LMFDB - Embedded newform 840.2.bj.b.517.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			517.19
Character	$\chi$	$=$	840.517
Dual form			840.2.bj.b.13.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08726 + 0.904365i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.364249 - 1.96655i) q^{4} +(-0.998967 + 2.00052i) q^{5} +(0.129323 - 1.40829i) q^{6} +(-2.62852 - 0.301481i) q^{7} +(1.38245 + 2.46756i) q^{8} -1.00000i q^{9} +(-0.723063 - 3.07850i) q^{10} -2.31287i q^{11} +(1.13300 + 1.64812i) q^{12} +(-3.26599 + 3.26599i) q^{13} +(3.13052 - 2.04935i) q^{14} +(-0.708202 - 2.12095i) q^{15} +(-3.73464 - 1.43263i) q^{16} +(2.54214 - 2.54214i) q^{17} +(0.904365 + 1.08726i) q^{18} -2.46154i q^{19} +(3.57024 + 2.69321i) q^{20} +(2.07182 - 1.64546i) q^{21} +(2.09168 + 2.51468i) q^{22} +(-2.20000 + 2.20000i) q^{23} +(-2.72236 - 0.767289i) q^{24} +(-3.00413 - 3.99690i) q^{25} +(0.597320 - 6.50462i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.55031 + 5.05930i) q^{28} +5.31262 q^{29} +(2.68811 + 1.66555i) q^{30} -0.162657i q^{31} +(5.35613 - 1.81985i) q^{32} +(1.63544 + 1.63544i) q^{33} +(-0.464934 + 5.06298i) q^{34} +(3.22892 - 4.95722i) q^{35} +(-1.96655 - 0.364249i) q^{36} +(-0.503633 + 0.503633i) q^{37} +(2.22613 + 2.67632i) q^{38} -4.61881i q^{39} +(-6.31741 + 0.300598i) q^{40} -0.552208i q^{41} +(-0.764501 + 3.66272i) q^{42} +(-5.38505 - 5.38505i) q^{43} +(-4.54837 - 0.842460i) q^{44} +(2.00052 + 0.998967i) q^{45} +(0.402359 - 4.38156i) q^{46} +(9.44984 - 9.44984i) q^{47} +(3.65381 - 1.62777i) q^{48} +(6.81822 + 1.58490i) q^{49} +(6.88091 + 1.62882i) q^{50} +3.59513i q^{51} +(5.23311 + 7.61238i) q^{52} +(2.25295 + 2.25295i) q^{53} +(-1.40829 - 0.129323i) q^{54} +(4.62693 + 2.31048i) q^{55} +(-2.88987 - 6.90280i) q^{56} +(1.74057 + 1.74057i) q^{57} +(-5.77617 + 4.80454i) q^{58} -0.0510421i q^{59} +(-4.42893 + 0.620159i) q^{60} -4.19768 q^{61} +(0.147101 + 0.176850i) q^{62} +(-0.301481 + 2.62852i) q^{63} +(-4.17768 + 6.82254i) q^{64} +(-3.27105 - 9.79629i) q^{65} +(-3.25718 - 0.299108i) q^{66} +(5.01239 - 5.01239i) q^{67} +(-4.07327 - 5.92522i) q^{68} -3.11126i q^{69} +(0.972475 + 8.30989i) q^{70} +14.1513 q^{71} +(2.46756 - 1.38245i) q^{72} +(7.08619 + 7.08619i) q^{73} +(0.0921099 - 1.00305i) q^{74} +(4.95047 + 0.701995i) q^{75} +(-4.84074 - 0.896614i) q^{76} +(-0.697286 + 6.07941i) q^{77} +(4.17709 + 5.02183i) q^{78} -16.6322i q^{79} +(6.59679 - 6.04007i) q^{80} -1.00000 q^{81} +(0.499398 + 0.600392i) q^{82} +(0.691321 - 0.691321i) q^{83} +(-2.48123 - 4.67370i) q^{84} +(2.54608 + 7.62511i) q^{85} +(10.7250 + 0.984876i) q^{86} +(-3.75659 + 3.75659i) q^{87} +(5.70713 - 3.19742i) q^{88} -12.0195 q^{89} +(-3.07850 + 0.723063i) q^{90} +(9.56936 - 7.60009i) q^{91} +(3.52506 + 5.12775i) q^{92} +(0.115016 + 0.115016i) q^{93} +(-1.72829 + 18.8205i) q^{94} +(4.92435 + 2.45900i) q^{95} +(-2.50053 + 5.07418i) q^{96} +(-1.80373 + 1.80373i) q^{97} +(-8.84647 + 4.44297i) q^{98} -2.31287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.08726	+	0.904365i	−0.768806	+	0.639482i
$2$	−1.08726	+	0.904365i	−0.768806	+	0.639482i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	0.364249	−	1.96655i	0.182125	−	0.983275i
$5$	−0.998967	+	2.00052i	−0.446752	+	0.894658i
$5$	−0.998967	+	2.00052i	−0.446752	+	0.894658i
$6$	0.129323	−	1.40829i	0.0527961	−	0.574931i
$7$	−2.62852	−	0.301481i	−0.993487	−	0.113949i
$7$	−2.62852	−	0.301481i	−0.993487	−	0.113949i
$8$	1.38245	+	2.46756i	0.488769	+	0.872413i
$9$		−	1.00000i		−	0.333333i
$10$	−0.723063	−	3.07850i	−0.228653	−	0.973508i
$11$		−	2.31287i		−	0.697356i	−0.937243	−	0.348678i	$-0.886631\pi$
$11$		−	2.31287i		−	0.697356i	0.937243	−	0.348678i	$-0.113369\pi$
$12$	1.13300	+	1.64812i	0.327068	+	0.475773i
$13$	−3.26599	+	3.26599i	−0.905823	+	0.905823i	−0.995932	−	0.0901086i	$-0.971279\pi$
$13$	−3.26599	+	3.26599i	−0.905823	+	0.905823i	0.0901086	+	0.995932i	$0.471279\pi$
$14$	3.13052	−	2.04935i	0.836667	−	0.547712i
$15$	−0.708202	−	2.12095i	−0.182857	−	0.547628i
$16$	−3.73464	−	1.43263i	−0.933661	−	0.358157i
$17$	2.54214	−	2.54214i	0.616559	−	0.616559i	−0.328088	−	0.944647i	$-0.606404\pi$
$17$	2.54214	−	2.54214i	0.616559	−	0.616559i	0.944647	+	0.328088i	$0.106404\pi$
$18$	0.904365	+	1.08726i	0.213161	+	0.256269i
$19$		−	2.46154i		−	0.564716i	−0.959309	−	0.282358i	$-0.908883\pi$
$19$		−	2.46154i		−	0.564716i	0.959309	−	0.282358i	$-0.0911166\pi$
$20$	3.57024	+	2.69321i	0.798331	+	0.602219i
$21$	2.07182	−	1.64546i	0.452109	−	0.359070i
$22$	2.09168	+	2.51468i	0.445947	+	0.536131i
$23$	−2.20000	+	2.20000i	−0.458731	+	0.458731i	−0.898239	−	0.439508i	$-0.855153\pi$
$23$	−2.20000	+	2.20000i	−0.458731	+	0.458731i	0.439508	+	0.898239i	$0.355153\pi$
$24$	−2.72236	−	0.767289i	−0.555700	−	0.156622i
$25$	−3.00413	−	3.99690i	−0.600826	−	0.799380i
$26$	0.597320	−	6.50462i	0.117144	−	1.27566i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.55031	+	5.05930i	−0.292982	+	0.956118i
$29$	5.31262			0.986528			0.493264	−	0.869880i	$-0.335804\pi$
$29$	5.31262			0.986528			0.493264	+	0.869880i	$0.335804\pi$
$30$	2.68811	+	1.66555i	0.490780	+	0.304086i
$31$		−	0.162657i		−	0.0292140i	−0.999893	−	0.0146070i	$-0.995350\pi$
$31$		−	0.162657i		−	0.0292140i	0.999893	−	0.0146070i	$-0.00464972\pi$
$32$	5.35613	−	1.81985i	0.946839	−	0.321706i
$33$	1.63544	+	1.63544i	0.284694	+	0.284694i
$34$	−0.464934	+	5.06298i	−0.0797356	+	0.868293i
$35$	3.22892	−	4.95722i	0.545787	−	0.837924i
$36$	−1.96655	−	0.364249i	−0.327758	−	0.0607082i
$37$	−0.503633	+	0.503633i	−0.0827967	+	0.0827967i	−0.747292	−	0.664496i	$-0.768646\pi$
$37$	−0.503633	+	0.503633i	−0.0827967	+	0.0827967i	0.664496	+	0.747292i	$0.268646\pi$
$38$	2.22613	+	2.67632i	0.361126	+	0.434157i
$39$		−	4.61881i		−	0.739602i
$40$	−6.31741	+	0.300598i	−0.998870	+	0.0475288i
$41$		−	0.552208i		−	0.0862405i	−0.999070	−	0.0431202i	$-0.986270\pi$
$41$		−	0.552208i		−	0.0862405i	0.999070	−	0.0431202i	$-0.0137299\pi$
$42$	−0.764501	+	3.66272i	−0.117965	+	0.565170i
$43$	−5.38505	−	5.38505i	−0.821212	−	0.821212i	0.165070	−	0.986282i	$-0.447215\pi$
$43$	−5.38505	−	5.38505i	−0.821212	−	0.821212i	−0.986282	+	0.165070i	$0.947215\pi$
$44$	−4.54837	−	0.842460i	−0.685693	−	0.127006i
$45$	2.00052	+	0.998967i	0.298219	+	0.148917i
$46$	0.402359	−	4.38156i	0.0593246	−	0.646025i
$47$	9.44984	−	9.44984i	1.37840	−	1.37840i	0.531079	−	0.847322i	$-0.321787\pi$
$47$	9.44984	−	9.44984i	1.37840	−	1.37840i	0.847322	−	0.531079i	$-0.178213\pi$
$48$	3.65381	−	1.62777i	0.527383	−	0.234948i
$49$	6.81822	+	1.58490i	0.974031	+	0.226414i
$50$	6.88091	+	1.62882i	0.973108	+	0.230350i
$51$			3.59513i			0.503419i
$52$	5.23311	+	7.61238i	0.725701	+	1.05565i
$53$	2.25295	+	2.25295i	0.309467	+	0.309467i	0.844703	−	0.535236i	$-0.179777\pi$
$53$	2.25295	+	2.25295i	0.309467	+	0.309467i	−0.535236	+	0.844703i	$0.679777\pi$
$54$	−1.40829	−	0.129323i	−0.191644	−	0.0175987i
$55$	4.62693	+	2.31048i	0.623895	+	0.311545i
$56$	−2.88987	−	6.90280i	−0.386175	−	0.922426i
$57$	1.74057	+	1.74057i	0.230544	+	0.230544i
$58$	−5.77617	+	4.80454i	−0.758449	+	0.630868i
$59$		−	0.0510421i		−	0.00664511i	−0.999994	−	0.00332256i	$-0.998942\pi$
$59$		−	0.0510421i		−	0.00664511i	0.999994	−	0.00332256i	$-0.00105760\pi$
$60$	−4.42893	+	0.620159i	−0.571772	+	0.0800622i
$61$	−4.19768			−0.537458			−0.268729	−	0.963216i	$-0.586604\pi$
$61$	−4.19768			−0.537458			−0.268729	+	0.963216i	$0.586604\pi$
$62$	0.147101	+	0.176850i	0.0186819	+	0.0224599i
$63$	−0.301481	+	2.62852i	−0.0379830	+	0.331162i
$64$	−4.17768	+	6.82254i	−0.522210	+	0.852817i
$65$	−3.27105	−	9.79629i	−0.405724	−	1.21508i
$66$	−3.25718	−	0.299108i	−0.400932	−	0.0368176i
$67$	5.01239	−	5.01239i	0.612361	−	0.612361i	−0.331199	−	0.943561i	$-0.607453\pi$
$67$	5.01239	−	5.01239i	0.612361	−	0.612361i	0.943561	+	0.331199i	$0.107453\pi$
$68$	−4.07327	−	5.92522i	−0.493957	−	0.718538i
$69$		−	3.11126i		−	0.374552i
$70$	0.972475	+	8.30989i	0.116233	+	0.993222i
$71$	14.1513			1.67945			0.839723	−	0.543015i	$-0.182717\pi$
$71$	14.1513			1.67945			0.839723	+	0.543015i	$0.182717\pi$
$72$	2.46756	−	1.38245i	0.290804	−	0.162923i
$73$	7.08619	+	7.08619i	0.829376	+	0.829376i	0.987430	−	0.158054i	$-0.0505220\pi$
$73$	7.08619	+	7.08619i	0.829376	+	0.829376i	−0.158054	+	0.987430i	$0.550522\pi$
$74$	0.0921099	−	1.00305i	0.0107076	−	0.116602i
$75$	4.95047	+	0.701995i	0.571632	+	0.0810594i
$76$	−4.84074	−	0.896614i	−0.555271	−	0.102849i
$77$	−0.697286	+	6.07941i	−0.0794631	+	0.692814i
$78$	4.17709	+	5.02183i	0.472962	+	0.568610i
$79$		−	16.6322i		−	1.87127i	−0.352974	−	0.935633i	$-0.614830\pi$
$79$		−	16.6322i		−	1.87127i	0.352974	−	0.935633i	$-0.385170\pi$
$80$	6.59679	−	6.04007i	0.737543	−	0.675300i
$81$	−1.00000			−0.111111
$82$	0.499398	+	0.600392i	0.0551493	+	0.0663022i
