LMFDB - Embedded newform 403.2.h.b.118.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, 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("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.5
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.51349 q^{2} +(1.68586 + 2.92000i) q^{3} +0.290659 q^{4} +(1.24235 - 2.15182i) q^{5} +(-2.55154 - 4.41940i) q^{6} +(-1.03520 - 1.79302i) q^{7} +2.58707 q^{8} +(-4.18427 + 7.24738i) q^{9} +O(q^{10})$	\(q-1.51349 q^{2} +(1.68586 + 2.92000i) q^{3} +0.290659 q^{4} +(1.24235 - 2.15182i) q^{5} +(-2.55154 - 4.41940i) q^{6} +(-1.03520 - 1.79302i) q^{7} +2.58707 q^{8} +(-4.18427 + 7.24738i) q^{9} +(-1.88029 + 3.25676i) q^{10} +(-2.30677 + 3.99544i) q^{11} +(0.490012 + 0.848726i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.56677 + 2.71372i) q^{14} +8.37775 q^{15} -4.49684 q^{16} +(1.97748 + 3.42510i) q^{17} +(6.33287 - 10.9688i) q^{18} +(3.35329 + 5.80806i) q^{19} +(0.361102 - 0.625447i) q^{20} +(3.49041 - 6.04557i) q^{21} +(3.49128 - 6.04707i) q^{22} -0.227498 q^{23} +(4.36145 + 7.55426i) q^{24} +(-0.586883 - 1.01651i) q^{25} +(0.756746 - 1.31072i) q^{26} -18.1013 q^{27} +(-0.300890 - 0.521158i) q^{28} -4.45086 q^{29} -12.6797 q^{30} +(5.05901 + 2.32517i) q^{31} +1.63178 q^{32} -15.5556 q^{33} +(-2.99290 - 5.18386i) q^{34} -5.14433 q^{35} +(-1.21620 + 2.10652i) q^{36} +(0.645467 + 1.11798i) q^{37} +(-5.07517 - 8.79046i) q^{38} -3.37173 q^{39} +(3.21406 - 5.56691i) q^{40} +(4.59513 - 7.95900i) q^{41} +(-5.28271 + 9.14992i) q^{42} +(1.49555 + 2.59037i) q^{43} +(-0.670484 + 1.16131i) q^{44} +(10.3967 + 18.0076i) q^{45} +0.344317 q^{46} -3.11747 q^{47} +(-7.58105 - 13.1308i) q^{48} +(1.35672 - 2.34992i) q^{49} +(0.888243 + 1.53848i) q^{50} +(-6.66753 + 11.5485i) q^{51} +(-0.145330 + 0.251718i) q^{52} +(3.23762 - 5.60773i) q^{53} +27.3962 q^{54} +(5.73164 + 9.92749i) q^{55} +(-2.67814 - 4.63867i) q^{56} +(-11.3064 + 19.5832i) q^{57} +6.73634 q^{58} +(-1.62720 - 2.81840i) q^{59} +2.43507 q^{60} -4.21429 q^{61} +(-7.65678 - 3.51912i) q^{62} +17.3262 q^{63} +6.52399 q^{64} +(1.24235 + 2.15182i) q^{65} +23.5433 q^{66} +(0.269832 - 0.467363i) q^{67} +(0.574773 + 0.995537i) q^{68} +(-0.383531 - 0.664295i) q^{69} +7.78591 q^{70} +(4.67631 - 8.09961i) q^{71} +(-10.8250 + 18.7495i) q^{72} +(1.94675 - 3.37187i) q^{73} +(-0.976909 - 1.69206i) q^{74} +(1.97881 - 3.42740i) q^{75} +(0.974665 + 1.68817i) q^{76} +9.55186 q^{77} +5.10308 q^{78} +(7.79892 + 13.5081i) q^{79} +(-5.58666 + 9.67638i) q^{80} +(-17.9635 - 31.1137i) q^{81} +(-6.95469 + 12.0459i) q^{82} +(6.02645 - 10.4381i) q^{83} +(1.01452 - 1.75720i) q^{84} +9.82692 q^{85} +(-2.26350 - 3.92050i) q^{86} +(-7.50354 - 12.9965i) q^{87} +(-5.96778 + 10.3365i) q^{88} -10.7386 q^{89} +(-15.7353 - 27.2544i) q^{90} +2.07040 q^{91} -0.0661245 q^{92} +(1.73931 + 18.6922i) q^{93} +4.71826 q^{94} +16.6639 q^{95} +(2.75096 + 4.76480i) q^{96} +3.72894 q^{97} +(-2.05339 + 3.55658i) q^{98} +(-19.3043 - 33.4360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.51349			−1.07020			−0.535100	−	0.844788i	$-0.679726\pi$
$2$	−1.51349			−1.07020			−0.535100	+	0.844788i	$0.679726\pi$
$3$	1.68586	+	2.92000i	0.973334	+	1.68586i	0.685327	+	0.728236i	$0.259659\pi$
$3$	1.68586	+	2.92000i	0.973334	+	1.68586i	0.288007	+	0.957628i	$0.407007\pi$
$4$	0.290659			0.145330
$5$	1.24235	−	2.15182i	0.555597	−	0.962323i	−0.442260	−	0.896887i	$-0.645823\pi$
$5$	1.24235	−	2.15182i	0.555597	−	0.962323i	0.997857	−	0.0654356i	$-0.0208437\pi$
$6$	−2.55154	−	4.41940i	−1.04166	−	1.80421i
$7$	−1.03520	−	1.79302i	−0.391269	−	0.677697i	0.601349	−	0.798987i	$-0.294630\pi$
$7$	−1.03520	−	1.79302i	−0.391269	−	0.677697i	−0.992617	+	0.121290i	$0.961297\pi$
$8$	2.58707			0.914669
$9$	−4.18427	+	7.24738i	−1.39476	+	2.41579i
$10$	−1.88029	+	3.25676i	−0.594601	+	1.02988i
$11$	−2.30677	+	3.99544i	−0.695517	+	1.20467i	0.274489	+	0.961590i	$0.411491\pi$
$11$	−2.30677	+	3.99544i	−0.695517	+	1.20467i	−0.970006	+	0.243080i	$0.921842\pi$
$12$	0.490012	+	0.848726i	0.141454	+	0.245006i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	1.56677	+	2.71372i	0.418736	+	0.725272i
$15$	8.37775			2.16313
$16$	−4.49684			−1.12421
$17$	1.97748	+	3.42510i	0.479609	+	0.830708i	0.999726	−	0.0233871i	$-0.00744502\pi$
$17$	1.97748	+	3.42510i	0.479609	+	0.830708i	−0.520117	+	0.854095i	$0.674112\pi$
$18$	6.33287	−	10.9688i	1.49267	−	2.58538i
$19$	3.35329	+	5.80806i	0.769297	+	1.33246i	0.937945	+	0.346785i	$0.112727\pi$
$19$	3.35329	+	5.80806i	0.769297	+	1.33246i	−0.168648	+	0.985676i	$0.553940\pi$
$20$	0.361102	−	0.625447i	0.0807448	−	0.139854i
$21$	3.49041	−	6.04557i	0.761670	−	1.31925i
$22$	3.49128	−	6.04707i	0.744343	−	1.28924i
$23$	−0.227498			−0.0474366			−0.0237183	−	0.999719i	$-0.507550\pi$
$23$	−0.227498			−0.0474366			−0.0237183	+	0.999719i	$0.507550\pi$
$24$	4.36145	+	7.55426i	0.890278	+	1.54201i
$25$	−0.586883	−	1.01651i	−0.117377	−	0.203302i
$26$	0.756746	−	1.31072i	0.148410	−	0.257054i
$27$	−18.1013			−3.48359
$28$	−0.300890	−	0.521158i	−0.0568630	−	0.0984895i
$29$	−4.45086			−0.826504			−0.413252	−	0.910617i	$-0.635607\pi$
$29$	−4.45086			−0.826504			−0.413252	+	0.910617i	$0.635607\pi$
$30$	−12.6797			−2.31498
$31$	5.05901	+	2.32517i	0.908625	+	0.417612i
$31$	5.05901	+	2.32517i	0.908625	+	0.417612i
$32$	1.63178			0.288461
$33$	−15.5556			−2.70788
$34$	−2.99290	−	5.18386i	−0.513278	−	0.889024i
$35$	−5.14433			−0.869551
$36$	−1.21620	+	2.10652i	−0.202700	+	0.351086i
$37$	0.645467	+	1.11798i	0.106114	+	0.183795i	0.914193	−	0.405279i	$-0.132826\pi$
$37$	0.645467	+	1.11798i	0.106114	+	0.183795i	−0.808079	+	0.589074i	$0.799492\pi$
$38$	−5.07517	−	8.79046i	−0.823302	−	1.42600i
$39$	−3.37173			−0.539909
$40$	3.21406	−	5.56691i	0.508187	−	0.880207i
$41$	4.59513	−	7.95900i	0.717639	−	1.24299i	−0.244294	−	0.969701i	$-0.578556\pi$
$41$	4.59513	−	7.95900i	0.717639	−	1.24299i	0.961933	−	0.273285i	$-0.0881103\pi$
$42$	−5.28271	+	9.14992i	−0.815140	+	1.41186i
$43$	1.49555	+	2.59037i	0.228069	+	0.395027i	0.957236	−	0.289309i	$-0.0934255\pi$
$43$	1.49555	+	2.59037i	0.228069	+	0.395027i	−0.729167	+	0.684336i	$0.760092\pi$
$44$	−0.670484	+	1.16131i	−0.101079	+	0.175074i
$45$	10.3967	+	18.0076i	1.54985	+	2.68441i
$46$	0.344317			0.0507667
$47$	−3.11747			−0.454729			−0.227365	−	0.973810i	$-0.573011\pi$
$47$	−3.11747			−0.454729			−0.227365	+	0.973810i	$0.573011\pi$
$48$	−7.58105	−	13.1308i	−1.09423	−	1.89526i
$49$	1.35672	−	2.34992i	0.193818	−	0.335702i
$50$	0.888243	+	1.53848i	0.125617	+	0.217574i
$51$	−6.66753	+	11.5485i	−0.933640	+	1.61711i
$52$	−0.145330	+	0.251718i	−0.0201536	+	0.0349071i
$53$	3.23762	−	5.60773i	0.444722	−	0.770281i	−0.553311	−	0.832975i	$-0.686636\pi$
$53$	3.23762	−	5.60773i	0.444722	−	0.770281i	0.998033	+	0.0626940i	$0.0199692\pi$
$54$	27.3962			3.72814
$55$	5.73164	+	9.92749i	0.772854	+	1.33862i
$56$	−2.67814	−	4.63867i	−0.357881	−	0.619868i
$57$	−11.3064	+	19.5832i	−1.49757	+	2.59386i
$58$	6.73634			0.884525
$59$	−1.62720	−	2.81840i	−0.211844	−	0.366924i	0.740448	−	0.672114i	$-0.234614\pi$
$59$	−1.62720	−	2.81840i	−0.211844	−	0.366924i	−0.952292	+	0.305190i	$0.901280\pi$
$60$	2.43507			0.314367
$61$	−4.21429			−0.539585			−0.269793	−	0.962918i	$-0.586955\pi$
$61$	−4.21429			−0.539585			−0.269793	+	0.962918i	$0.586955\pi$
$62$	−7.65678	−	3.51912i	−0.972411	−	0.446929i
$63$	17.3262			2.18290
$64$	6.52399			0.815498
$65$	1.24235	+	2.15182i	0.154095	+	0.266900i
$66$	23.5433			2.89798
$67$	0.269832	−	0.467363i	0.0329653	−	0.0570975i	−0.849072	−	0.528277i	$-0.822838\pi$
$67$	0.269832	−	0.467363i	0.0329653	−	0.0570975i	0.882037	+	0.471179i	$0.156172\pi$
$68$	0.574773	+	0.995537i	0.0697015	+	0.120727i
$69$	−0.383531	−	0.664295i	−0.0461717	−	0.0799717i
$70$	7.78591			0.930594
$71$	4.67631	−	8.09961i	0.554976	−	0.961247i	−0.442929	−	0.896557i	$-0.646061\pi$
$71$	4.67631	−	8.09961i	0.554976	−	0.961247i	0.997905	−	0.0646907i	$-0.0206061\pi$
$72$	−10.8250	+	18.7495i	−1.27574	+	2.20965i
$73$	1.94675	−	3.37187i	0.227850	−	0.394648i	−0.729321	−	0.684172i	$-0.760164\pi$
$73$	1.94675	−	3.37187i	0.227850	−	0.394648i	0.957171	+	0.289524i	$0.0934970\pi$
$74$	−0.976909	−	1.69206i	−0.113563	−	0.196698i
$75$	1.97881	−	3.42740i	0.228493	−	0.395762i
$76$	0.974665	+	1.68817i	0.111802	+	0.193646i
