LMFDB - Embedded newform 280.2.ba.b.59.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(19,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("280.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.12
Character	$\chi$	$=$	280.59
Dual form			280.2.ba.b.19.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.931410 + 1.06418i) q^{2} +(1.60233 - 2.77531i) q^{3} +(-0.264952 - 1.98237i) q^{4} +(2.12896 - 0.683763i) q^{5} +(1.46101 + 4.29012i) q^{6} +(2.23600 + 1.41432i) q^{7} +(2.35638 + 1.56444i) q^{8} +(-3.63491 - 6.29586i) q^{9} +O(q^{10})$	\(q+(-0.931410 + 1.06418i) q^{2} +(1.60233 - 2.77531i) q^{3} +(-0.264952 - 1.98237i) q^{4} +(2.12896 - 0.683763i) q^{5} +(1.46101 + 4.29012i) q^{6} +(2.23600 + 1.41432i) q^{7} +(2.35638 + 1.56444i) q^{8} +(-3.63491 - 6.29586i) q^{9} +(-1.25529 + 2.90246i) q^{10} +(-1.23701 + 2.14257i) q^{11} +(-5.92625 - 2.44109i) q^{12} +2.90697i q^{13} +(-3.58772 + 1.06219i) q^{14} +(1.51364 - 7.00414i) q^{15} +(-3.85960 + 1.05047i) q^{16} +(1.21515 - 2.10471i) q^{17} +(10.0855 + 1.99582i) q^{18} +(-3.38329 + 1.95334i) q^{19} +(-1.91954 - 4.03923i) q^{20} +(7.50799 - 3.93940i) q^{21} +(-1.12791 - 3.31201i) q^{22} +(-2.86568 - 4.96350i) q^{23} +(8.11752 - 4.03293i) q^{24} +(4.06494 - 2.91141i) q^{25} +(-3.09353 - 2.70758i) q^{26} -13.6833 q^{27} +(2.21128 - 4.80731i) q^{28} +4.71148i q^{29} +(6.04385 + 8.13451i) q^{30} +(-3.92617 + 6.80032i) q^{31} +(2.47699 - 5.08572i) q^{32} +(3.96419 + 6.86619i) q^{33} +(1.10798 + 3.25349i) q^{34} +(5.72741 + 1.48213i) q^{35} +(-11.5177 + 8.87385i) q^{36} +(1.67865 + 2.90751i) q^{37} +(1.07252 - 5.41978i) q^{38} +(8.06775 + 4.65792i) q^{39} +(6.08634 + 1.71944i) q^{40} -5.75850i q^{41} +(-2.80079 + 11.6590i) q^{42} -0.763818i q^{43} +(4.57511 + 1.88454i) q^{44} +(-12.0435 - 10.9182i) q^{45} +(7.95117 + 1.57346i) q^{46} +(-2.86896 + 1.65640i) q^{47} +(-3.26897 + 12.3948i) q^{48} +(2.99940 + 6.32484i) q^{49} +(-0.687865 + 7.03753i) q^{50} +(-3.89415 - 6.74487i) q^{51} +(5.76269 - 0.770206i) q^{52} +(-0.474139 + 0.821232i) q^{53} +(12.7448 - 14.5615i) q^{54} +(-1.16854 + 5.40726i) q^{55} +(3.05624 + 6.83077i) q^{56} +12.5196i q^{57} +(-5.01386 - 4.38832i) q^{58} +(-6.41474 - 3.70355i) q^{59} +(-14.2859 - 1.14483i) q^{60} +(-0.145254 - 0.251587i) q^{61} +(-3.57989 - 10.5120i) q^{62} +(0.776680 - 19.2185i) q^{63} +(3.10502 + 7.37284i) q^{64} +(1.98768 + 6.18882i) q^{65} +(-10.9991 - 2.17662i) q^{66} +(4.12005 + 2.37871i) q^{67} +(-4.49427 - 1.85124i) q^{68} -18.3670 q^{69} +(-6.91182 + 4.71452i) q^{70} -7.87114i q^{71} +(1.28429 - 20.5220i) q^{72} +(0.915891 - 1.58637i) q^{73} +(-4.65762 - 0.921698i) q^{74} +(-1.56671 - 15.9465i) q^{75} +(4.76866 + 6.18939i) q^{76} +(-5.79623 + 3.04125i) q^{77} +(-12.4712 + 4.24710i) q^{78} +(-1.69463 + 0.978393i) q^{79} +(-7.49866 + 4.87545i) q^{80} +(-11.0205 + 19.0880i) q^{81} +(6.12808 + 5.36353i) q^{82} +6.61627 q^{83} +(-9.79862 - 13.8399i) q^{84} +(1.14789 - 5.31172i) q^{85} +(0.812839 + 0.711428i) q^{86} +(13.0758 + 7.54934i) q^{87} +(-6.26679 + 3.11346i) q^{88} +(3.72584 - 2.15111i) q^{89} +(22.8363 - 2.64707i) q^{90} +(-4.11138 + 6.49998i) q^{91} +(-9.08023 + 6.99593i) q^{92} +(12.5820 + 21.7927i) q^{93} +(0.909478 - 4.59587i) q^{94} +(-5.86726 + 6.47195i) q^{95} +(-10.1455 - 15.0234i) q^{96} +15.9453 q^{97} +(-9.52443 - 2.69912i) q^{98} +17.9857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) $ 80 * q + 6 * q^4 - 52 * q^9	$ 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) $ 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.931410	+	1.06418i	−0.658606	+	0.752488i
$2$	−0.931410	+	1.06418i	−0.658606	+	0.752488i
$3$	1.60233	−	2.77531i	0.925105	−	1.60233i	0.133712	−	0.991020i	$-0.457310\pi$
$3$	1.60233	−	2.77531i	0.925105	−	1.60233i	0.791392	−	0.611308i	$-0.209356\pi$
$4$	−0.264952	−	1.98237i	−0.132476	−	0.991186i
$5$	2.12896	−	0.683763i	0.952100	−	0.305788i
$5$	2.12896	−	0.683763i	0.952100	−	0.305788i
$6$	1.46101	+	4.29012i	0.596453	+	1.75143i
$7$	2.23600	+	1.41432i	0.845129	+	0.534562i
$7$	2.23600	+	1.41432i	0.845129	+	0.534562i
$8$	2.35638	+	1.56444i	0.833105	+	0.553115i
$9$	−3.63491	−	6.29586i	−1.21164	−	2.09862i
$10$	−1.25529	+	2.90246i	−0.396957	+	0.917837i
$11$	−1.23701	+	2.14257i	−0.372973	+	0.646008i	−0.990021	−	0.140917i	$-0.954995\pi$
$11$	−1.23701	+	2.14257i	−0.372973	+	0.646008i	0.617049	+	0.786925i	$0.288328\pi$
$12$	−5.92625	−	2.44109i	−1.71076	−	0.704681i
$13$			2.90697i			0.806248i	0.915145	+	0.403124i	$0.132076\pi$
$13$			2.90697i			0.806248i	−0.915145	+	0.403124i	$0.867924\pi$
$14$	−3.58772	+	1.06219i	−0.958859	+	0.283883i
$15$	1.51364	−	7.00414i	0.390819	−	1.80846i
$16$	−3.85960	+	1.05047i	−0.964900	+	0.262617i
$17$	1.21515	−	2.10471i	0.294718	−	0.510467i	−0.680201	−	0.733026i	$-0.738108\pi$
$17$	1.21515	−	2.10471i	0.294718	−	0.510467i	0.974919	+	0.222559i	$0.0714409\pi$
$18$	10.0855	+	1.99582i	2.37718	+	0.470420i
$19$	−3.38329	+	1.95334i	−0.776179	+	0.448127i	−0.835075	−	0.550137i	$-0.814576\pi$
$19$	−3.38329	+	1.95334i	−0.776179	+	0.448127i	0.0588952	+	0.998264i	$0.481242\pi$
$20$	−1.91954	−	4.03923i	−0.429223	−	0.903198i
$21$	7.50799	−	3.93940i	1.63838	−	0.859648i
$22$	−1.12791	−	3.31201i	−0.240471	−	0.706122i
$23$	−2.86568	−	4.96350i	−0.597535	−	1.03496i	−0.993184	−	0.116559i	$-0.962814\pi$
$23$	−2.86568	−	4.96350i	−0.597535	−	1.03496i	0.395649	−	0.918402i	$-0.370520\pi$
$24$	8.11752	−	4.03293i	1.65698	−	0.823219i
$25$	4.06494	−	2.91141i	0.812987	−	0.582281i
$26$	−3.09353	−	2.70758i	−0.606692	−	0.531000i
$27$	−13.6833			−2.63336
$28$	2.21128	−	4.80731i	0.417892	−	0.908497i
$29$			4.71148i			0.874900i	0.899243	+	0.437450i	$0.144118\pi$
$29$			4.71148i			0.874900i	−0.899243	+	0.437450i	$0.855882\pi$
$30$	6.04385	+	8.13451i	1.10345	+	1.48515i
$31$	−3.92617	+	6.80032i	−0.705161	+	1.22137i	0.261473	+	0.965211i	$0.415792\pi$
$31$	−3.92617	+	6.80032i	−0.705161	+	1.22137i	−0.966634	+	0.256163i	$0.917542\pi$
$32$	2.47699	−	5.08572i	0.437873	−	0.899037i
$33$	3.96419	+	6.86619i	0.690078	+	1.19525i
$34$	1.10798	+	3.25349i	0.190017	+	0.557968i
$35$	5.72741	+	1.48213i	0.968110	+	0.250526i
$36$	−11.5177	+	8.87385i	−1.91961	+	1.47898i
$37$	1.67865	+	2.90751i	0.275969	+	0.477991i	0.970379	−	0.241588i	$-0.0776681\pi$
$37$	1.67865	+	2.90751i	0.275969	+	0.477991i	−0.694411	+	0.719579i	$0.744335\pi$
$38$	1.07252	−	5.41978i	0.173986	−	0.879205i
$39$	8.06775	+	4.65792i	1.29187	+	0.745864i
$40$	6.08634	+	1.71944i	0.962335	+	0.271867i
$41$		−	5.75850i		−	0.899327i	−0.893198	−	0.449664i	$-0.851544\pi$
$41$		−	5.75850i		−	0.899327i	0.893198	−	0.449664i	$-0.148456\pi$
$42$	−2.80079	+	11.6590i	−0.432171	+	1.79903i
$43$		−	0.763818i		−	0.116481i	−0.998303	−	0.0582406i	$-0.981451\pi$
$43$		−	0.763818i		−	0.116481i	0.998303	−	0.0582406i	$-0.0185491\pi$
$44$	4.57511	+	1.88454i	0.689724	+	0.284105i
$45$	−12.0435	−	10.9182i	−1.79533	−	1.62759i
$46$	7.95117	+	1.57346i	1.17234	+	0.231994i
$47$	−2.86896	+	1.65640i	−0.418481	+	0.241610i	−0.694427	−	0.719563i	$-0.744342\pi$
$47$	−2.86896	+	1.65640i	−0.418481	+	0.241610i	0.275946	+	0.961173i	$0.411009\pi$
$48$	−3.26897	+	12.3948i	−0.471836	+	1.78904i
$49$	2.99940	+	6.32484i	0.428486	+	0.903548i
$50$	−0.687865	+	7.03753i	−0.0972787	+	0.995257i
$51$	−3.89415	−	6.74487i	−0.545290	−	0.944471i
$52$	5.76269	−	0.770206i	0.799142	−	0.106808i
$53$	−0.474139	+	0.821232i	−0.0651280	+	0.112805i	−0.896751	−	0.442536i	$-0.854079\pi$
$53$	−0.474139	+	0.821232i	−0.0651280	+	0.112805i	0.831623	+	0.555341i	$0.187412\pi$
$54$	12.7448	−	14.5615i	1.73435	−	1.98157i
$55$	−1.16854	+	5.40726i	−0.157566	+	0.729114i
$56$	3.05624	+	6.83077i	0.408407	+	0.912800i
$57$			12.5196i			1.65826i
$58$	−5.01386	−	4.38832i	−0.658352	−	0.576215i
$59$	−6.41474	−	3.70355i	−0.835128	−	0.482161i	0.0204773	−	0.999790i	$-0.493481\pi$
$59$	−6.41474	−	3.70355i	−0.835128	−	0.482161i	−0.855605	+	0.517629i	$0.826815\pi$
$60$	−14.2859	−	1.14483i	−1.84430	−	0.147797i
$61$	−0.145254	−	0.251587i	−0.0185978	−	0.0322124i	0.856577	−	0.516020i	$-0.172587\pi$
$61$	−0.145254	−	0.251587i	−0.0185978	−	0.0322124i	−0.875175	+	0.483807i	$0.839254\pi$
$62$	−3.57989	−	10.5120i	−0.454646	−	1.33503i
$63$	0.776680	−	19.2185i	0.0978524	−	2.42130i
$64$	3.10502	+	7.37284i	0.388128	+	0.921605i
$65$	1.98768	+	6.18882i	0.246541	+	0.767628i
$66$	−10.9991	−	2.17662i	−1.35390	−	0.267924i
$67$	4.12005	+	2.37871i	0.503344	+	0.290606i	0.730094	−	0.683347i	$-0.239476\pi$
$67$	4.12005	+	2.37871i	0.503344	+	0.290606i	−0.226749	+	0.973953i	$0.572810\pi$
$68$	−4.49427	−	1.85124i	−0.545011	−	0.224496i
$69$	−18.3670			−2.21113
$70$	−6.91182	+	4.71452i	−0.826121	+	0.563493i
$71$		−	7.87114i		−	0.934132i	−0.884222	−	0.467066i	$-0.845311\pi$
$71$		−	7.87114i		−	0.934132i	0.884222	−	0.467066i	$-0.154689\pi$
$72$	1.28429	−	20.5220i	0.151355	−	2.41854i
$73$	0.915891	−	1.58637i	0.107197	−	0.185671i	−0.807437	−	0.589954i	$-0.799146\pi$
$73$	0.915891	−	1.58637i	0.107197	−	0.185671i	0.914634	+	0.404284i	$0.132479\pi$
$74$	−4.65762	−	0.921698i	−0.541437	−	0.107145i
$75$	−1.56671	−	15.9465i	−0.180908	−	1.84134i
