LMFDB - Embedded newform 819.2.r.a.781.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(625,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2, 0]))

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

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

chi := DirichletCharacter("819.625");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.r (of order $3$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			781.19
Character	$\chi$	$=$	819.781
Dual form			819.2.r.a.625.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.919929 q^{2} +(-1.24150 - 1.20776i) q^{3} -1.15373 q^{4} +(-1.17586 + 2.03665i) q^{5} +(1.14209 + 1.11105i) q^{6} +(-0.707790 + 2.54932i) q^{7} +2.90121 q^{8} +(0.0826321 + 2.99886i) q^{9} +O(q^{10})$	\(q-0.919929 q^{2} +(-1.24150 - 1.20776i) q^{3} -1.15373 q^{4} +(-1.17586 + 2.03665i) q^{5} +(1.14209 + 1.11105i) q^{6} +(-0.707790 + 2.54932i) q^{7} +2.90121 q^{8} +(0.0826321 + 2.99886i) q^{9} +(1.08171 - 1.87357i) q^{10} +(-0.445310 - 0.771300i) q^{11} +(1.43235 + 1.39343i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.651117 - 2.34519i) q^{14} +(3.91961 - 1.10834i) q^{15} -0.361441 q^{16} +(-2.19130 + 3.79544i) q^{17} +(-0.0760156 - 2.75874i) q^{18} +(-0.779295 - 1.34978i) q^{19} +(1.35663 - 2.34975i) q^{20} +(3.95769 - 2.31013i) q^{21} +(0.409654 + 0.709541i) q^{22} +(2.75776 - 4.77658i) q^{23} +(-3.60184 - 3.50396i) q^{24} +(-0.265294 - 0.459503i) q^{25} +(-0.459964 - 0.796682i) q^{26} +(3.51932 - 3.82288i) q^{27} +(0.816600 - 2.94123i) q^{28} +(-5.11053 + 8.85169i) q^{29} +(-3.60576 + 1.01959i) q^{30} +4.02208 q^{31} -5.46992 q^{32} +(-0.378694 + 1.49540i) q^{33} +(2.01584 - 3.49153i) q^{34} +(-4.35981 - 4.43916i) q^{35} +(-0.0953353 - 3.45988i) q^{36} +(0.764675 + 1.32446i) q^{37} +(0.716896 + 1.24170i) q^{38} +(0.425202 - 1.67905i) q^{39} +(-3.41141 + 5.90874i) q^{40} +(-4.06327 - 7.03779i) q^{41} +(-3.64079 + 2.12516i) q^{42} +(1.78818 - 3.09722i) q^{43} +(0.513768 + 0.889873i) q^{44} +(-6.20479 - 3.35795i) q^{45} +(-2.53694 + 4.39411i) q^{46} -11.4336 q^{47} +(0.448728 + 0.436534i) q^{48} +(-5.99807 - 3.60877i) q^{49} +(0.244051 + 0.422710i) q^{50} +(7.30446 - 2.06547i) q^{51} +(-0.576866 - 0.999161i) q^{52} +(2.34007 - 4.05312i) q^{53} +(-3.23752 + 3.51678i) q^{54} +2.09449 q^{55} +(-2.05345 + 7.39611i) q^{56} +(-0.662716 + 2.61695i) q^{57} +(4.70132 - 8.14292i) q^{58} -8.55287 q^{59} +(-4.52218 + 1.27872i) q^{60} -0.502618 q^{61} -3.70002 q^{62} +(-7.70354 - 1.91191i) q^{63} +5.75481 q^{64} -2.35172 q^{65} +(0.348371 - 1.37566i) q^{66} -5.53222 q^{67} +(2.52817 - 4.37891i) q^{68} +(-9.19271 + 2.59940i) q^{69} +(4.01071 + 4.08371i) q^{70} +1.96645 q^{71} +(0.239733 + 8.70032i) q^{72} +(-2.12101 + 3.67370i) q^{73} +(-0.703447 - 1.21841i) q^{74} +(-0.225607 + 0.890883i) q^{75} +(0.899097 + 1.55728i) q^{76} +(2.28148 - 0.589320i) q^{77} +(-0.391155 + 1.54460i) q^{78} +1.68564 q^{79} +(0.425004 - 0.736129i) q^{80} +(-8.98634 + 0.495605i) q^{81} +(3.73792 + 6.47426i) q^{82} +(-7.20538 + 12.4801i) q^{83} +(-4.56611 + 2.66527i) q^{84} +(-5.15332 - 8.92580i) q^{85} +(-1.64500 + 2.84922i) q^{86} +(17.0354 - 4.81706i) q^{87} +(-1.29194 - 2.23770i) q^{88} +(-1.05501 - 1.82733i) q^{89} +(5.70797 + 3.08907i) q^{90} +(-2.56167 + 0.661696i) q^{91} +(-3.18171 + 5.51089i) q^{92} +(-4.99340 - 4.85770i) q^{93} +10.5181 q^{94} +3.66537 q^{95} +(6.79089 + 6.60634i) q^{96} +(8.73516 - 15.1297i) q^{97} +(5.51779 + 3.31981i) q^{98} +(2.27623 - 1.39916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{2} + 96 q^{4} - 4 q^{5} + 6 q^{6} - 36 q^{8} - 8 q^{9}+O(q^{10}) $ 96 * q - 12 * q^2 + 96 * q^4 - 4 * q^5 + 6 * q^6 - 36 * q^8 - 8 * q^9	$ 96 q - 12 q^{2} + 96 q^{4} - 4 q^{5} + 6 q^{6} - 36 q^{8} - 8 q^{9} + 20 q^{11} - 15 q^{12} + 48 q^{13} + 7 q^{14} + 96 q^{16} - 3 q^{17} + 5 q^{18} - 12 q^{20} + 29 q^{23} - 2 q^{24} - 48 q^{25} - 6 q^{26} + 30 q^{28} + 10 q^{29} + 39 q^{30} - 18 q^{31} - 134 q^{32} - 16 q^{35} - 48 q^{36} - 6 q^{37} - 15 q^{38} - 12 q^{41} - 85 q^{42} + 29 q^{44} - 13 q^{45} - 6 q^{46} + 30 q^{47} - 86 q^{48} + 6 q^{49} + 2 q^{50} + 5 q^{51} + 48 q^{52} + 50 q^{53} + 19 q^{54} - 36 q^{55} + 22 q^{56} + 55 q^{57} + 6 q^{58} + 70 q^{59} - 35 q^{60} + 12 q^{61} - 38 q^{62} + 70 q^{63} + 96 q^{64} - 8 q^{65} - 71 q^{66} + 9 q^{68} + 50 q^{69} - 58 q^{71} + 6 q^{72} + 80 q^{74} - 34 q^{75} + q^{77} + 3 q^{78} - 12 q^{79} - 60 q^{80} - 24 q^{81} - 30 q^{82} - 34 q^{83} + 76 q^{84} + 27 q^{85} + 50 q^{86} + 20 q^{87} - 29 q^{89} - 43 q^{90} + 63 q^{92} + 25 q^{93} + 24 q^{94} - 132 q^{95} - 4 q^{96} - 64 q^{98} - 67 q^{99}+O(q^{100}) $ 96 * q - 12 * q^2 + 96 * q^4 - 4 * q^5 + 6 * q^6 - 36 * q^8 - 8 * q^9 + 20 * q^11 - 15 * q^12 + 48 * q^13 + 7 * q^14 + 96 * q^16 - 3 * q^17 + 5 * q^18 - 12 * q^20 + 29 * q^23 - 2 * q^24 - 48 * q^25 - 6 * q^26 + 30 * q^28 + 10 * q^29 + 39 * q^30 - 18 * q^31 - 134 * q^32 - 16 * q^35 - 48 * q^36 - 6 * q^37 - 15 * q^38 - 12 * q^41 - 85 * q^42 + 29 * q^44 - 13 * q^45 - 6 * q^46 + 30 * q^47 - 86 * q^48 + 6 * q^49 + 2 * q^50 + 5 * q^51 + 48 * q^52 + 50 * q^53 + 19 * q^54 - 36 * q^55 + 22 * q^56 + 55 * q^57 + 6 * q^58 + 70 * q^59 - 35 * q^60 + 12 * q^61 - 38 * q^62 + 70 * q^63 + 96 * q^64 - 8 * q^65 - 71 * q^66 + 9 * q^68 + 50 * q^69 - 58 * q^71 + 6 * q^72 + 80 * q^74 - 34 * q^75 + q^77 + 3 * q^78 - 12 * q^79 - 60 * q^80 - 24 * q^81 - 30 * q^82 - 34 * q^83 + 76 * q^84 + 27 * q^85 + 50 * q^86 + 20 * q^87 - 29 * q^89 - 43 * q^90 + 63 * q^92 + 25 * q^93 + 24 * q^94 - 132 * q^95 - 4 * q^96 - 64 * q^98 - 67 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.919929			−0.650488			−0.325244	−	0.945630i	$-0.605446\pi$
$2$	−0.919929			−0.650488			−0.325244	+	0.945630i	$0.605446\pi$
$3$	−1.24150	−	1.20776i	−0.716779	−	0.697300i
$3$	−1.24150	−	1.20776i	−0.716779	−	0.697300i
$4$	−1.15373			−0.576866
$5$	−1.17586	+	2.03665i	−0.525861	+	0.910817i	0.473686	+	0.880694i	$0.342923\pi$
$5$	−1.17586	+	2.03665i	−0.525861	+	0.910817i	−0.999546	+	0.0301233i	$0.990410\pi$
$6$	1.14209	+	1.11105i	0.466256	+	0.453585i
$7$	−0.707790	+	2.54932i	−0.267520	+	0.963552i
$7$	−0.707790	+	2.54932i	−0.267520	+	0.963552i
$8$	2.90121			1.02573
$9$	0.0826321	+	2.99886i	0.0275440	+	0.999621i
$10$	1.08171	−	1.87357i	0.342066	−	0.592475i
$11$	−0.445310	−	0.771300i	−0.134266	−	0.232556i	0.791051	−	0.611751i	$-0.209534\pi$
$11$	−0.445310	−	0.771300i	−0.134266	−	0.232556i	−0.925317	+	0.379195i	$0.876201\pi$
$12$	1.43235	+	1.39343i	0.413485	+	0.402249i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	0.651117	−	2.34519i	0.174018	−	0.626779i
$15$	3.91961	−	1.10834i	1.01204	−	0.286172i
$16$	−0.361441			−0.0903603
$17$	−2.19130	+	3.79544i	−0.531467	+	0.920528i	0.467858	+	0.883804i	$0.345026\pi$
$17$	−2.19130	+	3.79544i	−0.531467	+	0.920528i	−0.999325	+	0.0367249i	$0.988307\pi$
$18$	−0.0760156	−	2.75874i	−0.0179171	−	0.650241i
$19$	−0.779295	−	1.34978i	−0.178783	−	0.309661i	0.762681	−	0.646775i	$-0.223883\pi$
$19$	−0.779295	−	1.34978i	−0.178783	−	0.309661i	−0.941464	+	0.337114i	$0.890549\pi$
$20$	1.35663	−	2.34975i	0.303351	−	0.525419i
$21$	3.95769	−	2.31013i	0.863638	−	0.504112i
$22$	0.409654	+	0.709541i	0.0873385	+	0.151275i
$23$	2.75776	−	4.77658i	0.575032	−	0.995985i	−0.421006	−	0.907058i	$-0.638323\pi$
$23$	2.75776	−	4.77658i	0.575032	−	0.995985i	0.996038	−	0.0889274i	$-0.0283439\pi$
$24$	−3.60184	−	3.50396i	−0.735223	−	0.715243i
$25$	−0.265294	−	0.459503i	−0.0530588	−	0.0919005i
$26$	−0.459964	−	0.796682i	−0.0902064	−	0.156242i
$27$	3.51932	−	3.82288i	0.677293	−	0.735713i
$28$	0.816600	−	2.94123i	0.154323	−	0.555840i
$29$	−5.11053	+	8.85169i	−0.949001	+	1.64372i	−0.201466	+	0.979496i	$0.564571\pi$
$29$	−5.11053	+	8.85169i	−0.949001	+	1.64372i	−0.747535	+	0.664222i	$0.768763\pi$
$30$	−3.60576	+	1.01959i	−0.658319	+	0.186151i
$31$	4.02208			0.722387			0.361193	−	0.932491i	$-0.382369\pi$
$31$	4.02208			0.722387			0.361193	+	0.932491i	$0.382369\pi$
$32$	−5.46992			−0.966954
$33$	−0.378694	+	1.49540i	−0.0659221	+	0.260315i
$34$	2.01584	−	3.49153i	0.345713	−	0.598793i
$35$	−4.35981	−	4.43916i	−0.736942	−	0.750356i
$36$	−0.0953353	−	3.45988i	−0.0158892	−	0.576647i
$37$	0.764675	+	1.32446i	0.125712	+	0.217739i	0.922011	−	0.387164i	$-0.126545\pi$
$37$	0.764675	+	1.32446i	0.125712	+	0.217739i	−0.796299	+	0.604903i	$0.793212\pi$
$38$	0.716896	+	1.24170i	0.116296	+	0.201430i
$39$	0.425202	−	1.67905i	0.0680868	−	0.268863i
$40$	−3.41141	+	5.90874i	−0.539392	+	0.934254i
$41$	−4.06327	−	7.03779i	−0.634576	−	1.09912i	−0.986605	−	0.163129i	$-0.947841\pi$
$41$	−4.06327	−	7.03779i	−0.634576	−	1.09912i	0.352029	−	0.935989i	$-0.385492\pi$
$42$	−3.64079	+	2.12516i	−0.561786	+	0.327919i
$43$	1.78818	−	3.09722i	0.272695	−	0.472321i	−0.696856	−	0.717211i	$-0.745418\pi$
$43$	1.78818	−	3.09722i	0.272695	−	0.472321i	0.969551	+	0.244890i	$0.0787518\pi$
$44$	0.513768	+	0.889873i	0.0774535	+	0.134153i
$45$	−6.20479	−	3.35795i	−0.924956	−	0.500574i
$46$	−2.53694	+	4.39411i	−0.374052	+	0.647876i
$47$	−11.4336			−1.66777			−0.833883	−	0.551941i	$-0.813887\pi$
$47$	−11.4336			−1.66777			−0.833883	+	0.551941i	$0.813887\pi$
$48$	0.448728	+	0.436534i	0.0647683	+	0.0630083i
$49$	−5.99807	−	3.60877i	−0.856867	−	0.515538i
$50$	0.244051	+	0.422710i	0.0345141	+	0.0597802i
