LMFDB - Embedded newform 252.2.bi.c.139.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.22
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139426 - 1.40732i) q^{2} +(1.60547 - 0.649977i) q^{3} +(-1.96112 - 0.392436i) q^{4} +(-1.35495 - 0.782280i) q^{5} +(-0.690883 - 2.35004i) q^{6} +(-2.11799 - 1.58559i) q^{7} +(-0.825716 + 2.70522i) q^{8} +(2.15506 - 2.08703i) q^{9} +O(q^{10})$	\(q+(0.139426 - 1.40732i) q^{2} +(1.60547 - 0.649977i) q^{3} +(-1.96112 - 0.392436i) q^{4} +(-1.35495 - 0.782280i) q^{5} +(-0.690883 - 2.35004i) q^{6} +(-2.11799 - 1.58559i) q^{7} +(-0.825716 + 2.70522i) q^{8} +(2.15506 - 2.08703i) q^{9} +(-1.28984 + 1.79778i) q^{10} +(2.65503 - 1.53288i) q^{11} +(-3.40359 + 0.644639i) q^{12} +(-4.17891 - 2.41269i) q^{13} +(-2.52674 + 2.75963i) q^{14} +(-2.68379 - 0.375241i) q^{15} +(3.69199 + 1.53923i) q^{16} +0.603184i q^{17} +(-2.63666 - 3.32386i) q^{18} +5.64236 q^{19} +(2.35022 + 2.06588i) q^{20} +(-4.43097 - 1.16897i) q^{21} +(-1.78708 - 3.95021i) q^{22} +(7.81563 + 4.51236i) q^{23} +(0.432666 + 4.87984i) q^{24} +(-1.27608 - 2.21023i) q^{25} +(-3.97809 + 5.54468i) q^{26} +(2.10336 - 4.75141i) q^{27} +(3.53140 + 3.94071i) q^{28} +(3.38751 + 5.86734i) q^{29} +(-0.902277 + 3.72464i) q^{30} +(-0.860400 + 1.49026i) q^{31} +(2.68095 - 4.98121i) q^{32} +(3.26623 - 4.18670i) q^{33} +(0.848876 + 0.0840997i) q^{34} +(1.62940 + 3.80526i) q^{35} +(-5.04536 + 3.24720i) q^{36} -5.45766 q^{37} +(0.786694 - 7.94063i) q^{38} +(-8.27730 - 1.15731i) q^{39} +(3.23504 - 3.01949i) q^{40} +(-2.08830 - 1.20568i) q^{41} +(-2.26291 + 6.07283i) q^{42} +(0.473105 - 0.273147i) q^{43} +(-5.80838 + 1.96424i) q^{44} +(-4.55264 + 1.14196i) q^{45} +(7.44005 - 10.3700i) q^{46} +(1.83914 + 3.18549i) q^{47} +(6.92783 + 0.0714765i) q^{48} +(1.97180 + 6.71655i) q^{49} +(-3.28843 + 1.48769i) q^{50} +(0.392056 + 0.968394i) q^{51} +(7.24851 + 6.37153i) q^{52} -0.430107 q^{53} +(-6.39351 - 3.62258i) q^{54} -4.79657 q^{55} +(6.03823 - 4.42038i) q^{56} +(9.05864 - 3.66740i) q^{57} +(8.72955 - 3.94926i) q^{58} +(-2.05729 + 3.56332i) q^{59} +(5.11598 + 1.78911i) q^{60} +(11.3148 - 6.53263i) q^{61} +(1.97731 + 1.41864i) q^{62} +(-7.87359 + 1.00328i) q^{63} +(-6.63639 - 4.46748i) q^{64} +(3.77480 + 6.53815i) q^{65} +(-5.43664 - 5.18037i) q^{66} +(-1.39203 - 0.803692i) q^{67} +(0.236711 - 1.18292i) q^{68} +(15.4807 + 2.16447i) q^{69} +(5.58241 - 1.76254i) q^{70} -10.5254i q^{71} +(3.86641 + 7.55320i) q^{72} -1.88011i q^{73} +(-0.760941 + 7.68070i) q^{74} +(-3.48530 - 2.71903i) q^{75} +(-11.0654 - 2.21427i) q^{76} +(-8.05385 - 0.963155i) q^{77} +(-2.78278 + 11.4875i) q^{78} +(6.41918 - 3.70612i) q^{79} +(-3.79835 - 4.97374i) q^{80} +(0.288576 - 8.99537i) q^{81} +(-1.98795 + 2.77081i) q^{82} +(0.801117 + 1.38758i) q^{83} +(8.23092 + 4.03136i) q^{84} +(0.471859 - 0.817284i) q^{85} +(-0.318443 - 0.703896i) q^{86} +(9.25217 + 7.21803i) q^{87} +(1.95447 + 8.44814i) q^{88} +14.0535i q^{89} +(0.972354 + 6.56626i) q^{90} +(5.02536 + 11.7361i) q^{91} +(-13.5566 - 11.9164i) q^{92} +(-0.412714 + 2.95180i) q^{93} +(4.73944 - 2.14413i) q^{94} +(-7.64511 - 4.41391i) q^{95} +(1.06651 - 9.73974i) q^{96} +(-14.8174 + 8.55485i) q^{97} +(9.72728 - 1.83850i) q^{98} +(2.52257 - 8.84458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.139426	−	1.40732i	0.0985892	−	0.995128i
$2$	0.139426	−	1.40732i	0.0985892	−	0.995128i
$3$	1.60547	−	0.649977i	0.926918	−	0.375264i
$3$	1.60547	−	0.649977i	0.926918	−	0.375264i
$4$	−1.96112	−	0.392436i	−0.980560	−	0.196218i
$5$	−1.35495	−	0.782280i	−0.605951	−	0.349846i	0.165428	−	0.986222i	$-0.447099\pi$
$5$	−1.35495	−	0.782280i	−0.605951	−	0.349846i	−0.771379	+	0.636376i	$0.780433\pi$
$6$	−0.690883	−	2.35004i	−0.282052	−	0.959399i
$7$	−2.11799	−	1.58559i	−0.800527	−	0.599297i
$7$	−2.11799	−	1.58559i	−0.800527	−	0.599297i
$8$	−0.825716	+	2.70522i	−0.291935	+	0.956438i
$9$	2.15506	−	2.08703i	0.718354	−	0.695678i
$10$	−1.28984	+	1.79778i	−0.407882	+	0.568508i
$11$	2.65503	−	1.53288i	0.800521	−	0.462181i	−0.0431325	−	0.999069i	$-0.513734\pi$
$11$	2.65503	−	1.53288i	0.800521	−	0.462181i	0.843653	+	0.536889i	$0.180400\pi$
$12$	−3.40359	+	0.644639i	−0.982532	+	0.186091i
$13$	−4.17891	−	2.41269i	−1.15902	−	0.669160i	−0.207951	−	0.978139i	$-0.566679\pi$
$13$	−4.17891	−	2.41269i	−1.15902	−	0.669160i	−0.951069	+	0.308979i	$0.900013\pi$
$14$	−2.52674	+	2.75963i	−0.675301	+	0.737542i
$15$	−2.68379	−	0.375241i	−0.692952	−	0.0968869i
$16$	3.69199	+	1.53923i	0.922997	+	0.384807i
$17$			0.603184i			0.146294i	0.997321	+	0.0731468i	$0.0233042\pi$
$17$			0.603184i			0.146294i	−0.997321	+	0.0731468i	$0.976696\pi$
$18$	−2.63666	−	3.32386i	−0.621467	−	0.783440i
$19$	5.64236			1.29445			0.647224	−	0.762300i	$-0.275930\pi$
$19$	5.64236			1.29445			0.647224	+	0.762300i	$0.275930\pi$
$20$	2.35022	+	2.06588i	0.525526	+	0.461944i
$21$	−4.43097	−	1.16897i	−0.966917	−	0.255090i
$22$	−1.78708	−	3.95021i	−0.381006	−	0.842187i
$23$	7.81563	+	4.51236i	1.62967	+	0.940891i	0.984190	+	0.177116i	$0.0566767\pi$
$23$	7.81563	+	4.51236i	1.62967	+	0.940891i	0.645482	+	0.763776i	$0.276657\pi$
$24$	0.432666	+	4.87984i	0.0883175	+	0.996092i
$25$	−1.27608	−	2.21023i	−0.255215	−	0.442046i
$26$	−3.97809	+	5.54468i	−0.780167	+	1.08740i
$27$	2.10336	−	4.75141i	0.404792	−	0.914409i
$28$	3.53140	+	3.94071i	0.667372	+	0.744725i
$29$	3.38751	+	5.86734i	0.629045	+	1.08954i	0.987744	+	0.156084i	$0.0498871\pi$
$29$	3.38751	+	5.86734i	0.629045	+	1.08954i	−0.358699	+	0.933453i	$0.616780\pi$
$30$	−0.902277	+	3.72464i	−0.164732	+	0.680024i
$31$	−0.860400	+	1.49026i	−0.154532	+	0.267658i	−0.932889	−	0.360165i	$-0.882720\pi$
$31$	−0.860400	+	1.49026i	−0.154532	+	0.267658i	0.778356	+	0.627823i	$0.216054\pi$
$32$	2.68095	−	4.98121i	0.473930	−	0.880563i
$33$	3.26623	−	4.18670i	0.568577	−	0.728810i
$34$	0.848876	+	0.0840997i	0.145581	+	0.0144230i
$35$	1.62940	+	3.80526i	0.275418	+	0.643206i
$36$	−5.04536	+	3.24720i	−0.840894	+	0.541201i
$37$	−5.45766			−0.897234			−0.448617	−	0.893724i	$-0.648083\pi$
$37$	−5.45766			−0.897234			−0.448617	+	0.893724i	$0.648083\pi$
$38$	0.786694	−	7.94063i	0.127619	−	1.28814i
$39$	−8.27730	−	1.15731i	−1.32543	−	0.185318i
$40$	3.23504	−	3.01949i	0.511505	−	0.477423i
$41$	−2.08830	−	1.20568i	−0.326138	−	0.188296i	0.327987	−	0.944682i	$-0.393630\pi$
$41$	−2.08830	−	1.20568i	−0.326138	−	0.188296i	−0.654125	+	0.756386i	$0.726963\pi$
$42$	−2.26291	+	6.07283i	−0.349175	+	0.937057i
$43$	0.473105	−	0.273147i	0.0721478	−	0.0416546i	−0.463492	−	0.886101i	$-0.653404\pi$
$43$	0.473105	−	0.273147i	0.0721478	−	0.0416546i	0.535640	+	0.844446i	$0.320070\pi$
$44$	−5.80838	+	1.96424i	−0.875647	+	0.296120i
$45$	−4.55264	+	1.14196i	−0.678668	+	0.170234i
$46$	7.44005	−	10.3700i	1.09698	−	1.52897i
$47$	1.83914	+	3.18549i	0.268267	+	0.464651i	0.968414	−	0.249347i	$-0.0802158\pi$
$47$	1.83914	+	3.18549i	0.268267	+	0.464651i	−0.700148	+	0.713998i	$0.746883\pi$
$48$	6.92783	+	0.0714765i	0.999947	+	0.0103167i
$49$	1.97180	+	6.71655i	0.281686	+	0.959507i
$50$	−3.28843	+	1.48769i	−0.465054	+	0.210391i
$51$	0.392056	+	0.968394i	0.0548988	+	0.135602i
$52$	7.24851	+	6.37153i	1.00519	+	0.883572i
$53$	−0.430107			−0.0590798			−0.0295399	−	0.999564i	$-0.509404\pi$
$53$	−0.430107			−0.0590798			−0.0295399	+	0.999564i	$0.509404\pi$
$54$	−6.39351	−	3.62258i	−0.870046	−	0.492971i
$55$	−4.79657			−0.646769
$56$	6.03823	−	4.42038i	0.806892	−	0.590699i
$57$	9.05864	−	3.66740i	1.19985	−	0.485760i
$58$	8.72955	−	3.94926i	1.14625	−	0.518563i
$59$	−2.05729	+	3.56332i	−0.267836	+	0.463905i	−0.968303	−	0.249780i	$-0.919642\pi$
$59$	−2.05729	+	3.56332i	−0.267836	+	0.463905i	0.700467	+	0.713685i	$0.252975\pi$
$60$	5.11598	+	1.78911i	0.660470	+	0.230973i
$61$	11.3148	−	6.53263i	1.44872	−	0.836417i	0.450312	−	0.892871i	$-0.351313\pi$
$61$	11.3148	−	6.53263i	1.44872	−	0.836417i	0.998405	+	0.0564545i	$0.0179796\pi$
$62$	1.97731	+	1.41864i	0.251119	+	0.180168i
$63$	−7.87359	+	1.00328i	−0.991979	+	0.126402i
$64$	−6.63639	−	4.46748i	−0.829548	−	0.558435i
$65$	3.77480	+	6.53815i	0.468206	+	0.810957i
$66$	−5.43664	−	5.18037i	−0.669204	−	0.637660i
$67$	−1.39203	−	0.803692i	−0.170064	−	0.0981866i	0.412552	−	0.910934i	$-0.364638\pi$
$67$	−1.39203	−	0.803692i	−0.170064	−	0.0981866i	−0.582616	+	0.812748i	$0.697971\pi$
$68$	0.236711	−	1.18292i	0.0287054	−	0.143450i
$69$	15.4807	+	2.16447i	1.86365	+	0.260572i
$70$	5.58241	−	1.76254i	0.667226	−	0.210663i
$71$		−	10.5254i		−	1.24913i	−0.780973	−	0.624565i	$-0.785276\pi$
$71$		−	10.5254i		−	1.24913i	0.780973	−	0.624565i	$-0.214724\pi$
$72$	3.86641	+	7.55320i	0.455661	+	0.890153i
$73$		−	1.88011i		−	0.220051i	−0.993929	−	0.110025i	$-0.964907\pi$
$73$		−	1.88011i		−	0.220051i	0.993929	−	0.110025i	$-0.0350932\pi$
$74$	−0.760941	+	7.68070i	−0.0884576	+	0.892863i
$75$	−3.48530	−	2.71903i	−0.402448	−	0.313967i
$76$	−11.0654	−	2.21427i	−1.26928	−	0.253994i
$77$	−8.05385	−	0.963155i	−0.917822	−	0.109762i
$78$	−2.78278	+	11.4875i	−0.315088	+	1.30070i
$79$	6.41918	−	3.70612i	0.722215	−	0.416971i	−0.0933526	−	0.995633i	$-0.529758\pi$
$79$	6.41918	−	3.70612i	0.722215	−	0.416971i	0.815567	+	0.578662i	$0.196425\pi$
