LMFDB - Embedded newform 252.2.n.b.31.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(31,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.25
Character	$\chi$	$=$	252.31
Dual form			252.2.n.b.187.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.447581 + 1.34152i) q^{2} +(-0.385748 - 1.68855i) q^{3} +(-1.59934 + 1.20088i) q^{4} +3.94623i q^{5} +(2.09257 - 1.27325i) q^{6} +(-2.37341 - 1.16916i) q^{7} +(-2.32683 - 1.60806i) q^{8} +(-2.70240 + 1.30271i) q^{9} +(-5.29393 + 1.76626i) q^{10} +4.89244i q^{11} +(2.64468 + 2.23733i) q^{12} +(1.13829 + 0.657191i) q^{13} +(0.506153 - 3.70726i) q^{14} +(6.66340 - 1.52225i) q^{15} +(1.11579 - 3.84122i) q^{16} +(1.67931 + 0.969547i) q^{17} +(-2.95715 - 3.04225i) q^{18} +(1.49477 + 2.58902i) q^{19} +(-4.73893 - 6.31137i) q^{20} +(-1.05864 + 4.45862i) q^{21} +(-6.56330 + 2.18976i) q^{22} -3.37433i q^{23} +(-1.81771 + 4.54928i) q^{24} -10.5727 q^{25} +(-0.372157 + 1.82118i) q^{26} +(3.24213 + 4.06061i) q^{27} +(5.19991 - 0.980288i) q^{28} +(-1.32976 - 2.30322i) q^{29} +(5.02453 + 8.25774i) q^{30} +(-0.443302 - 0.767822i) q^{31} +(5.65248 - 0.222403i) q^{32} +(8.26113 - 1.88725i) q^{33} +(-0.549040 + 2.68677i) q^{34} +(4.61376 - 9.36601i) q^{35} +(2.75767 - 5.32872i) q^{36} +(0.237205 + 0.410852i) q^{37} +(-2.80419 + 3.16406i) q^{38} +(0.670607 - 2.17556i) q^{39} +(6.34576 - 9.18221i) q^{40} +(8.79016 + 5.07500i) q^{41} +(-6.45515 + 0.575406i) q^{42} +(2.31047 - 1.33395i) q^{43} +(-5.87522 - 7.82469i) q^{44} +(-5.14078 - 10.6643i) q^{45} +(4.52673 - 1.51029i) q^{46} +(-1.23083 + 2.13186i) q^{47} +(-6.91651 - 0.402326i) q^{48} +(4.26614 + 5.54978i) q^{49} +(-4.73214 - 14.1835i) q^{50} +(0.989340 - 3.20959i) q^{51} +(-2.60972 + 0.315870i) q^{52} +(6.34427 - 10.9886i) q^{53} +(-3.99627 + 6.16683i) q^{54} -19.3067 q^{55} +(3.64245 + 6.53701i) q^{56} +(3.79508 - 3.52270i) q^{57} +(2.49463 - 2.81478i) q^{58} +(3.49742 + 6.05771i) q^{59} +(-8.82902 + 10.4365i) q^{60} +(2.05369 + 1.18570i) q^{61} +(0.831634 - 0.938361i) q^{62} +(7.93697 + 0.0676656i) q^{63} +(2.82830 + 7.48336i) q^{64} +(-2.59342 + 4.49194i) q^{65} +(6.22930 + 10.2378i) q^{66} +(-1.20793 + 0.697399i) q^{67} +(-3.85009 + 0.465999i) q^{68} +(-5.69773 + 1.30164i) q^{69} +(14.6297 + 1.99739i) q^{70} +2.15535i q^{71} +(8.38286 + 1.31442i) q^{72} +(3.96915 + 2.29159i) q^{73} +(-0.444996 + 0.502105i) q^{74} +(4.07840 + 17.8525i) q^{75} +(-5.49974 - 2.34569i) q^{76} +(5.72003 - 11.6118i) q^{77} +(3.21871 - 0.0741104i) q^{78} +(-8.70741 - 5.02722i) q^{79} +(15.1583 + 4.40317i) q^{80} +(5.60590 - 7.04087i) q^{81} +(-2.87390 + 14.0636i) q^{82} +(1.29635 + 2.24535i) q^{83} +(-3.66112 - 8.40216i) q^{84} +(-3.82605 + 6.62692i) q^{85} +(2.82365 + 2.50249i) q^{86} +(-3.37615 + 3.13384i) q^{87} +(7.86733 - 11.3839i) q^{88} +(-11.6706 + 6.73801i) q^{89} +(12.0054 - 11.6696i) q^{90} +(-1.93326 - 2.89062i) q^{91} +(4.05215 + 5.39671i) q^{92} +(-1.12550 + 1.04472i) q^{93} +(-3.41082 - 0.697000i) q^{94} +(-10.2169 + 5.89870i) q^{95} +(-2.55597 - 9.45870i) q^{96} +(1.88401 - 1.08773i) q^{97} +(-5.53568 + 8.20708i) q^{98} +(-6.37343 - 13.2213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28}+ \cdots + 21 q^{98}+O(q^{100}) $ 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9 - 18 * q^10 + 9 * q^12 - 18 * q^13 - 25 * q^14 - 7 * q^16 + 6 * q^17 - 13 * q^18 + 24 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^24 - 32 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 14 * q^30 + 9 * q^32 - 6 * q^33 + 24 * q^34 - 38 * q^36 + 2 * q^37 - 6 * q^41 + 7 * q^42 - 13 * q^44 - 18 * q^45 + 10 * q^46 - 9 * q^48 + 2 * q^49 - 17 * q^50 - 2 * q^53 - 42 * q^54 - 32 * q^56 + 6 * q^57 + 26 * q^58 + 8 * q^60 - 24 * q^61 - 8 * q^64 + 50 * q^65 + 27 * q^66 + 18 * q^69 - 4 * q^70 - 7 * q^72 + 30 * q^73 + 46 * q^74 + 46 * q^77 + 15 * q^78 + 3 * q^80 - 26 * q^81 - 18 * q^82 + 29 * q^84 - 50 * q^85 + 18 * q^86 - 2 * q^88 - 102 * q^89 + 39 * q^90 + 28 * q^92 - 24 * q^93 + 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.447581	+	1.34152i	0.316488	+	0.948597i
$2$	0.447581	+	1.34152i	0.316488	+	0.948597i
$3$	−0.385748	−	1.68855i	−0.222712	−	0.974884i
$3$	−0.385748	−	1.68855i	−0.222712	−	0.974884i
$4$	−1.59934	+	1.20088i	−0.799671	+	0.600438i
$5$			3.94623i			1.76481i	0.470494	+	0.882403i	$0.344076\pi$
$5$			3.94623i			1.76481i	−0.470494	+	0.882403i	$0.655924\pi$
$6$	2.09257	−	1.27325i	0.854287	−	0.519802i
$7$	−2.37341	−	1.16916i	−0.897064	−	0.441900i
$7$	−2.37341	−	1.16916i	−0.897064	−	0.441900i
$8$	−2.32683	−	1.60806i	−0.822660	−	0.568534i
$9$	−2.70240	+	1.30271i	−0.900799	+	0.434236i
$10$	−5.29393	+	1.76626i	−1.67409	+	0.558539i
$11$			4.89244i			1.47513i	0.675278	+	0.737563i	$0.264024\pi$
$11$			4.89244i			1.47513i	−0.675278	+	0.737563i	$0.735976\pi$
$12$	2.64468	+	2.23733i	0.763454	+	0.645862i
$13$	1.13829	+	0.657191i	0.315704	+	0.182272i	0.649476	−	0.760382i	$-0.274988\pi$
$13$	1.13829	+	0.657191i	0.315704	+	0.182272i	−0.333772	+	0.942654i	$0.608322\pi$
$14$	0.506153	−	3.70726i	0.135275	−	0.990808i
$15$	6.66340	−	1.52225i	1.72048	−	0.393043i
$16$	1.11579	−	3.84122i	0.278948	−	0.960306i
$17$	1.67931	+	0.969547i	0.407291	+	0.235150i	0.689625	−	0.724166i	$-0.257775\pi$
$17$	1.67931	+	0.969547i	0.407291	+	0.235150i	−0.282334	+	0.959316i	$0.591109\pi$
$18$	−2.95715	−	3.04225i	−0.697007	−	0.717065i
$19$	1.49477	+	2.58902i	0.342924	+	0.593962i	0.984974	−	0.172701i	$-0.0552493\pi$
$19$	1.49477	+	2.58902i	0.342924	+	0.593962i	−0.642050	+	0.766662i	$0.721916\pi$
$20$	−4.73893	−	6.31137i	−1.05966	−	1.41126i
$21$	−1.05864	+	4.45862i	−0.231015	+	0.972950i
$22$	−6.56330	+	2.18976i	−1.39930	+	0.466859i
$23$		−	3.37433i		−	0.703597i	−0.936076	−	0.351798i	$-0.885570\pi$
$23$		−	3.37433i		−	0.703597i	0.936076	−	0.351798i	$-0.114430\pi$
$24$	−1.81771	+	4.54928i	−0.371039	+	0.928617i
$25$	−10.5727			−2.11454
$26$	−0.372157	+	1.82118i	−0.0729861	+	0.357163i
$27$	3.24213	+	4.06061i	0.623949	+	0.781465i
$28$	5.19991	−	0.980288i	0.982690	−	0.185257i
$29$	−1.32976	−	2.30322i	−0.246931	−	0.427697i	0.715742	−	0.698365i	$-0.246089\pi$
$29$	−1.32976	−	2.30322i	−0.246931	−	0.427697i	−0.962673	+	0.270668i	$0.912755\pi$
$30$	5.02453	+	8.25774i	0.917350	+	1.50765i
$31$	−0.443302	−	0.767822i	−0.0796195	−	0.137905i	0.823466	−	0.567365i	$-0.192037\pi$
$31$	−0.443302	−	0.767822i	−0.0796195	−	0.137905i	−0.903086	+	0.429460i	$0.858704\pi$
$32$	5.65248	−	0.222403i	0.999227	−	0.0393156i
$33$	8.26113	−	1.88725i	1.43808	−	0.328528i
$34$	−0.549040	+	2.68677i	−0.0941596	+	0.460777i
$35$	4.61376	−	9.36601i	0.779868	−	1.58314i
$36$	2.75767	−	5.32872i	0.459611	−	0.888120i
$37$	0.237205	+	0.410852i	0.0389963	+	0.0675436i	0.884865	−	0.465848i	$-0.154251\pi$
$37$	0.237205	+	0.410852i	0.0389963	+	0.0675436i	−0.845869	+	0.533391i	$0.820917\pi$
$38$	−2.80419	+	3.16406i	−0.454899	+	0.513278i
$39$	0.670607	−	2.17556i	0.107383	−	0.348369i
$40$	6.34576	−	9.18221i	1.00335	−	1.45183i
$41$	8.79016	+	5.07500i	1.37279	+	0.792582i	0.991279	−	0.131781i	$-0.0420696\pi$
$41$	8.79016	+	5.07500i	1.37279	+	0.792582i	0.381514	+	0.924363i	$0.375403\pi$
$42$	−6.45515	+	0.575406i	−0.996051	+	0.0887870i
$43$	2.31047	−	1.33395i	0.352344	−	0.203426i	−0.313373	−	0.949630i	$-0.601459\pi$
$43$	2.31047	−	1.33395i	0.352344	−	0.203426i	0.665717	+	0.746204i	$0.268126\pi$
$44$	−5.87522	−	7.82469i	−0.885722	−	1.17962i
$45$	−5.14078	−	10.6643i	−0.766343	−	1.58974i
$46$	4.52673	−	1.51029i	0.667430	−	0.222680i
$47$	−1.23083	+	2.13186i	−0.179535	+	0.310963i	−0.941721	−	0.336394i	$-0.890793\pi$
$47$	−1.23083	+	2.13186i	−0.179535	+	0.310963i	0.762186	+	0.647358i	$0.224126\pi$
$48$	−6.91651	−	0.402326i	−0.998312	−	0.0580708i
$49$	4.26614	+	5.54978i	0.609449	+	0.792825i
$50$	−4.73214	−	14.1835i	−0.669226	−	2.00585i
$51$	0.989340	−	3.20959i	0.138535	−	0.449433i
$52$	−2.60972	+	0.315870i	−0.361903	+	0.0438032i
$53$	6.34427	−	10.9886i	0.871453	−	1.50940i	0.0109585	−	0.999940i	$-0.496512\pi$
$53$	6.34427	−	10.9886i	0.871453	−	1.50940i	0.860494	−	0.509460i	$-0.170155\pi$
$54$	−3.99627	+	6.16683i	−0.543823	+	0.839200i
$55$	−19.3067			−2.60331
$56$	3.64245	+	6.53701i	0.486743	+	0.873545i
$57$	3.79508	−	3.52270i	0.502671	−	0.466594i
$58$	2.49463	−	2.81478i	0.327562	−	0.369599i
$59$	3.49742	+	6.05771i	0.455325	+	0.788646i	0.998707	−	0.0508394i	$-0.0161897\pi$
$59$	3.49742	+	6.05771i	0.455325	+	0.788646i	−0.543382	+	0.839486i	$0.682856\pi$
$60$	−8.82902	+	10.4365i	−1.13982	+	1.34735i
$61$	2.05369	+	1.18570i	0.262948	+	0.151813i	0.625679	−	0.780081i	$-0.284822\pi$
$61$	2.05369	+	1.18570i	0.262948	+	0.151813i	−0.362731	+	0.931894i	$0.618156\pi$
$62$	0.831634	−	0.938361i	0.105618	−	0.119172i
$63$	7.93697	+	0.0676656i	0.999964	+	0.00852507i
$64$	2.82830	+	7.48336i	0.353538	+	0.935420i
$65$	−2.59342	+	4.49194i	−0.321675	+	0.557157i
$66$	6.22930	+	10.2378i	0.766774	+	1.26018i
$67$	−1.20793	+	0.697399i	−0.147572	+	0.0852008i	−0.571968	−	0.820276i	$-0.693820\pi$
$67$	−1.20793	+	0.697399i	−0.147572	+	0.0852008i	0.424396	+	0.905477i	$0.360487\pi$
$68$	−3.85009	+	0.465999i	−0.466892	+	0.0565107i
$69$	−5.69773	+	1.30164i	−0.685925	+	0.156699i
$70$	14.6297	+	1.99739i	1.74858	+	0.238734i
$71$			2.15535i			0.255793i	0.991788	+	0.127896i	$0.0408225\pi$
$71$			2.15535i			0.255793i	−0.991788	+	0.127896i	$0.959177\pi$
