LMFDB - Embedded newform 546.2.by.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	546.19
Dual form			546.2.by.a.115.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.421063 - 0.112824i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.44466 + 1.01175i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.421063 - 0.112824i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.44466 + 1.01175i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +0.435917 q^{10} +(1.13468 + 1.13468i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.06233 - 3.44550i) q^{13} +(2.09950 + 1.61000i) q^{14} +(0.112824 + 0.421063i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.582739 - 1.00933i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(4.57550 + 4.57550i) q^{19} +(0.421063 + 0.112824i) q^{20} +(-1.01175 + 2.44466i) q^{21} +(0.802339 + 1.38969i) q^{22} +(-4.85037 + 2.80036i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.16556 + 2.40499i) q^{25} +(-0.134376 - 3.60305i) q^{26} -1.00000i q^{27} +(1.61126 + 2.09853i) q^{28} +(-1.92767 + 3.33883i) q^{29} +0.435917i q^{30} +(2.28207 - 8.51682i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.13468 + 1.13468i) q^{33} +(0.824118 - 0.824118i) q^{34} +(1.14351 + 0.150196i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(1.27404 - 4.75480i) q^{37} +(3.23537 + 5.60382i) q^{38} +(3.44550 - 1.06233i) q^{39} +(0.377515 + 0.217958i) q^{40} +(1.78730 - 0.478906i) q^{41} +(-1.61000 + 2.09950i) q^{42} +(-0.251976 + 0.145478i) q^{43} +(0.415321 + 1.55000i) q^{44} +(-0.421063 + 0.112824i) q^{45} +(-5.40989 + 1.44957i) q^{46} +(1.19456 + 4.45815i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(4.95272 + 4.94677i) q^{49} +(-4.64608 + 1.24491i) q^{50} +(1.00933 + 0.582739i) q^{51} +(0.802739 - 3.51505i) q^{52} +(-2.94607 - 5.10274i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.605790 + 0.349753i) q^{55} +(1.01322 + 2.44405i) q^{56} +(-4.57550 + 4.57550i) q^{57} +(-2.72614 + 2.72614i) q^{58} +(-3.35860 - 12.5345i) q^{59} +(-0.112824 + 0.421063i) q^{60} +0.413392i q^{61} +(4.40863 - 7.63597i) q^{62} +(-2.44466 - 1.01175i) q^{63} +1.00000i q^{64} +(-0.836043 - 1.33092i) q^{65} +(-1.38969 + 0.802339i) q^{66} +(-1.22023 + 1.22023i) q^{67} +(1.00933 - 0.582739i) q^{68} +(-2.80036 - 4.85037i) q^{69} +(1.06567 + 0.441039i) q^{70} +(-7.98595 - 2.13983i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(0.797676 + 0.213737i) q^{73} +(2.46126 - 4.26303i) q^{74} +(-2.40499 - 4.16556i) q^{75} +(1.67475 + 6.25025i) q^{76} +(1.62589 + 3.92191i) q^{77} +(3.60305 - 0.134376i) q^{78} +(4.79745 - 8.30943i) q^{79} +(0.308240 + 0.308240i) q^{80} +1.00000 q^{81} +1.85035 q^{82} +(-7.03301 - 7.03301i) q^{83} +(-2.09853 + 1.61126i) q^{84} +(0.131493 - 0.490740i) q^{85} +(-0.281043 + 0.0753052i) q^{86} +(-3.33883 - 1.92767i) q^{87} +1.60468i q^{88} +(6.66910 + 1.78698i) q^{89} -0.435917 q^{90} +(0.888935 - 9.49788i) q^{91} -5.60073 q^{92} +(8.51682 + 2.28207i) q^{93} +4.61542i q^{94} +(2.44280 + 1.41035i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(0.433491 - 1.61781i) q^{97} +(3.50364 + 6.06007i) q^{98} +(-1.13468 - 1.13468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.421063	−	0.112824i	0.188305	−	0.0504562i	−0.163434	−	0.986554i	$-0.552257\pi$
$5$	0.421063	−	0.112824i	0.188305	−	0.0504562i	0.351739	+	0.936098i	$0.385590\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	2.44466	+	1.01175i	0.923995	+	0.382406i
$7$	2.44466	+	1.01175i	0.923995	+	0.382406i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	0.435917			0.137849
$11$	1.13468	+	1.13468i	0.342118	+	0.342118i	0.857163	−	0.515045i	$-0.172225\pi$
$11$	1.13468	+	1.13468i	0.342118	+	0.342118i	−0.515045	+	0.857163i	$0.672225\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.06233	−	3.44550i	−0.294639	−	0.955609i
$13$	−1.06233	−	3.44550i	−0.294639	−	0.955609i
$14$	2.09950	+	1.61000i	0.561115	+	0.430291i
$15$	0.112824	+	0.421063i	0.0291309	+	0.108718i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.582739	−	1.00933i	0.141335	−	0.244799i	−0.786665	−	0.617381i	$-0.788194\pi$
$17$	0.582739	−	1.00933i	0.141335	−	0.244799i	0.928000	+	0.372581i	$0.121527\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	4.57550	+	4.57550i	1.04969	+	1.04969i	0.998699	+	0.0509932i	$0.0162387\pi$
$19$	4.57550	+	4.57550i	1.04969	+	1.04969i	0.0509932	+	0.998699i	$0.483761\pi$
$20$	0.421063	+	0.112824i	0.0941526	+	0.0252281i
$21$	−1.01175	+	2.44466i	−0.220782	+	0.533468i
$22$	0.802339	+	1.38969i	0.171059	+	0.296283i
$23$	−4.85037	+	2.80036i	−1.01137	+	0.583916i	−0.911593	−	0.411094i	$-0.865147\pi$
$23$	−4.85037	+	2.80036i	−1.01137	+	0.583916i	−0.0997790	+	0.995010i	$0.531814\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−4.16556	+	2.40499i	−0.833112	+	0.480998i
$26$	−0.134376	−	3.60305i	−0.0263534	−	0.706616i
$27$		−	1.00000i		−	0.192450i
$28$	1.61126	+	2.09853i	0.304500	+	0.396585i
$29$	−1.92767	+	3.33883i	−0.357960	+	0.620005i	−0.987620	−	0.156866i	$-0.949861\pi$
$29$	−1.92767	+	3.33883i	−0.357960	+	0.620005i	0.629660	+	0.776871i	$0.283194\pi$
$30$			0.435917i			0.0795871i
$31$	2.28207	−	8.51682i	0.409873	−	1.52967i	−0.385016	−	0.922910i	$-0.625804\pi$
$31$	2.28207	−	8.51682i	0.409873	−	1.52967i	0.794888	−	0.606756i	$-0.207529\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−1.13468	+	1.13468i	−0.197522	+	0.197522i
$34$	0.824118	−	0.824118i	0.141335	−	0.141335i
$35$	1.14351	+	0.150196i	0.193288	+	0.0253877i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	1.27404	−	4.75480i	0.209451	−	0.781684i	−0.778595	−	0.627527i	$-0.784067\pi$
$37$	1.27404	−	4.75480i	0.209451	−	0.781684i	0.988046	−	0.154157i	$-0.0492661\pi$
$38$	3.23537	+	5.60382i	0.524846	+	0.909060i
$39$	3.44550	−	1.06233i	0.551721	−	0.170110i
$40$	0.377515	+	0.217958i	0.0596904	+	0.0344622i
$41$	1.78730	−	0.478906i	0.279130	−	0.0747926i	−0.116538	−	0.993186i	$-0.537180\pi$
$41$	1.78730	−	0.478906i	0.279130	−	0.0747926i	0.395668	+	0.918394i	$0.370513\pi$
$42$	−1.61000	+	2.09950i	−0.248428	+	0.323960i
$43$	−0.251976	+	0.145478i	−0.0384260	+	0.0221853i	−0.519090	−	0.854720i	$-0.673729\pi$
$43$	−0.251976	+	0.145478i	−0.0384260	+	0.0221853i	0.480664	+	0.876905i	$0.340396\pi$
$44$	0.415321	+	1.55000i	0.0626120	+	0.233671i
$45$	−0.421063	+	0.112824i	−0.0627684	+	0.0168187i
$46$	−5.40989	+	1.44957i	−0.797644	+	0.213728i
$47$	1.19456	+	4.45815i	0.174244	+	0.650289i	0.996679	+	0.0814292i	$0.0259485\pi$
$47$	1.19456	+	4.45815i	0.174244	+	0.650289i	−0.822435	+	0.568859i	$0.807385\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	4.95272	+	4.94677i	0.707532	+	0.706682i
$50$	−4.64608	+	1.24491i	−0.657055	+	0.176057i
$51$	1.00933	+	0.582739i	0.141335	+	0.0815998i
$52$	0.802739	−	3.51505i	0.111320	−	0.487450i
$53$	−2.94607	−	5.10274i	−0.404673	−	0.700915i	0.589610	−	0.807688i	$-0.299281\pi$
$53$	−2.94607	−	5.10274i	−0.404673	−	0.700915i	−0.994283	+	0.106773i	$0.965948\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	0.605790	+	0.349753i	0.0816847	+	0.0471607i
$56$	1.01322	+	2.44405i	0.135397	+	0.326600i
$57$	−4.57550	+	4.57550i	−0.606040	+	0.606040i
$58$	−2.72614	+	2.72614i	−0.357960	+	0.357960i
$59$	−3.35860	−	12.5345i	−0.437252	−	1.63185i	−0.735619	−	0.677395i	$-0.763109\pi$
$59$	−3.35860	−	12.5345i	−0.437252	−	1.63185i	0.298367	−	0.954451i	$-0.403558\pi$
$60$	−0.112824	+	0.421063i	−0.0145655	+	0.0543590i
$61$			0.413392i			0.0529294i	0.999650	+	0.0264647i	$0.00842495\pi$
$61$			0.413392i			0.0529294i	−0.999650	+	0.0264647i	$0.991575\pi$
$62$	4.40863	−	7.63597i	0.559897	−	0.969769i
$63$	−2.44466	−	1.01175i	−0.307998	−	0.127469i
$64$			1.00000i			0.125000i
$65$	−0.836043	−	1.33092i	−0.103698	−	0.165080i
$66$	−1.38969	+	0.802339i	−0.171059	+	0.0987611i
$67$	−1.22023	+	1.22023i	−0.149075	+	0.149075i	−0.777705	−	0.628630i	$-0.783616\pi$
$67$	−1.22023	+	1.22023i	−0.149075	+	0.149075i	0.628630	+	0.777705i	$0.283616\pi$
$68$	1.00933	−	0.582739i	0.122400	−	0.0706675i
$69$	−2.80036	−	4.85037i	−0.337124	−	0.583916i
$70$	1.06567	+	0.441039i	0.127372	+	0.0527142i
$71$	−7.98595	−	2.13983i	−0.947758	−	0.253951i	−0.248347	−	0.968671i	$-0.579887\pi$
$71$	−7.98595	−	2.13983i	−0.947758	−	0.253951i	−0.699410	+	0.714720i	$0.746554\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	0.797676	+	0.213737i	0.0933609	+	0.0250160i	0.305197	−	0.952289i	$-0.401278\pi$
$73$	0.797676	+	0.213737i	0.0933609	+	0.0250160i	−0.211836	+	0.977305i	$0.567944\pi$
$74$	2.46126	−	4.26303i	0.286116	−	0.495568i
$75$	−2.40499	−	4.16556i	−0.277704	−	0.480998i
$76$	1.67475	+	6.25025i	0.192107	+	0.716953i
$77$	1.62589	+	3.92191i	0.185287	+	0.446943i
$78$	3.60305	−	0.134376i	0.407965	−	0.0152151i
$79$	4.79745	−	8.30943i	0.539755	−	0.934884i	−0.459161	−	0.888353i	$-0.651850\pi$
$79$	4.79745	−	8.30943i	0.539755	−	0.934884i	0.998917	−	0.0465310i	$-0.0148166\pi$
$80$	0.308240	+	0.308240i	0.0344622	+	0.0344622i
$81$	1.00000			0.111111
$82$	1.85035			0.204337
