LMFDB - Embedded newform 483.2.i.g.415.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
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} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} + \cdots + 6400 $ x^16 - x^15 + 16x^14 - 7x^13 + 161x^12 - 50x^11 + 929x^10 - 47x^9 + 3741x^8 - 158x^7 + 8993x^6 + 265x^5 + 15176x^4 + 383x^3 + 12649x^2 + 2960x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.6
Root			$-0.838903 - 1.45302i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.g.277.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.838903 - 1.45302i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.407518 - 0.705841i) q^{4} +(-1.47412 + 2.55325i) q^{5} -1.67781 q^{6} +(2.59341 + 0.523657i) q^{7} +1.98814 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.838903 - 1.45302i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.407518 - 0.705841i) q^{4} +(-1.47412 + 2.55325i) q^{5} -1.67781 q^{6} +(2.59341 + 0.523657i) q^{7} +1.98814 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.47329 + 4.28386i) q^{10} +(1.83154 + 3.17233i) q^{11} +(-0.407518 + 0.705841i) q^{12} +1.91805 q^{13} +(2.93651 - 3.32899i) q^{14} +2.94824 q^{15} +(2.48289 - 4.30050i) q^{16} +(-1.51422 - 2.62270i) q^{17} +(0.838903 + 1.45302i) q^{18} +(-1.08225 + 1.87451i) q^{19} +2.40292 q^{20} +(-0.843205 - 2.50779i) q^{21} +6.14595 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.994071 - 1.72178i) q^{24} +(-1.84606 - 3.19747i) q^{25} +(1.60906 - 2.78697i) q^{26} +1.00000 q^{27} +(-0.687242 - 2.04394i) q^{28} -0.852794 q^{29} +(2.47329 - 4.28386i) q^{30} +(-1.01172 - 1.75235i) q^{31} +(-2.17767 - 3.77184i) q^{32} +(1.83154 - 3.17233i) q^{33} -5.08113 q^{34} +(-5.16003 + 5.84970i) q^{35} +0.815035 q^{36} +(2.71717 - 4.70627i) q^{37} +(1.81581 + 3.14507i) q^{38} +(-0.959026 - 1.66108i) q^{39} +(-2.93076 + 5.07623i) q^{40} -1.41089 q^{41} +(-4.35124 - 0.878596i) q^{42} +6.68453 q^{43} +(1.49277 - 2.58556i) q^{44} +(-1.47412 - 2.55325i) q^{45} +(-0.838903 - 1.45302i) q^{46} +(-5.86116 + 10.1518i) q^{47} -4.96579 q^{48} +(6.45157 + 2.71612i) q^{49} -6.19467 q^{50} +(-1.51422 + 2.62270i) q^{51} +(-0.781640 - 1.35384i) q^{52} +(3.40300 + 5.89417i) q^{53} +(0.838903 - 1.45302i) q^{54} -10.7997 q^{55} +(5.15607 + 1.04110i) q^{56} +2.16450 q^{57} +(-0.715412 + 1.23913i) q^{58} +(-5.54782 - 9.60911i) q^{59} +(-1.20146 - 2.08099i) q^{60} +(1.08651 - 1.88189i) q^{61} -3.39495 q^{62} +(-1.75021 + 1.98413i) q^{63} +2.62414 q^{64} +(-2.82744 + 4.89727i) q^{65} +(-3.07298 - 5.32255i) q^{66} +(-5.74715 - 9.95435i) q^{67} +(-1.23414 + 2.13759i) q^{68} -1.00000 q^{69} +(4.17098 + 12.4050i) q^{70} -14.1534 q^{71} +(-0.994071 + 1.72178i) q^{72} +(-5.11498 - 8.85941i) q^{73} +(-4.55888 - 7.89622i) q^{74} +(-1.84606 + 3.19747i) q^{75} +1.76415 q^{76} +(3.08873 + 9.18625i) q^{77} -3.21812 q^{78} +(2.20288 - 3.81550i) q^{79} +(7.32017 + 12.6789i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.18360 + 2.05006i) q^{82} +14.2550 q^{83} +(-1.42648 + 1.61714i) q^{84} +8.92856 q^{85} +(5.60767 - 9.71278i) q^{86} +(0.426397 + 0.738542i) q^{87} +(3.64137 + 6.30704i) q^{88} +(-8.09248 + 14.0166i) q^{89} -4.94658 q^{90} +(4.97430 + 1.00440i) q^{91} -0.815035 q^{92} +(-1.01172 + 1.75235i) q^{93} +(9.83389 + 17.0328i) q^{94} +(-3.19074 - 5.52652i) q^{95} +(-2.17767 + 3.77184i) q^{96} +7.01439 q^{97} +(9.35882 - 7.09572i) q^{98} -3.66309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.838903	−	1.45302i	0.593194	−	1.02744i	−0.400605	−	0.916251i	$-0.631200\pi$
$2$	0.838903	−	1.45302i	0.593194	−	1.02744i	0.993799	−	0.111192i	$-0.0354667\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.407518	−	0.705841i	−0.203759	−	0.352921i
$5$	−1.47412	+	2.55325i	−0.659247	+	1.14185i	0.321564	+	0.946888i	$0.395791\pi$
$5$	−1.47412	+	2.55325i	−0.659247	+	1.14185i	−0.980811	+	0.194961i	$0.937542\pi$
$6$	−1.67781			−0.684962
$7$	2.59341	+	0.523657i	0.980217	+	0.197924i
$7$	2.59341	+	0.523657i	0.980217	+	0.197924i
$8$	1.98814			0.702914
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.47329	+	4.28386i	0.782123	+	1.35468i
$11$	1.83154	+	3.17233i	0.552231	+	0.956492i	0.998113	+	0.0614007i	$0.0195568\pi$
$11$	1.83154	+	3.17233i	0.552231	+	0.956492i	−0.445882	+	0.895092i	$0.647110\pi$
$12$	−0.407518	+	0.705841i	−0.117640	+	0.203759i
$13$	1.91805			0.531972			0.265986	−	0.963977i	$-0.414303\pi$
$13$	1.91805			0.531972			0.265986	+	0.963977i	$0.414303\pi$
$14$	2.93651	−	3.32899i	0.784815	−	0.889710i
$15$	2.94824			0.761232
$16$	2.48289	−	4.30050i	0.620724	−	1.07512i
$17$	−1.51422	−	2.62270i	−0.367252	−	0.636099i	0.621883	−	0.783110i	$-0.286368\pi$
$17$	−1.51422	−	2.62270i	−0.367252	−	0.636099i	−0.989135	+	0.147011i	$0.953035\pi$
$18$	0.838903	+	1.45302i	0.197731	+	0.342481i
$19$	−1.08225	+	1.87451i	−0.248285	+	0.430043i	−0.963050	−	0.269322i	$-0.913200\pi$
$19$	−1.08225	+	1.87451i	−0.248285	+	0.430043i	0.714765	+	0.699365i	$0.246534\pi$
$20$	2.40292			0.537309
$21$	−0.843205	−	2.50779i	−0.184002	−	0.547244i
$22$	6.14595			1.31032
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	−0.994071	−	1.72178i	−0.202914	−	0.351457i
$25$	−1.84606	−	3.19747i	−0.369212	−	0.639494i
$26$	1.60906	−	2.78697i	0.315563	−	0.546571i
$27$	1.00000			0.192450
$28$	−0.687242	−	2.04394i	−0.129877	−	0.386268i
$29$	−0.852794			−0.158360			−0.0791800	−	0.996860i	$-0.525230\pi$
$29$	−0.852794			−0.158360			−0.0791800	+	0.996860i	$0.525230\pi$
$30$	2.47329	−	4.28386i	0.451559	−	0.782123i
$31$	−1.01172	−	1.75235i	−0.181711	−	0.314732i	0.760753	−	0.649042i	$-0.224830\pi$
$31$	−1.01172	−	1.75235i	−0.181711	−	0.314732i	−0.942463	+	0.334310i	$0.891497\pi$
$32$	−2.17767	−	3.77184i	−0.384962	−	0.666774i
$33$	1.83154	−	3.17233i	0.318831	−	0.552231i
$34$	−5.08113			−0.871407
$35$	−5.16003	+	5.84970i	−0.872204	+	0.988779i
$36$	0.815035			0.135839
$37$	2.71717	−	4.70627i	0.446700	−	0.773707i	−0.551469	−	0.834195i	$-0.685933\pi$
$37$	2.71717	−	4.70627i	0.446700	−	0.773707i	0.998169	+	0.0604887i	$0.0192659\pi$
$38$	1.81581	+	3.14507i	0.294563	+	0.510198i
$39$	−0.959026	−	1.66108i	−0.153567	−	0.265986i
$40$	−2.93076	+	5.07623i	−0.463394	+	0.802622i
$41$	−1.41089			−0.220345			−0.110172	−	0.993913i	$-0.535140\pi$
$41$	−1.41089			−0.220345			−0.110172	+	0.993913i	$0.535140\pi$
$42$	−4.35124	−	0.878596i	−0.671411	−	0.135570i
$43$	6.68453			1.01938			0.509691	−	0.860358i	$-0.329760\pi$
$43$	6.68453			1.01938			0.509691	+	0.860358i	$0.329760\pi$
$44$	1.49277	−	2.58556i	0.225044	−	0.389788i
$45$	−1.47412	−	2.55325i	−0.219749	−	0.380616i
$46$	−0.838903	−	1.45302i	−0.123690	−	0.214237i
$47$	−5.86116	+	10.1518i	−0.854938	+	1.48080i	0.0217647	+	0.999763i	$0.493072\pi$
$47$	−5.86116	+	10.1518i	−0.854938	+	1.48080i	−0.876703	+	0.481033i	$0.840262\pi$
$48$	−4.96579			−0.716750
$49$	6.45157	+	2.71612i	0.921652	+	0.388017i
$50$	−6.19467			−0.876058
$51$	−1.51422	+	2.62270i	−0.212033	+	0.367252i
$52$	−0.781640	−	1.35384i	−0.108394	−	0.187744i
$53$	3.40300	+	5.89417i	0.467438	+	0.809627i	0.999308	−	0.0371994i	$-0.0118437\pi$
$53$	3.40300	+	5.89417i	0.467438	+	0.809627i	−0.531870	+	0.846826i	$0.678510\pi$
$54$	0.838903	−	1.45302i	0.114160	−	0.197731i
$55$	−10.7997			−1.45623
$56$	5.15607	+	1.04110i	0.689009	+	0.139123i
$57$	2.16450			0.286695
$58$	−0.715412	+	1.23913i	−0.0939382	+	0.162706i
$59$	−5.54782	−	9.60911i	−0.722265	−	1.25100i	−0.960090	−	0.279691i	$-0.909768\pi$
$59$	−5.54782	−	9.60911i	−0.722265	−	1.25100i	0.237825	−	0.971308i	$-0.423565\pi$
$60$	−1.20146	−	2.08099i	−0.155108	−	0.268655i
$61$	1.08651	−	1.88189i	0.139113	−	0.240951i	−0.788048	−	0.615614i	$-0.788908\pi$
$61$	1.08651	−	1.88189i	0.139113	−	0.240951i	0.927161	+	0.374663i	$0.122242\pi$
$62$	−3.39495			−0.431159
$63$	−1.75021	+	1.98413i	−0.220505	+	0.249977i
$64$	2.62414			0.328018
$65$	−2.82744	+	4.89727i	−0.350701	+	0.607431i
$66$	−3.07298	−	5.32255i	−0.378257	−	0.655161i
$67$	−5.74715	−	9.95435i	−0.702126	−	1.21612i	−0.967719	−	0.252032i	$-0.918901\pi$
$67$	−5.74715	−	9.95435i	−0.702126	−	1.21612i	0.265593	−	0.964085i	$-0.414432\pi$
$68$	−1.23414	+	2.13759i	−0.149662	+	0.259221i
$69$	−1.00000			−0.120386
$70$	4.17098	+	12.4050i	0.498528	+	1.48268i
$71$	−14.1534			−1.67970			−0.839848	−	0.542822i	$-0.817356\pi$
$71$	−14.1534			−1.67970			−0.839848	+	0.542822i	$0.817356\pi$
$72$	−0.994071	+	1.72178i	−0.117152	+	0.202914i
$73$	−5.11498	−	8.85941i	−0.598664	−	1.03692i	−0.993019	−	0.117958i	$-0.962365\pi$
