LMFDB - Embedded newform 403.2.r.a.218.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [403,2,Mod(218,403)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("403.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(403, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.22
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.720477 - 0.415968i) q^{2} +(-1.53222 - 2.65388i) q^{3} +(-0.653942 + 1.13266i) q^{4} +1.49771i q^{5} +(-2.20786 - 1.27471i) q^{6} +(1.75030 + 1.01053i) q^{7} +2.75195i q^{8} +(-3.19539 + 5.53457i) q^{9} +(0.622999 + 1.07907i) q^{10} +(-4.84342 + 2.79635i) q^{11} +4.00793 q^{12} +(-3.59428 + 0.284818i) q^{13} +1.68140 q^{14} +(3.97474 - 2.29482i) q^{15} +(-0.163162 - 0.282605i) q^{16} +(0.509189 - 0.881941i) q^{17} +5.31671i q^{18} +(5.64316 + 3.25808i) q^{19} +(-1.69640 - 0.979414i) q^{20} -6.19344i q^{21} +(-2.32638 + 4.02941i) q^{22} +(1.35457 + 2.34619i) q^{23} +(7.30334 - 4.21658i) q^{24} +2.75687 q^{25} +(-2.47113 + 1.70031i) q^{26} +10.3908 q^{27} +(-2.28918 + 1.32166i) q^{28} +(-1.95518 - 3.38647i) q^{29} +(1.90914 - 3.30673i) q^{30} -1.00000i q^{31} +(-5.00162 - 2.88769i) q^{32} +(14.8424 + 8.56924i) q^{33} -0.847225i q^{34} +(-1.51349 + 2.62143i) q^{35} +(-4.17919 - 7.23857i) q^{36} +(-9.35653 + 5.40200i) q^{37} +5.42102 q^{38} +(6.26310 + 9.10240i) q^{39} -4.12162 q^{40} +(-1.13050 + 0.652697i) q^{41} +(-2.57627 - 4.46223i) q^{42} +(-0.725927 + 1.25734i) q^{43} -7.31460i q^{44} +(-8.28918 - 4.78576i) q^{45} +(1.95188 + 1.12692i) q^{46} +8.81641i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.45764 - 2.52471i) q^{49} +(1.98626 - 1.14677i) q^{50} -3.12076 q^{51} +(2.02785 - 4.25736i) q^{52} -3.69910 q^{53} +(7.48635 - 4.32225i) q^{54} +(-4.18812 - 7.25404i) q^{55} +(-2.78093 + 4.81672i) q^{56} -19.9684i q^{57} +(-2.81733 - 1.62658i) q^{58} +(1.50669 + 0.869889i) q^{59} +6.00271i q^{60} +(5.78061 - 10.0123i) q^{61} +(-0.415968 - 0.720477i) q^{62} +(-11.1857 + 6.45809i) q^{63} -4.15209 q^{64} +(-0.426575 - 5.38319i) q^{65} +14.2581 q^{66} +(2.51865 - 1.45415i) q^{67} +(0.665960 + 1.15348i) q^{68} +(4.15100 - 7.18975i) q^{69} +2.51825i q^{70} +(-3.05994 - 1.76666i) q^{71} +(-15.2308 - 8.79353i) q^{72} +11.6544i q^{73} +(-4.49411 + 7.78403i) q^{74} +(-4.22412 - 7.31639i) q^{75} +(-7.38059 + 4.26119i) q^{76} -11.3032 q^{77} +(8.29873 + 3.95282i) q^{78} +14.5978 q^{79} +(0.423260 - 0.244369i) q^{80} +(-6.33484 - 10.9723i) q^{81} +(-0.543002 + 0.940507i) q^{82} +15.3384i q^{83} +(7.01506 + 4.05014i) q^{84} +(1.32089 + 0.762617i) q^{85} +1.20785i q^{86} +(-5.99153 + 10.3776i) q^{87} +(-7.69541 - 13.3288i) q^{88} +(0.250158 - 0.144429i) q^{89} -7.96289 q^{90} +(-6.57888 - 3.13363i) q^{91} -3.54325 q^{92} +(-2.65388 + 1.53222i) q^{93} +(3.66734 + 6.35203i) q^{94} +(-4.87966 + 8.45181i) q^{95} +17.6983i q^{96} +(-9.34768 - 5.39688i) q^{97} +(-2.10040 - 1.21266i) q^{98} -35.7417i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30}+ \cdots - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.720477	−	0.415968i	0.509454	−	0.294134i	−0.223155	−	0.974783i	$-0.571636\pi$
$2$	0.720477	−	0.415968i	0.509454	−	0.294134i	0.732609	+	0.680649i	$0.238302\pi$
$3$	−1.53222	−	2.65388i	−0.884627	−	1.53222i	−0.846141	−	0.532959i	$-0.821080\pi$
$3$	−1.53222	−	2.65388i	−0.884627	−	1.53222i	−0.0384860	−	0.999259i	$-0.512253\pi$
$4$	−0.653942	+	1.13266i	−0.326971	+	0.566330i
$5$			1.49771i			0.669796i	0.942254	+	0.334898i	$0.108702\pi$
$5$			1.49771i			0.669796i	−0.942254	+	0.334898i	$0.891298\pi$
$6$	−2.20786	−	1.27471i	−0.901354	−	0.520397i
$7$	1.75030	+	1.01053i	0.661550	+	0.381946i	0.792867	−	0.609394i	$-0.208587\pi$
$7$	1.75030	+	1.01053i	0.661550	+	0.381946i	−0.131317	+	0.991340i	$0.541921\pi$
$8$			2.75195i			0.972960i
$9$	−3.19539	+	5.53457i	−1.06513	+	1.84486i
$10$	0.622999	+	1.07907i	0.197010	+	0.341231i
$11$	−4.84342	+	2.79635i	−1.46035	+	0.843131i	−0.999027	−	0.0441027i	$-0.985957\pi$
$11$	−4.84342	+	2.79635i	−1.46035	+	0.843131i	−0.461319	+	0.887234i	$0.652624\pi$
$12$	4.00793			1.15699
$13$	−3.59428	+	0.284818i	−0.996875	+	0.0789943i
$13$	−3.59428	+	0.284818i	−0.996875	+	0.0789943i
$14$	1.68140			0.449373
$15$	3.97474	−	2.29482i	1.02627	−	0.592519i
$16$	−0.163162	−	0.282605i	−0.0407905	−	0.0706513i
$17$	0.509189	−	0.881941i	0.123496	−	0.213902i	−0.797648	−	0.603124i	$-0.793923\pi$
$17$	0.509189	−	0.881941i	0.123496	−	0.213902i	0.921144	+	0.389221i	$0.127256\pi$
$18$			5.31671i			1.25316i
$19$	5.64316	+	3.25808i	1.29463	+	0.747455i	0.979471	−	0.201585i	$-0.0646091\pi$
$19$	5.64316	+	3.25808i	1.29463	+	0.747455i	0.315158	+	0.949039i	$0.397942\pi$
$20$	−1.69640	−	0.979414i	−0.379326	−	0.219004i
$21$		−	6.19344i		−	1.35152i
$22$	−2.32638	+	4.02941i	−0.495987	+	0.859074i
$23$	1.35457	+	2.34619i	0.282448	+	0.489214i	0.971987	−	0.235034i	$-0.0755202\pi$
$23$	1.35457	+	2.34619i	0.282448	+	0.489214i	−0.689539	+	0.724248i	$0.742187\pi$
$24$	7.30334	−	4.21658i	1.49079	−	0.860706i
$25$	2.75687			0.551373
$26$	−2.47113	+	1.70031i	−0.484628	+	0.333459i
$27$	10.3908			1.99971
$28$	−2.28918	+	1.32166i	−0.432615	+	0.249770i
$29$	−1.95518	−	3.38647i	−0.363068	−	0.628852i	0.625396	−	0.780307i	$-0.284937\pi$
$29$	−1.95518	−	3.38647i	−0.363068	−	0.628852i	−0.988464	+	0.151455i	$0.951604\pi$
$30$	1.90914	−	3.30673i	0.348560	−	0.603723i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	−5.00162	−	2.88769i	−0.884170	−	0.510476i
$33$	14.8424	+	8.56924i	2.58372	+	1.49171i
$34$		−	0.847225i		−	0.145298i
$35$	−1.51349	+	2.62143i	−0.255826	+	0.443103i
$36$	−4.17919	−	7.23857i	−0.696532	−	1.20643i
$37$	−9.35653	+	5.40200i	−1.53820	+	0.888083i	−0.539260	+	0.842139i	$0.681296\pi$
$37$	−9.35653	+	5.40200i	−1.53820	+	0.888083i	−0.998944	+	0.0459436i	$0.985371\pi$
$38$	5.42102			0.879406
$39$	6.26310	+	9.10240i	1.00290	+	1.45755i
$40$	−4.12162			−0.651685
$41$	−1.13050	+	0.652697i	−0.176555	+	0.101934i	−0.585673	−	0.810547i	$-0.699170\pi$
$41$	−1.13050	+	0.652697i	−0.176555	+	0.101934i	0.409118	+	0.912481i	$0.365836\pi$
$42$	−2.57627	−	4.46223i	−0.397527	−	0.688537i
$43$	−0.725927	+	1.25734i	−0.110703	+	0.191743i	−0.916054	−	0.401055i	$-0.868644\pi$
$43$	−0.725927	+	1.25734i	−0.110703	+	0.191743i	0.805351	+	0.592798i	$0.201977\pi$
$44$		−	7.31460i		−	1.10272i
$45$	−8.28918	−	4.78576i	−1.23568	−	0.713419i
$46$	1.95188	+	1.12692i	0.287789	+	0.166155i
$47$			8.81641i			1.28601i	0.765864	+	0.643003i	$0.222312\pi$
$47$			8.81641i			1.28601i	−0.765864	+	0.643003i	$0.777688\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−1.45764	−	2.52471i	−0.208235	−	0.360673i
$50$	1.98626	−	1.14677i	0.280900	−	0.162177i
$51$	−3.12076			−0.436993
$52$	2.02785	−	4.25736i	0.281212	−	0.590389i
$53$	−3.69910			−0.508111			−0.254056	−	0.967190i	$-0.581765\pi$
$53$	−3.69910			−0.508111			−0.254056	+	0.967190i	$0.581765\pi$
$54$	7.48635	−	4.32225i	1.01876	−	0.588183i
$55$	−4.18812	−	7.25404i	−0.564726	−	0.978134i
$56$	−2.78093	+	4.81672i	−0.371618	+	0.643661i
$57$		−	19.9684i		−	2.64487i
$58$	−2.81733	−	1.62658i	−0.369933	−	0.213581i
$59$	1.50669	+	0.869889i	0.196155	+	0.113250i	0.594861	−	0.803829i	$-0.297207\pi$
$59$	1.50669	+	0.869889i	0.196155	+	0.113250i	−0.398706	+	0.917079i	$0.630541\pi$
$60$			6.00271i			0.774946i
$61$	5.78061	−	10.0123i	0.740131	−	1.28195i	−0.212304	−	0.977204i	$-0.568097\pi$
$61$	5.78061	−	10.0123i	0.740131	−	1.28195i	0.952435	−	0.304742i	$-0.0985701\pi$
$62$	−0.415968	−	0.720477i	−0.0528280	−	0.0915007i
$63$	−11.1857	+	6.45809i	−1.40927	+	0.813643i
$64$	−4.15209			−0.519011
$65$	−0.426575	−	5.38319i	−0.0529101	−	0.667703i
$66$	14.2581			1.75505
$67$	2.51865	−	1.45415i	0.307703	−	0.177652i	−0.338195	−	0.941076i	$-0.609816\pi$
$67$	2.51865	−	1.45415i	0.307703	−	0.177652i	0.645898	+	0.763424i	$0.276483\pi$
$68$	0.665960	+	1.15348i	0.0807595	+	0.139880i
$69$	4.15100	−	7.18975i	0.499722	−	0.865544i
$70$			2.51825i			0.300988i
$71$	−3.05994	−	1.76666i	−0.363149	−	0.209664i	0.307313	−	0.951609i	$-0.400570\pi$
$71$	−3.05994	−	1.76666i	−0.363149	−	0.209664i	−0.670461	+	0.741945i	$0.733904\pi$
$72$	−15.2308	−	8.79353i	−1.79497	−	1.03633i
$73$			11.6544i			1.36404i	0.731333	+	0.682021i	$0.238899\pi$
$73$			11.6544i			1.36404i	−0.731333	+	0.682021i	$0.761101\pi$
$74$	−4.49411	+	7.78403i	−0.522430	+	0.904875i
$75$	−4.22412	−	7.31639i	−0.487760	−	0.844824i
$76$	−7.38059	+	4.26119i	−0.846612	+	0.488792i
