LMFDB - Embedded newform 363.2.f.i.161.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.8
Character	$\chi$	$=$	363.161
Dual form			363.2.f.i.239.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93692 + 1.40726i) q^{2} +(1.72318 + 0.175035i) q^{3} +(1.15327 + 3.54939i) q^{4} +(-0.728450 - 1.00263i) q^{5} +(3.09136 + 2.76399i) q^{6} +(-2.68999 + 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(2.93873 + 0.603233i) q^{9} +O(q^{10})$	\(q+(1.93692 + 1.40726i) q^{2} +(1.72318 + 0.175035i) q^{3} +(1.15327 + 3.54939i) q^{4} +(-0.728450 - 1.00263i) q^{5} +(3.09136 + 2.76399i) q^{6} +(-2.68999 + 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(2.93873 + 0.603233i) q^{9} -2.96713i q^{10} +(1.36603 + 6.31812i) q^{12} +(1.96677 - 2.70702i) q^{13} +(-6.44030 - 2.09258i) q^{14} +(-1.07976 - 1.85521i) q^{15} +(-1.99350 + 1.44836i) q^{16} +(-3.35485 + 2.43744i) q^{17} +(4.84318 + 5.30396i) q^{18} +(-2.32960 - 0.756934i) q^{19} +(2.71861 - 3.74185i) q^{20} +(-4.78834 + 1.03528i) q^{21} +(-2.89847 + 6.57171i) q^{24} +(1.07047 - 3.29456i) q^{25} +(7.61896 - 2.47555i) q^{26} +(4.95838 + 1.55386i) q^{27} +(-6.20456 - 8.53985i) q^{28} +(-1.67792 - 5.16410i) q^{29} +(0.519350 - 5.11291i) q^{30} +(-0.158691 - 0.115296i) q^{31} +2.39417 q^{32} -9.92820 q^{34} +(2.83585 + 2.06037i) q^{35} +(1.24802 + 11.1264i) q^{36} +(-3.23359 - 9.95195i) q^{37} +(-3.44706 - 4.74448i) q^{38} +(3.86293 - 4.32045i) q^{39} +(4.88769 - 1.58811i) q^{40} +(-2.21952 + 6.83097i) q^{41} +(-10.7316 - 4.73318i) q^{42} +4.24264i q^{43} +(-1.53590 - 3.38587i) q^{45} +(3.22015 + 1.04629i) q^{47} +(-3.68868 + 2.14686i) q^{48} +(0.809017 - 0.587785i) q^{49} +(6.70970 - 4.87488i) q^{50} +(-6.20766 + 3.61295i) q^{51} +(11.8765 + 3.85891i) q^{52} +(-4.17551 + 5.74710i) q^{53} +(7.41732 + 9.98743i) q^{54} -11.7290i q^{56} +(-3.88185 - 1.71210i) q^{57} +(4.01722 - 12.3637i) q^{58} +(-12.0178 + 3.90481i) q^{59} +(5.33962 - 5.97205i) q^{60} +(2.65681 + 3.65679i) q^{61} +(-0.145121 - 0.446637i) q^{62} +(-8.43240 + 0.945846i) q^{63} +(8.62433 + 6.26594i) q^{64} -4.14682 q^{65} +2.00000 q^{67} +(-12.5205 - 9.09666i) q^{68} +(2.59336 + 7.98156i) q^{70} +(4.90396 + 6.74973i) q^{71} +(-6.14487 + 10.8169i) q^{72} +(7.70959 - 2.50500i) q^{73} +(7.74175 - 23.8267i) q^{74} +(2.42127 - 5.48976i) q^{75} -9.14162i q^{76} +(13.5622 - 2.93225i) q^{78} +(4.31932 - 5.94504i) q^{79} +(2.90433 + 0.943674i) q^{80} +(8.27222 + 3.54547i) q^{81} +(-13.9120 + 10.1076i) q^{82} +(-12.0015 + 8.71958i) q^{83} +(-9.19684 - 15.8017i) q^{84} +(4.88769 + 1.58811i) q^{85} +(-5.97049 + 8.21767i) q^{86} +(-1.98747 - 9.19239i) q^{87} +9.58244i q^{89} +(1.78987 - 8.71958i) q^{90} +(-2.92457 + 9.00090i) q^{91} +(-0.253272 - 0.226452i) q^{93} +(4.76479 + 6.55817i) q^{94} +(0.938079 + 2.88711i) q^{95} +(4.12560 + 0.419062i) q^{96} +(-1.83481 - 1.33307i) q^{97} +2.39417 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9}+O(q^{10}) $ 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9	$ 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9} + 16 q^{12} - 4 q^{15} + 8 q^{16} + 4 q^{27} + 40 q^{31} - 96 q^{34} + 40 q^{36} + 56 q^{37} - 64 q^{42} - 160 q^{45} - 28 q^{48} + 8 q^{49} - 104 q^{58} + 28 q^{60} + 16 q^{64} + 64 q^{67} + 16 q^{70} - 24 q^{75} + 240 q^{78} + 8 q^{81} - 96 q^{82} + 48 q^{91} - 56 q^{93} - 32 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9 + 16 * q^12 - 4 * q^15 + 8 * q^16 + 4 * q^27 + 40 * q^31 - 96 * q^34 + 40 * q^36 + 56 * q^37 - 64 * q^42 - 160 * q^45 - 28 * q^48 + 8 * q^49 - 104 * q^58 + 28 * q^60 + 16 * q^64 + 64 * q^67 + 16 * q^70 - 24 * q^75 + 240 * q^78 + 8 * q^81 - 96 * q^82 + 48 * q^91 - 56 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	1.93692	+	1.40726i	1.36961	+	0.995082i	0.997767	+	0.0667868i	$0.0212747\pi$
$2$	1.93692	+	1.40726i	1.36961	+	0.995082i	0.371845	+	0.928295i	$0.378725\pi$
$3$	1.72318	+	0.175035i	0.994881	+	0.101056i
$3$	1.72318	+	0.175035i	0.994881	+	0.101056i
$4$	1.15327	+	3.54939i	0.576634	+	1.77470i
$5$	−0.728450	−	1.00263i	−0.325773	−	0.448388i	0.614446	−	0.788959i	$-0.289380\pi$
$5$	−0.728450	−	1.00263i	−0.325773	−	0.448388i	−0.940219	+	0.340571i	$0.889380\pi$
$6$	3.09136	+	2.76399i	1.26204	+	1.12840i
$7$	−2.68999	+	0.874032i	−1.01672	+	0.330353i	−0.769528	−	0.638613i	$-0.779509\pi$
$7$	−2.68999	+	0.874032i	−1.01672	+	0.330353i	−0.247194	+	0.968966i	$0.579509\pi$
$8$	−1.28144	+	3.94386i	−0.453057	+	1.39437i
$9$	2.93873	+	0.603233i	0.979575	+	0.201078i
$10$		−	2.96713i		−	0.938288i
$11$		0			0
$11$		0			0
$12$	1.36603	+	6.31812i	0.394338	+	1.82388i
$13$	1.96677	−	2.70702i	0.545483	−	0.750793i	−0.443907	−	0.896073i	$-0.646408\pi$
$13$	1.96677	−	2.70702i	0.545483	−	0.750793i	0.989391	+	0.145279i	$0.0464081\pi$
$14$	−6.44030	−	2.09258i	−1.72124	−	0.559266i
$15$	−1.07976	−	1.85521i	−0.278793	−	0.479014i
$16$	−1.99350	+	1.44836i	−0.498375	+	0.362091i
$17$	−3.35485	+	2.43744i	−0.813671	+	0.591167i	−0.914893	−	0.403697i	$-0.867725\pi$
$17$	−3.35485	+	2.43744i	−0.813671	+	0.591167i	0.101222	+	0.994864i	$0.467725\pi$
$18$	4.84318	+	5.30396i	1.14155	+	1.25016i
$19$	−2.32960	−	0.756934i	−0.534448	−	0.173653i	0.0293444	−	0.999569i	$-0.490658\pi$
$19$	−2.32960	−	0.756934i	−0.534448	−	0.173653i	−0.563792	+	0.825917i	$0.690658\pi$
$20$	2.71861	−	3.74185i	0.607900	−	0.836703i
$21$	−4.78834	+	1.03528i	−1.04490	+	0.225916i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−2.89847	+	6.57171i	−0.591647	+	1.34144i
$25$	1.07047	−	3.29456i	0.214093	−	0.658911i
$26$	7.61896	−	2.47555i	1.49420	−	0.485495i
$27$	4.95838	+	1.55386i	0.954240	+	0.299041i
$28$	−6.20456	−	8.53985i	−1.17255	−	1.61388i
$29$	−1.67792	−	5.16410i	−0.311582	−	0.958949i	−0.977139	−	0.212603i	$-0.931806\pi$
$29$	−1.67792	−	5.16410i	−0.311582	−	0.958949i	0.665557	−	0.746347i	$-0.268194\pi$
$30$	0.519350	−	5.11291i	0.0948199	−	0.933485i
$31$	−0.158691	−	0.115296i	−0.0285017	−	0.0207077i	0.573443	−	0.819245i	$-0.305607\pi$
$31$	−0.158691	−	0.115296i	−0.0285017	−	0.0207077i	−0.601945	+	0.798538i	$0.705607\pi$
$32$	2.39417			0.423233
$33$		0			0
$34$	−9.92820			−1.70267
$35$	2.83585	+	2.06037i	0.479347	+	0.348266i
$36$	1.24802	+	11.1264i	0.208004	+	1.85440i
$37$	−3.23359	−	9.95195i	−0.531598	−	1.63609i	−0.750887	−	0.660431i	$-0.770374\pi$
$37$	−3.23359	−	9.95195i	−0.531598	−	1.63609i	0.219289	−	0.975660i	$-0.429626\pi$
$38$	−3.44706	−	4.74448i	−0.559188	−	0.769656i
$39$	3.86293	−	4.32045i	0.618563	−	0.691825i
$40$	4.88769	−	1.58811i	0.772811	−	0.251101i
$41$	−2.21952	+	6.83097i	−0.346630	+	1.06682i	0.614075	+	0.789248i	$0.289529\pi$
$41$	−2.21952	+	6.83097i	−0.346630	+	1.06682i	−0.960705	+	0.277571i	$0.910471\pi$
$42$	−10.7316	−	4.73318i	−1.65591	−	0.730345i
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$		0			0
$45$	−1.53590	−	3.38587i	−0.228958	−	0.504735i
$46$		0			0
$47$	3.22015	+	1.04629i	0.469707	+	0.152617i	0.534301	−	0.845294i	$-0.320575\pi$
$47$	3.22015	+	1.04629i	0.469707	+	0.152617i	−0.0645933	+	0.997912i	$0.520575\pi$
$48$	−3.68868	+	2.14686i	−0.532415	+	0.309873i
$49$	0.809017	−	0.587785i	0.115574	−	0.0839693i
$50$	6.70970	−	4.87488i	0.948895	−	0.689413i
$51$	−6.20766	+	3.61295i	−0.869247	+	0.505914i
$52$	11.8765	+	3.85891i	1.64697	+	0.535134i
$53$	−4.17551	+	5.74710i	−0.573551	+	0.789425i	−0.992970	−	0.118368i	$-0.962234\pi$
$53$	−4.17551	+	5.74710i	−0.573551	+	0.789425i	0.419419	+	0.907793i	$0.362234\pi$
$54$	7.41732	+	9.98743i	1.00937	+	1.35912i
$55$		0			0
$56$		−	11.7290i		−	1.56735i
$57$	−3.88185	−	1.71210i	−0.514163	−	0.226773i
$58$	4.01722	−	12.3637i	0.527487	−	1.62344i
$59$	−12.0178	+	3.90481i	−1.56458	+	0.508363i	−0.958027	−	0.286679i	$-0.907449\pi$
$59$	−12.0178	+	3.90481i	−1.56458	+	0.508363i	−0.606554	+	0.795042i	$0.707449\pi$
$60$	5.33962	−	5.97205i	0.689343	−	0.770988i
$61$	2.65681	+	3.65679i	0.340170	+	0.468204i	0.944491	−	0.328537i	$-0.106556\pi$
$61$	2.65681	+	3.65679i	0.340170	+	0.468204i	−0.604321	+	0.796741i	$0.706556\pi$
$62$	−0.145121	−	0.446637i	−0.0184304	−	0.0567230i
$63$	−8.43240	+	0.945846i	−1.06238	+	0.119165i
$64$	8.62433	+	6.26594i	1.07804	+	0.783243i
$65$	−4.14682			−0.514350
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−12.5205	−	9.09666i	−1.51833	−	1.10313i
$69$		0			0
$70$	2.59336	+	7.98156i	0.309966	+	0.953978i
$71$	4.90396	+	6.74973i	0.581994	+	0.801045i	0.993912	−	0.110175i	$-0.0351412\pi$
$71$	4.90396	+	6.74973i	0.581994	+	0.801045i	−0.411919	+	0.911221i	$0.635141\pi$
$72$	−6.14487	+	10.8169i	−0.724180	+	1.27479i
$73$	7.70959	−	2.50500i	0.902339	−	0.293188i	0.179137	−	0.983824i	$-0.442669\pi$
$73$	7.70959	−	2.50500i	0.902339	−	0.293188i	0.723202	+	0.690636i	$0.242669\pi$