$72$	8.38286	+	1.31442i	0.987929	+	0.154906i
$73$	3.96915	+	2.29159i	0.464554	+	0.268210i	0.713957	−	0.700189i	$-0.246901\pi$
$73$	3.96915	+	2.29159i	0.464554	+	0.268210i	−0.249403	+	0.968400i	$0.580234\pi$
$74$	−0.444996	+	0.502105i	−0.0517298	+	0.0583685i
$75$	4.07840	+	17.8525i	0.470933	+	2.06143i
$76$	−5.49974	−	2.34569i	−0.630864	−	0.269070i
$77$	5.72003	−	11.6118i	0.651858	−	1.32328i
$78$	3.21871	−	0.0741104i	0.364447	−	0.00839135i
$79$	−8.70741	−	5.02722i	−0.979660	−	0.565607i	−0.0774925	−	0.996993i	$-0.524691\pi$
$79$	−8.70741	−	5.02722i	−0.979660	−	0.565607i	−0.902167	+	0.431386i	$0.858025\pi$
$80$	15.1583	+	4.40317i	1.69475	+	0.492289i
$81$	5.60590	−	7.04087i	0.622878	−	0.782319i
$82$	−2.87390	+	14.0636i	−0.317369	+	1.55307i
$83$	1.29635	+	2.24535i	0.142293	+	0.246459i	0.928360	−	0.371683i	$-0.121219\pi$
$83$	1.29635	+	2.24535i	0.142293	+	0.246459i	−0.786067	+	0.618142i	$0.787886\pi$
$84$	−3.66112	−	8.40216i	−0.399461	−	0.916750i
$85$	−3.82605	+	6.62692i	−0.414994	+	0.718790i
$86$	2.82365	+	2.50249i	0.304481	+	0.269850i
$87$	−3.37615	+	3.13384i	−0.361961	+	0.335982i
$88$	7.86733	−	11.3839i	0.838660	−	1.21353i
$89$	−11.6706	+	6.73801i	−1.23708	+	0.714227i	−0.968496	−	0.249029i	$-0.919888\pi$
$89$	−11.6706	+	6.73801i	−1.23708	+	0.714227i	−0.268582	+	0.963257i	$0.586555\pi$
$90$	12.0054	−	11.6696i	1.26548	−	1.23008i
$91$	−1.93326	−	2.89062i	−0.202661	−	0.303019i
$92$	4.05215	+	5.39671i	0.422466	+	0.562646i
$93$	−1.12550	+	1.04472i	−0.116709	+	0.108333i
$94$	−3.41082	−	0.697000i	−0.351799	−	0.0718901i
$95$	−10.2169	+	5.89870i	−1.04823	+	0.605194i
$96$	−2.55597	−	9.45870i	−0.260868	−	0.965375i
$97$	1.88401	−	1.08773i	0.191292	−	0.110442i	−0.401295	−	0.915949i	$-0.631440\pi$
$97$	1.88401	−	1.08773i	0.191292	−	0.110442i	0.592587	+	0.805506i	$0.298107\pi$
$98$	−5.53568	+	8.20708i	−0.559188	+	0.829041i
$99$	−6.37343	−	13.2213i	−0.640553	−	1.32879i
$100$	16.9094	−	12.6965i	1.69094	−	1.26965i
$101$		−	0.713750i		−	0.0710208i	−0.999369	−	0.0355104i	$-0.988694\pi$
$101$		−	0.713750i		−	0.0710208i	0.999369	−	0.0355104i	$-0.0113057\pi$
$102$	4.74853	−	0.109334i	0.470175	−	0.0108257i
$103$	1.16468			0.114760			0.0573798	−	0.998352i	$-0.481725\pi$
$103$	1.16468			0.114760			0.0573798	+	0.998352i	$0.481725\pi$
$104$	−1.59180	−	3.35961i	−0.156089	−	0.329436i
$105$	−17.5947	−	4.17764i	−1.71707	−	0.407696i
$106$	17.5810	+	3.59267i	1.70762	+	0.348951i
$107$	−10.5529	+	6.09270i	−1.02018	+	0.589004i	−0.914157	−	0.405360i	$-0.867146\pi$
$107$	−10.5529	+	6.09270i	−1.02018	+	0.589004i	−0.106027	+	0.994363i	$0.533813\pi$
$108$	−10.0616	−	2.60091i	−0.968175	−	0.250273i
$109$	−4.74875	+	8.22508i	−0.454848	+	0.787820i	−0.998679	−	0.0513747i	$-0.983640\pi$
$109$	−4.74875	+	8.22508i	−0.454848	+	0.787820i	0.543832	+	0.839194i	$0.316973\pi$
$110$	−8.64130	−	25.9003i	−0.823916	−	2.46949i
$111$	0.602242	−	0.559018i	0.0571622	−	0.0530596i
$112$	−7.13923	+	7.81226i	−0.674594	+	0.738189i
$113$	−6.24802	+	10.8219i	−0.587764	+	1.01804i	0.406761	+	0.913535i	$0.366658\pi$
$113$	−6.24802	+	10.8219i	−0.587764	+	1.01804i	−0.994525	+	0.104502i	$0.966675\pi$
$114$	6.42438	+	3.51448i	0.601698	+	0.329161i
$115$	13.3159			1.24171
$116$	4.89263	+	2.08675i	0.454269	+	0.193750i
$117$	−3.93223	−	0.293133i	−0.363535	−	0.0271001i
$118$	−6.56115	+	7.40317i	−0.604003	+	0.681517i
$119$	−2.85213	−	4.26450i	−0.261454	−	0.390927i
$120$	−17.9525	−	7.17311i	−1.63883	−	0.654812i
$121$	−12.9360			−1.17600
$122$	−0.671443	+	3.28576i	−0.0607896	+	0.297478i
$123$	5.17860	−	16.8003i	0.466939	−	1.51483i
$124$	1.63105	+	0.695659i	0.146473	+	0.0624721i
$125$		−	21.9911i		−	1.96695i
$126$	3.46166	+	10.6779i	0.308389	+	0.951260i
$127$		−	6.01418i		−	0.533672i	−0.963742	−	0.266836i	$-0.914022\pi$
$127$		−	6.01418i		−	0.533672i	0.963742	−	0.266836i	$-0.0859782\pi$
$128$	−8.77317	+	7.14363i	−0.775446	+	0.631413i
$129$	−3.14370	−	3.38678i	−0.276788	−	0.298189i
$130$	−7.18679	−	1.46862i	−0.630323	−	0.128806i
$131$	−1.99858			−0.174617			−0.0873085	−	0.996181i	$-0.527827\pi$
$131$	−1.99858			−0.174617			−0.0873085	+	0.996181i	$0.527827\pi$
$132$	−10.9460	+	12.9389i	−0.952729	+	1.12619i
$133$	−0.520732	−	7.89243i	−0.0451532	−	0.684360i
$134$	−1.47622	−	1.30832i	−0.127526	−	0.113021i
$135$	−16.0241	+	12.7942i	−1.37913	+	1.10115i
$136$	−2.34837	−	4.95639i	−0.201371	−	0.425007i
$137$	10.0616			0.859622			0.429811	−	0.902919i	$-0.358580\pi$
$137$	10.0616			0.859622			0.429811	+	0.902919i	$0.358580\pi$
$138$	−4.29637	−	7.06101i	−0.365731	−	0.601073i
$139$	8.02010	−	13.8912i	0.680256	−	1.17824i	−0.294647	−	0.955606i	$-0.595202\pi$
$139$	8.02010	−	13.8912i	0.680256	−	1.17824i	0.974903	−	0.222631i	$-0.0714646\pi$
$140$	3.86844	+	20.5200i	0.326943	+	1.73426i
$141$	4.07454	+	1.25596i	0.343138	+	0.105771i
$142$	−2.89144	+	0.964693i	−0.242644	+	0.0809553i
$143$	−3.21527	+	5.56901i	−0.268874	+	0.465704i
$144$	1.98868	+	11.8341i	0.165724	+	0.986172i
$145$	9.08903	−	5.24755i	0.754803	−	0.435785i
$146$	−1.29769	+	6.35036i	−0.107398	+	0.525560i
$147$	7.72542	−	9.34441i	0.637182	−	0.770714i
$148$	−0.872754	−	0.372238i	−0.0717400	−	0.0305978i
$149$	9.69055			0.793881			0.396940	−	0.917844i	$-0.370072\pi$
$149$	9.69055			0.793881			0.396940	+	0.917844i	$0.370072\pi$
$150$	−22.1241	+	13.4617i	−1.80642	+	1.09914i
$151$			16.5476i			1.34663i	0.739357	+	0.673314i	$0.235130\pi$
$151$			16.5476i			1.34663i	−0.739357	+	0.673314i	$0.764870\pi$
$152$	0.685211	−	8.42789i	0.0555779	−	0.683592i
$153$	−5.80119	−	0.432456i	−0.468998	−	0.0349620i
$154$	18.1376	+	2.47632i	1.46157	+	0.199548i
$155$	3.03000	−	1.74937i	0.243375	−	0.140513i
$156$	1.54005	+	4.28479i	0.123303	+	0.343058i
$157$	11.3438	−	6.54936i	0.905335	−	0.522696i	0.0264079	−	0.999651i	$-0.491593\pi$
$157$	11.3438	−	6.54936i	0.905335	−	0.522696i	0.878927	+	0.476956i	$0.158260\pi$
$158$	2.84684	−	13.9312i	0.226483	−	1.10831i
$159$	−21.0021	−	6.47378i	−1.66557	−	0.513404i
$160$	0.877652	+	22.3060i	0.0693845	+	1.76344i
$161$	−3.94512	+	8.00867i	−0.310919	+	0.631172i
$162$	11.9546	+	4.36905i	0.939238	+	0.343265i
$163$	6.95666	−	4.01643i	0.544888	−	0.314591i	−0.202170	−	0.979350i	$-0.564799\pi$
$163$	6.95666	−	4.01643i	0.544888	−	0.314591i	0.747057	+	0.664759i	$0.231466\pi$
$164$	−20.1529	+	2.43923i	−1.57368	+	0.190472i
$165$	7.44751	+	32.6003i	0.579788	+	2.53793i
$166$	−2.43195	+	2.74405i	−0.188756	+	0.212980i
$167$	−4.83680	+	8.37758i	−0.374283	+	0.648277i	−0.990219	−	0.139519i	$-0.955444\pi$
$167$	−4.83680	+	8.37758i	−0.374283	+	0.648277i	0.615937	+	0.787796i	$0.288778\pi$
$168$	9.63300	−	8.67210i	0.743202	−	0.669067i
$169$	−5.63620	−	9.76219i	−0.433554	−	0.750937i
$170$	−10.6026	−	2.16664i	−0.813182	−	0.166173i
$171$	−7.41220	−	5.04931i	−0.566825	−	0.386130i
$172$	−2.09333	+	4.90804i	−0.159615	+	0.374234i
$173$	14.1923	+	8.19394i	1.07902	+	0.622974i	0.930633	−	0.365955i	$-0.119258\pi$
$173$	14.1923	+	8.19394i	1.07902	+	0.622974i	0.148390	+	0.988929i	$0.452591\pi$
$174$	−5.71520	−	3.12652i	−0.433268	−	0.237021i
$175$	25.0933	+	12.3611i	1.89688	+	0.934415i
$176$	18.7930	+	5.45895i	1.41657	+	0.411484i
$177$	8.87962	−	8.24231i	0.667433	−	0.619530i
$178$	−14.2627	−	12.6405i	−1.06903	−	0.947444i
$179$	16.0572	+	9.27065i	1.20017	+	0.692921i	0.960594	−	0.277955i	$-0.0896567\pi$
$179$	16.0572	+	9.27065i	1.20017	+	0.692921i	0.239581	+	0.970876i	$0.422990\pi$
$180$	21.0283	+	10.8824i	1.56736	+	0.811124i
$181$		−	23.0045i		−	1.70991i	−0.518700	−	0.854956i	$-0.673584\pi$
$181$		−	23.0045i		−	1.70991i	0.518700	−	0.854956i	$-0.326416\pi$
$182$	3.01253	−	3.88729i	0.223303	−	0.288145i
$183$	1.20990	−	3.92514i	0.0894386	−	0.290154i
$184$	−5.42612	+	7.85151i	−0.400019	+	0.578821i
$185$	−1.62131	+	0.936066i	−0.119201	+	0.0688209i
$186$	−1.90527	−	1.04228i	−0.139701	−	0.0764240i
$187$	−4.74345	+	8.21590i	−0.346876	+	0.600806i
$188$	−0.591581	−	4.88764i	−0.0431455	−	0.356468i
$189$	−2.94741	−	13.4281i	−0.214393	−	0.976748i
$190$	−12.4861	−	11.0660i	−0.905836	−	0.802808i
$191$	3.41570	+	1.97206i	0.247152	+	0.142693i	0.618459	−	0.785817i	$-0.287757\pi$
$191$	3.41570	+	1.97206i	0.247152	+	0.142693i	−0.371308	+	0.928510i	$0.621090\pi$
$192$	11.5450	−	7.66242i	0.833190	−	0.552987i
$193$	−2.87501	−	4.97966i	−0.206947	−	0.358443i	0.743804	−	0.668398i	$-0.233020\pi$
$193$	−2.87501	−	4.97966i	−0.206947	−	0.358443i	−0.950751	+	0.309954i	$0.899686\pi$
$194$	2.30246	+	2.04058i	0.165307	+	0.146505i
$195$	8.58527	+	2.64637i	0.614804	+	0.189510i
$196$	−13.4876	−	3.75289i	−0.963401	−	0.268063i
$197$	−16.6012			−1.18279			−0.591393	−	0.806384i	$-0.701422\pi$
$197$	−16.6012			−1.18279			−0.591393	+	0.806384i	$0.701422\pi$
$198$	14.8840	−	14.4677i	1.05776	−	1.02817i
$199$	6.23391	−	10.7974i	0.441910	−	0.765411i	−0.555921	−	0.831235i	$-0.687634\pi$
$199$	6.23391	−	10.7974i	0.441910	−	0.765411i	0.997831	+	0.0658244i	$0.0209677\pi$
$200$	24.6009	+	17.0015i	1.73955	+	1.20219i
$201$	1.64355	+	1.77063i	0.115927	+	0.124891i
$202$	0.957509	−	0.319461i	0.0673701	−	0.0224772i
$203$	0.463249	+	7.02119i	0.0325137	+	0.492791i
$204$	2.27203	+	6.32131i	0.159074	+	0.442580i
$205$	−20.0271	+	34.6880i	−1.39875	+	2.42271i
$206$	0.521290	+	1.56244i	0.0363200	+	0.108861i
$207$	4.39577	+	9.11878i	0.305527	+	0.633799i
