LMFDB - Embedded newform 585.2.bt.b.376.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.10
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71151 - 0.988142i) q^{2} +(1.03985 + 1.38517i) q^{3} +(0.952848 + 1.65038i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.410976 - 3.39826i) q^{6} +(-1.22619 - 0.707941i) q^{7} +0.186373i q^{8} +(-0.837406 + 2.88076i) q^{9} +O(q^{10})$	\(q+(-1.71151 - 0.988142i) q^{2} +(1.03985 + 1.38517i) q^{3} +(0.952848 + 1.65038i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.410976 - 3.39826i) q^{6} +(-1.22619 - 0.707941i) q^{7} +0.186373i q^{8} +(-0.837406 + 2.88076i) q^{9} +1.97628 q^{10} +(-2.00421 - 1.15713i) q^{11} +(-1.29524 + 3.03601i) q^{12} +(-0.495342 - 3.57136i) q^{13} +(1.39909 + 2.42330i) q^{14} +(-1.59313 - 0.679667i) q^{15} +(2.08986 - 3.61974i) q^{16} -3.18319 q^{17} +(4.27982 - 4.10297i) q^{18} -0.980755i q^{19} +(-1.65038 - 0.952848i) q^{20} +(-0.294438 - 2.43464i) q^{21} +(2.28682 + 3.96088i) q^{22} +(-1.24305 - 2.15303i) q^{23} +(-0.258158 + 0.193800i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.68123 + 6.60190i) q^{26} +(-4.86112 + 1.83562i) q^{27} -2.69824i q^{28} +(1.49087 - 2.58226i) q^{29} +(2.05505 + 2.73749i) q^{30} +(5.20727 - 3.00642i) q^{31} +(-6.83082 + 3.94378i) q^{32} +(-0.481260 - 3.97942i) q^{33} +(5.44807 + 3.14544i) q^{34} +1.41588 q^{35} +(-5.55226 + 1.36288i) q^{36} -3.28027i q^{37} +(-0.969125 + 1.67857i) q^{38} +(4.43187 - 4.39983i) q^{39} +(-0.0931864 - 0.161403i) q^{40} +(2.06830 - 1.19413i) q^{41} +(-1.90183 + 4.45786i) q^{42} +(4.60358 - 7.97363i) q^{43} -4.41028i q^{44} +(-0.715163 - 2.91351i) q^{45} +4.91325i q^{46} +(-5.30466 - 3.06265i) q^{47} +(7.18711 - 0.869189i) q^{48} +(-2.49764 - 4.32604i) q^{49} +(-1.71151 + 0.988142i) q^{50} +(-3.31006 - 4.40927i) q^{51} +(5.42212 - 4.22047i) q^{52} -9.53923 q^{53} +(10.1337 + 1.66180i) q^{54} +2.31426 q^{55} +(0.131941 - 0.228528i) q^{56} +(1.35851 - 1.01984i) q^{57} +(-5.10327 + 2.94638i) q^{58} +(1.50962 - 0.871582i) q^{59} +(-0.396297 - 3.27688i) q^{60} +(-2.11267 + 3.65926i) q^{61} -11.8831 q^{62} +(3.06622 - 2.93952i) q^{63} +7.22861 q^{64} +(2.21466 + 2.84522i) q^{65} +(-3.10855 + 7.28638i) q^{66} +(-11.5912 + 6.69216i) q^{67} +(-3.03310 - 5.25348i) q^{68} +(1.68972 - 3.96068i) q^{69} +(-2.42330 - 1.39909i) q^{70} -0.496012i q^{71} +(-0.536894 - 0.156070i) q^{72} +12.1586i q^{73} +(-3.24137 + 5.61422i) q^{74} +(1.71952 - 0.207954i) q^{75} +(1.61862 - 0.934510i) q^{76} +(1.63836 + 2.83772i) q^{77} +(-11.9329 + 3.15105i) q^{78} +(-2.20379 + 3.81708i) q^{79} +4.17972i q^{80} +(-7.59750 - 4.82472i) q^{81} -4.71989 q^{82} +(-6.14947 - 3.55040i) q^{83} +(3.73752 - 2.80577i) q^{84} +(2.75672 - 1.59160i) q^{85} +(-15.7582 + 9.09797i) q^{86} +(5.12716 - 0.620064i) q^{87} +(0.215658 - 0.373530i) q^{88} -9.63808i q^{89} +(-1.65495 + 5.69319i) q^{90} +(-1.92093 + 4.72984i) q^{91} +(2.36888 - 4.10302i) q^{92} +(9.57921 + 4.08673i) q^{93} +(6.05266 + 10.4835i) q^{94} +(0.490377 + 0.849359i) q^{95} +(-12.5659 - 5.36091i) q^{96} +(-10.4990 - 6.06159i) q^{97} +9.87209i q^{98} +(5.01175 - 4.80465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.71151	−	0.988142i	−1.21022	−	0.698722i	−0.247414	−	0.968910i	$-0.579581\pi$
$2$	−1.71151	−	0.988142i	−1.21022	−	0.698722i	−0.962808	+	0.270188i	$0.912914\pi$
$3$	1.03985	+	1.38517i	0.600360	+	0.799730i
$3$	1.03985	+	1.38517i	0.600360	+	0.799730i
$4$	0.952848	+	1.65038i	0.476424	+	0.825190i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−0.410976	−	3.39826i	−0.167780	−	1.38733i
$7$	−1.22619	−	0.707941i	−0.463456	−	0.267576i	0.250040	−	0.968235i	$-0.419556\pi$
$7$	−1.22619	−	0.707941i	−0.463456	−	0.267576i	−0.713496	+	0.700659i	$0.752889\pi$
$8$			0.186373i			0.0658927i
$9$	−0.837406	+	2.88076i	−0.279135	+	0.960252i
$10$	1.97628			0.624956
$11$	−2.00421	−	1.15713i	−0.604292	−	0.348888i	0.166436	−	0.986052i	$-0.446774\pi$
$11$	−2.00421	−	1.15713i	−0.604292	−	0.348888i	−0.770728	+	0.637164i	$0.780107\pi$
$12$	−1.29524	+	3.03601i	−0.373903	+	0.876422i
$13$	−0.495342	−	3.57136i	−0.137383	−	0.990518i
$13$	−0.495342	−	3.57136i	−0.137383	−	0.990518i
$14$	1.39909	+	2.42330i	0.373923	+	0.647653i
$15$	−1.59313	−	0.679667i	−0.411344	−	0.175489i
$16$	2.08986	−	3.61974i	0.522464	−	0.904935i
$17$	−3.18319			−0.772037			−0.386019	−	0.922491i	$-0.626150\pi$
$17$	−3.18319			−0.772037			−0.386019	+	0.922491i	$0.626150\pi$
$18$	4.27982	−	4.10297i	1.00876	−	0.967079i
$19$		−	0.980755i		−	0.225001i	−0.993652	−	0.112500i	$-0.964114\pi$
$19$		−	0.980755i		−	0.225001i	0.993652	−	0.112500i	$-0.0358859\pi$
$20$	−1.65038	−	0.952848i	−0.369036	−	0.213063i
$21$	−0.294438	−	2.43464i	−0.0642517	−	0.531282i
$22$	2.28682	+	3.96088i	0.487551	+	0.844463i
$23$	−1.24305	−	2.15303i	−0.259194	−	0.448938i	0.706832	−	0.707381i	$-0.250124\pi$
$23$	−1.24305	−	2.15303i	−0.259194	−	0.448938i	−0.966026	+	0.258444i	$0.916790\pi$
$24$	−0.258158	+	0.193800i	−0.0526964	+	0.0395594i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.68123	+	6.60190i	−0.525832	+	1.29474i
$27$	−4.86112	+	1.83562i	−0.935524	+	0.353264i
$28$		−	2.69824i		−	0.509919i
$29$	1.49087	−	2.58226i	0.276847	−	0.479513i	−0.693752	−	0.720214i	$-0.744044\pi$
$29$	1.49087	−	2.58226i	0.276847	−	0.479513i	0.970599	+	0.240700i	$0.0773771\pi$
$30$	2.05505	+	2.73749i	0.375199	+	0.499796i
$31$	5.20727	−	3.00642i	0.935254	−	0.539969i	0.0467843	−	0.998905i	$-0.485103\pi$
$31$	5.20727	−	3.00642i	0.935254	−	0.539969i	0.888469	+	0.458936i	$0.151769\pi$
$32$	−6.83082	+	3.94378i	−1.20753	+	0.697168i
$33$	−0.481260	−	3.97942i	−0.0837766	−	0.692729i
$34$	5.44807	+	3.14544i	0.934336	+	0.539439i
$35$	1.41588			0.239328
$36$	−5.55226	+	1.36288i	−0.925377	+	0.227147i
$37$		−	3.28027i		−	0.539273i	−0.962962	−	0.269636i	$-0.913096\pi$
$37$		−	3.28027i		−	0.539273i	0.962962	−	0.269636i	$-0.0869035\pi$
$38$	−0.969125	+	1.67857i	−0.157213	+	0.272301i
$39$	4.43187	−	4.39983i	0.709667	−	0.704537i
$40$	−0.0931864	−	0.161403i	−0.0147341	−	0.0255201i
$41$	2.06830	−	1.19413i	0.323014	−	0.186492i	−0.329721	−	0.944078i	$-0.606955\pi$
$41$	2.06830	−	1.19413i	0.323014	−	0.186492i	0.652735	+	0.757586i	$0.273621\pi$
$42$	−1.90183	+	4.45786i	−0.293459	+	0.687862i
$43$	4.60358	−	7.97363i	0.702039	−	1.21597i	−0.265711	−	0.964053i	$-0.585607\pi$
$43$	4.60358	−	7.97363i	0.702039	−	1.21597i	0.967750	−	0.251914i	$-0.0810601\pi$
$44$		−	4.41028i		−	0.664874i
$45$	−0.715163	−	2.91351i	−0.106610	−	0.434320i
$46$			4.91325i			0.724419i
$47$	−5.30466	−	3.06265i	−0.773765	−	0.446733i	0.0604513	−	0.998171i	$-0.480746\pi$
$47$	−5.30466	−	3.06265i	−0.773765	−	0.446733i	−0.834216	+	0.551438i	$0.814079\pi$
$48$	7.18711	−	0.869189i	1.03737	−	0.125457i
$49$	−2.49764	−	4.32604i	−0.356806	−	0.618006i
$50$	−1.71151	+	0.988142i	−0.242044	+	0.139744i
$51$	−3.31006	−	4.40927i	−0.463501	−	0.617421i
$52$	5.42212	−	4.22047i	0.751913	−	0.585274i
$53$	−9.53923			−1.31031			−0.655157	−	0.755493i	$-0.727397\pi$
$53$	−9.53923			−1.31031			−0.655157	+	0.755493i	$0.727397\pi$
$54$	10.1337	+	1.66180i	1.37902	+	0.226143i
$55$	2.31426			0.312055
$56$	0.131941	−	0.228528i	0.0176313	−	0.0305384i
$57$	1.35851	−	1.01984i	0.179940	−	0.135081i
$58$	−5.10327	+	2.94638i	−0.670093	+	0.386878i
$59$	1.50962	−	0.871582i	0.196536	−	0.113470i	−0.398503	−	0.917167i	$-0.630470\pi$
$59$	1.50962	−	0.871582i	0.196536	−	0.113470i	0.595039	+	0.803697i	$0.297137\pi$
$60$	−0.396297	−	3.27688i	−0.0511617	−	0.423044i
$61$	−2.11267	+	3.65926i	−0.270500	+	0.468520i	−0.968990	−	0.247100i	$-0.920522\pi$
$61$	−2.11267	+	3.65926i	−0.270500	+	0.468520i	0.698490	+	0.715620i	$0.253856\pi$
$62$	−11.8831			−1.50915
$63$	3.06622	−	2.93952i	0.386308	−	0.370344i
$64$	7.22861			0.903577
$65$	2.21466	+	2.84522i	0.274695	+	0.352906i
$66$	−3.10855	+	7.28638i	−0.382636	+	0.896891i
$67$	−11.5912	+	6.69216i	−1.41609	+	0.817578i	−0.995952	−	0.0898838i	$-0.971350\pi$
$67$	−11.5912	+	6.69216i	−1.41609	+	0.817578i	−0.420134	+	0.907462i	$0.638017\pi$
$68$	−3.03310	−	5.25348i	−0.367817	−	0.637078i
$69$	1.68972	−	3.96068i	0.203419	−	0.476810i
$70$	−2.42330	−	1.39909i	−0.289639	−	0.167223i
$71$		−	0.496012i		−	0.0588657i	−0.999567	−	0.0294329i	$-0.990630\pi$
$71$		−	0.496012i		−	0.0588657i	0.999567	−	0.0294329i	$-0.00937013\pi$
$72$	−0.536894	−	0.156070i	−0.0632736	−	0.0183930i
$73$			12.1586i			1.42306i	0.702658	+	0.711528i	$0.251997\pi$
$73$			12.1586i			1.42306i	−0.702658	+	0.711528i	$0.748003\pi$
$74$	−3.24137	+	5.61422i	−0.376802	+	0.652640i
$75$	1.71952	−	0.207954i	0.198553	−	0.0240125i
$76$	1.61862	−	0.934510i	0.185668	−	0.107196i
$77$	1.63836	+	2.83772i	0.186708	+	0.323388i
$78$	−11.9329	+	3.15105i	−1.35113	+	0.356786i
