LMFDB - Embedded newform 756.2.ci.a.95.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.17
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33299 - 0.472387i) q^{2} +(-1.55434 - 0.764214i) q^{3} +(1.55370 + 1.25937i) q^{4} +(3.05802 + 0.539212i) q^{5} +(1.71091 + 1.75294i) q^{6} +(-2.62079 - 0.362599i) q^{7} +(-1.47615 - 2.41267i) q^{8} +(1.83195 + 2.37570i) q^{9} +O(q^{10})$	\(q+(-1.33299 - 0.472387i) q^{2} +(-1.55434 - 0.764214i) q^{3} +(1.55370 + 1.25937i) q^{4} +(3.05802 + 0.539212i) q^{5} +(1.71091 + 1.75294i) q^{6} +(-2.62079 - 0.362599i) q^{7} +(-1.47615 - 2.41267i) q^{8} +(1.83195 + 2.37570i) q^{9} +(-3.82158 - 2.16333i) q^{10} +(0.575637 + 3.26460i) q^{11} +(-1.45255 - 3.14485i) q^{12} +(-0.0707741 + 0.401380i) q^{13} +(3.32218 + 1.72137i) q^{14} +(-4.34113 - 3.17510i) q^{15} +(0.827971 + 3.91337i) q^{16} +(-4.67173 + 2.69723i) q^{17} +(-1.31972 - 4.03216i) q^{18} +(4.67159 + 2.69714i) q^{19} +(4.07218 + 4.68896i) q^{20} +(3.79649 + 2.56645i) q^{21} +(0.774840 - 4.62359i) q^{22} +(-5.60139 - 4.70012i) q^{23} +(0.450642 + 4.87821i) q^{24} +(4.36228 + 1.58774i) q^{25} +(0.283947 - 0.501600i) q^{26} +(-1.03194 - 5.09265i) q^{27} +(-3.61527 - 3.86391i) q^{28} +(-4.92203 + 0.867886i) q^{29} +(4.28679 + 6.28306i) q^{30} +(-8.68640 - 1.53165i) q^{31} +(0.744953 - 5.60759i) q^{32} +(1.60012 - 5.51421i) q^{33} +(7.50149 - 1.38850i) q^{34} +(-7.81890 - 2.52199i) q^{35} +(-0.145580 + 5.99823i) q^{36} -0.873013 q^{37} +(-4.95306 - 5.80205i) q^{38} +(0.416747 - 0.569794i) q^{39} +(-3.21316 - 8.17396i) q^{40} +(-4.64047 - 0.818240i) q^{41} +(-3.84831 - 5.21445i) q^{42} +(6.26462 + 7.46588i) q^{43} +(-3.21697 + 5.79715i) q^{44} +(4.32115 + 8.25275i) q^{45} +(5.24629 + 8.91122i) q^{46} +(1.90566 + 10.8076i) q^{47} +(1.70370 - 6.71546i) q^{48} +(6.73704 + 1.90059i) q^{49} +(-5.06483 - 4.17712i) q^{50} +(9.32272 - 0.622205i) q^{51} +(-0.615447 + 0.534493i) q^{52} +(-6.39512 - 3.69223i) q^{53} +(-1.03015 + 7.27591i) q^{54} +10.2936i q^{55} +(2.99384 + 6.85835i) q^{56} +(-5.20004 - 7.76237i) q^{57} +(6.97097 + 1.16822i) q^{58} +(-2.78610 + 1.01406i) q^{59} +(-2.74619 - 10.4003i) q^{60} +(1.25754 + 7.13188i) q^{61} +(10.8553 + 6.14501i) q^{62} +(-3.93973 - 6.89047i) q^{63} +(-3.64197 + 7.12293i) q^{64} +(-0.432857 + 1.18927i) q^{65} +(-4.73778 + 6.59449i) q^{66} +(0.563236 - 0.671238i) q^{67} +(-10.6553 - 1.69276i) q^{68} +(5.11457 + 11.5863i) q^{69} +(9.23112 + 7.05533i) q^{70} +(-1.18599 + 2.05419i) q^{71} +(3.02755 - 7.92679i) q^{72} +15.4303 q^{73} +(1.16371 + 0.412400i) q^{74} +(-5.56710 - 5.80160i) q^{75} +(3.86154 + 10.0738i) q^{76} +(-0.324880 - 8.76454i) q^{77} +(-0.824681 + 0.562662i) q^{78} +(3.40949 + 4.06327i) q^{79} +(0.421817 + 12.4136i) q^{80} +(-2.28790 + 8.70434i) q^{81} +(5.79915 + 3.28280i) q^{82} +(1.93646 + 10.9822i) q^{83} +(2.66651 + 8.76868i) q^{84} +(-15.7406 + 5.72912i) q^{85} +(-4.82386 - 12.9112i) q^{86} +(8.31376 + 2.41249i) q^{87} +(7.02668 - 6.20786i) q^{88} +(-3.49680 - 2.01888i) q^{89} +(-1.86153 - 13.0420i) q^{90} +(0.331024 - 1.02627i) q^{91} +(-2.78368 - 14.3568i) q^{92} +(12.3311 + 9.01897i) q^{93} +(2.56513 - 15.3065i) q^{94} +(12.8315 + 10.7669i) q^{95} +(-5.44331 + 8.14680i) q^{96} +(-13.5183 + 11.3432i) q^{97} +(-8.08257 - 5.71595i) q^{98} +(-6.70117 + 7.34813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.33299	−	0.472387i	−0.942563	−	0.334028i
$2$	−1.33299	−	0.472387i	−0.942563	−	0.334028i
$3$	−1.55434	−	0.764214i	−0.897399	−	0.441219i
$3$	−1.55434	−	0.764214i	−0.897399	−	0.441219i
$4$	1.55370	+	1.25937i	0.776850	+	0.629685i
$5$	3.05802	+	0.539212i	1.36759	+	0.241143i	0.808759	−	0.588140i	$-0.200140\pi$
$5$	3.05802	+	0.539212i	1.36759	+	0.241143i	0.558829	+	0.829283i	$0.311251\pi$
$6$	1.71091	+	1.75294i	0.698476	+	0.715634i
$7$	−2.62079	−	0.362599i	−0.990564	−	0.137050i
$7$	−2.62079	−	0.362599i	−0.990564	−	0.137050i
$8$	−1.47615	−	2.41267i	−0.521898	−	0.853008i
$9$	1.83195	+	2.37570i	0.610651	+	0.791900i
$10$	−3.82158	−	2.16333i	−1.20849	−	0.684105i
$11$	0.575637	+	3.26460i	0.173561	+	0.984314i	0.939792	+	0.341748i	$0.111019\pi$
$11$	0.575637	+	3.26460i	0.173561	+	0.984314i	−0.766231	+	0.642566i	$0.777870\pi$
$12$	−1.45255	−	3.14485i	−0.419316	−	0.907841i
$13$	−0.0707741	+	0.401380i	−0.0196292	+	0.111323i	−0.993048	−	0.117709i	$-0.962445\pi$
$13$	−0.0707741	+	0.401380i	−0.0196292	+	0.111323i	0.973419	+	0.229032i	$0.0735560\pi$
$14$	3.32218	+	1.72137i	0.887891	+	0.460054i
$15$	−4.34113	−	3.17510i	−1.12088	−	0.819808i
$16$	0.827971	+	3.91337i	0.206993	+	0.978342i
$17$	−4.67173	+	2.69723i	−1.13306	+	0.654173i	−0.944703	−	0.327927i	$-0.893650\pi$
$17$	−4.67173	+	2.69723i	−1.13306	+	0.654173i	−0.188358	+	0.982100i	$0.560317\pi$
$18$	−1.31972	−	4.03216i	−0.311060	−	0.950390i
$19$	4.67159	+	2.69714i	1.07174	+	0.618767i	0.928655	−	0.370945i	$-0.120966\pi$
$19$	4.67159	+	2.69714i	1.07174	+	0.618767i	0.143080	+	0.989711i	$0.454299\pi$
$20$	4.07218	+	4.68896i	0.910567	+	1.04848i
$21$	3.79649	+	2.56645i	0.828463	+	0.560044i
$22$	0.774840	−	4.62359i	0.165196	−	0.985752i
$23$	−5.60139	−	4.70012i	−1.16797	−	0.980043i	−0.167987	−	0.985789i	$-0.553727\pi$
$23$	−5.60139	−	4.70012i	−1.16797	−	0.980043i	−0.999983	+	0.00574583i	$0.998171\pi$
$24$	0.450642	+	4.87821i	0.0919869	+	0.995760i
$25$	4.36228	+	1.58774i	0.872456	+	0.317548i
$26$	0.283947	−	0.501600i	0.0556867	−	0.0983719i
$27$	−1.03194	−	5.09265i	−0.198596	−	0.980081i
$28$	−3.61527	−	3.86391i	−0.683222	−	0.730211i
$29$	−4.92203	+	0.867886i	−0.913997	+	0.161162i	−0.610818	−	0.791771i	$-0.709159\pi$
$29$	−4.92203	+	0.867886i	−0.913997	+	0.161162i	−0.303179	+	0.952933i	$0.598048\pi$
$30$	4.28679	+	6.28306i	0.782657	+	1.14712i
$31$	−8.68640	−	1.53165i	−1.56012	−	0.275092i	−0.674068	−	0.738670i	$-0.735454\pi$
$31$	−8.68640	−	1.53165i	−1.56012	−	0.275092i	−0.886056	+	0.463578i	$0.846565\pi$
$32$	0.744953	−	5.60759i	0.131690	−	0.991291i
$33$	1.60012	−	5.51421i	0.278545	−	0.959901i
$34$	7.50149	−	1.38850i	1.28649	−	0.238125i
$35$	−7.81890	−	2.52199i	−1.32164	−	0.426295i
$36$	−0.145580	+	5.99823i	−0.0242633	+	0.999706i
$37$	−0.873013			−0.143523			−0.0717613	−	0.997422i	$-0.522862\pi$
$37$	−0.873013			−0.143523			−0.0717613	+	0.997422i	$0.522862\pi$
$38$	−4.95306	−	5.80205i	−0.803492	−	0.941216i
$39$	0.416747	−	0.569794i	0.0667329	−	0.0912401i
$40$	−3.21316	−	8.17396i	−0.508044	−	1.29242i
$41$	−4.64047	−	0.818240i	−0.724719	−	0.127788i	−0.200894	−	0.979613i	$-0.564385\pi$
$41$	−4.64047	−	0.818240i	−0.724719	−	0.127788i	−0.523826	+	0.851826i	$0.675496\pi$
$42$	−3.84831	−	5.21445i	−0.593808	−	0.804607i
$43$	6.26462	+	7.46588i	0.955345	+	1.13854i	0.990272	+	0.139146i	$0.0444357\pi$
$43$	6.26462	+	7.46588i	0.955345	+	1.13854i	−0.0349270	+	0.999390i	$0.511120\pi$
$44$	−3.21697	+	5.79715i	−0.484977	+	0.873953i
$45$	4.32115	+	8.25275i	0.644158	+	1.23025i
$46$	5.24629	+	8.91122i	0.773523	+	1.31389i
$47$	1.90566	+	10.8076i	0.277970	+	1.57644i	0.729368	+	0.684122i	$0.239814\pi$
$47$	1.90566	+	10.8076i	0.277970	+	1.57644i	−0.451398	+	0.892323i	$0.649075\pi$
$48$	1.70370	−	6.71546i	0.245909	−	0.969293i
$49$	6.73704	+	1.90059i	0.962435	+	0.271513i
$50$	−5.06483	−	4.17712i	−0.716275	−	0.590734i
$51$	9.32272	−	0.622205i	1.30544	−	0.0871261i
$52$	−0.615447	+	0.534493i	−0.0853472	+	0.0741208i
$53$	−6.39512	−	3.69223i	−0.878438	−	0.507166i	−0.00829466	−	0.999966i	$-0.502640\pi$
$53$	−6.39512	−	3.69223i	−0.878438	−	0.507166i	−0.870143	+	0.492799i	$0.835974\pi$
$54$	−1.03015	+	7.27591i	−0.140185	+	0.990125i
$55$			10.2936i			1.38799i
$56$	2.99384	+	6.85835i	0.400069	+	0.916485i