$76$	4.76866	+	6.18939i	0.547003	+	0.709972i
$77$	−5.79623	+	3.04125i	−0.660541	+	0.346583i
$78$	−12.4712	+	4.24710i	−1.41209	+	0.480889i
$79$	−1.69463	+	0.978393i	−0.190660	+	0.110078i	−0.592292	−	0.805724i	$-0.701777\pi$
$79$	−1.69463	+	0.978393i	−0.190660	+	0.110078i	0.401631	+	0.915801i	$0.368443\pi$
$80$	−7.49866	+	4.87545i	−0.838376	+	0.545092i
$81$	−11.0205	+	19.0880i	−1.22449	+	2.12089i
$82$	6.12808	+	5.36353i	0.676733	+	0.592302i
$83$	6.61627			0.726230			0.363115	−	0.931744i	$-0.381713\pi$
$83$	6.61627			0.726230			0.363115	+	0.931744i	$0.381713\pi$
$84$	−9.79862	−	13.8399i	−1.06912	−	1.51005i
$85$	1.14789	−	5.31172i	0.124506	−	0.576137i
$86$	0.812839	+	0.711428i	0.0876507	+	0.0767153i
$87$	13.0758	+	7.54934i	1.40188	+	0.809374i
$88$	−6.26679	+	3.11346i	−0.668042	+	0.331896i
$89$	3.72584	−	2.15111i	0.394938	−	0.228018i	−0.289359	−	0.957221i	$-0.593442\pi$
$89$	3.72584	−	2.15111i	0.394938	−	0.228018i	0.684298	+	0.729203i	$0.260109\pi$
$90$	22.8363	−	2.64707i	2.40716	−	0.279026i
$91$	−4.11138	+	6.49998i	−0.430990	+	0.681383i
$92$	−9.08023	+	6.99593i	−0.946680	+	0.729376i
$93$	12.5820	+	21.7927i	1.30469	+	2.25980i
$94$	0.909478	−	4.59587i	0.0938055	−	0.474028i
$95$	−5.86726	+	6.47195i	−0.601968	+	0.664008i
$96$	−10.1455	−	15.0234i	−1.03547	−	1.53332i
$97$	15.9453			1.61900			0.809498	−	0.587123i	$-0.199739\pi$
$97$	15.9453			1.61900			0.809498	+	0.587123i	$0.199739\pi$
$98$	−9.52443	−	2.69912i	−0.962113	−	0.272652i
$99$	17.9857			1.80763
$100$	−6.84851	−	7.28684i	−0.684851	−	0.728684i
$101$	−6.08259	+	10.5354i	−0.605240	+	1.04831i	0.386773	+	0.922175i	$0.373590\pi$
$101$	−6.08259	+	10.5354i	−0.605240	+	1.04831i	−0.992013	+	0.126132i	$0.959744\pi$
$102$	10.8048	+	2.13816i	1.06983	+	0.211710i
$103$	−10.9386	+	6.31541i	−1.07781	+	0.622276i	−0.930306	−	0.366785i	$-0.880458\pi$
$103$	−10.9386	+	6.31541i	−1.07781	+	0.622276i	−0.147507	+	0.989061i	$0.547125\pi$
$104$	−4.54779	+	6.84991i	−0.445948	+	0.671689i
$105$	13.2906	−	13.5205i	1.29703	−	1.31947i
$106$	−0.432320	−	1.26947i	−0.0419907	−	0.123302i
$107$	−8.49616	+	4.90526i	−0.821355	+	0.474209i	−0.850883	−	0.525355i	$-0.823933\pi$
$107$	−8.49616	+	4.90526i	−0.821355	+	0.474209i	0.0295287	+	0.999564i	$0.490599\pi$
$108$	3.62542	+	27.1255i	0.348857	+	2.61015i
$109$	2.87979	+	1.66265i	0.275834	+	0.159253i	0.631536	−	0.775347i	$-0.282425\pi$
$109$	2.87979	+	1.66265i	0.275834	+	0.159253i	−0.355702	+	0.934599i	$0.615758\pi$
$110$	−4.66590	−	6.27990i	−0.444876	−	0.598765i
$111$	10.7590			1.02120
$112$	−10.1158	−	3.10986i	−0.955850	−	0.293855i
$113$		−	6.24090i		−	0.587095i	−0.955945	−	0.293547i	$-0.905164\pi$
$113$		−	6.24090i		−	0.587095i	0.955945	−	0.293547i	$-0.0948358\pi$
$114$	−13.3231	−	11.6609i	−1.24782	−	1.09214i
$115$	−9.49476	−	8.60764i	−0.885391	−	0.802667i
$116$	9.33991	−	1.24832i	0.867189	−	0.115903i
$117$	18.3018	−	10.5666i	1.69201	−	0.976880i
$118$	9.91599	−	3.37690i	0.912841	−	0.310869i
$119$	5.69382	−	2.98751i	0.521951	−	0.273865i
$120$	14.5243	−	14.1364i	1.32588	−	1.29047i
$121$	2.43961	+	4.22553i	0.221783	+	0.384139i
$122$	0.403024	+	0.0797546i	0.0364881	+	0.00722064i
$123$	−15.9817	−	9.22701i	−1.44102	−	0.831972i
$124$	14.5210	+	5.98137i	1.30403	+	0.537143i
$125$	6.66337	−	8.97772i	0.595990	−	0.802992i
$126$	19.7285	+	18.7268i	1.75755	+	1.66832i
$127$	17.2612			1.53169			0.765843	−	0.643027i	$-0.222322\pi$
$127$	17.2612			1.53169			0.765843	+	0.643027i	$0.222322\pi$
$128$	−10.7381	−	3.56284i	−0.949120	−	0.314913i
$129$	−2.11984	−	1.22389i	−0.186641	−	0.107757i
$130$	−8.43735	−	3.64908i	−0.740004	−	0.320046i
$131$	1.77736	−	1.02616i	0.155289	−	0.0896562i	−0.420342	−	0.907366i	$-0.638090\pi$
$131$	1.77736	−	1.02616i	0.155289	−	0.0896562i	0.575631	+	0.817710i	$0.304757\pi$
$132$	12.5610	−	9.67772i	1.09330	−	0.842337i
$133$	−10.3277	−	0.417375i	−0.895524	−	0.0361910i
$134$	−6.36883	+	2.16891i	−0.550183	+	0.187366i
$135$	−29.1313	+	9.35616i	−2.50722	+	0.805250i
$136$	6.15606	−	3.05845i	0.527878	−	0.262259i
$137$	−7.40950	−	4.27788i	−0.633036	−	0.365484i	0.148891	−	0.988854i	$-0.452430\pi$
$137$	−7.40950	−	4.27788i	−0.633036	−	0.365484i	−0.781927	+	0.623370i	$0.785763\pi$
$138$	17.1072	−	19.5458i	1.45626	−	1.66385i
$139$			13.3454i			1.13194i	0.824426	+	0.565970i	$0.191498\pi$
$139$			13.3454i			1.13194i	−0.824426	+	0.565970i	$0.808502\pi$
$140$	1.42065	−	11.7466i	0.120067	−	0.992766i
$141$			10.6164i			0.894059i
$142$	8.37629	+	7.33125i	0.702923	+	0.615225i
$143$	−6.22837	−	3.59595i	−0.520842	−	0.300708i
$144$	20.6429	+	20.4811i	1.72024	+	1.70676i
$145$	3.22154	+	10.0306i	0.267534	+	0.832992i
$146$	0.835111	+	2.45223i	0.0691143	+	0.202948i
$147$	22.3594	+	1.81019i	1.84418	+	0.149302i
$148$	5.31900	−	4.09806i	0.437219	−	0.336859i
$149$	10.0494	−	5.80204i	0.823281	−	0.475321i	−0.0282658	−	0.999600i	$-0.508998\pi$
$149$	10.0494	−	5.80204i	0.823281	−	0.475321i	0.851547	+	0.524279i	$0.175665\pi$
$150$	18.4292	+	13.1855i	1.50474	+	1.07659i
$151$	−13.4070	−	7.74053i	−1.09104	−	0.629915i	−0.157190	−	0.987568i	$-0.550244\pi$
$151$	−13.4070	−	7.74053i	−1.09104	−	0.629915i	−0.933854	+	0.357653i	$0.883577\pi$
$152$	−11.0282	−	0.690157i	−0.894505	−	0.0559791i
$153$	−17.6679			−1.42837
$154$	2.16223	−	9.00087i	0.174238	−	0.725311i
$155$	−3.70884	+	17.1622i	−0.297902	+	1.37850i
$156$	7.09616	−	17.2274i	0.568148	−	1.37930i
$157$	−1.73719	−	1.00296i	−0.138643	−	0.0800453i	0.429074	−	0.903269i	$-0.358840\pi$
$157$	−1.73719	−	1.00296i	−0.138643	−	0.0800453i	−0.567717	+	0.823224i	$0.692173\pi$
$158$	0.537207	−	2.71467i	0.0427379	−	0.215967i
$159$	1.51945	+	2.63177i	0.120500	+	0.208713i
$160$	1.79598	−	12.5210i	0.141984	−	0.989869i
$161$	0.612315	−	15.1514i	0.0482572	−	1.19409i
$162$	−10.0485	−	29.5065i	−0.789482	−	2.31825i
$163$	14.2898	−	8.25020i	1.11926	−	0.646205i	0.178048	−	0.984022i	$-0.443022\pi$
$163$	14.2898	−	8.25020i	1.11926	−	0.646205i	0.941212	+	0.337816i	$0.109688\pi$
$164$	−11.4155	+	1.52573i	−0.891401	+	0.119139i
$165$	13.1345	+	11.9073i	1.02252	+	0.926979i
$166$	−6.16246	+	7.04090i	−0.478300	+	0.546480i
$167$		−	4.67196i		−	0.361527i	−0.983527	−	0.180763i	$-0.942143\pi$
$167$		−	4.67196i		−	0.361527i	0.983527	−	0.180763i	$-0.0578568\pi$
$168$	23.8546	+	2.46312i	1.84042	+	0.190034i
$169$	4.54954			0.349965
$170$	4.58346	+	6.16895i	0.351535	+	0.473137i
$171$	24.5959	+	14.2005i	1.88090	+	1.08594i
$172$	−1.51417	+	0.202375i	−0.115455	+	0.0154310i
$173$	6.44746	−	3.72244i	0.490191	−	0.283012i	−0.234463	−	0.972125i	$-0.575333\pi$
$173$	6.44746	−	3.72244i	0.490191	−	0.283012i	0.724654	+	0.689113i	$0.242000\pi$
$174$	−20.2128	+	6.88350i	−1.53233	+	0.521837i
$175$	13.2069	−	0.760790i	0.998345	−	0.0575103i
$176$	2.52367	−	9.56888i	0.190229	−	0.721282i
$177$	−20.5570	+	11.8686i	−1.54516	+	0.892099i
$178$	−1.18111	+	5.96853i	−0.0885282	+	0.447360i
$179$	−4.86291	+	8.42281i	−0.363471	+	0.629550i	−0.988530	−	0.151028i	$-0.951742\pi$
$179$	−4.86291	+	8.42281i	−0.363471	+	0.629550i	0.625059	+	0.780578i	$0.285075\pi$
$180$	−18.4530	+	26.7674i	−1.37541	+	1.99513i
$181$	−5.72502			−0.425537			−0.212769	−	0.977103i	$-0.568248\pi$
$181$	−5.72502			−0.425537			−0.212769	+	0.977103i	$0.568248\pi$
$182$	−3.08776	−	10.4294i	−0.228880	−	0.773078i
$183$	−0.930977			−0.0688198
$184$	1.01250	−	16.1791i	0.0746428	−	1.19274i
$185$	5.56183	+	5.04217i	0.408914	+	0.370708i
$186$	−34.9103	−	6.90842i	−2.55975	−	0.506550i
$187$	3.00632	+	5.20709i	0.219844	+	0.380780i
$188$	4.04373	+	5.24848i	0.294919	+	0.382785i
$189$	−30.5959	−	19.3526i	−2.22553	−	1.40769i
$190$	−1.42249	−	12.2718i	−0.103198	−	0.890294i
$191$	−2.66537	+	1.53885i	−0.192860	+	0.111347i	−0.593321	−	0.804966i	$-0.702183\pi$
$191$	−2.66537	+	1.53885i	−0.192860	+	0.111347i	0.400461	+	0.916314i	$0.368850\pi$
$192$	25.4372	+	3.19630i	1.83577	+	0.230673i
$193$	−16.3501	−	9.43976i	−1.17691	−	0.679488i	−0.221611	−	0.975135i	$-0.571132\pi$
$193$	−16.3501	−	9.43976i	−1.17691	−	0.679488i	−0.955297	+	0.295647i	$0.904465\pi$
$194$	−14.8516	+	16.9686i	−1.06628	+	1.21827i
$195$	20.3608	+	4.40009i	1.45807	+	0.315097i
$196$	11.7435	−	7.62171i	0.838821	−	0.544408i
$197$	4.81372			0.342964			0.171482	−	0.985187i	$-0.445145\pi$
$197$	4.81372			0.342964			0.171482	+	0.985187i	$0.445145\pi$
$198$	−16.7521	+	19.1400i	−1.19052	+	1.36022i
$199$	12.0922	−	20.9442i	0.857190	−	1.48470i	−0.0174086	−	0.999848i	$-0.505542\pi$
$199$	12.0922	−	20.9442i	0.857190	−	1.48470i	0.874598	−	0.484848i	$-0.161125\pi$
$200$	14.1333	−	0.501003i	0.999372	−	0.0354263i
$201$	13.2034	−	7.62296i	0.931293	−	0.537682i
$202$	−5.54612	−	16.2857i	−0.390223	−	1.14586i
$203$	−6.66354	+	10.5349i	−0.467689	+	0.739404i
$204$	−12.3391	+	9.50673i	−0.863908	+	0.665604i
$205$	−3.93745	−	12.2596i	−0.275004	−	0.856249i
$206$	3.46760	−	17.5229i	0.241599	−	1.22088i
$207$	−20.8330	+	36.0838i	−1.44799	+	2.50800i
$208$	−3.05367	−	11.2197i	−0.211734	−	0.777949i
$209$		−	9.66522i		−	0.668557i
$210$	2.00925	+	26.7367i	0.138652	+	1.84501i
$211$	−24.8628			−1.71163			−0.855814	−	0.517284i	$-0.826943\pi$
$211$	−24.8628			−1.71163			−0.855814	+	0.517284i	$0.826943\pi$
