LMFDB - Embedded newform 315.2.i.f.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 8 x^{14} - 10 x^{13} + 40 x^{12} - 45 x^{11} + 159 x^{10} - 180 x^{9} + 576 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 8x^14 - 10x^13 + 40x^12 - 45x^11 + 159x^10 - 180x^9 + 576x^8 - 540x^7 + 1431x^6 - 1215x^5 + 3240x^4 - 2430x^3 + 5832x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$-1.41596 + 0.997525i$ of defining polynomial
Character	$\chi$	$=$	315.211
Dual form			315.2.i.f.106.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978244 - 1.69437i) q^{2} +(-1.57186 - 0.727495i) q^{3} +(-0.913922 + 1.58296i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.305020 + 3.37498i) q^{6} +(0.500000 + 0.866025i) q^{7} -0.336819 q^{8} +(1.94150 + 2.28704i) q^{9} +O(q^{10})$	\(q+(-0.978244 - 1.69437i) q^{2} +(-1.57186 - 0.727495i) q^{3} +(-0.913922 + 1.58296i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.305020 + 3.37498i) q^{6} +(0.500000 + 0.866025i) q^{7} -0.336819 q^{8} +(1.94150 + 2.28704i) q^{9} +1.95649 q^{10} +(0.582651 + 1.00918i) q^{11} +(2.58816 - 1.82332i) q^{12} +(-2.22338 + 3.85101i) q^{13} +(0.978244 - 1.69437i) q^{14} +(1.41596 - 0.997525i) q^{15} +(2.15734 + 3.73662i) q^{16} -0.994717 q^{17} +(1.97583 - 5.52691i) q^{18} +7.73479 q^{19} +(-0.913922 - 1.58296i) q^{20} +(-0.155902 - 1.72502i) q^{21} +(1.13995 - 1.97445i) q^{22} +(0.300518 - 0.520512i) q^{23} +(0.529434 + 0.245034i) q^{24} +(-0.500000 - 0.866025i) q^{25} +8.70004 q^{26} +(-1.38796 - 5.00735i) q^{27} -1.82784 q^{28} +(-3.41734 - 5.91901i) q^{29} +(-3.07533 - 1.42334i) q^{30} +(-3.41871 + 5.92138i) q^{31} +(3.88398 - 6.72726i) q^{32} +(-0.181673 - 2.01017i) q^{33} +(0.973076 + 1.68542i) q^{34} -1.00000 q^{35} +(-5.39468 + 0.983140i) q^{36} +4.70104 q^{37} +(-7.56651 - 13.1056i) q^{38} +(6.29644 - 4.43576i) q^{39} +(0.168410 - 0.291694i) q^{40} +(-5.52906 + 9.57662i) q^{41} +(-2.77031 + 1.95165i) q^{42} +(2.55183 + 4.41989i) q^{43} -2.12999 q^{44} +(-2.95139 + 0.537868i) q^{45} -1.17592 q^{46} +(6.25988 + 10.8424i) q^{47} +(-0.672666 - 7.44290i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.978244 + 1.69437i) q^{50} +(1.56356 + 0.723652i) q^{51} +(-4.06400 - 7.03905i) q^{52} +8.43583 q^{53} +(-7.12653 + 7.25013i) q^{54} -1.16530 q^{55} +(-0.168410 - 0.291694i) q^{56} +(-12.1580 - 5.62702i) q^{57} +(-6.68599 + 11.5805i) q^{58} +(-2.49717 + 4.32523i) q^{59} +(0.284965 + 3.15307i) q^{60} +(0.303940 + 0.526439i) q^{61} +13.3773 q^{62} +(-1.00989 + 2.82491i) q^{63} -6.56859 q^{64} +(-2.22338 - 3.85101i) q^{65} +(-3.22824 + 2.27426i) q^{66} +(-2.67398 + 4.63147i) q^{67} +(0.909095 - 1.57460i) q^{68} +(-0.851043 + 0.599548i) q^{69} +(0.978244 + 1.69437i) q^{70} +4.95513 q^{71} +(-0.653936 - 0.770321i) q^{72} -9.75040 q^{73} +(-4.59876 - 7.96529i) q^{74} +(0.155902 + 1.72502i) q^{75} +(-7.06900 + 12.2439i) q^{76} +(-0.582651 + 1.00918i) q^{77} +(-13.6753 - 6.32924i) q^{78} +(0.188621 + 0.326701i) q^{79} -4.31467 q^{80} +(-1.46114 + 8.88060i) q^{81} +21.6351 q^{82} +(5.37082 + 9.30253i) q^{83} +(2.87312 + 1.32975i) q^{84} +(0.497359 - 0.861451i) q^{85} +(4.99262 - 8.64746i) q^{86} +(1.06554 + 11.7900i) q^{87} +(-0.196248 - 0.339912i) q^{88} -7.66903 q^{89} +(3.79853 + 4.47457i) q^{90} -4.44676 q^{91} +(0.549300 + 0.951415i) q^{92} +(9.68152 - 6.82050i) q^{93} +(12.2474 - 21.2131i) q^{94} +(-3.86739 + 6.69852i) q^{95} +(-10.9991 + 7.74874i) q^{96} +(-8.80909 - 15.2578i) q^{97} +1.95649 q^{98} +(-1.17682 + 3.29187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.978244	−	1.69437i	−0.691723	−	1.19810i	−0.971273	−	0.237968i	$-0.923519\pi$
$2$	−0.978244	−	1.69437i	−0.691723	−	1.19810i	0.279550	−	0.960131i	$-0.409815\pi$
$3$	−1.57186	−	0.727495i	−0.907515	−	0.420019i
$3$	−1.57186	−	0.727495i	−0.907515	−	0.420019i
$4$	−0.913922	+	1.58296i	−0.456961	+	0.791480i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.305020	+	3.37498i	0.124524	+	1.37783i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−0.336819			−0.119084
$9$	1.94150	+	2.28704i	0.647167	+	0.762348i
$10$	1.95649			0.618696
$11$	0.582651	+	1.00918i	0.175676	+	0.304279i	0.940395	−	0.340084i	$-0.110456\pi$
$11$	0.582651	+	1.00918i	0.175676	+	0.304279i	−0.764719	+	0.644364i	$0.777122\pi$
$12$	2.58816	−	1.82332i	0.747136	−	0.526348i
$13$	−2.22338	+	3.85101i	−0.616655	+	1.06808i	0.373436	+	0.927656i	$0.378179\pi$
$13$	−2.22338	+	3.85101i	−0.616655	+	1.06808i	−0.990092	+	0.140423i	$0.955154\pi$
$14$	0.978244	−	1.69437i	0.261447	−	0.452839i
$15$	1.41596	−	0.997525i	0.365599	−	0.257560i
$16$	2.15734	+	3.73662i	0.539334	+	0.934154i
$17$	−0.994717			−0.241254			−0.120627	−	0.992698i	$-0.538491\pi$
$17$	−0.994717			−0.241254			−0.120627	+	0.992698i	$0.538491\pi$
$18$	1.97583	−	5.52691i	0.465708	−	1.30270i
$19$	7.73479			1.77448			0.887241	−	0.461306i	$-0.152619\pi$
$19$	7.73479			1.77448			0.887241	+	0.461306i	$0.152619\pi$
$20$	−0.913922	−	1.58296i	−0.204359	−	0.353961i
$21$	−0.155902	−	1.72502i	−0.0340206	−	0.376430i
$22$	1.13995	−	1.97445i	0.243038	−	0.420954i
$23$	0.300518	−	0.520512i	0.0626623	−	0.108534i	−0.832992	−	0.553285i	$-0.813374\pi$
$23$	0.300518	−	0.520512i	0.0626623	−	0.108534i	0.895655	+	0.444750i	$0.146708\pi$
$24$	0.529434	+	0.245034i	0.108070	+	0.0500174i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	8.70004			1.70622
$27$	−1.38796	−	5.00735i	−0.267113	−	0.963665i
$28$	−1.82784			−0.345430
$29$	−3.41734	−	5.91901i	−0.634585	−	1.09913i	−0.986603	−	0.163140i	$-0.947838\pi$
$29$	−3.41734	−	5.91901i	−0.634585	−	1.09913i	0.352018	−	0.935993i	$-0.385496\pi$
$30$	−3.07533	−	1.42334i	−0.561476	−	0.259864i
$31$	−3.41871	+	5.92138i	−0.614019	+	1.06351i	0.376537	+	0.926401i	$0.377115\pi$
$31$	−3.41871	+	5.92138i	−0.614019	+	1.06351i	−0.990556	+	0.137110i	$0.956219\pi$
$32$	3.88398	−	6.72726i	0.686598	−	1.18922i
$33$	−0.181673	−	2.01017i	−0.0316252	−	0.349925i
$34$	0.973076	+	1.68542i	0.166881	+	0.289047i
$35$	−1.00000			−0.169031
$36$	−5.39468	+	0.983140i	−0.899114	+	0.163857i
$37$	4.70104			0.772845			0.386423	−	0.922322i	$-0.373711\pi$
$37$	4.70104			0.772845			0.386423	+	0.922322i	$0.373711\pi$
$38$	−7.56651	−	13.1056i	−1.22745	−	2.12601i
$39$	6.29644	−	4.43576i	1.00824	−	0.710290i
$40$	0.168410	−	0.291694i	0.0266279	−	0.0461209i
$41$	−5.52906	+	9.57662i	−0.863495	+	1.49562i	0.00503975	+	0.999987i	$0.498396\pi$
$41$	−5.52906	+	9.57662i	−0.863495	+	1.49562i	−0.868534	+	0.495629i	$0.834938\pi$
$42$	−2.77031	+	1.95165i	−0.427468	+	0.301146i
$43$	2.55183	+	4.41989i	0.389150	+	0.674027i	0.992335	−	0.123574i	$-0.0394355\pi$
$43$	2.55183	+	4.41989i	0.389150	+	0.674027i	−0.603186	+	0.797601i	$0.706102\pi$
$44$	−2.12999			−0.321108
$45$	−2.95139	+	0.537868i	−0.439967	+	0.0801807i
$46$	−1.17592			−0.173380
$47$	6.25988	+	10.8424i	0.913097	+	1.58153i	0.809663	+	0.586895i	$0.199650\pi$
$47$	6.25988	+	10.8424i	0.913097	+	1.58153i	0.103434	+	0.994636i	$0.467017\pi$
$48$	−0.672666	−	7.44290i	−0.0970910	−	1.07429i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.978244	+	1.69437i	−0.138345	+	0.239620i
$51$	1.56356	+	0.723652i	0.218942	+	0.101332i
$52$	−4.06400	−	7.03905i	−0.563575	−	0.976141i
$53$	8.43583			1.15875			0.579375	−	0.815061i	$-0.303297\pi$
$53$	8.43583			1.15875			0.579375	+	0.815061i	$0.303297\pi$
$54$	−7.12653	+	7.25013i	−0.969798	+	0.986617i
$55$	−1.16530			−0.157129
$56$	−0.168410	−	0.291694i	−0.0225047	−	0.0389793i
$57$	−12.1580	−	5.62702i	−1.61037	−	0.745317i
$58$	−6.68599	+	11.5805i	−0.877914	+	1.52059i
$59$	−2.49717	+	4.32523i	−0.325104	+	0.563097i	−0.981533	−	0.191291i	$-0.938733\pi$
$59$	−2.49717	+	4.32523i	−0.325104	+	0.563097i	0.656429	+	0.754387i	$0.272066\pi$
$60$	0.284965	+	3.15307i	0.0367888	+	0.407059i
$61$	0.303940	+	0.526439i	0.0389155	+	0.0674036i	0.884827	−	0.465919i	$-0.154276\pi$
$61$	0.303940	+	0.526439i	0.0389155	+	0.0674036i	−0.845912	+	0.533323i	$0.820943\pi$
$62$	13.3773			1.69892
$63$	−1.00989	+	2.82491i	−0.127234	+	0.355905i
$64$	−6.56859			−0.821073
$65$	−2.22338	−	3.85101i	−0.275777	−	0.477659i
$66$	−3.22824	+	2.27426i	−0.397369	+	0.279942i
$67$	−2.67398	+	4.63147i	−0.326679	+	0.565824i	−0.981851	−	0.189656i	$-0.939263\pi$
$67$	−2.67398	+	4.63147i	−0.326679	+	0.565824i	0.655172	+	0.755480i	$0.272596\pi$
$68$	0.909095	−	1.57460i	0.110244	−	0.190948i
$69$	−0.851043	+	0.599548i	−0.102453	+	0.0721771i
$70$	0.978244	+	1.69437i	0.116923	+	0.202516i
$71$	4.95513			0.588066			0.294033	−	0.955795i	$-0.405003\pi$
$71$	4.95513			0.588066			0.294033	+	0.955795i	$0.405003\pi$
$72$	−0.653936	−	0.770321i	−0.0770670	−	0.0907832i
$73$	−9.75040			−1.14120			−0.570599	−	0.821229i	$-0.693289\pi$