$79$	−2.20379	+	3.81708i	−0.247946	+	0.429455i	−0.962956	−	0.269660i	$-0.913089\pi$
$79$	−2.20379	+	3.81708i	−0.247946	+	0.429455i	0.715010	+	0.699114i	$0.246422\pi$
$80$			4.17972i			0.467306i
$81$	−7.59750	−	4.82472i	−0.844167	−	0.536080i
$82$	−4.71989			−0.521224
$83$	−6.14947	−	3.55040i	−0.674992	−	0.389707i	0.122974	−	0.992410i	$-0.460757\pi$
$83$	−6.14947	−	3.55040i	−0.674992	−	0.389707i	−0.797965	+	0.602703i	$0.794090\pi$
$84$	3.73752	−	2.80577i	0.407797	−	0.306135i
$85$	2.75672	−	1.59160i	0.299009	−	0.172633i
$86$	−15.7582	+	9.09797i	−1.69925	+	0.981060i
$87$	5.12716	−	0.620064i	0.549689	−	0.0664778i
$88$	0.215658	−	0.373530i	0.0229892	−	0.0398184i
$89$		−	9.63808i		−	1.02163i	−0.859689	−	0.510817i	$-0.829343\pi$
$89$		−	9.63808i		−	1.02163i	0.859689	−	0.510817i	$-0.170657\pi$
$90$	−1.65495	+	5.69319i	−0.174447	+	0.600115i
$91$	−1.92093	+	4.72984i	−0.201368	+	0.495822i
$92$	2.36888	−	4.10302i	0.246973	−	0.427769i
$93$	9.57921	+	4.08673i	0.993318	+	0.423774i
$94$	6.05266	+	10.4835i	0.624284	+	1.08129i
$95$	0.490377	+	0.849359i	0.0503117	+	0.0871424i
$96$	−12.5659	−	5.36091i	−1.28250	−	0.547146i
$97$	−10.4990	−	6.06159i	−1.06601	−	0.615461i	−0.138921	−	0.990303i	$-0.544364\pi$
$97$	−10.4990	−	6.06159i	−1.06601	−	0.615461i	−0.927089	+	0.374842i	$0.877697\pi$
$98$			9.87209i			0.997232i
$99$	5.01175	−	4.80465i	0.503699	−	0.482885i
$100$	1.90570			0.190570
$101$	3.93293	−	6.81203i	0.391341	−	0.677822i	−0.601286	−	0.799034i	$-0.705345\pi$
$101$	3.93293	−	6.81203i	0.391341	−	0.677822i	0.992627	+	0.121212i	$0.0386781\pi$
$102$	1.30822	+	10.8173i	0.129533	+	1.07107i
$103$	−5.27293	−	9.13298i	−0.519557	−	0.899899i	−0.999742	−	0.0227315i	$-0.992764\pi$
$103$	−5.27293	−	9.13298i	−0.519557	−	0.899899i	0.480185	−	0.877167i	$-0.340570\pi$
$104$	0.665605	−	0.0923182i	0.0652679	−	0.00905254i
$105$	1.47231	+	1.96124i	0.143683	+	0.191397i
$106$	16.3265	+	9.42611i	1.58577	+	0.915544i
$107$	−6.08240			−0.588007			−0.294004	−	0.955804i	$-0.594988\pi$
$107$	−6.08240			−0.588007			−0.294004	+	0.955804i	$0.594988\pi$
$108$	−7.66137	−	6.27364i	−0.737216	−	0.603681i
$109$			1.69203i			0.162067i	0.996711	+	0.0810337i	$0.0258221\pi$
$109$			1.69203i			0.162067i	−0.996711	+	0.0810337i	$0.974178\pi$
$110$	−3.96088	−	2.28682i	−0.377656	−	0.218040i
$111$	4.54374	−	3.41100i	0.431273	−	0.323758i
$112$	−5.12512	+	2.95899i	−0.484278	+	0.279598i
$113$	9.66178	+	16.7347i	0.908904	+	1.57427i	0.815589	+	0.578631i	$0.196413\pi$
$113$	9.66178	+	16.7347i	0.908904	+	1.57427i	0.0933149	+	0.995637i	$0.470254\pi$
$114$	−3.33286	+	0.403067i	−0.312151	+	0.0377507i
$115$	2.15303	+	1.24305i	0.200771	+	0.115915i
$116$	5.68228			0.527586
$117$	10.7030	+	1.56372i	0.989495	+	0.144566i
$118$	−3.44499			−0.317137
$119$	3.90319	+	2.25351i	0.357805	+	0.206579i
$120$	0.126671	−	0.296915i	0.0115635	−	0.0271045i
$121$	−2.82210	−	4.88802i	−0.256554	−	0.444365i
$122$	7.23173	−	4.17524i	0.654730	−	0.378008i
$123$	3.80481	+	1.62322i	0.343068	+	0.146361i
$124$	9.92347	+	5.72932i	0.891154	+	0.514508i
$125$			1.00000i			0.0894427i
$126$	−8.15253	+	2.00116i	−0.726285	+	0.178277i
$127$	7.92398			0.703139			0.351570	−	0.936162i	$-0.385648\pi$
$127$	7.92398			0.703139			0.351570	+	0.936162i	$0.385648\pi$
$128$	1.28979	+	0.744662i	0.114003	+	0.0658195i
$129$	15.8319	−	1.91467i	1.39392	−	0.168577i
$130$	−0.978936	−	7.05803i	−0.0858583	−	0.619030i
$131$	9.21543	+	15.9616i	0.805156	+	1.39457i	0.916186	+	0.400754i	$0.131252\pi$
$131$	9.21543	+	15.9616i	0.805156	+	1.39457i	−0.111029	+	0.993817i	$0.535415\pi$
$132$	6.10899	−	4.58605i	0.531720	−	0.399164i
$133$	−0.694316	+	1.20259i	−0.0602048	+	0.104278i
$134$	26.4512			2.28504
$135$	3.29205	−	4.02025i	0.283334	−	0.346008i
$136$		−	0.593260i		−	0.0508716i
$137$	−11.8392	−	6.83535i	−1.01149	−	0.583983i	−0.0998616	−	0.995001i	$-0.531840\pi$
$137$	−11.8392	−	6.83535i	−1.01149	−	0.583983i	−0.911627	+	0.411018i	$0.865173\pi$
$138$	−6.80570	+	5.10906i	−0.579339	+	0.434912i
$139$	1.20757	+	2.09158i	0.102425	+	0.177406i	0.912683	−	0.408668i	$-0.134006\pi$
$139$	1.20757	+	2.09158i	0.102425	+	0.177406i	−0.810258	+	0.586073i	$0.800673\pi$
$140$	1.34912	+	2.33674i	0.114021	+	0.197491i
$141$	−1.27378	−	10.5326i	−0.107272	−	0.887003i
$142$	−0.490130	+	0.848930i	−0.0411308	+	0.0712406i
$143$	−3.13977	+	7.73093i	−0.262560	+	0.646493i
$144$	8.67753	+	9.05156i	0.723127	+	0.754297i
$145$			2.98174i			0.247620i
$146$	12.0144	−	20.8096i	0.994320	−	1.72221i
$147$	3.39513	−	7.95811i	0.280026	−	0.656374i
$148$	5.41369	−	3.12560i	0.445003	−	0.256922i
$149$	10.4794	−	6.05030i	0.858507	−	0.495659i	−0.00500475	−	0.999987i	$-0.501593\pi$
$149$	10.4794	−	6.05030i	0.858507	−	0.495659i	0.863512	+	0.504328i	$0.168260\pi$
$150$	−3.14847	−	1.34322i	−0.257071	−	0.109673i
$151$	19.9813	+	11.5362i	1.62605	+	0.938802i	0.985255	+	0.171093i	$0.0547297\pi$
$151$	19.9813	+	11.5362i	1.62605	+	0.938802i	0.640798	+	0.767709i	$0.278604\pi$
$152$	0.182786			0.0148259
$153$	2.66562	−	9.17000i	0.215503	−	0.741350i
$154$		−	6.47572i		−	0.521829i
$155$	−3.00642	+	5.20727i	−0.241481	+	0.418258i
$156$	11.4843	+	3.12190i	0.919479	+	0.249952i
$157$	7.21401	+	12.4950i	0.575741	+	0.997212i	0.995961	+	0.0897898i	$0.0286195\pi$
$157$	7.21401	+	12.4950i	0.575741	+	0.997212i	−0.420220	+	0.907422i	$0.638047\pi$
$158$	7.54362	−	4.35531i	0.600138	−	0.346490i
$159$	−9.91941	−	13.2135i	−0.786660	−	1.04790i
$160$	3.94378	−	6.83082i	0.311783	−	0.540024i
$161$			3.52003i			0.277417i
$162$	8.23571	+	15.7650i	0.647058	+	1.23861i
$163$			8.75992i			0.686130i	0.939312	+	0.343065i	$0.111465\pi$
$163$			8.75992i			0.686130i	−0.939312	+	0.343065i	$0.888535\pi$
$164$	3.94154	+	2.27565i	0.307783	+	0.177699i
$165$	2.40649	+	3.20565i	0.187345	+	0.249560i
$166$	7.01659	+	12.1531i	0.544593	+	0.943263i
$167$	14.6376	−	8.45105i	1.13269	−	0.653962i	0.188083	−	0.982153i	$-0.439772\pi$
$167$	14.6376	−	8.45105i	1.13269	−	0.653962i	0.944611	+	0.328192i	$0.106439\pi$
$168$	0.453750	−	0.0548753i	0.0350076	−	0.00423372i
$169$	−12.5093	+	3.53809i	−0.962252	+	0.272161i
$170$	−6.29089			−0.482489
$171$	2.82531	+	0.821290i	0.216057	+	0.0628056i
$172$	17.5460			1.33787
$173$	2.01845	−	3.49605i	0.153460	−	0.265800i	−0.779037	−	0.626977i	$-0.784292\pi$
$173$	2.01845	−	3.49605i	0.153460	−	0.265800i	0.932497	+	0.361178i	$0.117625\pi$
$174$	−9.38790	−	4.00511i	−0.711695	−	0.303627i
$175$	−1.22619	+	0.707941i	−0.0926912	+	0.0535153i
$176$	−8.37702	+	4.83648i	−0.631442	+	0.364563i
$177$	2.77708	+	1.18477i	0.208738	+	0.0890529i
$178$	−9.52379	+	16.4957i	−0.713838	+	1.23640i
$179$	6.37013			0.476126			0.238063	−	0.971250i	$-0.423488\pi$
$179$	6.37013			0.476126			0.238063	+	0.971250i	$0.423488\pi$
$180$	4.12696	−	3.95642i	0.307605	−	0.294894i
$181$	−24.1388			−1.79423			−0.897113	−	0.441801i	$-0.854340\pi$
$181$	−24.1388			−1.79423			−0.897113	+	0.441801i	$0.854340\pi$
$182$	7.96144	−	6.19702i	0.590142	−	0.459354i
$183$	−7.26557	+	0.878678i	−0.537087	+	0.0649537i
$184$	0.401266	−	0.231671i	0.0295817	−	0.0170790i
$185$	1.64013	+	2.84080i	0.120585	+	0.208859i
$186$	−12.3567	−	16.4601i	−0.906035	−	1.20691i
$187$	6.37978	+	3.68337i	0.466536	+	0.269355i
$188$		−	11.6729i		−	0.851337i
$189$	7.26016	+	1.19058i	0.528099	+	0.0866016i
$190$		−	1.93825i		−	0.140615i
$191$	−5.23282	+	9.06351i	−0.378633	+	0.655812i	−0.990864	−	0.134867i	$-0.956939\pi$
$191$	−5.23282	+	9.06351i	−0.378633	+	0.655812i	0.612230	+	0.790680i	$0.290273\pi$
$192$	7.51671	+	10.0129i	0.542472	+	0.722617i
$193$	−1.18109	+	0.681901i	−0.0850165	+	0.0490843i	−0.541906	−	0.840439i	$-0.682297\pi$
$193$	−1.18109	+	0.681901i	−0.0850165	+	0.0490843i	0.456889	+	0.889524i	$0.348964\pi$
$194$	11.9794	+	20.7490i	0.860072	+	1.48969i
$195$	−1.63820	+	6.02630i	−0.117314	+	0.431552i
$196$	4.75974	−	8.24411i	0.339982	−	0.588865i
$197$		−	21.2075i		−	1.51097i	−0.655165	−	0.755486i	$-0.727401\pi$
$197$		−	21.2075i		−	1.51097i	0.655165	−	0.755486i	$-0.272599\pi$
$198$	−13.3253	+	3.27090i	−0.946990	+	0.232452i
$199$	−10.6575			−0.755489			−0.377745	−	0.925910i	$-0.623300\pi$
$199$	−10.6575			−0.755489			−0.377745	+	0.925910i	$0.623300\pi$
$200$	0.161403	+	0.0931864i	0.0114130	+	0.00658927i
$201$	−21.3229	−	9.09689i	−1.50400	−	0.641645i
$202$	−13.4625	+	7.77257i	−0.947218	+	0.546876i
$203$	−3.65617	+	2.11089i	−0.256613	+	0.148156i
$204$	4.12299	−	9.66421i	0.288667	−	0.676630i
$205$	−1.19413	+	2.06830i	−0.0834018	+	0.144456i
$206$			20.8416i			1.45210i
$207$	7.24329	−	1.77797i	0.503444	−	0.123578i
$208$	−13.9626	−	5.67063i	−0.968132	−	0.393188i
$209$	−1.13486	+	1.96564i	−0.0785000	+	0.135966i
$210$	−0.581893	−	4.81153i	−0.0401545	−	0.332027i
$211$	1.65684	+	2.86973i	0.114061	+	0.197560i	0.917404	−	0.397957i	$-0.130281\pi$
