LMFDB - Embedded newform 287.2.n.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(64,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("287.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	287.64
Dual form			287.2.n.a.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849806 - 2.61543i) q^{2} +0.744022i q^{3} +(-4.50028 + 3.26965i) q^{4} +(-1.22809 + 0.892261i) q^{5} +(1.94594 - 0.632274i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(7.92627 + 5.75877i) q^{8} +2.44643 q^{9} +O(q^{10})$	\(q+(-0.849806 - 2.61543i) q^{2} +0.744022i q^{3} +(-4.50028 + 3.26965i) q^{4} +(-1.22809 + 0.892261i) q^{5} +(1.94594 - 0.632274i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(7.92627 + 5.75877i) q^{8} +2.44643 q^{9} +(3.37729 + 2.45374i) q^{10} +(-0.874353 + 1.20344i) q^{11} +(-2.43269 - 3.34831i) q^{12} +(3.72894 - 1.21161i) q^{13} +2.75003i q^{14} +(-0.663862 - 0.913727i) q^{15} +(4.88798 - 15.0437i) q^{16} +(-0.144304 + 0.198618i) q^{17} +(-2.07899 - 6.39848i) q^{18} +(5.63170 + 1.82985i) q^{19} +(2.60938 - 8.03085i) q^{20} +(0.229915 - 0.707607i) q^{21} +(3.89056 + 1.26412i) q^{22} +(1.97398 + 6.07529i) q^{23} +(-4.28465 + 5.89732i) q^{24} +(-0.833005 + 2.56373i) q^{25} +(-6.33775 - 8.72316i) q^{26} +4.05226i q^{27} +(5.29040 - 1.71896i) q^{28} +(-1.66454 - 2.29104i) q^{29} +(-1.82564 + 2.51278i) q^{30} +(4.96714 + 3.60884i) q^{31} -23.9047 q^{32} +(-0.895389 - 0.650538i) q^{33} +(0.642101 + 0.208631i) q^{34} +(1.44371 - 0.469089i) q^{35} +(-11.0096 + 7.99897i) q^{36} +(-4.62630 + 3.36120i) q^{37} -16.2843i q^{38} +(0.901462 + 2.77441i) q^{39} -14.8725 q^{40} +(-3.92406 - 5.05982i) q^{41} -2.04608 q^{42} +(1.31974 + 4.06173i) q^{43} -8.27467i q^{44} +(-3.00444 + 2.18286i) q^{45} +(14.2120 - 10.3256i) q^{46} +(-2.90131 + 0.942693i) q^{47} +(11.1928 + 3.63676i) q^{48} +(0.809017 + 0.587785i) q^{49} +7.41314 q^{50} +(-0.147776 - 0.107365i) q^{51} +(-12.8198 + 17.6449i) q^{52} +(4.40459 + 6.06239i) q^{53} +(10.5984 - 3.44364i) q^{54} -2.25809i q^{55} +(-5.75877 - 7.92627i) q^{56} +(-1.36145 + 4.19011i) q^{57} +(-4.57753 + 6.30042i) q^{58} +(-3.49132 - 10.7452i) q^{59} +(5.97513 + 1.94144i) q^{60} +(3.14858 - 9.69032i) q^{61} +(5.21757 - 16.0580i) q^{62} +(-2.32669 - 0.755989i) q^{63} +(10.5384 + 32.4338i) q^{64} +(-3.49841 + 4.81515i) q^{65} +(-0.940532 + 2.89466i) q^{66} +(4.28220 + 5.89395i) q^{67} -1.36566i q^{68} +(-4.52015 + 1.46869i) q^{69} +(-2.45374 - 3.37729i) q^{70} +(-6.04701 + 8.32300i) q^{71} +(19.3911 + 14.0884i) q^{72} +12.8474 q^{73} +(12.7224 + 9.24340i) q^{74} +(-1.90747 - 0.619774i) q^{75} +(-31.3272 + 10.1788i) q^{76} +(1.20344 - 0.874353i) q^{77} +(6.49022 - 4.71542i) q^{78} -12.4968i q^{79} +(7.41998 + 22.8363i) q^{80} +4.32432 q^{81} +(-9.89892 + 14.5630i) q^{82} +3.20297 q^{83} +(1.27894 + 3.93617i) q^{84} -0.372678i q^{85} +(9.50166 - 6.90336i) q^{86} +(1.70458 - 1.23845i) q^{87} +(-13.8607 + 4.50362i) q^{88} +(9.72555 + 3.16002i) q^{89} +(8.26230 + 6.00291i) q^{90} -3.92084 q^{91} +(-28.7476 - 20.8863i) q^{92} +(-2.68505 + 3.69566i) q^{93} +(4.93110 + 6.78708i) q^{94} +(-8.54895 + 2.77772i) q^{95} -17.7856i q^{96} +(-7.50137 - 10.3247i) q^{97} +(0.849806 - 2.61543i) q^{98} +(-2.13905 + 2.94414i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.849806	−	2.61543i	−0.600903	−	1.84939i	−0.522820	−	0.852443i	$-0.675120\pi$
$2$	−0.849806	−	2.61543i	−0.600903	−	1.84939i	−0.0780834	−	0.996947i	$-0.524880\pi$
$3$			0.744022i			0.429561i	0.976662	+	0.214781i	$0.0689037\pi$
$3$			0.744022i			0.429561i	−0.976662	+	0.214781i	$0.931096\pi$
$4$	−4.50028	+	3.26965i	−2.25014	+	1.63482i
$5$	−1.22809	+	0.892261i	−0.549219	+	0.399031i	−0.827498	−	0.561469i	$-0.810236\pi$
$5$	−1.22809	+	0.892261i	−0.549219	+	0.399031i	0.278278	+	0.960501i	$0.410236\pi$
$6$	1.94594	−	0.632274i	0.794426	−	0.258125i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$8$	7.92627	+	5.75877i	2.80236	+	2.03603i
$9$	2.44643			0.815477
$10$	3.37729	+	2.45374i	1.06799	+	0.775942i
$11$	−0.874353	+	1.20344i	−0.263627	+	0.362852i	−0.920225	−	0.391389i	$-0.871995\pi$
$11$	−0.874353	+	1.20344i	−0.263627	+	0.362852i	0.656598	+	0.754241i	$0.271995\pi$
$12$	−2.43269	−	3.34831i	−0.702257	−	0.966574i
$13$	3.72894	−	1.21161i	1.03422	−	0.336039i	0.257764	−	0.966208i	$-0.417014\pi$
$13$	3.72894	−	1.21161i	1.03422	−	0.336039i	0.776458	+	0.630169i	$0.217014\pi$
$14$			2.75003i			0.734976i
$15$	−0.663862	−	0.913727i	−0.171408	−	0.235923i
$16$	4.88798	−	15.0437i	1.22199	−	3.76091i
$17$	−0.144304	+	0.198618i	−0.0349989	+	0.0481718i	−0.826158	−	0.563439i	$-0.809478\pi$
$17$	−0.144304	+	0.198618i	−0.0349989	+	0.0481718i	0.791159	+	0.611611i	$0.209478\pi$
$18$	−2.07899	−	6.39848i	−0.490023	−	1.50814i
$19$	5.63170	+	1.82985i	1.29200	+	0.419796i	0.872791	−	0.488093i	$-0.162307\pi$
$19$	5.63170	+	1.82985i	1.29200	+	0.419796i	0.419209	+	0.907890i	$0.362307\pi$
$20$	2.60938	−	8.03085i	0.583476	−	1.79575i
$21$	0.229915	−	0.707607i	0.0501717	−	0.154412i
$22$	3.89056	+	1.26412i	0.829469	+	0.269511i
$23$	1.97398	+	6.07529i	0.411604	+	1.26679i	0.915253	+	0.402878i	$0.131990\pi$
$23$	1.97398	+	6.07529i	0.411604	+	1.26679i	−0.503650	+	0.863908i	$0.668010\pi$
$24$	−4.28465	+	5.89732i	−0.874601	+	1.20378i
$25$	−0.833005	+	2.56373i	−0.166601	+	0.512745i
$26$	−6.33775	−	8.72316i	−1.24293	−	1.71075i
$27$			4.05226i			0.779859i
$28$	5.29040	−	1.71896i	0.999792	−	0.324852i
$29$	−1.66454	−	2.29104i	−0.309097	−	0.425435i	0.626002	−	0.779821i	$-0.284690\pi$
$29$	−1.66454	−	2.29104i	−0.309097	−	0.425435i	−0.935099	+	0.354386i	$0.884690\pi$
$30$	−1.82564	+	2.51278i	−0.333315	+	0.458768i
$31$	4.96714	+	3.60884i	0.892125	+	0.648166i	0.936431	−	0.350852i	$-0.114108\pi$
$31$	4.96714	+	3.60884i	0.892125	+	0.648166i	−0.0443065	+	0.999018i	$0.514108\pi$
$32$	−23.9047			−4.22579
$33$	−0.895389	−	0.650538i	−0.155867	−	0.113244i
$34$	0.642101	+	0.208631i	0.110119	+	0.0357800i
$35$	1.44371	−	0.469089i	0.244031	−	0.0792906i
$36$	−11.0096	+	7.99897i	−1.83494	+	1.33316i
$37$	−4.62630	+	3.36120i	−0.760558	+	0.552578i	−0.899082	−	0.437781i	$-0.855764\pi$
$37$	−4.62630	+	3.36120i	−0.760558	+	0.552578i	0.138523	+	0.990359i	$0.455764\pi$
$38$		−	16.2843i		−	2.64167i
$39$	0.901462	+	2.77441i	0.144349	+	0.444262i
$40$	−14.8725			−2.35155
$41$	−3.92406	−	5.05982i	−0.612836	−	0.790210i
$41$	−3.92406	−	5.05982i	−0.612836	−	0.790210i
$42$	−2.04608			−0.315717
$43$	1.31974	+	4.06173i	0.201258	+	0.619408i	0.999846	+	0.0175303i	$0.00558037\pi$
$43$	1.31974	+	4.06173i	0.201258	+	0.619408i	−0.798589	+	0.601877i	$0.794420\pi$
$44$		−	8.27467i		−	1.24745i
$45$	−3.00444	+	2.18286i	−0.447876	+	0.325401i
$46$	14.2120	−	10.3256i	2.09545	−	1.52243i
$47$	−2.90131	+	0.942693i	−0.423200	+	0.137506i	−0.512871	−	0.858465i	$-0.671418\pi$
$47$	−2.90131	+	0.942693i	−0.423200	+	0.137506i	0.0896716	+	0.995971i	$0.471418\pi$
$48$	11.1928	+	3.63676i	1.61554	+	0.524922i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	7.41314			1.04838
$51$	−0.147776	−	0.107365i	−0.0206928	−	0.0150342i
$52$	−12.8198	+	17.6449i	−1.77778	+	2.44691i
$53$	4.40459	+	6.06239i	0.605016	+	0.832734i	0.996156	−	0.0875978i	$-0.0279190\pi$
$53$	4.40459	+	6.06239i	0.605016	+	0.832734i	−0.391140	+	0.920331i	$0.627919\pi$
$54$	10.5984	−	3.44364i	1.44226	−	0.468620i
$55$		−	2.25809i		−	0.304481i
$56$	−5.75877	−	7.92627i	−0.769548	−	1.05919i
$57$	−1.36145	+	4.19011i	−0.180328	+	0.554993i
$58$	−4.57753	+	6.30042i	−0.601059	+	0.827286i
$59$	−3.49132	−	10.7452i	−0.454531	−	1.39890i	−0.871685	−	0.490066i	$-0.836972\pi$
$59$	−3.49132	−	10.7452i	−0.454531	−	1.39890i	0.417154	−	0.908836i	$-0.363028\pi$
$60$	5.97513	+	1.94144i	0.771386	+	0.250639i
$61$	3.14858	−	9.69032i	0.403134	−	1.24072i	−0.519310	−	0.854586i	$-0.673811\pi$
$61$	3.14858	−	9.69032i	0.403134	−	1.24072i	0.922443	−	0.386132i	$-0.126189\pi$
$62$	5.21757	−	16.0580i	0.662632	−	2.03937i
$63$	−2.32669	−	0.755989i	−0.293136	−	0.0952456i
$64$	10.5384	+	32.4338i	1.31730	+	4.05422i
$65$	−3.49841	+	4.81515i	−0.433925	+	0.597246i
$66$	−0.940532	+	2.89466i	−0.115771	+	0.356308i
$67$	4.28220	+	5.89395i	0.523154	+	0.720060i	0.986068	−	0.166343i	$-0.0531960\pi$
$67$	4.28220	+	5.89395i	0.523154	+	0.720060i	−0.462914	+	0.886403i	$0.653196\pi$
$68$		−	1.36566i		−	0.165610i
$69$	−4.52015	+	1.46869i	−0.544162	+	0.176809i
$70$	−2.45374	−	3.37729i	−0.293278	−	0.403663i
$71$	−6.04701	+	8.32300i	−0.717648	+	0.987758i	0.281950	+	0.959429i	$0.409019\pi$
$71$	−6.04701	+	8.32300i	−0.717648	+	0.987758i	−0.999599	+	0.0283292i	$0.990981\pi$
$72$	19.3911	+	14.0884i	2.28526	+	1.66034i
$73$	12.8474			1.50367			0.751837	−	0.659349i	$-0.229168\pi$
$73$	12.8474			1.50367			0.751837	+	0.659349i	$0.229168\pi$
$74$	12.7224	+	9.24340i	1.47895	+	1.07452i