$208$	3.79451	−	3.63913i	0.263102	−	0.252328i
$209$	−12.6666	+	7.31308i	−0.876169	+	0.505856i
$210$	−2.27068	−	25.4735i	−0.156692	−	1.75784i
$211$	−19.4166	−	11.2102i	−1.33669	−	0.771739i	−0.350376	−	0.936609i	$-0.613946\pi$
$211$	−19.4166	−	11.2102i	−1.33669	−	0.771739i	−0.986315	+	0.164870i	$0.947279\pi$
$212$	3.04929	+	25.1932i	0.209426	+	1.73028i
$213$	3.63941	−	0.831422i	0.249369	−	0.0569681i
$214$	−12.8967	−	11.4299i	−0.881603	−	0.781331i
$215$	5.26408	+	9.11765i	0.359007	+	0.621819i
$216$	−1.01420	−	14.6619i	−0.0690075	−	0.997616i
$217$	0.154433	+	2.34065i	0.0104836	+	0.158893i
$218$	−13.1595	−	2.68915i	−0.891277	−	0.182132i
$219$	2.33837	−	7.58608i	0.158013	−	0.512620i
$220$	30.8780	−	23.1849i	2.08179	−	1.56313i
$221$	1.27436	+	2.20725i	0.0857224	+	0.148476i
$222$	1.01948	+	0.557712i	0.0684233	+	0.0374312i
$223$	4.48502	+	7.76829i	0.300339	+	0.520203i	0.976213	−	0.216815i	$-0.0695668\pi$
$223$	4.48502	+	7.76829i	0.300339	+	0.520203i	−0.675873	+	0.737018i	$0.736233\pi$
$224$	−13.6757	−	6.08079i	−0.913744	−	0.406290i
$225$	28.5716	−	13.7732i	1.90478	−	0.918210i
$226$	−17.3142	−	3.53816i	−1.15173	−	0.235355i
$227$	7.79377			0.517291			0.258645	−	0.965972i	$-0.416724\pi$
$227$	7.79377			0.517291			0.258645	+	0.965972i	$0.416724\pi$
$228$	−1.83930	+	10.1914i	−0.121811	+	0.674944i
$229$			6.80092i			0.449417i	0.974426	+	0.224709i	$0.0721430\pi$
$229$			6.80092i			0.449417i	−0.974426	+	0.224709i	$0.927857\pi$
$230$	5.95993	+	17.8635i	0.392986	+	1.17788i
$231$	−21.8135	−	5.17934i	−1.43522	−	0.340776i
$232$	−0.609571	+	7.49755i	−0.0400203	+	0.492238i
$233$	8.45700	+	14.6480i	0.554037	+	0.959619i	0.997978	+	0.0635635i	$0.0202466\pi$
$233$	8.45700	+	14.6480i	0.554037	+	0.959619i	−0.443941	+	0.896056i	$0.646420\pi$
$234$	−1.36675	−	5.40636i	−0.0893473	−	0.353425i
$235$	−8.41279	−	4.85713i	−0.548790	−	0.316844i
$236$	−12.8681	−	5.48838i	−0.837644	−	0.357263i
$237$	−5.12985	+	16.6421i	−0.333220	+	1.08102i
$238$	4.44435	−	5.73489i	0.288085	−	0.371738i
$239$	16.8495	+	9.72804i	1.08990	+	0.629254i	0.933550	−	0.358447i	$-0.116694\pi$
$239$	16.8495	+	9.72804i	1.08990	+	0.629254i	0.156351	+	0.987702i	$0.450027\pi$
$240$	1.58767	−	27.2941i	0.102484	−	1.76183i
$241$		−	23.5574i		−	1.51747i	−0.651401	−	0.758734i	$-0.725818\pi$
$241$		−	23.5574i		−	1.51747i	0.651401	−	0.758734i	$-0.274182\pi$
$242$	−5.78990	−	17.3539i	−0.372189	−	1.11555i
$243$	−14.0513	−	6.74983i	−0.901393	−	0.433002i
$244$	−4.70843	+	0.569889i	−0.301426	+	0.0364834i
$245$	−21.9007	+	16.8352i	−1.39918	+	1.07556i
$246$	24.8557	−	0.572300i	1.58474	−	0.0364885i
$247$			3.92940i			0.250022i
$248$	−0.203212	+	2.49945i	−0.0129040	+	0.158715i
$249$	3.29131	−	3.05509i	0.208578	−	0.193609i
$250$	29.5015	−	9.84281i	1.86584	−	0.622514i
$251$	−4.53190			−0.286051			−0.143026	−	0.989719i	$-0.545683\pi$
$251$	−4.53190			−0.286051			−0.143026	+	0.989719i	$0.545683\pi$
$252$	−12.7752	+	9.42309i	−0.804761	+	0.593599i
$253$	16.5087			1.03789
$254$	8.06813	−	2.69183i	0.506240	−	0.168901i
$255$	12.6658	+	3.90416i	0.793161	+	0.244488i
$256$	−13.5100	−	8.57202i	−0.844376	−	0.535751i
$257$		−	23.8841i		−	1.48985i	−0.667149	−	0.744924i	$-0.732486\pi$
$257$		−	23.8841i		−	1.48985i	0.667149	−	0.744924i	$-0.267514\pi$
$258$	3.13636	−	5.73319i	0.195261	−	0.356933i
$259$	−0.0826350	−	1.25245i	−0.00513469	−	0.0778234i
$260$	−1.24649	−	10.2985i	−0.0773042	−	0.638688i
$261$	6.59398	+	4.49192i	0.408157	+	0.278043i
$262$	−0.894528	−	2.68113i	−0.0552641	−	0.165641i
$263$		−	27.2015i		−	1.67732i	−0.544656	−	0.838660i	$-0.683340\pi$
$263$		−	27.2015i		−	1.67732i	0.544656	−	0.838660i	$-0.316660\pi$
$264$	−22.2571	−	8.89306i	−1.36983	−	0.547330i
$265$	43.3635	+	25.0359i	2.66380	+	1.53794i
$266$	10.3548	−	4.23107i	0.634891	−	0.259424i
$267$	15.8794	+	17.1072i	0.971801	+	1.04694i
$268$	1.09440	−	2.56595i	0.0668514	−	0.156741i
$269$	15.8637	+	9.15891i	0.967227	+	0.558429i	0.898390	−	0.439199i	$-0.144738\pi$
$269$	15.8637	+	9.15891i	0.967227	+	0.558429i	0.0688372	+	0.997628i	$0.478071\pi$
$270$	−24.3357	−	15.7702i	−1.48102	−	0.959743i
$271$	0.772505	+	1.33802i	0.0469264	+	0.0812788i	0.888535	−	0.458810i	$-0.151724\pi$
$271$	0.772505	+	1.33802i	0.0469264	+	0.0812788i	−0.841608	+	0.540089i	$0.818391\pi$
$272$	5.59801	−	5.36878i	0.339429	−	0.325530i
$273$	−4.13520	+	4.37946i	−0.250274	+	0.265057i
$274$	4.50339	+	13.4978i	0.272060	+	0.815435i
$275$		−	51.7263i		−	3.11921i
$276$	7.54950	−	8.92403i	0.454427	−	0.537164i
$277$	0.486092			0.0292065			0.0146032	−	0.999893i	$-0.495351\pi$
$277$	0.486092			0.0292065			0.0146032	+	0.999893i	$0.495351\pi$
$278$	22.2250	+	4.54166i	1.33296	+	0.272391i
$279$	2.19823	+	1.49747i	0.131604	+	0.0896510i
$280$	−25.7965	+	14.3739i	−1.54164	+	0.859007i
$281$	−13.1672	−	22.8062i	−0.785489	−	1.36051i	−0.928707	−	0.370815i	$-0.879078\pi$
$281$	−13.1672	−	22.8062i	−0.785489	−	1.36051i	0.143218	−	0.989691i	$-0.454255\pi$
$282$	0.138799	+	6.02821i	0.00826535	+	0.358975i
$283$	8.58849	+	14.8757i	0.510533	+	0.884268i	0.999926	+	0.0122050i	$0.00388506\pi$
$283$	8.58849	+	14.8757i	0.510533	+	0.884268i	−0.489393	+	0.872063i	$0.662782\pi$
$284$	−2.58831	−	3.44714i	−0.153588	−	0.204550i
$285$	13.9014	+	14.9763i	0.823447	+	0.887117i
$286$	−8.91002	−	1.82076i	−0.526860	−	0.107664i
$287$	−14.9292	−	22.3221i	−0.881241	−	1.31763i
$288$	−14.9855	+	7.96456i	−0.883030	+	0.469316i
$289$	−6.61996	−	11.4661i	−0.389409	−	0.674476i
$290$	11.1078	+	9.84439i	0.652270	+	0.578082i
$291$	−2.56344	−	2.76165i	−0.150271	−	0.161891i
$292$	−9.09995	+	1.10142i	−0.532534	+	0.0644558i
$293$	−21.5170	−	12.4229i	−1.25704	−	0.725751i	−0.284540	−	0.958664i	$-0.591841\pi$
$293$	−21.5170	−	12.4229i	−1.25704	−	0.725751i	−0.972498	+	0.232913i	$0.925174\pi$
$294$	15.9934	+	6.18141i	0.932756	+	0.360507i
$295$	−23.9051	+	13.8016i	−1.39181	+	0.803561i
$296$	0.108736	−	1.33742i	0.00632016	−	0.0777361i
$297$	−19.8663	+	15.8619i	−1.15276	+	0.920403i
$298$	4.33730	+	13.0000i	0.251253	+	0.753072i
$299$	2.21758	−	3.84096i	0.128246	−	0.222128i
$300$	−27.9614	−	23.6546i	−1.61435	−	1.36570i
$301$	−7.04330	+	0.464708i	−0.405969	+	0.0267853i
$302$	−22.1990	+	7.40641i	−1.27741	+	0.426191i
$303$	−1.20520	+	0.275328i	−0.0692370	+	0.0158172i
$304$	11.6129	−	2.85294i	0.666043	−	0.163627i
$305$	−4.67903	+	8.10432i	−0.267921	+	0.464052i
$306$	−2.01635	−	7.97596i	−0.115267	−	0.455955i
$307$	32.0881			1.83136			0.915682	−	0.401904i	$-0.131652\pi$
$307$	32.0881			1.83136			0.915682	+	0.401904i	$0.131652\pi$
$308$	4.79600	+	25.4402i	0.273277	+	1.44959i
$309$	−0.449274	−	1.96662i	−0.0255583	−	0.111877i
$310$	3.70298	+	3.28181i	0.210315	+	0.186395i
$311$	−6.52427	−	11.3004i	−0.369957	−	0.640785i	0.619601	−	0.784917i	$-0.287294\pi$
$311$	−6.52427	−	11.3004i	−0.369957	−	0.640785i	−0.989559	+	0.144132i	$0.953961\pi$
$312$	−5.05882	+	3.98380i	−0.286399	+	0.225538i
$313$	11.5365	+	6.66061i	0.652083	+	0.376480i	0.789254	−	0.614067i	$-0.210468\pi$
$313$	11.5365	+	6.66061i	0.652083	+	0.376480i	−0.137171	+	0.990547i	$0.543801\pi$
$314$	13.8634	+	12.2866i	0.782355	+	0.693371i
$315$	−0.267024	+	31.3211i	−0.0150451	+	1.76474i
$316$	19.9632	−	2.41627i	1.12302	−	0.135926i
$317$	9.82677	−	17.0205i	0.551927	−	0.955965i	−0.446209	−	0.894929i	$-0.647226\pi$
$317$	9.82677	−	17.0205i	0.551927	−	0.955965i	0.998136	−	0.0610362i	$-0.0194405\pi$
$318$	−0.715434	−	31.0722i	−0.0401196	−	1.74244i
$319$	11.2684	−	6.50579i	0.630907	−	0.364255i
$320$	−29.5310	+	11.1611i	−1.65084	+	0.623925i
$321$	14.3586	+	15.4688i	0.801417	+	0.863384i
$322$	−12.5095	−	1.70793i	−0.697129	−	0.0951791i
$323$			5.79701i			0.322554i
$324$	−0.510534	+	17.9928i	−0.0283630	+	0.999598i
$325$	−12.0348	−	6.94828i	−0.667569	−	0.385421i
$326$	8.50178	+	7.53481i	0.470870	+	0.417314i
$327$	15.7203	+	4.84569i	0.869333	+	0.267967i
$328$	−12.2923	−	25.9438i	−0.678731	−	1.43250i
$329$	5.41374	−	3.62074i	0.298469	−	0.199618i
$330$	−40.4005	+	24.5822i	−2.22397	+	1.35321i
$331$	12.4763	+	7.20320i	0.685760	+	0.395924i	0.802022	−	0.597295i	$-0.203758\pi$
$331$	12.4763	+	7.20320i	0.685760	+	0.395924i	−0.116262	+	0.993219i	$0.537091\pi$
$332$	−4.76969	−	2.03432i	−0.261771	−	0.111648i
$333$	−1.17624	−	0.801275i	−0.0644577	−	0.0439096i
$334$	−13.4035	−	2.73901i	−0.733409	−	0.149872i
$335$	−2.75209	−	4.76677i	−0.150363	−	0.260436i
$336$	15.9453	+	9.04137i	0.869889	+	0.493247i
$337$	−0.489878	+	0.848494i	−0.0266854	+	0.0462204i	−0.879060	−	0.476712i	$-0.841829\pi$
$337$	−0.489878	+	0.848494i	−0.0266854	+	0.0462204i	0.852374	+	0.522932i	$0.175162\pi$
$338$	10.5735	−	11.9304i	0.575122	−	0.648930i
$339$	20.6834	+	6.37556i	1.12337	+	0.346273i
$340$	−1.83894	−	15.1933i	−0.0997305	−	0.823974i
$341$	3.75652	−	2.16883i	0.203427	−	0.117449i
$342$	3.45618	−	12.2036i	0.186889	−	0.659894i
$343$	−3.63674	−	18.1597i	−0.196365	−	0.980531i
$344$	−7.52116	−	0.611491i	−0.405514	−	0.0329694i
$345$	−5.13657	−	22.4845i	−0.276544	−	1.21053i
$346$	−4.64011	+	22.7067i	−0.249454	+	1.22072i
$347$	23.7580	−	13.7167i	1.27540	−	0.736351i	0.299399	−	0.954128i	$-0.403214\pi$
$347$	23.7580	−	13.7167i	1.27540	−	0.736351i	0.975998	+	0.217777i	$0.0698807\pi$
$348$	1.63627	−	9.06641i	0.0877130	−	0.486011i
$349$	−13.0352	+	7.52589i	−0.697760	+	0.402852i	−0.806512	−	0.591217i	$-0.798648\pi$