$77$	9.55186			1.08854
$78$	5.10308			0.577811
$79$	7.79892	+	13.5081i	0.877447	+	1.51978i	0.854133	+	0.520055i	$0.174088\pi$
$79$	7.79892	+	13.5081i	0.877447	+	1.51978i	0.0233142	+	0.999728i	$0.492578\pi$
$80$	−5.58666	+	9.67638i	−0.624607	+	1.08185i
$81$	−17.9635	−	31.1137i	−1.99594	−	3.45707i
$82$	−6.95469	+	12.0459i	−0.768017	+	1.33025i
$83$	6.02645	−	10.4381i	0.661489	−	1.14573i	−0.318735	−	0.947844i	$-0.603258\pi$
$83$	6.02645	−	10.4381i	0.661489	−	1.14573i	0.980224	−	0.197889i	$-0.0634086\pi$
$84$	1.01452	−	1.75720i	0.110693	−	0.191726i
$85$	9.82692			1.06588
$86$	−2.26350	−	3.92050i	−0.244080	−	0.422758i
$87$	−7.50354	−	12.9965i	−0.804464	−	1.39337i
$88$	−5.96778	+	10.3365i	−0.636167	+	1.10187i
$89$	−10.7386			−1.13829			−0.569144	−	0.822238i	$-0.692725\pi$
$89$	−10.7386			−1.13829			−0.569144	+	0.822238i	$0.692725\pi$
$90$	−15.7353	−	27.2544i	−1.65865	−	2.87286i
$91$	2.07040			0.217037
$92$	−0.0661245			−0.00689395
$93$	1.73931	+	18.6922i	0.180358	+	1.93829i
$94$	4.71826			0.486651
$95$	16.6639			1.70968
$96$	2.75096	+	4.76480i	0.280768	+	0.486305i
$97$	3.72894			0.378616			0.189308	−	0.981918i	$-0.439376\pi$
$97$	3.72894			0.378616			0.189308	+	0.981918i	$0.439376\pi$
$98$	−2.05339	+	3.55658i	−0.207424	+	0.359269i
$99$	−19.3043	−	33.4360i	−1.94015	−	3.36045i
$100$	−0.170583	−	0.295459i	−0.0170583	−	0.0295459i
$101$	−3.42045			−0.340348			−0.170174	−	0.985414i	$-0.554433\pi$
$101$	−3.42045			−0.340348			−0.170174	+	0.985414i	$0.554433\pi$
$102$	10.0912	−	17.4786i	0.999183	−	1.73064i
$103$	6.30533	−	10.9212i	0.621283	−	1.07609i	−0.367965	−	0.929840i	$-0.619945\pi$
$103$	6.30533	−	10.9212i	0.621283	−	1.07609i	0.989247	−	0.146253i	$-0.0467214\pi$
$104$	−1.29354	+	2.24047i	−0.126842	+	0.219696i
$105$	−8.67264	−	15.0215i	−0.846363	−	1.46594i
$106$	−4.90012	+	8.48726i	−0.475942	+	0.824355i
$107$	−4.00423	−	6.93552i	−0.387103	−	0.670482i	0.604955	−	0.796259i	$-0.293191\pi$
$107$	−4.00423	−	6.93552i	−0.387103	−	0.670482i	−0.992059	+	0.125777i	$0.959858\pi$
$108$	−5.26131			−0.506270
$109$	−6.40774			−0.613750			−0.306875	−	0.951750i	$-0.599283\pi$
$109$	−6.40774			−0.613750			−0.306875	+	0.951750i	$0.599283\pi$
$110$	−8.67480	−	15.0252i	−0.827109	−	1.43260i
$111$	−2.17634	+	3.76953i	−0.206569	+	0.357788i
$112$	4.65512	+	8.06291i	0.439868	+	0.761873i
$113$	−2.09670	+	3.63160i	−0.197241	+	0.341632i	−0.947633	−	0.319362i	$-0.896532\pi$
$113$	−2.09670	+	3.63160i	−0.197241	+	0.341632i	0.750392	+	0.660993i	$0.229865\pi$
$114$	17.1121	−	29.6390i	1.60270	−	2.77595i
$115$	−0.282633	+	0.489535i	−0.0263557	+	0.0456493i
$116$	−1.29368			−0.120116
$117$	−4.18427	−	7.24738i	−0.386836	−	0.670020i
$118$	2.46276	+	4.26563i	0.226716	+	0.392683i
$119$	4.09417	−	7.09131i	0.375312	−	0.650060i
$120$	21.6739			1.97854
$121$	−5.14236	−	8.90682i	−0.467487	−	0.809711i
$122$	6.37830			0.577464
$123$	30.9870			2.79401
$124$	1.47045	+	0.675832i	0.132050	+	0.0606915i
$125$	9.50707			0.850338
$126$	−26.2231			−2.33614
$127$	6.94088	+	12.0220i	0.615904	+	1.06678i	0.990225	+	0.139478i	$0.0445424\pi$
$127$	6.94088	+	12.0220i	0.615904	+	1.06678i	−0.374321	+	0.927299i	$0.622124\pi$
$128$	−13.1376			−1.16121
$129$	−5.04258	+	8.73401i	−0.443975	+	0.768987i
$130$	−1.88029	−	3.25676i	−0.164913	−	0.285637i
$131$	10.0475	+	17.4027i	0.877851	+	1.52048i	0.853694	+	0.520775i	$0.174357\pi$
$131$	10.0475	+	17.4027i	0.877851	+	1.52048i	0.0241576	+	0.999708i	$0.492310\pi$
$132$	−4.52138			−0.393535
$133$	6.94264	−	12.0250i	0.602003	−	1.04270i
$134$	−0.408389	+	0.707351i	−0.0352795	+	0.0611058i
$135$	−22.4882	+	38.9507i	−1.93547	+	3.35234i
$136$	5.11589	+	8.86098i	0.438684	+	0.759823i
$137$	−0.619096	+	1.07231i	−0.0528930	+	0.0916133i	−0.891260	−	0.453493i	$-0.850178\pi$
$137$	−0.619096	+	1.07231i	−0.0528930	+	0.0916133i	0.838367	+	0.545107i	$0.183511\pi$
$138$	0.580471	+	1.00540i	0.0494130	+	0.0855858i
$139$	−1.63014			−0.138267			−0.0691335	−	0.997607i	$-0.522023\pi$
$139$	−1.63014			−0.138267			−0.0691335	+	0.997607i	$0.522023\pi$
$140$	−1.49525			−0.126372
$141$	−5.25562	−	9.10300i	−0.442603	−	0.766611i
$142$	−7.07757	+	12.2587i	−0.593936	+	1.02873i
$143$	−2.30677	−	3.99544i	−0.192902	−	0.334115i
$144$	18.8160	−	32.5903i	1.56800	−	2.71585i
$145$	−5.52954	+	9.57744i	−0.459203	+	0.795364i
$146$	−2.94640	+	5.10331i	−0.243845	+	0.422353i
$147$	9.14901			0.754598
$148$	0.187611	+	0.324952i	0.0154215	+	0.0267109i
$149$	−10.4825	−	18.1562i	−0.858759	−	1.48741i	−0.873113	−	0.487517i	$-0.837903\pi$
$149$	−10.4825	−	18.1562i	−0.858759	−	1.48741i	0.0143541	−	0.999897i	$-0.495431\pi$
$150$	−2.99491	+	5.18734i	−0.244534	+	0.423545i
$151$	−0.0776759			−0.00632118			−0.00316059	−	0.999995i	$-0.501006\pi$
$151$	−0.0776759			−0.00632118			−0.00316059	+	0.999995i	$0.501006\pi$
$152$	8.67520	+	15.0259i	0.703652	+	1.21876i
$153$	−33.0973			−2.67576
$154$	−14.4567			−1.16495
$155$	11.2884	−	7.99740i	0.906708	−	0.642366i
$156$	−0.980025			−0.0784648
$157$	1.52670			0.121844			0.0609220	−	0.998143i	$-0.480596\pi$
$157$	1.52670			0.121844			0.0609220	+	0.998143i	$0.480596\pi$
$158$	−11.8036	−	20.4444i	−0.939045	−	1.62647i
$159$	21.8328			1.73145
$160$	2.02725	−	3.51129i	0.160268	−	0.277592i
$161$	0.235506	+	0.407908i	0.0185605	+	0.0321477i
$162$	27.1876	+	47.0903i	2.13606	+	3.69976i
$163$	20.0274			1.56867			0.784334	−	0.620338i	$-0.213005\pi$
$163$	20.0274			1.56867			0.784334	+	0.620338i	$0.213005\pi$
$164$	1.33562	−	2.31336i	0.104294	−	0.180643i
$165$	−19.3255	+	33.4728i	−1.50449	+	2.60585i
$166$	−9.12099	+	15.7980i	−0.707926	+	1.22616i
$167$	10.6277	+	18.4076i	0.822392	+	1.42443i	0.903896	+	0.427752i	$0.140694\pi$
$167$	10.6277	+	18.4076i	0.822392	+	1.42443i	−0.0815038	+	0.996673i	$0.525972\pi$
$168$	9.02995	−	15.6403i	0.696676	−	1.20668i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−14.8730			−1.14070
$171$	−56.1243			−4.29193
$172$	0.434695	+	0.752915i	0.0331452	+	0.0574092i
$173$	−9.27090	+	16.0577i	−0.704853	+	1.22084i	0.261891	+	0.965097i	$0.415654\pi$
$173$	−9.27090	+	16.0577i	−0.704853	+	1.22084i	−0.966744	+	0.255744i	$0.917679\pi$
$174$	11.3566	+	19.6701i	0.860938	+	1.49119i
$175$	−1.21508	+	2.10458i	−0.0918516	+	0.159092i
$176$	10.3732	−	17.9668i	0.781906	−	1.35430i
$177$	5.48649	−	9.50288i	0.412390	−	0.714280i
$178$	16.2528			1.21820
$179$	−11.0054	−	19.0620i	−0.822584	−	1.42476i	−0.903751	−	0.428058i	$-0.859198\pi$
$179$	−11.0054	−	19.0620i	−0.822584	−	1.42476i	0.0811670	−	0.996701i	$-0.474135\pi$
$180$	3.02190	+	5.23408i	0.225239	+	0.390125i
$181$	0.0848474	−	0.146960i	0.00630665	−	0.0109234i	−0.862855	−	0.505452i	$-0.831326\pi$
$181$	0.0848474	−	0.146960i	0.00630665	−	0.0109234i	0.869162	+	0.494528i	$0.164659\pi$
$182$	−3.13353			−0.232273
$183$	−7.10473	−	12.3057i	−0.525196	−	0.909667i
$184$	−0.588554			−0.0433888
$185$	3.20759			0.235827
$186$	−2.63243	−	28.2906i	−0.193019	−	2.07436i
$187$	−18.2464			−1.33431
$188$	−0.906121			−0.0660856
$189$	18.7384	+	32.4559i	1.36302	+	2.36082i
$190$	−25.2206			−1.82970
$191$	7.08863	−	12.2779i	0.512915	−	0.888395i	−0.486972	−	0.873417i	$-0.661899\pi$
$191$	7.08863	−	12.2779i	0.512915	−	0.888395i	0.999888	−	0.0149782i	$-0.00476787\pi$
$192$	10.9986	+	19.0501i	0.793752	+	1.37482i
$193$	3.40474	+	5.89718i	0.245079	+	0.424489i	0.962154	−	0.272507i	$-0.0878529\pi$
$193$	3.40474	+	5.89718i	0.245079	+	0.424489i	−0.717075	+	0.696996i	$0.754520\pi$
$194$	−5.64372			−0.405195
$195$	−4.18888	+	7.25535i	−0.299972	+	0.519566i
$196$	0.394345	−	0.683025i	0.0281675	−	0.0487875i
$197$	11.7086	−	20.2799i	0.834205	−	1.44489i	−0.0604713	−	0.998170i	$-0.519260\pi$
$197$	11.7086	−	20.2799i	0.834205	−	1.44489i	0.894676	−	0.446715i	$-0.147406\pi$
$198$	29.2169	+	50.6052i	2.07636	+	3.59635i
$199$	3.85860	−	6.68330i	0.273529	−	0.473766i	−0.696234	−	0.717815i	$-0.745142\pi$
$199$	3.85860	−	6.68330i	0.273529	−	0.473766i	0.969763	+	0.244049i	$0.0784756\pi$
$200$	−1.51831	−	2.62979i	−0.107361	−	0.185954i
$201$	1.81960			0.128345
$202$	5.17683			0.364240
$203$	4.60753	+	7.98047i	0.323385	+	0.560119i
$204$	−1.93798	+	3.35668i	−0.135686	+	0.235015i
$205$	−11.4175	−	19.7758i	−0.797436	−	1.38120i
$206$	−9.54307	+	16.5291i	−0.664897	+	1.15164i
$207$	0.951914	−	1.64876i	0.0661626	−	0.114597i