$75$	−1.90747	−	0.619774i	−0.220255	−	0.0715653i
$76$	−31.3272	+	10.1788i	−3.59348	+	1.16759i
$77$	1.20344	−	0.874353i	0.137145	−	0.0996418i
$78$	6.49022	−	4.71542i	0.734873	−	0.533917i
$79$		−	12.4968i		−	1.40600i	−0.711189	−	0.703001i	$-0.751843\pi$
$79$		−	12.4968i		−	1.40600i	0.711189	−	0.703001i	$-0.248157\pi$
$80$	7.41998	+	22.8363i	0.829579	+	2.55318i
$81$	4.32432			0.480480
$82$	−9.89892	+	14.5630i	−1.09315	+	1.60821i
$83$	3.20297			0.351572			0.175786	−	0.984428i	$-0.443753\pi$
$83$	3.20297			0.351572			0.175786	+	0.984428i	$0.443753\pi$
$84$	1.27894	+	3.93617i	0.139544	+	0.429472i
$85$		−	0.372678i		−	0.0404226i
$86$	9.50166	−	6.90336i	1.02459	−	0.744408i
$87$	1.70458	−	1.23845i	0.182751	−	0.132776i
$88$	−13.8607	+	4.50362i	−1.47756	+	0.480087i
$89$	9.72555	+	3.16002i	1.03091	+	0.334962i	0.775148	−	0.631779i	$-0.217675\pi$
$89$	9.72555	+	3.16002i	1.03091	+	0.334962i	0.255758	+	0.966741i	$0.417675\pi$
$90$	8.26230	+	6.00291i	0.870923	+	0.632763i
$91$	−3.92084			−0.411016
$92$	−28.7476	−	20.8863i	−2.99714	−	2.17755i
$93$	−2.68505	+	3.69566i	−0.278427	+	0.383222i
$94$	4.93110	+	6.78708i	0.508604	+	0.700034i
$95$	−8.54895	+	2.77772i	−0.877104	+	0.284988i
$96$		−	17.7856i		−	1.81524i
$97$	−7.50137	−	10.3247i	−0.761649	−	1.04832i	−0.997075	−	0.0764271i	$-0.975649\pi$
$97$	−7.50137	−	10.3247i	−0.761649	−	1.04832i	0.235427	−	0.971892i	$-0.424351\pi$
$98$	0.849806	−	2.61543i	0.0858433	−	0.264199i
$99$	−2.13905	+	2.94414i	−0.214982	+	0.295897i
$100$	−4.63372	−	14.2611i	−0.463372	−	1.42611i
$101$	−16.7585	−	5.44517i	−1.66753	−	0.541815i	−0.685104	−	0.728445i	$-0.740243\pi$
$101$	−16.7585	−	5.44517i	−1.66753	−	0.541815i	−0.982430	+	0.186630i	$0.940243\pi$
$102$	−0.155226	+	0.477738i	−0.0153697	+	0.0473031i
$103$	−2.96811	+	9.13489i	−0.292456	+	0.900087i	0.691608	+	0.722273i	$0.256903\pi$
$103$	−2.96811	+	9.13489i	−0.292456	+	0.900087i	−0.984064	+	0.177814i	$0.943097\pi$
$104$	36.5339	+	11.8706i	3.58245	+	1.16401i
$105$	0.349013	+	1.07415i	0.0340602	+	0.104826i
$106$	12.1127	−	16.6718i	1.17649	−	1.61930i
$107$	3.42491	−	10.5408i	0.331098	−	1.01902i	−0.637514	−	0.770439i	$-0.720037\pi$
$107$	3.42491	−	10.5408i	0.331098	−	1.01902i	0.968612	−	0.248577i	$-0.0799629\pi$
$108$	−13.2495	−	18.2363i	−1.27493	−	1.75479i
$109$			1.71182i			0.163963i	0.996634	+	0.0819814i	$0.0261248\pi$
$109$			1.71182i			0.163963i	−0.996634	+	0.0819814i	$0.973875\pi$
$110$	−5.90588	+	1.91894i	−0.563104	+	0.182964i
$111$	−2.50081	−	3.44207i	−0.237366	−	0.326706i
$112$	−9.29749	+	12.7969i	−0.878530	+	1.20919i
$113$	−7.61553	−	5.53301i	−0.716409	−	0.520501i	0.168826	−	0.985646i	$-0.446002\pi$
$113$	−7.61553	−	5.53301i	−0.716409	−	0.520501i	−0.885235	+	0.465144i	$0.846002\pi$
$114$	12.1159			1.13476
$115$	−7.84498	−	5.69971i	−0.731548	−	0.531501i
$116$	14.9818	+	4.86788i	1.39102	+	0.451971i
$117$	9.12260	−	2.96411i	0.843384	−	0.274032i
$118$	−25.1363	+	18.2626i	−2.31399	+	1.68121i
$119$	0.198618	−	0.144304i	0.0182072	−	0.0132283i
$120$		−	11.0655i		−	1.01014i
$121$	2.71540	+	8.35715i	0.246855	+	0.759741i
$122$	−28.0201			−2.53682
$123$	3.76461	−	2.91959i	0.339444	−	0.263250i
$124$	−34.1532			−3.06704
$125$	−3.60995	−	11.1103i	−0.322884	−	0.993735i
$126$			6.72776i			0.599356i
$127$	−8.95001	+	6.50257i	−0.794185	+	0.577009i	−0.909203	−	0.416354i	$-0.863308\pi$
$127$	−8.95001	+	6.50257i	−0.794185	+	0.577009i	0.115017	+	0.993363i	$0.463308\pi$
$128$	37.1942	−	27.0232i	3.28753	−	2.38853i
$129$	−3.02201	+	0.981912i	−0.266074	+	0.0864525i
$130$	15.5667	+	5.05792i	1.36529	+	0.443609i
$131$	15.2920	+	11.1103i	1.33607	+	0.970710i	0.999579	+	0.0290226i	$0.00923949\pi$
$131$	15.2920	+	11.1103i	1.33607	+	0.970710i	0.336489	+	0.941687i	$0.390761\pi$
$132$	6.15653			0.535857
$133$	−4.79061	−	3.48058i	−0.415399	−	0.301805i
$134$	11.7762	−	16.2085i	1.01731	−	1.40020i
$135$	−3.61568	−	4.97655i	−0.311188	−	0.428313i
$136$	−2.28759	+	0.743282i	−0.196159	+	0.0637359i
$137$			1.64142i			0.140236i	0.997539	+	0.0701181i	$0.0223376\pi$
$137$			1.64142i			0.140236i	−0.997539	+	0.0701181i	$0.977662\pi$
$138$	7.68250	+	10.5741i	0.653978	+	0.900123i
$139$	−0.0338601	+	0.104211i	−0.00287197	+	0.00883903i	−0.952482	−	0.304594i	$-0.901479\pi$
$139$	−0.0338601	+	0.104211i	−0.00287197	+	0.00883903i	0.949610	+	0.313433i	$0.101479\pi$
$140$	−4.96334	+	6.83145i	−0.419479	+	0.577363i
$141$	−0.701384	−	2.15864i	−0.0590672	−	0.181790i
$142$	26.9070	+	8.74262i	2.25799	+	0.733665i
$143$	−1.80231	+	5.54694i	−0.150717	+	0.463859i
$144$	11.9581	−	36.8033i	0.996509	−	3.06694i
$145$	4.08841	+	1.32840i	0.339524	+	0.110318i
$146$	−10.9178	−	33.6015i	−0.903562	−	2.78088i
$147$	−0.437325	+	0.601926i	−0.0360700	+	0.0496461i
$148$	9.82970	−	30.2527i	0.807997	−	2.48676i
$149$	−7.35329	−	10.1209i	−0.602405	−	0.829139i	0.393521	−	0.919316i	$-0.371257\pi$
$149$	−7.35329	−	10.1209i	−0.602405	−	0.829139i	−0.995926	+	0.0901765i	$0.971257\pi$
$150$			5.51554i			0.450342i
$151$	17.5242	−	5.69394i	1.42610	−	0.463367i	0.508562	−	0.861025i	$-0.330177\pi$
$151$	17.5242	−	5.69394i	1.42610	−	0.463367i	0.917534	+	0.397658i	$0.130177\pi$
$152$	34.1007	+	46.9356i	2.76593	+	3.80698i
$153$	−0.353030	+	0.485904i	−0.0285408	+	0.0392830i
$154$	−3.30951	−	2.40450i	−0.266688	−	0.193760i
$155$	−9.32013			−0.748611
$156$	−13.1282	−	9.53819i	−1.05110	−	0.763666i
$157$	−5.45389	−	1.77208i	−0.435268	−	0.141427i	0.0831835	−	0.996534i	$-0.473491\pi$
$157$	−5.45389	−	1.77208i	−0.435268	−	0.141427i	−0.518451	+	0.855107i	$0.673491\pi$
$158$	−32.6846	+	10.6199i	−2.60025	+	0.844872i
$159$	−4.51055	+	3.27711i	−0.357710	+	0.259892i
$160$	29.3571	−	21.3292i	2.32089	−	1.68622i
$161$		−	6.38794i		−	0.503440i
$162$	−3.67483	−	11.3100i	−0.288722	−	0.888595i
$163$	−12.9976			−1.01805			−0.509026	−	0.860751i	$-0.669994\pi$
$163$	−12.9976			−1.01805			−0.509026	+	0.860751i	$0.669994\pi$
$164$	34.2032	+	9.94030i	2.67082	+	0.776207i
$165$	1.68007			0.130793
$166$	−2.72190	−	8.37716i	−0.211261	−	0.650194i
$167$			5.81777i			0.450193i	0.974337	+	0.225096i	$0.0722697\pi$
$167$			5.81777i			0.450193i	−0.974337	+	0.225096i	$0.927730\pi$
$168$	5.89732	−	4.28465i	0.454988	−	0.330568i
$169$	1.91979	−	1.39481i	0.147676	−	0.107293i
$170$	−0.974713	+	0.316703i	−0.0747571	+	0.0242900i
$171$	13.7776	+	4.47660i	1.05360	+	0.342334i
$172$	−19.2196	−	13.9639i	−1.46548	−	1.06473i
$173$	−11.5221			−0.876007			−0.438004	−	0.898973i	$-0.644314\pi$
$173$	−11.5221			−0.876007			−0.438004	+	0.898973i	$0.644314\pi$
$174$	−4.68765	−	3.40578i	−0.355370	−	0.258191i
$175$	1.58447	−	2.18084i	0.119775	−	0.164856i
$176$	13.8304	+	19.0359i	1.04250	+	1.43488i
$177$	7.99464	−	2.59762i	0.600914	−	0.195249i
$178$		−	28.1219i		−	2.10783i
$179$	0.0852672	+	0.117360i	0.00637317	+	0.00877192i	0.812192	−	0.583391i	$-0.198274\pi$
$179$	0.0852672	+	0.117360i	0.00637317	+	0.00877192i	−0.805819	+	0.592163i	$0.798274\pi$
$180$	6.38368	−	19.6469i	0.475811	−	1.46440i
$181$	6.11598	−	8.41793i	0.454597	−	0.625700i	−0.518780	−	0.854908i	$-0.673614\pi$
$181$	6.11598	−	8.41793i	0.454597	−	0.625700i	0.973377	+	0.229208i	$0.0736137\pi$
$182$	3.33195	+	10.2547i	0.246981	+	0.760128i
$183$	7.20981	+	2.34261i	0.532965	+	0.173171i
$184$	−19.3399	+	59.5221i	−1.42576	+	4.38803i
$185$	2.68245	−	8.25573i	0.197218	−	0.606973i
$186$	11.9475	+	3.88199i	0.876035	+	0.284641i
$187$	−0.112852	−	0.347324i	−0.00825258	−	0.0253988i
$188$	9.97445	−	13.7287i	0.727462	−	1.00126i
$189$	1.25222	−	3.85393i	0.0910855	−	0.280332i
$190$	14.5299	+	19.9987i	1.05411	+	1.45086i
$191$			16.6172i			1.20238i	0.799106	+	0.601190i	$0.205307\pi$
$191$			16.6172i			1.20238i	−0.799106	+	0.601190i	$0.794693\pi$
$192$	−24.1314	+	7.84078i	−1.74154	+	0.565860i
$193$	2.06178	+	2.83780i	0.148410	+	0.204269i	0.876749	−	0.480948i	$-0.159707\pi$
$193$	2.06178	+	2.83780i	0.148410	+	0.204269i	−0.728339	+	0.685217i	$0.759707\pi$
$194$	−20.6290	+	28.3933i	−1.48107	+	2.03852i
$195$	−3.58258	−	2.60290i	−0.256554	−	0.186397i
$196$	−5.56266			−0.397333
$197$	−14.5901	−	10.6003i	−1.03950	−	0.755241i	−0.0693121	−	0.997595i	$-0.522080\pi$
$197$	−14.5901	−	10.6003i	−1.03950	−	0.755241i	−0.970188	+	0.242354i	$0.922080\pi$
$198$	9.51798	+	3.09258i	0.676413	+	0.219780i
$199$	−7.62651	+	2.47800i	−0.540629	+	0.175661i	−0.566587	−	0.824002i	$-0.691736\pi$
$199$	−7.62651	+	2.47800i	−0.540629	+	0.175661i	0.0259578	+	0.999663i	$0.491736\pi$
$200$	−21.3665	+	15.5237i	−1.51084	+	1.09769i
$201$	−4.38523	+	3.18605i	−0.309310	+	0.224727i
$202$			48.4581i			3.40950i
$203$	0.875099	+	2.69328i	0.0614199	+	0.189031i
$204$	1.01608			0.0711399
$205$	9.33379	+	2.71263i	0.651900	+	0.189458i
$206$	26.4140			1.84035
$207$	4.82921	+	14.8628i	0.335654	+	1.03304i
$208$		−	62.0192i		−	4.30026i
$209$	−7.12622	+	5.17750i	−0.492931	+	0.358135i
