LMFDB - Embedded newform 252.2.bi.c.139.8

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			139.8
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28849 - 0.582915i) q^{2} +(1.60547 - 0.649977i) q^{3} +(1.32042 + 1.50216i) q^{4} +(1.35495 + 0.782280i) q^{5} +(-2.44751 - 0.0983632i) q^{6} +(-0.314165 - 2.62703i) q^{7} +(-0.825716 - 2.70522i) q^{8} +(2.15506 - 2.08703i) q^{9} +O(q^{10})$	\(q+(-1.28849 - 0.582915i) q^{2} +(1.60547 - 0.649977i) q^{3} +(1.32042 + 1.50216i) q^{4} +(1.35495 + 0.782280i) q^{5} +(-2.44751 - 0.0983632i) q^{6} +(-0.314165 - 2.62703i) 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} +(3.09626 + 1.55343i) q^{12} +(4.17891 + 2.41269i) q^{13} +(-1.12654 + 3.56804i) q^{14} +(2.68379 + 0.375241i) q^{15} +(-0.512984 + 3.96697i) q^{16} -0.603184i q^{17} +(-3.99334 + 1.43291i) q^{18} +5.64236 q^{19} +(0.613989 + 3.06829i) q^{20} +(-2.21189 - 4.01342i) q^{21} +(4.31452 - 0.427448i) q^{22} +(-7.81563 - 4.51236i) q^{23} +(-3.08399 - 3.80644i) 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} +(-3.23931 - 2.04792i) q^{30} +(-0.860400 + 1.49026i) q^{31} +(2.97338 - 4.81238i) q^{32} +(-3.26623 + 4.18670i) q^{33} +(-0.351605 + 0.777198i) q^{34} +(1.62940 - 3.80526i) q^{35} +(5.98065 + 0.481490i) q^{36} -5.45766 q^{37} +(-7.27014 - 3.28902i) q^{38} +(8.27730 + 1.15731i) q^{39} +(0.997434 - 4.31137i) q^{40} +(2.08830 + 1.20568i) q^{41} +(0.510520 + 6.46060i) 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} +(1.75486 + 6.70227i) q^{48} +(-6.80260 + 1.65064i) q^{49} +(0.355837 + 3.59171i) q^{50} +(-0.392056 - 0.968394i) q^{51} +(1.89365 + 9.46316i) q^{52} -0.430107 q^{53} +(-5.47983 + 4.89607i) q^{54} -4.79657 q^{55} +(-6.84728 + 3.01907i) q^{56} +(9.05864 - 3.66740i) q^{57} +(-0.944615 - 9.53464i) q^{58} +(-2.05729 + 3.56332i) q^{59} +(2.98006 + 4.52697i) q^{60} +(-11.3148 + 6.53263i) q^{61} +(1.97731 - 1.41864i) q^{62} +(-6.15975 - 5.00574i) q^{63} +(-6.63639 + 4.46748i) q^{64} +(3.77480 + 6.53815i) q^{65} +(6.64899 - 3.49059i) q^{66} +(1.39203 + 0.803692i) q^{67} +(0.906081 - 0.796456i) q^{68} +(-15.4807 - 2.16447i) q^{69} +(-4.31761 + 3.95324i) q^{70} +10.5254i q^{71} +(-7.42535 - 4.10661i) q^{72} +1.88011i q^{73} +(7.03215 + 3.18135i) q^{74} +(-3.48530 - 2.71903i) q^{75} +(7.45029 + 8.47575i) q^{76} +(4.86104 + 6.49326i) q^{77} +(-9.99061 - 6.31615i) 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} +(3.10818 - 8.62202i) q^{84} +(0.471859 - 0.817284i) q^{85} +(0.768813 - 0.0761678i) q^{86} +(9.25217 + 7.21803i) q^{87} +(6.33907 + 5.91670i) q^{88} -14.0535i q^{89} +(-6.53171 - 1.18239i) q^{90} +(5.02536 - 11.7361i) q^{91} +(-3.54162 - 17.6986i) q^{92} +(-0.412714 + 2.95180i) q^{93} +(-0.512850 - 5.17654i) q^{94} +(7.64511 + 4.41391i) q^{95} +(1.64574 - 9.65875i) 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 $

$2$	−1.28849	−	0.582915i	−0.911101	−	0.412183i
$2$	−1.28849	−	0.582915i	−0.911101	−	0.412183i
$3$	1.60547	−	0.649977i	0.926918	−	0.375264i
$3$	1.60547	−	0.649977i	0.926918	−	0.375264i
$4$	1.32042	+	1.50216i	0.660210	+	0.751081i
$5$	1.35495	+	0.782280i	0.605951	+	0.349846i	0.771379	−	0.636376i	$-0.219567\pi$
$5$	1.35495	+	0.782280i	0.605951	+	0.349846i	−0.165428	+	0.986222i	$0.552901\pi$
$6$	−2.44751	−	0.0983632i	−0.999193	−	0.0401566i
$7$	−0.314165	−	2.62703i	−0.118743	−	0.992925i
$7$	−0.314165	−	2.62703i	−0.118743	−	0.992925i
$8$	−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	−0.843653	−	0.536889i	$-0.819600\pi$
$11$	−2.65503	+	1.53288i	−0.800521	+	0.462181i	0.0431325	+	0.999069i	$0.486266\pi$
$12$	3.09626	+	1.55343i	0.893814	+	0.448438i
$13$	4.17891	+	2.41269i	1.15902	+	0.669160i	0.951069	−	0.308979i	$-0.0999873\pi$
$13$	4.17891	+	2.41269i	1.15902	+	0.669160i	0.207951	+	0.978139i	$0.433321\pi$
$14$	−1.12654	+	3.56804i	−0.301080	+	0.953599i
$15$	2.68379	+	0.375241i	0.692952	+	0.0968869i
$16$	−0.512984	+	3.96697i	−0.128246	+	0.991742i
$17$		−	0.603184i		−	0.146294i	−0.997321	−	0.0731468i	$-0.976696\pi$
$17$		−	0.603184i		−	0.146294i	0.997321	−	0.0731468i	$-0.0233042\pi$
$18$	−3.99334	+	1.43291i	−0.941240	+	0.337740i
$19$	5.64236			1.29445			0.647224	−	0.762300i	$-0.275930\pi$
$19$	5.64236			1.29445			0.647224	+	0.762300i	$0.275930\pi$
$20$	0.613989	+	3.06829i	0.137292	+	0.686091i
$21$	−2.21189	−	4.01342i	−0.482674	−	0.875800i
$22$	4.31452	−	0.427448i	0.919858	−	0.0911321i
$23$	−7.81563	−	4.51236i	−1.62967	−	0.940891i	−0.984190	−	0.177116i	$-0.943323\pi$
$23$	−7.81563	−	4.51236i	−1.62967	−	0.940891i	−0.645482	−	0.763776i	$-0.723343\pi$
$24$	−3.08399	−	3.80644i	−0.629516	−	0.776987i
$25$	−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	$0.616780\pi$
$30$	−3.23931	−	2.04792i	−0.591414	−	0.373897i
$31$	−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	$0.216054\pi$
$32$	2.97338	−	4.81238i	0.525625	−	0.850717i
$33$	−3.26623	+	4.18670i	−0.568577	+	0.728810i
$34$	−0.351605	+	0.777198i	−0.0602998	+	0.133288i
$35$	1.62940	−	3.80526i	0.275418	−	0.643206i
$36$	5.98065	+	0.481490i	0.996775	+	0.0802484i
$37$	−5.45766			−0.897234			−0.448617	−	0.893724i	$-0.648083\pi$
$37$	−5.45766			−0.897234			−0.448617	+	0.893724i	$0.648083\pi$
$38$	−7.27014	−	3.28902i	−1.17937	−	0.533549i
$39$	8.27730	+	1.15731i	1.32543	+	0.185318i
$40$	0.997434	−	4.31137i	0.157708	−	0.681687i
$41$	2.08830	+	1.20568i	0.326138	+	0.188296i	0.654125	−	0.756386i	$-0.273037\pi$
$41$	2.08830	+	1.20568i	0.326138	+	0.188296i	−0.327987	+	0.944682i	$0.606370\pi$
$42$	0.510520	+	6.46060i	0.0787749	+	0.996892i
$43$	−0.473105	+	0.273147i	−0.0721478	+	0.0416546i	−0.535640	−	0.844446i	$-0.679930\pi$
$43$	−0.473105	+	0.273147i	−0.0721478	+	0.0416546i	0.463492	+	0.886101i	$0.346596\pi$
$44$	−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	$0.746883\pi$
$48$	1.75486	+	6.70227i	0.253292	+	0.967390i
$49$	−6.80260	+	1.65064i	−0.971800	+	0.235806i
$50$	0.355837	+	3.59171i	0.0503230	+	0.507944i
$51$	−0.392056	−	0.968394i	−0.0548988	−	0.135602i
$52$	1.89365	+	9.46316i	0.262602	+	1.31230i
$53$	−0.430107			−0.0590798			−0.0295399	−	0.999564i	$-0.509404\pi$
$53$	−0.430107			−0.0590798			−0.0295399	+	0.999564i	$0.509404\pi$
$54$	−5.47983	+	4.89607i	−0.745710	+	0.666270i
$55$	−4.79657			−0.646769
$56$	−6.84728	+	3.01907i	−0.915006	+	0.403440i
$57$	9.05864	−	3.66740i	1.19985	−	0.485760i
$58$	−0.944615	−	9.53464i	−0.124034	−	1.25196i
$59$	−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	$0.252975\pi$
$60$	2.98006	+	4.52697i	0.384724	+	0.584429i
$61$	−11.3148	+	6.53263i	−1.44872	+	0.836417i	−0.998405	−	0.0564545i	$-0.982020\pi$
$61$	−11.3148	+	6.53263i	−1.44872	+	0.836417i	−0.450312	+	0.892871i	$0.648687\pi$
$62$	1.97731	−	1.41864i	0.251119	−	0.180168i
$63$	−6.15975	−	5.00574i	−0.776056	−	0.630664i
$64$	−6.63639	+	4.46748i	−0.829548	+	0.558435i
$65$	3.77480	+	6.53815i	0.468206	+	0.810957i
$66$	6.64899	−	3.49059i	0.818435	−	0.429662i
$67$	1.39203	+	0.803692i	0.170064	+	0.0981866i	0.582616	−	0.812748i	$-0.302029\pi$
$67$	1.39203	+	0.803692i	0.170064	+	0.0981866i	−0.412552	+	0.910934i	$0.635362\pi$
$68$	0.906081	−	0.796456i	0.109878	−	0.0965845i
$69$	−15.4807	−	2.16447i	−1.86365	−	0.260572i
$70$	−4.31761	+	3.95324i	−0.516053	+	0.472503i
$71$			10.5254i			1.24913i	0.780973	+	0.624565i	$0.214724\pi$
$71$			10.5254i			1.24913i	−0.780973	+	0.624565i	$0.785276\pi$
$72$	−7.42535	−	4.10661i	−0.875085	−	0.483968i