$51$	7.30446	−	2.06547i	1.02283	−	0.289223i
$52$	−0.576866	−	0.999161i	−0.0799969	−	0.138559i
$53$	2.34007	−	4.05312i	0.321433	−	0.556739i	−0.659351	−	0.751835i	$-0.729169\pi$
$53$	2.34007	−	4.05312i	0.321433	−	0.556739i	0.980784	+	0.195097i	$0.0625021\pi$
$54$	−3.23752	+	3.51678i	−0.440571	+	0.478573i
$55$	2.09449			0.282421
$56$	−2.05345	+	7.39611i	−0.274403	+	0.988346i
$57$	−0.662716	+	2.61695i	−0.0877789	+	0.346623i
$58$	4.70132	−	8.14292i	0.617313	−	1.06922i
$59$	−8.55287			−1.11349			−0.556744	−	0.830684i	$-0.687950\pi$
$59$	−8.55287			−1.11349			−0.556744	+	0.830684i	$0.687950\pi$
$60$	−4.52218	+	1.27872i	−0.583811	+	0.165083i
$61$	−0.502618			−0.0643536			−0.0321768	−	0.999482i	$-0.510244\pi$
$61$	−0.502618			−0.0643536			−0.0321768	+	0.999482i	$0.510244\pi$
$62$	−3.70002			−0.469904
$63$	−7.70354	−	1.91191i	−0.970555	−	0.240878i
$64$	5.75481			0.719352
$65$	−2.35172			−0.291695
$66$	0.348371	−	1.37566i	0.0428815	−	0.169332i
$67$	−5.53222			−0.675868			−0.337934	−	0.941170i	$-0.609728\pi$
$67$	−5.53222			−0.675868			−0.337934	+	0.941170i	$0.609728\pi$
$68$	2.52817	−	4.37891i	0.306585	−	0.531021i
$69$	−9.19271	+	2.59940i	−1.10667	+	0.312931i
$70$	4.01071	+	4.08371i	0.479372	+	0.488097i
$71$	1.96645			0.233375			0.116687	−	0.993169i	$-0.462772\pi$
$71$	1.96645			0.233375			0.116687	+	0.993169i	$0.462772\pi$
$72$	0.239733	+	8.70032i	0.0282528	+	1.02534i
$73$	−2.12101	+	3.67370i	−0.248246	+	0.429974i	−0.963039	−	0.269362i	$-0.913187\pi$
$73$	−2.12101	+	3.67370i	−0.248246	+	0.429974i	0.714794	+	0.699336i	$0.246521\pi$
$74$	−0.703447	−	1.21841i	−0.0817740	−	0.141637i
$75$	−0.225607	+	0.890883i	−0.0260509	+	0.102870i
$76$	0.899097	+	1.55728i	0.103134	+	0.178633i
$77$	2.28148	−	0.589320i	0.259998	−	0.0671592i
$78$	−0.391155	+	1.54460i	−0.0442896	+	0.174892i
$79$	1.68564			0.189649			0.0948245	−	0.995494i	$-0.469771\pi$
$79$	1.68564			0.189649			0.0948245	+	0.995494i	$0.469771\pi$
$80$	0.425004	−	0.736129i	0.0475169	−	0.0823017i
$81$	−8.98634	+	0.495605i	−0.998483	+	0.0550672i
$82$	3.73792	+	6.47426i	0.412784	+	0.714963i
$83$	−7.20538	+	12.4801i	−0.790893	+	1.36987i	0.134521	+	0.990911i	$0.457050\pi$
$83$	−7.20538	+	12.4801i	−0.790893	+	1.36987i	−0.925415	+	0.378956i	$0.876283\pi$
$84$	−4.56611	+	2.66527i	−0.498203	+	0.290805i
$85$	−5.15332	−	8.92580i	−0.558956	−	0.968139i
$86$	−1.64500	+	2.84922i	−0.177385	+	0.307239i
$87$	17.0354	−	4.81706i	1.82639	−	0.516443i
$88$	−1.29194	−	2.23770i	−0.137721	−	0.238540i
$89$	−1.05501	−	1.82733i	−0.111831	−	0.193697i	0.804678	−	0.593712i	$-0.202338\pi$
$89$	−1.05501	−	1.82733i	−0.111831	−	0.193697i	−0.916508	+	0.400015i	$0.869005\pi$
$90$	5.70797	+	3.08907i	0.601673	+	0.325617i
$91$	−2.56167	+	0.661696i	−0.268536	+	0.0693645i
$92$	−3.18171	+	5.51089i	−0.331717	+	0.574550i
$93$	−4.99340	−	4.85770i	−0.517791	−	0.503720i
$94$	10.5181			1.08486
$95$	3.66537			0.376059
$96$	6.79089	+	6.60634i	0.693092	+	0.674257i
$97$	8.73516	−	15.1297i	0.886922	−	1.53619i	0.0434264	−	0.999057i	$-0.486173\pi$
$97$	8.73516	−	15.1297i	0.886922	−	1.53619i	0.843495	−	0.537137i	$-0.180494\pi$
$98$	5.51779	+	3.31981i	0.557381	+	0.335351i
$99$	2.27623	−	1.39916i	0.228769	−	0.140621i
$100$	0.306078	+	0.530143i	0.0306078	+	0.0530143i
$101$	−0.653537	−	1.13196i	−0.0650293	−	0.112634i	0.831678	−	0.555259i	$-0.187381\pi$
$101$	−0.653537	−	1.13196i	−0.0650293	−	0.112634i	−0.896707	+	0.442625i	$0.854047\pi$
$102$	−6.71959	+	1.90008i	−0.665338	+	0.188136i
$103$	8.08413	−	14.0021i	0.796553	−	1.37967i	−0.125295	−	0.992119i	$-0.539988\pi$
$103$	8.08413	−	14.0021i	0.796553	−	1.37967i	0.921848	−	0.387551i	$-0.126679\pi$
$104$	1.45060	+	2.51252i	0.142243	+	0.246373i
$105$	0.0512468	+	10.7768i	0.00500117	+	1.05171i
$106$	−2.15270	+	3.72858i	−0.209088	+	0.362152i
$107$	−7.76899	−	13.4563i	−0.751057	−	1.30087i	−0.947311	−	0.320315i	$-0.896211\pi$
$107$	−7.76899	−	13.4563i	−0.751057	−	1.30087i	0.196254	−	0.980553i	$-0.437122\pi$
$108$	−4.06035	+	4.41058i	−0.390707	+	0.424408i
$109$	6.35039	−	10.9992i	0.608257	−	1.05353i	−0.383270	−	0.923636i	$-0.625202\pi$
$109$	6.35039	−	10.9992i	0.608257	−	1.05353i	0.991528	−	0.129896i	$-0.0414645\pi$
$110$	−1.92678			−0.183711
$111$	0.650283	−	2.56785i	0.0617221	−	0.243730i
$112$	0.255824	−	0.921429i	0.0241731	−	0.0870668i
$113$	0.422841	+	0.732382i	0.0397775	+	0.0688967i	0.885229	−	0.465156i	$-0.154002\pi$
$113$	0.422841	+	0.732382i	0.0397775	+	0.0688967i	−0.845451	+	0.534053i	$0.820668\pi$
$114$	0.609651	−	2.40741i	0.0570991	−	0.225474i
$115$	6.48548	+	11.2332i	0.604774	+	1.04750i
$116$	5.89618	−	10.2125i	0.547446	−	0.948204i
$117$	−2.55577	+	1.57099i	−0.236281	+	0.145238i
$118$	7.86803			0.724311
$119$	−8.12480	−	8.27269i	−0.744800	−	0.758356i
$120$	11.3716	−	3.21552i	1.03808	−	0.293535i
$121$	5.10340	−	8.83934i	0.463945	−	0.803577i
$122$	0.462373			0.0418612
$123$	−3.45542	+	13.6449i	−0.311565	+	1.23031i
$124$	−4.64040			−0.416720
$125$	−10.5108			−0.940115
$126$	7.08671	+	1.75882i	0.631334	+	0.156688i
$127$	16.0121			1.42085			0.710424	−	0.703774i	$-0.248503\pi$
$127$	16.0121			1.42085			0.710424	+	0.703774i	$0.248503\pi$
$128$	5.64581			0.499024
$129$	−5.96071	+	1.68550i	−0.524811	+	0.148400i
$130$	2.16341			0.189744
$131$	1.70539	−	2.95383i	0.149001	−	0.258077i	−0.781858	−	0.623457i	$-0.785728\pi$
$131$	1.70539	−	2.95383i	0.149001	−	0.258077i	0.930858	+	0.365380i	$0.119061\pi$
$132$	0.436911	−	1.72528i	0.0380282	−	0.150167i
$133$	3.99260	−	1.03131i	0.346202	−	0.0894261i
$134$	5.08925			0.439644
$135$	3.64764	+	11.6628i	0.313939	+	1.00377i
$136$	−6.35741	+	11.0113i	−0.545143	+	0.944215i
$137$	1.49365	+	2.58708i	0.127611	+	0.221029i	0.922751	−	0.385397i	$-0.125936\pi$
$137$	1.49365	+	2.58708i	0.127611	+	0.221029i	−0.795139	+	0.606427i	$0.792602\pi$
$138$	8.45664	−	2.39126i	0.719877	−	0.203558i
$139$	9.36789	+	16.2257i	0.794574	+	1.37624i	0.923109	+	0.384538i	$0.125639\pi$
$139$	9.36789	+	16.2257i	0.794574	+	1.37624i	−0.128535	+	0.991705i	$0.541027\pi$
$140$	5.03005	+	5.12160i	0.425117	+	0.432855i
$141$	14.1948	+	13.8091i	1.19542	+	1.16293i
$142$	−1.80899			−0.151807
$143$	0.445310	−	0.771300i	0.0372387	−	0.0644994i
$144$	−0.0298666	−	1.08391i	−0.00248889	−	0.0903260i
$145$	−12.0185	−	20.8167i	−0.998084	−	1.72873i
$146$	1.95118	−	3.37954i	0.161481	−	0.279693i
$147$	3.08806	+	11.7245i	0.254699	+	0.967020i
$148$	−0.882230	−	1.52807i	−0.0725188	−	0.125606i
$149$	5.53043	−	9.57898i	0.453070	−	0.784741i	−0.545505	−	0.838108i	$-0.683662\pi$
$149$	5.53043	−	9.57898i	0.453070	−	0.784741i	0.998575	+	0.0533670i	$0.0169953\pi$
$150$	0.207542	−	0.819548i	0.0169458	−	0.0669158i
$151$	1.45712	+	2.52380i	0.118579	+	0.205384i	0.919205	−	0.393780i	$-0.128833\pi$
$151$	1.45712	+	2.52380i	0.118579	+	0.205384i	−0.800626	+	0.599164i	$0.795500\pi$
$152$	−2.26090	−	3.91599i	−0.183383	−	0.317629i
$153$	−11.5631	−	6.25777i	−0.934818	−	0.505911i
$154$	−2.09880	+	0.542132i	−0.169126	+	0.0436862i
$155$	−4.72940	+	8.19156i	−0.379875	+	0.657962i
$156$	−0.490569	+	1.93717i	−0.0392769	+	0.155098i
$157$	−17.7381			−1.41565			−0.707827	−	0.706386i	$-0.750324\pi$
$157$	−17.7381			−1.41565			−0.707827	+	0.706386i	$0.750324\pi$
$158$	−1.55067			−0.123364
$159$	−7.80038	+	2.20570i	−0.618611	+	0.174923i
$160$	6.43186	−	11.1403i	0.508483	−	0.880718i
$161$	10.2251	+	10.4112i	0.805852	+	0.820520i
$162$	8.26679	−	0.455921i	0.649501	−	0.0358205i
$163$	−7.43004	−	12.8692i	−0.581965	−	1.00799i	−0.995246	−	0.0973901i	$-0.968951\pi$
$163$	−7.43004	−	12.8692i	−0.581965	−	1.00799i	0.413281	−	0.910604i	$-0.364383\pi$
$164$	4.68792	+	8.11972i	0.366065	+	0.634044i
$165$	−2.60030	−	2.52964i	−0.202433	−	0.196932i
$166$	6.62843	−	11.4808i	0.514466	−	0.891082i
$167$	−4.62937	−	8.01830i	−0.358231	−	0.620475i	0.629434	−	0.777054i	$-0.283287\pi$
$167$	−4.62937	−	8.01830i	−0.358231	−	0.620475i	−0.987665	+	0.156579i	$0.949953\pi$
$168$	11.4821	−	6.70218i	0.885861	−	0.517084i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	4.74068	+	8.21110i	0.363594	+	0.629763i
$171$	3.98341	−	2.44853i	0.304619	−	0.187244i
$172$	−2.06308	+	3.57336i	−0.157308	+	0.272466i
$173$	12.7396			0.968576			0.484288	−	0.874909i	$-0.339079\pi$
$173$	12.7396			0.968576			0.484288	+	0.874909i	$0.339079\pi$
$174$	−15.6714	+	4.43136i	−1.18804	+	0.335940i
$175$	1.35919	−	0.351088i	0.102745	−	0.0265397i
$176$	0.160953	+	0.278779i	0.0121323	+	0.0210138i
$177$	10.6184	+	10.3298i	0.798125	+	0.776436i
$178$	0.970533	+	1.68101i	0.0727445	+	0.125997i
$179$	6.42429	−	11.1272i	0.480174	−	0.831685i	−0.519568	−	0.854429i	$-0.673907\pi$
$179$	6.42429	−	11.1272i	0.480174	−	0.831685i	0.999741	+	0.0227440i	$0.00724027\pi$
$180$	7.15867	+	3.87417i	0.533575	+	0.288764i
$181$	−16.6257			−1.23578			−0.617889	−	0.786265i	$-0.712012\pi$
$181$	−16.6257			−1.23578			−0.617889	+	0.786265i	$0.712012\pi$
$182$	2.35655	−	0.608713i	0.174679	−	0.0451208i
$183$	0.623999	+	0.607042i	0.0461273	+	0.0448738i
$184$	8.00083	−	13.8578i	0.589829	−	1.02161i
$185$	−3.59660			−0.264428
$186$	4.59357	+	4.46874i	0.336817	+	0.327664i
$187$	3.90323			0.285432
$188$	13.1913			0.962077
$189$	7.25480	+	11.6777i	0.527709	+	0.849425i
$190$	−3.37188			−0.244622
$191$	6.44280			0.466184			0.233092	−	0.972455i	$-0.425116\pi$
$191$	6.44280			0.466184			0.233092	+	0.972455i	$0.425116\pi$