$210$	2.51278	−	1.82564i	0.173398	−	0.125981i
$211$	11.9855	−	3.89433i	0.825118	−	0.268097i	0.134130	−	0.990964i	$-0.457176\pi$
$211$	11.9855	−	3.89433i	0.825118	−	0.268097i	0.690988	+	0.722867i	$0.257176\pi$
$212$	−39.6438	−	12.8810i	−2.72275	−	0.884674i
$213$	−6.19249	−	4.49911i	−0.424303	−	0.308274i
$214$	−30.4792			−2.08352
$215$	−5.24488	−	3.81063i	−0.357698	−	0.259883i
$216$	−23.3361	+	32.1193i	−1.58782	+	2.18544i
$217$	−3.60884	−	4.96714i	−0.244984	−	0.337191i
$218$	4.47716	−	1.45472i	0.303231	−	0.0985258i
$219$			9.55874i			0.645920i
$220$	7.38316	+	10.1620i	0.497773	+	0.685125i
$221$	−0.297455	+	0.915473i	−0.0200090	+	0.0615814i
$222$	−6.87729	+	9.46578i	−0.461574	+	0.635301i
$223$	−0.456893	−	1.40617i	−0.0305958	−	0.0941643i	0.934592	−	0.355720i	$-0.115764\pi$
$223$	−0.456893	−	1.40617i	−0.0305958	−	0.0941643i	−0.965188	+	0.261556i	$0.915764\pi$
$224$	22.7347	+	7.38695i	1.51903	+	0.493562i
$225$	−2.03789	+	6.27198i	−0.135859	+	0.418132i
$226$	−7.99949	+	24.6199i	−0.532118	+	1.63769i
$227$	3.97717	+	1.29226i	0.263974	+	0.0857704i	0.438014	−	0.898968i	$-0.355682\pi$
$227$	3.97717	+	1.29226i	0.263974	+	0.0857704i	−0.174040	+	0.984739i	$0.555682\pi$
$228$	−7.57327	−	23.3081i	−0.501552	−	1.54362i
$229$	16.2924	−	22.4246i	1.07663	−	1.48186i	0.213461	−	0.976952i	$-0.431527\pi$
$229$	16.2924	−	22.4246i	1.07663	−	1.48186i	0.863173	−	0.504908i	$-0.168473\pi$
$230$	−8.24050	+	25.3617i	−0.543363	+	1.67230i
$231$	0.650538	+	0.895389i	0.0428023	+	0.0589123i
$232$		−	27.7451i		−	1.82155i
$233$	4.59166	−	1.49192i	0.300809	−	0.0977389i	−0.154724	−	0.987958i	$-0.549449\pi$
$233$	4.59166	−	1.49192i	0.300809	−	0.0977389i	0.455533	+	0.890219i	$0.349449\pi$
$234$	−15.5049	−	21.3406i	−1.01358	−	1.39508i
$235$	2.72195	−	3.74644i	0.177560	−	0.244391i
$236$	50.8448	+	36.9409i	3.30972	+	2.40465i
$237$	9.29791			0.603964
$238$	−0.546204	−	0.396840i	−0.0354051	−	0.0257233i
$239$	2.87972	+	0.935677i	0.186274	+	0.0605239i	0.400668	−	0.916223i	$-0.368778\pi$
$239$	2.87972	+	0.935677i	0.186274	+	0.0605239i	−0.214395	+	0.976747i	$0.568778\pi$
$240$	−16.9907	+	5.52063i	−1.09675	+	0.356355i
$241$	−2.04663	+	1.48696i	−0.131835	+	0.0957838i	−0.651748	−	0.758435i	$-0.725964\pi$
$241$	−2.04663	+	1.48696i	−0.131835	+	0.0957838i	0.519913	+	0.854219i	$0.325964\pi$
$242$	19.5500	−	14.2039i	1.25672	−	0.913062i
$243$			15.3742i			0.986254i
$244$	17.5144	+	53.9039i	1.12125	+	3.45085i
$245$	−1.51801			−0.0969818
$246$	−10.8352	−	7.36501i	−0.690826	−	0.469576i
$247$	23.2173			1.47728
$248$	18.5884	+	57.2092i	1.18037	+	3.63279i
$249$			2.38308i			0.151022i
$250$	−25.9905	+	18.8832i	−1.64378	+	1.19428i
$251$	−1.65871	+	1.20513i	−0.104697	+	0.0760669i	−0.638902	−	0.769288i	$-0.720611\pi$
$251$	−1.65871	+	1.20513i	−0.104697	+	0.0760669i	0.534205	+	0.845355i	$0.320611\pi$
$252$	12.9426	−	4.20531i	0.815307	−	0.264909i
$253$	−9.03723	−	2.93638i	−0.568166	−	0.184608i
$254$	24.6128	+	17.8822i	1.54434	+	1.12203i
$255$	0.277280			0.0173640
$256$	−47.1054	−	34.2241i	−2.94409	−	2.13901i
$257$	8.01211	−	11.0277i	0.499782	−	0.687891i	−0.482373	−	0.875966i	$-0.660225\pi$
$257$	8.01211	−	11.0277i	0.499782	−	0.687891i	0.982155	+	0.188075i	$0.0602249\pi$
$258$	5.13625	+	7.06944i	0.319769	+	0.440124i
$259$	5.43854	−	1.76709i	0.337934	−	0.109801i
$260$		−	33.1081i		−	2.05328i
$261$	−4.07218	−	5.60487i	−0.252061	−	0.346933i
$262$	16.0630	−	49.4368i	0.992374	−	3.05421i
$263$	0.578063	−	0.795636i	0.0356449	−	0.0490610i	−0.790823	−	0.612045i	$-0.790347\pi$
$263$	0.578063	−	0.795636i	0.0356449	−	0.0490610i	0.826467	+	0.562984i	$0.190347\pi$
$264$	−3.35079	−	10.3127i	−0.206227	−	0.634701i
$265$	−10.8185	−	3.51513i	−0.664573	−	0.215933i
$266$	−5.03214	+	15.4873i	−0.308540	+	0.949589i
$267$	−2.35113	+	7.23602i	−0.143887	+	0.442837i
$268$	−38.5423	−	12.5231i	−2.35434	−	0.764972i
$269$	−5.59270	−	17.2126i	−0.340993	−	1.04947i	−0.963694	−	0.267008i	$-0.913965\pi$
$269$	−5.59270	−	17.2126i	−0.340993	−	1.04947i	0.622701	−	0.782460i	$-0.286035\pi$
$270$	−9.94322	+	13.6857i	−0.605125	+	0.832883i
$271$	7.50395	−	23.0948i	0.455832	−	1.40291i	−0.414323	−	0.910130i	$-0.635981\pi$
$271$	7.50395	−	23.0948i	0.455832	−	1.40291i	0.870155	−	0.492778i	$-0.164019\pi$
$272$	2.28258	+	3.14170i	0.138402	+	0.190494i
$273$		−	2.91719i		−	0.176556i
$274$	4.29303	−	1.39489i	0.259352	−	0.0842684i
$275$	−2.35696	−	3.24408i	−0.142130	−	0.195625i
$276$	15.5399	−	21.3888i	0.935391	−	1.28746i
$277$	−11.6298	−	8.44956i	−0.698768	−	0.507685i	0.180763	−	0.983527i	$-0.442143\pi$
$277$	−11.6298	−	8.44956i	−0.698768	−	0.507685i	−0.879531	+	0.475842i	$0.842143\pi$
$278$	0.301330			0.0180726
$279$	12.1518	+	8.82877i	0.727507	+	0.528565i
$280$	14.1446	+	4.59586i	0.845302	+	0.274655i
$281$	22.8784	−	7.43365i	1.36481	−	0.443455i	0.467166	−	0.884170i	$-0.345275\pi$
$281$	22.8784	−	7.43365i	1.36481	−	0.443455i	0.897647	+	0.440715i	$0.145275\pi$
$282$	−5.04974	+	3.66885i	−0.300707	+	0.218477i
$283$	−10.6473	+	7.73572i	−0.632916	+	0.459841i	−0.857409	−	0.514635i	$-0.827927\pi$
$283$	−10.6473	+	7.73572i	−0.632916	+	0.459841i	0.224493	+	0.974476i	$0.427927\pi$
$284$		−	57.2275i		−	3.39582i
$285$	−2.06669	−	6.36061i	−0.122420	−	0.376770i
$286$	16.0393			0.948422
$287$	2.16844	+	6.02477i	0.127999	+	0.355631i
$288$	−58.4812			−3.44604
$289$	5.23466	+	16.1106i	0.307921	+	0.947685i
$290$		−	11.8218i		−	0.694203i
$291$	7.68184	−	5.58118i	0.450317	−	0.327175i
$292$	−57.8169	+	42.0064i	−3.38348	+	2.45824i
$293$	6.07758	−	1.97473i	0.355056	−	0.115365i	−0.126058	−	0.992023i	$-0.540232\pi$
$293$	6.07758	−	1.97473i	0.355056	−	0.115365i	0.481114	+	0.876658i	$0.340232\pi$
$294$	1.94594	+	0.632274i	0.113489	+	0.0368750i
$295$	13.8752	+	10.0809i	0.807843	+	0.586932i
$296$	−56.0257			−3.25642
$297$	−4.87667	−	3.54311i	−0.282973	−	0.205592i
$298$	−20.2218	+	27.8329i	−1.17141	+	1.61231i
$299$	14.7217	+	20.2627i	0.851380	+	1.17182i
$300$	10.6106	−	3.44759i	0.612603	−	0.199047i
$301$		−	4.27075i		−	0.246162i
$302$	−29.7843	−	40.9945i	−1.71389	−	2.35897i
$303$	4.05133	−	12.4687i	0.232743	−	0.716308i
$304$	55.0553	−	75.7771i	3.15764	−	4.34611i
$305$	4.77955	+	14.7100i	0.273677	+	0.842290i
$306$	1.57086	+	0.510402i	0.0897999	+	0.0291778i
$307$	4.87157	−	14.9931i	0.278035	−	0.855704i	−0.710365	−	0.703833i	$-0.751470\pi$
$307$	4.87157	−	14.9931i	0.278035	−	0.855704i	0.988400	−	0.151871i	$-0.0485298\pi$
$308$	−2.55701	+	7.86967i	−0.145699	+	0.448416i
$309$	−6.79656	−	2.20834i	−0.386643	−	0.125628i
$310$	7.92030	+	24.3762i	0.449843	+	1.38447i
$311$	−9.22827	+	12.7016i	−0.523287	+	0.720243i	−0.986089	−	0.166219i	$-0.946844\pi$
$311$	−9.22827	+	12.7016i	−0.523287	+	0.720243i	0.462802	+	0.886462i	$0.346844\pi$
$312$	−8.83199	+	27.1821i	−0.500013	+	1.53888i
$313$	18.4317	+	25.3691i	1.04182	+	1.43394i	0.895690	+	0.444678i	$0.146682\pi$
$313$	18.4317	+	25.3691i	1.04182	+	1.43394i	0.146131	+	0.989265i	$0.453318\pi$
$314$			15.7702i			0.889964i
$315$	3.53193	−	1.14759i	0.199002	−	0.0646596i
$316$	40.8602	+	56.2393i	2.29857	+	3.16371i
$317$	18.5659	−	25.5537i	1.04276	−	1.43524i	0.147845	−	0.989011i	$-0.452766\pi$
$317$	18.5659	−	25.5537i	1.04276	−	1.43524i	0.894918	−	0.446230i	$-0.147234\pi$
$318$	12.4041	+	9.01214i	0.695590	+	0.505376i
$319$	4.21253			0.235856
$320$	−41.8815	−	30.4287i	−2.34125	−	1.70101i
$321$	7.84257	+	2.54821i	0.437730	+	0.142227i
$322$	−16.7072	+	5.42851i	−0.931058	+	0.302519i
$323$	−1.17612	+	0.854500i	−0.0654410	+	0.0475456i
$324$	−19.4607	+	14.1390i	−1.08115	+	0.785500i
$325$			10.5693i			0.586277i
$326$	11.0454	+	33.9944i	0.611750	+	1.88277i
$327$	−1.27363			−0.0704321
$328$	−1.96486	−	62.7032i	−0.108491	−	3.46221i
$329$	3.05062			0.168186
$330$	−1.42773	−	4.39411i	−0.0785941	−	0.241888i
$331$		−	20.2274i		−	1.11180i	−0.831249	−	0.555900i	$-0.812374\pi$
$331$		−	20.2274i		−	1.11180i	0.831249	−	0.555900i	$-0.187626\pi$
$332$	−14.4143	+	10.4726i	−0.791087	+	0.574758i
$333$	−11.3179	+	8.22295i	−0.620218	+	0.450615i
$334$	15.2160	−	4.94397i	0.832582	−	0.270522i
$335$	−10.5179	−	3.41747i	−0.574653	−	0.186716i
$336$	−9.52117	−	6.91754i	−0.519423	−	0.377383i
$337$	21.9745			1.19703			0.598515	−	0.801112i	$-0.295758\pi$
$337$	21.9745			1.19703			0.598515	+	0.801112i	$0.295758\pi$
$338$	−5.27946	−	3.83576i	−0.287165	−	0.208638i
$339$	4.11668	−	5.66612i	0.223587	−	0.307741i
$340$	1.21852	+	1.67715i	0.0660838	+	0.0909565i
$341$	−8.68607	+	2.82227i	−0.470377	+	0.152835i
$342$		−	39.8385i		−	2.15422i
$343$	−0.587785	−	0.809017i	−0.0317374	−	0.0436828i
$344$	−12.9300	+	39.7944i	−0.697138	+	2.14557i
$345$	4.24071	−	5.83684i	0.228312	−	0.314245i
$346$	9.79152	+	30.1352i	0.526396	+	1.62008i
$347$	−22.0448	−	7.16278i	−1.18343	−	0.384518i	−0.349787	−	0.936829i	$-0.613746\pi$