$77$	−11.3032			−1.28812
$78$	8.29873	+	3.95282i	0.939646	+	0.447569i
$79$	14.5978			1.64238			0.821188	−	0.570658i	$-0.193312\pi$
$79$	14.5978			1.64238			0.821188	+	0.570658i	$0.193312\pi$
$80$	0.423260	−	0.244369i	0.0473219	−	0.0273213i
$81$	−6.33484	−	10.9723i	−0.703871	−	1.21914i
$82$	−0.543002	+	0.940507i	−0.0599645	+	0.103862i
$83$			15.3384i			1.68361i	0.539779	+	0.841807i	$0.318508\pi$
$83$			15.3384i			1.68361i	−0.539779	+	0.841807i	$0.681492\pi$
$84$	7.01506	+	4.05014i	0.765405	+	0.441907i
$85$	1.32089	+	0.762617i	0.143271	+	0.0827174i
$86$			1.20785i			0.130246i
$87$	−5.99153	+	10.3776i	−0.642359	+	1.11260i
$88$	−7.69541	−	13.3288i	−0.820333	−	1.42086i
$89$	0.250158	−	0.144429i	0.0265166	−	0.0153094i	−0.486683	−	0.873579i	$-0.661793\pi$
$89$	0.250158	−	0.144429i	0.0265166	−	0.0153094i	0.513200	+	0.858269i	$0.328460\pi$
$90$	−7.96289			−0.839362
$91$	−6.57888	−	3.13363i	−0.689654	−	0.328494i
$92$	−3.54325			−0.369409
$93$	−2.65388	+	1.53222i	−0.275195	+	0.158884i
$94$	3.66734	+	6.35203i	0.378258	+	0.655162i
$95$	−4.87966	+	8.45181i	−0.500642	+	0.867138i
$96$			17.6983i			1.80632i
$97$	−9.34768	−	5.39688i	−0.949113	−	0.547971i	−0.0563077	−	0.998413i	$-0.517933\pi$
$97$	−9.34768	−	5.39688i	−0.949113	−	0.547971i	−0.892805	+	0.450443i	$0.851266\pi$
$98$	−2.10040	−	1.21266i	−0.212172	−	0.122498i
$99$		−	35.7417i		−	3.59218i
$100$	−1.80283	+	3.12259i	−0.180283	+	0.312259i
$101$	−3.39785	−	5.88524i	−0.338098	−	0.585604i	0.645977	−	0.763357i	$-0.276450\pi$
$101$	−3.39785	−	5.88524i	−0.338098	−	0.585604i	−0.984075	+	0.177754i	$0.943117\pi$
$102$	−2.24843	+	1.29813i	−0.222628	+	0.128534i
$103$	3.57498			0.352253			0.176126	−	0.984368i	$-0.443643\pi$
$103$	3.57498			0.352253			0.176126	+	0.984368i	$0.443643\pi$
$104$	−0.783804	−	9.89128i	−0.0768583	−	0.969919i
$105$	9.27597			0.905242
$106$	−2.66512	+	1.53871i	−0.258859	+	0.149453i
$107$	7.86970	+	13.6307i	0.760793	+	1.31773i	0.942442	+	0.334369i	$0.108523\pi$
$107$	7.86970	+	13.6307i	0.760793	+	1.31773i	−0.181649	+	0.983363i	$0.558144\pi$
$108$	−6.79499	+	11.7693i	−0.653848	+	1.13250i
$109$			4.63222i			0.443687i	0.975082	+	0.221843i	$0.0712074\pi$
$109$			4.63222i			0.443687i	−0.975082	+	0.221843i	$0.928793\pi$
$110$	−6.03489	−	3.48425i	−0.575404	−	0.332210i
$111$	28.6725	+	16.5541i	2.72147	+	1.57124i
$112$		−	0.659523i		−	0.0623191i
$113$	6.68385	−	11.5768i	0.628764	−	1.08905i	−0.359036	−	0.933324i	$-0.616895\pi$
$113$	6.68385	−	11.5768i	0.628764	−	1.08905i	0.987800	−	0.155727i	$-0.0497721\pi$
$114$	−8.30619	−	14.3868i	−0.777946	−	1.34744i
$115$	−3.51391	+	2.02876i	−0.327674	+	0.189183i
$116$	5.11429			0.474850
$117$	9.90878	−	20.8029i	0.916067	−	1.92323i
$118$	1.44738			0.133242
$119$	1.78246	−	1.02911i	0.163398	−	0.0943380i
$120$	6.31522	+	10.9383i	0.576498	+	0.998523i
$121$	10.1392	−	17.5615i	0.921741	−	1.59650i
$122$		−	9.61819i		−	0.870790i
$123$	3.46436	+	2.00015i	0.312371	+	0.180347i
$124$	1.13266	+	0.653942i	0.101716	+	0.0587257i
$125$			11.6175i			1.03910i
$126$	−5.37272	+	9.30582i	−0.478640	+	0.829029i
$127$	0.237217	+	0.410872i	0.0210496	+	0.0364590i	0.876358	−	0.481660i	$-0.159966\pi$
$127$	0.237217	+	0.410872i	0.0210496	+	0.0364590i	−0.855309	+	0.518119i	$0.826633\pi$
$128$	7.01175	−	4.04824i	0.619757	−	0.357817i
$129$	4.44912			0.391723
$130$	−2.54657	−	3.70103i	−0.223349	−	0.324602i
$131$	−8.54543			−0.746618			−0.373309	−	0.927707i	$-0.621777\pi$
$131$	−8.54543			−0.746618			−0.373309	+	0.927707i	$0.621777\pi$
$132$	−19.4121	+	11.2076i	−1.68960	+	0.975493i
$133$	6.58480	+	11.4052i	0.570974	+	0.988957i
$134$	1.20976	−	2.09536i	0.104507	−	0.181011i
$135$			15.5624i			1.33940i
$136$	2.42705	+	1.40126i	0.208118	+	0.120157i
$137$	3.86960	+	2.23411i	0.330602	+	0.190873i	0.656108	−	0.754667i	$-0.272201\pi$
$137$	3.86960	+	2.23411i	0.330602	+	0.190873i	−0.325506	+	0.945540i	$0.605535\pi$
$138$		−	6.90674i		−	0.587940i
$139$	6.64590	−	11.5110i	0.563698	−	0.976354i	−0.433471	−	0.901167i	$-0.642712\pi$
$139$	6.64590	−	11.5110i	0.563698	−	0.976354i	0.997170	−	0.0751863i	$-0.0239552\pi$
$140$	−1.97946	−	3.42853i	−0.167295	−	0.289764i
$141$	23.3977	−	13.5087i	1.97044	−	1.13764i
$142$	−2.93949			−0.246677
$143$	16.6122	−	11.4304i	1.38918	−	0.955856i
$144$	2.08546			0.173789
$145$	5.07195	−	2.92829i	0.421203	−	0.243181i
$146$	4.84785	+	8.39672i	0.401211	+	0.694917i
$147$	−4.46685	+	7.73682i	−0.368420	+	0.638122i
$148$		−	14.1304i		−	1.16151i
$149$	−3.64875	−	2.10661i	−0.298918	−	0.172580i	0.343039	−	0.939321i	$-0.388544\pi$
$149$	−3.64875	−	2.10661i	−0.298918	−	0.172580i	−0.641956	+	0.766741i	$0.721877\pi$
$150$	−6.08677	−	3.51420i	−0.496983	−	0.286933i
$151$		−	5.35318i		−	0.435635i	−0.975989	−	0.217818i	$-0.930106\pi$
$151$		−	5.35318i		−	0.435635i	0.975989	−	0.217818i	$-0.0698938\pi$
$152$	−8.96606	+	15.5297i	−0.727243	+	1.25962i
$153$	3.25411	+	5.63629i	0.263079	+	0.455667i
$154$	−8.14372	+	4.70178i	−0.656240	+	0.378880i
$155$	1.49771			0.120299
$156$	−14.4056	+	1.14153i	−1.15337	+	0.0913955i
$157$	22.7079			1.81229			0.906145	−	0.422968i	$-0.139012\pi$
$157$	22.7079			1.81229			0.906145	+	0.422968i	$0.139012\pi$
$158$	10.5174	−	6.07220i	0.836716	−	0.483078i
$159$	5.66784	+	9.81698i	0.449489	+	0.778537i
$160$	4.32491	−	7.49097i	0.341915	−	0.592213i
$161$			5.47537i			0.431519i
$162$	−9.12822	−	5.27018i	−0.717180	−	0.414064i
$163$	0.665811	+	0.384406i	0.0521503	+	0.0301090i	0.525848	−	0.850578i	$-0.323748\pi$
$163$	0.665811	+	0.384406i	0.0521503	+	0.0301090i	−0.473698	+	0.880687i	$0.657081\pi$
$164$		−	1.70730i		−	0.133318i
$165$	−12.8342	+	22.2295i	−0.999144	+	1.73057i
$166$	6.38030	+	11.0510i	0.495207	+	0.857724i
$167$	5.93541	−	3.42681i	0.459296	−	0.265175i	−0.252452	−	0.967609i	$-0.581237\pi$
$167$	5.93541	−	3.42681i	0.459296	−	0.265175i	0.711748	+	0.702435i	$0.247904\pi$
$168$	17.0440			1.31497
$169$	12.8378	−	2.04743i	0.987520	−	0.157495i
$170$	1.26890			0.0973200
$171$	−36.0642	+	20.8216i	−2.75789	+	1.59227i
$172$	−0.949428	−	1.64446i	−0.0723932	−	0.125389i
$173$	1.76070	−	3.04963i	0.133864	−	0.231859i	−0.791299	−	0.611429i	$-0.790595\pi$
$173$	1.76070	−	3.04963i	0.133864	−	0.231859i	0.925163	+	0.379571i	$0.123928\pi$
$174$			9.96913i			0.755758i
$175$	4.82533	+	2.78591i	0.364761	+	0.210595i
$176$	1.58053	+	0.912517i	0.119137	+	0.0687835i
$177$		−	5.33144i		−	0.400736i
$178$	0.120155	−	0.208115i	0.00900602	−	0.0155989i
$179$	−11.0673	−	19.1691i	−0.827208	−	1.43277i	−0.900220	−	0.435436i	$-0.856594\pi$
$179$	−11.0673	−	19.1691i	−0.827208	−	1.43277i	0.0730116	−	0.997331i	$-0.476739\pi$
$180$	10.8413	−	6.25922i	0.808061	−	0.466534i
$181$	4.41482			0.328151			0.164075	−	0.986448i	$-0.447536\pi$
$181$	4.41482			0.328151			0.164075	+	0.986448i	$0.447536\pi$
$182$	−6.04342	+	0.478893i	−0.447968	+	0.0354979i
$183$	−35.4286			−2.61896
$184$	−6.45659	+	3.72771i	−0.475986	+	0.274811i
$185$	−8.09062	−	14.0134i	−0.594834	−	1.03028i
$186$	−1.27471	+	2.20786i	−0.0934661	+	0.161888i
$187$			5.69548i			0.416495i
$188$	−9.98600	−	5.76542i	−0.728304	−	0.420486i
$189$	18.1870	+	10.5003i	1.32291	+	0.763782i
$190$			8.11912i			0.589023i
$191$	4.36959	−	7.56835i	0.316172	−	0.547627i	−0.663514	−	0.748164i	$-0.730936\pi$
$191$	4.36959	−	7.56835i	0.316172	−	0.547627i	0.979686	+	0.200538i	$0.0642689\pi$
$192$	6.36191	+	11.0192i	0.459131	+	0.795239i
$193$	−12.7744	+	7.37532i	−0.919524	+	0.530887i	−0.883483	−	0.468463i	$-0.844808\pi$
$193$	−12.7744	+	7.37532i	−0.919524	+	0.530887i	−0.0360409	+	0.999350i	$0.511475\pi$
$194$	−8.97972			−0.644706
$195$	−13.6327	+	9.38031i	−0.976261	+	0.671738i
$196$	3.81285			0.272347
$197$	−1.73925	+	1.00416i	−0.123916	+	0.0715431i	−0.560677	−	0.828035i	$-0.689459\pi$
$197$	−1.73925	+	1.00416i	−0.123916	+	0.0715431i	0.436761	+	0.899578i	$0.356126\pi$
$198$	−14.8674	−	25.7511i	−1.05658	−	1.83005i
$199$	−7.14092	+	12.3684i	−0.506206	+	0.876775i	0.493768	+	0.869594i	$0.335619\pi$
$199$	−7.14092	+	12.3684i	−0.506206	+	0.876775i	−0.999974	+	0.00718137i	$0.997714\pi$
$200$			7.58675i			0.536464i
$201$	−7.71826	−	4.45614i	−0.544404	−	0.314312i
$202$	−4.89614	−	2.82679i	−0.344492	−	0.198892i
$203$		−	7.90310i		−	0.554689i
$204$	2.04079	−	3.53475i	0.142884	−	0.247482i
$205$	−0.977551	−	1.69317i	−0.0682751	−	0.118256i
$206$	2.57569	−	1.48708i	0.179457	−	0.103609i
$207$	−17.3135			−1.20337
$208$	0.666942	+	0.969291i	0.0462441	+	0.0672083i