$57$	−5.20004	−	7.76237i	−0.688763	−	1.02815i
$58$	6.97097	+	1.16822i	0.915333	+	0.153395i
$59$	−2.78610	+	1.01406i	−0.362719	+	0.132019i	−0.516950	−	0.856016i	$-0.672933\pi$
$59$	−2.78610	+	1.01406i	−0.362719	+	0.132019i	0.154230	+	0.988035i	$0.450710\pi$
$60$	−2.74619	−	10.4003i	−0.354532	−	1.34267i
$61$	1.25754	+	7.13188i	0.161012	+	0.913143i	0.953082	+	0.302713i	$0.0978924\pi$
$61$	1.25754	+	7.13188i	0.161012	+	0.913143i	−0.792070	+	0.610430i	$0.790997\pi$
$62$	10.8553	+	6.14501i	1.37863	+	0.780417i
$63$	−3.93973	−	6.89047i	−0.496359	−	0.868117i
$64$	−3.64197	+	7.12293i	−0.455246	+	0.890366i
$65$	−0.432857	+	1.18927i	−0.0536893	+	0.147510i
$66$	−4.73778	+	6.59449i	−0.583180	+	0.811725i
$67$	0.563236	−	0.671238i	0.0688102	−	0.0820048i	−0.730541	−	0.682869i	$-0.760732\pi$
$67$	0.563236	−	0.671238i	0.0688102	−	0.0820048i	0.799351	+	0.600864i	$0.205177\pi$
$68$	−10.6553	−	1.69276i	−1.29214	−	0.205278i
$69$	5.11457	+	11.5863i	0.615722	+	1.39482i
$70$	9.23112	+	7.05533i	1.10333	+	0.843273i
$71$	−1.18599	+	2.05419i	−0.140751	+	0.243788i	−0.927780	−	0.373129i	$-0.878285\pi$
$71$	−1.18599	+	2.05419i	−0.140751	+	0.243788i	0.787029	+	0.616916i	$0.211618\pi$
$72$	3.02755	−	7.92679i	0.356800	−	0.934181i
$73$	15.4303			1.80597			0.902987	−	0.429667i	$-0.141369\pi$
$73$	15.4303			1.80597			0.902987	+	0.429667i	$0.141369\pi$
$74$	1.16371	+	0.412400i	0.135279	+	0.0479406i
$75$	−5.56710	−	5.80160i	−0.642833	−	0.669912i
$76$	3.86154	+	10.0738i	0.442949	+	1.15554i
$77$	−0.324880	−	8.76454i	−0.0370235	−	0.998812i
$78$	−0.824681	+	0.562662i	−0.0933768	+	0.0637089i
$79$	3.40949	+	4.06327i	0.383597	+	0.457153i	0.922946	−	0.384929i	$-0.125774\pi$
$79$	3.40949	+	4.06327i	0.383597	+	0.457153i	−0.539349	+	0.842082i	$0.681330\pi$
$80$	0.421817	+	12.4136i	0.0471606	+	1.38788i
$81$	−2.28790	+	8.70434i	−0.254211	+	0.967149i
$82$	5.79915	+	3.28280i	0.640409	+	0.362525i
$83$	1.93646	+	10.9822i	0.212554	+	1.20545i	0.885101	+	0.465398i	$0.154089\pi$
$83$	1.93646	+	10.9822i	0.212554	+	1.20545i	−0.672547	+	0.740054i	$0.734800\pi$
$84$	2.66651	+	8.76868i	0.290940	+	0.956741i
$85$	−15.7406	+	5.72912i	−1.70731	+	0.621410i
$86$	−4.82386	−	12.9112i	−0.520170	−	1.39225i
$87$	8.31376	+	2.41249i	0.891329	+	0.258646i
$88$	7.02668	−	6.20786i	0.749047	−	0.661760i
$89$	−3.49680	−	2.01888i	−0.370660	−	0.214001i	0.303087	−	0.952963i	$-0.401983\pi$
$89$	−3.49680	−	2.01888i	−0.370660	−	0.214001i	−0.673747	+	0.738962i	$0.735316\pi$
$90$	−1.86153	−	13.0420i	−0.196223	−	1.37475i
$91$	0.331024	−	1.02627i	0.0347007	−	0.107582i
$92$	−2.78368	−	14.3568i	−0.290219	−	1.49680i
$93$	12.3311	+	9.01897i	1.27868	+	0.935224i
$94$	2.56513	−	15.3065i	0.264573	−	1.57875i
$95$	12.8315	+	10.7669i	1.31648	+	1.10466i
$96$	−5.44331	+	8.14680i	−0.555556	+	0.831479i
$97$	−13.5183	+	11.3432i	−1.37258	+	1.15173i	−0.400710	+	0.916205i	$0.631237\pi$
$97$	−13.5183	+	11.3432i	−1.37258	+	1.15173i	−0.971868	+	0.235525i	$0.924319\pi$
$98$	−8.08257	−	5.71595i	−0.816462	−	0.577398i
$99$	−6.70117	+	7.34813i	−0.673493	+	0.738515i
$100$	4.77812	+	7.96060i	0.477812	+	0.796060i
$101$	−0.835454	−	0.995655i	−0.0831307	−	0.0990714i	0.722876	−	0.690978i	$-0.242820\pi$
$101$	−0.835454	−	0.995655i	−0.0831307	−	0.0990714i	−0.806007	+	0.591907i	$0.798375\pi$
$102$	−12.7210	−	3.57455i	−1.25956	−	0.353933i
$103$	−9.96189	−	1.75655i	−0.981574	−	0.173078i	−0.340239	−	0.940339i	$-0.610508\pi$
$103$	−9.96189	−	1.75655i	−0.981574	−	0.173078i	−0.641335	+	0.767261i	$0.721619\pi$
$104$	1.07287	−	0.421742i	0.105204	−	0.0413552i
$105$	10.2259	+	9.89536i	0.997945	+	0.965688i
$106$	6.78044	+	7.94266i	0.658575	+	0.771459i
$107$	4.47560	+	7.75197i	0.432673	+	0.749412i	0.997103	−	0.0760696i	$-0.0242371\pi$
$107$	4.47560	+	7.75197i	0.432673	+	0.749412i	−0.564429	+	0.825481i	$0.690904\pi$
$108$	4.81022	−	9.21205i	0.462863	−	0.886430i
$109$	3.66021	−	6.33967i	0.350585	−	0.607231i	−0.635767	−	0.771881i	$-0.719316\pi$
$109$	3.66021	−	6.33967i	0.350585	−	0.607231i	0.986352	+	0.164650i	$0.0526495\pi$
$110$	4.86257	−	13.7212i	0.463628	−	1.30827i
$111$	1.35696	+	0.667169i	0.128797	+	0.0633249i
$112$	−0.750949	−	10.5563i	−0.0709580	−	0.997479i
$113$	−6.03015	+	7.18645i	−0.567269	+	0.676044i	−0.971068	−	0.238803i	$-0.923245\pi$
$113$	−6.03015	+	7.18645i	−0.567269	+	0.676044i	0.403799	+	0.914848i	$0.367689\pi$
$114$	3.26474	+	12.8036i	0.305771	+	1.19916i
$115$	−14.5948	−	17.3934i	−1.36097	−	1.62194i
$116$	−8.74034	−	4.85022i	−0.811521	−	0.450332i
$117$	−1.08321	+	0.567171i	−0.100143	+	0.0524350i
$118$	4.19286	−	0.0356057i	0.385984	−	0.00327777i
$119$	13.2216	−	5.37489i	1.21202	−	0.492715i
$120$	−1.25231	+	15.1607i	−0.114320	+	1.38397i
$121$	0.0103665	−	0.00377310i	0.000942410	−	0.000343009i
$122$	1.69272	−	10.1007i	0.153252	−	0.914478i
$123$	6.58756	+	4.81813i	0.593980	+	0.434437i
$124$	−11.5672	−	13.3191i	−1.03876	−	1.19609i
$125$	−0.962081	−	0.555458i	−0.0860511	−	0.0496817i
$126$	1.99664	+	11.0460i	0.177874	+	0.984053i
$127$	5.39430	−	3.11440i	0.478666	−	0.276358i	−0.241194	−	0.970477i	$-0.577539\pi$
$127$	5.39430	−	3.11440i	0.478666	−	0.276358i	0.719861	+	0.694119i	$0.244206\pi$
$128$	8.21947	−	7.77434i	0.726505	−	0.687161i
$129$	−4.03182	−	16.3920i	−0.354982	−	1.44324i
$130$	1.13879	−	1.38080i	0.0998781	−	0.121104i
$131$	0.0518629	+	0.0435182i	0.00453129	+	0.00380220i	0.645050	−	0.764140i	$-0.276836\pi$
$131$	0.0518629	+	0.0435182i	0.00453129	+	0.00380220i	−0.640519	+	0.767942i	$0.721281\pi$
$132$	9.43054	−	6.55229i	0.820823	−	0.570304i
$133$	−11.2652	−	8.76254i	−0.976821	−	0.759809i
$134$	−1.06787	+	0.628685i	−0.0922499	+	0.0543101i
$135$	−0.409667	−	16.1299i	−0.0352585	−	1.38824i
$136$	13.4037	+	7.28985i	1.14936	+	0.625099i
$137$	5.40219	−	14.8424i	0.461541	−	1.26807i	−0.462786	−	0.886470i	$-0.653150\pi$
$137$	5.40219	−	14.8424i	0.461541	−	1.26807i	0.924327	−	0.381602i	$-0.124628\pi$
$138$	−1.34444	−	17.8604i	−0.114447	−	1.52038i
$139$	−3.55557	−	9.76884i	−0.301579	−	0.828582i	−0.994226	−	0.107305i	$-0.965778\pi$
$139$	−3.55557	−	9.76884i	−0.301579	−	0.828582i	0.692647	−	0.721277i	$-0.256444\pi$
$140$	−8.97211	−	13.7653i	−0.758281	−	1.16338i
$141$	5.29724	−	18.2550i	0.446108	−	1.53735i
$142$	2.55128	−	2.17796i	0.214098	−	0.182770i
$143$	−1.35108			−0.112983
$144$	−7.78019	+	9.13612i	−0.648349	+	0.761343i
$145$	−15.5196			−1.28884
$146$	−20.5683	−	7.28905i	−1.70224	−	0.603246i
$147$	−9.01921	−	8.10271i	−0.743892	−	0.668300i
$148$	−1.35640	−	1.09945i	−0.111496	−	0.0903740i
$149$	2.15408	+	5.91829i	0.176469	+	0.484845i	0.996119	−	0.0880203i	$-0.0280540\pi$
$149$	2.15408	+	5.91829i	0.176469	+	0.484845i	−0.819650	+	0.572865i	$0.805832\pi$
$150$	4.68025	+	10.3633i	0.382141	+	0.846158i
$151$	−0.312854	+	0.0551646i	−0.0254597	+	0.00448923i	−0.186364	−	0.982481i	$-0.559670\pi$
$151$	−0.312854	+	0.0551646i	−0.0254597	+	0.00448923i	0.160904	+	0.986970i	$0.448559\pi$
$152$	−0.388644	−	15.2524i	−0.0315232	−	1.23713i
$153$	−14.9662	−	6.15744i	−1.20994	−	0.497800i
$154$	−3.70720	+	11.8365i	−0.298735	+	0.953811i
$155$	−25.7373	−	9.36762i	−2.06727	−	0.752425i
$156$	1.36508	−	0.360451i	0.109294	−	0.0288592i
$157$	2.61190	−	0.950655i	0.208453	−	0.0758706i	−0.235684	−	0.971830i	$-0.575733\pi$
$157$	2.61190	−	0.950655i	0.208453	−	0.0758706i	0.444136	+	0.895959i	$0.353511\pi$
$158$	−2.62536	−	7.02688i	−0.208862	−	0.559028i
$159$	7.11855	+	10.6262i	0.564538	+	0.842714i
$160$	5.30176	−	16.7464i	0.419141	−	1.32392i
$161$	12.9758	+	14.3491i	1.02263	+	1.13087i
$162$	7.16155	−	10.5220i	0.562665	−	0.826685i
$163$	2.43859	−	1.40792i	0.191005	−	0.110277i	−0.401448	−	0.915882i	$-0.631493\pi$
