LMFDB - Embedded newform 770.2.m.d.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$1.14412 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	770.43
Dual form			770.2.m.d.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.61803 - 1.61803i) q^{3} +1.00000i q^{4} +(2.00000 + 1.00000i) q^{5} -2.28825i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.23607i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.61803 - 1.61803i) q^{3} +1.00000i q^{4} +(2.00000 + 1.00000i) q^{5} -2.28825i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.23607i q^{9} +(0.707107 + 2.12132i) q^{10} +(-1.00000 - 3.16228i) q^{11} +(1.61803 - 1.61803i) q^{12} +(1.74806 - 1.74806i) q^{13} -1.00000i q^{14} +(-1.61803 - 4.85410i) q^{15} -1.00000 q^{16} +(0.540182 + 0.540182i) q^{17} +(-1.58114 + 1.58114i) q^{18} +6.53089 q^{19} +(-1.00000 + 2.00000i) q^{20} +2.28825i q^{21} +(1.52896 - 2.94317i) q^{22} +(-4.85410 - 4.85410i) q^{23} +2.28825 q^{24} +(3.00000 + 4.00000i) q^{25} +2.47214 q^{26} +(-1.23607 + 1.23607i) q^{27} +(0.707107 - 0.707107i) q^{28} +10.0270 q^{29} +(2.28825 - 4.57649i) q^{30} -7.70820 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.49864 + 6.73471i) q^{33} +0.763932i q^{34} +(-0.707107 - 2.12132i) q^{35} -2.23607 q^{36} +(7.61803 - 7.61803i) q^{37} +(4.61803 + 4.61803i) q^{38} -5.65685 q^{39} +(-2.12132 + 0.707107i) q^{40} -7.61125i q^{41} +(-1.61803 + 1.61803i) q^{42} +(4.24264 - 4.24264i) q^{43} +(3.16228 - 1.00000i) q^{44} +(-2.23607 + 4.47214i) q^{45} -6.86474i q^{46} +(4.70820 - 4.70820i) q^{47} +(1.61803 + 1.61803i) q^{48} +1.00000i q^{49} +(-0.707107 + 4.94975i) q^{50} -1.74806i q^{51} +(1.74806 + 1.74806i) q^{52} +(-4.38197 - 4.38197i) q^{53} -1.74806 q^{54} +(1.16228 - 7.32456i) q^{55} +1.00000 q^{56} +(-10.5672 - 10.5672i) q^{57} +(7.09017 + 7.09017i) q^{58} +7.23607i q^{59} +(4.85410 - 1.61803i) q^{60} -2.82843i q^{61} +(-5.45052 - 5.45052i) q^{62} +(1.58114 - 1.58114i) q^{63} -1.00000i q^{64} +(5.24419 - 1.74806i) q^{65} +(-7.23607 + 2.28825i) q^{66} +(-6.23607 + 6.23607i) q^{67} +(-0.540182 + 0.540182i) q^{68} +15.7082i q^{69} +(1.00000 - 2.00000i) q^{70} +12.0000 q^{71} +(-1.58114 - 1.58114i) q^{72} +(-4.91034 + 4.91034i) q^{73} +10.7735 q^{74} +(1.61803 - 11.3262i) q^{75} +6.53089i q^{76} +(-1.52896 + 2.94317i) q^{77} +(-4.00000 - 4.00000i) q^{78} +7.19859 q^{79} +(-2.00000 - 1.00000i) q^{80} +10.7082 q^{81} +(5.38197 - 5.38197i) q^{82} +(-4.57649 + 4.57649i) q^{83} -2.28825 q^{84} +(0.540182 + 1.62054i) q^{85} +6.00000 q^{86} +(-16.2241 - 16.2241i) q^{87} +(2.94317 + 1.52896i) q^{88} +9.41641i q^{89} +(-4.74342 + 1.58114i) q^{90} -2.47214 q^{91} +(4.85410 - 4.85410i) q^{92} +(12.4721 + 12.4721i) q^{93} +6.65841 q^{94} +(13.0618 + 6.53089i) q^{95} +2.28825i q^{96} +(-13.3262 + 13.3262i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(7.07107 - 2.23607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 16 q^{5}+O(q^{10}) $ 8 * q - 4 * q^3 + 16 * q^5	$ 8 q - 4 q^{3} + 16 q^{5} - 8 q^{11} + 4 q^{12} - 4 q^{15} - 8 q^{16} - 8 q^{20} - 12 q^{23} + 24 q^{25} - 16 q^{26} + 8 q^{27} - 8 q^{31} + 4 q^{33} + 52 q^{37} + 28 q^{38} - 4 q^{42} - 16 q^{47} + 4 q^{48} - 44 q^{53} - 16 q^{55} + 8 q^{56} + 12 q^{58} + 12 q^{60} - 40 q^{66} - 32 q^{67} + 8 q^{70} + 96 q^{71} + 4 q^{75} - 32 q^{78} - 16 q^{80} + 32 q^{81} + 52 q^{82} + 48 q^{86} + 16 q^{91} + 12 q^{92} + 64 q^{93} - 44 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 + 16 * q^5 - 8 * q^11 + 4 * q^12 - 4 * q^15 - 8 * q^16 - 8 * q^20 - 12 * q^23 + 24 * q^25 - 16 * q^26 + 8 * q^27 - 8 * q^31 + 4 * q^33 + 52 * q^37 + 28 * q^38 - 4 * q^42 - 16 * q^47 + 4 * q^48 - 44 * q^53 - 16 * q^55 + 8 * q^56 + 12 * q^58 + 12 * q^60 - 40 * q^66 - 32 * q^67 + 8 * q^70 + 96 * q^71 + 4 * q^75 - 32 * q^78 - 16 * q^80 + 32 * q^81 + 52 * q^82 + 48 * q^86 + 16 * q^91 + 12 * q^92 + 64 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.61803	−	1.61803i	−0.934172	−	0.934172i	0.0637909	−	0.997963i	$-0.479681\pi$
$3$	−1.61803	−	1.61803i	−0.934172	−	0.934172i	−0.997963	+	0.0637909i	$0.979681\pi$
$4$			1.00000i			0.500000i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$		−	2.28825i		−	0.934172i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			2.23607i			0.745356i
$10$	0.707107	+	2.12132i	0.223607	+	0.670820i
$11$	−1.00000	−	3.16228i	−0.301511	−	0.953463i
$11$	−1.00000	−	3.16228i	−0.301511	−	0.953463i
$12$	1.61803	−	1.61803i	0.467086	−	0.467086i
$13$	1.74806	−	1.74806i	0.484826	−	0.484826i	−0.421843	−	0.906669i	$-0.638617\pi$
$13$	1.74806	−	1.74806i	0.484826	−	0.484826i	0.906669	+	0.421843i	$0.138617\pi$
$14$		−	1.00000i		−	0.267261i
$15$	−1.61803	−	4.85410i	−0.417775	−	1.25332i
$16$	−1.00000			−0.250000
$17$	0.540182	+	0.540182i	0.131013	+	0.131013i	0.769573	−	0.638559i	$-0.220469\pi$
$17$	0.540182	+	0.540182i	0.131013	+	0.131013i	−0.638559	+	0.769573i	$0.720469\pi$
$18$	−1.58114	+	1.58114i	−0.372678	+	0.372678i
$19$	6.53089			1.49829			0.749144	−	0.662407i	$-0.230465\pi$
$19$	6.53089			1.49829			0.749144	+	0.662407i	$0.230465\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$			2.28825i			0.499336i
$22$	1.52896	−	2.94317i	0.325976	−	0.627487i
$23$	−4.85410	−	4.85410i	−1.01215	−	1.01215i	−0.999925	−	0.0122250i	$-0.996109\pi$
$23$	−4.85410	−	4.85410i	−1.01215	−	1.01215i	−0.0122250	−	0.999925i	$-0.503891\pi$
$24$	2.28825			0.467086
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	2.47214			0.484826
$27$	−1.23607	+	1.23607i	−0.237881	+	0.237881i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	10.0270			1.86197			0.930985	−	0.365058i	$-0.118951\pi$
$29$	10.0270			1.86197			0.930985	+	0.365058i	$0.118951\pi$
$30$	2.28825	−	4.57649i	0.417775	−	0.835549i
$31$	−7.70820			−1.38443			−0.692217	−	0.721689i	$-0.743366\pi$
$31$	−7.70820			−1.38443			−0.692217	+	0.721689i	$0.743366\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.49864	+	6.73471i	−0.609035	+	1.17236i
$34$			0.763932i			0.131013i
$35$	−0.707107	−	2.12132i	−0.119523	−	0.358569i
$36$	−2.23607			−0.372678
$37$	7.61803	−	7.61803i	1.25240	−	1.25240i	0.297755	−	0.954642i	$-0.403762\pi$
$37$	7.61803	−	7.61803i	1.25240	−	1.25240i	0.954642	−	0.297755i	$-0.0962377\pi$
$38$	4.61803	+	4.61803i	0.749144	+	0.749144i
$39$	−5.65685			−0.905822
$40$	−2.12132	+	0.707107i	−0.335410	+	0.111803i
$41$		−	7.61125i		−	1.18868i	−0.804215	−	0.594339i	$-0.797414\pi$
$41$		−	7.61125i		−	1.18868i	0.804215	−	0.594339i	$-0.202586\pi$
$42$	−1.61803	+	1.61803i	−0.249668	+	0.249668i
$43$	4.24264	−	4.24264i	0.646997	−	0.646997i	−0.305269	−	0.952266i	$-0.598747\pi$
$43$	4.24264	−	4.24264i	0.646997	−	0.646997i	0.952266	+	0.305269i	$0.0987465\pi$
$44$	3.16228	−	1.00000i	0.476731	−	0.150756i
$45$	−2.23607	+	4.47214i	−0.333333	+	0.666667i
$46$		−	6.86474i		−	1.01215i
$47$	4.70820	−	4.70820i	0.686762	−	0.686762i	−0.274753	−	0.961515i	$-0.588596\pi$
$47$	4.70820	−	4.70820i	0.686762	−	0.686762i	0.961515	+	0.274753i	$0.0885960\pi$
$48$	1.61803	+	1.61803i	0.233543	+	0.233543i
$49$			1.00000i			0.142857i
$50$	−0.707107	+	4.94975i	−0.100000	+	0.700000i
$51$		−	1.74806i		−	0.244778i
$52$	1.74806	+	1.74806i	0.242413	+	0.242413i
$53$	−4.38197	−	4.38197i	−0.601909	−	0.601909i	0.338910	−	0.940819i	$-0.389942\pi$
$53$	−4.38197	−	4.38197i	−0.601909	−	0.601909i	−0.940819	+	0.338910i	$0.889942\pi$
$54$	−1.74806			−0.237881
$55$	1.16228	−	7.32456i	0.156721	−	0.987643i
$56$	1.00000			0.133631
$57$	−10.5672	−	10.5672i	−1.39966	−	1.39966i
$58$	7.09017	+	7.09017i	0.930985	+	0.930985i
$59$			7.23607i			0.942056i	0.882118	+	0.471028i	$0.156117\pi$
$59$			7.23607i			0.942056i	−0.882118	+	0.471028i	$0.843883\pi$
$60$	4.85410	−	1.61803i	0.626662	−	0.208887i
$61$		−	2.82843i		−	0.362143i	−0.983470	−	0.181071i	$-0.942043\pi$
$61$		−	2.82843i		−	0.362143i	0.983470	−	0.181071i	$-0.0579565\pi$
$62$	−5.45052	−	5.45052i	−0.692217	−	0.692217i
$63$	1.58114	−	1.58114i	0.199205	−	0.199205i
$64$		−	1.00000i		−	0.125000i
$65$	5.24419	−	1.74806i	0.650462	−	0.216821i
$66$	−7.23607	+	2.28825i	−0.890698	+	0.281664i
$67$	−6.23607	+	6.23607i	−0.761857	+	0.761857i	−0.976658	−	0.214801i	$-0.931090\pi$
$67$	−6.23607	+	6.23607i	−0.761857	+	0.761857i	0.214801	+	0.976658i	$0.431090\pi$
$68$	−0.540182	+	0.540182i	−0.0655066	+	0.0655066i
$69$			15.7082i			1.89105i
$70$	1.00000	−	2.00000i	0.119523	−	0.239046i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.58114	−	1.58114i	−0.186339	−	0.186339i