$73$	−9.75040			−1.14120			−0.570599	+	0.821229i	$0.693289\pi$
$74$	−4.59876	−	7.96529i	−0.534595	−	0.925946i
$75$	0.155902	+	1.72502i	0.0180020	+	0.199188i
$76$	−7.06900	+	12.2439i	−0.810870	+	1.40447i
$77$	−0.582651	+	1.00918i	−0.0663992	+	0.115007i
$78$	−13.6753	−	6.32924i	−1.54842	−	0.716645i
$79$	0.188621	+	0.326701i	0.0212215	+	0.0367567i	0.876441	−	0.481509i	$-0.159911\pi$
$79$	0.188621	+	0.326701i	0.0212215	+	0.0367567i	−0.855220	+	0.518266i	$0.826578\pi$
$80$	−4.31467			−0.482395
$81$	−1.46114	+	8.88060i	−0.162349	+	0.986733i
$82$	21.6351			2.38920
$83$	5.37082	+	9.30253i	0.589524	+	1.02109i	0.994295	+	0.106667i	$0.0340179\pi$
$83$	5.37082	+	9.30253i	0.589524	+	1.02109i	−0.404771	+	0.914418i	$0.632649\pi$
$84$	2.87312	+	1.32975i	0.313483	+	0.145087i
$85$	0.497359	−	0.861451i	0.0539461	−	0.0934374i
$86$	4.99262	−	8.64746i	0.538368	−	0.932480i
$87$	1.06554	+	11.7900i	0.114238	+	1.26402i
$88$	−0.196248	−	0.339912i	−0.0209201	−	0.0362347i
$89$	−7.66903			−0.812916			−0.406458	−	0.913670i	$-0.633236\pi$
$89$	−7.66903			−0.812916			−0.406458	+	0.913670i	$0.633236\pi$
$90$	3.79853	+	4.47457i	0.400400	+	0.471661i
$91$	−4.44676			−0.466148
$92$	0.549300	+	0.951415i	0.0572685	+	0.0991919i
$93$	9.68152	−	6.82050i	1.00393	−	0.707253i
$94$	12.2474	−	21.2131i	1.26322	−	2.18796i
$95$	−3.86739	+	6.69852i	−0.396786	+	0.687254i
$96$	−10.9991	+	7.74874i	−1.12259	+	0.790853i
$97$	−8.80909	−	15.2578i	−0.894428	−	1.54919i	−0.834511	−	0.550991i	$-0.814250\pi$
$97$	−8.80909	−	15.2578i	−0.894428	−	1.54919i	−0.0599170	−	0.998203i	$-0.519084\pi$
$98$	1.95649			0.197635
$99$	−1.17682	+	3.29187i	−0.118275	+	0.330846i
$100$	1.82784			0.182784
$101$	3.29807	+	5.71242i	0.328170	+	0.568407i	0.982149	−	0.188106i	$-0.0602348\pi$
$101$	3.29807	+	5.71242i	0.328170	+	0.568407i	−0.653979	+	0.756513i	$0.726901\pi$
$102$	−0.303409	−	3.35715i	−0.0300420	−	0.332408i
$103$	2.01785	−	3.49502i	0.198825	−	0.344374i	−0.749323	−	0.662205i	$-0.769621\pi$
$103$	2.01785	−	3.49502i	0.198825	−	0.344374i	0.948148	+	0.317830i	$0.102954\pi$
$104$	0.748878	−	1.29710i	0.0734336	−	0.127191i
$105$	1.57186	+	0.727495i	0.153398	+	0.0709962i
$106$	−8.25229	−	14.2934i	−0.801534	−	1.38830i
$107$	−7.69946			−0.744335			−0.372168	−	0.928166i	$-0.621385\pi$
$107$	−7.69946			−0.744335			−0.372168	+	0.928166i	$0.621385\pi$
$108$	9.19493	+	2.37924i	0.884782	+	0.228943i
$109$	−2.11167			−0.202261			−0.101130	−	0.994873i	$-0.532246\pi$
$109$	−2.11167			−0.202261			−0.101130	+	0.994873i	$0.532246\pi$
$110$	1.13995	+	1.97445i	0.108690	+	0.188256i
$111$	−7.38938	−	3.41998i	−0.701369	−	0.324610i
$112$	−2.15734	+	3.73662i	−0.203849	+	0.353077i
$113$	−2.00963	+	3.48078i	−0.189050	+	0.327444i	−0.944934	−	0.327262i	$-0.893874\pi$
$113$	−2.00963	+	3.48078i	−0.189050	+	0.327444i	0.755884	+	0.654706i	$0.227208\pi$
$114$	2.35927	+	26.1048i	0.220966	+	2.44494i
$115$	0.300518	+	0.520512i	0.0280234	+	0.0485380i
$116$	12.4928			1.15992
$117$	−13.1241	+	2.39177i	−1.21333	+	0.221120i
$118$	9.77137			0.899528
$119$	−0.497359	−	0.861451i	−0.0455928	−	0.0789690i
$120$	−0.476923	+	0.335986i	−0.0435369	+	0.0306712i
$121$	4.82104	−	8.35028i	0.438276	−	0.759116i
$122$	0.594654	−	1.02997i	0.0538375	−	0.0932493i
$123$	15.6579	−	11.0308i	1.41182	−	0.994610i
$124$	−6.24887	−	10.8234i	−0.561165	−	0.971967i
$125$	1.00000			0.0894427
$126$	5.77436	−	1.05233i	0.514421	−	0.0937492i
$127$	−5.30718			−0.470936			−0.235468	−	0.971882i	$-0.575662\pi$
$127$	−5.30718			−0.470936			−0.235468	+	0.971882i	$0.575662\pi$
$128$	−1.34229	−	2.32491i	−0.118642	−	0.205495i
$129$	−0.795669	−	8.80390i	−0.0700548	−	0.775140i
$130$	−4.35002	+	7.53446i	−0.381522	+	0.660816i
$131$	−1.25987	+	2.18216i	−0.110075	+	0.190656i	−0.915800	−	0.401633i	$-0.868443\pi$
$131$	−1.25987	+	2.18216i	−0.110075	+	0.190656i	0.805725	+	0.592290i	$0.201776\pi$
$132$	3.34805	+	1.54956i	0.291410	+	0.134872i
$133$	3.86739	+	6.69852i	0.335346	+	0.580836i
$134$	10.4632			0.903885
$135$	5.03047	+	1.30167i	0.432954	+	0.112030i
$136$	0.335040			0.0287295
$137$	−2.58234	−	4.47274i	−0.220624	−	0.382132i	0.734374	−	0.678745i	$-0.237476\pi$
$137$	−2.58234	−	4.47274i	−0.220624	−	0.382132i	−0.954998	+	0.296614i	$0.904143\pi$
$138$	1.84838	+	0.855475i	0.157345	+	0.0728229i
$139$	8.06702	−	13.9725i	0.684235	−	1.18513i	−0.289441	−	0.957196i	$-0.593469\pi$
$139$	8.06702	−	13.9725i	0.684235	−	1.18513i	0.973676	−	0.227935i	$-0.0731972\pi$
$140$	0.913922	−	1.58296i	0.0772405	−	0.133785i
$141$	−1.95186	−	21.5968i	−0.164376	−	1.81878i
$142$	−4.84732	−	8.39581i	−0.406778	−	0.704561i
$143$	−5.18182			−0.433326
$144$	−4.35733	+	12.1886i	−0.363111	+	1.01571i
$145$	6.83469			0.567590
$146$	9.53827	+	16.5208i	0.789393	+	1.36727i
$147$	1.41596	−	0.997525i	0.116786	−	0.0822745i
$148$	−4.29638	+	7.44155i	−0.353160	+	0.611692i
$149$	6.14743	−	10.6477i	0.503617	−	0.872290i	−0.496374	−	0.868109i	$-0.665336\pi$
$149$	6.14743	−	10.6477i	0.503617	−	0.872290i	0.999991	−	0.00418164i	$-0.00133106\pi$
$150$	2.77031	−	1.95165i	0.226195	−	0.159351i
$151$	−4.05278	−	7.01962i	−0.329811	−	0.571249i	0.652663	−	0.757648i	$-0.273652\pi$
$151$	−4.05278	−	7.01962i	−0.329811	−	0.571249i	−0.982474	+	0.186399i	$0.940318\pi$
$152$	−2.60523			−0.211312
$153$	−1.93125	−	2.27496i	−0.156132	−	0.183920i
$154$	2.27990			0.183719
$155$	−3.41871	−	5.92138i	−0.274597	−	0.475617i
$156$	1.26717	+	14.0210i	0.101455	+	1.12257i
$157$	−2.57677	+	4.46310i	−0.205649	+	0.356194i	−0.950339	−	0.311216i	$-0.899264\pi$
$157$	−2.57677	+	4.46310i	−0.205649	+	0.356194i	0.744690	+	0.667410i	$0.232597\pi$
$158$	0.369034	−	0.639186i	0.0293588	−	0.0508509i
$159$	−13.2600	−	6.13702i	−1.05158	−	0.486697i
$160$	3.88398	+	6.72726i	0.307056	+	0.531836i
$161$	0.601036			0.0473682
$162$	16.4764	−	6.21169i	1.29450	−	0.488036i
$163$	19.2444			1.50734			0.753670	−	0.657254i	$-0.228282\pi$
$163$	19.2444			1.50734			0.753670	+	0.657254i	$0.228282\pi$
$164$	−10.1063	−	17.5046i	−0.789167	−	1.36688i
$165$	1.83169	+	0.847751i	0.142597	+	0.0659973i
$166$	10.5079	−	18.2003i	0.815574	−	1.41262i
$167$	4.04302	−	7.00271i	0.312858	−	0.541886i	−0.666122	−	0.745843i	$-0.732047\pi$
$167$	4.04302	−	7.00271i	0.312858	−	0.541886i	0.978980	+	0.203957i	$0.0653802\pi$
$168$	0.0525108	+	0.581020i	0.00405130	+	0.0448267i
$169$	−3.38686	−	5.86621i	−0.260528	−	0.451247i
$170$	−1.94615			−0.149263
$171$	15.0171	+	17.6898i	1.14839	+	1.35277i
$172$	−9.32868			−0.711305
$173$	11.2178	+	19.4297i	0.852870	+	1.47721i	0.878607	+	0.477545i	$0.158473\pi$
$173$	11.2178	+	19.4297i	0.852870	+	1.47721i	−0.0257373	+	0.999669i	$0.508193\pi$
$174$	18.9342	−	13.3389i	1.43540	−	1.01122i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	−2.51395	+	4.35428i	−0.189496	+	0.328216i
$177$	7.07179	−	4.98198i	0.531548	−	0.374469i
$178$	7.50218	+	12.9942i	0.562312	+	0.973954i
$179$	−7.32628			−0.547592			−0.273796	−	0.961788i	$-0.588279\pi$
$179$	−7.32628			−0.547592			−0.273796	+	0.961788i	$0.588279\pi$
$180$	1.84592	−	5.16350i	0.137587	−	0.384865i
$181$	−16.0531			−1.19322			−0.596610	−	0.802531i	$-0.703486\pi$
$181$	−16.0531			−1.19322			−0.596610	+	0.802531i	$0.703486\pi$
$182$	4.35002	+	7.53446i	0.322445	+	0.558491i
$183$	−0.0947696	−	1.04860i	−0.00700557	−	0.0775151i
$184$	−0.101220	+	0.175319i	−0.00746205	+	0.0129247i
$185$	−2.35052	+	4.07122i	−0.172814	+	0.299322i
$186$	−21.0273	−	9.73194i	−1.54180	−	0.713581i
$187$	−0.579573	−	1.00385i	−0.0423826	−	0.0734087i
$188$	−22.8842			−1.66900
$189$	3.64251	−	3.70568i	0.264954	−	0.269549i
$190$	15.1330			1.09786
$191$	−4.68721	−	8.11849i	−0.339155	−	0.587433i	0.645119	−	0.764082i	$-0.276808\pi$
$191$	−4.68721	−	8.11849i	−0.339155	−	0.587433i	−0.984274	+	0.176649i	$0.943474\pi$
$192$	10.3249	+	4.77861i	0.745136	+	0.344867i
$193$	−11.1584	+	19.3270i	−0.803201	+	1.39119i	0.114298	+	0.993447i	$0.463538\pi$
$193$	−11.1584	+	19.3270i	−0.803201	+	1.39119i	−0.917499	+	0.397739i	$0.869795\pi$
$194$	−17.2349	+	29.8517i	−1.23739	+	2.14323i
$195$	0.693260	+	7.67076i	0.0496453	+	0.549314i
$196$	−0.913922	−	1.58296i	−0.0652802	−	0.113069i
$197$	11.8258			0.842556			0.421278	−	0.906932i	$-0.361582\pi$
$197$	11.8258			0.842556			0.421278	+	0.906932i	$0.361582\pi$
$198$	6.72887	−	1.22628i	0.478200	−	0.0871483i
$199$	12.3689			0.876809			0.438405	−	0.898778i	$-0.355544\pi$
$199$	12.3689			0.876809			0.438405	+	0.898778i	$0.355544\pi$
$200$	0.168410	+	0.291694i	0.0119084	+	0.0206259i
$201$	7.57250	−	5.33473i	0.534123	−	0.376283i
$202$	6.45263	−	11.1763i	0.454005	−	0.786361i
$203$	3.41734	−	5.91901i	0.239851	−	0.415433i
$204$	−2.57448	+	1.81369i	−0.180250	+	0.126984i
$205$	−5.52906	−	9.57662i	−0.386166	−	0.668860i
$206$	−7.89580			−0.550126
