LMFDB - Embedded newform 210.2.t.e.89.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,2,Mod(59,210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("210.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$210 = 2 \cdot 3 \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	210.t (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81$ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.3
Root			$1.72286 + 0.178197i$ of defining polynomial
Character	$\chi$	$=$	210.89
Dual form			210.2.t.e.59.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.01575 - 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 0.358719i) q^{5} +(0.707107 + 1.58114i) q^{6} +(-1.41421 + 2.23607i) q^{7} +1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +(-0.792893 + 2.09077i) q^{10} +(4.05781 - 2.34278i) q^{11} +(-1.72286 - 0.178197i) q^{12} -1.04456 q^{13} +(-1.22938 - 2.34278i) q^{14} +(1.73861 - 3.46081i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.73861 - 1.58114i) q^{17} +(2.93649 + 0.614017i) q^{18} +(-1.23861 - 0.715113i) q^{19} +(-1.41421 - 1.73205i) q^{20} +(1.70058 + 4.25535i) q^{21} +4.68556i q^{22} +(-2.23861 + 3.87739i) q^{23} +(1.01575 - 1.40294i) q^{24} +(4.74264 - 1.58346i) q^{25} +(0.522278 - 0.904612i) q^{26} +(-4.94975 - 1.58114i) q^{27} +(2.64360 + 0.106711i) q^{28} +6.92163i q^{29} +(2.12785 + 3.23609i) q^{30} +(-5.73861 + 3.31319i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.834952 - 8.07256i) q^{33} +3.16228i q^{34} +(-2.31920 + 5.44255i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(-2.30615 - 1.33146i) q^{37} +(1.23861 - 0.715113i) q^{38} +(-1.06101 + 1.46545i) q^{39} +(2.20711 - 0.358719i) q^{40} +1.04456 q^{41} +(-4.53553 - 0.654929i) q^{42} +6.92163i q^{43} +(-4.05781 - 2.34278i) q^{44} +(-3.08932 - 5.95450i) q^{45} +(-2.23861 - 3.87739i) q^{46} +(-9.71584 - 5.60944i) q^{47} +(0.707107 + 1.58114i) q^{48} +(-3.00000 - 6.32456i) q^{49} +(-1.00000 + 4.89898i) q^{50} +(0.563508 - 5.44816i) q^{51} +(0.522278 + 0.904612i) q^{52} +(-2.50000 - 4.33013i) q^{53} +(3.84418 - 3.49604i) q^{54} +(8.11562 - 6.62638i) q^{55} +(-1.41421 + 2.23607i) q^{56} +(-2.26139 + 1.01132i) q^{57} +(-5.99430 - 3.46081i) q^{58} +(5.28720 + 9.15769i) q^{59} +(-3.86646 + 0.224724i) q^{60} +(3.00000 + 1.73205i) q^{61} -6.62638i q^{62} +(7.69738 + 1.93657i) q^{63} +1.00000 q^{64} +(-2.30545 + 0.374703i) q^{65} +(6.57357 + 4.75937i) q^{66} +(-12.3583 + 7.13505i) q^{67} +(-2.73861 - 1.58114i) q^{68} +(3.16588 + 7.07912i) q^{69} +(-3.55378 - 4.72976i) q^{70} -6.92163i q^{71} +(-0.936492 - 2.85008i) q^{72} +(-1.75166 - 3.03397i) q^{73} +(2.30615 - 1.33146i) q^{74} +(2.59584 - 8.26206i) q^{75} +1.43023i q^{76} +(-0.500000 + 12.3867i) q^{77} +(-0.738613 - 1.65159i) q^{78} +(-5.73861 + 9.93957i) q^{79} +(-0.792893 + 2.09077i) q^{80} +(-7.24597 + 5.33816i) q^{81} +(-0.522278 + 0.904612i) q^{82} +4.06775i q^{83} +(2.83495 - 3.60042i) q^{84} +(5.47723 - 4.47214i) q^{85} +(-5.99430 - 3.46081i) q^{86} +(9.71064 + 7.03066i) q^{87} +(4.05781 - 2.34278i) q^{88} +(2.45877 - 4.25871i) q^{89} +(6.70141 + 0.301824i) q^{90} +(1.47723 - 2.33570i) q^{91} +4.47723 q^{92} +(-1.18080 + 11.4163i) q^{93} +(9.71584 - 5.60944i) q^{94} +(-2.99028 - 1.13402i) q^{95} +(-1.72286 - 0.178197i) q^{96} +11.9886 q^{97} +(6.97723 + 0.564201i) q^{98} +(-10.4772 - 9.37112i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 4 q^{2} - 4 q^{4} + 12 q^{5} + 8 q^{8} + 8 q^{9} - 12 q^{10} - 8 q^{15} - 4 q^{16} + 8 q^{18} + 12 q^{19} + 4 q^{21} + 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{35}+ \cdots - 40 q^{99}+O(q^{100})$ 8 * q - 4 * q^2 - 4 * q^4 + 12 * q^5 + 8 * q^8 + 8 * q^9 - 12 * q^10 - 8 * q^15 - 4 * q^16 + 8 * q^18 + 12 * q^19 + 4 * q^21 + 4 * q^23 + 4 * q^25 + 4 * q^30 - 24 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^35 - 16 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^40 - 8 * q^42 + 24 * q^45 + 4 * q^46 - 12 * q^47 - 24 * q^49 - 8 * q^50 + 20 * q^51 - 20 * q^53 - 40 * q^57 + 4 * q^60 + 24 * q^61 + 20 * q^63 + 8 * q^64 + 16 * q^65 + 12 * q^66 - 8 * q^70 + 8 * q^72 - 24 * q^75 - 4 * q^77 + 16 * q^78 - 24 * q^79 - 12 * q^80 + 4 * q^81 + 4 * q^84 + 12 * q^87 - 32 * q^91 - 8 * q^92 - 20 * q^93 + 12 * q^94 + 12 * q^95 + 12 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$ .

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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

)

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.01575	−	1.40294i	0.586445	−	0.809989i
$3$	1.01575	−	1.40294i	0.586445	−	0.809989i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$6$	0.707107	+	1.58114i	0.288675	+	0.645497i
$7$	−1.41421	+	2.23607i	−0.534522	+	0.845154i
$7$	−1.41421	+	2.23607i	−0.534522	+	0.845154i
$8$	1.00000			0.353553
$9$	−0.936492	−	2.85008i	−0.312164	−	0.950028i
$10$	−0.792893	+	2.09077i	−0.250735	+	0.661160i
$11$	4.05781	−	2.34278i	1.22348	−	0.706374i	0.257819	−	0.966193i	$-0.416996\pi$
$11$	4.05781	−	2.34278i	1.22348	−	0.706374i	0.965657	+	0.259819i	$0.0836628\pi$
$12$	−1.72286	−	0.178197i	−0.497347	−	0.0514410i
$13$	−1.04456			−0.289708			−0.144854	−	0.989453i	$-0.546271\pi$
$13$	−1.04456			−0.289708			−0.144854	+	0.989453i	$0.546271\pi$
$14$	−1.22938	−	2.34278i	−0.328567	−	0.626134i
$15$	1.73861	−	3.46081i	0.448908	−	0.893578i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.73861	−	1.58114i	0.664211	−	0.383482i	−0.129668	−	0.991557i	$-0.541391\pi$
$17$	2.73861	−	1.58114i	0.664211	−	0.383482i	0.793880	+	0.608075i	$0.208058\pi$
$18$	2.93649	+	0.614017i	0.692138	+	0.144725i
$19$	−1.23861	−	0.715113i	−0.284157	−	0.164058i	0.351147	−	0.936320i	$-0.385792\pi$
$19$	−1.23861	−	0.715113i	−0.284157	−	0.164058i	−0.635304	+	0.772262i	$0.719125\pi$
$20$	−1.41421	−	1.73205i	−0.316228	−	0.387298i
$21$	1.70058	+	4.25535i	0.371097	+	0.928594i
$22$			4.68556i			0.998964i
$23$	−2.23861	+	3.87739i	−0.466783	+	0.808492i	−0.999280	−	0.0379400i	$-0.987920\pi$
$23$	−2.23861	+	3.87739i	−0.466783	+	0.808492i	0.532497	+	0.846432i	$0.321254\pi$
$24$	1.01575	−	1.40294i	0.207340	−	0.286374i
$25$	4.74264	−	1.58346i	0.948528	−	0.316693i
$26$	0.522278	−	0.904612i	0.102427	−	0.177409i
$27$	−4.94975	−	1.58114i	−0.952579	−	0.304290i
$28$	2.64360	+	0.106711i	0.499593	+	0.0201665i
$29$			6.92163i			1.28531i	0.766154	+	0.642657i	$0.222168\pi$
$29$			6.92163i			1.28531i	−0.766154	+	0.642657i	$0.777832\pi$
$30$	2.12785	+	3.23609i	0.388490	+	0.590826i
$31$	−5.73861	+	3.31319i	−1.03069	+	0.595066i	−0.917181	−	0.398471i	$-0.869541\pi$
$31$	−5.73861	+	3.31319i	−1.03069	+	0.595066i	−0.113504	+	0.993537i	$0.536208\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.834952	−	8.07256i	0.145347	−	1.40525i
$34$			3.16228i			0.542326i
$35$	−2.31920	+	5.44255i	−0.392016	+	0.919958i
$36$	−2.00000	+	2.23607i	−0.333333	+	0.372678i
$37$	−2.30615	−	1.33146i	−0.379129	−	0.218890i	0.298310	−	0.954469i	$-0.403577\pi$
$37$	−2.30615	−	1.33146i	−0.379129	−	0.218890i	−0.677439	+	0.735579i	$0.736910\pi$
$38$	1.23861	−	0.715113i	0.200930	−	0.116007i
$39$	−1.06101	+	1.46545i	−0.169898	+	0.234660i
$40$	2.20711	−	0.358719i	0.348974	−	0.0567185i
$41$	1.04456			0.163132			0.0815661	−	0.996668i	$-0.474008\pi$
$41$	1.04456			0.163132			0.0815661	+	0.996668i	$0.474008\pi$
$42$	−4.53553	−	0.654929i	−0.699848	−	0.101058i
$43$			6.92163i			1.05554i	0.849388	+	0.527769i	$0.176971\pi$
$43$			6.92163i			1.05554i	−0.849388	+	0.527769i	$0.823029\pi$
$44$	−4.05781	−	2.34278i	−0.611738	−	0.353187i
$45$	−3.08932	−	5.95450i	−0.460528	−	0.887645i
$46$	−2.23861	−	3.87739i	−0.330065	−	0.571690i
$47$	−9.71584	−	5.60944i	−1.41720	−	0.818221i	−0.421149	−	0.906992i	$-0.638373\pi$
$47$	−9.71584	−	5.60944i	−1.41720	−	0.818221i	−0.996052	+	0.0887705i	$0.971706\pi$
$48$	0.707107	+	1.58114i	0.102062	+	0.228218i
$49$	−3.00000	−	6.32456i	−0.428571	−	0.903508i
$50$	−1.00000	+	4.89898i	−0.141421	+	0.692820i
$51$	0.563508	−	5.44816i	0.0789069	−	0.762895i
$52$	0.522278	+	0.904612i	0.0724269	+	0.125447i
$53$	−2.50000	−	4.33013i	−0.343401	−	0.594789i	0.641661	−	0.766989i	$-0.278246\pi$
$53$	−2.50000	−	4.33013i	−0.343401	−	0.594789i	−0.985062	+	0.172200i	$0.944912\pi$
$54$	3.84418	−	3.49604i	0.523127	−	0.475750i
$55$	8.11562	−	6.62638i	1.09431	−	0.893501i
$56$	−1.41421	+	2.23607i	−0.188982	+	0.298807i
$57$	−2.26139	+	1.01132i	−0.299528	+	0.133953i
$58$	−5.99430	−	3.46081i	−0.787091	−	0.454427i
$59$	5.28720	+	9.15769i	0.688334	+	1.19223i	0.972376	+	0.233418i	$0.0749911\pi$
$59$	5.28720	+	9.15769i	0.688334	+	1.19223i	−0.284042	+	0.958812i	$0.591676\pi$
$60$	−3.86646	+	0.224724i	−0.499158	+	0.0290117i
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	0.679605	−	0.733578i	$-0.262151\pi$
