LMFDB - Embedded newform 483.2.m.a.137.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(137,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("483.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.m (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.11
Character	$\chi$	$=$	483.137
Dual form			483.2.m.a.275.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55658 + 0.898694i) q^{2} +(0.279659 + 1.70932i) q^{3} +(0.615303 - 1.06574i) q^{4} +(-0.620314 - 1.07442i) q^{5} +(-1.97147 - 2.40938i) q^{6} +(-2.49407 + 0.882968i) q^{7} -1.38290i q^{8} +(-2.84358 + 0.956058i) q^{9} +O(q^{10})$	\(q+(-1.55658 + 0.898694i) q^{2} +(0.279659 + 1.70932i) q^{3} +(0.615303 - 1.06574i) q^{4} +(-0.620314 - 1.07442i) q^{5} +(-1.97147 - 2.40938i) q^{6} +(-2.49407 + 0.882968i) q^{7} -1.38290i q^{8} +(-2.84358 + 0.956058i) q^{9} +(1.93114 + 1.11495i) q^{10} +(1.65369 - 2.86428i) q^{11} +(1.99377 + 0.753710i) q^{12} -1.23140 q^{13} +(3.08871 - 3.61582i) q^{14} +(1.66305 - 1.36079i) q^{15} +(2.47341 + 4.28407i) q^{16} +(3.17428 - 5.49801i) q^{17} +(3.56707 - 4.04369i) q^{18} +(0.447270 - 0.258231i) q^{19} -1.52672 q^{20} +(-2.20677 - 4.01624i) q^{21} +5.94465i q^{22} +(-4.71286 + 0.888215i) q^{23} +(2.36382 - 0.386741i) q^{24} +(1.73042 - 2.99718i) q^{25} +(1.91678 - 1.10665i) q^{26} +(-2.42945 - 4.59323i) q^{27} +(-0.593596 + 3.20131i) q^{28} -1.86326i q^{29} +(-1.36574 + 3.61275i) q^{30} +(-1.88016 + 3.25653i) q^{31} +(-5.30489 - 3.06278i) q^{32} +(5.35845 + 2.02567i) q^{33} +11.4108i q^{34} +(2.49578 + 2.13195i) q^{35} +(-0.730759 + 3.61877i) q^{36} +(2.31050 - 1.33397i) q^{37} +(-0.464142 + 0.803918i) q^{38} +(-0.344372 - 2.10486i) q^{39} +(-1.48581 + 0.857831i) q^{40} -0.439801i q^{41} +(7.04439 + 4.26840i) q^{42} -2.93738i q^{43} +(-2.03504 - 3.52480i) q^{44} +(2.79112 + 2.46213i) q^{45} +(6.53773 - 5.61801i) q^{46} +(2.82618 - 1.63170i) q^{47} +(-6.63116 + 5.42594i) q^{48} +(5.44074 - 4.40436i) q^{49} +6.22048i q^{50} +(10.2856 + 3.88830i) q^{51} +(-0.757684 + 1.31235i) q^{52} +(-3.41084 + 5.90774i) q^{53} +(7.90955 + 4.96642i) q^{54} -4.10323 q^{55} +(1.22106 + 3.44904i) q^{56} +(0.566484 + 0.692312i) q^{57} +(1.67450 + 2.90032i) q^{58} +(1.01380 + 0.585318i) q^{59} +(-0.426963 - 2.60967i) q^{60} +(10.5195 - 6.07341i) q^{61} -6.75876i q^{62} +(6.24791 - 4.89526i) q^{63} +1.11638 q^{64} +(0.763854 + 1.32303i) q^{65} +(-10.1613 + 1.66248i) q^{66} +(-8.48919 - 4.90123i) q^{67} +(-3.90629 - 6.76589i) q^{68} +(-2.83624 - 7.80741i) q^{69} +(-5.80086 - 1.07561i) q^{70} -9.86872i q^{71} +(1.32213 + 3.93239i) q^{72} +(-1.05999 + 1.83596i) q^{73} +(-2.39766 + 4.15287i) q^{74} +(5.60708 + 2.11966i) q^{75} -0.635562i q^{76} +(-1.59535 + 8.60386i) q^{77} +(2.42767 + 2.96691i) q^{78} +(-1.21660 + 0.702404i) q^{79} +(3.06858 - 5.31494i) q^{80} +(7.17191 - 5.43725i) q^{81} +(0.395246 + 0.684587i) q^{82} -0.607683 q^{83} +(-5.63808 - 0.119372i) q^{84} -7.87619 q^{85} +(2.63980 + 4.57227i) q^{86} +(3.18491 - 0.521077i) q^{87} +(-3.96101 - 2.28689i) q^{88} +(-4.52399 - 7.83579i) q^{89} +(-6.55731 - 1.32415i) q^{90} +(3.07119 - 1.08729i) q^{91} +(-1.95324 + 5.56919i) q^{92} +(-6.09228 - 2.30308i) q^{93} +(-2.93279 + 5.07974i) q^{94} +(-0.554895 - 0.320369i) q^{95} +(3.75172 - 9.92432i) q^{96} -16.3689i q^{97} +(-4.51079 + 11.7453i) q^{98} +(-1.96399 + 9.72583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9}+O(q^{10}) $ 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9	$ 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9} + 14 q^{12} - 16 q^{13} - 60 q^{16} - 10 q^{18} - 24 q^{24} - 40 q^{25} - 20 q^{27} - 4 q^{31} + 64 q^{36} - 12 q^{39} - 20 q^{46} + 140 q^{48} - 48 q^{49} - 76 q^{52} - 2 q^{54} + 72 q^{55} - 28 q^{58} - 128 q^{64} - 20 q^{69} - 68 q^{70} + 6 q^{72} + 20 q^{73} + 20 q^{75} - 156 q^{78} - 62 q^{81} + 80 q^{82} + 112 q^{85} + 46 q^{87} - 38 q^{93} + 36 q^{94} + 72 q^{96}+O(q^{100}) $ 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9 + 14 * q^12 - 16 * q^13 - 60 * q^16 - 10 * q^18 - 24 * q^24 - 40 * q^25 - 20 * q^27 - 4 * q^31 + 64 * q^36 - 12 * q^39 - 20 * q^46 + 140 * q^48 - 48 * q^49 - 76 * q^52 - 2 * q^54 + 72 * q^55 - 28 * q^58 - 128 * q^64 - 20 * q^69 - 68 * q^70 + 6 * q^72 + 20 * q^73 + 20 * q^75 - 156 * q^78 - 62 * q^81 + 80 * q^82 + 112 * q^85 + 46 * q^87 - 38 * q^93 + 36 * q^94 + 72 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.55658	+	0.898694i	−1.10067	+	0.635473i	−0.936397	−	0.350942i	$-0.885861\pi$
$2$	−1.55658	+	0.898694i	−1.10067	+	0.635473i	−0.164274	+	0.986415i	$0.552528\pi$
$3$	0.279659	+	1.70932i	0.161461	+	0.986879i
$3$	0.279659	+	1.70932i	0.161461	+	0.986879i
$4$	0.615303	−	1.06574i	0.307652	−	0.532868i
$5$	−0.620314	−	1.07442i	−0.277413	−	0.480493i	0.693328	−	0.720622i	$-0.256144\pi$
$5$	−0.620314	−	1.07442i	−0.277413	−	0.480493i	−0.970741	+	0.240129i	$0.922810\pi$
$6$	−1.97147	−	2.40938i	−0.804851	−	0.983625i
$7$	−2.49407	+	0.882968i	−0.942669	+	0.333730i
$7$	−2.49407	+	0.882968i	−0.942669	+	0.333730i
$8$		−	1.38290i		−	0.488929i
$9$	−2.84358	+	0.956058i	−0.947860	+	0.318686i
$10$	1.93114	+	1.11495i	0.610681	+	0.352577i
$11$	1.65369	−	2.86428i	0.498607	−	0.863612i	−0.501392	−	0.865220i	$-0.667179\pi$
$11$	1.65369	−	2.86428i	0.498607	−	0.863612i	0.999999	+	0.00160808i	$0.000511867\pi$
$12$	1.99377	+	0.753710i	0.575550	+	0.217577i
$13$	−1.23140			−0.341529			−0.170764	−	0.985312i	$-0.554624\pi$
$13$	−1.23140			−0.341529			−0.170764	+	0.985312i	$0.554624\pi$
$14$	3.08871	−	3.61582i	0.825492	−	0.966368i
$15$	1.66305	−	1.36079i	0.429397	−	0.351354i
$16$	2.47341	+	4.28407i	0.618353	+	1.07102i
$17$	3.17428	−	5.49801i	0.769875	−	1.33346i	−0.167755	−	0.985829i	$-0.553652\pi$
$17$	3.17428	−	5.49801i	0.769875	−	1.33346i	0.937630	−	0.347635i	$-0.113015\pi$
$18$	3.56707	−	4.04369i	0.840767	−	0.953108i
$19$	0.447270	−	0.258231i	0.102611	−	0.0592423i	−0.447816	−	0.894126i	$-0.647798\pi$
$19$	0.447270	−	0.258231i	0.102611	−	0.0592423i	0.550427	+	0.834883i	$0.314465\pi$
$20$	−1.52672			−0.341386
$21$	−2.20677	−	4.01624i	−0.481556	−	0.876415i
$22$			5.94465i			1.26740i
$23$	−4.71286	+	0.888215i	−0.982700	+	0.185206i
$23$	−4.71286	+	0.888215i	−0.982700	+	0.185206i
$24$	2.36382	−	0.386741i	0.482513	−	0.0789431i
$25$	1.73042	−	2.99718i	0.346084	−	0.599436i
$26$	1.91678	−	1.10665i	0.375911	−	0.217032i
$27$	−2.42945	−	4.59323i	−0.467547	−	0.883968i
$28$	−0.593596	+	3.20131i	−0.112179	+	0.604991i
$29$		−	1.86326i		−	0.345998i	−0.984922	−	0.172999i	$-0.944654\pi$
$29$		−	1.86326i		−	0.345998i	0.984922	−	0.172999i	$-0.0553457\pi$
$30$	−1.36574	+	3.61275i	−0.249349	+	0.659595i
$31$	−1.88016	+	3.25653i	−0.337687	+	0.584890i	−0.983997	−	0.178184i	$-0.942978\pi$
$31$	−1.88016	+	3.25653i	−0.337687	+	0.584890i	0.646311	+	0.763075i	$0.276311\pi$
$32$	−5.30489	−	3.06278i	−0.937781	−	0.541428i
$33$	5.35845	+	2.02567i	0.932786	+	0.352624i
$34$			11.4108i			1.95694i
$35$	2.49578	+	2.13195i	0.421863	+	0.360365i
$36$	−0.730759	+	3.61877i	−0.121793	+	0.603129i
$37$	2.31050	−	1.33397i	0.379844	−	0.219303i	−0.297907	−	0.954595i	$-0.596288\pi$
$37$	2.31050	−	1.33397i	0.379844	−	0.219303i	0.677750	+	0.735292i	$0.262955\pi$
$38$	−0.464142	+	0.803918i	−0.0752938	+	0.130413i
$39$	−0.344372	−	2.10486i	−0.0551437	−	0.337047i
$40$	−1.48581	+	0.857831i	−0.234927	+	0.135635i
$41$		−	0.439801i		−	0.0686853i	−0.999410	−	0.0343427i	$-0.989066\pi$
$41$		−	0.439801i		−	0.0686853i	0.999410	−	0.0343427i	$-0.0109338\pi$
$42$	7.04439	+	4.26840i	1.08697	+	0.658629i
$43$		−	2.93738i		−	0.447946i	−0.974595	−	0.223973i	$-0.928097\pi$
$43$		−	2.93738i		−	0.447946i	0.974595	−	0.223973i	$-0.0719027\pi$
$44$	−2.03504	−	3.52480i	−0.306794	−	0.531383i
$45$	2.79112	+	2.46213i	0.416075	+	0.367033i
$46$	6.53773	−	5.61801i	0.963936	−	0.828330i
$47$	2.82618	−	1.63170i	0.412241	−	0.238007i	−0.279511	−	0.960142i	$-0.590172\pi$
$47$	2.82618	−	1.63170i	0.412241	−	0.238007i	0.691752	+	0.722135i	$0.256839\pi$
$48$	−6.63116	+	5.42594i	−0.957125	+	0.783167i
$49$	5.44074	−	4.40436i	0.777248	−	0.629194i
$50$			6.22048i			0.879709i
$51$	10.2856	+	3.88830i	1.44027	+	0.544471i
$52$	−0.757684	+	1.31235i	−0.105072	+	0.181990i
$53$	−3.41084	+	5.90774i	−0.468515	+	0.811491i	−0.999352	−	0.0359823i	$-0.988544\pi$
$53$	−3.41084	+	5.90774i	−0.468515	+	0.811491i	0.530838	+	0.847473i	$0.321877\pi$
$54$	7.90955	+	4.96642i	1.07635	+	0.675845i
$55$	−4.10323			−0.553279
$56$	1.22106	+	3.44904i	0.163170	+	0.460898i
$57$	0.566484	+	0.692312i	0.0750327	+	0.0916990i
$58$	1.67450	+	2.90032i	0.219872	+	0.380830i
$59$	1.01380	+	0.585318i	0.131986	+	0.0762019i	0.564539	−	0.825406i	$-0.309054\pi$
$59$	1.01380	+	0.585318i	0.131986	+	0.0762019i	−0.432553	+	0.901608i	$0.642387\pi$
$60$	−0.426963	−	2.60967i	−0.0551207	−	0.336907i
$61$	10.5195	−	6.07341i	1.34688	−	0.777621i	0.359072	−	0.933310i	$-0.383093\pi$
$61$	10.5195	−	6.07341i	1.34688	−	0.777621i	0.987806	+	0.155689i	$0.0497598\pi$
$62$		−	6.75876i		−	0.858363i
$63$	6.24791	−	4.89526i	0.787163	−	0.616745i
$64$	1.11638			0.139547
$65$	0.763854	+	1.32303i	0.0947444	+	0.164102i
$66$	−10.1613	+	1.66248i	−1.25077	+	0.204637i