$73$	−4.91034	+	4.91034i	−0.574712	+	0.574712i	−0.933442	−	0.358730i	$-0.883210\pi$
$73$	−4.91034	+	4.91034i	−0.574712	+	0.574712i	0.358730	+	0.933442i	$0.383210\pi$
$74$	10.7735			1.25240
$75$	1.61803	−	11.3262i	0.186834	−	1.30784i
$76$			6.53089i			0.749144i
$77$	−1.52896	+	2.94317i	−0.174241	+	0.335406i
$78$	−4.00000	−	4.00000i	−0.452911	−	0.452911i
$79$	7.19859			0.809904			0.404952	−	0.914338i	$-0.367288\pi$
$79$	7.19859			0.809904			0.404952	+	0.914338i	$0.367288\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$	10.7082			1.18980
$82$	5.38197	−	5.38197i	0.594339	−	0.594339i
$83$	−4.57649	+	4.57649i	−0.502335	+	0.502335i	−0.912163	−	0.409828i	$-0.865589\pi$
$83$	−4.57649	+	4.57649i	−0.502335	+	0.502335i	0.409828	+	0.912163i	$0.365589\pi$
$84$	−2.28825			−0.249668
$85$	0.540182	+	1.62054i	0.0585909	+	0.175773i
$86$	6.00000			0.646997
$87$	−16.2241	−	16.2241i	−1.73940	−	1.73940i
$88$	2.94317	+	1.52896i	0.313743	+	0.162988i
$89$			9.41641i			0.998137i	0.866562	+	0.499069i	$0.166324\pi$
$89$			9.41641i			0.998137i	−0.866562	+	0.499069i	$0.833676\pi$
$90$	−4.74342	+	1.58114i	−0.500000	+	0.166667i
$91$	−2.47214			−0.259150
$92$	4.85410	−	4.85410i	0.506075	−	0.506075i
$93$	12.4721	+	12.4721i	1.29330	+	1.29330i
$94$	6.65841			0.686762
$95$	13.0618	+	6.53089i	1.34011	+	0.670055i
$96$			2.28825i			0.233543i
$97$	−13.3262	+	13.3262i	−1.35307	+	1.35307i	−0.470874	+	0.882200i	$0.656061\pi$
$97$	−13.3262	+	13.3262i	−1.35307	+	1.35307i	−0.882200	+	0.470874i	$0.843939\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	7.07107	−	2.23607i	0.710669	−	0.224733i
$100$	−4.00000	+	3.00000i	−0.400000	+	0.300000i
$101$			6.32456i			0.629317i	0.949205	+	0.314658i	$0.101890\pi$
$101$			6.32456i			0.629317i	−0.949205	+	0.314658i	$0.898110\pi$
$102$	1.23607	−	1.23607i	0.122389	−	0.122389i
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$			2.47214i			0.242413i
$105$	−2.28825	+	4.57649i	−0.223310	+	0.446620i
$106$		−	6.19704i		−	0.601909i
$107$	−6.65841	−	6.65841i	−0.643692	−	0.643692i	0.307769	−	0.951461i	$-0.400418\pi$
$107$	−6.65841	−	6.65841i	−0.643692	−	0.643692i	−0.951461	+	0.307769i	$0.900418\pi$
$108$	−1.23607	−	1.23607i	−0.118941	−	0.118941i
$109$	−11.1074			−1.06389			−0.531947	−	0.846778i	$-0.678539\pi$
$109$	−11.1074			−1.06389			−0.531947	+	0.846778i	$0.678539\pi$
$110$	6.00110	−	4.35739i	0.572182	−	0.415461i
$111$	−24.6525			−2.33991
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−2.23607	−	2.23607i	−0.210352	−	0.210352i	0.594065	−	0.804417i	$-0.297522\pi$
$113$	−2.23607	−	2.23607i	−0.210352	−	0.210352i	−0.804417	+	0.594065i	$0.797522\pi$
$114$		−	14.9443i		−	1.39966i
$115$	−4.85410	−	14.5623i	−0.452647	−	1.35794i
$116$			10.0270i			0.930985i
$117$	3.90879	+	3.90879i	0.361368	+	0.361368i
$118$	−5.11667	+	5.11667i	−0.471028	+	0.471028i
$119$		−	0.763932i		−	0.0700295i
$120$	4.57649	+	2.28825i	0.417775	+	0.208887i
$121$	−9.00000	+	6.32456i	−0.818182	+	0.574960i
$122$	2.00000	−	2.00000i	0.181071	−	0.181071i
$123$	−12.3153	+	12.3153i	−1.11043	+	1.11043i
$124$		−	7.70820i		−	0.692217i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	2.23607			0.199205
$127$	−0.206331	−	0.206331i	−0.0183089	−	0.0183089i	0.697893	−	0.716202i	$-0.254121\pi$
$127$	−0.206331	−	0.206331i	−0.0183089	−	0.0183089i	−0.716202	+	0.697893i	$0.754121\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−13.7295			−1.20881
$130$	4.94427	+	2.47214i	0.433641	+	0.216821i
$131$			11.7751i			1.02879i	0.857552	+	0.514397i	$0.171984\pi$
$131$			11.7751i			1.02879i	−0.857552	+	0.514397i	$0.828016\pi$
$132$	−6.73471	−	3.49864i	−0.586181	−	0.304517i
$133$	−4.61803	−	4.61803i	−0.400434	−	0.400434i
$134$	−8.81913			−0.761857
$135$	−3.70820	+	1.23607i	−0.319151	+	0.106384i
$136$	−0.763932			−0.0655066
$137$	12.4164	−	12.4164i	1.06081	−	1.06081i	0.0627778	−	0.998028i	$-0.480004\pi$
$137$	12.4164	−	12.4164i	1.06081	−	1.06081i	0.998028	−	0.0627778i	$-0.0199959\pi$
$138$	−11.1074	+	11.1074i	−0.945523	+	0.945523i
$139$	17.4319			1.47856			0.739279	−	0.673400i	$-0.235167\pi$
$139$	17.4319			1.47856			0.739279	+	0.673400i	$0.235167\pi$
$140$	2.12132	−	0.707107i	0.179284	−	0.0597614i
$141$	−15.2361			−1.28311
$142$	8.48528	+	8.48528i	0.712069	+	0.712069i
$143$	−7.27593	−	3.77980i	−0.608444	−	0.316083i
$144$		−	2.23607i		−	0.186339i
$145$	20.0540	+	10.0270i	1.66540	+	0.832698i
$146$	−6.94427			−0.574712
$147$	1.61803	−	1.61803i	0.133453	−	0.133453i
$148$	7.61803	+	7.61803i	0.626199	+	0.626199i
$149$	−21.3407			−1.74830			−0.874150	−	0.485656i	$-0.838581\pi$
$149$	−21.3407			−1.74830			−0.874150	+	0.485656i	$0.838581\pi$
$150$	9.15298	−	6.86474i	0.747338	−	0.560503i
$151$			12.8554i			1.04616i	0.852283	+	0.523081i	$0.175217\pi$
$151$			12.8554i			1.04616i	−0.852283	+	0.523081i	$0.824783\pi$
$152$	−4.61803	+	4.61803i	−0.374572	+	0.374572i
$153$	−1.20788	+	1.20788i	−0.0976515	+	0.0976515i
$154$	−3.16228	+	1.00000i	−0.254824	+	0.0805823i
$155$	−15.4164	−	7.70820i	−1.23828	−	0.619138i
$156$		−	5.65685i		−	0.452911i
$157$	−14.4164	+	14.4164i	−1.15055	+	1.15055i	−0.164113	+	0.986442i	$0.552476\pi$
$157$	−14.4164	+	14.4164i	−1.15055	+	1.15055i	−0.986442	+	0.164113i	$0.947524\pi$
$158$	5.09017	+	5.09017i	0.404952	+	0.404952i
$159$			14.1803i			1.12457i
$160$	−0.707107	−	2.12132i	−0.0559017	−	0.167705i
$161$			6.86474i			0.541017i
$162$	7.57184	+	7.57184i	0.594900	+	0.594900i
$163$	1.76393	+	1.76393i	0.138162	+	0.138162i	0.772805	−	0.634643i	$-0.218853\pi$
$163$	1.76393	+	1.76393i	0.138162	+	0.138162i	−0.634643	+	0.772805i	$0.718853\pi$
$164$	7.61125			0.594339
$165$	−13.7320	+	9.97077i	−1.06903	+	0.776224i
$166$	−6.47214			−0.502335
$167$	13.0618	+	13.0618i	1.01075	+	1.01075i	0.999942	+	0.0108087i	$0.00344059\pi$
$167$	13.0618	+	13.0618i	1.01075	+	1.01075i	0.0108087	+	0.999942i	$0.496559\pi$
$168$	−1.61803	−	1.61803i	−0.124834	−	0.124834i
$169$			6.88854i			0.529888i
$170$	−0.763932	+	1.52786i	−0.0585909	+	0.117182i
$171$			14.6035i			1.11676i
$172$	4.24264	+	4.24264i	0.323498	+	0.323498i
$173$	7.07107	−	7.07107i	0.537603	−	0.537603i	−0.385221	−	0.922824i	$-0.625875\pi$
$173$	7.07107	−	7.07107i	0.537603	−	0.537603i	0.922824	+	0.385221i	$0.125875\pi$
$174$		−	22.9443i		−	1.73940i
$175$	0.707107	−	4.94975i	0.0534522	−	0.374166i
$176$	1.00000	+	3.16228i	0.0753778	+	0.238366i
$177$	11.7082	−	11.7082i	0.880042	−	0.880042i
$178$	−6.65841	+	6.65841i	−0.499069	+	0.499069i
$179$		−	1.70820i		−	0.127677i	−0.997960	−	0.0638386i	$-0.979666\pi$
$179$		−	1.70820i		−	0.127677i	0.997960	−	0.0638386i	$-0.0203343\pi$
$180$	−4.47214	−	2.23607i	−0.333333	−	0.166667i
$181$	1.52786			0.113565			0.0567826	−	0.998387i	$-0.481916\pi$
$181$	1.52786			0.113565			0.0567826	+	0.998387i	$0.481916\pi$
$182$	−1.74806	−	1.74806i	−0.129575	−	0.129575i
$183$	−4.57649	+	4.57649i	−0.338304	+	0.338304i
$184$	6.86474			0.506075
$185$	22.8541	−	7.61803i	1.68027	−	0.560089i
$186$			17.6383i			1.29330i
$187$	1.16802	−	2.24839i	0.0854143	−	0.164418i
$188$	4.70820	+	4.70820i	0.343381	+	0.343381i
$189$	1.74806			0.127153
$190$	4.61803	+	13.8541i	0.335027	+	1.00508i
$191$	6.65248			0.481356			0.240678	−	0.970605i	$-0.422630\pi$
$191$	6.65248			0.481356			0.240678	+	0.970605i	$0.422630\pi$
$192$	−1.61803	+	1.61803i	−0.116772	+	0.116772i
$193$	6.32456	−	6.32456i	0.455251	−	0.455251i	−0.441842	−	0.897093i	$-0.645675\pi$
$193$	6.32456	−	6.32456i	0.455251	−	0.455251i	0.897093	+	0.441842i	$0.145675\pi$
$194$	−18.8461			−1.35307
$195$	−11.3137	−	5.65685i	−0.810191	−	0.405096i
$196$	−1.00000			−0.0714286
$197$	−4.03631	−	4.03631i	−0.287575	−	0.287575i	0.548546	−	0.836121i	$-0.315182\pi$
$197$	−4.03631	−	4.03631i	−0.287575	−	0.287575i	−0.836121	+	0.548546i	$0.815182\pi$
$198$	6.58114	+	3.41886i	0.467701	+	0.242968i
$199$			3.52786i			0.250084i	0.992151	+	0.125042i	$0.0399065\pi$
$199$			3.52786i			0.250084i	−0.992151	+	0.125042i	$0.960093\pi$
$200$	−4.94975	−	0.707107i	−0.350000	−	0.0500000i
$201$	20.1803			1.42341
$202$	−4.47214	+	4.47214i	−0.314658	+	0.314658i
$203$	−7.09017	−	7.09017i	−0.497632	−	0.497632i
$204$	1.74806			0.122389
$205$	7.61125	−	15.2225i	0.531593	−	1.06319i
$206$		−	7.07107i		−	0.492665i
$207$	10.8541	−	10.8541i	0.754412	−	0.754412i
$208$	−1.74806	+	1.74806i	−0.121206	+	0.121206i
$209$	−6.53089	−	20.6525i	−0.451751	−	1.42856i
