LMFDB - Embedded newform 546.2.bz.a.73.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.10
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.a.187.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.96696 + 0.794994i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.29138 + 1.32272i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.96696 + 0.794994i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.29138 + 1.32272i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.53581 - 2.66010i) q^{10} +(-1.52783 - 5.70193i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.68342 - 2.40817i) q^{13} +(0.684600 + 2.55565i) q^{14} +(-2.17196 - 2.17196i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.42101 - 4.19331i) q^{17} +(0.965926 - 0.258819i) q^{18} +(2.47512 + 0.663207i) q^{19} +(-2.17196 - 2.17196i) q^{20} +(2.64575 + 0.000176542i) q^{21} -5.90308 q^{22} +(1.88034 - 1.08561i) q^{23} +(0.965926 - 0.258819i) q^{24} +(3.84069 + 2.21742i) q^{25} +(-1.63159 - 3.21526i) q^{26} -1.00000i q^{27} +(2.64575 + 0.000176542i) q^{28} +6.52905 q^{29} +(-2.66010 + 1.53581i) q^{30} +(-2.13374 - 7.96323i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.52783 + 5.70193i) q^{33} +(-3.42382 - 3.42382i) q^{34} +(-7.84997 + 2.10283i) q^{35} -1.00000i q^{36} +(-6.74944 - 1.80851i) q^{37} +(1.28122 - 2.21913i) q^{38} +(-3.52799 + 0.743825i) q^{39} +(-2.66010 + 1.53581i) q^{40} +(-0.208825 + 0.208825i) q^{41} +(0.684941 - 2.55555i) q^{42} +4.79294i q^{43} +(-1.52783 + 5.70193i) q^{44} +(0.794994 + 2.96696i) q^{45} +(-0.561954 - 2.09724i) q^{46} +(-2.11585 + 7.89646i) q^{47} -1.00000i q^{48} +(3.50081 - 6.06171i) q^{49} +(3.13591 - 3.13591i) q^{50} +(-4.19331 + 2.42101i) q^{51} +(-3.52799 + 0.743825i) q^{52} +(-3.36961 + 5.83633i) q^{53} +(-0.965926 - 0.258819i) q^{54} -18.1320i q^{55} +(0.684941 - 2.55555i) q^{56} +(-1.81191 - 1.81191i) q^{57} +(1.68984 - 6.30658i) q^{58} +(-5.22111 + 1.39899i) q^{59} +(0.794994 + 2.96696i) q^{60} +(-9.00344 + 5.19814i) q^{61} -8.24414 q^{62} +(-2.29120 - 1.32303i) q^{63} -1.00000i q^{64} +(9.87606 - 5.01163i) q^{65} +(5.11221 + 2.95154i) q^{66} +(13.0381 - 3.49354i) q^{67} +(-4.19331 + 2.42101i) q^{68} -2.17122 q^{69} +(-0.000542271 + 8.12674i) q^{70} +(7.97993 + 7.97993i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(15.5205 - 4.15870i) q^{73} +(-3.49377 + 6.05138i) q^{74} +(-2.21742 - 3.84069i) q^{75} +(-1.81191 - 1.81191i) q^{76} +(11.0429 + 11.0444i) q^{77} +(-0.194632 + 3.60029i) q^{78} +(-3.82489 - 6.62490i) q^{79} +(0.794994 + 2.96696i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.147662 + 0.255758i) q^{82} +(-5.84641 + 5.84641i) q^{83} +(-2.29120 - 1.32303i) q^{84} +(10.5167 - 10.5167i) q^{85} +(4.62962 + 1.24050i) q^{86} +(-5.65433 - 3.26453i) q^{87} +(5.11221 + 2.95154i) q^{88} +(0.865860 - 3.23143i) q^{89} +3.07162 q^{90} +(-2.96338 + 9.06743i) q^{91} -2.17122 q^{92} +(-2.13374 + 7.96323i) q^{93} +(7.07977 + 4.08751i) q^{94} +(6.81633 + 3.93541i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(-5.75747 + 5.75747i) q^{97} +(-4.94909 - 4.95041i) q^{98} +(4.17411 - 4.17411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 + 20 * q^9	$ 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.96696	+	0.794994i	1.32686	+	0.355532i	0.851545	−	0.524282i	$-0.175666\pi$
$5$	2.96696	+	0.794994i	1.32686	+	0.355532i	0.475318	+	0.879814i	$0.342333\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−2.29138	+	1.32272i	−0.866059	+	0.499942i
$7$	−2.29138	+	1.32272i	−0.866059	+	0.499942i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.53581	−	2.66010i	0.485666	−	0.841198i
$11$	−1.52783	−	5.70193i	−0.460658	−	1.71920i	−0.670899	−	0.741548i	$-0.734092\pi$
$11$	−1.52783	−	5.70193i	−0.460658	−	1.71920i	0.210242	−	0.977649i	$-0.432575\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	2.68342	−	2.40817i	0.744246	−	0.667905i
$13$	2.68342	−	2.40817i	0.744246	−	0.667905i
$14$	0.684600	+	2.55565i	0.182967	+	0.683025i
$15$	−2.17196	−	2.17196i	−0.560798	−	0.560798i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.42101	−	4.19331i	0.587181	−	1.01703i	−0.407419	−	0.913241i	$-0.633571\pi$
$17$	2.42101	−	4.19331i	0.587181	−	1.01703i	0.994600	−	0.103785i	$-0.0330955\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	2.47512	+	0.663207i	0.567832	+	0.152150i	0.531302	−	0.847182i	$-0.321703\pi$
$19$	2.47512	+	0.663207i	0.567832	+	0.152150i	0.0365298	+	0.999333i	$0.488370\pi$
$20$	−2.17196	−	2.17196i	−0.485666	−	0.485666i
$21$	2.64575		0.000176542i	0.577350		3.85247e-5i
$22$	−5.90308			−1.25854
$23$	1.88034	−	1.08561i	0.392077	−	0.226366i	−0.290983	−	0.956728i	$-0.593982\pi$
$23$	1.88034	−	1.08561i	0.392077	−	0.226366i	0.683060	+	0.730363i	$0.260649\pi$
$24$	0.965926	−	0.258819i	0.197169	−	0.0528312i
$25$	3.84069	+	2.21742i	0.768138	+	0.443484i
$26$	−1.63159	−	3.21526i	−0.319981	−	0.630565i
$27$		−	1.00000i		−	0.192450i
$28$	2.64575		0.000176542i	0.500000		3.33634e-5i
$29$	6.52905			1.21241			0.606207	−	0.795307i	$-0.292690\pi$
$29$	6.52905			1.21241			0.606207	+	0.795307i	$0.292690\pi$
$30$	−2.66010	+	1.53581i	−0.485666	+	0.280399i
$31$	−2.13374	−	7.96323i	−0.383231	−	1.43024i	−0.840936	−	0.541134i	$-0.817995\pi$
$31$	−2.13374	−	7.96323i	−0.383231	−	1.43024i	0.457705	−	0.889104i	$-0.348671\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−1.52783	+	5.70193i	−0.265961	+	0.992579i
$34$	−3.42382	−	3.42382i	−0.587181	−	0.587181i
$35$	−7.84997	+	2.10283i	−1.32689	+	0.355443i
$36$		−	1.00000i		−	0.166667i
$37$	−6.74944	−	1.80851i	−1.10960	−	0.297317i	−0.342933	−	0.939360i	$-0.611420\pi$
$37$	−6.74944	−	1.80851i	−1.10960	−	0.297317i	−0.766668	+	0.642043i	$0.778087\pi$
$38$	1.28122	−	2.21913i	0.207841	−	0.359991i
$39$	−3.52799	+	0.743825i	−0.564931	+	0.119107i
$40$	−2.66010	+	1.53581i	−0.420599	+	0.242833i
$41$	−0.208825	+	0.208825i	−0.0326131	+	0.0326131i	−0.723225	−	0.690612i	$-0.757341\pi$
$41$	−0.208825	+	0.208825i	−0.0326131	+	0.0326131i	0.690612	+	0.723225i	$0.257341\pi$
$42$	0.684941	−	2.55555i	0.105689	−	0.394331i
$43$			4.79294i			0.730916i	0.930828	+	0.365458i	$0.119088\pi$
$43$			4.79294i			0.730916i	−0.930828	+	0.365458i	$0.880912\pi$
$44$	−1.52783	+	5.70193i	−0.230329	+	0.859599i
$45$	0.794994	+	2.96696i	0.118511	+	0.442288i
$46$	−0.561954	−	2.09724i	−0.0828556	−	0.309221i
$47$	−2.11585	+	7.89646i	−0.308628	+	1.15182i	0.621149	+	0.783693i	$0.286666\pi$
$47$	−2.11585	+	7.89646i	−0.308628	+	1.15182i	−0.929777	+	0.368124i	$0.880000\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.50081	−	6.06171i	0.500116	−	0.865959i
$50$	3.13591	−	3.13591i	0.443484	−	0.443484i
$51$	−4.19331	+	2.42101i	−0.587181	+	0.339009i
$52$	−3.52799	+	0.743825i	−0.489244	+	0.103150i
$53$	−3.36961	+	5.83633i	−0.462851	+	0.801682i	−0.999102	−	0.0423768i	$-0.986507\pi$
$53$	−3.36961	+	5.83633i	−0.462851	+	0.801682i	0.536250	+	0.844059i	$0.319840\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$		−	18.1320i		−	2.44492i
$56$	0.684941	−	2.55555i	0.0915291	−	0.341500i
$57$	−1.81191	−	1.81191i	−0.239994	−	0.239994i
$58$	1.68984	−	6.30658i	0.221887	−	0.828095i
$59$	−5.22111	+	1.39899i	−0.679730	+	0.182133i	−0.582134	−	0.813093i	$-0.697782\pi$
$59$	−5.22111	+	1.39899i	−0.679730	+	0.182133i	−0.0975963	+	0.995226i	$0.531115\pi$
$60$	0.794994	+	2.96696i	0.102633	+	0.383032i
$61$	−9.00344	+	5.19814i	−1.15277	+	0.665553i	−0.949561	−	0.313582i	$-0.898471\pi$
$61$	−9.00344	+	5.19814i	−1.15277	+	0.665553i	−0.203211	+	0.979135i	$0.565138\pi$
$62$	−8.24414			−1.04701
$63$	−2.29120	−	1.32303i	−0.288664	−	0.166686i
$64$		−	1.00000i		−	0.125000i
$65$	9.87606	−	5.01163i	1.22497	−	0.621616i
$66$	5.11221	+	2.95154i	0.629270	+	0.363309i
$67$	13.0381	−	3.49354i	1.59285	−	0.426804i	0.649979	−	0.759952i	$-0.274778\pi$
$67$	13.0381	−	3.49354i	1.59285	−	0.426804i	0.942874	+	0.333149i	$0.108111\pi$
$68$	−4.19331	+	2.42101i	−0.508513	+	0.293590i
$69$	−2.17122			−0.261385
$70$	−0.000542271		8.12674i	−6.48137e−5		0.971331i
$71$	7.97993	+	7.97993i	0.947044	+	0.947044i	0.998667	−	0.0516228i	$-0.0164394\pi$
$71$	7.97993	+	7.97993i	0.947044	+	0.947044i	−0.0516228	+	0.998667i	$0.516439\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	15.5205	−	4.15870i	1.81653	−	0.486739i	0.820183	−	0.572101i	$-0.193872\pi$
$73$	15.5205	−	4.15870i	1.81653	−	0.486739i	0.996350	+	0.0853627i	$0.0272049\pi$
$74$	−3.49377	+	6.05138i	−0.406142	+	0.703459i
$75$	−2.21742	−	3.84069i	−0.256046	−	0.443484i
$76$	−1.81191	−	1.81191i	−0.207841	−	0.207841i
$77$	11.0429	+	11.0444i	1.25846	+	1.25862i
$78$	−0.194632	+	3.60029i	−0.0220377	+	0.407653i
$79$	−3.82489	−	6.62490i	−0.430333	−	0.745359i	0.566569	−	0.824015i	$-0.308271\pi$
$79$	−3.82489	−	6.62490i	−0.430333	−	0.745359i	−0.996902	+	0.0786554i	$0.974937\pi$
$80$	0.794994	+	2.96696i	0.0888830	+	0.331716i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.147662	+	0.255758i	0.0163065	+	0.0282437i
