LMFDB - Embedded newform 343.2.g.i.30.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(30,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([32]))

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

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

chi := DirichletCharacter("343.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.g (of order $21$, degree $12$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			30.2
Character	$\chi$	$=$	343.30
Dual form			343.2.g.i.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30646 + 0.890730i) q^{2} +(2.35796 - 2.18787i) q^{3} +(0.182757 - 0.465658i) q^{4} +(-0.379430 - 0.117039i) q^{5} +(-1.13178 + 4.95867i) q^{6} +(-0.527696 - 2.31199i) q^{8} +(0.549024 - 7.32622i) q^{9} +O(q^{10})$	\(q+(-1.30646 + 0.890730i) q^{2} +(2.35796 - 2.18787i) q^{3} +(0.182757 - 0.465658i) q^{4} +(-0.379430 - 0.117039i) q^{5} +(-1.13178 + 4.95867i) q^{6} +(-0.527696 - 2.31199i) q^{8} +(0.549024 - 7.32622i) q^{9} +(0.599961 - 0.185063i) q^{10} +(-0.165845 - 2.21305i) q^{11} +(-0.587864 - 1.49785i) q^{12} +(1.92814 + 0.928542i) q^{13} +(-1.15075 + 0.554171i) q^{15} +(3.48217 + 3.23098i) q^{16} +(-0.659554 - 0.0994118i) q^{17} +(5.80840 + 10.0604i) q^{18} +(0.781344 - 1.35333i) q^{19} +(-0.123844 + 0.155295i) q^{20} +(2.18790 + 2.74354i) q^{22} +(0.626297 - 0.0943991i) q^{23} +(-6.30262 - 4.29705i) q^{24} +(-4.00092 - 2.72778i) q^{25} +(-3.34612 + 0.504346i) q^{26} +(-8.71761 - 10.9315i) q^{27} +(3.83058 - 4.80339i) q^{29} +(1.00979 - 1.74901i) q^{30} +(1.69627 + 2.93803i) q^{31} +(-2.73733 - 0.412586i) q^{32} +(-5.23292 - 4.85544i) q^{33} +(0.950231 - 0.457607i) q^{34} +(-3.31117 - 1.59458i) q^{36} +(1.55284 + 3.95658i) q^{37} +(0.184654 + 2.46404i) q^{38} +(6.57801 - 2.02905i) q^{39} +(-0.0703683 + 0.938999i) q^{40} +(1.37484 + 6.02357i) q^{41} +(-1.37677 + 6.03200i) q^{43} +(-1.06083 - 0.327224i) q^{44} +(-1.06577 + 2.71553i) q^{45} +(-0.734148 + 0.681190i) q^{46} +(4.53069 - 3.08897i) q^{47} +15.2798 q^{48} +7.65677 q^{50} +(-1.77270 + 1.20861i) q^{51} +(0.784765 - 0.728155i) q^{52} +(3.34394 - 8.52021i) q^{53} +(21.1263 + 6.51659i) q^{54} +(-0.196086 + 0.859108i) q^{55} +(-1.11852 - 4.90058i) q^{57} +(-0.725974 + 9.68745i) q^{58} +(-7.95929 + 2.45512i) q^{59} +(0.0477466 + 0.637134i) q^{60} +(3.46607 + 8.83141i) q^{61} +(-4.83310 - 2.32750i) q^{62} +(-4.61591 + 2.22291i) q^{64} +(-0.622919 - 0.577984i) q^{65} +(11.1615 + 1.68232i) q^{66} +(0.892421 + 1.54572i) q^{67} +(-0.166830 + 0.288959i) q^{68} +(1.27025 - 1.59285i) q^{69} +(-1.30754 - 1.63960i) q^{71} +(-17.2279 + 2.59668i) q^{72} +(11.9415 + 8.14156i) q^{73} +(-5.55296 - 3.78595i) q^{74} +(-15.4021 + 2.32149i) q^{75} +(-0.487392 - 0.611170i) q^{76} +(-6.78657 + 8.51010i) q^{78} +(0.821284 - 1.42251i) q^{79} +(-0.943091 - 1.63348i) q^{80} +(-22.6785 - 3.41823i) q^{81} +(-7.16155 - 6.64495i) q^{82} +(-5.20544 + 2.50681i) q^{83} +(0.238620 + 0.114913i) q^{85} +(-3.57419 - 9.10690i) q^{86} +(-1.47684 - 19.7070i) q^{87} +(-5.02903 + 1.55125i) q^{88} +(-0.957805 + 12.7810i) q^{89} +(-1.02642 - 4.49705i) q^{90} +(0.0705027 - 0.308892i) q^{92} +(10.4278 + 3.21654i) q^{93} +(-3.16773 + 8.07124i) q^{94} +(-0.454857 + 0.422046i) q^{95} +(-7.35721 + 5.01606i) q^{96} -9.59518 q^{97} -16.3043 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9	$ 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9} + 7 q^{10} - 3 q^{11} - 63 q^{12} - 14 q^{13} - 12 q^{15} + 18 q^{16} + 14 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 20 q^{22} - 27 q^{23} - 77 q^{24} + 17 q^{25} - 21 q^{26} + 7 q^{27} + 12 q^{29} + 11 q^{30} + 35 q^{31} - 60 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 6 q^{37} + 35 q^{38} + 35 q^{39} + 105 q^{40} - 42 q^{41} - 30 q^{43} + 13 q^{44} - 35 q^{45} + 69 q^{46} - 42 q^{47} - 84 q^{48} + 40 q^{50} + 53 q^{51} - 7 q^{52} - 31 q^{53} + 70 q^{54} - 7 q^{55} - 12 q^{57} - 47 q^{58} + 35 q^{59} - 91 q^{60} - 14 q^{61} - 28 q^{62} - 32 q^{64} + 35 q^{65} - 35 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 19 q^{71} - 124 q^{72} - 35 q^{73} + 13 q^{74} - 119 q^{75} + 119 q^{76} + 28 q^{78} + 15 q^{79} + 70 q^{80} - 125 q^{81} - 98 q^{82} - 26 q^{85} + 9 q^{86} + 35 q^{87} + 49 q^{88} - 14 q^{89} - 182 q^{90} - 38 q^{92} + 46 q^{93} + 14 q^{94} + 128 q^{95} + 98 q^{96} - 16 q^{99}+O(q^{100}) $ 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9 + 7 * q^10 - 3 * q^11 - 63 * q^12 - 14 * q^13 - 12 * q^15 + 18 * q^16 + 14 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 20 * q^22 - 27 * q^23 - 77 * q^24 + 17 * q^25 - 21 * q^26 + 7 * q^27 + 12 * q^29 + 11 * q^30 + 35 * q^31 - 60 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 6 * q^37 + 35 * q^38 + 35 * q^39 + 105 * q^40 - 42 * q^41 - 30 * q^43 + 13 * q^44 - 35 * q^45 + 69 * q^46 - 42 * q^47 - 84 * q^48 + 40 * q^50 + 53 * q^51 - 7 * q^52 - 31 * q^53 + 70 * q^54 - 7 * q^55 - 12 * q^57 - 47 * q^58 + 35 * q^59 - 91 * q^60 - 14 * q^61 - 28 * q^62 - 32 * q^64 + 35 * q^65 - 35 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 19 * q^71 - 124 * q^72 - 35 * q^73 + 13 * q^74 - 119 * q^75 + 119 * q^76 + 28 * q^78 + 15 * q^79 + 70 * q^80 - 125 * q^81 - 98 * q^82 - 26 * q^85 + 9 * q^86 + 35 * q^87 + 49 * q^88 - 14 * q^89 - 182 * q^90 - 38 * q^92 + 46 * q^93 + 14 * q^94 + 128 * q^95 + 98 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−1.30646	+	0.890730i	−0.923807	+	0.629841i	−0.928974	−	0.370146i	$-0.879308\pi$
$2$	−1.30646	+	0.890730i	−0.923807	+	0.629841i	0.00516677	+	0.999987i	$0.498355\pi$
$3$	2.35796	−	2.18787i	1.36137	−	1.26317i	0.428223	−	0.903673i	$-0.359140\pi$
$3$	2.35796	−	2.18787i	1.36137	−	1.26317i	0.933147	−	0.359494i	$-0.117051\pi$
$4$	0.182757	−	0.465658i	0.0913786	−	0.232829i
$5$	−0.379430	−	0.117039i	−0.169686	−	0.0523413i	0.208748	−	0.977969i	$-0.433061\pi$
$5$	−0.379430	−	0.117039i	−0.169686	−	0.0523413i	−0.378434	+	0.925628i	$0.623537\pi$
$6$	−1.13178	+	4.95867i	−0.462049	+	2.02437i
$7$		0			0
$7$		0			0
$8$	−0.527696	−	2.31199i	−0.186569	−	0.817411i
$9$	0.549024	−	7.32622i	0.183008	−	2.44207i
$10$	0.599961	−	0.185063i	0.189724	−	0.0585222i
$11$	−0.165845	−	2.21305i	−0.0500042	−	0.667260i	−0.964740	−	0.263206i	$-0.915220\pi$
$11$	−0.165845	−	2.21305i	−0.0500042	−	0.667260i	0.914735	−	0.404053i	$-0.132399\pi$
$12$	−0.587864	−	1.49785i	−0.169702	−	0.432393i
$13$	1.92814	+	0.928542i	0.534769	+	0.257531i	0.681721	−	0.731612i	$-0.261232\pi$
$13$	1.92814	+	0.928542i	0.534769	+	0.257531i	−0.146952	+	0.989144i	$0.546946\pi$
$14$		0			0
$15$	−1.15075	+	0.554171i	−0.297122	+	0.143086i
$16$	3.48217	+	3.23098i	0.870543	+	0.807746i
$17$	−0.659554	−	0.0994118i	−0.159965	−	0.0241109i	0.0685712	−	0.997646i	$-0.478156\pi$
$17$	−0.659554	−	0.0994118i	−0.159965	−	0.0241109i	−0.228537	+	0.973535i	$0.573394\pi$
$18$	5.80840	+	10.0604i	1.36905	+	2.37127i
$19$	0.781344	−	1.35333i	0.179253	−	0.310475i	−0.762372	−	0.647139i	$-0.775965\pi$
$19$	0.781344	−	1.35333i	0.179253	−	0.310475i	0.941625	+	0.336664i	$0.109299\pi$
$20$	−0.123844	+	0.155295i	−0.0276923	+	0.0347250i
$21$		0			0
$22$	2.18790	+	2.74354i	0.466462	+	0.584924i
$23$	0.626297	−	0.0943991i	0.130592	−	0.0196836i	−0.0834210	−	0.996514i	$-0.526585\pi$
$23$	0.626297	−	0.0943991i	0.130592	−	0.0196836i	0.214013	+	0.976831i	$0.431347\pi$
$24$	−6.30262	−	4.29705i	−1.28652	−	0.877132i
$25$	−4.00092	−	2.72778i	−0.800185	−	0.545557i
$26$	−3.34612	+	0.504346i	−0.656227	+	0.0989104i
$27$	−8.71761	−	10.9315i	−1.67771	−	2.10378i
$28$		0			0
$29$	3.83058	−	4.80339i	0.711320	−	0.891967i	−0.286492	−	0.958083i	$-0.592489\pi$
$29$	3.83058	−	4.80339i	0.711320	−	0.891967i	0.997812	+	0.0661153i	$0.0210605\pi$
$30$	1.00979	−	1.74901i	0.184362	−	0.319324i
$31$	1.69627	+	2.93803i	0.304659	+	0.527685i	0.977185	−	0.212388i	$-0.0681241\pi$
$31$	1.69627	+	2.93803i	0.304659	+	0.527685i	−0.672526	+	0.740073i	$0.734791\pi$
$32$	−2.73733	−	0.412586i	−0.483897	−	0.0729357i
$33$	−5.23292	−	4.85544i	−0.910935	−	0.845224i
$34$	0.950231	−	0.457607i	0.162963	−	0.0784789i
$35$		0			0
$36$	−3.31117	−	1.59458i	−0.551862	−	0.265763i
$37$	1.55284	+	3.95658i	0.255286	+	0.650457i	0.999854	−	0.0170891i	$-0.00543990\pi$
$37$	1.55284	+	3.95658i	0.255286	+	0.650457i	−0.744568	+	0.667546i	$0.767345\pi$
$38$	0.184654	+	2.46404i	0.0299548	+	0.399719i
$39$	6.57801	−	2.02905i	1.05332	−	0.324908i
$40$	−0.0703683	+	0.938999i	−0.0111262	+	0.148469i
$41$	1.37484	+	6.02357i	0.214714	+	0.940724i	0.961315	+	0.275452i	$0.0888274\pi$
$41$	1.37484	+	6.02357i	0.214714	+	0.940724i	−0.746601	+	0.665272i	$0.768315\pi$
$42$		0			0
$43$	−1.37677	+	6.03200i	−0.209955	+	0.919872i	0.754641	+	0.656138i	$0.227811\pi$
$43$	−1.37677	+	6.03200i	−0.209955	+	0.919872i	−0.964596	+	0.263734i	$0.915046\pi$
$44$	−1.06083	−	0.327224i	−0.159927	−	0.0493308i
$45$	−1.06577	+	2.71553i	−0.158875	+	0.404808i
$46$	−0.734148	+	0.681190i	−0.108244	+	0.100436i
$47$	4.53069	−	3.08897i	0.660869	−	0.450573i	−0.185875	−	0.982573i	$-0.559512\pi$
$47$	4.53069	−	3.08897i	0.660869	−	0.450573i	0.846744	+	0.532000i	$0.178559\pi$
$48$	15.2798			2.20545
$49$		0			0
$50$	7.65677			1.08283
$51$	−1.77270	+	1.20861i	−0.248228	+	0.169239i
$52$	0.784765	−	0.728155i	0.108827	−	0.100977i