$349$	−13.0352	+	7.52589i	−0.697760	+	0.402852i	0.108753	+	0.994069i	$0.465314\pi$
$350$	−5.35140	+	39.1958i	−0.286045	+	2.09510i
$351$	1.02188	+	6.75285i	0.0545441	+	0.360440i
$352$	1.08809	+	27.6544i	0.0579955	+	1.47399i
$353$			18.5070i			0.985026i	0.870305	+	0.492513i	$0.163922\pi$
$353$			18.5070i			0.985026i	−0.870305	+	0.492513i	$0.836078\pi$
$354$	15.0316	+	8.22306i	0.798918	+	0.437051i
$355$	−8.50550			−0.451425
$356$	10.5737	−	24.7913i	0.560407	−	1.31394i
$357$	−6.10062	+	6.46098i	−0.322879	+	0.341951i
$358$	−5.24983	+	25.6904i	−0.277462	+	1.35778i
$359$	−5.04854	+	2.91478i	−0.266452	+	0.153836i	−0.627274	−	0.778799i	$-0.715829\pi$
$359$	−5.04854	+	2.91478i	−0.266452	+	0.153836i	0.360822	+	0.932635i	$0.382496\pi$
$360$	−5.18702	+	33.0806i	−0.273380	+	1.74350i
$361$	5.03132	−	8.71450i	0.264806	−	0.458658i
$362$	30.8610	−	10.2964i	1.62202	−	0.541166i
$363$	4.99003	+	21.8430i	0.261909	+	1.14646i
$364$	6.56323	+	2.30148i	0.344007	+	0.120630i
$365$	−9.04313	+	15.6632i	−0.473339	+	0.819848i
$366$	5.80717	−	0.133709i	0.303546	−	0.00698910i
$367$	−1.80797			−0.0943752			−0.0471876	−	0.998886i	$-0.515026\pi$
$367$	−1.80797			−0.0943752			−0.0471876	+	0.998886i	$0.515026\pi$
$368$	−12.9616	−	3.76505i	−0.675668	−	0.196267i
$369$	−30.3658	−	2.26365i	−1.58078	−	0.117841i
$370$	−1.98142	−	1.75606i	−0.103009	−	0.0912930i
$371$	−27.9050	+	18.6630i	−1.44875	+	0.968934i
$372$	0.545480	−	3.02246i	0.0282818	−	0.156707i
$373$	−5.95914			−0.308553			−0.154276	−	0.988028i	$-0.549305\pi$
$373$	−5.95914			−0.308553			−0.154276	+	0.988028i	$0.549305\pi$
$374$	−13.1449	−	2.68615i	−0.679705	−	0.138897i
$375$	−37.1331	+	8.48303i	−1.91755	+	0.438062i
$376$	6.29208	−	2.98123i	0.324489	−	0.153745i
$377$		−	3.49564i		−	0.180034i
$378$	16.6948	−	9.96415i	0.858687	−	0.512501i
$379$			16.5311i			0.849146i	0.905394	+	0.424573i	$0.139576\pi$
$379$			16.5311i			0.849146i	−0.905394	+	0.424573i	$0.860424\pi$
$380$	9.25664	−	21.7032i	0.474855	−	1.11335i
$381$	−10.1552	+	2.31996i	−0.520269	+	0.118855i
$382$	−1.11675	+	5.46489i	−0.0571378	+	0.279608i
$383$	−3.29801			−0.168520			−0.0842601	−	0.996444i	$-0.526853\pi$
$383$	−3.29801			−0.168520			−0.0842601	+	0.996444i	$0.526853\pi$
$384$	15.4466	+	12.0583i	0.788256	+	0.615347i
$385$	45.8226	+	22.5725i	2.33534	+	1.15040i
$386$	5.39350	−	6.08567i	0.274522	−	0.309753i
$387$	−4.50606	+	6.61474i	−0.229056	+	0.336246i
$388$	−1.70694	+	4.00211i	−0.0866567	+	0.203176i
$389$	9.64882			0.489215			0.244607	−	0.969622i	$-0.421341\pi$
$389$	9.64882			0.489215			0.244607	+	0.969622i	$0.421341\pi$
$390$	0.292457	+	12.7018i	0.0148091	+	0.643179i
$391$	3.27157	−	5.66653i	0.165451	−	0.286569i
$392$	−1.00224	−	19.7736i	−0.0506206	−	0.998718i
$393$	0.770949	+	3.37470i	0.0388892	+	0.170231i
$394$	−7.43037	−	22.2708i	−0.374337	−	1.12199i
$395$	19.8386	−	34.3614i	0.998186	−	1.72891i
$396$	26.0705	+	13.4917i	1.31009	+	0.677984i
$397$	−3.22184	+	1.86013i	−0.161700	+	0.0933573i	−0.578666	−	0.815565i	$-0.696427\pi$
$397$	−3.22184	+	1.86013i	−0.161700	+	0.0933573i	0.416967	+	0.908922i	$0.363093\pi$
$398$	17.2751	+	3.53017i	0.865925	+	0.176951i
$399$	−13.1259	+	3.92377i	−0.657116	+	0.196434i
$400$	−11.7969	+	40.6121i	−0.589847	+	2.03061i
$401$	−23.9720			−1.19711			−0.598553	−	0.801083i	$-0.704257\pi$
$401$	−23.9720			−1.19711			−0.598553	+	0.801083i	$0.704257\pi$
$402$	−1.63971	+	2.99735i	−0.0817813	+	0.149494i
$403$		−	1.16534i		−	0.0580496i
$404$	0.857125	+	1.14153i	0.0426436	+	0.0567933i
$405$	27.7849	+	22.1221i	1.38064	+	1.09926i
$406$	−9.21171	+	3.76401i	−0.457169	+	0.186805i
$407$	−2.01007	+	1.16051i	−0.0996353	+	0.0575245i
$408$	−7.46324	+	5.87727i	−0.369485	+	0.290968i
$409$	−19.1868	+	11.0775i	−0.948726	+	0.547747i	−0.892685	−	0.450681i	$-0.851181\pi$
$409$	−19.1868	+	11.0775i	−0.948726	+	0.547747i	−0.0560410	+	0.998428i	$0.517848\pi$
$410$	−55.4983	−	11.3411i	−2.74087	−	0.560095i
$411$	−3.88125	−	16.9895i	−0.191448	−	0.838032i
$412$	−1.86273	+	1.39864i	−0.0917700	+	0.0689061i
$413$	−1.21839	−	18.4665i	−0.0599532	−	0.908675i
$414$	−10.2656	+	9.97840i	−0.504524	+	0.490412i
$415$	−8.86064	+	5.11570i	−0.434952	+	0.251120i
$416$	6.58031	+	3.46160i	0.322626	+	0.169719i
$417$	−26.5497	−	8.18382i	−1.30015	−	0.400763i
$418$	−15.4800	−	13.7193i	−0.757150	−	0.671034i
$419$	−17.6835	+	30.6287i	−0.863895	+	1.49631i	0.00424524	+	0.999991i	$0.498649\pi$
$419$	−17.6835	+	30.6287i	−0.863895	+	1.49631i	−0.868140	+	0.496319i	$0.834685\pi$
$420$	33.1568	−	14.4476i	1.61789	−	0.704971i
$421$	−15.4856	−	26.8219i	−0.754723	−	1.30722i	−0.945512	−	0.325588i	$-0.894438\pi$
$421$	−15.4856	−	26.8219i	−0.754723	−	1.30722i	0.190788	−	0.981631i	$-0.438896\pi$
$422$	6.34815	−	31.0651i	0.309023	−	1.51223i
$423$	0.548997	−	7.36454i	0.0266932	−	0.358076i
$424$	−32.4324	+	15.3667i	−1.57505	+	0.746272i
$425$	−17.7548	−	10.2507i	−0.861234	−	0.497234i
$426$	2.74430	+	4.51021i	0.132962	+	0.218520i
$427$	−3.48798	−	5.21523i	−0.168795	−	0.252383i
$428$	9.56107	−	22.4170i	0.462152	−	1.08357i
$429$	10.6438	+	3.28090i	0.513889	+	0.158404i
$430$	−9.87539	+	11.1427i	−0.476234	+	0.537351i
$431$	4.22345	+	2.43841i	0.203437	+	0.117454i	0.598257	−	0.801304i	$-0.295860\pi$
$431$	4.22345	+	2.43841i	0.203437	+	0.117454i	−0.394821	+	0.918758i	$0.629193\pi$
$432$	19.2153	−	7.92296i	0.924495	−	0.381193i
$433$		−	13.0744i		−	0.628314i	−0.949371	−	0.314157i	$-0.898278\pi$
$433$		−	13.0744i		−	0.628314i	0.949371	−	0.314157i	$-0.101722\pi$
$434$	−3.07090	+	1.25480i	−0.147408	+	0.0602325i
$435$	−12.3668	−	13.3230i	−0.592944	−	0.638791i
$436$	−2.28242	−	18.8574i	−0.109308	−	0.903105i
$437$	8.73621	−	5.04385i	0.417910	−	0.241280i
$438$	11.2235	−	0.258419i	0.536279	−	0.0123478i
$439$	−0.958667	+	1.66046i	−0.0457547	+	0.0792494i	−0.887996	−	0.459852i	$-0.847903\pi$
$439$	−0.958667	+	1.66046i	−0.0457547	+	0.0792494i	0.842241	+	0.539101i	$0.181236\pi$
$440$	44.9234	+	31.0463i	2.14164	+	1.48007i
$441$	−18.7586	−	9.44016i	−0.893265	−	0.449531i
$442$	−2.39069	+	2.69749i	−0.113713	+	0.128307i
$443$	18.4381	+	10.6452i	0.876020	+	0.505770i	0.869344	−	0.494207i	$-0.164542\pi$
$443$	18.4381	+	10.6452i	0.876020	+	0.505770i	0.00667575	+	0.999978i	$0.497875\pi$
$444$	−0.291879	+	1.61728i	−0.0138520	+	0.0767527i
$445$	−26.5897	−	46.0547i	−1.26047	−	2.18320i
$446$	−8.41389	+	9.49368i	−0.398409	+	0.449539i
$447$	−3.73811	−	16.3630i	−0.176806	−	0.773942i
$448$	2.03651	−	21.0678i	0.0962162	−	0.995360i
$449$	5.99969			0.283143			0.141572	−	0.989928i	$-0.454784\pi$
$449$	5.99969			0.283143			0.141572	+	0.989928i	$0.454784\pi$
$450$	31.2651	+	32.1648i	1.47385	+	1.51626i
$451$	−24.8291	+	43.0053i	−1.16916	+	2.02504i
$452$	−3.00302	−	24.8110i	−0.141250	−	1.16701i
$453$	27.9415	−	6.38322i	1.31281	−	0.299910i
$454$	3.48834	+	10.4555i	0.163716	+	0.490700i
$455$	11.4070	−	7.62909i	0.534770	−	0.357657i
$456$	−14.4952	+	2.09403i	−0.678801	+	0.0980620i
$457$	12.6676	−	21.9408i	0.592563	−	1.02635i	−0.401323	−	0.915937i	$-0.631449\pi$
$457$	12.6676	−	21.9408i	0.592563	−	1.02635i	0.993886	−	0.110413i	$-0.0352173\pi$
$458$	−9.12356	+	3.04396i	−0.426316	+	0.142235i
$459$	1.50757	+	9.96241i	0.0703675	+	0.465005i
$460$	−21.2966	+	15.9907i	−0.992961	+	0.745571i
$461$	17.3693	−	10.0282i	0.808970	−	0.467059i	−0.0376278	−	0.999292i	$-0.511980\pi$
$461$	17.3693	−	10.0282i	0.808970	−	0.467059i	0.846598	+	0.532233i	$0.178647\pi$
$462$	−2.81514	−	31.5814i	−0.130972	−	1.46930i
$463$	33.2880	+	19.2188i	1.54702	+	0.893175i	0.998367	+	0.0571279i	$0.0181943\pi$
$463$	33.2880	+	19.2188i	1.54702	+	0.893175i	0.548658	+	0.836047i	$0.315139\pi$
$464$	−10.3309	+	2.53801i	−0.479601	+	0.117824i
$465$	−4.12272	−	4.44149i	−0.191186	−	0.205969i
$466$	−15.8653	+	17.9014i	−0.734946	+	0.829265i
$467$	−16.3595	−	28.3355i	−0.757028	−	1.31121i	−0.944360	−	0.328914i	$-0.893317\pi$
$467$	−16.3595	−	28.3355i	−0.757028	−	1.31121i	0.187332	−	0.982297i	$-0.440016\pi$
$468$	6.64100	−	4.25331i	0.306981	−	0.196609i
$469$	3.68228	−	0.242952i	0.170032	−	0.0112185i
$470$	2.75052	−	13.4599i	0.126872	−	0.620858i
$471$	−15.4348	−	16.6282i	−0.711196	−	0.766187i
$472$	1.60323	−	19.7193i	0.0737949	−	0.907656i
$473$	6.52628	+	11.3039i	0.300079	+	0.519752i
$474$	−24.6217	+	0.566913i	−1.13091	+	0.0260392i
$475$	−15.8038	−	27.3729i	−0.725126	−	1.25596i
$476$	9.68267	+	3.39535i	0.443804	+	0.155626i
$477$	−2.82979	+	37.9603i	−0.129567	+	1.73808i
$478$	−5.50884	+	26.9579i	−0.251969	+	1.23303i
$479$	−36.7966			−1.68128			−0.840639	−	0.541595i	$-0.817820\pi$
$479$	−36.7966			−1.68128			−0.840639	+	0.541595i	$0.817820\pi$
$480$	37.3262	−	10.0864i	1.70370	−	0.460381i
$481$			0.623556i			0.0284317i
$482$	31.6027	−	10.5439i	1.43946	−	0.480259i
$483$	15.0449	+	3.57221i	0.684565	+	0.162541i
$484$	20.6891	−	15.5345i	0.940412	−	0.706114i
$485$	4.29243	+	7.43471i	0.194909	+	0.337593i
$486$	2.76592	−	21.8712i	0.125465	−	0.992098i
$487$	−3.93075	−	2.26942i	−0.178119	−	0.102837i	0.408289	−	0.912853i	$-0.366125\pi$
$487$	−3.93075	−	2.26942i	−0.178119	−	0.102837i	−0.586409	+	0.810015i	$0.699459\pi$
$488$	−2.87192	−	6.06137i	−0.130006	−	0.274385i
$489$	−9.46546	−	10.1973i	−0.428043	−	0.461139i
$490$	−32.3870	−	21.8451i	−1.46310	−	0.986859i
$491$	10.6660	+	6.15804i	0.481351	+	0.277908i	0.720980	−	0.692956i	$-0.243692\pi$