$83$	−5.84641	+	5.84641i	−0.641726	+	0.641726i	−0.950980	−	0.309253i	$-0.899921\pi$
$83$	−5.84641	+	5.84641i	−0.641726	+	0.641726i	0.309253	+	0.950980i	$0.399921\pi$
$84$	−2.29120	−	1.32303i	−0.249990	−	0.144354i
$85$	10.5167	−	10.5167i	1.14069	−	1.14069i
$86$	4.62962	+	1.24050i	0.499225	+	0.133767i
$87$	−5.65433	−	3.26453i	−0.606207	−	0.349994i
$88$	5.11221	+	2.95154i	0.544964	+	0.314635i
$89$	0.865860	−	3.23143i	0.0917809	−	0.342531i	−0.904731	−	0.425984i	$-0.859928\pi$
$89$	0.865860	−	3.23143i	0.0917809	−	0.342531i	0.996512	+	0.0834526i	$0.0265947\pi$
$90$	3.07162			0.323777
$91$	−2.96338	+	9.06743i	−0.310647	+	0.950525i
$92$	−2.17122			−0.226366
$93$	−2.13374	+	7.96323i	−0.221259	+	0.825748i
$94$	7.07977	+	4.08751i	0.730222	+	0.421594i
$95$	6.81633	+	3.93541i	0.699341	+	0.403765i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	−5.75747	+	5.75747i	−0.584583	+	0.584583i	−0.936159	−	0.351576i	$-0.885646\pi$
$97$	−5.75747	+	5.75747i	−0.584583	+	0.584583i	0.351576	+	0.936159i	$0.385646\pi$
$98$	−4.94909	−	4.95041i	−0.499933	−	0.500067i
$99$	4.17411	−	4.17411i	0.419513	−	0.419513i
$100$	−2.21742	−	3.84069i	−0.221742	−	0.384069i
$101$	−5.76814	+	9.99071i	−0.573951	+	0.994113i	0.422203	+	0.906501i	$0.361257\pi$
$101$	−5.76814	+	9.99071i	−0.573951	+	0.994113i	−0.996155	+	0.0876118i	$0.972076\pi$
$102$	1.25321	+	4.67703i	0.124086	+	0.463095i
$103$	−2.88520	−	4.99732i	−0.284287	−	0.492400i	0.688149	−	0.725570i	$-0.258424\pi$
$103$	−2.88520	−	4.99732i	−0.284287	−	0.492400i	−0.972436	+	0.233170i	$0.925090\pi$
$104$	−0.194632	+	3.60029i	−0.0190852	+	0.353038i
$105$	7.84969	+	2.10388i	0.766051	+	0.205318i
$106$	4.76535	+	4.76535i	0.462851	+	0.462851i
$107$	8.29845	+	14.3733i	0.802242	+	1.38952i	0.918137	+	0.396262i	$0.129693\pi$
$107$	8.29845	+	14.3733i	0.802242	+	1.38952i	−0.115896	+	0.993261i	$0.536974\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−8.22262	+	2.20324i	−0.787584	+	0.211032i	−0.630126	−	0.776493i	$-0.716997\pi$
$109$	−8.22262	+	2.20324i	−0.787584	+	0.211032i	−0.157458	+	0.987526i	$0.550330\pi$
$110$	−17.5142	−	4.69291i	−1.66991	−	0.447451i
$111$	4.94093	+	4.94093i	0.468973	+	0.468973i
$112$	−2.29120	−	1.32303i	−0.216498	−	0.125014i
$113$	12.1545			1.14340			0.571700	−	0.820462i	$-0.306284\pi$
$113$	12.1545			1.14340			0.571700	+	0.820462i	$0.306284\pi$
$114$	−2.21913	+	1.28122i	−0.207841	+	0.119997i
$115$	6.44193	−	1.72611i	0.600713	−	0.160961i
$116$	−5.65433	−	3.26453i	−0.524991	−	0.303104i
$117$	3.42724	+	1.11982i	0.316849	+	0.103528i
$118$			5.40529i			0.497597i
$119$	−0.000854820		12.8108i	−7.83612e−5		1.17436i
$120$	3.07162			0.280399
$121$	−20.6515	+	11.9232i	−1.87741	+	1.08392i
$122$	2.69075	+	10.0420i	0.243609	+	0.909163i
$123$	0.285261	−	0.0764354i	0.0257211	−	0.00689195i
$124$	−2.13374	+	7.96323i	−0.191616	+	0.715119i
$125$	−1.22750	−	1.22750i	−0.109791	−	0.109791i
$126$	−1.87095	+	1.87070i	−0.166678	+	0.166656i
$127$			12.3327i			1.09435i	0.837017	+	0.547176i	$0.184297\pi$
$127$			12.3327i			1.09435i	−0.837017	+	0.547176i	$0.815703\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	2.39647	−	4.15080i	0.210997	−	0.365458i
$130$	−2.28475	−	10.8366i	−0.200386	−	0.950437i
$131$	14.4195	−	8.32511i	1.25984	−	0.727368i	0.286796	−	0.957992i	$-0.407410\pi$
$131$	14.4195	−	8.32511i	1.25984	−	0.727368i	0.973043	+	0.230624i	$0.0740766\pi$
$132$	4.17411	−	4.17411i	0.363309	−	0.363309i
$133$	−6.54867	+	1.75424i	−0.567842	+	0.152112i
$134$		−	13.4980i		−	1.16605i
$135$	0.794994	−	2.96696i	0.0684222	−	0.255355i
$136$	1.25321	+	4.67703i	0.107461	+	0.401052i
$137$	1.40781	+	5.25404i	0.120278	+	0.448883i	0.999627	−	0.0272939i	$-0.00868900\pi$
$137$	1.40781	+	5.25404i	0.120278	+	0.448883i	−0.879350	+	0.476176i	$0.842022\pi$
$138$	−0.561954	+	2.09724i	−0.0478367	+	0.178529i
$139$		−	13.3501i		−	1.13234i	−0.824289	−	0.566169i	$-0.808425\pi$
$139$		−	13.3501i		−	1.13234i	0.824289	−	0.566169i	$-0.191575\pi$
$140$	7.84969	+	2.10388i	0.663420	+	0.177810i
$141$	5.78061	−	5.78061i	0.486815	−	0.486815i
$142$	9.77338	−	5.64267i	0.820164	−	0.473522i
$143$	−17.8310	−	11.6214i	−1.49110	−	0.971831i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	19.3714	+	5.19055i	1.60871	+	0.431052i
$146$		−	16.0680i		−	1.32979i
$147$	−6.06264	+	3.49919i	−0.500039	+	0.288608i
$148$	4.94093	+	4.94093i	0.406142	+	0.406142i
$149$	0.193630	−	0.722637i	0.0158628	−	0.0592007i	−0.957541	−	0.288298i	$-0.906911\pi$
$149$	0.193630	−	0.722637i	0.0158628	−	0.0592007i	0.973404	+	0.229097i	$0.0735773\pi$
$150$	−4.28373	+	1.14782i	−0.349765	+	0.0937193i
$151$	2.27999	+	8.50906i	0.185543	+	0.692457i	0.994514	+	0.104608i	$0.0333586\pi$
$151$	2.27999	+	8.50906i	0.185543	+	0.692457i	−0.808970	+	0.587850i	$0.799975\pi$
$152$	−2.21913	+	1.28122i	−0.179995	+	0.103920i
$153$	4.84201			0.391454
$154$	13.5262	−	7.80813i	1.08997	−	0.629197i
$155$		−	25.3229i		−	2.03398i
$156$	3.42724	+	1.11982i	0.274399	+	0.0896577i
$157$	−6.98023	−	4.03003i	−0.557083	−	0.321632i	0.194891	−	0.980825i	$-0.437565\pi$
$157$	−6.98023	−	4.03003i	−0.557083	−	0.321632i	−0.751974	+	0.659193i	$0.770898\pi$
$158$	−7.38911	+	1.97991i	−0.587846	+	0.157513i
$159$	5.83633	−	3.36961i	0.462851	−	0.267227i
$160$	3.07162			0.242833
$161$	−2.87259	+	4.97471i	−0.226392	+	0.392062i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	7.92842	+	2.12441i	0.621002	+	0.166397i	0.555583	−	0.831461i	$-0.312495\pi$
$163$	7.92842	+	2.12441i	0.621002	+	0.166397i	0.0654186	+	0.997858i	$0.479162\pi$
$164$	0.285261	−	0.0764354i	0.0222751	−	0.00596860i
$165$	−9.06600	+	15.7028i	−0.705787	+	1.22246i
$166$	4.13403	+	7.16036i	0.320863	+	0.555751i
$167$	−9.83724	−	9.83724i	−0.761229	−	0.761229i	0.215316	−	0.976545i	$-0.430922\pi$
$167$	−9.83724	−	9.83724i	−0.761229	−	0.761229i	−0.976545	+	0.215316i	$0.930922\pi$
$168$	−1.87095	+	1.87070i	−0.144347	+	0.144328i
$169$	1.40146	−	12.9242i	0.107805	−	0.994172i
$170$	−7.43641	−	12.8802i	−0.570347	−	0.987870i
$171$	0.663207	+	2.47512i	0.0507167	+	0.189277i
$172$	2.39647	−	4.15080i	0.182729	−	0.316496i
$173$	−2.07735	−	3.59807i	−0.157938	−	0.273556i	0.776187	−	0.630503i	$-0.217151\pi$
$173$	−2.07735	−	3.59807i	−0.157938	−	0.273556i	−0.934125	+	0.356947i	$0.883818\pi$
$174$	−4.61674	+	4.61674i	−0.349994	+	0.349994i
$175$	−11.7335		0.000782937i	−0.886969		5.91845e-5i
$176$	4.17411	−	4.17411i	0.314635	−	0.314635i
$177$	5.22111	+	1.39899i	0.392442	+	0.105155i
$178$	−2.89722	−	1.67271i	−0.217156	−	0.125375i
$179$	8.74701	+	5.05009i	0.653782	+	0.377461i	0.789904	−	0.613231i	$-0.210130\pi$
$179$	8.74701	+	5.05009i	0.653782	+	0.377461i	−0.136122	+	0.990692i	$0.543464\pi$
$180$	0.794994	−	2.96696i	0.0592553	−	0.221144i
$181$	0.310365			0.0230693			0.0115346	−	0.999933i	$-0.496328\pi$
$181$	0.310365			0.0230693			0.0115346	+	0.999933i	$0.496328\pi$
$182$	7.99149	+	5.20923i	0.592369	+	0.386134i
$183$	10.3963			0.768515
$184$	−0.561954	+	2.09724i	−0.0414278	+	0.154611i
$185$	−18.5875	−	10.7315i	−1.36658	−	0.788997i
$186$	7.13963	+	4.12207i	0.523503	+	0.302245i
$187$	−27.6088	−	7.39777i	−2.01896	−	0.540978i
$188$	5.78061	−	5.78061i	0.421594	−	0.421594i
$189$	1.32272	+	2.29138i	0.0962139	+	0.166673i
$190$	5.56551	−	5.56551i	0.403765	−	0.403765i
$191$	6.20525	+	10.7478i	0.448996	+	0.777684i	0.998321	−	0.0579248i	$-0.0184484\pi$
$191$	6.20525	+	10.7478i	0.448996	+	0.777684i	−0.549325	+	0.835609i	$0.685115\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.92516	−	7.18478i	−0.138576	−	0.517172i	−0.999958	−	0.00921377i	$-0.997067\pi$
$193$	−1.92516	−	7.18478i	−0.138576	−	0.517172i	0.861382	−	0.507958i	$-0.169600\pi$
$194$	4.07115	+	7.05144i	0.292291	+	0.506264i
$195$	−11.0587	−	0.597834i	−0.791932	−	0.0428118i
$196$	−6.06264	+	3.49919i	−0.433046	+	0.249942i
$197$	1.90823	+	1.90823i	0.135956	+	0.135956i	0.771810	−	0.635854i	$-0.219352\pi$
$197$	1.90823	+	1.90823i	0.135956	+	0.135956i	−0.635854	+	0.771810i	$0.719352\pi$
$198$	−2.95154	−	5.11221i	−0.209757	−	0.363309i
$199$	−6.33316	+	10.9694i	−0.448946	+	0.777597i	−0.998318	−	0.0579808i	$-0.981534\pi$
$199$	−6.33316	+	10.9694i	−0.448946	+	0.777597i	0.549372	+	0.835578i	$0.314867\pi$
$200$	−4.28373	+	1.14782i	−0.302906	+	0.0811633i
$201$	−13.0381	−	3.49354i	−0.919634	−	0.246415i
$202$	8.15738	+	8.15738i	0.573951	+	0.573951i
$203$	−14.9605	+	8.63613i	−1.05002	+	0.606137i
$204$	4.84201			0.339009
$205$	−0.785591	+	0.453561i	−0.0548680	+	0.0316781i
$206$	−5.57378	+	1.49349i	−0.388344	+	0.104056i
$207$	1.88034	+	1.08561i	0.130692	+	0.0754553i
$208$	3.42724	+	1.11982i	0.237637	+	0.0776458i
$209$		−	15.1262i		−	1.04630i
$210$	4.06384	−	7.03769i	0.280432	−	0.485647i
$211$	−2.46343			−0.169589			−0.0847947	−	0.996398i	$-0.527023\pi$
$211$	−2.46343			−0.169589			−0.0847947	+	0.996398i	$0.527023\pi$
$212$	5.83633	−	3.36961i	0.400841	−	0.231426i
$213$	−2.92086	−	10.9008i	−0.200134	−	0.746910i
$214$	16.0314	−	4.29560i	1.09588	−	0.293641i
$215$	−3.81035	+	14.2204i	−0.259864	+	0.969825i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	15.4223	+	15.4244i	1.04694	+	1.04708i