$163$	2.43859	−	1.40792i	0.191005	−	0.110277i	0.592453	+	0.805605i	$0.298160\pi$
$164$	−6.17943	−	7.11537i	−0.482532	−	0.555617i
$165$	7.86652	−	15.9998i	0.612408	−	1.24558i
$166$	2.60658	−	15.5539i	0.202310	−	1.20721i
$167$	8.69860	+	7.29899i	0.673118	+	0.564813i	0.913986	−	0.405745i	$-0.132988\pi$
$167$	8.69860	+	7.29899i	0.673118	+	0.564813i	−0.240868	+	0.970558i	$0.577432\pi$
$168$	0.587798	−	12.9481i	0.0453496	−	0.998971i
$169$	12.0599	+	4.38945i	0.927685	+	0.337650i
$170$	23.6884	−	0.201161i	1.81682	−	0.0154284i
$171$	2.15053	+	16.0393i	0.164455	+	1.22656i
$172$	0.331028	+	19.4892i	0.0252406	+	1.48604i
$173$	−5.85092	+	16.0753i	−0.444837	+	1.22218i	0.491438	+	0.870912i	$0.336471\pi$
$173$	−5.85092	+	16.0753i	−0.444837	+	1.22218i	−0.936275	+	0.351267i	$0.885751\pi$
$174$	−9.94249	−	7.14313i	−0.753738	−	0.541519i
$175$	−10.8569	−	5.74289i	−0.820704	−	0.434121i
$176$	−12.2990	+	4.95567i	−0.927070	+	0.373548i
$177$	5.10551	+	0.552986i	0.383754	+	0.0415650i
$178$	3.70749	+	4.34298i	0.277888	+	0.325520i
$179$	−5.29260	−	9.16706i	−0.395588	−	0.685178i	0.597588	−	0.801803i	$-0.296126\pi$
$179$	−5.29260	−	9.16706i	−0.395588	−	0.685178i	−0.993176	+	0.116625i	$0.962792\pi$
$180$	−3.67950	+	18.2642i	−0.274254	+	1.36133i
$181$	−6.51928	−	11.2917i	−0.484574	−	0.839307i	0.515269	−	0.857029i	$-0.327692\pi$
$181$	−6.51928	−	11.2917i	−0.484574	−	0.839307i	−0.999843	+	0.0177216i	$0.994359\pi$
$182$	−0.926046	+	1.21163i	−0.0686431	+	0.0898119i
$183$	3.49563	−	12.0464i	0.258405	−	0.890496i
$184$	−3.07137	+	20.4524i	−0.226424	+	1.50777i
$185$	−2.66969	−	0.470739i	−0.196280	−	0.0346094i
$186$	−12.1768	−	17.8472i	−0.892844	−	1.30862i
$187$	−11.4946	−	13.6987i	−0.840567	−	1.00175i
$188$	−10.6499	+	19.1916i	−0.776723	+	1.39969i
$189$	0.857894	+	13.7209i	0.0624026	+	0.998051i
$190$	−12.0180	−	20.4135i	−0.871880	−	1.48095i
$191$	10.8883	−	9.13639i	0.787852	−	0.661086i	−0.157361	−	0.987541i	$-0.550299\pi$
$191$	10.8883	−	9.13639i	0.787852	−	0.661086i	0.945213	+	0.326455i	$0.105854\pi$
$192$	11.1043	−	8.28822i	0.801384	−	0.598151i
$193$	−1.87583	+	10.6383i	−0.135025	+	0.765765i	0.839817	+	0.542869i	$0.182662\pi$
$193$	−1.87583	+	10.6383i	−0.135025	+	0.765765i	−0.974842	+	0.222896i	$0.928449\pi$
$194$	23.3781	−	8.73447i	1.67845	−	0.627098i
$195$	1.58166	−	1.51773i	0.113265	−	0.108687i
$196$	8.07380	+	11.4374i	0.576700	+	0.816956i
$197$	−13.9163	+	8.03460i	−0.991498	+	0.572441i	−0.905722	−	0.423873i	$-0.860670\pi$
$197$	−13.9163	+	8.03460i	−0.991498	+	0.572441i	−0.0857759	+	0.996314i	$0.527337\pi$
$198$	12.4037	−	6.62941i	0.881494	−	0.471132i
$199$	7.35150	−	4.24439i	0.521134	−	0.300877i	−0.216265	−	0.976335i	$-0.569387\pi$
$199$	7.35150	−	4.24439i	0.521134	−	0.300877i	0.737398	+	0.675458i	$0.236054\pi$
$200$	−2.60868	−	12.8685i	−0.184462	−	0.909939i
$201$	−1.38843	+	0.612900i	−0.0979323	+	0.0432307i
$202$	0.643313	+	1.72185i	0.0452633	+	0.121149i
$203$	13.2143	−	0.489821i	0.927460	−	0.0343787i
$204$	15.2683	+	10.7740i	1.06900	+	0.754334i
$205$	−13.7494	−	5.00439i	−0.960303	−	0.349522i
$206$	12.4493	+	7.04733i	0.867383	+	0.491011i
$207$	0.904598	−	21.9176i	0.0628739	−	1.52338i
$208$	−1.62935	+	0.0553655i	−0.112975	+	0.00383890i
$209$	−6.11595	+	16.8034i	−0.423049	+	1.16232i
$210$	−8.95653	−	18.0209i	−0.618059	−	1.24356i
$211$	10.6728	−	12.7194i	0.734746	−	0.875637i	−0.261228	−	0.965277i	$-0.584127\pi$
$211$	10.6728	−	12.7194i	0.734746	−	0.875637i	0.995974	+	0.0896406i	$0.0285718\pi$
$212$	−5.28622	−	13.7904i	−0.363059	−	0.947131i
$213$	3.41327	−	2.28656i	0.233873	−	0.156673i
$214$	−2.30398	−	12.4475i	−0.157497	−	0.850893i
$215$	15.1316	+	26.2088i	1.03197	+	1.78742i
$216$	−10.7636	+	10.0072i	−0.732370	+	0.680906i
$217$	22.2098	+	7.16380i	1.50770	+	0.486311i
$218$	−7.87379	+	6.72166i	−0.533281	+	0.455248i
$219$	−23.9839	−	11.7920i	−1.62068	−	0.796831i
$220$	−12.9635	+	15.9932i	−0.873996	+	1.07826i
$221$	−0.751974	−	2.06603i	−0.0505833	−	0.138976i
$222$	−1.49365	−	1.53034i	−0.100247	−	0.102710i
$223$	−6.02876	+	16.5639i	−0.403716	+	1.10920i	0.556721	+	0.830700i	$0.312059\pi$
$223$	−6.02876	+	16.5639i	−0.403716	+	1.10920i	−0.960436	+	0.278500i	$0.910163\pi$
$224$	−3.98567	+	14.4262i	−0.266304	+	0.963889i
$225$	4.21950	+	13.2721i	0.281300	+	0.884808i
$226$	11.4329	−	6.73087i	0.760504	−	0.447731i
$227$	−0.486468	−	2.75889i	−0.0322880	−	0.183114i	0.964399	−	0.264453i	$-0.0851915\pi$
$227$	−0.486468	−	2.75889i	−0.0322880	−	0.183114i	−0.996686	+	0.0813390i	$0.974080\pi$
$228$	1.69639	−	18.6092i	0.112346	−	1.23242i
$229$	18.6656	−	6.79371i	1.23345	−	0.448941i	0.358676	−	0.933462i	$-0.383228\pi$
$229$	18.6656	−	6.79371i	1.23345	−	0.448941i	0.874779	+	0.484521i	$0.161006\pi$
$230$	11.2382	+	30.0796i	0.741027	+	1.98339i
$231$	−6.19301	+	13.8714i	−0.407470	+	0.912669i
$232$	9.35957	+	10.5941i	0.614486	+	0.695537i
$233$		−	8.76687i		−	0.574337i	−0.957880	−	0.287168i	$-0.907286\pi$
$233$		−	8.76687i		−	0.574337i	0.957880	−	0.287168i	$-0.0927139\pi$
$234$	1.71183	−	0.244335i	0.111906	−	0.0159727i
$235$			34.0773i			2.22296i
$236$	−5.60584	−	1.93319i	−0.364909	−	0.125840i
$237$	−2.19430	−	8.92128i	−0.142535	−	0.579500i
$238$	−20.1633	+	0.918918i	−1.30699	+	0.0595646i
$239$	14.4963	−	5.27621i	0.937686	−	0.341290i	0.172434	−	0.985021i	$-0.444837\pi$
$239$	14.4963	−	5.27621i	0.937686	−	0.341290i	0.765252	+	0.643731i	$0.222615\pi$
$240$	8.83102	−	19.6174i	0.570040	−	1.26629i
$241$	−15.0218	−	5.46749i	−0.967640	−	0.352192i	−0.190617	−	0.981664i	$-0.561049\pi$
$241$	−15.0218	−	5.46749i	−0.967640	−	0.352192i	−0.777023	+	0.629472i	$0.783271\pi$
$242$	−0.0156008		0.000132481i	−0.00100286		8.51623e-6i
$243$	10.2082	−	11.7811i	0.654853	−	0.755756i
$244$	−7.02783	+	12.6645i	−0.449911	+	0.810762i
$245$	19.5772	+	9.44474i	1.25074	+	0.603402i
$246$	−6.50509	−	9.53438i	−0.414750	−	0.607890i
$247$	−1.41320	+	1.68419i	−0.0899201	+	0.107163i
$248$	9.12707	+	23.2184i	0.579569	+	1.47437i
$249$	5.38283	−	18.5499i	0.341123	−	1.17556i
$250$	1.02005	+	1.19489i	0.0645136	+	0.0755716i
$251$	−1.27965	−	2.21641i	−0.0807705	−	0.139899i	0.822811	−	0.568316i	$-0.192405\pi$
$251$	−1.27965	−	2.21641i	−0.0807705	−	0.139899i	−0.903581	+	0.428417i	$0.859071\pi$
$252$	2.55649	−	15.6673i	0.161044	−	0.986947i
$253$	12.1197	−	20.9919i	0.761956	−	1.31975i
$254$	−8.66172	+	1.60325i	−0.543485	+	0.100597i
$255$	28.8446	+	3.12421i	1.80632	+	0.195645i
$256$	−14.6289	+	6.48031i	−0.914308	+	0.405019i
$257$	1.60523	+	4.41034i	0.100132	+	0.275110i	0.979636	−	0.200781i	$-0.0643480\pi$
$257$	1.60523	+	4.41034i	0.100132	+	0.275110i	−0.879504	+	0.475891i	$0.842126\pi$
$258$	−2.36903	+	23.7549i	−0.147489	+	1.47892i
$259$	2.28798	+	0.316554i	0.142168	+	0.0196697i
$260$	−2.17026	+	1.30263i	−0.134594	+	0.0807859i
$261$	−11.0788	−	10.1033i	−0.685758	−	0.625380i
$262$	−0.0485751	−	0.0825085i	−0.00300098	−	0.00509739i
$263$	18.3538	−	15.4007i	1.13174	−	0.949645i	0.132605	−	0.991169i	$-0.457666\pi$
$263$	18.3538	−	15.4007i	1.13174	−	0.949645i	0.999138	+	0.0415240i	$0.0132213\pi$
$264$	−15.6660	+	4.27924i	−0.964175	+	0.263369i
$265$	−17.5655	−	14.7392i	−1.07904	−	0.905423i
$266$	10.8771	+	17.0019i	0.666918	+	1.04245i
$267$	3.89237	+	5.81033i	0.238209	+	0.355587i
$268$	1.72044	−	0.333581i	0.105092	−	0.0203767i
$269$	−19.7504	−	11.4029i	−1.20420	−	0.695245i	−0.242714	−	0.970098i	$-0.578038\pi$
$269$	−19.7504	−	11.4029i	−1.20420	−	0.695245i	−0.961486	+	0.274853i	$0.911371\pi$
$270$	−7.07346	+	21.6944i	−0.430477	+	1.32028i
$271$	−21.7778	+	12.5734i	−1.32291	+	0.763780i	−0.984191	−	0.177109i	$-0.943326\pi$
