LMFDB - Embedded newform 273.2.bj.c.142.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 88x^{12} - 303x^{10} + 758x^{8} - 968x^{6} + 867x^{4} - 30x^{2} + 1 $ x^16 - 11x^14 + 88x^12 - 303x^10 + 758x^8 - 968x^6 + 867x^4 - 30*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			142.4
Root			$-0.161178 + 0.0930563i$ of defining polynomial
Character	$\chi$	$=$	273.142
Dual form			273.2.bj.c.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.161178 - 0.0930563i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.982681 - 1.70205i) q^{4} +(2.28561 + 1.31960i) q^{5} +0.186113i q^{6} +(-0.161178 - 2.64084i) q^{7} +0.738004i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.161178 - 0.0930563i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.982681 - 1.70205i) q^{4} +(2.28561 + 1.31960i) q^{5} +0.186113i q^{6} +(-0.161178 - 2.64084i) q^{7} +0.738004i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.245594 - 0.425381i) q^{10} +(1.56731 - 0.904889i) q^{11} +(-0.982681 + 1.70205i) q^{12} +(-2.45655 - 2.63920i) q^{13} +(-0.219768 + 0.440644i) q^{14} -2.63920i q^{15} +(-1.89669 + 3.28516i) q^{16} +(-3.13377 - 5.42785i) q^{17} +(0.161178 - 0.0930563i) q^{18} +(2.44679 + 1.41265i) q^{19} -5.18698i q^{20} +(-2.20644 + 1.46000i) q^{21} -0.336822 q^{22} +(2.12496 - 3.68054i) q^{23} +(0.639130 - 0.369002i) q^{24} +(0.982681 + 1.70205i) q^{25} +(0.150348 + 0.653979i) q^{26} +1.00000 q^{27} +(-4.33646 + 2.86943i) q^{28} +0.456550 q^{29} +(-0.245594 + 0.425381i) q^{30} +(-2.76356 + 1.59554i) q^{31} +(1.88967 - 1.09100i) q^{32} +(-1.56731 - 0.904889i) q^{33} +1.16647i q^{34} +(3.11645 - 6.24862i) q^{35} +1.96536 q^{36} +(3.00675 + 1.73595i) q^{37} +(-0.262913 - 0.455379i) q^{38} +(-1.05734 + 3.44703i) q^{39} +(-0.973869 + 1.68679i) q^{40} +7.18287i q^{41} +(0.491493 - 0.0299973i) q^{42} +7.23230 q^{43} +(-3.08034 - 1.77843i) q^{44} +(-2.28561 + 1.31960i) q^{45} +(-0.684995 + 0.395482i) q^{46} +(10.3082 + 5.95146i) q^{47} +3.79337 q^{48} +(-6.94804 + 0.851291i) q^{49} -0.365779i q^{50} +(-3.13377 + 5.42785i) q^{51} +(-2.07805 + 6.77467i) q^{52} +(2.23678 + 3.87422i) q^{53} +(-0.161178 - 0.0930563i) q^{54} +4.77636 q^{55} +(1.94895 - 0.118950i) q^{56} -2.82531i q^{57} +(-0.0735859 - 0.0424849i) q^{58} +(8.83136 - 5.09879i) q^{59} +(-4.49205 + 2.59349i) q^{60} +(-4.59032 + 7.95067i) q^{61} +0.593902 q^{62} +(2.36762 + 1.18083i) q^{63} +7.18065 q^{64} +(-2.13204 - 9.27384i) q^{65} +(0.168411 + 0.291697i) q^{66} +(1.40329 - 0.810192i) q^{67} +(-6.15900 + 10.6677i) q^{68} -4.24992 q^{69} +(-1.08378 + 0.717136i) q^{70} -1.85468i q^{71} +(-0.639130 - 0.369002i) q^{72} +(-12.3924 + 7.15475i) q^{73} +(-0.323082 - 0.559594i) q^{74} +(0.982681 - 1.70205i) q^{75} -5.55276i q^{76} +(-2.64228 - 3.99317i) q^{77} +(0.491188 - 0.457195i) q^{78} +(5.86235 - 10.1539i) q^{79} +(-8.67018 + 5.00573i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.668411 - 1.15772i) q^{82} +11.7617i q^{83} +(4.65323 + 2.32077i) q^{84} -16.5413i q^{85} +(-1.16569 - 0.673011i) q^{86} +(-0.228275 - 0.395384i) q^{87} +(0.667811 + 1.15668i) q^{88} +(0.0791688 + 0.0457081i) q^{89} +0.491188 q^{90} +(-6.57375 + 6.91273i) q^{91} -8.35264 q^{92} +(2.76356 + 1.59554i) q^{93} +(-1.10764 - 1.91849i) q^{94} +(3.72828 + 6.45756i) q^{95} +(-1.88967 - 1.09100i) q^{96} -1.62366i q^{97} +(1.19909 + 0.509350i) q^{98} +1.80978i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{13} + 40 q^{14} - 10 q^{16} - 8 q^{17} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} + 16 q^{27} - 36 q^{29} - 4 q^{30} - 14 q^{35} - 12 q^{36} - 26 q^{38} - 2 q^{39} + 6 q^{40} - 14 q^{42} + 32 q^{43} + 20 q^{48} - 46 q^{49} - 8 q^{51} + 40 q^{52} + 36 q^{53} - 8 q^{55} + 54 q^{56} + 12 q^{61} - 80 q^{62} - 56 q^{64} + 34 q^{65} + 4 q^{66} + 10 q^{68} + 16 q^{69} + 18 q^{74} - 6 q^{75} - 22 q^{77} + 8 q^{78} + 8 q^{79} - 8 q^{81} + 12 q^{82} + 18 q^{87} - 98 q^{88} + 8 q^{90} + 16 q^{91} + 40 q^{92} + 46 q^{94} + 38 q^{95}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^13 + 40 * q^14 - 10 * q^16 - 8 * q^17 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 + 16 * q^27 - 36 * q^29 - 4 * q^30 - 14 * q^35 - 12 * q^36 - 26 * q^38 - 2 * q^39 + 6 * q^40 - 14 * q^42 + 32 * q^43 + 20 * q^48 - 46 * q^49 - 8 * q^51 + 40 * q^52 + 36 * q^53 - 8 * q^55 + 54 * q^56 + 12 * q^61 - 80 * q^62 - 56 * q^64 + 34 * q^65 + 4 * q^66 + 10 * q^68 + 16 * q^69 + 18 * q^74 - 6 * q^75 - 22 * q^77 + 8 * q^78 + 8 * q^79 - 8 * q^81 + 12 * q^82 + 18 * q^87 - 98 * q^88 + 8 * q^90 + 16 * q^91 + 40 * q^92 + 46 * q^94 + 38 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.161178	−	0.0930563i	−0.113970	−	0.0658007i	0.441931	−	0.897049i	$-0.354294\pi$
$2$	−0.161178	−	0.0930563i	−0.113970	−	0.0658007i	−0.555902	+	0.831248i	$0.687627\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.982681	−	1.70205i	−0.491341	−	0.851027i
$5$	2.28561	+	1.31960i	1.02216	+	0.590142i	0.914728	−	0.404070i	$-0.132405\pi$
$5$	2.28561	+	1.31960i	1.02216	+	0.590142i	0.107429	+	0.994213i	$0.465738\pi$
$6$			0.186113i			0.0759802i
$7$	−0.161178	−	2.64084i	−0.0609197	−	0.998143i
$7$	−0.161178	−	2.64084i	−0.0609197	−	0.998143i
$8$			0.738004i			0.260924i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.245594	−	0.425381i	−0.0776636	−	0.134517i
$11$	1.56731	−	0.904889i	0.472563	−	0.272834i	−0.244749	−	0.969586i	$-0.578706\pi$
$11$	1.56731	−	0.904889i	0.472563	−	0.272834i	0.717312	+	0.696752i	$0.245372\pi$
$12$	−0.982681	+	1.70205i	−0.283676	+	0.491341i
$13$	−2.45655	−	2.63920i	−0.681324	−	0.731982i
$13$	−2.45655	−	2.63920i	−0.681324	−	0.731982i
$14$	−0.219768	+	0.440644i	−0.0587355	+	0.117767i
$15$		−	2.63920i		−	0.681438i
$16$	−1.89669	+	3.28516i	−0.474172	+	0.821289i
$17$	−3.13377	−	5.42785i	−0.760052	−	1.31645i	−0.942823	−	0.333293i	$-0.891840\pi$
$17$	−3.13377	−	5.42785i	−0.760052	−	1.31645i	0.182772	−	0.983155i	$-0.441493\pi$
$18$	0.161178	−	0.0930563i	0.0379901	−	0.0219336i
$19$	2.44679	+	1.41265i	0.561332	+	0.324085i	0.753680	−	0.657242i	$-0.228277\pi$
$19$	2.44679	+	1.41265i	0.561332	+	0.324085i	−0.192348	+	0.981327i	$0.561610\pi$
$20$		−	5.18698i		−	1.15984i
$21$	−2.20644	+	1.46000i	−0.481485	+	0.318599i
$22$	−0.336822			−0.0718108
$23$	2.12496	−	3.68054i	0.443085	−	0.767446i	−0.554832	−	0.831963i	$-0.687217\pi$
$23$	2.12496	−	3.68054i	0.443085	−	0.767446i	0.997917	+	0.0645169i	$0.0205506\pi$
$24$	0.639130	−	0.369002i	0.130462	−	0.0753222i
$25$	0.982681	+	1.70205i	0.196536	+	0.340411i
$26$	0.150348	+	0.653979i	0.0294858	+	0.128256i
$27$	1.00000			0.192450
$28$	−4.33646	+	2.86943i	−0.819514	+	0.542272i
$29$	0.456550			0.0847792			0.0423896	−	0.999101i	$-0.486503\pi$
$29$	0.456550			0.0847792			0.0423896	+	0.999101i	$0.486503\pi$
$30$	−0.245594	+	0.425381i	−0.0448391	+	0.0776636i
$31$	−2.76356	+	1.59554i	−0.496351	+	0.286568i	−0.727205	−	0.686420i	$-0.759181\pi$
$31$	−2.76356	+	1.59554i	−0.496351	+	0.286568i	0.230855	+	0.972988i	$0.425848\pi$
$32$	1.88967	−	1.09100i	0.334050	−	0.192864i
$33$	−1.56731	−	0.904889i	−0.272834	−	0.157521i
$34$			1.16647i			0.200048i
$35$	3.11645	−	6.24862i	0.526777	−	1.05621i
$36$	1.96536			0.327560
$37$	3.00675	+	1.73595i	0.494307	+	0.285388i	0.726359	−	0.687315i	$-0.241211\pi$
$37$	3.00675	+	1.73595i	0.494307	+	0.285388i	−0.232053	+	0.972703i	$0.574544\pi$
$38$	−0.262913	−	0.455379i	−0.0426501	−	0.0738721i
$39$	−1.05734	+	3.44703i	−0.169309	+	0.551967i
$40$	−0.973869	+	1.68679i	−0.153982	+	0.266705i
$41$			7.18287i			1.12178i	0.827892	+	0.560888i	$0.189540\pi$
$41$			7.18287i			1.12178i	−0.827892	+	0.560888i	$0.810460\pi$
$42$	0.491493	−	0.0299973i	0.0758390	−	0.00462868i
$43$	7.23230			1.10292			0.551458	−	0.834203i	$-0.314072\pi$
$43$	7.23230			1.10292			0.551458	+	0.834203i	$0.314072\pi$
$44$	−3.08034	−	1.77843i	−0.464378	−	0.268109i
$45$	−2.28561	+	1.31960i	−0.340719	+	0.196714i
$46$	−0.684995	+	0.395482i	−0.100997	+	0.0583107i
$47$	10.3082	+	5.95146i	1.50361	+	0.868110i	0.999991	+	0.00418434i	$0.00133192\pi$
$47$	10.3082	+	5.95146i	1.50361	+	0.868110i	0.503619	+	0.863926i	$0.332001\pi$
$48$	3.79337			0.547526
$49$	−6.94804	+	0.851291i	−0.992578	+	0.121613i
$50$		−	0.365779i		−	0.0517289i
$51$	−3.13377	+	5.42785i	−0.438816	+	0.760052i
$52$	−2.07805	+	6.77467i	−0.288174	+	0.939478i
$53$	2.23678	+	3.87422i	0.307246	+	0.532165i	0.977759	−	0.209733i	$-0.0672594\pi$
$53$	2.23678	+	3.87422i	0.307246	+	0.532165i	−0.670513	+	0.741898i	$0.733926\pi$
$54$	−0.161178	−	0.0930563i	−0.0219336	−	0.0126634i
$55$	4.77636			0.644044
$56$	1.94895	−	0.118950i	0.260439	−	0.0158954i
$57$		−	2.82531i		−	0.374221i
$58$	−0.0735859	−	0.0424849i	−0.00966231	−	0.00557854i
$59$	8.83136	−	5.09879i	1.14974	−	0.663805i	0.200920	−	0.979608i	$-0.435607\pi$
$59$	8.83136	−	5.09879i	1.14974	−	0.663805i	0.948825	+	0.315802i	$0.102274\pi$
$60$	−4.49205	+	2.59349i	−0.579922	+	0.334818i
$61$	−4.59032	+	7.95067i	−0.587731	+	1.01798i	0.406798	+	0.913518i	$0.366645\pi$
$61$	−4.59032	+	7.95067i	−0.587731	+	1.01798i	−0.994529	+	0.104461i	$0.966688\pi$