$192$	−7.14459	−	6.95043i	−0.515616	−	0.501604i
$193$	−18.8240			−1.35498			−0.677491	−	0.735531i	$-0.736933\pi$
$193$	−18.8240			−1.35498			−0.677491	+	0.735531i	$0.736933\pi$
$194$	−8.03573	+	13.9183i	−0.576932	+	0.999275i
$195$	2.91965	+	2.84031i	0.209081	+	0.203399i
$196$	6.92016	+	4.16355i	0.494297	+	0.297396i
$197$	−11.5353			−0.821854			−0.410927	−	0.911668i	$-0.634795\pi$
$197$	−11.5353			−0.821854			−0.410927	+	0.911668i	$0.634795\pi$
$198$	−2.09396	+	1.28713i	−0.148812	+	0.0914720i
$199$	−6.73008	+	11.6568i	−0.477082	+	0.826331i	−0.999655	−	0.0262637i	$-0.991639\pi$
$199$	−6.73008	+	11.6568i	−0.477082	+	0.826331i	0.522573	+	0.852595i	$0.324972\pi$
$200$	−0.769673	−	1.33311i	−0.0544241	−	0.0942653i
$201$	6.86824	+	6.68160i	0.484448	+	0.471283i
$202$	0.601207	+	1.04132i	0.0423008	+	0.0732671i
$203$	−18.9486	−	19.2935i	−1.32993	−	1.35414i
$204$	−8.42739	+	2.38299i	−0.590035	+	0.166843i
$205$	19.1113			1.33479
$206$	−7.43682	+	12.8810i	−0.518148	+	0.897459i
$207$	14.5522	+	7.87544i	1.01145	+	0.547381i
$208$	−0.180721	−	0.313017i	−0.0125307	−	0.0217038i
$209$	−0.694056	+	1.20214i	−0.0480089	+	0.0831538i
$210$	−0.0471434	−	9.91390i	−0.00325320	−	0.684124i
$211$	9.86569	+	17.0879i	0.679182	+	1.17638i	0.975228	+	0.221204i	$0.0709985\pi$
$211$	9.86569	+	17.0879i	0.679182	+	1.17638i	−0.296046	+	0.955174i	$0.595668\pi$
$212$	−2.69981	+	4.67621i	−0.185424	+	0.321163i
$213$	−2.44134	−	2.37500i	−0.167278	−	0.162732i
$214$	7.14692	+	12.3788i	0.488553	+	0.846199i
$215$	4.20530	+	7.28378i	0.286799	+	0.496750i
$216$	10.2103	−	11.0910i	0.694721	−	0.754645i
$217$	−2.84679	+	10.2536i	−0.193253	+	0.696057i
$218$	−5.84191	+	10.1185i	−0.395664	+	0.685310i
$219$	7.07017	−	1.99922i	0.477758	−	0.135094i
$220$	−2.41648			−0.162919
$221$	−4.38259			−0.294805
$222$	−0.598214	+	2.36224i	−0.0401495	+	0.158543i
$223$	8.88991	−	15.3978i	0.595312	−	1.03111i	−0.398190	−	0.917303i	$-0.630362\pi$
$223$	8.88991	−	15.3978i	0.595312	−	1.03111i	0.993503	−	0.113808i	$-0.0363050\pi$
$224$	3.87155	−	13.9446i	0.258679	−	0.931710i
$225$	1.35606	−	0.833549i	0.0904042	−	0.0555700i
$226$	−0.388983	−	0.673739i	−0.0258748	−	0.0448165i
$227$	−4.24327	−	7.34955i	−0.281635	−	0.487807i	0.690152	−	0.723664i	$-0.257544\pi$
$227$	−4.24327	−	7.34955i	−0.281635	−	0.487807i	−0.971788	+	0.235857i	$0.924210\pi$
$228$	0.764596	−	3.01926i	0.0506366	−	0.199955i
$229$	−14.8011	+	25.6362i	−0.978082	+	1.69409i	−0.308715	+	0.951154i	$0.599899\pi$
$229$	−14.8011	+	25.6362i	−0.978082	+	1.69409i	−0.669366	+	0.742933i	$0.733434\pi$
$230$	−5.96618	−	10.3337i	−0.393398	−	0.681385i
$231$	−3.54420	−	2.02384i	−0.233192	−	0.133159i
$232$	−14.8267	+	25.6806i	−0.973420	+	1.68601i
$233$	−1.03609	−	1.79456i	−0.0678765	−	0.117566i	0.830090	−	0.557630i	$-0.188289\pi$
$233$	−1.03609	−	1.79456i	−0.0678765	−	0.117566i	−0.897966	+	0.440064i	$0.854956\pi$
$234$	2.35113	−	1.44520i	0.153698	−	0.0944757i
$235$	13.4444	−	23.2863i	0.877013	−	1.51903i
$236$	9.86771			0.642333
$237$	−2.09271	−	2.03585i	−0.135936	−	0.132242i
$238$	7.47424	+	7.61028i	0.484483	+	0.493301i
$239$	13.8948	+	24.0664i	0.898777	+	1.55673i	0.829059	+	0.559160i	$0.188876\pi$
$239$	13.8948	+	24.0664i	0.898777	+	1.55673i	0.0697174	+	0.997567i	$0.477790\pi$
$240$	−1.41671	+	0.400599i	−0.0914481	+	0.0258586i
$241$	−0.0439378	−	0.0761025i	−0.00283028	−	0.00490219i	0.864607	−	0.502449i	$-0.167568\pi$
$241$	−0.0439378	−	0.0761025i	−0.00283028	−	0.00490219i	−0.867437	+	0.497547i	$0.834234\pi$
$242$	−4.69476	+	8.13156i	−0.301791	+	0.522717i
$243$	11.7551	+	10.2381i	0.754090	+	0.656771i
$244$	0.579886			0.0371234
$245$	14.4027	−	7.97255i	0.920154	−	0.509348i
$246$	3.17874	−	12.5523i	0.202669	−	0.800305i
$247$	0.779295	−	1.34978i	0.0495854	−	0.0858844i
$248$	11.6689			0.740975
$249$	24.0184	−	6.79162i	1.52210	−	0.430402i
$250$	9.66919			0.611533
$251$	−18.7552			−1.18382			−0.591909	−	0.806005i	$-0.701626\pi$
$251$	−18.7552			−1.18382			−0.591909	+	0.806005i	$0.701626\pi$
$252$	8.88782	+	2.20583i	0.559880	+	0.138954i
$253$	−4.91223			−0.308829
$254$	−14.7300			−0.924244
$255$	−4.38240	+	17.3053i	−0.274437	+	1.08370i
$256$	−16.7034			−1.04396
$257$	0.891933	−	1.54487i	0.0556372	−	0.0963665i	−0.836865	−	0.547409i	$-0.815614\pi$
$257$	0.891933	−	1.54487i	0.0556372	−	0.0963665i	0.892503	+	0.451042i	$0.148948\pi$
$258$	5.48343	−	1.55054i	0.341383	−	0.0965321i
$259$	−3.91769	+	1.01196i	−0.243434	+	0.0628804i
$260$	2.71325			0.168269
$261$	−26.9673	−	14.5943i	−1.66923	−	0.903366i
$262$	−1.56884	+	2.71731i	−0.0969232	+	0.167876i
$263$	−6.77617	−	11.7367i	−0.417836	−	0.723714i	0.577885	−	0.816118i	$-0.303878\pi$
$263$	−6.77617	−	11.7367i	−0.417836	−	0.723714i	−0.995722	+	0.0924042i	$0.970545\pi$
$264$	−1.09867	+	4.33845i	−0.0676184	+	0.267013i
$265$	5.50319	+	9.53180i	0.338058	+	0.585534i
$266$	−3.67290	+	0.948734i	−0.225200	+	0.0581706i
$267$	−0.897184	+	3.54282i	−0.0549068	+	0.216817i
$268$	6.38270			0.389885
$269$	−4.30637	+	7.45885i	−0.262564	+	0.454774i	−0.966923	−	0.255070i	$-0.917901\pi$
$269$	−4.30637	+	7.45885i	−0.262564	+	0.454774i	0.704359	+	0.709844i	$0.251235\pi$
$270$	−3.35557	−	10.7289i	−0.204213	−	0.652942i
$271$	10.5155	+	18.2133i	0.638768	+	1.10638i	0.985703	+	0.168490i	$0.0538890\pi$
$271$	10.5155	+	18.2133i	0.638768	+	1.10638i	−0.346935	+	0.937889i	$0.612778\pi$
$272$	0.792024	−	1.37183i	0.0480235	−	0.0831792i
$273$	3.97948	+	2.27239i	0.240849	+	0.137531i
$274$	−1.37405	−	2.37993i	−0.0830096	−	0.143777i
$275$	−0.236276	+	0.409242i	−0.0142480	+	0.0246782i
$276$	10.6059	−	2.99901i	0.638401	−	0.180519i
$277$	1.16337	+	2.01502i	0.0699002	+	0.121071i	0.898857	−	0.438242i	$-0.144399\pi$
$277$	1.16337	+	2.01502i	0.0699002	+	0.121071i	−0.828957	+	0.559312i	$0.811065\pi$
$278$	−8.61779	−	14.9265i	−0.516861	−	0.895229i
$279$	0.332353	+	12.0617i	0.0198974	+	0.722112i
$280$	−12.6487	−	12.8789i	−0.755905	−	0.769664i
$281$	−6.43733	+	11.1498i	−0.384019	+	0.665140i	−0.991633	−	0.129093i	$-0.958794\pi$
$281$	−6.43733	+	11.1498i	−0.384019	+	0.665140i	0.607614	+	0.794233i	$0.292127\pi$
$282$	−13.0582	−	12.7034i	−0.777606	−	0.756475i
$283$	−29.0249			−1.72535			−0.862674	−	0.505760i	$-0.831212\pi$
$283$	−29.0249			−1.72535			−0.862674	+	0.505760i	$0.831212\pi$
$284$	−2.26876			−0.134626
$285$	−4.55055	−	4.42689i	−0.269551	−	0.262226i
$286$	−0.409654	+	0.709541i	−0.0242233	+	0.0419560i
$287$	20.8175	−	5.37730i	1.22882	−	0.317412i
$288$	−0.451991	−	16.4035i	−0.0266338	−	0.966587i
$289$	−1.10356	−	1.91142i	−0.0649151	−	0.112436i
$290$	11.0562	+	19.1499i	0.649242	+	1.12452i
$291$	−29.1178	+	8.23356i	−1.70692	+	0.482660i
$292$	2.44708	−	4.23846i	0.143204	−	0.248037i
$293$	−2.02365	−	3.50506i	−0.118223	−	0.204768i	0.800841	−	0.598878i	$-0.204386\pi$
$293$	−2.02365	−	3.50506i	−0.118223	−	0.204768i	−0.919063	+	0.394110i	$0.871053\pi$
$294$	−2.84079	−	10.7857i	−0.165678	−	0.629035i
$295$	10.0570	−	17.4192i	0.585540	−	1.01418i
$296$	2.21848	+	3.84252i	0.128947	+	0.223342i
$297$	−4.51578	−	1.01208i	−0.262032	−	0.0587270i
$298$	−5.08760	+	8.81198i	−0.294717	+	0.510464i
$299$	5.51552			0.318971
$300$	0.260290	−	1.02784i	0.0150278	−	0.0593423i
$301$	6.63014	+	6.75082i	0.382155	+	0.389111i
$302$	−1.34045	−	2.32172i	−0.0771340	−	0.133600i
$303$	−0.555770	+	2.19464i	−0.0319282	+	0.126079i
$304$	0.281669	+	0.487865i	0.0161548	+	0.0279810i
$305$	0.591008	−	1.02366i	0.0338410	−	0.0586144i
$306$	10.6372	+	5.75670i	0.608088	+	0.329089i
$307$	−4.60984			−0.263098			−0.131549	−	0.991310i	$-0.541995\pi$
$307$	−4.60984			−0.263098			−0.131549	+	0.991310i	$0.541995\pi$
$308$	−2.63221	+	0.679917i	−0.149984	+	0.0387418i
$309$	−26.9476	+	7.61991i	−1.53300	+	0.433482i
$310$	4.35071	−	7.53565i	0.247104	−	0.427996i
$311$	5.48641			0.311106			0.155553	−	0.987828i	$-0.450284\pi$
$311$	5.48641			0.311106			0.155553	+	0.987828i	$0.450284\pi$
$312$	1.23360	−	4.87127i	0.0698388	−	0.275781i
$313$	−14.5615			−0.823063			−0.411532	−	0.911395i	$-0.635006\pi$
$313$	−14.5615			−0.823063			−0.411532	+	0.911395i	$0.635006\pi$
$314$	16.3178			0.920865
$315$	12.9522	−	13.4413i	0.729773	−	0.757330i
$316$	−1.94477			−0.109402
$317$	−21.3848			−1.20109			−0.600546	−	0.799590i	$-0.705050\pi$
$317$	−21.3848			−1.20109			−0.600546	+	0.799590i	$0.705050\pi$
$318$	7.17580	−	2.02908i	0.402399	−	0.113785i
$319$	9.10308			0.509675
$320$	−6.76686	+	11.7205i	−0.378279	+	0.655198i
$321$	−6.60678	+	26.0890i	−0.368755	+	1.45615i
$322$	−9.40637	−	9.57758i	−0.524197	−	0.533738i
$323$	6.83067			0.380068
$324$	10.3678	−	0.571795i	0.575990	−	0.0317664i
$325$	0.265294	−	0.459503i	0.0147159	−	0.0254886i
$326$	6.83510	+	11.8387i	0.378561	+	0.655688i
$327$	−21.1684	+	5.98573i	−1.17061	+	0.331012i
$328$	−11.7884	−	20.4181i	−0.650905	−	1.12740i
$329$	8.09262	−	29.1480i	0.446160	−	1.60698i
$330$	2.39209	+	2.32709i	0.131680	+	0.128102i
$331$	6.84026			0.375975			0.187987	−	0.982171i	$-0.439804\pi$
$331$	6.84026			0.375975			0.187987	+	0.982171i	$0.439804\pi$
$332$	8.31307	−	14.3987i	0.456239	−	0.790229i
$333$	−3.90867	+	2.40260i	−0.214194	+	0.131662i
$334$	4.25869	+	7.37626i	0.233025	+	0.403611i
$335$	6.50512	−	11.2672i	0.355413	−	0.615593i
$336$	−1.43047	+	0.834977i	−0.0780385	+	0.0455517i
$337$	−2.40428	−	4.16433i	−0.130969	−	0.226845i	0.793081	−	0.609116i	$-0.208476\pi$