$207$	1.77389	−	0.323278i	0.123294	−	0.0224694i
$208$	−19.1863			−1.33033
$209$	4.50668	+	7.80580i	0.311734	+	0.539938i
$210$	−0.305020	−	3.37498i	−0.0210484	−	0.232896i
$211$	6.46683	−	11.2009i	0.445195	−	0.771100i	−0.552871	−	0.833267i	$-0.686468\pi$
$211$	6.46683	−	11.2009i	0.445195	−	0.771100i	0.998066	+	0.0621670i	$0.0198011\pi$
$212$	−7.70969	+	13.3536i	−0.529504	+	0.917127i
$213$	−7.78878	−	3.60483i	−0.533678	−	0.246999i
$214$	7.53195	+	13.0457i	0.514874	+	0.891788i
$215$	−5.10365			−0.348066
$216$	0.467492	+	1.68657i	0.0318088	+	0.114757i
$217$	−6.83742			−0.464154
$218$	2.06572	+	3.57794i	0.139909	+	0.242329i
$219$	15.3263	+	7.09337i	1.03565	+	0.479325i
$220$	1.06500	−	1.84463i	0.0718019	−	0.124365i
$221$	2.21164	−	3.83067i	0.148771	−	0.257679i
$222$	1.43391	+	15.8659i	0.0962379	+	1.06485i
$223$	12.4664	+	21.5924i	0.834809	+	1.44593i	0.894186	+	0.447696i	$0.147755\pi$
$223$	12.4664	+	21.5924i	0.834809	+	1.44593i	−0.0593767	+	0.998236i	$0.518911\pi$
$224$	7.76797			0.519019
$225$	1.00989	−	2.82491i	0.0673258	−	0.188327i
$226$	7.86363			0.523081
$227$	−6.99580	−	12.1171i	−0.464328	−	0.804239i	0.534843	−	0.844951i	$-0.320371\pi$
$227$	−6.99580	−	12.1171i	−0.464328	−	0.804239i	−0.999171	+	0.0407123i	$0.987037\pi$
$228$	20.0188	−	14.1030i	1.32578	−	0.933994i
$229$	−0.781500	+	1.35360i	−0.0516430	+	0.0894482i	−0.890691	−	0.454609i	$-0.849779\pi$
$229$	−0.781500	+	1.35360i	−0.0516430	+	0.0894482i	0.839048	+	0.544057i	$0.183112\pi$
$230$	0.587959	−	1.01838i	0.0387689	−	0.0671497i
$231$	1.65002	−	1.16242i	0.108563	−	0.0764814i
$232$	1.15103	+	1.99364i	0.0755687	+	0.130889i
$233$	−24.2313			−1.58745			−0.793723	−	0.608279i	$-0.791860\pi$
$233$	−24.2313			−1.58745			−0.793723	+	0.608279i	$0.791860\pi$
$234$	16.8911	+	19.8974i	1.10421	+	1.30073i
$235$	−12.5198			−0.816699
$236$	−4.56444	−	7.90585i	−0.297120	−	0.514627i
$237$	−0.0588127	−	0.650749i	−0.00382030	−	0.0422707i
$238$	−0.973076	+	1.68542i	−0.0630752	+	0.109249i
$239$	−5.63781	+	9.76498i	−0.364680	+	0.631644i	−0.988725	−	0.149744i	$-0.952155\pi$
$239$	−5.63781	+	9.76498i	−0.364680	+	0.631644i	0.624045	+	0.781388i	$0.285488\pi$
$240$	6.78207	+	3.13890i	0.437781	+	0.202615i
$241$	−11.5696	−	20.0392i	−0.745266	−	1.29084i	−0.950070	−	0.312035i	$-0.898989\pi$
$241$	−11.5696	−	20.0392i	−0.745266	−	1.29084i	0.204805	−	0.978803i	$-0.434344\pi$
$242$	−18.8646			−1.21266
$243$	8.75730	−	12.8961i	0.561781	−	0.827286i
$244$	−1.11111			−0.0711315
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	−34.0074	−	15.7394i	−2.16823	−	1.00351i
$247$	−17.1974	+	29.7868i	−1.09424	+	1.89529i
$248$	1.15149	−	1.99444i	0.0731196	−	0.126647i
$249$	−1.67464	−	18.5295i	−0.106126	−	1.17426i
$250$	−0.978244	−	1.69437i	−0.0618696	−	0.107161i
$251$	0.0228942			0.00144507			0.000722536	−	1.00000i	$-0.499770\pi$
$251$	0.0228942			0.00144507			0.000722536		1.00000i	$0.499770\pi$
$252$	−3.54876	−	4.18036i	−0.223551	−	0.263338i
$253$	0.700388			0.0440330
$254$	5.19171	+	8.99231i	0.325757	+	0.564228i
$255$	−1.40848	+	0.992256i	−0.0882025	+	0.0621375i
$256$	−9.19475	+	15.9258i	−0.574672	+	0.995361i
$257$	9.94634	−	17.2276i	0.620435	−	1.07463i	−0.368969	−	0.929442i	$-0.620289\pi$
$257$	9.94634	−	17.2276i	0.620435	−	1.07463i	0.989405	−	0.145184i	$-0.0463774\pi$
$258$	−14.1387	+	9.96052i	−0.880236	+	0.620115i
$259$	2.35052	+	4.07122i	0.146054	+	0.252973i
$260$	8.12800			0.504077
$261$	6.90226	−	19.3074i	0.427239	−	1.19510i
$262$	4.92985			0.304567
$263$	10.3195	+	17.8739i	0.636328	+	1.10215i	0.986232	+	0.165366i	$0.0528807\pi$
$263$	10.3195	+	17.8739i	0.636328	+	1.10215i	−0.349905	+	0.936785i	$0.613786\pi$
$264$	0.0611909	+	0.677064i	0.00376604	+	0.0416704i
$265$	−4.21791	+	7.30564i	−0.259104	+	0.448782i
$266$	7.56651	−	13.1056i	0.463933	−	0.803555i
$267$	12.0547	+	5.57918i	0.737733	+	0.341440i
$268$	−4.88762	−	8.46561i	−0.298559	−	0.517119i
$269$	−0.384122			−0.0234203			−0.0117102	−	0.999931i	$-0.503728\pi$
$269$	−0.384122			−0.0234203			−0.0117102	+	0.999931i	$0.503728\pi$
$270$	−2.71553	−	9.79682i	−0.165262	−	0.596216i
$271$	1.71192			0.103991			0.0519957	−	0.998647i	$-0.483442\pi$
$271$	1.71192			0.103991			0.0519957	+	0.998647i	$0.483442\pi$
$272$	−2.14594	−	3.71688i	−0.130117	−	0.225369i
$273$	6.98970	+	3.23500i	0.423036	+	0.195791i
$274$	−5.05231	+	8.75085i	−0.305221	+	0.528658i
$275$	0.582651	−	1.00918i	0.0351352	−	0.0608559i
$276$	−0.171274	−	1.89511i	−0.0103095	−	0.114072i
$277$	−8.41731	−	14.5792i	−0.505747	−	0.875980i	−0.999978	−	0.00664883i	$-0.997884\pi$
$277$	−8.41731	−	14.5792i	−0.505747	−	0.875980i	0.494231	−	0.869331i	$-0.335450\pi$
$278$	−31.5660			−1.89321
$279$	−20.1799	+	3.67763i	−1.20814	+	0.220174i
$280$	0.336819			0.0201288
$281$	10.6994	+	18.5320i	0.638275	+	1.10552i	0.985811	+	0.167858i	$0.0536850\pi$
$281$	10.6994	+	18.5320i	0.638275	+	1.10552i	−0.347536	+	0.937666i	$0.612982\pi$
$282$	−34.6836	+	24.4341i	−2.06538	+	1.45503i
$283$	10.8237	−	18.7472i	0.643403	−	1.11441i	−0.341265	−	0.939967i	$-0.610855\pi$
$283$	10.8237	−	18.7472i	0.643403	−	1.11441i	0.984668	−	0.174439i	$-0.0558112\pi$
$284$	−4.52860	+	7.84377i	−0.268723	+	0.465442i
$285$	10.9522	−	7.71565i	0.648750	−	0.457035i
$286$	5.06908	+	8.77991i	0.299741	+	0.519167i
$287$	−11.0581			−0.652741
$288$	22.9263	−	4.17814i	1.35094	−	0.246199i
$289$	−16.0105			−0.941796
$290$	−6.68599	−	11.5805i	−0.392615	−	0.680029i
$291$	2.74671	+	30.3917i	0.161015	+	1.78159i
$292$	8.91111	−	15.4345i	0.521483	−	0.903235i
$293$	8.09115	−	14.0143i	0.472690	−	0.818723i	−0.526821	−	0.849976i	$-0.676616\pi$
$293$	8.09115	−	14.0143i	0.472690	−	0.818723i	0.999512	+	0.0312527i	$0.00994967\pi$
$294$	−3.07533	−	1.42334i	−0.179357	−	0.0830106i
$295$	−2.49717	−	4.32523i	−0.145391	−	0.251824i
$296$	−1.58340			−0.0920333
$297$	4.24462	−	4.31824i	0.246298	−	0.250570i
$298$	−24.0547			−1.39345
$299$	1.33633	+	2.31459i	0.0772821	+	0.133856i
$300$	−2.87312	−	1.32975i	−0.165880	−	0.0767730i
$301$	−2.55183	+	4.41989i	−0.147085	+	0.254758i
$302$	−7.92922	+	13.7338i	−0.456275	+	0.790292i
$303$	−1.02835	−	11.3785i	−0.0590772	−	0.653676i
$304$	16.6865	+	28.9019i	0.957039	+	1.65764i
$305$	−0.607879			−0.0348071
$306$	−1.96539	+	5.49771i	−0.112354	+	0.314283i
$307$	12.4852			0.712566			0.356283	−	0.934378i	$-0.384044\pi$
$307$	12.4852			0.712566			0.356283	+	0.934378i	$0.384044\pi$
$308$	−1.06500	−	1.84463i	−0.0606837	−	0.105107i
$309$	−5.71439	+	4.02571i	−0.325080	+	0.229015i
$310$	−6.68867	+	11.5851i	−0.379891	+	0.657990i
$311$	−8.30021	+	14.3764i	−0.470662	+	0.815210i	−0.999437	−	0.0335521i	$-0.989318\pi$
$311$	−8.30021	+	14.3764i	−0.470662	+	0.815210i	0.528775	+	0.848762i	$0.322651\pi$
$312$	−2.12076	+	1.49405i	−0.120065	+	0.0845839i
$313$	4.12400	+	7.14297i	0.233102	+	0.403745i	0.958719	−	0.284354i	$-0.0917790\pi$
$313$	4.12400	+	7.14297i	0.233102	+	0.403745i	−0.725617	+	0.688099i	$0.758446\pi$
$314$	10.0829			0.569008
$315$	−1.94150	−	2.28704i	−0.109391	−	0.128860i
$316$	−0.689539			−0.0387896
$317$	8.94572	+	15.4944i	0.502442	+	0.870255i	0.999996	+	0.00282203i	$0.000898281\pi$
$317$	8.94572	+	15.4944i	0.502442	+	0.870255i	−0.497554	+	0.867433i	$0.665768\pi$
$318$	2.57310	+	28.4707i	0.144292	+	1.59656i
$319$	3.98224	−	6.89743i	0.222962	−	0.386182i
$320$	3.28429	−	5.68856i	0.183598	−	0.318000i
$321$	12.1025	+	5.60132i	0.675496	+	0.312635i
$322$	−0.587959	−	1.01838i	−0.0327657	−	0.0567519i
$323$	−7.69393			−0.428102
$324$	−12.7223	−	10.4291i	−0.706793	−	0.579395i
$325$	4.44676			0.246662
$326$	−18.8257	−	32.6071i	−1.04266	−	1.80594i
$327$	3.31925	+	1.53623i	0.183555	+	0.0849535i
$328$	1.86230	−	3.22559i	0.102828	−	0.178103i
$329$	−6.25988	+	10.8424i	−0.345118	+	0.597762i
$330$	−0.355441	−	3.93287i	−0.0195664	−	0.216497i
$331$	−11.7025	−	20.2692i	−0.643225	−	1.11410i	−0.984708	−	0.174211i	$-0.944263\pi$
$331$	−11.7025	−	20.2692i	−0.643225	−	1.11410i	0.341483	−	0.939888i	$-0.389071\pi$
$332$	−19.6340			−1.07756
$333$	9.12707	+	10.7515i	0.500160	+	0.589177i
$334$	−15.8202			−0.865644
$335$	−2.67398	−	4.63147i	−0.146095	−	0.253044i
$336$	6.10941	−	4.30399i	0.333295	−	0.234802i
$337$	−17.2516	+	29.8806i	−0.939753	+	1.62770i	−0.173823	+	0.984777i	$0.555612\pi$
$337$	−17.2516	+	29.8806i	−0.939753	+	1.62770i	−0.765931	+	0.642923i	$0.777721\pi$
$338$	−6.62635	+	11.4772i	−0.360426	+	0.624276i
$339$	5.69111	−	4.00931i	0.309099	−	0.217756i
$340$	0.909095	+	1.57460i	0.0493026	+	0.0853946i
$341$	−7.96766			−0.431473
$342$	15.2826	−	42.7495i	0.826391	−	2.31163i
$343$	−1.00000			−0.0539949
$344$	−0.859504	−	1.48871i	−0.0463414	−	0.0802656i
$345$	−0.0937027	−	1.03680i	−0.00504478	−	0.0558194i
$346$	21.9474	−	38.0140i	1.17990	−	2.04365i