$53$	3.34394	−	8.52021i	0.459325	−	1.17034i	−0.494286	−	0.869299i	$-0.664571\pi$
$53$	3.34394	−	8.52021i	0.459325	−	1.17034i	0.953611	−	0.301041i	$-0.0973343\pi$
$54$	21.1263	+	6.51659i	2.87492	+	0.886796i
$55$	−0.196086	+	0.859108i	−0.0264402	+	0.115842i
$56$		0			0
$57$	−1.11852	−	4.90058i	−0.148152	−	0.649097i
$58$	−0.725974	+	9.68745i	−0.0953250	+	1.27202i
$59$	−7.95929	+	2.45512i	−1.03621	+	0.319629i	−0.765775	−	0.643109i	$-0.777644\pi$
$59$	−7.95929	+	2.45512i	−1.03621	+	0.319629i	−0.270436	+	0.962738i	$0.587168\pi$
$60$	0.0477466	+	0.637134i	0.00616406	+	0.0822536i
$61$	3.46607	+	8.83141i	0.443785	+	1.13075i	0.961405	+	0.275136i	$0.0887229\pi$
$61$	3.46607	+	8.83141i	0.443785	+	1.13075i	−0.517620	+	0.855611i	$0.673182\pi$
$62$	−4.83310	−	2.32750i	−0.613804	−	0.295592i
$63$		0			0
$64$	−4.61591	+	2.22291i	−0.576989	+	0.277863i
$65$	−0.622919	−	0.577984i	−0.0772635	−	0.0716901i
$66$	11.1615	+	1.68232i	1.37388	+	0.207080i
$67$	0.892421	+	1.54572i	0.109027	+	0.188840i	0.915376	−	0.402600i	$-0.131893\pi$
$67$	0.892421	+	1.54572i	0.109027	+	0.188840i	−0.806350	+	0.591439i	$0.798560\pi$
$68$	−0.166830	+	0.288959i	−0.0202311	+	0.0350414i
$69$	1.27025	−	1.59285i	0.152920	−	0.191756i
$70$		0			0
$71$	−1.30754	−	1.63960i	−0.155176	−	0.194585i	0.698166	−	0.715936i	$-0.254000\pi$
$71$	−1.30754	−	1.63960i	−0.155176	−	0.194585i	−0.853342	+	0.521351i	$0.825428\pi$
$72$	−17.2279	+	2.59668i	−2.03032	+	0.306022i
$73$	11.9415	+	8.14156i	1.39764	+	0.952898i	0.999365	+	0.0356340i	$0.0113451\pi$
$73$	11.9415	+	8.14156i	1.39764	+	0.952898i	0.398280	+	0.917264i	$0.369607\pi$
$74$	−5.55296	−	3.78595i	−0.645519	−	0.440107i
$75$	−15.4021	+	2.32149i	−1.77848	+	0.268062i
$76$	−0.487392	−	0.611170i	−0.0559076	−	0.0701060i
$77$		0			0
$78$	−6.78657	+	8.51010i	−0.768428	+	0.963579i
$79$	0.821284	−	1.42251i	0.0924017	−	0.160044i	−0.816120	−	0.577883i	$-0.803879\pi$
$79$	0.821284	−	1.42251i	0.0924017	−	0.160044i	0.908521	+	0.417839i	$0.137212\pi$
$80$	−0.943091	−	1.63348i	−0.105441	−	0.182629i
$81$	−22.6785	−	3.41823i	−2.51983	−	0.379803i
$82$	−7.16155	−	6.64495i	−0.790861	−	0.733812i
$83$	−5.20544	+	2.50681i	−0.571371	+	0.275158i	−0.697179	−	0.716897i	$-0.745562\pi$
$83$	−5.20544	+	2.50681i	−0.571371	+	0.275158i	0.125808	+	0.992055i	$0.459848\pi$
$84$		0			0
$85$	0.238620	+	0.114913i	0.0258820	+	0.0124641i
$86$	−3.57419	−	9.10690i	−0.385415	−	0.982022i
$87$	−1.47684	−	19.7070i	−0.158334	−	2.11281i
$88$	−5.02903	+	1.55125i	−0.536096	+	0.165364i
$89$	−0.957805	+	12.7810i	−0.101527	+	1.35479i	0.681052	+	0.732235i	$0.261523\pi$
$89$	−0.957805	+	12.7810i	−0.101527	+	1.35479i	−0.782580	+	0.622551i	$0.786097\pi$
$90$	−1.02642	−	4.49705i	−0.108194	−	0.474030i
$91$		0			0
$92$	0.0705027	−	0.308892i	0.00735041	−	0.0322043i
$93$	10.4278	+	3.21654i	1.08131	+	0.333539i
$94$	−3.16773	+	8.07124i	−0.326726	+	0.832485i
$95$	−0.454857	+	0.422046i	−0.0466674	+	0.0433010i
$96$	−7.35721	+	5.01606i	−0.750892	+	0.511950i
$97$	−9.59518			−0.974243			−0.487121	−	0.873334i	$-0.661953\pi$
$97$	−9.59518			−0.974243			−0.487121	+	0.873334i	$0.661953\pi$
$98$		0			0
$99$	−16.3043			−1.63865
$100$	−2.00141	+	1.36454i	−0.200141	+	0.136454i
$101$	−9.08602	+	8.43060i	−0.904093	+	0.838876i	−0.987497	−	0.157640i	$-0.949611\pi$
$101$	−9.08602	+	8.43060i	−0.904093	+	0.838876i	0.0834036	+	0.996516i	$0.473421\pi$
$102$	1.23942	−	3.15800i	0.122721	−	0.312689i
$103$	−1.30226	−	0.401694i	−0.128316	−	0.0395801i	0.229932	−	0.973207i	$-0.426150\pi$
$103$	−1.30226	−	0.401694i	−0.128316	−	0.0395801i	−0.358248	+	0.933627i	$0.616626\pi$
$104$	1.12931	−	4.94782i	0.110738	−	0.485174i
$105$		0			0
$106$	3.22048	+	14.1099i	0.312801	+	1.37047i
$107$	0.536614	−	7.16062i	0.0518765	−	0.692244i	−0.909270	−	0.416206i	$-0.863360\pi$
$107$	0.536614	−	7.16062i	0.0518765	−	0.692244i	0.961147	−	0.276038i	$-0.0890214\pi$
$108$	−6.68357	+	2.06161i	−0.643127	+	0.198378i
$109$	1.43723	+	19.1785i	0.137662	+	1.83697i	0.457159	+	0.889385i	$0.348867\pi$
$109$	1.43723	+	19.1785i	0.137662	+	1.83697i	−0.319497	+	0.947587i	$0.603514\pi$
$110$	−0.509055	−	1.29705i	−0.0485365	−	0.123669i
$111$	12.3180	+	5.93204i	1.16917	+	0.563045i
$112$		0			0
$113$	−3.02699	+	1.45772i	−0.284755	+	0.137131i	−0.570809	−	0.821083i	$-0.693370\pi$
$113$	−3.02699	+	1.45772i	−0.284755	+	0.137131i	0.286054	+	0.958213i	$0.407656\pi$
$114$	5.82640	+	5.40610i	0.545692	+	0.506328i
$115$	−0.248684	−	0.0374832i	−0.0231899	−	0.00349532i
$116$	−1.53667	−	2.66159i	−0.142676	−	0.247123i
$117$	7.86130	−	13.6162i	0.726778	−	1.25882i
$118$	8.21165	−	10.2971i	0.755944	−	0.947923i
$119$		0			0
$120$	1.88848	+	2.36808i	0.172394	+	0.216175i
$121$	6.00706	−	0.905418i	0.546096	−	0.0823107i
$122$	−12.3947	−	8.45056i	−1.12216	−	0.765077i
$123$	16.4206	+	11.1954i	1.48060	+	1.00945i
$124$	1.67812	−	0.252936i	0.150700	−	0.0227143i
$125$	2.43666	+	3.05548i	0.217942	+	0.273290i
$126$		0			0
$127$	2.74253	−	3.43902i	0.243360	−	0.305164i	−0.645118	−	0.764083i	$-0.723192\pi$
$127$	2.74253	−	3.43902i	0.243360	−	0.305164i	0.888478	+	0.458919i	$0.151763\pi$
$128$	6.81875	−	11.8104i	0.602698	−	1.04390i
$129$	9.95088	+	17.2354i	0.876126	+	1.51749i
$130$	1.32865	+	0.200261i	0.116530	+	0.0175641i
$131$	6.59619	+	6.12037i	0.576311	+	0.534739i	0.913574	−	0.406672i	$-0.133311\pi$
$131$	6.59619	+	6.12037i	0.576311	+	0.534739i	−0.337263	+	0.941410i	$0.609501\pi$
$132$	−3.21733	+	1.54938i	−0.280033	+	0.134857i
$133$		0			0
$134$	−2.54273	−	1.22451i	−0.219658	−	0.105782i
$135$	2.02831	+	5.16806i	0.174569	+	0.444796i
$136$	0.118205	+	1.57734i	0.0101360	+	0.135256i
$137$	−12.8379	+	3.95998i	−1.09682	+	0.338324i	−0.789790	−	0.613377i	$-0.789811\pi$
$137$	−12.8379	+	3.95998i	−1.09682	+	0.338324i	−0.307028	+	0.951701i	$0.599334\pi$
$138$	−0.240739	+	3.21244i	−0.0204931	+	0.273461i
$139$	0.369690	+	1.61972i	0.0313567	+	0.137383i	0.988183	−	0.153277i	$-0.0489826\pi$
$139$	0.369690	+	1.61972i	0.0313567	+	0.137383i	−0.956827	+	0.290659i	$0.906125\pi$
$140$		0			0
$141$	3.92493	−	17.1963i	0.330539	−	1.44819i
$142$	3.16868	+	0.977409i	0.265910	+	0.0820224i
$143$	1.73514	−	4.42106i	0.145100	−	0.369708i
$144$	25.5827	−	23.7373i	2.13189	−	1.97811i
$145$	−2.01562	+	1.37423i	−0.167388	+	0.114123i
$146$	−22.8530			−1.89133
$147$		0			0
$148$	2.12620			0.174773
$149$	−7.49519	+	5.11013i	−0.614030	+	0.418639i	−0.830002	−	0.557761i	$-0.811661\pi$
$149$	−7.49519	+	5.11013i	−0.614030	+	0.418639i	0.215972	+	0.976400i	$0.430708\pi$
$150$	18.0544	−	16.7520i	1.47413	−	1.36780i
$151$	3.34468	−	8.52211i	0.272186	−	0.693520i	−0.727784	−	0.685807i	$-0.759450\pi$
$151$	3.34468	−	8.52211i	0.272186	−	0.693520i	0.999970	−	0.00771305i	$-0.00245516\pi$
$152$	−3.54119	−	1.09231i	−0.287228	−	0.0885982i
$153$	−1.09042	+	4.77746i	−0.0881556	+	0.386235i
$154$		0			0
$155$	−0.299753	−	1.31331i	−0.0240768	−	0.105487i
$156$	0.257337	−	3.43393i	0.0206035	−	0.274934i
$157$	6.42813	−	1.98281i	0.513020	−	0.158246i	−0.0274267	−	0.999624i	$-0.508731\pi$
$157$	6.42813	−	1.98281i	0.513020	−	0.158246i	0.540447	+	0.841378i	$0.318255\pi$
$158$	0.194093	+	2.58999i	0.0154412	+	0.206049i
$159$	−10.7562	−	27.4064i	−0.853025	−	2.17347i
$160$	0.990338	+	0.476922i	0.0782931	+	0.0377040i
$161$		0			0
$162$	32.6733	−	15.7346i	2.56705	−	1.23623i
$163$	−2.07917	−	1.92919i	−0.162853	−	0.151106i	0.594537	−	0.804068i	$-0.297335\pi$
$163$	−2.07917	−	1.92919i	−0.162853	−	0.151106i	−0.757390	+	0.652962i	$0.773526\pi$
$164$	3.05619	+	0.460646i	0.238648	+	0.0359704i
$165$	1.41725	+	2.45476i	0.110333	+	0.191102i
$166$	4.56781	−	7.91168i	0.354531	−	0.614065i
$167$	3.84685	−	4.82380i	0.297678	−	0.373277i	−0.610389	−	0.792102i	$-0.708987\pi$
$167$	3.84685	−	4.82380i	0.297678	−	0.373277i	0.908067	+	0.418826i	$0.137558\pi$
$168$		0			0
$169$	−5.24984	−	6.58309i	−0.403834	−	0.506392i
$170$	−0.414104	+	0.0624161i	−0.0317603	+	0.00478710i
$171$	−9.48580	−	6.46731i	−0.725397	−	0.494567i
$172$	2.55724	+	1.74349i	0.194987	+	0.132940i
$173$	16.2753	−	2.45311i	1.23739	−	0.186506i	0.502429	−	0.864618i	$-0.332440\pi$
$173$	16.2753	−	2.45311i	1.23739	−	0.186506i	0.734959	+	0.678112i	$0.237202\pi$
$174$	19.4831	+	24.4310i	1.47701	+	1.85211i
$175$		0			0
$176$	6.57282	−	8.24206i	0.495445	−	0.621269i
$177$	−13.3962	+	23.2030i	−1.00692	+	1.74404i
$178$	−10.1331	−	17.5510i	−0.759508	−	1.31551i
$179$	15.9874	+	2.40972i	1.19496	+	0.180111i	0.716237	−	0.697858i	$-0.245863\pi$
$179$	15.9874	+	2.40972i	1.19496	+	0.180111i	0.478719	+	0.877968i	$0.341101\pi$
$180$	1.06973	+	0.992567i	0.0797332	+	0.0739816i
$181$	−6.74759	+	3.24947i	−0.501545	+	0.241531i	−0.667511	−	0.744600i	$-0.732640\pi$
$181$	−6.74759	+	3.24947i	−0.501545	+	0.241531i	0.165966	+	0.986131i	$0.446926\pi$
$182$		0			0
$183$	27.4949	+	13.2408i	2.03248	+	0.978790i
$184$	−0.548744	−	1.39818i	−0.0404540	−	0.103075i
$185$	−0.126122	−	1.68299i	−0.00927271	−	0.123736i
$186$	−16.4885	+	5.08604i	−1.20900	+	0.372926i
$187$	−0.110619	+	1.47611i	−0.00808929	+	0.107944i
$188$	−0.610388	−	2.67429i	−0.0445171	−	0.195042i
$189$		0			0
$190$	0.218324	−	0.956541i	0.0158389	−	0.0693948i
$191$	−21.1330	−	6.51866i	−1.52913	−	0.471674i	−0.587755	−	0.809039i	$-0.699988\pi$
$191$	−21.1330	−	6.51866i	−1.52913	−	0.471674i	−0.941374	+	0.337365i	$0.890464\pi$
