LMFDB - Embedded newform 374.2.g.e.69.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [374,2,Mod(69,374)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("374.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(374, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$374 = 2 \cdot 11 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	374.g (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25$ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.1
Root			$-0.762262 + 2.34600i$ of defining polynomial
Character	$\chi$	$=$	374.69
Dual form			374.2.g.e.103.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.280121 - 0.862123i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.99563 + 1.44991i) q^{5} +(-0.733366 - 0.532822i) q^{6} +(-0.733366 + 2.25707i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.76226 - 1.28036i) q^{9} +2.46673 q^{10} +(3.30902 + 0.224514i) q^{11} -0.906490 q^{12} +(0.424349 - 0.308308i) q^{13} +(0.733366 + 2.25707i) q^{14} +(0.690983 - 2.12663i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.673124 - 2.07166i) q^{18} +(-0.888631 - 2.73493i) q^{19} +(1.99563 - 1.44991i) q^{20} +2.15130 q^{21} +(2.80902 - 1.76336i) q^{22} -4.66708 q^{23} +(-0.733366 + 0.532822i) q^{24} +(0.335211 + 1.03167i) q^{25} +(0.162087 - 0.498852i) q^{26} +(-3.79757 - 2.75910i) q^{27} +(1.91998 + 1.39494i) q^{28} +(-1.96673 + 6.05298i) q^{29} +(-0.690983 - 2.12663i) q^{30} +(3.63548 - 2.64133i) q^{31} -1.00000 q^{32} +(-0.733366 - 2.91567i) q^{33} -1.00000 q^{34} +(-4.73607 + 3.44095i) q^{35} +(-0.673124 - 2.07166i) q^{36} +(-0.682648 + 2.10097i) q^{37} +(-2.32647 - 1.69028i) q^{38} +(-0.384668 - 0.279478i) q^{39} +(0.762262 - 2.34600i) q^{40} +(0.738770 + 2.27370i) q^{41} +(1.74044 - 1.26450i) q^{42} -9.13922 q^{43} +(1.23607 - 3.07768i) q^{44} +5.37322 q^{45} +(-3.77575 + 2.74324i) q^{46} +(-0.188534 - 0.580247i) q^{47} +(-0.280121 + 0.862123i) q^{48} +(1.10659 + 0.803983i) q^{49} +(0.877594 + 0.637609i) q^{50} +(-0.280121 + 0.862123i) q^{51} +(-0.162087 - 0.498852i) q^{52} +(10.2294 - 7.43207i) q^{53} -4.69406 q^{54} +(6.27804 + 5.24582i) q^{55} +2.37322 q^{56} +(-2.10892 + 1.53222i) q^{57} +(1.96673 + 6.05298i) q^{58} +(-3.37489 + 10.3868i) q^{59} +(-1.80902 - 1.31433i) q^{60} +(3.65400 + 2.65479i) q^{61} +(1.38863 - 4.27377i) q^{62} +(1.59747 + 4.91652i) q^{63} +(-0.809017 + 0.587785i) q^{64} +1.29386 q^{65} +(-2.30709 - 1.92777i) q^{66} -10.1916 q^{67} +(-0.809017 + 0.587785i) q^{68} +(1.30735 + 4.02360i) q^{69} +(-1.80902 + 5.56758i) q^{70} +(-3.83395 - 2.78553i) q^{71} +(-1.76226 - 1.28036i) q^{72} +(-2.97381 + 9.15243i) q^{73} +(0.682648 + 2.10097i) q^{74} +(0.795530 - 0.577987i) q^{75} -2.87567 q^{76} +(-2.93346 + 7.30403i) q^{77} -0.475476 q^{78} +(-8.33187 + 6.05346i) q^{79} +(-0.762262 - 2.34600i) q^{80} +(0.704470 - 2.16813i) q^{81} +(1.93413 + 1.40522i) q^{82} +(-6.16708 - 4.48065i) q^{83} +(0.664789 - 2.04601i) q^{84} +(-0.762262 - 2.34600i) q^{85} +(-7.39378 + 5.37190i) q^{86} +5.76934 q^{87} +(-0.809017 - 3.21644i) q^{88} -1.34084 q^{89} +(4.34703 - 3.15830i) q^{90} +(0.384668 + 1.18389i) q^{91} +(-1.44221 + 4.43866i) q^{92} +(-3.29553 - 2.39434i) q^{93} +(-0.493587 - 0.358612i) q^{94} +(2.19202 - 6.74633i) q^{95} +(0.280121 + 0.862123i) q^{96} +(5.57398 - 4.04973i) q^{97} +1.36782 q^{98} +(6.11881 - 3.84107i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 7 q^{9} + 4 q^{10} + 22 q^{11} - 2 q^{12} - 2 q^{14} + 10 q^{15} - 2 q^{16} - 2 q^{17} + 8 q^{18} + q^{20} + 24 q^{21} + 18 q^{22}+ \cdots + 3 q^{99}+O(q^{100})$ 8 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 7 * q^9 + 4 * q^10 + 22 * q^11 - 2 * q^12 - 2 * q^14 + 10 * q^15 - 2 * q^16 - 2 * q^17 + 8 * q^18 + q^20 + 24 * q^21 + 18 * q^22 + 2 * q^24 + 9 * q^25 + 5 * q^26 - 6 * q^27 - 3 * q^28 - 10 * q^30 + q^31 - 8 * q^32 + 2 * q^33 - 8 * q^34 - 20 * q^35 - 8 * q^36 - q^37 + 5 * q^38 - 2 * q^39 - q^40 - 22 * q^41 + 11 * q^42 - 8 * q^44 + 22 * q^45 - 10 * q^46 - 18 * q^47 + 3 * q^48 - 20 * q^49 + q^50 + 3 * q^51 - 5 * q^52 + q^53 + 26 * q^54 - q^55 - 2 * q^56 - 36 * q^57 - 31 * q^59 - 10 * q^60 + 26 * q^61 + 4 * q^62 + 12 * q^63 - 2 * q^64 - 6 * q^65 + 13 * q^66 - 30 * q^67 - 2 * q^68 - 19 * q^69 - 10 * q^70 - 33 * q^71 - 7 * q^72 - 13 * q^73 + q^74 + 15 * q^75 + 10 * q^76 + 8 * q^77 - 18 * q^78 - 23 * q^79 + q^80 - 3 * q^81 + 7 * q^82 - 12 * q^83 - q^84 + q^85 - 30 * q^86 + 44 * q^87 - 2 * q^88 - 36 * q^89 + 3 * q^90 + 2 * q^91 - 10 * q^92 - 35 * q^93 - 22 * q^94 - 13 * q^95 - 3 * q^96 + 23 * q^97 + 10 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$ .

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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

)

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.280121	−	0.862123i	−0.161728	−	0.497747i	0.837052	−	0.547123i	$-0.184277\pi$
$3$	−0.280121	−	0.862123i	−0.161728	−	0.497747i	−0.998780	+	0.0493755i	$0.984277\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	1.99563	+	1.44991i	0.892472	+	0.648419i	0.936521	−	0.350611i	$-0.114026\pi$
$5$	1.99563	+	1.44991i	0.892472	+	0.648419i	−0.0440494	+	0.999029i	$0.514026\pi$
$6$	−0.733366	−	0.532822i	−0.299395	−	0.217523i
$7$	−0.733366	+	2.25707i	−0.277186	+	0.853092i	0.711446	+	0.702740i	$0.248040\pi$
$7$	−0.733366	+	2.25707i	−0.277186	+	0.853092i	−0.988633	+	0.150351i	$0.951960\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	1.76226	−	1.28036i	0.587421	−	0.426786i
$10$	2.46673			0.780049
$11$	3.30902	+	0.224514i	0.997706	+	0.0676935i
$11$	3.30902	+	0.224514i	0.997706	+	0.0676935i
$12$	−0.906490			−0.261681
$13$	0.424349	−	0.308308i	0.117693	−	0.0855091i	−0.527382	−	0.849629i	$-0.676826\pi$
$13$	0.424349	−	0.308308i	0.117693	−	0.0855091i	0.645075	+	0.764119i	$0.276826\pi$
$14$	0.733366	+	2.25707i	0.196000	+	0.603227i
$15$	0.690983	−	2.12663i	0.178411	−	0.549093i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	0.673124	−	2.07166i	0.158657	−	0.488296i
$19$	−0.888631	−	2.73493i	−0.203866	−	0.627435i	−0.999758	−	0.0219965i	$-0.992998\pi$
$19$	−0.888631	−	2.73493i	−0.203866	−	0.627435i	0.795892	−	0.605439i	$-0.207002\pi$
$20$	1.99563	−	1.44991i	0.446236	−	0.324209i
$21$	2.15130			0.469453
$22$	2.80902	−	1.76336i	0.598884	−	0.375949i
$23$	−4.66708			−0.973154			−0.486577	−	0.873638i	$-0.661755\pi$
$23$	−4.66708			−0.973154			−0.486577	+	0.873638i	$0.661755\pi$
$24$	−0.733366	+	0.532822i	−0.149698	+	0.108762i
$25$	0.335211	+	1.03167i	0.0670422	+	0.206335i
$26$	0.162087	−	0.498852i	0.0317878	−	0.0978329i
$27$	−3.79757	−	2.75910i	−0.730843	−	0.530988i
$28$	1.91998	+	1.39494i	0.362842	+	0.263620i
$29$	−1.96673	+	6.05298i	−0.365213	+	1.12401i	0.584635	+	0.811297i	$0.301238\pi$
$29$	−1.96673	+	6.05298i	−0.365213	+	1.12401i	−0.949848	+	0.312713i	$0.898762\pi$
$30$	−0.690983	−	2.12663i	−0.126156	−	0.388267i
$31$	3.63548	−	2.64133i	0.652952	−	0.474398i	−0.211323	−	0.977416i	$-0.567777\pi$
$31$	3.63548	−	2.64133i	0.652952	−	0.474398i	0.864276	+	0.503019i	$0.167777\pi$
$32$	−1.00000			−0.176777
$33$	−0.733366	−	2.91567i	−0.127663	−	0.507553i
$34$	−1.00000			−0.171499
$35$	−4.73607	+	3.44095i	−0.800542	+	0.581628i
$36$	−0.673124	−	2.07166i	−0.112187	−	0.345277i
$37$	−0.682648	+	2.10097i	−0.112227	+	0.345398i	−0.991358	−	0.131181i	$-0.958123\pi$
$37$	−0.682648	+	2.10097i	−0.112227	+	0.345398i	0.879132	+	0.476579i	$0.158123\pi$
$38$	−2.32647	−	1.69028i	−0.377403	−	0.274199i
$39$	−0.384668	−	0.279478i	−0.0615962	−	0.0447523i
$40$	0.762262	−	2.34600i	0.120524	−	0.370935i
$41$	0.738770	+	2.27370i	0.115376	+	0.355092i	0.992025	−	0.126038i	$-0.0402262\pi$
$41$	0.738770	+	2.27370i	0.115376	+	0.355092i	−0.876649	+	0.481131i	$0.840226\pi$
$42$	1.74044	−	1.26450i	0.268556	−	0.195117i
$43$	−9.13922			−1.39372			−0.696859	−	0.717208i	$-0.745420\pi$
$43$	−9.13922			−1.39372			−0.696859	+	0.717208i	$0.745420\pi$
$44$	1.23607	−	3.07768i	0.186344	−	0.463978i
$45$	5.37322			0.800993
$46$	−3.77575	+	2.74324i	−0.556704	+	0.404469i
$47$	−0.188534	−	0.580247i	−0.0275005	−	0.0846377i	0.936364	−	0.351030i	$-0.114168\pi$
$47$	−0.188534	−	0.580247i	−0.0275005	−	0.0846377i	−0.963865	+	0.266392i	$0.914168\pi$
$48$	−0.280121	+	0.862123i	−0.0404320	+	0.124437i
$49$	1.10659	+	0.803983i	0.158084	+	0.114855i
$50$	0.877594	+	0.637609i	0.124111	+	0.0901716i
$51$	−0.280121	+	0.862123i	−0.0392248	+	0.120721i
$52$	−0.162087	−	0.498852i	−0.0224774	−	0.0691783i
$53$	10.2294	−	7.43207i	1.40511	−	1.02087i	0.411101	−	0.911590i	$-0.365144\pi$
$53$	10.2294	−	7.43207i	1.40511	−	1.02087i	0.994011	−	0.109283i	$-0.0348555\pi$
$54$	−4.69406			−0.638780
$55$	6.27804	+	5.24582i	0.846531	+	0.707346i
$56$	2.37322			0.317135