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	−0.295495	+	0.955344i	$0.595484\pi$
$62$		−	6.62638i		−	0.841551i
$63$	7.69738	+	1.93657i	0.969779	+	0.243985i
$64$	1.00000			0.125000
$65$	−2.30545	+	0.374703i	−0.285956	+	0.0464761i
$66$	6.57357	+	4.75937i	0.809150	+	0.585838i
$67$	−12.3583	+	7.13505i	−1.50980	+	0.871685i	−0.509868	+	0.860253i	$0.670306\pi$
$67$	−12.3583	+	7.13505i	−1.50980	+	0.871685i	−0.999935	+	0.0114319i	$0.996361\pi$
$68$	−2.73861	−	1.58114i	−0.332106	−	0.191741i
$69$	3.16588	+	7.07912i	0.381127	+	0.852225i
$70$	−3.55378	−	4.72976i	−0.424758	−	0.565314i
$71$		−	6.92163i		−	0.821446i	−0.911760	−	0.410723i	$-0.865276\pi$
$71$		−	6.92163i		−	0.821446i	0.911760	−	0.410723i	$-0.134724\pi$
$72$	−0.936492	−	2.85008i	−0.110367	−	0.335886i
$73$	−1.75166	−	3.03397i	−0.205017	−	0.355099i	0.745121	−	0.666929i	$-0.232392\pi$
$73$	−1.75166	−	3.03397i	−0.205017	−	0.355099i	−0.950138	+	0.311830i	$0.899058\pi$
$74$	2.30615	−	1.33146i	0.268084	−	0.154779i
$75$	2.59584	−	8.26206i	0.299742	−	0.954020i
$76$			1.43023i			0.164058i
$77$	−0.500000	+	12.3867i	−0.0569803	+	1.41160i
$78$	−0.738613	−	1.65159i	−0.0836314	−	0.187006i
$79$	−5.73861	+	9.93957i	−0.645644	+	1.11829i	0.338508	+	0.940964i	$0.390078\pi$
$79$	−5.73861	+	9.93957i	−0.645644	+	1.11829i	−0.984152	+	0.177325i	$0.943256\pi$
$80$	−0.792893	+	2.09077i	−0.0886482	+	0.233755i
$81$	−7.24597	+	5.33816i	−0.805107	+	0.593129i
$82$	−0.522278	+	0.904612i	−0.0576760	+	0.0998977i
$83$			4.06775i			0.446494i	0.974762	+	0.223247i	$0.0716656\pi$
$83$			4.06775i			0.446494i	−0.974762	+	0.223247i	$0.928334\pi$
$84$	2.83495	−	3.60042i	0.309319	−	0.392838i
$85$	5.47723	−	4.47214i	0.594089	−	0.485071i
$86$	−5.99430	−	3.46081i	−0.646382	−	0.373189i
$87$	9.71064	+	7.03066i	1.04109	+	0.753766i
$88$	4.05781	−	2.34278i	0.432564	−	0.249741i
$89$	2.45877	−	4.25871i	0.260629	−	0.451423i	−0.705780	−	0.708431i	$-0.749403\pi$
$89$	2.45877	−	4.25871i	0.260629	−	0.451423i	0.966409	+	0.257008i	$0.0827367\pi$
$90$	6.70141	+	0.301824i	0.706391	+	0.0318150i
$91$	1.47723	−	2.33570i	0.154855	−	0.244848i
$92$	4.47723			0.466783
$93$	−1.18080	+	11.4163i	−0.122443	+	1.18382i
$94$	9.71584	−	5.60944i	1.00211	−	0.578570i
$95$	−2.99028	−	1.13402i	−0.306796	−	0.116348i
$96$	−1.72286	−	0.178197i	−0.175839	−	0.0181872i
$97$	11.9886			1.21726			0.608629	−	0.793455i	$-0.291720\pi$
$97$	11.9886			1.21726			0.608629	+	0.793455i	$0.291720\pi$
$98$	6.97723	+	0.564201i	0.704806	+	0.0569930i
$99$	−10.4772	−	9.37112i	−1.05300	−	0.941833i
$100$	−3.74264	−	3.31552i	−0.374264	−	0.331552i
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	−0.997244	−	0.0741967i	$-0.976361\pi$
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	0.434366	−	0.900737i	$-0.356973\pi$
$102$	4.43649	+	3.21209i	0.439278	+	0.318045i
$103$	2.45877	−	4.25871i	0.242270	−	0.419624i	−0.719091	−	0.694916i	$-0.755441\pi$
$103$	2.45877	−	4.25871i	0.242270	−	0.419624i	0.961360	+	0.275293i	$0.0887748\pi$
$104$	−1.04456			−0.102427
$105$	5.27984	+	8.78198i	0.515260	+	0.857034i
$106$	5.00000			0.485643
$107$	2.73861	−	4.74342i	0.264752	−	0.458563i	−0.702747	−	0.711440i	$-0.748043\pi$
$107$	2.73861	−	4.74342i	0.264752	−	0.458563i	0.967499	+	0.252877i	$0.0813767\pi$
$108$	1.10557	+	5.07718i	0.106383	+	0.488552i
$109$	10.2158	+	17.6944i	0.978500	+	1.69481i	0.667866	+	0.744282i	$0.267208\pi$
$109$	10.2158	+	17.6944i	0.978500	+	1.69481i	0.310634	+	0.950529i	$0.399459\pi$
$110$	1.68080	+	10.3415i	0.160258	+	0.986026i
$111$	−4.21043	+	1.88296i	−0.399637	+	0.178723i
$112$	−1.22938	−	2.34278i	−0.116166	−	0.221372i
$113$	17.4772			1.64412			0.822060	−	0.569402i	$-0.192825\pi$
$113$	17.4772			1.64412			0.822060	+	0.569402i	$0.192825\pi$
$114$	0.254862	−	2.46408i	0.0238700	−	0.230782i
$115$	−3.54996	+	9.36085i	−0.331036	+	0.872904i
$116$	5.99430	−	3.46081i	0.556557	−	0.321328i
$117$	0.978218	+	2.97707i	0.0904363	+	0.275231i
$118$	−10.5744			−0.973452
$119$	−0.337449	+	8.35979i	−0.0309339	+	0.766341i
$120$	1.73861	−	3.46081i	0.158713	−	0.315928i
$121$	5.47723	−	9.48683i	0.497930	−	0.862439i
$122$	−3.00000	+	1.73205i	−0.271607	+	0.156813i
$123$	1.06101	−	1.46545i	0.0956682	−	0.132135i
$124$	5.73861	+	3.31319i	0.515343	+	0.297533i
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$	−5.52581	+	5.69784i	−0.492278	+	0.507604i
$127$		−	8.73085i		−	0.774738i	−0.921925	−	0.387369i	$-0.873384\pi$
$127$		−	8.73085i		−	0.774738i	0.921925	−	0.387369i	$-0.126616\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	9.71064	+	7.03066i	0.854974	+	0.619015i
$130$	0.828222	−	2.18393i	0.0726398	−	0.191543i
$131$	6.88624	−	11.9273i	0.601654	−	1.04209i	−0.390917	−	0.920426i	$-0.627842\pi$
$131$	6.88624	−	11.9273i	0.601654	−	1.04209i	0.992571	−	0.121669i	$-0.0388245\pi$
$132$	−7.40852	+	3.31319i	−0.644829	+	0.288376i
$133$	3.35071	−	1.75830i	0.290543	−	0.152464i
$134$		−	14.2701i		−	1.23275i
$135$	−11.4918	−	1.71417i	−0.989057	−	0.147532i
$136$	2.73861	−	1.58114i	0.234834	−	0.135582i
$137$	1.73861	+	3.01137i	0.148540	+	0.257278i	0.930688	−	0.365814i	$-0.119209\pi$
$137$	1.73861	+	3.01137i	0.148540	+	0.257278i	−0.782148	+	0.623092i	$0.785876\pi$
$138$	−7.71363	−	0.797828i	−0.656628	−	0.0679156i
$139$		−	20.1810i		−	1.71173i	−0.517202	−	0.855863i	$-0.673026\pi$
$139$		−	20.1810i		−	1.71173i	0.517202	−	0.855863i	$-0.326974\pi$
$140$	5.87298	−	0.712788i	0.496358	−	0.0602416i
$141$	−17.7386	+	7.93295i	−1.49386	+	0.668075i
$142$	5.99430	+	3.46081i	0.503031	+	0.290425i
$143$	−4.23861	+	2.44716i	−0.354451	+	0.204642i
$144$	2.93649	+	0.614017i	0.244708	+	0.0511681i
$145$	2.48292	+	15.2768i	0.206195	+	1.26867i
$146$	3.50333			0.289937
$147$	−11.9202	−	2.21536i	−0.983165	−	0.182720i
$148$			2.66291i			0.218890i
$149$	2.12132	+	1.22474i	0.173785	+	0.100335i	0.584370	−	0.811488i	$-0.301342\pi$
$149$	2.12132	+	1.22474i	0.173785	+	0.100335i	−0.410584	+	0.911823i	$0.634675\pi$
$150$	5.85723	+	6.37909i	0.478241	+	0.520851i
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−1.23861	−	0.715113i	−0.100465	−	0.0580034i
$153$	−7.07107	−	6.32456i	−0.571662	−	0.511310i
$154$	−10.4772	−	6.62638i	−0.844279	−	0.533969i
$155$	−11.4772	+	9.37112i	−0.921873	+	0.752706i
$156$	1.79962	+	0.186137i	0.144085	+	0.0149029i
$157$	−7.22369	−	12.5118i	−0.576513	−	0.998550i	−0.995875	−	0.0907311i	$-0.971080\pi$
$157$	−7.22369	−	12.5118i	−0.576513	−	0.998550i	0.419362	−	0.907819i	$-0.362254\pi$
$158$	−5.73861	−	9.93957i	−0.456540	−	0.790750i
$159$	−8.61430	−	0.890985i	−0.683158	−	0.0706597i
$160$	−1.41421	−	1.73205i	−0.111803	−	0.136931i
$161$	−5.50423	−	10.4891i	−0.433794	−	0.826661i
$162$	−1.00000	−	8.94427i	−0.0785674	−	0.702728i
$163$	−12.7279	−	7.34847i	−0.996928	−	0.575577i	−0.0895899	−	0.995979i	$-0.528556\pi$
$163$	−12.7279	−	7.34847i	−0.996928	−	0.575577i	−0.907338	+	0.420402i	$0.861889\pi$
$164$	−0.522278	−	0.904612i	−0.0407831	−	0.0706383i
$165$	−1.05296	−	18.1165i	−0.0819725	−	1.41037i
$166$	−3.52277	−	2.03387i	−0.273420	−	0.157859i
$167$			4.29068i			0.332023i	0.986124	+	0.166011i	$0.0530889\pi$
$167$			4.29068i			0.332023i	−0.986124	+	0.166011i	$0.946911\pi$
$168$	1.70058	+	4.25535i	0.131203	+	0.328308i
$169$	−11.9089			−0.916069
$170$	1.13437	+	6.97948i	0.0870023	+	0.535302i
$171$	−0.878183	+	4.19985i	−0.0671564	+	0.321170i
$172$	5.99430	−	3.46081i	0.457061	−	0.263885i
$173$	0.977226	+	0.564201i	0.0742971	+	0.0428954i	0.536688	−	0.843781i	$-0.319675\pi$
$173$	0.977226	+	0.564201i	0.0742971	+	0.0428954i	−0.462391	+	0.886676i	$0.653008\pi$
$174$	−10.9441	+	4.89433i	−0.829666	+	0.371038i
$175$	−3.16637	+	12.8442i	−0.239355	+	0.970932i
$176$			4.68556i			0.353187i
$177$	18.2182	+	1.88433i	1.36936	+	0.141635i
$178$	2.45877	+	4.25871i	0.184293	+	0.319204i
$179$	−16.7857	+	9.69125i	−1.25462	+	0.724358i	−0.972024	−	0.234880i	$-0.924530\pi$
$179$	−16.7857	+	9.69125i	−1.25462	+	0.724358i	−0.282600	+	0.959238i	$0.591197\pi$
$180$	−3.61209	+	5.65268i	−0.269229	+	0.421326i
$181$		−	3.16228i		−	0.235050i	−0.993070	−	0.117525i	$-0.962504\pi$
$181$		−	3.16228i		−	0.235050i	0.993070	−	0.117525i	$-0.0374961\pi$
$182$	1.28416	+	2.44716i	0.0951884	+	0.181396i
$183$	5.47723	−	2.44949i	0.404888	−	0.181071i
$184$	−2.23861	+	3.87739i	−0.165033	+	0.285845i
$185$	−5.56754	−	2.11140i	−0.409333	−	0.155234i
$186$	−9.29642	−	6.73076i	−0.681647	−	0.493524i
$187$	7.40852	−	12.8319i	0.541764	−	0.938364i
$188$			11.2189i			0.818221i
$189$	10.5355	−	8.83190i	0.766347	−	0.642426i
$190$	2.47723	−	2.02265i	0.179717	−	0.146738i
$191$	14.1099	+	8.14637i	1.02096	+	0.589451i	0.914381	−	0.404854i	$-0.132678\pi$
$191$	14.1099	+	8.14637i	1.02096	+	0.589451i	0.106577	+	0.994304i	$0.466011\pi$
$192$	1.01575	−	1.40294i	0.0733057	−	0.101249i
