LMFDB - Embedded newform 471.2.e.c.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.1
Character	$\chi$	$=$	471.301
Dual form			471.2.e.c.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59656 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.74215 q^{4} +(-0.824270 + 1.42768i) q^{5} +(1.29828 - 2.24869i) q^{6} +0.523535 q^{7} -7.12017 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-2.59656 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.74215 q^{4} +(-0.824270 + 1.42768i) q^{5} +(1.29828 - 2.24869i) q^{6} +0.523535 q^{7} -7.12017 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.14027 - 3.70706i) q^{10} +(-2.28219 + 3.95287i) q^{11} +(-2.37107 + 4.10682i) q^{12} +(-1.25497 - 2.17367i) q^{13} -1.35939 q^{14} +(-0.824270 - 1.42768i) q^{15} +9.00368 q^{16} +(1.81072 - 3.13625i) q^{17} +(1.29828 + 2.24869i) q^{18} +(-3.72719 + 6.45567i) q^{19} +(-3.90881 + 6.77026i) q^{20} +(-0.261768 + 0.453395i) q^{21} +(5.92586 - 10.2639i) q^{22} +2.22378 q^{23} +(3.56008 - 6.16625i) q^{24} +(1.14116 + 1.97655i) q^{25} +(3.25860 + 5.64407i) q^{26} +1.00000 q^{27} +2.48268 q^{28} +0.501196 q^{29} +(2.14027 + 3.70706i) q^{30} +(-2.75215 - 4.76687i) q^{31} -9.13830 q^{32} +(-2.28219 - 3.95287i) q^{33} +(-4.70164 + 8.14349i) q^{34} +(-0.431534 + 0.747439i) q^{35} +(-2.37107 - 4.10682i) q^{36} +(-2.94703 - 5.10440i) q^{37} +(9.67788 - 16.7626i) q^{38} +2.50993 q^{39} +(5.86894 - 10.1653i) q^{40} -8.08786 q^{41} +(0.679696 - 1.17727i) q^{42} +(1.43081 + 2.47823i) q^{43} +(-10.8225 + 18.7451i) q^{44} +1.64854 q^{45} -5.77419 q^{46} +(-2.41757 - 4.18735i) q^{47} +(-4.50184 + 7.79741i) q^{48} -6.72591 q^{49} +(-2.96309 - 5.13223i) q^{50} +(1.81072 + 3.13625i) q^{51} +(-5.95124 - 10.3079i) q^{52} +(-5.22713 - 9.05366i) q^{53} -2.59656 q^{54} +(-3.76228 - 6.51647i) q^{55} -3.72766 q^{56} +(-3.72719 - 6.45567i) q^{57} -1.30139 q^{58} -8.07787 q^{59} +(-3.90881 - 6.77026i) q^{60} +(-2.59489 + 4.49447i) q^{61} +(7.14614 + 12.3775i) q^{62} +(-0.261768 - 0.453395i) q^{63} +5.72083 q^{64} +4.13773 q^{65} +(5.92586 + 10.2639i) q^{66} +0.0931257 q^{67} +(8.58669 - 14.8726i) q^{68} +(-1.11189 + 1.92585i) q^{69} +(1.12051 - 1.94077i) q^{70} +(-4.73864 - 8.20756i) q^{71} +(3.56008 + 6.16625i) q^{72} +(-0.147965 + 0.256283i) q^{73} +(7.65214 + 13.2539i) q^{74} -2.28232 q^{75} +(-17.6749 + 30.6138i) q^{76} +(-1.19481 + 2.06947i) q^{77} -6.51721 q^{78} +10.9065 q^{79} +(-7.42146 + 12.8543i) q^{80} +(-0.500000 + 0.866025i) q^{81} +21.0006 q^{82} +(-4.18448 - 7.24774i) q^{83} +(-1.24134 + 2.15007i) q^{84} +(2.98504 + 5.17024i) q^{85} +(-3.71518 - 6.43488i) q^{86} +(-0.250598 + 0.434049i) q^{87} +(16.2496 - 28.1451i) q^{88} +(4.88663 - 8.46389i) q^{89} -4.28054 q^{90} +(-0.657020 - 1.13799i) q^{91} +10.5455 q^{92} +5.50430 q^{93} +(6.27738 + 10.8727i) q^{94} +(-6.14441 - 10.6424i) q^{95} +(4.56915 - 7.91400i) q^{96} +(-3.47444 - 6.01790i) q^{97} +17.4643 q^{98} +4.56439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.59656			−1.83605			−0.918024	−	0.396524i	$-0.870216\pi$
$2$	−2.59656			−1.83605			−0.918024	+	0.396524i	$0.870216\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	4.74215			2.37107
$5$	−0.824270	+	1.42768i	−0.368625	+	0.638476i	−0.989351	−	0.145551i	$-0.953505\pi$
$5$	−0.824270	+	1.42768i	−0.368625	+	0.638476i	0.620726	+	0.784027i	$0.286838\pi$
$6$	1.29828	−	2.24869i	0.530022	−	0.918024i
$7$	0.523535			0.197878			0.0989388	−	0.995094i	$-0.468455\pi$
$7$	0.523535			0.197878			0.0989388	+	0.995094i	$0.468455\pi$
$8$	−7.12017			−2.51736
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.14027	−	3.70706i	0.676813	−	1.17227i
$11$	−2.28219	+	3.95287i	−0.688107	+	1.19184i	0.284342	+	0.958723i	$0.408225\pi$
$11$	−2.28219	+	3.95287i	−0.688107	+	1.19184i	−0.972450	+	0.233114i	$0.925109\pi$
$12$	−2.37107	+	4.10682i	−0.684470	+	1.18554i
$13$	−1.25497	−	2.17367i	−0.348065	−	0.602867i	0.637840	−	0.770169i	$-0.279828\pi$
$13$	−1.25497	−	2.17367i	−0.348065	−	0.602867i	−0.985906	+	0.167302i	$0.946495\pi$
$14$	−1.35939			−0.363313
$15$	−0.824270	−	1.42768i	−0.212825	−	0.368625i
$16$	9.00368			2.25092
$17$	1.81072	−	3.13625i	0.439163	−	0.760653i	−0.558462	−	0.829530i	$-0.688608\pi$
$17$	1.81072	−	3.13625i	0.439163	−	0.760653i	0.997625	+	0.0688770i	$0.0219416\pi$
$18$	1.29828	+	2.24869i	0.306008	+	0.530022i
$19$	−3.72719	+	6.45567i	−0.855075	+	1.48103i	0.0215006	+	0.999769i	$0.493156\pi$
$19$	−3.72719	+	6.45567i	−0.855075	+	1.48103i	−0.876576	+	0.481264i	$0.840178\pi$
$20$	−3.90881	+	6.77026i	−0.874036	+	1.51388i
$21$	−0.261768	+	0.453395i	−0.0571224	+	0.0989388i
$22$	5.92586	−	10.2639i	1.26340	−	2.18827i
$23$	2.22378			0.463690			0.231845	−	0.972753i	$-0.425524\pi$
$23$	2.22378			0.463690			0.231845	+	0.972753i	$0.425524\pi$
$24$	3.56008	−	6.16625i	0.726699	−	1.25868i
$25$	1.14116	+	1.97655i	0.228232	+	0.395309i
$26$	3.25860	+	5.64407i	0.639065	+	1.10689i
$27$	1.00000			0.192450
$28$	2.48268			0.469183
$29$	0.501196			0.0930698			0.0465349	−	0.998917i	$-0.485182\pi$
$29$	0.501196			0.0930698			0.0465349	+	0.998917i	$0.485182\pi$
$30$	2.14027	+	3.70706i	0.390758	+	0.676813i
$31$	−2.75215	−	4.76687i	−0.494301	−	0.856154i	0.505677	−	0.862723i	$-0.331243\pi$
$31$	−2.75215	−	4.76687i	−0.494301	−	0.856154i	−0.999978	+	0.00656824i	$0.997909\pi$
$32$	−9.13830			−1.61544
$33$	−2.28219	−	3.95287i	−0.397279	−	0.688107i
$34$	−4.70164	+	8.14349i	−0.806325	+	1.39660i
$35$	−0.431534	+	0.747439i	−0.0729426	+	0.126340i
$36$	−2.37107	−	4.10682i	−0.395179	−	0.684470i
$37$	−2.94703	−	5.10440i	−0.484488	−	0.839158i	0.515353	−	0.856978i	$-0.327661\pi$
$37$	−2.94703	−	5.10440i	−0.484488	−	0.839158i	−0.999841	+	0.0178199i	$0.994327\pi$
$38$	9.67788	−	16.7626i	1.56996	−	2.71925i
$39$	2.50993			0.401911
$40$	5.86894	−	10.1653i	0.927960	−	1.60727i
$41$	−8.08786			−1.26311			−0.631555	−	0.775331i	$-0.717583\pi$
$41$	−8.08786			−1.26311			−0.631555	+	0.775331i	$0.717583\pi$
$42$	0.679696	−	1.17727i	0.104879	−	0.181657i
$43$	1.43081	+	2.47823i	0.218196	+	0.377926i	0.954256	−	0.298989i	$-0.0966495\pi$
$43$	1.43081	+	2.47823i	0.218196	+	0.377926i	−0.736061	+	0.676916i	$0.763316\pi$
$44$	−10.8225	+	18.7451i	−1.63155	+	2.82593i
$45$	1.64854			0.245750
$46$	−5.77419			−0.851358
$47$	−2.41757	−	4.18735i	−0.352639	−	0.610788i	0.634072	−	0.773274i	$-0.281382\pi$
$47$	−2.41757	−	4.18735i	−0.352639	−	0.610788i	−0.986711	+	0.162486i	$0.948049\pi$
$48$	−4.50184	+	7.79741i	−0.649784	+	1.12546i
$49$	−6.72591			−0.960844
$50$	−2.96309	−	5.13223i	−0.419045	−	0.725807i
$51$	1.81072	+	3.13625i	0.253551	+	0.439163i
$52$	−5.95124	−	10.3079i	−0.825289	−	1.42944i
$53$	−5.22713	−	9.05366i	−0.718002	−	1.24362i	−0.961790	−	0.273787i	$-0.911724\pi$
$53$	−5.22713	−	9.05366i	−0.718002	−	1.24362i	0.243789	−	0.969828i	$-0.421610\pi$
$54$	−2.59656			−0.353348
$55$	−3.76228	−	6.51647i	−0.507306	−	0.878680i
$56$	−3.72766			−0.498129
$57$	−3.72719	−	6.45567i	−0.493678	−	0.855075i
$58$	−1.30139			−0.170881
$59$	−8.07787			−1.05165			−0.525825	−	0.850593i	$-0.676243\pi$
$59$	−8.07787			−1.05165			−0.525825	+	0.850593i	$0.676243\pi$
$60$	−3.90881	−	6.77026i	−0.504625	−	0.874036i
$61$	−2.59489	+	4.49447i	−0.332241	+	0.575458i	−0.982951	−	0.183868i	$-0.941138\pi$
$61$	−2.59489	+	4.49447i	−0.332241	+	0.575458i	0.650710	+	0.759326i	$0.274471\pi$
$62$	7.14614	+	12.3775i	0.907561	+	1.57194i
$63$	−0.261768	−	0.453395i	−0.0329796	−	0.0571224i
$64$	5.72083			0.715103
$65$	4.13773			0.513222
$66$	5.92586	+	10.2639i	0.729423	+	1.26340i
$67$	0.0931257			0.0113771			0.00568856	−	0.999984i	$-0.498189\pi$
$67$	0.0931257			0.0113771			0.00568856	+	0.999984i	$0.498189\pi$
$68$	8.58669	−	14.8726i	1.04129	−	1.80357i
$69$	−1.11189	+	1.92585i	−0.133856	+	0.231845i
$70$	1.12051	−	1.94077i	0.133926	−	0.231967i
$71$	−4.73864	−	8.20756i	−0.562373	−	0.974058i	−0.997289	−	0.0735869i	$-0.976555\pi$
$71$	−4.73864	−	8.20756i	−0.562373	−	0.974058i	0.434916	−	0.900471i	$-0.356778\pi$
$72$	3.56008	+	6.16625i	0.419560	+	0.726699i
$73$	−0.147965	+	0.256283i	−0.0173180	+	0.0299957i	−0.874555	−	0.484927i	$-0.838846\pi$
$73$	−0.147965	+	0.256283i	−0.0173180	+	0.0299957i	0.857237	+	0.514923i	$0.172179\pi$
$74$	7.65214	+	13.2539i	0.889544	+	1.54073i