$57$	−2.10892	+	1.53222i	−0.279333	+	0.202947i
$58$	1.96673	+	6.05298i	0.258245	+	0.794795i
$59$	−3.37489	+	10.3868i	−0.439373	+	1.35225i	0.449164	+	0.893449i	$0.351722\pi$
$59$	−3.37489	+	10.3868i	−0.439373	+	1.35225i	−0.888538	+	0.458803i	$0.848278\pi$
$60$	−1.80902	−	1.31433i	−0.233543	−	0.169679i
$61$	3.65400	+	2.65479i	0.467847	+	0.339911i	0.796602	−	0.604504i	$-0.206629\pi$
$61$	3.65400	+	2.65479i	0.467847	+	0.339911i	−0.328754	+	0.944415i	$0.606629\pi$
$62$	1.38863	−	4.27377i	0.176356	−	0.542769i
$63$	1.59747	+	4.91652i	0.201263	+	0.619423i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.29386			0.160484
$66$	−2.30709	−	1.92777i	−0.283984	−	0.237292i
$67$	−10.1916			−1.24510			−0.622551	−	0.782579i	$-0.713904\pi$
$67$	−10.1916			−1.24510			−0.622551	+	0.782579i	$0.713904\pi$
$68$	−0.809017	+	0.587785i	−0.0981077	+	0.0712794i
$69$	1.30735	+	4.02360i	0.157386	+	0.484385i
$70$	−1.80902	+	5.56758i	−0.216219	+	0.665453i
$71$	−3.83395	−	2.78553i	−0.455006	−	0.330581i	0.336563	−	0.941661i	$-0.390736\pi$
$71$	−3.83395	−	2.78553i	−0.455006	−	0.330581i	−0.791569	+	0.611080i	$0.790736\pi$
$72$	−1.76226	−	1.28036i	−0.207685	−	0.150892i
$73$	−2.97381	+	9.15243i	−0.348058	+	1.07121i	0.611869	+	0.790959i	$0.290418\pi$
$73$	−2.97381	+	9.15243i	−0.348058	+	1.07121i	−0.959926	+	0.280252i	$0.909582\pi$
$74$	0.682648	+	2.10097i	0.0793562	+	0.244233i
$75$	0.795530	−	0.577987i	0.0918599	−	0.0667401i
$76$	−2.87567			−0.329862
$77$	−2.93346	+	7.30403i	−0.334299	+	0.832371i
$78$	−0.475476			−0.0538370
$79$	−8.33187	+	6.05346i	−0.937409	+	0.681067i	−0.947796	−	0.318879i	$-0.896694\pi$
$79$	−8.33187	+	6.05346i	−0.937409	+	0.681067i	0.0103868	+	0.999946i	$0.496694\pi$
$80$	−0.762262	−	2.34600i	−0.0852235	−	0.262291i
$81$	0.704470	−	2.16813i	0.0782744	−	0.240904i
$82$	1.93413	+	1.40522i	0.213588	+	0.155181i
$83$	−6.16708	−	4.48065i	−0.676925	−	0.491815i	0.195411	−	0.980721i	$-0.437396\pi$
$83$	−6.16708	−	4.48065i	−0.676925	−	0.491815i	−0.872336	+	0.488906i	$0.837396\pi$
$84$	0.664789	−	2.04601i	0.0725344	−	0.223238i
$85$	−0.762262	−	2.34600i	−0.0826789	−	0.254460i
$86$	−7.39378	+	5.37190i	−0.797292	+	0.579267i
$87$	5.76934			0.618538
$88$	−0.809017	−	3.21644i	−0.0862415	−	0.342874i
$89$	−1.34084			−0.142129			−0.0710646	−	0.997472i	$-0.522640\pi$
$89$	−1.34084			−0.142129			−0.0710646	+	0.997472i	$0.522640\pi$
$90$	4.34703	−	3.15830i	0.458217	−	0.332914i
$91$	0.384668	+	1.18389i	0.0403242	+	0.124105i
$92$	−1.44221	+	4.43866i	−0.150361	+	0.462762i
$93$	−3.29553	−	2.39434i	−0.341731	−	0.248282i
$94$	−0.493587	−	0.358612i	−0.0509097	−	0.0369880i
$95$	2.19202	−	6.74633i	0.224896	−	0.692159i
$96$	0.280121	+	0.862123i	0.0285897	+	0.0879901i
$97$	5.57398	−	4.04973i	0.565952	−	0.411188i	−0.267680	−	0.963508i	$-0.586257\pi$
$97$	5.57398	−	4.04973i	0.565952	−	0.411188i	0.833633	+	0.552320i	$0.186257\pi$
$98$	1.36782			0.138170
$99$	6.11881	−	3.84107i	0.614964	−	0.386043i
$100$	1.08477			0.108477
$101$	−3.54238	+	2.57369i	−0.352480	+	0.256092i	−0.749909	−	0.661541i	$-0.769903\pi$
$101$	−3.54238	+	2.57369i	−0.352480	+	0.256092i	0.397429	+	0.917633i	$0.369903\pi$
$102$	0.280121	+	0.862123i	0.0277361	+	0.0853629i
$103$	−2.92538	+	9.00340i	−0.288246	+	0.887131i	0.697160	+	0.716915i	$0.254447\pi$
$103$	−2.92538	+	9.00340i	−0.288246	+	0.887131i	−0.985407	+	0.170216i	$0.945553\pi$
$104$	−0.424349	−	0.308308i	−0.0416108	−	0.0302320i
$105$	4.29320	+	3.11919i	0.418973	+	0.304402i
$106$	3.90727	−	12.0253i	0.379508	−	1.16800i
$107$	−0.0168267	−	0.0517873i	−0.00162670	−	0.00500646i	0.950240	−	0.311519i	$-0.100838\pi$
$107$	−0.0168267	−	0.0517873i	−0.00162670	−	0.00500646i	−0.951867	+	0.306513i	$0.900838\pi$
$108$	−3.79757	+	2.75910i	−0.365421	+	0.265494i
$109$	−5.72896			−0.548734			−0.274367	−	0.961625i	$-0.588468\pi$
$109$	−5.72896			−0.548734			−0.274367	+	0.961625i	$0.588468\pi$
$110$	8.16246	+	0.553816i	0.778260	+	0.0528043i
$111$	2.00252			0.190071
$112$	1.91998	−	1.39494i	0.181421	−	0.131810i
$113$	−4.96799	−	15.2899i	−0.467349	−	1.43835i	−0.856004	−	0.516970i	$-0.827060\pi$
$113$	−4.96799	−	15.2899i	−0.467349	−	1.43835i	0.388654	−	0.921384i	$-0.372940\pi$
$114$	−0.805535	+	2.47918i	−0.0754453	+	0.232197i
$115$	−9.31376	−	6.76684i	−0.868513	−	0.631011i
$116$	5.14897	+	3.74095i	0.478070	+	0.347338i
$117$	0.353070	−	1.08664i	0.0326413	−	0.100460i
$118$	3.37489	+	10.3868i	0.310684	+	0.956187i
$119$	1.91998	−	1.39494i	0.176004	−	0.127874i
$120$	−2.23607			−0.204124
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$	4.51660			0.408914
$123$	1.75327	−	1.27382i	0.158087	−	0.114857i
$124$	−1.38863	−	4.27377i	−0.124703	−	0.383796i
$125$	2.98443	−	9.18514i	0.266936	−	0.821544i
$126$	4.18224	+	3.03857i	0.372583	+	0.270698i
$127$	−0.750816	−	0.545500i	−0.0666241	−	0.0484053i	0.553975	−	0.832534i	$-0.313110\pi$
$127$	−0.750816	−	0.545500i	−0.0666241	−	0.0484053i	−0.620599	+	0.784128i	$0.713110\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	2.56009	+	7.87913i	0.225403	+	0.693719i
$130$	1.04675	−	0.760512i	0.0918065	−	0.0667013i
$131$	12.8533			1.12300			0.561498	−	0.827478i	$-0.310225\pi$
$131$	12.8533			1.12300			0.561498	+	0.827478i	$0.310225\pi$
$132$	−2.99959	−	0.203520i	−0.261081	−	0.0177141i
$133$	6.82461			0.591768
$134$	−8.24518	+	5.99048i	−0.712275	+	0.517498i
$135$	−3.57810	−	11.0123i	−0.307954	−	0.947785i
$136$	−0.309017	+	0.951057i	−0.0264980	+	0.0815524i
$137$	−14.3258	−	10.4083i	−1.22394	−	0.889243i	−0.227517	−	0.973774i	$-0.573061\pi$
$137$	−14.3258	−	10.4083i	−1.22394	−	0.889243i	−0.996421	+	0.0845309i	$0.973061\pi$
$138$	3.42268	+	2.48672i	0.291358	+	0.211684i
$139$	3.32495	−	10.2332i	0.282019	−	0.867965i	−0.705258	−	0.708951i	$-0.749169\pi$
$139$	3.32495	−	10.2332i	0.282019	−	0.867965i	0.987276	−	0.159014i	$-0.0508314\pi$
$140$	1.80902	+	5.56758i	0.152890	+	0.470547i
$141$	−0.447432	+	0.325078i	−0.0376806	+	0.0273765i
$142$	−4.73902			−0.397690
$143$	1.47340	−	0.924923i	0.123212	−	0.0773459i
$144$	−2.17828			−0.181523
$145$	−12.7011	+	9.22791i	−1.05477	+	0.766336i
$146$	2.97381	+	9.15243i	0.246114	+	0.757461i
$147$	0.383154	−	1.17923i	0.0316020	−	0.0972611i
$148$	1.78719	+	1.29847i	0.146907	+	0.106734i
$149$	−12.9661	−	9.42042i	−1.06222	−	0.771751i	−0.0877253	−	0.996145i	$-0.527960\pi$
$149$	−12.9661	−	9.42042i	−1.06222	−	0.771751i	−0.974499	+	0.224394i	$0.927960\pi$
$150$	0.303866	−	0.935202i	0.0248105	−	0.0763589i
$151$	2.53453	+	7.80048i	0.206257	+	0.634794i	0.999659	+	0.0260965i	$0.00830770\pi$
$151$	2.53453	+	7.80048i	0.206257	+	0.634794i	−0.793402	+	0.608698i	$0.791692\pi$
$152$	−2.32647	+	1.69028i	−0.188701	+	0.137100i
$153$	−2.17828			−0.176103
$154$	1.91998	+	7.63333i	0.154716	+	0.615111i
$155$	11.0848			0.890350
$156$	−0.384668	+	0.279478i	−0.0307981	+	0.0223761i
$157$	5.74232	+	17.6731i	0.458287	+	1.41046i	0.867232	+	0.497904i	$0.165897\pi$
$157$	5.74232	+	17.6731i	0.458287	+	1.41046i	−0.408945	+	0.912559i	$0.634103\pi$
$158$	−3.18249	+	9.79470i	−0.253185	+	0.779225i
$159$	−9.27282	−	6.73710i	−0.735382	−	0.534286i
$160$	−1.99563	−	1.44991i	−0.157768	−	0.114625i
$161$	3.42268	−	10.5339i	0.269745	−	0.830189i
$162$	−0.704470	−	2.16813i	−0.0553484	−	0.170345i
$163$	4.11203	−	2.98756i	0.322079	−	0.234004i	−0.414983	−	0.909829i	$-0.636212\pi$
$163$	4.11203	−	2.98756i	0.322079	−	0.234004i	0.737062	+	0.675825i	$0.236212\pi$
$164$	2.39071			0.186683
$165$	2.76393	−	6.88191i	0.215172	−	0.535756i
$166$	−7.62293			−0.591654
$167$	5.64693	−	4.10273i	0.436973	−	0.317479i	−0.347458	−	0.937695i	$-0.612955\pi$
$167$	5.64693	−	4.10273i	0.436973	−	0.317479i	0.784431	+	0.620216i	$0.212955\pi$
$168$	−0.664789	−	2.04601i	−0.0512896	−	0.157853i
$169$	−3.93220	+	12.1021i	−0.302477	+	0.930929i
$170$	−1.99563	−	1.44991i	−0.153058	−	0.111203i
$171$	−5.06769	−	3.68189i	−0.387536	−	0.281561i
$172$	−2.82417	+	8.69191i	−0.215341	+	0.662752i
$173$	−0.729247	−	2.24439i	−0.0554436	−	0.170638i	0.919500	−	0.393090i	$-0.128594\pi$
$173$	−0.729247	−	2.24439i	−0.0554436	−	0.170638i	−0.974944	+	0.222452i	$0.928594\pi$
$174$	4.66749	−	3.39113i	0.353842	−	0.257081i
$175$	−2.57439			−0.194606
$176$	−2.54508	−	2.12663i	−0.191843	−	0.160301i
$177$	9.90012			0.744139
$178$	−1.08477	+	0.788128i	−0.0813066	+	0.0590727i
$179$	−7.43298	−	22.8764i	−0.555567	−	1.70986i	−0.694441	−	0.719550i	$-0.744348\pi$
$179$	−7.43298	−	22.8764i	−0.555567	−	1.70986i	0.138874	−	0.990310i	$-0.455652\pi$
$180$	1.66042	−	5.11024i	0.123760	−	0.380895i
$181$	13.6346	+	9.90611i	1.01345	+	0.736316i	0.964930	−	0.262507i	$-0.0845492\pi$
$181$	13.6346	+	9.90611i	1.01345	+	0.736316i	0.0485212	+	0.998822i	$0.484549\pi$