$67$	−8.48919	−	4.90123i	−1.03712	−	0.598781i	−0.118103	−	0.993001i	$-0.537681\pi$
$67$	−8.48919	−	4.90123i	−1.03712	−	0.598781i	−0.919016	+	0.394220i	$0.871015\pi$
$68$	−3.90629	−	6.76589i	−0.473707	−	0.820484i
$69$	−2.83624	−	7.80741i	−0.341444	−	0.939902i
$70$	−5.80086	−	1.07561i	−0.693335	−	0.128560i
$71$		−	9.86872i		−	1.17120i	−0.810600	−	0.585601i	$-0.800859\pi$
$71$		−	9.86872i		−	1.17120i	0.810600	−	0.585601i	$-0.199141\pi$
$72$	1.32213	+	3.93239i	0.155815	+	0.463436i
$73$	−1.05999	+	1.83596i	−0.124062	+	0.214882i	−0.921366	−	0.388696i	$-0.872926\pi$
$73$	−1.05999	+	1.83596i	−0.124062	+	0.214882i	0.797304	+	0.603578i	$0.206259\pi$
$74$	−2.39766	+	4.15287i	−0.278722	+	0.482761i
$75$	5.60708	+	2.11966i	0.647450	+	0.244758i
$76$		−	0.635562i		−	0.0729040i
$77$	−1.59535	+	8.60386i	−0.181807	+	0.980500i
$78$	2.42767	+	2.96691i	0.274880	+	0.335936i
$79$	−1.21660	+	0.702404i	−0.136878	+	0.0790266i	−0.566875	−	0.823804i	$-0.691848\pi$
$79$	−1.21660	+	0.702404i	−0.136878	+	0.0790266i	0.429997	+	0.902830i	$0.358515\pi$
$80$	3.06858	−	5.31494i	0.343078	−	0.594228i
$81$	7.17191	−	5.43725i	0.796879	−	0.604139i
$82$	0.395246	+	0.684587i	0.0436477	+	0.0756000i
$83$	−0.607683			−0.0667019			−0.0333510	−	0.999444i	$-0.510618\pi$
$83$	−0.607683			−0.0667019			−0.0333510	+	0.999444i	$0.510618\pi$
$84$	−5.63808	−	0.119372i	−0.615165	−	0.0130245i
$85$	−7.87619			−0.854293
$86$	2.63980	+	4.57227i	0.284657	+	0.493041i
$87$	3.18491	−	0.521077i	0.341458	−	0.0558653i
$88$	−3.96101	−	2.28689i	−0.422245	−	0.243783i
$89$	−4.52399	−	7.83579i	−0.479543	−	0.830592i	0.520182	−	0.854055i	$-0.325864\pi$
$89$	−4.52399	−	7.83579i	−0.479543	−	0.830592i	−0.999725	+	0.0234633i	$0.992531\pi$
$90$	−6.55731	−	1.32415i	−0.691201	−	0.139578i
$91$	3.07119	−	1.08729i	0.321948	−	0.113979i
$92$	−1.95324	+	5.56919i	−0.203639	+	0.580628i
$93$	−6.09228	−	2.30308i	−0.631740	−	0.238819i
$94$	−2.93279	+	5.07974i	−0.302494	+	0.523936i
$95$	−0.554895	−	0.320369i	−0.0569310	−	0.0328692i
$96$	3.75172	−	9.92432i	0.382909	−	1.01290i
$97$		−	16.3689i		−	1.66201i	−0.556262	−	0.831007i	$-0.687765\pi$
$97$		−	16.3689i		−	1.66201i	0.556262	−	0.831007i	$-0.312235\pi$
$98$	−4.51079	+	11.7453i	−0.455659	+	1.18646i
$99$	−1.96399	+	9.72583i	−0.197389	+	0.977483i
$100$	−2.12947	−	3.68835i	−0.212947	−	0.368835i
$101$	−2.30150	−	1.32877i	−0.229008	−	0.132218i	0.381106	−	0.924531i	$-0.375543\pi$
$101$	−2.30150	−	1.32877i	−0.229008	−	0.132218i	−0.610114	+	0.792313i	$0.708876\pi$
$102$	−19.5048	+	3.19114i	−1.93126	+	0.315970i
$103$	−14.2905	+	8.25062i	−1.40808	+	0.812957i	−0.995203	−	0.0978281i	$-0.968810\pi$
$103$	−14.2905	+	8.25062i	−1.40808	+	0.812957i	−0.412880	+	0.910785i	$0.635477\pi$
$104$			1.70290i			0.166983i
$105$	−2.94622	+	4.86231i	−0.287522	+	0.474513i
$106$		−	12.2612i		−	1.19091i
$107$	−2.50130	−	4.33238i	−0.241810	−	0.418827i	0.719420	−	0.694575i	$-0.244408\pi$
$107$	−2.50130	−	4.33238i	−0.241810	−	0.418827i	−0.961230	+	0.275748i	$0.911074\pi$
$108$	−6.39002	−	0.237081i	−0.614880	−	0.0228131i
$109$	9.04416	+	5.22165i	0.866274	+	0.500143i	0.866108	−	0.499857i	$-0.166614\pi$
$109$	9.04416	+	5.22165i	0.866274	+	0.500143i	0.000165530		1.00000i	$0.499947\pi$
$110$	6.38702	−	3.68755i	0.608979	−	0.351594i
$111$	2.92634	+	3.57634i	0.277756	+	0.339451i
$112$	−9.95155	−	8.50082i	−0.940333	−	0.803252i
$113$	−20.1331			−1.89396			−0.946980	−	0.321293i	$-0.895882\pi$
$113$	−20.1331			−1.89396			−0.946980	+	0.321293i	$0.895882\pi$
$114$	−1.50396	−	0.568546i	−0.140859	−	0.0532492i
$115$	3.87777	+	4.51260i	0.361604	+	0.420802i
$116$	−1.98574	−	1.14647i	−0.184371	−	0.106447i
$117$	3.50158	−	1.17729i	0.323721	−	0.108840i
$118$	−2.10409			−0.193697
$119$	−3.06229	+	16.5152i	−0.280720	+	1.51394i
$120$	−1.88183	−	2.29983i	−0.171787	−	0.209945i
$121$	0.0306095	+	0.0530172i	0.00278268	+	0.00481975i
$122$	−10.9163	+	18.9076i	−0.988314	+	1.71181i
$123$	0.751762	−	0.122994i	0.0677841	−	0.0110900i
$124$	2.31374	+	4.00751i	0.207780	+	0.359885i
$125$	−10.4968			−0.938858
$126$	−5.32606	+	13.2349i	−0.474483	+	1.17905i
$127$	−13.0147			−1.15487			−0.577433	−	0.816438i	$-0.695945\pi$
$127$	−13.0147			−1.15487			−0.577433	+	0.816438i	$0.695945\pi$
$128$	8.87205	−	5.12228i	0.784186	−	0.452750i
$129$	5.02093	−	0.821465i	0.442068	−	0.0723259i
$130$	−2.37801	−	1.37294i	−0.208565	−	0.120415i
$131$	−9.41742	+	5.43715i	−0.822804	+	0.475046i	−0.851382	−	0.524546i	$-0.824235\pi$
$131$	−9.41742	+	5.43715i	−0.822804	+	0.475046i	0.0285786	+	0.999592i	$0.490902\pi$
$132$	5.45591	−	4.46429i	0.474876	−	0.388567i
$133$	−0.887510	+	1.03897i	−0.0769569	+	0.0900902i
$134$	17.6188			1.52204
$135$	−3.42802	+	5.45948i	−0.295037	+	0.469877i
$136$	−7.60319	−	4.38971i	−0.651968	−	0.376414i
$137$	7.60654	−	13.1749i	0.649870	−	1.12561i	−0.333283	−	0.942827i	$-0.608157\pi$
$137$	7.60654	−	13.1749i	0.649870	−	1.12561i	0.983154	−	0.182781i	$-0.0585101\pi$
$138$	11.4313	+	9.60398i	0.973100	+	0.817545i
$139$	23.0698			1.95675			0.978375	−	0.206837i	$-0.0663170\pi$
$139$	23.0698			1.95675			0.978375	+	0.206837i	$0.0663170\pi$
$140$	3.80775	−	1.34805i	0.321814	−	0.113931i
$141$	3.57947	+	4.37454i	0.301445	+	0.368403i
$142$	8.86896	+	15.3615i	0.744267	+	1.28911i
$143$	−2.03635	+	3.52707i	−0.170288	+	0.294948i
$144$	−11.1292	−	9.81738i	−0.927430	−	0.818115i
$145$	−2.00191	+	1.15580i	−0.166250	+	0.0959843i
$146$		−	3.81043i		−	0.315353i
$147$	9.05004	+	8.06826i	0.746434	+	0.665459i
$148$		−	3.28318i		−	0.269876i
$149$	−9.13468	−	15.8217i	−0.748342	−	1.29617i	−0.948617	−	0.316426i	$-0.897517\pi$
$149$	−9.13468	−	15.8217i	−0.748342	−	1.29617i	0.200275	−	0.979740i	$-0.435816\pi$
$150$	−10.6328	+	1.73962i	−0.868166	+	0.142039i
$151$	2.41320	−	4.17979i	0.196384	−	0.340146i	−0.750970	−	0.660337i	$-0.770414\pi$
$151$	2.41320	−	4.17979i	0.196384	−	0.340146i	0.947353	+	0.320190i	$0.103747\pi$
$152$	−0.357108	−	0.618529i	−0.0289653	−	0.0501693i
$153$	−3.76990	+	18.6688i	−0.304778	+	1.50929i
$154$	−5.24894	−	14.8264i	−0.422971	−	1.19474i
$155$	4.66516			0.374714
$156$	−2.45512	−	0.928117i	−0.196567	−	0.0743089i
$157$	−10.6963	−	6.17552i	−0.853659	−	0.492860i	0.00822504	−	0.999966i	$-0.497382\pi$
$157$	−10.6963	−	6.17552i	−0.853659	−	0.492860i	−0.861884	+	0.507106i	$0.830715\pi$
$158$	1.26249	−	2.18670i	0.100439	−	0.173965i
$159$	−11.0521	−	4.17807i	−0.876491	−	0.331343i
$160$			7.59954i			0.600796i
$161$	10.9699	−	6.37657i	0.864551	−	0.502544i
$162$	−6.27725	+	14.9089i	−0.493187	+	1.17135i
$163$	8.09702	+	14.0244i	0.634207	+	1.09848i	0.986682	+	0.162658i	$0.0520068\pi$
$163$	8.09702	+	14.0244i	0.634207	+	1.09848i	−0.352475	+	0.935821i	$0.614660\pi$
$164$	−0.468712	−	0.270611i	−0.0366002	−	0.0211312i
$165$	−1.14751	−	7.01375i	−0.0893333	−	0.546020i
$166$	0.945910	−	0.546122i	0.0734169	−	0.0423873i
$167$		−	9.78443i		−	0.757142i	−0.925572	−	0.378571i	$-0.876416\pi$
$167$		−	9.78443i		−	0.757142i	0.925572	−	0.378571i	$-0.123584\pi$
$168$	−5.55405	+	3.05174i	−0.428505	+	0.235447i
$169$	−11.4837			−0.883358
$170$	12.2600	−	7.07829i	0.940296	−	0.542880i
$171$	−1.02496	+	1.16192i	−0.0783809	+	0.0888540i
$172$	−3.13047	−	1.80738i	−0.238696	−	0.137811i
$173$	0.00105854		0.000611150i	8.04795e−5		4.64648e-5i	−0.499960	−	0.866049i	$-0.666652\pi$
$173$	0.00105854		0.000611150i	8.04795e−5		4.64648e-5i	0.500040	+	0.866002i	$0.333319\pi$
$174$	−4.48929	+	3.67336i	−0.340332	+	0.278477i
$175$	−1.66937	+	9.00307i	−0.126193	+	0.680568i
$176$	16.3610			1.23326
$177$	−0.716980	+	1.89660i	−0.0538915	+	0.142558i
$178$	14.0840	+	8.13138i	1.05564	+	0.609473i
$179$	−11.2837	−	6.51465i	−0.843384	−	0.486928i	0.0150289	−	0.999887i	$-0.495216\pi$
$179$	−11.2837	−	6.51465i	−0.843384	−	0.486928i	−0.858413	+	0.512959i	$0.828549\pi$
$180$	4.34137	−	1.45964i	0.323586	−	0.108795i
$181$		−	18.1492i		−	1.34902i	−0.738266	−	0.674509i	$-0.764355\pi$
$181$		−	18.1492i		−	1.34902i	0.738266	−	0.674509i	$-0.235645\pi$
$182$	−3.80343	+	4.45251i	−0.281929	+	0.330042i
$183$	13.3233	+	16.2827i	0.984887	+	1.20365i
$184$	1.22831	+	6.51741i	0.0905524	+	0.480470i
$185$	−2.86647	−	1.65496i	−0.210747	−	0.121675i
$186$	11.5529	−	1.89015i	0.847100	−	0.138593i
$187$	−10.4986	−	18.1840i	−0.767730	−	1.32975i
$188$		−	4.01595i		−	0.292893i
$189$	10.1149	+	9.31070i	0.735749	+	0.677254i
$190$	1.15165			0.0835498
$191$	8.41969	+	14.5833i	0.609228	+	1.05521i	0.991368	+	0.131109i	$0.0418538\pi$
$191$	8.41969	+	14.5833i	0.609228	+	1.05521i	−0.382140	+	0.924104i	$0.624813\pi$
$192$	0.312205	+	1.90825i	0.0225314	+	0.137716i
$193$	−1.12242	+	1.94409i	−0.0807936	+	0.139939i	−0.903591	−	0.428396i	$-0.859079\pi$
$193$	−1.12242	+	1.94409i	−0.0807936	+	0.139939i	0.822797	+	0.568335i	$0.192412\pi$
$194$	14.7107	+	25.4796i	1.05617	+	1.82933i
$195$	−2.04787	+	1.67567i	−0.146651	+	0.119997i
$196$	−1.34619	−	8.50841i	−0.0961562	−	0.607743i
$197$		−	2.32167i		−	0.165412i	−0.996574	−	0.0827061i	$-0.973644\pi$
$197$		−	2.32167i		−	0.165412i	0.996574	−	0.0827061i	$-0.0263563\pi$
$198$	−5.68343	−	16.9041i	−0.403904	−	1.20132i
$199$	19.9886	+	11.5404i	1.41695	+	0.818079i	0.996030	−	0.0890176i	$-0.0283727\pi$