$75$	−2.28232			−0.263539
$76$	−17.6749	+	30.6138i	−2.02745	+	3.51164i
$77$	−1.19481	+	2.06947i	−0.136161	+	0.235838i
$78$	−6.51721			−0.737929
$79$	10.9065			1.22708			0.613540	−	0.789663i	$-0.289745\pi$
$79$	10.9065			1.22708			0.613540	+	0.789663i	$0.289745\pi$
$80$	−7.42146	+	12.8543i	−0.829744	+	1.43716i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	21.0006			2.31913
$83$	−4.18448	−	7.24774i	−0.459307	−	0.795543i	0.539618	−	0.841910i	$-0.318569\pi$
$83$	−4.18448	−	7.24774i	−0.459307	−	0.795543i	−0.998924	+	0.0463676i	$0.985235\pi$
$84$	−1.24134	+	2.15007i	−0.135441	+	0.234591i
$85$	2.98504	+	5.17024i	0.323773	+	0.560791i
$86$	−3.71518	−	6.43488i	−0.400618	−	0.693891i
$87$	−0.250598	+	0.434049i	−0.0268669	+	0.0465349i
$88$	16.2496	−	28.1451i	1.73221	−	3.00028i
$89$	4.88663	−	8.46389i	0.517982	−	0.897171i	−0.481800	−	0.876281i	$-0.660017\pi$
$89$	4.88663	−	8.46389i	0.517982	−	0.897171i	0.999782	−	0.0208895i	$-0.00664981\pi$
$90$	−4.28054			−0.451208
$91$	−0.657020	−	1.13799i	−0.0688744	−	0.119294i
$92$	10.5455			1.09944
$93$	5.50430			0.570770
$94$	6.27738	+	10.8727i	0.647462	+	1.12144i
$95$	−6.14441	−	10.6424i	−0.630403	−	1.09189i
$96$	4.56915	−	7.91400i	0.466337	−	0.807719i
$97$	−3.47444	−	6.01790i	−0.352775	−	0.611025i	0.633959	−	0.773367i	$-0.281429\pi$
$97$	−3.47444	−	6.01790i	−0.352775	−	0.611025i	−0.986735	+	0.162341i	$0.948095\pi$
$98$	17.4643			1.76416
$99$	4.56439			0.458738
$100$	5.41155	+	9.37307i	0.541155	+	0.937307i
$101$	15.4185			1.53420			0.767099	−	0.641529i	$-0.221700\pi$
$101$	15.4185			1.53420			0.767099	+	0.641529i	$0.221700\pi$
$102$	−4.70164	−	8.14349i	−0.465532	−	0.806325i
$103$	−9.78555			−0.964199			−0.482100	−	0.876116i	$-0.660126\pi$
$103$	−9.78555			−0.964199			−0.482100	+	0.876116i	$0.660126\pi$
$104$	8.93558	+	15.4769i	0.876205	+	1.51763i
$105$	−0.431534	−	0.747439i	−0.0421134	−	0.0729426i
$106$	13.5726	+	23.5084i	1.31829	+	2.28334i
$107$	9.33710	+	16.1723i	0.902652	+	1.56344i	0.824039	+	0.566534i	$0.191716\pi$
$107$	9.33710	+	16.1723i	0.902652	+	1.56344i	0.0786134	+	0.996905i	$0.474951\pi$
$108$	4.74215			0.456313
$109$	−4.55636	+	7.89185i	−0.436420	+	0.755902i	−0.997410	−	0.0719205i	$-0.977087\pi$
$109$	−4.55636	+	7.89185i	−0.436420	+	0.755902i	0.560990	+	0.827822i	$0.310421\pi$
$110$	9.76902	+	16.9204i	0.931439	+	1.61330i
$111$	5.89405			0.559439
$112$	4.71374			0.445407
$113$	−8.79601	+	15.2351i	−0.827459	+	1.43320i	0.0725661	+	0.997364i	$0.476881\pi$
$113$	−8.79601	+	15.2351i	−0.827459	+	1.43320i	−0.900025	+	0.435838i	$0.856452\pi$
$114$	9.67788	+	16.7626i	0.906416	+	1.56996i
$115$	−1.83299	+	3.17484i	−0.170928	+	0.296055i
$116$	2.37675			0.220675
$117$	−1.25497	+	2.17367i	−0.116022	+	0.200956i
$118$	20.9747			1.93088
$119$	0.947974	−	1.64194i	0.0869006	−	0.150516i
$120$	5.86894	+	10.1653i	0.535758	+	0.927960i
$121$	−4.91681	−	8.51616i	−0.446983	−	0.774197i
$122$	6.73779	−	11.6702i	0.610011	−	1.05657i
$123$	4.04393	−	7.00429i	0.364629	−	0.631555i
$124$	−13.0511	−	22.6052i	−1.17202	−	2.03001i
$125$	−12.0052			−1.07378
$126$	0.679696	+	1.17727i	0.0605522	+	0.104879i
$127$	1.94838	+	3.37469i	0.172891	+	0.299456i	0.939429	−	0.342743i	$-0.111356\pi$
$127$	1.94838	+	3.37469i	0.172891	+	0.299456i	−0.766539	+	0.642198i	$0.778023\pi$
$128$	3.42210			0.302474
$129$	−2.86161			−0.251951
$130$	−10.7439			−0.942300
$131$	9.85648	+	17.0719i	0.861165	+	1.49158i	0.870805	+	0.491628i	$0.163598\pi$
$131$	9.85648	+	17.0719i	0.861165	+	1.49158i	−0.00964032	+	0.999954i	$0.503069\pi$
$132$	−10.8225	−	18.7451i	−0.941978	−	1.63155i
$133$	−1.95131	+	3.37977i	−0.169200	+	0.293063i
$134$	−0.241807			−0.0208889
$135$	−0.824270	+	1.42768i	−0.0709418	+	0.122875i
$136$	−12.8926	+	22.3306i	−1.10553	+	1.91484i
$137$	−3.87944	+	6.71939i	−0.331443	+	0.574076i	−0.982795	−	0.184700i	$-0.940869\pi$
$137$	−3.87944	+	6.71939i	−0.331443	+	0.574076i	0.651352	+	0.758776i	$0.274202\pi$
$138$	2.88709	−	5.00059i	0.245766	−	0.425679i
$139$	−9.85625	−	17.0715i	−0.835996	−	1.44799i	−0.893217	−	0.449626i	$-0.851557\pi$
$139$	−9.85625	−	17.0715i	−0.835996	−	1.44799i	0.0572207	−	0.998362i	$-0.481776\pi$
$140$	−2.04640	+	3.54447i	−0.172952	+	0.299562i
$141$	4.83514			0.407192
$142$	12.3042	+	21.3115i	1.03254	+	1.78842i
$143$	11.4563			0.958025
$144$	−4.50184	−	7.79741i	−0.375153	−	0.649784i
$145$	−0.413121	+	0.715546i	−0.0343078	+	0.0594229i
$146$	0.384202	−	0.665457i	0.0317968	−	0.0550736i
$147$	3.36296	−	5.82481i	0.277372	−	0.480422i
$148$	−13.9752	−	24.2058i	−1.14876	−	1.98971i
$149$	−3.47126			−0.284377			−0.142188	−	0.989840i	$-0.545414\pi$
$149$	−3.47126			−0.284377			−0.142188	+	0.989840i	$0.545414\pi$
$150$	5.92619			0.483871
$151$	−3.74278	+	6.48269i	−0.304583	+	0.527554i	−0.977169	−	0.212466i	$-0.931851\pi$
$151$	−3.74278	+	6.48269i	−0.304583	+	0.527554i	0.672585	+	0.740020i	$0.265184\pi$
$152$	26.5382	−	45.9655i	2.15253	−	3.72829i
$153$	−3.62143			−0.292776
$154$	3.10240	−	5.37351i	0.249998	−	0.433010i
$155$	9.07406			0.728846
$156$	11.9025			0.952961
$157$	−12.3332	−	2.21191i	−0.984295	−	0.176529i
$157$	−12.3332	−	2.21191i	−0.984295	−	0.176529i
$158$	−28.3195			−2.25298
$159$	10.4543			0.829077
$160$	7.53242	−	13.0465i	0.595490	−	1.03142i
$161$	1.16423			0.0917539
$162$	1.29828	−	2.24869i	0.102003	−	0.176674i
$163$	−6.41699	+	11.1146i	−0.502617	+	0.870559i	0.497378	+	0.867534i	$0.334296\pi$
$163$	−6.41699	+	11.1146i	−0.502617	+	0.870559i	−0.999995	+	0.00302501i	$0.999037\pi$
$164$	−38.3538			−2.99493
$165$	7.52457			0.585787
$166$	10.8653	+	18.8192i	0.843309	+	1.46065i
$167$	8.59982	−	14.8953i	0.665474	−	1.15263i	−0.313683	−	0.949528i	$-0.601563\pi$
$167$	8.59982	−	14.8953i	0.665474	−	1.15263i	0.979157	−	0.203107i	$-0.0651038\pi$
$168$	1.86383	−	3.22825i	0.143798	−	0.249065i
$169$	3.35011	−	5.80257i	0.257701	−	0.446351i
$170$	−7.75084	−	13.4249i	−0.594463	−	1.02964i
$171$	7.45437			0.570050
$172$	6.78510	+	11.7521i	0.517359	+	0.896092i
$173$	2.42068			0.184041			0.0920204	−	0.995757i	$-0.470667\pi$
$173$	2.42068			0.184041			0.0920204	+	0.995757i	$0.470667\pi$
$174$	0.650694	−	1.12704i	0.0493290	−	0.0854403i
$175$	0.597437	+	1.03479i	0.0451620	+	0.0782229i
$176$	−20.5481	+	35.5904i	−1.54887	+	2.68273i
$177$	4.03893	−	6.99564i	0.303585	−	0.525825i
$178$	−12.6885	+	21.9770i	−0.951040	+	1.64725i
$179$	3.29047	−	5.69927i	0.245941	−	0.425983i	−0.716454	−	0.697634i	$-0.754236\pi$
$179$	3.29047	−	5.69927i	0.245941	−	0.425983i	0.962396	+	0.271651i	$0.0875696\pi$
$180$	7.81762			0.582691
$181$	−4.21105	+	7.29376i	−0.313005	+	0.542141i	−0.979011	−	0.203805i	$-0.934669\pi$
$181$	−4.21105	+	7.29376i	−0.313005	+	0.542141i	0.666006	+	0.745946i	$0.268002\pi$
$182$	1.70599	+	2.95487i	0.126457	+	0.219029i
$183$	−2.59489	−	4.49447i	−0.191819	−	0.332241i
$184$	−15.8337			−1.16727
$185$	9.71658			0.714377
$186$	−14.2923			−1.04796
$187$	8.26481	+	14.3151i	0.604383	+	1.04682i
$188$	−11.4645	−	19.8571i	−0.836133	−	1.44822i
$189$	0.523535			0.0380816
$190$	15.9544	+	27.6338i	1.15745	+	2.00476i
$191$	−5.79997	+	10.0458i	−0.419671	+	0.726891i	−0.995906	−	0.0903926i	$-0.971188\pi$
$191$	−5.79997	+	10.0458i	−0.419671	+	0.726891i	0.576235	+	0.817284i	$0.304521\pi$
$192$	−2.86041	+	4.95438i	−0.206433	+	0.357552i
$193$	−10.2579	−	17.7672i	−0.738380	−	1.27891i	−0.953225	−	0.302263i	$-0.902258\pi$
$193$	−10.2579	−	17.7672i	−0.738380	−	1.27891i	0.214845	−	0.976648i	$-0.431075\pi$
$194$	9.02160	+	15.6259i	0.647713	+	1.12187i
$195$	−2.06886	+	3.58338i	−0.148154	+	0.256611i
$196$	−31.8953			−2.27823
$197$	−4.88857	+	8.46725i	−0.348296	+	0.603267i	−0.985947	−	0.167059i	$-0.946573\pi$
$197$	−4.88857	+	8.46725i	−0.348296	+	0.603267i	0.637651	+	0.770326i	$0.279906\pi$
$198$	−11.8517			−0.842265
$199$	0.797369	−	1.38108i	0.0565240	−	0.0979025i	−0.836379	−	0.548152i	$-0.815332\pi$
$199$	0.797369	−	1.38108i	0.0565240	−	0.0979025i	0.892903	+	0.450249i	$0.148665\pi$
$200$	−8.12524	−	14.0733i	−0.574542	−	0.995135i
$201$	−0.0465628	+	0.0806492i	−0.00328429	+	0.00568856i
$202$	−40.0351			−2.81686
$203$	0.262394			0.0184164
$204$	8.58669	+	14.8726i	0.601188	+	1.04129i
$205$	6.66657	−	11.5468i	0.465614	−	0.806467i
$206$	25.4088			1.77032
$207$	−1.11189	−	1.92585i	−0.0772817	−	0.133856i