$74$	7.74175	−	23.8267i	0.899961	−	2.76979i
$75$	2.42127	−	5.48976i	0.279584	−	0.633903i
$76$		−	9.14162i		−	1.04862i
$77$		0			0
$78$	13.5622	−	2.93225i	1.53561	−	0.332012i
$79$	4.31932	−	5.94504i	0.485962	−	0.668869i	−0.493675	−	0.869646i	$-0.664347\pi$
$79$	4.31932	−	5.94504i	0.485962	−	0.668869i	0.979637	+	0.200778i	$0.0643468\pi$
$80$	2.90433	+	0.943674i	0.324714	+	0.105506i
$81$	8.27222	+	3.54547i	0.919135	+	0.393942i
$82$	−13.9120	+	10.1076i	−1.53632	+	1.11620i
$83$	−12.0015	+	8.71958i	−1.31733	+	0.957099i	−0.317372	+	0.948301i	$0.602800\pi$
$83$	−12.0015	+	8.71958i	−1.31733	+	0.957099i	−0.999961	+	0.00879766i	$0.997200\pi$
$84$	−9.19684	−	15.8017i	−1.00346	−	1.72411i
$85$	4.88769	+	1.58811i	0.530144	+	0.172254i
$86$	−5.97049	+	8.21767i	−0.643814	+	0.886135i
$87$	−1.98747	−	9.19239i	−0.213079	−	0.985527i
$88$		0			0
$89$			9.58244i			1.01574i	0.861435	+	0.507868i	$0.169566\pi$
$89$			9.58244i			1.01574i	−0.861435	+	0.507868i	$0.830434\pi$
$90$	1.78987	−	8.71958i	0.188669	−	0.919124i
$91$	−2.92457	+	9.00090i	−0.306578	+	0.943550i
$92$		0			0
$93$	−0.253272	−	0.226452i	−0.0262631	−	0.0234819i
$94$	4.76479	+	6.55817i	0.491451	+	0.676424i
$95$	0.938079	+	2.88711i	0.0962448	+	0.296211i
$96$	4.12560	+	0.419062i	0.421067	+	0.0427704i
$97$	−1.83481	−	1.33307i	−0.186297	−	0.135352i	0.490728	−	0.871313i	$-0.336731\pi$
$97$	−1.83481	−	1.33307i	−0.186297	−	0.135352i	−0.677025	+	0.735960i	$0.736731\pi$
$98$	2.39417			0.241848
$99$		0			0
$100$	12.9282			1.29282
$101$	−0.379932	−	0.276037i	−0.0378047	−	0.0274667i	0.568722	−	0.822529i	$-0.307438\pi$
$101$	−0.379932	−	0.276037i	−0.0378047	−	0.0274667i	−0.606527	+	0.795063i	$0.707438\pi$
$102$	−17.1081	−	1.73778i	−1.69396	−	0.172066i
$103$	3.93442	+	12.1089i	0.387670	+	1.19313i	0.934525	+	0.355898i	$0.115825\pi$
$103$	3.93442	+	12.1089i	0.387670	+	1.19313i	−0.546855	+	0.837227i	$0.684175\pi$
$104$	8.15584	+	11.2256i	0.799746	+	1.10076i
$105$	4.52606	+	4.04677i	0.441698	+	0.394924i
$106$	−16.1753	+	5.25568i	−1.57108	+	0.510476i
$107$	1.08320	−	3.33375i	0.104717	−	0.322285i	−0.884947	−	0.465692i	$-0.845806\pi$
$107$	1.08320	−	3.33375i	0.104717	−	0.322285i	0.989664	+	0.143406i	$0.0458056\pi$
$108$	0.203076	+	19.3912i	0.0195410	+	1.86592i
$109$		−	10.6945i		−	1.02435i	−0.858881	−	0.512175i	$-0.828840\pi$
$109$		−	10.6945i		−	1.02435i	0.858881	−	0.512175i	$-0.171160\pi$
$110$		0			0
$111$	−3.83013	−	17.7150i	−0.363540	−	1.68144i
$112$	4.09659	−	5.63847i	0.387091	−	0.532785i
$113$	12.3336	+	4.00743i	1.16025	+	0.376987i	0.824994	−	0.565141i	$-0.191178\pi$
$113$	12.3336	+	4.00743i	1.16025	+	0.376987i	0.335252	+	0.942128i	$0.391178\pi$
$114$	−5.10948	−	8.77896i	−0.478546	−	0.822225i
$115$		0			0
$116$	16.3943	−	11.9112i	1.52217	−	1.10592i
$117$	7.41276	−	6.76878i	0.685310	−	0.625774i
$118$	−28.7726	−	9.34878i	−2.64873	−	0.860625i
$119$	6.89413	−	9.48895i	0.631984	−	0.869851i
$120$	8.70035	−	1.88108i	0.794230	−	0.171719i
$121$		0			0
$122$			10.8217i			0.979755i
$123$	−5.02029	+	11.3825i	−0.452665	+	1.02633i
$124$	0.226216	−	0.696222i	0.0203148	−	0.0625226i
$125$	−9.97628	+	3.24149i	−0.892305	+	0.289928i
$126$	−17.6640	−	10.0345i	−1.57363	−	0.893947i
$127$	−8.47559	−	11.6657i	−0.752087	−	1.03516i	−0.997831	−	0.0658244i	$-0.979032\pi$
$127$	−8.47559	−	11.6657i	−0.752087	−	1.03516i	0.245744	−	0.969335i	$-0.420968\pi$
$128$	6.40720	+	19.7193i	0.566321	+	1.74296i
$129$	−0.742609	+	7.31085i	−0.0653830	+	0.643684i
$130$	−8.03209	−	5.83565i	−0.704460	−	0.511820i
$131$	13.5516			1.18401			0.592005	−	0.805934i	$-0.298337\pi$
$131$	13.5516			1.18401			0.592005	+	0.805934i	$0.298337\pi$
$132$		0			0
$133$	6.92820			0.600751
$134$	3.87385	+	2.81452i	0.334650	+	0.243137i
$135$	−2.05399	−	6.10331i	−0.176779	−	0.525289i
$136$	−5.31390	−	16.3545i	−0.455663	−	1.40239i
$137$	−10.4841	−	14.4301i	−0.895715	−	1.23285i	−0.971815	−	0.235746i	$-0.924247\pi$
$137$	−10.4841	−	14.4301i	−0.895715	−	1.23285i	0.0760994	−	0.997100i	$-0.475753\pi$
$138$		0			0
$139$	4.92303	−	1.59959i	0.417566	−	0.135675i	−0.0926959	−	0.995694i	$-0.529548\pi$
$139$	4.92303	−	1.59959i	0.417566	−	0.135675i	0.510262	+	0.860019i	$0.329548\pi$
$140$	−4.04256	+	12.4417i	−0.341658	+	1.05152i
$141$	5.36578	+	2.36659i	0.451880	+	0.199303i
$142$			19.9749i			1.67625i
$143$		0			0
$144$	−6.73205	+	3.05379i	−0.561004	+	0.254483i
$145$	−3.95538	+	5.44411i	−0.328476	+	0.452109i
$146$	18.4581	+	5.99739i	1.52760	+	0.496348i
$147$	1.49697	−	0.871256i	0.123468	−	0.0718600i
$148$	31.5942	−	22.9545i	2.59703	−	1.88685i
$149$	7.60863	−	5.52800i	0.623323	−	0.452871i	−0.230757	−	0.973011i	$-0.574120\pi$
$149$	7.60863	−	5.52800i	0.623323	−	0.452871i	0.854081	+	0.520140i	$0.174120\pi$
$150$	12.4153	−	7.22589i	1.01371	−	0.589992i
$151$	15.6830	+	5.09572i	1.27627	+	0.414684i	0.867263	−	0.497850i	$-0.165877\pi$
$151$	15.6830	+	5.09572i	1.27627	+	0.414684i	0.409002	+	0.912534i	$0.365877\pi$
$152$	5.97049	−	8.21767i	0.484271	−	0.666541i
$153$	−11.3293	+	5.13922i	−0.915922	+	0.415481i
$154$		0			0
$155$			0.243094i			0.0195258i
$156$	19.7899	+	8.72840i	1.58446	+	0.698832i
$157$	−3.54260	+	10.9030i	−0.282730	+	0.870155i	0.704339	+	0.709863i	$0.251243\pi$
$157$	−3.54260	+	10.9030i	−0.282730	+	0.870155i	−0.987070	+	0.160291i	$0.948757\pi$
$158$	16.7324	−	5.43669i	1.33116	−	0.432520i
$159$	−8.20112	+	9.17246i	−0.650391	+	0.727423i
$160$	−1.74403	−	2.40046i	−0.137878	−	0.189773i
$161$		0			0
$162$	11.0333	+	18.5085i	0.866855	+	1.45416i
$163$	−10.0256	−	7.28401i	−0.785264	−	0.570528i	0.121290	−	0.992617i	$-0.461297\pi$
$163$	−10.0256	−	7.28401i	−0.785264	−	0.570528i	−0.906554	+	0.422089i	$0.861297\pi$
$164$	−26.8055			−2.09316
$165$		0			0
$166$	−35.5167			−2.75663
$167$	4.25378	+	3.09055i	0.329167	+	0.239154i	0.740077	−	0.672522i	$-0.234789\pi$
$167$	4.25378	+	3.09055i	0.329167	+	0.239154i	−0.410910	+	0.911676i	$0.634789\pi$
$168$	2.05298	−	20.2112i	0.158391	−	1.55933i
$169$	0.557420	+	1.71556i	0.0428784	+	0.131966i
$170$	7.23220	+	9.95427i	0.554685	+	0.763458i
$171$	−6.38946	−	3.62972i	−0.488614	−	0.277571i
$172$	−15.0588	+	4.89290i	−1.14822	+	0.373080i
$173$	3.50096	−	10.7748i	0.266173	−	0.819196i	−0.725248	−	0.688488i	$-0.758275\pi$
$173$	3.50096	−	10.7748i	0.266173	−	0.819196i	0.991421	−	0.130708i	$-0.0417251\pi$
$174$	9.08649	−	20.6018i	0.688845	−	1.56182i
$175$			9.79796i			0.740656i
$176$		0			0
$177$	−21.3923	+	4.62518i	−1.60794	+	0.347650i
$178$	−13.4850	+	18.5605i	−1.01074	+	1.39116i
$179$	−21.6782	−	7.04368i	−1.62031	−	0.526470i	−0.648292	−	0.761391i	$-0.724517\pi$
$179$	−21.6782	−	7.04368i	−1.62031	−	0.526470i	−0.972014	+	0.234922i	$0.924517\pi$
$180$	10.2465	−	9.35631i	0.763727	−	0.697379i
$181$	−10.4011	+	7.55681i	−0.773104	+	0.561693i	−0.902901	−	0.429848i	$-0.858567\pi$
$181$	−10.4011	+	7.55681i	−0.773104	+	0.561693i	0.129797	+	0.991541i	$0.458567\pi$
$182$	−18.3312	+	13.3184i	−1.35880	+	0.987228i
$183$	3.93811	+	6.76636i	0.291114	+	0.500184i
$184$		0			0
$185$	−7.62258	+	10.4916i	−0.560423	+	0.771356i
$186$	−0.171894	−	0.795040i	−0.0126039	−	0.0582951i
$187$		0			0
$188$			12.6362i			0.921592i
$189$	−14.6961	+	0.153906i	−1.06899	+	0.0111950i
$190$	−2.24592	+	6.91223i	−0.162936	+	0.501466i
$191$	2.35731	−	0.765938i	0.170569	−	0.0554213i	−0.222487	−	0.974936i	$-0.571418\pi$
$191$	2.35731	−	0.765938i	0.170569	−	0.0554213i	0.393057	+	0.919514i	$0.371418\pi$
$192$	13.7645	+	12.3069i	0.993371	+	0.888176i
$193$	−1.68435	−	2.31831i	−0.121242	−	0.166876i	0.744082	−	0.668089i	$-0.232887\pi$
$193$	−1.68435	−	2.31831i	−0.121242	−	0.166876i	−0.865324	+	0.501213i	$0.832887\pi$
$194$	−1.67792	−	5.16410i	−0.120467	−	0.370761i
$195$	−7.14574	−	0.725837i	−0.511717	−	0.0519783i
$196$	3.01929	+	2.19364i	0.215664	+	0.156689i
$197$	−10.6878			−0.761476			−0.380738	−	0.924683i	$-0.624330\pi$
$197$	−10.6878			−0.761476			−0.380738	+	0.924683i	$0.624330\pi$
$198$		0			0
$199$	7.66025			0.543021			0.271511	−	0.962435i	$-0.412477\pi$
$199$	7.66025			0.543021			0.271511	+	0.962435i	$0.412477\pi$
$200$	11.6215	+	8.44355i	0.821767	+	0.597049i
$201$	3.44637	+	0.350069i	0.243088	+	0.0246920i
$202$	−0.347445	−	1.06933i	−0.0244461	−	0.0752375i
$203$	9.02718	+	12.4248i	0.633584	+	0.872053i
$204$	−19.9829	−	17.8667i	−1.39908	−	1.25092i
$205$	8.46572	−	2.75068i	0.591271	−	0.192116i
$206$	−9.41967	+	28.9908i	−0.656300	+	2.01988i
$207$		0			0
$208$			8.24504i			0.571691i
$209$		0			0
$210$	3.07180	+	14.2076i	0.211974	+	0.980419i
$211$	−1.11367	+	1.53283i	−0.0766681	+	0.105525i	−0.845629	−	0.533772i	$-0.820774\pi$
$211$	−1.11367	+	1.53283i	−0.0766681	+	0.105525i	0.768961	+	0.639296i	$0.220774\pi$
