LMFDB - Embedded newform 770.2.bi.a.27.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(27,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 10, 8]))

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

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

chi := DirichletCharacter("770.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bi (of order $20$, degree $8$, 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:	$384$
Relative dimension:	$48$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.8
Character	$\chi$	$=$	770.27
Dual form			770.2.bi.a.713.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.205427 - 1.29702i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.486212 - 2.18257i) q^{5} +(1.24891 + 0.405797i) q^{6} +(-0.970889 - 2.46117i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.21312 - 0.394165i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.205427 - 1.29702i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.486212 - 2.18257i) q^{5} +(1.24891 + 0.405797i) q^{6} +(-0.970889 - 2.46117i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.21312 - 0.394165i) q^{9} +(2.16542 + 0.557647i) q^{10} +(2.28175 + 2.40699i) q^{11} +(-0.928562 + 0.928562i) q^{12} +(0.860081 - 1.68800i) q^{13} +(2.63370 + 0.252281i) q^{14} +(-2.73095 + 1.07898i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.777984 - 1.52688i) q^{17} +(-0.199539 + 1.25984i) q^{18} +(0.719860 + 0.523009i) q^{19} +(-1.47995 + 1.67623i) q^{20} +(-2.99274 + 1.76485i) q^{21} +(-3.18054 + 0.940305i) q^{22} +(1.90910 - 1.90910i) q^{23} +(-0.405797 - 1.24891i) q^{24} +(-4.52720 + 2.12238i) q^{25} +(1.11355 + 1.53268i) q^{26} +(-2.54897 - 5.00263i) q^{27} +(-1.42046 + 2.23211i) q^{28} +(-2.82542 - 3.88885i) q^{29} +(0.278442 - 2.92314i) q^{30} +(-3.45658 + 1.12311i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.65318 - 3.45393i) q^{33} +1.71366 q^{34} +(-4.89962 + 3.31568i) q^{35} +(-1.03194 - 0.749746i) q^{36} +(-7.31639 - 1.15880i) q^{37} +(-0.792814 + 0.403959i) q^{38} +(-2.36606 - 0.768778i) q^{39} +(-0.821654 - 2.07964i) q^{40} +(1.75801 - 2.41969i) q^{41} +(-0.213820 - 3.46778i) q^{42} +(0.391437 - 0.391437i) q^{43} +(0.606117 - 3.26077i) q^{44} +(-1.45012 - 2.45606i) q^{45} +(0.834307 + 2.56773i) q^{46} +(0.864767 - 0.136966i) q^{47} +(1.29702 + 0.205427i) q^{48} +(-5.11475 + 4.77905i) q^{49} +(0.164251 - 4.99730i) q^{50} +(-1.82057 + 1.32272i) q^{51} +(-1.87117 + 0.296364i) q^{52} +(-3.98289 - 2.02939i) q^{53} +5.61458 q^{54} +(4.14401 - 6.15038i) q^{55} +(-1.34395 - 2.27899i) q^{56} +(0.530473 - 1.04111i) q^{57} +(4.74770 - 0.751963i) q^{58} +(-9.98591 + 7.25519i) q^{59} +(2.47813 + 1.57517i) q^{60} +(5.90414 + 1.91837i) q^{61} +(0.568555 - 3.58971i) q^{62} +(-2.14791 - 2.60300i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-4.10236 - 1.05646i) q^{65} +(1.87296 + 3.93205i) q^{66} +(11.1217 + 11.1217i) q^{67} +(-0.777984 + 1.52688i) q^{68} +(-2.86832 - 2.08395i) q^{69} +(-0.729913 - 5.87088i) q^{70} +(1.68794 - 5.19494i) q^{71} +(1.13652 - 0.579085i) q^{72} +(-2.95046 - 0.467306i) q^{73} +(4.35407 - 5.99287i) q^{74} +(3.68277 + 5.43586i) q^{75} -0.889796i q^{76} +(3.70870 - 7.95271i) q^{77} +(1.75915 - 1.75915i) q^{78} +(0.164177 - 0.0533443i) q^{79} +(2.22599 + 0.212036i) q^{80} +(-2.86906 + 2.08449i) q^{81} +(1.35784 + 2.66491i) q^{82} +(14.2748 - 7.27335i) q^{83} +(3.18688 + 1.38382i) q^{84} +(-2.95425 + 2.44039i) q^{85} +(0.171064 + 0.526481i) q^{86} +(-4.46349 + 4.46349i) q^{87} +(2.63020 + 2.02041i) q^{88} -1.92909 q^{89} +(2.84671 - 0.177042i) q^{90} +(-4.98952 - 0.477945i) q^{91} +(-2.66664 - 0.422354i) q^{92} +(2.16677 + 4.25252i) q^{93} +(-0.270559 + 0.832694i) q^{94} +(0.791498 - 1.82544i) q^{95} +(-0.771871 + 1.06239i) q^{96} +(-7.65359 - 3.89970i) q^{97} +(-1.93612 - 6.72692i) q^{98} +(3.71678 + 2.02057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 4 q^{7}+O(q^{10}) $ 384 * q - 4 * q^7	$ 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) $ 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.205427	−	1.29702i	−0.118604	−	0.748833i	−0.973271	−	0.229658i	$-0.926239\pi$
$3$	−0.205427	−	1.29702i	−0.118604	−	0.748833i	0.854668	−	0.519175i	$-0.173761\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−0.486212	−	2.18257i	−0.217440	−	0.976074i
$5$	−0.486212	−	2.18257i	−0.217440	−	0.976074i
$6$	1.24891	+	0.405797i	0.509867	+	0.165666i
$7$	−0.970889	−	2.46117i	−0.366961	−	0.930236i
$7$	−0.970889	−	2.46117i	−0.366961	−	0.930236i
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	1.21312	−	0.394165i	0.404372	−	0.131388i
$10$	2.16542	+	0.557647i	0.684765	+	0.176343i
$11$	2.28175	+	2.40699i	0.687974	+	0.725735i
$11$	2.28175	+	2.40699i	0.687974	+	0.725735i
$12$	−0.928562	+	0.928562i	−0.268053	+	0.268053i
$13$	0.860081	−	1.68800i	0.238544	−	0.468168i	−0.740436	−	0.672127i	$-0.765381\pi$
$13$	0.860081	−	1.68800i	0.238544	−	0.468168i	0.978979	+	0.203959i	$0.0653809\pi$
$14$	2.63370	+	0.252281i	0.703885	+	0.0674250i
$15$	−2.73095	+	1.07898i	−0.705127	+	0.278592i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.777984	−	1.52688i	−0.188689	−	0.370323i	0.777210	−	0.629241i	$-0.216634\pi$
$17$	−0.777984	−	1.52688i	−0.188689	−	0.370323i	−0.965899	+	0.258918i	$0.916634\pi$
$18$	−0.199539	+	1.25984i	−0.0470318	+	0.296947i
$19$	0.719860	+	0.523009i	0.165147	+	0.119986i	0.667289	−	0.744799i	$-0.267455\pi$
$19$	0.719860	+	0.523009i	0.165147	+	0.119986i	−0.502142	+	0.864785i	$0.667455\pi$
$20$	−1.47995	+	1.67623i	−0.330926	+	0.374817i
$21$	−2.99274	+	1.76485i	−0.653069	+	0.385122i
$22$	−3.18054	+	0.940305i	−0.678093	+	0.200474i
$23$	1.90910	−	1.90910i	0.398075	−	0.398075i	−0.479479	−	0.877554i	$-0.659174\pi$
$23$	1.90910	−	1.90910i	0.398075	−	0.398075i	0.877554	+	0.479479i	$0.159174\pi$
$24$	−0.405797	−	1.24891i	−0.0828329	−	0.254933i
$25$	−4.52720	+	2.12238i	−0.905439	+	0.424476i
$26$	1.11355	+	1.53268i	0.218386	+	0.300583i
$27$	−2.54897	−	5.00263i	−0.490549	−	0.962756i
$28$	−1.42046	+	2.23211i	−0.268441	+	0.421829i
$29$	−2.82542	−	3.88885i	−0.524667	−	0.722142i	0.461639	−	0.887068i	$-0.347261\pi$
$29$	−2.82542	−	3.88885i	−0.524667	−	0.722142i	−0.986306	+	0.164926i	$0.947261\pi$
$30$	0.278442	−	2.92314i	0.0508363	−	0.533690i
$31$	−3.45658	+	1.12311i	−0.620820	+	0.201717i	−0.602504	−	0.798116i	$-0.705830\pi$
$31$	−3.45658	+	1.12311i	−0.620820	+	0.201717i	−0.0183154	+	0.999832i	$0.505830\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.65318	−	3.45393i	0.461859	−	0.601253i
$34$	1.71366			0.293890
$35$	−4.89962	+	3.31568i	−0.828187	+	0.560452i
$36$	−1.03194	−	0.749746i	−0.171990	−	0.124958i
$37$	−7.31639	−	1.15880i	−1.20281	−	0.190506i	−0.477313	−	0.878734i	$-0.658389\pi$
$37$	−7.31639	−	1.15880i	−1.20281	−	0.190506i	−0.725495	+	0.688228i	$0.758389\pi$
$38$	−0.792814	+	0.403959i	−0.128611	+	0.0655308i
$39$	−2.36606	−	0.768778i	−0.378872	−	0.123103i
$40$	−0.821654	−	2.07964i	−0.129915	−	0.328819i
$41$	1.75801	−	2.41969i	0.274554	−	0.377892i	−0.649366	−	0.760476i	$-0.724966\pi$
$41$	1.75801	−	2.41969i	0.274554	−	0.377892i	0.923921	+	0.382584i	$0.124966\pi$
$42$	−0.213820	−	3.46778i	−0.0329931	−	0.535089i
$43$	0.391437	−	0.391437i	0.0596935	−	0.0596935i	−0.676630	−	0.736323i	$-0.736560\pi$
$43$	0.391437	−	0.391437i	0.0596935	−	0.0596935i	0.736323	+	0.676630i	$0.236560\pi$
$44$	0.606117	−	3.26077i	0.0913755	−	0.491580i
$45$	−1.45012	−	2.45606i	−0.216171	−	0.366127i
$46$	0.834307	+	2.56773i	0.123012	+	0.378592i
$47$	0.864767	−	0.136966i	0.126139	−	0.0199785i	−0.0930456	−	0.995662i	$-0.529660\pi$
$47$	0.864767	−	0.136966i	0.126139	−	0.0199785i	0.219185	+	0.975683i	$0.429660\pi$
$48$	1.29702	+	0.205427i	0.187208	+	0.0296509i
$49$	−5.11475	+	4.77905i	−0.730679	+	0.682722i
$50$	0.164251	−	4.99730i	0.0232286	−	0.706725i
$51$	−1.82057	+	1.32272i	−0.254931	+	0.185218i
$52$	−1.87117	+	0.296364i	−0.259484	+	0.0410983i
$53$	−3.98289	−	2.02939i	−0.547092	−	0.278758i	0.158520	−	0.987356i	$-0.449328\pi$
$53$	−3.98289	−	2.02939i	−0.547092	−	0.278758i	−0.705612	+	0.708598i	$0.749328\pi$
$54$	5.61458			0.764048
$55$	4.14401	−	6.15038i	0.558778	−	0.829318i
$56$	−1.34395	−	2.27899i	−0.179593	−	0.304543i
$57$	0.530473	−	1.04111i	0.0702628	−	0.137899i
$58$	4.74770	−	0.751963i	0.623404	−	0.0987375i
$59$	−9.98591	+	7.25519i	−1.30005	+	0.944545i	−0.999956	−	0.00936327i	$-0.997020\pi$
$59$	−9.98591	+	7.25519i	−1.30005	+	0.944545i	−0.300098	+	0.953908i	$0.597020\pi$
$60$	2.47813	+	1.57517i	0.319925	+	0.203354i
$61$	5.90414	+	1.91837i	0.755948	+	0.245622i	0.661539	−	0.749911i	$-0.269904\pi$
$61$	5.90414	+	1.91837i	0.755948	+	0.245622i	0.0944095	+	0.995533i	$0.469904\pi$
$62$	0.568555	−	3.58971i	0.0722065	−	0.455894i
$63$	−2.14791	−	2.60300i	−0.270611	−	0.327947i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	−4.10236	−	1.05646i	−0.508836	−	0.131037i
$66$	1.87296	+	3.93205i	0.230546	+	0.484002i
$67$	11.1217	+	11.1217i	1.35873	+	1.35873i	0.875488	+	0.483241i	$0.160540\pi$
$67$	11.1217	+	11.1217i	1.35873	+	1.35873i	0.483241	+	0.875488i	$0.339460\pi$
$68$	−0.777984	+	1.52688i	−0.0943445	+	0.185161i
$69$	−2.86832	−	2.08395i	−0.345305	−	0.250879i
$70$	−0.729913	−	5.87088i	−0.0872413	−	0.701704i
$71$	1.68794	−	5.19494i	0.200322	−	0.616527i	−0.799552	−	0.600598i	$-0.794929\pi$
$71$	1.68794	−	5.19494i	0.200322	−	0.616527i	0.999873	−	0.0159290i	$-0.00507057\pi$