$491$	10.6660	+	6.15804i	0.481351	+	0.277908i	−0.239628	+	0.970865i	$0.577025\pi$
$492$	11.8927	+	33.0883i	0.536165	+	1.49174i
$493$		−	5.15708i		−	0.232263i
$494$	−5.27136	+	1.75872i	−0.237170	+	0.0791288i
$495$	52.1743	−	25.1510i	2.34506	−	1.13045i
$496$	−3.44401	+	0.846093i	−0.154641	+	0.0379907i
$497$	2.51994	−	5.11553i	0.113035	−	0.229463i
$498$	5.57159	+	3.04796i	0.249669	+	0.136582i
$499$			12.9516i			0.579793i	0.957058	+	0.289896i	$0.0936209\pi$
$499$			12.9516i			0.579793i	−0.957058	+	0.289896i	$0.906379\pi$
$500$	26.4086	+	35.1713i	1.18103	+	1.57291i
$501$	16.0117	+	4.93554i	0.715352	+	0.220504i
$502$	−2.02839	−	6.07963i	−0.0905316	−	0.271347i
$503$	20.4872			0.913480			0.456740	−	0.889600i	$-0.349017\pi$
$503$	20.4872			0.913480			0.456740	+	0.889600i	$0.349017\pi$
$504$	−18.3592	−	12.9205i	−0.817783	−	0.575527i
$505$	2.81662			0.125338
$506$	7.38899	+	22.1467i	0.328481	+	0.984543i
$507$	−14.3098	+	13.2827i	−0.635520	+	0.589907i
$508$	7.22229	+	9.61873i	0.320437	+	0.426762i
$509$			28.4509i			1.26107i	0.776163	+	0.630533i	$0.217163\pi$
$509$			28.4509i			1.26107i	−0.776163	+	0.630533i	$0.782837\pi$
$510$	0.431458	+	18.7388i	0.0191053	+	0.829768i
$511$	−6.74119	−	10.0794i	−0.298213	−	0.445888i
$512$	5.45270	−	21.9606i	0.240977	−	0.970531i
$513$	−5.66676	+	14.4636i	−0.250194	+	0.638585i
$514$	32.0409	−	10.6901i	1.41327	−	0.471519i
$515$			4.59610i			0.202528i
$516$	9.09496	+	1.64142i	0.400383	+	0.0722594i
$517$	−10.4300	−	6.02176i	−0.458710	−	0.264837i
$518$	1.64320	−	0.671429i	0.0721980	−	0.0295009i
$519$	8.36122	−	27.1252i	0.367017	−	1.19067i
$520$	13.2578	−	6.28162i	0.581391	−	0.275467i
$521$	32.0751	+	18.5186i	1.40524	+	0.811314i	0.994924	−	0.100630i	$-0.0320858\pi$
$521$	32.0751	+	18.5186i	1.40524	+	0.811314i	0.410314	+	0.911944i	$0.365419\pi$
$522$	−3.07465	+	10.8564i	−0.134574	+	0.475173i
$523$	2.33168	+	4.03859i	0.101957	+	0.176595i	0.912491	−	0.409097i	$-0.134156\pi$
$523$	2.33168	+	4.03859i	0.101957	+	0.176595i	−0.810534	+	0.585692i	$0.800823\pi$
$524$	3.19642	−	2.40005i	0.139636	−	0.104847i
$525$	11.1927	−	47.1396i	0.488490	−	2.05734i
$526$	36.4914	−	12.1749i	1.59110	−	0.530851i
$527$		−	1.71921i		−	0.0748900i
$528$	1.96836	−	33.8386i	0.0856618	−	1.47264i
$529$	11.6139			0.504952
$530$	−14.1775	+	69.3785i	−0.615830	+	3.01361i
$531$	−17.3428	−	11.8142i	−0.752615	−	0.512693i
$532$	10.3107	+	11.9974i	0.447024	+	0.520151i
$533$	6.67049	+	11.5536i	0.288931	+	0.500443i
$534$	−15.8423	+	28.9593i	−0.685562	+	1.25319i
$535$	−24.0432	−	41.6440i	−1.03948	−	1.80043i
$536$	3.93211	+	0.319691i	0.169841	+	0.0138086i
$537$	9.45990	−	30.6896i	0.408225	−	1.32435i
$538$	−5.18656	+	25.3808i	−0.223608	+	1.09424i
$539$	−27.1520	+	20.8718i	−1.16952	+	0.899014i
$540$	10.2638	−	39.7052i	0.441683	−	1.70864i
$541$	11.6836	+	20.2366i	0.502318	+	0.870040i	0.999996	+	0.00267870i	$0.000852658\pi$
$541$	11.6836	+	20.2366i	0.502318	+	0.870040i	−0.497678	+	0.867362i	$0.665814\pi$
$542$	−1.44922	+	1.63520i	−0.0622492	+	0.0702379i
$543$	−38.8443	+	8.87395i	−1.66697	+	0.380817i
$544$	9.70787	+	5.10687i	0.416222	+	0.218955i
$545$	−32.4580	−	18.7396i	−1.39035	−	0.802718i
$546$	−7.72596	−	3.58729i	−0.330641	−	0.153522i
$547$	−21.8092	+	12.5915i	−0.932493	+	0.538375i	−0.887599	−	0.460617i	$-0.847628\pi$
$547$	−21.8092	+	12.5915i	−0.932493	+	0.538375i	−0.0448939	+	0.998992i	$0.514295\pi$
$548$	−16.0920	+	12.0828i	−0.687415	+	0.516150i
$549$	−7.09450	−	0.528867i	−0.302786	−	0.0225715i
$550$	69.3918	−	23.1517i	2.95888	−	0.987192i
$551$	3.97539	−	6.88557i	0.169357	−	0.293335i
$552$	15.3508	+	6.13357i	0.653372	+	0.261062i
$553$	14.7886	+	22.1120i	0.628876	+	0.940297i
$554$	0.217566	+	0.652102i	0.00924348	+	0.0277051i
$555$	2.20601	+	2.37658i	0.0936400	+	0.100880i
$556$	3.85475	+	31.8480i	0.163478	+	1.35065i
$557$	−3.17042	+	5.49134i	−0.134335	+	0.232675i	−0.925343	−	0.379130i	$-0.876223\pi$
$557$	−3.17042	+	5.49134i	−0.134335	+	0.232675i	0.791008	+	0.611806i	$0.209557\pi$
$558$	−1.02499	+	3.61920i	−0.0433914	+	0.153213i
$559$	3.50664			0.148315
$560$	−30.8289	−	28.1730i	−1.30276	−	1.19053i
$561$	15.7027	+	4.84029i	0.662970	+	0.204357i
$562$	24.7016	−	27.8717i	1.04197	−	1.17570i
$563$	−0.642577	−	1.11298i	−0.0270814	−	0.0469064i	0.852167	−	0.523270i	$-0.175288\pi$
$563$	−0.642577	−	1.11298i	−0.0270814	−	0.0469064i	−0.879248	+	0.476363i	$0.841955\pi$
$564$	−8.02483	+	2.88431i	−0.337906	+	0.121451i
$565$	−42.7056	−	24.6561i	−1.79664	−	1.03729i
$566$	−16.1120	+	18.1797i	−0.677237	+	0.764149i
$567$	−21.5370	+	10.1567i	−0.904468	+	0.426541i
$568$	3.46593	−	5.01514i	0.145427	−	0.210430i
$569$	9.93849	−	17.2140i	0.416643	−	0.721647i	−0.578956	−	0.815359i	$-0.696540\pi$
$569$	9.93849	−	17.2140i	0.416643	−	0.721647i	0.995599	+	0.0937117i	$0.0298732\pi$
$570$	−13.8689	+	25.3520i	−0.580905	+	1.06188i
$571$	−12.4246	+	7.17336i	−0.519954	+	0.300196i	−0.736916	−	0.675985i	$-0.763719\pi$
$571$	−12.4246	+	7.17336i	−0.519954	+	0.300196i	0.216962	+	0.976180i	$0.430385\pi$
$572$	−1.54537	−	12.7679i	−0.0646153	−	0.533852i
$573$	2.01232	−	6.52830i	0.0840657	−	0.272724i
$574$	23.2635	−	30.0187i	0.971001	−	1.25296i
$575$			35.6758i			1.48778i
$576$	−17.3918	−	16.5386i	−0.724660	−	0.689107i
$577$	10.9881	+	6.34398i	0.457440	+	0.264103i	0.710967	−	0.703225i	$-0.248257\pi$
$577$	10.9881	+	6.34398i	0.457440	+	0.264103i	−0.253527	+	0.967328i	$0.581591\pi$
$578$	12.4190	−	14.0128i	0.516563	−	0.582856i
$579$	−7.29937	+	6.77548i	−0.303351	+	0.281579i
$580$	−8.23481	+	19.3074i	−0.341932	+	0.801697i
$581$	−0.451609	−	6.84476i	−0.0187359	−	0.283969i
$582$	2.55745	−	4.67496i	0.106010	−	0.193783i
$583$	53.7611	+	31.0390i	2.22656	+	1.28550i
$584$	−5.55054	−	11.7148i	−0.229683	−	0.484761i
$585$	1.15677	−	15.5175i	0.0478264	−	0.641569i
$586$	7.03488	−	34.4257i	0.290608	−	1.42211i
$587$	−12.4489	−	21.5622i	−0.513823	−	0.889967i	−0.999871	−	0.0160352i	$-0.994896\pi$
$587$	−12.4489	−	21.5622i	−0.513823	−	0.889967i	0.486049	−	0.873932i	$-0.338438\pi$
$588$	−1.13411	+	24.2222i	−0.0467699	+	0.998906i
$589$	1.32527	−	2.29544i	0.0546068	−	0.0945818i
$590$	−29.2146	−	25.8918i	−1.20274	−	1.06595i
$591$	6.40387	+	28.0319i	0.263420	+	1.15308i
$592$	1.84285	−	0.452734i	0.0757405	−	0.0186072i
$593$	−22.9565	+	13.2540i	−0.942712	+	0.544275i	−0.890809	−	0.454377i	$-0.849862\pi$
$593$	−22.9565	+	13.2540i	−0.942712	+	0.544275i	−0.0519027	+	0.998652i	$0.516529\pi$
$594$	−30.1709	−	19.5515i	−1.23793	−	0.802208i
$595$	16.8287	−	11.2551i	0.689909	−	0.461415i
$596$	−15.4985	+	11.6371i	−0.634843	+	0.476676i
$597$	−20.6367	−	6.36117i	−0.844605	−	0.260345i
$598$	6.14527	+	1.25578i	0.251299	+	0.0513528i
$599$	−21.3471	+	12.3248i	−0.872219	+	0.503576i	−0.868085	−	0.496415i	$-0.834649\pi$
$599$	−21.3471	+	12.3248i	−0.872219	+	0.503576i	−0.00413416	+	0.999991i	$0.501316\pi$
$600$	19.2181	−	48.0981i	0.784577	−	1.96360i
$601$	−0.673377	+	0.388774i	−0.0274676	+	0.0158584i	−0.513671	−	0.857987i	$-0.671715\pi$
$601$	−0.673377	+	0.388774i	−0.0274676	+	0.0158584i	0.486203	+	0.873846i	$0.338381\pi$
$602$	−3.77586	−	9.24072i	−0.153893	−	0.376624i
$603$	2.35580	−	3.45823i	0.0959356	−	0.140830i
$604$	−19.8717	−	26.4653i	−0.808566	−	1.07686i
$605$		−	51.0483i		−	2.07541i
$606$	−0.908783	−	1.49357i	−0.0369168	−	0.0606721i
$607$	−42.1687			−1.71157			−0.855787	−	0.517328i	$-0.826927\pi$
$607$	−42.1687			−1.71157			−0.855787	+	0.517328i	$0.826927\pi$
$608$	9.02497	+	14.3019i	0.366011	+	0.580020i
$609$	11.6769	−	3.49063i	0.473173	−	0.141447i
$610$	−12.9663	−	2.64967i	−0.524992	−	0.107282i
$611$	−2.80208	+	1.61778i	−0.113360	+	0.0654483i
$612$	9.79741	−	6.27486i	0.396037	−	0.253646i
$613$	4.18716	−	7.25237i	0.169118	−	0.292921i	−0.768992	−	0.639258i	$-0.779241\pi$
$613$	4.18716	−	7.25237i	0.169118	−	0.292921i	0.938110	+	0.346338i	$0.112575\pi$
$614$	14.3620	+	43.0467i	0.579604	+	1.73723i
$615$	66.2977	+	20.4359i	2.67338	+	0.824057i
$616$	−31.9819	+	17.8205i	−1.28859	+	0.718008i
$617$	−8.84616	+	15.3220i	−0.356133	+	0.616840i	−0.987311	−	0.158797i	$-0.949238\pi$
$617$	−8.84616	+	15.3220i	−0.356133	+	0.616840i	0.631178	+	0.775638i	$0.282572\pi$
$618$	2.43718	−	1.48293i	0.0980376	−	0.0596523i
$619$	28.2667			1.13614			0.568068	−	0.822982i	$-0.307691\pi$
$619$	28.2667			1.13614			0.568068	+	0.822982i	$0.307691\pi$
$620$	−2.74523	+	6.43650i	−0.110251	+	0.258496i
$621$	13.7019	−	10.9400i	0.549836	−	0.439008i
$622$	12.2395	−	13.8103i	0.490760	−	0.553741i
$623$	35.5768	−	2.34732i	1.42536	−	0.0940432i
$624$	−7.60858	−	5.00343i	−0.304587	−	0.200298i
$625$	33.9185			1.35674
$626$	−3.77181	+	18.4576i	−0.150752	+	0.737715i
$627$	17.2346	+	18.5672i	0.688284	+	0.741503i
$628$	−10.2777	+	24.0972i	−0.410124	+	0.961582i
$629$			0.919927i			0.0366799i
$630$	−42.1373	+	13.6605i	−1.67879	+	0.544247i
$631$		−	21.2515i		−	0.846007i	−0.906128	−	0.423004i	$-0.860976\pi$
$631$		−	21.2515i		−	0.846007i	0.906128	−	0.423004i	$-0.139024\pi$
$632$	12.1766	+	25.6995i	0.484360	+	1.02227i
$633$	−11.4390	+	37.1101i	−0.454659	+	1.47499i
$634$	27.2316	+	5.56476i	1.08150	+	0.221005i
$635$	23.7333			0.941828
$636$	41.3637	−	14.8671i	1.64018	−	0.589519i
$637$	1.20884	+	9.12091i	0.0478958	+	0.361384i
$638$	13.7711	+	12.2049i	0.545205	+	0.483195i
$639$	−2.80779	−	5.82461i	−0.111075	−	0.230418i
$640$	−28.1904	−	34.6209i	−1.11432	−	1.36851i
