LMFDB - Embedded newform 546.2.u.a.185.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.18
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.69393 + 0.361382i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.0272832 + 0.0472559i) q^{5} +(-1.28630 - 1.15993i) q^{6} +(2.23165 - 1.42118i) q^{7} -1.00000i q^{8} +(2.73881 + 1.22431i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.69393 + 0.361382i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.0272832 + 0.0472559i) q^{5} +(-1.28630 - 1.15993i) q^{6} +(2.23165 - 1.42118i) q^{7} -1.00000i q^{8} +(2.73881 + 1.22431i) q^{9} -0.0545664i q^{10} +4.73776i q^{11} +(0.533999 + 1.64768i) q^{12} +(1.35013 + 3.34322i) q^{13} +(-2.64325 + 0.114956i) q^{14} +(0.0291384 + 0.0899079i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.64679 - 2.85233i) q^{17} +(-1.75972 - 2.42969i) q^{18} -0.566108i q^{19} +(-0.0272832 + 0.0472559i) q^{20} +(4.29384 - 1.60091i) q^{21} +(2.36888 - 4.10302i) q^{22} +(-5.33783 - 3.08180i) q^{23} +(0.361382 - 1.69393i) q^{24} +(2.49851 - 4.32755i) q^{25} +(0.502363 - 3.57038i) q^{26} +(4.19690 + 3.06366i) q^{27} +(2.34660 + 1.22207i) q^{28} +(0.837457 - 0.483506i) q^{29} +(0.0197193 - 0.0924317i) q^{30} +(5.91042 + 3.41238i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.71214 + 8.02543i) q^{33} +3.29359i q^{34} +(0.128046 + 0.0666840i) q^{35} +(0.309116 + 2.98403i) q^{36} +(-4.88894 + 8.46790i) q^{37} +(-0.283054 + 0.490264i) q^{38} +(1.07885 + 6.15110i) q^{39} +(0.0472559 - 0.0272832i) q^{40} +(0.229870 + 0.398146i) q^{41} +(-4.51903 - 0.760497i) q^{42} +(5.30399 - 9.18678i) q^{43} +(-4.10302 + 2.36888i) q^{44} +(0.0168673 + 0.162828i) q^{45} +(3.08180 + 5.33783i) q^{46} +(-2.56444 - 4.44174i) q^{47} +(-1.15993 + 1.28630i) q^{48} +(2.96049 - 6.34315i) q^{49} +(-4.32755 + 2.49851i) q^{50} +(-1.75877 - 5.42677i) q^{51} +(-2.22025 + 2.84086i) q^{52} +(4.60984 + 2.66149i) q^{53} +(-2.10279 - 4.75166i) q^{54} +(-0.223887 + 0.129261i) q^{55} +(-1.42118 - 2.23165i) q^{56} +(0.204582 - 0.958948i) q^{57} -0.967012 q^{58} +(4.92008 + 8.52182i) q^{59} +(-0.0632933 + 0.0701885i) q^{60} +1.14676i q^{61} +(-3.41238 - 5.91042i) q^{62} +(7.85202 - 1.16011i) q^{63} -1.00000 q^{64} +(-0.121151 + 0.155015i) q^{65} +(5.49547 - 6.09416i) q^{66} -3.18163 q^{67} +(1.64679 - 2.85233i) q^{68} +(-7.92821 - 7.14935i) q^{69} +(-0.0775487 - 0.121773i) q^{70} +(-0.679865 - 0.392520i) q^{71} +(1.22431 - 2.73881i) q^{72} +(-8.73107 - 5.04088i) q^{73} +(8.46790 - 4.88894i) q^{74} +(5.79621 - 6.42765i) q^{75} +(0.490264 - 0.283054i) q^{76} +(6.73321 + 10.5730i) q^{77} +(2.14124 - 5.86644i) q^{78} +(-4.29768 - 7.44380i) q^{79} -0.0545664 q^{80} +(6.00211 + 6.70631i) q^{81} -0.459740i q^{82} -12.9439 q^{83} +(3.53335 + 2.91813i) q^{84} +(0.0898595 - 0.155641i) q^{85} +(-9.18678 + 5.30399i) q^{86} +(1.59332 - 0.516383i) q^{87} +4.73776 q^{88} +(7.66189 - 13.2708i) q^{89} +(0.0668064 - 0.149447i) q^{90} +(7.76434 + 5.54211i) q^{91} -6.16359i q^{92} +(8.77867 + 7.91626i) q^{93} +5.12888i q^{94} +(0.0267519 - 0.0154452i) q^{95} +(1.64768 - 0.533999i) q^{96} +(-12.1215 - 6.99836i) q^{97} +(-5.73543 + 4.01308i) q^{98} +(-5.80050 + 12.9758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.69393	+	0.361382i	0.977992	+	0.208644i
$3$	1.69393	+	0.361382i	0.977992	+	0.208644i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.0272832	+	0.0472559i	0.0122014	+	0.0211335i	0.872062	−	0.489396i	$-0.162783\pi$
$5$	0.0272832	+	0.0472559i	0.0122014	+	0.0211335i	−0.859860	+	0.510530i	$0.829449\pi$
$6$	−1.28630	−	1.15993i	−0.525128	−	0.473540i
$7$	2.23165	−	1.42118i	0.843483	−	0.537156i
$7$	2.23165	−	1.42118i	0.843483	−	0.537156i
$8$		−	1.00000i		−	0.353553i
$9$	2.73881	+	1.22431i	0.912935	+	0.408105i
$10$		−	0.0545664i		−	0.0172554i
$11$			4.73776i			1.42849i	0.699897	+	0.714244i	$0.253229\pi$
$11$			4.73776i			1.42849i	−0.699897	+	0.714244i	$0.746771\pi$
$12$	0.533999	+	1.64768i	0.154152	+	0.475644i
$13$	1.35013	+	3.34322i	0.374459	+	0.927243i
$13$	1.35013	+	3.34322i	0.374459	+	0.927243i
$14$	−2.64325	+	0.114956i	−0.706439	+	0.0307234i
$15$	0.0291384	+	0.0899079i	0.00752350	+	0.0232141i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.64679	−	2.85233i	−0.399406	−	0.691791i	0.594247	−	0.804283i	$-0.297450\pi$
$17$	−1.64679	−	2.85233i	−0.399406	−	0.691791i	−0.993653	+	0.112491i	$0.964117\pi$
$18$	−1.75972	−	2.42969i	−0.414770	−	0.572683i
$19$		−	0.566108i		−	0.129874i	−0.997889	−	0.0649371i	$-0.979315\pi$
$19$		−	0.566108i		−	0.129874i	0.997889	−	0.0649371i	$-0.0206847\pi$
$20$	−0.0272832	+	0.0472559i	−0.00610071	+	0.0105667i
$21$	4.29384	−	1.60091i	0.936994	−	0.349346i
$22$	2.36888	−	4.10302i	0.505047	−	0.874766i
$23$	−5.33783	−	3.08180i	−1.11301	−	0.642599i	−0.173406	−	0.984850i	$-0.555477\pi$
$23$	−5.33783	−	3.08180i	−1.11301	−	0.642599i	−0.939608	+	0.342251i	$0.888811\pi$
$24$	0.361382	−	1.69393i	0.0737669	−	0.345772i
$25$	2.49851	−	4.32755i	0.499702	−	0.865510i
$26$	0.502363	−	3.57038i	0.0985215	−	0.700210i
$27$	4.19690	+	3.06366i	0.807694	+	0.589602i
$28$	2.34660	+	1.22207i	0.443466	+	0.230950i
$29$	0.837457	−	0.483506i	0.155512	−	0.0897848i	−0.420225	−	0.907420i	$-0.638049\pi$
$29$	0.837457	−	0.483506i	0.155512	−	0.0897848i	0.575736	+	0.817635i	$0.304715\pi$
$30$	0.0197193	−	0.0924317i	0.00360024	−	0.0168756i
$31$	5.91042	+	3.41238i	1.06154	+	0.612882i	0.925859	−	0.377870i	$-0.123343\pi$
$31$	5.91042	+	3.41238i	1.06154	+	0.612882i	0.135684	+	0.990752i	$0.456677\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.71214	+	8.02543i	−0.298046	+	1.39705i
$34$			3.29359i			0.564845i
$35$	0.128046	+	0.0666840i	0.0216437	+	0.0112717i
$36$	0.309116	+	2.98403i	0.0515193	+	0.497339i
$37$	−4.88894	+	8.46790i	−0.803737	+	1.39211i	0.113403	+	0.993549i	$0.463825\pi$
$37$	−4.88894	+	8.46790i	−0.803737	+	1.39211i	−0.917140	+	0.398564i	$0.869509\pi$
$38$	−0.283054	+	0.490264i	−0.0459174	+	0.0795313i
$39$	1.07885	+	6.15110i	0.172754	+	0.984965i
$40$	0.0472559	−	0.0272832i	0.00747181	−	0.00431385i
$41$	0.229870	+	0.398146i	0.0358996	+	0.0621800i	0.883417	−	0.468588i	$-0.155237\pi$
$41$	0.229870	+	0.398146i	0.0358996	+	0.0621800i	−0.847517	+	0.530768i	$0.821904\pi$
$42$	−4.51903	−	0.760497i	−0.697302	−	0.117347i
$43$	5.30399	−	9.18678i	0.808850	−	1.40097i	−0.104810	−	0.994492i	$-0.533423\pi$
$43$	5.30399	−	9.18678i	0.808850	−	1.40097i	0.913661	−	0.406478i	$-0.133243\pi$
$44$	−4.10302	+	2.36888i	−0.618553	+	0.357122i
$45$	0.0168673	+	0.162828i	0.00251443	+	0.0242729i
$46$	3.08180	+	5.33783i	0.454386	+	0.787020i
$47$	−2.56444	−	4.44174i	−0.374062	−	0.647895i	0.616124	−	0.787649i	$-0.288702\pi$
$47$	−2.56444	−	4.44174i	−0.374062	−	0.647895i	−0.990186	+	0.139754i	$0.955369\pi$
$48$	−1.15993	+	1.28630i	−0.167422	+	0.185661i
$49$	2.96049	−	6.34315i	0.422927	−	0.906164i
$50$	−4.32755	+	2.49851i	−0.612008	+	0.353343i
$51$	−1.75877	−	5.42677i	−0.246277	−	0.759900i
$52$	−2.22025	+	2.84086i	−0.307893	+	0.393956i
$53$	4.60984	+	2.66149i	0.633210	+	0.365584i	0.781994	−	0.623286i	$-0.214203\pi$
$53$	4.60984	+	2.66149i	0.633210	+	0.365584i	−0.148784	+	0.988870i	$0.547536\pi$
$54$	−2.10279	−	4.75166i	−0.286154	−	0.646619i
$55$	−0.223887	+	0.129261i	−0.0301889	+	0.0174296i
$56$	−1.42118	−	2.23165i	−0.189913	−	0.298216i
$57$	0.204582	−	0.958948i	0.0270975	−	0.127016i
$58$	−0.967012			−0.126975
$59$	4.92008	+	8.52182i	0.640540	+	1.10945i	0.985312	+	0.170761i	$0.0546226\pi$
$59$	4.92008	+	8.52182i	0.640540	+	1.10945i	−0.344773	+	0.938686i	$0.612044\pi$
$60$	−0.0632933	+	0.0701885i	−0.00817113	+	0.00906130i
$61$			1.14676i			0.146827i	0.997302	+	0.0734135i	$0.0233893\pi$
$61$			1.14676i			0.146827i	−0.997302	+	0.0734135i	$0.976611\pi$
$62$	−3.41238	−	5.91042i	−0.433373	−	0.750624i
$63$	7.85202	−	1.16011i	0.989261	−	0.146160i
$64$	−1.00000			−0.125000
$65$	−0.121151	+	0.155015i	−0.0150269	+	0.0192273i
$66$	5.49547	−	6.09416i	0.676446	−	0.750139i
$67$	−3.18163			−0.388698			−0.194349	−	0.980932i	$-0.562259\pi$
$67$	−3.18163			−0.388698			−0.194349	+	0.980932i	$0.562259\pi$
$68$	1.64679	−	2.85233i	0.199703	−	0.345896i
$69$	−7.92821	−	7.14935i	−0.954444	−	0.860680i
$70$	−0.0775487	−	0.121773i	−0.00926885	−	0.0145546i
$71$	−0.679865	−	0.392520i	−0.0806851	−	0.0465836i	0.459115	−	0.888377i	$-0.348167\pi$
$71$	−0.679865	−	0.392520i	−0.0806851	−	0.0465836i	−0.539800	+	0.841793i	$0.681500\pi$
$72$	1.22431	−	2.73881i	0.144287	−	0.322771i
$73$	−8.73107	−	5.04088i	−1.02189	−	0.589991i	−0.107242	−	0.994233i	$-0.534202\pi$
$73$	−8.73107	−	5.04088i	−1.02189	−	0.589991i	−0.914652	+	0.404242i	$0.867535\pi$
$74$	8.46790	−	4.88894i	0.984373	−	0.568328i
$75$	5.79621	−	6.42765i	0.669288	−	0.742201i
$76$	0.490264	−	0.283054i	0.0562372	−	0.0324685i
$77$	6.73321	+	10.5730i	0.767321	+	1.20490i
$78$	2.14124	−	5.86644i	0.242448	−	0.664243i
$79$	−4.29768	−	7.44380i	−0.483527	−	0.837493i	0.516294	−	0.856411i	$-0.327311\pi$