$182$	1.00707	+	0.731682i	0.0746493	+	0.0542359i
$183$	1.26519	−	3.89386i	0.0935258	−	0.287843i
$184$	1.44221	+	4.43866i	0.106321	+	0.327222i
$185$	−4.40853	+	3.20299i	−0.324122	+	0.235488i
$186$	−4.07350			−0.298683
$187$	−2.54508	−	2.12663i	−0.186115	−	0.155514i
$188$	−0.610108			−0.0444967
$189$	9.01248	−	6.54795i	0.655561	−	0.476293i
$190$	−2.19202	−	6.74633i	−0.159025	−	0.489430i
$191$	−3.12690	+	9.62360i	−0.226254	+	0.696339i	0.771908	+	0.635735i	$0.219303\pi$
$191$	−3.12690	+	9.62360i	−0.226254	+	0.696339i	−0.998162	+	0.0606043i	$0.980697\pi$
$192$	0.733366	+	0.532822i	0.0529261	+	0.0384531i
$193$	−1.53471	−	1.11503i	−0.110471	−	0.0802617i	0.531178	−	0.847260i	$-0.321749\pi$
$193$	−1.53471	−	1.11503i	−0.110471	−	0.0802617i	−0.641649	+	0.766998i	$0.721749\pi$
$194$	2.12907	−	6.55261i	0.152858	−	0.470450i
$195$	−0.362437	−	1.11547i	−0.0259547	−	0.0798803i
$196$	1.10659	−	0.803983i	0.0790420	−	0.0574274i
$197$	27.5571			1.96336			0.981682	−	0.190525i	$-0.0610190\pi$
$197$	27.5571			1.96336			0.981682	+	0.190525i	$0.0610190\pi$
$198$	2.69250	−	6.70404i	0.191347	−	0.476436i
$199$	16.8034			1.19116			0.595581	−	0.803295i	$-0.296922\pi$
$199$	16.8034			1.19116			0.595581	+	0.803295i	$0.296922\pi$
$200$	0.877594	−	0.637609i	0.0620553	−	0.0450858i
$201$	2.85488	+	8.78642i	0.201368	+	0.619746i
$202$	−1.35307	+	4.16432i	−0.0952017	+	0.293001i
$203$	−12.2197	−	8.87810i	−0.857651	−	0.623120i
$204$	0.733366	+	0.532822i	0.0513459	+	0.0373050i
$205$	−1.82235	+	5.60861i	−0.127278	+	0.391722i
$206$	2.92538	+	9.00340i	0.203821	+	0.627296i
$207$	−8.22462	+	5.97554i	−0.571651	+	0.415329i
$208$	−0.524524			−0.0363692
$209$	−2.32647	−	9.24943i	−0.160925	−	0.639796i
$210$	5.30669			0.366196
$211$	13.6022	−	9.88256i	0.936413	−	0.680344i	−0.0111419	−	0.999938i	$-0.503547\pi$
$211$	13.6022	−	9.88256i	0.936413	−	0.680344i	0.947554	+	0.319594i	$0.103547\pi$
$212$	−3.90727	−	12.0253i	−0.268352	−	0.825904i
$213$	−1.32750	+	4.08562i	−0.0909587	+	0.279942i
$214$	−0.0440529	−	0.0320063i	−0.00301139	−	0.00218790i
$215$	−18.2385	−	13.2510i	−1.24385	−	0.903713i
$216$	−1.45054	+	4.46431i	−0.0986969	+	0.303758i
$217$	3.29553	+	10.1426i	0.223715	+	0.688524i
$218$	−4.63482	+	3.36740i	−0.313910	+	0.228069i
$219$	8.72355			0.589483
$220$	6.92909	−	4.34973i	0.467159	−	0.293258i
$221$	−0.524524			−0.0352833
$222$	1.62007	−	1.17705i	0.108732	−	0.0789986i
$223$	−0.203209	−	0.625412i	−0.0136079	−	0.0418807i	0.944022	−	0.329882i	$-0.107009\pi$
$223$	−0.203209	−	0.625412i	−0.0136079	−	0.0418807i	−0.957630	+	0.288002i	$0.907009\pi$
$224$	0.733366	−	2.25707i	0.0490001	−	0.150807i
$225$	1.91164	+	1.38889i	0.127443	+	0.0925926i
$226$	−13.0064	−	9.44968i	−0.865171	−	0.628584i
$227$	−3.77241	+	11.6103i	−0.250384	+	0.770601i	0.744321	+	0.667822i	$0.232773\pi$
$227$	−3.77241	+	11.6103i	−0.250384	+	0.770601i	−0.994704	+	0.102779i	$0.967227\pi$
$228$	0.805535	+	2.47918i	0.0533479	+	0.164188i
$229$	20.6481	−	15.0017i	1.36446	−	0.991341i	0.366317	−	0.930490i	$-0.380619\pi$
$229$	20.6481	−	15.0017i	1.36446	−	0.991341i	0.998147	−	0.0608505i	$-0.0193813\pi$
$230$	−11.5124			−0.759108
$231$	7.11870	+	0.482997i	0.468376	+	0.0317789i
$232$	6.36448			0.417848
$233$	−6.40620	+	4.65438i	−0.419684	+	0.304918i	−0.777511	−	0.628870i	$-0.783518\pi$
$233$	−6.40620	+	4.65438i	−0.419684	+	0.304918i	0.357827	+	0.933788i	$0.383518\pi$
$234$	−0.353070	−	1.08664i	−0.0230809	−	0.0710357i
$235$	0.465062	−	1.43131i	0.0303373	−	0.0933686i
$236$	8.83558	+	6.41943i	0.575147	+	0.417869i
$237$	7.55276	+	5.48740i	0.490604	+	0.356445i
$238$	0.733366	−	2.25707i	0.0475371	−	0.146304i
$239$	−4.96721	−	15.2875i	−0.321302	−	0.988867i	−0.973082	−	0.230459i	$-0.925977\pi$
$239$	−4.96721	−	15.2875i	−0.321302	−	0.988867i	0.651780	−	0.758408i	$-0.274023\pi$
$240$	−1.80902	+	1.31433i	−0.116772	+	0.0848395i
$241$	−17.0644			−1.09921			−0.549607	−	0.835423i	$-0.685223\pi$
$241$	−17.0644			−1.09921			−0.549607	+	0.835423i	$0.685223\pi$
$242$	9.69098	−	5.20431i	0.622960	−	0.334546i
$243$	−16.1487			−1.03594
$244$	3.65400	−	2.65479i	0.233924	−	0.169955i
$245$	1.04264	+	3.20890i	0.0666115	+	0.205009i
$246$	0.669688	−	2.06109i	0.0426977	−	0.131410i
$247$	−1.22029	−	0.886591i	−0.0776451	−	0.0564124i
$248$	−3.63548	−	2.64133i	−0.230853	−	0.167725i
$249$	−2.13534	+	6.57191i	−0.135322	+	0.416478i
$250$	−2.98443	−	9.18514i	−0.188752	−	0.580920i
$251$	16.2720	−	11.8223i	1.02708	−	0.746217i	0.0593575	−	0.998237i	$-0.481095\pi$
$251$	16.2720	−	11.8223i	1.02708	−	0.746217i	0.967722	+	0.252020i	$0.0810948\pi$
$252$	5.16953			0.325650
$253$	−15.4435	−	1.04783i	−0.970922	−	0.0658762i
$254$	−0.928059			−0.0582316
$255$	−1.80902	+	1.31433i	−0.113285	+	0.0823064i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.56716	−	4.82322i	0.0977567	−	0.300864i	−0.890206	−	0.455559i	$-0.849439\pi$
$257$	1.56716	−	4.82322i	0.0977567	−	0.300864i	0.987962	+	0.154695i	$0.0494394\pi$
$258$	6.70239	+	4.86957i	0.417273	+	0.303166i
$259$	−4.24141	−	3.08156i	−0.263548	−	0.191479i
$260$	0.399825	−	1.23053i	0.0247961	−	0.0763145i
$261$	4.28408	+	13.1851i	0.265178	+	0.816134i
$262$	10.3985	−	7.55497i	0.642423	−	0.466748i
$263$	29.7148			1.83229			0.916147	−	0.400843i	$-0.131283\pi$
$263$	29.7148			1.83229			0.916147	+	0.400843i	$0.131283\pi$
$264$	−2.54635	+	1.59846i	−0.156717	+	0.0983787i
$265$	31.1898			1.91598
$266$	5.52122	−	4.01140i	0.338528	−	0.245955i
$267$	0.375598	+	1.15597i	0.0229863	+	0.0707444i
$268$	−3.14938	+	9.69279i	−0.192379	+	0.592082i
$269$	−19.9099	−	14.4654i	−1.21393	−	0.881972i	−0.218348	−	0.975871i	$-0.570067\pi$
$269$	−19.9099	−	14.4654i	−1.21393	−	0.881972i	−0.995582	+	0.0938991i	$0.970067\pi$
$270$	−9.36759	−	6.80595i	−0.570093	−	0.414197i
$271$	−1.74388	+	5.36710i	−0.105933	+	0.326028i	−0.989948	−	0.141430i	$-0.954830\pi$
$271$	−1.74388	+	5.36710i	−0.105933	+	0.326028i	0.884015	+	0.467458i	$0.154830\pi$
$272$	0.309017	+	0.951057i	0.0187369	+	0.0576663i
$273$	0.912903	−	0.663263i	0.0552514	−	0.0401425i
$274$	−17.7077			−1.06976
$275$	0.877594	+	3.48908i	0.0529209	+	0.210400i
$276$	4.23066			0.254656
$277$	−9.27760	+	6.74057i	−0.557437	+	0.405002i	−0.830520	−	0.556989i	$-0.811957\pi$
$277$	−9.27760	+	6.74057i	−0.557437	+	0.405002i	0.273083	+	0.961990i	$0.411957\pi$
$278$	−3.32495	−	10.2332i	−0.199417	−	0.613744i
$279$	3.02482	−	9.30944i	0.181091	−	0.557342i
$280$	4.73607	+	3.44095i	0.283034	+	0.205636i
$281$	3.65460	+	2.65523i	0.218015	+	0.158397i	0.691433	−	0.722441i	$-0.256980\pi$
$281$	3.65460	+	2.65523i	0.218015	+	0.158397i	−0.473417	+	0.880838i	$0.656980\pi$
$282$	−0.170904	+	0.525988i	−0.0101772	+	0.0313221i
$283$	5.62445	+	17.3103i	0.334339	+	1.02899i	0.967047	+	0.254598i	$0.0819432\pi$
$283$	5.62445	+	17.3103i	0.334339	+	1.02899i	−0.632708	+	0.774390i	$0.718057\pi$
$284$	−3.83395	+	2.78553i	−0.227503	+	0.165291i
$285$	−6.43020			−0.380892
$286$	0.648347	−	1.61432i	0.0383376	−	0.0954567i
$287$	−5.67369			−0.334907
$288$	−1.76226	+	1.28036i	−0.103842	+	0.0754458i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−4.85140	+	14.9311i	−0.284884	+	0.876783i
$291$	−5.05276	−	3.67104i	−0.296198	−	0.215200i
$292$	7.78552	+	5.65652i	0.455613	+	0.331023i
$293$	−1.07629	+	3.31248i	−0.0628775	+	0.193517i	−0.977560	−	0.210655i	$-0.932440\pi$
$293$	−1.07629	+	3.31248i	−0.0628775	+	0.193517i	0.914683	+	0.404172i	$0.132440\pi$
$294$	−0.383154	−	1.17923i	−0.0223460	−	0.0687739i
$295$	−21.7950	+	15.8350i	−1.26895	+	0.921949i
$296$	2.20909			0.128401
$297$	−11.9468	−	9.98251i	−0.693222	−	0.579244i
$298$	−16.0270			−0.928418
$299$	−1.98047	+	1.43890i	−0.114534	+	0.0832135i
$300$	−0.303866	−	0.935202i	−0.0175437	−	0.0539939i
$301$	6.70239	−	20.6278i	0.386319	−	1.18897i
$302$	6.63548	+	4.82096i	0.381829	+	0.277415i
$303$	3.21114	+	2.33303i	0.184475	+	0.134029i
$304$	−0.888631	+	2.73493i	−0.0509665	+	0.156859i
$305$	3.44283	+	10.5959i	0.197136	+	0.606722i
$306$	−1.76226	+	1.28036i	−0.100742	+	0.0731932i
$307$	−4.65092			−0.265442			−0.132721	−	0.991153i	$-0.542371\pi$
$307$	−4.65092			−0.265442			−0.132721	+	0.991153i	$0.542371\pi$
$308$	6.04005	+	5.04696i	0.344164	+	0.287577i
$309$	8.58150			0.488184
$310$	8.96776	−	6.51546i	0.509335	−	0.370053i
$311$	9.02696	+	27.7821i	0.511872	+	1.57538i	0.788902	+	0.614519i	$0.210650\pi$
$311$	9.02696	+	27.7821i	0.511872	+	1.57538i	−0.277031	+	0.960861i	$0.589350\pi$
$312$	−0.146930	+	0.452204i	−0.00831828	+	0.0256010i
$313$	3.81898	+	2.77465i	0.215862	+	0.156833i	0.690462	−	0.723369i	$-0.257407\pi$
$313$	3.81898	+	2.77465i	0.215862	+	0.156833i	−0.474600	+	0.880202i	$0.657407\pi$
$314$	15.0336	+	10.9226i	0.848395	+	0.616395i
$315$	−3.94054	+	12.1277i	−0.222024	+	0.683320i