$199$	19.9886	+	11.5404i	1.41695	+	0.818079i	0.420924	+	0.907096i	$0.361706\pi$
$200$	−4.14479	−	2.39300i	−0.293081	−	0.169211i
$201$	6.00372	−	15.8815i	0.423470	−	1.12019i
$202$	4.77664			0.336083
$203$	1.64520	+	4.64709i	0.115470	+	0.326161i
$204$	10.4727	−	8.56926i	0.733233	−	0.599968i
$205$	−0.472529	+	0.272814i	−0.0330028	+	0.0190542i
$206$	14.8296	−	25.6856i	1.03322	−	1.78960i
$207$	12.5522	−	7.03148i	0.872440	−	0.488722i
$208$	−3.04575	−	5.27540i	−0.211185	−	0.365783i
$209$		−	1.70814i		−	0.118154i
$210$	0.216305	−	10.2164i	0.0149264	−	0.704995i
$211$	−13.4680			−0.927177			−0.463589	−	0.886051i	$-0.653438\pi$
$211$	−13.4680			−0.927177			−0.463589	+	0.886051i	$0.653438\pi$
$212$	4.19740	+	7.27011i	0.288279	+	0.499313i
$213$	16.8688	−	2.75988i	1.15583	−	0.189104i
$214$	7.78697	+	4.49581i	0.532306	+	0.307327i
$215$	−3.15596	+	1.82209i	−0.215235	+	0.124266i
$216$	−6.35198	+	3.35968i	−0.432197	+	0.228597i
$217$	1.81383	−	9.78213i	0.123131	−	0.664054i
$218$	−18.7707			−1.27131
$219$	−3.43468	−	1.29842i	−0.232094	−	0.0877394i
$220$	−2.52473	+	4.37296i	−0.170217	+	0.294825i
$221$	−3.90880	+	6.77024i	−0.262934	+	0.455416i
$222$	−7.76912	−	2.93699i	−0.521429	−	0.197118i
$223$	25.9764			1.73951			0.869753	−	0.493488i	$-0.164278\pi$
$223$	25.9764			1.73951			0.869753	+	0.493488i	$0.164278\pi$
$224$	15.9351	+	2.95473i	1.06471	+	0.197421i
$225$	−2.05512	+	10.1771i	−0.137008	+	0.678473i
$226$	31.3388	−	18.0935i	2.08463	−	1.20356i
$227$	−1.31884	+	2.28430i	−0.0875348	+	0.151615i	−0.906469	−	0.422273i	$-0.861232\pi$
$227$	−1.31884	+	2.28430i	−0.0875348	+	0.151615i	0.818934	+	0.573888i	$0.194566\pi$
$228$	1.08638	−	0.177741i	0.0719474	−	0.0117712i
$229$	3.48282	−	2.01081i	0.230151	−	0.132878i	−0.380491	−	0.924785i	$-0.624245\pi$
$229$	3.48282	−	2.01081i	0.230151	−	0.132878i	0.610642	+	0.791907i	$0.290912\pi$
$230$	−10.0915	−	3.53931i	−0.665415	−	0.233375i
$231$	−15.1529	−	0.320824i	−0.996990	−	0.0211087i
$232$	−2.57670			−0.169168
$233$	−6.87369	+	3.96853i	−0.450311	+	0.259987i	−0.707961	−	0.706251i	$-0.750385\pi$
$233$	−6.87369	+	3.96853i	−0.450311	+	0.259987i	0.257651	+	0.966238i	$0.417052\pi$
$234$	−4.39249	+	4.97940i	−0.287146	+	0.325514i
$235$	−3.50624	−	2.02433i	−0.228722	−	0.132053i
$236$	1.24759	−	0.720296i	0.0812112	−	0.0468873i
$237$	−1.54087	−	1.88313i	−0.100090	−	0.122322i
$238$	−10.0754	−	28.4593i	−0.653090	−	1.84475i
$239$		−	2.46625i		−	0.159529i	−0.996814	−	0.0797644i	$-0.974583\pi$
$239$		−	2.46625i		−	0.159529i	0.996814	−	0.0797644i	$-0.0254168\pi$
$240$	9.94311	+	3.75883i	0.641825	+	0.242631i
$241$	6.24259	+	3.60416i	0.402121	+	0.232164i	0.687399	−	0.726280i	$-0.258753\pi$
$241$	6.24259	+	3.60416i	0.402121	+	0.232164i	−0.285278	+	0.958445i	$0.592086\pi$
$242$	−0.0952925	−	0.0550172i	−0.00612564	−	0.00353664i
$243$	11.2997	+	10.7385i	0.724878	+	0.688878i
$244$		−	14.9480i		−	0.956945i
$245$	−8.10708	−	3.11352i	−0.517942	−	0.198916i
$246$	−1.05965	+	0.867056i	−0.0675606	+	0.0552815i
$247$	−0.550767	+	0.317986i	−0.0350445	+	0.0202329i
$248$	4.50346	+	2.60007i	0.285970	+	0.165105i
$249$	−0.169944	−	1.03873i	−0.0107698	−	0.0658267i
$250$	16.3391	−	9.43338i	1.03337	−	0.596619i
$251$	−5.42169			−0.342214			−0.171107	−	0.985252i	$-0.554734\pi$
$251$	−5.42169			−0.342214			−0.171107	+	0.985252i	$0.554734\pi$
$252$	−1.37270	−	9.67070i	−0.0864719	−	0.609197i
$253$	−5.24953	+	14.9678i	−0.330035	+	0.941016i
$254$	20.2584	−	11.6962i	1.27113	−	0.733886i
$255$	−2.20265	−	13.4630i	−0.137935	−	0.843084i
$256$	−10.3231	+	17.8801i	−0.645194	+	1.11751i
$257$	17.7792	−	10.2648i	1.10903	−	0.640300i	0.170454	−	0.985366i	$-0.445476\pi$
$257$	17.7792	−	10.2648i	1.10903	−	0.640300i	0.938579	+	0.345065i	$0.112143\pi$
$258$	−7.07725	+	5.79096i	−0.440610	+	0.360529i
$259$	−4.58469	+	5.36710i	−0.284879	+	0.333495i
$260$	1.88001			0.116593
$261$	1.78138	+	5.29832i	0.110265	+	0.327958i
$262$	9.77267	−	16.9268i	0.603758	−	1.04574i
$263$	−12.0795	+	20.9222i	−0.744851	+	1.29012i	0.205413	+	0.978675i	$0.434146\pi$
$263$	−12.0795	+	20.9222i	−0.744851	+	1.29012i	−0.950264	+	0.311445i	$0.899187\pi$
$264$	2.80130	−	7.41020i	0.172408	−	0.456066i
$265$	8.46316			0.519888
$266$	0.447768	−	2.41485i	0.0274544	−	0.148064i
$267$	12.1287	−	9.92433i	0.742266	−	0.607359i
$268$	−10.4468	+	6.03149i	−0.638143	+	0.368432i
$269$	26.9028	+	15.5323i	1.64029	+	0.947024i	0.980729	+	0.195375i	$0.0625925\pi$
$269$	26.9028	+	15.5323i	1.64029	+	0.947024i	0.659564	+	0.751648i	$0.270741\pi$
$270$	0.429596	−	11.5789i	0.0261444	−	0.704668i
$271$	3.62999	+	6.28732i	0.220506	+	0.381928i	0.954962	−	0.296729i	$-0.0958958\pi$
$271$	3.62999	+	6.28732i	0.220506	+	0.381928i	−0.734456	+	0.678657i	$0.762562\pi$
$272$	31.4052			1.90422
$273$	2.71741	+	4.94559i	0.164465	+	0.299321i
$274$			27.3438i			1.65190i
$275$	−5.72317	−	9.91281i	−0.345120	−	0.597765i
$276$	−10.0658	−	1.78124i	−0.605890	−	0.107218i
$277$	−13.5553	+	23.4785i	−0.814459	+	1.41068i	0.0952569	+	0.995453i	$0.469633\pi$
$277$	−13.5553	+	23.4785i	−0.814459	+	1.41068i	−0.909716	+	0.415231i	$0.863701\pi$
$278$	−35.9100	+	20.7327i	−2.15374	+	1.24346i
$279$	2.23295	−	11.0578i	0.133683	−	0.662010i
$280$	2.94827	−	3.45141i	0.176193	−	0.206261i
$281$	−6.28047			−0.374661			−0.187331	−	0.982297i	$-0.559984\pi$
$281$	−6.28047			−0.374661			−0.187331	+	0.982297i	$0.559984\pi$
$282$	−9.50312	−	3.59249i	−0.565902	−	0.213930i
$283$	−16.1748	−	9.33855i	−0.961495	−	0.555119i	−0.0648619	−	0.997894i	$-0.520661\pi$
$283$	−16.1748	−	9.33855i	−0.961495	−	0.555119i	−0.896633	+	0.442775i	$0.853994\pi$
$284$	−10.5175	−	6.07226i	−0.624096	−	0.360322i
$285$	0.392433	−	1.03809i	0.0232457	−	0.0614912i
$286$		−	7.32024i		−	0.432855i
$287$	0.388330	+	1.09689i	0.0229224	+	0.0647475i
$288$	18.0131	+	3.63748i	1.06143	+	0.214341i
$289$	−11.6521	−	20.1820i	−0.685416	−	1.18718i
$290$	2.07743	−	3.59821i	0.121991	−	0.211294i
$291$	27.9798	−	4.57773i	1.64021	−	0.268351i
$292$	1.30443	+	2.25934i	0.0763360	+	0.132218i
$293$	16.2418			0.948855			0.474427	−	0.880295i	$-0.342655\pi$
$293$	16.2418			0.948855			0.474427	+	0.880295i	$0.342655\pi$
$294$	−21.3380	−	4.42571i	−1.24446	−	0.258113i
$295$		−	1.45232i		−	0.0845576i
$296$	−1.84474	−	3.19519i	−0.107223	−	0.185717i
$297$	−17.1738	−	0.637179i	−0.996528	−	0.0369729i
$298$	28.4378	+	16.4186i	1.64736	+	0.951102i
$299$	5.80341	−	1.09375i	0.335620	−	0.0632530i
$300$	5.70906	−	4.67143i	0.329613	−	0.269705i
$301$	2.59361	+	7.32601i	0.149493	+	0.422264i
$302$			8.67492i			0.499186i
$303$	1.62767	−	4.30562i	0.0935070	−	0.247351i
$304$	2.21256	+	1.27742i	0.126899	+	0.0732653i
$305$	−13.0507	−	7.53484i	−0.747283	−	0.431444i
$306$	−10.9094	−	32.4476i	−0.623649	−	1.85491i
$307$	30.0387			1.71440			0.857200	−	0.514984i	$-0.172202\pi$
$307$	30.0387			1.71440			0.857200	+	0.514984i	$0.172202\pi$
$308$	8.18782	+	6.99420i	0.466544	+	0.398532i
$309$	−18.0994	−	22.1197i	−1.02964	−	1.25835i
$310$	−7.26171	+	4.19255i	−0.412437	+	0.238121i
$311$	9.01639	+	5.20562i	0.511273	+	0.295183i	0.733357	−	0.679844i	$-0.237953\pi$
$311$	9.01639	+	5.20562i	0.511273	+	0.295183i	−0.222084	+	0.975028i	$0.571286\pi$
$312$	−2.91081	+	0.476232i	−0.164792	+	0.0269613i
$313$	−13.8814	+	8.01446i	−0.784626	+	0.453004i	−0.838067	−	0.545567i	$-0.816314\pi$
$313$	−13.8814	+	8.01446i	−0.784626	+	0.453004i	0.0534415	+	0.998571i	$0.482981\pi$
$314$	22.1996			1.25280
$315$	−9.13521	−	3.67625i	−0.514711	−	0.207133i
$316$			1.72877i			0.0972507i
$317$	−20.5913	+	11.8884i	−1.15653	+	0.667720i	−0.950469	−	0.310820i	$-0.899396\pi$
$317$	−20.5913	+	11.8884i	−1.15653	+	0.667720i	−0.206056	+	0.978540i	$0.566063\pi$
$318$	20.9584	−	3.42896i	1.17529	−	0.192287i
$319$	−5.33688	−	3.08125i	−0.298808	−	0.172517i
$320$	−0.692503	−	1.19945i	−0.0387121	−	0.0670513i
$321$	6.70593	−	5.48712i	0.374288	−	0.306261i
$322$	−11.3450	+	19.7843i	−0.632234	+	1.10254i
$323$		−	3.27879i		−	0.182437i
$324$	−1.38178	−	10.9889i	−0.0767657	−	0.610496i
$325$	−2.13084	+	3.69072i	−0.118198	+	0.204724i
$326$	−25.2074	−	14.5535i	−1.39611	−	0.806043i
$327$	−6.39621	+	16.9197i	−0.353711	+	0.935661i
$328$	−0.608200			−0.0335822
$329$	−5.60795	+	6.56498i	−0.309176	+	0.361939i
$330$	8.08941	+	9.88624i	0.445307	+	0.544220i
$331$	−12.2320	−	21.1865i	−0.672332	−	1.16451i	−0.977241	−	0.212132i	$-0.931959\pi$
$331$	−12.2320	−	21.1865i	−0.672332	−	1.16451i	0.304908	−	0.952382i	$-0.401374\pi$
$332$	−0.373910	+	0.647630i	−0.0205210	+	0.0355433i
$333$	−5.29474	+	6.00222i	−0.290150	+	0.328919i
$334$	8.79321	+	15.2303i	0.481143	+	0.833365i
$335$			12.1612i			0.664438i
$336$	11.7476	−	19.3878i	0.640885	−	1.05769i
$337$			27.0572i			1.47390i	0.675948	+	0.736949i	$0.263734\pi$
$337$			27.0572i			1.47390i	−0.675948	+	0.736949i	$0.736266\pi$
$338$	17.8753	−	10.3203i	0.972287	−	0.561350i
$339$	−5.63040	−	34.4139i	−0.305801	−	1.86911i
$340$	−4.84625	+	8.39395i	−0.262825	+	0.455226i
$341$	6.21841	+	10.7706i	0.336746	+	0.583261i
$342$	0.551234	−	2.72975i	0.0298073	−	0.147608i
$343$	−9.68065	+	15.7888i	−0.522706	+	0.852513i
$344$	−4.06209			−0.219013
$345$	−6.62904	+	7.89035i	−0.356896	+	0.424802i