$192$	−6.02072	+	15.3406i	−0.434508	+	1.10711i
$193$	15.4091	−	14.2976i	1.10917	−	1.02916i	0.109792	−	0.993955i	$-0.464981\pi$
$193$	15.4091	−	14.2976i	1.10917	−	1.02916i	0.999380	−	0.0352071i	$-0.0112091\pi$
$194$	12.5357	−	8.54671i	0.900012	−	0.613618i
$195$	−2.73337			−0.195741
$196$		0			0
$197$	14.9189			1.06293			0.531464	−	0.847081i	$-0.321642\pi$
$197$	14.9189			1.06293			0.531464	+	0.847081i	$0.321642\pi$
$198$	21.3010	−	14.5228i	1.51379	−	1.03209i
$199$	8.01604	−	7.43780i	0.568242	−	0.527251i	−0.342885	−	0.939377i	$-0.611404\pi$
$199$	8.01604	−	7.43780i	0.568242	−	0.527251i	0.911127	+	0.412126i	$0.135214\pi$
$200$	−4.19533	+	10.6895i	−0.296655	+	0.755864i
$201$	5.48613	+	1.69225i	0.386962	+	0.119362i
$202$	4.36115	−	19.1074i	0.306849	−	1.34439i
$203$		0			0
$204$	0.238824	+	1.04636i	0.0167210	+	0.0732596i
$205$	0.183335	−	2.44644i	0.0128047	−	0.170866i
$206$	2.05915	−	0.635165i	0.143468	−	0.0442540i
$207$	−0.347736	−	4.64022i	−0.0241693	−	0.322517i
$208$	3.71400	+	9.46312i	0.257520	+	0.656150i
$209$	−3.12456	−	1.50471i	−0.216131	−	0.104083i
$210$		0			0
$211$	−15.2742	+	7.35566i	−1.05152	+	0.506384i	−0.878106	−	0.478465i	$-0.841193\pi$
$211$	−15.2742	+	7.35566i	−1.05152	+	0.506384i	−0.173411	+	0.984850i	$0.555479\pi$
$212$	−3.35637	−	3.11426i	−0.230517	−	0.213888i
$213$	−6.67035	−	1.00539i	−0.457045	−	0.0688884i
$214$	5.67711	+	9.83305i	0.388079	+	0.672173i
$215$	1.22836	−	2.12759i	0.0837738	−	0.145100i
$216$	−20.6733	+	25.9236i	−1.40664	+	1.76387i
$217$		0			0
$218$	−18.9606	−	23.7758i	−1.28417	−	1.61030i
$219$	45.9703	−	6.92890i	3.10638	−	0.468212i
$220$	0.364215	+	0.248317i	0.0245553	+	0.0167415i
$221$	−1.17940	−	0.804104i	−0.0793353	−	0.0540899i
$222$	−21.3768	+	3.22204i	−1.43472	+	0.216249i
$223$	13.4548	+	16.8717i	0.900998	+	1.12982i	0.990998	+	0.133874i	$0.0427417\pi$
$223$	13.4548	+	16.8717i	0.900998	+	1.12982i	−0.0900007	+	0.995942i	$0.528687\pi$
$224$		0			0
$225$	−22.1810	+	27.8140i	−1.47873	+	1.85427i
$226$	2.65620	−	4.60068i	0.176688	−	0.306033i
$227$	8.44939	+	14.6348i	0.560806	+	0.971344i	0.997426	+	0.0716980i	$0.0228418\pi$
$227$	8.44939	+	14.6348i	0.560806	+	0.971344i	−0.436621	+	0.899646i	$0.643825\pi$
$228$	−2.48641	−	0.374766i	−0.164667	−	0.0248195i
$229$	−14.7824	−	13.7160i	−0.976846	−	0.906380i	0.0187790	−	0.999824i	$-0.494022\pi$
$229$	−14.7824	−	13.7160i	−0.976846	−	0.906380i	−0.995625	+	0.0934434i	$0.970213\pi$
$230$	0.358284	−	0.172540i	0.0236245	−	0.0113770i
$231$		0			0
$232$	−13.1268	−	6.32152i	−0.861814	−	0.415028i
$233$	−0.322765	−	0.822391i	−0.0211450	−	0.0538766i	0.919911	−	0.392126i	$-0.128260\pi$
$233$	−0.322765	−	0.822391i	−0.0211450	−	0.0538766i	−0.941056	+	0.338250i	$0.890165\pi$
$234$	1.85785	+	24.7913i	0.121451	+	1.62066i
$235$	−2.08061	+	0.641784i	−0.135724	+	0.0418654i
$236$	−0.311374	+	4.15500i	−0.0202687	+	0.270467i
$237$	−1.17570	−	5.15108i	−0.0763699	−	0.334599i
$238$		0			0
$239$	−0.533986	+	2.33954i	−0.0345407	+	0.151333i	−0.989258	−	0.146183i	$-0.953301\pi$
$239$	−0.533986	+	2.33954i	−0.0345407	+	0.151333i	0.954717	+	0.297516i	$0.0961582\pi$
$240$	−5.79762	−	1.78833i	−0.374235	−	0.115436i
$241$	7.61993	−	19.4153i	0.490843	−	1.25065i	−0.444140	−	0.895957i	$-0.646491\pi$
$241$	7.61993	−	19.4153i	0.490843	−	1.25065i	0.934984	−	0.354691i	$-0.115414\pi$
$242$	−7.04150	+	6.53355i	−0.452645	+	0.419993i
$243$	−26.2963	+	17.9285i	−1.68691	+	1.15012i
$244$	4.74587			0.303823
$245$		0			0
$246$	−31.4249			−2.00358
$247$	2.76316	−	1.88389i	0.175816	−	0.119869i
$248$	5.89757	−	5.47214i	0.374496	−	0.347481i
$249$	−6.78966	+	17.2998i	−0.430277	+	1.09633i
$250$	−5.90501	−	1.82145i	−0.373466	−	0.115199i
$251$	5.88168	−	25.7693i	0.371248	−	1.62655i	−0.352030	−	0.935989i	$-0.614508\pi$
$251$	5.88168	−	25.7693i	0.371248	−	1.62655i	0.723278	−	0.690557i	$-0.242634\pi$
$252$		0			0
$253$	−0.312778	−	1.37037i	−0.0196642	−	0.0861545i
$254$	−0.519766	+	6.93579i	−0.0326130	+	0.435190i
$255$	0.814072	−	0.251108i	0.0509792	−	0.0157250i
$256$	0.845739	+	11.2856i	0.0528587	+	0.705350i
$257$	4.11474	+	10.4842i	0.256671	+	0.653986i	0.999887	−	0.0150655i	$-0.00479569\pi$
$257$	4.11474	+	10.4842i	0.256671	+	0.653986i	−0.743216	+	0.669052i	$0.766700\pi$
$258$	−28.3525	−	13.6539i	−1.76515	−	0.850052i
$259$		0			0
$260$	−0.382986	+	0.184436i	−0.0237518	+	0.0114383i
$261$	−33.0876	−	30.7008i	−2.04807	−	1.90033i
$262$	−14.0692	−	2.12060i	−0.869201	−	0.131011i
$263$	−11.1542	−	19.3196i	−0.687795	−	1.19130i	−0.972550	−	0.232695i	$-0.925246\pi$
$263$	−11.1542	−	19.3196i	−0.687795	−	1.19130i	0.284755	−	0.958600i	$-0.408088\pi$
$264$	−8.46433	+	14.6606i	−0.520943	+	0.902301i
$265$	−2.26599	+	2.84146i	−0.139198	+	0.174549i
$266$		0			0
$267$	25.7047	+	32.2327i	1.57310	+	1.97261i
$268$	0.882873	−	0.133072i	0.0539300	−	0.00812864i
$269$	−16.4573	−	11.2204i	−1.00342	−	0.684119i	−0.0541331	−	0.998534i	$-0.517240\pi$
$269$	−16.4573	−	11.2204i	−1.00342	−	0.684119i	−0.949286	+	0.314414i	$0.898192\pi$
$270$	−7.25325	−	4.94518i	−0.441419	−	0.300954i
$271$	10.1145	−	1.52452i	0.614413	−	0.0926078i	0.165539	−	0.986203i	$-0.447064\pi$
$271$	10.1145	−	1.52452i	0.614413	−	0.0926078i	0.448873	+	0.893595i	$0.351825\pi$
$272$	−1.97548	−	2.47718i	−0.119781	−	0.150201i
$273$		0			0
$274$	13.2450	−	16.6087i	0.800158	−	1.00337i
$275$	−5.37319	+	9.30663i	−0.324015	+	0.561211i
$276$	−0.509574	−	0.882607i	−0.0306727	−	0.0531267i
$277$	−7.77152	−	1.17137i	−0.466945	−	0.0703807i	−0.0886443	−	0.996063i	$-0.528253\pi$
$277$	−7.77152	−	1.17137i	−0.466945	−	0.0703807i	−0.378301	+	0.925683i	$0.623492\pi$
$278$	−1.92571	−	1.78680i	−0.115497	−	0.107165i
$279$	22.4559	−	10.8142i	1.34440	−	0.647429i
$280$		0			0
$281$	−10.3585	−	4.98841i	−0.617939	−	0.297584i	0.0986041	−	0.995127i	$-0.468562\pi$
$281$	−10.3585	−	4.98841i	−0.617939	−	0.297584i	−0.716543	+	0.697543i	$0.754277\pi$
$282$	10.1894	+	25.9623i	0.606772	+	1.54603i
$283$	−0.603970	−	8.05941i	−0.0359023	−	0.479082i	−0.985957	−	0.166999i	$-0.946592\pi$
$283$	−0.603970	−	8.05941i	−0.0359023	−	0.479082i	0.950055	−	0.312083i	$-0.101027\pi$
$284$	−1.00245	+	0.309216i	−0.0594847	+	0.0183486i
$285$	−0.149155	+	1.99034i	−0.00883519	+	0.117897i
$286$	1.67108	+	7.32148i	0.0988130	+	0.432928i
$287$		0			0
$288$	−4.52556	+	19.8278i	−0.266671	+	1.16836i
$289$	−15.8196	−	4.87970i	−0.930565	−	0.287041i
$290$	1.40926	−	3.59074i	0.0827548	−	0.210856i
$291$	−22.6251	+	20.9930i	−1.32631	+	1.23063i
$292$	5.97358	−	4.07272i	0.349577	−	0.238338i
$293$	4.90918			0.286797			0.143399	−	0.989665i	$-0.454197\pi$
$293$	4.90918			0.286797			0.143399	+	0.989665i	$0.454197\pi$
$294$		0			0
$295$	3.30734			0.192561
$296$	8.32813	−	5.67802i	0.484063	−	0.330028i
$297$	−22.7463	+	21.1055i	−1.31987	+	1.22466i
$298$	5.24042	−	13.3524i	0.303569	−	0.773482i
$299$	1.29524	+	0.399529i	0.0749057	+	0.0231054i
$300$	−1.73382	+	7.59637i	−0.100102	+	0.438576i
$301$		0			0
$302$	3.22120	+	14.1130i	0.185359	+	0.812112i
$303$	−2.97946	+	39.7581i	−0.171165	+	2.28404i
$304$	7.09335	−	2.18801i	0.406832	−	0.125491i
$305$	−0.281516	−	3.75657i	−0.0161196	−	0.215101i
$306$	−2.83083	−	7.21284i	−0.161828	−	0.412330i
$307$	5.02321	+	2.41905i	0.286690	+	0.138063i	0.571702	−	0.820461i	$-0.306283\pi$
$307$	5.02321	+	2.41905i	0.286690	+	0.138063i	−0.285012	+	0.958524i	$0.591998\pi$
$308$		0			0
$309$	−3.94954	+	1.90200i	−0.224681	+	0.108201i
$310$	1.56142	+	1.44878i	0.0886825	+	0.0822853i
$311$	20.0116	+	3.01626i	1.13475	+	0.171036i	0.689442	−	0.724341i	$-0.257856\pi$
$311$	20.0116	+	3.01626i	1.13475	+	0.171036i	0.445309	+	0.895377i	$0.353094\pi$
$312$	−8.16232	−	14.1376i	−0.462101	−	0.800382i
$313$	6.09673	−	10.5598i	0.344607	−	0.596877i	−0.640675	−	0.767812i	$-0.721345\pi$
$313$	6.09673	−	10.5598i	0.344607	−	0.596877i	0.985282	+	0.170935i	$0.0546787\pi$
$314$	−6.63194	+	8.31619i	−0.374262	+	0.469310i
$315$		0			0
$316$	−0.512306	−	0.642411i	−0.0288194	−	0.0361384i
$317$	−8.59992	+	1.29623i	−0.483020	+	0.0728035i	−0.386039	−	0.922483i	$-0.626157\pi$
$317$	−8.59992	+	1.29623i	−0.483020	+	0.0728035i	−0.0969814	+	0.995286i	$0.530919\pi$
$318$	38.4643	+	26.2245i	2.15697	+	1.47060i
$319$	−11.2654	−	7.68064i	−0.630743	−	0.430033i
$320$	2.01158	−	0.303197i	0.112451	−	0.0169493i
$321$	−14.4012	−	18.0585i	−0.803796	−	1.00793i
$322$		0			0
$323$	−0.649876	+	0.814918i	−0.0361600	+	0.0453433i
$324$	−5.73639	+	9.93571i	−0.318688	+	0.551984i
$325$	−5.18147	−	8.97457i	−0.287416	−	0.497820i
$326$	4.43475	+	0.668430i	0.245618	+	0.0370209i
$327$	45.3491	+	42.0778i	2.50781	+	2.32691i
$328$	13.2009	−	6.35723i	0.728899	−	0.351019i
$329$		0			0
$330$	−4.03811	−	1.94465i	−0.222291	−	0.107050i
$331$	−11.4949	−	29.2885i	−0.631817	−	1.60984i	−0.783484	−	0.621412i	$-0.786559\pi$
$331$	−11.4949	−	29.2885i	−0.631817	−	1.60984i	0.151667	−	0.988432i	$-0.451536\pi$
$332$	0.215983	+	2.88209i	0.0118536	+	0.158175i
$333$	29.8393	−	9.20420i	1.63518	−	0.504387i
$334$	−0.729058	+	9.72860i	−0.0398923	+	0.532325i
$335$	−0.157703	−	0.690940i	−0.00861621	−	0.0377501i
$336$		0			0
$337$	6.27847	−	27.5078i	0.342010	−	1.49844i	−0.452814	−	0.891605i	$-0.649580\pi$
$337$	6.27847	−	27.5078i	0.342010	−	1.49844i	0.794824	−	0.606840i	$-0.207563\pi$
$338$	12.7225	+	3.92436i	0.692011	+	0.213457i