$80$	−3.79835	−	4.97374i	−0.424668	−	0.556081i
$81$	0.288576	−	8.99537i	0.0320639	−	0.999486i
$82$	−1.98795	+	2.77081i	−0.219532	+	0.305985i
$83$	0.801117	+	1.38758i	0.0879341	+	0.152306i	0.906638	−	0.421910i	$-0.138640\pi$
$83$	0.801117	+	1.38758i	0.0879341	+	0.152306i	−0.818704	+	0.574216i	$0.805307\pi$
$84$	8.23092	+	4.03136i	0.898067	+	0.439858i
$85$	0.471859	−	0.817284i	0.0511803	−	0.0886469i
$86$	−0.318443	−	0.703896i	−0.0343386	−	0.0759030i
$87$	9.25217	+	7.21803i	0.991937	+	0.773854i
$88$	1.95447	+	8.44814i	0.208348	+	0.900575i
$89$			14.0535i			1.48966i	0.667252	+	0.744832i	$0.267471\pi$
$89$			14.0535i			1.48966i	−0.667252	+	0.744832i	$0.732529\pi$
$90$	0.972354	+	6.56626i	0.102495	+	0.692145i
$91$	5.02536	+	11.7361i	0.526800	+	1.23028i
$92$	−13.5566	−	11.9164i	−1.41337	−	1.24237i
$93$	−0.412714	+	2.95180i	−0.0427964	+	0.306088i
$94$	4.73944	−	2.14413i	0.488836	−	0.221150i
$95$	−7.64511	−	4.41391i	−0.784372	−	0.452857i
$96$	1.06651	−	9.73974i	0.108850	−	0.994058i
$97$	−14.8174	+	8.55485i	−1.50448	+	0.868614i	−0.504496	+	0.863414i	$0.668322\pi$
$97$	−14.8174	+	8.55485i	−1.50448	+	0.868614i	−0.999986	+	0.00519970i	$0.998345\pi$
$98$	9.72728	−	1.83850i	0.982603	−	0.185717i
$99$	2.52257	−	8.84458i	0.253528	−	0.888914i
$100$	1.63517	+	4.83530i	0.163517	+	0.483530i
$101$	6.71208	−	3.87522i	0.667877	−	0.385599i	−0.127395	−	0.991852i	$-0.540662\pi$
$101$	6.71208	−	3.87522i	0.667877	−	0.385599i	0.795272	+	0.606253i	$0.207328\pi$
$102$	1.41751	−	0.416730i	0.140354	−	0.0412624i
$103$	−7.63585	+	13.2257i	−0.752382	+	1.30316i	0.194283	+	0.980946i	$0.437762\pi$
$103$	−7.63585	+	13.2257i	−0.752382	+	1.30316i	−0.946665	+	0.322219i	$0.895571\pi$
$104$	9.97744	−	9.31264i	0.978369	−	0.913180i
$105$	5.08928	+	5.05015i	0.496662	+	0.492845i
$106$	−0.0599682	+	0.605300i	−0.00582463	+	0.0587920i
$107$		−	6.97461i		−	0.674261i	−0.941458	−	0.337131i	$-0.890544\pi$
$107$		−	6.97461i		−	0.674261i	0.941458	−	0.337131i	$-0.109456\pi$
$108$	−5.98957	+	8.49265i	−0.576346	+	0.817206i
$109$	−9.19063			−0.880303			−0.440152	−	0.897924i	$-0.645075\pi$
$109$	−9.19063			−0.880303			−0.440152	+	0.897924i	$0.645075\pi$
$110$	−0.668767	+	6.75032i	−0.0637645	+	0.643618i
$111$	−8.76211	+	3.54735i	−0.831662	+	0.336700i
$112$	−5.37903	−	9.11406i	−0.508270	−	0.861198i
$113$	−2.66541	+	4.61663i	−0.250741	+	0.434296i	−0.963730	−	0.266879i	$-0.914008\pi$
$113$	−2.66541	+	4.61663i	−0.250741	+	0.434296i	0.712989	+	0.701175i	$0.247341\pi$
$114$	−3.89821	−	13.2598i	−0.365101	−	1.24189i
$115$	−7.05985	−	12.2280i	−0.658335	−	1.14027i
$116$	−4.34076	−	12.8359i	−0.403030	−	1.19179i
$117$	−14.0412	+	3.52202i	−1.29811	+	0.325611i
$118$	4.72791	+	3.39209i	0.435239	+	0.312267i
$119$	0.956404	−	1.27754i	0.0876734	−	0.117112i
$120$	3.23116	−	6.95039i	0.294963	−	0.634481i
$121$	−0.800555	+	1.38660i	−0.0727777	+	0.126055i
$122$	−7.61593	−	16.8345i	−0.689514	−	1.52412i
$123$	−4.13637	−	0.578337i	−0.372964	−	0.0521469i
$124$	2.27218	−	2.58492i	0.204048	−	0.232133i
$125$			11.8158i			1.05684i
$126$	0.314157	+	11.2206i	0.0279873	+	0.999608i
$127$		−	1.96179i		−	0.174080i	−0.996205	−	0.0870402i	$-0.972259\pi$
$127$		−	1.96179i		−	0.174080i	0.996205	−	0.0870402i	$-0.0277409\pi$
$128$	−7.21248	+	8.71666i	−0.637499	+	0.770451i
$129$	0.582016	−	0.746036i	0.0512436	−	0.0656848i
$130$	9.72760	−	4.40078i	0.853167	−	0.385974i
$131$	3.67079	−	6.35800i	0.320719	−	0.555501i	−0.659918	−	0.751338i	$-0.729409\pi$
$131$	3.67079	−	6.35800i	0.320719	−	0.555501i	0.980637	+	0.195837i	$0.0627423\pi$
$132$	−8.04847	+	6.92883i	−0.700530	+	0.603078i
$133$	−11.9505	−	8.94648i	−1.03624	−	0.775758i
$134$	−1.32514	+	1.84699i	−0.114475	+	0.159555i
$135$	−6.56688	+	4.79250i	−0.565187	+	0.412472i
$136$	−1.63174	−	0.498059i	−0.139921	−	0.0427082i
$137$	−1.48981	−	2.58042i	−0.127283	−	0.220460i	0.795340	−	0.606163i	$-0.207292\pi$
$137$	−1.48981	−	2.58042i	−0.127283	−	0.220460i	−0.922623	+	0.385703i	$0.873959\pi$
$138$	5.20453	−	21.4845i	0.443039	−	1.82889i
$139$	−0.156332	+	0.270775i	−0.0132599	+	0.0229668i	−0.872579	−	0.488473i	$-0.837554\pi$
$139$	−0.156332	+	0.270775i	−0.0132599	+	0.0229668i	0.859319	+	0.511439i	$0.170888\pi$
$140$	−1.70213	−	8.10201i	−0.143856	−	0.684744i
$141$	5.02318	+	3.91881i	0.423028	+	0.330023i
$142$	−14.8126	−	1.46751i	−1.24304	−	0.123151i
$143$	−14.7935			−1.23709
$144$	11.1689	−	4.38818i	0.930740	−	0.365681i
$145$		−	10.5999i		−	0.880276i
$146$	−2.64593	−	0.262137i	−0.218979	−	0.0216946i
$147$	7.53126	+	9.50158i	0.621168	+	0.783677i
$148$	10.7031	+	2.14178i	0.879792	+	0.176053i
$149$	6.08449	−	10.5386i	0.498461	−	0.863359i	−0.501538	−	0.865136i	$-0.667232\pi$
$149$	6.08449	−	10.5386i	0.498461	−	0.863359i	0.999998	+	0.00177667i	$0.000565533\pi$
$150$	−4.31250	+	4.52584i	−0.352114	+	0.369533i
$151$	−10.8594	+	6.26969i	−0.883727	+	0.510220i	−0.871885	−	0.489710i	$-0.837103\pi$
$151$	−10.8594	+	6.26969i	−0.883727	+	0.510220i	−0.0118414	+	0.999930i	$0.503769\pi$
$152$	−4.65899	+	15.2638i	−0.377894	+	1.23806i
$153$	1.25887	+	1.29990i	0.101773	+	0.105091i
$154$	−2.47839	+	11.2001i	−0.199714	+	0.902529i
$155$	2.33160	−	1.34615i	0.187278	−	0.108125i
$156$	15.7786	+	5.51793i	1.26330	+	0.441788i
$157$	9.12353	+	5.26748i	0.728137	+	0.420390i	0.817740	−	0.575587i	$-0.195226\pi$
$157$	9.12353	+	5.26748i	0.728137	+	0.420390i	−0.0896030	+	0.995978i	$0.528560\pi$
$158$	−4.32070	−	9.55060i	−0.343737	−	0.759805i
$159$	−0.690524	+	0.279560i	−0.0547621	+	0.0221705i
$160$	−7.52926	+	4.65203i	−0.595240	+	0.367776i
$161$	−9.39871	−	21.9495i	−0.740722	−	1.72987i
$162$	−12.6192	−	1.66031i	−0.991455	−	0.130446i
$163$			14.0402i			1.09971i	0.835260	+	0.549855i	$0.185317\pi$
$163$			14.0402i			1.09971i	−0.835260	+	0.549855i	$0.814683\pi$
$164$	3.62226	+	3.18401i	0.282851	+	0.248629i
$165$	−7.70074	+	3.11766i	−0.599502	+	0.242709i
$166$	2.06447	−	0.933967i	0.160234	−	0.0724899i
$167$	−0.653708	+	1.13226i	−0.0505854	+	0.0876165i	−0.890209	−	0.455552i	$-0.849442\pi$
$167$	−0.653708	+	1.13226i	−0.0505854	+	0.0876165i	0.839624	+	0.543168i	$0.182775\pi$
$168$	6.82104	−	11.0215i	0.526255	−	0.850327i
$169$	5.14217	+	8.90649i	0.395551	+	0.685115i
$170$	−1.08439	−	0.778009i	−0.0831692	−	0.0596706i
$171$	12.1596	−	11.7758i	0.929871	−	0.900518i
$172$	−1.03501	+	0.350011i	−0.0789186	+	0.0266881i
$173$	−11.3036	+	6.52614i	−0.859398	+	0.496173i	−0.863811	−	0.503817i	$-0.831929\pi$
$173$	−11.3036	+	6.52614i	−0.859398	+	0.496173i	0.00441290	+	0.999990i	$0.498595\pi$
$174$	11.4481	−	12.0144i	0.867878	−	0.910811i
$175$	−0.801797	+	6.70459i	−0.0606101	+	0.506819i
$176$	12.1618	−	1.57269i	0.916729	−	0.118546i
$177$	−0.986831	+	7.05799i	−0.0741748	+	0.530511i
$178$	19.7778	+	1.95942i	1.48241	+	0.146865i
$179$			14.5664i			1.08875i	0.838843	+	0.544373i	$0.183232\pi$
$179$			14.5664i			1.08875i	−0.838843	+	0.544373i	$0.816768\pi$
$180$	9.37643	−	0.452908i	0.698878	−	0.0337578i
$181$		−	12.3620i		−	0.918861i	−0.888214	−	0.459431i	$-0.848053\pi$
$181$		−	12.3620i		−	0.918861i	0.888214	−	0.459431i	$-0.151947\pi$
$182$	17.2172	−	5.43598i	1.27622	−	0.402942i
$183$	13.9196	−	17.8423i	1.02896	−	1.31894i
$184$	−18.6604	+	17.4170i	−1.37566	+	1.28400i
$185$	7.39485	+	4.26942i	0.543680	+	0.313894i
$186$	4.09660	+	0.992381i	0.300377	+	0.0727649i
$187$	0.924609	+	1.60147i	0.0676141	+	0.117111i
$188$	−2.35668	−	6.96888i	−0.171879	−	0.508258i
$189$	−11.9887	+	6.72839i	−0.872049	+	0.489418i
$190$	−7.27773	+	10.1437i	−0.527982	+	0.735904i
$191$	−6.72098	+	3.88036i	−0.486313	+	0.280773i	−0.723044	−	0.690802i	$-0.757257\pi$
$191$	−6.72098	+	3.88036i	−0.486313	+	0.280773i	0.236731	+	0.971575i	$0.423924\pi$
$192$	−13.5583	−	2.85890i	−0.978484	−	0.206324i
$193$	−1.26747	+	2.19532i	−0.0912343	+	0.158023i	−0.908031	−	0.418903i	$-0.862415\pi$
$193$	−1.26747	+	2.19532i	−0.0912343	+	0.158023i	0.816796	+	0.576926i	$0.195748\pi$
$194$	9.97351	+	22.0457i	0.716056	+	1.58279i
$195$	10.3100	+	8.04326i	0.738312	+	0.575990i
$196$	−1.23113	−	13.9458i	−0.0879377	−	0.996126i
$197$	27.5862			1.96544			0.982718	−	0.185109i	$-0.0592638\pi$
$197$	27.5862			1.96544			0.982718	+	0.185109i	$0.0592638\pi$
$198$	−12.0955	−	4.78324i	−0.859588	−	0.339930i
$199$	−2.26815			−0.160785			−0.0803925	−	0.996763i	$-0.525617\pi$
$199$	−2.26815			−0.160785			−0.0803925	+	0.996763i	$0.525617\pi$
$200$	7.03282	−	1.62704i	0.497296	−	0.115049i
$201$	−2.75725	−	0.385512i	−0.194481	−	0.0271919i
$202$	−4.51785	−	9.98638i	−0.317875	−	0.702639i
$203$	2.12847	−	17.7982i	0.149390	−	1.24919i
$204$	−0.388836	−	2.05299i	−0.0272240	−	0.143738i
$205$	1.88636	+	3.26727i	0.131749	+	0.228196i
$206$	17.5482	+	12.5901i	1.22264	+	0.877195i
$207$	26.2606	−	6.58709i	1.82524	−	0.457834i
$208$	−11.7148	−	15.3399i	−0.812274	−	1.06363i
$209$	14.9806	−	8.64907i	1.03623	−	0.598269i
$210$	7.81678	−	6.45814i	0.539409	−	0.445654i
$211$	3.25741	+	1.88067i	0.224249	+	0.129470i	0.607916	−	0.794001i	$-0.292006\pi$
$211$	3.25741	+	1.88067i	0.224249	+	0.129470i	−0.383667	+	0.923471i	$0.625339\pi$
$212$	0.843492	+	0.168789i	0.0579313	+	0.0115925i
$213$	−6.84123	−	16.8981i	−0.468753	−	1.15784i
