LMFDB - Embedded newform 363.2.f.i.161.7

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			161.7
Character	$\chi$	$=$	363.161
Dual form			363.2.f.i.239.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93692 + 1.40726i) q^{2} +(-1.49697 - 0.871256i) q^{3} +(1.15327 + 3.54939i) q^{4} +(0.728450 + 1.00263i) q^{5} +(-1.67343 - 3.79418i) q^{6} +(2.68999 - 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(1.48183 + 2.60848i) q^{9} +O(q^{10})$	\(q+(1.93692 + 1.40726i) q^{2} +(-1.49697 - 0.871256i) q^{3} +(1.15327 + 3.54939i) q^{4} +(0.728450 + 1.00263i) q^{5} +(-1.67343 - 3.79418i) q^{6} +(2.68999 - 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(1.48183 + 2.60848i) q^{9} +2.96713i q^{10} +(1.36603 - 6.31812i) q^{12} +(-1.96677 + 2.70702i) q^{13} +(6.44030 + 2.09258i) q^{14} +(-0.216923 - 2.13557i) q^{15} +(-1.99350 + 1.44836i) q^{16} +(-3.35485 + 2.43744i) q^{17} +(-0.800628 + 7.13775i) q^{18} +(2.32960 + 0.756934i) q^{19} +(-2.71861 + 3.74185i) q^{20} +(-4.78834 - 1.03528i) q^{21} +(5.35439 - 4.78738i) q^{24} +(1.07047 - 3.29456i) q^{25} +(-7.61896 + 2.47555i) q^{26} +(0.0544141 - 5.19587i) q^{27} +(6.20456 + 8.53985i) q^{28} +(-1.67792 - 5.16410i) q^{29} +(2.58513 - 4.44169i) q^{30} +(-0.158691 - 0.115296i) q^{31} +2.39417 q^{32} -9.92820 q^{34} +(2.83585 + 2.06037i) q^{35} +(-7.54959 + 8.26786i) q^{36} +(-3.23359 - 9.95195i) q^{37} +(3.44706 + 4.74448i) q^{38} +(5.30270 - 2.33877i) q^{39} +(-4.88769 + 1.58811i) q^{40} +(-2.21952 + 6.83097i) q^{41} +(-7.81775 - 8.74368i) q^{42} -4.24264i q^{43} +(-1.53590 + 3.38587i) q^{45} +(-3.22015 - 1.04629i) q^{47} +(4.24610 - 0.431303i) q^{48} +(0.809017 - 0.587785i) q^{49} +(6.70970 - 4.87488i) q^{50} +(7.14574 - 0.725837i) q^{51} +(-11.8765 - 3.85891i) q^{52} +(4.17551 - 5.74710i) q^{53} +(7.41732 - 9.98743i) q^{54} +11.7290i q^{56} +(-2.82786 - 3.16279i) q^{57} +(4.01722 - 12.3637i) q^{58} +(12.0178 - 3.90481i) q^{59} +(7.32979 - 3.23282i) q^{60} +(-2.65681 - 3.65679i) q^{61} +(-0.145121 - 0.446637i) q^{62} +(6.26600 + 5.72165i) 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} +(-12.1864 + 2.50150i) q^{72} +(-7.70959 + 2.50500i) q^{73} +(7.74175 - 23.8267i) q^{74} +(-4.47286 + 3.99919i) q^{75} +9.14162i q^{76} +(13.5622 + 2.93225i) q^{78} +(-4.31932 + 5.94504i) q^{79} +(-2.90433 - 0.943674i) q^{80} +(-4.60839 + 7.73064i) q^{81} +(-13.9120 + 10.1076i) q^{82} +(-12.0015 + 8.71958i) q^{83} +(-1.84764 - 18.1896i) q^{84} +(-4.88769 - 1.58811i) q^{85} +(5.97049 - 8.21767i) q^{86} +(-1.98747 + 9.19239i) q^{87} -9.58244i q^{89} +(-7.73971 + 4.39676i) q^{90} +(-2.92457 + 9.00090i) q^{91} +(0.137103 + 0.310854i) q^{93} +(-4.76479 - 6.55817i) q^{94} +(0.938079 + 2.88711i) q^{95} +(-3.58400 - 2.08594i) 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	$0.378725\pi$
$3$	−1.49697	−	0.871256i	−0.864275	−	0.503020i
$3$	−1.49697	−	0.871256i	−0.864275	−	0.503020i
$4$	1.15327	+	3.54939i	0.576634	+	1.77470i
$5$	0.728450	+	1.00263i	0.325773	+	0.448388i	0.940219	−	0.340571i	$-0.110620\pi$
$5$	0.728450	+	1.00263i	0.325773	+	0.448388i	−0.614446	+	0.788959i	$0.710620\pi$
$6$	−1.67343	−	3.79418i	−0.683175	−	1.54897i
$7$	2.68999	−	0.874032i	1.01672	−	0.330353i	0.247194	−	0.968966i	$-0.420491\pi$
$7$	2.68999	−	0.874032i	1.01672	−	0.330353i	0.769528	+	0.638613i	$0.220491\pi$
$8$	−1.28144	+	3.94386i	−0.453057	+	1.39437i
$9$	1.48183	+	2.60848i	0.493942	+	0.869495i
$10$			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	−0.989391	−	0.145279i	$-0.953592\pi$
$13$	−1.96677	+	2.70702i	−0.545483	+	0.750793i	0.443907	+	0.896073i	$0.353592\pi$
$14$	6.44030	+	2.09258i	1.72124	+	0.559266i
$15$	−0.216923	−	2.13557i	−0.0560092	−	0.551401i
$16$	−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	$0.467725\pi$
$18$	−0.800628	+	7.13775i	−0.188710	+	1.68238i
$19$	2.32960	+	0.756934i	0.534448	+	0.173653i	0.563792	−	0.825917i	$-0.309342\pi$
$19$	2.32960	+	0.756934i	0.534448	+	0.173653i	−0.0293444	+	0.999569i	$0.509342\pi$
$20$	−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			$\pi$
$24$	5.35439	−	4.78738i	1.09296	−	0.977219i
$25$	1.07047	−	3.29456i	0.214093	−	0.658911i
$26$	−7.61896	+	2.47555i	−1.49420	+	0.485495i
$27$	0.0544141	−	5.19587i	0.0104720	−	0.999945i
$28$	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	$-0.268194\pi$
$30$	2.58513	−	4.44169i	0.471978	−	0.810939i
$31$	−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
$36$	−7.54959	+	8.26786i	−1.25827	+	1.37798i
$37$	−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
$39$	5.30270	−	2.33877i	0.849111	−	0.374503i
$40$	−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	$0.910471\pi$
$42$	−7.81775	−	8.74368i	−1.20631	−	1.34918i
$43$		−	4.24264i		−	0.646997i	−0.946229	−	0.323498i	$-0.895141\pi$
$43$		−	4.24264i		−	0.646997i	0.946229	−	0.323498i	$-0.104859\pi$
$44$		0			0
$45$	−1.53590	+	3.38587i	−0.228958	+	0.504735i
$46$		0			0
$47$	−3.22015	−	1.04629i	−0.469707	−	0.152617i	0.0645933	−	0.997912i	$-0.479425\pi$
$47$	−3.22015	−	1.04629i	−0.469707	−	0.152617i	−0.534301	+	0.845294i	$0.679425\pi$
$48$	4.24610	−	0.431303i	0.612872	−	0.0622532i
$49$	0.809017	−	0.587785i	0.115574	−	0.0839693i
$50$	6.70970	−	4.87488i	0.948895	−	0.689413i
$51$	7.14574	−	0.725837i	1.00060	−	0.101638i
$52$	−11.8765	−	3.85891i	−1.64697	−	0.535134i
$53$	4.17551	−	5.74710i	0.573551	−	0.789425i	−0.419419	−	0.907793i	$-0.637766\pi$
$53$	4.17551	−	5.74710i	0.573551	−	0.789425i	0.992970	+	0.118368i	$0.0377661\pi$
$54$	7.41732	−	9.98743i	1.00937	−	1.35912i
$55$		0			0
$56$			11.7290i			1.56735i
$57$	−2.82786	−	3.16279i	−0.374559	−	0.418921i
$58$	4.01722	−	12.3637i	0.527487	−	1.62344i
$59$	12.0178	−	3.90481i	1.56458	−	0.508363i	0.606554	−	0.795042i	$-0.292551\pi$
$59$	12.0178	−	3.90481i	1.56458	−	0.508363i	0.958027	+	0.286679i	$0.0925515\pi$
$60$	7.32979	−	3.23282i	0.946271	−	0.417355i
