LMFDB - Embedded newform 43.2.c.b.6.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	43.6
Dual form			43.2.c.b.36.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.381966 q^{2} +(1.30902 - 2.26728i) q^{3} -1.85410 q^{4} +(-0.618034 + 1.07047i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.11803 + 3.66854i) q^{7} +1.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})$	\(q-0.381966 q^{2} +(1.30902 - 2.26728i) q^{3} -1.85410 q^{4} +(-0.618034 + 1.07047i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.11803 + 3.66854i) q^{7} +1.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(0.236068 - 0.408882i) q^{10} -3.61803 q^{11} +(-2.42705 + 4.20378i) q^{12} +(-0.690983 - 1.19682i) q^{13} +(-0.809017 - 1.40126i) q^{14} +(1.61803 + 2.80252i) q^{15} +3.14590 q^{16} +(-3.04508 - 5.27424i) q^{17} +(0.736068 + 1.27491i) q^{18} +(0.618034 - 1.07047i) q^{19} +(1.14590 - 1.98475i) q^{20} +11.0902 q^{21} +1.38197 q^{22} +(-2.19098 + 3.79489i) q^{23} +(1.92705 - 3.33775i) q^{24} +(1.73607 + 3.00696i) q^{25} +(0.263932 + 0.457144i) q^{26} -2.23607 q^{27} +(-3.92705 - 6.80185i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-0.618034 - 1.07047i) q^{30} -4.14590 q^{32} +(-4.73607 + 8.20311i) q^{33} +(1.16312 + 2.01458i) q^{34} -5.23607 q^{35} +(3.57295 + 6.18853i) q^{36} +(2.42705 - 4.20378i) q^{37} +(-0.236068 + 0.408882i) q^{38} -3.61803 q^{39} +(-0.909830 + 1.57587i) q^{40} +9.47214 q^{41} -4.23607 q^{42} +(-6.50000 + 0.866025i) q^{43} +6.70820 q^{44} +4.76393 q^{45} +(0.836881 - 1.44952i) q^{46} +1.14590 q^{47} +(4.11803 - 7.13264i) q^{48} +(-5.47214 + 9.47802i) q^{49} +(-0.663119 - 1.14856i) q^{50} -15.9443 q^{51} +(1.28115 + 2.21902i) q^{52} +(0.690983 - 1.19682i) q^{53} +0.854102 q^{54} +(2.23607 - 3.87298i) q^{55} +(3.11803 + 5.40059i) q^{56} +(-1.61803 - 2.80252i) q^{57} +(0.572949 + 0.992377i) q^{58} +5.09017 q^{59} +(-3.00000 - 5.19615i) q^{60} +(-1.42705 - 2.47172i) q^{61} +(8.16312 - 14.1389i) q^{63} -4.70820 q^{64} +1.70820 q^{65} +(1.80902 - 3.13331i) q^{66} +(1.92705 - 3.33775i) q^{67} +(5.64590 + 9.77898i) q^{68} +(5.73607 + 9.93516i) q^{69} +2.00000 q^{70} +(5.39919 + 9.35167i) q^{71} +(-2.83688 - 4.91362i) q^{72} +(-0.927051 - 1.60570i) q^{73} +(-0.927051 + 1.60570i) q^{74} +9.09017 q^{75} +(-1.14590 + 1.98475i) q^{76} +(-7.66312 - 13.2729i) q^{77} +1.38197 q^{78} +(0.690983 + 1.19682i) q^{79} +(-1.94427 + 3.36758i) q^{80} +(2.85410 - 4.94345i) q^{81} -3.61803 q^{82} +(-8.01722 + 13.8862i) q^{83} -20.5623 q^{84} +7.52786 q^{85} +(2.48278 - 0.330792i) q^{86} -7.85410 q^{87} -5.32624 q^{88} +(0.927051 - 1.60570i) q^{89} -1.81966 q^{90} +(2.92705 - 5.06980i) q^{91} +(4.06231 - 7.03612i) q^{92} -0.437694 q^{94} +(0.763932 + 1.32317i) q^{95} +(-5.42705 + 9.39993i) q^{96} -9.23607 q^{97} +(2.09017 - 3.62028i) q^{98} +(6.97214 + 12.0761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9	\( 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9} - 8 q^{10} - 10 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} + 2 q^{15} + 26 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 22 q^{21} + 10 q^{22} - 11 q^{23} + q^{24} - 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} - 30 q^{32} - 10 q^{33} - 11 q^{34} - 12 q^{35} + 21 q^{36} + 3 q^{37} + 8 q^{38} - 10 q^{39} - 26 q^{40} + 20 q^{41} - 8 q^{42} - 26 q^{43} + 28 q^{45} + 19 q^{46} + 18 q^{47} + 12 q^{48} - 4 q^{49} + 13 q^{50} - 28 q^{51} - 15 q^{52} + 5 q^{53} - 10 q^{54} + 8 q^{56} - 2 q^{57} + 9 q^{58} - 2 q^{59} - 12 q^{60} + q^{61} + 17 q^{63} + 8 q^{64} - 20 q^{65} + 5 q^{66} + q^{67} + 36 q^{68} + 14 q^{69} + 8 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} + 3 q^{74} + 14 q^{75} - 18 q^{76} - 15 q^{77} + 10 q^{78} + 5 q^{79} + 28 q^{80} - 2 q^{81} - 10 q^{82} - 3 q^{83} - 42 q^{84} + 48 q^{85} + 39 q^{86} - 18 q^{87} + 10 q^{88} - 3 q^{89} - 52 q^{90} + 5 q^{91} - 24 q^{92} - 42 q^{94} + 12 q^{95} - 15 q^{96} - 28 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9 - 8 * q^10 - 10 * q^11 - 3 * q^12 - 5 * q^13 - q^14 + 2 * q^15 + 26 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 22 * q^21 + 10 * q^22 - 11 * q^23 + q^24 - 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 - 30 * q^32 - 10 * q^33 - 11 * q^34 - 12 * q^35 + 21 * q^36 + 3 * q^37 + 8 * q^38 - 10 * q^39 - 26 * q^40 + 20 * q^41 - 8 * q^42 - 26 * q^43 + 28 * q^45 + 19 * q^46 + 18 * q^47 + 12 * q^48 - 4 * q^49 + 13 * q^50 - 28 * q^51 - 15 * q^52 + 5 * q^53 - 10 * q^54 + 8 * q^56 - 2 * q^57 + 9 * q^58 - 2 * q^59 - 12 * q^60 + q^61 + 17 * q^63 + 8 * q^64 - 20 * q^65 + 5 * q^66 + q^67 + 36 * q^68 + 14 * q^69 + 8 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 + 3 * q^74 + 14 * q^75 - 18 * q^76 - 15 * q^77 + 10 * q^78 + 5 * q^79 + 28 * q^80 - 2 * q^81 - 10 * q^82 - 3 * q^83 - 42 * q^84 + 48 * q^85 + 39 * q^86 - 18 * q^87 + 10 * q^88 - 3 * q^89 - 52 * q^90 + 5 * q^91 - 24 * q^92 - 42 * q^94 + 12 * q^95 - 15 * q^96 - 28 * q^97 - 14 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.381966			−0.270091			−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−0.381966			−0.270091			−0.135045	+	0.990839i	$0.543118\pi$
$3$	1.30902	−	2.26728i	0.755761	−	1.30902i	−0.189234	−	0.981932i	$-0.560600\pi$
$3$	1.30902	−	2.26728i	0.755761	−	1.30902i	0.944995	−	0.327085i	$-0.106066\pi$
$4$	−1.85410			−0.927051
$5$	−0.618034	+	1.07047i	−0.276393	+	0.478727i	−0.970486	−	0.241159i	$-0.922473\pi$
$5$	−0.618034	+	1.07047i	−0.276393	+	0.478727i	0.694092	+	0.719886i	$0.255806\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	0.919260	+	0.393651i	$0.128788\pi$
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	−0.118718	+	0.992928i	$0.537879\pi$
$8$	1.47214			0.520479
$9$	−1.92705	−	3.33775i	−0.642350	−	1.11258i
$10$	0.236068	−	0.408882i	0.0746512	−	0.129300i
$11$	−3.61803			−1.09088			−0.545439	−	0.838150i	$-0.683637\pi$
$11$	−3.61803			−1.09088			−0.545439	+	0.838150i	$0.683637\pi$
$12$	−2.42705	+	4.20378i	−0.700629	+	1.21353i
$13$	−0.690983	−	1.19682i	−0.191644	−	0.331937i	0.754151	−	0.656701i	$-0.228049\pi$
$13$	−0.690983	−	1.19682i	−0.191644	−	0.331937i	−0.945795	+	0.324763i	$0.894715\pi$
$14$	−0.809017	−	1.40126i	−0.216219	−	0.374502i
$15$	1.61803	+	2.80252i	0.417775	+	0.723607i
$16$	3.14590			0.786475
$17$	−3.04508	−	5.27424i	−0.738542	−	1.27919i	−0.953152	−	0.302492i	$-0.902182\pi$
$17$	−3.04508	−	5.27424i	−0.738542	−	1.27919i	0.214610	−	0.976700i	$-0.431152\pi$
$18$	0.736068	+	1.27491i	0.173493	+	0.300498i
$19$	0.618034	−	1.07047i	0.141787	−	0.245582i	−0.786383	−	0.617740i	$-0.788049\pi$
$19$	0.618034	−	1.07047i	0.141787	−	0.245582i	0.928170	+	0.372158i	$0.121382\pi$
$20$	1.14590	−	1.98475i	0.256231	−	0.443804i
$21$	11.0902			2.42007
$22$	1.38197			0.294636
$23$	−2.19098	+	3.79489i	−0.456852	+	0.791290i	−0.998793	−	0.0491264i	$-0.984356\pi$
$23$	−2.19098	+	3.79489i	−0.456852	+	0.791290i	0.541941	+	0.840417i	$0.317690\pi$
$24$	1.92705	−	3.33775i	0.393358	−	0.681315i
$25$	1.73607	+	3.00696i	0.347214	+	0.601392i
$26$	0.263932	+	0.457144i	0.0517613	+	0.0896533i
$27$	−2.23607			−0.430331
$28$	−3.92705	−	6.80185i	−0.742143	−	1.28543i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$	−0.618034	−	1.07047i	−0.112837	−	0.195440i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−4.14590			−0.732898
$33$	−4.73607	+	8.20311i	−0.824444	+	1.42798i
$34$	1.16312	+	2.01458i	0.199473	+	0.345498i
$35$	−5.23607			−0.885057
$36$	3.57295	+	6.18853i	0.595492	+	1.03142i
$37$	2.42705	−	4.20378i	0.399005	−	0.691096i	−0.594599	−	0.804023i	$-0.702689\pi$
$37$	2.42705	−	4.20378i	0.399005	−	0.691096i	0.993603	+	0.112926i	$0.0360224\pi$
$38$	−0.236068	+	0.408882i	−0.0382953	+	0.0663294i
$39$	−3.61803			−0.579349
$40$	−0.909830	+	1.57587i	−0.143857	+	0.249167i
$41$	9.47214			1.47930			0.739650	−	0.672992i	$-0.234991\pi$
$41$	9.47214			1.47930			0.739650	+	0.672992i	$0.234991\pi$
$42$	−4.23607			−0.653639
$43$	−6.50000	+	0.866025i	−0.991241	+	0.132068i
$43$	−6.50000	+	0.866025i	−0.991241	+	0.132068i
$44$	6.70820			1.01130
$45$	4.76393			0.710165
$46$	0.836881	−	1.44952i	0.123391	−	0.213720i
$47$	1.14590			0.167146			0.0835732	−	0.996502i	$-0.473367\pi$
$47$	1.14590			0.167146			0.0835732	+	0.996502i	$0.473367\pi$
$48$	4.11803	−	7.13264i	0.594387	−	1.02951i
$49$	−5.47214	+	9.47802i	−0.781734	+	1.35400i
$50$	−0.663119	−	1.14856i	−0.0937792	−	0.162430i
$51$	−15.9443			−2.23264
$52$	1.28115	+	2.21902i	0.177664	+	0.307723i
$53$	0.690983	−	1.19682i	0.0949138	−	0.164396i	−0.814659	−	0.579941i	$-0.803076\pi$
$53$	0.690983	−	1.19682i	0.0949138	−	0.164396i	0.909573	+	0.415545i	$0.136409\pi$
$54$	0.854102			0.116229
$55$	2.23607	−	3.87298i	0.301511	−	0.522233i