$83$	−7.03301	−	7.03301i	−0.771973	−	0.771973i	0.206478	−	0.978451i	$-0.433800\pi$
$83$	−7.03301	−	7.03301i	−0.771973	−	0.771973i	−0.978451	+	0.206478i	$0.933800\pi$
$84$	−2.09853	+	1.61126i	−0.228969	+	0.175803i
$85$	0.131493	−	0.490740i	0.0142625	−	0.0532282i
$86$	−0.281043	+	0.0753052i	−0.0303056	+	0.00812037i
$87$	−3.33883	−	1.92767i	−0.357960	−	0.206668i
$88$			1.60468i			0.171059i
$89$	6.66910	+	1.78698i	0.706923	+	0.189419i	0.594329	−	0.804222i	$-0.297418\pi$
$89$	6.66910	+	1.78698i	0.706923	+	0.189419i	0.112594	+	0.993641i	$0.464084\pi$
$90$	−0.435917			−0.0459497
$91$	0.888935	−	9.49788i	0.0931857	−	0.995649i
$92$	−5.60073			−0.583916
$93$	8.51682	+	2.28207i	0.883153	+	0.236640i
$94$			4.61542i			0.476044i
$95$	2.44280	+	1.41035i	0.250626	+	0.144699i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	0.433491	−	1.61781i	0.0440143	−	0.164264i	−0.940421	−	0.340014i	$-0.889568\pi$
$97$	0.433491	−	1.61781i	0.0440143	−	0.164264i	0.984435	+	0.175750i	$0.0562350\pi$
$98$	3.50364	+	6.06007i	0.353921	+	0.612160i
$99$	−1.13468	−	1.13468i	−0.114039	−	0.114039i
$100$	−4.80998			−0.480998
$101$	−19.3362			−1.92403			−0.962013	−	0.273004i	$-0.911983\pi$
$101$	−19.3362			−1.92403			−0.962013	+	0.273004i	$0.911983\pi$
$102$	0.824118	+	0.824118i	0.0815998	+	0.0815998i
$103$	9.71249	−	16.8225i	0.957000	−	1.65757i	0.227277	−	0.973830i	$-0.427018\pi$
$103$	9.71249	−	16.8225i	0.957000	−	1.65757i	0.729723	−	0.683743i	$-0.239649\pi$
$104$	1.68515	−	3.18752i	0.165243	−	0.312562i
$105$	−0.150196	+	1.14351i	−0.0146576	+	0.111595i
$106$	−1.52500	−	5.69136i	−0.148121	−	0.552794i
$107$	3.72496	+	6.45182i	0.360105	+	0.623721i	0.987978	−	0.154595i	$-0.0494074\pi$
$107$	3.72496	+	6.45182i	0.360105	+	0.623721i	−0.627872	+	0.778316i	$0.716074\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	2.40272	+	0.643807i	0.230139	+	0.0616656i	0.372045	−	0.928215i	$-0.378657\pi$
$109$	2.40272	+	0.643807i	0.230139	+	0.0616656i	−0.141906	+	0.989880i	$0.545323\pi$
$110$	0.494625	+	0.494625i	0.0471607	+	0.0471607i
$111$	4.75480	+	1.27404i	0.451305	+	0.120927i
$112$	0.346128	+	2.62301i	0.0327061	+	0.247851i
$113$	−4.14975	−	7.18757i	−0.390375	−	0.676150i	0.602124	−	0.798403i	$-0.294321\pi$
$113$	−4.14975	−	7.18757i	−0.390375	−	0.676150i	−0.992499	+	0.122253i	$0.960988\pi$
$114$	−5.60382	+	3.23537i	−0.524846	+	0.303020i
$115$	−1.72637	+	1.72637i	−0.160984	+	0.160984i
$116$	−3.33883	+	1.92767i	−0.310002	+	0.178980i
$117$	1.06233	+	3.44550i	0.0982129	+	0.318536i
$118$		−	12.9766i		−	1.19459i
$119$	2.44579	−	1.87789i	0.224205	−	0.172146i
$120$	−0.217958	+	0.377515i	−0.0198968	+	0.0344622i
$121$		−	8.42501i		−	0.765910i
$122$	−0.106994	+	0.399306i	−0.00968675	+	0.0361514i
$123$	0.478906	+	1.78730i	0.0431815	+	0.161156i
$124$	6.23474	−	6.23474i	0.559897	−	0.559897i
$125$	−3.02382	+	3.02382i	−0.270459	+	0.270459i
$126$	−2.09950	−	1.61000i	−0.187038	−	0.143430i
$127$	−6.99554	−	4.03888i	−0.620754	−	0.358393i	0.156408	−	0.987692i	$-0.450008\pi$
$127$	−6.99554	−	4.03888i	−0.620754	−	0.358393i	−0.777163	+	0.629300i	$0.783342\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−0.145478	−	0.251976i	−0.0128087	−	0.0221853i
$130$	−0.463089	−	1.50195i	−0.0406156	−	0.131730i
$131$	10.5709	+	6.10313i	0.923586	+	0.533233i	0.884777	−	0.466014i	$-0.154310\pi$
$131$	10.5709	+	6.10313i	0.923586	+	0.533233i	0.0388087	+	0.999247i	$0.487644\pi$
$132$	−1.55000	+	0.415321i	−0.134910	+	0.0361491i
$133$	6.55628	+	15.8148i	0.568502	+	1.37132i
$134$	−1.49447	+	0.862834i	−0.129103	+	0.0745375i
$135$	−0.112824	−	0.421063i	−0.00971031	−	0.0362394i
$136$	1.12577	−	0.301648i	0.0965336	−	0.0258661i
$137$	−3.17860	+	0.851705i	−0.271567	+	0.0727660i	−0.392032	−	0.919951i	$-0.628228\pi$
$137$	−3.17860	+	0.851705i	−0.271567	+	0.0727660i	0.120466	+	0.992717i	$0.461561\pi$
$138$	−1.44957	−	5.40989i	−0.123396	−	0.460520i
$139$	11.2104	−	6.47234i	0.950855	−	0.548976i	0.0575086	−	0.998345i	$-0.481684\pi$
$139$	11.2104	−	6.47234i	0.950855	−	0.548976i	0.893346	+	0.449369i	$0.148351\pi$
$140$	0.915207	+	0.701826i	0.0773491	+	0.0593151i
$141$	−4.45815	+	1.19456i	−0.375444	+	0.100600i
$142$	−7.16000	−	4.13383i	−0.600854	−	0.346903i
$143$	2.70412	−	5.11494i	0.226130	−	0.427733i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.434974	+	1.62334i	−0.0361226	+	0.134811i
$146$	0.715177	+	0.412908i	0.0591885	+	0.0341725i
$147$	−4.94677	+	4.95272i	−0.408003	+	0.408494i
$148$	3.48075	−	3.48075i	0.286116	−	0.286116i
$149$	−15.7855	+	15.7855i	−1.29320	+	1.29320i	−0.360400	+	0.932798i	$0.617360\pi$
$149$	−15.7855	+	15.7855i	−1.29320	+	1.29320i	−0.932798	+	0.360400i	$0.882640\pi$
$150$	−1.24491	−	4.64608i	−0.101647	−	0.379351i
$151$	−1.85599	+	6.92663i	−0.151038	+	0.563681i	0.848374	+	0.529397i	$0.177582\pi$
$151$	−1.85599	+	6.92663i	−0.151038	+	0.563681i	−0.999412	+	0.0342842i	$0.989085\pi$
$152$			6.47074i			0.524846i
$153$	−0.582739	+	1.00933i	−0.0471117	+	0.0815998i
$154$	0.555424	+	4.20909i	0.0447574	+	0.339178i
$155$		−	3.84359i		−	0.308725i
$156$	3.51505	+	0.802739i	0.281430	+	0.0642706i
$157$	13.2498	−	7.64980i	1.05745	−	0.610521i	0.132726	−	0.991153i	$-0.457627\pi$
$157$	13.2498	−	7.64980i	1.05745	−	0.610521i	0.924726	+	0.380632i	$0.124294\pi$
$158$	6.78462	−	6.78462i	0.539755	−	0.539755i
$159$	5.10274	−	2.94607i	0.404673	−	0.233638i
$160$	0.217958	+	0.377515i	0.0172311	+	0.0298452i
$161$	−14.6908	+	1.93857i	−1.15780	+	0.152781i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	2.31928	+	2.31928i	0.181660	+	0.181660i	0.792079	−	0.610419i	$-0.208999\pi$
$163$	2.31928	+	2.31928i	0.181660	+	0.181660i	−0.610419	+	0.792079i	$0.708999\pi$
$164$	1.78730	+	0.478906i	0.139565	+	0.0373963i
$165$	−0.349753	+	0.605790i	−0.0272282	+	0.0471607i
$166$	−4.97309	−	8.61364i	−0.385987	−	0.668548i
$167$	−4.22682	−	15.7747i	−0.327081	−	1.22068i	−0.912203	−	0.409738i	$-0.865620\pi$
$167$	−4.22682	−	15.7747i	−0.327081	−	1.22068i	0.585122	−	0.810945i	$-0.301047\pi$
$168$	−2.44405	+	1.01322i	−0.188563	+	0.0781716i
$169$	−10.7429	+	7.32054i	−0.826376	+	0.563119i
$170$	0.254026	−	0.439986i	0.0194829	−	0.0337453i
$171$	−4.57550	−	4.57550i	−0.349897	−	0.349897i
$172$	−0.290957			−0.0221853
$173$	−9.02660			−0.686280			−0.343140	−	0.939284i	$-0.611491\pi$
$173$	−9.02660			−0.686280			−0.343140	+	0.939284i	$0.611491\pi$
$174$	−2.72614	−	2.72614i	−0.206668	−	0.206668i
$175$	−12.6166	+	1.66487i	−0.953728	+	0.125852i
$176$	−0.415321	+	1.55000i	−0.0313060	+	0.116836i
$177$	12.5345	−	3.35860i	0.942147	−	0.252448i
$178$	5.97935	+	3.45218i	0.448171	+	0.258752i
$179$			9.80307i			0.732716i	0.930474	+	0.366358i	$0.119395\pi$
$179$			9.80307i			0.732716i	−0.930474	+	0.366358i	$0.880605\pi$
$180$	−0.421063	−	0.112824i	−0.0313842	−	0.00840937i
$181$	−12.5973			−0.936349			−0.468174	−	0.883636i	$-0.655088\pi$
$181$	−12.5973			−0.936349			−0.468174	+	0.883636i	$0.655088\pi$
$182$	3.31688	−	8.94418i	0.245863	−	0.662987i
$183$	−0.413392			−0.0305588
$184$	−5.40989	−	1.44957i	−0.398822	−	0.106864i
$185$		−	2.14581i		−	0.157763i
$186$	7.63597	+	4.40863i	0.559897	+	0.323256i
$187$	1.80649	−	0.484048i	0.132104	−	0.0353971i
$188$	−1.19456	+	4.45815i	−0.0871221	+	0.325144i
$189$	1.01175	−	2.44466i	0.0735940	−	0.177823i
$190$	1.99454	+	1.99454i	0.144699	+	0.144699i
$191$	19.7514			1.42916			0.714579	−	0.699554i	$-0.246618\pi$
$191$	19.7514			1.42916			0.714579	+	0.699554i	$0.246618\pi$
$192$	−1.00000			−0.0721688
$193$	13.3630	+	13.3630i	0.961892	+	0.961892i	0.999300	−	0.0374083i	$-0.0119102\pi$
$193$	13.3630	+	13.3630i	0.961892	+	0.961892i	−0.0374083	+	0.999300i	$0.511910\pi$
$194$	0.837440	−	1.45049i	0.0601247	−	0.104139i
$195$	1.33092	−	0.836043i	0.0953088	−	0.0598703i
$196$	1.81580	+	6.76039i	0.129700	+	0.482885i
$197$	5.41861	+	20.2225i	0.386060	+	1.44080i	0.836489	+	0.547984i	$0.184605\pi$
$197$	5.41861	+	20.2225i	0.386060	+	1.44080i	−0.450428	+	0.892813i	$0.648729\pi$
$198$	−0.802339	−	1.38969i	−0.0570197	−	0.0987611i
$199$	−7.58258	+	13.1334i	−0.537515	+	0.931003i	0.461522	+	0.887129i	$0.347303\pi$
$199$	−7.58258	+	13.1334i	−0.537515	+	0.931003i	−0.999037	+	0.0438744i	$0.986030\pi$
$200$	−4.64608	−	1.24491i	−0.328528	−	0.0880287i
$201$	−1.22023	−	1.22023i	−0.0860685	−	0.0860685i
$202$	−18.6774	−	5.00458i	−1.31413	−	0.352121i
$203$	−8.09057	+	6.21198i	−0.567846	+	0.435995i
$204$	0.582739	+	1.00933i	0.0407999	+	0.0706675i
$205$	0.698535	−	0.403299i	0.0487878	−	0.0281677i
$206$	13.7355	−	13.7355i	0.957000	−	0.957000i
$207$	4.85037	−	2.80036i	0.337124	−	0.194639i
$208$	2.45272	−	2.64276i	0.170066	−	0.183242i
$209$			10.3834i			0.718238i
$210$	−0.441039	+	1.06567i	−0.0304346	+	0.0735381i
$211$	−4.67336	+	8.09449i	−0.321727	+	0.557248i	−0.980845	−	0.194792i	$-0.937597\pi$
$211$	−4.67336	+	8.09449i	−0.321727	+	0.557248i	0.659117	+	0.752040i	$0.270930\pi$
$212$		−	5.89213i		−	0.404673i
$213$	2.13983	−	7.98595i	0.146619	−	0.547188i
$214$	1.92818	+	7.19607i	0.131808	+	0.491913i
$215$	−0.0896845	+	0.0896845i	−0.00611643	+	0.00611643i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	14.1958	−	18.5118i	0.963673	−	1.25667i