$210$	−4.85410	+	1.61803i	−0.334965	+	0.111655i
$211$		−	2.82843i		−	0.194717i	−0.995249	−	0.0973585i	$-0.968961\pi$
$211$		−	2.82843i		−	0.194717i	0.995249	−	0.0973585i	$-0.0310393\pi$
$212$	4.38197	−	4.38197i	0.300955	−	0.300955i
$213$	−19.4164	−	19.4164i	−1.33039	−	1.33039i
$214$		−	9.41641i		−	0.643692i
$215$	12.7279	−	4.24264i	0.868037	−	0.289346i
$216$		−	1.74806i		−	0.118941i
$217$	5.45052	+	5.45052i	0.370006	+	0.370006i
$218$	−7.85410	−	7.85410i	−0.531947	−	0.531947i
$219$	15.8902			1.07376
$220$	7.32456	+	1.16228i	0.493821	+	0.0783607i
$221$	1.88854			0.127037
$222$	−17.4319	−	17.4319i	−1.16995	−	1.16995i
$223$	11.7639	+	11.7639i	0.787771	+	0.787771i	0.981128	−	0.193357i	$-0.0619376\pi$
$223$	11.7639	+	11.7639i	0.787771	+	0.787771i	−0.193357	+	0.981128i	$0.561938\pi$
$224$			1.00000i			0.0668153i
$225$	−8.94427	+	6.70820i	−0.596285	+	0.447214i
$226$		−	3.16228i		−	0.210352i
$227$	−15.2712	−	15.2712i	−1.01359	−	1.01359i	−0.999906	−	0.0136792i	$-0.995646\pi$
$227$	−15.2712	−	15.2712i	−1.01359	−	1.01359i	−0.0136792	−	0.999906i	$-0.504354\pi$
$228$	10.5672	−	10.5672i	0.699830	−	0.699830i
$229$			16.7639i			1.10779i	0.832586	+	0.553896i	$0.186859\pi$
$229$			16.7639i			1.10779i	−0.832586	+	0.553896i	$0.813141\pi$
$230$	6.86474	−	13.7295i	0.452647	−	0.905295i
$231$	7.23607	−	2.28825i	0.476098	−	0.150556i
$232$	−7.09017	+	7.09017i	−0.465492	+	0.465492i
$233$	−7.07107	+	7.07107i	−0.463241	+	0.463241i	−0.899716	−	0.436475i	$-0.856227\pi$
$233$	−7.07107	+	7.07107i	−0.463241	+	0.463241i	0.436475	+	0.899716i	$0.356227\pi$
$234$			5.52786i			0.361368i
$235$	14.1246	−	4.70820i	0.921388	−	0.307129i
$236$	−7.23607			−0.471028
$237$	−11.6476	−	11.6476i	−0.756590	−	0.756590i
$238$	0.540182	−	0.540182i	0.0350148	−	0.0350148i
$239$	−18.0996			−1.17077			−0.585384	−	0.810756i	$-0.699056\pi$
$239$	−18.0996			−1.17077			−0.585384	+	0.810756i	$0.699056\pi$
$240$	1.61803	+	4.85410i	0.104444	+	0.313331i
$241$		−	4.78282i		−	0.308089i	−0.988064	−	0.154044i	$-0.950770\pi$
$241$		−	4.78282i		−	0.308089i	0.988064	−	0.154044i	$-0.0492299\pi$
$242$	−10.8361	−	1.89183i	−0.696571	−	0.121611i
$243$	−13.6180	−	13.6180i	−0.873597	−	0.873597i
$244$	2.82843			0.181071
$245$	−1.00000	+	2.00000i	−0.0638877	+	0.127775i
$246$	−17.4164			−1.11043
$247$	11.4164	−	11.4164i	0.726409	−	0.726409i
$248$	5.45052	−	5.45052i	0.346109	−	0.346109i
$249$	14.8098			0.938535
$250$	−6.36396	+	9.19239i	−0.402492	+	0.581378i
$251$	−8.94427			−0.564557			−0.282279	−	0.959332i	$-0.591090\pi$
$251$	−8.94427			−0.564557			−0.282279	+	0.959332i	$0.591090\pi$
$252$	1.58114	+	1.58114i	0.0996024	+	0.0996024i
$253$	−10.4959	+	20.2041i	−0.659873	+	1.27022i
$254$		−	0.291796i		−	0.0183089i
$255$	1.74806	−	3.49613i	0.109468	−	0.218936i
$256$	1.00000			0.0625000
$257$	5.14590	−	5.14590i	0.320992	−	0.320992i	−0.528155	−	0.849148i	$-0.677116\pi$
$257$	5.14590	−	5.14590i	0.320992	−	0.320992i	0.849148	+	0.528155i	$0.177116\pi$
$258$	−9.70820	−	9.70820i	−0.604406	−	0.604406i
$259$	−10.7735			−0.669434
$260$	1.74806	+	5.24419i	0.108410	+	0.325231i
$261$			22.4211i			1.38783i
$262$	−8.32624	+	8.32624i	−0.514397	+	0.514397i
$263$	3.70246	−	3.70246i	0.228303	−	0.228303i	−0.583680	−	0.811984i	$-0.698388\pi$
$263$	3.70246	−	3.70246i	0.228303	−	0.228303i	0.811984	+	0.583680i	$0.198388\pi$
$264$	−2.28825	−	7.23607i	−0.140832	−	0.445349i
$265$	−4.38197	−	13.1459i	−0.269182	−	0.807546i
$266$		−	6.53089i		−	0.400434i
$267$	15.2361	−	15.2361i	0.932432	−	0.932432i
$268$	−6.23607	−	6.23607i	−0.380928	−	0.380928i
$269$			12.1803i			0.742648i	0.928503	+	0.371324i	$0.121096\pi$
$269$			12.1803i			0.742648i	−0.928503	+	0.371324i	$0.878904\pi$
$270$	−3.49613	−	1.74806i	−0.212768	−	0.106384i
$271$			5.91189i			0.359122i	0.983747	+	0.179561i	$0.0574677\pi$
$271$			5.91189i			0.359122i	−0.983747	+	0.179561i	$0.942532\pi$
$272$	−0.540182	−	0.540182i	−0.0327533	−	0.0327533i
$273$	4.00000	+	4.00000i	0.242091	+	0.242091i
$274$	17.5595			1.06081
$275$	9.64911	−	13.4868i	0.581863	−	0.813287i
$276$	−15.7082			−0.945523
$277$	11.8539	+	11.8539i	0.712231	+	0.712231i	0.967002	−	0.254770i	$-0.0819999\pi$
$277$	11.8539	+	11.8539i	0.712231	+	0.712231i	−0.254770	+	0.967002i	$0.582000\pi$
$278$	12.3262	+	12.3262i	0.739279	+	0.739279i
$279$		−	17.2361i		−	1.03190i
$280$	2.00000	+	1.00000i	0.119523	+	0.0597614i
$281$		−	20.0540i		−	1.19632i	−0.801376	−	0.598162i	$-0.795898\pi$
$281$		−	20.0540i		−	1.19632i	0.801376	−	0.598162i	$-0.204102\pi$
$282$	−10.7735	−	10.7735i	−0.641554	−	0.641554i
$283$	5.45052	−	5.45052i	0.324000	−	0.324000i	−0.526299	−	0.850299i	$-0.676421\pi$
$283$	5.45052	−	5.45052i	0.324000	−	0.324000i	0.850299	+	0.526299i	$0.176421\pi$
$284$			12.0000i			0.712069i
$285$	−10.5672	−	31.7016i	−0.625947	−	1.87784i
$286$	−2.47214	−	7.81758i	−0.146180	−	0.462263i
$287$	−5.38197	+	5.38197i	−0.317687	+	0.317687i
$288$	1.58114	−	1.58114i	0.0931695	−	0.0931695i
$289$		−	16.4164i		−	0.965671i
$290$	7.09017	+	21.2705i	0.416349	+	1.24905i
$291$	43.1246			2.52801
$292$	−4.91034	−	4.91034i	−0.287356	−	0.287356i
$293$	13.0618	−	13.0618i	0.763077	−	0.763077i	−0.213800	−	0.976877i	$-0.568584\pi$
$293$	13.0618	−	13.0618i	0.763077	−	0.763077i	0.976877	+	0.213800i	$0.0685842\pi$
$294$	2.28825			0.133453
$295$	−7.23607	+	14.4721i	−0.421300	+	0.842600i
$296$			10.7735i			0.626199i
$297$	5.14486	+	2.67272i	0.298535	+	0.155087i
$298$	−15.0902	−	15.0902i	−0.874150	−	0.874150i
$299$	−16.9706			−0.981433
$300$	11.3262	+	1.61803i	0.653921	+	0.0934172i
$301$	−6.00000			−0.345834
$302$	−9.09017	+	9.09017i	−0.523081	+	0.523081i
$303$	10.2333	−	10.2333i	0.587890	−	0.587890i
$304$	−6.53089			−0.374572
$305$	2.82843	−	5.65685i	0.161955	−	0.323911i
$306$	−1.70820			−0.0976515
$307$	4.37016	+	4.37016i	0.249418	+	0.249418i	0.820732	−	0.571314i	$-0.193566\pi$
$307$	4.37016	+	4.37016i	0.249418	+	0.249418i	−0.571314	+	0.820732i	$0.693566\pi$
$308$	−2.94317	−	1.52896i	−0.167703	−	0.0871206i
$309$			16.1803i			0.920467i
$310$	−5.45052	−	16.3516i	−0.309569	−	0.928707i
$311$	24.1803			1.37114			0.685571	−	0.728006i	$-0.259553\pi$
$311$	24.1803			1.37114			0.685571	+	0.728006i	$0.259553\pi$
$312$	4.00000	−	4.00000i	0.226455	−	0.226455i
$313$	−0.381966	−	0.381966i	−0.0215900	−	0.0215900i	0.696229	−	0.717819i	$-0.254860\pi$
$313$	−0.381966	−	0.381966i	−0.0215900	−	0.0215900i	−0.717819	+	0.696229i	$0.754860\pi$
$314$	−20.3879			−1.15055
$315$	4.74342	−	1.58114i	0.267261	−	0.0890871i
$316$			7.19859i			0.404952i
$317$	−1.61803	+	1.61803i	−0.0908778	+	0.0908778i	−0.751084	−	0.660206i	$-0.770469\pi$
$317$	−1.61803	+	1.61803i	−0.0908778	+	0.0908778i	0.660206	+	0.751084i	$0.270469\pi$
$318$	−10.0270	+	10.0270i	−0.562287	+	0.562287i
$319$	−10.0270	−	31.7082i	−0.561405	−	1.77532i
$320$	1.00000	−	2.00000i	0.0559017	−	0.111803i
$321$			21.5471i			1.20264i
$322$	−4.85410	+	4.85410i	−0.270509	+	0.270509i
$323$	3.52786	+	3.52786i	0.196296	+	0.196296i
$324$			10.7082i			0.594900i
$325$	12.2364	+	1.74806i	0.678756	+	0.0969651i
$326$			2.49458i			0.138162i
$327$	17.9721	+	17.9721i	0.993860	+	0.993860i
$328$	5.38197	+	5.38197i	0.297169	+	0.297169i
$329$	−6.65841			−0.367090
$330$	−16.7604	−	2.65958i	−0.922629	−	0.146405i
$331$	−8.29180			−0.455758			−0.227879	−	0.973689i	$-0.573179\pi$
$331$	−8.29180			−0.455758			−0.227879	+	0.973689i	$0.573179\pi$
$332$	−4.57649	−	4.57649i	−0.251168	−	0.251168i
$333$	17.0344	+	17.0344i	0.933482	+	0.933482i
$334$			18.4721i			1.01075i
$335$	−18.7082	+	6.23607i	−1.02214	+	0.340713i
$336$		−	2.28825i		−	0.124834i
$337$	13.3956	+	13.3956i	0.729706	+	0.729706i	0.970561	−	0.240855i	$-0.0774278\pi$
$337$	13.3956	+	13.3956i	0.729706	+	0.729706i	−0.240855	+	0.970561i	$0.577428\pi$
$338$	−4.87094	+	4.87094i	−0.264944	+	0.264944i
$339$			7.23607i			0.393009i
$340$	−1.62054	+	0.540182i	−0.0878864	+	0.0292955i
$341$	7.70820	+	24.3755i	0.417423	+	1.32001i
$342$	−10.3262	+	10.3262i	−0.558379	+	0.558379i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$			6.00000i			0.323498i
$345$	−15.7082	+	31.4164i	−0.845701	+	1.69140i
$346$	10.0000			0.537603
$347$	6.40337	+	6.40337i	0.343751	+	0.343751i	0.857775	−	0.514025i	$-0.171846\pi$
$347$	6.40337	+	6.40337i	0.343751	+	0.343751i	−0.514025	+	0.857775i	$0.671846\pi$
$348$	16.2241	−	16.2241i	0.869700	−	0.869700i
$349$	8.74032			0.467859			0.233929	−	0.972254i	$-0.424842\pi$