$212$	1.75361	+	0.722333i	0.120439	+	0.0496100i
$213$	−21.8449	−	12.6121i	−1.49679	−	0.864170i
$214$	2.69333	−	13.6102i	0.184112	−	0.930377i
$215$	−0.522271	−	1.62614i	−0.0356186	−	0.110902i
$216$	−32.2431	−	21.4068i	−2.19386	−	1.45655i
$217$	−18.3967	+	9.65267i	−1.24885	+	0.655266i
$218$	−4.45161	+	1.51600i	−0.301501	+	0.102677i
$219$	−2.93512	−	5.08377i	−0.198337	−	0.343529i
$220$	11.0288	+	0.883816i	0.743562	+	0.0595869i
$221$	6.11832	+	3.53241i	0.411563	+	0.237616i
$222$	−10.0210	+	11.4495i	−0.672568	+	0.768440i
$223$			6.76281i			0.452871i	0.974026	+	0.226436i	$0.0727073\pi$
$223$			6.76281i			0.452871i	−0.974026	+	0.226436i	$0.927293\pi$
$224$	12.7314	−	7.86842i	0.850651	−	0.525731i
$225$	−33.1055	−	15.0095i	−2.20703	−	1.00064i
$226$	6.64143	+	5.81284i	0.441782	+	0.386664i
$227$	−4.30970	+	7.46462i	−0.286045	+	0.495444i	−0.972862	−	0.231386i	$-0.925674\pi$
$227$	−4.30970	+	7.46462i	−0.286045	+	0.495444i	0.686817	+	0.726830i	$0.259007\pi$
$228$	24.8185	−	3.31709i	1.64364	−	0.219679i
$229$	−10.3387	−	17.9071i	−0.683200	−	1.18334i	−0.973999	−	0.226552i	$-0.927255\pi$
$229$	−10.3387	−	17.9071i	−0.683200	−	1.18334i	0.290799	−	0.956784i	$-0.406079\pi$
$230$	18.0036	−	2.08688i	1.18712	−	0.137605i
$231$	−0.847038	+	20.9594i	−0.0557310	+	1.37903i
$232$	−7.37085	+	11.1020i	−0.483920	+	0.728884i
$233$	19.1261	−	11.0424i	1.25299	−	0.723414i	0.281287	−	0.959624i	$-0.409239\pi$
$233$	19.1261	−	11.0424i	1.25299	−	0.723414i	0.971702	+	0.236210i	$0.0759053\pi$
$234$	−5.80179	+	29.3182i	−0.379275	+	1.91659i
$235$	−4.97532	+	5.48809i	−0.324554	+	0.358003i
$236$	−5.64222	+	13.6977i	−0.367277	+	0.891642i
$237$			6.27083i			0.407334i
$238$	−2.12403	+	8.84184i	−0.137680	+	0.573131i
$239$			10.7855i			0.697656i	0.937187	+	0.348828i	$0.113420\pi$
$239$			10.7855i			0.697656i	−0.937187	+	0.348828i	$0.886580\pi$
$240$	1.51559	+	28.6232i	0.0978310	+	1.84762i
$241$	−15.4652	−	8.92882i	−0.996200	−	0.575156i	−0.0890780	−	0.996025i	$-0.528392\pi$
$241$	−15.4652	−	8.92882i	−0.996200	−	0.575156i	−0.907122	+	0.420868i	$0.861725\pi$
$242$	−6.76899	−	1.33952i	−0.435127	−	0.0861075i
$243$	14.7918	+	25.6201i	0.948893	+	1.64353i
$244$	−0.460254	+	0.354606i	−0.0294647	+	0.0227013i
$245$	10.7103	+	11.4144i	0.684256	+	0.729242i
$246$	24.7047	−	8.41321i	1.57511	−	0.536406i
$247$	−5.67830	−	9.83511i	−0.361302	−	0.625793i
$248$	−19.8903	+	9.88185i	−1.26303	+	0.627498i
$249$	10.6014	−	18.3622i	0.671839	−	1.16366i
$250$	3.34757	+	15.4530i	0.211719	+	0.977331i
$251$		−	11.0237i		−	0.695810i	−0.937530	−	0.347905i	$-0.886893\pi$
$251$		−	11.0237i		−	0.695810i	0.937530	−	0.347905i	$-0.113107\pi$
$252$	−38.3039	+	3.55230i	−2.41292	+	0.223774i
$253$	14.1795			0.891457
$254$	−16.0773	+	18.3690i	−1.00878	+	1.15258i
$255$	−12.9024	−	11.6969i	−0.807979	−	0.732487i
$256$	13.7930	−	8.10876i	0.862065	−	0.506798i
$257$	−15.5353	−	26.9079i	−0.969065	−	1.67847i	−0.698272	−	0.715832i	$-0.746048\pi$
$257$	−15.5353	−	26.9079i	−0.969065	−	1.67847i	−0.270793	−	0.962638i	$-0.587286\pi$
$258$	3.27687	−	1.11594i	0.204009	−	0.0694756i
$259$	−0.358681	+	8.87534i	−0.0222873	+	0.551487i
$260$	11.7419	−	5.58005i	0.728202	−	0.346060i
$261$	29.6628	−	17.1258i	1.83608	−	1.06006i
$262$	−0.563435	+	2.84721i	−0.0348091	+	0.175901i
$263$	9.32868	−	16.1577i	0.575231	−	0.996329i	−0.420786	−	0.907160i	$-0.638246\pi$
$263$	9.32868	−	16.1577i	0.575231	−	0.996329i	0.996017	−	0.0891689i	$-0.0284211\pi$
$264$	−1.40063	+	22.3811i	−0.0862031	+	1.37746i
$265$	−0.447894	+	2.07257i	−0.0275139	+	0.127317i
$266$	10.0635	−	10.6018i	0.617031	−	0.650035i
$267$		−	13.7872i		−	0.843761i
$268$	3.62388	−	8.79772i	0.221364	−	0.537406i
$269$	1.41984	−	2.45923i	0.0865689	−	0.149942i	−0.819490	−	0.573094i	$-0.805743\pi$
$269$	1.41984	−	2.45923i	0.0865689	−	0.149942i	0.906059	+	0.423152i	$0.139076\pi$
$270$	17.1765	−	39.7153i	1.04533	−	2.41699i
$271$	−9.37179	−	16.2324i	−0.569296	−	0.986049i	−0.996636	−	0.0819580i	$-0.973883\pi$
$271$	−9.37179	−	16.2324i	−0.569296	−	0.986049i	0.427340	−	0.904091i	$-0.359451\pi$
$272$	−2.47908	+	9.39981i	−0.150317	+	0.569947i
$273$	11.4517	+	21.8255i	0.693089	+	1.32094i
$274$	11.4537	−	3.90057i	0.691943	−	0.235642i
$275$	1.20951	+	12.3108i	0.0729362	+	0.742371i
$276$	4.86638	+	36.4103i	0.292921	+	2.19164i
$277$	−11.9110	+	20.6304i	−0.715661	+	1.23956i	0.247043	+	0.969004i	$0.420541\pi$
$277$	−11.9110	+	20.6304i	−0.715661	+	1.23956i	−0.962704	+	0.270557i	$0.912792\pi$
$278$	−14.2019	−	12.4300i	−0.851771	−	0.745502i
$279$	57.0851			3.41760
$280$	11.1772	+	12.4527i	0.667967	+	0.744191i
$281$	10.3608			0.618073			0.309037	−	0.951050i	$-0.399993\pi$
$281$	10.3608			0.618073			0.309037	+	0.951050i	$0.399993\pi$
$282$	−11.2977	−	9.88818i	−0.672768	−	0.588833i
$283$	4.67454	−	8.09653i	0.277872	−	0.481289i	−0.692983	−	0.720953i	$-0.743704\pi$
$283$	4.67454	−	8.09653i	0.277872	−	0.481289i	0.970856	+	0.239665i	$0.0770375\pi$
$284$	−15.6035	+	2.08547i	−0.925899	+	0.123750i
$285$	8.56043	+	26.6537i	0.507076	+	1.57883i
$286$	9.62789	−	3.27879i	0.569309	−	0.193879i
$287$	8.14436	−	12.8760i	0.480747	−	0.760047i
$288$	−41.0226	+	2.89140i	−2.41728	+	0.170378i
$289$	5.54680	+	9.60734i	0.326282	+	0.565138i
$290$	−13.6749	−	5.91427i	−0.803016	−	0.347298i
$291$	25.5495	−	44.2531i	1.49774	−	2.59416i
$292$	−3.38744	−	1.39533i	−0.198235	−	0.0816553i
$293$		−	16.0747i		−	0.939094i	−0.882907	−	0.469547i	$-0.844417\pi$
$293$		−	16.0747i		−	0.939094i	0.882907	−	0.469547i	$-0.155583\pi$
$294$	−22.7522	+	22.1084i	−1.32693	+	1.28939i
$295$	−16.1891	−	3.49855i	−0.942564	−	0.203693i
$296$	−0.593103	+	9.47734i	−0.0344734	+	0.550859i
$297$	16.9264	−	29.3174i	0.982171	−	1.70117i
$298$	−3.18573	+	16.0985i	−0.184544	+	0.932558i
$299$	14.4287	−	8.33043i	0.834435	−	0.481761i
$300$	−31.1968	+	7.33085i	−1.80115	+	0.423247i
$301$	1.08028	−	1.70790i	0.0622665	−	0.0984417i
$302$	20.7247	−	7.05782i	1.19257	−	0.406132i
$303$	19.4926	+	33.7622i	1.11982	+	1.93959i
$304$	11.0062	−	11.0931i	0.631250	−	0.636236i
$305$	−0.481265	−	0.436299i	−0.0275572	−	0.0249824i
$306$	16.4561	−	18.8018i	0.940731	−	1.07483i
$307$	−14.9824			−0.855091			−0.427545	−	0.903994i	$-0.640622\pi$
$307$	−14.9824			−0.855091			−0.427545	+	0.903994i	$0.640622\pi$
$308$	7.56461	+	10.6845i	0.431034	+	0.608806i
$309$			40.4774i			2.30268i
$310$	−14.8092	−	19.9319i	−0.841104	−	1.13206i
$311$	−15.4750	+	26.8036i	−0.877509	+	1.51989i	−0.0234437	+	0.999725i	$0.507463\pi$
$311$	−15.4750	+	26.8036i	−0.877509	+	1.51989i	−0.854066	+	0.520165i	$0.825870\pi$
$312$	11.7236	+	23.5974i	0.663718	+	1.33594i
$313$	1.57151	+	2.72194i	0.0888271	+	0.153853i	0.907016	−	0.421097i	$-0.138355\pi$
$313$	1.57151	+	2.72194i	0.0888271	+	0.153853i	−0.818189	+	0.574950i	$0.805021\pi$
$314$	2.68537	−	0.914505i	0.151544	−	0.0516085i
$315$	−11.4874	−	41.4464i	−0.647239	−	2.33524i
$316$	2.38853	+	3.10015i	0.134365	+	0.174397i
$317$	1.89262	+	3.27812i	0.106300	+	0.184118i	0.914269	−	0.405108i	$-0.132766\pi$
$317$	1.89262	+	3.27812i	0.106300	+	0.184118i	−0.807968	+	0.589226i	$0.799433\pi$
$318$	−4.21590	−	0.834286i	−0.236416	−	0.0467845i
$319$	−10.0947	−	5.82815i	−0.565192	−	0.326314i
$320$	11.6517	+	13.5734i	0.651353	+	0.758775i
$321$			31.4393i			1.75477i
$322$	15.5534	+	14.7637i	0.866759	+	0.822751i
$323$			9.49444i			0.528285i
$324$	40.7594	+	16.7892i	2.26441	+	0.932736i
$325$	8.46336	+	11.8166i	0.469463	+	0.655469i
$326$	−4.52994	+	22.8912i	−0.250890	+	1.26782i
$327$	9.22873	−	5.32821i	0.510350	−	0.294651i
$328$	9.00886	−	13.5692i	0.497431	−	0.749234i
$329$	−8.75767	−	0.353925i	−0.482826	−	0.0195125i
$330$	−24.9050	+	2.88686i	−1.37098	+	0.158917i
$331$	−3.83340	−	6.63965i	−0.210703	−	0.364948i	0.741232	−	0.671249i	$-0.234242\pi$
$331$	−3.83340	−	6.63965i	−0.210703	−	0.364948i	−0.951935	+	0.306301i	$0.900909\pi$
$332$	−1.75299	−	13.1159i	−0.0962080	−	0.719830i
$333$	12.2035	−	21.1371i	0.668748	−	1.15831i
$334$	4.97179	+	4.35150i	0.272045	+	0.238104i
$335$	10.3979	+	2.24704i	0.568098	+	0.122769i
$336$	−24.8396	+	23.0914i	−1.35511	+	1.25974i
$337$			24.8688i			1.35469i	0.735667	+	0.677344i	$0.236869\pi$
$337$			24.8688i			1.35469i	−0.735667	+	0.677344i	$0.763131\pi$
$338$	−4.23749	+	4.84152i	−0.230489	+	0.263344i
$339$	−17.3205	−	9.99998i	−0.940719	−	0.543124i
$340$	−10.8339	−	0.868200i	−0.587553	−	0.0470848i
$341$	−9.71342	−	16.8241i	−0.526011	−	0.911078i
$342$	−38.0207	+	12.9480i	−2.05592	+	0.700148i
$343$	−2.23868	+	18.3845i	−0.120877	+	0.992667i
$344$	1.19495	−	1.79984i	0.0644275	−	0.0970411i
$345$	−39.1026	+	12.5587i	−2.10522	+	0.676137i
$346$	−2.04388	+	10.3284i	−0.109880	+	0.555256i
$347$	19.3450	+	11.1689i	1.03850	+	0.599576i	0.919407	−	0.393308i	$-0.128669\pi$
$347$	19.3450	+	11.1689i	1.03850	+	0.599576i	0.119089	+	0.992884i	$0.462003\pi$
$348$	11.5011	−	27.9214i	0.616526	−	1.49674i
$349$	−6.23220			−0.333602			−0.166801	−	0.985991i	$-0.553344\pi$
$349$	−6.23220			−0.333602			−0.166801	+	0.985991i	$0.553344\pi$
$350$	−11.4914	+	14.7631i	−0.614240	+	0.789119i
$351$		−	39.7770i		−	2.12314i
$352$	7.83243	+	11.5982i	0.417470	+	0.618186i