$347$	−22.0448	−	7.16278i	−1.18343	−	0.384518i	−0.833638	+	0.552311i	$0.813746\pi$
$348$	−3.62181	+	11.1468i	−0.194149	+	0.597530i
$349$	2.14623	−	6.60542i	0.114885	−	0.353580i	−0.877038	−	0.480421i	$-0.840484\pi$
$349$	2.14623	−	6.60542i	0.114885	−	0.353580i	0.991923	+	0.126841i	$0.0404838\pi$
$350$	−7.05032	−	2.29079i	−0.376855	−	0.122448i
$351$	4.90975	+	15.1107i	0.262063	+	0.806547i
$352$	20.9011	−	28.7679i	1.11403	−	1.53334i
$353$	0.836589	−	2.57476i	0.0445271	−	0.137040i	−0.926321	−	0.376734i	$-0.877047\pi$
$353$	0.836589	−	2.57476i	0.0445271	−	0.137040i	0.970849	+	0.239694i	$0.0770470\pi$
$354$	−13.5878	−	18.7020i	−0.722183	−	0.993999i
$355$		−	15.6169i		−	0.828860i
$356$	−54.0999	+	17.5781i	−2.86729	+	0.931638i
$357$	0.107365	+	0.147776i	0.00568238	+	0.00782113i
$358$	0.234487	−	0.322744i	0.0123930	−	0.0170576i
$359$	−3.74569	−	2.72140i	−0.197690	−	0.143630i	0.484537	−	0.874771i	$-0.338988\pi$
$359$	−3.74569	−	2.72140i	−0.197690	−	0.143630i	−0.682226	+	0.731141i	$0.738988\pi$
$360$	−36.3846			−1.91764
$361$	12.9964	+	9.44241i	0.684019	+	0.496969i
$362$	−27.2139	−	8.84234i	−1.43033	−	0.464743i
$363$	−6.21790	+	2.02032i	−0.326355	+	0.106039i
$364$	17.6449	−	12.8198i	0.924844	−	0.671938i
$365$	−15.7778	+	11.4632i	−0.825847	+	0.600013i
$366$		−	20.8475i		−	1.08972i
$367$	3.63370	+	11.1834i	0.189678	+	0.583768i	0.999998	−	0.00221991i	$-0.000706621\pi$
$367$	3.63370	+	11.1834i	0.189678	+	0.583768i	−0.810320	+	0.585988i	$0.800707\pi$
$368$	101.043			5.26725
$369$	−9.59995	−	12.3785i	−0.499753	−	0.644398i
$370$	−23.8719			−1.24104
$371$	−2.31563	−	7.12677i	−0.120221	−	0.370003i
$372$		−	25.4107i		−	1.31748i
$373$	−10.2556	+	7.45114i	−0.531016	+	0.385805i	−0.820738	−	0.571305i	$-0.806437\pi$
$373$	−10.2556	+	7.45114i	−0.531016	+	0.385805i	0.289722	+	0.957111i	$0.406437\pi$
$374$	−0.812500	+	0.590315i	−0.0420134	+	0.0305245i
$375$	8.26630	−	2.68588i	0.426870	−	0.138698i
$376$	−28.4253	−	9.23595i	−1.46592	−	0.476308i
$377$	−8.98280	−	6.52639i	−0.462638	−	0.336126i
$378$	−11.1438			−0.573177
$379$	−21.5964	−	15.6907i	−1.10934	−	0.805979i	−0.126776	−	0.991931i	$-0.540463\pi$
$379$	−21.5964	−	15.6907i	−1.10934	−	0.805979i	−0.982559	+	0.185952i	$0.940463\pi$
$380$	29.3905	−	40.4526i	1.50770	−	2.07517i
$381$	−4.83805	−	6.65901i	−0.247861	−	0.341151i
$382$	43.4612	−	14.1214i	2.22367	−	0.722514i
$383$		−	30.8195i		−	1.57480i	−0.616440	−	0.787402i	$-0.711426\pi$
$383$		−	30.8195i		−	1.57480i	0.616440	−	0.787402i	$-0.288574\pi$
$384$	20.1058	+	27.6733i	1.02602	+	1.41220i
$385$	−0.697788	+	2.14757i	−0.0355626	+	0.109450i
$386$	5.66996	−	7.80404i	0.288594	−	0.397215i
$387$	3.22864	+	9.93674i	0.164121	+	0.505113i
$388$	67.5166	+	21.9375i	3.42763	+	1.11371i
$389$	−6.97506	+	21.4670i	−0.353649	+	1.08842i	0.603139	+	0.797636i	$0.293916\pi$
$389$	−6.97506	+	21.4670i	−0.353649	+	1.08842i	−0.956788	+	0.290785i	$0.906084\pi$
$390$	−3.76320	+	11.5819i	−0.190557	+	0.586475i
$391$	−1.49151	−	0.484622i	−0.0754291	−	0.0245084i
$392$	3.02757	+	9.31789i	0.152915	+	0.470624i
$393$	−8.26630	+	11.3776i	−0.416979	+	0.573923i
$394$	−15.3257	+	47.1676i	−0.772096	+	2.37627i
$395$	11.1504	+	15.3472i	0.561039	+	0.772204i
$396$		−	20.2434i		−	1.01727i
$397$	−17.1671	+	5.57794i	−0.861594	+	0.279949i	−0.706294	−	0.707918i	$-0.749634\pi$
$397$	−17.1671	+	5.57794i	−0.861594	+	0.279949i	−0.155300	+	0.987867i	$0.549634\pi$
$398$	12.9621	+	17.8408i	0.649731	+	0.894279i
$399$	2.58963	−	3.56432i	0.129644	−	0.178439i
$400$	34.4961	+	25.0629i	1.72480	+	1.25314i
$401$	−8.60959			−0.429942			−0.214971	−	0.976620i	$-0.568966\pi$
$401$	−8.60959			−0.429942			−0.214971	+	0.976620i	$0.568966\pi$
$402$	12.0595	+	8.76174i	0.601473	+	0.436996i
$403$	22.8947	+	7.43892i	1.14046	+	0.370559i
$404$	93.2219	−	30.2896i	4.63796	−	1.50697i
$405$	−5.31066	+	3.85842i	−0.263889	+	0.191727i
$406$	6.30042	−	4.57753i	0.312685	−	0.227179i
$407$		−	8.50636i		−	0.421645i
$408$	−0.553018	−	1.70201i	−0.0273785	−	0.0842623i
$409$	−16.2629			−0.804150			−0.402075	−	0.915607i	$-0.631711\pi$
$409$	−16.2629			−0.804150			−0.402075	+	0.915607i	$0.631711\pi$
$410$	−0.837202	−	26.7171i	−0.0413464	−	1.31946i
$411$	−1.22125			−0.0602401
$412$	−16.5105	−	50.8142i	−0.813416	−	2.50344i
$413$			11.2981i			0.555945i
$414$	34.7687	−	25.2610i	1.70879	−	1.24151i
$415$	−3.93354	+	2.85789i	−0.193090	+	0.140288i
$416$	−89.1391	+	28.9631i	−4.37041	+	1.42003i
$417$	−0.0775350	−	0.0251926i	−0.00379690	−	0.00123369i
$418$	19.5973	+	14.2383i	0.958535	+	0.696417i
$419$	29.8396			1.45776			0.728881	−	0.684641i	$-0.240041\pi$
$419$	29.8396			1.45776			0.728881	+	0.684641i	$0.240041\pi$
$420$	−5.08275	−	3.69283i	−0.248013	−	0.180192i
$421$	−4.82434	+	6.64013i	−0.235124	+	0.323620i	−0.910232	−	0.414098i	$-0.864097\pi$
$421$	−4.82434	+	6.64013i	−0.235124	+	0.323620i	0.675108	+	0.737719i	$0.264097\pi$
$422$	−20.3707	−	28.0379i	−0.991632	−	1.36486i
$423$	−7.09786	+	2.30623i	−0.345110	+	0.112133i
$424$			73.4171i			3.56545i
$425$	−0.388995	−	0.535406i	−0.0188690	−	0.0259710i
$426$	−6.50470	+	20.0194i	−0.315154	+	0.969944i
$427$	−5.98895	+	8.24308i	−0.289826	+	0.398911i
$428$	19.0516	+	58.6348i	0.920893	+	2.83422i
$429$	−4.12705	−	1.34096i	−0.199256	−	0.0647421i
$430$	−5.50931	+	16.9559i	−0.265683	+	0.817687i
$431$	−8.72690	+	26.8586i	−0.420360	+	1.29374i	0.487008	+	0.873398i	$0.338088\pi$
$431$	−8.72690	+	26.8586i	−0.420360	+	1.29374i	−0.907368	+	0.420338i	$0.861912\pi$
$432$	60.9609	+	19.8074i	2.93298	+	0.952983i
$433$	−5.79127	−	17.8237i	−0.278311	−	0.856552i	−0.988324	−	0.152364i	$-0.951311\pi$
$433$	−5.79127	−	17.8237i	−0.278311	−	0.856552i	0.710014	−	0.704188i	$-0.248689\pi$
$434$	−9.92441	+	13.6598i	−0.476387	+	0.655690i
$435$	−0.988362	+	3.04187i	−0.0473884	+	0.145846i
$436$	−5.59706	−	7.70369i	−0.268050	−	0.368940i
$437$			37.8263i			1.80948i
$438$	25.0002	−	8.12307i	1.19456	−	0.388135i
$439$	−9.47154	−	13.0365i	−0.452052	−	0.622196i	0.520785	−	0.853688i	$-0.325639\pi$
$439$	−9.47154	−	13.0365i	−0.452052	−	0.622196i	−0.972837	+	0.231492i	$0.925639\pi$
$440$	13.0038	−	17.8982i	0.619933	−	0.853265i
$441$	1.97920	+	1.43798i	0.0942478	+	0.0684751i
$442$	2.64714			0.125911
$443$	13.7011	+	9.95442i	0.650958	+	0.472949i	0.863597	−	0.504182i	$-0.168206\pi$
$443$	13.7011	+	9.95442i	0.650958	+	0.472949i	−0.212639	+	0.977131i	$0.568206\pi$
$444$	22.5087	+	7.31351i	1.06821	+	0.347084i
$445$	−14.7634	+	4.79693i	−0.699854	+	0.227396i
$446$	−3.28948	+	2.38995i	−0.155761	+	0.113167i
$447$	7.53020	−	5.47101i	0.356166	−	0.258770i
$448$		−	34.1029i		−	1.61121i
$449$	−0.925953	−	2.84979i	−0.0436984	−	0.134490i	0.926827	−	0.375489i	$-0.122525\pi$
$449$	−0.925953	−	2.84979i	−0.0436984	−	0.134490i	−0.970525	+	0.240999i	$0.922525\pi$
$450$	18.1357			0.854927
$451$	9.52022	−	0.298324i	0.448290	−	0.0140475i
$452$	52.3630			2.46295
$453$	4.23642	+	13.0384i	0.199044	+	0.612596i
$454$		−	11.5002i		−	0.539731i
$455$	4.81515	−	3.49841i	0.225738	−	0.164008i
$456$	−34.9211	+	25.3717i	−1.63533	+	1.18814i
$457$	20.7371	−	6.73789i	0.970040	−	0.315185i	0.219208	−	0.975678i	$-0.429653\pi$
$457$	20.7371	−	6.73789i	0.970040	−	0.315185i	0.750832	+	0.660493i	$0.229653\pi$
$458$	−72.4954	−	23.5552i	−3.38749	−	1.10066i
$459$	−0.804851	−	0.584758i	−0.0375672	−	0.0272942i
$460$	53.9407			2.51500
$461$	0.559802	+	0.406720i	0.0260726	+	0.0189429i	0.600745	−	0.799441i	$-0.294871\pi$
$461$	0.559802	+	0.406720i	0.0260726	+	0.0189429i	−0.574673	+	0.818383i	$0.694871\pi$
$462$	1.78900	−	2.46234i	0.0832317	−	0.114559i
$463$	−12.3613	−	17.0139i	−0.574479	−	0.790702i	0.418598	−	0.908172i	$-0.362522\pi$
$463$	−12.3613	−	17.0139i	−0.574479	−	0.790702i	−0.993076	+	0.117470i	$0.962522\pi$
$464$	−42.6018	+	13.8422i	−1.97774	+	0.642607i
$465$		−	6.93438i		−	0.321574i
$466$	−7.80403	−	10.7413i	−0.361515	−	0.497582i
$467$	−10.4301	+	32.1005i	−0.482647	+	1.48543i	0.352713	+	0.935731i	$0.385259\pi$
$467$	−10.4301	+	32.1005i	−0.482647	+	1.48543i	−0.835360	+	0.549703i	$0.814741\pi$
$468$	−31.3627	+	43.1670i	−1.44974	+	1.99540i
$469$	−2.25129	−	6.92875i	−0.103955	−	0.319940i
$470$	−12.1117	−	3.93533i	−0.558671	−	0.181523i
$471$	1.31846	−	4.05781i	0.0607516	−	0.186974i
$472$	34.2059	−	105.275i	1.57445	−	4.84567i
$473$	−6.04198	−	1.96316i	−0.277810	−	0.0902661i
$474$	−7.90142	−	24.3181i	−0.362924	−	1.11697i
$475$	−9.38247	+	12.9139i	−0.430497	+	0.592528i
$476$	−0.422012	+	1.29882i	−0.0193429	+	0.0595313i
$477$	10.7755	+	14.8312i	0.493377	+	0.679075i
$478$		−	8.32686i		−	0.380861i
$479$	−4.32243	+	1.40444i	−0.197497	+	0.0641706i	−0.406095	−	0.913831i	$-0.633110\pi$
$479$	−4.32243	+	1.40444i	−0.197497	+	0.0641706i	0.208598	+	0.978001i	$0.433110\pi$
$480$	15.8694	+	21.8424i	0.724336	+	0.996963i