$72$	1.13652	−	0.579085i	0.133940	−	0.0682459i
$73$	−2.95046	−	0.467306i	−0.345325	−	0.0546941i	−0.0186368	−	0.999826i	$-0.505933\pi$
$73$	−2.95046	−	0.467306i	−0.345325	−	0.0546941i	−0.326688	+	0.945132i	$0.605933\pi$
$74$	4.35407	−	5.99287i	0.506151	−	0.696657i
$75$	3.68277	+	5.43586i	0.425250	+	0.627679i
$76$		−	0.889796i		−	0.102067i
$77$	3.70870	−	7.95271i	0.422645	−	0.906295i
$78$	1.75915	−	1.75915i	0.199185	−	0.199185i
$79$	0.164177	−	0.0533443i	0.0184713	−	0.00600170i	−0.299767	−	0.954013i	$-0.596909\pi$
$79$	0.164177	−	0.0533443i	0.0184713	−	0.00600170i	0.318238	+	0.948011i	$0.396909\pi$
$80$	2.22599	+	0.212036i	0.248873	+	0.0237063i
$81$	−2.86906	+	2.08449i	−0.318784	+	0.231610i
$82$	1.35784	+	2.66491i	0.149948	+	0.294290i
$83$	14.2748	−	7.27335i	1.56686	−	0.798354i	0.567176	−	0.823596i	$-0.308036\pi$
$83$	14.2748	−	7.27335i	1.56686	−	0.798354i	0.999681	+	0.0252425i	$0.00803578\pi$
$84$	3.18688	+	1.38382i	0.347717	+	0.150987i
$85$	−2.95425	+	2.44039i	−0.320434	+	0.264697i
$86$	0.171064	+	0.526481i	0.0184463	+	0.0567719i
$87$	−4.46349	+	4.46349i	−0.478537	+	0.478537i
$88$	2.63020	+	2.02041i	0.280380	+	0.215377i
$89$	−1.92909			−0.204484			−0.102242	−	0.994760i	$-0.532602\pi$
$89$	−1.92909			−0.204484			−0.102242	+	0.994760i	$0.532602\pi$
$90$	2.84671	−	0.177042i	0.300069	−	0.0186618i
$91$	−4.98952	−	0.477945i	−0.523043	−	0.0501022i
$92$	−2.66664	−	0.422354i	−0.278016	−	0.0440334i
$93$	2.16677	+	4.25252i	0.224683	+	0.440966i
$94$	−0.270559	+	0.832694i	−0.0279060	+	0.0858858i
$95$	0.791498	−	1.82544i	0.0812059	−	0.187286i
$96$	−0.771871	+	1.06239i	−0.0787787	+	0.108430i
$97$	−7.65359	−	3.89970i	−0.777104	−	0.395954i	0.0199969	−	0.999800i	$-0.493634\pi$
$97$	−7.65359	−	3.89970i	−0.777104	−	0.395954i	−0.797101	+	0.603846i	$0.793634\pi$
$98$	−1.93612	−	6.72692i	−0.195577	−	0.679522i
$99$	3.71678	+	2.02057i	0.373550	+	0.203075i
$100$	4.37806	+	2.41508i	0.437806	+	0.241508i
$101$	1.39629	−	0.453682i	0.138936	−	0.0451430i	−0.238724	−	0.971088i	$-0.576729\pi$
$101$	1.39629	−	0.453682i	0.138936	−	0.0451430i	0.377660	+	0.925945i	$0.376729\pi$
$102$	−0.352032	−	2.22264i	−0.0348564	−	0.220075i
$103$	2.71298	+	0.429694i	0.267318	+	0.0423390i	0.288654	−	0.957433i	$-0.406792\pi$
$103$	2.71298	+	0.429694i	0.267318	+	0.0423390i	−0.0213366	+	0.999772i	$0.506792\pi$
$104$	0.585430	−	1.80177i	0.0574062	−	0.176678i
$105$	5.30701	+	5.67376i	0.517911	+	0.553702i
$106$	3.61639	−	2.62746i	0.351255	−	0.255202i
$107$	−0.206029	−	1.30082i	−0.0199176	−	0.125755i	0.975726	−	0.218994i	$-0.0702777\pi$
$107$	−0.206029	−	1.30082i	−0.0199176	−	0.125755i	−0.995644	+	0.0932399i	$0.970278\pi$
$108$	−2.54897	+	5.00263i	−0.245274	+	0.481378i
$109$		−	5.83806i		−	0.559184i	−0.960119	−	0.279592i	$-0.909801\pi$
$109$		−	5.83806i		−	0.559184i	0.960119	−	0.279592i	$-0.0901993\pi$
$110$	3.59869	+	6.48455i	0.343122	+	0.618278i
$111$			9.72754i			0.923297i
$112$	2.64074	−	0.162825i	0.249526	−	0.0153856i
$113$	−9.73460	+	1.54181i	−0.915754	+	0.145041i	−0.596486	−	0.802623i	$-0.703437\pi$
$113$	−9.73460	+	1.54181i	−0.915754	+	0.145041i	−0.319268	+	0.947664i	$0.603437\pi$
$114$	0.686808	+	0.945309i	0.0643254	+	0.0885363i
$115$	−5.09497	−	3.23851i	−0.475108	−	0.301993i
$116$	−1.48541	+	4.57162i	−0.137917	+	0.424464i
$117$	0.378025	−	2.38676i	0.0349485	−	0.220656i
$118$	−1.93091	−	12.1913i	−0.177755	−	1.12230i
$119$	−3.00258	+	3.39719i	−0.275246	+	0.311420i
$120$	−2.52853	+	1.49291i	−0.230822	+	0.136284i
$121$	−0.587215	+	10.9843i	−0.0533832	+	0.998574i
$122$	−4.38971	+	4.38971i	−0.397425	+	0.397425i
$123$	−3.49952	−	1.78309i	−0.315541	−	0.160776i
$124$	2.94034	+	2.13628i	0.264050	+	0.191844i
$125$	6.83341	+	8.84898i	0.611199	+	0.791477i
$126$	3.29442	−	0.732065i	0.293490	−	0.0652175i
$127$	18.5465	−	9.44994i	1.64574	−	0.838546i	0.648751	−	0.761001i	$-0.275292\pi$
$127$	18.5465	−	9.44994i	1.64574	−	0.838546i	0.996989	−	0.0775455i	$-0.0247083\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−0.588112	−	0.427288i	−0.0517804	−	0.0376206i
$130$	2.80375	−	3.17561i	0.245905	−	0.278520i
$131$		−	7.06822i		−	0.617553i	−0.951135	−	0.308776i	$-0.900081\pi$
$131$		−	7.06822i		−	0.617553i	0.951135	−	0.308776i	$-0.0999195\pi$
$132$	−4.35379	−	0.116293i	−0.378949	−	0.0101220i
$133$	0.588312	−	2.27948i	0.0510131	−	0.197656i
$134$	−14.9586	+	4.86035i	−1.29223	+	0.419870i
$135$	−9.67924	+	7.99563i	−0.833056	+	0.688154i
$136$	−1.00726	−	1.38638i	−0.0863721	−	0.118881i
$137$	12.7634	−	6.50328i	1.09045	−	0.555613i	0.186156	−	0.982520i	$-0.440397\pi$
$137$	12.7634	−	6.50328i	1.09045	−	0.555613i	0.904295	+	0.426907i	$0.140397\pi$
$138$	3.15901	−	1.60959i	0.268912	−	0.137018i
$139$	10.2531	−	7.44930i	0.869656	−	0.631842i	−0.0608389	−	0.998148i	$-0.519378\pi$
$139$	10.2531	−	7.44930i	0.869656	−	0.631842i	0.930495	+	0.366306i	$0.119378\pi$
$140$	5.56237	+	2.01497i	0.470106	+	0.170296i
$141$	−0.355294	−	1.09348i	−0.0299211	−	0.0920877i
$142$	3.86242	+	3.86242i	0.324127	+	0.324127i
$143$	6.02551	−	1.78140i	0.503878	−	0.148968i
$144$			1.27554i			0.106295i
$145$	−7.11393	+	8.05747i	−0.590780	+	0.669136i
$146$	1.75585	−	2.41672i	0.145315	−	0.200009i
$147$	7.24922	+	5.65217i	0.597906	+	0.466183i
$148$	3.36298	+	6.60021i	0.276435	+	0.542534i
$149$	11.2869	+	3.66734i	0.924660	+	0.300440i	0.732377	−	0.680899i	$-0.238411\pi$
$149$	11.2869	+	3.66734i	0.924660	+	0.300440i	0.192283	+	0.981340i	$0.438411\pi$
$150$	−6.51533	+	0.813546i	−0.531974	+	0.0664258i
$151$	9.42755	+	6.84952i	0.767203	+	0.557406i	0.901111	−	0.433588i	$-0.142753\pi$
$151$	9.42755	+	6.84952i	0.767203	+	0.557406i	−0.133908	+	0.990994i	$0.542753\pi$
$152$	0.792814	+	0.403959i	0.0643057	+	0.0327654i
$153$	−1.54563	−	1.54563i	−0.124957	−	0.124957i
$154$	5.40220	+	6.91493i	0.435322	+	0.557221i
$155$	4.13189	+	6.99814i	0.331881	+	0.562104i
$156$	0.768778	+	2.36606i	0.0615515	+	0.189436i
$157$	−14.9078	+	2.36117i	−1.18977	+	0.188442i	−0.719764	−	0.694219i	$-0.755750\pi$
$157$	−14.9078	+	2.36117i	−1.18977	+	0.188442i	−0.470010	+	0.882661i	$0.655750\pi$
$158$	−0.0270046	+	0.170500i	−0.00214837	+	0.0135643i
$159$	−1.81395	+	5.58277i	−0.143856	+	0.442743i
$160$	−1.19950	+	1.88711i	−0.0948291	+	0.149189i
$161$	−6.55215	−	2.84510i	−0.516382	−	0.224226i
$162$	−0.554771	−	3.50269i	−0.0435870	−	0.275197i
$163$	11.0389	+	5.62463i	0.864637	+	0.440555i	0.829289	−	0.558820i	$-0.188746\pi$
$163$	11.0389	+	5.62463i	0.864637	+	0.440555i	0.0353485	+	0.999375i	$0.488746\pi$
$164$	−2.99090			−0.233550
$165$	−8.82845	−	4.11139i	−0.687294	−	0.320071i
$166$			16.0209i			1.24347i
$167$	−17.1710	−	8.74905i	−1.32873	−	0.677021i	−0.361845	−	0.932238i	$-0.617853\pi$
$167$	−17.1710	−	8.74905i	−1.32873	−	0.677021i	−0.966884	+	0.255217i	$0.917853\pi$
$168$	−2.67981	+	2.21129i	−0.206752	+	0.170605i
$169$	5.53159	+	7.61358i	0.425507	+	0.585660i
$170$	−0.833200	−	3.74017i	−0.0639036	−	0.286858i
$171$	1.07943	+	0.350726i	0.0825457	+	0.0268207i
$172$	−0.546760	−	0.0865982i	−0.0416900	−	0.00660305i
$173$	−2.96809	−	18.7398i	−0.225660	−	1.42476i	−0.796967	−	0.604023i	$-0.793564\pi$
$173$	−2.96809	−	18.7398i	−0.225660	−	1.42476i	0.571308	−	0.820736i	$-0.306436\pi$
$174$	−1.95062	−	6.00338i	−0.147876	−	0.455115i
$175$	9.61895	+	9.08162i	0.727124	+	0.686506i
$176$	−2.99429	+	1.42627i	−0.225703	+	0.107509i
$177$	11.4615	+	11.4615i	0.861498	+	0.861498i
$178$	0.875790	−	1.71884i	0.0656433	−	0.128832i
$179$	−5.47825	+	7.54016i	−0.409463	+	0.563578i	−0.963087	−	0.269189i	$-0.913244\pi$
$179$	−5.47825	+	7.54016i	−0.409463	+	0.563578i	0.553624	+	0.832767i	$0.313244\pi$
$180$	−1.13463	+	2.61681i	−0.0845705	+	0.195045i
$181$	5.98952	+	1.94611i	0.445197	+	0.144653i	0.523032	−	0.852313i	$-0.324801\pi$
$181$	5.98952	+	1.94611i	0.445197	+	0.144653i	−0.0778349	+	0.996966i	$0.524801\pi$
$182$	2.69104	−	4.22871i	0.199474	−	0.313453i
$183$	1.27529	−	8.05187i	0.0942722	−	0.595211i
$184$	1.58695	−	2.18424i	0.116991	−	0.161025i
$185$	1.02815	+	16.5319i	0.0755911	+	1.21545i
$186$	−4.77272			−0.349953
$187$	1.90002	−	5.35656i	0.138943	−	0.391711i
$188$	−0.619104	−	0.619104i	−0.0451528	−	0.0451528i
$189$	−9.83758	+	11.1304i	−0.715578	+	0.809621i
$190$	1.26714	+	1.53396i	0.0919282	+	0.111285i
$191$	6.99159	−	5.07969i	0.505894	−	0.367553i	−0.305370	−	0.952234i	$-0.598780\pi$
$191$	6.99159	−	5.07969i	0.505894	−	0.367553i	0.811264	+	0.584681i	$0.198780\pi$
$192$	−0.596174	−	1.17006i	−0.0430251	−	0.0844416i
$193$	4.59314	+	9.01455i	0.330622	+	0.648881i	0.995149	−	0.0983829i	$-0.0313670\pi$
$193$	4.59314	+	9.01455i	0.330622	+	0.648881i	−0.664527	+	0.747264i	$0.731367\pi$
$194$	6.94931	−	5.04897i	0.498932	−	0.362495i
$195$	−0.527506	+	5.53786i	−0.0377755	+	0.396575i
$196$	6.87271	+	1.32886i	0.490908	+	0.0949189i
$197$	−13.2846	−	13.2846i	−0.946489	−	0.946489i	0.0521498	−	0.998639i	$-0.483393\pi$
$197$	−13.2846	−	13.2846i	−0.946489	−	0.946489i	−0.998639	+	0.0521498i	$0.983393\pi$
$198$	−3.48772	+	2.39436i	−0.247862	+	0.170159i
$199$	−21.8695			−1.55029			−0.775145	−	0.631783i	$-0.782323\pi$
$199$	−21.8695			−1.55029			−0.775145	+	0.631783i	$0.782323\pi$
$200$	−4.13945	+	2.80446i	−0.292703	+	0.198305i
$201$	12.1403	−	16.7097i	0.856311	−	1.17861i
$202$	−0.229668	+	1.45007i	−0.0161594	+	0.102027i
$203$	−6.82798	+	10.7295i	−0.479230	+	0.753062i
$204$	2.14021	+	0.695396i	0.149845	+	0.0486875i
$205$	−6.13589	−	2.66049i	−0.428549	−	0.185816i
$206$	−1.61453	+	2.22220i	−0.112489	+	0.154828i