$62$	0.593902			0.0754256
$63$	2.36762	+	1.18083i	0.298292	+	0.148771i
$64$	7.18065			0.897581
$65$	−2.13204	−	9.27384i	−0.264447	−	1.15028i
$66$	0.168411	+	0.291697i	0.0207300	+	0.0359054i
$67$	1.40329	−	0.810192i	0.171440	−	0.0989807i	−0.411825	−	0.911263i	$-0.635108\pi$
$67$	1.40329	−	0.810192i	0.171440	−	0.0989807i	0.583265	+	0.812282i	$0.301775\pi$
$68$	−6.15900	+	10.6677i	−0.746888	+	1.29365i
$69$	−4.24992			−0.511631
$70$	−1.08378	+	0.717136i	−0.129536	+	0.0857141i
$71$		−	1.85468i		−	0.220110i	−0.993926	−	0.110055i	$-0.964897\pi$
$71$		−	1.85468i		−	0.220110i	0.993926	−	0.110055i	$-0.0351027\pi$
$72$	−0.639130	−	0.369002i	−0.0753222	−	0.0434873i
$73$	−12.3924	+	7.15475i	−1.45042	+	0.837400i	−0.998505	−	0.0546615i	$-0.982592\pi$
$73$	−12.3924	+	7.15475i	−1.45042	+	0.837400i	−0.451914	+	0.892061i	$0.649259\pi$
$74$	−0.323082	−	0.559594i	−0.0375575	−	0.0650515i
$75$	0.982681	−	1.70205i	0.113470	−	0.196536i
$76$		−	5.55276i		−	0.636945i
$77$	−2.64228	−	3.99317i	−0.301116	−	0.455064i
$78$	0.491188	−	0.457195i	0.0556161	−	0.0517671i
$79$	5.86235	−	10.1539i	0.659566	−	1.14240i	−0.321162	−	0.947024i	$-0.604073\pi$
$79$	5.86235	−	10.1539i	0.659566	−	1.14240i	0.980728	−	0.195378i	$-0.0625934\pi$
$80$	−8.67018	+	5.00573i	−0.969355	+	0.559658i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.668411	−	1.15772i	0.0738137	−	0.127849i
$83$			11.7617i			1.29102i	0.763754	+	0.645508i	$0.223354\pi$
$83$			11.7617i			1.29102i	−0.763754	+	0.645508i	$0.776646\pi$
$84$	4.65323	+	2.32077i	0.507709	+	0.253216i
$85$		−	16.5413i		−	1.79415i
$86$	−1.16569	−	0.673011i	−0.125699	−	0.0725726i
$87$	−0.228275	−	0.395384i	−0.0244736	−	0.0423896i
$88$	0.667811	+	1.15668i	0.0711889	+	0.123303i
$89$	0.0791688	+	0.0457081i	0.00839188	+	0.00484505i	0.504190	−	0.863593i	$-0.331791\pi$
$89$	0.0791688	+	0.0457081i	0.00839188	+	0.00484505i	−0.495798	+	0.868438i	$0.665124\pi$
$90$	0.491188			0.0517758
$91$	−6.57375	+	6.91273i	−0.689116	+	0.724651i
$92$	−8.35264			−0.870823
$93$	2.76356	+	1.59554i	0.286568	+	0.165450i
$94$	−1.10764	−	1.91849i	−0.114245	−	0.197877i
$95$	3.72828	+	6.45756i	0.382513	+	0.662532i
$96$	−1.88967	−	1.09100i	−0.192864	−	0.111350i
$97$		−	1.62366i		−	0.164858i	−0.996597	−	0.0824291i	$-0.973732\pi$
$97$		−	1.62366i		−	0.164858i	0.996597	−	0.0824291i	$-0.0262678\pi$
$98$	1.19909	+	0.509350i	0.121127	+	0.0514521i
$99$			1.80978i			0.181889i
$100$	1.93132	−	3.34515i	0.193132	−	0.334515i
$101$	6.03046	+	10.4451i	0.600053	+	1.03932i	0.992812	+	0.119681i	$0.0381872\pi$
$101$	6.03046	+	10.4451i	0.600053	+	1.03932i	−0.392759	+	0.919641i	$0.628479\pi$
$102$	1.01019	−	0.583235i	0.100024	−	0.0577488i
$103$	2.11645	−	3.66581i	0.208540	−	0.361203i	−0.742715	−	0.669608i	$-0.766462\pi$
$103$	2.11645	−	3.66581i	0.208540	−	0.361203i	0.951255	+	0.308406i	$0.0997954\pi$
$104$	1.94774	−	1.81294i	0.190991	−	0.177774i
$105$	−6.96969	+	0.425381i	−0.680172	+	0.0415130i
$106$		−	0.832587i		−	0.0808680i
$107$	4.10734	−	7.11412i	0.397071	−	0.687748i	−0.596292	−	0.802768i	$-0.703360\pi$
$107$	4.10734	−	7.11412i	0.397071	−	0.687748i	0.993363	+	0.115020i	$0.0366932\pi$
$108$	−0.982681	−	1.70205i	−0.0945585	−	0.163780i
$109$	9.85516	−	5.68988i	0.943953	−	0.544992i	0.0527560	−	0.998607i	$-0.483199\pi$
$109$	9.85516	−	5.68988i	0.943953	−	0.544992i	0.891197	+	0.453616i	$0.149866\pi$
$110$	−0.769845	−	0.444470i	−0.0734019	−	0.0423786i
$111$		−	3.47190i		−	0.329538i
$112$	8.98127	+	4.47934i	0.848650	+	0.423258i
$113$	2.98299			0.280616			0.140308	−	0.990108i	$-0.455191\pi$
$113$	2.98299			0.280616			0.140308	+	0.990108i	$0.455191\pi$
$114$	−0.262913	+	0.455379i	−0.0246240	+	0.0426501i
$115$	9.71367	−	5.60819i	0.905805	−	0.522967i
$116$	−0.448643	−	0.777073i	−0.0416555	−	0.0721494i
$117$	3.51389	−	0.807836i	0.324859	−	0.0746845i
$118$	−1.89790			−0.174716
$119$	−13.8290	+	9.15064i	−1.26770	+	0.838838i
$120$	1.94774			0.177803
$121$	−3.86235	+	6.68979i	−0.351123	+	0.608163i
$122$	1.47972	−	0.854317i	0.133968	−	0.0773462i
$123$	6.22055	−	3.59143i	0.560888	−	0.323829i
$124$	5.43140	+	3.13582i	0.487754	+	0.281605i
$125$		−	8.00901i		−	0.716347i
$126$	−0.271725	−	0.410647i	−0.0242072	−	0.0365833i
$127$	−0.828621			−0.0735282			−0.0367641	−	0.999324i	$-0.511705\pi$
$127$	−0.828621			−0.0735282			−0.0367641	+	0.999324i	$0.511705\pi$
$128$	−4.93670	−	2.85021i	−0.436347	−	0.251925i
$129$	−3.61615	−	6.26335i	−0.318384	−	0.551458i
$130$	−0.519351	+	1.69314i	−0.0455501	+	0.148498i
$131$	0.956855	−	1.65732i	0.0836008	−	0.144801i	−0.821193	−	0.570650i	$-0.806691\pi$
$131$	0.956855	−	1.65732i	0.0836008	−	0.144801i	0.904794	+	0.425849i	$0.140025\pi$
$132$			3.55687i			0.309586i
$133$	3.33622	−	6.68926i	0.289287	−	0.580033i
$134$	−0.301574			−0.0260520
$135$	2.28561	+	1.31960i	0.196714	+	0.113573i
$136$	4.00578	−	2.31274i	0.343493	−	0.198316i
$137$	16.5705	−	9.56699i	1.41571	−	0.817363i	0.419795	−	0.907619i	$-0.362102\pi$
$137$	16.5705	−	9.56699i	1.41571	−	0.817363i	0.995919	+	0.0902558i	$0.0287685\pi$
$138$	0.684995	+	0.395482i	0.0583107	+	0.0336657i
$139$	−17.6202			−1.49452			−0.747262	−	0.664529i	$-0.768632\pi$
$139$	−17.6202			−1.49452			−0.747262	+	0.664529i	$0.768632\pi$
$140$	−13.6980	+	0.836028i	−1.15769	+	0.0706573i
$141$		−	11.9029i		−	1.00241i
$142$	−0.172590	+	0.298934i	−0.0144834	+	0.0250860i
$143$	−6.23836	−	1.91354i	−0.521678	−	0.160019i
$144$	−1.89669	−	3.28516i	−0.158057	−	0.273763i
$145$	1.04350	+	0.602463i	0.0866576	+	0.0500318i
$146$	2.66318			0.220406
$147$	4.21126	+	5.59154i	0.347339	+	0.461182i
$148$		−	6.82354i		−	0.560891i
$149$	−12.7634	−	7.36898i	−1.04562	−	0.603690i	−0.124202	−	0.992257i	$-0.539637\pi$
$149$	−12.7634	−	7.36898i	−1.04562	−	0.603690i	−0.921421	+	0.388567i	$0.872970\pi$
$150$	−0.316774	+	0.182889i	−0.0258645	+	0.0149329i
$151$	−19.9427	+	11.5139i	−1.62292	+	0.936992i	−0.636783	+	0.771043i	$0.719735\pi$
$151$	−19.9427	+	11.5139i	−1.62292	+	0.936992i	−0.986134	+	0.165948i	$0.946932\pi$
$152$	−1.04254	+	1.80574i	−0.0845616	+	0.146465i
$153$	6.26755			0.506701
$154$	0.0542884	+	0.889493i	0.00437469	+	0.0716774i
$155$	−8.42191			−0.676464
$156$	6.90606	−	1.58769i	0.552927	−	0.127117i
$157$	−9.76664	−	16.9163i	−0.779463	−	1.35007i	−0.932252	−	0.361810i	$-0.882159\pi$
$157$	−9.76664	−	16.9163i	−0.779463	−	1.35007i	0.152789	−	0.988259i	$-0.451175\pi$
$158$	−1.88977	+	1.09106i	−0.150342	+	0.0867999i
$159$	2.23678	−	3.87422i	0.177388	−	0.307246i
$160$	5.75873			0.455268
$161$	−10.0622	−	5.01845i	−0.793013	−	0.395510i
$162$			0.186113i			0.0146224i
$163$	3.93209	+	2.27020i	0.307985	+	0.177815i	0.646025	−	0.763317i	$-0.276430\pi$
$163$	3.93209	+	2.27020i	0.307985	+	0.177815i	−0.338039	+	0.941132i	$0.609764\pi$
$164$	12.2256	−	7.05847i	0.954661	−	0.551174i
$165$	−2.38818	−	4.13645i	−0.185920	−	0.322022i
$166$	1.09450	−	1.89573i	0.0849498	−	0.147137i
$167$		−	4.30788i		−	0.333354i	−0.986012	−	0.166677i	$-0.946696\pi$
$167$		−	4.30788i		−	0.333354i	0.986012	−	0.166677i	$-0.0533036\pi$
$168$	−1.07749	−	1.62836i	−0.0831300	−	0.125631i
$169$	−0.930724	+	12.9666i	−0.0715942	+	0.997434i
$170$	−1.53927	+	2.66610i	−0.118057	+	0.204480i
$171$	−2.44679	+	1.41265i	−0.187111	+	0.108028i
$172$	−7.10704	−	12.3098i	−0.541907	−	0.938610i
$173$	−9.68065	+	16.7674i	−0.736006	+	1.27480i	0.218275	+	0.975887i	$0.429957\pi$
$173$	−9.68065	+	16.7674i	−0.736006	+	1.27480i	−0.954281	+	0.298912i	$0.903376\pi$
$174$			0.0849697i			0.00644154i
$175$	4.33646	−	2.86943i	0.327806	−	0.216909i
$176$			6.86516i			0.517481i
$177$	−8.83136	−	5.09879i	−0.663805	−	0.383248i
$178$	−0.00850686	−	0.0147343i	−0.000637616	−	0.00110438i
$179$	3.17632	+	5.50154i	0.237409	+	0.411205i	0.959970	−	0.280103i	$-0.0903685\pi$
$179$	3.17632	+	5.50154i	0.237409	+	0.411205i	−0.722561	+	0.691307i	$0.757035\pi$
$180$	4.49205	+	2.59349i	0.334818	+	0.193307i
$181$	7.22425			0.536974			0.268487	−	0.963283i	$-0.413476\pi$
$181$	7.22425			0.536974			0.268487	+	0.963283i	$0.413476\pi$
$182$	1.70282	−	0.502453i	0.126221	−	0.0372443i
$183$	9.18065			0.678653
$184$	2.71625	+	1.56823i	0.200245	+	0.115611i
$185$	4.58151	+	7.93541i	0.336839	+	0.583423i
$186$	−0.296951	−	0.514334i	−0.0217735	−	0.0377128i
$187$	−9.82321	−	5.67143i	−0.718344	−	0.414736i
$188$		−	23.3936i		−	1.70615i
$189$	−0.161178	−	2.64084i	−0.0117240	−	0.192093i
$190$		−	1.38776i		−	0.100679i
$191$	−0.556285	+	0.963514i	−0.0402514	+	0.0697174i	−0.885449	−	0.464736i	$-0.846149\pi$
$191$	−0.556285	+	0.963514i	−0.0402514	+	0.0697174i	0.845198	+	0.534454i	$0.179483\pi$
$192$	−3.59032	−	6.21862i	−0.259109	−	0.448790i
$193$	23.5745	−	13.6108i	1.69693	−	0.979723i	0.748288	−	0.663374i	$-0.230876\pi$
$193$	23.5745	−	13.6108i	1.69693	−	0.979723i	0.948643	−	0.316350i	$-0.102457\pi$
$194$	−0.151092	+	0.261699i	−0.0108478	+	0.0187889i
$195$	−6.96536	+	6.48332i	−0.498800	+	0.464280i
$196$	8.27665	+	10.9894i	0.591190	+	0.784957i
$197$			19.0457i			1.35695i	0.734623	+	0.678476i	$0.237359\pi$
$197$			19.0457i			1.35695i	−0.734623	+	0.678476i	$0.762641\pi$