$56$	3.11803	+	5.40059i	0.416665	+	0.721685i
$57$	−1.61803	−	2.80252i	−0.214314	−	0.371202i
$58$	0.572949	+	0.992377i	0.0752319	+	0.130305i
$59$	5.09017			0.662684			0.331342	−	0.943511i	$-0.392499\pi$
$59$	5.09017			0.662684			0.331342	+	0.943511i	$0.392499\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	−1.42705	−	2.47172i	−0.182715	−	0.316472i	0.760089	−	0.649819i	$-0.225155\pi$
$61$	−1.42705	−	2.47172i	−0.182715	−	0.316472i	−0.942804	+	0.333347i	$0.891822\pi$
$62$		0			0
$63$	8.16312	−	14.1389i	1.02846	−	1.78134i
$64$	−4.70820			−0.588525
$65$	1.70820			0.211877
$66$	1.80902	−	3.13331i	0.222675	−	0.385684i
$67$	1.92705	−	3.33775i	0.235427	−	0.407771i	−0.723970	−	0.689832i	$-0.757685\pi$
$67$	1.92705	−	3.33775i	0.235427	−	0.407771i	0.959397	+	0.282061i	$0.0910179\pi$
$68$	5.64590	+	9.77898i	0.684666	+	1.18588i
$69$	5.73607	+	9.93516i	0.690541	+	1.19605i
$70$	2.00000			0.239046
$71$	5.39919	+	9.35167i	0.640766	+	1.10984i	0.985262	+	0.171051i	$0.0547163\pi$
$71$	5.39919	+	9.35167i	0.640766	+	1.10984i	−0.344497	+	0.938788i	$0.611950\pi$
$72$	−2.83688	−	4.91362i	−0.334330	−	0.579076i
$73$	−0.927051	−	1.60570i	−0.108503	−	0.187933i	0.806661	−	0.591015i	$-0.201272\pi$
$73$	−0.927051	−	1.60570i	−0.108503	−	0.187933i	−0.915164	+	0.403082i	$0.867939\pi$
$74$	−0.927051	+	1.60570i	−0.107767	+	0.186659i
$75$	9.09017			1.04964
$76$	−1.14590	+	1.98475i	−0.131444	+	0.227667i
$77$	−7.66312	−	13.2729i	−0.873293	−	1.51259i
$78$	1.38197			0.156477
$79$	0.690983	+	1.19682i	0.0777417	+	0.134653i	0.902275	−	0.431161i	$-0.141896\pi$
$79$	0.690983	+	1.19682i	0.0777417	+	0.134653i	−0.824534	+	0.565813i	$0.808562\pi$
$80$	−1.94427	+	3.36758i	−0.217376	+	0.376507i
$81$	2.85410	−	4.94345i	0.317122	−	0.549272i
$82$	−3.61803			−0.399545
$83$	−8.01722	+	13.8862i	−0.880004	+	1.52421i	−0.0286698	+	0.999589i	$0.509127\pi$
$83$	−8.01722	+	13.8862i	−0.880004	+	1.52421i	−0.851335	+	0.524623i	$0.824206\pi$
$84$	−20.5623			−2.24353
$85$	7.52786			0.816511
$86$	2.48278	−	0.330792i	0.267725	−	0.0356702i
$87$	−7.85410			−0.842048
$88$	−5.32624			−0.567779
$89$	0.927051	−	1.60570i	0.0982672	−	0.170204i	−0.812700	−	0.582682i	$-0.802003\pi$
$89$	0.927051	−	1.60570i	0.0982672	−	0.170204i	0.910968	+	0.412478i	$0.135337\pi$
$90$	−1.81966			−0.191809
$91$	2.92705	−	5.06980i	0.306838	−	0.531460i
$92$	4.06231	−	7.03612i	0.423525	−	0.733566i
$93$		0			0
$94$	−0.437694			−0.0451447
$95$	0.763932	+	1.32317i	0.0783778	+	0.135754i
$96$	−5.42705	+	9.39993i	−0.553896	+	0.959376i
$97$	−9.23607			−0.937781			−0.468890	−	0.883256i	$-0.655346\pi$
$97$	−9.23607			−0.937781			−0.468890	+	0.883256i	$0.655346\pi$
$98$	2.09017	−	3.62028i	0.211139	−	0.365704i
$99$	6.97214	+	12.0761i	0.700726	+	1.21369i
$100$	−3.21885	−	5.57521i	−0.321885	−	0.557521i
$101$	−1.88197	−	3.25966i	−0.187263	−	0.324348i	0.757074	−	0.653329i	$-0.226628\pi$
$101$	−1.88197	−	3.25966i	−0.187263	−	0.324348i	−0.944337	+	0.328981i	$0.893295\pi$
$102$	6.09017			0.603017
$103$	8.20820	+	14.2170i	0.808778	+	1.40085i	0.913710	+	0.406366i	$0.133204\pi$
$103$	8.20820	+	14.2170i	0.808778	+	1.40085i	−0.104932	+	0.994479i	$0.533463\pi$
$104$	−1.01722	−	1.76188i	−0.0997467	−	0.172766i
$105$	−6.85410	+	11.8717i	−0.668892	+	1.15855i
$106$	−0.263932	+	0.457144i	−0.0256353	+	0.0444017i
$107$	7.52786			0.727746			0.363873	−	0.931449i	$-0.381454\pi$
$107$	7.52786			0.727746			0.363873	+	0.931449i	$0.381454\pi$
$108$	4.14590			0.398939
$109$	6.92705	−	11.9980i	0.663491	−	1.14920i	−0.316201	−	0.948692i	$-0.602407\pi$
$109$	6.92705	−	11.9980i	0.663491	−	1.14920i	0.979692	−	0.200508i	$-0.0642593\pi$
$110$	−0.854102	+	1.47935i	−0.0814354	+	0.141050i
$111$	−6.35410	−	11.0056i	−0.603105	−	1.04461i
$112$	6.66312	+	11.5409i	0.629606	+	1.09051i
$113$	−15.6180			−1.46922			−0.734611	−	0.678489i	$-0.762635\pi$
$113$	−15.6180			−1.46922			−0.734611	+	0.678489i	$0.762635\pi$
$114$	0.618034	+	1.07047i	0.0578842	+	0.100258i
$115$	−2.70820	−	4.69075i	−0.252541	−	0.437414i
$116$	2.78115	+	4.81710i	0.258224	+	0.447256i
$117$	−2.66312	+	4.61266i	−0.246205	+	0.426440i
$118$	−1.94427			−0.178985
$119$	12.8992	−	22.3420i	1.18247	−	2.04809i
$120$	2.38197	+	4.12569i	0.217443	+	0.376622i
$121$	2.09017			0.190015
$122$	0.545085	+	0.944115i	0.0493497	+	0.0854761i
$123$	12.3992	−	21.4760i	1.11800	−	1.93643i
$124$		0			0
$125$	−10.4721			−0.936656
$126$	−3.11803	+	5.40059i	−0.277777	+	0.481123i
$127$	−14.6525			−1.30020			−0.650098	−	0.759850i	$-0.725272\pi$
$127$	−14.6525			−1.30020			−0.650098	+	0.759850i	$0.725272\pi$
$128$	10.0902			0.891853
$129$	−6.54508	+	15.8710i	−0.576263	+	1.39736i
$130$	−0.652476			−0.0572259
$131$	9.94427			0.868835			0.434418	−	0.900712i	$-0.356954\pi$
$131$	9.94427			0.868835			0.434418	+	0.900712i	$0.356954\pi$
$132$	8.78115	−	15.2094i	0.764301	−	1.32381i
$133$	5.23607			0.454025
$134$	−0.736068	+	1.27491i	−0.0635866	+	0.110135i
$135$	1.38197	−	2.39364i	0.118941	−	0.206011i
$136$	−4.48278	−	7.76440i	−0.384395	−	0.665792i
$137$	3.70820			0.316813			0.158407	−	0.987374i	$-0.449364\pi$
$137$	3.70820			0.316813			0.158407	+	0.987374i	$0.449364\pi$
$138$	−2.19098	−	3.79489i	−0.186509	−	0.323043i
$139$	2.64590	−	4.58283i	0.224422	−	0.388711i	−0.731724	−	0.681601i	$-0.761284\pi$
$139$	2.64590	−	4.58283i	0.224422	−	0.388711i	0.956146	+	0.292891i	$0.0946172\pi$
$140$	9.70820			0.820493
$141$	1.50000	−	2.59808i	0.126323	−	0.218797i
$142$	−2.06231	−	3.57202i	−0.173065	−	0.299757i
$143$	2.50000	+	4.33013i	0.209061	+	0.362103i
$144$	−6.06231	−	10.5002i	−0.505192	−	0.875018i
$145$	3.70820			0.307950
$146$	0.354102	+	0.613323i	0.0293057	+	0.0507589i
$147$	14.3262	+	24.8138i	1.18161	+	2.04661i
$148$	−4.50000	+	7.79423i	−0.369898	+	0.640682i
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$	−3.47214			−0.283499
$151$	−8.85410			−0.720537			−0.360268	−	0.932849i	$-0.617315\pi$
$151$	−8.85410			−0.720537			−0.360268	+	0.932849i	$0.617315\pi$
$152$	0.909830	−	1.57587i	0.0737970	−	0.127820i
$153$	−11.7361	+	20.3275i	−0.948805	+	1.64338i
$154$	2.92705	+	5.06980i	0.235868	+	0.408536i
$155$		0			0
$156$	6.70820			0.537086
$157$	2.57295	+	4.45648i	0.205344	+	0.355666i	0.950242	−	0.311512i	$-0.100835\pi$
$157$	2.57295	+	4.45648i	0.205344	+	0.355666i	−0.744898	+	0.667178i	$0.767502\pi$
$158$	−0.263932	−	0.457144i	−0.0209973	−	0.0363684i
$159$	−1.80902	−	3.13331i	−0.143464	−	0.248488i
$160$	2.56231	−	4.43804i	0.202568	−	0.350858i
$161$	−18.5623			−1.46291
$162$	−1.09017	+	1.88823i	−0.0856518	+	0.148353i
$163$	−7.00000	−	12.1244i	−0.548282	−	0.949653i	−0.998392	−	0.0566798i	$-0.981949\pi$
$163$	−7.00000	−	12.1244i	−0.548282	−	0.949653i	0.450110	−	0.892973i	$-0.351385\pi$
$164$	−17.5623			−1.37139
$165$	−5.85410	−	10.1396i	−0.455741	−	0.789367i
$166$	3.06231	−	5.30407i	0.237681	−	0.411676i
$167$	−7.11803	+	12.3288i	−0.550810	+	0.954031i	0.447406	+	0.894331i	$0.352348\pi$
$167$	−7.11803	+	12.3288i	−0.550810	+	0.954031i	−0.998216	+	0.0597001i	$0.980986\pi$
$168$	16.3262			1.25960
$169$	5.54508	−	9.60437i	0.426545	−	0.738798i
$170$	−2.87539			−0.220532
$171$	−4.76393			−0.364307
$172$	12.0517	−	1.60570i	0.918931	−	0.122433i
$173$	−3.76393			−0.286166			−0.143083	−	0.989711i	$-0.545702\pi$
$173$	−3.76393			−0.286166			−0.143083	+	0.989711i	$0.545702\pi$
$174$	3.00000			0.227429
$175$	−7.35410	+	12.7377i	−0.555918	+	0.962878i
$176$	−11.3820			−0.857948
$177$	6.66312	−	11.5409i	0.500831	−	0.867464i
$178$	−0.354102	+	0.613323i	−0.0265411	+	0.0459705i
$179$	−4.82624	−	8.35929i	−0.360730	−	0.624803i	0.627351	−	0.778736i	$-0.284139\pi$
$179$	−4.82624	−	8.35929i	−0.360730	−	0.624803i	−0.988081	+	0.153934i	$0.950806\pi$
$180$	−8.83282			−0.658359
$181$	9.69098	+	16.7853i	0.720325	+	1.24764i	0.960869	+	0.277002i	$0.0893407\pi$
$181$	9.69098	+	16.7853i	0.720325	+	1.24764i	−0.240544	+	0.970638i	$0.577326\pi$
$182$	−1.11803	+	1.93649i	−0.0828742	+	0.143542i
$183$	−7.47214			−0.552356
$184$	−3.22542	+	5.58660i	−0.237781	+	0.411850i
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	11.0172	+	19.0824i	0.805659	+	1.39544i
$188$	−2.12461			−0.154953
$189$	−4.73607	−	8.20311i	−0.344498	−	0.596688i
$190$	−0.291796	−	0.505406i	−0.0211691	−	0.0366660i
$191$	7.26393	−	12.5815i	0.525600	−	0.910365i	−0.473956	−	0.880549i	$-0.657174\pi$
$191$	7.26393	−	12.5815i	0.525600	−	0.910365i	0.999555	−	0.0298167i	$-0.00949234\pi$
$192$	−6.16312	+	10.6748i	−0.444785	+	0.770390i
$193$	2.70820			0.194941			0.0974704	−	0.995238i	$-0.468925\pi$
$193$	2.70820			0.194941			0.0974704	+	0.995238i	$0.468925\pi$
$194$	3.52786			0.253286
$195$	2.23607	−	3.87298i	0.160128	−	0.277350i
$196$	10.1459	−	17.5732i	0.724707	−	1.25523i