$353$	5.05250	−	8.75119i	0.268918	−	0.465779i	−0.699665	−	0.714471i	$-0.746667\pi$
$353$	5.05250	−	8.75119i	0.268918	−	0.465779i	0.968583	+	0.248692i	$0.0800008\pi$
$354$	6.51670	−	32.9309i	0.346359	−	1.75026i
$355$	−5.38199	−	16.7573i	−0.285646	−	0.889387i
$356$	−5.25148	−	6.81606i	−0.278328	−	0.361250i
$357$	0.832072	−	20.5891i	0.0440379	−	1.08969i
$358$	−4.43401	−	13.0201i	−0.234345	−	0.688133i
$359$	18.4425	−	10.6478i	0.973359	−	0.561969i	0.0731003	−	0.997325i	$-0.476711\pi$
$359$	18.4425	−	10.6478i	0.973359	−	0.561969i	0.900259	+	0.435356i	$0.143377\pi$
$360$	−11.2980	−	44.5687i	−0.595457	−	2.34898i
$361$	−1.86891	+	3.23705i	−0.0983638	+	0.170371i
$362$	5.33234	−	6.09244i	0.280262	−	0.320212i
$363$	15.6362			0.820689
$364$	13.9747	+	6.42810i	0.732473	+	0.336924i
$365$	0.865194	−	4.00357i	0.0452863	−	0.209556i
$366$	0.867121	−	0.990726i	0.0453252	−	0.0517861i
$367$	−26.2490	−	15.1549i	−1.37019	−	0.791077i	−0.379234	−	0.925301i	$-0.623813\pi$
$367$	−26.2490	−	15.1549i	−1.37019	−	0.791077i	−0.990951	+	0.134224i	$0.957146\pi$
$368$	16.2744	+	16.1468i	0.848359	+	0.841711i
$369$	−36.2547	+	20.9317i	−1.88734	+	1.08966i
$370$	−10.5461	+	1.22245i	−0.548266	+	0.0635522i
$371$	−2.22166	+	1.16569i	−0.115343	+	0.0605198i
$372$	39.8676	−	30.7163i	2.06704	−	1.59256i
$373$	−11.6702	−	20.2134i	−0.604260	−	1.04661i	−0.992168	−	0.124911i	$-0.960136\pi$
$373$	−11.6702	−	20.2134i	−0.604260	−	1.04661i	0.387908	−	0.921698i	$-0.373198\pi$
$374$	−8.34139	−	1.65068i	−0.431323	−	0.0853546i
$375$	−14.2391	−	32.8782i	−0.735303	−	1.69782i
$376$	−9.35169	−	0.585240i	−0.482277	−	0.0301814i
$377$	−13.6961			−0.705386
$378$	49.0920	−	14.5343i	2.52502	−	0.747566i
$379$	9.55433			0.490773			0.245387	−	0.969425i	$-0.421085\pi$
$379$	9.55433			0.490773			0.245387	+	0.969425i	$0.421085\pi$
$380$	14.3844	+	9.91634i	0.737902	+	0.508697i
$381$	27.6582	−	47.9053i	1.41697	−	2.45427i
$382$	0.844939	−	4.26973i	0.0432308	−	0.218459i
$383$	−16.2249	+	9.36744i	−0.829052	+	0.478654i	−0.853528	−	0.521047i	$-0.825542\pi$
$383$	−16.2249	+	9.36744i	−0.829052	+	0.478654i	0.0244757	+	0.999700i	$0.492208\pi$
$384$	−27.0939	+	24.0927i	−1.38263	+	1.22947i
$385$	−10.2604	+	10.4379i	−0.522920	+	0.531967i
$386$	25.2743	−	8.60718i	1.28643	−	0.438094i
$387$	−4.80889	+	2.77641i	−0.244450	+	0.141133i
$388$	−4.22473	−	31.6094i	−0.214478	−	1.60473i
$389$	−18.5104	−	10.6870i	−0.938515	−	0.541852i	−0.0490204	−	0.998798i	$-0.515610\pi$
$389$	−18.5104	−	10.6870i	−0.938515	−	0.541852i	−0.889494	+	0.456946i	$0.848943\pi$
$390$	−23.6467	+	17.5693i	−1.19740	+	0.889654i
$391$	−13.9290			−0.704417
$392$	−2.82714	+	19.5961i	−0.142792	+	0.989753i
$393$		−	6.57699i		−	0.331765i
$394$	−4.48355	+	5.12266i	−0.225878	+	0.258076i
$395$	−2.93880	+	3.24168i	−0.147867	+	0.163107i
$396$	−4.76535	−	35.6544i	−0.239468	−	1.79170i
$397$	−0.251200	+	0.145030i	−0.0126073	+	0.00727885i	−0.506290	−	0.862363i	$-0.668984\pi$
$397$	−0.251200	+	0.145030i	−0.0126073	+	0.00727885i	0.493683	+	0.869642i	$0.335650\pi$
$398$	11.0256	+	32.3759i	0.552666	+	1.62286i
$399$	−17.7067	+	27.9938i	−0.886443	+	1.40144i
$400$	−12.6307	+	15.5069i	−0.631535	+	0.775347i
$401$	13.4012	+	23.2115i	0.669223	+	1.15913i	0.978122	+	0.208033i	$0.0667063\pi$
$401$	13.4012	+	23.2115i	0.669223	+	1.15913i	−0.308899	+	0.951095i	$0.599960\pi$
$402$	−4.18554	+	21.1508i	−0.208756	+	1.05491i
$403$	−19.7683	−	11.4132i	−0.984730	−	0.568534i
$404$	22.4966	+	9.26660i	1.11925	+	0.461031i
$405$	−10.4104	+	48.1729i	−0.517299	+	2.39373i
$406$	−5.00451	−	16.9035i	−0.248369	−	0.838906i
$407$	−8.30603			−0.411715
$408$	1.37589	−	21.9856i	0.0681165	−	1.08845i
$409$	11.0759	+	6.39466i	0.547667	+	0.316195i	0.748180	−	0.663495i	$-0.230928\pi$
$409$	11.0759	+	6.39466i	0.547667	+	0.316195i	−0.200514	+	0.979691i	$0.564261\pi$
$410$	16.7138	+	7.22858i	0.825436	+	0.356994i
$411$	−23.7449	+	13.7091i	−1.17125	+	0.676221i
$412$	15.4177	+	20.0111i	0.759575	+	0.985877i
$413$	−9.10536	−	17.3536i	−0.448045	−	0.853916i
$414$	−18.9955	−	55.7788i	−0.933580	−	2.74138i
$415$	14.0858	−	4.52396i	0.691444	−	0.222073i
$416$	14.7840	+	7.20052i	0.724846	+	0.353034i
$417$	37.0376	+	21.3837i	1.81374	+	1.04716i
$418$	10.2855	+	9.00228i	0.503081	+	0.440316i
$419$		−	11.3606i		−	0.555002i	−0.960725	−	0.277501i	$-0.910494\pi$
$419$		−	11.3606i		−	0.555002i	0.960725	−	0.277501i	$-0.0895062\pi$
$420$	−30.3241	−	22.7646i	−1.47966	−	1.11080i
$421$			36.1939i			1.76398i	0.471266	+	0.881991i	$0.343797\pi$
$421$			36.1939i			1.76398i	−0.471266	+	0.881991i	$0.656203\pi$
$422$	23.1575	−	26.4585i	1.12729	−	1.28798i
$423$	20.8569	+	12.0417i	1.01409	+	0.585488i
$424$	−2.40202	+	1.19337i	−0.116653	+	0.0579551i
$425$	−1.18814	−	12.0933i	−0.0576332	−	0.586612i
$426$	33.7681	−	11.4998i	1.63607	−	0.557166i
$427$	0.0310367	−	0.767984i	0.00150197	−	0.0371654i
$428$	11.9751	+	15.5429i	0.578839	+	0.751294i
$429$	−19.9598	+	11.5238i	−0.963667	+	0.556374i
$430$	2.21695	+	0.958812i	0.106911	+	0.0462380i
$431$	26.0484	+	15.0391i	1.25471	+	0.724406i	0.972041	−	0.234812i	$-0.0754475\pi$
$431$	26.0484	+	15.0391i	1.25471	+	0.724406i	0.282667	+	0.959218i	$0.408781\pi$
$432$	52.8122	−	14.3739i	2.54093	−	0.691564i
$433$	−13.9510			−0.670442			−0.335221	−	0.942139i	$-0.608811\pi$
$433$	−13.9510			−0.670442			−0.335221	+	0.942139i	$0.608811\pi$
$434$	6.86274	−	28.5680i	0.329422	−	1.37131i
$435$	32.9999	+	7.13147i	1.58222	+	0.341928i
$436$	2.53298	−	6.14933i	0.121308	−	0.294500i
$437$	19.3908	+	11.1953i	0.927588	+	0.535543i
$438$	8.14384	+	1.61159i	0.389128	+	0.0770046i
$439$	5.58413	+	9.67200i	0.266516	+	0.461619i	0.967960	−	0.251106i	$-0.0807941\pi$
$439$	5.58413	+	9.67200i	0.266516	+	0.461619i	−0.701444	+	0.712725i	$0.747461\pi$
$440$	−11.2129	+	10.9134i	−0.534553	+	0.520277i
$441$	28.9177	−	41.8740i	1.37703	−	1.99400i
$442$	−9.45778	+	3.22086i	−0.449861	+	0.153201i
$443$	−16.0785	+	9.28292i	−0.763912	+	0.441045i	−0.830699	−	0.556722i	$-0.812059\pi$
$443$	−16.0785	+	9.28292i	−0.763912	+	0.441045i	0.0667865	+	0.997767i	$0.478725\pi$
$444$	−2.85062	−	21.3283i	−0.135284	−	1.01220i
$445$	6.46131	−	7.12722i	0.306295	−	0.337863i
$446$	−7.19684	−	6.29895i	−0.340780	−	0.298264i
$447$		−	37.1871i		−	1.75889i
$448$	−3.48472	+	20.8772i	−0.164637	+	0.986354i
$449$	−8.39895			−0.396371			−0.198186	−	0.980165i	$-0.563505\pi$
$449$	−8.39895			−0.396371			−0.198186	+	0.980165i	$0.563505\pi$
$450$	46.8076	−	21.2501i	2.20653	−	1.00174i
$451$	12.3380	+	7.12333i	0.580972	+	0.335424i
$452$	−12.3718	+	1.65354i	−0.581920	+	0.0777759i
$453$	−42.9648	+	24.8057i	−2.01866	+	1.16547i
$454$	−3.92959	−	11.5389i	−0.184425	−	0.541548i
$455$	−4.30852	+	16.6494i	−0.201986	+	0.780536i
$456$	−19.5862	+	29.5009i	−0.917208	+	1.38150i
$457$	24.5026	−	14.1466i	1.14618	−	0.661749i	0.198229	−	0.980156i	$-0.436481\pi$
$457$	24.5026	−	14.1466i	1.14618	−	0.661749i	0.947954	+	0.318406i	$0.103148\pi$
$458$	28.6859	+	5.67667i	1.34041	+	0.265253i
$459$	−16.6274	+	28.7994i	−0.776099	+	1.34424i
$460$	−14.5479	+	21.1028i	−0.678299	+	0.983922i
$461$	−31.5889			−1.47124			−0.735621	−	0.677393i	$-0.763110\pi$
$461$	−31.5889			−1.47124			−0.735621	+	0.677393i	$0.763110\pi$
$462$	−21.5156	−	20.4232i	−1.00100	−	0.950174i
$463$	20.6027			0.957487			0.478744	−	0.877955i	$-0.341092\pi$
$463$	20.6027			0.957487			0.478744	+	0.877955i	$0.341092\pi$
$464$	−4.94925	−	18.1844i	−0.229763	−	0.844192i
$465$	41.6877	+	37.7927i	1.93322	+	1.75259i
$466$	−6.06307	+	30.6386i	−0.280866	+	1.41930i
$467$	−8.18604	−	14.1786i	−0.378805	−	0.656109i	0.612084	−	0.790793i	$-0.290331\pi$
$467$	−8.18604	−	14.1786i	−0.378805	−	0.656109i	−0.990889	+	0.134684i	$0.956998\pi$
$468$	−25.7960	−	33.4814i	−1.19242	−	1.54768i
$469$	5.84818	+	11.1459i	0.270044	+	0.514669i
$470$	−1.20624	−	10.4063i	−0.0556399	−	0.480006i
$471$	−5.56708	+	3.21416i	−0.256518	+	0.148101i
$472$	−9.32154	−	18.7625i	−0.429059	−	0.863613i
$473$	1.63653	+	0.944851i	0.0752478	+	0.0434443i
$474$	−6.67328	−	5.84071i	−0.306514	−	0.268273i
$475$	−8.06588	+	17.7903i	−0.370088	+	0.816277i
$476$	−7.43095	−	10.4957i	−0.340597	−	0.481070i
$477$	6.89381			0.315646
$478$	−11.4777	−	10.0457i	−0.524978	−	0.459481i
$479$	−18.7679	+	32.5069i	−0.857526	+	1.48528i	0.0167554	+	0.999860i	$0.494666\pi$
$479$	−18.7679	+	32.5069i	−0.857526	+	1.48528i	−0.874282	+	0.485419i	$0.838667\pi$
$480$	−31.8719	−	25.0471i	−1.45474	−	1.14324i
$481$	−8.45203	+	4.87978i	−0.385379	+	0.222499i
$482$	23.9063	−	8.14132i	1.08890	−	0.370827i
$483$	−41.0687	−	25.9768i	−1.86869	−	1.18199i
$484$	7.73019	−	5.95578i	0.351372	−	0.270717i
$485$	33.9468	−	10.9028i	1.54145	−	0.495070i
$486$	−41.0416	−	8.12173i	−1.86168	−	0.368409i
$487$	12.1439	−	21.0339i	0.550294	−	0.953138i	−0.447959	−	0.894054i	$-0.647849\pi$
$487$	12.1439	−	21.0339i	0.550294	−	0.953138i	0.998253	−	0.0590835i	$-0.0188178\pi$
$488$	0.0513212	−	0.820075i	0.00232320	−	0.0371231i
$489$		−	52.8781i		−	2.39123i
$490$	−22.1227	+	0.766138i	−0.999401	+	0.0346106i
$491$	15.9769			0.721025			0.360513	−	0.932754i	$-0.382602\pi$