$193$	−6.36396	+	3.67423i	−0.458088	+	0.264477i	−0.711240	−	0.702949i	$-0.751866\pi$
$193$	−6.36396	+	3.67423i	−0.458088	+	0.264477i	0.253152	+	0.967427i	$0.418533\pi$
$194$	−5.99430	+	10.3824i	−0.430366	+	0.745416i
$195$	−1.81608	+	3.61501i	−0.130052	+	0.258877i
$196$	−3.97723	+	5.76035i	−0.284088	+	0.411454i
$197$	9.00000			0.641223			0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000			0.641223			0.320612	+	0.947211i	$0.396112\pi$
$198$	13.3542	−	4.38799i	0.949044	−	0.311841i
$199$	13.4317	−	7.75478i	0.952146	−	0.549722i	0.0583993	−	0.998293i	$-0.481400\pi$
$199$	13.4317	−	7.75478i	0.952146	−	0.549722i	0.893747	+	0.448571i	$0.148067\pi$
$200$	4.74264	−	1.58346i	0.335355	−	0.111968i
$201$	−2.54289	+	24.5854i	−0.179361	+	1.73412i
$202$	11.3137			0.796030
$203$	−15.4772	−	9.78866i	−1.08629	−	0.687029i
$204$	−5.00000	+	2.23607i	−0.350070	+	0.156556i
$205$	2.30545	−	0.374703i	0.161019	−	0.0261704i
$206$	2.45877	+	4.25871i	0.171311	+	0.296719i
$207$	13.1473	+	2.74909i	0.913803	+	0.191075i
$208$	0.522278	−	0.904612i	0.0362135	−	0.0627236i
$209$	−6.70141			−0.463546
$210$	−10.2453	+	0.181486i	−0.706996	+	0.0125237i
$211$	24.4772			1.68508			0.842541	−	0.538632i	$-0.181059\pi$
$211$	24.4772			1.68508			0.842541	+	0.538632i	$0.181059\pi$
$212$	−2.50000	+	4.33013i	−0.171701	+	0.297394i
$213$	−9.71064	−	7.03066i	−0.665362	−	0.481733i
$214$	2.73861	+	4.74342i	0.187208	+	0.324253i
$215$	2.48292	+	15.2768i	0.169334	+	1.04187i
$216$	−4.94975	−	1.58114i	−0.336788	−	0.107583i
$217$	0.707107	−	17.5175i	0.0480015	−	1.18916i
$218$	−20.4317			−1.38381
$219$	−6.03574	−	0.624282i	−0.407857	−	0.0421851i
$220$	−9.79642	−	3.71515i	−0.660475	−	0.250475i
$221$	−2.86064	+	1.65159i	−0.192427	+	0.111098i
$222$	0.474523	−	4.58782i	0.0318479	−	0.307915i
$223$	21.8881			1.46574			0.732868	−	0.680371i	$-0.238181\pi$
$223$	21.8881			1.46574			0.732868	+	0.680371i	$0.238181\pi$
$224$	2.64360	+	0.106711i	0.176633	+	0.00712992i
$225$	−8.95445	−	12.0340i	−0.596963	−	0.802268i
$226$	−8.73861	+	15.1357i	−0.581284	+	1.00681i
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	−0.170648	−	0.985332i	$-0.554586\pi$
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	0.767999	+	0.640451i	$0.221253\pi$
$228$	2.00653	+	1.45276i	0.132885	+	0.0962112i
$229$	−11.7386	−	6.77729i	−0.775709	−	0.447856i	0.0591982	−	0.998246i	$-0.481146\pi$
$229$	−11.7386	−	6.77729i	−0.775709	−	0.447856i	−0.834908	+	0.550390i	$0.814479\pi$
$230$	−6.33175	−	7.75478i	−0.417503	−	0.511335i
$231$	16.8700	+	13.2833i	1.10996	+	0.873979i
$232$			6.92163i			0.454427i
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	−0.793047	−	0.609160i	$-0.791507\pi$
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	0.924072	+	0.382219i	$0.124840\pi$
$234$	−3.06733	−	0.641375i	−0.200518	−	0.0419280i
$235$	−23.4561	−	8.89538i	−1.53011	−	0.580270i
$236$	5.28720	−	9.15769i	0.344167	−	0.596115i
$237$	8.11562	+	18.1471i	0.527166	+	1.17878i
$238$	−7.07107	−	4.47214i	−0.458349	−	0.289886i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	2.12785	+	3.23609i	0.137352	+	0.208889i
$241$	−18.4545	+	10.6547i	−1.18876	+	0.686328i	−0.958024	−	0.286689i	$-0.907445\pi$
$241$	−18.4545	+	10.6547i	−1.18876	+	0.686328i	−0.230732	+	0.973017i	$0.574112\pi$
$242$	5.47723	+	9.48683i	0.352089	+	0.609837i
$243$	0.129018	+	15.5879i	0.00827648	+	0.999966i
$244$		−	3.46410i		−	0.221766i
$245$	−8.89006	−	12.8828i	−0.567965	−	0.823053i
$246$	0.738613	+	1.65159i	0.0470922	+	0.105301i
$247$	1.29380	+	0.746976i	0.0823226	+	0.0475290i
$248$	−5.73861	+	3.31319i	−0.364402	+	0.210388i
$249$	5.70682	+	4.13183i	0.361655	+	0.261844i
$250$	−0.449747	+	11.1713i	−0.0284445	+	0.706534i
$251$	8.85494			0.558919			0.279459	−	0.960158i	$-0.409845\pi$
$251$	8.85494			0.558919			0.279459	+	0.960158i	$0.409845\pi$
$252$	−2.17157	−	7.63441i	−0.136796	−	0.480923i
$253$			20.9783i			1.31889i
$254$	7.56114	+	4.36543i	0.474428	+	0.273911i
$255$	−0.710638	−	12.2268i	−0.0445019	−	0.765673i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.52277	−	5.49798i	−0.594014	−	0.342954i	0.172669	−	0.984980i	$-0.444761\pi$
$257$	−9.52277	−	5.49798i	−0.594014	−	0.342954i	−0.766683	+	0.642026i	$0.778094\pi$
$258$	−10.9441	+	4.89433i	−0.681347	+	0.304708i
$259$	6.23861	−	3.27374i	0.387649	−	0.203421i
$260$	1.47723	+	1.80922i	0.0916136	+	0.112203i
$261$	19.7272	−	6.48204i	1.22108	−	0.401229i
$262$	6.88624	+	11.9273i	0.425433	+	0.736872i
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	0.895209	−	0.445647i	$-0.147026\pi$
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	−0.833546	+	0.552450i	$0.813693\pi$
$264$	0.834952	−	8.07256i	0.0513878	−	0.496832i
$265$	−7.07107	−	8.66025i	−0.434372	−	0.531995i
$266$	−0.152621	+	3.78095i	−0.00935778	+	0.231825i
$267$	−3.47723	−	7.77531i	−0.212803	−	0.475841i
$268$	12.3583	+	7.13505i	0.754901	+	0.435842i
$269$	−8.79052	−	15.2256i	−0.535968	−	0.928323i	−0.999116	−	0.0420423i	$-0.986614\pi$
$269$	−8.79052	−	15.2256i	−0.535968	−	0.928323i	0.463148	−	0.886281i	$-0.346720\pi$
$270$	7.23042	−	9.09511i	0.440029	−	0.553511i
$271$	−5.47723	−	3.16228i	−0.332718	−	0.192095i	0.324329	−	0.945944i	$-0.394861\pi$
$271$	−5.47723	−	3.16228i	−0.332718	−	0.192095i	−0.657047	+	0.753850i	$0.728195\pi$
$272$			3.16228i			0.191741i
$273$	−1.77635	−	4.44495i	−0.107510	−	0.269021i
$274$	−3.47723			−0.210067
$275$	15.5350	−	17.5364i	0.936798	−	1.05748i
$276$	4.54776	−	6.28129i	0.273743	−	0.378089i
$277$	8.48528	−	4.89898i	0.509831	−	0.294351i	−0.222933	−	0.974834i	$-0.571563\pi$
$277$	8.48528	−	4.89898i	0.509831	−	0.294351i	0.732764	+	0.680483i	$0.238230\pi$
$278$	17.4772	+	10.0905i	1.04821	+	0.605187i
$279$	14.8170	+	13.2528i	0.887073	+	0.793422i
$280$	−2.31920	+	5.44255i	−0.138599	+	0.325254i
$281$		−	1.80922i		−	0.107929i	−0.998543	−	0.0539646i	$-0.982814\pi$
$281$		−	1.80922i		−	0.107929i	0.998543	−	0.0539646i	$-0.0171858\pi$
$282$	1.99917	−	19.3286i	0.119049	−	1.15100i
$283$	−4.61230	−	7.98873i	−0.274173	−	0.474881i	0.695753	−	0.718281i	$-0.255071\pi$
$283$	−4.61230	−	7.98873i	−0.274173	−	0.474881i	−0.969926	+	0.243400i	$0.921737\pi$
$284$	−5.99430	+	3.46081i	−0.355696	+	0.205361i
$285$	−4.62834	+	3.04330i	−0.274159	+	0.180270i
$286$		−	4.89433i		−	0.289408i
$287$	−1.47723	+	2.33570i	−0.0871979	+	0.137872i
$288$	−2.00000	+	2.23607i	−0.117851	+	0.131762i
$289$	−3.50000	+	6.06218i	−0.205882	+	0.356599i
$290$	−14.4715	−	5.48811i	−0.849797	−	0.322273i
$291$	12.1775	−	16.8193i	0.713856	−	0.985966i
$292$	−1.75166	+	3.03397i	−0.102508	+	0.177550i
$293$		−	8.05661i		−	0.470672i	−0.971914	−	0.235336i	$-0.924381\pi$
$293$		−	8.05661i		−	0.470672i	0.971914	−	0.235336i	$-0.0756190\pi$
$294$	7.87868	−	9.21555i	0.459494	−	0.537462i
$295$	14.9545	+	18.3154i	0.870682	+	1.06636i
$296$	−2.30615	−	1.33146i	−0.134042	−	0.0773893i
$297$	−23.7894	+	5.18020i	−1.38040	+	0.300586i
$298$	−2.12132	+	1.22474i	−0.122885	+	0.0709476i
$299$	2.33836	−	4.05015i	0.135231	−	0.234226i
$300$	−8.45307	+	1.88296i	−0.488038	+	0.108713i
$301$	−15.4772	−	9.78866i	−0.892092	−	0.564209i
$302$	−2.00000			−0.115087
$303$	−19.4919	−	2.01607i	−1.11978	−	0.115820i
$304$	1.23861	−	0.715113i	0.0710393	−	0.0410146i
$305$	7.24264	+	2.74666i	0.414712	+	0.157273i
$306$	9.01276	−	2.96145i	0.515225	−	0.169295i
$307$	−11.9886			−0.684226			−0.342113	−	0.939659i	$-0.611143\pi$
$307$	−11.9886			−0.684226			−0.342113	+	0.939659i	$0.611143\pi$
$308$	10.9772	−	5.76035i	0.625485	−	0.328227i
$309$	−3.47723	−	7.77531i	−0.197812	−	0.442322i
$310$	−2.37701	−	14.6251i	−0.135005	−	0.830651i
$311$	−8.79052	−	15.2256i	−0.498465	−	0.863366i	0.501534	−	0.865138i	$-0.332769\pi$
$311$	−8.79052	−	15.2256i	−0.498465	−	0.863366i	−0.999998	+	0.00177176i	$0.999436\pi$
$312$	−1.06101	+	1.46545i	−0.0600679	+	0.0829649i
$313$	−11.6190	+	20.1246i	−0.656742	+	1.13751i	0.324712	+	0.945813i	$0.394733\pi$
$313$	−11.6190	+	20.1246i	−0.656742	+	1.13751i	−0.981454	+	0.191697i	$0.938601\pi$
$314$	14.4474			0.815313
$315$	17.6836	+	1.51301i	0.996360	+	0.0852487i
$316$	11.4772			0.645644
$317$	4.95445	−	8.58136i	0.278270	−	0.481977i	−0.692685	−	0.721240i	$-0.743572\pi$
$317$	4.95445	−	8.58136i	0.278270	−	0.481977i	0.970955	+	0.239263i	$0.0769058\pi$
$318$	5.07877	−	7.01471i	0.284803	−	0.393365i
$319$	16.2158	+	28.0867i	0.907913	+	1.57255i
$320$	2.20711	−	0.358719i	0.123381	−	0.0200530i
$321$	−3.87298	−	8.66025i	−0.216169	−	0.483368i
$322$	11.8360	+	0.477769i	0.659594	+	0.0266250i
$323$	−4.52277			−0.251654
$324$	8.24597	+	3.60611i	0.458109	+	0.200339i
$325$	−4.95395	+	1.65402i	−0.274796	+	0.0917484i
$326$	12.7279	−	7.34847i	0.704934	−	0.406994i
$327$	35.2009	+	3.64086i	1.94662	+	0.201340i
$328$	1.04456			0.0576760