$212$	−25.2142	−	8.19259i	−1.73172	−	0.562669i
$213$	7.26900	+	12.4894i	0.498063	+	0.855759i
$214$	6.78952	−	4.93287i	0.464122	−	0.337204i
$215$	4.25378	−	3.09055i	0.290105	−	0.210774i
$216$	−12.4821	+	17.5640i	−0.849298	+	1.19508i
$217$	0.527649	+	0.171444i	0.0358191	+	0.0116383i
$218$	15.0500	−	20.7145i	1.01931	−	1.40296i
$219$	13.7235	−	2.96713i	0.927349	−	0.200500i
$220$		0			0
$221$			13.8755i			0.933370i
$222$	17.5110	−	39.7027i	1.17526	−	2.66467i
$223$	3.99503	−	12.2955i	0.267527	−	0.823364i	−0.723573	−	0.690248i	$-0.757502\pi$
$223$	3.99503	−	12.2955i	0.267527	−	0.823364i	0.991100	−	0.133117i	$-0.0424985\pi$
$224$	−6.44030	+	2.09258i	−0.430311	+	0.139816i
$225$	5.13319	−	9.03606i	0.342213	−	0.602404i
$226$	18.2497	+	25.1186i	1.21396	+	1.67087i
$227$	1.62480	+	5.00062i	0.107842	+	0.331903i	0.990387	−	0.138325i	$-0.0441718\pi$
$227$	1.62480	+	5.00062i	0.107842	+	0.331903i	−0.882545	+	0.470228i	$0.844172\pi$
$228$	1.60010	−	15.7527i	0.105969	−	1.04325i
$229$	−4.47864	−	3.25392i	−0.295957	−	0.215025i	0.429891	−	0.902881i	$-0.358552\pi$
$229$	−4.47864	−	3.25392i	−0.295957	−	0.215025i	−0.725847	+	0.687856i	$0.758552\pi$
$230$		0			0
$231$		0			0
$232$	22.5167			1.47829
$233$	−4.39285	−	3.19159i	−0.287785	−	0.209088i	0.434521	−	0.900662i	$-0.356918\pi$
$233$	−4.39285	−	3.19159i	−0.287785	−	0.209088i	−0.722306	+	0.691574i	$0.756918\pi$
$234$	23.8834	−	2.67895i	1.56130	−	0.175129i
$235$	−1.29668	−	3.99078i	−0.0845862	−	0.260330i
$236$	−27.7194	−	38.1525i	−1.80438	−	2.48351i
$237$	8.48357	−	9.48836i	0.551067	−	0.616335i
$238$	26.7068	−	8.67757i	1.73115	−	0.562483i
$239$	−3.10448	+	9.55460i	−0.200812	+	0.618036i	0.799047	+	0.601268i	$0.205338\pi$
$239$	−3.10448	+	9.55460i	−0.200812	+	0.618036i	−0.999859	+	0.0167678i	$0.994662\pi$
$240$	4.83952	+	2.13448i	0.312390	+	0.137780i
$241$		−	3.76217i		−	0.242343i	−0.992632	−	0.121171i	$-0.961335\pi$
$241$		−	3.76217i		−	0.242343i	0.992632	−	0.121171i	$-0.0386650\pi$
$242$		0			0
$243$	13.6340	+	7.55743i	0.874620	+	0.484809i
$244$	−9.91537	+	13.6473i	−0.634766	+	0.873681i
$245$	−1.17866	−	0.382969i	−0.0753017	−	0.0244670i
$246$	−25.7421	+	14.9823i	−1.64126	+	0.955234i
$247$	−6.63083	+	4.81758i	−0.421909	+	0.306535i
$248$	0.658062	−	0.478110i	0.0417870	−	0.0303600i
$249$	−22.2070	+	12.9248i	−1.40731	+	0.819074i
$250$	−23.8849	−	7.76067i	−1.51061	−	0.490828i
$251$	−5.04685	+	6.94640i	−0.318554	+	0.438453i	−0.938025	−	0.346567i	$-0.887347\pi$
$251$	−5.04685	+	6.94640i	−0.318554	+	0.438453i	0.619471	+	0.785020i	$0.287347\pi$
$252$	−13.0820	−	28.8391i	−0.824088	−	1.81669i
$253$		0			0
$254$		−	34.5228i		−	2.16615i
$255$	8.14441	+	3.59211i	0.510023	+	0.224947i
$256$	−8.75152	+	26.9344i	−0.546970	+	1.68340i
$257$	21.9940	−	7.14630i	1.37195	−	0.445774i	0.471936	−	0.881633i	$-0.343555\pi$
$257$	21.9940	−	7.14630i	1.37195	−	0.445774i	0.900015	+	0.435859i	$0.143555\pi$
$258$	−11.7266	+	13.1155i	−0.730068	+	0.816537i
$259$	17.3967	+	23.9444i	1.08098	+	1.48783i
$260$	−4.78240	−	14.7187i	−0.296592	−	0.912815i
$261$	−1.81578	−	16.1881i	−0.112394	−	1.00202i
$262$	26.2484	+	19.0706i	1.62163	+	1.17819i
$263$	23.4721			1.44735			0.723675	−	0.690141i	$-0.242451\pi$
$263$	23.4721			1.44735			0.723675	+	0.690141i	$0.242451\pi$
$264$		0			0
$265$	8.80385			0.540816
$266$	13.4194	+	9.74977i	0.822797	+	0.597797i
$267$	−1.67726	+	16.5123i	−0.102646	+	1.01054i
$268$	2.30653	+	7.09878i	0.140894	+	0.433627i
$269$	−9.61274	−	13.2308i	−0.586099	−	0.806696i	0.408248	−	0.912871i	$-0.366140\pi$
$269$	−9.61274	−	13.2308i	−0.586099	−	0.806696i	−0.994348	+	0.106175i	$0.966140\pi$
$270$	4.61050	−	14.7121i	0.280586	−	0.895353i
$271$	−8.69420	+	2.82492i	−0.528135	+	0.171601i	−0.560934	−	0.827861i	$-0.689558\pi$
$271$	−8.69420	+	2.82492i	−0.528135	+	0.171601i	0.0327991	+	0.999462i	$0.489558\pi$
$272$	3.15760	−	9.71808i	0.191457	−	0.589245i
$273$	−6.61504	+	14.9983i	−0.400360	+	0.907738i
$274$		−	42.7038i		−	2.57983i
$275$		0			0
$276$		0			0
$277$	3.68896	−	5.07741i	0.221648	−	0.305072i	−0.683683	−	0.729779i	$-0.739623\pi$
$277$	3.68896	−	5.07741i	0.221648	−	0.305072i	0.905331	+	0.424707i	$0.139623\pi$
$278$	11.7866	+	3.82969i	0.706912	+	0.229690i
$279$	−0.396798	−	0.434549i	−0.0237557	−	0.0260158i
$280$	−11.7598	+	8.54399i	−0.702782	+	0.510601i
$281$	0.658062	−	0.478110i	0.0392567	−	0.0285217i	−0.567984	−	0.823040i	$-0.692276\pi$
$281$	0.658062	−	0.478110i	0.0392567	−	0.0285217i	0.607241	+	0.794518i	$0.292276\pi$
$282$	7.06270	+	12.1349i	0.420578	+	0.722625i
$283$	6.46116	+	2.09936i	0.384076	+	0.124794i	0.494690	−	0.869070i	$-0.335282\pi$
$283$	6.46116	+	2.09936i	0.384076	+	0.124794i	−0.110614	+	0.993863i	$0.535282\pi$
$284$	−18.3018	+	25.1903i	−1.08601	+	1.49477i
$285$	1.11114	+	5.13922i	0.0658181	+	0.304421i
$286$		0			0
$287$		−	20.3152i		−	1.19917i
$288$	7.03581	+	1.44424i	0.414589	+	0.0851029i
$289$	0.0606144	−	0.186552i	0.00356555	−	0.0109736i
$290$	−15.3225	+	4.97860i	−0.899771	+	0.292353i
$291$	−2.92838	−	2.61827i	−0.171665	−	0.153486i
$292$	17.7824	+	24.4754i	1.04064	+	1.43232i
$293$	−10.0533	−	30.9408i	−0.587319	−	1.80758i	−0.589753	−	0.807584i	$-0.700775\pi$
$293$	−10.0533	−	30.9408i	−0.587319	−	1.80758i	0.00243453	−	0.999997i	$-0.499225\pi$
$294$	4.12560	+	0.419062i	0.240610	+	0.0244402i
$295$	12.6694	+	9.20487i	0.737642	+	0.535928i
$296$	43.3928			2.52215
$297$		0			0
$298$	22.5167			1.30436
$299$		0			0
$300$	22.2777	+	2.26288i	1.28620	+	0.130648i
$301$	−3.70820	−	11.4127i	−0.213737	−	0.657816i
$302$	23.2058	+	31.9401i	1.33534	+	1.83794i
$303$	−0.606377	−	0.542164i	−0.0348355	−	0.0311465i
$304$	5.74038	−	1.86516i	0.329233	−	0.106974i
$305$	1.73104	−	5.32758i	0.0991188	−	0.305056i
$306$	−29.1763	−	5.98902i	−1.66790	−	0.342370i
$307$			31.1870i			1.77994i	0.456021	+	0.889969i	$0.349274\pi$
$307$			31.1870i			1.77994i	−0.456021	+	0.889969i	$0.650726\pi$
$308$		0			0
$309$	4.66025	+	21.5545i	0.265113	+	1.22619i
$310$	−0.342096	+	0.470855i	−0.0194298	+	0.0267428i
$311$	−0.631641	−	0.205232i	−0.0358171	−	0.0116377i	0.291054	−	0.956707i	$-0.405994\pi$
$311$	−0.631641	−	0.205232i	−0.0358171	−	0.0116377i	−0.326871	+	0.945069i	$0.605994\pi$
$312$	12.0892	+	20.7712i	0.684414	+	1.17594i
$313$	5.98050	−	4.34509i	0.338038	−	0.245599i	−0.405796	−	0.913964i	$-0.633006\pi$
$313$	5.98050	−	4.34509i	0.338038	−	0.245599i	0.743834	+	0.668365i	$0.233006\pi$
$314$	−22.2051	+	16.1329i	−1.25311	+	0.910435i
$315$	7.09091	+	7.76554i	0.399528	+	0.437539i
$316$	26.0826	+	8.47475i	1.46726	+	0.476742i
$317$	14.4644	−	19.9085i	0.812402	−	1.11818i	−0.178546	−	0.983931i	$-0.557139\pi$
$317$	14.4644	−	19.9085i	0.812402	−	1.11818i	0.990948	−	0.134244i	$-0.0428605\pi$
$318$	−28.7930	+	6.22526i	−1.61463	+	0.349095i
$319$		0			0
$320$		−	13.2114i		−	0.738540i
$321$	2.45007	−	5.55506i	0.136750	−	0.310053i
$322$		0			0
$323$	9.66046	−	3.13887i	0.537522	−	0.174652i
$324$	−3.04420	+	33.4502i	−0.169122	+	1.85835i
$325$	−6.81308	−	9.37740i	−0.377922	−	0.520165i
$326$	−9.16831	−	28.2172i	−0.507786	−	1.56280i
$327$	1.87191	−	18.4287i	0.103517	−	1.01911i
$328$	−24.0963	−	17.5070i	−1.33049	−	0.966660i
$329$	−9.57668			−0.527979
$330$		0			0
$331$	−0.392305			−0.0215630			−0.0107815	−	0.999942i	$-0.503432\pi$
$331$	−0.392305			−0.0215630			−0.0107815	+	0.999942i	$0.503432\pi$
$332$	−44.7901	−	32.5419i	−2.45818	−	1.78597i
$333$	−3.49927	−	31.1967i	−0.191759	−	1.70957i
$334$	3.89005	+	11.9723i	0.212854	+	0.655097i
$335$	−1.45690	−	2.00525i	−0.0795990	−	0.109559i
$336$	8.04610	−	8.99908i	0.438951	−	0.490940i
$337$	−8.10533	+	2.63358i	−0.441525	+	0.143460i	−0.521339	−	0.853349i	$-0.674567\pi$
$337$	−8.10533	+	2.63358i	−0.441525	+	0.143460i	0.0798139	+	0.996810i	$0.474567\pi$
$338$	−1.33456	+	4.10734i	−0.0725903	+	0.223410i
$339$	20.5516	+	9.06434i	1.11621	+	0.492307i
$340$			19.1798i			1.04017i
$341$		0			0
$342$	−7.26795	−	16.0221i	−0.393006	−	0.866376i
$343$	9.97505	−	13.7295i	0.538602	−	0.741322i
$344$	−16.7324	−	5.43669i	−0.902151	−	0.293126i
$345$		0			0
$346$	21.9441	−	15.9433i	1.17972	−	0.857117i
$347$	−1.03799	+	0.754147i	−0.0557225	+	0.0404847i	−0.615298	−	0.788295i	$-0.710964\pi$
$347$	−1.03799	+	0.754147i	−0.0557225	+	0.0404847i	0.559575	+	0.828779i	$0.310964\pi$
$348$	30.3353	−	17.6556i	1.62614	−	0.946438i
$349$	−19.3223	−	6.27818i	−1.03430	−	0.336063i	−0.257809	−	0.966196i	$-0.583001\pi$
$349$	−19.3223	−	6.27818i	−1.03430	−	0.336063i	−0.776488	+	0.630132i	$0.783001\pi$
$350$	−13.7883	+	18.9779i	−0.737013	+	1.01441i
$351$	13.9583	−	10.3664i	0.745040	−	0.553316i
$352$		0			0
$353$		−	9.58244i		−	0.510022i	−0.966938	−	0.255011i	$-0.917921\pi$