$209$	−36.4429			−2.52081
$210$	6.68312	−	3.85850i	0.461179	−	0.266262i
$211$	−1.88634	−	3.26723i	−0.129861	−	0.224926i	0.793762	−	0.608229i	$-0.208120\pi$
$211$	−1.88634	−	3.26723i	−0.129861	−	0.224926i	−0.923623	+	0.383303i	$0.874786\pi$
$212$	2.41900	−	4.18983i	0.166137	−	0.287758i
$213$			10.8276i			0.741897i
$214$	11.3399	+	6.54709i	0.775179	+	0.447550i
$215$	−1.88313	−	1.08723i	−0.128429	−	0.0741483i
$216$			28.5950i			1.94564i
$217$	1.01053	−	1.75030i	0.0685995	−	0.118818i
$218$	1.92686	+	3.33741i	0.130503	+	0.226038i
$219$	30.9293	−	17.8571i	2.09001	−	1.20667i
$220$	10.9551			0.738596
$221$	−1.57898	+	3.31497i	−0.106214	+	0.222989i
$222$	27.5439			1.84862
$223$	24.6060	−	14.2063i	1.64774	−	0.951324i	0.669775	−	0.742564i	$-0.266391\pi$
$223$	24.6060	−	14.2063i	1.64774	−	0.951324i	0.977967	−	0.208760i	$-0.0669428\pi$
$224$	−5.83621	−	10.1086i	−0.389948	−	0.675410i
$225$	−8.80926	+	15.2581i	−0.587284	+	1.01721i
$226$		−	11.1211i		−	0.739762i
$227$	−10.7151	−	6.18635i	−0.711185	−	0.410603i	0.100315	−	0.994956i	$-0.468015\pi$
$227$	−10.7151	−	6.18635i	−0.711185	−	0.410603i	−0.811500	+	0.584353i	$0.801348\pi$
$228$	22.6174	+	13.0581i	1.49787	+	0.864796i
$229$			26.4190i			1.74582i	0.487883	+	0.872909i	$0.337769\pi$
$229$			26.4190i			1.74582i	−0.487883	+	0.872909i	$0.662231\pi$
$230$	−1.68779	+	2.92335i	−0.111290	+	0.192760i
$231$	17.3190	+	29.9974i	1.13951	+	1.97369i
$232$	9.31939	−	5.38055i	0.611848	−	0.353250i
$233$	−17.2631			−1.13094			−0.565472	−	0.824768i	$-0.691306\pi$
$233$	−17.2631			−1.13094			−0.565472	+	0.824768i	$0.691306\pi$
$234$	−1.51430	−	19.1098i	−0.0989926	−	1.24925i
$235$	−13.2044			−0.861362
$236$	−1.97058	+	1.13771i	−0.128274	+	0.0740588i
$237$	−22.3670	−	38.7407i	−1.45289	−	2.51648i
$238$	0.856150	−	1.48289i	0.0554959	−	0.0961218i
$239$			19.6451i			1.27074i	0.772210	+	0.635368i	$0.219151\pi$
$239$			19.6451i			1.27074i	−0.772210	+	0.635368i	$0.780849\pi$
$240$	−1.29705	−	0.748855i	−0.0837245	−	0.0483384i
$241$	16.0493	+	9.26606i	1.03383	+	0.596879i	0.918078	−	0.396400i	$-0.129740\pi$
$241$	16.0493	+	9.26606i	1.03383	+	0.596879i	0.115747	+	0.993279i	$0.463074\pi$
$242$		−	16.8702i		−	1.08446i
$243$	−3.82649	+	6.62768i	−0.245469	+	0.425166i
$244$	7.56036	+	13.0949i	0.484003	+	0.838317i
$245$	3.78128	−	2.18312i	0.241577	−	0.139475i
$246$	3.32799			0.212185
$247$	−21.2111	−	10.1032i	−1.34963	−	0.642850i
$248$	2.75195			0.174749
$249$	40.7064	−	23.5019i	2.57966	−	1.48937i
$250$	4.83252	+	8.37017i	0.305635	+	0.529376i
$251$	−8.11034	+	14.0475i	−0.511920	+	0.886671i	0.487985	+	0.872852i	$0.337732\pi$
$251$	−8.11034	+	14.0475i	−0.511920	+	0.886671i	−0.999905	+	0.0138191i	$0.995601\pi$
$252$		−	16.8929i		−	1.06415i
$253$	−13.1215	−	7.57572i	−0.824944	−	0.476282i
$254$	0.341819	+	0.197350i	0.0214477	+	0.0123828i
$255$		−	4.67398i		−	0.292696i
$256$	7.51996	−	13.0250i	0.469998	−	0.814060i
$257$	0.918472	+	1.59084i	0.0572927	+	0.0992339i	0.893249	−	0.449562i	$-0.148420\pi$
$257$	0.918472	+	1.59084i	0.0572927	+	0.0992339i	−0.835957	+	0.548796i	$0.815087\pi$
$258$	3.20549	−	1.85069i	0.199565	−	0.115219i
$259$	−21.8356			−1.35680
$260$	6.37628	+	3.03713i	0.395440	+	0.188355i
$261$	24.9902			1.54686
$262$	−6.15679	+	3.55463i	−0.380368	+	0.219605i
$263$	15.4862	+	26.8228i	0.954918	+	1.65397i	0.734556	+	0.678548i	$0.237390\pi$
$263$	15.4862	+	26.8228i	0.954918	+	1.65397i	0.220362	+	0.975418i	$0.429276\pi$
$264$	−23.5821	+	40.8454i	−1.45138	+	2.51386i
$265$		−	5.54018i		−	0.340331i
$266$	9.48840	+	5.47813i	0.581771	+	0.335886i
$267$	−0.766592	−	0.442592i	−0.0469147	−	0.0270862i
$268$			3.80371i			0.232348i
$269$	−10.4643	+	18.1247i	−0.638021	+	1.10509i	0.347845	+	0.937552i	$0.386914\pi$
$269$	−10.4643	+	18.1247i	−0.638021	+	1.10509i	−0.985866	+	0.167533i	$0.946420\pi$
$270$	6.47347	+	11.2124i	0.393963	+	0.682363i
$271$	18.0501	−	10.4212i	1.09646	−	0.633044i	0.161174	−	0.986926i	$-0.448472\pi$
$271$	18.0501	−	10.4212i	1.09646	−	0.633044i	0.935290	+	0.353882i	$0.115138\pi$
$272$	−0.332321			−0.0201499
$273$	1.76400	+	22.2610i	0.106762	+	1.34729i
$274$	3.71728			0.224569
$275$	−13.3527	+	7.70917i	−0.805196	+	0.464880i
$276$	5.42903	+	9.40335i	0.326789	+	0.566015i
$277$	6.49340	−	11.2469i	0.390151	−	0.675761i	−0.602318	−	0.798256i	$-0.705756\pi$
$277$	6.49340	−	11.2469i	0.390151	−	0.675761i	0.992469	+	0.122495i	$0.0390896\pi$
$278$		−	11.0579i		−	0.663210i
$279$	5.53457	+	3.19539i	0.331346	+	0.191303i
$280$	−7.21405	−	4.16503i	−0.431122	−	0.248908i
$281$		−	5.18043i		−	0.309038i	−0.987990	−	0.154519i	$-0.950617\pi$
$281$		−	5.18043i		−	0.309038i	0.987990	−	0.154519i	$-0.0493828\pi$
$282$	11.2383	−	19.4654i	0.669234	−	1.15915i
$283$	14.1912	+	24.5798i	0.843577	+	1.46112i	0.886851	+	0.462055i	$0.152888\pi$
$283$	14.1912	+	24.5798i	0.843577	+	1.46112i	−0.0432745	+	0.999063i	$0.513779\pi$
$284$	4.00205	−	2.31058i	0.237478	−	0.137108i
$285$	29.9068			1.77153
$286$	7.21403	−	15.1455i	0.426575	−	0.895570i
$287$	−2.63829			−0.155733
$288$	31.9642	−	18.4546i	1.88351	−	1.08744i
$289$	7.98145	+	13.8243i	0.469497	+	0.813193i
$290$	2.43615	−	4.21954i	0.143056	−	0.247780i
$291$			33.0768i			1.93900i
$292$	−13.2004	−	7.62128i	−0.772498	−	0.446002i
$293$	−9.48668	−	5.47714i	−0.554218	−	0.319978i	0.196604	−	0.980483i	$-0.437009\pi$
$293$	−9.48668	−	5.47714i	−0.554218	−	0.319978i	−0.750821	+	0.660505i	$0.770342\pi$
$294$			7.43227i			0.433459i
$295$	−1.30284	+	2.25659i	−0.0758543	+	0.131384i
$296$	−14.8660	−	25.7487i	−0.864069	−	1.49661i
$297$	−50.3271	+	29.0564i	−2.92027	+	1.68602i
$298$	−3.50513			−0.203046
$299$	−5.53696	−	8.04706i	−0.320210	−	0.465374i
$300$	11.0493			0.637933
$301$	−2.54118	+	1.46715i	−0.146471	+	0.0845650i
$302$	−2.22675	−	3.85684i	−0.128135	−	0.221936i
$303$	−10.4125	+	18.0350i	−0.598182	+	1.03608i
$304$		−	2.12638i		−	0.121956i
$305$	14.9955	+	8.65768i	0.858642	+	0.495737i
$306$	4.68903	+	2.70721i	0.268054	+	0.154761i
$307$		−	20.4028i		−	1.16445i	−0.813028	−	0.582224i	$-0.802183\pi$
$307$		−	20.4028i		−	1.16445i	0.813028	−	0.582224i	$-0.197817\pi$
$308$	7.39165	−	12.8027i	0.421178	−	0.729502i
$309$	−5.47765	−	9.48756i	−0.311612	−	0.539728i
$310$	1.07907	−	0.622999i	0.0612868	−	0.0353840i
$311$	9.75439			0.553121			0.276560	−	0.960997i	$-0.410805\pi$
$311$	9.75439			0.553121			0.276560	+	0.960997i	$0.410805\pi$
$312$	−25.0493	+	17.2357i	−1.41814	+	0.975780i
$313$	−17.9950			−1.01714			−0.508568	−	0.861022i	$-0.669825\pi$
$313$	−17.9950			−1.01714			−0.508568	+	0.861022i	$0.669825\pi$
$314$	16.3605	−	9.44576i	0.923279	−	0.533055i
$315$	−9.67235	−	16.7530i	−0.544975	−	0.943925i
$316$	−9.54608	+	16.5343i	−0.537009	+	0.930127i
$317$		−	22.7973i		−	1.28043i	−0.768198	−	0.640213i	$-0.778846\pi$
$317$		−	22.7973i		−	1.28043i	0.768198	−	0.640213i	$-0.221154\pi$
$318$	8.16710	+	4.71527i	0.457988	+	0.264419i
$319$	18.9395	+	10.9347i	1.06041	+	0.612228i
$320$		−	6.21862i		−	0.347632i
$321$	24.1162	−	41.7705i	1.34604	−	2.33140i
$322$	2.27758	+	3.94488i	0.126924	+	0.219839i
$323$	5.74687	−	3.31796i	0.319764	−	0.184616i
$324$	16.5705			0.920581
$325$	−9.90896	+	0.785206i	−0.549650	+	0.0435554i
$326$	0.639602			0.0354243
$327$	12.2934	−	7.09758i	0.679825	−	0.392497i
$328$	−1.79619	−	3.11109i	−0.0991778	−	0.171781i
$329$	−8.90929	+	15.4313i	−0.491185	+	0.850757i
$330$			21.3545i			1.17553i
$331$	−1.52038	−	0.877792i	−0.0835677	−	0.0482478i	0.457634	−	0.889141i	$-0.348697\pi$
$331$	−1.52038	−	0.877792i	−0.0835677	−	0.0482478i	−0.541202	+	0.840893i	$0.682030\pi$
$332$	−17.3732	−	10.0304i	−0.953481	−	0.550492i
$333$		−	69.0459i		−	3.78369i
$334$	2.85089	−	4.93788i	0.155994	−	0.270189i
$335$	2.17789	+	3.77221i	0.118991	+	0.206098i
$336$	−1.75030	+	1.01053i	−0.0954865	+	0.0551291i
$337$	9.12206			0.496910			0.248455	−	0.968643i	$-0.420077\pi$
$337$	9.12206			0.496910			0.248455	+	0.968643i	$0.420077\pi$
$338$	8.39765	−	6.81522i	0.456772	−	0.370699i
$339$	−40.9645			−2.22489
$340$	−1.72757	+	0.997414i	−0.0936907	+	0.0540924i
$341$	2.79635	+	4.84342i	0.151431	+	0.262286i
$342$	−17.3223	+	30.0031i	−0.936681	+	1.62238i
$343$		−	20.0395i		−	1.08203i
$344$	−3.46014	−	1.99771i	−0.186558	−	0.107709i
$345$	10.7682	+	6.21700i	0.579738	+	0.334712i
$346$		−	2.92958i		−	0.157495i
$347$	−15.7978	+	27.3626i	−0.848071	+	1.46890i	0.0348570	+	0.999392i	$0.488902\pi$
$347$	−15.7978	+	27.3626i	−0.848071	+	1.46890i	−0.882928	+	0.469509i	$0.844431\pi$