$218$	2.15422	+	1.24374i	0.145902	+	0.0842367i
$219$	−0.213737	+	0.797676i	−0.0144430	+	0.0539020i
$220$	0.349753	+	0.605790i	0.0235803	+	0.0408423i
$221$	−4.09672	−	0.935575i	−0.275575	−	0.0629336i
$222$	4.26303	+	2.46126i	0.286116	+	0.165189i
$223$	0.548487	−	0.146967i	0.0367294	−	0.00984161i	−0.240408	−	0.970672i	$-0.577281\pi$
$223$	0.548487	−	0.146967i	0.0367294	−	0.00984161i	0.277137	+	0.960830i	$0.410614\pi$
$224$	−0.344551	+	2.62322i	−0.0230213	+	0.175271i
$225$	4.16556	−	2.40499i	0.277704	−	0.160333i
$226$	−2.14807	−	8.01670i	−0.142887	−	0.533263i
$227$	−12.6834	+	3.39850i	−0.841826	+	0.225566i	−0.653866	−	0.756610i	$-0.726854\pi$
$227$	−12.6834	+	3.39850i	−0.841826	+	0.225566i	−0.187959	+	0.982177i	$0.560187\pi$
$228$	−6.25025	+	1.67475i	−0.413933	+	0.110913i
$229$	6.73106	+	25.1207i	0.444801	+	1.66002i	0.716461	+	0.697627i	$0.245761\pi$
$229$	6.73106	+	25.1207i	0.444801	+	1.66002i	−0.271660	+	0.962393i	$0.587573\pi$
$230$	−2.11436	+	1.22072i	−0.139417	+	0.0804922i
$231$	−3.92191	+	1.62589i	−0.258043	+	0.106976i
$232$	−3.72398	+	0.997837i	−0.244491	+	0.0655112i
$233$	8.06058	+	4.65378i	0.528066	+	0.304879i	0.740229	−	0.672355i	$-0.234717\pi$
$233$	8.06058	+	4.65378i	0.528066	+	0.304879i	−0.212162	+	0.977234i	$0.568051\pi$
$234$	0.134376	+	3.60305i	0.00878447	+	0.235539i
$235$	1.00597	+	1.74239i	0.0656222	+	0.113661i
$236$	3.35860	−	12.5345i	0.218626	−	0.815923i
$237$	8.30943	+	4.79745i	0.539755	+	0.311628i
$238$	2.84849	−	1.18089i	0.184640	−	0.0765455i
$239$	−14.8784	+	14.8784i	−0.962402	+	0.962402i	−0.999318	−	0.0369162i	$-0.988247\pi$
$239$	−14.8784	+	14.8784i	−0.962402	+	0.962402i	0.0369162	+	0.999318i	$0.488247\pi$
$240$	−0.308240	+	0.308240i	−0.0198968	+	0.0198968i
$241$	2.35351	+	8.78342i	0.151603	+	0.565790i	0.999372	+	0.0354249i	$0.0112785\pi$
$241$	2.35351	+	8.78342i	0.151603	+	0.565790i	−0.847769	+	0.530365i	$0.822055\pi$
$242$	2.18055	−	8.13794i	0.140171	−	0.523126i
$243$			1.00000i			0.0641500i
$244$	−0.206696	+	0.358008i	−0.0132323	+	0.0229191i
$245$	2.64352	+	1.52412i	0.168888	+	0.0973724i
$246$			1.85035i			0.117974i
$247$	10.9042	−	20.6256i	0.693815	−	1.31237i
$248$	7.63597	−	4.40863i	0.484885	−	0.279948i
$249$	7.03301	−	7.03301i	0.445699	−	0.445699i
$250$	−3.70341	+	2.13817i	−0.234224	+	0.135230i
$251$	−9.81192	−	16.9947i	−0.619323	−	1.07270i	−0.989610	−	0.143781i	$-0.954074\pi$
$251$	−9.81192	−	16.9947i	−0.619323	−	1.07270i	0.370287	−	0.928918i	$-0.379259\pi$
$252$	−1.61126	−	2.09853i	−0.101500	−	0.132195i
$253$	−8.68112	−	2.32610i	−0.545777	−	0.146241i
$254$	−5.71184	−	5.71184i	−0.358393	−	0.358393i
$255$	0.490740	+	0.131493i	0.0307313	+	0.00823444i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.3779	+	17.9750i	0.647354	+	1.12125i	0.983752	+	0.179531i	$0.0574579\pi$
$257$	10.3779	+	17.9750i	0.647354	+	1.12125i	−0.336398	+	0.941720i	$0.609209\pi$
$258$	−0.0753052	−	0.281043i	−0.00468830	−	0.0174970i
$259$	7.92527	−	10.3348i	0.492452	−	0.642176i
$260$	−0.0585770	−	1.57063i	−0.00363279	−	0.0974062i
$261$	1.92767	−	3.33883i	0.119320	−	0.206668i
$262$	8.63112	+	8.63112i	0.533233	+	0.533233i
$263$	27.4496			1.69262			0.846308	−	0.532694i	$-0.178820\pi$
$263$	27.4496			1.69262			0.846308	+	0.532694i	$0.178820\pi$
$264$	−1.60468			−0.0987611
$265$	−1.81619	−	1.81619i	−0.111568	−	0.111568i
$266$	2.23971	+	16.9728i	0.137325	+	1.04067i
$267$	−1.78698	+	6.66910i	−0.109361	+	0.408142i
$268$	−1.66687	+	0.446636i	−0.101820	+	0.0272826i
$269$	6.51347	+	3.76055i	0.397133	+	0.229285i	0.685246	−	0.728311i	$-0.259695\pi$
$269$	6.51347	+	3.76055i	0.397133	+	0.229285i	−0.288113	+	0.957596i	$0.593028\pi$
$270$		−	0.435917i		−	0.0265290i
$271$	0.352934	+	0.0945684i	0.0214392	+	0.00574462i	0.269523	−	0.962994i	$-0.413134\pi$
$271$	0.352934	+	0.0945684i	0.0214392	+	0.00574462i	−0.248084	+	0.968739i	$0.579801\pi$
$272$	1.16548			0.0706675
$273$	9.49788	+	0.888935i	0.574838	+	0.0538008i
$274$	−3.29073			−0.198800
$275$	−7.45546	−	1.99768i	−0.449581	−	0.120465i
$276$		−	5.60073i		−	0.337124i
$277$	−25.2730	−	14.5914i	−1.51851	−	0.876711i	−0.999763	−	0.0217819i	$-0.993066\pi$
$277$	−25.2730	−	14.5914i	−1.51851	−	0.876711i	−0.518745	−	0.854929i	$-0.673601\pi$
$278$	12.5036	−	3.35033i	0.749916	−	0.200939i
$279$	−2.28207	+	8.51682i	−0.136624	+	0.509889i
$280$	0.702376	+	0.914785i	0.0419750	+	0.0546689i
$281$	0.535962	+	0.535962i	0.0319728	+	0.0319728i	0.722912	−	0.690940i	$-0.242803\pi$
$281$	0.535962	+	0.535962i	0.0319728	+	0.0319728i	−0.690940	+	0.722912i	$0.742803\pi$
$282$	−4.61542			−0.274844
$283$	1.61700			0.0961207			0.0480604	−	0.998844i	$-0.484696\pi$
$283$	1.61700			0.0961207			0.0480604	+	0.998844i	$0.484696\pi$
$284$	−5.84612	−	5.84612i	−0.346903	−	0.346903i
$285$	−1.41035	+	2.44280i	−0.0835420	+	0.144699i
$286$	3.93582	−	4.24077i	0.232730	−	0.250762i
$287$	4.85388	+	0.637541i	0.286515	+	0.0376329i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	7.82083	+	13.5461i	0.460049	+	0.796828i
$290$	−0.840305	+	1.45545i	−0.0493444	+	0.0854670i
$291$	1.61781	+	0.433491i	0.0948377	+	0.0254117i
$292$	0.583940	+	0.583940i	0.0341725	+	0.0341725i
$293$	−23.2061	−	6.21805i	−1.35571	−	0.363262i	−0.493473	−	0.869761i	$-0.664273\pi$
$293$	−23.2061	−	6.21805i	−1.35571	−	0.363262i	−0.862240	+	0.506499i	$0.830939\pi$
$294$	−6.06007	+	3.50364i	−0.353431	+	0.204337i
$295$	−2.82836	−	4.89887i	−0.164674	−	0.285223i
$296$	4.26303	−	2.46126i	0.247784	−	0.143058i
$297$	1.13468	−	1.13468i	0.0658407	−	0.0658407i
$298$	−19.3332	+	11.1620i	−1.11994	+	0.646599i
$299$	14.8014	+	13.7370i	0.855985	+	0.794432i
$300$		−	4.80998i		−	0.277704i
$301$	−0.763184	+	0.100708i	−0.0439892	+	0.00580474i
$302$	−3.58549	+	6.21025i	−0.206322	+	0.357360i
$303$		−	19.3362i		−	1.11084i
$304$	−1.67475	+	6.25025i	−0.0960535	+	0.358477i
$305$	0.0466403	+	0.174064i	0.00267062	+	0.00996688i
$306$	−0.824118	+	0.824118i	−0.0471117	+	0.0471117i
$307$	−15.4981	+	15.4981i	−0.884523	+	0.884523i	−0.993990	−	0.109467i	$-0.965086\pi$
$307$	−15.4981	+	15.4981i	−0.884523	+	0.884523i	0.109467	+	0.993990i	$0.465086\pi$
$308$	−0.552894	+	4.20942i	−0.0315040	+	0.239854i
$309$	16.8225	+	9.71249i	0.957000	+	0.552524i
$310$	0.994795	−	3.71262i	0.0565005	−	0.210863i
$311$	0.950990	+	1.64716i	0.0539257	+	0.0934020i	0.891728	−	0.452571i	$-0.149493\pi$
$311$	0.950990	+	1.64716i	0.0539257	+	0.0934020i	−0.837802	+	0.545973i	$0.816160\pi$
$312$	3.18752	+	1.68515i	0.180458	+	0.0954028i
$313$	−17.7365	−	10.2402i	−1.00253	−	0.578808i	−0.0935309	−	0.995616i	$-0.529815\pi$
$313$	−17.7365	−	10.2402i	−1.00253	−	0.578808i	−0.908995	+	0.416808i	$0.863149\pi$
$314$	14.7783	−	3.95983i	0.833987	−	0.223466i
$315$	−1.14351	−	0.150196i	−0.0644292	−	0.00846257i
$316$	8.30943	−	4.79745i	0.467442	−	0.269878i
$317$	−7.08481	−	26.4409i	−0.397923	−	1.48507i	−0.816745	−	0.576999i	$-0.804223\pi$
$317$	−7.08481	−	26.4409i	−0.397923	−	1.48507i	0.418822	−	0.908068i	$-0.362443\pi$
$318$	5.69136	−	1.52500i	0.319156	−	0.0855175i
$319$	−5.97579	+	1.60121i	−0.334580	+	0.0896504i
$320$	0.112824	+	0.421063i	0.00630703	+	0.0235381i
$321$	−6.45182	+	3.72496i	−0.360105	+	0.207907i
$322$	−14.6919	−	1.92974i	−0.818750	−	0.107540i
$323$	7.28453	−	1.95188i	0.405322	−	0.108606i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	12.7116	+	11.7975i	0.705113	+	0.654409i
$326$	1.63998	+	2.84053i	0.0908300	+	0.157322i
$327$	−0.643807	+	2.40272i	−0.0356026	+	0.132871i
$328$	1.60245	+	0.925176i	0.0884806	+	0.0510843i
$329$	−1.59025	+	12.1073i	−0.0876733	+	0.667495i
$330$	−0.494625	+	0.494625i	−0.0272282	+	0.0272282i
$331$	−9.26114	+	9.26114i	−0.509038	+	0.509038i	−0.914231	−	0.405193i	$-0.867204\pi$
$331$	−9.26114	+	9.26114i	−0.509038	+	0.509038i	0.405193	+	0.914231i	$0.367204\pi$
$332$	−2.57426	−	9.60727i	−0.141281	−	0.527267i
$333$	−1.27404	+	4.75480i	−0.0698172	+	0.260561i
$334$		−	16.3312i		−	0.893602i
$335$	−0.376124	+	0.651465i	−0.0205498	+	0.0355933i
$336$	−2.62301	+	0.346128i	−0.143097	+	0.0188828i
$337$		0	0.000853258i		0	4.64799e-5i	−1.00000		2.32400e-5i	$-0.999993\pi$
$337$		0	0.000853258i		0	4.64799e-5i	1.00000		2.32400e-5i	$-7.39751e-6\pi$
$338$	−12.2715	+	4.29064i	−0.667483	+	0.233380i
$339$	7.18757	−	4.14975i	0.390375	−	0.225383i
$340$	0.359247	−	0.359247i	0.0194829	−	0.0194829i
$341$	12.2533	−	7.07443i	0.663552	−	0.383102i
$342$	−3.23537	−	5.60382i	−0.174949	−	0.303020i
$343$	7.10282	+	17.1041i	0.383516	+	0.923534i
$344$	−0.281043	−	0.0753052i	−0.0151528	−	0.00406018i
$345$	−1.72637	−	1.72637i	−0.0929444	−	0.0929444i
$346$	−8.71903	−	2.33626i	−0.468738	−	0.125598i
$347$	−1.22911	+	2.12888i	−0.0659820	+	0.114284i	−0.897129	−	0.441768i	$-0.854351\pi$
$347$	−1.22911	+	2.12888i	−0.0659820	+	0.114284i	0.831147	+	0.556053i	$0.187685\pi$
$348$	−1.92767	−	3.33883i	−0.103334	−	0.178980i
$349$	6.98477	+	26.0675i	0.373886	+	1.39536i	0.854965	+	0.518685i	$0.173578\pi$
$349$	6.98477	+	26.0675i	0.373886	+	1.39536i	−0.481079	+	0.876677i	$0.659755\pi$