$61$	−2.65681	−	3.65679i	−0.340170	−	0.468204i	0.604321	−	0.796741i	$-0.293444\pi$
$61$	−2.65681	−	3.65679i	−0.340170	−	0.468204i	−0.944491	+	0.328537i	$0.893444\pi$
$62$	−0.145121	−	0.446637i	−0.0184304	−	0.0567230i
$63$	6.26600	+	5.72165i	0.789442	+	0.720860i
$64$	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	0.411919	−	0.911221i	$-0.364859\pi$
$71$	−4.90396	−	6.74973i	−0.581994	−	0.801045i	−0.993912	+	0.110175i	$0.964859\pi$
$72$	−12.1864	+	2.50150i	−1.43618	+	0.294805i
$73$	−7.70959	+	2.50500i	−0.902339	+	0.293188i	−0.723202	−	0.690636i	$-0.757331\pi$
$73$	−7.70959	+	2.50500i	−0.902339	+	0.293188i	−0.179137	+	0.983824i	$0.557331\pi$
$74$	7.74175	−	23.8267i	0.899961	−	2.76979i
$75$	−4.47286	+	3.99919i	−0.516481	+	0.461787i
$76$			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	−0.979637	−	0.200778i	$-0.935653\pi$
$79$	−4.31932	+	5.94504i	−0.485962	+	0.668869i	0.493675	+	0.869646i	$0.335653\pi$
$80$	−2.90433	−	0.943674i	−0.324714	−	0.105506i
$81$	−4.60839	+	7.73064i	−0.512043	+	0.858960i
$82$	−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	$0.997200\pi$
$84$	−1.84764	−	18.1896i	−0.201594	−	1.98465i
$85$	−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	$-0.830434\pi$
$89$		−	9.58244i		−	1.01574i	0.861435	−	0.507868i	$-0.169566\pi$
$90$	−7.73971	+	4.39676i	−0.815837	+	0.463460i
$91$	−2.92457	+	9.00090i	−0.306578	+	0.943550i
$92$		0			0
$93$	0.137103	+	0.310854i	0.0142169	+	0.0322340i
$94$	−4.76479	−	6.55817i	−0.491451	−	0.676424i
$95$	0.938079	+	2.88711i	0.0962448	+	0.296211i
$96$	−3.58400	−	2.08594i	−0.365790	−	0.212895i
$97$	−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	$0.707438\pi$
$102$	14.8622	+	8.65001i	1.47158	+	0.856478i
$103$	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
$105$	−2.45007	−	5.55506i	−0.239103	−	0.542118i
$106$	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	$0.0458056\pi$
$108$	18.5049	−	5.79909i	1.78064	−	0.558017i
$109$			10.6945i			1.02435i	0.858881	+	0.512175i	$0.171160\pi$
$109$			10.6945i			1.02435i	−0.858881	+	0.512175i	$0.828840\pi$
$110$		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	−0.335252	−	0.942128i	$-0.608822\pi$
$113$	−12.3336	−	4.00743i	−1.16025	−	0.376987i	−0.824994	+	0.565141i	$0.808822\pi$
$114$	−1.02649	−	10.1056i	−0.0961395	−	0.946477i
$115$		0			0
$116$	16.3943	−	11.9112i	1.52217	−	1.10592i
$117$	−9.97564	−	1.11895i	−0.922248	−	0.103447i
$118$	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
$123$	9.27407	−	8.29198i	0.836215	−	0.747663i
$124$	0.226216	−	0.696222i	0.0203148	−	0.0625226i
$125$	9.97628	−	3.24149i	0.892305	−	0.289928i
$126$	4.08494	+	19.9003i	0.363915	+	1.77286i
$127$	8.47559	+	11.6657i	0.752087	+	1.03516i	0.997831	+	0.0658244i	$0.0209677\pi$
$127$	8.47559	+	11.6657i	0.752087	+	1.03516i	−0.245744	+	0.969335i	$0.579032\pi$
$128$	6.40720	+	19.7193i	0.566321	+	1.74296i
$129$	−3.69643	+	6.35110i	−0.325452	+	0.559183i
$130$	−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
$135$	5.24915	−	3.73037i	0.451775	−	0.321059i
$136$	−5.31390	−	16.3545i	−0.455663	−	1.40239i
$137$	10.4841	+	14.4301i	0.895715	+	1.23285i	0.971815	+	0.235746i	$0.0757534\pi$
$137$	10.4841	+	14.4301i	0.895715	+	1.23285i	−0.0760994	+	0.997100i	$0.524247\pi$
$138$		0			0
$139$	−4.92303	+	1.59959i	−0.417566	+	0.135675i	−0.510262	−	0.860019i	$-0.670452\pi$
$139$	−4.92303	+	1.59959i	−0.417566	+	0.135675i	0.0926959	+	0.995694i	$0.470452\pi$
$140$	−4.04256	+	12.4417i	−0.341658	+	1.05152i
$141$	3.90888	+	4.37184i	0.329187	+	0.368175i
$142$		−	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
$147$	−1.72318	+	0.175035i	−0.142126	+	0.0144366i
$148$	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	$0.174120\pi$
$150$	−14.2915	+	1.45167i	−1.16689	+	0.118529i
$151$	−15.6830	−	5.09572i	−1.27627	−	0.414684i	−0.409002	−	0.912534i	$-0.634123\pi$
$151$	−15.6830	−	5.09572i	−1.27627	−	0.414684i	−0.867263	+	0.497850i	$0.834123\pi$
$152$	−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
$156$	14.4166	+	16.1241i	1.15425	+	1.29096i
$157$	−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
$159$	−11.2578	+	4.96528i	−0.892802	+	0.393773i
$160$	1.74403	+	2.40046i	0.137878	+	0.189773i
$161$		0			0
$162$	−19.8051	+	8.48847i	−1.55604	+	0.666917i
$163$	−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	$0.634789\pi$
$168$	10.2190	−	17.5579i	0.788410	−	1.35462i
$169$	0.557420	+	1.71556i	0.0428784	+	0.131966i
$170$	−7.23220	−	9.95427i	−0.554685	−	0.763458i
$171$	1.47761	+	7.19838i	0.112996	+	0.550474i
$172$	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	$-0.0417251\pi$
$174$	−16.7856	+	15.0081i	−1.27252	+	1.13776i
$175$		−	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	0.972014	−	0.234922i	$-0.0754835\pi$
$179$	21.6782	+	7.04368i	1.62031	+	0.526470i	0.648292	+	0.761391i	$0.275483\pi$
$180$	−13.7891	−	1.54669i	−1.02778	−	0.115284i
$181$	−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
$183$	0.791163	+	7.78886i	0.0584845	+	0.575769i
$184$		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
$189$	−4.39498	−	14.0244i	−0.319688	−	1.02013i
$190$	−2.24592	+	6.91223i	−0.162936	+	0.501466i
$191$	−2.35731	+	0.765938i	−0.170569	+	0.0554213i	−0.393057	−	0.919514i	$-0.628582\pi$
$191$	−2.35731	+	0.765938i	−0.170569	+	0.0554213i	0.222487	+	0.974936i	$0.428582\pi$
$192$	−7.45110	−	16.8939i	−0.537737	−	1.21921i
$193$	1.68435	+	2.31831i	0.121242	+	0.166876i	0.865324	−	0.501213i	$-0.167113\pi$
$193$	1.68435	+	2.31831i	0.121242	+	0.166876i	−0.744082	+	0.668089i	$0.767113\pi$
$194$	−1.67792	−	5.16410i	−0.120467	−	0.370761i
$195$	6.20766	+	3.61295i	0.444540	+	0.258728i
$196$	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
$201$	−2.99394	−	1.74251i	−0.211176	−	0.122907i
$202$	−0.347445	−	1.06933i	−0.0244461	−	0.0752375i