$337$	−2.40428	−	4.16433i	−0.130969	−	0.226845i	−0.924050	+	0.382271i	$0.875142\pi$
$338$	0.459964	−	0.796682i	0.0250188	−	0.0433338i
$339$	0.359586	−	1.41994i	0.0195300	−	0.0771206i
$340$	5.94554	+	10.2980i	0.322442	+	0.558486i
$341$	−1.79107	−	3.10223i	−0.0969920	−	0.167995i
$342$	−3.66445	+	2.25248i	−0.198151	+	0.121800i
$343$	13.4453	−	12.7367i	0.725977	−	0.687719i
$344$	5.18788	−	8.98567i	0.279712	−	0.484475i
$345$	5.51528	−	21.7789i	0.296932	−	1.17253i
$346$	−11.7195			−0.630047
$347$	12.5502			0.673732			0.336866	−	0.941553i	$-0.390633\pi$
$347$	12.5502			0.673732			0.336866	+	0.941553i	$0.390633\pi$
$348$	−19.6543	+	5.55760i	−1.05358	+	0.297919i
$349$	−7.59288	+	13.1513i	−0.406438	+	0.703971i	−0.994488	−	0.104854i	$-0.966563\pi$
$349$	−7.59288	+	13.1513i	−0.406438	+	0.703971i	0.588050	+	0.808825i	$0.299896\pi$
$350$	−1.25036	+	0.322976i	−0.0668345	+	0.0172638i
$351$	5.07037	+	1.13638i	0.270636	+	0.0606554i
$352$	2.43581	+	4.21895i	0.129829	+	0.224871i
$353$	3.11778	+	5.40015i	0.165943	+	0.287421i	0.936990	−	0.349357i	$-0.113600\pi$
$353$	3.11778	+	5.40015i	0.165943	+	0.287421i	−0.771047	+	0.636778i	$0.780267\pi$
$354$	−9.76813	−	9.50269i	−0.519171	−	0.505062i
$355$	−2.31227	+	4.00497i	−0.122723	+	0.212562i
$356$	1.21720	+	2.10825i	0.0645113	+	0.111737i
$357$	0.0955018	+	20.0833i	0.00505449	+	1.06292i
$358$	−5.90989	+	10.2362i	−0.312347	+	0.541001i
$359$	3.87141	+	6.70548i	0.204325	+	0.353902i	0.949918	−	0.312501i	$-0.101167\pi$
$359$	3.87141	+	6.70548i	0.204325	+	0.353902i	−0.745592	+	0.666402i	$0.767833\pi$
$360$	−18.0014	−	9.74211i	−0.948757	−	0.513454i
$361$	8.28540	−	14.3507i	0.436074	−	0.755302i
$362$	15.2945			0.803859
$363$	−17.0117	+	4.81034i	−0.892881	+	0.252478i
$364$	2.95548	−	0.763419i	0.154909	−	0.0400140i
$365$	−4.98802	−	8.63951i	−0.261085	−	0.452213i
$366$	−0.574034	−	0.558435i	−0.0300053	−	0.0291899i
$367$	−2.27090	−	3.93331i	−0.118540	−	0.205317i	0.800649	−	0.599133i	$-0.204488\pi$
$367$	−2.27090	−	3.93331i	−0.118540	−	0.205317i	−0.919189	+	0.393816i	$0.871155\pi$
$368$	−0.996767	+	1.72645i	−0.0519601	+	0.0899975i
$369$	20.7696	−	12.7667i	1.08122	−	0.664610i
$370$	3.30862			0.172007
$371$	8.67642	+	8.83434i	0.450457	+	0.458656i
$372$	5.76104	+	5.60449i	0.298696	+	0.290579i
$373$	6.12636	−	10.6112i	0.317211	−	0.549425i	−0.662694	−	0.748890i	$-0.730587\pi$
$373$	6.12636	−	10.6112i	0.317211	−	0.549425i	0.979905	+	0.199465i	$0.0639204\pi$
$374$	−3.59069			−0.185670
$375$	13.0491	+	12.6945i	0.673855	+	0.655543i
$376$	−33.1713			−1.71068
$377$	−10.2211			−0.526411
$378$	−6.67390	−	10.7426i	−0.343268	−	0.552541i
$379$	8.36007			0.429428			0.214714	−	0.976677i	$-0.431118\pi$
$379$	8.36007			0.429428			0.214714	+	0.976677i	$0.431118\pi$
$380$	−4.22885			−0.216935
$381$	−19.8790	−	19.3388i	−1.01843	−	0.990758i
$382$	−5.92691			−0.303247
$383$	3.94634	−	6.83526i	0.201649	−	0.349266i	−0.747411	−	0.664362i	$-0.768703\pi$
$383$	3.94634	−	6.83526i	0.201649	−	0.349266i	0.949060	+	0.315096i	$0.102037\pi$
$384$	−7.00926	−	6.81879i	−0.357690	−	0.347970i
$385$	−1.48246	+	5.33953i	−0.0755532	+	0.272127i
$386$	17.3167			0.881399
$387$	9.43588	+	5.10657i	0.479653	+	0.259582i
$388$	−10.0780	+	17.4557i	−0.511635	+	0.886177i
$389$	−5.96375	−	10.3295i	−0.302374	−	0.523727i	0.674299	−	0.738458i	$-0.264446\pi$
$389$	−5.96375	−	10.3295i	−0.302374	−	0.523727i	−0.976673	+	0.214731i	$0.931112\pi$
$390$	−2.68587	−	2.61289i	−0.136005	−	0.132309i
$391$	12.0861	+	20.9338i	0.611222	+	1.05867i
$392$	−17.4016	−	10.4698i	−0.878915	−	0.528804i
$393$	−5.68475	+	1.60746i	−0.286758	+	0.0810858i
$394$	10.6116			0.534606
$395$	−1.98207	+	3.43305i	−0.0997289	+	0.172736i
$396$	−2.62615	+	1.61425i	−0.131969	+	0.0811193i
$397$	−1.09701	−	1.90008i	−0.0550575	−	0.0953624i	0.837183	−	0.546923i	$-0.184201\pi$
$397$	−1.09701	−	1.90008i	−0.0550575	−	0.0953624i	−0.892241	+	0.451560i	$0.850868\pi$
$398$	6.19119	−	10.7235i	0.310336	−	0.537518i
$399$	−6.20238	−	3.54173i	−0.310507	−	0.177308i
$400$	0.0958881	+	0.166083i	0.00479441	+	0.00830415i
$401$	−14.0427	+	24.3226i	−0.701257	+	1.21461i	0.266768	+	0.963761i	$0.414044\pi$
$401$	−14.0427	+	24.3226i	−0.701257	+	1.21461i	−0.968025	+	0.250853i	$0.919289\pi$
$402$	−6.31829	−	6.14659i	−0.315128	−	0.306564i
$403$	2.01104	+	3.48322i	0.100177	+	0.173512i
$404$	0.754006	+	1.30598i	0.0375132	+	0.0649748i
$405$	9.55731	−	18.8848i	0.474907	−	0.938393i
$406$	17.4314	+	17.7487i	0.865104	+	0.880851i
$407$	0.681036	−	1.17959i	0.0337577	−	0.0584700i
$408$	21.1918	−	5.99234i	1.04915	−	0.296665i
$409$	−33.5146			−1.65719			−0.828596	−	0.559848i	$-0.810860\pi$
$409$	−33.5146			−1.65719			−0.828596	+	0.559848i	$0.810860\pi$
$410$	−17.5811			−0.868267
$411$	1.27021	−	5.01583i	0.0626547	−	0.247413i
$412$	−9.32691	+	16.1547i	−0.459504	+	0.795884i
$413$	6.05364	−	21.8040i	0.297880	−	1.07290i
$414$	−13.3870	−	7.24484i	−0.657933	−	0.356065i
$415$	−16.9450	−	29.3497i	−0.831799	−	1.44072i
$416$	−2.73496	−	4.73709i	−0.134092	−	0.232255i
$417$	7.96650	−	31.4583i	0.390121	−	1.54052i
$418$	0.638482	−	1.10588i	0.0312292	−	0.0540905i
$419$	−17.7237	−	30.6983i	−0.865859	−	1.49971i	−0.866192	−	0.499711i	$-0.833440\pi$
$419$	−17.7237	−	30.6983i	−0.865859	−	1.49971i	0.000333594	−	1.00000i	$-0.499894\pi$
$420$	−0.0591250	−	12.4335i	−0.00288500	−	0.606695i
$421$	6.15206	−	10.6557i	0.299833	−	0.519326i	−0.676264	−	0.736659i	$-0.736402\pi$
$421$	6.15206	−	10.6557i	0.299833	−	0.519326i	0.976098	+	0.217333i	$0.0697356\pi$
$422$	−9.07573	−	15.7196i	−0.441799	−	0.765219i
$423$	−0.944785	−	34.2879i	−0.0459370	−	1.66713i
$424$	6.78903	−	11.7589i	0.329704	−	0.571065i
$425$	2.32535			0.112796
$426$	2.24586	+	2.18483i	0.108812	+	0.105855i
$427$	0.355748	−	1.28133i	0.0172159	−	0.0620081i
$428$	8.96333	+	15.5249i	0.433259	+	0.750426i
$429$	−1.48440	+	0.419739i	−0.0716674	+	0.0202652i
$430$	−3.86857	−	6.70056i	−0.186559	−	0.323130i
$431$	10.9063	−	18.8903i	0.525338	−	0.909912i	−0.474227	−	0.880403i	$-0.657272\pi$
$431$	10.9063	−	18.8903i	0.525338	−	0.909912i	0.999565	−	0.0295091i	$-0.00939441\pi$
$432$	−1.27203	+	1.38175i	−0.0612004	+	0.0664793i
$433$	23.1815			1.11403			0.557017	−	0.830501i	$-0.311946\pi$
$433$	23.1815			1.11403			0.557017	+	0.830501i	$0.311946\pi$
$434$	2.61884	−	9.43255i	0.125708	−	0.452777i
$435$	−10.2206	+	40.3594i	−0.490040	+	1.93508i
$436$	−7.32665	+	12.6901i	−0.350883	+	0.607747i
$437$	−8.59643			−0.411223
$438$	−6.50406	+	1.83914i	−0.310776	+	0.0878773i
$439$	−25.8054			−1.23163			−0.615813	−	0.787893i	$-0.711172\pi$
$439$	−25.8054			−1.23163			−0.615813	+	0.787893i	$0.711172\pi$
$440$	6.07655			0.289688
$441$	10.3266	−	18.2856i	0.491741	−	0.870741i
$442$	4.03167			0.191767
$443$	−15.4278			−0.732999			−0.366499	−	0.930418i	$-0.619444\pi$
$443$	−15.4278			−0.732999			−0.366499	+	0.930418i	$0.619444\pi$
$444$	−0.750252	+	2.96261i	−0.0356054	+	0.140599i
$445$	4.96217			0.235230
$446$	−8.17808	+	14.1649i	−0.387243	+	0.670725i
$447$	−18.4351	+	5.21285i	−0.871951	+	0.246559i
$448$	−4.07320	+	14.6709i	−0.192441	+	0.693133i
$449$	36.1491			1.70598			0.852990	−	0.521927i	$-0.174787\pi$
$449$	36.1491			1.70598			0.852990	+	0.521927i	$0.174787\pi$
$450$	−1.24748	+	0.766806i	−0.0588068	+	0.0361476i
$451$	−3.61883	+	6.26800i	−0.170404	+	0.295149i
$452$	−0.487845	−	0.844972i	−0.0229463	−	0.0397441i
$453$	1.23914	−	4.89315i	0.0582199	−	0.229900i
$454$	3.90350	+	6.76106i	0.183200	+	0.317312i
$455$	1.66452	−	5.99529i	0.0780341	−	0.281063i
$456$	−1.92268	+	7.59231i	−0.0900376	+	0.355543i
$457$	−20.0448			−0.937657			−0.468828	−	0.883289i	$-0.655324\pi$
$457$	−20.0448			−0.937657			−0.468828	+	0.883289i	$0.655324\pi$
$458$	13.6159	−	23.5835i	0.636230	−	1.10198i
$459$	6.79763	+	21.7344i	0.317286	+	1.01448i
$460$	−7.48250	−	12.9601i	−0.348873	−	0.604266i
$461$	−4.65477	+	8.06229i	−0.216794	+	0.375498i	−0.953826	−	0.300359i	$-0.902893\pi$
$461$	−4.65477	+	8.06229i	−0.216794	+	0.375498i	0.737032	+	0.675858i	$0.236227\pi$
$462$	3.26042	+	1.86179i	0.151688	+	0.0866181i
$463$	−7.80494	−	13.5186i	−0.362726	−	0.628260i	0.625682	−	0.780078i	$-0.284821\pi$
$463$	−7.80494	−	13.5186i	−0.362726	−	0.628260i	−0.988409	+	0.151818i	$0.951487\pi$
$464$	1.84715	−	3.19936i	0.0857520	−	0.148527i
$465$	15.7650	−	4.45782i	0.731083	−	0.206727i
$466$	0.953129	+	1.65087i	0.0441528	+	0.0764749i
$467$	20.9803	+	36.3389i	0.970851	+	1.68156i	0.692998	+	0.720940i	$0.256290\pi$
$467$	20.9803	+	36.3389i	0.970851	+	1.68156i	0.277853	+	0.960623i	$0.410377\pi$
$468$	2.94868	−	1.81250i	0.136303	−	0.0837830i
$469$	3.91565	−	14.1034i	0.180808	−	0.651235i
$470$	−12.3678	+	21.4217i	−0.570486	+	0.988111i
$471$	22.0218	+	21.4234i	1.01471	+	0.987136i
$472$	−24.8136			−1.14214
$473$	−3.18518			−0.146455
$474$	1.92515	+	1.87283i	0.0884250	+	0.0860220i
$475$	−0.413485	+	0.716176i	−0.0189720	+	0.0328604i
$476$	9.37384	+	9.54446i	0.429649	+	0.437470i
$477$	12.3481	+	6.68263i	0.565381	+	0.305976i
$478$	−12.7822	−	22.1394i	−0.584643	−	1.01263i
$479$	−3.27603	−	5.67424i	−0.149685	−	0.259263i	0.781426	−	0.623998i	$-0.214493\pi$
$479$	−3.27603	−	5.67424i	−0.149685	−	0.259263i	−0.931111	+	0.364735i	$0.881159\pi$
$480$	−21.4399	+	6.06252i	−0.978595	+	0.276715i
$481$	−0.764675	+	1.32446i	−0.0348662	+	0.0603900i
$482$	0.0404196	+	0.0700088i	0.00184106	+	0.00318882i