$79$	−4.29768	−	7.44380i	−0.483527	−	0.837493i	−0.999821	+	0.0189184i	$0.993978\pi$
$80$	−0.0545664			−0.00610071
$81$	6.00211	+	6.70631i	0.666901	+	0.745146i
$82$		−	0.459740i		−	0.0507697i
$83$	−12.9439			−1.42077			−0.710387	−	0.703811i	$-0.751480\pi$
$83$	−12.9439			−1.42077			−0.710387	+	0.703811i	$0.751480\pi$
$84$	3.53335	+	2.91813i	0.385520	+	0.318394i
$85$	0.0898595	−	0.155641i	0.00974664	−	0.0168817i
$86$	−9.18678	+	5.30399i	−0.990635	+	0.571944i
$87$	1.59332	−	0.516383i	0.170822	−	0.0553621i
$88$	4.73776			0.505047
$89$	7.66189	−	13.2708i	0.812159	−	1.40670i	−0.0991917	−	0.995068i	$-0.531626\pi$
$89$	7.66189	−	13.2708i	0.812159	−	1.40670i	0.911350	−	0.411632i	$-0.135041\pi$
$90$	0.0668064	−	0.149447i	0.00704201	−	0.0157531i
$91$	7.76434	+	5.54211i	0.813924	+	0.580971i
$92$		−	6.16359i		−	0.642599i
$93$	8.77867	+	7.91626i	0.910306	+	0.820878i
$94$			5.12888i			0.529004i
$95$	0.0267519	−	0.0154452i	0.00274469	−	0.00158465i
$96$	1.64768	−	0.533999i	0.168165	−	0.0545011i
$97$	−12.1215	−	6.99836i	−1.23075	−	0.710575i	−0.263566	−	0.964641i	$-0.584899\pi$
$97$	−12.1215	−	6.99836i	−1.23075	−	0.710575i	−0.967187	+	0.254066i	$0.918232\pi$
$98$	−5.73543	+	4.01308i	−0.579366	+	0.405383i
$99$	−5.80050	+	12.9758i	−0.582972	+	1.30412i
$100$	4.99702			0.499702
$101$	2.77670			0.276292			0.138146	−	0.990412i	$-0.455886\pi$
$101$	2.77670			0.276292			0.138146	+	0.990412i	$0.455886\pi$
$102$	−1.19024	+	5.57911i	−0.117852	+	0.552414i
$103$	−8.11913	+	4.68758i	−0.800002	+	0.461881i	−0.843472	−	0.537174i	$-0.819492\pi$
$103$	−8.11913	+	4.68758i	−0.800002	+	0.461881i	0.0434701	+	0.999055i	$0.486159\pi$
$104$	3.34322	−	1.35013i	0.327830	−	0.132391i
$105$	0.192802	+	0.159232i	0.0188155	+	0.0155394i
$106$	−2.66149	−	4.60984i	−0.258507	−	0.447747i
$107$	−1.71030	−	0.987440i	−0.165341	−	0.0954595i	0.415046	−	0.909800i	$-0.363765\pi$
$107$	−1.71030	−	0.987440i	−0.165341	−	0.0954595i	−0.580387	+	0.814341i	$0.697099\pi$
$108$	−0.554755	+	5.16645i	−0.0533814	+	0.497142i
$109$	0.563497	−	0.976006i	0.0539732	−	0.0934844i	−0.837776	−	0.546013i	$-0.816145\pi$
$109$	0.563497	−	0.976006i	0.0539732	−	0.0934844i	0.891750	+	0.452529i	$0.149478\pi$
$110$	0.258522			0.0246491
$111$	−11.3417	+	12.5773i	−1.07650	+	1.19378i
$112$	0.114956	+	2.64325i	0.0108624	+	0.249764i
$113$	−7.98058	−	4.60759i	−0.750750	−	0.433445i	0.0752152	−	0.997167i	$-0.476036\pi$
$113$	−7.98058	−	4.60759i	−0.750750	−	0.433445i	−0.825965	+	0.563722i	$0.809369\pi$
$114$	−0.656647	+	0.728183i	−0.0615006	+	0.0682006i
$115$		−	0.336325i		−	0.0313625i
$116$	0.837457	+	0.483506i	0.0777559	+	0.0448924i
$117$	−0.395406	+	10.8094i	−0.0365553	+	0.999332i
$118$		−	9.84016i		−	0.905860i
$119$	−7.72874	−	4.02500i	−0.708492	−	0.368971i
$120$	0.0899079	−	0.0291384i	0.00820743	−	0.00265996i
$121$	−11.4463			−1.04058
$122$	0.573378	−	0.993119i	0.0519112	−	0.0899128i
$123$	0.245501	+	0.757503i	0.0221360	+	0.0683018i
$124$			6.82476i			0.612882i
$125$	0.545501			0.0487911
$126$	−7.38010	−	2.92133i	−0.657471	−	0.260253i
$127$	−0.435625	−	0.754524i	−0.0386554	−	0.0669532i	0.846050	−	0.533103i	$-0.178974\pi$
$127$	−0.435625	−	0.754524i	−0.0386554	−	0.0669532i	−0.884706	+	0.466150i	$0.845641\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	12.3045	−	13.6450i	1.08335	−	1.20138i
$130$	0.182428	−	0.0736718i	0.0160000	−	0.00646145i
$131$	5.35095	+	9.26812i	0.467515	+	0.809760i	0.999311	−	0.0371126i	$-0.0118160\pi$
$131$	5.35095	+	9.26812i	0.467515	+	0.809760i	−0.531796	+	0.846872i	$0.678483\pi$
$132$	−7.80630	+	2.52996i	−0.679451	+	0.220205i
$133$	−0.804543	−	1.26335i	−0.0697627	−	0.109547i
$134$	2.75537	+	1.59081i	0.238028	+	0.137425i
$135$	−0.0302710	+	0.281915i	−0.00260531	+	0.0242634i
$136$	−2.85233	+	1.64679i	−0.244585	+	0.141211i
$137$	−4.05094	+	2.33881i	−0.346095	+	0.199818i	−0.662964	−	0.748651i	$-0.730702\pi$
$137$	−4.05094	+	2.33881i	−0.346095	+	0.199818i	0.316869	+	0.948469i	$0.397368\pi$
$138$	3.29135	+	10.1556i	0.280179	+	0.864504i
$139$	−16.9346	−	9.77718i	−1.43637	−	0.829289i	−0.438776	−	0.898597i	$-0.644588\pi$
$139$	−16.9346	−	9.77718i	−1.43637	−	0.829289i	−0.997595	+	0.0693072i	$0.977921\pi$
$140$	0.00627275	+	0.144233i	0.000530144	+	0.0121899i
$141$	−2.73882	−	8.45075i	−0.230650	−	0.711682i
$142$	0.392520	+	0.679865i	0.0329396	+	0.0570530i
$143$	−15.8394	+	6.39660i	−1.32456	+	0.534910i
$144$	−2.42969	+	1.75972i	−0.202474	+	0.146643i
$145$	0.0456970	+	0.0263832i	0.00379493	+	0.00219100i
$146$	5.04088	+	8.73107i	0.417187	+	0.722588i
$147$	7.30716	−	9.67499i	0.602685	−	0.797980i
$148$	−9.77788			−0.803737
$149$		−	23.3685i		−	1.91442i	−0.289396	−	0.957209i	$-0.593454\pi$
$149$		−	23.3685i		−	1.91442i	0.289396	−	0.957209i	$-0.406546\pi$
$150$	−8.23349	+	2.66841i	−0.672261	+	0.217874i
$151$	−9.78550	+	16.9490i	−0.796333	+	1.37929i	0.125656	+	0.992074i	$0.459896\pi$
$151$	−9.78550	+	16.9490i	−0.796333	+	1.37929i	−0.921989	+	0.387215i	$0.873437\pi$
$152$	−0.566108			−0.0459174
$153$	−1.01810	−	9.82817i	−0.0823085	−	0.794560i
$154$	−0.544635	−	12.5231i	−0.0438880	−	1.00914i
$155$			0.372403i			0.0299121i
$156$	−4.78759	+	4.00986i	−0.383314	+	0.321046i
$157$	−7.99582	−	4.61639i	−0.638136	−	0.368428i	0.145760	−	0.989320i	$-0.453437\pi$
$157$	−7.99582	−	4.61639i	−0.638136	−	0.368428i	−0.783896	+	0.620892i	$0.786771\pi$
$158$			8.59536i			0.683810i
$159$	6.84693	+	6.17429i	0.542997	+	0.489653i
$160$	0.0472559	+	0.0272832i	0.00373590	+	0.00215693i
$161$	−16.2919	+	0.708544i	−1.28398	+	0.0558411i
$162$	−1.84482	−	8.80889i	−0.144943	−	0.692092i
$163$	4.23279			0.331538			0.165769	−	0.986165i	$-0.446989\pi$
$163$	4.23279			0.331538			0.165769	+	0.986165i	$0.446989\pi$
$164$	−0.229870	+	0.398146i	−0.0179498	+	0.0310900i
$165$	−0.425962	+	0.138051i	−0.0331611	+	0.0107472i
$166$	11.2097	+	6.47194i	0.870043	+	0.502320i
$167$	5.39330	+	9.34146i	0.417346	+	0.722864i	0.995672	−	0.0929418i	$-0.0296270\pi$
$167$	5.39330	+	9.34146i	0.417346	+	0.722864i	−0.578326	+	0.815806i	$0.696294\pi$
$168$	−1.60091	−	4.29384i	−0.123513	−	0.331277i
$169$	−9.35429	+	9.02759i	−0.719561	+	0.694430i
$170$	−0.155641	+	0.0898595i	−0.0119371	+	0.00689191i
$171$	0.693094	−	1.55046i	0.0530022	−	0.118567i
$172$	10.6080			0.808850
$173$	−25.4354			−1.93382			−0.966908	−	0.255124i	$-0.917884\pi$
$173$	−25.4354			−1.93382			−0.966908	+	0.255124i	$0.917884\pi$
$174$	−1.63805	−	0.349461i	−0.124180	−	0.0264926i
$175$	−0.574440	−	13.2084i	−0.0434236	−	0.998461i
$176$	−4.10302	−	2.36888i	−0.309277	−	0.178561i
$177$	5.25464	+	16.2134i	0.394963	+	1.21867i
$178$	−13.2708	+	7.66189i	−0.994687	+	0.574283i
$179$		−	4.85816i		−	0.363116i	−0.983380	−	0.181558i	$-0.941886\pi$
$179$		−	4.85816i		−	0.363116i	0.983380	−	0.181558i	$-0.0581140\pi$
$180$	−0.132579	+	0.0960215i	−0.00988188	+	0.00715702i
$181$			6.63622i			0.493266i	0.969109	+	0.246633i	$0.0793243\pi$
$181$			6.63622i			0.493266i	−0.969109	+	0.246633i	$0.920676\pi$
$182$	−3.95306	−	8.68178i	−0.293021	−	0.643536i
$183$	−0.414417	+	1.94252i	−0.0306346	+	0.143596i
$184$	−3.08180	+	5.33783i	−0.227193	+	0.393510i
$185$	−0.533544			−0.0392269
$186$	−3.64442	−	11.2450i	−0.267222	−	0.824525i
$187$	13.5136	−	7.80210i	0.988215	−	0.570546i
$188$	2.56444	−	4.44174i	0.187031	−	0.323947i
$189$	13.7200	+	0.872442i	0.997984	+	0.0634608i
$190$	−0.0308905			−0.00224103
$191$			11.7572i			0.850724i	0.905023	+	0.425362i	$0.139853\pi$
$191$			11.7572i			0.850724i	−0.905023	+	0.425362i	$0.860147\pi$
$192$	−1.69393	−	0.361382i	−0.122249	−	0.0260805i
$193$	23.3987			1.68427			0.842137	−	0.539263i	$-0.181297\pi$
$193$	23.3987			1.68427			0.842137	+	0.539263i	$0.181297\pi$
$194$	6.99836	+	12.1215i	0.502453	+	0.870274i
$195$	−0.261241	+	0.218804i	−0.0187079	+	0.0156689i
$196$	6.97357	−	0.607718i	0.498112	−	0.0434084i
$197$	8.57934	−	4.95328i	0.611253	−	0.352907i	−0.162203	−	0.986757i	$-0.551860\pi$
$197$	8.57934	−	4.95328i	0.611253	−	0.352907i	0.773456	+	0.633851i	$0.218527\pi$
$198$	11.5113	−	8.33712i	0.818071	−	0.592493i
$199$	2.66634	−	1.53941i	0.189012	−	0.109126i	−0.402508	−	0.915416i	$-0.631861\pi$
$199$	2.66634	−	1.53941i	0.189012	−	0.109126i	0.591520	+	0.806290i	$0.298528\pi$
$200$	−4.32755	−	2.49851i	−0.306004	−	0.176671i
$201$	−5.38946	−	1.14978i	−0.380143	−	0.0810996i
$202$	−2.40470	−	1.38835i	−0.169194	−	0.0976841i
$203$	1.18176	−	2.26919i	0.0829431	−	0.159266i
$204$	3.82034	−	4.23653i	0.267477	−	0.296616i
$205$	−0.0125432	+	0.0217254i	−0.000876052	+	0.00151737i
$206$	9.37516			0.653199
$207$	−10.8462	−	14.9756i	−0.753862	−	1.04088i
$208$	−3.57038	−	0.502363i	−0.247561	−	0.0348326i
$209$	2.68208			0.185524
$210$	−0.0873557	−	0.234300i	−0.00602811	−	0.0161682i
$211$	1.29565	+	2.24413i	0.0891960	+	0.154492i	0.907172	−	0.420761i	$-0.138237\pi$
$211$	1.29565	+	2.24413i	0.0891960	+	0.154492i	−0.817976	+	0.575253i	$0.804904\pi$
$212$			5.32298i			0.365584i
$213$	−1.00979	−	0.910593i	−0.0691900	−	0.0623928i