$207$	1.56346	−	3.06846i	0.108668	−	0.213273i
$208$	1.33961	+	1.33961i	0.0928851	+	0.0928851i
$209$	0.383664	+	2.92607i	0.0265386	+	0.202401i
$210$	−7.46469	+	2.15275i	−0.515113	+	0.148554i
$211$	8.40265	+	25.8607i	0.578462	+	1.78032i	0.624075	+	0.781364i	$0.285476\pi$
$211$	8.40265	+	25.8607i	0.578462	+	1.78032i	−0.0456128	+	0.998959i	$0.514524\pi$
$212$	0.699279	+	4.41507i	0.0480266	+	0.303228i
$213$	−7.08468	−	1.12210i	−0.485435	−	0.0768853i
$214$	1.25257	+	0.406985i	0.0856239	+	0.0278209i
$215$	−1.04466	−	0.664016i	−0.0712451	−	0.0452855i
$216$	−3.30017	−	4.54229i	−0.224548	−	0.309064i
$217$	6.12012	+	7.41682i	0.415461	+	0.503487i
$218$	5.20175	+	2.65042i	0.352307	+	0.179509i
$219$			3.92279i			0.265078i
$220$	−7.41155	+	0.262534i	−0.499687	+	0.0177000i
$221$	−3.24651			−0.218384
$222$	−8.66730	−	4.41621i	−0.581711	−	0.296397i
$223$	1.46601	+	9.25600i	0.0981710	+	0.619828i	0.986892	+	0.161380i	$0.0515944\pi$
$223$	1.46601	+	9.25600i	0.0981710	+	0.619828i	−0.888721	+	0.458448i	$0.848406\pi$
$224$	−1.05379	+	2.42683i	−0.0704093	+	0.162150i
$225$	−4.65544	+	4.35915i	−0.310363	+	0.290610i
$226$	3.04565	−	9.37356i	0.202594	−	0.623520i
$227$	−2.20430	+	13.9174i	−0.146304	+	0.923730i	0.799894	+	0.600142i	$0.204889\pi$
$227$	−2.20430	+	13.9174i	−0.146304	+	0.923730i	−0.946198	+	0.323588i	$0.895111\pi$
$228$	−1.15408	+	0.182788i	−0.0764309	+	0.0121055i
$229$	−0.454971	−	1.40026i	−0.0300653	−	0.0925315i	0.934898	−	0.354917i	$-0.115491\pi$
$229$	−0.454971	−	1.40026i	−0.0300653	−	0.0925315i	−0.964963	+	0.262385i	$0.915491\pi$
$230$	5.19860	−	3.06939i	0.342786	−	0.202390i
$231$	−11.0767	−	3.17654i	−0.728791	−	0.209001i
$232$	−3.39898	−	3.39898i	−0.223154	−	0.223154i
$233$	−4.25316	−	2.16709i	−0.278633	−	0.141971i	0.309090	−	0.951033i	$-0.399976\pi$
$233$	−4.25316	−	2.16709i	−0.278633	−	0.141971i	−0.587723	+	0.809062i	$0.699976\pi$
$234$	1.95500	+	1.42039i	0.127802	+	0.0928537i
$235$	−0.719396	−	1.82082i	−0.0469282	−	0.118777i
$236$	11.7391	+	3.81428i	0.764153	+	0.248288i
$237$	−0.102915	−	0.201982i	−0.00668504	−	0.0131201i
$238$	−1.66377	−	4.21761i	−0.107846	−	0.273387i
$239$	−6.16905	+	8.49097i	−0.399043	+	0.549235i	−0.960503	−	0.278268i	$-0.910240\pi$
$239$	−6.16905	+	8.49097i	−0.399043	+	0.549235i	0.561461	+	0.827503i	$0.310240\pi$
$240$	−0.182266	−	2.93071i	−0.0117652	−	0.189176i
$241$		−	13.0134i		−	0.838270i	−0.907924	−	0.419135i	$-0.862333\pi$
$241$		−	13.0134i		−	0.838270i	0.907924	−	0.419135i	$-0.137667\pi$
$242$	−9.52051	−	5.50999i	−0.612001	−	0.354195i
$243$	−8.61732	−	8.61732i	−0.552801	−	0.552801i
$244$	−1.91837	−	5.90414i	−0.122811	−	0.377974i
$245$	12.9174	+	8.83966i	0.825266	+	0.564745i
$246$	3.17750	−	2.30859i	0.202590	−	0.147190i
$247$	1.50198	−	0.765297i	0.0955687	−	0.0486947i
$248$	−3.23833	+	1.65001i	−0.205634	+	0.104776i
$249$	−12.3661	−	17.0205i	−0.783669	−	1.07863i
$250$	−10.9868	+	2.07126i	−0.694867	+	0.130998i
$251$	20.9182	−	6.79672i	1.32034	−	0.429005i	0.437730	−	0.899106i	$-0.355783\pi$
$251$	20.9182	−	6.79672i	1.32034	−	0.429005i	0.882613	+	0.470101i	$0.155783\pi$
$252$	−0.843360	+	3.26770i	−0.0531267	+	0.205846i
$253$	8.95128	+	0.239095i	0.562762	+	0.0150317i
$254$			20.8153i			1.30607i
$255$	3.77211	+	3.33040i	0.236219	+	0.208557i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	4.03785	−	25.4940i	0.251874	−	1.59027i	−0.459971	−	0.887934i	$-0.652140\pi$
$257$	4.03785	−	25.4940i	0.251874	−	1.59027i	0.711845	−	0.702337i	$-0.247860\pi$
$258$	0.647714	−	0.330027i	0.0403249	−	0.0205466i
$259$	4.25139	+	19.1320i	0.264168	+	1.18880i
$260$	1.55662	+	3.93985i	0.0965373	+	0.244339i
$261$	−4.96041	−	3.60395i	−0.307041	−	0.223079i
$262$	6.29783	+	3.20890i	0.389081	+	0.198247i
$263$	13.0437	−	13.0437i	0.804306	−	0.804306i	−0.179459	−	0.983765i	$-0.557435\pi$
$263$	13.0437	−	13.0437i	0.804306	−	0.804306i	0.983765	+	0.179459i	$0.0574348\pi$
$264$	2.08020	−	3.82646i	0.128027	−	0.235502i
$265$	−2.49274	+	9.67964i	−0.153128	+	0.594616i
$266$	1.76395	+	1.55905i	0.108155	+	0.0955917i
$267$	0.396289	+	2.50207i	0.0242525	+	0.153124i
$268$	2.46047	−	15.5348i	0.150297	−	0.948937i
$269$	−2.02121	+	6.22065i	−0.123236	+	0.379280i	−0.993575	−	0.113171i	$-0.963899\pi$
$269$	−2.02121	+	6.22065i	−0.123236	+	0.379280i	0.870340	+	0.492451i	$0.163899\pi$
$270$	−2.72987	−	12.2542i	−0.166135	−	0.745767i
$271$	8.26217	+	11.3719i	0.501891	+	0.690794i	0.982526	−	0.186127i	$-0.0595936\pi$
$271$	8.26217	+	11.3719i	0.501891	+	0.690794i	−0.480635	+	0.876921i	$0.659594\pi$
$272$	1.69256	−	0.268075i	0.102627	−	0.0162544i
$273$	0.405080	+	6.56967i	0.0245166	+	0.397615i
$274$			14.3247i			0.865387i
$275$	−15.4385	−	6.05418i	−0.930976	−	0.365081i
$276$			3.54544i			0.213410i
$277$	3.14752	−	6.17736i	0.189116	−	0.371161i	−0.776908	−	0.629615i	$-0.783213\pi$
$277$	3.14752	−	6.17736i	0.189116	−	0.371161i	0.966024	+	0.258453i	$0.0832128\pi$
$278$	1.98257	+	12.5175i	0.118907	+	0.750749i
$279$	−3.75054	+	2.72492i	−0.224539	+	0.163137i
$280$	−4.32061	+	4.04133i	−0.258206	+	0.241516i
$281$	9.56842	−	29.4486i	0.570804	−	1.75675i	−0.0792374	−	0.996856i	$-0.525249\pi$
$281$	9.56842	−	29.4486i	0.570804	−	1.75675i	0.650042	−	0.759899i	$-0.274751\pi$
$282$	1.13560	+	0.179861i	0.0676239	+	0.0107106i
$283$	2.97387	+	18.7763i	0.176778	+	1.11613i	0.903306	+	0.428997i	$0.141133\pi$
$283$	2.97387	+	18.7763i	0.176778	+	1.11613i	−0.726528	+	0.687137i	$0.758867\pi$
$284$	−5.19494	+	1.68794i	−0.308263	+	0.100161i
$285$	−2.53022	−	0.651592i	−0.149877	−	0.0385970i
$286$	−1.14828	+	6.17750i	−0.0678994	+	0.365283i
$287$	−7.66210	−	1.97751i	−0.452279	−	0.116729i
$288$	−1.13652	−	0.579085i	−0.0669700	−	0.0341229i
$289$	8.26625	−	11.3775i	0.486250	−	0.669265i
$290$	−3.94960	−	9.99657i	−0.231928	−	0.587019i
$291$	−3.48572	+	10.7279i	−0.204337	+	0.628883i
$292$	1.35618	+	2.66165i	0.0793642	+	0.155761i
$293$	32.1364	+	5.08991i	1.87743	+	0.297356i	0.987363	−	0.158473i	$-0.0506570\pi$
$293$	32.1364	+	5.08991i	1.87743	+	0.297356i	0.890068	+	0.455829i	$0.150657\pi$
$294$	−8.32720	+	3.89307i	−0.485652	+	0.227049i
$295$	20.6902	+	18.2674i	1.20463	+	1.06357i
$296$	−7.40759			−0.430557
$297$	6.22518	−	17.5501i	0.361221	−	1.01836i
$298$	−8.39178	+	8.39178i	−0.486122	+	0.486122i
$299$	−1.58059	−	4.86455i	−0.0914078	−	0.281324i
$300$	2.23302	−	6.17454i	0.128924	−	0.356487i
$301$	−1.34343	−	0.583352i	−0.0774343	−	0.0336239i
$302$	−10.3830	+	5.29039i	−0.597473	+	0.304428i
$303$	−0.875269	−	1.71781i	−0.0502829	−	0.0986857i
$304$	−0.719860	+	0.523009i	−0.0412868	+	0.0299966i
$305$	1.31631	−	13.8189i	0.0753719	−	0.791269i
$306$	2.07886	−	0.675464i	0.118841	−	0.0386137i
$307$	9.86427	−	9.86427i	0.562984	−	0.562984i	−0.367170	−	0.930154i	$-0.619673\pi$
$307$	9.86427	−	9.86427i	0.562984	−	0.562984i	0.930154	+	0.367170i	$0.119673\pi$
$308$	−8.61379	+	1.67409i	−0.490816	+	0.0953899i
$309$		−	3.60705i		−	0.205198i
$310$	−8.11123	+	0.504452i	−0.460687	+	0.0286509i
$311$	9.41140	−	12.9537i	0.533672	−	0.734536i	−0.454013	−	0.890995i	$-0.650008\pi$
$311$	9.41140	−	12.9537i	0.533672	−	0.734536i	0.987684	+	0.156459i	$0.0500079\pi$
$312$	−2.45719	−	0.389181i	−0.139111	−	0.0220330i
$313$	−15.8908	+	8.09678i	−0.898203	+	0.457657i	−0.841205	−	0.540717i	$-0.818153\pi$
$313$	−15.8908	+	8.09678i	−0.898203	+	0.457657i	−0.0569984	+	0.998374i	$0.518153\pi$
$314$	4.66420	−	14.3549i	0.263216	−	0.810095i
$315$	−4.63688	+	5.95356i	−0.261258	+	0.335445i
$316$	−0.139657	−	0.101467i	−0.00785633	−	0.00570795i
$317$	5.84797	−	11.4773i	0.328455	−	0.644628i	−0.666439	−	0.745560i	$-0.732182\pi$
$317$	5.84797	−	11.4773i	0.328455	−	0.644628i	0.994893	+	0.100931i	$0.0321822\pi$
$318$	−4.15077	−	4.15077i	−0.232764	−	0.232764i
$319$	2.91353	−	15.6741i	0.163127	−	0.877584i
$320$	−1.13686	−	1.92550i	−0.0635527	−	0.107639i
$321$	−1.64486	+	0.534446i	−0.0918069	+	0.0298299i
$322$	5.50962	−	4.54636i	0.307039	−	0.253359i
$323$	0.238532	−	1.50603i	0.0132723	−	0.0837979i
$324$	3.37278	+	1.09588i	0.187377	+	0.0608824i
$325$	−0.311172	+	9.46735i	−0.0172607	+	0.525154i
$326$	−10.0232	+	7.28225i	−0.555131	+	0.403326i
$327$	−7.57206	+	1.19930i	−0.418736	+	0.0663213i
$328$	1.35784	−	2.66491i	0.0749741	−	0.147145i
$329$	−1.17669	−	1.99536i	−0.0648729	−	0.110008i
$330$	7.67131	−	5.99967i	0.422292	−	0.330271i
$331$	21.3521			1.17362			0.586808	−	0.809726i	$-0.300384\pi$
$331$	21.3521			1.17362			0.586808	+	0.809726i	$0.300384\pi$
$332$	−14.2748	−	7.27335i	−0.783429	−	0.399177i
$333$	−9.33239	+	1.47810i	−0.511412	+	0.0809996i
$334$	15.5909	−	11.3275i	0.853097	−	0.619811i
$335$	18.8663	−	29.6813i	1.03078	−	1.62166i
$336$	−0.753667	−	3.39163i	−0.0411159	−	0.185029i
$337$	−30.3244	−	4.80291i	−1.65187	−	0.261631i	−0.740152	−	0.672440i	$-0.765246\pi$
$337$	−30.3244	−	4.80291i	−1.65187	−	0.261631i	−0.911722	+	0.410809i	$0.865246\pi$
$338$	−9.29504	+	1.47219i	−0.505583	+	0.0800765i
$339$	3.99951	+	12.3092i	0.217223	+	0.668545i
$340$	3.71078	+	0.955616i	0.201246	+	0.0518256i
$341$	−10.5904	−	5.75729i	−0.573501	−	0.311775i
$342$	−0.802548	+	0.802548i	−0.0433968	+	0.0433968i
$343$	16.7279	+	7.94836i	0.903223	+	0.429171i
$344$	0.325383	−	0.447852i	0.0175435	−	0.0241465i
$345$	−3.15376	+	7.27354i	−0.169793	+	0.391594i
$346$	18.0447	+	5.86309i	0.970091	+	0.315202i
$347$	15.1298	−	7.70902i	0.812211	−	0.413842i	0.00201260	−	0.999998i	$-0.499359\pi$
$347$	15.1298	−	7.70902i	0.812211	−	0.413842i	0.810198	+	0.586156i	$0.199359\pi$