$348$	−7.83622	−	13.5727i	−0.420065	−	0.727574i
$349$	−3.47285	+	2.00505i	−0.185898	+	0.107328i	−0.590061	−	0.807359i	$-0.700896\pi$
$349$	−3.47285	+	2.00505i	−0.185898	+	0.107328i	0.404163	+	0.914687i	$0.367563\pi$
$350$	4.63539			0.247772
$351$	−37.3475	+	2.95949i	−1.99346	+	0.157966i
$352$	32.2999			1.72159
$353$	−6.23031	+	3.59707i	−0.331606	+	0.191453i	−0.656554	−	0.754279i	$-0.727987\pi$
$353$	−6.23031	+	3.59707i	−0.331606	+	0.191453i	0.324948	+	0.945732i	$0.394653\pi$
$354$	−2.21771	−	3.84118i	−0.117870	−	0.204157i
$355$	2.64594	−	4.58291i	0.140432	−	0.243235i
$356$			0.377791i			0.0200229i
$357$	−5.46225	−	3.15363i	−0.289093	−	0.166908i
$358$	−15.9475	−	9.20728i	−0.842850	−	0.486620i
$359$		−	11.3596i		−	0.599539i	−0.954012	−	0.299769i	$-0.903090\pi$
$359$		−	11.3596i		−	0.599539i	0.954012	−	0.299769i	$-0.0969098\pi$
$360$	13.1702	−	22.8114i	0.694128	−	1.20227i
$361$	11.7302	+	20.3172i	0.617377	+	1.06933i
$362$	3.18078	−	1.83642i	0.167178	−	0.0965202i
$363$	−62.1416			−3.26159
$364$	7.85154	−	5.40242i	0.411533	−	0.283164i
$365$	−17.4549			−0.913630
$366$	−25.5255	+	14.7372i	−1.33424	+	0.770324i
$367$	5.00983	+	8.67728i	0.261511	+	0.452950i	0.966644	−	0.256125i	$-0.0824459\pi$
$367$	5.00983	+	8.67728i	0.261511	+	0.452950i	−0.705133	+	0.709075i	$0.749113\pi$
$368$	0.442030	−	0.765618i	0.0230424	−	0.0399106i
$369$		−	8.34248i		−	0.434292i
$370$	−11.6582	−	6.73088i	−0.606082	−	0.349922i
$371$	−6.47453	−	3.73807i	−0.336141	−	0.194071i
$372$		−	4.00793i		−	0.207801i
$373$	−9.00207	+	15.5920i	−0.466109	+	0.807325i	−0.999251	−	0.0387009i	$-0.987678\pi$
$373$	−9.00207	+	15.5920i	−0.466109	+	0.807325i	0.533141	+	0.846026i	$0.321011\pi$
$374$	2.36914	+	4.10347i	0.122505	+	0.212185i
$375$	30.8315	−	17.8006i	1.59213	−	0.919219i
$376$	−24.2623			−1.25123
$377$	7.99200	+	11.6151i	0.411609	+	0.598207i
$378$	17.4711			0.898616
$379$	−5.56688	+	3.21404i	−0.285952	+	0.165094i	−0.636115	−	0.771594i	$-0.719460\pi$
$379$	−5.56688	+	3.21404i	−0.285952	+	0.165094i	0.350163	+	0.936689i	$0.386126\pi$
$380$	−6.38202	−	11.0540i	−0.327391	−	0.567057i
$381$	0.726937	−	1.25909i	0.0372421	−	0.0645053i
$382$		−	7.27043i		−	0.371988i
$383$	4.33125	+	2.50065i	0.221317	+	0.127777i	0.606560	−	0.795038i	$-0.292549\pi$
$383$	4.33125	+	2.50065i	0.221317	+	0.127777i	−0.385243	+	0.922815i	$0.625882\pi$
$384$	−21.4871	−	12.4056i	−1.09651	−	0.633069i
$385$		−	16.9290i		−	0.862779i
$386$	−6.13580	+	10.6275i	−0.312304	+	0.540926i
$387$	−4.63924	−	8.03540i	−0.235826	−	0.408462i
$388$	12.2257	−	7.05849i	0.620664	−	0.358341i
$389$	21.2028			1.07502			0.537512	−	0.843256i	$-0.319364\pi$
$389$	21.2028			1.07502			0.537512	+	0.843256i	$0.319364\pi$
$390$	−5.92018	+	12.4291i	−0.299780	+	0.629371i
$391$	2.75893			0.139525
$392$	6.94787	−	4.01135i	0.350920	−	0.202604i
$393$	13.0935	+	22.6786i	0.660478	+	1.14398i
$394$	−0.835393	+	1.44694i	−0.0420865	+	0.0728959i
$395$			21.8632i			1.10006i
$396$	40.4832	+	23.3730i	2.03436	+	1.17454i
$397$	−2.21384	−	1.27816i	−0.111109	−	0.0641489i	0.443416	−	0.896316i	$-0.353767\pi$
$397$	−2.21384	−	1.27816i	−0.111109	−	0.0641489i	−0.554525	+	0.832167i	$0.687100\pi$
$398$			11.8816i			0.595569i
$399$	20.1787	−	34.9505i	1.01020	−	1.74972i
$400$	−0.449816	−	0.779104i	−0.0224908	−	0.0389552i
$401$	−20.8544	+	12.0403i	−1.04142	+	0.601264i	−0.920235	−	0.391366i	$-0.872003\pi$
$401$	−20.8544	+	12.0403i	−1.04142	+	0.601264i	−0.121184	+	0.992630i	$0.538669\pi$
$402$	−7.41444			−0.369799
$403$	0.284818	+	3.59428i	0.0141878	+	0.179044i
$404$	8.88797			0.442193
$405$	16.4333	−	9.48775i	0.816575	−	0.471450i
$406$	−3.28744	−	5.69401i	−0.163153	−	0.282589i
$407$	30.2117	−	52.3283i	1.49754	−	2.59382i
$408$		−	8.58815i		−	0.425177i
$409$	19.7862	+	11.4236i	0.978366	+	0.564860i	0.901776	−	0.432203i	$-0.142264\pi$
$409$	19.7862	+	11.4236i	0.978366	+	0.564860i	0.0765893	+	0.997063i	$0.475597\pi$
$410$	−1.40861	−	0.813259i	−0.0695661	−	0.0401640i
$411$		−	13.6926i		−	0.675406i
$412$	−2.33783	+	4.04923i	−0.115176	+	0.199491i
$413$	1.75810	+	3.04513i	0.0865107	+	0.149841i
$414$	−12.4740	+	7.20188i	−0.613064	+	0.353953i
$415$	−22.9725			−1.12768
$416$	18.7997	+	8.95461i	0.921731	+	0.439036i
$417$	−40.7319			−1.99465
$418$	−26.2563	+	15.1591i	−1.28424	+	0.741455i
$419$	−8.68199	−	15.0376i	−0.424143	−	0.734637i	0.572197	−	0.820116i	$-0.306091\pi$
$419$	−8.68199	−	15.0376i	−0.424143	−	0.734637i	−0.996340	+	0.0854792i	$0.972758\pi$
$420$	−6.06594	+	10.5065i	−0.295988	+	0.512665i
$421$			3.16733i			0.154366i	0.997017	+	0.0771832i	$0.0245926\pi$
$421$			3.16733i			0.154366i	−0.997017	+	0.0771832i	$0.975407\pi$
$422$	−2.71813	−	1.56931i	−0.132316	−	0.0763929i
$423$	−48.7951	−	28.1719i	−2.37250	−	1.36976i
$424$		−	10.1797i		−	0.494372i
$425$	1.40377	−	2.43139i	0.0680927	−	0.117940i
$426$	4.50395	+	7.80106i	0.218217	+	0.377963i
$427$	20.2356	−	11.6830i	0.979268	−	0.565380i
$428$	−20.5853			−0.995028
$429$	−55.7883	−	26.5729i	−2.69349	−	1.28295i
$430$	−1.80901			−0.0872381
$431$	9.69038	−	5.59474i	0.466769	−	0.269489i	−0.248117	−	0.968730i	$-0.579812\pi$
$431$	9.69038	−	5.59474i	0.466769	−	0.269489i	0.714886	+	0.699241i	$0.246478\pi$
$432$	−1.69539	−	2.93650i	−0.0815693	−	0.141282i
$433$	−15.5991	+	27.0183i	−0.749643	+	1.29842i	0.198352	+	0.980131i	$0.436441\pi$
$433$	−15.5991	+	27.0183i	−0.749643	+	1.29842i	−0.947994	+	0.318288i	$0.896892\pi$
$434$		−	1.68140i		−	0.0807097i
$435$	−15.5427	−	8.97357i	−0.745214	−	0.430250i
$436$	−5.24674	−	3.02920i	−0.251273	−	0.145073i
$437$			17.6532i			0.844468i
$438$	14.8559	−	25.7312i	0.709843	−	1.22948i
$439$	−3.28051	−	5.68202i	−0.156570	−	0.271188i	0.777059	−	0.629427i	$-0.216710\pi$
$439$	−3.28051	−	5.68202i	−0.156570	−	0.271188i	−0.933630	+	0.358239i	$0.883377\pi$
$440$	19.9627	−	11.5255i	0.951685	−	0.549456i
$441$	18.6309			0.887187
$442$	0.241305	+	3.04517i	0.0114777	+	0.144844i
$443$	−7.46246			−0.354552			−0.177276	−	0.984161i	$-0.556729\pi$
$443$	−7.46246			−0.354552			−0.177276	+	0.984161i	$0.556729\pi$
$444$	−37.5003	+	21.6508i	−1.77968	+	1.02750i
$445$	0.216312	+	0.374663i	0.0102542	+	0.0177607i
$446$	11.8187	−	20.4706i	0.559633	−	0.969313i
$447$			12.9111i			0.610676i
$448$	−7.26739	−	4.19583i	−0.343352	−	0.198234i
$449$	6.19599	+	3.57726i	0.292407	+	0.168821i	0.639027	−	0.769184i	$-0.279337\pi$
$449$	6.19599	+	3.57726i	0.292407	+	0.168821i	−0.346620	+	0.938006i	$0.612671\pi$
$450$			14.6575i			0.690960i
$451$	3.65034	−	6.32257i	0.171888	−	0.297718i
$452$	8.74169	+	15.1411i	0.411175	+	0.712176i
$453$	−14.2067	+	8.20224i	−0.667489	+	0.385375i
$454$	−10.2933			−0.483088
$455$	4.69327	−	9.85325i	0.220024	−	0.461927i
$456$	54.9518			2.57336
$457$	9.15194	−	5.28387i	0.428110	−	0.247169i	−0.270431	−	0.962739i	$-0.587166\pi$
$457$	9.15194	−	5.28387i	0.428110	−	0.247169i	0.698541	+	0.715570i	$0.253833\pi$
$458$	10.9895	+	19.0343i	0.513504	+	0.889415i
$459$	5.29089	−	9.16409i	0.246958	−	0.427743i
$460$		−	5.30675i		−	0.247429i
$461$	27.4427	+	15.8440i	1.27813	+	0.737930i	0.976505	−	0.215495i	$-0.0691366\pi$
$461$	27.4427	+	15.8440i	1.27813	+	0.737930i	0.301628	+	0.953426i	$0.402470\pi$
$462$	24.9559	+	14.4083i	1.16105	+	0.670335i
$463$			37.4935i			1.74247i	0.490864	+	0.871236i	$0.336681\pi$
$463$			37.4935i			1.74247i	−0.490864	+	0.871236i	$0.663319\pi$
$464$	−0.638023	+	1.10509i	−0.0296195	+	0.0513024i
$465$	−2.29482	−	3.97474i	−0.106420	−	0.184324i
$466$	−12.4377	+	7.18090i	−0.576164	+	0.332649i
$467$	−7.61460			−0.352362			−0.176181	−	0.984358i	$-0.556374\pi$
$467$	−7.61460			−0.352362			−0.176181	+	0.984358i	$0.556374\pi$
$468$	17.0829	+	24.8272i	0.789657	+	1.14764i
$469$	5.87786			0.271414
$470$	−9.51349	+	5.49262i	−0.438825	+	0.253355i
$471$	−34.7935	−	60.2641i	−1.60320	−	2.77682i
$472$	−2.39389	+	4.14633i	−0.110188	+	0.190850i
$473$		−	8.11979i		−	0.373348i
$474$	−32.2298	−	18.6079i	−1.48036	−	0.854688i
$475$	15.5574	+	8.98209i	0.713824	+	0.412127i
$476$			2.69190i			0.123383i
$477$	11.8201	−	20.4730i	0.541204	−	0.937393i
$478$	8.17173	+	14.1538i	0.373766	+	0.647382i
$479$	7.20059	−	4.15726i	0.329003	−	0.189950i	−0.326395	−	0.945233i	$-0.605834\pi$
$479$	7.20059	−	4.15726i	0.329003	−	0.189950i	0.655398	+	0.755283i	$0.272501\pi$
$480$	−26.5069			−1.20987
$481$	32.0914	−	22.0812i	1.46324	−	1.00682i
$482$	15.4175			0.702249
$483$	14.5310	−	8.38946i	0.661182	−	0.381734i