$198$	0.168411	−	0.291697i	0.0119685	−	0.0207300i
$199$	−1.03031	−	1.78455i	−0.0730367	−	0.126503i	0.827194	−	0.561916i	$-0.189936\pi$
$199$	−1.03031	−	1.78455i	−0.0730367	−	0.126503i	−0.900231	+	0.435413i	$0.856602\pi$
$200$	−1.25612	+	0.725222i	−0.0888212	+	0.0512810i
$201$	−1.40329	−	0.810192i	−0.0989807	−	0.0571466i
$202$		−	2.24469i		−	0.157936i
$203$	−0.0735859	−	1.20567i	−0.00516472	−	0.0846217i
$204$	12.3180			0.862432
$205$	−9.47850	+	16.4172i	−0.662007	+	1.14663i
$206$	−0.682253	+	0.393899i	−0.0475348	+	0.0274442i
$207$	2.12496	+	3.68054i	0.147695	+	0.255815i
$208$	13.3295	−	3.06442i	0.924233	−	0.212480i
$209$	5.11318			0.353686
$210$	1.16295	+	0.580011i	0.0802510	+	0.0400246i
$211$	6.57689			0.452772			0.226386	−	0.974038i	$-0.427309\pi$
$211$	6.57689			0.452772			0.226386	+	0.974038i	$0.427309\pi$
$212$	4.39609	−	7.61424i	0.301924	−	0.522948i
$213$	−1.60620	+	0.927340i	−0.110055	+	0.0635403i
$214$	−1.32403	+	0.764427i	−0.0905086	+	0.0522552i
$215$	16.5302	+	9.54373i	1.12735	+	0.650877i
$216$			0.738004i			0.0502148i
$217$	4.65900	+	7.04096i	0.316273	+	0.477971i
$218$	−2.11792			−0.143443
$219$	12.3924	+	7.15475i	0.837400	+	0.483473i
$220$	−4.69364	−	8.12962i	−0.316445	−	0.548099i
$221$	−6.62691	+	21.6044i	−0.445774	+	1.45327i
$222$	−0.323082	+	0.559594i	−0.0216838	+	0.0375575i
$223$			28.1666i			1.88617i	0.332547	+	0.943087i	$0.392092\pi$
$223$			28.1666i			1.88617i	−0.332547	+	0.943087i	$0.607908\pi$
$224$	−3.18573	−	4.81446i	−0.212856	−	0.321680i
$225$	−1.96536			−0.131024
$226$	−0.480793	−	0.277586i	−0.0319818	−	0.0184647i
$227$	−5.22162	+	3.01470i	−0.346571	+	0.200093i	−0.663174	−	0.748465i	$-0.730791\pi$
$227$	−5.22162	+	3.01470i	−0.346571	+	0.200093i	0.316603	+	0.948558i	$0.397458\pi$
$228$	−4.80883	+	2.77638i	−0.318472	+	0.183870i
$229$	−13.4054	−	7.73962i	−0.885855	−	0.511449i	−0.0132706	−	0.999912i	$-0.504224\pi$
$229$	−13.4054	−	7.73962i	−0.885855	−	0.511449i	−0.872584	+	0.488463i	$0.837558\pi$
$230$	−2.08751			−0.137646
$231$	−2.13705	+	4.28487i	−0.140607	+	0.281924i
$232$			0.336936i			0.0221209i
$233$	−7.79695	+	13.5047i	−0.510795	+	0.884723i	0.489127	+	0.872213i	$0.337316\pi$
$233$	−7.79695	+	13.5047i	−0.510795	+	0.884723i	−0.999922	+	0.0125105i	$0.996018\pi$
$234$	−0.641536	−	0.196784i	−0.0419385	−	0.0128642i
$235$	15.7071	+	27.2055i	1.02462	+	1.77469i
$236$	−17.3568	−	10.0210i	−1.12983	−	0.652309i
$237$	−11.7247			−0.761602
$238$	3.08046	−	0.188010i	0.199676	−	0.0121868i
$239$			2.96980i			0.192100i	0.995376	+	0.0960502i	$0.0306209\pi$
$239$			2.96980i			0.192100i	−0.995376	+	0.0960502i	$0.969379\pi$
$240$	8.67018	+	5.00573i	0.559658	+	0.323118i
$241$	−3.64444	+	2.10412i	−0.234759	+	0.135538i	−0.612765	−	0.790265i	$-0.709943\pi$
$241$	−3.64444	+	2.10412i	−0.234759	+	0.135538i	0.378007	+	0.925803i	$0.376610\pi$
$242$	1.24505	−	0.718833i	0.0800352	−	0.0462083i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	18.0433			1.15510
$245$	−17.0039	−	7.22291i	−1.08634	−	0.461455i
$246$	−1.33682			−0.0852327
$247$	−2.28239	−	9.92782i	−0.145225	−	0.631692i
$248$	−1.17752	−	2.03952i	−0.0747725	−	0.129510i
$249$	10.1859	−	5.88086i	0.645508	−	0.372684i
$250$	−0.745289	+	1.29088i	−0.0471362	+	0.0816423i
$251$	−9.80053			−0.618604			−0.309302	−	0.950964i	$-0.600095\pi$
$251$	−9.80053			−0.618604			−0.309302	+	0.950964i	$0.600095\pi$
$252$	−0.316774	−	5.19020i	−0.0199549	−	0.326952i
$253$		−	7.69141i		−	0.483555i
$254$	0.133556	+	0.0771084i	0.00838003	+	0.00483821i
$255$	−14.3252	+	8.27065i	−0.897077	+	0.517928i
$256$	−6.65019	−	11.5185i	−0.415637	−	0.719904i
$257$	12.4615	−	21.5839i	0.777326	−	1.34637i	−0.156151	−	0.987733i	$-0.549909\pi$
$257$	12.4615	−	21.5839i	0.777326	−	1.34637i	0.933478	−	0.358636i	$-0.116758\pi$
$258$			1.34602i			0.0837997i
$259$	4.09974	−	8.22014i	0.254745	−	0.510775i
$260$	−13.6895	+	12.7421i	−0.848984	+	0.790230i
$261$	−0.228275	+	0.395384i	−0.0141299	+	0.0244736i
$262$	−0.308449	+	0.178083i	−0.0190560	+	0.0110020i
$263$	−8.95686	−	15.5137i	−0.552303	−	0.956617i	−0.998108	−	0.0614871i	$-0.980416\pi$
$263$	−8.95686	−	15.5137i	−0.552303	−	0.956617i	0.445805	−	0.895130i	$-0.352918\pi$
$264$	0.667811	−	1.15668i	0.0411009	−	0.0711889i
$265$			11.8066i			0.725275i
$266$	−1.16020	+	0.767707i	−0.0711367	+	0.0470712i
$267$		−	0.0914163i		−	0.00559458i
$268$	−2.75798	−	1.59232i	−0.168470	−	0.0972665i
$269$	15.6070	+	27.0322i	0.951578	+	1.64818i	0.742011	+	0.670387i	$0.233872\pi$
$269$	15.6070	+	27.0322i	0.951578	+	1.64818i	0.209567	+	0.977794i	$0.432795\pi$
$270$	−0.245594	−	0.425381i	−0.0149464	−	0.0258879i
$271$	−19.6854	−	11.3654i	−1.19581	−	0.690399i	−0.236188	−	0.971707i	$-0.575898\pi$
$271$	−19.6854	−	11.3654i	−1.19581	−	0.690399i	−0.959617	+	0.281309i	$0.909232\pi$
$272$	23.7751			1.44158
$273$	9.27347	+	2.23667i	0.561256	+	0.135369i
$274$	−3.56107			−0.215132
$275$	3.08034	+	1.77843i	0.185751	+	0.107244i
$276$	4.17632	+	7.23360i	0.251385	+	0.435411i
$277$	−5.81069	−	10.0644i	−0.349131	−	0.604712i	0.636965	−	0.770893i	$-0.280190\pi$
$277$	−5.81069	−	10.0644i	−0.349131	−	0.604712i	−0.986095	+	0.166181i	$0.946856\pi$
$278$	2.83999	+	1.63967i	0.170331	+	0.0983408i
$279$		−	3.19109i		−	0.191045i
$280$	4.61151	+	2.29996i	0.275590	+	0.137449i
$281$			17.6385i			1.05223i	0.850415	+	0.526113i	$0.176351\pi$
$281$			17.6385i			1.05223i	−0.850415	+	0.526113i	$0.823649\pi$
$282$	−1.10764	+	1.91849i	−0.0659591	+	0.114245i
$283$	−4.66423	−	8.07869i	−0.277260	−	0.480228i	0.693443	−	0.720512i	$-0.256093\pi$
$283$	−4.66423	−	8.07869i	−0.277260	−	0.480228i	−0.970703	+	0.240283i	$0.922760\pi$
$284$	−3.15676	+	1.82256i	−0.187319	+	0.108149i
$285$	3.72828	−	6.45756i	0.220844	−	0.382513i
$286$	0.827421	+	0.888941i	0.0489264	+	0.0525642i
$287$	18.9688	−	1.15772i	1.11969	−	0.0683382i
$288$			2.18200i			0.128576i
$289$	−11.1411	+	19.2969i	−0.655357	+	1.13511i
$290$	−0.112126	−	0.194208i	−0.00658426	−	0.0114043i
$291$	−1.40613	+	0.811832i	−0.0824291	+	0.0475904i
$292$	24.3555	+	14.0617i	1.42530	+	0.822897i
$293$		−	8.28665i		−	0.484111i	−0.970262	−	0.242056i	$-0.922178\pi$
$293$		−	8.28665i		−	0.484111i	0.970262	−	0.242056i	$-0.0778217\pi$
$294$	−0.158436	−	1.29312i	−0.00924018	−	0.0754162i
$295$	26.9134			1.56696
$296$	−1.28114	+	2.21899i	−0.0744646	+	0.128976i
$297$	1.56731	−	0.904889i	0.0909447	−	0.0525070i
$298$	1.37146	+	2.37544i	0.0794466	+	0.137605i
$299$	−14.9337	+	3.43324i	−0.863641	+	0.198549i
$300$	−3.86265			−0.223010
$301$	−1.16569	−	19.0993i	−0.0671892	−	1.10087i
$302$	4.28578			0.246619
$303$	6.03046	−	10.4451i	0.346441	−	0.600053i
$304$	−9.28159	+	5.35873i	−0.532335	+	0.307344i
$305$	−20.9834	+	12.1148i	−1.20151	+	0.693690i
$306$	−1.01019	−	0.583235i	−0.0577488	−	0.0333413i
$307$		−	13.9886i		−	0.798373i	−0.916870	−	0.399186i	$-0.869293\pi$
$307$		−	13.9886i		−	0.798373i	0.916870	−	0.399186i	$-0.130707\pi$
$308$	−4.20007	+	8.42131i	−0.239321	+	0.479849i
$309$	−4.23291			−0.240802
$310$	1.35743	+	0.783712i	0.0770968	+	0.0445119i
$311$	10.9344	+	18.9390i	0.620035	+	1.07393i	0.989479	+	0.144679i	$0.0462151\pi$
$311$	10.9344	+	18.9390i	0.620035	+	1.07393i	−0.369443	+	0.929253i	$0.620452\pi$
$312$	−2.54392	−	0.780319i	−0.144021	−	0.0441768i
$313$	−4.22949	+	7.32568i	−0.239065	+	0.414072i	−0.960446	−	0.278466i	$-0.910174\pi$
$313$	−4.22949	+	7.32568i	−0.239065	+	0.414072i	0.721382	+	0.692538i	$0.243507\pi$
$314$			3.63539i			0.205157i
$315$	3.85324	+	5.82324i	0.217105	+	0.328102i
$316$	−23.0433			−1.29629
$317$	22.5868	+	13.0405i	1.26860	+	0.732426i	0.974723	−	0.223418i	$-0.0717215\pi$
$317$	22.5868	+	13.0405i	1.26860	+	0.732426i	0.293876	+	0.955844i	$0.405055\pi$
$318$	−0.721041	+	0.416293i	−0.0404340	+	0.0233446i
$319$	0.715557	−	0.413127i	0.0400635	−	0.0231307i
$320$	16.4122	+	9.47557i	0.917468	+	0.529701i
$321$	−8.21467			−0.458498
$322$	1.15481	+	1.74522i	0.0643551	+	0.0972572i
$323$		−	17.7078i		−	0.985286i
$324$	−0.982681	+	1.70205i	−0.0545934	+	0.0945585i
$325$	2.07805	−	6.77467i	0.115269	−	0.375791i
$326$	−0.422512	−	0.731812i	−0.0234008	−	0.0405313i
$327$	−9.85516	−	5.68988i	−0.544992	−	0.314651i
$328$	−5.30098			−0.292698
$329$	14.0554	−	28.1816i	0.774898	−	1.55370i
$330$			0.888941i			0.0489346i
$331$	3.92512	+	2.26617i	0.215744	+	0.124560i	0.603978	−	0.797001i	$-0.293581\pi$
$331$	3.92512	+	2.26617i	0.215744	+	0.124560i	−0.388234	+	0.921561i	$0.626915\pi$
$332$	20.0191	−	11.5580i	1.09869	−	0.634328i
$333$	−3.00675	+	1.73595i	−0.164769	+	0.0951294i
$334$	−0.400875	+	0.694336i	−0.0219349	+	0.0379924i
$335$	4.27651			0.233651
$336$	−0.611409	−	10.0177i	−0.0333551	−	0.546509i
$337$	−15.1893			−0.827414			−0.413707	−	0.910410i	$-0.635766\pi$
$337$	−15.1893			−0.827414			−0.413707	+	0.910410i	$0.635766\pi$
$338$	1.35664	−	2.00333i	0.0737915	−	0.108967i
$339$	−1.49149	−	2.58334i	−0.0810068	−	0.140308i
$340$	−28.1542	+	16.2548i	−1.52687	+	0.881541i
$341$	−2.88758	+	5.00143i	−0.156371	+	0.270843i
$342$	0.525826			0.0284334
$343$	3.36799	+	18.2114i	0.181855	+	0.983325i
$344$			5.33746i			0.287777i
$345$	−9.71367	−	5.60819i	−0.522967	−	0.301935i