$316$	3.18249	+	9.79470i	0.179029	+	0.550995i
$317$	13.5625	−	9.85376i	0.761748	−	0.553442i	−0.137698	−	0.990474i	$-0.543970\pi$
$317$	13.5625	−	9.85376i	0.761748	−	0.553442i	0.899446	+	0.437032i	$0.143970\pi$
$318$	−11.4618			−0.642748
$319$	−7.86693	+	19.5878i	−0.440463	+	1.09671i
$320$	−2.46673			−0.137894
$321$	−0.0399335	+	0.0290134i	−0.00222887	+	0.00161937i
$322$	−3.42268	−	10.5339i	−0.190738	−	0.587033i
$323$	−0.888631	+	2.73493i	−0.0494448	+	0.152175i
$324$	−1.84433	−	1.33998i	−0.102463	−	0.0744434i
$325$	0.460319	+	0.334441i	0.0255339	+	0.0185515i
$326$	1.57066	−	4.83398i	0.0869906	−	0.267729i
$327$	1.60480	+	4.93907i	0.0887456	+	0.273131i
$328$	1.93413	−	1.40522i	0.106794	−	0.0775905i
$329$	1.44792			0.0798264
$330$	−1.80902	−	7.19218i	−0.0995831	−	0.395916i
$331$	12.5653			0.690653			0.345327	−	0.938483i	$-0.387768\pi$
$331$	12.5653			0.690653			0.345327	+	0.938483i	$0.387768\pi$
$332$	−6.16708	+	4.48065i	−0.338463	+	0.245907i
$333$	1.48699	+	4.57650i	0.0814868	+	0.250791i
$334$	2.15694	−	6.63836i	0.118022	−	0.363235i
$335$	−20.3387	−	14.7769i	−1.11122	−	0.807348i
$336$	−1.74044	−	1.26450i	−0.0949488	−	0.0689843i
$337$	−7.72723	+	23.7820i	−0.420929	+	1.29549i	0.485910	+	0.874009i	$0.338488\pi$
$337$	−7.72723	+	23.7820i	−0.420929	+	1.29549i	−0.906839	+	0.421477i	$0.861512\pi$
$338$	3.93220	+	12.1021i	0.213884	+	0.658266i
$339$	−11.7901	+	8.56605i	−0.640353	+	0.465244i
$340$	−2.46673			−0.133777
$341$	12.6229	−	7.92400i	0.683568	−	0.429109i
$342$	−6.26400			−0.338719
$343$	−16.0660	+	11.6726i	−0.867483	+	0.630264i
$344$	2.82417	+	8.69191i	0.152269	+	0.468637i
$345$	−3.22487	+	9.92514i	−0.173621	+	0.534352i
$346$	−1.90919	−	1.38711i	−0.102639	−	0.0745715i
$347$	0.210882	+	0.153215i	0.0113208	+	0.00822501i	0.593431	−	0.804885i	$-0.297773\pi$
$347$	0.210882	+	0.153215i	0.0113208	+	0.00822501i	−0.582110	+	0.813110i	$0.697773\pi$
$348$	1.78282	−	5.48696i	0.0955693	−	0.294132i
$349$	−5.20161	−	16.0089i	−0.278436	−	0.856938i	−0.988290	−	0.152589i	$-0.951239\pi$
$349$	−5.20161	−	16.0089i	−0.278436	−	0.856938i	0.709854	−	0.704349i	$-0.248761\pi$
$350$	−2.08273	+	1.51319i	−0.111326	+	0.0808833i
$351$	−2.46215			−0.131420
$352$	−3.30902	−	0.224514i	−0.176371	−	0.0119666i
$353$	−11.1557			−0.593760			−0.296880	−	0.954915i	$-0.595946\pi$
$353$	−11.1557			−0.593760			−0.296880	+	0.954915i	$0.595946\pi$
$354$	8.00937	−	5.81915i	0.425693	−	0.309284i
$355$	−3.61238	−	11.1178i	−0.191725	−	0.590069i
$356$	−0.414344	+	1.27522i	−0.0219602	+	0.0675865i
$357$	−1.74044	−	1.26450i	−0.0921139	−	0.0669246i
$358$	−19.4598	−	14.1384i	−1.02848	−	0.747236i
$359$	−1.51651	+	4.66735i	−0.0800386	+	0.246333i	−0.983067	−	0.183248i	$-0.941339\pi$
$359$	−1.51651	+	4.66735i	−0.0800386	+	0.246333i	0.903028	+	0.429581i	$0.141339\pi$
$360$	−1.66042	−	5.11024i	−0.0875117	−	0.269333i
$361$	8.68117	−	6.30724i	0.456904	−	0.331960i
$362$	16.8533			0.885789
$363$	−1.77211	−	9.81266i	−0.0930117	−	0.515031i
$364$	1.24481			0.0652459
$365$	−19.2048	+	13.9531i	−1.00523	+	0.730339i
$366$	−1.26519	−	3.89386i	−0.0661327	−	0.203536i
$367$	6.78512	−	20.8824i	0.354180	−	1.09005i	−0.602303	−	0.798267i	$-0.705750\pi$
$367$	6.78512	−	20.8824i	0.354180	−	1.09005i	0.956483	−	0.291787i	$-0.0942499\pi$
$368$	3.77575	+	2.74324i	0.196825	+	0.143001i
$369$	4.21306	+	3.06097i	0.219323	+	0.159348i
$370$	−1.68391	+	5.18254i	−0.0875423	+	0.269427i
$371$	9.27282	+	28.5388i	0.481421	+	1.48166i
$372$	−3.29553	+	2.39434i	−0.170865	+	0.124141i
$373$	−24.1531			−1.25060			−0.625300	−	0.780384i	$-0.715023\pi$
$373$	−24.1531			−1.25060			−0.625300	+	0.780384i	$0.715023\pi$
$374$	−3.30902	−	0.224514i	−0.171105	−	0.0116093i
$375$	−8.75473			−0.452092
$376$	−0.493587	+	0.358612i	−0.0254548	+	0.0184940i
$377$	1.03160	+	3.17493i	0.0531300	+	0.163517i
$378$	3.44246	−	10.5948i	0.177061	−	0.544938i
$379$	−1.10562	−	0.803278i	−0.0567918	−	0.0412616i	0.559027	−	0.829149i	$-0.311175\pi$
$379$	−1.10562	−	0.803278i	−0.0567918	−	0.0412616i	−0.615819	+	0.787888i	$0.711175\pi$
$380$	−5.73877	−	4.16946i	−0.294393	−	0.213889i
$381$	−0.259969	+	0.800102i	−0.0133186	+	0.0409905i
$382$	3.12690	+	9.62360i	0.159986	+	0.492386i
$383$	7.69176	−	5.58839i	0.393031	−	0.285554i	−0.373666	−	0.927563i	$-0.621899\pi$
$383$	7.69176	−	5.58839i	0.393031	−	0.285554i	0.766696	+	0.642010i	$0.221899\pi$
$384$	0.906490			0.0462591
$385$	−16.4443	+	10.3229i	−0.838078	+	0.526102i
$386$	−1.89700			−0.0965550
$387$	−16.1057	+	11.7015i	−0.818699	+	0.594819i
$388$	−2.12907	−	6.55261i	−0.108087	−	0.332658i
$389$	6.78702	−	20.8883i	0.344115	−	1.05908i	−0.617940	−	0.786225i	$-0.712033\pi$
$389$	6.78702	−	20.8883i	0.344115	−	1.05908i	0.962056	−	0.272853i	$-0.0879673\pi$
$390$	−0.948873	−	0.689397i	−0.0480481	−	0.0349090i
$391$	3.77575	+	2.74324i	0.190948	+	0.138732i
$392$	0.422679	−	1.30087i	0.0213485	−	0.0657040i
$393$	−3.60047	−	11.0811i	−0.181620	−	0.558968i
$394$	22.2942	−	16.1977i	1.12317	−	0.816027i
$395$	−25.4043			−1.27823
$396$	−1.76226	−	7.00629i	−0.0885570	−	0.352080i
$397$	−12.6412			−0.634442			−0.317221	−	0.948352i	$-0.602750\pi$
$397$	−12.6412			−0.634442			−0.317221	+	0.948352i	$0.602750\pi$
$398$	13.5943	−	9.87680i	0.681418	−	0.495079i
$399$	−1.91171	−	5.88365i	−0.0957054	−	0.294551i
$400$	0.335211	−	1.03167i	0.0167606	−	0.0515837i
$401$	11.4792	+	8.34013i	0.573244	+	0.416486i	0.836282	−	0.548299i	$-0.184724\pi$
$401$	11.4792	+	8.34013i	0.573244	+	0.416486i	−0.263038	+	0.964785i	$0.584724\pi$
$402$	7.47418	+	5.43031i	0.372778	+	0.270839i
$403$	0.728371	−	2.24169i	0.0362827	−	0.111667i
$404$	1.35307	+	4.16432i	0.0673177	+	0.207183i
$405$	4.54946	−	3.30537i	0.226064	−	0.164245i
$406$	−15.1043			−0.749615
$407$	−2.73059	+	6.79889i	−0.135350	+	0.337009i
$408$	0.906490			0.0448779
$409$	−26.2553	+	19.0756i	−1.29824	+	0.943228i	−0.999937	−	0.0112420i	$-0.996421\pi$
$409$	−26.2553	+	19.0756i	−1.29824	+	0.943228i	−0.298306	+	0.954470i	$0.596421\pi$
$410$	1.82235	+	5.60861i	0.0899993	+	0.276989i
$411$	−4.96030	+	15.2662i	−0.244673	+	0.753027i
$412$	7.65875	+	5.56441i	0.377319	+	0.274139i
$413$	−20.9688	−	15.2347i	−1.03181	−	0.749652i
$414$	−3.14153	+	9.66862i	−0.154398	+	0.475187i
$415$	−5.81067	−	17.8834i	−0.285235	−	0.877862i
$416$	−0.424349	+	0.308308i	−0.0208054	+	0.0151160i
$417$	−9.75363			−0.477637
$418$	−7.31883	−	6.11548i	−0.357976	−	0.299118i
$419$	30.0753			1.46927			0.734636	−	0.678461i	$-0.237353\pi$
$419$	30.0753			1.46927			0.734636	+	0.678461i	$0.237353\pi$
$420$	4.29320	−	3.11919i	0.209487	−	0.152201i
$421$	4.54140	+	13.9770i	0.221334	+	0.681196i	0.998643	+	0.0520772i	$0.0165842\pi$
$421$	4.54140	+	13.9770i	0.221334	+	0.681196i	−0.777309	+	0.629119i	$0.783416\pi$
$422$	5.19557	−	15.9903i	0.252916	−	0.778397i
$423$	−1.07517	−	0.781156i	−0.0522765	−	0.0379811i
$424$	−10.2294	−	7.43207i	−0.496782	−	0.360933i
$425$	0.335211	−	1.03167i	0.0162601	−	0.0500435i
$426$	1.32750	+	4.08562i	0.0643175	+	0.197949i
$427$	−8.67176	+	6.30040i	−0.419656	+	0.304898i
$428$	−0.0544523			−0.00263205
$429$	−1.21013	−	1.01116i	−0.0584255	−	0.0488193i
$430$	−22.5440			−1.08717
$431$	−25.1006	+	18.2367i	−1.20905	+	0.878430i	−0.995145	−	0.0984238i	$-0.968620\pi$
$431$	−25.1006	+	18.2367i	−1.20905	+	0.878430i	−0.213910	+	0.976853i	$0.568620\pi$
$432$	1.45054	+	4.46431i	0.0697893	+	0.214789i
$433$	−4.04405	+	12.4463i	−0.194345	+	0.598132i	0.805639	+	0.592407i	$0.201822\pi$
$433$	−4.04405	+	12.4463i	−0.194345	+	0.598132i	−0.999984	+	0.00572471i	$0.998178\pi$
$434$	8.62781	+	6.26847i	0.414148	+	0.300896i
$435$	11.5134	+	8.36501i	0.552028	+	0.401072i
$436$	−1.77034	+	5.44856i	−0.0847841	+	0.260939i
$437$	4.14732	+	12.7641i	0.198393	+	0.610591i
$438$	7.05750	−	5.12757i	0.337220	−	0.245005i
$439$	32.8517			1.56793			0.783964	−	0.620806i	$-0.213195\pi$
$439$	32.8517			1.56793			0.783964	+	0.620806i	$0.213195\pi$
$440$	3.04905	−	7.59182i	0.145358	−	0.361926i
$441$	2.97948			0.141880
$442$	−0.424349	+	0.308308i	−0.0201842	+	0.0146647i
$443$	2.43758	+	7.50211i	0.115813	+	0.356436i	0.992116	−	0.125325i	$-0.0399974\pi$
$443$	2.43758	+	7.50211i	0.115813	+	0.356436i	−0.876303	+	0.481761i	$0.839997\pi$
$444$	0.618813	−	1.90451i	0.0293676	−	0.0903841i
$445$	−2.67583	−	1.94410i	−0.126846	−	0.0921593i
$446$	−0.532007	−	0.386526i	−0.0251913	−	0.0183025i
$447$	−4.48949	+	13.8172i	−0.212346	+	0.653532i
$448$	−0.733366	−	2.25707i	−0.0346483	−	0.106636i
$449$	−19.5858	+	14.2299i	−0.924309	+	0.671550i	−0.944593	−	0.328244i	$-0.893543\pi$
$449$	−19.5858	+	14.2299i	−0.924309	+	0.671550i	0.0202837	+	0.999794i	$0.493543\pi$
$450$	2.36292			0.111389
$451$	1.93413	+	7.68958i	0.0910744	+	0.362088i
$452$	−16.0768			−0.756187