$73$	−5.11498	−	8.85941i	−0.598664	−	1.03692i	0.394355	−	0.918958i	$-0.370968\pi$
$74$	−4.55888	−	7.89622i	−0.529959	−	0.917917i
$75$	−1.84606	+	3.19747i	−0.213165	+	0.369212i
$76$	1.76415			0.202361
$77$	3.08873	+	9.18625i	0.351994	+	1.04687i
$78$	−3.21812			−0.364380
$79$	2.20288	−	3.81550i	0.247843	−	0.429277i	−0.715084	−	0.699039i	$-0.753612\pi$
$79$	2.20288	−	3.81550i	0.247843	−	0.429277i	0.962927	+	0.269762i	$0.0869449\pi$
$80$	7.32017	+	12.6789i	0.818420	+	1.41754i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.18360	+	2.05006i	−0.130707	+	0.226391i
$83$	14.2550			1.56469			0.782344	−	0.622847i	$-0.214024\pi$
$83$	14.2550			1.56469			0.782344	+	0.622847i	$0.214024\pi$
$84$	−1.42648	+	1.61714i	−0.155642	+	0.176444i
$85$	8.92856			0.968438
$86$	5.60767	−	9.71278i	0.604691	−	1.04736i
$87$	0.426397	+	0.738542i	0.0457146	+	0.0791800i
$88$	3.64137	+	6.30704i	0.388171	+	0.672332i
$89$	−8.09248	+	14.0166i	−0.857802	+	1.48576i	0.0162198	+	0.999868i	$0.494837\pi$
$89$	−8.09248	+	14.0166i	−0.857802	+	1.48576i	−0.874021	+	0.485887i	$0.838496\pi$
$90$	−4.94658			−0.521415
$91$	4.97430	+	1.00440i	0.521448	+	0.105290i
$92$	−0.815035			−0.0849733
$93$	−1.01172	+	1.75235i	−0.104911	+	0.181711i
$94$	9.83389	+	17.0328i	1.01429	+	1.75680i
$95$	−3.19074	−	5.52652i	−0.327363	−	0.567009i
$96$	−2.17767	+	3.77184i	−0.222258	+	0.384962i
$97$	7.01439			0.712203			0.356102	−	0.934447i	$-0.384106\pi$
$97$	7.01439			0.712203			0.356102	+	0.934447i	$0.384106\pi$
$98$	9.35882	−	7.09572i	0.945384	−	0.716776i
$99$	−3.66309			−0.368154
$100$	−1.50461	+	2.60605i	−0.150461	+	0.260605i
$101$	−4.46842	−	7.73953i	−0.444625	−	0.770112i	0.553401	−	0.832915i	$-0.313330\pi$
$101$	−4.46842	−	7.73953i	−0.444625	−	0.770112i	−0.998026	+	0.0628024i	$0.979996\pi$
$102$	2.54056	+	4.40039i	0.251553	+	0.435703i
$103$	−0.574873	+	0.995710i	−0.0566439	+	0.0981102i	−0.892957	−	0.450142i	$-0.851373\pi$
$103$	−0.574873	+	0.995710i	−0.0566439	+	0.0981102i	0.836313	+	0.548252i	$0.184707\pi$
$104$	3.81336			0.373931
$105$	7.64600	+	1.54387i	0.746173	+	0.150666i
$106$	11.4192			1.10913
$107$	−1.47593	+	2.55639i	−0.142684	+	0.247135i	−0.928506	−	0.371317i	$-0.878906\pi$
$107$	−1.47593	+	2.55639i	−0.142684	+	0.247135i	0.785823	+	0.618452i	$0.212240\pi$
$108$	−0.407518	−	0.705841i	−0.0392134	−	0.0679196i
$109$	5.38701	+	9.33058i	0.515982	+	0.893707i	0.999828	+	0.0185541i	$0.00590628\pi$
$109$	5.38701	+	9.33058i	0.515982	+	0.893707i	−0.483846	+	0.875153i	$0.660760\pi$
$110$	−9.05987	+	15.6922i	−0.863825	+	1.49619i
$111$	−5.43434			−0.515804
$112$	8.69115	−	9.85278i	0.821237	−	0.931000i
$113$	−3.85957			−0.363078			−0.181539	−	0.983384i	$-0.558108\pi$
$113$	−3.85957			−0.363078			−0.181539	+	0.983384i	$0.558108\pi$
$114$	1.81581	−	3.14507i	0.170066	−	0.294563i
$115$	1.47412	+	2.55325i	0.137462	+	0.238092i
$116$	0.347529	+	0.601937i	0.0322672	+	0.0558885i
$117$	−0.959026	+	1.66108i	−0.0886620	+	0.153567i
$118$	−18.6163			−1.71377
$119$	−2.55359	−	7.59468i	−0.234088	−	0.696203i
$120$	5.86152			0.535081
$121$	−1.20910	+	2.09423i	−0.109919	+	0.190384i
$122$	−1.82295	−	3.15744i	−0.165042	−	0.285861i
$123$	0.705447	+	1.22187i	0.0636080	+	0.110172i
$124$	−0.824589	+	1.42823i	−0.0740503	+	0.128259i
$125$	−3.85594			−0.344885
$126$	1.41474	+	4.20758i	0.126035	+	0.374841i
$127$	−18.7188			−1.66102			−0.830512	−	0.557001i	$-0.811952\pi$
$127$	−18.7188			−1.66102			−0.830512	+	0.557001i	$0.811952\pi$
$128$	6.55675	−	11.3566i	0.579540	−	1.00379i
$129$	−3.34226	−	5.78897i	−0.294270	−	0.509691i
$130$	4.74390	+	8.21667i	0.416067	+	0.720650i
$131$	6.37556	−	11.0428i	0.557035	−	0.964813i	−0.440707	−	0.897651i	$-0.645272\pi$
$131$	6.37556	−	11.0428i	0.557035	−	0.964813i	0.997742	−	0.0671618i	$-0.0213944\pi$
$132$	−2.98555			−0.259858
$133$	−3.78833	+	4.29466i	−0.328490	+	0.372394i
$134$	−19.2852			−1.66599
$135$	−1.47412	+	2.55325i	−0.126872	+	0.219749i
$136$	−3.01048	−	5.21430i	−0.258147	−	0.447123i
$137$	−9.77031	−	16.9227i	−0.834734	−	1.44580i	−0.894247	−	0.447574i	$-0.852288\pi$
$137$	−9.77031	−	16.9227i	−0.834734	−	1.44580i	0.0595126	−	0.998228i	$-0.481045\pi$
$138$	−0.838903	+	1.45302i	−0.0714122	+	0.123690i
$139$	−7.65626			−0.649395			−0.324698	−	0.945818i	$-0.605263\pi$
$139$	−7.65626			−0.649395			−0.324698	+	0.945818i	$0.605263\pi$
$140$	6.23176	+	1.25831i	0.526680	+	0.106346i
$141$	11.7223			0.987197
$142$	−11.8733	+	20.5652i	−0.996386	+	1.72579i
$143$	3.51300	+	6.08469i	0.293771	+	0.508827i
$144$	2.48289	+	4.30050i	0.206908	+	0.358375i
$145$	1.25712	−	2.17740i	0.104398	−	0.180823i
$146$	−17.1639			−1.42050
$147$	−0.873557	−	6.94528i	−0.0720497	−	0.572837i
$148$	−4.42918			−0.364076
$149$	4.22573	−	7.31919i	0.346186	−	0.599611i	−0.639383	−	0.768889i	$-0.720810\pi$
$149$	4.22573	−	7.31919i	0.346186	−	0.599611i	0.985568	+	0.169277i	$0.0541434\pi$
$150$	3.09733	+	5.36474i	0.252896	+	0.438029i
$151$	−2.46322	−	4.26642i	−0.200454	−	0.347196i	0.748221	−	0.663450i	$-0.230908\pi$
$151$	−2.46322	−	4.26642i	−0.200454	−	0.347196i	−0.948675	+	0.316253i	$0.897575\pi$
$152$	−2.15167	+	3.72680i	−0.174523	+	0.302283i
$153$	3.02844			0.244835
$154$	15.9390	+	3.21837i	1.28440	+	0.259344i
$155$	5.96560			0.479168
$156$	−0.781640	+	1.35384i	−0.0625813	+	0.108394i
$157$	6.76902	+	11.7243i	0.540227	+	0.935700i	0.998891	+	0.0470905i	$0.0149949\pi$
$157$	6.76902	+	11.7243i	0.540227	+	0.935700i	−0.458664	+	0.888610i	$0.651672\pi$
$158$	−3.69601	−	6.40167i	−0.294038	−	0.509289i
$159$	3.40300	−	5.89417i	0.269876	−	0.467438i
$160$	12.8406			1.01514
$161$	1.75021	−	1.98413i	0.137936	−	0.156371i
$162$	−1.67781			−0.131821
$163$	−6.83865	+	11.8449i	−0.535645	+	0.927764i	0.463487	+	0.886104i	$0.346598\pi$
$163$	−6.83865	+	11.8449i	−0.535645	+	0.927764i	−0.999132	+	0.0416601i	$0.986735\pi$
$164$	0.574964	+	0.995867i	0.0448971	+	0.0777641i
$165$	5.39983	+	9.35278i	0.420376	+	0.728113i
$166$	11.9586	−	20.7128i	0.928164	−	1.60763i
$167$	4.39959			0.340450			0.170225	−	0.985405i	$-0.445550\pi$
$167$	4.39959			0.340450			0.170225	+	0.985405i	$0.445550\pi$
$168$	−1.67641	−	4.98584i	−0.129338	−	0.384666i
$169$	−9.32108			−0.717006
$170$	7.49020	−	12.9734i	0.574472	−	0.995014i
$171$	−1.08225	−	1.87451i	−0.0827618	−	0.143348i
$172$	−2.72406	−	4.71822i	−0.207708	−	0.359761i
$173$	−0.900113	+	1.55904i	−0.0684343	+	0.118532i	−0.898212	−	0.439562i	$-0.855134\pi$
$173$	−0.900113	+	1.55904i	−0.0684343	+	0.118532i	0.829778	+	0.558094i	$0.188467\pi$
$174$	1.43082			0.108471
$175$	−3.11322	−	9.25906i	−0.235337	−	0.699919i
$176$	18.1901			1.37113
$177$	−5.54782	+	9.60911i	−0.417000	+	0.722265i
$178$	13.5776	+	23.5171i	1.01769	+	1.76268i
$179$	−10.7405	−	18.6031i	−0.802783	−	1.39046i	−0.917777	−	0.397095i	$-0.870018\pi$
$179$	−10.7405	−	18.6031i	−0.802783	−	1.39046i	0.114994	−	0.993366i	$-0.463315\pi$
$180$	−1.20146	+	2.08099i	−0.0895515	+	0.155108i
$181$	−21.2920			−1.58262			−0.791310	−	0.611416i	$-0.790600\pi$
$181$	−21.2920			−1.58262			−0.791310	+	0.611416i	$0.790600\pi$
$182$	5.63237	−	6.38517i	0.417499	−	0.473301i
$183$	−2.17302			−0.160634
$184$	0.994071	−	1.72178i	0.0732839	−	0.126931i
$185$	8.01087	+	13.8752i	0.588971	+	1.02013i
$186$	1.69747	+	2.94011i	0.124465	+	0.215579i
$187$	5.54671	−	9.60719i	0.405616	−	0.702547i
$188$	9.55410			0.696805
$189$	2.59341	+	0.523657i	0.188643	+	0.0380905i
$190$	−10.7069			−0.776759
$191$	−3.84724	+	6.66361i	−0.278376	+	0.482162i	−0.970981	−	0.239155i	$-0.923130\pi$
$191$	−3.84724	+	6.66361i	−0.278376	+	0.482162i	0.692605	+	0.721317i	$0.256463\pi$
$192$	−1.31207	−	2.27257i	−0.0946906	−	0.164009i
$193$	7.57345	+	13.1176i	0.545149	+	0.944225i	0.998598	+	0.0529427i	$0.0168601\pi$
$193$	7.57345	+	13.1176i	0.545149	+	0.944225i	−0.453449	+	0.891282i	$0.649807\pi$
$194$	5.88439	−	10.1921i	0.422475	−	0.731748i
$195$	5.65488			0.404954
$196$	−0.711980	−	5.66065i	−0.0508557	−	0.404332i
$197$	8.95690			0.638153			0.319076	−	0.947729i	$-0.396627\pi$
$197$	8.95690			0.638153			0.319076	+	0.947729i	$0.396627\pi$
$198$	−3.07298	+	5.32255i	−0.218387	+	0.378257i
$199$	−8.32877	−	14.4259i	−0.590411	−	1.02262i	−0.994177	−	0.107759i	$-0.965632\pi$
$199$	−8.32877	−	14.4259i	−0.590411	−	1.02262i	0.403766	−	0.914862i	$-0.367701\pi$
$200$	−3.67023	−	6.35703i	−0.259525	−	0.449510i
$201$	−5.74715	+	9.95435i	−0.405373	+	0.702126i
$202$	−14.9943			−1.05499
$203$	−2.21165	−	0.446572i	−0.155227	−	0.0313432i
$204$	2.46828			0.172814