$218$			8.51268i			0.576552i
$219$	−15.5205	−	4.15870i	−1.04878	−	0.281019i
$220$	−9.06600	+	15.7028i	−0.611230	+	1.05868i
$221$	−3.60161	−	17.0826i	−0.242271	−	1.14910i
$222$	6.05138	−	3.49377i	0.406142	−	0.234486i
$223$	−0.344118	+	0.344118i	−0.0230438	+	0.0230438i	−0.718535	−	0.695491i	$-0.755187\pi$
$223$	−0.344118	+	0.344118i	−0.0230438	+	0.0230438i	0.695491	+	0.718535i	$0.255187\pi$
$224$	−1.87095	+	1.87070i	−0.125008	+	0.124992i
$225$			4.43484i			0.295656i
$226$	3.14582	−	11.7404i	0.209257	−	0.780957i
$227$	3.56655	+	13.3105i	0.236720	+	0.883452i	0.977366	+	0.211556i	$0.0678531\pi$
$227$	3.56655	+	13.3105i	0.236720	+	0.883452i	−0.740646	+	0.671896i	$0.765480\pi$
$228$	0.663207	+	2.47512i	0.0439219	+	0.163919i
$229$	0.175058	−	0.653325i	0.0115681	−	0.0431729i	−0.959901	−	0.280341i	$-0.909553\pi$
$229$	0.175058	−	0.653325i	0.0115681	−	0.0431729i	0.971469	+	0.237168i	$0.0762192\pi$
$230$		−	6.66917i		−	0.439752i
$231$	−4.04125	−	15.0862i	−0.265895	−	0.992597i
$232$	−4.61674	+	4.61674i	−0.303104	+	0.303104i
$233$	−8.54221	+	4.93184i	−0.559618	+	0.323096i	−0.752992	−	0.658029i	$-0.771390\pi$
$233$	−8.54221	+	4.93184i	−0.559618	+	0.323096i	0.193374	+	0.981125i	$0.438057\pi$
$234$	1.96870	−	3.02063i	0.128698	−	0.197465i
$235$	−12.5553	+	21.7464i	−0.819015	+	1.41858i
$236$	5.22111	+	1.39899i	0.339865	+	0.0910666i
$237$			7.64977i			0.496906i
$238$	12.3740	+	3.31650i	0.802089	+	0.214977i
$239$	−10.5301	−	10.5301i	−0.681133	−	0.681133i	0.279123	−	0.960255i	$-0.409956\pi$
$239$	−10.5301	−	10.5301i	−0.681133	−	0.681133i	−0.960255	+	0.279123i	$0.909956\pi$
$240$	0.794994	−	2.96696i	0.0513166	−	0.191516i
$241$	6.79487	−	1.82068i	0.437696	−	0.117280i	−0.0332405	−	0.999447i	$-0.510583\pi$
$241$	6.79487	−	1.82068i	0.437696	−	0.117280i	0.470937	+	0.882167i	$0.343916\pi$
$242$	6.17188	+	23.0338i	0.396743	+	1.48067i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	10.3963			0.665553
$245$	15.2058	−	15.2017i	0.971461	−	0.971202i
$246$		−	0.295324i		−	0.0188292i
$247$	8.23890	−	4.18085i	0.524229	−	0.266021i
$248$	7.13963	+	4.12207i	0.453367	+	0.261752i
$249$	7.98634	−	2.13993i	0.506114	−	0.135613i
$250$	−1.50337	+	0.867971i	−0.0950814	+	0.0548953i
$251$	−1.52426			−0.0962101			−0.0481051	−	0.998842i	$-0.515318\pi$
$251$	−1.52426			−0.0962101			−0.0481051	+	0.998842i	$0.515318\pi$
$252$	1.32272	+	2.29138i	0.0833237	+	0.144343i
$253$	−9.06292	−	9.06292i	−0.569781	−	0.569781i
$254$	11.9125	+	3.19194i	0.747457	+	0.200280i
$255$	−14.3660	+	3.84937i	−0.899637	+	0.241057i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.1470	+	21.0392i	0.757709	+	1.31239i	0.944016	+	0.329899i	$0.107015\pi$
$257$	12.1470	+	21.0392i	0.757709	+	1.31239i	−0.186307	+	0.982491i	$0.559652\pi$
$258$	−3.38912	−	3.38912i	−0.210997	−	0.210997i
$259$	17.8577	−	4.78367i	1.10962	−	0.297243i
$260$	−11.0587	−	0.597834i	−0.685834	−	0.0370761i
$261$	3.26453	+	5.65433i	0.202069	+	0.349994i
$262$	−4.30939	−	16.0829i	−0.266235	−	0.993603i
$263$	1.46899	−	2.54437i	0.0905818	−	0.156892i	−0.817174	−	0.576391i	$-0.804461\pi$
$263$	1.46899	−	2.54437i	0.0905818	−	0.156892i	0.907756	+	0.419498i	$0.137794\pi$
$264$	−2.95154	−	5.11221i	−0.181655	−	0.314635i
$265$	−14.6373	+	14.6373i	−0.899164	+	0.899164i
$266$	−0.000452378		6.77956i	−2.77371e−5		0.415682i
$267$	−2.36557	+	2.36557i	−0.144771	+	0.144771i
$268$	−13.0381	−	3.49354i	−0.796427	−	0.213402i
$269$	−5.80466	−	3.35132i	−0.353916	−	0.204334i	0.312493	−	0.949920i	$-0.398836\pi$
$269$	−5.80466	−	3.35132i	−0.353916	−	0.204334i	−0.666409	+	0.745587i	$0.732169\pi$
$270$	−2.66010	−	1.53581i	−0.161889	−	0.0934664i
$271$	0.485997	−	1.81377i	0.0295222	−	0.110178i	−0.949593	−	0.313487i	$-0.898503\pi$
$271$	0.485997	−	1.81377i	0.0295222	−	0.110178i	0.979115	+	0.203309i	$0.0651695\pi$
$272$	4.84201			0.293590
$273$	7.10008	−	6.37094i	0.429716	−	0.385587i
$274$	5.43938			0.328605
$275$	6.77568	−	25.2872i	0.408589	−	1.52487i
$276$	1.88034	+	1.08561i	0.113183	+	0.0653462i
$277$	14.2965	+	8.25410i	0.858995	+	0.495941i	0.863676	−	0.504048i	$-0.168157\pi$
$277$	14.2965	+	8.25410i	0.858995	+	0.495941i	−0.00468078	+	0.999989i	$0.501490\pi$
$278$	−12.8952	−	3.45525i	−0.773401	−	0.207232i
$279$	5.82949	−	5.82949i	0.349002	−	0.349002i
$280$	4.06384	−	7.03769i	0.242861	−	0.420583i
$281$	−21.8287	+	21.8287i	−1.30219	+	1.30219i	−0.375281	+	0.926911i	$0.622454\pi$
$281$	−21.8287	+	21.8287i	−1.30219	+	1.30219i	−0.926911	+	0.375281i	$0.877546\pi$
$282$	−4.08751	−	7.07977i	−0.243407	−	0.421594i
$283$	−6.88809	+	11.9305i	−0.409455	+	0.709196i	−0.994829	−	0.101567i	$-0.967614\pi$
$283$	−6.88809	+	11.9305i	−0.409455	+	0.709196i	0.585374	+	0.810763i	$0.300948\pi$
$284$	−2.92086	−	10.9008i	−0.173321	−	0.646843i
$285$	−3.93541	−	6.81633i	−0.233114	−	0.403765i
$286$	−15.8404	+	14.2156i	−0.936664	+	0.840586i
$287$	0.202279	−	0.754716i	0.0119402	−	0.0445495i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−3.22255	−	5.58163i	−0.189562	−	0.328331i
$290$	10.0274	−	17.3679i	0.588828	−	1.01988i
$291$	7.86486	−	2.10738i	0.461046	−	0.123537i
$292$	−15.5205	−	4.15870i	−0.908266	−	0.243369i
$293$	−6.85005	−	6.85005i	−0.400184	−	0.400184i	0.478114	−	0.878298i	$-0.341321\pi$
$293$	−6.85005	−	6.85005i	−0.400184	−	0.400184i	−0.878298	+	0.478114i	$0.841321\pi$
$294$	1.81083	+	6.76172i	0.105610	+	0.394352i
$295$	−16.6030			−0.966663
$296$	6.05138	−	3.49377i	0.351730	−	0.203071i
$297$	−5.70193	+	1.52783i	−0.330860	+	0.0886536i
$298$	−0.647899	−	0.374064i	−0.0375318	−	0.0216690i
$299$	2.43139	−	7.44131i	0.140611	−	0.430342i
$300$			4.43484i			0.256046i
$301$	−6.33973	−	10.9824i	−0.365416	−	0.633016i
$302$	8.80922			0.506914
$303$	9.99071	−	5.76814i	0.573951	−	0.331371i
$304$	0.663207	+	2.47512i	0.0380375	+	0.141958i
$305$	−30.8453	+	8.26497i	−1.76620	+	0.473251i
$306$	1.25321	−	4.67703i	0.0716410	−	0.267368i
$307$	−19.4318	−	19.4318i	−1.10903	−	1.10903i	−0.993278	−	0.115753i	$-0.963072\pi$
$307$	−19.4318	−	19.4318i	−1.10903	−	1.10903i	−0.115753	−	0.993278i	$-0.536928\pi$
$308$	−4.04125	−	15.0862i	−0.230271	−	0.859614i
$309$			5.77040i			0.328267i
$310$	−24.4600	−	6.55404i	−1.38923	−	0.372244i
$311$	3.78351	−	6.55324i	0.214543	−	0.371600i	−0.738588	−	0.674157i	$-0.764507\pi$
$311$	3.78351	−	6.55324i	0.214543	−	0.371600i	0.953131	+	0.302557i	$0.0978404\pi$
$312$	1.96870	−	3.02063i	0.111456	−	0.171010i
$313$	22.0207	−	12.7136i	1.24468	−	0.718617i	0.274638	−	0.961548i	$-0.411442\pi$
$313$	22.0207	−	12.7136i	1.24468	−	0.718617i	0.970044	+	0.242930i	$0.0781086\pi$
$314$	−5.69933	+	5.69933i	−0.321632	+	0.321632i
$315$	−5.74609	−	5.74686i	−0.323755	−	0.323799i
$316$			7.64977i			0.430333i
$317$	1.44748	−	5.40208i	0.0812987	−	0.303411i	−0.913289	−	0.407312i	$-0.866466\pi$
$317$	1.44748	−	5.40208i	0.0812987	−	0.303411i	0.994588	+	0.103901i	$0.0331327\pi$
$318$	−1.74424	−	6.50959i	−0.0978120	−	0.365039i
$319$	−9.97527	−	37.2282i	−0.558508	−	2.08438i
$320$	0.794994	−	2.96696i	0.0444415	−	0.165858i
$321$		−	16.5969i		−	0.926349i
$322$	4.06172	+	4.06226i	0.226351	+	0.226381i
$323$	8.77332	−	8.77332i	0.488161	−	0.488161i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	15.6461	−	3.29875i	0.867889	−	0.182982i
$326$	4.10405	−	7.10843i	0.227302	−	0.393699i
$327$	8.22262	+	2.20324i	0.454712	+	0.121840i
$328$		−	0.295324i		−	0.0163065i
$329$	−5.59662	−	20.8924i	−0.308551	−	1.15184i
$330$	12.8213	+	12.8213i	0.705787	+	0.705787i
$331$	2.05126	−	7.65539i	0.112747	−	0.420778i	−0.886361	−	0.462994i	$-0.846775\pi$
$331$	2.05126	−	7.65539i	0.112747	−	0.420778i	0.999109	+	0.0422159i	$0.0134417\pi$
$332$	7.98634	−	2.13993i	0.438307	−	0.117444i
$333$	−1.80851	−	6.74944i	−0.0991056	−	0.369867i
$334$	−12.0481	+	6.95598i	−0.659244	+	0.380614i
$335$	41.4607			2.26524
$336$	1.32272	+	2.29138i	0.0721604	+	0.125005i
$337$			31.5803i			1.72029i	0.510051	+	0.860144i	$0.329626\pi$
$337$			31.5803i			1.72029i	−0.510051	+	0.860144i	$0.670374\pi$
$338$	−12.1211	−	4.69875i	−0.659303	−	0.255578i
$339$	−10.5261	−	6.07726i	−0.571700	−	0.330071i
$340$	−14.3660	+	3.84937i	−0.779108	+	0.208761i
$341$	−42.1458	+	24.3329i	−2.28232	+	1.31770i
$342$	2.56243			0.138561
$343$	−0.00370739	+	18.5203i	−0.000200180	+	1.00000i
$344$	−3.38912	−	3.38912i	−0.182729	−	0.182729i
$345$	−6.44193	−	1.72611i	−0.346822	−	0.0929306i
$346$	−4.01312	+	1.07531i	−0.215747	+	0.0578092i
$347$	−0.408592	+	0.707702i	−0.0219344	+	0.0379914i	−0.876784	−	0.480884i	$-0.840316\pi$
$347$	−0.408592	+	0.707702i	−0.0219344	+	0.0379914i	0.854850	+	0.518875i	$0.173649\pi$
$348$	3.26453	+	5.65433i	0.174997	+	0.303104i
$349$	−11.6786	−	11.6786i	−0.625140	−	0.625140i	0.321701	−	0.946841i	$-0.395745\pi$
$349$	−11.6786	−	11.6786i	−0.625140	−	0.625140i	−0.946841	+	0.321701i	$0.895745\pi$
$350$	−3.03761	+	11.3335i	−0.162367	+	0.605800i
$351$	−2.40817	−	2.68342i	−0.128538	−	0.143230i
$352$	−2.95154	−	5.11221i	−0.157318	−	0.272482i