$211$	1.65684	+	2.86973i	0.114061	+	0.197560i	−0.803343	+	0.595517i	$0.796947\pi$
$212$	−9.08943	−	15.7434i	−0.624265	−	1.08126i
$213$	0.687062	−	0.515780i	0.0470767	−	0.0353407i
$214$	10.4101	+	6.01027i	0.711619	+	0.410853i
$215$			9.20715i			0.627923i
$216$	−0.342109	−	0.905981i	−0.0232775	−	0.0616442i
$217$	−8.51347			−0.577932
$218$	1.67197	−	2.89593i	0.113240	−	0.196137i
$219$	−16.8418	+	12.6432i	−1.13806	+	0.854346i
$220$	2.20514	+	3.81941i	0.148670	+	0.257505i
$221$	1.57677	+	11.3683i	0.106065	+	0.764717i
$222$	−11.1472	+	1.34811i	−0.748152	+	0.0904794i
$223$	13.5170	+	7.80407i	0.905168	+	0.522599i	0.878873	−	0.477055i	$-0.158296\pi$
$223$	13.5170	+	7.80407i	0.905168	+	0.522599i	0.0262948	+	0.999654i	$0.491629\pi$
$224$	11.1678			0.746183
$225$	2.07610	+	2.16559i	0.138407	+	0.144373i
$226$		−	38.1888i		−	2.54028i
$227$	5.58421	+	3.22405i	0.370637	+	0.213987i	0.673737	−	0.738971i	$-0.264688\pi$
$227$	5.58421	+	3.22405i	0.370637	+	0.213987i	−0.303100	+	0.952959i	$0.598021\pi$
$228$	2.97759	+	1.27031i	0.197195	+	0.0841285i
$229$	−20.5653	+	11.8734i	−1.35900	+	0.784616i	−0.989488	−	0.144612i	$-0.953807\pi$
$229$	−20.5653	+	11.8734i	−1.35900	+	0.784616i	−0.369507	+	0.929228i	$0.620473\pi$
$230$	−2.45662	−	4.25500i	−0.161985	−	0.280566i
$231$	−2.22708	+	5.22023i	−0.146531	+	0.343466i
$232$	0.481262	+	0.277857i	0.0315964	+	0.0182422i
$233$	−10.6980			−0.700851			−0.350426	−	0.936591i	$-0.613963\pi$
$233$	−10.6980			−0.700851			−0.350426	+	0.936591i	$0.613963\pi$
$234$	−16.7732	−	13.2524i	−1.09650	−	0.866339i
$235$	6.12530			0.399570
$236$	2.87688	+	1.66097i	0.187269	+	0.108120i
$237$	−7.57893	+	0.916574i	−0.492304	+	0.0595379i
$238$	−4.45357	−	7.71382i	−0.288682	−	0.500013i
$239$	−1.28938	+	0.744425i	−0.0834032	+	0.0481528i	−0.541122	−	0.840944i	$-0.682000\pi$
$239$	−1.28938	+	0.744425i	−0.0834032	+	0.0481528i	0.457718	+	0.889097i	$0.348667\pi$
$240$	−5.78963	+	4.34630i	−0.373719	+	0.280552i
$241$	17.5519	+	10.1336i	1.13062	+	0.652763i	0.944090	−	0.329687i	$-0.106943\pi$
$241$	17.5519	+	10.1336i	1.13062	+	0.652763i	0.186528	+	0.982450i	$0.440277\pi$
$242$			11.1545i			0.717040i
$243$	−1.21723	−	15.5409i	−0.0780851	−	0.996947i
$244$	−8.05222			−0.515491
$245$	4.32604	+	2.49764i	0.276381	+	0.159568i
$246$	−4.90799	−	6.53786i	−0.312922	−	0.416838i
$247$	−3.50263	+	0.485809i	−0.222867	+	0.0309113i
$248$	0.560315	+	0.970493i	0.0355800	+	0.0616264i
$249$	−1.47664	−	12.2100i	−0.0935782	−	0.773775i
$250$	0.988142	−	1.71151i	0.0624956	−	0.108245i
$251$	−11.9532			−0.754480			−0.377240	−	0.926116i	$-0.623127\pi$
$251$	−11.9532			−0.754480			−0.377240	+	0.926116i	$0.623127\pi$
$252$	7.77296	+	2.25952i	0.489651	+	0.142336i
$253$			5.75350i			0.361719i
$254$	−13.5620	−	7.83001i	−0.850954	−	0.491299i
$255$	5.07123	+	2.16351i	0.317573	+	0.135484i
$256$	−8.70028	−	15.0693i	−0.543767	−	0.941833i
$257$	−0.381495	−	0.660769i	−0.0237970	−	0.0412177i	0.853882	−	0.520467i	$-0.174242\pi$
$257$	−0.381495	−	0.660769i	−0.0237970	−	0.0412177i	−0.877679	+	0.479250i	$0.840909\pi$
$258$	−28.9884	−	12.3672i	−1.80474	−	0.769948i
$259$	−2.32224	+	4.02223i	−0.144297	+	0.249929i
$260$	−2.58546	+	6.36609i	−0.160344	+	0.394808i
$261$	6.19039	+	6.45722i	0.383176	+	0.399692i
$262$		−	36.4246i		−	2.25032i
$263$	4.79584	−	8.30663i	0.295724	−	0.512209i	−0.679429	−	0.733741i	$-0.737772\pi$
$263$	4.79584	−	8.30663i	0.295724	−	0.512209i	0.975153	+	0.221532i	$0.0711058\pi$
$264$	0.741656	−	0.0896938i	0.0456458	−	0.00552027i
$265$	8.26121	−	4.76961i	0.507482	−	0.292995i
$266$	2.37666	−	1.37217i	0.145722	−	0.0841329i
$267$	13.3504	−	10.0222i	0.817032	−	0.613349i
$268$	−22.0892	−	12.7532i	−1.34931	−	0.779027i
$269$	−0.453046			−0.0276227			−0.0138113	−	0.999905i	$-0.504396\pi$
$269$	−0.453046			−0.0276227			−0.0138113	+	0.999905i	$0.504396\pi$
$270$	−9.60696	+	3.62770i	−0.584661	+	0.220775i
$271$		−	24.8382i		−	1.50881i	−0.656409	−	0.754405i	$-0.727925\pi$
$271$		−	24.8382i		−	1.50881i	0.656409	−	0.754405i	$-0.272075\pi$
$272$	−6.65242	+	11.5223i	−0.403362	+	0.698644i
$273$	−8.54913	+	2.25752i	−0.517417	+	0.136632i
$274$	13.5086	+	23.3976i	0.816084	+	1.41350i
$275$	−2.00421	+	1.15713i	−0.120858	+	0.0697776i
$276$	8.14668	−	0.985236i	0.490372	−	0.0593043i
$277$	8.68367	−	15.0406i	0.521751	−	0.903699i	−0.477929	−	0.878399i	$-0.658612\pi$
$277$	8.68367	−	15.0406i	0.521751	−	0.903699i	0.999680	−	0.0253007i	$-0.00805433\pi$
$278$		−	4.77302i		−	0.286267i
$279$	4.30016	+	17.5185i	0.257444	+	1.04880i
$280$			0.263882i			0.0157699i
$281$	−17.4145	−	10.0542i	−1.03886	−	0.599786i	−0.119350	−	0.992852i	$-0.538081\pi$
$281$	−17.4145	−	10.0542i	−1.03886	−	0.599786i	−0.919510	+	0.393066i	$0.871414\pi$
$282$	−8.22759	+	19.2853i	−0.489946	+	1.14842i
$283$	−1.18881	−	2.05907i	−0.0706672	−	0.122399i	0.828527	−	0.559950i	$-0.189179\pi$
$283$	−1.18881	−	2.05907i	−0.0706672	−	0.122399i	−0.899194	+	0.437550i	$0.855846\pi$
$284$	0.818608	−	0.472623i	0.0485754	−	0.0280450i
$285$	−0.666587	+	1.56247i	−0.0394852	+	0.0925525i
$286$	13.0130	−	10.1290i	0.769475	−	0.598943i
$287$	−3.38150			−0.199603
$288$	−5.64089	−	22.9805i	−0.332393	−	1.35414i
$289$	−6.86729			−0.403958
$290$	2.94638	−	5.10327i	0.173017	−	0.299675i
$291$	−2.52106	−	20.8461i	−0.147787	−	1.22202i
$292$	−20.0663	+	11.5853i	−1.17429	+	0.677978i
$293$	5.26375	−	3.03903i	0.307511	−	0.177542i	−0.338301	−	0.941038i	$-0.609852\pi$
$293$	5.26375	−	3.03903i	0.307511	−	0.177542i	0.645812	+	0.763496i	$0.276519\pi$
$294$	−13.6745	+	10.2655i	−0.797516	+	0.598698i
$295$	−0.871582	+	1.50962i	−0.0507455	+	0.0878937i
$296$	0.611353			0.0355341
$297$	11.8668	+	1.94600i	0.688579	+	0.112918i
$298$	−23.9142			−1.38531
$299$	−7.07352	+	5.50588i	−0.409072	+	0.318413i
$300$	1.98165	+	2.63972i	0.114410	+	0.152404i
$301$	−11.2897	+	6.51812i	−0.650728	+	0.375698i
$302$	−22.7988	−	39.4887i	−1.31192	−	2.27232i
$303$	13.5255	−	1.63574i	0.777020	−	0.0939706i
$304$	−3.55008	−	2.04964i	−0.203611	−	0.117555i
$305$		−	4.22535i		−	0.241943i
$306$	−13.6235	+	13.0605i	−0.778804	+	0.746621i
$307$		−	4.96898i		−	0.283595i	−0.989896	−	0.141797i	$-0.954712\pi$
$307$		−	4.96898i		−	0.283595i	0.989896	−	0.141797i	$-0.0452881\pi$
$308$	−3.12221	+	5.40783i	−0.177905	+	0.308140i
$309$	7.16767	−	16.8009i	0.407755	−	0.955768i
$310$	10.2910	−	5.94154i	0.584492	−	0.337457i
$311$	16.8635	+	29.2084i	0.956240	+	1.65626i	0.731505	+	0.681837i	$0.238818\pi$
$311$	16.8635	+	29.2084i	0.956240	+	1.65626i	0.224736	+	0.974420i	$0.427848\pi$
$312$	0.820009	+	0.825980i	0.0464238	+	0.0467619i
$313$	−11.3401	+	19.6416i	−0.640979	+	1.11021i	0.344235	+	0.938883i	$0.388138\pi$
$313$	−11.3401	+	19.6416i	−0.640979	+	1.11021i	−0.985215	+	0.171325i	$0.945195\pi$
$314$		−	28.5139i		−	1.60913i
$315$	−1.18567	+	4.07881i	−0.0668048	+	0.229815i
$316$	−8.39950			−0.472509
$317$	17.3120	+	9.99507i	0.972338	+	0.561379i	0.899948	−	0.435997i	$-0.143604\pi$
$317$	17.3120	+	9.99507i	0.972338	+	0.561379i	0.0723895	+	0.997376i	$0.476938\pi$
$318$	3.92039	+	32.4168i	0.219845	+	1.81784i
$319$	−5.97602	+	3.45026i	−0.334593	+	0.193177i
$320$	−6.26016	+	3.61431i	−0.349954	+	0.202046i
$321$	−6.32481	−	8.42517i	−0.353016	−	0.470247i
$322$	3.47829	−	6.02457i	0.193837	−	0.335736i
$323$			3.12193i			0.173709i
$324$	0.723363	−	17.1360i	0.0401868	−	0.952000i
$325$	−3.34056	−	1.35670i	−0.185301	−	0.0752563i
$326$	8.65605	−	14.9927i	0.479414	−	0.830369i
$327$	−2.34376	+	1.75947i	−0.129610	+	0.0972988i
$328$	0.222554	+	0.385474i	0.0122885	+	0.0212842i
$329$	4.33635	+	7.51077i	0.239070	+	0.414082i
$330$	−0.951106	−	7.86447i	−0.0523567	−	0.432925i
$331$	−5.16112	−	2.97977i	−0.283681	−	0.163783i	0.351408	−	0.936222i	$-0.385703\pi$
$331$	−5.16112	−	2.97977i	−0.283681	−	0.163783i	−0.635089	+	0.772439i	$0.719036\pi$
$332$		−	13.5319i		−	0.742662i
$333$	9.44965	+	2.74692i	0.517838	+	0.150530i
$334$	−33.4033			−1.82775
$335$	6.69216	−	11.5912i	0.365632	−	0.633293i
$336$	−9.42809	−	4.02226i	−0.514345	−	0.219432i
$337$	−9.62249	−	16.6666i	−0.524170	−	0.907890i	−0.999604	−	0.0281382i	$-0.991042\pi$
$337$	−9.62249	−	16.6666i	−0.524170	−	0.907890i	0.475434	−	0.879752i	$-0.342291\pi$
$338$	24.9059	+	6.30545i	1.35470	+	0.342971i
$339$	−13.1336	+	30.7849i	−0.713319	+	1.67201i
$340$	5.25348	+	3.03310i	0.284910	+	0.164493i
$341$	−13.9153			−0.753555
$342$	−4.02401	−	4.19746i	−0.217593	−	0.226973i
$343$			16.9839i			0.917044i
$344$	1.48607	+	0.857981i	0.0801234	+	0.0462592i
$345$	0.516996	+	4.27491i	0.0278341	+	0.230154i
$346$	−6.90919	+	3.98902i	−0.371440	+	0.214451i
$347$	−9.13406	−	15.8207i	−0.490342	−	0.849297i	0.509596	−	0.860414i	$-0.329795\pi$
$347$	−9.13406	−	15.8207i	−0.490342	−	0.849297i	−0.999938	+	0.0111165i	$0.996461\pi$