$349$	8.74032			0.467859			0.233929	+	0.972254i	$0.424842\pi$
$350$	4.00000	−	3.00000i	0.213809	−	0.160357i
$351$			4.32145i			0.230662i
$352$	−1.52896	+	2.94317i	−0.0814939	+	0.156872i
$353$	−18.0902	−	18.0902i	−0.962843	−	0.962843i	0.0364914	−	0.999334i	$-0.488382\pi$
$353$	−18.0902	−	18.0902i	−0.962843	−	0.962843i	−0.999334	+	0.0364914i	$0.988382\pi$
$354$	16.5579			0.880042
$355$	24.0000	+	12.0000i	1.27379	+	0.636894i
$356$	−9.41641			−0.499069
$357$	−1.23607	+	1.23607i	−0.0654197	+	0.0654197i
$358$	1.20788	−	1.20788i	0.0638386	−	0.0638386i
$359$	−20.6730			−1.09108			−0.545540	−	0.838085i	$-0.683675\pi$
$359$	−20.6730			−1.09108			−0.545540	+	0.838085i	$0.683675\pi$
$360$	−1.58114	−	4.74342i	−0.0833333	−	0.250000i
$361$	23.6525			1.24487
$362$	1.08036	+	1.08036i	0.0567826	+	0.0567826i
$363$	24.7957	+	4.32896i	1.30143	+	0.227211i
$364$		−	2.47214i		−	0.129575i
$365$	−14.7310	+	4.91034i	−0.771057	+	0.257019i
$366$	−6.47214			−0.338304
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	−0.781058	−	0.624459i	$-0.785320\pi$
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	0.624459	+	0.781058i	$0.285320\pi$
$368$	4.85410	+	4.85410i	0.253038	+	0.253038i
$369$	17.0193			0.885988
$370$	21.5471	+	10.7735i	1.12018	+	0.560089i
$371$			6.19704i			0.321734i
$372$	−12.4721	+	12.4721i	−0.646650	+	0.646650i
$373$	−7.94510	+	7.94510i	−0.411382	+	0.411382i	−0.882220	−	0.470838i	$-0.843952\pi$
$373$	−7.94510	+	7.94510i	−0.411382	+	0.411382i	0.470838	+	0.882220i	$0.343952\pi$
$374$	2.41577	−	0.763932i	0.124916	−	0.0395020i
$375$	14.5623	−	21.0344i	0.751994	−	1.08621i
$376$			6.65841i			0.343381i
$377$	17.5279	−	17.5279i	0.902731	−	0.902731i
$378$	1.23607	+	1.23607i	0.0635765	+	0.0635765i
$379$			31.8885i			1.63800i	0.573790	+	0.819002i	$0.305472\pi$
$379$			31.8885i			1.63800i	−0.573790	+	0.819002i	$0.694528\pi$
$380$	−6.53089	+	13.0618i	−0.335027	+	0.670055i
$381$			0.667701i			0.0342074i
$382$	4.70401	+	4.70401i	0.240678	+	0.240678i
$383$	1.76393	+	1.76393i	0.0901327	+	0.0901327i	0.750736	−	0.660603i	$-0.229699\pi$
$383$	1.76393	+	1.76393i	0.0901327	+	0.0901327i	−0.660603	+	0.750736i	$0.729699\pi$
$384$	−2.28825			−0.116772
$385$	−6.00110	+	4.35739i	−0.305844	+	0.222073i
$386$	8.94427			0.455251
$387$	9.48683	+	9.48683i	0.482243	+	0.482243i
$388$	−13.3262	−	13.3262i	−0.676537	−	0.676537i
$389$		−	6.18034i		−	0.313356i	−0.987650	−	0.156678i	$-0.949922\pi$
$389$		−	6.18034i		−	0.313356i	0.987650	−	0.156678i	$-0.0500784\pi$
$390$	−4.00000	−	12.0000i	−0.202548	−	0.607644i
$391$		−	5.24419i		−	0.265210i
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	19.0525	−	19.0525i	0.961070	−	0.961070i
$394$		−	5.70820i		−	0.287575i
$395$	14.3972	+	7.19859i	0.724400	+	0.362200i
$396$	2.23607	+	7.07107i	0.112367	+	0.355335i
$397$	−2.05573	+	2.05573i	−0.103174	+	0.103174i	−0.756810	−	0.653635i	$-0.773243\pi$
$397$	−2.05573	+	2.05573i	−0.103174	+	0.103174i	0.653635	+	0.756810i	$0.273243\pi$
$398$	−2.49458	+	2.49458i	−0.125042	+	0.125042i
$399$			14.9443i			0.748149i
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	−2.29180			−0.114447			−0.0572234	−	0.998361i	$-0.518225\pi$
$401$	−2.29180			−0.114447			−0.0572234	+	0.998361i	$0.518225\pi$
$402$	14.2697	+	14.2697i	0.711706	+	0.711706i
$403$	−13.4744	+	13.4744i	−0.671209	+	0.671209i
$404$	−6.32456			−0.314658
$405$	21.4164	+	10.7082i	1.06419	+	0.532095i
$406$		−	10.0270i		−	0.497632i
$407$	−31.7084	−	16.4723i	−1.57173	−	0.816502i
$408$	1.23607	+	1.23607i	0.0611945	+	0.0611945i
$409$	11.7751			0.582240			0.291120	−	0.956687i	$-0.405972\pi$
$409$	11.7751			0.582240			0.291120	+	0.956687i	$0.405972\pi$
$410$	16.1459	−	5.38197i	0.797389	−	0.265796i
$411$	−40.1803			−1.98195
$412$	5.00000	−	5.00000i	0.246332	−	0.246332i
$413$	5.11667	−	5.11667i	0.251775	−	0.251775i
$414$	15.3500			0.754412
$415$	−13.7295	+	4.57649i	−0.673953	+	0.224651i
$416$	−2.47214			−0.121206
$417$	−28.2055	−	28.2055i	−1.38123	−	1.38123i
$418$	9.98547	−	19.2215i	0.488405	−	0.940156i
$419$		−	32.3607i		−	1.58092i	−0.612512	−	0.790461i	$-0.709841\pi$
$419$		−	32.3607i		−	1.58092i	0.612512	−	0.790461i	$-0.290159\pi$
$420$	−4.57649	−	2.28825i	−0.223310	−	0.111655i
$421$	1.23607			0.0602423			0.0301211	−	0.999546i	$-0.490411\pi$
$421$	1.23607			0.0602423			0.0301211	+	0.999546i	$0.490411\pi$
$422$	2.00000	−	2.00000i	0.0973585	−	0.0973585i
$423$	10.5279	+	10.5279i	0.511882	+	0.511882i
$424$	6.19704			0.300955
$425$	−0.540182	+	3.78127i	−0.0262027	+	0.183419i
$426$		−	27.4589i		−	1.33039i
$427$	−2.00000	+	2.00000i	−0.0967868	+	0.0967868i
$428$	6.65841	−	6.65841i	0.321846	−	0.321846i
$429$	5.65685	+	17.8885i	0.273115	+	0.863667i
$430$	12.0000	+	6.00000i	0.578691	+	0.289346i
$431$		−	8.27895i		−	0.398783i	−0.979920	−	0.199392i	$-0.936103\pi$
$431$		−	8.27895i		−	0.398783i	0.979920	−	0.199392i	$-0.0638965\pi$
$432$	1.23607	−	1.23607i	0.0594703	−	0.0594703i
$433$	−15.6180	−	15.6180i	−0.750555	−	0.750555i	0.224028	−	0.974583i	$-0.428079\pi$
$433$	−15.6180	−	15.6180i	−0.750555	−	0.750555i	−0.974583	+	0.224028i	$0.928079\pi$
$434$			7.70820i			0.370006i
$435$	−16.2241	−	48.6722i	−0.777884	−	2.33365i
$436$		−	11.1074i		−	0.531947i
$437$	−31.7016	−	31.7016i	−1.51649	−	1.51649i
$438$	11.2361	+	11.2361i	0.536880	+	0.536880i
$439$	5.91189			0.282159			0.141080	−	0.989998i	$-0.454943\pi$
$439$	5.91189			0.282159			0.141080	+	0.989998i	$0.454943\pi$
$440$	4.35739	+	6.00110i	0.207730	+	0.286091i
$441$	−2.23607			−0.106479
$442$	1.33540	+	1.33540i	0.0635186	+	0.0635186i
$443$	16.5279	+	16.5279i	0.785263	+	0.785263i	0.980713	−	0.195451i	$-0.0626170\pi$
$443$	16.5279	+	16.5279i	0.785263	+	0.785263i	−0.195451	+	0.980713i	$0.562617\pi$
$444$		−	24.6525i		−	1.16995i
$445$	−9.41641	+	18.8328i	−0.446381	+	0.892761i
$446$			16.6367i			0.787771i
$447$	34.5300	+	34.5300i	1.63321	+	1.63321i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$		−	25.2361i		−	1.19096i	−0.803369	−	0.595482i	$-0.796961\pi$
$449$		−	25.2361i		−	1.19096i	0.803369	−	0.595482i	$-0.203039\pi$
$450$	−11.0680	−	1.58114i	−0.521749	−	0.0745356i
$451$	−24.0689	+	7.61125i	−1.13336	+	0.358400i
$452$	2.23607	−	2.23607i	0.105176	−	0.105176i
$453$	20.8005	−	20.8005i	0.977295	−	0.977295i
$454$		−	21.5967i		−	1.01359i
$455$	−4.94427	−	2.47214i	−0.231791	−	0.115896i
$456$	14.9443			0.699830
$457$	23.2163	+	23.2163i	1.08601	+	1.08601i	0.995935	+	0.0900783i	$0.0287117\pi$
$457$	23.2163	+	23.2163i	1.08601	+	1.08601i	0.0900783	+	0.995935i	$0.471288\pi$
$458$	−11.8539	+	11.8539i	−0.553896	+	0.553896i
$459$	−1.33540			−0.0623312
$460$	14.5623	−	4.85410i	0.678971	−	0.226324i
$461$		−	3.90879i		−	0.182051i	−0.995849	−	0.0910253i	$-0.970986\pi$
$461$		−	3.90879i		−	0.182051i	0.995849	−	0.0910253i	$-0.0290144\pi$
$462$	6.73471	+	3.49864i	0.313327	+	0.162771i
$463$	8.27051	+	8.27051i	0.384363	+	0.384363i	0.872671	−	0.488308i	$-0.162386\pi$
$463$	8.27051	+	8.27051i	0.384363	+	0.384363i	−0.488308	+	0.872671i	$0.662386\pi$
$464$	−10.0270			−0.465492
$465$	12.4721	+	37.4164i	0.578381	+	1.73514i
$466$	−10.0000			−0.463241
$467$	−10.3820	+	10.3820i	−0.480420	+	0.480420i	−0.905266	−	0.424846i	$-0.860328\pi$
$467$	−10.3820	+	10.3820i	−0.480420	+	0.480420i	0.424846	+	0.905266i	$0.360328\pi$
$468$	−3.90879	+	3.90879i	−0.180684	+	0.180684i
$469$	8.81913			0.407230
$470$	13.3168	+	6.65841i	0.614259	+	0.307129i
$471$	46.6525			2.14963
$472$	−5.11667	−	5.11667i	−0.235514	−	0.235514i
$473$	−17.6590	−	9.17377i	−0.811964	−	0.421810i
$474$		−	16.4721i		−	0.756590i
$475$	19.5927	+	26.1235i	0.898973	+	1.19863i
$476$	0.763932			0.0350148
$477$	9.79837	−	9.79837i	0.448637	−	0.448637i
$478$	−12.7984	−	12.7984i	−0.585384	−	0.585384i
$479$	29.6197			1.35336			0.676679	−	0.736278i	$-0.263419\pi$
$479$	29.6197			1.35336			0.676679	+	0.736278i	$0.263419\pi$
$480$	−2.28825	+	4.57649i	−0.104444	+	0.208887i
$481$		−	26.6336i		−	1.21439i
$482$	3.38197	−	3.38197i	0.154044	−	0.154044i
$483$	11.1074	−	11.1074i	0.505403	−	0.505403i
$484$	−6.32456	−	9.00000i	−0.287480	−	0.409091i
$485$	−39.9787	+	13.3262i	−1.81534	+	0.605113i
$486$		−	19.2588i		−	0.873597i
$487$	−10.3820	+	10.3820i	−0.470452	+	0.470452i	−0.902061	−	0.431609i	$-0.857946\pi$
$487$	−10.3820	+	10.3820i	−0.470452	+	0.470452i	0.431609	+	0.902061i	$0.357946\pi$
$488$	2.00000	+	2.00000i	0.0905357	+	0.0905357i
$489$		−	5.70820i		−	0.258134i