$214$	−9.81554	−	0.972444i	−0.670976	−	0.0664749i
$215$	−0.854710			−0.0582908
$216$	11.1168	+	9.61336i	0.756403	+	0.654106i
$217$	4.18526	−	1.79211i	0.284114	−	0.121657i
$218$	−1.28142	+	12.9342i	−0.0867884	+	0.876014i
$219$	−1.22203	−	3.01846i	−0.0825771	−	0.203969i
$220$	9.40664	+	1.88234i	0.634196	+	0.126908i
$221$	1.45530	−	2.52065i	0.0978939	−	0.169557i
$222$	3.77061	+	12.8257i	0.253067	+	0.860806i
$223$	−7.77796	−	13.4718i	−0.520850	−	0.902139i	−0.999706	−	0.0242457i	$-0.992282\pi$
$223$	−7.77796	−	13.4718i	−0.520850	−	0.902139i	0.478856	−	0.877894i	$-0.341052\pi$
$224$	−13.5764	+	6.29929i	−0.907112	+	0.420889i
$225$	−7.36285	−	2.09996i	−0.490856	−	0.139998i
$226$	6.12546	+	4.39478i	0.407460	+	0.292336i
$227$	8.59421	+	14.8856i	0.570418	+	0.987992i	0.996523	+	0.0833188i	$0.0265520\pi$
$227$	8.59421	+	14.8856i	0.570418	+	0.987992i	−0.426105	+	0.904674i	$0.640115\pi$
$228$	−19.2043	+	3.63729i	−1.27184	+	0.240885i
$229$	14.8935	+	8.59879i	0.984193	+	0.568224i	0.903533	−	0.428518i	$-0.140964\pi$
$229$	14.8935	+	8.59879i	0.984193	+	0.568224i	0.0806596	+	0.996742i	$0.474297\pi$
$230$	−18.1931	+	8.23059i	−1.19962	+	0.542709i
$231$	−13.5562	+	3.68850i	−0.891935	+	0.242686i
$232$	−18.6695	+	4.31919i	−1.22572	+	0.283569i
$233$	−12.6033			−0.825667			−0.412834	−	0.910806i	$-0.635461\pi$
$233$	−12.6033			−0.825667			−0.412834	+	0.910806i	$0.635461\pi$
$234$	2.99892	+	20.2515i	0.196045	+	1.32388i
$235$		−	5.75490i		−	0.375408i
$236$	5.43296	−	6.18075i	0.353656	−	0.402333i
$237$	7.89691	−	10.1224i	0.512959	−	0.657519i
$238$	−1.66457	−	1.52409i	−0.107898	−	0.0987922i
$239$	2.38860	+	1.37906i	0.154506	+	0.0892038i	0.575259	−	0.817971i	$-0.304901\pi$
$239$	2.38860	+	1.37906i	0.154506	+	0.0892038i	−0.420754	+	0.907175i	$0.638234\pi$
$240$	−9.33094	−	5.51635i	−0.602310	−	0.356079i
$241$	−18.4108	+	10.6295i	−1.18594	+	0.684705i	−0.957382	−	0.288824i	$-0.906736\pi$
$241$	−18.4108	+	10.6295i	−1.18594	+	0.684705i	−0.228562	+	0.973529i	$0.573402\pi$
$242$	1.83978	+	1.31997i	0.118266	+	0.0848508i
$243$	−5.38348	−	14.6294i	−0.345351	−	0.938474i
$244$	−24.7534	+	8.37092i	−1.58467	+	0.535893i
$245$	2.58253	−	10.6431i	0.164992	−	0.679961i
$246$	−1.39063	+	5.74057i	−0.0886630	+	0.366005i
$247$	−23.5789	−	13.6133i	−1.50029	−	0.866193i
$248$	−3.32102	−	3.55810i	−0.210885	−	0.225939i
$249$	2.18806	+	1.70700i	0.138663	+	0.108177i
$250$	16.6286	+	1.64743i	1.05169	+	0.104193i
$251$	21.6486			1.36645			0.683225	−	0.730208i	$-0.260577\pi$
$251$	21.6486			1.36645			0.683225	+	0.730208i	$0.260577\pi$
$252$	15.8348	+	1.12232i	0.997498	+	0.0706996i
$253$	27.6676			1.73945
$254$	−2.76087	−	0.273524i	−0.173232	−	0.0171625i
$255$	0.226340	−	1.61882i	0.0141739	−	0.101374i
$256$	11.2616	+	11.3656i	0.703847	+	0.710351i
$257$	−1.58731	−	0.916432i	−0.0990135	−	0.0571655i	0.449676	−	0.893192i	$-0.351540\pi$
$257$	−1.58731	−	0.916432i	−0.0990135	−	0.0571655i	−0.548689	+	0.836026i	$0.684873\pi$
$258$	−0.968766	−	0.923102i	−0.0603128	−	0.0574698i
$259$	11.5593	+	8.65362i	0.718260	+	0.537710i
$260$	−4.83704	−	14.3035i	−0.299980	−	0.887063i
$261$	19.5456	+	5.57462i	1.20984	+	0.345061i
$262$	−8.43596	−	6.05247i	−0.521175	−	0.373923i
$263$	−4.14197	+	2.39137i	−0.255405	+	0.147458i	−0.622237	−	0.782829i	$-0.713776\pi$
$263$	−4.14197	+	2.39137i	−0.255405	+	0.147458i	0.366832	+	0.930287i	$0.380443\pi$
$264$	8.62894	+	12.2929i	0.531075	+	0.756574i
$265$	0.582773	+	0.336464i	0.0357995	+	0.0206688i
$266$	−14.2568	+	15.5708i	−0.874141	+	0.954710i
$267$	9.13442	+	22.5624i	0.559018	+	1.38080i
$268$	2.41455	+	2.12242i	0.147492	+	0.129647i
$269$			7.26728i			0.443094i	0.975150	+	0.221547i	$0.0711106\pi$
$269$			7.26728i			0.443094i	−0.975150	+	0.221547i	$0.928889\pi$
$270$	5.82900	+	9.90992i	0.354742	+	0.603099i
$271$	22.6258			1.37442			0.687209	−	0.726460i	$-0.258836\pi$
$271$	22.6258			1.37442			0.687209	+	0.726460i	$0.258836\pi$
$272$	−0.928438	+	2.22695i	−0.0562948	+	0.135029i
$273$	15.6962	+	15.5756i	0.949980	+	0.942677i
$274$	−3.83921	+	1.73686i	−0.231935	+	0.104928i
$275$	−6.77603	−	3.91214i	−0.408610	−	0.235911i
$276$	−29.5101	−	10.3200i	−1.77630	−	0.621189i
$277$	−4.33032	−	7.50034i	−0.260184	−	0.450652i	0.706107	−	0.708105i	$-0.250450\pi$
$277$	−4.33032	−	7.50034i	−0.260184	−	0.450652i	−0.966291	+	0.257454i	$0.917116\pi$
$278$	0.359271	+	0.257763i	0.0215477	+	0.0154596i
$279$	1.25600	+	5.00728i	0.0751949	+	0.299778i
$280$	−11.6395	+	1.26581i	−0.695591	+	0.0756466i
$281$	−12.3243	−	21.3464i	−0.735207	−	1.27342i	−0.954632	−	0.297787i	$-0.903751\pi$
$281$	−12.3243	−	21.3464i	−0.735207	−	1.27342i	0.219425	−	0.975629i	$-0.429582\pi$
$282$	6.21539	−	6.52286i	0.370121	−	0.388431i
$283$	11.4042	−	19.7527i	0.677910	−	1.17418i	−0.297699	−	0.954660i	$-0.596219\pi$
$283$	11.4042	−	19.7527i	0.677910	−	1.17418i	0.975609	−	0.219515i	$-0.0704476\pi$
$284$	−4.13052	+	20.6415i	−0.245101	+	1.22485i
$285$	−15.1429	−	2.11725i	−0.896990	−	0.125415i
$286$	−2.06260	+	20.8192i	−0.121964	+	1.23107i
$287$	2.51129	+	5.86482i	0.148237	+	0.346189i
$288$	−4.61835	−	16.3301i	−0.272139	−	0.962258i
$289$	16.6362			0.978598
$290$	−14.9175	−	1.47791i	−0.875987	−	0.0867857i
$291$	−18.2285	+	23.3655i	−1.06857	+	1.36971i
$292$	−0.737824	+	3.68713i	−0.0431779	+	0.215773i
$293$	−8.93196	−	5.15687i	−0.521811	−	0.301268i	0.215864	−	0.976423i	$-0.430743\pi$
$293$	−8.93196	−	5.15687i	−0.521811	−	0.301268i	−0.737675	+	0.675156i	$0.764076\pi$
$294$	14.4219	−	9.27416i	0.841100	−	0.540880i
$295$	5.57503	−	3.21875i	0.324591	−	0.187403i
$296$	4.50648	−	14.7642i	0.261934	−	0.858149i
$297$	−1.69886	−	15.8393i	−0.0985780	−	0.919090i
$298$	−13.9829	−	10.0322i	−0.810010	−	0.581150i
$299$	−21.7739	−	37.7134i	−1.25921	−	2.18102i
$300$	5.76804	+	6.70011i	0.333018	+	0.386831i
$301$	−1.43513	−	0.171627i	−0.0827197	−	0.00989239i
$302$	7.30939	+	16.1569i	0.420608	+	0.929724i
$303$	8.25723	−	10.5842i	0.474366	−	0.608049i
$304$	20.8315	+	8.68488i	1.19477	+	0.498112i
$305$	−20.4414			−1.17047
$306$	2.00490	−	1.59039i	0.114612	−	0.0909167i
$307$	15.9763			0.911818			0.455909	−	0.890026i	$-0.349314\pi$
$307$	15.9763			0.911818			0.455909	+	0.890026i	$0.349314\pi$
$308$	15.4166	+	5.04948i	0.878442	+	0.287721i
$309$	−3.66274	+	26.1965i	−0.208366	+	1.49027i
$310$	−1.56938	−	3.46900i	−0.0891348	−	0.197026i
$311$	−11.9638	+	20.7219i	−0.678405	+	1.17503i	0.297056	+	0.954860i	$0.403995\pi$
$311$	−11.9638	+	20.7219i	−0.678405	+	1.17503i	−0.975461	+	0.220172i	$0.929338\pi$
$312$	9.96547	−	21.4363i	0.564184	−	1.21359i
$313$	12.2943	−	7.09809i	0.694913	−	0.401208i	−0.110537	−	0.993872i	$-0.535257\pi$
$313$	12.2943	−	7.09809i	0.694913	−	0.401208i	0.805450	+	0.592664i	$0.201924\pi$
$314$	8.68510	−	12.1053i	0.490129	−	0.683144i
$315$	11.4532	+	4.79996i	0.645312	+	0.270447i
$316$	−14.0432	+	4.74903i	−0.789992	+	0.267154i
$317$	0.252032	+	0.436532i	0.0141555	+	0.0245181i	0.873016	−	0.487691i	$-0.162161\pi$
$317$	0.252032	+	0.436532i	0.0141555	+	0.0245181i	−0.858861	+	0.512209i	$0.828827\pi$
$318$	0.297154	+	1.01077i	0.0166636	+	0.0566811i
$319$	17.9879	+	10.3853i	1.00713	+	0.581465i
$320$	5.49714	+	11.2447i	0.307300	+	0.628599i
$321$	−4.53333	−	11.1975i	−0.253026	−	0.624985i
$322$	−32.2005	+	10.1667i	−1.79447	+	0.566567i
$323$			3.40339i			0.189369i
$324$	−4.09604	+	17.5278i	−0.227558	+	0.973765i
$325$			12.3151i			0.683120i
$326$	19.7590	+	1.95757i	1.09435	+	0.108420i
$327$	−14.7553	+	5.97370i	−0.815969	+	0.330346i
$328$	4.98597	−	4.65375i	0.275304	−	0.256961i
$329$	1.15559	−	9.66298i	0.0637097	−	0.532737i
$330$	3.31387	+	11.2721i	0.182422	+	0.620510i
$331$	21.6527	−	12.5012i	1.19014	−	0.687128i	0.231802	−	0.972763i	$-0.425538\pi$
$331$	21.6527	−	12.5012i	1.19014	−	0.687128i	0.958338	+	0.285635i	$0.0922045\pi$
$332$	−1.02655	−	3.03559i	−0.0563394	−	0.166600i
$333$	−11.7616	+	11.3903i	−0.644531	+	0.624186i
$334$	1.50231	+	1.07784i	0.0822025	+	0.0589770i
$335$	1.25742	+	2.17792i	0.0687004	+	0.118993i
$336$	−14.5598	−	11.1361i	−0.794301	−	0.607524i
$337$	−7.55413	+	13.0841i	−0.411500	+	0.712739i	−0.995054	−	0.0993356i	$-0.968328\pi$
$337$	−7.55413	+	13.0841i	−0.411500	+	0.712739i	0.583554	+	0.812074i	$0.301662\pi$
$338$	13.2513	−	5.99489i	0.720774	−	0.326079i
$339$	−1.27854	+	9.14431i	−0.0694405	+	0.496651i
$340$	−1.24610	+	1.41762i	−0.0675795	+	0.0768811i
$341$			5.27556i			0.285688i
$342$	−14.8770	−	18.7544i	−0.804456	−	1.01412i
$343$	6.47343	−	17.3521i	0.349532	−	0.936924i
$344$	0.348272	+	1.50539i	0.0187776	+	0.0811653i
$345$	−19.2823	−	15.0430i	−1.03812	−	0.809886i
$346$	7.60838	+	16.8178i	0.409029	+	0.904128i
$347$	6.57640	+	3.79689i	0.353040	+	0.203828i	0.666023	−	0.745931i	$-0.267995\pi$
$347$	6.57640	+	3.79689i	0.353040	+	0.203828i	−0.312983	+	0.949759i	$0.601328\pi$
$348$	−15.3120	−	17.7863i	−0.820810	−	0.953446i
$349$	−15.5492	+	8.97732i	−0.832329	+	0.480545i	−0.854649	−	0.519206i	$-0.826228\pi$
$349$	−15.5492	+	8.97732i	−0.832329	+	0.480545i	0.0223207	+	0.999751i	$0.492894\pi$
$350$	9.32374	+	2.06318i	0.498375	+	0.110282i
$351$	−20.2534	+	14.7809i	−1.08105	+	0.788947i
$352$	−0.517607	−	17.3348i	−0.0275885	−	0.923950i
