 12 q^{42} - 3 q^{43} + 12 q^{45} - 30 q^{48} - 18 q^{49} + 36 q^{50} + 24 q^{51} + 23 q^{52} - 18 q^{53} + 18 q^{54} + 16 q^{55} - 15 q^{56} + 6 q^{58} - 9 q^{59} + 10 q^{61} - 33 q^{62} + 63 q^{63} + 38 q^{64} + 60 q^{65} - 68 q^{66} - 18 q^{67} + 18 q^{68} - 5 q^{69} - 54 q^{71} + 27 q^{72} - 18 q^{74} + 8 q^{75} + 54 q^{76} + 12 q^{77} + 57 q^{78} - 56 q^{79} + 24 q^{80} + 15 q^{81} - 11 q^{82} + 15 q^{84} + 33 q^{85} + 5 q^{88} + 21 q^{89} - 38 q^{90} + 42 q^{91} + 8 q^{92} - 42 q^{93} - 14 q^{94} - 36 q^{95} - 30 q^{97} - 15 q^{98}+O(q^{100}) \) 18 * q + 5 * q^3 + 4 * q^4 - 3 * q^7 - 6 * q^9 - 11 * q^10 + 2 * q^12 + 2 * q^13 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 15 * q^17 + 6 * q^19 + 6 * q^20 - 8 * q^22 + 9 * q^23 + 24 * q^24 + 16 * q^25 + 18 * q^26 - 34 * q^27 - 24 * q^28 + 15 * q^29 + 4 * q^30 + 27 * q^32 - 18 * q^33 - 12 * q^35 - 20 * q^36 - 6 * q^37 - 30 * q^38 + 12 * q^39 - 52 * q^40 - 6 * q^41 + 12 * q^42 - 3 * q^43 + 12 * q^45 - 30 * q^48 - 18 * q^49 + 36 * q^50 + 24 * q^51 + 23 * q^52 - 18 * q^53 + 18 * q^54 + 16 * q^55 - 15 * q^56 + 6 * q^58 - 9 * q^59 + 10 * q^61 - 33 * q^62 + 63 * q^63 + 38 * q^64 + 60 * q^65 - 68 * q^66 - 18 * q^67 + 18 * q^68 - 5 * q^69 - 54 * q^71 + 27 * q^72 - 18 * q^74 + 8 * q^75 + 54 * q^76 + 12 * q^77 + 57 * q^78 - 56 * q^79 + 24 * q^80 + 15 * q^81 - 11 * q^82 + 15 * q^84 + 33 * q^85 + 5 * q^88 + 21 * q^89 - 38 * q^90 + 42 * q^91 + 8 * q^92 - 42 * q^93 - 14 * q^94 - 36 * q^95 - 30 * q^97 - 15 * q^98

Introduction

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