$348$	6.23461	+	0.987466i	0.334210	+	0.0529337i
$349$	10.5150	+	7.63960i	0.562855	+	0.408938i	0.832503	−	0.554021i	$-0.186907\pi$
$349$	10.5150	+	7.63960i	0.562855	+	0.408938i	−0.269648	+	0.962959i	$0.586907\pi$
$350$	−12.4587	+	4.44757i	−0.665945	+	0.237733i
$351$	−10.6368			−0.567749
$352$	0.0885576	−	3.31544i	0.00472014	−	0.176714i
$353$	11.1665	+	11.1665i	0.594332	+	0.594332i	0.938799	−	0.344467i	$-0.111940\pi$
$353$	11.1665	+	11.1665i	0.594332	+	0.594332i	−0.344467	+	0.938799i	$0.611940\pi$
$354$	−15.4157	+	5.00885i	−0.819333	+	0.266218i
$355$	−12.1590	−	1.15820i	−0.645333	−	0.0614708i
$356$	1.13389	+	1.56067i	0.0600962	+	0.0827153i
$357$	5.02302	+	3.19653i	0.265847	+	0.169178i
$358$	−4.23126	−	8.30431i	−0.223629	−	0.438897i
$359$	−21.0588	−	28.9850i	−1.11144	−	1.52977i	−0.819275	−	0.573401i	$-0.805624\pi$
$359$	−21.0588	−	28.9850i	−1.11144	−	1.52977i	−0.292167	−	0.956367i	$-0.594376\pi$
$360$	−1.81648	−	2.19897i	−0.0957370	−	0.115896i
$361$	−5.62666	−	17.3171i	−0.296140	−	0.911426i
$362$	−4.45318	+	4.45318i	−0.234054	+	0.234054i
$363$	14.3675	−	1.49485i	0.754097	−	0.0784593i
$364$	2.54610	+	4.31753i	0.133452	+	0.226300i
$365$	0.414619	+	6.66678i	0.0217021	+	0.348955i
$366$	6.59530	+	4.79176i	0.344742	+	0.250469i
$367$	0.992532	−	6.26660i	0.0518098	−	0.327114i	−0.948147	−	0.317832i	$-0.897045\pi$
$367$	0.992532	−	6.26660i	0.0518098	−	0.327114i	0.999957	−	0.00928229i	$-0.00295469\pi$
$368$	1.22572	+	2.40561i	0.0638950	+	0.125401i
$369$	1.17891	−	3.62830i	0.0613715	−	0.188882i
$370$	−15.1968	−	6.58925i	−0.790046	−	0.342559i
$371$	−1.12772	+	11.7729i	−0.0585485	+	0.611218i
$372$	2.16677	−	4.25252i	0.112342	−	0.220483i
$373$	−10.0143	+	10.0143i	−0.518521	+	0.518521i	−0.917124	−	0.398603i	$-0.869495\pi$
$373$	−10.0143	+	10.0143i	−0.518521	+	0.518521i	0.398603	+	0.917124i	$0.369495\pi$
$374$	3.91014	+	4.12476i	0.202189	+	0.213286i
$375$	10.0735	−	10.6809i	0.520194	−	0.551558i
$376$	0.832694	−	0.270559i	0.0429429	−	0.0139530i
$377$	−8.99449	+	1.42459i	−0.463240	+	0.0733700i
$378$	−5.45113	−	13.8185i	−0.280376	−	0.710745i
$379$	2.17008	+	0.705101i	0.111469	+	0.0362186i	0.364221	−	0.931313i	$-0.381335\pi$
$379$	2.17008	+	0.705101i	0.111469	+	0.0362186i	−0.252751	+	0.967531i	$0.581335\pi$
$380$	−1.94204	+	0.432629i	−0.0996245	+	0.0221934i
$381$	−16.0667	−	22.1139i	−0.823122	−	1.13293i
$382$	1.35192	+	8.53568i	0.0691702	+	0.436723i
$383$	7.97074	−	15.6435i	0.407286	−	0.799343i	−0.592696	−	0.805426i	$-0.701936\pi$
$383$	7.97074	−	15.6435i	0.407286	−	0.799343i	0.999981	+	0.00608332i	$0.00193639\pi$
$384$	1.31319			0.0670132
$385$	−19.1605	−	4.22778i	−0.976511	−	0.215468i
$386$	−10.1173			−0.514955
$387$	0.320567	−	0.629148i	0.0162953	−	0.0319814i
$388$	1.34374	+	8.48407i	0.0682183	+	0.430713i
$389$	14.6081	+	20.1063i	0.740660	+	1.01943i	0.998580	+	0.0532650i	$0.0169628\pi$
$389$	14.6081	+	20.1063i	0.740660	+	1.01943i	−0.257920	+	0.966166i	$0.583037\pi$
$390$	−4.69479	−	2.98415i	−0.237730	−	0.151108i
$391$	−4.40022	−	1.42972i	−0.222529	−	0.0723039i
$392$	−4.30417	+	5.52034i	−0.217393	+	0.278819i
$393$	−9.16760	+	1.45201i	−0.462444	+	0.0732440i
$394$	17.8678	−	5.80559i	0.900165	−	0.292481i
$395$	−0.196252	−	0.332390i	−0.00987451	−	0.0167244i
$396$	−0.549992	−	4.19460i	−0.0276381	−	0.210787i
$397$	9.82584	−	9.82584i	0.493145	−	0.493145i	−0.416151	−	0.909296i	$-0.636621\pi$
$397$	9.82584	−	9.82584i	0.493145	−	0.493145i	0.909296	+	0.416151i	$0.136621\pi$
$398$	9.92856	−	19.4859i	0.497674	−	0.976740i
$399$	−3.07739	−	0.294782i	−0.154062	−	0.0147576i
$400$	−0.619522	−	4.96147i	−0.0309761	−	0.248074i
$401$	8.01231	−	24.6594i	0.400116	−	1.23143i	−0.524789	−	0.851232i	$-0.675856\pi$
$401$	8.01231	−	24.6594i	0.400116	−	1.23143i	0.924905	−	0.380198i	$-0.124144\pi$
$402$	9.37687	+	18.4031i	0.467676	+	0.917865i
$403$	−1.07712	+	6.80068i	−0.0536553	+	0.338766i
$404$	−1.18775	−	0.862954i	−0.0590930	−	0.0429336i
$405$	5.94451	+	5.24841i	0.295385	+	0.260795i
$406$	−6.46020	−	10.9549i	−0.320614	−	0.543680i
$407$	−13.9050	−	20.2546i	−0.689243	−	1.00398i
$408$	−1.59124	+	1.59124i	−0.0787780	+	0.0787780i
$409$	−0.389181	−	1.19778i	−0.0192438	−	0.0592263i	0.940973	−	0.338480i	$-0.109913\pi$
$409$	−0.389181	−	1.19778i	−0.0192438	−	0.0592263i	−0.960217	+	0.279254i	$0.909913\pi$
$410$	5.15615	−	4.25929i	0.254644	−	0.210351i
$411$	−11.0568	−	15.2184i	−0.545393	−	0.750669i
$412$	−1.24702	−	2.44741i	−0.0614362	−	0.120575i
$413$	27.5515	+	17.5331i	1.35572	+	0.862746i
$414$	2.02422	+	2.78610i	0.0994851	+	0.136929i
$415$	−22.8151	−	27.6192i	−1.11995	−	1.35577i
$416$	−1.80177	+	0.585430i	−0.0883390	+	0.0287031i
$417$	−11.7681	−	11.7681i	−0.576289	−	0.576289i
$418$	−2.78133	−	0.986562i	−0.136039	−	0.0482543i
$419$	−11.7070			−0.571925			−0.285963	−	0.958241i	$-0.592313\pi$
$419$	−11.7070			−0.571925			−0.285963	+	0.958241i	$0.592313\pi$
$420$	1.47078	−	7.62842i	0.0717670	−	0.372229i
$421$	1.18102	+	0.858059i	0.0575592	+	0.0418192i	0.616193	−	0.787595i	$-0.288674\pi$
$421$	1.18102	+	0.858059i	0.0575592	+	0.0418192i	−0.558634	+	0.829415i	$0.688674\pi$
$422$	−26.8568	−	4.25369i	−1.30737	−	0.207067i
$423$	0.995074	−	0.507016i	0.0483822	−	0.0246520i
$424$	−4.25132	−	1.38134i	−0.206462	−	0.0670837i
$425$	6.76271	+	5.26131i	0.328039	+	0.255211i
$426$	4.21618	−	5.80308i	0.204275	−	0.281160i
$427$	−1.01082	−	16.3936i	−0.0489169	−	0.793344i
$428$	−0.931281	+	0.931281i	−0.0450152	+	0.0450152i
$429$	−3.54831	−	7.44924i	−0.171314	−	0.359653i
$430$	1.06591	−	0.629340i	0.0514026	−	0.0303495i
$431$	4.62840	+	14.2447i	0.222942	+	0.686145i	0.998494	+	0.0548615i	$0.0174717\pi$
$431$	4.62840	+	14.2447i	0.222942	+	0.686145i	−0.775552	+	0.631284i	$0.782528\pi$
$432$	5.54546	−	0.878314i	0.266806	−	0.0422579i
$433$	16.9782	+	2.68908i	0.815920	+	0.129229i	0.550426	−	0.834884i	$-0.314465\pi$
$433$	16.9782	+	2.68908i	0.815920	+	0.129229i	0.265493	+	0.964113i	$0.414465\pi$
$434$	−9.38691	+	2.08590i	−0.450586	+	0.100126i
$435$	11.9121	+	7.57167i	0.571140	+	0.363034i
$436$	−4.72309	+	3.43152i	−0.226195	+	0.164340i
$437$	2.37276	−	0.375808i	0.113505	−	0.0179774i
$438$	−3.49523	−	1.78091i	−0.167009	−	0.0850952i
$439$	23.6822			1.13029			0.565146	−	0.824991i	$-0.308820\pi$
$439$	23.6822			1.13029			0.565146	+	0.824991i	$0.308820\pi$
$440$	3.13085	−	6.72293i	0.149258	−	0.320503i
$441$	−4.32105	+	7.81360i	−0.205764	+	0.372076i
$442$	1.47389	−	2.89266i	0.0701056	−	0.137590i
$443$	−18.2562	+	2.89150i	−0.867380	+	0.137380i	−0.574237	−	0.818689i	$-0.694701\pi$
$443$	−18.2562	+	2.89150i	−0.867380	+	0.137380i	−0.293143	+	0.956069i	$0.594701\pi$
$444$	7.86974	−	5.71770i	0.373482	−	0.271350i
$445$	0.937948	+	4.21038i	0.0444630	+	0.199591i
$446$	−8.91271	−	2.89591i	−0.422029	−	0.137126i
$447$	2.43796	−	15.3927i	0.115312	−	0.728050i
$448$	−1.68391	−	2.04069i	−0.0795575	−	0.0964137i
$449$	−4.18923	+	1.36116i	−0.197702	+	0.0642372i	−0.406194	−	0.913787i	$-0.633144\pi$
$449$	−4.18923	+	1.36116i	−0.197702	+	0.0642372i	0.208492	+	0.978024i	$0.433144\pi$
$450$	−1.77051	−	6.12704i	−0.0834625	−	0.288832i
$451$	9.83550	−	1.28962i	0.463136	−	0.0607259i
$452$	6.96920	+	6.96920i	0.327804	+	0.327804i
$453$	6.94726	−	13.6348i	0.326411	−	0.640618i
$454$	−11.3998	−	8.28241i	−0.535017	−	0.388713i
$455$	1.38281	+	11.1223i	0.0648273	+	0.521423i
$456$	0.361076	−	1.11128i	0.0169089	−	0.0520404i
$457$	−28.8634	+	14.7066i	−1.35017	+	0.687948i	−0.971379	−	0.237533i	$-0.923661\pi$
$457$	−28.8634	+	14.7066i	−1.35017	+	0.687948i	−0.378794	+	0.925481i	$0.623661\pi$
$458$	1.45419	+	0.230321i	0.0679498	+	0.0107622i
$459$	−5.65536	+	7.78394i	−0.263970	+	0.363323i
$460$	0.374734	+	6.02546i	0.0174721	+	0.280939i
$461$		−	11.6851i		−	0.544231i	−0.962265	−	0.272116i	$-0.912277\pi$
$461$		−	11.6851i		−	0.544231i	0.962265	−	0.272116i	$-0.0877233\pi$
$462$	7.85902	−	8.42727i	0.365635	−	0.392072i
$463$	23.2762	−	23.2762i	1.08174	−	1.08174i	0.0853888	−	0.996348i	$-0.472787\pi$
$463$	23.2762	−	23.2762i	1.08174	−	1.08174i	0.996348	−	0.0853888i	$-0.0272132\pi$
$464$	4.57162	−	1.48541i	0.212232	−	0.0689584i
$465$	8.22791	−	6.79674i	0.381560	−	0.315191i
$466$	3.86178	−	2.80575i	0.178894	−	0.129974i
$467$	12.0832	+	23.7146i	0.559143	+	1.09738i	0.981591	+	0.190993i	$0.0611709\pi$
$467$	12.0832	+	23.7146i	0.559143	+	1.09738i	−0.422448	+	0.906387i	$0.638829\pi$
$468$	−2.15313	+	1.09707i	−0.0995283	+	0.0507122i
$469$	16.5745	−	38.1703i	0.765337	−	1.76254i
$470$	1.94896	+	0.185647i	0.0898987	+	0.00856325i
$471$	6.12495	+	18.8507i	0.282223	+	0.868593i
$472$	−8.72800	+	8.72800i	−0.401739	+	0.401739i
$473$	1.83535	+	0.0490233i	0.0843893	+	0.00225409i
$474$	0.226689			0.0104122
$475$	−4.36897	−	0.839949i	−0.200462	−	0.0385395i
$476$	4.51325	+	0.432324i	0.206865	+	0.0198155i
$477$	−5.63162	−	0.891961i	−0.257854	−	0.0408401i
$478$	−4.76482	−	9.35149i	−0.217938	−	0.427727i
$479$	−6.80872	+	20.9551i	−0.311098	+	0.957463i	0.666232	+	0.745744i	$0.267906\pi$
$479$	−6.80872	+	20.9551i	−0.311098	+	0.957463i	−0.977331	+	0.211718i	$0.932094\pi$
$480$	2.69403	+	1.16811i	0.122965	+	0.0533169i
$481$	−8.24876	+	11.3534i	−0.376111	+	0.517672i
$482$	11.5951	+	5.90798i	0.528141	+	0.269101i
$483$	−2.34416	+	9.08272i	−0.106663	+	0.413278i
$484$	9.23165	−	5.98135i	0.419621	−	0.271880i
$485$	−4.79009	+	18.6006i	−0.217507	+	0.844608i
$486$	11.5903	−	3.76591i	0.525745	−	0.170825i