$491$	15.9769			0.721025			0.360513	+	0.932754i	$0.382602\pi$
$492$	−14.0570	+	34.1263i	−0.633739	+	1.53853i
$493$	9.91630	+	5.72518i	0.446608	+	0.257849i
$494$	15.7551	+	3.11779i	0.708857	+	0.140276i
$495$	38.2908	−	12.2980i	1.72105	−	0.552752i
$496$	8.00993	−	30.3708i	0.359657	−	1.36369i
$497$	11.1323	−	17.5999i	0.499352	−	0.789462i
$498$	9.66641	+	28.3846i	0.433162	+	1.27194i
$499$	7.03517	+	12.1853i	0.314937	+	0.545487i	0.979424	−	0.201813i	$-0.0646832\pi$
$499$	7.03517	+	12.1853i	0.314937	+	0.545487i	−0.664487	+	0.747300i	$0.731350\pi$
$500$	−19.5627	−	10.8306i	−0.874869	−	0.484360i
$501$	−12.9661	−	7.48601i	−0.579285	−	0.334450i
$502$	11.7312	+	10.2676i	0.523588	+	0.458265i
$503$			8.77499i			0.391258i	0.980678	+	0.195629i	$0.0626748\pi$
$503$			8.77499i			0.391258i	−0.980678	+	0.195629i	$0.937325\pi$
$504$	31.8964	−	44.0709i	1.42078	−	1.96307i
$505$	−5.74590	+	26.5884i	−0.255689	+	1.18317i
$506$	−13.2069	+	15.0895i	−0.587119	+	0.670810i
$507$	7.28986	−	12.6264i	0.323754	−	0.560758i
$508$	−4.57340	−	34.2182i	−0.202912	−	1.51819i
$509$	17.8686	+	30.9493i	0.792011	+	1.37180i	0.924720	+	0.380649i	$0.124299\pi$
$509$	17.8686	+	30.9493i	0.792011	+	1.37180i	−0.132709	+	0.991155i	$0.542367\pi$
$510$	24.4650	−	2.83585i	1.08333	−	0.125574i
$511$	4.29157	−	2.25176i	0.189848	−	0.0996121i
$512$	−4.21780	+	22.2308i	−0.186402	+	0.982474i
$513$	46.2946	−	26.7282i	2.04396	−	1.18008i
$514$	43.1046	+	8.52997i	1.90126	+	0.376241i
$515$	−18.9696	+	20.9247i	−0.835901	+	0.922051i
$516$	−1.86455	+	4.52658i	−0.0820821	+	0.199271i
$517$		−	8.19591i		−	0.360456i
$518$	−9.11087	−	8.64828i	−0.400309	−	0.379984i
$519$		−	23.8583i		−	1.04726i
$520$	−4.99835	+	17.6928i	−0.219192	+	0.775880i
$521$	−34.6318	−	19.9947i	−1.51724	−	0.875982i	−0.999795	−	0.0202683i	$-0.993548\pi$
$521$	−34.6318	−	19.9947i	−1.51724	−	0.875982i	−0.517450	−	0.855713i	$-0.673119\pi$
$522$	−9.40329	+	47.5177i	−0.411571	+	2.07979i
$523$	17.3266	+	30.0106i	0.757641	+	1.31227i	0.944050	+	0.329801i	$0.106982\pi$
$523$	17.3266	+	30.0106i	0.757641	+	1.31227i	−0.186409	+	0.982472i	$0.559685\pi$
$524$	−2.50515	−	3.25152i	−0.109438	−	0.142043i
$525$	19.0503	−	37.8722i	0.831423	−	1.65288i
$526$	8.50590	+	24.9769i	0.370875	+	1.08904i
$527$	9.54180	+	16.5269i	0.415647	+	0.719922i
$528$	−22.5129	−	22.3365i	−0.979749	−	0.972071i
$529$	−4.92420	+	8.52897i	−0.214096	+	0.370825i
$530$	−1.78841	−	2.40705i	−0.0776836	−	0.104556i
$531$			53.8484i			2.33682i
$532$	1.90895	+	20.5839i	0.0827633	+	0.892425i
$533$	16.7398			0.725080
$534$	14.6720	+	12.8415i	0.634920	+	0.555706i
$535$	−14.7339	+	16.2525i	−0.637004	+	0.702655i
$536$	5.98703	+	12.0507i	0.258600	+	0.520513i
$537$	15.5840	+	26.9922i	0.672497	+	1.16480i
$538$	1.29461	+	3.80151i	0.0558145	+	0.163895i
$539$	−17.2617	−	1.39748i	−0.743513	−	0.0601938i
$540$	26.2658	+	55.2701i	1.13030	+	2.37845i
$541$	−24.2321	+	13.9904i	−1.04182	+	0.601495i	−0.920348	−	0.391100i	$-0.872095\pi$
$541$	−24.2321	+	13.9904i	−1.04182	+	0.601495i	−0.121472	+	0.992595i	$0.538761\pi$
$542$	26.0032	+	5.14577i	1.11693	+	0.221030i
$543$	−9.17336	+	15.8887i	−0.393667	+	0.681851i
$544$	−7.69404	−	11.3933i	−0.329879	−	0.488482i
$545$	7.26781	+	1.57061i	0.311319	+	0.0672777i
$546$	−33.8924	−	8.14180i	−1.45046	−	0.348437i
$547$		−	11.5628i		−	0.494391i	−0.968966	−	0.247196i	$-0.920491\pi$
$547$		−	11.5628i		−	0.494391i	0.968966	−	0.247196i	$-0.0795090\pi$
$548$	−6.51718	+	15.8218i	−0.278400	+	0.675875i
$549$	−1.05597	+	1.82899i	−0.0450677	+	0.0780596i
$550$	−14.2275	−	10.1793i	−0.606661	−	0.434047i
$551$	−9.20314	−	15.9403i	−0.392067	−	0.679080i
$552$	−43.2796	−	28.7342i	−1.84210	−	1.22301i
$553$	−5.17295	−	0.209055i	−0.219976	−	0.00888993i
$554$	−10.8604	−	31.8908i	−0.461416	−	1.35491i
$555$	22.9055	−	7.35661i	0.972283	−	0.312271i
$556$	26.4555	−	3.53588i	1.12196	−	0.149955i
$557$	−22.6698	+	39.2653i	−0.960552	+	1.66372i	−0.239434	+	0.970913i	$0.576962\pi$
$557$	−22.6698	+	39.2653i	−0.960552	+	1.66372i	−0.721118	+	0.692812i	$0.756371\pi$
$558$	−53.1696	+	60.7488i	−2.25085	+	2.57170i
$559$	2.22040			0.0939127
$560$	−23.6625	+	0.296011i	−0.999922	+	0.0125087i
$561$	19.2684			0.813514
$562$	−9.65015	+	11.0257i	−0.407067	+	0.465093i
$563$	5.15902	−	8.93569i	0.217427	−	0.376594i	−0.736594	−	0.676335i	$-0.763567\pi$
$563$	5.15902	−	8.93569i	0.217427	−	0.376594i	0.954021	+	0.299741i	$0.0969003\pi$
$564$	21.0456	−	2.81282i	0.886179	−	0.118441i
$565$	−4.26730	−	13.2866i	−0.179527	−	0.558973i
$566$	4.26225	+	12.5157i	0.179156	+	0.526075i
$567$	−51.6383	+	27.0943i	−2.16860	+	1.13785i
$568$	12.3140	−	18.5474i	0.516682	−	0.778230i
$569$	−4.72049	−	8.17613i	−0.197893	−	0.342761i	0.749952	−	0.661492i	$-0.230077\pi$
$569$	−4.72049	−	8.17613i	−0.197893	−	0.342761i	−0.947845	+	0.318731i	$0.896743\pi$
$570$	−36.3375	−	15.7157i	−1.52201	−	0.658257i
$571$	14.8128	−	25.6565i	0.619895	−	1.07369i	−0.369609	−	0.929187i	$-0.620508\pi$
$571$	14.8128	−	25.6565i	0.619895	−	1.07369i	0.989504	−	0.144503i	$-0.0461582\pi$
$572$	−5.47829	+	13.2997i	−0.229059	+	0.556088i
$573$			9.86299i			0.412032i
$574$	6.11664	+	20.6599i	0.255304	+	0.862328i
$575$	−26.0996	−	11.8332i	−1.08843	−	0.493477i
$576$	35.1319	−	46.3484i	1.46383	−	1.93118i
$577$	−7.61237	+	13.1850i	−0.316907	+	0.548899i	−0.979841	−	0.199779i	$-0.935978\pi$
$577$	−7.61237	+	13.1850i	−0.316907	+	0.548899i	0.662934	+	0.748678i	$0.269311\pi$
$578$	−15.3903	−	3.04558i	−0.640151	−	0.126680i
$579$	−52.3966	+	30.2512i	−2.17753	+	1.25720i
$580$	19.0307	−	9.04390i	0.790209	−	0.375528i
$581$	14.7940	+	9.35752i	0.613758	+	0.388216i
$582$	23.2961	+	68.4070i	0.965655	+	2.83556i
$583$	−1.17303	−	2.03175i	−0.0485819	−	0.0841463i
$584$	4.63997	−	2.30522i	0.192003	−	0.0953909i
$585$	31.7389	−	35.0099i	1.31224	−	1.44748i
$586$	17.1064	+	14.9721i	0.706657	+	0.618493i
$587$	24.3201			1.00380			0.501899	−	0.864926i	$-0.332635\pi$
$587$	24.3201			1.00380			0.501899	+	0.864926i	$0.332635\pi$
$588$	−2.33571	−	44.8044i	−0.0963229	−	1.84770i
$589$		−	30.6766i		−	1.26401i
$590$	18.8017	−	13.9695i	0.774055	−	0.575114i
$591$	7.71317	−	13.3596i	0.317277	−	0.549540i
$592$	−9.53316	−	9.45846i	−0.391811	−	0.388740i
$593$	4.82898	+	8.36403i	0.198302	+	0.343470i	0.947978	−	0.318336i	$-0.103124\pi$
$593$	4.82898	+	8.36403i	0.198302	+	0.343470i	−0.749676	+	0.661805i	$0.769791\pi$
$594$	15.4335	+	45.3193i	0.633246	+	1.85947i
$595$	10.0792	−	10.2535i	0.413205	−	0.420353i
$596$	−14.1644	−	18.3844i	−0.580197	−	0.753056i
$597$	−38.7512	−	67.1190i	−1.58598	−	2.74700i
$598$	−4.57399	+	23.1138i	−0.187044	+	0.945193i
$599$	−9.10218	−	5.25515i	−0.371905	−	0.214719i	0.302385	−	0.953186i	$-0.402217\pi$
$599$	−9.10218	−	5.25515i	−0.371905	−	0.214719i	−0.674290	+	0.738466i	$0.735550\pi$
$600$	21.2557	−	40.0270i	0.867760	−	1.63410i
$601$		−	9.14888i		−	0.373191i	−0.982437	−	0.186595i	$-0.940255\pi$
$601$		−	9.14888i		−	0.373191i	0.982437	−	0.186595i	$-0.0597453\pi$
$602$	0.811323	+	2.74037i	0.0330671	+	0.111689i
$603$		−	34.5857i		−	1.40844i
$604$	−11.7924	+	28.6285i	−0.479826	+	1.16488i
$605$	8.08309	+	7.32786i	0.328624	+	0.297920i
$606$	−54.0846	−	10.7028i	−2.19704	−	0.434772i
$607$	42.1138	−	24.3144i	1.70935	−	0.986892i	0.773981	−	0.633209i	$-0.218263\pi$
$607$	42.1138	−	24.3144i	1.70935	−	0.986892i	0.935366	−	0.353682i	$-0.115071\pi$
$608$	1.55379	+	22.0448i	0.0630146	+	0.894037i
$609$	18.5604	+	35.3738i	0.752106	+	1.43342i
$610$	0.912556	−	0.105779i	0.0369483	−	0.00428286i
$611$	−4.81509	−	8.33998i	−0.194798	−	0.337399i
$612$	4.68115	+	35.0244i	0.189224	+	1.41578i
$613$	2.92021	−	5.05795i	0.117946	−	0.204289i	−0.801008	−	0.598654i	$-0.795702\pi$
$613$	2.92021	−	5.05795i	0.117946	−	0.204289i	0.918954	+	0.394366i	$0.129036\pi$
$614$	13.9548	−	15.9440i	0.563168	−	0.643446i
$615$	−40.3334	−	8.71627i	−1.62640	−	0.351474i
$616$	−18.4160	−	1.90155i	−0.742000	−	0.0766156i
$617$		−	49.5048i		−	1.99299i	−0.0836564	−	0.996495i	$-0.526660\pi$
$617$		−	49.5048i		−	1.99299i	0.0836564	−	0.996495i	$-0.473340\pi$
$618$	−43.0752	−	37.7011i	−1.73274	−	1.51656i
$619$	8.25280	+	4.76475i	0.331708	+	0.191512i	0.656599	−	0.754240i	$-0.271994\pi$
$619$	8.25280	+	4.76475i	0.331708	+	0.191512i	−0.324891	+	0.945751i	$0.605328\pi$
$620$	35.0045	+	2.80516i	1.40581	+	0.112658i
$621$	39.2120	+	67.9172i	1.57352	+	2.72542i
$622$	−14.1102	−	41.4333i	−0.565766	−	1.66132i
$623$	11.3733	+	0.459633i	0.455663	+	0.0184148i
$624$	−36.0313	−	9.50280i	−1.44241	−	0.380416i
$625$	8.04742	−	23.6694i	0.321897	−	0.946775i
$626$	−4.36035	−	0.862871i	−0.174275	−	0.0344873i
$627$	−26.8240	−	15.4869i	−1.07125	−	0.618485i
$628$	−1.52798	+	3.70949i	−0.0609730	+	0.148025i
$629$	8.15928			0.325332
$630$	54.8058	+	26.3790i	2.18352	+	1.05096i
$631$		−	7.60958i		−	0.302933i	−0.988462	−	0.151466i	$-0.951601\pi$
$631$		−	7.60958i		−	0.302933i	0.988462	−	0.151466i	$-0.0483995\pi$
$632$	−5.52382	−	0.345687i	−0.219726	−	0.0137507i
$633$	−39.8384	+	69.0021i	−1.58343	+	2.74259i
$634$	−5.25131	−	1.03918i	−0.208556	−	0.0412712i
$635$	36.7485	−	11.8026i	1.45832	−	0.468371i
$636$	4.81456	−	3.70941i	0.190910	−	0.147088i
