LMFDB - Embedded newform 1190.2.ba.a.611.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1190,2,Mod(611,1190)] 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("1190.611"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1190 = 2 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1190.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.50219784053$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.17
Character	$\chi$	$=$	1190.611
Dual form			1190.2.ba.a.781.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.29617 - 0.748343i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.49669i q^{6} +(2.63849 + 0.195927i) q^{7} +1.00000 q^{8} +(-0.379966 + 0.658120i) q^{9} +(0.866025 - 0.500000i) q^{10} +(-4.84516 + 2.79736i) q^{11} +(-1.29617 - 0.748343i) q^{12} +0.757861 q^{13} +(-1.48892 + 2.18703i) q^{14} -1.49669 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.80668 - 1.58404i) q^{17} +(-0.379966 - 0.658120i) q^{18} +(-4.08113 + 7.06872i) q^{19} +1.00000i q^{20} +(3.56654 - 1.72054i) q^{21} -5.59471i q^{22} +(6.94442 + 4.00936i) q^{23} +(1.29617 - 0.748343i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.378930 + 0.656327i) q^{26} +5.62744i q^{27} +(-1.14957 - 2.38296i) q^{28} +1.97624i q^{29} +(0.748343 - 1.29617i) q^{30} +(-4.71971 + 2.72493i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.18676 + 7.25169i) q^{33} +(-0.531519 + 4.08870i) q^{34} +(-2.18703 - 1.48892i) q^{35} +0.759931 q^{36} +(8.54672 + 4.93445i) q^{37} +(-4.08113 - 7.06872i) q^{38} +(0.982315 - 0.567140i) q^{39} +(-0.866025 - 0.500000i) q^{40} -10.8917i q^{41} +(-0.293240 + 3.94899i) q^{42} -1.98174 q^{43} +(4.84516 + 2.79736i) q^{44} +(0.658120 - 0.379966i) q^{45} +(-6.94442 + 4.00936i) q^{46} +(6.18089 - 10.7056i) q^{47} +1.49669i q^{48} +(6.92323 + 1.03390i) q^{49} -1.00000 q^{50} +(3.74869 - 4.90189i) q^{51} +(-0.378930 - 0.656327i) q^{52} +(-2.26988 - 3.93154i) q^{53} +(-4.87350 - 2.81372i) q^{54} +5.59471 q^{55} +(2.63849 + 0.195927i) q^{56} +12.2163i q^{57} +(-1.71148 - 0.988122i) q^{58} +(-1.97140 - 3.41457i) q^{59} +(0.748343 + 1.29617i) q^{60} +(10.0495 + 5.80208i) q^{61} -5.44985i q^{62} +(-1.13148 + 1.66199i) q^{63} +1.00000 q^{64} +(-0.656327 - 0.378930i) q^{65} +(-4.18676 - 7.25169i) q^{66} +(3.69120 + 6.39335i) q^{67} +(-3.27516 - 2.50466i) q^{68} +12.0015 q^{69} +(2.38296 - 1.14957i) q^{70} +12.1163i q^{71} +(-0.379966 + 0.658120i) q^{72} +(-7.07727 + 4.08606i) q^{73} +(-8.54672 + 4.93445i) q^{74} +(1.29617 + 0.748343i) q^{75} +8.16225 q^{76} +(-13.3320 + 6.43149i) q^{77} +1.13428i q^{78} +(6.57142 + 3.79401i) q^{79} +(0.866025 - 0.500000i) q^{80} +(3.07136 + 5.31974i) q^{81} +(9.43253 + 5.44587i) q^{82} -3.31908 q^{83} +(-3.27330 - 2.22845i) q^{84} +(-4.08870 - 0.531519i) q^{85} +(0.990868 - 1.71623i) q^{86} +(1.47891 + 2.56154i) q^{87} +(-4.84516 + 2.79736i) q^{88} +(-3.41890 + 5.92171i) q^{89} +0.759931i q^{90} +(1.99961 + 0.148485i) q^{91} -8.01872i q^{92} +(-4.07836 + 7.06392i) q^{93} +(6.18089 + 10.7056i) q^{94} +(7.06872 - 4.08113i) q^{95} +(-1.29617 - 0.748343i) q^{96} -1.62950i q^{97} +(-4.35700 + 5.47874i) q^{98} -4.25159i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 16 q^{9} - 16 q^{13} - 8 q^{15} - 24 q^{16} - 6 q^{17} + 16 q^{18} + 16 q^{19} + 68 q^{21} + 24 q^{25} + 8 q^{26} + 4 q^{30} - 24 q^{32} + 20 q^{33} + 12 q^{34} - 4 q^{35}+ \cdots + 12 q^{94}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 16 * q^9 - 16 * q^13 - 8 * q^15 - 24 * q^16 - 6 * q^17 + 16 * q^18 + 16 * q^19 + 68 * q^21 + 24 * q^25 + 8 * q^26 + 4 * q^30 - 24 * q^32 + 20 * q^33 + 12 * q^34 - 4 * q^35 - 32 * q^36 + 16 * q^38 - 40 * q^42 - 40 * q^43 + 12 * q^47 - 12 * q^49 - 48 * q^50 + 20 * q^51 + 8 * q^52 + 24 * q^53 + 40 * q^55 + 20 * q^59 + 4 * q^60 + 48 * q^64 + 20 * q^66 + 48 * q^67 - 6 * q^68 + 24 * q^69 + 8 * q^70 + 16 * q^72 - 32 * q^76 - 12 * q^77 - 64 * q^81 - 56 * q^83 - 28 * q^84 + 12 * q^85 + 20 * q^86 + 8 * q^87 - 24 * q^89 + 36 * q^93 + 12 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1190\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.29617	−	0.748343i	0.748343	−	0.432056i	−0.0767519	−	0.997050i	$-0.524455\pi$
$3$	1.29617	−	0.748343i	0.748343	−	0.432056i	0.825095	+	0.564994i	$0.191122\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$			1.49669i			0.611020i
$7$	2.63849	+	0.195927i	0.997254	+	0.0740533i
$7$	2.63849	+	0.195927i	0.997254	+	0.0740533i
$8$	1.00000			0.353553
$9$	−0.379966	+	0.658120i	−0.126655	+	0.219373i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	−4.84516	+	2.79736i	−1.46087	+	0.843434i	−0.999052	−	0.0435396i	$-0.986137\pi$
$11$	−4.84516	+	2.79736i	−1.46087	+	0.843434i	−0.461819	+	0.886974i	$0.652803\pi$
$12$	−1.29617	−	0.748343i	−0.374172	−	0.216028i
$13$	0.757861			0.210193			0.105096	−	0.994462i	$-0.466485\pi$
$13$	0.757861			0.210193			0.105096	+	0.994462i	$0.466485\pi$
$14$	−1.48892	+	2.18703i	−0.397931	+	0.584509i
$15$	−1.49669			−0.386443
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.80668	−	1.58404i	0.923255	−	0.384187i
$17$	3.80668	−	1.58404i	0.923255	−	0.384187i
$18$	−0.379966	−	0.658120i	−0.0895587	−	0.155120i
$19$	−4.08113	+	7.06872i	−0.936274	+	1.62167i	−0.163929	+	0.986472i	$0.552417\pi$
$19$	−4.08113	+	7.06872i	−0.936274	+	1.62167i	−0.772346	+	0.635202i	$0.780917\pi$
$20$			1.00000i			0.223607i
$21$	3.56654	−	1.72054i	0.778283	−	0.375452i
$22$		−	5.59471i		−	1.19280i
$23$	6.94442	+	4.00936i	1.44801	+	0.836009i	0.998363	−	0.0571964i	$-0.0182161\pi$
$23$	6.94442	+	4.00936i	1.44801	+	0.836009i	0.449648	+	0.893206i	$0.351549\pi$
$24$	1.29617	−	0.748343i	0.264579	−	0.152755i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.378930	+	0.656327i	−0.0743144	+	0.128716i
$27$			5.62744i			1.08300i
$28$	−1.14957	−	2.38296i	−0.217248	−	0.450337i
$29$			1.97624i			0.366979i	0.983022	+	0.183490i	$0.0587394\pi$
$29$			1.97624i			0.366979i	−0.983022	+	0.183490i	$0.941261\pi$
$30$	0.748343	−	1.29617i	0.136628	−	0.236647i
$31$	−4.71971	+	2.72493i	−0.847685	+	0.489411i	−0.859869	−	0.510515i	$-0.829455\pi$
$31$	−4.71971	+	2.72493i	−0.847685	+	0.489411i	0.0121841	+	0.999926i	$0.496122\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.18676	+	7.25169i	−0.728822	+	1.26236i
$34$	−0.531519	+	4.08870i	−0.0911548	+	0.701207i
$35$	−2.18703	−	1.48892i	−0.369676	−	0.251674i
$36$	0.759931			0.126655
$37$	8.54672	+	4.93445i	1.40507	+	0.811219i	0.994907	−	0.100793i	$-0.0321378\pi$
$37$	8.54672	+	4.93445i	1.40507	+	0.811219i	0.410165	+	0.912011i	$0.365471\pi$
$38$	−4.08113	−	7.06872i	−0.662046	−	1.14670i
$39$	0.982315	−	0.567140i	0.157296	−	0.0908150i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$		−	10.8917i		−	1.70100i	−0.525971	−	0.850502i	$-0.676298\pi$
$41$		−	10.8917i		−	1.70100i	0.525971	−	0.850502i	$-0.323702\pi$
$42$	−0.293240	+	3.94899i	−0.0452480	+	0.609342i
$43$	−1.98174			−0.302212			−0.151106	−	0.988518i	$-0.548283\pi$
$43$	−1.98174			−0.302212			−0.151106	+	0.988518i	$0.548283\pi$
$44$	4.84516	+	2.79736i	0.730436	+	0.421717i
$45$	0.658120	−	0.379966i	0.0981067	−	0.0566419i
$46$	−6.94442	+	4.00936i	−1.02390	+	0.591148i
$47$	6.18089	−	10.7056i	0.901576	−	1.56158i	0.0761271	−	0.997098i	$-0.475745\pi$
$47$	6.18089	−	10.7056i	0.901576	−	1.56158i	0.825449	−	0.564477i	$-0.190922\pi$
$48$			1.49669i			0.216028i
$49$	6.92323	+	1.03390i	0.989032	+	0.147700i
$50$	−1.00000			−0.141421
$51$	3.74869	−	4.90189i	0.524922	−	0.686401i
$52$	−0.378930	−	0.656327i	−0.0525482	−	0.0910161i
$53$	−2.26988	−	3.93154i	−0.311791	−	0.540039i	0.666959	−	0.745095i	$-0.267596\pi$
$53$	−2.26988	−	3.93154i	−0.311791	−	0.540039i	−0.978750	+	0.205056i	$0.934262\pi$
$54$	−4.87350	−	2.81372i	−0.663200	−	0.382899i
$55$	5.59471			0.754391
$56$	2.63849	+	0.195927i	0.352583	+	0.0261818i
$57$			12.2163i			1.61809i
$58$	−1.71148	−	0.988122i	−0.224728	−	0.129747i
$59$	−1.97140	−	3.41457i	−0.256655	−	0.444540i	0.708689	−	0.705521i	$-0.249287\pi$
$59$	−1.97140	−	3.41457i	−0.256655	−	0.444540i	−0.965344	+	0.260982i	$0.915954\pi$
$60$	0.748343	+	1.29617i	0.0966107	+	0.167335i
$61$	10.0495	+	5.80208i	1.28671	+	0.742881i	0.978066	−	0.208298i	$-0.0667922\pi$
$61$	10.0495	+	5.80208i	1.28671	+	0.742881i	0.308642	+	0.951178i	$0.400126\pi$
$62$		−	5.44985i		−	0.692132i
$63$	−1.13148	+	1.66199i	−0.142553	+	0.209392i
$64$	1.00000			0.125000
$65$	−0.656327	−	0.378930i	−0.0814073	−	0.0470005i
$66$	−4.18676	−	7.25169i	−0.515355	−	0.892621i
$67$	3.69120	+	6.39335i	0.450952	+	0.781072i	0.998445	−	0.0557383i	$-0.0177513\pi$
$67$	3.69120	+	6.39335i	0.450952	+	0.781072i	−0.547494	+	0.836810i	$0.684418\pi$
$68$	−3.27516	−	2.50466i	−0.397172	−	0.303735i
$69$	12.0015			1.44481
$70$	2.38296	−	1.14957i	0.284818	−	0.137399i