$641$	−34.5020			−1.36275			−0.681373	−	0.731936i	$-0.738617\pi$
$641$	−34.5020			−1.36275			−0.681373	+	0.731936i	$0.738617\pi$
$642$	−14.3250	+	26.1858i	−0.565364	+	1.03347i
$643$	3.50574	−	6.07213i	0.138253	−	0.239461i	−0.788582	−	0.614929i	$-0.789185\pi$
$643$	3.50574	−	6.07213i	0.138253	−	0.239461i	0.926835	+	0.375468i	$0.122518\pi$
$644$	−3.30782	−	17.5462i	−0.130346	−	0.691418i
$645$	13.3650	−	12.4058i	0.526246	−	0.488477i
$646$	−7.77679	+	2.59463i	−0.305974	+	0.102084i
$647$	−0.330066	+	0.571691i	−0.0129762	+	0.0224755i	−0.872441	−	0.488720i	$-0.837464\pi$
$647$	−0.330066	+	0.571691i	−0.0129762	+	0.0224755i	0.859464	+	0.511196i	$0.170797\pi$
$648$	−24.3661	+	7.36833i	−0.957192	+	0.289455i
$649$	−29.6370	+	17.1109i	−1.16335	+	0.671662i
$650$	3.93471	−	19.2548i	0.154332	−	0.755235i
$651$	3.89272	−	1.16367i	0.152568	−	0.0456077i
$652$	−6.30285	+	14.7777i	−0.246839	+	0.578741i
$653$	2.38048			0.0931552			0.0465776	−	0.998915i	$-0.485169\pi$
$653$	2.38048			0.0931552			0.0465776	+	0.998915i	$0.485169\pi$
$654$	0.535510	+	23.2579i	0.0209401	+	0.909455i
$655$		−	7.88686i		−	0.308165i
$656$	29.3022	−	28.1023i	1.14406	−	1.09721i
$657$	−13.7115	−	1.02214i	−0.534937	−	0.0398774i
$658$	7.28037	+	5.64205i	0.283819	+	0.219950i
$659$	4.53599	−	2.61885i	0.176697	−	0.102016i	−0.409043	−	0.912515i	$-0.634137\pi$
$659$	4.53599	−	2.61885i	0.176697	−	0.102016i	0.585740	+	0.810499i	$0.300804\pi$
$660$	−51.0600	−	43.1955i	−1.98751	−	1.68138i
$661$	−6.35756	+	3.67054i	−0.247280	+	0.142767i	−0.618518	−	0.785770i	$-0.712267\pi$
$661$	−6.35756	+	3.67054i	−0.247280	+	0.142767i	0.371238	+	0.928538i	$0.378933\pi$
$662$	−4.07906	+	19.9612i	−0.158537	+	0.775814i
$663$	3.23547	−	3.00325i	0.125655	−	0.116637i
$664$	0.594254	−	7.30915i	0.0230615	−	0.283650i
$665$	31.1453	−	2.05493i	1.20776	−	0.0796867i
$666$	0.548461	−	1.93659i	0.0212524	−	0.0750412i
$667$	−7.77183	+	4.48707i	−0.300926	+	0.173740i
$668$	−2.32474	−	19.2070i	−0.0899469	−	0.743142i
$669$	11.3870	−	10.5698i	0.440249	−	0.408651i
$670$	5.16292	−	5.82550i	0.199461	−	0.225059i
$671$	−5.80096	+	10.0476i	−0.223943	+	0.387881i
$672$	−4.99234	+	25.4377i	−0.192584	+	0.981281i
$673$	6.21172	+	10.7590i	0.239444	+	0.414730i	0.960555	−	0.278090i	$-0.0897014\pi$
$673$	6.21172	+	10.7590i	0.239444	+	0.414730i	−0.721111	+	0.692820i	$0.756368\pi$
$674$	−1.35753	−	0.277411i	−0.0522901	−	0.0106855i
$675$	−34.2781	−	42.9316i	−1.31936	−	1.65244i
$676$	20.7374	+	8.84470i	0.797592	+	0.340181i
$677$	25.8330	+	14.9147i	0.992843	+	0.573218i	0.906123	−	0.423014i	$-0.139028\pi$
$677$	25.8330	+	14.9147i	0.992843	+	0.573218i	0.0867203	+	0.996233i	$0.472361\pi$
$678$	0.704580	+	30.6008i	0.0270592	+	1.17522i
$679$	−5.74324	+	0.378932i	−0.220405	+	0.0145421i
$680$	19.5591	−	9.26722i	0.750055	−	0.355382i
$681$	−3.00643	−	13.1602i	−0.115207	−	0.504298i
$682$	4.59087	+	4.06872i	0.175794	+	0.155799i
$683$	9.32990	+	5.38662i	0.356999	+	0.206113i	0.667763	−	0.744374i	$-0.267252\pi$
$683$	9.32990	+	5.38662i	0.356999	+	0.206113i	−0.310765	+	0.950487i	$0.600585\pi$
$684$	17.9182	−	0.825568i	0.685121	−	0.0315664i
$685$			39.7054i			1.51707i
$686$	22.7338	−	13.0067i	0.867981	−	0.496597i
$687$	11.4837	−	2.62344i	0.438130	−	0.100091i
$688$	−2.54600	−	10.3635i	−0.0970654	−	0.395103i
$689$	14.4432	−	8.33879i	0.550243	−	0.317683i
$690$	27.8643	−	16.9544i	1.06078	−	0.645445i
$691$	23.6969	−	41.0442i	0.901471	−	1.56139i	0.0758850	−	0.997117i	$-0.475822\pi$
$691$	23.6969	−	41.0442i	0.901471	−	1.56139i	0.825586	−	0.564277i	$-0.190845\pi$
$692$	−32.5383	+	3.93831i	−1.23692	+	0.149712i
$693$	−0.331050	+	38.8311i	−0.0125756	+	1.47507i
$694$	29.0348	+	25.7325i	1.10215	+	0.976791i
$695$	54.8179	+	31.6491i	2.07936	+	1.20052i
$696$	12.8951	−	1.86287i	0.488788	−	0.0706120i
$697$	9.84091	+	17.0450i	0.372751	+	0.645624i
$698$	−15.9304	−	14.1185i	−0.602976	−	0.534395i
$699$	21.4715	−	19.9305i	0.812128	−	0.753840i
$700$	−54.9771	+	10.3643i	−2.07794	+	0.391733i
$701$	−39.5982			−1.49560			−0.747801	−	0.663923i	$-0.768890\pi$
$701$	−39.5982			−1.49560			−0.747801	+	0.663923i	$0.768890\pi$
$702$	−8.60169	+	4.39332i	−0.324650	+	0.165815i
$703$	−0.709135	+	1.22826i	−0.0267455	+	0.0463246i
$704$	−36.6119	+	13.8373i	−1.37986	+	0.521513i
$705$	−4.95628	+	16.0790i	−0.186664	+	0.605572i
$706$	−24.8274	+	8.28336i	−0.934392	+	0.311749i
$707$	−0.834486	+	1.69402i	−0.0313841	+	0.0637102i
$708$	−4.30355	+	23.8456i	−0.161737	+	0.896173i
$709$	−13.7496	+	23.8150i	−0.516378	+	0.894393i	0.483441	+	0.875377i	$0.339387\pi$
$709$	−13.7496	+	23.8150i	−0.516378	+	0.894393i	−0.999819	+	0.0190160i	$0.993947\pi$
$710$	−3.80690	−	11.4103i	−0.142870	−	0.428220i
$711$	30.0799	+	2.24234i	1.12808	+	0.0840942i
$712$	37.9906	+	3.08874i	1.42376	+	0.115755i
$713$	−2.59089	+	1.49585i	−0.0970295	+	0.0560200i
$714$	−11.3980	−	5.29229i	−0.426561	−	0.198059i
$715$	−21.9766	−	12.6882i	−0.821877	−	0.474511i
$716$	−36.8139	+	4.45581i	−1.37580	+	0.166521i
$717$	9.92662	−	32.2037i	0.370717	−	1.20267i
$718$	−6.16986	−	5.46811i	−0.230257	−	0.204068i
$719$	26.4956	+	45.8917i	0.988118	+	1.71147i	0.627164	+	0.778887i	$0.284216\pi$
$719$	26.4956	+	45.8917i	0.988118	+	1.71147i	0.360954	+	0.932584i	$0.382451\pi$
$720$	−46.6999	+	7.84779i	−1.74040	+	0.292470i
$721$	−2.76427	−	1.36170i	−0.102947	−	0.0507123i
$722$	13.9426	+	2.84916i	0.518889	+	0.106035i
$723$	−39.7779	+	9.08723i	−1.47935	+	0.337958i
$724$	27.6256	+	36.7921i	1.02670	+	1.36737i
$725$	14.0592	+	24.3513i	0.522146	+	0.904383i
$726$	−27.0694	+	16.4707i	−1.00464	+	0.611287i
$727$	−15.2977	−	26.4963i	−0.567359	−	0.982694i	−0.996826	−	0.0796118i	$-0.974632\pi$
$727$	−15.2977	−	26.4963i	−0.567359	−	0.982694i	0.429467	−	0.903082i	$-0.358701\pi$
$728$	−0.149904	+	9.83479i	−0.00555580	+	0.364502i
$729$	−5.97715	+	26.3301i	−0.221376	+	0.975189i
$730$	−25.0600	−	5.12099i	−0.927511	−	0.189536i
$731$	5.17332			0.191342
$732$	2.77855	+	7.73058i	0.102698	+	0.285730i
$733$			0.705255i			0.0260492i	0.999915	+	0.0130246i	$0.00414597\pi$
$733$			0.705255i			0.0260492i	−0.999915	+	0.0130246i	$0.995854\pi$
$734$	−0.809212	−	2.42542i	−0.0298686	−	0.0895240i
$735$	36.8751	+	30.4862i	1.36016	+	1.12450i
$736$	−0.750461	−	19.0733i	−0.0276624	−	0.703053i
$737$	−3.41198	−	5.90973i	−0.125682	−	0.217688i
$738$	−10.5544	−	41.7494i	−0.388513	−	1.53682i
$739$	−29.5374	−	17.0534i	−1.08655	−	0.627321i	−0.153896	−	0.988087i	$-0.549182\pi$
$739$	−29.5374	−	17.0534i	−1.08655	−	0.627321i	−0.932656	+	0.360766i	$0.882515\pi$
$740$	1.46894	−	3.44409i	0.0539992	−	0.126607i
$741$	6.63498	−	1.51576i	0.243742	−	0.0556828i
$742$	−37.5265	−	29.0818i	−1.37764	−	1.06763i
$743$	−32.7970	−	18.9353i	−1.20320	−	0.694670i	−0.241938	−	0.970292i	$-0.577783\pi$
$743$	−32.7970	−	18.9353i	−1.20320	−	0.694670i	−0.961266	+	0.275621i	$0.911116\pi$
$744$	4.29883	−	0.621024i	0.157603	−	0.0227678i
$745$			38.2411i			1.40105i
$746$	−2.66720	−	7.99429i	−0.0976530	−	0.292692i
$747$	−6.42829	−	4.37905i	−0.235199	−	0.160221i
$748$	−2.27987	−	18.8363i	−0.0833605	−	0.688725i
$749$	32.1696	−	2.12251i	1.17545	−	0.0775548i
$750$	−28.0002	−	46.0179i	−1.02242	−	1.68034i
$751$			18.1205i			0.661227i	0.943766	+	0.330613i	$0.107256\pi$
$751$			18.1205i			0.661227i	−0.943766	+	0.330613i	$0.892744\pi$
$752$	6.81560	+	7.10660i	0.248539	+	0.259151i
$753$	1.74817	+	7.65234i	0.0637069	+	0.278867i
$754$	4.68946	−	1.56458i	0.170780	−	0.0569787i
$755$	−65.3007			−2.37654
$756$	20.8394	+	17.9366i	0.757920	+	0.652347i
$757$	−30.0755			−1.09311			−0.546555	−	0.837423i	$-0.684061\pi$
$757$	−30.0755			−1.09311			−0.546555	+	0.837423i	$0.684061\pi$
$758$	−22.1768	+	7.39901i	−0.805497	+	0.268744i
$759$	−6.36820	−	27.8758i	−0.231151	−	1.01183i
$760$	33.2584	+	2.70400i	1.20641	+	0.0980842i
$761$		−	22.2505i		−	0.806579i	−0.915072	−	0.403290i	$-0.867867\pi$
$761$		−	22.2505i		−	0.806579i	0.915072	−	0.403290i	$-0.132133\pi$
$762$	−7.65756	−	12.5851i	−0.277404	−	0.455909i
$763$	20.8871	−	13.9694i	0.756165	−	0.505728i
$764$	−7.83108	+	0.947842i	−0.283318	+	0.0342917i
$765$	1.70657	−	22.8928i	0.0617011	−	0.827691i
$766$	−1.47613	−	4.42434i	−0.0533346	−	0.159858i
$767$			9.19389i			0.331972i
$768$	−9.26282	+	26.1190i	−0.334243	+	0.942487i
$769$	−9.46235	−	5.46309i	−0.341221	−	0.197004i	0.319591	−	0.947556i	$-0.396455\pi$
$769$	−9.46235	−	5.46309i	−0.341221	−	0.197004i	−0.660812	+	0.750552i	$0.729788\pi$
$770$	−9.77213	+	71.5750i	−0.352163	+	2.57938i
$771$	−40.3295	+	9.21324i	−1.45243	+	0.331807i
$772$	10.5781	+	4.51165i	0.380713	+	0.162378i
$773$	−10.6286	−	6.13643i	−0.382284	−	0.220712i	0.296527	−	0.955024i	$-0.404171\pi$
$773$	−10.6286	−	6.13643i	−0.382284	−	0.220712i	−0.678812	+	0.734312i	$0.737505\pi$
$774$	−10.8906	−	3.08433i	−0.391455	−	0.110864i
$775$	4.68690	+	8.11795i	0.168359	+	0.291605i
$776$	−6.13290	−	0.498621i	−0.220158	−	0.0178995i
$777$	−2.08295	+	0.622663i	−0.0747253	+	0.0223379i
$778$	4.31863	+	12.9441i	0.154830	+	0.464067i
$779$			30.3439i			1.08718i
$780$	−16.9087	+	6.07740i	−0.605430	+	0.217606i
$781$	−10.5449			−0.377327
$782$	9.06605	+	1.85264i	0.324201	+	0.0662504i
$783$	5.04121	−	12.8670i	0.180158	−	0.459829i
$784$	26.0781	−	10.1948i	0.931360	−	0.364100i
$785$	25.8452	+	44.7653i	0.922456	+	1.59774i
$786$	−4.18217	+	2.54470i	−0.149173	+	0.0907663i