$350$	−12.6176	−	1.65728i	−0.674441	−	0.0885855i
$351$	−3.44550	+	1.06233i	−0.183907	+	0.0567032i
$352$	−0.802339	+	1.38969i	−0.0427648	+	0.0740708i
$353$	1.47723	+	1.47723i	0.0786250	+	0.0786250i	0.745326	−	0.666701i	$-0.232294\pi$
$353$	1.47723	+	1.47723i	0.0786250	+	0.0786250i	−0.666701	+	0.745326i	$0.732294\pi$
$354$	12.9766			0.689700
$355$	−3.60401			−0.191281
$356$	4.88212	+	4.88212i	0.258752	+	0.258752i
$357$	1.87789	+	2.44579i	0.0993885	+	0.129445i
$358$	−2.53722	+	9.46904i	−0.134096	+	0.500454i
$359$	36.0238	−	9.65254i	1.90126	−	0.509442i	0.904756	−	0.425931i	$-0.140053\pi$
$359$	36.0238	−	9.65254i	1.90126	−	0.509442i	0.996507	−	0.0835107i	$-0.0266133\pi$
$360$	−0.377515	−	0.217958i	−0.0198968	−	0.0114874i
$361$			22.8704i			1.20371i
$362$	−12.1680	−	3.26042i	−0.639538	−	0.171364i
$363$	8.42501			0.442198
$364$	5.51878	−	7.78094i	0.289263	−	0.407832i
$365$	0.359987			0.0188426
$366$	−0.399306	−	0.106994i	−0.0208720	−	0.00559265i
$367$			27.0247i			1.41068i	0.708871	+	0.705338i	$0.249205\pi$
$367$			27.0247i			1.41068i	−0.708871	+	0.705338i	$0.750795\pi$
$368$	−4.85037	−	2.80036i	−0.252843	−	0.145979i
$369$	−1.78730	+	0.478906i	−0.0930432	+	0.0249309i
$370$	0.555377	−	2.07269i	0.0288727	−	0.107754i
$371$	−2.03943	−	15.4551i	−0.105882	−	0.802391i
$372$	6.23474	+	6.23474i	0.323256	+	0.323256i
$373$	11.0566			0.572490			0.286245	−	0.958156i	$-0.407593\pi$
$373$	11.0566			0.572490			0.286245	+	0.958156i	$0.407593\pi$
$374$	1.87022			0.0967066
$375$	−3.02382	−	3.02382i	−0.156150	−	0.156150i
$376$	−2.30771	+	3.99707i	−0.119011	+	0.206133i
$377$	13.5518	+	3.09484i	0.697951	+	0.159392i
$378$	1.61000	−	2.09950i	0.0828095	−	0.107987i
$379$	−2.53287	−	9.45279i	−0.130105	−	0.485557i	0.869865	−	0.493289i	$-0.164206\pi$
$379$	−2.53287	−	9.45279i	−0.130105	−	0.485557i	−0.999970	+	0.00773179i	$0.997539\pi$
$380$	1.41035	+	2.44280i	0.0723495	+	0.125313i
$381$	4.03888	−	6.99554i	0.206918	−	0.358393i
$382$	19.0784	+	5.11203i	0.976134	+	0.261554i
$383$	13.9940	+	13.9940i	0.715058	+	0.715058i	0.967589	−	0.252531i	$-0.0812630\pi$
$383$	13.9940	+	13.9940i	0.715058	+	0.715058i	−0.252531	+	0.967589i	$0.581263\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	1.12709	+	1.46793i	0.0574417	+	0.0748129i
$386$	9.44909	+	16.3663i	0.480946	+	0.833023i
$387$	0.251976	−	0.145478i	0.0128087	−	0.00739509i
$388$	1.18432	−	1.18432i	0.0601247	−	0.0601247i
$389$	19.6684	−	11.3556i	0.997229	−	0.575751i	0.0898021	−	0.995960i	$-0.471377\pi$
$389$	19.6684	−	11.3556i	0.997229	−	0.575751i	0.907427	+	0.420209i	$0.138043\pi$
$390$	1.50195	−	0.463089i	0.0760542	−	0.0234494i
$391$			6.52752i			0.330111i
$392$	0.00420831	+	7.00000i	0.000212552	+	0.353553i
$393$	−6.10313	+	10.5709i	−0.307862	+	0.533233i
$394$			20.9359i			1.05474i
$395$	1.08253	−	4.04006i	0.0544680	−	0.203278i
$396$	−0.415321	−	1.55000i	−0.0208707	−	0.0778904i
$397$	−2.21072	+	2.21072i	−0.110953	+	0.110953i	−0.760404	−	0.649451i	$-0.774999\pi$
$397$	−2.21072	+	2.21072i	−0.110953	+	0.110953i	0.649451	+	0.760404i	$0.274999\pi$
$398$	−10.7234	+	10.7234i	−0.537515	+	0.537515i
$399$	−15.8148	+	6.55628i	−0.791731	+	0.328225i
$400$	−4.16556	−	2.40499i	−0.208278	−	0.120249i
$401$	−3.15586	+	11.7778i	−0.157596	+	0.588157i	0.841273	+	0.540611i	$0.181807\pi$
$401$	−3.15586	+	11.7778i	−0.157596	+	0.588157i	−0.998869	+	0.0475461i	$0.984860\pi$
$402$	−0.862834	−	1.49447i	−0.0430342	−	0.0745375i
$403$	−31.7690	+	1.18483i	−1.58253	+	0.0590207i
$404$	−16.7457	−	9.66811i	−0.833128	−	0.481006i
$405$	0.421063	−	0.112824i	0.0209228	−	0.00560625i
$406$	−9.42267	+	3.90631i	−0.467639	+	0.193867i
$407$	6.84079	−	3.94953i	0.339085	−	0.195771i
$408$	0.301648	+	1.12577i	0.0149338	+	0.0557337i
$409$	−6.80871	+	1.82439i	−0.336669	+	0.0902102i	−0.423193	−	0.906040i	$-0.639091\pi$
$409$	−6.80871	+	1.82439i	−0.336669	+	0.0902102i	0.0865239	+	0.996250i	$0.472424\pi$
$410$	0.779115	−	0.208763i	0.0384777	−	0.0103101i
$411$	−0.851705	−	3.17860i	−0.0420115	−	0.156789i
$412$	16.8225	−	9.71249i	0.828786	−	0.478500i
$413$	4.47111	−	34.0405i	0.220009	−	1.67502i
$414$	5.40989	−	1.44957i	0.265881	−	0.0712427i
$415$	−3.75483	−	2.16785i	−0.184317	−	0.106416i
$416$	3.05314	−	1.91790i	0.149693	−	0.0940326i
$417$	6.47234	+	11.2104i	0.316952	+	0.548976i
$418$	−2.68743	+	10.0296i	−0.131447	+	0.490566i
$419$	−0.343937	−	0.198572i	−0.0168024	−	0.00970087i	0.491575	−	0.870835i	$-0.336421\pi$
$419$	−0.343937	−	0.198572i	−0.0168024	−	0.00970087i	−0.508378	+	0.861134i	$0.669755\pi$
$420$	−0.701826	+	0.915207i	−0.0342456	+	0.0446575i
$421$	13.3307	−	13.3307i	0.649699	−	0.649699i	−0.303221	−	0.952920i	$-0.598062\pi$
$421$	13.3307	−	13.3307i	0.649699	−	0.649699i	0.952920	+	0.303221i	$0.0980621\pi$
$422$	−6.60913	+	6.60913i	−0.321727	+	0.321727i
$423$	−1.19456	−	4.45815i	−0.0580814	−	0.216763i
$424$	1.52500	−	5.69136i	0.0740604	−	0.276397i
$425$			5.60592i			0.271927i
$426$	4.13383	−	7.16000i	0.200285	−	0.346903i
$427$	−0.418249	+	1.01060i	−0.0202405	+	0.0489064i
$428$			7.44992i			0.360105i
$429$	5.11494	+	2.70412i	0.246952	+	0.130556i
$430$	−0.109841	+	0.0634165i	−0.00529698	+	0.00305822i
$431$	23.7482	−	23.7482i	1.14391	−	1.14391i	0.156184	−	0.987728i	$-0.450081\pi$
$431$	23.7482	−	23.7482i	1.14391	−	1.14391i	0.987728	−	0.156184i	$-0.0499193\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−3.78238	−	6.55128i	−0.181770	−	0.314834i	0.760714	−	0.649088i	$-0.224849\pi$
$433$	−3.78238	−	6.55128i	−0.181770	−	0.314834i	−0.942483	+	0.334253i	$0.891516\pi$
$434$	18.5033	−	14.2069i	0.888187	−	0.681954i
$435$	−1.62334	−	0.434974i	−0.0778334	−	0.0208554i
$436$	1.75891	+	1.75891i	0.0842367	+	0.0842367i
$437$	−35.0059	−	9.37982i	−1.67456	−	0.448697i
$438$	−0.412908	+	0.715177i	−0.0197295	+	0.0341725i
$439$	−3.81378	−	6.60566i	−0.182022	−	0.315271i	0.760547	−	0.649283i	$-0.224931\pi$
$439$	−3.81378	−	6.60566i	−0.182022	−	0.315271i	−0.942569	+	0.334012i	$0.891597\pi$
$440$	0.181045	+	0.675671i	0.00863100	+	0.0322113i
$441$	−4.95272	−	4.94677i	−0.235844	−	0.235561i
$442$	−3.71498	−	1.96401i	−0.176704	−	0.0934182i
$443$	−15.6206	+	27.0557i	−0.742157	+	1.28545i	0.209354	+	0.977840i	$0.432864\pi$
$443$	−15.6206	+	27.0557i	−0.742157	+	1.28545i	−0.951511	+	0.307614i	$0.900470\pi$
$444$	3.48075	+	3.48075i	0.165189	+	0.165189i
$445$	3.00973			0.142675
$446$	0.567835			0.0268878
$447$	−15.7855	−	15.7855i	−0.746628	−	0.746628i
$448$	−1.01175	+	2.44466i	−0.0478007	+	0.115499i
$449$	4.76539	−	17.7847i	0.224893	−	0.839312i	−0.757555	−	0.652772i	$-0.773606\pi$
$449$	4.76539	−	17.7847i	0.224893	−	0.839312i	0.982447	−	0.186540i	$-0.0597273\pi$
$450$	4.64608	−	1.24491i	0.219018	−	0.0586858i
$451$	2.57142	+	1.48461i	0.121083	+	0.0699075i
$452$		−	8.29950i		−	0.390375i
$453$	−6.92663	−	1.85599i	−0.325442	−	0.0872018i
$454$	−13.1308			−0.616259
$455$	−0.697287	−	4.09950i	−0.0326893	−	0.192188i
$456$	−6.47074			−0.303020
$457$	−19.1040	−	5.11890i	−0.893647	−	0.239452i	−0.217361	−	0.976091i	$-0.569745\pi$
$457$	−19.1040	−	5.11890i	−0.893647	−	0.239452i	−0.676286	+	0.736639i	$0.736412\pi$
$458$			26.0068i			1.21522i
$459$	−1.00933	−	0.582739i	−0.0471117	−	0.0271999i
$460$	−2.35826	+	0.631894i	−0.109954	+	0.0294622i
$461$	3.36881	−	12.5726i	0.156901	−	0.585563i	−0.842034	−	0.539425i	$-0.818642\pi$
$461$	3.36881	−	12.5726i	0.156901	−	0.585563i	0.998935	−	0.0461384i	$-0.0146915\pi$
$462$	−4.20909	+	0.555424i	−0.195825	+	0.0258407i
$463$	−26.9528	−	26.9528i	−1.25260	−	1.25260i	−0.954550	−	0.298051i	$-0.903663\pi$
$463$	−26.9528	−	26.9528i	−1.25260	−	1.25260i	−0.298051	−	0.954550i	$-0.596337\pi$
$464$	−3.85535			−0.178980
$465$	3.84359			0.178242
$466$	6.58144	+	6.58144i	0.304879	+	0.304879i
$467$	−3.15831	+	5.47035i	−0.146149	+	0.253138i	−0.929801	−	0.368063i	$-0.880021\pi$
$467$	−3.15831	+	5.47035i	−0.146149	+	0.253138i	0.783652	+	0.621200i	$0.213355\pi$
$468$	−0.802739	+	3.51505i	−0.0371066	+	0.162483i
$469$	−4.21762	+	1.74848i	−0.194752	+	0.0807373i
$470$	0.520728	+	1.94338i	0.0240194	+	0.0896416i
$471$	7.64980	+	13.2498i	0.352484	+	0.610521i
$472$	6.48831	−	11.2381i	0.298649	−	0.517275i
$473$	−0.450983	−	0.120841i	−0.0207362	−	0.00555625i
$474$	6.78462	+	6.78462i	0.311628	+	0.311628i
$475$	−30.0636	−	8.05551i	−1.37941	−	0.369612i
$476$	3.05706	−	0.403405i	0.140120	−	0.0184900i
$477$	2.94607	+	5.10274i	0.134891	+	0.233638i
$478$	−18.2222	+	10.5206i	−0.833465	+	0.481201i
$479$	22.9359	−	22.9359i	1.04797	−	1.04797i	0.0491799	−	0.998790i	$-0.484339\pi$
$479$	22.9359	−	22.9359i	1.04797	−	1.04797i	0.998790	−	0.0491799i	$-0.0156608\pi$
$480$	−0.377515	+	0.217958i	−0.0172311	+	0.00994839i
$481$	−17.7361	+	0.661472i	−0.808696	+	0.0301605i
$482$			9.09327i			0.414187i
$483$	−1.93857	−	14.6908i	−0.0882080	−	0.668453i
$484$	4.21251	−	7.29627i	0.191478	−	0.331649i
$485$		−	0.730108i		−	0.0331525i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	−6.90163	−	25.7572i	−0.312743	−	1.16717i	−0.926073	−	0.377345i	$-0.876837\pi$
$487$	−6.90163	−	25.7572i	−0.312743	−	1.16717i	0.613330	−	0.789827i	$-0.289830\pi$