$348$	5.90874	+	7.87094i	0.316742	+	0.421926i
$349$	−19.1163	−	11.0368i	−1.02327	−	0.590787i	−0.108222	−	0.994127i	$-0.534516\pi$
$349$	−19.1163	−	11.0368i	−1.02327	−	0.590787i	−0.915050	+	0.403340i	$0.867849\pi$
$350$	2.79818			0.149569
$351$	8.96357	+	16.4516i	0.478440	+	0.878120i
$352$	18.2539			0.972934
$353$	−22.5935	−	13.0444i	−1.20253	−	0.694282i	−0.241414	−	0.970422i	$-0.577611\pi$
$353$	−22.5935	−	13.0444i	−1.20253	−	0.694282i	−0.961117	+	0.276140i	$0.910945\pi$
$354$	−3.58228	−	4.77190i	−0.190396	−	0.253624i
$355$	0.248006	+	0.429559i	0.0131628	+	0.0227986i
$356$	15.9065	−	9.18362i	0.843043	−	0.486731i
$357$	0.937253	+	7.74992i	0.0496047	+	0.410169i
$358$	−10.9025	−	6.29459i	−0.576217	−	0.332679i
$359$		−	4.20431i		−	0.221895i	−0.993826	−	0.110947i	$-0.964611\pi$
$359$		−	4.20431i		−	0.221895i	0.993826	−	0.110947i	$-0.0353885\pi$
$360$	0.542999	−	0.133287i	0.0286185	−	0.00702484i
$361$	18.0381			0.949375
$362$	41.3139	+	23.8526i	2.17141	+	1.25366i
$363$	3.83617	−	8.99192i	0.201347	−	0.471953i
$364$	−9.63639	+	1.33655i	−0.505084	+	0.0700543i
$365$	−6.07930	−	10.5297i	−0.318205	−	0.551147i
$366$	13.3034	+	5.67555i	0.695378	+	0.296666i
$367$	2.24078	−	3.88114i	0.116968	−	0.202594i	−0.801597	−	0.597865i	$-0.796016\pi$
$367$	2.24078	−	3.88114i	0.116968	−	0.202594i	0.918565	+	0.395271i	$0.129349\pi$
$368$	−10.3912			−0.541679
$369$	1.70800	+	6.95823i	0.0889148	+	0.362231i
$370$		−	6.48274i		−	0.337022i
$371$	11.6969	+	6.75320i	0.607272	+	0.350609i
$372$	2.38287	+	19.7034i	0.123546	+	1.02157i
$373$	16.4696	+	28.5261i	0.852762	+	1.47703i	0.878706	+	0.477363i	$0.158407\pi$
$373$	16.4696	+	28.5261i	0.852762	+	1.47703i	−0.0259441	+	0.999663i	$0.508259\pi$
$374$	−7.27938	−	12.6083i	−0.376408	−	0.651957i
$375$	−1.38517	+	1.03985i	−0.0715300	+	0.0536979i
$376$	0.570794	−	0.988644i	0.0294365	−	0.0509854i
$377$	−9.96067	−	4.04533i	−0.513001	−	0.208345i
$378$	−11.2494	−	9.21175i	−0.578606	−	0.473801i
$379$		−	16.1499i		−	0.829565i	−0.909921	−	0.414783i	$-0.863858\pi$
$379$		−	16.1499i		−	0.829565i	0.909921	−	0.414783i	$-0.136142\pi$
$380$	−0.934510	+	1.61862i	−0.0479394	+	0.0830334i
$381$	8.23979	+	10.9761i	0.422137	+	0.562322i
$382$	17.9121	−	10.3415i	0.916461	−	0.529119i
$383$	5.46094	−	3.15287i	0.279041	−	0.161104i	−0.353948	−	0.935265i	$-0.615161\pi$
$383$	5.46094	−	3.15287i	0.279041	−	0.161104i	0.632989	+	0.774161i	$0.281828\pi$
$384$	0.309711	+	2.56093i	0.0158049	+	0.130687i
$385$	−2.83772	−	1.63836i	−0.144624	−	0.0834985i
$386$	2.69526			0.137185
$387$	19.1150	+	19.9389i	0.971671	+	1.01355i
$388$		−	23.1031i		−	1.17288i
$389$	−6.91245	+	11.9727i	−0.350475	+	0.607041i	−0.986333	−	0.164766i	$-0.947313\pi$
$389$	−6.91245	+	11.9727i	−0.350475	+	0.607041i	0.635858	+	0.771806i	$0.280647\pi$
$390$	8.75863	−	8.69531i	0.443511	−	0.440304i
$391$	3.95687	+	6.85351i	0.200108	+	0.346597i
$392$	0.806256	−	0.465492i	0.0407221	−	0.0235109i
$393$	−12.5269	+	29.3627i	−0.631896	+	1.48115i
$394$	−20.9560	+	36.2969i	−1.05575	+	1.82861i
$395$		−	4.40758i		−	0.221769i
$396$	12.7049	+	3.69319i	0.638447	+	0.185590i
$397$		−	10.3783i		−	0.520873i	−0.965491	−	0.260436i	$-0.916134\pi$
$397$		−	10.3783i		−	0.520873i	0.965491	−	0.260436i	$-0.0838665\pi$
$398$	18.2404	+	10.5311i	0.914309	+	0.527877i
$399$	−2.38778	+	0.288772i	−0.119539	+	0.0144567i
$400$	−2.08986	−	3.61974i	−0.104493	−	0.180987i
$401$	2.56352	−	1.48005i	0.128016	−	0.0739101i	−0.434624	−	0.900612i	$-0.643119\pi$
$401$	2.56352	−	1.48005i	0.128016	−	0.0739101i	0.562640	+	0.826702i	$0.309786\pi$
$402$	27.5054	+	36.6395i	1.37185	+	1.82741i
$403$	−13.3164	−	17.1079i	−0.663337	−	0.852203i
$404$	14.9899			0.745776
$405$	8.99199	+	0.379579i	0.446816	+	0.0188615i
$406$	8.34344			0.414078
$407$	−3.79570	+	6.57434i	−0.188146	+	0.325878i
$408$	0.821767	−	0.616904i	0.0406836	−	0.0305413i
$409$	−22.9348	+	13.2414i	−1.13405	+	0.654745i	−0.944951	−	0.327212i	$-0.893891\pi$
$409$	−22.9348	+	13.2414i	−1.13405	+	0.654745i	−0.189101	+	0.981958i	$0.560557\pi$
$410$	4.08754	−	2.35994i	0.201869	−	0.116549i
$411$	−2.84288	−	23.5071i	−0.140229	−	1.15952i
$412$	10.0486	−	17.4047i	0.495059	−	0.857466i
$413$	−2.46811			−0.121448
$414$	−14.1539	−	4.11438i	−0.695625	−	0.202211i
$415$	7.10079			0.348564
$416$	17.4683	+	22.4418i	0.856452	+	1.10030i
$417$	−1.64150	+	3.84764i	−0.0803845	+	0.188420i
$418$	3.88466	−	2.24281i	0.190005	−	0.109699i
$419$	−14.8689	−	25.7537i	−0.726393	−	1.25815i	−0.958398	−	0.285435i	$-0.907862\pi$
$419$	−14.8689	−	25.7537i	−0.726393	−	1.25815i	0.232005	−	0.972715i	$-0.425471\pi$
$420$	−1.83390	+	4.29863i	−0.0894854	+	0.209752i
$421$	−18.2103	−	10.5137i	−0.887516	−	0.512408i	−0.0143871	−	0.999896i	$-0.504580\pi$
$421$	−18.2103	−	10.5137i	−0.887516	−	0.512408i	−0.873129	+	0.487489i	$0.837913\pi$
$422$		−	6.54876i		−	0.318789i
$423$	13.2649	−	12.7168i	0.644961	−	0.618310i
$424$		−	1.77785i		−	0.0863401i
$425$	−1.59160	+	2.75672i	−0.0772037	+	0.133721i
$426$	−1.68558	+	0.203849i	−0.0816665	+	0.00987651i
$427$	5.18107	−	2.99129i	0.250730	−	0.144759i
$428$	−5.79560	−	10.0383i	−0.280141	−	0.485218i
$429$	−13.9736	+	3.68993i	−0.674651	+	0.178151i
$430$	9.09797	−	15.7582i	0.438743	−	0.759925i
$431$			9.68227i			0.466378i	0.972431	+	0.233189i	$0.0749161\pi$
$431$			9.68227i			0.466378i	−0.972431	+	0.233189i	$0.925084\pi$
$432$	−3.51461	+	21.4322i	−0.169097	+	1.03116i
$433$	31.1909			1.49894			0.749470	−	0.662038i	$-0.230308\pi$
$433$	31.1909			1.49894			0.749470	+	0.662038i	$0.230308\pi$
$434$	14.5709	+	8.41251i	0.699425	+	0.403813i
$435$	−4.13022	+	3.10057i	−0.198029	+	0.148661i
$436$	−2.79250	+	1.61225i	−0.133736	+	0.0772128i
$437$	−2.11159	+	1.21913i	−0.101011	+	0.0583189i
$438$	41.3181	−	4.99689i	1.97426	−	0.238761i
$439$	2.17718	−	3.77099i	0.103911	−	0.179980i	−0.809382	−	0.587283i	$-0.800198\pi$
$439$	2.17718	−	3.77099i	0.103911	−	0.179980i	0.913293	+	0.407303i	$0.133531\pi$
$440$			0.431315i			0.0205621i
$441$	14.5538	−	3.57244i	0.693038	−	0.170116i
$442$	8.53487	−	21.0151i	0.405962	−	0.999587i
$443$	13.1513	−	22.7787i	0.624838	−	1.08225i	−0.363734	−	0.931503i	$-0.618498\pi$
$443$	13.1513	−	22.7787i	0.624838	−	1.08225i	0.988572	−	0.150748i	$-0.0481683\pi$
$444$	9.95894	+	4.24873i	0.472630	+	0.201636i
$445$	4.81904	+	8.34682i	0.228444	+	0.395677i
$446$	−15.4230	−	26.7135i	−0.730303	−	1.26492i
$447$	19.2778	+	8.22438i	0.911807	+	0.389000i
$448$	−8.86365	−	5.11743i	−0.418768	−	0.241776i
$449$		−	13.3071i		−	0.628003i	−0.949423	−	0.314001i	$-0.898330\pi$
$449$		−	13.3071i		−	0.628003i	0.949423	−	0.314001i	$-0.101670\pi$
$450$	−1.41337	−	5.75792i	−0.0666267	−	0.271431i
$451$	−5.52707			−0.260259
$452$	−18.4124	+	31.8912i	−0.866047	+	1.50004i
$453$	4.79800	+	39.6735i	0.225430	+	1.86402i
$454$	−6.37163	−	11.0360i	−0.299035	−	0.517944i
$455$	−0.701345	−	5.05663i	−0.0328796	−	0.237058i
$456$	0.190071	+	0.253190i	0.00890088	+	0.0118567i
$457$	−23.9756	−	13.8423i	−1.12153	−	0.647517i	−0.179741	−	0.983714i	$-0.557526\pi$
$457$	−23.9756	−	13.8423i	−1.12153	−	0.647517i	−0.941792	+	0.336197i	$0.890859\pi$
$458$	46.9304			2.19291
$459$	15.4739	−	5.84311i	0.722259	−	0.272733i
$460$			4.73776i			0.220899i
$461$	−32.2477	−	18.6182i	−1.50193	−	0.867137i	−0.999998	−	0.00222758i	$-0.999291\pi$
$461$	−32.2477	−	18.6182i	−1.50193	−	0.867137i	−0.501928	−	0.864909i	$-0.667376\pi$
$462$	8.96999	−	6.73381i	0.417322	−	0.313285i
$463$	6.17329	−	3.56415i	0.286897	−	0.165640i	−0.349645	−	0.936882i	$-0.613698\pi$
$463$	6.17329	−	3.56415i	0.286897	−	0.165640i	0.636542	+	0.771242i	$0.280364\pi$
$464$	−6.23140	−	10.7931i	−0.289286	−	0.501057i
$465$	−10.3392	+	1.25039i	−0.479469	+	0.0579857i
$466$	18.3098	+	10.5712i	0.848185	+	0.489700i
$467$	−16.2693			−0.752854			−0.376427	−	0.926446i	$-0.622847\pi$
$467$	−16.2693			−0.752854			−0.376427	+	0.926446i	$0.622847\pi$
$468$	7.61762	+	19.1541i	0.352125	+	0.885397i
$469$	18.9506			0.875058
$470$	−10.4835	−	6.05266i	−0.483569	−	0.279188i
$471$	−9.80625	+	22.9857i	−0.451848	+	1.05912i
$472$	0.162439	+	0.281353i	0.00747687	+	0.0129503i
$473$	−18.4531	+	10.6539i	−0.848473	+	0.489866i
$474$	13.8771	+	5.92033i	0.637398	+	0.271930i
$475$	−0.849359	−	0.490377i	−0.0389712	−	0.0225001i
$476$			8.58901i			0.393677i
$477$	7.98820	−	27.4802i	0.365755	−	1.25823i
$478$	2.94239			0.134582
$479$	18.9675	+	10.9509i	0.866646	+	0.500358i	0.866232	−	0.499642i	$-0.166535\pi$
$479$	18.9675	+	10.9509i	0.866646	+	0.500358i	0.000413810		1.00000i	$0.499868\pi$
$480$	13.5628	−	1.64025i	0.619055	−	0.0748668i
$481$	−11.7150	+	1.62485i	−0.534159	+	0.0740870i
$482$	−20.0269	−	34.6875i	−0.912199	−	1.57997i
$483$	−4.87585	+	3.66032i	−0.221859	+	0.166550i
$484$	5.37806	−	9.31507i	0.244457	−	0.423412i
$485$	12.1232			0.550485