$214$	0.987440	+	1.71030i	0.0675000	+	0.116913i
$215$	0.578839			0.0394765
$216$	3.06366	−	4.19690i	0.208456	−	0.285563i
$217$	18.0396	−	0.784550i	1.22461	−	0.0532587i
$218$	−0.976006	+	0.563497i	−0.0661035	+	0.0381649i
$219$	−12.9681	−	11.6942i	−0.876306	−	0.790218i
$220$	−0.223887	−	0.129261i	−0.0150944	−	0.00871478i
$221$	7.31259	−	9.35662i	0.491898	−	0.629394i
$222$	16.1108	−	5.22138i	1.08129	−	0.350436i
$223$	−20.4174	+	11.7880i	−1.36725	+	0.789382i	−0.990576	−	0.136964i	$-0.956265\pi$
$223$	−20.4174	+	11.7880i	−1.36725	+	0.789382i	−0.376673	+	0.926346i	$0.622932\pi$
$224$	1.22207	−	2.34660i	0.0816531	−	0.156789i
$225$	12.1412	−	8.79335i	0.809414	−	0.586223i
$226$	4.60759	+	7.98058i	0.306492	+	0.530860i
$227$	13.0526	+	22.6078i	0.866331	+	1.50053i	0.865719	+	0.500530i	$0.166861\pi$
$227$	13.0526	+	22.6078i	0.866331	+	1.50053i	0.000611932		1.00000i	$0.499805\pi$
$228$	0.932764	−	0.302301i	0.0617738	−	0.0200204i
$229$	−18.5664	+	10.7193i	−1.22690	+	0.708351i	−0.966380	−	0.257118i	$-0.917227\pi$
$229$	−18.5664	+	10.7193i	−1.22690	+	0.708351i	−0.260519	+	0.965469i	$0.583894\pi$
$230$	−0.168163	+	0.291266i	−0.0110883	+	0.0192055i
$231$	7.58470	+	20.3432i	0.499037	+	1.33848i
$232$	−0.483506	−	0.837457i	−0.0317437	−	0.0549817i
$233$	22.2853	−	12.8664i	1.45996	−	0.842909i	0.460953	−	0.887425i	$-0.347508\pi$
$233$	22.2853	−	12.8664i	1.45996	−	0.842909i	0.999009	+	0.0445157i	$0.0141745\pi$
$234$	5.74714	−	9.16353i	0.375703	−	0.599039i
$235$	0.139932	−	0.242370i	0.00912818	−	0.0158105i
$236$	−4.92008	+	8.52182i	−0.320270	+	0.554724i
$237$	−4.58992	−	14.1624i	−0.298147	−	0.919946i
$238$	4.68078	+	7.35012i	0.303410	+	0.476437i
$239$			4.85891i			0.314297i	0.987575	+	0.157148i	$0.0502301\pi$
$239$			4.85891i			0.314297i	−0.987575	+	0.157148i	$0.949770\pi$
$240$	−0.0924317	−	0.0197193i	−0.00596644	−	0.00127288i
$241$	2.50327	−	1.44527i	0.161250	−	0.0930978i	−0.417203	−	0.908813i	$-0.636990\pi$
$241$	2.50327	−	1.44527i	0.161250	−	0.0930978i	0.578454	+	0.815715i	$0.303656\pi$
$242$	9.91282	+	5.72317i	0.637220	+	0.367899i
$243$	7.74362	+	13.5291i	0.496753	+	0.867892i
$244$	−0.993119	+	0.573378i	−0.0635779	+	0.0367067i
$245$	0.380522	−	0.0331609i	0.0243107	−	0.00211858i
$246$	0.166142	−	0.778767i	0.0105928	−	0.0496524i
$247$	1.89263	−	0.764321i	0.120425	−	0.0486326i
$248$	3.41238	−	5.91042i	0.216687	−	0.375312i
$249$	−21.9260	−	4.67769i	−1.38951	−	0.296436i
$250$	−0.472418	−	0.272751i	−0.0298783	−	0.0172503i
$251$	3.89281	−	6.74254i	0.245712	−	0.425586i	−0.716620	−	0.697464i	$-0.754312\pi$
$251$	3.89281	−	6.74254i	0.245712	−	0.425586i	0.962332	+	0.271879i	$0.0876449\pi$
$252$	4.93069	+	6.21999i	0.310604	+	0.391823i
$253$	14.6008	−	25.2893i	0.917945	−	1.58993i
$254$			0.871249i			0.0546670i
$255$	0.208462	−	0.231172i	0.0130544	−	0.0144765i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.05714	−	10.4913i	0.377834	−	0.654428i	−0.612913	−	0.790151i	$-0.710002\pi$
$257$	6.05714	−	10.4913i	0.377834	−	0.654428i	0.990747	+	0.135723i	$0.0433356\pi$
$258$	−17.4785	+	5.66465i	−1.08817	+	0.352666i
$259$	1.12403	+	25.8454i	0.0698438	+	1.60596i
$260$	−0.194823	−	0.0274121i	−0.0120824	−	0.00170003i
$261$	2.88559	−	0.298919i	0.178614	−	0.0185026i
$262$		−	10.7019i		−	0.661166i
$263$		−	9.10252i		−	0.561285i	−0.959812	−	0.280643i	$-0.909452\pi$
$263$		−	9.10252i		−	0.561285i	0.959812	−	0.280643i	$-0.0905476\pi$
$264$	8.02543	+	1.71214i	0.493931	+	0.105375i
$265$			0.290456i			0.0178426i
$266$	0.0650778	+	1.49637i	0.00399017	+	0.0917482i
$267$	17.7745	−	19.7109i	1.08778	−	1.20629i
$268$	−1.59081	−	2.75537i	−0.0971745	−	0.168311i
$269$	5.77027	+	9.99440i	0.351819	+	0.609369i	0.986568	−	0.163349i	$-0.0522298\pi$
$269$	5.77027	+	9.99440i	0.351819	+	0.609369i	−0.634749	+	0.772719i	$0.718896\pi$
$270$	0.167173	−	0.229010i	0.0101738	−	0.0139371i
$271$	6.55095	+	3.78219i	0.397942	+	0.229752i	0.685595	−	0.727983i	$-0.259542\pi$
$271$	6.55095	+	3.78219i	0.397942	+	0.229752i	−0.287654	+	0.957734i	$0.592875\pi$
$272$	3.29359			0.199703
$273$	11.1494	+	12.1938i	0.674795	+	0.738005i
$274$	4.67762			0.282586
$275$	20.5029	+	11.8373i	1.23637	+	0.713818i
$276$	2.22741	−	10.4407i	0.134075	−	0.628456i
$277$	−12.2398	−	21.2000i	−0.735419	−	1.27378i	−0.954539	−	0.298085i	$-0.903652\pi$
$277$	−12.2398	−	21.2000i	−0.735419	−	1.27378i	0.219121	−	0.975698i	$-0.429681\pi$
$278$	9.77718	+	16.9346i	0.586396	+	1.01567i
$279$	12.0097	+	16.5821i	0.719000	+	0.992742i
$280$	0.0666840	−	0.128046i	0.00398513	−	0.00765219i
$281$		−	22.3416i		−	1.33279i	−0.745599	−	0.666394i	$-0.767837\pi$
$281$		−	22.3416i		−	1.33279i	0.745599	−	0.666394i	$-0.232163\pi$
$282$	−1.85349	+	8.68797i	−0.110374	+	0.517361i
$283$			16.8284i			1.00034i	0.865927	+	0.500171i	$0.166730\pi$
$283$			16.8284i			1.00034i	−0.865927	+	0.500171i	$0.833270\pi$
$284$		−	0.785040i		−	0.0465836i
$285$	0.0508976	−	0.0164955i	0.00301491	−	0.000977109i
$286$	16.9156	+	2.38007i	1.00024	+	0.140737i
$287$	1.07883	+	0.561835i	0.0636811	+	0.0331640i
$288$	2.98403	−	0.309116i	0.175836	−	0.0182148i
$289$	3.07615	−	5.32804i	0.180950	−	0.313414i
$290$	−0.0263832	−	0.0456970i	−0.00154927	−	0.00268342i
$291$	−18.0039	−	16.2352i	−1.05541	−	0.951726i
$292$		−	10.0818i		−	0.589991i
$293$	−0.258953	+	0.448519i	−0.0151282	+	0.0262028i	−0.873490	−	0.486841i	$-0.838149\pi$
$293$	−0.258953	+	0.448519i	−0.0151282	+	0.0262028i	0.858362	+	0.513044i	$0.171482\pi$
$294$	−11.1657	+	4.72520i	−0.651196	+	0.275580i
$295$	−0.268471	+	0.465005i	−0.0156310	+	0.0270736i
$296$	8.46790	+	4.88894i	0.492186	+	0.284164i
$297$	−14.5149	+	19.8839i	−0.842238	+	1.15378i
$298$	−11.6842	+	20.2377i	−0.676849	+	1.17234i
$299$	3.09636	−	22.0064i	0.179067	−	1.27266i
$300$	8.46461	+	1.80584i	0.488705	+	0.104260i
$301$	−1.21945	−	28.0396i	−0.0702882	−	1.61617i
$302$	16.9490	−	9.78550i	0.975305	−	0.563092i
$303$	4.70355	+	1.00345i	0.270212	+	0.0576468i
$304$	0.490264	+	0.283054i	0.0281186	+	0.0162343i
$305$	−0.0541909	+	0.0312871i	−0.00310296	+	0.00179150i
$306$	−4.03238	+	9.02049i	−0.230516	+	0.515667i
$307$			5.00175i			0.285465i	0.989761	+	0.142732i	$0.0455888\pi$
$307$			5.00175i			0.285465i	−0.989761	+	0.142732i	$0.954411\pi$
$308$	−5.78988	+	11.1176i	−0.329909	+	0.633486i
$309$	−15.4473	+	5.00633i	−0.878764	+	0.284800i
$310$	0.186201	−	0.322510i	0.0105755	−	0.0183173i
$311$	−11.8105	+	20.4564i	−0.669712	+	1.15998i	0.308272	+	0.951298i	$0.400249\pi$
$311$	−11.8105	+	20.4564i	−0.669712	+	1.15998i	−0.977985	+	0.208677i	$0.933084\pi$
$312$	6.15110	−	1.07885i	0.348238	−	0.0610778i
$313$	24.0008	−	13.8569i	1.35661	−	0.783238i	0.367443	−	0.930046i	$-0.380233\pi$
$313$	24.0008	−	13.8569i	1.35661	−	0.783238i	0.989165	+	0.146808i	$0.0469000\pi$
$314$	4.61639	+	7.99582i	0.260518	+	0.451230i
$315$	0.269050	+	0.339403i	0.0151592	+	0.0191232i
$316$	4.29768	−	7.44380i	0.241763	−	0.418746i
$317$	9.71277	−	5.60767i	0.545524	−	0.314958i	−0.201791	−	0.979429i	$-0.564676\pi$
$317$	9.71277	−	5.60767i	0.545524	−	0.314958i	0.747315	+	0.664470i	$0.231343\pi$
$318$	−2.84247	−	8.77056i	−0.159398	−	0.491829i
$319$	2.29073	+	3.96767i	0.128256	+	0.222147i
$320$	−0.0272832	−	0.0472559i	−0.00152518	−	0.00264168i
$321$	−2.54028	−	2.29073i	−0.141785	−	0.127856i
$322$	14.4635	+	7.53235i	0.806019	+	0.419761i
$323$	−1.61473	+	0.932263i	−0.0898458	+	0.0518725i
$324$	−2.80678	+	8.55114i	−0.155932	+	0.475063i
$325$	17.8413	+	2.51032i	0.989656	+	0.139248i
$326$	−3.66571	−	2.11640i	−0.203025	−	0.117216i
$327$	1.30724	−	1.44965i	0.0722904	−	0.0801658i
$328$	0.398146	−	0.229870i	0.0219839	−	0.0126924i
$329$	−12.0354	−	6.26786i	−0.663536	−	0.345558i
$330$	0.437919	+	0.0934254i	0.0241066	+	0.00514290i
$331$	−16.6502			−0.915180			−0.457590	−	0.889163i	$-0.651287\pi$
$331$	−16.6502			−0.915180			−0.457590	+	0.889163i	$0.651287\pi$
$332$	−6.47194	−	11.2097i	−0.355194	−	0.615213i
$333$	−23.7572	+	17.2063i	−1.30189	+	0.942901i
$334$		−	10.7866i		−	0.590216i
$335$	−0.0868050	−	0.150351i	−0.00474266	−	0.00821453i
$336$	−0.760497	+	4.51903i	−0.0414885	+	0.246533i
$337$	8.79331			0.479002			0.239501	−	0.970896i	$-0.423016\pi$
$337$	8.79331			0.479002			0.239501	+	0.970896i	$0.423016\pi$
$338$	12.6148	−	3.14097i	0.686157	−	0.170846i
$339$	−11.8534	−	10.6890i	−0.643791	−	0.580546i
$340$	0.179719			0.00974664
$341$	−16.1670	+	28.0021i	−0.875494	+	1.51640i
$342$	−1.37547	+	0.996191i	−0.0743768	+	0.0538678i
$343$	−2.40801	−	18.3630i	−0.130020	−	0.991511i
$344$	−9.18678	−	5.30399i	−0.495318	−	0.285972i
$345$	0.121542	−	0.569711i	0.00654360	−	0.0306722i
$346$	22.0277	+	12.7177i	1.18422	+	0.683708i
$347$	23.6601	−	13.6602i	1.27014	−	0.733316i	0.295126	−	0.955458i	$-0.404638\pi$
$347$	23.6601	−	13.6602i	1.27014	−	0.733316i	0.975014	+	0.222142i	$0.0713049\pi$
$348$	1.24386	+	1.12167i	0.0666781	+	0.0601277i
$349$	−0.474380	+	0.273884i	−0.0253930	+	0.0146606i	−0.512643	−	0.858602i	$-0.671333\pi$
$349$	−0.474380	+	0.273884i	−0.0253930	+	0.0146606i	0.487250	+	0.873263i	$0.338000\pi$