$83$	0.691321	−	0.691321i	0.0758823	−	0.0758823i	−0.668147	−	0.744029i	$-0.732912\pi$
$83$	0.691321	−	0.691321i	0.0758823	−	0.0758823i	0.744029	+	0.668147i	$0.232912\pi$
$84$	−2.48123	−	4.67370i	−0.270724	−	0.509943i
$85$	2.54608	+	7.62511i	0.276161	+	0.827059i
$86$	10.7250	+	0.984876i	1.15650	+	0.106202i
$87$	−3.75659	+	3.75659i	−0.402749	+	0.402749i
$88$	5.70713	−	3.19742i	0.608382	−	0.340846i
$89$	−12.0195			−1.27407			−0.637034	−	0.770835i	$-0.719839\pi$
$89$	−12.0195			−1.27407			−0.637034	+	0.770835i	$0.719839\pi$
$90$	−3.07850	+	0.723063i	−0.324503	+	0.0762176i
$91$	9.56936	−	7.60009i	1.00314	−	0.796706i
$92$	3.52506	+	5.12775i	0.367513	+	0.534605i
$93$	0.115016	+	0.115016i	0.0119266	+	0.0119266i
$94$	−1.72829	+	18.8205i	−0.178260	+	1.94119i
$95$	4.92435	+	2.45900i	0.505227	+	0.252288i
$96$	−2.50053	+	5.07418i	−0.255209	+	0.517882i
$97$	−1.80373	+	1.80373i	−0.183141	+	0.183141i	−0.792723	−	0.609582i	$-0.791337\pi$
$97$	−1.80373	+	1.80373i	−0.183141	+	0.183141i	0.609582	+	0.792723i	$0.291337\pi$
$98$	−8.84647	+	4.44297i	−0.893628	+	0.448807i
$99$	−2.31287			−0.232452
$100$	−8.95436	+	4.45190i	−0.895436	+	0.445190i
$101$	−7.38166			−0.734502			−0.367251	−	0.930122i	$-0.619701\pi$
$101$	−7.38166			−0.734502			−0.367251	+	0.930122i	$0.619701\pi$
$102$	−3.25131	−	3.90882i	−0.321927	−	0.387031i
$103$	−0.579644	−	0.579644i	−0.0571140	−	0.0571140i	0.677973	−	0.735087i	$-0.262859\pi$
$103$	−0.579644	−	0.579644i	−0.0571140	−	0.0571140i	−0.735087	+	0.677973i	$0.762859\pi$
$104$	−12.5741	−	3.54396i	−1.23299	−	0.347514i
$105$	1.22209	+	5.78848i	0.119264	+	0.564898i
$106$	−4.48703	−	0.412045i	−0.435819	−	0.0400213i
$107$	−8.13173	+	8.13173i	−0.786124	+	0.786124i	−0.980856	−	0.194732i	$-0.937616\pi$
$107$	−8.13173	+	8.13173i	−0.786124	+	0.786124i	0.194732	+	0.980856i	$0.437616\pi$
$108$	1.64812	−	1.13300i	0.158591	−	0.109023i
$109$	17.0197			1.63020			0.815098	−	0.579323i	$-0.196683\pi$
$109$	17.0197			1.63020			0.815098	+	0.579323i	$0.196683\pi$
$110$	−7.12017	+	1.67235i	−0.678881	+	0.159452i
$111$		−	0.712244i		−	0.0676032i
$112$	9.38467	+	4.89162i	0.886768	+	0.462214i
$113$	11.0513	−	11.0513i	1.03962	−	1.03962i	0.0404416	−	0.999182i	$-0.487124\pi$
$113$	11.0513	−	11.0513i	1.03962	−	1.03962i	0.999182	−	0.0404416i	$-0.0128765\pi$
$114$	−3.46656	−	0.318335i	−0.324673	−	0.0298148i
$115$	−2.20340	−	6.59885i	−0.205468	−	0.615346i
$116$	1.93512	−	10.4475i	0.179671	−	0.970029i
$117$	3.26599	+	3.26599i	0.301941	+	0.301941i
$118$	0.0461607	+	0.0554958i	0.00424943	+	0.00510880i
$119$	−7.44847	+	5.91565i	−0.682800	+	0.542287i
$120$	4.25453	−	4.67964i	0.388383	−	0.427190i
$121$	5.65064			0.513695
$122$	4.56395	−	3.79623i	0.413201	−	0.343695i
$123$	0.390470	+	0.390470i	0.0352075	+	0.0352075i
$124$	−0.319873	−	0.0592477i	−0.0287254	−	0.00532060i
$125$	10.9969	−	2.01704i	0.983592	−	0.180409i
$126$	−2.04935	−	3.13052i	−0.182571	−	0.278889i
$127$	0.514788	+	0.514788i	0.0456800	+	0.0456800i	0.729578	−	0.683898i	$-0.239717\pi$
$127$	0.514788	+	0.514788i	0.0456800	+	0.0456800i	−0.683898	+	0.729578i	$0.739717\pi$
$128$	−1.62785	−	11.1960i	−0.143883	−	0.989595i
$129$	7.61561			0.670517
$130$	12.4159	+	7.69285i	1.08895	+	0.674707i
$131$	1.94528			0.169960			0.0849800	−	0.996383i	$-0.472917\pi$
$131$	1.94528			0.169960			0.0849800	+	0.996383i	$0.472917\pi$
$132$	3.81189	−	2.62048i	0.331783	−	0.228083i
$133$	−0.742107	+	6.47020i	−0.0643489	+	0.561038i
$134$	−0.916721	+	9.98278i	−0.0791926	+	0.862381i
$135$	−2.12095	+	0.708202i	−0.182543	+	0.0609523i
$136$	9.78725	+	2.75850i	0.839250	+	0.236540i
$137$	−4.28204	−	4.28204i	−0.365839	−	0.365839i	0.500118	−	0.865957i	$-0.333290\pi$
$137$	−4.28204	−	4.28204i	−0.365839	−	0.365839i	−0.865957	+	0.500118i	$0.833290\pi$
$138$	2.81372	+	3.38274i	0.239520	+	0.287958i
$139$		−	11.7747i		−	0.998718i	−0.866395	−	0.499359i	$-0.833569\pi$
$139$		−	11.7747i		−	0.998718i	0.866395	−	0.499359i	$-0.166431\pi$
$140$	−8.57250	−	8.15550i	−0.724509	−	0.689266i
$141$			13.3641i			1.12546i
$142$	−15.3860	+	12.7979i	−1.29117	+	1.07398i
$143$	7.55381	+	7.55381i	0.631681	+	0.631681i
$144$	−1.43263	+	3.73464i	−0.119386	+	0.311220i
$145$	−5.30713	+	10.6280i	−0.440733	+	0.882606i
$146$	−14.1130	−	1.29600i	−1.16800	−	0.107258i
$147$	−5.94190	+	3.70052i	−0.490080	+	0.305213i
$148$	0.806972	+	1.17387i	0.0663327	+	0.0964913i
$149$	−14.1744			−1.16121			−0.580607	−	0.814184i	$-0.697185\pi$
$149$	−14.1744			−1.16121			−0.580607	+	0.814184i	$0.697185\pi$
$150$	−6.01729	+	3.71379i	−0.491310	+	0.303229i
$151$	−10.0615			−0.818795			−0.409397	−	0.912356i	$-0.634261\pi$
$151$	−10.0615			−0.818795			−0.409397	+	0.912356i	$0.634261\pi$
$152$	6.07399	−	3.40295i	0.492666	−	0.276015i
$153$	−2.54214	−	2.54214i	−0.205520	−	0.205520i
$154$	−4.73988	−	7.24048i	−0.381950	−	0.583454i
$155$	0.325398	+	0.162489i	0.0261366	+	0.0130514i
$156$	−9.08313	−	1.68240i	−0.727232	−	0.134700i
$157$	−16.2573	−	16.2573i	−1.29747	−	1.29747i	−0.930055	−	0.367420i	$-0.880241\pi$
$157$	−16.2573	−	16.2573i	−1.29747	−	1.29747i	−0.367420	−	0.930055i	$-0.619759\pi$
$158$	15.0416	+	18.0834i	1.19664	+	1.43864i
$159$	−3.18616			−0.252679
$160$	−1.70997	+	12.5330i	−0.135185	+	0.990820i
$161$	6.44599	−	5.11947i	0.508015	−	0.403471i
$162$	1.08726	−	0.904365i	0.0854229	−	0.0710536i
$163$	−15.5575	−	15.5575i	−1.21856	−	1.21856i	−0.968136	−	0.250424i	$-0.919430\pi$
$163$	−15.5575	−	15.5575i	−1.21856	−	1.21856i	−0.250424	−	0.968136i	$-0.580570\pi$
$164$	−1.08595	−	0.201141i	−0.0847981	−	0.0157065i
$165$	−4.90549	+	1.63798i	−0.381892	+	0.127516i
$166$	−0.126436	+	1.37685i	−0.00981336	+	0.106864i
$167$	10.2946	−	10.2946i	0.796620	−	0.796620i	−0.185941	−	0.982561i	$-0.559533\pi$
$167$	10.2946	−	10.2946i	0.796620	−	0.796620i	0.982561	+	0.185941i	$0.0595334\pi$
$168$	6.92446	+	2.83757i	0.534234	+	0.218924i
$169$		−	8.33342i		−	0.641032i
$170$	−9.66411	−	5.98786i	−0.741204	−	0.459248i
$171$	−2.46154			−0.188239
$172$	−12.5515	+	8.62847i	−0.957041	+	0.657915i
$173$	−7.39614	+	7.39614i	−0.562318	+	0.562318i	−0.929965	−	0.367647i	$-0.880163\pi$
$173$	−7.39614	+	7.39614i	−0.562318	+	0.562318i	0.367647	+	0.929965i	$0.380163\pi$
$174$	0.687046	−	7.48170i	0.0520848	−	0.567186i
$175$	6.69142	+	11.4116i	0.505824	+	0.862637i
$176$	−3.31348	+	8.63774i	−0.249763	+	0.651094i
$177$	0.0360922	+	0.0360922i	0.00271286	+	0.00271286i
$178$	13.0683	−	10.8700i	0.979511	−	0.814744i
$179$	0.300643			0.0224711			0.0112356	−	0.999937i	$-0.496424\pi$
$179$	0.300643			0.0224711			0.0112356	+	0.999937i	$0.496424\pi$
$180$	2.69321	−	3.57024i	0.200740	−	0.266110i
$181$	−14.2273			−1.05751			−0.528754	−	0.848775i	$-0.677341\pi$
$181$	−14.2273			−1.05751			−0.528754	+	0.848775i	$0.677341\pi$
$182$	−3.53109	+	16.9174i	−0.261742	+	1.25400i
$183$	2.96821	−	2.96821i	0.219416	−	0.219416i
$184$	−8.47000	−	2.38724i	−0.624416	−	0.175990i
$185$	−0.504413	−	1.51064i	−0.0370852	−	0.111064i
$186$	−0.229068	−	0.0210353i	−0.0167961	−	0.00154239i
$187$	−5.87963	−	5.87963i	−0.429961	−	0.429961i
$188$	−15.1415	−	22.0257i	−1.10431	−	1.60639i
$189$	−1.64546	−	2.07182i	−0.119690	−	0.150703i
$190$	−7.57785	+	1.77985i	−0.549755	+	0.129124i
$191$	−8.69992			−0.629504			−0.314752	−	0.949174i	$-0.601921\pi$
$191$	−8.69992			−0.629504			−0.314752	+	0.949174i	$0.601921\pi$
$192$	−1.87019	−	7.77833i	−0.134970	−	0.561352i
$193$	−15.6265	+	15.6265i	−1.12482	+	1.12482i	−0.133811	+	0.991007i	$0.542721\pi$
$193$	−15.6265	+	15.6265i	−1.12482	+	1.12482i	−0.991007	+	0.133811i	$0.957279\pi$
$194$	0.329886	−	3.59235i	0.0236844	−	0.257916i
$195$	9.24001	+	4.61404i	0.661691	+	0.330418i
$196$	5.60031	−	12.8311i	0.400022	−	0.916505i
$197$	4.85702	−	4.85702i	0.346048	−	0.346048i	−0.512587	−	0.858635i	$-0.671313\pi$
$197$	4.85702	−	4.85702i	0.346048	−	0.346048i	0.858635	+	0.512587i	$0.171313\pi$
$198$	2.51468	−	2.09168i	0.178710	−	0.148649i
$199$	−26.5795			−1.88417			−0.942086	−	0.335370i	$-0.891139\pi$
$199$	−26.5795			−1.88417			−0.942086	+	0.335370i	$0.891139\pi$
$200$	5.70953	−	12.9384i	0.403725	−	0.914880i
$201$			7.08859i			0.499991i
$202$	8.02575	−	6.67571i	0.564690	−	0.469701i
$203$	−13.9643	−	1.60165i	−0.980103	−	0.112414i
$204$	7.07000	+	1.30952i	0.494999	+	0.0916849i
$205$	1.10470	+	0.551638i	0.0771557	+	0.0385281i
$206$	1.15443	+	0.106012i	0.0804330	+	0.00738618i
$207$	2.20000	+	2.20000i	0.152910	+	0.152910i
$208$	16.8763	−	7.51837i	1.17016	−	0.521305i
$209$	−5.69321			−0.393808
$210$	−6.56362	−	5.18834i	−0.452933	−	0.358029i
$211$		−	21.8210i		−	1.50222i	−0.660179	−	0.751108i	$-0.729520\pi$
$211$		−	21.8210i		−	1.50222i	0.660179	−	0.751108i	$-0.270480\pi$
$212$	5.25119	−	3.60991i	0.360653	−	0.247930i
$213$	−10.0065	+	10.0065i	−0.685631	+	0.685631i
$214$	1.48722	−	16.1953i	0.101664	−	1.10709i