$73$			1.88011i			0.220051i	0.993929	+	0.110025i	$0.0350932\pi$
$73$			1.88011i			0.220051i	−0.993929	+	0.110025i	$0.964907\pi$
$74$	7.03215	+	3.18135i	0.817471	+	0.369825i
$75$	−3.48530	−	2.71903i	−0.402448	−	0.313967i
$76$	7.45029	+	8.47575i	0.854607	+	0.972235i
$77$	4.86104	+	6.49326i	0.553967	+	0.739976i
$78$	−9.99061	−	6.31615i	−1.13121	−	0.715163i
$79$	−6.41918	+	3.70612i	−0.722215	+	0.416971i	−0.815567	−	0.578662i	$-0.803575\pi$
$79$	−6.41918	+	3.70612i	−0.722215	+	0.416971i	0.0933526	+	0.995633i	$0.470242\pi$
$80$	−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	$0.805307\pi$
$84$	3.10818	−	8.62202i	0.339131	−	0.940739i
$85$	0.471859	−	0.817284i	0.0511803	−	0.0886469i
$86$	0.768813	−	0.0761678i	0.0829033	−	0.00821338i
$87$	9.25217	+	7.21803i	0.991937	+	0.773854i
$88$	6.33907	+	5.91670i	0.675747	+	0.630722i
$89$		−	14.0535i		−	1.48966i	−0.667252	−	0.744832i	$-0.732529\pi$
$89$		−	14.0535i		−	1.48966i	0.667252	−	0.744832i	$-0.267471\pi$
$90$	−6.53171	−	1.18239i	−0.688502	−	0.124635i
$91$	5.02536	−	11.7361i	0.526800	−	1.23028i
$92$	−3.54162	−	17.6986i	−0.369239	−	1.84520i
$93$	−0.412714	+	2.95180i	−0.0427964	+	0.306088i
$94$	−0.512850	−	5.17654i	−0.0528964	−	0.533919i
$95$	7.64511	+	4.41391i	0.784372	+	0.452857i
$96$	1.64574	−	9.65875i	0.167968	−	0.985793i
$97$	14.8174	−	8.55485i	1.50448	−	0.868614i	0.504496	−	0.863414i	$-0.331678\pi$
$97$	14.8174	−	8.55485i	1.50448	−	0.868614i	0.999986	−	0.00519970i	$-0.00165512\pi$
$98$	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	−0.795272	−	0.606253i	$-0.792672\pi$
$101$	−6.71208	+	3.87522i	−0.667877	+	0.385599i	0.127395	+	0.991852i	$0.459338\pi$
$102$	−0.0593311	+	1.47630i	−0.00587466	+	0.146176i
$103$	−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	$0.895571\pi$
$104$	3.07626	−	13.2970i	0.301653	−	1.30388i
$105$	0.142618	−	7.16829i	0.0139181	−	0.699554i
$106$	0.554190	+	0.250716i	0.0538276	+	0.0243517i
$107$			6.97461i			0.674261i	0.941458	+	0.337131i	$0.109456\pi$
$107$			6.97461i			0.674261i	−0.941458	+	0.337131i	$0.890544\pi$
$108$	9.91470	−	3.11426i	0.954043	−	0.299670i
$109$	−9.19063			−0.880303			−0.440152	−	0.897924i	$-0.645075\pi$
$109$	−9.19063			−0.880303			−0.440152	+	0.897924i	$0.645075\pi$
$110$	6.18033	+	2.79599i	0.589272	+	0.266587i
$111$	−8.76211	+	3.54735i	−0.831662	+	0.336700i
$112$	10.5825	+	0.101343i	0.999954	+	0.00957598i
$113$	−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	$0.247341\pi$
$114$	−13.8098	−	0.555001i	−1.29340	−	0.0519806i
$115$	−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
$119$	−1.58458	+	0.189499i	−0.145259	+	0.0173714i
$120$	−1.20094	−	7.57008i	−0.109630	−	0.691050i
$121$	−0.800555	+	1.38660i	−0.0727777	+	0.126055i
$122$	18.3870	−	1.82164i	1.66468	−	0.164923i
$123$	4.13637	+	0.578337i	0.372964	+	0.0521469i
$124$	−3.37470	+	0.675304i	−0.303057	+	0.0606441i
$125$		−	11.8158i		−	1.05684i
$126$	5.01886	+	10.0405i	0.447116	+	0.894476i
$127$			1.96179i			0.174080i	0.996205	+	0.0870402i	$0.0277409\pi$
$127$			1.96179i			0.174080i	−0.996205	+	0.0870402i	$0.972259\pi$
$128$	11.1551	−	1.88786i	0.985980	−	0.166865i
$129$	−0.582016	+	0.746036i	−0.0512436	+	0.0656848i
$130$	−1.05261	−	10.6247i	−0.0923202	−	0.931851i
$131$	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	$0.0627423\pi$
$132$	−10.6019	+	0.621794i	−0.922776	+	0.0541202i
$133$	−1.77263	−	14.8227i	−0.153707	−	1.28529i
$134$	−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	$0.873959\pi$
$138$	18.6850	+	11.8128i	1.59057	+	1.00557i
$139$	−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	$0.170888\pi$
$140$	7.86761	−	2.57692i	0.664934	−	0.217789i
$141$	5.02318	+	3.91881i	0.423028	+	0.330023i
$142$	6.13539	−	13.5618i	0.514870	−	1.13808i
$143$	−14.7935			−1.23709
$144$	7.17369	+	9.61968i	0.597808	+	0.801640i
$145$			10.5999i			0.880276i
$146$	1.09595	−	2.42251i	0.0907012	−	0.200488i
$147$	−9.84848	+	7.07159i	−0.812289	+	0.583255i
$148$	−7.20640	−	8.19830i	−0.592363	−	0.673896i
$149$	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	$0.000565533\pi$
$150$	2.90581	+	5.53509i	0.237258	+	0.451938i
$151$	10.8594	−	6.26969i	0.883727	−	0.510220i	0.0118414	−	0.999930i	$-0.496231\pi$
$151$	10.8594	−	6.26969i	0.883727	−	0.510220i	0.871885	+	0.489710i	$0.162897\pi$
$152$	−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
$156$	9.19103	+	13.9620i	0.735872	+	1.11785i
$157$	−9.12353	−	5.26748i	−0.728137	−	0.420390i	0.0896030	−	0.995978i	$-0.471440\pi$
$157$	−9.12353	−	5.26748i	−0.728137	−	0.420390i	−0.817740	+	0.575587i	$0.804774\pi$
$158$	10.4314	−	1.03346i	0.829879	−	0.0822177i
$159$	−0.690524	+	0.279560i	−0.0547621	+	0.0221705i
$160$	7.79341	−	4.19451i	0.616123	−	0.331605i
$161$	−9.39871	+	21.9495i	−0.740722	+	1.72987i
$162$	−5.61537	+	11.4222i	−0.441185	+	0.897416i
$163$		−	14.0402i		−	1.09971i	−0.835260	−	0.549855i	$-0.814683\pi$
$163$		−	14.0402i		−	1.09971i	0.835260	−	0.549855i	$-0.185317\pi$
$164$	0.946305	+	4.72897i	0.0738940	+	0.369271i
$165$	−7.70074	+	3.11766i	−0.599502	+	0.242709i
$166$	−0.223394	−	2.25486i	−0.0173387	−	0.175011i
$167$	−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	$0.182775\pi$
$168$	−9.03077	+	9.29759i	−0.696739	+	0.717325i
$169$	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	−0.00441290	−	0.999990i	$-0.501405\pi$
$173$	11.3036	−	6.52614i	0.859398	−	0.496173i	0.863811	+	0.503817i	$0.168071\pi$
$174$	−7.71385	−	14.6936i	−0.584785	−	1.11392i
$175$	−5.40545	+	4.04667i	−0.408613	+	0.305900i
$176$	−4.71890	−	11.3188i	−0.355701	−	0.853183i
$177$	−0.986831	+	7.05799i	−0.0741748	+	0.530511i
$178$	−8.19198	+	18.1078i	−0.614015	+	1.35723i
$179$		−	14.5664i		−	1.08875i	−0.838843	−	0.544373i	$-0.816768\pi$
$179$		−	14.5664i		−	1.08875i	0.838843	−	0.544373i	$-0.183232\pi$
$180$	7.72681	+	5.33094i	0.575923	+	0.397345i
$181$			12.3620i			0.918861i	0.888214	+	0.459431i	$0.151947\pi$
$181$			12.3620i			0.918861i	−0.888214	+	0.459431i	$0.848053\pi$
$182$	−13.3163	+	12.1925i	−0.987068	+	0.903769i
$183$	−13.9196	+	17.8423i	−1.02896	+	1.31894i
$184$	−5.75341	+	24.8689i	−0.424147	+	1.83336i
$185$	−7.39485	−	4.26942i	−0.543680	−	0.313894i
$186$	2.25243	−	3.56279i	0.165156	−	0.261237i
$187$	0.924609	+	1.60147i	0.0676141	+	0.117111i
$188$	−2.35668	+	6.96888i	−0.171879	+	0.508258i
$189$	−13.1429	−	4.03287i	−0.956006	−	0.293348i
$190$	−7.27773	−	10.1437i	−0.527982	−	0.735904i
$191$	6.72098	−	3.88036i	0.486313	−	0.280773i	−0.236731	−	0.971575i	$-0.576076\pi$
$191$	6.72098	−	3.88036i	0.486313	−	0.280773i	0.723044	+	0.690802i	$0.242743\pi$
$192$	−7.75076	+	11.4859i	−0.559363	+	0.828923i
$193$	−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	$0.195748\pi$
$194$	−24.0789	+	2.38554i	−1.72876	+	0.171272i
$195$	10.3100	+	8.04326i	0.738312	+	0.575990i
$196$	−11.4618	−	8.03907i	−0.818702	−	0.574219i
$197$	27.5862			1.96544			0.982718	−	0.185109i	$-0.0592638\pi$
$197$	27.5862			1.96544			0.982718	+	0.185109i	$0.0592638\pi$
$198$	8.40595	−	9.92572i	0.597385	−	0.705390i
$199$	−2.26815			−0.160785			−0.0803925	−	0.996763i	$-0.525617\pi$
$199$	−2.26815			−0.160785			−0.0803925	+	0.996763i	$0.525617\pi$
$200$	−4.92547	+	5.27708i	−0.348283	+	0.373146i
$201$	2.75725	+	0.385512i	0.194481	+	0.0271919i
$202$	10.9074	−	1.08061i	0.767441	−	0.0760318i
$203$	14.3495	−	10.7424i	1.00713	−	0.753969i