$490$	−2.12132	+	0.707107i	−0.0958315	+	0.0319438i
$491$		−	35.2765i		−	1.59201i	−0.605292	−	0.796004i	$-0.706944\pi$
$491$		−	35.2765i		−	1.59201i	0.605292	−	0.796004i	$-0.293056\pi$
$492$	−12.3153	−	12.3153i	−0.555215	−	0.555215i
$493$	5.41641	+	5.41641i	0.243943	+	0.243943i
$494$	16.1452			0.726409
$495$	16.3782	+	2.59893i	0.736146	+	0.116813i
$496$	7.70820			0.346109
$497$	−8.48528	−	8.48528i	−0.380617	−	0.380617i
$498$	10.4721	+	10.4721i	0.469268	+	0.469268i
$499$			3.70820i			0.166002i	0.996549	+	0.0830010i	$0.0264505\pi$
$499$			3.70820i			0.166002i	−0.996549	+	0.0830010i	$0.973550\pi$
$500$	−11.0000	+	2.00000i	−0.491935	+	0.0894427i
$501$		−	42.2688i		−	1.88843i
$502$	−6.32456	−	6.32456i	−0.282279	−	0.282279i
$503$	−9.15298	+	9.15298i	−0.408111	+	0.408111i	−0.881080	−	0.472968i	$-0.843183\pi$
$503$	−9.15298	+	9.15298i	−0.408111	+	0.408111i	0.472968	+	0.881080i	$0.343183\pi$
$504$			2.23607i			0.0996024i
$505$	−6.32456	+	12.6491i	−0.281439	+	0.562878i
$506$	−21.7082	+	6.86474i	−0.965047	+	0.305175i
$507$	11.1459	−	11.1459i	0.495007	−	0.495007i
$508$	0.206331	−	0.206331i	0.00915446	−	0.00915446i
$509$			5.52786i			0.245018i	0.992467	+	0.122509i	$0.0390941\pi$
$509$			5.52786i			0.245018i	−0.992467	+	0.122509i	$0.960906\pi$
$510$	3.70820	−	1.23607i	0.164202	−	0.0547340i
$511$	6.94427			0.307197
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−8.07262	+	8.07262i	−0.356415	+	0.356415i
$514$	7.27740			0.320992
$515$	−5.00000	−	15.0000i	−0.220326	−	0.660979i
$516$		−	13.7295i		−	0.604406i
$517$	−19.5969	−	10.1804i	−0.861869	−	0.447735i
$518$	−7.61803	−	7.61803i	−0.334717	−	0.334717i
$519$	−22.8825			−1.00443
$520$	−2.47214	+	4.94427i	−0.108410	+	0.216821i
$521$	−9.81966			−0.430207			−0.215104	−	0.976591i	$-0.569009\pi$
$521$	−9.81966			−0.430207			−0.215104	+	0.976591i	$0.569009\pi$
$522$	−15.8541	+	15.8541i	−0.693915	+	0.693915i
$523$	−24.4242	+	24.4242i	−1.06800	+	1.06800i	−0.0704822	+	0.997513i	$0.522454\pi$
$523$	−24.4242	+	24.4242i	−1.06800	+	1.06800i	−0.997513	+	0.0704822i	$0.977546\pi$
$524$	−11.7751			−0.514397
$525$	−9.15298	+	6.86474i	−0.399469	+	0.299602i
$526$	5.23607			0.228303
$527$	−4.16383	−	4.16383i	−0.181379	−	0.181379i
$528$	3.49864	−	6.73471i	0.152259	−	0.293090i
$529$			24.1246i			1.04890i
$530$	6.19704	−	12.3941i	0.269182	−	0.538364i
$531$	−16.1803			−0.702167
$532$	4.61803	−	4.61803i	0.200217	−	0.200217i
$533$	−13.3050	−	13.3050i	−0.576301	−	0.576301i
$534$	21.5471			0.932432
$535$	−6.65841	−	19.9752i	−0.287868	−	0.863604i
$536$		−	8.81913i		−	0.380928i
$537$	−2.76393	+	2.76393i	−0.119272	+	0.119272i
$538$	−8.61280	+	8.61280i	−0.371324	+	0.371324i
$539$	3.16228	−	1.00000i	0.136209	−	0.0430730i
$540$	−1.23607	−	3.70820i	−0.0531919	−	0.159576i
$541$			8.69161i			0.373682i	0.982390	+	0.186841i	$0.0598249\pi$
$541$			8.69161i			0.373682i	−0.982390	+	0.186841i	$0.940175\pi$
$542$	−4.18034	+	4.18034i	−0.179561	+	0.179561i
$543$	−2.47214	−	2.47214i	−0.106090	−	0.106090i
$544$		−	0.763932i		−	0.0327533i
$545$	−22.2148	−	11.1074i	−0.951576	−	0.475788i
$546$			5.65685i			0.242091i
$547$	23.9628	+	23.9628i	1.02458	+	1.02458i	0.999690	+	0.0248859i	$0.00792223\pi$
$547$	23.9628	+	23.9628i	1.02458	+	1.02458i	0.0248859	+	0.999690i	$0.492078\pi$
$548$	12.4164	+	12.4164i	0.530403	+	0.530403i
$549$	6.32456			0.269925
$550$	16.3596	−	2.71368i	0.697575	−	0.115712i
$551$	65.4853			2.78977
$552$	−11.1074	−	11.1074i	−0.472761	−	0.472761i
$553$	−5.09017	−	5.09017i	−0.216456	−	0.216456i
$554$			16.7639i			0.712231i
$555$	−49.3050	−	24.6525i	−2.09288	−	1.04644i
$556$			17.4319i			0.739279i
$557$	13.6507	+	13.6507i	0.578397	+	0.578397i	0.934461	−	0.356064i	$-0.115882\pi$
$557$	13.6507	+	13.6507i	0.578397	+	0.578397i	−0.356064	+	0.934461i	$0.615882\pi$
$558$	12.1877	−	12.1877i	0.515948	−	0.515948i
$559$		−	14.8328i		−	0.627361i
$560$	0.707107	+	2.12132i	0.0298807	+	0.0896421i
$561$	−5.52786	+	1.74806i	−0.233387	+	0.0738033i
$562$	14.1803	−	14.1803i	0.598162	−	0.598162i
$563$	6.99226	−	6.99226i	0.294688	−	0.294688i	−0.544241	−	0.838929i	$-0.683182\pi$
$563$	6.99226	−	6.99226i	0.294688	−	0.294688i	0.838929	+	0.544241i	$0.183182\pi$
$564$		−	15.2361i		−	0.641554i
$565$	−2.23607	−	6.70820i	−0.0940721	−	0.282216i
$566$	7.70820			0.324000
$567$	−7.57184	−	7.57184i	−0.317988	−	0.317988i
$568$	−8.48528	+	8.48528i	−0.356034	+	0.356034i
$569$	39.4404			1.65343			0.826713	−	0.562624i	$-0.190208\pi$
$569$	39.4404			1.65343			0.826713	+	0.562624i	$0.190208\pi$
$570$	14.9443	−	29.8885i	0.625947	−	1.25189i
$571$		−	26.5362i		−	1.11051i	−0.831682	−	0.555253i	$-0.812621\pi$
$571$		−	26.5362i		−	1.11051i	0.831682	−	0.555253i	$-0.187379\pi$
$572$	3.77980	−	7.27593i	0.158041	−	0.304222i
$573$	−10.7639	−	10.7639i	−0.449670	−	0.449670i
$574$	−7.61125			−0.317687
$575$	4.85410	−	33.9787i	0.202430	−	1.41701i
$576$	2.23607			0.0931695
$577$	5.61803	−	5.61803i	0.233882	−	0.233882i	−0.580429	−	0.814311i	$-0.697115\pi$
$577$	5.61803	−	5.61803i	0.233882	−	0.233882i	0.814311	+	0.580429i	$0.197115\pi$
$578$	11.6082	−	11.6082i	0.482836	−	0.482836i
$579$	−20.4667			−0.850567
$580$	−10.0270	+	20.0540i	−0.416349	+	0.832698i
$581$	6.47214			0.268509
$582$	30.4937	+	30.4937i	1.26400	+	1.26400i
$583$	−9.47503	+	18.2390i	−0.392416	+	0.755381i
$584$		−	6.94427i		−	0.287356i
$585$	3.90879	+	11.7264i	0.161609	+	0.484826i
$586$	18.4721			0.763077
$587$	−1.79837	+	1.79837i	−0.0742268	+	0.0742268i	−0.743246	−	0.669019i	$-0.766715\pi$
$587$	−1.79837	+	1.79837i	−0.0742268	+	0.0742268i	0.669019	+	0.743246i	$0.266715\pi$
$588$	1.61803	+	1.61803i	0.0667266	+	0.0667266i
$589$	−50.3414			−2.07428
$590$	−15.3500	+	5.11667i	−0.631950	+	0.210650i
$591$			13.0618i			0.537290i
$592$	−7.61803	+	7.61803i	−0.313099	+	0.313099i
$593$	−19.0525	+	19.0525i	−0.782391	+	0.782391i	−0.980234	−	0.197842i	$-0.936607\pi$
$593$	−19.0525	+	19.0525i	−0.782391	+	0.782391i	0.197842	+	0.980234i	$0.436607\pi$
$594$	1.74806	+	5.52786i	0.0717239	+	0.226811i
$595$	0.763932	−	1.52786i	0.0313182	−	0.0626363i
$596$		−	21.3407i		−	0.874150i
$597$	5.70820	−	5.70820i	0.233621	−	0.233621i
$598$	−12.0000	−	12.0000i	−0.490716	−	0.490716i
$599$			12.0000i			0.490307i	0.969484	+	0.245153i	$0.0788383\pi$
$599$			12.0000i			0.490307i	−0.969484	+	0.245153i	$0.921162\pi$
$600$	6.86474	+	9.15298i	0.280252	+	0.373669i
$601$		−	8.02391i		−	0.327302i	−0.986518	−	0.163651i	$-0.947673\pi$
$601$		−	8.02391i		−	0.327302i	0.986518	−	0.163651i	$-0.0523271\pi$
$602$	−4.24264	−	4.24264i	−0.172917	−	0.172917i
$603$	−13.9443	−	13.9443i	−0.567855	−	0.567855i
$604$	−12.8554			−0.523081
$605$	−24.3246	+	3.64911i	−0.988934	+	0.148357i
$606$	14.4721			0.587890
$607$	3.16228	+	3.16228i	0.128353	+	0.128353i	0.768365	−	0.640012i	$-0.221071\pi$
$607$	3.16228	+	3.16228i	0.128353	+	0.128353i	−0.640012	+	0.768365i	$0.721071\pi$
$608$	−4.61803	−	4.61803i	−0.187286	−	0.187286i
$609$			22.9443i			0.929749i
$610$	6.00000	−	2.00000i	0.242933	−	0.0809776i
$611$		−	16.4605i		−	0.665920i
$612$	−1.20788	−	1.20788i	−0.0488258	−	0.0488258i
$613$	19.7202	−	19.7202i	0.796491	−	0.796491i	−0.186050	−	0.982540i	$-0.559569\pi$
$613$	19.7202	−	19.7202i	0.796491	−	0.796491i	0.982540	+	0.186050i	$0.0595686\pi$
$614$			6.18034i			0.249418i
$615$	−36.9458	+	12.3153i	−1.48980	+	0.496599i
$616$	−1.00000	−	3.16228i	−0.0402911	−	0.127412i
$617$	26.8885	−	26.8885i	1.08249	−	1.08249i	0.0862155	−	0.996277i	$-0.472523\pi$
$617$	26.8885	−	26.8885i	1.08249	−	1.08249i	0.996277	−	0.0862155i	$-0.0274774\pi$
$618$	−11.4412	+	11.4412i	−0.460234	+	0.460234i
$619$		−	22.4721i		−	0.903231i	−0.892213	−	0.451616i	$-0.850848\pi$
$619$		−	22.4721i		−	0.903231i	0.892213	−	0.451616i	$-0.149152\pi$
$620$	7.70820	−	15.4164i	0.309569	−	0.619138i
$621$	12.0000			0.481543
$622$	17.0981	+	17.0981i	0.685571	+	0.685571i
$623$	6.65841	−	6.65841i	0.266763	−	0.266763i
$624$	5.65685			0.226455
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		−	0.540182i		−	0.0215900i
$627$	−22.8492	+	43.9836i	−0.912510	+	1.75654i
$628$	−14.4164	−	14.4164i	−0.575277	−	0.575277i
$629$	8.23024			0.328161
$630$	4.47214	+	2.23607i	0.178174	+	0.0890871i
$631$	−6.47214			−0.257652			−0.128826	−	0.991667i	$-0.541121\pi$
$631$	−6.47214			−0.257652			−0.128826	+	0.991667i	$0.541121\pi$
$632$	−5.09017	+	5.09017i	−0.202476	+	0.202476i
$633$	−4.57649	+	4.57649i	−0.181899	+	0.181899i