$205$	2.07983	−	3.60237i	0.145261	−	0.251600i
$206$	0.964526	+	1.67061i	0.0672017	+	0.116397i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	4.76232	−	8.24858i	0.330207	−	0.571936i
$209$	−7.92876			−0.548444
$210$	8.65753	−	9.81466i	0.597426	−	0.677276i
$211$	−0.555224			−0.0382232			−0.0191116	−	0.999817i	$-0.506084\pi$
$211$	−0.555224			−0.0382232			−0.0191116	+	0.999817i	$0.506084\pi$
$212$	2.77357	−	4.80396i	0.190489	−	0.329937i
$213$	7.07669	+	12.2572i	0.484887	+	0.839848i
$214$	2.47633	+	4.28912i	0.169278	+	0.293198i
$215$	−9.85380	+	17.0673i	−0.672024	+	1.16398i
$216$	1.98814			0.135276
$217$	−1.70618	−	5.07437i	−0.115823	−	0.344471i
$218$	18.0767			1.22431
$219$	−5.11498	+	8.85941i	−0.345639	+	0.598664i
$220$	4.40105	+	7.62285i	0.296719	+	0.513932i
$221$	−2.90435	−	5.03048i	−0.195368	−	0.338387i
$222$	−4.55888	+	7.89622i	−0.305972	+	0.529959i
$223$	15.1938			1.01745			0.508727	−	0.860928i	$-0.330116\pi$
$223$	15.1938			1.01745			0.508727	+	0.860928i	$0.330116\pi$
$224$	−3.67245	−	10.9223i	−0.245376	−	0.729777i
$225$	3.69212			0.246142
$226$	−3.23781	+	5.60804i	−0.215376	+	0.373042i
$227$	−13.5780	−	23.5177i	−0.901201	−	1.56093i	−0.825936	−	0.563763i	$-0.809353\pi$
$227$	−13.5780	−	23.5177i	−0.901201	−	1.56093i	−0.0752650	−	0.997164i	$-0.523980\pi$
$228$	−0.882073	−	1.52780i	−0.0584167	−	0.101181i
$229$	11.0742	−	19.1811i	0.731806	−	1.26753i	−0.224304	−	0.974519i	$-0.572011\pi$
$229$	11.0742	−	19.1811i	0.731806	−	1.26753i	0.956111	−	0.293006i	$-0.0946557\pi$
$230$	4.94658			0.326168
$231$	6.41116	−	7.26805i	0.421823	−	0.478202i
$232$	−1.69548			−0.111313
$233$	1.57911	−	2.73509i	0.103451	−	0.179182i	−0.809653	−	0.586908i	$-0.800345\pi$
$233$	1.57911	−	2.73509i	0.103451	−	0.179182i	0.913104	+	0.407726i	$0.133678\pi$
$234$	1.60906	+	2.78697i	0.105188	+	0.182190i
$235$	−17.2801	−	29.9300i	−1.12723	−	1.95242i
$236$	−4.52167	+	7.83176i	−0.294336	+	0.509804i
$237$	−4.40576			−0.286185
$238$	−13.1775	−	2.66077i	−0.854168	−	0.172472i
$239$	26.3726			1.70590			0.852952	−	0.521990i	$-0.174810\pi$
$239$	26.3726			1.70590			0.852952	+	0.521990i	$0.174810\pi$
$240$	7.32017	−	12.6789i	0.472515	−	0.818420i
$241$	6.27226	+	10.8639i	0.404032	+	0.699803i	0.994208	−	0.107471i	$-0.0342752\pi$
$241$	6.27226	+	10.8639i	0.404032	+	0.699803i	−0.590177	+	0.807274i	$0.700942\pi$
$242$	2.02864	+	3.51371i	0.130406	+	0.225870i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.77109			−0.113382
$245$	−16.4453	+	12.4686i	−1.05065	+	0.796589i
$246$	2.36721			0.150928
$247$	−2.07581	+	3.59542i	−0.132081	+	0.228771i
$248$	−2.01145	−	3.48393i	−0.127727	−	0.221230i
$249$	−7.12749	−	12.3452i	−0.451687	−	0.782344i
$250$	−3.23476	+	5.60277i	−0.204584	+	0.354350i
$251$	20.5316			1.29595			0.647973	−	0.761663i	$-0.275617\pi$
$251$	20.5316			1.29595			0.647973	+	0.761663i	$0.275617\pi$
$252$	2.11372	+	0.426799i	0.133152	+	0.0268858i
$253$	3.66309			0.230296
$254$	−15.7032	+	27.1988i	−0.985309	+	1.70661i
$255$	−4.46428	−	7.73236i	−0.279564	−	0.484219i
$256$	−8.37682	−	14.5091i	−0.523551	−	0.906817i
$257$	−5.05349	+	8.75290i	−0.315228	+	0.545991i	−0.979486	−	0.201513i	$-0.935414\pi$
$257$	−5.05349	+	8.75290i	−0.315228	+	0.545991i	0.664258	+	0.747503i	$0.268748\pi$
$258$	−11.2153			−0.698237
$259$	9.51121	−	10.7824i	0.590998	−	0.669988i
$260$	4.60893			0.285833
$261$	0.426397	−	0.738542i	0.0263933	−	0.0457146i
$262$	−10.6969	−	18.5277i	−0.660860	−	1.14464i
$263$	3.64611	+	6.31525i	0.224829	+	0.389415i	0.956268	−	0.292492i	$-0.0944844\pi$
$263$	3.64611	+	6.31525i	0.224829	+	0.389415i	−0.731439	+	0.681907i	$0.761151\pi$
$264$	3.64137	−	6.30704i	0.224111	−	0.388171i
$265$	−20.0657			−1.23263
$266$	3.06220	+	9.10733i	0.187755	+	0.558406i
$267$	16.1850			0.990504
$268$	−4.68413	+	8.11315i	−0.286129	+	0.495589i
$269$	9.49686	+	16.4490i	0.579034	+	1.00292i	0.995590	+	0.0938060i	$0.0299033\pi$
$269$	9.49686	+	16.4490i	0.579034	+	1.00292i	−0.416557	+	0.909110i	$0.636763\pi$
$270$	2.47329	+	4.28386i	0.150520	+	0.260708i
$271$	4.17789	−	7.23632i	0.253789	−	0.439575i	−0.710777	−	0.703417i	$-0.751657\pi$
$271$	4.17789	−	7.23632i	0.253789	−	0.439575i	0.964566	+	0.263842i	$0.0849898\pi$
$272$	−15.0386			−0.911847
$273$	−1.61731	−	4.81007i	−0.0978841	−	0.291119i
$274$	−32.7854			−1.98064
$275$	6.76228	−	11.7126i	0.407781	−	0.706298i
$276$	0.407518	+	0.705841i	0.0245297	+	0.0424866i
$277$	−5.72499	−	9.91597i	−0.343981	−	0.595793i	0.641187	−	0.767385i	$-0.278442\pi$
$277$	−5.72499	−	9.91597i	−0.343981	−	0.595793i	−0.985168	+	0.171592i	$0.945109\pi$
$278$	−6.42286	+	11.1247i	−0.385218	+	0.667216i
$279$	2.02344			0.121140
$280$	−10.2589	+	11.6300i	−0.613085	+	0.695027i
$281$	−6.28234			−0.374773			−0.187387	−	0.982286i	$-0.560002\pi$
$281$	−6.28234			−0.374773			−0.187387	+	0.982286i	$0.560002\pi$
$282$	9.83389	−	17.0328i	0.585600	−	1.01429i
$283$	7.76954	+	13.4572i	0.461851	+	0.799950i	0.999053	−	0.0435037i	$-0.0138520\pi$
$283$	7.76954	+	13.4572i	0.461851	+	0.799950i	−0.537202	+	0.843454i	$0.680519\pi$
$284$	5.76775	+	9.99003i	0.342253	+	0.592799i
$285$	−3.19074	+	5.52652i	−0.189003	+	0.327363i
$286$	11.7883			0.697054
$287$	−3.65903	−	0.738825i	−0.215986	−	0.0436114i
$288$	4.35535			0.256641
$289$	3.91429	−	6.77975i	0.230252	−	0.398809i
$290$	−2.10921	−	3.65325i	−0.123857	−	0.214526i
$291$	−3.50719	−	6.07464i	−0.205595	−	0.356102i
$292$	−4.16889	+	7.22073i	−0.243966	+	0.422562i
$293$	13.8483			0.809026			0.404513	−	0.914532i	$-0.367441\pi$
$293$	13.8483			0.809026			0.404513	+	0.914532i	$0.367441\pi$
$294$	−10.8245	−	4.55712i	−0.631297	−	0.265777i
$295$	32.7126			1.90460
$296$	5.40212	−	9.35674i	0.313992	−	0.543849i
$297$	1.83154	+	3.17233i	0.106277	+	0.184077i
$298$	−7.08997	−	12.2802i	−0.410711	−	0.711372i
$299$	0.959026	−	1.66108i	0.0554619	−	0.0960628i
$300$	3.00921			0.173737
$301$	17.3357	+	3.50040i	0.999215	+	0.201760i
$302$	−8.26561			−0.475632
$303$	−4.46842	+	7.73953i	−0.256704	+	0.444625i
$304$	5.37423	+	9.30844i	0.308233	+	0.533876i
$305$	3.20329	+	5.54826i	0.183420	+	0.317692i
$306$	2.54056	−	4.40039i	0.145234	−	0.251553i
$307$	−20.5112			−1.17064			−0.585318	−	0.810804i	$-0.699030\pi$
$307$	−20.5112			−1.17064			−0.585318	+	0.810804i	$0.699030\pi$
$308$	5.22532	−	5.92371i	0.297740	−	0.337535i
$309$	1.14975			0.0654068
$310$	5.00456	−	8.66815i	0.284240	−	0.492318i
$311$	0.490808	+	0.850105i	0.0278312	+	0.0482050i	0.879606	−	0.475704i	$-0.157807\pi$
$311$	0.490808	+	0.850105i	0.0278312	+	0.0482050i	−0.851774	+	0.523909i	$0.824473\pi$
$312$	−1.90668	−	3.30247i	−0.107944	−	0.186965i
$313$	2.02216	−	3.50248i	0.114299	−	0.197972i	−0.803200	−	0.595709i	$-0.796871\pi$
$313$	2.02216	−	3.50248i	0.114299	−	0.197972i	0.917499	+	0.397737i	$0.130204\pi$
$314$	22.7142			1.28184
$315$	−2.48597	−	7.39356i	−0.140069	−	0.416580i
$316$	−3.59085			−0.202001
$317$	7.45352	−	12.9099i	0.418631	−	0.725091i	−0.577171	−	0.816623i	$-0.695843\pi$
$317$	7.45352	−	12.9099i	0.418631	−	0.725091i	0.995802	+	0.0915329i	$0.0291767\pi$
$318$	−5.70958	−	9.88928i	−0.320177	−	0.554563i
$319$	−1.56193	−	2.70534i	−0.0874513	−	0.151470i
$320$	−3.86830	+	6.70010i	−0.216245	+	0.374547i
$321$	2.95186			0.164757
$322$	−1.41474	−	4.20758i	−0.0788401	−	0.234480i
$323$	6.55506			0.364733
$324$	−0.407518	+	0.705841i	−0.0226399	+	0.0392134i
$325$	−3.54084	−	6.13292i	−0.196411	−	0.340193i
$326$	11.4739	+	19.8734i	0.635483	+	1.10069i
$327$	5.38701	−	9.33058i	0.297902	−	0.515982i
$328$	−2.80506			−0.154883
$329$	−20.5165	+	23.2586i	−1.13111	+	1.28229i
$330$	18.1197			0.997459
$331$	4.06385	−	7.03880i	0.223369	−	0.386887i	−0.732460	−	0.680811i	$-0.761628\pi$
$331$	4.06385	−	7.03880i	0.223369	−	0.386887i	0.955829	+	0.293923i	$0.0949610\pi$
$332$	−5.80916	−	10.0618i	−0.318819	−	0.552211i
$333$	2.71717	+	4.70627i	0.148900	+	0.257902i
$334$	3.69083	−	6.39271i	0.201953	−	0.349793i
$335$	33.8880			1.85150
$336$	−12.8783	−	2.60037i	−0.702571	−	0.141862i
$337$	3.74188			0.203833			0.101917	−	0.994793i	$-0.467503\pi$
$337$	3.74188			0.203833			0.101917	+	0.994793i	$0.467503\pi$
$338$	−7.81948	+	13.5437i	−0.425324	+	0.736682i
$339$	1.92978	+	3.34249i	0.104812	+	0.181539i
$340$	−3.63854	−	6.30214i	−0.197328	−	0.341782i
$341$	3.70602	−	6.41902i	0.200692	−	0.347610i
$342$	−3.63162			−0.196375
$343$	15.3093	+	10.4224i	0.826622	+	0.562758i
$344$	13.2898			0.716538
$345$	1.47412	−	2.55325i	0.0793640	−	0.137462i
$346$	1.51022	+	2.61577i	0.0811897	+	0.140625i