$208$	2.24842	−	3.89437i	0.155900	−	0.270026i
$209$	−30.9410			−2.14024
$210$	13.1260	+	22.7349i	0.905779	+	1.56885i
$211$	2.07315	+	3.59080i	0.142721	+	0.247201i	0.928520	−	0.371281i	$-0.121081\pi$
$211$	2.07315	+	3.59080i	0.142721	+	0.247201i	−0.785799	+	0.618482i	$0.787748\pi$
$212$	0.941046	−	1.62994i	0.0646313	−	0.111945i
$213$	31.5345			2.16071
$214$	6.06037	+	10.4969i	0.414278	+	0.717551i
$215$	7.43200			0.506858
$216$	−46.8294			−3.18633
$217$	−1.06802	−	11.4779i	−0.0725018	−	0.779171i
$218$	9.69806			0.656836
$219$	13.1278			0.887097
$220$	1.66596	+	2.88552i	0.112319	+	0.194542i
$221$	−3.95496			−0.266039
$222$	3.29387	−	5.70515i	0.221070	−	0.382905i
$223$	5.43039	+	9.40572i	0.363646	+	0.629853i	0.988558	−	0.150842i	$-0.0481984\pi$
$223$	5.43039	+	9.40572i	0.363646	+	0.629853i	−0.624912	+	0.780695i	$0.714865\pi$
$224$	−1.68922	−	2.92581i	−0.112866	−	0.195489i
$225$	9.82272			0.654848
$226$	3.17334	−	5.49639i	0.211088	−	0.365615i
$227$	−1.07379	+	1.85985i	−0.0712696	+	0.123443i	−0.899458	−	0.437007i	$-0.856038\pi$
$227$	−1.07379	+	1.85985i	−0.0712696	+	0.123443i	0.828188	+	0.560450i	$0.189372\pi$
$228$	−3.28630	+	5.69205i	−0.217641	+	0.376965i
$229$	−8.06398	−	13.9672i	−0.532883	−	0.922980i	−0.999263	−	0.0383953i	$-0.987775\pi$
$229$	−8.06398	−	13.9672i	−0.532883	−	0.922980i	0.466380	−	0.884584i	$-0.345558\pi$
$230$	0.427763	−	0.740907i	0.0282058	−	0.0488540i
$231$	16.1031	+	27.8914i	1.05951	+	1.83512i
$232$	−11.5147			−0.755977
$233$	−9.52903			−0.624268			−0.312134	−	0.950038i	$-0.601044\pi$
$233$	−9.52903			−0.624268			−0.312134	+	0.950038i	$0.601044\pi$
$234$	6.33287	+	10.9688i	0.413992	+	0.717056i
$235$	−3.87299	+	6.70822i	−0.252646	+	0.437596i
$236$	−0.472962	−	0.819195i	−0.0307872	−	0.0533250i
$237$	−26.2958	+	45.5457i	−1.70810	+	2.95851i
$238$	−6.19650	+	10.7327i	−0.401659	+	0.695694i
$239$	−4.49601	+	7.78732i	−0.290823	+	0.503720i	−0.974005	−	0.226528i	$-0.927262\pi$
$239$	−4.49601	+	7.78732i	−0.290823	+	0.503720i	0.683182	+	0.730248i	$0.260596\pi$
$240$	−37.6734			−2.43181
$241$	10.6597	+	18.4631i	0.686649	+	1.18931i	0.972915	+	0.231161i	$0.0742525\pi$
$241$	10.6597	+	18.4631i	0.686649	+	1.18931i	−0.286266	+	0.958150i	$0.592414\pi$
$242$	7.78292	+	13.4804i	0.500305	+	0.866554i
$243$	33.4160	−	57.8783i	2.14364	−	3.71289i
$244$	−1.22492			−0.0784177
$245$	−3.37106	−	5.83885i	−0.215369	−	0.373031i
$246$	−46.8987			−2.99015
$247$	−6.70657			−0.426729
$248$	13.0880	+	6.01538i	0.831091	+	0.381977i
$249$	40.6391			2.57540
$250$	−14.3889			−0.910032
$251$	−0.497471	−	0.861645i	−0.0314001	−	0.0543866i	0.849898	−	0.526947i	$-0.176663\pi$
$251$	−0.497471	−	0.861645i	−0.0314001	−	0.0543866i	−0.881298	+	0.472560i	$0.843330\pi$
$252$	5.03603			0.317240
$253$	0.524785	−	0.908955i	0.0329930	−	0.0571455i
$254$	−10.5050	−	18.1952i	−0.659141	−	1.14167i
$255$	16.5668	+	28.6946i	1.03746	+	1.79693i
$256$	6.83563			0.427227
$257$	−13.1651	+	22.8026i	−0.821216	+	1.42239i	0.0835617	+	0.996503i	$0.473370\pi$
$257$	−13.1651	+	22.8026i	−0.821216	+	1.42239i	−0.904777	+	0.425885i	$0.859963\pi$
$258$	7.63191	−	13.2189i	0.475142	−	0.822970i
$259$	1.33637	−	2.31467i	0.0830382	−	0.143826i
$260$	0.361102	+	0.625447i	0.0223946	+	0.0387885i
$261$	18.6236	−	32.2571i	1.15277	−	1.99666i
$262$	−15.2068	−	26.3389i	−0.939477	−	1.62722i
$263$	6.63694			0.409251			0.204626	−	0.978840i	$-0.434402\pi$
$263$	6.63694			0.409251			0.204626	+	0.978840i	$0.434402\pi$
$264$	−40.2435			−2.47681
$265$	−8.04454	−	13.9336i	−0.494172	−	0.855932i
$266$	−10.5076	+	18.1998i	−0.644264	+	1.11590i
$267$	−18.1038	−	31.3567i	−1.10793	−	1.91900i
$268$	0.0784293	−	0.135844i	0.00479083	−	0.00829797i
$269$	6.97798	−	12.0862i	0.425455	−	0.736910i	−0.571008	−	0.820945i	$-0.693447\pi$
$269$	6.97798	−	12.0862i	0.425455	−	0.736910i	0.996463	+	0.0840350i	$0.0267808\pi$
$270$	34.0357	−	58.9516i	2.07135	−	3.58768i
$271$	−9.87890			−0.600101			−0.300050	−	0.953923i	$-0.597003\pi$
$271$	−9.87890			−0.600101			−0.300050	+	0.953923i	$0.597003\pi$
$272$	−8.89240	−	15.4021i	−0.539181	−	0.933889i
$273$	3.49041	+	6.04557i	0.211249	+	0.365894i
$274$	0.936998	−	1.62293i	0.0566061	−	0.0980447i
$275$	5.41521			0.326550
$276$	−0.111477	−	0.193084i	−0.00671012	−	0.0116223i
$277$	21.2475			1.27664			0.638318	−	0.769772i	$-0.279630\pi$
$277$	21.2475			1.27664			0.638318	+	0.769772i	$0.279630\pi$
$278$	2.46721			0.147974
$279$	−38.0196	+	26.9354i	−2.27618	+	1.61258i
$280$	−13.3088			−0.795351
$281$	−7.20545			−0.429841			−0.214921	−	0.976632i	$-0.568949\pi$
$281$	−7.20545			−0.429841			−0.214921	+	0.976632i	$0.568949\pi$
$282$	7.95434	+	13.7773i	0.473674	+	0.820428i
$283$	−8.50797			−0.505747			−0.252873	−	0.967499i	$-0.581376\pi$
$283$	−8.50797			−0.505747			−0.252873	+	0.967499i	$0.581376\pi$
$284$	1.35922	−	2.35423i	0.0806546	−	0.139698i
$285$	28.0930	+	48.6585i	1.66409	+	2.88228i
$286$	3.49128	+	6.04707i	0.206443	+	0.357571i
$287$	−19.0275			−1.12316
$288$	−6.82781	+	11.8261i	−0.402333	+	0.696861i
$289$	0.679143	−	1.17631i	0.0399496	−	0.0691947i
$290$	8.36892	−	14.4954i	0.491440	−	0.851199i
$291$	6.28648	+	10.8885i	0.368520	+	0.638295i
$292$	0.565842	−	0.980067i	0.0331134	−	0.0573541i
$293$	−0.756852	−	1.31091i	−0.0442158	−	0.0765839i	0.843071	−	0.537803i	$-0.180746\pi$
$293$	−0.756852	−	1.31091i	−0.0442158	−	0.0765839i	−0.887286	+	0.461219i	$0.847412\pi$
$294$	−13.8470			−0.807571
$295$	−8.08625			−0.470800
$296$	1.66987	+	2.89230i	0.0970592	+	0.168112i
$297$	41.7555	−	72.3226i	2.42290	−	4.19658i
$298$	15.8652	+	27.4793i	0.919045	+	1.59183i
$299$	0.113749	−	0.197019i	0.00657828	−	0.0113939i
$300$	0.575160	−	0.996206i	0.0332069	−	0.0575160i
$301$	3.09638	−	5.36309i	0.178473	−	0.309123i
$302$	0.117562			0.00676493
$303$	−5.76642	−	9.98773i	−0.331272	−	0.573780i
$304$	−15.0792	−	26.1179i	−0.864850	−	1.49796i
$305$	−5.23564	+	9.06840i	−0.299792	+	0.519255i
$306$	50.0925			2.86360
$307$	−13.8161	−	23.9302i	−0.788527	−	1.36577i	−0.926869	−	0.375384i	$-0.877511\pi$
$307$	−13.8161	−	23.9302i	−0.788527	−	1.36577i	0.138342	−	0.990384i	$-0.455823\pi$
$308$	2.77634			0.158197
$309$	42.5197			2.41886
$310$	−17.0849	+	12.1040i	−0.970359	+	0.687461i
$311$	0.509613			0.0288975			0.0144488	−	0.999896i	$-0.495401\pi$
$311$	0.509613			0.0288975			0.0144488	+	0.999896i	$0.495401\pi$
$312$	−8.72291			−0.493837
$313$	4.14898	+	7.18624i	0.234514	+	0.406190i	0.959131	−	0.282961i	$-0.0913168\pi$
$313$	4.14898	+	7.18624i	0.234514	+	0.406190i	−0.724617	+	0.689152i	$0.757983\pi$
$314$	−2.31065			−0.130398
$315$	21.5253	−	37.2829i	1.21281	−	2.10065i
$316$	2.26683	+	3.92626i	0.127519	+	0.220870i
$317$	−5.13601	−	8.89583i	−0.288467	−	0.499640i	0.684977	−	0.728565i	$-0.259812\pi$
$317$	−5.13601	−	8.89583i	−0.288467	−	0.499640i	−0.973444	+	0.228925i	$0.926479\pi$
$318$	−33.0437			−1.85300
$319$	10.2671	−	17.7831i	0.574847	−	0.995665i
$320$	8.10510	−	14.0384i	0.453089	−	0.784772i
$321$	13.5012	−	23.3847i	0.753561	−	1.30521i
$322$	−0.356436	−	0.617366i	−0.0198634	−	0.0344044i
$323$	−13.2621	+	22.9707i	−0.737924	+	1.27812i
$324$	−5.22125	−	9.04348i	−0.290070	−	0.502415i
$325$	1.17377			0.0651088
$326$	−30.3114			−1.67879
$327$	−10.8026	−	18.7106i	−0.597384	−	1.03470i
$328$	11.8879	−	20.5905i	0.656402	−	1.13692i
$329$	3.22720	+	5.58967i	0.177921	+	0.308168i
$330$	29.2491	−	50.6608i	1.61011	−	2.78879i
$331$	13.0318	−	22.5717i	0.716290	−	1.24065i	−0.246169	−	0.969227i	$-0.579172\pi$
$331$	13.0318	−	22.5717i	0.716290	−	1.24065i	0.962460	−	0.271424i	$-0.0874947\pi$
$332$	1.75165	−	3.03394i	0.0961341	−	0.166509i
$333$	−10.8032			−0.592014
$334$	−16.0849	−	27.8598i	−0.880125	−	1.52442i
$335$	−0.670454	−	1.16126i	−0.0366308	−	0.0634465i
$336$	−15.6958	+	27.1859i	−0.856276	+	1.48311i
$337$	−6.86791			−0.374119			−0.187059	−	0.982349i	$-0.559896\pi$
$337$	−6.86791			−0.374119			−0.187059	+	0.982349i	$0.559896\pi$
$338$	0.756746	+	1.31072i	0.0411616	+	0.0712939i
$339$	−14.1390			−0.767926
$340$	2.85629			0.154904
$341$	−20.9600	+	14.8494i	−1.13505	+	0.804137i
$342$	84.9437			4.59323
$343$	−20.1107			−1.08588
$344$	3.86910	+	6.70147i	0.208608	+	0.361319i
$345$	−1.90592			−0.102611
$346$	14.0314	−	24.3032i	0.754335	−	1.30655i
$347$	−0.184403	−	0.319396i	−0.00989929	−	0.0171461i	0.861033	−	0.508549i	$-0.169818\pi$