$271$	−21.7778	+	12.5734i	−1.32291	+	0.763780i	−0.338715	+	0.940889i	$0.609992\pi$
$272$	−14.4233	−	16.0490i	−0.874541	−	0.973113i
$273$	−1.29881	+	1.34220i	−0.0786077	+	0.0812335i
$274$	−14.2124	+	17.2328i	−0.858603	+	1.04107i
$275$	−2.67224	+	15.1551i	−0.161142	+	0.913884i
$276$	−6.64489	+	24.4427i	−0.399975	+	1.47128i
$277$	0.0806907	−	0.0677075i	0.00484823	−	0.00406815i	−0.640360	−	0.768075i	$-0.721215\pi$
$277$	0.0806907	−	0.0677075i	0.00484823	−	0.00406815i	0.645209	+	0.764007i	$0.276770\pi$
$278$	0.124843	+	14.7013i	0.00748761	+	0.881727i
$279$	−12.2743	−	23.4422i	−0.734846	−	1.40345i
$280$	5.45712	+	22.5873i	0.326126	+	1.34985i
$281$	3.97276	+	4.73455i	0.236995	+	0.282440i	0.871412	−	0.490551i	$-0.163204\pi$
$281$	3.97276	+	4.73455i	0.236995	+	0.282440i	−0.634418	+	0.772990i	$0.718760\pi$
$282$	−15.6846	+	21.8313i	−0.934002	+	1.30003i
$283$	−8.10413	+	9.65813i	−0.481741	+	0.574116i	−0.951097	−	0.308893i	$-0.900042\pi$
$283$	−8.10413	+	9.65813i	−0.481741	+	0.574116i	0.469356	+	0.883009i	$0.344486\pi$
$284$	−4.42966	+	1.69800i	−0.262852	+	0.100758i
$285$	−11.7163	−	26.5414i	−0.694013	−	1.57218i
$286$	1.80098	+	0.638235i	0.106494	+	0.0377396i
$287$	11.8650	+	3.82706i	0.700368	+	0.225904i
$288$	14.6867	−	8.50305i	0.865420	−	0.501047i
$289$	6.05006	−	10.4790i	0.355886	−	0.616412i
$290$	20.6874	+	7.33128i	1.21481	+	0.430507i
$291$	29.6807	−	7.30034i	1.73992	−	0.427954i
$292$	23.9740	+	19.4324i	1.40297	+	1.13720i
$293$	−0.431940	−	1.18675i	−0.0252342	−	0.0693304i	0.926436	−	0.376453i	$-0.122856\pi$
$293$	−0.431940	−	1.18675i	−0.0252342	−	0.0693304i	−0.951670	+	0.307122i	$0.900634\pi$
$294$	8.19485	+	15.0614i	0.477934	+	0.878396i
$295$	−9.06675	+	1.59871i	−0.527886	+	0.0930806i
$296$	1.28870	+	2.10629i	0.0749041	+	0.122426i
$297$	16.0314	−	6.30038i	0.930239	−	0.365585i
$298$	−0.0756343	−	8.90655i	−0.00438138	−	0.515943i
$299$	2.28297	−	1.91564i	0.132027	−	0.110784i
$300$	−1.34323	−	16.0250i	−0.0775514	−	0.925203i
$301$	−13.7111	−	21.8380i	−0.790295	−	1.25872i
$302$	0.443089	+	0.0742546i	0.0254969	+	0.00427287i
$303$	0.537686	+	2.18605i	0.0308893	+	0.125585i
$304$	−6.68698	+	20.5148i	−0.383524	+	1.17660i
$305$			22.4875i			1.28763i
$306$	17.0410	+	15.2776i	0.974170	+	0.873363i
$307$	−3.98009	−	2.29791i	−0.227156	−	0.131148i	0.382104	−	0.924120i	$-0.375200\pi$
$307$	−3.98009	−	2.29791i	−0.227156	−	0.131148i	−0.609259	+	0.792971i	$0.708533\pi$
$308$	10.5330	−	14.0266i	0.600176	−	0.799241i
$309$	14.1418	+	10.3433i	0.804499	+	0.588410i
$310$	29.8823	+	24.6449i	1.69720	+	1.39973i
$311$	−12.6522	−	10.6165i	−0.717442	−	0.602005i	0.209234	−	0.977865i	$-0.432903\pi$
$311$	−12.6522	−	10.6165i	−0.717442	−	0.602005i	−0.926676	+	0.375860i	$0.877347\pi$
$312$	−1.98991	−	0.164372i	−0.112656	−	0.00930574i
$313$	−6.02132	−	2.19158i	−0.340345	−	0.123876i	0.166192	−	0.986093i	$-0.446853\pi$
$313$	−6.02132	−	2.19158i	−0.340345	−	0.123876i	−0.506538	+	0.862218i	$0.669075\pi$
$314$	−3.93071	+	0.0333795i	−0.221823	+	0.00188371i
$315$	−8.33236	−	23.1955i	−0.469475	−	1.30692i
$316$	0.180160	+	10.6069i	0.0101348	+	0.596685i
$317$	14.3405	−	2.52861i	0.805441	−	0.142021i	0.244255	−	0.969711i	$-0.421456\pi$
$317$	14.3405	−	2.52861i	0.805441	−	0.142021i	0.561186	+	0.827690i	$0.310345\pi$
$318$	−4.46923	−	17.5273i	−0.250622	−	0.982883i
$319$	−5.66660	−	15.5689i	−0.317269	−	0.871689i
$320$	−14.9780	+	19.8183i	−0.837294	+	1.10787i
$321$	−1.03245	−	15.4695i	−0.0576256	−	0.863425i
$322$	−10.5182	−	25.2567i	−0.586157	−	1.40750i
$323$	−29.0992			−1.61912
$324$	−14.5167	+	10.6426i	−0.806483	+	0.591257i
$325$	−0.946022	+	1.63856i	−0.0524759	+	0.0908909i
$326$	−3.91569	+	0.724779i	−0.216870	+	0.0401418i
$327$	−10.5341	+	7.05683i	−0.582536	+	0.390244i
$328$	4.87588	+	12.4038i	0.269225	+	0.684883i
$329$	−1.07553	−	29.0153i	−0.0592957	−	1.59966i
$330$	−18.0440	+	17.6114i	−0.993292	+	0.969477i
$331$	18.1027	−	3.19199i	0.995014	−	0.175448i	0.347647	−	0.937626i	$-0.386981\pi$
$331$	18.1027	−	3.19199i	0.995014	−	0.175448i	0.647368	+	0.762178i	$0.275870\pi$
$332$	−10.8220	+	19.5018i	−0.593933	+	1.07030i
$333$	−1.59932	−	2.07402i	−0.0876422	−	0.113655i
$334$	−8.14716	−	13.8386i	−0.445793	−	0.757212i
$335$	2.08433	−	1.74896i	0.113879	−	0.0955557i
$336$	−6.90007	+	16.9820i	−0.376429	+	0.926445i
$337$	2.78629	−	15.8018i	0.151779	−	0.860782i	−0.809893	−	0.586578i	$-0.800475\pi$
$337$	2.78629	−	15.8018i	0.151779	−	0.860782i	0.961672	−	0.274203i	$-0.0884142\pi$
$338$	−14.0022	−	11.5480i	−0.761617	−	0.628129i
$339$	14.8649	−	6.56187i	0.807350	−	0.356392i
$340$	−31.6713	−	10.9220i	−1.71762	−	0.592326i
$341$		−	29.2393i		−	1.58340i
$342$	4.71015	−	22.3961i	0.254696	−	1.21104i
$343$	−16.9672	−	7.42389i	−0.916143	−	0.400852i
$344$	8.76520	−	26.1352i	0.472588	−	1.40912i
$345$	9.39301	+	38.1888i	0.505703	+	2.05602i
$346$	15.3929	−	18.6642i	0.827529	−	1.00339i
$347$	2.02373	−	11.4772i	0.108640	−	0.616126i	−0.881064	−	0.472996i	$-0.843172\pi$
$347$	2.02373	−	11.4772i	0.108640	−	0.616126i	0.989704	−	0.143130i	$-0.0457165\pi$
$348$	9.87887	+	14.2184i	0.529563	+	0.762186i
$349$	3.03140	+	17.1919i	0.162267	+	0.920262i	0.951838	+	0.306603i	$0.0991923\pi$
$349$	3.03140	+	17.1919i	0.162267	+	0.920262i	−0.789571	+	0.613660i	$0.789697\pi$
$350$	11.7592	+	12.7838i	0.628556	+	0.683325i
$351$	2.11712	−	0.0537708i	0.113004	−	0.00287007i
$352$	18.7354	−	0.795961i	0.998598	−	0.0424248i
$353$	2.01748	−	5.54299i	0.107380	−	0.295024i	−0.874352	−	0.485292i	$-0.838713\pi$
$353$	2.01748	−	5.54299i	0.107380	−	0.295024i	0.981732	+	0.190268i	$0.0609357\pi$
$354$	−6.54435	−	3.14890i	−0.347828	−	0.167362i
$355$	−4.73442	+	5.64226i	−0.251277	+	0.299460i
$356$	−2.89047	−	7.54050i	−0.153194	−	0.399646i
$357$	−24.6585	−	1.74975i	−1.30507	−	0.0926064i
$358$	2.72456	+	14.7197i	0.143998	+	0.777961i
$359$	−1.01348	+	1.75539i	−0.0534892	+	0.0926460i	−0.891530	−	0.452961i	$-0.850368\pi$
$359$	−1.01348	+	1.75539i	−0.0534892	+	0.0926460i	0.838041	+	0.545607i	$0.183701\pi$
$360$	13.5325	−	22.6078i	0.713226	−	1.19154i
$361$	5.04914	+	8.74537i	0.265744	+	0.460282i
$362$	3.35604	+	18.1313i	0.176389	+	0.952961i
$363$	−0.0189965	−	0.00205755i	−0.000997060	−	0.000107993i
$364$	1.80676	−	1.17763i	0.0947001	−	0.0617246i
$365$	47.1860	+	8.32017i	2.46983	+	0.435498i
$366$	−10.3502	+	14.4064i	−0.541013	+	0.753034i
$367$	17.0877	−	3.01303i	0.891972	−	0.157279i	0.291165	−	0.956673i	$-0.405957\pi$
$367$	17.0877	−	3.01303i	0.891972	−	0.157279i	0.600807	+	0.799394i	$0.294846\pi$
$368$	13.7555	−	25.8119i	0.717057	−	1.34554i
$369$	−6.55723	−	12.5233i	−0.341356	−	0.651939i
$370$	3.33629	+	1.88862i	0.173446	+	0.0981845i
$371$	15.4215	+	11.9954i	0.800642	+	0.622770i
$372$	7.80064	+	29.5422i	0.404445	+	1.53169i
$373$	−2.74435	+	15.5640i	−0.142097	+	0.805873i	0.827555	+	0.561385i	$0.189731\pi$
$373$	−2.74435	+	15.5640i	−0.142097	+	0.805873i	−0.969652	+	0.244489i	$0.921380\pi$
$374$	8.85102	+	23.6901i	0.457675	+	1.22498i
$375$	1.07091	+	1.59861i	0.0553017	+	0.0825517i
$376$	23.2620	−	20.5513i	1.19965	−	1.05985i
$377$		−	2.03702i		−	0.104912i
$378$	5.33803	−	18.6951i	0.274559	−	0.961570i
$379$			6.93686i			0.356322i	0.984001	+	0.178161i	$0.0570149\pi$
$379$			6.93686i			0.356322i	−0.984001	+	0.178161i	$0.942985\pi$
$380$	6.37677	+	32.8881i	0.327121	+	1.68712i
$381$	−10.7646	+	0.718440i	−0.551490	+	0.0368068i
$382$	−18.8299	+	7.03517i	−0.963421	+	0.359951i
$383$	−2.85330	+	16.1819i	−0.145797	+	0.826855i	0.820927	+	0.571033i	$0.193457\pi$
$383$	−2.85330	+	16.1819i	−0.145797	+	0.826855i	−0.966724	+	0.255822i	$0.917654\pi$
$384$	−18.7171	+	5.80254i	−0.955154	+	0.296110i
$385$	3.73245	−	26.9773i	0.190223	−	1.37489i