$71$			12.1163i			1.43794i	0.695043	+	0.718969i	$0.255386\pi$
$71$			12.1163i			1.43794i	−0.695043	+	0.718969i	$0.744614\pi$
$72$	−0.379966	+	0.658120i	−0.0447794	+	0.0775601i
$73$	−7.07727	+	4.08606i	−0.828331	+	0.478237i	−0.853281	−	0.521451i	$-0.825391\pi$
$73$	−7.07727	+	4.08606i	−0.828331	+	0.478237i	0.0249497	+	0.999689i	$0.492057\pi$
$74$	−8.54672	+	4.93445i	−0.993536	+	0.573618i
$75$	1.29617	+	0.748343i	0.149669	+	0.0864112i
$76$	8.16225			0.936274
$77$	−13.3320	+	6.43149i	−1.51932	+	0.732936i
$78$			1.13428i			0.128432i
$79$	6.57142	+	3.79401i	0.739343	+	0.426860i	0.821830	−	0.569732i	$-0.192953\pi$
$79$	6.57142	+	3.79401i	0.739343	+	0.426860i	−0.0824874	+	0.996592i	$0.526286\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	3.07136	+	5.31974i	0.341262	+	0.591083i
$82$	9.43253	+	5.44587i	1.04165	+	0.601396i
$83$	−3.31908			−0.364316			−0.182158	−	0.983269i	$-0.558308\pi$
$83$	−3.31908			−0.364316			−0.182158	+	0.983269i	$0.558308\pi$
$84$	−3.27330	−	2.22845i	−0.357147	−	0.243143i
$85$	−4.08870	−	0.531519i	−0.443482	−	0.0576514i
$86$	0.990868	−	1.71623i	0.106848	−	0.185066i
$87$	1.47891	+	2.56154i	0.158556	+	0.274626i
$88$	−4.84516	+	2.79736i	−0.516496	+	0.298199i
$89$	−3.41890	+	5.92171i	−0.362403	+	0.627700i	−0.988356	−	0.152161i	$-0.951377\pi$
$89$	−3.41890	+	5.92171i	−0.362403	+	0.627700i	0.625953	+	0.779861i	$0.284710\pi$
$90$			0.759931i			0.0801038i
$91$	1.99961	+	0.148485i	0.209616	+	0.0155655i
$92$		−	8.01872i		−	0.836009i
$93$	−4.07836	+	7.06392i	−0.422906	+	0.732495i
$94$	6.18089	+	10.7056i	0.637510	+	1.10420i
$95$	7.06872	−	4.08113i	0.725235	−	0.418715i
$96$	−1.29617	−	0.748343i	−0.132290	−	0.0763774i
$97$		−	1.62950i		−	0.165450i	−0.996572	−	0.0827252i	$-0.973638\pi$
$97$		−	1.62950i		−	0.165450i	0.996572	−	0.0827252i	$-0.0263624\pi$
$98$	−4.35700	+	5.47874i	−0.440123	+	0.553436i
$99$		−	4.25159i		−	0.427301i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−6.19735	−	10.7341i	−0.616659	−	1.06809i	−0.990091	−	0.140428i	$-0.955152\pi$
$101$	−6.19735	−	10.7341i	−0.616659	−	1.06809i	0.373431	−	0.927658i	$-0.378181\pi$
$102$	2.37081	+	5.69740i	0.234746	+	0.564127i
$103$	3.82319	−	6.62196i	0.376710	−	0.652481i	−0.613871	−	0.789406i	$-0.710389\pi$
$103$	3.82319	−	6.62196i	0.376710	−	0.652481i	0.990581	+	0.136925i	$0.0437220\pi$
$104$	0.757861			0.0743144
$105$	−3.94899	−	0.293240i	−0.385382	−	0.0286173i
$106$	4.53975			0.440940
$107$	0.234019	+	0.135111i	0.0226235	+	0.0130617i	0.511269	−	0.859421i	$-0.329176\pi$
$107$	0.234019	+	0.135111i	0.0226235	+	0.0130617i	−0.488646	+	0.872482i	$0.662509\pi$
$108$	4.87350	−	2.81372i	0.468953	−	0.270750i
$109$	−6.14370	+	3.54707i	−0.588460	+	0.339747i	−0.764488	−	0.644638i	$-0.777008\pi$
$109$	−6.14370	+	3.54707i	−0.588460	+	0.339747i	0.176029	+	0.984385i	$0.443675\pi$
$110$	−2.79736	+	4.84516i	−0.266717	+	0.461968i
$111$	14.7706			1.40197
$112$	−1.48892	+	2.18703i	−0.140690	+	0.206655i
$113$			2.75153i			0.258842i	0.991590	+	0.129421i	$0.0413119\pi$
$113$			2.75153i			0.258842i	−0.991590	+	0.129421i	$0.958688\pi$
$114$	−10.5796	−	6.10816i	−0.990875	−	0.572082i
$115$	−4.00936	−	6.94442i	−0.373875	−	0.647570i
$116$	1.71148	−	0.988122i	0.158907	−	0.0917448i
$117$	−0.287961	+	0.498763i	−0.0266220	+	0.0461107i
$118$	3.94281			0.362965
$119$	10.3542	−	3.43364i	0.949171	−	0.314762i
$120$	−1.49669			−0.136628
$121$	10.1504	−	17.5810i	0.922763	−	1.59827i
$122$	−10.0495	+	5.80208i	−0.909839	+	0.525296i
$123$	−8.15076	−	14.1175i	−0.734929	−	1.27293i
$124$	4.71971	+	2.72493i	0.423843	+	0.244706i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.873591	−	1.81089i	−0.0778257	−	0.161326i
$127$	−8.06162			−0.715353			−0.357677	−	0.933846i	$-0.616431\pi$
$127$	−8.06162			−0.715353			−0.357677	+	0.933846i	$0.616431\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.56866	+	1.48302i	−0.226158	+	0.130572i
$130$	0.656327	−	0.378930i	0.0575637	−	0.0332344i
$131$	−8.36888	−	4.83177i	−0.731192	−	0.422154i	0.0876660	−	0.996150i	$-0.472059\pi$
$131$	−8.36888	−	4.83177i	−0.731192	−	0.422154i	−0.818858	+	0.573996i	$0.805392\pi$
$132$	8.37352			0.728822
$133$	−12.1529	+	17.8511i	−1.05379	+	1.54789i
$134$	−7.38240			−0.637742
$135$	2.81372	−	4.87350i	0.242166	−	0.419444i
$136$	3.80668	−	1.58404i	0.326420	−	0.135830i
$137$	−1.26684	−	2.19424i	−0.108234	−	0.187466i	0.806821	−	0.590796i	$-0.201186\pi$
$137$	−1.26684	−	2.19424i	−0.108234	−	0.187466i	−0.915055	+	0.403330i	$0.867853\pi$
$138$	−6.00075	+	10.3936i	−0.510818	+	0.884763i
$139$			17.8442i			1.51352i	0.653691	+	0.756761i	$0.273220\pi$
$139$			17.8442i			1.51352i	−0.653691	+	0.756761i	$0.726780\pi$
$140$	−0.195927	+	2.63849i	−0.0165588	+	0.222993i
$141$		−	18.5017i		−	1.55813i
$142$	−10.4930	−	6.05814i	−0.880553	−	0.508388i
$143$	−3.67196	+	2.12001i	−0.307065	+	0.177284i
$144$	−0.379966	−	0.658120i	−0.0316638	−	0.0548433i
$145$	0.988122	−	1.71148i	0.0820591	−	0.142130i
$146$		−	8.17212i		−	0.676330i
$147$	9.74738	−	3.84084i	0.803950	−	0.316787i
$148$		−	9.86890i		−	0.811219i
$149$	−10.3718	+	17.9645i	−0.849692	+	1.47171i	0.0317922	+	0.999494i	$0.489879\pi$
$149$	−10.3718	+	17.9645i	−0.849692	+	1.47171i	−0.881484	+	0.472214i	$0.843455\pi$
$150$	−1.29617	+	0.748343i	−0.105832	+	0.0611020i
$151$	−6.16379	−	10.6760i	−0.501602	−	0.868800i	−0.999998	−	0.00185102i	$-0.999411\pi$
$151$	−6.16379	−	10.6760i	−0.501602	−	0.868800i	0.498396	−	0.866949i	$-0.333923\pi$
$152$	−4.08113	+	7.06872i	−0.331023	+	0.573349i
$153$	−0.403918	+	3.10713i	−0.0326548	+	0.251197i
$154$	1.09615	−	14.7616i	0.0883305	−	1.18952i
$155$	5.44985			0.437743
$156$	−0.982315	−	0.567140i	−0.0786481	−	0.0454075i
$157$	0.553270	+	0.958292i	0.0441558	+	0.0764801i	0.887259	−	0.461272i	$-0.152607\pi$
$157$	0.553270	+	0.958292i	0.0441558	+	0.0764801i	−0.843103	+	0.537752i	$0.819274\pi$
$158$	−6.57142	+	3.79401i	−0.522794	+	0.301836i
$159$	−5.88428	−	3.39729i	−0.466654	−	0.269423i
$160$			1.00000i			0.0790569i
$161$	17.5372	+	11.9392i	1.38213	+	0.940944i
$162$	−6.14271			−0.482617
$163$	1.87265	+	1.08118i	0.146678	+	0.0846844i	0.571543	−	0.820572i	$-0.306345\pi$
$163$	1.87265	+	1.08118i	0.146678	+	0.0846844i	−0.424865	+	0.905257i	$0.639678\pi$
$164$	−9.43253	+	5.44587i	−0.736557	+	0.425251i
$165$	7.25169	−	4.18676i	0.564543	−	0.325939i
$166$	1.65954	−	2.87441i	0.128805	−	0.223097i
$167$		−	9.25328i		−	0.716041i	−0.933714	−	0.358020i	$-0.883452\pi$
$167$		−	9.25328i		−	0.716041i	0.933714	−	0.358020i	$-0.116548\pi$
$168$	3.56654	−	1.72054i	0.275165	−	0.132743i
$169$	−12.4256			−0.955819
$170$	2.50466	−	3.27516i	0.192099	−	0.251193i
$171$	−3.10137	−	5.37174i	−0.237168	−	0.410787i
$172$	0.990868	+	1.71623i	0.0755530	+	0.130862i
$173$	1.73801	+	1.00344i	0.132139	+	0.0762902i	0.564612	−	0.825356i	$-0.309026\pi$
$173$	1.73801	+	1.00344i	0.132139	+	0.0762902i	−0.432474	+	0.901647i	$0.642359\pi$
$174$	−2.95782			−0.224232
$175$	1.14957	+	2.38296i	0.0868990	+	0.180135i
$176$		−	5.59471i		−	0.421717i
$177$	−5.11054	−	2.95057i	−0.384132	−	0.221779i
$178$	−3.41890	−	5.92171i	−0.256257	−	0.443851i
$179$	−6.00255	−	10.3967i	−0.448651	−	0.777087i	0.549647	−	0.835397i	$-0.314762\pi$
$179$	−6.00255	−	10.3967i	−0.448651	−	0.777087i	−0.998299	+	0.0583100i	$0.981429\pi$
$180$	−0.658120	−	0.379966i	−0.0490533	−	0.0283210i
$181$		−	0.934493i		−	0.0694603i	−0.999397	−	0.0347302i	$-0.988943\pi$
$181$		−	0.934493i		−	0.0694603i	0.999397	−	0.0347302i	$-0.0110572\pi$
$182$	−1.12839	+	1.65747i	−0.0836422	+	0.122860i
$183$	17.3678			1.28386
$184$	6.94442	+	4.00936i	0.511949	+	0.295574i
$185$	−4.93445	−	8.54672i	−0.362788	−	0.628367i
$186$	−4.07836	−	7.06392i	−0.299040	−	0.517952i
$187$	−14.0128	+	18.3236i	−1.02472	+	1.33995i
$188$	−12.3618			−0.901576
$189$	−1.10256	+	14.8479i	−0.0801997	+	1.08003i
$190$			8.16225i			0.592152i
$191$	1.81144	−	3.13751i	0.131072	−	0.227023i	−0.793018	−	0.609198i	$-0.791492\pi$
$191$	1.81144	−	3.13751i	0.131072	−	0.227023i	0.924090	+	0.382175i	$0.124825\pi$
$192$	1.29617	−	0.748343i	0.0935429	−	0.0540070i
$193$	14.0996	−	8.14040i	1.01491	−	0.585959i	0.102285	−	0.994755i	$-0.467385\pi$
$193$	14.0996	−	8.14040i	1.01491	−	0.585959i	0.912626	+	0.408796i	$0.134051\pi$
$194$	1.41119	+	0.814748i	0.101317	+	0.0584955i
$195$	−1.13428			−0.0812274
$196$	−2.56623	−	6.51264i	−0.183302	−	0.465188i
$197$		−	19.8616i		−	1.41508i	−0.706672	−	0.707541i	$-0.749805\pi$
$197$		−	19.8616i		−	1.41508i	0.706672	−	0.707541i	$-0.250195\pi$
$198$	3.68199	+	2.12580i	0.261668	+	0.151074i
$199$	1.25080	−	0.722149i	0.0886668	−	0.0511918i	−0.455011	−	0.890486i	$-0.650365\pi$
$199$	1.25080	−	0.722149i	0.0886668	−	0.0511918i	0.543678	+	0.839294i	$0.317031\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	9.56883	+	5.52457i	0.674933	+	0.389673i