$208$	−11.2993	−	19.5710i	−0.783467	−	1.35700i
$209$	−17.0123	−	29.4662i	−1.17677	−	2.03822i
$210$	1.12051	+	1.94077i	0.0773223	+	0.133926i
$211$	17.2111			1.18486			0.592430	−	0.805622i	$-0.298169\pi$
$211$	17.2111			1.18486			0.592430	+	0.805622i	$0.298169\pi$
$212$	−24.7878	−	42.9338i	−1.70244	−	2.94870i
$213$	9.47727			0.649372
$214$	−24.2444	−	41.9925i	−1.65731	−	2.87055i
$215$	−4.71748			−0.321730
$216$	−7.12017			−0.484466
$217$	−1.44085	−	2.49562i	−0.0978111	−	0.169414i
$218$	11.8309	−	20.4917i	0.801289	−	1.38787i
$219$	−0.147965	−	0.256283i	−0.00999857	−	0.0173180i
$220$	−17.8413	−	30.9021i	−1.20286	−	2.08342i
$221$	−9.08956			−0.611430
$222$	−15.3043			−1.02716
$223$	11.9714	+	20.7351i	0.801665	+	1.38853i	0.918519	+	0.395376i	$0.129386\pi$
$223$	11.9714	+	20.7351i	0.801665	+	1.38853i	−0.116854	+	0.993149i	$0.537281\pi$
$224$	−4.78422			−0.319659
$225$	1.14116	−	1.97655i	0.0760773	−	0.131770i
$226$	22.8394	−	39.5590i	1.51926	−	2.63143i
$227$	−14.1794	+	24.5595i	−0.941122	+	1.63007i	−0.177785	+	0.984069i	$0.556893\pi$
$227$	−14.1794	+	24.5595i	−0.941122	+	1.63007i	−0.763336	+	0.646001i	$0.776440\pi$
$228$	−17.6749	−	30.6138i	−1.17055	−	2.02745i
$229$	10.3736	+	17.9676i	0.685505	+	1.18733i	0.973278	+	0.229631i	$0.0737520\pi$
$229$	10.3736	+	17.9676i	0.685505	+	1.18733i	−0.287772	+	0.957699i	$0.592915\pi$
$230$	4.75949	−	8.24368i	0.313831	−	0.543572i
$231$	−1.19481	−	2.06947i	−0.0786126	−	0.136161i
$232$	−3.56860			−0.234290
$233$	0.790176	−	1.36863i	0.0517662	−	0.0896616i	−0.838981	−	0.544160i	$-0.816848\pi$
$233$	0.790176	−	1.36863i	0.0517662	−	0.0896616i	0.890747	+	0.454499i	$0.150182\pi$
$234$	3.25860	−	5.64407i	0.213022	−	0.368964i
$235$	7.97092			0.519965
$236$	−38.3065			−2.49354
$237$	−5.45326	+	9.44533i	−0.354228	+	0.613540i
$238$	−2.46148	+	4.26340i	−0.159554	+	0.276355i
$239$	−12.9291			−0.836314			−0.418157	−	0.908375i	$-0.637324\pi$
$239$	−12.9291			−0.836314			−0.418157	+	0.908375i	$0.637324\pi$
$240$	−7.42146	−	12.8543i	−0.479053	−	0.829744i
$241$	−5.88551	+	10.1940i	−0.379119	+	0.656654i	−0.990934	−	0.134347i	$-0.957106\pi$
$241$	−5.88551	+	10.1940i	−0.379119	+	0.656654i	0.611815	+	0.791001i	$0.290440\pi$
$242$	12.7668	+	22.1128i	0.820682	+	1.42146i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−12.3053	+	21.3135i	−0.787768	+	1.36445i
$245$	5.54396	−	9.60243i	0.354191	−	0.613477i
$246$	−10.5003	+	18.1871i	−0.669476	+	1.15957i
$247$	18.7100			1.19049
$248$	19.5958	+	33.9409i	1.24433	+	2.15525i
$249$	8.36897			0.530362
$250$	31.1722			1.97151
$251$	14.3408	+	24.8389i	0.905181	+	1.56782i	0.820674	+	0.571397i	$0.193598\pi$
$251$	14.3408	+	24.8389i	0.905181	+	1.56782i	0.0845079	+	0.996423i	$0.473068\pi$
$252$	−1.24134	−	2.15007i	−0.0781971	−	0.135441i
$253$	−5.07509	+	8.79032i	−0.319068	+	0.552643i
$254$	−5.05910	−	8.76261i	−0.317436	−	0.549815i
$255$	−5.97008			−0.373861
$256$	−20.3274			−1.27046
$257$	−3.69377	−	6.39780i	−0.230411	−	0.399084i	0.727518	−	0.686089i	$-0.240674\pi$
$257$	−3.69377	−	6.39780i	−0.230411	−	0.399084i	−0.957929	+	0.287005i	$0.907340\pi$
$258$	7.43036			0.462594
$259$	−1.54287	−	2.67233i	−0.0958694	−	0.166051i
$260$	19.6217			1.21689
$261$	−0.250598	−	0.434049i	−0.0155116	−	0.0268669i
$262$	−25.5930	−	44.3284i	−1.58114	−	2.73862i
$263$	8.11204	+	14.0505i	0.500210	+	0.866389i	1.00000		0.000242362i	$7.71462e-5\pi$
$263$	8.11204	+	14.0505i	0.500210	+	0.866389i	−0.499790	+	0.866147i	$0.666590\pi$
$264$	16.2496	+	28.1451i	1.00009	+	1.73221i
$265$	17.2343			1.05869
$266$	5.06671	−	8.77580i	0.310660	−	0.538079i
$267$	4.88663	+	8.46389i	0.299057	+	0.517982i
$268$	0.441616			0.0269760
$269$	3.44117			0.209812			0.104906	−	0.994482i	$-0.466546\pi$
$269$	3.44117			0.209812			0.104906	+	0.994482i	$0.466546\pi$
$270$	2.14027	−	3.70706i	0.130253	−	0.225604i
$271$	13.8598	+	24.0059i	0.841924	+	1.45825i	0.888266	+	0.459329i	$0.151910\pi$
$271$	13.8598	+	24.0059i	0.841924	+	1.45825i	−0.0463425	+	0.998926i	$0.514757\pi$
$272$	16.3031	−	28.2378i	0.988521	−	1.71217i
$273$	1.31404			0.0795293
$274$	10.0732	−	17.4473i	0.608545	−	1.05403i
$275$	−10.4174			−0.628192
$276$	−5.27275	+	9.13267i	−0.317382	+	0.549722i
$277$	−5.93208	−	10.2747i	−0.356424	−	0.617345i	0.630937	−	0.775834i	$-0.282671\pi$
$277$	−5.93208	−	10.2747i	−0.356424	−	0.617345i	−0.987361	+	0.158490i	$0.949337\pi$
$278$	25.5924	+	44.3273i	1.53493	+	2.65858i
$279$	−2.75215	+	4.76687i	−0.164767	+	0.285385i
$280$	3.07259	−	5.32189i	0.183623	−	0.318044i
$281$	10.5937	+	18.3489i	0.631969	+	1.09460i	0.987149	+	0.159804i	$0.0510863\pi$
$281$	10.5937	+	18.3489i	0.631969	+	1.09460i	−0.355180	+	0.934798i	$0.615580\pi$
$282$	−12.5548			−0.747625
$283$	−7.11718	−	12.3273i	−0.423073	−	0.732783i	0.573166	−	0.819440i	$-0.305715\pi$
$283$	−7.11718	−	12.3273i	−0.423073	−	0.732783i	−0.996238	+	0.0866562i	$0.972382\pi$
$284$	−22.4713	−	38.9215i	−1.33343	−	2.30956i
$285$	12.2888			0.727927
$286$	−29.7471			−1.75898
$287$	−4.23428			−0.249941
$288$	4.56915	+	7.91400i	0.269240	+	0.466337i
$289$	1.94261	+	3.36470i	0.114271	+	0.197923i
$290$	1.07269	−	1.85796i	0.0629908	−	0.109103i
$291$	6.94887			0.407350
$292$	−0.701674	+	1.21533i	−0.0410623	+	0.0711221i
$293$	8.76086	−	15.1743i	0.511815	−	0.886490i	−0.488091	−	0.872793i	$-0.662307\pi$
$293$	8.76086	−	15.1743i	0.511815	−	0.886490i	0.999906	−	0.0136971i	$-0.00436007\pi$
$294$	−8.73213	+	15.1245i	−0.509268	+	0.882079i
$295$	6.65834	−	11.5326i	0.387664	−	0.671453i
$296$	20.9833	+	36.3442i	1.21963	+	2.11246i
$297$	−2.28219	+	3.95287i	−0.132426	+	0.229369i
$298$	9.01335			0.522130
$299$	−2.79077	−	4.83376i	−0.161394	−	0.279543i
$300$	−10.8231			−0.624872
$301$	0.749077	+	1.29744i	0.0431761	+	0.0747832i
$302$	9.71838	−	16.8327i	0.559230	−	0.968615i
$303$	−7.70925	+	13.3528i	−0.442885	+	0.767099i
$304$	−33.5584	+	58.1248i	−1.92470	+	3.33369i
$305$	−4.27777	−	7.40931i	−0.244944	−	0.424256i
$306$	9.40329			0.537550
$307$	14.7465			0.841625			0.420813	−	0.907148i	$-0.361745\pi$
$307$	14.7465			0.841625			0.420813	+	0.907148i	$0.361745\pi$
$308$	−5.66596	+	9.81373i	−0.322848	+	0.559189i
$309$	4.89278	−	8.47454i	0.278340	−	0.482100i
$310$	−23.5614			−1.33820
$311$	4.68473	−	8.11420i	0.265647	−	0.460114i	−0.702086	−	0.712092i	$-0.747748\pi$
$311$	4.68473	−	8.11420i	0.265647	−	0.460114i	0.967733	+	0.251978i	$0.0810811\pi$
$312$	−17.8712			−1.01175
$313$	−10.8973			−0.615950			−0.307975	−	0.951394i	$-0.599651\pi$
$313$	−10.8973			−0.615950			−0.307975	+	0.951394i	$0.599651\pi$
$314$	32.0239	+	5.74336i	1.80721	+	0.324116i
$315$	0.863068			0.0486284
$316$	51.7204			2.90950
$317$	−6.51533	+	11.2849i	−0.365937	+	0.633822i	−0.988926	−	0.148409i	$-0.952585\pi$
$317$	−6.51533	+	11.2849i	−0.365937	+	0.633822i	0.622989	+	0.782231i	$0.285918\pi$
$318$	−27.1452			−1.52223
$319$	−1.14383	+	1.98117i	−0.0640420	+	0.110924i
$320$	−4.71550	+	8.16749i	−0.263605	+	0.456577i
$321$	−18.6742			−1.04229
$322$	−3.02299			−0.168465
$323$	13.4978	+	23.3788i	0.751035	+	1.30083i
$324$	−2.37107	+	4.10682i	−0.131726	+	0.228157i
$325$	2.86424	−	4.96100i	0.158879	−	0.275187i
$326$	16.6621	−	28.8597i	0.922830	−	1.59839i
$327$	−4.55636	−	7.89185i	−0.251967	−	0.436420i
$328$	57.5869			3.17970
$329$	−1.26568	−	2.19223i	−0.0697793	−	0.120861i
$330$	−19.5380			−1.07553
$331$	2.12578	−	3.68195i	0.116843	−	0.202378i	−0.801672	−	0.597764i	$-0.796056\pi$
$331$	2.12578	−	3.68195i	0.116843	−	0.202378i	0.918515	+	0.395386i	$0.129389\pi$
$332$	−19.8434	−	34.3698i	−1.08905	−	1.88629i
$333$	−2.94703	+	5.10440i	−0.161496	+	0.279719i
$334$	−22.3300	+	38.6767i	−1.22184	+	2.11629i
$335$	−0.0767607	+	0.132953i	−0.00419388	+	0.00726402i
$336$	−2.35687	+	4.08222i	−0.128578	+	0.222703i
$337$	−9.29270			−0.506205			−0.253103	−	0.967439i	$-0.581451\pi$
$337$	−9.29270			−0.506205			−0.253103	+	0.967439i	$0.581451\pi$
$338$	−8.69879	+	15.0667i	−0.473152	+	0.819523i
$339$	−8.79601	−	15.2351i	−0.477734	−	0.827459i
$340$	14.1555	+	24.5180i	0.767689	+	1.32968i
$341$	25.1238			1.36053
$342$	−19.3558			−1.04664
$343$	−7.18600			−0.388007
$344$	−10.1876	−	17.6454i	−0.549277	−	0.951377i
$345$	−1.83299	−	3.17484i	−0.0986851	−	0.170928i
$346$	−6.28545			−0.337908
$347$	−7.50251	−	12.9947i	−0.402756	−	0.697594i	0.591301	−	0.806451i	$-0.298614\pi$