$339$	−3.94822	+	10.0599i	−0.214438	+	0.546379i
$340$	0.0971198	−	0.0901140i	0.00526706	−	0.00488712i
$341$	6.22068	−	4.24119i	0.336869	−	0.229673i
$342$	18.1534			0.981626
$343$		0			0
$344$	14.6724			0.791085
$345$	−0.668397	+	0.455705i	−0.0359853	+	0.0245344i
$346$	−19.0780	+	17.7018i	−1.02564	+	0.951653i
$347$	2.60737	−	6.64348i	0.139971	−	0.356641i	−0.843649	−	0.536895i	$-0.819597\pi$
$347$	2.60737	−	6.64348i	0.139971	−	0.356641i	0.983620	+	0.180255i	$0.0576922\pi$
$348$	−9.44664	−	2.91390i	−0.506393	−	0.156202i
$349$	−6.57045	+	28.7870i	−0.351708	+	1.54093i	0.421528	+	0.906815i	$0.361494\pi$
$349$	−6.57045	+	28.7870i	−0.351708	+	1.54093i	−0.773236	+	0.634118i	$0.781363\pi$
$350$		0			0
$351$	−6.65836	−	29.1722i	−0.355397	−	1.55710i
$352$	−0.459101	+	6.12628i	−0.0244702	+	0.326532i
$353$	−15.5482	+	4.79598i	−0.827546	+	0.255264i	−0.679462	−	0.733711i	$-0.737787\pi$
$353$	−15.5482	+	4.79598i	−0.827546	+	0.255264i	−0.148084	+	0.988975i	$0.547311\pi$
$354$	−3.16591	−	42.2462i	−0.168266	−	2.24536i
$355$	0.304222	+	0.775146i	0.0161464	+	0.0411405i
$356$	5.77654	+	2.78183i	0.306156	+	0.147437i
$357$		0			0
$358$	−23.0333	+	11.0923i	−1.21735	+	0.586244i
$359$	19.2326	+	17.8452i	1.01506	+	0.941834i	0.998315	−	0.0580255i	$-0.0184805\pi$
$359$	19.2326	+	17.8452i	1.01506	+	0.941834i	0.0167409	+	0.999860i	$0.494671\pi$
$360$	6.84068	+	1.03107i	0.360536	+	0.0543420i
$361$	8.27900	+	14.3397i	0.435737	+	0.754719i
$362$	5.92107	−	10.2556i	0.311204	−	0.539022i
$363$	12.1835	−	15.2776i	0.639467	−	0.801866i
$364$		0			0
$365$	−3.57808	−	4.48677i	−0.187285	−	0.234848i
$366$	−47.7149	+	7.19187i	−2.49410	+	0.375925i
$367$	17.3840	+	11.8522i	0.907435	+	0.618679i	0.924503	−	0.381175i	$-0.124481\pi$
$367$	17.3840	+	11.8522i	0.907435	+	0.618679i	−0.0170673	+	0.999854i	$0.505433\pi$
$368$	2.48588	+	1.69484i	0.129585	+	0.0883497i
$369$	44.8848	−	6.76530i	2.33661	−	0.352188i
$370$	1.66386	+	2.08642i	0.0865000	+	0.108468i
$371$		0			0
$372$	3.40356	−	4.26792i	0.176466	−	0.221282i
$373$	2.07271	−	3.59004i	0.107321	−	0.185885i	−0.807363	−	0.590055i	$-0.799106\pi$
$373$	2.07271	−	3.59004i	0.107321	−	0.185885i	0.914684	+	0.404170i	$0.132439\pi$
$374$	−1.17030	−	2.02702i	−0.0605147	−	0.104814i
$375$	12.4306	+	1.87361i	0.641911	+	0.0967526i
$376$	−9.53250	−	8.84487i	−0.491601	−	0.456139i
$377$	11.8460	−	5.70475i	0.610102	−	0.293810i
$378$		0			0
$379$	17.7420	+	8.54409i	0.911344	+	0.438880i	0.829973	−	0.557804i	$-0.188356\pi$
$379$	17.7420	+	8.54409i	0.911344	+	0.438880i	0.0813713	+	0.996684i	$0.474070\pi$
$380$	0.113401	+	0.288940i	0.00581733	+	0.0148223i
$381$	−1.05735	−	14.1094i	−0.0541697	−	0.722845i
$382$	33.4158	−	10.3074i	1.70970	−	0.527372i
$383$	−0.336592	+	4.49151i	−0.0171991	+	0.229506i	0.981980	+	0.188986i	$0.0605202\pi$
$383$	−0.336592	+	4.49151i	−0.0171991	+	0.229506i	−0.999179	+	0.0405191i	$0.987099\pi$
$384$	−9.76131	−	42.7671i	−0.498130	−	2.18245i
$385$		0			0
$386$	−7.39613	+	32.4046i	−0.376453	+	1.64935i
$387$	43.4359	+	13.3982i	2.20797	+	0.681069i
$388$	−1.75359	+	4.46807i	−0.0890250	+	0.226832i
$389$	−18.4377	+	17.1077i	−0.934830	+	0.867395i	−0.991382	−	0.131005i	$-0.958180\pi$
$389$	−18.4377	+	17.1077i	−0.934830	+	0.867395i	0.0565522	+	0.998400i	$0.481989\pi$
$390$	3.57104	−	2.43470i	0.180827	−	0.123286i
$391$	−0.422461			−0.0213648
$392$		0			0
$393$	28.9441			1.46004
$394$	−19.4910	+	13.2887i	−0.981940	+	0.669476i
$395$	−0.478109	+	0.443620i	−0.0240562	+	0.0223209i
$396$	−2.97974	+	7.59225i	−0.149737	+	0.381525i
$397$	−22.6206	−	6.97754i	−1.13530	−	0.350193i	−0.330537	−	0.943793i	$-0.607230\pi$
$397$	−22.6206	−	6.97754i	−1.13530	−	0.350193i	−0.804760	+	0.593600i	$0.797706\pi$
$398$	−3.84757	+	16.8573i	−0.192861	+	0.844980i
$399$		0			0
$400$	−5.11848	−	22.4255i	−0.255924	−	1.12128i
$401$	−0.996145	+	13.2926i	−0.0497451	+	0.663803i	0.915477	+	0.402371i	$0.131814\pi$
$401$	−0.996145	+	13.2926i	−0.0497451	+	0.663803i	−0.965222	+	0.261432i	$0.915805\pi$
$402$	−8.67474	+	2.67580i	−0.432657	+	0.133457i
$403$	0.542561	+	7.23998i	0.0270269	+	0.360649i
$404$	2.26524	+	5.77173i	0.112700	+	0.287154i
$405$	8.20484	+	3.95124i	0.407702	+	0.196339i
$406$		0			0
$407$	8.49857	−	4.09269i	0.421258	−	0.202867i
$408$	3.72974	+	3.46069i	0.184650	+	0.171330i
$409$	−32.5988	−	4.91348i	−1.61191	−	0.242956i	−0.719601	−	0.694388i	$-0.755675\pi$
$409$	−32.5988	−	4.91348i	−1.61191	−	0.242956i	−0.892306	+	0.451432i	$0.850913\pi$
$410$	1.93959	+	3.35947i	0.0957896	+	0.165913i
$411$	−21.6074	+	37.4252i	−1.06582	+	1.84605i
$412$	−0.425050	+	0.532996i	−0.0209407	+	0.0262588i
$413$		0			0
$414$	4.58748	+	5.75252i	0.225462	+	0.282721i
$415$	2.26849	−	0.341920i	0.111356	−	0.0167842i
$416$	−4.89485	−	3.33725i	−0.239990	−	0.163622i
$417$	4.41544	+	3.01040i	0.216225	+	0.147420i
$418$	5.42241	−	0.817296i	0.265219	−	0.0399753i
$419$	−24.5840	−	30.8274i	−1.20101	−	1.50602i	−0.810834	−	0.585276i	$-0.800986\pi$
$419$	−24.5840	−	30.8274i	−1.20101	−	1.50602i	−0.390175	−	0.920741i	$-0.627585\pi$
$420$		0			0
$421$	−2.04607	+	2.56569i	−0.0997194	+	0.125044i	−0.829187	−	0.558971i	$-0.811196\pi$
$421$	−2.04607	+	2.56569i	−0.0997194	+	0.125044i	0.729468	+	0.684015i	$0.239768\pi$
$422$	13.4032	−	23.2150i	0.652458	−	1.13009i
$423$	−20.1430	−	34.8888i	−0.979388	−	1.69635i
$424$	−21.4632	−	3.23506i	−1.04235	−	0.157108i
$425$	2.36765	+	2.19686i	0.114848	+	0.106563i
$426$	9.61008	−	4.62797i	0.465610	−	0.224226i
$427$		0			0
$428$	−3.23633	−	1.55853i	−0.156434	−	0.0753346i
$429$	−5.58131	−	14.2210i	−0.269468	−	0.686594i
$430$	0.290298	+	3.87375i	0.0139994	+	0.186809i
$431$	6.63928	−	2.04795i	0.319803	−	0.0986461i	−0.130698	−	0.991422i	$-0.541722\pi$
$431$	6.63928	−	2.04795i	0.319803	−	0.0986461i	0.450501	+	0.892776i	$0.351246\pi$
$432$	4.96340	−	66.2319i	0.238802	−	3.18659i
$433$	−2.49996	−	10.9530i	−0.120140	−	0.526370i	−0.998802	−	0.0489252i	$-0.984420\pi$
$433$	−2.49996	−	10.9530i	−0.120140	−	0.526370i	0.878662	−	0.477444i	$-0.158437\pi$
$434$		0			0
$435$	−1.74613	+	7.65029i	−0.0837205	+	0.366803i
$436$	9.19331	+	2.83576i	0.440280	+	0.135808i
$437$	0.361601	−	0.921343i	0.0172977	−	0.0440738i
$438$	−53.8865	+	49.9994i	−2.57480	+	2.38906i
$439$	−24.8653	+	16.9529i	−1.18675	+	0.809115i	−0.985375	−	0.170398i	$-0.945495\pi$
$439$	−24.8653	+	16.9529i	−1.18675	+	0.809115i	−0.201379	+	0.979513i	$0.564542\pi$
$440$	2.08972			0.0996236
$441$		0			0
$442$	2.25708			0.107359
$443$	−10.9498	+	7.46545i	−0.520241	+	0.354694i	−0.794796	−	0.606877i	$-0.792422\pi$
$443$	−10.9498	+	7.46545i	−0.520241	+	0.354694i	0.274554	+	0.961572i	$0.411470\pi$
$444$	5.01351	−	4.65186i	0.237931	−	0.220767i
$445$	1.85929	−	4.73741i	0.0881390	−	0.224575i
$446$	−32.6063	−	10.0577i	−1.54395	−	0.476246i
$447$	−6.49307	+	28.4480i	−0.307112	+	1.34554i
$448$		0			0
$449$	8.14714	+	35.6949i	0.384487	+	1.68455i	0.683221	+	0.730212i	$0.260579\pi$
$449$	8.14714	+	35.6949i	0.384487	+	1.68455i	−0.298734	+	0.954336i	$0.596564\pi$
$450$	4.20375	−	56.0952i	0.198167	−	2.64435i
$451$	13.1025	−	4.04157i	0.616970	−	0.190310i
$452$	0.125595	+	1.67595i	0.00590749	+	0.0788300i
$453$	−10.7586	−	27.4126i	−0.505485	−	1.28795i
$454$	−24.0744	−	11.5936i	−1.12987	−	0.544116i
$455$		0			0
$456$	−10.7398	+	5.17203i	−0.502939	+	0.242203i
$457$	6.16441	+	5.71974i	0.288359	+	0.267558i	0.811066	−	0.584954i	$-0.198887\pi$
$457$	6.16441	+	5.71974i	0.288359	+	0.267558i	−0.522707	+	0.852512i	$0.675078\pi$
$458$	31.5298	+	4.75236i	1.47329	+	0.222063i
$459$	4.66302	+	8.07658i	0.217651	+	0.376982i
$460$	−0.0629032	+	0.108952i	−0.00293288	+	0.00507989i
$461$	−12.9757	+	16.2710i	−0.604338	+	0.757816i	−0.986047	−	0.166467i	$-0.946764\pi$
$461$	−12.9757	+	16.2710i	−0.604338	+	0.757816i	0.381709	+	0.924282i	$0.375336\pi$
$462$		0			0
$463$	1.03419	+	1.29683i	0.0480628	+	0.0602689i	0.805282	−	0.592892i	$-0.202014\pi$
$463$	1.03419	+	1.29683i	0.0480628	+	0.0602689i	−0.757219	+	0.653161i	$0.773443\pi$
$464$	28.8584	−	4.34970i	1.33972	−	0.201930i
$465$	−3.58015	−	2.44090i	−0.166025	−	0.113194i
$466$	1.15421	+	0.786925i	0.0534676	+	0.0364536i
$467$	−33.6707	+	5.07504i	−1.55809	+	0.234845i	−0.870838	−	0.491571i	$-0.836423\pi$
$467$	−33.6707	+	5.07504i	−1.55809	+	0.234845i	−0.687256	+	0.726416i	$0.741185\pi$
$468$	−4.90377	−	6.14913i	−0.226677	−	0.284244i
$469$		0			0
$470$	2.14658	−	2.69173i	0.0990144	−	0.124160i
$471$	10.8191	−	18.7393i	0.498520	−	0.863462i
$472$	9.87628	+	17.1062i	0.454593	+	0.787378i
$473$	13.5775	+	2.04647i	0.624292	+	0.0940969i
$474$	6.12422	+	5.68245i	0.281295	+	0.261004i
$475$	−6.81768	+	3.28322i	−0.312817	+	0.150645i
$476$		0			0
$477$	−60.5850	−	29.1762i	−2.77400	−	1.33589i
$478$	−1.38627	−	3.53216i	−0.0634065	−	0.161557i
$479$	1.87728	+	25.0506i	0.0857753	+	1.14459i	0.859523	+	0.511098i	$0.170761\pi$
$479$	1.87728	+	25.0506i	0.0857753	+	1.14459i	−0.773747	+	0.633495i	$0.781620\pi$
$480$	3.37862	−	1.04217i	0.154212	−	0.0475682i
$481$	−0.679755	+	9.07070i	−0.0309942	+	0.413589i
$482$	7.33862	+	32.1526i	0.334265	+	1.46451i
$483$		0			0
$484$	0.676218	−	2.96271i	0.0307372	−	0.134668i
$485$	3.64070	+	1.12301i	0.165316	+	0.0509931i
$486$	18.3856	−	46.8459i	0.833990	−	2.12497i
$487$	16.9634	−	15.7397i	0.768685	−	0.713235i	−0.194846	−	0.980834i	$-0.562421\pi$