$215$	16.1524	−	5.39339i	1.10158	−	0.367826i
$216$	−0.767289	+	2.72236i	−0.0522074	+	0.185233i
$217$	−0.0490380	+	0.427547i	−0.00332891	+	0.0290238i
$218$	−18.5048	+	15.3921i	−1.25330	+	1.04248i
$219$	−10.0214			−0.677183
$220$	6.22903	−	8.25750i	0.419961	−	0.556721i
$221$			16.6052i			1.11699i
$222$	0.644129	+	0.774392i	0.0432311	+	0.0519738i
$223$	−8.64542	−	8.64542i	−0.578940	−	0.578940i	0.355671	−	0.934611i	$-0.384252\pi$
$223$	−8.64542	−	8.64542i	−0.578940	−	0.578940i	−0.934611	+	0.355671i	$0.884252\pi$
$224$	−14.6273	+	3.16873i	−0.977330	+	0.211720i
$225$	−3.99690	+	3.00413i	−0.266460	+	0.200275i
$226$	−2.02119	+	22.0101i	−0.134448	+	1.46409i
$227$	−8.50479	−	8.50479i	−0.564483	−	0.564483i	0.366095	−	0.930578i	$-0.380695\pi$
$227$	−8.50479	−	8.50479i	−0.564483	−	0.564483i	−0.930578	+	0.366095i	$0.880695\pi$
$228$	4.05692	−	2.78892i	0.268676	−	0.184701i
$229$		−	5.12037i		−	0.338364i	−0.985585	−	0.169182i	$-0.945887\pi$
$229$		−	5.12037i		−	0.338364i	0.985585	−	0.169182i	$-0.0541125\pi$
$230$	8.36343	+	5.18196i	0.551468	+	0.341688i
$231$	−3.80574	−	4.79185i	−0.250399	−	0.315281i
$232$	7.34441	+	13.1092i	0.482184	+	0.860661i
$233$	−6.17616	+	6.17616i	−0.404614	+	0.404614i	−0.879855	−	0.475241i	$-0.842361\pi$
$233$	−6.17616	+	6.17616i	−0.404614	+	0.404614i	0.475241	+	0.879855i	$0.342361\pi$
$234$	−6.50462	−	0.597320i	−0.425220	−	0.0390481i
$235$	9.46448	+	28.3446i	0.617394	+	1.84900i
$236$	−0.100377	−	0.0185920i	−0.00653398	−	0.00121024i
$237$	11.7607	+	11.7607i	0.763941	+	0.763941i
$238$	2.74848	−	13.1680i	0.178157	−	0.853552i
$239$		−	7.51408i		−	0.486046i	−0.970021	−	0.243023i	$-0.921861\pi$
$239$		−	7.51408i		−	0.486046i	0.970021	−	0.243023i	$-0.0781390\pi$
$240$	−0.393660	+	8.93560i	−0.0254106	+	0.576791i
$241$		−	24.2934i		−	1.56488i	−0.622728	−	0.782438i	$-0.713976\pi$
$241$		−	24.2934i		−	1.56488i	0.622728	−	0.782438i	$-0.286024\pi$
$242$	−6.14369	+	5.11024i	−0.394932	+	0.328499i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−1.52900	+	8.25495i	−0.0978843	+	0.528469i
$245$	−9.98179	+	12.0567i	−0.637713	+	0.770274i
$246$	−0.777669	−	0.0714135i	−0.0495823	−	0.00455316i
$247$	8.03937	+	8.03937i	0.511533	+	0.511533i
$248$	0.401365	−	0.224865i	0.0254867	−	0.0142789i
$249$			0.977675i			0.0619577i
$250$	−10.1323	+	12.1382i	−0.640822	+	0.767689i
$251$	21.2390			1.34059			0.670296	−	0.742094i	$-0.266167\pi$
$251$	21.2390			1.34059			0.670296	+	0.742094i	$0.266167\pi$
$252$	5.05930	+	1.55031i	0.318706	+	0.0976606i
$253$	5.08830	+	5.08830i	0.319899	+	0.319899i
$254$	−1.02526	−	0.0941500i	−0.0643307	−	0.00590750i
$255$	−7.19211	−	3.59142i	−0.450388	−	0.224903i
$256$	11.8951	+	10.7007i	0.743447	+	0.668795i
$257$	12.3818	−	12.3818i	0.772356	−	0.772356i	−0.206162	−	0.978518i	$-0.566097\pi$
$257$	12.3818	−	12.3818i	0.772356	−	0.772356i	0.978518	+	0.206162i	$0.0660974\pi$
$258$	−8.28011	+	6.88729i	−0.515497	+	0.428784i
$259$	1.47564	−	1.17197i	0.0916921	−	0.0728228i
$260$	−20.4564	+	2.86440i	−1.26865	+	0.177642i
$261$		−	5.31262i		−	0.328843i
$262$	−2.11502	+	1.75924i	−0.130666	+	0.108686i
$263$	−13.1541	+	13.1541i	−0.811114	+	0.811114i	−0.984801	−	0.173687i	$-0.944432\pi$
$263$	−13.1541	+	13.1541i	−0.811114	+	0.811114i	0.173687	+	0.984801i	$0.444432\pi$
$264$	−1.77464	+	6.29647i	−0.109221	+	0.387521i
$265$	−6.75770	+	2.25644i	−0.415122	+	0.138612i
$266$	−5.04456	−	7.70590i	−0.309302	−	0.472479i
$267$	8.49910	−	8.49910i	0.520136	−	0.520136i
$268$	−8.03137	−	11.6829i	−0.490594	−	0.713646i
$269$			12.3724i			0.754355i	0.926141	+	0.377178i	$0.123105\pi$
$269$			12.3724i			0.754355i	−0.926141	+	0.377178i	$0.876895\pi$
$270$	1.66555	−	2.68811i	0.101362	−	0.163593i
$271$			16.3605i			0.993827i	0.867800	+	0.496913i	$0.165533\pi$
$271$			16.3605i			0.993827i	−0.867800	+	0.496913i	$0.834467\pi$
$272$	−13.1359	+	5.85205i	−0.796483	+	0.354832i
$273$	−1.39248	+	12.1406i	−0.0842770	+	0.734784i
$274$	8.52820	+	0.783146i	0.515207	+	0.0473116i
$275$	−9.24430	+	6.94815i	−0.557452	+	0.418989i
$276$	−6.11846	−	1.13328i	−0.368288	−	0.0682152i
$277$	11.7509	−	11.7509i	0.706043	−	0.706043i	−0.259657	−	0.965701i	$-0.583610\pi$
$277$	11.7509	−	11.7509i	0.706043	−	0.706043i	0.965701	+	0.259657i	$0.0836096\pi$
$278$	10.6486	+	12.8021i	0.638662	+	0.767820i
$279$	−0.162657			−0.00973801
$280$	16.6960	+	1.11445i	0.997780	+	0.0666012i
$281$	22.4586			1.33977			0.669885	−	0.742465i	$-0.266344\pi$
$281$	22.4586			1.33977			0.669885	+	0.742465i	$0.266344\pi$
$282$	−12.0860	−	14.5302i	−0.719712	−	0.865260i
$283$	13.2506	−	13.2506i	0.787663	−	0.787663i	−0.193447	−	0.981111i	$-0.561967\pi$
$283$	13.2506	−	13.2506i	0.787663	−	0.787663i	0.981111	+	0.193447i	$0.0619668\pi$
$284$	5.15459	−	27.8292i	0.305869	−	1.65136i
$285$	−5.22081	+	1.74327i	−0.309254	+	0.103262i
$286$	−15.0443	−	1.38152i	−0.889589	−	0.0816912i
$287$	−0.166480	+	1.45149i	−0.00982703	+	0.0856787i
$288$	−1.81985	−	5.35613i	−0.107235	−	0.315613i
$289$			4.07505i			0.239709i
$290$	−3.84136	−	16.3549i	−0.225572	−	0.960393i
$291$		−	2.55086i		−	0.149534i
$292$	16.5165	−	11.3542i	0.966555	−	0.664456i
$293$	−16.2062	+	16.2062i	−0.946775	+	0.946775i	−0.998653	−	0.0518781i	$-0.983479\pi$
$293$	−16.2062	+	16.2062i	−0.946775	+	0.946775i	0.0518781	+	0.998653i	$0.483479\pi$
$294$	3.11375	−	9.39705i	0.181597	−	0.548047i
$295$	0.102111	+	0.0509894i	0.00594510	+	0.00296872i
$296$	−1.93899	−	0.546497i	−0.112701	−	0.0317645i
$297$	1.63544	−	1.63544i	0.0948981	−	0.0948981i
$298$	15.4112	−	12.8189i	0.892749	−	0.742576i
$299$		−	14.3703i		−	0.831058i
$300$	3.18372	−	9.47966i	0.183812	−	0.547308i
$301$	12.5312	+	15.7782i	0.722287	+	0.909440i
$302$	10.9394	−	9.09928i	0.629494	−	0.523605i
$303$	5.21962	−	5.21962i	0.299859	−	0.299859i
$304$	−3.52647	+	9.19297i	−0.202257	+	0.527253i
$305$	4.19334	−	8.39753i	0.240110	−	0.480841i
$306$	5.06298	+	0.464934i	0.289431	+	0.0265785i
$307$	−13.8124	−	13.8124i	−0.788316	−	0.788316i	0.192902	−	0.981218i	$-0.438210\pi$
$307$	−13.8124	−	13.8124i	−0.788316	−	0.788316i	−0.981218	+	0.192902i	$0.938210\pi$
$308$	11.7015	+	3.58567i	0.666754	+	0.204313i
$309$	0.819740			0.0466334
$310$	−0.500740	+	0.117611i	−0.0284401	+	0.00667987i
$311$			22.6395i			1.28377i	0.766803	+	0.641883i	$0.221846\pi$
$311$			22.6395i			1.28377i	−0.766803	+	0.641883i	$0.778154\pi$
$312$	11.3972	−	6.38526i	0.645238	−	0.361494i
$313$	2.43152	+	2.43152i	0.137437	+	0.137437i	0.772478	−	0.635041i	$-0.219017\pi$
$313$	2.43152	+	2.43152i	0.137437	+	0.137437i	−0.635041	+	0.772478i	$0.719017\pi$
$314$	32.3784	+	2.97332i	1.82722	+	0.167794i
$315$	−4.95722	−	3.22892i	−0.279308	−	0.181929i
$316$	−32.7080	−	6.05826i	−1.83997	−	0.340804i
$317$	22.2671	−	22.2671i	1.25065	−	1.25065i	0.295216	−	0.955431i	$-0.404608\pi$
$317$	22.2671	−	22.2671i	1.25065	−	1.25065i	0.955431	−	0.295216i	$-0.0953915\pi$
$318$	3.46417	−	2.88145i	0.194261	−	0.161584i
$319$		−	12.2874i		−	0.687961i
$320$	−9.47523	−	15.1730i	−0.529681	−	0.848197i
$321$		−	11.5000i		−	0.641868i
$322$	−2.37857	+	11.3957i	−0.132552	+	0.635057i
$323$	−6.25758	−	6.25758i	−0.348181	−	0.348181i
$324$	−0.364249	+	1.96655i	−0.0202361	+	0.109253i
$325$	22.8653	+	3.24238i	1.26834	+	0.179855i
$326$	30.9847	+	2.84533i	1.71608	+	0.157588i
$327$	−12.0348	+	12.0348i	−0.665525	+	0.665525i
$328$	1.36261	−	0.763399i	0.0752373	−	0.0421517i
$329$	−27.6880	+	21.9901i	−1.52649	+	1.21236i
$330$	3.85219	−	6.21725i	0.212056	−	0.342248i
$331$			20.5985i			1.13220i	0.824338	+	0.566099i	$0.191548\pi$
$331$			20.5985i			1.13220i	−0.824338	+	0.566099i	$0.808452\pi$
$332$	−1.10770	−	1.61133i	−0.0607932	−	0.0884333i
$333$	0.503633	+	0.503633i	0.0275989	+	0.0275989i
$334$	−1.88279	+	20.5029i	−0.103022	+	1.12187i
$335$	5.02016	+	15.0346i	0.274280	+	0.821427i
$336$	−10.0949	+	3.17707i	−0.550720	+	0.173323i
$337$	10.8982	+	10.8982i	0.593665	+	0.593665i	0.938620	−	0.344954i	$-0.112106\pi$
$337$	10.8982	+	10.8982i	0.593665	+	0.593665i	−0.344954	+	0.938620i	$0.612106\pi$
$338$	7.53645	+	9.06055i	0.409929	+	0.492829i
$339$			15.6290i			0.848849i
$340$	15.9226	−	2.22955i	0.863522	−	0.120914i
$341$	−0.376204			−0.0203726
$342$	2.67632	−	2.22613i	0.144719	−	0.120375i
$343$	−17.4440	−	6.22149i	−0.941887	−	0.335929i
$344$	5.84337	−	20.7325i	0.315053	−	1.11782i
$345$	6.22413	+	3.10805i	0.335096	+	0.167332i
$346$	1.35269	−	14.7303i	0.0727209	−	0.791906i
$347$	13.2150	−	13.2150i	0.709421	−	0.709421i	−0.256992	−	0.966413i	$-0.582732\pi$
$347$	13.2150	−	13.2150i	0.709421	−	0.709421i	0.966413	+	0.256992i	$0.0827315\pi$
$348$	6.01919	+	8.75586i	0.322662	+	0.469363i
$349$		−	10.1105i		−	0.541204i	−0.962691	−	0.270602i	$-0.912777\pi$
$349$		−	10.1105i		−	0.541204i	0.962691	−	0.270602i	$-0.0872227\pi$
$350$	−17.5955	−	6.35586i	−0.940521	−	0.339735i
$351$	−4.61881			−0.246534
$352$	−4.20906	−	12.3880i	−0.224344	−	0.660284i