$347$	−7.50251	−	12.9947i	−0.402756	−	0.697594i	−0.994057	+	0.108857i	$0.965281\pi$
$348$	−1.18837	+	2.05832i	−0.0637035	+	0.110338i
$349$	15.5717	−	26.9710i	0.833533	−	1.44372i	−0.0616858	−	0.998096i	$-0.519648\pi$
$349$	15.5717	−	26.9710i	0.833533	−	1.44372i	0.895219	−	0.445626i	$-0.147019\pi$
$350$	−1.55128	−	2.68690i	−0.0829196	−	0.143621i
$351$	−1.25497	−	2.17367i	−0.0669852	−	0.116022i
$352$	20.8554	−	36.1225i	1.11159	−	1.92534i
$353$	5.44659			0.289893			0.144946	−	0.989440i	$-0.453699\pi$
$353$	5.44659			0.289893			0.144946	+	0.989440i	$0.453699\pi$
$354$	−10.4874	+	18.1646i	−0.557397	+	0.965439i
$355$	15.6237			0.829217
$356$	23.1731	−	40.1370i	1.22817	−	2.12726i
$357$	0.947974	+	1.64194i	0.0501721	+	0.0869006i
$358$	−8.54392	+	14.7985i	−0.451560	+	0.782126i
$359$	11.0145			0.581321			0.290661	−	0.956826i	$-0.406125\pi$
$359$	11.0145			0.581321			0.290661	+	0.956826i	$0.406125\pi$
$360$	−11.7379			−0.618640
$361$	−18.2838	−	31.6685i	−0.962306	−	1.66676i
$362$	10.9343	−	18.9387i	0.574692	−	0.995397i
$363$	9.83362			0.516131
$364$	−3.11568	−	5.39652i	−0.163306	−	0.282855i
$365$	−0.243927	−	0.422493i	−0.0127677	−	0.0221143i
$366$	6.73779	+	11.6702i	0.352190	+	0.610011i
$367$	6.33526	+	10.9730i	0.330698	+	0.572786i	0.982649	−	0.185475i	$-0.0593825\pi$
$367$	6.33526	+	10.9730i	0.330698	+	0.572786i	−0.651951	+	0.758261i	$0.726049\pi$
$368$	20.0222			1.04373
$369$	4.04393	+	7.00429i	0.210518	+	0.364629i
$370$	−25.2297			−1.31163
$371$	−2.73659	−	4.73991i	−0.142076	−	0.246084i
$372$	26.1022			1.35334
$373$	−34.6424			−1.79371			−0.896857	−	0.442321i	$-0.854155\pi$
$373$	−34.6424			−1.79371			−0.896857	+	0.442321i	$0.854155\pi$
$374$	−21.4601	−	37.1700i	−1.10968	−	1.92202i
$375$	6.00259	−	10.3968i	0.309973	−	0.536888i
$376$	17.2135	+	29.8147i	0.887718	+	1.53757i
$377$	−0.628985	−	1.08943i	−0.0323944	−	0.0561087i
$378$	−1.35939			−0.0699196
$379$	−2.27947			−0.117089			−0.0585443	−	0.998285i	$-0.518646\pi$
$379$	−2.27947			−0.117089			−0.0585443	+	0.998285i	$0.518646\pi$
$380$	−29.1377	−	50.4680i	−1.49473	−	2.58895i
$381$	−3.89676			−0.199637
$382$	15.0600	−	26.0847i	0.770536	−	1.33461i
$383$	−12.5860	+	21.7996i	−0.643116	+	1.11391i	0.341618	+	0.939839i	$0.389025\pi$
$383$	−12.5860	+	21.7996i	−0.643116	+	1.11391i	−0.984733	+	0.174070i	$0.944308\pi$
$384$	−1.71105	+	2.96362i	−0.0873166	+	0.151237i
$385$	−1.96969	−	3.41160i	−0.100385	−	0.173871i
$386$	26.6353	+	46.1337i	1.35570	+	2.34814i
$387$	1.43081	−	2.47823i	0.0727320	−	0.125975i
$388$	−16.4763	−	28.5378i	−0.836457	−	1.44879i
$389$	−12.5729			−0.637470			−0.318735	−	0.947844i	$-0.603258\pi$
$389$	−12.5729			−0.637470			−0.318735	+	0.947844i	$0.603258\pi$
$390$	5.37194	−	9.30447i	0.272019	−	0.471150i
$391$	4.02664	−	6.97434i	0.203636	−	0.352707i
$392$	47.8896			2.41879
$393$	−19.7130			−0.994388
$394$	12.6935	−	21.9858i	0.639489	−	1.10763i
$395$	−8.98992	+	15.5710i	−0.452332	+	0.783462i
$396$	21.6450			1.08770
$397$	−12.7148	−	22.0228i	−0.638140	−	1.10529i	−0.985841	−	0.167685i	$-0.946371\pi$
$397$	−12.7148	−	22.0228i	−0.638140	−	1.10529i	0.347701	−	0.937605i	$-0.386962\pi$
$398$	−2.07042	+	3.58607i	−0.103781	+	0.179754i
$399$	−1.95131	−	3.37977i	−0.0976878	−	0.169200i
$400$	10.2746	+	17.7962i	0.513731	+	0.889809i
$401$	2.03917	−	3.53195i	0.101831	−	0.176377i	−0.810608	−	0.585589i	$-0.800863\pi$
$401$	2.03917	−	3.53195i	0.101831	−	0.176377i	0.912439	+	0.409212i	$0.134196\pi$
$402$	0.120903	−	0.209411i	0.00603011	−	0.0104445i
$403$	−6.90772	+	11.9645i	−0.344098	+	0.595995i
$404$	73.1168			3.63770
$405$	−0.824270	−	1.42768i	−0.0409583	−	0.0709418i
$406$	−0.681323			−0.0338135
$407$	26.9027			1.33352
$408$	−12.8926	−	22.3306i	−0.638279	−	1.10553i
$409$	15.1997	+	26.3266i	0.751575	+	1.30177i	0.947059	+	0.321059i	$0.104039\pi$
$409$	15.1997	+	26.3266i	0.751575	+	1.30177i	−0.195485	+	0.980707i	$0.562628\pi$
$410$	−17.3102	+	29.9821i	−0.854889	+	1.48071i
$411$	−3.87944	−	6.71939i	−0.191359	−	0.331443i
$412$	−46.4045			−2.28619
$413$	−4.22905			−0.208098
$414$	2.88709	+	5.00059i	0.141893	+	0.245766i
$415$	13.7966			0.677247
$416$	11.4683	+	19.8636i	0.562278	+	0.973894i
$417$	19.7125			0.965325
$418$	44.1736	+	76.5109i	2.16060	+	3.74227i
$419$	−11.3511	−	19.6607i	−0.554539	−	0.960490i	−0.997939	−	0.0641662i	$-0.979561\pi$
$419$	−11.3511	−	19.6607i	−0.554539	−	0.960490i	0.443400	−	0.896324i	$-0.353772\pi$
$420$	−2.04640	−	3.54447i	−0.0998540	−	0.172952i
$421$	−8.33945	−	14.4443i	−0.406440	−	0.703974i	0.588048	−	0.808826i	$-0.299897\pi$
$421$	−8.33945	−	14.4443i	−0.406440	−	0.703974i	−0.994488	+	0.104852i	$0.966563\pi$
$422$	−44.6897			−2.17546
$423$	−2.41757	+	4.18735i	−0.117546	+	0.203596i
$424$	37.2180	+	64.4635i	1.80747	+	3.13063i
$425$	8.26527			0.400924
$426$	−24.6083			−1.19228
$427$	−1.35851	+	2.35301i	−0.0657431	+	0.113870i
$428$	44.2779	+	76.6916i	2.14025	+	3.70703i
$429$	−5.72816	+	9.92146i	−0.276558	+	0.479012i
$430$	12.2492			0.590711
$431$	−9.39231	+	16.2680i	−0.452412	+	0.783600i	−0.998535	−	0.0541048i	$-0.982770\pi$
$431$	−9.39231	+	16.2680i	−0.452412	+	0.783600i	0.546124	+	0.837705i	$0.316103\pi$
$432$	9.00368			0.433190
$433$	−2.66167	+	4.61015i	−0.127912	+	0.221550i	−0.922867	−	0.385118i	$-0.874161\pi$
$433$	−2.66167	+	4.61015i	−0.127912	+	0.221550i	0.794956	+	0.606668i	$0.207494\pi$
$434$	3.74125	+	6.48004i	0.179586	+	0.311052i
$435$	−0.413121	−	0.715546i	−0.0198076	−	0.0343078i
$436$	−21.6069	+	37.4243i	−1.03478	+	1.79230i
$437$	−8.28844	+	14.3560i	−0.396490	+	0.686741i
$438$	0.384202	+	0.665457i	0.0183579	+	0.0317968i
$439$	19.8584			0.947792			0.473896	−	0.880581i	$-0.342847\pi$
$439$	19.8584			0.947792			0.473896	+	0.880581i	$0.342847\pi$
$440$	26.7881	+	46.3983i	1.27707	+	2.21195i
$441$	3.36296	+	5.82481i	0.160141	+	0.277372i
$442$	23.6016			1.12262
$443$	−24.5628			−1.16701			−0.583507	−	0.812108i	$-0.698320\pi$
$443$	−24.5628			−1.16701			−0.583507	+	0.812108i	$0.698320\pi$
$444$	27.9505			1.32647
$445$	8.05580	+	13.9531i	0.381882	+	0.661438i
$446$	−31.0846	−	53.8400i	−1.47190	−	2.54940i
$447$	1.73563	−	3.00620i	0.0820925	−	0.142188i
$448$	2.99505			0.141503
$449$	11.9577	−	20.7113i	0.564318	−	0.977428i	−0.432794	−	0.901493i	$-0.642472\pi$
$449$	11.9577	−	20.7113i	0.564318	−	0.977428i	0.997113	−	0.0759355i	$-0.0241943\pi$
$450$	−2.96309	+	5.13223i	−0.139682	+	0.241936i
$451$	18.4580	−	31.9703i	0.869156	−	1.50542i
$452$	−41.7120	+	72.2473i	−1.96197	+	3.39823i
$453$	−3.74278	−	6.48269i	−0.175851	−	0.304583i
$454$	36.8178	−	63.7703i	1.72795	−	2.99289i
$455$	2.16624			0.101555
$456$	26.5382	+	45.9655i	1.24276	+	2.15253i
$457$	34.4429			1.61117			0.805586	−	0.592478i	$-0.201850\pi$
$457$	34.4429			1.61117			0.805586	+	0.592478i	$0.201850\pi$
$458$	−26.9357	−	46.6539i	−1.25862	−	2.18000i
$459$	1.81072	−	3.13625i	0.0845170	−	0.146388i
$460$	−8.69233	+	15.0556i	−0.405282	+	0.701969i
$461$	−17.3853	+	30.1122i	−0.809714	+	1.40247i	0.103347	+	0.994645i	$0.467045\pi$
$461$	−17.3853	+	30.1122i	−0.809714	+	1.40247i	−0.913062	+	0.407821i	$0.866289\pi$
$462$	3.10240	+	5.37351i	0.144337	+	0.249998i
$463$	23.9159			1.11146			0.555732	−	0.831361i	$-0.312438\pi$
$463$	23.9159			1.11146			0.555732	+	0.831361i	$0.312438\pi$
$464$	4.51261			0.209493
$465$	−4.53703	+	7.85837i	−0.210400	+	0.364423i
$466$	−2.05174	+	3.55373i	−0.0950452	+	0.164623i
$467$	−6.25093			−0.289258			−0.144629	−	0.989486i	$-0.546199\pi$
$467$	−6.25093			−0.289258			−0.144629	+	0.989486i	$0.546199\pi$
$468$	−5.95124	+	10.3079i	−0.275096	+	0.476481i
$469$	0.0487546			0.00225128
$470$	−20.6970			−0.954681
$471$	8.08216	−	9.57490i	0.372406	−	0.441188i
$472$	57.5158			2.64738
$473$	−13.0615			−0.600569
$474$	14.1598	−	24.5254i	0.650379	−	1.12649i
$475$	−17.0132			−0.780621
$476$	4.49543	−	7.78632i	0.206048	−	0.356885i
$477$	−5.22713	+	9.05366i	−0.239334	+	0.414538i
$478$	33.5712			1.53551
$479$	2.90636			0.132795			0.0663975	−	0.997793i	$-0.478849\pi$
$479$	2.90636			0.132795			0.0663975	+	0.997793i	$0.478849\pi$
$480$	7.53242	+	13.0465i	0.343806	+	0.595490i
$481$	−7.39684	+	12.8117i	−0.337267	+	0.584164i
$482$	15.2821	−	26.4694i	0.696081	−	1.20565i
$483$	−0.582113	+	1.00825i	−0.0264871	+	0.0458770i