$484$	13.2608	+	22.9684i	0.602765	+	1.04402i
$485$	8.08296	−	14.0001i	0.367028	−	0.635712i
$486$			6.36679i			0.288803i
$487$	−2.73749	−	1.58049i	−0.124048	−	0.0716190i	0.436692	−	0.899611i	$-0.356150\pi$
$487$	−2.73749	−	1.58049i	−0.124048	−	0.0716190i	−0.560740	+	0.827992i	$0.689483\pi$
$488$	27.5533	+	15.9079i	1.24728	+	0.720118i
$489$		−	2.35598i		−	0.106541i
$490$	1.81622	−	3.14578i	0.0820484	−	0.142112i
$491$	17.1620	+	29.7255i	0.774511	+	1.34149i	0.935069	+	0.354467i	$0.115338\pi$
$491$	17.1620	+	29.7255i	0.774511	+	1.34149i	−0.160557	+	0.987027i	$0.551329\pi$
$492$	−4.53098	+	2.61596i	−0.204272	+	0.117937i
$493$	−3.98223			−0.179350
$494$	−19.4847	+	1.54401i	−0.876658	+	0.0694681i
$495$	53.5307			2.40602
$496$	−0.282605	+	0.163162i	−0.0126893	+	0.00732619i
$497$	−3.57054	−	6.18435i	−0.160161	−	0.277406i
$498$	19.5520	−	33.8651i	0.876147	−	1.51753i
$499$		−	36.5003i		−	1.63398i	−0.576652	−	0.816990i	$-0.695641\pi$
$499$		−	36.5003i		−	1.63398i	0.576652	−	0.816990i	$-0.304359\pi$
$500$	−13.1587	−	7.59719i	−0.588476	−	0.339757i
$501$	−18.1887	−	10.5012i	−0.812611	−	0.469161i
$502$			13.4946i			0.602292i
$503$	−2.16613	+	3.75185i	−0.0965831	+	0.167287i	−0.910268	−	0.414019i	$-0.864125\pi$
$503$	−2.16613	+	3.75185i	−0.0965831	+	0.167287i	0.813685	+	0.581306i	$0.197458\pi$
$504$	−17.7723	−	30.7826i	−0.791642	−	1.37116i
$505$	8.81438	−	5.08899i	0.392235	−	0.226457i
$506$	−12.6050			−0.560362
$507$	−25.1039	−	30.9328i	−1.11490	−	1.37377i
$508$	−0.620505			−0.0275305
$509$	−12.4356	+	7.17972i	−0.551200	+	0.318236i	−0.749606	−	0.661884i	$-0.769757\pi$
$509$	−12.4356	+	7.17972i	−0.551200	+	0.318236i	0.198406	+	0.980120i	$0.436424\pi$
$510$	−1.94423	−	3.36750i	−0.0860918	−	0.149115i
$511$	−11.7771	+	20.3986i	−0.520990	+	0.902382i
$512$			3.68070i			0.162665i
$513$	58.6370	+	33.8541i	2.58889	+	1.49469i
$514$	1.32348	+	0.764110i	0.0583760	+	0.0337034i
$515$			5.35428i			0.235938i
$516$	−2.90946	+	5.03934i	−0.128082	+	0.221844i
$517$	−24.6538	−	42.7016i	−1.08427	−	1.87801i
$518$	−15.7321	+	9.08291i	−0.691227	+	0.399080i
$519$	−10.7911			−0.473678
$520$	14.8143	−	1.17391i	0.649648	−	0.0514794i
$521$	−12.7273			−0.557593			−0.278797	−	0.960350i	$-0.589936\pi$
$521$	−12.7273			−0.557593			−0.278797	+	0.960350i	$0.589936\pi$
$522$	18.0049	−	10.3951i	0.788053	−	0.454983i
$523$	9.12642	+	15.8074i	0.399071	+	0.691211i	0.993611	−	0.112855i	$-0.0359995\pi$
$523$	9.12642	+	15.8074i	0.399071	+	0.691211i	−0.594541	+	0.804065i	$0.702666\pi$
$524$	5.58821	−	9.67907i	0.244122	−	0.422832i
$525$		−	17.0745i		−	0.745191i
$526$	22.3149	+	12.8835i	0.972974	+	0.561747i
$527$	−0.881941	−	0.509189i	−0.0384180	−	0.0221806i
$528$		−	5.59270i		−	0.243391i
$529$	7.83026	−	13.5624i	0.340446	−	0.589670i
$530$	−2.30454	−	3.99158i	−0.100103	−	0.173383i
$531$	−9.62893	+	5.55926i	−0.417860	+	0.241251i
$532$	−17.2243			−0.746768
$533$	3.87745	−	2.66797i	0.167951	−	0.115562i
$534$	−0.736416			−0.0318678
$535$	−20.4149	+	11.7865i	−0.882612	+	0.509576i
$536$	4.00173	+	6.93120i	0.172848	+	0.299382i
$537$	−33.9150	+	58.7425i	−1.46354	+	2.53493i
$538$			17.4113i			0.750654i
$539$	14.1200	+	8.15216i	0.608189	+	0.351138i
$540$	−17.6269	−	10.1769i	−0.758542	−	0.437945i
$541$		−	24.0161i		−	1.03253i	−0.856428	−	0.516267i	$-0.827321\pi$
$541$		−	24.0161i		−	1.03253i	0.856428	−	0.516267i	$-0.172679\pi$
$542$	8.66979	−	15.0165i	0.372399	−	0.645014i
$543$	−6.76447	−	11.7164i	−0.290291	−	0.502799i
$544$	−5.09354	+	2.94076i	−0.218384	+	0.126084i
$545$	−6.93773			−0.297180
$546$	10.5308	+	15.3048i	0.450675	+	0.654983i
$547$	17.8886			0.764860			0.382430	−	0.923984i	$-0.375087\pi$
$547$	17.8886			0.764860			0.382430	+	0.923984i	$0.375087\pi$
$548$	−5.06098	+	2.92196i	−0.216194	+	0.124820i
$549$	36.9426	+	63.9864i	1.57667	+	2.73087i
$550$	−6.41353	+	11.1086i	−0.273474	+	0.473671i
$551$		−	25.4805i		−	1.08551i
$552$	19.7858	+	11.4233i	0.842140	+	0.486210i
$553$	25.5504	+	14.7515i	1.08651	+	0.627299i
$554$		−	10.8042i		−	0.459026i
$555$	−24.7932	+	42.9431i	−1.05241	+	1.82283i
$556$	8.69206	+	15.0551i	0.368626	+	0.638478i
$557$	7.51808	−	4.34057i	0.318551	−	0.183916i	−0.332195	−	0.943211i	$-0.607789\pi$
$557$	7.51808	−	4.34057i	0.318551	−	0.183916i	0.650747	+	0.759295i	$0.274456\pi$
$558$	5.31671			0.225074
$559$	2.25108	−	4.72601i	0.0952103	−	0.199889i
$560$	0.987774			0.0417411
$561$	15.1151	−	8.72673i	0.638161	−	0.368443i
$562$	−2.15489	−	3.73238i	−0.0908986	−	0.157441i
$563$	−15.3358	+	26.5625i	−0.646329	+	1.11947i	0.337664	+	0.941267i	$0.390363\pi$
$563$	−15.3358	+	26.5625i	−0.646329	+	1.11947i	−0.983993	+	0.178208i	$0.942970\pi$
$564$			35.3355i			1.48789i
$565$	17.3386	+	10.0105i	0.729442	+	0.421143i
$566$	20.4488	+	11.8061i	0.859528	+	0.496249i
$567$		−	25.6063i		−	1.07536i
$568$	4.86175	−	8.42080i	0.203995	−	0.353329i
$569$	2.22636	+	3.85616i	0.0933337	+	0.161659i	0.908912	−	0.416988i	$-0.136914\pi$
$569$	2.22636	+	3.85616i	0.0933337	+	0.161659i	−0.815578	+	0.578647i	$0.803581\pi$
$570$	21.5472	−	12.4403i	0.902512	−	0.521065i
$571$	−20.9889			−0.878359			−0.439179	−	0.898399i	$-0.644731\pi$
$571$	−20.9889			−0.878359			−0.439179	+	0.898399i	$0.644731\pi$
$572$	2.08333	+	26.2907i	0.0871084	+	1.09927i
$573$	−26.7807			−1.11878
$574$	−1.90083	+	1.09744i	−0.0793390	+	0.0458064i
$575$	3.73438	+	6.46813i	0.155734	+	0.269740i
$576$	13.2675	−	22.9800i	0.552814	−	0.957502i
$577$		−	10.6421i		−	0.443035i	−0.975156	−	0.221518i	$-0.928899\pi$
$577$		−	10.6421i		−	0.443035i	0.975156	−	0.221518i	$-0.0711010\pi$
$578$	11.5009	+	6.64006i	0.478375	+	0.276190i
$579$	39.1465	+	22.6012i	1.62687	+	0.939275i
$580$			7.65973i			0.318053i
$581$	−15.5000	+	26.8468i	−0.643049	+	1.11379i
$582$	13.7589	+	23.8311i	0.570325	+	0.987831i
$583$	17.9163	−	10.3440i	0.742018	−	0.428404i
$584$	−32.0722			−1.32716
$585$	31.1567	+	14.8405i	1.28817	+	0.613578i
$586$	−9.11325			−0.376465
$587$	19.7842	−	11.4224i	0.816580	−	0.471452i	−0.0326560	−	0.999467i	$-0.510397\pi$
$587$	19.7842	−	11.4224i	0.816580	−	0.471452i	0.849236	+	0.528014i	$0.177063\pi$
$588$	−5.84212	−	10.1189i	−0.240925	−	0.417294i
$589$	3.25808	−	5.64316i	0.134247	−	0.232522i
$590$			2.16776i			0.0892452i
$591$	5.32982	+	3.07717i	0.219239	+	0.126578i
$592$	3.05326	+	1.76280i	0.125488	+	0.0724507i
$593$			25.3190i			1.03973i	0.854250	+	0.519863i	$0.174017\pi$
$593$			25.3190i			1.03973i	−0.854250	+	0.519863i	$0.825983\pi$
$594$	−24.1730	+	41.8689i	−0.991831	+	1.71790i
$595$	1.54130	+	2.66961i	0.0631872	+	0.109443i
$596$	4.77214	−	2.75520i	0.195475	−	0.112857i
$597$	43.7658			1.79121
$598$	−7.33657	−	3.49453i	−0.300015	−	0.142902i
$599$	−12.2836			−0.501894			−0.250947	−	0.968001i	$-0.580742\pi$
$599$	−12.2836			−0.501894			−0.250947	+	0.968001i	$0.580742\pi$
$600$	20.1343	−	11.6246i	0.821980	−	0.474571i
$601$	−13.6249	−	23.5991i	−0.555773	−	0.962627i	−0.997843	−	0.0656462i	$-0.979089\pi$
$601$	−13.6249	−	23.5991i	−0.555773	−	0.962627i	0.442070	−	0.896980i	$-0.354244\pi$
$602$	−1.22057	+	2.11409i	−0.0497468	+	0.0861641i
$603$			18.5862i			0.756890i
$604$	6.06333	+	3.50066i	0.246713	+	0.142440i
$605$	26.3021	+	15.1855i	1.06933	+	0.617379i
$606$			17.3250i			0.703782i
$607$	−2.34092	+	4.05460i	−0.0950151	+	0.164571i	−0.909615	−	0.415452i	$-0.863623\pi$
$607$	−2.34092	+	4.05460i	−0.0950151	+	0.164571i	0.814600	+	0.580023i	$0.196957\pi$
$608$	−18.8166	−	32.5913i	−0.763115	−	1.32175i
$609$	−20.9739	+	12.1093i	−0.849905	+	0.490693i
$610$	14.4053			0.583252
$611$	−2.51107	−	31.6887i	−0.101587	−	1.28199i
$612$	−8.51200			−0.344077
$613$	−17.8198	+	10.2883i	−0.719736	+	0.415540i	−0.814655	−	0.579945i	$-0.803074\pi$
$613$	−17.8198	+	10.2883i	−0.719736	+	0.415540i	0.0949195	+	0.995485i	$0.469741\pi$
$614$	−8.48690	−	14.6997i	−0.342503	−	0.593233i
$615$	−2.99564	+	5.18860i	−0.120796	+	0.209225i
$616$		−	31.1059i		−	1.25329i
$617$	−22.4196	−	12.9440i	−0.902580	−	0.521105i	−0.0245439	−	0.999699i	$-0.507813\pi$
$617$	−22.4196	−	12.9440i	−0.902580	−	0.521105i	−0.878036	+	0.478594i	$0.841147\pi$
$618$	−7.89304	−	4.55705i	−0.317505	−	0.183311i
$619$			13.0268i			0.523589i	0.965124	+	0.261795i	$0.0843143\pi$
$619$			13.0268i			0.523589i	−0.965124	+	0.261795i	$0.915686\pi$
$620$	−0.979414	+	1.69640i	−0.0393342	+	0.0681289i
$621$	14.0751	+	24.3788i	0.564815	+	0.978288i
$622$	7.02782	−	4.05751i	0.281790	−	0.162691i
$623$	0.583800			0.0233894