$353$	0.0721014	+	0.0721014i	0.00383757	+	0.00383757i	0.709023	−	0.705185i	$-0.249136\pi$
$353$	0.0721014	+	0.0721014i	0.00383757	+	0.00383757i	−0.705185	+	0.709023i	$0.749136\pi$
$354$	−0.0718820	−	0.00660094i	−0.00382048	−	0.000350836i
$355$	−14.1367	+	28.3098i	−0.750296	+	1.50253i
$356$	−4.37811	+	23.6370i	−0.232039	+	1.25276i
$357$	1.08386	−	9.44986i	0.0573641	−	0.500140i
$358$	−0.326876	+	0.271891i	−0.0172759	+	0.0143699i
$359$			27.6009i			1.45672i	0.685195	+	0.728359i	$0.259717\pi$
$359$			27.6009i			1.45672i	−0.685195	+	0.728359i	$0.740283\pi$
$360$	0.300598	+	6.31741i	0.0158429	+	0.332957i
$361$	12.9408			0.681096
$362$	15.4687	−	12.8667i	0.813019	−	0.676258i
$363$	−3.99561	+	3.99561i	−0.209715	+	0.209715i
$364$	−11.4603	−	21.5870i	−0.600684	−	1.13146i
$365$	−21.2549	+	7.09717i	−1.11253	+	0.371483i
$366$	−0.542858	+	5.91154i	−0.0283757	+	0.309001i
$367$	−7.73673	+	7.73673i	−0.403854	+	0.403854i	−0.879589	−	0.475735i	$-0.842182\pi$
$367$	−7.73673	+	7.73673i	−0.403854	+	0.403854i	0.475735	+	0.879589i	$0.342182\pi$
$368$	11.3680	−	5.06443i	0.592597	−	0.264001i
$369$	−0.552208			−0.0287468
$370$	1.91459	+	1.18628i	0.0995350	+	0.0616716i
$371$	−5.24271	−	6.60116i	−0.272188	−	0.342715i
$372$	0.268079	−	0.184290i	0.0138992	−	0.00955499i
$373$	−10.9013	−	10.9013i	−0.564446	−	0.564446i	0.366121	−	0.930567i	$-0.380686\pi$
$373$	−10.9013	−	10.9013i	−0.564446	−	0.564446i	−0.930567	+	0.366121i	$0.880686\pi$
$374$	11.7100	+	1.07533i	0.605509	+	0.0556041i
$375$	−6.34972	+	9.20223i	−0.327898	+	0.475201i
$376$	36.3819	+	10.2541i	1.87626	+	0.528816i
$377$	−17.3510	+	17.3510i	−0.893621	+	0.893621i
$378$	3.66272	+	0.764501i	0.188390	+	0.0393217i
$379$	22.6624			1.16409			0.582043	−	0.813158i	$-0.302253\pi$
$379$	22.6624			1.16409			0.582043	+	0.813158i	$0.302253\pi$
$380$	6.62943	−	8.78829i	0.340083	−	0.450830i
$381$	−0.728020			−0.0372976
$382$	9.45904	−	7.86790i	0.483966	−	0.402557i
$383$	−1.18684	−	1.18684i	−0.0606449	−	0.0606449i	0.676134	−	0.736779i	$-0.263654\pi$
$383$	−1.18684	−	1.18684i	−0.0606449	−	0.0606449i	−0.736779	+	0.676134i	$0.763654\pi$
$384$	9.06782	+	6.76569i	0.462740	+	0.345260i
$385$	−11.4654	−	7.46807i	−0.584331	−	0.380608i
$386$	2.85794	−	31.1220i	0.145465	−	1.58407i
$387$	−5.38505	+	5.38505i	−0.273737	+	0.273737i
$388$	2.89012	+	4.20414i	0.146724	+	0.213433i
$389$	25.1866			1.27701			0.638506	−	0.769617i	$-0.279553\pi$
$389$	25.1866			1.27701			0.638506	+	0.769617i	$0.279553\pi$
$390$	−14.2190	+	3.33969i	−0.720008	+	0.169112i
$391$			11.1854i			0.565670i
$392$	5.51500	+	19.0154i	0.278550	+	0.960422i
$393$	−1.37552	+	1.37552i	−0.0693859	+	0.0693859i
$394$	−0.888304	+	9.67333i	−0.0447521	+	0.487336i
$395$	33.2729	+	16.6150i	1.67414	+	0.835991i
$396$	−0.842460	+	4.54837i	−0.0423352	+	0.228564i
$397$	−3.05179	−	3.05179i	−0.153165	−	0.153165i	0.626365	−	0.779530i	$-0.284542\pi$
$397$	−3.05179	−	3.05179i	−0.153165	−	0.153165i	−0.779530	+	0.626365i	$0.784542\pi$
$398$	28.8987	−	24.0376i	1.44856	−	1.20490i
$399$	−4.05037	−	5.09987i	−0.202772	−	0.255313i
$400$	5.49328	+	19.2308i	0.274664	+	0.961540i
$401$	0.131175			0.00655057			0.00327529	−	0.999995i	$-0.498957\pi$
$401$	0.131175			0.00655057			0.00327529	+	0.999995i	$0.498957\pi$
$402$	−6.41067	−	7.70711i	−0.319735	−	0.384396i
$403$	0.531236	+	0.531236i	0.0264628	+	0.0264628i
$404$	−2.68876	+	14.5164i	−0.133771	+	0.722218i
$405$	0.998967	−	2.00052i	0.0496391	−	0.0994064i
$406$	16.6313	−	10.8874i	0.825395	−	0.540334i
$407$	1.16484	+	1.16484i	0.0577388	+	0.0577388i
$408$	−8.87119	+	4.97007i	−0.439189	+	0.246055i
$409$	24.7028			1.22148			0.610738	−	0.791833i	$-0.290873\pi$
$409$	24.7028			1.22148			0.610738	+	0.791833i	$0.290873\pi$
$410$	−1.69998	+	0.399282i	−0.0839558	+	0.0197191i
$411$	6.05572			0.298707
$412$	−1.35103	+	0.928764i	−0.0665607	+	0.0457569i
$413$	−0.0153882	+	0.134165i	−0.000757205	+	0.00660183i
$414$	−4.38156	−	0.402359i	−0.215342	−	0.0197749i
$415$	0.692392	+	2.07361i	0.0339882	+	0.101789i
$416$	−11.5495	+	23.4367i	−0.566260	+	1.14908i
$417$	8.32598	+	8.32598i	0.407725	+	0.407725i
$418$	6.18998	−	5.14874i	0.302762	−	0.251833i
$419$			27.2210i			1.32983i	0.746917	+	0.664917i	$0.231533\pi$
$419$			27.2210i			1.32983i	−0.746917	+	0.664917i	$0.768467\pi$
$420$	11.8285	−	0.294861i	0.577171	−	0.0143878i
$421$		−	14.2584i		−	0.694911i	−0.937697	−	0.347455i	$-0.887046\pi$
$421$		−	14.2584i		−	0.694911i	0.937697	−	0.347455i	$-0.112954\pi$
$422$	19.7341	+	23.7250i	0.960641	+	1.15491i
$423$	−9.44984	−	9.44984i	−0.459467	−	0.459467i
$424$	−2.44470	+	8.67389i	−0.118725	+	0.421241i
$425$	−17.7976	−	2.52376i	−0.863310	−	0.122420i
$426$	1.83009	−	19.9291i	0.0886681	−	0.965566i
$427$	11.0337	+	1.26552i	0.533957	+	0.0612429i
$428$	13.0295	+	18.9534i	0.629804	+	0.916149i
$429$	−10.6827			−0.515766
$430$	−12.6842	+	20.4716i	−0.611684	+	0.987229i
$431$	−30.6115			−1.47450			−0.737252	−	0.675618i	$-0.763877\pi$
$431$	−30.6115			−1.47450			−0.737252	+	0.675618i	$0.763877\pi$
$432$	−1.62777	−	3.65381i	−0.0783162	−	0.175794i
$433$	−0.411449	−	0.411449i	−0.0197730	−	0.0197730i	0.697151	−	0.716924i	$-0.254451\pi$
$433$	−0.411449	−	0.411449i	−0.0197730	−	0.0197730i	−0.716924	+	0.697151i	$0.754451\pi$
$434$	−0.333341	−	0.509201i	−0.0160009	−	0.0244424i
$435$	−3.76241	−	11.2678i	−0.180394	−	0.540251i
$436$	6.19943	−	33.4702i	0.296899	−	1.60293i
$437$	5.41538	+	5.41538i	0.259053	+	0.259053i
$438$	10.8958	−	9.06299i	0.520622	−	0.433047i
$439$	−19.5289			−0.932063			−0.466031	−	0.884768i	$-0.654317\pi$
$439$	−19.5289			−0.932063			−0.466031	+	0.884768i	$0.654317\pi$
$440$	0.695244	+	14.6113i	0.0331445	+	0.696568i
$441$	1.58490	−	6.81822i	0.0754713	−	0.324677i
$442$	−15.0172	−	18.0541i	−0.714294	−	0.858747i
$443$	6.17122	+	6.17122i	0.293204	+	0.293204i	0.838344	−	0.545141i	$-0.183524\pi$
$443$	6.17122	+	6.17122i	0.293204	+	0.293204i	−0.545141	+	0.838344i	$0.683524\pi$
$444$	−1.40066	−	0.259434i	−0.0664726	−	0.0123122i
$445$	12.0071	−	24.0453i	0.569192	−	1.13986i
$446$	17.2184	+	1.58117i	0.815315	+	0.0748705i
$447$	10.0228	−	10.0228i	0.474064	−	0.474064i
$448$	13.0380	−	16.6737i	0.615986	−	0.787757i
$449$		−	12.9112i		−	0.609317i	−0.952462	−	0.304659i	$-0.901458\pi$
$449$		−	12.9112i		−	0.609317i	0.952462	−	0.304659i	$-0.0985424\pi$
$450$	1.62882	−	6.88091i	0.0767835	−	0.324369i
$451$	−1.27718			−0.0601403
$452$	−17.7076	−	25.7585i	−0.832895	−	1.21158i
$453$	7.11457	−	7.11457i	0.334271	−	0.334271i
$454$	16.9383	+	1.55545i	0.794955	+	0.0730009i
$455$	5.64462	+	26.7359i	0.264624	+	1.25340i
$456$	−1.88871	+	6.70121i	−0.0884470	+	0.313813i
$457$	−3.16432	−	3.16432i	−0.148021	−	0.148021i	0.629213	−	0.777233i	$-0.283377\pi$
$457$	−3.16432	−	3.16432i	−0.148021	−	0.148021i	−0.777233	+	0.629213i	$0.783377\pi$
$458$	4.63068	+	5.56715i	0.216378	+	0.260136i
$459$	3.59513			0.167806
$460$	−13.7796	+	1.92948i	−0.642476	+	0.0899624i
$461$	35.7469			1.66490			0.832449	−	0.554102i	$-0.186938\pi$
$461$	35.7469			1.66490			0.832449	+	0.554102i	$0.186938\pi$
$462$	8.47139	+	1.76819i	0.394125	+	0.0822636i
$463$	28.0663	−	28.0663i	1.30435	−	1.30435i	0.378925	−	0.925428i	$-0.376294\pi$
$463$	28.0663	−	28.0663i	1.30435	−	1.30435i	0.925428	−	0.378925i	$-0.123706\pi$
$464$	−19.8407	−	7.61101i	−0.921083	−	0.353332i
$465$	−0.344988	+	0.115194i	−0.0159984	+	0.00534199i
$466$	1.12956	−	12.3006i	0.0523261	−	0.569813i
$467$	−2.71591	−	2.71591i	−0.125677	−	0.125677i	0.641471	−	0.767148i	$-0.278325\pi$
$467$	−2.71591	−	2.71591i	−0.125677	−	0.125677i	−0.767148	+	0.641471i	$0.778325\pi$
$468$	7.61238	−	5.23311i	0.351882	−	0.241900i
$469$	−14.6863	+	11.6640i	−0.678151	+	0.538595i
$470$	−35.9242	−	22.2585i	−1.65706	−	1.02671i
$471$	22.9913			1.05938
$472$	0.125949	−	0.0705630i	0.00579729	−	0.00324792i
$473$	−12.4549	+	12.4549i	−0.572677	+	0.572677i
$474$	−23.4229	−	2.15093i	−1.07585	−	0.0987955i
$475$	−9.83852	+	7.39478i	−0.451422	+	0.339296i
$476$	8.92034	+	16.8026i	0.408863	+	0.770144i
$477$	2.25295	−	2.25295i	0.103156	−	0.103156i
$478$	6.79547	+	8.16973i	0.310818	+	0.373675i
$479$	1.09107			0.0498525			0.0249262	−	0.999689i	$-0.492065\pi$
$479$	1.09107			0.0498525			0.0249262	+	0.999689i	$0.492065\pi$
$480$	−7.65304	−	10.0713i	−0.349312	−	0.459690i
$481$		−	3.28972i		−	0.149998i
$482$	21.9701	+	26.4132i	1.00071	+	1.20309i
$483$	−0.937987	+	8.17802i	−0.0426799	+	0.372113i
$484$	2.05824	−	11.1123i	0.0935565	−	0.505104i
$485$	−1.80653	−	5.41026i	−0.0820301	−	0.245667i
$486$	−0.129323	+	1.40829i	−0.00586623	+	0.0638812i
$487$	12.7356	+	12.7356i	0.577106	+	0.577106i	0.934105	−	0.356999i	$-0.116200\pi$
$487$	12.7356	+	12.7356i	0.577106	+	0.577106i	−0.356999	+	0.934105i	$0.616200\pi$
$488$	−5.80307	−	10.3580i	−0.262693	−	0.468885i
$489$	22.0017			0.994950