$481$	−13.1787	+	18.1390i	−0.600898	+	0.827066i
$482$	5.62829	+	4.08919i	0.256362	+	0.186258i
$483$	4.75277			0.216259
$484$	−39.5450	−	28.7311i	−1.79750	−	1.30596i
$485$	18.4247	+	5.98656i	0.836624	+	0.271836i
$486$	40.2101	−	13.0651i	1.82397	−	0.592643i
$487$	12.0461	−	8.75198i	0.545859	−	0.396590i	−0.280397	−	0.959884i	$-0.590466\pi$
$487$	12.0461	−	8.75198i	0.545859	−	0.396590i	0.826256	+	0.563294i	$0.190466\pi$
$488$	80.7608	−	58.6762i	3.65587	−	2.65614i
$489$		−	9.67051i		−	0.437315i
$490$	1.29001	+	3.97024i	0.0582767	+	0.179357i
$491$	−28.3817			−1.28085			−0.640424	−	0.768022i	$-0.721241\pi$
$491$	−28.3817			−1.28085			−0.640424	+	0.768022i	$0.721241\pi$
$492$	−7.39580	+	25.4479i	−0.333429	+	1.14728i
$493$	0.695240			0.0313121
$494$	−19.7302	−	60.7234i	−0.887704	−	2.73207i
$495$		−	5.52426i		−	0.248297i
$496$	78.5694	−	57.0840i	3.52787	−	2.56315i
$497$	8.32300	−	6.04701i	0.373337	−	0.271246i
$498$	6.23279	−	2.02516i	0.279298	−	0.0907494i
$499$	−6.91186	−	2.24580i	−0.309417	−	0.100536i	0.150192	−	0.988657i	$-0.452011\pi$
$499$	−6.91186	−	2.24580i	−0.309417	−	0.100536i	−0.459610	+	0.888121i	$0.652011\pi$
$500$	52.5725	+	38.1962i	2.35112	+	1.70819i
$501$	−4.32855			−0.193385
$502$	4.56151	+	3.31413i	0.203590	+	0.147917i
$503$	−14.0115	+	19.2852i	−0.624743	+	0.859885i	−0.997687	−	0.0679688i	$-0.978348\pi$
$503$	−14.0115	+	19.2852i	−0.624743	+	0.859885i	0.372945	+	0.927854i	$0.378348\pi$
$504$	−14.0884	−	19.3911i	−0.627549	−	0.863747i
$505$	25.4395	−	8.26580i	1.13204	−	0.367823i
$506$			26.1316i			1.16169i
$507$	1.03777	+	1.42836i	0.0460888	+	0.0634358i
$508$	19.0165	−	58.5268i	0.843721	−	2.59671i
$509$	21.2449	−	29.2411i	0.941664	−	1.29609i	−0.0134676	−	0.999909i	$-0.504287\pi$
$509$	21.2449	−	29.2411i	0.941664	−	1.29609i	0.955132	−	0.296180i	$-0.0957130\pi$
$510$	−0.235634	−	0.725208i	−0.0104341	−	0.0321127i
$511$	−12.2186	−	3.97006i	−0.540519	−	0.175625i
$512$	−21.0665	+	64.8362i	−0.931019	+	2.86538i
$513$	−7.41504	+	22.8211i	−0.327382	+	1.00758i
$514$	−35.6510	−	11.5837i	−1.57250	−	0.510936i
$515$	−4.50560	−	13.8668i	−0.198540	−	0.611045i
$516$	10.3894	−	14.2998i	0.457369	−	0.629514i
$517$	1.40229	−	4.31581i	0.0616728	−	0.189809i
$518$	−9.24340	−	12.7224i	−0.406132	−	0.558992i
$519$		−	8.57268i		−	0.376299i
$520$	−55.4587	+	18.0196i	−2.43203	+	0.790213i
$521$	−19.8491	−	27.3199i	−0.869604	−	1.19691i	−0.979193	−	0.202931i	$-0.934953\pi$
$521$	−19.8491	−	27.3199i	−0.869604	−	1.19691i	0.109589	−	0.993977i	$-0.465047\pi$
$522$	−11.1986	+	15.4136i	−0.490149	+	0.674633i
$523$	−18.5912	−	13.5073i	−0.812938	−	0.590634i	0.101743	−	0.994811i	$-0.467558\pi$
$523$	−18.5912	−	13.5073i	−0.812938	−	0.590634i	−0.914681	+	0.404177i	$0.867558\pi$
$524$	−105.145			−4.59328
$525$	1.62259	+	1.17888i	0.0708156	+	0.0514506i
$526$	−2.57217	−	0.835749i	−0.112152	−	0.0364404i
$527$	−1.43356	+	0.465791i	−0.0624467	+	0.0202902i
$528$	−14.1631	+	10.2901i	−0.616370	+	0.447819i
$529$	−14.4052	+	10.4660i	−0.626313	+	0.455043i
$530$			31.2822i			1.35881i
$531$	−8.54127	−	26.2873i	−0.370660	−	1.14077i
$532$	32.9394			1.42810
$533$	−20.7631	−	14.1133i	−0.899350	−	0.611316i
$534$	20.9233			0.905441
$535$	5.19903	+	16.0010i	0.224774	+	0.691782i
$536$			71.3772i			3.08303i
$537$	−0.0873186	+	0.0634407i	−0.00376808	+	0.00273767i
$538$	−40.2656	+	29.2546i	−1.73597	+	1.26126i
$539$	−1.41473	+	0.459675i	−0.0609369	+	0.0197996i
$540$	32.5431	+	10.5739i	1.40043	+	0.455029i
$541$	−24.7243	−	17.9632i	−1.06298	−	0.772300i	−0.0883420	−	0.996090i	$-0.528157\pi$
$541$	−24.7243	−	17.9632i	−1.06298	−	0.772300i	−0.974637	+	0.223791i	$0.928157\pi$
$542$	−66.7797			−2.86844
$543$	6.26312	+	4.55042i	0.268776	+	0.195277i
$544$	3.44954	−	4.74789i	0.147898	−	0.203564i
$545$	−1.52739	−	2.10228i	−0.0654263	−	0.0900516i
$546$	−7.62972	+	2.47905i	−0.326522	+	0.106093i
$547$			10.7155i			0.458160i	0.973408	+	0.229080i	$0.0735718\pi$
$547$			10.7155i			0.458160i	−0.973408	+	0.229080i	$0.926428\pi$
$548$	−5.36688	−	7.38687i	−0.229262	−	0.315551i
$549$	7.70278	−	23.7067i	0.328746	−	1.01178i
$550$	−6.48171	+	8.92130i	−0.276381	+	0.380406i
$551$	−5.18192	−	15.9483i	−0.220757	−	0.679420i
$552$	−44.2858	−	14.3893i	−1.88493	−	0.612450i
$553$	−3.86173	+	11.8852i	−0.164218	+	0.505410i
$554$	−12.2162	+	37.5975i	−0.519015	+	1.59736i
$555$	6.14244	+	1.99580i	0.260732	+	0.0847170i
$556$	−0.188352	−	0.579688i	−0.00798790	−	0.0245842i
$557$	7.16730	−	9.86494i	0.303688	−	0.417991i	−0.629712	−	0.776829i	$-0.716827\pi$
$557$	7.16730	−	9.86494i	0.303688	−	0.417991i	0.933400	+	0.358838i	$0.116827\pi$
$558$	12.7644	−	39.2849i	0.540361	−	1.66306i
$559$	9.84243	+	13.5469i	0.416290	+	0.572974i
$560$		−	24.0116i		−	1.01467i
$561$	0.258417	−	0.0839646i	0.0109104	−	0.00354499i
$562$	−38.8844	−	53.5198i	−1.64024	−	2.25760i
$563$	−7.40031	+	10.1857i	−0.311886	+	0.429274i	−0.935968	−	0.352084i	$-0.885473\pi$
$563$	−7.40031	+	10.1857i	−0.311886	+	0.429274i	0.624082	+	0.781359i	$0.285473\pi$
$564$	10.2144	+	7.42121i	0.430105	+	0.312489i
$565$	14.2895			0.601162
$566$	29.2804	+	21.2734i	1.23075	+	0.894189i
$567$	−4.11267	−	1.33629i	−0.172716	−	0.0561188i
$568$	−95.8605	+	31.1470i	−4.02222	+	1.30690i
$569$	−4.36132	+	3.16869i	−0.182836	+	0.132838i	−0.675439	−	0.737416i	$-0.736046\pi$
$569$	−4.36132	+	3.16869i	−0.182836	+	0.132838i	0.492602	+	0.870254i	$0.336046\pi$
$570$	−14.8795	+	10.8106i	−0.623232	+	0.452804i
$571$		−	36.3500i		−	1.52120i	−0.649221	−	0.760600i	$-0.724905\pi$
$571$		−	36.3500i		−	1.52120i	0.649221	−	0.760600i	$-0.275095\pi$
$572$	−10.0256	−	30.8557i	−0.419193	−	1.29014i
$573$	−12.3636			−0.516496
$574$	13.9146	−	10.7913i	0.580786	−	0.450420i
$575$	−17.2197			−0.718112
$576$	25.7814	+	79.3470i	1.07423	+	3.30612i
$577$			29.0168i			1.20799i	0.796990	+	0.603993i	$0.206425\pi$
$577$			29.0168i			1.20799i	−0.796990	+	0.603993i	$0.793575\pi$
$578$	37.6878	−	27.3818i	1.56761	−	1.13893i
$579$	−2.11139	+	1.53401i	−0.0877463	+	0.0637514i
$580$	−22.7424	+	7.38946i	−0.944328	+	0.306831i
$581$	−3.04621	−	0.989773i	−0.126378	−	0.0410627i
$582$	−21.1253	−	15.3484i	−0.875671	−	0.636212i
$583$	−11.1469			−0.461658
$584$	101.832	+	73.9852i	4.21383	+	3.06153i
$585$	−8.55863	+	11.7799i	−0.353856	+	0.487040i
$586$	−10.3295	−	14.2174i	−0.426709	−	0.587314i
$587$	34.4292	−	11.1867i	1.42104	−	0.461725i	0.505111	−	0.863055i	$-0.331452\pi$
$587$	34.4292	−	11.1867i	1.42104	−	0.461725i	0.915934	+	0.401329i	$0.131452\pi$
$588$		−	4.13874i		−	0.170679i
$589$	21.3698	+	29.4130i	0.880527	+	1.21194i
$590$	14.5747	−	44.8563i	0.600031	−	1.84671i
$591$	7.88686	−	10.8553i	0.324422	−	0.446529i
$592$	27.9515	+	86.0259i	1.14880	+	3.53564i
$593$	1.00891	+	0.327815i	0.0414310	+	0.0134617i	0.329659	−	0.944100i	$-0.393066\pi$
$593$	1.00891	+	0.327815i	0.0414310	+	0.0134617i	−0.288228	+	0.957562i	$0.593066\pi$
$594$	−5.12254	+	15.7656i	−0.210180	+	0.646869i
$595$	−0.115164	+	0.354437i	−0.00472125	+	0.0145305i
$596$	66.1838	+	21.5044i	2.71099	+	0.880855i
$597$	−1.84369	−	5.67429i	−0.0754572	−	0.232233i
$598$	40.4852	−	55.7231i	1.65556	−	2.27869i
$599$	8.10453	−	24.9432i	0.331142	−	1.01915i	−0.637449	−	0.770492i	$-0.720010\pi$
$599$	8.10453	−	24.9432i	0.331142	−	1.01915i	0.968591	−	0.248658i	$-0.0799896\pi$
$600$	−11.5500	−	15.8972i	−0.471526	−	0.648999i
$601$		−	22.0853i		−	0.900878i	−0.892807	−	0.450439i	$-0.851268\pi$
$601$		−	22.0853i		−	0.900878i	0.892807	−	0.450439i	$-0.148732\pi$
$602$	−11.1699	+	3.62931i	−0.455250	+	0.147920i
$603$	10.4761	+	14.4191i	0.426620	+	0.587193i
$604$	−60.2465	+	82.9222i	−2.45140	+	3.37406i
$605$	−10.7915	−	7.84050i	−0.438738	−	0.318762i
$606$	−36.0539			−1.46459
$607$	−17.4591	−	12.6848i	−0.708643	−	0.514860i	0.174092	−	0.984729i	$-0.444301\pi$
$607$	−17.4591	−	12.6848i	−0.708643	−	0.514860i	−0.882736	+	0.469870i	$0.844301\pi$
$608$	−134.624	−	43.7420i	−5.45972	−	1.77397i
$609$	−2.00386	+	0.651093i	−0.0812004	+	0.0263836i
$610$	34.4112	−	25.0012i	1.39327	−	1.01227i
$611$	−9.67664	+	7.03049i	−0.391475	+	0.284423i
$612$		−	3.34099i		−	0.135052i
$613$	8.74390	+	26.9110i	0.353163	+	1.08692i	0.957067	+	0.289867i	$0.0936109\pi$
$613$	8.74390	+	26.9110i	0.353163	+	1.08692i	−0.603904	+	0.797057i	$0.706389\pi$
$614$	−43.3534			−1.74960
$615$	−2.01826	+	6.94454i	−0.0813840	+	0.280031i
$616$	14.5740			0.587204
$617$	−0.799350	−	2.46015i	−0.0321806	−	0.0990418i	0.933676	−	0.358119i	$-0.116582\pi$
$617$	−0.799350	−	2.46015i	−0.0321806	−	0.0990418i	−0.965857	+	0.259077i	$0.916582\pi$
$618$			19.6526i			0.790543i
$619$	−16.0976	+	11.6956i	−0.647018	+	0.470086i	−0.862254	−	0.506476i	$-0.830948\pi$
$619$	−16.0976	+	11.6956i	−0.647018	+	0.470086i	0.215236	+	0.976562i	$0.430948\pi$
$620$	41.9432	−	30.4735i	1.68448	−	1.22385i
$621$	−24.6187	+	7.99910i	−0.987914	+	0.320993i