$483$	−0.120190	−	25.2750i	−0.00546882	−	1.15005i
$484$	−5.88795	+	10.1982i	−0.267634	+	0.463556i
$485$	20.5427	+	35.5809i	0.932794	+	1.61565i
$486$	−10.8138	−	9.41828i	−0.490526	−	0.427222i
$487$	−6.03483	+	10.4526i	−0.273464	+	0.473654i	−0.969747	−	0.244114i	$-0.921503\pi$
$487$	−6.03483	+	10.4526i	−0.273464	+	0.473654i	0.696282	+	0.717768i	$0.254836\pi$
$488$	−1.45820			−0.0660096
$489$	−6.31853	+	24.9508i	−0.285734	+	1.12831i
$490$	−13.2494	+	7.33418i	−0.598549	+	0.331324i
$491$	14.5456	+	25.1937i	0.656432	+	1.13697i	0.981533	+	0.191294i	$0.0612685\pi$
$491$	14.5456	+	25.1937i	0.656432	+	1.13697i	−0.325101	+	0.945679i	$0.605398\pi$
$492$	3.98663	−	15.7425i	0.179731	−	0.709727i
$493$	−22.3974	−	38.7934i	−1.00873	−	1.74716i
$494$	−0.716896	+	1.24170i	−0.0322547	+	0.0558667i
$495$	0.173072	+	6.28109i	0.00777902	+	0.282314i
$496$	−1.45374			−0.0652750
$497$	−1.39183	+	5.01311i	−0.0624323	+	0.224869i
$498$	−22.0952	+	6.24781i	−0.990110	+	0.279971i
$499$	−20.4974	+	35.5025i	−0.917589	+	1.58931i	−0.114523	+	0.993421i	$0.536534\pi$
$499$	−20.4974	+	35.5025i	−0.917589	+	1.58931i	−0.803066	+	0.595890i	$0.796799\pi$
$500$	12.1266			0.542320
$501$	−3.93683	+	15.5459i	−0.175885	+	0.694538i
$502$	17.2535			0.770060
$503$	−3.88786			−0.173351			−0.0866755	−	0.996237i	$-0.527624\pi$
$503$	−3.88786			−0.173351			−0.0866755	+	0.996237i	$0.527624\pi$
$504$	−22.3496	−	5.54685i	−0.995530	−	0.247076i
$505$	3.07387			0.136785
$506$	4.51890			0.200890
$507$	1.66670	−	0.471288i	0.0740207	−	0.0209307i
$508$	−18.4737			−0.819638
$509$	17.7911	−	30.8151i	0.788577	−	1.36586i	−0.138262	−	0.990396i	$-0.544151\pi$
$509$	17.7911	−	30.8151i	0.788577	−	1.36586i	0.926839	−	0.375460i	$-0.122515\pi$
$510$	4.03149	−	15.9197i	0.178518	−	0.704935i
$511$	−7.86420	−	8.00734i	−0.347892	−	0.354224i
$512$	4.07428			0.180060
$513$	−7.90263	−	1.77115i	−0.348910	−	0.0781981i
$514$	−0.820515	+	1.42117i	−0.0361913	+	0.0626853i
$515$	19.0116	+	32.9291i	0.837752	+	1.45103i
$516$	6.87706	−	1.94461i	0.302746	−	0.0856066i
$517$	5.09151	+	8.81876i	0.223925	+	0.387849i
$518$	3.60400	−	0.930935i	0.158351	−	0.0409029i
$519$	−15.8162	−	15.3864i	−0.694255	−	0.675388i
$520$	−6.82283			−0.299201
$521$	−9.35370	+	16.2011i	−0.409793	+	0.709783i	−0.994866	−	0.101198i	$-0.967732\pi$
$521$	−9.35370	+	16.2011i	−0.409793	+	0.709783i	0.585073	+	0.810981i	$0.301066\pi$
$522$	24.8080	+	13.4257i	1.08582	+	0.587629i
$523$	−11.0542	−	19.1465i	−0.483368	−	0.837218i	0.516450	−	0.856317i	$-0.327253\pi$
$523$	−11.0542	−	19.1465i	−0.483368	−	0.837218i	−0.999818	+	0.0190999i	$0.993920\pi$
$524$	−1.96756	+	3.40792i	−0.0859534	+	0.148876i
$525$	−2.11146	−	1.20570i	−0.0921518	−	0.0526212i
$526$	6.23359	+	10.7969i	0.271797	+	0.470767i
$527$	−8.81356	+	15.2655i	−0.383925	+	0.664977i
$528$	0.136875	−	0.540497i	0.00595674	−	0.0235221i
$529$	−3.71047	−	6.42672i	−0.161325	−	0.279423i
$530$	−5.06254	−	8.76858i	−0.219903	−	0.380883i
$531$	−0.706741	−	25.6489i	−0.0306700	−	1.11307i
$532$	−4.60638	+	1.18986i	−0.199712	+	0.0515869i
$533$	4.06327	−	7.03779i	0.176000	−	0.304841i
$534$	0.825345	−	3.25914i	0.0357162	−	0.141037i
$535$	36.5410			1.57980
$536$	−16.0501			−0.693260
$537$	−21.4147	+	6.05538i	−0.924113	+	0.261309i
$538$	3.96155	−	6.86161i	0.170795	−	0.295825i
$539$	−0.112443	+	6.23333i	−0.00484326	+	0.268489i
$540$	−4.20840	−	13.4557i	−0.181101	−	0.579042i
$541$	−3.92007	−	6.78976i	−0.168537	−	0.291915i	0.769369	−	0.638805i	$-0.220571\pi$
$541$	−3.92007	−	6.78976i	−0.168537	−	0.291915i	−0.937906	+	0.346890i	$0.887238\pi$
$542$	−9.67346	−	16.7549i	−0.415511	−	0.719686i
$543$	20.6408	+	20.0799i	0.885780	+	0.861709i
$544$	11.9862	−	20.7607i	0.513904	−	0.890108i
$545$	14.9343	+	25.8671i	0.639717	+	1.10802i
$546$	−3.66084	−	2.09044i	−0.156669	−	0.0894624i
$547$	8.12851	−	14.0790i	0.347550	−	0.601974i	−0.638264	−	0.769818i	$-0.720347\pi$
$547$	8.12851	−	14.0790i	0.347550	−	0.601974i	0.985814	+	0.167844i	$0.0536804\pi$
$548$	−1.72327	−	2.98480i	−0.0736146	−	0.127504i
$549$	−0.0415324	−	1.50728i	−0.00177256	−	0.0643292i
$550$	0.217357	−	0.376474i	0.00926814	−	0.0160529i
$551$	15.9304			0.678659
$552$	−26.6700	+	7.54140i	−1.13515	+	0.320983i
$553$	−1.19308	+	4.29723i	−0.0507348	+	0.182737i
$554$	−1.07022	−	1.85367i	−0.0454692	−	0.0787550i
$555$	4.46518	+	4.34383i	0.189536	+	0.184386i
$556$	−10.8080	−	18.7201i	−0.458363	−	0.793908i
$557$	−18.2227	+	31.5626i	−0.772119	+	1.33735i	0.164281	+	0.986414i	$0.447470\pi$
$557$	−18.2227	+	31.5626i	−0.772119	+	1.33735i	−0.936400	+	0.350935i	$0.885864\pi$
$558$	−0.305741	−	11.0959i	−0.0129430	−	0.469725i
$559$	3.57636			0.151264
$560$	1.57581	+	1.60450i	0.0665903	+	0.0678023i
$561$	−4.84585	−	4.71416i	−0.204592	−	0.199032i
$562$	5.92188	−	10.2570i	0.249799	−	0.432665i
$563$	−10.8503			−0.457285			−0.228642	−	0.973510i	$-0.573429\pi$
$563$	−10.8503			−0.457285			−0.228642	+	0.973510i	$0.573429\pi$
$564$	−16.3770	−	15.9320i	−0.689597	−	0.670857i
$565$	−1.98881			−0.0836697
$566$	26.7008			1.12232
$567$	5.09699	−	23.2599i	0.214054	−	0.976822i
$568$	5.70508			0.239380
$569$	5.70887			0.239328			0.119664	−	0.992814i	$-0.461818\pi$
$569$	5.70887			0.239328			0.119664	+	0.992814i	$0.461818\pi$
$570$	4.18618	+	4.07242i	0.175340	+	0.170575i
$571$	38.4857			1.61057			0.805287	−	0.592885i	$-0.202011\pi$
$571$	38.4857			1.61057			0.805287	+	0.592885i	$0.202011\pi$
$572$	−0.513768	+	0.889873i	−0.0214817	+	0.0372075i
$573$	−7.99872	−	7.78135i	−0.334151	−	0.325071i
$574$	−19.1506	+	4.94673i	−0.799332	+	0.206472i
$575$	−2.92647			−0.122042
$576$	0.475532	+	17.2579i	0.0198139	+	0.719079i
$577$	−13.2218	+	22.9007i	−0.550429	+	0.953371i	0.447815	+	0.894126i	$0.352202\pi$
$577$	−13.2218	+	22.9007i	−0.550429	+	0.953371i	−0.998244	+	0.0592442i	$0.981131\pi$
$578$	1.01519	+	1.75837i	0.0422265	+	0.0731385i
$579$	23.3699	+	22.7349i	0.971222	+	0.944829i
$580$	13.8662	+	24.0169i	0.575761	+	0.997247i
$581$	−26.7158	−	27.2021i	−1.10836	−	1.12853i
$582$	26.7863	−	7.57429i	1.11033	−	0.313964i
$583$	−4.16823			−0.172630
$584$	−6.15349	+	10.6582i	−0.254633	+	0.441038i
$585$	−0.194328	−	7.05248i	−0.00803446	−	0.291584i
$586$	1.86161	+	3.22441i	0.0769025	+	0.133199i
$587$	14.1682	−	24.5401i	0.584785	−	1.01288i	−0.410117	−	0.912033i	$-0.634512\pi$
$587$	14.1682	−	24.5401i	0.584785	−	1.01288i	0.994902	−	0.100844i	$-0.0321544\pi$
$588$	−3.56279	−	13.5269i	−0.146927	−	0.557841i
$589$	−3.13439	−	5.42892i	−0.129150	−	0.223695i
$590$	−9.25170	+	16.0244i	−0.380886	+	0.659715i
$591$	14.3210	+	13.9318i	0.589088	+	0.573079i
$592$	−0.276385	−	0.478713i	−0.0113594	−	0.0196750i
$593$	11.3491	+	19.6571i	0.466050	+	0.807222i	0.999248	−	0.0387685i	$-0.0123435\pi$
$593$	11.3491	+	19.6571i	0.466050	+	0.807222i	−0.533199	+	0.845990i	$0.679010\pi$
$594$	4.15419	+	0.931043i	0.170449	+	0.0382012i
$595$	26.4022	−	6.81985i	1.08238	−	0.279587i
$596$	−6.38063	+	11.0516i	−0.261361	+	0.452690i
$597$	22.4340	−	6.34361i	0.918164	−	0.259627i
$598$	−5.07388			−0.207486
$599$	−16.3597			−0.668439			−0.334219	−	0.942495i	$-0.608473\pi$
$599$	−16.3597			−0.668439			−0.334219	+	0.942495i	$0.608473\pi$
$600$	−0.654533	+	2.58464i	−0.0267212	+	0.105517i
$601$	−11.3314	+	19.6266i	−0.462219	+	0.800587i	−0.999071	−	0.0430892i	$-0.986280\pi$
$601$	−11.3314	+	19.6266i	−0.462219	+	0.800587i	0.536852	+	0.843676i	$0.319613\pi$
$602$	−6.09925	−	6.21027i	−0.248587	−	0.253112i
$603$	−0.457139	−	16.5904i	−0.0186161	−	0.675612i
$604$	−1.68112	−	2.91179i	−0.0684040	−	0.118479i
$605$	12.0018	+	20.7877i	0.487941	+	0.845139i
$606$	0.511269	−	2.01891i	0.0207689	−	0.0820127i
$607$	7.00233	−	12.1284i	0.284216	−	0.492276i	−0.688203	−	0.725518i	$-0.741600\pi$
$607$	7.00233	−	12.1284i	0.284216	−	0.492276i	0.972419	+	0.233242i	$0.0749335\pi$
$608$	4.26268	+	7.38318i	0.172874	+	0.299427i
$609$	0.222729	+	46.8382i	0.00902543	+	1.89798i
$610$	−0.543685	+	0.941691i	−0.0220132	+	0.0381279i
$611$	−5.71682	−	9.90182i	−0.231278	−	0.400585i
$612$	13.3407	+	7.21978i	0.539264	+	0.291843i
$613$	−13.0375	+	22.5816i	−0.526580	+	0.912063i	0.472941	+	0.881094i	$0.343193\pi$
$613$	−13.0375	+	22.5816i	−0.526580	+	0.912063i	−0.999520	+	0.0309687i	$0.990141\pi$
$614$	4.24073			0.171142
$615$	−23.7267	−	23.0819i	−0.956752	−	0.930753i
$616$	6.61904	−	1.70974i	0.266689	−	0.0688873i
$617$	−4.34395	−	7.52394i	−0.174881	−	0.302903i	0.765239	−	0.643746i	$-0.222621\pi$
$617$	−4.34395	−	7.52394i	−0.174881	−	0.302903i	−0.940120	+	0.340843i	$0.889287\pi$
$618$	24.7899	−	7.00978i	0.997196	−	0.281975i
$619$	11.7545	+	20.3594i	0.472454	+	0.818314i	0.999503	−	0.0315207i	$-0.0100350\pi$
$619$	11.7545	+	20.3594i	0.472454	+	0.818314i	−0.527049	+	0.849835i	$0.676702\pi$
$620$	5.45646	−	9.45086i	0.219137	−	0.379556i
$621$	−8.55485	−	27.3529i	−0.343294	−	1.09763i
$622$	−5.04711			−0.202371
$623$	5.40517	−	1.39619i	0.216554	−	0.0559372i
$624$	−0.153685	+	0.606877i	−0.00615234	+	0.0242945i
$625$	13.6857	−	23.7043i	0.547428	−	0.948174i
$626$	13.3955			0.535393
$627$	2.31357	−	0.654202i	0.0923950	−	0.0261263i
$628$	20.4650			0.816642
$629$	−6.70252			−0.267247
$630$	−11.9151	+	12.3650i	−0.474708	+	0.492634i
$631$	5.28315			0.210319			0.105160	−	0.994455i	$-0.466465\pi$
$631$	5.28315			0.210319			0.105160	+	0.994455i	$0.466465\pi$
$632$	4.89038			0.194529