$203$	−9.02718	−	12.4248i	−0.633584	−	0.872053i
$204$	10.8172	+	24.5259i	0.757358	+	1.71716i
$205$	−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	−0.768961	−	0.639296i	$-0.779226\pi$
$211$	1.11367	−	1.53283i	0.0766681	−	0.105525i	0.845629	+	0.533772i	$0.179226\pi$
$212$	25.2142	+	8.19259i	1.73172	+	0.562669i
$213$	1.46033	+	14.3767i	0.100060	+	0.985078i
$214$	6.78952	−	4.93287i	0.464122	−	0.337204i
$215$	4.25378	−	3.09055i	0.290105	−	0.210774i
$216$	20.4221	+	6.87279i	1.38955	+	0.467634i
$217$	−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
$222$	−32.3483	+	28.9227i	−2.17107	+	1.94116i
$223$	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
$225$	10.1800	−	2.08966i	0.678670	−	0.139311i
$226$	−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	$0.844172\pi$
$228$	7.96469	−	13.6847i	0.527475	−	0.906292i
$229$	−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	$0.756918\pi$
$234$	−17.7474	−	16.2056i	−1.16018	−	1.05939i
$235$	−1.29668	−	3.99078i	−0.0845862	−	0.260330i
$236$	27.7194	+	38.1525i	1.80438	+	2.48351i
$237$	11.6455	−	5.13629i	0.756459	−	0.333638i
$238$	−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	$0.994662\pi$
$240$	3.52551	+	3.94307i	0.227571	+	0.254524i
$241$			3.76217i			0.242343i	0.992632	+	0.121171i	$0.0386650\pi$
$241$			3.76217i			0.242343i	−0.992632	+	0.121171i	$0.961335\pi$
$242$		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
$246$	29.6321	−	3.00992i	1.88928	−	0.191906i
$247$	−6.63083	+	4.81758i	−0.421909	+	0.306535i
$248$	0.658062	−	0.478110i	0.0417870	−	0.0303600i
$249$	25.5628	−	2.59657i	1.61998	−	0.164551i
$250$	23.8849	+	7.76067i	1.51061	+	0.490828i
$251$	5.04685	−	6.94640i	0.318554	−	0.438453i	−0.619471	−	0.785020i	$-0.712653\pi$
$251$	5.04685	−	6.94640i	0.318554	−	0.438453i	0.938025	+	0.346567i	$0.112653\pi$
$252$	−13.0820	+	28.8391i	−0.824088	+	1.81669i
$253$		0			0
$254$			34.5228i			2.16615i
$255$	5.93306	+	6.63577i	0.371543	+	0.415548i
$256$	−8.75152	+	26.9344i	−0.546970	+	1.68340i
$257$	−21.9940	+	7.14630i	−1.37195	+	0.445774i	−0.900015	−	0.435859i	$-0.856445\pi$
$257$	−21.9940	+	7.14630i	−1.37195	+	0.445774i	−0.471936	+	0.881633i	$0.656445\pi$
$258$	−16.0973	+	7.09977i	−1.00218	+	0.442012i
$259$	−17.3967	−	23.9444i	−1.08098	−	1.48783i
$260$	−4.78240	−	14.7187i	−0.296592	−	0.912815i
$261$	10.9841	−	12.0291i	0.679899	−	0.744584i
$262$	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
$267$	−8.34876	+	14.3446i	−0.510936	+	0.877875i
$268$	2.30653	+	7.09878i	0.140894	+	0.433627i
$269$	9.61274	+	13.2308i	0.586099	+	0.806696i	0.994348	−	0.106175i	$-0.0338602\pi$
$269$	9.61274	+	13.2308i	0.586099	+	0.806696i	−0.408248	+	0.912871i	$0.633860\pi$
$270$	15.4168	+	0.161454i	0.938237	+	0.00982575i
$271$	8.69420	−	2.82492i	0.528135	−	0.171601i	−0.0327991	−	0.999462i	$-0.510442\pi$
$271$	8.69420	−	2.82492i	0.528135	−	0.171601i	0.560934	+	0.827861i	$0.310442\pi$
$272$	3.15760	−	9.71808i	0.191457	−	0.589245i
$273$	12.2201	−	10.9260i	0.739592	−	0.661272i
$274$			42.7038i			2.57983i
$275$		0			0
$276$		0			0
$277$	−3.68896	+	5.07741i	−0.221648	+	0.305072i	−0.905331	−	0.424707i	$-0.860377\pi$
$277$	−3.68896	+	5.07741i	−0.221648	+	0.305072i	0.683683	+	0.729779i	$0.260377\pi$
$278$	−11.7866	−	3.82969i	−0.706912	−	0.229690i
$279$	0.0655948	−	0.584790i	0.00392706	−	0.0350105i
$280$	−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	$0.292276\pi$
$282$	1.41889	+	13.9687i	0.0844937	+	0.831825i
$283$	−6.46116	−	2.09936i	−0.384076	−	0.124794i	0.110614	−	0.993863i	$-0.464718\pi$
$283$	−6.46116	−	2.09936i	−0.384076	−	0.124794i	−0.494690	+	0.869070i	$0.664718\pi$
$284$	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
$288$	3.54774	+	6.24516i	0.209053	+	0.367999i
$289$	0.0606144	−	0.186552i	0.00356555	−	0.0109736i
$290$	15.3225	−	4.97860i	0.899771	−	0.292353i
$291$	1.58521	+	3.59415i	0.0929265	+	0.210693i
$292$	−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	$-0.499225\pi$
$294$	−3.58400	−	2.08594i	−0.209023	−	0.121654i
$295$	12.6694	+	9.20487i	0.737642	+	0.535928i
$296$	43.3928			2.52215
$297$		0			0
$298$	22.5167			1.30436
$299$		0			0
$300$	−19.3531	−	11.2638i	−1.11735	−	0.650314i
$301$	−3.70820	−	11.4127i	−0.213737	−	0.657816i
$302$	−23.2058	−	31.9401i	−1.33534	−	1.83794i
$303$	0.328248	+	0.744237i	0.0188573	+	0.0427553i
$304$	−5.74038	+	1.86516i	−0.329233	+	0.106974i
$305$	1.73104	−	5.32758i	0.0991188	−	0.305056i
$306$	−14.7119	−	25.8976i	−0.841021	−	1.48047i
$307$		−	31.1870i		−	1.77994i	−0.456021	−	0.889969i	$-0.650726\pi$
$307$		−	31.1870i		−	1.77994i	0.456021	−	0.889969i	$-0.349274\pi$
$308$		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	0.326871	−	0.945069i	$-0.394006\pi$
$311$	0.631641	+	0.205232i	0.0358171	+	0.0116377i	−0.291054	+	0.956707i	$0.594006\pi$
$312$	2.42870	+	23.9101i	0.137498	+	1.35364i
$313$	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
$315$	−1.17220	+	10.4504i	−0.0660460	+	0.588813i
$316$	−26.0826	−	8.47475i	−1.46726	−	0.476742i
$317$	−14.4644	+	19.9085i	−0.812402	+	1.11818i	0.178546	+	0.983931i	$0.442861\pi$
$317$	−14.4644	+	19.9085i	−0.812402	+	1.11818i	−0.990948	+	0.134244i	$0.957139\pi$
$318$	−28.7930	−	6.22526i	−1.61463	−	0.349095i
$319$		0			0
$320$			13.2114i			0.738540i
$321$	−4.52606	+	4.04677i	−0.252620	+	0.225868i
$322$		0			0
$323$	−9.66046	+	3.13887i	−0.537522	+	0.174652i
$324$	−32.7538	−	7.44148i	−1.81965	−	0.413416i
$325$	6.81308	+	9.37740i	0.377922	+	0.520165i
$326$	−9.16831	−	28.2172i	−0.507786	−	1.56280i
$327$	9.31768	−	16.0094i	0.515269	−	0.885320i
$328$	−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
$333$	21.1679	−	23.1818i	1.15999	−	1.27036i
$334$	3.89005	+	11.9723i	0.212854	+	0.655097i
$335$	1.45690	+	2.00525i	0.0795990	+	0.109559i
$336$	11.0450	−	4.87143i	0.602555	−	0.265758i
$337$	8.10533	−	2.63358i	0.441525	−	0.143460i	−0.0798139	−	0.996810i	$-0.525433\pi$