$350$	−6.10672	+	11.7260i	−0.326418	+	0.626782i
$351$	−4.57613	+	18.1675i	−0.244256	+	0.969711i
$352$	2.36888	+	4.10302i	0.126262	+	0.218692i
$353$	−21.8838			−1.16476			−0.582378	−	0.812918i	$-0.697878\pi$
$353$	−21.8838			−1.16476			−0.582378	+	0.812918i	$0.697878\pi$
$354$	3.55606	−	16.6685i	0.189002	−	0.885923i
$355$		−	0.0428368i		−	0.00227354i
$356$	15.3238			0.812159
$357$	−11.6374	−	9.61110i	−0.615916	−	0.508673i
$358$	−2.42908	+	4.20729i	−0.128381	+	0.222362i
$359$	20.1753	−	11.6482i	1.06481	−	0.614771i	0.138054	−	0.990425i	$-0.455915\pi$
$359$	20.1753	−	11.6482i	1.06481	−	0.614771i	0.926760	+	0.375654i	$0.122582\pi$
$360$	0.162828	−	0.0168673i	0.00858178	−	0.000888987i
$361$	18.6795			0.983133
$362$	3.31811	−	5.74713i	0.174396	−	0.302063i
$363$	−19.3893	−	4.13650i	−1.01767	−	0.217110i
$364$	−0.917435	+	9.49517i	−0.0480867	+	0.497682i
$365$		−	0.550126i		−	0.0287949i
$366$	1.33016	−	1.47507i	0.0695285	−	0.0771030i
$367$			4.33758i			0.226420i	0.993571	+	0.113210i	$0.0361132\pi$
$367$			4.33758i			0.226420i	−0.993571	+	0.113210i	$0.963887\pi$
$368$	5.33783	−	3.08180i	0.278254	−	0.160650i
$369$	0.142113	+	1.37188i	0.00739810	+	0.0714171i
$370$	0.462062	+	0.266772i	0.0240215	+	0.0138688i
$371$	14.0700	−	0.611911i	0.730477	−	0.0317688i
$372$	−2.46635	+	11.5607i	−0.127874	+	0.599393i
$373$	−9.31427			−0.482274			−0.241137	−	0.970491i	$-0.577520\pi$
$373$	−9.31427			−0.482274			−0.241137	+	0.970491i	$0.577520\pi$
$374$	−15.6042			−0.806874
$375$	0.924042	+	0.197135i	0.0477173	+	0.0101800i
$376$	−4.44174	+	2.56444i	−0.229065	+	0.132251i
$377$	2.74714	+	2.14701i	0.141485	+	0.110577i
$378$	−11.4457	−	7.61557i	−0.588701	−	0.391702i
$379$	3.73379	+	6.46712i	0.191792	+	0.332194i	0.945844	−	0.324621i	$-0.105237\pi$
$379$	3.73379	+	6.46712i	0.191792	+	0.332194i	−0.754052	+	0.656815i	$0.771903\pi$
$380$	0.0267519	+	0.0154452i	0.00137235	+	0.000792324i
$381$	−0.465247	−	1.43554i	−0.0238353	−	0.0735449i
$382$	5.87862	−	10.1821i	0.300776	−	0.520960i
$383$	−11.5239			−0.588841			−0.294421	−	0.955676i	$-0.595127\pi$
$383$	−11.5239			−0.588841			−0.294421	+	0.955676i	$0.595127\pi$
$384$	1.28630	+	1.15993i	0.0656410	+	0.0591925i
$385$	−0.315933	+	0.606649i	−0.0161014	+	0.0309177i
$386$	−20.2639	−	11.6993i	−1.03140	−	0.595481i
$387$	25.7741	−	18.6670i	1.31017	−	0.948899i
$388$		−	13.9967i		−	0.710575i
$389$	−9.47378	−	5.46969i	−0.480340	−	0.277324i	0.240218	−	0.970719i	$-0.422781\pi$
$389$	−9.47378	−	5.46969i	−0.480340	−	0.277324i	−0.720558	+	0.693395i	$0.756114\pi$
$390$	0.335644	−	0.0588689i	0.0169960	−	0.00298094i
$391$			20.3003i			1.02663i
$392$	−6.34315	−	2.96049i	−0.320377	−	0.149527i
$393$	5.71481	+	17.6333i	0.288274	+	0.889483i
$394$	−9.90657			−0.499086
$395$	0.234509	−	0.406181i	0.0117994	−	0.0204372i
$396$	−14.1376	+	1.46452i	−0.710442	+	0.0735947i
$397$			4.07431i			0.204484i	0.994760	+	0.102242i	$0.0326016\pi$
$397$			4.07431i			0.204484i	−0.994760	+	0.102242i	$0.967398\pi$
$398$	−3.07882			−0.154328
$399$	−0.906286	−	2.43078i	−0.0453711	−	0.121691i
$400$	2.49851	+	4.32755i	0.124926	+	0.216377i
$401$	−6.30564	−	3.64056i	−0.314889	−	0.181801i	0.334223	−	0.942494i	$-0.391526\pi$
$401$	−6.30564	−	3.64056i	−0.314889	−	0.181801i	−0.649112	+	0.760693i	$0.724859\pi$
$402$	4.09252	+	3.69047i	0.204116	+	0.184064i
$403$	−3.42851	+	24.3670i	−0.170786	+	1.21381i
$404$	1.38835	+	2.40470i	0.0690731	+	0.119638i
$405$	−0.153156	+	0.466605i	−0.00761038	+	0.0231858i
$406$	−2.15803	+	1.37430i	−0.107101	+	0.0682053i
$407$	−40.1188	−	23.1626i	−1.98862	−	1.14813i
$408$	−5.42677	+	1.75877i	−0.268665	+	0.0870722i
$409$	−11.8222	+	6.82554i	−0.584569	+	0.337501i	−0.762947	−	0.646461i	$-0.776248\pi$
$409$	−11.8222	+	6.82554i	−0.584569	+	0.337501i	0.178378	+	0.983962i	$0.442915\pi$
$410$	0.0217254	−	0.0125432i	0.00107294	−	0.000619463i
$411$	−7.70722	+	2.49785i	−0.380169	+	0.123210i
$412$	−8.11913	−	4.68758i	−0.400001	−	0.230941i
$413$	23.0909	+	12.0254i	1.13623	+	0.591730i
$414$	1.90527	+	18.3924i	0.0936387	+	0.903935i
$415$	−0.353150	−	0.611674i	−0.0173355	−	0.0300259i
$416$	2.84086	+	2.22025i	0.139285	+	0.108857i
$417$	−25.1527	−	22.6817i	−1.23173	−	1.11073i
$418$	−2.32275	−	1.34104i	−0.113610	−	0.0655925i
$419$	7.63041	+	13.2163i	0.372770	+	0.645657i	0.989991	−	0.141134i	$-0.0450747\pi$
$419$	7.63041	+	13.2163i	0.372770	+	0.645657i	−0.617221	+	0.786790i	$0.711741\pi$
$420$	−0.0414976	+	0.246587i	−0.00202487	+	0.0120322i
$421$	−17.2971			−0.843008			−0.421504	−	0.906827i	$-0.638498\pi$
$421$	−17.2971			−0.843008			−0.421504	+	0.906827i	$0.638498\pi$
$422$		−	2.59129i		−	0.126142i
$423$	−1.58542	−	15.3048i	−0.0770857	−	0.744142i
$424$	2.66149	−	4.60984i	0.129253	−	0.223873i
$425$	−16.4581			−0.798336
$426$	0.419211	+	1.29349i	0.0203108	+	0.0626700i
$427$	1.62975	+	2.55915i	0.0788690	+	0.123846i
$428$		−	1.97488i		−	0.0954595i
$429$	−29.1424	+	5.11132i	−1.40701	+	0.246777i
$430$	−0.501289	−	0.289419i	−0.0241743	−	0.0139570i
$431$			37.2206i			1.79285i	0.443191	+	0.896427i	$0.353846\pi$
$431$			37.2206i			1.79285i	−0.443191	+	0.896427i	$0.646154\pi$
$432$	−4.75166	+	2.10279i	−0.228614	+	0.101171i
$433$	1.96666	+	1.13545i	0.0945115	+	0.0545662i	0.546511	−	0.837452i	$-0.315956\pi$
$433$	1.96666	+	1.13545i	0.0945115	+	0.0545662i	−0.451999	+	0.892018i	$0.649289\pi$
$434$	−16.0150	−	8.34035i	−0.768745	−	0.400350i
$435$	0.0678731	+	0.0612053i	0.00325427	+	0.00293457i
$436$	1.12699			0.0539732
$437$	−1.74463	+	3.02179i	−0.0834570	+	0.144552i
$438$	5.38366	+	16.6115i	0.257241	+	0.793729i
$439$	21.5971	+	12.4691i	1.03077	+	0.595117i	0.917206	−	0.398413i	$-0.130439\pi$
$439$	21.5971	+	12.4691i	1.03077	+	0.595117i	0.113567	+	0.993530i	$0.463772\pi$
$440$	0.129261	+	0.223887i	0.00616228	+	0.0106734i
$441$	15.8742	−	13.7481i	0.755914	−	0.654671i
$442$	−11.0112	+	4.44678i	−0.523749	+	0.211512i
$443$	−23.2821	+	13.4420i	−1.10617	+	0.638647i	−0.937834	−	0.347084i	$-0.887172\pi$
$443$	−23.2821	+	13.4420i	−1.10617	+	0.638647i	−0.168334	+	0.985730i	$0.553839\pi$
$444$	−16.5631	−	3.53356i	−0.786048	−	0.167695i
$445$	0.836163			0.0396379
$446$	23.5760			1.11635
$447$	8.44495	−	39.5846i	0.399432	−	1.87229i
$448$	−2.23165	+	1.42118i	−0.105435	+	0.0671445i
$449$	33.0058	+	19.0559i	1.55764	+	0.899304i	0.997482	+	0.0709182i	$0.0225929\pi$
$449$	33.0058	+	19.0559i	1.55764	+	0.899304i	0.560158	+	0.828386i	$0.310740\pi$
$450$	−14.9113	+	1.54466i	−0.702924	+	0.0728159i
$451$	−1.88632	+	1.08907i	−0.0888233	+	0.0512822i
$452$		−	9.21518i		−	0.433445i
$453$	−22.7010	+	25.1741i	−1.06659	+	1.18278i
$454$		−	26.1052i		−	1.22518i
$455$	−0.0500611	+	0.518117i	−0.00234690	+	0.0242897i
$456$	−0.958948	−	0.204582i	−0.0449069	−	0.00958041i
$457$	13.9866	−	24.2255i	0.654267	−	1.13322i	−0.327811	−	0.944743i	$-0.606311\pi$
$457$	13.9866	−	24.2255i	0.654267	−	1.13322i	0.982077	−	0.188480i	$-0.0603559\pi$
$458$	21.4386			1.00176
$459$	1.82713	−	17.0162i	0.0852833	−	0.794246i
$460$	0.291266	−	0.168163i	0.0135803	−	0.00784062i
$461$	−4.40994	+	7.63823i	−0.205391	+	0.355748i	−0.950257	−	0.311466i	$-0.899180\pi$
$461$	−4.40994	+	7.63823i	−0.205391	+	0.355748i	0.744866	+	0.667214i	$0.232513\pi$
$462$	3.60305	−	21.4101i	0.167629	−	0.996087i
$463$	−1.13863			−0.0529167			−0.0264583	−	0.999650i	$-0.508423\pi$
$463$	−1.13863			−0.0529167			−0.0264583	+	0.999650i	$0.508423\pi$
$464$			0.967012i			0.0448924i
$465$	−0.134580	+	0.630825i	−0.00624099	+	0.0292538i
$466$	−25.7329			−1.19205
$467$	−5.62914	−	9.74995i	−0.260485	−	0.451174i	0.705886	−	0.708326i	$-0.250549\pi$
$467$	−5.62914	−	9.74995i	−0.260485	−	0.451174i	−0.966371	+	0.257152i	$0.917216\pi$
$468$	−9.55894	+	5.06228i	−0.441862	+	0.234004i
$469$	−7.10027	+	4.52167i	−0.327860	+	0.208791i
$470$	−0.242370	+	0.139932i	−0.0111797	+	0.00645460i
$471$	−11.8761	−	10.7094i	−0.547221	−	0.493463i
$472$	8.52182	−	4.92008i	0.392249	−	0.226465i
$473$	43.5247	+	25.1290i	2.00127	+	1.15543i
$474$	−3.10621	+	14.5599i	−0.142673	+	0.668761i
$475$	−2.44986	−	1.41443i	−0.112407	−	0.0648984i
$476$	−0.378619	−	8.70578i	−0.0173540	−	0.399029i
$477$	9.36695	+	12.9332i	0.428883	+	0.592170i
$478$	2.42945	−	4.20794i	0.111121	−	0.192467i
$479$	32.8473			1.50083			0.750416	−	0.660966i	$-0.229853\pi$
$479$	32.8473			1.50083			0.750416	+	0.660966i	$0.229853\pi$
$480$	0.0701885	+	0.0632933i	0.00320365	+	0.00288893i
$481$	−34.9108	−	4.91205i	−1.59179	−	0.223970i
$482$	−2.89053			−0.131660
$483$	−27.8535	−	4.68739i	−1.26738	−	0.213284i
$484$	−5.72317	−	9.91282i	−0.260144	−	0.450583i
$485$		−	0.763750i		−	0.0346801i
$486$	0.0583746	−	15.5883i	0.00264792	−	0.707102i
$487$	−7.63011	−	13.2157i	−0.345753	−	0.598862i	0.639737	−	0.768594i	$-0.279043\pi$
$487$	−7.63011	−	13.2157i	−0.345753	−	0.598862i	−0.985490	+	0.169732i	$0.945710\pi$
$488$	1.14676			0.0519112
$489$	7.17006	+	1.52966i	0.324241	+	0.0691735i
$490$	−0.346123	−	0.161543i	−0.0156362	−	0.00729777i