$346$	3.12062	−	1.80169i	0.167766	−	0.0968595i
$347$	−16.9646	−	29.3836i	−0.910708	−	1.57739i	−0.813067	−	0.582171i	$-0.802204\pi$
$347$	−16.9646	−	29.3836i	−0.910708	−	1.57739i	−0.0976411	−	0.995222i	$-0.531130\pi$
$348$	−0.448643	+	0.777073i	−0.0240498	+	0.0416555i
$349$			10.1701i			0.544391i	0.962242	+	0.272195i	$0.0877497\pi$
$349$			10.1701i			0.544391i	−0.962242	+	0.272195i	$0.912250\pi$
$350$	−0.965962	+	0.0589556i	−0.0516328	+	0.00315131i
$351$	−2.45655	−	2.63920i	−0.131121	−	0.140870i
$352$	1.97447	−	3.41988i	0.105240	−	0.182280i
$353$	15.9965	−	9.23561i	0.851410	−	0.491562i	−0.00971638	−	0.999953i	$-0.503093\pi$
$353$	15.9965	−	9.23561i	0.851410	−	0.491562i	0.861126	+	0.508391i	$0.169760\pi$
$354$	0.948948	+	1.64363i	0.0504360	+	0.0873578i
$355$	2.44743	−	4.23908i	0.129896	−	0.224987i
$356$		−	0.179666i		−	0.00952228i
$357$	14.8392	+	7.40093i	0.785373	+	0.391699i
$358$		−	1.18231i		−	0.0624868i
$359$	14.1209	+	8.15269i	0.745271	+	0.430283i	0.823983	−	0.566615i	$-0.191747\pi$
$359$	14.1209	+	8.15269i	0.745271	+	0.430283i	−0.0787114	+	0.996897i	$0.525081\pi$
$360$	−0.973869	−	1.68679i	−0.0513274	−	0.0889017i
$361$	−5.50881	−	9.54154i	−0.289937	−	0.502186i
$362$	−1.16439	−	0.672262i	−0.0611991	−	0.0353333i
$363$	7.72471			0.405442
$364$	18.2257	+	4.39586i	0.955288	+	0.230406i
$365$	−37.7656			−1.97674
$366$	−1.47972	−	0.854317i	−0.0773462	−	0.0446559i
$367$	12.9612	+	22.4494i	0.676568	+	1.17185i	0.976008	+	0.217735i	$0.0698670\pi$
$367$	12.9612	+	22.4494i	0.676568	+	1.17185i	−0.299440	+	0.954115i	$0.596800\pi$
$368$	8.06077	+	13.9617i	0.420197	+	0.727802i
$369$	−6.22055	−	3.59143i	−0.323829	−	0.186963i
$370$		−	1.70535i		−	0.0886571i
$371$	9.87066	−	6.53142i	0.512459	−	0.339094i
$372$		−	6.27164i		−	0.325170i
$373$	11.7329	−	20.3220i	0.607507	−	1.05223i	−0.384143	−	0.923274i	$-0.625503\pi$
$373$	11.7329	−	20.3220i	0.607507	−	1.05223i	0.991650	−	0.128959i	$-0.0411637\pi$
$374$	1.05552	+	1.82822i	0.0545799	+	0.0945351i
$375$	−6.93600	+	4.00450i	−0.358174	+	0.206792i
$376$	−4.39220	+	7.60752i	−0.226511	+	0.392328i
$377$	−1.12154	−	1.20493i	−0.0577621	−	0.0620568i
$378$	−0.219768	+	0.440644i	−0.0113037	+	0.0226643i
$379$		−	14.6833i		−	0.754232i	−0.926166	−	0.377116i	$-0.876916\pi$
$379$		−	14.6833i		−	0.754232i	0.926166	−	0.377116i	$-0.123084\pi$
$380$	7.32741	−	12.6914i	0.375888	−	0.651057i
$381$	0.414310	+	0.717607i	0.0212258	+	0.0367641i
$382$	0.179322	−	0.103532i	0.00917492	−	0.00529714i
$383$	−19.7717	−	11.4152i	−1.01029	−	0.583291i	−0.0990126	−	0.995086i	$-0.531568\pi$
$383$	−19.7717	−	11.4152i	−1.01029	−	0.583291i	−0.911276	+	0.411796i	$0.864902\pi$
$384$			5.70041i			0.290898i
$385$	−0.769845	−	12.6136i	−0.0392349	−	0.642848i
$386$	−5.06627			−0.257866
$387$	−3.61615	+	6.26335i	−0.183819	+	0.318384i
$388$	−2.76356	+	1.59554i	−0.140299	+	0.0810015i
$389$	−12.7928	−	22.1577i	−0.648619	−	1.12344i	−0.983453	−	0.181164i	$-0.942013\pi$
$389$	−12.7928	−	22.1577i	−0.648619	−	1.12344i	0.334834	−	0.942277i	$-0.391320\pi$
$390$	1.72598	−	0.396799i	0.0873983	−	0.0200927i
$391$	−26.6366			−1.34707
$392$	−0.628256	−	5.12768i	−0.0317317	−	0.258987i
$393$	−1.91371			−0.0965339
$394$	1.77232	−	3.06976i	0.0892884	−	0.154652i
$395$	26.7981	−	15.4719i	1.34836	−	0.778476i
$396$	3.08034	−	1.77843i	0.154793	−	0.0893697i
$397$	−16.1690	−	9.33517i	−0.811498	−	0.468519i	0.0359778	−	0.999353i	$-0.488545\pi$
$397$	−16.1690	−	9.33517i	−0.811498	−	0.468519i	−0.847476	+	0.530834i	$0.821879\pi$
$398$			0.383507i			0.0192235i
$399$	−7.46118	+	0.455379i	−0.373526	+	0.0227974i
$400$	−7.45535			−0.372768
$401$	−7.30019	−	4.21476i	−0.364554	−	0.210475i	0.306523	−	0.951863i	$-0.400834\pi$
$401$	−7.30019	−	4.21476i	−0.364554	−	0.210475i	−0.671077	+	0.741388i	$0.734168\pi$
$402$	0.150787	+	0.261171i	0.00752057	+	0.0130260i
$403$	10.9998	+	3.37406i	0.547938	+	0.168074i
$404$	11.8520	−	20.5283i	0.589661	−	1.02132i
$405$		−	2.63920i		−	0.131143i
$406$	−0.100335	+	0.201176i	−0.00497955	+	0.00998420i
$407$	6.28336			0.311455
$408$	−4.00578	−	2.31274i	−0.198316	−	0.114498i
$409$	11.7518	−	6.78491i	0.581090	−	0.335492i	−0.180477	−	0.983579i	$-0.557764\pi$
$409$	11.7518	−	6.78491i	0.581090	−	0.335492i	0.761566	+	0.648087i	$0.224431\pi$
$410$	3.05546	−	1.76407i	0.150898	−	0.0871212i
$411$	−16.5705	−	9.56699i	−0.817363	−	0.471905i
$412$	−8.31920			−0.409857
$413$	−14.8885	−	22.5004i	−0.732614	−	1.10717i
$414$		−	0.790964i		−	0.0388738i
$415$	−15.5207	+	26.8827i	−0.761883	+	1.31962i
$416$	−7.52143	−	2.30711i	−0.368769	−	0.113115i
$417$	8.81009	+	15.2595i	0.431432	+	0.747262i
$418$	−0.824134	−	0.475814i	−0.0403097	−	0.0232728i
$419$	−3.04148			−0.148586			−0.0742931	−	0.997236i	$-0.523670\pi$
$419$	−3.04148			−0.148586			−0.0742931	+	0.997236i	$0.523670\pi$
$420$	7.57300	+	11.4448i	0.369525	+	0.558448i
$421$		−	2.97464i		−	0.144975i	−0.997369	−	0.0724874i	$-0.976906\pi$
$421$		−	2.97464i		−	0.144975i	0.997369	−	0.0724874i	$-0.0230937\pi$
$422$	−1.06005	−	0.612021i	−0.0516025	−	0.0297927i
$423$	−10.3082	+	5.95146i	−0.501204	+	0.289370i
$424$	−2.85919	+	1.65075i	−0.138855	+	0.0801677i
$425$	6.15900	−	10.6677i	0.298755	−	0.517459i
$426$	0.345179			0.0167240
$427$	21.7363	+	10.8408i	1.05189	+	0.524624i
$428$	−16.1448			−0.780389
$429$	1.46200	+	6.35935i	0.0705862	+	0.307032i
$430$	−1.77621	−	3.07648i	−0.0856564	−	0.148361i
$431$	30.8470	−	17.8095i	1.48585	−	0.857854i	0.485977	−	0.873972i	$-0.338464\pi$
$431$	30.8470	−	17.8095i	1.48585	−	0.857854i	0.999870	+	0.0161177i	$0.00513064\pi$
$432$	−1.89669	+	3.28516i	−0.0912544	+	0.158057i
$433$	−13.5181			−0.649637			−0.324819	−	0.945776i	$-0.605303\pi$
$433$	−13.5181			−0.649637			−0.324819	+	0.945776i	$0.605303\pi$
$434$	−0.0957241	−	1.56840i	−0.00459490	−	0.0752855i
$435$		−	1.20493i		−	0.0577718i
$436$	−19.3690	−	11.1827i	−0.927605	−	0.535553i
$437$	10.3987	−	6.00367i	0.497436	−	0.287195i
$438$	−1.33159	−	2.30638i	−0.0636258	−	0.110203i
$439$	16.3570	−	28.3311i	0.780675	−	1.35217i	−0.150873	−	0.988553i	$-0.548209\pi$
$439$	16.3570	−	28.3311i	0.780675	−	1.35217i	0.931549	−	0.363616i	$-0.118458\pi$
$440$			3.52497i			0.168046i
$441$	2.73678	−	6.44283i	0.130323	−	0.306801i
$442$	3.07854	−	2.86549i	0.146431	−	0.136297i
$443$	10.6845	−	18.5061i	0.507637	−	0.879253i	−0.492324	−	0.870412i	$-0.663853\pi$
$443$	10.6845	−	18.5061i	0.507637	−	0.879253i	0.999961	−	0.00884084i	$-0.00281416\pi$
$444$	−5.90936	+	3.41177i	−0.280446	+	0.161915i
$445$	0.120633	+	0.208942i	0.00571854	+	0.00990481i
$446$	2.62108	−	4.53984i	0.124112	−	0.214968i
$447$			14.7380i			0.697082i
$448$	−1.15736	−	18.9629i	−0.0546803	−	0.895914i
$449$			19.2606i			0.908962i	0.890756	+	0.454481i	$0.150175\pi$
$449$			19.2606i			0.908962i	−0.890756	+	0.454481i	$0.849825\pi$
$450$	0.316774	+	0.182889i	0.0149329	+	0.00862149i
$451$	6.49969	+	11.2578i	0.306059	+	0.530109i
$452$	−2.93132	−	5.07720i	−0.137878	−	0.238812i
$453$	19.9427	+	11.5139i	0.936992	+	0.540972i
$454$	1.12215			0.0526650
$455$	−24.1471	+	7.12511i	−1.13203	+	0.334030i
$456$	2.08509			0.0976433
$457$	10.7224	+	6.19059i	0.501574	+	0.289584i	0.729363	−	0.684127i	$-0.239816\pi$
$457$	10.7224	+	6.19059i	0.501574	+	0.289584i	−0.227790	+	0.973710i	$0.573150\pi$
$458$	1.44044	+	2.49492i	0.0673074	+	0.116580i
$459$	−3.13377	−	5.42785i	−0.146272	−	0.253351i
$460$	−19.0909	−	11.0221i	−0.890117	−	0.513909i
$461$			23.1820i			1.07969i	0.841763	+	0.539847i	$0.181518\pi$
$461$			23.1820i			1.07969i	−0.841763	+	0.539847i	$0.818482\pi$
$462$	0.743179	−	0.491762i	0.0345758	−	0.0228788i
$463$			17.2760i			0.802885i	0.915884	+	0.401442i	$0.131491\pi$
$463$			17.2760i			0.802885i	−0.915884	+	0.401442i	$0.868509\pi$
$464$	−0.865932	+	1.49984i	−0.0401999	+	0.0696282i
$465$	4.21096	+	7.29359i	0.195278	+	0.338232i
$466$	2.51340	−	1.45111i	0.116431	−	0.0672214i
$467$	4.45237	−	7.71173i	0.206031	−	0.356856i	−0.744430	−	0.667701i	$-0.767278\pi$
$467$	4.45237	−	7.71173i	0.206031	−	0.356856i	0.950461	+	0.310844i	$0.100612\pi$
$468$	−4.82801	−	5.18698i	−0.223175	−	0.239768i
$469$	−2.36577	−	3.57529i	−0.109241	−	0.165091i
$470$		−	5.84657i		−	0.269682i
$471$	−9.76664	+	16.9163i	−0.450023	+	0.779463i
$472$	3.76292	+	6.51757i	0.173203	+	0.299996i
$473$	11.3353	−	6.54442i	0.521196	−	0.300913i
$474$	1.88977	+	1.09106i	0.0867999	+	0.0501140i
$475$			5.55276i			0.254778i
$476$	29.1644	+	14.5455i	1.33675	+	0.666693i
$477$	−4.47356			−0.204830
$478$	0.276359	−	0.478667i	0.0126403	−	0.0218937i
$479$	14.7459	−	8.51355i	0.673758	−	0.388994i	−0.123741	−	0.992315i	$-0.539489\pi$
$479$	14.7459	−	8.51355i	0.673758	−	0.388994i	0.797499	+	0.603320i	$0.206156\pi$
$480$	−2.87937	−	4.98721i	−0.131425	−	0.227634i
$481$	−2.80472	−	12.1999i	−0.127884	−	0.556266i
$482$	0.783205			0.0356740
$483$	0.684995	+	11.2234i	0.0311684	+	0.510680i
$484$	15.1818			0.690084
$485$	2.14259	−	3.71107i	0.0972898	−	0.168511i
$486$	0.161178	−	0.0930563i	0.00731119	−	0.00422112i
$487$	−24.3358	+	14.0503i	−1.10276	+	0.636680i	−0.936945	−	0.349477i	$-0.886359\pi$