$624$	1.55048	−	3.25515i	0.0620690	−	0.130310i
$625$	−3.61535			−0.144614
$626$	−12.9650	+	7.48533i	−0.518185	+	0.299174i
$627$	55.8385	+	96.7152i	2.22998	+	3.86243i
$628$	−14.8497	+	25.7203i	−0.592566	+	1.02635i
$629$			11.0025i			0.438700i
$630$	−13.9374	−	8.04677i	−0.555280	−	0.320591i
$631$	−14.6600	−	8.46393i	−0.583604	−	0.336944i	0.178960	−	0.983856i	$-0.442727\pi$
$631$	−14.6600	−	8.46393i	−0.583604	−	0.336944i	−0.762564	+	0.646912i	$0.776060\pi$
$632$			40.1722i			1.59797i
$633$	−5.78057	+	10.0122i	−0.229757	+	0.397951i
$634$	−9.48296	−	16.4250i	−0.376616	−	0.652319i
$635$	−0.615367	+	0.355283i	−0.0244201	+	0.0140990i
$636$	−14.8257			−0.587879
$637$	5.95826	+	8.65937i	0.236075	+	0.343097i
$638$	18.1940			0.720307
$639$	19.5554	−	11.2903i	0.773600	−	0.446638i
$640$	6.06308	+	10.5016i	0.239664	+	0.415111i
$641$	1.11590	−	1.93280i	0.0440755	−	0.0763410i	−0.843146	−	0.537685i	$-0.819299\pi$
$641$	1.11590	−	1.93280i	0.0440755	−	0.0763410i	0.887222	+	0.461344i	$0.152632\pi$
$642$		−	40.1263i		−	1.58366i
$643$	12.6232	+	7.28802i	0.497811	+	0.287411i	0.727809	−	0.685780i	$-0.240539\pi$
$643$	12.6232	+	7.28802i	0.497811	+	0.287411i	−0.229998	+	0.973191i	$0.573872\pi$
$644$	−6.20173	−	3.58057i	−0.244382	−	0.141094i
$645$			6.66348i			0.262374i
$646$	2.76033	−	4.78103i	0.108604	−	0.188107i
$647$	−18.4836	−	32.0145i	−0.726664	−	1.25862i	−0.958285	−	0.285813i	$-0.907736\pi$
$647$	−18.4836	−	32.0145i	−0.726664	−	1.25862i	0.231621	−	0.972806i	$-0.425597\pi$
$648$	30.1951	−	17.4331i	1.18617	−	0.684838i
$649$	−9.73006			−0.381938
$650$	−6.81256	+	4.68753i	−0.267211	+	0.183860i
$651$	−6.19344			−0.242740
$652$	−0.870802	+	0.502758i	−0.0341033	+	0.0196895i
$653$	0.823360	+	1.42610i	0.0322206	+	0.0558076i	0.881686	−	0.471837i	$-0.156409\pi$
$653$	0.823360	+	1.42610i	0.0322206	+	0.0558076i	−0.849465	+	0.527644i	$0.823075\pi$
$654$	5.90473	−	10.2273i	0.230893	−	0.399919i
$655$		−	12.7986i		−	0.500082i
$656$	0.368911	+	0.212991i	0.0144036	+	0.00831589i
$657$	−64.5020	−	37.2403i	−2.51646	−	1.45288i
$658$			14.8239i			0.577896i
$659$	8.92854	−	15.4647i	0.347806	−	0.602418i	−0.638053	−	0.769992i	$-0.720260\pi$
$659$	8.92854	−	15.4647i	0.347806	−	0.602418i	0.985860	+	0.167574i	$0.0535933\pi$
$660$	−16.7857	−	29.0736i	−0.653381	−	1.13169i
$661$	−26.3168	+	15.1940i	−1.02360	+	0.590978i	−0.915146	−	0.403123i	$-0.867925\pi$
$661$	−26.3168	+	15.1940i	−1.02360	+	0.590978i	−0.108459	+	0.994101i	$0.534591\pi$
$662$	−1.46053			−0.0567652
$663$	11.2169	−	0.888848i	0.435628	−	0.0345200i
$664$	−42.2106			−1.63809
$665$	−17.0817	+	9.86211i	−0.662399	+	0.382436i
$666$	−28.7209	−	49.7460i	−1.11291	−	1.92762i
$667$	5.29687	−	9.17445i	0.205096	−	0.355236i
$668$			8.96374i			0.346817i
$669$	−75.4036	−	43.5343i	−2.91527	−	1.68313i
$670$	3.13824	+	1.81186i	0.121241	+	0.0699984i
$671$			64.6585i			2.49611i
$672$	−17.8847	+	30.9772i	−0.689917	+	1.19497i
$673$	−15.0214	−	26.0178i	−0.579032	−	1.00291i	−0.995591	−	0.0938040i	$-0.970097\pi$
$673$	−15.0214	−	26.0178i	−0.579032	−	1.00291i	0.416559	−	0.909109i	$-0.363236\pi$
$674$	6.57224	−	3.79448i	0.253153	−	0.146158i
$675$	28.6461			1.10259
$676$	−6.07610	+	15.8797i	−0.233696	+	0.610758i
$677$	14.9123			0.573128			0.286564	−	0.958061i	$-0.407487\pi$
$677$	14.9123			0.573128			0.286564	+	0.958061i	$0.407487\pi$
$678$	−29.5140	+	17.0399i	−1.13348	+	0.654414i
$679$	−10.9075	−	18.8923i	−0.418590	−	0.725020i
$680$	−2.09868	+	3.63502i	−0.0804808	+	0.139397i
$681$			37.9154i			1.45292i
$682$	4.02941	+	2.32638i	0.154294	+	0.0890818i
$683$	−28.1539	−	16.2547i	−1.07728	−	0.621967i	−0.147118	−	0.989119i	$-0.547000\pi$
$683$	−28.1539	−	16.2547i	−1.07728	−	0.621967i	−0.930161	+	0.367152i	$0.880333\pi$
$684$		−	54.4646i		−	2.08250i
$685$	−3.34605	+	5.79553i	−0.127846	+	0.221436i
$686$	−8.33577	−	14.4380i	−0.318261	−	0.551245i
$687$	70.1129	−	40.4797i	2.67498	−	1.54440i
$688$	0.473775			0.0180625
$689$	13.2956	−	1.05357i	0.506523	−	0.0401379i
$690$	10.3443			0.393800
$691$	−10.7982	+	6.23432i	−0.410782	+	0.237165i	−0.691126	−	0.722735i	$-0.742885\pi$
$691$	−10.7982	+	6.23432i	−0.410782	+	0.237165i	0.280344	+	0.959900i	$0.409552\pi$
$692$	2.30279	+	3.98855i	0.0875390	+	0.151622i
$693$	36.1182	−	62.5585i	1.37202	−	2.37640i
$694$			26.2855i			0.997785i
$695$	17.2402	+	9.95363i	0.653958	+	0.377563i
$696$	−28.5587	−	16.4884i	−1.08251	−	0.624990i
$697$			1.32938i			0.0503540i
$698$	−1.66807	+	2.88919i	−0.0631375	+	0.109357i
$699$	26.4508	+	45.8142i	1.00046	+	1.73285i
$700$	−6.31097	+	3.64364i	−0.238532	+	0.137717i
$701$	36.8033			1.39004			0.695021	−	0.718989i	$-0.255395\pi$
$701$	36.8033			1.39004			0.695021	+	0.718989i	$0.255395\pi$
$702$	−25.6770	+	17.6676i	−0.969116	+	0.666822i
$703$	−70.4005			−2.65521
$704$	20.1103	−	11.6107i	0.757936	−	0.437595i
$705$	20.2321	+	35.0430i	0.761984	+	1.31979i
$706$	−2.99253	+	5.18322i	−0.112625	+	0.195073i
$707$		−	13.7346i		−	0.516541i
$708$	6.03871	+	3.48645i	0.226949	+	0.131029i
$709$	−36.5498	−	21.1020i	−1.37266	−	0.792503i	−0.381393	−	0.924413i	$-0.624556\pi$
$709$	−36.5498	−	21.1020i	−1.37266	−	0.792503i	−0.991262	+	0.131910i	$0.957889\pi$
$710$		−	4.40251i		−	0.165223i
$711$	−46.6455	+	80.7924i	−1.74934	+	3.02995i
$712$	0.397459	+	0.688420i	0.0148954	+	0.0257996i
$713$	2.34619	−	1.35457i	0.0878655	−	0.0507292i
$714$	−5.24723			−0.196373
$715$	17.1194	+	24.8802i	0.640228	+	0.930467i
$716$	28.9494			1.08189
$717$	52.1357	−	30.1006i	1.94704	−	1.12413i
$718$	−4.72525	−	8.18437i	−0.176345	−	0.305438i
$719$	−2.03072	+	3.51731i	−0.0757331	+	0.131174i	−0.901405	−	0.432977i	$-0.857463\pi$
$719$	−2.03072	+	3.51731i	−0.0757331	+	0.131174i	0.825672	+	0.564151i	$0.190796\pi$
$720$			3.12342i			0.116403i
$721$	6.25727	+	3.61264i	0.233033	+	0.134542i
$722$	16.9026	+	9.75874i	0.629051	+	0.363183i
$723$		−	56.7905i		−	2.11206i
$724$	−2.88703	+	5.00049i	−0.107296	+	0.185842i
$725$	−5.39017	−	9.33605i	−0.200186	−	0.346732i
$726$	−44.7716	+	25.8489i	−1.66163	+	0.959343i
$727$	5.61475			0.208240			0.104120	−	0.994565i	$-0.466797\pi$
$727$	5.61475			0.208240			0.104120	+	0.994565i	$0.466797\pi$
$728$	8.62358	−	18.1047i	0.319611	−	0.671006i
$729$	−14.5570			−0.539146
$730$	−12.5758	+	7.26067i	−0.465453	+	0.268729i
$731$	0.739268	+	1.28045i	0.0273428	+	0.0473592i
$732$	23.1683	−	40.1286i	0.856323	−	1.48320i
$733$		−	11.2823i		−	0.416720i	−0.978052	−	0.208360i	$-0.933187\pi$
$733$		−	11.2823i		−	0.416720i	0.978052	−	0.208360i	$-0.0668125\pi$
$734$	7.21894	+	4.16785i	0.266456	+	0.153838i
$735$	−11.5875	−	6.69005i	−0.427412	−	0.246766i
$736$		−	15.6463i		−	0.576731i
$737$	−8.13260	+	14.0861i	−0.299568	+	0.518868i
$738$	−3.47020	−	6.01057i	−0.127740	−	0.221252i
$739$	−8.51900	+	4.91844i	−0.313376	+	0.180928i	−0.648436	−	0.761269i	$-0.724577\pi$
$739$	−8.51900	+	4.91844i	−0.313376	+	0.180928i	0.335060	+	0.942197i	$0.391243\pi$
$740$	21.1632			0.777974
$741$	5.68735	+	71.7719i	0.208930	+	2.63661i
$742$	−6.21967			−0.228331
$743$	34.1306	−	19.7053i	1.25213	−	0.722917i	0.280597	−	0.959826i	$-0.409468\pi$
$743$	34.1306	−	19.7053i	1.25213	−	0.722917i	0.971532	+	0.236909i	$0.0761342\pi$
$744$	−4.21658	−	7.30334i	−0.154587	−	0.267753i
$745$	3.15509	−	5.46477i	0.115593	−	0.200214i
$746$			14.9783i			0.548394i
$747$	−84.8917	−	49.0123i	−3.10603	−	1.79327i
$748$	−6.45105	−	3.72451i	−0.235874	−	0.136182i
$749$			31.8104i			1.16233i
$750$	14.8090	−	25.6499i	0.540746	−	0.936600i
$751$	0.269911	+	0.467500i	0.00984920	+	0.0170593i	0.870908	−	0.491446i	$-0.163532\pi$
$751$	0.269911	+	0.467500i	0.00984920	+	0.0170593i	−0.861059	+	0.508505i	$0.830198\pi$
$752$	2.49156	−	1.43850i	0.0908579	−	0.0524569i
$753$	49.7072			1.81143
$754$	10.5896	+	5.04398i	0.385649	+	0.183691i
$755$	8.01750			0.291787
$756$	−23.7865	+	13.7331i	−0.865106	+	0.499469i
$757$	4.69490	+	8.13181i	0.170639	+	0.295556i	0.938644	−	0.344889i	$-0.112083\pi$
$757$	4.69490	+	8.13181i	0.170639	+	0.295556i	−0.768004	+	0.640445i	$0.778750\pi$
$758$	−2.67388	+	4.63129i	−0.0971196	+	0.168216i
$759$			46.4306i			1.68533i
$760$	−23.2589	−	13.4285i	−0.843690	−	0.487105i
$761$	2.68784	+	1.55183i	0.0974341	+	0.0562536i	0.547925	−	0.836527i	$-0.315418\pi$
$761$	2.68784	+	1.55183i	0.0974341	+	0.0562536i	−0.450491	+	0.892781i	$0.648751\pi$
$762$		−	1.20953i		−	0.0438167i
$763$	−4.68102	+	8.10776i	−0.169464	+	0.293521i
$764$	5.71491	+	9.89852i	0.206758	+	0.358116i