$337$	8.10533	−	2.63358i	0.441525	−	0.143460i	0.521339	+	0.853349i	$0.325433\pi$
$338$	−1.33456	+	4.10734i	−0.0725903	+	0.223410i
$339$	14.9715	+	16.7447i	0.813140	+	0.909448i
$340$		−	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	$0.310964\pi$
$348$	−34.9195	+	3.54699i	−1.87188	+	0.190138i
$349$	19.3223	+	6.27818i	1.03430	+	0.336063i	0.776488	−	0.630132i	$-0.216999\pi$
$349$	19.3223	+	6.27818i	1.03430	+	0.336063i	0.257809	+	0.966196i	$0.416999\pi$
$350$	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	$0.0820790\pi$
$353$			9.58244i			0.510022i	−0.966938	+	0.255011i	$0.917921\pi$
$354$	−34.9265	−	39.0631i	−1.85632	−	2.07618i
$355$	3.19516	−	9.83368i	0.169581	−	0.521918i
$356$	34.0118	−	11.0511i	1.80262	−	0.585708i
$357$	18.5876	−	8.19811i	0.983760	−	0.433890i
$358$	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	$0.536616\pi$
$360$	−11.3852	−	10.3962i	−0.600055	−	0.547926i
$361$	−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
$366$	−9.42852	+	16.1998i	−0.492836	+	0.846778i
$367$	−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
$369$	−21.1074	+	4.33273i	−1.09881	+	0.225553i
$370$	29.5287	−	9.59446i	1.53512	−	0.498792i
$371$	6.20896	−	19.1092i	0.322353	−	0.992100i
$372$	−0.945226	+	0.845129i	−0.0490077	+	0.0438179i
$373$			9.62209i			0.498213i	0.968476	+	0.249107i	$0.0801369\pi$
$373$			9.62209i			0.498213i	−0.968476	+	0.249107i	$0.919863\pi$
$374$		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
$378$	11.2232	−	33.3491i	0.577260	−	1.71529i
$379$	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
$381$	−2.52392	−	24.8475i	−0.129304	−	1.27298i
$382$	−5.64381	−	1.83379i	−0.288763	−	0.0938246i
$383$	−5.58011	+	7.68037i	−0.285131	+	0.392448i	−0.927425	−	0.374010i	$-0.877983\pi$
$383$	−5.58011	+	7.68037i	−0.285131	+	0.392448i	0.642294	+	0.766458i	$0.277983\pi$
$384$	7.58922	−	35.1015i	0.387286	−	1.79127i
$385$		0			0
$386$			6.86071i			0.349201i
$387$	11.0669	−	6.28685i	0.562560	−	0.319579i
$388$	2.61555	−	8.04984i	0.132784	−	0.408669i
$389$	−18.1423	+	5.89478i	−0.919849	+	0.298877i	−0.730405	−	0.683015i	$-0.760669\pi$
$389$	−18.1423	+	5.89478i	−0.919849	+	0.298877i	−0.189444	+	0.981892i	$0.560669\pi$
$390$	6.93943	+	15.7338i	0.351391	+	0.796711i
$391$		0			0
$392$	1.28144	+	3.94386i	0.0647225	+	0.199195i
$393$	−20.2863	−	11.8069i	−1.02331	−	0.595581i
$394$	−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
$399$	−10.3713	−	6.03624i	−0.519214	−	0.302190i
$400$	2.63774	+	8.11812i	0.131887	+	0.405906i
$401$	0.728450	+	1.00263i	0.0363771	+	0.0500687i	0.826818	−	0.562469i	$-0.190149\pi$
$401$	0.728450	+	1.00263i	0.0363771	+	0.0500687i	−0.790441	+	0.612538i	$0.790149\pi$
$402$	−3.34686	−	7.58835i	−0.166926	−	0.378473i
$403$	0.624215	−	0.202820i	0.0310944	−	0.0101032i
$404$	0.541600	−	1.66687i	0.0269456	−	0.0829300i
$405$	−11.1079	+	1.01090i	−0.551957	+	0.0502319i
$406$		−	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	$0.506763\pi$
$409$	−19.5265	+	26.8759i	−0.965522	+	1.32893i	−0.944277	+	0.329152i	$0.893237\pi$
$410$	−20.2684	−	6.58559i	−1.00098	−	0.325239i
$411$	−3.12202	−	30.7357i	−0.153998	−	1.51608i
$412$	−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	$0.0871151\pi$
$419$			11.0648i			0.540553i	−0.962783	+	0.270277i	$0.912885\pi$
$420$	16.8915	−	15.1027i	0.824221	−	0.736938i
$421$	−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
$423$	−2.04247	−	9.95014i	−0.0993082	−	0.483792i
$424$	17.3151	+	23.8322i	0.840897	+	1.15740i
$425$	4.43904	+	13.6619i	0.215325	+	0.662702i
$426$	−17.4032	+	29.9017i	−0.843189	+	1.44874i
$427$	−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	$0.532044\pi$
$432$	7.41703	+	10.4368i	0.356852	+	0.502140i
$433$	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
$435$	−10.6643	+	4.70351i	−0.511314	+	0.225516i
$436$	−37.9591	+	12.3337i	−1.81791	+	0.590675i
$437$		0			0
$438$	22.4059	+	25.0596i	1.07059	+	1.19739i
$439$			8.38375i			0.400134i	0.979782	+	0.200067i	$0.0641160\pi$
$439$			8.38375i			0.400134i	−0.979782	+	0.200067i	$0.935884\pi$
$440$		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	−0.330695	−	0.943738i	$-0.607283\pi$
$443$	−24.2667	−	7.88474i	−1.15295	−	0.374615i	−0.822253	+	0.569122i	$0.807283\pi$
$444$	−67.2947	+	6.83555i	−3.19367	+	0.324401i
$445$	9.60760	−	6.98033i	0.455444	−	0.330899i
$446$	25.0410	−	18.1933i	1.18572	−	0.861478i
$447$	−16.2062	+	1.64616i	−0.766526	+	0.0778608i
$448$	28.6760	+	9.31740i	1.35481	+	0.440206i
$449$	23.6868	−	32.6020i	1.11785	−	1.53859i	0.308530	−	0.951215i	$-0.400163\pi$
$449$	23.6868	−	32.6020i	1.11785	−	1.53859i	0.809318	−	0.587371i	$-0.199837\pi$
$450$	22.6587	+	10.2784i	1.06814	+	0.484530i
$451$		0			0
$452$		−	48.3984i		−	2.27647i
$453$	19.0373	+	21.2920i	0.894449	+	1.00039i
$454$	−3.89005	+	11.9723i	−0.182569	+	0.561889i
$455$	−11.1549	+	3.62446i	−0.522951	+	0.169917i
$456$	16.0973	−	7.09977i	0.753827	−	0.332477i
$457$	10.8281	+	14.9037i	0.506519	+	0.697164i	0.983328	−	0.181843i	$-0.0582064\pi$
$457$	10.8281	+	14.9037i	0.506519	+	0.697164i	−0.476808	+	0.879007i	$0.658206\pi$
$458$	−4.09568	−	12.6052i	−0.191378	−	0.589002i
$459$	12.4821	+	17.5640i	0.582613	+	0.819817i
$460$		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
$465$	−0.211797	+	0.363904i	−0.00982187	+	0.0168757i
$466$	−4.01722	−	12.3637i	−0.186094	−	0.572739i
$467$	−11.4077	−	15.7014i	−0.527886	−	0.726573i	0.458920	−	0.888477i	$-0.348236\pi$
$467$	−11.4077	−	15.7014i	−0.527886	−	0.726573i	−0.986806	+	0.161904i	$0.948236\pi$
$468$	−7.53299	−	36.6979i	−0.348213	−	1.69636i
$469$	5.37999	−	1.74806i	0.248425	−	0.0807181i
$470$	3.10448	−	9.55460i	0.143199	−	0.440721i
$471$	14.8025	−	13.2349i	0.682062	−	0.609834i
$472$			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
$477$	21.1786	+	2.37556i	0.969702	+	0.108770i