$487$	−24.3358	+	14.0503i	−1.10276	+	0.636680i	−0.165817	+	0.986157i	$0.553026\pi$
$488$	−5.86763	−	3.38768i	−0.265615	−	0.153353i
$489$		−	4.54039i		−	0.205324i
$490$	2.06852	+	2.74650i	0.0934462	+	0.124074i
$491$	3.95609			0.178536			0.0892680	−	0.996008i	$-0.471547\pi$
$491$	3.95609			0.178536			0.0892680	+	0.996008i	$0.471547\pi$
$492$	−12.2256	−	7.05847i	−0.551174	−	0.318220i
$493$	−1.43072	−	2.47809i	−0.0644366	−	0.111607i
$494$	−0.555975	+	1.81254i	−0.0250145	+	0.0815500i
$495$	−2.38818	+	4.13645i	−0.107341	+	0.185920i
$496$		−	12.1050i		−	0.543530i
$497$	−4.89791	+	0.298934i	−0.219701	+	0.0134090i
$498$	−2.18900			−0.0980916
$499$	10.5959	+	6.11754i	0.474337	+	0.273859i	0.718054	−	0.695988i	$-0.245033\pi$
$499$	10.5959	+	6.11754i	0.474337	+	0.273859i	−0.243716	+	0.969847i	$0.578367\pi$
$500$	−13.6318	+	7.87030i	−0.609631	+	0.351971i
$501$	−3.73073	+	2.15394i	−0.166677	+	0.0962309i
$502$	1.57963	+	0.912001i	0.0705024	+	0.0407046i
$503$	−30.6178			−1.36518			−0.682589	−	0.730802i	$-0.739146\pi$
$503$	−30.6178			−1.36518			−0.682589	+	0.730802i	$0.739146\pi$
$504$	−0.871460	+	1.74731i	−0.0388179	+	0.0778315i
$505$			31.8311i			1.41647i
$506$	−0.715734	+	1.23969i	−0.0318183	+	0.0551109i
$507$	11.6948	−	5.67729i	0.519384	−	0.252137i
$508$	0.814270	+	1.41036i	0.0361274	+	0.0625745i
$509$	9.63176	+	5.56090i	0.426920	+	0.246483i	0.698034	−	0.716065i	$-0.254059\pi$
$509$	9.63176	+	5.56090i	0.426920	+	0.246483i	−0.271113	+	0.962547i	$0.587392\pi$
$510$	3.07854			0.136320
$511$	20.8919	+	31.5731i	0.924204	+	1.39671i
$512$			13.8762i			0.613247i
$513$	2.44679	+	1.41265i	0.108028	+	0.0623702i
$514$	−4.01704	+	2.31924i	−0.177184	+	0.102297i
$515$	9.67479	−	5.58574i	0.426322	−	0.246137i
$516$	−7.10704	+	12.3098i	−0.312870	+	0.541907i
$517$	21.5416			0.947400
$518$	−1.42572	+	0.943401i	−0.0626427	+	0.0414507i
$519$	19.3613			0.849866
$520$	6.84413	−	1.57345i	0.300135	−	0.0690005i
$521$	0.749617	+	1.29837i	0.0328413	+	0.0568828i	0.881979	−	0.471289i	$-0.156211\pi$
$521$	0.749617	+	1.29837i	0.0328413	+	0.0568828i	−0.849138	+	0.528172i	$0.822878\pi$
$522$	0.0735859	−	0.0424849i	0.00322077	−	0.00185951i
$523$	15.8262	−	27.4118i	0.692031	−	1.19863i	−0.279140	−	0.960250i	$-0.590049\pi$
$523$	15.8262	−	27.4118i	0.692031	−	1.19863i	0.971171	−	0.238383i	$-0.0766174\pi$
$524$	−3.76113			−0.164306
$525$	−4.65323	−	2.32077i	−0.203084	−	0.101287i
$526$			3.33397i			0.145368i
$527$	17.3208	+	10.0001i	0.754504	+	0.435613i
$528$	5.94540	−	3.43258i	0.258740	−	0.149384i
$529$	2.46908	+	4.27657i	0.107351	+	0.185938i
$530$	1.09868	−	1.90297i	0.0477236	−	0.0826597i
$531$			10.1976i			0.442537i
$532$	−14.6639	+	0.894984i	−0.635762	+	0.0388025i
$533$	18.9570	−	17.6451i	0.821119	−	0.764293i
$534$	−0.00850686	+	0.0147343i	−0.000368128	+	0.000637616i
$535$	18.7756	−	10.8401i	0.811738	−	0.468657i
$536$	0.597925	+	1.03564i	0.0258264	+	0.0447327i
$537$	3.17632	−	5.50154i	0.137068	−	0.237409i
$538$		−	5.80933i		−	0.250458i
$539$	−10.1194	+	7.62144i	−0.435875	+	0.328279i
$540$		−	5.18698i		−	0.223212i
$541$	−11.6353	−	6.71764i	−0.500241	−	0.288814i	0.228572	−	0.973527i	$-0.426594\pi$
$541$	−11.6353	−	6.71764i	−0.500241	−	0.288814i	−0.728813	+	0.684713i	$0.759928\pi$
$542$	2.11524	+	3.66371i	0.0908575	+	0.157370i
$543$	−3.61213	−	6.25639i	−0.155011	−	0.268487i
$544$	−11.8436	−	6.83790i	−0.507790	−	0.293173i
$545$	30.0334			1.28649
$546$	−1.28655	−	1.22346i	−0.0550591	−	0.0523591i
$547$	−6.82740			−0.291919			−0.145959	−	0.989291i	$-0.546627\pi$
$547$	−6.82740			−0.291919			−0.145959	+	0.989291i	$0.546627\pi$
$548$	−32.5670	−	18.8026i	−1.39120	−	0.803207i
$549$	−4.59032	−	7.95067i	−0.195910	−	0.339326i
$550$	−0.330989	−	0.573290i	−0.0141134	−	0.0244452i
$551$	1.11708	+	0.644948i	0.0475893	+	0.0274757i
$552$		−	3.13646i		−	0.133497i
$553$	−27.7597	−	13.8449i	−1.18046	−	0.588747i
$554$			2.16289i			0.0918922i
$555$	4.58151	−	7.93541i	0.194474	−	0.336839i
$556$	17.3150	+	29.9905i	0.734320	+	1.27188i
$557$	−40.2049	+	23.2123i	−1.70354	+	0.983537i	−0.761415	+	0.648265i	$0.775495\pi$
$557$	−40.2049	+	23.2123i	−1.70354	+	0.983537i	−0.942121	+	0.335272i	$0.891172\pi$
$558$	−0.296951	+	0.514334i	−0.0125709	+	0.0217735i
$559$	−17.7665	−	19.0875i	−0.751443	−	0.807314i
$560$	14.6168	+	22.0897i	0.617671	+	0.933461i
$561$			11.3429i			0.478896i
$562$	1.64138	−	2.84294i	0.0692372	−	0.119922i
$563$	−11.9697	−	20.7321i	−0.504462	−	0.873754i	−0.999987	−	0.00516032i	$-0.998357\pi$
$563$	−11.9697	−	20.7321i	−0.504462	−	0.873754i	0.495524	−	0.868594i	$-0.334976\pi$
$564$	−20.2594	+	11.6968i	−0.853075	+	0.492523i
$565$	6.81795	+	3.93634i	0.286833	+	0.165603i
$566$			1.73615i			0.0729756i
$567$	−2.20644	+	1.46000i	−0.0926619	+	0.0613144i
$568$	1.36876			0.0574319
$569$	−20.3776	+	35.2950i	−0.854272	+	1.47964i	0.0230475	+	0.999734i	$0.492663\pi$
$569$	−20.3776	+	35.2950i	−0.854272	+	1.47964i	−0.877319	+	0.479907i	$0.840670\pi$
$570$	−1.20183	+	0.693879i	−0.0503393	+	0.0290634i
$571$	−6.04808	−	10.4756i	−0.253104	−	0.438390i	0.711275	−	0.702914i	$-0.248118\pi$
$571$	−6.04808	−	10.4756i	−0.253104	−	0.438390i	−0.964379	+	0.264525i	$0.914785\pi$
$572$	2.87337	+	12.4984i	0.120141	+	0.522586i
$573$	1.11257			0.0464783
$574$	−3.16509	−	1.57857i	−0.132108	−	0.0658881i
$575$	8.35264			0.348329
$576$	−3.59032	+	6.21862i	−0.149597	+	0.259109i
$577$	−7.30707	+	4.21874i	−0.304197	+	0.175628i	−0.644327	−	0.764750i	$-0.722862\pi$
$577$	−7.30707	+	4.21874i	−0.304197	+	0.175628i	0.340130	+	0.940379i	$0.389529\pi$
$578$	3.59140	−	2.07349i	0.149382	−	0.0862460i
$579$	−23.5745	−	13.6108i	−0.979723	−	0.565644i
$580$		−	2.36811i		−	0.0983306i
$581$	31.0608	−	1.89573i	1.28862	−	0.0786482i
$582$	0.302184			0.0125259
$583$	7.01147	+	4.04808i	0.290386	+	0.167654i
$584$	−5.28023	−	9.14563i	−0.218498	−	0.378449i
$585$	9.09740	+	2.79052i	0.376131	+	0.115374i
$586$	−0.771125	+	1.33563i	−0.0318549	+	0.0551743i
$587$		−	15.6268i		−	0.644987i	−0.946572	−	0.322493i	$-0.895479\pi$
$587$		−	15.6268i		−	0.644987i	0.946572	−	0.322493i	$-0.104521\pi$
$588$	5.37877	−	12.6625i	0.221817	−	0.522192i
$589$	−9.01581			−0.371490
$590$	−4.33785	−	2.50446i	−0.178587	−	0.103107i
$591$	16.4941	−	9.52286i	0.678476	−	0.391718i
$592$	−11.4057	+	6.58510i	−0.468773	+	0.270646i
$593$	1.81608	+	1.04852i	0.0745776	+	0.0430574i	0.536825	−	0.843694i	$-0.319623\pi$
$593$	1.81608	+	1.04852i	0.0745776	+	0.0430574i	−0.462247	+	0.886751i	$0.652957\pi$
$594$	−0.336822			−0.0138200
$595$	−43.6829	+	2.66610i	−1.79082	+	0.109299i
$596$			28.9654i			1.18647i
$597$	−1.03031	+	1.78455i	−0.0421678	+	0.0730367i
$598$	2.72648	+	0.836316i	0.111494	+	0.0341995i
$599$	10.9316	+	18.9341i	0.446654	+	0.773628i	0.998166	−	0.0605394i	$-0.0192821\pi$
$599$	10.9316	+	18.9341i	0.446654	+	0.773628i	−0.551512	+	0.834167i	$0.685949\pi$
$600$	1.25612	+	0.725222i	0.0512810	+	0.0296071i
$601$	−11.3022			−0.461026			−0.230513	−	0.973069i	$-0.574040\pi$
$601$	−11.3022			−0.461026			−0.230513	+	0.973069i	$0.574040\pi$
$602$	−1.58943	+	3.18687i	−0.0647803	+	0.129887i
$603$			1.62038i			0.0659872i
$604$	39.1947	+	22.6291i	1.59481	+	0.920764i
$605$	−17.6557	+	10.1935i	−0.717806	+	0.414425i
$606$	−1.94396	+	1.12234i	−0.0789679	+	0.0455921i
$607$	−3.58151	+	6.20336i	−0.145369	+	0.251787i	−0.929511	−	0.368795i	$-0.879770\pi$
$607$	−3.58151	+	6.20336i	−0.145369	+	0.251787i	0.784142	+	0.620582i	$0.213104\pi$
$608$	6.16483			0.250017
$609$	−1.00735	+	0.666564i	−0.0408199	+	0.0270106i
$610$	4.50942			0.182581
$611$	−9.61561	−	41.8255i	−0.389006	−	1.69208i
$612$	−6.15900	−	10.6677i	−0.248963	−	0.431216i
$613$	9.29011	−	5.36365i	0.375224	−	0.216636i	−0.300514	−	0.953777i	$-0.597158\pi$
$613$	9.29011	−	5.36365i	0.375224	−	0.216636i	0.675738	+	0.737142i	$0.263825\pi$
$614$	−1.30173	+	2.25466i	−0.0525335	+	0.0909907i
$615$	18.9570			0.764420
$616$	2.94698	−	1.95001i	0.118737	−	0.0785683i
$617$			25.5275i			1.02770i	0.857881	+	0.513849i	$0.171781\pi$
$617$			25.5275i			1.02770i	−0.857881	+	0.513849i	$0.828219\pi$
$618$	0.682253	+	0.393899i	0.0274442	+	0.0158449i
$619$	−17.3694	+	10.0282i	−0.698136	+	0.403069i	−0.806653	−	0.591026i	$-0.798723\pi$
$619$	−17.3694	+	10.0282i	−0.698136	+	0.403069i	0.108517	+	0.994095i	$0.465390\pi$
$620$	8.27605	+	14.3345i	0.332374	+	0.575689i
$621$	2.12496	−	3.68054i	0.0852718	−	0.147695i
$622$		−	4.07008i		−	0.163195i
$623$	0.107947	−	0.216439i	0.00432482	−	0.00867145i
$624$	−9.31861	−	10.0115i	−0.373043	−	0.400779i
$625$	15.4821	−	26.8158i	0.619283	−	1.07263i
$626$	1.36340	−	0.787161i	0.0544925	−	0.0314613i
$627$	−2.55659	−	4.42814i	−0.102100	−	0.176843i
$628$	−19.1950	+	33.2467i	−0.765963	+	1.32669i
$629$		−	21.7603i		−	0.867639i
$630$	−0.0791688	−	1.29715i	−0.00315416	−	0.0516796i
$631$			28.7829i			1.14583i	0.819615	+	0.572915i	$0.194188\pi$
$631$			28.7829i			1.14583i	−0.819615	+	0.572915i	$0.805812\pi$
$632$	7.49361	+	4.32644i	0.298080	+	0.172097i
$633$	−3.28844	−	5.69575i	−0.130704	−	0.226386i
$634$	−2.42700	−	4.20368i	−0.0963883	−	0.166949i