$765$	−8.44152	+	4.87371i	−0.305204	+	0.176210i
$766$	4.16076			0.150334
$767$	−5.66324	−	2.69749i	−0.204488	−	0.0974009i
$768$	−46.0889			−1.66309
$769$	−16.5943	+	9.58071i	−0.598405	+	0.345489i	−0.768414	−	0.639953i	$-0.778954\pi$
$769$	−16.5943	+	9.58071i	−0.598405	+	0.345489i	0.170009	+	0.985443i	$0.445620\pi$
$770$	−7.04190	−	12.1969i	−0.253772	−	0.439547i
$771$	2.81460	−	4.87503i	0.101365	−	0.175570i
$772$		−	19.2921i		−	0.694339i
$773$	22.8771	+	13.2081i	0.822831	+	0.475061i	0.851392	−	0.524531i	$-0.175759\pi$
$773$	22.8771	+	13.2081i	0.822831	+	0.475061i	−0.0285611	+	0.999592i	$0.509093\pi$
$774$	−6.68493	−	3.85955i	−0.240285	−	0.138729i
$775$		−	2.75687i		−	0.0990296i
$776$	14.8519	−	25.7243i	0.533153	−	0.923449i
$777$	33.4569	+	57.9491i	1.20026	+	2.07891i
$778$	15.2761	−	8.81968i	0.547676	−	0.316201i
$779$	−8.50615			−0.304765
$780$	−1.70968	−	21.5754i	−0.0612164	−	0.772525i
$781$	19.7608			0.707097
$782$	1.98775	−	1.14763i	0.0710818	−	0.0410391i
$783$	−20.3159	−	35.1882i	−0.726032	−	1.25752i
$784$	−0.475664	+	0.823874i	−0.0169880	+	0.0294241i
$785$			34.0099i			1.21386i
$786$	18.8671	+	10.8929i	0.672967	+	0.388538i
$787$	29.7004	+	17.1475i	1.05870	+	0.611243i	0.925073	−	0.379789i	$-0.124003\pi$
$787$	29.7004	+	17.1475i	1.05870	+	0.611243i	0.133630	+	0.991031i	$0.457337\pi$
$788$		−	2.62664i		−	0.0935700i
$789$	47.4564	−	82.1969i	1.68949	−	2.92629i
$790$	9.09439	+	15.7519i	0.323564	+	0.560429i
$791$	23.3974	−	13.5085i	0.831917	−	0.480307i
$792$	98.3592			3.49504
$793$	−17.9255	+	37.6335i	−0.636552	+	1.33641i
$794$	−2.12669			−0.0754735
$795$	−14.7030	+	8.48877i	−0.521461	+	0.301066i
$796$	−9.33949	−	16.1765i	−0.331029	−	0.573360i
$797$	23.1887	−	40.1640i	0.821385	−	1.42268i	−0.0832657	−	0.996527i	$-0.526535\pi$
$797$	23.1887	−	40.1640i	0.821385	−	1.42268i	0.904651	−	0.426153i	$-0.140132\pi$
$798$		−	33.5748i		−	1.18853i
$799$	7.77556	+	4.48922i	0.275080	+	0.158817i
$800$	−13.7888	−	7.96097i	−0.487508	−	0.281463i
$801$			1.84602i			0.0652259i
$802$	−10.0168	+	17.3495i	−0.353704	+	0.612633i
$803$	−32.5897	−	56.4471i	−1.15007	−	1.99197i
$804$	10.0946	−	5.82811i	0.356008	−	0.205542i
$805$	−8.20051			−0.289030
$806$	1.70031	+	2.47113i	0.0598909	+	0.0870417i
$807$	64.1346			2.25764
$808$	16.1959	−	9.35069i	0.569769	−	0.328956i
$809$	−3.50932	−	6.07832i	−0.123381	−	0.213702i	0.797718	−	0.603031i	$-0.206040\pi$
$809$	−3.50932	−	6.07832i	−0.123381	−	0.213702i	−0.921099	+	0.389328i	$0.872707\pi$
$810$	7.89320	−	13.6714i	0.277339	−	0.480365i
$811$		−	1.60718i		−	0.0564356i	−0.999602	−	0.0282178i	$-0.991017\pi$
$811$		−	1.60718i		−	0.0564356i	0.999602	−	0.0282178i	$-0.00898319\pi$
$812$	8.95153	+	5.16817i	0.314137	+	0.181367i
$813$	−55.3134	−	31.9352i	−1.93992	−	1.12002i
$814$		−	50.2685i		−	1.76191i
$815$	−0.575728	+	0.997191i	−0.0201669	+	0.0349301i
$816$	0.509189	+	0.881941i	0.0178252	+	0.0308741i
$817$	−8.19305	+	4.73026i	−0.286638	+	0.165491i
$818$	19.0074			0.664577
$819$	38.3654	−	26.3981i	1.34059	−	0.922425i
$820$	2.55704			0.0892958
$821$	27.7575	−	16.0258i	0.968745	−	0.559305i	0.0698915	−	0.997555i	$-0.477735\pi$
$821$	27.7575	−	16.0258i	0.968745	−	0.559305i	0.898853	+	0.438249i	$0.144401\pi$
$822$	−5.69568	−	9.86521i	−0.198660	−	0.344089i
$823$	7.89566	−	13.6757i	0.275225	−	0.476704i	−0.694967	−	0.719042i	$-0.744581\pi$
$823$	7.89566	−	13.6757i	0.275225	−	0.476704i	0.970192	+	0.242338i	$0.0779142\pi$
$824$			9.83814i			0.342728i
$825$	40.9184	+	23.6243i	1.42460	+	0.822491i
$826$	2.53335	+	1.46263i	0.0881465	+	0.0508914i
$827$			20.7307i			0.720877i	0.932783	+	0.360439i	$0.117373\pi$
$827$			20.7307i			0.720877i	−0.932783	+	0.360439i	$0.882627\pi$
$828$	11.3220	−	19.6104i	0.393468	−	0.681507i
$829$	−10.2008	−	17.6683i	−0.354289	−	0.613646i	0.632707	−	0.774391i	$-0.281944\pi$
$829$	−10.2008	−	17.6683i	−0.354289	−	0.613646i	−0.986996	+	0.160745i	$0.948610\pi$
$830$	−16.5512	+	9.55583i	−0.574500	+	0.331688i
$831$	−39.7972			−1.38055
$832$	14.9238	−	1.18259i	0.517389	−	0.0409989i
$833$	−2.96886			−0.102865
$834$	−29.3464	+	16.9432i	−1.01618	+	0.586694i
$835$	5.13237	+	8.88952i	0.177613	+	0.307635i
$836$	23.8315	−	41.2774i	0.824231	−	1.42761i
$837$		−	10.3908i		−	0.359159i
$838$	−12.5104	−	7.22286i	−0.432163	−	0.249509i
$839$	34.5711	+	19.9597i	1.19353	+	0.689084i	0.959105	−	0.283051i	$-0.0913466\pi$
$839$	34.5711	+	19.9597i	1.19353	+	0.689084i	0.234423	+	0.972135i	$0.424680\pi$
$840$			25.5270i			0.880764i
$841$	6.85454	−	11.8724i	0.236363	−	0.409393i
$842$	1.31751	+	2.28199i	0.0454043	+	0.0786426i
$843$	−13.7482	+	7.93754i	−0.473514	+	0.273384i
$844$	4.93422			0.169843
$845$	3.06646	+	19.2272i	0.105489	+	0.661437i
$846$	−46.8743			−1.61157
$847$	35.4930	−	20.4919i	1.21956	−	0.704111i
$848$	0.603553	+	1.04539i	0.0207261	+	0.0358987i
$849$	43.4879	−	75.3233i	1.49250	−	2.58509i
$850$		−	2.33569i		−	0.0801134i
$851$	−25.3482	−	14.6348i	−0.868925	−	0.501674i
$852$	−12.2640	−	7.08064i	−0.420159	−	0.242579i
$853$		−	18.6811i		−	0.639628i	−0.947480	−	0.319814i	$-0.896380\pi$
$853$		−	18.6811i		−	0.639628i	0.947480	−	0.319814i	$-0.103620\pi$
$854$	9.71951	−	16.8347i	0.332595	−	0.576071i
$855$	−31.1848	−	54.0136i	−1.06650	−	1.84723i
$856$	−37.5110	+	21.6570i	−1.28210	+	0.740221i
$857$	30.2414			1.03303			0.516514	−	0.856279i	$-0.327229\pi$
$857$	30.2414			1.03303			0.516514	+	0.856279i	$0.327229\pi$
$858$	−51.2477	+	4.06097i	−1.74957	+	0.138639i
$859$	30.8023			1.05096			0.525481	−	0.850805i	$-0.323885\pi$
$859$	30.8023			1.05096			0.525481	+	0.850805i	$0.323885\pi$
$860$	2.46292	−	1.42197i	0.0839849	−	0.0484887i
$861$	4.04244	+	7.00171i	0.137766	+	0.238618i
$862$	4.65447	−	8.06177i	0.158532	−	0.274585i
$863$			51.1994i			1.74285i	0.490532	+	0.871423i	$0.336803\pi$
$863$			51.1994i			1.74285i	−0.490532	+	0.871423i	$0.663197\pi$
$864$	−51.9709	−	30.0054i	−1.76809	−	1.02080i
$865$	4.56745	+	2.63702i	0.155298	+	0.0896614i
$866$			25.9548i			0.881980i
$867$	24.4587	−	42.3636i	0.830660	−	1.43874i
$868$	1.32166	+	2.28918i	0.0448601	+	0.0776999i
$869$	−70.7031	+	40.8204i	−2.39844	+	1.38474i
$870$	−14.9309			−0.506204
$871$	−8.63859	+	5.94397i	−0.292708	+	0.201404i
$872$	−12.7476			−0.431689
$873$	59.7389	−	34.4903i	2.02186	−	1.16732i
$874$	7.34317	+	12.7187i	0.248387	+	0.430218i
$875$	−11.7399	+	20.3341i	−0.396881	+	0.687419i
$876$			46.7099i			1.57818i
$877$	−7.88404	−	4.55185i	−0.266225	−	0.153705i	0.360946	−	0.932587i	$-0.382454\pi$
$877$	−7.88404	−	4.55185i	−0.266225	−	0.153705i	−0.627171	+	0.778882i	$0.715787\pi$
$878$	−4.72707	−	2.72918i	−0.159531	−	0.0921053i
$879$			33.5687i			1.13224i
$880$	−1.36668	+	2.36717i	−0.0460709	+	0.0797972i
$881$	−27.5119	−	47.6520i	−0.926899	−	1.60544i	−0.788478	−	0.615063i	$-0.789131\pi$
$881$	−27.5119	−	47.6520i	−0.926899	−	1.60544i	−0.138421	−	0.990373i	$-0.544203\pi$
$882$	13.4232	−	7.74987i	0.451981	−	0.260952i
$883$	−48.5436			−1.63362			−0.816811	−	0.576905i	$-0.804260\pi$
$883$	−48.5436			−1.63362			−0.816811	+	0.576905i	$0.804260\pi$
$884$	−2.72218	−	3.95624i	−0.0915568	−	0.133063i
$885$	7.98495			0.268411
$886$	−5.37653	+	3.10414i	−0.180628	+	0.104286i
$887$	21.5606	+	37.3441i	0.723936	+	1.25389i	0.959411	+	0.282013i	$0.0910021\pi$
$887$	21.5606	+	37.3441i	0.723936	+	1.25389i	−0.235475	+	0.971880i	$0.575665\pi$
$888$	−45.5559	+	78.9052i	−1.52876	+	2.64788i
$889$			0.958864i			0.0321593i
$890$	0.311696	+	0.179958i	0.0104481	+	0.00603219i
$891$	61.3646	+	35.4289i	2.05579	+	1.18691i
$892$			37.1604i			1.24422i
$893$	−28.7246	+	49.7524i	−0.961231	+	1.66490i
$894$	5.37062	+	9.30218i	0.179620	+	0.311112i
$895$	28.7098	−	16.5756i	0.959661	−	0.554061i
$896$	16.3635			0.546667
$897$	−12.8721	+	27.0243i	−0.429787	+	0.902314i
$898$	5.95210			0.198624
$899$	−3.38647	+	1.95518i	−0.112945	+	0.0652089i
$900$	−11.5215	−	19.9558i	−0.384049	−	0.665193i
$901$	−1.88354	+	3.26239i	−0.0627499	+	0.108686i
$902$		−	6.07370i		−	0.202232i
$903$	7.78727	+	4.49598i	0.259144	+	0.149617i
$904$	31.8586	+	18.3936i	1.05960	+	0.611762i
$905$			6.61212i			0.219794i
$906$	−6.82373	+	11.8191i	−0.226703	+	0.392662i
$907$	16.8029	+	29.1034i	0.557930	+	0.966364i	0.997669	+	0.0682381i	$0.0217377\pi$
$907$	16.8029	+	29.1034i	0.557930	+	0.966364i	−0.439739	+	0.898126i	$0.644929\pi$
$908$	14.0141	−	8.09103i	0.465073	−	0.268510i
$909$	43.4298			1.44047
$910$	−0.717242	−	9.05129i	−0.0237763	−	0.300047i