$478$	−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	$0.252255\pi$
$480$	−0.519350	−	5.11291i	−0.0237050	−	0.233371i
$481$	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
$486$	37.0432	+	4.54835i	1.68032	+	0.206317i
$487$	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
$489$	8.66174	+	19.6388i	0.391697	+	0.888097i
$490$	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	$0.743627\pi$
$492$	40.1270	+	23.3545i	1.80906	+	1.05290i
$493$	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
$498$	53.1673	+	30.9441i	2.38248	+	1.38664i
$499$	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
$501$	−3.67511	−	8.33259i	−0.164192	−	0.372273i
$502$	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	$0.0750997\pi$
$504$	−30.5949	+	17.3803i	−1.36280	+	0.774181i
$505$		−	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	0.545611	−	0.838038i	$-0.316297\pi$
$509$	11.1549	+	3.62446i	0.494434	+	0.160651i	−0.0511777	+	0.998690i	$0.516297\pi$
$510$	2.15365	+	21.2023i	0.0953653	+	0.938855i
$511$	−18.5493	+	13.4769i	−0.820573	+	0.596181i
$512$	−21.3062	+	15.4798i	−0.941608	+	0.684119i
$513$	4.05969	−	12.0631i	0.179240	−	0.532600i
$514$	−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
$519$	−14.6285	+	13.0794i	−0.642118	+	0.574120i
$520$	5.31390	−	16.3545i	0.233030	−	0.717193i
$521$	−2.35731	+	0.765938i	−0.103276	+	0.0335564i	−0.360199	−	0.932875i	$-0.617291\pi$
$521$	−2.35731	+	0.765938i	−0.103276	+	0.0335564i	0.256923	+	0.966432i	$0.417291\pi$
$522$	38.2034	−	7.84203i	1.67212	−	0.343236i
$523$	−21.2108	−	29.1942i	−0.927485	−	1.27657i	−0.960833	−	0.277129i	$-0.910617\pi$
$523$	−21.2108	−	29.1942i	−0.927485	−	1.27657i	0.0333482	−	0.999444i	$-0.489383\pi$
$524$	15.6286	+	48.1000i	0.682740	+	2.10126i
$525$	−8.53653	+	14.6672i	−0.372565	+	0.640130i
$526$	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
$531$	27.9939	+	25.5619i	1.21483	+	1.10929i
$532$	7.99007	+	24.5909i	0.346413	+	1.06615i
$533$	−14.1263	−	19.4432i	−0.611879	−	0.842180i
$534$	−36.3575	+	16.0355i	−1.57334	+	0.693926i
$535$	4.13156	−	1.34242i	0.178623	−	0.0580381i
$536$	−2.56288	+	7.88773i	−0.110699	+	0.340698i
$537$	−26.3148	−	29.4315i	−1.13557	−	1.27006i
$538$			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	−0.737104	−	0.675779i	$-0.763807\pi$
$541$	3.10228	−	4.26992i	0.133378	−	0.183578i	0.870482	+	0.492201i	$0.163807\pi$
$542$	20.8154	+	6.76333i	0.894097	+	0.290510i
$543$	22.1540	−	2.25031i	0.950717	−	0.0965703i
$544$	−8.03209	+	5.83565i	−0.344373	+	0.250201i
$545$	−10.7226	+	7.79044i	−0.459306	+	0.333706i
$546$	39.0451	−	3.96605i	1.67097	−	0.169731i
$547$	−20.0784	−	6.52386i	−0.858490	−	0.278940i	−0.153492	−	0.988150i	$-0.549052\pi$
$547$	−20.0784	−	6.52386i	−0.858490	−	0.278940i	−0.704998	+	0.709210i	$0.749052\pi$
$548$	−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
$555$	−20.5516	+	9.06434i	−0.872367	+	0.384760i
$556$	−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	$0.970645\pi$
$558$	0.950002	−	1.04039i	0.0402168	−	0.0440430i
$559$	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	$0.967980\pi$
$564$	−11.0094	+	18.9160i	−0.463579	+	0.796509i
$565$	−4.96646	−	15.2852i	−0.208940	−	0.643053i
$566$	−9.56044	−	13.1588i	−0.401855	−	0.553106i
$567$	−5.63971	+	24.8232i	−0.236846	+	1.04248i
$568$	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	$0.871133\pi$
$570$	9.38439	−	8.39061i	0.393069	−	0.351444i
$571$			27.3233i			1.14345i	0.820447	+	0.571723i	$0.193725\pi$
$571$			27.3233i			1.14345i	−0.820447	+	0.571723i	$0.806275\pi$
$572$		0			0
$573$	4.19615	+	0.907241i	0.175297	+	0.0379005i
$574$	−28.5887	+	39.3490i	−1.19327	+	1.64240i
$575$		0			0
$576$	−3.56487	+	31.7815i	−0.148536	+	1.32423i
$577$	−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
$579$	−0.501577	−	4.93794i	−0.0208448	−	0.205214i
$580$	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
$585$	−6.14487	−	10.8169i	−0.254059	−	0.447225i
$586$	24.0692	−	74.0775i	0.994292	−	3.06011i
$587$	−6.20911	+	2.01746i	−0.256277	+	0.0832695i	−0.434338	−	0.900750i	$-0.643018\pi$
$587$	−6.20911	+	2.01746i	−0.256277	+	0.0832695i	0.178061	+	0.984020i	$0.443018\pi$
$588$	−2.60856	−	5.91439i	−0.107575	−	0.243905i
$589$	−0.282415	−	0.388711i	−0.0116367	−	0.0160166i
$590$	11.5861	+	35.6583i	0.476991	+	1.46803i
$591$	15.9993	+	9.31183i	0.658124	+	0.383037i
$592$	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
$597$	−11.4672	−	6.67404i	−0.469319	−	0.273150i
$598$		0			0
$599$	1.59979	+	2.20192i	0.0653656	+	0.0899680i	0.840448	−	0.541892i	$-0.182292\pi$
$599$	1.59979	+	2.20192i	0.0653656	+	0.0899680i	−0.775083	+	0.631860i	$0.782292\pi$
$600$	−10.0406	−	22.7651i	−0.409905	−	0.929380i
$601$	−39.4972	+	12.8334i	−1.61113	+	0.523486i	−0.969825	−	0.243804i	$-0.921605\pi$
$601$	−39.4972	+	12.8334i	−1.61113	+	0.523486i	−0.641300	+	0.767290i	$0.721605\pi$
$602$	8.87807	−	27.3239i	0.361843	−	1.11364i
$603$	2.96365	+	5.21697i	0.120689	+	0.212451i
$604$		−	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	$-0.442851\pi$
$607$	26.0950	−	35.9167i	1.05916	−	1.45781i	0.880586	−	0.473886i	$-0.157149\pi$
$608$	5.57747	+	1.81223i	0.226196	+	0.0734956i
$609$	2.68817	+	26.4646i	0.108930	+	1.07240i
$610$	10.8502	−	7.88311i	0.439310	−	0.319178i
$611$	9.16562	−	6.65922i	0.370801	−	0.269403i
$612$	5.17534	−	46.1391i	0.209201	−	1.86506i
$613$	−14.6631	−	4.76432i	−0.592235	−	0.192429i	−0.00246086	−	0.999997i	$-0.500783\pi$
$613$	−14.6631	−	4.76432i	−0.592235	−	0.192429i	−0.589774	+	0.807568i	$0.700783\pi$
$614$	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	$0.0884828\pi$
$617$			13.6325i			0.548822i	−0.961613	+	0.274411i	$0.911517\pi$
$618$	39.3593	−	35.1913i	1.58326	−	1.41560i
$619$	−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
$624$	−7.18355	+	12.3426i	−0.287572	+	0.494098i