$490$	−0.0508929	−	22.1359i	−0.00229911	−	0.999997i
$491$		−	9.01506i		−	0.406844i	−0.979091	−	0.203422i	$-0.934794\pi$
$491$		−	9.01506i		−	0.406844i	0.979091	−	0.203422i	$-0.0652063\pi$
$492$	0.910108	−	0.625651i	0.0410308	−	0.0282065i
$493$	13.5054	−	13.5054i	0.608253	−	0.608253i
$494$	−16.0114	−	1.47033i	−0.720385	−	0.0661532i
$495$	2.31048	−	4.62693i	0.103848	−	0.207965i
$496$	−0.233027	+	0.607466i	−0.0104632	+	0.0272760i
$497$	−37.1969	−	4.26634i	−1.66851	−	0.191371i
$498$	−0.884175	−	1.06298i	−0.0396208	−	0.0476334i
$499$	34.2778			1.53448			0.767242	−	0.641358i	$-0.221629\pi$
$499$	34.2778			1.53448			0.767242	+	0.641358i	$0.221629\pi$
$500$	0.0390054	−	22.3606i	0.00174437	−	0.999998i
$501$			14.5588i			0.650437i
$502$	−23.0922	+	19.2078i	−1.03065	+	0.857285i
$503$	−15.8199	−	15.8199i	−0.705374	−	0.705374i	0.260185	−	0.965559i	$-0.416216\pi$
$503$	−15.8199	−	15.8199i	−0.705374	−	0.705374i	−0.965559	+	0.260185i	$0.916216\pi$
$504$	−6.90280	+	2.88987i	−0.307475	+	0.128725i
$505$	7.37403	−	14.7671i	0.328140	−	0.657128i
$506$	−10.1340	−	0.930604i	−0.450509	−	0.0413704i
$507$	5.89261	+	5.89261i	0.261700	+	0.261700i
$508$	1.19987	−	0.824846i	0.0532355	−	0.0365966i
$509$		−	35.5921i		−	1.57759i	−0.614654	−	0.788797i	$-0.710704\pi$
$509$		−	35.5921i		−	1.57759i	0.614654	−	0.788797i	$-0.289296\pi$
$510$	11.0676	−	2.59951i	0.490082	−	0.115108i
$511$	−16.4898	−	20.7625i	−0.729468	−	0.918481i
$512$	−22.6104	−	0.876872i	−0.999249	−	0.0387526i
$513$	1.74057	−	1.74057i	0.0768481	−	0.0768481i
$514$	−2.26452	+	24.6599i	−0.0998837	+	1.08770i
$515$	1.73863	−	0.580541i	0.0766133	−	0.0255817i
$516$	2.77398	−	14.9765i	0.122118	−	0.659303i
$517$	−21.8562	−	21.8562i	−0.961236	−	0.961236i
$518$	−0.544512	+	2.60875i	−0.0239245	+	0.114622i
$519$		−	10.4597i		−	0.459131i
$520$	19.6509	−	21.6144i	0.861747	−	0.947852i
$521$		−	35.8489i		−	1.57057i	−0.619134	−	0.785285i	$-0.712516\pi$
$521$		−	35.8489i		−	1.57057i	0.619134	−	0.785285i	$-0.287484\pi$
$522$	4.80454	+	5.77617i	0.210289	+	0.252816i
$523$	−12.5603	+	12.5603i	−0.549225	+	0.549225i	−0.926217	−	0.376992i	$-0.876958\pi$
$523$	−12.5603	+	12.5603i	−0.549225	+	0.549225i	0.376992	+	0.926217i	$0.376958\pi$
$524$	0.708567	−	3.82549i	0.0309539	−	0.167118i
$525$	−12.8008	−	3.33768i	−0.558672	−	0.145668i
$526$	2.40576	−	26.1979i	0.104896	−	1.14228i
$527$	−0.413497	−	0.413497i	−0.0180122	−	0.0180122i
$528$	−3.76482	−	8.45079i	−0.163843	−	0.367773i
$529$			13.3200i			0.579132i
$530$	5.30670	−	8.56476i	0.230508	−	0.372029i
$531$	−0.0510421			−0.00221504
$532$	12.4537	+	3.81616i	0.539935	+	0.165451i
$533$	1.80351	+	1.80351i	0.0781186	+	0.0781186i
$534$	−1.55441	+	16.9270i	−0.0672658	+	0.732502i
$535$	−8.14433	−	24.3910i	−0.352110	−	1.05451i
$536$	19.2977	+	5.43900i	0.833535	+	0.234929i
$537$	−0.212587	+	0.212587i	−0.00917380	+	0.00917380i
$538$	−11.1891	−	13.4519i	−0.482397	−	0.579953i
$539$	3.66566	−	15.7696i	0.157891	−	0.679246i
$540$	0.620159	+	4.42893i	0.0266874	+	0.190591i
$541$		−	32.5384i		−	1.39893i	−0.714665	−	0.699467i	$-0.753421\pi$
$541$		−	32.5384i		−	1.39893i	0.714665	−	0.699467i	$-0.246579\pi$
$542$	−14.7958	−	17.7880i	−0.635535	−	0.764060i
$543$	10.0602	−	10.0602i	0.431726	−	0.431726i
$544$	8.98973	−	18.2423i	0.385432	−	0.782134i
$545$	−17.0022	+	34.0483i	−0.728293	+	1.45847i
$546$	−9.46557	−	14.4593i	−0.405089	−	0.618800i
$547$	−0.172929	+	0.172929i	−0.00739389	+	0.00739389i	−0.710794	−	0.703400i	$-0.751664\pi$
$547$	−0.172929	+	0.172929i	−0.00739389	+	0.00739389i	0.703400	+	0.710794i	$0.251664\pi$
$548$	−9.98058	+	6.86112i	−0.426349	+	0.293093i
$549$			4.19768i			0.179153i
$550$	3.76725	−	15.9146i	0.160636	−	0.678602i
$551$		−	13.0772i		−	0.557108i
$552$	7.67722	−	4.30116i	0.326764	−	0.183069i
$553$	−5.01429	+	43.7180i	−0.213229	+	1.85908i
$554$	−2.14913	+	23.4033i	−0.0913079	+	0.994313i
$555$	1.42486	+	0.711509i	0.0604818	+	0.0302019i
$556$	−23.1556	−	4.28893i	−0.982015	−	0.181891i
$557$	−14.5689	+	14.5689i	−0.617302	+	0.617302i	−0.944839	−	0.327536i	$-0.893782\pi$
$557$	−14.5689	+	14.5689i	−0.617302	+	0.617302i	0.327536	+	0.944839i	$0.393782\pi$
$558$	0.176850	−	0.147101i	0.00748664	−	0.00622729i
$559$	35.1751			1.48775
$560$	−19.1607	+	13.8876i	−0.809689	+	0.586859i
$561$	8.31506			0.351062
$562$	−24.4183	+	20.3108i	−1.03002	+	0.856759i
$563$	−18.2210	+	18.2210i	−0.767924	+	0.767924i	−0.977741	−	0.209817i	$-0.932713\pi$
$563$	−18.2210	+	18.2210i	−0.767924	+	0.767924i	0.209817	+	0.977741i	$0.432713\pi$
$564$	26.2812	+	4.86786i	1.10664	+	0.204974i
$565$	11.0685	+	33.1483i	0.465654	+	1.39456i
$566$	−2.42341	+	26.3901i	−0.101863	+	1.10926i
$567$	2.62852	+	0.301481i	0.110387	+	0.0126610i
$568$	19.5634	+	34.9191i	0.820861	+	1.46517i
$569$			1.67927i			0.0703986i	0.999380	+	0.0351993i	$0.0112066\pi$
$569$			1.67927i			0.0703986i	−0.999380	+	0.0351993i	$0.988793\pi$
$570$	4.09981	−	6.61689i	0.171722	−	0.277151i
$571$			27.8353i			1.16487i	0.812877	+	0.582435i	$0.197900\pi$
$571$			27.8353i			1.16487i	−0.812877	+	0.582435i	$0.802100\pi$
$572$	17.6064	−	12.1035i	0.736161	−	0.506072i
$573$	6.15177	−	6.15177i	0.256994	−	0.256994i
$574$	−1.13167	−	1.72870i	−0.0472350	−	0.0721545i
$575$	15.4022	+	2.18409i	0.642318	+	0.0910830i
$576$	6.82254	+	4.17768i	0.284272	+	0.174070i
$577$	−26.4367	+	26.4367i	−1.10057	+	1.10057i	−0.106233	+	0.994341i	$0.533879\pi$
$577$	−26.4367	+	26.4367i	−1.10057	+	1.10057i	−0.994341	+	0.106233i	$0.966121\pi$
$578$	−3.68533	−	4.43062i	−0.153290	−	0.184290i
$579$		−	22.0992i		−	0.918410i
$580$	18.9673	+	14.3080i	0.787576	+	0.594106i
$581$	−2.02557	+	1.60873i	−0.0840348	+	0.0667413i
$582$	2.30691	+	2.77344i	0.0956245	+	0.114963i
$583$	5.21079	−	5.21079i	0.215809	−	0.215809i
$584$	−7.68930	+	27.2819i	−0.318186	+	1.12893i
$585$	−9.79629	+	3.27105i	−0.405027	+	0.135241i
$586$	2.96396	−	32.2766i	0.122440	−	1.33333i
$587$	−15.3996	−	15.3996i	−0.635608	−	0.635608i	0.313861	−	0.949469i	$-0.398377\pi$
$587$	−15.3996	−	15.3996i	−0.635608	−	0.635608i	−0.949469	+	0.313861i	$0.898377\pi$
$588$	5.11292	+	13.0330i	0.210853	+	0.537470i
$589$	−0.400386			−0.0164976
$590$	−0.157133	+	0.0369067i	−0.00646907	+	0.00151942i
$591$			6.86886i			0.282547i
$592$	2.60241	−	1.15937i	0.106958	−	0.0476498i
$593$	12.9349	+	12.9349i	0.531172	+	0.531172i	0.920921	−	0.389749i	$-0.127438\pi$
$593$	12.9349	+	12.9349i	0.531172	+	0.531172i	−0.389749	+	0.920921i	$0.627438\pi$
$594$	−0.299108	+	3.25718i	−0.0122725	+	0.133644i
$595$	−4.39359	−	20.8103i	−0.180119	−	0.853140i
$596$	−5.16303	+	27.8747i	−0.211486	+	1.14179i
$597$	18.7946	−	18.7946i	0.769210	−	0.769210i
$598$	12.9960	+	15.6242i	0.531447	+	0.638922i
$599$			30.7540i			1.25658i	0.777981	+	0.628288i	$0.216244\pi$
$599$			30.7540i			1.25658i	−0.777981	+	0.628288i	$0.783756\pi$
$600$	5.11156	+	13.1861i	0.208678	+	0.538318i
$601$		−	13.2033i		−	0.538574i	−0.963060	−	0.269287i	$-0.913212\pi$
$601$		−	13.2033i		−	0.538574i	0.963060	−	0.269287i	$-0.0867881\pi$
$602$	−27.8939	−	5.82214i	−1.13687	−	0.237293i
$603$	−5.01239	−	5.01239i	−0.204120	−	0.204120i
$604$	−3.66490	+	19.7865i	−0.149123	+	0.805101i
$605$	−5.64481	+	11.3042i	−0.229494	+	0.459581i
$606$	−0.954621	+	10.3955i	−0.0387788	+	0.422288i
$607$	18.1850	−	18.1850i	0.738105	−	0.738105i	−0.234106	−	0.972211i	$-0.575216\pi$
$607$	18.1850	−	18.1850i	0.738105	−	0.738105i	0.972211	+	0.234106i	$0.0752164\pi$
$608$	−4.47962	−	13.1843i	−0.181673	−	0.534695i
$609$	11.0068	−	8.74172i	0.446018	−	0.354232i
$610$	3.03519	+	12.9226i	0.122891	+	0.523220i
$611$			61.7262i			2.49718i
$612$	−5.92522	+	4.07327i	−0.239513	+	0.164652i
$613$	−12.7804	−	12.7804i	−0.516195	−	0.516195i	0.400223	−	0.916418i	$-0.368933\pi$
$613$	−12.7804	−	12.7804i	−0.516195	−	0.516195i	−0.916418	+	0.400223i	$0.868933\pi$
$614$	27.5091	+	2.52616i	1.11018	+	0.101948i
$615$	−1.17121	+	0.391075i	−0.0472277	+	0.0157697i
$616$	−15.9653	+	6.68388i	−0.643259	+	0.269301i
$617$	−32.5397	−	32.5397i	−1.31000	−	1.31000i	−0.921412	−	0.388588i	$-0.872963\pi$
$617$	−32.5397	−	32.5397i	−1.31000	−	1.31000i	−0.388588	−	0.921412i	$-0.627037\pi$
$618$	−0.891267	+	0.741344i	−0.0358520	+	0.0298212i
$619$			4.66489i			0.187498i	0.995596	+	0.0937488i	$0.0298851\pi$
$619$			4.66489i			0.187498i	−0.995596	+	0.0937488i	$0.970115\pi$
$620$	0.438069	−	0.580725i	0.0175933	−	0.0233225i
$621$	−3.11126			−0.124851
$622$	−20.4743	−	24.6149i	−0.820946	−	0.986967i
$623$	31.5936	+	3.62366i	1.26577	+	0.145179i
$624$	−6.61704	+	17.2496i	−0.264894	+	0.690537i
$625$	−6.95042	+	24.0144i	−0.278017	+	0.960576i
$626$	−4.84265	−	0.444702i	−0.193551	−	0.0177739i
$627$	4.02571	−	4.02571i	0.160771	−	0.160771i
$628$	−37.8926	+	26.0491i	−1.51208	+	1.03947i
$629$			2.56061i			0.102098i
$630$	8.30989	−	0.972475i	0.331074	−	0.0387443i
$631$	−12.9180			−0.514258			−0.257129	−	0.966377i	$-0.582777\pi$