$347$	−0.184403	−	0.319396i	−0.00989929	−	0.0171461i	−0.870933	+	0.491402i	$0.836484\pi$
$348$	−2.18098	−	3.77756i	−0.116913	−	0.202499i
$349$	−14.9318			−0.799279			−0.399640	−	0.916672i	$-0.630865\pi$
$349$	−14.9318			−0.799279			−0.399640	+	0.916672i	$0.630865\pi$
$350$	1.83902	−	3.18527i	0.0982996	−	0.170260i
$351$	9.05064	−	15.6762i	0.483087	−	0.836732i
$352$	−3.76414	+	6.51968i	−0.200629	+	0.347500i
$353$	10.2030	+	17.6721i	0.543050	+	0.940591i	0.998727	+	0.0504455i	$0.0160641\pi$
$353$	10.2030	+	17.6721i	0.543050	+	0.940591i	−0.455676	+	0.890146i	$0.650603\pi$
$354$	−8.30376	+	14.3825i	−0.441340	+	0.764423i
$355$	−11.6193	−	20.1252i	−0.616687	−	1.06813i
$356$	−3.12127			−0.165427
$357$	27.6089			1.46122
$358$	16.6566	+	28.8501i	0.880331	+	1.52478i
$359$	−0.527237	+	0.913201i	−0.0278265	+	0.0481969i	−0.879603	−	0.475708i	$-0.842192\pi$
$359$	−0.527237	+	0.913201i	−0.0278265	+	0.0481969i	0.851777	+	0.523905i	$0.175525\pi$
$360$	26.8970	+	46.5870i	1.41760	+	2.45535i
$361$	−12.9891	+	22.4977i	−0.683635	+	1.18409i
$362$	−0.128416	+	0.222423i	−0.00674939	+	0.0116903i
$363$	17.3386	−	30.0314i	0.910042	−	1.57624i
$364$	0.601781			0.0315419
$365$	−4.83711	−	8.37812i	−0.253186	−	0.438531i
$366$	10.7529	+	18.6247i	0.562066	+	0.973526i
$367$	−3.27934	+	5.67998i	−0.171180	+	0.296493i	−0.938833	−	0.344374i	$-0.888091\pi$
$367$	−3.27934	+	5.67998i	−0.171180	+	0.296493i	0.767653	+	0.640866i	$0.221425\pi$
$368$	1.02302			0.0533287
$369$	38.4546	+	66.6052i	2.00186	+	3.46733i
$370$	−4.85466			−0.252382
$371$	−13.4063			−0.696023
$372$	0.505547	+	5.43308i	0.0262114	+	0.281692i
$373$	−28.6295			−1.48238			−0.741189	−	0.671296i	$-0.765738\pi$
$373$	−28.6295			−1.48238			−0.741189	+	0.671296i	$0.765738\pi$
$374$	27.6157			1.42797
$375$	16.0276	+	27.7607i	0.827663	+	1.43355i
$376$	−8.06511			−0.415926
$377$	2.22543	−	3.85456i	0.114615	−	0.198520i
$378$	−28.3605	−	49.1218i	−1.45871	−	2.52655i
$379$	−2.09363	−	3.62626i	−0.107542	−	0.186269i	0.807232	−	0.590235i	$-0.200965\pi$
$379$	−2.09363	−	3.62626i	−0.107542	−	0.186269i	−0.914774	+	0.403966i	$0.867631\pi$
$380$	4.84351			0.248467
$381$	−23.4028	+	40.5348i	−1.19896	+	2.07666i
$382$	−10.7286	+	18.5825i	−0.548922	+	0.950762i
$383$	−2.03964	+	3.53276i	−0.104221	+	0.180515i	−0.913420	−	0.407019i	$-0.866568\pi$
$383$	−2.03964	+	3.53276i	−0.104221	+	0.180515i	0.809199	+	0.587535i	$0.199901\pi$
$384$	−22.1481	−	38.3617i	−1.13024	−	1.95764i
$385$	11.8668	−	20.5539i	0.604787	−	1.04752i
$386$	−5.15305	−	8.92534i	−0.262283	−	0.454288i
$387$	−25.0311			−1.27240
$388$	1.08385			0.0550242
$389$	1.52561	+	2.64244i	0.0773517	+	0.133977i	0.902107	−	0.431513i	$-0.142020\pi$
$389$	1.52561	+	2.64244i	0.0773517	+	0.133977i	−0.824755	+	0.565490i	$0.808687\pi$
$390$	6.33983	−	10.9809i	0.321030	−	0.556040i
$391$	−0.449873	−	0.779203i	−0.0227510	−	0.0394060i
$392$	3.50995	−	6.07941i	0.177279	−	0.307056i
$393$	−33.8773	+	58.6773i	−1.70889	+	2.95988i
$394$	−17.7209	+	30.6935i	−0.892767	+	1.54632i
$395$	38.7561			1.95003
$396$	−5.61098	−	9.71850i	−0.281962	−	0.488373i
$397$	0.627543	+	1.08694i	0.0314955	+	0.0545518i	0.881344	−	0.472476i	$-0.156640\pi$
$397$	0.627543	+	1.08694i	0.0314955	+	0.0545518i	−0.849848	+	0.527028i	$0.823306\pi$
$398$	−5.83997	+	10.1151i	−0.292731	+	0.507025i
$399$	46.8174			2.34380
$400$	2.63912	+	4.57109i	0.131956	+	0.228554i
$401$	31.0198			1.54905			0.774527	−	0.632540i	$-0.217988\pi$
$401$	31.0198			1.54905			0.774527	+	0.632540i	$0.217988\pi$
$402$	−2.75395			−0.137355
$403$	−4.54316	+	3.21865i	−0.226311	+	0.160332i
$404$	−0.994187			−0.0494626
$405$	−89.2679			−4.43576
$406$	−6.97346	−	12.0784i	−0.346087	−	0.599440i
$407$	−5.95577			−0.295216
$408$	−17.2494	+	29.8768i	−0.853972	+	1.47912i
$409$	13.8765	+	24.0348i	0.686149	+	1.18845i	0.973074	+	0.230492i	$0.0740337\pi$
$409$	13.8765	+	24.0348i	0.686149	+	1.18845i	−0.286925	+	0.957953i	$0.592633\pi$
$410$	17.2804	+	29.9305i	0.853417	+	1.47816i
$411$	−4.17485			−0.205930
$412$	1.83270	−	3.17434i	0.0902908	−	0.156388i
$413$	−3.36896	+	5.83521i	−0.165776	+	0.287132i
$414$	−1.44071	+	2.49539i	−0.0708073	+	0.122642i
$415$	−14.9740	−	25.9357i	−0.735043	−	1.27313i
$416$	−0.815890	+	1.41316i	−0.0400023	+	0.0692860i
$417$	−2.74820	−	4.76003i	−0.134580	−	0.233099i
$418$	46.8290			2.29048
$419$	13.2957			0.649539			0.324770	−	0.945793i	$-0.394713\pi$
$419$	13.2957			0.649539			0.324770	+	0.945793i	$0.394713\pi$
$420$	−2.52079	−	4.36613i	−0.123002	−	0.213045i
$421$	18.4570	−	31.9684i	0.899537	−	1.55804i	0.0714506	−	0.997444i	$-0.477237\pi$
$421$	18.4570	−	31.9684i	0.899537	−	1.55804i	0.828087	−	0.560600i	$-0.189429\pi$
$422$	−3.13769	−	5.43464i	−0.152740	−	0.264554i
$423$	13.0443	−	22.5934i	0.634237	−	1.09853i
$424$	8.37597	−	14.5076i	0.406773	−	0.704552i
$425$	2.32110	−	4.02026i	0.112590	−	0.195011i
$426$	−47.7273			−2.31239
$427$	4.36263	+	7.55630i	0.211123	+	0.365675i
$428$	−1.16387	−	2.01588i	−0.0562576	−	0.0974410i
$429$	7.77779	−	13.4715i	0.375515	−	0.650412i
$430$	−11.2483			−0.542440
$431$	−8.32396	−	14.4175i	−0.400951	−	0.694467i	0.592890	−	0.805283i	$-0.297987\pi$
$431$	−8.32396	−	14.4175i	−0.400951	−	0.694467i	−0.993841	+	0.110816i	$0.964654\pi$
$432$	81.3985			3.91629
$433$	39.9660			1.92064			0.960322	−	0.278893i	$-0.0899674\pi$
$433$	39.9660			1.92064			0.960322	+	0.278893i	$0.0899674\pi$
$434$	1.61644	+	17.3717i	0.0775915	+	0.833870i
$435$	−37.2882			−1.78783
$436$	−1.86247			−0.0891961
$437$	−0.762866	−	1.32132i	−0.0364928	−	0.0632075i
$438$	−19.8689			−0.949372
$439$	−6.69445	+	11.5951i	−0.319509	+	0.553405i	−0.980386	−	0.197089i	$-0.936851\pi$
$439$	−6.69445	+	11.5951i	−0.319509	+	0.553405i	0.660877	+	0.750494i	$0.270184\pi$
$440$	14.8282	+	25.6832i	0.706906	+	1.22440i
$441$	11.3538	+	19.6654i	0.540658	+	0.936447i
$442$	5.98580			0.284716
$443$	−17.8174	+	30.8606i	−0.846530	+	1.46623i	0.0377563	+	0.999287i	$0.487979\pi$
$443$	−17.8174	+	30.8606i	−0.846530	+	1.46623i	−0.884286	+	0.466946i	$0.845354\pi$
$444$	−0.632573	+	1.09565i	−0.0300206	+	0.0519972i
$445$	−13.3411	+	23.1075i	−0.632430	+	1.09540i
$446$	−8.21886	−	14.2355i	−0.389174	−	0.674070i
$447$	35.3441	−	61.2178i	1.67172	−	2.89550i
$448$	−6.75363	−	11.6976i	−0.319079	−	0.552661i
$449$	−24.1648			−1.14041			−0.570204	−	0.821503i	$-0.693136\pi$
$449$	−24.1648			−1.14041			−0.570204	+	0.821503i	$0.693136\pi$
$450$	−14.8666			−0.700819
$451$	21.1998	+	36.7191i	0.998259	+	1.72904i
$452$	−0.609427	+	1.05556i	−0.0286650	+	0.0496493i
$453$	−0.130951	−	0.226814i	−0.00615262	−	0.0106566i
$454$	1.62517	−	2.81487i	0.0762728	−	0.132108i
$455$	2.57217	−	4.45512i	0.120585	−	0.208859i
$456$	−29.2504	+	50.6632i	−1.36978	+	2.37252i
$457$	22.0308			1.03056			0.515279	−	0.857022i	$-0.327688\pi$
$457$	22.0308			1.03056			0.515279	+	0.857022i	$0.327688\pi$
$458$	12.2048	+	21.1393i	0.570291	+	0.987774i
$459$	−35.7949	−	61.9986i	−1.67076	−	2.89385i
$460$	−0.0821499	+	0.142288i	−0.00383026	+	0.00663421i
$461$	−5.24478			−0.244274			−0.122137	−	0.992513i	$-0.538975\pi$
$461$	−5.24478			−0.244274			−0.122137	+	0.992513i	$0.538975\pi$
$462$	−24.3720	−	42.2135i	−1.13389	−	1.96395i
$463$	31.5239			1.46504			0.732520	−	0.680745i	$-0.238344\pi$
$463$	31.5239			1.46504			0.732520	+	0.680745i	$0.238344\pi$
$464$	20.0148			0.929163
$465$	42.3832	+	19.4797i	1.96547	+	0.903349i
$466$	14.4221			0.668092
$467$	22.1963			1.02712			0.513562	−	0.858052i	$-0.328326\pi$
$467$	22.1963			1.02712			0.513562	+	0.858052i	$0.328326\pi$
$468$	−1.21620	−	2.10652i	−0.0562188	−	0.0973738i
$469$	−1.11732			−0.0515931
$470$	5.86175	−	10.1528i	0.270382	−	0.468316i
$471$	2.57381	+	4.45797i	0.118595	+	0.205412i
$472$	−4.20970	−	7.29141i	−0.193767	−	0.335614i
$473$	−13.7995			−0.634503
$474$	39.7986	−	68.9331i	1.82801	−	3.16620i
$475$	3.93598	−	6.81731i	0.180595	−	0.312800i
$476$	1.19001	−	2.06116i	0.0545440	−	0.0944730i
$477$	27.0942	+	46.9285i	1.24056	+	2.14871i
$478$	6.80468	−	11.7861i	0.311239	−	0.539082i
$479$	−15.4756	−	26.8046i	−0.707100	−	1.22473i	−0.965928	−	0.258810i	$-0.916670\pi$
$479$	−15.4756	−	26.8046i	−0.707100	−	1.22473i	0.258828	−	0.965923i	$-0.416664\pi$
$480$	13.6706			0.623977
$481$	−1.29093			−0.0588615
$482$	−16.1333	−	27.9437i	−0.734853	−	1.27280i