$347$	−11.5262	−	19.9640i	−0.618760	−	1.07172i	−0.989712	−	0.143072i	$-0.954302\pi$
$347$	−11.5262	−	19.9640i	−0.618760	−	1.07172i	0.370952	−	0.928652i	$-0.379031\pi$
$348$	0.347529	−	0.601937i	0.0186295	−	0.0322672i
$349$	26.4338			1.41497			0.707484	−	0.706729i	$-0.249830\pi$
$349$	26.4338			1.41497			0.707484	+	0.706729i	$0.249830\pi$
$350$	−16.0653	−	3.24388i	−0.858728	−	0.173393i
$351$	1.91805			0.102378
$352$	7.97701	−	13.8166i	0.425176	−	0.736427i
$353$	6.02238	+	10.4311i	0.320539	+	0.555189i	0.980599	−	0.196023i	$-0.0628027\pi$
$353$	6.02238	+	10.4311i	0.320539	+	0.555189i	−0.660061	+	0.751212i	$0.729469\pi$
$354$	9.30817	+	16.1222i	0.494724	+	0.856887i
$355$	20.8638	−	36.1371i	1.10733	−	1.91796i
$356$	13.1913			0.699139
$357$	−5.30039	+	6.00882i	−0.280526	+	0.318020i
$358$	−36.0410			−1.90483
$359$	−3.31751	+	5.74610i	−0.175092	+	0.303268i	−0.940193	−	0.340642i	$-0.889356\pi$
$359$	−3.31751	+	5.74610i	−0.175092	+	0.303268i	0.765101	+	0.643910i	$0.222689\pi$
$360$	−2.93076	−	5.07623i	−0.154465	−	0.267541i
$361$	7.15746	+	12.3971i	0.376709	+	0.652479i
$362$	−17.8619	+	30.9377i	−0.938801	+	1.62605i
$363$	2.41821			0.126923
$364$	−1.31817	−	3.92038i	−0.0690907	−	0.205484i
$365$	30.1604			1.57867
$366$	−1.82295	+	3.15744i	−0.0952872	+	0.165042i
$367$	−17.8768	−	30.9636i	−0.933163	−	1.61629i	−0.777877	−	0.628417i	$-0.783703\pi$
$367$	−17.8768	−	30.9636i	−0.933163	−	1.61629i	−0.155287	−	0.987869i	$-0.549630\pi$
$368$	−2.48289	−	4.30050i	−0.129430	−	0.224179i
$369$	0.705447	−	1.22187i	0.0367241	−	0.0636080i
$370$	26.8814			1.39750
$371$	5.73886	+	17.0680i	0.297947	+	0.886128i
$372$	1.64918			0.0855059
$373$	−16.2626	+	28.1677i	−0.842048	+	1.45847i	0.0461125	+	0.998936i	$0.485317\pi$
$373$	−16.2626	+	28.1677i	−0.842048	+	1.45847i	−0.888160	+	0.459533i	$0.848017\pi$
$374$	−9.30631	−	16.1190i	−0.481218	−	0.833494i
$375$	1.92797	+	3.33934i	0.0995599	+	0.172443i
$376$	−11.6528	+	20.1833i	−0.600948	+	1.04087i
$377$	−1.63570			−0.0842430
$378$	2.93651	−	3.32899i	0.151038	−	0.171225i
$379$	−8.00325			−0.411100			−0.205550	−	0.978647i	$-0.565898\pi$
$379$	−8.00325			−0.411100			−0.205550	+	0.978647i	$0.565898\pi$
$380$	−2.60056	+	4.50431i	−0.133406	+	0.231066i
$381$	9.35939	+	16.2109i	0.479496	+	0.830512i
$382$	6.45492	+	11.1803i	0.330263	+	0.572032i
$383$	3.09259	−	5.35652i	0.158024	−	0.273706i	−0.776132	−	0.630570i	$-0.782821\pi$
$383$	3.09259	−	5.35652i	0.158024	−	0.273706i	0.934156	+	0.356865i	$0.116154\pi$
$384$	−13.1135			−0.669196
$385$	−28.0080	−	5.65532i	−1.42742	−	0.288222i
$386$	25.4136			1.29352
$387$	−3.34226	+	5.78897i	−0.169897	+	0.294270i
$388$	−2.85849	−	4.95104i	−0.145118	−	0.251351i
$389$	2.47171	+	4.28113i	0.125321	+	0.217062i	0.921858	−	0.387527i	$-0.126671\pi$
$389$	2.47171	+	4.28113i	0.125321	+	0.217062i	−0.796538	+	0.604589i	$0.793337\pi$
$390$	4.74390	−	8.21667i	0.240217	−	0.416067i
$391$	−3.02844			−0.153155
$392$	12.8266	+	5.40003i	0.647843	+	0.272742i
$393$	−12.7511			−0.643208
$394$	7.51397	−	13.0146i	0.378549	−	0.655665i
$395$	6.49462	+	11.2490i	0.326780	+	0.565999i
$396$	1.49277	+	2.58556i	0.0750146	+	0.129929i
$397$	−10.9400	+	18.9486i	−0.549060	+	0.951001i	0.449279	+	0.893392i	$0.351681\pi$
$397$	−10.9400	+	18.9486i	−0.549060	+	0.951001i	−0.998339	+	0.0576089i	$0.981652\pi$
$398$	−27.9481			−1.40091
$399$	5.61345	+	1.13346i	0.281024	+	0.0567438i
$400$	−18.3343			−0.916715
$401$	−11.3865	+	19.7220i	−0.568615	+	0.984870i	0.428088	+	0.903737i	$0.359187\pi$
$401$	−11.3865	+	19.7220i	−0.568615	+	0.984870i	−0.996703	+	0.0811332i	$0.974146\pi$
$402$	9.64260	+	16.7015i	0.480929	+	0.832994i
$403$	−1.94053	−	3.36110i	−0.0966649	−	0.167429i
$404$	−3.64192	+	6.30799i	−0.181192	+	0.313834i
$405$	2.94824			0.146499
$406$	−2.50424	+	2.83894i	−0.124283	+	0.140894i
$407$	19.9064			0.986726
$408$	−3.01048	+	5.21430i	−0.149041	+	0.258147i
$409$	9.14036	+	15.8316i	0.451962	+	0.782821i	0.998508	−	0.0546084i	$-0.0173910\pi$
$409$	9.14036	+	15.8316i	0.451962	+	0.782821i	−0.546546	+	0.837429i	$0.684058\pi$
$410$	−3.48955	−	6.04407i	−0.172336	−	0.298496i
$411$	−9.77031	+	16.9227i	−0.481934	+	0.834734i
$412$	0.937084			0.0461668
$413$	−9.35590	−	27.8255i	−0.460374	−	1.36920i
$414$	1.67781			0.0824597
$415$	−21.0136	+	36.3966i	−1.03152	+	1.78664i
$416$	−4.17689	−	7.23459i	−0.204789	−	0.354705i
$417$	3.82813	+	6.63051i	0.187464	+	0.324698i
$418$	−6.65146	+	11.5207i	−0.325334	+	0.563495i
$419$	−7.08048			−0.345904			−0.172952	−	0.984930i	$-0.555331\pi$
$419$	−7.08048			−0.345904			−0.172952	+	0.984930i	$0.555331\pi$
$420$	−2.02615	−	6.02602i	−0.0988662	−	0.294039i
$421$	23.8313			1.16147			0.580734	−	0.814093i	$-0.302766\pi$
$421$	23.8313			1.16147			0.580734	+	0.814093i	$0.302766\pi$
$422$	−0.465779	+	0.806753i	−0.0226738	+	0.0392721i
$423$	−5.86116	−	10.1518i	−0.284979	−	0.493599i
$424$	6.76565	+	11.7185i	0.328569	+	0.569098i
$425$	−5.59068	+	9.68334i	−0.271188	+	0.469711i
$426$	23.7466			1.15053
$427$	3.80323	−	4.31155i	0.184051	−	0.208651i
$428$	2.40587			0.116292
$429$	3.51300	−	6.08469i	0.169609	−	0.293771i
$430$	16.5328	+	28.6356i	0.797281	+	1.38093i
$431$	2.76391	+	4.78724i	0.133133	+	0.230593i	0.924883	−	0.380253i	$-0.124163\pi$
$431$	2.76391	+	4.78724i	0.133133	+	0.230593i	−0.791750	+	0.610846i	$0.790830\pi$
$432$	2.48289	−	4.30050i	0.119458	−	0.206908i
$433$	17.6961			0.850422			0.425211	−	0.905094i	$-0.360200\pi$
$433$	17.6961			0.850422			0.425211	+	0.905094i	$0.360200\pi$
$434$	−8.80449	−	1.77779i	−0.422629	−	0.0853366i
$435$	−2.51424			−0.120549
$436$	4.39060	−	7.60475i	0.210272	−	0.364202i
$437$	1.08225	+	1.87451i	0.0517711	+	0.0896702i
$438$	8.58196	+	14.8644i	0.410062	+	0.710248i
$439$	1.76490	−	3.05690i	0.0842342	−	0.145898i	−0.820830	−	0.571172i	$-0.806489\pi$
$439$	1.76490	−	3.05690i	0.0842342	−	0.145898i	0.905065	+	0.425274i	$0.139822\pi$
$440$	−21.4713			−1.02360
$441$	−5.57801	+	4.22916i	−0.265620	+	0.201389i
$442$	−9.74587			−0.463564
$443$	−18.7987	+	32.5603i	−0.893154	+	1.54699i	−0.0570809	+	0.998370i	$0.518179\pi$
$443$	−18.7987	+	32.5603i	−0.893154	+	1.54699i	−0.836073	+	0.548618i	$0.815154\pi$
$444$	2.21459	+	3.83578i	0.105100	+	0.182038i
$445$	−23.8586	−	41.3243i	−1.13101	−	1.95896i
$446$	12.7462	−	22.0770i	0.603548	−	1.04538i
$447$	−8.45147			−0.399741
$448$	6.80548	+	1.37415i	0.321529	+	0.0649225i
$449$	−38.6628			−1.82461			−0.912305	−	0.409512i	$-0.865699\pi$
$449$	−38.6628			−1.82461			−0.912305	+	0.409512i	$0.865699\pi$
$450$	3.09733	−	5.36474i	0.146010	−	0.252896i
$451$	−2.58411	−	4.47582i	−0.121681	−	0.210758i
$452$	1.57284	+	2.72424i	0.0739803	+	0.128138i
$453$	−2.46322	+	4.26642i	−0.115732	+	0.200454i
$454$	−45.5624			−2.13835
$455$	−9.89720	+	11.2200i	−0.463988	+	0.526003i
$456$	4.30334			0.201522
$457$	−16.4480	+	28.4888i	−0.769405	+	1.33265i	0.168482	+	0.985705i	$0.446114\pi$
$457$	−16.4480	+	28.4888i	−0.769405	+	1.33265i	−0.937886	+	0.346943i	$0.887220\pi$
$458$	−18.5804	−	32.1822i	−0.868206	−	1.50378i
$459$	−1.51422	−	2.62270i	−0.0706776	−	0.122417i
$460$	1.20146	−	2.08099i	0.0560184	−	0.0970266i
$461$	33.3004			1.55095			0.775477	−	0.631376i	$-0.217509\pi$
$461$	33.3004			1.55095			0.775477	+	0.631376i	$0.217509\pi$
$462$	−5.18230	−	15.4128i	−0.241102	−	0.717066i
$463$	−41.9745			−1.95072			−0.975359	−	0.220622i	$-0.929191\pi$
$463$	−41.9745			−1.95072			−0.975359	+	0.220622i	$0.929191\pi$
$464$	−2.11740	+	3.66744i	−0.0982977	+	0.170257i
$465$	−2.98280	−	5.16636i	−0.138324	−	0.239584i
$466$	−2.64944	−	4.58896i	−0.122733	−	0.212579i
$467$	18.9354	−	32.7971i	0.876226	−	1.51767i	0.0207751	−	0.999784i	$-0.493387\pi$
$467$	18.9354	−	32.7971i	0.876226	−	1.51767i	0.855451	−	0.517884i	$-0.173280\pi$
$468$	1.56328			0.0722626
$469$	−9.69205	−	28.8253i	−0.447537	−	1.33103i
$470$	−57.9854			−2.67467
$471$	6.76902	−	11.7243i	0.311900	−	0.540227i
$472$	−11.0299	−	19.1043i	−0.507690	−	0.879345i
$473$	12.2430	+	21.2055i	0.562934	+	0.975030i
$474$	−3.69601	+	6.40167i	−0.169763	+	0.294038i
$475$	7.99161			0.366680
$476$	−4.32000	+	4.89740i	−0.198007	+	0.224472i
$477$	−6.80600			−0.311626
$478$	22.1241	−	38.3200i	1.01193	−	1.75272i
$479$	6.32758	+	10.9597i	0.289115	+	0.500761i	0.973599	−	0.228267i	$-0.0733058\pi$
$479$	6.32758	+	10.9597i	0.289115	+	0.500761i	−0.684484	+	0.729028i	$0.739972\pi$
$480$	−6.42031	−	11.1203i	−0.293046	−	0.507570i
$481$	5.21167	−	9.02688i	0.237632	−	0.411590i
$482$	21.0473			0.958677