$329$	26.2834	−	13.7923i	1.44905	−	0.760396i
$330$	16.2158	+	8.14637i	0.892653	+	0.448443i
$331$	−10.7158	+	18.5604i	−0.588996	+	1.02017i	0.405369	+	0.914153i	$0.367143\pi$
$331$	−10.7158	+	18.5604i	−0.588996	+	1.02017i	−0.994364	+	0.106017i	$0.966190\pi$
$332$	3.52277	−	2.03387i	0.193337	−	0.111623i
$333$	−1.63507	+	7.81962i	−0.0896014	+	0.428512i
$334$	−3.71584	−	2.14534i	−0.203322	−	0.117388i
$335$	−24.7165	+	20.1810i	−1.35041	+	1.10260i
$336$	−4.53553	−	0.654929i	−0.247434	−	0.0357293i
$337$			17.1464i			0.934025i	0.884251	+	0.467013i	$0.154670\pi$
$337$			17.1464i			0.934025i	−0.884251	+	0.467013i	$0.845330\pi$
$338$	5.95445	−	10.3134i	0.323879	−	0.560976i
$339$	17.7525	−	24.5195i	0.964186	−	1.33172i
$340$	−6.61160	−	2.50735i	−0.358564	−	0.135980i
$341$	−15.5241	+	26.8886i	−0.840679	+	1.45610i
$342$	−3.19808	−	2.86045i	−0.172933	−	0.154676i
$343$	18.3848	+	2.23607i	0.992685	+	0.120736i
$344$			6.92163i			0.373189i
$345$	9.52684	+	14.4887i	0.512908	+	0.780045i
$346$	−0.977226	+	0.564201i	−0.0525360	+	0.0303317i
$347$	8.73861	+	15.1357i	0.469113	+	0.812528i	0.999377	−	0.0353049i	$-0.0112402\pi$
$347$	8.73861	+	15.1357i	0.469113	+	0.812528i	−0.530263	+	0.847833i	$0.677907\pi$
$348$	1.23341	−	11.9250i	0.0661179	−	0.639247i
$349$			11.7436i			0.628623i	0.949320	+	0.314311i	$0.101774\pi$
$349$			11.7436i			0.628623i	−0.949320	+	0.314311i	$0.898226\pi$
$350$	−9.54024	−	9.16427i	−0.509947	−	0.489851i
$351$	5.17029	+	1.65159i	0.275970	+	0.0881553i
$352$	−4.05781	−	2.34278i	−0.216282	−	0.124871i
$353$	0.522774	−	0.301824i	0.0278245	−	0.0160645i	−0.486023	−	0.873946i	$-0.661553\pi$
$353$	0.522774	−	0.301824i	0.0278245	−	0.0160645i	0.513848	+	0.857881i	$0.328220\pi$
$354$	−10.7410	+	14.8353i	−0.570876	+	0.788485i
$355$	−2.48292	−	15.2768i	−0.131780	−	0.810807i
$356$	−4.91754			−0.260629
$357$	11.3855	+	8.96491i	0.602587	+	0.474473i
$358$		−	19.3825i		−	1.02440i
$359$	−9.86729	−	5.69688i	−0.520775	−	0.300670i	0.216476	−	0.976288i	$-0.430544\pi$
$359$	−9.86729	−	5.69688i	−0.520775	−	0.300670i	−0.737252	+	0.675618i	$0.763877\pi$
$360$	−3.08932	−	5.95450i	−0.162821	−	0.313830i
$361$	−8.47723	−	14.6830i	−0.446170	−	0.772789i
$362$	2.73861	+	1.58114i	0.143938	+	0.0831028i
$363$	−7.74597	−	17.3205i	−0.406558	−	0.909091i
$364$	−2.76139	−	0.111466i	−0.144736	−	0.00584238i
$365$	−4.95445	−	6.06794i	−0.259328	−	0.317610i
$366$	−0.617292	+	5.96816i	−0.0322664	+	0.311961i
$367$	−0.184829	−	0.320133i	−0.00964798	−	0.0167108i	0.861161	−	0.508332i	$-0.169738\pi$
$367$	−0.184829	−	0.320133i	−0.00964798	−	0.0167108i	−0.870809	+	0.491621i	$0.836404\pi$
$368$	−2.23861	−	3.87739i	−0.116696	−	0.202123i
$369$	−0.978218	−	2.97707i	−0.0509240	−	0.154980i
$370$	4.61230	−	3.76593i	0.239782	−	0.195781i
$371$	13.2180	+	0.533554i	0.686244	+	0.0277008i
$372$	10.4772	−	4.68556i	0.543219	−	0.242935i
$373$	20.1042	+	11.6072i	1.04096	+	0.600997i	0.920104	−	0.391673i	$-0.128104\pi$
$373$	20.1042	+	11.6072i	1.04096	+	0.600997i	0.120853	+	0.992670i	$0.461437\pi$
$374$	7.40852	+	12.8319i	0.383085	+	0.663523i
$375$	2.76554	−	19.1664i	0.142812	−	0.989750i
$376$	−9.71584	−	5.60944i	−0.501056	−	0.289285i
$377$		−	7.23003i		−	0.372365i
$378$	2.38089	+	13.5400i	0.122460	+	0.696422i
$379$	−20.4772			−1.05184			−0.525922	−	0.850533i	$-0.676280\pi$
$379$	−20.4772			−1.05184			−0.525922	+	0.850533i	$0.676280\pi$
$380$	0.513050	+	3.15666i	0.0263189	+	0.161933i
$381$	−12.2489	−	8.86839i	−0.627529	−	0.454341i
$382$	−14.1099	+	8.14637i	−0.721927	+	0.416805i
$383$	15.7158	+	9.07354i	0.803042	+	0.463636i	0.844534	−	0.535502i	$-0.179878\pi$
$383$	15.7158	+	9.07354i	0.803042	+	0.463636i	−0.0414919	+	0.999139i	$0.513211\pi$
$384$	0.707107	+	1.58114i	0.0360844	+	0.0806872i
$385$	3.33981	+	27.5182i	0.170212	+	1.40246i
$386$		−	7.34847i		−	0.374027i
$387$	19.7272	−	6.48204i	1.00279	−	0.329501i
$388$	−5.99430	−	10.3824i	−0.304315	−	0.527088i
$389$	−6.36396	+	3.67423i	−0.322666	+	0.186291i	−0.652580	−	0.757720i	$-0.726313\pi$
$389$	−6.36396	+	3.67423i	−0.322666	+	0.186291i	0.329914	+	0.944011i	$0.392980\pi$
$390$	−2.22265	−	3.38028i	−0.112548	−	0.171167i
$391$			14.1582i			0.716012i
$392$	−3.00000	−	6.32456i	−0.151523	−	0.319438i
$393$	−9.73861	−	21.7762i	−0.491248	−	1.09846i
$394$	−4.50000	+	7.79423i	−0.226707	+	0.392668i
$395$	−9.10021	+	23.9962i	−0.457881	+	1.20738i
$396$	−2.87701	+	13.7591i	−0.144575	+	0.691421i
$397$	−7.44073	+	12.8877i	−0.373439	+	0.646816i	−0.990092	−	0.140419i	$-0.955155\pi$
$397$	−7.44073	+	12.8877i	−0.373439	+	0.646816i	0.616653	+	0.787235i	$0.288488\pi$
$398$			15.5096i			0.777424i
$399$	0.936697	−	6.48684i	0.0468935	−	0.324748i
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$	0.827520	+	0.477769i	0.0413244	+	0.0238586i	0.520520	−	0.853850i	$-0.325738\pi$
$401$	0.827520	+	0.477769i	0.0413244	+	0.0238586i	−0.479195	+	0.877708i	$0.659072\pi$
$402$	−20.0201	−	14.4949i	−0.998513	−	0.722939i
$403$	5.99430	−	3.46081i	0.298598	−	0.172395i
$404$	−5.65685	+	9.79796i	−0.281439	+	0.487467i
$405$	−14.0777	+	14.3812i	−0.699528	+	0.714606i
$406$	16.2158	−	8.50934i	0.804779	−	0.422312i
$407$	−12.4772			−0.618473
$408$	0.563508	−	5.44816i	0.0278978	−	0.269724i
$409$	13.4317	−	7.75478i	0.664154	−	0.383449i	−0.129704	−	0.991553i	$-0.541403\pi$
$409$	13.4317	−	7.75478i	0.664154	−	0.383449i	0.793858	+	0.608103i	$0.208069\pi$
$410$	−0.828222	+	2.18393i	−0.0409029	+	0.107856i
$411$	5.99077	+	0.619631i	0.295503	+	0.0305641i
$412$	−4.91754			−0.242270
$413$	−27.9545	−	1.12840i	−1.37555	−	0.0555251i
$414$	−8.95445	+	10.0114i	−0.440087	+	0.492033i
$415$	1.45918	+	8.97796i	0.0716284	+	0.440711i
$416$	0.522278	+	0.904612i	0.0256068	+	0.0443523i
$417$	−28.3127	−	20.4989i	−1.38648	−	1.00383i
$418$	3.35071	−	5.80359i	0.163888	−	0.283863i
$419$	−8.85494			−0.432592			−0.216296	−	0.976328i	$-0.569398\pi$
$419$	−8.85494			−0.432592			−0.216296	+	0.976328i	$0.569398\pi$
$420$	4.96550	−	8.96347i	0.242292	−	0.437373i
$421$	18.9545			0.923783			0.461892	−	0.886936i	$-0.347171\pi$
$421$	18.9545			0.923783			0.461892	+	0.886936i	$0.347171\pi$
$422$	−12.2386	+	21.1979i	−0.595766	+	1.03190i
$423$	−6.88858	+	32.9442i	−0.334934	+	1.60180i
$424$	−2.50000	−	4.33013i	−0.121411	−	0.210290i
$425$	10.4846	−	11.8353i	0.508577	−	0.574095i
$426$	10.9441	−	4.89433i	0.530241	−	0.237131i
$427$	−8.11562	+	4.25871i	−0.392743	+	0.206094i
$428$	−5.47723			−0.264752
$429$	−0.872155	+	8.43224i	−0.0421080	+	0.407112i
$430$	−14.4715	−	5.48811i	−0.697879	−	0.264660i
$431$	−6.63699	+	3.83187i	−0.319693	+	0.184575i	−0.651256	−	0.758858i	$-0.725757\pi$
$431$	−6.63699	+	3.83187i	−0.319693	+	0.184575i	0.331563	+	0.943433i	$0.392424\pi$
$432$	3.84418	−	3.49604i	0.184953	−	0.168203i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	14.8170	+	9.37112i	0.711240	+	0.449828i
$435$	23.9545	+	12.0340i	1.14853	+	0.576987i
$436$	10.2158	−	17.6944i	0.489250	−	0.847406i
$437$	5.54555	−	3.20172i	0.265280	−	0.153159i
$438$	3.55851	−	4.91496i	0.170032	−	0.234846i
$439$	−7.69306	−	4.44159i	−0.367170	−	0.211986i	0.305051	−	0.952336i	$-0.401326\pi$
$439$	−7.69306	−	4.44159i	−0.367170	−	0.211986i	−0.672221	+	0.740350i	$0.734660\pi$
$440$	8.11562	−	6.62638i	0.386897	−	0.315900i
$441$	−15.2160	+	14.4731i	−0.724574	+	0.689198i
$442$		−	3.30318i		−	0.157116i
$443$	7.52277	−	13.0298i	0.357418	−	0.619066i	−0.630111	−	0.776505i	$-0.716991\pi$
$443$	7.52277	−	13.0298i	0.357418	−	0.619066i	0.987529	+	0.157439i	$0.0503239\pi$
$444$	3.73591	+	2.70486i	0.177298	+	0.128367i
$445$	3.89908	−	10.2814i	0.184834	−	0.487387i
$446$	−10.9441	+	18.9557i	−0.518216	+	0.897576i
$447$	3.87298	−	1.73205i	0.183186	−	0.0819232i
$448$	−1.41421	+	2.23607i	−0.0668153	+	0.105644i
$449$		−	25.8773i		−	1.22122i	−0.791930	−	0.610612i	$-0.790923\pi$
$449$		−	25.8773i		−	1.22122i	0.791930	−	0.610612i	$-0.209077\pi$
$450$	14.8990	−	1.73777i	0.702346	−	0.0819192i
$451$	4.23861	−	2.44716i	0.199588	−	0.115232i
$452$	−8.73861	−	15.1357i	−0.411030	−	0.711924i
$453$	3.44572	+	0.356394i	0.161894	+	0.0167448i
$454$			10.3923i			0.487735i
$455$	2.42253	−	5.68505i	0.113570	−	0.266519i
$456$	−2.26139	+	1.01132i	−0.105899	+	0.0473595i
$457$	−9.59425	−	5.53924i	−0.448800	−	0.259115i	0.258523	−	0.966005i	$-0.416764\pi$
$457$	−9.59425	−	5.53924i	−0.448800	−	0.259115i	−0.707323	+	0.706890i	$0.750098\pi$
$458$	11.7386	−	6.77729i	0.548509	−	0.316682i
$459$	−16.0554	+	3.49611i	−0.749404	+	0.163184i
$460$	9.88171	−	1.60607i	0.460737	−	0.0748833i
$461$	−31.7876			−1.48050			−0.740248	−	0.672334i	$-0.765292\pi$
$461$	−31.7876			−1.48050			−0.740248	+	0.672334i	$0.765292\pi$
$462$	−19.9387	+	7.96817i	−0.927632	+	0.370713i
$463$		−	22.5741i		−	1.04911i	−0.851377	−	0.524554i	$-0.824232\pi$