$386$	7.52587	−	13.2946i	0.383057	−	0.676680i
$387$	−6.26020	+	28.5600i	−0.318224	+	1.45179i
$388$	−35.2888	+	0.599386i	−1.79152	+	0.0304292i
$389$	−20.9863	+	3.70045i	−1.06405	+	0.187620i	−0.678152	−	0.734922i	$-0.737219\pi$
$389$	−20.9863	+	3.70045i	−1.06405	+	0.187620i	−0.385896	+	0.922542i	$0.626108\pi$
$390$	−2.82529	+	1.27595i	−0.143064	+	0.0646104i
$391$	38.8455	+	6.84951i	1.96450	+	0.346394i
$392$	−5.35938	−	19.0598i	−0.270690	−	0.962667i
$393$	−0.0473555	−	0.107276i	−0.00238877	−	0.00541138i
$394$	22.3457	−	4.13610i	1.12576	−	0.208374i
$395$	8.23532	+	14.2640i	0.414364	+	0.717699i
$396$	−19.6656	+	2.97755i	−0.988235	+	0.149627i
$397$	−4.71392	+	8.16476i	−0.236585	+	0.409777i	−0.959732	−	0.280917i	$-0.909362\pi$
$397$	−4.71392	+	8.16476i	−0.236585	+	0.409777i	0.723147	+	0.690694i	$0.242695\pi$
$398$	−11.8044	+	2.18496i	−0.591703	+	0.109522i
$399$	10.8136	+	22.2290i	0.541356	+	1.11284i
$400$	−2.60157	+	18.3858i	−0.130079	+	0.919291i
$401$	5.15280	−	6.14086i	0.257318	−	0.306660i	−0.621883	−	0.783110i	$-0.713632\pi$
$401$	5.15280	−	6.14086i	0.257318	−	0.306660i	0.879202	+	0.476450i	$0.158077\pi$
$402$	2.14028	−	0.161111i	0.106748	−	0.00803546i
$403$	1.22954	−	3.37814i	0.0612479	−	0.168277i
$404$	−0.0441461	−	2.59910i	−0.00219635	−	0.129310i
$405$	−11.6899	+	25.3844i	−0.580876	+	1.26136i
$406$	−17.8458	−	5.58933i	−0.885673	−	0.277394i
$407$	−0.502539	−	2.85004i	−0.0249099	−	0.141271i
$408$	−15.2629	−	21.5742i	−0.755627	−	1.06808i
$409$	−3.58000	+	20.3032i	−0.177019	+	1.00393i	0.758768	+	0.651361i	$0.225802\pi$
$409$	−3.58000	+	20.3032i	−0.177019	+	1.00393i	−0.935787	+	0.352566i	$0.885309\pi$
$410$	15.9638	+	13.1658i	0.788396	+	0.650214i
$411$	−19.7396	+	18.9417i	−0.973684	+	0.934327i
$412$	−13.2656	−	15.2749i	−0.653552	−	0.752539i
$413$	7.66947	−	1.64739i	0.377390	−	0.0810628i
$414$	−11.5594	+	28.7885i	−0.568115	+	1.41488i
$415$			34.6279i			1.69982i
$416$	2.19805	+	0.695881i	0.107768	+	0.0341184i
$417$	−1.93892	+	17.9013i	−0.0949495	+	0.876632i
$418$	16.0902	−	19.5096i	0.786997	−	0.954247i
$419$	−4.26529	+	24.1896i	−0.208373	+	1.18174i	0.683670	+	0.729791i	$0.260383\pi$
$419$	−4.26529	+	24.1896i	−0.208373	+	1.18174i	−0.892043	+	0.451950i	$0.850729\pi$
$420$	3.42606	+	28.2526i	0.167175	+	1.37859i
$421$	18.8987	−	15.8579i	0.921064	−	0.772864i	−0.0531276	−	0.998588i	$-0.516919\pi$
$421$	18.8987	−	15.8579i	0.921064	−	0.772864i	0.974191	+	0.225723i	$0.0724746\pi$
$422$	−20.2352	+	11.9130i	−0.985032	+	0.579917i
$423$	−22.1844	+	24.3262i	−1.07864	+	1.18278i
$424$	0.532030	+	20.8796i	0.0258377	+	1.01400i
$425$	−24.6619	+	4.34856i	−1.19628	+	0.210936i
$426$	−5.62998	+	1.43557i	−0.272774	+	0.0695536i
$427$	−0.709737	−	19.1471i	−0.0343466	−	0.926594i
$428$	−2.80886	+	17.6807i	−0.135771	+	0.854629i
$429$	2.10005	+	1.03252i	0.101391	+	0.0498504i
$430$	−7.78957	−	42.0839i	−0.375646	−	2.02947i
$431$	−6.94183	+	12.0236i	−0.334376	+	0.579157i	−0.983365	−	0.181641i	$-0.941859\pi$
$431$	−6.94183	+	12.0236i	−0.334376	+	0.579157i	0.648989	+	0.760798i	$0.275192\pi$
$432$	19.0750	−	8.25492i	0.917747	−	0.397165i
$433$	21.8624			1.05064			0.525320	−	0.850905i	$-0.323945\pi$
$433$	21.8624			1.05064			0.525320	+	0.850905i	$0.323945\pi$
$434$	−26.2213	−	20.0409i	−1.25866	−	0.961993i
$435$	24.1228	+	11.8603i	1.15660	+	0.568659i
$436$	13.6709	−	5.24039i	0.654716	−	0.250969i
$437$	−13.4905	−	37.0648i	−0.645337	−	1.77305i
$438$	26.3998	+	27.0483i	1.26143	+	1.29242i
$439$	−22.7841	+	4.01745i	−1.08743	+	0.191742i	−0.688497	−	0.725239i	$-0.741729\pi$
$439$	−22.7841	+	4.01745i	−1.08743	+	0.191742i	−0.398929	+	0.916982i	$0.630618\pi$
$440$	24.8351	−	15.1949i	1.18397	−	0.724388i
$441$	7.82672	+	19.4870i	0.372701	+	0.927952i
$442$	0.0264034	+	3.10921i	0.00125588	+	0.147890i
$443$	−31.7504	−	11.5562i	−1.50851	−	0.549051i	−0.550259	−	0.834994i	$-0.685471\pi$
$443$	−31.7504	−	11.5562i	−1.50851	−	0.549051i	−0.958247	+	0.285942i	$0.907693\pi$
$444$	1.26810	+	2.74550i	0.0601812	+	0.130296i
$445$	−9.60469	−	8.05929i	−0.455306	−	0.382047i
$446$	15.8608	−	19.2315i	0.751031	−	0.910638i
$447$	1.17466	−	10.8452i	0.0555597	−	0.512961i
$448$	12.1276	−	17.3471i	0.572974	−	0.819573i
$449$	10.7635	+	6.21431i	0.507961	+	0.293271i	0.731995	−	0.681310i	$-0.238589\pi$
$449$	10.7635	+	6.21431i	0.507961	+	0.293271i	−0.224034	+	0.974581i	$0.571923\pi$
$450$	0.645055	−	19.6848i	0.0304082	−	0.927950i
$451$		−	15.6203i		−	0.735530i
$452$	−18.4194	+	3.57140i	−0.866378	+	0.167985i
$453$	0.528439	+	0.153343i	0.0248282	+	0.00720467i
$454$	−0.654812	+	3.90737i	−0.0307319	+	0.183382i
$455$	1.56565	−	2.95986i	0.0733989	−	0.138760i
$456$	−11.0520	+	24.0044i	−0.517558	+	1.12411i
$457$	13.8452	−	11.6175i	0.647651	−	0.543444i	−0.258706	−	0.965956i	$-0.583296\pi$
$457$	13.8452	−	11.6175i	0.647651	−	0.543444i	0.906357	+	0.422512i	$0.138852\pi$
$458$	−28.0902	+	0.238541i	−1.31257	+	0.0111463i
$459$	18.5570	+	21.0081i	0.866165	+	0.980576i
$460$	−0.771202	−	45.4044i	−0.0359575	−	2.11699i
$461$	−5.75332	+	1.01447i	−0.267959	+	0.0472484i	−0.306013	−	0.952027i	$-0.598995\pi$
$461$	−5.75332	+	1.01447i	−0.267959	+	0.0472484i	0.0380542	+	0.999276i	$0.487884\pi$
$462$	14.8079	−	15.5648i	0.688924	−	0.724142i
$463$	3.55969	+	9.78017i	0.165433	+	0.454523i	0.994514	−	0.104606i	$-0.0333580\pi$
$463$	3.55969	+	9.78017i	0.165433	+	0.454523i	−0.829081	+	0.559129i	$0.811136\pi$
$464$	−7.47165	−	18.5431i	−0.346863	−	0.860843i
$465$	32.8457	+	34.2293i	1.52318	+	1.58735i
$466$	−4.14136	+	11.6861i	−0.191845	+	0.541349i
$467$	14.1362	−	24.4846i	0.654145	−	1.13301i	−0.327962	−	0.944691i	$-0.606362\pi$
$467$	14.1362	−	24.4846i	0.654145	−	1.13301i	0.982107	−	0.188322i	$-0.0603048\pi$
$468$	−2.39727	−	0.482952i	−0.110814	−	0.0223245i
$469$	−1.71951	+	1.55494i	−0.0793996	+	0.0718006i
$470$	16.0977	−	45.4245i	0.742531	−	2.09528i
$471$	−4.78629	−	0.518412i	−0.220541	−	0.0238871i
$472$	6.55929	+	5.22504i	0.301916	+	0.240502i
$473$	−20.7670	+	24.7491i	−0.954866	+	1.13796i
$474$	−1.28933	+	12.9285i	−0.0592210	+	0.593826i
$475$	16.0964	+	19.1829i	0.738553	+	0.880174i
$476$	27.3114	+	8.29996i	1.25182	+	0.380428i
$477$	−2.94395	−	21.9569i	−0.134794	−	1.00534i
$478$	−21.8157	+	0.185259i	−0.997829	+	0.00847354i
$479$	−12.2803	+	10.3044i	−0.561103	+	0.470821i	−0.878680	−	0.477411i	$-0.841575\pi$
$479$	−12.2803	+	10.3044i	−0.561103	+	0.470821i	0.317577	+	0.948232i	$0.397131\pi$
$480$	−21.0386	+	21.9780i	−0.960277	+	1.00315i
$481$	0.0617867	−	0.350410i	0.00281723	−	0.0159773i
$482$	17.4411	+	14.3842i	0.794420	+	0.655182i
$483$	−9.20302	−	32.2196i	−0.418752	−	1.46604i
$484$	0.0208582	+	0.00719301i	0.000948099	+	0.000326955i
$485$	−47.4557	+	27.3986i	−2.15485	+	1.24411i
$486$	−19.1725	+	10.8818i	−0.869684	+	0.493608i
$487$	2.86191	+	1.65233i	0.129686	+	0.0748740i	0.563439	−	0.826157i	$-0.309478\pi$
$487$	2.86191	+	1.65233i	0.129686	+	0.0748740i	−0.433754	+	0.901031i	$0.642811\pi$
$488$	15.3506	−	13.5618i	0.694887	−	0.613912i
$489$	−4.86636	+	0.324784i	−0.220064	+	0.0146872i
$490$	−21.6345	−	21.8377i	−0.977349	−	0.986527i
$491$	19.4554	+	16.3250i	0.878009	+	0.736737i	0.965769	−	0.259405i	$-0.0835263\pi$
$491$	19.4554	+	16.3250i	0.878009	+	0.736737i	−0.0877597	+	0.996142i	$0.527971\pi$
$492$	4.16728	+	15.7821i	0.187875	+	0.711513i
$493$	20.6535	−	17.3303i	0.930187	−	0.780520i
$494$	2.67937	−	1.57742i	0.120551	−	0.0709716i
$495$	−24.4545	+	18.8574i	−1.09915	+	0.847577i
$496$	−1.19818	−	35.2613i	−0.0538000	−	1.58328i
$497$	3.85307	−	4.95356i	0.172834	−	0.222197i
$498$	−15.9380	+	22.1840i	−0.714199	+	0.994090i