$486$	−13.2733	+	27.8012i	−0.602088	+	1.26109i
$487$			38.2626i			1.73384i	0.498444	+	0.866922i	$0.333905\pi$
$487$			38.2626i			1.73384i	−0.498444	+	0.866922i	$0.666095\pi$
$488$	−0.681986	−	0.393745i	−0.0308720	−	0.0178240i
$489$	−12.1340	+	9.10905i	−0.548719	+	0.411925i
$490$	−4.93604	−	8.54948i	−0.222988	−	0.386226i
$491$	2.61014	+	4.52090i	0.117794	+	0.204025i	0.918893	−	0.394506i	$-0.129084\pi$
$491$	2.61014	+	4.52090i	0.117794	+	0.204025i	−0.801099	+	0.598532i	$0.795751\pi$
$492$	0.946462	+	7.82606i	0.0426698	+	0.352826i
$493$	−4.74572	+	8.21982i	−0.213736	+	0.370202i
$494$	6.47484	+	2.62963i	0.291317	+	0.118313i
$495$	−1.93798	+	6.66682i	−0.0871055	+	0.299651i
$496$		−	25.1320i		−	1.12846i
$497$	−0.351147	+	0.608204i	−0.0157511	+	0.0272817i
$498$	−9.53789	+	22.3566i	−0.427403	+	1.00182i
$499$	24.5153	−	14.1539i	1.09746	−	0.633616i	0.161904	−	0.986806i	$-0.448236\pi$
$499$	24.5153	−	14.1539i	1.09746	−	0.633616i	0.935552	+	0.353190i	$0.114903\pi$
$500$	−1.65038	+	0.952848i	−0.0738073	+	0.0426126i
$501$	26.9272	+	11.4878i	1.20302	+	0.513237i
$502$	20.4581	+	11.8115i	0.913088	+	0.527171i
$503$	43.1996			1.92617			0.963087	−	0.269191i	$-0.0867562\pi$
$503$	43.1996			1.92617			0.963087	+	0.269191i	$0.0867562\pi$
$504$	0.547846	+	0.571460i	0.0244030	+	0.0254548i
$505$			7.86585i			0.350026i
$506$	5.68527	−	9.84718i	0.252741	−	0.437760i
$507$	−17.9087	−	13.6484i	−0.795353	−	0.606147i
$508$	7.55035	+	13.0776i	0.334992	+	0.580224i
$509$	24.7633	−	14.2971i	1.09762	−	0.633709i	0.162022	−	0.986787i	$-0.448198\pi$
$509$	24.7633	−	14.2971i	1.09762	−	0.633709i	0.935594	+	0.353078i	$0.114865\pi$
$510$	−6.54161	−	8.71397i	−0.289667	−	0.385861i
$511$	8.60756	−	14.9087i	0.380776	−	0.659524i
$512$			31.4098i			1.38813i
$513$	1.80029	+	4.76757i	0.0794847	+	0.210493i
$514$			1.50789i			0.0665100i
$515$	9.13298	+	5.27293i	0.402447	+	0.232353i
$516$	18.2453	+	24.3043i	0.803205	+	1.06994i
$517$	7.08777	+	12.2764i	0.311720	+	0.539914i
$518$	7.94906	−	4.58939i	0.349262	−	0.201646i
$519$	6.94152	−	0.839488i	0.304699	−	0.0368494i
$520$	−0.530271	+	0.412752i	−0.0232539	+	0.0181004i
$521$	−26.9407			−1.18030			−0.590148	−	0.807295i	$-0.700930\pi$
$521$	−26.9407			−1.18030			−0.590148	+	0.807295i	$0.700930\pi$
$522$	−4.21428	−	17.1686i	−0.184454	−	0.751449i
$523$	42.0516			1.83879			0.919394	−	0.393338i	$-0.128680\pi$
$523$	42.0516			1.83879			0.919394	+	0.393338i	$0.128680\pi$
$524$	−17.5618	+	30.4179i	−0.767191	+	1.32881i
$525$	−2.25568	−	0.962328i	−0.0984458	−	0.0419994i
$526$	−16.4163	+	9.47793i	−0.715783	+	0.413257i
$527$	−16.5757	+	9.57001i	−0.722051	+	0.416876i
$528$	−15.4102	−	6.57439i	−0.670645	−	0.286114i
$529$	8.40964	−	14.5659i	0.365637	−	0.633301i
$530$	−18.8522			−0.818888
$531$	1.24665	+	5.07873i	0.0540999	+	0.220398i
$532$	−2.64631			−0.114732
$533$	−5.28919	−	6.79514i	−0.229100	−	0.294330i
$534$	−32.7527	+	3.96102i	−1.41735	+	0.171410i
$535$	5.26751	−	3.04120i	0.227734	−	0.131482i
$536$	−1.24724	−	2.16028i	−0.0538724	−	0.0933098i
$537$	6.62400	+	8.82372i	0.285847	+	0.380772i
$538$	0.775393	+	0.447673i	0.0334296	+	0.0193006i
$539$			11.5604i			0.497941i
$540$	9.77176	+	1.60245i	0.420510	+	0.0689583i
$541$			8.88208i			0.381870i	0.981603	+	0.190935i	$0.0611520\pi$
$541$			8.88208i			0.381870i	−0.981603	+	0.190935i	$0.938848\pi$
$542$	−24.5436	+	42.5108i	−1.05424	+	1.82599i
$543$	−25.1009	−	33.4365i	−1.07718	−	1.43490i
$544$	21.7438	−	12.5538i	0.932259	−	0.538240i
$545$	−0.846016	−	1.46534i	−0.0362394	−	0.0627684i
$546$	16.8627	+	4.58397i	0.721656	+	0.196176i
$547$	19.4682	−	33.7200i	0.832402	−	1.44176i	−0.0637268	−	0.997967i	$-0.520299\pi$
$547$	19.4682	−	33.7200i	0.832402	−	1.44176i	0.896128	−	0.443795i	$-0.146368\pi$
$548$		−	26.0522i		−	1.11289i
$549$	−8.77226	−	9.15038i	−0.374391	−	0.390529i
$550$	4.57364			0.195020
$551$	−2.53256	−	1.46218i	−0.107891	−	0.0622908i
$552$	0.738163	+	0.314919i	0.0314183	+	0.0134038i
$553$	5.40453	−	3.12030i	0.229824	−	0.132689i
$554$	−29.7244	+	17.1614i	−1.26287	+	0.729117i
$555$	−2.22949	+	5.22588i	−0.0946366	+	0.221826i
$556$	−2.30127	+	3.98592i	−0.0975956	+	0.169040i
$557$			7.23411i			0.306519i	0.988186	+	0.153260i	$0.0489770\pi$
$557$			7.23411i			0.306519i	−0.988186	+	0.153260i	$0.951023\pi$
$558$	9.95095	−	34.2322i	0.421257	−	1.44917i
$559$	−30.7571	−	12.4914i	−1.30089	−	0.528329i
$560$	2.95899	−	5.12512i	0.125040	−	0.216576i
$561$	1.53194	+	12.6673i	0.0646787	+	0.534812i
$562$	19.8700	+	34.4159i	0.838167	+	1.45175i
$563$	0.937061	+	1.62304i	0.0394924	+	0.0684029i	0.885096	−	0.465408i	$-0.154093\pi$
$563$	0.937061	+	1.62304i	0.0394924	+	0.0684029i	−0.845604	+	0.533811i	$0.820759\pi$
$564$	16.1690	−	12.1382i	0.680840	−	0.511109i
$565$	−16.7347	−	9.66178i	−0.704034	−	0.406474i
$566$			4.69883i			0.197507i
$567$	5.90036	+	11.2946i	0.247792	+	0.474329i
$568$	0.0924430			0.00387882
$569$	14.2621	−	24.7027i	0.597899	−	1.03559i	−0.395231	−	0.918582i	$-0.629336\pi$
$569$	14.2621	−	24.7027i	0.597899	−	1.03559i	0.993131	−	0.117011i	$-0.0373311\pi$
$570$	2.68481	−	2.01550i	0.112454	−	0.0844199i
$571$	−9.84138	−	17.0458i	−0.411849	−	0.713343i	0.583243	−	0.812298i	$-0.301784\pi$
$571$	−9.84138	−	17.0458i	−0.411849	−	0.713343i	−0.995092	+	0.0989544i	$0.968450\pi$
$572$	−15.7507	+	2.18459i	−0.658570	+	0.0913425i
$573$	−17.9959	+	2.17637i	−0.751789	+	0.0909193i
$574$	5.78747	+	3.34140i	0.241564	+	0.139467i
$575$	−2.48611			−0.103678
$576$	−6.05328	+	20.8239i	−0.252220	+	0.867661i
$577$			28.2701i			1.17690i	0.808533	+	0.588451i	$0.200262\pi$
$577$			28.2701i			1.17690i	−0.808533	+	0.588451i	$0.799738\pi$
$578$	11.7534	+	6.78586i	0.488879	+	0.282254i
$579$	−2.17271	−	0.926931i	−0.0902946	−	0.0385219i
$580$	−4.92100	+	2.84114i	−0.204333	+	0.117972i
$581$	5.02694	+	8.70691i	0.208553	+	0.361224i
$582$	−16.2840	+	38.1695i	−0.674995	+	1.58217i
$583$	19.1186	+	11.0381i	0.791812	+	0.457153i
$584$	−2.26603			−0.0937690
$585$	−10.0510	+	3.99729i	−0.415556	+	0.165268i
$586$	−12.0120			−0.496209
$587$	−11.3964	−	6.57969i	−0.470378	−	0.271573i	0.246020	−	0.969265i	$-0.420877\pi$
$587$	−11.3964	−	6.57969i	−0.470378	−	0.271573i	−0.716398	+	0.697692i	$0.754211\pi$
$588$	16.3690	−	1.97962i	0.675044	−	0.0816380i
$589$	−2.94856	−	5.10706i	−0.121493	−	0.210433i
$590$	2.98345	−	1.72249i	0.122826	−	0.0709139i
$591$	29.3761	−	22.0527i	1.20837	−	0.907128i
$592$	−11.8737	−	6.85530i	−0.488007	−	0.281751i
$593$			17.1582i			0.704602i	0.935887	+	0.352301i	$0.114601\pi$
$593$			17.1582i			0.704602i	−0.935887	+	0.352301i	$0.885399\pi$
$594$	−18.3872	−	15.0566i	−0.754434	−	0.617781i
$595$	−4.50702			−0.184770
$596$	19.9706	+	11.5300i	0.818027	+	0.472288i
$597$	−11.0822	−	14.7625i	−0.453566	−	0.604187i
$598$	17.5470	−	2.43374i	0.717550	−	0.0995229i
$599$	−19.6101	−	33.9657i	−0.801246	−	1.38780i	−0.918796	−	0.394732i	$-0.870837\pi$
$599$	−19.6101	−	33.9657i	−0.801246	−	1.38780i	0.117550	−	0.993067i	$-0.462496\pi$
$600$	0.0387570	+	0.320472i	0.00158225	+	0.0130832i
$601$	−12.2038	+	21.1375i	−0.497802	+	0.862218i	−0.999997	−	0.00253654i	$-0.999193\pi$
$601$	−12.2038	+	21.1375i	−0.497802	+	0.862218i	0.502195	+	0.864754i	$0.332526\pi$
$602$	25.7633			1.05003
$603$	−9.57198	−	38.9954i	−0.389801	−	1.58801i
$604$			43.9689i			1.78907i
$605$	4.88802	+	2.82210i	0.198726	+	0.114735i
$606$	−24.7654	−	10.5655i	−1.00603	−	0.429195i
$607$	−18.5929	−	32.2039i	−0.754663	−	1.30711i	−0.945542	−	0.325501i	$-0.894467\pi$
$607$	−18.5929	−	32.2039i	−0.754663	−	1.30711i	0.190879	−	0.981614i	$-0.438866\pi$
$608$	3.86788	+	6.69936i	0.156863	+	0.271695i
$609$	−6.72583	−	2.86941i	−0.272545	−	0.116274i
$610$	−4.17524	+	7.23173i	−0.169051	+	0.292804i
$611$	−8.31021	+	20.4619i	−0.336195	+	0.827801i
$612$	17.6739	−	4.33832i	0.714426	−	0.175366i
$613$			46.1767i			1.86506i	0.361092	+	0.932530i	$0.382404\pi$
$613$			46.1767i			1.86506i	−0.361092	+	0.932530i	$0.617596\pi$
$614$	−4.91006	+	8.50447i	−0.198154	+	0.343212i
$615$	−4.10667	+	0.496649i	−0.165597	+	0.0200268i
$616$	−0.528874	+	0.305345i	−0.0213089	+	0.0123027i
$617$	−32.0251	+	18.4897i	−1.28928	+	0.744367i	−0.978526	−	0.206122i	$-0.933915\pi$
$617$	−32.0251	+	18.4897i	−1.28928	+	0.744367i	−0.310756	+	0.950490i	$0.600582\pi$
$618$	−28.8692	+	21.6722i	−1.16129	+	0.871785i
$619$	27.7138	+	16.0006i	1.11391	+	0.643117i	0.939840	−	0.341616i	$-0.110974\pi$
$619$	27.7138	+	16.0006i	1.11391	+	0.643117i	0.174072	+	0.984733i	$0.444307\pi$
$620$	−11.4586			−0.460190
$621$	9.99477	+	8.18438i	0.401076	+	0.328428i
$622$		−	66.6540i		−	2.67258i
$623$	−6.82319	+	11.8181i	−0.273365	+	0.473483i
$624$	−6.66427	−	25.2372i	−0.266784	−	1.01030i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	38.8174	−	22.4112i	1.55145	−	0.895732i