$491$	5.43320	−	3.13686i	0.245197	−	0.141564i	−0.372366	−	0.928086i	$-0.621453\pi$
$491$	5.43320	−	3.13686i	0.245197	−	0.141564i	0.617563	+	0.786521i	$0.288120\pi$
$492$	−0.533267	+	0.591361i	−0.0240415	+	0.0266606i
$493$	−2.75824	−	1.59247i	−0.124225	−	0.0717211i
$494$	−2.02122	−	0.284392i	−0.0909391	−	0.0127954i
$495$	−0.771439	+	0.0799133i	−0.0346736	+	0.00359184i
$496$	−5.91042	+	3.41238i	−0.265386	+	0.153220i
$497$	−2.07506	+	0.0902454i	−0.0930792	+	0.00404806i
$498$	16.6497	+	15.0140i	0.746089	+	0.672794i
$499$	5.83077	+	10.0992i	0.261021	+	0.452102i	0.966513	−	0.256616i	$-0.0826075\pi$
$499$	5.83077	+	10.0992i	0.261021	+	0.452102i	−0.705493	+	0.708717i	$0.749274\pi$
$500$	0.272751	+	0.472418i	0.0121978	+	0.0211272i
$501$	5.76003	+	17.7728i	0.257339	+	0.794032i
$502$	−6.74254	+	3.89281i	−0.300934	+	0.173745i
$503$	0.152024	−	0.263314i	0.00677843	−	0.0117406i	−0.862616	−	0.505859i	$-0.831176\pi$
$503$	0.152024	−	0.263314i	0.00677843	−	0.0117406i	0.869395	+	0.494118i	$0.164509\pi$
$504$	−1.16011	−	7.85202i	−0.0516752	−	0.349757i
$505$	0.0757573	+	0.131216i	0.00337116	+	0.00583902i
$506$	−25.2893	+	14.6008i	−1.12425	+	0.649085i
$507$	−19.1079	+	11.9116i	−0.848613	+	0.529014i
$508$	0.435625	−	0.754524i	0.0193277	−	0.0334766i
$509$	3.39059	−	5.87267i	0.150285	−	0.260302i	−0.781047	−	0.624472i	$-0.785314\pi$
$509$	3.39059	−	5.87267i	0.150285	−	0.260302i	0.931332	+	0.364171i	$0.118647\pi$
$510$	−0.296119	+	0.0959699i	−0.0131124	+	0.00424962i
$511$	−26.6487	+	1.15896i	−1.17887	+	0.0512695i
$512$			1.00000i			0.0441942i
$513$	1.73436	−	2.37590i	0.0765740	−	0.104899i
$514$	−10.4913	+	6.05714i	−0.462751	+	0.267169i
$515$	−0.443032	−	0.255784i	−0.0195223	−	0.0112712i
$516$	17.9692	+	3.83354i	0.791049	+	0.168762i
$517$	21.0439	−	12.1497i	0.925509	−	0.534343i
$518$	11.9493	−	22.9448i	0.525021	−	1.00814i
$519$	−43.0858	−	9.19190i	−1.89126	−	0.403480i
$520$	0.155015	+	0.121151i	0.00679788	+	0.00531282i
$521$	−2.15594	+	3.73419i	−0.0944533	+	0.163598i	−0.909380	−	0.415966i	$-0.863444\pi$
$521$	−2.15594	+	3.73419i	−0.0944533	+	0.163598i	0.814927	+	0.579564i	$0.196777\pi$
$522$	−2.64846	−	1.18393i	−0.115920	−	0.0518190i
$523$	−4.42230	−	2.55322i	−0.193374	−	0.111644i	0.400187	−	0.916433i	$-0.368945\pi$
$523$	−4.42230	−	2.55322i	−0.193374	−	0.111644i	−0.593561	+	0.804789i	$0.702278\pi$
$524$	−5.35095	+	9.26812i	−0.233758	+	0.404880i
$525$	3.80022	−	22.5817i	0.165855	−	0.985546i
$526$	−4.55126	+	7.88301i	−0.198444	+	0.343716i
$527$		−	22.4779i		−	0.979155i
$528$	−6.09416	−	5.49547i	−0.265214	−	0.239160i
$529$	7.49494	+	12.9816i	0.325867	+	0.564418i
$530$	0.145228	−	0.251542i	0.00630830	−	0.0109263i
$531$	3.04175	+	29.3633i	0.132001	+	1.27426i
$532$	0.691825	−	1.32843i	0.0299944	−	0.0575948i
$533$	−1.02074	+	1.30606i	−0.0442130	+	0.0565716i
$534$	−25.2487	+	8.18289i	−1.09262	+	0.354108i
$535$		−	0.107762i		−	0.00465896i
$536$			3.18163i			0.137425i
$537$	1.75565	−	8.22939i	0.0757621	−	0.355125i
$538$		−	11.5405i		−	0.497548i
$539$	30.0523	+	14.0261i	1.29444	+	0.604145i
$540$	−0.259281	+	0.114742i	−0.0111577	+	0.00493771i
$541$	−2.52578	−	4.37478i	−0.108592	−	0.188086i	0.806608	−	0.591086i	$-0.201301\pi$
$541$	−2.52578	−	4.37478i	−0.108592	−	0.188086i	−0.915200	+	0.403000i	$0.867967\pi$
$542$	−3.78219	−	6.55095i	−0.162459	−	0.281387i
$543$	−2.39821	+	11.2413i	−0.102917	+	0.482410i
$544$	−2.85233	−	1.64679i	−0.122293	−	0.0706057i
$545$	0.0614960			0.00263420
$546$	−3.55878	−	16.1349i	−0.152302	−	0.690510i
$547$	32.1836			1.37607			0.688037	−	0.725676i	$-0.258473\pi$
$547$	32.1836			1.37607			0.688037	+	0.725676i	$0.258473\pi$
$548$	−4.05094	−	2.33881i	−0.173048	−	0.0999091i
$549$	−1.40399	+	3.14074i	−0.0599208	+	0.134044i
$550$	−11.8373	−	20.5029i	−0.504746	−	0.874245i
$551$	−0.273717	−	0.474091i	−0.0116607	−	0.0201970i
$552$	−7.14935	+	7.92821i	−0.304296	+	0.337447i
$553$	−20.1699	−	10.5041i	−0.857711	−	0.446682i
$554$			24.4796i			1.04004i
$555$	−0.903786	−	0.192813i	−0.0383636	−	0.00818447i
$556$		−	19.5544i		−	0.829289i
$557$		−	37.4217i		−	1.58561i	−0.609477	−	0.792804i	$-0.708620\pi$
$557$		−	37.4217i		−	1.58561i	0.609477	−	0.792804i	$-0.291380\pi$
$558$	−2.10964	−	20.3653i	−0.0893083	−	0.862133i
$559$	37.8745	+	5.32906i	1.60192	+	0.225395i
$560$	−0.121773	+	0.0775487i	−0.00514584	+	0.00327703i
$561$	25.7107	−	8.33264i	1.08551	−	0.351804i
$562$	−11.1708	+	19.3484i	−0.471212	+	0.816163i
$563$	13.5997	+	23.5555i	0.573161	+	0.992744i	0.996239	+	0.0866505i	$0.0276164\pi$
$563$	13.5997	+	23.5555i	0.573161	+	0.992744i	−0.423078	+	0.906093i	$0.639050\pi$
$564$	5.94915	−	6.59726i	0.250505	−	0.277795i
$565$		−	0.502839i		−	0.0211546i
$566$	8.41418	−	14.5738i	0.353674	−	0.612582i
$567$	22.9255	+	6.43603i	0.962780	+	0.270288i
$568$	−0.392520	+	0.679865i	−0.0164698	+	0.0285265i
$569$	31.0496	+	17.9265i	1.30167	+	0.751517i	0.980690	−	0.195570i	$-0.0626557\pi$
$569$	31.0496	+	17.9265i	1.30167	+	0.751517i	0.320976	+	0.947087i	$0.395989\pi$
$570$	−0.0523263	−	0.0111633i	−0.00219171	−	0.000467578i
$571$	3.22192	−	5.58053i	0.134833	−	0.233538i	−0.790700	−	0.612203i	$-0.790283\pi$
$571$	3.22192	−	5.58053i	0.134833	−	0.233538i	0.925534	+	0.378665i	$0.123617\pi$
$572$	−13.4593	−	10.5190i	−0.562762	−	0.439822i
$573$	−4.24886	+	19.9160i	−0.177499	+	0.832001i
$574$	−0.653373	−	1.02598i	−0.0272713	−	0.0428234i
$575$	−26.6732	+	15.3998i	−1.11235	+	0.642216i
$576$	−2.73881	−	1.22431i	−0.114117	−	0.0510131i
$577$	13.5099	+	7.79997i	0.562427	+	0.324717i	0.754119	−	0.656738i	$-0.228064\pi$
$577$	13.5099	+	7.79997i	0.562427	+	0.324717i	−0.191692	+	0.981455i	$0.561398\pi$
$578$	−5.32804	+	3.07615i	−0.221617	+	0.127951i
$579$	39.6358	+	8.45588i	1.64721	+	0.351414i
$580$			0.0527663i			0.00219100i
$581$	−28.8861	+	18.3956i	−1.19840	+	0.763178i
$582$	7.47423	+	23.0621i	0.309817	+	0.955954i
$583$	−12.6095	+	21.8403i	−0.522232	+	0.904532i
$584$	−5.04088	+	8.73107i	−0.208593	+	0.361294i
$585$	−0.521597	+	0.276230i	−0.0215654	+	0.0114207i
$586$	0.448519	−	0.258953i	0.0185282	−	0.0106972i
$587$	−1.29017	−	2.23464i	−0.0532510	−	0.0922335i	0.838171	−	0.545407i	$-0.183625\pi$
$587$	−1.29017	−	2.23464i	−0.0532510	−	0.0922335i	−0.891422	+	0.453174i	$0.850292\pi$
$588$	12.0324	+	1.49069i	0.496206	+	0.0614752i
$589$	1.93178	−	3.34594i	0.0795975	−	0.137867i
$590$	0.465005	−	0.268471i	0.0191440	−	0.0110528i
$591$	16.3228	−	5.29010i	0.671432	−	0.217606i
$592$	−4.88894	−	8.46790i	−0.200934	−	0.348028i
$593$	9.35407	+	16.2017i	0.384125	+	0.665325i	0.991647	−	0.128978i	$-0.0411697\pi$
$593$	9.35407	+	16.2017i	0.384125	+	0.665325i	−0.607522	+	0.794303i	$0.707836\pi$
$594$	22.5122	−	9.96253i	0.923687	−	0.408768i
$595$	−0.0206599	−	0.475043i	−0.000846971	−	0.0194749i
$596$	20.2377	−	11.6842i	0.828968	−	0.478605i
$597$	5.07291	−	1.64409i	0.207621	−	0.0672881i
$598$	−13.6847	+	17.5099i	−0.559610	+	0.716033i
$599$	9.48179	+	5.47431i	0.387415	+	0.223674i	0.681040	−	0.732247i	$-0.261528\pi$
$599$	9.48179	+	5.47431i	0.387415	+	0.223674i	−0.293624	+	0.955921i	$0.594861\pi$
$600$	−6.42765	−	5.79621i	−0.262408	−	0.236629i
$601$	11.4546	−	6.61334i	0.467244	−	0.269764i	−0.247841	−	0.968801i	$-0.579721\pi$
$601$	11.4546	−	6.61334i	0.467244	−	0.269764i	0.715085	+	0.699037i	$0.246388\pi$
$602$	−12.9637	+	24.8927i	−0.528361	+	1.01455i
$603$	−8.71386	−	3.89531i	−0.354856	−	0.158629i
$604$	−19.5710			−0.796333
$605$	−0.312293	−	0.540907i	−0.0126965	−	0.0219910i
$606$	−3.57166	−	3.22079i	−0.145089	−	0.130836i
$607$		−	28.4807i		−	1.15600i	−0.816038	−	0.577999i	$-0.803834\pi$
$607$		−	28.4807i		−	1.15600i	0.816038	−	0.577999i	$-0.196166\pi$
$608$	−0.283054	−	0.490264i	−0.0114794	−	0.0198828i
$609$	2.82186	−	3.41679i	0.114348	−	0.138455i
$610$	0.0625743			0.00253356
$611$	11.3874	−	14.5704i	0.460685	−	0.589457i
$612$	8.00239	−	5.79578i	0.323478	−	0.234281i
$613$	35.9381			1.45152			0.725762	−	0.687946i	$-0.241487\pi$
$613$	35.9381			1.45152			0.725762	+	0.687946i	$0.241487\pi$
$614$	2.50087	−	4.33164i	0.100927	−	0.174811i
$615$	−0.0290984	+	0.0322684i	−0.00117336	+	0.00130119i
$616$	10.5730	−	6.73321i	0.425998	−	0.271289i
$617$	31.2556	+	18.0454i	1.25830	+	0.726481i	0.972744	−	0.231881i	$-0.0744879\pi$
$617$	31.2556	+	18.0454i	1.25830	+	0.726481i	0.285558	+	0.958362i	$0.407821\pi$
$618$	15.8809	+	3.38802i	0.638823	+	0.136286i
$619$	−34.4650	−	19.8984i	−1.38527	−	0.799784i	−0.392489	−	0.919757i	$-0.628386\pi$
$619$	−34.4650	−	19.8984i	−1.38527	−	0.799784i	−0.992777	+	0.119973i	$0.961719\pi$
$620$	−0.322510	+	0.186201i	−0.0129523	+	0.00747803i
$621$	−12.9608	−	29.2873i	−0.520098	−	1.17526i
$622$	20.4564	−	11.8105i	0.820226	−	0.473558i
$623$	−1.76157	−	40.5046i	−0.0705756	−	1.62278i
$624$	−5.86644	−	2.14124i	−0.234845	−	0.0857183i
$625$	−12.4777	−	21.6120i	−0.499107	−	0.864479i
$626$	−27.7138			−1.10767
$627$	4.54326	+	0.969258i	0.181440	+	0.0387084i
$628$		−	9.23278i		−	0.368428i
$629$	32.2043			1.28407