$204$	0.937007	−	1.86762i	0.0656036	−	0.130759i
$205$	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
$210$	−4.36227	+	9.15315i	−0.301025	+	0.631627i
$211$	−3.25741	−	1.88067i	−0.224249	−	0.129470i	0.383667	−	0.923471i	$-0.374661\pi$
$211$	−3.25741	−	1.88067i	−0.224249	−	0.129470i	−0.607916	+	0.794001i	$0.707994\pi$
$212$	−0.567922	−	0.646091i	−0.0390051	−	0.0443737i
$213$	6.84123	+	16.8981i	0.468753	+	1.15784i
$214$	4.06561	−	8.98672i	0.277919	−	0.614320i
$215$	−0.854710			−0.0582908
$216$	−14.5904	−	1.76673i	−0.992748	−	0.120211i
$217$	4.18526	+	1.79211i	0.284114	+	0.121657i
$218$	11.8421	+	5.35736i	0.802045	+	0.362846i
$219$	1.22203	+	3.01846i	0.0825771	+	0.203969i
$220$	−6.33348	−	7.20522i	−0.427003	−	0.485776i
$221$	1.45530	−	2.52065i	0.0978939	−	0.169557i
$222$	13.3577	+	0.536833i	0.896510	+	0.0360299i
$223$	−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	$0.640115\pi$
$228$	17.4702	+	8.76504i	1.15700	+	0.580479i
$229$	−14.8935	−	8.59879i	−0.984193	−	0.568224i	−0.0806596	−	0.996742i	$-0.525703\pi$
$229$	−14.8935	−	8.59879i	−0.984193	−	0.568224i	−0.903533	+	0.428518i	$0.859036\pi$
$230$	1.96866	+	19.8710i	0.129809	+	1.31025i
$231$	12.0247	+	7.26517i	0.791169	+	0.478013i
$232$	13.0753	−	14.0087i	0.858435	−	0.919716i
$233$	−12.6033			−0.825667			−0.412834	−	0.910806i	$-0.635461\pi$
$233$	−12.6033			−0.825667			−0.412834	+	0.910806i	$0.635461\pi$
$234$	−20.1450	−	3.64672i	−1.31692	−	0.238393i
$235$			5.75490i			0.375408i
$236$	−8.06917	+	1.61470i	−0.525258	+	0.105108i
$237$	−7.89691	+	10.1224i	−0.512959	+	0.657519i
$238$	2.15219	+	0.679510i	0.139505	+	0.0440461i
$239$	−2.38860	−	1.37906i	−0.154506	−	0.0892038i	0.420754	−	0.907175i	$-0.361766\pi$
$239$	−2.38860	−	1.37906i	−0.154506	−	0.0892038i	−0.575259	+	0.817971i	$0.695099\pi$
$240$	−2.86531	+	10.4540i	−0.184955	+	0.674804i
$241$	18.4108	−	10.6295i	1.18594	−	0.684705i	0.228562	−	0.973529i	$-0.426598\pi$
$241$	18.4108	−	10.6295i	1.18594	−	0.684705i	0.957382	+	0.288824i	$0.0932642\pi$
$242$	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
$245$	−10.5084	−	3.08500i	−0.671360	−	0.197094i
$246$	−4.99255	−	3.15633i	−0.318313	−	0.201240i
$247$	23.5789	+	13.6133i	1.50029	+	0.866193i
$248$	4.74191	+	1.09704i	0.301112	+	0.0696621i
$249$	2.18806	+	1.70700i	0.138663	+	0.108177i
$250$	−6.88761	+	15.2245i	−0.435610	+	0.962885i
$251$	21.6486			1.36645			0.683225	−	0.730208i	$-0.260577\pi$
$251$	21.6486			1.36645			0.683225	+	0.730208i	$0.260577\pi$
$252$	−0.614019	−	15.8626i	−0.0386796	−	0.999252i
$253$	27.6676			1.73945
$254$	1.14355	−	2.52774i	0.0717530	−	0.158605i
$255$	0.226340	−	1.61882i	0.0141739	−	0.101374i
$256$	−15.4737	−	4.06998i	−0.967106	−	0.254374i
$257$	1.58731	+	0.916432i	0.0990135	+	0.0571655i	0.548689	−	0.836026i	$-0.315127\pi$
$257$	1.58731	+	0.916432i	0.0990135	+	0.0571655i	−0.449676	+	0.893192i	$0.648460\pi$
$258$	1.18480	−	0.621996i	0.0737623	−	0.0387237i
$259$	1.71461	+	14.3375i	0.106540	+	0.890886i
$260$	−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	−0.366832	−	0.930287i	$-0.619557\pi$
$263$	4.14197	−	2.39137i	0.255405	−	0.147458i	0.622237	+	0.782829i	$0.286224\pi$
$264$	14.0229	+	5.37883i	0.863050	+	0.331044i
$265$	−0.582773	−	0.336464i	−0.0357995	−	0.0206688i
$266$	−6.35634	+	20.1322i	−0.389732	+	1.23438i
$267$	−9.13442	−	22.5624i	−0.559018	−	1.38080i
$268$	0.630795	+	3.15227i	0.0385319	+	0.192556i
$269$		−	7.26728i		−	0.443094i	−0.975150	−	0.221547i	$-0.928889\pi$
$269$		−	7.26728i		−	0.443094i	0.975150	−	0.221547i	$-0.0711106\pi$
$270$	−11.2550	+	2.34716i	−0.684956	+	0.142844i
$271$	22.6258			1.37442			0.687209	−	0.726460i	$-0.258836\pi$
$271$	22.6258			1.37442			0.687209	+	0.726460i	$0.258836\pi$
$272$	2.39281	+	0.309424i	0.145086	+	0.0187616i
$273$	0.439860	−	22.1083i	0.0266215	−	1.33806i
$274$	0.415436	+	4.19328i	0.0250974	+	0.253325i
$275$	6.77603	+	3.91214i	0.408610	+	0.235911i
$276$	−17.1896	−	26.1125i	−1.03469	−	1.57179i
$277$	−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	$-0.429582\pi$
$282$	−4.18799	−	7.97744i	−0.249391	−	0.475049i
$283$	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	$-0.0704476\pi$
$284$	−15.8108	+	13.8979i	−0.938198	+	0.824687i
$285$	15.1429	+	2.11725i	0.896990	+	0.125415i
$286$	19.0613	+	8.62334i	1.12712	+	0.509909i
$287$	2.51129	−	5.86482i	0.148237	−	0.346189i
$288$	−3.63578	−	16.5765i	−0.214240	−	0.976781i
$289$	16.6362			0.978598
$290$	6.17886	−	13.6579i	0.362835	−	0.802020i
$291$	18.2285	−	23.3655i	1.06857	−	1.36971i
$292$	−2.82424	+	2.48254i	−0.165276	+	0.145280i
$293$	8.93196	+	5.15687i	0.521811	+	0.301268i	0.737675	−	0.675156i	$-0.235924\pi$
$293$	8.93196	+	5.15687i	0.521811	+	0.301268i	−0.215864	+	0.976423i	$0.569257\pi$
$294$	16.8118	−	3.37085i	0.980485	−	0.196592i
$295$	−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
$300$	−0.517625	−	8.82575i	−0.0298851	−	0.509555i
$301$	0.866200	+	1.15705i	0.0499269	+	0.0666912i
$302$	−17.6470	+	1.74832i	−1.01547	+	0.100604i
$303$	−8.25723	+	10.5842i	−0.474366	+	0.608049i
$304$	−2.89444	+	22.3831i	−0.166008	+	1.28376i
$305$	−20.4414			−1.17047
$306$	0.864307	+	2.40872i	0.0494092	+	0.137697i
$307$	15.9763			0.911818			0.455909	−	0.890026i	$-0.349314\pi$
$307$	15.9763			0.911818			0.455909	+	0.890026i	$0.349314\pi$
$308$	−3.33532	+	15.8759i	−0.190048	+	0.904614i
$309$	−3.66274	+	26.1965i	−0.208366	+	1.49027i
$310$	3.78893	−	0.375377i	0.215197	−	0.0213200i
$311$	−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	$0.929338\pi$
$312$	−3.70392	−	23.3475i	−0.209693	−	1.32179i
$313$	−12.2943	+	7.09809i	−0.694913	+	0.401208i	−0.805450	−	0.592664i	$-0.798076\pi$
$313$	−12.2943	+	7.09809i	−0.694913	+	0.401208i	0.110537	+	0.993872i	$0.464743\pi$
$314$	8.68510	+	12.1053i	0.490129	+	0.683144i
$315$	−4.43025	−	11.6012i	−0.249617	−	0.653652i
$316$	−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	$0.828827\pi$
$318$	1.05269	+	0.0423067i	0.0590321	+	0.00237244i
$319$	−17.9879	−	10.3853i	−1.00713	−	0.581465i
$320$	−12.4868	+	0.861693i	−0.698032	+	0.0481701i
$321$	4.53333	+	11.1975i	0.253026	+	0.624985i
$322$	24.9049	−	22.8031i	1.38789	−	1.27077i
$323$		−	3.40339i		−	0.189369i
$324$	13.8936	−	11.4442i	0.771864	−	0.635788i
$325$		−	12.3151i		−	0.683120i
$326$	−8.18422	+	18.0906i	−0.453282	+	1.00195i
$327$	−14.7553	+	5.97370i	−0.815969	+	0.330346i
$328$	1.53728	−	6.64485i	0.0848823	−	0.366901i
$329$	7.79059	−	5.83226i	0.429509	−	0.321543i
$330$	11.7397	+	0.471805i	0.646247	+	0.0259720i
$331$	−21.6527	+	12.5012i	−1.19014	+	0.687128i	−0.958338	−	0.285635i	$-0.907796\pi$
$331$	−21.6527	+	12.5012i	−1.19014	+	0.687128i	−0.231802	+	0.972763i	$0.574462\pi$
$332$	−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
$336$	17.0558	−	6.71569i	0.930469	−	0.366371i
$337$	−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	$0.301662\pi$
$338$	−1.43391	−	14.4734i	−0.0779942	−	0.787248i
$339$	−1.27854	+	9.14431i	−0.0694405	+	0.496651i
$340$	1.85074	−	0.370349i	0.100371	−	0.0200850i
$341$		−	5.27556i		−	0.285688i
$342$	−22.5319	+	8.08499i	−1.21838	+	0.437186i
$343$	6.47343	+	17.3521i	0.349532	+	0.936924i
$344$	1.12957	+	1.05431i	0.0609025	+	0.0568445i
$345$	−19.2823	−	15.0430i	−1.03812	−	0.809886i
$346$	−18.3688	+	1.81983i	−0.987512	+	0.0978347i
$347$	−6.57640	−	3.79689i	−0.353040	−	0.203828i	0.312983	−	0.949759i	$-0.398672\pi$