$627$	−3.90284	+	0.471998i	−0.155864	+	0.0188498i
$628$	−13.7477	+	23.8117i	−0.548593	+	0.950191i
$629$			10.4417i			0.416339i
$630$	6.05972	−	5.80932i	0.241425	−	0.231449i
$631$			29.5469i			1.17625i	0.808772	+	0.588123i	$0.200133\pi$
$631$			29.5469i			1.17625i	−0.808772	+	0.588123i	$0.799867\pi$
$632$	−0.711399	−	0.410726i	−0.0282979	−	0.0163378i
$633$	−2.25220	+	5.27910i	−0.0895168	+	0.209826i
$634$	−19.7531	−	34.2134i	−0.784496	−	1.35879i
$635$	−6.86237	+	3.96199i	−0.272325	+	0.157227i
$636$	12.3556	−	28.9612i	0.489930	−	1.14839i
$637$	−14.2127	+	11.0629i	−0.563127	+	0.438326i
$638$	13.6374			0.539909
$639$	1.42889	+	0.415363i	0.0565259	+	0.0164315i
$640$	−1.48932			−0.0588707
$641$	−9.45016	+	16.3682i	−0.373259	+	0.646503i	−0.990065	−	0.140612i	$-0.955093\pi$
$641$	−9.45016	+	16.3682i	−0.373259	+	0.646503i	0.616806	+	0.787115i	$0.288426\pi$
$642$	2.49972	+	20.6696i	0.0986561	+	0.815763i
$643$	35.0392	−	20.2299i	1.38181	−	0.797788i	0.389436	−	0.921054i	$-0.372670\pi$
$643$	35.0392	−	20.2299i	1.38181	−	0.797788i	0.992374	+	0.123266i	$0.0393368\pi$
$644$	−5.80939	+	3.35405i	−0.228922	+	0.132168i
$645$	−12.7535	+	9.57410i	−0.502168	+	0.376980i
$646$	3.08491	−	5.34322i	0.121374	−	0.210226i
$647$	8.57838			0.337251			0.168626	−	0.985680i	$-0.446067\pi$
$647$	8.57838			0.337251			0.168626	+	0.985680i	$0.446067\pi$
$648$	0.899196	−	1.41597i	0.0353238	−	0.0556245i
$649$	−4.03414			−0.158354
$650$	4.37680	+	5.62296i	0.171672	+	0.220551i
$651$	−8.85276	−	11.7926i	−0.346967	−	0.462189i
$652$	−14.4572	+	8.34687i	−0.566188	+	0.326889i
$653$	−17.6875	−	30.6357i	−0.692167	−	1.19887i	−0.971127	−	0.238565i	$-0.923323\pi$
$653$	−17.6875	−	30.6357i	−0.692167	−	1.19887i	0.278960	−	0.960303i	$-0.410010\pi$
$654$	5.74997	−	0.695385i	0.224842	−	0.0271917i
$655$	−15.9616	−	9.21543i	−0.623671	−	0.360077i
$656$		−	9.98226i		−	0.389742i
$657$	−35.0259	−	10.1817i	−1.36649	−	0.397225i
$658$		−	17.1397i		−	0.668175i
$659$	0.467515	−	0.809759i	0.0182118	−	0.0315437i	−0.856776	−	0.515689i	$-0.827536\pi$
$659$	0.467515	−	0.809759i	0.0182118	−	0.0315437i	0.874988	+	0.484145i	$0.160869\pi$
$660$	−2.99752	+	7.02613i	−0.116678	+	0.273492i
$661$	−20.4363	+	11.7989i	−0.794880	+	0.458924i	−0.841678	−	0.539980i	$-0.818432\pi$
$661$	−20.4363	+	11.7989i	−0.794880	+	0.458924i	0.0467979	+	0.998904i	$0.485098\pi$
$662$	5.88888	+	10.1998i	0.228878	+	0.396428i
$663$	−14.1075	+	14.0055i	−0.547890	+	0.543929i
$664$	0.661697	−	1.14609i	0.0256788	−	0.0444770i
$665$		−	1.38863i		−	0.0538488i
$666$	−13.4588	−	14.0390i	−0.521520	−	0.543999i
$667$	−7.41291			−0.287029
$668$	27.8949	+	16.1051i	1.07929	+	0.623126i
$669$	3.24578	+	26.8385i	0.125489	+	1.03764i
$670$	−22.9074	+	13.2256i	−0.884991	+	0.510950i
$671$	8.46848	−	4.88928i	0.326922	−	0.188748i
$672$	11.6129	+	15.4694i	0.447979	+	0.596745i
$673$	−3.28480	+	5.68944i	−0.126620	+	0.219312i	−0.922365	−	0.386320i	$-0.873746\pi$
$673$	−3.28480	+	5.68944i	−0.126620	+	0.219312i	0.795745	+	0.605631i	$0.207079\pi$
$674$			38.0335i			1.46500i
$675$	−0.840872	+	5.12766i	−0.0323652	+	0.197364i
$676$	−17.7586	−	17.2738i	−0.683024	−	0.664377i
$677$	25.1692	−	43.5943i	0.967330	−	1.67546i	0.264109	−	0.964493i	$-0.414922\pi$
$677$	25.1692	−	43.5943i	0.967330	−	1.67546i	0.703221	−	0.710971i	$-0.251744\pi$
$678$	52.8981	−	39.7108i	2.03154	−	1.52509i
$679$	8.58249	+	14.8653i	0.329366	+	0.570478i
$680$	0.296630	+	0.513778i	0.0113752	+	0.0197025i
$681$	1.34091	+	11.0876i	0.0513837	+	0.424879i
$682$	23.8162	+	13.7503i	0.911968	+	0.526525i
$683$		−	41.3176i		−	1.58097i	−0.612479	−	0.790487i	$-0.709827\pi$
$683$		−	41.3176i		−	1.58097i	0.612479	−	0.790487i	$-0.290173\pi$
$684$	1.33665	+	5.44541i	0.0511083	+	0.208210i
$685$	13.6707			0.522331
$686$	16.7825	−	29.0681i	0.640758	−	1.10983i
$687$	−37.8317	−	16.1399i	−1.44337	−	0.615776i
$688$	−19.2416	−	33.3275i	−0.733581	−	1.27060i
$689$	4.72518	+	34.0680i	0.180015	+	1.29789i
$690$	3.33937	−	7.82743i	0.127128	−	0.297985i
$691$	−7.76180	−	4.48128i	−0.295273	−	0.170476i	0.345044	−	0.938586i	$-0.387864\pi$
$691$	−7.76180	−	4.48128i	−0.295273	−	0.170476i	−0.640317	+	0.768110i	$0.721197\pi$
$692$	7.69309			0.292447
$693$	−9.54675	+	2.34339i	−0.362651	+	0.0890180i
$694$			36.1030i			1.37045i
$695$	−2.09158	−	1.20757i	−0.0793382	−	0.0458059i
$696$	0.115563	+	0.955562i	0.00438040	+	0.0362205i
$697$	−6.58379	+	3.80115i	−0.249379	+	0.143979i
$698$	21.8119	+	37.7792i	0.825591	+	1.42997i
$699$	−11.1244	−	14.8186i	−0.420763	−	0.560491i
$700$	−2.33674	−	1.34912i	−0.0883206	−	0.0509919i
$701$	−12.7281			−0.480735			−0.240367	−	0.970682i	$-0.577268\pi$
$701$	−12.7281			−0.480735			−0.240367	+	0.970682i	$0.577268\pi$
$702$	0.915245	−	37.0143i	0.0345437	−	1.39702i
$703$	−3.21714			−0.121337
$704$	−14.4877	−	8.36445i	−0.546024	−	0.315247i
$705$	6.36942	+	8.48459i	0.239886	+	0.319548i
$706$	25.7794	+	44.6512i	0.970220	+	1.68047i
$707$	−9.64502	+	5.56855i	−0.362738	+	0.209427i
$708$	0.690811	+	5.71215i	0.0259623	+	0.214676i
$709$	−12.1726	−	7.02783i	−0.457150	−	0.263936i	0.253695	−	0.967284i	$-0.418354\pi$
$709$	−12.1726	−	7.02783i	−0.457150	−	0.263936i	−0.710845	+	0.703349i	$0.751687\pi$
$710$		−	0.980259i		−	0.0367885i
$711$	−9.15060	−	9.54502i	−0.343174	−	0.357966i
$712$	1.79628			0.0673183
$713$	−12.9458	−	7.47428i	−0.484825	−	0.279914i
$714$	6.05390	−	14.1902i	0.226561	−	0.531056i
$715$	−1.14635	−	8.26507i	−0.0428711	−	0.309096i
$716$	6.06976	+	10.5131i	0.226838	+	0.392894i
$717$	−2.37193	−	1.01192i	−0.0885812	−	0.0377909i
$718$	−4.15445	+	7.19572i	−0.155043	+	0.268542i
$719$	41.1269			1.53378			0.766888	−	0.641781i	$-0.221804\pi$
$719$	41.1269			1.53378			0.766888	+	0.641781i	$0.221804\pi$
$720$	−12.0407	−	3.50012i	−0.448732	−	0.130442i
$721$			14.9317i			0.556085i
$722$	−30.8724	−	17.8242i	−1.14895	−	0.663349i
$723$	4.21465	+	34.8499i	0.156744	+	1.29608i
$724$	−23.0006	−	39.8383i	−0.854812	−	1.48058i
$725$	−1.49087	−	2.58226i	−0.0553694	−	0.0959027i
$726$	−15.4509	+	11.5991i	−0.573438	+	0.430482i
$727$	3.16503	−	5.48199i	0.117384	−	0.203316i	−0.801346	−	0.598201i	$-0.795882\pi$
$727$	3.16503	−	5.48199i	0.117384	−	0.203316i	0.918730	+	0.394885i	$0.129216\pi$
$728$	−0.881513	−	0.358009i	−0.0326710	−	0.0132687i
$729$	20.2610	−	17.8463i	0.750409	−	0.660974i
$730$			24.0288i			0.889347i
$731$	−14.6541	+	25.3816i	−0.542000	+	0.938772i
$732$	−8.37314	−	11.1537i	−0.309480	−	0.412253i
$733$	33.9154	−	19.5810i	1.25269	−	0.723242i	0.281049	−	0.959693i	$-0.409318\pi$
$733$	33.9154	−	19.5810i	1.25269	−	0.723242i	0.971643	+	0.236451i	$0.0759843\pi$
$734$	−7.67023	+	4.42841i	−0.283113	+	0.163455i
$735$	1.03879	+	8.58949i	0.0383163	+	0.316828i
$736$	16.9821	+	9.80465i	0.625970	+	0.361404i
$737$	30.9748			1.14097
$738$	3.95246	−	13.5968i	0.145492	−	0.500506i
$739$		−	10.0932i		−	0.371283i	−0.982618	−	0.185641i	$-0.940564\pi$
$739$		−	10.0932i		−	0.371283i	0.982618	−	0.185641i	$-0.0594363\pi$
$740$	−3.12560	+	5.41369i	−0.114899	+	0.199011i
$741$	−4.31516	−	4.34658i	−0.158521	−	0.159676i
$742$	−13.3462	−	23.1164i	−0.489956	−	0.848629i
$743$	−37.6176	+	21.7185i	−1.38006	+	0.796776i	−0.992166	−	0.124930i	$-0.960129\pi$
$743$	−37.6176	+	21.7185i	−1.38006	+	0.796776i	−0.387890	+	0.921706i	$0.626796\pi$
$744$	−0.761655	+	1.78530i	−0.0279236	+	0.0654524i
$745$	−6.05030	+	10.4794i	−0.221666	+	0.383936i
$746$		−	65.0971i		−	2.38337i
$747$	15.3774	−	14.7420i	0.562630	−	0.539381i
$748$			14.0388i			0.513308i
$749$	7.45817	+	4.30597i	0.272515	+	0.157337i
$750$	3.39826	−	0.410976i	0.124087	−	0.0150067i
$751$	16.9962	+	29.4383i	0.620200	+	1.07422i	0.989448	+	0.144887i	$0.0462818\pi$
$751$	16.9962	+	29.4383i	0.620200	+	1.07422i	−0.369249	+	0.929331i	$0.620385\pi$
$752$	−22.1720	+	12.8010i	−0.808529	+	0.466804i
$753$	−12.4296	−	16.5573i	−0.452960	−	0.603380i
$754$	13.0504	+	16.7662i	0.475269	+	0.610588i
$755$	−23.0724			−0.839690
$756$	4.95293	+	13.1165i	0.180136	+	0.477041i
$757$	29.6328			1.07702			0.538512	−	0.842618i	$-0.318987\pi$
$757$	29.6328			1.07702			0.538512	+	0.842618i	$0.318987\pi$
$758$	−15.9584	+	27.6408i	−0.579635	+	1.00396i
$759$	−7.96959	+	5.98280i	−0.289278	+	0.217162i
$760$	−0.158297	+	0.0913930i	−0.00574205	+	0.00331517i
$761$	10.9826	−	6.34081i	0.398119	−	0.229854i	−0.287553	−	0.957765i	$-0.592842\pi$
$761$	10.9826	−	6.34081i	0.398119	−	0.229854i	0.685672	+	0.727910i	$0.259508\pi$
$762$	−3.25657	−	26.9278i	−0.117973	−	0.975490i
$763$	1.19786	−	2.07475i	0.0433654	−	0.0751111i
$764$	−19.9443			−0.721560
$765$	2.27650	+	9.27426i	0.0823071	+	0.335312i
$766$	−12.4619			−0.450268
$767$	−3.86052	−	4.95969i	−0.139395	−	0.179084i
$768$	11.8266	−	27.7213i	0.426755	−	1.00031i
$769$	−4.22386	+	2.43865i	−0.152316	+	0.0879398i	−0.574221	−	0.818700i	$-0.694695\pi$