$347$	13.4122	−	23.2306i	0.720003	−	1.24708i	−0.240994	−	0.970527i	$-0.577474\pi$
$347$	13.4122	−	23.2306i	0.720003	−	1.24708i	0.960998	−	0.276556i	$-0.0891931\pi$
$348$	−19.6369	−	9.08841i	−1.05265	−	0.487190i
$349$	−12.3883	−	21.4572i	−0.663132	−	1.14858i	−0.979788	−	0.200038i	$-0.935893\pi$
$349$	−12.3883	−	21.4572i	−0.663132	−	1.14858i	0.316656	−	0.948540i	$-0.397440\pi$
$350$	−1.95649			−0.104579
$351$	22.3693	+	5.78820i	1.19399	+	0.308951i
$352$	9.05202			0.482474
$353$	−17.4059	−	30.1480i	−0.926425	−	1.60461i	−0.789254	−	0.614067i	$-0.789532\pi$
$353$	−17.4059	−	30.1480i	−0.926425	−	1.60461i	−0.137171	−	0.990547i	$-0.543801\pi$
$354$	−15.3593	−	7.10862i	−0.816335	−	0.377819i
$355$	−2.47756	+	4.29127i	−0.131495	+	0.227757i
$356$	7.00890	−	12.1398i	0.371471	−	0.643406i
$357$	0.155078	+	1.71591i	0.00820762	+	0.0908155i
$358$	7.16688	+	12.4134i	0.378782	+	0.656069i
$359$	2.88997			0.152527			0.0762634	−	0.997088i	$-0.475701\pi$
$359$	2.88997			0.152527			0.0762634	+	0.997088i	$0.475701\pi$
$360$	0.994085	−	0.181164i	0.0523929	−	0.00954821i
$361$	40.8270			2.14879
$362$	15.7039	+	27.1999i	0.825378	+	1.42960i
$363$	−13.6528	+	9.61821i	−0.716586	+	0.504825i
$364$	4.06400	−	7.03905i	0.213011	−	0.368947i
$365$	4.87520	−	8.44409i	0.255180	−	0.441984i
$366$	−1.68401	+	1.18637i	−0.0880248	+	0.0620123i
$367$	−5.62134	−	9.73645i	−0.293432	−	0.508239i	0.681187	−	0.732109i	$-0.261464\pi$
$367$	−5.62134	−	9.73645i	−0.293432	−	0.508239i	−0.974619	+	0.223871i	$0.928131\pi$
$368$	2.59327			0.135184
$369$	−32.6368	+	5.94781i	−1.69901	+	0.309631i
$370$	9.19752			0.478156
$371$	4.21791	+	7.30564i	0.218983	+	0.379290i
$372$	1.94842	+	21.5589i	0.101021	+	1.11777i
$373$	9.72983	−	16.8526i	0.503792	−	0.872592i	−0.496199	−	0.868209i	$-0.665271\pi$
$373$	9.72983	−	16.8526i	0.503792	−	0.872592i	0.999990	−	0.00438361i	$-0.00139535\pi$
$374$	−1.13393	+	1.96402i	−0.0586340	+	0.101557i
$375$	−1.57186	−	0.727495i	−0.0811706	−	0.0375677i
$376$	−2.10845	−	3.65194i	−0.108735	−	0.188334i
$377$	30.3923			1.56528
$378$	−9.84206	−	2.54669i	−0.506221	−	0.130988i
$379$	−6.59079			−0.338546			−0.169273	−	0.985569i	$-0.554142\pi$
$379$	−6.59079			−0.338546			−0.169273	+	0.985569i	$0.554142\pi$
$380$	−7.06900	−	12.2439i	−0.362632	−	0.628097i
$381$	8.34215	+	3.86094i	0.427381	+	0.197802i
$382$	−9.17047	+	15.8837i	−0.469202	+	0.812682i
$383$	6.20254	−	10.7431i	0.316935	−	0.548947i	−0.662912	−	0.748697i	$-0.730680\pi$
$383$	6.20254	−	10.7431i	0.316935	−	0.548947i	0.979847	+	0.199750i	$0.0640130\pi$
$384$	0.418530	+	4.63094i	0.0213580	+	0.236322i
$385$	−0.582651	−	1.00918i	−0.0296946	−	0.0514326i
$386$	43.6627			2.22237
$387$	−5.15411	+	14.4174i	−0.261998	+	0.732876i
$388$	32.2033			1.63488
$389$	10.4896	+	18.1685i	0.531844	+	0.921180i	0.999309	+	0.0371689i	$0.0118339\pi$
$389$	10.4896	+	18.1685i	0.531844	+	0.921180i	−0.467465	+	0.884011i	$0.654833\pi$
$390$	12.3189	−	8.67851i	0.623792	−	0.439453i
$391$	−0.298930	+	0.517763i	−0.0151176	+	0.0261844i
$392$	0.168410	−	0.291694i	0.00850597	−	0.0147328i
$393$	3.56786	−	2.51351i	0.179974	−	0.126790i
$394$	−11.5686	−	20.0373i	−0.582815	−	1.00947i
$395$	−0.377242			−0.0189811
$396$	−4.13538	−	4.87138i	−0.207811	−	0.244796i
$397$	12.3241			0.618531			0.309265	−	0.950976i	$-0.399917\pi$
$397$	12.3241			0.618531			0.309265	+	0.950976i	$0.399917\pi$
$398$	−12.0998	−	20.9575i	−0.606509	−	1.05050i
$399$	−1.20587	−	13.3427i	−0.0603690	−	0.667969i
$400$	2.15734	−	3.73662i	0.107867	−	0.186831i
$401$	8.43307	−	14.6065i	0.421127	−	0.729414i	−0.574923	−	0.818208i	$-0.694968\pi$
$401$	8.43307	−	14.6065i	0.421127	−	0.729414i	0.996050	+	0.0887937i	$0.0283012\pi$
$402$	−16.4467	−	7.61194i	−0.820289	−	0.379649i
$403$	−15.2022	−	26.3310i	−0.757276	−	1.31164i
$404$	−12.0567			−0.599844
$405$	−6.96026	−	5.70568i	−0.345858	−	0.283518i
$406$	−13.3720			−0.663641
$407$	2.73906	+	4.74419i	0.135770	+	0.235161i
$408$	−0.526637	−	0.243740i	−0.0260724	−	0.0120669i
$409$	−4.09798	+	7.09791i	−0.202632	+	0.350969i	−0.949376	−	0.314143i	$-0.898283\pi$
$409$	−4.09798	+	7.09791i	−0.202632	+	0.350969i	0.746744	+	0.665112i	$0.231616\pi$
$410$	−10.8175	+	18.7365i	−0.534240	+	0.925332i
$411$	0.805182	+	8.90916i	0.0397167	+	0.439456i
$412$	3.68832	+	6.38835i	0.181710	+	0.314731i
$413$	−4.99434			−0.245756
$414$	−2.28305	−	2.68938i	−0.112206	−	0.132176i
$415$	−10.7416			−0.527286
$416$	17.2712	+	29.9145i	0.846788	+	1.46668i
$417$	−22.8451	+	16.0941i	−1.11873	+	0.788132i
$418$	8.81727	−	15.2720i	0.431267	−	0.746976i
$419$	16.2440	−	28.1354i	0.793570	−	1.37450i	−0.130173	−	0.991491i	$-0.541553\pi$
$419$	16.2440	−	28.1354i	0.793570	−	1.37450i	0.923743	−	0.383012i	$-0.125113\pi$
$420$	−2.58816	+	1.82332i	−0.126289	+	0.0889690i
$421$	6.29850	+	10.9093i	0.306970	+	0.531687i	0.977698	−	0.210016i	$-0.0673516\pi$
$421$	6.29850	+	10.9093i	0.306970	+	0.531687i	−0.670728	+	0.741703i	$0.734018\pi$
$422$	−25.3045			−1.23181
$423$	−12.6435	+	35.3672i	−0.614750	+	1.71961i
$424$	−2.84135			−0.137988
$425$	0.497359	+	0.861451i	0.0241254	+	0.0417865i
$426$	1.51142	+	16.7235i	0.0732283	+	0.810255i
$427$	−0.303940	+	0.526439i	−0.0147087	+	0.0254762i
$428$	7.03671	−	12.1879i	0.340132	−	0.589127i
$429$	8.14511	+	3.76975i	0.393250	+	0.182005i
$430$	4.99262	+	8.64746i	0.240765	+	0.417018i
$431$	10.8445			0.522362			0.261181	−	0.965290i	$-0.415888\pi$
$431$	10.8445			0.522362			0.261181	+	0.965290i	$0.415888\pi$
$432$	15.7163	−	15.9888i	0.756148	−	0.769262i
$433$	7.76721			0.373268			0.186634	−	0.982429i	$-0.440242\pi$
$433$	7.76721			0.373268			0.186634	+	0.982429i	$0.440242\pi$
$434$	6.68867	+	11.5851i	0.321066	+	0.556103i
$435$	−10.7432	−	4.97220i	−0.515097	−	0.238399i
$436$	1.92990	−	3.34268i	0.0924254	−	0.160086i
$437$	2.32444	−	4.02605i	0.111193	−	0.192592i
$438$	−2.97407	−	32.9074i	−0.142107	−	1.57238i
$439$	19.5764	+	33.9073i	0.934331	+	1.61831i	0.775822	+	0.630952i	$0.217335\pi$
$439$	19.5764	+	33.9073i	0.934331	+	1.61831i	0.158509	+	0.987357i	$0.449331\pi$
$440$	0.392496			0.0187115
$441$	−2.95139	+	0.537868i	−0.140542	+	0.0256128i
$442$	−8.65408			−0.411633
$443$	12.6684	+	21.9423i	0.601893	+	1.04251i	0.992534	+	0.121966i	$0.0389199\pi$
$443$	12.6684	+	21.9423i	0.601893	+	1.04251i	−0.390641	+	0.920543i	$0.627747\pi$
$444$	12.1670	−	8.57150i	0.577421	−	0.406785i
$445$	3.83452	−	6.64157i	0.181773	−	0.314841i
$446$	24.3903	−	42.2452i	1.15491	−	2.00037i
$447$	−17.4090	+	12.2644i	−0.823419	+	0.580088i
$448$	−3.28429	−	5.68856i	−0.155168	−	0.268759i
$449$	25.0325			1.18135			0.590677	−	0.806908i	$-0.298861\pi$
$449$	25.0325			1.18135			0.590677	+	0.806908i	$0.298861\pi$
$450$	−5.77436	+	1.05233i	−0.272206	+	0.0496074i
$451$	−12.8860			−0.606780
$452$	−3.67329	−	6.36233i	−0.172777	−	0.299259i
$453$	1.26367	+	13.9823i	0.0593725	+	0.656944i
$454$	−13.6872	+	23.7069i	−0.642372	+	1.11262i
$455$	2.22338	−	3.85101i	0.104234	−	0.180538i
$456$	4.09506	+	1.89529i	0.191769	+	0.0887551i
$457$	−0.0997169	−	0.172715i	−0.00466456	−	0.00807926i	0.863684	−	0.504034i	$-0.168151\pi$
$457$	−0.0997169	−	0.172715i	−0.00466456	−	0.00807926i	−0.868348	+	0.495955i	$0.834818\pi$
$458$	3.05799			0.142891
$459$	1.38063	+	4.98090i	0.0644422	+	0.232488i
$460$	−1.09860			−0.0512225
$461$	9.38421	+	16.2539i	0.437066	+	0.757021i	0.997462	−	0.0712040i	$-0.0226841\pi$
$461$	9.38421	+	16.2539i	0.437066	+	0.757021i	−0.560395	+	0.828225i	$0.689351\pi$
$462$	−3.58369	−	1.65861i	−0.166728	−	0.0771657i
$463$	−5.80351	+	10.0520i	−0.269712	+	0.467155i	−0.968787	−	0.247893i	$-0.920262\pi$
$463$	−5.80351	+	10.0520i	−0.269712	+	0.467155i	0.699075	+	0.715048i	$0.253595\pi$
$464$	14.7447	−	25.5386i	0.684507	−	1.18560i
$465$	1.06597	+	11.7947i	0.0494331	+	0.546966i
$466$	23.7041	+	41.0568i	1.09807	+	1.90192i
$467$	14.9973			0.693993			0.346997	−	0.937866i	$-0.387201\pi$
$467$	14.9973			0.693993			0.346997	+	0.937866i	$0.387201\pi$
$468$	8.20836	−	22.9609i	0.379431	−	1.06137i
$469$	−5.34796			−0.246946
$470$	12.2474	+	21.2131i	0.564929	+	0.978487i
$471$	7.29722	−	5.14079i	0.336238	−	0.236875i
$472$	0.841096	−	1.45682i	0.0387146	−	0.0670556i
$473$	−2.97365	+	5.15051i	−0.136728	+	0.236820i
$474$	−1.04508	+	0.736242i	−0.0480019	+	0.0338167i
$475$	−3.86739	−	6.69852i	−0.177448	−	0.307349i
$476$	1.81819			0.0833366
$477$	16.3782	+	19.2931i	0.749905	+	0.883370i
$478$	22.0606			1.00903
$479$	5.57631	+	9.65845i	0.254788	+	0.441306i	0.964838	−	0.262846i	$-0.0846610\pi$
$479$	5.57631	+	9.65845i	0.254788	+	0.441306i	−0.710050	+	0.704151i	$0.751328\pi$
$480$	−1.21104	−	13.3999i	−0.0552762	−	0.611619i
$481$	−10.4522	+	18.1037i	−0.476579	+	0.825460i
$482$	−22.6359	+	39.2065i	−1.03103	+	1.78581i