$633$	8.38982	−	33.1299i	0.333465	−	1.31680i
$634$	19.6725			0.781296
$635$	−18.8280	+	32.6111i	−0.747168	+	1.29413i
$636$	8.99955	−	2.54478i	0.356855	−	0.100907i
$637$	0.126252	−	6.99886i	0.00500230	−	0.277305i
$638$	−8.37418			−0.331537
$639$	0.162492	+	5.89711i	0.00642808	+	0.233286i
$640$	−6.63869	+	11.4985i	−0.262417	+	0.454520i
$641$	14.3457	+	24.8475i	0.566621	+	0.981417i	0.996897	+	0.0787190i	$0.0250830\pi$
$641$	14.3457	+	24.8475i	0.566621	+	0.981417i	−0.430276	+	0.902697i	$0.641584\pi$
$642$	6.07777	−	24.0000i	0.239870	−	0.947206i
$643$	5.74466	+	9.95005i	0.226547	+	0.392392i	0.956783	−	0.290804i	$-0.0939228\pi$
$643$	5.74466	+	9.95005i	0.226547	+	0.392392i	−0.730235	+	0.683196i	$0.760589\pi$
$644$	−11.7970	−	12.0118i	−0.464868	−	0.473330i
$645$	3.57620	−	14.1218i	0.140813	−	0.556045i
$646$	−6.28373			−0.247230
$647$	15.5033	−	26.8525i	0.609498	−	1.05568i	−0.381826	−	0.924234i	$-0.624704\pi$
$647$	15.5033	−	26.8525i	0.609498	−	1.05568i	0.991323	−	0.131447i	$-0.0419622\pi$
$648$	−26.0712	+	1.43785i	−1.02418	+	0.0564842i
$649$	3.80868	+	6.59683i	0.149504	+	0.258948i
$650$	−0.244051	+	0.422710i	−0.00957249	+	0.0165800i
$651$	15.9181	−	9.29154i	0.623880	−	0.364164i
$652$	8.57227	+	14.8476i	0.335716	+	0.581477i
$653$	20.1569	−	34.9127i	0.788799	−	1.36624i	−0.137905	−	0.990446i	$-0.544037\pi$
$653$	20.1569	−	34.9127i	0.788799	−	1.36624i	0.926703	−	0.375794i	$-0.122630\pi$
$654$	19.4734	−	5.50645i	0.761471	−	0.215319i
$655$	4.01060	+	6.94657i	0.156707	+	0.271425i
$656$	1.46863	+	2.54375i	0.0573405	+	0.0993166i
$657$	−11.1922	−	6.05705i	−0.436648	−	0.236308i
$658$	−7.44463	+	26.8141i	−0.290222	+	1.04532i
$659$	−8.37378	+	14.5038i	−0.326196	+	0.564988i	−0.981754	−	0.190157i	$-0.939100\pi$
$659$	−8.37378	+	14.5038i	−0.326196	+	0.564988i	0.655558	+	0.755145i	$0.272434\pi$
$660$	3.00005	+	2.91853i	0.116777	+	0.113604i
$661$	−7.82431			−0.304330			−0.152165	−	0.988355i	$-0.548625\pi$
$661$	−7.82431			−0.304330			−0.152165	+	0.988355i	$0.548625\pi$
$662$	−6.29255			−0.244567
$663$	5.44098	+	5.29312i	0.211310	+	0.205568i
$664$	−20.9043	+	36.2073i	−0.811244	+	1.40512i
$665$	−2.59431	+	9.34420i	−0.100603	+	0.362352i
$666$	3.59570	−	2.21022i	0.139331	−	0.0856442i
$667$	28.1872	+	48.8217i	1.09141	+	1.89038i
$668$	5.34105	+	9.25096i	0.206651	+	0.357930i
$669$	−29.6336	+	8.37942i	−1.14570	+	0.323967i
$670$	−5.98424	+	10.3650i	−0.231192	+	0.400436i
$671$	0.223821	+	0.387669i	0.00864051	+	0.0149658i
$672$	−21.6482	+	12.6362i	−0.835098	+	0.487453i
$673$	8.26302	−	14.3120i	0.318516	−	0.551686i	−0.661663	−	0.749802i	$-0.730149\pi$
$673$	8.26302	−	14.3120i	0.318516	−	0.551686i	0.980179	+	0.198116i	$0.0634822\pi$
$674$	2.21176	+	3.83088i	0.0851939	+	0.147560i
$675$	−2.69028	−	0.602949i	−0.103549	−	0.0232075i
$676$	0.576866	−	0.999161i	0.0221871	−	0.0384293i
$677$	−1.18695			−0.0456181			−0.0228090	−	0.999740i	$-0.507261\pi$
$677$	−1.18695			−0.0456181			−0.0228090	+	0.999740i	$0.507261\pi$
$678$	−0.330793	+	1.30624i	−0.0127040	+	0.0501660i
$679$	32.3879	+	32.9774i	1.24293	+	1.26556i
$680$	−14.9508	−	25.8956i	−0.573338	−	0.993051i
$681$	−3.60849	+	14.2493i	−0.138278	+	0.546034i
$682$	1.64766	+	2.85383i	0.0630921	+	0.109279i
$683$	−12.3761	+	21.4361i	−0.473560	+	0.820230i	−0.999542	−	0.0302659i	$-0.990365\pi$
$683$	−12.3761	+	21.4361i	−0.473560	+	0.820230i	0.525982	+	0.850496i	$0.323698\pi$
$684$	−4.59578	+	2.82495i	−0.175724	+	0.108015i
$685$	−7.02531			−0.268423
$686$	−12.3687	+	11.7169i	−0.472239	+	0.447353i
$687$	49.3378	−	13.9511i	1.88236	−	0.532269i
$688$	−0.646321	+	1.11946i	−0.0246408	+	0.0426790i
$689$	4.68014			0.178299
$690$	−5.07366	+	20.0350i	−0.193151	+	0.762719i
$691$	−48.8972			−1.86014			−0.930069	−	0.367386i	$-0.880253\pi$
$691$	−48.8972			−1.86014			−0.930069	+	0.367386i	$0.880253\pi$
$692$	−14.6981			−0.558738
$693$	1.95581	+	6.79314i	0.0742951	+	0.258050i
$694$	−11.5453			−0.438254
$695$	−44.0613			−1.67134
$696$	49.4233	−	13.9753i	1.87339	−	0.529733i
$697$	35.6153			1.34903
$698$	6.98491	−	12.0982i	0.264383	−	0.457924i
$699$	−0.881095	+	3.47929i	−0.0333261	+	0.131599i
$700$	−1.56814	+	0.405061i	−0.0592702	+	0.0153099i
$701$	1.18495			0.0447551			0.0223776	−	0.999750i	$-0.492876\pi$
$701$	1.18495			0.0447551			0.0223776	+	0.999750i	$0.492876\pi$
$702$	−4.66438	−	1.04539i	−0.176046	−	0.0394556i
$703$	1.19182	−	2.06429i	0.0449502	−	0.0778560i
$704$	−2.56268	−	4.43869i	−0.0965846	−	0.167289i
$705$	−44.8154	+	12.6723i	−1.68785	+	0.477268i
$706$	−2.86813	−	4.96775i	−0.107944	−	0.186964i
$707$	3.34829	−	0.864885i	0.125926	−	0.0325273i
$708$	−12.2507	−	11.9178i	−0.460411	−	0.447899i
$709$	1.47303			0.0553207			0.0276603	−	0.999617i	$-0.491194\pi$
$709$	1.47303			0.0553207			0.0276603	+	0.999617i	$0.491194\pi$
$710$	2.12712	−	3.68429i	0.0798295	−	0.138269i
$711$	0.139288	+	5.05499i	0.00522370	+	0.189577i
$712$	−3.06080	−	5.30146i	−0.114708	−	0.198681i
$713$	11.0919	−	19.2118i	0.415396	−	0.719486i
$714$	−0.0878549	−	18.4752i	−0.00328789	−	0.691418i
$715$	1.04725	+	1.81388i	0.0391648	+	0.0678353i
$716$	−7.41190	+	12.8378i	−0.276996	+	0.479771i
$717$	11.8162	−	46.6599i	0.441282	−	1.74255i
$718$	−3.56142	−	6.16856i	−0.132911	−	0.230209i
$719$	−12.0381	−	20.8507i	−0.448947	−	0.777598i	0.549371	−	0.835578i	$-0.314867\pi$
$719$	−12.0381	−	20.8507i	−0.448947	−	0.777598i	−0.998318	+	0.0579801i	$0.981534\pi$
$720$	2.24267	+	1.21370i	0.0835793	+	0.0452320i
$721$	29.9740	+	30.5196i	1.11629	+	1.13661i
$722$	−7.62197	+	13.2016i	−0.283661	+	0.491314i
$723$	−0.0373649	+	0.147547i	−0.00138961	+	0.00548734i
$724$	19.1816			0.712878
$725$	5.42317			0.201411
$726$	15.6495	−	4.42517i	0.580808	−	0.164234i
$727$	20.4028	−	35.3387i	0.756699	−	1.31064i	−0.187827	−	0.982202i	$-0.560144\pi$
$727$	20.4028	−	35.3387i	0.756699	−	1.31064i	0.944525	−	0.328438i	$-0.106522\pi$
$728$	−7.43194	+	1.91972i	−0.275446	+	0.0711494i
$729$	−2.22881	−	26.9079i	−0.0825485	−	0.996587i
$730$	4.58863	+	7.94773i	0.169833	+	0.294159i
$731$	7.83686	+	13.5738i	0.289857	+	0.502046i
$732$	−0.719927	−	0.700363i	−0.0266093	−	0.0258862i
$733$	6.33462	−	10.9719i	0.233975	−	0.405256i	−0.725000	−	0.688749i	$-0.758160\pi$
$733$	6.33462	−	10.9719i	0.233975	−	0.405256i	0.958974	+	0.283493i	$0.0914934\pi$
$734$	2.08906	+	3.61836i	0.0771087	+	0.133556i
$735$	−27.5098	−	7.49708i	−1.01471	−	0.276534i
$736$	−15.0847	+	26.1275i	−0.556030	+	0.963072i
$737$	2.46356	+	4.26700i	0.0907462	+	0.157177i
$738$	−19.1066	+	11.7445i	−0.703322	+	0.432320i
$739$	14.7739	−	25.5891i	0.543467	−	0.941312i	−0.455235	−	0.890371i	$-0.650445\pi$
$739$	14.7739	−	25.5891i	0.543467	−	0.941312i	0.998702	−	0.0509406i	$-0.0162219\pi$
$740$	4.14952			0.152539
$741$	−2.59770	+	0.734546i	−0.0954290	+	0.0269842i
$742$	−7.98169	−	8.12697i	−0.293017	−	0.298350i
$743$	2.89933	+	5.02179i	0.106366	+	0.184232i	0.914296	−	0.405048i	$-0.132745\pi$
$743$	2.89933	+	5.02179i	0.106366	+	0.184232i	−0.807929	+	0.589279i	$0.799412\pi$
$744$	−14.4869	−	14.0932i	−0.531115	−	0.516682i
$745$	13.0060	+	22.5271i	0.476504	+	0.825329i
$746$	−5.63581	+	9.76151i	−0.206342	+	0.357394i
$747$	−38.0214	−	20.5767i	−1.39113	−	0.752861i
$748$	−4.50328			−0.164656
$749$	39.8032	−	10.2814i	1.45438	−	0.375675i
$750$	−12.0043	−	11.6781i	−0.438334	−	0.426423i
$751$	−17.3734	+	30.0916i	−0.633963	+	1.09806i	0.352770	+	0.935710i	$0.385240\pi$
$751$	−17.3734	+	30.0916i	−0.633963	+	1.09806i	−0.986734	+	0.162347i	$0.948094\pi$
$752$	4.13258			0.150700
$753$	23.2846	+	22.6518i	0.848536	+	0.825477i
$754$	9.40264			0.342424
$755$	−6.85347			−0.249423
$756$	−8.37009	−	13.4729i	−0.304417	−	0.490004i
$757$	31.3112			1.13802			0.569012	−	0.822329i	$-0.307326\pi$
$757$	31.3112			1.13802			0.569012	+	0.822329i	$0.307326\pi$
$758$	−7.69067			−0.279338
$759$	6.09853	+	5.93280i	0.221362	+	0.215347i
$760$	10.6340			0.385736
$761$	−11.7886	+	20.4185i	−0.427337	+	0.740169i	−0.996635	−	0.0819619i	$-0.973881\pi$
$761$	−11.7886	+	20.4185i	−0.427337	+	0.740169i	0.569299	+	0.822131i	$0.307215\pi$
$762$	18.2873	+	17.7903i	0.662479	+	0.644476i
$763$	23.5457	+	23.9743i	0.852413	+	0.867929i
$764$	−7.43326			−0.268926
$765$	26.3414	−	16.1916i	0.952376	−	0.585410i
$766$	−3.63035	+	6.28795i	−0.131170	+	0.227193i
$767$	−4.27643	−	7.40700i	−0.154413	−	0.267451i
$768$	20.7372	+	20.1737i	0.748289	+	0.727954i
$769$	4.36059	+	7.55277i	0.157247	+	0.272360i	0.933875	−	0.357600i	$-0.116405\pi$
$769$	4.36059	+	7.55277i	0.157247	+	0.272360i	−0.776628	+	0.629960i	$0.783071\pi$
$770$	1.36376	−	4.91198i	0.0491464	−	0.177016i
$771$	−2.97317	+	0.840715i	−0.107076	+	0.0302776i
$772$	21.7178			0.781642
$773$	10.3067	−	17.8517i	0.370707	−	0.642083i	−0.618968	−	0.785416i	$-0.712449\pi$
$773$	10.3067	−	17.8517i	0.370707	−	0.642083i	0.989674	+	0.143334i	$0.0457822\pi$
$774$	−8.68034	−	4.69768i	−0.312008	−	0.168855i
$775$	−1.06703	−	1.84815i	−0.0383289	−	0.0663877i
$776$	25.3425	−	43.8945i	0.909744	−	1.57572i
$777$	6.08602	+	3.47528i	0.218335	+	0.124675i
$778$	5.48622	+	9.50241i	0.196691	+	0.340678i
$779$	−6.33297	+	10.9690i	−0.226902	+	0.393006i
$780$	−3.36850	−	3.27696i	−0.120612	−	0.117334i
$781$	−0.875681	−	1.51672i	−0.0313343	−	0.0542726i
$782$	−11.1184	−	19.2576i	−0.397592	−	0.688650i
$783$	15.8534	+	50.6888i	0.566554	+	1.81147i
$784$	2.16795	+	1.30436i	0.0774267	+	0.0465842i