$625$	−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
$630$	−16.9769	+	18.5920i	−0.676374	+	0.740724i
$631$	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
$633$	−3.00262	+	1.32431i	−0.119343	+	0.0526367i
$634$	−56.0329	+	18.2062i	−2.22535	+	0.723061i
$635$	−5.52224	+	16.9957i	−0.219143	+	0.674454i
$636$	−30.6070	−	34.2321i	−1.21365	−	1.35739i
$637$			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	−0.776290	−	0.630376i	$-0.782901\pi$
$641$	−44.9356	−	14.6004i	−1.77485	−	0.576683i	−0.998557	+	0.0536929i	$0.982901\pi$
$642$	−14.4615	+	1.46894i	−0.570749	+	0.0579746i
$643$	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
$645$	−9.06044	+	0.920325i	−0.356754	+	0.0362378i
$646$	−23.1288	−	7.51499i	−0.909989	−	0.295673i
$647$	9.80793	−	13.4995i	0.385589	−	0.530718i	−0.571465	−	0.820626i	$-0.693625\pi$
$647$	9.80793	−	13.4995i	0.385589	−	0.530718i	0.957055	+	0.289908i	$0.0936247\pi$
$648$	−24.5832	−	28.0812i	−0.965720	−	1.10313i
$649$		0			0
$650$			27.7511i			1.08849i
$651$	0.640502	+	0.716363i	0.0251033	+	0.0280765i
$652$	14.2916	−	43.9851i	0.559704	−	1.72259i
$653$	36.9161	−	11.9948i	1.44464	−	0.469392i	0.521300	−	0.853374i	$-0.325447\pi$
$653$	36.9161	−	11.9948i	1.44464	−	0.469392i	0.923341	+	0.383982i	$0.125447\pi$
$654$	40.5770	−	17.8966i	1.58668	−	0.699811i
$655$	9.87168	+	13.5872i	0.385718	+	0.530896i
$656$	−5.46912	−	16.8322i	−0.213533	−	0.657187i
$657$	−17.9585	−	16.3984i	−0.700628	−	0.639762i
$658$	−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
$663$	−12.0892	+	20.7712i	−0.469504	+	0.806688i
$664$	−19.0097	−	58.5058i	−0.737719	−	2.27047i
$665$	5.04685	+	6.94640i	0.195709	+	0.269370i
$666$	73.6234	−	15.1127i	2.85285	−	0.585606i
$667$		0			0
$668$	−6.06384	+	18.6626i	−0.234617	+	0.722076i
$669$	−16.6929	+	14.9252i	−0.645386	+	0.577041i
$670$			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	$-0.552569\pi$
$673$	21.3899	−	29.4406i	0.824519	−	1.13485i	0.988919	−	0.148459i	$-0.0474313\pi$
$674$	19.4055	+	6.30524i	0.747473	+	0.242869i
$675$	−17.0598	−	5.74127i	−0.656633	−	0.220982i
$676$	−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	$0.229063\pi$
$678$	5.43453	+	53.5020i	0.208712	+	2.05473i
$679$	−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	$0.289944\pi$
$683$			41.2946i			1.58009i	−0.613047	+	0.790046i	$0.710056\pi$
$684$	−23.8458	+	13.5463i	−0.911766	+	0.517955i
$685$	−6.83086	+	21.0232i	−0.260994	+	0.803256i
$686$	−38.6418	+	12.5555i	−1.47535	+	0.479371i
$687$	3.86938	+	8.77305i	0.147626	+	0.334713i
$688$	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
$696$	−33.7067	−	19.6178i	−1.27765	−	0.743610i
$697$	−9.20395	−	28.3268i	−0.348624	−	1.07296i
$698$	28.5907	+	39.3518i	1.08218	+	1.48949i
$699$	3.79526	+	8.60500i	0.143550	+	0.325471i
$700$	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	$-0.0227686\pi$
$702$	12.4481	+	39.7218i	0.469821	+	1.49920i
$703$		−	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
$708$	−8.25446	−	81.2637i	−0.310222	−	3.05408i
$709$	−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
$711$	−21.9080	−	2.45738i	−0.821615	−	0.0921590i
$712$	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
$717$	12.9718	−	11.5981i	0.484441	−	0.433140i
$718$	−25.4931	+	78.4597i	−0.951394	+	2.92809i
$719$	34.0964	−	11.0786i	1.27158	−	0.413162i	0.405975	−	0.913884i	$-0.366932\pi$
$719$	34.0964	−	11.0786i	1.27158	−	0.413162i	0.865608	+	0.500722i	$0.166932\pi$
$720$	−1.84215	−	8.97427i	−0.0686529	−	0.334451i
$721$	21.1671	+	29.1341i	0.788305	+	1.08501i
$722$	−9.61791	−	29.6009i	−0.357942	−	1.10163i
$723$	3.27781	−	5.63184i	0.121903	−	0.209451i
$724$	−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
$729$	−26.9941	−	0.565457i	−0.999781	−	0.0209428i
$730$	−7.43265	−	22.8753i	−0.275095	−	0.846654i
$731$	10.3412	+	14.2334i	0.382483	+	0.526442i
$732$	−26.7333	+	11.7908i	−0.988091	+	0.435800i
$733$	27.2957	−	8.86890i	1.00819	−	0.327580i	0.242056	−	0.970262i	$-0.422178\pi$
$733$	27.2957	−	8.86890i	1.00819	−	0.327580i	0.766133	+	0.642682i	$0.222178\pi$
$734$	17.6499	−	54.3208i	0.651470	−	2.00502i
$735$	−1.43075	−	1.60020i	−0.0527739	−	0.0590244i
$736$		0			0
$737$		0			0
$738$	−46.9808	−	21.3114i	−1.72939	−	0.784484i
$739$	13.2404	−	18.2238i	0.487055	−	0.670374i	−0.492786	−	0.870150i	$-0.664022\pi$
$739$	13.2404	−	18.2238i	0.487055	−	0.670374i	0.979842	+	0.199776i	$0.0640216\pi$
$740$	46.0296	+	14.9559i	1.69208	+	0.549791i
$741$	14.1235	−	1.43461i	0.518839	−	0.0527017i
$742$	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	$0.474327\pi$
$744$	−1.40165	+	0.142375i	−0.0513871	+	0.00521971i
$745$	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
$750$	−28.9934	−	32.4273i	−1.05869	−	1.18408i
$751$	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
$753$	−13.6071	+	6.00143i	−0.495869	+	0.218704i
$754$	25.5680	+	35.1913i	0.931131	+	1.28159i
$755$	−6.31519	−	19.4362i	−0.229833	−	0.707354i
$756$	44.7095	−	31.7734i	1.62607	−	1.15559i
$757$	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	$0.875504\pi$
$762$	30.0782	−	51.6796i	1.08962	−	1.87215i
$763$	9.34737	+	28.7682i	0.338397	+	1.04148i
$764$	−5.43723	−	7.48370i	−0.196712	−	0.270751i
$765$	−3.10015	−	15.1027i	−0.112086	−	0.546041i
$766$	−21.6165	+	7.02363i	−0.781037	+	0.253774i
$767$	−13.0657	+	40.2122i	−0.471777	+	1.45198i
$768$	36.5675	−	32.6951i	1.31952	−	1.17978i
$769$			11.9329i			0.430311i	0.976580	+	0.215155i	$0.0690258\pi$
$769$			11.9329i			0.430311i	−0.976580	+	0.215155i	$0.930974\pi$
$770$		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	0.785330	−	0.619078i	$-0.212493\pi$
$773$	29.3818	+	9.54673i	1.05679	+	0.343372i	0.271460	+	0.962450i	$0.412493\pi$
$774$	30.2829	+	3.39678i	1.08850	+	0.122095i
$775$	−0.549721	+	0.399395i	−0.0197465	+	0.0143467i
$776$	7.60863	−	5.52800i	0.273134	−	0.198443i