$353$		−	9.58244i		−	0.510022i	0.966938	−	0.255011i	$-0.0820790\pi$
$354$	−47.9441	−	21.1459i	−2.54820	−	1.12389i
$355$	3.19516	−	9.83368i	0.169581	−	0.521918i
$356$	−34.0118	+	11.0511i	−1.80262	+	0.585708i
$357$	13.5407	−	15.1445i	0.716652	−	0.801532i
$358$	−32.0768	−	44.1499i	−1.69531	−	2.33340i
$359$	10.6480	+	32.7712i	0.561980	+	1.72960i	0.676759	+	0.736204i	$0.263384\pi$
$359$	10.6480	+	32.7712i	0.561980	+	1.72960i	−0.114780	+	0.993391i	$0.536616\pi$
$360$	15.3216	−	1.71859i	0.807517	−	0.0905777i
$361$	−10.5172	−	7.64121i	−0.553538	−	0.402169i
$362$	−30.7804			−1.61778
$363$		0			0
$364$	−35.3205			−1.85130
$365$	−8.12763	−	5.90507i	−0.425420	−	0.309085i
$366$	−1.89418	+	18.6479i	−0.0990104	+	0.974740i
$367$	−7.37204	−	22.6888i	−0.384817	−	1.18435i	−0.936613	−	0.350366i	$-0.886057\pi$
$367$	−7.37204	−	22.6888i	−0.384817	−	1.18435i	0.551796	−	0.833979i	$-0.313943\pi$
$368$		0			0
$369$	−10.6432	+	18.7355i	−0.554064	+	0.975330i
$370$	−29.5287	+	9.59446i	−1.53512	+	0.498792i
$371$	6.20896	−	19.1092i	0.322353	−	0.992100i
$372$	0.511675	−	1.16012i	0.0265291	−	0.0601495i
$373$		−	9.62209i		−	0.498213i	−0.968476	−	0.249107i	$-0.919863\pi$
$373$		−	9.62209i		−	0.498213i	0.968476	−	0.249107i	$-0.0801369\pi$
$374$		0			0
$375$	−17.7583	+	3.83949i	−0.917036	+	0.198270i
$376$	−8.25286	+	11.3591i	−0.425609	+	0.585800i
$377$	−17.2794	−	5.61442i	−0.889935	−	0.289157i
$378$	−28.6819	−	20.3831i	−1.47524	−	1.04840i
$379$	24.7466	−	17.9794i	1.27115	−	0.923542i	0.271899	−	0.962326i	$-0.412348\pi$
$379$	24.7466	−	17.9794i	1.27115	−	0.923542i	0.999248	+	0.0387838i	$0.0123484\pi$
$380$	−9.16562	+	6.65922i	−0.470187	+	0.341611i
$381$	−12.5631	−	21.5856i	−0.643628	−	1.10586i
$382$	5.64381	+	1.83379i	0.288763	+	0.0938246i
$383$	5.58011	−	7.68037i	0.285131	−	0.392448i	−0.642294	−	0.766458i	$-0.722017\pi$
$383$	5.58011	−	7.68037i	0.285131	−	0.392448i	0.927425	+	0.374010i	$0.122017\pi$
$384$	7.58922	+	35.1015i	0.387286	+	1.79127i
$385$		0			0
$386$		−	6.86071i		−	0.349201i
$387$	−2.55930	+	12.4680i	−0.130097	+	0.633782i
$388$	2.61555	−	8.04984i	0.132784	−	0.408669i
$389$	18.1423	−	5.89478i	0.919849	−	0.298877i	0.189444	−	0.981892i	$-0.439331\pi$
$389$	18.1423	−	5.89478i	0.919849	−	0.298877i	0.730405	+	0.683015i	$0.239331\pi$
$390$	−12.8193	−	11.4618i	−0.649131	−	0.580390i
$391$		0			0
$392$	1.28144	+	3.94386i	0.0647225	+	0.199195i
$393$	23.3519	+	2.37200i	1.17795	+	0.119652i
$394$	−20.7015	−	15.0405i	−1.04293	−	0.757730i
$395$	−9.10706			−0.458226
$396$		0			0
$397$	−21.1962			−1.06380			−0.531902	−	0.846806i	$-0.678523\pi$
$397$	−21.1962			−1.06380			−0.531902	+	0.846806i	$0.678523\pi$
$398$	14.8373	+	10.7800i	0.743728	+	0.540350i
$399$	11.9386	+	1.21267i	0.597676	+	0.0607097i
$400$	2.63774	+	8.11812i	0.131887	+	0.405906i
$401$	−0.728450	−	1.00263i	−0.0363771	−	0.0500687i	0.790441	−	0.612538i	$-0.209851\pi$
$401$	−0.728450	−	1.00263i	−0.0363771	−	0.0500687i	−0.826818	+	0.562469i	$0.809851\pi$
$402$	6.18272	+	5.52799i	0.308366	+	0.275711i
$403$	−0.624215	+	0.202820i	−0.0310944	+	0.0101032i
$404$	0.541600	−	1.66687i	0.0269456	−	0.0829300i
$405$	−2.47112	−	10.8766i	−0.122791	−	0.540465i
$406$			36.7696i			1.82484i
$407$		0			0
$408$	−6.29423	−	29.1120i	−0.311611	−	1.44126i
$409$	19.5265	−	26.8759i	0.965522	−	1.32893i	0.0212450	−	0.999774i	$-0.493237\pi$
$409$	19.5265	−	26.8759i	0.965522	−	1.32893i	0.944277	−	0.329152i	$-0.106763\pi$
$410$	20.2684	+	6.58559i	1.00098	+	0.325239i
$411$	−15.5402	−	26.7008i	−0.766543	−	1.31705i
$412$	−38.4418	+	27.9296i	−1.89389	+	1.37599i
$413$	28.9148	−	21.0078i	1.42280	−	1.03373i
$414$		0			0
$415$	17.4850	+	5.68121i	0.858303	+	0.278880i
$416$	4.70878	−	6.48108i	0.230867	−	0.317761i
$417$	8.76327	−	1.89469i	0.429139	−	0.0927832i
$418$		0			0
$419$		−	11.0648i		−	0.540553i	−0.962783	−	0.270277i	$-0.912885\pi$
$419$		−	11.0648i		−	0.540553i	0.962783	−	0.270277i	$-0.0871151\pi$
$420$	−9.14380	+	20.7318i	−0.446172	+	1.01161i
$421$	−5.93194	+	18.2566i	−0.289105	+	0.889774i	0.696033	+	0.718010i	$0.254947\pi$
$421$	−5.93194	+	18.2566i	−0.289105	+	0.889774i	−0.985138	+	0.171764i	$0.945053\pi$
$422$	−4.31419	+	1.40176i	−0.210011	+	0.0682368i
$423$	8.83199	+	5.01726i	0.429426	+	0.243948i
$424$	−17.3151	−	23.8322i	−0.840897	−	1.15740i
$425$	4.43904	+	13.6619i	0.215325	+	0.662702i
$426$	−3.49629	+	34.4204i	−0.169396	+	1.66767i
$427$	−10.3430	−	7.51461i	−0.500531	−	0.363657i
$428$	13.0820			0.632342
$429$		0			0
$430$	12.5885			0.607069
$431$	16.9133	+	12.2882i	0.814686	+	0.591904i	0.915185	−	0.403033i	$-0.132044\pi$
$431$	16.9133	+	12.2882i	0.814686	+	0.591904i	−0.100499	+	0.994937i	$0.532044\pi$
$432$	−12.1351	+	4.08391i	−0.583849	+	0.196487i
$433$	4.03346	+	12.4137i	0.193836	+	0.596565i	0.999988	+	0.00485736i	$0.00154615\pi$
$433$	4.03346	+	12.4137i	0.193836	+	0.596565i	−0.806152	+	0.591708i	$0.798454\pi$
$434$	0.780751	+	1.07461i	0.0374772	+	0.0515830i
$435$	−7.76876	+	8.68888i	−0.372483	+	0.416600i
$436$	37.9591	−	12.3337i	1.81791	−	0.590675i
$437$		0			0
$438$	30.7569	+	13.5654i	1.46962	+	0.648180i
$439$		−	8.38375i		−	0.400134i	−0.979782	−	0.200067i	$-0.935884\pi$
$439$		−	8.38375i		−	0.400134i	0.979782	−	0.200067i	$-0.0641160\pi$
$440$		0			0
$441$	2.73205	−	1.23931i	0.130098	−	0.0590149i
$442$	−19.5265	+	26.8759i	−0.928779	+	1.27836i
$443$	24.2667	+	7.88474i	1.15295	+	0.374615i	0.822253	−	0.569122i	$-0.192717\pi$
$443$	24.2667	+	7.88474i	1.15295	+	0.374615i	0.330695	+	0.943738i	$0.392717\pi$
$444$	58.4604	−	34.0248i	2.77441	−	1.61474i
$445$	9.60760	−	6.98033i	0.455444	−	0.330899i
$446$	25.0410	−	18.1933i	1.18572	−	0.861478i
$447$	14.0787	−	8.19398i	0.665898	−	0.387562i
$448$	−28.6760	−	9.31740i	−1.35481	−	0.440206i
$449$	−23.6868	+	32.6020i	−1.11785	+	1.53859i	−0.308530	+	0.951215i	$0.599837\pi$
$449$	−23.6868	+	32.6020i	−1.11785	+	1.53859i	−0.809318	+	0.587371i	$0.800163\pi$
$450$	22.6587	−	10.2784i	1.06814	−	0.484530i
$451$		0			0
$452$			48.3984i			2.27647i
$453$	26.1328	+	11.5259i	1.22783	+	0.541535i
$454$	−3.89005	+	11.9723i	−0.182569	+	0.561889i
$455$	11.1549	−	3.62446i	0.522951	−	0.169917i
$456$	11.7266	−	13.1155i	0.549150	−	0.614191i
$457$	−10.8281	−	14.9037i	−0.506519	−	0.697164i	0.476808	−	0.879007i	$-0.341794\pi$
$457$	−10.8281	−	14.9037i	−0.506519	−	0.697164i	−0.983328	+	0.181843i	$0.941794\pi$
$458$	−4.09568	−	12.6052i	−0.191378	−	0.589002i
$459$	−20.4221	+	6.87279i	−0.953221	+	0.320794i
$460$		0			0
$461$	2.86379			0.133380			0.0666901	−	0.997774i	$-0.478756\pi$
$461$	2.86379			0.133380			0.0666901	+	0.997774i	$0.478756\pi$
$462$		0			0
$463$	−1.26795			−0.0589266			−0.0294633	−	0.999566i	$-0.509380\pi$
$463$	−1.26795			−0.0589266			−0.0294633	+	0.999566i	$0.509380\pi$
$464$	10.8244	+	7.86440i	0.502511	+	0.365096i
$465$	−0.0425499	+	0.418896i	−0.00197320	+	0.0194259i
$466$	−4.01722	−	12.3637i	−0.186094	−	0.572739i
$467$	11.4077	+	15.7014i	0.527886	+	0.726573i	0.986806	−	0.161904i	$-0.0517636\pi$
$467$	11.4077	+	15.7014i	0.527886	+	0.726573i	−0.458920	+	0.888477i	$0.651764\pi$
$468$	32.5739	+	18.5046i	1.50573	+	0.855374i
$469$	−5.37999	+	1.74806i	−0.248425	+	0.0807181i
$470$	3.10448	−	9.55460i	0.143199	−	0.440721i
$471$	−8.01296	+	18.1678i	−0.369218	+	0.837129i
$472$		−	52.4002i		−	2.41192i
$473$		0			0
$474$	29.7846	−	6.43966i	1.36805	−	0.295784i
$475$	−4.98752	+	6.86474i	−0.228843	+	0.314976i
$476$	41.6308	+	13.5267i	1.90814	+	0.619993i
$477$	−15.7375	+	14.3703i	−0.720572	+	0.657973i
$478$	−19.4589	+	14.1377i	−0.890031	+	0.646645i
$479$	5.29178	−	3.84470i	0.241787	−	0.175669i	−0.460292	−	0.887768i	$-0.652255\pi$
$479$	5.29178	−	3.84470i	0.241787	−	0.175669i	0.702079	+	0.712099i	$0.252255\pi$
$480$	−2.58513	−	4.44169i	−0.117994	−	0.202735i
$481$	−33.2999	−	10.8198i	−1.51834	−	0.493340i
$482$	5.29434	−	7.28703i	0.241151	−	0.331915i
$483$		0			0
$484$		0			0
$485$			2.81070i			0.127627i
$486$	15.7727	+	33.8247i	0.715465	+	1.53432i
$487$	10.2522	−	31.5531i	0.464573	−	1.42981i	−0.394946	−	0.918704i	$-0.629237\pi$
$487$	10.2522	−	31.5531i	0.464573	−	1.42981i	0.859519	−	0.511104i	$-0.170763\pi$
$488$	−17.8264	+	5.79216i	−0.806965	+	0.262199i
$489$	−16.0010	−	14.3065i	−0.723589	−	0.646963i
$490$	−1.74403	−	2.40046i	−0.0787874	−	0.108442i
$491$	6.46031	+	19.8828i	0.291550	+	0.897298i	0.984359	+	0.176177i	$0.0563731\pi$
$491$	6.46031	+	19.8828i	0.291550	+	0.897298i	−0.692809	+	0.721121i	$0.743627\pi$
$492$	−46.1908	−	4.69189i	−2.08244	−	0.211527i
$493$	18.2164	+	13.2350i	0.820424	+	0.596073i
$494$	−19.6230			−0.882880
$495$		0			0
$496$	0.483340			0.0217026
$497$	−19.0911	−	13.8705i	−0.856353	−	0.622177i
$498$	−61.2017	−	6.21664i	−2.74252	−	0.278574i