$353$	0.187291	+	0.698979i	0.00996848	+	0.0372029i	0.970731	−	0.240170i	$-0.0772031\pi$
$353$	0.187291	+	0.698979i	0.00996848	+	0.0372029i	−0.960762	+	0.277372i	$0.910536\pi$
$354$	2.70264	−	4.68112i	0.143644	−	0.248799i
$355$	17.3321	+	30.0201i	0.919893	+	1.59330i
$356$	−2.36557	+	2.36557i	−0.125375	+	0.125375i
$357$	6.40612	−	11.0940i	0.339048	−	0.587158i
$358$	7.14190	−	7.14190i	0.377461	−	0.377461i
$359$	−8.87176	−	2.37718i	−0.468233	−	0.125463i	0.0169851	−	0.999856i	$-0.494593\pi$
$359$	−8.87176	−	2.37718i	−0.468233	−	0.125463i	−0.485218	+	0.874393i	$0.661260\pi$
$360$	−2.66010	−	1.53581i	−0.140200	−	0.0809443i
$361$	−10.7681	−	6.21696i	−0.566742	−	0.327209i
$362$	0.0803284	−	0.299790i	0.00422197	−	0.0157566i
$363$	23.8463			1.25161
$364$	7.10008	−	6.37094i	0.372145	−	0.333928i
$365$	49.3547			2.58334
$366$	2.69075	−	10.0420i	0.140648	−	0.524905i
$367$	23.2287	+	13.4111i	1.21253	+	0.700055i	0.963310	−	0.268392i	$-0.0864923\pi$
$367$	23.2287	+	13.4111i	1.21253	+	0.700055i	0.249221	+	0.968447i	$0.419826\pi$
$368$	1.88034	+	1.08561i	0.0980192	+	0.0565914i
$369$	−0.285261	−	0.0764354i	−0.0148501	−	0.00397907i
$370$	−15.1767	+	15.1767i	−0.788997	+	0.788997i
$371$	0.00118976	−	17.8303i	6.17691e−5	−	0.925703i
$372$	5.82949	−	5.82949i	0.302245	−	0.302245i
$373$	16.4439	+	28.4817i	0.851434	+	1.47473i	0.879915	+	0.475132i	$0.157600\pi$
$373$	16.4439	+	28.4817i	0.851434	+	1.47473i	−0.0284810	+	0.999594i	$0.509067\pi$
$374$	−14.2914	+	24.7534i	−0.738990	+	1.27997i
$375$	0.449295	+	1.67679i	0.0232015	+	0.0865891i
$376$	−4.08751	−	7.07977i	−0.210797	−	0.365111i
$377$	17.5202	−	15.7231i	0.902335	−	0.809778i
$378$	2.55565	−	0.684600i	0.131448	−	0.0352120i
$379$	−15.9720	−	15.9720i	−0.820427	−	0.820427i	0.165742	−	0.986169i	$-0.446998\pi$
$379$	−15.9720	−	15.9720i	−0.820427	−	0.820427i	−0.986169	+	0.165742i	$0.946998\pi$
$380$	−3.93541	−	6.81633i	−0.201882	−	0.349671i
$381$	6.16636	−	10.6805i	0.315912	−	0.547176i
$382$	11.9876	−	3.21207i	0.613340	−	0.164344i
$383$	3.78871	+	1.01518i	0.193594	+	0.0518733i	0.354313	−	0.935127i	$-0.384715\pi$
$383$	3.78871	+	1.01518i	0.193594	+	0.0518733i	−0.160719	+	0.987000i	$0.551381\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	23.9836	+	41.5472i	1.22232	+	2.11744i
$386$	−7.43823			−0.378596
$387$	−4.15080	+	2.39647i	−0.210997	+	0.121819i
$388$	7.86486	−	2.10738i	0.399278	−	0.106986i
$389$	3.83759	+	2.21563i	0.194573	+	0.112337i	0.594122	−	0.804375i	$-0.297500\pi$
$389$	3.83759	+	2.21563i	0.194573	+	0.112337i	−0.399548	+	0.916712i	$0.630833\pi$
$390$	−3.43967	+	10.5272i	−0.174175	+	0.533065i
$391$		−	10.5131i		−	0.531670i
$392$	1.81083	+	6.76172i	0.0914608	+	0.341519i
$393$	−16.6502			−0.839892
$394$	2.33710	−	1.34933i	0.117741	−	0.0679781i
$395$	−6.08152	−	22.6965i	−0.305994	−	1.14199i
$396$	−5.70193	+	1.52783i	−0.286533	+	0.0767763i
$397$	−0.690075	+	2.57540i	−0.0346339	+	0.129255i	−0.981078	−	0.193611i	$-0.937980\pi$
$397$	−0.690075	+	2.57540i	−0.0346339	+	0.129255i	0.946444	+	0.322867i	$0.104647\pi$
$398$	8.95644	+	8.95644i	0.448946	+	0.448946i
$399$	6.54844	+	1.75512i	0.327832	+	0.0878658i
$400$			4.43484i			0.221742i
$401$	13.0686	+	3.50173i	0.652617	+	0.174868i	0.569912	−	0.821706i	$-0.306977\pi$
$401$	13.0686	+	3.50173i	0.652617	+	0.174868i	0.0827052	+	0.996574i	$0.473644\pi$
$402$	−6.74900	+	11.6896i	−0.336609	+	0.583025i
$403$	−24.9025	−	16.2303i	−1.24048	−	0.808487i
$404$	9.99071	−	5.76814i	0.497057	−	0.286976i
$405$	−2.17196	+	2.17196i	−0.107926	+	0.107926i
$406$	4.46979	+	16.6859i	0.221832	+	0.828109i
$407$			41.2480i			2.04459i
$408$	1.25321	−	4.67703i	0.0620429	−	0.231547i
$409$	1.28627	+	4.80044i	0.0636022	+	0.237367i	0.990408	−	0.138175i	$-0.0441235\pi$
$409$	1.28627	+	4.80044i	0.0636022	+	0.237367i	−0.926806	+	0.375541i	$0.877457\pi$
$410$	0.234780	+	0.876213i	0.0115950	+	0.0432731i
$411$	1.40781	−	5.25404i	0.0694424	−	0.259162i
$412$			5.77040i			0.284287i
$413$	10.1130	−	10.1117i	0.497630	−	0.497564i
$414$	1.53529	−	1.53529i	0.0754553	−	0.0754553i
$415$	−21.9939	+	12.6982i	−1.07964	+	0.623329i
$416$	1.96870	−	3.02063i	0.0965236	−	0.148099i
$417$	−6.67503	+	11.5615i	−0.326878	+	0.566169i
$418$	−14.6108	−	3.91496i	−0.714639	−	0.191487i
$419$			0.419506i			0.0204942i	0.999947	+	0.0102471i	$0.00326181\pi$
$419$			0.419506i			0.0204942i	−0.999947	+	0.0102471i	$0.996738\pi$
$420$	−5.74609	−	5.74686i	−0.280380	−	0.280418i
$421$	−4.28704	−	4.28704i	−0.208937	−	0.208937i	0.594878	−	0.803816i	$-0.297200\pi$
$421$	−4.28704	−	4.28704i	−0.208937	−	0.208937i	−0.803816	+	0.594878i	$0.797200\pi$
$422$	−0.637582	+	2.37949i	−0.0310370	+	0.115832i
$423$	−7.89646	+	2.11585i	−0.383939	+	0.102876i
$424$	−1.74424	−	6.50959i	−0.0847077	−	0.316133i
$425$	18.5967	−	10.7368i	0.902071	−	0.520811i
$426$	−11.2853			−0.546776
$427$	13.7546	−	23.8199i	0.665630	−	1.15273i
$428$		−	16.5969i		−	0.802242i
$429$	9.63141	+	18.9799i	0.465009	+	0.916360i
$430$	12.7497	+	7.36104i	0.614845	+	0.354981i
$431$	3.67742	−	0.985361i	0.177135	−	0.0474632i	−0.169161	−	0.985588i	$-0.554106\pi$
$431$	3.67742	−	0.985361i	0.177135	−	0.0474632i	0.346296	+	0.938125i	$0.387439\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	11.7518			0.564755			0.282378	−	0.959303i	$-0.408877\pi$
$433$	11.7518			0.564755			0.282378	+	0.959303i	$0.408877\pi$
$434$	18.8904	−	10.9047i	0.906769	−	0.523443i
$435$	−14.1809	−	14.1809i	−0.679920	−	0.679920i
$436$	8.22262	+	2.20324i	0.393792	+	0.105516i
$437$	5.37404	−	1.43997i	0.257075	−	0.0688831i
$438$	−8.03398	+	13.9153i	−0.383879	+	0.664897i
$439$	−14.9568	−	25.9060i	−0.713850	−	1.23643i	−0.963401	−	0.268064i	$-0.913616\pi$
$439$	−14.9568	−	25.9060i	−0.713850	−	1.23643i	0.249551	−	0.968362i	$-0.419717\pi$
$440$	12.8213	+	12.8213i	0.611230	+	0.611230i
$441$	7.00000		0.000934174i	0.333333		4.44845e-5i
$442$	−17.4327	−	0.942409i	−0.829188	−	0.0448258i
$443$	11.4444	+	19.8222i	0.543738	+	0.941782i	0.998685	+	0.0512637i	$0.0163249\pi$
$443$	11.4444	+	19.8222i	0.543738	+	0.941782i	−0.454947	+	0.890519i	$0.650342\pi$
$444$	−1.80851	−	6.74944i	−0.0858280	−	0.320314i
$445$	5.13794	−	8.89917i	0.243562	−	0.421861i
$446$	0.243328	+	0.421457i	0.0115219	+	0.0199565i
$447$	−0.529007	+	0.529007i	−0.0250212	+	0.0250212i
$448$	1.32272	+	2.29138i	0.0624928	+	0.108257i
$449$	17.0633	−	17.0633i	0.805268	−	0.805268i	−0.178646	−	0.983913i	$-0.557172\pi$
$449$	17.0633	−	17.0633i	0.805268	−	0.805268i	0.983913	+	0.178646i	$0.0571716\pi$
$450$	4.28373	+	1.14782i	0.201937	+	0.0541089i
$451$	1.50976	+	0.871659i	0.0710917	+	0.0410448i
$452$	−10.5261	−	6.07726i	−0.495107	−	0.285850i
$453$	2.27999	−	8.50906i	0.107123	−	0.399790i
$454$	13.7801			0.646732
$455$	−16.0008	+	24.5468i	−0.750128	+	1.15077i
$456$	2.56243			0.119997
$457$	−6.90941	+	25.7863i	−0.323209	+	1.20623i	0.592892	+	0.805282i	$0.297986\pi$
$457$	−6.90941	+	25.7863i	−0.323209	+	1.20623i	−0.916100	+	0.400949i	$0.868680\pi$
$458$	−0.585755	−	0.338186i	−0.0273705	−	0.0158024i
$459$	−4.19331	−	2.42101i	−0.195727	−	0.113003i
$460$	−6.44193	−	1.72611i	−0.300356	−	0.0804803i
$461$	−11.2132	+	11.2132i	−0.522249	+	0.522249i	−0.918250	−	0.396001i	$-0.870398\pi$
$461$	−11.2132	+	11.2132i	−0.522249	+	0.522249i	0.396001	+	0.918250i	$0.370398\pi$
$462$	−15.6181	−	0.00104214i	−0.726618	−	4.84849e-5i
$463$	−20.4265	+	20.4265i	−0.949301	+	0.949301i	−0.998775	−	0.0494742i	$-0.984245\pi$
$463$	−20.4265	+	20.4265i	−0.949301	+	0.949301i	0.0494742	+	0.998775i	$0.484245\pi$
$464$	3.26453	+	5.65433i	0.151552	+	0.262495i
$465$	−12.6614	+	21.9302i	−0.587160	+	1.01699i
$466$	2.55291	+	9.52759i	0.118261	+	0.441357i
$467$	11.6541	+	20.1855i	0.539288	+	0.934075i	0.998943	+	0.0459766i	$0.0146400\pi$
$467$	11.6541	+	20.1855i	0.539288	+	0.934075i	−0.459654	+	0.888098i	$0.652027\pi$
$468$	−2.40817	−	2.68342i	−0.111318	−	0.124041i
$469$	−25.2541	+	25.2508i	−1.16613	+	1.16597i
$470$	17.7558	+	17.7558i	0.819015	+	0.819015i
$471$	4.03003	+	6.98023i	0.185694	+	0.321632i
$472$	2.70264	−	4.68112i	0.124399	−	0.215466i
$473$	27.3290	−	7.32278i	1.25659	−	0.336702i
$474$	7.38911	+	1.97991i	0.339393	+	0.0909401i
$475$	8.03556	+	8.03556i	0.368697	+	0.368697i
$476$	6.40612	−	11.0940i	0.293624	−	0.508494i
$477$	−6.73922			−0.308568
$478$	−12.8966	+	7.44587i	−0.589878	+	0.340566i
$479$	16.3812	−	4.38934i	0.748477	−	0.200554i	0.135635	−	0.990759i	$-0.456693\pi$
$479$	16.3812	−	4.38934i	0.748477	−	0.200554i	0.612843	+	0.790205i	$0.290026\pi$
$480$	−2.66010	−	1.53581i	−0.121416	−	0.0700998i
$481$	−22.4668	+	11.4008i	−1.02440	+	0.519832i
$482$		−	7.03457i		−	0.320416i
$483$	4.97509	−	2.87193i	0.226374	−	0.130677i
$484$	23.8463			1.08392
$485$	−21.6593	+	12.5050i	−0.983499	+	0.567824i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	22.0493	−	5.90808i	0.999148	−	0.267721i	0.278059	−	0.960564i	$-0.410309\pi$
$487$	22.0493	−	5.90808i	0.999148	−	0.267721i	0.721088	+	0.692843i	$0.243642\pi$
$488$	2.69075	−	10.0420i	0.121805	−	0.454581i