$346$	−0.00109847	+	0.00190261i	−5.90543e−5	+	0.000102285i
$347$	27.6834	+	15.9830i	1.48612	+	0.858012i	0.999875	−	0.0158094i	$-0.00503250\pi$
$347$	27.6834	+	15.9830i	1.48612	+	0.858012i	0.486246	+	0.873822i	$0.338366\pi$
$348$	1.40435	−	3.71490i	0.0752813	−	0.199139i
$349$	20.4414			1.09420			0.547102	−	0.837066i	$-0.315731\pi$
$349$	20.4414			1.09420			0.547102	+	0.837066i	$0.315731\pi$
$350$	−5.49248	−	15.5143i	−0.293586	−	0.829274i
$351$	2.99162	+	5.65610i	0.159681	+	0.301900i
$352$	−17.5453	+	10.1298i	−0.935168	+	0.539920i
$353$	1.05894	+	0.611380i	0.0563618	+	0.0325405i	0.527916	−	0.849297i	$-0.322974\pi$
$353$	1.05894	+	0.611380i	0.0563618	+	0.0325405i	−0.471554	+	0.881837i	$0.656307\pi$
$354$	−0.588428	−	3.59657i	−0.0312746	−	0.191156i
$355$	−10.6031	+	6.12170i	−0.562754	+	0.324906i
$356$	−11.1345			−0.590128
$357$	−29.0862	−	0.615825i	−1.53941	−	0.0325929i
$358$	23.4187			1.23772
$359$	15.7270	+	27.2400i	0.830039	+	1.43767i	0.898006	+	0.439982i	$0.145015\pi$
$359$	15.7270	+	27.2400i	0.830039	+	1.43767i	−0.0679673	+	0.997688i	$0.521651\pi$
$360$	3.40488	−	3.85983i	0.179453	−	0.203431i
$361$	−9.36663	+	16.2235i	−0.492981	+	0.853868i
$362$	16.3106	+	28.2507i	0.857265	+	1.48483i
$363$	−0.0820634	+	0.0671483i	−0.00430721	+	0.00352437i
$364$	0.730954	−	3.94209i	0.0383124	−	0.206622i
$365$	2.63011			0.137666
$366$	−35.3720	−	13.3718i	−1.84892	−	0.698955i
$367$	−9.86515	−	5.69564i	−0.514956	−	0.297310i	0.219912	−	0.975520i	$-0.429423\pi$
$367$	−9.86515	−	5.69564i	−0.514956	−	0.297310i	−0.734869	+	0.678209i	$0.762756\pi$
$368$	−15.4620	−	17.9933i	−0.806014	−	0.937967i
$369$	0.420475	+	1.25061i	0.0218890	+	0.0651041i
$370$	5.94920			0.309284
$371$	3.29051	−	17.7460i	0.170835	−	0.921325i
$372$	−6.20308	+	5.07567i	−0.321615	+	0.263161i
$373$	−22.1188	+	12.7703i	−1.14527	+	0.661222i	−0.947730	−	0.319073i	$-0.896629\pi$
$373$	−22.1188	+	12.7703i	−1.14527	+	0.661222i	−0.197540	+	0.980295i	$0.563295\pi$
$374$	32.6838	+	18.8700i	1.69004	+	0.975743i
$375$	−2.93552	−	17.9424i	−0.151589	−	0.926540i
$376$	−2.25647	−	3.90832i	−0.116369	−	0.201556i
$377$			2.29441i			0.118168i
$378$	−24.1121	−	5.40271i	−1.24019	−	0.277885i
$379$		−	1.14645i		−	0.0588893i	−0.999566	−	0.0294447i	$-0.990626\pi$
$379$		−	1.14645i		−	0.0588893i	0.999566	−	0.0294447i	$-0.00937388\pi$
$380$	−0.682858	+	0.394248i	−0.0350299	+	0.0202245i
$381$	−3.63968	−	22.2463i	−0.186466	−	1.13971i
$382$	−26.2119	−	15.1335i	−1.34112	−	0.774295i
$383$	−6.26291	−	10.8477i	−0.320020	−	0.554290i	0.660472	−	0.750851i	$-0.270356\pi$
$383$	−6.26291	−	10.8477i	−0.320020	−	0.554290i	−0.980492	+	0.196560i	$0.937023\pi$
$384$	11.2368	+	13.7327i	0.573425	+	0.700795i
$385$	10.2337	−	3.62302i	0.521559	−	0.184646i
$386$		−	4.03485i		−	0.205369i
$387$	2.80830	+	8.35266i	0.142754	+	0.424590i
$388$	−17.4450	−	10.0719i	−0.885635	−	0.511321i
$389$	−16.9692	+	29.3915i	−0.860373	+	1.49021i	0.0111972	+	0.999937i	$0.496436\pi$
$389$	−16.9692	+	29.3915i	−0.860373	+	1.49021i	−0.871570	+	0.490272i	$0.836898\pi$
$390$	1.68177	−	4.44874i	0.0851598	−	0.225271i
$391$	−10.0765	+	28.7308i	−0.509591	+	1.45298i
$392$	−6.09079	−	7.52399i	−0.307631	−	0.380019i
$393$	−11.9275	−	14.5769i	−0.601664	−	0.735306i
$394$	2.08647	+	3.61388i	0.105115	+	0.182064i
$395$	1.50935	+	0.871422i	0.0759435	+	0.0438460i
$396$	9.15672	+	8.07743i	0.460143	+	0.405906i
$397$	1.63662	+	2.83471i	0.0821397	+	0.142270i	0.904169	−	0.427175i	$-0.140491\pi$
$397$	1.63662	+	2.83471i	0.0821397	+	0.142270i	−0.822029	+	0.569445i	$0.807158\pi$
$398$	−41.4852			−2.07947
$399$	−2.02414	−	1.22649i	−0.101334	−	0.0614011i
$400$	17.1202			0.856008
$401$	−7.66782	−	13.2811i	−0.382913	−	0.663224i	0.608564	−	0.793504i	$-0.291746\pi$
$401$	−7.66782	−	13.2811i	−0.382913	−	0.663224i	−0.991477	+	0.130280i	$0.958412\pi$
$402$	4.92728	+	30.1163i	0.245750	+	1.50207i
$403$	2.31523	−	4.01009i	0.115330	−	0.199757i
$404$	−2.83224	+	1.63520i	−0.140909	+	0.0813540i
$405$	−10.2907	−	4.33280i	−0.511349	−	0.215299i
$406$	−6.73719	−	5.75505i	−0.334361	−	0.285618i
$407$		−	8.82388i		−	0.437384i
$408$	5.37713	−	14.2239i	0.266207	−	0.704190i
$409$	−2.00954	+	3.48063i	−0.0993654	+	0.172106i	−0.911422	−	0.411473i	$-0.865015\pi$
$409$	−2.00954	+	3.48063i	−0.0993654	+	0.172106i	0.812057	+	0.583578i	$0.198348\pi$
$410$	0.490354	−	0.849317i	0.0242168	−	0.0419448i
$411$	24.6474	+	9.31755i	1.21577	+	0.459601i
$412$			20.3065i			1.00043i
$413$	−3.04530	−	0.564669i	−0.149850	−	0.0277855i
$414$	−13.2194	+	22.2257i	−0.649700	+	1.09233i
$415$	0.376954	+	0.652904i	0.0185040	+	0.0320498i
$416$	6.53244	+	3.77150i	0.320279	+	0.184913i
$417$	6.45167	+	39.4337i	0.315940	+	1.93108i
$418$	1.53510	+	2.65886i	0.0750840	+	0.130049i
$419$	−16.5585			−0.808934			−0.404467	−	0.914553i	$-0.632543\pi$
$419$	−16.5585			−0.808934			−0.404467	+	0.914553i	$0.632543\pi$
$420$	3.36913	+	6.13169i	0.164397	+	0.299196i
$421$		−	27.5675i		−	1.34356i	−0.740751	−	0.671780i	$-0.765530\pi$
$421$		−	27.5675i		−	1.34356i	0.740751	−	0.671780i	$-0.234470\pi$
$422$	20.9641	−	12.1036i	1.02052	−	0.589196i
$423$	−6.47648	+	7.34185i	−0.314897	+	0.356973i
$424$	8.16981	+	4.71684i	0.396761	+	0.229070i
$425$	−10.9857	−	19.0277i	−0.532884	−	0.922981i
$426$	−23.7775	+	19.4559i	−1.15202	+	0.942643i
$427$	−20.8736	+	24.4358i	−1.01014	+	1.18253i
$428$	−6.15623			−0.297573
$429$	−6.59839	−	2.49441i	−0.318573	−	0.120431i
$430$	3.27501	−	5.67249i	0.157935	−	0.273552i
$431$	9.07515	−	15.7186i	0.437135	−	0.757139i	−0.560333	−	0.828268i	$-0.689327\pi$
$431$	9.07515	−	15.7186i	0.437135	−	0.757139i	0.997467	+	0.0711284i	$0.0226600\pi$
$432$	13.6687	−	21.7689i	0.657637	−	1.04736i
$433$		−	18.9311i		−	0.909770i	−0.890550	−	0.454885i	$-0.849680\pi$
$433$		−	18.9311i		−	0.909770i	0.890550	−	0.454885i	$-0.150320\pi$
$434$	5.96776	+	16.8568i	0.286462	+	0.809152i
$435$	−2.53550	−	3.09868i	−0.121568	−	0.148571i
$436$	11.1298	−	6.42580i	0.533021	−	0.307740i
$437$	−1.87856	+	1.61428i	−0.0898635	+	0.0772215i
$438$	6.51326	−	1.06562i	0.311215	−	0.0509174i
$439$	−13.9956	−	24.2411i	−0.667975	−	1.15697i	−0.978470	−	0.206391i	$-0.933828\pi$
$439$	−13.9956	−	24.2411i	−0.667975	−	1.15697i	0.310495	−	0.950575i	$-0.399505\pi$
$440$			5.67435i			0.270514i
$441$	−11.2604	+	17.7258i	−0.536207	+	0.844086i
$442$		−	14.0513i		−	0.668351i
$443$	10.4233	−	6.01791i	0.495227	−	0.285919i	−0.231513	−	0.972832i	$-0.574368\pi$
$443$	10.4233	−	6.01791i	0.495227	−	0.285919i	0.726740	+	0.686912i	$0.241034\pi$
$444$	5.61202	−	0.918172i	0.266335	−	0.0435745i
$445$	−5.61259	+	9.72130i	−0.266062	+	0.460834i
$446$	−40.4344	+	23.3448i	−1.91462	+	1.10541i
$447$	24.4899	−	20.0388i	1.15833	−	0.947804i
$448$	−2.78431	+	0.985723i	−0.131546	+	0.0465711i
$449$		−	28.2703i		−	1.33416i	−0.744987	−	0.667079i	$-0.767545\pi$
$449$		−	28.2703i		−	1.33416i	0.744987	−	0.667079i	$-0.232455\pi$
$450$	−5.94714	−	17.6884i	−0.280351	−	0.833841i
$451$	−1.25971	−	0.727295i	−0.0593175	−	0.0342470i
$452$	−12.3879	+	21.4565i	−0.582680	+	1.00923i
$453$	7.81949	+	2.95603i	0.367392	+	0.138886i
$454$		−	4.74095i		−	0.222504i
$455$	−3.07330	−	2.62528i	−0.144078	−	0.123075i
$456$	0.957398	−	0.783391i	0.0448343	−	0.0366856i
$457$	14.7585	−	8.52083i	0.690374	−	0.398587i	−0.113378	−	0.993552i	$-0.536167\pi$
$457$	14.7585	−	8.52083i	0.690374	−	0.398587i	0.803752	+	0.594964i	$0.202834\pi$
$458$	−3.61420	+	6.25998i	−0.168880	+	0.292510i
$459$	−32.9654	−	1.22307i	−1.53869	−	0.0570881i
$460$	7.19524	−	1.35606i	0.335480	−	0.0632266i
$461$			24.2583i			1.12982i	0.825151	+	0.564912i	$0.191090\pi$
$461$			24.2583i			1.12982i	−0.825151	+	0.564912i	$0.808910\pi$
$462$	23.8751	−	13.1185i	1.11077	−	0.610326i
$463$	21.8434			1.01515			0.507574	−	0.861608i	$-0.330542\pi$
$463$	21.8434			1.01515			0.507574	+	0.861608i	$0.330542\pi$
$464$	7.98232	−	4.60860i	0.370570	−	0.213949i
$465$	1.30466	+	7.97427i	0.0605019	+	0.369798i
$466$	7.13299	−	12.3547i	0.330429	−	0.572320i
$467$	15.7765	+	27.3257i	0.730049	+	1.26448i	0.956862	+	0.290543i	$0.0938359\pi$
$467$	15.7765	+	27.3257i	0.730049	+	1.26448i	−0.226813	+	0.973938i	$0.572831\pi$
$468$	0.899856	−	4.45615i	0.0415959	−	0.205986i
$469$	25.5002	+	4.72833i	1.17749	+	0.218334i
$470$	7.27701			0.335663
$471$	7.56464	−	20.0105i	0.348560	−	0.922036i
$472$	0.809436	−	1.40198i	0.0372573	−	0.0645316i
$473$	−8.41346	−	4.85751i	−0.386851	−	0.223349i
$474$	4.09085	+	1.54648i	0.187899	+	0.0710321i
$475$		−	1.78740i		−	0.0820113i
$476$	15.7166	+	13.4254i	0.720369	+	0.615354i
$477$	4.05085	−	20.0601i	0.185476	−	0.918489i
$478$	2.21641	+	3.83893i	0.101376	+	0.175589i
$479$	−8.84486	+	15.3197i	−0.404132	+	0.699977i	−0.994220	−	0.107362i	$-0.965760\pi$
$479$	−8.84486	+	15.3197i	−0.404132	+	0.699977i	0.590088	+	0.807339i	$0.299093\pi$
$480$	−12.9901	+	2.12528i	−0.592913	+	0.0970055i
$481$	−2.84515	+	1.64265i	−0.129728	+	0.0748982i
$482$	−12.9562			−0.590137
$483$	13.9675	+	16.9679i	0.635542	+	0.772066i
$484$	0.0753365			0.00342439
$485$	−17.5870	+	10.1539i	−0.798586	+	0.461064i
$486$	−27.2396	−	6.56044i	−1.23562	−	0.297588i