$634$	−2.28825			−0.0908778
$635$	−0.206331	−	0.618993i	−0.00818800	−	0.0245640i
$636$	−14.1803			−0.562287
$637$	1.74806	+	1.74806i	0.0692608	+	0.0692608i
$638$	15.3309	−	29.5113i	0.606957	−	1.16836i
$639$			26.8328i			1.06149i
$640$	2.12132	−	0.707107i	0.0838525	−	0.0279508i
$641$	−18.8328			−0.743851			−0.371926	−	0.928262i	$-0.621302\pi$
$641$	−18.8328			−0.743851			−0.371926	+	0.928262i	$0.621302\pi$
$642$	−15.2361	+	15.2361i	−0.601320	+	0.601320i
$643$	30.2705	+	30.2705i	1.19375	+	1.19375i	0.976005	+	0.217747i	$0.0698708\pi$
$643$	30.2705	+	30.2705i	1.19375	+	1.19375i	0.217747	+	0.976005i	$0.430129\pi$
$644$	−6.86474			−0.270509
$645$	−27.4589	−	13.7295i	−1.08119	−	0.540597i
$646$			4.98915i			0.196296i
$647$	−9.76393	+	9.76393i	−0.383860	+	0.383860i	−0.872491	−	0.488631i	$-0.837496\pi$
$647$	−9.76393	+	9.76393i	−0.383860	+	0.383860i	0.488631	+	0.872491i	$0.337496\pi$
$648$	−7.57184	+	7.57184i	−0.297450	+	0.297450i
$649$	22.8825	−	7.23607i	0.898215	−	0.284041i
$650$	7.41641	+	9.88854i	0.290895	+	0.387861i
$651$		−	17.6383i		−	0.691298i
$652$	−1.76393	+	1.76393i	−0.0690809	+	0.0690809i
$653$	−1.90983	−	1.90983i	−0.0747374	−	0.0747374i	0.668750	−	0.743487i	$-0.266830\pi$
$653$	−1.90983	−	1.90983i	−0.0747374	−	0.0747374i	−0.743487	+	0.668750i	$0.766830\pi$
$654$			25.4164i			0.993860i
$655$	−11.7751	+	23.5502i	−0.460090	+	0.920181i
$656$			7.61125i			0.297169i
$657$	−10.9799	−	10.9799i	−0.428365	−	0.428365i
$658$	−4.70820	−	4.70820i	−0.183545	−	0.183545i
$659$	15.2225			0.592984			0.296492	−	0.955035i	$-0.404183\pi$
$659$	15.2225			0.592984			0.296492	+	0.955035i	$0.404183\pi$
$660$	−9.97077	−	13.7320i	−0.388112	−	0.534517i
$661$	33.4164			1.29975			0.649874	−	0.760042i	$-0.274822\pi$
$661$	33.4164			1.29975			0.649874	+	0.760042i	$0.274822\pi$
$662$	−5.86319	−	5.86319i	−0.227879	−	0.227879i
$663$	−3.05573	−	3.05573i	−0.118675	−	0.118675i
$664$		−	6.47214i		−	0.251168i
$665$	−4.61803	−	13.8541i	−0.179080	−	0.537239i
$666$			24.0903i			0.933482i
$667$	−48.6722	−	48.6722i	−1.88459	−	1.88459i
$668$	−13.0618	+	13.0618i	−0.505375	+	0.505375i
$669$		−	38.0689i		−	1.47183i
$670$	−17.6383	−	8.81913i	−0.681426	−	0.340713i
$671$	−8.94427	+	2.82843i	−0.345290	+	0.109190i
$672$	1.61803	−	1.61803i	0.0624170	−	0.0624170i
$673$	−19.0525	+	19.0525i	−0.734419	+	0.734419i	−0.971492	−	0.237073i	$-0.923812\pi$
$673$	−19.0525	+	19.0525i	−0.734419	+	0.734419i	0.237073	+	0.971492i	$0.423812\pi$
$674$			18.9443i			0.729706i
$675$	−8.65248	−	1.23607i	−0.333034	−	0.0475763i
$676$	−6.88854			−0.264944
$677$	17.5595	+	17.5595i	0.674865	+	0.674865i	0.958833	−	0.283969i	$-0.0916513\pi$
$677$	17.5595	+	17.5595i	0.674865	+	0.674865i	−0.283969	+	0.958833i	$0.591651\pi$
$678$	−5.11667	+	5.11667i	−0.196505	+	0.196505i
$679$	18.8461			0.723249
$680$	−1.52786	−	0.763932i	−0.0585909	−	0.0292955i
$681$			49.4187i			1.89373i
$682$	−11.7855	+	22.6866i	−0.451292	+	0.868714i
$683$	−20.8885	−	20.8885i	−0.799278	−	0.799278i	0.183704	−	0.982982i	$-0.441191\pi$
$683$	−20.8885	−	20.8885i	−0.799278	−	0.799278i	−0.982982	+	0.183704i	$0.941191\pi$
$684$	−14.6035			−0.558379
$685$	37.2492	−	12.4164i	1.42322	−	0.474407i
$686$	1.00000			0.0381802
$687$	27.1246	−	27.1246i	1.03487	−	1.03487i
$688$	−4.24264	+	4.24264i	−0.161749	+	0.161749i
$689$	−15.3199			−0.583642
$690$	−33.3221	+	11.1074i	−1.26855	+	0.422851i
$691$	−12.3607			−0.470222			−0.235111	−	0.971968i	$-0.575545\pi$
$691$	−12.3607			−0.470222			−0.235111	+	0.971968i	$0.575545\pi$
$692$	7.07107	+	7.07107i	0.268802	+	0.268802i
$693$	−6.58114	−	3.41886i	−0.249997	−	0.129872i
$694$			9.05573i			0.343751i
$695$	34.8639	+	17.4319i	1.32246	+	0.661231i
$696$	22.9443			0.869700
$697$	4.11146	−	4.11146i	0.155733	−	0.155733i
$698$	6.18034	+	6.18034i	0.233929	+	0.233929i
$699$	22.8825			0.865494
$700$	4.94975	+	0.707107i	0.187083	+	0.0267261i
$701$			47.2092i			1.78307i	0.452954	+	0.891534i	$0.350370\pi$
$701$			47.2092i			1.78307i	−0.452954	+	0.891534i	$0.649630\pi$
$702$	−3.05573	+	3.05573i	−0.115331	+	0.115331i
$703$	49.7525	−	49.7525i	1.87645	−	1.87645i
$704$	−3.16228	+	1.00000i	−0.119183	+	0.0376889i
$705$	−30.4721	−	15.2361i	−1.14765	−	0.573824i
$706$		−	25.5834i		−	0.962843i
$707$	4.47214	−	4.47214i	0.168192	−	0.168192i
$708$	11.7082	+	11.7082i	0.440021	+	0.440021i
$709$		−	8.11146i		−	0.304632i	−0.988332	−	0.152316i	$-0.951327\pi$
$709$		−	8.11146i		−	0.304632i	0.988332	−	0.152316i	$-0.0486732\pi$
$710$	8.48528	+	25.4558i	0.318447	+	0.955341i
$711$			16.0965i			0.603667i
$712$	−6.65841	−	6.65841i	−0.249534	−	0.249534i
$713$	37.4164	+	37.4164i	1.40126	+	1.40126i
$714$	−1.74806			−0.0654197
$715$	−10.7721	−	14.8355i	−0.402852	−	0.554817i
$716$	1.70820			0.0638386
$717$	29.2858	+	29.2858i	1.09370	+	1.09370i
$718$	−14.6180	−	14.6180i	−0.545540	−	0.545540i
$719$			8.94427i			0.333565i	0.985994	+	0.166783i	$0.0533378\pi$
$719$			8.94427i			0.333565i	−0.985994	+	0.166783i	$0.946662\pi$
$720$	2.23607	−	4.47214i	0.0833333	−	0.166667i
$721$			7.07107i			0.263340i
$722$	16.7248	+	16.7248i	0.622434	+	0.622434i
$723$	−7.73877	+	7.73877i	−0.287808	+	0.287808i
$724$			1.52786i			0.0567826i
$725$	30.0810	+	40.1081i	1.11718	+	1.48958i
$726$	14.4721	+	20.5942i	0.537111	+	0.764323i
$727$	−1.58359	+	1.58359i	−0.0587322	+	0.0587322i	−0.735863	−	0.677131i	$-0.763223\pi$
$727$	−1.58359	+	1.58359i	−0.0587322	+	0.0587322i	0.677131	+	0.735863i	$0.263223\pi$
$728$	1.74806	−	1.74806i	0.0647876	−	0.0647876i
$729$			11.9443i			0.442380i
$730$	−13.8885	−	6.94427i	−0.514038	−	0.257019i
$731$	4.58359			0.169530
$732$	−4.57649	−	4.57649i	−0.169152	−	0.169152i
$733$	−19.4651	+	19.4651i	−0.718961	+	0.718961i	−0.968393	−	0.249431i	$-0.919756\pi$
$733$	−19.4651	+	19.4651i	−0.718961	+	0.718961i	0.249431	+	0.968393i	$0.419756\pi$
$734$	−4.24264			−0.156599
$735$	4.85410	−	1.61803i	0.179046	−	0.0596821i
$736$			6.86474i			0.253038i
$737$	25.9562	+	13.4841i	0.956111	+	0.496694i
$738$	12.0344	+	12.0344i	0.442994	+	0.442994i
$739$	−19.6414			−0.722519			−0.361260	−	0.932465i	$-0.617653\pi$
$739$	−19.6414			−0.722519			−0.361260	+	0.932465i	$0.617653\pi$
$740$	7.61803	+	22.8541i	0.280044	+	0.840133i
$741$	−36.9443			−1.35718
$742$	−4.38197	+	4.38197i	−0.160867	+	0.160867i
$743$	−23.0888	+	23.0888i	−0.847045	+	0.847045i	−0.989763	−	0.142718i	$-0.954416\pi$
$743$	−23.0888	+	23.0888i	−0.847045	+	0.847045i	0.142718	+	0.989763i	$0.454416\pi$
$744$	−17.6383			−0.646650
$745$	−42.6814	−	21.3407i	−1.56373	−	0.781864i
$746$	−11.2361			−0.411382
$747$	−10.2333	−	10.2333i	−0.374419	−	0.374419i
$748$	2.24839	+	1.16802i	0.0822091	+	0.0427071i
$749$			9.41641i			0.344068i
$750$	25.1707	−	4.57649i	0.919104	−	0.167110i
$751$	−24.9443			−0.910229			−0.455115	−	0.890433i	$-0.650402\pi$
$751$	−24.9443			−0.910229			−0.455115	+	0.890433i	$0.650402\pi$
$752$	−4.70820	+	4.70820i	−0.171691	+	0.171691i
$753$	14.4721	+	14.4721i	0.527394	+	0.527394i
$754$	24.7881			0.902731
$755$	−12.8554	+	25.7109i	−0.467857	+	0.935715i
$756$			1.74806i			0.0635765i
$757$	−27.0344	+	27.0344i	−0.982584	+	0.982584i	−0.999851	−	0.0172674i	$-0.994503\pi$
$757$	−27.0344	+	27.0344i	−0.982584	+	0.982584i	0.0172674	+	0.999851i	$0.494503\pi$
$758$	−22.5486	+	22.5486i	−0.819002	+	0.819002i
$759$	49.6737	−	15.7082i	1.80304	−	0.570172i
$760$	−13.8541	+	4.61803i	−0.502541	+	0.167514i
$761$		−	21.7534i		−	0.788560i	−0.918990	−	0.394280i	$-0.870994\pi$
$761$		−	21.7534i		−	0.788560i	0.918990	−	0.394280i	$-0.129006\pi$
$762$	−0.472136	+	0.472136i	−0.0171037	+	0.0171037i
$763$	7.85410	+	7.85410i	0.284338	+	0.284338i
$764$			6.65248i			0.240678i
$765$	−3.62365	+	1.20788i	−0.131013	+	0.0436711i
$766$			2.49458i			0.0901327i
$767$	12.6491	+	12.6491i	0.456733	+	0.456733i
$768$	−1.61803	−	1.61803i	−0.0583858	−	0.0583858i
$769$	10.8523			0.391345			0.195673	−	0.980669i	$-0.437311\pi$
$769$	10.8523			0.391345			0.195673	+	0.980669i	$0.437311\pi$
$770$	−7.32456	−	1.16228i	−0.263959	−	0.0418856i
$771$	−16.6525			−0.599724
$772$	6.32456	+	6.32456i	0.227626	+	0.227626i
$773$	−17.3607	−	17.3607i	−0.624420	−	0.624420i	0.322238	−	0.946659i	$-0.395565\pi$
$773$	−17.3607	−	17.3607i	−0.624420	−	0.624420i	−0.946659	+	0.322238i	$0.895565\pi$
$774$			13.4164i			0.482243i
$775$	−23.1246	−	30.8328i	−0.830661	−	1.10755i
$776$		−	18.8461i		−	0.676537i
$777$	17.4319	+	17.4319i	0.625367	+	0.625367i