$197$	1.47214	+	2.54981i	0.104885	+	0.181667i	0.913691	−	0.406409i	$-0.133219\pi$
$197$	1.47214	+	2.54981i	0.104885	+	0.181667i	−0.808806	+	0.588076i	$0.799886\pi$
$198$	−2.66312	−	4.61266i	−0.189260	−	0.327807i
$199$	1.94427			0.137826			0.0689129	−	0.997623i	$-0.478047\pi$
$199$	1.94427			0.137826			0.0689129	+	0.997623i	$0.478047\pi$
$200$	2.55573	+	4.42665i	0.180717	+	0.313011i
$201$	−5.04508	−	8.73834i	−0.355853	−	0.616355i
$202$	0.718847	+	1.24508i	0.0505779	+	0.0876035i
$203$	6.35410	−	11.0056i	0.445971	−	0.772444i
$204$	29.5623			2.06978
$205$	−5.85410	+	10.1396i	−0.408868	+	0.708181i
$206$	−3.13525	−	5.43042i	−0.218444	−	0.378355i
$207$	16.8885			1.17383
$208$	−2.17376	−	3.76507i	−0.150723	−	0.261060i
$209$	−2.23607	+	3.87298i	−0.154672	+	0.267900i
$210$	2.61803	−	4.53457i	0.180662	−	0.312915i
$211$	−9.23607			−0.635837			−0.317919	−	0.948118i	$-0.602984\pi$
$211$	−9.23607			−0.635837			−0.317919	+	0.948118i	$0.602984\pi$
$212$	−1.28115	+	2.21902i	−0.0879899	+	0.152403i
$213$	28.2705			1.93706
$214$	−2.87539			−0.196557
$215$	3.09017	−	7.49326i	0.210748	−	0.511036i
$216$	−3.29180			−0.223978
$217$		0			0
$218$	−2.64590	+	4.58283i	−0.179203	+	0.310388i
$219$	−4.85410			−0.328010
$220$	−4.14590	+	7.18091i	−0.279516	+	0.484137i
$221$	−4.20820	+	7.28882i	−0.283074	+	0.490299i
$222$	2.42705	+	4.20378i	0.162893	+	0.282139i
$223$	2.76393			0.185087			0.0925433	−	0.995709i	$-0.470500\pi$
$223$	2.76393			0.185087			0.0925433	+	0.995709i	$0.470500\pi$
$224$	−8.78115	−	15.2094i	−0.586715	−	1.01622i
$225$	6.69098	−	11.5891i	0.446066	−	0.772608i
$226$	5.96556			0.396823
$227$	0.736068	−	1.27491i	0.0488545	−	0.0846186i	−0.840564	−	0.541712i	$-0.817776\pi$
$227$	0.736068	−	1.27491i	0.0488545	−	0.0846186i	0.889419	+	0.457094i	$0.151110\pi$
$228$	3.00000	+	5.19615i	0.198680	+	0.344124i
$229$	1.14590	+	1.98475i	0.0757231	+	0.131156i	0.901400	−	0.432986i	$-0.142540\pi$
$229$	1.14590	+	1.98475i	0.0757231	+	0.131156i	−0.825677	+	0.564143i	$0.809207\pi$
$230$	1.03444	+	1.79171i	0.0682091	+	0.118142i
$231$	−40.1246			−2.64001
$232$	−2.20820	−	3.82472i	−0.144976	−	0.251105i
$233$	−9.01722	−	15.6183i	−0.590738	−	1.02319i	−0.994133	−	0.108162i	$-0.965503\pi$
$233$	−9.01722	−	15.6183i	−0.590738	−	1.02319i	0.403395	−	0.915026i	$-0.367830\pi$
$234$	1.01722	−	1.76188i	0.0664978	−	0.115178i
$235$	−0.708204	+	1.22665i	−0.0461981	+	0.0800175i
$236$	−9.43769			−0.614342
$237$	3.61803			0.235017
$238$	−4.92705	+	8.53390i	−0.319373	+	0.553171i
$239$	4.14590	−	7.18091i	0.268176	−	0.464494i	−0.700215	−	0.713932i	$-0.746913\pi$
$239$	4.14590	−	7.18091i	0.268176	−	0.464494i	0.968391	+	0.249438i	$0.0802458\pi$
$240$	5.09017	+	8.81643i	0.328569	+	0.569098i
$241$	−2.13525	−	3.69837i	−0.137544	−	0.238233i	0.789022	−	0.614364i	$-0.210587\pi$
$241$	−2.13525	−	3.69837i	−0.137544	−	0.238233i	−0.926566	+	0.376131i	$0.877254\pi$
$242$	−0.798374			−0.0513214
$243$	−10.8262	−	18.7516i	−0.694503	−	1.20292i
$244$	2.64590	+	4.58283i	0.169386	+	0.293386i
$245$	−6.76393	−	11.7155i	−0.432132	−	0.748474i
$246$	−4.73607	+	8.20311i	−0.301961	+	0.523011i
$247$	−1.70820			−0.108690
$248$		0			0
$249$	20.9894	+	36.3546i	1.33015	+	2.30388i
$250$	4.00000			0.252982
$251$	14.5902	+	25.2709i	0.920923	+	1.59509i	0.797990	+	0.602671i	$0.205897\pi$
$251$	14.5902	+	25.2709i	0.920923	+	1.59509i	0.122934	+	0.992415i	$0.460770\pi$
$252$	−15.1353	+	26.2150i	−0.953431	+	1.65139i
$253$	7.92705	−	13.7301i	0.498369	−	0.863201i
$254$	5.59675			0.351171
$255$	9.85410	−	17.0678i	0.617088	−	1.06883i
$256$	5.56231			0.347644
$257$	3.43769			0.214437			0.107219	−	0.994235i	$-0.465805\pi$
$257$	3.43769			0.214437			0.107219	+	0.994235i	$0.465805\pi$
$258$	2.50000	−	6.06218i	0.155643	−	0.377415i
$259$	20.5623			1.27768
$260$	−3.16718			−0.196420
$261$	−5.78115	+	10.0133i	−0.357844	+	0.619805i
$262$	−3.79837			−0.234664
$263$	−13.7533	+	23.8214i	−0.848064	+	1.46889i	0.0348693	+	0.999392i	$0.488899\pi$
$263$	−13.7533	+	23.8214i	−0.848064	+	1.46889i	−0.882933	+	0.469498i	$0.844435\pi$
$264$	−6.97214	+	12.0761i	−0.429105	+	0.743232i
$265$	0.854102	+	1.47935i	0.0524671	+	0.0908756i
$266$	−2.00000			−0.122628
$267$	−2.42705	−	4.20378i	−0.148533	−	0.257267i
$268$	−3.57295	+	6.18853i	−0.218253	+	0.378025i
$269$	11.5623			0.704966			0.352483	−	0.935818i	$-0.385337\pi$
$269$	11.5623			0.704966			0.352483	+	0.935818i	$0.385337\pi$
$270$	−0.527864	+	0.914287i	−0.0321248	+	0.0556418i
$271$	−6.92705	−	11.9980i	−0.420788	−	0.728827i	0.575228	−	0.817993i	$-0.304913\pi$
$271$	−6.92705	−	11.9980i	−0.420788	−	0.728827i	−0.996017	+	0.0891660i	$0.971580\pi$
$272$	−9.57953	−	16.5922i	−0.580844	−	1.00605i
$273$	−7.66312	−	13.2729i	−0.463793	−	0.803313i
$274$	−1.41641			−0.0855683
$275$	−6.28115	−	10.8793i	−0.378768	−	0.656045i
$276$	−10.6353	−	18.4208i	−0.640167	−	1.10880i
$277$	6.23607	−	10.8012i	0.374689	−	0.648980i	−0.615591	−	0.788065i	$-0.711083\pi$
$277$	6.23607	−	10.8012i	0.374689	−	0.648980i	0.990280	+	0.139085i	$0.0444161\pi$
$278$	−1.01064	+	1.75049i	−0.0606143	+	0.104987i
$279$		0			0
$280$	−7.70820			−0.460653
$281$	−3.73607	+	6.47106i	−0.222875	+	0.386031i	−0.955680	−	0.294408i	$-0.904878\pi$
$281$	−3.73607	+	6.47106i	−0.222875	+	0.386031i	0.732805	+	0.680439i	$0.238211\pi$
$282$	−0.572949	+	0.992377i	−0.0341186	+	0.0590952i
$283$	−5.38197	−	9.32184i	−0.319925	−	0.554126i	0.660547	−	0.750784i	$-0.270324\pi$
$283$	−5.38197	−	9.32184i	−0.319925	−	0.554126i	−0.980472	+	0.196659i	$0.936991\pi$
$284$	−10.0106	−	17.3389i	−0.594022	−	1.02888i
$285$	4.00000			0.236940
$286$	−0.954915	−	1.65396i	−0.0564653	−	0.0978008i
$287$	20.0623	+	34.7489i	1.18424	+	2.05116i
$288$	7.98936	+	13.8380i	0.470777	+	0.815410i
$289$	−10.0451	+	17.3986i	−0.590887	+	1.02345i
$290$	−1.41641			−0.0831743
$291$	−12.0902	+	20.9408i	−0.708738	+	1.22757i
$292$	1.71885	+	2.97713i	0.100588	+	0.174223i
$293$	−12.0902			−0.706315			−0.353158	−	0.935564i	$-0.614892\pi$
$293$	−12.0902			−0.706315			−0.353158	+	0.935564i	$0.614892\pi$
$294$	−5.47214	−	9.47802i	−0.319141	−	0.552769i
$295$	−3.14590	+	5.44886i	−0.183161	+	0.317245i
$296$	3.57295	−	6.18853i	0.207673	−	0.359701i
$297$	8.09017			0.469439
$298$	1.71885	−	2.97713i	0.0995701	−	0.172461i
$299$	6.05573			0.350212
$300$	−16.8541			−0.973072
$301$	−16.9443	−	22.0113i	−0.976652	−	1.26871i
$302$	3.38197			0.194610
$303$	−9.85410			−0.566103
$304$	1.94427	−	3.36758i	0.111512	−	0.193144i
$305$	3.52786			0.202005
$306$	4.48278	−	7.76440i	0.256263	−	0.443861i
$307$	11.6074	−	20.1046i	0.662469	−	1.14743i	−0.317496	−	0.948260i	$-0.602842\pi$
$307$	11.6074	−	20.1046i	0.662469	−	1.14743i	0.979965	−	0.199170i	$-0.0638246\pi$
$308$	14.2082	+	24.6093i	0.809588	+	1.40225i
$309$	42.9787			2.44497
$310$		0			0
$311$	14.9164	−	25.8360i	0.845832	−	1.46502i	−0.0390649	−	0.999237i	$-0.512438\pi$
$311$	14.9164	−	25.8360i	0.845832	−	1.46502i	0.884897	−	0.465787i	$-0.154229\pi$
$312$	−5.32624			−0.301539
$313$	−6.56231	+	11.3662i	−0.370923	+	0.642458i	−0.989708	−	0.143103i	$-0.954292\pi$
$313$	−6.56231	+	11.3662i	−0.370923	+	0.642458i	0.618784	+	0.785561i	$0.287625\pi$
$314$	−0.982779	−	1.70222i	−0.0554614	−	0.0960620i
$315$	10.0902	+	17.4767i	0.568517	+	0.984700i
$316$	−1.28115	−	2.21902i	−0.0720705	−	0.124830i
$317$	33.3050			1.87059			0.935296	−	0.353866i	$-0.115133\pi$
$317$	33.3050			1.87059			0.935296	+	0.353866i	$0.115133\pi$
$318$	0.690983	+	1.19682i	0.0387484	+	0.0671142i
$319$	5.42705	+	9.39993i	0.303857	+	0.526295i
$320$	2.90983	−	5.03997i	0.162664	−	0.281743i
$321$	9.85410	−	17.0678i	0.550002	−	0.952632i
$322$	7.09017			0.395120
$323$	−7.52786			−0.418862
$324$	−5.29180	+	9.16566i	−0.293989	+	0.509203i
$325$	2.39919	−	4.15551i	0.133083	−	0.230506i
$326$	2.67376	+	4.63109i	0.148086	+	0.256492i
$327$	−18.1353	−	31.4112i	−1.00288	−	1.73704i
$328$	13.9443			0.769944
$329$	2.42705	+	4.20378i	0.133808	+	0.231762i
$330$	2.23607	+	3.87298i	0.123091	+	0.213201i
$331$	2.73607	+	4.73901i	0.150388	+	0.260479i	0.931370	−	0.364074i	$-0.118614\pi$
$331$	2.73607	+	4.73901i	0.150388	+	0.260479i	−0.780982	+	0.624553i	$0.785281\pi$
$332$	14.8647	−	25.7465i	0.815809	−	1.41302i
$333$	−18.7082			−1.02520
$334$	2.71885	−	4.70918i	0.148769	−	0.257675i
$335$	2.38197	+	4.12569i	0.130141	+	0.225410i
$336$	34.8885			1.90333
$337$	−14.0000	−	24.2487i	−0.762629	−	1.32091i	−0.941491	−	0.337037i	$-0.890575\pi$
$337$	−14.0000	−	24.2487i	−0.762629	−	1.32091i	0.178863	−	0.983874i	$-0.442758\pi$
$338$	−2.11803	+	3.66854i	−0.115206	+	0.199542i
$339$	−20.4443	+	35.4105i	−1.11038	+	1.92324i
$340$	−13.9574			−0.756948
$341$		0			0
$342$	1.81966			0.0983959
$343$	−16.7082			−0.902158
$344$	−9.56888	+	1.27491i	−0.515920	+	0.0687384i