$487$	4.27482	+	26.9902i	0.193711	+	1.22304i	0.872465	+	0.488676i	$0.162520\pi$
$487$	4.27482	+	26.9902i	0.193711	+	1.22304i	−0.678755	+	0.734365i	$0.737480\pi$
$488$	6.13155	+	0.971143i	0.277562	+	0.0439616i
$489$	5.02754	−	15.4732i	0.227353	−	0.699721i
$490$	−13.7406	+	7.49641i	−0.620737	+	0.338653i
$491$	9.64348	−	7.00640i	0.435204	−	0.316194i	−0.348522	−	0.937300i	$-0.613316\pi$
$491$	9.64348	−	7.00640i	0.435204	−	0.316194i	0.783726	+	0.621106i	$0.213316\pi$
$492$	0.614412	+	3.87925i	0.0276999	+	0.174890i
$493$	−3.73968	+	7.33954i	−0.168427	+	0.330556i
$494$			1.68571i			0.0758437i
$495$	2.60289	−	9.09455i	0.116991	−	0.408769i
$496$		−	3.63446i		−	0.163192i
$497$	−14.4245	+	0.889400i	−0.647026	+	0.0398950i
$498$	20.7794	−	3.29114i	0.931148	−	0.147479i
$499$	−7.62346	−	10.4928i	−0.341273	−	0.469722i	0.603540	−	0.797333i	$-0.293756\pi$
$499$	−7.62346	−	10.4928i	−0.341273	−	0.469722i	−0.944813	+	0.327611i	$0.893756\pi$
$500$	3.14240	−	10.7296i	0.140532	−	0.479844i
$501$	−7.82028	+	24.0683i	−0.349384	+	1.07529i
$502$	−3.44072	+	21.7239i	−0.153567	+	0.969583i
$503$	5.10653	+	32.2414i	0.227689	+	1.43757i	0.791248	+	0.611495i	$0.209432\pi$
$503$	5.10653	+	32.2414i	0.227689	+	1.43757i	−0.563559	+	0.826076i	$0.690568\pi$
$504$	−2.52866	−	2.23494i	−0.112636	−	0.0995523i
$505$	−1.66908	−	2.82691i	−0.0742732	−	0.125796i
$506$	−4.27683	+	7.86710i	−0.190128	+	0.349735i
$507$	8.73861	−	8.73861i	0.388095	−	0.388095i
$508$	−18.5465	−	9.44994i	−0.822870	−	0.419273i
$509$	−2.89936	−	2.10651i	−0.128512	−	0.0933694i	0.521672	−	0.853146i	$-0.325308\pi$
$509$	−2.89936	−	2.10651i	−0.128512	−	0.0933694i	−0.650184	+	0.759777i	$0.725308\pi$
$510$	−4.67991	+	1.84901i	−0.207230	+	0.0818755i
$511$	1.71444	+	7.71529i	0.0758425	+	0.341304i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	0.781520	−	4.93432i	0.0345050	−	0.217856i
$514$	20.8822	+	15.1718i	0.921072	+	0.669198i
$515$	−0.381247	−	6.13018i	−0.0167997	−	0.270128i
$516$			0.726947i			0.0320020i
$517$	2.30286	+	1.76896i	0.101280	+	0.0777990i
$518$	−18.9768	−	4.89772i	−0.833793	−	0.215194i
$519$	−23.6961	+	7.69933i	−1.04014	+	0.337963i
$520$	−4.21712	−	0.401700i	−0.184933	−	0.0176157i
$521$	−17.6793	−	24.3335i	−0.774546	−	1.06607i	−0.995863	−	0.0908694i	$-0.971035\pi$
$521$	−17.6793	−	24.3335i	−0.774546	−	1.06607i	0.221317	−	0.975202i	$-0.428965\pi$
$522$	5.46312	−	2.78360i	0.239114	−	0.121835i
$523$	−28.2984	+	14.4188i	−1.23740	+	0.630488i	−0.945395	−	0.325928i	$-0.894323\pi$
$523$	−28.2984	+	14.4188i	−1.23740	+	0.630488i	−0.292008	+	0.956416i	$0.594323\pi$
$524$	−5.71831	+	4.15459i	−0.249805	+	0.181494i
$525$	9.80303	−	14.3416i	0.427839	−	0.625917i
$526$	5.70029	+	17.5437i	0.248544	+	0.764941i
$527$	4.40402	+	4.40402i	0.191842	+	0.191842i
$528$	2.46501	+	3.59064i	0.107276	+	0.156263i
$529$			15.7107i			0.683073i
$530$	−7.49294	−	6.61551i	−0.325473	−	0.287360i
$531$	−9.25432	+	12.7375i	−0.401603	+	0.552759i
$532$	−2.18994	+	0.863893i	−0.0949460	+	0.0374545i
$533$	−2.57242	−	5.04865i	−0.111424	−	0.218681i
$534$	−2.40927	−	0.782820i	−0.104259	−	0.0338759i
$535$	−2.73894	+	1.08214i	−0.118415	+	0.0467851i
$536$	12.7246	+	9.24493i	0.549617	+	0.399320i
$537$	10.9051	+	5.55643i	0.470590	+	0.239777i
$538$	−4.62503	−	4.62503i	−0.199399	−	0.199399i
$539$	−23.1737	−	1.40655i	−0.998163	−	0.0605845i
$540$	12.1579	+	3.13095i	0.523193	+	0.134735i
$541$	3.72136	+	11.4532i	0.159994	+	0.492410i	0.998633	−	0.0522778i	$-0.0166481\pi$
$541$	3.72136	+	11.4532i	0.159994	+	0.492410i	−0.838639	+	0.544688i	$0.816648\pi$
$542$	−13.8834	+	2.19891i	−0.596342	+	0.0944514i
$543$	1.29373	−	8.16829i	0.0555193	−	0.350535i
$544$	−0.529549	+	1.62979i	−0.0227042	+	0.0698765i
$545$	−12.7420	+	2.83853i	−0.545805	+	0.121589i
$546$	−6.03752	−	2.62164i	−0.258382	−	0.112196i
$547$	3.71458	+	23.4530i	0.158824	+	1.00278i	0.930375	+	0.366609i	$0.119481\pi$
$547$	3.71458	+	23.4530i	0.158824	+	1.00278i	−0.771551	+	0.636167i	$0.780519\pi$
$548$	−12.7634	−	6.50328i	−0.545226	−	0.277806i
$549$	7.91856			0.337956
$550$	12.4032	−	11.0073i	0.528876	−	0.469351i
$551$		−	4.27715i		−	0.182213i
$552$	−3.15901	−	1.60959i	−0.134456	−	0.0685089i
$553$	−0.290687	−	0.352276i	−0.0123613	−	0.0149803i
$554$	4.07512	+	5.60892i	0.173135	+	0.238300i
$555$	21.2310	−	4.72964i	0.901206	−	0.200762i
$556$	−12.0532	−	3.91633i	−0.511171	−	0.166089i
$557$	0.812690	+	0.128717i	0.0344348	+	0.00545393i	0.173628	−	0.984811i	$-0.444451\pi$
$557$	0.812690	+	0.128717i	0.0344348	+	0.00545393i	−0.139193	+	0.990265i	$0.544451\pi$
$558$	−0.725217	−	4.57884i	−0.0307009	−	0.193838i
$559$	−0.324080	−	0.997414i	−0.0137071	−	0.0421861i
$560$	−1.63933	−	5.68442i	−0.0692745	−	0.240210i
$561$	−7.33788	−	1.36398i	−0.309805	−	0.0575871i
$562$	21.8949	+	21.8949i	0.923580	+	0.923580i
$563$	−9.85314	+	19.3379i	−0.415260	+	0.814994i	0.584733	+	0.811226i	$0.301199\pi$
$563$	−9.85314	+	19.3379i	−0.415260	+	0.814994i	−0.999993	+	0.00376806i	$0.998801\pi$
$564$	−0.675808	+	0.930170i	−0.0284567	+	0.0391672i
$565$	8.09818	+	20.4968i	0.340693	+	0.862306i
$566$	−18.0799	−	5.87451i	−0.759954	−	0.246924i
$567$	7.91583	+	5.03744i	0.332434	+	0.211553i
$568$	0.854490	−	5.39504i	0.0358536	−	0.226371i
$569$	25.7230	−	35.4047i	1.07837	−	1.48424i	0.217058	−	0.976159i	$-0.430354\pi$
$569$	25.7230	−	35.4047i	1.07837	−	1.48424i	0.861307	−	0.508084i	$-0.169646\pi$
$570$	1.72927	−	1.95862i	0.0724310	−	0.0820377i
$571$	10.4604			0.437755			0.218878	−	0.975752i	$-0.429760\pi$
$571$	10.4604			0.437755			0.218878	+	0.975752i	$0.429760\pi$
$572$	−4.98289	−	3.82766i	−0.208345	−	0.160042i
$573$	−8.02471	−	8.02471i	−0.335237	−	0.335237i
$574$	5.24049	−	5.92921i	0.218734	−	0.247480i
$575$	−4.59104	+	12.6947i	−0.191460	+	0.529406i
$576$	1.03194	−	0.749746i	0.0429974	−	0.0312394i
$577$	7.30274	+	14.3324i	0.304017	+	0.596667i	0.991586	−	0.129453i	$-0.0413220\pi$
$577$	7.30274	+	14.3324i	0.304017	+	0.596667i	−0.687569	+	0.726119i	$0.741322\pi$
$578$	6.38464	+	12.5306i	0.265566	+	0.521203i
$579$	10.7485	−	7.80922i	0.446691	−	0.324540i
$580$	10.7001	+	1.01923i	0.444297	+	0.0423212i
$581$	−31.7602	−	28.0710i	−1.31763	−	1.16458i
$582$	−7.97619	−	7.97619i	−0.330624	−	0.330624i
$583$	−4.20326	−	14.2173i	−0.174081	−	0.588822i
$584$	−2.98723			−0.123613
$585$	−5.39306	+	0.335404i	−0.222976	+	0.0138672i
$586$	−19.1248	+	26.3230i	−0.790038	+	1.08739i
$587$	−5.14812	+	32.5040i	−0.212486	+	1.34158i	0.618717	+	0.785614i	$0.287653\pi$
$587$	−5.14812	+	32.5040i	−0.212486	+	1.34158i	−0.831203	+	0.555969i	$0.812347\pi$
$588$	0.311718	−	9.18701i	0.0128550	−	0.378866i
$589$	−3.07565	−	0.999339i	−0.126730	−	0.0411770i
$590$	−25.6695	+	10.1419i	−1.05680	+	0.417535i
$591$	−14.5014	+	19.9594i	−0.596506	+	0.821020i
$592$	3.36298	−	6.60021i	0.138217	−	0.271267i
$593$	−9.17885	−	9.17885i	−0.376930	−	0.376930i	0.493063	−	0.869993i	$-0.335877\pi$
$593$	−9.17885	−	9.17885i	−0.376930	−	0.376930i	−0.869993	+	0.493063i	$0.835877\pi$
$594$	12.8111	+	13.5143i	0.525645	+	0.554496i
$595$	8.87448	+	4.90158i	0.363818	+	0.200945i
$596$	−3.66734	−	11.2869i	−0.150220	−	0.462330i
$597$	4.49260	+	28.3652i	0.183870	+	1.16091i
$598$	5.05192	+	0.800145i	0.206588	+	0.0327204i
$599$	−3.92211	−	1.27437i	−0.160253	−	0.0520694i	0.227792	−	0.973710i	$-0.426849\pi$
$599$	−3.92211	−	1.27437i	−0.160253	−	0.0520694i	−0.388045	+	0.921640i	$0.626849\pi$
$600$	4.48779	+	4.79282i	0.183213	+	0.195666i
$601$	−7.10255	−	9.77582i	−0.289719	−	0.398764i	0.639204	−	0.769037i	$-0.279264\pi$
$601$	−7.10255	−	9.77582i	−0.289719	−	0.398764i	−0.928923	+	0.370273i	$0.879264\pi$
$602$	1.12968	−	0.932173i	0.0460422	−	0.0379925i
$603$	17.8756	+	9.10809i	0.727952	+	0.370910i
$604$		−	11.6531i		−	0.474158i
$605$	24.2595	−	4.05906i	0.986289	−	0.165024i
$606$	1.92795			0.0783174
$607$	−35.0030	−	17.8349i	−1.42073	−	0.723897i	−0.436320	−	0.899792i	$-0.643718\pi$
$607$	−35.0030	−	17.8349i	−1.42073	−	0.723897i	−0.984409	+	0.175894i	$0.943718\pi$
$608$	−0.139195	−	0.878841i	−0.00564509	−	0.0356417i
$609$	15.3190	+	6.65187i	0.620756	+	0.269548i
$610$	11.7152	+	7.44650i	0.474333	+	0.301500i
$611$	0.512571	−	1.57753i	0.0207364	−	0.0638201i
$612$	−0.341942	+	2.15894i	−0.0138222	+	0.0872698i
$613$	−19.0227	+	3.01291i	−0.768321	+	0.121690i	−0.528277	−	0.849072i	$-0.677162\pi$
$613$	−19.0227	+	3.01291i	−0.768321	+	0.121690i	−0.240044	+	0.970762i	$0.577162\pi$
$614$	4.31084	+	13.2674i	0.173972	+	0.535429i
$615$	−2.19022	+	8.50490i	−0.0883180	+	0.342951i
$616$	2.41896	−	8.43497i	0.0974626	−	0.339854i
$617$	6.17359	+	6.17359i	0.248539	+	0.248539i	0.820371	−	0.571832i	$-0.193767\pi$
$617$	6.17359	+	6.17359i	0.248539	+	0.248539i	−0.571832	+	0.820371i	$0.693767\pi$
$618$	3.21391	+	1.63757i	0.129282	+	0.0658726i
$619$	−33.9147	−	24.6405i	−1.36315	−	0.990384i	−0.998238	−	0.0593415i	$-0.981100\pi$
$619$	−33.9147	−	24.6405i	−1.36315	−	0.990384i	−0.364910	−	0.931043i	$-0.618900\pi$
$620$	3.23295	−	7.45617i	0.129838	−	0.299447i
$621$	−14.4168	−	4.68429i	−0.578524	−	0.187974i
$622$	7.26913	+	14.2665i	0.291466	+	0.572033i
$623$	1.87294	+	4.74784i	0.0750376	+	0.190218i
$624$	1.46230	−	2.01269i	0.0585390	−	0.0805720i
$625$	15.9910	−	19.2169i	0.639641	−	0.768674i
$626$		−	17.8347i		−	0.712818i
$627$	3.71635	−	1.09871i	0.148417	−	0.0438784i
$628$	10.6728	+	10.6728i	0.425892	+	0.425892i
$629$	3.92269	+	12.0728i	0.156408	+	0.481373i
$630$	−3.19956	−	6.83435i	−0.127474	−	0.272287i