$353$	−14.9938	+	8.65665i	−0.798037	+	0.460747i	−0.842784	−	0.538251i	$-0.819085\pi$
$353$	−14.9938	+	8.65665i	−0.798037	+	0.460747i	0.0447470	+	0.998998i	$0.485752\pi$
$354$	9.79529	+	2.37286i	0.520614	+	0.126116i
$355$	−8.23377	+	14.2613i	−0.437003	+	0.756912i
$356$	5.51508	−	27.5605i	0.292299	−	1.46071i
$357$	0.705105	−	2.67269i	0.0373181	−	0.141454i
$358$	20.4997	+	2.03094i	1.08344	+	0.107339i
$359$		−	1.14980i		−	0.0606842i	−0.999540	−	0.0303421i	$-0.990340\pi$
$359$		−	1.14980i		−	0.0606842i	0.999540	−	0.0303421i	$-0.00965967\pi$
$360$	0.669932	−	13.2588i	0.0353085	−	0.698801i
$361$	12.8363			0.675593
$362$	−17.3974	−	1.72359i	−0.914385	−	0.0905899i
$363$	−0.384007	+	2.74649i	−0.0201552	+	0.144153i
$364$	−5.24966	−	24.9880i	−0.275157	−	1.30973i
$365$	−1.47077	+	2.54746i	−0.0769839	+	0.133340i
$366$	−23.1692	−	22.0770i	−1.21107	−	1.15398i
$367$	−10.8257	−	18.7507i	−0.565099	−	0.978780i	−0.997040	−	0.0768781i	$-0.975505\pi$
$367$	−10.8257	−	18.7507i	−0.565099	−	0.978780i	0.431942	−	0.901901i	$-0.357829\pi$
$368$	21.9097	+	28.6896i	1.14212	+	1.49555i
$369$	−7.01671	+	1.76004i	−0.365275	+	0.0916240i
$370$	7.03949	−	9.81168i	0.365966	−	0.510085i
$371$	0.910965	+	0.681974i	0.0472949	+	0.0354063i
$372$	1.96777	−	5.62688i	0.102024	−	0.291740i
$373$	8.98723	−	15.5663i	0.465341	−	0.805995i	−0.533876	−	0.845563i	$-0.679265\pi$
$373$	8.98723	−	15.5663i	0.465341	−	0.805995i	0.999217	+	0.0395683i	$0.0125983\pi$
$374$	2.38270	−	1.07794i	0.123207	−	0.0557388i
$375$	7.67999	+	18.9699i	0.396593	+	0.979601i
$376$	−10.1360	+	2.34497i	−0.522727	+	0.120933i
$377$		−	32.6921i		−	1.68373i
$378$	7.79748	+	17.8101i	0.401059	+	0.916052i
$379$		−	32.3368i		−	1.66103i	−0.556997	−	0.830515i	$-0.688047\pi$
$379$		−	32.3368i		−	1.66103i	0.556997	−	0.830515i	$-0.311953\pi$
$380$	13.2608	+	11.6564i	0.680265	+	0.597962i
$381$	−1.27511	−	3.14959i	−0.0653261	−	0.161358i
$382$	4.52384	+	9.99962i	0.231460	+	0.511625i
$383$	6.36839	−	11.0304i	0.325410	−	0.563626i	−0.656186	−	0.754600i	$-0.727831\pi$
$383$	6.36839	−	11.0304i	0.325410	−	0.563626i	0.981595	+	0.190974i	$0.0611645\pi$
$384$	−5.91378	+	18.6823i	−0.301786	+	0.953376i
$385$	10.1591	+	7.60539i	0.517756	+	0.387607i
$386$	2.91281	+	2.08982i	0.148258	+	0.106369i
$387$	0.449502	−	1.57603i	0.0228495	−	0.0801144i
$388$	32.4160	−	10.9622i	1.64567	−	0.556522i
$389$	−1.75350	−	3.03715i	−0.0889058	−	0.153989i	0.818143	−	0.575015i	$-0.195004\pi$
$389$	−1.75350	−	3.03715i	−0.0889058	−	0.153989i	−0.907049	+	0.421025i	$0.861670\pi$
$390$	12.7570	−	13.3880i	0.645973	−	0.677929i
$391$	−2.72178	+	4.71427i	−0.137646	+	0.238411i
$392$	−19.7979	−	0.211810i	−0.999943	−	0.0106980i
$393$	1.76079	−	12.5935i	0.0888203	−	0.635258i
$394$	3.84624	−	38.8227i	0.193771	−	1.95586i
$395$	−11.5969			−0.583503
$396$	−8.41800	+	16.3553i	−0.423020	+	0.821887i
$397$		−	21.6449i		−	1.08633i	−0.839626	−	0.543164i	$-0.817226\pi$
$397$		−	21.6449i		−	1.08633i	0.839626	−	0.543164i	$-0.182774\pi$
$398$	−0.316240	+	3.19203i	−0.0158517	+	0.160002i
$399$	−25.0012	−	6.59576i	−1.25162	−	0.330201i
$400$	−1.30921	−	10.1243i	−0.0654607	−	0.506216i
$401$	−4.98422	+	8.63291i	−0.248900	+	0.431107i	−0.963221	−	0.268711i	$-0.913402\pi$
$401$	−4.98422	+	8.63291i	−0.248900	+	0.431107i	0.714321	+	0.699818i	$0.246736\pi$
$402$	−0.926973	+	3.82659i	−0.0462332	+	0.190853i
$403$	7.19106	−	4.15176i	0.358212	−	0.206814i
$404$	−14.6840	+	4.96571i	−0.730555	+	0.247054i
$405$	−7.42790	+	11.9625i	−0.369096	+	0.594422i
$406$	−24.7511	−	5.47699i	−1.22837	−	0.271818i
$407$	−14.4902	+	8.36594i	−0.718255	+	0.414684i
$408$	−2.94344	+	0.260977i	−0.145722	+	0.0129203i
$409$	−13.7025	−	7.91112i	−0.677543	−	0.391180i	0.121386	−	0.992605i	$-0.461266\pi$
$409$	−13.7025	−	7.91112i	−0.677543	−	0.391180i	−0.798929	+	0.601426i	$0.794600\pi$
$410$	4.86112	−	2.19918i	0.240073	−	0.108610i
$411$	−4.06905	−	3.17445i	−0.200711	−	0.156584i
$412$	20.1650	−	22.9406i	0.993460	−	1.13020i
$413$	10.0073	−	4.28508i	0.492427	−	0.210855i
$414$	−5.60875	−	37.8756i	−0.275655	−	1.86148i
$415$		−	2.50679i		−	0.123054i
$416$	−23.2216	+	14.3477i	−1.13853	+	0.703454i
$417$	−0.0749888	+	0.536333i	−0.00367222	+	0.0262643i
$418$	−10.0833	−	22.2885i	−0.493193	−	1.09017i
$419$	−14.6538	+	25.3811i	−0.715884	+	1.23995i	0.246733	+	0.969083i	$0.420643\pi$
$419$	−14.6538	+	25.3811i	−0.715884	+	1.23995i	−0.962617	+	0.270865i	$0.912690\pi$
$420$	−7.99882	−	11.9012i	−0.390303	−	0.580718i
$421$	−13.4680	−	23.3272i	−0.656389	−	1.13690i	−0.981544	−	0.191238i	$-0.938750\pi$
$421$	−13.4680	−	23.3272i	−0.656389	−	1.13690i	0.325155	−	0.945661i	$-0.394584\pi$
$422$	3.10087	−	4.32201i	0.150948	−	0.210392i
$423$	10.6117	+	3.02657i	0.515958	+	0.147157i
$424$	0.355146	−	1.16353i	0.0172474	−	0.0565062i
$425$	1.33318	−	0.769709i	0.0646685	−	0.0373364i
$426$	−24.7350	+	7.27179i	−1.19841	+	0.352319i
$427$	−34.3228	−	4.10464i	−1.66100	−	0.198638i
$428$	−2.73709	+	13.6781i	−0.132302	+	0.661154i
$429$	−23.7505	+	9.61541i	−1.14668	+	0.464236i
$430$	−0.119169	+	1.20285i	−0.00574684	+	0.0580068i
$431$			6.40732i			0.308630i	0.988022	+	0.154315i	$0.0493170\pi$
$431$			6.40732i			0.308630i	−0.988022	+	0.154315i	$0.950683\pi$
$432$	15.0791	−	14.3046i	0.725493	−	0.688230i
$433$			37.1536i			1.78549i	0.450563	+	0.892745i	$0.351223\pi$
$433$			37.1536i			1.78549i	−0.450563	+	0.892745i	$0.648777\pi$
$434$	−1.93855	−	6.13989i	−0.0930533	−	0.294724i
$435$	−6.88970	−	17.0178i	−0.330336	−	0.815943i
$436$	18.0239	+	3.60673i	0.863190	+	0.172731i
$437$	44.0986	+	25.4604i	2.10952	+	1.21793i
$438$	−4.41834	+	1.29894i	−0.211116	+	0.0620657i
$439$	18.7727	+	32.5154i	0.895974	+	1.55187i	0.832594	+	0.553884i	$0.186855\pi$
$439$	18.7727	+	32.5154i	0.895974	+	1.55187i	0.0633805	+	0.997989i	$0.479812\pi$
$440$	3.96060	−	12.9757i	0.188814	−	0.618594i
$441$	18.2670	+	10.3593i	0.869858	+	0.493302i
$442$	−3.34446	−	2.39952i	−0.159080	−	0.114134i
$443$	−4.69335	+	2.70971i	−0.222988	+	0.128742i	−0.607333	−	0.794447i	$-0.707761\pi$
$443$	−4.69335	+	2.70971i	−0.222988	+	0.128742i	0.384345	+	0.923189i	$0.374427\pi$
$444$	18.5757	−	3.51822i	0.881562	−	0.166967i
$445$	10.9937	−	19.0417i	0.521153	−	0.902664i
$446$	−20.0437	+	9.06778i	−0.949095	+	0.429372i
$447$	2.91859	−	20.8742i	0.138044	−	0.987317i
$448$	6.97223	+	19.9847i	0.329407	+	0.944188i
$449$	−28.7353			−1.35610			−0.678051	−	0.735015i	$-0.737175\pi$
$449$	−28.7353			−1.35610			−0.678051	+	0.735015i	$0.737175\pi$
$450$	−3.98190	+	10.0691i	−0.187709	+	0.474663i
$451$	−7.39266			−0.348107
$452$	7.03892	−	8.00776i	0.331083	−	0.376653i
$453$	−13.3593	+	17.1242i	−0.627675	+	0.804563i
$454$	22.1471	−	10.0194i	1.03942	−	0.470233i
$455$	2.37182	−	19.8330i	0.111193	−	0.929788i
$456$	2.44126	+	27.5338i	0.114322	+	1.28939i
$457$	8.27639	+	14.3351i	0.387153	+	0.670569i	0.992065	−	0.125723i	$-0.0401251\pi$
$457$	8.27639	+	14.3351i	0.387153	+	0.670569i	−0.604912	+	0.796292i	$0.706792\pi$
$458$	14.1778	−	19.7611i	0.662487	−	0.923378i
$459$	2.86597	+	1.26871i	0.133772	+	0.0592185i
$460$	9.04651	+	26.7512i	0.421796	+	1.24728i
$461$	5.03928	−	2.90943i	0.234703	−	0.135506i	−0.378037	−	0.925790i	$-0.623401\pi$
$461$	5.03928	−	2.90943i	0.234703	−	0.135506i	0.612740	+	0.790285i	$0.290067\pi$
$462$	3.30082	+	19.5923i	0.153568	+	0.911516i
$463$	3.49676	+	2.01885i	0.162508	+	0.0938240i	0.579048	−	0.815293i	$-0.303424\pi$
$463$	3.49676	+	2.01885i	0.162508	+	0.0938240i	−0.416540	+	0.909117i	$0.636758\pi$
$464$	3.47547	+	26.8763i	0.161345	+	1.24770i
$465$	2.86834	−	3.67668i	0.133016	−	0.170502i
$466$	−1.75723	+	17.7369i	−0.0814019	+	0.821645i
$467$	13.6718			0.632656			0.316328	−	0.948650i	$-0.397550\pi$
$467$	13.6718			0.632656			0.316328	+	0.948650i	$0.397550\pi$
$468$	28.9186	−	1.39685i	1.33676	−	0.0645694i
$469$	1.67400	+	3.90941i	0.0772979	+	0.180520i
$470$	−8.09901	−	0.802384i	−0.373579	−	0.0370112i
$471$	18.0713	+	2.52668i	0.832681	+	0.116423i
$472$	−7.94082	−	8.50769i	−0.365506	−	0.391598i
$473$	0.837404	−	1.45043i	0.0385039	−	0.0666907i
$474$	−13.1444	−	12.5248i	−0.603743	−	0.575285i
$475$	−7.20009	−	12.4709i	−0.330363	−	0.572205i
$476$	−2.37698	+	2.13009i	−0.108949	+	0.0976323i
$477$	−0.926907	+	0.897649i	−0.0424402	+	0.0411005i
$478$	2.27381	−	3.16925i	0.104002	−	0.144958i
$479$	2.35070	+	4.07154i	0.107406	+	0.186033i	0.914719	−	0.404091i	$-0.132412\pi$
$479$	2.35070	+	4.07154i	0.107406	+	0.186033i	−0.807312	+	0.590124i	$0.799079\pi$
$480$	−9.06427	+	12.3625i	−0.413726	+	0.564270i
$481$	22.8071	+	13.1677i	1.03991	+	0.600394i
$482$	12.3922	+	27.3920i	0.564448	+	1.24767i
$483$	−29.3560	−	29.1304i	−1.33575	−	1.32548i
$484$	2.11414	−	2.40513i	0.0960972	−	0.109324i
$485$	26.7692			1.21552
$486$	−21.3388	+	5.53659i	−0.967950	+	0.251145i
$487$			0.965533i			0.0437525i	0.999761	+	0.0218762i	$0.00696398\pi$
$487$			0.965533i			0.0437525i	−0.999761	+	0.0218762i	$0.993036\pi$
$488$	8.32932	+	36.0032i	0.377051	+	1.62979i
$489$	9.12577	+	22.5410i	0.412682	+	1.01934i
$490$	−14.6182	−	5.11838i	−0.660382	−	0.231225i
$491$	26.2795	+	15.1725i	1.18598	+	0.684724i	0.957390	−	0.288799i	$-0.0932560\pi$
$491$	26.2795	+	15.1725i	1.18598	+	0.684724i	0.228587	+	0.973523i	$0.426589\pi$