$202$	12.3947			0.872088
$203$	−0.387199	+	5.21429i	−0.0271760	+	0.365972i
$204$	−6.11950	−	0.795518i	−0.428451	−	0.0556974i
$205$	−5.44587	+	9.43253i	−0.380356	+	0.658796i
$206$	3.82319	+	6.62196i	0.266374	+	0.461374i
$207$	−5.27728	+	3.04684i	−0.366796	+	0.211770i
$208$	−0.378930	+	0.656327i	−0.0262741	+	0.0455081i
$209$		−	45.6654i		−	3.15874i
$210$	2.22845	−	3.27330i	0.153777	−	0.225879i
$211$			4.44364i			0.305913i	0.988233	+	0.152957i	$0.0488795\pi$
$211$			4.44364i			0.305913i	−0.988233	+	0.152957i	$0.951121\pi$
$212$	−2.26988	+	3.93154i	−0.155896	+	0.270019i
$213$	9.06713	+	15.7047i	0.621269	+	1.07607i
$214$	−0.234019	+	0.135111i	−0.0159972	+	0.00923601i
$215$	1.71623	+	0.990868i	0.117046	+	0.0675766i
$216$			5.62744i			0.382899i
$217$	−12.9868	+	6.26497i	−0.881600	+	0.425294i
$218$		−	7.09413i		−	0.480475i
$219$	−6.11555	+	10.5924i	−0.413251	+	0.715771i
$220$	−2.79736	−	4.84516i	−0.188598	−	0.326661i
$221$	2.88493	−	1.20048i	0.194062	−	0.0807532i
$222$	−7.38532	+	12.7918i	−0.495671	+	0.858527i
$223$	−12.2113			−0.817728			−0.408864	−	0.912595i	$-0.634075\pi$
$223$	−12.2113			−0.817728			−0.408864	+	0.912595i	$0.634075\pi$
$224$	−1.14957	−	2.38296i	−0.0768086	−	0.159218i
$225$	−0.759931			−0.0506621
$226$	−2.38290	−	1.37577i	−0.158508	−	0.0915145i
$227$	6.75821	−	3.90185i	0.448558	−	0.258975i	−0.258663	−	0.965968i	$-0.583282\pi$
$227$	6.75821	−	3.90185i	0.448558	−	0.258975i	0.707221	+	0.706993i	$0.249949\pi$
$228$	10.5796	−	6.10816i	0.700654	−	0.404523i
$229$	−0.721607	+	1.24986i	−0.0476851	+	0.0825931i	−0.888883	−	0.458135i	$-0.848518\pi$
$229$	−0.721607	+	1.24986i	−0.0476851	+	0.0825931i	0.841198	+	0.540728i	$0.181851\pi$
$230$	8.01872			0.528739
$231$	−12.4675	+	18.3132i	−0.820302	+	1.20492i
$232$			1.97624i			0.129747i
$233$	11.4315	+	6.59995i	0.748900	+	0.432377i	0.825296	−	0.564700i	$-0.191008\pi$
$233$	11.4315	+	6.59995i	0.748900	+	0.432377i	−0.0763965	+	0.997078i	$0.524341\pi$
$234$	−0.287961	−	0.498763i	−0.0188246	−	0.0326052i
$235$	−10.7056	+	6.18089i	−0.698358	+	0.403197i
$236$	−1.97140	+	3.41457i	−0.128328	+	0.222270i
$237$	11.3569			0.737710
$238$	−2.20349	+	10.6838i	−0.142831	+	0.692531i
$239$	3.79985			0.245792			0.122896	−	0.992420i	$-0.460782\pi$
$239$	3.79985			0.245792			0.122896	+	0.992420i	$0.460782\pi$
$240$	0.748343	−	1.29617i	0.0483053	−	0.0836673i
$241$	20.1496	−	11.6334i	1.29795	−	0.749370i	0.317898	−	0.948125i	$-0.397023\pi$
$241$	20.1496	−	11.6334i	1.29795	−	0.749370i	0.980049	+	0.198755i	$0.0636898\pi$
$242$	10.1504	+	17.5810i	0.652492	+	1.13015i
$243$	−6.65852	−	3.84430i	−0.427144	−	0.246612i
$244$		−	11.6042i		−	0.742881i
$245$	−5.47874	−	4.35700i	−0.350024	−	0.278358i
$246$	16.3015			1.03935
$247$	−3.09292	+	5.35710i	−0.196798	+	0.340864i
$248$	−4.71971	+	2.72493i	−0.299702	+	0.173033i
$249$	−4.30209	+	2.48381i	−0.272634	+	0.157405i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	11.0969			0.700431			0.350215	−	0.936669i	$-0.386108\pi$
$251$	11.0969			0.700431			0.350215	+	0.936669i	$0.386108\pi$
$252$	2.00507	+	0.148891i	0.126307	+	0.00937923i
$253$	−44.8624			−2.82048
$254$	4.03081	−	6.98157i	0.252915	−	0.438062i
$255$	−5.69740	+	2.37081i	−0.356785	+	0.148466i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.78708	+	4.82736i	−0.173853	+	0.301122i	−0.939764	−	0.341825i	$-0.888955\pi$
$257$	−2.78708	+	4.82736i	−0.173853	+	0.301122i	0.765911	+	0.642947i	$0.222288\pi$
$258$		−	2.96604i		−	0.184657i
$259$	21.5836	+	14.6940i	1.34114	+	0.913042i
$260$			0.757861i			0.0470005i
$261$	−1.30061	−	0.750905i	−0.0805054	−	0.0464798i
$262$	8.36888	−	4.83177i	0.517031	−	0.298508i
$263$	5.94980	+	10.3054i	0.366881	+	0.635456i	0.989076	−	0.147406i	$-0.0470925\pi$
$263$	5.94980	+	10.3054i	0.366881	+	0.635456i	−0.622196	+	0.782862i	$0.713759\pi$
$264$	−4.18676	+	7.25169i	−0.257677	+	0.446310i
$265$			4.53975i			0.278875i
$266$	−9.38305	−	19.4503i	−0.575311	−	1.19258i
$267$			10.2340i			0.626313i
$268$	3.69120	−	6.39335i	0.225476	−	0.390536i
$269$	6.93088	−	4.00154i	0.422583	−	0.243978i	−0.273599	−	0.961844i	$-0.588214\pi$
$269$	6.93088	−	4.00154i	0.422583	−	0.243978i	0.696182	+	0.717866i	$0.254881\pi$
$270$	2.81372	+	4.87350i	0.171237	+	0.296592i
$271$	2.01142	−	3.48388i	0.122185	−	0.211630i	−0.798444	−	0.602069i	$-0.794343\pi$
$271$	2.01142	−	3.48388i	0.122185	−	0.211630i	0.920629	+	0.390439i	$0.127677\pi$
$272$	−0.531519	+	4.08870i	−0.0322281	+	0.247914i
$273$	2.70294	−	1.30393i	0.163590	−	0.0789174i
$274$	2.53368			0.153065
$275$	−4.84516	−	2.79736i	−0.292174	−	0.168687i
$276$	−6.00075	−	10.3936i	−0.361203	−	0.625622i
$277$	14.8686	−	8.58441i	0.893369	−	0.515787i	0.0183263	−	0.999832i	$-0.494166\pi$
$277$	14.8686	−	8.58441i	0.893369	−	0.515787i	0.875043	+	0.484045i	$0.160833\pi$
$278$	−15.4535	−	8.92209i	−0.926840	−	0.535111i
$279$		−	4.14151i		−	0.247946i
$280$	−2.18703	−	1.48892i	−0.130700	−	0.0889800i
$281$	−4.03860			−0.240923			−0.120461	−	0.992718i	$-0.538437\pi$
$281$	−4.03860			−0.240923			−0.120461	+	0.992718i	$0.538437\pi$
$282$	16.0230	+	9.25086i	0.954153	+	0.550880i
$283$	27.8807	−	16.0969i	1.65734	−	0.956863i	0.683398	−	0.730046i	$-0.260501\pi$
$283$	27.8807	−	16.0969i	1.65734	−	0.956863i	0.973937	−	0.226818i	$-0.0728321\pi$
$284$	10.4930	−	6.05814i	0.622645	−	0.359484i
$285$	6.10816	−	10.5796i	0.361816	−	0.626684i
$286$		−	4.24001i		−	0.250717i
$287$	2.13398	−	28.7377i	0.125965	−	1.69633i
$288$	0.759931			0.0447794
$289$	11.9816	−	12.0599i	0.704801	−	0.709405i
$290$	0.988122	+	1.71148i	0.0580245	+	0.100501i
$291$	−1.21942	−	2.11210i	−0.0714838	−	0.123814i
$292$	7.07727	+	4.08606i	0.414166	+	0.239119i
$293$	22.0279			1.28688			0.643441	−	0.765496i	$-0.277506\pi$
$293$	22.0279			1.28688			0.643441	+	0.765496i	$0.277506\pi$
$294$	−1.54742	+	10.3619i	−0.0902475	+	0.604318i
$295$			3.94281i			0.229559i
$296$	8.54672	+	4.93445i	0.496768	+	0.286809i
$297$	−15.7419	−	27.2658i	−0.913440	−	1.58212i
$298$	−10.3718	−	17.9645i	−0.600823	−	1.04066i
$299$	5.26290	+	3.03854i	0.304361	+	0.175723i
$300$		−	1.49669i		−	0.0864112i
$301$	−5.22878	−	0.388275i	−0.301382	−	0.0223798i
$302$	12.3276			0.709373
$303$	−16.0656	−	9.27549i	−0.922946	−	0.532863i
$304$	−4.08113	−	7.06872i	−0.234069	−	0.405419i
$305$	−5.80208	−	10.0495i	−0.332226	−	0.575433i
$306$	−2.48890	−	1.90337i	−0.142281	−	0.108808i
$307$	−6.90454			−0.394063			−0.197031	−	0.980397i	$-0.563130\pi$
$307$	−6.90454			−0.394063			−0.197031	+	0.980397i	$0.563130\pi$
$308$	12.2358	+	8.33008i	0.697200	+	0.474650i
$309$		−	11.4442i		−	0.651039i
$310$	−2.72493	+	4.71971i	−0.154765	+	0.268062i
$311$	9.67048	−	5.58326i	0.548363	−	0.316597i	−0.200099	−	0.979776i	$-0.564126\pi$
$311$	9.67048	−	5.58326i	0.548363	−	0.316597i	0.748461	+	0.663178i	$0.230793\pi$
$312$	0.982315	−	0.567140i	0.0556126	−	0.0321080i
$313$	−12.6610	−	7.30981i	−0.715640	−	0.413175i	0.0975058	−	0.995235i	$-0.468914\pi$
$313$	−12.6610	−	7.30981i	−0.715640	−	0.413175i	−0.813146	+	0.582060i	$0.802247\pi$
$314$	−1.10654			−0.0624457
$315$	1.81089	−	0.873591i	0.102032	−	0.0492213i
$316$		−	7.58803i		−	0.426860i
$317$	−24.4502	−	14.1163i	−1.37326	−	0.792852i	−0.381924	−	0.924194i	$-0.624738\pi$
$317$	−24.4502	−	14.1163i	−1.37326	−	0.792852i	−0.991337	+	0.131342i	$0.958072\pi$
$318$	5.88428	−	3.39729i	0.329974	−	0.190511i
$319$	−5.52826	−	9.57522i	−0.309523	−	0.536110i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	0.404438			0.0225735
$322$	−19.1083	+	9.21805i	−1.06486	+	0.513702i
$323$	−4.33839	+	33.3730i	−0.241395	+	1.85692i
$324$	3.07136	−	5.31974i	0.170631	−	0.295541i
$325$	0.378930	+	0.656327i	0.0210193	+	0.0364065i
$326$	−1.87265	+	1.08118i	−0.103717	+	0.0598809i
$327$	−5.30884	+	9.19519i	−0.293580	+	0.508495i
$328$		−	10.8917i		−	0.601396i
$329$	18.4057	−	27.0356i	1.01474	−	1.49052i
$330$			8.37352i			0.460947i
$331$	1.23656	−	2.14179i	0.0679675	−	0.117723i	−0.830039	−	0.557705i	$-0.811682\pi$
$331$	1.23656	−	2.14179i	0.0679675	−	0.117723i	0.898007	+	0.439982i	$0.145015\pi$
$332$	1.65954	+	2.87441i	0.0910791	+	0.157754i
$333$	−6.49492	+	3.74984i	−0.355919	+	0.205490i
$334$	8.01358	+	4.62664i	0.438484	+	0.253159i
$335$		−	7.38240i		−	0.403344i
$336$	−0.293240	+	3.94899i	−0.0159976	+	0.215435i
$337$		−	10.1811i		−	0.554601i	−0.960783	−	0.277300i	$-0.910560\pi$
$337$		−	10.1811i		−	0.554601i	0.960783	−	0.277300i	$-0.0894397\pi$
$338$	6.21282	−	10.7609i	0.337933	−	0.585317i
$339$	2.05909	+	3.56645i	0.111834	+	0.193703i
$340$	1.58404	+	3.80668i	0.0859067	+	0.206446i
$341$	15.2452	−	26.4054i	0.825572	−	1.42993i
$342$	6.20275			0.335406
$343$	18.0643	+	4.08437i	0.975379	+	0.220535i
$344$	−1.98174			−0.106848
$345$	−10.3936	−	6.00075i	−0.559573	−	0.323070i