$453$	6.01500	−	4.37015i	0.282609	−	0.205328i
$454$	3.77241	+	11.6103i	0.177048	+	0.544897i
$455$	−0.948873	+	2.92033i	−0.0444839	+	0.136907i
$456$	2.10892	+	1.53222i	0.0987592	+	0.0717528i
$457$	22.5238	+	16.3645i	1.05362	+	0.765497i	0.972897	−	0.231240i	$-0.0742781\pi$
$457$	22.5238	+	16.3645i	1.05362	+	0.765497i	0.0807198	+	0.996737i	$0.474278\pi$
$458$	7.88686	−	24.2733i	0.368529	−	1.13422i
$459$	1.45054	+	4.46431i	0.0677055	+	0.208376i
$460$	−9.31376	+	6.76684i	−0.434256	+	0.315506i
$461$	22.5328			1.04946			0.524729	−	0.851269i	$-0.324167\pi$
$461$	22.5328			1.04946			0.524729	+	0.851269i	$0.324167\pi$
$462$	6.04304	−	3.79351i	0.281148	−	0.176490i
$463$	−14.8466			−0.689980			−0.344990	−	0.938606i	$-0.612118\pi$
$463$	−14.8466			−0.689980			−0.344990	+	0.938606i	$0.612118\pi$
$464$	5.14897	−	3.74095i	0.239035	−	0.173669i
$465$	−3.10507	−	9.55644i	−0.143994	−	0.443169i
$466$	−2.44695	+	7.53094i	−0.113353	+	0.348864i
$467$	33.6191	+	24.4257i	1.55571	+	1.13029i	0.939421	+	0.342764i	$0.111363\pi$
$467$	33.6191	+	24.4257i	1.55571	+	1.13029i	0.616285	+	0.787523i	$0.288637\pi$
$468$	−0.924349	−	0.671579i	−0.0427280	−	0.0310437i
$469$	7.47418	−	23.0032i	0.345125	−	1.06219i
$470$	−0.465062	−	1.43131i	−0.0214517	−	0.0660216i
$471$	13.6278	−	9.90118i	0.627936	−	0.456222i
$472$	10.9214			0.502697
$473$	−30.2418	−	2.05188i	−1.39052	−	0.0943456i
$474$	9.33572			0.428804
$475$	2.52367	−	1.83355i	0.115794	−	0.0841293i
$476$	−0.733366	−	2.25707i	−0.0336138	−	0.103453i
$477$	8.51111	−	26.1945i	0.389697	−	1.19936i
$478$	−13.0043	−	9.44820i	−0.594804	−	0.432151i
$479$	20.6821	+	15.0264i	0.944991	+	0.686576i	0.949617	−	0.313413i	$-0.101473\pi$
$479$	20.6821	+	15.0264i	0.944991	+	0.686576i	−0.00462622	+	0.999989i	$0.501473\pi$
$480$	−0.690983	+	2.12663i	−0.0315389	+	0.0970668i
$481$	0.358065	+	1.10201i	0.0163264	+	0.0502474i
$482$	−13.8054	+	10.0302i	−0.628818	+	0.456863i
$483$	−10.0403			−0.456850
$484$	4.78115	−	9.90659i	0.217325	−	0.450300i
$485$	16.9953			0.771719
$486$	−13.0646	+	9.49197i	−0.592621	+	0.430564i
$487$	4.19653	+	12.9156i	0.190163	+	0.585261i	0.999999	−	0.00139499i	$-0.000444038\pi$
$487$	4.19653	+	12.9156i	0.190163	+	0.585261i	−0.809836	+	0.586656i	$0.800444\pi$
$488$	1.39571	−	4.29554i	0.0631806	−	0.194450i
$489$	−3.72751	−	2.70820i	−0.168564	−	0.122469i
$490$	2.72966	+	1.98321i	0.123313	+	0.0895923i
$491$	11.9138	−	36.6670i	0.537663	−	1.65476i	−0.200160	−	0.979763i	$-0.564146\pi$
$491$	11.9138	−	36.6670i	0.537663	−	1.65476i	0.737823	−	0.674994i	$-0.235854\pi$
$492$	−0.669688	−	2.06109i	−0.0301919	−	0.0929210i
$493$	5.14897	−	3.74095i	0.231898	−	0.168484i
$494$	−1.50836			−0.0678643
$495$	17.7801	+	1.20636i	0.799155	+	0.0542220i
$496$	−4.49371			−0.201773
$497$	9.09881	−	6.61068i	0.408138	−	0.296529i
$498$	2.13534	+	6.57191i	0.0956870	+	0.294494i
$499$	6.76790	−	20.8294i	0.302973	−	0.932454i	−0.677453	−	0.735566i	$-0.736916\pi$
$499$	6.76790	−	20.8294i	0.302973	−	0.932454i	0.980426	−	0.196888i	$-0.0630836\pi$
$500$	−7.81335	−	5.67673i	−0.349424	−	0.253871i
$501$	−5.11889	−	3.71909i	−0.228695	−	0.166157i
$502$	6.21535	−	19.1289i	0.277405	−	0.853764i
$503$	−7.38348	−	22.7240i	−0.329213	−	1.01321i	−0.969503	−	0.245080i	$-0.921186\pi$
$503$	−7.38348	−	22.7240i	−0.329213	−	1.01321i	0.640290	−	0.768134i	$-0.278814\pi$
$504$	4.18224	−	3.03857i	0.186292	−	0.135349i
$505$	−10.8009			−0.480634
$506$	−13.1099	+	8.22973i	−0.582807	+	0.365856i
$507$	11.5350			0.512286
$508$	−0.750816	+	0.545500i	−0.0333121	+	0.0242026i
$509$	0.773612	+	2.38093i	0.0342897	+	0.105533i	0.966736	−	0.255775i	$-0.0823305\pi$
$509$	0.773612	+	2.38093i	0.0342897	+	0.105533i	−0.932447	+	0.361307i	$0.882330\pi$
$510$	−0.690983	+	2.12663i	−0.0305972	+	0.0941686i
$511$	−18.4768	−	13.4242i	−0.817365	−	0.593850i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−4.17128	+	12.8379i	−0.184167	+	0.566807i
$514$	−1.56716	−	4.82322i	−0.0691244	−	0.212743i
$515$	−18.8921	+	13.7259i	−0.832484	+	0.604835i
$516$	8.28461			0.364710
$517$	−0.493587	−	1.96237i	−0.0217079	−	0.0863051i
$518$	−5.24267			−0.230350
$519$	−1.73066	+	1.25740i	−0.0759677	+	0.0551938i
$520$	−0.399825	−	1.23053i	−0.0175335	−	0.0539625i
$521$	5.77002	−	17.7583i	0.252789	−	0.778005i	−0.741468	−	0.670988i	$-0.765870\pi$
$521$	5.77002	−	17.7583i	0.252789	−	0.778005i	0.994257	−	0.107017i	$-0.0341299\pi$
$522$	11.2159	+	8.14881i	0.490906	+	0.356664i
$523$	31.2594	+	22.7113i	1.36688	+	0.993094i	0.997974	+	0.0636264i	$0.0202666\pi$
$523$	31.2594	+	22.7113i	1.36688	+	0.993094i	0.368903	+	0.929468i	$0.379733\pi$
$524$	3.97188	−	12.2242i	0.173513	−	0.534017i
$525$	0.721140	+	2.21944i	0.0314731	+	0.0968644i
$526$	24.0398	−	17.4659i	1.04818	−	0.761551i
$527$	−4.49371			−0.195749
$528$	−1.12048	+	2.78989i	−0.0487628	+	0.121414i
$529$	−1.21834			−0.0529715
$530$	25.2331	−	18.3329i	1.09606	−	0.796331i
$531$	7.35144	+	22.6254i	0.319026	+	0.981860i
$532$	2.10892	−	6.49059i	0.0914332	−	0.281403i
$533$	1.01450	+	0.737074i	0.0439427	+	0.0319262i
$534$	0.983329	+	0.714431i	0.0425528	+	0.0309164i
$535$	0.0415070	−	0.127745i	0.00179450	−	0.00552291i
$536$	3.14938	+	9.69279i	0.136032	+	0.418665i
$537$	−17.6401	+	12.8163i	−0.761227	+	0.553064i
$538$	−24.6100			−1.06101
$539$	3.48121	+	2.90884i	0.149946	+	0.125293i
$540$	−11.5790			−0.498280
$541$	31.4945	−	22.8821i	1.35405	−	0.983778i	0.355256	−	0.934769i	$-0.384394\pi$
$541$	31.4945	−	22.8821i	1.35405	−	0.983778i	0.998798	−	0.0490094i	$-0.0156064\pi$
$542$	1.74388	+	5.36710i	0.0749059	+	0.230537i
$543$	4.72096	−	14.5296i	0.202596	−	0.623525i
$544$	0.809017	+	0.587785i	0.0346863	+	0.0252011i
$545$	−11.4329	−	8.30646i	−0.489730	−	0.355810i
$546$	0.348698	−	1.07318i	0.0149229	−	0.0459279i
$547$	−4.41957	−	13.6020i	−0.188967	−	0.581581i	0.811027	−	0.585009i	$-0.198909\pi$
$547$	−4.41957	−	13.6020i	−0.188967	−	0.581581i	−0.999994	+	0.00342778i	$0.998909\pi$
$548$	−14.3258	+	10.4083i	−0.611969	+	0.444622i
$549$	9.83839			0.419892
$550$	2.76082	+	2.30689i	0.117722	+	0.0983662i
$551$	18.3021			0.779698
$552$	3.42268	−	2.48672i	0.145679	−	0.105842i
$553$	−7.55276	−	23.2450i	−0.321176	−	0.988478i
$554$	−3.54373	+	10.9065i	−0.150559	+	0.463372i
$555$	3.99629	+	2.90347i	0.169633	+	0.123246i
$556$	−8.70484	−	6.32444i	−0.369167	−	0.268216i
$557$	3.57598	−	11.0057i	0.151519	−	0.466328i	−0.846273	−	0.532750i	$-0.821159\pi$
$557$	3.57598	−	11.0057i	0.151519	−	0.466328i	0.997792	+	0.0664226i	$0.0211586\pi$
$558$	−3.02482	−	9.30944i	−0.128051	−	0.394100i
$559$	−3.87822	+	2.81769i	−0.164031	+	0.119176i
$560$	5.85410			0.247381
$561$	−1.12048	+	2.78989i	−0.0473068	+	0.117789i
$562$	4.51734			0.190552
$563$	37.6295	−	27.3394i	1.58590	−	1.15222i	0.676378	−	0.736555i	$-0.263549\pi$
$563$	37.6295	−	27.3394i	1.58590	−	1.15222i	0.909518	−	0.415665i	$-0.136451\pi$
$564$	0.170904	+	0.525988i	0.00719635	+	0.0221481i
$565$	12.2547	−	37.7161i	0.515559	−	1.58673i
$566$	14.7250	+	10.6983i	0.618938	+	0.449684i
$567$	4.37699	+	3.18007i	0.183816	+	0.133550i
$568$	−1.46444	+	4.50708i	−0.0614465	+	0.189113i
$569$	−3.63012	−	11.1724i	−0.152182	−	0.468369i	0.845682	−	0.533687i	$-0.179194\pi$
$569$	−3.63012	−	11.1724i	−0.152182	−	0.468369i	−0.997865	+	0.0653176i	$0.979194\pi$
$570$	−5.20214	+	3.77957i	−0.217894	+	0.158309i
$571$	−7.82989			−0.327671			−0.163835	−	0.986488i	$-0.552387\pi$
$571$	−7.82989			−0.327671			−0.163835	+	0.986488i	$0.552387\pi$
$572$	−0.424349	−	1.68710i	−0.0177429	−	0.0705412i
$573$	9.17264			0.383192
$574$	−4.59011	+	3.33491i	−0.191587	+	0.139196i
$575$	−1.56446	−	4.81491i	−0.0652424	−	0.200795i
$576$	−0.673124	+	2.07166i	−0.0280468	+	0.0863193i
$577$	−0.0666543	−	0.0484272i	−0.00277486	−	0.00201605i	0.586397	−	0.810024i	$-0.300546\pi$
$577$	−0.0666543	−	0.0484272i	−0.00277486	−	0.00201605i	−0.589172	+	0.808008i	$0.700546\pi$
$578$	0.809017	+	0.587785i	0.0336507	+	0.0244486i
$579$	−0.531391	+	1.63545i	−0.0220838	+	0.0679671i
$580$	4.85140	+	14.9311i	0.201443	+	0.619979i
$581$	14.6359	−	10.6336i	0.607198	−	0.441155i
$582$	−6.24555			−0.258887
$583$	35.5177	−	22.2962i	1.47099	−	0.923414i
$584$	9.62344			0.398221
$585$	2.28012	−	1.65660i	0.0942714	−	0.0684922i
$586$	1.07629	+	3.31248i	0.0444611	+	0.136837i
$587$	9.74001	−	29.9767i	0.402013	−	1.23727i	−0.521350	−	0.853343i	$-0.674572\pi$
$587$	9.74001	−	29.9767i	0.402013	−	1.23727i	0.923364	−	0.383927i	$-0.125428\pi$
$588$	−1.00311	−	0.728803i	−0.0413676	−	0.0300553i
$589$	−10.4545	−	7.59561i	−0.430768	−	0.312972i
$590$	−8.32495	+	25.6216i	−0.342733	+	1.05482i
$591$	−7.71933	−	23.7577i	−0.317531	−	0.977259i
$592$	1.78719	−	1.29847i	0.0734533	−	0.0533669i