$499$	7.97383	+	24.5409i	0.356958	+	1.09860i	0.954866	+	0.297038i	$0.0959987\pi$
$499$	7.97383	+	24.5409i	0.356958	+	1.09860i	−0.597908	+	0.801565i	$0.704001\pi$
$500$	−23.0106	−	31.6714i	−1.02907	−	1.41639i
$501$	6.78909	+	6.07015i	0.303314	+	0.271194i
$502$	−19.5507	+	6.35242i	−0.872592	+	0.283522i
$503$	1.08320	−	3.33375i	0.0482975	−	0.148644i	−0.923999	−	0.382394i	$-0.875100\pi$
$503$	1.08320	−	3.33375i	0.0482975	−	0.148644i	0.972297	+	0.233750i	$0.0750997\pi$
$504$	7.07532	−	34.4683i	0.315160	−	1.53534i
$505$			0.582009i			0.0258991i
$506$		0			0
$507$	0.660254	+	3.05379i	0.0293229	+	0.135624i
$508$	31.6313	−	43.5368i	1.40341	−	1.93163i
$509$	−11.1549	−	3.62446i	−0.494434	−	0.160651i	0.0511777	−	0.998690i	$-0.483703\pi$
$509$	−11.1549	−	3.62446i	−0.494434	−	0.160651i	−0.545611	+	0.838038i	$0.683703\pi$
$510$	10.7201	+	18.4189i	0.474693	+	0.815604i
$511$	−18.5493	+	13.4769i	−0.820573	+	0.596181i
$512$	−21.3062	+	15.4798i	−0.941608	+	0.684119i
$513$	−10.3749	−	7.37304i	−0.458062	−	0.325528i
$514$	52.6575	+	17.1095i	2.32262	+	0.754666i
$515$	9.27467	−	12.7655i	0.408691	−	0.562514i
$516$	−26.8055	+	5.79555i	−1.18005	+	0.255135i
$517$		0			0
$518$			70.8601i			3.11342i
$519$	7.91876	−	17.9542i	0.347595	−	0.788104i
$520$	5.31390	−	16.3545i	0.233030	−	0.717193i
$521$	2.35731	−	0.765938i	0.103276	−	0.0335564i	−0.256923	−	0.966432i	$-0.582709\pi$
$521$	2.35731	−	0.765938i	0.103276	−	0.0335564i	0.360199	+	0.932875i	$0.382709\pi$
$522$	19.2637	−	33.9103i	0.843150	−	1.48421i
$523$	21.2108	+	29.1942i	0.927485	+	1.27657i	0.960833	+	0.277129i	$0.0893830\pi$
$523$	21.2108	+	29.1942i	0.927485	+	1.27657i	−0.0333482	+	0.999444i	$0.510617\pi$
$524$	15.6286	+	48.1000i	0.682740	+	2.10126i
$525$	−1.71498	+	16.8837i	−0.0748479	+	0.736864i
$526$	45.4636	+	33.0313i	1.98231	+	1.44023i
$527$	0.813410			0.0354327
$528$		0			0
$529$	23.0000			1.00000
$530$	17.0524	+	12.3893i	0.740708	+	0.538156i
$531$	−37.6724	+	4.22565i	−1.63484	+	0.183377i
$532$	7.99007	+	24.5909i	0.346413	+	1.06615i
$533$	14.1263	+	19.4432i	0.611879	+	0.842180i
$534$	−26.4858	+	29.6227i	−1.14615	+	1.28190i
$535$	−4.13156	+	1.34242i	−0.178623	+	0.0580381i
$536$	−2.56288	+	7.88773i	−0.110699	+	0.340698i
$537$	−36.1227	−	15.9320i	−1.55881	−	0.687516i
$538$		−	39.1547i		−	1.68808i
$539$		0			0
$540$	19.2942	−	14.3292i	0.830291	−	0.616629i
$541$	−3.10228	+	4.26992i	−0.133378	+	0.183578i	−0.870482	−	0.492201i	$-0.836193\pi$
$541$	−3.10228	+	4.26992i	−0.133378	+	0.183578i	0.737104	+	0.675779i	$0.236193\pi$
$542$	−20.8154	−	6.76333i	−0.894097	−	0.290510i
$543$	−19.2456	+	11.2012i	−0.825909	+	0.480691i
$544$	−8.03209	+	5.83565i	−0.344373	+	0.250201i
$545$	−10.7226	+	7.79044i	−0.459306	+	0.333706i
$546$	−33.9193	+	19.7415i	−1.45161	+	0.844858i
$547$	20.0784	+	6.52386i	0.858490	+	0.278940i	0.704998	−	0.709210i	$-0.250948\pi$
$547$	20.0784	+	6.52386i	0.858490	+	0.278940i	0.153492	+	0.988150i	$0.450948\pi$
$548$	39.1271	−	53.8539i	1.67143	−	2.30052i
$549$	5.60175	+	12.3490i	0.239077	+	0.527042i
$550$		0			0
$551$			13.3004i			0.566615i
$552$		0			0
$553$	−6.42280	+	19.7673i	−0.273125	+	0.840593i
$554$	14.2905	−	4.64325i	0.607144	−	0.197273i
$555$	−14.9715	+	16.7447i	−0.635504	+	0.710773i
$556$	11.3551	+	15.6290i	0.481565	+	0.662818i
$557$	−3.21071	−	9.88156i	−0.136042	−	0.418695i	0.859708	−	0.510785i	$-0.170645\pi$
$557$	−3.21071	−	9.88156i	−0.136042	−	0.418695i	−0.995751	+	0.0920900i	$0.970645\pi$
$558$	−0.157045	−	1.40009i	−0.00664825	−	0.0592704i
$559$	11.4849	+	8.34429i	0.485761	+	0.352926i
$560$	−8.63744			−0.364998
$561$		0			0
$562$	1.94744			0.0821478
$563$	−28.6367	−	20.8058i	−1.20689	−	0.876858i	−0.211947	−	0.977281i	$-0.567980\pi$
$563$	−28.6367	−	20.8058i	−1.20689	−	0.876858i	−0.994945	+	0.100423i	$0.967980\pi$
$564$	−2.21178	+	21.7746i	−0.0931326	+	0.916874i
$565$	−4.96646	−	15.2852i	−0.208940	−	0.643053i
$566$	9.56044	+	13.1588i	0.401855	+	0.553106i
$567$	−25.3511	−	2.30712i	−1.06465	−	0.0968900i
$568$	−32.9041	+	10.6912i	−1.38063	+	0.448593i
$569$	−9.70991	+	29.8840i	−0.407061	+	1.25280i	0.512101	+	0.858925i	$0.328867\pi$
$569$	−9.70991	+	29.8840i	−0.407061	+	1.25280i	−0.919162	+	0.393879i	$0.871133\pi$
$570$	−5.08001	+	11.5179i	−0.212778	+	0.482433i
$571$		−	27.3233i		−	1.14345i	−0.820447	−	0.571723i	$-0.806275\pi$
$571$		−	27.3233i		−	1.14345i	0.820447	−	0.571723i	$-0.193725\pi$
$572$		0			0
$573$	4.19615	−	0.907241i	0.175297	−	0.0379005i
$574$	28.5887	−	39.3490i	1.19327	−	1.64240i
$575$		0			0
$576$	21.5647	+	23.6164i	0.898529	+	0.984015i
$577$	−3.88639	+	2.82363i	−0.161793	+	0.117549i	−0.665736	−	0.746188i	$-0.731882\pi$
$577$	−3.88639	+	2.82363i	−0.161793	+	0.117549i	0.503943	+	0.863737i	$0.331882\pi$
$578$	0.379932	−	0.276037i	0.0158031	−	0.0114816i
$579$	−2.49666	−	4.28970i	−0.103758	−	0.178274i
$580$	−23.8849	−	7.76067i	−0.991767	−	0.322244i
$581$	24.6627	−	33.9453i	1.02318	−	1.40829i
$582$	−1.98747	−	9.19239i	−0.0823831	−	0.381037i
$583$		0			0
$584$			33.6156i			1.39102i
$585$	−12.1864	−	2.50150i	−0.503845	−	0.103424i
$586$	24.0692	−	74.0775i	0.994292	−	3.06011i
$587$	6.20911	−	2.01746i	0.256277	−	0.0832695i	−0.178061	−	0.984020i	$-0.556982\pi$
$587$	6.20911	−	2.01746i	0.256277	−	0.0832695i	0.434338	+	0.900750i	$0.356982\pi$
$588$	4.81883	+	4.30853i	0.198725	+	0.177681i
$589$	0.282415	+	0.388711i	0.0116367	+	0.0160166i
$590$	11.5861	+	35.6583i	0.476991	+	1.46803i
$591$	−18.4171	−	1.87074i	−0.757577	−	0.0769518i
$592$	20.8602	+	15.1558i	0.857348	+	0.622900i
$593$	−26.3359			−1.08148			−0.540742	−	0.841188i	$-0.681857\pi$
$593$	−26.3359			−1.08148			−0.540742	+	0.841188i	$0.681857\pi$
$594$		0			0
$595$	−14.5359			−0.595914
$596$	28.3958	+	20.6308i	1.16314	+	0.845069i
$597$	13.2000	+	1.34081i	0.540241	+	0.0548757i
$598$		0			0
$599$	−1.59979	−	2.20192i	−0.0653656	−	0.0899680i	0.775083	−	0.631860i	$-0.217708\pi$
$599$	−1.59979	−	2.20192i	−0.0653656	−	0.0899680i	−0.840448	+	0.541892i	$0.817708\pi$
$600$	18.5481	+	16.5840i	0.757225	+	0.677037i
$601$	39.4972	−	12.8334i	1.61113	−	0.523486i	0.641300	−	0.767290i	$-0.278395\pi$
$601$	39.4972	−	12.8334i	1.61113	−	0.523486i	0.969825	+	0.243804i	$0.0783952\pi$
$602$	8.87807	−	27.3239i	0.361843	−	1.11364i
$603$	5.87745	+	1.20647i	0.239348	+	0.0491311i
$604$			61.5419i			2.50410i
$605$		0			0
$606$	−0.411543	−	1.90346i	−0.0167178	−	0.0773228i
$607$	−26.0950	+	35.9167i	−1.05916	+	1.45781i	−0.178576	+	0.983926i	$0.557149\pi$
$607$	−26.0950	+	35.9167i	−1.05916	+	1.45781i	−0.880586	+	0.473886i	$0.842851\pi$
$608$	−5.57747	−	1.81223i	−0.226196	−	0.0734956i
$609$	13.3807	+	22.9904i	0.542214	+	0.931616i
$610$	10.8502	−	7.88311i	0.439310	−	0.319178i
$611$	9.16562	−	6.65922i	0.370801	−	0.269403i
$612$	−31.3068	−	34.2854i	−1.26550	−	1.38590i
$613$	14.6631	+	4.76432i	0.592235	+	0.192429i	0.589774	−	0.807568i	$-0.299217\pi$
$613$	14.6631	+	4.76432i	0.592235	+	0.192429i	0.00246086	+	0.999997i	$0.499217\pi$
$614$	−43.8882	+	60.4069i	−1.77118	+	2.43782i
$615$	15.0695	−	3.25813i	0.607659	−	0.131381i
$616$		0			0
$617$		−	13.6325i		−	0.548822i	−0.961613	−	0.274411i	$-0.911517\pi$
$617$		−	13.6325i		−	0.548822i	0.961613	−	0.274411i	$-0.0884828\pi$
$618$	−21.3062	+	48.3077i	−0.857062	+	1.94322i
$619$	−0.0443728	+	0.136566i	−0.00178350	+	0.00548903i	−0.951944	−	0.306271i	$-0.900919\pi$
$619$	−0.0443728	+	0.136566i	−0.00178350	+	0.00548903i	0.950161	+	0.311760i	$0.100919\pi$
$620$	−0.862837	+	0.280353i	−0.0346524	+	0.0112592i
$621$		0			0
$622$	−0.934625	−	1.28640i	−0.0374750	−	0.0515800i
$623$	−8.37536	−	25.7767i	−0.335552	−	1.03272i
$624$	−1.44317	+	14.2077i	−0.0577729	+	0.568764i
$625$	−3.49536	−	2.53953i	−0.139815	−	0.101581i
$626$	17.6984			0.707372
$627$		0			0
$628$	−42.7846			−1.70729
$629$	35.1055	+	25.5056i	1.39975	+	1.01698i
$630$	2.80645	+	25.0200i	0.111812	+	0.996821i
$631$	8.44250	+	25.9833i	0.336091	+	1.03438i	0.966182	+	0.257860i	$0.0830173\pi$
$631$	8.44250	+	25.9833i	0.336091	+	1.03438i	−0.630092	+	0.776521i	$0.716983\pi$
$632$	17.9115	+	24.6530i	0.712480	+	0.980645i
$633$	−2.18736	+	2.44642i	−0.0869396	+	0.0972366i
$634$	56.0329	−	18.2062i	2.22535	−	0.723061i
$635$	−5.52224	+	16.9957i	−0.219143	+	0.674454i
$636$	−42.0147	−	18.5307i	−1.66599	−	0.734790i
$637$		−	3.34607i		−	0.132576i
$638$		0			0
$639$	10.3397	+	22.7938i	0.409034	+	0.901710i
$640$	15.1038	−	20.7886i	0.597029	−	0.821740i
$641$	44.9356	+	14.6004i	1.77485	+	0.576683i	0.998557	−	0.0536929i	$-0.0170992\pi$
$641$	44.9356	+	14.6004i	1.77485	+	0.576683i	0.776290	+	0.630376i	$0.217099\pi$
$642$	12.5630	−	7.31185i	0.495822	−	0.288576i
$643$	3.07738	−	2.23585i	0.121360	−	0.0881731i	−0.525450	−	0.850825i	$-0.676103\pi$