$463$		−	22.5741i		−	1.04911i	0.851377	−	0.524554i	$-0.175768\pi$
$464$	−5.99430	−	3.46081i	−0.278279	−	0.160664i
$465$	1.48910	+	25.6206i	0.0690555	+	1.18813i
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	−24.2614	−	14.0073i	−1.12268	−	0.648181i	−0.180599	−	0.983557i	$-0.557803\pi$
$467$	−24.2614	−	14.0073i	−1.12268	−	0.648181i	−0.942085	+	0.335375i	$0.891137\pi$
$468$	2.08911	−	2.33570i	0.0965693	−	0.107968i
$469$	1.52277	−	37.7244i	0.0703152	−	1.74195i
$470$	19.4317	−	15.8659i	0.896316	−	0.731839i
$471$	−24.8908	−	2.57448i	−1.14691	−	0.118626i
$472$	5.28720	+	9.15769i	0.243363	+	0.421517i
$473$	16.2158	+	28.0867i	0.745605	+	1.29143i
$474$	−19.7737	−	2.04521i	−0.908234	−	0.0939395i
$475$	−7.00665	−	1.43023i	−0.321487	−	0.0656233i
$476$	7.40852	−	3.88766i	0.339569	−	0.178190i
$477$	−10.0000	+	11.1803i	−0.457869	+	0.511913i
$478$		0			0
$479$	21.1810	+	36.6866i	0.967784	+	1.67625i	0.701940	+	0.712236i	$0.252317\pi$
$479$	21.1810	+	36.6866i	0.967784	+	1.67625i	0.265844	+	0.964016i	$0.414349\pi$
$480$	−3.86646	+	0.224724i	−0.176479	+	0.0102572i
$481$	2.40890	+	1.39078i	0.109836	+	0.0634141i
$482$		−	21.3094i		−	0.970615i
$483$	−20.3066	−	2.93227i	−0.923983	−	0.133423i
$484$	−10.9545			−0.497930
$485$	26.4601	−	4.30055i	1.20149	−	0.195278i
$486$	−13.5640	−	7.68223i	−0.615278	−	0.348473i
$487$	14.7526	−	8.51743i	0.668505	−	0.385962i	−0.127005	−	0.991902i	$-0.540536\pi$
$487$	14.7526	−	8.51743i	0.668505	−	0.385962i	0.795510	+	0.605941i	$0.207203\pi$
$488$	3.00000	+	1.73205i	0.135804	+	0.0784063i
$489$	−23.2379	+	10.3923i	−1.05085	+	0.469956i
$490$	15.6019	−	1.25761i	0.704821	−	0.0568132i
$491$			13.8433i			0.624737i	0.949961	+	0.312369i	$0.101122\pi$
$491$			13.8433i			0.624737i	−0.949961	+	0.312369i	$0.898878\pi$
$492$	−1.79962	−	0.186137i	−0.0811333	−	0.00839169i
$493$	10.9441	+	18.9557i	0.492895	+	0.853720i
$494$	−1.29380	+	0.746976i	−0.0582108	+	0.0336080i
$495$	−26.4860	−	16.9247i	−1.19046	−	0.760707i
$496$		−	6.62638i		−	0.297533i
$497$	15.4772	+	9.78866i	0.694248	+	0.439081i
$498$	−6.43168	+	2.87633i	−0.288210	+	0.128892i
$499$	−0.954451	+	1.65316i	−0.0427271	+	0.0740055i	−0.886598	−	0.462541i	$-0.846938\pi$
$499$	−0.954451	+	1.65316i	−0.0427271	+	0.0740055i	0.843871	+	0.536546i	$0.180271\pi$
$500$	−9.44975	−	5.97514i	−0.422606	−	0.267216i
$501$	6.01958	+	4.35827i	0.268935	+	0.194713i
$502$	−4.42747	+	7.66860i	−0.197608	+	0.342266i
$503$		−	15.5096i		−	0.691537i	−0.938320	−	0.345769i	$-0.887618\pi$
$503$		−	15.5096i		−	0.691537i	0.938320	−	0.345769i	$-0.112382\pi$
$504$	7.69738	+	1.93657i	0.342869	+	0.0862617i
$505$	−16.0000	−	19.5959i	−0.711991	−	0.872007i
$506$	−18.1677	−	10.4891i	−0.807655	−	0.466300i
$507$	−12.0965	+	16.7075i	−0.537225	+	0.742006i
$508$	−7.56114	+	4.36543i	−0.335471	+	0.193684i
$509$	12.3583	−	21.4051i	0.547770	−	0.948766i	−0.450656	−	0.892697i	$-0.648810\pi$
$509$	12.3583	−	21.4051i	0.547770	−	0.948766i	0.998427	−	0.0560688i	$-0.0178566\pi$
$510$	10.9441	+	5.49798i	0.484611	+	0.243454i
$511$	9.26139	+	0.373843i	0.409700	+	0.0165378i
$512$	1.00000			0.0441942
$513$	5.00013	+	5.49805i	0.220761	+	0.242745i
$514$	9.52277	−	5.49798i	0.420032	−	0.242505i
$515$	3.89908	−	10.2814i	0.171814	−	0.453055i
$516$	1.23341	−	11.9250i	0.0542980	−	0.524968i
$517$	−52.5667			−2.31188
$518$	−0.284162	+	7.03967i	−0.0124853	+	0.309305i
$519$	1.78416	−	0.797901i	0.0783160	−	0.0350240i
$520$	−2.30545	+	0.374703i	−0.101101	+	0.0164318i
$521$	17.7981	+	30.8272i	0.779748	+	1.35056i	0.932087	+	0.362235i	$0.117986\pi$
$521$	17.7981	+	30.8272i	0.779748	+	1.35056i	−0.152339	+	0.988328i	$0.548680\pi$
$522$	−4.24999	+	20.3253i	−0.186017	+	0.889614i
$523$	8.45307	−	14.6412i	0.369627	−	0.640213i	−0.619880	−	0.784697i	$-0.712819\pi$
$523$	8.45307	−	14.6412i	0.369627	−	0.640213i	0.989507	+	0.144484i	$0.0461521\pi$
$524$	−13.7725			−0.601654
$525$	14.8034	+	17.4888i	0.646075	+	0.763274i
$526$	−2.00000			−0.0872041
$527$	−10.4772	+	18.1471i	−0.456395	+	0.790500i
$528$	6.57357	+	4.75937i	0.286078	+	0.207125i
$529$	1.47723	+	2.55863i	0.0642272	+	0.111245i
$530$	11.0355	−	1.79360i	0.479353	−	0.0779089i
$531$	21.1488	−	23.6451i	0.917779	−	1.02611i
$532$	−3.19808	−	2.02265i	−0.138655	−	0.0876928i
$533$	−1.09110			−0.0472607
$534$	8.47223	+	0.876291i	0.366629	+	0.0379208i
$535$	4.34286	−	11.4516i	0.187758	−	0.495097i
$536$	−12.3583	+	7.13505i	−0.533796	+	0.308187i
$537$	−3.45390	+	33.3933i	−0.149047	+	1.44103i
$538$	17.5810			0.757973
$539$	−26.9905	−	18.6355i	−1.16256	−	0.802689i
$540$	4.26139	+	10.8093i	0.183381	+	0.465157i
$541$	−4.26139	+	7.38094i	−0.183211	+	0.317331i	−0.942972	−	0.332871i	$-0.891983\pi$
$541$	−4.26139	+	7.38094i	−0.183211	+	0.317331i	0.759761	+	0.650202i	$0.225316\pi$
$542$	5.47723	−	3.16228i	0.235267	−	0.135831i
$543$	−4.43649	−	3.21209i	−0.190388	−	0.137844i
$544$	−2.73861	−	1.58114i	−0.117417	−	0.0677908i
$545$	28.8948	+	35.3887i	1.23772	+	1.51589i
$546$	4.73762	+	0.684110i	0.202751	+	0.0292772i
$547$			3.61845i			0.154714i	0.997003	+	0.0773569i	$0.0246481\pi$
$547$			3.61845i			0.154714i	−0.997003	+	0.0773569i	$0.975352\pi$
$548$	1.73861	−	3.01137i	0.0742699	−	0.128639i
$549$	2.12702	−	10.1723i	0.0907789	−	0.434143i
$550$	7.41941	+	22.2219i	0.316365	+	0.947546i
$551$	4.94975	−	8.57321i	0.210866	−	0.365231i
$552$	3.16588	+	7.07912i	0.134749	+	0.301307i
$553$	−14.1099	−	26.8886i	−0.600015	−	1.14342i
$554$			9.79796i			0.416275i
$555$	−8.61742	+	5.66626i	−0.365789	+	0.240520i
$556$	−17.4772	+	10.0905i	−0.741199	+	0.427932i
$557$	−13.9317	−	24.1304i	−0.590304	−	1.02244i	−0.994191	−	0.107628i	$-0.965674\pi$
$557$	−13.9317	−	24.1304i	−0.590304	−	1.02244i	0.403887	−	0.914809i	$-0.367659\pi$
$558$	−18.8857	+	6.20555i	−0.799497	+	0.262702i
$559$		−	7.23003i		−	0.305798i
$560$	−3.55378	−	4.72976i	−0.150175	−	0.199869i
$561$	−10.4772	−	23.4278i	−0.442349	−	0.989122i
$562$	1.56683	+	0.904612i	0.0660929	+	0.0381588i
$563$	9.00000	−	5.19615i	0.379305	−	0.218992i	−0.298211	−	0.954500i	$-0.596390\pi$
$563$	9.00000	−	5.19615i	0.379305	−	0.218992i	0.677516	+	0.735508i	$0.263057\pi$
$564$	15.7394	+	11.3956i	0.662750	+	0.479842i
$565$	38.5741	−	6.26942i	1.62282	−	0.263757i
$566$	9.22460			0.387739
$567$	−1.68915	−	23.7518i	−0.0709375	−	0.997481i
$568$		−	6.92163i		−	0.290425i
$569$	6.54879	+	3.78095i	0.274540	+	0.158505i	0.630949	−	0.775824i	$-0.282666\pi$
$569$	6.54879	+	3.78095i	0.274540	+	0.158505i	−0.356409	+	0.934330i	$0.615999\pi$
$570$	−0.321406	−	5.52991i	−0.0134622	−	0.231623i
$571$	−7.47723	−	12.9509i	−0.312912	−	0.541980i	0.666079	−	0.745881i	$-0.267971\pi$
$571$	−7.47723	−	12.9509i	−0.312912	−	0.541980i	−0.978991	+	0.203901i	$0.934638\pi$
$572$	4.23861	+	2.44716i	0.177225	+	0.102321i
$573$	25.7611	−	11.5207i	1.07618	−	0.481284i
$574$	−1.28416	−	2.44716i	−0.0535999	−	0.102143i
$575$	−4.47723	+	21.9338i	−0.186713	+	0.914704i
$576$	−0.936492	−	2.85008i	−0.0390205	−	0.118754i
$577$	0.337449	+	0.584480i	0.0140482	+	0.0243322i	0.872964	−	0.487785i	$-0.162195\pi$
$577$	0.337449	+	0.584480i	0.0140482	+	0.0243322i	−0.858916	+	0.512117i	$0.828862\pi$
$578$	−3.50000	−	6.06218i	−0.145581	−	0.252153i
$579$	−1.30948	+	12.6604i	−0.0544199	+	0.526148i
$580$	11.9886	−	9.78866i	0.497800	−	0.406452i
$581$	−9.09576	−	5.75267i	−0.377356	−	0.238661i
$582$	8.47723	+	18.9557i	0.351392	+	0.785737i
$583$	−20.2891	−	11.7139i	−0.840287	−	0.485140i
$584$	−1.75166	−	3.03397i	−0.0724843	−	0.125547i
$585$	3.22697	+	6.21981i	0.133419	+	0.257158i
$586$	6.97723	+	4.02830i	0.288227	+	0.166408i
$587$			21.0864i			0.870330i	0.900351	+	0.435165i	$0.143310\pi$
$587$			21.0864i			0.870330i	−0.900351	+	0.435165i	$0.856690\pi$
$588$	4.04156	+	11.4309i	0.166671	+	0.471403i
$589$	9.47723			0.390502
$590$	−23.3388	+	3.79324i	−0.960844	+	0.156165i
$591$	9.14178	−	12.6265i	0.376042	−	0.519384i
$592$	2.30615	−	1.33146i	0.0947821	−	0.0547225i
$593$	−1.43168	−	0.826579i	−0.0587919	−	0.0339435i	0.470316	−	0.882498i	$-0.344140\pi$
$593$	−1.43168	−	0.826579i	−0.0587919	−	0.0339435i	−0.529108	+	0.848555i	$0.677473\pi$
$594$	7.40852	−	23.1923i	0.303975	−	0.951593i
$595$	2.25403	+	18.5720i	0.0924064	+	0.761378i
$596$		−	2.44949i		−	0.100335i
$597$	2.76376	−	26.7208i	0.113113	−	1.09361i
$598$	2.33836	+	4.05015i	0.0956225	+	0.165623i
$599$	20.4739	−	11.8206i	0.836540	−	0.482977i	−0.0195464	−	0.999809i	$-0.506222\pi$
$599$	20.4739	−	11.8206i	0.836540	−	0.482977i	0.856087	+	0.516832i	$0.172889\pi$
$600$	2.59584	−	8.26206i	0.105975	−	0.337297i
$601$			4.06775i			0.165927i	0.996553	+	0.0829635i	$0.0264385\pi$
$601$			4.06775i			0.165927i	−0.996553	+	0.0829635i	$0.973562\pi$
$602$	16.2158	−	8.50934i	0.660908	−	0.346815i
$603$	31.9089	+	28.5402i	1.29943	+	1.16225i