$593$	−17.2977			−0.710330			−0.355165	−	0.934804i	$-0.615575\pi$
$593$	−17.2977			−0.710330			−0.355165	+	0.934804i	$0.615575\pi$
$594$	−15.5327	−	1.05388i	−0.637315	−	0.0432413i
$595$	5.85410			0.239995
$596$	−12.9661	+	9.42042i	−0.531112	+	0.385875i
$597$	−4.70699	−	14.4866i	−0.192644	−	0.592898i
$598$	−0.756473	+	2.32818i	−0.0309345	+	0.0952065i
$599$	−14.0959	−	10.2413i	−0.575942	−	0.418446i	0.261317	−	0.965253i	$-0.415843\pi$
$599$	−14.0959	−	10.2413i	−0.575942	−	0.418446i	−0.837259	+	0.546807i	$0.815843\pi$
$600$	−0.795530	−	0.577987i	−0.0324774	−	0.0235962i
$601$	−7.42957	+	22.8659i	−0.303059	+	0.932719i	0.677336	+	0.735674i	$0.263134\pi$
$601$	−7.42957	+	22.8659i	−0.303059	+	0.932719i	−0.980395	+	0.197045i	$0.936866\pi$
$602$	−6.70239	−	20.6278i	−0.273169	−	0.840728i
$603$	−17.9603	+	13.0489i	−0.731399	+	0.531393i
$604$	8.20191			0.333731
$605$	19.5964	+	18.7680i	0.796706	+	0.763028i
$606$	3.96918			0.161237
$607$	28.9016	−	20.9982i	1.17308	−	0.852291i	0.181704	−	0.983353i	$-0.441839\pi$
$607$	28.9016	−	20.9982i	1.17308	−	0.852291i	0.991374	+	0.131062i	$0.0418387\pi$
$608$	0.888631	+	2.73493i	0.0360388	+	0.110916i
$609$	−4.23103	+	13.0218i	−0.171450	+	0.527669i
$610$	9.01345	+	6.54865i	0.364944	+	0.265147i
$611$	−0.258898	−	0.188101i	−0.0104739	−	0.00760974i
$612$	−0.673124	+	2.07166i	−0.0272094	+	0.0837420i
$613$	−5.93568	−	18.2682i	−0.239740	−	0.737844i	−0.996457	−	0.0841015i	$-0.973198\pi$
$613$	−5.93568	−	18.2682i	−0.239740	−	0.737844i	0.756717	−	0.653742i	$-0.226802\pi$
$614$	−3.76267	+	2.73374i	−0.151849	+	0.110325i
$615$	5.34579			0.215563
$616$	7.85303	+	0.532822i	0.316408	+	0.0214680i
$617$	−40.3313			−1.62368			−0.811839	−	0.583881i	$-0.801533\pi$
$617$	−40.3313			−1.62368			−0.811839	+	0.583881i	$0.801533\pi$
$618$	6.94258	−	5.04408i	0.279271	−	0.202903i
$619$	10.9173	+	33.6001i	0.438805	+	1.35050i	0.889137	+	0.457641i	$0.151305\pi$
$619$	10.9173	+	33.6001i	0.438805	+	1.35050i	−0.450332	+	0.892861i	$0.648695\pi$
$620$	3.42538	−	10.5422i	0.137567	−	0.423386i
$621$	17.7236	+	12.8769i	0.711223	+	0.516733i
$622$	23.6329	+	17.1703i	0.947592	+	0.688466i
$623$	0.983329	−	3.02638i	0.0393963	−	0.121249i
$624$	0.146930	+	0.452204i	0.00588191	+	0.0181027i
$625$	23.6614	−	17.1910i	0.946456	−	0.687641i
$626$	4.72052			0.188670
$627$	−7.32245	+	4.59666i	−0.292431	+	0.183573i
$628$	18.5826			0.741525
$629$	1.78719	−	1.29847i	0.0712601	−	0.0517735i
$630$	3.94054	+	12.1277i	0.156995	+	0.483180i
$631$	−4.21627	+	12.9764i	−0.167847	+	0.516580i	−0.999235	−	0.0391125i	$-0.987547\pi$
$631$	−4.21627	+	12.9764i	−0.167847	+	0.516580i	0.831388	+	0.555693i	$0.187547\pi$
$632$	8.33187	+	6.05346i	0.331424	+	0.240794i
$633$	−12.3302	−	8.95844i	−0.490083	−	0.356066i
$634$	5.18043	−	15.9437i	0.205741	−	0.633206i
$635$	−0.707425	−	2.17723i	−0.0280733	−	0.0864007i
$636$	−9.27282	+	6.73710i	−0.367691	+	0.267143i
$637$	0.717453			0.0284265
$638$	5.14897	+	20.4710i	0.203850	+	0.810453i
$639$	−10.3229			−0.408368
$640$	−1.99563	+	1.44991i	−0.0788841	+	0.0573127i
$641$	4.85964	+	14.9564i	0.191944	+	0.590743i	0.999999	+	0.00163569i	$0.000520657\pi$
$641$	4.85964	+	14.9564i	0.191944	+	0.590743i	−0.808054	+	0.589108i	$0.799479\pi$
$642$	−0.0152532	+	0.0469446i	−0.000601997	+	0.00185276i
$643$	−3.33446	−	2.42262i	−0.131498	−	0.0955389i	0.520092	−	0.854110i	$-0.325898\pi$
$643$	−3.33446	−	2.42262i	−0.131498	−	0.0955389i	−0.651590	+	0.758571i	$0.725898\pi$
$644$	−8.96069	−	6.51032i	−0.353101	−	0.256543i
$645$	−6.31504	+	19.4357i	−0.248655	+	0.765280i
$646$	0.888631	+	2.73493i	0.0349627	+	0.107604i
$647$	−17.2497	+	12.5327i	−0.678157	+	0.492710i	−0.872746	−	0.488175i	$-0.837663\pi$
$647$	−17.2497	+	12.5327i	−0.678157	+	0.492710i	0.194589	+	0.980885i	$0.437663\pi$
$648$	−2.27971			−0.0895555
$649$	−13.4996	+	33.6126i	−0.529904	+	1.31941i
$650$	0.568986			0.0223175
$651$	7.82102	−	5.68231i	0.306530	−	0.222707i
$652$	−1.57066	−	4.83398i	−0.0615116	−	0.189313i
$653$	−13.4615	+	41.4301i	−0.526788	+	1.62129i	0.233965	+	0.972245i	$0.424830\pi$
$653$	−13.4615	+	41.4301i	−0.526788	+	1.62129i	−0.760753	+	0.649042i	$0.775170\pi$
$654$	4.20142	+	3.05251i	0.164289	+	0.119363i
$655$	25.6504	+	18.6361i	1.00224	+	0.728172i
$656$	0.738770	−	2.27370i	0.0288441	−	0.0887731i
$657$	6.47777	+	19.9365i	0.252722	+	0.777798i
$658$	1.17139	−	0.851066i	0.0456656	−	0.0331780i
$659$	−13.0539			−0.508507			−0.254253	−	0.967138i	$-0.581830\pi$
$659$	−13.0539			−0.508507			−0.254253	+	0.967138i	$0.581830\pi$
$660$	−5.69098	−	4.75528i	−0.221521	−	0.185099i
$661$	−2.30481			−0.0896469			−0.0448234	−	0.998995i	$-0.514273\pi$
$661$	−2.30481			−0.0896469			−0.0448234	+	0.998995i	$0.514273\pi$
$662$	10.1656	−	7.38572i	0.395096	−	0.287054i
$663$	0.146930	+	0.452204i	0.00570629	+	0.0175622i
$664$	−2.35562	+	7.24984i	−0.0914156	+	0.281348i
$665$	13.6194	+	9.89506i	0.528137	+	0.383714i
$666$	3.89300	+	2.82843i	0.150851	+	0.109600i
$667$	9.17890	−	28.2497i	0.355408	−	1.09383i
$668$	−2.15694	−	6.63836i	−0.0834543	−	0.256846i
$669$	−0.482259	+	0.350382i	−0.0186452	+	0.0135465i
$670$	−25.1400			−0.971241
$671$	11.4951	+	9.60512i	0.443764	+	0.370801i
$672$	−2.15130			−0.0829883
$673$	5.46465	−	3.97030i	0.210647	−	0.153044i	−0.477459	−	0.878654i	$-0.658442\pi$
$673$	5.46465	−	3.97030i	0.210647	−	0.153044i	0.688106	+	0.725610i	$0.258442\pi$
$674$	7.72723	+	23.7820i	0.297642	+	0.916047i
$675$	1.57350	−	4.84273i	0.0605640	−	0.186397i
$676$	10.2946	+	7.47949i	0.395948	+	0.287673i
$677$	−39.4195	−	28.6400i	−1.51502	−	1.10072i	−0.963890	−	0.266301i	$-0.914198\pi$
$677$	−39.4195	−	28.6400i	−1.51502	−	1.10072i	−0.551126	−	0.834422i	$-0.685802\pi$
$678$	−4.50344	+	13.8602i	−0.172953	+	0.532296i
$679$	5.05276	+	15.5508i	0.193907	+	0.596785i
$680$	−1.99563	+	1.44991i	−0.0765288	+	0.0556015i
$681$	11.0662			0.424059
$682$	5.55453	−	13.8302i	0.212694	−	0.529586i
$683$	−7.39739			−0.283053			−0.141527	−	0.989934i	$-0.545201\pi$
$683$	−7.39739			−0.283053			−0.141527	+	0.989934i	$0.545201\pi$
$684$	−5.06769	+	3.68189i	−0.193768	+	0.140781i
$685$	−13.4979	−	41.5423i	−0.515729	−	1.58725i
$686$	−6.13667	+	18.8867i	−0.234299	+	0.721099i
$687$	−18.7173	−	13.5989i	−0.714109	−	0.518830i
$688$	7.39378	+	5.37190i	0.281885	+	0.204802i
$689$	2.04946	−	6.30758i	0.0780781	−	0.240300i
$690$	3.22487	+	9.92514i	0.122769	+	0.377844i
$691$	−12.0403	+	8.74779i	−0.458035	+	0.332782i	−0.792760	−	0.609534i	$-0.791357\pi$
$691$	−12.0403	+	8.74779i	−0.458035	+	0.332782i	0.334725	+	0.942316i	$0.391357\pi$
$692$	−2.35989			−0.0897096
$693$	4.18224	+	16.6275i	0.158870	+	0.631626i
$694$	0.260665			0.00989471
$695$	21.4725	−	15.6007i	0.814499	−	0.591768i
$696$	−1.78282	−	5.48696i	−0.0675777	−	0.207983i
$697$	0.738770	−	2.27370i	0.0279829	−	0.0861225i
$698$	−13.6180	−	9.89405i	−0.515449	−	0.374495i
$699$	5.80716	+	4.21915i	0.219647	+	0.159583i
$700$	−0.795530	+	2.44839i	−0.0300682	+	0.0925405i
$701$	−3.31982	−	10.2173i	−0.125388	−	0.385904i	0.868584	−	0.495542i	$-0.165031\pi$
$701$	−3.31982	−	10.2173i	−0.125388	−	0.385904i	−0.993972	+	0.109639i	$0.965031\pi$
$702$	−1.99192	+	1.44721i	−0.0751801	+	0.0546215i
$703$	6.35263			0.239594
$704$	−2.80902	+	1.76336i	−0.105869	+	0.0664590i
$705$	−1.36424			−0.0513803
$706$	−9.02519	+	6.55718i	−0.339667	+	0.246783i
$707$	−3.21114	−	9.88286i	−0.120767	−	0.371683i
$708$	3.05931	−	9.41558i	0.114976	−	0.353859i
$709$	−3.67513	−	2.67014i	−0.138022	−	0.100279i	0.516632	−	0.856208i	$-0.327186\pi$
$709$	−3.67513	−	2.67014i	−0.138022	−	0.100279i	−0.654654	+	0.755929i	$0.727186\pi$
$710$	−9.45733	−	6.87115i	−0.354927	−	0.257870i
$711$	−6.93234	+	21.3356i	−0.259983	+	0.800146i
$712$	0.414344	+	1.27522i	0.0155282	+	0.0477908i
$713$	−16.9671	+	12.3273i	−0.635423	+	0.461662i
$714$	−2.15130			−0.0805105
$715$	4.28141	+	0.290490i	0.160115	+	0.0108637i
$716$	−24.0536			−0.898927
$717$	−11.7883	+	8.56470i	−0.440242	+	0.319855i
$718$	1.51651	+	4.66735i	0.0565958	+	0.174184i
$719$	−0.375412	+	1.15540i	−0.0140005	+	0.0430891i	−0.957813	−	0.287393i	$-0.907211\pi$
$719$	−0.375412	+	1.15540i	−0.0140005	+	0.0430891i	0.943812	+	0.330482i	$0.107211\pi$
$720$	−4.34703	−	3.15830i	−0.162004	−	0.117703i
$721$	−18.1759	−	13.2056i	−0.676906	−	0.491801i
$722$	3.31591	−	10.2053i	0.123405	−	0.379803i
$723$	4.78009	+	14.7116i	0.177774	+	0.547131i
$724$	13.6346	−	9.90611i	0.506726	−	0.368158i
$725$	−6.90397			−0.256407
$726$	−7.20140	−	6.89699i	−0.267269	−	0.255971i
$727$	23.4837			0.870962			0.435481	−	0.900198i	$-0.356578\pi$
$727$	23.4837			0.870962			0.435481	+	0.900198i	$0.356578\pi$
$728$	1.00707	−	0.731682i	0.0373247	−	0.0271179i
$729$	2.41018	+	7.41777i	0.0892659	+	0.274732i