$487$	16.9634	−	15.7397i	0.768685	−	0.713235i	0.963530	+	0.267599i	$0.0862302\pi$
$488$	18.5891	−	12.6738i	0.841488	−	0.573717i
$489$	−9.12344			−0.412576
$490$		0			0
$491$	−16.8361			−0.759804			−0.379902	−	0.925027i	$-0.624042\pi$
$491$	−16.8361			−0.759804			−0.379902	+	0.925027i	$0.624042\pi$
$492$	8.21421	−	5.60035i	0.370325	−	0.252483i
$493$	−3.00399	+	2.78729i	−0.135293	+	0.125533i
$494$	−1.93192	+	4.92246i	−0.0869213	+	0.221472i
$495$	6.18636	+	1.90824i	0.278056	+	0.0857690i
$496$	−3.58601	+	15.7113i	−0.161017	+	0.705459i
$497$		0			0
$498$	−6.53900	−	28.6492i	−0.293019	−	1.28380i
$499$	0.633778	−	8.45718i	0.0283718	−	0.378595i	−0.964886	−	0.262669i	$-0.915397\pi$
$499$	0.633778	−	8.45718i	0.0283718	−	0.378595i	0.993258	−	0.115926i	$-0.0369837\pi$
$500$	1.86813	−	0.576241i	0.0835452	−	0.0257703i
$501$	−1.48311	−	19.7907i	−0.0662605	−	0.884185i
$502$	15.2693	+	38.9056i	0.681503	+	1.73644i
$503$	30.2302	+	14.5581i	1.34790	+	0.649113i	0.961904	−	0.273388i	$-0.0881444\pi$
$503$	30.2302	+	14.5581i	1.34790	+	0.649113i	0.385993	+	0.922502i	$0.373859\pi$
$504$		0			0
$505$	4.43422	−	2.13541i	0.197320	−	0.0950244i
$506$	1.62926	+	1.51173i	0.0724295	+	0.0672048i
$507$	−26.7819	−	4.03672i	−1.18943	−	0.179277i
$508$	−1.10019	−	1.90559i	−0.0488130	−	0.0845467i
$509$	−11.3032	+	19.5777i	−0.501005	+	0.867765i	0.498995	+	0.866605i	$0.333703\pi$
$509$	−11.3032	+	19.5777i	−0.501005	+	0.867765i	−0.999999	+	0.00116035i	$0.999631\pi$
$510$	−0.839884	+	1.05318i	−0.0371907	+	0.0466356i
$511$		0			0
$512$	5.84834	+	7.33358i	0.258462	+	0.324102i
$513$	−21.6054	+	3.25649i	−0.953902	+	0.143778i
$514$	−14.7143	−	10.0321i	−0.649021	−	0.442495i
$515$	0.447104	+	0.304830i	0.0197017	+	0.0134324i
$516$	9.84441	−	1.48381i	0.433376	−	0.0653209i
$517$	−7.58745	−	9.51436i	−0.333695	−	0.418441i
$518$		0			0
$519$	33.0095	−	41.3926i	1.44896	−	1.81693i
$520$	−1.00758	+	1.74518i	−0.0441853	+	0.0765312i
$521$	5.31567	+	9.20700i	0.232884	+	0.403366i	0.958655	−	0.284569i	$-0.0918506\pi$
$521$	5.31567	+	9.20700i	0.232884	+	0.403366i	−0.725772	+	0.687935i	$0.758517\pi$
$522$	70.5738	+	10.6373i	3.08893	+	0.465582i
$523$	−9.93813	−	9.22123i	−0.434564	−	0.403216i	0.432325	−	0.901718i	$-0.357693\pi$
$523$	−9.93813	−	9.22123i	−0.434564	−	0.403216i	−0.866889	+	0.498501i	$0.833884\pi$
$524$	4.05550	−	1.95302i	0.177165	−	0.0853183i
$525$		0			0
$526$	31.7810	+	15.3049i	1.38572	+	0.667326i
$527$	−0.826708	−	2.10642i	−0.0360120	−	0.0917570i
$528$	−2.53408	−	33.8149i	−0.110282	−	1.47161i
$529$	−21.5948	+	6.66113i	−0.938906	+	0.289614i
$530$	0.429451	−	5.73063i	0.0186542	−	0.248923i
$531$	13.6169	+	59.6594i	0.590922	+	2.58900i
$532$		0			0
$533$	−2.94226	+	12.8909i	−0.127443	+	0.558366i
$534$	−62.2928	−	19.2148i	−2.69568	−	0.831506i
$535$	−1.04168	+	2.65415i	−0.0450357	+	0.114749i
$536$	3.10276	−	2.87894i	0.134019	−	0.124351i
$537$	42.9699	−	29.2964i	1.85429	−	1.26423i
$538$	31.4951			1.35785
$539$		0			0
$540$	2.77724			0.119513
$541$	19.9030	−	13.5696i	0.855697	−	0.583404i	−0.0540640	−	0.998537i	$-0.517217\pi$
$541$	19.9030	−	13.5696i	0.855697	−	0.583404i	0.909761	+	0.415133i	$0.136265\pi$
$542$	−11.8563	+	11.0010i	−0.509270	+	0.472534i
$543$	−8.80116	+	22.4250i	−0.377694	+	0.962348i
$544$	1.76440	+	0.544246i	0.0756482	+	0.0233344i
$545$	1.69930	−	7.44514i	0.0727902	−	0.318915i
$546$		0			0
$547$	3.58775	+	15.7189i	0.153401	+	0.672093i	0.991882	+	0.127163i	$0.0405870\pi$
$547$	3.58775	+	15.7189i	0.153401	+	0.672093i	−0.838481	+	0.544931i	$0.816556\pi$
$548$	−0.502230	+	6.70180i	−0.0214542	+	0.286287i
$549$	66.6038	−	20.5446i	2.84258	−	0.876821i
$550$	−1.26984	−	16.9448i	−0.0541461	−	0.722529i
$551$	−3.50756	−	8.93713i	−0.149427	−	0.380734i
$552$	−4.35295	−	2.09627i	−0.185274	−	0.0892232i
$553$		0			0
$554$	11.1966	−	5.39198i	0.475696	−	0.229083i
$555$	−3.97955	−	3.69248i	−0.168922	−	0.156737i
$556$	0.821797	+	0.123866i	0.0348520	+	0.00525309i
$557$	4.30428	+	7.45523i	0.182378	+	0.315888i	0.942690	−	0.333670i	$-0.108287\pi$
$557$	4.30428	+	7.45523i	0.182378	+	0.315888i	−0.760312	+	0.649558i	$0.774954\pi$
$558$	−19.7052	+	34.1305i	−0.834189	+	1.44486i
$559$	−8.25557	+	10.3522i	−0.349173	+	0.437849i
$560$		0			0
$561$	2.96871	+	3.72264i	0.125339	+	0.157170i
$562$	17.9763	−	2.70950i	0.758286	−	0.114293i
$563$	7.17927	+	4.89475i	0.302570	+	0.206289i	0.705082	−	0.709126i	$-0.250910\pi$
$563$	7.17927	+	4.89475i	0.302570	+	0.206289i	−0.402511	+	0.915415i	$0.631863\pi$
$564$	−7.29026	−	4.97042i	−0.306975	−	0.209292i
$565$	1.31914	−	0.198828i	0.0554966	−	0.00836477i
$566$	7.96782	+	9.99133i	0.334912	+	0.419967i
$567$		0			0
$568$	−3.10075	+	3.88822i	−0.130105	+	0.163146i
$569$	−16.8304	+	29.1511i	−0.705566	+	1.22208i	0.260921	+	0.965360i	$0.415974\pi$
$569$	−16.8304	+	29.1511i	−0.705566	+	1.22208i	−0.966487	+	0.256716i	$0.917359\pi$
$570$	−1.57799	−	2.73315i	−0.0660946	−	0.114479i
$571$	−10.9925	−	1.65686i	−0.460023	−	0.0693373i	−0.0850573	−	0.996376i	$-0.527107\pi$
$571$	−10.9925	−	1.65686i	−0.460023	−	0.0693373i	−0.374965	+	0.927039i	$0.622345\pi$
$572$	−1.74159	−	1.61596i	−0.0728196	−	0.0675668i
$573$	−64.0928	+	30.8654i	−2.67751	+	1.28942i
$574$		0			0
$575$	−2.76327	−	1.33072i	−0.115236	−	0.0554948i
$576$	13.7513	+	35.0376i	0.572969	+	1.45990i
$577$	1.81312	+	24.1944i	0.0754811	+	1.00723i	0.898432	+	0.439113i	$0.144707\pi$
$577$	1.81312	+	24.1944i	0.0754811	+	1.00723i	−0.822951	+	0.568112i	$0.807674\pi$
$578$	25.0142	−	7.71585i	1.04045	−	0.320937i
$579$	5.05290	−	67.4263i	0.209991	−	2.80214i
$580$	0.271550	+	1.18974i	0.0112755	+	0.0494012i
$581$		0			0
$582$	10.8597	−	47.5793i	0.450148	−	1.97223i
$583$	−19.4102	−	5.98726i	−0.803889	−	0.247967i
$584$	12.5217	−	31.9048i	0.518153	−	1.32023i
$585$	−4.57644	+	4.24631i	−0.189212	+	0.175563i
$586$	−6.41365	+	4.37275i	−0.264945	+	0.180637i
$587$	18.8678			0.778758			0.389379	−	0.921078i	$-0.372690\pi$
$587$	18.8678			0.778758			0.389379	+	0.921078i	$0.372690\pi$
$588$		0			0
$589$	5.30148			0.218444
$590$	−4.32091	+	2.94594i	−0.177889	+	0.121283i
$591$	35.1782	−	32.6406i	1.44704	−	1.34266i
$592$	−7.37637	+	18.7947i	−0.303167	+	0.772456i
$593$	−16.8454	−	5.19612i	−0.691759	−	0.213379i	−0.0711104	−	0.997468i	$-0.522654\pi$
$593$	−16.8454	−	5.19612i	−0.691759	−	0.213379i	−0.620648	+	0.784089i	$0.713130\pi$
$594$	10.9178	−	47.8342i	0.447965	−	1.96266i
$595$		0			0
$596$	1.00977	+	4.42411i	0.0413620	+	0.181219i
$597$	2.62859	−	35.0761i	0.107581	−	1.43557i
$598$	−2.04805	+	0.631741i	−0.0837511	+	0.0258338i
$599$	−2.34957	−	31.3529i	−0.0960009	−	1.28104i	−0.812296	−	0.583246i	$-0.801782\pi$
$599$	−2.34957	−	31.3529i	−0.0960009	−	1.28104i	0.716295	−	0.697798i	$-0.245837\pi$
$600$	13.4949	+	34.3844i	0.550926	+	1.40374i
$601$	−10.7945	−	5.19834i	−0.440315	−	0.212045i	0.200573	−	0.979679i	$-0.435720\pi$
$601$	−10.7945	−	5.19834i	−0.440315	−	0.212045i	−0.640888	+	0.767634i	$0.721434\pi$
$602$		0			0
$603$	11.8142	−	5.68944i	0.481113	−	0.231692i
$604$	−3.35712	−	3.11496i	−0.136599	−	0.126746i
$605$	−2.38523	−	0.359515i	−0.0969733	−	0.0146164i
$606$	−31.5211	−	54.5962i	−1.28046	−	2.21782i
$607$	16.2197	−	28.0934i	0.658338	−	1.14028i	−0.322707	−	0.946499i	$-0.604593\pi$
$607$	16.2197	−	28.0934i	0.658338	−	1.14028i	0.981046	−	0.193777i	$-0.0620737\pi$
$608$	−2.69716	+	3.38214i	−0.109384	+	0.137164i
$609$		0			0
$610$	3.71388	+	4.65706i	0.150371	+	0.188559i
$611$	11.6040	−	1.74903i	0.469449	−	0.0707581i
$612$	2.02538	+	1.38088i	0.0818711	+	0.0558188i
$613$	−20.8727	−	14.2308i	−0.843041	−	0.574776i	0.0629766	−	0.998015i	$-0.479941\pi$
$613$	−20.8727	−	14.2308i	−0.843041	−	0.574776i	−0.906018	+	0.423239i	$0.860893\pi$
$614$	−8.71735	+	1.31393i	−0.351804	+	0.0530259i
$615$	−4.92019	−	6.16972i	−0.198401	−	0.248787i
$616$		0			0
$617$	−14.9776	+	18.7813i	−0.602974	+	0.756105i	−0.985838	−	0.167699i	$-0.946366\pi$
$617$	−14.9776	+	18.7813i	−0.602974	+	0.756105i	0.382865	+	0.923805i	$0.374938\pi$
$618$	3.46575	−	6.00286i	0.139413	−	0.241470i
$619$	−11.6230	−	20.1316i	−0.467166	−	0.809156i	0.532130	−	0.846663i	$-0.321392\pi$
$619$	−11.6230	−	20.1316i	−0.467166	−	0.809156i	−0.999296	+	0.0375069i	$0.988058\pi$
$620$	−0.666333	−	0.100434i	−0.0267606	−	0.00403351i
$621$	−6.49174	−	6.02346i	−0.260505	−	0.241713i
$622$	−28.8310	+	13.8843i	−1.15602	+	0.556708i
$623$		0			0
$624$	29.4616	+	14.1879i	1.17941	+	0.567972i
$625$	8.27858	+	21.0935i	0.331143	+	0.843739i
$626$	1.44083	+	19.2265i	0.0575872	+	0.768447i
$627$	−10.6597	+	3.28809i	−0.425708	+	0.131314i
$628$	0.251474	−	3.35568i	0.0100349	−	0.133906i
$629$	−0.630853	−	2.76395i	−0.0251538	−	0.110206i
$630$		0			0
$631$	−0.318104	+	1.39370i	−0.0126635	+	0.0554824i	−0.980865	−	0.194690i	$-0.937630\pi$
$631$	−0.318104	+	1.39370i	−0.0126635	+	0.0554824i	0.968201	+	0.250172i	$0.0804872\pi$
$632$	−3.72221	−	1.14815i	−0.148061	−	0.0456709i
$633$	−19.9227	+	50.7623i	−0.791857	+	2.01762i
$634$	10.0809	−	9.35368i	0.400362	−	0.371482i
$635$	−1.44310	+	0.983886i	−0.0572675	+	0.0390443i
$636$	−14.7278			−0.583995
$637$		0			0
$638$	21.5592			0.853537
$639$	−12.7299	+	8.67912i	−0.503588	+	0.343341i
$640$	−3.96952	+	3.68317i	−0.156909	+	0.145590i
$641$	−8.64566	+	22.0288i	−0.341483	+	0.870084i	0.652219	+	0.758030i	$0.273838\pi$