$483$	−0.944745	−	0.437250i	−0.0429874	−	0.0198956i
$484$	8.81211	+	15.2630i	0.400550	+	0.693773i
$485$	17.6182			0.800001
$486$	−30.4175	−	2.22255i	−1.37977	−	0.100817i
$487$	35.3058			1.59986			0.799930	−	0.600093i	$-0.204870\pi$
$487$	35.3058			1.59986			0.799930	+	0.600093i	$0.204870\pi$
$488$	−0.102373	−	0.177315i	−0.00463420	−	0.00802667i
$489$	−30.2496	−	14.0002i	−1.36793	−	0.633112i
$490$	−0.978244	+	1.69437i	−0.0441926	+	0.0765438i
$491$	−15.3559	+	26.5972i	−0.693002	+	1.20031i	0.277848	+	0.960625i	$0.410379\pi$
$491$	−15.3559	+	26.5972i	−0.693002	+	1.20031i	−0.970850	+	0.239689i	$0.922954\pi$
$492$	3.15118	+	34.8670i	0.142066	+	1.57193i
$493$	3.39929	+	5.88775i	0.153096	+	0.265171i
$494$	67.2930			3.02765
$495$	−2.26243	−	2.66510i	−0.101689	−	0.119787i
$496$	−29.5012			−1.32464
$497$	2.47756	+	4.29127i	0.111134	+	0.192490i
$498$	−29.7576	+	20.9639i	−1.33347	+	0.939413i
$499$	5.87892	−	10.1826i	0.263177	−	0.455836i	−0.703908	−	0.710292i	$-0.748563\pi$
$499$	5.87892	−	10.1826i	0.263177	−	0.455836i	0.967084	+	0.254456i	$0.0818964\pi$
$500$	−0.913922	+	1.58296i	−0.0408719	+	0.0707921i
$501$	−11.4495	+	8.06602i	−0.511526	+	0.360363i
$502$	−0.0223961	−	0.0387913i	−0.000999589	−	0.00173134i
$503$	−31.4630			−1.40287			−0.701433	−	0.712735i	$-0.747456\pi$
$503$	−31.4630			−1.40287			−0.701433	+	0.712735i	$0.747456\pi$
$504$	0.340150	−	0.951485i	0.0151515	−	0.0423825i
$505$	−6.59614			−0.293524
$506$	−0.685150	−	1.18671i	−0.0304586	−	0.0527559i
$507$	1.05604	+	11.6848i	0.0469002	+	0.518940i
$508$	4.85035	−	8.40105i	0.215199	−	0.372736i
$509$	4.07345	−	7.05543i	0.180553	−	0.312726i	−0.761516	−	0.648146i	$-0.775545\pi$
$509$	4.07345	−	7.05543i	0.180553	−	0.312726i	0.942069	+	0.335419i	$0.108878\pi$
$510$	3.05908	+	1.41582i	0.135459	+	0.0626934i
$511$	−4.87520	−	8.44409i	−0.215666	−	0.373545i
$512$	30.6097			1.35277
$513$	−10.7356	−	38.7308i	−0.473988	−	1.71001i
$514$	−38.9198			−1.71668
$515$	2.01785	+	3.49502i	0.0889171	+	0.154009i
$516$	14.6634	+	6.78657i	0.645520	+	0.298762i
$517$	−7.29465	+	12.6347i	−0.320818	+	0.555673i
$518$	4.59876	−	7.96529i	0.202058	−	0.349975i
$519$	−3.49774	−	38.7017i	−0.153534	−	1.69882i
$520$	0.748878	+	1.29710i	0.0328405	+	0.0568814i
$521$	4.66869			0.204539			0.102270	−	0.994757i	$-0.467390\pi$
$521$	4.66869			0.204539			0.102270	+	0.994757i	$0.467390\pi$
$522$	−39.4659	+	7.19237i	−1.72738	+	0.314801i
$523$	−40.7724			−1.78285			−0.891426	−	0.453167i	$-0.850294\pi$
$523$	−40.7724			−1.78285			−0.891426	+	0.453167i	$0.850294\pi$
$524$	−2.30285	−	3.98865i	−0.100600	−	0.174245i
$525$	−1.41596	+	0.997525i	−0.0617976	+	0.0435356i
$526$	20.1900	−	34.9701i	0.880325	−	1.52477i
$527$	3.40065	−	5.89010i	0.148135	−	0.256577i
$528$	7.11930	−	5.01545i	0.309828	−	0.218269i
$529$	11.3194	+	19.6057i	0.492147	+	0.852423i
$530$	16.5046			0.716914
$531$	−14.7402	+	2.68630i	−0.639672	+	0.116575i
$532$	−14.1380			−0.612960
$533$	−24.5864	−	42.5850i	−1.06496	−	1.84456i
$534$	−2.33921	−	25.8828i	−0.101228	−	1.12006i
$535$	3.84973	−	6.66793i	0.166438	−	0.288280i
$536$	0.900649	−	1.55997i	0.0389021	−	0.0673804i
$537$	11.5159	+	5.32983i	0.496948	+	0.229999i
$538$	0.375765	+	0.650844i	0.0162004	+	0.0280599i
$539$	−1.16530			−0.0501931
$540$	−6.65795	+	6.77342i	−0.286512	+	0.291481i
$541$	38.4016			1.65101			0.825506	−	0.564393i	$-0.190890\pi$
$541$	38.4016			1.65101			0.825506	+	0.564393i	$0.190890\pi$
$542$	−1.67467	−	2.90061i	−0.0719333	−	0.124592i
$543$	25.2333	+	11.6786i	1.08287	+	0.501176i
$544$	−3.86347	+	6.69172i	−0.165645	+	0.286905i
$545$	1.05583	−	1.82876i	0.0452269	−	0.0783353i
$546$	−1.35635	−	15.0077i	−0.0580466	−	0.642272i
$547$	5.16174	+	8.94040i	0.220700	+	0.382264i	0.955021	−	0.296539i	$-0.0958324\pi$
$547$	5.16174	+	8.94040i	0.220700	+	0.382264i	−0.734321	+	0.678803i	$0.762499\pi$
$548$	9.44022			0.403266
$549$	−0.613890	+	1.71721i	−0.0262002	+	0.0732886i
$550$	−2.27990			−0.0972152
$551$	−26.4324	−	45.7823i	−1.12606	−	1.95039i
$552$	0.286648	−	0.201939i	0.0122005	−	0.00859511i
$553$	−0.188621	+	0.326701i	−0.00802097	+	0.0138927i
$554$	−16.4684	+	28.5240i	−0.699674	+	1.21187i
$555$	6.65648	−	4.68940i	0.282552	−	0.199054i
$556$	14.7453	+	25.5395i	0.625338	+	1.08312i
$557$	19.8980			0.843104			0.421552	−	0.906804i	$-0.361485\pi$
$557$	19.8980			0.843104			0.421552	+	0.906804i	$0.361485\pi$
$558$	25.9721	+	30.5945i	1.09949	+	1.29517i
$559$	−22.6947			−0.959885
$560$	−2.15734	−	3.73662i	−0.0911641	−	0.157901i
$561$	0.180713	+	1.99955i	0.00762971	+	0.0844210i
$562$	20.9333	−	36.2576i	0.883019	−	1.52943i
$563$	−5.96899	+	10.3386i	−0.251563	+	0.435719i	−0.963956	−	0.266061i	$-0.914278\pi$
$563$	−5.96899	+	10.3386i	−0.251563	+	0.435719i	0.712394	+	0.701780i	$0.247611\pi$
$564$	35.9708	+	16.6481i	1.51464	+	0.701013i
$565$	−2.00963	−	3.48078i	−0.0845457	−	0.146438i
$566$	−42.3529			−1.78023
$567$	−8.42140	+	3.17492i	−0.353665	+	0.133334i
$568$	−1.66898			−0.0700290
$569$	−15.9693	−	27.6597i	−0.669470	−	1.15956i	−0.978053	−	0.208358i	$-0.933188\pi$
$569$	−15.9693	−	27.6597i	−0.669470	−	1.15956i	0.308583	−	0.951197i	$-0.400145\pi$
$570$	−23.7870	−	11.0092i	−0.996329	−	0.461125i
$571$	13.7905	−	23.8859i	0.577115	−	0.999592i	−0.418693	−	0.908128i	$-0.637512\pi$
$571$	13.7905	−	23.8859i	0.577115	−	0.999592i	0.995808	−	0.0914647i	$-0.0291549\pi$
$572$	4.73578	−	8.20262i	0.198013	−	0.342969i
$573$	1.46149	+	16.1711i	0.0610547	+	0.675556i
$574$	10.8175	+	18.7365i	0.451516	+	0.782048i
$575$	−0.601036			−0.0250649
$576$	−12.7529	−	15.0226i	−0.531372	−	0.625944i
$577$	−30.3543			−1.26367			−0.631834	−	0.775104i	$-0.717698\pi$
$577$	−30.3543			−1.26367			−0.631834	+	0.775104i	$0.717698\pi$
$578$	15.6622	+	27.1277i	0.651462	+	1.12837i
$579$	31.5998	−	22.2616i	1.31324	−	0.925161i
$580$	−6.24638	+	10.8190i	−0.259367	+	0.449236i
$581$	−5.37082	+	9.30253i	−0.222819	+	0.385934i
$582$	48.8078	−	34.3845i	2.02315	−	1.42528i
$583$	4.91514	+	8.51327i	0.203564	+	0.352584i
$584$	3.28412			0.135898
$585$	4.49073	−	12.5617i	0.185669	−	0.519363i
$586$	−31.6605			−1.30788
$587$	3.81547	+	6.60859i	0.157481	+	0.272766i	0.933960	−	0.357378i	$-0.116329\pi$
$587$	3.81547	+	6.60859i	0.157481	+	0.272766i	−0.776478	+	0.630144i	$0.782996\pi$
$588$	0.284965	+	3.15307i	0.0117517	+	0.130030i
$589$	−26.4430	+	45.8006i	−1.08957	+	1.88718i
$590$	−4.88569	+	8.46226i	−0.201140	+	0.348386i
$591$	−18.5886	−	8.60324i	−0.764632	−	0.353890i
$592$	10.1417	+	17.5660i	0.416822	+	0.721957i
$593$	7.70845			0.316548			0.158274	−	0.987395i	$-0.449407\pi$
$593$	7.70845			0.316548			0.158274	+	0.987395i	$0.449407\pi$
$594$	−11.4690	−	2.96767i	−0.470577	−	0.121765i
$595$	0.994717			0.0407794
$596$	11.2365	+	19.4623i	0.460267	+	0.797206i
$597$	−19.4422	−	8.99833i	−0.795718	−	0.368277i
$598$	2.61452	−	4.52848i	0.106916	−	0.185183i
$599$	15.7229	−	27.2328i	0.642419	−	1.11270i	−0.342473	−	0.939528i	$-0.611264\pi$
$599$	15.7229	−	27.2328i	0.642419	−	1.11270i	0.984891	−	0.173174i	$-0.0554022\pi$
$600$	−0.0525108	−	0.581020i	−0.00214375	−	0.0237201i
$601$	−19.5176	−	33.8054i	−0.796138	−	1.37895i	−0.922114	−	0.386918i	$-0.873540\pi$
$601$	−19.5176	−	33.8054i	−0.796138	−	1.37895i	0.125976	−	0.992033i	$-0.459794\pi$
$602$	9.98523			0.406968
$603$	−15.7839	+	2.87650i	−0.642771	+	0.117140i
$604$	14.8157			0.602843
$605$	4.82104	+	8.35028i	0.196003	+	0.339487i
$606$	−18.2733	+	12.8733i	−0.742304	+	0.522943i
$607$	16.0094	−	27.7291i	0.649801	−	1.12549i	−0.333369	−	0.942797i	$-0.608185\pi$
$607$	16.0094	−	27.7291i	0.649801	−	1.12549i	0.983170	−	0.182693i	$-0.0584813\pi$
$608$	30.0418	−	52.0339i	1.21836	−	2.11025i
$609$	−9.67765	+	6.81777i	−0.392158	+	0.276270i
$610$	0.594654	+	1.02997i	0.0240769	+	0.0417023i
$611$	−55.6724			−2.25227
$612$	5.36618	−	0.977946i	0.216915	−	0.0395311i
$613$	−30.1674			−1.21845			−0.609226	−	0.792997i	$-0.708520\pi$
$613$	−30.1674			−1.21845			−0.609226	+	0.792997i	$0.708520\pi$
$614$	−12.2135	−	21.1545i	−0.492899	−	0.853725i
$615$	1.72398	+	19.0755i	0.0695177	+	0.769198i
$616$	0.196248	−	0.339912i	0.00790706	−	0.0136954i
$617$	13.8089	−	23.9177i	0.555925	−	0.962891i	−0.441906	−	0.897062i	$-0.645697\pi$
$617$	13.8089	−	23.9177i	0.555925	−	0.962891i	0.997831	−	0.0658293i	$-0.0209693\pi$
$618$	12.4111	+	5.74415i	0.499248	+	0.231064i
$619$	2.44649	+	4.23744i	0.0983327	+	0.170317i	0.910995	−	0.412418i	$-0.135316\pi$
$619$	2.44649	+	4.23744i	0.0983327	+	0.170317i	−0.812662	+	0.582735i	$0.801982\pi$
$620$	12.4977			0.501922
$621$	−3.02349	−	0.782348i	−0.121329	−	0.0313945i
$622$	32.4785			1.30227
$623$	−3.83452	−	6.64157i	−0.153627	−	0.266089i
$624$	30.1583	+	13.9580i	1.20730	+	0.558766i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.06855	−	13.9751i	0.322484	−	0.558559i