$787$	−1.13525	−	1.96631i	−0.0404672	−	0.0700913i	0.845082	−	0.534636i	$-0.179551\pi$
$787$	−1.13525	−	1.96631i	−0.0404672	−	0.0700913i	−0.885550	+	0.464545i	$0.846218\pi$
$788$	26.5510	−	19.9360i	0.945839	−	0.710189i
$789$	−45.9311	+	10.4929i	−1.63519	+	0.373559i
$790$	54.9758	+	11.2343i	1.95595	+	0.399698i
$791$	27.4816	−	18.3798i	0.977133	−	0.653512i
$792$	−6.43074	+	41.0126i	−0.228507	+	1.45732i
$793$	1.55846	+	2.69933i	0.0553425	+	0.0958560i
$794$	−3.93743	−	3.48960i	−0.139734	−	0.123841i
$795$	25.5470	−	82.8790i	0.906059	−	2.93941i
$796$	2.99624	+	24.7550i	0.106199	+	0.877416i
$797$	−4.92030	−	2.84074i	−0.174286	−	0.100624i	0.410319	−	0.911942i	$-0.365417\pi$
$797$	−4.92030	−	2.84074i	−0.174286	−	0.100624i	−0.584605	+	0.811318i	$0.698751\pi$
$798$	−11.1387	−	15.8524i	−0.394306	−	0.561169i
$799$	−4.13388	+	2.38669i	−0.146246	+	0.0844352i
$800$	−59.7620	+	2.35140i	−2.11290	+	0.0831345i
$801$	22.7609	−	33.4121i	0.804215	−	1.18056i
$802$	−10.7294	−	32.1589i	−0.378869	−	1.13557i
$803$	−11.2115	+	19.4188i	−0.395644	+	0.685276i
$804$	−4.75490	−	0.858144i	−0.167693	−	0.0302644i
$805$	−31.6040	−	15.5684i	−1.11390	−	0.548712i
$806$	1.56332	−	0.521583i	0.0550656	−	0.0183720i
$807$	9.34588	−	30.3197i	0.328991	−	1.06730i
$808$	−1.14775	+	1.66078i	−0.0403777	+	0.0584259i
$809$	−8.28527	+	14.3505i	−0.291295	+	0.504537i	−0.974116	−	0.226048i	$-0.927419\pi$
$809$	−8.28527	+	14.3505i	−0.291295	+	0.504537i	0.682821	+	0.730585i	$0.260753\pi$
$810$	−17.2413	+	47.1754i	−0.605797	+	1.65757i
$811$	10.2931			0.361438			0.180719	−	0.983535i	$-0.442158\pi$
$811$	10.2931			0.361438			0.180719	+	0.983535i	$0.442158\pi$
$812$	−9.17247	−	10.6730i	−0.321891	−	0.374548i
$813$	1.96132	−	1.82055i	0.0687864	−	0.0638495i
$814$	−2.45652	−	2.17712i	−0.0861009	−	0.0763080i
$815$	15.8497	+	27.4526i	0.555192	+	0.961621i
$816$	−11.2249	−	7.38151i	−0.392949	−	0.258405i
$817$	6.90726	+	3.98791i	0.241654	+	0.139519i
$818$	−23.4483	−	20.7814i	−0.819851	−	0.726603i
$819$	8.99008	+	5.29312i	0.314139	+	0.184957i
$820$	−9.62575	−	79.5280i	−0.336146	−	2.77724i
$821$	0.0507961	−	0.0879815i	0.00177280	−	0.00307058i	−0.865138	−	0.501535i	$-0.832769\pi$
$821$	0.0507961	−	0.0879815i	0.00177280	−	0.00307058i	0.866910	+	0.498464i	$0.166102\pi$
$822$	21.0546	−	12.8110i	0.734364	−	0.446834i
$823$	47.7924	−	27.5929i	1.66594	−	0.961829i	0.696144	−	0.717902i	$-0.254898\pi$
$823$	47.7924	−	27.5929i	1.66594	−	0.961829i	0.969794	−	0.243927i	$-0.0784358\pi$
$824$	−2.71002	−	1.87288i	−0.0944081	−	0.0652448i
$825$	−87.3424	+	19.9533i	−3.04087	+	0.694685i
$826$	24.2278	−	9.89973i	0.842991	−	0.344456i
$827$		−	37.1634i		−	1.29230i	−0.763211	−	0.646149i	$-0.776378\pi$
$827$		−	37.1634i		−	1.29230i	0.763211	−	0.646149i	$-0.223622\pi$
$828$	−17.9809	−	9.30528i	−0.624879	−	0.323381i
$829$	33.4823	+	19.3310i	1.16289	+	0.671393i	0.951994	−	0.306116i	$-0.0990295\pi$
$829$	33.4823	+	19.3310i	1.16289	+	0.671393i	0.210893	+	0.977509i	$0.432363\pi$
$830$	−10.8287	−	9.59703i	−0.375868	−	0.333118i
$831$	−0.187509	−	0.820791i	−0.00650462	−	0.0284729i
$832$	−1.69858	+	10.3770i	−0.0588876	+	0.359756i
$833$	1.78338	+	13.4560i	0.0617906	+	0.466223i
$834$	−0.904414	−	39.2799i	−0.0313173	−	1.36015i
$835$	−33.0598	−	19.0871i	−1.14408	−	0.660537i
$836$	11.4762	−	26.9072i	0.396912	−	0.930604i
$837$	1.68058	−	4.28946i	0.0580895	−	0.148265i
$838$	−49.0038	−	10.0139i	−1.69281	−	0.345924i
$839$	−2.58403	−	4.47567i	−0.0892106	−	0.154517i	0.817967	−	0.575265i	$-0.195101\pi$
$839$	−2.58403	−	4.47567i	−0.0892106	−	0.154517i	−0.907178	+	0.420748i	$0.861768\pi$
$840$	34.2221	+	38.0140i	1.18077	+	1.31161i
$841$	10.9635	−	18.9893i	0.378050	−	0.654802i
$842$	29.0510	−	32.7792i	1.00116	−	1.12965i
$843$	−33.4302	+	31.0309i	−1.15140	+	1.06876i
$844$	44.5157	−	5.38801i	1.53229	−	0.185463i
$845$	38.5238	−	22.2417i	1.32526	−	0.765138i
$846$	10.1254	−	2.55974i	0.348118	−	0.0880056i
$847$	30.7024	+	15.1242i	1.05495	+	0.519673i
$848$	−35.1308	−	36.6308i	−1.20640	−	1.25791i
$849$	21.8054	−	20.2404i	0.748358	−	0.694647i
$850$	5.80484	−	28.4064i	0.199104	−	0.974332i
$851$	1.38635	−	0.800409i	0.0475234	−	0.0274377i
$852$	−4.82223	+	5.70021i	−0.165207	+	0.195286i
$853$	30.1332	−	17.3974i	1.03174	−	0.595675i	0.114257	−	0.993451i	$-0.463551\pi$
$853$	30.1332	−	17.3974i	1.03174	−	0.595675i	0.917483	+	0.397776i	$0.130218\pi$
$854$	5.43518	−	7.01342i	0.185988	−	0.239994i
$855$	19.9257	−	29.2502i	0.681445	−	1.00034i
$856$	34.3522	+	2.79293i	1.17413	+	0.0954602i
$857$			42.8423i			1.46347i	0.681592	+	0.731733i	$0.261288\pi$
$857$			42.8423i			1.46347i	−0.681592	+	0.731733i	$0.738712\pi$
$858$	0.362581	+	15.7474i	0.0123783	+	0.537606i
$859$	31.9433			1.08989			0.544945	−	0.838472i	$-0.316550\pi$
$859$	31.9433			1.08989			0.544945	+	0.838472i	$0.316550\pi$
$860$	−19.3682	−	8.26074i	−0.660451	−	0.281689i
$861$	−31.9331	+	33.8194i	−1.08828	+	1.15256i
$862$	−1.38084	+	6.75722i	−0.0470315	+	0.230152i
$863$	30.0490	−	17.3488i	1.02288	−	0.590560i	0.107943	−	0.994157i	$-0.465574\pi$
$863$	30.0490	−	17.3488i	1.02288	−	0.590560i	0.914937	+	0.403597i	$0.132240\pi$
$864$	19.2292	+	22.2315i	0.654190	+	0.756330i
$865$	−32.3352	+	56.0061i	−1.09943	+	1.90427i
$866$	17.5395	−	5.85184i	0.596017	−	0.198854i
$867$	−16.8074	+	15.6011i	−0.570811	+	0.529843i
$868$	−3.05782	−	3.55804i	−0.103789	−	0.120768i
$869$	24.5954	−	42.6005i	0.834342	−	1.44512i
$870$	12.3379	−	22.5535i	0.418295	−	0.764634i
$871$	−1.83330			−0.0621189
$872$	24.2760	−	11.5021i	0.822088	−	0.389511i
$873$	−3.67433	+	5.39379i	−0.124357	+	0.182552i
$874$	10.6766	+	9.46225i	0.361141	+	0.320065i
$875$	−25.7111	+	52.1939i	−0.869193	+	1.76448i
$876$	5.37009	+	14.9408i	0.181439	+	0.504804i
$877$	−22.2426			−0.751081			−0.375540	−	0.926806i	$-0.622543\pi$
$877$	−22.2426			−0.751081			−0.375540	+	0.926806i	$0.622543\pi$
$878$	−2.65662	−	0.542879i	−0.0896565	−	0.0183213i
$879$	−12.6765	+	41.1246i	−0.427566	+	1.38710i
$880$	−21.5422	+	74.1613i	−0.726189	+	2.49998i
$881$			20.4228i			0.688061i	0.938958	+	0.344031i	$0.111792\pi$
$881$			20.4228i			0.688061i	−0.938958	+	0.344031i	$0.888208\pi$
$882$	4.26817	−	29.3902i	0.143717	−	0.989619i
$883$		−	11.6027i		−	0.390461i	−0.980757	−	0.195231i	$-0.937454\pi$
$883$		−	11.6027i		−	0.390461i	0.980757	−	0.195231i	$-0.0625456\pi$
$884$	−4.68876	−	1.99980i	−0.157700	−	0.0672606i
$885$	32.5260	+	35.0410i	1.09335	+	1.17789i
$886$	−6.02824	+	29.4996i	−0.202523	+	0.991059i
$887$	−53.0798			−1.78225			−0.891123	−	0.453763i	$-0.850081\pi$
$887$	−53.0798			−1.78225			−0.891123	+	0.453763i	$0.850081\pi$
$888$	−2.30025	+	0.332302i	−0.0771913	+	0.0111513i
$889$	−7.03152	+	14.2741i	−0.235830	+	0.478738i
$890$	49.8822	−	56.2838i	1.67206	−	1.88664i
$891$	34.4471	+	27.4265i	1.15402	+	0.918823i
$892$	−16.5018	−	7.03819i	−0.552522	−	0.235656i
$893$	−7.35923			−0.246267
$894$	20.2781	−	12.3385i	0.678201	−	0.412661i
$895$	−36.5841	+	63.3655i	−1.22287	+	2.11808i
$896$	29.1744	−	6.69753i	0.974647	−	0.223749i
$897$	−7.34108	−	2.26285i	−0.245111	−	0.0755543i
$898$	2.68535	+	8.04870i	0.0896113	+	0.268589i
$899$	−1.17898	+	2.04205i	−0.0393210	+	0.0681060i
$900$	−29.1560	+	56.3390i	−0.971866	+	1.87797i
$901$	21.3079	−	12.3021i	0.709870	−	0.409844i
$902$	−68.8055	−	14.0604i	−2.29097	−	0.468159i
$903$	3.50162	+	11.7137i	0.116527	+	0.389807i
$904$	31.9403	−	15.1335i	1.06232	−	0.503334i
$905$	90.7810			3.01766
$906$	21.0693	+	34.6270i	0.699980	+	1.15041i
$907$			54.6847i			1.81578i	0.419213	+	0.907888i	$0.362306\pi$
$907$			54.6847i			1.81578i	−0.419213	+	0.907888i	$0.637694\pi$
$908$	−12.4649	+	9.35935i	−0.413662	+	0.310601i
$909$	0.929808	+	1.92884i	0.0308398	+	0.0639754i
$910$	15.3401	+	11.8881i	0.508521	+	0.394087i
$911$	1.27865	−	0.738229i	0.0423636	−	0.0244586i	−0.478669	−	0.877996i	$-0.658880\pi$
$911$	1.27865	−	0.738229i	0.0423636	−	0.0244586i	0.521032	+	0.853537i	$0.325547\pi$
$912$	−9.29697	−	18.5084i	−0.307853	−	0.612873i
$913$	−10.9852	+	6.34232i	−0.363558	+	0.209900i
$914$	35.1038	+	7.17345i	1.16113	+	0.237277i
$915$	15.4895	+	4.77455i	0.512066	+	0.157842i
$916$	−8.16706	−	10.8770i	−0.269847	−	0.359386i
$917$	4.74345	+	2.33666i	0.156643	+	0.0771632i
$918$	−12.6900	+	6.48142i	−0.418832	+	0.213919i
$919$	16.9505	−	9.78639i	0.559146	−	0.322823i	−0.193657	−	0.981069i	$-0.562035\pi$
$919$	16.9505	−	9.78639i	0.559146	−	0.322823i	0.752803	+	0.658246i	$0.228701\pi$
$920$	−30.9838	−	21.4127i	−1.02151	−	0.705956i
$921$	−12.3779	−	54.1823i	−0.407866	−	1.78537i
$922$	21.2272	+	18.8128i	0.699080	+	0.619568i
$923$	−1.41648	+	2.45341i	−0.0466239	+	0.0807549i
$924$	41.1070	−	17.9118i	1.35232	−	0.589255i
$925$	−2.50790	−	4.34381i	−0.0824592	−	0.142824i
$926$	−10.8833	+	53.2584i	−0.357649	+	1.75018i
$927$	−3.14744	+	1.51724i	−0.103375	+	0.0498328i
$928$	−8.02871	−	12.7232i	−0.263555	−	0.417658i
$929$	−12.5102	−	7.22275i	−0.410445	−	0.236971i	0.280536	−	0.959844i	$-0.409488\pi$
$929$	−12.5102	−	7.22275i	−0.410445	−	0.236971i	−0.690981	+	0.722873i	$0.742821\pi$
$930$	4.11309	−	7.51862i	0.134873	−	0.246545i
$931$	−7.99158	+	19.3408i	−0.261913	+	0.633868i
$932$	−31.1160	−	13.2713i	−1.01924	−	0.434715i
$933$	−16.5645	+	15.3756i	−0.542298	+	0.503376i
$934$	30.6904	−	34.6290i	1.00422	−	1.13310i
$935$	−32.4218	−	18.7187i	−1.06031	−	0.612168i