$769$	−4.22386	+	2.43865i	−0.152316	+	0.0879398i	0.421905	+	0.906640i	$0.361362\pi$
$770$	3.23786	+	5.60814i	0.116684	+	0.202103i
$771$	0.518580	−	1.21554i	0.0186762	−	0.0437766i
$772$	−2.25079	−	1.29949i	−0.0810077	−	0.0467698i
$773$		−	15.0432i		−	0.541066i	−0.962711	−	0.270533i	$-0.912800\pi$
$773$		−	15.0432i		−	0.541066i	0.962711	−	0.270533i	$-0.0872000\pi$
$774$	−13.0131	−	53.0141i	−0.467745	−	1.90555i
$775$		−	6.01284i		−	0.215988i
$776$	1.12971	−	1.95672i	0.0405544	−	0.0702423i
$777$	−7.98627	+	0.965837i	−0.286506	+	0.0346492i
$778$	23.6615	−	13.6610i	0.848305	−	0.489769i
$779$	−1.17115	−	2.02849i	−0.0419608	−	0.0726783i
$780$	−11.5066	+	3.03850i	−0.412004	+	0.108796i
$781$	−0.573950	+	0.994111i	−0.0205376	+	0.0355721i
$782$		−	15.6398i		−	0.559278i
$783$	−2.50726	+	15.2893i	−0.0896021	+	0.546396i
$784$	−20.8789			−0.745673
$785$	−12.4950	−	7.21401i	−0.445967	−	0.257479i
$786$	50.4544	−	37.8763i	1.79965	−	1.35100i
$787$	29.5539	−	17.0630i	1.05348	−	0.608229i	0.129861	−	0.991532i	$-0.458547\pi$
$787$	29.5539	−	17.0630i	1.05348	−	0.608229i	0.923623	+	0.383303i	$0.125214\pi$
$788$	35.0005	−	20.2075i	1.24684	−	0.719863i
$789$	16.4931	−	1.99463i	0.587170	−	0.0710106i
$790$	−4.35531	+	7.54362i	−0.154955	+	0.268390i
$791$		−	27.3599i		−	0.972805i
$792$	0.895455	+	0.934053i	0.0318186	+	0.0331901i
$793$	14.1150	+	5.73254i	0.501239	+	0.203568i
$794$	−10.2553	+	17.7626i	−0.363945	+	0.630372i
$795$	15.1972	+	6.48350i	0.538989	+	0.229946i
$796$	−10.1550	−	17.5889i	−0.359933	−	0.623422i
$797$	−11.0039	−	19.0594i	−0.389780	−	0.675118i	0.602640	−	0.798013i	$-0.294116\pi$
$797$	−11.0039	−	19.0594i	−0.389780	−	0.675118i	−0.992420	+	0.122895i	$0.960782\pi$
$798$	4.37207	+	1.86523i	0.154769	+	0.0660285i
$799$	16.8858	+	9.74900i	0.597375	+	0.344895i
$800$			7.88756i			0.278867i
$801$	27.7650	+	8.07098i	0.981027	+	0.285174i
$802$	−5.84999			−0.206570
$803$	14.0691	−	24.3684i	0.496487	−	0.859941i
$804$	−5.30417	−	43.8589i	−0.187064	−	1.54678i
$805$	−1.76001	−	3.04843i	−0.0620324	−	0.107443i
$806$	5.88618	+	42.4388i	0.207332	+	1.49484i
$807$	−0.471101	−	0.627546i	−0.0165836	−	0.0220907i
$808$	1.26958	+	0.732990i	0.0446635	+	0.0257865i
$809$	35.0622			1.23272			0.616360	−	0.787464i	$-0.288606\pi$
$809$	35.0622			1.23272			0.616360	+	0.787464i	$0.288606\pi$
$810$	−15.0148	−	9.53502i	−0.527567	−	0.335026i
$811$		−	23.0860i		−	0.810659i	−0.914171	−	0.405329i	$-0.867157\pi$
$811$		−	23.0860i		−	0.810659i	0.914171	−	0.405329i	$-0.132843\pi$
$812$	−6.96755	−	4.02272i	−0.244513	−	0.141170i
$813$	34.4051	−	25.8281i	1.20664	−	0.905830i
$814$	12.9928	−	7.50138i	0.455396	−	0.262923i
$815$	−4.37996	−	7.58632i	−0.153423	−	0.265737i
$816$	−22.8780	+	2.76680i	−0.800889	+	0.0968572i
$817$	−7.82018	−	4.51498i	−0.273593	−	0.157959i
$818$	52.3375			1.82994
$819$	−12.0169	−	9.49452i	−0.419905	−	0.331766i
$820$	−4.55130			−0.158938
$821$	19.7852	+	11.4230i	0.690509	+	0.398666i	0.803803	−	0.594896i	$-0.202807\pi$
$821$	19.7852	+	11.4230i	0.690509	+	0.398666i	−0.113294	+	0.993562i	$0.536140\pi$
$822$	−18.3627	+	43.0418i	−0.640472	+	1.50125i
$823$	1.15184	+	1.99504i	0.0401505	+	0.0695426i	0.885402	−	0.464826i	$-0.153883\pi$
$823$	1.15184	+	1.99504i	0.0401505	+	0.0695426i	−0.845252	+	0.534368i	$0.820550\pi$
$824$	1.70214	−	0.982729i	0.0592968	−	0.0342350i
$825$	−3.68691	−	1.57293i	−0.128362	−	0.0547623i
$826$	4.22420	+	2.43884i	0.146979	+	0.0848583i
$827$			29.4957i			1.02567i	0.858489	+	0.512833i	$0.171404\pi$
$827$			29.4957i			1.02567i	−0.858489	+	0.512833i	$0.828596\pi$
$828$	9.83608	+	10.2601i	0.341828	+	0.356562i
$829$	−24.1393			−0.838394			−0.419197	−	0.907895i	$-0.637688\pi$
$829$	−24.1393			−0.838394			−0.419197	+	0.907895i	$0.637688\pi$
$830$	−12.1531	−	7.01659i	−0.421840	−	0.243549i
$831$	29.8635	−	3.61161i	1.03595	−	0.125285i
$832$	−3.58064	−	25.8160i	−0.124136	−	0.895009i
$833$	7.95047	+	13.7706i	0.275467	+	0.477124i
$834$	6.61145	−	4.96324i	0.228936	−	0.171863i
$835$	−8.45105	+	14.6376i	−0.292460	+	0.506556i
$836$	−4.32540			−0.149597
$837$	−19.7946	+	24.1731i	−0.684200	+	0.835545i
$838$			58.7703i			2.03019i
$839$	13.4456	+	7.76280i	0.464193	+	0.268002i	0.713805	−	0.700344i	$-0.246970\pi$
$839$	13.4456	+	7.76280i	0.464193	+	0.268002i	−0.249613	+	0.968346i	$0.580303\pi$
$840$	−0.365522	+	0.274398i	−0.0126117	+	0.00946765i
$841$	10.0546	+	17.4151i	0.346711	+	0.600522i
$842$	20.7781	+	35.9887i	0.716061	+	1.24025i
$843$	−4.18164	−	34.5770i	−0.144023	−	1.19089i
$844$	−3.15743	+	5.46883i	−0.108683	+	0.188245i
$845$	9.06430	−	9.31871i	0.311821	−	0.320573i
$846$	−35.2690	+	8.65728i	−1.21257	+	0.297643i
$847$			7.99151i			0.274591i
$848$	−19.9356	+	34.5295i	−0.684592	+	1.18575i
$849$	1.61599	−	3.78784i	0.0554605	−	0.129998i
$850$	5.44807	−	3.14544i	0.186867	−	0.107888i
$851$	−7.06252	+	4.07755i	−0.242100	+	0.139776i
$852$	1.50590	+	0.642453i	0.0515912	+	0.0220101i
$853$	−29.7052	−	17.1503i	−1.01709	−	0.587215i	−0.103828	−	0.994595i	$-0.533109\pi$
$853$	−29.7052	−	17.1503i	−1.01709	−	0.587215i	−0.913259	+	0.407380i	$0.866442\pi$
$854$	−11.8233			−0.404585
$855$	−2.85744	+	0.701400i	−0.0977224	+	0.0239874i
$856$		−	1.13359i		−	0.0387454i
$857$	−21.6564	+	37.5100i	−0.739768	+	1.28132i	0.212832	+	0.977089i	$0.431731\pi$
$857$	−21.6564	+	37.5100i	−0.739768	+	1.28132i	−0.952600	+	0.304227i	$0.901602\pi$
$858$	27.5621	+	7.49252i	0.940955	+	0.255790i
$859$	4.14294	+	7.17579i	0.141355	+	0.244835i	0.928007	−	0.372562i	$-0.121521\pi$
$859$	4.14294	+	7.17579i	0.141355	+	0.244835i	−0.786652	+	0.617397i	$0.788187\pi$
$860$	−15.1953	+	8.77302i	−0.518156	+	0.299157i
$861$	−3.51626	−	4.68396i	−0.119834	−	0.159629i
$862$	9.56745	−	16.5713i	0.325869	−	0.564421i
$863$			19.1400i			0.651532i	0.945450	+	0.325766i	$0.105622\pi$
$863$			19.1400i			0.651532i	−0.945450	+	0.325766i	$0.894378\pi$
$864$	25.9662	−	31.7100i	0.883389	−	1.07879i
$865$			4.03689i			0.137258i
$866$	−53.3836	−	30.8211i	−1.81405	−	1.04734i
$867$	−7.14098	−	9.51238i	−0.242520	−	0.323057i
$868$	−8.11204	−	14.0505i	−0.275340	−	0.476904i
$869$	8.83371	−	5.10015i	0.299663	−	0.173011i
$870$	10.1327	−	1.22542i	0.343531	−	0.0415457i
$871$	29.6417	+	38.0814i	1.00437	+	1.29034i
$872$	−0.315349			−0.0106791
$873$	26.2539	−	25.1690i	0.888558	−	0.851841i
$874$	4.81869			0.162995
$875$	0.707941	−	1.22619i	0.0239328	−	0.0414528i
$876$	−36.9137	−	15.7483i	−1.24720	−	0.532085i
$877$	2.47326	−	1.42794i	0.0835162	−	0.0482181i	−0.457660	−	0.889127i	$-0.651312\pi$
$877$	2.47326	−	1.42794i	0.0835162	−	0.0482181i	0.541177	+	0.840909i	$0.317979\pi$
$878$	−7.45255	+	4.30273i	−0.251511	+	0.145210i
$879$	9.68311	+	4.13105i	0.326603	+	0.139337i
$880$	4.83648	−	8.37702i	0.163038	−	0.282389i
$881$	15.3248			0.516307			0.258153	−	0.966104i	$-0.416886\pi$
$881$	15.3248			0.516307			0.258153	+	0.966104i	$0.416886\pi$
$882$	−28.4391	−	8.26694i	−0.957594	−	0.278362i
$883$	−10.8428			−0.364890			−0.182445	−	0.983216i	$-0.558401\pi$
$883$	−10.8428			−0.364890			−0.182445	+	0.983216i	$0.558401\pi$
$884$	−17.2597	+	13.4346i	−0.580505	+	0.451853i
$885$	−2.99741	+	0.362498i	−0.100757	+	0.0121852i
$886$	−45.0173	+	25.9907i	−1.51238	+	0.873176i
$887$	11.3250	+	19.6155i	0.380258	+	0.658626i	0.991099	−	0.133128i	$-0.0425020\pi$
$887$	11.3250	+	19.6155i	0.380258	+	0.658626i	−0.610841	+	0.791753i	$0.709169\pi$
$888$	0.635718	+	0.846829i	0.0213333	+	0.0284177i
$889$	−9.71630	−	5.60971i	−0.325874	−	0.188144i
$890$		−	19.0476i		−	0.638476i
$891$	9.64415	+	18.4611i	0.323091	+	0.618469i
$892$			29.7444i			0.995915i
$893$	−3.00371	+	5.20257i	−0.100515	+	0.174097i
$894$	−24.8673	−	33.1253i	−0.831686	−	1.10788i
$895$	−5.51669	+	3.18506i	−0.184403	+	0.106465i
$896$	−1.05435	−	1.82619i	−0.0352235	−	0.0610088i
$897$	−14.9820	−	4.07273i	−0.500235	−	0.135984i
$898$	−13.1493	+	22.7753i	−0.438799	+	0.760022i
$899$		−	17.9287i		−	0.597955i
$900$	−1.59584	+	5.48984i	−0.0531947	+	0.182995i
$901$	30.3652			1.01161
$902$	9.45964	+	5.46152i	0.314971	+	0.181849i
$903$	−20.7684	−	8.86030i	−0.691128	−	0.294852i
$904$	−3.11889	+	1.80069i	−0.103733	+	0.0598901i
$905$	20.9048	−	12.0694i	0.694901	−	0.401201i
$906$	30.9912	−	72.6427i	1.02961	−	2.41339i
$907$	−21.7436	+	37.6610i	−0.721983	+	1.25051i	0.238220	+	0.971211i	$0.423436\pi$
$907$	−21.7436	+	37.6610i	−0.721983	+	1.25051i	−0.960204	+	0.279301i	$0.909897\pi$
$908$			12.2881i			0.407795i
$909$	16.3303	+	17.0342i	0.541643	+	0.564990i
$910$	−3.79630	+	9.34750i	−0.125846	+	0.309867i
$911$	24.0812	−	41.7098i	0.797846	−	1.38191i	−0.123171	−	0.992385i	$-0.539306\pi$
$911$	24.0812	−	41.7098i	0.797846	−	1.38191i	0.921017	−	0.389523i	$-0.127360\pi$
$912$	−0.852461	−	7.04880i	−0.0282278	−	0.233409i