$635$	−1.89391	−	1.09345i	−0.0751573	−	0.0433921i
$636$	−8.79217			−0.348632
$637$	19.3149	+	16.2460i	0.765286	+	0.643691i
$638$	−0.153776			−0.00608806
$639$	1.60620	+	0.927340i	0.0635403	+	0.0366850i
$640$	−7.52226	−	13.0289i	−0.297343	−	0.515014i
$641$	21.4397	+	37.1346i	0.846817	+	1.46673i	0.884034	+	0.467422i	$0.154817\pi$
$641$	21.4397	+	37.1346i	0.846817	+	1.46673i	−0.0372174	+	0.999307i	$0.511849\pi$
$642$	1.32403	+	0.764427i	0.0522552	+	0.0301695i
$643$			26.0950i			1.02909i	0.857465	+	0.514543i	$0.172038\pi$
$643$			26.0950i			1.02909i	−0.857465	+	0.514543i	$0.827962\pi$
$644$	1.34626	+	22.0580i	0.0530502	+	0.869205i
$645$		−	19.0875i		−	0.751568i
$646$	−1.64782	+	2.85411i	−0.0648326	+	0.112293i
$647$	11.7761	+	20.3967i	0.462965	+	0.801879i	0.999107	−	0.0422490i	$-0.0134523\pi$
$647$	11.7761	+	20.3967i	0.462965	+	0.801879i	−0.536142	+	0.844128i	$0.680119\pi$
$648$	0.639130	−	0.369002i	0.0251074	−	0.0144958i
$649$	9.22766	−	15.9828i	0.362218	−	0.627379i
$650$	−0.965362	+	0.898554i	−0.0378646	+	0.0352442i
$651$	3.76815	−	7.55529i	0.147685	−	0.296115i
$652$		−	8.92351i		−	0.349472i
$653$	−20.3276	+	35.2084i	−0.795479	+	1.37781i	0.127056	+	0.991896i	$0.459447\pi$
$653$	−20.3276	+	35.2084i	−0.795479	+	1.37781i	−0.922535	+	0.385914i	$0.873886\pi$
$654$	1.05896	+	1.83417i	0.0414086	+	0.0717217i
$655$	4.37400	−	2.52533i	0.170906	−	0.0986728i
$656$	−23.5968	−	13.6236i	−0.921302	−	0.531914i
$657$		−	14.3095i		−	0.558267i
$658$	−4.88790	+	3.23432i	−0.190550	+	0.126087i
$659$	−34.6922			−1.35142			−0.675708	−	0.737170i	$-0.736162\pi$
$659$	−34.6922			−1.35142			−0.675708	+	0.737170i	$0.736162\pi$
$660$	−4.69364	+	8.12962i	−0.182700	+	0.316445i
$661$	−21.6501	+	12.4997i	−0.842093	+	0.486183i	−0.857975	−	0.513691i	$-0.828278\pi$
$661$	−21.6501	+	12.4997i	−0.842093	+	0.486183i	0.0158820	+	0.999874i	$0.494944\pi$
$662$	−0.421762	−	0.730514i	−0.0163923	−	0.0283922i
$663$	22.0234	−	5.06315i	0.855320	−	0.196636i
$664$	−8.68019			−0.336857
$665$	16.4525	−	10.8866i	0.637999	−	0.422164i
$666$	0.646164			0.0250383
$667$	0.970151	−	1.68035i	0.0375644	−	0.0650634i
$668$	−7.33224	+	4.23327i	−0.283693	+	0.163790i
$669$	24.3930	−	14.0833i	0.943087	−	0.544491i
$670$	−0.689281	−	0.397957i	−0.0266293	−	0.0153744i
$671$			16.6149i			0.641412i
$672$	−2.57658	+	5.16616i	−0.0993938	+	0.199289i
$673$	16.8725			0.650388			0.325194	−	0.945647i	$-0.394570\pi$
$673$	16.8725			0.650388			0.325194	+	0.945647i	$0.394570\pi$
$674$	2.44819	+	1.41346i	0.0943006	+	0.0544445i
$675$	0.982681	+	1.70205i	0.0378234	+	0.0655121i
$676$	22.9845	−	11.1579i	0.884020	−	0.429151i
$677$	−6.44341	+	11.1603i	−0.247640	+	0.428926i	−0.962871	−	0.269963i	$-0.912988\pi$
$677$	−6.44341	+	11.1603i	−0.247640	+	0.428926i	0.715230	+	0.698889i	$0.246322\pi$
$678$			0.555171i			0.0213212i
$679$	−4.28783	+	0.261699i	−0.164552	+	0.0100431i
$680$	12.2075			0.468138
$681$	5.22162	+	3.01470i	0.200093	+	0.115524i
$682$	0.930830	−	0.537415i	0.0356433	−	0.0205787i
$683$	−10.7961	+	6.23311i	−0.413100	+	0.238503i	−0.692121	−	0.721782i	$-0.743323\pi$
$683$	−10.7961	+	6.23311i	−0.413100	+	0.238503i	0.279021	+	0.960285i	$0.409990\pi$
$684$	4.80883	+	2.77638i	0.183870	+	0.106157i
$685$	50.4983			1.92944
$686$	1.15184	−	3.24870i	0.0439775	−	0.124036i
$687$			15.4792i			0.590570i
$688$	−13.7174	+	23.7592i	−0.522971	+	0.905812i
$689$	4.73006	−	15.4205i	0.180201	−	0.587475i
$690$	1.04376	+	1.80784i	0.0397351	+	0.0688232i
$691$	28.3069	+	16.3430i	1.07685	+	0.621717i	0.930044	−	0.367449i	$-0.119769\pi$
$691$	28.3069	+	16.3430i	1.07685	+	0.621717i	0.146802	+	0.989166i	$0.453102\pi$
$692$	38.0520			1.44652
$693$	4.77933	−	0.291697i	0.181552	−	0.0110806i
$694$			6.31465i			0.239701i
$695$	−40.2729	−	23.2516i	−1.52764	−	0.881982i
$696$	0.291795	−	0.168468i	0.0110605	−	0.00638576i
$697$	38.9876	−	22.5095i	1.47676	−	0.852607i
$698$	0.946388	−	1.63919i	0.0358213	−	0.0620443i
$699$	15.5939			0.589816
$700$	−9.14529	−	4.56115i	−0.345659	−	0.172395i
$701$	13.3789			0.505315			0.252657	−	0.967556i	$-0.418695\pi$
$701$	13.3789			0.505315			0.252657	+	0.967556i	$0.418695\pi$
$702$	0.150348	+	0.653979i	0.00567454	+	0.0246828i
$703$	4.90459	+	8.49500i	0.184980	+	0.320395i
$704$	11.2543	−	6.49768i	0.424163	−	0.244891i
$705$	15.7071	−	27.2055i	0.591563	−	1.02462i
$706$	−3.43773			−0.129381
$707$	26.6117	−	17.6090i	1.00084	−	0.662254i
$708$			20.0419i			0.753221i
$709$	11.2668	+	6.50488i	0.423133	+	0.244296i	0.696417	−	0.717638i	$-0.254777\pi$
$709$	11.2668	+	6.50488i	0.423133	+	0.244296i	−0.273284	+	0.961933i	$0.588110\pi$
$710$	−0.788946	+	0.455498i	−0.0296086	+	0.0170945i
$711$	5.86235	+	10.1539i	0.219855	+	0.380801i
$712$	−0.0337328	+	0.0584269i	−0.00126419	+	0.00218964i
$713$			13.5619i			0.507896i
$714$	−1.70305	−	2.57375i	−0.0637350	−	0.0963201i
$715$	−11.7334	−	12.6058i	−0.438803	−	0.471428i
$716$	6.24262	−	10.8125i	0.233297	−	0.404083i
$717$	2.57192	−	1.48490i	0.0960502	−	0.0554546i
$718$	−1.51732	−	2.62807i	−0.0566258	−	0.0980788i
$719$	−6.10225	+	10.5694i	−0.227576	+	0.394173i	−0.957089	−	0.289794i	$-0.906413\pi$
$719$	−6.10225	+	10.5694i	−0.227576	+	0.394173i	0.729513	+	0.683966i	$0.239747\pi$
$720$		−	10.0115i		−	0.373105i
$721$	−10.0219	−	4.99836i	−0.373236	−	0.186149i
$722$			2.05052i			0.0763124i
$723$	3.64444	+	2.10412i	0.135538	+	0.0782529i
$724$	−7.09914	−	12.2961i	−0.263837	−	0.456980i
$725$	0.448643	+	0.777073i	0.0166622	+	0.0288597i
$726$	−1.24505	−	0.718833i	−0.0462083	−	0.0266784i
$727$	29.5079			1.09439			0.547194	−	0.837006i	$-0.315696\pi$
$727$	29.5079			1.09439			0.547194	+	0.837006i	$0.315696\pi$
$728$	−5.10162	−	4.85145i	−0.189079	−	0.179807i
$729$	1.00000			0.0370370
$730$	6.08699	+	3.51433i	0.225290	+	0.130071i
$731$	−22.6644	−	39.2559i	−0.838272	−	1.45193i
$732$	−9.02165	−	15.6260i	−0.333450	−	0.577552i
$733$	20.7832	+	11.9992i	0.767646	+	0.443201i	0.832034	−	0.554724i	$-0.187176\pi$
$733$	20.7832	+	11.9992i	0.767646	+	0.443201i	−0.0643881	+	0.997925i	$0.520510\pi$
$734$		−	4.82448i		−	0.178075i
$735$	2.24673	+	18.3373i	0.0828717	+	0.676380i
$736$		−	9.27334i		−	0.341820i
$737$	1.46627	−	2.53965i	0.0540106	−	0.0935492i
$738$	0.668411	+	1.15772i	0.0246046	+	0.0426163i
$739$	1.62405	−	0.937647i	0.0597417	−	0.0344919i	−0.469832	−	0.882756i	$-0.655685\pi$
$739$	1.62405	−	0.937647i	0.0597417	−	0.0344919i	0.529573	+	0.848264i	$0.322352\pi$
$740$	9.00433	−	15.5960i	0.331006	−	0.573319i
$741$	−7.45655	+	6.94051i	−0.273923	+	0.254966i
$742$	−2.19873	+	0.134195i	−0.0807178	+	0.00492645i
$743$		−	26.7562i		−	0.981590i	−0.871275	−	0.490795i	$-0.836706\pi$
$743$		−	26.7562i		−	0.981590i	0.871275	−	0.490795i	$-0.163294\pi$
$744$	−1.17752	+	2.03952i	−0.0431699	+	0.0747725i
$745$	−19.4482	−	33.6853i	−0.712527	−	1.23413i
$746$	−3.78218	+	2.18364i	−0.138475	+	0.0799488i
$747$	−10.1859	−	5.88086i	−0.372684	−	0.215169i
$748$			22.2928i			0.815107i
$749$	−19.4492	−	9.70017i	−0.710660	−	0.354436i
$750$	1.49058			0.0544282
$751$	−0.160060	+	0.277231i	−0.00584066	+	0.0101163i	−0.868931	−	0.494933i	$-0.835192\pi$
$751$	−0.160060	+	0.277231i	−0.00584066	+	0.0101163i	0.863090	+	0.505050i	$0.168526\pi$
$752$	−39.1030	+	22.5761i	−1.42594	+	0.823266i
$753$	4.90026	+	8.48751i	0.178576	+	0.309302i
$754$	0.0686416	+	0.298574i	0.00249978	+	0.0108734i
$755$	−60.7751			−2.21183
$756$	−4.33646	+	2.86943i	−0.157716	+	0.104360i
$757$	−18.5240			−0.673267			−0.336633	−	0.941636i	$-0.609288\pi$
$757$	−18.5240			−0.673267			−0.336633	+	0.941636i	$0.609288\pi$
$758$	−1.36638	+	2.36663i	−0.0496290	+	0.0859600i
$759$	−6.66096	+	3.84571i	−0.241777	+	0.139590i
$760$	−4.76571	+	2.75148i	−0.172870	+	0.0998067i
$761$	4.87428	+	2.81417i	0.176693	+	0.102014i	0.585738	−	0.810501i	$-0.300805\pi$
$761$	4.87428	+	2.81417i	0.176693	+	0.102014i	−0.409045	+	0.912514i	$0.634138\pi$
$762$		−	0.154217i		−	0.00558668i
$763$	−16.6145	−	25.1088i	−0.601485	−	0.909000i
$764$	2.18660			0.0791086
$765$	14.3252	+	8.27065i	0.517928	+	0.299026i
$766$	2.12452	+	3.67977i	0.0767619	+	0.132956i
$767$	−35.1514	−	10.7823i	−1.26924	−	0.389325i
$768$	−6.65019	+	11.5185i	−0.239968	+	0.415637i
$769$		−	19.6058i		−	0.707003i	−0.935434	−	0.353501i	$-0.884991\pi$
$769$		−	19.6058i		−	0.707003i	0.935434	−	0.353501i	$-0.115009\pi$
$770$	−1.04969	+	2.10467i	−0.0378283	+	0.0758472i
$771$	−24.9230			−0.897579
$772$	−46.3325	−	26.7501i	−1.66754	−	0.962756i
$773$	−28.2961	+	16.3368i	−1.01774	+	0.587593i	−0.913449	−	0.406953i	$-0.866591\pi$
$773$	−28.2961	+	16.3368i	−1.01774	+	0.587593i	−0.104293	+	0.994547i	$0.533258\pi$
$774$	1.16569	−	0.673011i	0.0418998	−	0.0241909i
$775$	−5.43140	−	3.13582i	−0.195102	−	0.112642i
$776$	1.19827			0.0430154
$777$	−9.16872	+	0.559594i	−0.328926	+	0.0200753i
$778$			4.76179i			0.170719i
$779$	−10.1469	+	17.5750i	−0.363551	+	0.629689i
$780$	17.8797	+	5.48438i	0.640195	+	0.196372i
$781$	−1.67828	−	2.90686i	−0.0600535	−	0.104016i
$782$	4.29324	+	2.47870i	0.153526	+	0.0886382i
$783$	0.456550			0.0163158
$784$	10.3816	−	24.4400i	0.370773	−	0.872859i
$785$		−	51.5522i		−	1.83998i