$347$	−6.57640	−	3.79689i	−0.353040	−	0.203828i	−0.666023	+	0.745931i	$0.732005\pi$
$348$	1.37410	+	23.4291i	0.0736596	+	1.25593i
$349$	15.5492	−	8.97732i	0.832329	−	0.480545i	−0.0223207	−	0.999751i	$-0.507106\pi$
$349$	15.5492	−	8.97732i	0.832329	−	0.480545i	0.854649	+	0.519206i	$0.173772\pi$
$350$	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	−0.0447470	−	0.998998i	$-0.514248\pi$
$353$	14.9938	−	8.65665i	0.798037	−	0.460747i	0.842784	+	0.538251i	$0.180915\pi$
$354$	5.38573	−	8.51892i	0.286249	−	0.452776i
$355$	−8.23377	+	14.2613i	−0.437003	+	0.756912i
$356$	21.1106	−	18.5565i	1.11886	−	0.983491i
$357$	−2.42083	+	1.33418i	−0.128124	+	0.0706122i
$358$	−8.49099	+	18.7687i	−0.448763	+	0.991958i
$359$			1.14980i			0.0606842i	0.999540	+	0.0303421i	$0.00965967\pi$
$359$			1.14980i			0.0606842i	−0.999540	+	0.0303421i	$0.990340\pi$
$360$	−6.84845	−	11.3729i	−0.360945	−	0.599407i
$361$	12.8363			0.675593
$362$	7.20601	−	15.9283i	0.378739	−	0.837175i
$363$	−0.384007	+	2.74649i	−0.0201552	+	0.144153i
$364$	24.2651	−	7.94768i	1.27184	−	0.416572i
$365$	−1.47077	+	2.54746i	−0.0769839	+	0.133340i
$366$	28.3358	−	14.8757i	1.48114	−	0.777567i
$367$	−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
$371$	0.135125	+	1.12991i	0.00701532	+	0.0586618i
$372$	−4.97904	+	3.27765i	−0.258151	+	0.169938i
$373$	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	$0.0125983\pi$
$374$	−0.257830	−	2.60245i	−0.0133321	−	0.134569i
$375$	−7.67999	−	18.9699i	−0.396593	−	0.979601i
$376$	7.09883	−	7.60559i	0.366094	−	0.392228i
$377$			32.6921i			1.68373i
$378$	14.5837	+	12.8575i	0.750104	+	0.661319i
$379$			32.3368i			1.66103i	0.556997	+	0.830515i	$0.311953\pi$
$379$			32.3368i			1.66103i	−0.556997	+	0.830515i	$0.688047\pi$
$380$	3.46435	+	17.3124i	0.177717	+	0.888108i
$381$	1.27511	+	3.14959i	0.0653261	+	0.161358i
$382$	−10.9218	+	1.08205i	−0.558810	+	0.0553624i
$383$	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	$0.0611645\pi$
$384$	16.6821	−	10.2814i	0.851304	−	0.524673i
$385$	1.50691	+	12.6007i	0.0767994	+	0.642193i
$386$	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	$0.861670\pi$
$390$	−8.59576	−	16.3735i	−0.435263	−	0.829105i
$391$	−2.72178	+	4.71427i	−0.137646	+	0.238411i
$392$	10.0824	+	17.0395i	0.509236	+	0.860627i
$393$	1.76079	−	12.5935i	0.0888203	−	0.635258i
$394$	−35.5446	−	16.0804i	−1.79071	−	0.810120i
$395$	−11.5969			−0.583503
$396$	−16.6169	+	7.88925i	−0.835028	+	0.396450i
$397$			21.6449i			1.08633i	0.839626	+	0.543164i	$0.182774\pi$
$397$			21.6449i			1.08633i	−0.839626	+	0.543164i	$0.817226\pi$
$398$	2.92250	+	1.32214i	0.146491	+	0.0662729i
$399$	−12.4803	−	22.6452i	−0.624796	−	1.13368i
$400$	9.42252	−	3.92834i	0.471126	−	0.196417i
$401$	−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	$0.246736\pi$
$402$	−3.32797	−	2.10397i	−0.165984	−	0.104937i
$403$	−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
$408$	−2.29599	+	1.86021i	−0.113668	+	0.0920943i
$409$	13.7025	+	7.91112i	0.677543	+	0.391180i	0.798929	−	0.601426i	$-0.205400\pi$
$409$	13.7025	+	7.91112i	0.677543	+	0.391180i	−0.121386	+	0.992605i	$0.538734\pi$
$410$	−0.526016	−	5.30944i	−0.0259781	−	0.262214i
$411$	−4.06905	−	3.17445i	−0.200711	−	0.156584i
$412$	−29.9496	+	5.99316i	−1.47551	+	0.295262i
$413$	10.0073	+	4.28508i	0.492427	+	0.210855i
$414$	37.6763	+	6.82030i	1.85169	+	0.335200i
$415$			2.50679i			0.123054i
$416$	24.0363	−	12.9366i	1.17848	−	0.634270i
$417$	−0.0749888	+	0.536333i	−0.00367222	+	0.0262643i
$418$	24.3441	−	2.41181i	1.19071	−	0.117966i
$419$	−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	$0.912690\pi$
$420$	10.9563	−	9.25092i	0.534611	−	0.451399i
$421$	−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
$426$	1.03531	−	25.7609i	0.0501608	−	1.24812i
$427$	20.7161	+	27.6721i	1.00252	+	1.33915i
$428$	−10.4770	+	9.20941i	−0.506425	+	0.445154i
$429$	−23.7505	+	9.61541i	−1.14668	+	0.464236i
$430$	1.10129	+	0.498224i	0.0531088	+	0.0240265i
$431$		−	6.40732i		−	0.308630i	−0.988022	−	0.154315i	$-0.950683\pi$
$431$		−	6.40732i		−	0.308630i	0.988022	−	0.154315i	$-0.0493170\pi$
$432$	17.7697	+	10.7814i	0.854945	+	0.518718i
$433$		−	37.1536i		−	1.78549i	−0.450563	−	0.892745i	$-0.648777\pi$
$433$		−	37.1536i		−	1.78549i	0.450563	−	0.892745i	$-0.351223\pi$
$434$	−4.34802	−	4.74878i	−0.208712	−	0.227949i
$435$	6.88970	+	17.0178i	0.330336	+	0.815943i
$436$	−12.1355	−	13.8058i	−0.581185	−	0.661179i
$437$	−44.0986	−	25.4604i	−2.10952	−	1.21793i
$438$	0.184934	−	4.60160i	0.00883648	−	0.219873i
$439$	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
$441$	−11.2151	+	17.7545i	−0.534051	+	0.845452i
$442$	−3.34446	+	2.39952i	−0.159080	+	0.114134i
$443$	4.69335	−	2.70971i	0.222988	−	0.128742i	−0.384345	−	0.923189i	$-0.625573\pi$
$443$	4.69335	−	2.70971i	0.222988	−	0.128742i	0.607333	+	0.794447i	$0.292239\pi$
$444$	−16.8984	−	8.47811i	−0.801961	−	0.402354i
$445$	10.9937	−	19.0417i	0.521153	−	0.902664i
$446$	2.16890	+	21.8922i	0.102701	+	1.03663i
$447$	2.91859	−	20.8742i	0.138044	−	0.987317i
$448$	13.8211	+	16.0305i	0.652987	+	0.757369i
$449$	−28.7353			−1.35610			−0.678051	−	0.735015i	$-0.737175\pi$
$449$	−28.7353			−1.35610			−0.678051	+	0.735015i	$0.737175\pi$
$450$	8.26286	+	6.99770i	0.389515	+	0.329875i
$451$	−7.39266			−0.348107
$452$	−10.4544	+	2.09201i	−0.491733	+	0.0983996i
$453$	13.3593	−	17.1242i	0.627675	−	0.804563i
$454$	−2.39652	−	24.1897i	−0.112474	−	1.13528i
$455$	15.9900	−	11.9706i	0.749623	−	0.561190i
$456$	−17.4010	−	21.4773i	−0.814876	−	1.00577i
$457$	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	−0.612740	−	0.790285i	$-0.709933\pi$
$461$	−5.03928	+	2.90943i	−0.234703	+	0.135506i	0.378037	+	0.925790i	$0.376599\pi$
$462$	−11.2588	−	16.3705i	−0.523806	−	0.761625i
$463$	−3.49676	−	2.01885i	−0.162508	−	0.0938240i	0.416540	−	0.909117i	$-0.363242\pi$
$463$	−3.49676	−	2.01885i	−0.162508	−	0.0938240i	−0.579048	+	0.815293i	$0.696576\pi$
$464$	−25.0133	+	10.4283i	−1.16121	+	0.484122i
$465$	−2.86834	+	3.67668i	−0.133016	+	0.170502i
$466$	16.2392	+	7.34664i	0.752266	+	0.340326i
$467$	13.6718			0.632656			0.316328	−	0.948650i	$-0.397550\pi$
$467$	13.6718			0.632656			0.316328	+	0.948650i	$0.397550\pi$
$468$	23.8309	+	16.4416i	1.10158	+	0.760012i
$469$	1.67400	−	3.90941i	0.0772979	−	0.180520i
$470$	3.35462	−	7.41514i	0.154737	−	0.342035i
$471$	−18.0713	−	2.52668i	−0.832681	−	0.116423i
$472$	11.3383	+	2.62311i	0.521887	+	0.120738i
$473$	0.837404	−	1.45043i	0.0385039	−	0.0666907i
$474$	16.0756	−	8.43936i	0.738376	−	0.387633i
$475$	−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	$0.799079\pi$
$480$	9.78574	−	11.7997i	0.446656	−	0.538580i
$481$	−22.8071	−	13.1677i	−1.03991	−	0.600394i
$482$	−29.9183	+	2.96406i	−1.36274	+	0.135009i
$483$	−0.822651	+	41.3482i	−0.0374319	+	1.88141i
$484$	−3.13997	+	0.628333i	−0.142726	+	0.0285606i
$485$	26.7692			1.21552
$486$	−1.59111	+	21.9879i	−0.0721740	+	0.997392i
$487$		−	0.965533i		−	0.0437525i	−0.999761	−	0.0218762i	$-0.993036\pi$
$487$		−	0.965533i		−	0.0437525i	0.999761	−	0.0218762i	$-0.00696398\pi$
$488$	27.0150	+	25.2150i	1.22291	+	1.14143i
$489$	−9.12577	−	22.5410i	−0.412682	−	1.01934i
$490$	11.7417	+	10.1005i	0.530438	+	0.456295i
$491$	−26.2795	−	15.1725i	−1.18598	−	0.684724i	−0.228587	−	0.973523i	$-0.573411\pi$