$483$	−0.794061	+	1.37535i	−0.0361310	+	0.0625808i
$484$	−1.49467	−	2.58885i	−0.0679398	−	0.117675i
$485$	4.63266	−	8.02399i	0.210358	−	0.364351i
$486$	−50.5749	+	87.5983i	−2.29412	+	3.97354i
$487$	−1.87396	+	3.24580i	−0.0849173	+	0.147081i	−0.905356	−	0.424653i	$-0.860396\pi$
$487$	−1.87396	+	3.24580i	−0.0849173	+	0.147081i	0.820439	+	0.571735i	$0.193729\pi$
$488$	−10.9027			−0.493542
$489$	33.7635	+	58.4801i	1.52684	+	2.64456i
$490$	5.10208	+	8.83706i	0.230488	+	0.399218i
$491$	14.3858	−	24.9169i	0.649221	−	1.12448i	−0.334088	−	0.942542i	$-0.608428\pi$
$491$	14.3858	−	24.9169i	0.649221	−	1.12448i	0.983309	−	0.181942i	$-0.0582382\pi$
$492$	9.00668			0.406052
$493$	−8.80149	−	15.2446i	−0.396399	−	0.686583i
$494$	10.1503			0.456686
$495$	−95.9310			−4.31178
$496$	−22.7495	−	10.4559i	−1.02148	−	0.469484i
$497$	−19.3637			−0.868579
$498$	−61.5070			−2.75619
$499$	−7.30744	−	12.6569i	−0.327126	−	0.566599i	0.654814	−	0.755790i	$-0.272747\pi$
$499$	−7.30744	−	12.6569i	−0.327126	−	0.566599i	−0.981940	+	0.189191i	$0.939414\pi$
$500$	2.76332			0.123579
$501$	−35.8335	+	62.0655i	−1.60092	+	2.77288i
$502$	0.752919	+	1.30409i	0.0336044	+	0.0582046i
$503$	10.1977	+	17.6630i	0.454695	+	0.787554i	0.998671	−	0.0515465i	$-0.0164150\pi$
$503$	10.1977	+	17.6630i	0.454695	+	0.787554i	−0.543976	+	0.839101i	$0.683082\pi$
$504$	44.8242			1.99663
$505$	−4.24941	+	7.36019i	−0.189096	+	0.327524i
$506$	−0.794258	+	1.37570i	−0.0353091	+	0.0611571i
$507$	1.68586	−	2.92000i	0.0748718	−	0.129682i
$508$	2.01743	+	3.49430i	0.0895091	+	0.155034i
$509$	5.05525	−	8.75595i	0.224070	−	0.388101i	−0.731970	−	0.681337i	$-0.761399\pi$
$509$	5.05525	−	8.75595i	0.224070	−	0.388101i	0.956040	+	0.293236i	$0.0947322\pi$
$510$	−25.0738	−	43.4291i	−1.11029	−	1.92307i
$511$	−8.06111			−0.356602
$512$	15.9295			0.703989
$513$	−60.6988	−	105.133i	−2.67992	−	4.64175i
$514$	19.9253	−	34.5116i	0.878866	−	1.52224i
$515$	−15.6669	−	27.1359i	−0.690366	−	1.19575i
$516$	−1.46567	+	2.53862i	−0.0645227	+	0.111757i
$517$	7.19127	−	12.4556i	0.316272	−	0.547799i
$518$	−2.02259	+	3.50323i	−0.0888676	+	0.153923i
$519$	−62.5179			−2.74423
$520$	3.21406	+	5.56691i	0.140946	+	0.244125i
$521$	−4.49005	−	7.77699i	−0.196713	−	0.340716i	0.750748	−	0.660589i	$-0.229693\pi$
$521$	−4.49005	−	7.77699i	−0.196713	−	0.340716i	−0.947461	+	0.319873i	$0.896360\pi$
$522$	−28.1867	+	48.8208i	−1.23370	+	2.13683i
$523$	9.07959			0.397023			0.198511	−	0.980099i	$-0.436389\pi$
$523$	9.07959			0.397023			0.198511	+	0.980099i	$0.436389\pi$
$524$	2.92039	+	5.05827i	0.127578	+	0.220971i
$525$	−8.19385			−0.357609
$526$	−10.0450			−0.437981
$527$	2.04017	+	21.9256i	0.0888713	+	0.955093i
$528$	69.9509			3.04422
$529$	−22.9482			−0.997750
$530$	12.1754	+	21.0883i	0.528864	+	0.916019i
$531$	27.2347			1.18188
$532$	2.01794	−	3.49518i	0.0874890	−	0.151535i
$533$	4.59513	+	7.95900i	0.199037	+	0.344742i
$534$	27.4000	+	47.4581i	1.18571	+	2.05371i
$535$	−19.8987			−0.860294
$536$	0.698076	−	1.20910i	0.0301523	−	0.0522253i
$537$	37.1073	−	64.2718i	1.60130	−	2.77353i
$538$	−10.5611	+	18.2924i	−0.455322	+	0.788641i
$539$	6.25930	+	10.8414i	0.269607	+	0.466973i
$540$	−6.53640	+	11.3214i	−0.281282	+	0.487195i
$541$	0.878149	+	1.52100i	0.0377546	+	0.0653928i	0.884285	−	0.466947i	$-0.154646\pi$
$541$	0.878149	+	1.52100i	0.0377546	+	0.0653928i	−0.846531	+	0.532340i	$0.821313\pi$
$542$	14.9516			0.642228
$543$	0.572164			0.0245539
$544$	3.22681	+	5.58900i	0.138348	+	0.239626i
$545$	−7.96067	+	13.7883i	−0.340998	+	0.590625i
$546$	−5.28271	−	9.14992i	−0.226079	−	0.391580i
$547$	−9.92760	+	17.1951i	−0.424474	+	0.735210i	−0.996371	−	0.0851153i	$-0.972874\pi$
$547$	−9.92760	+	17.1951i	−0.424474	+	0.735210i	0.571898	+	0.820325i	$0.306207\pi$
$548$	−0.179946	+	0.311676i	−0.00768692	+	0.0133141i
$549$	17.6338	−	30.5426i	0.752591	−	1.30352i
$550$	−8.19588			−0.349474
$551$	−14.9250	−	25.8509i	−0.635827	−	1.10128i
$552$	−0.992222	−	1.71858i	−0.0422318	−	0.0731476i
$553$	16.1469	−	27.9672i	0.686635	−	1.18929i
$554$	−32.1579			−1.36626
$555$	5.40756	+	9.36617i	0.229538	+	0.397572i
$556$	−0.473817			−0.0200943
$557$	4.01710			0.170210			0.0851050	−	0.996372i	$-0.472877\pi$
$557$	4.01710			0.170210			0.0851050	+	0.996372i	$0.472877\pi$
$558$	57.5425	−	40.7665i	2.43597	−	1.72579i
$559$	−2.99110			−0.126510
$560$	23.1332			0.977557
$561$	−30.7609	−	53.2794i	−1.29872	−	2.24946i
$562$	10.9054			0.460016
$563$	−0.794428	+	1.37599i	−0.0334811	+	0.0579910i	−0.882280	−	0.470724i	$-0.843993\pi$
$563$	−0.794428	+	1.37599i	−0.0334811	+	0.0579910i	0.848799	+	0.528715i	$0.177326\pi$
$564$	−1.52760	−	2.64587i	−0.0643234	−	0.111411i
$565$	5.20969	+	9.02345i	0.219173	+	0.379619i
$566$	12.8768			0.541250
$567$	−37.1916	+	64.4177i	−1.56190	+	2.70529i
$568$	12.0980	−	20.9543i	0.507620	−	0.879223i
$569$	−8.75399	+	15.1624i	−0.366986	+	0.635639i	−0.989093	−	0.147294i	$-0.952944\pi$
$569$	−8.75399	+	15.1624i	−0.366986	+	0.635639i	0.622107	+	0.782933i	$0.286277\pi$
$570$	−42.5186	−	73.6443i	−1.78091	−	3.08462i
$571$	−18.1894	+	31.5051i	−0.761205	+	1.31845i	0.181025	+	0.983478i	$0.442058\pi$
$571$	−18.1894	+	31.5051i	−0.761205	+	1.31845i	−0.942230	+	0.334967i	$0.891275\pi$
$572$	−0.670484	−	1.16131i	−0.0280343	−	0.0485569i
$573$	47.8019			1.99695
$574$	28.7980			1.20200
$575$	0.133515	+	0.231254i	0.00556795	+	0.00964397i
$576$	−27.2981	+	47.2818i	−1.13742	+	1.97007i
$577$	−6.54217	−	11.3314i	−0.272354	−	0.471731i	0.697110	−	0.716964i	$-0.254469\pi$
$577$	−6.54217	−	11.3314i	−0.272354	−	0.471731i	−0.969464	+	0.245233i	$0.921136\pi$
$578$	−1.02788	+	1.78034i	−0.0427541	+	0.0740522i
$579$	−11.4799	+	19.8837i	−0.477087	+	0.826338i
$580$	−1.60721	+	2.78377i	−0.0667359	+	0.115590i
$581$	−24.9543			−1.03528
$582$	−9.51454	−	16.4797i	−0.394390	−	0.683104i
$583$	14.9369	+	25.8715i	0.618623	+	1.07149i
$584$	5.03639	−	8.72329i	0.208407	−	0.360972i
$585$	−20.7934			−0.859701
$586$	1.14549	+	1.98405i	0.0473197	+	0.0819602i
$587$	−11.6897			−0.482484			−0.241242	−	0.970465i	$-0.577555\pi$
$587$	−11.6897			−0.482484			−0.241242	+	0.970465i	$0.577555\pi$
$588$	2.65925			0.109666
$589$	3.45960	+	37.1800i	0.142550	+	1.53198i
$590$	12.2385			0.503850
$591$	78.9566			3.24784
$592$	−2.90256	−	5.02738i	−0.119294	−	0.206624i
$593$	9.88948			0.406112			0.203056	−	0.979167i	$-0.434913\pi$
$593$	9.88948			0.406112			0.203056	+	0.979167i	$0.434913\pi$
$594$	−63.1966	+	109.460i	−2.59299	+	4.49118i
$595$	−10.1728	−	17.6198i	−0.417045	−	0.722343i
$596$	−3.04684	−	5.27727i	−0.124803	−	0.216166i
$597$	26.0203			1.06494
$598$	−0.172158	+	0.298187i	−0.00704008	+	0.0121938i
$599$	4.07327	−	7.05511i	0.166429	−	0.288264i	−0.770733	−	0.637159i	$-0.780110\pi$
$599$	4.07327	−	7.05511i	0.166429	−	0.288264i	0.937162	+	0.348895i	$0.113443\pi$
$600$	5.11933	−	8.86694i	0.208996	−	0.361991i
$601$	−13.0094	−	22.5330i	−0.530665	−	0.919139i	−0.999360	−	0.0357787i	$-0.988609\pi$
$601$	−13.0094	−	22.5330i	−0.530665	−	0.919139i	0.468695	−	0.883360i	$-0.344724\pi$
$602$	−4.68635	+	8.11700i	−0.191001	+	0.330824i
$603$	2.25810	+	3.91115i	0.0919571	+	0.159274i
$604$	−0.0225772			−0.000918655
$605$	−25.5545			−1.03894
$606$	8.72743	+	15.1163i	0.354528	+	0.614060i
$607$	−3.31423	+	5.74042i	−0.134520	+	0.232996i	−0.925414	−	0.378957i	$-0.876283\pi$
$607$	−3.31423	+	5.74042i	−0.134520	+	0.232996i	0.790894	+	0.611954i	$0.209616\pi$
$608$	5.47182	+	9.47748i	0.221912	+	0.384363i
$609$	−15.5353	+	26.9080i	−0.629523	+	1.09037i
$610$	7.92410	−	13.7250i	0.320838	−	0.555707i
$611$	1.55873	−	2.69980i	0.0630596	−	0.109222i
$612$	−9.62004			−0.388867
$613$	−12.3700	−	21.4256i	−0.499622	−	0.865370i	0.500378	−	0.865807i	$-0.333194\pi$
$613$	−12.3700	−	21.4256i	−0.499622	−	0.865370i	−1.00000		0.000436995i	$0.999861\pi$
$614$	20.9106	+	36.2182i	0.843882	+	1.46165i
$615$	38.4969	−	66.6785i	1.55234	−	2.68874i
$616$	24.7114			0.995649
$617$	−0.704018	−	1.21940i	−0.0283427	−	0.0490910i	0.851506	−	0.524345i	$-0.175690\pi$
$617$	−0.704018	−	1.21940i	−0.0283427	−	0.0490910i	−0.879849	+	0.475254i	$0.842356\pi$
$618$	−64.3533			−2.58867
$619$	−37.5779			−1.51038			−0.755192	−	0.655504i	$-0.772456\pi$
$619$	−37.5779			−1.51038			−0.755192	+	0.655504i	$0.772456\pi$
$620$	3.28109	−	2.32452i	0.131772	−	0.0933549i