$786$	0.308449	+	0.178083i	0.0110020	+	0.00635200i
$787$	−2.90270	+	1.67588i	−0.103470	+	0.0597385i	−0.550842	−	0.834609i	$-0.685693\pi$
$787$	−2.90270	+	1.67588i	−0.103470	+	0.0597385i	0.447372	+	0.894348i	$0.352360\pi$
$788$	32.4168	−	18.7159i	1.15480	−	0.666725i
$789$	−8.95686	+	15.5137i	−0.318872	+	0.552303i
$790$	−5.75903			−0.204897
$791$	−0.480793	−	7.87758i	−0.0170950	−	0.280095i
$792$	−1.33562			−0.0474593
$793$	32.2598	−	7.41646i	1.14558	−	0.263366i
$794$	1.73739	+	3.00925i	0.0616577	+	0.106794i
$795$	10.2248	−	5.90331i	0.362637	−	0.209369i
$796$	−2.02493	+	3.50728i	−0.0717718	+	0.124312i
$797$	−43.8379			−1.55282			−0.776409	−	0.630230i	$-0.782961\pi$
$797$	−43.8379			−1.55282			−0.776409	+	0.630230i	$0.782961\pi$
$798$	1.24496	+	0.620913i	0.0440710	+	0.0219801i
$799$		−	74.6021i		−	2.63923i
$800$	3.71388	+	2.14421i	0.131306	+	0.0758094i
$801$	−0.0791688	+	0.0457081i	−0.00279729	+	0.00161502i
$802$	0.784421	+	1.35866i	0.0276989	+	0.0479758i
$803$	−12.9485	+	22.4275i	−0.456943	+	0.791448i
$804$			3.18464i			0.112314i
$805$	−16.3760	−	24.7483i	−0.577177	−	0.872263i
$806$	−1.45895	−	1.56742i	−0.0513893	−	0.0552102i
$807$	15.6070	−	27.0322i	0.549394	−	0.951578i
$808$	−7.70850	+	4.45050i	−0.271184	+	0.156568i
$809$	−7.66720	−	13.2800i	−0.269564	−	0.466899i	0.699185	−	0.714941i	$-0.253546\pi$
$809$	−7.66720	−	13.2800i	−0.269564	−	0.466899i	−0.968749	+	0.248042i	$0.920213\pi$
$810$	−0.245594	+	0.425381i	−0.00862929	+	0.0149464i
$811$		−	50.2060i		−	1.76297i	−0.472211	−	0.881485i	$-0.656544\pi$
$811$		−	50.2060i		−	1.76297i	0.472211	−	0.881485i	$-0.343456\pi$
$812$	−1.97981	+	1.31004i	−0.0694777	+	0.0459734i
$813$			22.7308i			0.797204i
$814$	−1.01274	−	0.584706i	−0.0354966	−	0.0204939i
$815$	5.99149	+	10.3776i	0.209873	+	0.363510i
$816$	−11.8876	−	20.5899i	−0.416148	−	0.720790i
$817$	17.6959	+	10.2167i	0.619102	+	0.357439i
$818$	−2.52552			−0.0883026
$819$	−2.69973	−	9.14940i	−0.0943361	−	0.319706i
$820$	37.2574			1.30108
$821$	37.9067	+	21.8855i	1.32295	+	0.763808i	0.984199	−	0.177067i	$-0.0566609\pi$
$821$	37.9067	+	21.8855i	1.32295	+	0.763808i	0.338755	+	0.940875i	$0.389994\pi$
$822$	1.78054	+	3.08398i	0.0621034	+	0.107566i
$823$	16.2062	+	28.0699i	0.564911	+	0.978455i	0.997058	+	0.0766519i	$0.0244230\pi$
$823$	16.2062	+	28.0699i	0.564911	+	0.978455i	−0.432146	+	0.901803i	$0.642244\pi$
$824$	2.70538	+	1.56195i	0.0942464	+	0.0544132i
$825$		−	3.55687i		−	0.123834i
$826$	0.305900	+	5.01204i	0.0106436	+	0.174391i
$827$		−	45.6351i		−	1.58689i	−0.608642	−	0.793445i	$-0.708286\pi$
$827$		−	45.6351i		−	1.58689i	0.608642	−	0.793445i	$-0.291714\pi$
$828$	4.17632	−	7.23360i	0.145137	−	0.251385i
$829$	12.4703	+	21.5992i	0.433111	+	0.750171i	0.997139	−	0.0755847i	$-0.0240823\pi$
$829$	12.4703	+	21.5992i	0.433111	+	0.750171i	−0.564028	+	0.825756i	$0.690749\pi$
$830$	5.00321	−	2.88861i	0.173664	−	0.100265i
$831$	−5.81069	+	10.0644i	−0.201571	+	0.349131i
$832$	−17.6396	−	18.9511i	−0.611544	−	0.657013i
$833$	26.3943	+	35.0452i	0.914507	+	1.21424i
$834$		−	3.27934i		−	0.113554i
$835$	5.68467	−	9.84614i	0.196726	−	0.340740i
$836$	−5.02463	−	8.70291i	−0.173780	−	0.300996i
$837$	−2.76356	+	1.59554i	−0.0955227	+	0.0551501i
$838$	0.490221	+	0.283029i	0.0169344	+	0.00977709i
$839$			48.0402i			1.65853i	0.558854	+	0.829266i	$0.311241\pi$
$839$			48.0402i			1.65853i	−0.558854	+	0.829266i	$0.688759\pi$
$840$	−0.313933	−	5.14366i	−0.0108317	−	0.177473i
$841$	−28.7916			−0.992812
$842$	−0.276809	+	0.479447i	−0.00953945	+	0.0165228i
$843$	15.2754	−	8.81926i	0.526113	−	0.303751i
$844$	−6.46298	−	11.1942i	−0.222465	−	0.385321i
$845$	−19.2380	+	28.4085i	−0.661809	+	0.977283i
$846$	2.21528			0.0761630
$847$	18.2892	+	9.12160i	0.628424	+	0.313422i
$848$	−16.9699			−0.582749
$849$	−4.66423	+	8.07869i	−0.160076	+	0.277260i
$850$	−1.98539	+	1.14627i	−0.0680984	+	0.0393166i
$851$	12.7785	−	7.37765i	0.438040	−	0.252902i
$852$	3.15676	+	1.82256i	0.108149	+	0.0624398i
$853$		−	7.77367i		−	0.266165i	−0.991105	−	0.133083i	$-0.957512\pi$
$853$		−	7.77367i		−	0.266165i	0.991105	−	0.133083i	$-0.0424876\pi$
$854$	−2.49461	−	3.77000i	−0.0853638	−	0.129007i
$855$	−7.45655			−0.255009
$856$	5.25025	+	3.03123i	0.179450	+	0.103605i
$857$	−6.99073	−	12.1083i	−0.238799	−	0.413611i	0.721571	−	0.692340i	$-0.243420\pi$
$857$	−6.99073	−	12.1083i	−0.238799	−	0.413611i	−0.960370	+	0.278729i	$0.910087\pi$
$858$	0.356135	−	1.16104i	0.0121582	−	0.0396372i
$859$	−8.95534	+	15.5111i	−0.305552	+	0.529232i	−0.977384	−	0.211472i	$-0.932174\pi$
$859$	−8.95534	+	15.5111i	−0.305552	+	0.529232i	0.671832	+	0.740704i	$0.265508\pi$
$860$		−	37.5138i		−	1.27921i
$861$	−10.4870	−	15.8486i	−0.357396	−	0.540118i
$862$	−6.62915			−0.225790
$863$	−4.00982	−	2.31507i	−0.136496	−	0.0788059i	0.430197	−	0.902735i	$-0.358444\pi$
$863$	−4.00982	−	2.31507i	−0.136496	−	0.0788059i	−0.566693	+	0.823929i	$0.691777\pi$
$864$	1.88967	−	1.09100i	0.0642879	−	0.0371166i
$865$	−44.2524	+	25.5491i	−1.50463	+	0.868697i
$866$	2.17882	+	1.25794i	0.0740393	+	0.0427466i
$867$	22.2821			0.756741
$868$	7.40577	−	14.8489i	0.251368	−	0.504004i
$869$		−	21.2191i		−	0.719809i
$870$	−0.112126	+	0.194208i	−0.00380142	+	0.00658426i
$871$	−5.58552	−	1.71329i	−0.189258	−	0.0580527i
$872$	4.19915	+	7.27315i	0.142201	+	0.246300i
$873$	1.40613	+	0.811832i	0.0475904	+	0.0274764i
$874$	−2.23472			−0.0755905
$875$	−21.1505	+	1.29088i	−0.715017	+	0.0436396i
$876$		−	28.1233i		−	0.950200i
$877$	−5.52010	−	3.18703i	−0.186401	−	0.107618i	0.403896	−	0.914805i	$-0.367656\pi$
$877$	−5.52010	−	3.18703i	−0.186401	−	0.107618i	−0.590296	+	0.807187i	$0.700989\pi$
$878$	−5.27277	+	3.04424i	−0.177948	+	0.102738i
$879$	−7.17645	+	4.14333i	−0.242056	+	0.139751i
$880$	−9.05925	+	15.6911i	−0.305387	+	0.528946i
$881$	3.66287			0.123405			0.0617026	−	0.998095i	$-0.480347\pi$
$881$	3.66287			0.123405			0.0617026	+	0.998095i	$0.480347\pi$
$882$	−1.04066	+	0.783769i	−0.0350407	+	0.0263909i
$883$	26.1018			0.878395			0.439198	−	0.898390i	$-0.355263\pi$
$883$	26.1018			0.878395			0.439198	+	0.898390i	$0.355263\pi$
$884$	43.2841	−	9.95092i	1.45580	−	0.334686i
$885$	−13.4567	−	23.3077i	−0.452342	−	0.783479i
$886$	−3.44422	+	1.98852i	−0.115711	+	0.0668058i
$887$	−29.3395	+	50.8175i	−0.985124	+	1.70628i	−0.343738	+	0.939066i	$0.611693\pi$
$887$	−29.3395	+	50.8175i	−0.985124	+	1.70628i	−0.641386	+	0.767219i	$0.721640\pi$
$888$	2.56227			0.0859843
$889$	0.133556	+	2.18825i	0.00447931	+	0.0733916i
$890$		−	0.0449026i		−	0.00150514i
$891$	−1.56731	−	0.904889i	−0.0525070	−	0.0303149i
$892$	47.9410	−	27.6788i	1.60518	−	0.926753i
$893$	16.8147	+	29.1240i	0.562683	+	0.974596i
$894$	1.37146	−	2.37544i	0.0458685	−	0.0794466i
$895$			16.7659i			0.560421i
$896$	−6.73124	+	13.4964i	−0.224875	+	0.450884i
$897$	10.4401	+	11.2164i	0.348586	+	0.374504i
$898$	1.79232	−	3.10438i	0.0598104	−	0.103595i
$899$	−1.26171	+	0.728446i	−0.0420802	+	0.0242950i
$900$	1.93132	+	3.34515i	0.0643775	+	0.111505i
$901$	14.0191	−	24.2819i	0.467045	−	0.808946i
$902$		−	2.41935i		−	0.0805556i
$903$	−15.9577	+	10.5592i	−0.531037	+	0.351387i
$904$			2.20146i			0.0732193i
$905$	16.5118	+	9.53311i	0.548872	+	0.316891i
$906$	−2.14289	−	3.71160i	−0.0711928	−	0.123309i
$907$	−24.8995	−	43.1272i	−0.826775	−	1.43202i	−0.900555	−	0.434741i	$-0.856840\pi$
$907$	−24.8995	−	43.1272i	−0.826775	−	1.43202i	0.0737808	−	0.997274i	$-0.476493\pi$
$908$	10.2624	+	5.92498i	0.340569	+	0.196627i
$909$	−12.0609			−0.400035
$910$	4.55502	+	1.09862i	0.150997	+	0.0364190i
$911$	11.6112			0.384696			0.192348	−	0.981327i	$-0.438390\pi$
$911$	11.6112			0.384696			0.192348	+	0.981327i	$0.438390\pi$
$912$	9.28159	+	5.35873i	0.307344	+	0.177445i
$913$	10.6430	+	18.4343i	0.352233	+	0.610086i
$914$	−1.15215	−	1.99558i	−0.0381096	−	0.0660078i
$915$	20.9834	+	12.1148i	0.693690	+	0.400502i
$916$			30.4223i			1.00518i
$917$	−4.53094	−	2.25977i	−0.149625	−	0.0746243i
$918$			1.16647i			0.0384992i
$919$	−17.6160	+	30.5118i	−0.581098	+	1.00649i	0.414251	+	0.910163i	$0.364044\pi$
$919$	−17.6160	+	30.5118i	−0.581098	+	1.00649i	−0.995350	+	0.0963293i	$0.969290\pi$
$920$	4.13887	+	7.16873i	0.136454	+	0.236346i
$921$	−12.1145	+	6.99431i	−0.399186	+	0.230470i
$922$	2.15723	−	3.73643i	0.0710446	−	0.123053i
$923$	−4.89487	+	4.55611i	−0.161116	+	0.149966i
$924$	9.39311	−	0.573290i	0.309011	−	0.0188598i
$925$			6.82354i			0.224356i
$926$	1.60764	−	2.78452i	0.0528304	−	0.0915049i
$927$	2.11645	+	3.66581i	0.0695135	+	0.120401i
$928$	0.862729	−	0.498097i	0.0283205	−	0.0163508i
$929$	−13.5692	−	7.83421i	−0.445192	−	0.257032i	0.260605	−	0.965445i	$-0.416078\pi$
$929$	−13.5692	−	7.83421i	−0.445192	−	0.257032i	−0.705798	+	0.708414i	$0.749411\pi$
$930$		−	1.56742i		−	0.0513979i
$931$	−18.2030	−	7.73226i	−0.596579	−	0.253414i
$932$	30.6477			1.00390
$933$	10.9344	−	18.9390i	0.357978	−	0.620035i
$934$	−1.43525	+	0.828643i	−0.0469628	+	0.0271140i
$935$	−14.9680	−	25.9254i	−0.489507	−	0.847851i
$936$	0.596186	+	2.59326i	0.0194870	+	0.0847634i