$778$	4.37016	−	4.37016i	0.156678	−	0.156678i
$779$		−	49.7082i		−	1.78098i
$780$	5.65685	−	11.3137i	0.202548	−	0.405096i
$781$	−12.0000	−	37.9473i	−0.429394	−	1.35786i
$782$	3.70820	−	3.70820i	0.132605	−	0.132605i
$783$	−12.3941	+	12.3941i	−0.442928	+	0.442928i
$784$		−	1.00000i		−	0.0357143i
$785$	−43.2492	+	14.4164i	−1.54363	+	0.514544i
$786$	26.9443			0.961070
$787$	−14.8098	−	14.8098i	−0.527914	−	0.527914i	0.392036	−	0.919950i	$-0.371771\pi$
$787$	−14.8098	−	14.8098i	−0.527914	−	0.527914i	−0.919950	+	0.392036i	$0.871771\pi$
$788$	4.03631	−	4.03631i	0.143788	−	0.143788i
$789$	−11.9814			−0.426549
$790$	5.09017	+	15.2705i	0.181100	+	0.543300i
$791$			3.16228i			0.112438i
$792$	−3.41886	+	6.58114i	−0.121484	+	0.233851i
$793$	−4.94427	−	4.94427i	−0.175576	−	0.175576i
$794$	−2.90724			−0.103174
$795$	−14.1803	+	28.3607i	−0.502925	+	1.00585i
$796$	−3.52786			−0.125042
$797$	−35.9443	+	35.9443i	−1.27321	+	1.27321i	−0.328818	+	0.944393i	$0.606650\pi$
$797$	−35.9443	+	35.9443i	−1.27321	+	1.27321i	−0.944393	+	0.328818i	$0.893350\pi$
$798$	−10.5672	+	10.5672i	−0.374075	+	0.374075i
$799$	5.08657			0.179950
$800$	0.707107	−	4.94975i	0.0250000	−	0.175000i
$801$	−21.0557			−0.743968
$802$	−1.62054	−	1.62054i	−0.0572234	−	0.0572234i
$803$	20.4382	+	10.6175i	0.721249	+	0.374684i
$804$			20.1803i			0.711706i
$805$	−6.86474	+	13.7295i	−0.241950	+	0.483900i
$806$	−19.0557			−0.671209
$807$	19.7082	−	19.7082i	0.693762	−	0.693762i
$808$	−4.47214	−	4.47214i	−0.157329	−	0.157329i
$809$	−24.2179			−0.851455			−0.425727	−	0.904852i	$-0.639982\pi$
$809$	−24.2179			−0.851455			−0.425727	+	0.904852i	$0.639982\pi$
$810$	7.57184	+	22.7155i	0.266047	+	0.798142i
$811$			24.1692i			0.848694i	0.905500	+	0.424347i	$0.139496\pi$
$811$			24.1692i			0.848694i	−0.905500	+	0.424347i	$0.860504\pi$
$812$	7.09017	−	7.09017i	0.248816	−	0.248816i
$813$	9.56564	−	9.56564i	0.335482	−	0.335482i
$814$	−10.7735	−	34.0689i	−0.377612	−	1.19411i
$815$	1.76393	+	5.29180i	0.0617878	+	0.185364i
$816$			1.74806i			0.0611945i
$817$	27.7082	−	27.7082i	0.969387	−	0.969387i
$818$	8.32624	+	8.32624i	0.291120	+	0.291120i
$819$		−	5.52786i		−	0.193159i
$820$	15.2225	+	7.61125i	0.531593	+	0.265796i
$821$		−	50.7054i		−	1.76963i	−0.465943	−	0.884815i	$-0.654285\pi$
$821$		−	50.7054i		−	1.76963i	0.465943	−	0.884815i	$-0.345715\pi$
$822$	−28.4118	−	28.4118i	−0.990975	−	0.990975i
$823$	24.2705	+	24.2705i	0.846017	+	0.846017i	0.989633	−	0.143617i	$-0.0458732\pi$
$823$	24.2705	+	24.2705i	0.846017	+	0.846017i	−0.143617	+	0.989633i	$0.545873\pi$
$824$	7.07107			0.246332
$825$	−37.4347	+	6.20957i	−1.30331	+	0.216189i
$826$	7.23607			0.251775
$827$	18.7186	+	18.7186i	0.650910	+	0.650910i	0.953212	−	0.302302i	$-0.0977550\pi$
$827$	18.7186	+	18.7186i	0.650910	+	0.650910i	−0.302302	+	0.953212i	$0.597755\pi$
$828$	10.8541	+	10.8541i	0.377206	+	0.377206i
$829$			38.1803i			1.32606i	0.748594	+	0.663029i	$0.230729\pi$
$829$			38.1803i			1.32606i	−0.748594	+	0.663029i	$0.769271\pi$
$830$	−12.9443	−	6.47214i	−0.449302	−	0.224651i
$831$		−	38.3600i		−	1.33069i
$832$	−1.74806	−	1.74806i	−0.0606032	−	0.0606032i
$833$	−0.540182	+	0.540182i	−0.0187162	+	0.0187162i
$834$		−	39.8885i		−	1.38123i
$835$	13.0618	+	39.1853i	0.452021	+	1.35606i
$836$	20.6525	−	6.53089i	0.714281	−	0.225875i
$837$	9.52786	−	9.52786i	0.329331	−	0.329331i
$838$	22.8825	−	22.8825i	0.790461	−	0.790461i
$839$			17.5967i			0.607507i	0.952751	+	0.303754i	$0.0982400\pi$
$839$			17.5967i			0.607507i	−0.952751	+	0.303754i	$0.901760\pi$
$840$	−1.61803	−	4.85410i	−0.0558275	−	0.167482i
$841$	71.5410			2.46693
$842$	0.874032	+	0.874032i	0.0301211	+	0.0301211i
$843$	−32.4481	+	32.4481i	−1.11757	+	1.11757i
$844$	2.82843			0.0973585
$845$	−6.88854	+	13.7771i	−0.236973	+	0.473946i
$846$			14.8886i			0.511882i
$847$	10.8361	+	1.89183i	0.372333	+	0.0650039i
$848$	4.38197	+	4.38197i	0.150477	+	0.150477i
$849$	−17.6383			−0.605344
$850$	−3.05573	+	2.29180i	−0.104811	+	0.0786080i
$851$	−73.9574			−2.53523
$852$	19.4164	−	19.4164i	0.665195	−	0.665195i
$853$	9.23179	−	9.23179i	0.316091	−	0.316091i	−0.531173	−	0.847263i	$-0.678249\pi$
$853$	9.23179	−	9.23179i	0.316091	−	0.316091i	0.847263	+	0.531173i	$0.178249\pi$
$854$	−2.82843			−0.0967868
$855$	−14.6035	+	29.2070i	−0.499429	+	0.998859i
$856$	9.41641			0.321846
$857$	−32.1142	−	32.1142i	−1.09700	−	1.09700i	−0.994760	−	0.102242i	$-0.967398\pi$
$857$	−32.1142	−	32.1142i	−1.09700	−	1.09700i	−0.102242	−	0.994760i	$-0.532602\pi$
$858$	−8.64911	+	16.6491i	−0.295276	+	0.568391i
$859$			26.8328i			0.915524i	0.889075	+	0.457762i	$0.151349\pi$
$859$			26.8328i			0.915524i	−0.889075	+	0.457762i	$0.848651\pi$
$860$	4.24264	+	12.7279i	0.144673	+	0.434019i
$861$	17.4164			0.593550
$862$	5.85410	−	5.85410i	0.199392	−	0.199392i
$863$	9.03444	+	9.03444i	0.307536	+	0.307536i	0.843953	−	0.536417i	$-0.180223\pi$
$863$	9.03444	+	9.03444i	0.307536	+	0.307536i	−0.536417	+	0.843953i	$0.680223\pi$
$864$	1.74806			0.0594703
$865$	21.2132	−	7.07107i	0.721271	−	0.240424i
$866$		−	22.0872i		−	0.750555i
$867$	−26.5623	+	26.5623i	−0.902103	+	0.902103i
$868$	−5.45052	+	5.45052i	−0.185003	+	0.185003i
$869$	−7.19859	−	22.7639i	−0.244195	−	0.772214i
$870$	22.9443	−	45.8885i	0.777884	−	1.55577i
$871$			21.8021i			0.738736i
$872$	7.85410	−	7.85410i	0.265973	−	0.265973i
$873$	−29.7984	−	29.7984i	−1.00852	−	1.00852i
$874$		−	44.8328i		−	1.51649i
$875$	6.36396	−	9.19239i	0.215141	−	0.310759i
$876$			15.8902i			0.536880i
$877$	28.4118	+	28.4118i	0.959398	+	0.959398i	0.999207	−	0.0398093i	$-0.0126750\pi$
$877$	28.4118	+	28.4118i	0.959398	+	0.959398i	−0.0398093	+	0.999207i	$0.512675\pi$
$878$	4.18034	+	4.18034i	0.141080	+	0.141080i
$879$	−42.2688			−1.42569
$880$	−1.16228	+	7.32456i	−0.0391804	+	0.246911i
$881$	−17.4164			−0.586774			−0.293387	−	0.955994i	$-0.594782\pi$
$881$	−17.4164			−0.586774			−0.293387	+	0.955994i	$0.594782\pi$
$882$	−1.58114	−	1.58114i	−0.0532397	−	0.0532397i
$883$	−7.29180	−	7.29180i	−0.245388	−	0.245388i	0.573686	−	0.819075i	$-0.305513\pi$
$883$	−7.29180	−	7.29180i	−0.245388	−	0.245388i	−0.819075	+	0.573686i	$0.805513\pi$
$884$			1.88854i			0.0635186i
$885$	35.1246	−	11.7082i	1.18070	−	0.393567i
$886$			23.3739i			0.785263i
$887$	0.255039	+	0.255039i	0.00856338	+	0.00856338i	0.711376	−	0.702812i	$-0.248073\pi$
$887$	0.255039	+	0.255039i	0.00856338	+	0.00856338i	−0.702812	+	0.711376i	$0.748073\pi$
$888$	17.4319	−	17.4319i	0.584977	−	0.584977i
$889$			0.291796i			0.00978653i
$890$	−19.9752	+	6.65841i	−0.669571	+	0.223190i
$891$	−10.7082	−	33.8623i	−0.358738	−	1.13443i
$892$	−11.7639	+	11.7639i	−0.393886	+	0.393886i
$893$	30.7487	−	30.7487i	1.02897	−	1.02897i
$894$			48.8328i			1.63321i
$895$	1.70820	−	3.41641i	0.0570990	−	0.114198i
$896$	−1.00000			−0.0334077
$897$	27.4589	+	27.4589i	0.916828	+	0.916828i
$898$	17.8446	−	17.8446i	0.595482	−	0.595482i
$899$	−77.2903			−2.57777
$900$	−6.70820	−	8.94427i	−0.223607	−	0.298142i
$901$		−	4.73411i		−	0.157716i
$902$	−22.4012	−	11.6373i	−0.745880	−	0.387480i
$903$	9.70820	+	9.70820i	0.323069	+	0.323069i
$904$	3.16228			0.105176
$905$	3.05573	+	1.52786i	0.101576	+	0.0507879i
$906$	29.4164			0.977295
$907$	−35.0689	+	35.0689i	−1.16444	+	1.16444i	−0.180951	+	0.983492i	$0.557918\pi$
$907$	−35.0689	+	35.0689i	−1.16444	+	1.16444i	−0.983492	+	0.180951i	$0.942082\pi$
$908$	15.2712	−	15.2712i	0.506793	−	0.506793i
$909$	−14.1421			−0.469065
$910$	−1.74806	−	5.24419i	−0.0579478	−	0.173843i
$911$	10.6525			0.352932			0.176466	−	0.984307i	$-0.443533\pi$
$911$	10.6525			0.352932			0.176466	+	0.984307i	$0.443533\pi$
$912$	10.5672	+	10.5672i	0.349915	+	0.349915i
$913$	19.0486	+	9.89564i	0.630418	+	0.327498i
$914$			32.8328i			1.08601i
$915$	−13.7295	+	4.57649i	−0.453882	+	0.151294i
$916$	−16.7639			−0.553896
$917$	8.32624	−	8.32624i	0.274957	−	0.274957i
$918$	−0.944272	−	0.944272i	−0.0311656	−	0.0311656i
$919$	23.7565			0.783654			0.391827	−	0.920039i	$-0.371843\pi$
$919$	23.7565			0.783654			0.391827	+	0.920039i	$0.371843\pi$
$920$	13.7295	+	6.86474i	0.452647	+	0.226324i
$921$		−	14.1421i		−	0.465999i
$922$	2.76393	−	2.76393i	0.0910253	−	0.0910253i
$923$	20.9768	−	20.9768i	0.690459	−	0.690459i
$924$	2.28825	+	7.23607i	0.0752778	+	0.238049i
$925$	53.3262	+	7.61803i	1.75336	+	0.250479i
$926$			11.6963i			0.384363i
$927$	11.1803	−	11.1803i	0.367211	−	0.367211i