$491$	−26.2795	−	15.1725i	−1.18598	−	0.684724i	−0.957390	+	0.288799i	$0.906744\pi$
$492$	4.59298	+	6.97714i	0.207068	+	0.314554i
$493$	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
$497$	27.6504	−	3.30670i	1.24029	−	0.148326i
$498$	−1.82426	−	3.47491i	−0.0817470	−	0.155715i
$499$	9.79493	+	5.65511i	0.438481	+	0.253157i	0.702953	−	0.711236i	$-0.251864\pi$
$499$	9.79493	+	5.65511i	0.438481	+	0.253157i	−0.264472	+	0.964393i	$0.585198\pi$
$500$	17.7492	−	15.6018i	0.793770	−	0.697734i
$501$	−0.313568	+	2.24270i	−0.0140092	+	0.100196i
$502$	−27.8941	−	12.6193i	−1.24497	−	0.563228i
$503$	−41.8216			−1.86473			−0.932367	−	0.361513i	$-0.882260\pi$
$503$	−41.8216			−1.86473			−0.932367	+	0.361513i	$0.882260\pi$
$504$	−8.45541	+	20.7968i	−0.376634	+	0.926362i
$505$	−12.1260			−0.539601
$506$	−35.6495	−	16.1279i	−1.58481	−	0.716971i
$507$	14.0446	+	10.9568i	0.623742	+	0.486609i
$508$	−2.94692	+	2.59038i	−0.130748	+	0.114930i
$509$	−2.37262	−	1.36983i	−0.105164	−	0.0607167i	0.446495	−	0.894786i	$-0.352672\pi$
$509$	−2.37262	−	1.36983i	−0.105164	−	0.0607167i	−0.551660	+	0.834069i	$0.686005\pi$
$510$	−1.23527	+	1.95390i	−0.0546988	+	0.0865201i
$511$	4.93912	−	0.590666i	0.218494	−	0.0261295i
$512$	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
$516$	−1.88917	+	0.110799i	−0.0831662	+	0.00487765i
$517$	−9.76595	−	5.63837i	−0.429506	−	0.247975i
$518$	6.14827	−	19.4732i	0.270139	−	0.855602i
$519$	13.9058	−	17.8246i	0.610395	−	0.782413i
$520$	14.5702	−	15.6103i	0.638945	−	0.684557i
$521$		−	5.74317i		−	0.251613i	−0.992055	−	0.125806i	$-0.959848\pi$
$521$		−	5.74317i		−	0.251613i	0.992055	−	0.125806i	$-0.0401518\pi$
$522$	−21.9348	−	18.5763i	−0.960062	−	0.813062i
$523$	−17.8387			−0.780032			−0.390016	−	0.920808i	$-0.627530\pi$
$523$	−17.8387			−0.780032			−0.390016	+	0.920808i	$0.627530\pi$
$524$	14.3977	−	2.88110i	0.628968	−	0.125861i
$525$	−6.04803	+	10.0102i	−0.263958	+	0.436882i
$526$	−6.73086	+	0.666839i	−0.293479	+	0.0290756i
$527$	0.898900	+	0.518980i	0.0391567	+	0.0226071i
$528$	−14.9330	−	15.1047i	−0.649874	−	0.657349i
$529$	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
$534$	−1.38234	+	34.3961i	−0.0598199	+	1.48846i
$535$	−5.45610	+	9.45024i	−0.235888	+	0.408569i
$536$	1.02473	−	4.42938i	0.0442618	−	0.191320i
$537$	−9.46784	−	23.3860i	−0.408567	−	1.00918i
$538$	−4.23621	+	9.36383i	−0.182636	+	0.403703i
$539$	15.5308	−	14.8101i	0.668961	−	0.637915i
$540$	15.8701	+	3.53641i	0.682942	+	0.152183i
$541$	−20.7375			−0.891575			−0.445788	−	0.895139i	$-0.647076\pi$
$541$	−20.7375			−0.891575			−0.445788	+	0.895139i	$0.647076\pi$
$542$	−29.1531	−	13.1889i	−1.25223	−	0.566512i
$543$	8.03502	+	19.8468i	0.344816	+	0.851709i
$544$	−2.90275	−	1.79350i	−0.124454	−	0.0768956i
$545$	−12.4528	−	7.18965i	−0.533421	−	0.307971i
$546$	−13.4540	+	28.2300i	−0.575779	+	1.20813i
$547$	30.0061	−	17.3240i	1.28297	−	0.740722i	0.305578	−	0.952167i	$-0.401150\pi$
$547$	30.0061	−	17.3240i	1.28297	−	0.740722i	0.977390	+	0.211445i	$0.0678171\pi$
$548$	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
$552$	6.92728	+	43.6658i	0.294845	+	1.85854i
$553$	11.7528	+	15.6991i	0.499779	+	0.667593i
$554$	1.20752	+	12.1883i	0.0513026	+	0.517832i
$555$	−14.6472	−	2.04794i	−0.621740	−	0.0869302i
$556$	−0.613172	+	0.122701i	−0.0260043	+	0.00520366i
$557$	6.03515			0.255717			0.127859	−	0.991792i	$-0.459190\pi$
$557$	6.03515			0.255717			0.127859	+	0.991792i	$0.459190\pi$
$558$	1.30047	−	7.18398i	0.0550534	−	0.304122i
$559$	−2.63608			−0.111494
$560$	14.2595	+	8.41581i	0.602573	+	0.355633i
$561$	2.52535	+	1.97014i	0.106620	+	0.0831792i
$562$	3.43667	+	34.6886i	0.144967	+	1.46325i
$563$	−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	$0.974440\pi$
$564$	0.746026	+	12.7201i	0.0314134	+	0.535613i
$565$	−7.22299	+	4.17019i	−0.303873	+	0.175441i
$566$	−26.2084	+	18.8035i	−1.10162	+	0.790369i
$567$	−23.7218	+	2.06793i	−0.996222	+	0.0868450i
$568$	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	$-0.463214\pi$
$570$	−18.2774	−	11.5551i	−0.765554	−	0.483990i
$571$	−6.91177	−	3.99051i	−0.289248	−	0.166998i	0.348354	−	0.937363i	$-0.386741\pi$
$571$	−6.91177	−	3.99051i	−0.289248	−	0.166998i	−0.637603	+	0.770365i	$0.720074\pi$
$572$	−19.5336	−	22.2222i	−0.816741	−	0.929157i
$573$	8.26818	−	10.5983i	0.345408	−	0.442749i
$574$	−6.65447	+	6.09289i	−0.277752	+	0.254312i
$575$			23.0324i			0.960519i
$576$	−4.97803	+	23.4781i	−0.207418	+	0.978252i
$577$			9.07042i			0.377607i	0.982015	+	0.188803i	$0.0604609\pi$
$577$			9.07042i			0.377607i	−0.982015	+	0.188803i	$0.939539\pi$
$578$	−21.4356	−	9.69748i	−0.891602	−	0.403362i
$579$	−0.607975	+	4.34834i	−0.0252666	+	0.180711i
$580$	−15.9228	+	13.9963i	−0.661158	+	0.581167i
$581$	3.39352	−	2.54049i	0.140787	−	0.105397i
$582$	−37.1074	+	19.4806i	−1.53815	+	0.807498i
$583$	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	$0.966824\pi$
$588$	−23.6268	−	5.45656i	−0.974353	−	0.225025i
$589$	−4.85469	+	8.40857i	−0.200034	+	0.346469i
$590$	9.05963	−	0.897555i	0.372979	−	0.0369518i
$591$	44.2888	−	17.9304i	1.82180	−	0.737558i
$592$	2.79969	−	21.6504i	0.115067	−	0.889825i
$593$			36.7145i			1.50768i	0.657056	+	0.753842i	$0.271802\pi$
$593$			36.7145i			1.50768i	−0.657056	+	0.753842i	$0.728198\pi$
$594$	7.04401	−	21.3991i	0.289019	−	0.878016i
$595$	−2.29527	−	0.982827i	−0.0940970	−	0.0402920i
$596$	23.8648	−	4.77554i	0.977541	−	0.195614i
$597$	−3.64145	+	1.47425i	−0.149035	+	0.0603369i
$598$	6.07169	+	61.2857i	0.248290	+	2.50616i
$599$	12.5041	+	7.21925i	0.510904	+	0.294971i	0.733205	−	0.680008i	$-0.238024\pi$
$599$	12.5041	+	7.21925i	0.510904	+	0.294971i	−0.222301	+	0.974978i	$0.571357\pi$
$600$	−4.47771	+	11.6736i	−0.182802	+	0.476574i
$601$	−21.1289	+	12.1988i	−0.861867	+	0.497599i	−0.864637	−	0.502397i	$-0.832452\pi$
$601$	−21.1289	+	12.1988i	−0.861867	+	0.497599i	0.00276977	+	0.999996i	$0.499118\pi$
$602$	−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
$606$	16.8091	−	8.82443i	0.682822	−	0.358468i
$607$	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	$-0.0433402\pi$
$608$	16.7769	−	27.1532i	0.680393	−	1.10121i
$609$	16.0553	−	26.5734i	0.650593	−	1.07681i
$610$	26.3385	+	11.9156i	1.06642	+	0.482448i
$611$			17.7491i			0.718054i
$612$	0.290427	−	3.60743i	0.0117398	−	0.145822i
$613$	−36.9378			−1.49190			−0.745952	−	0.665999i	$-0.768005\pi$
$613$	−36.9378			−1.49190			−0.745952	+	0.665999i	$0.768005\pi$
$614$	−20.5854	−	9.31285i	−0.830758	−	0.375836i
$615$	5.15214	+	4.01941i	0.207754	+	0.162078i
$616$	13.5518	−	18.5118i	0.546019	−	0.745860i
$617$	−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	$0.224927\pi$
$618$	19.9898	−	31.6189i	0.804106	−	1.27190i
$619$	−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
$623$	−36.9189	+	4.41511i	−1.47913	+	0.176888i
$624$	−8.83714	+	32.2421i	−0.353769	+	1.29072i
$625$	2.86288	−	4.95865i	0.114515	−	0.198346i
$626$	19.9786	−	1.97932i	0.798507	−	0.0791096i
$627$	−18.4292	+	23.6229i	−0.735993	+	0.943407i
$628$	−4.13429	−	20.6603i	−0.164976	−	0.824436i
$629$			3.29198i			0.131260i
$630$	−1.05416	+	17.5305i	−0.0419986	+	0.698431i
$631$		−	34.9573i		−	1.39163i	−0.718223	−	0.695813i	$-0.755044\pi$
$631$		−	34.9573i		−	1.39163i	0.718223	−	0.695813i	$-0.244956\pi$
$632$	15.3263	+	14.3051i	0.609646	+	0.569025i
$633$	−6.45205	−	0.902111i	−0.256446	−	0.0358557i