$777$	5.18049	+	51.0010i	0.185849	+	1.82965i
$778$	−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
$783$	−26.9233	+	8.43724i	−0.962160	+	0.301522i
$784$	−0.761449	+	2.34350i	−0.0271946	+	0.0836964i
$785$	−13.5122	+	4.39040i	−0.482273	+	0.156700i
$786$	−22.6777	−	51.4172i	−0.808886	−	1.83399i
$787$	26.7632	+	36.8364i	0.954004	+	1.31307i	0.949726	+	0.313083i	$0.101362\pi$
$787$	26.7632	+	36.8364i	0.954004	+	1.31307i	0.00427854	+	0.999991i	$0.498638\pi$
$788$	−12.3259	−	37.9353i	−0.439092	−	1.35139i
$789$	−35.1369	−	20.4502i	−1.25091	−	0.728046i
$790$	−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
$795$	−13.1791	−	7.67041i	−0.467414	−	0.272041i
$796$	8.83432	+	27.1892i	0.313124	+	0.963697i
$797$	−9.02718	−	12.4248i	−0.319759	−	0.440111i	0.618635	−	0.785679i	$-0.287686\pi$
$797$	−9.02718	−	12.4248i	−0.319759	−	0.440111i	−0.938394	+	0.345568i	$0.887686\pi$
$798$	−11.5939	−	26.2868i	−0.410419	−	0.930544i
$799$	13.3534	−	4.33878i	0.472409	−	0.153495i
$800$	2.56288	−	7.88773i	0.0906114	−	0.278873i
$801$	24.9956	−	14.1995i	0.883178	−	0.501715i
$802$			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
$807$	−2.86254	−	28.1812i	−0.100766	−	0.992027i
$808$	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	$0.934832\pi$
$810$	−22.9378	−	13.6737i	−0.805952	−	0.480444i
$811$	24.7376	+	8.03773i	0.868654	+	0.282243i	0.709239	−	0.704969i	$-0.249039\pi$
$811$	24.7376	+	8.03773i	0.868654	+	0.282243i	0.159416	+	0.987212i	$0.449039\pi$
$812$	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
$816$	−13.1938	+	11.7966i	−0.461874	+	0.412963i
$817$	3.21140	−	9.88367i	0.112353	−	0.345786i
$818$	−75.6426	+	24.5778i	−2.64478	+	0.859342i
$819$	−27.8124	+	5.70906i	−0.971844	+	0.199491i
$820$	−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	$-0.224490\pi$
$822$	37.2060	−	63.9262i	1.29771	−	2.22968i
$823$	−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
$831$	9.94598	−	4.38670i	0.345022	−	0.152173i
$832$	−33.9241	+	11.0226i	−1.17611	+	0.382140i
$833$	−1.28144	+	3.94386i	−0.0443992	+	0.136647i
$834$	14.3075	+	16.0020i	0.495428	+	0.554106i
$835$			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	0.600113	−	0.799915i	$-0.295122\pi$
$839$	17.8264	+	5.79216i	0.615437	+	0.199968i	0.0153236	+	0.999883i	$0.495122\pi$
$840$	25.0480	−	2.54428i	0.864239	−	0.0877861i
$841$	−0.391030	+	0.284100i	−0.0134838	+	0.00979655i
$842$	−37.1815	+	27.0139i	−1.28136	+	0.930962i
$843$	−1.40165	+	0.142375i	−0.0482755	+	0.00490365i
$844$	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
$849$	7.84307	+	8.77200i	0.269173	+	0.301054i
$850$	−10.6278	+	32.7090i	−0.364531	+	1.12191i
$851$		0			0
$852$	−49.3445	+	21.7635i	−1.69051	+	0.745606i
$853$	−25.0191	−	34.4359i	−0.856639	−	1.17906i	−0.982360	−	0.186997i	$-0.940125\pi$
$853$	−25.0191	−	34.4359i	−0.856639	−	1.17906i	0.125721	−	0.992066i	$-0.459875\pi$
$854$	−9.45856	−	29.1104i	−0.323665	−	0.996139i
$855$	−6.14091	+	6.72516i	−0.210015	+	0.229995i
$856$	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
$861$	17.6998	−	30.4112i	0.603206	−	1.03641i
$862$	15.4671	+	47.6028i	0.526811	+	1.62136i
$863$	16.9878	+	23.3817i	0.578272	+	0.795924i	0.993505	−	0.113792i	$-0.0362996\pi$
$863$	16.9878	+	23.3817i	0.578272	+	0.795924i	−0.415232	+	0.909715i	$0.636300\pi$
$864$	0.130277	−	12.4398i	0.00443210	−	0.423210i
$865$	13.3534	−	4.33878i	0.454029	−	0.147523i
$866$	−9.65680	+	29.7206i	−0.328151	+	1.00995i
$867$	−0.253272	+	0.226452i	−0.00860158	+	0.00769070i
$868$		−	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
$873$	0.758419	−	6.76145i	0.0256686	−	0.228840i
$874$		0			0
$875$	24.0030	−	17.4392i	0.811448	−	0.589552i
$876$	5.29537	+	52.1320i	0.178914	+	1.76138i
$877$	27.3664	+	8.89187i	0.924097	+	0.300257i	0.732146	−	0.681147i	$-0.238519\pi$
$877$	27.3664	+	8.89187i	0.924097	+	0.300257i	0.191950	+	0.981405i	$0.438519\pi$
$878$	−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	$0.0737563\pi$
$881$			13.6325i			0.459289i	−0.973275	+	0.229644i	$0.926244\pi$
$882$	3.54774	+	6.24516i	0.119459	+	0.210285i
$883$	−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
$885$	−10.9459	−	24.8177i	−0.367943	−	0.834238i
$886$	−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	$-0.375195\pi$
$888$	−64.9576	−	37.8062i	−2.17983	−	1.26869i
$889$	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
$894$	−33.7067	−	19.6178i	−1.12732	−	0.656117i
$895$	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
$900$	19.1573	+	33.7230i	0.638578	+	1.12410i
$901$			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
$906$	6.91038	+	68.0314i	0.229582	+	2.26019i
$907$	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
$909$	0.157045	−	1.40009i	0.00520886	−	0.0464379i
$910$	−26.7068	−	8.67757i	−0.885322	−	0.287659i
$911$	18.6922	−	25.7276i	0.619301	−	0.852395i	−0.378001	−	0.925805i	$-0.623388\pi$
$911$	18.6922	−	25.7276i	0.619301	−	0.852395i	0.997302	+	0.0734107i	$0.0233884\pi$
$912$	10.2182	+	2.20925i	0.338358	+	0.0731557i
$913$		0			0
$914$			44.1053i			1.45887i
$915$	−7.23299	+	6.46704i	−0.239115	+	0.213794i
$916$	6.38437	−	19.6491i	0.210946	−	0.649224i
$917$	36.4538	−	11.8445i	1.20381	−	0.391141i
$918$	−0.540234	+	51.5856i	−0.0178304	+	1.70258i
$919$	−22.9330	−	31.5646i	−0.756490	−	1.04122i	−0.997498	−	0.0706963i	$-0.977478\pi$
$919$	−22.9330	−	31.5646i	−0.756490	−	1.04122i	0.241008	−	0.970523i	$-0.422522\pi$
$920$		0			0
$921$	−27.1719	+	46.6860i	−0.895344	+	1.53836i
$922$	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
$927$	−25.7558	+	28.2061i	−0.845930	+	0.926411i
$928$	−4.01722	−	12.3637i	−0.131872	−	0.405859i
$929$	−18.7828	−	25.8523i	−0.616244	−	0.848187i	0.380829	−	0.924646i	$-0.375639\pi$
$929$	−18.7828	−	25.8523i	−0.616244	−	0.848187i	−0.997073	+	0.0764586i	$0.975639\pi$
$930$	−0.922343	+	0.406802i	−0.0302448	+	0.0133396i