$637$	−18.3861	+	8.71916i	−0.728484	+	0.345466i
$638$	15.6045	−	5.31412i	0.617786	−	0.210388i
$639$	−49.5555	+	28.6109i	−1.96039	+	1.13183i
$640$	−25.2971	−	0.242843i	−0.999954	−	0.00959921i
$641$	−10.7911	+	18.6907i	−0.426222	+	0.738238i	−0.996534	−	0.0831906i	$-0.973489\pi$
$641$	−10.7911	+	18.6907i	−0.426222	+	0.738238i	0.570312	+	0.821428i	$0.306822\pi$
$642$	−33.4571	−	29.2829i	−1.32045	−	1.15570i
$643$	−35.1575			−1.38648			−0.693239	−	0.720708i	$-0.743817\pi$
$643$	−35.1575			−1.38648			−0.693239	+	0.720708i	$0.743817\pi$
$644$	−30.1979	+	2.80055i	−1.18996	+	0.110357i
$645$	−5.34990	−	1.15614i	−0.210652	−	0.0455231i
$646$	−10.1038	−	8.84322i	−0.397528	−	0.347932i
$647$	−0.0712919	−	0.0411604i	−0.00280277	−	0.00161818i	0.498598	−	0.866833i	$-0.333848\pi$
$647$	−0.0712919	−	0.0411604i	−0.00280277	−	0.00161818i	−0.501401	+	0.865215i	$0.667182\pi$
$648$	−55.8304	+	27.7376i	−2.19323	+	1.08964i
$649$	15.8702	−	9.16266i	0.622960	−	0.359666i
$650$	−20.4579	−	1.99960i	−0.802424	−	0.0784308i
$651$	−2.68843	+	66.5235i	−0.105368	+	2.60726i
$652$	−20.1411	−	26.1417i	−0.788785	−	1.02379i
$653$	−12.0368	−	20.8484i	−0.471037	−	0.815859i	0.528415	−	0.848987i	$-0.322787\pi$
$653$	−12.0368	−	20.8484i	−0.471037	−	0.815859i	−0.999451	+	0.0331271i	$0.989453\pi$
$654$	−2.92556	+	14.7838i	−0.114399	+	0.578091i
$655$	3.08229	−	3.39995i	0.120435	−	0.132847i
$656$	6.04911	+	22.2255i	0.236178	+	0.867761i
$657$	−13.3167			−0.519536
$658$	8.53362	−	8.99008i	0.332675	−	0.350470i
$659$	41.3082			1.60914			0.804569	−	0.593859i	$-0.202396\pi$
$659$	41.3082			1.60914			0.804569	+	0.593859i	$0.202396\pi$
$660$	20.1246	−	29.1922i	0.783350	−	1.13631i
$661$	−9.80101	+	16.9759i	−0.381215	+	0.660284i	−0.991236	−	0.132101i	$-0.957828\pi$
$661$	−9.80101	+	16.9759i	−0.381215	+	0.660284i	0.610021	+	0.792385i	$0.291161\pi$
$662$	10.6362	+	2.10481i	0.413389	+	0.0818057i
$663$	19.6071	−	11.3202i	0.761477	−	0.439639i
$664$	15.5904	+	10.3508i	0.605026	+	0.401689i
$665$	−22.2726	+	6.17311i	−0.863695	+	0.239383i
$666$	11.1272	+	32.6740i	0.431169	+	1.26609i
$667$	23.3854	−	13.5016i	0.905487	−	0.522783i
$668$	−9.26156	+	1.23784i	−0.358340	+	0.0478936i
$669$	18.7689	+	10.8362i	0.725648	+	0.418953i
$670$	−12.0760	+	8.97230i	−0.466535	+	0.346630i
$671$	0.718722			0.0277460
$672$	−1.43750	−	47.9414i	−0.0554530	−	1.84938i
$673$			38.8213i			1.49645i	0.663444	+	0.748226i	$0.269094\pi$
$673$			38.8213i			1.49645i	−0.663444	+	0.748226i	$0.730906\pi$
$674$	−26.4648	−	23.1630i	−1.01939	−	0.892206i
$675$	−55.6219	+	39.8377i	−2.14089	+	1.53336i
$676$	−1.20541	−	9.01889i	−0.0463619	−	0.346880i
$677$	−33.5675	+	19.3802i	−1.29010	+	0.744842i	−0.978672	−	0.205427i	$-0.934142\pi$
$677$	−33.5675	+	19.3802i	−1.29010	+	0.744842i	−0.311431	+	0.950269i	$0.600808\pi$
$678$	26.7742	−	9.11799i	1.02826	−	0.350174i
$679$	35.6536	+	22.5517i	1.36826	+	0.865454i
$680$	11.0148	−	10.7206i	0.422397	−	0.411116i
$681$	13.8111	+	23.9216i	0.529243	+	0.916676i
$682$	26.9511	+	5.33335i	1.03201	+	0.204225i
$683$	31.8093	+	18.3651i	1.21715	+	0.702721i	0.964307	−	0.264786i	$-0.0853013\pi$
$683$	31.8093	+	18.3651i	1.21715	+	0.702721i	0.252842	+	0.967508i	$0.418635\pi$
$684$	21.6339	−	52.5207i	0.827191	−	2.00818i
$685$	−18.6996	−	4.04108i	−0.714474	−	0.154402i
$686$	−17.4792	−	19.5058i	−0.667360	−	0.744736i
$687$	−66.2639			−2.52812
$688$	0.802366	+	2.94803i	0.0305899	+	0.112393i
$689$	−2.38730	−	1.37831i	−0.0909487	−	0.0525093i
$690$	23.0559	−	53.3095i	0.877723	−	2.02946i
$691$	23.1244	−	13.3509i	0.879693	−	0.507891i	0.00913605	−	0.999958i	$-0.497092\pi$
$691$	23.1244	−	13.3509i	0.879693	−	0.507891i	0.870557	+	0.492067i	$0.163759\pi$
$692$	−9.08753	−	11.7950i	−0.345456	−	0.448378i
$693$	40.2161	+	25.4375i	1.52768	+	0.966292i
$694$	−29.9038	+	10.1838i	−1.13513	+	0.386571i
$695$	9.12507	+	28.4118i	0.346134	+	1.07772i
$696$	19.0011	+	38.2455i	0.720234	+	1.44969i
$697$	−12.1200	−	6.99747i	−0.459077	−	0.265048i
$698$	5.80473	−	6.63217i	0.219712	−	0.251031i
$699$		−	70.7744i		−	2.67693i
$700$	−5.00735	−	25.9793i	−0.189260	−	0.981927i
$701$		−	28.7252i		−	1.08494i	−0.840076	−	0.542468i	$-0.817490\pi$
$701$		−	28.7252i		−	1.08494i	0.840076	−	0.542468i	$-0.182510\pi$
$702$	42.3298	+	37.0487i	1.59764	+	1.39831i
$703$	−11.3587	−	6.55796i	−0.428402	−	0.247338i
$704$	−19.6377	−	2.46757i	−0.740125	−	0.0930000i
$705$	7.25907	+	22.6018i	0.273392	+	0.851233i
$706$	4.60688	+	13.5277i	0.173382	+	0.509122i
$707$	−28.5010	+	14.9543i	−1.07189	+	0.562416i
$708$	28.9746	+	37.6071i	1.08893	+	1.41336i
$709$	26.2847	−	15.1755i	0.987142	−	0.569927i	0.0827230	−	0.996573i	$-0.473638\pi$
$709$	26.2847	−	15.1755i	0.987142	−	0.569927i	0.904419	+	0.426646i	$0.140305\pi$
$710$	22.8456	+	9.88054i	0.857381	+	0.370810i
$711$	12.3196	+	7.11275i	0.462023	+	0.266749i
$712$	12.1448	+	0.760034i	0.455145	+	0.0284835i
$713$	45.0045			1.68543
$714$	21.1355	+	20.0624i	0.790976	+	0.750815i
$715$	−15.7187	−	3.39690i	−0.587847	−	0.127037i
$716$	17.9856	+	7.40846i	0.672152	+	0.276867i
$717$	29.9332	+	17.2819i	1.11787	+	0.645405i
$718$	−5.84639	+	29.5436i	−0.218185	+	1.10256i
$719$	−23.6997	−	41.0491i	−0.883849	−	1.53087i	−0.847027	−	0.531549i	$-0.821610\pi$
$719$	−23.6997	−	41.0491i	−0.883849	−	1.53087i	−0.0368218	−	0.999322i	$-0.511723\pi$
$720$	57.9521	+	29.4887i	2.15975	+	1.09898i
$721$	−33.3907	−	1.34943i	−1.24354	−	0.0502553i
$722$	−1.70408	−	5.00387i	−0.0634192	−	0.186225i
$723$	−49.5606	+	28.6138i	−1.84318	+	1.06416i
$724$	1.51685	+	11.3491i	0.0563735	+	0.421787i
$725$	13.7170	+	19.1519i	0.509438	+	0.711283i
$726$	−14.5637	+	16.6397i	−0.540511	+	0.617559i
$727$			14.3064i			0.530595i	0.964167	+	0.265297i	$0.0854701\pi$
$727$			14.3064i			0.530595i	−0.964167	+	0.265297i	$0.914530\pi$
$728$	−19.8568	+	8.88438i	−0.735943	+	0.329277i
$729$	28.6824			1.06231
$730$	3.45466	+	4.64968i	0.127863	+	0.172093i
$731$	−1.60762	−	0.928157i	−0.0594598	−	0.0343291i
$732$	0.246664	+	1.84554i	0.00911697	+	0.0682133i
$733$	6.48221	−	3.74251i	0.239426	−	0.138233i	−0.375487	−	0.926828i	$-0.622524\pi$
$733$	6.48221	−	3.74251i	0.239426	−	0.138233i	0.614913	+	0.788595i	$0.289191\pi$
$734$	40.5760	−	13.8182i	1.49769	−	0.510040i
$735$	48.8401	−	11.4347i	1.80149	−	0.421777i
$736$	−32.3412	+	2.27951i	−1.19211	+	0.0840239i
$737$	−10.1931	+	5.88498i	−0.375467	+	0.216776i
$738$	11.4930	−	58.0774i	0.423062	−	2.13786i
$739$	11.8579	−	20.5385i	0.436199	−	0.755519i	−0.561193	−	0.827685i	$-0.689658\pi$
$739$	11.8579	−	20.5385i	0.436199	−	0.755519i	0.997393	+	0.0721655i	$0.0229910\pi$
$740$	8.52184	−	12.3615i	0.313269	−	0.454419i
$741$	−36.3940			−1.33697
$742$	0.828770	−	3.44998i	0.0304251	−	0.126653i
$743$	−4.32810			−0.158783			−0.0793914	−	0.996844i	$-0.525298\pi$
$743$	−4.32810			−0.158783			−0.0793914	+	0.996844i	$0.525298\pi$
$744$	−4.44549	+	71.0357i	−0.162980	+	2.60430i
$745$	17.4276	−	19.2237i	0.638498	−	0.704303i
$746$	32.3804	+	6.40776i	1.18553	+	0.234605i
$747$	−24.0496	−	41.6551i	−0.879928	−	1.52408i
$748$	9.52587	−	7.33927i	0.348300	−	0.268350i
$749$	−25.9350	−	1.04812i	−0.947645	−	0.0382974i
$750$	48.2507	+	15.4702i	1.76187	+	0.564890i
$751$	1.87523	−	1.08267i	0.0684282	−	0.0395071i	−0.465396	−	0.885103i	$-0.654088\pi$
$751$	1.87523	−	1.08267i	0.0684282	−	0.0395071i	0.533824	+	0.845596i	$0.320755\pi$
$752$	9.33306	−	9.40677i	0.340342	−	0.343030i
$753$	−30.5942	−	17.6636i	−1.11492	−	0.643697i
$754$	12.7567	−	14.5751i	0.464572	−	0.530795i
$755$	−33.8356	−	7.31207i	−1.23140	−	0.266113i
$756$	−30.2576	+	65.7801i	−1.10046	+	2.39240i
$757$	−21.9602			−0.798158			−0.399079	−	0.916917i	$-0.630670\pi$
$757$	−21.9602			−0.798158			−0.399079	+	0.916917i	$0.630670\pi$
$758$	−8.89900	+	10.1675i	−0.323226	+	0.369301i
$759$	22.7202	−	39.3525i	0.824691	−	1.42841i
$760$	−23.9505	+	6.07135i	−0.868775	+	0.220231i
$761$	−5.54542	+	3.20165i	−0.201021	+	0.116060i	−0.597132	−	0.802143i	$-0.703693\pi$
$761$	−5.54542	+	3.20165i	−0.201021	+	0.116060i	0.396110	+	0.918203i	$0.370360\pi$
$762$	25.2188	+	74.0527i	0.913579	+	2.68265i
$763$	4.08769	+	7.79062i	0.147984	+	0.282039i
$764$	3.75677	+	4.87604i	0.135915	+	0.176409i
$765$	−37.6143	+	12.0807i	−1.35995	+	0.436777i
$766$	5.14338	−	25.9911i	0.185838	−	0.939096i
$767$	10.7661	−	18.6474i	0.388741	−	0.673320i
$768$	−0.403385	−	51.2729i	−0.0145559	−	1.85015i
$769$		−	12.2214i		−	0.440714i	−0.975419	−	0.220357i	$-0.929278\pi$
$769$		−	12.2214i		−	0.440714i	0.975419	−	0.220357i	$-0.0707222\pi$
$770$	−1.55116	−	20.6409i	−0.0558999	−	0.743848i
$771$	−99.5706			−3.58595
$772$	−14.3811	+	34.9131i	−0.517588	+	1.25655i
$773$	41.6408	+	24.0413i	1.49772	+	0.864706i	0.999997	−	0.00263190i	$-0.000837761\pi$
$773$	41.6408	+	24.0413i	1.49772	+	0.864706i	0.497719	+	0.867338i	$0.334171\pi$
$774$	1.52445	−	7.70350i	0.0547951	−	0.276896i
$775$	3.83888	+	39.0736i	0.137897	+	1.40356i
$776$	37.5730	+	24.9455i	1.34879	+	0.895490i
$777$	24.0571	+	15.2167i	0.863045	+	0.545895i
$778$	28.6136	−	9.74441i	1.02585	−	0.349354i
$779$	11.2483	+	19.4827i	0.403013	+	0.698039i
$780$	3.32798	−	41.5285i	0.119161	−	1.48696i