$483$	−2.59341	−	0.523657i	−0.118004	−	0.0238272i
$484$	1.97092			0.0895875
$485$	−10.3400	+	17.9095i	−0.469517	+	0.813228i
$486$	0.838903	+	1.45302i	0.0380534	+	0.0659105i
$487$	9.35525	+	16.2038i	0.423927	+	0.734263i	0.996320	−	0.0857169i	$-0.0273181\pi$
$487$	9.35525	+	16.2038i	0.423927	+	0.734263i	−0.572393	+	0.819980i	$0.693985\pi$
$488$	2.16013	−	3.74146i	0.0977846	−	0.169368i
$489$	13.6773			0.618509
$490$	4.32112	+	34.3554i	0.195208	+	1.55202i
$491$	41.6265			1.87858			0.939288	−	0.343129i	$-0.111487\pi$
$491$	41.6265			1.87858			0.939288	+	0.343129i	$0.111487\pi$
$492$	0.574964	−	0.995867i	0.0259214	−	0.0448971i
$493$	1.29132	+	2.23663i	0.0581580	+	0.100733i
$494$	3.48281	+	6.03241i	0.156699	+	0.271411i
$495$	5.39983	−	9.35278i	0.242704	−	0.420376i
$496$	−10.0480			−0.451168
$497$	−36.7055	−	7.41151i	−1.64647	−	0.332452i
$498$	−23.9171			−1.07175
$499$	−11.8505	+	20.5257i	−0.530503	+	0.918858i	0.468864	+	0.883271i	$0.344664\pi$
$499$	−11.8505	+	20.5257i	−0.530503	+	0.918858i	−0.999367	+	0.0355876i	$0.988670\pi$
$500$	1.57136	+	2.72168i	0.0702734	+	0.121717i
$501$	−2.19979	−	3.81016i	−0.0982796	−	0.170225i
$502$	17.2241	−	29.8330i	0.768748	−	1.33151i
$503$	9.78650			0.436359			0.218179	−	0.975909i	$-0.429988\pi$
$503$	9.78650			0.436359			0.218179	+	0.975909i	$0.429988\pi$
$504$	−3.47966	+	3.94474i	−0.154996	+	0.175712i
$505$	26.3480			1.17247
$506$	3.07298	−	5.32255i	0.136610	−	0.236616i
$507$	4.66054	+	8.07229i	0.206982	+	0.358503i
$508$	7.62823	+	13.2125i	0.338448	+	0.586209i
$509$	16.3444	−	28.3093i	0.724452	−	1.25479i	−0.234747	−	0.972056i	$-0.575426\pi$
$509$	16.3444	−	28.3093i	0.724452	−	1.25479i	0.959199	−	0.282731i	$-0.0912403\pi$
$510$	−14.9804			−0.663343
$511$	−8.62596	−	25.6546i	−0.381590	−	1.13489i
$512$	−1.88236			−0.0831892
$513$	−1.08225	+	1.87451i	−0.0477826	+	0.0827618i
$514$	8.47878	+	14.6857i	0.373983	+	0.647757i
$515$	−1.69486	−	2.93559i	−0.0746847	−	0.129358i
$516$	−2.72406	+	4.71822i	−0.119920	+	0.207708i
$517$	−42.9399			−1.88849
$518$	−7.68815	−	22.8654i	−0.337798	−	1.00465i
$519$	1.80023			0.0790211
$520$	−5.62135	+	9.73646i	−0.246513	+	0.426972i
$521$	−4.68578	−	8.11600i	−0.205288	−	0.355569i	0.744937	−	0.667135i	$-0.232480\pi$
$521$	−4.68578	−	8.11600i	−0.205288	−	0.355569i	−0.950224	+	0.311567i	$0.899146\pi$
$522$	−0.715412	−	1.23913i	−0.0313127	−	0.0542353i
$523$	−15.1971	+	26.3221i	−0.664523	+	1.15099i	0.314892	+	0.949128i	$0.398032\pi$
$523$	−15.1971	+	26.3221i	−0.664523	+	1.15099i	−0.979415	+	0.201859i	$0.935302\pi$
$524$	−10.3926			−0.454003
$525$	−6.46198	+	7.32566i	−0.282024	+	0.319718i
$526$	12.2349			0.533469
$527$	−3.06393	+	5.30689i	−0.133467	+	0.231172i
$528$	−9.09506	−	15.7531i	−0.395812	−	0.685566i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−16.8332	+	29.1560i	−0.731188	+	1.26646i
$531$	11.0956			0.481510
$532$	4.57516	+	0.923808i	0.198358	+	0.0400521i
$533$	−2.70617			−0.117217
$534$	13.5776	−	23.5171i	0.587561	−	1.01769i
$535$	−4.35140	−	7.53684i	−0.188127	−	0.325846i
$536$	−11.4261	−	19.7907i	−0.493534	−	0.854827i
$537$	−10.7405	+	18.6031i	−0.463487	+	0.802783i
$538$	31.8678			1.37392
$539$	3.19991	+	25.4412i	0.137830	+	1.09583i
$540$	2.40292			0.103405
$541$	−6.79237	+	11.7647i	−0.292027	+	0.505805i	−0.974289	−	0.225303i	$-0.927663\pi$
$541$	−6.79237	+	11.7647i	−0.292027	+	0.505805i	0.682262	+	0.731108i	$0.260996\pi$
$542$	−7.00969	−	12.1411i	−0.301092	−	0.521507i
$543$	10.6460	+	18.4394i	0.456863	+	0.791310i
$544$	−6.59495	+	11.4228i	−0.282756	+	0.489748i
$545$	−31.7644			−1.36064
$546$	−8.34591	−	1.68519i	−0.357172	−	0.0721195i
$547$	−38.4666			−1.64471			−0.822357	−	0.568971i	$-0.807341\pi$
$547$	−38.4666			−1.64471			−0.822357	+	0.568971i	$0.807341\pi$
$548$	−7.96315	+	13.7926i	−0.340169	+	0.589190i
$549$	1.08651	+	1.88189i	0.0463710	+	0.0803170i
$550$	−11.3458	−	19.6515i	−0.483787	−	0.837943i
$551$	0.922938	−	1.59858i	0.0393185	−	0.0681016i
$552$	−1.98814			−0.0846209
$553$	7.71099	−	8.74160i	0.327904	−	0.371731i
$554$	−19.2108			−0.816190
$555$	8.01087	−	13.8752i	0.340042	−	0.588971i
$556$	3.12006	+	5.40410i	0.132320	+	0.229185i
$557$	18.0764	+	31.3093i	0.765922	+	1.32662i	0.939758	+	0.341841i	$0.111050\pi$
$557$	18.0764	+	31.3093i	0.765922	+	1.32662i	−0.173836	+	0.984775i	$0.555616\pi$
$558$	1.69747	−	2.94011i	0.0718598	−	0.124465i
$559$	12.8213			0.542282
$560$	12.3448	+	36.7149i	0.521663	+	1.55149i
$561$	−11.0934			−0.468365
$562$	−5.27028	+	9.12839i	−0.222313	+	0.385058i
$563$	−4.55667	−	7.89238i	−0.192041	−	0.332624i	0.753886	−	0.657006i	$-0.228177\pi$
$563$	−4.55667	−	7.89238i	−0.192041	−	0.332624i	−0.945926	+	0.324381i	$0.894844\pi$
$564$	−4.77705	−	8.27410i	−0.201150	−	0.348402i
$565$	5.68947	−	9.85445i	0.239358	−	0.414580i
$566$	26.0716			1.09587
$567$	−0.843205	−	2.50779i	−0.0354113	−	0.105317i
$568$	−28.1389			−1.18068
$569$	3.42210	−	5.92724i	0.143462	−	0.248483i	−0.785336	−	0.619069i	$-0.787510\pi$
$569$	3.42210	−	5.92724i	0.143462	−	0.248483i	0.928798	+	0.370586i	$0.120843\pi$
$570$	5.35344	+	9.27243i	0.224231	+	0.388379i
$571$	7.13561	+	12.3592i	0.298616	+	0.517218i	0.975820	−	0.218578i	$-0.0701417\pi$
$571$	7.13561	+	12.3592i	0.298616	+	0.517218i	−0.677204	+	0.735796i	$0.736808\pi$
$572$	2.86322	−	4.95923i	0.119717	−	0.207356i
$573$	7.69448			0.321441
$574$	−4.14310	+	4.69685i	−0.172930	+	0.196043i
$575$	−3.69212			−0.153972
$576$	−1.31207	+	2.27257i	−0.0546696	+	0.0946906i
$577$	6.80830	+	11.7923i	0.283433	+	0.490921i	0.972228	−	0.234036i	$-0.0751933\pi$
$577$	6.80830	+	11.7923i	0.283433	+	0.490921i	−0.688795	+	0.724956i	$0.741860\pi$
$578$	−6.56742	−	11.3751i	−0.273169	−	0.473142i
$579$	7.57345	−	13.1176i	0.314742	−	0.545149i
$580$	−2.04920			−0.0850883
$581$	36.9690	+	7.46473i	1.53373	+	0.309689i
$582$	−11.7688			−0.487832
$583$	−12.4655	+	21.5909i	−0.516268	+	0.894202i
$584$	−10.1693	−	17.6138i	−0.420809	−	0.728863i
$585$	−2.82744	−	4.89727i	−0.116900	−	0.202477i
$586$	11.6174	−	20.1219i	0.479910	−	0.831228i
$587$	16.3493			0.674807			0.337403	−	0.941360i	$-0.390451\pi$
$587$	16.3493			0.674807			0.337403	+	0.941360i	$0.390451\pi$
$588$	−4.54627	+	3.44692i	−0.187485	+	0.142148i
$589$	4.37975			0.180464
$590$	27.4427	−	47.5322i	1.12980	−	1.95687i
$591$	−4.47845	−	7.75690i	−0.184219	−	0.319076i
$592$	−13.4929	−	23.3704i	−0.554554	−	0.960516i
$593$	5.52181	−	9.56405i	0.226754	−	0.392749i	−0.730091	−	0.683350i	$-0.760522\pi$
$593$	5.52181	−	9.56405i	0.226754	−	0.392749i	0.956844	+	0.290602i	$0.0938555\pi$
$594$	6.14595			0.252171
$595$	23.1554	+	4.67550i	0.949280	+	0.191677i
$596$	−6.88824			−0.282154
$597$	−8.32877	+	14.4259i	−0.340874	+	0.590411i
$598$	−1.60906	−	2.78697i	−0.0657994	−	0.113968i
$599$	0.732085	+	1.26801i	0.0299122	+	0.0518094i	0.880594	−	0.473872i	$-0.157144\pi$
$599$	0.732085	+	1.26801i	0.0299122	+	0.0518094i	−0.850682	+	0.525681i	$0.823811\pi$
$600$	−3.67023	+	6.35703i	−0.149837	+	0.259525i
$601$	−12.5553			−0.512141			−0.256071	−	0.966658i	$-0.582428\pi$
$601$	−12.5553			−0.512141			−0.256071	+	0.966658i	$0.582428\pi$
$602$	19.6292	−	22.2527i	0.800025	−	0.906953i
$603$	11.4943			0.468084
$604$	−2.00761	+	3.47728i	−0.0816885	+	0.141489i
$605$	−3.56473	−	6.17429i	−0.144927	−	0.251021i
$606$	7.49715	+	12.9854i	0.304551	+	0.527497i
$607$	−0.907639	+	1.57208i	−0.0368399	+	0.0638086i	−0.883857	−	0.467756i	$-0.845063\pi$
$607$	−0.907639	+	1.57208i	−0.0368399	+	0.0638086i	0.847018	+	0.531565i	$0.178396\pi$
$608$	9.42716			0.382322
$609$	0.719081	+	2.13863i	0.0291386	+	0.0866616i
$610$	10.7490			0.435214
$611$	−11.2420	+	19.4717i	−0.454803	+	0.787742i
$612$	−1.23414	−	2.13759i	−0.0498872	−	0.0864072i
$613$	24.3541	+	42.1826i	0.983654	+	1.70374i	0.647773	+	0.761834i	$0.275701\pi$
$613$	24.3541	+	42.1826i	0.983654	+	1.70374i	0.335881	+	0.941905i	$0.390966\pi$
$614$	−17.2069	+	29.8033i	−0.694415	+	1.20276i
$615$	−4.15965			−0.167733
$616$	6.14084	+	18.2636i	0.247422	+	0.735860i
$617$	−5.07884			−0.204466			−0.102233	−	0.994760i	$-0.532599\pi$
$617$	−5.07884			−0.204466			−0.102233	+	0.994760i	$0.532599\pi$
$618$	0.964526	−	1.67061i	0.0387989	−	0.0672017i
$619$	7.63782	+	13.2291i	0.306990	+	0.531722i	0.977702	−	0.209995i	$-0.0673449\pi$
$619$	7.63782	+	13.2291i	0.306990	+	0.531722i	−0.670713	+	0.741717i	$0.734012\pi$
$620$	−2.43109	−	4.21076i	−0.0976348	−	0.169108i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	1.64696			0.0660372
$623$	−28.3270	+	32.1131i	−1.13490	+	1.28658i