$484$	−23.3162	−	40.3849i	−1.05983	−	1.83568i
$485$	11.4555			0.520167
$486$	1.29828	+	2.24869i	0.0588913	+	0.102003i
$487$	−14.2063			−0.643750			−0.321875	−	0.946782i	$-0.604313\pi$
$487$	−14.2063			−0.643750			−0.321875	+	0.946782i	$0.604313\pi$
$488$	18.4760	−	32.0014i	0.836370	−	1.44864i
$489$	−6.41699	−	11.1146i	−0.290186	−	0.502617i
$490$	−14.3953	+	24.9333i	−0.650312	+	1.12637i
$491$	−21.5330	+	37.2963i	−0.971772	+	1.68316i	−0.281570	+	0.959541i	$0.590855\pi$
$491$	−21.5330	+	37.2963i	−0.971772	+	1.68316i	−0.690202	+	0.723617i	$0.742478\pi$
$492$	19.1769	−	33.2154i	0.864562	−	1.49746i
$493$	0.907524	−	1.57188i	0.0408728	−	0.0707938i
$494$	−48.5817			−2.18579
$495$	−3.76228	+	6.51647i	−0.169102	+	0.292893i
$496$	−24.7795	−	42.9193i	−1.11263	−	1.92713i
$497$	−2.48084	−	4.29694i	−0.111281	−	0.192744i
$498$	−21.7306			−0.973770
$499$	30.3527			1.35877			0.679386	−	0.733781i	$-0.262246\pi$
$499$	30.3527			1.35877			0.679386	+	0.733781i	$0.262246\pi$
$500$	−56.9304			−2.54600
$501$	8.59982	+	14.8953i	0.384211	+	0.665474i
$502$	−37.2367	−	64.4959i	−1.66196	−	2.87859i
$503$	−41.4994			−1.85037			−0.925184	−	0.379519i	$-0.876089\pi$
$503$	−41.4994			−1.85037			−0.925184	+	0.379519i	$0.876089\pi$
$504$	1.86383	+	3.22825i	0.0830215	+	0.143798i
$505$	−12.7090	+	22.0126i	−0.565543	+	0.979549i
$506$	13.1778	−	22.8246i	0.585825	−	1.01468i
$507$	3.35011	+	5.80257i	0.148784	+	0.257701i
$508$	9.23951	+	16.0033i	0.409937	+	0.710032i
$509$	7.50019	−	12.9907i	0.332440	−	0.575803i	−0.650550	−	0.759464i	$-0.725461\pi$
$509$	7.50019	−	12.9907i	0.332440	−	0.575803i	0.982990	+	0.183661i	$0.0587948\pi$
$510$	15.5017			0.686426
$511$	−0.0774651	+	0.134173i	−0.00342685	+	0.00593548i
$512$	45.9371			2.03015
$513$	−3.72719	+	6.45567i	−0.164559	+	0.285025i
$514$	9.59112	+	16.6123i	0.423046	+	0.732738i
$515$	8.06593	−	13.9706i	0.355427	−	0.615618i
$516$	−13.5702			−0.597394
$517$	22.0694			0.970613
$518$	4.00617	+	6.93888i	0.176021	+	0.304877i
$519$	−1.21034	+	2.09637i	−0.0531280	+	0.0920204i
$520$	−29.4613			−1.29196
$521$	−14.3236	−	24.8092i	−0.627528	−	1.08691i	−0.988046	−	0.154158i	$-0.950734\pi$
$521$	−14.3236	−	24.8092i	−0.627528	−	1.08691i	0.360518	−	0.932752i	$-0.382600\pi$
$522$	0.650694	+	1.12704i	0.0284801	+	0.0493290i
$523$	−9.47902	−	16.4181i	−0.414489	−	0.717915i	0.580886	−	0.813985i	$-0.302706\pi$
$523$	−9.47902	−	16.4181i	−0.414489	−	0.717915i	−0.995375	+	0.0960697i	$0.969373\pi$
$524$	46.7409	+	80.9576i	2.04189	+	3.53665i
$525$	−1.19487			−0.0521486
$526$	−21.0634	−	36.4829i	−0.918410	−	1.59073i
$527$	−19.9335			−0.868315
$528$	−20.5481	−	35.5904i	−0.894242	−	1.54887i
$529$	−18.0548			−0.784991
$530$	−44.7499			−1.94381
$531$	4.03893	+	6.99564i	0.175275	+	0.303585i
$532$	−9.25341	+	16.0274i	−0.401186	+	0.694875i
$533$	10.1500	+	17.5803i	0.439645	+	0.761488i
$534$	−12.6885	−	21.9770i	−0.549083	−	0.951040i
$535$	−30.7852			−1.33096
$536$	−0.663070			−0.0286403
$537$	3.29047	+	5.69927i	0.141994	+	0.245941i
$538$	−8.93521			−0.385224
$539$	15.3498	−	26.5867i	0.661164	−	1.14517i
$540$	−3.90881	+	6.77026i	−0.168208	+	0.291345i
$541$	−15.0157	+	26.0079i	−0.645574	+	1.11817i	0.338595	+	0.940932i	$0.390048\pi$
$541$	−15.0157	+	26.0079i	−0.645574	+	1.11817i	−0.984169	+	0.177234i	$0.943285\pi$
$542$	−35.9879	−	62.3329i	−1.54581	−	2.67743i
$543$	−4.21105	−	7.29376i	−0.180714	−	0.313005i
$544$	−16.5469	+	28.6600i	−0.709441	+	1.22879i
$545$	−7.51134	−	13.0100i	−0.321750	−	0.557288i
$546$	−3.41199			−0.146020
$547$	9.44610	−	16.3611i	0.403886	−	0.699551i	−0.590305	−	0.807180i	$-0.700993\pi$
$547$	9.44610	−	16.3611i	0.403886	−	0.699551i	0.994191	+	0.107629i	$0.0343259\pi$
$548$	−18.3969	+	31.8643i	−0.785876	+	1.36118i
$549$	5.18977			0.221494
$550$	27.0494			1.15339
$551$	−1.86805	+	3.23556i	−0.0795816	+	0.137839i
$552$	7.91684	−	13.7124i	0.336963	−	0.583637i
$553$	5.70995			0.242812
$554$	15.4030	+	26.6788i	0.654412	+	1.13347i
$555$	−4.85829	+	8.41480i	−0.206223	+	0.357188i
$556$	−46.7398	−	80.9557i	−1.98221	−	3.43329i
$557$	0.538440	+	0.932606i	0.0228144	+	0.0395158i	0.877207	−	0.480112i	$-0.159404\pi$
$557$	0.538440	+	0.932606i	0.0228144	+	0.0395158i	−0.854393	+	0.519628i	$0.826071\pi$
$558$	7.14614	−	12.3775i	0.302520	−	0.523980i
$559$	3.59123	−	6.22019i	0.151893	−	0.263086i
$560$	−3.88539	+	6.72970i	−0.164188	+	0.284382i
$561$	−16.5296			−0.697881
$562$	−27.5073	−	47.6440i	−1.16033	−	2.00974i
$563$	−5.61481			−0.236636			−0.118318	−	0.992976i	$-0.537750\pi$
$563$	−5.61481			−0.236636			−0.118318	+	0.992976i	$0.537750\pi$
$564$	22.9289			0.965483
$565$	−14.5006	−	25.1157i	−0.610044	−	1.05663i
$566$	18.4802	+	32.0087i	0.776782	+	1.34543i
$567$	−0.261768	+	0.453395i	−0.0109932	+	0.0190408i
$568$	33.7399	+	58.4392i	1.41569	+	2.45205i
$569$	−30.0148			−1.25829			−0.629144	−	0.777289i	$-0.716594\pi$
$569$	−30.0148			−1.25829			−0.629144	+	0.777289i	$0.716594\pi$
$570$	−31.9087			−1.33651
$571$	11.9480	+	20.6946i	0.500009	+	0.866040i	1.00000		9.92878e-6i	$3.16043e-6\pi$
$571$	11.9480	+	20.6946i	0.500009	+	0.866040i	−0.499991	+	0.866030i	$0.666664\pi$
$572$	54.3275			2.27155
$573$	−5.79997	−	10.0458i	−0.242297	−	0.419671i
$574$	10.9946			0.458905
$575$	2.53769	+	4.39540i	0.105829	+	0.183301i
$576$	−2.86041	−	4.95438i	−0.119184	−	0.206433i
$577$	−13.1121	−	22.7108i	−0.545862	−	0.945461i	−0.998552	−	0.0537931i	$-0.982869\pi$
$577$	−13.1121	−	22.7108i	−0.545862	−	0.945461i	0.452690	−	0.891668i	$-0.350464\pi$
$578$	−5.04411	−	8.73665i	−0.209807	−	0.363397i
$579$	20.5158			0.852607
$580$	−1.95908	+	3.39323i	−0.0813464	+	0.140896i
$581$	−2.19072	−	3.79445i	−0.0908865	−	0.157420i
$582$	−18.0432			−0.747914
$583$	47.7173			1.97625
$584$	1.05354	−	1.82478i	0.0435957	−	0.0755100i
$585$	−2.06886	−	3.58338i	−0.0855370	−	0.148154i
$586$	−22.7482	+	39.4010i	−0.939717	+	1.62764i
$587$	6.66513			0.275100			0.137550	−	0.990495i	$-0.456077\pi$
$587$	6.66513			0.275100			0.137550	+	0.990495i	$0.456077\pi$
$588$	15.9476	−	27.6221i	0.657669	−	1.13912i
$589$	41.0311			1.69066
$590$	−17.2888	+	29.9451i	−0.711769	+	1.23282i
$591$	−4.88857	−	8.46725i	−0.201089	−	0.348296i
$592$	−26.5341	−	45.9584i	−1.09054	−	1.88888i
$593$	0.979588	−	1.69670i	0.0402269	−	0.0696750i	−0.845211	−	0.534433i	$-0.820525\pi$
$593$	0.979588	−	1.69670i	0.0402269	−	0.0696750i	0.885438	+	0.464758i	$0.153859\pi$
$594$	5.92586	−	10.2639i	0.243141	−	0.421133i
$595$	1.56277	+	2.70680i	0.0640674	+	0.110968i
$596$	−16.4612			−0.674278
$597$	0.797369	+	1.38108i	0.0326342	+	0.0565240i
$598$	7.24642	+	12.5512i	0.296328	+	0.513255i
$599$	−30.3223			−1.23894			−0.619468	−	0.785022i	$-0.712651\pi$
$599$	−30.3223			−1.23894			−0.619468	+	0.785022i	$0.712651\pi$
$600$	16.2505			0.663423
$601$	−36.8214			−1.50198			−0.750988	−	0.660316i	$-0.770422\pi$
$601$	−36.8214			−1.50198			−0.750988	+	0.660316i	$0.770422\pi$
$602$	−1.94503	−	3.36889i	−0.0792734	−	0.137306i
$603$	−0.0465628	−	0.0806492i	−0.00189619	−	0.00328429i
$604$	−17.7488	+	30.7419i	−0.722190	+	1.25087i
$605$	16.2111			0.659075
$606$	20.0176	−	34.6714i	0.813158	−	1.40843i
$607$	8.41564	−	14.5763i	0.341580	−	0.591635i	−0.643146	−	0.765744i	$-0.722371\pi$
$607$	8.41564	−	14.5763i	0.341580	−	0.591635i	0.984726	+	0.174109i	$0.0557045\pi$
$608$	34.0601	−	58.9939i	1.38132	−	2.39252i
$609$	−0.131197	+	0.227240i	−0.00531637	+	0.00920822i
$610$	11.1075	+	19.2388i	0.449730	+	0.778955i
$611$	−6.06794	+	10.5100i	−0.245483	+	0.425188i
$612$	−17.1734			−0.694193
$613$	0.133512	+	0.231249i	0.00539250	+	0.00934008i	0.868709	−	0.495323i	$-0.164950\pi$
$613$	0.133512	+	0.231249i	0.00539250	+	0.00934008i	−0.863317	+	0.504663i	$0.831617\pi$
$614$	−38.2901			−1.54526
$615$	6.66657	+	11.5468i	0.268822	+	0.465614i
$616$	8.50723	−	14.7350i	0.342766	−	0.593688i
$617$	18.6353	−	32.2772i	0.750228	−	1.29943i	−0.197484	−	0.980306i	$-0.563277\pi$
$617$	18.6353	−	32.2772i	0.750228	−	1.29943i	0.947712	−	0.319127i	$-0.103390\pi$
$618$	−12.7044	+	22.0047i	−0.511046	+	0.885158i
$619$	−15.3707	−	26.6229i	−0.617802	−	1.07006i	−0.989886	−	0.141865i	$-0.954690\pi$
$619$	−15.3707	−	26.6229i	−0.617802	−	1.07006i	0.372084	−	0.928199i	$-0.378643\pi$
$620$	43.0305			1.72815
$621$	2.22378			0.0892372