$643$	3.07738	−	2.23585i	0.121360	−	0.0881731i	0.646810	+	0.762652i	$0.276103\pi$
$644$		0			0
$645$	7.87100	−	4.58103i	0.309920	−	0.180378i
$646$	23.1288	+	7.51499i	0.909989	+	0.295673i
$647$	−9.80793	+	13.4995i	−0.385589	+	0.530718i	−0.957055	−	0.289908i	$-0.906375\pi$
$647$	−9.80793	+	13.4995i	−0.385589	+	0.530718i	0.571465	+	0.820626i	$0.306375\pi$
$648$	−24.5832	+	28.0812i	−0.965720	+	1.10313i
$649$		0			0
$650$		−	27.7511i		−	1.08849i
$651$	0.879227	+	0.387785i	0.0344596	+	0.0151985i
$652$	14.2916	−	43.9851i	0.559704	−	1.72259i
$653$	−36.9161	+	11.9948i	−1.44464	+	0.469392i	−0.923341	−	0.383982i	$-0.874553\pi$
$653$	−36.9161	+	11.9948i	−1.44464	+	0.469392i	−0.521300	+	0.853374i	$0.674553\pi$
$654$	29.5596	−	33.0606i	1.15587	−	1.29277i
$655$	−9.87168	−	13.5872i	−0.385718	−	0.530896i
$656$	−5.46912	−	16.8322i	−0.213533	−	0.657187i
$657$	24.1675	−	2.71082i	0.942863	−	0.105759i
$658$	−18.5493	−	13.4769i	−0.723127	−	0.525383i
$659$	−13.5516			−0.527896			−0.263948	−	0.964537i	$-0.585025\pi$
$659$	−13.5516			−0.527896			−0.263948	+	0.964537i	$0.585025\pi$
$660$		0			0
$661$	3.19615			0.124316			0.0621580	−	0.998066i	$-0.480202\pi$
$661$	3.19615			0.124316			0.0621580	+	0.998066i	$0.480202\pi$
$662$	−0.759865	−	0.552074i	−0.0295330	−	0.0214570i
$663$	−2.42870	+	23.9101i	−0.0943229	+	0.928592i
$664$	−19.0097	−	58.5058i	−0.737719	−	2.27047i
$665$	−5.04685	−	6.94640i	−0.195709	−	0.269370i
$666$	37.1239	−	65.3500i	1.43852	−	2.53226i
$667$		0			0
$668$	−6.06384	+	18.6626i	−0.234617	+	0.722076i
$669$	9.03631	−	20.4881i	0.349364	−	0.792114i
$670$		−	5.93426i		−	0.229260i
$671$		0			0
$672$	−11.4641	+	2.47863i	−0.442237	+	0.0956151i
$673$	−21.3899	+	29.4406i	−0.824519	+	1.13485i	0.164400	+	0.986394i	$0.447431\pi$
$673$	−21.3899	+	29.4406i	−0.824519	+	1.13485i	−0.988919	+	0.148459i	$0.952569\pi$
$674$	−19.4055	−	6.30524i	−0.747473	−	0.242869i
$675$	10.4271	−	14.6723i	0.401338	−	0.564737i
$676$	−5.44634	+	3.95700i	−0.209475	+	0.152192i
$677$	9.30469	−	6.76025i	0.357608	−	0.259818i	−0.394446	−	0.918919i	$-0.629063\pi$
$677$	9.30469	−	6.76025i	0.357608	−	0.259818i	0.752054	+	0.659102i	$0.229063\pi$
$678$	27.0510	+	46.4783i	1.03889	+	1.78499i
$679$	6.10077	+	1.98226i	0.234126	+	0.0760722i
$680$	−12.5265	+	17.2413i	−0.480371	+	0.661174i
$681$	1.92455	+	8.90138i	0.0737488	+	0.341102i
$682$		0			0
$683$		−	41.2946i		−	1.58009i	−0.613047	−	0.790046i	$-0.710056\pi$
$683$		−	41.2946i		−	1.58009i	0.613047	−	0.790046i	$-0.289944\pi$
$684$	5.51453	−	26.8647i	0.210853	−	1.02720i
$685$	−6.83086	+	21.0232i	−0.260994	+	0.803256i
$686$	38.6418	−	12.5555i	1.47535	−	0.479371i
$687$	−7.14797	−	6.39102i	−0.272712	−	0.243833i
$688$	−6.14488	−	8.45770i	−0.234271	−	0.322447i
$689$	7.34527	+	22.6064i	0.279833	+	0.861236i
$690$		0			0
$691$	−2.09411	−	1.52146i	−0.0796635	−	0.0578790i	0.547241	−	0.836975i	$-0.315678\pi$
$691$	−2.09411	−	1.52146i	−0.0796635	−	0.0578790i	−0.626904	+	0.779096i	$0.715678\pi$
$692$	42.2817			1.60731
$693$		0			0
$694$	−3.07180			−0.116604
$695$	−5.18997	−	3.77074i	−0.196867	−	0.143032i
$696$	38.8003	+	3.94119i	1.47072	+	0.149391i
$697$	−9.20395	−	28.3268i	−0.348624	−	1.07296i
$698$	−28.5907	−	39.3518i	−1.08218	−	1.48949i
$699$	−7.01104	−	6.26860i	−0.265182	−	0.237100i
$700$	−34.7768	+	11.2997i	−1.31444	+	0.427087i
$701$	6.15584	−	18.9457i	0.232503	−	0.715570i	−0.764940	−	0.644102i	$-0.777231\pi$
$701$	6.15584	−	18.9457i	0.232503	−	0.715570i	0.997443	−	0.0714686i	$-0.0227686\pi$
$702$	41.6244	−	0.435914i	1.57101	−	0.0164525i
$703$			25.6317i			0.966718i
$704$		0			0
$705$	−1.53590	−	7.10381i	−0.0578453	−	0.267545i
$706$	13.4850	−	18.5605i	0.507513	−	0.698532i
$707$	1.26328	+	0.410465i	0.0475106	+	0.0154371i
$708$	−41.0876	−	70.5956i	−1.54417	−	2.65314i
$709$	−31.8110	+	23.1120i	−1.19469	+	0.867990i	−0.993752	−	0.111615i	$-0.964398\pi$
$709$	−31.8110	+	23.1120i	−1.19469	+	0.867990i	−0.200934	+	0.979605i	$0.564398\pi$
$710$	20.0273	−	14.5507i	0.751611	−	0.546078i
$711$	16.2795	−	14.8653i	0.610531	−	0.557491i
$712$	−37.7918	−	12.2793i	−1.41631	−	0.460187i
$713$		0			0
$714$	47.5396	−	10.2784i	1.77913	−	0.384661i
$715$		0			0
$716$		−	85.0677i		−	3.17913i
$717$	−7.02197	+	15.9209i	−0.262240	+	0.594579i
$718$	−25.4931	+	78.4597i	−0.951394	+	2.92809i
$719$	−34.0964	+	11.0786i	−1.27158	+	0.413162i	−0.865608	−	0.500722i	$-0.833068\pi$
$719$	−34.0964	+	11.0786i	−1.27158	+	0.413162i	−0.405975	+	0.913884i	$0.633068\pi$
$720$	7.96578	+	4.52519i	0.296867	+	0.168644i
$721$	−21.1671	−	29.1341i	−0.788305	−	1.08501i
$722$	−9.61791	−	29.6009i	−0.357942	−	1.10163i
$723$	0.658509	−	6.48291i	0.0244902	−	0.241102i
$724$	−38.8173	−	28.2024i	−1.44263	−	1.04813i
$725$	−18.8096			−0.698570
$726$		0			0
$727$	−28.9282			−1.07289			−0.536444	−	0.843936i	$-0.680233\pi$
$727$	−28.9282			−1.07289			−0.536444	+	0.843936i	$0.680233\pi$
$728$	−31.7507	−	23.0682i	−1.17676	−	0.854964i
$729$	22.1710	+	15.4093i	0.821149	+	0.570713i
$730$	−7.43265	−	22.8753i	−0.275095	−	0.846654i
$731$	−10.3412	−	14.2334i	−0.382483	−	0.526442i
$732$	−19.4748	+	21.7813i	−0.719808	+	0.805061i
$733$	−27.2957	+	8.86890i	−1.00819	+	0.327580i	−0.766133	−	0.642682i	$-0.777822\pi$
$733$	−27.2957	+	8.86890i	−1.00819	+	0.327580i	−0.242056	+	0.970262i	$0.577822\pi$
$734$	17.6499	−	54.3208i	0.651470	−	2.00502i
$735$	−1.96401	−	0.866232i	−0.0724436	−	0.0319514i
$736$		0			0
$737$		0			0
$738$	−46.9808	+	21.3114i	−1.72939	+	0.784484i
$739$	−13.2404	+	18.2238i	−0.487055	+	0.670374i	−0.979842	−	0.199776i	$-0.935978\pi$
$739$	−13.2404	+	18.2238i	−0.487055	+	0.670374i	0.492786	+	0.870150i	$0.335978\pi$
$740$	−46.0296	−	14.9559i	−1.69208	−	0.549791i
$741$	−12.2694	+	7.14095i	−0.450727	+	0.262329i
$742$	38.9179	−	28.2755i	1.42872	−	1.03803i
$743$	−22.9650	+	16.6850i	−0.842503	+	0.612114i	−0.923069	−	0.384635i	$-0.874327\pi$
$743$	−22.9650	+	16.6850i	−0.842503	+	0.612114i	0.0805659	+	0.996749i	$0.474327\pi$
$744$	1.21765	−	0.708688i	0.0446411	−	0.0259818i
$745$	−11.0850	−	3.60174i	−0.406124	−	0.131958i
$746$	13.5408	−	18.6373i	0.495763	−	0.682359i
$747$	−40.5290	+	18.3848i	−1.48288	+	0.672664i
$748$		0			0
$749$			9.91451i			0.362268i
$750$	−39.7997	−	17.5538i	−1.45328	−	0.640972i
$751$	1.50666	−	4.63701i	0.0549787	−	0.169207i	−0.919797	−	0.392395i	$-0.871647\pi$
$751$	1.50666	−	4.63701i	0.0549787	−	0.169207i	0.974775	+	0.223188i	$0.0716465\pi$
$752$	−7.93478	+	2.57817i	−0.289352	+	0.0940161i
$753$	−9.91251	+	11.0865i	−0.361232	+	0.404016i
$754$	−25.5680	−	35.1913i	−0.931131	−	1.28159i
$755$	−6.31519	−	19.4362i	−0.229833	−	0.707354i
$756$	−17.4948	−	51.9848i	−0.636281	−	1.89067i
$757$	5.38826	+	3.91480i	0.195840	+	0.142286i	0.681384	−	0.731926i	$-0.261379\pi$
$757$	5.38826	+	3.91480i	0.195840	+	0.142286i	−0.485544	+	0.874212i	$0.661379\pi$
$758$	73.2340			2.65998
$759$		0			0
$760$	−12.5885			−0.456631
$761$	−23.3822	−	16.9881i	−0.847603	−	0.615819i	0.0768814	−	0.997040i	$-0.475504\pi$
$761$	−23.3822	−	16.9881i	−0.847603	−	0.615819i	−0.924484	+	0.381221i	$0.875504\pi$
$762$	6.04269	−	59.4892i	0.218903	−	2.15507i
$763$	9.34737	+	28.7682i	0.338397	+	1.04148i
$764$	5.43723	+	7.48370i	0.196712	+	0.270751i
$765$	13.4056	+	7.61542i	0.484679	+	0.275336i
$766$	21.6165	−	7.02363i	0.781037	−	0.253774i
$767$	−13.0657	+	40.2122i	−0.471777	+	1.45198i
$768$	−19.7949	+	44.8811i	−0.714288	+	1.61951i
$769$		−	11.9329i		−	0.430311i	−0.976580	−	0.215155i	$-0.930974\pi$
$769$		−	11.9329i		−	0.430311i	0.976580	−	0.215155i	$-0.0690258\pi$
$770$		0			0
$771$	39.1506	−	8.46467i	1.40998	−	0.304848i
$772$	6.28609	−	8.65206i	0.226241	−	0.311394i
$773$	−29.3818	−	9.54673i	−1.05679	−	0.343372i	−0.271460	−	0.962450i	$-0.587507\pi$
$773$	−29.3818	−	9.54673i	−1.05679	−	0.343372i	−0.785330	+	0.619078i	$0.787507\pi$
$774$	−22.5028	+	20.5479i	−0.808847	+	0.738579i
$775$	−0.549721	+	0.399395i	−0.0197465	+	0.0143467i
$776$	7.60863	−	5.52800i	0.273134	−	0.198443i
$777$	25.7865	+	44.3057i	0.925086	+	1.58946i
$778$	43.4356	+	14.1131i	1.55724	+	0.505979i
$779$	10.3412	−	14.2334i	0.370512	−	0.509966i
$780$	−5.66467	−	26.2001i	−0.202828	−	0.938115i
$781$		0			0
$782$		0			0
$783$	−0.295461	−	28.2128i	−0.0105589	−	1.00824i
$784$	−0.761449	+	2.34350i	−0.0271946	+	0.0836964i
$785$	13.5122	−	4.39040i	0.482273	−	0.156700i
$786$	41.8929	+	37.4566i	1.49427	+	1.33603i
$787$	−26.7632	−	36.8364i	−0.954004	−	1.31307i	−0.949726	−	0.313083i	$-0.898638\pi$
$787$	−26.7632	−	36.8364i	−0.954004	−	1.31307i	−0.00427854	−	0.999991i	$-0.501362\pi$
$788$	−12.3259	−	37.9353i	−0.439092	−	1.35139i
$789$	40.4467	+	4.10842i	1.43994	+	0.146264i
$790$	−17.6397	−	12.8160i	−0.627592	−	0.455972i