$488$	−0.292312	+	0.292312i	−0.0132323	+	0.0132323i
$489$	−2.31928	+	2.31928i	−0.104881	+	0.104881i
$490$	2.15897	+	2.15638i	0.0975325	+	0.0974153i
$491$	7.04676	+	4.06845i	0.318016	+	0.183607i	0.650508	−	0.759500i	$-0.274556\pi$
$491$	7.04676	+	4.06845i	0.318016	+	0.183607i	−0.332492	+	0.943106i	$0.607889\pi$
$492$	−0.478906	+	1.78730i	−0.0215908	+	0.0805778i
$493$	2.24666	+	3.89133i	0.101185	+	0.175257i
$494$	15.8709	−	17.1006i	0.714066	−	0.769392i
$495$	−0.605790	−	0.349753i	−0.0272282	−	0.0157202i
$496$	8.51682	−	2.28207i	0.382416	−	0.102468i
$497$	−17.3580	−	13.3109i	−0.778611	−	0.597077i
$498$	8.61364	−	4.97309i	0.385987	−	0.222849i
$499$	1.84669	+	6.89194i	0.0826691	+	0.308525i	0.994863	−	0.101234i	$-0.0322792\pi$
$499$	1.84669	+	6.89194i	0.0826691	+	0.308525i	−0.912193	+	0.409760i	$0.865613\pi$
$500$	−4.13062	+	1.10680i	−0.184727	+	0.0494974i
$501$	15.7747	−	4.22682i	0.704762	−	0.188840i
$502$	−5.07902	−	18.9552i	−0.226688	−	0.846011i
$503$	30.4903	−	17.6036i	1.35950	−	0.784905i	0.369940	−	0.929056i	$-0.379378\pi$
$503$	30.4903	−	17.6036i	1.35950	−	0.784905i	0.989556	+	0.144150i	$0.0460448\pi$
$504$	−1.01322	−	2.44405i	−0.0451324	−	0.108867i
$505$	−8.14177	+	2.18158i	−0.362304	+	0.0970791i
$506$	−7.78328	−	4.49368i	−0.346009	−	0.199768i
$507$	−7.32054	−	10.7429i	−0.325117	−	0.477108i
$508$	−4.03888	−	6.99554i	−0.179196	−	0.310377i
$509$	−0.523767	+	1.95473i	−0.0232156	+	0.0866417i	−0.976562	−	0.215238i	$-0.930947\pi$
$509$	−0.523767	+	1.95473i	−0.0232156	+	0.0866417i	0.953346	+	0.301879i	$0.0976140\pi$
$510$	0.439986	+	0.254026i	0.0194829	+	0.0112484i
$511$	1.73380	+	1.32956i	0.0766987	+	0.0588164i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.57550	−	4.57550i	0.202013	−	0.202013i
$514$	5.37199	+	20.0485i	0.236948	+	0.884302i
$515$	2.19160	−	8.17915i	0.0965732	−	0.360416i
$516$		−	0.290957i		−	0.0128087i
$517$	−3.70313	+	6.41401i	−0.162863	+	0.282088i
$518$	10.3301	−	7.93148i	0.453877	−	0.348489i
$519$		−	9.02660i		−	0.396224i
$520$	0.349927	−	1.53227i	0.0153453	−	0.0671945i
$521$	−1.84182	+	1.06338i	−0.0806917	+	0.0465874i	−0.539803	−	0.841791i	$-0.681501\pi$
$521$	−1.84182	+	1.06338i	−0.0806917	+	0.0465874i	0.459111	+	0.888379i	$0.348168\pi$
$522$	2.72614	−	2.72614i	0.119320	−	0.119320i
$523$	27.5109	−	15.8834i	1.20297	−	0.694533i	0.241753	−	0.970338i	$-0.422278\pi$
$523$	27.5109	−	15.8834i	1.20297	−	0.694533i	0.961214	+	0.275805i	$0.0889443\pi$
$524$	6.10313	+	10.5709i	0.266616	+	0.461793i
$525$	−1.66487	−	12.6166i	−0.0726608	−	0.550635i
$526$	26.5143	+	7.10448i	1.15608	+	0.309770i
$527$	−7.26646	−	7.26646i	−0.316532	−	0.316532i
$528$	−1.55000	−	0.415321i	−0.0674551	−	0.0180745i
$529$	4.18406	−	7.24701i	0.181916	−	0.315087i
$530$	−1.28424	−	2.22437i	−0.0557838	−	0.0966204i
$531$	3.35860	+	12.5345i	0.145751	+	0.543949i
$532$	−2.22950	+	16.9742i	−0.0966611	+	0.735924i
$533$	−3.54878	−	5.64938i	−0.153715	−	0.244702i
$534$	−3.45218	+	5.97935i	−0.149390	+	0.258752i
$535$	2.29636	+	2.29636i	0.0992803	+	0.0992803i
$536$	−1.72567			−0.0745375
$537$	−9.80307			−0.423034
$538$	5.31823	+	5.31823i	0.229285	+	0.229285i
$539$	0.00675298	+	11.2327i	0.000290871	+	0.483828i
$540$	0.112824	−	0.421063i	0.00485515	−	0.0181197i
$541$	−20.2886	+	5.43630i	−0.872273	+	0.233725i	−0.667071	−	0.744995i	$-0.732452\pi$
$541$	−20.2886	+	5.43630i	−0.872273	+	0.233725i	−0.205203	+	0.978719i	$0.565785\pi$
$542$	0.316432	+	0.182692i	0.0135919	+	0.00784730i
$543$		−	12.5973i		−	0.540601i
$544$	1.12577	+	0.301648i	0.0482668	+	0.0129331i
$545$	1.08433			0.0464478
$546$	8.94418	+	3.31688i	0.382775	+	0.141949i
$547$	−19.0247			−0.813436			−0.406718	−	0.913554i	$-0.633327\pi$
$547$	−19.0247			−0.813436			−0.406718	+	0.913554i	$0.633327\pi$
$548$	−3.17860	−	0.851705i	−0.135783	−	0.0363830i
$549$		−	0.413392i		−	0.0176431i
$550$	−6.68438	−	3.85923i	−0.285023	−	0.164558i
$551$	−24.0969	+	6.45674i	−1.02656	+	0.275066i
$552$	1.44957	−	5.40989i	0.0616980	−	0.230260i
$553$	20.1352	−	15.4599i	0.856236	−	0.657422i
$554$	−20.6353	−	20.6353i	−0.876711	−	0.876711i
$555$	2.14581			0.0910846
$556$	12.9447			0.548976
$557$	−18.1456	−	18.1456i	−0.768855	−	0.768855i	0.209050	−	0.977905i	$-0.432963\pi$
$557$	−18.1456	−	18.1456i	−0.768855	−	0.768855i	−0.977905	+	0.209050i	$0.932963\pi$
$558$	−4.40863	+	7.63597i	−0.186632	+	0.323256i
$559$	0.768929	+	0.713636i	0.0325222	+	0.0301836i
$560$	0.441679	+	1.06540i	0.0186644	+	0.0450215i
$561$	0.484048	+	1.80649i	0.0204365	+	0.0762701i
$562$	0.378983	+	0.656417i	0.0159864	+	0.0276893i
$563$	−6.74430	+	11.6815i	−0.284238	+	0.492315i	−0.972424	−	0.233219i	$-0.925074\pi$
$563$	−6.74430	+	11.6815i	−0.284238	+	0.492315i	0.688186	+	0.725534i	$0.258407\pi$
$564$	−4.45815	−	1.19456i	−0.187722	−	0.0503000i
$565$	−2.55823	−	2.55823i	−0.107626	−	0.107626i
$566$	1.56190	+	0.418511i	0.0656517	+	0.0175913i
$567$	2.44466	+	1.01175i	0.102666	+	0.0424895i
$568$	−4.13383	−	7.16000i	−0.173452	−	0.300427i
$569$	−21.3242	+	12.3115i	−0.893957	+	0.516126i	−0.875235	−	0.483699i	$-0.839293\pi$
$569$	−21.3242	+	12.3115i	−0.893957	+	0.516126i	−0.0187221	+	0.999825i	$0.505960\pi$
$570$	−1.99454	+	1.99454i	−0.0835420	+	0.0835420i
$571$	−30.3631	+	17.5301i	−1.27065	+	0.733613i	−0.975111	−	0.221717i	$-0.928834\pi$
$571$	−30.3631	+	17.5301i	−1.27065	+	0.733613i	−0.295543	+	0.955329i	$0.595501\pi$
$572$	4.89931	−	3.07761i	0.204850	−	0.128681i
$573$			19.7514i			0.825125i
$574$	4.52348	+	1.87209i	0.188806	+	0.0781397i
$575$	13.4697	−	23.3302i	0.561724	−	0.972935i
$576$		−	1.00000i		−	0.0416667i
$577$	−5.27409	+	19.6832i	−0.219563	+	0.819422i	0.764947	+	0.644094i	$0.222765\pi$
$577$	−5.27409	+	19.6832i	−0.219563	+	0.819422i	−0.984510	+	0.175328i	$0.943901\pi$
$578$	4.04836	+	15.1087i	0.168390	+	0.628438i
$579$	−13.3630	+	13.3630i	−0.555348	+	0.555348i
$580$	−1.18837	+	1.18837i	−0.0493444	+	0.0493444i
$581$	−10.0777	−	24.3090i	−0.418092	−	1.00851i
$582$	1.45049	+	0.837440i	0.0601247	+	0.0347130i
$583$	2.44713	−	9.13280i	0.101350	−	0.378242i
$584$	0.412908	+	0.715177i	0.0170862	+	0.0295942i
$585$	0.836043	+	1.33092i	0.0345661	+	0.0550266i
$586$	−20.8060	−	12.0123i	−0.859488	−	0.496225i
$587$	−6.30452	+	1.68929i	−0.260215	+	0.0697245i	−0.386568	−	0.922261i	$-0.626340\pi$
$587$	−6.30452	+	1.68929i	−0.260215	+	0.0697245i	0.126353	+	0.991985i	$0.459673\pi$
$588$	−6.76039	+	1.81580i	−0.278794	+	0.0748822i
$589$	49.4104	−	28.5271i	2.03592	−	1.17544i
$590$	−1.46407	−	5.46398i	−0.0602747	−	0.224948i
$591$	−20.2225	+	5.41861i	−0.831844	+	0.222892i
$592$	4.75480	−	1.27404i	0.195421	−	0.0523629i
$593$	−2.72689	−	10.1769i	−0.111980	−	0.417915i	0.887063	−	0.461648i	$-0.152742\pi$
$593$	−2.72689	−	10.1769i	−0.111980	−	0.417915i	−0.999043	+	0.0437330i	$0.986075\pi$
$594$	1.38969	−	0.802339i	0.0570197	−	0.0329204i
$595$	0.817963	−	1.06665i	0.0335332	−	0.0437285i
$596$	−21.5634	+	5.77789i	−0.883271	+	0.236672i
$597$	−13.1334	−	7.58258i	−0.537515	−	0.310334i
$598$	10.7416	+	17.0998i	0.439257	+	0.699263i
$599$	9.33086	+	16.1615i	0.381249	+	0.660342i	0.991241	−	0.132065i	$-0.0421609\pi$
$599$	9.33086	+	16.1615i	0.381249	+	0.660342i	−0.609992	+	0.792407i	$0.708828\pi$
$600$	1.24491	−	4.64608i	0.0508234	−	0.189675i
$601$	−10.9044	−	6.29568i	−0.444802	−	0.256806i	0.260831	−	0.965385i	$-0.416004\pi$
$601$	−10.9044	−	6.29568i	−0.444802	−	0.256806i	−0.705632	+	0.708578i	$0.749337\pi$
$602$	−0.763244	−	0.100250i	−0.0311075	−	0.00408587i
$603$	1.22023	−	1.22023i	0.0496916	−	0.0496916i
$604$	−5.07065	+	5.07065i	−0.206322	+	0.206322i
$605$	−0.950540	−	3.54746i	−0.0386449	−	0.144225i
$606$	5.00458	−	18.6774i	0.203297	−	0.758716i
$607$		−	20.7550i		−	0.842419i	−0.906963	−	0.421209i	$-0.861606\pi$
$607$		−	20.7550i		−	0.842419i	0.906963	−	0.421209i	$-0.138394\pi$
$608$	−3.23537	+	5.60382i	−0.131212	+	0.227265i
$609$	−6.21198	−	8.09057i	−0.251722	−	0.327846i
$610$			0.180204i			0.00729626i
$611$	14.0915	−	8.85190i	0.570082	−	0.358110i
$612$	−1.00933	+	0.582739i	−0.0407999	+	0.0235558i
$613$	−12.7096	+	12.7096i	−0.513336	+	0.513336i	−0.915547	−	0.402211i	$-0.868242\pi$
$613$	−12.7096	+	12.7096i	−0.513336	+	0.513336i	0.402211	+	0.915547i	$0.368242\pi$
$614$	−18.9812	+	10.9588i	−0.766020	+	0.442262i
$615$	0.403299	+	0.698535i	0.0162626	+	0.0281677i
$616$	−1.62353	+	3.92289i	−0.0654140	+	0.158058i
$617$	1.11387	+	0.298460i	0.0448427	+	0.0120156i	0.281171	−	0.959658i	$-0.409277\pi$
$617$	1.11387	+	0.298460i	0.0448427	+	0.0120156i	−0.236328	+	0.971673i	$0.575944\pi$
$618$	13.7355	+	13.7355i	0.552524	+	0.552524i
$619$	−3.86266	−	1.03500i	−0.155254	−	0.0416001i	0.180355	−	0.983602i	$-0.442275\pi$
$619$	−3.86266	−	1.03500i	−0.155254	−	0.0416001i	−0.335609	+	0.942001i	$0.608942\pi$
$620$	1.92180	−	3.32865i	0.0771812	−	0.133682i
$621$	2.80036	+	4.85037i	0.112375	+	0.194639i
$622$	0.492269	+	1.83717i	0.0197382	+	0.0736639i
$623$	14.4957	+	11.1160i	0.580758	+	0.445354i
$624$	2.64276	+	2.45272i	0.105795	+	0.0981874i
$625$	11.0929	−	19.2134i	0.443715	−	0.768537i