$604$	1.00000	−	1.73205i	0.0406894	−	0.0704761i
$605$	8.68571	−	22.9032i	0.353124	−	0.931149i
$606$	11.4919	−	15.8725i	0.466828	−	0.644775i
$607$	−6.14692	+	10.6468i	−0.249496	+	0.432140i	−0.963386	−	0.268118i	$-0.913598\pi$
$607$	−6.14692	+	10.6468i	−0.249496	+	0.432140i	0.713890	+	0.700258i	$0.246932\pi$
$608$			1.43023i			0.0580034i
$609$	−29.4540	+	11.7708i	−1.19353	+	0.476976i
$610$	−6.00000	+	4.89898i	−0.242933	+	0.198354i
$611$	10.1487	+	5.85938i	0.410574	+	0.237045i
$612$	−1.94169	+	9.28600i	−0.0784882	+	0.375364i
$613$	−5.07016	+	2.92726i	−0.204782	+	0.118231i	−0.598884	−	0.800836i	$-0.704389\pi$
$613$	−5.07016	+	2.92726i	−0.204782	+	0.118231i	0.394102	+	0.919067i	$0.371056\pi$
$614$	5.99430	−	10.3824i	0.241910	−	0.419001i
$615$	1.81608	−	3.61501i	0.0732314	−	0.145771i
$616$	−0.500000	+	12.3867i	−0.0201456	+	0.499076i
$617$	14.5228			0.584665			0.292332	−	0.956317i	$-0.405569\pi$
$617$	14.5228			0.584665			0.292332	+	0.956317i	$0.405569\pi$
$618$	8.47223	+	0.876291i	0.340803	+	0.0352496i
$619$	26.1475	−	15.0963i	1.05096	−	0.606771i	0.128040	−	0.991769i	$-0.459131\pi$
$619$	26.1475	−	15.0963i	1.05096	−	0.606771i	0.922917	+	0.384998i	$0.125798\pi$
$620$	13.8542	+	5.25401i	0.556400	+	0.211006i
$621$	17.2113	−	15.6525i	0.690664	−	0.628115i
$622$	17.5810			0.704936
$623$	6.04555	+	11.5207i	0.242210	+	0.461567i
$624$	−0.738613	−	1.65159i	−0.0295682	−	0.0661165i
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	−11.6190	−	20.1246i	−0.464387	−	0.804341i
$627$	−6.80698	+	9.40169i	−0.271845	+	0.375467i
$628$	−7.22369	+	12.5118i	−0.288257	+	0.499275i
$629$	−8.42087			−0.335762
$630$	−10.1521	+	14.5580i	−0.404470	+	0.580003i
$631$	3.47723			0.138426			0.0692131	−	0.997602i	$-0.477951\pi$
$631$	3.47723			0.138426			0.0692131	+	0.997602i	$0.477951\pi$
$632$	−5.73861	+	9.93957i	−0.228270	+	0.395375i
$633$	24.8628	−	34.3401i	0.988208	−	1.36490i
$634$	4.95445	+	8.58136i	0.196766	+	0.340809i
$635$	−3.13193	−	19.2699i	−0.124287	−	0.764703i
$636$	3.53553	+	7.90569i	0.140193	+	0.313481i
$637$	3.13367	+	6.60635i	0.124160	+	0.261753i
$638$	−32.4317			−1.28398
$639$	−19.7272	+	6.48204i	−0.780397	+	0.256426i
$640$	−0.792893	+	2.09077i	−0.0313419	+	0.0826450i
$641$	−13.9251	+	8.03966i	−0.550008	+	0.317547i	−0.749125	−	0.662428i	$-0.769526\pi$
$641$	−13.9251	+	8.03966i	−0.550008	+	0.317547i	0.199117	+	0.979976i	$0.436193\pi$
$642$	9.43649	+	0.976025i	0.372429	+	0.0385206i
$643$	26.0663			1.02796			0.513978	−	0.857803i	$-0.328171\pi$
$643$	26.0663			1.02796			0.513978	+	0.857803i	$0.328171\pi$
$644$	−6.33175	+	10.0114i	−0.249506	+	0.394504i
$645$	23.9545	+	12.0340i	0.943206	+	0.473839i
$646$	2.26139	−	3.91684i	0.0889731	−	0.154106i
$647$	17.6703	−	10.2019i	0.694691	−	0.401080i	−0.110676	−	0.993857i	$-0.535302\pi$
$647$	17.6703	−	10.2019i	0.694691	−	0.401080i	0.805367	+	0.592777i	$0.201968\pi$
$648$	−7.24597	+	5.33816i	−0.284648	+	0.209703i
$649$	42.9089	+	24.7735i	1.68432	+	0.972444i
$650$	1.04456	−	5.11726i	0.0409709	−	0.200715i
$651$	−23.8578	−	18.7855i	−0.935060	−	0.736261i
$652$			14.6969i			0.575577i
$653$	−19.9317	+	34.5227i	−0.779987	+	1.35098i	0.151962	+	0.988386i	$0.451441\pi$
$653$	−19.9317	+	34.5227i	−0.779987	+	1.35098i	−0.931949	+	0.362590i	$0.881892\pi$
$654$	−20.7535	+	28.6645i	−0.811528	+	1.12087i
$655$	10.9201	−	28.7951i	0.426684	−	1.12512i
$656$	−0.522278	+	0.904612i	−0.0203915	+	0.0353192i
$657$	−7.00665	+	7.83368i	−0.273356	+	0.305621i
$658$	−1.19718	+	29.6582i	−0.0466708	+	1.15620i
$659$		−	34.2929i		−	1.33586i	−0.744224	−	0.667930i	$-0.767181\pi$
$659$		−	34.2929i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$660$	−15.1629	+	9.97014i	−0.590214	+	0.388087i
$661$	0.522774	−	0.301824i	0.0203336	−	0.0117396i	−0.489799	−	0.871836i	$-0.662930\pi$
$661$	0.522774	−	0.301824i	0.0203336	−	0.0117396i	0.510132	+	0.860096i	$0.329596\pi$
$662$	−10.7158	−	18.5604i	−0.416483	−	0.721370i
$663$	−0.588616	+	5.69091i	−0.0228600	+	0.221017i
$664$			4.06775i			0.157859i
$665$	6.76463	−	5.08272i	0.262321	−	0.197099i
$666$	−5.95445	−	5.32582i	−0.230730	−	0.206371i
$667$	−26.8378	−	15.4948i	−1.03917	−	0.599963i
$668$	3.71584	−	2.14534i	0.143770	−	0.0830057i
$669$	22.2329	−	30.7077i	0.859574	−	1.18723i
$670$	−5.11896	−	31.4956i	−0.197763	−	1.21678i
$671$	16.2312			0.626600
$672$	2.83495	−	3.60042i	0.109361	−	0.138889i
$673$		−	14.1585i		−	0.545771i	−0.962047	−	0.272885i	$-0.912022\pi$
$673$		−	14.1585i		−	0.545771i	0.962047	−	0.272885i	$-0.0879780\pi$
$674$	−14.8492	−	8.57321i	−0.571971	−	0.330228i
$675$	−25.9786	+	0.338975i	−0.999915	+	0.0130472i
$676$	5.95445	+	10.3134i	0.229017	+	0.396670i
$677$	−28.5000	−	16.4545i	−1.09534	−	0.632397i	−0.160350	−	0.987060i	$-0.551262\pi$
$677$	−28.5000	−	16.4545i	−1.09534	−	0.632397i	−0.934994	+	0.354663i	$0.884596\pi$
$678$	12.3583	+	27.6339i	0.474616	+	1.06127i
$679$	−16.9545	+	26.8073i	−0.650652	+	1.02877i
$680$	5.47723	−	4.47214i	0.210042	−	0.171499i
$681$	1.85188	−	17.9045i	0.0709641	−	0.686101i
$682$	−15.5241	−	26.8886i	−0.594450	−	1.02962i
$683$	9.47723	+	16.4150i	0.362636	+	0.628104i	0.988394	−	0.151913i	$-0.0485435\pi$
$683$	9.47723	+	16.4150i	0.362636	+	0.628104i	−0.625758	+	0.780017i	$0.715210\pi$
$684$	4.07627	−	1.33940i	0.155860	−	0.0512131i
$685$	4.91754	+	6.02273i	0.187890	+	0.230117i
$686$	−11.1289	+	14.8036i	−0.424903	+	0.565206i
$687$	−21.4317	+	9.58454i	−0.817669	+	0.365673i
$688$	−5.99430	−	3.46081i	−0.228531	−	0.131942i
$689$	2.61139	+	4.52306i	0.0994861	+	0.172315i
$690$	−17.3110	+	1.00614i	−0.659019	+	0.0383030i
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$		−	1.12840i		−	0.0428954i
$693$	35.7715	−	10.1750i	1.35885	−	0.386517i
$694$	−17.4772			−0.663426
$695$	−7.23930	−	44.5415i	−0.274602	−	1.68956i
$696$	9.71064	+	7.03066i	0.368081	+	0.266497i
$697$	2.86064	−	1.65159i	0.108354	−	0.0625584i
$698$	−10.1703	−	5.87182i	−0.384951	−	0.222252i
$699$	−2.82843	−	6.32456i	−0.106981	−	0.239217i
$700$	12.7066	−	3.67995i	0.480265	−	0.139089i
$701$			51.7546i			1.95474i	0.211531	+	0.977371i	$0.432155\pi$
$701$			51.7546i			1.95474i	−0.211531	+	0.977371i	$0.567845\pi$
$702$	−4.01546	+	3.65181i	−0.151554	+	0.137829i
$703$	1.90428	+	3.29832i	0.0718214	+	0.124398i
$704$	4.05781	−	2.34278i	0.152935	−	0.0882968i
$705$	−36.3053	+	23.8721i	−1.36734	+	0.899073i
$706$			0.603648i			0.0227186i
$707$	29.9089	+	1.20730i	1.12484	+	0.0454050i
$708$	−7.47723	−	16.7196i	−0.281011	−	0.628360i
$709$	11.2158	−	19.4264i	0.421220	−	0.729574i	−0.574839	−	0.818266i	$-0.694935\pi$
$709$	11.2158	−	19.4264i	0.421220	−	0.729574i	0.996059	+	0.0886924i	$0.0282688\pi$
$710$	14.4715	+	5.48811i	0.543107	+	0.205965i
$711$	33.7028	+	7.04721i	1.26395	+	0.264291i
$712$	2.45877	−	4.25871i	0.0921463	−	0.159602i
$713$		−	29.6678i		−	1.11107i
$714$	−13.4566	+	5.37771i	−0.503601	+	0.201256i
$715$	−8.47723	+	6.92163i	−0.317030	+	0.258854i
$716$	16.7857	+	9.69125i	0.627312	+	0.362179i
$717$		0			0
$718$	9.86729	−	5.69688i	0.368244	−	0.212606i
$719$	−0.401865	+	0.696051i	−0.0149870	+	0.0259583i	−0.873422	−	0.486965i	$-0.838104\pi$
$719$	−0.401865	+	0.696051i	−0.0149870	+	0.0259583i	0.858435	+	0.512923i	$0.171437\pi$
$720$	6.70141	+	0.301824i	0.249747	+	0.0112483i
$721$	6.04555	+	11.5207i	0.225148	+	0.429054i
$722$	16.9545			0.630979
$723$	−3.79726	+	36.7130i	−0.141222	+	1.36537i
$724$	−2.73861	+	1.58114i	−0.101780	+	0.0587626i
$725$	10.9601	+	32.8268i	0.407050	+	1.21916i
$726$	18.8730	+	1.95205i	0.700442	+	0.0724474i
$727$	15.1223			0.560854			0.280427	−	0.959875i	$-0.409524\pi$
$727$	15.1223			0.560854			0.280427	+	0.959875i	$0.409524\pi$
$728$	1.47723	−	2.33570i	0.0547496	−	0.0865668i
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	7.73221	−	1.25671i	0.286182	−	0.0465130i
$731$	10.9441	+	18.9557i	0.404780	+	0.701100i
$732$	−4.85993	−	3.51867i	−0.179628	−	0.130054i
$733$	−1.19718	+	2.07357i	−0.0442187	+	0.0765891i	−0.887288	−	0.461216i	$-0.847413\pi$
$733$	−1.19718	+	2.07357i	−0.0442187	+	0.0765891i	0.843069	+	0.537805i	$0.180747\pi$
$734$	0.369657			0.0136443
$735$	−27.1039	−	0.613514i	−0.999744	−	0.0226298i
$736$	4.47723			0.165033
$737$	−33.4317	+	57.9054i	−1.23147	+	2.13297i
$738$	3.06733	+	0.641375i	0.112910	+	0.0236093i
$739$	−3.23861	−	5.60944i	−0.119134	−	0.206347i	0.800291	−	0.599612i	$-0.204679\pi$
$739$	−3.23861	−	5.60944i	−0.119134	−	0.206347i	−0.919425	+	0.393266i	$0.871345\pi$
$740$	0.955238	+	5.87733i	0.0351153	+	0.216055i
$741$	2.36215	−	1.05638i	0.0867756	−	0.0388072i
$742$	−7.07107	+	11.1803i	−0.259587	+	0.410443i
$743$	13.4317			0.492760			0.246380	−	0.969173i	$-0.420759\pi$
$743$	13.4317			0.492760			0.246380	+	0.969173i	$0.420759\pi$
$744$	−1.18080	+	11.4163i	−0.0432903	+	0.418543i