$631$	−12.9180			−0.514258			−0.257129	+	0.966377i	$0.582777\pi$
$632$	41.0409	−	22.9931i	1.63252	−	0.914617i
$633$	15.4297	+	15.4297i	0.613277	+	0.613277i
$634$	−4.07246	+	44.3477i	−0.161738	+	1.76127i
$635$	−1.54410	+	0.515585i	−0.0612757	+	0.0204604i
$636$	−1.16056	+	6.26574i	−0.0460190	+	0.248453i
$637$	−27.4445	+	17.0920i	−1.08739	+	0.677209i
$638$	11.1123	+	13.3595i	0.439939	+	0.528909i
$639$		−	14.1513i		−	0.559815i
$640$	24.0239	+	7.92788i	0.949629	+	0.313377i
$641$	−25.0301			−0.988631			−0.494316	−	0.869282i	$-0.664581\pi$
$641$	−25.0301			−0.988631			−0.494316	+	0.869282i	$0.664581\pi$
$642$	10.4002	+	12.5034i	0.410463	+	0.493472i
$643$	−5.60693	+	5.60693i	−0.221116	+	0.221116i	−0.808968	−	0.587852i	$-0.799974\pi$
$643$	−5.60693	+	5.60693i	−0.221116	+	0.221116i	0.587852	+	0.808968i	$0.299974\pi$
$644$	−7.71976	−	14.5411i	−0.304201	−	0.573001i
$645$	−7.60774	+	15.2351i	−0.299555	+	0.599883i
$646$	12.4627	+	1.14445i	0.490339	+	0.0450279i
$647$	13.6806	−	13.6806i	0.537840	−	0.537840i	−0.385054	−	0.922894i	$-0.625817\pi$
$647$	13.6806	−	13.6806i	0.537840	−	0.537840i	0.922894	+	0.385054i	$0.125817\pi$
$648$	−1.38245	−	2.46756i	−0.0543076	−	0.0969348i
$649$	−0.118054			−0.00463401
$650$	−27.7927	+	17.1533i	−1.09012	+	0.672807i
$651$	−0.267646	−	0.336996i	−0.0104899	−	0.0132079i
$652$	−36.2615	+	24.9279i	−1.42011	+	0.976251i
$653$	−27.3390	−	27.3390i	−1.06986	−	1.06986i	−0.997369	−	0.0724880i	$-0.976906\pi$
$653$	−27.3390	−	27.3390i	−1.06986	−	1.06986i	−0.0724880	−	0.997369i	$-0.523094\pi$
$654$	2.20105	−	23.9687i	0.0860679	−	0.937251i
$655$	−1.94327	+	3.89157i	−0.0759299	+	0.152056i
$656$	−0.791110	+	2.06230i	−0.0308877	+	0.0805194i
$657$	7.08619	−	7.08619i	0.276459	−	0.276459i
$658$	10.2169	−	48.9490i	0.398295	−	1.90823i
$659$	10.1015			0.393499			0.196749	−	0.980454i	$-0.436961\pi$
$659$	10.1015			0.393499			0.196749	+	0.980454i	$0.436961\pi$
$660$	1.43435	+	10.2435i	0.0558318	+	0.398729i
$661$	24.0594			0.935801			0.467901	−	0.883781i	$-0.345010\pi$
$661$	24.0594			0.935801			0.467901	+	0.883781i	$0.345010\pi$
$662$	−18.6286	−	22.3959i	−0.724020	−	0.870440i
$663$	−11.7417	−	11.7417i	−0.456008	−	0.456008i
$664$	2.66159	+	0.750160i	0.103290	+	0.0291118i
$665$	−12.2024	−	7.94812i	−0.473189	−	0.308215i
$666$	−1.00305	−	0.0921099i	−0.0388672	−	0.00356919i
$667$	−11.6877	+	11.6877i	−0.452551	+	0.452551i
$668$	−16.4950	−	23.9946i	−0.638213	−	0.928381i
$669$	12.2265			0.472703
$670$	−19.0549	−	11.8064i	−0.736157	−	0.456121i
$671$			9.70868i			0.374799i
$672$	8.10246	−	12.5837i	0.312559	−	0.485428i
$673$	12.9529	−	12.9529i	0.499298	−	0.499298i	−0.411922	−	0.911219i	$-0.635142\pi$
$673$	12.9529	−	12.9529i	0.499298	−	0.499298i	0.911219	+	0.411922i	$0.135142\pi$
$674$	−21.7052	−	1.99319i	−0.836052	−	0.0767748i
$675$	0.701995	−	4.95047i	0.0270198	−	0.190544i
$676$	−16.3881	−	3.03544i	−0.630311	−	0.116748i
$677$	0.136604	+	0.136604i	0.00525011	+	0.00525011i	0.709727	−	0.704477i	$-0.248818\pi$
$677$	0.136604	+	0.136604i	0.00525011	+	0.00525011i	−0.704477	+	0.709727i	$0.748818\pi$
$678$	−14.1343	−	16.9927i	−0.542824	−	0.652600i
$679$	5.28493	−	4.19735i	0.202817	−	0.161080i
$680$	−15.2956	+	16.8239i	−0.586558	+	0.645167i
$681$	12.0276			0.460898
$682$	0.409030	−	0.340225i	0.0156626	−	0.0130279i
$683$	28.1468	+	28.1468i	1.07701	+	1.07701i	0.996776	+	0.0802303i	$0.0255656\pi$
$683$	28.1468	+	28.1468i	1.07701	+	1.07701i	0.0802303	+	0.996776i	$0.474434\pi$
$684$	−0.896614	+	4.84074i	−0.0342829	+	0.185090i
$685$	12.8439	−	4.28867i	0.490740	−	0.163862i
$686$	24.5926	−	9.01138i	0.938949	−	0.344056i
$687$	3.62065	+	3.62065i	0.138136	+	0.138136i
$688$	12.3965	+	27.8260i	0.472611	+	1.06086i
$689$	−14.7163			−0.560645
$690$	−9.57804	+	2.24964i	−0.364630	+	0.0856424i
$691$	4.83484			0.183926			0.0919630	−	0.995762i	$-0.470686\pi$
$691$	4.83484			0.183926			0.0919630	+	0.995762i	$0.470686\pi$
$692$	11.8508	+	17.2389i	0.450502	+	0.655326i
$693$	6.07941	+	0.697286i	0.230938	+	0.0264877i
$694$	−2.41691	+	26.3194i	−0.0917447	+	0.999069i
$695$	23.5555	+	11.7625i	0.893511	+	0.446179i
$696$	−14.4629	−	4.07631i	−0.548214	−	0.154512i
$697$	−1.40379	−	1.40379i	−0.0531724	−	0.0531724i
$698$	9.14360	+	10.9927i	0.346090	+	0.416080i
$699$		−	8.73442i		−	0.330366i
$700$	24.8789	−	9.00234i	0.940333	−	0.340257i
$701$			34.1137i			1.28846i	0.764833	+	0.644229i	$0.222822\pi$
$701$			34.1137i			1.28846i	−0.764833	+	0.644229i	$0.777178\pi$
$702$	5.02183	−	4.17709i	0.189537	−	0.157654i
$703$	1.23971	+	1.23971i	0.0467566	+	0.0467566i
$704$	15.7796	+	9.66242i	0.594717	+	0.364166i
$705$	−26.7351	−	13.3503i	−1.00690	−	0.502801i
$706$	−0.143599	−	0.0131867i	−0.00540440	−	0.000496287i
$707$	19.4028	+	2.22543i	0.729718	+	0.0836959i
$708$	0.0841237	−	0.0578306i	0.00316156	−	0.00217341i
$709$	−1.70158			−0.0639041			−0.0319521	−	0.999489i	$-0.510172\pi$
$709$	−1.70158			−0.0639041			−0.0319521	+	0.999489i	$0.510172\pi$
$710$	−10.2323	−	43.5647i	−0.384010	−	1.63495i
$711$	−16.6322			−0.623755
$712$	−16.6164	−	29.6589i	−0.622725	−	1.11151i
$713$	0.357845	+	0.357845i	0.0134014	+	0.0134014i
$714$	7.36768	+	11.2546i	0.275729	+	0.421194i
$715$	−22.6575	+	7.56551i	−0.847343	+	0.282934i
$716$	0.109509	−	0.591230i	0.00409254	−	0.0220953i
$717$	5.31326	+	5.31326i	0.198427	+	0.198427i
$718$	−24.9613	−	30.0092i	−0.931546	−	1.11993i
$719$	19.1925			0.715758			0.357879	−	0.933768i	$-0.383500\pi$
$719$	19.1925			0.715758			0.357879	+	0.933768i	$0.383500\pi$
$720$	−6.04007	−	6.59679i	−0.225100	−	0.245848i
$721$	1.34885	+	1.69836i	0.0502339	+	0.0632501i
$722$	−14.0700	+	11.7032i	−0.523631	+	0.435549i
$723$	17.1780	+	17.1780i	0.638858	+	0.638858i
$724$	−5.18229	+	27.9788i	−0.192598	+	1.03982i
$725$	−15.9598	−	21.2340i	−0.592732	−	0.788611i
$726$	0.730761	−	7.95773i	0.0271211	−	0.295339i
$727$	−22.5433	+	22.5433i	−0.836086	+	0.836086i	−0.988341	−	0.152256i	$-0.951346\pi$
$727$	−22.5433	+	22.5433i	−0.836086	+	0.836086i	0.152256	+	0.988341i	$0.451346\pi$
$728$	31.9828	+	13.1062i	1.18536	+	0.485749i
$729$			1.00000i			0.0370370i
$730$	16.6911	−	26.9386i	0.617765	−	0.997044i
$731$	−27.3791			−1.01265
$732$	−4.75596	−	6.91830i	−0.175785	−	0.255708i
$733$	−7.22303	+	7.22303i	−0.266789	+	0.266789i	−0.827805	−	0.561016i	$-0.810411\pi$
$733$	−7.22303	+	7.22303i	−0.266789	+	0.266789i	0.561016	+	0.827805i	$0.310411\pi$
$734$	1.41498	−	15.4086i	0.0522278	−	0.568743i
$735$	−1.46718	−	15.5836i	−0.0541177	−	0.574808i
$736$	−7.77982	+	15.7871i	−0.286768	+	0.581921i
$737$	−11.5930	−	11.5930i	−0.427034	−	0.427034i
$738$	0.600392	−	0.499398i	0.0221007	−	0.0183831i
$739$	−37.2974			−1.37201			−0.686004	−	0.727598i	$-0.740637\pi$
$739$	−37.2974			−1.37201			−0.686004	+	0.727598i	$0.740637\pi$
$740$	−3.15448	+	0.441705i	−0.115961	+	0.0162374i
$741$	−11.3694			−0.417665
$742$	11.6700	+	2.43582i	0.428420	+	0.0894218i
$743$	9.27408	−	9.27408i	0.340233	−	0.340233i	−0.516222	−	0.856455i	$-0.672662\pi$
$743$	9.27408	−	9.27408i	0.340233	−	0.340233i	0.856455	+	0.516222i	$0.172662\pi$
$744$	−0.124805	+	0.442811i	−0.00457557	+	0.0162343i
$745$	14.1598	−	28.3562i	0.518775	−	1.03889i
$746$	21.7112	+	1.99374i	0.794903	+	0.0729961i
$747$	−0.691321	−	0.691321i	−0.0252941	−	0.0252941i
$748$	−13.7042	+	9.42094i	−0.501077	+	0.344464i
$749$	23.8260	−	18.9228i	0.870582	−	0.691426i
$750$	−1.41841	−	15.7476i	−0.0517931	−	0.575022i
$751$	22.2185			0.810765			0.405382	−	0.914147i	$-0.367138\pi$
$751$	22.2185			0.810765			0.405382	+	0.914147i	$0.367138\pi$
$752$	−48.8299	+	21.7537i	−1.78064	+	0.793275i
$753$	−15.0182	+	15.0182i	−0.547294	+	0.547294i
$754$	3.17334	−	34.5565i	0.115566	−	1.25848i
$755$	10.0511	−	20.1282i	0.365798	−	0.732541i
$756$	−4.67370	+	2.48123i	−0.169981	+	0.0902414i
$757$	−32.1590	+	32.1590i	−1.16884	+	1.16884i	−0.186355	+	0.982482i	$0.559668\pi$
$757$	−32.1590	+	32.1590i	−1.16884	+	1.16884i	−0.982482	+	0.186355i	$0.940332\pi$
$758$	−24.6398	+	20.4950i	−0.894957	+	0.744413i
$759$	−7.19594			−0.261196
$760$	0.739935	+	15.5505i	0.0268402	+	0.564078i
$761$		−	6.53097i		−	0.236747i	−0.992969	−	0.118374i	$-0.962232\pi$
$761$		−	6.53097i		−	0.236747i	0.992969	−	0.118374i	$-0.0377681\pi$
$762$	0.791544	−	0.658396i	0.0286746	−	0.0238512i
$763$	−44.7367	−	5.13113i	−1.61958	−	0.185759i
$764$	−3.16894	+	17.1088i	−0.114648	+	0.618976i
$765$	7.62511	−	2.54608i	0.275686	−	0.0920536i
$766$	2.36374	+	0.217063i	0.0854055	+	0.00784280i
$767$	0.166703	+	0.166703i	0.00601930	+	0.00601930i
$768$	−15.9777	+	0.844584i	−0.576545	+	0.0304763i
$769$	45.0123			1.62319			0.811593	−	0.584224i	$-0.198601\pi$
$769$	45.0123			1.62319			0.811593	+	0.584224i	$0.198601\pi$
$770$	19.2197	−	2.24921i	0.692629	−	0.0810557i
$771$			17.5105i			0.630626i
$772$	25.0383	+	36.4222i	0.901149	+	1.31086i