$346$	−1.73801	+	1.00344i	−0.0934360	+	0.0539453i
$347$	4.50028	−	2.59824i	0.241588	−	0.139481i	−0.374318	−	0.927300i	$-0.622123\pi$
$347$	4.50028	−	2.59824i	0.241588	−	0.139481i	0.615906	+	0.787819i	$0.288790\pi$
$348$	1.47891	−	2.56154i	0.0792778	−	0.137313i
$349$	7.30956			0.391272			0.195636	−	0.980677i	$-0.437323\pi$
$349$	7.30956			0.391272			0.195636	+	0.980677i	$0.437323\pi$
$350$	−2.63849	−	0.195927i	−0.141033	−	0.0104727i
$351$			4.26481i			0.227639i
$352$	4.84516	+	2.79736i	0.258248	+	0.149100i
$353$	13.3122	+	23.0574i	0.708538	+	1.22722i	0.965399	+	0.260776i	$0.0839784\pi$
$353$	13.3122	+	23.0574i	0.708538	+	1.22722i	−0.256861	+	0.966448i	$0.582688\pi$
$354$	5.11054	−	2.95057i	0.271622	−	0.156821i
$355$	6.05814	−	10.4930i	0.321533	−	0.556911i
$356$	6.83780			0.362403
$357$	10.8513	−	12.1991i	0.574311	−	0.645645i
$358$	12.0051			0.634489
$359$	−13.5013	+	23.3849i	−0.712571	+	1.23421i	0.251318	+	0.967905i	$0.419136\pi$
$359$	−13.5013	+	23.3849i	−0.712571	+	1.23421i	−0.963889	+	0.266304i	$0.914197\pi$
$360$	0.658120	−	0.379966i	0.0346859	−	0.0200259i
$361$	−23.8112	−	41.2421i	−1.25322	−	2.17064i
$362$	0.809295	+	0.467247i	0.0425356	+	0.0245579i
$363$		−	30.3839i		−	1.59474i
$364$	−0.871211	−	1.80595i	−0.0456639	−	0.0946576i
$365$	8.17212			0.427748
$366$	−8.68390	+	15.0410i	−0.453915	+	0.786203i
$367$	−4.46139	+	2.57579i	−0.232883	+	0.134455i	−0.611901	−	0.790934i	$-0.709595\pi$
$367$	−4.46139	+	2.57579i	−0.232883	+	0.134455i	0.379019	+	0.925389i	$0.376262\pi$
$368$	−6.94442	+	4.00936i	−0.362003	+	0.209002i
$369$	7.16807	+	4.13849i	0.373155	+	0.215441i
$370$	9.86890			0.513060
$371$	−5.21875	−	10.8180i	−0.270944	−	0.561645i
$372$	8.15672			0.422906
$373$	2.78675	−	4.82680i	0.144293	−	0.249922i	−0.784816	−	0.619729i	$-0.787243\pi$
$373$	2.78675	−	4.82680i	0.144293	−	0.249922i	0.929109	+	0.369807i	$0.120576\pi$
$374$	−8.86226	−	21.2973i	−0.458256	−	1.10126i
$375$	−0.748343	−	1.29617i	−0.0386443	−	0.0669338i
$376$	6.18089	−	10.7056i	0.318755	−	0.552100i
$377$			1.49772i			0.0771364i
$378$	−12.3074	−	8.37881i	−0.633024	−	0.430959i
$379$			17.3172i			0.889527i	0.895648	+	0.444763i	$0.146712\pi$
$379$			17.3172i			0.889527i	−0.895648	+	0.444763i	$0.853288\pi$
$380$	−7.06872	−	4.08113i	−0.362617	−	0.209357i
$381$	−10.4492	+	6.03286i	−0.535329	+	0.309073i
$382$	1.81144	+	3.13751i	0.0926816	+	0.160529i
$383$	−13.9955	+	24.2408i	−0.715134	+	1.23865i	0.247774	+	0.968818i	$0.420301\pi$
$383$	−13.9955	+	24.2408i	−0.715134	+	1.23865i	−0.962908	+	0.269831i	$0.913032\pi$
$384$			1.49669i			0.0763774i
$385$	14.7616	+	1.09615i	0.752319	+	0.0558651i
$386$			16.2808i			0.828671i
$387$	0.752991	−	1.30422i	0.0382767	−	0.0662972i
$388$	−1.41119	+	0.814748i	−0.0716421	+	0.0413626i
$389$	−11.9147	−	20.6368i	−0.604098	−	1.04633i	−0.992193	−	0.124709i	$-0.960200\pi$
$389$	−11.9147	−	20.6368i	−0.604098	−	1.04633i	0.388095	−	0.921619i	$-0.373133\pi$
$390$	0.567140	−	0.982315i	0.0287182	−	0.0497414i
$391$	32.7862	+	4.26211i	1.65807	+	0.215544i
$392$	6.92323	+	1.03390i	0.349676	+	0.0522198i
$393$	−14.4633			−0.729577
$394$	17.2007	+	9.93081i	0.866557	+	0.500307i
$395$	−3.79401	−	6.57142i	−0.190898	−	0.330644i
$396$	−3.68199	+	2.12580i	−0.185027	+	0.106825i
$397$	−17.3258	−	10.0030i	−0.869555	−	0.502038i	−0.00235495	−	0.999997i	$-0.500750\pi$
$397$	−17.3258	−	10.0030i	−0.869555	−	0.502038i	−0.867200	+	0.497959i	$0.834083\pi$
$398$			1.44430i			0.0723961i
$399$	−2.39350	+	32.2326i	−0.119825	+	1.61365i
$400$	−1.00000			−0.0500000
$401$	−19.0441	−	10.9951i	−0.951018	−	0.549071i	−0.0576212	−	0.998339i	$-0.518352\pi$
$401$	−19.0441	−	10.9951i	−0.951018	−	0.549071i	−0.893397	+	0.449268i	$0.851685\pi$
$402$	−9.56883	+	5.52457i	−0.477250	+	0.275540i
$403$	−3.57688	+	2.06511i	−0.178177	+	0.102871i
$404$	−6.19735	+	10.7341i	−0.308330	+	0.534043i
$405$		−	6.14271i		−	0.305234i
$406$	−4.32211	−	2.94247i	−0.214503	−	0.146032i
$407$	−55.2137			−2.73684
$408$	3.74869	−	4.90189i	0.185588	−	0.242680i
$409$	−15.6041	−	27.0271i	−0.771575	−	1.33641i	−0.936700	−	0.350134i	$-0.886136\pi$
$409$	−15.6041	−	27.0271i	−0.771575	−	1.33641i	0.165125	−	0.986273i	$-0.447197\pi$
$410$	−5.44587	−	9.43253i	−0.268952	−	0.465839i
$411$	−3.28408	−	1.89607i	−0.161992	−	0.0935260i
$412$	−7.64638			−0.376710
$413$	−4.53252	−	9.39556i	−0.223031	−	0.462325i
$414$		−	6.09367i		−	0.299488i
$415$	2.87441	+	1.65954i	0.141099	+	0.0814636i
$416$	−0.378930	−	0.656327i	−0.0185786	−	0.0321791i
$417$	13.3536	+	23.1290i	0.653927	+	1.13263i
$418$	39.5474	+	22.8327i	1.93433	+	1.11678i
$419$			15.2940i			0.747162i	0.927598	+	0.373581i	$0.121870\pi$
$419$			15.2940i			0.747162i	−0.927598	+	0.373581i	$0.878130\pi$
$420$	1.72054	+	3.56654i	0.0839537	+	0.174029i
$421$	−3.62570			−0.176706			−0.0883530	−	0.996089i	$-0.528160\pi$
$421$	−3.62570			−0.176706			−0.0883530	+	0.996089i	$0.528160\pi$
$422$	−3.84831	−	2.22182i	−0.187333	−	0.108157i
$423$	4.69705	+	8.13553i	0.228378	+	0.395563i
$424$	−2.26988	−	3.93154i	−0.110235	−	0.190933i
$425$	3.27516	+	2.50466i	0.158869	+	0.121494i
$426$	−18.1343			−0.878608
$427$	25.3787	+	17.2777i	1.22816	+	0.836126i
$428$		−	0.270222i		−	0.0130617i
$429$	−3.17298	+	5.49577i	−0.153193	+	0.265338i
$430$	−1.71623	+	0.990868i	−0.0827641	+	0.0477839i
$431$	4.19428	−	2.42157i	0.202031	−	0.116643i	−0.395571	−	0.918435i	$-0.629453\pi$
$431$	4.19428	−	2.42157i	0.202031	−	0.116643i	0.597603	+	0.801792i	$0.296120\pi$
$432$	−4.87350	−	2.81372i	−0.234477	−	0.135375i
$433$	18.0806			0.868899			0.434450	−	0.900696i	$-0.356943\pi$
$433$	18.0806			0.868899			0.434450	+	0.900696i	$0.356943\pi$
$434$	1.06777	−	14.3794i	0.0512546	−	0.690232i
$435$		−	2.95782i		−	0.141816i
$436$	6.14370	+	3.54707i	0.294230	+	0.169874i
$437$	−56.6821	+	32.7254i	−2.71147	+	1.56547i
$438$	−6.11555	−	10.5924i	−0.292212	−	0.506127i
$439$	−33.3159	−	19.2350i	−1.59008	−	0.918035i	−0.993291	−	0.115638i	$-0.963109\pi$
$439$	−33.3159	−	19.2350i	−1.59008	−	0.918035i	−0.596791	−	0.802396i	$-0.703558\pi$
$440$	5.59471			0.266717
$441$	−3.31102	+	4.16346i	−0.157667	+	0.198260i
$442$	−0.402818	+	3.09867i	−0.0191601	+	0.147389i
$443$	15.5424	−	26.9203i	0.738443	−	1.27902i	−0.214753	−	0.976668i	$-0.568895\pi$
$443$	15.5424	−	26.9203i	0.738443	−	1.27902i	0.953196	−	0.302353i	$-0.0977720\pi$
$444$	−7.38532	−	12.7918i	−0.350492	−	0.607070i
$445$	5.92171	−	3.41890i	0.280716	−	0.162071i
$446$	6.10564	−	10.5753i	0.289110	−	0.500754i
$447$			31.0467i			1.46846i
$448$	2.63849	+	0.195927i	0.124657	+	0.00925666i
$449$			0.662281i			0.0312550i	0.999878	+	0.0156275i	$0.00497459\pi$
$449$			0.662281i			0.0312550i	−0.999878	+	0.0156275i	$0.995025\pi$
$450$	0.379966	−	0.658120i	0.0179117	−	0.0310241i
$451$	30.4681	+	52.7723i	1.43469	+	2.48495i
$452$	2.38290	−	1.37577i	0.112082	−	0.0647105i
$453$	−15.9786	−	9.22526i	−0.750741	−	0.433440i
$454$			7.80371i			0.366246i
$455$	−1.65747	−	1.12839i	−0.0777032	−	0.0529000i
$456$			12.2163i			0.572082i
$457$	16.8463	−	29.1787i	0.788038	−	1.36492i	−0.139129	−	0.990274i	$-0.544430\pi$
$457$	16.8463	−	29.1787i	0.788038	−	1.36492i	0.927167	−	0.374647i	$-0.122236\pi$
$458$	−0.721607	−	1.24986i	−0.0337185	−	0.0584021i
$459$	8.91409	+	21.4218i	0.416074	+	0.999886i
$460$	−4.00936	+	6.94442i	−0.186937	+	0.323785i
$461$	14.6782			0.683631			0.341816	−	0.939767i	$-0.388958\pi$
$461$	14.6782			0.683631			0.341816	+	0.939767i	$0.388958\pi$
$462$	−9.62592	−	19.9538i	−0.447838	−	0.928334i
$463$	29.7205			1.38123			0.690615	−	0.723223i	$-0.257340\pi$
$463$	29.7205			1.38123			0.690615	+	0.723223i	$0.257340\pi$
$464$	−1.71148	−	0.988122i	−0.0794534	−	0.0458724i
$465$	7.06392	−	4.07836i	0.327582	−	0.189129i
$466$	−11.4315	+	6.59995i	−0.529552	+	0.305737i
$467$	−1.48936	+	2.57965i	−0.0689194	+	0.119372i	−0.898426	−	0.439125i	$-0.855288\pi$
$467$	−1.48936	+	2.57965i	−0.0689194	+	0.119372i	0.829506	+	0.558497i	$0.188622\pi$
$468$	0.575922			0.0266220
$469$	8.48656	+	17.5920i	0.391873	+	0.812321i
$470$		−	12.3618i		−	0.570207i
$471$	1.43426	+	0.828072i	0.0660873	+	0.0381555i
$472$	−1.97140	−	3.41457i	−0.0907413	−	0.157168i
$473$	9.60183	−	5.54362i	0.441493	−	0.254896i
$474$	−5.67845	+	9.83536i	−0.260820	+	0.451753i
$475$	−8.16225			−0.374510
$476$	−8.15074	−	7.25020i	−0.373588	−	0.332313i
$477$	3.44990			0.157960
$478$	−1.89992	+	3.29076i	−0.0869005	+	0.150516i
$479$	17.5314	−	10.1218i	0.801032	−	0.462476i	−0.0427999	−	0.999084i	$-0.513628\pi$
$479$	17.5314	−	10.1218i	0.801032	−	0.462476i	0.843832	+	0.536608i	$0.180294\pi$
$480$	0.748343	+	1.29617i	0.0341570	+	0.0591617i
$481$	6.47722	+	3.73963i	0.295336	+	0.170512i
$482$			23.2667i			1.05977i
$483$	31.6658	+	2.35141i	1.44084	+	0.106993i
$484$	−20.3008			−0.922763