$630$	−0.0633027	−	0.428456i	−0.00252204	−	0.0170701i
$631$	−18.0785	+	31.3129i	−0.719695	+	1.24655i	0.241426	+	0.970419i	$0.422385\pi$
$631$	−18.0785	+	31.3129i	−0.719695	+	1.24655i	−0.961121	+	0.276129i	$0.910948\pi$
$632$	−7.44380	+	4.29768i	−0.296098	+	0.170953i
$633$	1.38375	+	4.26962i	0.0549991	+	0.169702i
$634$	−11.2153			−0.445418
$635$	0.0237705	−	0.0411716i	0.000943302	−	0.00163385i
$636$	−1.92363	+	9.01676i	−0.0762769	+	0.357538i
$637$	25.2036	+	1.33348i	0.998603	+	0.0528345i
$638$		−	4.58147i		−	0.181382i
$639$	−1.38145	−	1.90740i	−0.0546493	−	0.0754558i
$640$			0.0545664i			0.00215693i
$641$	−7.06718	+	4.08024i	−0.279137	+	0.161160i	−0.633032	−	0.774125i	$-0.718190\pi$
$641$	−7.06718	+	4.08024i	−0.279137	+	0.161160i	0.353896	+	0.935285i	$0.384857\pi$
$642$	1.05458	+	3.25397i	0.0416211	+	0.128424i
$643$	16.4057	+	9.47185i	0.646979	+	0.373533i	0.787298	−	0.616573i	$-0.211479\pi$
$643$	16.4057	+	9.47185i	0.646979	+	0.373533i	−0.140319	+	0.990106i	$0.544813\pi$
$644$	−8.75959	−	13.7550i	−0.345176	−	0.542021i
$645$	0.980513	+	0.209182i	0.0386077	+	0.00823654i
$646$	1.86453			0.0733588
$647$	−20.3288			−0.799208			−0.399604	−	0.916688i	$-0.630852\pi$
$647$	−20.3288			−0.799208			−0.399604	+	0.916688i	$0.630852\pi$
$648$	6.70631	−	6.00211i	0.263449	−	0.235785i
$649$	−40.3743	+	23.3101i	−1.58483	+	0.915003i
$650$	−14.1958	−	11.0946i	−0.556807	−	0.435168i
$651$	30.8413	+	5.19021i	1.20877	+	0.203420i
$652$	2.11640	+	3.66571i	0.0828845	+	0.143560i
$653$	−20.1946	−	11.6594i	−0.790277	−	0.456267i	0.0497829	−	0.998760i	$-0.484147\pi$
$653$	−20.1946	−	11.6594i	−0.790277	−	0.456267i	−0.840060	+	0.542493i	$0.817480\pi$
$654$	−1.85692	+	0.601814i	−0.0726115	+	0.0235328i
$655$	−0.291982	+	0.505728i	−0.0114087	+	0.0197604i
$656$	−0.459740			−0.0179498
$657$	−17.7411	−	24.4956i	−0.692145	−	0.955663i
$658$	7.28907	+	11.4458i	0.284158	+	0.446206i
$659$	−35.4529	−	20.4688i	−1.38105	−	0.797349i	−0.388766	−	0.921337i	$-0.627099\pi$
$659$	−35.4529	−	20.4688i	−1.38105	−	0.797349i	−0.992284	+	0.123987i	$0.960432\pi$
$660$	−0.332536	−	0.299868i	−0.0129440	−	0.0116724i
$661$		−	9.31221i		−	0.362203i	−0.983464	−	0.181102i	$-0.942034\pi$
$661$		−	9.31221i		−	0.362203i	0.983464	−	0.181102i	$-0.0579663\pi$
$662$	14.4195	+	8.32512i	0.560431	+	0.323565i
$663$	15.7683	−	13.2068i	0.612391	−	0.512911i
$664$			12.9439i			0.502320i
$665$	0.0377504	−	0.0724877i	0.00146390	−	0.00281095i
$666$	29.1775	−	3.02250i	1.13061	−	0.117120i
$667$	−5.96027			−0.230782
$668$	−5.39330	+	9.34146i	−0.208673	+	0.361432i
$669$	−38.8456	+	12.5896i	−1.50186	+	0.486740i
$670$			0.173610i			0.00670714i
$671$	−5.43305			−0.209740
$672$	2.91813	−	3.53335i	0.112569	−	0.136302i
$673$	5.08322	+	8.80440i	0.195944	+	0.339385i	0.947210	−	0.320615i	$-0.103890\pi$
$673$	5.08322	+	8.80440i	0.195944	+	0.339385i	−0.751266	+	0.660000i	$0.770556\pi$
$674$	−7.61523	−	4.39666i	−0.293328	−	0.169353i
$675$	23.7441	−	10.5077i	0.913912	−	0.404442i
$676$	−12.4953	−	3.58726i	−0.480587	−	0.137971i
$677$	−10.0028	−	17.3253i	−0.384438	−	0.665866i	0.607253	−	0.794508i	$-0.292271\pi$
$677$	−10.0028	−	17.3253i	−0.384438	−	0.665866i	−0.991691	+	0.128642i	$0.958938\pi$
$678$	4.92090	+	15.1836i	0.188986	+	0.583125i
$679$	−36.9968	+	1.60901i	−1.41981	+	0.0617482i
$680$	−0.155641	−	0.0898595i	−0.00596857	−	0.00344596i
$681$	13.9402	+	43.0130i	0.534188	+	1.64826i
$682$	28.0021	−	16.1670i	1.07226	−	0.619068i
$683$	7.68727	−	4.43825i	0.294145	−	0.169825i	−0.345664	−	0.938358i	$-0.612346\pi$
$683$	7.68727	−	4.43825i	0.294145	−	0.169825i	0.639810	+	0.768533i	$0.279013\pi$
$684$	1.68929	−	0.174993i	0.0645914	−	0.00669103i
$685$	−0.221045	−	0.127620i	−0.00844570	−	0.00487613i
$686$	−7.09613	+	17.1069i	−0.270931	+	0.653143i
$687$	−35.3239	+	11.4482i	−1.34769	+	0.436776i
$688$	5.30399	+	9.18678i	0.202213	+	0.350243i
$689$	−2.67407	+	19.0051i	−0.101874	+	0.724036i
$690$	−0.390114	+	0.432614i	−0.0148514	+	0.0164693i
$691$	−10.3616	−	5.98230i	−0.394175	−	0.227577i	0.289792	−	0.957090i	$-0.406414\pi$
$691$	−10.3616	−	5.98230i	−0.394175	−	0.227577i	−0.683968	+	0.729512i	$0.739747\pi$
$692$	−12.7177	−	22.0277i	−0.483454	−	0.837367i
$693$	5.49630	+	37.2009i	0.208787	+	1.41315i
$694$	−27.3203			−1.03707
$695$		−	1.06701i		−	0.0404740i
$696$	−0.516383	−	1.59332i	−0.0195735	−	0.0603948i
$697$	0.757096	−	1.31133i	0.0286771	−	0.0496701i
$698$	0.547767			0.0207333
$699$	42.3995	−	13.7413i	1.60370	−	0.519746i
$700$	11.1516	−	7.10168i	0.421490	−	0.268418i
$701$			21.0976i			0.796847i	0.917202	+	0.398423i	$0.130443\pi$
$701$			21.0976i			0.796847i	−0.917202	+	0.398423i	$0.869557\pi$
$702$	13.0468	−	13.4455i	0.492420	−	0.507467i
$703$	4.79375	+	2.76767i	0.180800	+	0.104385i
$704$		−	4.73776i		−	0.178561i
$705$	0.324624	−	0.359989i	0.0122260	−	0.0135580i
$706$	18.9519	+	10.9419i	0.713264	+	0.411803i
$707$	6.19662	−	3.94620i	0.233048	−	0.148412i
$708$	−11.4139	+	12.6574i	−0.428961	+	0.475693i
$709$	28.8724			1.08432			0.542162	−	0.840274i	$-0.317606\pi$
$709$	28.8724			1.08432			0.542162	+	0.840274i	$0.317606\pi$
$710$	−0.0214184	+	0.0370978i	−0.000803819	+	0.00139225i
$711$	−2.65696	−	25.6488i	−0.0996439	−	0.961906i
$712$	−13.2708	−	7.66189i	−0.497344	−	0.287141i
$713$	−21.0325	−	36.4294i	−0.787675	−	1.36429i
$714$	5.27272	+	14.1421i	0.197327	+	0.529256i
$715$	−0.734426	−	0.573984i	−0.0274660	−	0.0214658i
$716$	4.20729	−	2.42908i	0.157234	−	0.0907790i
$717$	−1.75592	+	8.23066i	−0.0655762	+	0.307379i
$718$	−23.2965			−0.869417
$719$	−29.5891			−1.10349			−0.551744	−	0.834013i	$-0.686038\pi$
$719$	−29.5891			−1.10349			−0.551744	+	0.834013i	$0.686038\pi$
$720$	−0.149447	−	0.0668064i	−0.00556955	−	0.00248973i
$721$	−11.4571	+	21.9998i	−0.426685	+	0.819315i
$722$	−16.1769	−	9.33976i	−0.602043	−	0.347590i
$723$	4.76267	−	1.54354i	0.177126	−	0.0574049i
$724$	−5.74713	+	3.31811i	−0.213591	+	0.123317i
$725$		−	4.83218i		−	0.179463i
$726$	14.7234	+	13.2770i	0.546436	+	0.492755i
$727$			19.8262i			0.735312i	0.929962	+	0.367656i	$0.119840\pi$
$727$			19.8262i			0.735312i	−0.929962	+	0.367656i	$0.880160\pi$
$728$	5.54211	−	7.76434i	0.205404	−	0.287766i
$729$	8.22798	+	25.7158i	0.304740	+	0.952436i
$730$	−0.275063	+	0.476423i	−0.0101805	+	0.0176332i
$731$	−34.9383			−1.29224
$732$	−1.88948	+	0.612367i	−0.0698374	+	0.0226337i
$733$	12.7910	−	7.38488i	0.472446	−	0.272767i	−0.244817	−	0.969569i	$-0.578728\pi$
$733$	12.7910	−	7.38488i	0.472446	−	0.272767i	0.717263	+	0.696803i	$0.245395\pi$
$734$	2.16879	−	3.75645i	0.0800514	−	0.138653i
$735$	0.656563	+	0.0813418i	0.0242177	+	0.00300034i
$736$	−6.16359			−0.227193
$737$		−	15.0738i		−	0.555250i
$738$	0.562865	−	1.25914i	0.0207194	−	0.0463495i
$739$	−0.502545			−0.0184864			−0.00924321	−	0.999957i	$-0.502942\pi$
$739$	−0.502545			−0.0184864			−0.00924321	+	0.999957i	$0.502942\pi$
$740$	−0.266772	−	0.462062i	−0.00980673	−	0.0169858i
$741$	3.48219	−	0.610745i	0.127921	−	0.0224363i
$742$	−12.4909	−	6.50506i	−0.458556	−	0.238808i
$743$	−9.20149	+	5.31248i	−0.337570	+	0.194896i	−0.659197	−	0.751970i	$-0.729104\pi$
$743$	−9.20149	+	5.31248i	−0.337570	+	0.194896i	0.321627	+	0.946866i	$0.395770\pi$
$744$	7.91626	−	8.77867i	0.290224	−	0.321842i
$745$	1.10430	−	0.637566i	0.0404583	−	0.0233586i
$746$	8.06639	+	4.65713i	0.295332	+	0.170510i
$747$	−35.4507	−	15.8474i	−1.29707	−	0.579825i
$748$	13.5136	+	7.80210i	0.494108	+	0.285273i
$749$	−5.22011	+	0.227025i	−0.190739	+	0.00829532i
$750$	−0.701676	−	0.632744i	−0.0256216	−	0.0231046i
$751$	16.9041	−	29.2787i	0.616838	−	1.06839i	−0.373221	−	0.927742i	$-0.621747\pi$
$751$	16.9041	−	29.2787i	0.616838	−	1.06839i	0.990059	−	0.140652i	$-0.0449199\pi$
$752$	5.12888			0.187031
$753$	9.03079	−	10.0146i	0.329100	−	0.364953i
$754$	−1.30559	−	3.23294i	−0.0475469	−	0.117737i
$755$	−1.06792			−0.0388656
$756$	6.10445	+	12.3181i	0.222017	+	0.448005i
$757$	23.7078	+	41.0631i	0.861675	+	1.49246i	0.870312	+	0.492501i	$0.163917\pi$
$757$	23.7078	+	41.0631i	0.861675	+	1.49246i	−0.00863717	+	0.999963i	$0.502749\pi$
$758$		−	7.46759i		−	0.271235i
$759$	33.8719	−	37.5619i	1.22947	−	1.36341i
$760$	−0.0154452	−	0.0267519i	−0.000560258	−	0.000970395i
$761$	−20.3127			−0.736334			−0.368167	−	0.929760i	$-0.620015\pi$
$761$	−20.3127			−0.736334			−0.368167	+	0.929760i	$0.620015\pi$
$762$	−0.314854	+	1.47584i	−0.0114060	+	0.0534639i
$763$	−0.129555	−	2.97893i	−0.00469021	−	0.107845i
$764$	−10.1821	+	5.87862i	−0.368374	+	0.212681i
$765$	0.436662	−	0.316255i	0.0157875	−	0.0114342i
$766$	9.97995	+	5.76193i	0.360590	+	0.208187i
$767$	−21.8476	+	27.9545i	−0.788871	+	1.00938i
$768$	−0.533999	−	1.64768i	−0.0192690	−	0.0594555i
$769$	−17.3839	+	10.0366i	−0.626879	+	0.361929i	−0.779542	−	0.626350i	$-0.784548\pi$
$769$	−17.3839	+	10.0366i	−0.626879	+	0.361929i	0.152664	+	0.988278i	$0.451215\pi$
$770$	0.576930	−	0.367407i	0.0207911	−	0.0132404i
$771$	14.0517	−	15.5826i	0.506061	−	0.561192i