$622$	41.0625	+	13.3420i	1.64646	+	0.534966i
$623$	−8.27304	−	6.01072i	−0.331452	−	0.240814i
$624$	46.1436			1.84722
$625$	3.44246	+	2.50109i	0.137698	+	0.100044i
$626$	50.6877	−	69.7656i	2.02589	−	2.78839i
$627$	−3.85217	−	5.30206i	−0.153841	−	0.211744i
$628$	30.3381	−	9.85745i	1.21062	−	0.393355i
$629$		−	1.40390i		−	0.0559771i
$630$	−6.00291	−	8.26230i	−0.239162	−	0.329178i
$631$	−13.7827	+	42.4187i	−0.548679	+	1.68866i	0.163398	+	0.986560i	$0.447755\pi$
$631$	−13.7827	+	42.4187i	−0.548679	+	1.68866i	−0.712077	+	0.702101i	$0.752245\pi$
$632$	71.9664	−	99.0532i	2.86267	−	3.94012i
$633$	2.89747	+	8.91750i	0.115164	+	0.354439i
$634$	−82.6114	−	26.8421i	−3.28092	−	1.06604i
$635$	5.18945	−	15.9715i	0.205937	−	0.633810i
$636$	9.58378	−	29.4958i	0.380022	−	1.16959i
$637$	3.72894	+	1.21161i	0.147746	+	0.0480056i
$638$	−3.57983	−	11.0176i	−0.141727	−	0.436191i
$639$	−14.7936	+	20.3616i	−0.585226	+	0.805494i
$640$	−21.5662	+	66.3738i	−0.852478	+	2.62366i
$641$	4.47348	+	6.15722i	0.176692	+	0.243195i	0.888172	−	0.459510i	$-0.151975\pi$
$641$	4.47348	+	6.15722i	0.176692	+	0.243195i	−0.711481	+	0.702706i	$0.751975\pi$
$642$		−	22.6772i		−	0.894998i
$643$	24.7347	−	8.03680i	0.975442	−	0.316940i	0.222431	−	0.974948i	$-0.428601\pi$
$643$	24.7347	−	8.03680i	0.975442	−	0.316940i	0.753011	+	0.658008i	$0.228601\pi$
$644$	20.8863	+	28.7476i	0.823036	+	1.13281i
$645$	2.83519	−	3.90230i	0.111635	−	0.153653i
$646$	3.23436	+	2.34990i	0.127254	+	0.0924555i
$647$	24.5356			0.964592			0.482296	−	0.876008i	$-0.339803\pi$
$647$	24.5356			0.964592			0.482296	+	0.876008i	$0.339803\pi$
$648$	34.2757	+	24.9028i	1.34648	+	0.978273i
$649$	15.9839	+	5.19347i	0.627421	+	0.203862i
$650$	27.6432	−	8.98181i	1.08425	−	0.352296i
$651$	3.69566	−	2.68505i	0.144844	−	0.105236i
$652$	58.4929	−	42.4976i	2.29076	−	1.66433i
$653$			4.73401i			0.185256i	0.995701	+	0.0926280i	$0.0295267\pi$
$653$			4.73401i			0.185256i	−0.995701	+	0.0926280i	$0.970473\pi$
$654$	1.08234	+	3.33110i	0.0423229	+	0.130256i
$655$	−28.6932			−1.12114
$656$	−95.2989	+	34.3000i	−3.72080	+	1.33919i
$657$	31.4303			1.22621
$658$	−2.59243	−	7.97869i	−0.101064	−	0.311042i
$659$			35.6222i			1.38765i	0.720146	+	0.693823i	$0.244075\pi$
$659$			35.6222i			1.38765i	−0.720146	+	0.693823i	$0.755925\pi$
$660$	−7.56079	+	5.49323i	−0.294303	+	0.213824i
$661$	23.7760	−	17.2743i	0.924778	−	0.671891i	−0.0199307	−	0.999801i	$-0.506345\pi$
$661$	23.7760	−	17.2743i	0.924778	−	0.671891i	0.944709	+	0.327911i	$0.106345\pi$
$662$	−52.9034	+	17.1894i	−2.05615	+	0.668084i
$663$	−0.681132	−	0.221313i	−0.0264530	−	0.00859509i
$664$	25.3876	+	18.4452i	0.985231	+	0.715812i
$665$	8.98890			0.348574
$666$	31.1246	+	22.6133i	1.20605	+	0.876249i
$667$	10.6330	−	14.6350i	0.411710	−	0.566671i
$668$	−19.0221	−	26.1816i	−0.735986	−	1.01300i
$669$	1.04622	−	0.339939i	0.0404493	−	0.0131428i
$670$			30.4130i			1.17496i
$671$	8.90879	+	12.2619i	0.343920	+	0.473365i
$672$	−5.49606	+	16.9151i	−0.212015	+	0.652515i
$673$	−8.44194	+	11.6193i	−0.325413	+	0.447892i	−0.940110	−	0.340871i	$-0.889278\pi$
$673$	−8.44194	+	11.6193i	−0.325413	+	0.447892i	0.614697	+	0.788763i	$0.289278\pi$
$674$	−18.6741	−	57.4729i	−0.719299	−	2.21377i
$675$	−10.3889	−	3.37556i	−0.399869	−	0.129925i
$676$	−4.07906	+	12.5540i	−0.156887	+	0.482848i
$677$	−3.61855	+	11.1367i	−0.139072	+	0.428020i	−0.996201	−	0.0870819i	$-0.972246\pi$
$677$	−3.61855	+	11.1367i	−0.139072	+	0.428020i	0.857129	+	0.515102i	$0.172246\pi$
$678$	−18.3177	−	5.95179i	−0.703488	−	0.228577i
$679$	3.94370	+	12.1375i	0.151345	+	0.465793i
$680$	2.14616	−	2.95394i	0.0823017	−	0.113279i
$681$	−0.961470	+	2.95910i	−0.0368436	+	0.113393i
$682$	14.7629	+	20.3194i	0.565302	+	0.778072i
$683$		−	29.5836i		−	1.13198i	−0.824411	−	0.565992i	$-0.808493\pi$
$683$		−	29.5836i		−	1.13198i	0.824411	−	0.565992i	$-0.191507\pi$
$684$	−76.6399	+	24.9018i	−2.93040	+	0.952144i
$685$	−1.46458	−	2.01582i	−0.0559586	−	0.0770205i
$686$	−1.61643	+	2.22482i	−0.0617154	+	0.0849440i
$687$	16.6844	+	12.1219i	0.636549	+	0.462480i
$688$	67.5541			2.57547
$689$	23.7697	+	17.2697i	0.905552	+	0.657922i
$690$	−18.8696	−	6.13112i	−0.718355	−	0.233408i
$691$	4.46161	−	1.44966i	0.169728	−	0.0551479i	−0.222920	−	0.974837i	$-0.571559\pi$
$691$	4.46161	−	1.44966i	0.169728	−	0.0551479i	0.392648	+	0.919689i	$0.371559\pi$
$692$	51.8526	−	37.6731i	1.97114	−	1.43212i
$693$	2.94414	−	2.13905i	0.111839	−	0.0812556i
$694$			63.7436i			2.41967i
$695$	−0.0513998	−	0.158192i	−0.00194970	−	0.00600057i
$696$	20.6430			0.782469
$697$	1.57123	−	0.0492357i	0.0595145	−	0.00186493i
$698$	−19.0999			−0.722942
$699$	1.11002	+	3.41629i	0.0419848	+	0.129216i
$700$			14.9950i			0.566759i
$701$	11.4470	−	8.31673i	0.432347	−	0.314118i	−0.350240	−	0.936660i	$-0.613900\pi$
$701$	11.4470	−	8.31673i	0.432347	−	0.314118i	0.782587	+	0.622542i	$0.213900\pi$
$702$	35.3486	−	25.6822i	1.33415	−	0.969313i
$703$	−32.2044	+	10.4638i	−1.21461	+	0.394651i
$704$	−48.2465	−	15.6762i	−1.81836	−	0.590820i
$705$	2.78743	+	2.02519i	0.104981	+	0.0762731i
$706$	−7.44504			−0.280198
$707$	14.2556	+	10.3573i	0.536139	+	0.389528i
$708$	−27.4849	+	37.8297i	−1.03294	+	1.42173i
$709$	2.47741	+	3.40986i	0.0930409	+	0.128060i	0.853000	−	0.521912i	$-0.174781\pi$
$709$	2.47741	+	3.40986i	0.0930409	+	0.128060i	−0.759959	+	0.649971i	$0.774781\pi$
$710$	−40.8450	+	13.2713i	−1.53289	+	0.498065i
$711$		−	30.5726i		−	1.14656i
$712$	58.8894	+	81.0544i	2.20698	+	3.03764i
$713$	−12.1197	+	37.3006i	−0.453887	+	1.39692i
$714$	0.295258	−	0.406388i	0.0110498	−	0.0152087i
$715$	−2.73592	−	8.42029i	−0.102317	−	0.314901i
$716$	−0.767454	−	0.249361i	−0.0286811	−	0.00931905i
$717$	−0.696165	+	2.14257i	−0.0259987	+	0.0800159i
$718$	−3.93453	+	12.1092i	−0.146835	+	0.451913i
$719$	1.62983	+	0.529565i	0.0607826	+	0.0197495i	0.339250	−	0.940696i	$-0.389827\pi$
$719$	1.62983	+	0.529565i	0.0607826	+	0.0197495i	−0.278468	+	0.960446i	$0.589827\pi$
$720$	18.1525	+	55.8675i	0.676502	+	2.08206i
$721$	5.64567	−	7.77060i	0.210256	−	0.289392i
$722$	13.6516	−	42.0153i	0.508060	−	1.56365i
$723$	−1.10633	−	1.52274i	−0.0411450	−	0.0566312i
$724$			57.8802i			2.15110i
$725$	7.26016	−	2.35897i	0.269636	−	0.0876100i
$726$	10.5680	+	14.5456i	0.392216	+	0.539839i
$727$	−3.29067	+	4.52922i	−0.122044	+	0.167980i	−0.865668	−	0.500619i	$-0.833106\pi$
$727$	−3.29067	+	4.52922i	−0.122044	+	0.167980i	0.743623	+	0.668599i	$0.233106\pi$
$728$	−31.0776	−	22.5792i	−1.15181	−	0.836842i
$729$	1.53423			0.0568234
$730$	43.3893	+	31.5242i	1.60591	+	1.16676i
$731$	−0.997174	−	0.324001i	−0.0368818	−	0.0119836i
$732$	−40.1057	+	13.0311i	−1.48235	+	0.481645i
$733$	−15.5254	+	11.2799i	−0.573444	+	0.416631i	−0.836354	−	0.548189i	$-0.815317\pi$
$733$	−15.5254	+	11.2799i	−0.573444	+	0.416631i	0.262911	+	0.964820i	$0.415317\pi$
$734$	26.1614	−	19.0074i	0.965637	−	0.701576i
$735$		−	1.12943i		−	0.0416596i
$736$	−47.1874	−	145.228i	−1.73935	−	5.35317i
$737$	−10.8372			−0.399193
$738$	−24.2170	+	35.6273i	−0.891441	+	1.31146i
$739$	−41.9976			−1.54491			−0.772453	−	0.635072i	$-0.780971\pi$
$739$	−41.9976			−1.54491			−0.772453	+	0.635072i	$0.780971\pi$
$740$	14.9215	+	45.9238i	0.548527	+	1.68819i
$741$			17.2742i			0.634584i
$742$	−16.6718	+	12.1127i	−0.612039	+	0.444673i
$743$	0.784797	−	0.570188i	0.0287914	−	0.0209182i	−0.573296	−	0.819348i	$-0.694336\pi$
$743$	0.784797	−	0.570188i	0.0287914	−	0.0209182i	0.602088	+	0.798430i	$0.294336\pi$
$744$	−42.5649	+	13.8302i	−1.56051	+	0.507039i
$745$	18.0610	+	5.86838i	0.661705	+	0.215001i
$746$	28.2032	+	20.4909i	1.03259	+	0.750223i
$747$	7.83585			0.286699
$748$	1.64349	+	1.19407i	0.0600921	+	0.0436595i
$749$	−6.51456	+	8.96653i	−0.238037	+	0.327630i
$750$	−14.0495	−	19.3375i	−0.513015	−	0.706105i
$751$	10.0186	−	3.25523i	0.365583	−	0.118785i	−0.120464	−	0.992718i	$-0.538438\pi$
$751$	10.0186	−	3.25523i	0.365583	−	0.118785i	0.486047	+	0.873933i	$0.338438\pi$
$752$			48.2542i			1.75965i
$753$	−0.896640	−	1.23412i	−0.0326754	−	0.0449738i
$754$	−9.43569	+	29.0401i	−0.343627	+	1.05758i
$755$	−16.4408	+	22.6288i	−0.598342	+	0.823547i
$756$	6.96566	+	21.4381i	0.253339	+	0.779696i
$757$	−46.4052	−	15.0779i	−1.68662	−	0.548017i	−0.700446	−	0.713706i	$-0.747015\pi$
$757$	−46.4052	−	15.0779i	−1.68662	−	0.548017i	−0.986178	+	0.165688i	$0.947015\pi$
$758$	−22.6853	+	69.8181i	−0.823967	+	2.53591i
$759$	2.18473	−	6.72390i	0.0793006	−	0.244062i
$760$	−83.7575	−	27.2145i	−3.03820	−	0.987173i
$761$	−6.95442	−	21.4035i	−0.252098	−	0.775877i	−0.994388	−	0.105798i	$-0.966260\pi$
$761$	−6.95442	−	21.4035i	−0.252098	−	0.775877i	0.742290	−	0.670079i	$-0.233740\pi$
$762$	−13.3048	+	18.3125i	−0.481981	+	0.663390i
$763$	0.528982	−	1.62804i	0.0191504	−	0.0589390i