$485$	−0.814748	+	1.41119i	−0.0369958	+	0.0640786i
$486$	6.65852	−	3.84430i	0.302037	−	0.174381i
$487$	−4.32530	+	2.49721i	−0.195998	+	0.113159i	−0.594787	−	0.803883i	$-0.702764\pi$
$487$	−4.32530	+	2.49721i	−0.195998	+	0.113159i	0.398789	+	0.917043i	$0.369430\pi$
$488$	10.0495	+	5.80208i	0.454920	+	0.262648i
$489$	3.23637			0.146354
$490$	6.51264	−	2.56623i	0.294211	−	0.115930i
$491$	−14.9690			−0.675541			−0.337771	−	0.941228i	$-0.609673\pi$
$491$	−14.9690			−0.675541			−0.337771	+	0.941228i	$0.609673\pi$
$492$	−8.15076	+	14.1175i	−0.367465	+	0.636467i
$493$	3.13045	+	7.52293i	0.140989	+	0.338816i
$494$	−3.09292	−	5.35710i	−0.139157	−	0.241027i
$495$	−2.12580	+	3.68199i	−0.0955475	+	0.165493i
$496$		−	5.44985i		−	0.244706i
$497$	−2.37390	+	31.9686i	−0.106484	+	1.43399i
$498$		−	4.96762i		−	0.222604i
$499$	25.7514	+	14.8676i	1.15279	+	0.665565i	0.949566	−	0.313567i	$-0.101524\pi$
$499$	25.7514	+	14.8676i	1.15279	+	0.665565i	0.203227	+	0.979132i	$0.434857\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−6.92463	−	11.9938i	−0.309370	−	0.535844i
$502$	−5.54845	+	9.61020i	−0.247640	+	0.428924i
$503$		−	30.0516i		−	1.33993i	−0.742391	−	0.669967i	$-0.766308\pi$
$503$		−	30.0516i		−	1.33993i	0.742391	−	0.669967i	$-0.233692\pi$
$504$	−1.13148	+	1.66199i	−0.0504000	+	0.0740311i
$505$			12.3947i			0.551557i
$506$	22.4312	−	38.8520i	0.997189	−	1.72718i
$507$	−16.1057	+	9.29865i	−0.715280	+	0.412967i
$508$	4.03081	+	6.98157i	0.178838	+	0.309757i
$509$	−3.75051	+	6.49607i	−0.166238	+	0.287933i	−0.937094	−	0.349076i	$-0.886495\pi$
$509$	−3.75051	+	6.49607i	−0.166238	+	0.287933i	0.770856	+	0.637009i	$0.219829\pi$
$510$	0.795518	−	6.11950i	0.0352261	−	0.270976i
$511$	−19.4738	+	9.39440i	−0.861472	+	0.415584i
$512$	1.00000			0.0441942
$513$	−39.7787	−	22.9663i	−1.75627	−	1.01399i
$514$	−2.78708	−	4.82736i	−0.122933	−	0.212926i
$515$	−6.62196	+	3.82319i	−0.291798	+	0.168470i
$516$	2.56866	+	1.48302i	0.113079	+	0.0652862i
$517$			69.1606i			3.04168i
$518$	−23.5172	+	11.3450i	−1.03329	+	0.498469i
$519$	3.00367			0.131847
$520$	−0.656327	−	0.378930i	−0.0287818	−	0.0166172i
$521$	3.70381	−	2.13840i	0.162267	−	0.0936848i	−0.416667	−	0.909059i	$-0.636802\pi$
$521$	3.70381	−	2.13840i	0.162267	−	0.0936848i	0.578934	+	0.815374i	$0.303469\pi$
$522$	1.30061	−	0.750905i	0.0569259	−	0.0328662i
$523$	9.68237	−	16.7704i	0.423380	−	0.733316i	−0.572887	−	0.819634i	$-0.694177\pi$
$523$	9.68237	−	16.7704i	0.423380	−	0.733316i	0.996268	+	0.0863178i	$0.0275101\pi$
$524$			9.66355i			0.422154i
$525$	3.27330	+	2.22845i	0.142859	+	0.0972574i
$526$	−11.8996			−0.518847
$527$	−13.6500	+	17.8491i	−0.594605	+	0.777521i
$528$	−4.18676	−	7.25169i	−0.182205	−	0.315589i
$529$	20.6499	+	35.7668i	0.897824	+	1.55508i
$530$	−3.93154	−	2.26988i	−0.170775	−	0.0985971i
$531$	2.99626			0.130027
$532$	21.5360	+	1.59920i	0.933704	+	0.0693342i
$533$		−	8.25442i		−	0.357539i
$534$	−8.86294	−	5.11702i	−0.383537	−	0.221435i
$535$	−0.135111	−	0.234019i	−0.00584136	−	0.0101175i
$536$	3.69120	+	6.39335i	0.159436	+	0.276151i
$537$	−15.5606	−	8.98393i	−0.671490	−	0.387685i
$538$			8.00309i			0.345038i
$539$	−36.4363	+	14.3573i	−1.56942	+	0.618413i
$540$	−5.62744			−0.242166
$541$	−6.79470	−	3.92292i	−0.292127	−	0.168660i	0.346774	−	0.937949i	$-0.387277\pi$
$541$	−6.79470	−	3.92292i	−0.292127	−	0.168660i	−0.638901	+	0.769289i	$0.720610\pi$
$542$	2.01142	+	3.48388i	0.0863977	+	0.149645i
$543$	−0.699322	−	1.21126i	−0.0300108	−	0.0519802i
$544$	−3.27516	−	2.50466i	−0.140421	−	0.107386i
$545$	7.09413			0.303879
$546$	−0.222235	+	2.99278i	−0.00951080	+	0.128079i
$547$			29.1986i			1.24844i	0.781248	+	0.624220i	$0.214583\pi$
$547$			29.1986i			1.24844i	−0.781248	+	0.624220i	$0.785417\pi$
$548$	−1.26684	+	2.19424i	−0.0541168	+	0.0937331i
$549$	−7.63693	+	4.40918i	−0.325936	+	0.188179i
$550$	4.84516	−	2.79736i	0.206598	−	0.119280i
$551$	−13.9695	−	8.06530i	−0.595121	−	0.343593i
$552$	12.0015			0.510818
$553$	16.5953	+	11.2980i	0.705703	+	0.480439i
$554$			17.1688i			0.729433i
$555$	−12.7918	−	7.38532i	−0.542980	−	0.313490i
$556$	15.4535	−	8.92209i	0.655375	−	0.378381i
$557$	−11.9801	−	20.7501i	−0.507611	−	0.879208i	−0.999961	−	0.00881111i	$-0.997195\pi$
$557$	−11.9801	−	20.7501i	−0.507611	−	0.879208i	0.492350	−	0.870397i	$-0.336138\pi$
$558$	3.58665	+	2.07076i	0.151835	+	0.0876621i
$559$	−1.50188			−0.0635227
$560$	2.38296	−	1.14957i	0.100698	−	0.0485780i
$561$	−4.45069	+	34.2369i	−0.187908	+	1.44548i
$562$	2.01930	−	3.49753i	0.0851790	−	0.147534i
$563$	13.3319	+	23.0916i	0.561873	+	0.973193i	0.997333	+	0.0729851i	$0.0232525\pi$
$563$	13.3319	+	23.0916i	0.561873	+	0.973193i	−0.435460	+	0.900208i	$0.643414\pi$
$564$	−16.0230	+	9.25086i	−0.674688	+	0.389531i
$565$	1.37577	−	2.38290i	0.0578789	−	0.100249i
$566$			32.1939i			1.35321i
$567$	7.06145	+	14.6378i	0.296553	+	0.614731i
$568$			12.1163i			0.508388i
$569$	−16.4525	+	28.4965i	−0.689723	+	1.19464i	0.282204	+	0.959354i	$0.408934\pi$
$569$	−16.4525	+	28.4965i	−0.689723	+	1.19464i	−0.971927	+	0.235281i	$0.924399\pi$
$570$	6.10816	+	10.5796i	0.255843	+	0.443133i
$571$	−18.2525	+	10.5381i	−0.763845	+	0.441006i	−0.830674	−	0.556759i	$-0.812045\pi$
$571$	−18.2525	+	10.5381i	−0.763845	+	0.441006i	0.0668298	+	0.997764i	$0.478712\pi$
$572$	3.67196	+	2.12001i	0.153532	+	0.0886419i
$573$		−	5.42233i		−	0.226521i
$574$	23.8206	+	16.2169i	0.994253	+	0.676882i
$575$			8.01872i			0.334404i
$576$	−0.379966	+	0.658120i	−0.0158319	+	0.0274216i
$577$	2.92767	+	5.07086i	0.121880	+	0.211103i	0.920509	−	0.390721i	$-0.127774\pi$
$577$	2.92767	+	5.07086i	0.121880	+	0.211103i	−0.798629	+	0.601824i	$0.794441\pi$
$578$	4.45335	+	16.4063i	0.185235	+	0.682413i
$579$	12.1836	−	21.1027i	0.506334	−	0.876997i
$580$	−1.97624			−0.0820591
$581$	−8.75735	−	0.650296i	−0.363316	−	0.0269788i
$582$	2.43884			0.101093
$583$	21.9958	+	12.6993i	0.910974	+	0.525951i
$584$	−7.07727	+	4.08606i	−0.292859	+	0.169082i
$585$	0.498763	−	0.287961i	0.0206213	−	0.0119057i
$586$	−11.0139	+	19.0767i	−0.454981	+	0.788051i
$587$	6.45643			0.266486			0.133243	−	0.991083i	$-0.457461\pi$
$587$	6.45643			0.266486			0.133243	+	0.991083i	$0.457461\pi$
$588$	−8.19995	−	6.52105i	−0.338160	−	0.268924i
$589$		−	44.4831i		−	1.83289i
$590$	−3.41457	−	1.97140i	−0.140576	−	0.0811615i
$591$	−14.8633	−	25.7440i	−0.611395	−	1.05897i
$592$	−8.54672	+	4.93445i	−0.351268	+	0.202805i
$593$	2.79084	−	4.83387i	0.114606	−	0.198503i	−0.803016	−	0.595957i	$-0.796773\pi$
$593$	2.79084	−	4.83387i	0.114606	−	0.198503i	0.917622	+	0.397454i	$0.130106\pi$
$594$	31.4839			1.29180
$595$	−10.6838	−	2.20349i	−0.437995	−	0.0903344i
$596$	20.7436			0.849692
$597$	1.08083	−	1.87205i	0.0442354	−	0.0766180i
$598$	−5.26290	+	3.03854i	−0.215216	+	0.124255i
$599$	−13.8045	−	23.9101i	−0.564037	−	0.976940i	−0.997139	−	0.0755954i	$-0.975914\pi$
$599$	−13.8045	−	23.9101i	−0.564037	−	0.976940i	0.433102	−	0.901345i	$-0.357419\pi$
$600$	1.29617	+	0.748343i	0.0529158	+	0.0305510i
$601$			0.761649i			0.0310683i	0.999879	+	0.0155342i	$0.00494487\pi$
$601$			0.761649i			0.0310683i	−0.999879	+	0.0155342i	$0.995055\pi$
$602$	2.95065	−	4.33412i	0.120259	−	0.176646i
$603$	−5.61012			−0.228462
$604$	−6.16379	+	10.6760i	−0.250801	+	0.434400i
$605$	−17.5810	+	10.1504i	−0.714769	+	0.412672i
$606$	16.0656	−	9.27549i	0.652621	−	0.376791i
$607$	22.3930	+	12.9286i	0.908902	+	0.524755i	0.880078	−	0.474830i	$-0.157490\pi$
$607$	22.3930	+	12.9286i	0.908902	+	0.524755i	0.0288243	+	0.999584i	$0.490824\pi$
$608$	8.16225			0.331023
$609$	3.40021	+	7.04836i	0.137783	+	0.285614i
$610$	11.6042			0.469839
$611$	4.68426	−	8.11337i	0.189505	−	0.328232i
$612$	2.89281	−	1.20376i	0.116935	−	0.0486592i
$613$	−13.7392	−	23.7971i	−0.554922	−	0.961154i	−0.997910	−	0.0646259i	$-0.979415\pi$
$613$	−13.7392	−	23.7971i	−0.554922	−	0.961154i	0.442987	−	0.896528i	$-0.353919\pi$
$614$	3.45227	−	5.97950i	0.139322	−	0.241313i
$615$			16.3015i			0.657341i
$616$	−13.3320	+	6.43149i	−0.537160	+	0.259132i
$617$		−	29.7531i		−	1.19782i	−0.800818	−	0.598908i	$-0.795602\pi$
$617$		−	29.7531i		−	1.19782i	0.800818	−	0.598908i	$-0.204398\pi$
$618$	9.91099	+	5.72211i	0.398679	+	0.230177i
$619$	24.0352	−	13.8767i	0.966055	−	0.557752i	0.0680239	−	0.997684i	$-0.478331\pi$
$619$	24.0352	−	13.8767i	0.966055	−	0.557752i	0.898031	+	0.439931i	$0.144997\pi$
$620$	−2.72493	−	4.71971i	−0.109436	−	0.189548i
$621$	−22.5624	+	39.0793i	−0.905399	+	1.56820i
$622$			11.1665i			0.447736i
$623$	−10.1809	+	14.9545i	−0.407891	+	0.599139i
$624$			1.13428i			0.0454075i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	12.6610	−	7.30981i	0.506034	−	0.292159i
$627$	−34.1734	−	59.1901i	−1.36475	−	2.36382i
$628$	0.553270	−	0.958292i	0.0220779	−	0.0382400i