$791$	−36.6799			−1.30419
$792$		0			0
$793$	15.1244			0.537082
$794$	−41.0553	−	29.8285i	−1.45700	−	1.05857i
$795$	15.1706	+	1.54098i	0.538047	+	0.0546528i
$796$	8.83432	+	27.1892i	0.313124	+	0.963697i
$797$	9.02718	+	12.4248i	0.319759	+	0.440111i	0.938394	−	0.345568i	$-0.112314\pi$
$797$	9.02718	+	12.4248i	0.319759	+	0.440111i	−0.618635	+	0.785679i	$0.712314\pi$
$798$	21.4176	+	19.1495i	0.758173	+	0.677885i
$799$	−13.3534	+	4.33878i	−0.472409	+	0.153495i
$800$	2.56288	−	7.88773i	0.0906114	−	0.278873i
$801$	−5.78045	+	28.1602i	−0.204242	+	0.994990i
$802$		−	2.96713i		−	0.104773i
$803$		0			0
$804$	2.73205	+	12.6362i	0.0963520	+	0.445646i
$805$		0			0
$806$	−1.49448	−	0.485585i	−0.0526407	−	0.0171040i
$807$	−14.2487	−	24.4817i	−0.501577	−	0.861796i
$808$	1.57551	−	1.14468i	0.0554264	−	0.0402696i
$809$	−41.9543	+	30.4816i	−1.47503	+	1.07167i	−0.495918	+	0.868369i	$0.665168\pi$
$809$	−41.9543	+	30.4816i	−1.47503	+	1.07167i	−0.979115	+	0.203306i	$0.934832\pi$
$810$	10.5199	−	24.5447i	0.369631	−	0.862414i
$811$	−24.7376	−	8.03773i	−0.868654	−	0.282243i	−0.159416	−	0.987212i	$-0.550961\pi$
$811$	−24.7376	−	8.03773i	−0.868654	−	0.282243i	−0.709239	+	0.704969i	$0.750961\pi$
$812$	−33.6899	+	46.3702i	−1.18228	+	1.62727i
$813$	−15.4762	+	3.34607i	−0.542773	+	0.117352i
$814$		0			0
$815$			15.3580i			0.537966i
$816$	7.14212	−	16.1934i	0.250024	−	0.566881i
$817$	3.21140	−	9.88367i	0.112353	−	0.345786i
$818$	75.6426	−	24.5778i	2.64478	−	0.859342i
$819$	−14.0241	+	24.6870i	−0.490043	+	0.862632i
$820$	19.5265	+	26.8759i	0.681894	+	0.938546i
$821$	−6.75056	−	20.7761i	−0.235596	−	0.725090i	−0.997042	−	0.0768614i	$-0.975510\pi$
$821$	−6.75056	−	20.7761i	−0.235596	−	0.725090i	0.761446	−	0.648229i	$-0.224490\pi$
$822$	7.47464	−	73.5865i	0.260708	−	2.56662i
$823$	−26.5970	−	19.3238i	−0.927112	−	0.673586i	0.0181723	−	0.999835i	$-0.494215\pi$
$823$	−26.5970	−	19.3238i	−0.927112	−	0.673586i	−0.945284	+	0.326249i	$0.894215\pi$
$824$	−52.7976			−1.83929
$825$		0			0
$826$	85.5692			2.97733
$827$	15.2173	+	11.0560i	0.529156	+	0.384454i	0.820042	−	0.572303i	$-0.193950\pi$
$827$	15.2173	+	11.0560i	0.529156	+	0.384454i	−0.290886	+	0.956758i	$0.593950\pi$
$828$		0			0
$829$	6.05317	+	18.6297i	0.210235	+	0.647037i	0.999458	+	0.0329299i	$0.0104838\pi$
$829$	6.05317	+	18.6297i	0.210235	+	0.647037i	−0.789223	+	0.614107i	$0.789516\pi$
$830$	25.8721	+	35.6099i	0.898034	+	1.23604i
$831$	7.24547	−	8.10362i	0.251343	−	0.281112i
$832$	33.9241	−	11.0226i	1.17611	−	0.382140i
$833$	−1.28144	+	3.94386i	−0.0443992	+	0.136647i
$834$	19.6401	+	8.66232i	0.680081	+	0.299952i
$835$		−	6.51626i		−	0.225505i
$836$		0			0
$837$	−0.607695	−	0.818262i	−0.0210050	−	0.0282833i
$838$	15.5711	−	21.4318i	0.537894	−	0.740348i
$839$	−17.8264	−	5.79216i	−0.615437	−	0.199968i	−0.0153236	−	0.999883i	$-0.504878\pi$
$839$	−17.8264	−	5.79216i	−0.615437	−	0.199968i	−0.600113	+	0.799915i	$0.704878\pi$
$840$	−21.7598	+	12.6645i	−0.750783	+	0.436966i
$841$	−0.391030	+	0.284100i	−0.0134838	+	0.00979655i
$842$	−37.1815	+	27.0139i	−1.28136	+	0.930962i
$843$	1.21765	−	0.708688i	0.0419380	−	0.0244085i
$844$	−6.72499	−	2.18508i	−0.231484	−	0.0752136i
$845$	1.31401	−	1.80858i	0.0452034	−	0.0622172i
$846$	10.0463	+	22.1469i	0.345399	+	0.761428i
$847$		0			0
$848$		−	17.5045i		−	0.601107i
$849$	10.7663	+	4.74851i	0.369499	+	0.162968i
$850$	−10.6278	+	32.7090i	−0.364531	+	1.12191i
$851$		0			0
$852$	−35.9466	+	40.2041i	−1.23151	+	1.37737i
$853$	25.0191	+	34.4359i	0.856639	+	1.17906i	0.982360	+	0.186997i	$0.0598755\pi$
$853$	25.0191	+	34.4359i	0.856639	+	1.17906i	−0.125721	+	0.992066i	$0.540125\pi$
$854$	−9.45856	−	29.1104i	−0.323665	−	0.996139i
$855$	1.01516	+	9.05030i	0.0347176	+	0.309514i
$856$	11.7598	+	8.54399i	0.401941	+	0.292027i
$857$	56.3029			1.92327			0.961635	−	0.274332i	$-0.0884568\pi$
$857$	56.3029			1.92327			0.961635	+	0.274332i	$0.0884568\pi$
$858$		0			0
$859$	1.12436			0.0383625			0.0191813	−	0.999816i	$-0.493894\pi$
$859$	1.12436			0.0383625			0.0191813	+	0.999816i	$0.493894\pi$
$860$	15.8753	+	11.5341i	0.541344	+	0.393310i
$861$	3.55586	−	35.0068i	0.121183	−	1.19303i
$862$	15.4671	+	47.6028i	0.526811	+	1.62136i
$863$	−16.9878	−	23.3817i	−0.578272	−	0.795924i	0.415232	−	0.909715i	$-0.363700\pi$
$863$	−16.9878	−	23.3817i	−0.578272	−	0.795924i	−0.993505	+	0.113792i	$0.963700\pi$
$864$	11.8712	+	3.72021i	0.403866	+	0.126564i
$865$	−13.3534	+	4.33878i	−0.454029	+	0.147523i
$866$	−9.65680	+	29.7206i	−0.328151	+	1.00995i
$867$	0.137103	−	0.310854i	0.00465626	−	0.0105572i
$868$			2.07055i			0.0702791i
$869$		0			0
$870$	−27.2750	+	5.89706i	−0.924709	+	0.199929i
$871$	3.93354	−	5.41405i	0.133283	−	0.183448i
$872$	42.1778	+	13.7044i	1.42832	+	0.464089i
$873$	−4.58785	−	5.02434i	−0.155275	−	0.170048i
$874$		0			0
$875$	24.0030	−	17.4392i	0.811448	−	0.589552i
$876$	26.3584	+	45.2882i	0.890567	+	1.53015i
$877$	−27.3664	−	8.89187i	−0.924097	−	0.300257i	−0.191950	−	0.981405i	$-0.561481\pi$
$877$	−27.3664	−	8.89187i	−0.924097	−	0.300257i	−0.732146	+	0.681147i	$0.761481\pi$
$878$	11.7981	−	16.2387i	0.398166	−	0.548029i
$879$	−11.9079	−	55.0764i	−0.401645	−	1.85768i
$880$		0			0
$881$		−	13.6325i		−	0.459289i	−0.973275	−	0.229644i	$-0.926244\pi$
$881$		−	13.6325i		−	0.459289i	0.973275	−	0.229644i	$-0.0737563\pi$
$882$	7.03581	+	1.44424i	0.236908	+	0.0486302i
$883$	−3.54260	+	10.9030i	−0.119218	+	0.366915i	−0.992803	−	0.119756i	$-0.961789\pi$
$883$	−3.54260	+	10.9030i	−0.119218	+	0.366915i	0.873585	+	0.486671i	$0.161789\pi$
$884$	−49.2497	+	16.0022i	−1.65645	+	0.538213i
$885$	20.2206	+	18.0793i	0.679707	+	0.607728i
$886$	35.9070	+	49.4217i	1.20632	+	1.66035i
$887$	−14.0038	−	43.0994i	−0.470203	−	1.44713i	−0.852320	−	0.523021i	$-0.824805\pi$
$887$	−14.0038	−	43.0994i	−0.470203	−	1.44713i	0.382117	−	0.924114i	$-0.375195\pi$
$888$	74.7738	+	7.59524i	2.50924	+	0.254879i
$889$	32.9954	+	23.9726i	1.10663	+	0.804015i
$890$	28.4323			0.953053
$891$		0			0
$892$	48.2487			1.61549
$893$	−6.70970	−	4.87488i	−0.224532	−	0.163132i
$894$	38.8003	+	3.94119i	1.29768	+	0.131813i
$895$	8.72933	+	26.8661i	0.291789	+	0.898035i
$896$	−34.4706	−	47.4448i	−1.15158	−	1.58502i
$897$		0			0
$898$	−91.7590	+	29.8143i	−3.06204	+	0.994916i
$899$	−0.329128	+	1.01295i	−0.0109770	+	0.0337838i
$900$	37.9924	+	7.79872i	1.26641	+	0.259957i
$901$		−	29.4582i		−	0.981397i
$902$		0			0
$903$	−4.39230	−	20.3152i	−0.146167	−	0.676048i
$904$	−31.6095	+	43.5067i	−1.05132	+	1.44701i
$905$	15.1533	+	4.92360i	0.503713	+	0.163666i
$906$	34.3973	+	59.1004i	1.14277	+	1.96348i
$907$	21.3943	−	15.5439i	0.710388	−	0.516127i	−0.172911	−	0.984937i	$-0.555317\pi$
$907$	21.3943	−	15.5439i	0.710388	−	0.516127i	0.883299	+	0.468811i	$0.155317\pi$
$908$	−15.8753	+	11.5341i	−0.526841	+	0.382773i
$909$	−0.950002	−	1.04039i	−0.0315096	−	0.0345074i
$910$	26.7068	+	8.67757i	0.885322	+	0.287659i
$911$	−18.6922	+	25.7276i	−0.619301	+	0.852395i	−0.997302	−	0.0734107i	$-0.976612\pi$
$911$	−18.6922	+	25.7276i	−0.619301	+	0.852395i	0.378001	+	0.925805i	$0.376612\pi$
$912$	10.2182	−	2.20925i	0.338358	−	0.0731557i
$913$		0			0
$914$		−	44.1053i		−	1.45887i
$915$	3.91540	−	8.87741i	0.129439	−	0.293478i
$916$	6.38437	−	19.6491i	0.210946	−	0.649224i
$917$	−36.4538	+	11.8445i	−1.20381	+	0.391141i
$918$	−49.2278	−	15.4270i	−1.62476	−	0.509168i
$919$	22.9330	+	31.5646i	0.756490	+	1.04122i	0.997498	+	0.0706963i	$0.0225221\pi$
$919$	22.9330	+	31.5646i	0.756490	+	1.04122i	−0.241008	+	0.970523i	$0.577478\pi$
$920$		0			0
$921$	−5.45881	+	53.7410i	−0.179874	+	1.77083i
$922$	5.54695	+	4.03009i	0.182679	+	0.132724i
$923$	27.9166			0.918887
$924$		0			0
$925$	−36.2487			−1.19185
$926$	−2.45592	−	1.78433i	−0.0807066	−	0.0586368i
$927$	4.25769	+	37.9581i	0.139841	+	1.24671i
$928$	−4.01722	−	12.3637i	−0.131872	−	0.405859i
$929$	18.7828	+	25.8523i	0.616244	+	0.848187i	0.997073	−	0.0764586i	$-0.0243613\pi$
$929$	18.7828	+	25.8523i	0.616244	+	0.848187i	−0.380829	+	0.924646i	$0.624361\pi$
$930$	−0.671911	+	0.751492i	−0.0220328	+	0.0246424i
$931$	−2.32960	+	0.756934i	−0.0763497	+	0.0248075i
$932$	6.26207	−	19.2727i	0.205121	−	0.631298i
$933$	−1.05251	−	0.464212i	−0.0344576	−	0.0151976i
$934$			46.4660i			1.52041i
$935$		0			0
$936$	17.1962	+	37.9087i	0.562074	+	1.23908i
$937$	16.8100	−	23.1369i	0.549158	−	0.755851i	−0.440740	−	0.897635i	$-0.645284\pi$
$937$	16.8100	−	23.1369i	0.549158	−	0.755851i	0.989898	+	0.141784i	$0.0452838\pi$
$938$	−12.8806	−	4.18516i	−0.420567	−	0.136650i
$939$	11.0660	−	6.44059i	0.361127	−	0.210181i
$940$	12.6694	−	9.20487i	0.413231	−	0.300230i
$941$	−1.65879	+	1.20518i	−0.0540752	+	0.0392879i	−0.614494	−	0.788921i	$-0.710640\pi$