$931$	2.32960	−	0.756934i	0.0763497	−	0.0248075i
$932$	6.26207	−	19.2727i	0.205121	−	0.631298i
$933$	−0.766736	−	0.857547i	−0.0251018	−	0.0280748i
$934$		−	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	−0.989898	−	0.141784i	$-0.954716\pi$
$937$	−16.8100	+	23.1369i	−0.549158	+	0.755851i	0.440740	+	0.897635i	$0.354716\pi$
$938$	12.8806	+	4.18516i	0.420567	+	0.136650i
$939$	−12.7383	+	1.29391i	−0.415699	+	0.0422251i
$940$	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	$0.310640\pi$
$942$	47.2962	−	4.80417i	1.54100	−	0.156528i
$943$		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	$-0.836571\pi$
$947$		−	30.2297i		−	0.982334i	0.871065	−	0.491167i	$-0.163429\pi$
$948$	31.6611	+	35.4110i	1.02831	+	1.15010i
$949$	8.38189	−	25.7968i	0.272088	−	0.837399i
$950$	19.3209	−	6.27774i	0.626853	−	0.203677i
$951$	38.9982	−	17.2002i	1.26460	−	0.557756i
$952$	−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	$0.549386\pi$
$954$	37.6783	+	34.4051i	1.21988	+	1.11390i
$955$	−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
$960$	11.5105	−	19.7770i	0.371500	−	0.638301i
$961$	−9.56764	−	29.4462i	−0.308633	−	0.949876i
$962$	49.2731	+	67.8186i	1.58863	+	2.18656i
$963$	10.3011	−	2.11452i	0.331950	−	0.0681394i
$964$	−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	$-0.742125\pi$
$967$		−	45.0518i		−	1.44877i	0.689397	−	0.724383i	$-0.257875\pi$
$968$		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	0.193335	−	0.981133i	$-0.438070\pi$
$971$	−7.07194	−	2.29781i	−0.226949	−	0.0737404i	−0.420284	+	0.907392i	$0.638070\pi$
$972$	42.5479	+	39.6766i	1.36472	+	1.27263i
$973$	−11.8448	+	8.60577i	−0.379728	+	0.275888i
$974$	64.2612	−	46.6885i	2.05906	−	1.49600i
$975$	−2.02884	−	19.9736i	−0.0649750	−	0.639668i
$976$	10.5927	+	3.44178i	0.339065	+	0.110169i
$977$	6.55605	−	9.02363i	0.209747	−	0.288692i	−0.691162	−	0.722700i	$-0.742901\pi$
$977$	6.55605	−	9.02363i	0.209747	−	0.288692i	0.900909	+	0.434008i	$0.142901\pi$
$978$	−10.8597	+	50.2281i	−0.347255	+	1.60612i
$979$		0			0
$980$			4.62518i			0.147746i
$981$	−27.8965	+	15.8474i	−0.890668	+	0.505970i
$982$	−15.4671	+	47.6028i	−0.493575	+	1.51907i
$983$	0.462393	−	0.150241i	0.0147480	−	0.00479193i	−0.301634	−	0.953424i	$-0.597532\pi$
$983$	0.462393	−	0.150241i	0.0147480	−	0.00479193i	0.316382	+	0.948632i	$0.397532\pi$
$984$	20.8183	+	47.2014i	0.663662	+	1.50472i
$985$	−7.78554	−	10.7159i	−0.248068	−	0.341436i
$986$	16.6587	+	51.2702i	0.530521	+	1.63278i
$987$	14.3360	+	8.34374i	0.456319	+	0.265584i
$988$	−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
$993$	0.587268	+	0.341798i	0.0186364	+	0.0108466i
$994$	−17.4587	−	53.7322i	−0.553755	−	1.70428i
$995$	5.58011	+	7.68037i	0.176902	+	0.243484i
$996$	38.6970	+	87.7379i	1.22616	+	2.78008i
$997$	−57.5098	+	18.6861i	−1.82135	+	0.591794i	−0.821590	+	0.570078i	$0.806913\pi$
$997$	−57.5098	+	18.6861i	−1.82135	+	0.591794i	−0.999764	+	0.0217156i	$0.993087\pi$
$998$	−19.0907	+	58.7551i	−0.604306	+	1.85986i
$999$	−51.8850	+	16.2598i	−1.64157	+	0.514436i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.93692 + 1.40726i) q^{2} +(-1.49697 - 0.871256i) q^{3} +(1.15327 + 3.54939i) q^{4} +(0.728450 + 1.00263i) q^{5} +(-1.67343 - 3.79418i) q^{6} +(2.68999 - 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(1.48183 + 2.60848i) q^{9} +O(q^{10})\)	\(q+(1.93692 + 1.40726i) q^{2} +(-1.49697 - 0.871256i) q^{3} +(1.15327 + 3.54939i) q^{4} +(0.728450 + 1.00263i) q^{5} +(-1.67343 - 3.79418i) q^{6} +(2.68999 - 0.874032i) q^{7} +(-1.28144 + 3.94386i) q^{8} +(1.48183 + 2.60848i) q^{9} +2.96713i q^{10} +(1.36603 - 6.31812i) q^{12} +(-1.96677 + 2.70702i) q^{13} +(6.44030 + 2.09258i) q^{14} +(-0.216923 - 2.13557i) q^{15} +(-1.99350 + 1.44836i) q^{16} +(-3.35485 + 2.43744i) q^{17} +(-0.800628 + 7.13775i) q^{18} +(2.32960 + 0.756934i) q^{19} +(-2.71861 + 3.74185i) q^{20} +(-4.78834 - 1.03528i) q^{21} +(5.35439 - 4.78738i) q^{24} +(1.07047 - 3.29456i) q^{25} +(-7.61896 + 2.47555i) q^{26} +(0.0544141 - 5.19587i) q^{27} +(6.20456 + 8.53985i) q^{28} +(-1.67792 - 5.16410i) q^{29} +(2.58513 - 4.44169i) q^{30} +(-0.158691 - 0.115296i) q^{31} +2.39417 q^{32} -9.92820 q^{34} +(2.83585 + 2.06037i) q^{35} +(-7.54959 + 8.26786i) q^{36} +(-3.23359 - 9.95195i) q^{37} +(3.44706 + 4.74448i) q^{38} +(5.30270 - 2.33877i) q^{39} +(-4.88769 + 1.58811i) q^{40} +(-2.21952 + 6.83097i) q^{41} +(-7.81775 - 8.74368i) q^{42} -4.24264i q^{43} +(-1.53590 + 3.38587i) q^{45} +(-3.22015 - 1.04629i) q^{47} +(4.24610 - 0.431303i) q^{48} +(0.809017 - 0.587785i) q^{49} +(6.70970 - 4.87488i) q^{50} +(7.14574 - 0.725837i) q^{51} +(-11.8765 - 3.85891i) q^{52} +(4.17551 - 5.74710i) q^{53} +(7.41732 - 9.98743i) q^{54} +11.7290i q^{56} +(-2.82786 - 3.16279i) q^{57} +(4.01722 - 12.3637i) q^{58} +(12.0178 - 3.90481i) q^{59} +(7.32979 - 3.23282i) q^{60} +(-2.65681 - 3.65679i) q^{61} +(-0.145121 - 0.446637i) q^{62} +(6.26600 + 5.72165i) 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} +(-12.1864 + 2.50150i) q^{72} +(-7.70959 + 2.50500i) q^{73} +(7.74175 - 23.8267i) q^{74} +(-4.47286 + 3.99919i) q^{75} +9.14162i q^{76} +(13.5622 + 2.93225i) q^{78} +(-4.31932 + 5.94504i) q^{79} +(-2.90433 - 0.943674i) q^{80} +(-4.60839 + 7.73064i) q^{81} +(-13.9120 + 10.1076i) q^{82} +(-12.0015 + 8.71958i) q^{83} +(-1.84764 - 18.1896i) q^{84} +(-4.88769 - 1.58811i) q^{85} +(5.97049 - 8.21767i) q^{86} +(-1.98747 + 9.19239i) q^{87} -9.58244i q^{89} +(-7.73971 + 4.39676i) q^{90} +(-2.92457 + 9.00090i) q^{91} +(0.137103 + 0.310854i) q^{93} +(-4.76479 - 6.55817i) q^{94} +(0.938079 + 2.88711i) q^{95} +(-3.58400 - 2.08594i) 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

Varieties

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Database

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