$629$	40.3510	+	5.24551i	1.60890	+	0.209152i
$630$	−0.148891	+	2.00507i	−0.00593195	+	0.0798838i
$631$	−40.2086			−1.60068			−0.800340	−	0.599547i	$-0.795348\pi$
$631$	−40.2086			−1.60068			−0.800340	+	0.599547i	$0.795348\pi$
$632$	6.57142	+	3.79401i	0.261397	+	0.150918i
$633$	3.32537	+	5.75971i	0.132172	+	0.228928i
$634$	24.4502	−	14.1163i	0.971042	−	0.560631i
$635$	6.98157	+	4.03081i	0.277055	+	0.159958i
$636$			6.79458i			0.269423i
$637$	5.24684	+	0.783551i	0.207887	+	0.0310454i
$638$	11.0565			0.437732
$639$	−7.97396	−	4.60377i	−0.315445	−	0.182122i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	28.2733	−	16.3236i	1.11673	−	0.644744i	0.176166	−	0.984360i	$-0.443630\pi$
$641$	28.2733	−	16.3236i	1.11673	−	0.644744i	0.940564	+	0.339616i	$0.110297\pi$
$642$	−0.202219	+	0.350253i	−0.00798094	+	0.0138234i
$643$			0.700838i			0.0276384i	0.999905	+	0.0138192i	$0.00439892\pi$
$643$			0.700838i			0.0276384i	−0.999905	+	0.0138192i	$0.995601\pi$
$644$	1.57108	−	21.1573i	0.0619092	−	0.833714i
$645$	2.96604			0.116788
$646$	−26.7327	−	20.4437i	−1.05178	−	0.804345i
$647$	1.94439	+	3.36778i	0.0764417	+	0.132401i	0.901712	−	0.432337i	$-0.142311\pi$
$647$	1.94439	+	3.36778i	0.0764417	+	0.132401i	−0.825271	+	0.564737i	$0.808977\pi$
$648$	3.07136	+	5.31974i	0.120654	+	0.208979i
$649$	19.1035	+	11.0294i	0.749880	+	0.432943i
$650$	−0.757861			−0.0297257
$651$	−12.1447	+	17.8390i	−0.475989	+	0.699166i
$652$		−	2.16235i		−	0.0846844i
$653$	23.3201	+	13.4638i	0.912584	+	0.526881i	0.881262	−	0.472628i	$-0.156695\pi$
$653$	23.3201	+	13.4638i	0.912584	+	0.526881i	0.0313227	+	0.999509i	$0.490028\pi$
$654$	−5.30884	−	9.19519i	−0.207592	−	0.359560i
$655$	4.83177	+	8.36888i	0.188793	+	0.326999i
$656$	9.43253	+	5.44587i	0.368278	+	0.212626i
$657$		−	6.21025i		−	0.242285i
$658$	14.2107	+	29.4576i	0.553990	+	1.14838i
$659$	3.91848			0.152642			0.0763212	−	0.997083i	$-0.475683\pi$
$659$	3.91848			0.152642			0.0763212	+	0.997083i	$0.475683\pi$
$660$	−7.25169	−	4.18676i	−0.282271	−	0.162970i
$661$	16.0960	+	27.8791i	0.626062	+	1.08437i	0.988334	+	0.152299i	$0.0486676\pi$
$661$	16.0960	+	27.8791i	0.626062	+	1.08437i	−0.362273	+	0.932072i	$0.617999\pi$
$662$	1.23656	+	2.14179i	0.0480603	+	0.0832429i
$663$	2.84099	−	3.71495i	0.110335	−	0.144277i
$664$	−3.31908			−0.128805
$665$	19.4503	−	9.38305i	0.754251	−	0.363859i
$666$		−	7.49969i		−	0.290607i
$667$	−7.92348	+	13.7239i	−0.306798	+	0.531390i
$668$	−8.01358	+	4.62664i	−0.310055	+	0.179010i
$669$	−15.8279	+	9.13823i	−0.611941	+	0.353304i
$670$	6.39335	+	3.69120i	0.246997	+	0.142604i
$671$	−64.9220			−2.50628
$672$	−3.27330	−	2.22845i	−0.126270	−	0.0859642i
$673$			4.49772i			0.173375i	0.996236	+	0.0866873i	$0.0276281\pi$
$673$			4.49772i			0.173375i	−0.996236	+	0.0866873i	$0.972372\pi$
$674$	8.81711	+	5.09056i	0.339622	+	0.196081i
$675$	−4.87350	+	2.81372i	−0.187581	+	0.108300i
$676$	6.21282	+	10.7609i	0.238955	+	0.413882i
$677$	32.7628	+	18.9156i	1.25918	+	0.726986i	0.972914	−	0.231166i	$-0.0742540\pi$
$677$	32.7628	+	18.9156i	1.25918	+	0.726986i	0.286262	+	0.958151i	$0.407587\pi$
$678$	−4.11818			−0.158158
$679$	0.319262	−	4.29941i	0.0122521	−	0.164996i
$680$	−4.08870	−	0.531519i	−0.156795	−	0.0203828i
$681$	5.83985	−	10.1149i	0.223784	−	0.387604i
$682$	15.2452	+	26.4054i	0.583768	+	1.01112i
$683$	−10.0498	+	5.80228i	−0.384547	+	0.222018i	−0.679795	−	0.733403i	$-0.737931\pi$
$683$	−10.0498	+	5.80228i	−0.384547	+	0.222018i	0.295248	+	0.955421i	$0.404598\pi$
$684$	−3.10137	+	5.37174i	−0.118584	+	0.205393i
$685$			2.53368i			0.0968071i
$686$	−12.5693	+	13.6019i	−0.479898	+	0.519324i
$687$			2.16004i			0.0824106i
$688$	0.990868	−	1.71623i	0.0377765	−	0.0654308i
$689$	−1.72025	−	2.97956i	−0.0655363	−	0.113512i
$690$	10.3936	−	6.00075i	0.395678	−	0.228445i
$691$	13.2433	+	7.64600i	0.503798	+	0.290868i	0.730280	−	0.683147i	$-0.239389\pi$
$691$	13.2433	+	7.64600i	0.503798	+	0.290868i	−0.226483	+	0.974015i	$0.572723\pi$
$692$		−	2.00688i		−	0.0762902i
$693$	0.833000	−	11.2178i	0.0316431	−	0.426128i
$694$			5.19648i			0.197256i
$695$	8.92209	−	15.4535i	0.338434	−	0.586185i
$696$	1.47891	+	2.56154i	0.0560579	+	0.0970951i
$697$	−17.2530	−	41.4614i	−0.653503	−	1.57046i
$698$	−3.65478	+	6.33027i	−0.138336	+	0.239604i
$699$	19.7561			0.747245
$700$	1.48892	−	2.18703i	0.0562759	−	0.0826621i
$701$	25.2845			0.954983			0.477491	−	0.878636i	$-0.341546\pi$
$701$	25.2845			0.954983			0.477491	+	0.878636i	$0.341546\pi$
$702$	−3.69344	−	2.13241i	−0.139400	−	0.0804825i
$703$	−69.7605	+	40.2762i	−2.63107	+	1.51905i
$704$	−4.84516	+	2.79736i	−0.182609	+	0.105429i
$705$	−9.25086	+	16.0230i	−0.348407	+	0.603459i
$706$	−26.6244			−1.00202
$707$	−14.2485	−	29.5361i	−0.535871	−	1.11082i
$708$			5.90115i			0.221779i
$709$	−17.9473	−	10.3619i	−0.674024	−	0.389148i	0.123576	−	0.992335i	$-0.460564\pi$
$709$	−17.9473	−	10.3619i	−0.674024	−	0.389148i	−0.797600	+	0.603187i	$0.793897\pi$
$710$	6.05814	+	10.4930i	0.227358	+	0.393795i
$711$	−4.99383	+	2.88319i	−0.187283	+	0.108128i
$712$	−3.41890	+	5.92171i	−0.128129	+	0.221925i
$713$	−43.7008			−1.63661
$714$	5.13909	+	15.4970i	0.192326	+	0.579962i
$715$	4.24001			0.158567
$716$	−6.00255	+	10.3967i	−0.224326	+	0.388543i
$717$	4.92524	−	2.84359i	0.183936	−	0.106196i
$718$	−13.5013	−	23.3849i	−0.503864	−	0.872718i
$719$	−6.42865	−	3.71158i	−0.239748	−	0.138419i	0.375313	−	0.926898i	$-0.377535\pi$
$719$	−6.42865	−	3.71158i	−0.239748	−	0.138419i	−0.615061	+	0.788479i	$0.710869\pi$
$720$			0.759931i			0.0283210i
$721$	11.3849	−	16.7229i	0.423994	−	0.622793i
$722$	47.6223			1.77232
$723$	17.4115	−	30.1576i	0.647540	−	1.12157i
$724$	−0.809295	+	0.467247i	−0.0300772	+	0.0173651i
$725$	−1.71148	+	0.988122i	−0.0635627	+	0.0366979i
$726$	26.3132	+	15.1920i	0.976576	+	0.563826i
$727$	−1.28840			−0.0477841			−0.0238920	−	0.999715i	$-0.507606\pi$
$727$	−1.28840			−0.0477841			−0.0238920	+	0.999715i	$0.507606\pi$
$728$	1.99961	+	0.148485i	0.0741103	+	0.00550322i
$729$	−29.9356			−1.10872
$730$	−4.08606	+	7.07727i	−0.151232	+	0.261941i
$731$	−7.54383	+	3.13915i	−0.279019	+	0.116106i
$732$	−8.68390	−	15.0410i	−0.320966	−	0.555930i
$733$	−12.6812	+	21.9645i	−0.468392	+	0.811278i	−0.999347	−	0.0361215i	$-0.988500\pi$
$733$	−12.6812	+	21.9645i	−0.468392	+	0.811278i	0.530956	+	0.847400i	$0.321833\pi$
$734$		−	5.15157i		−	0.190148i
$735$	−10.3619	−	1.54742i	−0.382204	−	0.0570775i
$736$		−	8.01872i		−	0.295574i
$737$	−35.7689	−	20.6512i	−1.31757	−	0.760697i
$738$	−7.16807	+	4.13849i	−0.263860	+	0.152340i
$739$	27.1482	+	47.0220i	0.998662	+	1.72973i	0.544113	+	0.839012i	$0.316866\pi$
$739$	27.1482	+	47.0220i	0.998662	+	1.72973i	0.454549	+	0.890722i	$0.349801\pi$
$740$	−4.93445	+	8.54672i	−0.181394	+	0.314184i
$741$			9.25827i			0.340111i
$742$	11.9781	+	0.889458i	0.439729	+	0.0326530i
$743$			16.1785i			0.593530i	0.954951	+	0.296765i	$0.0959078\pi$
$743$			16.1785i			0.593530i	−0.954951	+	0.296765i	$0.904092\pi$
$744$	−4.07836	+	7.06392i	−0.149520	+	0.258976i
$745$	17.9645	−	10.3718i	0.658168	−	0.379994i
$746$	2.78675	+	4.82680i	0.102030	+	0.176722i
$747$	1.26114	−	2.18435i	0.0461426	−	0.0799213i
$748$	22.8751	+	2.97370i	0.836397	+	0.108729i
$749$	0.590985	+	0.402340i	0.0215941	+	0.0147012i
$750$	1.49669			0.0546512
$751$	27.0394	+	15.6112i	0.986682	+	0.569661i	0.904281	−	0.426938i	$-0.140408\pi$
$751$	27.0394	+	15.6112i	0.986682	+	0.569661i	0.0824009	+	0.996599i	$0.473741\pi$
$752$	6.18089	+	10.7056i	0.225394	+	0.390394i
$753$	14.3835	−	8.30429i	0.524162	−	0.302625i
$754$	−1.29706	−	0.748859i	−0.0472362	−	0.0272718i
$755$			12.3276i			0.448647i
$756$	13.4100	−	6.46911i	0.487715	−	0.235279i
$757$	0.668327			0.0242908			0.0121454	−	0.999926i	$-0.496134\pi$
$757$	0.668327			0.0242908			0.0121454	+	0.999926i	$0.496134\pi$
$758$	−14.9972	−	8.65862i	−0.544722	−	0.314495i
$759$	−58.1492	+	33.5725i	−2.11068	+	1.21860i
$760$	7.06872	−	4.08113i	0.256409	−	0.148038i
$761$	3.81452	−	6.60694i	0.138276	−	0.239502i	−0.788568	−	0.614948i	$-0.789177\pi$
$761$	3.81452	−	6.60694i	0.138276	−	0.239502i	0.926844	+	0.375446i	$0.122510\pi$
$762$		−	12.0657i		−	0.437095i
$763$	−16.9050	+	8.15517i	−0.612003	+	0.295237i
$764$	−3.62289			−0.131072
$765$	1.90337	−	2.48890i	0.0688165	−	0.0899862i
$766$	−13.9955	−	24.2408i	−0.505676	−	0.875857i
$767$	−1.49405	−	2.58777i	−0.0539470	−	0.0934390i
$768$	−1.29617	−	0.748343i	−0.0467714	−	0.0270035i
$769$	−14.9761			−0.540050			−0.270025	−	0.962853i	$-0.587032\pi$
$769$	−14.9761			−0.540050			−0.270025	+	0.962853i	$0.587032\pi$
$770$	−8.33008	+	12.2358i	−0.300195	+	0.440948i
$771$			8.34276i			0.300457i
$772$	−14.0996	−	8.14040i	−0.507455	−	0.292979i