$634$	−0.0702796	−	0.709380i	−0.00279116	−	0.0281731i
$635$	−1.53467	+	2.65812i	−0.0609014	+	0.105484i
$636$	−1.33173	−	0.668143i	−0.0528063	−	0.0264936i
$637$	−32.4099	−	9.51470i	−1.28413	−	0.376986i
$638$	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	$0.624889\pi$
$642$	0.686045	−	17.0705i	0.0270760	−	0.673717i
$643$	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	$0.103399\pi$
$644$	−45.3820	+	14.8642i	−1.78830	+	0.585732i
$645$	−1.37221	+	0.555542i	−0.0540307	+	0.0218744i
$646$	−1.98389	+	4.38523i	−0.0780549	+	0.172535i
$647$	10.3033			0.405063			0.202532	−	0.979276i	$-0.435083\pi$
$647$	10.3033			0.405063			0.202532	+	0.979276i	$0.435083\pi$
$648$	−24.5727	+	6.64696i	−0.965307	+	0.261117i
$649$		−	12.6143i		−	0.495154i
$650$	−7.17867	+	15.8679i	−0.281571	+	0.622391i
$651$	7.88414	+	0.156860i	0.309004	+	0.00614784i
$652$	21.0906	−	18.5389i	0.825971	−	0.726039i
$653$	−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	$0.971966\pi$
$654$	22.4942	+	0.904020i	0.879593	+	0.0353500i
$655$	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	$-0.277341\pi$
$659$	41.8028	−	24.1349i	1.62841	−	0.940162i	0.984568	−	0.175001i	$-0.0559928\pi$
$660$	−14.8514	−	7.45115i	−0.578091	−	0.290035i
$661$	40.1854	+	23.2010i	1.56303	+	0.902416i	0.996948	+	0.0780662i	$0.0248746\pi$
$661$	40.1854	+	23.2010i	1.56303	+	0.902416i	0.566081	+	0.824349i	$0.308459\pi$
$662$	35.1865	−	3.48599i	1.36756	−	0.135487i
$663$	0.698072	−	4.99273i	0.0271109	−	0.193902i
$664$	3.09220	−	3.31294i	0.120001	−	0.128567i
$665$	9.19365	−	21.4707i	0.356515	−	0.832596i
$666$	21.7943	−	7.82033i	0.844512	−	0.303032i
$667$		−	61.1426i		−	2.36745i
$668$	−2.56400	+	0.513077i	−0.0992041	+	0.0198515i
$669$	−21.2436	−	16.5731i	−0.821326	−	0.640753i
$670$	−0.350636	−	3.53920i	−0.0135462	−	0.136731i
$671$	20.0275	−	34.6886i	0.773152	−	1.33914i
$672$	−25.8909	−	1.28897i	−0.998763	−	0.0497230i
$673$	−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	0.0488191	−	0.998808i	$-0.484454\pi$
$677$	24.4118	−	14.0942i	0.938221	−	0.541682i	0.889402	+	0.457125i	$0.151121\pi$
$678$	6.97774	−	11.0371i	0.267978	−	0.423877i
$679$	−27.1290	−	36.2383i	−1.04112	−	1.39070i
$680$	−2.60055	−	0.601636i	−0.0997265	−	0.0230717i
$681$	23.4730	+	18.3123i	0.899489	+	0.701731i
$682$	−3.07521	+	6.79752i	−0.117756	+	0.260290i
$683$			1.45337i			0.0556116i	0.999613	+	0.0278058i	$0.00885200\pi$
$683$			1.45337i			0.0556116i	−0.999613	+	0.0278058i	$0.991148\pi$
$684$	33.7450	+	2.71674i	1.29027	+	0.103877i
$685$		−	4.66178i		−	0.178118i
$686$	1.77383	−	26.1315i	0.0677252	−	0.997704i
$687$	−29.5001	−	4.12464i	−1.12550	−	0.157365i
$688$	−0.840871	−	2.01691i	−0.0320579	−	0.0768941i
$689$	−1.79738	−	1.03772i	−0.0684746	−	0.0395338i
$690$	16.0763	+	30.6227i	0.612014	+	1.16579i
$691$	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
$693$	24.0275	+	3.84822i	0.912730	+	0.146182i
$694$	6.26038	+	8.72575i	0.237641	+	0.331225i
$695$	−0.423644	+	0.244591i	−0.0160697	+	0.00927786i
$696$	11.8867	−	30.9892i	0.450563	−	1.17464i
$697$	0.727248	−	1.25963i	0.0275465	−	0.0477119i
$698$	−25.2680	+	2.50335i	−0.956408	+	0.0947532i
$699$	−20.2342	+	8.19183i	−0.765326	+	0.309843i
$700$	−13.2162	−	2.77655i	−0.499526	−	0.104944i
$701$	11.1081			0.419546			0.209773	−	0.977750i	$-0.432727\pi$
$701$	11.1081			0.419546			0.209773	+	0.977750i	$0.432727\pi$
$702$	−34.7124	+	7.23906i	−1.31013	+	0.273221i
$703$	−30.7941			−1.16142
$704$	10.7717	−	22.0341i	0.405973	−	0.830440i
$705$	3.74055	+	9.23931i	0.140877	+	0.347973i
$706$	−24.3654	+	2.41393i	−0.917005	+	0.0908494i
$707$	12.2890	+	16.4154i	0.462177	+	0.617364i
$708$	−11.9053	+	7.83713i	−0.447428	+	0.294537i
$709$	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
$714$	3.89693	−	0.307938i	0.145839	−	0.0115243i
$715$	−20.0444	−	11.5726i	−0.749618	−	0.432792i
$716$	21.8811	−	19.2338i	0.817737	−	0.718801i
$717$	−4.73117	−	0.661502i	−0.176689	−	0.0247042i
$718$	0.670237	−	1.48151i	0.0250130	−	0.0552894i
$719$	18.7468			0.699137			0.349569	−	0.936911i	$-0.386328\pi$
$719$	18.7468			0.699137			0.349569	+	0.936911i	$0.386328\pi$
$720$	2.19470	+	18.6460i	0.0817917	+	0.694895i
$721$	37.1432	+	15.9046i	1.38328	+	0.592317i
$722$	−16.5394	−	7.48246i	−0.615534	−	0.278468i
$723$	22.6491	−	29.0319i	0.842328	−	1.07971i
$724$	−18.5698	+	16.3230i	−0.690140	+	0.606641i
$725$	8.64544	−	14.9743i	0.321084	−	0.556133i
$726$	2.09576	−	3.31498i	0.0777810	−	0.123031i
$727$	−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
$732$	−45.1817	+	2.64988i	−1.66996	+	0.0979424i
$733$	10.6133	+	6.12762i	0.392013	+	0.226329i	0.683032	−	0.730389i	$-0.260661\pi$
$733$	10.6133	+	6.12762i	0.392013	+	0.226329i	−0.291019	+	0.956717i	$0.593994\pi$
$734$	3.01878	+	30.4706i	0.111425	+	1.12469i
$735$	−18.8762	+	1.87736i	−0.696257	+	0.0692476i
$736$	−44.9540	+	24.1948i	−1.65703	+	0.891833i
$737$	−4.92785			−0.181520
$738$	−10.0669	−	1.82235i	−0.370569	−	0.0670818i
$739$			11.3906i			0.419011i	0.977807	+	0.209506i	$0.0671855\pi$
$739$			11.3906i			0.419011i	−0.977807	+	0.209506i	$0.932815\pi$
$740$	−3.35095	−	16.7457i	−0.123183	−	0.615584i
$741$	46.7035	+	6.52997i	1.71570	+	0.239885i
$742$	0.484532	−	1.53464i	0.0177877	−	0.0563384i
$743$	−28.6884	−	16.5632i	−1.05247	−	0.607646i	−0.129133	−	0.991627i	$-0.541219\pi$
$743$	−28.6884	−	16.5632i	−1.05247	−	0.607646i	−0.923341	+	0.383981i	$0.874553\pi$
$744$	8.32605	−	1.32087i	0.305248	−	0.0484254i
$745$	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
$749$	18.3225	−	2.19118i	0.669491	−	0.0800639i
$750$	−1.16224	+	28.9193i	−0.0424390	+	1.05598i
$751$	−9.23549	−	5.33211i	−0.337008	−	0.194572i	0.321940	−	0.946760i	$-0.395665\pi$
$751$	−9.23549	−	5.33211i	−0.337008	−	0.194572i	−0.658948	+	0.752188i	$0.728998\pi$
$752$	−13.5802	+	5.66172i	−0.495219	+	0.206462i
$753$	34.7562	−	14.0711i	1.26659	−	0.512779i
$754$	19.0567	−	42.1234i	0.694004	−	1.53405i
$755$	19.6186			0.713994
$756$	−11.2961	−	25.0679i	−0.410836	−	0.911709i
$757$	−25.8612			−0.939941			−0.469970	−	0.882682i	$-0.655735\pi$
$757$	−25.8612			−0.939941			−0.469970	+	0.882682i	$0.655735\pi$
$758$	18.8496	−	41.6657i	0.684648	−	1.51337i
$759$	44.4195	−	17.9833i	1.61233	−	0.652752i
$760$	5.62788	−	24.3263i	0.204145	−	0.882408i
$761$	41.2900	+	23.8388i	1.49676	+	0.864157i	0.999993	−	0.00372570i	$-0.00118593\pi$
$761$	41.2900	+	23.8388i	1.49676	+	0.864157i	0.496770	+	0.867882i	$0.334519\pi$
$762$	0.192967	−	4.80150i	0.00699047	−	0.173940i
$763$	2.88737	+	24.1441i	0.104530	+	0.874075i
$764$	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
$768$	−27.4879	+	3.52331i	−0.991885	+	0.127136i
$769$	26.7936	+	15.4693i	0.966203	+	0.557838i	0.898077	−	0.439839i	$-0.144964\pi$
$769$	26.7936	+	15.4693i	0.966203	+	0.557838i	0.0681267	+	0.997677i	$0.478298\pi$
$770$	5.40352	−	17.1143i	0.194729	−	0.616758i
$771$	3.14403	+	0.439591i	0.113230	+	0.0158315i
$772$	−4.97132	+	0.994800i	−0.178922	+	0.0358036i
$773$		−	18.7467i		−	0.674273i	−0.941456	−	0.337136i	$-0.890542\pi$
$773$		−	18.7467i		−	0.674273i	0.941456	−	0.337136i	$-0.109458\pi$
$774$	1.49787	−	1.76869i	0.0538400	−	0.0635741i
$775$	4.39175			0.157756
$776$	−35.3777	−	33.0205i	−1.26999	−	1.18537i
$777$	12.0718	+	21.9039i	0.433072	+	0.785798i
$778$	0.488967	+	4.93548i	0.0175303	+	0.176945i
$779$	11.7830	+	6.80289i	0.422168	+	0.243739i