$641$	−8.64566	+	22.0288i	−0.341483	+	0.870084i	−0.993702	+	0.112054i	$0.964257\pi$
$642$	34.8998	+	10.7652i	1.37739	+	0.424868i
$643$	1.85767	−	8.13897i	0.0732592	−	0.320969i	−0.924999	−	0.379970i	$-0.875934\pi$
$643$	1.85767	−	8.13897i	0.0732592	−	0.320969i	0.998258	+	0.0590007i	$0.0187914\pi$
$644$		0			0
$645$	−1.75845	−	7.70428i	−0.0692390	−	0.303356i
$646$	0.123165	−	1.64352i	0.00484586	−	0.0646635i
$647$	1.74068	−	0.536928i	0.0684331	−	0.0211088i	−0.260350	−	0.965514i	$-0.583838\pi$
$647$	1.74068	−	0.536928i	0.0684331	−	0.0211088i	0.328783	+	0.944406i	$0.393362\pi$
$648$	4.06444	+	54.2362i	0.159666	+	2.13060i
$649$	6.75330	+	17.2071i	0.265090	+	0.675439i
$650$	14.7633	+	7.10963i	0.579064	+	0.278863i
$651$		0			0
$652$	−1.27833	+	0.615610i	−0.0500632	+	0.0241092i
$653$	5.11394	+	4.74505i	0.200124	+	0.185688i	0.773868	−	0.633346i	$-0.218319\pi$
$653$	5.11394	+	4.74505i	0.200124	+	0.185688i	−0.573744	+	0.819035i	$0.694510\pi$
$654$	−96.7268	−	14.5792i	−3.78232	−	0.570092i
$655$	−1.78647	−	3.09426i	−0.0698033	−	0.120903i
$656$	−14.6746	+	25.4172i	−0.572948	+	0.992375i
$657$	66.2031	−	83.0160i	2.58283	−	3.23876i
$658$		0			0
$659$	−29.5248	−	37.0229i	−1.15012	−	1.44221i	−0.877171	−	0.480178i	$-0.840572\pi$
$659$	−29.5248	−	37.0229i	−1.15012	−	1.44221i	−0.272950	−	0.962028i	$-0.587999\pi$
$660$	1.40209	−	0.211331i	0.0545763	−	0.00822605i
$661$	10.8524	+	7.39904i	0.422109	+	0.287789i	0.755687	−	0.654934i	$-0.227303\pi$
$661$	10.8524	+	7.39904i	0.422109	+	0.287789i	−0.333577	+	0.942723i	$0.608256\pi$
$662$	41.1058	+	28.0255i	1.59762	+	1.08924i
$663$	−4.54027	+	0.684335i	−0.176329	+	0.0265774i
$664$	8.54259	+	10.7121i	0.331517	+	0.415709i
$665$		0			0
$666$	−30.7854	+	38.6037i	−1.19291	+	1.49586i
$667$	1.94564	−	3.36995i	0.0753356	−	0.130485i
$668$	−1.54320	−	2.67290i	−0.0597082	−	0.103418i
$669$	68.6390	+	10.3457i	2.65374	+	0.399987i
$670$	0.821473	+	0.762216i	0.0317363	+	0.0294470i
$671$	18.9695	−	9.13524i	0.732310	−	0.352662i
$672$		0			0
$673$	9.88389	+	4.75983i	0.380996	+	0.183478i	0.614572	−	0.788860i	$-0.289329\pi$
$673$	9.88389	+	4.75983i	0.380996	+	0.183478i	−0.233576	+	0.972338i	$0.575043\pi$
$674$	16.2994	+	41.5303i	0.627830	+	1.59969i
$675$	5.05963	+	67.5160i	0.194745	+	2.59869i
$676$	−4.02492	+	1.24152i	−0.154804	+	0.0477509i
$677$	−1.06853	+	14.2586i	−0.0410670	+	0.548001i	0.938288	+	0.345854i	$0.112411\pi$
$677$	−1.06853	+	14.2586i	−0.0410670	+	0.548001i	−0.979355	+	0.202147i	$0.935208\pi$
$678$	−3.80246	−	16.6597i	−0.146033	−	0.639810i
$679$		0			0
$680$	0.139759	−	0.612326i	0.00535953	−	0.0234816i
$681$	51.9423	+	16.0221i	1.99043	+	0.613967i
$682$	−4.34932	+	11.0819i	−0.166544	+	0.424347i
$683$	20.6344	−	19.1459i	0.789554	−	0.732599i	−0.178337	−	0.983969i	$-0.557072\pi$
$683$	20.6344	−	19.1459i	0.789554	−	0.732599i	0.967891	+	0.251371i	$0.0808813\pi$
$684$	−4.74515	+	3.23519i	−0.181435	+	0.123701i
$685$	5.33457			0.203823
$686$		0			0
$687$	−64.8651			−2.47476
$688$	−24.2834	+	16.5562i	−0.925797	+	0.631198i
$689$	14.3589	−	13.3232i	0.547032	−	0.507572i
$690$	0.467324	−	1.19072i	0.0177907	−	0.0453300i
$691$	10.9397	+	3.37446i	0.416166	+	0.128370i	0.495765	−	0.868457i	$-0.334888\pi$
$691$	10.9397	+	3.37446i	0.416166	+	0.128370i	−0.0795987	+	0.996827i	$0.525364\pi$
$692$	1.83212	−	8.02705i	0.0696468	−	0.305143i
$693$		0			0
$694$	2.51111	+	11.0019i	0.0953206	+	0.417627i
$695$	0.0492981	−	0.657838i	0.00186998	−	0.0249532i
$696$	−44.7831	+	13.8138i	−1.69750	+	0.523609i
$697$	−0.307968	−	4.10955i	−0.0116651	−	0.155660i
$698$	−17.0574	−	43.4616i	−0.645633	−	1.64505i
$699$	−2.56035	−	1.23300i	−0.0968414	−	0.0466363i
$700$		0			0
$701$	9.58967	−	4.61814i	0.362197	−	0.174425i	−0.243930	−	0.969793i	$-0.578437\pi$
$701$	9.58967	−	4.61814i	0.362197	−	0.174425i	0.606127	+	0.795368i	$0.292722\pi$
$702$	34.6834	+	32.1815i	1.30904	+	1.21461i
$703$	6.56785	+	0.989944i	0.247711	+	0.0373364i
$704$	5.68493	+	9.84659i	0.214259	+	0.371107i
$705$	−3.50187	+	6.06541i	−0.131888	+	0.228437i
$706$	16.0412	−	20.1150i	0.603717	−	0.757037i
$707$		0			0
$708$	8.35638	+	10.4786i	0.314052	+	0.393809i
$709$	−15.0214	+	2.26411i	−0.564141	+	0.0850306i	−0.424920	−	0.905231i	$-0.639698\pi$
$709$	−15.0214	+	2.26411i	−0.564141	+	0.0850306i	−0.139221	+	0.990261i	$0.544460\pi$
$710$	−1.08790	−	0.741717i	−0.0408281	−	0.0278362i
$711$	−9.97069	−	6.79790i	−0.373930	−	0.254941i
$712$	30.0550	−	4.53006i	1.12636	−	0.169771i
$713$	1.33972	+	1.67995i	0.0501728	+	0.0629147i
$714$		0			0
$715$	−1.17580	+	1.47441i	−0.0439724	+	0.0551396i
$716$	4.04392	−	7.00427i	0.151128	−	0.261762i
$717$	3.85950	+	6.68485i	0.144136	+	0.249650i
$718$	−41.0218	−	6.18305i	−1.53092	−	0.230749i
$719$	−14.6926	−	13.6327i	−0.547940	−	0.508414i	0.356913	−	0.934138i	$-0.383829\pi$
$719$	−14.6926	−	13.6327i	−0.547940	−	0.508414i	−0.904853	+	0.425723i	$0.860020\pi$
$720$	−12.4850	+	6.01247i	−0.465289	+	0.224072i
$721$		0			0
$722$	−23.5889	−	11.3598i	−0.877889	−	0.422769i
$723$	−24.5106	−	62.4519i	−0.911558	−	2.32261i
$724$	0.279970	+	3.73594i	0.0104050	+	0.138845i
$725$	−28.4285	+	8.76902i	−1.05581	+	0.325673i
$726$	−2.30902	+	30.8118i	−0.0856958	+	1.14353i
$727$	−11.1011	−	48.6369i	−0.411716	−	1.80384i	−0.576021	−	0.817435i	$-0.695395\pi$
$727$	−11.1011	−	48.6369i	−0.411716	−	1.80384i	0.164305	−	0.986410i	$-0.447462\pi$
$728$		0			0
$729$	−7.47016	+	32.7289i	−0.276673	+	1.21218i
$730$	8.67112	+	2.67469i	0.320933	+	0.0989946i
$731$	1.50770	−	3.84157i	0.0557645	−	0.142086i
$732$	11.1906	−	10.3833i	0.413616	−	0.383779i
$733$	8.11028	−	5.52950i	0.299560	−	0.204237i	−0.404207	−	0.914668i	$-0.632452\pi$
$733$	8.11028	−	5.52950i	0.299560	−	0.204237i	0.703767	+	0.710431i	$0.251500\pi$
$734$	−33.2685			−1.22796
$735$		0			0
$736$	−1.75333			−0.0646286
$737$	3.27275	−	2.23132i	0.120553	−	0.0821918i
$738$	−52.6142	+	48.8189i	−1.93676	+	1.79705i
$739$	−9.27165	+	23.6238i	−0.341063	+	0.869014i	0.652712	+	0.757606i	$0.273631\pi$
$739$	−9.27165	+	23.6238i	−0.341063	+	0.869014i	−0.993775	+	0.111408i	$0.964464\pi$
$740$	−0.806746	−	0.248848i	−0.0296566	−	0.00914785i
$741$	2.39372	−	10.4876i	0.0879356	−	0.385271i
$742$		0			0
$743$	2.74476	+	12.0256i	0.100696	+	0.441176i	0.999993	+	0.00383783i	$0.00122162\pi$
$743$	2.74476	+	12.0256i	0.100696	+	0.441176i	−0.899297	+	0.437338i	$0.855921\pi$
$744$	1.93391	−	25.8062i	0.0709005	−	0.946102i
$745$	3.44199	−	1.06171i	0.126105	−	0.0388981i
$746$	0.489841	+	6.53647i	0.0179344	+	0.239317i
$747$	15.5075	+	39.5125i	0.567390	+	1.44569i
$748$	0.667148	+	0.321281i	0.0243933	+	0.0117472i
$749$		0			0
$750$	−17.9089	+	8.62447i	−0.653941	+	0.314921i
$751$	22.4960	+	20.8732i	0.820889	+	0.761674i	0.974003	−	0.226534i	$-0.0727396\pi$
$751$	22.4960	+	20.8732i	0.820889	+	0.761674i	−0.153114	+	0.988209i	$0.548930\pi$
$752$	25.7571	+	3.88225i	0.939263	+	0.141571i
$753$	−42.5112	−	73.6315i	−1.54919	−	2.68328i
$754$	−10.3950	+	18.0046i	−0.378563	+	0.655690i
$755$	−2.26649	+	2.84209i	−0.0824861	+	0.103434i
$756$		0			0
$757$	−7.11089	−	8.91678i	−0.258450	−	0.324086i	0.635630	−	0.771994i	$-0.280741\pi$
$757$	−7.11089	−	8.91678i	−0.258450	−	0.324086i	−0.894079	+	0.447908i	$0.852169\pi$
$758$	−30.7897	+	4.64079i	−1.11833	+	0.168561i
$759$	−3.73571	−	2.54697i	−0.135598	−	0.0924490i
$760$	1.21579	+	0.828913i	0.0441014	+	0.0300678i
$761$	−14.7945	+	2.22991i	−0.536299	+	0.0808341i	−0.411607	−	0.911361i	$-0.635032\pi$
$761$	−14.7945	+	2.22991i	−0.536299	+	0.0808341i	−0.124692	+	0.992195i	$0.539794\pi$
$762$	13.9490	+	17.4915i	0.505320	+	0.633651i
$763$		0			0
$764$	−6.89767	+	8.64941i	−0.249549	+	0.312925i
$765$	0.972888	−	1.68509i	0.0351748	−	0.0609246i
$766$	−3.56098	−	6.16780i	−0.128663	−	0.222852i
$767$	−17.6263	−	2.65674i	−0.636448	−	0.0959291i
$768$	26.6857	+	24.7607i	0.962936	+	0.893474i
$769$	−6.62237	+	3.18917i	−0.238809	+	0.115004i	−0.549461	−	0.835519i	$-0.685167\pi$
$769$	−6.62237	+	3.18917i	−0.238809	+	0.115004i	0.310652	+	0.950524i	$0.399453\pi$
$770$		0			0
$771$	32.6405	+	15.7188i	1.17552	+	0.566100i
$772$	−3.84165	−	9.78836i	−0.138264	−	0.352291i
$773$	−3.11733	−	41.5979i	−0.112123	−	1.49617i	−0.715441	−	0.698673i	$-0.753774\pi$
$773$	−3.11733	−	41.5979i	−0.112123	−	1.49617i	0.603318	−	0.797501i	$-0.293845\pi$
$774$	−68.6815	+	21.1854i	−2.46870	+	0.761494i
$775$	1.22765	−	16.3819i	0.0440986	−	0.588455i
$776$	5.06334	+	22.1839i	0.181763	+	0.796357i
$777$		0			0
$778$	8.84981	−	38.7736i	0.317281	−	1.39010i
$779$	9.22609	+	2.84587i	0.330559	+	0.101964i
$780$	−0.499544	+	1.27282i	−0.0178865	+	0.0455742i
$781$	−3.41166	+	3.16556i	−0.122079	+	0.113273i
$782$	0.551929	−	0.376299i	0.0197369	−	0.0134564i
$783$	−85.9020			−3.06989
$784$		0			0
$785$	−2.67109			−0.0953354
$786$	−37.8143	+	25.7814i	−1.34879	+	0.919592i
$787$	−16.7505	+	15.5421i	−0.597089	+	0.554018i	−0.919754	−	0.392496i	$-0.871612\pi$
$787$	−16.7505	+	15.5421i	−0.597089	+	0.554018i	0.322665	+	0.946513i	$0.395421\pi$
$788$	2.72654	−	6.94711i	0.0971289	−	0.247480i
$789$	−68.5698	−	21.1510i	−2.44115	−	0.752995i
$790$	0.229484	−	1.00544i	0.00816469	−	0.0357718i
$791$		0			0
$792$	8.60374	+	37.6954i	0.305721	+	1.33945i
$793$	−1.51727	+	20.2466i	−0.0538799	+	0.718977i
$794$	35.7681	−	11.0330i	1.26936	−	0.391546i