$621$	4.11801			0.165250
$622$	−0.771295			−0.0309261
$623$	11.1166	+	19.2545i	0.445376	+	0.771415i
$624$	15.1621			0.606970
$625$	14.7456	−	25.5400i	0.589822	−	1.02160i
$626$	−6.27945	−	10.8763i	−0.250977	−	0.434705i
$627$	−52.1624	−	90.3478i	−2.08316	−	3.60815i
$628$	0.443750			0.0177076
$629$	−2.55280	+	4.42157i	−0.101787	+	0.176300i
$630$	−32.5784	+	56.4274i	−1.29795	+	2.24812i
$631$	−3.12870	+	5.41907i	−0.124552	+	0.215730i	−0.921558	−	0.388242i	$-0.873083\pi$
$631$	−3.12870	+	5.41907i	−0.124552	+	0.215730i	0.797006	+	0.603971i	$0.206416\pi$
$632$	20.1764	+	34.9465i	0.802573	+	1.39010i
$633$	−6.99009	+	12.1072i	−0.277831	+	0.481217i
$634$	7.77331	+	13.4638i	0.308718	+	0.534715i
$635$	34.4921			1.36878
$636$	6.34590			0.251631
$637$	1.35672	+	2.34992i	0.0537554	+	0.0931071i
$638$	−15.5392	+	26.9147i	−0.615202	+	1.06556i
$639$	39.1340	+	67.7820i	1.54812	+	2.68141i
$640$	−16.3215	+	28.2697i	−0.645164	+	1.11746i
$641$	20.9057	−	36.2097i	0.825724	−	1.43020i	−0.0756413	−	0.997135i	$-0.524100\pi$
$641$	20.9057	−	36.2097i	0.825724	−	1.43020i	0.901365	−	0.433060i	$-0.142566\pi$
$642$	−20.4339	+	35.3926i	−0.806462	+	1.39683i
$643$	2.87978			0.113567			0.0567837	−	0.998387i	$-0.481915\pi$
$643$	2.87978			0.113567			0.0567837	+	0.998387i	$0.481915\pi$
$644$	0.0684520	+	0.118562i	0.00269739	+	0.00467201i
$645$	12.5293	+	21.7015i	0.493342	+	0.854494i
$646$	20.0721	−	34.7659i	0.789727	−	1.36785i
$647$	34.1653			1.34318			0.671588	−	0.740925i	$-0.265613\pi$
$647$	34.1653			1.34318			0.671588	+	0.740925i	$0.265613\pi$
$648$	−46.4728	−	80.4933i	−1.82563	−	3.16208i
$649$	15.0143			0.589364
$650$	−1.77649			−0.0696795
$651$	31.7150	−	22.4688i	1.24301	−	0.880622i
$652$	5.82116			0.227974
$653$	21.3121			0.834008			0.417004	−	0.908905i	$-0.363080\pi$
$653$	21.3121			0.834008			0.417004	+	0.908905i	$0.363080\pi$
$654$	16.3496	+	28.3184i	0.639320	+	1.10734i
$655$	49.9300			1.95093
$656$	−20.6635	+	35.7903i	−0.806776	+	1.39738i
$657$	16.2915	+	28.2177i	0.635592	+	1.10088i
$658$	−4.88434	−	8.45992i	−0.190411	−	0.329802i
$659$	45.3383			1.76613			0.883064	−	0.469252i	$-0.155477\pi$
$659$	45.3383			1.76613			0.883064	+	0.469252i	$0.155477\pi$
$660$	−5.61715	+	9.72919i	−0.218647	+	0.378708i
$661$	−12.4143	+	21.5022i	−0.482861	+	0.836341i	−0.999806	−	0.0196781i	$-0.993736\pi$
$661$	−12.4143	+	21.5022i	−0.482861	+	0.836341i	0.516945	+	0.856019i	$0.327069\pi$
$662$	−19.7235	+	34.1621i	−0.766574	+	1.32775i
$663$	−6.66753	−	11.5485i	−0.258945	−	0.448506i
$664$	15.5909	−	27.0042i	0.605044	−	1.04797i
$665$	−17.2504	−	29.8786i	−0.668943	−	1.15864i
$666$	16.3506			0.633574
$667$	1.01256			0.0392066
$668$	3.08903	+	5.35035i	0.119518	+	0.207011i
$669$	−18.3098	+	31.7135i	−0.707898	+	1.22612i
$670$	1.01473	+	1.75756i	0.0392023	+	0.0679004i
$671$	9.72140	−	16.8380i	0.375290	−	0.650022i
$672$	5.69558	−	9.86503i	0.219712	−	0.380552i
$673$	−4.90548	+	8.49654i	−0.189092	+	0.327518i	−0.944948	−	0.327221i	$-0.893888\pi$
$673$	−4.90548	+	8.49654i	−0.189092	+	0.327518i	0.755856	+	0.654738i	$0.227221\pi$
$674$	10.3945			0.400382
$675$	10.6233	+	18.4002i	0.408892	+	0.708223i
$676$	−0.145330	−	0.251718i	−0.00558961	−	0.00968148i
$677$	1.59090	−	2.75553i	0.0611434	−	0.105904i	−0.833833	−	0.552016i	$-0.813859\pi$
$677$	1.59090	−	2.75553i	0.0611434	−	0.105904i	0.894977	+	0.446113i	$0.147192\pi$
$678$	21.3993			0.821835
$679$	−3.86019	−	6.68605i	−0.148141	−	0.256587i
$680$	25.4230			0.974926
$681$	−7.24102			−0.277477
$682$	31.7228	−	22.4744i	1.21473	−	0.860589i
$683$	13.3662			0.511443			0.255721	−	0.966751i	$-0.417687\pi$
$683$	13.3662			0.511443			0.255721	+	0.966751i	$0.417687\pi$
$684$	−16.3131			−0.623745
$685$	1.53827	+	2.66437i	0.0587744	+	0.101800i
$686$	30.4374			1.16211
$687$	27.1895	−	47.0937i	1.03735	−	1.79674i
$688$	−6.72524	−	11.6485i	−0.256397	−	0.444093i
$689$	3.23762	+	5.60773i	0.123344	+	0.213637i
$690$	2.88460			0.109815
$691$	0.173108	−	0.299831i	0.00658533	−	0.0114061i	−0.862714	−	0.505692i	$-0.831237\pi$
$691$	0.173108	−	0.299831i	0.00658533	−	0.0114061i	0.869299	+	0.494286i	$0.164570\pi$
$692$	−2.69467	+	4.66731i	−0.102436	+	0.177425i
$693$	−39.9676	+	69.2259i	−1.51824	+	2.62967i
$694$	0.279093	+	0.483403i	0.0105942	+	0.0183497i
$695$	−2.02522	+	3.50778i	−0.0768208	+	0.133058i
$696$	−19.4122	−	33.6230i	−0.735818	−	1.27447i
$697$	36.3471			1.37674
$698$	22.5991			0.855389
$699$	−16.0647	−	27.8248i	−0.607621	−	1.05243i
$700$	−0.353175	+	0.611717i	−0.0133488	+	0.0231207i
$701$	0.318617	+	0.551862i	0.0120340	+	0.0208435i	0.871980	−	0.489542i	$-0.162836\pi$
$701$	0.318617	+	0.551862i	0.0120340	+	0.0208435i	−0.859946	+	0.510386i	$0.829503\pi$
$702$	−13.6981	+	23.7258i	−0.517001	+	0.895471i
$703$	−4.32887	+	7.49782i	−0.163266	+	0.282786i
$704$	−15.0493	+	26.0662i	−0.567193	+	0.982407i
$705$	−26.1174			−0.983636
$706$	−15.4422	−	26.7466i	−0.581173	−	1.00662i
$707$	3.54085	+	6.13293i	0.133167	+	0.230653i
$708$	1.59470	−	2.76210i	0.0599325	−	0.103806i
$709$	−5.12268			−0.192386			−0.0961931	−	0.995363i	$-0.530667\pi$
$709$	−5.12268			−0.192386			−0.0961931	+	0.995363i	$0.530667\pi$
$710$	17.5857	+	30.4593i	0.659979	+	1.14312i
$711$	−130.531			−4.89531
$712$	−27.7815			−1.04116
$713$	−1.15092	−	0.528971i	−0.0431021	−	0.0198101i
$714$	−41.7858			−1.56379
$715$	−11.4633			−0.428702
$716$	−3.19883	−	5.54054i	−0.119546	−	0.207060i
$717$	−30.3187			−1.13227
$718$	0.797969	−	1.38212i	0.0297799	−	0.0515804i
$719$	−6.24342	−	10.8139i	−0.232840	−	0.403292i	0.725802	−	0.687903i	$-0.241469\pi$
$719$	−6.24342	−	10.8139i	−0.232840	−	0.403292i	−0.958643	+	0.284612i	$0.908135\pi$
$720$	−46.7522	−	80.9772i	−1.74235	−	3.01784i
$721$	−26.1091			−0.972353
$722$	19.6589	−	34.0501i	0.731627	−	1.26722i
$723$	−35.9415	+	62.2525i	−1.33668	+	2.31519i
$724$	0.0246617	−	0.0427153i	0.000916544	−	0.00158750i
$725$	2.61213	+	4.52435i	0.0970123	+	0.168030i
$726$	−26.2419	+	45.4523i	−0.973928	+	1.68689i
$727$	3.70845	+	6.42323i	0.137539	+	0.238224i	0.926564	−	0.376136i	$-0.122747\pi$
$727$	3.70845	+	6.42323i	0.137539	+	0.238224i	−0.789026	+	0.614360i	$0.789414\pi$
$728$	5.35627			0.198517
$729$	117.559			4.35402
$730$	7.32093	+	12.6802i	0.270960	+	0.469316i
$731$	−5.91484	+	10.2448i	−0.218768	+	0.378918i
$732$	−2.06506	−	3.57678i	−0.0763267	−	0.132202i
$733$	3.49544	−	6.05428i	0.129107	−	0.223620i	−0.794224	−	0.607625i	$-0.792122\pi$
$733$	3.49544	−	6.05428i	0.129107	−	0.223620i	0.923331	+	0.384005i	$0.125456\pi$
$734$	4.96326	−	8.59661i	0.183197	−	0.317307i
$735$	11.3663	−	19.6870i	0.419253	−	0.726167i
$736$	−0.371227			−0.0136836
$737$	1.24488	+	2.15620i	0.0458558	+	0.0794246i
$738$	−58.2007	−	100.807i	−2.14240	−	3.71074i
$739$	−18.5794	+	32.1805i	−0.683455	+	1.18378i	0.290465	+	0.956886i	$0.406190\pi$
$739$	−18.5794	+	32.1805i	−0.683455	+	1.18378i	−0.973920	+	0.226893i	$0.927143\pi$
$740$	0.932317			0.0342726
$741$	−11.3064	−	19.5832i	−0.415350	−	0.719407i
$742$	20.2904			0.744884
$743$	−20.9212			−0.767523			−0.383761	−	0.923432i	$-0.625372\pi$
$743$	−20.9212			−0.767523			−0.383761	+	0.923432i	$0.625372\pi$
$744$	4.49973	+	48.3582i	0.164968	+	1.77290i
$745$	−52.0918			−1.90850
$746$	43.3305			1.58644
$747$	50.4327	+	87.3519i	1.84523	+	3.19604i
$748$	−5.30348			−0.193914
$749$	−8.29034	+	14.3593i	−0.302923	+	0.524677i
$750$	−24.2577	−	42.0155i	−0.885765	−	1.53419i
$751$	2.52793	+	4.37850i	0.0922454	+	0.159774i	0.908456	−	0.417981i	$-0.137262\pi$
$751$	2.52793	+	4.37850i	0.0922454	+	0.159774i	−0.816210	+	0.577755i	$0.803929\pi$
$752$	14.0187			0.511210
$753$	1.67734	−	2.90523i	0.0611256	−	0.105873i
$754$	−3.36817	+	5.83384i	−0.122662	+	0.212456i
$755$	−0.0965009	+	0.167145i	−0.00351203	+	0.00608301i
$756$	5.44650	+	9.43362i	0.198087	+	0.343097i
$757$	−13.4559	+	23.3063i	−0.489064	+	0.847083i	−0.999921	−	0.0125824i	$-0.995995\pi$
$757$	−13.4559	+	23.3063i	−0.489064	+	0.847083i	0.510857	+	0.859666i	$0.329328\pi$
$758$	3.16869	+	5.48832i	0.115092	+	0.199345i
$759$	3.53887			0.128453
$760$	43.1107			1.56379
$761$	12.6158	+	21.8512i	0.457323	+	0.792107i	0.998818	−	0.0485968i	$-0.0154749\pi$
$761$	12.6158	+	21.8512i	0.457323	+	0.792107i	−0.541495	+	0.840704i	$0.682142\pi$
$762$	35.4199	−	61.3491i	1.28313	−	2.22244i
$763$	6.63328	+	11.4892i	0.240141	+	0.415936i