$627$	−1.40520	−	15.5482i	−0.0561183	−	0.620936i
$628$	−4.70994	−	8.15786i	−0.187947	−	0.325534i
$629$	−4.67620			−0.186452
$630$	−1.97583	+	5.52691i	−0.0787190	+	0.220197i
$631$	−3.28394			−0.130732			−0.0653658	−	0.997861i	$-0.520821\pi$
$631$	−3.28394			−0.130732			−0.0653658	+	0.997861i	$0.520821\pi$
$632$	−0.0635311	−	0.110039i	−0.00252713	−	0.00437712i
$633$	−18.3135	+	12.9016i	−0.727898	+	0.512794i
$634$	17.5022	−	30.3147i	0.695101	−	1.20395i
$635$	2.65359	−	4.59615i	0.105304	−	0.182393i
$636$	21.8332	−	15.3812i	0.865744	−	0.609905i
$637$	−2.22338	−	3.85101i	−0.0880936	−	0.152583i
$638$	−15.5824			−0.616913
$639$	9.62039	+	11.3326i	0.380577	+	0.448311i
$640$	2.68457			0.106117
$641$	10.7728	+	18.6590i	0.425500	+	0.736987i	0.996467	−	0.0839856i	$-0.0267650\pi$
$641$	10.7728	+	18.6590i	0.425500	+	0.736987i	−0.570967	+	0.820973i	$0.693432\pi$
$642$	−2.34849	−	25.9855i	−0.0926876	−	1.02557i
$643$	16.7769	−	29.0585i	0.661618	−	1.14596i	−0.318572	−	0.947899i	$-0.603203\pi$
$643$	16.7769	−	29.0585i	0.661618	−	1.14596i	0.980190	−	0.198058i	$-0.0634633\pi$
$644$	−0.549300	+	0.951415i	−0.0216455	+	0.0374910i
$645$	8.02224	+	3.71288i	0.315875	+	0.146195i
$646$	7.52654	+	13.0364i	0.296128	+	0.512908i
$647$	−5.72656			−0.225134			−0.112567	−	0.993644i	$-0.535907\pi$
$647$	−5.72656			−0.225134			−0.112567	+	0.993644i	$0.535907\pi$
$648$	0.492140	−	2.99116i	0.0193331	−	0.117504i
$649$	−5.81991			−0.228452
$650$	−4.35002	−	7.53446i	−0.170622	−	0.295526i
$651$	10.7475	+	4.97419i	0.421227	+	0.194954i
$652$	−17.5879	+	30.4631i	−0.688796	+	1.19303i
$653$	−12.7523	+	22.0875i	−0.499034	+	0.864353i	−0.999999	−	0.00111488i	$-0.999645\pi$
$653$	−12.7523	+	22.0875i	−0.499034	+	0.864353i	0.500965	+	0.865467i	$0.332978\pi$
$654$	−0.644101	−	7.12683i	−0.0251864	−	0.278681i
$655$	−1.25987	−	2.18216i	−0.0492272	−	0.0852641i
$656$	−47.7122			−1.86285
$657$	−18.9304	−	22.2996i	−0.738546	−	0.869990i
$658$	24.4948			0.954905
$659$	−22.7222	−	39.3561i	−0.885133	−	1.53310i	−0.845561	−	0.533879i	$-0.820734\pi$
$659$	−22.7222	−	39.3561i	−0.885133	−	1.53310i	−0.0395722	−	0.999217i	$-0.512600\pi$
$660$	−3.01598	+	2.12472i	−0.117397	+	0.0827046i
$661$	5.45128	−	9.44189i	0.212030	−	0.367247i	−0.740320	−	0.672255i	$-0.765326\pi$
$661$	5.45128	−	9.44189i	0.212030	−	0.367247i	0.952350	+	0.305008i	$0.0986591\pi$
$662$	−22.8957	+	39.6565i	−0.889867	+	1.54129i
$663$	−6.26318	+	4.41233i	−0.243242	+	0.171361i
$664$	−1.80900	−	3.13327i	−0.0702026	−	0.121595i
$665$	−7.73479			−0.299942
$666$	9.28846	−	25.9822i	0.359920	−	1.00679i
$667$	−4.10789			−0.159058
$668$	7.39001	+	12.7999i	0.285928	+	0.495242i
$669$	−3.88706	−	43.0094i	−0.150282	−	1.66284i
$670$	−5.23161	+	9.06142i	−0.202115	+	0.350073i
$671$	−0.354181	+	0.613460i	−0.0136730	+	0.0236824i
$672$	−12.2102	−	5.65116i	−0.471018	−	0.217998i
$673$	15.3950	+	26.6649i	0.593432	+	1.02785i	0.993766	+	0.111485i	$0.0355609\pi$
$673$	15.3950	+	26.6649i	0.593432	+	1.02785i	−0.400334	+	0.916369i	$0.631106\pi$
$674$	67.5050			2.60020
$675$	−3.64251	+	3.70568i	−0.140200	+	0.142632i
$676$	12.3813			0.476204
$677$	−17.7144	−	30.6823i	−0.680821	−	1.17922i	−0.974731	−	0.223384i	$-0.928290\pi$
$677$	−17.7144	−	30.6823i	−0.680821	−	1.17922i	0.293909	−	0.955833i	$-0.405044\pi$
$678$	−12.3605	−	5.72075i	−0.474704	−	0.219704i
$679$	8.80909	−	15.2578i	0.338062	−	0.585541i
$680$	−0.167520	+	0.290153i	−0.00642410	+	0.0111269i
$681$	2.18132	+	24.1358i	0.0835883	+	0.924886i
$682$	7.79431	+	13.5001i	0.298460	+	0.516947i
$683$	3.62098			0.138553			0.0692764	−	0.997598i	$-0.477931\pi$
$683$	3.62098			0.138553			0.0692764	+	0.997598i	$0.477931\pi$
$684$	−41.7267	+	7.60438i	−1.59546	+	0.290761i
$685$	5.16467			0.197332
$686$	0.978244	+	1.69437i	0.0373495	+	0.0646913i
$687$	2.21315	−	1.55913i	0.0844368	−	0.0594846i
$688$	−11.0103	+	19.0704i	−0.419763	+	0.727052i
$689$	−18.7561	+	32.4865i	−0.714549	+	1.23764i
$690$	−1.66505	+	1.17301i	−0.0633875	+	0.0446557i
$691$	22.3328	+	38.6815i	0.849578	+	1.47151i	0.881585	+	0.472025i	$0.156477\pi$
$691$	22.3328	+	38.6815i	0.849578	+	1.47151i	−0.0320066	+	0.999488i	$0.510190\pi$
$692$	−41.0086			−1.55891
$693$	−3.43926	+	0.626779i	−0.130647	+	0.0238093i
$694$	−52.4815			−1.99217
$695$	8.06702	+	13.9725i	0.305999	+	0.530006i
$696$	−0.358895	−	3.97109i	−0.0136039	−	0.150524i
$697$	5.49986	−	9.52603i	0.208322	−	0.360824i
$698$	−24.2376	+	41.9808i	−0.917407	+	1.58900i
$699$	38.0883	+	17.6282i	1.44063	+	0.666759i
$700$	0.913922	+	1.58296i	0.0345430	+	0.0598303i
$701$	−16.5211			−0.623992			−0.311996	−	0.950083i	$-0.600998\pi$
$701$	−16.5211			−0.623992			−0.311996	+	0.950083i	$0.600998\pi$
$702$	−12.0753	−	43.5642i	−0.455753	−	1.64422i
$703$	36.3615			1.37140
$704$	−3.82719	−	6.62889i	−0.144243	−	0.249836i
$705$	19.6793	+	9.10806i	0.741167	+	0.343029i
$706$	−34.0545	+	58.9841i	−1.28166	+	2.21990i
$707$	−3.29807	+	5.71242i	−0.124037	+	0.214838i
$708$	1.42321	+	15.7475i	0.0534876	+	0.591828i
$709$	19.1641	+	33.1932i	0.719722	+	1.24660i	0.961110	+	0.276167i	$0.0890642\pi$
$709$	19.1641	+	33.1932i	0.719722	+	1.24660i	−0.241387	+	0.970429i	$0.577602\pi$
$710$	9.69465			0.363834
$711$	−0.380971	+	1.06567i	−0.0142875	+	0.0399659i
$712$	2.58308			0.0968050
$713$	2.05477	+	3.55896i	0.0769516	+	0.133284i
$714$	2.75567	−	1.94134i	0.103129	−	0.0726527i
$715$	2.59091	−	4.48759i	0.0968946	−	0.167826i
$716$	6.69565	−	11.5972i	0.250228	−	0.433408i
$717$	15.9658	−	11.2477i	0.596255	−	0.420054i
$718$	−2.82710	−	4.89667i	−0.105506	−	0.182742i
$719$	−20.7838			−0.775106			−0.387553	−	0.921847i	$-0.626680\pi$
$719$	−20.7838			−0.775106			−0.387553	+	0.921847i	$0.626680\pi$
$720$	−8.37695	−	9.86785i	−0.312190	−	0.367753i
$721$	4.03570			0.150297
$722$	−39.9387	−	69.1759i	−1.48637	−	2.57446i
$723$	3.60746	+	39.9157i	0.134163	+	1.48448i
$724$	14.6713	−	25.4115i	0.545256	−	0.944410i
$725$	−3.41734	+	5.91901i	−0.126917	+	0.219827i
$726$	29.6526	+	13.7239i	1.10051	+	0.509342i
$727$	−6.61504	−	11.4576i	−0.245338	−	0.424938i	0.716888	−	0.697188i	$-0.245566\pi$
$727$	−6.61504	−	11.4576i	−0.245338	−	0.424938i	−0.962227	+	0.272250i	$0.912232\pi$
$728$	1.49776			0.0555106
$729$	−23.1471	+	13.9000i	−0.857301	+	0.514815i
$730$	−19.0765			−0.706054
$731$	−2.53835	−	4.39654i	−0.0938841	−	0.162612i
$732$	1.74651	+	0.808327i	0.0645529	+	0.0298766i
$733$	−8.01306	+	13.8790i	−0.295969	+	0.512634i	−0.975210	−	0.221282i	$-0.928976\pi$
$733$	−8.01306	+	13.8790i	−0.295969	+	0.512634i	0.679241	+	0.733916i	$0.262309\pi$
$734$	−10.9981	+	19.0493i	−0.405947	+	0.703121i
$735$	0.155902	+	1.72502i	0.00575053	+	0.0636283i
$736$	−2.33441	−	4.04332i	−0.0860476	−	0.149039i
$737$	−6.23199			−0.229558
$738$	42.0046	+	49.4804i	1.54621	+	1.82140i
$739$	5.24035			0.192769			0.0963846	−	0.995344i	$-0.469272\pi$
$739$	5.24035			0.192769			0.0963846	+	0.995344i	$0.469272\pi$
$740$	−4.29638	−	7.44155i	−0.157938	−	0.273557i
$741$	48.7017	−	34.3097i	1.78910	−	1.26040i
$742$	8.25229	−	14.2934i	0.302951	−	0.524727i
$743$	1.11026	−	1.92302i	0.0407313	−	0.0705487i	−0.844941	−	0.534859i	$-0.820365\pi$
$743$	1.11026	−	1.92302i	0.0407313	−	0.0705487i	0.885672	+	0.464311i	$0.153698\pi$
$744$	−3.26092	+	2.29728i	−0.119551	+	0.0842223i
$745$	6.14743	+	10.6477i	0.225224	+	0.390100i
$746$	−38.0726			−1.39394
$747$	−10.8478	+	30.3442i	−0.396902	+	1.11024i
$748$	2.11874			0.0774687
$749$	−3.84973	−	6.66793i	−0.140666	−	0.243641i
$750$	0.305020	+	3.37498i	0.0111378	+	0.123237i
$751$	−20.5697	+	35.6278i	−0.750599	+	1.30008i	0.196933	+	0.980417i	$0.436902\pi$
$751$	−20.5697	+	35.6278i	−0.750599	+	1.30008i	−0.947533	+	0.319659i	$0.896431\pi$
$752$	−27.0093	+	46.7815i	−0.984929	+	1.70595i
$753$	−0.0359866	−	0.0166554i	−0.00131142	−	0.000606958i
$754$	−29.7310	−	51.4957i	−1.08274	−	1.87536i
$755$	8.10556			0.294992
$756$	2.53698	+	9.15266i	0.0922690	+	0.332879i
$757$	17.3037			0.628914			0.314457	−	0.949272i	$-0.398178\pi$
$757$	17.3037			0.628914			0.314457	+	0.949272i	$0.398178\pi$
$758$	6.44740	+	11.1672i	0.234180	+	0.405612i
$759$	−1.10091	−	0.509528i	−0.0399606	−	0.0184947i
$760$	1.30261	−	2.25619i	0.0472508	−	0.0818407i
$761$	8.66798	−	15.0134i	0.314214	−	0.544235i	−0.665056	−	0.746793i	$-0.731592\pi$
$761$	8.66798	−	15.0134i	0.314214	−	0.544235i	0.979270	+	0.202559i	$0.0649257\pi$
$762$	−1.61880	−	17.9116i	−0.0586428	−	0.648870i
$763$	−1.05583	−	1.82876i	−0.0382237	−	0.0662054i
$764$	17.1350			0.619922
$765$	2.93580	−	0.535027i	0.106144	−	0.0193439i
$766$	−24.2704			−0.876925
$767$	−11.1043	−	19.2333i	−0.400954	−	0.694473i
$768$	26.0388	−	18.3440i	0.939595	−	0.661932i
$769$	−14.7789	+	25.5978i	−0.532941	+	0.923081i	0.466319	+	0.884617i	$0.345580\pi$