$941$	−1.65879	+	1.20518i	−0.0540752	+	0.0392879i	0.560419	+	0.828209i	$0.310640\pi$
$942$	−41.0873	+	23.9134i	−1.33870	+	0.779140i
$943$		0			0
$944$	18.3018	−	25.1903i	0.595674	−	0.819875i
$945$	10.8597	+	14.6226i	0.353266	+	0.475674i
$946$		0			0
$947$			30.2297i			0.982334i	0.871065	+	0.491167i	$0.163429\pi$
$947$			30.2297i			0.982334i	−0.871065	+	0.491167i	$0.836571\pi$
$948$	43.4617	+	19.1689i	1.41157	+	0.622577i
$949$	8.38189	−	25.7968i	0.272088	−	0.837399i
$950$	−19.3209	+	6.27774i	−0.626853	+	0.203677i
$951$	28.4095	−	31.7743i	0.921242	−	1.03035i
$952$	28.5887	+	39.3490i	0.926566	+	1.27531i
$953$	17.0163	+	52.3708i	0.551212	+	1.69646i	0.705742	+	0.708468i	$0.250614\pi$
$953$	17.0163	+	52.3708i	0.551212	+	1.69646i	−0.154530	+	0.987988i	$0.549386\pi$
$954$	−50.7052	+	5.68751i	−1.64164	+	0.184140i
$955$	−2.48514	−	1.80556i	−0.0804171	−	0.0584264i
$956$	−37.4933			−1.21262
$957$		0			0
$958$	15.6603			0.505960
$959$	40.8145	+	29.6535i	1.31797	+	0.957560i
$960$	2.31245	−	22.7657i	0.0746340	−	0.734759i
$961$	−9.56764	−	29.4462i	−0.308633	−	0.949876i
$962$	−49.2731	−	67.8186i	−1.58863	−	2.18656i
$963$	5.19425	−	9.14354i	0.167383	−	0.294647i
$964$	13.3534	−	4.33878i	0.430084	−	0.139743i
$965$	−1.09743	+	3.37755i	−0.0353276	+	0.108727i
$966$		0			0
$967$			45.0518i			1.44877i	0.689397	+	0.724383i	$0.257875\pi$
$967$			45.0518i			1.44877i	−0.689397	+	0.724383i	$0.742125\pi$
$968$		0			0
$969$	17.1962	−	3.71794i	0.552420	−	0.119437i
$970$	−3.95538	+	5.44411i	−0.127000	+	0.174800i
$971$	7.07194	+	2.29781i	0.226949	+	0.0737404i	0.420284	−	0.907392i	$-0.361930\pi$
$971$	7.07194	+	2.29781i	0.226949	+	0.0737404i	−0.193335	+	0.981133i	$0.561930\pi$
$972$	−11.1007	+	57.1080i	−0.356054	+	1.83174i
$973$	−11.8448	+	8.60577i	−0.379728	+	0.275888i
$974$	64.2612	−	46.6885i	2.05906	−	1.49600i
$975$	−10.0988	−	17.3515i	−0.323421	−	0.555693i
$976$	−10.5927	−	3.44178i	−0.339065	−	0.110169i
$977$	−6.55605	+	9.02363i	−0.209747	+	0.288692i	−0.900909	−	0.434008i	$-0.857099\pi$
$977$	−6.55605	+	9.02363i	−0.209747	+	0.288692i	0.691162	+	0.722700i	$0.257099\pi$
$978$	−10.8597	−	50.2281i	−0.347255	−	1.60612i
$979$		0			0
$980$		−	4.62518i		−	0.147746i
$981$	6.45130	−	31.4283i	0.205974	−	1.00343i
$982$	−15.4671	+	47.6028i	−0.493575	+	1.51907i
$983$	−0.462393	+	0.150241i	−0.0147480	+	0.00479193i	−0.316382	−	0.948632i	$-0.602468\pi$
$983$	−0.462393	+	0.150241i	−0.0147480	+	0.00479193i	0.301634	+	0.953424i	$0.402468\pi$
$984$	−38.4580	−	34.3854i	−1.22599	−	1.09617i
$985$	7.78554	+	10.7159i	0.248068	+	0.341436i
$986$	16.6587	+	51.2702i	0.530521	+	1.63278i
$987$	−16.5024	−	1.67625i	−0.525277	−	0.0533556i
$988$	−24.7466	−	17.9794i	−0.787294	−	0.572002i
$989$		0			0
$990$		0			0
$991$	19.8564			0.630760			0.315380	−	0.948966i	$-0.397868\pi$
$991$	19.8564			0.630760			0.315380	+	0.948966i	$0.397868\pi$
$992$	−0.379932	−	0.276037i	−0.0120629	−	0.00876419i
$993$	−0.676013	−	0.0686669i	−0.0214526	−	0.00217908i
$994$	−17.4587	−	53.7322i	−0.553755	−	1.70428i
$995$	−5.58011	−	7.68037i	−0.176902	−	0.243484i
$996$	−71.4857	−	63.9156i	−2.26511	−	2.02524i
$997$	57.5098	−	18.6861i	1.82135	−	0.591794i	0.821590	−	0.570078i	$-0.193087\pi$
$997$	57.5098	−	18.6861i	1.82135	−	0.591794i	0.999764	−	0.0217156i	$-0.00691282\pi$
$998$	−19.0907	+	58.7551i	−0.604306	+	1.85986i
$999$	−0.569395	−	54.3701i	−0.0180148	−	1.72019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.i.161.8		32
3.2	odd	2	inner	363.2.f.i.161.1		32
11.2	odd	10	inner	363.2.f.i.215.8		32
11.3	even	5	inner	363.2.f.i.239.7		32
11.4	even	5	inner	363.2.f.i.233.1		32
11.5	even	5		363.2.d.e.362.2	yes	8
11.6	odd	10		363.2.d.e.362.8	yes	8
11.7	odd	10	inner	363.2.f.i.233.7		32
11.8	odd	10	inner	363.2.f.i.239.1		32
11.9	even	5	inner	363.2.f.i.215.2		32
11.10	odd	2	inner	363.2.f.i.161.2		32
33.2	even	10	inner	363.2.f.i.215.1		32
33.5	odd	10		363.2.d.e.362.7	yes	8
33.8	even	10	inner	363.2.f.i.239.8		32
33.14	odd	10	inner	363.2.f.i.239.2		32
33.17	even	10		363.2.d.e.362.1	✓	8
33.20	odd	10	inner	363.2.f.i.215.7		32
33.26	odd	10	inner	363.2.f.i.233.8		32
33.29	even	10	inner	363.2.f.i.233.2		32
33.32	even	2	inner	363.2.f.i.161.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.e.362.1	✓	8	33.17	even	10
363.2.d.e.362.2	yes	8	11.5	even	5
363.2.d.e.362.7	yes	8	33.5	odd	10
363.2.d.e.362.8	yes	8	11.6	odd	10
363.2.f.i.161.1		32	3.2	odd	2	inner
363.2.f.i.161.2		32	11.10	odd	2	inner
363.2.f.i.161.7		32	33.32	even	2	inner
363.2.f.i.161.8		32	1.1	even	1	trivial
363.2.f.i.215.1		32	33.2	even	10	inner
363.2.f.i.215.2		32	11.9	even	5	inner
363.2.f.i.215.7		32	33.20	odd	10	inner
363.2.f.i.215.8		32	11.2	odd	10	inner
363.2.f.i.233.1		32	11.4	even	5	inner
363.2.f.i.233.2		32	33.29	even	10	inner
363.2.f.i.233.7		32	11.7	odd	10	inner
363.2.f.i.233.8		32	33.26	odd	10	inner
363.2.f.i.239.1		32	11.8	odd	10	inner
363.2.f.i.239.2		32	33.14	odd	10	inner
363.2.f.i.239.7		32	11.3	even	5	inner
363.2.f.i.239.8		32	33.8	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93692 + 1.40726i) q^{2} +(1.72318 + 0.175035i) q^{3} +(1.15327 + 3.54939i) q^{4} +(-0.728450 - 1.00263i) q^{5} +(3.09136 + 2.76399i) q^{6} +(-2.68999 + 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(2.93873 + 0.603233i) q^{9} +O(q^{10})\)	\(q+(1.93692 + 1.40726i) q^{2} +(1.72318 + 0.175035i) q^{3} +(1.15327 + 3.54939i) q^{4} +(-0.728450 - 1.00263i) q^{5} +(3.09136 + 2.76399i) q^{6} +(-2.68999 + 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(2.93873 + 0.603233i) q^{9} -2.96713i q^{10} +(1.36603 + 6.31812i) q^{12} +(1.96677 - 2.70702i) q^{13} +(-6.44030 - 2.09258i) q^{14} +(-1.07976 - 1.85521i) q^{15} +(-1.99350 + 1.44836i) q^{16} +(-3.35485 + 2.43744i) q^{17} +(4.84318 + 5.30396i) q^{18} +(-2.32960 - 0.756934i) q^{19} +(2.71861 - 3.74185i) q^{20} +(-4.78834 + 1.03528i) q^{21} +(-2.89847 + 6.57171i) q^{24} +(1.07047 - 3.29456i) q^{25} +(7.61896 - 2.47555i) q^{26} +(4.95838 + 1.55386i) q^{27} +(-6.20456 - 8.53985i) q^{28} +(-1.67792 - 5.16410i) q^{29} +(0.519350 - 5.11291i) q^{30} +(-0.158691 - 0.115296i) q^{31} +2.39417 q^{32} -9.92820 q^{34} +(2.83585 + 2.06037i) q^{35} +(1.24802 + 11.1264i) q^{36} +(-3.23359 - 9.95195i) q^{37} +(-3.44706 - 4.74448i) q^{38} +(3.86293 - 4.32045i) q^{39} +(4.88769 - 1.58811i) q^{40} +(-2.21952 + 6.83097i) q^{41} +(-10.7316 - 4.73318i) q^{42} +4.24264i q^{43} +(-1.53590 - 3.38587i) q^{45} +(3.22015 + 1.04629i) q^{47} +(-3.68868 + 2.14686i) q^{48} +(0.809017 - 0.587785i) q^{49} +(6.70970 - 4.87488i) q^{50} +(-6.20766 + 3.61295i) q^{51} +(11.8765 + 3.85891i) q^{52} +(-4.17551 + 5.74710i) q^{53} +(7.41732 + 9.98743i) q^{54} -11.7290i q^{56} +(-3.88185 - 1.71210i) q^{57} +(4.01722 - 12.3637i) q^{58} +(-12.0178 + 3.90481i) q^{59} +(5.33962 - 5.97205i) q^{60} +(2.65681 + 3.65679i) q^{61} +(-0.145121 - 0.446637i) q^{62} +(-8.43240 + 0.945846i) q^{63} +(8.62433 + 6.26594i) q^{64} -4.14682 q^{65} +2.00000 q^{67} +(-12.5205 - 9.09666i) q^{68} +(2.59336 + 7.98156i) q^{70} +(4.90396 + 6.74973i) q^{71} +(-6.14487 + 10.8169i) q^{72} +(7.70959 - 2.50500i) q^{73} +(7.74175 - 23.8267i) q^{74} +(2.42127 - 5.48976i) q^{75} -9.14162i q^{76} +(13.5622 - 2.93225i) q^{78} +(4.31932 - 5.94504i) q^{79} +(2.90433 + 0.943674i) q^{80} +(8.27222 + 3.54547i) q^{81} +(-13.9120 + 10.1076i) q^{82} +(-12.0015 + 8.71958i) q^{83} +(-9.19684 - 15.8017i) q^{84} +(4.88769 + 1.58811i) q^{85} +(-5.97049 + 8.21767i) q^{86} +(-1.98747 - 9.19239i) q^{87} +9.58244i q^{89} +(1.78987 - 8.71958i) q^{90} +(-2.92457 + 9.00090i) q^{91} +(-0.253272 - 0.226452i) q^{93} +(4.76479 + 6.55817i) q^{94} +(0.938079 + 2.88711i) q^{95} +(4.12560 + 0.419062i) q^{96} +(-1.83481 - 1.33307i) q^{97} +2.39417 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9}+O(q^{10}) \) 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9	\( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9} + 16 q^{12} - 4 q^{15} + 8 q^{16} + 4 q^{27} + 40 q^{31} - 96 q^{34} + 40 q^{36} + 56 q^{37} - 64 q^{42} - 160 q^{45} - 28 q^{48} + 8 q^{49} - 104 q^{58} + 28 q^{60} + 16 q^{64} + 64 q^{67} + 16 q^{70} - 24 q^{75} + 240 q^{78} + 8 q^{81} - 96 q^{82} + 48 q^{91} - 56 q^{93} - 32 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9 + 16 * q^12 - 4 * q^15 + 8 * q^16 + 4 * q^27 + 40 * q^31 - 96 * q^34 + 40 * q^36 + 56 * q^37 - 64 * q^42 - 160 * q^45 - 28 * q^48 + 8 * q^49 - 104 * q^58 + 28 * q^60 + 16 * q^64 + 64 * q^67 + 16 * q^70 - 24 * q^75 + 240 * q^78 + 8 * q^81 - 96 * q^82 + 48 * q^91 - 56 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

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