$780$	1.53120	+	26.1077i	0.0548258	+	0.934806i
$781$	−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
$786$	−9.60971	+	15.2002i	−0.342767	+	0.542174i
$787$	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	$0.136857\pi$
$788$	36.4254	+	41.4390i	1.29760	+	1.47620i
$789$	5.09547	−	6.53145i	0.181404	−	0.232526i
$790$	14.9425	+	6.76000i	0.531630	+	0.240510i
$791$	12.9654	+	5.55174i	0.460997	+	0.197397i
$792$	26.0094	−	0.479015i	0.924205	−	0.0170210i
$793$	−63.0449			−2.23879
$794$	12.6172	−	27.8893i	0.447766	−	0.989755i
$795$	−1.15432	−	0.161394i	−0.0409394	−	0.00572406i
$796$	−2.99491	−	3.40713i	−0.106152	−	0.120763i
$797$	7.80761	+	4.50773i	0.276560	+	0.159672i	0.631865	−	0.775078i	$-0.282290\pi$
$797$	7.80761	+	4.50773i	0.276560	+	0.159672i	−0.355305	+	0.934750i	$0.615623\pi$
$798$	2.88054	+	36.4531i	0.101970	+	1.29042i
$799$	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
$804$	3.06162	+	4.65087i	0.107975	+	0.164024i
$805$	−29.9055	+	22.3881i	−1.05403	+	0.789076i
$806$	11.6857	−	1.15773i	0.411613	−	0.0407793i
$807$	−4.72356	−	11.6674i	−0.166277	−	0.410712i
$808$	16.0256	+	14.9578i	0.563778	+	0.526213i
$809$	54.2083			1.90586			0.952932	−	0.303184i	$-0.0980498\pi$
$809$	54.2083			1.90586			0.952932	+	0.303184i	$0.0980498\pi$
$810$	−16.5439	+	11.0838i	−0.581294	+	0.389444i
$811$	−30.9693			−1.08748			−0.543740	−	0.839254i	$-0.682992\pi$
$811$	−30.9693			−1.08748			−0.543740	+	0.839254i	$0.682992\pi$
$812$	35.0841	+	7.37072i	1.23121	+	0.258662i
$813$	36.3250	−	14.7062i	1.27397	−	0.515770i
$814$	−23.5472	+	2.33286i	−0.825328	+	0.0817669i
$815$	10.9833	−	19.0237i	0.384729	−	0.666370i
$816$	4.04271	−	1.05850i	0.141523	−	0.0370550i
$817$	−2.66943	+	1.54120i	−0.0933915	+	0.0539196i
$818$	−13.0440	−	18.1808i	−0.456072	−	0.635676i
$819$	−13.6637	−	35.7801i	−0.477448	−	1.25026i
$820$	−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	$0.588659\pi$
$822$	3.39250	+	6.46216i	0.118327	+	0.225394i
$823$	27.7720	+	16.0342i	0.968073	+	0.558917i	0.898648	−	0.438670i	$-0.144550\pi$
$823$	27.7720	+	16.0342i	0.968073	+	0.558917i	0.0694246	+	0.997587i	$0.477884\pi$
$824$	42.0833	+	9.73596i	1.46604	+	0.339168i
$825$	13.4215	+	1.87656i	0.467277	+	0.0653336i
$826$	−10.3965	−	11.3547i	−0.361739	−	0.395080i
$827$			30.1201i			1.04738i	0.851909	+	0.523689i	$0.175445\pi$
$827$			30.1201i			1.04738i	−0.851909	+	0.523689i	$0.824555\pi$
$828$	−44.5699	−	30.7500i	−1.54891	−	1.06864i
$829$		−	8.36044i		−	0.290370i	−0.989405	−	0.145185i	$-0.953622\pi$
$829$		−	8.36044i		−	0.290370i	0.989405	−	0.145185i	$-0.0463777\pi$
$830$	1.46125	−	3.22998i	0.0507206	−	0.112114i
$831$	−11.8272	−	9.22695i	−0.410282	−	0.320079i
$832$	−38.5115	+	2.65762i	−1.33515	+	0.0921363i
$833$	0.995642	+	4.10322i	0.0344969	+	0.142168i
$834$	0.409259	−	0.647349i	0.0141715	−	0.0224158i
$835$	−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	$0.704705\pi$
$840$	−19.5095	+	5.53316i	−0.673143	+	0.190912i
$841$	−8.45044	+	14.6366i	−0.291394	+	0.504710i
$842$	3.75558	+	37.9076i	0.129426	+	1.30638i
$843$	−33.6609	−	26.2604i	−1.15934	−	0.904456i
$844$	−1.47608	−	7.37642i	−0.0508088	−	0.253907i
$845$			16.0904i			0.553528i
$846$	−11.9088	−	10.0854i	−0.409434	−	0.346744i
$847$	3.89416	+	1.66746i	0.133805	+	0.0572947i
$848$	0.220638	−	1.70622i	0.00757674	−	0.0585919i
$849$	5.47034	−	39.1248i	0.187741	−	1.34276i
$850$	2.16646	−	0.214635i	0.0743090	−	0.00736193i
$851$	42.6551	+	24.6269i	1.46220	+	0.844200i
$852$	−16.3504	+	32.5893i	−0.560156	+	1.11649i
$853$	−43.8698	+	25.3282i	−1.50207	+	0.867222i	−0.502075	+	0.864824i	$0.667430\pi$
$853$	−43.8698	+	25.3282i	−1.50207	+	0.867222i	−0.999997	+	0.00239737i	$0.999237\pi$
$854$	−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	−0.999199	−	0.0400164i	$-0.987259\pi$
$857$	−42.8622	+	24.7465i	−1.46414	+	0.845324i	−0.464944	+	0.885340i	$0.653926\pi$
$858$	36.2072	+	1.45513i	1.23609	+	0.0496774i
$859$	−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	$0.176593\pi$
$860$	−1.12858	−	1.28391i	−0.0384841	−	0.0437811i
$861$	0.219809	−	11.0481i	0.00749106	−	0.376517i
$862$	−3.73493	+	8.25578i	−0.127212	+	0.281193i
$863$		−	43.2686i		−	1.47288i	−0.676502	−	0.736441i	$-0.736505\pi$
$863$		−	43.2686i		−	1.47288i	0.676502	−	0.736441i	$-0.263495\pi$
$864$	−16.6115	−	24.2499i	−0.565134	−	0.824999i
$865$	20.4211			0.694338
$866$	−21.6574	+	47.8721i	−0.735949	+	1.62676i
$867$	26.7089	−	10.8131i	0.907080	−	0.367233i
$868$	2.83426	+	8.65329i	0.0962009	+	0.293712i
$869$	11.3621	−	19.6797i	0.385432	−	0.667588i
$870$	1.04264	−	25.9435i	0.0353489	−	0.879566i
$871$	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
$875$	−31.0405	+	3.71211i	−1.04936	+	0.125492i
$876$	−2.92063	+	5.82133i	−0.0986790	+	0.196684i
$877$	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	$-0.103839\pi$
$878$	−5.23483	−	52.8387i	−0.176667	−	1.78322i
$879$	17.6918	+	2.47363i	0.596731	+	0.0834334i
$880$	2.46056	−	19.0278i	0.0829455	−	0.641428i
$881$		−	28.6591i		−	0.965549i	−0.875745	−	0.482775i	$-0.839629\pi$
$881$		−	28.6591i		−	0.965549i	0.875745	−	0.482775i	$-0.160371\pi$
$882$	24.7999	−	16.3391i	0.835056	−	0.550165i
$883$			8.34232i			0.280741i	0.990099	+	0.140371i	$0.0448294\pi$
$883$			8.34232i			0.280741i	−0.990099	+	0.140371i	$0.955171\pi$
$884$	5.70803	−	1.14222i	0.191982	−	0.0384171i
$885$	−6.85843	+	8.79124i	−0.230544	+	0.295514i
$886$	−7.62687	+	0.755609i	−0.256230	+	0.0253852i
$887$	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	$-0.0665453\pi$
$888$	16.8314	+	20.7743i	0.564824	+	0.697139i
$889$	5.15368	−	0.616324i	0.172849	−	0.0206709i
$890$	−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
$894$	−15.9285	+	25.1950i	−0.532728	+	0.842646i
$895$	11.3950	−	19.7368i	0.380894	−	0.659727i
$896$	−8.46400	−	28.7117i	−0.282762	−	0.959190i
$897$	−59.4701	−	46.3952i	−1.98565	−	1.54909i
$898$	37.0252	+	16.7502i	1.23555	+	0.558962i
$899$	−11.6585			−0.388831
$900$	−6.56756	−	13.8330i	−0.218919	−	0.461101i
$901$			0.259434i			0.00864300i
$902$	9.52538	+	4.30929i	0.317160	+	0.143484i
$903$	2.14271	+	1.29460i	0.0713050	+	0.0430815i
$904$	14.6898	+	3.39849i	0.488577	+	0.113032i
$905$	−9.67056	+	16.7499i	−0.321460	+	0.556785i
$906$	−27.1953	+	14.2770i	−0.903503	+	0.474321i
$907$	13.2688	−	7.66077i	0.440585	−	0.254372i	−0.263261	−	0.964725i	$-0.584798\pi$
$907$	13.2688	−	7.66077i	0.440585	−	0.254372i	0.703846	+	0.710353i	$0.251465\pi$
$908$	−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	−0.347676	−	0.937615i	$-0.613029\pi$
$911$	8.76762	−	5.06199i	0.290484	−	0.167711i	0.638160	+	0.769904i	$0.279696\pi$
$912$	9.90155	+	37.8167i	0.327873	+	1.25224i
$913$	−4.25398	−	2.45603i	−0.140786	−	0.0812829i
$914$	−2.30789	−	23.2951i	−0.0763383	−	0.770534i
$915$	−32.8180	+	13.2864i	−1.08493	+	0.439235i
$916$	−6.74895	−	33.7265i	−0.222991	−	1.11436i
$917$	−17.8559	−	7.64583i	−0.589654	−	0.252488i
$918$	2.95323	+	3.30535i	0.0974711	+	0.109093i
$919$			0.699191i			0.0230642i	0.999934	+	0.0115321i	$0.00367086\pi$
$919$			0.699191i			0.0230642i	−0.999934	+	0.0115321i	$0.996329\pi$
$920$	−27.2500	+	29.1953i	−0.898406	+	0.962540i
$921$	25.6495	−	10.3842i	0.845180	−	0.342173i
$922$	8.18902	−	0.811301i	0.269691	−	0.0267188i
$923$	−25.3944	+	43.9844i	−0.835868	+	1.44777i
$924$	4.96422	+	27.6562i	0.163311	+	0.909821i