$769$	−14.7789	+	25.5978i	−0.532941	+	0.923081i	−0.999260	+	0.0384643i	$0.987753\pi$
$770$	−1.13995	+	1.97445i	−0.0410809	+	0.0711542i
$771$	−28.1672	+	19.8434i	−1.01442	+	0.714644i
$772$	−20.3959	−	35.3267i	−0.734064	−	1.27144i
$773$	25.5827			0.920145			0.460072	−	0.887881i	$-0.347823\pi$
$773$	25.5827			0.920145			0.460072	+	0.887881i	$0.347823\pi$
$774$	29.4703	−	5.37074i	1.05929	−	0.193047i
$775$	6.83742			0.245607
$776$	2.96707	+	5.13912i	0.106512	+	0.184484i
$777$	−0.732901	−	8.10938i	−0.0262927	−	0.290922i
$778$	20.5228	−	35.5465i	0.735777	−	1.27440i
$779$	−42.7661	+	74.0731i	−1.53226	+	2.65394i
$780$	−12.7761	−	5.91308i	−0.457457	−	0.211722i
$781$	2.88711	+	5.00062i	0.103309	+	0.178936i
$782$	1.16971			0.0418286
$783$	−24.8954	+	25.3272i	−0.889690	+	0.905120i
$784$	−4.31467			−0.154095
$785$	−2.57677	−	4.46310i	−0.0919690	−	0.159295i
$786$	−7.74904	−	3.58644i	−0.276399	−	0.127924i
$787$	14.9643	−	25.9189i	0.533419	−	0.923909i	−0.465819	−	0.884880i	$-0.654240\pi$
$787$	14.9643	−	25.9189i	0.533419	−	0.923909i	0.999238	−	0.0390288i	$-0.0124264\pi$
$788$	−10.8079	+	18.7198i	−0.385015	+	0.666866i
$789$	−3.21766	−	35.6027i	−0.114552	−	1.26749i
$790$	0.369034	+	0.639186i	0.0131296	+	0.0227412i
$791$	−4.01926			−0.142908
$792$	0.396377	−	1.10877i	0.0140846	−	0.0393983i
$793$	−2.70310			−0.0959898
$794$	−12.0560	−	20.8816i	−0.427852	−	0.741061i
$795$	11.9448	−	8.41495i	0.423638	−	0.298447i
$796$	−11.3042	+	19.5795i	−0.400668	+	0.693977i
$797$	−5.55316	+	9.61835i	−0.196703	+	0.340699i	−0.947457	−	0.319882i	$-0.896357\pi$
$797$	−5.55316	+	9.61835i	−0.196703	+	0.340699i	0.750755	+	0.660581i	$0.229690\pi$
$798$	−21.4278	+	15.0956i	−0.758534	+	0.534377i
$799$	−6.22681	−	10.7852i	−0.220289	−	0.381551i
$800$	−7.76797			−0.274639
$801$	−14.8894	−	17.5394i	−0.526092	−	0.619725i
$802$	−32.9984			−1.16521
$803$	−5.68108	−	9.83991i	−0.200481	−	0.347243i
$804$	1.52398	+	16.8625i	0.0537466	+	0.594694i
$805$	−0.300518	+	0.520512i	−0.0105919	+	0.0183456i
$806$	−29.7429	+	51.5163i	−1.04765	+	1.81458i
$807$	0.603787	+	0.279447i	0.0212543	+	0.00983700i
$808$	−1.11085	−	1.92405i	−0.0390797	−	0.0676880i
$809$	−29.1875			−1.02618			−0.513089	−	0.858336i	$-0.671499\pi$
$809$	−29.1875			−1.02618			−0.513089	+	0.858336i	$0.671499\pi$
$810$	−2.85870	+	17.3748i	−0.100445	+	0.610488i
$811$	1.81592			0.0637656			0.0318828	−	0.999492i	$-0.489850\pi$
$811$	1.81592			0.0637656			0.0318828	+	0.999492i	$0.489850\pi$
$812$	6.24638	+	10.8190i	0.219205	+	0.379674i
$813$	−2.69089	−	1.24541i	−0.0943738	−	0.0436784i
$814$	5.35894	−	9.28196i	0.187831	−	0.325332i
$815$	−9.62221	+	16.6662i	−0.337051	+	0.583790i
$816$	0.669113	+	7.40358i	0.0234236	+	0.259177i
$817$	19.7378	+	34.1869i	0.690539	+	1.19605i
$818$	16.0353			0.560661
$819$	−8.63340	−	10.1699i	−0.301676	−	0.355367i
$820$	20.2125			0.705852
$821$	−2.95728	−	5.12216i	−0.103210	−	0.178765i	0.809796	−	0.586712i	$-0.199578\pi$
$821$	−2.95728	−	5.12216i	−0.103210	−	0.178765i	−0.913005	+	0.407948i	$0.866245\pi$
$822$	14.3077	−	10.0796i	0.499039	−	0.351567i
$823$	17.3923	−	30.1243i	0.606256	−	1.05007i	−0.385595	−	0.922668i	$-0.626004\pi$
$823$	17.3923	−	30.1243i	0.606256	−	1.05007i	0.991852	−	0.127399i	$-0.0406627\pi$
$824$	−0.679651	+	1.17719i	−0.0236768	+	0.0410094i
$825$	−1.65002	+	1.16242i	−0.0574463	+	0.0404702i
$826$	4.88569	+	8.46226i	0.169995	+	0.294440i
$827$	0.182732			0.00635420			0.00317710	−	0.999995i	$-0.498989\pi$
$827$	0.182732			0.00635420			0.00317710	+	0.999995i	$0.498989\pi$
$828$	−1.10946	+	3.10345i	−0.0385565	+	0.107852i
$829$	17.2296			0.598409			0.299204	−	0.954189i	$-0.403279\pi$
$829$	17.2296			0.598409			0.299204	+	0.954189i	$0.403279\pi$
$830$	10.5079	+	18.2003i	0.364736	+	0.631741i
$831$	2.62455	+	29.0401i	0.0910446	+	1.00739i
$832$	14.6045	−	25.2957i	0.506319	−	0.876971i
$833$	0.497359	−	0.861451i	0.0172325	−	0.0298475i
$834$	49.6175	+	22.9641i	1.71811	+	0.795183i
$835$	4.04302	+	7.00271i	0.139914	+	0.242339i
$836$	−16.4750			−0.569801
$837$	34.3955	+	8.90004i	1.18888	+	0.307630i
$838$	−63.5623			−2.19572
$839$	4.60127	+	7.96963i	0.158854	+	0.275142i	0.934456	−	0.356080i	$-0.115887\pi$
$839$	4.60127	+	7.96963i	0.158854	+	0.275142i	−0.775602	+	0.631222i	$0.782554\pi$
$840$	−0.529434	−	0.245034i	−0.0182672	−	0.00845449i
$841$	−8.85648	+	15.3399i	−0.305396	+	0.528961i
$842$	12.3229	−	21.3439i	0.424676	−	0.735561i
$843$	−3.33613	−	36.9135i	−0.114902	−	1.27137i
$844$	11.8204	+	20.4735i	0.406873	+	0.704725i
$845$	6.77372			0.233023
$846$	72.2936	−	13.1750i	2.48550	−	0.452964i
$847$	9.64207			0.331306
$848$	18.1989	+	31.5214i	0.624953	+	1.08245i
$849$	−30.6519	+	21.5938i	−1.05197	+	0.741099i
$850$	0.973076	−	1.68542i	0.0333762	−	0.0578093i
$851$	1.41274	−	2.44695i	0.0484283	−	0.0838802i
$852$	12.8246	−	9.03479i	0.439365	−	0.309527i
$853$	11.5322	+	19.9744i	0.394856	+	0.683911i	0.993083	−	0.117416i	$-0.0374611\pi$
$853$	11.5322	+	19.9744i	0.394856	+	0.683911i	−0.598227	+	0.801327i	$0.704128\pi$
$854$	1.18931			0.0406973
$855$	−22.8284	+	4.16030i	−0.780714	+	0.142279i
$856$	2.59333			0.0886382
$857$	−9.60156	−	16.6304i	−0.327983	−	0.568083i	0.654128	−	0.756384i	$-0.273036\pi$
$857$	−9.60156	−	16.6304i	−0.327983	−	0.568083i	−0.982112	+	0.188300i	$0.939702\pi$
$858$	−1.58056	−	17.4885i	−0.0539595	−	0.597049i
$859$	−16.5118	+	28.5992i	−0.563374	+	0.975792i	0.433825	+	0.900997i	$0.357164\pi$
$859$	−16.5118	+	28.5992i	−0.563374	+	0.975792i	−0.997199	+	0.0747949i	$0.976170\pi$
$860$	4.66434	−	8.07888i	0.159053	−	0.275487i
$861$	17.3819	+	8.04473i	0.592372	+	0.274164i
$862$	−10.6086	−	18.3746i	−0.361330	−	0.625842i
$863$	−0.0361626			−0.00123099			−0.000615494	−	1.00000i	$-0.500196\pi$
$863$	−0.0361626			−0.00123099			−0.000615494		1.00000i	$0.500196\pi$
$864$	−39.0766	−	10.1113i	−1.32941	−	0.343993i
$865$	−22.4355			−0.762830
$866$	−7.59823	−	13.1605i	−0.258198	−	0.447213i
$867$	25.1664	+	11.6476i	0.854694	+	0.395573i
$868$	6.24887	−	10.8234i	0.212101	−	0.367369i
$869$	−0.219800	+	0.380705i	−0.00745620	+	0.0129145i
$870$	2.08472	+	23.0669i	0.0706786	+	0.782043i
$871$	−11.8906	−	20.5951i	−0.402896	−	0.697837i
$872$	0.711250			0.0240860
$873$	17.7924	−	49.7698i	0.602181	−	1.68445i
$874$	−9.09549			−0.307659
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$	−25.2355	+	17.7781i	−0.852630	+	0.600667i
$877$	−9.44791	+	16.3643i	−0.319033	+	0.552582i	−0.980287	−	0.197581i	$-0.936692\pi$
$877$	−9.44791	+	16.3643i	−0.319033	+	0.552582i	0.661253	+	0.750163i	$0.270025\pi$
$878$	38.3010	−	66.3393i	1.29260	−	2.23884i
$879$	−22.9135	+	16.1423i	−0.772853	+	0.544465i
$880$	−2.51395	−	4.35428i	−0.0847451	−	0.146783i
$881$	34.0718			1.14791			0.573953	−	0.818888i	$-0.305409\pi$
$881$	34.0718			1.14791			0.573953	+	0.818888i	$0.305409\pi$
$882$	3.79853	+	4.47457i	0.127903	+	0.150667i
$883$	35.8685			1.20707			0.603536	−	0.797336i	$-0.293758\pi$
$883$	35.8685			1.20707			0.603536	+	0.797336i	$0.293758\pi$
$884$	4.04253	+	7.00187i	0.135965	+	0.235498i
$885$	0.778628	+	8.61534i	0.0261733	+	0.289602i
$886$	24.7855	−	42.9298i	0.832686	−	1.44225i
$887$	27.0541	−	46.8591i	0.908389	−	1.57338i	0.0920868	−	0.995751i	$-0.470646\pi$
$887$	27.0541	−	46.8591i	0.908389	−	1.57338i	0.816302	−	0.577625i	$-0.196020\pi$
$888$	2.48889	+	1.15192i	0.0835216	+	0.0386558i
$889$	−2.65359	−	4.59615i	−0.0889985	−	0.154150i
$890$	−15.0044			−0.502947
$891$	−9.81346	+	3.69973i	−0.328763	+	0.123946i
$892$	−45.5731			−1.52590
$893$	48.4189	+	83.8639i	1.62028	+	2.80640i
$894$	37.8107	+	17.4997i	1.26458	+	0.585278i
$895$	3.66314	−	6.34474i	0.122445	−	0.212081i
$896$	1.34229	−	2.32491i	0.0448426	−	0.0776697i
$897$	−0.416674	−	4.61040i	−0.0139123	−	0.153937i
$898$	−24.4879	−	42.4142i	−0.817170	−	1.41538i
$899$	46.7316			1.55859
$900$	3.54876	+	4.18036i	0.118292	+	0.139345i
$901$	−8.39126			−0.279553
$902$	12.6057	+	21.8337i	0.419724	+	0.726983i
$903$	7.22657	−	5.09102i	0.240485	−	0.169419i
$904$	0.676882	−	1.17239i	0.0225128	−	0.0389933i
$905$	8.02657	−	13.9024i	0.266812	−	0.462132i
$906$	22.4549	−	15.8192i	0.746014	−	0.525557i
$907$	2.43278	+	4.21369i	0.0807790	+	0.139913i	0.903585	−	0.428409i	$-0.140926\pi$
$907$	2.43278	+	4.21369i	0.0807790	+	0.139913i	−0.822806	+	0.568323i	$0.807593\pi$
$908$	25.5745			0.848719
$909$	−6.66135	+	18.6335i	−0.220943	+	0.618034i
$910$	−8.70004			−0.288404
$911$	−2.40200	−	4.16038i	−0.0795817	−	0.137840i	0.823488	−	0.567334i	$-0.192025\pi$
$911$	−2.40200	−	4.16038i	−0.0795817	−	0.137840i	−0.903070	+	0.429494i	$0.858692\pi$
$912$	−5.20293	−	57.5692i	−0.172286	−	1.90631i
$913$	−6.25862	+	10.8402i	−0.207130	+	0.358760i