$773$	32.6049	−	32.6049i	1.17272	−	1.17272i	0.191156	−	0.981560i	$-0.438776\pi$
$773$	32.6049	−	32.6049i	1.17272	−	1.17272i	0.981560	−	0.191156i	$-0.0612235\pi$
$774$	0.984876	−	10.7250i	0.0354006	−	0.385501i
$775$	−0.650123	+	0.488642i	−0.0233531	+	0.0175525i
$776$	−6.94438	−	1.95725i	−0.249289	−	0.0702611i
$777$	−0.214728	+	1.87215i	−0.00770333	+	0.0671629i
$778$	−27.3843	+	22.7779i	−0.981774	+	0.816626i
$779$	−1.35928			−0.0487013
$780$	12.4394	−	16.4903i	0.445402	−	0.590447i
$781$		−	32.7300i		−	1.17117i
$782$	−10.1157	−	12.1614i	−0.361736	−	0.434890i
$783$	3.75659	+	3.75659i	0.134250	+	0.134250i
$784$	−23.1931	−	15.6870i	−0.828323	−	0.560250i
$785$	48.7635	−	16.2825i	1.74045	−	0.581147i
$786$	0.251570	−	2.73952i	0.00897322	−	0.0977153i
$787$	−10.7855	−	10.7855i	−0.384460	−	0.384460i	0.488246	−	0.872706i	$-0.337637\pi$
$787$	−10.7855	−	10.7855i	−0.384460	−	0.384460i	−0.872706	+	0.488246i	$0.837637\pi$
$788$	−7.78241	−	11.3207i	−0.277237	−	0.403285i
$789$		−	18.6026i		−	0.662272i
$790$	−51.2022	+	12.0261i	−1.82169	+	0.427870i
$791$	−32.3804	+	25.7169i	−1.15132	+	0.914388i
$792$	−3.19742	−	5.70713i	−0.113615	−	0.202794i
$793$	13.7096	−	13.7096i	0.486842	−	0.486842i
$794$	6.07802	+	0.558146i	0.215701	+	0.0198078i
$795$	3.18287	−	6.37396i	0.112885	−	0.226061i
$796$	−9.68157	+	52.2700i	−0.343154	+	1.85266i
$797$	10.1693	+	10.1693i	0.360215	+	0.360215i	0.863892	−	0.503677i	$-0.168020\pi$
$797$	10.1693	+	10.1693i	0.360215	+	0.360215i	−0.503677	+	0.863892i	$0.668020\pi$
$798$	9.01593	+	1.88185i	0.319161	+	0.0666167i
$799$		−	48.0456i		−	1.69973i
$800$	−23.3643	−	15.9409i	−0.826051	−	0.563595i
$801$			12.0195i			0.424690i
$802$	−0.142621	+	0.118630i	−0.00503612	+	0.00418898i
$803$	16.3894	−	16.3894i	0.578370	−	0.578370i
$804$	13.9401	+	2.58202i	0.491629	+	0.0910607i
$805$	3.80226	+	18.0095i	0.134012	+	0.634751i
$806$	−1.05802	−	0.0971583i	−0.0372672	−	0.00342225i
$807$	−8.74857	−	8.74857i	−0.307964	−	0.307964i
$808$	−10.2047	−	18.2147i	−0.359002	−	0.640790i
$809$			4.16194i			0.146326i	0.997320	+	0.0731630i	$0.0233093\pi$
$809$			4.16194i			0.146326i	−0.997320	+	0.0731630i	$0.976691\pi$
$810$	0.723063	+	3.07850i	0.0254059	+	0.108168i
$811$	15.5083			0.544569			0.272285	−	0.962217i	$-0.412221\pi$
$811$	15.5083			0.544569			0.272285	+	0.962217i	$0.412221\pi$
$812$	−8.23623	+	26.8781i	−0.289035	+	0.943238i
$813$	−11.5686	−	11.5686i	−0.405728	−	0.405728i
$814$	−2.31991	−	0.213038i	−0.0813128	−	0.00746698i
$815$	46.6646	−	15.5816i	1.63459	−	0.545801i
$816$	5.15049	−	13.4265i	0.180303	−	0.470023i
$817$	−13.2555	+	13.2555i	−0.463751	+	0.463751i
$818$	−26.8583	+	22.3404i	−0.939078	+	0.781112i
$819$	−7.60009	−	9.56936i	−0.265569	−	0.334380i
$820$	1.48721	−	1.97152i	0.0519357	−	0.0688484i
$821$		−	45.0658i		−	1.57281i	−0.617713	−	0.786404i	$-0.711940\pi$
$821$		−	45.0658i		−	1.57281i	0.617713	−	0.786404i	$-0.288060\pi$
$822$	−6.58411	+	5.47658i	−0.229647	+	0.191018i
$823$	−9.79135	+	9.79135i	−0.341305	+	0.341305i	−0.856858	−	0.515553i	$-0.827587\pi$
$823$	−9.79135	+	9.79135i	−0.341305	+	0.341305i	0.515553	+	0.856858i	$0.327587\pi$
$824$	0.628977	−	2.23163i	0.0219115	−	0.0777425i
$825$	1.62362	−	11.4498i	0.0565273	−	0.398631i
$826$	−0.104603	−	0.159788i	−0.00363961	−	0.00555975i
$827$	5.62483	−	5.62483i	0.195595	−	0.195595i	−0.602514	−	0.798108i	$-0.705834\pi$
$827$	5.62483	−	5.62483i	0.195595	−	0.195595i	0.798108	+	0.602514i	$0.205834\pi$
$828$	5.12775	−	3.52506i	0.178202	−	0.122504i
$829$		−	39.0436i		−	1.35604i	−0.735043	−	0.678021i	$-0.762838\pi$
$829$		−	39.0436i		−	1.35604i	0.735043	−	0.678021i	$-0.237162\pi$
$830$	−2.62810	−	1.62836i	−0.0912228	−	0.0565214i
$831$			16.6183i			0.576482i
$832$	−8.63808	−	35.9266i	−0.299471	−	1.24553i
$833$	21.3619	−	13.3038i	0.740146	−	0.460951i
$834$	−16.5822	−	1.52275i	−0.574194	−	0.0527284i
$835$	10.3105	+	30.8785i	0.356811	+	1.06859i
$836$	−2.07375	+	11.1960i	−0.0717221	+	0.387222i
$837$	0.115016	−	0.115016i	0.00397553	−	0.00397553i
$838$	−24.6177	−	29.5962i	−0.850406	−	1.02238i
$839$	−46.3596			−1.60051			−0.800256	−	0.599659i	$-0.795303\pi$
$839$	−46.3596			−1.60051			−0.800256	+	0.599659i	$0.795303\pi$
$840$	−12.5939	+	11.0179i	−0.434532	+	0.380152i
$841$	−0.776086			−0.0267616
$842$	12.8948	+	15.5025i	0.444383	+	0.534251i
$843$	−15.8806	+	15.8806i	−0.546958	+	0.546958i
$844$	−42.9120	−	7.94827i	−1.47709	−	0.273591i
$845$	16.6711	+	8.32481i	0.573504	+	0.286382i
$846$	18.8205	+	1.72829i	0.647062	+	0.0594198i
$847$	−14.8528	−	1.70356i	−0.510349	−	0.0585351i
$848$	−5.18634	−	11.6416i	−0.178100	−	0.399775i
$849$			18.7391i			0.643125i
$850$	21.6329	−	13.3515i	0.742004	−	0.457954i
$851$		−	2.21598i		−	0.0759628i
$852$	16.0334	+	23.3230i	0.549294	+	0.799035i
$853$	−18.0092	+	18.0092i	−0.616623	+	0.616623i	−0.944664	−	0.328041i	$-0.893612\pi$
$853$	−18.0092	+	18.0092i	−0.616623	+	0.616623i	0.328041	+	0.944664i	$0.393612\pi$
$854$	−13.1409	+	8.60252i	−0.449673	+	0.294372i
$855$	2.45900	−	4.92435i	0.0840959	−	0.168409i
$856$	−31.3072	−	8.82383i	−1.07006	−	0.301592i
$857$	−22.3652	+	22.3652i	−0.763980	+	0.763980i	−0.977039	−	0.213059i	$-0.931657\pi$
$857$	−22.3652	+	22.3652i	−0.763980	+	0.763980i	0.213059	+	0.977039i	$0.431657\pi$
$858$	11.6148	−	9.66105i	0.396524	−	0.329823i
$859$			6.28238i			0.214352i	0.994240	+	0.107176i	$0.0341808\pi$
$859$			6.28238i			0.214352i	−0.994240	+	0.107176i	$0.965819\pi$
$860$	−4.72289	−	33.7290i	−0.161049	−	1.15015i
$861$	−0.908639	−	1.14408i	−0.0309663	−	0.0389901i
$862$	33.2825	−	27.6840i	1.13361	−	0.942919i
$863$	30.3333	−	30.3333i	1.03256	−	1.03256i	0.0331053	−	0.999452i	$-0.489460\pi$
$863$	30.3333	−	30.3333i	1.03256	−	1.03256i	0.999452	−	0.0331053i	$-0.0105397\pi$
$864$	5.07418	+	2.50053i	0.172627	+	0.0850698i
$865$	−7.40759	−	22.1846i	−0.251866	−	0.754299i
$866$	0.819450	+	0.0752503i	0.0278460	+	0.00255711i
$867$	−2.88150	−	2.88150i	−0.0978608	−	0.0978608i
$868$	0.822930	+	0.252169i	0.0279321	+	0.00855918i
$869$	−38.4680			−1.30494
$870$	14.2809	+	8.84842i	0.484169	+	0.299989i
$871$			32.7409i			1.10938i
$872$	23.5289	+	41.9972i	0.796789	+	1.42220i
$873$	1.80373	+	1.80373i	0.0610471	+	0.0610471i
$874$	−10.7854	−	0.990423i	−0.364821	−	0.0335016i
$875$	−29.5136	+	1.98646i	−0.997743	+	0.0671546i
$876$	−3.65028	+	19.7076i	−0.123332	+	0.665857i
$877$	−9.46290	+	9.46290i	−0.319539	+	0.319539i	−0.848590	−	0.529051i	$-0.822548\pi$
$877$	−9.46290	+	9.46290i	−0.319539	+	0.319539i	0.529051	+	0.848590i	$0.322548\pi$
$878$	21.2329	−	17.6612i	0.716575	−	0.596038i
$879$		−	22.9190i		−	0.773039i
$880$	−13.9699	−	15.2575i	−0.470924	−	0.514330i
$881$		−	7.77655i		−	0.261999i	−0.991382	−	0.130999i	$-0.958181\pi$
$881$		−	7.77655i		−	0.261999i	0.991382	−	0.130999i	$-0.0418186\pi$
$882$	4.44297	+	8.84647i	0.149602	+	0.297876i
$883$	5.40461	+	5.40461i	0.181880	+	0.181880i	0.792174	−	0.610295i	$-0.208949\pi$
$883$	5.40461	+	5.40461i	0.181880	+	0.181880i	−0.610295	+	0.792174i	$0.708949\pi$
$884$	32.6550	+	6.04844i	1.09831	+	0.203431i
$885$	−0.108258	+	0.0361481i	−0.00363905	+	0.00121511i
$886$	−12.2907	−	1.12866i	−0.412915	−	0.0379181i
$887$	10.3564	−	10.3564i	0.347733	−	0.347733i	−0.511531	−	0.859265i	$-0.670922\pi$
$887$	10.3564	−	10.3564i	0.347733	−	0.347733i	0.859265	+	0.511531i	$0.170922\pi$
$888$	1.75750	−	0.984640i	0.0589780	−	0.0330424i
$889$	−1.19793	−	1.50833i	−0.0401773	−	0.0505877i
$890$	8.69089	+	37.0022i	0.291319	+	1.24032i
$891$			2.31287i			0.0774840i
$892$	−20.1507	+	13.8526i	−0.674697	+	0.463818i
$893$	−23.2612	−	23.2612i	−0.778405	−	0.778405i
$894$	−1.83309	+	19.9617i	−0.0613076	+	0.667619i
$895$	−0.300333	+	0.601441i	−0.0100390	+	0.0201040i
$896$	0.903466	+	29.9196i	0.0301827	+	0.999544i
$897$	10.1614	+	10.1614i	0.339278	+	0.339278i
$898$	11.6764	+	14.0378i	0.389648	+	0.468447i
$899$		−	0.864134i		−	0.0288205i
$900$	4.45190	+	8.95436i	0.148397	+	0.298479i
$901$	11.4547			0.381610
$902$	1.38863	−	1.15504i	0.0462362	−	0.0384587i
$903$	−20.0178	−	2.29596i	−0.666150	−	0.0764048i
$904$	42.5477	+	11.9919i	1.41512	+	0.398846i
$905$	14.2126	−	28.4620i	0.472444	−	0.946109i
$906$	−1.30119	+	14.1695i	−0.0432291	+	0.470751i
$907$	−9.06746	+	9.06746i	−0.301080	+	0.301080i	−0.841436	−	0.540356i	$-0.818289\pi$
$907$	−9.06746	+	9.06746i	−0.301080	+	0.301080i	0.540356	+	0.841436i	$0.318289\pi$
$908$	−19.8230	+	13.6272i	−0.657849	+	0.452236i
$909$			7.38166i			0.244834i
$910$	−30.3161	−	23.9639i	−1.00497	−	0.794397i
$911$	−11.0036			−0.364564			−0.182282	−	0.983246i	$-0.558348\pi$
$911$	−11.0036			−0.364564			−0.182282	+	0.983246i	$0.558348\pi$
$912$	−4.00682	−	8.99401i	−0.132679	−	0.297821i
$913$	−1.59893	−	1.59893i	−0.0529170	−	0.0529170i
$914$	6.30212	+	0.578725i	0.208456	+	0.0191425i
$915$	2.97280	+	8.90309i	0.0982779	+	0.294327i