$624$	−9.52464			−0.381291
$625$	14.9144	−	25.8325i	0.596577	−	1.03330i
$626$	−3.39279	−	5.87649i	−0.135603	−	0.234872i
$627$	3.96438	+	6.86651i	0.158322	+	0.274222i
$628$	5.51699	−	9.55571i	0.220152	−	0.381314i
$629$	−16.4575			−0.656205
$630$	−12.8285	−	2.59031i	−0.511100	−	0.103200i
$631$	22.5888			0.899247			0.449623	−	0.893218i	$-0.351558\pi$
$631$	22.5888			0.899247			0.449623	+	0.893218i	$0.351558\pi$
$632$	4.37964	−	7.58575i	0.174213	−	0.301745i
$633$	0.277612	+	0.480838i	0.0110341	+	0.0191116i
$634$	−12.5056	−	21.6603i	−0.496659	−	0.860239i
$635$	27.5937	−	47.7937i	1.09502	−	1.89664i
$636$	−5.54713			−0.219958
$637$	12.3744	+	5.20965i	0.490293	+	0.206414i
$638$	−5.24123			−0.207502
$639$	7.07669	−	12.2572i	0.279949	−	0.484887i
$640$	19.3309	+	33.4821i	0.764120	+	1.32349i
$641$	−2.80032	−	4.85030i	−0.110606	−	0.191575i	0.805409	−	0.592720i	$-0.201946\pi$
$641$	−2.80032	−	4.85030i	−0.110606	−	0.191575i	−0.916015	+	0.401144i	$0.868613\pi$
$642$	2.47633	−	4.28912i	0.0977328	−	0.169278i
$643$	−11.5110			−0.453951			−0.226975	−	0.973900i	$-0.572884\pi$
$643$	−11.5110			−0.453951			−0.226975	+	0.973900i	$0.572884\pi$
$644$	−2.11372	−	0.426799i	−0.0832923	−	0.0168182i
$645$	19.7076			0.775986
$646$	5.49906	−	9.52465i	0.216358	−	0.374742i
$647$	7.76978	+	13.4577i	0.305462	+	0.529075i	0.977364	−	0.211565i	$-0.0678559\pi$
$647$	7.76978	+	13.4577i	0.305462	+	0.529075i	−0.671902	+	0.740640i	$0.734523\pi$
$648$	−0.994071	−	1.72178i	−0.0390508	−	0.0676380i
$649$	20.3222	−	35.1990i	0.797714	−	1.38168i
$650$	−11.8817			−0.466038
$651$	−3.54144	+	4.01478i	−0.138800	+	0.157352i
$652$	11.1475			0.436569
$653$	15.8240	−	27.4079i	0.619239	−	1.07255i	−0.370385	−	0.928878i	$-0.620774\pi$
$653$	15.8240	−	27.4079i	0.619239	−	1.07255i	0.989625	−	0.143676i	$-0.0458923\pi$
$654$	−9.03837	−	15.6549i	−0.353428	−	0.612155i
$655$	18.7967	+	32.5568i	0.734447	+	1.27210i
$656$	−3.50310	+	6.06755i	−0.136773	+	0.236898i
$657$	10.2300			0.399109
$658$	16.5840	+	49.3226i	0.646511	+	1.92280i
$659$	−34.2553			−1.33440			−0.667199	−	0.744880i	$-0.732507\pi$
$659$	−34.2553			−1.33440			−0.667199	+	0.744880i	$0.732507\pi$
$660$	4.40105	−	7.62285i	0.171311	−	0.296719i
$661$	−0.545729	−	0.945230i	−0.0212264	−	0.0367652i	0.855217	−	0.518270i	$-0.173424\pi$
$661$	−0.545729	−	0.945230i	−0.0212264	−	0.0367652i	−0.876443	+	0.481505i	$0.840090\pi$
$662$	−6.81836	−	11.8097i	−0.265003	−	0.458998i
$663$	−2.90435	+	5.03048i	−0.112796	+	0.195368i
$664$	28.3409			1.09984
$665$	−5.38089	−	16.0034i	−0.208662	−	0.620585i
$666$	9.11777			0.353306
$667$	−0.426397	+	0.738542i	−0.0165102	+	0.0285964i
$668$	−1.79291	−	3.10541i	−0.0693698	−	0.120152i
$669$	−7.59692	−	13.1583i	−0.293714	−	0.508727i
$670$	28.4287	−	49.2400i	1.09830	−	1.90231i
$671$	7.95995			0.307290
$672$	−7.62276	+	8.64159i	−0.294054	+	0.333356i
$673$	4.74037			0.182728			0.0913639	−	0.995818i	$-0.470877\pi$
$673$	4.74037			0.182728			0.0913639	+	0.995818i	$0.470877\pi$
$674$	3.13907	−	5.43704i	0.120913	−	0.209427i
$675$	−1.84606	−	3.19747i	−0.0710549	−	0.123071i
$676$	3.79850	+	6.57920i	0.146096	+	0.253046i
$677$	−20.3654	+	35.2738i	−0.782704	+	1.35568i	0.147657	+	0.989039i	$0.452827\pi$
$677$	−20.3654	+	35.2738i	−0.782704	+	1.35568i	−0.930361	+	0.366645i	$0.880506\pi$
$678$	6.47561			0.248694
$679$	18.1912	+	3.67313i	0.698114	+	0.140962i
$680$	17.7512			0.680729
$681$	−13.5780	+	23.5177i	−0.520309	+	0.901201i
$682$	−6.21799	−	10.7699i	−0.238099	−	0.412400i
$683$	−19.6014	−	33.9506i	−0.750026	−	1.29908i	−0.947809	−	0.318837i	$-0.896708\pi$
$683$	−19.6014	−	33.9506i	−0.750026	−	1.29908i	0.197783	−	0.980246i	$-0.436626\pi$
$684$	−0.882073	+	1.52780i	−0.0337269	+	0.0584167i
$685$	57.6105			2.20118
$686$	27.9870	−	13.5013i	1.06855	−	0.515482i
$687$	−22.1485			−0.845017
$688$	16.5970	−	28.7468i	0.632754	−	1.09596i
$689$	6.52714	+	11.3053i	0.248664	+	0.430699i
$690$	−2.47329	−	4.28386i	−0.0941565	−	0.163084i
$691$	6.74020	−	11.6744i	0.256409	−	0.444114i	−0.708868	−	0.705341i	$-0.750794\pi$
$691$	6.74020	−	11.6744i	0.256409	−	0.444114i	0.965277	+	0.261227i	$0.0841272\pi$
$692$	1.46725			0.0557764
$693$	−9.49989	−	1.91820i	−0.360871	−	0.0728665i
$694$	−38.6776			−1.46818
$695$	11.2862	−	19.5484i	0.428112	−	0.741511i
$696$	0.847738	+	1.46833i	0.0321334	+	0.0556567i
$697$	2.13640	+	3.70035i	0.0809219	+	0.140161i
$698$	22.1754	−	38.4089i	0.839351	−	1.45380i
$699$	−3.15821			−0.119455
$700$	−5.26674	+	5.97067i	−0.199064	+	0.225670i
$701$	13.4433			0.507745			0.253873	−	0.967238i	$-0.418296\pi$
$701$	13.4433			0.507745			0.253873	+	0.967238i	$0.418296\pi$
$702$	1.60906	−	2.78697i	0.0607301	−	0.105188i
$703$	5.88132	+	10.1867i	0.221818	+	0.384200i
$704$	4.80623	+	8.32464i	0.181142	+	0.313747i
$705$	−17.2801	+	29.9300i	−0.650806	+	1.12723i
$706$	20.2088			0.760567
$707$	−7.53559	−	22.4117i	−0.283405	−	0.842879i
$708$	9.04334			0.339869
$709$	−0.0225554	+	0.0390671i	−0.000847086	+	0.00146720i	−0.866449	−	0.499266i	$-0.833603\pi$
$709$	−0.0225554	+	0.0390671i	−0.000847086	+	0.00146720i	0.865602	+	0.500733i	$0.166936\pi$
$710$	−35.0054	−	60.6311i	−1.31373	−	2.27544i
$711$	2.20288	+	3.81550i	0.0826144	+	0.143092i
$712$	−16.0890	+	27.8670i	−0.602961	+	1.04436i
$713$	−2.02344			−0.0757785
$714$	4.28444	+	12.7424i	0.160341	+	0.476872i
$715$	−20.7143			−0.774671
$716$	−8.75389	+	15.1622i	−0.327148	+	0.566638i
$717$	−13.1863	−	22.8394i	−0.492452	−	0.852952i
$718$	5.56615	+	9.64085i	0.207727	+	0.359793i
$719$	15.2918	−	26.4862i	0.570289	−	0.987769i	−0.426247	−	0.904607i	$-0.640165\pi$
$719$	15.2918	−	26.4862i	0.570289	−	0.987769i	0.996536	−	0.0831623i	$-0.0265020\pi$
$720$	−14.6403			−0.545613
$721$	−2.01229	+	2.28125i	−0.0749417	+	0.0849581i
$722$	24.0177			0.893846
$723$	6.27226	−	10.8639i	0.233268	−	0.404032i
$724$	8.67685	+	15.0287i	0.322473	+	0.558539i
$725$	1.57431	+	2.72679i	0.0584684	+	0.101270i
$726$	2.02864	−	3.51371i	0.0752900	−	0.130406i
$727$	−27.1973			−1.00869			−0.504347	−	0.863501i	$-0.668267\pi$
$727$	−27.1973			−1.00869			−0.504347	+	0.863501i	$0.668267\pi$
$728$	9.88961	+	1.99689i	0.366533	+	0.0740098i
$729$	1.00000			0.0370370
$730$	25.3017	−	43.8238i	0.936457	−	1.62199i
$731$	−10.1218	−	17.5315i	−0.374370	−	0.648427i
$732$	0.885543	+	1.53380i	0.0327306	+	0.0566910i
$733$	17.9460	−	31.0833i	0.662849	−	1.14809i	−0.317015	−	0.948421i	$-0.602681\pi$
$733$	17.9460	−	31.0833i	0.662849	−	1.14809i	0.979864	−	0.199667i	$-0.0639861\pi$
$734$	−59.9878			−2.21419
$735$	19.0208	+	8.00777i	0.701592	+	0.295371i
$736$	−4.35535			−0.160540
$737$	21.0523	−	36.4637i	0.775472	−	1.34316i
$738$	−1.18360	−	2.05006i	−0.0435690	−	0.0754638i
$739$	−2.09206	−	3.62356i	−0.0769577	−	0.133295i	0.824978	−	0.565165i	$-0.191187\pi$
$739$	−2.09206	−	3.62356i	−0.0769577	−	0.133295i	−0.901936	+	0.431870i	$0.857854\pi$
$740$	6.52914	−	11.3088i	0.240016	−	0.415720i
$741$	4.15163			0.152514
$742$	29.6146	+	5.97973i	1.08719	+	0.219523i
$743$	17.5835			0.645075			0.322537	−	0.946557i	$-0.395464\pi$
$743$	17.5835			0.645075			0.322537	+	0.946557i	$0.395464\pi$
$744$	−2.01145	+	3.48393i	−0.0737432	+	0.127727i
$745$	12.4585	+	21.5787i	0.456443	+	0.790583i
$746$	27.2856	+	47.2600i	0.998996	+	1.73031i
$747$	−7.12749	+	12.3452i	−0.260781	+	0.451687i
$748$	−9.04153			−0.330591
$749$	−5.16636	+	5.85688i	−0.188775	+	0.214006i
$750$	6.46952			0.236233
$751$	−15.3689	+	26.6197i	−0.560819	+	0.971367i	0.436606	+	0.899653i	$0.356180\pi$
$751$	−15.3689	+	26.6197i	−0.560819	+	0.971367i	−0.997425	+	0.0717145i	$0.977153\pi$
$752$	29.1053	+	50.4118i	1.06136	+	1.83833i
$753$	−10.2658	−	17.7809i	−0.374107	−	0.647973i
$754$	−1.37220	+	2.37672i	−0.0499725	+	0.0865549i
$755$	14.5243			0.528594
$756$	−0.687242	−	2.04394i	−0.0249948	−	0.0743372i
$757$	4.05528			0.147392			0.0736959	−	0.997281i	$-0.476521\pi$
$757$	4.05528			0.147392			0.0736959	+	0.997281i	$0.476521\pi$
$758$	−6.71396	+	11.6289i	−0.243862	+	0.422381i
$759$	−1.83154	−	3.17233i	−0.0664808	−	0.115148i
$760$	−6.34364	−	10.9875i	−0.230108	−	0.398559i
$761$	−14.4445	+	25.0187i	−0.523614	+	0.906926i	0.476008	+	0.879441i	$0.342083\pi$
$761$	−14.4445	+	25.0187i	−0.523614	+	0.906926i	−0.999622	+	0.0274851i	$0.991250\pi$
$762$	31.4065			1.13774
$763$	9.08472	+	27.0190i	0.328889	+	0.978153i
$764$	6.27127			0.226887
$765$	−4.46428	+	7.73236i	−0.161406	+	0.279564i
$766$	−5.18877	−	8.98721i	−0.187478	−	0.324721i
$767$	−10.6410	−	18.4308i	−0.384225	−	0.665496i