$764$	2.06038	−	3.56868i	0.0745419	−	0.129110i
$765$	−41.1185	+	71.2193i	−1.48664	+	2.57494i
$766$	3.08698	−	5.34680i	0.111537	−	0.193188i
$767$	3.25441			0.117510
$768$	11.5239	+	19.9601i	0.415834	+	0.720246i
$769$	10.7481	+	18.6163i	0.387587	+	0.671320i	0.992124	−	0.125256i	$-0.0399754\pi$
$769$	10.7481	+	18.6163i	0.387587	+	0.671320i	−0.604537	+	0.796577i	$0.706642\pi$
$770$	−17.9603	+	31.1081i	−0.647244	+	1.12106i
$771$	−88.7782			−3.19727
$772$	0.989620	+	1.71407i	0.0356172	+	0.0616908i
$773$	−38.1580			−1.37245			−0.686225	−	0.727390i	$-0.740733\pi$
$773$	−38.1580			−1.37245			−0.686225	+	0.727390i	$0.740733\pi$
$774$	37.8844			1.36173
$775$	−0.605489	−	6.50714i	−0.0217498	−	0.233744i
$776$	9.64703			0.346308
$777$	9.01178			0.323296
$778$	−2.30901	−	3.99932i	−0.0827819	−	0.143382i
$779$	61.6351			2.20831
$780$	−1.21754	+	2.10884i	−0.0435948	+	0.0755084i
$781$	21.5743	+	37.3679i	0.771991	+	1.33713i
$782$	0.680879	+	1.17932i	0.0243482	+	0.0421723i
$783$	80.5663			2.87920
$784$	−6.10097	+	10.5672i	−0.217892	+	0.377400i
$785$	1.89670	−	3.28519i	0.0676962	−	0.117253i
$786$	51.2731	−	88.8076i	1.82885	−	3.16766i
$787$	0.626469	+	1.08508i	0.0223312	+	0.0386788i	0.876975	−	0.480536i	$-0.159558\pi$
$787$	0.626469	+	1.08508i	0.0223312	+	0.0386788i	−0.854644	+	0.519215i	$0.826224\pi$
$788$	3.40322	−	5.89455i	0.121235	−	0.209985i
$789$	11.1890	+	19.3799i	0.398338	+	0.689942i
$790$	−58.6570			−2.08692
$791$	8.68202			0.308697
$792$	−49.9416	−	86.5015i	−1.77460	−	3.07370i
$793$	2.10715	−	3.64969i	0.0748270	−	0.129604i
$794$	−0.949782	−	1.64507i	−0.0337065	−	0.0583814i
$795$	27.1240	−	46.9802i	0.961990	−	1.66621i
$796$	1.12154	−	1.94256i	0.0397519	−	0.0688524i
$797$	3.78211	−	6.55080i	0.133969	−	0.232041i	−0.791234	−	0.611513i	$-0.790561\pi$
$797$	3.78211	−	6.55080i	0.133969	−	0.232041i	0.925203	+	0.379472i	$0.123894\pi$
$798$	−70.8578			−2.50834
$799$	−6.16473	−	10.6776i	−0.218092	−	0.377747i
$800$	−0.957664	−	1.65872i	−0.0338585	−	0.0586447i
$801$	44.9332	−	77.8266i	1.58764	−	2.74987i
$802$	−46.9482			−1.65780
$803$	8.98141	+	15.5563i	0.316947	+	0.548969i
$804$	0.528885			0.0186523
$805$	1.17033			0.0412486
$806$	6.87604	−	4.87140i	0.242198	−	0.171588i
$807$	47.0557			1.65644
$808$	−8.84896			−0.311305
$809$	−24.3288	−	42.1387i	−0.855355	−	1.48152i	−0.876316	−	0.481737i	$-0.840006\pi$
$809$	−24.3288	−	42.1387i	−0.855355	−	1.48152i	0.0209612	−	0.999780i	$-0.493327\pi$
$810$	135.106			4.74715
$811$	4.45058	−	7.70862i	0.156281	−	0.270686i	−0.777244	−	0.629200i	$-0.783383\pi$
$811$	4.45058	−	7.70862i	0.156281	−	0.270686i	0.933525	+	0.358513i	$0.116716\pi$
$812$	1.33922	+	2.31960i	0.0469975	+	0.0814020i
$813$	−16.6545	−	28.8464i	−0.584098	−	1.01169i
$814$	9.01401			0.315941
$815$	24.8811	−	43.0954i	0.871548	−	1.50957i
$816$	29.9828	−	51.9317i	1.04961	−	1.81797i
$817$	−10.0300	+	17.3725i	−0.350906	+	0.607786i
$818$	−21.0020	−	36.3765i	−0.734318	−	1.27188i
$819$	−8.66311	+	15.0050i	−0.302714	+	0.524316i
$820$	−3.31862	−	5.74801i	−0.115891	−	0.200729i
$821$	28.9555			1.01055			0.505277	−	0.862957i	$-0.331390\pi$
$821$	28.9555			1.01055			0.505277	+	0.862957i	$0.331390\pi$
$822$	6.31860			0.220387
$823$	18.4285	+	31.9191i	0.642378	+	1.11263i	0.984901	+	0.173121i	$0.0553852\pi$
$823$	18.4285	+	31.9191i	0.642378	+	1.11263i	−0.342523	+	0.939509i	$0.611281\pi$
$824$	16.3124	−	28.2538i	0.568268	−	0.984269i
$825$	9.12931	+	15.8124i	0.317842	+	0.550518i
$826$	5.09890	−	8.83155i	0.177413	−	0.307289i
$827$	15.2884	−	26.4803i	0.531630	−	0.920810i	−0.467689	−	0.883893i	$-0.654913\pi$
$827$	15.2884	−	26.4803i	0.531630	−	0.920810i	0.999318	−	0.0369165i	$-0.0117535\pi$
$828$	0.276683	−	0.479229i	0.00961539	−	0.0166543i
$829$	−40.5735			−1.40918			−0.704588	−	0.709616i	$-0.748868\pi$
$829$	−40.5735			−1.40918			−0.704588	+	0.709616i	$0.748868\pi$
$830$	22.6630	+	39.2534i	0.786644	+	1.36251i
$831$	35.8203	+	62.0427i	1.24259	+	2.15224i
$832$	−3.26199	+	5.64994i	−0.113089	+	0.195876i
$833$	10.7316			0.371827
$834$	4.15938	+	7.20426i	0.144028	+	0.249463i
$835$	52.8132			1.82768
$836$	−8.99330			−0.311040
$837$	−91.5746	−	42.0885i	−3.16528	−	1.45479i
$838$	−20.1230			−0.695137
$839$	−13.1509			−0.454019			−0.227010	−	0.973893i	$-0.572895\pi$
$839$	−13.1509			−0.454019			−0.227010	+	0.973893i	$0.572895\pi$
$840$	−22.4368	−	38.8616i	−0.774142	−	1.34085i
$841$	−9.18985			−0.316891
$842$	−27.9345	+	48.3839i	−0.962685	+	1.66742i
$843$	−12.1474	−	21.0399i	−0.418379	−	0.724653i
$844$	0.602580	+	1.04370i	0.0207416	+	0.0359256i
$845$	−2.48471			−0.0854765
$846$	−19.7425	+	34.1950i	−0.678761	+	1.17565i
$847$	−10.6467	+	18.4407i	−0.365826	+	0.633629i
$848$	−14.5591	+	25.2170i	−0.499960	+	0.865957i
$849$	−14.3433	−	24.8433i	−0.492260	−	0.852620i
$850$	−3.51297	+	6.08464i	−0.120494	+	0.208701i
$851$	−0.146842	−	0.254339i	−0.00503369	−	0.00871861i
$852$	9.16581			0.314015
$853$	−26.1873			−0.896636			−0.448318	−	0.893874i	$-0.647977\pi$
$853$	−26.1873			−0.896636			−0.448318	+	0.893874i	$0.647977\pi$
$854$	−6.60281	−	11.4364i	−0.225944	−	0.391346i
$855$	−69.7262	+	120.769i	−2.38459	+	4.13022i
$856$	−10.3592	−	17.9427i	−0.354071	−	0.613269i
$857$	−19.0777	+	33.0435i	−0.651681	+	1.12875i	0.331033	+	0.943619i	$0.392603\pi$
$857$	−19.0777	+	33.0435i	−0.651681	+	1.12875i	−0.982715	+	0.185126i	$0.940731\pi$
$858$	−11.7716	+	20.3891i	−0.401877	+	0.696071i
$859$	5.23802	−	9.07251i	0.178719	−	0.309550i	−0.762723	−	0.646725i	$-0.776138\pi$
$859$	5.23802	−	9.07251i	0.178719	−	0.309550i	0.941442	+	0.337175i	$0.109471\pi$
$860$	2.16018			0.0736616
$861$	−32.0778	−	55.5603i	−1.09321	−	1.89349i
$862$	12.5982	+	21.8208i	0.429098	+	0.743220i
$863$	2.34440	−	4.06061i	0.0798042	−	0.138225i	−0.823361	−	0.567518i	$-0.807904\pi$
$863$	2.34440	−	4.06061i	0.0798042	−	0.138225i	0.903165	+	0.429293i	$0.141237\pi$
$864$	−29.5373			−1.00488
$865$	23.0355	+	39.8986i	0.783229	+	1.35659i
$866$	−60.4883			−2.05548
$867$	4.57977			0.155537
$868$	−0.310430	−	3.33616i	−0.0105367	−	0.113237i
$869$	−71.9612			−2.44112
$870$	56.4354			1.91334
$871$	0.269832	+	0.467363i	0.00914292	+	0.0158360i
$872$	−16.5773			−0.561378
$873$	−15.6029	+	27.0250i	−0.528078	+	0.914657i
$874$	1.15459	+	1.99981i	0.0390547	+	0.0676447i
$875$	−9.84171	−	17.0463i	−0.332711	−	0.576272i
$876$	3.81573			0.128922
$877$	16.9044	−	29.2792i	0.570820	−	0.988690i	−0.425662	−	0.904882i	$-0.639959\pi$
$877$	16.9044	−	29.2792i	0.570820	−	0.988690i	0.996482	−	0.0838073i	$-0.0267080\pi$
$878$	10.1320	−	17.5491i	0.341938	−	0.592254i
$879$	2.55190	−	4.42002i	0.0860734	−	0.149083i
$880$	−25.7743	−	44.6423i	−0.868850	−	1.50489i
$881$	8.70001	−	15.0689i	0.293111	−	0.507683i	−0.681433	−	0.731881i	$-0.738643\pi$
$881$	8.70001	−	15.0689i	0.293111	−	0.507683i	0.974544	+	0.224198i	$0.0719761\pi$
$882$	−17.1839	−	29.7634i	−0.578613	−	1.00219i
$883$	−53.7058			−1.80734			−0.903672	−	0.428226i	$-0.859139\pi$
$883$	−53.7058			−1.80734			−0.903672	+	0.428226i	$0.859139\pi$
$884$	−1.14955			−0.0386634
$885$	−13.6323	−	23.6119i	−0.458245	−	0.793704i
$886$	26.9665	−	46.7073i	0.905957	−	1.56916i
$887$	−20.3069	−	35.1725i	−0.681838	−	1.18098i	−0.974419	−	0.224738i	$-0.927847\pi$
$887$	−20.3069	−	35.1725i	−0.681838	−	1.18098i	0.292581	−	0.956241i	$-0.405486\pi$
$888$	−5.63035	+	9.75205i	−0.188942	+	0.327257i
$889$	14.3704	−	24.8903i	0.481968	−	0.834792i
$890$	20.1917	−	34.9730i	0.676827	−	1.17230i
$891$	165.750			5.55284
$892$	1.57840	+	2.73386i	0.0528486	+	0.0915364i
$893$	−10.4538	−	18.1064i	−0.349822	−	0.605909i
$894$	−53.4930	+	92.6527i	−1.78907	+	3.09877i
$895$	−54.6905			−1.82810
$896$	13.6000	+	23.5559i	0.454344	+	0.786947i
$897$	0.767061			0.0256114
$898$	36.5733			1.22047
$899$	−22.5170	−	10.3490i	−0.750982	−	0.345158i
$900$	2.85507			0.0951689
$901$	25.6093			0.853171
$902$	−32.0857	−	55.5741i	−1.06834	−	1.85042i
$903$	20.8803			0.694853
$904$	−5.42433	+	9.39521i	−0.180410	+	0.312480i
$905$	−0.210821	−	0.365152i	−0.00700792	−	0.0121381i
$906$	0.198193	+	0.343281i	0.00658453	+	0.0114047i
$907$	−12.1458			−0.403294			−0.201647	−	0.979458i	$-0.564629\pi$
$907$	−12.1458			−0.403294			−0.201647	+	0.979458i	$0.564629\pi$
$908$	−0.312106	+	0.540583i	−0.0103576	+	0.0179399i
$909$	14.3121	−	24.7893i	0.474703	−	0.822209i