$916$	−10.0695	−	1.86509i	−0.332705	−	0.0616244i
$917$	−5.11321	−	0.586466i	−0.168853	−	0.0193668i
$918$	−3.90882	+	3.25131i	−0.129010	+	0.107309i
$919$			9.80357i			0.323390i	0.986841	+	0.161695i	$0.0516961\pi$
$919$			9.80357i			0.323390i	−0.986841	+	0.161695i	$0.948304\pi$
$920$	13.2370	−	14.5596i	0.436410	−	0.480015i
$921$	19.5337			0.643657
$922$	−38.8660	+	32.3282i	−1.27998	+	1.06467i
$923$	−46.2179	+	46.2179i	−1.52128	+	1.52128i
$924$	−10.8097	+	5.73875i	−0.355612	+	0.188791i
$925$	3.52595	+	0.499992i	0.115932	+	0.0164396i
$926$	−5.13307	+	55.8974i	−0.168683	+	1.83690i
$927$	−0.579644	+	0.579644i	−0.0190380	+	0.0190380i
$928$	28.4551	−	9.66815i	0.934084	−	0.317373i
$929$	41.4727			1.36068			0.680338	−	0.732899i	$-0.261833\pi$
$929$	41.4727			1.36068			0.680338	+	0.732899i	$0.261833\pi$
$930$	0.270913	−	0.437240i	0.00888358	−	0.0143377i
$931$	3.90129	−	16.7833i	0.127859	−	0.550051i
$932$	9.89608	+	14.3954i	0.324157	+	0.471537i
$933$	−16.0085	−	16.0085i	−0.524095	−	0.524095i
$934$	5.40905	+	0.496715i	0.176990	+	0.0162530i
$935$	17.6359	−	5.88874i	0.576754	−	0.192582i
$936$	−3.54396	+	12.5741i	−0.115838	+	0.410997i
$937$	31.6887	−	31.6887i	1.03522	−	1.03522i	0.0358673	−	0.999357i	$-0.488581\pi$
$937$	31.6887	−	31.6887i	1.03522	−	1.03522i	0.999357	−	0.0358673i	$-0.0114194\pi$
$938$	5.41924	−	25.9636i	0.176944	−	0.847740i
$939$	−3.43868			−0.112217
$940$	59.1886	−	8.28786i	1.93052	−	0.270320i
$941$	−56.1142			−1.82927			−0.914635	−	0.404280i	$-0.867522\pi$
$941$	−56.1142			−1.82927			−0.914635	+	0.404280i	$0.867522\pi$
$942$	−24.9974	+	20.7925i	−0.814460	+	0.677457i
$943$	1.21486	+	1.21486i	0.0395612	+	0.0395612i
$944$	−0.0731244	+	0.190624i	−0.00238000	+	0.00620429i
$945$	5.78848	−	1.22209i	0.188299	−	0.0397547i
$946$	2.27789	−	24.8054i	0.0740605	−	0.806494i
$947$	−12.3422	+	12.3422i	−0.401068	+	0.401068i	−0.878609	−	0.477541i	$-0.841528\pi$
$947$	−12.3422	+	12.3422i	−0.401068	+	0.401068i	0.477541	+	0.878609i	$0.341528\pi$
$948$	27.4119	−	18.8442i	0.890297	−	0.612032i
$949$	−46.2869			−1.50254
$950$	4.00941	−	16.9376i	0.130083	−	0.549529i
$951$			31.4905i			1.02115i
$952$	−24.8943	−	10.2014i	−0.806830	−	0.330631i
$953$	−2.79458	+	2.79458i	−0.0905252	+	0.0905252i	−0.750919	−	0.660394i	$-0.770389\pi$
$953$	−2.79458	+	2.79458i	−0.0905252	+	0.0905252i	0.660394	+	0.750919i	$0.270389\pi$
$954$	−0.412045	+	4.48703i	−0.0133404	+	0.145273i
$955$	8.69093	−	17.4043i	0.281232	−	0.563191i
$956$	−14.7768	−	2.73700i	−0.477917	−	0.0885209i
$957$	8.68849	+	8.68849i	0.280859	+	0.280859i
$958$	−1.18628	+	0.986729i	−0.0383269	+	0.0318798i
$959$	9.96447	+	12.5464i	0.321769	+	0.405144i
$960$	17.4289	+	4.02894i	0.562516	+	0.130033i
$961$	30.9735			0.999147
$962$	2.97511	+	3.57677i	0.0959213	+	0.115320i
$963$	8.13173	+	8.13173i	0.262041	+	0.262041i
$964$	−47.7743	−	8.84886i	−1.53871	−	0.285003i
$965$	−15.6507	−	46.8713i	−0.503813	−	1.50884i
$966$	−6.37608	−	9.73988i	−0.205147	−	0.313375i
$967$	17.4876	+	17.4876i	0.562364	+	0.562364i	0.929978	−	0.367615i	$-0.119825\pi$
$967$	17.4876	+	17.4876i	0.562364	+	0.562364i	−0.367615	+	0.929978i	$0.619825\pi$
$968$	7.81172	+	13.9433i	0.251078	+	0.448154i
$969$	8.84955			0.284288
$970$	6.85701	+	4.24858i	0.220165	+	0.136414i
$971$	−36.6445			−1.17598			−0.587989	−	0.808869i	$-0.700080\pi$
$971$	−36.6445			−1.17598			−0.587989	+	0.808869i	$0.700080\pi$
$972$	−1.13300	−	1.64812i	−0.0363409	−	0.0528636i
$973$	−3.54985	+	30.9500i	−0.113803	+	0.992213i
$974$	−25.3645	−	2.32923i	−0.812731	−	0.0746333i
$975$	−18.4609	+	13.8755i	−0.591223	+	0.444372i
$976$	15.6768	+	6.01372i	0.501804	+	0.192494i
$977$	9.57551	+	9.57551i	0.306348	+	0.306348i	0.843491	−	0.537143i	$-0.180497\pi$
$977$	9.57551	+	9.57551i	0.306348	+	0.306348i	−0.537143	+	0.843491i	$0.680497\pi$
$978$	−23.9214	+	19.8975i	−0.764924	+	0.636253i
$979$			27.7996i			0.888479i
$980$	20.0742	+	24.0213i	0.641248	+	0.767333i
$981$		−	17.0197i		−	0.543399i
$982$	8.15290	+	9.80167i	0.260170	+	0.312784i
$983$	30.6927	+	30.6927i	0.978946	+	0.978946i	0.999783	−	0.0208366i	$-0.00663298\pi$
$983$	30.6927	+	30.6927i	0.978946	+	0.978946i	−0.0208366	+	0.999783i	$0.506633\pi$
$984$	−0.423703	+	1.50331i	−0.0135072	+	0.0479239i
$985$	4.86454	+	14.5685i	0.154997	+	0.464192i
$986$	−2.47002	+	26.8977i	−0.0786614	+	0.856596i
$987$	4.02902	−	35.1278i	0.128245	−	1.11813i
$988$	18.7382	−	12.8815i	0.596140	−	0.409815i
$989$	23.6942			0.753431
$990$	1.67235	+	7.12017i	0.0531508	+	0.226294i
$991$	−8.89844			−0.282668			−0.141334	−	0.989962i	$-0.545139\pi$
$991$	−8.89844			−0.282668			−0.141334	+	0.989962i	$0.545139\pi$
$992$	−0.296011	−	0.871212i	−0.00939835	−	0.0276610i
$993$	−14.5654	−	14.5654i	−0.462218	−	0.462218i
$994$	44.3008	−	29.0009i	1.40514	−	0.919854i
$995$	26.5521	−	53.1728i	0.841757	−	1.68569i
$996$	1.92265	+	0.356118i	0.0609214	+	0.0112840i
$997$	−4.86884	−	4.86884i	−0.154198	−	0.154198i	0.625792	−	0.779990i	$-0.284776\pi$
$997$	−4.86884	−	4.86884i	−0.154198	−	0.154198i	−0.779990	+	0.625792i	$0.784776\pi$
$998$	−37.2687	+	30.9996i	−1.17972	+	0.981275i
$999$	−0.712244			−0.0225344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.517.19	yes	184
5.3	odd	4	inner	840.2.bj.b.13.65	yes	184
7.6	odd	2	inner	840.2.bj.b.517.20	yes	184
8.5	even	2	inner	840.2.bj.b.517.66	yes	184
35.13	even	4	inner	840.2.bj.b.13.66	yes	184
40.13	odd	4	inner	840.2.bj.b.13.20	yes	184
56.13	odd	2	inner	840.2.bj.b.517.65	yes	184
280.13	even	4	inner	840.2.bj.b.13.19	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.19	✓	184	280.13	even	4	inner
840.2.bj.b.13.20	yes	184	40.13	odd	4	inner
840.2.bj.b.13.65	yes	184	5.3	odd	4	inner
840.2.bj.b.13.66	yes	184	35.13	even	4	inner
840.2.bj.b.517.19	yes	184	1.1	even	1	trivial
840.2.bj.b.517.20	yes	184	7.6	odd	2	inner
840.2.bj.b.517.65	yes	184	56.13	odd	2	inner
840.2.bj.b.517.66	yes	184	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08726 + 0.904365i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.364249 - 1.96655i) q^{4} +(-0.998967 + 2.00052i) q^{5} +(0.129323 - 1.40829i) q^{6} +(-2.62852 - 0.301481i) q^{7} +(1.38245 + 2.46756i) q^{8} -1.00000i q^{9} +(-0.723063 - 3.07850i) q^{10} -2.31287i q^{11} +(1.13300 + 1.64812i) q^{12} +(-3.26599 + 3.26599i) q^{13} +(3.13052 - 2.04935i) q^{14} +(-0.708202 - 2.12095i) q^{15} +(-3.73464 - 1.43263i) q^{16} +(2.54214 - 2.54214i) q^{17} +(0.904365 + 1.08726i) q^{18} -2.46154i q^{19} +(3.57024 + 2.69321i) q^{20} +(2.07182 - 1.64546i) q^{21} +(2.09168 + 2.51468i) q^{22} +(-2.20000 + 2.20000i) q^{23} +(-2.72236 - 0.767289i) q^{24} +(-3.00413 - 3.99690i) q^{25} +(0.597320 - 6.50462i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.55031 + 5.05930i) q^{28} +5.31262 q^{29} +(2.68811 + 1.66555i) q^{30} -0.162657i q^{31} +(5.35613 - 1.81985i) q^{32} +(1.63544 + 1.63544i) q^{33} +(-0.464934 + 5.06298i) q^{34} +(3.22892 - 4.95722i) q^{35} +(-1.96655 - 0.364249i) q^{36} +(-0.503633 + 0.503633i) q^{37} +(2.22613 + 2.67632i) q^{38} -4.61881i q^{39} +(-6.31741 + 0.300598i) q^{40} -0.552208i q^{41} +(-0.764501 + 3.66272i) q^{42} +(-5.38505 - 5.38505i) q^{43} +(-4.54837 - 0.842460i) q^{44} +(2.00052 + 0.998967i) q^{45} +(0.402359 - 4.38156i) q^{46} +(9.44984 - 9.44984i) q^{47} +(3.65381 - 1.62777i) q^{48} +(6.81822 + 1.58490i) q^{49} +(6.88091 + 1.62882i) q^{50} +3.59513i q^{51} +(5.23311 + 7.61238i) q^{52} +(2.25295 + 2.25295i) q^{53} +(-1.40829 - 0.129323i) q^{54} +(4.62693 + 2.31048i) q^{55} +(-2.88987 - 6.90280i) q^{56} +(1.74057 + 1.74057i) q^{57} +(-5.77617 + 4.80454i) q^{58} -0.0510421i q^{59} +(-4.42893 + 0.620159i) q^{60} -4.19768 q^{61} +(0.147101 + 0.176850i) q^{62} +(-0.301481 + 2.62852i) q^{63} +(-4.17768 + 6.82254i) q^{64} +(-3.27105 - 9.79629i) q^{65} +(-3.25718 - 0.299108i) q^{66} +(5.01239 - 5.01239i) q^{67} +(-4.07327 - 5.92522i) q^{68} -3.11126i q^{69} +(0.972475 + 8.30989i) q^{70} +14.1513 q^{71} +(2.46756 - 1.38245i) q^{72} +(7.08619 + 7.08619i) q^{73} +(0.0921099 - 1.00305i) q^{74} +(4.95047 + 0.701995i) q^{75} +(-4.84074 - 0.896614i) q^{76} +(-0.697286 + 6.07941i) q^{77} +(4.17709 + 5.02183i) q^{78} -16.6322i q^{79} +(6.59679 - 6.04007i) q^{80} -1.00000 q^{81} +(0.499398 + 0.600392i) q^{82} +(0.691321 - 0.691321i) q^{83} +(-2.48123 - 4.67370i) q^{84} +(2.54608 + 7.62511i) q^{85} +(10.7250 + 0.984876i) q^{86} +(-3.75659 + 3.75659i) q^{87} +(5.70713 - 3.19742i) q^{88} -12.0195 q^{89} +(-3.07850 + 0.723063i) q^{90} +(9.56936 - 7.60009i) q^{91} +(3.52506 + 5.12775i) q^{92} +(0.115016 + 0.115016i) q^{93} +(-1.72829 + 18.8205i) q^{94} +(4.92435 + 2.45900i) q^{95} +(-2.50053 + 5.07418i) q^{96} +(-1.80373 + 1.80373i) q^{97} +(-8.84647 + 4.44297i) q^{98} -2.31287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

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