$768$	−8.37682	+	14.5091i	−0.302272	+	0.523551i
$769$	42.5217			1.53337			0.766685	−	0.642023i	$-0.221905\pi$
$769$	42.5217			1.53337			0.766685	+	0.642023i	$0.221905\pi$
$770$	−31.7133	+	35.9520i	−1.14287	+	1.29562i
$771$	10.1070			0.363994
$772$	6.17262	−	10.6913i	0.222158	−	0.384788i
$773$	8.50326	+	14.7281i	0.305841	+	0.529732i	0.977448	−	0.211175i	$-0.0677291\pi$
$773$	8.50326	+	14.7281i	0.305841	+	0.529732i	−0.671607	+	0.740907i	$0.734396\pi$
$774$	5.60767	+	9.71278i	0.201564	+	0.349119i
$775$	−3.73540	+	6.46990i	−0.134180	+	0.232406i
$776$	13.9456			0.500618
$777$	−14.0935	−	2.84573i	−0.505600	−	0.102090i
$778$	8.29411			0.297358
$779$	1.52694	−	2.64474i	0.0547084	−	0.0947577i
$780$	−2.30446	−	3.99145i	−0.0825130	−	0.142917i
$781$	−25.9225	−	44.8991i	−0.927581	−	1.60662i
$782$	−2.54056	+	4.40039i	−0.0908504	+	0.157358i
$783$	−0.852794			−0.0304764
$784$	27.6992	−	21.0011i	0.989258	−	0.750040i
$785$	−39.9134			−1.42457
$786$	−10.6969	+	18.5277i	−0.381548	+	0.660860i
$787$	−9.68118	−	16.7683i	−0.345097	−	0.597725i	0.640275	−	0.768146i	$-0.278821\pi$
$787$	−9.68118	−	16.7683i	−0.345097	−	0.597725i	−0.985371	+	0.170421i	$0.945487\pi$
$788$	−3.65009	−	6.32215i	−0.130029	−	0.225217i
$789$	3.64611	−	6.31525i	0.129805	−	0.224829i
$790$	21.7934			0.775375
$791$	−10.0095	−	2.02109i	−0.355895	−	0.0718617i
$792$	−7.28274			−0.258781
$793$	2.08398	−	3.60956i	0.0740043	−	0.128179i
$794$	18.3551	+	31.7920i	0.651399	+	1.12826i
$795$	10.0329	+	17.3774i	0.355829	+	0.616314i
$796$	−6.78824	+	11.7576i	−0.240603	+	0.416736i
$797$	−20.7380			−0.734579			−0.367289	−	0.930107i	$-0.619714\pi$
$797$	−20.7380			−0.734579			−0.367289	+	0.930107i	$0.619714\pi$
$798$	6.35608	−	7.20561i	0.225003	−	0.255076i
$799$	35.5003			1.25591
$800$	−8.04024	+	13.9261i	−0.284265	+	0.492362i
$801$	−8.09248	−	14.0166i	−0.285934	−	0.495252i
$802$	19.1044	+	33.0897i	0.674598	+	1.16844i
$803$	18.7366	−	32.4528i	0.661202	−	1.14523i
$804$	9.36826			0.330393
$805$	2.48597	+	7.39356i	0.0876190	+	0.260589i
$806$	−6.51168			−0.229364
$807$	9.49686	−	16.4490i	0.334305	−	0.579034i
$808$	−8.88385	−	15.3873i	−0.312533	−	0.541323i
$809$	14.1601	+	24.5260i	0.497843	+	0.862289i	0.999997	−	0.00248937i	$-0.000792392\pi$
$809$	14.1601	+	24.5260i	0.497843	+	0.862289i	−0.502154	+	0.864778i	$0.667459\pi$
$810$	2.47329	−	4.28386i	0.0869025	−	0.150520i
$811$	−18.6782			−0.655881			−0.327940	−	0.944698i	$-0.606354\pi$
$811$	−18.6782			−0.655881			−0.327940	+	0.944698i	$0.606354\pi$
$812$	0.586076	+	1.74306i	0.0205672	+	0.0611693i
$813$	−8.35578			−0.293050
$814$	16.6996	−	28.9245i	0.585320	−	1.01380i
$815$	−20.1620	−	34.9216i	−0.706244	−	1.22325i
$816$	7.51929	+	13.0238i	0.263228	+	0.455924i
$817$	−7.23434	+	12.5302i	−0.253098	+	0.438378i
$818$	30.6715			1.07240
$819$	−3.35699	+	3.80567i	−0.117303	+	0.132981i
$820$	−3.39026			−0.118393
$821$	12.2080	−	21.1449i	0.426063	−	0.737963i	−0.570456	−	0.821328i	$-0.693233\pi$
$821$	12.2080	−	21.1449i	0.426063	−	0.737963i	0.996519	+	0.0833650i	$0.0265667\pi$
$822$	16.3927	+	28.3930i	0.571761	+	0.990319i
$823$	18.5031	+	32.0483i	0.644977	+	1.11713i	0.984307	+	0.176466i	$0.0564665\pi$
$823$	18.5031	+	32.0483i	0.644977	+	1.11713i	−0.339330	+	0.940668i	$0.610200\pi$
$824$	−1.14293	+	1.97961i	−0.0398158	+	0.0689631i
$825$	−13.5246			−0.470865
$826$	−48.2798	−	9.74858i	−1.67987	−	0.339197i
$827$	−42.8466			−1.48992			−0.744961	−	0.667108i	$-0.767532\pi$
$827$	−42.8466			−1.48992			−0.744961	+	0.667108i	$0.767532\pi$
$828$	0.407518	−	0.705841i	0.0141622	−	0.0245297i
$829$	−6.68745	−	11.5830i	−0.232265	−	0.402294i	0.726210	−	0.687473i	$-0.241280\pi$
$829$	−6.68745	−	11.5830i	−0.232265	−	0.402294i	−0.958474	+	0.285179i	$0.907947\pi$
$830$	35.2567	+	61.0664i	1.22378	+	2.11965i
$831$	−5.72499	+	9.91597i	−0.198598	+	0.343981i
$832$	5.03324			0.174496
$833$	−2.64551	−	21.0333i	−0.0916615	−	0.728762i
$834$	12.8457			0.444811
$835$	−6.48552	+	11.2333i	−0.224441	+	0.388743i
$836$	3.23111	+	5.59645i	0.111750	+	0.193557i
$837$	−1.01172	−	1.75235i	−0.0349702	−	0.0605702i
$838$	−5.93983	+	10.2881i	−0.205188	+	0.355396i
$839$	−53.2311			−1.83774			−0.918871	−	0.394559i	$-0.870897\pi$
$839$	−53.2311			−1.83774			−0.918871	+	0.394559i	$0.870897\pi$
$840$	15.2013	+	3.06943i	0.524496	+	0.105905i
$841$	−28.2727			−0.974922
$842$	19.9922	−	34.6275i	0.688976	−	1.19334i
$843$	3.14117	+	5.44067i	0.108188	+	0.187387i
$844$	0.226264	+	0.391900i	0.00778831	+	0.0134898i
$845$	13.7404	−	23.7991i	0.472684	−	0.818712i
$846$	−19.6678			−0.676192
$847$	−4.23236	+	4.79804i	−0.145426	+	0.164863i
$848$	33.7972			1.16060
$849$	7.76954	−	13.4572i	0.266650	−	0.461851i
$850$	9.38008	+	16.2468i	0.321734	+	0.557260i
$851$	−2.71717	−	4.70627i	−0.0931433	−	0.161329i
$852$	5.76775	−	9.99003i	0.197600	−	0.342253i
$853$	37.5791			1.28668			0.643341	−	0.765579i	$-0.277548\pi$
$853$	37.5791			1.28668			0.643341	+	0.765579i	$0.277548\pi$
$854$	−3.07424	−	9.14315i	−0.105198	−	0.312872i
$855$	6.38147			0.218242
$856$	−2.93436	+	5.08246i	−0.100294	+	0.173715i
$857$	2.68703	+	4.65407i	0.0917871	+	0.158980i	0.908263	−	0.418399i	$-0.137409\pi$
$857$	2.68703	+	4.65407i	0.0917871	+	0.158980i	−0.816476	+	0.577379i	$0.804075\pi$
$858$	−5.89413	−	10.2089i	−0.201222	−	0.348527i
$859$	−10.3374	+	17.9050i	−0.352709	+	0.610910i	−0.986723	−	0.162412i	$-0.948073\pi$
$859$	−10.3374	+	17.9050i	−0.352709	+	0.610910i	0.634014	+	0.773322i	$0.281406\pi$
$860$	16.0624			0.547723
$861$	1.18967	+	3.53822i	0.0405440	+	0.120582i
$862$	9.27462			0.315895
$863$	20.4030	−	35.3390i	0.694526	−	1.20296i	−0.275814	−	0.961211i	$-0.588947\pi$
$863$	20.4030	−	35.3390i	0.694526	−	1.20296i	0.970340	−	0.241744i	$-0.0777194\pi$
$864$	−2.17767	−	3.77184i	−0.0740860	−	0.128321i
$865$	−2.65375	−	4.59643i	−0.0902302	−	0.156283i
$866$	14.8453	−	25.7129i	0.504465	−	0.873760i
$867$	−7.82858			−0.265872
$868$	−2.88640	+	3.27219i	−0.0979708	+	0.111065i
$869$	16.1387			0.547467
$870$	−2.10921	+	3.65325i	−0.0715088	+	0.123857i
$871$	−11.0233	−	19.0930i	−0.373511	−	0.646940i
$872$	10.7101	+	18.5505i	0.362691	+	0.628200i
$873$	−3.50719	+	6.07464i	−0.118701	+	0.205595i
$874$	3.63162			0.122841
$875$	−10.0000	−	2.01919i	−0.338063	−	0.0682610i
$876$	8.33779			0.281708
$877$	21.1081	−	36.5603i	0.712771	−	1.23455i	−0.251043	−	0.967976i	$-0.580773\pi$
$877$	21.1081	−	36.5603i	0.712771	−	1.23455i	0.963813	−	0.266579i	$-0.0858933\pi$
$878$	−2.96116	−	5.12889i	−0.0999344	−	0.173092i
$879$	−6.92415	−	11.9930i	−0.233546	−	0.404513i
$880$	−26.8144	+	46.4439i	−0.903914	+	1.56562i
$881$	−34.8993			−1.17579			−0.587893	−	0.808938i	$-0.700043\pi$
$881$	−34.8993			−1.17579			−0.587893	+	0.808938i	$0.700043\pi$
$882$	1.46566	+	11.6528i	0.0493513	+	0.392371i
$883$	−56.9299			−1.91585			−0.957923	−	0.287027i	$-0.907333\pi$
$883$	−56.9299			−1.91585			−0.957923	+	0.287027i	$0.907333\pi$
$884$	−2.36715	+	4.10002i	−0.0796157	+	0.137899i
$885$	−16.3563	−	28.3300i	−0.549811	−	0.952301i
$886$	31.5406	+	54.6299i	1.05963	+	1.83533i
$887$	−20.4084	+	35.3484i	−0.685246	+	1.18688i	0.288113	+	0.957596i	$0.406972\pi$
$887$	−20.4084	+	35.3484i	−0.685246	+	1.18688i	−0.973359	+	0.229285i	$0.926361\pi$
$888$	−10.8042			−0.362566
$889$	−48.5455	−	9.80222i	−1.62816	−	0.328756i
$890$	−80.0602			−2.68362
$891$	1.83154	−	3.17233i	0.0613590	−	0.106277i
$892$	−6.19176	−	10.7244i	−0.207315	−	0.359081i
$893$	−12.6865	−	21.9737i	−0.424537	−	0.735320i
$894$	−7.08997	+	12.2802i	−0.237124	+	0.410711i
$895$	63.3312			2.11693
$896$	22.9513	−	26.0189i	0.766750	−	0.869231i
$897$	−1.91805			−0.0640419
$898$	−32.4343	+	56.1779i	−1.08235	+	1.87468i
$899$	0.862791	+	1.49440i	0.0287757	+	0.0498409i
$900$	−1.50461	−	2.60605i	−0.0501535	−	0.0868684i
$901$	10.3058	−	17.8501i	0.343335	−	0.594674i
$902$	−8.67129			−0.288722
$903$	−5.63643	−	16.7634i	−0.187569	−	0.557851i
$904$	−7.67337			−0.255213
$905$	31.3869	−	54.3637i	1.04334	−	1.80711i
$906$	4.13280	+	7.15823i	0.137303	+	0.237816i
$907$	24.8218	+	42.9926i	0.824194	+	1.42755i	0.902534	+	0.430620i	$0.141705\pi$
$907$	24.8218	+	42.9926i	0.824194	+	1.42755i	−0.0783393	+	0.996927i	$0.524962\pi$
$908$	−11.0665	+	19.1678i	−0.367255	+	0.636105i
$909$	8.93684			0.296416
$910$	8.00016	+	23.7934i	0.265203	+	0.788743i
$911$	−33.8661			−1.12203			−0.561016	−	0.827805i	$-0.689589\pi$
$911$	−33.8661			−1.12203			−0.561016	+	0.827805i	$0.689589\pi$
$912$	5.37423	−	9.30844i	0.177959	−	0.308233i