$487$	2.96296	−	5.13199i	0.134264	−	0.232553i	−0.791052	−	0.611749i	$-0.790466\pi$
$487$	2.96296	−	5.13199i	0.134264	−	0.232553i	0.925316	+	0.379196i	$0.123800\pi$
$488$	−8.39892	−	14.5473i	−0.380201	−	0.658528i
$489$	−21.7079	+	17.7625i	−0.981666	+	0.803248i
$490$	15.4175	−	2.43932i	0.696489	−	0.110197i
$491$		−	4.63723i		−	0.209275i	−0.994510	−	0.104638i	$-0.966632\pi$
$491$		−	4.63723i		−	0.209275i	0.994510	−	0.104638i	$-0.0333683\pi$
$492$	0.331482	−	0.876859i	0.0149444	−	0.0395319i
$493$	−10.2442	−	5.91449i	−0.461376	−	0.266375i
$494$	0.571544	−	0.989943i	0.0257150	−	0.0445396i
$495$	11.6679	−	3.92292i	0.524432	−	0.176322i
$496$	−18.6016			−0.835238
$497$	8.71376	+	24.6132i	0.390866	+	1.10405i
$498$	1.19803	+	1.46414i	0.0536851	+	0.0656097i
$499$	−7.60903	−	13.1792i	−0.340627	−	0.589983i	0.643922	−	0.765091i	$-0.277306\pi$
$499$	−7.60903	−	13.1792i	−0.340627	−	0.589983i	−0.984549	+	0.175108i	$0.943973\pi$
$500$	−6.45869	+	11.1868i	−0.288841	+	0.500288i
$501$	16.7248	−	2.73631i	0.747208	−	0.122249i
$502$	8.43931	−	4.87244i	0.376665	−	0.217468i
$503$	21.5709			0.961797			0.480899	−	0.876776i	$-0.340311\pi$
$503$	21.5709			0.961797			0.480899	+	0.876776i	$0.340311\pi$
$504$	−6.76965	−	8.64023i	−0.301544	−	0.384867i
$505$			3.29702i			0.146716i
$506$	−5.28013	−	28.0163i	−0.234730	−	1.24548i
$507$	−3.21151	−	19.6293i	−0.142628	−	0.871768i
$508$	−8.00797	+	13.8702i	−0.355296	+	0.615391i
$509$	−7.12428	+	4.11321i	−0.315778	+	0.182315i	−0.649509	−	0.760354i	$-0.725026\pi$
$509$	−7.12428	+	4.11321i	−0.315778	+	0.182315i	0.333731	+	0.942668i	$0.391692\pi$
$510$	15.5277	+	18.9767i	0.687579	+	0.840304i
$511$	1.02259	−	5.51493i	0.0452369	−	0.243966i
$512$		−	16.6201i		−	0.734514i
$513$	−2.27273	−	1.42705i	−0.100344	−	0.0630060i
$514$	−18.4498	+	31.9560i	−0.813787	+	1.40952i
$515$	17.7292	+	10.2359i	0.781241	+	0.451049i
$516$	2.21393	−	5.85644i	0.0974628	−	0.257815i
$517$		−	10.7933i		−	0.474688i
$518$	2.31307	−	12.4746i	0.101631	−	0.548102i
$519$	0.00134068	+	0.00163848i	5.88495e−5	+	7.19212e-5i
$520$	1.82962	−	1.05633i	0.0802342	−	0.0463233i
$521$	8.40691	−	14.5612i	0.368313	−	0.637937i	−0.620989	−	0.783820i	$-0.713269\pi$
$521$	8.40691	−	14.5612i	0.368313	−	0.637937i	0.989302	+	0.145882i	$0.0466020\pi$
$522$	−7.53444	−	6.64637i	−0.329773	−	0.290904i
$523$	35.9841	−	20.7754i	1.57348	−	0.908447i	0.577737	−	0.816223i	$-0.303936\pi$
$523$	35.9841	−	20.7754i	1.57348	−	0.908447i	0.995738	−	0.0922237i	$-0.0293975\pi$
$524$			13.3820i			0.584595i
$525$	−15.8560	−	0.335710i	−0.692014	−	0.0146516i
$526$		−	43.4230i		−	1.89333i
$527$	11.9363	+	20.6743i	0.519953	+	0.900586i
$528$	4.57552	+	27.9663i	0.199124	+	1.21708i
$529$	21.4221	−	8.37207i	0.931398	−	0.364003i
$530$	−13.1736	+	7.60579i	−0.572226	+	0.330375i
$531$	−3.44242	−	0.695148i	−0.149388	−	0.0301668i
$532$	0.561181	+	1.58513i	0.0243303	+	0.0687243i
$533$			0.541570i			0.0234580i
$534$	−9.96045	+	26.3481i	−0.431031	+	1.14019i
$535$	−3.10318	+	5.37487i	−0.134162	+	0.232376i
$536$	−6.77791	+	11.7397i	−0.292761	+	0.507077i
$537$	7.98006	−	21.1094i	0.344365	−	0.910938i
$538$	−55.8353			−2.40723
$539$	−3.61802	−	22.8672i	−0.155839	−	0.984961i
$540$	3.70910	+	7.01260i	0.159614	+	0.301774i
$541$	−19.1831	−	33.2261i	−0.824745	−	1.42850i	−0.902114	−	0.431498i	$-0.857985\pi$
$541$	−19.1831	−	33.2261i	−0.824745	−	1.42850i	0.0773689	−	0.997003i	$-0.475348\pi$
$542$	−11.3008	−	6.52450i	−0.485409	−	0.280251i
$543$	31.0229	−	5.07559i	1.33132	−	0.217815i
$544$	−33.6784	+	19.4442i	−1.44395	+	0.833665i
$545$		−	12.9562i		−	0.554985i
$546$	−8.67446	−	5.25611i	−0.371232	−	0.224941i
$547$	−14.9714			−0.640130			−0.320065	−	0.947396i	$-0.603705\pi$
$547$	−14.9714			−0.640130			−0.320065	+	0.947396i	$0.603705\pi$
$548$	−9.36065	−	16.2131i	−0.399867	−	0.692590i
$549$	−24.1064	+	27.3274i	−1.02884	+	1.16631i
$550$	17.8172	+	10.2868i	0.759727	+	0.438629i
$551$	−0.481151	−	0.833378i	−0.0204977	−	0.0355031i
$552$	−10.7969	+	3.92224i	−0.459545	+	0.166942i
$553$	2.41408	−	2.82606i	0.102657	−	0.120176i
$554$		−	48.7283i		−	2.07027i
$555$	2.02722	−	5.36255i	0.0860508	−	0.227628i
$556$	14.1949	−	24.5863i	0.601998	−	1.04269i
$557$	15.4112	−	26.6929i	0.652992	−	1.13102i	−0.329401	−	0.944190i	$-0.606847\pi$
$557$	15.4112	−	26.6929i	0.652992	−	1.13102i	0.982393	−	0.186825i	$-0.0598199\pi$
$558$	6.46176	+	19.2191i	0.273548	+	0.813608i
$559$			3.61708i			0.152986i
$560$	−2.96033	+	15.9653i	−0.125097	+	0.674656i
$561$	28.1464	−	23.0308i	1.18834	−	0.972360i
$562$	9.77608	−	5.64422i	0.412379	−	0.238087i
$563$	3.58644	−	6.21190i	0.151150	−	0.261800i	−0.780500	−	0.625156i	$-0.785036\pi$
$563$	3.58644	−	6.21190i	0.151150	−	0.261800i	0.931651	+	0.363355i	$0.118369\pi$
$564$	6.86456	−	1.12310i	0.289050	−	0.0472910i
$565$	12.4888	+	21.6313i	0.525409	+	0.910034i
$566$	33.5700			1.41105
$567$	−13.0863	+	19.8934i	−0.549573	+	0.835446i
$568$	−13.6474			−0.572634
$569$	14.6499	+	25.3744i	0.614157	+	1.06375i	0.990532	+	0.137283i	$0.0438370\pi$
$569$	14.6499	+	25.3744i	0.614157	+	1.06375i	−0.376375	+	0.926467i	$0.622830\pi$
$570$	0.322071	+	1.96855i	0.0134901	+	0.0824536i
$571$	−1.19873	−	0.692088i	−0.0501653	−	0.0289630i	0.474708	−	0.880144i	$-0.342554\pi$
$571$	−1.19873	−	0.692088i	−0.0501653	−	0.0289630i	−0.524873	+	0.851181i	$0.675887\pi$
$572$	2.50595	+	4.34043i	0.104779	+	0.181483i
$573$	−22.5730	+	18.4704i	−0.943001	+	0.771610i
$574$	−1.59024	−	1.35842i	−0.0663753	−	0.0566992i
$575$	−5.49310	+	15.6623i	−0.229078	+	0.653162i
$576$	−3.17450	+	1.06732i	−0.132271	+	0.0444716i
$577$	15.1530	−	26.2458i	0.630830	−	1.09263i	−0.356553	−	0.934275i	$-0.616048\pi$
$577$	15.1530	−	26.2458i	0.630830	−	1.09263i	0.987382	−	0.158354i	$-0.0506186\pi$
$578$	36.2749	+	20.9433i	1.50884	+	0.871127i
$579$	−3.63697	−	1.37490i	−0.151147	−	0.0571388i
$580$			2.84468i			0.118119i
$581$	1.51560	−	0.536565i	0.0628778	−	0.0222605i
$582$	−39.4390	+	32.2709i	−1.63480	+	1.33767i
$583$	11.2809	+	19.5392i	0.467209	+	0.809230i
$584$	2.53894	+	1.46586i	0.105062	+	0.0606577i
$585$	−3.43698	−	3.03186i	−0.142101	−	0.125352i
$586$	−25.2817	+	14.5964i	−1.04438	+	0.602971i
$587$			28.4567i			1.17453i	0.809393	+	0.587267i	$0.199796\pi$
$587$			28.4567i			1.17453i	−0.809393	+	0.587267i	$0.800204\pi$
$588$	14.1672	−	4.68053i	0.584244	−	0.193022i
$589$			1.94206i			0.0800214i
$590$	1.30520	+	2.26066i	0.0537340	+	0.0930701i
$591$	3.96849	−	0.649277i	0.163242	−	0.0267077i
$592$	11.4296	+	6.59890i	0.469755	+	0.271213i
$593$	27.3639	−	15.7985i	1.12370	−	0.648768i	0.181356	−	0.983417i	$-0.441951\pi$
$593$	27.3639	−	15.7985i	1.12370	−	0.648768i	0.942343	+	0.334650i	$0.108618\pi$
$594$	27.3052	−	14.4422i	1.12034	−	0.592571i
$595$	19.6437	−	6.95443i	0.805315	−	0.285104i
$596$	−22.4824			−0.920914
$597$	−14.1363	+	37.3944i	−0.578561	+	1.53045i
$598$	−8.05056	+	6.91801i	−0.329212	+	0.282898i
$599$	16.0664	+	9.27593i	0.656455	+	0.379004i	0.790925	−	0.611913i	$-0.209600\pi$
$599$	16.0664	+	9.27593i	0.656455	+	0.379004i	−0.134470	+	0.990918i	$0.542933\pi$
$600$	2.93128	−	7.75402i	0.119669	−	0.316557i
$601$	11.6313			0.474452			0.237226	−	0.971455i	$-0.423762\pi$
$601$	11.6313			0.474452			0.237226	+	0.971455i	$0.423762\pi$
$602$	−10.6210	−	9.07269i	−0.432880	−	0.369775i
$603$	28.8256	+	5.82091i	1.17387	+	0.237046i
$604$	−2.96970	−	5.14367i	−0.120835	−	0.209293i
$605$	0.0379750	−	0.0657746i	0.00154390	−	0.00267412i
$606$	1.33583	+	8.16483i	0.0542645	+	0.331674i
$607$	8.13848	+	14.0963i	0.330331	+	0.572150i	0.982577	−	0.185858i	$-0.0595063\pi$
$607$	8.13848	+	14.0963i	0.330331	+	0.572150i	−0.652246	+	0.758008i	$0.726173\pi$
$608$	−3.16362			−0.128302
$609$	−7.48328	+	4.11177i	−0.303238	+	0.166618i
$610$	27.0861			1.09668
$611$	−3.48015	+	2.00927i	−0.140792	+	0.0812863i
$612$	17.5764	+	15.5047i	0.710485	+	0.626741i
$613$	−11.4761	−	6.62573i	−0.463515	−	0.267611i	0.250006	−	0.968244i	$-0.419567\pi$
$613$	−11.4761	−	6.62573i	−0.463515	−	0.267611i	−0.713521	+	0.700634i	$0.752901\pi$
$614$	−46.7578	+	26.9956i	−1.88699	+	1.08945i
$615$	−0.598476	−	0.731409i	−0.0241329	−	0.0294933i
$616$	11.8983	+	2.20621i	0.479395	+	0.0888907i
$617$	13.7930			0.555285			0.277643	−	0.960684i	$-0.410447\pi$
$617$	13.7930			0.555285			0.277643	+	0.960684i	$0.410447\pi$
$618$	48.0522	+	18.1653i	1.93294	+	0.730717i
$619$	24.4248	+	14.1017i	0.981717	+	0.566795i	0.902788	−	0.430086i	$-0.141517\pi$
$619$	24.4248	+	14.1017i	0.981717	+	0.566795i	0.0789289	+	0.996880i	$0.474850\pi$
$620$	2.87049	−	4.97183i	0.115281	−	0.199673i
$621$	15.5294	+	19.4894i	0.623175	+	0.782083i
$622$	−18.7130			−0.750324
$623$	18.2019	+	15.5484i	0.729243	+	0.622935i
$624$	8.16560	−	6.68150i	0.326886	−	0.267474i
$625$	−2.14082	−	3.70802i	−0.0856330	−	0.148321i
$626$	14.4051	−	24.9504i	0.575743	−	0.997217i
$627$	2.91976	−	0.477697i	0.116604	−	0.0190774i
$628$	−13.1630	+	7.59963i	−0.525259	+	0.303258i
$629$		−	16.9375i		−	0.675344i
$630$	17.5236	−	2.48736i	0.698155	−	0.0990990i
$631$			34.4366i			1.37090i	0.728119	+	0.685450i	$0.240395\pi$
$631$			34.4366i			1.37090i	−0.728119	+	0.685450i	$0.759605\pi$
$632$	0.971354	+	1.68243i	0.0386384	+	0.0669236i