$631$	10.6577	−	7.74324i	0.424274	−	0.308253i	−0.355081	−	0.934836i	$-0.615547\pi$
$631$	10.6577	−	7.74324i	0.424274	−	0.308253i	0.779355	+	0.626582i	$0.215547\pi$
$632$	0.153811	−	0.0783704i	0.00611826	−	0.00311741i
$633$	31.8156	−	16.2109i	1.26456	−	0.644325i
$634$	7.57141	+	10.4212i	0.300699	+	0.413877i
$635$	−29.6427	−	35.8844i	−1.17633	−	1.42403i
$636$	5.58277	−	1.81395i	0.221371	−	0.0719279i
$637$	3.66796	+	12.7441i	0.145330	+	0.504939i
$638$	12.6431	+	9.71189i	0.500543	+	0.384497i
$639$		−	6.96739i		−	0.275626i
$640$	2.23176	−	0.138797i	0.0882179	−	0.00548643i
$641$	−2.64502	−	1.92172i	−0.104472	−	0.0759035i	0.534323	−	0.845281i	$-0.320567\pi$
$641$	−2.64502	−	1.92172i	−0.104472	−	0.0759035i	−0.638795	+	0.769377i	$0.720567\pi$
$642$	0.270554	−	1.70821i	0.0106779	−	0.0674177i
$643$	−28.4377	+	14.4897i	−1.12147	+	0.571420i	−0.913550	−	0.406725i	$-0.866671\pi$
$643$	−28.4377	+	14.4897i	−1.12147	+	0.571420i	−0.207924	+	0.978145i	$0.566671\pi$
$644$	1.54952	+	6.97311i	0.0610597	+	0.274779i
$645$	−0.646639	+	1.49135i	−0.0254614	+	0.0587217i
$646$	1.23359	+	0.896258i	0.0485351	+	0.0352628i
$647$	22.1714	+	11.2969i	0.871647	+	0.444126i	0.831797	−	0.555079i	$-0.187312\pi$
$647$	22.1714	+	11.2969i	0.871647	+	0.444126i	0.0398495	+	0.999206i	$0.487312\pi$
$648$	−2.50765	+	2.50765i	−0.0985097	+	0.0985097i
$649$	−40.2485	−	7.48146i	−1.57989	−	0.293673i
$650$	−8.29420	−	4.57534i	−0.325325	−	0.179460i
$651$	8.36251	−	9.46152i	0.327753	−	0.370826i
$652$	−1.93811	−	12.2368i	−0.0759024	−	0.479229i
$653$	−6.48807	+	40.9641i	−0.253898	+	1.60305i	0.450189	+	0.892933i	$0.351357\pi$
$653$	−6.48807	+	40.9641i	−0.253898	+	1.60305i	−0.704087	+	0.710114i	$0.748643\pi$
$654$	2.36906	−	7.29123i	0.0926377	−	0.285110i
$655$	−15.4269	+	3.43665i	−0.602777	+	0.134281i
$656$	1.75801	+	2.41969i	0.0686386	+	0.0944729i
$657$	−3.76344	+	0.596070i	−0.146826	+	0.0232549i
$658$	2.31209	−	0.142561i	0.0901345	−	0.00555761i
$659$			38.4071i			1.49613i	0.663626	+	0.748065i	$0.269017\pi$
$659$			38.4071i			1.49613i	−0.663626	+	0.748065i	$0.730983\pi$
$660$	1.86305	+	9.55898i	0.0725190	+	0.372083i
$661$			31.8029i			1.23699i	0.785788	+	0.618495i	$0.212257\pi$
$661$			31.8029i			1.23699i	−0.785788	+	0.618495i	$0.787743\pi$
$662$	−9.69364	+	19.0248i	−0.376754	+	0.739422i
$663$	0.666922	+	4.21078i	0.0259011	+	0.163533i
$664$	12.9612	−	9.41687i	0.502992	−	0.365445i
$665$	−5.26117	−	0.175718i	−0.204019	−	0.00681407i
$666$	2.91981	−	8.98626i	0.113140	−	0.348211i
$667$	−12.8182	−	2.03020i	−0.496323	−	0.0786099i
$668$	3.01472	+	19.0342i	0.116643	+	0.736454i
$669$	11.7040	−	3.80287i	0.452504	−	0.147028i
$670$	17.8811	+	30.2850i	0.690807	+	1.17001i
$671$	8.85429	+	18.5885i	0.341816	+	0.717600i
$672$	3.36412	+	0.868247i	0.129774	+	0.0334933i
$673$	7.41995	+	3.78066i	0.286018	+	0.145734i	0.591114	−	0.806588i	$-0.298688\pi$
$673$	7.41995	+	3.78066i	0.286018	+	0.145734i	−0.305096	+	0.952322i	$0.598688\pi$
$674$	18.0464	−	24.8387i	0.695121	−	0.956752i
$675$	22.1571	+	17.2380i	0.852829	+	0.663491i
$676$	2.90813	−	8.95030i	0.111851	−	0.344242i
$677$	11.6987	+	22.9601i	0.449619	+	0.882427i	0.998905	+	0.0467924i	$0.0148999\pi$
$677$	11.6987	+	22.9601i	0.449619	+	0.882427i	−0.549286	+	0.835635i	$0.685100\pi$
$678$	−12.7833	−	2.02468i	−0.490941	−	0.0777574i
$679$	−2.16705	+	22.6230i	−0.0831638	+	0.868191i
$680$	−2.53612	+	2.87249i	−0.0972558	+	0.110155i
$681$	18.5039			0.709072
$682$	9.93771	−	6.82233i	0.380535	−	0.261241i
$683$	−31.4996	+	31.4996i	−1.20530	+	1.20530i	−0.232767	+	0.972533i	$0.574778\pi$
$683$	−31.4996	+	31.4996i	−1.20530	+	1.20530i	−0.972533	+	0.232767i	$0.925222\pi$
$684$	−0.350726	−	1.07943i	−0.0134104	−	0.0412728i
$685$	−20.3996	−	24.6950i	−0.779427	−	0.943548i
$686$	−14.6764	+	11.2962i	−0.560346	+	0.431291i
$687$	−1.72269	+	0.877756i	−0.0657248	+	0.0334885i
$688$	0.251318	+	0.493239i	0.00958140	+	0.0188046i
$689$	−6.85122	+	4.97771i	−0.261011	+	0.189635i
$690$	−5.04899	−	6.11214i	−0.192212	−	0.232685i
$691$	16.3964	−	5.32752i	0.623750	−	0.202669i	0.0199453	−	0.999801i	$-0.493651\pi$
$691$	16.3964	−	5.32752i	0.623750	−	0.202669i	0.603804	+	0.797132i	$0.293651\pi$
$692$	−13.4162	+	13.4162i	−0.510007	+	0.510007i
$693$	1.36440	−	11.1094i	0.0518291	−	0.422011i
$694$			16.9806i			0.644574i
$695$	−21.2438	−	18.7561i	−0.805822	−	0.711460i
$696$	−3.71029	+	5.10678i	−0.140638	+	0.193572i
$697$	−5.06228	−	0.801786i	−0.191747	−	0.0303698i
$698$	−11.5806	+	5.90063i	−0.438334	+	0.223342i
$699$	−1.93704	+	5.96160i	−0.0732656	+	0.225488i
$700$	1.69331	−	13.1199i	0.0640012	−	0.495887i
$701$	−2.52160	−	1.83205i	−0.0952395	−	0.0691955i	0.539146	−	0.842212i	$-0.318747\pi$
$701$	−2.52160	−	1.83205i	−0.0952395	−	0.0691955i	−0.634386	+	0.773017i	$0.718747\pi$
$702$	4.82900	−	9.47744i	0.182259	−	0.357703i
$703$	−4.66071	−	4.66071i	−0.175782	−	0.175782i
$704$	2.91388	+	1.58408i	0.109821	+	0.0597024i
$705$	−2.21385	+	1.30712i	−0.0833783	+	0.0492288i
$706$	−15.0189	+	4.87993i	−0.565243	+	0.183659i
$707$	−2.47223	−	2.99603i	−0.0929778	−	0.112677i
$708$	2.53564	−	16.0094i	0.0952954	−	0.601671i
$709$	37.1009	+	12.0548i	1.39335	+	0.452728i	0.907036	−	0.421054i	$-0.138340\pi$
$709$	37.1009	+	12.0548i	1.39335	+	0.452728i	0.486318	+	0.873782i	$0.338340\pi$
$710$	6.55204	−	10.3079i	0.245894	−	0.386850i
$711$	0.178139	−	0.129425i	0.00668073	−	0.00485383i
$712$	−1.90534	+	0.301777i	−0.0714058	+	0.0113096i
$713$	−4.45482	+	8.74308i	−0.166834	+	0.327431i
$714$	−5.12853	+	3.02435i	−0.191930	+	0.113184i
$715$	−6.81769	−	12.2849i	−0.254967	−	0.459430i
$716$	9.32015			0.348310
$717$	12.2802	+	6.25709i	0.458614	+	0.233675i
$718$	35.3863	−	5.60464i	1.32060	−	0.209163i
$719$	−12.3328	+	8.96033i	−0.459937	+	0.334164i	−0.793507	−	0.608562i	$-0.791747\pi$
$719$	−12.3328	+	8.96033i	−0.459937	+	0.334164i	0.333569	+	0.942726i	$0.391747\pi$
$720$	2.78396	−	0.620185i	0.103752	−	0.0231129i
$721$	−1.57645	−	7.09429i	−0.0587100	−	0.264205i
$722$	17.9841	+	2.84840i	0.669298	+	0.106006i
$723$	−16.8787	+	2.67332i	−0.627724	+	0.0994218i
$724$	−1.94611	−	5.98952i	−0.0723267	−	0.222599i
$725$	21.0448	+	11.6090i	0.781585	+	0.431147i
$726$	−5.19078	+	13.4802i	−0.192648	+	0.500296i
$727$	34.9186	−	34.9186i	1.29506	−	1.29506i	0.363441	−	0.931617i	$-0.381602\pi$
$727$	34.9186	−	34.9186i	1.29506	−	1.29506i	0.931617	−	0.363441i	$-0.118398\pi$
$728$	−5.00285	+	0.308472i	−0.185418	+	0.0114327i
$729$	−15.6601	+	21.5542i	−0.580002	+	0.798305i
$730$	−6.12838	−	2.65723i	−0.226821	−	0.0983484i
$731$	−0.902209	−	0.293145i	−0.0333694	−	0.0108424i
$732$	−7.26369	+	3.70104i	−0.268474	+	0.136794i
$733$	0.368364	+	0.0583431i	0.0136058	+	0.00215495i	0.163234	−	0.986587i	$-0.447808\pi$
$733$	0.368364	+	0.0583431i	0.0136058	+	0.00215495i	−0.149628	+	0.988742i	$0.547808\pi$
$734$	5.13298	+	3.72933i	0.189462	+	0.137652i
$735$	8.81159	−	18.5701i	0.325020	−	0.684967i
$736$	−2.69988			−0.0995187
$737$	−1.39287	+	52.1467i	−0.0513071	+	1.92085i
$738$	2.69763	+	2.69763i	0.0993011	+	0.0993011i
$739$	42.6321	−	13.8520i	1.56825	−	0.509555i	0.609253	−	0.792976i	$-0.291469\pi$
$739$	42.6321	−	13.8520i	1.56825	−	0.509555i	0.958996	+	0.283421i	$0.0914693\pi$
$740$	12.7703	−	10.5490i	0.469445	−	0.387790i
$741$	−1.30115	−	1.79088i	−0.0477990	−	0.0657897i
$742$	−9.97775	−	6.34959i	−0.366295	−	0.233101i
$743$	−7.49083	−	14.7016i	−0.274812	−	0.539349i	0.711810	−	0.702372i	$-0.247876\pi$
$743$	−7.49083	−	14.7016i	−0.274812	−	0.539349i	−0.986622	+	0.163023i	$0.947876\pi$
$744$	2.80533	+	3.86121i	0.102849	+	0.141559i
$745$	2.51639	−	26.4175i	0.0921933	−	0.967864i
$746$	−4.37641	−	13.4692i	−0.160232	−	0.493142i
$747$	14.4500	−	14.4500i	0.528699	−	0.528699i
$748$	−5.45036	+	1.61136i	−0.199285	+	0.0589172i
$749$	−3.00150	+	1.77002i	−0.109672	+	0.0646751i
$750$	4.94345	+	13.8246i	0.180509	+	0.504803i
$751$	3.88317	+	2.82129i	0.141699	+	0.102950i	0.656376	−	0.754434i	$-0.272088\pi$
$751$	3.88317	+	2.82129i	0.141699	+	0.102950i	−0.514677	+	0.857384i	$0.672088\pi$
$752$	−0.136966	+	0.864767i	−0.00499462	+	0.0315348i
$753$	−13.1126	−	25.7350i	−0.477851	−	0.937835i
$754$	2.81410	−	8.66090i	0.102483	−	0.315411i
$755$	10.3657	−	23.9066i	0.377248	−	0.870049i
$756$	14.7871	+	1.41645i	0.537802	+	0.0515159i
$757$	7.55085	−	14.8194i	0.274440	−	0.538620i	−0.712112	−	0.702066i	$-0.752261\pi$
$757$	7.55085	−	14.8194i	0.274440	−	0.538620i	0.986552	+	0.163446i	$0.0522611\pi$
$758$	−1.61344	+	1.61344i	−0.0586029	+	0.0586029i
$759$	−1.52873	−	11.6591i	−0.0554893	−	0.423198i
$760$	0.496192	−	1.92678i	0.0179988	−	0.0698916i
$761$	19.5360	−	6.34764i	0.708181	−	0.230102i	0.0672895	−	0.997733i	$-0.478565\pi$
$761$	19.5360	−	6.34764i	0.708181	−	0.230102i	0.640891	+	0.767632i	$0.278565\pi$
$762$	26.9978	−	4.27603i	0.978026	−	0.154904i
$763$	−14.3685	+	5.66810i	−0.520174	+	0.205199i
$764$	−8.21910	−	2.67055i	−0.297357	−	0.0966171i
$765$	−2.62193	+	4.12494i	−0.0947962	+	0.149137i
$766$	10.3198	+	14.2040i	0.372869	+	0.513210i
$767$	3.65810	+	23.0963i	0.132086	+	0.833960i
$768$	−0.596174	+	1.17006i	−0.0215126	+	0.0422208i
$769$	−13.3753			−0.482324			−0.241162	−	0.970485i	$-0.577529\pi$
$769$	−13.3753			−0.482324			−0.241162	+	0.970485i	$0.577529\pi$
$770$	12.4657	−	15.1528i	0.449232	−	0.546068i
$771$	−33.8956			−1.22072
$772$	4.59314	−	9.01455i	0.165311	−	0.324441i
$773$	−5.80231	−	36.6343i	−0.208695	−	1.31765i	−0.840201	−	0.542275i	$-0.817563\pi$