$773$	−2.22528	−	3.85429i	−0.0800376	−	0.138629i	0.823228	−	0.567711i	$-0.192171\pi$
$773$	−2.22528	−	3.85429i	−0.0800376	−	0.138629i	−0.903266	+	0.429081i	$0.858837\pi$
$774$	0.752991	+	1.30422i	0.0270657	+	0.0468792i
$775$	−4.71971	−	2.72493i	−0.169537	−	0.0978822i
$776$		−	1.62950i		−	0.0584955i
$777$	38.9722	+	2.89396i	1.39812	+	0.103820i
$778$	23.8294			0.854324
$779$	76.9906	+	44.4506i	2.75848	+	1.59261i
$780$	0.567140	+	0.982315i	0.0203069	+	0.0351725i
$781$	−33.8935	−	58.7053i	−1.21281	−	2.10064i
$782$	−20.0842	+	26.2626i	−0.718209	+	0.939149i
$783$	−11.1212			−0.397439
$784$	−4.35700	+	5.47874i	−0.155607	+	0.195669i
$785$		−	1.10654i		−	0.0394941i
$786$	7.23165	−	12.5256i	0.257944	−	0.446773i
$787$	−13.9567	+	8.05789i	−0.497502	+	0.287233i	−0.727681	−	0.685915i	$-0.759402\pi$
$787$	−13.9567	+	8.05789i	−0.497502	+	0.287233i	0.230179	+	0.973148i	$0.426069\pi$
$788$	−17.2007	+	9.93081i	−0.612748	+	0.353770i
$789$	15.4239	+	8.90499i	0.549105	+	0.317026i
$790$	7.58803			0.269970
$791$	−0.539098	+	7.25988i	−0.0191681	+	0.258131i
$792$		−	4.25159i		−	0.151074i
$793$	7.61613	+	4.39717i	0.270457	+	0.156148i
$794$	17.3258	−	10.0030i	0.614869	−	0.354995i
$795$	3.39729	+	5.88428i	0.120490	+	0.208694i
$796$	−1.25080	−	0.722149i	−0.0443334	−	0.0255959i
$797$	−14.7782			−0.523472			−0.261736	−	0.965140i	$-0.584295\pi$
$797$	−14.7782			−0.523472			−0.261736	+	0.965140i	$0.584295\pi$
$798$	−26.7175	−	18.1891i	−0.945790	−	0.643889i
$799$	6.57053	−	50.5437i	0.232449	−	1.78811i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−2.59813	−	4.50009i	−0.0918003	−	0.159003i
$802$	19.0441	−	10.9951i	0.672471	−	0.388252i
$803$	22.8603	−	39.5953i	0.806724	−	1.39729i
$804$		−	11.0491i		−	0.389673i
$805$	−9.21805	−	19.1083i	−0.324894	−	0.673479i
$806$		−	4.13023i		−	0.145481i
$807$	5.98905	−	10.3733i	0.210825	−	0.365159i
$808$	−6.19735	−	10.7341i	−0.218022	−	0.377625i
$809$	−48.4119	+	27.9506i	−1.70207	+	0.982692i	−0.758414	+	0.651773i	$0.774026\pi$
$809$	−48.4119	+	27.9506i	−1.70207	+	0.982692i	−0.943659	+	0.330920i	$0.892641\pi$
$810$	5.31974	+	3.07136i	0.186917	+	0.107916i
$811$		−	36.2727i		−	1.27371i	−0.770985	−	0.636854i	$-0.780236\pi$
$811$		−	36.2727i		−	1.27371i	0.770985	−	0.636854i	$-0.219764\pi$
$812$	4.70931	−	2.27182i	0.165264	−	0.0797254i
$813$		−	6.02092i		−	0.211163i
$814$	27.6068	−	47.8164i	0.967619	−	1.67596i
$815$	−1.08118	−	1.87265i	−0.0378720	−	0.0655962i
$816$	2.37081	+	5.69740i	0.0829951	+	0.199449i
$817$	8.08771	−	14.0083i	0.282953	−	0.490089i
$818$	31.2083			1.09117
$819$	−0.857502	+	1.25956i	−0.0299635	+	0.0440126i
$820$	10.8917			0.380356
$821$	−16.3954	−	9.46590i	−0.572204	−	0.330362i	0.185825	−	0.982583i	$-0.440504\pi$
$821$	−16.3954	−	9.46590i	−0.572204	−	0.330362i	−0.758029	+	0.652221i	$0.773838\pi$
$822$	3.28408	−	1.89607i	0.114545	−	0.0661329i
$823$	−1.47574	+	0.852017i	−0.0514410	+	0.0296995i	−0.525500	−	0.850794i	$-0.676122\pi$
$823$	−1.47574	+	0.852017i	−0.0514410	+	0.0296995i	0.474059	+	0.880493i	$0.342788\pi$
$824$	3.82319	−	6.62196i	0.133187	−	0.230687i
$825$	−8.37352			−0.291529
$826$	10.4031	+	0.772501i	0.361968	+	0.0268787i
$827$		−	52.5283i		−	1.82659i	−0.407301	−	0.913294i	$-0.633530\pi$
$827$		−	52.5283i		−	1.82659i	0.407301	−	0.913294i	$-0.366470\pi$
$828$	5.27728	+	3.04684i	0.183398	+	0.105885i
$829$	15.8799	+	27.5048i	0.551532	+	0.955282i	0.998164	+	0.0605640i	$0.0192899\pi$
$829$	15.8799	+	27.5048i	0.551532	+	0.955282i	−0.446632	+	0.894718i	$0.647377\pi$
$830$	−2.87441	+	1.65954i	−0.0997722	+	0.0576035i
$831$	12.8482	−	22.2537i	0.445698	−	0.771971i
$832$	0.757861			0.0262741
$833$	27.9922	−	7.03096i	0.969874	−	0.243608i
$834$	−26.7071			−0.924792
$835$	−4.62664	+	8.01358i	−0.160112	+	0.277321i
$836$	−39.5474	+	22.8327i	−1.36778	+	0.789686i
$837$	−15.3343	−	26.5599i	−0.530033	−	0.918043i
$838$	−13.2450	−	7.64701i	−0.457541	−	0.264162i
$839$			41.3871i			1.42884i	0.699717	+	0.714420i	$0.253309\pi$
$839$			41.3871i			1.42884i	−0.699717	+	0.714420i	$0.746691\pi$
$840$	−3.94899	−	0.293240i	−0.136253	−	0.0101178i
$841$	25.0945			0.865326
$842$	1.81285	−	3.13995i	0.0624750	−	0.108210i
$843$	−5.23470	+	3.02226i	−0.180293	+	0.104092i
$844$	3.84831	−	2.22182i	0.132464	−	0.0764783i
$845$	10.7609	+	6.21282i	0.370187	+	0.213728i
$846$	−9.39410			−0.322976
$847$	30.2263	−	44.3985i	1.03859	−	1.52555i
$848$	4.53975			0.155896
$849$	24.0921	−	41.7287i	0.826837	−	1.43212i
$850$	−3.80668	+	1.58404i	−0.130568	+	0.0543322i
$851$	39.5680	+	68.5338i	1.35637	+	2.34931i
$852$	9.06713	−	15.7047i	0.310635	−	0.538035i
$853$			17.1859i			0.588435i	0.955738	+	0.294218i	$0.0950590\pi$
$853$			17.1859i			0.588435i	−0.955738	+	0.294218i	$0.904941\pi$
$854$	−27.6523	+	13.3398i	−0.946241	+	0.456477i
$855$			6.20275i			0.212129i
$856$	0.234019	+	0.135111i	0.00799862	+	0.00461800i
$857$	1.71203	−	0.988439i	0.0584817	−	0.0337644i	−0.470474	−	0.882414i	$-0.655917\pi$
$857$	1.71203	−	0.988439i	0.0584817	−	0.0337644i	0.528956	+	0.848649i	$0.322584\pi$
$858$	−3.17298	−	5.49577i	−0.108324	−	0.187622i
$859$	26.3524	−	45.6437i	0.899132	−	1.55734i	0.0705255	−	0.997510i	$-0.477532\pi$
$859$	26.3524	−	45.6437i	0.899132	−	1.55734i	0.828606	−	0.559832i	$-0.189134\pi$
$860$		−	1.98174i		−	0.0675766i
$861$	−18.7397	−	38.8459i	−0.638646	−	1.32386i
$862$			4.84313i			0.164958i
$863$	−14.3099	+	24.7855i	−0.487115	+	0.843708i	−0.999890	−	0.0148147i	$-0.995284\pi$
$863$	−14.3099	+	24.7855i	−0.487115	+	0.843708i	0.512775	+	0.858523i	$0.328617\pi$
$864$	4.87350	−	2.81372i	0.165800	−	0.0957246i
$865$	−1.00344	−	1.73801i	−0.0341180	−	0.0590941i
$866$	−9.04031	+	15.6583i	−0.307202	+	0.532090i
$867$	6.50527	−	24.5980i	0.220931	−	0.835392i
$868$	11.9190	+	8.11440i	0.404558	+	0.275421i
$869$	−42.4528			−1.44011
$870$	2.56154	+	1.47891i	0.0868445	+	0.0501397i
$871$	2.79742	+	4.84527i	0.0947868	+	0.164176i
$872$	−6.14370	+	3.54707i	−0.208052	+	0.120119i
$873$	1.07240	+	0.619153i	0.0362954	+	0.0209551i
$874$		−	65.4508i		−	2.21391i
$875$	0.195927	−	2.63849i	0.00662353	−	0.0891971i
$876$	12.2311			0.413251
$877$	4.34481	+	2.50848i	0.146714	+	0.0847053i	0.571560	−	0.820560i	$-0.306338\pi$
$877$	4.34481	+	2.50848i	0.146714	+	0.0847053i	−0.424846	+	0.905266i	$0.639672\pi$
$878$	33.3159	−	19.2350i	1.12436	−	0.649149i
$879$	28.5518	−	16.4844i	0.963029	−	0.556005i
$880$	−2.79736	+	4.84516i	−0.0942988	+	0.163330i
$881$			10.5538i			0.355566i	0.984070	+	0.177783i	$0.0568925\pi$
$881$			10.5538i			0.355566i	−0.984070	+	0.177783i	$0.943108\pi$
$882$	−1.95016	−	4.94916i	−0.0656652	−	0.166647i
$883$	44.1941			1.48725			0.743625	−	0.668597i	$-0.233105\pi$
$883$	44.1941			1.48725			0.743625	+	0.668597i	$0.233105\pi$
$884$	−2.48212	−	1.89818i	−0.0834826	−	0.0638428i
$885$	2.95057	+	5.11054i	0.0991825	+	0.171789i
$886$	15.5424	+	26.9203i	0.522158	+	0.904404i
$887$	38.6563	+	22.3182i	1.29795	+	0.749373i	0.980050	−	0.198751i	$-0.0636884\pi$
$887$	38.6563	+	22.3182i	1.29795	+	0.749373i	0.317902	+	0.948124i	$0.397022\pi$
$888$	14.7706			0.495671
$889$	−21.2705	−	1.57948i	−0.713389	−	0.0529742i
$890$			6.83780i			0.229204i
$891$	−29.7624	−	17.1833i	−0.997079	−	0.575664i
$892$	6.10564	+	10.5753i	0.204432	+	0.354087i
$893$	50.4500	+	87.3819i	1.68824	+	2.92413i
$894$	−26.8872	−	15.5233i	−0.899243	−	0.519178i
$895$			12.0051i			0.401286i
$896$	−1.48892	+	2.18703i	−0.0497414	+	0.0730637i
$897$	9.09547			0.303689
$898$	−0.573553	−	0.331141i	−0.0191397	−	0.0110503i
$899$	−5.38512	−	9.32730i	−0.179604	−	0.311083i
$900$	0.379966	+	0.658120i	0.0126655	+	0.0219373i
$901$	−14.8684	−	11.3705i	−0.495339	−	0.378808i
$902$	−60.9362			−2.02895
$903$	−7.06794	+	3.40965i	−0.235206	+	0.113466i
$904$			2.75153i			0.0915145i
$905$	−0.467247	+	0.809295i	−0.0155318	+	0.0269019i
$906$	15.9786	−	9.22526i	0.530854	−	0.306489i
$907$	31.4228	−	18.1420i	1.04338	−	0.602394i	0.122589	−	0.992458i	$-0.460880\pi$
$907$	31.4228	−	18.1420i	1.04338	−	0.602394i	0.920788	+	0.390063i	$0.127547\pi$
$908$	−6.75821	−	3.90185i	−0.224279	−	0.129488i
$909$	9.41912			0.312412
$910$	1.80595	−	0.871211i	0.0598667	−	0.0288804i
$911$		−	15.1508i		−	0.501967i	−0.967991	−	0.250984i	$-0.919246\pi$
$911$		−	15.1508i		−	0.501967i	0.967991	−	0.250984i	$-0.0807541\pi$
$912$	−10.5796	−	6.10816i	−0.350327	−	0.202261i
$913$	16.0815	−	9.28465i	0.532219	−	0.307277i
$914$	16.8463	+	29.1787i	0.557227	+	0.965145i
$915$	−15.0410	−	8.68390i	−0.497239	−	0.287081i
$916$	1.44321			0.0476851
$917$	−21.1345	−	14.3883i	−0.697923	−	0.475142i
$918$	−23.0089	−	2.99109i	−0.759407	−	0.0987207i
$919$	−7.53698	+	13.0544i	−0.248622	+	0.430626i	−0.963144	−	0.268987i	$-0.913311\pi$
$919$	−7.53698	+	13.0544i	−0.248622	+	0.430626i	0.714522	+	0.699613i	$0.246644\pi$
$920$	−4.00936	−	6.94442i	−0.132185	−	0.228951i