$781$	16.8644	+	9.73668i	0.603456	+	0.348406i
$782$	12.9736	−	14.8229i	0.463934	−	0.530066i
$783$		−	64.4688i		−	2.30393i
$784$	−18.2205	−	21.2606i	−0.650733	−	0.759307i
$785$	−4.38419	−	0.947448i	−0.156478	−	0.0338159i
$786$	6.99910	+	6.12588i	0.249650	+	0.218503i
$787$	13.4764	−	23.3419i	0.480384	−	0.832049i	−0.519363	−	0.854554i	$-0.673831\pi$
$787$	13.4764	−	23.3419i	0.480384	−	0.832049i	0.999747	+	0.0225049i	$0.00716414\pi$
$788$	−1.27541	−	9.54259i	−0.0454344	−	0.339941i
$789$	−29.8952	−	51.7800i	−1.06430	−	1.84342i
$790$	−0.712499	−	6.14674i	−0.0253496	−	0.218691i
$791$	8.82663	−	13.9547i	0.313839	−	0.496171i
$792$	42.3811	+	28.1376i	1.50595	+	0.999828i
$793$	0.731355	−	0.422248i	0.0259712	−	0.0149945i
$794$	0.0796318	−	0.402404i	0.00282603	−	0.0142808i
$795$	5.03436	+	4.56398i	0.178550	+	0.161868i
$796$	−44.7231	−	18.4219i	−1.58517	−	0.652948i
$797$		−	1.04481i		−	0.0370090i	−0.999829	−	0.0185045i	$-0.994109\pi$
$797$		−	1.04481i		−	0.0370090i	0.999829	−	0.0185045i	$-0.00589050\pi$
$798$	−13.2982	−	44.9168i	−0.470752	−	1.59004i
$799$			8.05110i			0.284828i
$800$	−4.73781	−	27.8846i	−0.167507	−	0.985871i
$801$	−27.0862	−	15.6382i	−0.957044	−	0.552550i
$802$	−37.1832	−	7.35819i	−1.31298	−	0.259827i
$803$	2.26593	+	3.92471i	0.0799631	+	0.138500i
$804$	−18.6098	−	24.1542i	−0.656317	−	0.851854i
$805$	−9.05635	−	32.6753i	−0.319194	−	1.15165i
$806$	30.5581	−	10.4066i	1.07636	−	0.366557i
$807$	−4.55009	−	7.88098i	−0.160171	−	0.277424i
$808$	−30.8149	+	15.3094i	−1.08406	+	0.538583i
$809$	−20.5368	+	35.5707i	−0.722034	+	1.25060i	0.238150	+	0.971229i	$0.423459\pi$
$809$	−20.5368	+	35.5707i	−0.722034	+	1.25060i	−0.960183	+	0.279371i	$0.909874\pi$
$810$	−41.5682	−	55.9473i	−1.46056	−	1.96579i
$811$		−	52.7552i		−	1.85249i	−0.376926	−	0.926244i	$-0.623019\pi$
$811$		−	52.7552i		−	1.85249i	0.376926	−	0.926244i	$-0.376981\pi$
$812$	22.6496	+	10.4184i	0.794844	+	0.365614i
$813$	−60.0667			−2.10663
$814$	7.73632	−	8.83910i	0.271158	−	0.309810i
$815$	24.7811	−	27.3351i	0.868046	−	0.957508i
$816$	22.1151	+	21.9418i	0.774184	+	0.768118i
$817$	1.49200	+	2.58422i	0.0521984	+	0.0904103i
$818$	−17.1212	+	5.83066i	−0.598630	+	0.203864i
$819$	55.8675	+	2.25778i	1.95217	+	0.0788933i
$820$	−23.2599	+	11.0537i	−0.812271	+	0.386012i
$821$	25.0058	−	14.4371i	0.872710	−	0.503859i	0.00446216	−	0.999990i	$-0.498580\pi$
$821$	25.0058	−	14.4371i	0.872710	−	0.503859i	0.868248	+	0.496131i	$0.165246\pi$
$822$	7.52728	−	38.0376i	0.262544	−	1.32671i
$823$	6.70757	−	11.6178i	0.233811	−	0.404973i	−0.725115	−	0.688627i	$-0.758214\pi$
$823$	6.70757	−	11.6178i	0.233811	−	0.404973i	0.958926	+	0.283655i	$0.0915469\pi$
$824$	−35.6556	−	2.23137i	−1.24212	−	0.0777334i
$825$	36.1045	+	16.3692i	1.25700	+	0.569903i
$826$	26.9482	+	6.47362i	0.937647	+	0.225246i
$827$			30.8083i			1.07131i	0.844437	+	0.535655i	$0.179935\pi$
$827$			30.8083i			1.07131i	−0.844437	+	0.535655i	$0.820065\pi$
$828$	77.0512	+	31.7383i	2.67771	+	1.10298i
$829$	8.18705	−	14.1804i	0.284348	−	0.492505i	−0.688103	−	0.725613i	$-0.741556\pi$
$829$	8.18705	−	14.1804i	0.284348	−	0.492505i	0.972451	+	0.233108i	$0.0748896\pi$
$830$	−8.30533	+	19.2034i	−0.288282	+	0.666561i
$831$	38.1706	+	66.1134i	1.32412	+	2.29345i
$832$	−21.4326	+	9.02620i	−0.743042	+	0.312927i
$833$	16.9567	+	1.37279i	0.587514	+	0.0475643i
$834$	−57.2532	+	19.4977i	−1.98252	+	0.675149i
$835$	−3.19451	−	9.94640i	−0.110551	−	0.344210i
$836$	−19.1601	+	2.56082i	−0.662665	+	0.0885677i
$837$	53.7231	−	93.0511i	1.85694	−	3.21632i
$838$	12.0897	+	10.5814i	0.417632	+	0.365528i
$839$	23.6109			0.815137			0.407569	−	0.913175i	$-0.366377\pi$
$839$	23.6109			0.815137			0.407569	+	0.913175i	$0.366377\pi$
$840$	52.4697	−	11.0670i	1.81038	−	0.381849i
$841$	6.80193			0.234549
$842$	−38.5168	−	33.7113i	−1.32738	−	1.16177i
$843$	16.6014	−	28.7545i	0.571783	−	0.990356i
$844$	6.58745	+	49.2874i	0.226749	+	1.69654i
$845$	9.68579	−	3.11081i	0.333201	−	0.107015i
$846$	−32.2408	+	10.9796i	−1.10846	+	0.377488i
$847$	−0.521277	+	12.8987i	−0.0179113	+	0.443204i
$848$	0.967309	−	3.66770i	0.0332175	−	0.125949i
$849$	−14.9803	−	25.9466i	−0.514122	−	0.890485i
$850$	13.9761	+	9.99944i	0.479376	+	0.342978i
$851$	9.62094	−	16.6640i	0.329802	−	0.571233i
$852$	−19.2141	+	46.6463i	−0.658265	+	1.59808i
$853$			38.4550i			1.31667i	0.752724	+	0.658336i	$0.228740\pi$
$853$			38.4550i			1.31667i	−0.752724	+	0.658336i	$0.771260\pi$
$854$	0.788364	+	0.748336i	0.0269773	+	0.0256075i
$855$	62.0734	+	13.4144i	2.12287	+	0.458764i
$856$	−27.6942	−	1.73313i	−0.946567	−	0.0592372i
$857$	−8.83986	+	15.3111i	−0.301964	+	0.523017i	−0.976581	−	0.215151i	$-0.930976\pi$
$857$	−8.83986	+	15.3111i	−0.301964	+	0.523017i	0.674617	+	0.738168i	$0.264309\pi$
$858$	6.32737	−	31.9741i	0.216013	−	1.09158i
$859$	10.4581	−	6.03798i	0.356825	−	0.206013i	−0.310862	−	0.950455i	$-0.600618\pi$
$859$	10.4581	−	6.03798i	0.356825	−	0.206013i	0.667687	+	0.744442i	$0.267284\pi$
$860$	−3.08524	+	1.46618i	−0.105206	+	0.0499964i
$861$	−22.6851	−	43.2348i	−0.773105	−	1.47344i
$862$	−40.2660	+	13.7126i	−1.37146	+	0.467054i
$863$	−3.86108	−	6.68759i	−0.131433	−	0.227648i	0.792796	−	0.609487i	$-0.208624\pi$
$863$	−3.86108	−	6.68759i	−0.131433	−	0.227648i	−0.924229	+	0.381838i	$0.875291\pi$
$864$	−33.8934	+	69.5896i	−1.15308	+	2.36749i
$865$	11.1811	−	12.3335i	0.380169	−	0.419350i
$866$	12.9941	−	14.8464i	0.441557	−	0.504500i
$867$	35.5512			1.20738
$868$	24.0094	+	33.9117i	0.814934	+	1.15104i
$869$		−	4.84113i		−	0.164224i
$870$	−38.3256	+	28.4755i	−1.29936	+	0.965409i
$871$	−6.91484	+	11.9769i	−0.234300	+	0.405820i
$872$	4.18475	+	8.42309i	0.141713	+	0.285242i
$873$	−57.9596	−	100.389i	−1.96164	−	3.39765i
$874$	−29.9746	+	10.2079i	−1.01391	+	0.345287i
$875$	27.5967	−	10.6501i	0.932938	−	0.360038i
$876$	−9.30026	+	7.16545i	−0.314227	+	0.242098i
$877$	4.57193	+	7.91882i	0.154383	+	0.267399i	0.932834	−	0.360306i	$-0.117328\pi$
$877$	4.57193	+	7.91882i	0.154383	+	0.267399i	−0.778451	+	0.627705i	$0.783994\pi$
$878$	−15.4938	−	3.06608i	−0.522892	−	0.103475i
$879$	−44.6123	−	25.7570i	−1.50474	−	0.868760i
$880$	−1.17005	−	22.0974i	−0.0394423	−	0.744902i
$881$			4.52233i			0.152361i	0.997094	+	0.0761805i	$0.0242725\pi$
$881$			4.52233i			0.152361i	−0.997094	+	0.0761805i	$0.975727\pi$
$882$	17.6272	+	69.7755i	0.593539	+	2.34946i
$883$		−	37.8342i		−	1.27322i	−0.771185	−	0.636611i	$-0.780336\pi$
$883$		−	37.8342i		−	1.27322i	0.771185	−	0.636611i	$-0.219664\pi$
$884$	5.38150	−	13.0647i	0.180999	−	0.439414i
$885$	−35.6498	+	39.3239i	−1.19835	+	1.32186i
$886$	5.09698	−	25.7566i	0.171236	−	0.865309i
$887$	−13.0412	+	7.52933i	−0.437880	+	0.252810i	−0.702698	−	0.711488i	$-0.748021\pi$
$887$	−13.0412	+	7.52933i	−0.437880	+	0.252810i	0.264818	+	0.964298i	$0.414688\pi$
$888$	25.3523	+	16.8319i	0.850766	+	0.564840i
$889$	38.5961	+	24.4129i	1.29447	+	0.818782i
$890$	1.56651	+	13.5144i	0.0525097	+	0.453002i
$891$	−27.2648	−	47.2241i	−0.913406	−	1.58207i
$892$	13.4064	−	1.79182i	0.448880	−	0.0599945i
$893$	6.47101	−	11.2081i	0.216544	−	0.375066i
$894$	39.5737	+	34.6364i	1.32354	+	1.15841i
$895$	−4.59373	+	21.2569i	−0.153552	+	0.710539i
$896$	−18.9713	−	23.1536i	−0.633788	−	0.773507i
$897$		−	53.3923i		−	1.78272i
$898$	7.82286	−	8.93798i	0.261052	−	0.298264i
$899$	−32.0396	−	18.4981i	−1.06858	−	0.616945i
$900$	−20.9831	+	69.6042i	−0.699438	+	2.32014i
$901$	1.15230	+	1.99585i	0.0383888	+	0.0664913i
$902$	−19.0722	+	6.49506i	−0.635035	+	0.216262i
$903$	−3.00899	−	5.73474i	−0.100133	−	0.190840i
$904$	9.76355	−	14.7059i	0.324731	−	0.489112i
$905$	−12.1883	+	3.91456i	−0.405154	+	0.130124i
$906$	13.6201	−	68.8265i	0.452497	−	2.28661i
$907$	38.3608	+	22.1476i	1.27375	+	0.735400i	0.975692	−	0.219148i	$-0.0703279\pi$
$907$	38.3608	+	22.1476i	1.27375	+	0.735400i	0.298058	+	0.954548i	$0.403661\pi$
$908$	15.9395	+	6.56567i	0.528972	+	0.217889i
$909$	88.4388			2.93333
$910$	−13.7049	−	20.0924i	−0.454315	−	0.666058i
$911$			41.0968i			1.36160i	0.732470	+	0.680799i	$0.238367\pi$
$911$			41.0968i			1.36160i	−0.732470	+	0.680799i	$0.761633\pi$
$912$	−13.1514	−	48.3206i	−0.435486	−	1.60005i
$913$	−8.18440	+	14.1758i	−0.270864	+	0.469150i
$914$	−7.76747	+	39.2514i	−0.256925	+	1.29832i
$915$	−1.98201	+	0.636568i	−0.0655233	+	0.0210443i
$916$	−32.7593	+	25.2397i	−1.08240	+	0.833942i
$917$	5.42551	+	0.219262i	0.179166	+	0.00724068i
$918$	−15.1608	−	44.5185i	−0.500383	−	1.46933i
$919$	13.1904	−	7.61549i	0.435112	−	0.251212i	−0.266410	−	0.963860i	$-0.585838\pi$
$919$	13.1904	−	7.61549i	0.435112	−	0.251212i	0.701522	+	0.712648i	$0.252504\pi$
$920$	−8.90706	−	35.1369i	−0.293657	−	1.15843i
$921$	−24.0067	+	41.5809i	−0.791049	+	1.37014i
$922$	29.4222	−	33.6162i	0.968969	−	1.10709i
$923$	22.8811			0.753142
$924$	41.7738	−	3.87410i	1.37426	−	0.127448i
$925$	15.2886	+	6.93160i	0.502684	+	0.227910i
$926$	−19.1895	+	21.9249i	−0.630607	+	0.720498i
$927$	79.5218	+	45.9119i	2.61184	+	1.50795i
$928$	23.9613	+	11.6703i	0.786567	+	0.383096i
$929$	−6.33630	+	3.65826i	−0.207887	+	0.120024i	−0.600329	−	0.799753i	$-0.704964\pi$