$772$	11.6993	+	20.2639i	0.421069	+	0.729312i
$773$	9.71340	+	16.8241i	0.349367	+	0.605121i	0.986137	−	0.165933i	$-0.0530635\pi$
$773$	9.71340	+	16.8241i	0.349367	+	0.605121i	−0.636770	+	0.771053i	$0.719730\pi$
$774$	−31.6545	+	3.27909i	−1.13780	+	0.117865i
$775$	29.5345	−	17.0518i	1.06091	−	0.612517i
$776$	−6.99836	+	12.1215i	−0.251226	+	0.435137i
$777$	−7.43605	+	44.1866i	−0.266767	+	1.58518i
$778$	5.46969	+	9.47378i	0.196098	+	0.339651i
$779$	0.225394	−	0.130131i	0.00807557	−	0.00466243i
$780$	−0.320110	−	0.116840i	−0.0114618	−	0.00418354i
$781$	1.85967	−	3.22103i	0.0665440	−	0.115258i
$782$	10.1502	−	17.5806i	0.362969	−	0.628681i
$783$	4.99602	+	0.536455i	0.178543	+	0.0191713i
$784$	4.01308	+	5.73543i	0.143324	+	0.204837i
$785$		−	0.503799i		−	0.0179814i
$786$	3.86748	−	18.1283i	0.137948	−	0.646615i
$787$	22.2608	−	12.8523i	0.793511	−	0.458134i	−0.0476862	−	0.998862i	$-0.515185\pi$
$787$	22.2608	−	12.8523i	0.793511	−	0.458134i	0.841197	+	0.540729i	$0.181851\pi$
$788$	8.57934	+	4.95328i	0.305626	+	0.176453i
$789$	3.28949	−	15.4190i	0.117109	−	0.548932i
$790$	−0.406181	+	0.234509i	−0.0144513	+	0.00834345i
$791$	−24.3580	+	1.05934i	−0.866072	+	0.0376659i
$792$	12.9758	+	5.80050i	0.461075	+	0.206112i
$793$	−3.83386	+	1.54827i	−0.136144	+	0.0549807i
$794$	2.03716	−	3.52846i	0.0722959	−	0.125220i
$795$	−0.104966	+	0.492012i	−0.00372275	+	0.0174499i
$796$	2.66634	+	1.53941i	0.0945059	+	0.0545630i
$797$	−1.38387	+	2.39693i	−0.0490191	+	0.0849037i	−0.889494	−	0.456947i	$-0.848943\pi$
$797$	−1.38387	+	2.39693i	−0.0490191	+	0.0849037i	0.840475	+	0.541851i	$0.182276\pi$
$798$	−0.430524	+	2.55826i	−0.0152404	+	0.0905615i
$799$	−8.44621	+	14.6293i	−0.298805	+	0.517546i
$800$		−	4.99702i		−	0.176671i
$801$	37.2320	−	26.9655i	1.31553	−	0.952780i
$802$	3.64056	+	6.30564i	0.128553	+	0.222660i
$803$	23.8825	−	41.3657i	0.842795	−	1.45976i
$804$	−1.69899	−	5.24230i	−0.0599187	−	0.184882i
$805$	−0.477979	−	0.750558i	−0.0168465	−	0.0264537i
$806$	15.1527	−	19.3882i	0.533731	−	0.682920i
$807$	6.16264	+	19.0151i	0.216935	+	0.669363i
$808$		−	2.77670i		−	0.0976841i
$809$			38.6212i			1.35785i	0.734208	+	0.678925i	$0.237554\pi$
$809$			38.6212i			1.35785i	−0.734208	+	0.678925i	$0.762446\pi$
$810$	0.365939	−	0.327514i	0.0128578	−	0.0115077i
$811$		−	13.2231i		−	0.464327i	−0.972677	−	0.232163i	$-0.925420\pi$
$811$		−	13.2231i		−	0.464327i	0.972677	−	0.232163i	$-0.0745804\pi$
$812$	2.55606	−	0.111164i	0.0897000	−	0.00390110i
$813$	9.73003	+	8.77417i	0.341247	+	0.307723i
$814$	23.1626	+	40.1188i	0.811849	+	1.40616i
$815$	0.115484	+	0.200024i	0.00404523	+	0.00700655i
$816$	5.57911	+	1.19024i	0.195308	+	0.0416669i
$817$	−5.20071	−	3.00263i	−0.181950	−	0.105049i
$818$	13.6511			0.477299
$819$	14.4797	+	24.6848i	0.505963	+	0.862555i
$820$	−0.0250863			−0.000876052
$821$	−24.6007	−	14.2032i	−0.858569	−	0.495695i	0.00496391	−	0.999988i	$-0.498420\pi$
$821$	−24.6007	−	14.2032i	−0.858569	−	0.495695i	−0.863533	+	0.504293i	$0.831753\pi$
$822$	7.92357	+	1.69041i	0.276366	+	0.0589598i
$823$	23.5065	+	40.7144i	0.819385	+	1.41922i	0.906136	+	0.422986i	$0.139018\pi$
$823$	23.5065	+	40.7144i	0.819385	+	1.41922i	−0.0867511	+	0.996230i	$0.527648\pi$
$824$	4.68758	+	8.11913i	0.163300	+	0.282843i
$825$	30.4526	+	27.4610i	1.06023	+	0.956070i
$826$	−13.9846	−	21.9597i	−0.486588	−	0.764077i
$827$		−	40.5886i		−	1.41141i	−0.708508	−	0.705703i	$-0.750631\pi$
$827$		−	40.5886i		−	1.41141i	0.708508	−	0.705703i	$-0.249369\pi$
$828$	7.54617	−	16.8809i	0.262248	−	0.586651i
$829$			34.3548i			1.19319i	0.802542	+	0.596595i	$0.203480\pi$
$829$			34.3548i			1.19319i	−0.802542	+	0.596595i	$0.796520\pi$
$830$			0.706300i			0.0245160i
$831$	−13.0721	−	40.3345i	−0.453466	−	1.39919i
$832$	−1.35013	−	3.34322i	−0.0468074	−	0.115905i
$833$	−22.9681	+	2.00157i	−0.795796	+	0.0693503i
$834$	10.4420	+	32.2193i	0.361577	+	1.11566i
$835$	−0.294293	+	0.509730i	−0.0101844	+	0.0176399i
$836$	1.34104	+	2.32275i	0.0463809	+	0.0803341i
$837$	14.3511	+	32.4289i	0.496046	+	1.12091i
$838$		−	15.2608i		−	0.527176i
$839$	−13.4933	+	23.3711i	−0.465840	+	0.806858i	−0.999239	−	0.0390053i	$-0.987581\pi$
$839$	−13.4933	+	23.3711i	−0.465840	+	0.806858i	0.533399	+	0.845864i	$0.320914\pi$
$840$	0.159232	−	0.192802i	0.00549401	−	0.00665230i
$841$	−14.0324	+	24.3049i	−0.483877	+	0.838100i
$842$	14.9797	+	8.64854i	0.516235	+	0.298048i
$843$	8.07386	−	37.8451i	0.278079	−	1.30346i
$844$	−1.29565	+	2.24413i	−0.0445980	+	0.0772460i
$845$	−0.681821	−	0.195744i	−0.0234554	−	0.00673379i
$846$	−6.27936	+	14.0470i	−0.215889	+	0.482946i
$847$	−25.5442	+	16.2673i	−0.877708	+	0.558952i
$848$	−4.60984	+	2.66149i	−0.158302	+	0.0913959i
$849$	−6.08147	+	28.5061i	−0.208716	+	0.978327i
$850$	14.2532	+	8.22906i	0.488879	+	0.282254i
$851$	52.1927	−	30.1335i	1.78914	−	1.03296i
$852$	0.283700	−	1.32980i	0.00971939	−	0.0455583i
$853$		−	3.02494i		−	0.103572i	−0.998658	−	0.0517859i	$-0.983509\pi$
$853$		−	3.02494i		−	0.103572i	0.998658	−	0.0517859i	$-0.0164914\pi$
$854$	−0.131827	−	3.03116i	−0.00451102	−	0.103724i
$855$	0.0921782	−	0.00954874i	0.00315243	−	0.000326560i
$856$	−0.987440	+	1.71030i	−0.0337500	+	0.0584567i
$857$	−19.9436	+	34.5434i	−0.681262	+	1.17998i	0.293334	+	0.956010i	$0.405235\pi$
$857$	−19.9436	+	34.5434i	−0.681262	+	1.17998i	−0.974596	+	0.223970i	$0.928098\pi$
$858$	27.7937	+	10.1447i	0.948863	+	0.346334i
$859$	−14.9753	+	8.64597i	−0.510949	+	0.294997i	−0.733224	−	0.679987i	$-0.761985\pi$
$859$	−14.9753	+	8.64597i	−0.510949	+	0.294997i	0.222274	+	0.974984i	$0.428652\pi$
$860$	0.289419	+	0.501289i	0.00986912	+	0.0170938i
$861$	1.62442	+	1.34158i	0.0553601	+	0.0457208i
$862$	18.6103	−	32.2340i	0.633870	−	1.09789i
$863$	−11.2753	+	6.50978i	−0.383815	+	0.221596i	−0.679477	−	0.733697i	$-0.737793\pi$
$863$	−11.2753	+	6.50978i	−0.383815	+	0.221596i	0.295662	+	0.955293i	$0.404460\pi$
$864$	5.16645	+	0.554755i	0.175766	+	0.0188732i
$865$	−0.693959	−	1.20197i	−0.0235953	−	0.0408683i
$866$	−1.13545	−	1.96666i	−0.0385842	−	0.0668297i
$867$	7.13624	−	7.91367i	0.242359	−	0.268762i
$868$	9.69923	+	15.2305i	0.329213	+	0.516955i
$869$	35.2669	−	20.3614i	1.19635	−	0.690712i
$870$	−0.0281772	−	0.0869419i	−0.000955296	−	0.00294761i
$871$	−4.29562	−	10.6369i	−0.145551	−	0.360417i
$872$	−0.976006	−	0.563497i	−0.0330517	−	0.0190824i
$873$	−24.6303	−	34.0077i	−0.833608	−	1.15099i
$874$	3.02179	−	1.74463i	0.102214	−	0.0590130i
$875$	1.21737	−	0.775256i	0.0411545	−	0.0262085i
$876$	3.64337	−	17.0778i	0.123098	−	0.577006i
$877$	11.8222			0.399206			0.199603	−	0.979877i	$-0.436035\pi$
$877$	11.8222			0.399206			0.199603	+	0.979877i	$0.436035\pi$
$878$	−12.4691	−	21.5971i	−0.420812	−	0.728867i
$879$	−0.600735	+	0.666180i	−0.0202623	+	0.0224697i
$880$		−	0.258522i		−	0.00871478i
$881$	−25.6398	−	44.4094i	−0.863827	−	1.49619i	−0.868207	−	0.496202i	$-0.834728\pi$
$881$	−25.6398	−	44.4094i	−0.863827	−	1.49619i	0.00438035	−	0.999990i	$-0.498606\pi$
$882$	−20.6215	+	3.96909i	−0.694362	+	0.133646i
$883$	41.8667			1.40893			0.704464	−	0.709740i	$-0.251188\pi$
$883$	41.8667			1.40893			0.704464	+	0.709740i	$0.251188\pi$
$884$	11.7594	+	1.65458i	0.395510	+	0.0556494i
$885$	−0.622816	+	0.690666i	−0.0209357	+	0.0232165i
$886$	26.8839			0.903183
$887$	12.3927	−	21.4648i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$887$	12.3927	−	21.4648i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$888$	12.5773	+	11.3417i	0.422065	+	0.380602i
$889$	−2.04448	−	1.06473i	−0.0685695	−	0.0357099i
$890$	−0.724139	−	0.418082i	−0.0242732	−	0.0140141i
$891$	−31.7729	+	28.4365i	−1.06443	+	0.952660i
$892$	−20.4174	−	11.7880i	−0.683625	−	0.394691i
$893$	−2.51451	+	1.45175i	−0.0841448	+	0.0485810i
$894$	−27.1058	+	30.0588i	−0.906554	+	1.00532i
$895$	0.229577	−	0.132546i	0.00767390	−	0.00443053i
$896$	2.64325	−	0.114956i	0.0883049	−	0.00384042i
$897$	13.1977	−	36.1583i	0.440660	−	1.20729i
$898$	−19.0559	−	33.0058i	−0.635904	−	1.10142i
$899$	6.59963			0.220110
$900$	13.6859	+	6.11792i	0.456196	+	0.203931i
$901$		−	17.5317i		−	0.584065i
$902$	2.17813			0.0725239
$903$	8.06733	−	47.9378i	0.268464	−	1.59527i
$904$	−4.60759	+	7.98058i	−0.153246	+	0.265430i
$905$	−0.313600	+	0.181057i	−0.0104244	+	0.00601855i
$906$	32.2467	−	10.4509i	1.07133	−	0.347208i
$907$	−56.3523			−1.87115			−0.935574	−	0.353130i	$-0.885117\pi$
$907$	−56.3523			−1.87115			−0.935574	+	0.353130i	$0.885117\pi$
$908$	−13.0526	+	22.6078i	−0.433166	+	0.750265i
$909$	7.60485	+	3.39956i	0.252237	+	0.112756i
$910$	0.302413	−	0.423672i	0.0100249	−	0.0140446i
$911$			36.7197i			1.21658i	0.793716	+	0.608288i	$0.208144\pi$
$911$			36.7197i			1.21658i	−0.793716	+	0.608288i	$0.791856\pi$
$912$	0.728183	+	0.656647i	0.0241125	+	0.0217438i
$913$		−	61.3249i		−	2.02956i
$914$	−24.2255	+	13.9866i	−0.801310	+	0.462636i
$915$	−0.103102	+	0.0334146i	−0.00340846	+	0.00110465i
$916$	−18.5664	−	10.7193i	−0.613450	−	0.354175i