$913$	8.21655	+	14.2315i	0.271928	+	0.470993i
$914$	27.3564	+	47.3826i	0.904868	+	1.56728i
$915$	5.85283	−	4.39374i	0.193489	−	0.145253i
$916$	−39.1913	−	22.6271i	−1.29492	−	0.747620i
$917$		−	26.0959i		−	0.861763i
$918$	−32.2576	−	5.28983i	−1.06466	−	0.174591i
$919$	22.0524			0.727440			0.363720	−	0.931508i	$-0.381506\pi$
$919$	22.0524			0.727440			0.363720	+	0.931508i	$0.381506\pi$
$920$	−0.231671	+	0.401266i	−0.00763797	+	0.0132294i
$921$	6.88290	−	5.16702i	0.226799	−	0.170259i
$922$	36.7949	+	63.7306i	1.21177	+	2.09886i
$923$	−1.77144	+	0.245695i	−0.0583076	+	0.00808716i
$924$	−10.7374	+	1.29855i	−0.353235	+	0.0427193i
$925$	−2.84080	−	1.64013i	−0.0934048	−	0.0539273i
$926$	−14.0875			−0.462945
$927$	30.7254	−	7.54201i	1.00916	−	0.247712i
$928$			23.5186i			0.772036i
$929$	−18.8343	−	10.8740i	−0.617932	−	0.356763i	0.158131	−	0.987418i	$-0.449453\pi$
$929$	−18.8343	−	10.8740i	−0.617932	−	0.356763i	−0.776063	+	0.630655i	$0.782786\pi$
$930$	18.9312	+	8.07654i	0.620780	+	0.264840i
$931$	−4.24278	+	2.44957i	−0.139052	+	0.0802815i
$932$	−10.1936	−	17.6558i	−0.333902	−	0.578336i
$933$	−22.9231	+	53.7313i	−0.750469	+	1.75908i
$934$	27.8451	+	16.0764i	0.911120	+	0.526035i
$935$	−7.36674			−0.240918
$936$	−0.291435	+	1.99475i	−0.00952585	+	0.0652005i
$937$	2.95440			0.0965162			0.0482581	−	0.998835i	$-0.484633\pi$
$937$	2.95440			0.0965162			0.0482581	+	0.998835i	$0.484633\pi$
$938$	−32.4342	−	18.7259i	−1.05901	−	0.611422i
$939$	−38.9990	+	4.71643i	−1.27269	+	0.153915i
$940$	5.83647	+	10.1091i	0.190365	+	0.329722i
$941$	44.1732	−	25.5034i	1.44001	−	0.831387i	0.442156	−	0.896938i	$-0.354214\pi$
$941$	44.1732	−	25.5034i	1.44001	−	0.831387i	0.997849	+	0.0655509i	$0.0208805\pi$
$942$	39.4966	−	29.6503i	1.28687	−	0.966058i
$943$	−5.14200	−	2.96874i	−0.167447	−	0.0966754i
$944$		−	7.28593i		−	0.237137i
$945$	−6.88277	+	2.59901i	−0.223897	+	0.0845459i
$946$	42.1102			1.36912
$947$	−40.1773	−	23.1964i	−1.30559	−	0.753781i	−0.324230	−	0.945978i	$-0.605105\pi$
$947$	−40.1773	−	23.1964i	−1.30559	−	0.753781i	−0.981356	+	0.192197i	$0.938439\pi$
$948$	−8.73426	−	11.6348i	−0.283676	−	0.377880i
$949$	43.4228	−	6.02266i	1.40956	−	0.195504i
$950$	0.969125	+	1.67857i	0.0314426	+	0.0544601i
$951$	4.15703	+	34.3735i	0.134801	+	1.11464i
$952$	−0.419993	+	0.727449i	−0.0136120	+	0.0235768i
$953$	−37.3280			−1.20917			−0.604586	−	0.796540i	$-0.706662\pi$
$953$	−37.3280			−1.20917			−0.604586	+	0.796540i	$0.706662\pi$
$954$	−40.8262	+	39.1392i	−1.32180	+	1.26718i
$955$		−	10.4656i		−	0.338660i
$956$	−2.45717	−	1.41865i	−0.0794705	−	0.0458823i
$957$	−10.9934	−	4.69005i	−0.355366	−	0.151608i
$958$	−21.6420	−	37.4851i	−0.699222	−	1.21109i
$959$	9.67804	+	16.7629i	0.312520	+	0.541301i
$960$	−11.5161	−	4.91305i	−0.371680	−	0.158568i
$961$	2.57712	−	4.46370i	0.0831329	−	0.143990i
$962$	21.6560	+	8.79515i	0.698217	+	0.283567i
$963$	5.09343	−	17.5219i	0.164134	−	0.564635i
$964$			38.6231i			1.24397i
$965$	0.681901	−	1.18109i	0.0219512	−	0.0380205i
$966$	11.9620	−	1.44665i	0.384870	−	0.0465451i
$967$	29.1234	−	16.8144i	0.936545	−	0.540715i	0.0476696	−	0.998863i	$-0.484821\pi$
$967$	29.1234	−	16.8144i	0.936545	−	0.540715i	0.888876	+	0.458149i	$0.151487\pi$
$968$	0.910993	−	0.525962i	0.0292804	−	0.0169051i
$969$	−4.32441	+	3.24635i	−0.138920	+	0.104288i
$970$	−20.7490	−	11.9794i	−0.666209	−	0.384636i
$971$	41.0713			1.31804			0.659021	−	0.752125i	$-0.270971\pi$
$971$	41.0713			1.31804			0.659021	+	0.752125i	$0.270971\pi$
$972$	24.4885	−	16.8170i	0.785469	−	0.539404i
$973$		−	3.41956i		−	0.109626i
$974$	37.8089	−	65.4869i	1.21147	−	2.09834i
$975$	−1.59443	−	6.03803i	−0.0510626	−	0.193372i
$976$	8.83037	+	15.2947i	0.282653	+	0.489570i
$977$	13.3198	−	7.69020i	0.426139	−	0.246031i	−0.271562	−	0.962421i	$-0.587540\pi$
$977$	13.3198	−	7.69020i	0.426139	−	0.246031i	0.697700	+	0.716390i	$0.254207\pi$
$978$	29.7685	−	3.60012i	0.951892	−	0.115119i
$979$	−11.1525	+	19.3167i	−0.356436	+	0.617365i
$980$			9.51948i			0.304089i
$981$	−4.87433	−	1.41692i	−0.155625	−	0.0452387i
$982$		−	10.3168i		−	0.329221i
$983$	35.6115	+	20.5603i	1.13583	+	0.655773i	0.945395	−	0.325927i	$-0.105676\pi$
$983$	35.6115	+	20.5603i	1.13583	+	0.655773i	0.190436	+	0.981700i	$0.439010\pi$
$984$	−0.302525	+	0.709112i	−0.00964414	+	0.0226057i
$985$	10.6038	+	18.3662i	0.337864	+	0.585197i
$986$	16.2447	−	9.37888i	0.517337	−	0.298684i
$987$	−5.89455	+	13.8167i	−0.187625	+	0.439790i
$988$	−4.13924	−	5.31777i	−0.131687	−	0.169181i
$989$	−22.8900			−0.727858
$990$	9.90463	−	9.49535i	0.314790	−	0.301782i
$991$	−28.8830			−0.917498			−0.458749	−	0.888566i	$-0.651702\pi$
$991$	−28.8830			−0.917498			−0.458749	+	0.888566i	$0.651702\pi$
$992$	−23.7133	+	41.0727i	−0.752898	+	1.30406i
$993$	−1.23931	−	10.2476i	−0.0393284	−	0.325197i
$994$	1.20198	−	0.693965i	0.0381246	−	0.0220112i
$995$	9.22966	−	5.32874i	0.292600	−	0.168933i
$996$	18.7441	−	14.0713i	0.593929	−	0.445865i
$997$	−3.87517	+	6.71199i	−0.122728	+	0.212571i	−0.920843	−	0.389935i	$-0.872498\pi$
$997$	−3.87517	+	6.71199i	−0.122728	+	0.212571i	0.798115	+	0.602506i	$0.205831\pi$
$998$	−55.9443			−1.77089
$999$	6.02131	+	15.9458i	0.190506	+	0.504502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.10	✓	108
9.4	even	3	inner	585.2.bt.b.571.45	yes	108
13.12	even	2	inner	585.2.bt.b.376.45	yes	108
117.103	even	6	inner	585.2.bt.b.571.10	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.10	✓	108	1.1	even	1	trivial
585.2.bt.b.376.45	yes	108	13.12	even	2	inner
585.2.bt.b.571.10	yes	108	117.103	even	6	inner
585.2.bt.b.571.45	yes	108	9.4	even	3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71151 - 0.988142i) q^{2} +(1.03985 + 1.38517i) q^{3} +(0.952848 + 1.65038i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.410976 - 3.39826i) q^{6} +(-1.22619 - 0.707941i) q^{7} +0.186373i q^{8} +(-0.837406 + 2.88076i) q^{9} +O(q^{10})\)	\(q+(-1.71151 - 0.988142i) q^{2} +(1.03985 + 1.38517i) q^{3} +(0.952848 + 1.65038i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.410976 - 3.39826i) q^{6} +(-1.22619 - 0.707941i) q^{7} +0.186373i q^{8} +(-0.837406 + 2.88076i) q^{9} +1.97628 q^{10} +(-2.00421 - 1.15713i) q^{11} +(-1.29524 + 3.03601i) q^{12} +(-0.495342 - 3.57136i) q^{13} +(1.39909 + 2.42330i) q^{14} +(-1.59313 - 0.679667i) q^{15} +(2.08986 - 3.61974i) q^{16} -3.18319 q^{17} +(4.27982 - 4.10297i) q^{18} -0.980755i q^{19} +(-1.65038 - 0.952848i) q^{20} +(-0.294438 - 2.43464i) q^{21} +(2.28682 + 3.96088i) q^{22} +(-1.24305 - 2.15303i) q^{23} +(-0.258158 + 0.193800i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.68123 + 6.60190i) q^{26} +(-4.86112 + 1.83562i) q^{27} -2.69824i q^{28} +(1.49087 - 2.58226i) q^{29} +(2.05505 + 2.73749i) q^{30} +(5.20727 - 3.00642i) q^{31} +(-6.83082 + 3.94378i) q^{32} +(-0.481260 - 3.97942i) q^{33} +(5.44807 + 3.14544i) q^{34} +1.41588 q^{35} +(-5.55226 + 1.36288i) q^{36} -3.28027i q^{37} +(-0.969125 + 1.67857i) q^{38} +(4.43187 - 4.39983i) q^{39} +(-0.0931864 - 0.161403i) q^{40} +(2.06830 - 1.19413i) q^{41} +(-1.90183 + 4.45786i) q^{42} +(4.60358 - 7.97363i) q^{43} -4.41028i q^{44} +(-0.715163 - 2.91351i) q^{45} +4.91325i q^{46} +(-5.30466 - 3.06265i) q^{47} +(7.18711 - 0.869189i) q^{48} +(-2.49764 - 4.32604i) q^{49} +(-1.71151 + 0.988142i) q^{50} +(-3.31006 - 4.40927i) q^{51} +(5.42212 - 4.22047i) q^{52} -9.53923 q^{53} +(10.1337 + 1.66180i) q^{54} +2.31426 q^{55} +(0.131941 - 0.228528i) q^{56} +(1.35851 - 1.01984i) q^{57} +(-5.10327 + 2.94638i) q^{58} +(1.50962 - 0.871582i) q^{59} +(-0.396297 - 3.27688i) q^{60} +(-2.11267 + 3.65926i) q^{61} -11.8831 q^{62} +(3.06622 - 2.93952i) q^{63} +7.22861 q^{64} +(2.21466 + 2.84522i) q^{65} +(-3.10855 + 7.28638i) q^{66} +(-11.5912 + 6.69216i) q^{67} +(-3.03310 - 5.25348i) q^{68} +(1.68972 - 3.96068i) q^{69} +(-2.42330 - 1.39909i) q^{70} -0.496012i q^{71} +(-0.536894 - 0.156070i) q^{72} +12.1586i q^{73} +(-3.24137 + 5.61422i) q^{74} +(1.71952 - 0.207954i) q^{75} +(1.61862 - 0.934510i) q^{76} +(1.63836 + 2.83772i) q^{77} +(-11.9329 + 3.15105i) q^{78} +(-2.20379 + 3.81708i) q^{79} +4.17972i q^{80} +(-7.59750 - 4.82472i) q^{81} -4.71989 q^{82} +(-6.14947 - 3.55040i) q^{83} +(3.73752 - 2.80577i) q^{84} +(2.75672 - 1.59160i) q^{85} +(-15.7582 + 9.09797i) q^{86} +(5.12716 - 0.620064i) q^{87} +(0.215658 - 0.373530i) q^{88} -9.63808i q^{89} +(-1.65495 + 5.69319i) q^{90} +(-1.92093 + 4.72984i) q^{91} +(2.36888 - 4.10302i) q^{92} +(9.57921 + 4.08673i) q^{93} +(6.05266 + 10.4835i) q^{94} +(0.490377 + 0.849359i) q^{95} +(-12.5659 - 5.36091i) q^{96} +(-10.4990 - 6.06159i) q^{97} +9.87209i q^{98} +(5.01175 - 4.80465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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