$633$	−3.76646	−	23.0212i	−0.149703	−	0.915012i
$634$	21.3681	−	37.0106i	0.848636	−	1.46988i
$635$	8.07318	+	13.9832i	0.320374	+	0.554905i
$636$	−11.2531	+	9.20787i	−0.446216	+	0.365116i
$637$	−6.69972	+	5.42353i	−0.265452	+	0.214888i
$638$	11.0764			0.438519
$639$	9.43506	+	28.0625i	0.373245	+	1.11014i
$640$	−11.0069	−	6.35484i	−0.435086	−	0.251197i
$641$	12.0508	−	20.8726i	0.475979	−	0.824420i	−0.523642	−	0.851938i	$-0.675427\pi$
$641$	12.0508	−	20.8726i	0.475979	−	0.824420i	0.999621	+	0.0275185i	$0.00876052\pi$
$642$	−5.50710	+	14.5678i	−0.217348	+	0.574943i
$643$			10.3619i			0.408635i	0.978905	+	0.204317i	$0.0654974\pi$
$643$			10.3619i			0.408635i	−0.978905	+	0.204317i	$0.934503\pi$
$644$	−0.0459155	−	15.6146i	−0.00180933	−	0.615301i
$645$	−3.99714	−	4.88499i	−0.157387	−	0.192346i
$646$	2.94663	+	5.10371i	0.115934	+	0.200803i
$647$	−24.1978	−	13.9706i	−0.951313	−	0.549241i	−0.0578243	−	0.998327i	$-0.518416\pi$
$647$	−24.1978	−	13.9706i	−0.951313	−	0.549241i	−0.893488	+	0.449086i	$0.851750\pi$
$648$	−7.51917	−	9.91802i	−0.295381	−	0.389617i
$649$	3.35303	−	1.93587i	0.131618	−	0.0759896i
$650$		−	7.65989i		−	0.300446i
$651$	17.2281	+	0.364760i	0.675222	+	0.0142961i
$652$	19.9285			0.780460
$653$	−25.4257	+	14.6796i	−0.994986	+	0.574456i	−0.906761	−	0.421645i	$-0.861453\pi$
$653$	−25.4257	+	14.6796i	−0.994986	+	0.574456i	−0.0882252	+	0.996101i	$0.528120\pi$
$654$	−5.24940	−	32.0852i	−0.205268	−	1.25463i
$655$	11.6835	+	6.74548i	0.456513	+	0.263568i
$656$	1.88414	−	1.08781i	0.0735632	−	0.0424718i
$657$	1.25889	−	6.23410i	0.0491139	−	0.243215i
$658$	2.82933	−	15.2588i	0.110299	−	0.594849i
$659$	−39.1495			−1.52505			−0.762523	−	0.646961i	$-0.776040\pi$
$659$	−39.1495			−1.52505			−0.762523	+	0.646961i	$0.776040\pi$
$660$	−8.18088	−	3.09264i	−0.318440	−	0.120381i
$661$	9.27345	+	5.35403i	0.360696	+	0.208248i	0.669386	−	0.742915i	$-0.266557\pi$
$661$	9.27345	+	5.35403i	0.360696	+	0.208248i	−0.308690	+	0.951163i	$0.599891\pi$
$662$	38.0803	+	21.9857i	1.48003	+	0.854498i
$663$	−12.6657	−	4.78805i	−0.491894	−	0.185952i
$664$			0.840365i			0.0326125i
$665$	1.66682	+	0.309067i	0.0646365	+	0.0119851i
$666$	2.84756	−	14.1013i	0.110341	−	0.546415i
$667$	1.65497	+	8.78127i	0.0640808	+	0.340012i
$668$	−10.4276	−	6.02039i	−0.403457	−	0.232936i
$669$	7.26453	+	44.4020i	0.280863	+	1.71668i
$670$	−10.9292	−	18.9300i	−0.422232	−	0.731328i
$671$		−	40.1742i		−	1.55091i
$672$	−0.594194	+	28.0646i	−0.0229215	+	1.08261i
$673$	10.5400			0.406286			0.203143	−	0.979149i	$-0.434884\pi$
$673$	10.5400			0.406286			0.203143	+	0.979149i	$0.434884\pi$
$674$	−24.3161	−	42.1168i	−0.936622	−	1.62228i
$675$	−17.9707	−	0.666743i	−0.691693	−	0.0256630i
$676$	−7.06593	+	12.2386i	−0.271767	+	0.470714i
$677$	−17.9812	−	31.1443i	−0.691073	−	1.19697i	−0.971487	−	0.237095i	$-0.923805\pi$
$677$	−17.9812	−	31.1443i	−0.691073	−	1.19697i	0.280413	−	0.959879i	$-0.409528\pi$
$678$	39.6918	+	48.5082i	1.52435	+	1.86295i
$679$	14.4532	+	40.8252i	0.554665	+	1.56673i
$680$			10.8920i			0.417688i
$681$	−4.27345	−	1.61551i	−0.163759	−	0.0619063i
$682$	−19.3590	−	11.1769i	−0.741293	−	0.427986i
$683$	−37.1504	−	21.4488i	−1.42152	−	0.820716i	−0.425093	−	0.905150i	$-0.639759\pi$
$683$	−37.1504	−	21.4488i	−1.42152	−	0.820716i	−0.996429	+	0.0844335i	$0.973092\pi$
$684$	0.607634	+	1.80727i	0.0232335	+	0.0691028i
$685$	−18.8738			−0.721129
$686$	0.879470	−	33.2765i	0.0335783	−	1.27050i
$687$	4.41112	+	5.39092i	0.168295	+	0.205677i
$688$	12.5839	−	7.26533i	0.479758	−	0.276988i
$689$	4.20010	−	7.27479i	0.160011	−	0.277147i
$690$	3.22765	−	18.2395i	0.122874	−	0.694365i
$691$	−22.6677	−	39.2616i	−0.862320	−	1.49358i	−0.869684	−	0.493610i	$-0.835677\pi$
$691$	−22.6677	−	39.2616i	−0.862320	−	1.49358i	0.00736324	−	0.999973i	$-0.497656\pi$
$692$		−	0.00150417i		−	5.71799e-5i
$693$	−3.68927	−	25.9910i	−0.140144	−	0.987317i
$694$	−57.4553			−2.18097
$695$	−14.3105	−	24.7865i	−0.542828	−	0.940205i
$696$	−0.720597	−	4.40441i	−0.0273142	−	0.166949i
$697$	−2.41803	−	1.39605i	−0.0915894	−	0.0528791i
$698$	−31.8188	+	18.3706i	−1.20436	+	0.695336i
$699$	−8.70580	−	10.6395i	−0.329283	−	0.402424i
$700$	8.56773	+	7.31873i	0.323830	+	0.276622i
$701$	5.13343			0.193887			0.0969435	−	0.995290i	$-0.469093\pi$
$701$	5.13343			0.193887			0.0969435	+	0.995290i	$0.469093\pi$
$702$	−9.73981	−	6.11565i	−0.367606	−	0.230820i
$703$	0.688944	−	1.19329i	0.0259840	−	0.0450057i
$704$	1.84614	−	3.19761i	0.0695790	−	0.120514i
$705$	2.47968	−	6.55942i	0.0933901	−	0.247042i
$706$	−2.19778			−0.0827144
$707$	6.91336	+	1.28190i	0.260004	+	0.0482106i
$708$	1.58012	+	1.93110i	0.0593846	+	0.0725751i
$709$	−1.78691	+	1.03167i	−0.0671089	+	0.0387454i	−0.533179	−	0.846002i	$-0.679003\pi$
$709$	−1.78691	+	1.03167i	−0.0671089	+	0.0387454i	0.466070	+	0.884748i	$0.345669\pi$
$710$	11.0031	−	19.0579i	0.412938	−	0.715230i
$711$	2.78796	−	3.16048i	0.104557	−	0.118527i
$712$	−10.8361	+	6.25623i	−0.406100	+	0.234462i
$713$	5.96843	−	17.0176i	0.223520	−	0.637313i
$714$	45.8286	−	25.1810i	1.71509	−	0.942377i
$715$	5.05271			0.188961
$716$	−13.8858	+	8.01698i	−0.518937	+	0.299608i
$717$	4.21563	−	0.689711i	0.157436	−	0.0257577i
$718$	−48.9608	−	28.2675i	−1.82720	−	1.05493i
$719$	−19.2048	+	11.0879i	−0.716218	+	0.413509i	−0.813359	−	0.581762i	$-0.802364\pi$
$719$	−19.2048	+	11.0879i	−0.716218	+	0.413509i	0.0971411	+	0.995271i	$0.469030\pi$
$720$	−3.64437	+	18.0472i	−0.135818	+	0.672579i
$721$	28.3564	−	33.1956i	1.05605	−	1.23627i
$722$		−	33.6710i		−	1.25310i
$723$	−4.41488	+	11.6786i	−0.164191	+	0.434330i
$724$	−19.3423	−	11.1673i	−0.718849	−	0.415028i
$725$	−5.58451	−	3.22422i	−0.207404	−	0.119744i
$726$	0.0673927	−	0.178272i	0.00250118	−	0.00661629i
$727$		−	9.16580i		−	0.339941i	−0.985449	−	0.169970i	$-0.945633\pi$
$727$		−	9.16580i		−	0.339941i	0.985449	−	0.169970i	$-0.0543672\pi$
$728$	−1.50361	−	4.24715i	−0.0557274	−	0.157410i
$729$	−15.1956	+	22.3180i	−0.562799	+	0.826594i
$730$	−4.09398	+	2.36366i	−0.151525	+	0.0874830i
$731$	−16.1497	−	9.32404i	−0.597319	−	0.344862i
$732$	25.5509	−	4.18034i	0.944389	−	0.154510i
$733$	8.69575	−	5.02049i	0.321185	−	0.185436i	−0.330736	−	0.943723i	$-0.607297\pi$
$733$	8.69575	−	5.02049i	0.321185	−	0.185436i	0.651921	+	0.758287i	$0.273964\pi$
$734$	20.4746			0.755730
$735$	3.05480	−	14.7283i	0.112678	−	0.543263i
$736$	27.7216	+	9.72258i	1.02183	+	0.358379i
$737$	−28.0770	+	16.2103i	−1.03423	+	0.597113i
$738$	−1.77842	−	1.56880i	−0.0654645	−	0.0577483i
$739$	−9.56908	+	16.5741i	−0.352004	+	0.609689i	−0.986601	−	0.163155i	$-0.947833\pi$
$739$	−9.56908	+	16.5741i	−0.352004	+	0.609689i	0.634596	+	0.772844i	$0.281166\pi$
$740$	−3.52750	+	2.03660i	−0.129673	+	0.0748669i
$741$	−0.697568	−	0.852513i	−0.0256258	−	0.0313178i
$742$	10.8262	+	30.5803i	0.397444	+	1.12264i
$743$	17.5553			0.644043			0.322022	−	0.946732i	$-0.395638\pi$
$743$	17.5553			0.644043			0.322022	+	0.946732i	$0.395638\pi$
$744$	−3.18493	+	8.42500i	−0.116765	+	0.308876i
$745$	−11.3327	+	19.6289i	−0.415199	+	0.719146i
$746$	22.9532	−	39.7562i	0.840377	−	1.45558i
$747$	1.72800	−	0.580980i	0.0632241	−	0.0212570i
$748$	−25.8392			−0.944774
$749$	10.0638	+	8.59667i	0.367722	+	0.314116i
$750$	20.6941	+	25.2907i	0.755641	+	0.923485i
$751$	25.7696	−	14.8781i	0.940346	−	0.542909i	0.0502776	−	0.998735i	$-0.483989\pi$
$751$	25.7696	−	14.8781i	0.940346	−	0.542909i	0.890069	+	0.455826i	$0.150656\pi$
$752$	13.9806	+	8.07171i	0.509820	+	0.294345i
$753$	−1.51623	−	9.26742i	−0.0552543	−	0.337724i
$754$	−2.06197	−	3.57145i	−0.0750927	−	0.130064i
$755$	−5.98777			−0.217917
$756$	16.1465	−	5.05089i	0.587242	−	0.183699i
$757$		−	1.77643i		−	0.0645655i	−0.999479	−	0.0322828i	$-0.989722\pi$
$757$		−	1.77643i		−	0.0645655i	0.999479	−	0.0322828i	$-0.0102777\pi$
$758$	1.03031	+	1.78455i	0.0374226	+	0.0648178i
$759$	−27.0529	−	4.78726i	−0.981957	−	0.173767i
$760$	−0.443038	+	0.767364i	−0.0160707	+	0.0278352i
$761$	−23.1425	+	13.3613i	−0.838915	+	0.484348i	−0.856895	−	0.515490i	$-0.827610\pi$
$761$	−23.1425	+	13.3613i	−0.838915	+	0.484348i	0.0179801	+	0.999838i	$0.494276\pi$
$762$	25.6581	+	31.3573i	0.929494	+	1.13595i
$763$	−27.1673	−	5.03744i	−0.983522	−	0.182367i
$764$	20.7227			0.749720
$765$	22.3966	−	7.53009i	0.809751	−	0.272251i
$766$	19.4975	+	11.2569i	0.704473	+	0.406728i
$767$	−1.24839	−	0.720760i	−0.0450769	−	0.0260251i
$768$	−33.4499	−	12.6452i	−1.20702	−	0.456294i
$769$			29.7586i			1.07312i	0.843861	+	0.536562i	$0.180277\pi$
$769$			29.7586i			1.07312i	−0.843861	+	0.536562i	$0.819723\pi$
$770$	−12.6737	+	14.8365i	−0.456728	+	0.534672i
$771$	22.5180	+	27.5197i	0.810965	+	0.991098i
$772$	1.38126	+	2.39241i	0.0497126	+	0.0861047i
$773$	−2.68908	+	4.65762i	−0.0967195	+	0.167523i	−0.910325	−	0.413894i	$-0.864168\pi$
$773$	−2.68908	+	4.65762i	−0.0967195	+	0.167523i	0.813605	+	0.581417i	$0.197502\pi$
$774$	−11.8778	−	10.4778i	−0.426940	−	0.376618i
$775$	6.50694	+	11.2703i	0.233736	+	0.404843i
$776$	−22.6366			−0.812606
$777$	−10.4563	−	6.33576i	−0.375117	−	0.227294i
$778$		−	61.0005i		−	2.18697i
$779$	−0.113570	−	0.196710i	−0.00406908	−	0.00704785i