$489$	−5.80401	−	5.80401i	−0.262466	−	0.262466i
$490$	−10.7482	−	18.6221i	−0.485553	−	0.841262i
$491$		−	16.7305i		−	0.755037i	−0.926002	−	0.377518i	$-0.876778\pi$
$491$		−	16.7305i		−	0.755037i	0.926002	−	0.377518i	$-0.123222\pi$
$492$	−0.285261	−	0.0764354i	−0.0128606	−	0.00344597i
$493$	15.8069	−	27.3783i	0.711906	−	1.23306i
$494$	−1.90600	−	9.04025i	−0.0857551	−	0.406740i
$495$	15.7028	−	9.06600i	0.705787	−	0.407486i
$496$	5.82949	−	5.82949i	0.261752	−	0.261752i
$497$	−28.8403	−	7.72979i	−1.29366	−	0.346728i
$498$		−	8.26807i		−	0.370501i
$499$	4.00692	−	14.9540i	0.179375	−	0.669435i	−0.816390	−	0.577500i	$-0.804028\pi$
$499$	4.00692	−	14.9540i	0.179375	−	0.669435i	0.995765	−	0.0919347i	$-0.0293051\pi$
$500$	0.449295	+	1.67679i	0.0200931	+	0.0749884i
$501$	3.60068	+	13.4379i	0.160867	+	0.600362i
$502$	−0.394506	+	1.47232i	−0.0176077	+	0.0657127i
$503$			40.0305i			1.78487i	0.451173	+	0.892437i	$0.351006\pi$
$503$			40.0305i			1.78487i	−0.451173	+	0.892437i	$0.648994\pi$
$504$	2.55565	−	0.684600i	0.113837	−	0.0304945i
$505$	−25.0564	+	25.0564i	−1.11499	+	1.11499i
$506$	−11.0998	+	6.40845i	−0.493445	+	0.284890i
$507$	−7.67582	+	10.4920i	−0.340895	+	0.465965i
$508$	6.16636	−	10.6805i	0.273588	−	0.473869i
$509$	35.1260	+	9.41197i	1.55693	+	0.417178i	0.931690	−	0.363254i	$-0.118334\pi$
$509$	35.1260	+	9.41197i	1.55693	+	0.417178i	0.625241	+	0.780432i	$0.285001\pi$
$510$			14.8728i			0.658580i
$511$	−30.0624	+	30.0584i	−1.32988	+	1.32971i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.663207	−	2.47512i	0.0292813	−	0.109279i
$514$	23.4662	−	6.28775i	1.03505	−	0.277341i
$515$	−4.58743	−	17.1205i	−0.202146	−	0.754421i
$516$	−4.15080	+	2.39647i	−0.182729	+	0.105499i
$517$	48.2577			2.12237
$518$	0.00123360	−	18.4873i	5.42011e−5	−	0.812285i
$519$			4.15469i			0.182371i
$520$	−3.43967	+	10.5272i	−0.150840	+	0.461648i
$521$	−2.65237	−	1.53135i	−0.116202	−	0.0670895i	0.440772	−	0.897619i	$-0.354705\pi$
$521$	−2.65237	−	1.53135i	−0.116202	−	0.0670895i	−0.556975	+	0.830529i	$0.688038\pi$
$522$	6.30658	−	1.68984i	0.276032	−	0.0739624i
$523$	24.6781	−	14.2479i	1.07910	−	0.623018i	0.148445	−	0.988921i	$-0.452573\pi$
$523$	24.6781	−	14.2479i	1.07910	−	0.623018i	0.930653	+	0.365903i	$0.119240\pi$
$524$	−16.6502			−0.727368
$525$	10.1611	+	5.86743i	0.443467	+	0.256075i
$526$	−2.07747	−	2.07747i	−0.0905818	−	0.0905818i
$527$	−38.5581	−	10.3316i	−1.67962	−	0.450052i
$528$	−5.70193	+	1.52783i	−0.248145	+	0.0664902i
$529$	−9.14289	+	15.8360i	−0.397517	+	0.688520i
$530$	10.3502	+	17.9270i	0.449582	+	0.778699i
$531$	−3.82212	−	3.82212i	−0.165866	−	0.165866i
$532$	6.54844	+	1.75512i	0.283911	+	0.0760940i
$533$	−0.0574793	+	1.06325i	−0.00248971	+	0.0460546i
$534$	1.67271	+	2.89722i	0.0723853	+	0.125375i
$535$	13.1944	+	49.2423i	0.570445	+	2.12893i
$536$	−6.74900	+	11.6896i	−0.291512	+	0.504914i
$537$	−5.05009	−	8.74701i	−0.217927	−	0.377461i
$538$	−4.73948	+	4.73948i	−0.204334	+	0.204334i
$539$	−39.9121	−	10.7001i	−1.71914	−	0.460887i
$540$	−2.17196	+	2.17196i	−0.0934664	+	0.0934664i
$541$	−11.9489	−	3.20169i	−0.513722	−	0.137651i	−0.00736102	−	0.999973i	$-0.502343\pi$
$541$	−11.9489	−	3.20169i	−0.513722	−	0.137651i	−0.506361	+	0.862321i	$0.669010\pi$
$542$	−1.62618	−	0.938874i	−0.0698503	−	0.0403281i
$543$	−0.268784	−	0.155183i	−0.0115346	−	0.00665952i
$544$	1.25321	−	4.67703i	0.0537307	−	0.200526i
$545$	−26.1477			−1.12005
$546$	−4.31622	−	8.50707i	−0.184717	−	0.364069i
$547$	−12.6971			−0.542891			−0.271445	−	0.962454i	$-0.587502\pi$
$547$	−12.6971			−0.542891			−0.271445	+	0.962454i	$0.587502\pi$
$548$	1.40781	−	5.25404i	0.0601389	−	0.224441i
$549$	−9.00344	−	5.19814i	−0.384257	−	0.221851i
$550$	−22.6719	−	13.0896i	−0.966732	−	0.558143i
$551$	16.1602	+	4.33011i	0.688448	+	0.184469i
$552$	1.53529	−	1.53529i	0.0653462	−	0.0653462i
$553$	17.5272	+	10.1209i	0.745330	+	0.430383i
$554$	11.6731	−	11.6731i	0.495941	−	0.495941i
$555$	10.7315	+	18.5875i	0.455528	+	0.788997i
$556$	−6.67503	+	11.5615i	−0.283084	+	0.490317i
$557$	−10.3162	−	38.5005i	−0.437110	−	1.63132i	−0.735965	−	0.677020i	$-0.763271\pi$
$557$	−10.3162	−	38.5005i	−0.437110	−	1.63132i	0.298854	−	0.954299i	$-0.403396\pi$
$558$	−4.12207	−	7.13963i	−0.174501	−	0.302245i
$559$	11.5422	+	12.8614i	0.488183	+	0.543981i
$560$	−5.74609	−	5.74686i	−0.242817	−	0.242849i
$561$	20.2111	+	20.2111i	0.853312	+	0.853312i
$562$	15.4352	+	26.7346i	0.651096	+	1.12773i
$563$	21.4420	−	37.1387i	0.903674	−	1.56521i	0.0809857	−	0.996715i	$-0.474193\pi$
$563$	21.4420	−	37.1387i	0.903674	−	1.56521i	0.822688	−	0.568493i	$-0.192473\pi$
$564$	−7.89646	+	2.11585i	−0.332501	+	0.0890933i
$565$	36.0619	+	9.66276i	1.51714	+	0.406516i
$566$	9.74124	+	9.74124i	0.409455	+	0.409455i
$567$	0.000176542	−	2.64575i	7.41408e−6	−	0.111111i
$568$	−11.2853			−0.473522
$569$	22.5850	−	13.0394i	0.946812	−	0.546642i	0.0547228	−	0.998502i	$-0.482572\pi$
$569$	22.5850	−	13.0394i	0.946812	−	0.546642i	0.892089	+	0.451859i	$0.149239\pi$
$570$	−7.60263	+	2.03712i	−0.318439	+	0.0853255i
$571$	−25.7575	−	14.8711i	−1.07792	−	0.622337i	−0.147585	−	0.989049i	$-0.547150\pi$
$571$	−25.7575	−	14.8711i	−1.07792	−	0.622337i	−0.930334	+	0.366713i	$0.880483\pi$
$572$	9.63141	+	18.9799i	0.402709	+	0.793591i
$573$		−	12.4105i		−	0.518456i
$574$	−0.676646	−	0.390722i	−0.0282426	−	0.0163084i
$575$	9.62904			0.401559
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	−4.76511	−	17.7836i	−0.198374	−	0.740343i	−0.991367	−	0.131112i	$-0.958145\pi$
$577$	−4.76511	−	17.7836i	−0.198374	−	0.740343i	0.792993	−	0.609230i	$-0.208522\pi$
$578$	−6.22550	+	1.66812i	−0.258947	+	0.0693845i
$579$	−1.92516	+	7.18478i	−0.0800068	+	0.298589i
$580$	−14.1809	−	14.1809i	−0.588828	−	0.588828i
$581$	5.66314	−	21.1295i	0.234947	−	0.876599i
$582$		−	8.14230i		−	0.337509i
$583$	38.4266	+	10.2964i	1.59147	+	0.426432i
$584$	−8.03398	+	13.9153i	−0.332449	+	0.575818i
$585$	9.27823	+	6.04711i	0.383607	+	0.250017i
$586$	−8.38956	+	4.84372i	−0.346570	+	0.200092i
$587$	−25.6401	+	25.6401i	−1.05828	+	1.05828i	−0.0600864	+	0.998193i	$0.519138\pi$
$587$	−25.6401	+	25.6401i	−1.05828	+	1.05828i	−0.998193	+	0.0600864i	$0.980862\pi$
$588$	7.00000		0.000934174i	0.288675		3.85247e-5i
$589$		−	21.1251i		−	0.870443i
$590$	−4.29717	+	16.0373i	−0.176912	+	0.660243i
$591$	−0.698462	−	2.60670i	−0.0287309	−	0.107225i
$592$	−1.80851	−	6.74944i	−0.0743292	−	0.277400i
$593$	10.6370	−	39.6977i	0.436808	−	1.63019i	−0.299895	−	0.953972i	$-0.596952\pi$
$593$	10.6370	−	39.6977i	0.436808	−	1.63019i	0.736703	−	0.676217i	$-0.236382\pi$
$594$			5.90308i			0.242206i
$595$	−10.1870	+	38.0083i	−0.417627	+	1.55819i
$596$	−0.529007	+	0.529007i	−0.0216690	+	0.0216690i
$597$	10.9694	−	6.33316i	0.448946	−	0.259199i
$598$	−6.55847	−	4.27450i	−0.268196	−	0.174797i
$599$	1.86438	−	3.22921i	0.0761766	−	0.131942i	−0.825421	−	0.564518i	$-0.809062\pi$
$599$	1.86438	−	3.22921i	0.0761766	−	0.131942i	0.901597	+	0.432576i	$0.142395\pi$
$600$	4.28373	+	1.14782i	0.174883	+	0.0468596i
$601$		−	12.0150i		−	0.490102i	−0.969510	−	0.245051i	$-0.921195\pi$
$601$		−	12.0150i		−	0.490102i	0.969510	−	0.245051i	$-0.0788048\pi$
$602$	−12.2490	+	3.28125i	−0.499234	+	0.133734i
$603$	9.54453	+	9.54453i	0.388683	+	0.388683i
$604$	2.27999	−	8.50906i	0.0927717	−	0.346229i
$605$	−70.7510	+	18.9577i	−2.87644	+	0.770739i
$606$	−2.98581	−	11.1432i	−0.121290	−	0.452661i
$607$	−15.5379	+	8.97079i	−0.630663	+	0.364113i	−0.781009	−	0.624520i	$-0.785295\pi$
$607$	−15.5379	+	8.97079i	−0.630663	+	0.364113i	0.150346	+	0.988633i	$0.451961\pi$
$608$	2.56243			0.103920
$609$	17.2742	+	0.00115265i	0.699988	+	4.67079e-5i
$610$			31.9334i			1.29295i
$611$	13.3383	+	26.2848i	0.539609	+	1.06337i
$612$	−4.19331	−	2.42101i	−0.169504	−	0.0978634i
$613$	9.59970	−	2.57223i	0.387728	−	0.103891i	−0.0596885	−	0.998217i	$-0.519011\pi$
$613$	9.59970	−	2.57223i	0.387728	−	0.103891i	0.447417	+	0.894326i	$0.352344\pi$
$614$	−23.7990	+	13.7404i	−0.960449	+	0.554516i
$615$	0.907122			0.0365787
$616$	−15.6181	−	0.00104214i	−0.629270	−	4.19891e-5i
$617$	−16.3453	−	16.3453i	−0.658037	−	0.658037i	0.296878	−	0.954915i	$-0.404054\pi$
$617$	−16.3453	−	16.3453i	−0.658037	−	0.658037i	−0.954915	+	0.296878i	$0.904054\pi$
$618$	5.57378	+	1.49349i	0.224210	+	0.0600770i
$619$	35.1193	−	9.41019i	1.41156	−	0.378228i	0.529081	−	0.848571i	$-0.322537\pi$
$619$	35.1193	−	9.41019i	1.41156	−	0.378228i	0.882483	+	0.470344i	$0.155870\pi$
$620$	−12.6614	+	21.9302i	−0.508495	+	0.880739i
$621$	−1.08561	−	1.88034i	−0.0435641	−	0.0754553i
$622$	−5.35069	−	5.35069i	−0.214543	−	0.214543i
$623$	2.29028	+	8.54972i	0.0917581	+	0.342537i
$624$	−2.40817	−	2.68342i	−0.0964038	−	0.107423i
$625$	−13.7532	−	23.8212i	−0.550128	−	0.952849i
$626$	−6.58106	−	24.5609i	−0.263032	−	0.981650i
$627$	−7.56312	+	13.0997i	−0.302042	+	0.523152i
$628$	4.03003	+	6.98023i	0.160816	+	0.278541i
$629$	−23.9241	+	23.9241i	−0.953915	+	0.953915i