$492$	7.88495	+	2.75745i	0.355481	+	0.124315i
$493$	−3.53909	+	2.04329i	−0.159392	+	0.0920253i
$494$	−22.4458	+	31.2851i	−1.00989	+	1.40758i
$495$	−10.3369	+	10.0106i	−0.464609	+	0.449943i
$496$	−5.47043	+	4.17766i	−0.245630	+	0.187582i
$497$	−16.6889	+	22.2926i	−0.748600	+	0.999961i
$498$	2.70738	−	2.84131i	0.121321	−	0.127322i
$499$	−9.79493	−	5.65511i	−0.438481	−	0.253157i	0.264472	−	0.964393i	$-0.414802\pi$
$499$	−9.79493	−	5.65511i	−0.438481	−	0.253157i	−0.702953	+	0.711236i	$0.748136\pi$
$500$	4.63694	−	23.1722i	0.207370	−	1.03629i
$501$	−0.313568	+	2.24270i	−0.0140092	+	0.100196i
$502$	3.01839	−	30.4666i	0.134717	−	1.35979i
$503$	−41.8216			−1.86473			−0.932367	−	0.361513i	$-0.882260\pi$
$503$	−41.8216			−1.86473			−0.932367	+	0.361513i	$0.882260\pi$
$504$	3.78725	−	22.1282i	0.168698	−	0.985668i
$505$	−12.1260			−0.539601
$506$	3.85759	−	38.9373i	0.171491	−	1.73097i
$507$	14.0446	+	10.9568i	0.623742	+	0.486609i
$508$	−0.769875	+	3.84730i	−0.0341577	+	0.170696i
$509$	2.37262	+	1.36983i	0.105164	+	0.0607167i	0.551660	−	0.834069i	$-0.313995\pi$
$509$	2.37262	+	1.36983i	0.105164	+	0.0607167i	−0.446495	+	0.894786i	$0.647328\pi$
$510$	−2.24665	−	0.544239i	−0.0994832	−	0.0240993i
$511$	−2.98109	+	3.98207i	−0.131876	+	0.176156i
$512$	17.5653	−	14.2640i	0.776282	−	0.630385i
$513$	11.8679	−	26.8092i	0.523982	−	1.18365i
$514$	−1.51103	+	2.10608i	−0.0666486	+	0.0928952i
$515$	20.6924	−	11.9467i	0.911814	−	0.526436i
$516$	−1.43417	+	1.23466i	−0.0631360	+	0.0543530i
$517$	9.76595	+	5.63837i	0.429506	+	0.247975i
$518$	13.7901	−	15.0611i	0.605903	−	0.661748i
$519$	−13.9058	+	17.8246i	−0.610395	+	0.782413i
$520$	−20.8040	+	4.81300i	−0.912316	+	0.211064i
$521$			5.74317i			0.251613i	0.992055	+	0.125806i	$0.0401518\pi$
$521$			5.74317i			0.251613i	−0.992055	+	0.125806i	$0.959848\pi$
$522$	10.5705	−	26.7298i	0.462657	−	1.16993i
$523$	−17.8387			−0.780032			−0.390016	−	0.920808i	$-0.627530\pi$
$523$	−17.8387			−0.780032			−0.390016	+	0.920808i	$0.627530\pi$
$524$	−9.69397	+	11.0283i	−0.423483	+	0.481772i
$525$	3.07057	+	11.2852i	0.134010	+	0.492525i
$526$	2.78793	+	6.16252i	0.121560	+	0.268698i
$527$	−0.898900	−	0.518980i	−0.0391567	−	0.0226071i
$528$	18.5032	−	10.4298i	0.805246	−	0.453897i
$529$	29.2227	+	50.6152i	1.27055	+	2.20066i
$530$	0.554768	−	0.773239i	0.0240976	−	0.0335873i
$531$	3.00320	+	11.9728i	0.130328	+	0.519575i
$532$	19.9254	+	22.2349i	0.863878	+	0.964007i
$533$	5.81787	+	10.0769i	0.252000	+	0.436477i
$534$	33.0262	−	9.70930i	1.42918	−	0.420163i
$535$	−5.45610	+	9.45024i	−0.235888	+	0.408569i
$536$	3.32359	−	3.10213i	0.143557	−	0.133992i
$537$	9.46784	+	23.3860i	0.408567	+	1.00918i
$538$	10.2274	+	1.01325i	0.440935	+	0.0436843i
$539$	15.5308	+	14.8101i	0.668961	+	0.637915i
$540$	14.7592	−	6.82159i	0.635134	−	0.293554i
$541$	−20.7375			−0.891575			−0.445788	−	0.895139i	$-0.647076\pi$
$541$	−20.7375			−0.891575			−0.445788	+	0.895139i	$0.647076\pi$
$542$	3.15463	−	31.8418i	0.135503	−	1.36772i
$543$	−8.03502	−	19.8468i	−0.344816	−	0.851709i
$544$	3.00459	+	1.61711i	0.128821	+	0.0693329i
$545$	12.4528	+	7.18965i	0.533421	+	0.307971i
$546$	24.1084	−	19.9181i	1.03174	−	0.852414i
$547$	−30.0061	+	17.3240i	−1.28297	+	0.740722i	−0.977390	−	0.211445i	$-0.932183\pi$
$547$	−30.0061	+	17.3240i	−1.28297	+	0.740722i	−0.305578	+	0.952167i	$0.598850\pi$
$548$	1.90904	+	5.64517i	0.0815502	+	0.241150i
$549$	10.7504	−	37.6927i	0.458814	−	1.60868i
$550$	−6.45041	+	8.99062i	−0.275046	+	0.383361i
$551$	19.1136	+	33.1057i	0.814265	+	1.41035i
$552$	−18.6380	+	40.0913i	−0.793286	+	1.70640i
$553$	−19.4722	−	2.32866i	−0.828041	−	0.0990249i
$554$	−11.1592	+	5.04842i	−0.474107	+	0.214487i
$555$	14.6472	+	2.04794i	0.621740	+	0.0869302i
$556$	0.412848	−	0.469672i	0.0175087	−	0.0199185i
$557$	6.03515			0.255717			0.127859	−	0.991792i	$-0.459190\pi$
$557$	6.03515			0.255717			0.127859	+	0.991792i	$0.459190\pi$
$558$	7.22198	−	1.06946i	0.305731	−	0.0452737i
$559$	−2.63608			−0.111494
$560$	0.158557	+	16.5570i	0.00670024	+	0.699660i
$561$	2.52535	+	1.97014i	0.106620	+	0.0831792i
$562$	−31.7596	+	14.3681i	−1.33970	+	0.606080i
$563$	−13.4738	+	23.3374i	−0.567854	+	0.983553i	0.428923	+	0.903341i	$0.358893\pi$
$563$	−13.4738	+	23.3374i	−0.567854	+	0.983553i	−0.996778	+	0.0802118i	$0.974440\pi$
$564$	−8.31319	−	9.65653i	−0.350048	−	0.406613i
$565$	7.22299	−	4.17019i	0.303873	−	0.175441i
$566$	−26.2084	−	18.8035i	−1.10162	−	0.790369i
$567$	−14.8742	+	18.5946i	−0.624657	+	0.780899i
$568$	28.4733	+	8.69095i	1.19472	+	0.364664i
$569$	−19.1448	−	33.1598i	−0.802593	−	1.39013i	−0.917904	−	0.396803i	$-0.870120\pi$
$569$	−19.1448	−	33.1598i	−0.802593	−	1.39013i	0.115311	−	0.993329i	$-0.463214\pi$
$570$	−5.09098	+	21.0158i	−0.213237	+	0.880255i
$571$	6.91177	+	3.99051i	0.289248	+	0.166998i	0.637603	−	0.770365i	$-0.279926\pi$
$571$	6.91177	+	3.99051i	0.289248	+	0.166998i	−0.348354	+	0.937363i	$0.613259\pi$
$572$	29.0118	+	5.80549i	1.21304	+	0.242740i
$573$	−8.26818	+	10.5983i	−0.345408	+	0.442749i
$574$	8.60384	−	2.71649i	0.359117	−	0.113384i
$575$		−	23.0324i		−	0.960519i
$576$	−23.6256	+	4.22268i	−0.984400	+	0.175945i
$577$		−	9.07042i		−	0.377607i	−0.982015	−	0.188803i	$-0.939539\pi$
$577$		−	9.07042i		−	0.377607i	0.982015	−	0.188803i	$-0.0604609\pi$
$578$	2.31952	−	23.4125i	0.0964793	−	0.973831i
$579$	−0.607975	+	4.34834i	−0.0252666	+	0.180711i
$580$	−4.15979	+	20.7877i	−0.172726	+	0.863163i
$581$	0.503366	−	4.20912i	0.0208831	−	0.174624i
$582$	30.3413	+	28.9111i	1.25769	+	1.19841i
$583$	−1.14195	+	0.659303i	−0.0472946	+	0.0273055i
$584$	5.08611	+	1.55244i	0.210465	+	0.0642404i
$585$	21.7803	+	6.21197i	0.900503	+	0.256833i
$586$	−8.50273	+	11.8512i	−0.351245	+	0.489567i
$587$	−9.86537	−	17.0873i	−0.407187	−	0.705269i	0.587386	−	0.809307i	$-0.300157\pi$
$587$	−9.86537	−	17.0873i	−0.407187	−	0.705269i	−0.994573	+	0.104038i	$0.966824\pi$
$588$	−11.0410	−	21.5893i	−0.455321	−	0.890327i
$589$	−4.85469	+	8.40857i	−0.200034	+	0.346469i
$590$	−3.75251	−	8.29465i	−0.154488	−	0.341485i
$591$	44.2888	−	17.9304i	1.82180	−	0.737558i
$592$	−20.1496	−	8.40059i	−0.828145	−	0.345262i
$593$		−	36.7145i		−	1.50768i	−0.657056	−	0.753842i	$-0.728198\pi$
$593$		−	36.7145i		−	1.50768i	0.657056	−	0.753842i	$-0.271802\pi$
$594$	−22.5279	+	0.182434i	−0.924331	+	0.00748535i
$595$	−2.29527	+	0.982827i	−0.0940970	+	0.0402920i
$596$	−16.0682	+	18.2798i	−0.658177	+	0.748769i
$597$	−3.64145	+	1.47425i	−0.149035	+	0.0603369i
$598$	−56.1108	+	25.3846i	−2.29454	+	1.03805i
$599$	−12.5041	−	7.21925i	−0.510904	−	0.294971i	0.222301	−	0.974978i	$-0.428643\pi$
$599$	−12.5041	−	7.21925i	−0.510904	−	0.294971i	−0.733205	+	0.680008i	$0.761976\pi$
$600$	10.2334	−	7.18333i	0.417778	−	0.293258i
$601$	21.1289	−	12.1988i	0.861867	−	0.497599i	−0.00276977	−	0.999996i	$-0.500882\pi$
$601$	21.1289	−	12.1988i	0.861867	−	0.497599i	0.864637	+	0.502397i	$0.167548\pi$
$602$	−0.441629	+	1.99577i	−0.0179995	+	0.0813414i
$603$	−4.67725	+	1.17322i	−0.190472	+	0.0477772i
$604$	23.7571	−	8.03399i	0.966662	−	0.326898i
$605$	2.16942	−	1.25252i	0.0881995	−	0.0509220i
$606$	−13.7442	−	13.0963i	−0.558319	−	0.532002i
$607$	15.1008	−	26.1554i	0.612924	−	1.06162i	−0.377821	−	0.925879i	$-0.623326\pi$
$607$	15.1008	−	26.1554i	0.612924	−	1.06162i	0.990745	−	0.135737i	$-0.0433402\pi$
$608$	15.1269	−	28.1058i	0.613477	−	1.13984i
$609$	−8.15121	−	29.9579i	−0.330304	−	1.21396i
$610$	−2.85006	+	28.7676i	−0.115396	+	1.16477i
$611$		−	17.7491i		−	0.718054i
$612$	−1.95866	−	3.04328i	−0.0791742	−	0.123017i
$613$	−36.9378			−1.49190			−0.745952	−	0.665999i	$-0.768005\pi$
$613$	−36.9378			−1.49190			−0.745952	+	0.665999i	$0.768005\pi$
$614$	2.22752	−	22.4839i	0.0898954	−	0.907376i
$615$	5.15214	+	4.01941i	0.207754	+	0.162078i
$616$	9.25574	−	20.9921i	0.372924	−	0.845797i
$617$	−4.52107	+	7.83072i	−0.182011	+	0.315253i	−0.942565	−	0.334022i	$-0.891594\pi$
$617$	−4.52107	+	7.83072i	−0.182011	+	0.315253i	0.760554	+	0.649275i	$0.224927\pi$
$618$	36.3563	+	8.80714i	1.46247	+	0.354275i
$619$	−11.4714	−	19.8691i	−0.461076	−	0.798608i	0.537938	−	0.842984i	$-0.319203\pi$
$619$	−11.4714	−	19.8691i	−0.461076	−	0.798608i	−0.999015	+	0.0443763i	$0.985870\pi$
$620$	−5.10082	+	1.72496i	−0.204854	+	0.0692759i
$621$	37.8791	−	27.6441i	1.52004	−	1.10932i
$622$	27.4944	+	19.7261i	1.10242	+	0.790945i
$623$	22.2831	−	29.7652i	0.892752	−	1.19252i
$624$	−28.7783	−	17.0134i	−1.15205	−	0.681082i
$625$	2.86288	−	4.95865i	0.114515	−	0.198346i
$626$	−8.27518	−	18.2917i	−0.330743	−	0.731082i
$627$	18.4292	−	23.6229i	0.735993	−	0.943407i
$628$	−15.8252	−	13.9106i	−0.631494	−	0.555092i
$629$		−	3.29198i		−	0.131260i
$630$	8.35196	−	15.4491i	0.332750	−	0.615505i
$631$			34.9573i			1.39163i	0.718223	+	0.695813i	$0.244956\pi$
$631$			34.9573i			1.39163i	−0.718223	+	0.695813i	$0.755044\pi$
$632$	4.72543	+	20.4255i	0.187967	+	0.812482i
$633$	6.45205	+	0.902111i	0.256446	+	0.0358557i
$634$	0.649481	−	0.293826i	0.0257942	−	0.0116693i
$635$	−1.53467	+	2.65812i	−0.0609014	+	0.105484i
$636$	1.46391	−	0.277264i	0.0580478	−	0.0109942i
$637$	7.96499	−	32.8252i	0.315584	−	1.30058i