$929$	−6.33630	+	3.65826i	−0.207887	+	0.120024i	0.392442	+	0.919777i	$0.371630\pi$
$930$	−79.0464	+	9.16266i	−2.59203	+	0.300455i
$931$	−22.5024	−	15.5399i	−0.737487	−	0.509299i
$932$	−26.9577	−	34.9892i	−0.883029	−	1.14611i
$933$	49.5922	+	85.8962i	1.62358	+	2.81212i
$934$	22.7132	+	4.49471i	0.743197	+	0.147071i
$935$	9.96074	+	9.03008i	0.325751	+	0.295315i
$936$	59.6569	+	3.73339i	1.94995	+	0.122030i
$937$	−18.5605			−0.606347			−0.303173	−	0.952935i	$-0.598046\pi$
$937$	−18.5605			−0.606347			−0.303173	+	0.952935i	$0.598046\pi$
$938$	−17.3082	−	4.15787i	−0.565134	−	0.135759i
$939$	10.0723			0.328698
$940$	12.1977	+	8.40886i	0.397844	+	0.274267i
$941$	7.91298	−	13.7057i	0.257956	−	0.446792i	−0.707738	−	0.706475i	$-0.750284\pi$
$941$	7.91298	−	13.7057i	0.257956	−	0.446792i	0.965694	+	0.259682i	$0.0836178\pi$
$942$	1.76480	−	8.91807i	0.0575003	−	0.290566i
$943$	−28.5823	+	16.5020i	−0.930768	+	0.537379i
$944$	28.6488	+	7.55576i	0.932439	+	0.245919i
$945$	−78.3701	−	20.2805i	−2.54938	−	0.659726i
$946$	−2.52977	+	0.861517i	−0.0822500	+	0.0280103i
$947$	13.2327	−	7.63993i	0.430006	−	0.248264i	−0.269343	−	0.963044i	$-0.586807\pi$
$947$	13.2327	−	7.63993i	0.430006	−	0.248264i	0.699349	+	0.714780i	$0.253473\pi$
$948$	12.4311	−	1.66147i	0.403744	−	0.0539619i
$949$	4.61153	+	2.66247i	0.149696	+	0.0864273i
$950$	−11.4195	−	25.1536i	−0.370496	−	0.816091i
$951$	12.1304			0.393356
$952$	18.0906	+	1.86795i	0.586319	+	0.0605406i
$953$		−	13.4292i		−	0.435014i	−0.976059	−	0.217507i	$-0.930208\pi$
$953$		−	13.4292i		−	0.435014i	0.976059	−	0.217507i	$-0.0697924\pi$
$954$	−6.42097	+	7.33625i	−0.207886	+	0.237520i
$955$	−4.62226	+	5.09864i	−0.149573	+	0.164988i
$956$	21.3809	−	2.85764i	0.691507	−	0.0924227i
$957$	−32.3499	+	18.6772i	−1.04572	+	0.603749i
$958$	−17.1126	−	50.2496i	−0.552882	−	1.62349i
$959$	−10.5174	−	20.0447i	−0.339623	−	0.647278i
$960$	56.3403	−	10.5882i	1.81838	−	0.341734i
$961$	−15.3296	−	26.5516i	−0.494503	−	0.856504i
$962$	2.67934	−	13.5395i	0.0863855	−	0.436533i
$963$	61.7656	+	35.6604i	1.99037	+	1.14914i
$964$	−13.6027	+	33.0235i	−0.438114	+	1.06361i
$965$	−41.2633	−	8.91724i	−1.32831	−	0.287056i
$966$	65.8958	−	19.5093i	2.12016	−	0.627702i
$967$	20.1963			0.649468			0.324734	−	0.945805i	$-0.394725\pi$
$967$	20.1963			0.649468			0.324734	+	0.945805i	$0.394725\pi$
$968$	−0.861966	+	13.7736i	−0.0277046	+	0.442699i
$969$	26.3501	+	15.2132i	0.846486	+	0.488719i
$970$	−20.0159	+	46.2804i	−0.642671	+	1.48597i
$971$	−24.0745	+	13.8994i	−0.772587	+	0.446053i	−0.833797	−	0.552071i	$-0.813838\pi$
$971$	−24.0745	+	13.8994i	−0.772587	+	0.446053i	0.0612095	+	0.998125i	$0.480504\pi$
$972$	46.8695	−	36.1109i	1.50334	−	1.15826i
$973$	−18.8746	+	29.8403i	−0.605092	+	0.956635i
$974$	11.0729	+	32.5145i	0.354797	+	1.04183i
$975$	46.3560	−	4.55436i	1.48458	−	0.145856i
$976$	0.824905	+	0.818441i	0.0264046	+	0.0261977i
$977$	35.2559	+	20.3550i	1.12794	+	0.651214i	0.943415	−	0.331615i	$-0.107593\pi$
$977$	35.2559	+	20.3550i	1.12794	+	0.651214i	0.184521	+	0.982829i	$0.440927\pi$
$978$	56.2717	+	49.2512i	1.79937	+	1.57488i
$979$			10.6438i			0.340177i
$980$	19.7900	−	24.2561i	0.632168	−	0.774832i
$981$		−	24.1743i		−	0.771826i
$982$	−14.8810	+	17.0022i	−0.474872	+	0.542563i
$983$	−34.7777	−	20.0789i	−1.10924	−	0.640418i	−0.170605	−	0.985339i	$-0.554572\pi$
$983$	−34.7777	−	20.0789i	−1.10924	−	0.640418i	−0.938632	+	0.344921i	$0.887906\pi$
$984$	−23.2237	−	46.7447i	−0.740343	−	1.49017i
$985$	10.2482	−	3.29145i	0.326536	−	0.104874i
$986$	−15.3287	+	5.22022i	−0.488167	+	0.166246i
$987$	−15.0149	+	23.7382i	−0.477930	+	0.755595i
$988$	−17.9924	+	13.8623i	−0.572413	+	0.441020i
$989$	−3.79121	+	2.18886i	−0.120553	+	0.0696016i
$990$	−22.5772	+	52.2027i	−0.717552	+	1.65911i
$991$	−6.03398	−	3.48372i	−0.191676	−	0.110664i	0.401091	−	0.916038i	$-0.368631\pi$
$991$	−6.03398	−	3.48372i	−0.191676	−	0.110664i	−0.592767	+	0.805374i	$0.701964\pi$
$992$	24.8595	+	36.8117i	0.789289	+	1.16877i
$993$	−24.5695			−0.779689
$994$	8.36067	+	28.2394i	0.265184	+	0.895701i
$995$	11.4228	−	52.8576i	0.362128	−	1.67570i
$996$	−39.2097	−	16.1509i	−1.24241	−	0.511761i
$997$	−13.7596	−	7.94408i	−0.435770	−	0.251592i	0.266032	−	0.963964i	$-0.414287\pi$
$997$	−13.7596	−	7.94408i	−0.435770	−	0.251592i	−0.701802	+	0.712373i	$0.747621\pi$
$998$	−19.5199	−	3.86280i	−0.617892	−	0.122275i
$999$	−22.9695	−	39.7844i	−0.726724	−	1.25872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.ba.b.59.12	yes	80
4.3	odd	2		1120.2.bq.b.1039.1		80
5.4	even	2	inner	280.2.ba.b.59.29	yes	80
7.5	odd	6	inner	280.2.ba.b.19.38	yes	80
8.3	odd	2	inner	280.2.ba.b.59.3	yes	80
8.5	even	2		1120.2.bq.b.1039.2		80
20.19	odd	2		1120.2.bq.b.1039.39		80
28.19	even	6		1120.2.bq.b.719.40		80
35.19	odd	6	inner	280.2.ba.b.19.3	✓	80
40.19	odd	2	inner	280.2.ba.b.59.38	yes	80
40.29	even	2		1120.2.bq.b.1039.40		80
56.5	odd	6		1120.2.bq.b.719.39		80
56.19	even	6	inner	280.2.ba.b.19.29	yes	80
140.19	even	6		1120.2.bq.b.719.2		80
280.19	even	6	inner	280.2.ba.b.19.12	yes	80
280.229	odd	6		1120.2.bq.b.719.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.3	✓	80	35.19	odd	6	inner
280.2.ba.b.19.12	yes	80	280.19	even	6	inner
280.2.ba.b.19.29	yes	80	56.19	even	6	inner
280.2.ba.b.19.38	yes	80	7.5	odd	6	inner
280.2.ba.b.59.3	yes	80	8.3	odd	2	inner
280.2.ba.b.59.12	yes	80	1.1	even	1	trivial
280.2.ba.b.59.29	yes	80	5.4	even	2	inner
280.2.ba.b.59.38	yes	80	40.19	odd	2	inner
1120.2.bq.b.719.1		80	280.229	odd	6
1120.2.bq.b.719.2		80	140.19	even	6
1120.2.bq.b.719.39		80	56.5	odd	6
1120.2.bq.b.719.40		80	28.19	even	6
1120.2.bq.b.1039.1		80	4.3	odd	2
1120.2.bq.b.1039.2		80	8.5	even	2
1120.2.bq.b.1039.39		80	20.19	odd	2
1120.2.bq.b.1039.40		80	40.29	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.931410 + 1.06418i) q^{2} +(1.60233 - 2.77531i) q^{3} +(-0.264952 - 1.98237i) q^{4} +(2.12896 - 0.683763i) q^{5} +(1.46101 + 4.29012i) q^{6} +(2.23600 + 1.41432i) q^{7} +(2.35638 + 1.56444i) q^{8} +(-3.63491 - 6.29586i) q^{9} +O(q^{10})\)	\(q+(-0.931410 + 1.06418i) q^{2} +(1.60233 - 2.77531i) q^{3} +(-0.264952 - 1.98237i) q^{4} +(2.12896 - 0.683763i) q^{5} +(1.46101 + 4.29012i) q^{6} +(2.23600 + 1.41432i) q^{7} +(2.35638 + 1.56444i) q^{8} +(-3.63491 - 6.29586i) q^{9} +(-1.25529 + 2.90246i) q^{10} +(-1.23701 + 2.14257i) q^{11} +(-5.92625 - 2.44109i) q^{12} +2.90697i q^{13} +(-3.58772 + 1.06219i) q^{14} +(1.51364 - 7.00414i) q^{15} +(-3.85960 + 1.05047i) q^{16} +(1.21515 - 2.10471i) q^{17} +(10.0855 + 1.99582i) q^{18} +(-3.38329 + 1.95334i) q^{19} +(-1.91954 - 4.03923i) q^{20} +(7.50799 - 3.93940i) q^{21} +(-1.12791 - 3.31201i) q^{22} +(-2.86568 - 4.96350i) q^{23} +(8.11752 - 4.03293i) q^{24} +(4.06494 - 2.91141i) q^{25} +(-3.09353 - 2.70758i) q^{26} -13.6833 q^{27} +(2.21128 - 4.80731i) q^{28} +4.71148i q^{29} +(6.04385 + 8.13451i) q^{30} +(-3.92617 + 6.80032i) q^{31} +(2.47699 - 5.08572i) q^{32} +(3.96419 + 6.86619i) q^{33} +(1.10798 + 3.25349i) q^{34} +(5.72741 + 1.48213i) q^{35} +(-11.5177 + 8.87385i) q^{36} +(1.67865 + 2.90751i) q^{37} +(1.07252 - 5.41978i) q^{38} +(8.06775 + 4.65792i) q^{39} +(6.08634 + 1.71944i) q^{40} -5.75850i q^{41} +(-2.80079 + 11.6590i) q^{42} -0.763818i q^{43} +(4.57511 + 1.88454i) q^{44} +(-12.0435 - 10.9182i) q^{45} +(7.95117 + 1.57346i) q^{46} +(-2.86896 + 1.65640i) q^{47} +(-3.26897 + 12.3948i) q^{48} +(2.99940 + 6.32484i) q^{49} +(-0.687865 + 7.03753i) q^{50} +(-3.89415 - 6.74487i) q^{51} +(5.76269 - 0.770206i) q^{52} +(-0.474139 + 0.821232i) q^{53} +(12.7448 - 14.5615i) q^{54} +(-1.16854 + 5.40726i) q^{55} +(3.05624 + 6.83077i) q^{56} +12.5196i q^{57} +(-5.01386 - 4.38832i) q^{58} +(-6.41474 - 3.70355i) q^{59} +(-14.2859 - 1.14483i) q^{60} +(-0.145254 - 0.251587i) q^{61} +(-3.57989 - 10.5120i) q^{62} +(0.776680 - 19.2185i) q^{63} +(3.10502 + 7.37284i) q^{64} +(1.98768 + 6.18882i) q^{65} +(-10.9991 - 2.17662i) q^{66} +(4.12005 + 2.37871i) q^{67} +(-4.49427 - 1.85124i) q^{68} -18.3670 q^{69} +(-6.91182 + 4.71452i) q^{70} -7.87114i q^{71} +(1.28429 - 20.5220i) q^{72} +(0.915891 - 1.58637i) q^{73} +(-4.65762 - 0.921698i) q^{74} +(-1.56671 - 15.9465i) q^{75} +(4.76866 + 6.18939i) q^{76} +(-5.79623 + 3.04125i) q^{77} +(-12.4712 + 4.24710i) q^{78} +(-1.69463 + 0.978393i) q^{79} +(-7.49866 + 4.87545i) q^{80} +(-11.0205 + 19.0880i) q^{81} +(6.12808 + 5.36353i) q^{82} +6.61627 q^{83} +(-9.79862 - 13.8399i) q^{84} +(1.14789 - 5.31172i) q^{85} +(0.812839 + 0.711428i) q^{86} +(13.0758 + 7.54934i) q^{87} +(-6.26679 + 3.11346i) q^{88} +(3.72584 - 2.15111i) q^{89} +(22.8363 - 2.64707i) q^{90} +(-4.11138 + 6.49998i) q^{91} +(-9.08023 + 6.99593i) q^{92} +(12.5820 + 21.7927i) q^{93} +(0.909478 - 4.59587i) q^{94} +(-5.86726 + 6.47195i) q^{95} +(-10.1455 - 15.0234i) q^{96} +15.9453 q^{97} +(-9.52443 - 2.69912i) q^{98} +17.9857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) \) 80 * q + 6 * q^4 - 52 * q^9	\( 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) \) 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

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