$630$	−7.03823	+	4.06290i	−0.280410	+	0.161870i
$631$	−6.57428	+	6.57428i	−0.261718	+	0.261718i	−0.825752	−	0.564034i	$-0.809249\pi$
$631$	−6.57428	+	6.57428i	−0.261718	+	0.261718i	0.564034	+	0.825752i	$0.309249\pi$
$632$	7.38911	+	1.97991i	0.293923	+	0.0787565i
$633$	2.13339	+	1.23171i	0.0847947	+	0.0489563i
$634$	−4.84337	−	2.79632i	−0.192355	−	0.111056i
$635$	−9.80444	+	36.5907i	−0.389077	+	1.45206i
$636$	−6.73922			−0.267227
$637$	−5.20348	−	24.6966i	−0.206169	−	0.978516i
$638$	−38.5415			−1.52587
$639$	−2.92086	+	10.9008i	−0.115547	+	0.431229i
$640$	−2.66010	−	1.53581i	−0.105150	−	0.0607082i
$641$	38.1760	+	22.0409i	1.50786	+	0.870565i	0.999958	+	0.00915082i	$0.00291284\pi$
$641$	38.1760	+	22.0409i	1.50786	+	0.870565i	0.507904	+	0.861414i	$0.330420\pi$
$642$	−16.0314	−	4.29560i	−0.632708	−	0.169534i
$643$	14.2127	−	14.2127i	0.560493	−	0.560493i	−0.368955	−	0.929447i	$-0.620284\pi$
$643$	14.2127	−	14.2127i	0.560493	−	0.560493i	0.929447	+	0.368955i	$0.120284\pi$
$644$	4.97509	−	2.87193i	0.196046	−	0.113170i
$645$	10.4101	−	10.4101i	0.409896	−	0.409896i
$646$	−6.20367	−	10.7451i	−0.244080	−	0.422759i
$647$	−0.119454	+	0.206900i	−0.00469621	+	0.00813408i	−0.868364	−	0.495927i	$-0.834828\pi$
$647$	−0.119454	+	0.206900i	−0.00469621	+	0.00813408i	0.863668	+	0.504062i	$0.168162\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	15.9539	+	27.6330i	0.626246	+	1.08469i
$650$	0.863161	−	15.9667i	0.0338559	−	0.626267i
$651$	−5.64394	−	21.0691i	−0.221203	−	0.825763i
$652$	−5.80401	−	5.80401i	−0.227302	−	0.227302i
$653$	16.1851	+	28.0335i	0.633374	+	1.09704i	0.986857	+	0.161595i	$0.0516637\pi$
$653$	16.1851	+	28.0335i	0.633374	+	1.09704i	−0.353484	+	0.935441i	$0.615003\pi$
$654$	4.25634	−	7.37220i	0.166436	−	0.288276i
$655$	49.4005	−	13.2368i	1.93024	−	0.517205i
$656$	−0.285261	−	0.0764354i	−0.0111376	−	0.00298430i
$657$	11.3618	+	11.3618i	0.443265	+	0.443265i
$658$	−21.6290	−	0.00144324i	−0.843188	−	5.62632e-5i
$659$	3.84485			0.149774			0.0748870	−	0.997192i	$-0.476140\pi$
$659$	3.84485			0.149774			0.0748870	+	0.997192i	$0.476140\pi$
$660$	15.7028	−	9.06600i	0.611230	−	0.352894i
$661$	−22.7070	+	6.08432i	−0.883199	+	0.236652i	−0.671787	−	0.740745i	$-0.734473\pi$
$661$	−22.7070	+	6.08432i	−0.883199	+	0.236652i	−0.211412	+	0.977397i	$0.567806\pi$
$662$	−6.86364	−	3.96272i	−0.266763	−	0.154016i
$663$	−5.42221	+	16.5948i	−0.210581	+	0.644487i
$664$		−	8.26807i		−	0.320863i
$665$	−20.8242	−	0.00138953i	−0.807529	−	5.38838e-5i
$666$	−6.98754			−0.270762
$667$	12.2768	−	7.08802i	0.475360	−	0.274449i
$668$	3.60068	+	13.4379i	0.139315	+	0.519929i
$669$	0.470074	−	0.125956i	0.0181741	−	0.00486974i
$670$	10.7308	−	40.0480i	0.414568	−	1.54719i
$671$	43.3952	+	43.3952i	1.67525	+	1.67525i
$672$	2.55565	−	0.684600i	0.0985862	−	0.0264090i
$673$		−	6.31552i		−	0.243445i	−0.992564	−	0.121723i	$-0.961158\pi$
$673$		−	6.31552i		−	0.243445i	0.992564	−	0.121723i	$-0.0388418\pi$
$674$	30.5042	+	8.17358i	1.17498	+	0.314835i
$675$	2.21742	−	3.84069i	0.0853486	−	0.147828i
$676$	−7.67582	+	10.4920i	−0.295224	+	0.403538i
$677$	−14.6587	+	8.46318i	−0.563378	+	0.325266i	−0.754500	−	0.656300i	$-0.772121\pi$
$677$	−14.6587	+	8.46318i	−0.563378	+	0.325266i	0.191122	+	0.981566i	$0.438787\pi$
$678$	−8.59454	+	8.59454i	−0.330071	+	0.330071i
$679$	5.57700	−	20.8081i	0.214025	−	0.798541i
$680$			14.8728i			0.570347i
$681$	3.56655	−	13.3105i	0.136670	−	0.510061i
$682$	12.5956	+	47.0075i	0.482312	+	1.80001i
$683$	9.44047	+	35.2323i	0.361230	+	1.34813i	0.872461	+	0.488684i	$0.162523\pi$
$683$	9.44047	+	35.2323i	0.361230	+	1.34813i	−0.511231	+	0.859443i	$0.670810\pi$
$684$	0.663207	−	2.47512i	0.0253583	−	0.0946386i
$685$			16.7077i			0.638368i
$686$	17.8882	+	4.79698i	0.682976	+	0.183149i
$687$	−0.478267	+	0.478267i	−0.0182470	+	0.0182470i
$688$	−4.15080	+	2.39647i	−0.158248	+	0.0913645i
$689$	5.01280	+	23.7759i	0.190972	+	0.905790i
$690$	−3.33459	+	5.77567i	−0.126946	+	0.219876i
$691$	−22.9557	−	6.15096i	−0.873276	−	0.233994i	−0.205772	−	0.978600i	$-0.565971\pi$
$691$	−22.9557	−	6.15096i	−0.873276	−	0.233994i	−0.667504	+	0.744606i	$0.732637\pi$
$692$			4.15469i			0.157938i
$693$	−4.04326	+	15.0856i	−0.153591	+	0.573056i
$694$	0.577836	+	0.577836i	0.0219344	+	0.0219344i
$695$	10.6132	−	39.6091i	0.402582	−	1.50246i
$696$	6.30658	−	1.68984i	0.239050	−	0.0640533i
$697$	0.370101	+	1.38124i	0.0140186	+	0.0523181i
$698$	−14.3033	+	8.25800i	−0.541387	+	0.312570i
$699$	9.86369			0.373079
$700$	10.1611	+	5.86743i	0.384054	+	0.221768i
$701$		−	44.2139i		−	1.66994i	−0.550298	−	0.834969i	$-0.685486\pi$
$701$		−	44.2139i		−	1.66994i	0.550298	−	0.834969i	$-0.314514\pi$
$702$	−3.21526	+	1.63159i	−0.121352	+	0.0615804i
$703$	−15.5063	−	8.95255i	−0.584830	−	0.337652i
$704$	−5.70193	+	1.52783i	−0.214900	+	0.0575822i
$705$	21.7464	−	12.5553i	0.819015	−	0.472859i
$706$	0.723636			0.0272344
$707$	0.00203664	−	30.5221i	7.65958e−5	−	1.14790i
$708$	−3.82212	−	3.82212i	−0.143644	−	0.143644i
$709$	−1.28248	−	0.343638i	−0.0481644	−	0.0129056i	0.234656	−	0.972078i	$-0.424604\pi$
$709$	−1.28248	−	0.343638i	−0.0481644	−	0.0129056i	−0.282821	+	0.959173i	$0.591270\pi$
$710$	33.4831	−	8.97176i	1.25660	−	0.336704i
$711$	3.82489	−	6.62490i	0.143444	−	0.248453i
$712$	1.67271	+	2.89722i	0.0626875	+	0.108578i
$713$	−12.6571	−	12.6571i	−0.474013	−	0.474013i
$714$	−9.05798	−	9.05918i	−0.338986	−	0.339031i
$715$	−43.6649	−	48.6557i	−1.63297	−	1.81962i
$716$	−5.05009	−	8.74701i	−0.188731	−	0.326891i
$717$	3.85427	+	14.3843i	0.143940	+	0.537192i
$718$	−4.59236	+	7.95420i	−0.171385	+	0.296848i
$719$	2.56157	+	4.43677i	0.0955304	+	0.165463i	0.909830	−	0.414982i	$-0.136212\pi$
$719$	2.56157	+	4.43677i	0.0955304	+	0.165463i	−0.814299	+	0.580445i	$0.802879\pi$
$720$	−2.17196	+	2.17196i	−0.0809443	+	0.0809443i
$721$	13.2211	+	7.63441i	0.492381	+	0.284320i
$722$	−8.79212	+	8.79212i	−0.327209	+	0.327209i
$723$	−6.79487	−	1.82068i	−0.252704	−	0.0677118i
$724$	−0.268784	−	0.155183i	−0.00998928	−	0.00576731i
$725$	25.0761	+	14.4777i	0.931301	+	0.537687i
$726$	6.17188	−	23.0338i	0.229060	−	0.854863i
$727$	29.9307			1.11007			0.555035	−	0.831827i	$-0.312705\pi$
$727$	29.9307			1.11007			0.555035	+	0.831827i	$0.312705\pi$
$728$	−4.31622	−	8.50707i	−0.159970	−	0.315293i
$729$	−1.00000			−0.0370370
$730$	12.7739	−	47.6730i	0.472784	−	1.76446i
$731$	20.0983	+	11.6037i	0.743361	+	0.429180i
$732$	−9.00344	−	5.19814i	−0.332777	−	0.192129i
$733$	−37.1354	−	9.95040i	−1.37163	−	0.367526i	−0.503554	−	0.863964i	$-0.667975\pi$
$733$	−37.1354	−	9.95040i	−1.37163	−	0.367526i	−0.868073	+	0.496437i	$0.834641\pi$
$734$	18.9662	−	18.9662i	0.700055	−	0.700055i
$735$	−20.7694	+	5.56218i	−0.766092	+	0.205164i
$736$	1.53529	−	1.53529i	0.0565914	−	0.0565914i
$737$	−39.8399	−	69.0047i	−1.46752	−	2.54182i
$738$	−0.147662	+	0.255758i	−0.00543551	+	0.00941458i
$739$	−6.59845	−	24.6258i	−0.242728	−	0.905873i	−0.974512	−	0.224336i	$-0.927979\pi$
$739$	−6.59845	−	24.6258i	−0.242728	−	0.905873i	0.731784	−	0.681537i	$-0.238688\pi$
$740$	10.7315	+	18.5875i	0.394499	+	0.683292i
$741$	−9.22552	−	0.498731i	−0.338908	−	0.0183213i
$742$	−17.2224	−	4.61597i	−0.632256	−	0.169458i
$743$	31.5747	+	31.5747i	1.15836	+	1.15836i	0.984828	+	0.173535i	$0.0555190\pi$
$743$	31.5747	+	31.5747i	1.15836	+	1.15836i	0.173535	+	0.984828i	$0.444481\pi$
$744$	−4.12207	−	7.13963i	−0.151122	−	0.261752i
$745$	1.14898	−	1.99010i	0.0420955	−	0.0729115i
$746$	31.7672	−	8.51200i	1.16308	−	0.311646i
$747$	−7.98634	−	2.13993i	−0.292205	−	0.0782961i
$748$	20.2111	+	20.2111i	0.738990	+	0.738990i
$749$	−38.0268	−	21.9582i	−1.38947	−	0.802334i
$750$	1.73594			0.0633876
$751$	9.27559	−	5.35527i	0.338471	−	0.195416i	−0.321125	−	0.947037i	$-0.604061\pi$
$751$	9.27559	−	5.35527i	0.338471	−	0.195416i	0.659596	+	0.751621i	$0.270727\pi$
$752$	−7.89646	+	2.11585i	−0.287954	+	0.0771571i
$753$	1.32004	+	0.762128i	0.0481051	+	0.0277735i
$754$	−10.6527	−	20.9926i	−0.387950	−	0.764506i
$755$			27.0586i			0.984762i
$756$	0.000176542	−	2.64575i	6.42078e−6	−	0.0962250i
$757$	−13.0217			−0.473281			−0.236641	−	0.971597i	$-0.576046\pi$
$757$	−13.0217			−0.473281			−0.236641	+	0.971597i	$0.576046\pi$
$758$	−19.5616	+	11.2939i	−0.710511	+	0.410214i
$759$	3.31726	+	12.3802i	0.120409	+	0.449372i
$760$	−7.60263	+	2.03712i	−0.275776	+	0.0738941i
$761$	11.1082	−	41.4565i	0.402674	−	1.50280i	−0.405633	−	0.914036i	$-0.632949\pi$
$761$	11.1082	−	41.4565i	0.402674	−	1.50280i	0.808306	−	0.588762i	$-0.200385\pi$
$762$	−8.72056	−	8.72056i	−0.315912	−	0.315912i
$763$	15.9268	−	15.9247i	0.576590	−	0.576513i
$764$		−	12.4105i		−	0.448996i
$765$	14.3660	+	3.84937i	0.519406	+	0.139174i
$766$	1.96118	−	3.39686i	0.0708602	−	0.122734i
$767$	−10.6414	+	16.3274i	−0.384239	+	0.589547i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	7.07285	−	7.07285i	0.255053	−	0.255053i	−0.567985	−	0.823039i	$-0.692277\pi$
$769$	7.07285	−	7.07285i	0.255053	−	0.255053i	0.823039	+	0.567985i	$0.192277\pi$