$910$	−3.89295	+	6.74279i	−0.129050	+	0.223521i
$911$	16.4911	+	28.5635i	0.546376	+	0.946351i	0.998519	+	0.0544053i	$0.0173263\pi$
$911$	16.4911	+	28.5635i	0.546376	+	0.946351i	−0.452143	+	0.891945i	$0.649340\pi$
$912$	50.8429	−	88.0625i	1.68358	−	2.91604i
$913$	27.8033	+	48.1567i	0.920154	+	1.59375i
$914$	−33.3435			−1.10291
$915$	−35.3063			−1.16719
$916$	−2.34387	−	4.05970i	−0.0774437	−	0.134136i
$917$	20.8023	−	36.0306i	0.686951	−	1.18983i
$918$	54.1754	+	93.8345i	1.78805	+	3.09700i
$919$	19.3357	−	33.4904i	0.637826	−	1.10475i	−0.348083	−	0.937464i	$-0.613167\pi$
$919$	19.3357	−	33.4904i	0.637826	−	1.10475i	0.985909	−	0.167284i	$-0.0534995\pi$
$920$	−0.731192	+	1.26646i	−0.0241067	+	0.0417540i
$921$	46.5842	−	80.6861i	1.53500	−	2.65870i
$922$	7.93793			0.261422
$923$	4.67631	+	8.09961i	0.153923	+	0.266602i
$924$	4.68053	+	8.10691i	0.153978	+	0.266698i
$925$	0.757627	−	1.31225i	0.0249106	−	0.0431465i
$926$	−47.7112			−1.56789
$927$	52.7665	+	91.3942i	1.73308	+	3.00178i
$928$	−7.26282			−0.238414
$929$	−9.49720			−0.311593			−0.155797	−	0.987789i	$-0.549794\pi$
$929$	−9.49720			−0.311593			−0.155797	+	0.987789i	$0.549794\pi$
$930$	−64.1466	−	29.4823i	−2.10345	−	0.966764i
$931$	18.1980			0.596414
$932$	−2.76970			−0.0907247
$933$	0.859138	+	1.48807i	0.0281269	+	0.0487173i
$934$	−33.5940			−1.09923
$935$	−22.6684	+	39.2628i	−0.741336	+	1.28403i
$936$	−10.8250	−	18.7495i	−0.353827	−	0.612846i
$937$	8.10859	+	14.0445i	0.264896	+	0.458814i	0.967536	−	0.252732i	$-0.0813290\pi$
$937$	8.10859	+	14.0445i	0.264896	+	0.458814i	−0.702640	+	0.711545i	$0.747996\pi$
$938$	1.69106			0.0552150
$939$	−13.9892	+	24.2300i	−0.456521	+	0.790718i
$940$	−1.12572	+	1.94981i	−0.0367170	+	0.0635957i
$941$	3.27031	−	5.66434i	0.106609	−	0.184652i	−0.807785	−	0.589477i	$-0.799334\pi$
$941$	3.27031	−	5.66434i	0.106609	−	0.184652i	0.914394	+	0.404824i	$0.132667\pi$
$942$	−3.89544	−	6.74711i	−0.126920	−	0.219833i
$943$	−1.04538	+	1.81066i	−0.0340423	+	0.0589631i
$944$	7.31727	+	12.6739i	0.238157	+	0.412500i
$945$	93.1190			3.02916
$946$	20.8855			0.679046
$947$	−1.98141	−	3.43190i	−0.0643871	−	0.111522i	0.832035	−	0.554723i	$-0.187176\pi$
$947$	−1.98141	−	3.43190i	−0.0643871	−	0.111522i	−0.896422	+	0.443202i	$0.853843\pi$
$948$	−7.64313	+	13.2383i	−0.248237	+	0.429960i
$949$	1.94675	+	3.37187i	0.0631943	+	0.109456i
$950$	−5.95707	+	10.3179i	−0.193273	+	0.334758i
$951$	17.3172	−	29.9943i	0.561550	−	0.972632i
$952$	10.5919	−	18.3458i	0.343286	−	0.594589i
$953$	−25.5203			−0.826683			−0.413341	−	0.910576i	$-0.635638\pi$
$953$	−25.5203			−0.826683			−0.413341	+	0.910576i	$0.635638\pi$
$954$	−41.0069	−	71.0260i	−1.32765	−	2.29955i
$955$	−17.6132	−	30.5069i	−0.569949	−	0.987180i
$956$	−1.30681	+	2.26346i	−0.0422652	+	0.0732055i
$957$	69.2357			2.23807
$958$	23.4223	+	40.5686i	0.756739	+	1.31071i
$959$	2.56355			0.0827814
$960$	54.6564			1.76403
$961$	20.1872	+	23.5261i	0.651200	+	0.758906i
$962$	1.95382			0.0629936
$963$	67.0191			2.15966
$964$	3.09833	+	5.36647i	0.0997905	+	0.172842i
$965$	16.9196			0.544660
$966$	1.20181	−	2.08159i	0.0386675	−	0.0669740i
$967$	23.9201	+	41.4309i	0.769219	+	1.33233i	0.937987	+	0.346671i	$0.112688\pi$
$967$	23.9201	+	41.4309i	0.769219	+	1.33233i	−0.168767	+	0.985656i	$0.553979\pi$
$968$	−13.3037	−	23.0426i	−0.427596	−	0.740618i
$969$	−89.4325			−2.87299
$970$	−7.01149	+	12.1443i	−0.225125	+	0.389929i
$971$	−27.1142	+	46.9632i	−0.870136	+	1.50712i	−0.00828016	+	0.999966i	$0.502636\pi$
$971$	−27.1142	+	46.9632i	−0.870136	+	1.50712i	−0.861856	+	0.507154i	$0.830698\pi$
$972$	9.71268	−	16.8229i	0.311534	−	0.539594i
$973$	1.68752	+	2.92288i	0.0540996	+	0.0937032i
$974$	2.83623	−	4.91249i	0.0908786	−	0.157406i
$975$	1.97881	+	3.42740i	0.0633726	+	0.109765i
$976$	18.9510			0.606606
$977$	−14.8889			−0.476337			−0.238168	−	0.971224i	$-0.576547\pi$
$977$	−14.8889			−0.476337			−0.238168	+	0.971224i	$0.576547\pi$
$978$	−51.1008	−	88.5092i	−1.63402	−	2.83021i
$979$	24.7714	−	42.9054i	0.791698	−	1.37126i
$980$	−0.979831	−	1.69712i	−0.0312996	−	0.0542124i
$981$	26.8117	−	46.4393i	0.856033	−	1.48269i
$982$	−21.7728	+	37.7115i	−0.694797	+	1.20342i
$983$	−28.6618	+	49.6437i	−0.914170	+	1.58339i	−0.106059	+	0.994360i	$0.533823\pi$
$983$	−28.6618	+	49.6437i	−0.914170	+	1.58339i	−0.808111	+	0.589030i	$0.799510\pi$
$984$	80.1658			2.55559
$985$	−29.0925	−	50.3897i	−0.926964	−	1.60555i
$986$	13.3210	+	23.0726i	0.424227	+	0.734782i
$987$	−10.8812	+	18.8468i	−0.346353	+	0.599902i
$988$	−1.94933			−0.0620164
$989$	−0.340234	−	0.589303i	−0.0108188	−	0.0187388i
$990$	145.191			4.61447
$991$	−52.5955			−1.67075			−0.835376	−	0.549679i	$-0.814750\pi$
$991$	−52.5955			−1.67075			−0.835376	+	0.549679i	$0.814750\pi$
$992$	8.25519	+	3.79416i	0.262103	+	0.120465i
$993$	87.8791			2.78876
$994$	29.3068			0.929554
$995$	−9.58750	−	16.6060i	−0.303944	−	0.526447i
$996$	11.8121			0.374282
$997$	4.42324	−	7.66127i	0.140085	−	0.242635i	−0.787443	−	0.616387i	$-0.788596\pi$
$997$	4.42324	−	7.66127i	0.140085	−	0.242635i	0.927529	+	0.373752i	$0.121929\pi$
$998$	11.0598	+	19.1561i	0.350091	+	0.606375i
$999$	−11.6838	−	20.2369i	−0.369658	−	0.640267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.5	✓	34
31.5	even	3	inner	403.2.h.b.222.5	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.5	✓	34	1.1	even	1	trivial
403.2.h.b.222.5	yes	34	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.51349 q^{2} +(1.68586 + 2.92000i) q^{3} +0.290659 q^{4} +(1.24235 - 2.15182i) q^{5} +(-2.55154 - 4.41940i) q^{6} +(-1.03520 - 1.79302i) q^{7} +2.58707 q^{8} +(-4.18427 + 7.24738i) q^{9} +O(q^{10})\)	\(q-1.51349 q^{2} +(1.68586 + 2.92000i) q^{3} +0.290659 q^{4} +(1.24235 - 2.15182i) q^{5} +(-2.55154 - 4.41940i) q^{6} +(-1.03520 - 1.79302i) q^{7} +2.58707 q^{8} +(-4.18427 + 7.24738i) q^{9} +(-1.88029 + 3.25676i) q^{10} +(-2.30677 + 3.99544i) q^{11} +(0.490012 + 0.848726i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.56677 + 2.71372i) q^{14} +8.37775 q^{15} -4.49684 q^{16} +(1.97748 + 3.42510i) q^{17} +(6.33287 - 10.9688i) q^{18} +(3.35329 + 5.80806i) q^{19} +(0.361102 - 0.625447i) q^{20} +(3.49041 - 6.04557i) q^{21} +(3.49128 - 6.04707i) q^{22} -0.227498 q^{23} +(4.36145 + 7.55426i) q^{24} +(-0.586883 - 1.01651i) q^{25} +(0.756746 - 1.31072i) q^{26} -18.1013 q^{27} +(-0.300890 - 0.521158i) q^{28} -4.45086 q^{29} -12.6797 q^{30} +(5.05901 + 2.32517i) q^{31} +1.63178 q^{32} -15.5556 q^{33} +(-2.99290 - 5.18386i) q^{34} -5.14433 q^{35} +(-1.21620 + 2.10652i) q^{36} +(0.645467 + 1.11798i) q^{37} +(-5.07517 - 8.79046i) q^{38} -3.37173 q^{39} +(3.21406 - 5.56691i) q^{40} +(4.59513 - 7.95900i) q^{41} +(-5.28271 + 9.14992i) q^{42} +(1.49555 + 2.59037i) q^{43} +(-0.670484 + 1.16131i) q^{44} +(10.3967 + 18.0076i) q^{45} +0.344317 q^{46} -3.11747 q^{47} +(-7.58105 - 13.1308i) q^{48} +(1.35672 - 2.34992i) q^{49} +(0.888243 + 1.53848i) q^{50} +(-6.66753 + 11.5485i) q^{51} +(-0.145330 + 0.251718i) q^{52} +(3.23762 - 5.60773i) q^{53} +27.3962 q^{54} +(5.73164 + 9.92749i) q^{55} +(-2.67814 - 4.63867i) q^{56} +(-11.3064 + 19.5832i) q^{57} +6.73634 q^{58} +(-1.62720 - 2.81840i) q^{59} +2.43507 q^{60} -4.21429 q^{61} +(-7.65678 - 3.51912i) q^{62} +17.3262 q^{63} +6.52399 q^{64} +(1.24235 + 2.15182i) q^{65} +23.5433 q^{66} +(0.269832 - 0.467363i) q^{67} +(0.574773 + 0.995537i) q^{68} +(-0.383531 - 0.664295i) q^{69} +7.78591 q^{70} +(4.67631 - 8.09961i) q^{71} +(-10.8250 + 18.7495i) q^{72} +(1.94675 - 3.37187i) q^{73} +(-0.976909 - 1.69206i) q^{74} +(1.97881 - 3.42740i) q^{75} +(0.974665 + 1.68817i) q^{76} +9.55186 q^{77} +5.10308 q^{78} +(7.79892 + 13.5081i) q^{79} +(-5.58666 + 9.67638i) q^{80} +(-17.9635 - 31.1137i) q^{81} +(-6.95469 + 12.0459i) q^{82} +(6.02645 - 10.4381i) q^{83} +(1.01452 - 1.75720i) q^{84} +9.82692 q^{85} +(-2.26350 - 3.92050i) q^{86} +(-7.50354 - 12.9965i) q^{87} +(-5.96778 + 10.3365i) q^{88} -10.7386 q^{89} +(-15.7353 - 27.2544i) q^{90} +2.07040 q^{91} -0.0661245 q^{92} +(1.73931 + 18.6922i) q^{93} +4.71826 q^{94} +16.6639 q^{95} +(2.75096 + 4.76480i) q^{96} +3.72894 q^{97} +(-2.05339 + 3.55658i) q^{98} +(-19.3043 - 33.4360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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