$345$	−14.1803			−0.763444
$346$	1.43769			0.0772909
$347$	−5.04508	+	8.73834i	−0.270834	+	0.469099i	−0.969076	−	0.246764i	$-0.920633\pi$
$347$	−5.04508	+	8.73834i	−0.270834	+	0.469099i	0.698241	+	0.715862i	$0.253966\pi$
$348$	14.5623			0.780622
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	0.443720	+	0.896166i	$0.353659\pi$
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	−0.997962	+	0.0638103i	$0.979675\pi$
$350$	2.80902	−	4.86536i	0.150148	−	0.260064i
$351$	1.54508	+	2.67617i	0.0824705	+	0.142843i
$352$	15.0000			0.799503
$353$	8.61803	+	14.9269i	0.458692	+	0.794477i	0.998892	−	0.0470591i	$-0.0149849\pi$
$353$	8.61803	+	14.9269i	0.458692	+	0.794477i	−0.540200	+	0.841536i	$0.681652\pi$
$354$	−2.54508	+	4.40822i	−0.135270	+	0.234294i
$355$	−13.3475			−0.708413
$356$	−1.71885	+	2.97713i	−0.0910987	+	0.157788i
$357$	−33.7705	−	58.4922i	−1.78732	−	3.09574i
$358$	1.84346	+	3.19296i	0.0974298	+	0.168753i
$359$	2.67376	+	4.63109i	0.141116	+	0.244420i	0.927917	−	0.372787i	$-0.121598\pi$
$359$	2.67376	+	4.63109i	0.141116	+	0.244420i	−0.786801	+	0.617206i	$0.788264\pi$
$360$	7.01316			0.369626
$361$	8.73607	+	15.1313i	0.459793	+	0.796385i
$362$	−3.70163	−	6.41140i	−0.194553	−	0.336976i
$363$	2.73607	−	4.73901i	0.143606	−	0.248733i
$364$	−5.42705	+	9.39993i	−0.284455	+	0.492690i
$365$	2.29180			0.119958
$366$	2.85410			0.149186
$367$	−9.59017	+	16.6107i	−0.500603	+	0.867069i	0.499397	+	0.866373i	$0.333555\pi$
$367$	−9.59017	+	16.6107i	−0.500603	+	0.867069i	−1.00000		0.000696189i	$0.999778\pi$
$368$	−6.89261	+	11.9383i	−0.359302	+	0.622329i
$369$	−18.2533	−	31.6156i	−0.950228	−	1.64584i
$370$	−1.14590	−	1.98475i	−0.0595724	−	0.103182i
$371$	5.85410			0.303930
$372$		0			0
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	0.777847	−	0.628454i	$-0.216312\pi$
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	−0.933181	+	0.359408i	$0.882979\pi$
$374$	−4.20820	−	7.28882i	−0.217601	−	0.376896i
$375$	−13.7082	+	23.7433i	−0.707889	+	1.22610i
$376$	1.68692			0.0869961
$377$	−2.07295	+	3.59045i	−0.106762	+	0.184918i
$378$	1.80902	+	3.13331i	0.0930458	+	0.161160i
$379$	−27.3607			−1.40542			−0.702712	−	0.711475i	$-0.748028\pi$
$379$	−27.3607			−1.40542			−0.702712	+	0.711475i	$0.748028\pi$
$380$	−1.41641	−	2.45329i	−0.0726602	−	0.125851i
$381$	−19.1803	+	33.2213i	−0.982639	+	1.70198i
$382$	−2.77458	+	4.80571i	−0.141960	+	0.245881i
$383$	38.1246			1.94808			0.974038	−	0.226383i	$-0.0726901\pi$
$383$	38.1246			1.94808			0.974038	+	0.226383i	$0.0726901\pi$
$384$	13.2082	−	22.8773i	0.674028	−	1.16745i
$385$	18.9443			0.965489
$386$	−1.03444			−0.0526517
$387$	15.4164	+	20.0265i	0.783660	+	1.01800i
$388$	17.1246			0.869370
$389$	−35.0689			−1.77806			−0.889031	−	0.457846i	$-0.848621\pi$
$389$	−35.0689			−1.77806			−0.889031	+	0.457846i	$0.848621\pi$
$390$	−0.854102	+	1.47935i	−0.0432491	+	0.0749097i
$391$	26.6869			1.34962
$392$	−8.05573	+	13.9529i	−0.406876	+	0.704729i
$393$	13.0172	−	22.5465i	0.656632	−	1.13732i
$394$	−0.562306	−	0.973942i	−0.0283286	−	0.0490665i
$395$	−1.70820			−0.0859491
$396$	−12.9271	−	22.3903i	−0.649609	−	1.12516i
$397$	−16.2082	+	28.0734i	−0.813466	+	1.40897i	0.0969574	+	0.995289i	$0.469089\pi$
$397$	−16.2082	+	28.0734i	−0.813466	+	1.40897i	−0.910424	+	0.413677i	$0.864244\pi$
$398$	−0.742646			−0.0372255
$399$	6.85410	−	11.8717i	0.343134	−	0.594326i
$400$	5.46149	+	9.45958i	0.273075	+	0.472979i
$401$	12.7082	+	22.0113i	0.634617	+	1.09919i	0.986596	+	0.163182i	$0.0521756\pi$
$401$	12.7082	+	22.0113i	0.634617	+	1.09919i	−0.351979	+	0.936008i	$0.614491\pi$
$402$	1.92705	+	3.33775i	0.0961126	+	0.166472i
$403$		0			0
$404$	3.48936	+	6.04374i	0.173602	+	0.300687i
$405$	3.52786	+	6.11044i	0.175301	+	0.303630i
$406$	−2.42705	+	4.20378i	−0.120453	+	0.208630i
$407$	−8.78115	+	15.2094i	−0.435266	+	0.753902i
$408$	−23.4721			−1.16204
$409$	8.90983			0.440563			0.220281	−	0.975436i	$-0.429302\pi$
$409$	8.90983			0.440563			0.220281	+	0.975436i	$0.429302\pi$
$410$	2.23607	−	3.87298i	0.110432	−	0.191273i
$411$	4.85410	−	8.40755i	0.239435	−	0.414714i
$412$	−15.2188	−	26.3598i	−0.749779	−	1.29865i
$413$	10.7812	+	18.6735i	0.530506	+	0.918863i
$414$	−6.45085			−0.317042
$415$	−9.90983	−	17.1643i	−0.486454	−	0.842564i
$416$	2.86475	+	4.96188i	0.140456	+	0.243276i
$417$	−6.92705	−	11.9980i	−0.339219	−	0.587545i
$418$	0.854102	−	1.47935i	0.0417755	−	0.0723573i
$419$	−10.2361			−0.500065			−0.250032	−	0.968237i	$-0.580441\pi$
$419$	−10.2361			−0.500065			−0.250032	+	0.968237i	$0.580441\pi$
$420$	12.7082	−	22.0113i	0.620097	−	1.07404i
$421$	3.82624	+	6.62724i	0.186479	+	0.322992i	0.944074	−	0.329734i	$-0.106959\pi$
$421$	3.82624	+	6.62724i	0.186479	+	0.322992i	−0.757595	+	0.652725i	$0.773626\pi$
$422$	3.52786			0.171734
$423$	−2.20820	−	3.82472i	−0.107367	−	0.185964i
$424$	1.01722	−	1.76188i	0.0494006	−	0.0855644i
$425$	10.5729	−	18.3129i	0.512863	−	0.888305i
$426$	−10.7984			−0.523183
$427$	6.04508	−	10.4704i	0.292542	−	0.506698i
$428$	−13.9574			−0.674658
$429$	13.0902			0.631999
$430$	−1.18034	+	2.86217i	−0.0569210	+	0.138026i
$431$	−24.7984			−1.19450			−0.597248	−	0.802057i	$-0.703739\pi$
$431$	−24.7984			−1.19450			−0.597248	+	0.802057i	$0.703739\pi$
$432$	−7.03444			−0.338445
$433$	17.3541	−	30.0582i	0.833985	−	1.44450i	−0.0608693	−	0.998146i	$-0.519387\pi$
$433$	17.3541	−	30.0582i	0.833985	−	1.44450i	0.894854	−	0.446359i	$-0.147279\pi$
$434$		0			0
$435$	4.85410	−	8.40755i	0.232736	−	0.403111i
$436$	−12.8435	+	22.2455i	−0.615090	+	1.06537i
$437$	2.70820	+	4.69075i	0.129551	+	0.224389i
$438$	1.85410			0.0885924
$439$	−0.572949	−	0.992377i	−0.0273454	−	0.0473636i	0.852029	−	0.523495i	$-0.175372\pi$
$439$	−0.572949	−	0.992377i	−0.0273454	−	0.0473636i	−0.879374	+	0.476131i	$0.842039\pi$
$440$	3.29180	−	5.70156i	0.156930	−	0.271811i
$441$	42.1803			2.00859
$442$	1.60739	−	2.78408i	0.0764558	−	0.132425i
$443$	−1.23607	−	2.14093i	−0.0587274	−	0.101719i	0.835167	−	0.549996i	$-0.185371\pi$
$443$	−1.23607	−	2.14093i	−0.0587274	−	0.101719i	−0.893894	+	0.448278i	$0.852038\pi$
$444$	11.7812	+	20.4056i	0.559109	+	0.968405i
$445$	1.14590	+	1.98475i	0.0543208	+	0.0940863i
$446$	−1.05573			−0.0499902
$447$	11.7812	+	20.4056i	0.557229	+	0.965150i
$448$	−9.97214	−	17.2722i	−0.471139	−	0.816037i
$449$	16.4164	−	28.4341i	0.774738	−	1.34189i	−0.160203	−	0.987084i	$-0.551215\pi$
$449$	16.4164	−	28.4341i	0.774738	−	1.34189i	0.934942	−	0.354802i	$-0.115452\pi$
$450$	−2.55573	+	4.42665i	−0.120478	+	0.208674i
$451$	−34.2705			−1.61374
$452$	28.9574			1.36204
$453$	−11.5902	+	20.0748i	−0.544554	+	0.943195i
$454$	−0.281153	+	0.486971i	−0.0131952	+	0.0228547i
$455$	3.61803	+	6.26662i	0.169616	+	0.293784i
$456$	−2.38197	−	4.12569i	−0.111546	−	0.193203i
$457$	−15.7082			−0.734799			−0.367399	−	0.930063i	$-0.619752\pi$
$457$	−15.7082			−0.734799			−0.367399	+	0.930063i	$0.619752\pi$
$458$	−0.437694	−	0.758108i	−0.0204521	−	0.0354241i
$459$	6.80902	+	11.7936i	0.317818	+	0.550476i
$460$	5.02129	+	8.69712i	0.234119	+	0.405505i
$461$	15.7984	−	27.3636i	0.735804	−	1.27445i	−0.218566	−	0.975822i	$-0.570138\pi$
$461$	15.7984	−	27.3636i	0.735804	−	1.27445i	0.954370	−	0.298627i	$-0.0965287\pi$
$462$	15.3262			0.713041
$463$	14.9164	−	25.8360i	0.693224	−	1.20070i	−0.277551	−	0.960711i	$-0.589523\pi$
$463$	14.9164	−	25.8360i	0.693224	−	1.20070i	0.970776	−	0.239989i	$-0.0771438\pi$
$464$	−4.71885	−	8.17328i	−0.219067	−	0.379435i
$465$		0			0
$466$	3.44427	+	5.96565i	0.159553	+	0.276354i
$467$	7.52786	−	13.0386i	0.348348	−	0.603356i	−0.637608	−	0.770361i	$-0.720076\pi$
$467$	7.52786	−	13.0386i	0.348348	−	0.603356i	0.985956	+	0.167004i	$0.0534094\pi$
$468$	4.93769	−	8.55234i	0.228245	−	0.395332i
$469$	16.3262			0.753876
$470$	0.270510	−	0.468537i	0.0124777	−	0.0216120i
$471$	13.4721			0.620763
$472$	7.49342			0.344913
$473$	23.5172	−	3.13331i	1.08132	−	0.144070i
$474$	−1.38197			−0.0634758
$475$	4.29180			0.196921
$476$	−23.9164	+	41.4244i	−1.09621	+	1.89869i
$477$	−5.32624			−0.243872
$478$	−1.58359	+	2.74286i	−0.0724318	+	0.125456i
$479$	6.90983	−	11.9682i	0.315718	−	0.546840i	−0.663872	−	0.747846i	$-0.731088\pi$
$479$	6.90983	−	11.9682i	0.315718	−	0.546840i	0.979590	+	0.201007i	$0.0644212\pi$
$480$	−6.70820	−	11.6190i	−0.306186	−	0.530330i
$481$	−6.70820			−0.305868
$482$	0.815595	+	1.41265i	0.0371493	+	0.0643445i
$483$	−24.2984	+	42.0860i	−1.10561	+	1.91498i
$484$	−3.87539			−0.176154
$485$	5.70820	−	9.88690i	0.259196	−	0.448941i
$486$	4.13525	+	7.16247i	0.187579	+	0.324896i
$487$	−0.663119	−	1.14856i	−0.0300488	−	0.0520460i	0.850610	−	0.525797i	$-0.176233\pi$