$730$	−7.33558	+	22.5766i	−0.271502	+	0.835597i
$731$	7.39378	+	5.37190i	0.273469	+	0.198687i
$732$	−3.31232	−	2.40654i	−0.122427	−	0.0889483i
$733$	8.47323	−	26.0779i	0.312966	−	0.963210i	−0.663618	−	0.748072i	$-0.730980\pi$
$733$	8.47323	−	26.0779i	0.312966	−	0.963210i	0.976584	−	0.215138i	$-0.0690202\pi$
$734$	−6.78512	−	20.8824i	−0.250443	−	0.770785i
$735$	2.47441	−	1.79776i	0.0912698	−	0.0663114i
$736$	4.66708			0.172031
$737$	−33.7242	−	2.28816i	−1.24225	−	0.0842854i
$738$	5.20763			0.191695
$739$	−42.1074	+	30.5928i	−1.54894	+	1.12537i	−0.604546	+	0.796571i	$0.706645\pi$
$739$	−42.1074	+	30.5928i	−1.54894	+	1.12537i	−0.944399	+	0.328803i	$0.893355\pi$
$740$	1.68391	+	5.18254i	0.0619017	+	0.190514i
$741$	−0.422523	+	1.30039i	−0.0155218	+	0.0477711i
$742$	24.2766	+	17.6379i	0.891220	+	0.647509i
$743$	−9.03323	−	6.56303i	−0.331397	−	0.240774i	0.409626	−	0.912253i	$-0.365659\pi$
$743$	−9.03323	−	6.56303i	−0.331397	−	0.240774i	−0.741023	+	0.671479i	$0.765659\pi$
$744$	−1.25878	+	3.87413i	−0.0461491	+	0.142032i
$745$	−12.2168	−	37.5993i	−0.447587	−	1.37753i
$746$	−19.5403	+	14.1968i	−0.715420	+	0.519783i
$747$	−16.6048			−0.607540
$748$	−2.80902	+	1.76336i	−0.102708	+	0.0644747i
$749$	0.129227			0.00472187
$750$	−7.08273	+	5.14590i	−0.258625	+	0.187902i
$751$	−11.6881	−	35.9723i	−0.426506	−	1.31265i	−0.901545	−	0.432685i	$-0.857566\pi$
$751$	−11.6881	−	35.9723i	−0.426506	−	1.31265i	0.475039	−	0.879965i	$-0.342434\pi$
$752$	−0.188534	+	0.580247i	−0.00687511	+	0.0211594i
$753$	−14.7504	−	10.7168i	−0.537535	−	0.390542i
$754$	2.70076	+	1.96222i	0.0983558	+	0.0714597i
$755$	−6.25200	+	19.2417i	−0.227534	+	0.700277i
$756$	−3.44246	−	10.5948i	−0.125201	−	0.385329i
$757$	25.7645	−	18.7190i	0.936426	−	0.680353i	−0.0111318	−	0.999938i	$-0.503543\pi$
$757$	25.7645	−	18.7190i	0.936426	−	0.680353i	0.947558	+	0.319585i	$0.103543\pi$
$758$	−1.36662			−0.0496378
$759$	3.42268	+	13.6077i	0.124235	+	0.493927i
$760$	−7.09351			−0.257309
$761$	11.3222	−	8.22607i	0.410430	−	0.298195i	−0.363346	−	0.931654i	$-0.618366\pi$
$761$	11.3222	−	8.22607i	0.410430	−	0.298195i	0.773776	+	0.633460i	$0.218366\pi$
$762$	0.259969	+	0.800102i	0.00941768	+	0.0289846i
$763$	4.20142	−	12.9306i	0.152102	−	0.468121i
$764$	8.18632	+	5.94771i	0.296171	+	0.215181i
$765$	−4.34703	−	3.15830i	−0.157167	−	0.114189i
$766$	2.93799	−	9.04221i	0.106154	−	0.326708i
$767$	1.77021	+	5.44815i	0.0639187	+	0.196721i
$768$	0.733366	−	0.532822i	0.0264631	−	0.0192265i
$769$	−6.75134			−0.243460			−0.121730	−	0.992563i	$-0.538844\pi$
$769$	−6.75134			−0.243460			−0.121730	+	0.992563i	$0.538844\pi$
$770$	−7.23607	+	18.0171i	−0.260770	+	0.649290i
$771$	−4.59721			−0.165564
$772$	−1.53471	+	1.11503i	−0.0552354	+	0.0401309i
$773$	−13.7889	−	42.4377i	−0.495950	−	1.52638i	−0.815470	−	0.578799i	$-0.803522\pi$
$773$	−13.7889	−	42.4377i	−0.495950	−	1.52638i	0.319520	−	0.947580i	$-0.396478\pi$
$774$	−6.15183	+	18.9334i	−0.221123	+	0.680546i
$775$	3.94365	+	2.86523i	0.141660	+	0.102922i
$776$	−5.57398	−	4.04973i	−0.200094	−	0.145377i
$777$	−1.46858	+	4.51983i	−0.0526851	+	0.162148i
$778$	−6.78702	−	20.8883i	−0.243326	−	0.748881i
$779$	5.56191	−	4.04096i	0.199276	−	0.144783i
$780$	−1.17287			−0.0419955
$781$	−12.0612	−	10.0781i	−0.431584	−	0.360624i
$782$	4.66708			0.166895
$783$	24.1696	−	17.5602i	0.863749	−	0.627551i
$784$	−0.422679	−	1.30087i	−0.0150957	−	0.0464597i
$785$	−14.1648	+	43.5947i	−0.505562	+	1.55596i
$786$	−9.42616	−	6.84851i	−0.336220	−	0.244278i
$787$	−6.36300	−	4.62299i	−0.226816	−	0.164792i	0.468573	−	0.883425i	$-0.344768\pi$
$787$	−6.36300	−	4.62299i	−0.226816	−	0.164792i	−0.695390	+	0.718633i	$0.744768\pi$
$788$	8.51562	−	26.2084i	0.303357	−	0.933635i
$789$	−8.32374	−	25.6178i	−0.296333	−	0.912019i
$790$	−20.5525	+	14.9323i	−0.731225	+	0.531266i
$791$	38.1537			1.35659
$792$	−5.54390	−	4.63238i	−0.196994	−	0.164604i
$793$	2.36906			0.0841279
$794$	−10.2269	+	7.43029i	−0.362940	+	0.263691i
$795$	−8.73692	−	26.8895i	−0.309867	−	0.953671i
$796$	5.19254	−	15.9810i	0.184045	−	0.566432i
$797$	42.3555	+	30.7731i	1.50031	+	1.09004i	0.970258	+	0.242073i	$0.0778275\pi$
$797$	42.3555	+	30.7731i	1.50031	+	1.09004i	0.530052	+	0.847965i	$0.322173\pi$
$798$	−5.00493	−	3.63630i	−0.177173	−	0.128724i
$799$	−0.188534	+	0.580247i	−0.00666984	+	0.0205277i
$800$	−0.335211	−	1.03167i	−0.0118515	−	0.0364752i
$801$	−2.36292	+	1.71676i	−0.0834896	+	0.0606588i
$802$	14.1891			0.501034
$803$	−11.8952	+	29.6179i	−0.419773	+	1.04519i
$804$	9.23859			0.325820
$805$	22.1036	−	16.0592i	0.779050	−	0.566013i
$806$	−0.728371	−	2.24169i	−0.0256558	−	0.0789603i
$807$	−6.89378	+	21.2169i	−0.242673	+	0.746870i
$808$	3.54238	+	2.57369i	0.124621	+	0.0905422i
$809$	−30.0045	−	21.7995i	−1.05490	−	0.766431i	−0.0817629	−	0.996652i	$-0.526055\pi$
$809$	−30.0045	−	21.7995i	−1.05490	−	0.766431i	−0.973138	+	0.230221i	$0.926055\pi$
$810$	1.73774	−	5.34821i	0.0610579	−	0.187917i
$811$	−6.97364	−	21.4626i	−0.244877	−	0.753655i	−0.995657	−	0.0931021i	$-0.970322\pi$
$811$	−6.97364	−	21.4626i	−0.244877	−	0.753655i	0.750779	−	0.660553i	$-0.229678\pi$
$812$	−12.2197	+	8.87810i	−0.428826	+	0.311560i
$813$	5.11560			0.179412
$814$	1.78719	+	7.10542i	0.0626412	+	0.249045i
$815$	12.5378			0.439179
$816$	0.733366	−	0.532822i	0.0256729	−	0.0186525i
$817$	8.12140	+	24.9951i	0.284132	+	0.874467i
$818$	−10.0286	+	30.8650i	−0.350643	+	1.07917i
$819$	2.19369	+	1.59381i	0.0766536	+	0.0556921i
$820$	4.77097	+	3.46631i	0.166609	+	0.121049i
$821$	−7.56059	+	23.2691i	−0.263866	+	0.812097i	0.728086	+	0.685486i	$0.240410\pi$
$821$	−7.56059	+	23.2691i	−0.263866	+	0.812097i	−0.991952	+	0.126612i	$0.959590\pi$
$822$	4.96030	+	15.2662i	0.173010	+	0.532471i
$823$	−28.9711	+	21.0487i	−1.00987	+	0.733713i	−0.964182	−	0.265243i	$-0.914548\pi$
$823$	−28.9711	+	21.0487i	−1.00987	+	0.733713i	−0.0456872	+	0.998956i	$0.514548\pi$
$824$	9.46673			0.329789
$825$	2.76219	−	1.73396i	0.0961671	−	0.0603687i
$826$	−25.9189			−0.901832
$827$	−19.8101	+	14.3929i	−0.688866	+	0.500490i	−0.876287	−	0.481789i	$-0.839987\pi$
$827$	−19.8101	+	14.3929i	−0.688866	+	0.500490i	0.187421	+	0.982280i	$0.439987\pi$
$828$	3.14153	+	9.66862i	0.109176	+	0.336008i
$829$	0.740513	−	2.27906i	0.0257191	−	0.0791552i	−0.937373	−	0.348327i	$-0.886750\pi$
$829$	0.740513	−	2.27906i	0.0257191	−	0.0791552i	0.963092	+	0.269172i	$0.0867499\pi$
$830$	−15.2125	−	11.0526i	−0.528035	−	0.383640i
$831$	8.41005	+	6.11026i	0.291741	+	0.211963i
$832$	−0.162087	+	0.498852i	−0.00561935	+	0.0172946i
$833$	−0.422679	−	1.30087i	−0.0146450	−	0.0450725i
$834$	−7.89085	+	5.73304i	−0.273238	+	0.198519i
$835$	17.2178			0.595845
$836$	−9.51565	−	0.645628i	−0.329105	−	0.0223295i
$837$	−21.0937			−0.729105
$838$	24.3314	−	17.6778i	0.840514	−	0.610669i
$839$	15.5643	+	47.9021i	0.537341	+	1.65377i	0.738536	+	0.674214i	$0.235517\pi$
$839$	15.5643	+	47.9021i	0.537341	+	1.65377i	−0.201195	+	0.979551i	$0.564483\pi$
$840$	1.63986	−	5.04696i	0.0565804	−	0.174137i
$841$	−9.30902	−	6.76340i	−0.321001	−	0.233221i
$842$	11.8895	+	8.63825i	0.409740	+	0.297694i
$843$	1.26540	−	3.89450i	0.0435827	−	0.134134i
$844$	−5.19557	−	15.9903i	−0.178839	−	0.550409i
$845$	−25.3941	+	18.4499i	−0.873584	+	0.634696i
$846$	−1.32898			−0.0456914
$847$	−11.3467	+	23.5105i	−0.389878	+	0.807832i
$848$	−12.6442			−0.434203
$849$	13.3481	−	9.69793i	0.458104	−	0.332832i
$850$	−0.335211	−	1.03167i	−0.0114976	−	0.0353861i
$851$	3.18597	−	9.80542i	0.109214	−	0.336125i
$852$	3.47544	+	2.52505i	0.119067	+	0.0865069i
$853$	30.3717	+	22.0663i	1.03991	+	0.755537i	0.970267	−	0.242036i	$-0.0778151\pi$
$853$	30.3717	+	22.0663i	1.03991	+	0.755537i	0.0696396	+	0.997572i	$0.477815\pi$
$854$	−3.31232	+	10.1943i	−0.113345	+	0.348841i
$855$	−4.77481	−	14.6954i	−0.163295	−	0.502571i
$856$	−0.0440529	+	0.0320063i	−0.00150570	+	0.00109395i
$857$	8.97785			0.306677			0.153339	−	0.988174i	$-0.450997\pi$
$857$	8.97785			0.306677			0.153339	+	0.988174i	$0.450997\pi$
$858$	−1.57336	−	0.106751i	−0.0537136	−	0.00364442i
$859$	−43.3878			−1.48037			−0.740187	−	0.672401i	$-0.765263\pi$
$859$	−43.3878			−1.48037			−0.740187	+	0.672401i	$0.765263\pi$
$860$	−18.2385	+	13.2510i	−0.621927	+	0.451856i
$861$	1.58932	+	4.89142i	0.0541638	+	0.166699i
$862$	−9.58759	+	29.5076i	−0.326554	+	1.00503i
$863$	−10.4679	−	7.60539i	−0.356332	−	0.258890i	0.395188	−	0.918600i	$-0.370679\pi$
$863$	−10.4679	−	7.60539i	−0.356332	−	0.258890i	−0.751521	+	0.659710i	$0.770679\pi$
$864$	3.79757	+	2.75910i	0.129196	+	0.0938664i
$865$	1.79886	−	5.53631i	0.0611629	−	0.188240i
$866$	4.04405	+	12.4463i	0.137423	+	0.422943i
$867$	0.733366	−	0.532822i	0.0249064	−	0.0180956i