$499$	−6.22262	−	17.0965i	−0.278563	−	0.765345i	−0.997526	−	0.0702967i	$-0.977605\pi$
$499$	−6.22262	−	17.0965i	−0.278563	−	0.765345i	0.718964	−	0.695048i	$-0.244617\pi$
$500$	−0.795259	−	2.07463i	−0.0355650	−	0.0927804i
$501$	−7.94260	−	17.9927i	−0.354849	−	0.803856i
$502$	0.658745	+	3.55893i	0.0294012	+	0.158843i
$503$	1.01575	−	1.75933i	0.0452901	−	0.0784447i	−0.842492	−	0.538709i	$-0.818912\pi$
$503$	1.01575	−	1.75933i	0.0452901	−	0.0784447i	0.887782	+	0.460265i	$0.152245\pi$
$504$	−10.8088	+	19.6766i	−0.481462	+	0.876467i
$505$	−2.01797	−	3.49522i	−0.0897983	−	0.155535i
$506$	−26.0716	+	22.2567i	−1.15902	+	0.989430i
$507$	−15.3907	−	16.0391i	−0.683526	−	0.712319i
$508$	12.3033	+	1.95458i	0.545871	+	0.0867203i
$509$	26.6383	−	31.7462i	1.18072	−	1.40713i	0.287338	−	0.957829i	$-0.407230\pi$
$509$	26.6383	−	31.7462i	1.18072	−	1.40713i	0.893382	−	0.449298i	$-0.148326\pi$
$510$	−36.9736	−	17.7903i	−1.63722	−	0.787769i
$511$	−40.4394	−	5.59500i	−1.78893	−	0.247508i
$512$	22.5614	−	1.72764i	0.997081	−	0.0763516i
$513$	8.91482	−	26.5740i	0.393599	−	1.17327i
$514$	−0.0563631	−	6.63721i	−0.00248607	−	0.292755i
$515$	−29.5165	−	10.7431i	−1.30065	−	0.473399i
$516$	14.3794	−	30.5459i	0.633018	−	1.34471i
$517$	−34.1854	+	12.4425i	−1.50347	+	0.547219i
$518$	−2.90031	−	1.50278i	−0.127432	−	0.0660282i
$519$	21.3793	−	20.5151i	0.938445	−	0.900512i
$520$	3.50827	−	0.711191i	0.153848	−	0.0311878i
$521$			36.7752i			1.61115i	0.592493	+	0.805576i	$0.298144\pi$
$521$			36.7752i			1.61115i	−0.592493	+	0.805576i	$0.701856\pi$
$522$	9.99514	+	18.7011i	0.437475	+	0.818523i
$523$			14.8131i			0.647731i	0.946103	+	0.323866i	$0.104983\pi$
$523$			14.8131i			0.647731i	−0.946103	+	0.323866i	$0.895017\pi$
$524$	0.0257740	+	0.132929i	0.00112594	+	0.00580702i
$525$	12.4865	+	17.2234i	0.544956	+	0.751690i
$526$	−31.7404	+	11.8588i	−1.38395	+	0.517066i
$527$	44.7117	−	16.2737i	1.94767	−	0.708895i
$528$	22.9040	+	1.69625i	0.996769	+	0.0738196i
$529$	5.29049	+	30.0039i	0.230021	+	1.30452i
$530$	16.4520	+	27.9449i	0.714628	+	1.21385i
$531$	−7.51310	−	4.76123i	−0.326041	−	0.206620i
$532$	−6.46753	−	27.8015i	−0.280403	−	1.20535i
$533$	0.656849	−	1.80468i	0.0284513	−	0.0781693i
$534$	−2.44374	−	9.58380i	−0.105751	−	0.414731i
$535$	9.50654	+	26.1190i	0.411003	+	1.12922i
$536$	−2.45090	−	0.368055i	−0.105863	−	0.0158975i
$537$	1.22092	+	18.2934i	0.0526864	+	0.789419i
$538$	20.9404	+	24.5297i	0.902803	+	1.05755i
$539$	−2.32658	+	23.0878i	−0.100213	+	0.994462i
$540$	19.6770	−	25.5769i	0.846763	−	1.10065i
$541$	4.86824	+	8.43204i	0.209302	+	0.362522i	0.951495	−	0.307665i	$-0.0995475\pi$
$541$	4.86824	+	8.43204i	0.209302	+	0.362522i	−0.742193	+	0.670186i	$0.766214\pi$
$542$	34.9690	−	6.47263i	1.50205	−	0.278023i
$543$	1.50389	+	22.5333i	0.0645380	+	0.966997i
$544$	11.6447	+	28.2065i	0.499263	+	1.20934i
$545$	14.6114	−	17.4132i	0.625885	−	0.745901i
$546$	2.36533	−	1.17559i	0.101227	−	0.0503105i
$547$	11.3771	−	31.2583i	0.486449	−	1.33651i	−0.417426	−	0.908711i	$-0.637068\pi$
$547$	11.3771	−	31.2583i	0.486449	−	1.33651i	0.903875	−	0.427796i	$-0.140710\pi$
$548$	27.0855	−	16.2573i	1.15703	−	0.694477i
$549$	−14.6394	+	16.0528i	−0.624796	+	0.685117i
$550$	10.7211	−	18.9391i	0.457150	−	0.807567i
$551$	−25.3345	−	9.22100i	−1.07928	−	0.392828i
$552$	20.4040	−	29.4428i	0.868450	−	1.25317i
$553$	−7.46220	−	11.8852i	−0.317325	−	0.505412i
$554$	−0.139544	+	0.0521359i	−0.00592864	+	0.00221504i
$555$	3.78987	+	2.77191i	0.160871	+	0.117661i
$556$	6.77831	−	19.6556i	0.287464	−	0.833585i
$557$	26.9984	−	15.5875i	1.14396	−	0.660466i	0.196552	−	0.980493i	$-0.437026\pi$
$557$	26.9984	−	15.5875i	1.14396	−	0.660466i	0.947408	+	0.320028i	$0.103692\pi$
$558$	5.28774	+	37.0463i	0.223848	+	1.56830i
$559$	−3.44002	+	1.98610i	−0.145498	+	0.0840030i
$560$	3.39568	−	32.6864i	0.143494	−	1.38125i
$561$	7.39775	+	30.0768i	0.312333	+	1.26984i
$562$	−3.05909	−	8.18777i	−0.129040	−	0.345380i
$563$	−0.450331	+	2.55395i	−0.0189792	+	0.107636i	−0.992826	−	0.119571i	$-0.961848\pi$
$563$	−0.450331	+	2.55395i	−0.0189792	+	0.107636i	0.973847	+	0.227207i	$0.0729594\pi$
$564$	31.2201	−	21.6916i	1.31460	−	0.913380i
$565$	−22.3153	+	18.7248i	−0.938813	+	0.787758i
$566$	15.3651	−	9.04586i	0.645842	−	0.380226i
$567$	9.15227	−	21.9826i	0.384359	−	0.923184i
$568$	6.70678	−	0.170894i	0.281410	−	0.00717057i
$569$	28.5779	+	34.0579i	1.19805	+	1.42778i	0.876847	+	0.480770i	$0.159643\pi$
$569$	28.5779	+	34.0579i	1.19805	+	1.42778i	0.321203	+	0.947010i	$0.395913\pi$
$570$	3.07981	+	40.9139i	0.128999	+	1.71370i
$571$	−15.2082	−	2.68162i	−0.636445	−	0.112222i	−0.153890	−	0.988088i	$-0.549180\pi$
$571$	−15.2082	−	2.68162i	−0.636445	−	0.112222i	−0.482555	+	0.875866i	$0.660291\pi$
$572$	−2.09918	−	1.70152i	−0.0877711	−	0.0711439i
$573$	−23.9063	+	5.88005i	−0.998701	+	0.245643i
$574$	−14.0080	−	10.7063i	−0.584682	−	0.446872i
$575$	−16.9722	−	29.3968i	−0.707792	−	1.22593i
$576$	−23.5938	+	4.39665i	−0.983077	+	0.183194i
$577$	8.86803	+	15.3599i	0.369181	+	0.639440i	0.989438	−	0.144959i	$-0.0463049\pi$
$577$	8.86803	+	15.3599i	0.369181	+	0.639440i	−0.620257	+	0.784399i	$0.712972\pi$
$578$	−13.0148	+	11.1104i	−0.541344	+	0.462131i
$579$	11.0457	−	15.1021i	0.459042	−	0.627621i
$580$	−24.1129	−	19.5450i	−1.00123	−	0.811561i
$581$	−1.09291	−	29.4841i	−0.0453413	−	1.22321i
$582$	−43.0126	−	4.28956i	−1.78293	−	0.177808i
$583$	8.37237	−	23.0029i	0.346748	−	0.952683i
$584$	−22.7774	−	37.2281i	−0.942534	−	1.54051i
$585$	−3.61831	+	1.15034i	−0.149599	+	0.0475607i
$586$	0.0151663	+	1.78596i	0.000626515	+	0.0737772i
$587$	0.830855	+	0.302407i	0.0342931	+	0.0124817i	0.359110	−	0.933295i	$-0.383080\pi$
$587$	0.830855	+	0.302407i	0.0342931	+	0.0124817i	−0.324817	+	0.945777i	$0.605303\pi$
$588$	−3.80883	−	23.9477i	−0.157073	−	0.987587i
$589$	−36.4482	−	30.5837i	−1.50182	−	1.26018i
$590$	12.8411	+	2.15196i	0.528658	+	0.0885946i
$591$	27.7709	−	1.85345i	1.14234	−	0.0762406i
$592$	−0.722829	−	3.41642i	−0.0297081	−	0.140414i
$593$	12.7489	−	7.36060i	0.523536	−	0.302263i	−0.214844	−	0.976648i	$-0.568924\pi$
$593$	12.7489	−	7.36060i	0.523536	−	0.302263i	0.738380	+	0.674385i	$0.235591\pi$
$594$	−24.3459	+	0.825262i	−0.998925	+	0.0338609i
$595$	43.3302	−	9.30726i	1.77637	−	0.381561i
$596$	−4.10652	+	11.9080i	−0.168210	+	0.487772i
$597$	−14.6704	+	0.979110i	−0.600418	+	0.0400723i
$598$	−3.94808	+	1.47507i	−0.161449	+	0.0603201i
$599$	21.5884	−	7.85755i	0.882080	−	0.321051i	0.139031	−	0.990288i	$-0.455601\pi$
$599$	21.5884	−	7.85755i	0.882080	−	0.321051i	0.743049	+	0.669237i	$0.233379\pi$
$600$	−5.77950	+	21.9956i	−0.235947	+	0.897967i
$601$	20.2131	+	7.35696i	0.824509	+	0.300097i	0.719603	−	0.694385i	$-0.244324\pi$
$601$	20.2131	+	7.35696i	0.824509	+	0.300097i	0.104906	+	0.994482i	$0.466546\pi$
$602$	7.96069	+	35.5867i	0.324454	+	1.45041i
$603$	2.62648	+	0.108402i	0.106959	+	0.00441447i
$604$	−0.555554	−	0.308290i	−0.0226052	−	0.0125441i
$605$	0.0337355	−	0.00594848i	0.00137154	−	0.000241840i
$606$	0.315936	−	3.16797i	0.0128340	−	0.128690i
$607$	−0.383702	−	1.05421i	−0.0155740	−	0.0427892i	0.931662	−	0.363326i	$-0.118359\pi$
$607$	−0.383702	−	1.05421i	−0.0155740	−	0.0427892i	−0.947236	+	0.320537i	$0.896137\pi$
$608$	18.6046	−	24.1871i	0.754515	−	0.980916i
$609$	−20.9138	−	9.33719i	−0.847471	−	0.378362i
$610$	10.6228	−	29.9755i	0.430105	−	1.21367i
$611$	−4.47281			−0.180950
$612$	−15.4985	−	28.4148i	−0.626489	−	1.14860i
$613$	−17.4430			−0.704518			−0.352259	−	0.935903i	$-0.614586\pi$
$613$	−17.4430			−0.704518			−0.352259	+	0.935903i	$0.614586\pi$
$614$	4.21990	+	4.94322i	0.170301	+	0.199492i