$745$	5.12132	+	1.94218i	0.187631	+	0.0711561i
$746$	−20.1042	+	11.6072i	−0.736068	+	0.424969i
$747$	11.5934	−	3.80941i	0.424181	−	0.139379i
$748$	−14.8170			−0.541764
$749$	6.73362	+	12.8319i	0.246041	+	0.468868i
$750$	15.2158	+	11.9782i	0.555604	+	0.437384i
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	9.71584	−	5.60944i	0.354300	−	0.204555i
$753$	8.99443	−	12.4230i	0.327775	−	0.452718i
$754$	6.26139	+	3.61501i	0.228026	+	0.131651i
$755$	2.82843	+	3.46410i	0.102937	+	0.126072i
$756$	−12.9164	−	4.70809i	−0.469766	−	0.171232i
$757$		−	48.1361i		−	1.74954i	−0.484541	−	0.874768i	$-0.661014\pi$
$757$		−	48.1361i		−	1.74954i	0.484541	−	0.874768i	$-0.338986\pi$
$758$	10.2386	−	17.7338i	0.371883	−	0.644121i
$759$	29.4313	+	21.3088i	1.06829	+	0.773459i
$760$	−2.99028	−	1.13402i	−0.108469	−	0.0411351i
$761$	0.891935	−	1.54488i	0.0323326	−	0.0560018i	−0.849406	−	0.527739i	$-0.823040\pi$
$761$	0.891935	−	1.54488i	0.0323326	−	0.0560018i	0.881739	+	0.471738i	$0.156373\pi$
$762$	13.8047	−	6.17364i	0.500091	−	0.223648i
$763$	−54.0131	−	2.18028i	−1.95541	−	0.0789315i
$764$		−	16.2927i		−	0.589451i
$765$	−17.8753	−	11.4224i	−0.646284	−	0.412979i
$766$	−15.7158	+	9.07354i	−0.567836	+	0.327840i
$767$	−5.52277	−	9.56573i	−0.199416	−	0.345398i
$768$	−1.72286	−	0.178197i	−0.0621683	−	0.00643013i
$769$			16.1921i			0.583902i	0.956433	+	0.291951i	$0.0943045\pi$
$769$			16.1921i			0.583902i	−0.956433	+	0.291951i	$0.905696\pi$
$770$	−25.5014	−	10.8667i	−0.919005	−	0.391610i
$771$	−17.3861	+	7.77531i	−0.626146	+	0.280021i
$772$	6.36396	+	3.67423i	0.229044	+	0.132239i
$773$	−14.0228	+	8.09605i	−0.504364	+	0.291195i	−0.730514	−	0.682898i	$-0.760719\pi$
$773$	−14.0228	+	8.09605i	−0.504364	+	0.291195i	0.226150	+	0.974093i	$0.427386\pi$
$774$	−4.24999	+	20.3253i	−0.152763	+	0.730578i
$775$	−21.9699	+	24.8002i	−0.789181	+	0.890848i
$776$	11.9886			0.430366
$777$	1.74402	−	12.0777i	0.0625663	−	0.433286i
$778$		−	7.34847i		−	0.263455i
$779$	−1.29380	−	0.746976i	−0.0463552	−	0.0267632i
$780$	4.03873	−	0.234736i	0.144610	−	0.00840491i
$781$	−16.2158	−	28.0867i	−0.580248	−	1.00502i
$782$	−12.2614	−	7.07912i	−0.438466	−	0.253149i
$783$	10.9441	−	34.2603i	0.391108	−	1.22436i
$784$	6.97723	+	0.564201i	0.249187	+	0.0201501i
$785$	−20.4317	−	25.0236i	−0.729238	−	0.893130i
$786$	23.7280	+	2.45421i	0.846351	+	0.0875389i
$787$	25.0862	+	43.4506i	0.894226	+	1.54884i	0.834760	+	0.550615i	$0.185607\pi$
$787$	25.0862	+	43.4506i	0.894226	+	1.54884i	0.0594664	+	0.998230i	$0.481060\pi$
$788$	−4.50000	−	7.79423i	−0.160306	−	0.277658i
$789$	3.44572	+	0.356394i	0.122671	+	0.0126880i
$790$	−16.2312	−	19.8791i	−0.577482	−	0.707268i
$791$	−24.7165	+	39.0803i	−0.878819	+	1.38953i
$792$	−10.4772	−	9.37112i	−0.372292	−	0.332988i
$793$	−3.13367	−	1.80922i	−0.111280	−	0.0642474i
$794$	−7.44073	−	12.8877i	−0.264061	−	0.457368i
$795$	−19.3323	+	1.12362i	−0.685646	+	0.0398506i
$796$	−13.4317	−	7.75478i	−0.476073	−	0.274861i
$797$		−	54.2183i		−	1.92051i	−0.279121	−	0.960256i	$-0.590043\pi$
$797$		−	54.2183i		−	1.92051i	0.279121	−	0.960256i	$-0.409957\pi$
$798$	5.14942	+	4.05462i	0.182288	+	0.143532i
$799$	−35.4772			−1.25509
$800$	−3.74264	−	3.31552i	−0.132322	−	0.117221i
$801$	−14.4403	−	3.01945i	−0.510223	−	0.106687i
$802$	−0.827520	+	0.477769i	−0.0292207	+	0.0168706i
$803$	−14.2158	−	8.20752i	−0.501666	−	0.289637i
$804$	22.5630	−	10.0905i	0.795736	−	0.355864i
$805$	−15.9111	−	21.1762i	−0.560792	−	0.746363i
$806$			6.92163i			0.243804i
$807$	−30.2897	−	3.13289i	−1.06625	−	0.110283i
$808$	−5.65685	−	9.79796i	−0.199007	−	0.344691i
$809$	−7.65776	+	4.42121i	−0.269233	+	0.155441i	−0.628539	−	0.777778i	$-0.716347\pi$
$809$	−7.65776	+	4.42121i	−0.269233	+	0.155441i	0.359306	+	0.933220i	$0.383013\pi$
$810$	−5.41559	−	19.3822i	−0.190284	−	0.681023i
$811$			38.3280i			1.34588i	0.739697	+	0.672940i	$0.234969\pi$
$811$			38.3280i			1.34588i	−0.739697	+	0.672940i	$0.765031\pi$
$812$	−0.738613	+	18.2980i	−0.0259202	+	0.642134i
$813$	−10.0000	+	4.47214i	−0.350715	+	0.156845i
$814$	6.23861	−	10.8056i	0.218663	−	0.378736i
$815$	−30.7279	−	11.6531i	−1.07635	−	0.408190i
$816$	4.43649	+	3.21209i	0.155308	+	0.112446i
$817$	4.94975	−	8.57321i	0.173170	−	0.299939i
$818$			15.5096i			0.542279i
$819$	−8.04035	−	2.02286i	−0.280953	−	0.0706843i
$820$	−1.47723	−	1.80922i	−0.0515870	−	0.0631809i
$821$	−10.1403	−	5.85452i	−0.353900	−	0.204324i	0.312502	−	0.949917i	$-0.398833\pi$
$821$	−10.1403	−	5.85452i	−0.353900	−	0.204324i	−0.666401	+	0.745593i	$0.732166\pi$
$822$	−3.53200	+	4.87835i	−0.123193	+	0.170152i
$823$	2.76401	−	1.59580i	0.0963474	−	0.0556262i	−0.451052	−	0.892498i	$-0.648951\pi$
$823$	2.76401	−	1.59580i	0.0963474	−	0.0556262i	0.547400	+	0.836871i	$0.315618\pi$
$824$	2.45877	−	4.25871i	0.0856553	−	0.148359i
$825$	−8.82273	−	39.6074i	−0.307168	−	1.37895i
$826$	14.9545	−	23.6451i	0.520332	−	0.822717i
$827$	−3.90890			−0.135926			−0.0679629	−	0.997688i	$-0.521650\pi$
$827$	−3.90890			−0.135926			−0.0679629	+	0.997688i	$0.521650\pi$
$828$	−4.19288	−	12.7605i	−0.145713	−	0.443457i
$829$	−43.6931	+	25.2262i	−1.51752	+	0.876142i	−0.517735	+	0.855541i	$0.673225\pi$
$829$	−43.6931	+	25.2262i	−1.51752	+	0.876142i	−0.999788	+	0.0206012i	$0.993442\pi$
$830$	−8.50473	−	3.22529i	−0.295203	−	0.111951i
$831$	1.74597	−	16.8805i	0.0605669	−	0.585578i
$832$	−1.04456			−0.0362135
$833$	−18.2158	−	12.5771i	−0.631141	−	0.435770i
$834$	31.9089	−	14.2701i	1.10491	−	0.494133i
$835$	1.53915	+	9.46999i	0.0532645	+	0.327723i
$836$	3.35071	+	5.80359i	0.115887	+	0.200721i
$837$	33.6433	−	7.32591i	1.16288	−	0.253220i
$838$	4.42747	−	7.66860i	0.152944	−	0.264907i
$839$	40.1440			1.38593			0.692963	−	0.720973i	$-0.256305\pi$
$839$	40.1440			1.38593			0.692963	+	0.720973i	$0.256305\pi$
$840$	5.27984	+	8.78198i	0.182172	+	0.303007i
$841$	−18.9089			−0.652031
$842$	−9.47723	+	16.4150i	−0.326607	+	0.565700i
$843$	−2.53824	−	1.83773i	−0.0874215	−	0.0632946i
$844$	−12.2386	−	21.1979i	−0.421270	−	0.729662i
$845$	−26.2842	+	4.27196i	−0.904205	+	0.146960i
$846$	−25.0862	−	22.4378i	−0.862481	−	0.771426i
$847$	13.4672	+	25.6639i	0.462740	+	0.881821i
$848$	5.00000			0.171701
$849$	−15.8927	−	1.64380i	−0.545436	−	0.0564149i
$850$	5.00735	+	14.9975i	0.171751	+	0.514412i
$851$	10.3251	−	5.96123i	0.353942	−	0.204348i
$852$	−1.23341	+	11.9250i	−0.0422560	+	0.408543i
$853$	−31.2891			−1.07132			−0.535659	−	0.844434i	$-0.679937\pi$
$853$	−31.2891			−1.07132			−0.535659	+	0.844434i	$0.679937\pi$
$854$	0.369657	−	9.15769i	0.0126494	−	0.313370i
$855$	−0.431677	+	9.58454i	−0.0147630	+	0.327784i
$856$	2.73861	−	4.74342i	0.0936039	−	0.162127i
$857$	13.0455	−	7.53185i	0.445627	−	0.257283i	−0.260354	−	0.965513i	$-0.583839\pi$
$857$	13.0455	−	7.53185i	0.445627	−	0.257283i	0.705982	+	0.708230i	$0.250506\pi$
$858$	−6.86646	−	4.97143i	−0.234417	−	0.169722i
$859$	−26.4772	−	15.2866i	−0.903391	−	0.521573i	−0.0250924	−	0.999685i	$-0.507988\pi$
$859$	−26.4772	−	15.2866i	−0.903391	−	0.521573i	−0.878299	+	0.478112i	$0.841321\pi$
$860$	11.9886	−	9.78866i	0.408808	−	0.333790i
$861$	1.77635	+	4.44495i	0.0605380	+	0.151484i
$862$		−	7.66374i		−	0.261028i
$863$	13.2386	−	22.9299i	0.450648	−	0.780545i	−0.547779	−	0.836623i	$-0.684526\pi$
$863$	13.2386	−	22.9299i	0.450648	−	0.780545i	0.998426	+	0.0560787i	$0.0178598\pi$
$864$	1.10557	+	5.07718i	0.0376122	+	0.172729i
$865$	2.35923	+	0.894703i	0.0802163	+	0.0304208i
$866$		0			0
$867$	4.94975	+	11.0680i	0.168102	+	0.375888i
$868$	−15.5241	+	8.14637i	−0.526924	+	0.276506i
$869$			53.7772i			1.82427i
$870$	−22.3990	+	14.7281i	−0.759397	+	0.499331i
$871$	12.9089	−	7.45296i	0.437401	−	0.252534i
$872$	10.2158	+	17.6944i	0.345952	+	0.599206i
$873$	−11.2272	−	34.1685i	−0.379984	−	1.15643i
$874$			6.40345i			0.216600i
$875$	−2.38105	+	29.4844i	−0.0804942	+	0.996755i
$876$	2.47723	+	5.53924i	0.0836977	+	0.187154i
$877$	48.2359	+	27.8490i	1.62881	+	0.940394i	0.984449	+	0.175673i	$0.0562101\pi$
$877$	48.2359	+	27.8490i	1.62881	+	0.940394i	0.644361	+	0.764721i	$0.277123\pi$
$878$	7.69306	−	4.44159i	0.259628	−	0.149896i
$879$	−11.3029	−	8.18352i	−0.381239	−	0.276023i
$880$	1.68080	+	10.3415i	0.0566598	+	0.348613i
$881$	18.7544			0.631853			0.315926	−	0.948784i	$-0.397685\pi$
$881$	18.7544			0.631853			0.315926	+	0.948784i	$0.397685\pi$
$882$	−4.92609	−	20.4141i	−0.165870	−	0.687377i
$883$			24.3833i			0.820564i	0.911959	+	0.410282i	$0.134570\pi$
$883$			24.3833i			0.820564i	−0.911959	+	0.410282i	$0.865430\pi$
$884$	2.86064	+	1.65159i	0.0962136	+	0.0555489i
$885$	40.8855	−	2.37632i	1.37435	−	0.0798790i
$886$	7.52277	+	13.0298i	0.252733	+	0.437746i
$887$	3.00000	+	1.73205i	0.100730	+	0.0581566i	0.549519	−	0.835481i	$-0.314811\pi$