$487$	−0.663119	−	1.14856i	−0.0300488	−	0.0520460i	−0.880659	+	0.473751i	$0.842900\pi$
$488$	−2.10081	−	3.63871i	−0.0950993	−	0.164717i
$489$	−36.6525			−1.65748
$490$	2.58359	+	4.47491i	0.116715	+	0.202156i
$491$	−10.8262	−	18.7516i	−0.488581	−	0.846248i	0.511332	−	0.859383i	$-0.329152\pi$
$491$	−10.8262	−	18.7516i	−0.488581	−	0.846248i	−0.999914	+	0.0131354i	$0.995819\pi$
$492$	−22.9894	+	39.8187i	−1.03644	+	1.79517i
$493$	−9.13525	+	15.8227i	−0.411431	+	0.712620i
$494$	0.652476			0.0293563
$495$	−17.2361			−0.774704
$496$		0			0
$497$	−22.8713	+	39.6143i	−1.02592	+	1.77694i
$498$	−8.01722	−	13.8862i	−0.359260	−	0.622257i
$499$	−6.92705	−	11.9980i	−0.310097	−	0.537104i	0.668286	−	0.743905i	$-0.267028\pi$
$499$	−6.92705	−	11.9980i	−0.310097	−	0.537104i	−0.978383	+	0.206800i	$0.933695\pi$
$500$	19.4164			0.868328
$501$	18.6353	+	32.2772i	0.832562	+	1.44204i
$502$	−5.57295	−	9.65263i	−0.248733	−	0.430818i
$503$	6.73607	+	11.6672i	0.300346	+	0.520215i	0.976214	−	0.216807i	$-0.0695644\pi$
$503$	6.73607	+	11.6672i	0.300346	+	0.520215i	−0.675868	+	0.737023i	$0.736231\pi$
$504$	12.0172	−	20.8144i	0.535290	−	0.927149i
$505$	4.65248			0.207032
$506$	−3.02786	+	5.24441i	−0.134605	+	0.233143i
$507$	−14.5172	−	25.1446i	−0.644732	−	1.11671i
$508$	27.1672			1.20535
$509$	−9.35410	−	16.2018i	−0.414613	−	0.718131i	0.580774	−	0.814064i	$-0.302750\pi$
$509$	−9.35410	−	16.2018i	−0.414613	−	0.718131i	−0.995388	+	0.0959332i	$0.969416\pi$
$510$	−3.76393	+	6.51932i	−0.166670	+	0.288680i
$511$	3.92705	−	6.80185i	0.173723	−	0.300896i
$512$	−22.3050			−0.985749
$513$	−1.38197	+	2.39364i	−0.0610153	+	0.105682i
$514$	−1.31308			−0.0579176
$515$	−20.2918			−0.894163
$516$	12.1353	−	29.4264i	0.534225	−	1.29543i
$517$	−4.14590			−0.182336
$518$	−7.85410			−0.345089
$519$	−4.92705	+	8.53390i	−0.216274	+	0.374597i
$520$	2.51471			0.110277
$521$	11.0172	−	19.0824i	0.482673	−	0.836015i	−0.517129	−	0.855908i	$-0.672999\pi$
$521$	11.0172	−	19.0824i	0.482673	−	0.836015i	0.999802	+	0.0198930i	$0.00633256\pi$
$522$	2.20820	−	3.82472i	0.0966505	−	0.167404i
$523$	−17.9164	−	31.0321i	−0.783430	−	1.35694i	−0.929933	−	0.367730i	$-0.880135\pi$
$523$	−17.9164	−	31.0321i	−0.783430	−	1.35694i	0.146503	−	0.989210i	$-0.453198\pi$
$524$	−18.4377			−0.805454
$525$	19.2533	+	33.3477i	0.840282	+	1.45541i
$526$	5.25329	−	9.09896i	0.229054	−	0.396734i
$527$		0			0
$528$	−14.8992	+	25.8061i	−0.648404	+	1.12307i
$529$	1.89919	+	3.28949i	0.0825733	+	0.143021i
$530$	−0.326238	−	0.565061i	−0.0141709	−	0.0245447i
$531$	−9.80902	−	16.9897i	−0.425675	−	0.737291i
$532$	−9.70820			−0.420904
$533$	−6.54508	−	11.3364i	−0.283499	−	0.491035i
$534$	0.927051	+	1.60570i	0.0401174	+	0.0694854i
$535$	−4.65248	+	8.05832i	−0.201144	+	0.348392i
$536$	2.83688	−	4.91362i	0.122535	−	0.212236i
$537$	−25.2705			−1.09050
$538$	−4.41641			−0.190405
$539$	19.7984	−	34.2918i	0.852776	−	1.47705i
$540$	−2.56231	+	4.43804i	−0.110264	+	0.190983i
$541$	18.9721	+	32.8607i	0.815676	+	1.41279i	0.908842	+	0.417141i	$0.136968\pi$
$541$	18.9721	+	32.8607i	0.815676	+	1.41279i	−0.0931658	+	0.995651i	$0.529699\pi$
$542$	2.64590	+	4.58283i	0.113651	+	0.196849i
$543$	50.7426			2.17758
$544$	12.6246	+	21.8665i	0.541276	+	0.937517i
$545$	8.56231	+	14.8303i	0.366769	+	0.635262i
$546$	2.92705	+	5.06980i	0.125266	+	0.216967i
$547$	−10.5000	+	18.1865i	−0.448948	+	0.777600i	−0.998318	−	0.0579790i	$-0.981534\pi$
$547$	−10.5000	+	18.1865i	−0.448948	+	0.777600i	0.549370	+	0.835579i	$0.314868\pi$
$548$	−6.87539			−0.293702
$549$	−5.50000	+	9.52628i	−0.234734	+	0.406572i
$550$	2.39919	+	4.15551i	0.102302	+	0.177192i
$551$	−3.70820			−0.157975
$552$	8.44427	+	14.6259i	0.359412	+	0.622520i
$553$	−2.92705	+	5.06980i	−0.124471	+	0.215590i
$554$	−2.38197	+	4.12569i	−0.101200	+	0.175284i
$555$	15.7082			0.666776
$556$	−4.90576	+	8.49703i	−0.208051	+	0.360354i
$557$	−38.5623			−1.63394			−0.816969	−	0.576682i	$-0.804347\pi$
$557$	−38.5623			−1.63394			−0.816969	+	0.576682i	$0.804347\pi$
$558$		0			0
$559$	5.52786	+	7.18091i	0.233804	+	0.303720i
$560$	−16.4721			−0.696075
$561$	57.6869			2.43554
$562$	1.42705	−	2.47172i	0.0601965	−	0.104263i
$563$	−1.32624			−0.0558943			−0.0279471	−	0.999609i	$-0.508897\pi$
$563$	−1.32624			−0.0558943			−0.0279471	+	0.999609i	$0.508897\pi$
$564$	−2.78115	+	4.81710i	−0.117108	+	0.202836i
$565$	9.65248	−	16.7186i	0.406083	−	0.703356i
$566$	2.05573	+	3.56063i	0.0864087	+	0.149664i
$567$	24.1803			1.01548
$568$	7.94834	+	13.7669i	0.333505	+	0.577647i
$569$	12.9721	−	22.4684i	0.543820	−	0.941924i	−0.454860	−	0.890563i	$-0.650311\pi$
$569$	12.9721	−	22.4684i	0.543820	−	0.941924i	0.998680	−	0.0513613i	$-0.0163560\pi$
$570$	−1.52786			−0.0639952
$571$	21.5902	−	37.3953i	0.903520	−	1.56494i	0.0806295	−	0.996744i	$-0.474307\pi$
$571$	21.5902	−	37.3953i	0.903520	−	1.56494i	0.822891	−	0.568199i	$-0.192360\pi$
$572$	−4.63525	−	8.02850i	−0.193810	−	0.335688i
$573$	−19.0172	−	32.9388i	−0.794456	−	1.37604i
$574$	−7.66312	−	13.2729i	−0.319852	−	0.554001i
$575$	−15.2148			−0.634500
$576$	9.07295	+	15.7148i	0.378040	+	0.654784i
$577$	14.1074	+	24.4347i	0.587298	+	1.01723i	0.994585	+	0.103930i	$0.0331418\pi$
$577$	14.1074	+	24.4347i	0.587298	+	1.01723i	−0.407286	+	0.913301i	$0.633525\pi$
$578$	3.83688	−	6.64567i	0.159593	−	0.276424i
$579$	3.54508	−	6.14027i	0.147329	−	0.255181i
$580$	−6.87539			−0.285485
$581$	−67.9230			−2.81792
$582$	4.61803	−	7.99867i	0.191424	−	0.331556i
$583$	−2.50000	+	4.33013i	−0.103539	+	0.179336i
$584$	−1.36475	−	2.36381i	−0.0564736	−	0.0978151i
$585$	−3.29180	−	5.70156i	−0.136099	−	0.235730i
$586$	4.61803			0.190769
$587$	−7.87132	−	13.6335i	−0.324884	−	0.562716i	0.656605	−	0.754235i	$-0.271992\pi$
$587$	−7.87132	−	13.6335i	−0.324884	−	0.562716i	−0.981489	+	0.191519i	$0.938659\pi$
$588$	−26.5623	−	46.0073i	−1.09541	−	1.89731i
$589$		0			0
$590$	1.20163	−	2.08128i	0.0494702	−	0.0856848i
$591$	7.70820			0.317073
$592$	7.63525	−	13.2246i	0.313807	−	0.543530i
$593$	15.2361	+	26.3896i	0.625670	+	1.08369i	0.988411	+	0.151803i	$0.0485078\pi$
$593$	15.2361	+	26.3896i	0.625670	+	1.08369i	−0.362741	+	0.931890i	$0.618159\pi$
$594$	−3.09017			−0.126791
$595$	15.9443	+	27.6163i	0.653651	+	1.13216i
$596$	8.34346	−	14.4513i	0.341761	−	0.591948i
$597$	2.54508	−	4.40822i	0.104163	−	0.180416i
$598$	−2.31308			−0.0945890
$599$	−18.1180	+	31.3814i	−0.740283	+	1.28221i	0.212084	+	0.977252i	$0.431975\pi$
$599$	−18.1180	+	31.3814i	−0.740283	+	1.28221i	−0.952366	+	0.304956i	$0.901358\pi$
$600$	13.3820			0.546316
$601$	29.4164			1.19992			0.599960	−	0.800030i	$-0.295183\pi$
$601$	29.4164			1.19992			0.599960	+	0.800030i	$0.295183\pi$
$602$	6.47214	+	8.40755i	0.263785	+	0.342666i
$603$	−14.8541			−0.604906
$604$	16.4164			0.667974
$605$	−1.29180	+	2.23746i	−0.0525190	+	0.0909655i
$606$	3.76393			0.152899
$607$	11.9271	−	20.6583i	0.484104	−	0.838493i	−0.515729	−	0.856752i	$-0.672479\pi$
$607$	11.9271	−	20.6583i	0.484104	−	0.838493i	0.999833	+	0.0182588i	$0.00581228\pi$
$608$	−2.56231	+	4.43804i	−0.103915	+	0.179986i
$609$	−16.6353	−	28.8131i	−0.674095	−	1.16757i
$610$	−1.34752			−0.0545597
$611$	−0.791796	−	1.37143i	−0.0320326	−	0.0554822i
$612$	21.7599	−	37.6892i	0.879590	−	1.52350i
$613$	5.20163			0.210092			0.105046	−	0.994467i	$-0.466501\pi$
$613$	5.20163			0.210092			0.105046	+	0.994467i	$0.466501\pi$
$614$	−4.43363	+	7.67927i	−0.178927	+	0.309910i
$615$	15.3262	+	26.5458i	0.618014	+	1.07043i
$616$	−11.2812	−	19.5395i	−0.454531	−	0.787270i
$617$	−4.85410	−	8.40755i	−0.195419	−	0.338475i	0.751619	−	0.659598i	$-0.229273\pi$
$617$	−4.85410	−	8.40755i	−0.195419	−	0.338475i	−0.947038	+	0.321122i	$0.895940\pi$
$618$	−16.4164			−0.660365
$619$	15.1353	+	26.2150i	0.608337	+	1.05367i	0.991514	+	0.129996i	$0.0414965\pi$
$619$	15.1353	+	26.2150i	0.608337	+	1.05367i	−0.383177	+	0.923675i	$0.625170\pi$
$620$		0			0
$621$	4.89919	−	8.48564i	0.196598	−	0.340517i
$622$	−5.69756	+	9.86846i	−0.228451	+	0.395689i
$623$	7.85410			0.314668
$624$	−11.3820			−0.455643
$625$	−2.20820	+	3.82472i	−0.0883282	+	0.152989i
$626$	2.50658	−	4.34152i	0.100183	−	0.173522i
$627$	5.85410	+	10.1396i	0.233790	+	0.404937i
$628$	−4.77051	−	8.26277i	−0.190364	−	0.329720i
$629$	−29.5623			−1.17873
$630$	−3.85410	−	6.67550i	−0.153551	−	0.265958i
$631$	13.5451	+	23.4608i	0.539221	+	0.933959i	0.998946	+	0.0458973i	$0.0146147\pi$
$631$	13.5451	+	23.4608i	0.539221	+	0.933959i	−0.459725	+	0.888061i	$0.652052\pi$
$632$	1.01722	+	1.76188i	0.0404629	+	0.0700838i
$633$	−12.0902	+	20.9408i	−0.480541	+	0.832322i
$634$	−12.7214			−0.505230
$635$	9.05573	−	15.6850i	0.359366	−	0.622439i
$636$	3.35410	+	5.80948i	0.132999	+	0.230361i
$637$	15.1246			0.599259