$785$	20.8575	−	36.1263i	0.744437	−	1.28940i
$786$	5.22957	−	1.47875i	0.186532	−	0.0527453i
$787$	14.9745			0.533784			0.266892	−	0.963726i	$-0.414003\pi$
$787$	14.9745			0.533784			0.266892	+	0.963726i	$0.414003\pi$
$788$	13.3086			0.474100
$789$	−5.76248	+	22.7550i	−0.205150	+	0.810100i
$790$	1.82337	−	3.15816i	0.0648725	−	0.112362i
$791$	−2.16636	+	0.559584i	−0.0770268	+	0.0198965i
$792$	6.60380	−	4.05925i	0.234656	−	0.144239i
$793$	−0.251309	−	0.435280i	−0.00892424	−	0.0154572i
$794$	1.00917	+	1.74794i	0.0358142	+	0.0620320i
$795$	4.67993	−	18.4802i	0.165980	−	0.655427i
$796$	7.76470	−	13.4489i	0.275213	−	0.476682i
$797$	−7.12448	−	12.3400i	−0.252362	−	0.437104i	0.711814	−	0.702368i	$-0.247874\pi$
$797$	−7.12448	−	12.3400i	−0.252362	−	0.437104i	−0.964176	+	0.265265i	$0.914541\pi$
$798$	5.70574	+	3.25813i	0.201981	+	0.115337i
$799$	25.0545	−	43.3956i	0.886364	−	1.53523i
$800$	1.45114	+	2.51344i	0.0513054	+	0.0888635i
$801$	5.39273	−	3.31482i	0.190543	−	0.117124i
$802$	12.9183	−	22.3751i	0.456159	−	0.790091i
$803$	3.77803			0.133324
$804$	−7.92410	−	7.70877i	−0.279462	−	0.271867i
$805$	−33.2273	+	8.58282i	−1.17111	+	0.302505i
$806$	−1.85001	−	3.20432i	−0.0651639	−	0.112867i
$807$	14.3548	−	4.05908i	0.505315	−	0.142887i
$808$	−1.89605	−	3.28405i	−0.0667027	−	0.115532i
$809$	−21.8571	+	37.8575i	−0.768453	+	1.33100i	0.169948	+	0.985453i	$0.445640\pi$
$809$	−21.8571	+	37.8575i	−0.768453	+	1.33100i	−0.938401	+	0.345547i	$0.887693\pi$
$810$	−8.79204	+	17.3727i	−0.308921	+	0.610413i
$811$	−50.4077			−1.77005			−0.885027	−	0.465540i	$-0.845860\pi$
$811$	−50.4077			−1.77005			−0.885027	+	0.465540i	$0.845860\pi$
$812$	21.8616	+	22.2595i	0.767192	+	0.781156i
$813$	8.94238	−	35.3119i	0.313623	−	1.23844i
$814$	−0.626504	+	1.08514i	−0.0219590	+	0.0380340i
$815$	34.9467			1.22413
$816$	−2.64013	+	0.746544i	−0.0924231	+	0.0261343i
$817$	−5.57408			−0.195012
$818$	30.8311			1.07798
$819$	−2.19601	−	7.62742i	−0.0767348	−	0.266524i
$820$	−22.0494			−0.769997
$821$	−52.4248			−1.82964			−0.914819	−	0.403865i	$-0.867667\pi$
$821$	−52.4248			−1.82964			−0.914819	+	0.403865i	$0.867667\pi$
$822$	−1.16850	+	4.61420i	−0.0407561	+	0.160939i
$823$	4.88854			0.170404			0.0852019	−	0.996364i	$-0.472846\pi$
$823$	4.88854			0.170404			0.0852019	+	0.996364i	$0.472846\pi$
$824$	23.4537	−	40.6231i	0.817050	−	1.41517i
$825$	0.787603	−	0.222709i	0.0274208	−	0.00775372i
$826$	−5.56891	+	20.0581i	−0.193767	+	0.697911i
$827$	−8.10961			−0.281999			−0.140999	−	0.990010i	$-0.545032\pi$
$827$	−8.10961			−0.281999			−0.140999	+	0.990010i	$0.545032\pi$
$828$	−16.7893	−	9.08614i	−0.583469	−	0.315765i
$829$	9.33525	−	16.1691i	0.324227	−	0.561577i	−0.657129	−	0.753778i	$-0.728229\pi$
$829$	9.33525	−	16.1691i	0.324227	−	0.561577i	0.981356	+	0.192201i	$0.0615626\pi$
$830$	15.5882	+	26.9996i	0.541075	+	0.937170i
$831$	0.989336	−	3.90671i	0.0343197	−	0.135522i
$832$	2.87741	+	4.98381i	0.0997561	+	0.172783i
$833$	26.8404	−	14.8574i	0.929964	−	0.514778i
$834$	−7.32861	+	28.9394i	−0.253769	+	1.00209i
$835$	21.7740			0.753519
$836$	0.800755	−	1.38695i	0.0276947	−	0.0479686i
$837$	14.1550	−	15.3759i	0.489267	−	0.531469i
$838$	16.3045	+	28.2403i	0.563230	+	0.975544i
$839$	−18.3244	+	31.7388i	−0.632629	+	1.09575i	0.354383	+	0.935100i	$0.384691\pi$
$839$	−18.3244	+	31.7388i	−0.632629	+	1.09575i	−0.987012	+	0.160646i	$0.948642\pi$
$840$	0.148677	+	31.2658i	0.00512986	+	1.07877i
$841$	−37.7350	−	65.3589i	−1.30121	−	2.25375i
$842$	−5.65946	+	9.80247i	−0.195038	+	0.337815i
$843$	21.4582	−	6.06767i	0.739059	−	0.208982i
$844$	−11.3824	−	19.7148i	−0.391797	−	0.678612i
$845$	−1.17586	−	2.03665i	−0.0404508	−	0.0700629i
$846$	0.869135	+	31.5424i	0.0298815	+	1.08445i
$847$	18.9222	+	19.2666i	0.650174	+	0.662008i
$848$	−0.845797	+	1.46496i	−0.0290448	+	0.0503071i
$849$	36.0343	+	35.0551i	1.23669	+	1.20309i
$850$	−2.13916			−0.0733724
$851$	8.43516			0.289154
$852$	2.81665	+	2.74011i	0.0964970	+	0.0938747i
$853$	5.20839	−	9.02120i	0.178332	−	0.308880i	−0.762977	−	0.646425i	$-0.776263\pi$
$853$	5.20839	−	9.02120i	0.178332	−	0.308880i	0.941309	+	0.337545i	$0.109597\pi$
$854$	−0.327263	+	1.17874i	−0.0111987	+	0.0403355i
$855$	0.302877	+	10.9919i	0.0103582	+	0.375916i
$856$	−22.5395	−	39.0395i	−0.770383	−	1.33434i
$857$	2.30659	+	3.99514i	0.0787917	+	0.136471i	0.902729	−	0.430210i	$-0.141560\pi$
$857$	2.30659	+	3.99514i	0.0787917	+	0.136471i	−0.823937	+	0.566681i	$0.808227\pi$
$858$	1.36554	−	0.386130i	0.0466187	−	0.0131823i
$859$	−0.448524	+	0.776866i	−0.0153034	+	0.0265063i	−0.873576	−	0.486688i	$-0.838205\pi$
$859$	−0.448524	+	0.776866i	−0.0153034	+	0.0265063i	0.858272	+	0.513195i	$0.171538\pi$
$860$	−4.85178	−	8.40353i	−0.165444	−	0.286558i
$861$	−32.3394	−	18.4667i	−1.10212	−	0.629342i
$862$	−10.0330	+	17.3777i	−0.341726	+	0.591887i
$863$	3.15345	+	5.46194i	0.107345	+	0.185926i	0.914694	−	0.404148i	$-0.132432\pi$
$863$	3.15345	+	5.46194i	0.107345	+	0.185926i	−0.807349	+	0.590074i	$0.799098\pi$
$864$	−19.2504	+	20.9108i	−0.654911	+	0.711401i
$865$	−14.9800	+	25.9462i	−0.509336	+	0.882196i
$866$	−21.3254			−0.724665
$867$	−0.938470	+	3.70585i	−0.0318721	+	0.125857i
$868$	3.28443	−	11.8299i	0.111481	−	0.401532i
$869$	−0.750632	−	1.30013i	−0.0254634	−	0.0441040i
$870$	9.40223	−	37.1277i	0.318765	−	1.25875i
$871$	−2.76611	−	4.79104i	−0.0937261	−	0.162338i
$872$	18.4238	−	31.9110i	0.623909	−	1.08064i
$873$	46.0938	+	24.9453i	1.56004	+	0.844272i
$874$	7.90810			0.267496
$875$	7.43945	−	26.7954i	0.251499	−	0.905850i
$876$	−8.15708	+	2.30656i	−0.275602	+	0.0779314i
$877$	7.36529	−	12.7571i	0.248708	−	0.430775i	−0.714459	−	0.699677i	$-0.753327\pi$
$877$	7.36529	−	12.7571i	0.248708	−	0.430775i	0.963168	+	0.268902i	$0.0866607\pi$
$878$	23.7391			0.801157
$879$	−1.72092	+	6.79561i	−0.0580452	+	0.229210i
$880$	−0.757035			−0.0255196
$881$	6.12069			0.206211			0.103106	−	0.994670i	$-0.467122\pi$
$881$	6.12069			0.206211			0.103106	+	0.994670i	$0.467122\pi$
$882$	−9.49970	+	16.8214i	−0.319872	+	0.566407i
$883$	−52.9297			−1.78123			−0.890614	−	0.454761i	$-0.849725\pi$
$883$	−52.9297			−1.78123			−0.890614	+	0.454761i	$0.849725\pi$
$884$	5.05633			0.170063
$885$	−33.5239	+	9.47947i	−1.12689	+	0.318649i
$886$	14.1925			0.476807
$887$	−20.4432	+	35.4087i	−0.686415	+	1.18891i	0.286574	+	0.958058i	$0.407483\pi$
$887$	−20.4432	+	35.4087i	−0.686415	+	1.18891i	−0.972990	+	0.230848i	$0.925850\pi$
$888$	1.88661	−	7.44988i	0.0633103	−	0.250001i
$889$	−11.3332	+	40.8201i	−0.380105	+	1.36906i
$890$	−4.56485			−0.153014
$891$	4.38397	+	6.71047i	0.146869	+	0.224809i
$892$	−10.2566	+	17.7649i	−0.343415	+	0.594813i
$893$	8.91018	+	15.4329i	0.298168	+	0.516442i
$894$	16.9590	−	4.79545i	0.567194	−	0.160384i
$895$	15.1081	+	26.1680i	0.505009	+	0.874701i
$896$	−3.99605	+	14.3930i	−0.133499	+	0.480836i
$897$	−6.84750	−	6.66142i	−0.228631	−	0.222418i
$898$	−33.2546			−1.10972
$899$	−20.5549	+	35.6022i	−0.685546	+	1.18740i
$900$	−1.56453	+	0.961692i	−0.0521511	+	0.0320564i
$901$	10.2556	+	17.7632i	0.341663	+	0.591777i
$902$	3.32907	−	5.76611i	0.110846	−	0.191991i
$903$	−0.0779330	−	16.3887i	−0.00259345	−	0.545383i
$904$	1.22675	+	2.12479i	0.0408011	+	0.0706695i
$905$	19.5495	−	33.8607i	0.649847	−	1.12557i
$906$	−1.13992	+	4.50135i	−0.0378713	+	0.149547i
$907$	20.5944	+	35.6705i	0.683825	+	1.18442i	0.973805	+	0.227387i	$0.0730181\pi$
$907$	20.5944	+	35.6705i	0.683825	+	1.18442i	−0.289980	+	0.957033i	$0.593649\pi$
$908$	4.89559	+	8.47941i	0.162466	+	0.281399i
$909$	3.34059	−	2.05340i	0.110800	−	0.0681071i
$910$	−1.53124	+	5.51524i	−0.0507602	+	0.182828i
$911$	−1.35254	+	2.34267i	−0.0448117	+	0.0776161i	−0.887561	−	0.460690i	$-0.847602\pi$
$911$	−1.35254	+	2.34267i	−0.0448117	+	0.0776161i	0.842750	+	0.538306i	$0.180935\pi$
$912$	0.239533	−	0.945873i	0.00793172	−	0.0313210i
$913$	12.8345			0.424761
$914$	18.4398			0.609934
$915$	−1.97007	+	0.557071i	−0.0651284	+	0.0184162i
$916$	17.0764	−	29.5773i	0.564222	−	0.977261i
$917$	6.32319	+	6.43828i	0.208810	+	0.212611i
$918$	−6.25333	−	19.9941i	−0.206391	−	0.659904i
$919$	15.0159	+	26.0083i	0.495329	+	0.857935i	0.999985	−	0.00538539i	$-0.00171423\pi$
$919$	15.0159	+	26.0083i	0.495329	+	0.857935i	−0.504657	+	0.863320i	$0.668381\pi$
$920$	18.8157	+	32.5898i	0.620336	+	1.07445i
$921$	5.72311	+	5.56758i	0.188583	+	0.183458i
$922$	4.28205	−	7.41673i	0.141022	−	0.244257i
$923$	0.983225	+	1.70300i	0.0323633	+	0.0560548i
$924$	4.08906	+	2.33497i	0.134520	+	0.0768147i
$925$	0.405727	−	0.702740i	0.0133402	−	0.0231060i
$926$	7.17999	+	12.4361i	0.235949	+	0.408676i
$927$	42.6584	+	23.0862i	1.40109	+	0.758249i
$928$	27.9541	−	48.4180i	0.917640	−	1.58940i
$929$	51.0968			1.67643			0.838216	−	0.545338i	$-0.183599\pi$
$929$	51.0968			1.67643			0.838216	+	0.545338i	$0.183599\pi$
$930$	−14.5027	+	4.10088i	−0.475561	+	0.134473i
$931$	−0.196776	+	10.9084i	−0.00644907	+	0.357507i
$932$	1.19537	+	2.07044i	0.0391556	+	0.0678195i
$933$	−6.81137	−	6.62627i	−0.222994	−	0.216934i
$934$	−19.3003	−	33.4292i	−0.631527	−	1.09384i
$935$	−4.58965	+	7.94951i	−0.150098	+	0.259977i
$936$	−7.41483	+	4.55778i	−0.242361	+	0.148976i
$937$	8.55313			0.279419			0.139709	−	0.990193i	$-0.455383\pi$
$937$	8.55313			0.279419			0.139709	+	0.990193i	$0.455383\pi$