$764$	−54.3325	−	74.7822i	−1.96568	−	2.70553i
$765$		−	0.911730i		−	0.0329637i
$766$	−80.6064	+	26.1906i	−2.91243	+	0.946305i
$767$	−26.0378	−	35.8380i	−0.940172	−	1.29404i
$768$	25.4635	−	35.0475i	0.918834	−	1.26467i
$769$	33.9200	+	24.6443i	1.22319	+	0.888697i	0.996361	−	0.0852388i	$-0.0271653\pi$
$769$	33.9200	+	24.6443i	1.22319	+	0.888697i	0.226825	+	0.973935i	$0.427165\pi$
$770$	6.20981			0.223786
$771$	8.20487	+	5.96119i	0.295491	+	0.214687i
$772$	−18.5572	−	6.02961i	−0.667889	−	0.217010i
$773$	24.8048	−	8.05956i	0.892165	−	0.289882i	0.173166	−	0.984893i	$-0.444600\pi$
$773$	24.8048	−	8.05956i	0.892165	−	0.289882i	0.719000	+	0.695011i	$0.244600\pi$
$774$	23.2451	−	16.8886i	0.835530	−	0.607048i
$775$	−13.3897	+	9.72820i	−0.480973	+	0.349447i
$776$		−	125.035i		−	4.48851i
$777$	1.31475	+	4.04639i	0.0471665	+	0.145163i
$778$	62.0730			2.22542
$779$	−12.8404	−	35.6758i	−0.460056	−	1.27822i
$780$	24.6332			0.882009
$781$	−4.72904	−	14.5545i	−0.169218	−	0.520800i
$782$			4.31279i			0.154225i
$783$	9.28390	−	6.74515i	0.331779	−	0.241052i
$784$	12.7969	−	9.29749i	0.457032	−	0.332053i
$785$	8.27903	−	2.69002i	0.295491	−	0.0960109i
$786$	36.7820	+	11.9512i	1.31197	+	0.426285i
$787$	−0.880014	−	0.639368i	−0.0313691	−	0.0227910i	0.571990	−	0.820260i	$-0.306172\pi$
$787$	−0.880014	−	0.639368i	−0.0313691	−	0.0227910i	−0.603359	+	0.797469i	$0.706172\pi$
$788$	100.319			3.57371
$789$	0.591970	+	0.430092i	0.0210747	+	0.0153117i
$790$	30.6640	−	42.2054i	1.09098	−	1.50160i
$791$	5.53301	+	7.61553i	0.196731	+	0.270777i
$792$	−33.9093	+	11.0178i	−1.20491	+	0.391500i
$793$		−	39.9495i		−	1.41865i
$794$	29.1775	+	40.1593i	1.03547	+	1.42520i
$795$	2.61534	−	8.04918i	0.0927565	−	0.285475i
$796$	26.2193	−	36.0877i	0.929317	−	1.27910i
$797$	8.81741	+	27.1372i	0.312329	+	0.961249i	0.976840	+	0.213971i	$0.0686398\pi$
$797$	8.81741	+	27.1372i	0.312329	+	0.961249i	−0.664511	+	0.747278i	$0.731360\pi$
$798$	−11.5229	−	3.74402i	−0.407907	−	0.132537i
$799$	0.231436	−	0.712286i	0.00818761	−	0.0251989i
$800$	19.9127	−	61.2850i	0.704021	−	2.16675i
$801$	23.7929	+	7.73078i	0.840680	+	0.273154i
$802$	7.31648	+	22.5178i	0.258354	+	0.795131i
$803$	−11.2332	+	15.4611i	−0.396410	+	0.545611i
$804$	9.31749	−	28.6763i	0.328603	−	1.01133i
$805$	5.69971	+	7.84498i	0.200888	+	0.276499i
$806$		−	66.2011i		−	2.33183i
$807$	12.8065	−	4.16109i	0.450811	−	0.146477i
$808$	−101.475	−	139.668i	−3.56988	−	4.91352i
$809$	−9.12085	+	12.5538i	−0.320672	+	0.441367i	−0.938672	−	0.344811i	$-0.887943\pi$
$809$	−9.12085	+	12.5538i	−0.320672	+	0.441367i	0.618000	+	0.786178i	$0.287943\pi$
$810$	14.6045	+	10.6108i	0.513149	+	0.372824i
$811$	10.7023			0.375810			0.187905	−	0.982187i	$-0.439830\pi$
$811$	10.7023			0.375810			0.187905	+	0.982187i	$0.439830\pi$
$812$	−12.7443	−	9.25925i	−0.447236	−	0.324936i
$813$	17.1830	+	5.58310i	0.602635	+	0.195808i
$814$	−22.2478	+	7.22876i	−0.779786	+	0.253368i
$815$	15.9623	−	11.5973i	0.559134	−	0.406234i
$816$	−2.33749	+	1.69829i	−0.0818287	+	0.0594520i
$817$			25.2893i			0.884762i
$818$	13.8203	+	42.5346i	0.483217	+	1.48719i
$819$	−9.59207			−0.335174
$820$	−50.8740	+	18.3106i	−1.77660	+	0.639433i
$821$	27.8175			0.970837			0.485418	−	0.874282i	$-0.338667\pi$
$821$	27.8175			0.970837			0.485418	+	0.874282i	$0.338667\pi$
$822$	1.03783	+	3.19411i	0.0361985	+	0.111407i
$823$			7.88735i			0.274936i	0.990506	+	0.137468i	$0.0438964\pi$
$823$			7.88735i			0.274936i	−0.990506	+	0.137468i	$0.956104\pi$
$824$	−76.1317	+	55.3129i	−2.65217	+	1.92692i
$825$	2.41366	−	1.75363i	0.0840330	−	0.0610535i
$826$	29.5495	−	9.60122i	1.02816	−	0.334069i
$827$	28.0036	+	9.09891i	0.973779	+	0.316400i	0.752341	−	0.658774i	$-0.228925\pi$
$827$	28.0036	+	9.09891i	0.973779	+	0.316400i	0.221438	+	0.975174i	$0.428925\pi$
$828$	−70.3289	−	51.0969i	−2.44410	−	1.77574i
$829$	32.5061			1.12898			0.564492	−	0.825438i	$-0.309072\pi$
$829$	32.5061			1.12898			0.564492	+	0.825438i	$0.309072\pi$
$830$	10.8174	+	7.85927i	0.375476	+	0.272799i
$831$	6.28666	−	8.65284i	0.218082	−	0.300164i
$832$	78.5939	+	108.175i	2.72475	+	3.75030i
$833$	−0.233489	+	0.0758652i	−0.00808991	+	0.00262857i
$834$			0.224196i			0.00776328i
$835$	−5.19097	−	7.14476i	−0.179641	−	0.247255i
$836$	15.1414	−	46.6004i	0.523676	−	1.61171i
$837$	−14.6240	+	20.1282i	−0.505478	+	0.695731i
$838$	−25.3579	−	78.0435i	−0.875974	−	2.69597i
$839$	23.8596	+	7.75244i	0.823723	+	0.267644i	0.690399	−	0.723429i	$-0.257435\pi$
$839$	23.8596	+	7.75244i	0.823723	+	0.267644i	0.133324	+	0.991072i	$0.457435\pi$
$840$	−3.41942	+	10.5239i	−0.117981	+	0.363109i
$841$	6.48332	−	19.9536i	0.223563	−	0.688055i
$842$	21.4666	+	6.97491i	0.739787	+	0.240371i
$843$	5.53080	+	17.0221i	0.190491	+	0.586271i
$844$	−41.2052	+	56.7141i	−1.41834	+	1.95218i
$845$	−1.11314	+	3.42590i	−0.0382933	+	0.117855i
$846$	12.0636	+	16.6041i	0.414755	+	0.570861i
$847$		−	8.78723i		−	0.301933i
$848$	112.730	−	36.6282i	3.87117	−	1.25782i
$849$	−5.75554	−	7.92183i	−0.197530	−	0.271876i
$850$	−1.06975	+	1.47238i	−0.0366920	+	0.0505022i
$851$	−29.5525	−	21.4712i	−1.01305	−	0.736022i
$852$	42.5785			1.45871
$853$	−41.5778	−	30.2080i	−1.42360	−	1.03430i	−0.991165	−	0.132635i	$-0.957656\pi$
$853$	−41.5778	−	30.2080i	−1.42360	−	1.03430i	−0.432430	−	0.901667i	$-0.642344\pi$
$854$	26.6487	+	8.65867i	0.911898	+	0.296294i
$855$	−20.9144	+	6.79551i	−0.715258	+	0.232401i
$856$	87.8487	−	63.8258i	3.00261	−	2.18152i
$857$	−14.0150	+	10.1825i	−0.478742	+	0.347826i	−0.800838	−	0.598881i	$-0.795612\pi$
$857$	−14.0150	+	10.1825i	−0.478742	+	0.347826i	0.322097	+	0.946707i	$0.395612\pi$
$858$			11.9336i			0.407405i
$859$	−4.36580	−	13.4366i	−0.148959	−	0.458450i	0.848540	−	0.529132i	$-0.177482\pi$
$859$	−4.36580	−	13.4366i	−0.148959	−	0.458450i	−0.997499	+	0.0706823i	$0.977482\pi$
$860$	36.0628			1.22973
$861$	−4.48256	+	1.61336i	−0.152765	+	0.0549833i
$862$	77.6631			2.64522
$863$	9.79666	+	30.1510i	0.333482	+	1.02635i	0.967465	+	0.253005i	$0.0814190\pi$
$863$	9.79666	+	30.1510i	0.333482	+	1.02635i	−0.633983	+	0.773347i	$0.718581\pi$
$864$		−	96.8681i		−	3.29552i
$865$	14.1502	−	10.2807i	0.481120	−	0.349554i
$866$	−41.6952	+	30.2934i	−1.41686	+	1.02941i
$867$	−11.9867	+	3.89470i	−0.407089	+	0.132271i
$868$	32.4816	+	10.5539i	1.10250	+	0.358223i
$869$	15.0392	+	10.9266i	0.510171	+	0.370661i
$870$	8.79571			0.298203
$871$	23.1092	+	16.7898i	0.783026	+	0.568902i
$872$	−9.85800	+	13.5684i	−0.333834	+	0.459483i
$873$	−18.3516	−	25.2588i	−0.621107	−	0.854880i
$874$	98.9322	−	32.1450i	3.34643	−	1.08732i
$875$			11.6821i			0.394925i
$876$	−31.2537	−	43.0170i	−1.05597	−	1.45341i
$877$	−11.1273	+	34.2464i	−0.375744	+	1.15642i	0.567232	+	0.823558i	$0.308014\pi$
$877$	−11.1273	+	34.2464i	−0.375744	+	1.15642i	−0.942976	+	0.332862i	$0.891986\pi$
$878$	−26.0470	+	35.8506i	−0.879044	+	1.20990i
$879$	1.46924	+	4.52186i	0.0495562	+	0.152518i
$880$	−33.9699	−	11.0375i	−1.14513	−	0.372074i
$881$	7.61919	−	23.4495i	0.256697	−	0.790033i	−0.736793	−	0.676118i	$-0.763661\pi$
$881$	7.61919	−	23.4495i	0.256697	−	0.790033i	0.993491	−	0.113915i	$-0.0363390\pi$
$882$	2.07899	−	6.39848i	0.0700033	−	0.215448i
$883$	−9.61240	−	3.12326i	−0.323483	−	0.105106i	0.142774	−	0.989755i	$-0.454398\pi$
$883$	−9.61240	−	3.12326i	−0.323483	−	0.105106i	−0.466257	+	0.884649i	$0.654398\pi$
$884$	−1.65464	−	5.09246i	−0.0556516	−	0.171278i
$885$	−7.50040	+	10.3234i	−0.252123	+	0.347018i
$886$	14.3919	−	44.2936i	0.483504	−	1.48807i
$887$	9.34254	+	12.8589i	0.313692	+	0.431760i	0.936528	−	0.350592i	$-0.114020\pi$
$887$	9.34254	+	12.8589i	0.313692	+	0.431760i	−0.622836	+	0.782352i	$0.714020\pi$
$888$		−	41.6843i		−	1.39883i
$889$	10.5214	−	3.41860i	0.352876	−	0.114656i
$890$	25.0921	+	34.5363i	0.841089	+	1.15766i
$891$	−3.78098	+	5.20408i	−0.126668	+	0.174343i
$892$	6.65384	+	4.83430i	0.222787	+	0.161864i
$893$	−18.0643			−0.604499
$894$	−20.7083	−	15.0454i	−0.692588	−	0.503194i
$895$	−0.209432	−	0.0680486i	−0.00700054	−	0.00227461i
$896$	−43.7244	+	14.2069i	−1.46073	+	0.474620i
$897$	−15.0759	+	10.9533i	−0.503370	+	0.365720i
$898$	−6.66656	+	4.84354i	−0.222466	+	0.161631i
$899$		−	17.3870i		−	0.579888i
$900$	−11.3361	−	34.8889i	−0.377869	−	1.16296i
$901$	−1.83970			−0.0612892
$902$	−8.87058	−	24.6460i	−0.295358	−	0.820621i
$903$	3.17753			0.105742
$904$	−28.4994	−	87.7122i	−0.947877	−	2.91726i
$905$			15.7950i			0.525045i
$906$	30.5008	−	22.1601i	1.01332	−	0.736221i
$907$	3.97598	−	2.88872i	0.132020	−	0.0959183i	−0.519815	−	0.854279i	$-0.673999\pi$
$907$	3.97598	−	2.88872i	0.132020	−	0.0959183i	0.651836	+	0.758360i	$0.273999\pi$
$908$	−22.1236	+	7.18840i	−0.734198	+	0.238556i
$909$	−40.9986	−	13.3212i	−1.35984	−	0.441838i
$910$	−13.2418	−	9.62073i	−0.438962	−	0.318924i