$638$	−2.07295	−	3.59045i	−0.0820688	−	0.142147i
$639$	20.8090	−	36.0423i	0.823192	−	1.42581i
$640$	−6.23607	+	10.8012i	−0.246502	+	0.426954i
$641$	10.8197			0.427351			0.213675	−	0.976905i	$-0.431457\pi$
$641$	10.8197			0.427351			0.213675	+	0.976905i	$0.431457\pi$
$642$	−3.76393	+	6.51932i	−0.148551	+	0.257297i
$643$	9.43769			0.372186			0.186093	−	0.982532i	$-0.440417\pi$
$643$	9.43769			0.372186			0.186093	+	0.982532i	$0.440417\pi$
$644$	34.4164			1.35620
$645$	−12.9443	−	16.8151i	−0.509680	−	0.662094i
$646$	2.87539			0.113131
$647$	−21.6738			−0.852084			−0.426042	−	0.904703i	$-0.640092\pi$
$647$	−21.6738			−0.852084			−0.426042	+	0.904703i	$0.640092\pi$
$648$	4.20163	−	7.27743i	0.165055	−	0.285884i
$649$	−18.4164			−0.722907
$650$	−0.916408	+	1.58726i	−0.0359445	+	0.0622577i
$651$		0			0
$652$	12.9787	+	22.4798i	0.508286	+	0.880377i
$653$	−32.8885			−1.28703			−0.643514	−	0.765434i	$-0.722524\pi$
$653$	−32.8885			−1.28703			−0.643514	+	0.765434i	$0.722524\pi$
$654$	6.92705	+	11.9980i	0.270869	+	0.469159i
$655$	−6.14590	+	10.6450i	−0.240140	+	0.415935i
$656$	29.7984			1.16343
$657$	−3.57295	+	6.18853i	−0.139394	+	0.241438i
$658$	−0.927051	−	1.60570i	−0.0361402	−	0.0625967i
$659$	14.6803	+	25.4271i	0.571865	+	0.990499i	0.996375	+	0.0850756i	$0.0271132\pi$
$659$	14.6803	+	25.4271i	0.571865	+	0.990499i	−0.424510	+	0.905423i	$0.639553\pi$
$660$	10.8541	+	18.7999i	0.422495	+	0.731783i
$661$	−43.3951			−1.68787			−0.843937	−	0.536442i	$-0.819768\pi$
$661$	−43.3951			−1.68787			−0.843937	+	0.536442i	$0.819768\pi$
$662$	−1.04508	−	1.81014i	−0.0406184	−	0.0703531i
$663$	11.0172	+	19.0824i	0.427873	+	0.741098i
$664$	−11.8024	+	20.4424i	−0.458023	+	0.793320i
$665$	−3.23607	+	5.60503i	−0.125489	+	0.217354i
$666$	7.14590			0.276898
$667$	13.1459			0.509011
$668$	13.1976	−	22.8588i	0.510629	−	0.884435i
$669$	3.61803	−	6.26662i	0.139881	−	0.242281i
$670$	−0.909830	−	1.57587i	−0.0351498	−	0.0608812i
$671$	5.16312	+	8.94278i	0.199320	+	0.345232i
$672$	−45.9787			−1.77367
$673$	−6.91641	−	11.9796i	−0.266608	−	0.461778i	0.701376	−	0.712792i	$-0.252570\pi$
$673$	−6.91641	−	11.9796i	−0.266608	−	0.461778i	−0.967984	+	0.251013i	$0.919236\pi$
$674$	5.34752	+	9.26218i	0.205979	+	0.356766i
$675$	−3.88197	−	6.72376i	−0.149417	−	0.258798i
$676$	−10.2812	+	17.8075i	−0.395429	+	0.684903i
$677$	−31.7639			−1.22079			−0.610394	−	0.792098i	$-0.708989\pi$
$677$	−31.7639			−1.22079			−0.610394	+	0.792098i	$0.708989\pi$
$678$	7.80902	−	13.5256i	0.299903	−	0.519448i
$679$	−19.5623	−	33.8829i	−0.750732	−	1.30031i
$680$	11.0820			0.424977
$681$	−1.92705	−	3.33775i	−0.0738448	−	0.127903i
$682$		0			0
$683$	5.56231	−	9.63420i	0.212836	−	0.368642i	−0.739765	−	0.672865i	$-0.765063\pi$
$683$	5.56231	−	9.63420i	0.212836	−	0.368642i	0.952601	+	0.304223i	$0.0983968\pi$
$684$	8.83282			0.337731
$685$	−2.29180	+	3.96951i	−0.0875650	+	0.151667i
$686$	6.38197			0.243665
$687$	6.00000			0.228914
$688$	−20.4483	+	2.72443i	−0.779586	+	0.103868i
$689$	−1.90983			−0.0727587
$690$	5.41641			0.206199
$691$	−7.86475	+	13.6221i	−0.299189	+	0.518211i	−0.975951	−	0.217992i	$-0.930049\pi$
$691$	−7.86475	+	13.6221i	−0.299189	+	0.518211i	0.676762	+	0.736202i	$0.263383\pi$
$692$	6.97871			0.265291
$693$	−29.5344	+	51.1552i	−1.12192	+	1.94322i
$694$	1.92705	−	3.33775i	0.0731499	−	0.126699i
$695$	3.27051	+	5.66469i	0.124058	+	0.214874i
$696$	−11.5623			−0.438268
$697$	−28.8435	−	49.9583i	−1.09252	−	1.89231i
$698$	3.95492	−	6.85011i	0.149696	−	0.259281i
$699$	−47.2148			−1.78583
$700$	13.6353	−	23.6170i	0.515364	−	0.892637i
$701$	7.25329	+	12.5631i	0.273953	+	0.474500i	0.969870	−	0.243621i	$-0.0783354\pi$
$701$	7.25329	+	12.5631i	0.273953	+	0.474500i	−0.695917	+	0.718122i	$0.745002\pi$
$702$	−0.590170	−	1.02220i	−0.0222745	−	0.0385806i
$703$	−3.00000	−	5.19615i	−0.113147	−	0.195977i
$704$	17.0344			0.642010
$705$	1.85410	+	3.21140i	0.0698295	+	0.120948i
$706$	−3.29180	−	5.70156i	−0.123888	−	0.214581i
$707$	7.97214	−	13.8081i	0.299823	−	0.519309i
$708$	−12.3541	+	21.3979i	−0.464296	+	0.804184i
$709$	28.8885			1.08493			0.542466	−	0.840078i	$-0.317491\pi$
$709$	28.8885			1.08493			0.542466	+	0.840078i	$0.317491\pi$
$710$	5.09830			0.191336
$711$	2.66312	−	4.61266i	0.0998748	−	0.172988i
$712$	1.36475	−	2.36381i	0.0511460	−	0.0885874i
$713$		0			0
$714$	12.8992	+	22.3420i	0.482740	+	0.836130i
$715$	−6.18034			−0.231132
$716$	8.94834	+	15.4990i	0.334415	+	0.579224i
$717$	−10.8541	−	18.7999i	−0.405354	−	0.702093i
$718$	−1.02129	−	1.76892i	−0.0381141	−	0.0660155i
$719$	5.39919	−	9.35167i	0.201356	−	0.348758i	−0.747610	−	0.664138i	$-0.768799\pi$
$719$	5.39919	−	9.35167i	0.201356	−	0.348758i	0.948965	+	0.315380i	$0.102132\pi$
$720$	14.9868			0.558527
$721$	−34.7705	+	60.2243i	−1.29492	+	2.24287i
$722$	−3.33688	−	5.77965i	−0.124186	−	0.215096i
$723$	−11.1803			−0.415801
$724$	−17.9681	−	31.1216i	−0.667778	−	1.15663i
$725$	5.20820	−	9.02087i	0.193428	−	0.335027i
$726$	−1.04508	+	1.81014i	−0.0387867	+	0.0671806i
$727$	−17.9787			−0.666794			−0.333397	−	0.942787i	$-0.608195\pi$
$727$	−17.9787			−0.666794			−0.333397	+	0.942787i	$0.608195\pi$
$728$	4.30902	−	7.46344i	0.159703	−	0.276613i
$729$	−39.5623			−1.46527
$730$	−0.875388			−0.0323996
$731$	24.3607	+	31.6455i	0.901012	+	1.17045i
$732$	13.8541			0.512062
$733$	24.5410			0.906443			0.453222	−	0.891398i	$-0.350275\pi$
$733$	24.5410			0.906443			0.453222	+	0.891398i	$0.350275\pi$
$734$	3.66312	−	6.34471i	0.135208	−	0.234187i
$735$	−35.4164			−1.30635
$736$	9.08359	−	15.7332i	0.334826	−	0.579935i
$737$	−6.97214	+	12.0761i	−0.256822	+	0.444829i
$738$	6.97214	+	12.0761i	0.256648	+	0.444527i
$739$	49.5410			1.82240			0.911198	−	0.411969i	$-0.135159\pi$
$739$	49.5410			1.82240			0.911198	+	0.411969i	$0.135159\pi$
$740$	−5.56231	−	9.63420i	−0.204474	−	0.354160i
$741$	−2.23607	+	3.87298i	−0.0821440	+	0.142278i
$742$	−2.23607			−0.0820886
$743$	−16.6803	+	28.8912i	−0.611942	+	1.05992i	0.378970	+	0.925409i	$0.376278\pi$
$743$	−16.6803	+	28.8912i	−0.611942	+	1.05992i	−0.990913	+	0.134506i	$0.957055\pi$
$744$		0			0
$745$	−5.56231	−	9.63420i	−0.203787	−	0.352970i
$746$	1.14590	+	1.98475i	0.0419543	+	0.0726670i
$747$	61.7984			2.26108
$748$	−20.4271	−	35.3807i	−0.746887	−	1.29365i
$749$	15.9443	+	27.6163i	0.582591	+	1.00908i
$750$	5.23607	−	9.06914i	0.191194	−	0.331158i
$751$	18.9894	−	32.8905i	0.692931	−	1.20019i	−0.277942	−	0.960598i	$-0.589652\pi$
$751$	18.9894	−	32.8905i	0.692931	−	1.20019i	0.970873	−	0.239595i	$-0.0770145\pi$
$752$	3.60488			0.131456
$753$	76.3951			2.78399
$754$	0.791796	−	1.37143i	0.0288355	−	0.0499446i
$755$	5.47214	−	9.47802i	0.199151	−	0.344940i
$756$	8.78115	+	15.2094i	0.319367	+	0.553161i
$757$	15.4894	+	26.8284i	0.562970	+	0.975093i	0.997235	+	0.0743080i	$0.0236748\pi$
$757$	15.4894	+	26.8284i	0.562970	+	0.975093i	−0.434265	+	0.900785i	$0.642992\pi$
$758$	10.4508			0.379592
$759$	−20.7533	−	35.9458i	−0.753297	−	1.30475i
$760$	1.12461	+	1.94788i	0.0407940	+	0.0706572i
$761$	−0.545085	−	0.944115i	−0.0197593	−	0.0342241i	0.855977	−	0.517014i	$-0.172957\pi$
$761$	−0.545085	−	0.944115i	−0.0197593	−	0.0342241i	−0.875736	+	0.482790i	$0.839623\pi$
$762$	7.32624	−	12.6894i	0.265402	−	0.459689i
$763$	58.6869			2.12461
$764$	−13.4681	+	23.3274i	−0.487258	+	0.843955i
$765$	−14.5066	−	25.1261i	−0.524486	−	0.908437i
$766$	−14.5623			−0.526157
$767$	−3.51722	−	6.09201i	−0.126999	−	0.219970i
$768$	7.28115	−	12.6113i	0.262736	−	0.455072i
$769$	−9.94427	+	17.2240i	−0.358600	+	0.621113i	−0.987727	−	0.156189i	$-0.950079\pi$
$769$	−9.94427	+	17.2240i	−0.358600	+	0.621113i	0.629128	+	0.777302i	$0.283412\pi$
$770$	−7.23607			−0.260770
$771$	4.50000	−	7.79423i	0.162064	−	0.280702i
$772$	−5.02129			−0.180720
$773$	15.5967			0.560976			0.280488	−	0.959858i	$-0.409504\pi$
$773$	15.5967			0.560976			0.280488	+	0.959858i	$0.409504\pi$
$774$	−5.88854	−	7.64944i	−0.211659	−	0.274954i
$775$		0			0
$776$	−13.5967			−0.488095
$777$	26.9164	−	46.6206i	0.965621	−	1.67250i
$778$	13.3951			0.480238
$779$	5.85410	−	10.1396i	0.209745	−	0.363289i
$780$	−4.14590	+	7.18091i	−0.148447	+	0.257118i
$781$	−19.5344	−	33.8346i	−0.698997	−	1.21070i
$782$	−10.1935			−0.364519
$783$	3.35410	+	5.80948i	0.119866	+	0.207614i
$784$	−17.2148	+	29.8169i	−0.614814	+	1.06489i
$785$	−6.36068			−0.227022
$786$	−4.97214	+	8.61199i	−0.177350	+	0.307180i
$787$	−5.22542	−	9.05070i	−0.186266	−	0.322623i	0.757736	−	0.652561i	$-0.226305\pi$
$787$	−5.22542	−	9.05070i	−0.186266	−	0.322623i	−0.944002	+	0.329938i	$0.892972\pi$
$788$	−2.72949	−	4.72762i	−0.0972341	−	0.168414i
$789$	36.0066	+	62.3652i	1.28187	+	2.22026i
$790$	0.652476			0.0232140