$928$	−7.09017	−	7.09017i	−0.232746	−	0.232746i
$929$			8.29180i			0.272045i	0.990706	+	0.136023i	$0.0434319\pi$
$929$			8.29180i			0.272045i	−0.990706	+	0.136023i	$0.956568\pi$
$930$	−17.6383	+	35.2765i	−0.578381	+	1.15676i
$931$			6.53089i			0.214041i
$932$	−7.07107	−	7.07107i	−0.231621	−	0.231621i
$933$	−39.1246	−	39.1246i	−1.28088	−	1.28088i
$934$	−14.6823			−0.480420
$935$	4.58443	−	3.32875i	0.149927	−	0.108862i
$936$	−5.52786			−0.180684
$937$	−1.87558	−	1.87558i	−0.0612726	−	0.0612726i	0.675806	−	0.737079i	$-0.263796\pi$
$937$	−1.87558	−	1.87558i	−0.0612726	−	0.0612726i	−0.737079	+	0.675806i	$0.763796\pi$
$938$	6.23607	+	6.23607i	0.203615	+	0.203615i
$939$			1.23607i			0.0403376i
$940$	4.70820	+	14.1246i	0.153565	+	0.460694i
$941$			20.4667i			0.667195i	0.942716	+	0.333598i	$0.108263\pi$
$941$			20.4667i			0.667195i	−0.942716	+	0.333598i	$0.891737\pi$
$942$	32.9883	+	32.9883i	1.07482	+	1.07482i
$943$	−36.9458	+	36.9458i	−1.20312	+	1.20312i
$944$		−	7.23607i		−	0.235514i
$945$	3.49613	+	1.74806i	0.113729	+	0.0568645i
$946$	−6.00000	−	18.9737i	−0.195077	−	0.616887i
$947$	−2.23607	+	2.23607i	−0.0726624	+	0.0726624i	−0.742504	−	0.669842i	$-0.766362\pi$
$947$	−2.23607	+	2.23607i	−0.0726624	+	0.0726624i	0.669842	+	0.742504i	$0.266362\pi$
$948$	11.6476	−	11.6476i	0.378295	−	0.378295i
$949$			17.1672i			0.557270i
$950$	−4.61803	+	32.3262i	−0.149829	+	1.04880i
$951$	5.23607			0.169791
$952$	0.540182	+	0.540182i	0.0175074	+	0.0175074i
$953$	14.5548	−	14.5548i	0.471476	−	0.471476i	−0.430916	−	0.902392i	$-0.641809\pi$
$953$	14.5548	−	14.5548i	0.471476	−	0.471476i	0.902392	+	0.430916i	$0.141809\pi$
$954$	13.8570			0.448637
$955$	13.3050	+	6.65248i	0.430538	+	0.215269i
$956$		−	18.0996i		−	0.585384i
$957$	−35.0809	+	67.5290i	−1.13400	+	2.18290i
$958$	20.9443	+	20.9443i	0.676679	+	0.676679i
$959$	−17.5595			−0.567024
$960$	−4.85410	+	1.61803i	−0.156665	+	0.0522218i
$961$	28.4164			0.916658
$962$	18.8328	−	18.8328i	0.607194	−	0.607194i
$963$	14.8886	−	14.8886i	0.479780	−	0.479780i
$964$	4.78282			0.154044
$965$	18.9737	−	6.32456i	0.610784	−	0.203595i
$966$	15.7082			0.505403
$967$	−9.35931	−	9.35931i	−0.300975	−	0.300975i	0.540420	−	0.841395i	$-0.318265\pi$
$967$	−9.35931	−	9.35931i	−0.300975	−	0.300975i	−0.841395	+	0.540420i	$0.818265\pi$
$968$	1.89183	−	10.8361i	0.0608056	−	0.348285i
$969$		−	11.4164i		−	0.366748i
$970$	−37.6923	−	18.8461i	−1.21023	−	0.605113i
$971$	−52.5410			−1.68612			−0.843061	−	0.537818i	$-0.819249\pi$
$971$	−52.5410			−1.68612			−0.843061	+	0.537818i	$0.819249\pi$
$972$	13.6180	−	13.6180i	0.436799	−	0.436799i
$973$	−12.3262	−	12.3262i	−0.395161	−	0.395161i
$974$	−14.6823			−0.470452
$975$	−16.9706	−	22.6274i	−0.543493	−	0.724657i
$976$			2.82843i			0.0905357i
$977$	−6.70820	+	6.70820i	−0.214614	+	0.214614i	−0.806224	−	0.591610i	$-0.798493\pi$
$977$	−6.70820	+	6.70820i	−0.214614	+	0.214614i	0.591610	+	0.806224i	$0.298493\pi$
$978$	4.03631	−	4.03631i	0.129067	−	0.129067i
$979$	29.7773	−	9.41641i	0.951687	−	0.300950i
$980$	−2.00000	−	1.00000i	−0.0638877	−	0.0319438i
$981$		−	24.8369i		−	0.792980i
$982$	24.9443	−	24.9443i	0.796004	−	0.796004i
$983$	33.0689	+	33.0689i	1.05473	+	1.05473i	0.998413	+	0.0563209i	$0.0179370\pi$
$983$	33.0689	+	33.0689i	1.05473	+	1.05473i	0.0563209	+	0.998413i	$0.482063\pi$
$984$		−	17.4164i		−	0.555215i
$985$	−4.03631	−	12.1089i	−0.128608	−	0.385823i
$986$			7.65996i			0.243943i
$987$	10.7735	+	10.7735i	0.342925	+	0.342925i
$988$	11.4164	+	11.4164i	0.363204	+	0.363204i
$989$	−41.1884			−1.30972
$990$	9.74342	+	13.4189i	0.309666	+	0.426479i
$991$	−5.12461			−0.162789			−0.0813943	−	0.996682i	$-0.525937\pi$
$991$	−5.12461			−0.162789			−0.0813943	+	0.996682i	$0.525937\pi$
$992$	5.45052	+	5.45052i	0.173054	+	0.173054i
$993$	13.4164	+	13.4164i	0.425757	+	0.425757i
$994$		−	12.0000i		−	0.380617i
$995$	−3.52786	+	7.05573i	−0.111841	+	0.223682i
$996$			14.8098i			0.469268i
$997$	−17.9721	−	17.9721i	−0.569183	−	0.569183i	0.362717	−	0.931899i	$-0.381849\pi$
$997$	−17.9721	−	17.9721i	−0.569183	−	0.569183i	−0.931899	+	0.362717i	$0.881849\pi$
$998$	−2.62210	+	2.62210i	−0.0830010	+	0.0830010i
$999$			18.8328i			0.595844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.d.43.3	yes	8
5.2	odd	4	inner	770.2.m.d.197.1	yes	8
11.10	odd	2	inner	770.2.m.d.43.1	✓	8
55.32	even	4	inner	770.2.m.d.197.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.d.43.1	✓	8	11.10	odd	2	inner
770.2.m.d.43.3	yes	8	1.1	even	1	trivial
770.2.m.d.197.1	yes	8	5.2	odd	4	inner
770.2.m.d.197.3	yes	8	55.32	even	4	inner

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.61803 - 1.61803i) q^{3} +1.00000i q^{4} +(2.00000 + 1.00000i) q^{5} -2.28825i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.23607i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.61803 - 1.61803i) q^{3} +1.00000i q^{4} +(2.00000 + 1.00000i) q^{5} -2.28825i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.23607i q^{9} +(0.707107 + 2.12132i) q^{10} +(-1.00000 - 3.16228i) q^{11} +(1.61803 - 1.61803i) q^{12} +(1.74806 - 1.74806i) q^{13} -1.00000i q^{14} +(-1.61803 - 4.85410i) q^{15} -1.00000 q^{16} +(0.540182 + 0.540182i) q^{17} +(-1.58114 + 1.58114i) q^{18} +6.53089 q^{19} +(-1.00000 + 2.00000i) q^{20} +2.28825i q^{21} +(1.52896 - 2.94317i) q^{22} +(-4.85410 - 4.85410i) q^{23} +2.28825 q^{24} +(3.00000 + 4.00000i) q^{25} +2.47214 q^{26} +(-1.23607 + 1.23607i) q^{27} +(0.707107 - 0.707107i) q^{28} +10.0270 q^{29} +(2.28825 - 4.57649i) q^{30} -7.70820 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.49864 + 6.73471i) q^{33} +0.763932i q^{34} +(-0.707107 - 2.12132i) q^{35} -2.23607 q^{36} +(7.61803 - 7.61803i) q^{37} +(4.61803 + 4.61803i) q^{38} -5.65685 q^{39} +(-2.12132 + 0.707107i) q^{40} -7.61125i q^{41} +(-1.61803 + 1.61803i) q^{42} +(4.24264 - 4.24264i) q^{43} +(3.16228 - 1.00000i) q^{44} +(-2.23607 + 4.47214i) q^{45} -6.86474i q^{46} +(4.70820 - 4.70820i) q^{47} +(1.61803 + 1.61803i) q^{48} +1.00000i q^{49} +(-0.707107 + 4.94975i) q^{50} -1.74806i q^{51} +(1.74806 + 1.74806i) q^{52} +(-4.38197 - 4.38197i) q^{53} -1.74806 q^{54} +(1.16228 - 7.32456i) q^{55} +1.00000 q^{56} +(-10.5672 - 10.5672i) q^{57} +(7.09017 + 7.09017i) q^{58} +7.23607i q^{59} +(4.85410 - 1.61803i) q^{60} -2.82843i q^{61} +(-5.45052 - 5.45052i) q^{62} +(1.58114 - 1.58114i) q^{63} -1.00000i q^{64} +(5.24419 - 1.74806i) q^{65} +(-7.23607 + 2.28825i) q^{66} +(-6.23607 + 6.23607i) q^{67} +(-0.540182 + 0.540182i) q^{68} +15.7082i q^{69} +(1.00000 - 2.00000i) q^{70} +12.0000 q^{71} +(-1.58114 - 1.58114i) q^{72} +(-4.91034 + 4.91034i) q^{73} +10.7735 q^{74} +(1.61803 - 11.3262i) q^{75} +6.53089i q^{76} +(-1.52896 + 2.94317i) q^{77} +(-4.00000 - 4.00000i) q^{78} +7.19859 q^{79} +(-2.00000 - 1.00000i) q^{80} +10.7082 q^{81} +(5.38197 - 5.38197i) q^{82} +(-4.57649 + 4.57649i) q^{83} -2.28825 q^{84} +(0.540182 + 1.62054i) q^{85} +6.00000 q^{86} +(-16.2241 - 16.2241i) q^{87} +(2.94317 + 1.52896i) q^{88} +9.41641i q^{89} +(-4.74342 + 1.58114i) q^{90} -2.47214 q^{91} +(4.85410 - 4.85410i) q^{92} +(12.4721 + 12.4721i) q^{93} +6.65841 q^{94} +(13.0618 + 6.53089i) q^{95} +2.28825i q^{96} +(-13.3262 + 13.3262i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(7.07107 - 2.23607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 16 q^{5}+O(q^{10}) \) 8 * q - 4 * q^3 + 16 * q^5	\( 8 q - 4 q^{3} + 16 q^{5} - 8 q^{11} + 4 q^{12} - 4 q^{15} - 8 q^{16} - 8 q^{20} - 12 q^{23} + 24 q^{25} - 16 q^{26} + 8 q^{27} - 8 q^{31} + 4 q^{33} + 52 q^{37} + 28 q^{38} - 4 q^{42} - 16 q^{47} + 4 q^{48} - 44 q^{53} - 16 q^{55} + 8 q^{56} + 12 q^{58} + 12 q^{60} - 40 q^{66} - 32 q^{67} + 8 q^{70} + 96 q^{71} + 4 q^{75} - 32 q^{78} - 16 q^{80} + 32 q^{81} + 52 q^{82} + 48 q^{86} + 16 q^{91} + 12 q^{92} + 64 q^{93} - 44 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 + 16 * q^5 - 8 * q^11 + 4 * q^12 - 4 * q^15 - 8 * q^16 - 8 * q^20 - 12 * q^23 + 24 * q^25 - 16 * q^26 + 8 * q^27 - 8 * q^31 + 4 * q^33 + 52 * q^37 + 28 * q^38 - 4 * q^42 - 16 * q^47 + 4 * q^48 - 44 * q^53 - 16 * q^55 + 8 * q^56 + 12 * q^58 + 12 * q^60 - 40 * q^66 - 32 * q^67 + 8 * q^70 + 96 * q^71 + 4 * q^75 - 32 * q^78 - 16 * q^80 + 32 * q^81 + 52 * q^82 + 48 * q^86 + 16 * q^91 + 12 * q^92 + 64 * q^93 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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