$937$	24.1364			0.788503			0.394251	−	0.919003i	$-0.371004\pi$
$937$	24.1364			0.788503			0.394251	+	0.919003i	$0.371004\pi$
$938$	0.0486072	+	0.796408i	0.00158708	+	0.0260036i
$939$	8.45897			0.276048
$940$	30.8701	−	53.4686i	1.00687	−	1.74395i
$941$	−30.0408	+	17.3441i	−0.979302	+	0.565400i	−0.902059	−	0.431612i	$-0.857945\pi$
$941$	−30.0408	+	17.3441i	−0.979302	+	0.565400i	−0.0772426	+	0.997012i	$0.524612\pi$
$942$	3.14834	−	1.81770i	0.102578	−	0.0592237i
$943$	26.4368	+	15.2633i	0.860902	+	0.497042i
$944$			38.6832i			1.25903i
$945$	3.11645	−	6.24862i	0.101378	−	0.203268i
$946$	−2.43600			−0.0792012
$947$	−40.5508	−	23.4120i	−1.31772	−	0.760788i	−0.334362	−	0.942445i	$-0.608521\pi$
$947$	−40.5508	−	23.4120i	−1.31772	−	0.760788i	−0.983362	+	0.181657i	$0.941854\pi$
$948$	11.5216	+	19.9561i	0.374206	+	0.648143i
$949$	49.3253	+	15.1300i	1.60117	+	0.491139i
$950$	0.516719	−	0.894984i	0.0167646	−	0.0290371i
$951$		−	26.0809i		−	0.845732i
$952$	−6.75321	−	10.2058i	−0.218873	−	0.330773i
$953$	45.1284			1.46185			0.730926	−	0.682457i	$-0.239088\pi$
$953$	45.1284			1.46185			0.730926	+	0.682457i	$0.239088\pi$
$954$	0.721041	+	0.416293i	0.0233446	+	0.0134780i
$955$	−2.54290	+	1.46815i	−0.0822865	+	0.0475081i
$956$	5.05476	−	2.91837i	0.163483	−	0.0943867i
$957$	−0.715557	−	0.413127i	−0.0231307	−	0.0133545i
$958$	−3.16896			−0.102384
$959$	−27.9357	−	42.2180i	−0.902090	−	1.36329i
$960$		−	18.9511i		−	0.611645i
$961$	−10.4085	+	18.0280i	−0.335757	+	0.581549i
$962$	−0.683213	+	2.22735i	−0.0220277	+	0.0718126i
$963$	4.10734	+	7.11412i	0.132357	+	0.229249i
$964$	7.16264	+	4.13535i	0.230693	+	0.133191i
$965$	71.8429			2.31271
$966$	0.933998	−	1.87270i	0.0300509	−	0.0602533i
$967$			40.1853i			1.29227i	0.763223	+	0.646135i	$0.223616\pi$
$967$			40.1853i			1.29227i	−0.763223	+	0.646135i	$0.776384\pi$
$968$	−4.93709	−	2.85043i	−0.158684	−	0.0916164i
$969$	−15.3354	+	8.85388i	−0.492643	+	0.284428i
$970$	−0.690676	+	0.398762i	−0.0221763	+	0.0128035i
$971$	26.4954	−	45.8913i	0.850277	−	1.47272i	−0.0306815	−	0.999529i	$-0.509768\pi$
$971$	26.4954	−	45.8913i	0.850277	−	1.47272i	0.880958	−	0.473194i	$-0.156899\pi$
$972$	1.96536			0.0630390
$973$	2.83999	+	46.5320i	0.0910459	+	1.49175i
$974$	5.22988			0.167576
$975$	−6.90606	+	1.58769i	−0.221171	+	0.0508468i
$976$	−17.4128	−	30.1599i	−0.557370	−	0.965394i
$977$	−34.1202	+	19.6993i	−1.09160	+	0.630236i	−0.934002	−	0.357267i	$-0.883708\pi$
$977$	−34.1202	+	19.6993i	−1.09160	+	0.630236i	−0.157598	+	0.987503i	$0.550375\pi$
$978$	−0.422512	+	0.731812i	−0.0135104	+	0.0234008i
$979$	0.165443			0.00528758
$980$	4.41563	+	36.0393i	0.141052	+	1.15123i
$981$			11.3798i			0.363328i
$982$	−0.637636	−	0.368140i	−0.0203478	−	0.0117478i
$983$	1.01967	−	0.588707i	0.0325225	−	0.0187768i	−0.483651	−	0.875261i	$-0.660689\pi$
$983$	1.01967	−	0.588707i	0.0325225	−	0.0187768i	0.516173	+	0.856484i	$0.327356\pi$
$984$	2.65049	+	4.59079i	0.0844946	+	0.146349i
$985$	−25.1327	+	43.5311i	−0.800795	+	1.38702i
$986$			0.532552i			0.0169599i
$987$	−31.4337	+	1.91849i	−1.00055	+	0.0610663i
$988$	−14.6548	+	13.6406i	−0.466232	+	0.433966i
$989$	15.3684	−	26.6188i	0.488685	−	0.846428i
$990$	0.769845	−	0.444470i	0.0244673	−	0.0141262i
$991$	7.48344	+	12.9617i	0.237719	+	0.411742i	0.960059	−	0.279796i	$-0.0902668\pi$
$991$	7.48344	+	12.9617i	0.237719	+	0.411742i	−0.722340	+	0.691538i	$0.756933\pi$
$992$	−3.48148	+	6.03010i	−0.110537	+	0.191456i
$993$		−	4.53233i		−	0.143829i
$994$	0.817254	+	0.407599i	0.0259217	+	0.0129283i
$995$		−	5.43838i		−	0.172408i
$996$	−20.0191	−	11.5580i	−0.634328	−	0.366230i
$997$	−14.6275	−	25.3355i	−0.463257	−	0.802385i	0.535864	−	0.844304i	$-0.319986\pi$
$997$	−14.6275	−	25.3355i	−0.463257	−	0.802385i	−0.999121	+	0.0419198i	$0.986653\pi$
$998$	−1.13855	−	1.97203i	−0.0360402	−	0.0624235i
$999$	3.00675	+	1.73595i	0.0951294	+	0.0549230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.c.142.4	yes	16
3.2	odd	2		819.2.dl.f.415.5		16
7.2	even	3		1911.2.c.n.883.5		8
7.4	even	3	inner	273.2.bj.c.25.5	yes	16
7.5	odd	6		1911.2.c.k.883.5		8
13.12	even	2	inner	273.2.bj.c.142.5	yes	16
21.11	odd	6		819.2.dl.f.298.4		16
39.38	odd	2		819.2.dl.f.415.4		16
91.12	odd	6		1911.2.c.k.883.4		8
91.25	even	6	inner	273.2.bj.c.25.4	✓	16
91.51	even	6		1911.2.c.n.883.4		8
273.116	odd	6		819.2.dl.f.298.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.c.25.4	✓	16	91.25	even	6	inner
273.2.bj.c.25.5	yes	16	7.4	even	3	inner
273.2.bj.c.142.4	yes	16	1.1	even	1	trivial
273.2.bj.c.142.5	yes	16	13.12	even	2	inner
819.2.dl.f.298.4		16	21.11	odd	6
819.2.dl.f.298.5		16	273.116	odd	6
819.2.dl.f.415.4		16	39.38	odd	2
819.2.dl.f.415.5		16	3.2	odd	2
1911.2.c.k.883.4		8	91.12	odd	6
1911.2.c.k.883.5		8	7.5	odd	6
1911.2.c.n.883.4		8	91.51	even	6
1911.2.c.n.883.5		8	7.2	even	3

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.161178 - 0.0930563i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.982681 - 1.70205i) q^{4} +(2.28561 + 1.31960i) q^{5} +0.186113i q^{6} +(-0.161178 - 2.64084i) q^{7} +0.738004i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.161178 - 0.0930563i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.982681 - 1.70205i) q^{4} +(2.28561 + 1.31960i) q^{5} +0.186113i q^{6} +(-0.161178 - 2.64084i) q^{7} +0.738004i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.245594 - 0.425381i) q^{10} +(1.56731 - 0.904889i) q^{11} +(-0.982681 + 1.70205i) q^{12} +(-2.45655 - 2.63920i) q^{13} +(-0.219768 + 0.440644i) q^{14} -2.63920i q^{15} +(-1.89669 + 3.28516i) q^{16} +(-3.13377 - 5.42785i) q^{17} +(0.161178 - 0.0930563i) q^{18} +(2.44679 + 1.41265i) q^{19} -5.18698i q^{20} +(-2.20644 + 1.46000i) q^{21} -0.336822 q^{22} +(2.12496 - 3.68054i) q^{23} +(0.639130 - 0.369002i) q^{24} +(0.982681 + 1.70205i) q^{25} +(0.150348 + 0.653979i) q^{26} +1.00000 q^{27} +(-4.33646 + 2.86943i) q^{28} +0.456550 q^{29} +(-0.245594 + 0.425381i) q^{30} +(-2.76356 + 1.59554i) q^{31} +(1.88967 - 1.09100i) q^{32} +(-1.56731 - 0.904889i) q^{33} +1.16647i q^{34} +(3.11645 - 6.24862i) q^{35} +1.96536 q^{36} +(3.00675 + 1.73595i) q^{37} +(-0.262913 - 0.455379i) q^{38} +(-1.05734 + 3.44703i) q^{39} +(-0.973869 + 1.68679i) q^{40} +7.18287i q^{41} +(0.491493 - 0.0299973i) q^{42} +7.23230 q^{43} +(-3.08034 - 1.77843i) q^{44} +(-2.28561 + 1.31960i) q^{45} +(-0.684995 + 0.395482i) q^{46} +(10.3082 + 5.95146i) q^{47} +3.79337 q^{48} +(-6.94804 + 0.851291i) q^{49} -0.365779i q^{50} +(-3.13377 + 5.42785i) q^{51} +(-2.07805 + 6.77467i) q^{52} +(2.23678 + 3.87422i) q^{53} +(-0.161178 - 0.0930563i) q^{54} +4.77636 q^{55} +(1.94895 - 0.118950i) q^{56} -2.82531i q^{57} +(-0.0735859 - 0.0424849i) q^{58} +(8.83136 - 5.09879i) q^{59} +(-4.49205 + 2.59349i) q^{60} +(-4.59032 + 7.95067i) q^{61} +0.593902 q^{62} +(2.36762 + 1.18083i) q^{63} +7.18065 q^{64} +(-2.13204 - 9.27384i) q^{65} +(0.168411 + 0.291697i) q^{66} +(1.40329 - 0.810192i) q^{67} +(-6.15900 + 10.6677i) q^{68} -4.24992 q^{69} +(-1.08378 + 0.717136i) q^{70} -1.85468i q^{71} +(-0.639130 - 0.369002i) q^{72} +(-12.3924 + 7.15475i) q^{73} +(-0.323082 - 0.559594i) q^{74} +(0.982681 - 1.70205i) q^{75} -5.55276i q^{76} +(-2.64228 - 3.99317i) q^{77} +(0.491188 - 0.457195i) q^{78} +(5.86235 - 10.1539i) q^{79} +(-8.67018 + 5.00573i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.668411 - 1.15772i) q^{82} +11.7617i q^{83} +(4.65323 + 2.32077i) q^{84} -16.5413i q^{85} +(-1.16569 - 0.673011i) q^{86} +(-0.228275 - 0.395384i) q^{87} +(0.667811 + 1.15668i) q^{88} +(0.0791688 + 0.0457081i) q^{89} +0.491188 q^{90} +(-6.57375 + 6.91273i) q^{91} -8.35264 q^{92} +(2.76356 + 1.59554i) q^{93} +(-1.10764 - 1.91849i) q^{94} +(3.72828 + 6.45756i) q^{95} +(-1.88967 - 1.09100i) q^{96} -1.62366i q^{97} +(1.19909 + 0.509350i) q^{98} +1.80978i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{13} + 40 q^{14} - 10 q^{16} - 8 q^{17} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} + 16 q^{27} - 36 q^{29} - 4 q^{30} - 14 q^{35} - 12 q^{36} - 26 q^{38} - 2 q^{39} + 6 q^{40} - 14 q^{42} + 32 q^{43} + 20 q^{48} - 46 q^{49} - 8 q^{51} + 40 q^{52} + 36 q^{53} - 8 q^{55} + 54 q^{56} + 12 q^{61} - 80 q^{62} - 56 q^{64} + 34 q^{65} + 4 q^{66} + 10 q^{68} + 16 q^{69} + 18 q^{74} - 6 q^{75} - 22 q^{77} + 8 q^{78} + 8 q^{79} - 8 q^{81} + 12 q^{82} + 18 q^{87} - 98 q^{88} + 8 q^{90} + 16 q^{91} + 40 q^{92} + 46 q^{94} + 38 q^{95}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^13 + 40 * q^14 - 10 * q^16 - 8 * q^17 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 + 16 * q^27 - 36 * q^29 - 4 * q^30 - 14 * q^35 - 12 * q^36 - 26 * q^38 - 2 * q^39 + 6 * q^40 - 14 * q^42 + 32 * q^43 + 20 * q^48 - 46 * q^49 - 8 * q^51 + 40 * q^52 + 36 * q^53 - 8 * q^55 + 54 * q^56 + 12 * q^61 - 80 * q^62 - 56 * q^64 + 34 * q^65 + 4 * q^66 + 10 * q^68 + 16 * q^69 + 18 * q^74 - 6 * q^75 - 22 * q^77 + 8 * q^78 + 8 * q^79 - 8 * q^81 + 12 * q^82 + 18 * q^87 - 98 * q^88 + 8 * q^90 + 16 * q^91 + 40 * q^92 + 46 * q^94 + 38 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more