$938$	−3.60212	+	12.9741i	−0.117613	+	0.423620i
$939$	18.0780	+	17.5868i	0.589954	+	0.573922i
$940$	−15.5112	+	26.8661i	−0.505919	+	0.876277i
$941$	−0.496939			−0.0161997			−0.00809987	−	0.999967i	$-0.502578\pi$
$941$	−0.496939			−0.0161997			−0.00809987	+	0.999967i	$0.502578\pi$
$942$	−20.2585	−	19.7080i	−0.660057	−	0.642120i
$943$	−44.8221			−1.45961
$944$	3.09136			0.100615
$945$	−32.3139	+	1.04419i	−1.05117	+	0.0339676i
$946$	2.93014			0.0952669
$947$	−48.9953			−1.59213			−0.796067	−	0.605208i	$-0.793090\pi$
$947$	−48.9953			−1.59213			−0.796067	+	0.605208i	$0.793090\pi$
$948$	2.41443	+	2.34882i	0.0784171	+	0.0762861i
$949$	−4.24202			−0.137702
$950$	0.380376	−	0.658831i	0.0123410	−	0.0213753i
$951$	26.5492	+	25.8278i	0.860918	+	0.837523i
$952$	−23.5717	−	24.0008i	−0.763965	−	0.777870i
$953$	−59.0964			−1.91432			−0.957161	−	0.289557i	$-0.906492\pi$
$953$	−59.0964			−1.91432			−0.957161	+	0.289557i	$0.906492\pi$
$954$	−11.3594	−	6.14754i	−0.367773	−	0.199034i
$955$	−7.57583	+	13.1217i	−0.245148	+	0.424609i
$956$	−16.0308	−	27.7662i	−0.518474	−	0.898023i
$957$	−11.3015	−	10.9943i	−0.365324	−	0.355396i
$958$	3.01371	+	5.21990i	0.0973685	+	0.168647i
$959$	−7.65249	+	1.97669i	−0.247112	+	0.0638305i
$960$	22.5566	−	6.37828i	0.728012	−	0.205858i
$961$	−14.8229			−0.478158
$962$	0.703447	−	1.21841i	0.0226800	−	0.0392830i
$963$	39.7116	−	24.4101i	1.27969	−	0.786603i
$964$	0.0506924	+	0.0878018i	0.00163269	+	0.00282791i
$965$	22.1344	−	38.3379i	0.712531	−	1.23414i
$966$	0.110566	+	23.2512i	0.00355740	+	0.748095i
$967$	−11.6586	−	20.1934i	−0.374917	−	0.649375i	0.615398	−	0.788217i	$-0.288995\pi$
$967$	−11.6586	−	20.1934i	−0.374917	−	0.649375i	−0.990315	+	0.138842i	$0.955662\pi$
$968$	14.8060	−	25.6448i	0.475883	−	0.824254i
$969$	−8.48026	−	8.24981i	−0.272425	−	0.265022i
$970$	−18.8978	−	32.7319i	−0.606771	−	1.05096i
$971$	−19.6700	−	34.0695i	−0.631241	−	1.09334i	−0.987298	−	0.158878i	$-0.949212\pi$
$971$	−19.6700	−	34.0695i	−0.631241	−	1.09334i	0.356057	−	0.934464i	$-0.384121\pi$
$972$	−13.5622	−	11.8120i	−0.435008	−	0.378869i
$973$	−47.9949	+	12.3974i	−1.53865	+	0.397442i
$974$	5.55162	−	9.61568i	0.177885	−	0.308106i
$975$	−0.884330	+	0.250060i	−0.0283212	+	0.00800833i
$976$	0.181667			0.00581501
$977$	−7.01823			−0.224533			−0.112267	−	0.993678i	$-0.535811\pi$
$977$	−7.01823			−0.224533			−0.112267	+	0.993678i	$0.535811\pi$
$978$	5.81260	−	22.9529i	0.185866	−	0.733954i
$979$	−0.939613	+	1.62746i	−0.0300302	+	0.0520138i
$980$	−16.6168	+	9.19818i	−0.530805	+	0.293825i
$981$	33.5098	+	18.1351i	1.06989	+	0.579008i
$982$	−13.3809	−	23.1764i	−0.427001	−	0.739587i
$983$	2.60590	+	4.51354i	0.0831152	+	0.143960i	0.904586	−	0.426290i	$-0.140180\pi$
$983$	2.60590	+	4.51354i	0.0831152	+	0.143960i	−0.821471	+	0.570250i	$0.806846\pi$
$984$	−10.0249	+	39.5866i	−0.319582	+	1.26197i
$985$	13.5639	−	23.4933i	0.432181	−	0.748559i
$986$	20.6040	+	35.6871i	0.656164	+	1.13651i
$987$	−45.2507	+	26.4132i	−1.44035	+	0.840742i
$988$	−0.899097	+	1.55728i	−0.0286041	+	0.0495438i
$989$	−9.86273	−	17.0827i	−0.313617	−	0.543200i
$990$	−0.159214	−	5.77815i	−0.00506015	−	0.183642i
$991$	4.40660	−	7.63246i	0.139980	−	0.242453i	−0.787509	−	0.616304i	$-0.788629\pi$
$991$	4.40660	−	7.63246i	0.139980	−	0.242453i	0.927489	+	0.373851i	$0.121963\pi$
$992$	−22.0004			−0.698514
$993$	−8.49217	−	8.26140i	−0.269491	−	0.262167i
$994$	1.28039	−	4.61170i	0.0406115	−	0.146274i
$995$	−15.8273	−	27.4136i	−0.501758	−	0.869070i
$996$	−27.7108	+	7.83571i	−0.878050	+	0.248284i
$997$	−9.83491	−	17.0346i	−0.311475	−	0.539490i	0.667207	−	0.744872i	$-0.267490\pi$
$997$	−9.83491	−	17.0346i	−0.311475	−	0.539490i	−0.978682	+	0.205382i	$0.934156\pi$
$998$	18.8561	−	32.6598i	0.596880	−	1.03383i
$999$	7.75437	+	1.73792i	0.245337	+	0.0549854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.r.a.781.19	yes	96
7.2	even	3		819.2.q.b.79.30	✓	96
9.4	even	3		819.2.q.b.508.30	yes	96
63.58	even	3	inner	819.2.r.a.625.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.q.b.79.30	✓	96	7.2	even	3
819.2.q.b.508.30	yes	96	9.4	even	3
819.2.r.a.625.19	yes	96	63.58	even	3	inner
819.2.r.a.781.19	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.919929 q^{2} +(-1.24150 - 1.20776i) q^{3} -1.15373 q^{4} +(-1.17586 + 2.03665i) q^{5} +(1.14209 + 1.11105i) q^{6} +(-0.707790 + 2.54932i) q^{7} +2.90121 q^{8} +(0.0826321 + 2.99886i) q^{9} +O(q^{10})\)	\(q-0.919929 q^{2} +(-1.24150 - 1.20776i) q^{3} -1.15373 q^{4} +(-1.17586 + 2.03665i) q^{5} +(1.14209 + 1.11105i) q^{6} +(-0.707790 + 2.54932i) q^{7} +2.90121 q^{8} +(0.0826321 + 2.99886i) q^{9} +(1.08171 - 1.87357i) q^{10} +(-0.445310 - 0.771300i) q^{11} +(1.43235 + 1.39343i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.651117 - 2.34519i) q^{14} +(3.91961 - 1.10834i) q^{15} -0.361441 q^{16} +(-2.19130 + 3.79544i) q^{17} +(-0.0760156 - 2.75874i) q^{18} +(-0.779295 - 1.34978i) q^{19} +(1.35663 - 2.34975i) q^{20} +(3.95769 - 2.31013i) q^{21} +(0.409654 + 0.709541i) q^{22} +(2.75776 - 4.77658i) q^{23} +(-3.60184 - 3.50396i) q^{24} +(-0.265294 - 0.459503i) q^{25} +(-0.459964 - 0.796682i) q^{26} +(3.51932 - 3.82288i) q^{27} +(0.816600 - 2.94123i) q^{28} +(-5.11053 + 8.85169i) q^{29} +(-3.60576 + 1.01959i) q^{30} +4.02208 q^{31} -5.46992 q^{32} +(-0.378694 + 1.49540i) q^{33} +(2.01584 - 3.49153i) q^{34} +(-4.35981 - 4.43916i) q^{35} +(-0.0953353 - 3.45988i) q^{36} +(0.764675 + 1.32446i) q^{37} +(0.716896 + 1.24170i) q^{38} +(0.425202 - 1.67905i) q^{39} +(-3.41141 + 5.90874i) q^{40} +(-4.06327 - 7.03779i) q^{41} +(-3.64079 + 2.12516i) q^{42} +(1.78818 - 3.09722i) q^{43} +(0.513768 + 0.889873i) q^{44} +(-6.20479 - 3.35795i) q^{45} +(-2.53694 + 4.39411i) q^{46} -11.4336 q^{47} +(0.448728 + 0.436534i) q^{48} +(-5.99807 - 3.60877i) q^{49} +(0.244051 + 0.422710i) q^{50} +(7.30446 - 2.06547i) q^{51} +(-0.576866 - 0.999161i) q^{52} +(2.34007 - 4.05312i) q^{53} +(-3.23752 + 3.51678i) q^{54} +2.09449 q^{55} +(-2.05345 + 7.39611i) q^{56} +(-0.662716 + 2.61695i) q^{57} +(4.70132 - 8.14292i) q^{58} -8.55287 q^{59} +(-4.52218 + 1.27872i) q^{60} -0.502618 q^{61} -3.70002 q^{62} +(-7.70354 - 1.91191i) q^{63} +5.75481 q^{64} -2.35172 q^{65} +(0.348371 - 1.37566i) q^{66} -5.53222 q^{67} +(2.52817 - 4.37891i) q^{68} +(-9.19271 + 2.59940i) q^{69} +(4.01071 + 4.08371i) q^{70} +1.96645 q^{71} +(0.239733 + 8.70032i) q^{72} +(-2.12101 + 3.67370i) q^{73} +(-0.703447 - 1.21841i) q^{74} +(-0.225607 + 0.890883i) q^{75} +(0.899097 + 1.55728i) q^{76} +(2.28148 - 0.589320i) q^{77} +(-0.391155 + 1.54460i) q^{78} +1.68564 q^{79} +(0.425004 - 0.736129i) q^{80} +(-8.98634 + 0.495605i) q^{81} +(3.73792 + 6.47426i) q^{82} +(-7.20538 + 12.4801i) q^{83} +(-4.56611 + 2.66527i) q^{84} +(-5.15332 - 8.92580i) q^{85} +(-1.64500 + 2.84922i) q^{86} +(17.0354 - 4.81706i) q^{87} +(-1.29194 - 2.23770i) q^{88} +(-1.05501 - 1.82733i) q^{89} +(5.70797 + 3.08907i) q^{90} +(-2.56167 + 0.661696i) q^{91} +(-3.18171 + 5.51089i) q^{92} +(-4.99340 - 4.85770i) q^{93} +10.5181 q^{94} +3.66537 q^{95} +(6.79089 + 6.60634i) q^{96} +(8.73516 - 15.1297i) q^{97} +(5.51779 + 3.31981i) q^{98} +(2.27623 - 1.39916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{2} + 96 q^{4} - 4 q^{5} + 6 q^{6} - 36 q^{8} - 8 q^{9}+O(q^{10}) \) 96 * q - 12 * q^2 + 96 * q^4 - 4 * q^5 + 6 * q^6 - 36 * q^8 - 8 * q^9	\( 96 q - 12 q^{2} + 96 q^{4} - 4 q^{5} + 6 q^{6} - 36 q^{8} - 8 q^{9} + 20 q^{11} - 15 q^{12} + 48 q^{13} + 7 q^{14} + 96 q^{16} - 3 q^{17} + 5 q^{18} - 12 q^{20} + 29 q^{23} - 2 q^{24} - 48 q^{25} - 6 q^{26} + 30 q^{28} + 10 q^{29} + 39 q^{30} - 18 q^{31} - 134 q^{32} - 16 q^{35} - 48 q^{36} - 6 q^{37} - 15 q^{38} - 12 q^{41} - 85 q^{42} + 29 q^{44} - 13 q^{45} - 6 q^{46} + 30 q^{47} - 86 q^{48} + 6 q^{49} + 2 q^{50} + 5 q^{51} + 48 q^{52} + 50 q^{53} + 19 q^{54} - 36 q^{55} + 22 q^{56} + 55 q^{57} + 6 q^{58} + 70 q^{59} - 35 q^{60} + 12 q^{61} - 38 q^{62} + 70 q^{63} + 96 q^{64} - 8 q^{65} - 71 q^{66} + 9 q^{68} + 50 q^{69} - 58 q^{71} + 6 q^{72} + 80 q^{74} - 34 q^{75} + q^{77} + 3 q^{78} - 12 q^{79} - 60 q^{80} - 24 q^{81} - 30 q^{82} - 34 q^{83} + 76 q^{84} + 27 q^{85} + 50 q^{86} + 20 q^{87} - 29 q^{89} - 43 q^{90} + 63 q^{92} + 25 q^{93} + 24 q^{94} - 132 q^{95} - 4 q^{96} - 64 q^{98} - 67 q^{99}+O(q^{100}) \) 96 * q - 12 * q^2 + 96 * q^4 - 4 * q^5 + 6 * q^6 - 36 * q^8 - 8 * q^9 + 20 * q^11 - 15 * q^12 + 48 * q^13 + 7 * q^14 + 96 * q^16 - 3 * q^17 + 5 * q^18 - 12 * q^20 + 29 * q^23 - 2 * q^24 - 48 * q^25 - 6 * q^26 + 30 * q^28 + 10 * q^29 + 39 * q^30 - 18 * q^31 - 134 * q^32 - 16 * q^35 - 48 * q^36 - 6 * q^37 - 15 * q^38 - 12 * q^41 - 85 * q^42 + 29 * q^44 - 13 * q^45 - 6 * q^46 + 30 * q^47 - 86 * q^48 + 6 * q^49 + 2 * q^50 + 5 * q^51 + 48 * q^52 + 50 * q^53 + 19 * q^54 - 36 * q^55 + 22 * q^56 + 55 * q^57 + 6 * q^58 + 70 * q^59 - 35 * q^60 + 12 * q^61 - 38 * q^62 + 70 * q^63 + 96 * q^64 - 8 * q^65 - 71 * q^66 + 9 * q^68 + 50 * q^69 - 58 * q^71 + 6 * q^72 + 80 * q^74 - 34 * q^75 + q^77 + 3 * q^78 - 12 * q^79 - 60 * q^80 - 24 * q^81 - 30 * q^82 - 34 * q^83 + 76 * q^84 + 27 * q^85 + 50 * q^86 + 20 * q^87 - 29 * q^89 - 43 * q^90 + 63 * q^92 + 25 * q^93 + 24 * q^94 - 132 * q^95 - 4 * q^96 - 64 * q^98 - 67 * q^99

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