$914$	−0.195095	+	0.337914i	−0.00645317	+	0.0111772i
$915$	0.955503	+	0.442229i	0.0315879	+	0.0146196i
$916$	−1.42846	−	2.47417i	−0.0471977	−	0.0817488i
$917$	−2.51974			−0.0832092
$918$	7.08889	−	7.21183i	0.233968	−	0.238026i
$919$	54.9683			1.81324			0.906618	−	0.421952i	$-0.138655\pi$
$919$	54.9683			1.81324			0.906618	+	0.421952i	$0.138655\pi$
$920$	−0.101220	−	0.175319i	−0.00333713	−	0.00578008i
$921$	−19.6250	−	9.08290i	−0.646665	−	0.299292i
$922$	18.3601	−	31.8006i	0.604658	−	1.04730i
$923$	−11.0171	+	19.0823i	−0.362634	+	0.628100i
$924$	0.332070	+	3.67428i	0.0109243	+	0.120875i
$925$	−2.35052	−	4.07122i	−0.0772845	−	0.133861i
$926$	22.7090			0.746264
$927$	11.9109	−	2.17067i	0.391206	−	0.0712943i
$928$	−53.0916			−1.74282
$929$	6.54699	+	11.3397i	0.214800	+	0.372044i	0.953211	−	0.302307i	$-0.0977568\pi$
$929$	6.54699	+	11.3397i	0.214800	+	0.372044i	−0.738411	+	0.674351i	$0.764423\pi$
$930$	18.9418	−	13.3442i	0.621125	−	0.437574i
$931$	−3.86739	+	6.69852i	−0.126749	+	0.219535i
$932$	22.1456	−	38.3572i	0.725402	−	1.25643i
$933$	23.5055	−	16.5593i	0.769536	−	0.542128i
$934$	−14.6710	−	25.4110i	−0.480051	−	0.831473i
$935$	1.15915			0.0379081
$936$	4.42046	−	0.805596i	0.144487	−	0.0263317i
$937$	−26.5980			−0.868919			−0.434460	−	0.900691i	$-0.643061\pi$
$937$	−26.5980			−0.868919			−0.434460	+	0.900691i	$0.643061\pi$
$938$	5.23161	+	9.06142i	0.170818	+	0.295866i
$939$	−1.28588	−	14.2280i	−0.0419631	−	0.464312i
$940$	11.4421	−	19.8183i	0.373200	−	0.646401i
$941$	−7.06457	+	12.2362i	−0.230298	+	0.398888i	−0.957896	−	0.287116i	$-0.907304\pi$
$941$	−7.06457	+	12.2362i	−0.230298	+	0.398888i	0.727598	+	0.686004i	$0.240637\pi$
$942$	−15.8489	−	7.33523i	−0.516384	−	0.238995i
$943$	3.32316	+	5.75589i	0.108217	+	0.187438i
$944$	−21.5490			−0.701359
$945$	1.38796	+	5.00735i	0.0451504	+	0.162889i
$946$	11.6358			0.378313
$947$	8.92078	+	15.4513i	0.289887	+	0.502098i	0.973782	−	0.227481i	$-0.0730491\pi$
$947$	8.92078	+	15.4513i	0.289887	+	0.502098i	−0.683896	+	0.729580i	$0.739716\pi$
$948$	1.08386	+	0.501636i	0.0352021	+	0.0162924i
$949$	21.6789	−	37.5489i	0.703726	−	1.21889i
$950$	−7.56651	+	13.1056i	−0.245490	+	0.425201i
$951$	−2.78931	−	30.8631i	−0.0904497	−	1.00080i
$952$	0.167520	+	0.290153i	0.00542936	+	0.00940392i
$953$	11.6377			0.376983			0.188491	−	0.982075i	$-0.439640\pi$
$953$	11.6377			0.376983			0.188491	+	0.982075i	$0.439640\pi$
$954$	16.6678	−	46.6240i	0.539639	−	1.50951i
$955$	9.37442			0.303349
$956$	−10.3050	−	17.8489i	−0.333289	−	0.577274i
$957$	−11.2774	+	7.94476i	−0.364546	+	0.256818i
$958$	10.9100	−	18.8966i	0.352485	−	0.610522i
$959$	2.58234	−	4.47274i	0.0833879	−	0.144432i
$960$	−9.30086	+	6.55233i	−0.300184	+	0.211476i
$961$	−7.87517	−	13.6402i	−0.254038	−	0.440006i
$962$	40.8992			1.31864
$963$	−14.9485	−	17.6090i	−0.481710	−	0.567442i
$964$	42.2950			1.36223
$965$	−11.1584	−	19.3270i	−0.359202	−	0.622157i
$966$	0.183328	+	2.02848i	0.00589849	+	0.0652654i
$967$	−1.77330	+	3.07145i	−0.0570256	+	0.0987712i	−0.893129	−	0.449801i	$-0.851495\pi$
$967$	−1.77330	+	3.07145i	−0.0570256	+	0.0987712i	0.836103	+	0.548572i	$0.184828\pi$
$968$	−1.62382	+	2.81254i	−0.0521915	+	0.0903983i
$969$	12.0938	+	5.59730i	0.388509	+	0.179811i
$970$	−17.2349	−	29.8517i	−0.553379	−	0.958480i
$971$	5.28759			0.169687			0.0848433	−	0.996394i	$-0.472961\pi$
$971$	5.28759			0.169687			0.0848433	+	0.996394i	$0.472961\pi$
$972$	12.4105	+	25.6485i	0.398068	+	0.822676i
$973$	16.1340			0.517233
$974$	−34.5377	−	59.8211i	−1.10666	−	1.91679i
$975$	−6.98970	−	3.23500i	−0.223850	−	0.103603i
$976$	−1.31140	+	2.27141i	−0.0419769	+	0.0727061i
$977$	−17.2641	+	29.9023i	−0.552327	+	0.956658i	0.445780	+	0.895143i	$0.352927\pi$
$977$	−17.2641	+	29.9023i	−0.552327	+	0.956658i	−0.998106	+	0.0615150i	$0.980407\pi$
$978$	5.86994	+	64.9495i	0.187700	+	2.07686i
$979$	−4.46837	−	7.73944i	−0.142810	−	0.247353i
$980$	1.82784			0.0583884
$981$	−4.09980	−	4.82947i	−0.130897	−	0.154193i
$982$	60.0872			1.91746
$983$	−7.29386	−	12.6333i	−0.232638	−	0.402941i	0.725946	−	0.687752i	$-0.241402\pi$
$983$	−7.29386	−	12.6333i	−0.232638	−	0.402941i	−0.958584	+	0.284811i	$0.908069\pi$
$984$	−5.27387	+	3.71537i	−0.168125	+	0.118442i
$985$	−5.91292	+	10.2415i	−0.188401	+	0.326320i
$986$	6.65067	−	11.5193i	0.211801	−	0.366849i
$987$	17.7275	−	12.4888i	0.564272	−	0.397522i
$988$	−31.4342	−	54.4456i	−1.00005	−	1.73214i
$989$	3.06748			0.0975401
$990$	−2.30244	+	6.44051i	−0.0731763	+	0.204693i
$991$	7.14170			0.226864			0.113432	−	0.993546i	$-0.463816\pi$
$991$	7.14170			0.226864			0.113432	+	0.993546i	$0.463816\pi$
$992$	26.5564	+	45.9971i	0.843167	+	1.46041i
$993$	3.64887	+	40.3739i	0.115793	+	1.28123i
$994$	4.84732	−	8.39581i	0.153748	−	0.266299i
$995$	−6.18446	+	10.7118i	−0.196061	+	0.339587i
$996$	30.8620	+	14.2837i	0.977900	+	0.452595i
$997$	−2.04138	−	3.53578i	−0.0646512	−	0.111979i	0.831888	−	0.554944i	$-0.187260\pi$
$997$	−2.04138	−	3.53578i	−0.0646512	−	0.111979i	−0.896539	+	0.442964i	$0.853927\pi$
$998$	−23.0041			−0.728182
$999$	−6.52485	−	23.5397i	−0.206437	−	0.744764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.f.211.2	yes	16
3.2	odd	2		945.2.i.f.631.7		16
9.2	odd	6		945.2.i.f.316.7		16
9.4	even	3		2835.2.a.x.1.7		8
9.5	odd	6		2835.2.a.y.1.2		8
9.7	even	3	inner	315.2.i.f.106.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.f.106.2	✓	16	9.7	even	3	inner
315.2.i.f.211.2	yes	16	1.1	even	1	trivial
945.2.i.f.316.7		16	9.2	odd	6
945.2.i.f.631.7		16	3.2	odd	2
2835.2.a.x.1.7		8	9.4	even	3
2835.2.a.y.1.2		8	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.978244 - 1.69437i) q^{2} +(-1.57186 - 0.727495i) q^{3} +(-0.913922 + 1.58296i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.305020 + 3.37498i) q^{6} +(0.500000 + 0.866025i) q^{7} -0.336819 q^{8} +(1.94150 + 2.28704i) q^{9} +O(q^{10})\)	\(q+(-0.978244 - 1.69437i) q^{2} +(-1.57186 - 0.727495i) q^{3} +(-0.913922 + 1.58296i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.305020 + 3.37498i) q^{6} +(0.500000 + 0.866025i) q^{7} -0.336819 q^{8} +(1.94150 + 2.28704i) q^{9} +1.95649 q^{10} +(0.582651 + 1.00918i) q^{11} +(2.58816 - 1.82332i) q^{12} +(-2.22338 + 3.85101i) q^{13} +(0.978244 - 1.69437i) q^{14} +(1.41596 - 0.997525i) q^{15} +(2.15734 + 3.73662i) q^{16} -0.994717 q^{17} +(1.97583 - 5.52691i) q^{18} +7.73479 q^{19} +(-0.913922 - 1.58296i) q^{20} +(-0.155902 - 1.72502i) q^{21} +(1.13995 - 1.97445i) q^{22} +(0.300518 - 0.520512i) q^{23} +(0.529434 + 0.245034i) q^{24} +(-0.500000 - 0.866025i) q^{25} +8.70004 q^{26} +(-1.38796 - 5.00735i) q^{27} -1.82784 q^{28} +(-3.41734 - 5.91901i) q^{29} +(-3.07533 - 1.42334i) q^{30} +(-3.41871 + 5.92138i) q^{31} +(3.88398 - 6.72726i) q^{32} +(-0.181673 - 2.01017i) q^{33} +(0.973076 + 1.68542i) q^{34} -1.00000 q^{35} +(-5.39468 + 0.983140i) q^{36} +4.70104 q^{37} +(-7.56651 - 13.1056i) q^{38} +(6.29644 - 4.43576i) q^{39} +(0.168410 - 0.291694i) q^{40} +(-5.52906 + 9.57662i) q^{41} +(-2.77031 + 1.95165i) q^{42} +(2.55183 + 4.41989i) q^{43} -2.12999 q^{44} +(-2.95139 + 0.537868i) q^{45} -1.17592 q^{46} +(6.25988 + 10.8424i) q^{47} +(-0.672666 - 7.44290i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.978244 + 1.69437i) q^{50} +(1.56356 + 0.723652i) q^{51} +(-4.06400 - 7.03905i) q^{52} +8.43583 q^{53} +(-7.12653 + 7.25013i) q^{54} -1.16530 q^{55} +(-0.168410 - 0.291694i) q^{56} +(-12.1580 - 5.62702i) q^{57} +(-6.68599 + 11.5805i) q^{58} +(-2.49717 + 4.32523i) q^{59} +(0.284965 + 3.15307i) q^{60} +(0.303940 + 0.526439i) q^{61} +13.3773 q^{62} +(-1.00989 + 2.82491i) q^{63} -6.56859 q^{64} +(-2.22338 - 3.85101i) q^{65} +(-3.22824 + 2.27426i) q^{66} +(-2.67398 + 4.63147i) q^{67} +(0.909095 - 1.57460i) q^{68} +(-0.851043 + 0.599548i) q^{69} +(0.978244 + 1.69437i) q^{70} +4.95513 q^{71} +(-0.653936 - 0.770321i) q^{72} -9.75040 q^{73} +(-4.59876 - 7.96529i) q^{74} +(0.155902 + 1.72502i) q^{75} +(-7.06900 + 12.2439i) q^{76} +(-0.582651 + 1.00918i) q^{77} +(-13.6753 - 6.32924i) q^{78} +(0.188621 + 0.326701i) q^{79} -4.31467 q^{80} +(-1.46114 + 8.88060i) q^{81} +21.6351 q^{82} +(5.37082 + 9.30253i) q^{83} +(2.87312 + 1.32975i) q^{84} +(0.497359 - 0.861451i) q^{85} +(4.99262 - 8.64746i) q^{86} +(1.06554 + 11.7900i) q^{87} +(-0.196248 - 0.339912i) q^{88} -7.66903 q^{89} +(3.79853 + 4.47457i) q^{90} -4.44676 q^{91} +(0.549300 + 0.951415i) q^{92} +(9.68152 - 6.82050i) q^{93} +(12.2474 - 21.2131i) q^{94} +(-3.86739 + 6.69852i) q^{95} +(-10.9991 + 7.74874i) q^{96} +(-8.80909 - 15.2578i) q^{97} +1.95649 q^{98} +(-1.17682 + 3.29187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Introduction

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