$770$	46.3390	−	12.4132i	1.66994	−	0.447340i
$771$		−	24.2940i		−	0.874927i
$772$	−1.92516	+	7.18478i	−0.0692879	+	0.258586i
$773$	−1.65259	−	6.16754i	−0.0594395	−	0.221831i	0.929817	−	0.368023i	$-0.119965\pi$
$773$	−1.65259	−	6.16754i	−0.0594395	−	0.221831i	−0.989256	+	0.146192i	$0.953298\pi$
$774$	1.24050	+	4.62962i	0.0445890	+	0.166408i
$775$	9.46281	−	35.3157i	0.339914	−	1.26858i
$776$		−	8.14230i		−	0.292291i
$777$	−17.8570	−	4.78605i	−0.640617	−	0.171699i
$778$	3.13338	−	3.13338i	0.112337	−	0.112337i
$779$	−0.655363	+	0.378374i	−0.0234808	+	0.0135567i
$780$	9.27823	+	6.04711i	0.332214	+	0.216521i
$781$	33.3091	−	57.6930i	1.19189	−	2.06442i
$782$	−10.1549	−	2.72099i	−0.363138	−	0.0973024i
$783$		−	6.52905i		−	0.233329i
$784$	7.00000		0.000934174i	0.250000		3.33634e-5i
$785$	−17.5062	−	17.5062i	−0.624822	−	0.624822i
$786$	−4.30939	+	16.0829i	−0.153711	+	0.573657i
$787$	−45.6854	+	12.2414i	−1.62851	+	0.436357i	−0.953485	−	0.301439i	$-0.902533\pi$
$787$	−45.6854	+	12.2414i	−1.62851	+	0.436357i	−0.675023	+	0.737797i	$0.735866\pi$
$788$	−0.698462	−	2.60670i	−0.0248817	−	0.0928597i
$789$	−2.54437	+	1.46899i	−0.0905818	+	0.0522974i
$790$	−23.4972			−0.835992
$791$	−27.8506	+	16.0771i	−0.990252	+	0.571634i
$792$			5.90308i			0.209757i
$793$	−11.6420	+	35.6306i	−0.413420	+	1.26528i
$794$	2.30904	+	1.33312i	0.0819447	+	0.0473108i
$795$	19.9950	−	5.35764i	0.709148	−	0.190016i
$796$	10.9694	−	6.33316i	0.388799	−	0.224473i
$797$	−17.5325			−0.621032			−0.310516	−	0.950568i	$-0.600502\pi$
$797$	−17.5325			−0.621032			−0.310516	+	0.950568i	$0.600502\pi$
$798$	3.39017	−	5.87105i	0.120011	−	0.207833i
$799$	27.9898	+	27.9898i	0.990207	+	0.990207i
$800$	4.28373	+	1.14782i	0.151453	+	0.0405816i
$801$	3.23143	−	0.865860i	0.114177	−	0.0305936i
$802$	6.76483	−	11.7170i	0.238874	−	0.413743i
$803$	−47.4252	−	82.1429i	−1.67360	−	2.89876i
$804$	9.54453	+	9.54453i	0.336609	+	0.336609i
$805$	−12.4777	+	12.4760i	−0.439782	+	0.439723i
$806$	−22.1225	+	19.8533i	−0.779231	+	0.699301i
$807$	3.35132	+	5.80466i	0.117972	+	0.204334i
$808$	−2.98581	−	11.1432i	−0.105040	−	0.392016i
$809$	−12.5604	+	21.7553i	−0.441601	+	0.764875i	−0.997808	−	0.0661682i	$-0.978923\pi$
$809$	−12.5604	+	21.7553i	−0.441601	+	0.764875i	0.556208	+	0.831043i	$0.312256\pi$
$810$	1.53581	+	2.66010i	0.0539628	+	0.0934664i
$811$	10.8821	−	10.8821i	0.382120	−	0.382120i	−0.489745	−	0.871866i	$-0.662910\pi$
$811$	10.8821	−	10.8821i	0.382120	−	0.382120i	0.871866	+	0.489745i	$0.162910\pi$
$812$	17.2742	+	0.00115265i	0.606207	+	4.04502e-5i
$813$	−1.32777	+	1.32777i	−0.0465669	+	0.0465669i
$814$	39.8425	+	10.6758i	1.39648	+	0.374185i
$815$	21.8344	+	12.6061i	0.764825	+	0.441572i
$816$	−4.19331	−	2.42101i	−0.146795	−	0.0847522i
$817$	−3.17871	+	11.8631i	−0.111209	+	0.415037i
$818$	4.96978			0.173764
$819$	−9.33432	+	1.96735i	−0.326168	+	0.0687449i
$820$	0.907122			0.0316781
$821$	−0.365994	+	1.36591i	−0.0127733	+	0.0476705i	−0.972018	−	0.234905i	$-0.924522\pi$
$821$	−0.365994	+	1.36591i	−0.0127733	+	0.0476705i	0.959245	+	0.282575i	$0.0911888\pi$
$822$	−4.71064	−	2.71969i	−0.164302	−	0.0948600i
$823$	18.6219	+	10.7514i	0.649119	+	0.374769i	0.788119	−	0.615523i	$-0.211055\pi$
$823$	18.6219	+	10.7514i	0.649119	+	0.374769i	−0.139000	+	0.990292i	$0.544389\pi$
$824$	5.57378	+	1.49349i	0.194172	+	0.0520282i
$825$	−18.5115	+	18.5115i	−0.644488	+	0.644488i
$826$	−7.14970	−	12.3855i	−0.248770	−	0.430948i
$827$	−38.0970	+	38.0970i	−1.32476	+	1.32476i	−0.414889	+	0.909872i	$0.636180\pi$
$827$	−38.0970	+	38.0970i	−1.32476	+	1.32476i	−0.909872	+	0.414889i	$0.863820\pi$
$828$	−1.08561	−	1.88034i	−0.0377276	−	0.0653462i
$829$	4.11746	−	7.13165i	0.143005	−	0.247692i	−0.785622	−	0.618707i	$-0.787657\pi$
$829$	4.11746	−	7.13165i	0.143005	−	0.247692i	0.928627	+	0.371015i	$0.120990\pi$
$830$	6.57306	+	24.5310i	0.228154	+	0.851483i
$831$	−8.25410	−	14.2965i	−0.286332	−	0.495941i
$832$	−2.40817	−	2.68342i	−0.0834882	−	0.0930308i
$833$	−16.9431	−	29.3554i	−0.587045	−	1.01710i
$834$	9.43992	+	9.43992i	0.326878	+	0.326878i
$835$	−21.3661	−	37.0072i	−0.739405	−	1.28069i
$836$	−7.56312	+	13.0997i	−0.261576	+	0.453063i
$837$	−7.96323	+	2.13374i	−0.275249	+	0.0737528i
$838$	0.405212	+	0.108576i	0.0139978	+	0.00375070i
$839$	5.95998	+	5.95998i	0.205761	+	0.205761i	0.802463	−	0.596702i	$-0.203522\pi$
$839$	5.95998	+	5.95998i	0.205761	+	0.205761i	−0.596702	+	0.802463i	$0.703522\pi$
$840$	−7.03823	+	4.06290i	−0.242842	+	0.140183i
$841$	13.6285			0.469949
$842$	−5.25053	+	3.03139i	−0.180945	+	0.104469i
$843$	29.8186	−	7.98987i	1.02701	−	0.275186i
$844$	2.13339	+	1.23171i	0.0734344	+	0.0423974i
$845$	14.4328	−	37.2315i	0.496502	−	1.28080i
$846$			8.17501i			0.281063i
$847$	31.5493	−	54.6367i	1.08405	−	1.87734i
$848$	−6.73922			−0.231426
$849$	11.9305	−	6.88809i	0.409455	−	0.236399i
$850$	−5.55777	−	20.7419i	−0.190630	−	0.711441i
$851$	−14.6545	+	3.92667i	−0.502351	+	0.134605i
$852$	−2.92086	+	10.9008i	−0.100067	+	0.373455i
$853$	−17.6393	−	17.6393i	−0.603958	−	0.603958i	0.337402	−	0.941361i	$-0.390452\pi$
$853$	−17.6393	−	17.6393i	−0.603958	−	0.603958i	−0.941361	+	0.337402i	$0.890452\pi$
$854$	−19.4484	−	19.4509i	−0.665509	−	0.665598i
$855$			7.87082i			0.269176i
$856$	−16.0314	−	4.29560i	−0.547941	−	0.146820i
$857$	0.860571	−	1.49055i	0.0293965	−	0.0509163i	−0.850953	−	0.525242i	$-0.823975\pi$
$857$	0.860571	−	1.49055i	0.0293965	−	0.0509163i	0.880349	+	0.474326i	$0.157308\pi$
$858$	20.8260	−	4.39086i	0.710988	−	0.149901i
$859$	2.12428	−	1.22645i	0.0724794	−	0.0418460i	−0.463322	−	0.886190i	$-0.653343\pi$
$859$	2.12428	−	1.22645i	0.0724794	−	0.0418460i	0.535802	+	0.844344i	$0.320009\pi$
$860$	10.4101	−	10.4101i	0.354981	−	0.354981i
$861$	−0.552537	+	0.552463i	−0.0188304	+	0.0188279i
$862$		−	3.80714i		−	0.129672i
$863$	−10.7683	+	40.1877i	−0.366556	+	1.36801i	0.498742	+	0.866750i	$0.333795\pi$
$863$	−10.7683	+	40.1877i	−0.366556	+	1.36801i	−0.865299	+	0.501257i	$0.832871\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	−3.30295	−	12.3268i	−0.112304	−	0.419123i
$866$	3.04159	−	11.3514i	0.103357	−	0.385735i
$867$			6.44511i			0.218887i
$868$	−5.64394	−	21.0691i	−0.191568	−	0.715132i
$869$	−31.9310	+	31.9310i	−1.08318	+	1.08318i
$870$	−17.3679	+	10.0274i	−0.588828	+	0.339960i
$871$	26.5735	−	40.7725i	0.900410	−	1.38152i
$872$	4.25634	−	7.37220i	0.144138	−	0.249654i
$873$	−7.86486	−	2.10738i	−0.266185	−	0.0713241i
$874$		−	5.56362i		−	0.188192i
$875$	4.43629	+	1.18902i	0.149974	+	0.0401962i
$876$	11.3618	+	11.3618i	0.383879	+	0.383879i
$877$	6.03538	−	22.5243i	0.203800	−	0.760592i	−0.786012	−	0.618212i	$-0.787858\pi$
$877$	6.03538	−	22.5243i	0.203800	−	0.760592i	0.989812	−	0.142381i	$-0.0454758\pi$
$878$	−28.8944	+	7.74222i	−0.975138	+	0.261287i
$879$	2.50729	+	9.35734i	0.0845688	+	0.315615i
$880$	15.7028	−	9.06600i	0.529340	−	0.305615i
$881$	−17.7592			−0.598324			−0.299162	−	0.954202i	$-0.596707\pi$
$881$	−17.7592			−0.598324			−0.299162	+	0.954202i	$0.596707\pi$
$882$	1.81264	−	6.76124i	0.0610346	−	0.227663i
$883$		−	15.0945i		−	0.507969i	−0.967208	−	0.253985i	$-0.918259\pi$
$883$		−	15.0945i		−	0.507969i	0.967208	−	0.253985i	$-0.0817413\pi$
$884$	−5.42221	+	16.5948i	−0.182369	+	0.558142i
$885$	14.3786	+	8.30149i	0.483332	+	0.279052i
$886$	22.1088	−	5.92404i	0.742760	−	0.199022i
$887$	24.7751	−	14.3039i	0.831865	−	0.480278i	−0.0226255	−	0.999744i	$-0.507203\pi$
$887$	24.7751	−	14.3039i	0.831865	−	0.480278i	0.854491	+	0.519466i	$0.173869\pi$
$888$	−6.98754			−0.234486
$889$	−16.3128	−	28.2589i	−0.547113	−	0.947774i
$890$	−7.26614	−	7.26614i	−0.243562	−	0.243562i
$891$	5.70193	+	1.52783i	0.191022	+	0.0511842i
$892$	0.470074	−	0.125956i	0.0157392	−	0.00421731i
$893$	−10.4740	+	18.1414i	−0.350498	+	0.607080i
$894$	0.374064	+	0.647899i	0.0125106	+	0.0216690i
$895$	21.9372	+	21.9372i	0.733280	+	0.733280i
$896$	2.55565	−	0.684600i	0.0853781	−	0.0228709i
$897$	−5.82630	+	5.22867i	−0.194535	+	0.174580i
$898$	−12.0656	−	20.8982i	−0.402634	−	0.697382i
$899$	−13.9313	−	51.9923i	−0.464635	−	1.73404i
$900$	2.21742	−	3.84069i	0.0739141	−	0.128023i
$901$	16.3157	+	28.2596i	0.543555	+	0.941464i
$902$	1.23271	−	1.23271i	0.0410448	−	0.0410448i
$903$	−0.000846156		12.6809i	−2.81583e−5		0.421994i
$904$	−8.59454	+	8.59454i	−0.285850	+	0.285850i
$905$	0.920840	+	0.246738i	0.0306097	+	0.00820186i
$906$	−7.62901	−	4.40461i	−0.253457	−	0.146333i
$907$	3.23783	+	1.86936i	0.107510	+	0.0620712i	0.552791	−	0.833320i	$-0.313563\pi$
$907$	3.23783	+	1.86936i	0.107510	+	0.0620712i	−0.445281	+	0.895391i	$0.646896\pi$
$908$	3.56655	−	13.3105i	0.118360	−	0.441726i
$909$	−11.5363			−0.382634
$910$	19.5691	+	21.8087i	0.648709	+	0.722953i
$911$	57.9435			1.91975			0.959877	−	0.280420i	$-0.0904738\pi$
$911$	57.9435			1.91975			0.959877	+	0.280420i	$0.0904738\pi$
$912$	0.663207	−	2.47512i	0.0219610	−	0.0819595i
$913$	42.2681	+	24.4035i	1.39887	+	0.807638i