$638$	17.1234	−	23.8668i	0.677924	−	0.944894i
$639$	−21.9668	−	22.6828i	−0.868992	−	0.897317i
$640$	16.5914	−	6.16845i	0.655833	−	0.243829i
$641$	15.4196	+	26.7076i	0.609039	+	1.05489i	0.991399	+	0.130873i	$0.0417779\pi$
$641$	15.4196	+	26.7076i	0.609039	+	1.05489i	−0.382360	+	0.924013i	$0.624889\pi$
$642$	−16.3906	+	4.81864i	−0.646885	+	0.190177i
$643$	5.00696	−	8.67231i	0.197455	−	0.342003i	−0.750247	−	0.661157i	$-0.770066\pi$
$643$	5.00696	−	8.67231i	0.197455	−	0.342003i	0.947703	+	0.319155i	$0.103399\pi$
$644$	9.81822	+	46.7341i	0.386892	+	1.84158i
$645$	−1.37221	+	0.555542i	−0.0540307	+	0.0218744i
$646$	4.78967	+	0.474521i	0.188447	+	0.0186698i
$647$	10.3033			0.405063			0.202532	−	0.979276i	$-0.435083\pi$
$647$	10.3033			0.405063			0.202532	+	0.979276i	$0.435083\pi$
$648$	24.0961	+	8.20828i	0.946586	+	0.322452i
$649$			12.6143i			0.495154i
$650$	17.3314	+	1.71705i	0.679792	+	0.0673483i
$651$	5.55448	−	5.59750i	0.217697	−	0.219384i
$652$	5.50986	−	27.5344i	0.215783	−	1.07833i
$653$	−14.6739	+	25.4160i	−0.574235	+	0.994604i	0.421889	+	0.906647i	$0.361367\pi$
$653$	−14.6739	+	25.4160i	−0.574235	+	0.994604i	−0.996124	+	0.0879568i	$0.971966\pi$
$654$	6.34965	+	21.5983i	0.248291	+	0.844562i
$655$	−9.94747	+	5.74317i	−0.388680	+	0.224404i
$656$	−5.85416	−	7.66573i	−0.228567	−	0.299296i
$657$	−3.92386	−	4.05176i	−0.153084	−	0.158074i
$658$	−13.4378	−	2.97356i	−0.523861	−	0.115921i
$659$	−41.8028	+	24.1349i	−1.62841	+	0.940162i	−0.643839	+	0.765161i	$0.722659\pi$
$659$	−41.8028	+	24.1349i	−1.62841	+	0.940162i	−0.984568	+	0.175001i	$0.944007\pi$
$660$	16.3256	−	3.09205i	0.635471	−	0.120358i
$661$	−40.1854	−	23.2010i	−1.56303	−	0.902416i	−0.996948	−	0.0780662i	$-0.975125\pi$
$661$	−40.1854	−	23.2010i	−1.56303	−	0.902416i	−0.566081	−	0.824349i	$-0.691541\pi$
$662$	−14.5743	−	32.2154i	−0.566445	−	1.25209i
$663$	0.698072	−	4.99273i	0.0271109	−	0.193902i
$664$	−4.41519	+	1.02145i	−0.171343	+	0.0396400i
$665$	9.19365	+	21.4707i	0.356515	+	0.832596i
$666$	14.3900	+	18.1405i	0.557601	+	0.702929i
$667$			61.1426i			2.36745i
$668$	1.72634	−	1.96395i	0.0667940	−	0.0759875i
$669$	−21.2436	−	16.5731i	−0.821326	−	0.640753i
$670$	3.24036	−	1.46594i	0.125186	−	0.0566343i
$671$	20.0275	−	34.6886i	0.773152	−	1.33914i
$672$	−17.7021	+	18.9377i	−0.682874	+	0.730536i
$673$	−19.5864	−	33.9247i	−0.755001	−	1.30770i	−0.945374	−	0.325989i	$-0.894303\pi$
$673$	−19.5864	−	33.9247i	−0.755001	−	1.30770i	0.190372	−	0.981712i	$-0.439031\pi$
$674$	17.3604	+	12.4554i	0.668697	+	0.479763i
$675$	−13.1857	+	1.41425i	−0.507520	+	0.0544346i
$676$	−6.58918	−	19.4847i	−0.253430	−	0.749411i
$677$	−24.4118	+	14.0942i	−0.938221	+	0.541682i	−0.889402	−	0.457125i	$-0.848879\pi$
$677$	−24.4118	+	14.0942i	−0.938221	+	0.541682i	−0.0488191	+	0.998808i	$0.515546\pi$
$678$	12.6907	+	3.07427i	0.487385	+	0.118067i
$679$	44.9477	+	5.37527i	1.72494	+	0.206284i
$680$	1.82131	+	1.95132i	0.0698439	+	0.0748299i
$681$	23.4730	+	18.3123i	0.899489	+	0.701731i
$682$	7.42443	+	0.735552i	0.284296	+	0.0281657i
$683$		−	1.45337i		−	0.0556116i	−0.999613	−	0.0278058i	$-0.991148\pi$
$683$		−	1.45337i		−	0.0556116i	0.999613	−	0.0278058i	$-0.00885200\pi$
$684$	−28.4678	+	18.3219i	−1.08849	+	0.700555i
$685$			4.66178i			0.178118i
$686$	−23.5174	−	11.5295i	−0.897900	−	0.440200i
$687$	29.5001	+	4.12464i	1.12550	+	0.157365i
$688$	2.16713	−	0.280240i	0.0826212	−	0.0106841i
$689$	1.79738	+	1.03772i	0.0684746	+	0.0395338i
$690$	−23.8588	+	25.0391i	−0.908289	+	0.953221i
$691$	11.6279	+	20.1401i	0.442346	+	0.766166i	0.997863	−	0.0653391i	$-0.0208129\pi$
$691$	11.6279	+	20.1401i	0.442346	+	0.766166i	−0.555517	+	0.831505i	$0.687480\pi$
$692$	24.7288	−	8.36261i	0.940049	−	0.317899i
$693$	−19.3667	+	14.7330i	−0.735679	+	0.559661i
$694$	6.26038	−	8.72575i	0.237641	−	0.331225i
$695$	0.423644	−	0.244591i	0.0160697	−	0.00927786i
$696$	−27.1660	+	19.0691i	−1.02972	+	0.722812i
$697$	0.727248	−	1.25963i	0.0275465	−	0.0477119i
$698$	10.4660	+	23.1344i	0.396145	+	0.875650i
$699$	−20.2342	+	8.19183i	−0.765326	+	0.309843i
$700$	4.20354	−	12.8339i	0.158879	−	0.485074i
$701$	11.1081			0.419546			0.209773	−	0.977750i	$-0.432727\pi$
$701$	11.1081			0.419546			0.209773	+	0.977750i	$0.432727\pi$
$702$	17.9777	+	30.5640i	0.678524	+	1.15356i
$703$	−30.7941			−1.16142
$704$	−24.4679	−	1.68849i	−0.922169	−	0.0636374i
$705$	−3.74055	−	9.23931i	−0.140877	−	0.347973i
$706$	10.0922	+	22.3080i	0.379825	+	0.839574i
$707$	−20.3607	−	2.43492i	−0.765741	−	0.0915745i
$708$	4.70510	−	13.4543i	0.176829	−	0.505644i
$709$	3.16379	+	5.47984i	0.118819	+	0.205800i	0.919300	−	0.393558i	$-0.128756\pi$
$709$	3.16379	+	5.47984i	0.118819	+	0.205800i	−0.800481	+	0.599358i	$0.795423\pi$
$710$	18.9223	+	13.5760i	0.710140	+	0.509497i
$711$	6.09894	−	21.3840i	0.228728	−	0.801961i
$712$	−38.0177	−	11.6042i	−1.42477	−	0.434885i
$713$	−13.4491	+	7.76487i	−0.503674	+	0.290797i
$714$	−3.66303	−	1.36495i	−0.137086	−	0.0510821i
$715$	20.0444	+	11.5726i	0.749618	+	0.432792i
$716$	5.71639	−	28.5665i	0.213631	−	1.06758i
$717$	4.73117	+	0.661502i	0.176689	+	0.0247042i
$718$	−1.61814	−	0.160312i	−0.0603885	−	0.00598281i
$719$	18.7468			0.699137			0.349569	−	0.936911i	$-0.386328\pi$
$719$	18.7468			0.699137			0.349569	+	0.936911i	$0.386328\pi$
$720$	−18.5660	−	2.79144i	−0.691916	−	0.104031i
$721$	37.1432	−	15.9046i	1.38328	−	0.592317i
$722$	1.78971	−	18.0648i	0.0666062	−	0.672302i
$723$	−22.6491	+	29.0319i	−0.842328	+	1.07971i
$724$	−4.85130	+	24.2434i	−0.180297	+	0.900999i
$725$	8.64544	−	14.9743i	0.321084	−	0.556133i
$726$	3.81166	+	0.923356i	0.141464	+	0.0342689i
$727$	−0.671041	−	1.16228i	−0.0248875	−	0.0431065i	0.853313	−	0.521398i	$-0.174589\pi$
$727$	−0.671041	−	1.16228i	−0.0248875	−	0.0431065i	−0.878201	+	0.478292i	$0.841256\pi$
$728$	−35.8982	+	3.90398i	−1.33048	+	0.144691i
$729$	−18.1518	−	19.9878i	−0.672287	−	0.740290i
$730$	3.38003	+	2.42504i	0.125101	+	0.0897547i
$731$	0.164758	+	0.285369i	0.00609380	+	0.0105548i
$732$	−34.2999	+	29.5284i	−1.26776	+	1.09140i
$733$	−10.6133	−	6.12762i	−0.392013	−	0.226329i	0.291019	−	0.956717i	$-0.406006\pi$
$733$	−10.6133	−	6.12762i	−0.392013	−	0.226329i	−0.683032	+	0.730389i	$0.739339\pi$
$734$	−27.8977	+	12.6210i	−1.02972	+	0.465848i
$735$	−2.77158	−	18.7657i	−0.102231	−	0.692184i
$736$	43.4303	−	26.8339i	1.60086	−	0.989111i
$737$	−4.92785			−0.181520
$738$	1.49863	+	10.1202i	0.0551654	+	0.372529i
$739$		−	11.3906i		−	0.419011i	−0.977807	−	0.209506i	$-0.932815\pi$
$739$		−	11.3906i		−	0.419011i	0.977807	−	0.209506i	$-0.0671855\pi$
$740$	−12.8267	−	11.2749i	−0.471520	−	0.414472i
$741$	−46.7035	−	6.52997i	−1.71570	−	0.239885i
$742$	1.08677	−	1.18694i	0.0398966	−	0.0435738i
$743$	28.6884	+	16.5632i	1.05247	+	0.607646i	0.923341	−	0.383981i	$-0.125447\pi$
$743$	28.6884	+	16.5632i	1.05247	+	0.607646i	0.129133	+	0.991627i	$0.458781\pi$
$744$	−7.64448	−	3.55383i	−0.280260	−	0.130290i
$745$	−16.4883	+	9.51954i	−0.604086	+	0.348769i
$746$	−20.6538	−	14.8183i	−0.756191	−	0.542537i
$747$	4.62238	+	1.31835i	0.169124	+	0.0482360i
$748$	−1.18480	−	3.50353i	−0.0433204	−	0.128102i
$749$	−11.0589	+	14.7722i	−0.404083	+	0.539764i
$750$	27.7676	−	8.16333i	1.01393	−	0.298083i
$751$	9.23549	+	5.33211i	0.337008	+	0.194572i	0.658948	−	0.752188i	$-0.271002\pi$
$751$	9.23549	+	5.33211i	0.337008	+	0.194572i	−0.321940	+	0.946760i	$0.604335\pi$
$752$	1.88690	+	14.5917i	0.0688082	+	0.532103i
$753$	34.7562	−	14.0711i	1.26659	−	0.512779i
$754$	−46.0083	−	4.55813i	−1.67552	−	0.165997i
$755$	19.6186			0.713994
$756$	26.1517	−	8.49039i	0.951129	−	0.308792i
$757$	−25.8612			−0.939941			−0.469970	−	0.882682i	$-0.655735\pi$
$757$	−25.8612			−0.939941			−0.469970	+	0.882682i	$0.655735\pi$
$758$	−45.5083	−	4.50860i	−1.65294	−	0.163760i
$759$	44.4195	−	17.9833i	1.61233	−	0.652752i
$760$	18.2533	−	17.0370i	0.662116	−	0.617999i
$761$	−41.2900	−	23.8388i	−1.49676	−	0.864157i	−0.496770	−	0.867882i	$-0.665481\pi$
$761$	−41.2900	−	23.8388i	−1.49676	−	0.864157i	−0.999993	+	0.00372570i	$0.998814\pi$
$762$	−4.61027	+	1.35536i	−0.167013	+	0.0490997i
$763$	19.4657	+	14.5726i	0.704706	+	0.527563i
$764$	14.7034	−	4.97230i	0.531952	−	0.179891i
$765$	−0.688814	−	2.74608i	−0.0249041	−	0.0992848i
$766$	−14.6354	−	10.5003i	−0.528798	−	0.379392i
$767$	17.1944	−	9.92719i	0.620854	−	0.358450i
$768$	25.4675	+	10.9274i	0.918978	+	0.394309i
$769$	−26.7936	−	15.4693i	−0.966203	−	0.557838i	−0.0681267	−	0.997677i	$-0.521702\pi$
$769$	−26.7936	−	15.4693i	−0.966203	−	0.557838i	−0.898077	+	0.439839i	$0.855036\pi$
$770$	12.1197	−	13.2368i	0.436764	−	0.477019i
$771$	−3.14403	−	0.439591i	−0.113230	−	0.0158315i
$772$	3.34718	−	3.80789i	0.120468	−	0.137049i
$773$			18.7467i			0.674273i	0.941456	+	0.337136i	$0.109458\pi$
$773$			18.7467i			0.674273i	−0.941456	+	0.337136i	$0.890542\pi$
$774$	−2.15532	−	0.852336i	−0.0774713	−	0.0306366i
$775$	4.39175			0.157756
$776$	−10.9077	−	47.1482i	−0.391565	−	1.69252i
$777$	24.1827	+	6.37985i	0.867551	+	0.228876i
$778$	−4.51873	+	2.04428i	−0.162004	+	0.0732910i
$779$	−11.7830	−	6.80289i	−0.422168	−	0.243739i