$791$	−33.0795	−	57.2954i	−1.17617	−	2.03719i
$792$	10.2639	+	17.7777i	0.364713	+	0.631701i
$793$	−1.97214	+	3.41584i	−0.0700326	+	0.121300i
$794$	6.19098	−	10.7231i	0.219710	−	0.380548i
$795$	4.47214			0.158610
$796$	−3.60488			−0.127772
$797$	4.11803	−	7.13264i	0.145868	−	0.252651i	−0.783828	−	0.620978i	$-0.786736\pi$
$797$	4.11803	−	7.13264i	0.145868	−	0.252651i	0.929697	+	0.368326i	$0.120069\pi$
$798$	−2.61803	+	4.53457i	−0.0926774	+	0.160522i
$799$	−3.48936	−	6.04374i	−0.123445	−	0.213812i
$800$	−7.19756	−	12.4665i	−0.254472	−	0.440759i
$801$	−7.14590			−0.252488
$802$	−4.85410	−	8.40755i	−0.171404	−	0.296881i
$803$	3.35410	+	5.80948i	0.118364	+	0.205012i
$804$	9.35410	+	16.2018i	0.329894	+	0.571393i
$805$	11.4721	−	19.8703i	0.404340	−	0.700337i
$806$		0			0
$807$	15.1353	−	26.2150i	0.532786	−	0.922813i
$808$	−2.77051	−	4.79866i	−0.0974662	−	0.168816i
$809$	4.74265			0.166743			0.0833713	−	0.996519i	$-0.473431\pi$
$809$	4.74265			0.166743			0.0833713	+	0.996519i	$0.473431\pi$
$810$	−1.34752	−	2.33398i	−0.0473472	−	0.0820077i
$811$	−23.6976	+	41.0454i	−0.832134	+	1.44130i	0.0642089	+	0.997936i	$0.479548\pi$
$811$	−23.6976	+	41.0454i	−0.832134	+	1.44130i	−0.896343	+	0.443362i	$0.853786\pi$
$812$	−11.7812	+	20.4056i	−0.413437	+	0.716095i
$813$	−36.2705			−1.27206
$814$	3.35410	−	5.80948i	0.117561	−	0.203622i
$815$	17.3050			0.606166
$816$	−50.1591			−1.75592
$817$	−3.09017	+	7.49326i	−0.108111	+	0.262156i
$818$	−3.40325			−0.118992
$819$	−22.5623			−0.788391
$820$	10.8541	−	18.7999i	0.379042	−	0.656519i
$821$	0.326238			0.0113858			0.00569289	−	0.999984i	$-0.498188\pi$
$821$	0.326238			0.0113858			0.00569289	+	0.999984i	$0.498188\pi$
$822$	−1.85410	+	3.21140i	−0.0646692	+	0.112010i
$823$	−26.0066	+	45.0447i	−0.906532	+	1.57016i	−0.0876853	+	0.996148i	$0.527947\pi$
$823$	−26.0066	+	45.0447i	−0.906532	+	1.57016i	−0.818847	+	0.574012i	$0.805386\pi$
$824$	12.0836	+	20.9294i	0.420952	+	0.729110i
$825$	−32.8885			−1.14503
$826$	−4.11803	−	7.13264i	−0.143285	−	0.248176i
$827$	−4.59017	+	7.95041i	−0.159616	+	0.276463i	−0.934730	−	0.355358i	$-0.884359\pi$
$827$	−4.59017	+	7.95041i	−0.159616	+	0.276463i	0.775114	+	0.631821i	$0.217692\pi$
$828$	−31.3131			−1.08820
$829$	−14.0795	+	24.3865i	−0.489002	+	0.846977i	−0.999920	−	0.0126530i	$-0.995972\pi$
$829$	−14.0795	+	24.3865i	−0.489002	+	0.846977i	0.510918	+	0.859630i	$0.329306\pi$
$830$	3.78522	+	6.55619i	0.131387	+	0.227569i
$831$	−16.3262	−	28.2779i	−0.566351	−	0.980949i
$832$	3.25329	+	5.63486i	0.112787	+	0.195354i
$833$	66.6525			2.30937
$834$	2.64590	+	4.58283i	0.0916200	+	0.158690i
$835$	−8.79837	−	15.2392i	−0.304480	−	0.527375i
$836$	4.14590	−	7.18091i	0.143389	−	0.248357i
$837$		0			0
$838$	3.90983			0.135063
$839$	25.8885			0.893772			0.446886	−	0.894591i	$-0.352533\pi$
$839$	25.8885			0.893772			0.446886	+	0.894591i	$0.352533\pi$
$840$	−10.0902	+	17.4767i	−0.348144	+	0.603003i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−1.46149	−	2.53138i	−0.0503664	−	0.0872371i
$843$	9.78115	+	16.9415i	0.336881	+	0.583495i
$844$	17.1246			0.589453
$845$	6.85410	+	11.8717i	0.235788	+	0.408397i
$846$	0.843459	+	1.46091i	0.0289987	+	0.0502272i
$847$	4.42705	+	7.66788i	0.152115	+	0.263471i
$848$	2.17376	−	3.76507i	0.0746473	−	0.129293i
$849$	−28.1803			−0.967147
$850$	−4.03851	+	6.99490i	−0.138520	+	0.239923i
$851$	10.6353	+	18.4208i	0.364572	+	0.631457i
$852$	−52.4164			−1.79576
$853$	−5.62868	−	9.74915i	−0.192722	−	0.333805i	0.753429	−	0.657529i	$-0.228398\pi$
$853$	−5.62868	−	9.74915i	−0.192722	−	0.333805i	−0.946151	+	0.323724i	$0.895065\pi$
$854$	−2.30902	+	3.99933i	−0.0790129	+	0.136854i
$855$	2.94427	−	5.09963i	0.100692	−	0.174404i
$856$	11.0820			0.378776
$857$	18.0902	−	31.3331i	0.617948	−	1.07032i	−0.371911	−	0.928268i	$-0.621297\pi$
$857$	18.0902	−	31.3331i	0.617948	−	1.07032i	0.989860	−	0.142050i	$-0.0453693\pi$
$858$	−5.00000			−0.170697
$859$	−49.4164			−1.68607			−0.843033	−	0.537862i	$-0.819232\pi$
$859$	−49.4164			−1.68607			−0.843033	+	0.537862i	$0.819232\pi$
$860$	−5.72949	+	13.8933i	−0.195374	+	0.473757i
$861$	105.048			3.58001
$862$	9.47214			0.322622
$863$	−4.75329	+	8.23294i	−0.161804	+	0.280252i	−0.935516	−	0.353285i	$-0.885065\pi$
$863$	−4.75329	+	8.23294i	−0.161804	+	0.280252i	0.773712	+	0.633538i	$0.218398\pi$
$864$	9.27051			0.315389
$865$	2.32624	−	4.02916i	0.0790945	−	0.136996i
$866$	−6.62868	+	11.4812i	−0.225252	+	0.390147i
$867$	26.2984	+	45.5501i	0.893140	+	1.54696i
$868$		0			0
$869$	−2.50000	−	4.33013i	−0.0848067	−	0.146889i
$870$	−1.85410	+	3.21140i	−0.0628599	+	0.108877i
$871$	−5.32624			−0.180473
$872$	10.1976	−	17.6627i	0.345333	−	0.598134i
$873$	17.7984	+	30.8277i	0.602384	+	1.04336i
$874$	−1.03444	−	1.79171i	−0.0349905	−	0.0606054i
$875$	−22.1803	−	38.4175i	−0.749832	−	1.29875i
$876$	9.00000			0.304082
$877$	3.82624	+	6.62724i	0.129203	+	0.223786i	0.923368	−	0.383916i	$-0.125425\pi$
$877$	3.82624	+	6.62724i	0.129203	+	0.223786i	−0.794165	+	0.607702i	$0.792091\pi$
$878$	0.218847	+	0.379054i	0.00738573	+	0.0127925i
$879$	−15.8262	+	27.4118i	−0.533806	+	0.924579i
$880$	7.03444	−	12.1840i	0.237131	−	0.410723i
$881$	33.7639			1.13754			0.568768	−	0.822498i	$-0.307420\pi$
$881$	33.7639			1.13754			0.568768	+	0.822498i	$0.307420\pi$
$882$	−16.1115			−0.542501
$883$	−6.56231	+	11.3662i	−0.220839	+	0.382505i	−0.955063	−	0.296403i	$-0.904213\pi$
$883$	−6.56231	+	11.3662i	−0.220839	+	0.382505i	0.734224	+	0.678907i	$0.237546\pi$
$884$	7.80244	−	13.5142i	0.262424	−	0.454532i
$885$	8.23607	+	14.2653i	0.276852	+	0.479522i
$886$	0.472136	+	0.817763i	0.0158617	+	0.0274733i
$887$	−52.9574			−1.77814			−0.889068	−	0.457775i	$-0.848647\pi$
$887$	−52.9574			−1.77814			−0.889068	+	0.457775i	$0.848647\pi$
$888$	−9.35410	−	16.2018i	−0.313903	−	0.543696i
$889$	−31.0344	−	53.7532i	−1.04086	−	1.80283i
$890$	−0.437694	−	0.758108i	−0.0146715	−	0.0254119i
$891$	−10.3262	+	17.8856i	−0.345942	+	0.599189i
$892$	−5.12461			−0.171585
$893$	0.708204	−	1.22665i	0.0236991	−	0.0410481i
$894$	−4.50000	−	7.79423i	−0.150503	−	0.260678i
$895$	11.9311			0.398813
$896$	21.3713	+	37.0162i	0.713966	+	1.23663i
$897$	7.92705	−	13.7301i	0.264677	−	0.458433i
$898$	−6.27051	+	10.8608i	−0.209250	+	0.362431i
$899$		0			0
$900$	−12.4058	+	21.4874i	−0.413525	+	0.716247i
$901$	−8.41641			−0.280391
$902$	13.0902			0.435855
$903$	−72.0861	+	9.60437i	−2.39888	+	0.319613i
$904$	−22.9919			−0.764698
$905$	−23.9574			−0.796372
$906$	4.42705	−	7.66788i	0.147079	−	0.254748i
$907$	−21.7082			−0.720809			−0.360405	−	0.932796i	$-0.617361\pi$
$907$	−21.7082			−0.720809			−0.360405	+	0.932796i	$0.617361\pi$
$908$	−1.36475	+	2.36381i	−0.0452907	+	0.0784457i
$909$	−7.25329	+	12.5631i	−0.240576	+	0.416691i
$910$	−1.38197	−	2.39364i	−0.0458117	−	0.0793482i
$911$	−42.9787			−1.42395			−0.711974	−	0.702206i	$-0.752199\pi$
$911$	−42.9787			−1.42395			−0.711974	+	0.702206i	$0.752199\pi$
$912$	−5.09017	−	8.81643i	−0.168552	−	0.291941i
$913$	29.0066	−	50.2409i	0.959978	−	1.66273i
$914$	6.00000			0.198462
$915$	4.61803	−	7.99867i	0.152667	−	0.264428i
$916$	−2.12461	−	3.67994i	−0.0701991	−	0.121588i
$917$	21.0623	+	36.4810i	0.695539	+	1.20471i
$918$	−2.60081	−	4.50474i	−0.0858396	−	0.148679i
$919$	29.3951			0.969656			0.484828	−	0.874610i	$-0.338882\pi$
$919$	29.3951			0.969656			0.484828	+	0.874610i	$0.338882\pi$
$920$	−3.98684	−	6.90542i	−0.131442	−	0.227665i
$921$	−30.3885	−	52.6345i	−1.00134	−	1.73437i
$922$	−6.03444	+	10.4520i	−0.198734	+	0.344217i
$923$	7.46149	−	12.9237i	0.245598	−	0.425388i
$924$	74.3951			2.44742
$925$	16.8541			0.554159
$926$	−5.69756	+	9.86846i	−0.187233	+	0.324298i
$927$	31.6353	−	54.7939i	1.03904	−	1.79967i
$928$	6.21885	+	10.7714i	0.204144	+	0.353587i
$929$	−17.6180	−	30.5153i	−0.578029	−	1.00118i	−0.995705	−	0.0925796i	$-0.970489\pi$
$929$	−17.6180	−	30.5153i	−0.578029	−	1.00118i	0.417676	−	0.908596i	$-0.362845\pi$
$930$		0			0
$931$	6.76393	+	11.7155i	0.221679	+	0.383959i
$932$	16.7188	+	28.9579i	0.547644	+	0.948547i
$933$	−39.0517	−	67.6395i	−1.27849	−	2.21442i
$934$	−2.87539	+	4.98032i	−0.0940856	+	0.162961i
$935$	−27.2361			−0.890715
$936$	−3.92047	+	6.79046i	−0.128145	+	0.221953i
$937$	27.6631	+	47.9139i	0.903715	+	1.56528i	0.822633	+	0.568572i	$0.192504\pi$
$937$	27.6631	+	47.9139i	0.903715	+	1.56528i	0.0810814	+	0.996707i	$0.474163\pi$
$938$	−6.23607			−0.203615
$939$	17.1803	+	29.7572i	0.560659	+	0.971090i
$940$	1.31308	−	2.27433i	0.0428280	−	0.0741803i
$941$	13.1180	−	22.7211i	0.427636	−	0.740687i	−0.569027	−	0.822319i	$-0.692680\pi$
$941$	13.1180	−	22.7211i	0.427636	−	0.740687i	0.996663	+	0.0816322i	$0.0260133\pi$
$942$	−5.14590			−0.167662