$868$	10.6646			0.361979
$869$	−28.9294	+	18.1604i	−0.981362	+	0.616049i
$870$	14.2314			0.482490
$871$	−4.32480	+	3.14215i	−0.146540	+	0.106468i
$872$	1.77034	+	5.44856i	0.0599514	+	0.184512i
$873$	4.63770	−	14.2734i	0.156963	−	0.483081i
$874$	10.8578	+	7.88866i	0.367271	+	0.266838i
$875$	18.5428	+	13.4721i	0.626862	+	0.455442i
$876$	2.69573	−	8.29659i	0.0910801	−	0.280316i
$877$	−13.3989	−	41.2375i	−0.452448	−	1.39249i	−0.874105	−	0.485736i	$-0.838552\pi$
$877$	−13.3989	−	41.2375i	−0.452448	−	1.39249i	0.421658	−	0.906755i	$-0.361448\pi$
$878$	26.5776	−	19.3098i	0.896951	−	0.651673i
$879$	3.15725			0.106492
$880$	−1.99563	−	7.93410i	−0.0672726	−	0.267458i
$881$	−19.4820			−0.656366			−0.328183	−	0.944614i	$-0.606436\pi$
$881$	−19.4820			−0.656366			−0.328183	+	0.944614i	$0.606436\pi$
$882$	2.41045	−	1.75130i	0.0811642	−	0.0589692i
$883$	−2.64223	−	8.13196i	−0.0889182	−	0.273662i	0.896703	−	0.442633i	$-0.145956\pi$
$883$	−2.64223	−	8.13196i	−0.0889182	−	0.273662i	−0.985621	+	0.168971i	$0.945956\pi$
$884$	−0.162087	+	0.498852i	−0.00545157	+	0.0167782i
$885$	19.7570	+	14.3543i	0.664123	+	0.482514i
$886$	6.38168	+	4.63656i	0.214397	+	0.155768i
$887$	1.66606	−	5.12762i	0.0559410	−	0.172169i	−0.919182	−	0.393833i	$-0.871149\pi$
$887$	1.66606	−	5.12762i	0.0559410	−	0.172169i	0.975123	+	0.221664i	$0.0711489\pi$
$888$	−0.618813	−	1.90451i	−0.0207660	−	0.0639112i
$889$	1.78185	−	1.29459i	0.0597614	−	0.0434192i
$890$	−3.30750			−0.110868
$891$	2.81788	−	7.01623i	0.0944025	−	0.235053i
$892$	−0.657597			−0.0220180
$893$	−1.41940	+	1.03125i	−0.0474982	+	0.0345095i
$894$	4.48949	+	13.8172i	0.150151	+	0.462117i
$895$	18.3352	−	56.4299i	0.612877	−	1.88624i
$896$	−1.91998	−	1.39494i	−0.0641419	−	0.0466018i
$897$	1.79528	+	1.30435i	0.0599426	+	0.0435508i
$898$	−7.48109	+	23.0244i	−0.249647	+	0.768336i
$899$	8.83791	+	27.2003i	0.294761	+	0.907181i
$900$	1.91164	−	1.38889i	0.0637214	−	0.0462963i
$901$	−12.6442			−0.421239
$902$	6.08456	+	5.08415i	0.202594	+	0.169284i
$903$	−19.6612			−0.654284
$904$	−13.0064	+	9.44968i	−0.432586	+	0.314292i
$905$	12.8466	+	39.5378i	0.427036	+	1.31428i
$906$	2.29753	−	7.07106i	0.0763302	−	0.234920i
$907$	20.5312	+	14.9168i	0.681728	+	0.495304i	0.873930	−	0.486051i	$-0.161563\pi$
$907$	20.5312	+	14.9168i	0.681728	+	0.495304i	−0.192203	+	0.981355i	$0.561563\pi$
$908$	9.87629	+	7.17555i	0.327756	+	0.238129i
$909$	−2.94736	+	9.07104i	−0.0977577	+	0.300867i
$910$	0.948873	+	2.92033i	0.0314548	+	0.0968080i
$911$	−31.2813	+	22.7272i	−1.03640	+	0.752985i	−0.969579	−	0.244780i	$-0.921284\pi$
$911$	−31.2813	+	22.7272i	−1.03640	+	0.752985i	−0.0668168	+	0.997765i	$0.521284\pi$
$912$	2.60677			0.0863187
$913$	−19.4010	−	16.2111i	−0.642080	−	0.536510i
$914$	27.8409			0.920895
$915$	8.17060	−	5.93629i	0.270112	−	0.196248i
$916$	−7.88686	−	24.2733i	−0.260589	−	0.802012i
$917$	−9.42616	+	29.0107i	−0.311279	+	0.958019i
$918$	3.79757	+	2.75910i	0.125339	+	0.0910638i
$919$	32.4781	+	23.5967i	1.07135	+	0.778385i	0.976155	−	0.217074i	$-0.0696512\pi$
$919$	32.4781	+	23.5967i	1.07135	+	0.778385i	0.0951993	+	0.995458i	$0.469651\pi$
$920$	−3.55754	+	10.9490i	−0.117289	+	0.360977i
$921$	1.30282	+	4.00966i	0.0429293	+	0.132123i
$922$	18.2294	−	13.2445i	0.600354	−	0.436183i
$923$	−2.48573			−0.0818189
$924$	2.65916	−	6.62103i	0.0874798	−	0.217816i
$925$	−2.39635			−0.0787915
$926$	−12.0112	+	8.72662i	−0.394711	+	0.286774i
$927$	6.37229	+	19.6119i	0.209293	+	0.644139i
$928$	1.96673	−	6.05298i	0.0645611	−	0.198699i
$929$	7.02481	+	5.10383i	0.230477	+	0.167451i	0.697030	−	0.717042i	$-0.254504\pi$
$929$	7.02481	+	5.10383i	0.230477	+	0.167451i	−0.466553	+	0.884493i	$0.654504\pi$
$930$	−8.12919	−	5.90620i	−0.266567	−	0.193672i
$931$	1.21549	−	3.74088i	0.0398359	−	0.122602i
$932$	2.44695	+	7.53094i	0.0801525	+	0.246684i
$933$	21.4230	−	15.5647i	0.701357	−	0.509566i
$934$	41.5555			1.35974
$935$	−1.99563	−	7.93410i	−0.0652640	−	0.259473i
$936$	−1.14256			−0.0373457
$937$	7.60718	−	5.52694i	0.248516	−	0.180557i	−0.456553	−	0.889696i	$-0.650916\pi$
$937$	7.60718	−	5.52694i	0.248516	−	0.180557i	0.705069	+	0.709139i	$0.250916\pi$
$938$	−7.47418	−	23.0032i	−0.244041	−	0.751079i
$939$	1.32232	−	4.06967i	0.0431522	−	0.132809i
$940$	−1.21755	−	0.884600i	−0.0397120	−	0.0288525i
$941$	−10.4641	−	7.60265i	−0.341121	−	0.247839i	0.404013	−	0.914753i	$-0.367615\pi$
$941$	−10.4641	−	7.60265i	−0.341121	−	0.247839i	−0.745135	+	0.666914i	$0.767615\pi$
$942$	5.20536	−	16.0205i	0.169600	−	0.521975i
$943$	−3.44790	−	10.6115i	−0.112279	−	0.345560i
$944$	8.83558	−	6.41943i	0.287574	−	0.208935i
$945$	27.4795			0.893908
$946$	−25.6722	+	16.1157i	−0.834676	+	0.523966i
$947$	13.8517			0.450121			0.225060	−	0.974345i	$-0.427742\pi$
$947$	13.8517			0.450121			0.225060	+	0.974345i	$0.427742\pi$
$948$	7.55276	−	5.48740i	0.245302	−	0.178222i
$949$	1.55983	+	4.80067i	0.0506343	+	0.155836i
$950$	0.963957	−	2.96675i	0.0312749	−	0.0962542i
$951$	−12.2943	−	8.93233i	−0.398670	−	0.289651i
$952$	−1.91998	−	1.39494i	−0.0622268	−	0.0452104i
$953$	−7.37860	+	22.7090i	−0.239016	+	0.735617i	0.757547	+	0.652781i	$0.226398\pi$
$953$	−7.37860	+	22.7090i	−0.239016	+	0.735617i	−0.996563	+	0.0828359i	$0.973602\pi$
$954$	−8.51111	−	26.1945i	−0.275557	−	0.848078i
$955$	−20.1935	+	14.6714i	−0.653445	+	0.474756i
$956$	−16.0742			−0.519878
$957$	19.0908	+	1.29530i	0.617119	+	0.0418710i
$958$	25.5645			0.825952
$959$	33.9984	−	24.7013i	1.09786	−	0.797645i
$960$	0.690983	+	2.12663i	0.0223014	+	0.0686366i
$961$	−3.33943	+	10.2777i	−0.107723	+	0.331539i
$962$	0.937427	+	0.681080i	0.0302239	+	0.0219589i
$963$	−0.0959593	−	0.0697185i	−0.00309225	−	0.00224665i
$964$	−5.27319	+	16.2292i	−0.169838	+	0.522707i
$965$	−1.44601	−	4.45038i	−0.0465489	−	0.143263i
$966$	−8.12278	+	5.90154i	−0.261346	+	0.189879i
$967$	−26.9263			−0.865891			−0.432945	−	0.901420i	$-0.642526\pi$
$967$	−26.9263			−0.865891			−0.432945	+	0.901420i	$0.642526\pi$
$968$	−1.95492	−	10.8249i	−0.0628333	−	0.347925i
$969$	2.60677			0.0837414
$970$	13.7495	−	9.98961i	0.441470	−	0.320747i
$971$	−5.76735	−	17.7501i	−0.185083	−	0.569627i	0.814867	−	0.579649i	$-0.196810\pi$
$971$	−5.76735	−	17.7501i	−0.185083	−	0.569627i	−0.999950	+	0.0100210i	$0.996810\pi$
$972$	−4.99022	+	15.3583i	−0.160062	+	0.492619i
$973$	20.6585	+	15.0093i	0.662282	+	0.481176i
$974$	10.9867	+	7.98227i	0.352035	+	0.255768i
$975$	0.159385	−	0.490536i	0.00510440	−	0.0157097i
$976$	−1.39571	−	4.29554i	−0.0446754	−	0.137497i
$977$	12.2460	−	8.89724i	0.391784	−	0.284648i	−0.374402	−	0.927266i	$-0.622152\pi$
$977$	12.2460	−	8.89724i	0.391784	−	0.284648i	0.766186	+	0.642619i	$0.222152\pi$
$978$	−4.60746			−0.147330
$979$	−4.43688	−	0.301038i	−0.141803	−	0.00962123i
$980$	3.37404			0.107780
$981$	−10.0959	+	7.33512i	−0.322338	+	0.234192i
$982$	−11.9138	−	36.6670i	−0.380185	−	1.17009i
$983$	−9.90404	+	30.4815i	−0.315890	+	0.972209i	0.659497	+	0.751707i	$0.270769\pi$
$983$	−9.90404	+	30.4815i	−0.315890	+	0.972209i	−0.975387	+	0.220502i	$0.929231\pi$
$984$	−1.75327	−	1.27382i	−0.0558921	−	0.0406080i
$985$	54.9938	+	39.9553i	1.75225	+	1.27308i
$986$	1.96673	−	6.05298i	0.0626335	−	0.192766i
$987$	−0.405593	−	1.24829i	−0.0129102	−	0.0397334i
$988$	−1.22029	+	0.886591i	−0.0388225	+	0.0282062i
$989$	42.6535			1.35630
$990$	15.0935	−	9.47490i	0.479702	−	0.301132i
$991$	−18.8884			−0.600009			−0.300005	−	0.953938i	$-0.596988\pi$
$991$	−18.8884			−0.600009			−0.300005	+	0.953938i	$0.596988\pi$
$992$	−3.63548	+	2.64133i	−0.115427	+	0.0838624i
$993$	−3.51981	−	10.8329i	−0.111698	−	0.343771i
$994$	3.47544	−	10.6963i	0.110234	−	0.339266i
$995$	33.5334	+	24.3634i	1.06308	+	0.772372i
$996$	5.59040	+	4.06166i	0.177139	+	0.128699i
$997$	−1.53464	+	4.72314i	−0.0486026	+	0.149583i	−0.972412	−	0.233268i	$-0.925058\pi$
$997$	−1.53464	+	4.72314i	−0.0486026	+	0.149583i	0.923810	+	0.382852i	$0.125058\pi$
$998$	−6.76790	−	20.8294i	−0.214234	−	0.659344i
$999$	8.38919	−	6.09511i	0.265422	−	0.192841i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.e.69.1	✓	8
11.2	odd	10		4114.2.a.ba.1.2		4
11.4	even	5	inner	374.2.g.e.103.1	yes	8
11.9	even	5		4114.2.a.v.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.e.69.1	✓	8	1.1	even	1	trivial
374.2.g.e.103.1	yes	8	11.4	even	5	inner
4114.2.a.v.1.2		4	11.9	even	5
4114.2.a.ba.1.2		4	11.2	odd	10

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Classical	Maass
Hilbert	Bianchi

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

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	374.2.g.e.69.1

Level	$374$
Weight	$2$
Character	374.69
Analytic conductor	$2.986$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$