$911$	21.1755			0.701576			0.350788	−	0.936455i	$-0.385914\pi$
$911$	21.1755			0.701576			0.350788	+	0.936455i	$0.385914\pi$
$912$	−5.64316	+	3.25808i	−0.186864	+	0.107886i
$913$	−42.8917	−	74.2906i	−1.41951	−	2.45866i
$914$	4.39584	−	7.61382i	0.145402	−	0.251843i
$915$		−	53.0618i		−	1.75417i
$916$	−29.9238	−	17.2765i	−0.988709	−	0.570832i
$917$	−14.9570	−	8.63545i	−0.493925	−	0.285168i
$918$		−	8.80336i		−	0.290554i
$919$	−19.2620	+	33.3628i	−0.635395	+	1.10054i	0.351036	+	0.936362i	$0.385829\pi$
$919$	−19.2620	+	33.3628i	−0.635395	+	1.10054i	−0.986431	+	0.164175i	$0.947504\pi$
$920$	−5.58303	−	9.67009i	−0.184067	−	0.318813i
$921$	−54.1465	+	31.2615i	−1.78419	+	1.03010i
$922$	26.3624			0.868201
$923$	11.5015	+	5.47835i	0.378576	+	0.180322i
$924$	−45.3025			−1.49034
$925$	−25.7947	+	14.8926i	−0.848125	+	0.489665i
$926$	15.5961	+	27.0132i	0.512520	+	0.887710i
$927$	−11.4234	+	19.7860i	−0.375195	+	0.649857i
$928$			22.5838i			0.741349i
$929$	−45.6673	−	26.3661i	−1.49830	−	0.865042i	−0.498299	−	0.867005i	$-0.666042\pi$
$929$	−45.6673	−	26.3661i	−1.49830	−	0.865042i	−0.999998	+	0.00196329i	$0.999375\pi$
$930$	−3.30673	−	1.90914i	−0.108432	−	0.0626032i
$931$		−	18.9965i		−	0.622584i
$932$	11.2891	−	19.5532i	0.369785	−	0.640487i
$933$	−14.9459	−	25.8870i	−0.489305	−	0.847502i
$934$	−5.48615	+	3.16743i	−0.179512	+	0.103641i
$935$	−8.53018			−0.278967
$936$	57.2485	+	27.2684i	1.87123	+	0.891297i
$937$	−28.5850			−0.933830			−0.466915	−	0.884302i	$-0.654635\pi$
$937$	−28.5850			−0.933830			−0.466915	+	0.884302i	$0.654635\pi$
$938$	4.23486	−	2.44500i	0.138273	−	0.0798320i
$939$	27.5722	+	47.7565i	0.899786	+	1.55848i
$940$	8.63492	−	14.9561i	0.281640	−	0.487815i
$941$		−	44.7743i		−	1.45960i	−0.683660	−	0.729801i	$-0.739613\pi$
$941$		−	44.7743i		−	1.45960i	0.683660	−	0.729801i	$-0.260387\pi$
$942$	−50.1359	−	28.9459i	−1.63351	−	0.943110i
$943$	−3.06270	−	1.76825i	−0.0997353	−	0.0575822i
$944$		−	0.567731i		−	0.0184781i
$945$	−15.7264	+	27.2388i	−0.511578	+	0.886080i
$946$	−3.37757	−	5.85012i	−0.109814	−	0.190204i
$947$	−46.5264	+	26.8621i	−1.51191	+	0.872899i	−0.512003	+	0.858984i	$0.671096\pi$
$947$	−46.5264	+	26.8621i	−1.51191	+	0.872899i	−0.999903	+	0.0139157i	$0.995570\pi$
$948$	58.5067			1.90021
$949$	−3.31938	−	41.8892i	−0.107752	−	1.35978i
$950$	14.9450			0.484881
$951$	−60.5014	+	34.9305i	−1.96189	+	1.13270i
$952$	2.83204	+	4.90524i	0.0917870	+	0.158980i
$953$	7.42269	−	12.8565i	0.240445	−	0.416462i	−0.720396	−	0.693563i	$-0.756040\pi$
$953$	7.42269	−	12.8565i	0.240445	−	0.416462i	0.960841	+	0.277100i	$0.0893734\pi$
$954$		−	19.6671i		−	0.636745i
$955$	11.3352	+	6.54437i	0.366798	+	0.211771i
$956$	−22.2512	−	12.8467i	−0.719656	−	0.415493i
$957$		−	67.0176i		−	2.16637i
$958$	3.45857	−	5.99043i	0.111741	−	0.193542i
$959$	4.51529	+	7.82072i	0.145806	+	0.252544i
$960$	−16.5035	+	9.52829i	−0.532648	+	0.307524i
$961$	−1.00000			−0.0322581
$962$	13.9361	−	29.2580i	0.449317	−	0.943317i
$963$	−100.587			−3.24137
$964$	−20.9906	+	12.1189i	−0.676061	+	0.390324i
$965$	−11.0461	−	19.1324i	−0.355586	−	0.615894i
$966$	6.97949	−	12.0888i	0.224561	−	0.388952i
$967$			0.771974i			0.0248250i	0.999923	+	0.0124125i	$0.00395112\pi$
$967$			0.771974i			0.0248250i	−0.999923	+	0.0124125i	$0.996049\pi$
$968$	48.3284	+	27.9024i	1.55333	+	0.896817i
$969$	−17.6109	−	10.1677i	−0.565744	−	0.326633i
$970$		−	13.4490i		−	0.431822i
$971$	25.5192	−	44.2006i	0.818951	−	1.41846i	−0.0875048	−	0.996164i	$-0.527889\pi$
$971$	25.5192	−	44.2006i	0.818951	−	1.41846i	0.906456	−	0.422301i	$-0.138777\pi$
$972$	−5.00460	−	8.66823i	−0.160523	−	0.278033i
$973$	23.2646	−	13.4318i	0.745829	−	0.430604i
$974$	−2.62974			−0.0842622
$975$	17.2665	+	25.0941i	0.552972	+	0.803654i
$976$	−3.77271			−0.120761
$977$	−18.7545	+	10.8279i	−0.600010	+	0.346416i	−0.769046	−	0.639194i	$-0.779268\pi$
$977$	−18.7545	+	10.8279i	−0.600010	+	0.346416i	0.169035	+	0.985610i	$0.445935\pi$
$978$	−0.980010	−	1.69743i	−0.0313373	−	0.0542777i
$979$	−0.807745	+	1.39906i	−0.0258157	+	0.0447140i
$980$			5.71054i			0.182417i
$981$	−25.6374	−	14.8018i	−0.818539	−	0.472584i
$982$	24.7297	+	14.2777i	0.789157	+	0.455620i
$983$			27.0623i			0.863152i	0.902077	+	0.431576i	$0.142042\pi$
$983$			27.0623i			0.863152i	−0.902077	+	0.431576i	$0.857958\pi$
$984$	−5.50430	+	9.53373i	−0.175471	+	0.303924i
$985$	−1.50393	−	2.60489i	−0.0479193	−	0.0829987i
$986$	−2.86910	+	1.65648i	−0.0913709	+	0.0527530i
$987$	54.6039			1.73806
$988$	25.3143	−	17.4180i	0.805355	−	0.554142i
$989$	−3.93329			−0.125071
$990$	38.5676	−	22.2670i	1.22576	−	0.707693i
$991$	−14.7710	−	25.5842i	−0.469217	−	0.812708i	0.530163	−	0.847896i	$-0.322131\pi$
$991$	−14.7710	−	25.5842i	−0.469217	−	0.812708i	−0.999381	+	0.0351872i	$0.988797\pi$
$992$	−2.88769	+	5.00162i	−0.0916841	+	0.158802i
$993$			5.37988i			0.170725i
$994$	−5.14498	−	2.97046i	−0.163189	−	0.0942172i
$995$	−18.5243	−	10.6950i	−0.587260	−	0.339055i
$996$			61.4753i			1.94792i
$997$	−7.40350	+	12.8232i	−0.234471	+	0.406116i	−0.959119	−	0.283003i	$-0.908669\pi$
$997$	−7.40350	+	12.8232i	−0.234471	+	0.406116i	0.724648	+	0.689120i	$0.242003\pi$
$998$	−15.1830	−	26.2977i	−0.480608	−	0.832438i
$999$	−97.2220	+	56.1311i	−3.07597	+	1.77591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.22	✓	68
13.2	odd	12		5239.2.a.r.1.22		34
13.4	even	6	inner	403.2.r.a.342.22	yes	68
13.11	odd	12		5239.2.a.q.1.13		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.22	✓	68	1.1	even	1	trivial
403.2.r.a.342.22	yes	68	13.4	even	6	inner
5239.2.a.q.1.13		34	13.11	odd	12
5239.2.a.r.1.22		34	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.720477 - 0.415968i) q^{2} +(-1.53222 - 2.65388i) q^{3} +(-0.653942 + 1.13266i) q^{4} +1.49771i q^{5} +(-2.20786 - 1.27471i) q^{6} +(1.75030 + 1.01053i) q^{7} +2.75195i q^{8} +(-3.19539 + 5.53457i) q^{9} +(0.622999 + 1.07907i) q^{10} +(-4.84342 + 2.79635i) q^{11} +4.00793 q^{12} +(-3.59428 + 0.284818i) q^{13} +1.68140 q^{14} +(3.97474 - 2.29482i) q^{15} +(-0.163162 - 0.282605i) q^{16} +(0.509189 - 0.881941i) q^{17} +5.31671i q^{18} +(5.64316 + 3.25808i) q^{19} +(-1.69640 - 0.979414i) q^{20} -6.19344i q^{21} +(-2.32638 + 4.02941i) q^{22} +(1.35457 + 2.34619i) q^{23} +(7.30334 - 4.21658i) q^{24} +2.75687 q^{25} +(-2.47113 + 1.70031i) q^{26} +10.3908 q^{27} +(-2.28918 + 1.32166i) q^{28} +(-1.95518 - 3.38647i) q^{29} +(1.90914 - 3.30673i) q^{30} -1.00000i q^{31} +(-5.00162 - 2.88769i) q^{32} +(14.8424 + 8.56924i) q^{33} -0.847225i q^{34} +(-1.51349 + 2.62143i) q^{35} +(-4.17919 - 7.23857i) q^{36} +(-9.35653 + 5.40200i) q^{37} +5.42102 q^{38} +(6.26310 + 9.10240i) q^{39} -4.12162 q^{40} +(-1.13050 + 0.652697i) q^{41} +(-2.57627 - 4.46223i) q^{42} +(-0.725927 + 1.25734i) q^{43} -7.31460i q^{44} +(-8.28918 - 4.78576i) q^{45} +(1.95188 + 1.12692i) q^{46} +8.81641i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.45764 - 2.52471i) q^{49} +(1.98626 - 1.14677i) q^{50} -3.12076 q^{51} +(2.02785 - 4.25736i) q^{52} -3.69910 q^{53} +(7.48635 - 4.32225i) q^{54} +(-4.18812 - 7.25404i) q^{55} +(-2.78093 + 4.81672i) q^{56} -19.9684i q^{57} +(-2.81733 - 1.62658i) q^{58} +(1.50669 + 0.869889i) q^{59} +6.00271i q^{60} +(5.78061 - 10.0123i) q^{61} +(-0.415968 - 0.720477i) q^{62} +(-11.1857 + 6.45809i) q^{63} -4.15209 q^{64} +(-0.426575 - 5.38319i) q^{65} +14.2581 q^{66} +(2.51865 - 1.45415i) q^{67} +(0.665960 + 1.15348i) q^{68} +(4.15100 - 7.18975i) q^{69} +2.51825i q^{70} +(-3.05994 - 1.76666i) q^{71} +(-15.2308 - 8.79353i) q^{72} +11.6544i q^{73} +(-4.49411 + 7.78403i) q^{74} +(-4.22412 - 7.31639i) q^{75} +(-7.38059 + 4.26119i) q^{76} -11.3032 q^{77} +(8.29873 + 3.95282i) q^{78} +14.5978 q^{79} +(0.423260 - 0.244369i) q^{80} +(-6.33484 - 10.9723i) q^{81} +(-0.543002 + 0.940507i) q^{82} +15.3384i q^{83} +(7.01506 + 4.05014i) q^{84} +(1.32089 + 0.762617i) q^{85} +1.20785i q^{86} +(-5.99153 + 10.3776i) q^{87} +(-7.69541 - 13.3288i) q^{88} +(0.250158 - 0.144429i) q^{89} -7.96289 q^{90} +(-6.57888 - 3.13363i) q^{91} -3.54325 q^{92} +(-2.65388 + 1.53222i) q^{93} +(3.66734 + 6.35203i) q^{94} +(-4.87966 + 8.45181i) q^{95} +17.6983i q^{96} +(-9.34768 - 5.39688i) q^{97} +(-2.10040 - 1.21266i) q^{98} -35.7417i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30}+ \cdots - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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