$925$	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	−0.963614	−	0.267299i	$-0.913869\pi$
$929$	−37.0000	+	21.3620i	−1.21393	+	0.700864i	−0.250319	+	0.968164i	$0.580535\pi$
$930$	5.83903	−	3.06537i	0.191469	−	0.100518i
$931$	−38.3827	+	9.31353i	−1.25794	+	0.305239i
$932$	−16.6416	−	18.9322i	−0.545114	−	0.620143i
$933$	−5.73875	+	41.0446i	−0.187878	+	1.34374i
$934$	−17.6160	−	7.96951i	−0.576413	−	0.260770i
$935$			2.89321i			0.0946182i
$936$	−21.1218	−	35.0762i	−0.690389	−	1.14650i
$937$			22.0770i			0.721224i	0.932716	+	0.360612i	$0.117432\pi$
$937$			22.0770i			0.721224i	−0.932716	+	0.360612i	$0.882568\pi$
$938$	−4.43579	+	4.06145i	−0.144834	+	0.132611i
$939$	−15.1245	+	19.3868i	−0.493568	+	0.632663i
$940$	−8.64479	+	7.59888i	−0.281962	+	0.247848i
$941$	29.8416	+	17.2290i	0.972807	+	0.561650i	0.900091	−	0.435702i	$-0.143500\pi$
$941$	29.8416	+	17.2290i	0.972807	+	0.561650i	0.0727161	+	0.997353i	$0.476833\pi$
$942$	21.8119	+	13.7896i	0.710669	+	0.449291i
$943$	−10.8809	−	18.8463i	−0.354332	−	0.613720i
$944$	−13.0802	−	9.98911i	−0.425725	−	0.325118i
$945$	−14.6531	−	15.7458i	−0.476666	−	0.512210i
$946$	−1.92446	+	1.38073i	−0.0625697	+	0.0448913i
$947$	−34.9193	+	20.1606i	−1.13472	+	0.655133i	−0.945119	−	0.326728i	$-0.894054\pi$
$947$	−34.9193	+	20.1606i	−1.13472	+	0.655133i	−0.189605	+	0.981861i	$0.560721\pi$
$948$	−25.6327	+	1.50334i	−0.832511	+	0.0488263i
$949$	−4.53613	+	7.85682i	−0.147249	+	0.255043i
$950$	2.00776	+	20.2657i	0.0651404	+	0.657506i
$951$	0.688364	+	0.537023i	0.0223217	+	0.0174142i
$952$	1.82105	+	4.13017i	0.0590207	+	0.133860i
$953$	−40.6441			−1.31659			−0.658296	−	0.752759i	$-0.728722\pi$
$953$	−40.6441			−1.31659			−0.658296	+	0.752759i	$0.728722\pi$
$954$	1.71757	−	0.616304i	0.0556082	−	0.0199536i
$955$	12.1421			0.392909
$956$	−1.08238	−	5.40900i	−0.0350068	−	0.174939i
$957$	−35.6291	−	4.98158i	−1.15173	−	0.161032i
$958$	−0.655500	−	6.61641i	−0.0211782	−	0.213766i
$959$	−6.31080	+	4.72445i	−0.203786	+	0.152560i
$960$	−19.4871	+	9.49954i	−0.628942	+	0.306596i
$961$	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
$966$	25.1625	−	52.7973i	0.809590	−	1.69873i
$967$	−13.2891	−	7.67248i	−0.427349	−	0.246730i	0.270867	−	0.962617i	$-0.412689\pi$
$967$	−13.2891	−	7.67248i	−0.427349	−	0.246730i	−0.698217	+	0.715886i	$0.746023\pi$
$968$	4.41209	+	1.02074i	0.141810	+	0.0328077i
$969$	−2.21212	−	5.46403i	−0.0710636	−	0.175530i
$970$	−34.4918	−	15.6041i	−1.10747	−	0.501019i
$971$	−7.47337			−0.239832			−0.119916	−	0.992784i	$-0.538263\pi$
$971$	−7.47337			−0.239832			−0.119916	+	0.992784i	$0.538263\pi$
$972$	14.8672	−	27.4038i	0.476866	−	0.878976i
$973$	0.760449	+	0.325621i	0.0243789	+	0.0104389i
$974$	−0.562824	+	1.24408i	−0.0180340	+	0.0398629i
$975$	−8.00454	−	19.7715i	−0.256350	−	0.633196i
$976$	−20.1104	−	48.2368i	−0.643718	−	1.54402i
$977$	−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	$0.332537\pi$
$978$	−1.38103	+	34.3635i	−0.0441606	+	1.09882i
$979$	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	$0.843702\pi$
$984$	−1.85094	−	11.6673i	−0.0590057	−	0.371940i
$985$	37.3779	+	21.5801i	1.19096	+	0.687600i
$986$	−5.75115	+	0.569777i	−0.183154	+	0.0181454i
$987$	8.71672	−	14.4272i	0.277456	−	0.459223i
$988$	10.6847	+	53.3946i	0.339925	+	1.69871i
$989$	4.93015			0.156770
$990$	19.1543	−	6.87304i	0.608764	−	0.218439i
$991$			26.6788i			0.847480i	0.905784	+	0.423740i	$0.139283\pi$
$991$			26.6788i			0.847480i	−0.905784	+	0.423740i	$0.860717\pi$
$992$	4.61338	+	8.57168i	0.146475	+	0.272151i
$993$	−26.6373	+	34.1440i	−0.845308	+	1.08353i
$994$	−37.5549	−	11.8572i	−1.19117	−	0.376088i
$995$	−3.07323	−	1.77433i	−0.0974279	−	0.0562501i
$996$	0.324963	+	5.54078i	0.0102969	+	0.175566i
$997$	7.46362	−	4.30912i	0.236375	−	0.136471i	−0.377134	−	0.926159i	$-0.623091\pi$
$997$	7.46362	−	4.30912i	0.236375	−	0.136471i	0.613510	+	0.789687i	$0.289757\pi$
$998$	−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.139.8	yes	80
3.2	odd	2		756.2.bi.c.307.33		80
4.3	odd	2	inner	252.2.bi.c.139.21	yes	80
7.6	odd	2	inner	252.2.bi.c.139.7	✓	80
9.2	odd	6		756.2.bi.c.559.20		80
9.7	even	3	inner	252.2.bi.c.223.22	yes	80
12.11	even	2		756.2.bi.c.307.19		80
21.20	even	2		756.2.bi.c.307.34		80
28.27	even	2	inner	252.2.bi.c.139.22	yes	80
36.7	odd	6	inner	252.2.bi.c.223.7	yes	80
36.11	even	6		756.2.bi.c.559.34		80
63.20	even	6		756.2.bi.c.559.19		80
63.34	odd	6	inner	252.2.bi.c.223.21	yes	80
84.83	odd	2		756.2.bi.c.307.20		80
252.83	odd	6		756.2.bi.c.559.33		80
252.223	even	6	inner	252.2.bi.c.223.8	yes	80

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

\(f(q)\)	\(=\)	\(q+(-1.28849 - 0.582915i) q^{2} +(1.60547 - 0.649977i) q^{3} +(1.32042 + 1.50216i) q^{4} +(1.35495 + 0.782280i) q^{5} +(-2.44751 - 0.0983632i) q^{6} +(-0.314165 - 2.62703i) q^{7} +(-0.825716 - 2.70522i) q^{8} +(2.15506 - 2.08703i) q^{9} +O(q^{10})\)	\(q+(-1.28849 - 0.582915i) q^{2} +(1.60547 - 0.649977i) q^{3} +(1.32042 + 1.50216i) q^{4} +(1.35495 + 0.782280i) q^{5} +(-2.44751 - 0.0983632i) q^{6} +(-0.314165 - 2.62703i) 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} +(3.09626 + 1.55343i) q^{12} +(4.17891 + 2.41269i) q^{13} +(-1.12654 + 3.56804i) q^{14} +(2.68379 + 0.375241i) q^{15} +(-0.512984 + 3.96697i) q^{16} -0.603184i q^{17} +(-3.99334 + 1.43291i) q^{18} +5.64236 q^{19} +(0.613989 + 3.06829i) q^{20} +(-2.21189 - 4.01342i) q^{21} +(4.31452 - 0.427448i) q^{22} +(-7.81563 - 4.51236i) q^{23} +(-3.08399 - 3.80644i) 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} +(-3.23931 - 2.04792i) q^{30} +(-0.860400 + 1.49026i) q^{31} +(2.97338 - 4.81238i) q^{32} +(-3.26623 + 4.18670i) q^{33} +(-0.351605 + 0.777198i) q^{34} +(1.62940 - 3.80526i) q^{35} +(5.98065 + 0.481490i) q^{36} -5.45766 q^{37} +(-7.27014 - 3.28902i) q^{38} +(8.27730 + 1.15731i) q^{39} +(0.997434 - 4.31137i) q^{40} +(2.08830 + 1.20568i) q^{41} +(0.510520 + 6.46060i) 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} +(1.75486 + 6.70227i) q^{48} +(-6.80260 + 1.65064i) q^{49} +(0.355837 + 3.59171i) q^{50} +(-0.392056 - 0.968394i) q^{51} +(1.89365 + 9.46316i) q^{52} -0.430107 q^{53} +(-5.47983 + 4.89607i) q^{54} -4.79657 q^{55} +(-6.84728 + 3.01907i) q^{56} +(9.05864 - 3.66740i) q^{57} +(-0.944615 - 9.53464i) q^{58} +(-2.05729 + 3.56332i) q^{59} +(2.98006 + 4.52697i) q^{60} +(-11.3148 + 6.53263i) q^{61} +(1.97731 - 1.41864i) q^{62} +(-6.15975 - 5.00574i) q^{63} +(-6.63639 + 4.46748i) q^{64} +(3.77480 + 6.53815i) q^{65} +(6.64899 - 3.49059i) q^{66} +(1.39203 + 0.803692i) q^{67} +(0.906081 - 0.796456i) q^{68} +(-15.4807 - 2.16447i) q^{69} +(-4.31761 + 3.95324i) q^{70} +10.5254i q^{71} +(-7.42535 - 4.10661i) q^{72} +1.88011i q^{73} +(7.03215 + 3.18135i) q^{74} +(-3.48530 - 2.71903i) q^{75} +(7.45029 + 8.47575i) q^{76} +(4.86104 + 6.49326i) q^{77} +(-9.99061 - 6.31615i) 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} +(3.10818 - 8.62202i) q^{84} +(0.471859 - 0.817284i) q^{85} +(0.768813 - 0.0761678i) q^{86} +(9.25217 + 7.21803i) q^{87} +(6.33907 + 5.91670i) q^{88} -14.0535i q^{89} +(-6.53171 - 1.18239i) q^{90} +(5.02536 - 11.7361i) q^{91} +(-3.54162 - 17.6986i) q^{92} +(-0.412714 + 2.95180i) q^{93} +(-0.512850 - 5.17654i) q^{94} +(7.64511 + 4.41391i) q^{95} +(1.64574 - 9.65875i) 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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