$887$	3.00000	+	1.73205i	0.100730	+	0.0581566i	−0.448789	+	0.893638i	$0.648144\pi$
$888$	−4.21043	+	1.88296i	−0.141293	+	0.0631881i
$889$	19.5228	+	12.3473i	0.654773	+	0.414115i
$890$	6.95445	+	8.51743i	0.233114	+	0.285505i
$891$	−16.8966	+	38.6370i	−0.566059	+	1.29439i
$892$	−10.9441	−	18.9557i	−0.366434	−	0.634682i
$893$	8.02277	+	13.8959i	0.268472	+	0.465007i
$894$	−0.436492	+	4.22013i	−0.0145985	+	0.141142i
$895$	−33.5715	+	27.4110i	−1.12217	+	0.916248i
$896$	−1.22938	−	2.34278i	−0.0410709	−	0.0782667i
$897$	−3.30694	−	7.39453i	−0.110415	−	0.246896i
$898$	22.4104	+	12.9386i	0.747844	+	0.431768i
$899$	−22.9327	−	39.7205i	−0.764847	−	1.32475i
$900$	−5.94455	+	13.7718i	−0.198152	+	0.459060i
$901$	−13.6931	−	7.90569i	−0.456182	−	0.263377i
$902$			4.89433i			0.162963i
$903$	−29.4540	+	11.7708i	−0.980166	+	0.391707i
$904$	17.4772			0.581284
$905$	−1.13437	−	6.97948i	−0.0377078	−	0.232006i
$906$	−2.03151	+	2.80588i	−0.0674923	+	0.0932192i
$907$	8.48528	−	4.89898i	0.281749	−	0.162668i	−0.352466	−	0.935825i	$-0.614657\pi$
$907$	8.48528	−	4.89898i	0.281749	−	0.162668i	0.634215	+	0.773157i	$0.281323\pi$
$908$	−9.00000	−	5.19615i	−0.298675	−	0.172440i
$909$	−22.6274	+	25.2982i	−0.750504	+	0.839089i
$910$	3.71213	+	4.94050i	0.123056	+	0.163776i
$911$		−	24.0681i		−	0.797410i	−0.917079	−	0.398705i	$-0.869460\pi$
$911$		−	24.0681i		−	0.797410i	0.917079	−	0.398705i	$-0.130540\pi$
$912$	0.254862	−	2.46408i	0.00843933	−	0.0815939i
$913$	9.52984	+	16.5062i	0.315392	+	0.546274i
$914$	9.59425	−	5.53924i	0.317350	−	0.183222i
$915$	11.2101	−	7.37107i	0.370596	−	0.243680i
$916$			13.5546i			0.447856i
$917$	16.9317	+	32.2659i	0.559133	+	1.06551i
$918$	5.00000	−	15.6525i	0.165025	−	0.516609i
$919$	−0.215838	+	0.373843i	−0.00711985	+	0.0123319i	−0.869563	−	0.493821i	$-0.835600\pi$
$919$	−0.215838	+	0.373843i	−0.00711985	+	0.0123319i	0.862444	+	0.506153i	$0.168933\pi$
$920$	−3.54996	+	9.36085i	−0.117039	+	0.308618i
$921$	−12.1775	+	16.8193i	−0.401261	+	0.554215i
$922$	15.8938	−	27.5289i	0.523434	−	0.906615i
$923$			7.23003i			0.237979i
$924$	3.06871	−	21.2515i	0.100953	−	0.699123i
$925$	−13.0455	−	2.66291i	−0.428935	−	0.0875560i
$926$	19.5497	+	11.2871i	0.642444	+	0.370916i
$927$	−14.4403	−	3.01945i	−0.474282	−	0.0991718i
$928$	5.99430	−	3.46081i	0.196773	−	0.113607i
$929$	−7.96300	+	13.7923i	−0.261258	+	0.452512i	−0.966576	−	0.256379i	$-0.917471\pi$
$929$	−7.96300	+	13.7923i	−0.261258	+	0.452512i	0.705319	+	0.708890i	$0.250804\pi$
$930$	−22.9327	−	11.5207i	−0.751991	−	0.377779i
$931$	−0.806936	+	9.97902i	−0.0264463	+	0.327049i
$932$	−4.00000			−0.131024
$933$	−30.2897	−	3.13289i	−0.991640	−	0.102566i
$934$	24.2614	−	14.0073i	0.793857	−	0.458333i
$935$	11.7483	−	30.9790i	0.384211	−	1.01312i
$936$	0.978218	+	2.97707i	0.0319741	+	0.0973087i
$937$	53.6757			1.75351			0.876754	−	0.480938i	$-0.159704\pi$
$937$	53.6757			1.75351			0.876754	+	0.480938i	$0.159704\pi$
$938$	31.9089	+	20.1810i	1.04186	+	0.658932i
$939$	16.4317	+	36.7423i	0.536228	+	1.19904i
$940$	4.02443	+	24.7613i	0.131262	+	0.807624i
$941$	10.2369	+	17.7309i	0.333715	+	0.578011i	0.983237	−	0.182331i	$-0.0583644\pi$
$941$	10.2369	+	17.7309i	0.333715	+	0.578011i	−0.649522	+	0.760343i	$0.725031\pi$
$942$	14.6750	−	20.2688i	0.478136	−	0.660394i
$943$	−2.33836	+	4.05015i	−0.0761474	+	0.131891i
$944$	−10.5744			−0.344167
$945$	20.0849	−	23.2723i	0.653361	−	0.757047i
$946$	−32.4317			−1.05444
$947$	−16.4317	+	28.4605i	−0.533958	+	0.924842i	0.465255	+	0.885177i	$0.345963\pi$
$947$	−16.4317	+	28.4605i	−0.533958	+	0.924842i	−0.999213	+	0.0396654i	$0.987371\pi$
$948$	11.6580	−	16.1019i	0.378635	−	0.522965i
$949$	1.82971	+	3.16915i	0.0593949	+	0.102875i
$950$	4.74194	−	5.35283i	0.153849	−	0.173669i
$951$	−7.00665	−	15.6674i	−0.227206	−	0.508049i
$952$	−0.337449	+	8.35979i	−0.0109368	+	0.270942i
$953$	46.9545			1.52100			0.760502	−	0.649336i	$-0.224953\pi$
$953$	46.9545			1.52100			0.760502	+	0.649336i	$0.224953\pi$
$954$	−4.68246	−	14.2504i	−0.151600	−	0.461375i
$955$	34.0644	+	12.9184i	1.10230	+	0.418030i
$956$		0			0
$957$	55.8752	+	5.77923i	1.80619	+	0.186816i
$958$	−42.3620			−1.36865
$959$	−9.19239	−	0.371058i	−0.296838	−	0.0119821i
$960$	1.73861	−	3.46081i	0.0561135	−	0.111697i
$961$	6.45445	−	11.1794i	0.208208	−	0.360627i
$962$	−2.40890	+	1.39078i	−0.0776661	+	0.0448406i
$963$	−16.0838	−	3.36311i	−0.518294	−	0.108375i
$964$	18.4545	+	10.6547i	0.594378	+	0.343164i
$965$	−12.7279	+	10.3923i	−0.409726	+	0.334540i
$966$	12.6927	−	16.1199i	0.408382	−	0.518649i
$967$			7.23690i			0.232723i	0.993207	+	0.116361i	$0.0371231\pi$
$967$			7.23690i			0.232723i	−0.993207	+	0.116361i	$0.962877\pi$
$968$	5.47723	−	9.48683i	0.176045	−	0.304918i
$969$	−4.59402	+	6.34519i	−0.147581	+	0.203837i
$970$	−9.50569	+	25.0654i	−0.305209	+	0.804802i
$971$	18.8748	−	32.6922i	0.605723	−	1.04914i	−0.386214	−	0.922409i	$-0.626217\pi$
$971$	18.8748	−	32.6922i	0.605723	−	1.04914i	0.991937	−	0.126733i	$-0.0404492\pi$
$972$	13.4350	−	7.90569i	0.430929	−	0.253575i
$973$	45.1260	+	28.5402i	1.44667	+	0.914956i
$974$			17.0349i			0.545832i
$975$	−2.71150	+	8.63018i	−0.0868376	+	0.276387i
$976$	−3.00000	+	1.73205i	−0.0960277	+	0.0554416i
$977$	−1.95445	−	3.38521i	−0.0625284	−	0.108302i	0.833067	−	0.553173i	$-0.186583\pi$
$977$	−1.95445	−	3.38521i	−0.0625284	−	0.108302i	−0.895595	+	0.444870i	$0.853250\pi$
$978$	2.61895	−	25.3208i	0.0837448	−	0.809669i
$979$		−	23.0414i		−	0.736407i
$980$	−6.71181	+	14.1404i	−0.214401	+	0.451699i
$981$	40.8634	−	45.6866i	1.30467	−	1.45866i
$982$	−11.9886	−	6.92163i	−0.382572	−	0.220878i
$983$	−45.7158	+	26.3941i	−1.45811	+	0.841840i	−0.998918	−	0.0464984i	$-0.985194\pi$
$983$	−45.7158	+	26.3941i	−1.45811	+	0.841840i	−0.459190	+	0.888338i	$0.651860\pi$
$984$	1.06101	−	1.46545i	0.0338238	−	0.0467169i
$985$	19.8640	−	3.22848i	0.632918	−	0.102868i
$986$	−21.8881			−0.697059
$987$	7.34757	−	50.8836i	0.233876	−	1.61964i
$988$		−	1.49395i		−	0.0475290i
$989$	−26.8378	−	15.4948i	−0.853394	−	0.492707i
$990$	27.9002	−	14.4752i	0.886726	−	0.460051i
$991$	−5.26139	−	9.11299i	−0.167133	−	0.289484i	0.770277	−	0.637709i	$-0.220118\pi$
$991$	−5.26139	−	9.11299i	−0.167133	−	0.289484i	−0.937411	+	0.348225i	$0.886784\pi$
$992$	5.73861	+	3.31319i	0.182201	+	0.105194i
$993$	15.1545	+	33.8865i	0.480913	+	1.07535i
$994$	−16.2158	+	8.50934i	−0.514335	+	0.269900i
$995$	26.8634	−	21.9338i	0.851626	−	0.695349i
$996$	0.724861	−	7.00816i	0.0229681	−	0.222062i
$997$	−7.74597	−	13.4164i	−0.245317	−	0.424902i	0.716904	−	0.697172i	$-0.245559\pi$
$997$	−7.74597	−	13.4164i	−0.245317	−	0.424902i	−0.962221	+	0.272270i	$0.912225\pi$
$998$	−0.954451	−	1.65316i	−0.0302126	−	0.0523298i
$999$	9.30964	+	10.2367i	0.294544	+	0.323875i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.t.e.89.3	yes	8
3.2	odd	2		210.2.t.f.89.1	yes	8
5.2	odd	4		1050.2.s.i.551.1		16
5.3	odd	4		1050.2.s.i.551.8		16
5.4	even	2		210.2.t.f.89.2	yes	8
7.2	even	3		1470.2.d.f.1469.7		8
7.3	odd	6	inner	210.2.t.e.59.4	yes	8
7.5	odd	6		1470.2.d.f.1469.2		8
15.2	even	4		1050.2.s.i.551.7		16
15.8	even	4		1050.2.s.i.551.2		16
15.14	odd	2	inner	210.2.t.e.89.4	yes	8
21.2	odd	6		1470.2.d.e.1469.6		8
21.5	even	6		1470.2.d.e.1469.3		8
21.17	even	6		210.2.t.f.59.2	yes	8
35.3	even	12		1050.2.s.i.101.2		16
35.9	even	6		1470.2.d.e.1469.2		8
35.17	even	12		1050.2.s.i.101.7		16
35.19	odd	6		1470.2.d.e.1469.7		8
35.24	odd	6		210.2.t.f.59.1	yes	8
105.17	odd	12		1050.2.s.i.101.1		16
105.38	odd	12		1050.2.s.i.101.8		16
105.44	odd	6		1470.2.d.f.1469.3		8
105.59	even	6	inner	210.2.t.e.59.3	✓	8
105.89	even	6		1470.2.d.f.1469.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.3	✓	8	105.59	even	6	inner
210.2.t.e.59.4	yes	8	7.3	odd	6	inner
210.2.t.e.89.3	yes	8	1.1	even	1	trivial
210.2.t.e.89.4	yes	8	15.14	odd	2	inner
210.2.t.f.59.1	yes	8	35.24	odd	6
210.2.t.f.59.2	yes	8	21.17	even	6
210.2.t.f.89.1	yes	8	3.2	odd	2
210.2.t.f.89.2	yes	8	5.4	even	2
1050.2.s.i.101.1		16	105.17	odd	12
1050.2.s.i.101.2		16	35.3	even	12
1050.2.s.i.101.7		16	35.17	even	12
1050.2.s.i.101.8		16	105.38	odd	12
1050.2.s.i.551.1		16	5.2	odd	4
1050.2.s.i.551.2		16	15.8	even	4
1050.2.s.i.551.7		16	15.2	even	4
1050.2.s.i.551.8		16	5.3	odd	4
1470.2.d.e.1469.2		8	35.9	even	6
1470.2.d.e.1469.3		8	21.5	even	6
1470.2.d.e.1469.6		8	21.2	odd	6
1470.2.d.e.1469.7		8	35.19	odd	6
1470.2.d.f.1469.2		8	7.5	odd	6
1470.2.d.f.1469.3		8	105.44	odd	6
1470.2.d.f.1469.6		8	105.89	even	6
1470.2.d.f.1469.7		8	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	210.2.t.e.89.3

Level	$210$
Weight	$2$
Character	210.89
Analytic conductor	$1.677$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$