$795$	0.873626	+	11.6577i	0.0309843	+	0.413457i
$796$	−1.99848	−	5.09204i	−0.0708342	−	0.180483i
$797$	44.6791	+	21.5163i	1.58261	+	0.762147i	0.998764	−	0.0497137i	$-0.0158309\pi$
$797$	44.6791	+	21.5163i	1.58261	+	0.762147i	0.583851	+	0.811861i	$0.301545\pi$
$798$		0			0
$799$	−3.29532	+	1.58694i	−0.116580	+	0.0561420i
$800$	9.82641	+	9.11758i	0.347416	+	0.322355i
$801$	93.1107	+	14.0342i	3.28990	+	0.495873i
$802$	−10.5387	−	18.2536i	−0.372135	−	0.644557i
$803$	16.0372	−	27.7773i	0.565942	−	0.980241i
$804$	1.79064	−	2.24539i	0.0631509	−	0.0791887i
$805$		0			0
$806$	−7.15770	−	8.97547i	−0.252119	−	0.316147i
$807$	−63.3545	+	9.54915i	−2.23018	+	0.336146i
$808$	24.2861	+	16.5580i	0.854382	+	0.582508i
$809$	17.9228	+	12.2195i	0.630130	+	0.429616i	0.835821	−	0.549001i	$-0.184992\pi$
$809$	17.9228	+	12.2195i	0.630130	+	0.429616i	−0.205691	+	0.978617i	$0.565944\pi$
$810$	−14.2388	+	2.14615i	−0.500300	+	0.0754081i
$811$	−12.7005	−	15.9259i	−0.445974	−	0.559233i	0.507133	−	0.861868i	$-0.330705\pi$
$811$	−12.7005	−	15.9259i	−0.445974	−	0.559233i	−0.953107	+	0.302634i	$0.902134\pi$
$812$		0			0
$813$	20.5142	−	25.7240i	0.719464	−	0.902180i
$814$	−7.45756	+	12.9169i	−0.261387	+	0.452736i
$815$	0.563112	+	0.975338i	0.0197249	+	0.0341646i
$816$	−10.0779	−	1.51899i	−0.352796	−	0.0531754i
$817$	7.08755	+	6.57628i	0.247962	+	0.230075i
$818$	46.9656	−	22.6174i	1.64211	−	0.790800i
$819$		0			0
$820$	−1.10570	−	0.532475i	−0.0386126	−	0.0185948i
$821$	−8.64479	−	22.0266i	−0.301705	−	0.768732i	−0.998667	−	0.0516237i	$-0.983560\pi$
$821$	−8.64479	−	22.0266i	−0.301705	−	0.768732i	0.696961	−	0.717109i	$-0.254535\pi$
$822$	−5.10646	−	68.1409i	−0.178108	−	2.37669i
$823$	2.21680	−	0.683793i	0.0772728	−	0.0238355i	−0.255878	−	0.966709i	$-0.582364\pi$
$823$	2.21680	−	0.683793i	0.0772728	−	0.0238355i	0.333151	+	0.942874i	$0.391888\pi$
$824$	−0.241514	+	3.22279i	−0.00841355	+	0.112271i
$825$	7.69193	+	33.7005i	0.267799	+	1.17330i
$826$		0			0
$827$	−5.58131	+	24.4533i	−0.194081	+	0.850326i	0.780297	+	0.625409i	$0.215068\pi$
$827$	−5.58131	+	24.4533i	−0.194081	+	0.850326i	−0.974378	+	0.224916i	$0.927789\pi$
$828$	−2.22431	−	0.686108i	−0.0773000	−	0.0238439i
$829$	3.93834	−	10.0347i	0.136784	−	0.348520i	−0.846025	−	0.533142i	$-0.821011\pi$
$829$	3.93834	−	10.0347i	0.136784	−	0.348520i	0.982810	+	0.184622i	$0.0591062\pi$
$830$	−2.65914	+	2.46732i	−0.0923000	+	0.0856419i
$831$	−20.8878	+	14.2410i	−0.724588	+	0.494016i
$832$	−10.9642			−0.380115
$833$		0			0
$834$	−8.45005			−0.292601
$835$	−2.02418	+	1.38006i	−0.0700497	+	0.0477591i
$836$	−1.27172	+	1.17998i	−0.0439833	+	0.0408105i
$837$	17.3297	−	44.1554i	0.599003	−	1.52623i
$838$	59.5769	+	18.3771i	2.05805	+	0.634825i
$839$	−1.66884	+	7.31166i	−0.0576147	+	0.252426i	−0.995531	−	0.0944351i	$-0.969896\pi$
$839$	−1.66884	+	7.31166i	−0.0576147	+	0.252426i	0.937916	+	0.346862i	$0.112753\pi$
$840$		0			0
$841$	−1.94614	−	8.52662i	−0.0671084	−	0.294021i
$842$	0.387773	−	5.17447i	0.0133635	−	0.178324i
$843$	−35.3390	+	10.9007i	−1.21714	+	0.375438i
$844$	0.633753	+	8.45684i	0.0218147	+	0.291097i
$845$	1.22147	+	3.11226i	0.0420199	+	0.107065i
$846$	57.3926	+	27.6388i	1.97320	+	0.950241i
$847$		0			0
$848$	39.1728	−	18.8646i	1.34520	−	0.647814i
$849$	−19.0571	−	17.6824i	−0.654038	−	0.606858i
$850$	−5.05005	−	0.761173i	−0.173215	−	0.0261080i
$851$	1.34604	+	2.33141i	0.0461416	+	0.0799195i
$852$	−1.68722	+	2.92236i	−0.0578034	+	0.100118i
$853$	−6.28444	+	7.88043i	−0.215175	+	0.269821i	−0.877691	−	0.479227i	$-0.840917\pi$
$853$	−6.28444	+	7.88043i	−0.215175	+	0.269821i	0.662516	+	0.749048i	$0.269489\pi$
$854$		0			0
$855$	2.84227	+	3.56410i	0.0972037	+	0.121890i
$856$	−16.8384	+	2.53799i	−0.575526	+	0.0867466i
$857$	−35.7245	−	24.3566i	−1.22033	−	0.832004i	−0.230332	−	0.973112i	$-0.573981\pi$
$857$	−35.7245	−	24.3566i	−1.22033	−	0.832004i	−0.989994	+	0.141108i	$0.954933\pi$
$858$	19.9588	+	13.6077i	0.681382	+	0.464558i
$859$	50.0098	−	7.53777i	1.70631	−	0.257185i	0.777807	−	0.628503i	$-0.216332\pi$
$859$	50.0098	−	7.53777i	1.70631	−	0.257185i	0.928506	+	0.371318i	$0.121094\pi$
$860$	−0.766237	−	0.960830i	−0.0261285	−	0.0327640i
$861$		0			0
$862$	−6.84979	+	8.58936i	−0.233305	+	0.292555i
$863$	8.61615	−	14.9236i	0.293297	−	0.508006i	−0.681290	−	0.732013i	$-0.738581\pi$
$863$	8.61615	−	14.9236i	0.293297	−	0.508006i	0.974587	+	0.224008i	$0.0719141\pi$
$864$	19.3528	+	33.5200i	0.658396	+	1.14037i
$865$	−6.46245	−	0.974058i	−0.219730	−	0.0331190i
$866$	13.0223	+	12.0829i	0.442516	+	0.410594i
$867$	−47.9782	+	23.1051i	−1.62943	+	0.784690i
$868$		0			0
$869$	−3.28428	−	1.58163i	−0.111412	−	0.0536530i
$870$	−4.53309	−	11.5501i	−0.153686	−	0.391586i
$871$	0.285446	+	3.80901i	0.00967196	+	0.129063i
$872$	43.5822	−	13.4433i	1.47588	−	0.455248i
$873$	−5.26799	+	70.2964i	−0.178294	+	2.37917i
$874$	0.348251	+	1.52579i	0.0117798	+	0.0516105i
$875$		0			0
$876$	5.17490	−	22.6727i	0.174844	−	0.766040i
$877$	34.5556	+	10.6590i	1.16686	+	0.359929i	0.816869	−	0.576824i	$-0.195708\pi$
$877$	34.5556	+	10.6590i	1.16686	+	0.359929i	0.349992	+	0.936753i	$0.386184\pi$
$878$	17.3851	−	44.2965i	0.586718	−	1.49493i
$879$	11.5757	−	10.7406i	0.390437	−	0.362273i
$880$	−3.45857	+	2.35801i	−0.116588	+	0.0794886i
$881$	23.7204			0.799162			0.399581	−	0.916698i	$-0.369156\pi$
$881$	23.7204			0.799162			0.399581	+	0.916698i	$0.369156\pi$
$882$		0			0
$883$	−44.4089			−1.49448			−0.747240	−	0.664554i	$-0.768621\pi$
$883$	−44.4089			−1.49448			−0.747240	+	0.664554i	$0.768621\pi$
$884$	−0.589982	+	0.402243i	−0.0198432	+	0.0135289i
$885$	7.79858	−	7.23603i	0.262146	−	0.243236i
$886$	7.65579	−	19.5066i	0.257201	−	0.655338i
$887$	6.52505	+	2.01271i	0.219090	+	0.0675802i	0.402357	−	0.915483i	$-0.368191\pi$
$887$	6.52505	+	2.01271i	0.219090	+	0.0675802i	−0.183267	+	0.983063i	$0.558667\pi$
$888$	7.21465	−	31.6094i	0.242108	−	1.06074i
$889$		0			0
$890$	1.79065	+	7.84536i	0.0600228	+	0.262977i
$891$	−3.80360	+	50.7555i	−0.127425	+	1.70037i
$892$	10.3154	−	3.18189i	0.345386	−	0.106537i
$893$	−0.640364	−	8.54506i	−0.0214290	−	0.285950i
$894$	−16.8565	−	42.9498i	−0.563767	−	1.43646i
$895$	−5.78408	−	2.78547i	−0.193340	−	0.0931079i
$896$		0			0
$897$	3.92825	−	1.89174i	0.131160	−	0.0631635i
$898$	−42.4384	−	39.3771i	−1.41619	−	1.31403i
$899$	20.6102	+	3.10649i	0.687388	+	0.103607i
$900$	8.89810	+	15.4120i	0.296603	+	0.513732i
$901$	−3.05252	+	5.28711i	−0.101694	+	0.176139i
$902$	−13.5179	+	16.9509i	−0.450096	+	0.564403i
$903$		0			0
$904$	4.96756	+	6.22912i	0.165219	+	0.207178i
$905$	2.94056	−	0.443217i	0.0977474	−	0.0147330i
$906$	38.4729	+	26.2304i	1.27818	+	0.871446i
$907$	6.18242	+	4.21510i	0.205284	+	0.139960i	0.661598	−	0.749858i	$-0.269878\pi$
$907$	6.18242	+	4.21510i	0.205284	+	0.139960i	−0.456314	+	0.889819i	$0.650831\pi$
$908$	8.35898	−	1.25991i	0.277403	−	0.0418117i
$909$	56.7760	+	71.1948i	1.88314	+	2.36138i
$910$		0			0
$911$	−18.6126	+	23.3394i	−0.616662	+	0.773270i	−0.987871	−	0.155280i	$-0.950372\pi$
$911$	−18.6126	+	23.3394i	−0.616662	+	0.773270i	0.371208	+	0.928550i	$0.378944\pi$
$912$	11.9388	−	20.6786i	0.395332	−	0.684736i
$913$	6.41098	+	11.1041i	0.212173	+	0.367494i
$914$	−13.1483	−	1.98179i	−0.434907	−	0.0655517i
$915$	−8.88269	−	8.24193i	−0.293653	−	0.272470i
$916$	−9.08856	+	4.37682i	−0.300294	+	0.144614i
$917$		0			0
$918$	−13.2861	−	6.39825i	−0.438506	−	0.211174i
$919$	11.7153	+	29.8500i	0.386451	+	0.984660i	0.983249	+	0.182269i	$0.0583441\pi$
$919$	11.7153	+	29.8500i	0.386451	+	0.984660i	−0.596798	+	0.802391i	$0.703561\pi$
$920$	0.0445692	+	0.594735i	0.00146940	+	0.0196078i
$921$	17.1371	−	5.28610i	0.564687	−	0.174183i
$922$	2.45916	−	32.8152i	0.0809882	−	1.08071i
$923$	−0.998674	−	4.37547i	−0.0328717	−	0.144021i
$924$		0			0
$925$	4.57988	−	20.0658i	0.150586	−	0.659759i
$926$	−2.50625	−	0.773077i	−0.0823606	−	0.0254049i
$927$	−3.65788	+	9.32012i	−0.120140	+	0.306113i
$928$	−12.4674	+	11.5680i	−0.409262	+	0.379739i
$929$	−7.60515	+	5.18511i	−0.249517	+	0.170118i	−0.681620	−	0.731707i	$-0.738724\pi$
$929$	−7.60515	+	5.18511i	−0.249517	+	0.170118i	0.432103	+	0.901824i	$0.357772\pi$
$930$	6.85151			0.224670
$931$		0			0
$932$	−0.441940			−0.0144762
$933$	53.7857	−	36.6705i	1.76086	−	1.20054i
$934$	39.4689	−	36.6218i	1.29146	−	1.19830i
$935$	0.214735	−	0.547135i	0.00702258	−	0.0178932i
$936$	−35.6288	−	10.9900i	−1.16456	−	0.359220i
$937$	−4.81044	+	21.0759i	−0.157150	+	0.688520i	0.833549	+	0.552446i	$0.186305\pi$
$937$	−4.81044	+	21.0759i	−0.157150	+	0.688520i	−0.990699	+	0.136074i	$0.956552\pi$
$938$		0			0
$939$	−8.72770	−	38.2385i	−0.284818	−	1.24787i
$940$	−0.0813953	+	1.08614i	−0.00265482	+	0.0354261i
$941$	−54.3410	+	16.7620i	−1.77147	+	0.546425i	−0.996348	−	0.0853898i	$-0.972786\pi$
$941$	−54.3410	+	16.7620i	−1.77147	+	0.546425i	−0.775119	+	0.631815i	$0.782310\pi$
$942$	2.55687	+	34.1191i	0.0833074	+	1.11166i
$943$	1.42968	+	3.64276i	0.0465567	+	0.118625i
$944$	−35.6480	−	17.1672i	−1.16024	−	0.558744i
$945$		0			0
$946$	−19.5613	+	9.42020i	−0.635991	+	0.306277i
$947$	−23.9289	−	22.2028i	−0.777584	−	0.721493i	0.187833	−	0.982201i	$-0.439854\pi$
$947$	−23.9289	−	22.2028i	−0.777584	−	0.721493i	−0.965418	+	0.260708i	$0.916044\pi$