$943$	−20.7533	+	35.9458i	−0.675820	+	1.17055i
$944$	16.0132			0.521184
$945$	11.7082			0.380868
$946$	−8.98278	+	1.19682i	−0.292055	+	0.0389119i
$947$	25.3607			0.824111			0.412056	−	0.911159i	$-0.364811\pi$
$947$	25.3607			0.824111			0.412056	+	0.911159i	$0.364811\pi$
$948$	−6.70820			−0.217872
$949$	−1.28115	+	2.21902i	−0.0415880	+	0.0720325i
$950$	−1.63932			−0.0531866
$951$	43.5967	−	75.5118i	1.41372	−	2.44864i
$952$	18.9894	−	32.8905i	0.615449	−	1.06599i
$953$	19.4443	+	33.6785i	0.629862	+	1.09095i	0.987579	+	0.157123i	$0.0502218\pi$
$953$	19.4443	+	33.6785i	0.629862	+	1.09095i	−0.357717	+	0.933830i	$0.616445\pi$
$954$	2.03444			0.0658675
$955$	8.97871	+	15.5516i	0.290544	+	0.503238i
$956$	−7.68692	+	13.3141i	−0.248613	+	0.430610i
$957$	28.4164			0.918572
$958$	−2.63932	+	4.57144i	−0.0852726	+	0.147696i
$959$	7.85410	+	13.6037i	0.253622	+	0.439287i
$960$	−7.61803	−	13.1948i	−0.245871	−	0.425861i
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	2.56231			0.0826121
$963$	−14.5066	−	25.1261i	−0.467468	−	0.809678i
$964$	3.95898	+	6.85716i	0.127510	+	0.220854i
$965$	−1.67376	+	2.89904i	−0.0538803	+	0.0933234i
$966$	9.28115	−	16.0754i	0.298616	−	0.517218i
$967$	38.1033			1.22532			0.612660	−	0.790346i	$-0.290099\pi$
$967$	38.1033			1.22532			0.612660	+	0.790346i	$0.290099\pi$
$968$	3.07701			0.0988990
$969$	−9.85410	+	17.0678i	−0.316559	+	0.548297i
$970$	−2.18034	+	3.77646i	−0.0700065	+	0.121255i
$971$	8.68034	+	15.0348i	0.278565	+	0.482489i	0.971028	−	0.238964i	$-0.0768078\pi$
$971$	8.68034	+	15.0348i	0.278565	+	0.482489i	−0.692463	+	0.721453i	$0.743474\pi$
$972$	20.0729	+	34.7674i	0.643840	+	1.11516i
$973$	22.4164			0.718637
$974$	0.253289	+	0.438709i	0.00811590	+	0.0140572i
$975$	−6.28115	−	10.8793i	−0.201158	−	0.348416i
$976$	−4.48936	−	7.77579i	−0.143701	−	0.248897i
$977$	−20.6180	+	35.7115i	−0.659629	+	1.14251i	0.321082	+	0.947051i	$0.395953\pi$
$977$	−20.6180	+	35.7115i	−0.659629	+	1.14251i	−0.980712	+	0.195460i	$0.937380\pi$
$978$	14.0000			0.447671
$979$	−3.35410	+	5.80948i	−0.107198	+	0.185672i
$980$	12.5410	+	21.7217i	0.400608	+	0.693874i
$981$	−53.3951			−1.70478
$982$	4.13525	+	7.16247i	0.131961	+	0.228564i
$983$	5.23607	−	9.06914i	0.167005	−	0.289261i	−0.770361	−	0.637608i	$-0.779924\pi$
$983$	5.23607	−	9.06914i	0.167005	−	0.289261i	0.937365	+	0.348348i	$0.113257\pi$
$984$	18.2533	−	31.6156i	0.581894	−	1.00787i
$985$	−3.63932			−0.115958
$986$	3.48936	−	6.04374i	0.111124	−	0.192472i
$987$	12.7082			0.404507
$988$	3.16718			0.100762
$989$	10.9549	−	26.5643i	0.348346	−	0.844694i
$990$	6.58359			0.209240
$991$	−10.8197			−0.343698			−0.171849	−	0.985123i	$-0.554974\pi$
$991$	−10.8197			−0.343698			−0.171849	+	0.985123i	$0.554974\pi$
$992$		0			0
$993$	14.3262			0.454629
$994$	8.73607	−	15.1313i	0.277091	−	0.479936i
$995$	−1.20163	+	2.08128i	−0.0380941	+	0.0659809i
$996$	−38.9164	−	67.4052i	−1.23311	−	2.13582i
$997$	−19.4508			−0.616015			−0.308007	−	0.951384i	$-0.599662\pi$
$997$	−19.4508			−0.616015			−0.308007	+	0.951384i	$0.599662\pi$
$998$	2.64590	+	4.58283i	0.0837544	+	0.145067i
$999$	−5.42705	+	9.39993i	−0.171704	+	0.297401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.c.b.6.2	✓	4
3.2	odd	2		387.2.h.d.307.1		4
4.3	odd	2		688.2.i.e.49.1		4
43.6	even	3		1849.2.a.e.1.2		2
43.36	even	3	inner	43.2.c.b.36.2	yes	4
43.37	odd	6		1849.2.a.h.1.1		2
129.122	odd	6		387.2.h.d.208.1		4
172.79	odd	6		688.2.i.e.337.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.b.6.2	✓	4	1.1	even	1	trivial
43.2.c.b.36.2	yes	4	43.36	even	3	inner
387.2.h.d.208.1		4	129.122	odd	6
387.2.h.d.307.1		4	3.2	odd	2
688.2.i.e.49.1		4	4.3	odd	2
688.2.i.e.337.1		4	172.79	odd	6
1849.2.a.e.1.2		2	43.6	even	3
1849.2.a.h.1.1		2	43.37	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.381966 q^{2} +(1.30902 - 2.26728i) q^{3} -1.85410 q^{4} +(-0.618034 + 1.07047i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.11803 + 3.66854i) q^{7} +1.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\)	\(q-0.381966 q^{2} +(1.30902 - 2.26728i) q^{3} -1.85410 q^{4} +(-0.618034 + 1.07047i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.11803 + 3.66854i) q^{7} +1.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(0.236068 - 0.408882i) q^{10} -3.61803 q^{11} +(-2.42705 + 4.20378i) q^{12} +(-0.690983 - 1.19682i) q^{13} +(-0.809017 - 1.40126i) q^{14} +(1.61803 + 2.80252i) q^{15} +3.14590 q^{16} +(-3.04508 - 5.27424i) q^{17} +(0.736068 + 1.27491i) q^{18} +(0.618034 - 1.07047i) q^{19} +(1.14590 - 1.98475i) q^{20} +11.0902 q^{21} +1.38197 q^{22} +(-2.19098 + 3.79489i) q^{23} +(1.92705 - 3.33775i) q^{24} +(1.73607 + 3.00696i) q^{25} +(0.263932 + 0.457144i) q^{26} -2.23607 q^{27} +(-3.92705 - 6.80185i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-0.618034 - 1.07047i) q^{30} -4.14590 q^{32} +(-4.73607 + 8.20311i) q^{33} +(1.16312 + 2.01458i) q^{34} -5.23607 q^{35} +(3.57295 + 6.18853i) q^{36} +(2.42705 - 4.20378i) q^{37} +(-0.236068 + 0.408882i) q^{38} -3.61803 q^{39} +(-0.909830 + 1.57587i) q^{40} +9.47214 q^{41} -4.23607 q^{42} +(-6.50000 + 0.866025i) q^{43} +6.70820 q^{44} +4.76393 q^{45} +(0.836881 - 1.44952i) q^{46} +1.14590 q^{47} +(4.11803 - 7.13264i) q^{48} +(-5.47214 + 9.47802i) q^{49} +(-0.663119 - 1.14856i) q^{50} -15.9443 q^{51} +(1.28115 + 2.21902i) q^{52} +(0.690983 - 1.19682i) q^{53} +0.854102 q^{54} +(2.23607 - 3.87298i) q^{55} +(3.11803 + 5.40059i) q^{56} +(-1.61803 - 2.80252i) q^{57} +(0.572949 + 0.992377i) q^{58} +5.09017 q^{59} +(-3.00000 - 5.19615i) q^{60} +(-1.42705 - 2.47172i) q^{61} +(8.16312 - 14.1389i) q^{63} -4.70820 q^{64} +1.70820 q^{65} +(1.80902 - 3.13331i) q^{66} +(1.92705 - 3.33775i) q^{67} +(5.64590 + 9.77898i) q^{68} +(5.73607 + 9.93516i) q^{69} +2.00000 q^{70} +(5.39919 + 9.35167i) q^{71} +(-2.83688 - 4.91362i) q^{72} +(-0.927051 - 1.60570i) q^{73} +(-0.927051 + 1.60570i) q^{74} +9.09017 q^{75} +(-1.14590 + 1.98475i) q^{76} +(-7.66312 - 13.2729i) q^{77} +1.38197 q^{78} +(0.690983 + 1.19682i) q^{79} +(-1.94427 + 3.36758i) q^{80} +(2.85410 - 4.94345i) q^{81} -3.61803 q^{82} +(-8.01722 + 13.8862i) q^{83} -20.5623 q^{84} +7.52786 q^{85} +(2.48278 - 0.330792i) q^{86} -7.85410 q^{87} -5.32624 q^{88} +(0.927051 - 1.60570i) q^{89} -1.81966 q^{90} +(2.92705 - 5.06980i) q^{91} +(4.06231 - 7.03612i) q^{92} -0.437694 q^{94} +(0.763932 + 1.32317i) q^{95} +(-5.42705 + 9.39993i) q^{96} -9.23607 q^{97} +(2.09017 - 3.62028i) q^{98} +(6.97214 + 12.0761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9	\( 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9} - 8 q^{10} - 10 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} + 2 q^{15} + 26 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 22 q^{21} + 10 q^{22} - 11 q^{23} + q^{24} - 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} - 30 q^{32} - 10 q^{33} - 11 q^{34} - 12 q^{35} + 21 q^{36} + 3 q^{37} + 8 q^{38} - 10 q^{39} - 26 q^{40} + 20 q^{41} - 8 q^{42} - 26 q^{43} + 28 q^{45} + 19 q^{46} + 18 q^{47} + 12 q^{48} - 4 q^{49} + 13 q^{50} - 28 q^{51} - 15 q^{52} + 5 q^{53} - 10 q^{54} + 8 q^{56} - 2 q^{57} + 9 q^{58} - 2 q^{59} - 12 q^{60} + q^{61} + 17 q^{63} + 8 q^{64} - 20 q^{65} + 5 q^{66} + q^{67} + 36 q^{68} + 14 q^{69} + 8 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} + 3 q^{74} + 14 q^{75} - 18 q^{76} - 15 q^{77} + 10 q^{78} + 5 q^{79} + 28 q^{80} - 2 q^{81} - 10 q^{82} - 3 q^{83} - 42 q^{84} + 48 q^{85} + 39 q^{86} - 18 q^{87} + 10 q^{88} - 3 q^{89} - 52 q^{90} + 5 q^{91} - 24 q^{92} - 42 q^{94} + 12 q^{95} - 15 q^{96} - 28 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9 - 8 * q^10 - 10 * q^11 - 3 * q^12 - 5 * q^13 - q^14 + 2 * q^15 + 26 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 22 * q^21 + 10 * q^22 - 11 * q^23 + q^24 - 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 - 30 * q^32 - 10 * q^33 - 11 * q^34 - 12 * q^35 + 21 * q^36 + 3 * q^37 + 8 * q^38 - 10 * q^39 - 26 * q^40 + 20 * q^41 - 8 * q^42 - 26 * q^43 + 28 * q^45 + 19 * q^46 + 18 * q^47 + 12 * q^48 - 4 * q^49 + 13 * q^50 - 28 * q^51 - 15 * q^52 + 5 * q^53 - 10 * q^54 + 8 * q^56 - 2 * q^57 + 9 * q^58 - 2 * q^59 - 12 * q^60 + q^61 + 17 * q^63 + 8 * q^64 - 20 * q^65 + 5 * q^66 + q^67 + 36 * q^68 + 14 * q^69 + 8 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 + 3 * q^74 + 14 * q^75 - 18 * q^76 - 15 * q^77 + 10 * q^78 + 5 * q^79 + 28 * q^80 - 2 * q^81 - 10 * q^82 - 3 * q^83 - 42 * q^84 + 48 * q^85 + 39 * q^86 - 18 * q^87 + 10 * q^88 - 3 * q^89 - 52 * q^90 + 5 * q^91 - 24 * q^92 - 42 * q^94 + 12 * q^95 - 15 * q^96 - 28 * q^97 - 14 * q^98 + 10 * q^99

Introduction

L-functions

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