$780$	0.525762	+	3.21354i	0.0188253	+	0.115063i
$781$	−28.2668	−	16.3198i	−1.01146	−	0.583969i
$782$	−10.1353	−	53.7776i	−0.362436	−	1.92308i
$783$	−8.55837	+	4.52668i	−0.305851	+	0.161770i
$784$	32.3258	+	12.4147i	1.15449	+	0.443383i
$785$			15.3230i			0.546903i
$786$	31.6664	+	11.9709i	1.12950	+	0.426989i
$787$	18.4233	+	10.6367i	0.656721	+	0.379158i	0.791026	−	0.611782i	$-0.209547\pi$
$787$	18.4233	+	10.6367i	0.656721	+	0.379158i	−0.134306	+	0.990940i	$0.542880\pi$
$788$	−2.47429	−	1.42853i	−0.0881429	−	0.0508893i
$789$	−39.1410	−	14.7966i	−1.39346	−	0.526773i
$790$	−3.13257			−0.111452
$791$	50.2132	−	17.7768i	1.78538	−	0.632072i
$792$	13.4498	+	2.71600i	0.477919	+	0.0965089i
$793$	−12.9536	+	7.47879i	−0.459998	+	0.265580i
$794$	−5.09508	−	2.94164i	−0.180818	−	0.104395i
$795$	2.36680	+	14.4663i	0.0839418	+	0.513066i
$796$	24.5981	−	14.2017i	0.871856	−	0.503366i
$797$	−35.2930			−1.25014			−0.625072	−	0.780567i	$-0.714930\pi$
$797$	−35.2930			−1.25014			−0.625072	+	0.780567i	$0.714930\pi$
$798$	4.25298	+	0.0900457i	0.150554	+	0.00318758i
$799$		−	20.7178i		−	0.732944i
$800$	−18.3594	+	10.5998i	−0.649103	+	0.374760i
$801$	20.3558	+	17.9565i	0.719237	+	0.634462i
$802$	23.8712	+	13.7821i	0.842922	+	0.486661i
$803$	3.50579	+	6.07221i	0.123717	+	0.214284i
$804$	−13.2313	−	16.1703i	−0.466633	−	0.570282i
$805$	−13.6559	−	7.83078i	−0.481307	−	0.275999i
$806$			8.32273i			0.293155i
$807$	−19.0262	+	50.3294i	−0.669754	+	1.77168i
$808$	−1.83756	+	3.18274i	−0.0646451	+	0.111969i
$809$	5.48572	+	3.16718i	0.192868	+	0.111352i	0.593324	−	0.804964i	$-0.297815\pi$
$809$	5.48572	+	3.16718i	0.192868	+	0.111352i	−0.400457	+	0.916316i	$0.631149\pi$
$810$	19.9122	−	2.50383i	0.699644	−	0.0879755i
$811$	−4.84777			−0.170228			−0.0851141	−	0.996371i	$-0.527125\pi$
$811$	−4.84777			−0.170228			−0.0851141	+	0.996371i	$0.527125\pi$
$812$	5.96486	+	1.10602i	0.209326	+	0.0388138i
$813$	−9.73191	+	7.96314i	−0.341313	+	0.279279i
$814$	7.92997	+	13.7351i	0.277945	+	0.481416i
$815$	10.0454	−	17.3991i	0.351874	−	0.609465i
$816$	8.78275	+	53.6816i	0.307458	+	1.87923i
$817$	−0.758522	−	1.31380i	−0.0265373	−	0.0459640i
$818$		−	7.22385i		−	0.252576i
$819$	−7.69367	+	6.02802i	−0.268839	+	0.210636i
$820$			0.671455i			0.0234482i
$821$	28.8271	−	16.6433i	1.00607	−	0.580856i	0.0960327	−	0.995378i	$-0.469385\pi$
$821$	28.8271	−	16.6433i	1.00607	−	0.580856i	0.910039	+	0.414522i	$0.136051\pi$
$822$	−46.7394	+	7.64695i	−1.63023	+	0.266718i
$823$	24.1387	−	41.8095i	0.841422	−	1.45739i	−0.0472704	−	0.998882i	$-0.515052\pi$
$823$	24.1387	−	41.8095i	0.841422	−	1.45739i	0.888692	−	0.458504i	$-0.151614\pi$
$824$	11.4098	+	19.7623i	0.397478	+	0.688452i
$825$	15.3437	−	12.5550i	0.534198	−	0.437108i
$826$	5.24774	−	1.85784i	0.182592	−	0.0646426i
$827$	−25.6322			−0.891319			−0.445659	−	0.895203i	$-0.647031\pi$
$827$	−25.6322			−0.891319			−0.445659	+	0.895203i	$0.647031\pi$
$828$	0.229719	−	17.7039i	0.00798327	−	0.615252i
$829$	17.6570	−	30.5828i	0.613253	−	1.06219i	−0.377435	−	0.926036i	$-0.623194\pi$
$829$	17.6570	−	30.5828i	0.613253	−	1.06219i	0.990688	−	0.136150i	$-0.0434729\pi$
$830$	−1.17352	−	0.677534i	−0.0407336	−	0.0235175i
$831$	−43.9232	−	16.6044i	−1.52368	−	0.576001i
$832$	−1.37470			−0.0476593
$833$	−6.94482	−	43.8939i	−0.240624	−	1.52083i
$834$	−45.4814	−	55.5838i	−1.57489	−	1.92471i
$835$	−10.5125	+	6.06942i	−0.363802	+	0.210041i
$836$	−1.82043	−	1.05102i	−0.0629608	−	0.0363504i
$837$	19.5258	+	0.724438i	0.674909	+	0.0250403i
$838$	25.7747	−	14.8810i	0.890371	−	0.514056i
$839$	−30.7859			−1.06285			−0.531424	−	0.847106i	$-0.678343\pi$
$839$	−30.7859			−1.06285			−0.531424	+	0.847106i	$0.678343\pi$
$840$	6.72409	+	4.07432i	0.232003	+	0.140578i
$841$	25.5283			0.880285
$842$	24.7748	+	42.9112i	0.853796	+	1.47882i
$843$	−1.75639	−	10.7354i	−0.0604934	−	0.369745i
$844$	−8.28692	+	14.3534i	−0.285248	+	0.494063i
$845$	7.12347	+	12.3382i	0.245055	+	0.424447i
$846$	3.48310	−	17.2486i	0.119752	−	0.593019i
$847$	−0.123155	−	0.105201i	−0.00423164	−	0.00361476i
$848$	−33.7456			−1.15883
$849$	11.4392	−	30.2597i	0.392591	−	1.03851i
$850$	34.2003	+	19.7455i	1.17306	+	0.677266i
$851$	−9.70422	+	8.33903i	−0.332656	+	0.285858i
$852$	7.43815	−	19.6759i	0.254827	−	0.674086i
$853$	−44.5316			−1.52473			−0.762367	−	0.647145i	$-0.775963\pi$
$853$	−44.5316			−1.52473			−0.762367	+	0.647145i	$0.775963\pi$
$854$	10.5312	−	56.7954i	0.360369	−	1.94350i
$855$	1.88418	+	0.380483i	0.0644376	+	0.0130122i
$856$	−5.99124	+	3.45905i	−0.204776	+	0.118228i
$857$	−0.612262	−	0.353490i	−0.0209145	−	0.0120750i	0.489506	−	0.872000i	$-0.337177\pi$
$857$	−0.612262	−	0.353490i	−0.0209145	−	0.0120750i	−0.510421	+	0.859925i	$0.670510\pi$
$858$	12.5127	−	2.04717i	0.427175	−	0.0698894i
$859$	−12.6944	−	21.9873i	−0.433127	−	0.750198i	0.564014	−	0.825766i	$-0.309257\pi$
$859$	−12.6944	−	21.9873i	−0.433127	−	0.750198i	−0.997141	+	0.0755673i	$0.975923\pi$
$860$			4.48456i			0.152922i
$861$	−1.76634	+	0.970538i	−0.0601969	+	0.0330759i
$862$			32.6231i			1.11115i
$863$	17.7334	−	10.2384i	0.603651	−	0.348518i	−0.166826	−	0.985986i	$-0.553352\pi$
$863$	17.7334	−	10.2384i	0.603651	−	0.348518i	0.770476	+	0.637469i	$0.220018\pi$
$864$	−1.18011	+	31.8075i	−0.0401482	+	1.08211i
$865$	−0.00131326		0.000758209i	−4.46521e−5		2.57799e-5i
$866$	17.0133	+	29.4678i	0.578134	+	1.00136i
$867$	31.2390	−	25.5613i	1.06093	−	0.868106i
$868$	−9.30912	−	7.95204i	−0.315972	−	0.269910i
$869$			4.64624i			0.157613i
$870$	6.73148	+	2.54473i	0.228219	+	0.0862743i
$871$	10.4536	+	6.03537i	0.354206	+	0.204501i
$872$	7.22101	−	12.5072i	0.244534	−	0.423546i
$873$	15.6497	+	46.5464i	0.529660	+	1.57536i
$874$	1.47339	−	4.20101i	0.0498380	−	0.142101i
$875$	26.1796	−	9.26830i	0.885032	−	0.313326i
$876$	−3.49715	+	2.86154i	−0.118158	+	0.0966825i
$877$	−7.92846	−	13.7325i	−0.267725	−	0.463713i	0.700549	−	0.713604i	$-0.252939\pi$
$877$	−7.92846	−	13.7325i	−0.267725	−	0.463713i	−0.968274	+	0.249891i	$0.919605\pi$
$878$	43.5707	+	25.1556i	1.47044	+	0.848960i
$879$	4.54217	+	27.7625i	0.153203	+	0.936405i
$880$	−10.1490	−	17.5785i	−0.342122	−	0.592572i
$881$	25.4647			0.857926			0.428963	−	0.903322i	$-0.358879\pi$
$881$	25.4647			0.857926			0.428963	+	0.903322i	$0.358879\pi$
$882$	1.59759	−	37.7113i	0.0537938	−	1.26981i
$883$	6.13224			0.206366			0.103183	−	0.994662i	$-0.467097\pi$
$883$	6.13224			0.206366			0.103183	+	0.994662i	$0.467097\pi$
$884$	4.81020	+	8.33151i	0.161784	+	0.280219i
$885$	2.48249	−	0.406156i	0.0834481	−	0.0136528i
$886$	−10.8165	+	18.7348i	−0.363388	+	0.629407i
$887$	21.6944	−	12.5252i	0.728425	−	0.420556i	−0.0894206	−	0.995994i	$-0.528502\pi$
$887$	21.6944	−	12.5252i	0.728425	−	0.420556i	0.817846	+	0.575437i	$0.195168\pi$
$888$	4.94571	−	4.04683i	0.165967	−	0.135803i
$889$	32.4595	−	11.4915i	1.08866	−	0.385414i
$890$		−	20.1760i		−	0.676302i
$891$	−3.71368	−	29.5339i	−0.124413	−	0.989422i
$892$	15.9833	−	27.6840i	0.535162	−	0.926927i
$893$	0.842710	−	1.45962i	0.0282002	−	0.0488442i
$894$	−20.1118	+	53.2010i	−0.672638	+	1.77931i
$895$			16.1645i			0.540320i
$896$	−17.6047	+	20.6090i	−0.588131	+	0.688500i
$897$	3.49255	+	9.61404i	0.116613	+	0.321003i
$898$	25.4063	+	44.0051i	0.847821	+	1.46847i
$899$	6.06775	+	3.50322i	0.202371	+	0.116839i
$900$	9.58159	+	8.45222i	0.319386	+	0.281741i
$901$	21.6539	+	37.5056i	0.721396	+	1.24949i
$902$	2.61446			0.0870521
$903$	−11.7972	+	6.48211i	−0.392586	+	0.215711i
$904$			27.8420i			0.926011i
$905$	−19.4998	+	11.2582i	−0.648194	+	0.374235i
$906$	−14.8283	+	2.42602i	−0.492636	+	0.0805992i
$907$	4.98981	+	2.88087i	0.165684	+	0.0956576i	0.580549	−	0.814225i	$-0.302838\pi$
$907$	4.98981	+	2.88087i	0.165684	+	0.0956576i	−0.414865	+	0.909883i	$0.636171\pi$
$908$	1.62298	+	2.81108i	0.0538604	+	0.0932890i
$909$	7.81489	+	1.57810i	0.259203	+	0.0523424i
$910$	7.14317	+	1.32451i	0.236794	+	0.0439070i
$911$	8.98721			0.297760			0.148880	−	0.988855i	$-0.452433\pi$
$911$	8.98721			0.297760			0.148880	+	0.988855i	$0.452433\pi$
$912$	−1.56477	+	4.13923i	−0.0518146	+	0.137064i
$913$	−1.00492	+	1.74057i	−0.0332580	+	0.0576046i
$914$	−15.3152	+	26.5268i	−0.506583	+	0.877428i
$915$	9.22973	−	24.4151i	0.305126	−	0.807139i
$916$		−	4.94902i		−	0.163520i
$917$	18.6868	−	21.8759i	0.617094	−	0.722406i
$918$	52.4126	−	27.7220i	1.72987	−	0.914962i
$919$	−12.7630	+	7.36873i	−0.421013	+	0.243072i	−0.695511	−	0.718516i	$-0.744822\pi$
$919$	−12.7630	+	7.36873i	−0.421013	+	0.243072i	0.274498	+	0.961588i	$0.411488\pi$
$920$	6.24047	−	5.36256i	0.205742	−	0.176798i
$921$	8.40061	+	51.3459i	0.276810	+	1.69191i
$922$	−21.8008	−	37.7602i	−0.717972	−	1.24356i
$923$			12.1523i			0.399999i
$924$	−9.66557	+	15.9516i	−0.317974	+	0.524770i
$925$		−	9.23330i		−	0.303589i
$926$	−34.0011	+	19.6305i	−1.11734	+	0.645099i
$927$	32.7481	−	37.1238i	1.07559	−	1.21931i
$928$	−5.70675	+	9.88437i	−0.187333	+	0.324470i
$929$	−34.0660	+	19.6680i	−1.11767	+	0.645287i	−0.940805	−	0.338948i	$-0.889929\pi$
$929$	−34.0660	+	19.6680i	−1.11767	+	0.645287i	−0.176865	+	0.984235i	$0.556596\pi$