$948$	−2.61351	−	0.393923i	−0.0848828	−	0.0127940i
$949$	15.4650	+	26.7862i	0.502016	+	0.869518i
$950$	5.98257	−	10.3621i	0.194100	−	0.336191i
$951$	−17.4423	+	21.8720i	−0.565606	+	0.709247i
$952$		0			0
$953$	−28.0427	−	35.1645i	−0.908393	−	1.13909i	−0.989808	−	0.142409i	$-0.954515\pi$
$953$	−28.0427	−	35.1645i	−0.908393	−	1.13909i	0.0814149	−	0.996680i	$-0.474056\pi$
$954$	105.140	−	15.8473i	3.40403	−	0.513076i
$955$	7.25556	+	4.94675i	0.234784	+	0.160073i
$956$	0.991838	+	0.676224i	0.0320783	+	0.0218706i
$957$	−43.3677	+	6.53663i	−1.40188	+	0.211299i
$958$	−24.7659	−	31.0555i	−0.800151	−	1.00336i
$959$		0			0
$960$	4.07988	−	5.11601i	0.131678	−	0.165119i
$961$	9.74533	−	16.8794i	0.314366	−	0.544497i
$962$	−7.19147	−	12.4560i	−0.231862	−	0.401597i
$963$	−52.1657	−	7.86271i	−1.68102	−	0.253372i
$964$	−7.64828	−	7.09657i	−0.246335	−	0.228565i
$965$	−7.52006	+	3.62147i	−0.242079	+	0.116579i
$966$		0			0
$967$	21.8585	+	10.5265i	0.702922	+	0.338509i	0.750970	−	0.660336i	$-0.229586\pi$
$967$	21.8585	+	10.5265i	0.702922	+	0.338509i	−0.0480488	+	0.998845i	$0.515300\pi$
$968$	−5.26322	−	13.4105i	−0.169166	−	0.431028i
$969$	0.250552	+	3.34339i	0.00804891	+	0.107405i
$970$	−5.75673	+	1.77572i	−0.184837	+	0.0570148i
$971$	2.05228	−	27.3858i	0.0658608	−	0.878852i	−0.862235	−	0.506509i	$-0.830936\pi$
$971$	2.05228	−	27.3858i	0.0658608	−	0.878852i	0.928095	−	0.372343i	$-0.121445\pi$
$972$	3.54272	+	15.5217i	0.113633	+	0.497858i
$973$		0			0
$974$	−8.14216	+	35.6731i	−0.260892	+	1.14304i
$975$	−31.8529	−	9.82532i	−1.02011	−	0.314662i
$976$	−16.4647	+	41.9513i	−0.527021	+	1.34283i
$977$	−7.76406	+	7.20400i	−0.248394	+	0.230476i	−0.794537	−	0.607216i	$-0.792286\pi$
$977$	−7.76406	+	7.20400i	−0.248394	+	0.230476i	0.546142	+	0.837692i	$0.316096\pi$
$978$	11.9194	−	8.12651i	0.381141	−	0.259857i
$979$	28.4439			0.909070
$980$		0			0
$981$	141.295			4.51121
$982$	21.9957	−	14.9964i	0.701912	−	0.478556i
$983$	−30.9237	+	28.6930i	−0.986312	+	0.915163i	−0.996399	−	0.0847858i	$-0.972979\pi$
$983$	−30.9237	+	28.6930i	−0.986312	+	0.915163i	0.0100877	+	0.999949i	$0.496789\pi$
$984$	17.2185	−	43.8720i	0.548906	−	1.39859i
$985$	−5.66069	−	1.74609i	−0.180364	−	0.0556351i
$986$	1.44187	−	6.31723i	0.0459184	−	0.201182i
$987$		0			0
$988$	−0.372261	−	1.63098i	−0.0118432	−	0.0518885i
$989$	−0.292849	+	3.90779i	−0.00931204	+	0.124261i
$990$	−9.78196	+	3.01734i	−0.310891	+	0.0958972i
$991$	3.66005	+	48.8399i	0.116265	+	1.55145i	0.684763	+	0.728766i	$0.259906\pi$
$991$	3.66005	+	48.8399i	0.116265	+	1.55145i	−0.568497	+	0.822685i	$0.692475\pi$
$992$	−3.43107	−	8.74221i	−0.108936	−	0.277565i
$993$	−91.1841	−	43.9119i	−2.89364	−	1.39350i
$994$		0			0
$995$	−3.91204	+	1.88394i	−0.124020	+	0.0597249i
$996$	6.81492	+	6.32332i	0.215939	+	0.200362i
$997$	−35.6515	−	5.37360i	−1.12909	−	0.170183i	−0.442183	−	0.896925i	$-0.645796\pi$
$997$	−35.6515	−	5.37360i	−1.12909	−	0.170183i	−0.686911	+	0.726742i	$0.741034\pi$
$998$	6.70505	+	11.6135i	0.212245	+	0.367619i
$999$	29.7144	−	51.4669i	0.940122	−	1.62834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.g.i.30.2		48
7.2	even	3		343.2.e.d.197.6		48
7.3	odd	6		343.2.g.g.116.2		48
7.4	even	3		49.2.g.a.32.2	yes	48
7.5	odd	6		343.2.e.c.197.6		48
7.6	odd	2		343.2.g.h.30.2		48
21.11	odd	6		441.2.bb.d.424.3		48
28.11	odd	6		784.2.bg.c.81.4		48
49.2	even	21		2401.2.a.h.1.7		24
49.4	even	21	inner	343.2.g.i.263.2		48
49.22	even	7		49.2.g.a.23.2	✓	48
49.23	even	21		343.2.e.d.148.6		48
49.26	odd	42		343.2.e.c.148.6		48
49.27	odd	14		343.2.g.g.275.2		48
49.45	odd	42		343.2.g.h.263.2		48
49.47	odd	42		2401.2.a.i.1.7		24
147.71	odd	14		441.2.bb.d.415.3		48
196.71	odd	14		784.2.bg.c.513.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.2	✓	48	49.22	even	7
49.2.g.a.32.2	yes	48	7.4	even	3
343.2.e.c.148.6		48	49.26	odd	42
343.2.e.c.197.6		48	7.5	odd	6
343.2.e.d.148.6		48	49.23	even	21
343.2.e.d.197.6		48	7.2	even	3
343.2.g.g.116.2		48	7.3	odd	6
343.2.g.g.275.2		48	49.27	odd	14
343.2.g.h.30.2		48	7.6	odd	2
343.2.g.h.263.2		48	49.45	odd	42
343.2.g.i.30.2		48	1.1	even	1	trivial
343.2.g.i.263.2		48	49.4	even	21	inner
441.2.bb.d.415.3		48	147.71	odd	14
441.2.bb.d.424.3		48	21.11	odd	6
784.2.bg.c.81.4		48	28.11	odd	6
784.2.bg.c.513.4		48	196.71	odd	14
2401.2.a.h.1.7		24	49.2	even	21
2401.2.a.i.1.7		24	49.47	odd	42

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30646 + 0.890730i) q^{2} +(2.35796 - 2.18787i) q^{3} +(0.182757 - 0.465658i) q^{4} +(-0.379430 - 0.117039i) q^{5} +(-1.13178 + 4.95867i) q^{6} +(-0.527696 - 2.31199i) q^{8} +(0.549024 - 7.32622i) q^{9} +O(q^{10})\)	\(q+(-1.30646 + 0.890730i) q^{2} +(2.35796 - 2.18787i) q^{3} +(0.182757 - 0.465658i) q^{4} +(-0.379430 - 0.117039i) q^{5} +(-1.13178 + 4.95867i) q^{6} +(-0.527696 - 2.31199i) q^{8} +(0.549024 - 7.32622i) q^{9} +(0.599961 - 0.185063i) q^{10} +(-0.165845 - 2.21305i) q^{11} +(-0.587864 - 1.49785i) q^{12} +(1.92814 + 0.928542i) q^{13} +(-1.15075 + 0.554171i) q^{15} +(3.48217 + 3.23098i) q^{16} +(-0.659554 - 0.0994118i) q^{17} +(5.80840 + 10.0604i) q^{18} +(0.781344 - 1.35333i) q^{19} +(-0.123844 + 0.155295i) q^{20} +(2.18790 + 2.74354i) q^{22} +(0.626297 - 0.0943991i) q^{23} +(-6.30262 - 4.29705i) q^{24} +(-4.00092 - 2.72778i) q^{25} +(-3.34612 + 0.504346i) q^{26} +(-8.71761 - 10.9315i) q^{27} +(3.83058 - 4.80339i) q^{29} +(1.00979 - 1.74901i) q^{30} +(1.69627 + 2.93803i) q^{31} +(-2.73733 - 0.412586i) q^{32} +(-5.23292 - 4.85544i) q^{33} +(0.950231 - 0.457607i) q^{34} +(-3.31117 - 1.59458i) q^{36} +(1.55284 + 3.95658i) q^{37} +(0.184654 + 2.46404i) q^{38} +(6.57801 - 2.02905i) q^{39} +(-0.0703683 + 0.938999i) q^{40} +(1.37484 + 6.02357i) q^{41} +(-1.37677 + 6.03200i) q^{43} +(-1.06083 - 0.327224i) q^{44} +(-1.06577 + 2.71553i) q^{45} +(-0.734148 + 0.681190i) q^{46} +(4.53069 - 3.08897i) q^{47} +15.2798 q^{48} +7.65677 q^{50} +(-1.77270 + 1.20861i) q^{51} +(0.784765 - 0.728155i) q^{52} +(3.34394 - 8.52021i) q^{53} +(21.1263 + 6.51659i) q^{54} +(-0.196086 + 0.859108i) q^{55} +(-1.11852 - 4.90058i) q^{57} +(-0.725974 + 9.68745i) q^{58} +(-7.95929 + 2.45512i) q^{59} +(0.0477466 + 0.637134i) q^{60} +(3.46607 + 8.83141i) q^{61} +(-4.83310 - 2.32750i) q^{62} +(-4.61591 + 2.22291i) q^{64} +(-0.622919 - 0.577984i) q^{65} +(11.1615 + 1.68232i) q^{66} +(0.892421 + 1.54572i) q^{67} +(-0.166830 + 0.288959i) q^{68} +(1.27025 - 1.59285i) q^{69} +(-1.30754 - 1.63960i) q^{71} +(-17.2279 + 2.59668i) q^{72} +(11.9415 + 8.14156i) q^{73} +(-5.55296 - 3.78595i) q^{74} +(-15.4021 + 2.32149i) q^{75} +(-0.487392 - 0.611170i) q^{76} +(-6.78657 + 8.51010i) q^{78} +(0.821284 - 1.42251i) q^{79} +(-0.943091 - 1.63348i) q^{80} +(-22.6785 - 3.41823i) q^{81} +(-7.16155 - 6.64495i) q^{82} +(-5.20544 + 2.50681i) q^{83} +(0.238620 + 0.114913i) q^{85} +(-3.57419 - 9.10690i) q^{86} +(-1.47684 - 19.7070i) q^{87} +(-5.02903 + 1.55125i) q^{88} +(-0.957805 + 12.7810i) q^{89} +(-1.02642 - 4.49705i) q^{90} +(0.0705027 - 0.308892i) q^{92} +(10.4278 + 3.21654i) q^{93} +(-3.16773 + 8.07124i) q^{94} +(-0.454857 + 0.422046i) q^{95} +(-7.35721 + 5.01606i) q^{96} -9.59518 q^{97} -16.3043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9	\( 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9} + 7 q^{10} - 3 q^{11} - 63 q^{12} - 14 q^{13} - 12 q^{15} + 18 q^{16} + 14 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 20 q^{22} - 27 q^{23} - 77 q^{24} + 17 q^{25} - 21 q^{26} + 7 q^{27} + 12 q^{29} + 11 q^{30} + 35 q^{31} - 60 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 6 q^{37} + 35 q^{38} + 35 q^{39} + 105 q^{40} - 42 q^{41} - 30 q^{43} + 13 q^{44} - 35 q^{45} + 69 q^{46} - 42 q^{47} - 84 q^{48} + 40 q^{50} + 53 q^{51} - 7 q^{52} - 31 q^{53} + 70 q^{54} - 7 q^{55} - 12 q^{57} - 47 q^{58} + 35 q^{59} - 91 q^{60} - 14 q^{61} - 28 q^{62} - 32 q^{64} + 35 q^{65} - 35 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 19 q^{71} - 124 q^{72} - 35 q^{73} + 13 q^{74} - 119 q^{75} + 119 q^{76} + 28 q^{78} + 15 q^{79} + 70 q^{80} - 125 q^{81} - 98 q^{82} - 26 q^{85} + 9 q^{86} + 35 q^{87} + 49 q^{88} - 14 q^{89} - 182 q^{90} - 38 q^{92} + 46 q^{93} + 14 q^{94} + 128 q^{95} + 98 q^{96} - 16 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9 + 7 * q^10 - 3 * q^11 - 63 * q^12 - 14 * q^13 - 12 * q^15 + 18 * q^16 + 14 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 20 * q^22 - 27 * q^23 - 77 * q^24 + 17 * q^25 - 21 * q^26 + 7 * q^27 + 12 * q^29 + 11 * q^30 + 35 * q^31 - 60 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 6 * q^37 + 35 * q^38 + 35 * q^39 + 105 * q^40 - 42 * q^41 - 30 * q^43 + 13 * q^44 - 35 * q^45 + 69 * q^46 - 42 * q^47 - 84 * q^48 + 40 * q^50 + 53 * q^51 - 7 * q^52 - 31 * q^53 + 70 * q^54 - 7 * q^55 - 12 * q^57 - 47 * q^58 + 35 * q^59 - 91 * q^60 - 14 * q^61 - 28 * q^62 - 32 * q^64 + 35 * q^65 - 35 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 19 * q^71 - 124 * q^72 - 35 * q^73 + 13 * q^74 - 119 * q^75 + 119 * q^76 + 28 * q^78 + 15 * q^79 + 70 * q^80 - 125 * q^81 - 98 * q^82 - 26 * q^85 + 9 * q^86 + 35 * q^87 + 49 * q^88 - 14 * q^89 - 182 * q^90 - 38 * q^92 + 46 * q^93 + 14 * q^94 + 128 * q^95 + 98 * q^96 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more