$936$	8.67828	+	7.00533i	0.283658	+	0.228976i
$937$		−	31.4809i		−	1.02844i	−0.857659	−	0.514218i	$-0.828082\pi$
$937$		−	31.4809i		−	1.02844i	0.857659	−	0.514218i	$-0.171918\pi$
$938$	1.97404	+	4.83111i	0.0644548	+	0.157741i
$939$	6.79658	−	22.0493i	0.221798	−	0.719552i
$940$	19.2878	−	2.33451i	0.629097	−	0.0761434i
$941$	−34.9308	+	20.1673i	−1.13871	+	0.657435i	−0.946111	−	0.323842i	$-0.895025\pi$
$941$	−34.9308	+	20.1673i	−1.13871	+	0.657435i	−0.192600	+	0.981277i	$0.561692\pi$
$942$	15.3987	−	28.1485i	0.501717	−	0.917127i
$943$	17.1247	−	29.6609i	0.557658	−	0.965892i
$944$	27.1714	−	6.67523i	0.884354	−	0.217260i
$945$	52.9902	−	11.6312i	1.72377	−	0.378361i
$946$	−12.2433	+	13.8145i	−0.398064	+	0.449149i
$947$	−12.8689	−	7.42986i	−0.418183	−	0.241438i	0.276117	−	0.961124i	$-0.410952\pi$
$947$	−12.8689	−	7.42986i	−0.418183	−	0.241438i	−0.694300	+	0.719686i	$0.744286\pi$
$948$	−11.7807	−	32.7768i	−0.382621	−	1.06454i
$949$	3.01202	+	5.21698i	0.0977745	+	0.169350i
$950$	29.6478	−	33.4526i	0.961902	−	1.08535i
$951$	−32.5306	−	10.0274i	−1.05488	−	0.325160i
$952$	−0.221152	+	14.5092i	−0.00716757	+	0.470245i
$953$	−11.8041			−0.382371			−0.191185	−	0.981554i	$-0.561233\pi$
$953$	−11.8041			−0.382371			−0.191185	+	0.981554i	$0.561233\pi$
$954$	−52.1910	+	13.1941i	−1.68975	+	0.427174i
$955$	−7.78219	+	13.4791i	−0.251826	+	0.436175i
$956$	−38.6302	+	4.67565i	−1.24939	+	0.151221i
$957$	−15.3321	−	16.5176i	−0.495617	−	0.533938i
$958$	−16.4694	−	49.3633i	−0.532104	−	1.59486i
$959$	−23.8803	−	11.7636i	−0.771137	−	0.379867i
$960$	30.2376	+	45.5592i	0.975915	+	1.47042i
$961$	15.1070	−	26.1660i	0.487321	−	0.844066i
$962$	−0.836512	+	0.279092i	−0.0269702	+	0.00899829i
$963$	20.5810	−	30.2122i	0.663214	−	0.973575i
$964$	28.2895	+	37.6764i	0.911145	+	1.21347i
$965$	19.6508	−	11.3454i	0.632583	−	0.365222i
$966$	1.94161	+	21.7818i	0.0624703	+	0.700818i
$967$	−2.41663	−	1.39524i	−0.0777137	−	0.0448680i	0.460640	−	0.887587i	$-0.347620\pi$
$967$	−2.41663	−	1.39524i	−0.0777137	−	0.0448680i	−0.538353	+	0.842719i	$0.680953\pi$
$968$	30.0999	+	20.8018i	0.967446	+	0.668595i
$969$	9.78853	−	2.23618i	0.314453	−	0.0718366i
$970$	−8.05259	+	9.08601i	−0.258553	+	0.291734i
$971$	26.2483	+	45.4633i	0.842347	+	1.45899i	0.887905	+	0.460026i	$0.152160\pi$
$971$	26.2483	+	45.4633i	0.842347	+	1.45899i	−0.0455582	+	0.998962i	$0.514507\pi$
$972$	30.5786	−	6.07861i	0.980809	−	0.194971i
$973$	−35.2760	+	23.5928i	−1.13090	+	0.756350i
$974$	1.28514	−	6.28893i	0.0411786	−	0.201510i
$975$	−7.09012	+	23.0016i	−0.227066	+	0.736641i
$976$	6.84602	−	6.56569i	0.219136	−	0.210163i
$977$	5.14397	+	8.90962i	0.164570	+	0.285044i	0.936503	−	0.350661i	$-0.114043\pi$
$977$	5.14397	+	8.90962i	0.164570	+	0.285044i	−0.771932	+	0.635705i	$0.780710\pi$
$978$	9.44335	−	17.2622i	0.301965	−	0.551985i
$979$	−32.9653	−	57.0976i	−1.05358	−	1.82485i
$980$	14.8097	−	53.2252i	0.473080	−	1.70022i
$981$	2.11813	−	28.4137i	0.0676266	−	0.907179i
$982$	−3.48721	+	17.0649i	−0.111281	+	0.544563i
$983$	−32.9047			−1.04950			−0.524749	−	0.851257i	$-0.675841\pi$
$983$	−32.9047			−1.04950			−0.524749	+	0.851257i	$0.675841\pi$
$984$	−39.0656	+	30.7640i	−1.24537	+	0.980720i
$985$		−	65.5120i		−	2.08739i
$986$	6.91832	−	2.30821i	0.220324	−	0.0735084i
$987$	−8.20214	−	7.74467i	−0.261077	−	0.246516i
$988$	−4.71872	−	6.28445i	−0.150123	−	0.199935i
$989$	−4.50120	−	7.79630i	−0.143130	−	0.247908i
$990$	57.0927	+	58.7357i	1.81453	+	1.86674i
$991$	48.3716	+	27.9273i	1.53657	+	0.887141i	0.999036	+	0.0439007i	$0.0139785\pi$
$991$	48.3716	+	27.9273i	1.53657	+	0.887141i	0.537537	+	0.843240i	$0.319355\pi$
$992$	−2.67652	−	4.24151i	−0.0849797	−	0.134668i
$993$	7.35024	−	23.8455i	0.233253	−	0.756713i
$994$	7.99045	+	1.09094i	0.253442	+	0.0346024i
$995$	42.6092	+	24.6004i	1.35080	+	0.779885i
$996$	−1.59515	+	8.83860i	−0.0505443	+	0.280062i
$997$			0.253367i			0.00802422i	0.999992	+	0.00401211i	$0.00127710\pi$
$997$			0.253367i			0.00802422i	−0.999992	+	0.00401211i	$0.998723\pi$
$998$	−17.3748	+	5.79689i	−0.549990	+	0.183497i
$999$	−0.899258	+	2.29523i	−0.0284513	+	0.0726180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.n.b.31.25	yes	84
3.2	odd	2		756.2.n.b.199.18		84
4.3	odd	2	inner	252.2.n.b.31.4	✓	84
7.5	odd	6		252.2.bj.b.103.31	yes	84
9.2	odd	6		756.2.bj.b.451.12		84
9.7	even	3		252.2.bj.b.115.31	yes	84
12.11	even	2		756.2.n.b.199.39		84
21.5	even	6		756.2.bj.b.523.12		84
28.19	even	6		252.2.bj.b.103.32	yes	84
36.7	odd	6		252.2.bj.b.115.32	yes	84
36.11	even	6		756.2.bj.b.451.11		84
63.47	even	6		756.2.n.b.19.39		84
63.61	odd	6	inner	252.2.n.b.187.4	yes	84
84.47	odd	6		756.2.bj.b.523.11		84
252.47	odd	6		756.2.n.b.19.18		84
252.187	even	6	inner	252.2.n.b.187.25	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.4	✓	84	4.3	odd	2	inner
252.2.n.b.31.25	yes	84	1.1	even	1	trivial
252.2.n.b.187.4	yes	84	63.61	odd	6	inner
252.2.n.b.187.25	yes	84	252.187	even	6	inner
252.2.bj.b.103.31	yes	84	7.5	odd	6
252.2.bj.b.103.32	yes	84	28.19	even	6
252.2.bj.b.115.31	yes	84	9.7	even	3
252.2.bj.b.115.32	yes	84	36.7	odd	6
756.2.n.b.19.18		84	252.47	odd	6
756.2.n.b.19.39		84	63.47	even	6
756.2.n.b.199.18		84	3.2	odd	2
756.2.n.b.199.39		84	12.11	even	2
756.2.bj.b.451.11		84	36.11	even	6
756.2.bj.b.451.12		84	9.2	odd	6
756.2.bj.b.523.11		84	84.47	odd	6
756.2.bj.b.523.12		84	21.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.447581 + 1.34152i) q^{2} +(-0.385748 - 1.68855i) q^{3} +(-1.59934 + 1.20088i) q^{4} +3.94623i q^{5} +(2.09257 - 1.27325i) q^{6} +(-2.37341 - 1.16916i) q^{7} +(-2.32683 - 1.60806i) q^{8} +(-2.70240 + 1.30271i) q^{9} +(-5.29393 + 1.76626i) q^{10} +4.89244i q^{11} +(2.64468 + 2.23733i) q^{12} +(1.13829 + 0.657191i) q^{13} +(0.506153 - 3.70726i) q^{14} +(6.66340 - 1.52225i) q^{15} +(1.11579 - 3.84122i) q^{16} +(1.67931 + 0.969547i) q^{17} +(-2.95715 - 3.04225i) q^{18} +(1.49477 + 2.58902i) q^{19} +(-4.73893 - 6.31137i) q^{20} +(-1.05864 + 4.45862i) q^{21} +(-6.56330 + 2.18976i) q^{22} -3.37433i q^{23} +(-1.81771 + 4.54928i) q^{24} -10.5727 q^{25} +(-0.372157 + 1.82118i) q^{26} +(3.24213 + 4.06061i) q^{27} +(5.19991 - 0.980288i) q^{28} +(-1.32976 - 2.30322i) q^{29} +(5.02453 + 8.25774i) q^{30} +(-0.443302 - 0.767822i) q^{31} +(5.65248 - 0.222403i) q^{32} +(8.26113 - 1.88725i) q^{33} +(-0.549040 + 2.68677i) q^{34} +(4.61376 - 9.36601i) q^{35} +(2.75767 - 5.32872i) q^{36} +(0.237205 + 0.410852i) q^{37} +(-2.80419 + 3.16406i) q^{38} +(0.670607 - 2.17556i) q^{39} +(6.34576 - 9.18221i) q^{40} +(8.79016 + 5.07500i) q^{41} +(-6.45515 + 0.575406i) q^{42} +(2.31047 - 1.33395i) q^{43} +(-5.87522 - 7.82469i) q^{44} +(-5.14078 - 10.6643i) q^{45} +(4.52673 - 1.51029i) q^{46} +(-1.23083 + 2.13186i) q^{47} +(-6.91651 - 0.402326i) q^{48} +(4.26614 + 5.54978i) q^{49} +(-4.73214 - 14.1835i) q^{50} +(0.989340 - 3.20959i) q^{51} +(-2.60972 + 0.315870i) q^{52} +(6.34427 - 10.9886i) q^{53} +(-3.99627 + 6.16683i) q^{54} -19.3067 q^{55} +(3.64245 + 6.53701i) q^{56} +(3.79508 - 3.52270i) q^{57} +(2.49463 - 2.81478i) q^{58} +(3.49742 + 6.05771i) q^{59} +(-8.82902 + 10.4365i) q^{60} +(2.05369 + 1.18570i) q^{61} +(0.831634 - 0.938361i) q^{62} +(7.93697 + 0.0676656i) q^{63} +(2.82830 + 7.48336i) q^{64} +(-2.59342 + 4.49194i) q^{65} +(6.22930 + 10.2378i) q^{66} +(-1.20793 + 0.697399i) q^{67} +(-3.85009 + 0.465999i) q^{68} +(-5.69773 + 1.30164i) q^{69} +(14.6297 + 1.99739i) q^{70} +2.15535i q^{71} +(8.38286 + 1.31442i) q^{72} +(3.96915 + 2.29159i) q^{73} +(-0.444996 + 0.502105i) q^{74} +(4.07840 + 17.8525i) q^{75} +(-5.49974 - 2.34569i) q^{76} +(5.72003 - 11.6118i) q^{77} +(3.21871 - 0.0741104i) q^{78} +(-8.70741 - 5.02722i) q^{79} +(15.1583 + 4.40317i) q^{80} +(5.60590 - 7.04087i) q^{81} +(-2.87390 + 14.0636i) q^{82} +(1.29635 + 2.24535i) q^{83} +(-3.66112 - 8.40216i) q^{84} +(-3.82605 + 6.62692i) q^{85} +(2.82365 + 2.50249i) q^{86} +(-3.37615 + 3.13384i) q^{87} +(7.86733 - 11.3839i) q^{88} +(-11.6706 + 6.73801i) q^{89} +(12.0054 - 11.6696i) q^{90} +(-1.93326 - 2.89062i) q^{91} +(4.05215 + 5.39671i) q^{92} +(-1.12550 + 1.04472i) q^{93} +(-3.41082 - 0.697000i) q^{94} +(-10.2169 + 5.89870i) q^{95} +(-2.55597 - 9.45870i) q^{96} +(1.88401 - 1.08773i) q^{97} +(-5.53568 + 8.20708i) q^{98} +(-6.37343 - 13.2213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28}+ \cdots + 21 q^{98}+O(q^{100}) \) 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9 - 18 * q^10 + 9 * q^12 - 18 * q^13 - 25 * q^14 - 7 * q^16 + 6 * q^17 - 13 * q^18 + 24 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^24 - 32 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 14 * q^30 + 9 * q^32 - 6 * q^33 + 24 * q^34 - 38 * q^36 + 2 * q^37 - 6 * q^41 + 7 * q^42 - 13 * q^44 - 18 * q^45 + 10 * q^46 - 9 * q^48 + 2 * q^49 - 17 * q^50 - 2 * q^53 - 42 * q^54 - 32 * q^56 + 6 * q^57 + 26 * q^58 + 8 * q^60 - 24 * q^61 - 8 * q^64 + 50 * q^65 + 27 * q^66 + 18 * q^69 - 4 * q^70 - 7 * q^72 + 30 * q^73 + 46 * q^74 + 46 * q^77 + 15 * q^78 + 3 * q^80 - 26 * q^81 - 18 * q^82 + 29 * q^84 - 50 * q^85 + 18 * q^86 - 2 * q^88 - 102 * q^89 + 39 * q^90 + 28 * q^92 - 24 * q^93 + 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^98

Introduction

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