$773$	−5.80231	−	36.6343i	−0.208695	−	1.31765i	0.631506	−	0.775371i	$-0.282437\pi$
$774$	0.415041	+	0.571255i	0.0149183	+	0.0205333i
$775$	13.2649	−	12.4207i	0.476491	−	0.446165i
$776$	−8.16941	−	2.65440i	−0.293265	−	0.0952875i
$777$	23.9412	−	9.44436i	0.858884	−	0.338814i
$778$	−24.5468	+	3.88783i	−0.880046	+	0.139386i
$779$	2.53104	−	0.822384i	0.0906838	−	0.0294649i
$780$	4.79029	−	2.82831i	0.171520	−	0.101270i
$781$	16.3556	−	7.79072i	0.585251	−	0.278774i
$782$	3.27154	−	3.27154i	0.116990	−	0.116990i
$783$	−12.2526	+	24.0471i	−0.437872	+	0.859372i
$784$	−2.96460	−	6.34122i	−0.105879	−	0.226472i
$785$	12.4018	+	31.3893i	0.442638	+	1.12033i
$786$	2.86826	−	8.82759i	0.102307	−	0.314870i
$787$	5.74823	+	11.2815i	0.204902	+	0.402143i	0.970474	−	0.241208i	$-0.0775435\pi$
$787$	5.74823	+	11.2815i	0.204902	+	0.402143i	−0.765571	+	0.643351i	$0.777544\pi$
$788$	−2.93898	+	18.5560i	−0.104697	+	0.661029i
$789$	−19.5974	−	14.2383i	−0.697685	−	0.506898i
$790$	0.385258	−	0.0239599i	0.0137069	−	0.000852455i
$791$	13.2459	+	22.4616i	0.470969	+	0.798643i
$792$	3.98711	+	1.41426i	0.141676	+	0.0502536i
$793$	8.31627	−	8.31627i	0.295319	−	0.295319i
$794$	4.29405	+	13.2157i	0.152390	+	0.469009i
$795$	13.0667	+	1.24466i	0.463430	+	0.0441437i
$796$	12.8546	+	17.6928i	0.455619	+	0.627106i
$797$	21.1492	+	41.5076i	0.749142	+	1.47027i	0.878025	+	0.478614i	$0.158861\pi$
$797$	21.1492	+	41.5076i	0.749142	+	1.47027i	−0.128883	+	0.991660i	$0.541139\pi$
$798$	1.65976	−	2.60814i	0.0587548	−	0.0923273i
$799$	−0.881905	−	1.21384i	−0.0311996	−	0.0429425i
$800$	4.70196	+	1.70046i	0.166239	+	0.0601204i
$801$	−2.34021	+	0.760381i	−0.0826874	+	0.0268668i
$802$	18.3341	+	18.3341i	0.647401	+	0.647401i
$803$	−5.60741	−	8.16800i	−0.197881	−	0.288242i
$804$	−20.6543			−0.728422
$805$	−3.02390	+	15.6838i	−0.106578	+	0.552782i
$806$	−5.57045	−	4.04717i	−0.196211	−	0.142555i
$807$	8.48351	+	1.34366i	0.298634	+	0.0472989i
$808$	1.30813	−	0.666524i	0.0460197	−	0.0234482i
$809$	12.4482	+	4.04466i	0.437654	+	0.142203i	0.519553	−	0.854438i	$-0.326098\pi$
$809$	12.4482	+	4.04466i	0.437654	+	0.142203i	−0.0818988	+	0.996641i	$0.526098\pi$
$810$	−7.37512	+	2.91387i	−0.259135	+	0.102383i
$811$	17.4301	−	23.9904i	0.612052	−	0.842417i	−0.384692	−	0.923045i	$-0.625692\pi$
$811$	17.4301	−	23.9904i	0.612052	−	0.842417i	0.996744	+	0.0806276i	$0.0256924\pi$
$812$	12.6937	−	0.782683i	0.445462	−	0.0274668i
$813$	13.0523	−	13.0523i	0.457763	−	0.457763i
$814$	24.3597	−	3.19402i	0.853807	−	0.111950i
$815$	6.90886	−	26.8280i	0.242007	−	0.939744i
$816$	−0.695396	−	2.14021i	−0.0243437	−	0.0749223i
$817$	0.486504	−	0.0770547i	0.0170206	−	0.00269580i
$818$	1.24391	+	0.197016i	0.0434924	+	0.00688851i
$819$	−6.24125	+	1.38689i	−0.218087	+	0.0484619i
$820$	1.45421	+	6.52784i	0.0507832	+	0.227962i
$821$	37.9912	−	27.6022i	1.32590	−	0.963325i	0.326065	−	0.945347i	$-0.394277\pi$
$821$	37.9912	−	27.6022i	1.32590	−	0.963325i	0.999838	−	0.0179774i	$-0.00572270\pi$
$822$	18.5794	−	2.94269i	0.648031	−	0.102638i
$823$	−14.9233	−	7.60381i	−0.520194	−	0.265052i	0.174120	−	0.984725i	$-0.444292\pi$
$823$	−14.9233	−	7.60381i	−0.520194	−	0.265052i	−0.694314	+	0.719672i	$0.744292\pi$
$824$	2.74680			0.0956892
$825$	−4.68089	+	21.2677i	−0.162968	+	0.740446i
$826$	−28.1302	+	16.5887i	−0.978775	+	0.577195i
$827$	2.85504	−	5.60334i	0.0992796	−	0.194847i	−0.836025	−	0.548692i	$-0.815126\pi$
$827$	2.85504	−	5.60334i	0.0992796	−	0.194847i	0.935304	+	0.353845i	$0.115126\pi$
$828$	−3.40141	+	0.538731i	−0.118207	+	0.0187222i
$829$	37.0324	−	26.9056i	1.28619	−	0.934470i	0.286467	−	0.958090i	$-0.407519\pi$
$829$	37.0324	−	26.9056i	1.28619	−	0.934470i	0.999721	+	0.0236201i	$0.00751921\pi$
$830$	34.9668	−	7.78956i	1.21371	−	0.270380i
$831$	−8.65873	−	2.81339i	−0.300368	−	0.0975954i
$832$	0.296364	−	1.87117i	0.0102746	−	0.0648711i
$833$	11.2762	+	4.09159i	0.390698	+	0.141765i
$834$	15.8281	−	5.14287i	0.548083	−	0.178083i
$835$	−10.7467	+	41.7307i	−0.371903	+	1.44415i
$836$	2.14173	−	2.03029i	0.0740733	−	0.0702192i
$837$	14.4292	+	14.4292i	0.498746	+	0.498746i
$838$	5.31487	−	10.4310i	0.183599	−	0.360334i
$839$	15.0381	+	10.9258i	0.519171	+	0.377200i	0.816292	−	0.577640i	$-0.196026\pi$
$839$	15.0381	+	10.9258i	0.519171	+	0.377200i	−0.297120	+	0.954840i	$0.596026\pi$
$840$	6.12925	+	4.77371i	0.211479	+	0.164709i
$841$	1.82130	−	5.60539i	0.0628035	−	0.193289i
$842$	−1.30071	+	0.662743i	−0.0448253	+	0.0228396i
$843$	−40.1609	−	6.36087i	−1.38322	−	0.219080i
$844$	15.9828	−	21.9984i	0.550150	−	0.757217i
$845$	13.9276	−	15.7749i	0.479125	−	0.542672i
$846$			1.11680i			0.0383963i
$847$	27.6044	−	9.21931i	0.948499	−	0.316779i
$848$	3.16084	−	3.16084i	0.108544	−	0.108544i
$849$	23.7422	−	7.71432i	0.814832	−	0.264755i
$850$	−7.75807	+	3.63703i	−0.266099	+	0.124749i
$851$	−16.1800	+	11.7555i	−0.554643	+	0.402972i
$852$	3.25647	+	6.39119i	0.111565	+	0.218958i
$853$	−43.2857	+	22.0552i	−1.48208	+	0.755155i	−0.993114	−	0.117150i	$-0.962624\pi$
$853$	−43.2857	+	22.0552i	−1.48208	+	0.755155i	−0.488961	+	0.872305i	$0.662624\pi$
$854$	15.0658	+	6.54192i	0.515539	+	0.223860i
$855$	0.240655	−	2.52644i	0.00823023	−	0.0864026i
$856$	−0.406985	−	1.25257i	−0.0139104	−	0.0428120i
$857$	−19.6847	+	19.6847i	−0.672416	+	0.672416i	−0.958272	−	0.285857i	$-0.907722\pi$
$857$	−19.6847	+	19.6847i	−0.672416	+	0.672416i	0.285857	+	0.958272i	$0.407722\pi$
$858$	8.24822	+	0.220315i	0.281590	+	0.00752144i
$859$	−16.2961			−0.556016			−0.278008	−	0.960579i	$-0.589674\pi$
$859$	−16.2961			−0.556016			−0.278008	+	0.960579i	$0.589674\pi$
$860$	0.0768345	+	1.23544i	0.00262003	+	0.0421283i
$861$	−0.990861	+	10.3441i	−0.0337684	+	0.352526i
$862$	−14.7934	−	2.34305i	−0.503866	−	0.0798045i
$863$	−3.92060	−	7.69461i	−0.133459	−	0.261928i	0.814600	−	0.580023i	$-0.196957\pi$
$863$	−3.92060	−	7.69461i	−0.133459	−	0.261928i	−0.948059	+	0.318096i	$0.896957\pi$
$864$	−1.73500	+	5.33978i	−0.0590259	+	0.181663i
$865$	−39.4577	+	15.5895i	−1.34160	+	0.530061i
$866$	−10.1039	+	13.9069i	−0.343345	+	0.472574i
$867$	−16.4549	−	8.38421i	−0.558839	−	0.284743i
$868$	2.40302	−	9.31078i	0.0815638	−	0.316028i
$869$	0.503010	+	0.273454i	0.0170634	+	0.00927628i
$870$	−12.1544	+	7.17627i	−0.412072	+	0.243298i
$871$	28.3390	−	9.20789i	0.960229	−	0.311997i
$872$	−0.913273	−	5.76618i	−0.0309273	−	0.195268i
$873$	−10.8218	−	1.71401i	−0.366263	−	0.0580103i
$874$	−0.742363	+	2.28476i	−0.0251108	+	0.0772831i
$875$	15.1444	−	25.4096i	0.511974	−	0.859001i
$876$	3.17361	−	2.30576i	0.107226	−	0.0779044i
$877$	5.94558	+	37.5389i	0.200768	+	1.26760i	0.857898	+	0.513821i	$0.171770\pi$
$877$	5.94558	+	37.5389i	0.200768	+	1.26760i	−0.657130	+	0.753778i	$0.728230\pi$
$878$	−10.7515	+	21.1010i	−0.362846	+	0.712125i
$879$		−	42.7271i		−	1.44115i
$880$	4.56879	+	5.84176i	0.154014	+	0.196926i
$881$			49.8070i			1.67804i	0.544101	+	0.839020i	$0.316871\pi$
$881$			49.8070i			1.67804i	−0.544101	+	0.839020i	$0.683129\pi$
$882$	−5.00025	−	7.39738i	−0.168367	−	0.249083i
$883$	−44.8607	+	7.10523i	−1.50968	+	0.239110i	−0.855729	−	0.517425i	$-0.826891\pi$
$883$	−44.8607	+	7.10523i	−1.50968	+	0.239110i	−0.653953	+	0.756535i	$0.726891\pi$
$884$	1.90825	+	2.62648i	0.0641814	+	0.0883382i
$885$	19.4428	−	30.5882i	0.653561	−	1.02821i
$886$	5.71181	−	17.5791i	0.191892	−	0.590583i
$887$	2.12987	−	13.4475i	0.0715142	−	0.451523i	−0.925783	−	0.378054i	$-0.876593\pi$
$887$	2.12987	−	13.4475i	0.0715142	−	0.451523i	0.997298	−	0.0734683i	$-0.0234068\pi$
$888$	1.52172	+	9.60778i	0.0510657	+	0.322416i
$889$	−41.2646	−	36.4714i	−1.38397	−	1.22321i
$890$	−4.17729	−	1.07575i	−0.140023	−	0.0360593i
$891$	−11.5638	−	2.14950i	−0.387403	−	0.0720110i
$892$	6.62656	−	6.62656i	0.221874	−	0.221874i
$893$	0.694145	+	0.353685i	0.0232287	+	0.0118356i
$894$	12.6082	+	9.16038i	0.421681	+	0.306369i
$895$	19.1205	+	8.29052i	0.639127	+	0.277122i
$896$	2.58275	−	0.573923i	0.0862837	−	0.0191734i
$897$	−5.98471	+	3.04936i	−0.199824	+	0.101815i
$898$	0.689065	−	4.35059i	0.0229944	−	0.145181i
$899$	14.1339	+	10.2689i	0.471391	+	0.342486i
$900$	6.26303	+	1.20409i	0.208768	+	0.0401362i
$901$			7.66023i			0.255199i
$902$	−3.31616	+	9.34897i	−0.110416	+	0.311287i
$903$	−0.480640	+	1.86230i	−0.0159947	+	0.0619733i
$904$	−9.37356	+	3.04565i	−0.311760	+	0.101297i
$905$	1.33535	−	14.0187i	0.0443884	−	0.465999i
$906$	8.99468	+	12.3801i	0.298828	+	0.411302i
$907$	1.41947	−	0.723255i	0.0471326	−	0.0240153i	−0.430265	−	0.902702i	$-0.641580\pi$
$907$	1.41947	−	0.723255i	0.0471326	−	0.0240153i	0.477398	+	0.878687i	$0.341580\pi$
$908$	12.5551	−	6.39712i	0.416654	−	0.212296i
$909$	1.51503	−	1.10074i	0.0502505	−	0.0365091i
$910$	−10.5379	−	3.81734i	−0.349327	−	0.126544i
$911$	−13.2263	−	40.7064i	−0.438207	−	1.34866i	−0.889764	−	0.456421i	$-0.849131\pi$
$911$	−13.2263	−	40.7064i	−0.438207	−	1.34866i	0.451557	−	0.892243i	$-0.350869\pi$
$912$	0.826231	+	0.826231i	0.0273592	+	0.0273592i
$913$	50.0783	+	17.7632i	1.65735	+	0.587877i
$914$		−	32.3942i		−	1.07150i
$915$	−18.1938	+	1.13150i	−0.601468	+	0.0374064i
$916$	−0.865406	+	1.19113i	−0.0285938	+	0.0393560i
$917$	−17.3961	+	6.86245i	−0.574470	+	0.226618i
$918$	−4.36806	−	8.57280i	−0.144167	−	0.282944i
$919$	−13.1300	−	4.26620i	−0.433119	−	0.140729i	0.0843397	−	0.996437i	$-0.473122\pi$
$919$	−13.1300	−	4.26620i	−0.433119	−	0.140729i	−0.517459	+	0.855708i	$0.673122\pi$
$920$	−5.53885	−	2.40161i	−0.182611	−	0.0791788i