$921$	−8.94944	+	5.16696i	−0.294894	+	0.170257i
$922$	−7.33909	+	12.7117i	−0.241700	+	0.418637i
$923$			9.18245i			0.302244i
$924$	22.0934	+	1.64060i	0.726821	+	0.0539716i
$925$			9.86890i			0.324488i
$926$	−14.8603	+	25.7387i	−0.488338	+	0.845827i
$927$	2.90536	+	5.03223i	0.0954245	+	0.165280i
$928$	1.71148	−	0.988122i	0.0561820	−	0.0324367i
$929$	28.8962	+	16.6832i	0.948052	+	0.547358i	0.892475	−	0.451096i	$-0.148967\pi$
$929$	28.8962	+	16.6832i	0.948052	+	0.547358i	0.0555770	+	0.998454i	$0.482300\pi$
$930$			8.15672i			0.267469i
$931$	−35.5629	+	44.7188i	−1.16553	+	1.46560i
$932$		−	13.1999i		−	0.432377i
$933$	8.35638	−	14.4737i	0.273576	−	0.473847i
$934$	−1.48936	−	2.57965i	−0.0487334	−	0.0844087i
$935$	21.2973	−	8.86226i	0.696495	−	0.289827i
$936$	−0.287961	+	0.498763i	−0.00941230	+	0.0163026i
$937$	23.6977			0.774169			0.387084	−	0.922044i	$-0.373482\pi$
$937$	23.6977			0.774169			0.387084	+	0.922044i	$0.373482\pi$
$938$	−19.4784	−	1.44641i	−0.635991	−	0.0472269i
$939$	−21.8810			−0.714059
$940$	10.7056	+	6.18089i	0.349179	+	0.201598i
$941$	37.8427	−	21.8485i	1.23364	−	0.712241i	0.265851	−	0.964014i	$-0.414347\pi$
$941$	37.8427	−	21.8485i	1.23364	−	0.712241i	0.967786	+	0.251773i	$0.0810136\pi$
$942$	−1.43426	+	0.828072i	−0.0467308	+	0.0269800i
$943$	43.6689	−	75.6368i	1.42206	−	2.46307i
$944$	3.94281			0.128328
$945$	8.37881	−	12.3074i	0.272563	−	0.400359i
$946$			11.0872i			0.360477i
$947$	−2.20134	−	1.27094i	−0.0715338	−	0.0413001i	0.463806	−	0.885937i	$-0.346483\pi$
$947$	−2.20134	−	1.27094i	−0.0715338	−	0.0413001i	−0.535340	+	0.844636i	$0.679817\pi$
$948$	−5.67845	−	9.83536i	−0.184427	−	0.319438i
$949$	−5.36358	+	3.09667i	−0.174109	+	0.100522i
$950$	4.08113	−	7.06872i	0.132409	−	0.229339i
$951$	−42.2554			−1.37023
$952$	10.3542	−	3.43364i	0.335583	−	0.111285i
$953$	11.4238			0.370054			0.185027	−	0.982733i	$-0.440763\pi$
$953$	11.4238			0.370054			0.185027	+	0.982733i	$0.440763\pi$
$954$	−1.72495	+	2.98770i	−0.0558473	+	0.0967304i
$955$	−3.13751	+	1.81144i	−0.101528	+	0.0586170i
$956$	−1.89992	−	3.29076i	−0.0614479	−	0.106431i
$957$	−14.3311	−	8.27407i	−0.463259	−	0.267463i
$958$			20.2436i			0.654040i
$959$	−2.91264	−	6.03767i	−0.0940540	−	0.194967i
$960$	−1.49669			−0.0483053
$961$	−0.649555	+	1.12506i	−0.0209534	+	0.0362923i
$962$	−6.47722	+	3.73963i	−0.208834	+	0.120570i
$963$	−0.177839	+	0.102675i	−0.00573077	+	0.00330866i
$964$	−20.1496	−	11.6334i	−0.648974	−	0.374685i
$965$	−16.2808			−0.524098
$966$	−17.8693	+	26.2477i	−0.574935	+	0.844506i
$967$	−33.8972			−1.09006			−0.545030	−	0.838417i	$-0.683482\pi$
$967$	−33.8972			−1.09006			−0.545030	+	0.838417i	$0.683482\pi$
$968$	10.1504	−	17.5810i	0.326246	−	0.565075i
$969$	19.3512	+	46.5036i	0.621649	+	1.49391i
$970$	−0.814748	−	1.41119i	−0.0261600	−	0.0453104i
$971$	−6.12925	+	10.6162i	−0.196697	+	0.340689i	−0.947456	−	0.319888i	$-0.896355\pi$
$971$	−6.12925	+	10.6162i	−0.196697	+	0.340689i	0.750758	+	0.660577i	$0.229688\pi$
$972$			7.68860i			0.246612i
$973$	−3.49615	+	47.0816i	−0.112081	+	1.50937i
$974$		−	4.99442i		−	0.160032i
$975$	0.982315	+	0.567140i	0.0314593	+	0.0181630i
$976$	−10.0495	+	5.80208i	−0.321677	+	0.185720i
$977$	−14.6265	−	25.3339i	−0.467945	−	0.810504i	0.531384	−	0.847131i	$-0.321672\pi$
$977$	−14.6265	−	25.3339i	−0.467945	−	0.810504i	−0.999329	+	0.0366271i	$0.988339\pi$
$978$	−1.61818	+	2.80278i	−0.0517438	+	0.0896229i
$979$		−	38.2555i		−	1.22265i
$980$	−1.03390	+	6.92323i	−0.0330267	+	0.221154i
$981$		−	5.39105i		−	0.172123i
$982$	7.48450	−	12.9635i	0.238840	−	0.413683i
$983$	53.9186	−	31.1299i	1.71974	−	0.992890i	0.800350	−	0.599533i	$-0.204647\pi$
$983$	53.9186	−	31.1299i	1.71974	−	0.992890i	0.919386	−	0.393357i	$-0.128686\pi$
$984$	−8.15076	−	14.1175i	−0.259837	−	0.450050i
$985$	−9.93081	+	17.2007i	−0.316422	+	0.548059i
$986$	−8.08028	−	1.05041i	−0.257328	−	0.0334519i
$987$	3.62498	−	48.8165i	0.115384	−	1.55385i
$988$	6.18585			0.196798
$989$	−13.7620	−	7.94549i	−0.437606	−	0.252652i
$990$	−2.12580	−	3.68199i	−0.0675623	−	0.117021i
$991$	−23.9261	+	13.8137i	−0.760036	+	0.438807i	−0.829309	−	0.558791i	$-0.811266\pi$
$991$	−23.9261	+	13.8137i	−0.760036	+	0.438807i	0.0692726	+	0.997598i	$0.477932\pi$
$992$	4.71971	+	2.72493i	0.149851	+	0.0865165i
$993$		−	3.70149i		−	0.117463i
$994$	−26.4987	−	18.0402i	−0.840488	−	0.572200i
$995$	−1.44430			−0.0457873
$996$	4.30209	+	2.48381i	0.136317	+	0.0787026i
$997$	2.18039	−	1.25885i	0.0690535	−	0.0398681i	−0.465076	−	0.885271i	$-0.653973\pi$
$997$	2.18039	−	1.25885i	0.0690535	−	0.0398681i	0.534129	+	0.845403i	$0.320640\pi$
$998$	−25.7514	+	14.8676i	−0.815148	+	0.470626i
$999$	−27.7683	+	48.0961i	−0.878550	+	1.52169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1190.2.ba.a.611.17	yes	48
7.4	even	3	inner	1190.2.ba.a.781.8	yes	48
17.16	even	2	inner	1190.2.ba.a.611.8	✓	48
119.67	even	6	inner	1190.2.ba.a.781.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.ba.a.611.8	✓	48	17.16	even	2	inner
1190.2.ba.a.611.17	yes	48	1.1	even	1	trivial
1190.2.ba.a.781.8	yes	48	7.4	even	3	inner
1190.2.ba.a.781.17	yes	48	119.67	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.29617 - 0.748343i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.49669i q^{6} +(2.63849 + 0.195927i) q^{7} +1.00000 q^{8} +(-0.379966 + 0.658120i) q^{9} +(0.866025 - 0.500000i) q^{10} +(-4.84516 + 2.79736i) q^{11} +(-1.29617 - 0.748343i) q^{12} +0.757861 q^{13} +(-1.48892 + 2.18703i) q^{14} -1.49669 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.80668 - 1.58404i) q^{17} +(-0.379966 - 0.658120i) q^{18} +(-4.08113 + 7.06872i) q^{19} +1.00000i q^{20} +(3.56654 - 1.72054i) q^{21} -5.59471i q^{22} +(6.94442 + 4.00936i) q^{23} +(1.29617 - 0.748343i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.378930 + 0.656327i) q^{26} +5.62744i q^{27} +(-1.14957 - 2.38296i) q^{28} +1.97624i q^{29} +(0.748343 - 1.29617i) q^{30} +(-4.71971 + 2.72493i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.18676 + 7.25169i) q^{33} +(-0.531519 + 4.08870i) q^{34} +(-2.18703 - 1.48892i) q^{35} +0.759931 q^{36} +(8.54672 + 4.93445i) q^{37} +(-4.08113 - 7.06872i) q^{38} +(0.982315 - 0.567140i) q^{39} +(-0.866025 - 0.500000i) q^{40} -10.8917i q^{41} +(-0.293240 + 3.94899i) q^{42} -1.98174 q^{43} +(4.84516 + 2.79736i) q^{44} +(0.658120 - 0.379966i) q^{45} +(-6.94442 + 4.00936i) q^{46} +(6.18089 - 10.7056i) q^{47} +1.49669i q^{48} +(6.92323 + 1.03390i) q^{49} -1.00000 q^{50} +(3.74869 - 4.90189i) q^{51} +(-0.378930 - 0.656327i) q^{52} +(-2.26988 - 3.93154i) q^{53} +(-4.87350 - 2.81372i) q^{54} +5.59471 q^{55} +(2.63849 + 0.195927i) q^{56} +12.2163i q^{57} +(-1.71148 - 0.988122i) q^{58} +(-1.97140 - 3.41457i) q^{59} +(0.748343 + 1.29617i) q^{60} +(10.0495 + 5.80208i) q^{61} -5.44985i q^{62} +(-1.13148 + 1.66199i) q^{63} +1.00000 q^{64} +(-0.656327 - 0.378930i) q^{65} +(-4.18676 - 7.25169i) q^{66} +(3.69120 + 6.39335i) q^{67} +(-3.27516 - 2.50466i) q^{68} +12.0015 q^{69} +(2.38296 - 1.14957i) q^{70} +12.1163i q^{71} +(-0.379966 + 0.658120i) q^{72} +(-7.07727 + 4.08606i) q^{73} +(-8.54672 + 4.93445i) q^{74} +(1.29617 + 0.748343i) q^{75} +8.16225 q^{76} +(-13.3320 + 6.43149i) q^{77} +1.13428i q^{78} +(6.57142 + 3.79401i) q^{79} +(0.866025 - 0.500000i) q^{80} +(3.07136 + 5.31974i) q^{81} +(9.43253 + 5.44587i) q^{82} -3.31908 q^{83} +(-3.27330 - 2.22845i) q^{84} +(-4.08870 - 0.531519i) q^{85} +(0.990868 - 1.71623i) q^{86} +(1.47891 + 2.56154i) q^{87} +(-4.84516 + 2.79736i) q^{88} +(-3.41890 + 5.92171i) q^{89} +0.759931i q^{90} +(1.99961 + 0.148485i) q^{91} -8.01872i q^{92} +(-4.07836 + 7.06392i) q^{93} +(6.18089 + 10.7056i) q^{94} +(7.06872 - 4.08113i) q^{95} +(-1.29617 - 0.748343i) q^{96} -1.62950i q^{97} +(-4.35700 + 5.47874i) q^{98} -4.25159i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 16 q^{9} - 16 q^{13} - 8 q^{15} - 24 q^{16} - 6 q^{17} + 16 q^{18} + 16 q^{19} + 68 q^{21} + 24 q^{25} + 8 q^{26} + 4 q^{30} - 24 q^{32} + 20 q^{33} + 12 q^{34} - 4 q^{35}+ \cdots + 12 q^{94}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 16 * q^9 - 16 * q^13 - 8 * q^15 - 24 * q^16 - 6 * q^17 + 16 * q^18 + 16 * q^19 + 68 * q^21 + 24 * q^25 + 8 * q^26 + 4 * q^30 - 24 * q^32 + 20 * q^33 + 12 * q^34 - 4 * q^35 - 32 * q^36 + 16 * q^38 - 40 * q^42 - 40 * q^43 + 12 * q^47 - 12 * q^49 - 48 * q^50 + 20 * q^51 + 8 * q^52 + 24 * q^53 + 40 * q^55 + 20 * q^59 + 4 * q^60 + 48 * q^64 + 20 * q^66 + 48 * q^67 - 6 * q^68 + 24 * q^69 + 8 * q^70 + 16 * q^72 - 32 * q^76 - 12 * q^77 - 64 * q^81 - 56 * q^83 - 28 * q^84 + 12 * q^85 + 20 * q^86 + 8 * q^87 - 24 * q^89 + 36 * q^93 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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