$626$	−14.4818	−	14.4818i	−0.578808	−	0.578808i
$627$	−10.3834			−0.414675
$628$	15.2996			0.610521
$629$	−4.05674	−	4.05674i	−0.161753	−	0.161753i
$630$	−1.06567	−	0.441039i	−0.0424572	−	0.0175714i
$631$	6.47088	−	24.1497i	0.257602	−	0.961383i	−0.709023	−	0.705186i	$-0.750864\pi$
$631$	6.47088	−	24.1497i	0.257602	−	0.961383i	0.966625	−	0.256197i	$-0.0824697\pi$
$632$	9.26796	−	2.48334i	0.368660	−	0.0987821i
$633$	−8.09449	−	4.67336i	−0.321727	−	0.185749i
$634$		−	27.3736i		−	1.08715i
$635$	−3.40125	−	0.911361i	−0.134974	−	0.0361663i
$636$	5.89213			0.233638
$637$	11.7826	−	22.3197i	0.466845	−	0.884339i
$638$	−6.18659			−0.244929
$639$	7.98595	+	2.13983i	0.315919	+	0.0846503i
$640$			0.435917i			0.0172311i
$641$	−9.36501	−	5.40689i	−0.369896	−	0.213559i	0.303517	−	0.952826i	$-0.401839\pi$
$641$	−9.36501	−	5.40689i	−0.369896	−	0.213559i	−0.673413	+	0.739267i	$0.735172\pi$
$642$	−7.19607	+	1.92818i	−0.284006	+	0.0760992i
$643$	2.27198	−	8.47915i	0.0895981	−	0.334385i	−0.906547	−	0.422105i	$-0.861291\pi$
$643$	2.27198	−	8.47915i	0.0895981	−	0.334385i	0.996145	+	0.0877200i	$0.0279581\pi$
$644$	−13.6919	−	5.66654i	−0.539535	−	0.223293i
$645$	−0.0896845	−	0.0896845i	−0.00353132	−	0.00353132i
$646$	7.54150			0.296717
$647$	32.4239			1.27471			0.637357	−	0.770569i	$-0.280028\pi$
$647$	32.4239			1.27471			0.637357	+	0.770569i	$0.280028\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	10.4116	−	18.0335i	0.408693	−	0.707877i
$650$	9.22504	+	14.6855i	0.361836	+	0.576014i
$651$	18.5118	+	14.1958i	0.725536	+	0.556377i
$652$	0.848915	+	3.16820i	0.0332461	+	0.124076i
$653$	10.0799	+	17.4589i	0.394458	+	0.683222i	0.993032	−	0.117846i	$-0.0375990\pi$
$653$	10.0799	+	17.4589i	0.394458	+	0.683222i	−0.598574	+	0.801068i	$0.704266\pi$
$654$	−1.24374	+	2.15422i	−0.0486341	+	0.0842367i
$655$	5.13960	+	1.37715i	0.200821	+	0.0538098i
$656$	1.30840	+	1.30840i	0.0510843	+	0.0510843i
$657$	−0.797676	−	0.213737i	−0.0311203	−	0.00833866i
$658$	−4.66965	+	11.2831i	−0.182042	+	0.439862i
$659$	23.4367	+	40.5936i	0.912966	+	1.58130i	0.809853	+	0.586633i	$0.199547\pi$
$659$	23.4367	+	40.5936i	0.912966	+	1.58130i	0.103113	+	0.994670i	$0.467120\pi$
$660$	−0.605790	+	0.349753i	−0.0235803	+	0.0136141i
$661$	−16.4446	+	16.4446i	−0.639622	+	0.639622i	−0.950462	−	0.310840i	$-0.899390\pi$
$661$	−16.4446	+	16.4446i	−0.639622	+	0.639622i	0.310840	+	0.950462i	$0.399390\pi$
$662$	−11.3425	+	6.54861i	−0.440840	+	0.254519i
$663$	0.935575	−	4.09672i	0.0363347	−	0.159103i
$664$		−	9.94618i		−	0.385987i
$665$	4.54489	+	5.91933i	0.176243	+	0.229542i
$666$	−2.46126	+	4.26303i	−0.0953720	+	0.165189i
$667$		−	21.5927i		−	0.836074i
$668$	4.22682	−	15.7747i	0.163541	−	0.610342i
$669$	0.146967	+	0.548487i	0.00568206	+	0.0212057i
$670$	−0.531919	+	0.531919i	−0.0205498	+	0.0205498i
$671$	−0.469066	+	0.469066i	−0.0181081	+	0.0181081i
$672$	−2.62322	−	0.344551i	−0.101193	−	0.0132914i
$673$	24.1177	+	13.9244i	0.929670	+	0.536745i	0.886707	−	0.462332i	$-0.152987\pi$
$673$	24.1177	+	13.9244i	0.929670	+	0.536745i	0.0429627	+	0.999077i	$0.486320\pi$
$674$	0.000220839	0	0.000824184i	8.50642e−6	0	3.17464e-5i
$675$	2.40499	+	4.16556i	0.0925680	+	0.160333i
$676$	−12.9639	+	0.968329i	−0.498611	+	0.0372434i
$677$	−17.7894	−	10.2707i	−0.683702	−	0.394736i	0.117546	−	0.993067i	$-0.462497\pi$
$677$	−17.7894	−	10.2707i	−0.683702	−	0.394736i	−0.801249	+	0.598332i	$0.795831\pi$
$678$	8.01670	−	2.14807i	0.307879	−	0.0824960i
$679$	2.69656	−	3.51641i	0.103484	−	0.134947i
$680$	0.439986	−	0.254026i	0.0168727	−	0.00974144i
$681$	−3.39850	−	12.6834i	−0.130231	−	0.486028i
$682$	13.6667	−	3.66199i	0.523327	−	0.140225i
$683$	−13.5145	+	3.62120i	−0.517117	+	0.138561i	−0.507933	−	0.861397i	$-0.669590\pi$
$683$	−13.5145	+	3.62120i	−0.517117	+	0.138561i	−0.00918453	+	0.999958i	$0.502924\pi$
$684$	−1.67475	−	6.25025i	−0.0640357	−	0.238984i
$685$	−1.24230	+	0.717243i	−0.0474659	+	0.0274044i
$686$	2.43394	+	18.3596i	0.0929281	+	0.700974i
$687$	−25.1207	+	6.73106i	−0.958413	+	0.256806i
$688$	−0.251976	−	0.145478i	−0.00960650	−	0.00554632i
$689$	−14.4518	+	15.5715i	−0.550568	+	0.593226i
$690$	−1.22072	−	2.11436i	−0.0464722	−	0.0804922i
$691$	−13.3643	+	49.8763i	−0.508402	+	1.89738i	−0.0725483	+	0.997365i	$0.523113\pi$
$691$	−13.3643	+	49.8763i	−0.508402	+	1.89738i	−0.435854	+	0.900017i	$0.643554\pi$
$692$	−7.81727	−	4.51330i	−0.297168	−	0.171570i
$693$	−1.62589	−	3.92191i	−0.0617625	−	0.148981i
$694$	−1.73822	+	1.73822i	−0.0659820	+	0.0659820i
$695$	3.99006	−	3.99006i	0.151352	−	0.151352i
$696$	−0.997837	−	3.72398i	−0.0378229	−	0.141157i
$697$	0.558155	−	2.08306i	0.0211416	−	0.0789016i
$698$			26.9871i			1.02148i
$699$	−4.65378	+	8.06058i	−0.176022	+	0.304879i
$700$	−11.7588	−	4.86650i	−0.444439	−	0.183936i
$701$		−	11.6574i		−	0.440296i	−0.975467	−	0.220148i	$-0.929346\pi$
$701$		−	11.6574i		−	0.440296i	0.975467	−	0.220148i	$-0.0706540\pi$
$702$	−3.60305	+	0.134376i	−0.135988	+	0.00507171i
$703$	27.5850	−	15.9262i	1.04039	−	0.600668i
$704$	−1.13468	+	1.13468i	−0.0427648	+	0.0427648i
$705$	−1.74239	+	1.00597i	−0.0656222	+	0.0378870i
$706$	1.04456	+	1.80923i	0.0393125	+	0.0680913i
$707$	−47.2705	−	19.5634i	−1.77779	−	0.735758i
$708$	12.5345	+	3.35860i	0.471074	+	0.126224i
$709$	5.41429	+	5.41429i	0.203338	+	0.203338i	0.801429	−	0.598091i	$-0.204074\pi$
$709$	5.41429	+	5.41429i	0.203338	+	0.203338i	−0.598091	+	0.801429i	$0.704074\pi$
$710$	−3.48121	−	0.932787i	−0.130647	−	0.0350069i
$711$	−4.79745	+	8.30943i	−0.179918	+	0.311628i
$712$	3.45218	+	5.97935i	0.129376	+	0.224086i
$713$	12.7813	+	47.7004i	0.478662	+	1.78639i
$714$	1.18089	+	2.84849i	0.0441935	+	0.106602i
$715$	0.561521	−	2.45880i	0.0209997	−	0.0919539i
$716$	−4.90153	+	8.48971i	−0.183179	+	0.317275i
$717$	−14.8784	−	14.8784i	−0.555643	−	0.555643i
$718$	37.2946			1.39182
$719$	−5.02603			−0.187439			−0.0937196	−	0.995599i	$-0.529876\pi$
$719$	−5.02603			−0.187439			−0.0937196	+	0.995599i	$0.529876\pi$
$720$	−0.308240	−	0.308240i	−0.0114874	−	0.0114874i
$721$	40.7639	−	31.2987i	1.51813	−	1.16563i
$722$	−5.91931	+	22.0911i	−0.220294	+	0.822147i
$723$	−8.78342	+	2.35351i	−0.326659	+	0.0875280i
$724$	−10.9096	−	6.29864i	−0.405451	−	0.234087i
$725$		−	18.5441i		−	0.688712i
$726$	8.13794	+	2.18055i	0.302027	+	0.0809279i
$727$	5.39123			0.199950			0.0999748	−	0.994990i	$-0.468124\pi$
$727$	5.39123			0.199950			0.0999748	+	0.994990i	$0.468124\pi$
$728$	7.34459	−	6.08745i	0.272209	−	0.225616i
$729$	−1.00000			−0.0370370
$730$	0.347720	+	0.0931714i	0.0128697	+	0.00344843i
$731$			0.339104i			0.0125422i
$732$	−0.358008	−	0.206696i	−0.0132323	−	0.00763970i
$733$	13.3220	−	3.56963i	0.492061	−	0.131847i	−0.00425205	−	0.999991i	$-0.501353\pi$
$733$	13.3220	−	3.56963i	0.492061	−	0.131847i	0.496313	+	0.868144i	$0.334687\pi$
$734$	−6.99450	+	26.1038i	−0.258172	+	0.963510i
$735$	−1.52412	+	2.64352i	−0.0562180	+	0.0975078i
$736$	−3.96031	−	3.96031i	−0.145979	−	0.145979i
$737$	−2.76914			−0.102003
$738$	−1.85035			−0.0681124
$739$	13.0475	+	13.0475i	0.479959	+	0.479959i	0.905118	−	0.425159i	$-0.139782\pi$
$739$	13.0475	+	13.0475i	0.479959	+	0.479959i	−0.425159	+	0.905118i	$0.639782\pi$
$740$	1.07291	−	1.85833i	0.0394408	−	0.0683135i
$741$	20.6256	+	10.9042i	0.757700	+	0.400574i
$742$	2.03014	−	15.4564i	0.0745289	−	0.567421i
$743$	3.40539	+	12.7091i	0.124932	+	0.466251i	0.999837	−	0.0180423i	$-0.00574335\pi$
$743$	3.40539	+	12.7091i	0.124932	+	0.466251i	−0.874906	+	0.484294i	$0.839077\pi$
$744$	4.40863	+	7.63597i	0.161628	+	0.279948i
$745$	−4.86572	+	8.42767i	−0.178266	+	0.308766i
$746$	10.6799	+	2.86166i	0.391018	+	0.104773i
$747$	7.03301	+	7.03301i	0.257324	+	0.257324i
$748$	1.80649	+	0.484048i	0.0660518	+	0.0176985i
$749$	2.57863	+	19.5412i	0.0942210	+	0.714021i
$750$	−2.13817	−	3.70341i	−0.0780748	−	0.135230i
$751$	−38.7295	+	22.3605i	−1.41326	+	0.815946i	−0.995694	−	0.0927008i	$-0.970450\pi$
$751$	−38.7295	+	22.3605i	−1.41326	+	0.815946i	−0.417566	+	0.908647i	$0.637117\pi$
$752$	−3.26360	+	3.26360i	−0.119011	+	0.119011i
$753$	16.9947	−	9.81192i	0.619323	−	0.357566i
$754$	12.2890	+	6.49684i	0.447539	+	0.236601i
$755$			3.12595i			0.113765i
$756$	2.09853	−	1.61126i	0.0763228	−	0.0586010i
$757$	24.1166	−	41.7713i	0.876534	−	1.51820i	0.0214152	−	0.999771i	$-0.493183\pi$
$757$	24.1166	−	41.7713i	0.876534	−	1.51820i	0.855119	−	0.518431i	$-0.173484\pi$
$758$		−	9.78625i		−	0.355453i
$759$	2.32610	−	8.68112i	0.0844321	−	0.315105i
$760$	0.730052	+	2.72459i	0.0264818	+	0.0988312i
$761$	−5.29625	+	5.29625i	−0.191989	+	0.191989i	−0.796555	−	0.604566i	$-0.793347\pi$
$761$	−5.29625	+	5.29625i	−0.191989	+	0.191989i	0.604566	+	0.796555i	$0.293347\pi$
$762$	5.71184	−	5.71184i	0.206918	−	0.206918i
$763$	5.22246	+	4.00484i	0.189066	+	0.144985i
$764$	17.1052	+	9.87568i	0.618844	+	0.357290i
$765$	−0.131493	+	0.490740i	−0.00475415	+	0.0177427i
$766$	9.89522	+	17.1390i	0.357529	+	0.619258i