$921$	−14.8205	−	10.7677i	−0.488353	−	0.354809i
$922$	10.4115	+	5.30494i	0.342886	+	0.174709i
$923$	−7.31733	−	7.31733i	−0.240853	−	0.240853i
$924$	3.94083	+	10.8283i	0.129644	+	0.356226i
$925$	35.5822	−	10.2820i	1.16993	−	0.338071i
$926$	10.1721	+	31.3064i	0.334275	+	1.02879i
$927$	3.46053	−	0.548093i	0.113659	−	0.0180017i
$928$	−0.751963	+	4.74770i	−0.0246844	+	0.155851i
$929$	−11.7975	+	36.3089i	−0.387063	+	1.19126i	0.547909	+	0.836538i	$0.315424\pi$
$929$	−11.7975	+	36.3089i	−0.387063	+	1.19126i	−0.934973	+	0.354720i	$0.884576\pi$
$930$	2.32055	+	10.4168i	0.0760939	+	0.341580i
$931$	−6.18139	+	0.765187i	−0.202587	+	0.0250780i
$932$	0.746729	+	4.71466i	0.0244599	+	0.154434i
$933$	−18.7345	−	9.54571i	−0.613341	−	0.312513i
$934$	−26.6155			−0.870886
$935$	−12.6149	−	1.54250i	−0.412550	−	0.0504451i
$936$		−	2.41651i		−	0.0789861i
$937$	6.85999	+	3.49534i	0.224106	+	0.114188i	0.562439	−	0.826839i	$-0.309863\pi$
$937$	6.85999	+	3.49534i	0.224106	+	0.114188i	−0.338333	+	0.941026i	$0.609863\pi$
$938$	26.4853	+	32.0969i	0.864776	+	1.04800i
$939$	13.7661	+	18.9474i	0.449239	+	0.618325i
$940$	−1.05022	+	1.65225i	−0.0342544	+	0.0538905i
$941$	−39.0914	−	12.7016i	−1.27434	−	0.414059i	−0.407758	−	0.913090i	$-0.633689\pi$
$941$	−39.0914	−	12.7016i	−1.27434	−	0.414059i	−0.866584	+	0.499031i	$0.833689\pi$
$942$	−19.5767	−	3.10065i	−0.637844	−	0.101025i
$943$	−1.26322	−	7.97563i	−0.0411360	−	0.259722i
$944$	−3.81428	−	11.7391i	−0.124144	−	0.382076i
$945$	29.0761	+	16.0594i	0.945845	+	0.522413i
$946$	−0.876910	+	1.61305i	−0.0285108	+	0.0524448i
$947$	−11.8721	−	11.8721i	−0.385790	−	0.385790i	0.487393	−	0.873183i	$-0.337948\pi$
$947$	−11.8721	−	11.8721i	−0.385790	−	0.385790i	−0.873183	+	0.487393i	$0.837948\pi$
$948$	−0.102915	+	0.201982i	−0.00334252	+	0.00656006i
$949$	−3.32645	+	4.57846i	−0.107981	+	0.148623i
$950$	2.73187	−	3.51145i	0.0886336	−	0.113927i
$951$	−16.0876	−	5.22717i	−0.521675	−	0.169503i
$952$	−2.43418	+	3.82507i	−0.0788922	+	0.123971i
$953$	3.04557	−	19.2290i	0.0986557	−	0.622888i	−0.887972	−	0.459898i	$-0.847886\pi$
$953$	3.04557	−	19.2290i	0.0986557	−	0.622888i	0.986628	−	0.162990i	$-0.0521139\pi$
$954$	3.35145	−	4.61287i	0.108507	−	0.149347i
$955$	−14.4861	−	12.7898i	−0.468761	−	0.413868i
$956$	10.4954			0.339446
$957$	−20.9282	−	0.559005i	−0.676512	−	0.0180701i
$958$	−15.5800	−	15.5800i	−0.503368	−	0.503368i
$959$	−28.3976	−	25.0990i	−0.917005	−	0.810489i
$960$	−2.26386	+	1.87008i	−0.0730658	+	0.0603567i
$961$	−14.3930	+	10.4571i	−0.464290	+	0.337326i
$962$	−6.37113	−	12.5040i	−0.205414	−	0.403147i
$963$	−0.762673	−	1.49683i	−0.0245768	−	0.0482346i
$964$	−10.5281	+	7.64911i	−0.339087	+	0.246361i
$965$	17.4416	−	14.4078i	0.561465	−	0.463804i
$966$	−7.02853	−	6.21213i	−0.226139	−	0.199872i
$967$	−25.4840	−	25.4840i	−0.819509	−	0.819509i	0.166528	−	0.986037i	$-0.446744\pi$
$967$	−25.4840	−	25.4840i	−0.819509	−	0.819509i	−0.986037	+	0.166528i	$0.946744\pi$
$968$	1.13834	+	10.9409i	0.0365876	+	0.351655i
$969$	−2.00235			−0.0643248
$970$	−14.3986	−	12.7125i	−0.462310	−	0.408173i
$971$	−17.9001	+	24.6374i	−0.574443	+	0.790653i	−0.993072	−	0.117504i	$-0.962511\pi$
$971$	−17.9001	+	24.6374i	−0.574443	+	0.790653i	0.418629	+	0.908157i	$0.362511\pi$
$972$	−1.90642	+	12.0367i	−0.0611486	+	0.386077i
$973$	−28.2886	−	18.0022i	−0.906892	−	0.577124i
$974$	−25.9891	−	8.44439i	−0.832746	−	0.270576i
$975$	12.3432	−	1.54126i	0.395300	−	0.0493597i
$976$	−3.64896	+	5.02237i	−0.116800	+	0.160762i
$977$	8.65189	−	16.9803i	0.276799	−	0.543248i	−0.710195	−	0.704005i	$-0.751393\pi$
$977$	8.65189	−	16.9803i	0.276799	−	0.543248i	0.986994	+	0.160757i	$0.0513935\pi$
$978$	11.5042	+	11.5042i	0.367865	+	0.367865i
$979$	−4.40171	−	4.64331i	−0.140679	−	0.148401i
$980$	−0.441255	−	15.6463i	−0.0140954	−	0.499801i
$981$	−2.30116	−	7.08224i	−0.0734703	−	0.226118i
$982$	1.86470	+	11.7732i	0.0595049	+	0.375699i
$983$	−3.70836	−	0.587347i	−0.118278	−	0.0187335i	0.0970146	−	0.995283i	$-0.469071\pi$
$983$	−3.70836	−	0.587347i	−0.118278	−	0.0187335i	−0.215293	+	0.976549i	$0.569071\pi$
$984$	−3.73537	−	1.21370i	−0.119079	−	0.0386912i
$985$	−22.5354	+	35.4537i	−0.718038	+	1.12965i
$986$	−4.84180	−	6.66416i	−0.154194	−	0.212230i
$987$	−2.34630	+	1.93609i	−0.0746834	+	0.0616263i
$988$	−1.50198	−	0.765297i	−0.0477843	−	0.0243473i
$989$		−	1.49458i		−	0.0475250i
$990$	6.92161	+	6.44803i	0.219983	+	0.204932i
$991$	−57.0499			−1.81225			−0.906124	−	0.423011i	$-0.860973\pi$
$991$	−57.0499			−1.81225			−0.906124	+	0.423011i	$0.860973\pi$
$992$	3.23833	+	1.65001i	0.102817	+	0.0523879i
$993$	−4.38630	−	27.6940i	−0.139195	−	0.878844i
$994$	5.75611	−	13.2561i	0.182573	−	0.420457i
$995$	10.6332	+	47.7317i	0.337096	+	1.51320i
$996$	−6.50124	+	20.0088i	−0.206000	+	0.634002i
$997$	1.27303	−	8.03760i	0.0403173	−	0.254553i	−0.959295	−	0.282407i	$-0.908867\pi$
$997$	1.27303	−	8.03760i	0.0403173	−	0.254553i	0.999612	+	0.0278535i	$0.00886718\pi$
$998$	12.8101	−	2.02892i	0.405497	−	0.0642244i
$999$	12.8522	+	39.5549i	0.406625	+	1.25146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bi.a.27.8	✓	384
5.3	odd	4	inner	770.2.bi.a.643.41	yes	384
7.6	odd	2	inner	770.2.bi.a.27.17	yes	384
11.9	even	5	inner	770.2.bi.a.97.32	yes	384
35.13	even	4	inner	770.2.bi.a.643.32	yes	384
55.53	odd	20	inner	770.2.bi.a.713.17	yes	384
77.20	odd	10	inner	770.2.bi.a.97.41	yes	384
385.328	even	20	inner	770.2.bi.a.713.8	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bi.a.27.8	✓	384	1.1	even	1	trivial
770.2.bi.a.27.17	yes	384	7.6	odd	2	inner
770.2.bi.a.97.32	yes	384	11.9	even	5	inner
770.2.bi.a.97.41	yes	384	77.20	odd	10	inner
770.2.bi.a.643.32	yes	384	35.13	even	4	inner
770.2.bi.a.643.41	yes	384	5.3	odd	4	inner
770.2.bi.a.713.8	yes	384	385.328	even	20	inner
770.2.bi.a.713.17	yes	384	55.53	odd	20	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.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.205427 - 1.29702i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.486212 - 2.18257i) q^{5} +(1.24891 + 0.405797i) q^{6} +(-0.970889 - 2.46117i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.21312 - 0.394165i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.205427 - 1.29702i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.486212 - 2.18257i) q^{5} +(1.24891 + 0.405797i) q^{6} +(-0.970889 - 2.46117i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.21312 - 0.394165i) q^{9} +(2.16542 + 0.557647i) q^{10} +(2.28175 + 2.40699i) q^{11} +(-0.928562 + 0.928562i) q^{12} +(0.860081 - 1.68800i) q^{13} +(2.63370 + 0.252281i) q^{14} +(-2.73095 + 1.07898i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.777984 - 1.52688i) q^{17} +(-0.199539 + 1.25984i) q^{18} +(0.719860 + 0.523009i) q^{19} +(-1.47995 + 1.67623i) q^{20} +(-2.99274 + 1.76485i) q^{21} +(-3.18054 + 0.940305i) q^{22} +(1.90910 - 1.90910i) q^{23} +(-0.405797 - 1.24891i) q^{24} +(-4.52720 + 2.12238i) q^{25} +(1.11355 + 1.53268i) q^{26} +(-2.54897 - 5.00263i) q^{27} +(-1.42046 + 2.23211i) q^{28} +(-2.82542 - 3.88885i) q^{29} +(0.278442 - 2.92314i) q^{30} +(-3.45658 + 1.12311i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.65318 - 3.45393i) q^{33} +1.71366 q^{34} +(-4.89962 + 3.31568i) q^{35} +(-1.03194 - 0.749746i) q^{36} +(-7.31639 - 1.15880i) q^{37} +(-0.792814 + 0.403959i) q^{38} +(-2.36606 - 0.768778i) q^{39} +(-0.821654 - 2.07964i) q^{40} +(1.75801 - 2.41969i) q^{41} +(-0.213820 - 3.46778i) q^{42} +(0.391437 - 0.391437i) q^{43} +(0.606117 - 3.26077i) q^{44} +(-1.45012 - 2.45606i) q^{45} +(0.834307 + 2.56773i) q^{46} +(0.864767 - 0.136966i) q^{47} +(1.29702 + 0.205427i) q^{48} +(-5.11475 + 4.77905i) q^{49} +(0.164251 - 4.99730i) q^{50} +(-1.82057 + 1.32272i) q^{51} +(-1.87117 + 0.296364i) q^{52} +(-3.98289 - 2.02939i) q^{53} +5.61458 q^{54} +(4.14401 - 6.15038i) q^{55} +(-1.34395 - 2.27899i) q^{56} +(0.530473 - 1.04111i) q^{57} +(4.74770 - 0.751963i) q^{58} +(-9.98591 + 7.25519i) q^{59} +(2.47813 + 1.57517i) q^{60} +(5.90414 + 1.91837i) q^{61} +(0.568555 - 3.58971i) q^{62} +(-2.14791 - 2.60300i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-4.10236 - 1.05646i) q^{65} +(1.87296 + 3.93205i) q^{66} +(11.1217 + 11.1217i) q^{67} +(-0.777984 + 1.52688i) q^{68} +(-2.86832 - 2.08395i) q^{69} +(-0.729913 - 5.87088i) q^{70} +(1.68794 - 5.19494i) q^{71} +(1.13652 - 0.579085i) q^{72} +(-2.95046 - 0.467306i) q^{73} +(4.35407 - 5.99287i) q^{74} +(3.68277 + 5.43586i) q^{75} -0.889796i q^{76} +(3.70870 - 7.95271i) q^{77} +(1.75915 - 1.75915i) q^{78} +(0.164177 - 0.0533443i) q^{79} +(2.22599 + 0.212036i) q^{80} +(-2.86906 + 2.08449i) q^{81} +(1.35784 + 2.66491i) q^{82} +(14.2748 - 7.27335i) q^{83} +(3.18688 + 1.38382i) q^{84} +(-2.95425 + 2.44039i) q^{85} +(0.171064 + 0.526481i) q^{86} +(-4.46349 + 4.46349i) q^{87} +(2.63020 + 2.02041i) q^{88} -1.92909 q^{89} +(2.84671 - 0.177042i) q^{90} +(-4.98952 - 0.477945i) q^{91} +(-2.66664 - 0.422354i) q^{92} +(2.16677 + 4.25252i) q^{93} +(-0.270559 + 0.832694i) q^{94} +(0.791498 - 1.82544i) q^{95} +(-0.771871 + 1.06239i) q^{96} +(-7.65359 - 3.89970i) q^{97} +(-1.93612 - 6.72692i) q^{98} +(3.71678 + 2.02057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 4 q^{7}+O(q^{10}) \) 384 * q - 4 * q^7	\( 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) \) 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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