$914$	23.1193	+	13.3480i	0.764720	+	0.441511i
$915$	30.8453	+	8.26497i	1.01971	+	0.273232i
$916$	−0.478267	+	0.478267i	−0.0158024	+	0.0158024i
$917$	−22.0287	+	38.1490i	−0.727452	+	1.25979i
$918$	−3.42382	+	3.42382i	−0.113003	+	0.113003i
$919$	1.96112	+	3.39677i	0.0646915	+	0.112049i	0.896557	−	0.442928i	$-0.146060\pi$
$919$	1.96112	+	3.39677i	0.0646915	+	0.112049i	−0.831866	+	0.554977i	$0.812727\pi$
$920$	−3.33459	+	5.77567i	−0.109938	+	0.190418i
$921$	7.11253	+	26.5443i	0.234366	+	0.874665i
$922$	7.92891	+	13.7333i	0.261125	+	0.452281i
$923$	40.6305	+	2.19648i	1.33737	+	0.0722981i
$924$	−4.04326	+	15.0856i	−0.133014	+	0.496281i
$925$	−21.9123	−	21.9123i	−0.720471	−	0.720471i
$926$	14.4437	+	25.0173i	0.474651	+	0.822119i
$927$	2.88520	−	4.99732i	0.0947624	−	0.164133i
$928$	6.30658	−	1.68984i	0.207024	−	0.0554718i
$929$	−10.4487	−	2.79972i	−0.342810	−	0.0918558i	0.0833063	−	0.996524i	$-0.473452\pi$
$929$	−10.4487	−	2.79972i	−0.342810	−	0.0918558i	−0.426117	+	0.904668i	$0.640119\pi$
$930$	17.9060	+	17.9060i	0.587160	+	0.587160i
$931$	12.6851	−	12.6817i	0.415737	−	0.415626i
$932$	9.86369			0.323096
$933$	−6.55324	+	3.78351i	−0.214543	+	0.123867i
$934$	22.5140	−	6.03261i	0.736681	−	0.197393i
$935$	−76.0331	−	43.8977i	−2.48655	−	1.43561i
$936$	−3.21526	+	1.63159i	−0.105094	+	0.0533302i
$937$			56.8526i			1.85729i	0.370964	+	0.928647i	$0.379027\pi$
$937$			56.8526i			1.85729i	−0.370964	+	0.928647i	$0.620973\pi$
$938$	17.8541	+	30.9290i	0.582957	+	1.00987i
$939$	−25.4273			−0.829788
$940$	21.7464	−	12.5553i	0.709288	−	0.409508i
$941$	−4.17659	−	15.5873i	−0.136153	−	0.508130i	−0.999990	−	0.00435933i	$-0.998612\pi$
$941$	−4.17659	−	15.5873i	−0.136153	−	0.508130i	0.863838	−	0.503771i	$-0.168054\pi$
$942$	7.78543	−	2.08610i	0.253663	−	0.0679688i
$943$	−0.165958	+	0.619365i	−0.00540435	+	0.0201693i
$944$	−3.82212	−	3.82212i	−0.124399	−	0.124399i
$945$	2.10283	+	7.84997i	0.0684051	+	0.255360i
$946$		−	28.2931i		−	0.919887i
$947$	21.8848	+	5.86400i	0.711159	+	0.190555i	0.596224	−	0.802818i	$-0.296667\pi$
$947$	21.8848	+	5.86400i	0.711159	+	0.190555i	0.114936	+	0.993373i	$0.463334\pi$
$948$	3.82489	−	6.62490i	0.124227	−	0.215167i
$949$	31.6331	−	48.5354i	1.02685	−	1.57553i
$950$	9.84151	−	5.68200i	0.319301	−	0.184348i
$951$	−3.95460	+	3.95460i	−0.128237	+	0.128237i
$952$	−9.05798	−	9.05918i	−0.293571	−	0.293610i
$953$		−	48.8561i		−	1.58260i	−0.611426	−	0.791302i	$-0.709404\pi$
$953$		−	48.8561i		−	1.58260i	0.611426	−	0.791302i	$-0.290596\pi$
$954$	−1.74424	+	6.50959i	−0.0564718	+	0.210756i
$955$	9.86627	+	36.8214i	0.319265	+	1.19151i
$956$	3.85427	+	14.3843i	0.124656	+	0.465222i
$957$	−9.97527	+	37.2282i	−0.322455	+	1.20342i
$958$		−	16.9591i		−	0.547923i
$959$	−10.1755	−	10.1768i	−0.328583	−	0.328627i
$960$	−2.17196	+	2.17196i	−0.0700998	+	0.0700998i
$961$	−32.0133	+	18.4829i	−1.03269	+	0.596223i
$962$	5.19750	+	24.6520i	0.167574	+	0.794811i
$963$	−8.29845	+	14.3733i	−0.267414	+	0.463174i
$964$	−6.79487	−	1.82068i	−0.218848	−	0.0586401i
$965$		−	22.8474i		−	0.735484i
$966$	−1.48642	−	5.54888i	−0.0478248	−	0.178532i
$967$	22.5427	+	22.5427i	0.724923	+	0.724923i	0.969604	−	0.244681i	$-0.0786831\pi$
$967$	22.5427	+	22.5427i	0.724923	+	0.724923i	−0.244681	+	0.969604i	$0.578683\pi$
$968$	6.17188	−	23.0338i	0.198372	−	0.740333i
$969$	−11.9846	+	3.21126i	−0.385000	+	0.103160i
$970$	6.47307	+	24.1578i	0.207838	+	0.775662i
$971$	−20.9522	+	12.0968i	−0.672389	+	0.388204i	−0.796981	−	0.604004i	$-0.793571\pi$
$971$	−20.9522	+	12.0968i	−0.672389	+	0.388204i	0.124592	+	0.992208i	$0.460238\pi$
$972$	−1.00000			−0.0320750
$973$	17.6584	+	30.5900i	0.566103	+	0.980671i
$974$		−	22.8271i		−	0.731427i
$975$	−15.1993	−	4.96625i	−0.486767	−	0.159047i
$976$	−9.00344	−	5.19814i	−0.288193	−	0.166388i
$977$	−5.86888	+	1.57256i	−0.187762	+	0.0503107i	−0.351475	−	0.936197i	$-0.614320\pi$
$977$	−5.86888	+	1.57256i	−0.187762	+	0.0503107i	0.163713	+	0.986508i	$0.447653\pi$
$978$	−7.10843	+	4.10405i	−0.227302	+	0.131233i
$979$	−19.7483			−0.631158
$980$	−20.7694	+	5.56218i	−0.663455	+	0.177677i
$981$	−6.01937	−	6.01937i	−0.192184	−	0.192184i
$982$	−16.1604	−	4.33017i	−0.515700	−	0.138181i
$983$	5.74747	−	1.54003i	0.183316	−	0.0491193i	−0.165993	−	0.986127i	$-0.553083\pi$
$983$	5.74747	−	1.54003i	0.183316	−	0.0491193i	0.349309	+	0.937008i	$0.386416\pi$
$984$	−0.147662	+	0.255758i	−0.00470729	+	0.00815326i
$985$	4.14462	+	7.17868i	0.132058	+	0.228732i
$986$	−22.3543	−	22.3543i	−0.711906	−	0.711906i
$987$	−5.59940	+	20.8917i	−0.178231	+	0.664990i
$988$	−9.22552	−	0.498731i	−0.293503	−	0.0158667i
$989$	5.20327	+	9.01233i	0.165454	+	0.286575i
$990$	−4.69291	−	17.5142i	−0.149150	−	0.556637i
$991$	−4.04363	+	7.00377i	−0.128450	+	0.222482i	−0.923076	−	0.384617i	$-0.874334\pi$
$991$	−4.04363	+	7.00377i	−0.128450	+	0.222482i	0.794626	+	0.607099i	$0.207667\pi$
$992$	−4.12207	−	7.13963i	−0.130876	−	0.226684i
$993$	−5.60414	+	5.60414i	−0.177842	+	0.177842i
$994$	−14.9308	+	25.8569i	−0.473577	+	0.820132i
$995$	−27.5108	+	27.5108i	−0.872151	+	0.872151i
$996$	−7.98634	−	2.13993i	−0.253057	−	0.0678064i
$997$	11.2729	+	6.50844i	0.357018	+	0.206124i	0.667772	−	0.744366i	$-0.267248\pi$
$997$	11.2729	+	6.50844i	0.357018	+	0.206124i	−0.310754	+	0.950490i	$0.600582\pi$
$998$	−13.4074	−	7.74078i	−0.424405	−	0.245030i
$999$	−1.80851	+	6.74944i	−0.0572186	+	0.213543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.a.73.10	✓	40
7.5	odd	6		546.2.bz.b.229.5	yes	40
13.5	odd	4		546.2.bz.b.31.5	yes	40
91.5	even	12	inner	546.2.bz.a.187.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.10	✓	40	1.1	even	1	trivial
546.2.bz.a.187.10	yes	40	91.5	even	12	inner
546.2.bz.b.31.5	yes	40	13.5	odd	4
546.2.bz.b.229.5	yes	40	7.5	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.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.96696 + 0.794994i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.29138 + 1.32272i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.96696 + 0.794994i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.29138 + 1.32272i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.53581 - 2.66010i) q^{10} +(-1.52783 - 5.70193i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.68342 - 2.40817i) q^{13} +(0.684600 + 2.55565i) q^{14} +(-2.17196 - 2.17196i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.42101 - 4.19331i) q^{17} +(0.965926 - 0.258819i) q^{18} +(2.47512 + 0.663207i) q^{19} +(-2.17196 - 2.17196i) q^{20} +(2.64575 + 0.000176542i) q^{21} -5.90308 q^{22} +(1.88034 - 1.08561i) q^{23} +(0.965926 - 0.258819i) q^{24} +(3.84069 + 2.21742i) q^{25} +(-1.63159 - 3.21526i) q^{26} -1.00000i q^{27} +(2.64575 + 0.000176542i) q^{28} +6.52905 q^{29} +(-2.66010 + 1.53581i) q^{30} +(-2.13374 - 7.96323i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.52783 + 5.70193i) q^{33} +(-3.42382 - 3.42382i) q^{34} +(-7.84997 + 2.10283i) q^{35} -1.00000i q^{36} +(-6.74944 - 1.80851i) q^{37} +(1.28122 - 2.21913i) q^{38} +(-3.52799 + 0.743825i) q^{39} +(-2.66010 + 1.53581i) q^{40} +(-0.208825 + 0.208825i) q^{41} +(0.684941 - 2.55555i) q^{42} +4.79294i q^{43} +(-1.52783 + 5.70193i) q^{44} +(0.794994 + 2.96696i) q^{45} +(-0.561954 - 2.09724i) q^{46} +(-2.11585 + 7.89646i) q^{47} -1.00000i q^{48} +(3.50081 - 6.06171i) q^{49} +(3.13591 - 3.13591i) q^{50} +(-4.19331 + 2.42101i) q^{51} +(-3.52799 + 0.743825i) q^{52} +(-3.36961 + 5.83633i) q^{53} +(-0.965926 - 0.258819i) q^{54} -18.1320i q^{55} +(0.684941 - 2.55555i) q^{56} +(-1.81191 - 1.81191i) q^{57} +(1.68984 - 6.30658i) q^{58} +(-5.22111 + 1.39899i) q^{59} +(0.794994 + 2.96696i) q^{60} +(-9.00344 + 5.19814i) q^{61} -8.24414 q^{62} +(-2.29120 - 1.32303i) q^{63} -1.00000i q^{64} +(9.87606 - 5.01163i) q^{65} +(5.11221 + 2.95154i) q^{66} +(13.0381 - 3.49354i) q^{67} +(-4.19331 + 2.42101i) q^{68} -2.17122 q^{69} +(-0.000542271 + 8.12674i) q^{70} +(7.97993 + 7.97993i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(15.5205 - 4.15870i) q^{73} +(-3.49377 + 6.05138i) q^{74} +(-2.21742 - 3.84069i) q^{75} +(-1.81191 - 1.81191i) q^{76} +(11.0429 + 11.0444i) q^{77} +(-0.194632 + 3.60029i) q^{78} +(-3.82489 - 6.62490i) q^{79} +(0.794994 + 2.96696i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.147662 + 0.255758i) q^{82} +(-5.84641 + 5.84641i) q^{83} +(-2.29120 - 1.32303i) q^{84} +(10.5167 - 10.5167i) q^{85} +(4.62962 + 1.24050i) q^{86} +(-5.65433 - 3.26453i) q^{87} +(5.11221 + 2.95154i) q^{88} +(0.865860 - 3.23143i) q^{89} +3.07162 q^{90} +(-2.96338 + 9.06743i) q^{91} -2.17122 q^{92} +(-2.13374 + 7.96323i) q^{93} +(7.07977 + 4.08751i) q^{94} +(6.81633 + 3.93541i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(-5.75747 + 5.75747i) q^{97} +(-4.94909 - 4.95041i) q^{98} +(4.17411 - 4.17411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 + 20 * q^9	\( 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

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