$780$	−17.0626	−	19.8198i	−0.610940	−	0.709663i
$781$	−16.1341	−	27.9451i	−0.577324	−	0.999954i
$782$	6.25501	+	4.48772i	0.223679	+	0.160481i
$783$	35.0033	−	3.75431i	1.25091	−	0.134168i
$784$	−3.05843	+	27.8325i	−0.109230	+	0.994017i
$785$	−8.24128	−	14.2743i	−0.294144	−	0.509472i
$786$	−17.4776	−	4.23387i	−0.623406	−	0.151017i
$787$	2.62341	−	4.54387i	0.0935143	−	0.161972i	−0.815473	−	0.578795i	$-0.803523\pi$
$787$	2.62341	−	4.54387i	0.0935143	−	0.161972i	0.908988	+	0.416823i	$0.136857\pi$
$788$	−54.0999	−	10.8258i	−1.92723	−	0.385654i
$789$	−5.09547	+	6.53145i	−0.181404	+	0.232526i
$790$	−1.61691	+	16.3206i	−0.0575271	+	0.580660i
$791$	12.9654	−	5.55174i	0.460997	−	0.197397i
$792$	21.8436	+	14.1272i	0.776178	+	0.501989i
$793$	−63.0449			−2.23879
$794$	−30.4614	−	3.01787i	−1.08104	−	0.107100i
$795$	1.15432	+	0.161394i	0.0409394	+	0.00572406i
$796$	4.44812	+	0.890104i	0.157659	+	0.0315489i
$797$	−7.80761	−	4.50773i	−0.276560	−	0.159672i	0.355305	−	0.934750i	$-0.384377\pi$
$797$	−7.80761	−	4.50773i	−0.276560	−	0.159672i	−0.631865	+	0.775078i	$0.717710\pi$
$798$	−12.7682	+	34.2651i	−0.451989	+	1.21297i
$799$	−1.92144	+	1.10934i	−0.0679756	+	0.0392457i
$800$	−14.4307	+	0.430892i	−0.510203	+	0.0152343i
$801$	29.3301	+	30.2861i	1.03633	+	1.07011i
$802$	11.4544	+	8.21806i	0.404468	+	0.290190i
$803$	−2.88199	−	4.99175i	−0.101703	−	0.176155i
$804$	5.25601	+	1.83808i	0.185365	+	0.0648240i
$805$	−4.43592	+	37.0929i	−0.156345	+	1.30735i
$806$	−4.84025	−	10.6990i	−0.170491	−	0.376857i
$807$	4.72356	+	11.6674i	0.166277	+	0.410712i
$808$	4.94104	+	21.3575i	0.173825	+	0.751353i
$809$	54.2083			1.90586			0.952932	−	0.303184i	$-0.0980498\pi$
$809$	54.2083			1.90586			0.952932	+	0.303184i	$0.0980498\pi$
$810$	15.7995	+	12.1214i	0.555138	+	0.425901i
$811$	−30.9693			−1.08748			−0.543740	−	0.839254i	$-0.682992\pi$
$811$	−30.9693			−1.08748			−0.543740	+	0.839254i	$0.682992\pi$
$812$	−11.1588	+	34.0691i	−0.391599	+	1.19559i
$813$	36.3250	−	14.7062i	1.27397	−	0.515770i
$814$	9.75327	+	21.5589i	0.341852	+	0.755639i
$815$	10.9833	−	19.0237i	0.384729	−	0.666370i
$816$	−0.0431135	+	4.17876i	−0.00150927	+	0.146286i
$817$	2.66943	−	1.54120i	0.0933915	−	0.0539196i
$818$	−13.0440	+	18.1808i	−0.456072	+	0.635676i
$819$	35.3236	+	14.8039i	1.23431	+	0.517291i
$820$	−2.41719	−	7.14779i	−0.0844118	−	0.249612i
$821$	19.9190	+	34.5007i	0.695178	+	1.20408i	0.970121	+	0.242623i	$0.0780079\pi$
$821$	19.9190	+	34.5007i	0.695178	+	1.20408i	−0.274942	+	0.961461i	$0.588659\pi$
$822$	−5.03481	+	5.28387i	−0.175609	+	0.184296i
$823$	−27.7720	−	16.0342i	−0.968073	−	0.558917i	−0.0694246	−	0.997587i	$-0.522116\pi$
$823$	−27.7720	−	16.0342i	−0.968073	−	0.558917i	−0.898648	+	0.438670i	$0.855450\pi$
$824$	−29.4733	−	31.5773i	−1.02675	−	1.10005i
$825$	−13.4215	−	1.87656i	−0.467277	−	0.0653336i
$826$	−4.63522	−	14.6810i	−0.161280	−	0.510816i
$827$		−	30.1201i		−	1.04738i	−0.851909	−	0.523689i	$-0.824555\pi$
$827$		−	30.1201i		−	1.04738i	0.851909	−	0.523689i	$-0.175445\pi$
$828$	−54.0852	+	2.61247i	−1.87959	+	0.0907896i
$829$			8.36044i			0.290370i	0.989405	+	0.145185i	$0.0463777\pi$
$829$			8.36044i			0.290370i	−0.989405	+	0.145185i	$0.953622\pi$
$830$	−3.52787	−	0.349513i	−0.122454	−	0.0121318i
$831$	−11.8272	−	9.22695i	−0.410282	−	0.320079i
$832$	16.9542	+	34.6807i	0.587780	+	1.20234i
$833$	−4.05132	+	1.18936i	−0.140370	+	0.0412089i
$834$	0.744339	+	0.180312i	0.0257744	+	0.00624371i
$835$	1.77148	−	1.02277i	0.0613046	−	0.0353942i
$836$	−32.7730	+	11.0829i	−1.13348	+	0.383311i
$837$	5.27109	+	7.22266i	0.182195	+	0.249652i
$838$	33.6763	+	24.1614i	1.16333	+	0.834642i
$839$	11.3890	+	19.7262i	0.393190	+	0.681026i	0.992868	−	0.119216i	$-0.0380380\pi$
$839$	11.3890	+	19.7262i	0.393190	+	0.681026i	−0.599678	+	0.800241i	$0.704705\pi$
$840$	−17.8641	+	9.59760i	−0.616368	+	0.331149i
$841$	−8.45044	+	14.6366i	−0.291394	+	0.504710i
$842$	−34.7067	+	15.7014i	−1.19607	+	0.541105i
$843$	−33.6609	−	26.2604i	−1.15934	−	0.904456i
$844$	−5.65013	−	4.96653i	−0.194485	−	0.170955i
$845$		−	16.0904i		−	0.553528i
$846$	5.73891	−	14.5121i	0.197308	−	0.498936i
$847$	3.89416	−	1.66746i	0.133805	−	0.0572947i
$848$	−1.58795	−	0.662033i	−0.0545305	−	0.0227343i
$849$	5.47034	−	39.1248i	0.187741	−	1.34276i
$850$	−0.897350	−	1.98353i	−0.0307789	−	0.0680344i
$851$	−42.6551	−	24.6269i	−1.46220	−	0.844200i
$852$	6.78505	+	35.8240i	0.232452	+	1.22731i
$853$	43.8698	−	25.3282i	1.50207	−	0.867222i	0.502075	−	0.864824i	$-0.332570\pi$
$853$	43.8698	−	25.3282i	1.50207	−	0.867222i	0.999997	−	0.00239737i	$-0.000763106\pi$
$854$	−10.5621	+	47.7311i	−0.361427	+	1.63332i
$855$	−25.6877	+	6.44337i	−0.878499	+	0.220359i
$856$	18.8678	+	5.75905i	0.644889	+	0.196840i
$857$	42.8622	−	24.7465i	1.46414	−	0.845324i	0.464944	−	0.885340i	$-0.346074\pi$
$857$	42.8622	−	24.7465i	1.46414	−	0.845324i	0.999199	+	0.0400164i	$0.0127410\pi$
$858$	10.2206	+	34.7652i	0.348924	+	1.18687i
$859$	−0.913832	+	1.58280i	−0.0311795	+	0.0540046i	−0.881194	−	0.472755i	$-0.843260\pi$
$859$	−0.913832	+	1.58280i	−0.0311795	+	0.0540046i	0.850015	+	0.526759i	$0.176593\pi$
$860$	1.67619	+	0.335419i	0.0571576	+	0.0114377i
$861$	7.84379	+	7.78350i	0.267316	+	0.265261i
$862$	9.01718	+	0.893349i	0.307126	+	0.0304276i
$863$			43.2686i			1.47288i	0.676502	+	0.736441i	$0.263495\pi$
$863$			43.2686i			1.47288i	−0.676502	+	0.736441i	$0.736505\pi$
$864$	−18.0288	−	23.2156i	−0.613351	−	0.789810i
$865$	20.4211			0.694338
$866$	52.2872	+	5.18019i	1.77679	+	0.176030i
$867$	26.7089	−	10.8131i	0.907080	−	0.367233i
$868$	−8.91109	+	1.87210i	−0.302462	+	0.0635434i
$869$	11.3621	−	19.6797i	0.385432	−	0.667588i
$870$	−24.9102	+	7.32331i	−0.844536	+	0.248283i
$871$	3.87812	+	6.71710i	0.131405	+	0.227600i
$872$	7.58885	−	24.8626i	0.256991	−	0.841956i
$873$	−14.0782	+	49.3607i	−0.476475	+	1.67061i
$874$	41.9795	−	58.5112i	1.41998	−	1.97917i
$875$	18.7350	−	25.0258i	0.633359	−	0.846026i
$876$	1.21199	+	6.39914i	0.0409495	+	0.216207i
$877$	22.2450	−	38.5295i	0.751160	−	1.30105i	−0.196100	−	0.980584i	$-0.562828\pi$
$877$	22.2450	−	38.5295i	0.751160	−	1.30105i	0.947261	−	0.320464i	$-0.103839\pi$
$878$	48.3770	−	21.8858i	1.63265	−	0.738611i
$879$	−17.6918	−	2.47363i	−0.596731	−	0.0834334i
$880$	−17.7089	−	7.38301i	−0.596966	−	0.248881i
$881$			28.6591i			0.965549i	0.875745	+	0.482775i	$0.160371\pi$
$881$			28.6591i			0.965549i	−0.875745	+	0.482775i	$0.839629\pi$
$882$	17.1259	−	24.2632i	0.576658	−	0.816986i
$883$		−	8.34232i		−	0.280741i	−0.990099	−	0.140371i	$-0.955171\pi$
$883$		−	8.34232i		−	0.280741i	0.990099	−	0.140371i	$-0.0448294\pi$
$884$	−3.84321	+	4.37219i	−0.129261	+	0.147053i
$885$	6.85843	−	8.79124i	0.230544	−	0.295514i
$886$	3.15906	+	6.98287i	0.106131	+	0.234594i
$887$	19.9200	−	34.5024i	0.668847	−	1.15848i	−0.309379	−	0.950939i	$-0.600121\pi$
$887$	19.9200	−	34.5024i	0.668847	−	1.15848i	0.978227	−	0.207539i	$-0.0665453\pi$
$888$	−2.36134	−	26.6325i	−0.0792415	−	0.893728i
$889$	−3.11059	+	4.15505i	−0.104326	+	0.139356i
$890$	−25.2651	−	18.1267i	−0.846887	−	0.607608i
$891$	−13.0227	−	24.3253i	−0.436275	−	0.814928i
$892$	9.96669	+	29.4722i	0.333709	+	0.986802i
$893$	10.3771	+	17.9737i	0.347257	+	0.601467i
$894$	−28.9699	−	7.01781i	−0.968898	−	0.234711i
$895$	11.3950	−	19.7368i	0.380894	−	0.659727i
$896$	29.0970	−	7.02580i	0.972064	−	0.234716i
$897$	−59.4701	−	46.3952i	−1.98565	−	1.54909i
$898$	−4.00645	+	40.4398i	−0.133697	+	1.34949i
$899$	−11.6585			−0.388831
$900$	13.6153	+	7.00773i	0.453844	+	0.233591i
$901$		−	0.259434i		−	0.00864300i
$902$	−1.03073	+	10.4039i	−0.0343196	+	0.346411i
$903$	−2.41562	+	0.657262i	−0.0803866	+	0.0218723i
$904$	−10.2881	−	11.0225i	−0.342177	−	0.366604i
$905$	−9.67056	+	16.7499i	−0.321460	+	0.556785i
$906$	22.2366	+	21.1884i	0.738761	+	0.703938i
$907$	−13.2688	+	7.66077i	−0.440585	+	0.254372i	−0.703846	−	0.710353i	$-0.748535\pi$
$907$	−13.2688	+	7.66077i	−0.440585	+	0.254372i	0.263261	+	0.964725i	$0.415202\pi$
$908$	−11.0126	−	32.5651i	−0.365467	−	1.08071i
$909$	6.37722	−	22.3597i	0.211519	−	0.741624i
$910$	−27.5808	−	6.10317i	−0.914296	−	0.202318i
$911$	−8.76762	+	5.06199i	−0.290484	+	0.167711i	−0.638160	−	0.769904i	$-0.720304\pi$
$911$	−8.76762	+	5.06199i	−0.290484	+	0.167711i	0.347676	+	0.937615i	$0.386971\pi$
$912$	39.0894	+	0.403296i	1.29438	+	0.0133545i
$913$	4.25398	+	2.45603i	0.140786	+	0.0812829i
$914$	21.3281	−	9.64887i	0.705471	−	0.319156i
$915$	−32.8180	+	13.2864i	−1.08493	+	0.439235i
$916$	−25.8336	−	22.7080i	−0.853565	−	0.750294i
$917$	−17.8559	+	7.64583i	−0.589654	+	0.252488i
$918$	2.18508	−	3.85646i	0.0721185	−	0.127282i
$919$		−	0.699191i		−	0.0230642i	−0.999934	−	0.0115321i	$-0.996329\pi$
$919$		−	0.699191i		−	0.0230642i	0.999934	−	0.0115321i	$-0.00367086\pi$
$920$	38.9089	−	9.00155i	1.28279	−	0.296772i
$921$	25.6495	−	10.3842i	0.845180	−	0.342173i
$922$	−3.39190	−	7.49755i	−0.111706	−	0.246919i
$923$	−25.3944	+	43.9844i	−0.835868	+	1.44777i
$924$	28.0329	−	1.91364i	0.922215	−	0.0629542i
$925$	6.96439	+	12.0627i	0.228988	+	0.396619i
$926$	3.32872	−	4.63959i	0.109388	−	0.152466i
$927$	11.1467	+	44.4384i	0.366106	+	1.45955i