$615$	17.5469	+	18.2860i	0.707559	+	0.737364i
$616$	−20.6664	+	13.7216i	−0.832673	+	0.552859i
$617$	−2.26555	−	6.22455i	−0.0912077	−	0.250591i	0.885698	−	0.464262i	$-0.153680\pi$
$617$	−2.26555	−	6.22455i	−0.0912077	−	0.250591i	−0.976906	+	0.213671i	$0.931458\pi$
$618$	−13.9648	−	20.4679i	−0.561745	−	0.823339i
$619$	−16.2381	+	44.6139i	−0.652665	+	1.79318i	−0.0450043	+	0.998987i	$0.514330\pi$
$619$	−16.2381	+	44.6139i	−0.652665	+	1.79318i	−0.607661	+	0.794197i	$0.707892\pi$
$620$	−28.1908	−	46.9673i	−1.13217	−	1.88625i
$621$	−18.1558	+	33.3762i	−0.728568	+	1.33934i
$622$	11.8501	+	20.1284i	0.475147	+	0.807074i
$623$	8.43233	+	6.55899i	0.337834	+	0.262780i
$624$	2.57487	+	1.15911i	0.103077	+	0.0464016i
$625$	−20.4234	−	17.1372i	−0.816935	−	0.685490i
$626$	6.99106	+	5.76575i	0.279419	+	0.230446i
$627$	22.3477	−	21.4444i	0.892481	−	0.856406i
$628$	5.25534	+	1.81232i	0.209711	+	0.0723195i
$629$	4.07849	−	2.35471i	0.162620	−	0.0938886i
$630$	0.149640	+	34.8554i	0.00596178	+	1.38867i
$631$	−32.5614	−	18.7993i	−1.29625	−	0.748389i	−0.316494	−	0.948594i	$-0.602506\pi$
$631$	−32.5614	−	18.7993i	−1.29625	−	0.748389i	−0.979754	+	0.200205i	$0.935839\pi$
$632$	4.77042	−	14.2240i	0.189757	−	0.565799i
$633$	−26.3095	+	11.6139i	−1.04571	+	0.461611i
$634$	−20.3101	−	3.40365i	−0.806618	−	0.135176i
$635$	18.1752	−	6.61523i	0.721261	−	0.262517i
$636$	−2.32226	+	25.4749i	−0.0920835	+	1.01014i
$637$	−1.23967	+	2.56960i	−0.0491174	+	0.101811i
$638$	0.198966	+	23.4299i	0.00787715	+	0.927598i
$639$	−7.05281	+	0.945631i	−0.279005	+	0.0374086i
$640$	29.3273	−	19.3421i	1.15926	−	0.764562i
$641$	23.7652	+	28.3222i	0.938668	+	1.11866i	0.992759	+	0.120125i	$0.0383296\pi$
$641$	23.7652	+	28.3222i	0.938668	+	1.11866i	−0.0540906	+	0.998536i	$0.517226\pi$
$642$	−5.93137	+	21.1084i	−0.234093	+	0.833081i
$643$	3.74837	−	4.46713i	0.147821	−	0.176166i	−0.687053	−	0.726607i	$-0.741096\pi$
$643$	3.74837	−	4.46713i	0.147821	−	0.176166i	0.834874	+	0.550441i	$0.185540\pi$
$644$	2.08967	+	38.6355i	0.0823445	+	1.52245i
$645$	−3.49062	−	52.3012i	−0.137443	−	2.05936i
$646$	38.7888	+	13.7461i	1.52613	+	0.540833i
$647$	16.5030	−	28.5840i	0.648800	−	1.12375i	−0.334610	−	0.942357i	$-0.608605\pi$
$647$	16.5030	−	28.5840i	0.648800	−	1.12375i	0.983410	−	0.181397i	$-0.0580621\pi$
$648$	24.3780	−	7.32897i	0.957658	−	0.287909i
$649$	−4.91428	−	8.51177i	−0.192902	−	0.334116i
$650$	2.03507	−	1.73729i	0.0798220	−	0.0681420i
$651$	−29.0470	−	28.1081i	−1.13844	−	1.10164i
$652$	5.56194	+	0.883603i	0.217822	+	0.0346046i
$653$	3.53719	+	0.623703i	0.138421	+	0.0244074i	0.242429	−	0.970169i	$-0.422056\pi$
$653$	3.53719	+	0.623703i	0.138421	+	0.0244074i	−0.104008	+	0.994576i	$0.533167\pi$
$654$	17.3753	−	4.43048i	0.679430	−	0.173246i
$655$	0.135132	+	0.161045i	0.00528006	+	0.00629253i
$656$	−0.640096	−	18.8373i	−0.0249916	−	0.735475i
$657$	28.2675	+	36.6576i	1.10282	+	1.43015i
$658$	−12.2728	+	39.1850i	−0.478443	+	1.52759i
$659$	−6.60048	+	5.53846i	−0.257118	+	0.215748i	−0.762230	−	0.647306i	$-0.775896\pi$
$659$	−6.60048	+	5.53846i	−0.257118	+	0.215748i	0.505112	+	0.863054i	$0.331451\pi$
$660$	32.3719	−	14.9520i	1.26007	−	0.582005i
$661$	−6.10255	−	5.12064i	−0.237362	−	0.199170i	0.516346	−	0.856380i	$-0.327292\pi$
$661$	−6.10255	−	5.12064i	−0.237362	−	0.199170i	−0.753707	+	0.657210i	$0.771736\pi$
$662$	−25.6385	−	4.29660i	−0.996468	−	0.166992i
$663$	−0.410067	+	3.78599i	−0.0159257	+	0.147036i
$664$	23.6379	−	20.8834i	0.917329	−	0.810433i
$665$	−29.7245	−	32.8704i	−1.15267	−	1.27466i
$666$	1.15213	+	3.52013i	0.0446441	+	0.136402i
$667$	31.6494	+	18.2728i	1.22547	+	0.707524i
$668$	4.32288	+	22.2952i	0.167257	+	0.862628i
$669$	22.0291	−	21.1387i	0.851694	−	0.817268i
$670$	−3.60456	+	1.34673i	−0.139256	+	0.0520285i
$671$	−22.5588	+	8.21074i	−0.870874	+	0.316972i
$672$	17.2198	−	19.3773i	0.664267	−	0.747495i
$673$	7.73366	+	43.8598i	0.298111	+	1.69067i	0.654284	+	0.756249i	$0.272970\pi$
$673$	7.73366	+	43.8598i	0.298111	+	1.69067i	−0.356173	+	0.934420i	$0.615919\pi$
$674$	−11.1787	+	19.7474i	−0.430587	+	0.760642i
$675$	3.58421	−	23.8540i	0.137956	−	0.918141i
$676$	13.2095	+	22.0078i	0.508059	+	0.846453i
$677$	−22.6437	−	26.9858i	−0.870270	−	1.03715i	−0.998966	−	0.0454633i	$-0.985524\pi$
$677$	−22.6437	−	26.9858i	−0.870270	−	1.03715i	0.128696	−	0.991684i	$-0.458921\pi$
$678$	−22.9144	+	1.72489i	−0.880023	+	0.0662440i
$679$	39.5417	−	24.8264i	1.51747	−	0.952751i
$680$	37.0580	+	29.5199i	1.42111	+	1.13204i
$681$	−1.35225	+	4.66003i	−0.0518183	+	0.178573i
$682$	−13.8123	+	38.9756i	−0.528899	+	1.49245i
$683$	−6.88783			−0.263556			−0.131778	−	0.991279i	$-0.542069\pi$
$683$	−6.88783			−0.263556			−0.131778	+	0.991279i	$0.542069\pi$
$684$	−16.8582	+	27.6286i	−0.644588	+	1.05641i
$685$	24.5232	−	42.4755i	0.936984	−	1.62290i
$686$	19.1101	+	17.9110i	0.729626	+	0.683846i
$687$	−34.2045	−	3.70475i	−1.30498	−	0.141345i
$688$	−24.0298	+	30.6973i	−0.916128	+	1.17032i
$689$	1.93459	−	2.30556i	0.0737021	−	0.0878348i
$690$	5.51918	−	55.3423i	0.210111	−	2.10685i
$691$	7.43029	−	20.4146i	0.282662	−	0.776607i	−0.714381	−	0.699757i	$-0.753292\pi$
$691$	7.43029	−	20.4146i	0.282662	−	0.776607i	0.997043	−	0.0768497i	$-0.0244862\pi$
$692$	−29.3353	+	17.6077i	−1.11516	+	0.669343i
$693$	20.2268	−	16.8281i	0.768351	−	0.639245i
$694$	−8.11927	+	14.3429i	−0.308203	+	0.544449i
$695$	−5.60553	−	31.7905i	−0.212630	−	1.20588i
$696$	−6.45180	−	23.6196i	−0.244555	−	0.895297i
$697$	23.8860	−	8.69379i	0.904747	−	0.329301i
$698$	4.08043	−	24.3486i	0.154447	−	0.921607i
$699$	−6.69977	+	13.6267i	−0.253408	+	0.515409i
$700$	−9.63593	−	22.5956i	−0.364204	−	0.854032i
$701$			44.5061i			1.68097i	0.541832	+	0.840487i	$0.317731\pi$
$701$			44.5061i			1.68097i	−0.541832	+	0.840487i	$0.682269\pi$
$702$	−2.84749	−	0.928426i	−0.107472	−	0.0350412i
$703$	−4.07836	−	2.35464i	−0.153818	−	0.0888069i
$704$	−25.3500	−	7.78934i	−0.955412	−	0.293572i
$705$	26.0424	−	52.9677i	0.980812	−	1.99488i
$706$	−5.30772	+	6.43569i	−0.199759	+	0.242211i
$707$	1.82852	+	2.91233i	0.0687686	+	0.109530i
$708$	7.23602	+	7.28890i	0.271946	+	0.273934i
$709$	−6.17939	−	35.0451i	−0.232072	−	1.31614i	−0.848693	−	0.528885i	$-0.822610\pi$
$709$	−6.17939	−	35.0451i	−0.232072	−	1.31614i	0.616622	−	0.787260i	$-0.288501\pi$
$710$	8.97624	−	5.28457i	0.336872	−	0.198326i
$711$	−3.40708	+	15.5436i	−0.127776	+	0.582932i
$712$	0.290910	+	11.4168i	0.0109023	+	0.427863i
$713$	41.4570	+	49.4065i	1.55258	+	1.85029i
$714$	32.0428	+	13.9807i	1.19917	+	0.523216i
$715$	−4.13164	−	0.728520i	−0.154515	−	0.0272451i
$716$	3.32160	−	20.9082i	0.124134	−	0.781377i
$717$	−26.5643	−	2.87723i	−0.992062	−	0.107452i
$718$	2.18017	−	1.86116i	0.0813633	−	0.0694578i
$719$	−24.2072			−0.902777			−0.451389	−	0.892327i	$-0.649071\pi$
$719$	−24.2072			−0.902777			−0.451389	+	0.892327i	$0.649071\pi$
$720$	−28.7183	+	23.7433i	−1.07027	+	0.884860i
$721$	25.4711	+	8.21572i	0.948592	+	0.305969i
$722$	−2.59923	−	14.0426i	−0.0967333	−	0.522611i
$723$	19.1707	+	19.9782i	0.712966	+	0.742998i
$724$	4.09146	−	25.7541i	0.152058	−	0.957145i
$725$	−22.8492	−	4.02893i	−0.848599	−	0.149631i
$726$	0.0243502	+	0.0117164i	0.000903719	+	0.000434837i
$727$	16.4786	−	2.90561i	0.611156	−	0.107763i	0.140501	−	0.990081i	$-0.455129\pi$
$727$	16.4786	−	2.90561i	0.611156	−	0.107763i	0.470655	+	0.882317i	$0.344018\pi$
$728$	−2.96469	+	0.716273i	−0.109879	+	0.0265469i
$729$	−24.8702	+	10.5106i	−0.921119	+	0.389281i
$730$	−58.9679	−	33.3807i	−2.18250	−	1.23548i
$731$	−49.4038	−	17.9815i	−1.82726	−	0.665070i
$732$	20.6021	−	14.3142i	0.761474	−	0.529068i