$767$	−39.6195	+	24.8878i	−1.43058	+	0.898647i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	10.6482	−	2.85317i	0.383983	−	0.102888i	−0.0616632	−	0.998097i	$-0.519640\pi$
$769$	10.6482	−	2.85317i	0.383983	−	0.102888i	0.445647	+	0.895209i	$0.352974\pi$
$770$	0.708753	+	1.70963i	0.0255417	+	0.0616107i
$771$	−17.9750	+	10.3779i	−0.647354	+	0.373750i
$772$	4.89121	+	18.2542i	0.176038	+	0.656984i
$773$	−30.0960	+	8.06419i	−1.08248	+	0.290049i	−0.755610	−	0.655022i	$-0.772659\pi$
$773$	−30.0960	+	8.06419i	−1.08248	+	0.290049i	−0.326866	+	0.945071i	$0.605993\pi$
$774$	0.281043	−	0.0753052i	0.0101019	−	0.00270679i
$775$	10.9767	+	40.9657i	0.394296	+	1.47153i
$776$	1.45049	−	0.837440i	0.0520695	−	0.0300623i
$777$	10.3348	+	7.92527i	0.370760	+	0.284317i
$778$	21.9373	−	5.87808i	0.786490	−	0.210739i
$779$	10.3690	+	5.98657i	0.371509	+	0.214491i
$780$	1.57063	−	0.0585770i	0.0562375	−	0.00209739i
$781$	−6.63346	−	11.4895i	−0.237364	−	0.411127i
$782$	−1.68945	+	6.30510i	−0.0604145	+	0.225470i
$783$	3.33883	+	1.92767i	0.119320	+	0.0688894i
$784$	−1.80767	+	6.76257i	−0.0645596	+	0.241520i
$785$	4.71594	−	4.71594i	0.168319	−	0.168319i
$786$	−8.63112	+	8.63112i	−0.307862	+	0.307862i
$787$	1.78437	+	6.65937i	0.0636061	+	0.237381i	0.990409	−	0.138167i	$-0.0441211\pi$
$787$	1.78437	+	6.65937i	0.0636061	+	0.237381i	−0.926803	+	0.375548i	$0.877454\pi$
$788$	−5.41861	+	20.2225i	−0.193030	+	0.720398i
$789$			27.4496i			0.977232i
$790$	2.09129	−	3.62222i	0.0744047	−	0.128873i
$791$	−2.87269	−	21.7697i	−0.102141	−	0.774041i
$792$		−	1.60468i		−	0.0570197i
$793$	1.42434	−	0.439160i	0.0505798	−	0.0155950i
$794$	−2.70757	+	1.56321i	−0.0960880	+	0.0554764i
$795$	1.81619	−	1.81619i	0.0644136	−	0.0644136i
$796$	−13.1334	+	7.58258i	−0.465502	+	0.268757i
$797$	−3.10072	−	5.37060i	−0.109833	−	0.190236i	0.805869	−	0.592093i	$-0.201698\pi$
$797$	−3.10072	−	5.37060i	−0.109833	−	0.190236i	−0.915703	+	0.401857i	$0.868365\pi$
$798$	−16.9728	+	2.23971i	−0.600832	+	0.0792847i
$799$	5.19588	+	1.39223i	0.183817	+	0.0492536i
$800$	−3.40117	−	3.40117i	−0.120249	−	0.120249i
$801$	−6.66910	−	1.78698i	−0.235641	−	0.0631398i
$802$	−6.09665	+	10.5597i	−0.215280	+	0.372876i
$803$	0.662584	+	1.14763i	0.0233821	+	0.0404989i
$804$	−0.446636	−	1.66687i	−0.0157516	−	0.0587858i
$805$	−5.96703	+	2.47373i	−0.210310	+	0.0871874i
$806$	−30.9931	−	7.07796i	−1.09169	−	0.249311i
$807$	−3.76055	+	6.51347i	−0.132378	+	0.229285i
$808$	−13.6728	−	13.6728i	−0.481006	−	0.481006i
$809$	26.7793			0.941509			0.470754	−	0.882264i	$-0.343982\pi$
$809$	26.7793			0.941509			0.470754	+	0.882264i	$0.343982\pi$
$810$	0.435917			0.0153166
$811$	31.7654	+	31.7654i	1.11544	+	1.11544i	0.992403	+	0.123033i	$0.0392621\pi$
$811$	31.7654	+	31.7654i	1.11544	+	1.11544i	0.123033	+	0.992403i	$0.460738\pi$
$812$	−10.1126	+	1.33444i	−0.354884	+	0.0468298i
$813$	−0.0945684	+	0.352934i	−0.00331666	+	0.0123779i
$814$	7.62991	−	2.04443i	0.267428	−	0.0716572i
$815$	1.23823	+	0.714894i	0.0433734	+	0.0250416i
$816$			1.16548i			0.0407999i
$817$	−1.81855	−	0.487280i	−0.0636232	−	0.0170478i
$818$	−7.04890			−0.246459
$819$	−0.888935	+	9.49788i	−0.0310619	+	0.331883i
$820$	0.806599			0.0281677
$821$	11.3615	+	3.04430i	0.396519	+	0.106247i	0.451568	−	0.892237i	$-0.350865\pi$
$821$	11.3615	+	3.04430i	0.396519	+	0.106247i	−0.0550491	+	0.998484i	$0.517532\pi$
$822$		−	3.29073i		−	0.114778i
$823$	14.6017	+	8.43032i	0.508985	+	0.293862i	0.732416	−	0.680857i	$-0.238393\pi$
$823$	14.6017	+	8.43032i	0.508985	+	0.293862i	−0.223432	+	0.974720i	$0.571726\pi$
$824$	18.7631	−	5.02756i	0.653643	−	0.175143i
$825$	1.99768	−	7.45546i	0.0695504	−	0.259566i
$826$	13.1291	−	31.7234i	0.456820	−	1.10380i
$827$	18.4681	+	18.4681i	0.642199	+	0.642199i	0.951096	−	0.308896i	$-0.0999597\pi$
$827$	18.4681	+	18.4681i	0.642199	+	0.642199i	−0.308896	+	0.951096i	$0.599960\pi$
$828$	5.60073			0.194639
$829$	12.7985			0.444510			0.222255	−	0.974989i	$-0.428658\pi$
$829$	12.7985			0.444510			0.222255	+	0.974989i	$0.428658\pi$
$830$	−3.06581	−	3.06581i	−0.106416	−	0.106416i
$831$	14.5914	−	25.2730i	0.506169	−	0.876711i
$832$	3.44550	−	1.06233i	0.119451	−	0.0368298i
$833$	7.87909	−	2.11627i	0.272994	−	0.0733245i
$834$	3.35033	+	12.5036i	0.116012	+	0.432964i
$835$	−3.55952	−	6.16526i	−0.123182	−	0.213358i
$836$	−5.19172	+	8.99233i	−0.179559	+	0.311006i
$837$	−8.51682	−	2.28207i	−0.294384	−	0.0788800i
$838$	−0.280823	−	0.280823i	−0.00970087	−	0.00970087i
$839$	25.9817	+	6.96178i	0.896988	+	0.240347i	0.677722	−	0.735318i	$-0.262967\pi$
$839$	25.9817	+	6.96178i	0.896988	+	0.240347i	0.219266	+	0.975665i	$0.429634\pi$
$840$	−0.914785	+	0.702376i	−0.0315631	+	0.0242343i
$841$	7.06815	+	12.2424i	0.243729	+	0.422151i
$842$	16.3267	−	9.42623i	0.562656	−	0.324850i
$843$	−0.535962	+	0.535962i	−0.0184595	+	0.0184595i
$844$	−8.09449	+	4.67336i	−0.278624	+	0.160864i
$845$	−3.69751	+	4.29446i	−0.127198	+	0.147734i
$846$		−	4.61542i		−	0.158681i
$847$	8.52401	−	20.5963i	0.292888	−	0.707697i
$848$	2.94607	−	5.10274i	0.101168	−	0.175229i
$849$			1.61700i			0.0554953i
$850$	−1.45092	+	5.41491i	−0.0497661	+	0.185730i
$851$	7.13557	+	26.6303i	0.244604	+	0.912875i
$852$	5.84612	−	5.84612i	0.200285	−	0.200285i
$853$	−23.9325	+	23.9325i	−0.819435	+	0.819435i	−0.986026	−	0.166591i	$-0.946724\pi$
$853$	−23.9325	+	23.9325i	−0.819435	+	0.819435i	0.166591	+	0.986026i	$0.446724\pi$
$854$	−0.665561	+	0.867916i	−0.0227750	+	0.0296995i
$855$	−2.44280	−	1.41035i	−0.0835420	−	0.0482330i
$856$	−1.92818	+	7.19607i	−0.0659039	+	0.245957i
$857$	2.16796	+	3.75501i	0.0740560	+	0.128269i	0.900675	−	0.434493i	$-0.143072\pi$
$857$	2.16796	+	3.75501i	0.0740560	+	0.128269i	−0.826619	+	0.562761i	$0.809739\pi$
$858$	4.24077	+	3.93582i	0.144778	+	0.134367i
$859$	9.02380	+	5.20989i	0.307888	+	0.177759i	0.645981	−	0.763353i	$-0.276448\pi$
$859$	9.02380	+	5.20989i	0.307888	+	0.177759i	−0.338093	+	0.941113i	$0.609782\pi$
$860$	−0.122511	+	0.0328268i	−0.00417760	+	0.00111938i
$861$	−0.637541	+	4.85388i	−0.0217273	+	0.165420i
$862$	29.0855	−	16.7925i	0.990657	−	0.571956i
$863$	14.4796	+	54.0385i	0.492890	+	1.83949i	0.541538	+	0.840676i	$0.317842\pi$
$863$	14.4796	+	54.0385i	0.492890	+	1.83949i	−0.0486480	+	0.998816i	$0.515491\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−3.80077	+	1.01841i	−0.129230	+	0.0346271i
$866$	−1.95791	−	7.30700i	−0.0665324	−	0.248302i
$867$	−13.5461	+	7.82083i	−0.460049	+	0.265609i
$868$	21.5498	−	8.93382i	0.731449	−	0.303234i
$869$	14.8721	−	3.98497i	0.504501	−	0.135181i
$870$	−1.45545	−	0.840305i	−0.0493444	−	0.0284890i
$871$	5.50059	+	2.90801i	0.186381	+	0.0985341i
$872$	1.24374	+	2.15422i	0.0421184	+	0.0729511i
$873$	−0.433491	+	1.61781i	−0.0146714	+	0.0547546i
$874$	−31.3855	−	18.1204i	−1.06163	−	0.612932i
$875$	−10.4516	+	4.33287i	−0.353328	+	0.146478i
$876$	−0.583940	+	0.583940i	−0.0197295	+	0.0197295i
$877$	11.2140	−	11.2140i	0.378671	−	0.378671i	−0.491952	−	0.870623i	$-0.663716\pi$
$877$	11.2140	−	11.2140i	0.378671	−	0.378671i	0.870623	+	0.491952i	$0.163716\pi$
$878$	−1.97416	−	7.36765i	−0.0666246	−	0.248646i
$879$	6.21805	−	23.2061i	0.209730	−	0.782721i
$880$			0.699506i			0.0235803i
$881$	16.5769	−	28.7120i	0.558490	−	0.967332i	−0.439133	−	0.898422i	$-0.644714\pi$
$881$	16.5769	−	28.7120i	0.558490	−	0.967332i	0.997623	−	0.0689103i	$-0.0219522\pi$
$882$	−3.50364	−	6.06007i	−0.117974	−	0.204053i
$883$		−	39.9244i		−	1.34356i	−0.740749	−	0.671782i	$-0.765529\pi$
$883$		−	39.9244i		−	1.34356i	0.740749	−	0.671782i	$-0.234471\pi$
$884$	−3.08008	−	2.85859i	−0.103594	−	0.0961449i
$885$	4.89887	−	2.82836i	0.164674	−	0.0950744i
$886$	−22.0909	+	22.0909i	−0.742157	+	0.742157i
$887$	8.71285	−	5.03037i	0.292549	−	0.168903i	−0.346542	−	0.938034i	$-0.612644\pi$
$887$	8.71285	−	5.03037i	0.292549	−	0.168903i	0.639091	+	0.769131i	$0.279311\pi$
$888$	2.46126	+	4.26303i	0.0825946	+	0.143058i
$889$	−13.0154	−	16.9514i	−0.436522	−	0.568533i
$890$	2.90717	+	0.778974i	0.0974486	+	0.0261113i
$891$	1.13468	+	1.13468i	0.0380132	+	0.0380132i
$892$	0.548487	+	0.146967i	0.0183647	+	0.00492081i
$893$	−14.9326	+	25.8640i	−0.499700	+	0.865506i
$894$	−11.1620	−	19.3332i	−0.373314	−	0.646599i
$895$	1.10602	+	4.12771i	0.0369701	+	0.137974i
$896$	−1.61000	+	2.09950i	−0.0537863	+	0.0701394i
$897$	−13.7370	+	14.8014i	−0.458665	+	0.494203i
$898$	9.20604	−	15.9453i	0.307209	−	0.532102i
$899$	24.0371	+	24.0371i	0.801682	+	0.801682i
$900$	4.80998			0.160333
$901$	−6.86715			−0.228778
$902$	2.09955	+	2.09955i	0.0699075	+	0.0699075i
$903$	−0.100708	−	0.763184i	−0.00335137	−	0.0253972i
$904$	2.14807	−	8.01670i	0.0714437	−	0.266631i
$905$	−5.30425	+	1.42127i	−0.176319	+	0.0472446i
$906$	−6.21025	−	3.58549i	−0.206322	−	0.119120i
$907$			50.1122i			1.66395i	0.554815	+	0.831974i	$0.312789\pi$
$907$			50.1122i			1.66395i	−0.554815	+	0.831974i	$0.687211\pi$
$908$	−12.6834	−	3.39850i	−0.420913	−	0.112783i
$909$	19.3362			0.641342
$910$	0.387502	−	4.14029i	0.0128456	−	0.137249i
$911$	3.13043			0.103716			0.0518578	−	0.998654i	$-0.483486\pi$