$622$	−12.1642	+	21.0690i	−0.487741	+	0.844792i
$623$	2.55832	−	4.43114i	0.102497	−	0.177530i
$624$	22.5986			0.904670
$625$	4.18972	−	7.25680i	0.167589	−	0.290272i
$626$	28.2955			1.13091
$627$	34.0246			1.35881
$628$	−58.4858	−	10.4892i	−2.33384	−	0.418564i
$629$	−21.3449			−0.851078
$630$	−2.24101			−0.0892841
$631$	−12.7797	+	22.1350i	−0.508751	+	0.881182i	0.491198	+	0.871048i	$0.336559\pi$
$631$	−12.7797	+	22.1350i	−0.508751	+	0.881182i	−0.999949	+	0.0101339i	$0.996774\pi$
$632$	−77.6563			−3.08900
$633$	−8.60555	+	14.9052i	−0.342040	+	0.592430i
$634$	16.9175	−	29.3019i	0.671879	−	1.16373i
$635$	−6.42396			−0.254927
$636$	49.5757			1.96580
$637$	8.44080	+	14.6199i	0.334437	+	0.579261i
$638$	2.97002	−	5.14422i	0.117584	−	0.203662i
$639$	−4.73864	+	8.20756i	−0.187458	+	0.324686i
$640$	−2.82073	+	4.88565i	−0.111499	+	0.193122i
$641$	12.2649	+	21.2433i	0.484433	+	0.839062i	0.999840	−	0.0178834i	$-0.00569276\pi$
$641$	12.2649	+	21.2433i	0.484433	+	0.839062i	−0.515408	+	0.856945i	$0.672359\pi$
$642$	48.4888			1.91370
$643$	4.01497	+	6.95413i	0.158335	+	0.274244i	0.934268	−	0.356571i	$-0.116054\pi$
$643$	4.01497	+	6.95413i	0.158335	+	0.274244i	−0.775934	+	0.630815i	$0.782721\pi$
$644$	5.52094			0.217555
$645$	2.35874	−	4.08546i	0.0928753	−	0.160865i
$646$	−35.0478	−	60.7046i	−1.37894	−	2.38839i
$647$	−3.04487	+	5.27387i	−0.119706	+	0.207337i	−0.919651	−	0.392736i	$-0.871529\pi$
$647$	−3.04487	+	5.27387i	−0.119706	+	0.207337i	0.799945	+	0.600073i	$0.204862\pi$
$648$	3.56008	−	6.16625i	0.139853	−	0.242233i
$649$	18.4353	−	31.9308i	0.723647	−	1.25339i
$650$	−7.43717	+	12.8816i	−0.291710	+	0.505256i
$651$	2.88170			0.112943
$652$	−30.4303	+	52.7069i	−1.19174	+	2.06416i
$653$	17.1073	+	29.6307i	0.669461	+	1.15954i	0.978055	+	0.208346i	$0.0668081\pi$
$653$	17.1073	+	29.6307i	0.669461	+	1.15954i	−0.308594	+	0.951194i	$0.599859\pi$
$654$	11.8309	+	20.4917i	0.462624	+	0.801289i
$655$	−32.4976			−1.26979
$656$	−72.8204			−2.84316
$657$	0.295931			0.0115454
$658$	3.28643	+	5.69226i	0.128118	+	0.221907i
$659$	−6.28777	−	10.8907i	−0.244937	−	0.424243i	0.717177	−	0.696891i	$-0.245434\pi$
$659$	−6.28777	−	10.8907i	−0.244937	−	0.424243i	−0.962114	+	0.272648i	$0.912100\pi$
$660$	35.6826			1.38894
$661$	10.6318	+	18.4149i	0.413530	+	0.716256i	0.995273	−	0.0971172i	$-0.0309622\pi$
$661$	10.6318	+	18.4149i	0.413530	+	0.716256i	−0.581742	+	0.813373i	$0.697629\pi$
$662$	−5.51972	+	9.56043i	−0.214530	+	0.371577i
$663$	4.54478	−	7.87179i	0.176505	−	0.305715i
$664$	29.7942	+	51.6051i	1.15624	+	2.00267i
$665$	−3.21681	−	5.57169i	−0.124743	−	0.216061i
$666$	7.65214	−	13.2539i	0.296515	−	0.513578i
$667$	1.11455			0.0431556
$668$	40.7816	−	70.6358i	1.57789	−	2.73298i
$669$	−23.9428			−0.925683
$670$	0.199314	−	0.345222i	0.00770017	−	0.0133371i
$671$	−11.8441	−	20.5145i	−0.457235	−	0.791954i
$672$	2.39211	−	4.14326i	0.0922776	−	0.159830i
$673$	37.0808			1.42936			0.714680	−	0.699452i	$-0.246573\pi$
$673$	37.0808			1.42936			0.714680	+	0.699452i	$0.246573\pi$
$674$	24.1291			0.929418
$675$	1.14116	+	1.97655i	0.0439232	+	0.0760773i
$676$	15.8867	−	27.5166i	0.611028	−	1.05833i
$677$	33.7894			1.29863			0.649316	−	0.760519i	$-0.275055\pi$
$677$	33.7894			1.29863			0.649316	+	0.760519i	$0.275055\pi$
$678$	22.8394	+	39.5590i	0.877142	+	1.51926i
$679$	−1.81899	−	3.15058i	−0.0698064	−	0.120908i
$680$	−21.2540	−	36.8130i	−0.815052	−	1.41171i
$681$	−14.1794	−	24.5595i	−0.543357	−	0.941122i
$682$	−65.2355			−2.49800
$683$	7.19690	+	12.4654i	0.275382	+	0.476975i	0.970231	−	0.242180i	$-0.0778625\pi$
$683$	7.19690	+	12.4654i	0.275382	+	0.476975i	−0.694850	+	0.719155i	$0.744529\pi$
$684$	35.3497			1.35163
$685$	−6.39541	−	11.0772i	−0.244356	−	0.423237i
$686$	18.6589			0.712400
$687$	−20.7472			−0.791553
$688$	12.8825	+	22.3132i	0.491141	+	0.850682i
$689$	−13.1198	+	22.7241i	−0.499823	+	0.865719i
$690$	4.75949	+	8.24368i	0.181191	+	0.313831i
$691$	−10.6817	−	18.5012i	−0.406350	−	0.703818i	0.588128	−	0.808768i	$-0.299865\pi$
$691$	−10.6817	−	18.5012i	−0.406350	−	0.703818i	−0.994478	+	0.104950i	$0.966532\pi$
$692$	11.4792			0.436375
$693$	2.38962			0.0907740
$694$	19.4808	+	33.7417i	0.739479	+	1.28082i
$695$	32.4968			1.23267
$696$	1.78430	−	3.09050i	0.0676337	−	0.117145i
$697$	−14.6448	+	25.3656i	−0.554712	+	0.960789i
$698$	−40.4329	+	70.0318i	−1.53041	+	2.65074i
$699$	0.790176	+	1.36863i	0.0298872	+	0.0517662i
$700$	2.83313	+	4.90713i	0.107082	+	0.185472i
$701$	13.3076	−	23.0494i	0.502620	−	0.870563i	−0.497376	−	0.867535i	$-0.665703\pi$
$701$	13.3076	−	23.0494i	0.502620	−	0.870563i	0.999995	−	0.00302761i	$-0.000963719\pi$
$702$	3.25860	+	5.64407i	0.122988	+	0.213022i
$703$	43.9364			1.65709
$704$	−13.0560	+	22.6137i	−0.492068	+	0.852286i
$705$	−3.98546	+	6.90302i	−0.150101	+	0.259983i
$706$	−14.1424			−0.532257
$707$	8.07212			0.303583
$708$	19.1532	−	33.1744i	0.719822	−	1.24677i
$709$	−25.0185	+	43.3333i	−0.939588	+	1.62741i	−0.173348	+	0.984861i	$0.555458\pi$
$709$	−25.0185	+	43.3333i	−0.939588	+	1.62741i	−0.766240	+	0.642554i	$0.777875\pi$
$710$	−40.5678			−1.52248
$711$	−5.45326	−	9.44533i	−0.204513	−	0.354228i
$712$	−34.7936	+	60.2643i	−1.30395	+	2.25850i
$713$	−6.12018	−	10.6005i	−0.229203	−	0.396990i
$714$	−2.46148	−	4.26340i	−0.0921184	−	0.159554i
$715$	−9.44309	+	16.3559i	−0.353151	+	0.611676i
$716$	15.6039	−	27.0268i	0.583145	−	1.01004i
$717$	6.46455	−	11.1969i	0.241423	−	0.418157i
$718$	−28.5998			−1.06733
$719$	−8.30403	−	14.3830i	−0.309688	−	0.536396i	0.668606	−	0.743617i	$-0.266891\pi$
$719$	−8.30403	−	14.3830i	−0.309688	−	0.536396i	−0.978294	+	0.207221i	$0.933558\pi$
$720$	14.8429			0.553163
$721$	−5.12308			−0.190793
$722$	47.4751	+	82.2293i	1.76684	+	3.06026i
$723$	−5.88551	−	10.1940i	−0.218885	−	0.379119i
$724$	−19.9694	+	34.5881i	−0.742158	+	1.28546i
$725$	0.571945	+	0.990637i	0.0212415	+	0.0367913i
$726$	−25.5336			−0.947642
$727$	18.2383			0.676420			0.338210	−	0.941071i	$-0.390179\pi$
$727$	18.2383			0.676420			0.338210	+	0.941071i	$0.390179\pi$
$728$	4.67809	+	8.10269i	0.173382	+	0.300306i
$729$	1.00000			0.0370370
$730$	0.633371	+	1.09703i	0.0234421	+	0.0406030i
$731$	10.3631			0.383295
$732$	−12.3053	−	21.3135i	−0.454818	−	0.787768i
$733$	8.77307	+	15.1954i	0.324041	+	0.561255i	0.981318	−	0.192394i	$-0.0616252\pi$
$733$	8.77307	+	15.1954i	0.324041	+	0.561255i	−0.657277	+	0.753649i	$0.728292\pi$
$734$	−16.4499	−	28.4921i	−0.607178	−	1.05166i
$735$	5.54396	+	9.60243i	0.204492	+	0.354191i
$736$	−20.3216			−0.749063
$737$	−0.212531	+	0.368114i	−0.00782867	+	0.0135597i
$738$	−10.5003	−	18.1871i	−0.386522	−	0.669476i
$739$	32.8248			1.20748			0.603739	−	0.797182i	$-0.293677\pi$
$739$	32.8248			1.20748			0.603739	+	0.797182i	$0.293677\pi$
$740$	46.0775			1.69384
$741$	−9.35499	+	16.2033i	−0.343664	+	0.595244i
$742$	7.10572	+	12.3075i	0.260859	+	0.451822i
$743$	12.0440	−	20.8609i	0.441852	−	0.765310i	−0.555975	−	0.831199i	$-0.687655\pi$
$743$	12.0440	−	20.8609i	0.441852	−	0.765310i	0.997827	+	0.0658887i	$0.0209882\pi$
$744$	−39.1916			−1.43683
$745$	2.86125	−	4.95584i	0.104828	−	0.181568i
$746$	89.9511			3.29334
$747$	−4.18448	+	7.24774i	−0.153102	+	0.265181i
$748$	39.1930	+	67.8842i	1.43304	+	2.48209i
$749$	4.88830	+	8.46679i	0.178615	+	0.309370i
$750$	−15.5861	+	26.9960i	−0.569125	+	0.985753i
$751$	12.2821	−	21.2733i	0.448182	−	0.776274i	−0.550086	−	0.835108i	$-0.685405\pi$
$751$	12.2821	−	21.2733i	0.448182	−	0.776274i	0.998268	+	0.0588343i	$0.0187384\pi$
$752$	−21.7670	−	37.7016i	−0.793761	−	1.37483i
$753$	−28.6815			−1.04521
$754$	1.63320	+	2.82879i	0.0594776	+	0.103018i
$755$	−6.17013	−	10.6870i	−0.224554	−	0.388939i
$756$	2.48268			0.0902943
$757$	8.57492			0.311661			0.155830	−	0.987784i	$-0.450195\pi$
$757$	8.57492			0.311661			0.155830	+	0.987784i	$0.450195\pi$
$758$	5.91879			0.214980
$759$	−5.07509	−	8.79032i	−0.184214	−	0.319068i
$760$	43.7492	+	75.7759i	1.58695	+	2.74868i
$761$	3.76402	−	6.51947i	0.136446	−	0.236331i	−0.789703	−	0.613489i	$-0.789765\pi$
$761$	3.76402	−	6.51947i	0.136446	−	0.236331i	0.926149	+	0.377158i	$0.123099\pi$
$762$	10.1182			0.366543
$763$	−2.38542	+	4.13166i	−0.0863578	+	0.149576i
$764$	−27.5043	+	47.6388i	−0.995071	+	1.72351i