$911$	14.1304			0.468162			0.234081	−	0.972217i	$-0.424792\pi$
$911$	14.1304			0.468162			0.234081	+	0.972217i	$0.424792\pi$
$912$	56.3798	+	40.9623i	1.86692	+	1.35640i
$913$	−2.80053	+	3.85460i	−0.0926840	+	0.127569i
$914$	−35.2450	−	48.5105i	−1.16580	−	1.60459i
$915$	−10.9445	+	3.55609i	−0.361815	+	0.117561i
$916$			154.188i			5.09450i
$917$	−11.1103	−	15.2920i	−0.366894	−	0.504986i
$918$	−0.845430	+	2.60196i	−0.0279033	+	0.0858776i
$919$	31.6748	−	43.5967i	1.04486	−	1.43812i	0.151673	−	0.988431i	$-0.451534\pi$
$919$	31.6748	−	43.5967i	1.04486	−	1.43812i	0.893184	−	0.449691i	$-0.148466\pi$
$920$	−29.3581	−	90.3549i	−0.967907	−	2.97891i
$921$	11.1552	+	3.62455i	0.367577	+	0.119433i
$922$	0.588026	−	1.80976i	0.0193656	−	0.0596012i
$923$	−12.4648	+	38.3626i	−0.410282	+	1.26272i
$924$	−5.85521	−	1.90247i	−0.192622	−	0.0625868i
$925$	−4.76347	−	14.6605i	−0.156622	−	0.482033i
$926$	−33.9939	+	46.7887i	−1.11711	+	1.53757i
$927$	−7.26127	+	22.3479i	−0.238491	+	0.734001i
$928$	39.7902	+	54.7666i	1.30618	+	1.79780i
$929$			8.86601i			0.290884i	0.989367	+	0.145442i	$0.0464605\pi$
$929$			8.86601i			0.290884i	−0.989367	+	0.145442i	$0.953540\pi$
$930$	−18.1364	+	5.89287i	−0.594716	+	0.193235i
$931$	3.48058	+	4.79061i	0.114071	+	0.157006i
$932$	−15.7857	+	21.7272i	−0.517078	+	0.711697i
$933$	−9.45029	−	6.86604i	−0.309388	−	0.224784i
$934$	92.8203			3.03717
$935$	0.448497	+	0.325852i	0.0146674	+	0.0106565i
$936$	89.3778	+	29.0406i	2.92140	+	0.949222i
$937$	25.1814	−	8.18194i	0.822641	−	0.267292i	0.132698	−	0.991156i	$-0.457636\pi$
$937$	25.1814	−	8.18194i	0.822641	−	0.267292i	0.689942	+	0.723864i	$0.257636\pi$
$938$	−16.2085	+	11.7762i	−0.529227	+	0.384506i
$939$	−18.8751	+	13.7136i	−0.615967	+	0.447526i
$940$			25.7599i			0.840194i
$941$	1.98587	+	6.11187i	0.0647374	+	0.199241i	0.978193	−	0.207696i	$-0.0665966\pi$
$941$	1.98587	+	6.11187i	0.0647374	+	0.199241i	−0.913456	+	0.406938i	$0.866597\pi$
$942$	−11.7334			−0.382294
$943$	22.9938	−	33.8278i	0.748782	−	1.10159i
$944$	−178.712			−5.81658
$945$	1.90087	+	5.85029i	0.0618354	+	0.190310i
$946$			17.4707i			0.568021i
$947$	−22.5671	+	16.3960i	−0.733333	+	0.532797i	−0.890616	−	0.454756i	$-0.849726\pi$
$947$	−22.5671	+	16.3960i	−0.733333	+	0.532797i	0.157283	+	0.987554i	$0.449726\pi$
$948$	−41.8432	+	30.4009i	−1.35901	+	0.987375i
$949$	47.9072	−	15.5660i	1.55513	−	0.505293i
$950$	41.7486	+	13.5649i	1.35450	+	0.440105i
$951$	19.0125	+	13.8134i	0.616524	+	0.447931i
$952$	2.40531			0.0779566
$953$	4.83353	+	3.51176i	0.156573	+	0.113757i	0.663313	−	0.748342i	$-0.269150\pi$
$953$	4.83353	+	3.51176i	0.156573	+	0.113757i	−0.506740	+	0.862099i	$0.669150\pi$
$954$	29.6330	−	40.7863i	0.959403	−	1.32050i
$955$	−14.8269	−	20.4075i	−0.479787	−	0.660370i
$956$	−16.0189	+	5.20485i	−0.518088	+	0.168337i
$957$			3.13422i			0.101315i
$958$	7.34645	+	10.1115i	0.237353	+	0.326688i
$959$	0.507228	−	1.56109i	0.0163792	−	0.0504101i
$960$	22.6396	−	31.1607i	0.730690	−	1.00571i
$961$	2.06924	+	6.36845i	0.0667495	+	0.205434i
$962$	58.6406	+	19.0535i	1.89065	+	0.614309i
$963$	8.37880	−	25.7873i	0.270003	−	0.830984i
$964$	4.34857	−	13.3835i	0.140058	−	0.431054i
$965$	−5.06412	−	1.64543i	−0.163020	−	0.0529683i
$966$	−4.03893	−	12.4305i	−0.129950	−	0.399946i
$967$	25.0970	−	34.5431i	0.807066	−	1.11083i	−0.184703	−	0.982794i	$-0.559132\pi$
$967$	25.0970	−	34.5431i	0.807066	−	1.11083i	0.991769	−	0.128037i	$-0.0408676\pi$
$968$	−26.6039	+	81.8784i	−0.855082	+	2.63167i
$969$	−0.635767	−	0.875058i	−0.0204238	−	0.0281109i
$970$		−	53.2761i		−	1.71059i
$971$	51.7828	−	16.8253i	1.66179	−	0.539948i	0.680543	−	0.732708i	$-0.261744\pi$
$971$	51.7828	−	16.8253i	1.66179	−	0.539948i	0.981246	+	0.192760i	$0.0617438\pi$
$972$	−50.2682	−	69.1882i	−1.61235	−	2.21921i
$973$	0.0644057	−	0.0886468i	0.00206475	−	0.00284189i
$974$	−33.1270	−	24.0682i	−1.06146	−	0.771194i
$975$	−7.86376			−0.251842
$976$	−130.388	−	94.7322i	−4.17361	−	3.03230i
$977$	38.5267	+	12.5181i	1.23258	+	0.400489i	0.851648	−	0.524114i	$-0.175603\pi$
$977$	38.5267	+	12.5181i	1.23258	+	0.400489i	0.380931	+	0.924603i	$0.375603\pi$
$978$	−25.2926	+	8.21805i	−0.808767	+	0.262784i
$979$	−12.3065	+	8.94117i	−0.393317	+	0.285761i
$980$	6.83145	−	4.96334i	0.218223	−	0.158548i
$981$			4.18786i			0.133708i
$982$	24.1189	+	74.2304i	0.769666	+	2.36879i
$983$	11.5656			0.368885			0.184443	−	0.982843i	$-0.440952\pi$
$983$	11.5656			0.368885			0.184443	+	0.982843i	$0.440952\pi$
$984$	46.6526	−	1.46190i	1.48723	−	0.0466035i
$985$	27.3762			0.872278
$986$	−0.590819	−	1.81835i	−0.0188155	−	0.0579082i
$987$			2.26973i			0.0722462i
$988$	−104.485	+	75.9125i	−3.32410	+	2.41510i
$989$	−22.0711	+	16.0356i	−0.701819	+	0.509901i
$990$	−14.4483	+	4.69455i	−0.459198	+	0.149203i
$991$	−46.5960	−	15.1400i	−1.48017	−	0.480936i	−0.546006	−	0.837781i	$-0.683853\pi$
$991$	−46.5960	−	15.1400i	−1.48017	−	0.480936i	−0.934164	+	0.356845i	$0.883853\pi$
$992$	−118.738	−	86.2681i	−3.76993	−	2.73902i
$993$	15.0496			0.477586
$994$	−22.8885	−	16.6295i	−0.725979	−	0.527454i
$995$	7.15503	−	9.84805i	0.226830	−	0.312204i
$996$	−7.79184	−	10.7245i	−0.246894	−	0.339820i
$997$	4.63374	−	1.50559i	0.146752	−	0.0476826i	−0.234720	−	0.972063i	$-0.575417\pi$
$997$	4.63374	−	1.50559i	0.146752	−	0.0476826i	0.381472	+	0.924380i	$0.375417\pi$
$998$			19.9860i			0.632645i
$999$	−13.6205	−	18.7470i	−0.430933	−	0.593128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.n.a.64.1	✓	88
41.25	even	10	inner	287.2.n.a.148.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.n.a.64.1	✓	88	1.1	even	1	trivial
287.2.n.a.148.1	yes	88	41.25	even	10	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.849806 - 2.61543i) q^{2} +0.744022i q^{3} +(-4.50028 + 3.26965i) q^{4} +(-1.22809 + 0.892261i) q^{5} +(1.94594 - 0.632274i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(7.92627 + 5.75877i) q^{8} +2.44643 q^{9} +O(q^{10})\)	\(q+(-0.849806 - 2.61543i) q^{2} +0.744022i q^{3} +(-4.50028 + 3.26965i) q^{4} +(-1.22809 + 0.892261i) q^{5} +(1.94594 - 0.632274i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(7.92627 + 5.75877i) q^{8} +2.44643 q^{9} +(3.37729 + 2.45374i) q^{10} +(-0.874353 + 1.20344i) q^{11} +(-2.43269 - 3.34831i) q^{12} +(3.72894 - 1.21161i) q^{13} +2.75003i q^{14} +(-0.663862 - 0.913727i) q^{15} +(4.88798 - 15.0437i) q^{16} +(-0.144304 + 0.198618i) q^{17} +(-2.07899 - 6.39848i) q^{18} +(5.63170 + 1.82985i) q^{19} +(2.60938 - 8.03085i) q^{20} +(0.229915 - 0.707607i) q^{21} +(3.89056 + 1.26412i) q^{22} +(1.97398 + 6.07529i) q^{23} +(-4.28465 + 5.89732i) q^{24} +(-0.833005 + 2.56373i) q^{25} +(-6.33775 - 8.72316i) q^{26} +4.05226i q^{27} +(5.29040 - 1.71896i) q^{28} +(-1.66454 - 2.29104i) q^{29} +(-1.82564 + 2.51278i) q^{30} +(4.96714 + 3.60884i) q^{31} -23.9047 q^{32} +(-0.895389 - 0.650538i) q^{33} +(0.642101 + 0.208631i) q^{34} +(1.44371 - 0.469089i) q^{35} +(-11.0096 + 7.99897i) q^{36} +(-4.62630 + 3.36120i) q^{37} -16.2843i q^{38} +(0.901462 + 2.77441i) q^{39} -14.8725 q^{40} +(-3.92406 - 5.05982i) q^{41} -2.04608 q^{42} +(1.31974 + 4.06173i) q^{43} -8.27467i q^{44} +(-3.00444 + 2.18286i) q^{45} +(14.2120 - 10.3256i) q^{46} +(-2.90131 + 0.942693i) q^{47} +(11.1928 + 3.63676i) q^{48} +(0.809017 + 0.587785i) q^{49} +7.41314 q^{50} +(-0.147776 - 0.107365i) q^{51} +(-12.8198 + 17.6449i) q^{52} +(4.40459 + 6.06239i) q^{53} +(10.5984 - 3.44364i) q^{54} -2.25809i q^{55} +(-5.75877 - 7.92627i) q^{56} +(-1.36145 + 4.19011i) q^{57} +(-4.57753 + 6.30042i) q^{58} +(-3.49132 - 10.7452i) q^{59} +(5.97513 + 1.94144i) q^{60} +(3.14858 - 9.69032i) q^{61} +(5.21757 - 16.0580i) q^{62} +(-2.32669 - 0.755989i) q^{63} +(10.5384 + 32.4338i) q^{64} +(-3.49841 + 4.81515i) q^{65} +(-0.940532 + 2.89466i) q^{66} +(4.28220 + 5.89395i) q^{67} -1.36566i q^{68} +(-4.52015 + 1.46869i) q^{69} +(-2.45374 - 3.37729i) q^{70} +(-6.04701 + 8.32300i) q^{71} +(19.3911 + 14.0884i) q^{72} +12.8474 q^{73} +(12.7224 + 9.24340i) q^{74} +(-1.90747 - 0.619774i) q^{75} +(-31.3272 + 10.1788i) q^{76} +(1.20344 - 0.874353i) q^{77} +(6.49022 - 4.71542i) q^{78} -12.4968i q^{79} +(7.41998 + 22.8363i) q^{80} +4.32432 q^{81} +(-9.89892 + 14.5630i) q^{82} +3.20297 q^{83} +(1.27894 + 3.93617i) q^{84} -0.372678i q^{85} +(9.50166 - 6.90336i) q^{86} +(1.70458 - 1.23845i) q^{87} +(-13.8607 + 4.50362i) q^{88} +(9.72555 + 3.16002i) q^{89} +(8.26230 + 6.00291i) q^{90} -3.92084 q^{91} +(-28.7476 - 20.8863i) q^{92} +(-2.68505 + 3.69566i) q^{93} +(4.93110 + 6.78708i) q^{94} +(-8.54895 + 2.77772i) q^{95} -17.7856i q^{96} +(-7.50137 - 10.3247i) q^{97} +(0.849806 - 2.61543i) q^{98} +(-2.13905 + 2.94414i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

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