$928$	38.3082	−	1.14386i	1.25753	−	0.0375490i
$929$	37.0000	−	21.3620i	1.21393	−	0.700864i	0.250319	−	0.968164i	$-0.419465\pi$
$929$	37.0000	−	21.3620i	1.21393	−	0.700864i	0.963614	+	0.267299i	$0.0861313\pi$
$930$	−4.77436	−	4.54931i	−0.156557	−	0.149178i
$931$	11.1256	+	37.8972i	0.364628	+	1.24203i
$932$	24.7165	+	4.94597i	0.809617	+	0.162011i
$933$	−5.73875	+	41.0446i	−0.187878	+	1.34374i
$934$	1.90621	−	19.2407i	0.0623731	−	0.629574i
$935$		−	2.89321i		−	0.0946182i
$936$	2.06619	−	40.8926i	0.0675355	−	1.33662i
$937$		−	22.0770i		−	0.721224i	−0.932716	−	0.360612i	$-0.882568\pi$
$937$		−	22.0770i		−	0.721224i	0.932716	−	0.360612i	$-0.117432\pi$
$938$	5.73521	−	1.81078i	0.187261	−	0.0591240i
$939$	15.1245	−	19.3868i	0.493568	−	0.632663i
$940$	−2.25843	+	11.2861i	−0.0736618	+	0.368110i
$941$	−29.8416	−	17.2290i	−0.972807	−	0.561650i	−0.0727161	−	0.997353i	$-0.523167\pi$
$941$	−29.8416	−	17.2290i	−0.972807	−	0.561650i	−0.900091	+	0.435702i	$0.856500\pi$
$942$	6.07547	−	25.0799i	0.197950	−	0.817146i
$943$	−10.8809	−	18.8463i	−0.354332	−	0.613720i
$944$	−13.0802	+	9.98911i	−0.425725	+	0.325118i
$945$	21.5075	+	0.261897i	0.699641	+	0.00851952i
$946$	−1.92446	−	1.38073i	−0.0625697	−	0.0448913i
$947$	34.9193	−	20.1606i	1.13472	−	0.655133i	0.189605	−	0.981861i	$-0.439279\pi$
$947$	34.9193	−	20.1606i	1.13472	−	0.655133i	0.945119	+	0.326728i	$0.105946\pi$
$948$	−19.4592	+	16.7522i	−0.632005	+	0.544085i
$949$	−4.53613	+	7.85682i	−0.147249	+	0.255043i
$950$	−18.5545	+	8.39408i	−0.601987	+	0.272340i
$951$	0.688364	+	0.537023i	0.0223217	+	0.0174142i
$952$	2.66631	+	3.64216i	0.0864155	+	0.118043i
$953$	−40.6441			−1.31659			−0.658296	−	0.752759i	$-0.728722\pi$
$953$	−40.6441			−1.31659			−0.658296	+	0.752759i	$0.728722\pi$
$954$	1.13405	+	1.42961i	0.0367161	+	0.0462855i
$955$	12.1421			0.392909
$956$	−4.14314	−	3.64187i	−0.133999	−	0.117786i
$957$	35.6291	+	4.98158i	1.15173	+	0.161032i
$958$	6.05773	−	2.74052i	0.195716	−	0.0885423i
$959$	−0.936090	+	7.82754i	−0.0302279	+	0.252764i
$960$	16.1343	+	14.4800i	0.520732	+	0.467341i
$961$	14.0194	+	24.2824i	0.452239	+	0.783302i
$962$	21.7111	−	30.2610i	0.699993	−	0.975654i
$963$	−14.5563	−	15.0307i	−0.469069	−	0.484358i
$964$	40.2772	−	13.6206i	1.29724	−	0.438691i
$965$	3.43471	−	1.98303i	0.110567	−	0.0638360i
$966$	−45.0889	+	37.2519i	−1.45071	+	1.19856i
$967$	13.2891	+	7.67248i	0.427349	+	0.246730i	0.698217	−	0.715886i	$-0.253977\pi$
$967$	13.2891	+	7.67248i	0.427349	+	0.246730i	−0.270867	+	0.962617i	$0.587311\pi$
$968$	−3.09003	−	3.31061i	−0.0993172	−	0.106407i
$969$	2.21212	+	5.46403i	0.0710636	+	0.175530i
$970$	3.73232	−	37.6729i	0.119838	−	1.20960i
$971$	−7.47337			−0.239832			−0.119916	−	0.992784i	$-0.538263\pi$
$971$	−7.47337			−0.239832			−0.119916	+	0.992784i	$0.538263\pi$
$972$	4.81657	+	30.8026i	0.154492	+	0.987994i
$973$	0.760449	−	0.325621i	0.0243789	−	0.0104389i
$974$	1.35882	+	0.134621i	0.0435393	+	0.00431352i
$975$	8.00454	+	19.7715i	0.256350	+	0.633196i
$976$	51.8295	−	6.70226i	1.65902	−	0.214534i
$977$	−15.5607	+	26.9520i	−0.497832	+	0.862271i	−0.999997	−	0.00250126i	$-0.999204\pi$
$977$	−15.5607	+	26.9520i	−0.497832	+	0.862271i	0.502165	+	0.864772i	$0.332537\pi$
$978$	32.9949	−	9.70010i	1.05506	−	0.310175i
$979$	21.5423	+	37.3123i	0.688494	+	1.19251i
$980$	−9.24138	+	19.8589i	−0.295205	+	0.634369i
$981$	−19.8064	+	19.1812i	−0.632369	+	0.612408i
$982$	25.0166	−	34.8683i	0.798313	−	1.11269i
$983$	−1.02115	−	1.76868i	−0.0325696	−	0.0564123i	0.849281	−	0.527941i	$-0.177036\pi$
$983$	−1.02115	−	1.76868i	−0.0325696	−	0.0564123i	−0.881851	+	0.471529i	$0.843702\pi$
$984$	4.97999	−	10.7122i	0.158756	−	0.341493i
$985$	−37.3779	−	21.5801i	−1.19096	−	0.687600i
$986$	2.38213	+	5.26553i	0.0758626	+	0.167689i
$987$	−4.42545	−	16.2647i	−0.140864	−	0.517712i
$988$	40.8987	+	35.9505i	1.30116	+	1.14374i
$989$	4.93015			0.156770
$990$	12.6469	+	15.9431i	0.401945	+	0.506705i
$991$		−	26.6788i		−	0.847480i	−0.905784	−	0.423740i	$-0.860717\pi$
$991$		−	26.6788i		−	0.847480i	0.905784	−	0.423740i	$-0.139283\pi$
$992$	5.11660	+	8.28115i	0.162452	+	0.262927i
$993$	26.6373	−	34.1440i	0.845308	−	1.08353i
$994$	29.0461	+	26.5949i	0.921286	+	0.843538i
$995$	3.07323	+	1.77433i	0.0974279	+	0.0562501i
$996$	−3.62116	−	4.20631i	−0.114741	−	0.133282i
$997$	−7.46362	+	4.30912i	−0.236375	+	0.136471i	−0.613510	−	0.789687i	$-0.710243\pi$
$997$	−7.46362	+	4.30912i	−0.236375	+	0.136471i	0.377134	+	0.926159i	$0.376909\pi$
$998$	−9.32424	+	12.9962i	−0.295154	+	0.411387i
$999$	−11.4794	+	25.9316i	−0.363193	+	0.820439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.139.22	yes	80
3.2	odd	2		756.2.bi.c.307.20		80
4.3	odd	2	inner	252.2.bi.c.139.7	✓	80
7.6	odd	2	inner	252.2.bi.c.139.21	yes	80
9.2	odd	6		756.2.bi.c.559.33		80
9.7	even	3	inner	252.2.bi.c.223.8	yes	80
12.11	even	2		756.2.bi.c.307.34		80
21.20	even	2		756.2.bi.c.307.19		80
28.27	even	2	inner	252.2.bi.c.139.8	yes	80
36.7	odd	6	inner	252.2.bi.c.223.21	yes	80
36.11	even	6		756.2.bi.c.559.19		80
63.20	even	6		756.2.bi.c.559.34		80
63.34	odd	6	inner	252.2.bi.c.223.7	yes	80
84.83	odd	2		756.2.bi.c.307.33		80
252.83	odd	6		756.2.bi.c.559.20		80
252.223	even	6	inner	252.2.bi.c.223.22	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.7	✓	80	4.3	odd	2	inner
252.2.bi.c.139.8	yes	80	28.27	even	2	inner
252.2.bi.c.139.21	yes	80	7.6	odd	2	inner
252.2.bi.c.139.22	yes	80	1.1	even	1	trivial
252.2.bi.c.223.7	yes	80	63.34	odd	6	inner
252.2.bi.c.223.8	yes	80	9.7	even	3	inner
252.2.bi.c.223.21	yes	80	36.7	odd	6	inner
252.2.bi.c.223.22	yes	80	252.223	even	6	inner
756.2.bi.c.307.19		80	21.20	even	2
756.2.bi.c.307.20		80	3.2	odd	2
756.2.bi.c.307.33		80	84.83	odd	2
756.2.bi.c.307.34		80	12.11	even	2
756.2.bi.c.559.19		80	36.11	even	6
756.2.bi.c.559.20		80	252.83	odd	6
756.2.bi.c.559.33		80	9.2	odd	6
756.2.bi.c.559.34		80	63.20	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.139426 - 1.40732i) q^{2} +(1.60547 - 0.649977i) q^{3} +(-1.96112 - 0.392436i) q^{4} +(-1.35495 - 0.782280i) q^{5} +(-0.690883 - 2.35004i) q^{6} +(-2.11799 - 1.58559i) q^{7} +(-0.825716 + 2.70522i) q^{8} +(2.15506 - 2.08703i) q^{9} +O(q^{10})\)	\(q+(0.139426 - 1.40732i) q^{2} +(1.60547 - 0.649977i) q^{3} +(-1.96112 - 0.392436i) q^{4} +(-1.35495 - 0.782280i) q^{5} +(-0.690883 - 2.35004i) q^{6} +(-2.11799 - 1.58559i) q^{7} +(-0.825716 + 2.70522i) q^{8} +(2.15506 - 2.08703i) q^{9} +(-1.28984 + 1.79778i) q^{10} +(2.65503 - 1.53288i) q^{11} +(-3.40359 + 0.644639i) q^{12} +(-4.17891 - 2.41269i) q^{13} +(-2.52674 + 2.75963i) q^{14} +(-2.68379 - 0.375241i) q^{15} +(3.69199 + 1.53923i) q^{16} +0.603184i q^{17} +(-2.63666 - 3.32386i) q^{18} +5.64236 q^{19} +(2.35022 + 2.06588i) q^{20} +(-4.43097 - 1.16897i) q^{21} +(-1.78708 - 3.95021i) q^{22} +(7.81563 + 4.51236i) q^{23} +(0.432666 + 4.87984i) q^{24} +(-1.27608 - 2.21023i) q^{25} +(-3.97809 + 5.54468i) q^{26} +(2.10336 - 4.75141i) q^{27} +(3.53140 + 3.94071i) q^{28} +(3.38751 + 5.86734i) q^{29} +(-0.902277 + 3.72464i) q^{30} +(-0.860400 + 1.49026i) q^{31} +(2.68095 - 4.98121i) q^{32} +(3.26623 - 4.18670i) q^{33} +(0.848876 + 0.0840997i) q^{34} +(1.62940 + 3.80526i) q^{35} +(-5.04536 + 3.24720i) q^{36} -5.45766 q^{37} +(0.786694 - 7.94063i) q^{38} +(-8.27730 - 1.15731i) q^{39} +(3.23504 - 3.01949i) q^{40} +(-2.08830 - 1.20568i) q^{41} +(-2.26291 + 6.07283i) q^{42} +(0.473105 - 0.273147i) q^{43} +(-5.80838 + 1.96424i) q^{44} +(-4.55264 + 1.14196i) q^{45} +(7.44005 - 10.3700i) q^{46} +(1.83914 + 3.18549i) q^{47} +(6.92783 + 0.0714765i) q^{48} +(1.97180 + 6.71655i) q^{49} +(-3.28843 + 1.48769i) q^{50} +(0.392056 + 0.968394i) q^{51} +(7.24851 + 6.37153i) q^{52} -0.430107 q^{53} +(-6.39351 - 3.62258i) q^{54} -4.79657 q^{55} +(6.03823 - 4.42038i) q^{56} +(9.05864 - 3.66740i) q^{57} +(8.72955 - 3.94926i) q^{58} +(-2.05729 + 3.56332i) q^{59} +(5.11598 + 1.78911i) q^{60} +(11.3148 - 6.53263i) q^{61} +(1.97731 + 1.41864i) q^{62} +(-7.87359 + 1.00328i) q^{63} +(-6.63639 - 4.46748i) q^{64} +(3.77480 + 6.53815i) q^{65} +(-5.43664 - 5.18037i) q^{66} +(-1.39203 - 0.803692i) q^{67} +(0.236711 - 1.18292i) q^{68} +(15.4807 + 2.16447i) q^{69} +(5.58241 - 1.76254i) q^{70} -10.5254i q^{71} +(3.86641 + 7.55320i) q^{72} -1.88011i q^{73} +(-0.760941 + 7.68070i) q^{74} +(-3.48530 - 2.71903i) q^{75} +(-11.0654 - 2.21427i) q^{76} +(-8.05385 - 0.963155i) q^{77} +(-2.78278 + 11.4875i) q^{78} +(6.41918 - 3.70612i) q^{79} +(-3.79835 - 4.97374i) q^{80} +(0.288576 - 8.99537i) q^{81} +(-1.98795 + 2.77081i) q^{82} +(0.801117 + 1.38758i) q^{83} +(8.23092 + 4.03136i) q^{84} +(0.471859 - 0.817284i) q^{85} +(-0.318443 - 0.703896i) q^{86} +(9.25217 + 7.21803i) q^{87} +(1.95447 + 8.44814i) q^{88} +14.0535i q^{89} +(0.972354 + 6.56626i) q^{90} +(5.02536 + 11.7361i) q^{91} +(-13.5566 - 11.9164i) q^{92} +(-0.412714 + 2.95180i) q^{93} +(4.73944 - 2.14413i) q^{94} +(-7.64511 - 4.41391i) q^{95} +(1.06651 - 9.73974i) q^{96} +(-14.8174 + 8.55485i) q^{97} +(9.72728 - 1.83850i) q^{98} +(2.52257 - 8.84458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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