$930$	−9.19723	−	11.2401i	−0.301589	−	0.368578i
$931$	1.29613	−	3.37491i	0.0424790	−	0.110608i
$932$			9.76740i			0.319942i
$933$	−6.37657	+	16.8677i	−0.208759	+	0.552225i
$934$	−49.1149	−	28.3565i	−1.60709	−	0.927852i
$935$	−13.0248	+	22.5596i	−0.425956	+	0.737778i
$936$	−1.62807	−	4.84234i	−0.0532152	−	0.158277i
$937$			8.44592i			0.275916i	0.990438	+	0.137958i	$0.0440539\pi$
$937$			8.44592i			0.275916i	−0.990438	+	0.137958i	$0.955946\pi$
$938$	−43.9426	+	15.5569i	−1.43478	+	0.507950i
$939$	−17.5814	−	21.4866i	−0.573747	−	0.701188i
$940$	−4.31480	+	2.49115i	−0.140733	+	0.0812524i
$941$	−13.5892	+	23.5372i	−0.442996	+	0.767292i	−0.997910	−	0.0646157i	$-0.979418\pi$
$941$	−13.5892	+	23.5372i	−0.442996	+	0.767292i	0.554914	+	0.831908i	$0.312751\pi$
$942$	6.20833	+	37.9463i	0.202278	+	1.23636i
$943$	0.390638	+	2.07272i	0.0127209	+	0.0674971i
$944$			5.79093i			0.188479i
$945$	3.72916	−	16.6431i	0.121310	−	0.541401i
$946$	17.4617			0.567728
$947$	−34.0827	+	19.6777i	−1.10754	+	0.639439i	−0.938191	−	0.346117i	$-0.887500\pi$
$947$	−34.0827	+	19.6777i	−1.10754	+	0.639439i	−0.169349	+	0.985556i	$0.554167\pi$
$948$	−2.95502	+	0.483466i	−0.0959747	+	0.0157022i
$949$	1.30527	−	2.26079i	0.0423709	−	0.0733885i
$950$	1.60632	+	2.78223i	0.0521160	+	0.0902675i
$951$	−26.0797	−	31.8726i	−0.845693	−	1.03354i
$952$	22.8388	+	4.23484i	0.740211	+	0.137252i
$953$	17.0773			0.553188			0.276594	−	0.960987i	$-0.410794\pi$
$953$	17.0773			0.553188			0.276594	+	0.960987i	$0.410794\pi$
$954$	11.7224	+	34.8657i	0.379527	+	1.12882i
$955$	10.4457	−	18.0925i	0.338015	−	0.585459i
$956$	−2.62838	−	1.51749i	−0.0850078	−	0.0490793i
$957$	3.77435	−	9.98417i	0.122007	−	0.322742i
$958$		−	31.7953i		−	1.02726i
$959$	−7.33819	+	39.5754i	−0.236962	+	1.27796i
$960$	1.85658	−	1.51915i	0.0599210	−	0.0490304i
$961$	8.43000	+	14.6012i	0.271935	+	0.471006i
$962$	2.95247	−	5.11383i	0.0951916	−	0.164877i
$963$	11.2547	+	9.92808i	0.362676	+	0.319928i
$964$	7.68217	−	4.43531i	0.247426	−	0.142852i
$965$	2.78501			0.0896527
$966$	−36.9905	−	13.8595i	−1.19015	−	0.445921i
$967$	21.4244			0.688963			0.344481	−	0.938793i	$-0.388055\pi$
$967$	21.4244			0.688963			0.344481	+	0.938793i	$0.388055\pi$
$968$	0.0733174	−	0.0423298i	0.00235651	−	0.00136053i
$969$	5.60452	−	0.916945i	0.180043	−	0.0294565i
$970$	18.2505	−	31.6107i	0.585987	−	1.01496i
$971$	−14.5454	−	25.1934i	−0.466785	−	0.808496i	0.532495	−	0.846433i	$-0.321255\pi$
$971$	−14.5454	−	25.1934i	−0.466785	−	0.808496i	−0.999280	+	0.0379376i	$0.987921\pi$
$972$	18.3972	−	5.43507i	0.590091	−	0.174330i
$973$	−57.5375	+	20.3698i	−1.84457	+	0.653027i
$974$			10.6512i			0.341285i
$975$	−6.90455	−	2.61015i	−0.221123	−	0.0835917i
$976$	52.0379	+	30.0441i	1.66569	+	0.961688i
$977$	27.1495	−	47.0244i	0.868591	−	1.50444i	0.00515336	−	0.999987i	$-0.498360\pi$
$977$	27.1495	−	47.0244i	0.868591	−	1.50444i	0.863437	−	0.504456i	$-0.168307\pi$
$978$	17.8272	−	47.1576i	0.570050	−	1.50793i
$979$	−29.9252			−0.956412
$980$	−8.30650	+	6.72425i	−0.265342	+	0.214798i
$981$	−30.7100	−	6.20144i	−0.980495	−	0.197997i
$982$	4.16745	+	7.21824i	0.132989	+	0.230343i
$983$	−15.4936	+	26.8356i	−0.494168	+	0.855924i	−0.999977	−	0.00672150i	$-0.997860\pi$
$983$	−15.4936	+	26.8356i	−0.494168	+	0.855924i	0.505810	+	0.862645i	$0.331194\pi$
$984$	−0.170089	−	1.03961i	−0.00542224	−	0.0331416i
$985$	−2.49444	+	1.44016i	−0.0794794	+	0.0458874i
$986$	21.2613			0.677097
$987$	−12.7900	−	7.74984i	−0.407110	−	0.246680i
$988$			0.782631i			0.0248988i
$989$	2.60902	+	13.8434i	0.0829620	+	0.440196i
$990$	−14.6365	+	16.5922i	−0.465179	+	0.527335i
$991$	−8.27070	+	14.3253i	−0.262727	+	0.455057i	−0.966966	−	0.254906i	$-0.917955\pi$
$991$	−8.27070	+	14.3253i	−0.262727	+	0.455057i	0.704238	+	0.709964i	$0.251289\pi$
$992$	19.9481	−	11.5170i	0.633352	−	0.365666i
$993$	32.7938	−	26.8335i	1.04068	−	0.851535i
$994$	−35.6835	−	30.4816i	−1.13181	−	0.966817i
$995$		−	28.6347i		−	0.907782i
$996$	−1.21158	−	0.458017i	−0.0383903	−	0.0145128i
$997$	−18.7766	+	32.5221i	−0.594662	+	1.02998i	0.398933	+	0.916980i	$0.369381\pi$
$997$	−18.7766	+	32.5221i	−0.594662	+	1.02998i	−0.993595	+	0.113004i	$0.963953\pi$
$998$	23.6882	+	13.6764i	0.749836	+	0.432918i
$999$	−11.7405	−	7.37186i	−0.371452	−	0.233235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.m.a.137.11	✓	120
3.2	odd	2	inner	483.2.m.a.137.50	yes	120
7.2	even	3	inner	483.2.m.a.275.49	yes	120
21.2	odd	6	inner	483.2.m.a.275.12	yes	120
23.22	odd	2	inner	483.2.m.a.137.12	yes	120
69.68	even	2	inner	483.2.m.a.137.49	yes	120
161.114	odd	6	inner	483.2.m.a.275.50	yes	120
483.275	even	6	inner	483.2.m.a.275.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.m.a.137.11	✓	120	1.1	even	1	trivial
483.2.m.a.137.12	yes	120	23.22	odd	2	inner
483.2.m.a.137.49	yes	120	69.68	even	2	inner
483.2.m.a.137.50	yes	120	3.2	odd	2	inner
483.2.m.a.275.11	yes	120	483.275	even	6	inner
483.2.m.a.275.12	yes	120	21.2	odd	6	inner
483.2.m.a.275.49	yes	120	7.2	even	3	inner
483.2.m.a.275.50	yes	120	161.114	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55658 + 0.898694i) q^{2} +(0.279659 + 1.70932i) q^{3} +(0.615303 - 1.06574i) q^{4} +(-0.620314 - 1.07442i) q^{5} +(-1.97147 - 2.40938i) q^{6} +(-2.49407 + 0.882968i) q^{7} -1.38290i q^{8} +(-2.84358 + 0.956058i) q^{9} +O(q^{10})\)	\(q+(-1.55658 + 0.898694i) q^{2} +(0.279659 + 1.70932i) q^{3} +(0.615303 - 1.06574i) q^{4} +(-0.620314 - 1.07442i) q^{5} +(-1.97147 - 2.40938i) q^{6} +(-2.49407 + 0.882968i) q^{7} -1.38290i q^{8} +(-2.84358 + 0.956058i) q^{9} +(1.93114 + 1.11495i) q^{10} +(1.65369 - 2.86428i) q^{11} +(1.99377 + 0.753710i) q^{12} -1.23140 q^{13} +(3.08871 - 3.61582i) q^{14} +(1.66305 - 1.36079i) q^{15} +(2.47341 + 4.28407i) q^{16} +(3.17428 - 5.49801i) q^{17} +(3.56707 - 4.04369i) q^{18} +(0.447270 - 0.258231i) q^{19} -1.52672 q^{20} +(-2.20677 - 4.01624i) q^{21} +5.94465i q^{22} +(-4.71286 + 0.888215i) q^{23} +(2.36382 - 0.386741i) q^{24} +(1.73042 - 2.99718i) q^{25} +(1.91678 - 1.10665i) q^{26} +(-2.42945 - 4.59323i) q^{27} +(-0.593596 + 3.20131i) q^{28} -1.86326i q^{29} +(-1.36574 + 3.61275i) q^{30} +(-1.88016 + 3.25653i) q^{31} +(-5.30489 - 3.06278i) q^{32} +(5.35845 + 2.02567i) q^{33} +11.4108i q^{34} +(2.49578 + 2.13195i) q^{35} +(-0.730759 + 3.61877i) q^{36} +(2.31050 - 1.33397i) q^{37} +(-0.464142 + 0.803918i) q^{38} +(-0.344372 - 2.10486i) q^{39} +(-1.48581 + 0.857831i) q^{40} -0.439801i q^{41} +(7.04439 + 4.26840i) q^{42} -2.93738i q^{43} +(-2.03504 - 3.52480i) q^{44} +(2.79112 + 2.46213i) q^{45} +(6.53773 - 5.61801i) q^{46} +(2.82618 - 1.63170i) q^{47} +(-6.63116 + 5.42594i) q^{48} +(5.44074 - 4.40436i) q^{49} +6.22048i q^{50} +(10.2856 + 3.88830i) q^{51} +(-0.757684 + 1.31235i) q^{52} +(-3.41084 + 5.90774i) q^{53} +(7.90955 + 4.96642i) q^{54} -4.10323 q^{55} +(1.22106 + 3.44904i) q^{56} +(0.566484 + 0.692312i) q^{57} +(1.67450 + 2.90032i) q^{58} +(1.01380 + 0.585318i) q^{59} +(-0.426963 - 2.60967i) q^{60} +(10.5195 - 6.07341i) q^{61} -6.75876i q^{62} +(6.24791 - 4.89526i) q^{63} +1.11638 q^{64} +(0.763854 + 1.32303i) q^{65} +(-10.1613 + 1.66248i) q^{66} +(-8.48919 - 4.90123i) q^{67} +(-3.90629 - 6.76589i) q^{68} +(-2.83624 - 7.80741i) q^{69} +(-5.80086 - 1.07561i) q^{70} -9.86872i q^{71} +(1.32213 + 3.93239i) q^{72} +(-1.05999 + 1.83596i) q^{73} +(-2.39766 + 4.15287i) q^{74} +(5.60708 + 2.11966i) q^{75} -0.635562i q^{76} +(-1.59535 + 8.60386i) q^{77} +(2.42767 + 2.96691i) q^{78} +(-1.21660 + 0.702404i) q^{79} +(3.06858 - 5.31494i) q^{80} +(7.17191 - 5.43725i) q^{81} +(0.395246 + 0.684587i) q^{82} -0.607683 q^{83} +(-5.63808 - 0.119372i) q^{84} -7.87619 q^{85} +(2.63980 + 4.57227i) q^{86} +(3.18491 - 0.521077i) q^{87} +(-3.96101 - 2.28689i) q^{88} +(-4.52399 - 7.83579i) q^{89} +(-6.55731 - 1.32415i) q^{90} +(3.07119 - 1.08729i) q^{91} +(-1.95324 + 5.56919i) q^{92} +(-6.09228 - 2.30308i) q^{93} +(-2.93279 + 5.07974i) q^{94} +(-0.554895 - 0.320369i) q^{95} +(3.75172 - 9.92432i) q^{96} -16.3689i q^{97} +(-4.51079 + 11.7453i) q^{98} +(-1.96399 + 9.72583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9}+O(q^{10}) \) 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9	\( 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9} + 14 q^{12} - 16 q^{13} - 60 q^{16} - 10 q^{18} - 24 q^{24} - 40 q^{25} - 20 q^{27} - 4 q^{31} + 64 q^{36} - 12 q^{39} - 20 q^{46} + 140 q^{48} - 48 q^{49} - 76 q^{52} - 2 q^{54} + 72 q^{55} - 28 q^{58} - 128 q^{64} - 20 q^{69} - 68 q^{70} + 6 q^{72} + 20 q^{73} + 20 q^{75} - 156 q^{78} - 62 q^{81} + 80 q^{82} + 112 q^{85} + 46 q^{87} - 38 q^{93} + 36 q^{94} + 72 q^{96}+O(q^{100}) \) 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9 + 14 * q^12 - 16 * q^13 - 60 * q^16 - 10 * q^18 - 24 * q^24 - 40 * q^25 - 20 * q^27 - 4 * q^31 + 64 * q^36 - 12 * q^39 - 20 * q^46 + 140 * q^48 - 48 * q^49 - 76 * q^52 - 2 * q^54 + 72 * q^55 - 28 * q^58 - 128 * q^64 - 20 * q^69 - 68 * q^70 + 6 * q^72 + 20 * q^73 + 20 * q^75 - 156 * q^78 - 62 * q^81 + 80 * q^82 + 112 * q^85 + 46 * q^87 - 38 * q^93 + 36 * q^94 + 72 * q^96

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