$765$	2.98504	−	5.17024i	0.107924	−	0.186930i
$766$	32.6804	−	56.6042i	1.18079	−	2.04519i
$767$	10.1375	+	17.5586i	0.366043	+	0.634004i
$768$	10.1637	−	17.6040i	0.366750	−	0.635230i
$769$	−24.7941			−0.894099			−0.447049	−	0.894509i	$-0.647525\pi$
$769$	−24.7941			−0.894099			−0.447049	+	0.894509i	$0.647525\pi$
$770$	5.11442	+	8.85844i	0.184311	+	0.319236i
$771$	7.38755			0.266056
$772$	−48.6445	−	84.2547i	−1.75075	−	3.03239i
$773$	12.0209	−	20.8209i	0.432363	−	0.748874i	−0.564713	−	0.825287i	$-0.691013\pi$
$773$	12.0209	−	20.8209i	0.432363	−	0.748874i	0.997076	+	0.0764126i	$0.0243466\pi$
$774$	−3.71518	+	6.43488i	−0.133539	+	0.231297i
$775$	6.28129	−	10.8795i	0.225630	−	0.390803i
$776$	24.7386	+	42.8484i	0.888063	+	1.53817i
$777$	3.08574			0.110700
$778$	32.6463			1.17043
$779$	30.1449	−	52.2126i	1.08005	−	1.87071i
$780$	−9.81086	+	16.9929i	−0.351285	+	0.608443i
$781$	43.2579			1.54789
$782$	−10.4554	+	18.1093i	−0.373885	+	0.647588i
$783$	0.501196			0.0179113
$784$	−60.5579			−2.16278
$785$	13.3238	−	15.7846i	0.475545	−	0.563376i
$786$	51.1860			1.82574
$787$	−35.2774			−1.25750			−0.628752	−	0.777606i	$-0.716434\pi$
$787$	−35.2774			−1.25750			−0.628752	+	0.777606i	$0.716434\pi$
$788$	−23.1823	+	40.1530i	−0.825836	+	1.43039i
$789$	−16.2241			−0.577593
$790$	23.3429	−	40.4311i	0.830503	−	1.43847i
$791$	−4.60502	+	7.97613i	−0.163736	+	0.283599i
$792$	−32.4992			−1.15481
$793$	13.0260			0.462566
$794$	33.0149	+	57.1835i	1.17166	+	2.02937i
$795$	−8.61713	+	14.9253i	−0.305618	+	0.529346i
$796$	3.78124	−	6.54931i	0.134023	−	0.232134i
$797$	21.1703	−	36.6680i	0.749890	−	1.29885i	−0.197985	−	0.980205i	$-0.563440\pi$
$797$	21.1703	−	36.6680i	0.749890	−	1.29885i	0.947875	−	0.318642i	$-0.103227\pi$
$798$	5.06671	+	8.77580i	0.179360	+	0.310660i
$799$	−17.5101			−0.619464
$800$	−10.4283	−	18.0623i	−0.368694	−	0.638597i
$801$	−9.77326			−0.345321
$802$	−5.29484	+	9.17094i	−0.186967	+	0.323837i
$803$	−0.675371	−	1.16978i	−0.0238333	−	0.0412805i
$804$	−0.220808	+	0.382450i	−0.00778729	+	0.0134880i
$805$	−0.959637	+	1.66214i	−0.0338228	+	0.0585827i
$806$	17.9363	−	31.0667i	0.631781	−	1.09428i
$807$	−1.72058	+	2.98014i	−0.0605674	+	0.104906i
$808$	−109.782			−3.86213
$809$	−10.0923	+	17.4803i	−0.354825	+	0.614575i	−0.987088	−	0.160179i	$-0.948793\pi$
$809$	−10.0923	+	17.4803i	−0.354825	+	0.614575i	0.632263	+	0.774754i	$0.282126\pi$
$810$	2.14027	+	3.70706i	0.0752014	+	0.130253i
$811$	−13.2981	−	23.0330i	−0.466960	−	0.808798i	0.532328	−	0.846538i	$-0.321317\pi$
$811$	−13.2981	−	23.0330i	−0.466960	−	0.808798i	−0.999288	+	0.0377400i	$0.987984\pi$
$812$	1.24431			0.0436667
$813$	−27.7196			−0.972170
$814$	−69.8547			−2.44841
$815$	−10.5787	−	18.3228i	−0.370554	−	0.641819i
$816$	16.3031	+	28.2378i	0.570723	+	0.988521i
$817$	−21.3315			−0.746295
$818$	−39.4669	−	68.3587i	−1.37993	−	2.39010i
$819$	−0.657020	+	1.13799i	−0.0229581	+	0.0397646i
$820$	31.6139	−	54.7569i	1.10400	−	1.91219i
$821$	23.5292	+	40.7537i	0.821174	+	1.42232i	0.904809	+	0.425819i	$0.140014\pi$
$821$	23.5292	+	40.7537i	0.821174	+	1.42232i	−0.0836345	+	0.996496i	$0.526653\pi$
$822$	10.0732	+	17.4473i	0.351344	+	0.608545i
$823$	20.6526	−	35.7713i	0.719903	−	1.24691i	−0.241135	−	0.970492i	$-0.577520\pi$
$823$	20.6526	−	35.7713i	0.719903	−	1.24691i	0.961038	−	0.276417i	$-0.0891470\pi$
$824$	69.6748			2.42724
$825$	5.20869	−	9.02172i	0.181343	−	0.314096i
$826$	10.9810			0.382078
$827$	−24.0605	+	41.6740i	−0.836665	+	1.44915i	0.0560031	+	0.998431i	$0.482164\pi$
$827$	−24.0605	+	41.6740i	−0.836665	+	1.44915i	−0.892668	+	0.450715i	$0.851169\pi$
$828$	−5.27275	−	9.13267i	−0.183241	−	0.317382i
$829$	−8.38562	+	14.5243i	−0.291245	+	0.504450i	−0.974104	−	0.226099i	$-0.927403\pi$
$829$	−8.38562	+	14.5243i	−0.291245	+	0.504450i	0.682860	+	0.730550i	$0.260736\pi$
$830$	−35.8237			−1.24346
$831$	11.8642			0.411563
$832$	−7.17945	−	12.4352i	−0.248903	−	0.431112i
$833$	−12.1787	+	21.0942i	−0.421968	+	0.730869i
$834$	−51.1848			−1.77238
$835$	14.1771	+	24.5555i	0.490620	+	0.849779i
$836$	−80.6749	−	139.733i	−2.79020	−	4.83277i
$837$	−2.75215	−	4.76687i	−0.0951283	−	0.164767i
$838$	29.4740	+	51.0504i	1.01816	+	1.76351i
$839$	39.6384			1.36847			0.684235	−	0.729262i	$-0.260136\pi$
$839$	39.6384			1.36847			0.684235	+	0.729262i	$0.260136\pi$
$840$	3.07259	+	5.32189i	0.106015	+	0.183623i
$841$	−28.7488			−0.991338
$842$	21.6539	+	37.5057i	0.746243	+	1.29253i
$843$	−21.1875			−0.729735
$844$	81.6176			2.80939
$845$	5.52279	+	9.56576i	0.189990	+	0.329072i
$846$	6.27738	−	10.8727i	0.215821	−	0.373812i
$847$	−2.57412	−	4.45851i	−0.0884479	−	0.153196i
$848$	−47.0634	−	81.5162i	−1.61616	−	2.79928i
$849$	14.2344			0.488522
$850$	−21.4613			−0.736116
$851$	−6.55354	−	11.3511i	−0.224652	−	0.389109i
$852$	44.9426			1.53971
$853$	−4.57897	+	7.93100i	−0.156781	+	0.271552i	−0.933706	−	0.358041i	$-0.883445\pi$
$853$	−4.57897	+	7.93100i	−0.156781	+	0.271552i	0.776925	+	0.629593i	$0.216778\pi$
$854$	3.52747	−	6.10975i	0.120707	−	0.209071i
$855$	−6.14441	+	10.6424i	−0.210134	+	0.363963i
$856$	−66.4817	−	115.150i	−2.27230	−	3.93574i
$857$	8.20620	+	14.2136i	0.280318	+	0.485526i	0.971463	−	0.237191i	$-0.0762266\pi$
$857$	8.20620	+	14.2136i	0.280318	+	0.485526i	−0.691145	+	0.722716i	$0.742893\pi$
$858$	14.8735	−	25.7617i	0.507774	−	0.879490i
$859$	11.9582	+	20.7122i	0.408008	+	0.706691i	0.994666	−	0.103144i	$-0.0328902\pi$
$859$	11.9582	+	20.7122i	0.408008	+	0.706691i	−0.586658	+	0.809834i	$0.699557\pi$
$860$	−22.3710			−0.762845
$861$	2.11714	−	3.66699i	0.0721519	−	0.124971i
$862$	24.3877	−	42.2408i	0.830650	−	1.43873i
$863$	32.8563			1.11844			0.559222	−	0.829018i	$-0.311100\pi$
$863$	32.8563			1.11844			0.559222	+	0.829018i	$0.311100\pi$
$864$	−9.13830			−0.310891
$865$	−1.99529	+	3.45595i	−0.0678420	+	0.117506i
$866$	6.91121	−	11.9706i	0.234852	−	0.406776i
$867$	−3.88522			−0.131949
$868$	−6.83271	−	11.8346i	−0.231917	−	0.401693i
$869$	−24.8908	+	43.1121i	−0.844363	+	1.46248i
$870$	1.07269	+	1.85796i	0.0363678	+	0.0629908i
$871$	−0.116870	−	0.202424i	−0.00395998	−	0.00685888i
$872$	32.4421	−	56.1913i	1.09863	−	1.90288i
$873$	−3.47444	+	6.01790i	−0.117592	+	0.203675i
$874$	21.5215	−	37.2763i	0.727975	−	1.26089i
$875$	−6.28514			−0.212476
$876$	−0.701674	−	1.21533i	−0.0237074	−	0.0410623i
$877$	16.6169			0.561112			0.280556	−	0.959838i	$-0.409481\pi$
$877$	16.6169			0.561112			0.280556	+	0.959838i	$0.409481\pi$
$878$	−51.5637			−1.74019
$879$	8.76086	+	15.1743i	0.295497	+	0.511815i
$880$	−33.8744	−	58.6722i	−1.14191	−	1.97784i
$881$	−12.9171	+	22.3731i	−0.435189	+	0.753770i	−0.997311	−	0.0732847i	$-0.976652\pi$
$881$	−12.9171	+	22.3731i	−0.435189	+	0.753770i	0.562122	+	0.827054i	$0.309985\pi$
$882$	−8.73213	−	15.1245i	−0.294026	−	0.509268i
$883$	−23.3814			−0.786846			−0.393423	−	0.919358i	$-0.628709\pi$
$883$	−23.3814			−0.786846			−0.393423	+	0.919358i	$0.628709\pi$
$884$	−43.1041			−1.44975
$885$	6.65834	+	11.5326i	0.223818	+	0.387664i
$886$	63.7789			2.14270
$887$	−10.9268	−	18.9259i	−0.366888	−	0.635468i	0.622189	−	0.782867i	$-0.286243\pi$
$887$	−10.9268	−	18.9259i	−0.366888	−	0.635468i	−0.989077	+	0.147399i	$0.952910\pi$
$888$	−41.9666			−1.40831
$889$	1.02005	+	1.76677i	0.0342112	+	0.0592556i
$890$	−20.9174	−	36.2300i	−0.701153	−	1.21443i
$891$	−2.28219	−	3.95287i	−0.0764563	−	0.132426i
$892$	56.7702	+	98.3289i	1.90081	+	3.29230i
$893$	36.0429			1.20613
$894$	−4.50668	+	7.80579i	−0.150726	+	0.261065i
$895$	5.42447	+	9.39546i	0.181320	+	0.314056i
$896$	1.79159			0.0598528
$897$	5.58154			0.186362
$898$	−31.0489	+	53.7783i	−1.03612	+	1.79461i
$899$	−1.37937	−	2.38914i	−0.0460045	−	0.0796821i
$900$	5.41155	−	9.37307i	0.180385	−	0.312436i
$901$	−37.8594			−1.26128
$902$	−47.9275	+	83.0129i	−1.59581	+	2.76403i
$903$	−1.49815			−0.0498555
$904$	62.6291	−	108.477i	2.08301	−	3.60788i
$905$	−6.94208	−	12.0240i	−0.230763	−	0.399693i
$906$	9.71838	+	16.8327i	0.322872	+	0.559230i
$907$	−19.5431	+	33.8497i	−0.648918	+	1.12396i	0.334463	+	0.942409i	$0.391445\pi$
$907$	−19.5431	+	33.8497i	−0.648918	+	1.12396i	−0.983382	+	0.181551i	$0.941888\pi$
$908$	−67.2410	+	116.465i	−2.23147	+	3.86502i
$909$	−7.70925	−	13.3528i	−0.255700	−	0.442885i
$910$	−5.62480			−0.186460