$917$	25.1131	+	13.0785i	0.829308	+	0.431890i
$918$	−10.0904	+	13.8229i	−0.333034	+	0.456222i
$919$	57.6337			1.90116			0.950581	−	0.310477i	$-0.100489\pi$
$919$	57.6337			1.90116			0.950581	+	0.310477i	$0.100489\pi$
$920$	−0.336325			−0.0110883
$921$	−1.80754	+	8.47261i	−0.0595606	+	0.279182i
$922$	7.63823	−	4.40994i	0.251552	−	0.145234i
$923$	0.394375	−	2.80289i	0.0129810	−	0.0922584i
$924$	−13.8254	+	16.7401i	−0.454821	+	0.550710i
$925$	24.4302	+	42.3143i	0.803259	+	1.39128i
$926$	0.986083	+	0.569315i	0.0324047	+	0.0187089i
$927$	−27.9758	+	2.89801i	−0.918845	+	0.0951832i
$928$	0.483506	−	0.837457i	0.0158719	−	0.0274909i
$929$	−33.9404			−1.11355			−0.556774	−	0.830664i	$-0.687961\pi$
$929$	−33.9404			−1.11355			−0.556774	+	0.830664i	$0.687961\pi$
$930$	0.431962	−	0.479020i	0.0141646	−	0.0157077i
$931$	−3.59091	−	1.67596i	−0.117687	−	0.0549272i
$932$	22.2853	+	12.8664i	0.729981	+	0.421455i
$933$	−27.3988	+	30.3836i	−0.896995	+	0.994715i
$934$			11.2583i			0.368382i
$935$	0.737390	+	0.425733i	0.0241152	+	0.0139229i
$936$	10.8094	+	0.395406i	0.353317	+	0.0129242i
$937$		−	9.87231i		−	0.322514i	−0.986912	−	0.161257i	$-0.948445\pi$
$937$		−	9.87231i		−	0.322514i	0.986912	−	0.161257i	$-0.0515549\pi$
$938$	8.40985	−	0.365749i	0.274591	−	0.0119421i
$939$	45.6634	−	14.7991i	1.49017	−	0.482952i
$940$	0.279865			0.00912818
$941$	−3.85294	+	6.67349i	−0.125602	+	0.217550i	−0.921968	−	0.387266i	$-0.873420\pi$
$941$	−3.85294	+	6.67349i	−0.125602	+	0.217550i	0.796366	+	0.604815i	$0.206753\pi$
$942$	4.93030	+	15.2126i	0.160638	+	0.495655i
$943$		−	2.83365i		−	0.0922763i
$944$	−9.84016			−0.320270
$945$	0.333098	+	0.672154i	0.0108357	+	0.0218652i
$946$	−25.1290	−	43.5247i	−0.817014	−	1.41511i
$947$	−7.21820	−	4.16743i	−0.234560	−	0.135423i	0.378114	−	0.925759i	$-0.376573\pi$
$947$	−7.21820	−	4.16743i	−0.234560	−	0.135423i	−0.612674	+	0.790336i	$0.709906\pi$
$948$	9.97003	−	11.0562i	0.323812	−	0.359088i
$949$	5.06471	−	35.9958i	0.164407	−	1.16847i
$950$	1.41443	+	2.44986i	0.0458901	+	0.0794840i
$951$	18.4793	−	5.98899i	0.599232	−	0.194206i
$952$	−4.02500	+	7.72874i	−0.130451	+	0.250490i
$953$	−25.9527	−	14.9838i	−0.840689	−	0.485372i	0.0168091	−	0.999859i	$-0.494649\pi$
$953$	−25.9527	−	14.9838i	−0.840689	−	0.485372i	−0.857499	+	0.514486i	$0.827983\pi$
$954$	−1.64542	−	15.8839i	−0.0532724	−	0.514262i
$955$	−0.555599	+	0.320775i	−0.0179788	+	0.0103800i
$956$	−4.20794	+	2.42945i	−0.136094	+	0.0785742i
$957$	2.44650	+	7.54878i	0.0790841	+	0.244017i
$958$	−28.4466	−	16.4237i	−0.919068	−	0.530624i
$959$	−5.71639	+	10.9765i	−0.184592	+	0.354450i
$960$	−0.0291384	−	0.0899079i	−0.000940438	−	0.00290176i
$961$	7.78871	+	13.4904i	0.251249	+	0.435175i
$962$	27.7776	+	21.7094i	0.895586	+	0.699938i
$963$	−3.47523	−	4.79835i	−0.111988	−	0.154625i
$964$	2.50327	+	1.44527i	0.0806250	+	0.0465489i
$965$	0.638391	+	1.10573i	0.0205505	+	0.0355946i
$966$	21.7781	+	17.9861i	0.700699	+	0.578695i
$967$	−29.0892			−0.935445			−0.467723	−	0.883875i	$-0.654925\pi$
$967$	−29.0892			−0.935445			−0.467723	+	0.883875i	$0.654925\pi$
$968$			11.4463i			0.367899i
$969$	−3.07214	+	0.995656i	−0.0986914	+	0.0319851i
$970$	−0.381875	+	0.661427i	−0.0122613	+	0.0212371i
$971$	44.4307			1.42585			0.712924	−	0.701241i	$-0.247370\pi$
$971$	44.4307			1.42585			0.712924	+	0.701241i	$0.247370\pi$
$972$	−7.84473	+	13.4707i	−0.251620	+	0.432073i
$973$	−51.6871	+	2.24790i	−1.65701	+	0.0720643i
$974$			15.2602i			0.488969i
$975$	29.3147	+	10.6998i	0.938822	+	0.342669i
$976$	−0.993119	−	0.573378i	−0.0317890	−	0.0183534i
$977$			3.93630i			0.125934i	0.998016	+	0.0629668i	$0.0200562\pi$
$977$			3.93630i			0.125934i	−0.998016	+	0.0629668i	$0.979944\pi$
$978$	−5.44463	−	4.90975i	−0.174100	−	0.156997i
$979$	62.8737	+	36.3002i	2.00945	+	1.16016i
$980$	0.218979	+	0.312962i	0.00699504	+	0.00999719i
$981$	2.73825	−	1.98319i	0.0874255	−	0.0633185i
$982$	−6.27372			−0.200202
$983$	23.1093	−	40.0264i	0.737071	−	1.27664i	−0.216737	−	0.976230i	$-0.569542\pi$
$983$	23.1093	−	40.0264i	0.737071	−	1.27664i	0.953809	−	0.300415i	$-0.0971252\pi$
$984$	0.757503	−	0.245501i	0.0241483	−	0.00782627i
$985$	0.468143	+	0.270283i	0.0149163	+	0.00861193i
$986$	1.59247	+	2.75824i	0.0507145	+	0.0878401i
$987$	−18.1221	−	14.9667i	−0.576834	−	0.476396i
$988$	1.60823	+	1.25690i	0.0511648	+	0.0399874i
$989$	−56.6236	+	32.6916i	−1.80052	+	1.03953i
$990$	0.708042	+	0.316512i	0.0225031	+	0.0100594i
$991$	6.04064			0.191887			0.0959436	−	0.995387i	$-0.469413\pi$
$991$	6.04064			0.191887			0.0959436	+	0.995387i	$0.469413\pi$
$992$	6.82476			0.216687
$993$	−28.2044	−	6.01711i	−0.895039	−	0.190947i
$994$	1.84218	+	0.959375i	0.0584303	+	0.0304295i
$995$	0.145493	+	0.0840002i	0.00461242	+	0.00266298i
$996$	−6.91202	−	21.3273i	−0.219016	−	0.675783i
$997$	34.3556	−	19.8352i	1.08805	−	0.628188i	0.154996	−	0.987915i	$-0.450464\pi$
$997$	34.3556	−	19.8352i	1.08805	−	0.628188i	0.933057	+	0.359727i	$0.117130\pi$
$998$		−	11.6615i		−	0.369139i
$999$	−46.4612	+	20.5609i	−1.46997	+	0.650518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.185.18	✓	76
3.2	odd	2	inner	546.2.u.a.185.21	yes	76
7.5	odd	6		546.2.bb.a.341.33	yes	76
13.9	even	3		546.2.bb.a.269.26	yes	76
21.5	even	6		546.2.bb.a.341.7	yes	76
39.35	odd	6		546.2.bb.a.269.14	yes	76
91.61	odd	6	inner	546.2.u.a.425.21	yes	76
273.152	even	6	inner	546.2.u.a.425.18	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.18	✓	76	1.1	even	1	trivial
546.2.u.a.185.21	yes	76	3.2	odd	2	inner
546.2.u.a.425.18	yes	76	273.152	even	6	inner
546.2.u.a.425.21	yes	76	91.61	odd	6	inner
546.2.bb.a.269.14	yes	76	39.35	odd	6
546.2.bb.a.269.26	yes	76	13.9	even	3
546.2.bb.a.341.7	yes	76	21.5	even	6
546.2.bb.a.341.33	yes	76	7.5	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.69393 + 0.361382i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.0272832 + 0.0472559i) q^{5} +(-1.28630 - 1.15993i) q^{6} +(2.23165 - 1.42118i) q^{7} -1.00000i q^{8} +(2.73881 + 1.22431i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.69393 + 0.361382i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.0272832 + 0.0472559i) q^{5} +(-1.28630 - 1.15993i) q^{6} +(2.23165 - 1.42118i) q^{7} -1.00000i q^{8} +(2.73881 + 1.22431i) q^{9} -0.0545664i q^{10} +4.73776i q^{11} +(0.533999 + 1.64768i) q^{12} +(1.35013 + 3.34322i) q^{13} +(-2.64325 + 0.114956i) q^{14} +(0.0291384 + 0.0899079i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.64679 - 2.85233i) q^{17} +(-1.75972 - 2.42969i) q^{18} -0.566108i q^{19} +(-0.0272832 + 0.0472559i) q^{20} +(4.29384 - 1.60091i) q^{21} +(2.36888 - 4.10302i) q^{22} +(-5.33783 - 3.08180i) q^{23} +(0.361382 - 1.69393i) q^{24} +(2.49851 - 4.32755i) q^{25} +(0.502363 - 3.57038i) q^{26} +(4.19690 + 3.06366i) q^{27} +(2.34660 + 1.22207i) q^{28} +(0.837457 - 0.483506i) q^{29} +(0.0197193 - 0.0924317i) q^{30} +(5.91042 + 3.41238i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.71214 + 8.02543i) q^{33} +3.29359i q^{34} +(0.128046 + 0.0666840i) q^{35} +(0.309116 + 2.98403i) q^{36} +(-4.88894 + 8.46790i) q^{37} +(-0.283054 + 0.490264i) q^{38} +(1.07885 + 6.15110i) q^{39} +(0.0472559 - 0.0272832i) q^{40} +(0.229870 + 0.398146i) q^{41} +(-4.51903 - 0.760497i) q^{42} +(5.30399 - 9.18678i) q^{43} +(-4.10302 + 2.36888i) q^{44} +(0.0168673 + 0.162828i) q^{45} +(3.08180 + 5.33783i) q^{46} +(-2.56444 - 4.44174i) q^{47} +(-1.15993 + 1.28630i) q^{48} +(2.96049 - 6.34315i) q^{49} +(-4.32755 + 2.49851i) q^{50} +(-1.75877 - 5.42677i) q^{51} +(-2.22025 + 2.84086i) q^{52} +(4.60984 + 2.66149i) q^{53} +(-2.10279 - 4.75166i) q^{54} +(-0.223887 + 0.129261i) q^{55} +(-1.42118 - 2.23165i) q^{56} +(0.204582 - 0.958948i) q^{57} -0.967012 q^{58} +(4.92008 + 8.52182i) q^{59} +(-0.0632933 + 0.0701885i) q^{60} +1.14676i q^{61} +(-3.41238 - 5.91042i) q^{62} +(7.85202 - 1.16011i) q^{63} -1.00000 q^{64} +(-0.121151 + 0.155015i) q^{65} +(5.49547 - 6.09416i) q^{66} -3.18163 q^{67} +(1.64679 - 2.85233i) q^{68} +(-7.92821 - 7.14935i) q^{69} +(-0.0775487 - 0.121773i) q^{70} +(-0.679865 - 0.392520i) q^{71} +(1.22431 - 2.73881i) q^{72} +(-8.73107 - 5.04088i) q^{73} +(8.46790 - 4.88894i) q^{74} +(5.79621 - 6.42765i) q^{75} +(0.490264 - 0.283054i) q^{76} +(6.73321 + 10.5730i) q^{77} +(2.14124 - 5.86644i) q^{78} +(-4.29768 - 7.44380i) q^{79} -0.0545664 q^{80} +(6.00211 + 6.70631i) q^{81} -0.459740i q^{82} -12.9439 q^{83} +(3.53335 + 2.91813i) q^{84} +(0.0898595 - 0.155641i) q^{85} +(-9.18678 + 5.30399i) q^{86} +(1.59332 - 0.516383i) q^{87} +4.73776 q^{88} +(7.66189 - 13.2708i) q^{89} +(0.0668064 - 0.149447i) q^{90} +(7.76434 + 5.54211i) q^{91} -6.16359i q^{92} +(8.77867 + 7.91626i) q^{93} +5.12888i q^{94} +(0.0267519 - 0.0154452i) q^{95} +(1.64768 - 0.533999i) q^{96} +(-12.1215 - 6.99836i) q^{97} +(-5.73543 + 4.01308i) q^{98} +(-5.80050 + 12.9758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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