$911$	3.13043			0.103716			0.0518578	+	0.998654i	$0.483486\pi$
$912$	−6.25025	−	1.67475i	−0.206967	−	0.0554565i
$913$		−	15.9604i		−	0.528212i
$914$	−17.1282	−	9.88896i	−0.566550	−	0.327098i
$915$	−0.174064	+	0.0466403i	−0.00575438	+	0.00154188i
$916$	−6.73106	+	25.1207i	−0.222401	+	0.830010i
$917$	19.6675	+	25.6152i	0.649477	+	0.845889i
$918$	−0.824118	−	0.824118i	−0.0271999	−	0.0271999i
$919$	45.7305			1.50851			0.754254	−	0.656582i	$-0.227999\pi$
$919$	45.7305			1.50851			0.754254	+	0.656582i	$0.227999\pi$
$920$	−2.44145			−0.0804922
$921$	−15.4981	−	15.4981i	−0.510680	−	0.510680i
$922$	6.50804	−	11.2723i	0.214331	−	0.371232i
$923$	1.11098	+	29.7888i	0.0365683	+	0.980509i
$924$	−4.20942	−	0.552894i	−0.138480	−	0.0181889i
$925$	6.12812	+	22.8705i	0.201491	+	0.751976i
$926$	−19.0585	−	33.0103i	−0.626301	−	1.08478i
$927$	−9.71249	+	16.8225i	−0.319000	+	0.552524i
$928$	−3.72398	−	0.997837i	−0.122246	−	0.0327556i
$929$	−35.2842	−	35.2842i	−1.15764	−	1.15764i	−0.984983	−	0.172653i	$-0.944766\pi$
$929$	−35.2842	−	35.2842i	−1.15764	−	1.15764i	−0.172653	−	0.984983i	$-0.555234\pi$
$930$	3.71262	+	0.994795i	0.121742	+	0.0326206i
$931$	0.0272309	+	45.2952i	0.000892455	+	1.48449i
$932$	4.65378	+	8.06058i	0.152440	+	0.264033i
$933$	−1.64716	+	0.950990i	−0.0539257	+	0.0311340i
$934$	−4.46652	+	4.46652i	−0.146149	+	0.146149i
$935$	0.706035	−	0.407629i	0.0230898	−	0.0133309i
$936$	−1.68515	+	3.18752i	−0.0550808	+	0.104187i
$937$			36.5761i			1.19489i	0.801910	+	0.597445i	$0.203817\pi$
$937$			36.5761i			1.19489i	−0.801910	+	0.597445i	$0.796183\pi$
$938$	−4.52645	+	0.597302i	−0.147794	+	0.0195026i
$939$	10.2402	−	17.7365i	0.334175	−	0.578808i
$940$			2.01194i			0.0656222i
$941$	−1.63114	+	6.08751i	−0.0531738	+	0.198447i	−0.987403	−	0.158226i	$-0.949422\pi$
$941$	−1.63114	+	6.08751i	−0.0531738	+	0.198447i	0.934229	+	0.356674i	$0.116089\pi$
$942$	3.95983	+	14.7783i	0.129018	+	0.481502i
$943$	−7.32797	+	7.32797i	−0.238631	+	0.238631i
$944$	9.17586	−	9.17586i	0.298649	−	0.298649i
$945$	0.150196	−	1.14351i	0.00488587	−	0.0371982i
$946$	−0.404340	−	0.233446i	−0.0131462	−	0.00758999i
$947$	13.3018	−	49.6430i	0.432250	−	1.61318i	−0.315311	−	0.948988i	$-0.602109\pi$
$947$	13.3018	−	49.6430i	0.432250	−	1.61318i	0.747562	−	0.664192i	$-0.231224\pi$
$948$	4.79745	+	8.30943i	0.155814	+	0.269878i
$949$	−0.110970	−	2.97545i	−0.00360224	−	0.0965872i
$950$	−26.9543	−	15.5620i	−0.874512	−	0.504899i
$951$	26.4409	−	7.08481i	0.857404	−	0.229741i
$952$	3.05731	+	0.401567i	0.0990879	+	0.0130149i
$953$	47.6293	−	27.4988i	1.54286	−	0.890773i	0.544207	−	0.838951i	$-0.316830\pi$
$953$	47.6293	−	27.4988i	1.54286	−	0.890773i	0.998656	−	0.0518222i	$-0.0165029\pi$
$954$	1.52500	+	5.69136i	0.0493736	+	0.184265i
$955$	8.31657	−	2.22842i	0.269118	−	0.0721100i
$956$	−20.3242	+	5.44586i	−0.657333	+	0.176132i
$957$	−1.60121	−	5.97579i	−0.0517597	−	0.193170i
$958$	28.0907	−	16.2182i	0.907569	−	0.523985i
$959$	−8.63232	−	1.13383i	−0.278752	−	0.0366132i
$960$	−0.421063	+	0.112824i	−0.0135898	+	0.00364136i
$961$	−40.4815	−	23.3720i	−1.30586	−	0.753937i
$962$	−17.3029	−	3.95151i	−0.557869	−	0.127402i
$963$	−3.72496	−	6.45182i	−0.120035	−	0.207907i
$964$	−2.35351	+	8.78342i	−0.0758015	+	0.282895i
$965$	7.13434	+	4.11902i	0.229663	+	0.132596i
$966$	1.92974	−	14.6919i	0.0620883	−	0.472705i
$967$	−6.03011	+	6.03011i	−0.193915	+	0.193915i	−0.797385	−	0.603470i	$-0.793784\pi$
$967$	−6.03011	+	6.03011i	−0.193915	+	0.193915i	0.603470	+	0.797385i	$0.293784\pi$
$968$	5.95738	−	5.95738i	0.191478	−	0.191478i
$969$	1.95188	+	7.28453i	0.0627036	+	0.234013i
$970$	0.188966	−	0.705230i	0.00606733	−	0.0226436i
$971$			0.109991i			0.00352977i	0.999998	+	0.00176489i	$0.000561781\pi$
$971$			0.109991i			0.00352977i	−0.999998	+	0.00176489i	$0.999438\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	33.9540	−	4.48052i	1.08852	−	0.143639i
$974$		−	26.6659i		−	0.854429i
$975$	−11.7975	+	12.7116i	−0.377823	+	0.407097i
$976$	−0.358008	+	0.206696i	−0.0114595	+	0.00661617i
$977$	3.23594	−	3.23594i	0.103527	−	0.103527i	−0.653446	−	0.756973i	$-0.726677\pi$
$977$	3.23594	−	3.23594i	0.103527	−	0.103527i	0.756973	+	0.653446i	$0.226677\pi$
$978$	−2.84053	+	1.63998i	−0.0908300	+	0.0524407i
$979$	5.53963	+	9.59493i	0.177047	+	0.306655i
$980$	1.52730	+	2.64169i	0.0487877	+	0.0843856i
$981$	−2.40272	−	0.643807i	−0.0767130	−	0.0205552i
$982$	5.75366	+	5.75366i	0.183607	+	0.183607i
$983$	−36.9311	−	9.89567i	−1.17792	−	0.315623i	−0.383819	−	0.923408i	$-0.625391\pi$
$983$	−36.9311	−	9.89567i	−1.17792	−	0.315623i	−0.794101	+	0.607785i	$0.792058\pi$
$984$	−0.925176	+	1.60245i	−0.0294935	+	0.0510843i
$985$	4.56316	+	7.90362i	0.145394	+	0.251830i
$986$	1.16296	+	4.34022i	0.0370361	+	0.138221i
$987$	−12.1073	−	1.59025i	−0.385378	−	0.0506182i
$988$	19.7561	−	12.4102i	0.628524	−	0.394821i
$989$	0.814785	−	1.41125i	0.0259087	−	0.0448751i
$990$	−0.494625	−	0.494625i	−0.0157202	−	0.0157202i
$991$	−38.8996			−1.23569			−0.617843	−	0.786302i	$-0.711993\pi$
$991$	−38.8996			−1.23569			−0.617843	+	0.786302i	$0.711993\pi$
$992$	8.81726			0.279948
$993$	−9.26114	−	9.26114i	−0.293893	−	0.293893i
$994$	−13.3214	−	17.3499i	−0.422528	−	0.550307i
$995$	−1.71099	+	6.38549i	−0.0542419	+	0.202434i
$996$	9.60727	−	2.57426i	0.304418	−	0.0815686i
$997$	−26.0548	−	15.0428i	−0.825164	−	0.476409i	0.0270299	−	0.999635i	$-0.491395\pi$
$997$	−26.0548	−	15.0428i	−0.825164	−	0.476409i	−0.852194	+	0.523226i	$0.824728\pi$
$998$			7.13506i			0.225856i
$999$	−4.75480	−	1.27404i	−0.150435	−	0.0403090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.19.7	✓	32
7.3	odd	6		546.2.cg.a.409.3	yes	32
13.11	odd	12		546.2.cg.a.271.3	yes	32
91.24	even	12	inner	546.2.by.a.115.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.7	✓	32	1.1	even	1	trivial
546.2.by.a.115.7	yes	32	91.24	even	12	inner
546.2.cg.a.271.3	yes	32	13.11	odd	12
546.2.cg.a.409.3	yes	32	7.3	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.421063 - 0.112824i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.44466 + 1.01175i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.421063 - 0.112824i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.44466 + 1.01175i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +0.435917 q^{10} +(1.13468 + 1.13468i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.06233 - 3.44550i) q^{13} +(2.09950 + 1.61000i) q^{14} +(0.112824 + 0.421063i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.582739 - 1.00933i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(4.57550 + 4.57550i) q^{19} +(0.421063 + 0.112824i) q^{20} +(-1.01175 + 2.44466i) q^{21} +(0.802339 + 1.38969i) q^{22} +(-4.85037 + 2.80036i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.16556 + 2.40499i) q^{25} +(-0.134376 - 3.60305i) q^{26} -1.00000i q^{27} +(1.61126 + 2.09853i) q^{28} +(-1.92767 + 3.33883i) q^{29} +0.435917i q^{30} +(2.28207 - 8.51682i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.13468 + 1.13468i) q^{33} +(0.824118 - 0.824118i) q^{34} +(1.14351 + 0.150196i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(1.27404 - 4.75480i) q^{37} +(3.23537 + 5.60382i) q^{38} +(3.44550 - 1.06233i) q^{39} +(0.377515 + 0.217958i) q^{40} +(1.78730 - 0.478906i) q^{41} +(-1.61000 + 2.09950i) q^{42} +(-0.251976 + 0.145478i) q^{43} +(0.415321 + 1.55000i) q^{44} +(-0.421063 + 0.112824i) q^{45} +(-5.40989 + 1.44957i) q^{46} +(1.19456 + 4.45815i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(4.95272 + 4.94677i) q^{49} +(-4.64608 + 1.24491i) q^{50} +(1.00933 + 0.582739i) q^{51} +(0.802739 - 3.51505i) q^{52} +(-2.94607 - 5.10274i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.605790 + 0.349753i) q^{55} +(1.01322 + 2.44405i) q^{56} +(-4.57550 + 4.57550i) q^{57} +(-2.72614 + 2.72614i) q^{58} +(-3.35860 - 12.5345i) q^{59} +(-0.112824 + 0.421063i) q^{60} +0.413392i q^{61} +(4.40863 - 7.63597i) q^{62} +(-2.44466 - 1.01175i) q^{63} +1.00000i q^{64} +(-0.836043 - 1.33092i) q^{65} +(-1.38969 + 0.802339i) q^{66} +(-1.22023 + 1.22023i) q^{67} +(1.00933 - 0.582739i) q^{68} +(-2.80036 - 4.85037i) q^{69} +(1.06567 + 0.441039i) q^{70} +(-7.98595 - 2.13983i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(0.797676 + 0.213737i) q^{73} +(2.46126 - 4.26303i) q^{74} +(-2.40499 - 4.16556i) q^{75} +(1.67475 + 6.25025i) q^{76} +(1.62589 + 3.92191i) q^{77} +(3.60305 - 0.134376i) q^{78} +(4.79745 - 8.30943i) q^{79} +(0.308240 + 0.308240i) q^{80} +1.00000 q^{81} +1.85035 q^{82} +(-7.03301 - 7.03301i) q^{83} +(-2.09853 + 1.61126i) q^{84} +(0.131493 - 0.490740i) q^{85} +(-0.281043 + 0.0753052i) q^{86} +(-3.33883 - 1.92767i) q^{87} +1.60468i q^{88} +(6.66910 + 1.78698i) q^{89} -0.435917 q^{90} +(0.888935 - 9.49788i) q^{91} -5.60073 q^{92} +(8.51682 + 2.28207i) q^{93} +4.61542i q^{94} +(2.44280 + 1.41035i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(0.433491 - 1.61781i) q^{97} +(3.50364 + 6.06007i) q^{98} +(-1.13468 - 1.13468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more