$911$	−6.71831	−	11.6365i	−0.222588	−	0.385533i	0.733005	−	0.680223i	$-0.238117\pi$
$911$	−6.71831	−	11.6365i	−0.222588	−	0.385533i	−0.955593	+	0.294690i	$0.904784\pi$
$912$	−33.5584	−	58.1248i	−1.11123	−	1.92470i
$913$	38.1992			1.26421
$914$	−89.4333			−2.95819
$915$	8.55554			0.282837
$916$	49.1930	+	85.2049i	1.62538	+	2.81525i
$917$	5.16022	+	8.93776i	0.170405	+	0.295151i
$918$	−4.70164	+	8.14349i	−0.155177	+	0.268775i
$919$	−38.8990			−1.28316			−0.641580	−	0.767056i	$-0.721721\pi$
$919$	−38.8990			−1.28316			−0.641580	+	0.767056i	$0.721721\pi$
$920$	13.0512	−	22.6054i	0.430286	−	0.745277i
$921$	−7.37323	+	12.7708i	−0.242956	+	0.420813i
$922$	45.1421	−	78.1884i	1.48667	−	2.57500i
$923$	−11.8937	+	20.6004i	−0.391485	+	0.678072i
$924$	−5.66596	−	9.81373i	−0.186396	−	0.322848i
$925$	6.72605	−	11.6499i	0.221151	−	0.383045i
$926$	−62.0991			−2.04070
$927$	4.89278	+	8.47454i	0.160700	+	0.278340i
$928$	−4.58008			−0.150348
$929$	1.70202	+	2.94799i	0.0558416	+	0.0967205i	0.892595	−	0.450860i	$-0.148882\pi$
$929$	1.70202	+	2.94799i	0.0558416	+	0.0967205i	−0.836753	+	0.547580i	$0.815549\pi$
$930$	11.7807	−	20.4048i	0.386304	−	0.669098i
$931$	25.0687	−	43.4203i	0.821594	−	1.42304i
$932$	3.74713	−	6.49023i	0.122741	−	0.212594i
$933$	4.68473	+	8.11420i	0.153371	+	0.265647i
$934$	16.2309			0.531093
$935$	−27.2497			−0.891161
$936$	8.93558	−	15.4769i	0.292068	−	0.505877i
$937$	−16.6441	+	28.8284i	−0.543739	+	0.941784i	0.454946	+	0.890519i	$0.349659\pi$
$937$	−16.6441	+	28.8284i	−0.543739	+	0.941784i	−0.998685	+	0.0512649i	$0.983675\pi$
$938$	−0.126594			−0.00413345
$939$	5.44864	−	9.43731i	0.177809	−	0.307975i
$940$	37.7993			1.23288
$941$	−33.1093			−1.07933			−0.539665	−	0.841880i	$-0.681449\pi$
$941$	−33.1093			−1.07933			−0.539665	+	0.841880i	$0.681449\pi$
$942$	−20.9859	+	24.8618i	−0.683756	+	0.810043i
$943$	−17.9856			−0.585692
$944$	−72.7305			−2.36718
$945$	−0.431534	+	0.747439i	−0.0140378	+	0.0243142i
$946$	33.9150			1.10267
$947$	−25.0267	+	43.3475i	−0.813258	+	1.40860i	0.0973142	+	0.995254i	$0.468975\pi$
$947$	−25.0267	+	43.3475i	−0.813258	+	1.40860i	−0.910572	+	0.413350i	$0.864358\pi$
$948$	−25.8602	+	44.7912i	−0.839900	+	1.45475i
$949$	0.742767			0.0241112
$950$	44.1760			1.43326
$951$	−6.51533	−	11.2849i	−0.211274	−	0.365937i
$952$	−6.74973	+	11.6909i	−0.218760	+	0.378904i
$953$	12.0404	−	20.8547i	0.390028	−	0.675549i	−0.602425	−	0.798176i	$-0.705799\pi$
$953$	12.0404	−	20.8547i	0.390028	−	0.675549i	0.992453	+	0.122627i	$0.0391319\pi$
$954$	13.5726	−	23.5084i	0.439429	−	0.761113i
$955$	−9.56147	−	16.5610i	−0.309402	−	0.535900i
$956$	−61.3117			−1.98296
$957$	−1.14383	−	1.98117i	−0.0369747	−	0.0640420i
$958$	−7.54655			−0.243818
$959$	−2.03102	+	3.51783i	−0.0655851	+	0.113597i
$960$	−4.71550	−	8.16749i	−0.152192	−	0.263605i
$961$	0.351327	−	0.608517i	0.0113331	−	0.0196296i
$962$	19.2064	−	33.2664i	0.619239	−	1.07255i
$963$	9.33710	−	16.1723i	0.300884	−	0.521146i
$964$	−27.9100	+	48.3415i	−0.898920	+	1.55698i
$965$	33.8211			1.08874
$966$	1.51150	−	2.61799i	0.0486316	−	0.0842323i
$967$	−30.1214	−	52.1719i	−0.968640	−	1.67773i	−0.699500	−	0.714633i	$-0.746594\pi$
$967$	−30.1214	−	52.1719i	−0.968640	−	1.67773i	−0.269140	−	0.963101i	$-0.586740\pi$
$968$	35.0085	+	60.6365i	1.12522	+	1.94893i
$969$	−26.9955			−0.867221
$970$	−29.7449			−0.955052
$971$	−27.8224			−0.892864			−0.446432	−	0.894818i	$-0.647305\pi$
$971$	−27.8224			−0.892864			−0.446432	+	0.894818i	$0.647305\pi$
$972$	−2.37107	−	4.10682i	−0.0760522	−	0.131726i
$973$	−5.16009	−	8.93754i	−0.165425	−	0.286524i
$974$	36.8877			1.18196
$975$	2.86424	+	4.96100i	0.0917289	+	0.158879i
$976$	−23.3635	+	40.4668i	−0.747848	+	1.29531i
$977$	5.28524	−	9.15431i	0.169090	−	0.292872i	−0.769010	−	0.639237i	$-0.779250\pi$
$977$	5.28524	−	9.15431i	0.169090	−	0.292872i	0.938100	+	0.346364i	$0.112584\pi$
$978$	16.6621	+	28.8597i	0.532796	+	0.922830i
$979$	22.3045	+	38.6325i	0.712854	+	1.23470i
$980$	26.2903	−	45.5361i	0.839813	−	1.45460i
$981$	9.11272			0.290947
$982$	55.9119	−	96.8422i	1.78422	−	3.09036i
$983$	−1.10956			−0.0353895			−0.0176947	−	0.999843i	$-0.505633\pi$
$983$	−1.10956			−0.0353895			−0.0176947	+	0.999843i	$0.505633\pi$
$984$	−28.7934	+	49.8717i	−0.917901	+	1.58985i
$985$	−8.05900	−	13.9586i	−0.256781	−	0.444758i
$986$	−2.35645	+	4.08148i	−0.0750445	+	0.129981i
$987$	2.53136			0.0805742
$988$	88.7255			2.82273
$989$	3.18180	+	5.51104i	0.101175	+	0.175241i
$990$	9.76902	−	16.9204i	0.310480	−	0.537767i
$991$	−3.92983			−0.124835			−0.0624175	−	0.998050i	$-0.519881\pi$
$991$	−3.92983			−0.124835			−0.0624175	+	0.998050i	$0.519881\pi$
$992$	25.1500	+	43.5610i	0.798513	+	1.38306i
$993$	2.12578	+	3.68195i	0.0674595	+	0.116843i
$994$	6.44167	+	11.1573i	0.204317	+	0.353888i
$995$	1.31449	+	2.27677i	0.0416723	+	0.0721785i
$996$	39.6869			1.25753
$997$	−21.5422	−	37.3122i	−0.682249	−	1.18169i	−0.974293	−	0.225285i	$-0.927669\pi$
$997$	−21.5422	−	37.3122i	−0.682249	−	1.18169i	0.292044	−	0.956405i	$-0.405665\pi$
$998$	−78.8127			−2.49477
$999$	−2.94703	−	5.10440i	−0.0932398	−	0.161496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.301.1	yes	28
157.12	even	3	inner	471.2.e.c.169.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.1	✓	28	157.12	even	3	inner
471.2.e.c.301.1	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.59656 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.74215 q^{4} +(-0.824270 + 1.42768i) q^{5} +(1.29828 - 2.24869i) q^{6} +0.523535 q^{7} -7.12017 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-2.59656 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.74215 q^{4} +(-0.824270 + 1.42768i) q^{5} +(1.29828 - 2.24869i) q^{6} +0.523535 q^{7} -7.12017 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.14027 - 3.70706i) q^{10} +(-2.28219 + 3.95287i) q^{11} +(-2.37107 + 4.10682i) q^{12} +(-1.25497 - 2.17367i) q^{13} -1.35939 q^{14} +(-0.824270 - 1.42768i) q^{15} +9.00368 q^{16} +(1.81072 - 3.13625i) q^{17} +(1.29828 + 2.24869i) q^{18} +(-3.72719 + 6.45567i) q^{19} +(-3.90881 + 6.77026i) q^{20} +(-0.261768 + 0.453395i) q^{21} +(5.92586 - 10.2639i) q^{22} +2.22378 q^{23} +(3.56008 - 6.16625i) q^{24} +(1.14116 + 1.97655i) q^{25} +(3.25860 + 5.64407i) q^{26} +1.00000 q^{27} +2.48268 q^{28} +0.501196 q^{29} +(2.14027 + 3.70706i) q^{30} +(-2.75215 - 4.76687i) q^{31} -9.13830 q^{32} +(-2.28219 - 3.95287i) q^{33} +(-4.70164 + 8.14349i) q^{34} +(-0.431534 + 0.747439i) q^{35} +(-2.37107 - 4.10682i) q^{36} +(-2.94703 - 5.10440i) q^{37} +(9.67788 - 16.7626i) q^{38} +2.50993 q^{39} +(5.86894 - 10.1653i) q^{40} -8.08786 q^{41} +(0.679696 - 1.17727i) q^{42} +(1.43081 + 2.47823i) q^{43} +(-10.8225 + 18.7451i) q^{44} +1.64854 q^{45} -5.77419 q^{46} +(-2.41757 - 4.18735i) q^{47} +(-4.50184 + 7.79741i) q^{48} -6.72591 q^{49} +(-2.96309 - 5.13223i) q^{50} +(1.81072 + 3.13625i) q^{51} +(-5.95124 - 10.3079i) q^{52} +(-5.22713 - 9.05366i) q^{53} -2.59656 q^{54} +(-3.76228 - 6.51647i) q^{55} -3.72766 q^{56} +(-3.72719 - 6.45567i) q^{57} -1.30139 q^{58} -8.07787 q^{59} +(-3.90881 - 6.77026i) q^{60} +(-2.59489 + 4.49447i) q^{61} +(7.14614 + 12.3775i) q^{62} +(-0.261768 - 0.453395i) q^{63} +5.72083 q^{64} +4.13773 q^{65} +(5.92586 + 10.2639i) q^{66} +0.0931257 q^{67} +(8.58669 - 14.8726i) q^{68} +(-1.11189 + 1.92585i) q^{69} +(1.12051 - 1.94077i) q^{70} +(-4.73864 - 8.20756i) q^{71} +(3.56008 + 6.16625i) q^{72} +(-0.147965 + 0.256283i) q^{73} +(7.65214 + 13.2539i) q^{74} -2.28232 q^{75} +(-17.6749 + 30.6138i) q^{76} +(-1.19481 + 2.06947i) q^{77} -6.51721 q^{78} +10.9065 q^{79} +(-7.42146 + 12.8543i) q^{80} +(-0.500000 + 0.866025i) q^{81} +21.0006 q^{82} +(-4.18448 - 7.24774i) q^{83} +(-1.24134 + 2.15007i) q^{84} +(2.98504 + 5.17024i) q^{85} +(-3.71518 - 6.43488i) q^{86} +(-0.250598 + 0.434049i) q^{87} +(16.2496 - 28.1451i) q^{88} +(4.88663 - 8.46389i) q^{89} -4.28054 q^{90} +(-0.657020 - 1.13799i) q^{91} +10.5455 q^{92} +5.50430 q^{93} +(6.27738 + 10.8727i) q^{94} +(-6.14441 - 10.6424i) q^{95} +(4.56915 - 7.91400i) q^{96} +(-3.47444 - 6.01790i) q^{97} +17.4643 q^{98} +4.56439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

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