$913$	26.1086	+	45.2215i	0.864070	+	1.49661i
$914$	27.5965	+	47.7986i	0.912813	+	1.58104i
$915$	3.20329	−	5.54826i	0.105897	−	0.183420i
$916$	−18.0518			−0.596448
$917$	22.3171	−	25.2999i	0.736975	−	0.835476i
$918$	−5.08113			−0.167702
$919$	−7.37949	+	12.7817i	−0.243427	+	0.421628i	−0.961688	−	0.274146i	$-0.911605\pi$
$919$	−7.37949	+	12.7817i	−0.243427	+	0.421628i	0.718261	+	0.695774i	$0.244938\pi$
$920$	2.93076	+	5.07623i	0.0966243	+	0.167358i
$921$	10.2556	+	17.7632i	0.337934	+	0.585318i
$922$	27.9358	−	48.3862i	0.920017	−	1.59352i
$923$	−27.1469			−0.893551
$924$	−7.74275	−	1.56340i	−0.254718	−	0.0514322i
$925$	−20.0642			−0.659708
$926$	−35.2125	+	60.9899i	−1.15716	+	2.00425i
$927$	−0.574873	−	0.995710i	−0.0188813	−	0.0327034i
$928$	1.85711	+	3.21661i	0.0609626	+	0.105590i
$929$	12.5881	−	21.8031i	0.413001	−	0.715338i	−0.582216	−	0.813034i	$-0.697814\pi$
$929$	12.5881	−	21.8031i	0.413001	−	0.715338i	0.995216	+	0.0976963i	$0.0311474\pi$
$930$	−10.0091			−0.328212
$931$	−12.0736	+	9.15403i	−0.395697	+	0.300011i
$932$	−2.57406			−0.0843160
$933$	0.490808	−	0.850105i	0.0160683	−	0.0278312i
$934$	−31.7699	−	55.0272i	−1.03954	−	1.80054i
$935$	16.3530	+	28.3243i	0.534802	+	0.926304i
$936$	−1.90668	+	3.30247i	−0.0623218	+	0.107944i
$937$	1.20275			0.0392923			0.0196461	−	0.999807i	$-0.493746\pi$
$937$	1.20275			0.0392923			0.0196461	+	0.999807i	$0.493746\pi$
$938$	−50.0145	−	10.0988i	−1.63303	−	0.329739i
$939$	−4.04432			−0.131981
$940$	−14.0839	+	24.3940i	−0.459366	+	0.795645i
$941$	4.13733	+	7.16606i	0.134873	+	0.233607i	0.925549	−	0.378628i	$-0.123604\pi$
$941$	4.13733	+	7.16606i	0.134873	+	0.233607i	−0.790676	+	0.612235i	$0.790271\pi$
$942$	−11.3571	−	19.6711i	−0.370035	−	0.640919i
$943$	−0.705447	+	1.22187i	−0.0229725	+	0.0397896i
$944$	−55.0986			−1.79331
$945$	−5.16003	+	5.84970i	−0.167856	+	0.190291i
$946$	41.0828			1.33572
$947$	16.5976	−	28.7478i	0.539349	−	0.934180i	−0.459590	−	0.888131i	$-0.652004\pi$
$947$	16.5976	−	28.7478i	0.539349	−	0.934180i	0.998939	−	0.0460485i	$-0.0146629\pi$
$948$	1.79542	+	3.10977i	0.0583127	+	0.101000i
$949$	−9.81081	−	16.9928i	−0.318472	−	0.551610i
$950$	6.70419	−	11.6120i	0.217513	−	0.376743i
$951$	−14.9070			−0.483394
$952$	−5.07691	−	15.0993i	−0.164543	−	0.489371i
$953$	14.3543			0.464982			0.232491	−	0.972599i	$-0.425312\pi$
$953$	14.3543			0.464982			0.232491	+	0.972599i	$0.425312\pi$
$954$	−5.70958	+	9.88928i	−0.184854	+	0.320177i
$955$	−11.3426	−	19.6459i	−0.367037	−	0.635727i
$956$	−10.7473	−	18.6149i	−0.347593	−	0.602048i
$957$	−1.56193	+	2.70534i	−0.0504900	+	0.0874513i
$958$	21.2329			0.686004
$959$	−16.4768	−	49.0038i	−0.532062	−	1.58241i
$960$	7.73660			0.249698
$961$	13.4528	−	23.3010i	0.433963	−	0.751645i
$962$	−8.74417	−	15.1454i	−0.281923	−	0.488306i
$963$	−1.47593	−	2.55639i	−0.0475612	−	0.0823784i
$964$	5.11211	−	8.85444i	0.164650	−	0.285182i
$965$	−44.6567			−1.43755
$966$	−2.93651	+	3.32899i	−0.0944806	+	0.107108i
$967$	−37.8148			−1.21604			−0.608021	−	0.793921i	$-0.708036\pi$
$967$	−37.8148			−1.21604			−0.608021	+	0.793921i	$0.708036\pi$
$968$	−2.40387	+	4.16362i	−0.0772633	+	0.133824i
$969$	−3.27753	−	5.67685i	−0.105289	−	0.182367i
$970$	17.3486	+	30.0487i	0.557030	+	0.964804i
$971$	15.5209	−	26.8829i	0.498088	−	0.862714i	−0.501909	−	0.864920i	$-0.667369\pi$
$971$	15.5209	−	26.8829i	0.498088	−	0.862714i	0.999998	+	0.00220588i	$0.000702154\pi$
$972$	0.815035			0.0261423
$973$	−19.8558	−	4.00925i	−0.636549	−	0.128531i
$974$	31.3926			1.00588
$975$	−3.54084	+	6.13292i	−0.113398	+	0.196411i
$976$	−5.39537	−	9.34505i	−0.172702	−	0.299128i
$977$	26.4808	+	45.8661i	0.847196	+	1.46739i	0.883701	+	0.468052i	$0.155044\pi$
$977$	26.4808	+	45.8661i	0.847196	+	1.46739i	−0.0365051	+	0.999333i	$0.511623\pi$
$978$	11.4739	−	19.8734i	0.366896	−	0.635483i
$979$	−59.2869			−1.89482
$980$	15.5026	+	6.52661i	0.495212	+	0.208485i
$981$	−10.7740			−0.343988
$982$	34.9206	−	60.4842i	1.11436	−	1.93013i
$983$	23.7571	+	41.1485i	0.757734	+	1.31243i	0.944004	+	0.329935i	$0.107027\pi$
$983$	23.7571	+	41.1485i	0.757734	+	1.31243i	−0.186269	+	0.982499i	$0.559640\pi$
$984$	1.40253	+	2.42925i	0.0447110	+	0.0774417i
$985$	−13.2035	+	22.8692i	−0.420700	+	0.728674i
$986$	4.33316			0.137996
$987$	30.4008	+	6.13848i	0.967668	+	0.195390i
$988$	3.38372			0.107651
$989$	3.34226	−	5.78897i	0.106278	−	0.184079i
$990$	−9.05987	−	15.6922i	−0.287942	−	0.498730i
$991$	8.66006	+	14.9997i	0.275096	+	0.476480i	0.970159	−	0.242468i	$-0.0779571\pi$
$991$	8.66006	+	14.9997i	0.275096	+	0.476480i	−0.695063	+	0.718948i	$0.744624\pi$
$992$	−4.40640	+	7.63211i	−0.139903	+	0.242320i
$993$	−8.12770			−0.257925
$994$	−41.5615	+	47.1164i	−1.31825	+	1.49444i
$995$	49.1104			1.55691
$996$	−5.80916	+	10.0618i	−0.184070	+	0.318819i
$997$	−2.75044	−	4.76391i	−0.0871074	−	0.150874i	0.819180	−	0.573537i	$-0.194429\pi$
$997$	−2.75044	−	4.76391i	−0.0871074	−	0.150874i	−0.906287	+	0.422662i	$0.861096\pi$
$998$	19.8829	+	34.4382i	0.629383	+	1.09012i
$999$	2.71717	−	4.70627i	0.0859674	−	0.148900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.g.415.6	yes	16
7.2	even	3		3381.2.a.bf.1.3		8
7.4	even	3	inner	483.2.i.g.277.6	✓	16
7.5	odd	6		3381.2.a.be.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.6	✓	16	7.4	even	3	inner
483.2.i.g.415.6	yes	16	1.1	even	1	trivial
3381.2.a.be.1.3		8	7.5	odd	6
3381.2.a.bf.1.3		8	7.2	even	3

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.838903 - 1.45302i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.407518 - 0.705841i) q^{4} +(-1.47412 + 2.55325i) q^{5} -1.67781 q^{6} +(2.59341 + 0.523657i) q^{7} +1.98814 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.838903 - 1.45302i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.407518 - 0.705841i) q^{4} +(-1.47412 + 2.55325i) q^{5} -1.67781 q^{6} +(2.59341 + 0.523657i) q^{7} +1.98814 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.47329 + 4.28386i) q^{10} +(1.83154 + 3.17233i) q^{11} +(-0.407518 + 0.705841i) q^{12} +1.91805 q^{13} +(2.93651 - 3.32899i) q^{14} +2.94824 q^{15} +(2.48289 - 4.30050i) q^{16} +(-1.51422 - 2.62270i) q^{17} +(0.838903 + 1.45302i) q^{18} +(-1.08225 + 1.87451i) q^{19} +2.40292 q^{20} +(-0.843205 - 2.50779i) q^{21} +6.14595 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.994071 - 1.72178i) q^{24} +(-1.84606 - 3.19747i) q^{25} +(1.60906 - 2.78697i) q^{26} +1.00000 q^{27} +(-0.687242 - 2.04394i) q^{28} -0.852794 q^{29} +(2.47329 - 4.28386i) q^{30} +(-1.01172 - 1.75235i) q^{31} +(-2.17767 - 3.77184i) q^{32} +(1.83154 - 3.17233i) q^{33} -5.08113 q^{34} +(-5.16003 + 5.84970i) q^{35} +0.815035 q^{36} +(2.71717 - 4.70627i) q^{37} +(1.81581 + 3.14507i) q^{38} +(-0.959026 - 1.66108i) q^{39} +(-2.93076 + 5.07623i) q^{40} -1.41089 q^{41} +(-4.35124 - 0.878596i) q^{42} +6.68453 q^{43} +(1.49277 - 2.58556i) q^{44} +(-1.47412 - 2.55325i) q^{45} +(-0.838903 - 1.45302i) q^{46} +(-5.86116 + 10.1518i) q^{47} -4.96579 q^{48} +(6.45157 + 2.71612i) q^{49} -6.19467 q^{50} +(-1.51422 + 2.62270i) q^{51} +(-0.781640 - 1.35384i) q^{52} +(3.40300 + 5.89417i) q^{53} +(0.838903 - 1.45302i) q^{54} -10.7997 q^{55} +(5.15607 + 1.04110i) q^{56} +2.16450 q^{57} +(-0.715412 + 1.23913i) q^{58} +(-5.54782 - 9.60911i) q^{59} +(-1.20146 - 2.08099i) q^{60} +(1.08651 - 1.88189i) q^{61} -3.39495 q^{62} +(-1.75021 + 1.98413i) q^{63} +2.62414 q^{64} +(-2.82744 + 4.89727i) q^{65} +(-3.07298 - 5.32255i) q^{66} +(-5.74715 - 9.95435i) q^{67} +(-1.23414 + 2.13759i) q^{68} -1.00000 q^{69} +(4.17098 + 12.4050i) q^{70} -14.1534 q^{71} +(-0.994071 + 1.72178i) q^{72} +(-5.11498 - 8.85941i) q^{73} +(-4.55888 - 7.89622i) q^{74} +(-1.84606 + 3.19747i) q^{75} +1.76415 q^{76} +(3.08873 + 9.18625i) q^{77} -3.21812 q^{78} +(2.20288 - 3.81550i) q^{79} +(7.32017 + 12.6789i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.18360 + 2.05006i) q^{82} +14.2550 q^{83} +(-1.42648 + 1.61714i) q^{84} +8.92856 q^{85} +(5.60767 - 9.71278i) q^{86} +(0.426397 + 0.738542i) q^{87} +(3.64137 + 6.30704i) q^{88} +(-8.09248 + 14.0166i) q^{89} -4.94658 q^{90} +(4.97430 + 1.00440i) q^{91} -0.815035 q^{92} +(-1.01172 + 1.75235i) q^{93} +(9.83389 + 17.0328i) q^{94} +(-3.19074 - 5.52652i) q^{95} +(-2.17767 + 3.77184i) q^{96} +7.01439 q^{97} +(9.35882 - 7.09572i) q^{98} -3.66309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Introduction

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