$733$	13.4298	+	11.2689i	0.496040	+	0.416227i	0.856185	−	0.516670i	$-0.172828\pi$
$733$	13.4298	+	11.2689i	0.496040	+	0.416227i	−0.360145	+	0.932896i	$0.617273\pi$
$734$	−24.2010	−	4.05570i	−0.893276	−	0.149699i
$735$	−23.2118	−	29.6415i	−0.856182	−	1.09334i
$736$	−30.5291	+	27.9089i	−1.12532	+	1.02874i
$737$	2.51554	+	1.45235i	0.0926612	+	0.0534980i
$738$	2.82483	+	19.7910i	0.103983	+	0.728516i
$739$	15.9113	−	9.18638i	0.585306	−	0.337926i	−0.177933	−	0.984043i	$-0.556941\pi$
$739$	15.9113	−	9.18638i	0.585306	−	0.337926i	0.763239	+	0.646116i	$0.223608\pi$
$740$	−3.55507	−	4.09352i	−0.130687	−	0.150481i
$741$	3.48369	−	1.53782i	0.127976	−	0.0564931i
$742$	−14.8901	−	23.2746i	−0.546633	−	0.854437i
$743$	6.15568	−	34.9106i	0.225830	−	1.28074i	−0.635262	−	0.772296i	$-0.719108\pi$
$743$	6.15568	−	34.9106i	0.225830	−	1.28074i	0.861092	−	0.508449i	$-0.169781\pi$
$744$	3.55724	−	43.0643i	0.130415	−	1.57881i
$745$	3.39601	+	19.2598i	0.124420	+	0.705623i
$746$	11.0104	−	19.4502i	0.403120	−	0.712122i
$747$	−22.5429	+	24.7193i	−0.824801	+	0.904432i
$748$	−0.607384	−	35.7596i	−0.0222082	−	1.30750i
$749$	−8.91874	−	21.9391i	−0.325884	−	0.801638i
$750$	−0.672351	−	2.63681i	−0.0245508	−	0.0962825i
$751$	−20.3278	−	3.58434i	−0.741773	−	0.130795i	−0.210024	−	0.977696i	$-0.567354\pi$
$751$	−20.3278	−	3.58434i	−0.741773	−	0.130795i	−0.531749	+	0.846902i	$0.678465\pi$
$752$	−40.7161	+	16.4059i	−1.48476	+	0.598262i
$753$	0.295193	+	4.42298i	0.0107574	+	0.161182i
$754$	−0.962265	+	2.71532i	−0.0350436	+	0.0988863i
$755$	−0.986459			−0.0359009
$756$	−15.9468	+	22.3986i	−0.579981	+	0.814630i
$757$	−19.3224			−0.702286			−0.351143	−	0.936322i	$-0.614207\pi$
$757$	−19.3224			−0.702286			−0.351143	+	0.936322i	$0.614207\pi$
$758$	3.27688	−	9.24673i	0.119022	−	0.335856i
$759$	−34.8804	+	23.3665i	−1.26608	+	0.848150i
$760$	7.03578	−	46.8517i	0.255215	−	1.69949i
$761$	28.7883	+	5.07615i	1.04357	+	0.184010i	0.669058	−	0.743210i	$-0.266698\pi$
$761$	28.7883	+	5.07615i	1.04357	+	0.184010i	0.374516	+	0.927220i	$0.377809\pi$
$762$	14.6885	+	4.12741i	0.532108	+	0.149520i
$763$	−11.8914	+	15.2877i	−0.430498	+	0.553453i
$764$	28.4233	−	0.482775i	1.02832	−	0.0174662i
$765$	−42.4468	−	26.8995i	−1.53467	−	0.972554i
$766$	11.4475	−	20.2223i	0.413615	−	0.730662i
$767$	−0.209838	−	1.19005i	−0.00757683	−	0.0429703i
$768$	27.6907	+	1.10702i	0.999202	+	0.0399462i
$769$	8.89882	−	50.4677i	0.320900	−	1.81991i	−0.216148	−	0.976361i	$-0.569350\pi$
$769$	8.89882	−	50.4677i	0.320900	−	1.81991i	0.537048	−	0.843552i	$-0.319539\pi$
$770$	−17.7191	+	34.1972i	−0.638550	+	1.23238i
$771$	0.875366	−	8.08192i	0.0315255	−	0.291063i
$772$	−16.3121	+	14.1664i	−0.587085	+	0.509861i
$773$	−27.7466	+	16.0195i	−0.997977	+	0.576182i	−0.907649	−	0.419730i	$-0.862125\pi$
$773$	−27.7466	+	16.0195i	−0.997977	+	0.576182i	−0.0903281	+	0.995912i	$0.528792\pi$
$774$	21.8361	−	35.1128i	0.784883	−	1.26210i
$775$	−35.4606	−	20.4732i	−1.27378	−	0.735420i
$776$	47.3225	+	15.8710i	1.69878	+	0.569735i
$777$	−3.31439	−	2.24054i	−0.118903	−	0.0803790i
$778$	29.7225	+	4.98101i	1.06560	+	0.178578i
$779$	−19.4714	−	16.3385i	−0.697636	−	0.585386i
$780$	4.36881	−	0.366197i	0.156428	−	0.0131120i
$781$	−7.38881	−	2.68931i	−0.264392	−	0.0962309i
$782$	−48.5448	−	27.4804i	−1.73596	−	0.982697i
$783$	9.49906	+	24.1706i	0.339469	+	0.863785i
$784$	−1.85964	+	27.9382i	−0.0664157	+	0.997792i
$785$	8.49986	−	1.49875i	0.303373	−	0.0534929i
$786$	0.0124481	+	0.165368i	0.000444010	+	0.00589849i
$787$	−39.8143	−	7.02033i	−1.41923	−	0.250248i	−0.589207	−	0.807982i	$-0.700560\pi$
$787$	−39.8143	−	7.02033i	−1.41923	−	0.250248i	−0.830020	+	0.557734i	$0.811671\pi$
$788$	−31.7403	−	5.04246i	−1.13070	−	0.179630i
$789$	−40.2974	+	9.91165i	−1.43463	+	0.352864i
$790$	−4.23943	−	22.9040i	−0.150832	−	0.814886i
$791$	18.4095	−	16.6476i	0.654568	−	0.591921i
$792$	27.6206	+	5.32077i	0.981454	+	0.189065i
$793$	−2.95159			−0.104814
$794$	10.1405	−	8.65670i	0.359874	−	0.307215i
$795$	16.0389	+	36.3336i	0.568841	+	1.28862i
$796$	16.7673	+	2.66375i	0.594301	+	0.0944142i
$797$	−3.86909	−	0.682224i	−0.137050	−	0.0241656i	0.104702	−	0.994504i	$-0.466611\pi$
$797$	−3.86909	−	0.682224i	−0.137050	−	0.0241656i	−0.241752	+	0.970338i	$0.577722\pi$
$798$	−3.91362	−	34.7392i	−0.138541	−	1.22975i
$799$	−38.0532	−	45.3500i	−1.34622	−	1.60437i
$800$	12.1531	−	23.2791i	0.429676	−	0.823039i
$801$	−1.60973	−	12.0058i	−0.0568769	−	0.424206i
$802$	−9.76947	+	5.75157i	−0.344972	+	0.203095i
$803$	8.88222	+	50.3736i	0.313447	+	1.77765i
$804$	−2.92907	−	0.796285i	−0.103300	−	0.0280828i
$805$	31.9430	+	50.8765i	1.12584	+	1.79316i
$806$	−3.23476	+	3.92220i	−0.113939	+	0.138153i
$807$	21.9846	+	32.8175i	0.773893	+	1.15523i
$808$	−1.16893	+	3.48541i	−0.0411229	+	0.122616i
$809$	45.1828	+	26.0863i	1.58854	+	0.917145i	0.993548	+	0.113415i	$0.0361789\pi$
$809$	45.1828	+	26.0863i	1.58854	+	0.917145i	0.594994	+	0.803730i	$0.297154\pi$
$810$	27.5737	−	28.3149i	0.968843	−	0.994883i
$811$			7.76598i			0.272700i	0.990661	+	0.136350i	$0.0435373\pi$
$811$			7.76598i			0.272700i	−0.990661	+	0.136350i	$0.956463\pi$
$812$	21.1479	+	15.8806i	0.742145	+	0.557301i
$813$	43.4589	−	2.90048i	1.52417	−	0.101724i
$814$	−0.676445	+	4.03645i	−0.0237094	+	0.141478i
$815$	8.21643	−	2.99054i	0.287809	−	0.104754i
$816$	10.1539	+	35.9681i	0.355456	+	1.25914i
$817$	9.12916	+	51.7740i	0.319389	+	1.81134i
$818$	14.3630	−	25.3727i	0.502192	−	0.887135i
$819$	3.04452	−	1.09366i	0.106384	−	0.0382156i
$820$	−15.0601	−	25.0910i	−0.525923	−	0.876214i
$821$	−5.98666	+	16.4482i	−0.208936	+	0.574047i	−0.999253	−	0.0386516i	$-0.987694\pi$
$821$	−5.98666	+	16.4482i	−0.208936	+	0.574047i	0.790317	+	0.612698i	$0.209916\pi$
$822$	35.2605	−	15.9243i	1.22985	−	0.555424i
$823$	−18.6904	+	22.2743i	−0.651505	+	0.776433i	−0.986140	−	0.165915i	$-0.946942\pi$
$823$	−18.6904	+	22.2743i	−0.651505	+	0.776433i	0.334635	+	0.942348i	$0.391387\pi$
$824$	10.4673	+	26.6277i	0.364644	+	0.927620i
$825$	15.7353	−	21.5140i	0.547832	−	0.749020i
$826$	−11.0015	−	1.42701i	−0.382791	−	0.0496521i
$827$	11.2350	−	19.4595i	0.390678	−	0.676674i	−0.601861	−	0.798601i	$-0.705574\pi$
$827$	11.2350	−	19.4595i	0.390678	−	0.676674i	0.992539	+	0.121927i	$0.0389074\pi$
$828$	29.0079	−	32.9142i	1.00809	−	1.14385i
$829$	18.4990			0.642498			0.321249	−	0.946995i	$-0.395897\pi$
$829$	18.4990			0.642498			0.321249	+	0.946995i	$0.395897\pi$
$830$	16.3578	−	46.1585i	0.567787	−	1.60219i
$831$	−0.177164	+	0.0435756i	−0.00614575	+	0.00151162i
$832$	−2.60124	−	1.96593i	−0.0901818	−	0.0681563i
$833$	−36.6000	+	9.29228i	−1.26811	+	0.321958i
$834$	11.0409	−	22.9463i	0.382316	−	0.794565i
$835$	22.6648	+	27.0109i	0.784348	+	0.934749i
$836$	−30.6641	+	18.4053i	−1.06054	+	0.636559i
$837$	1.16367	+	45.8174i	0.0402224	+	1.58368i
$838$	17.1124	−	30.2296i	0.591139	−	1.04426i
$839$	6.91719	+	39.2293i	0.238808	+	1.35435i	0.834444	+	0.551092i	$0.185789\pi$
$839$	6.91719	+	39.2293i	0.238808	+	1.35435i	−0.595637	+	0.803254i	$0.703100\pi$
$840$	8.77929	−	39.2788i	0.302914	−	1.35525i
$841$	−3.77797	+	1.37507i	−0.130275	+	0.0474162i
$842$	−32.6827	+	12.2108i	−1.12632	+	0.420812i
$843$	−2.55681	−	10.3951i	−0.0880613	−	0.358028i
$844$	32.6007	−	6.32105i	1.12216	−	0.217579i
$845$	34.5126	+	19.9259i	1.18727	+	0.685471i
$846$	41.0629	−	21.9469i	1.41177	−	0.754549i
$847$	−0.0285365	+	0.00612960i	−0.000980527	+	0.000210616i
$848$	9.15407	−	28.0835i	0.314352	−	0.964393i
$849$	19.9775	−	8.81874i	0.685625	−	0.302658i
$850$	34.9281	+	5.85340i	1.19803	+	0.200770i
$851$	4.89009	+	4.10327i	0.167630	+	0.140658i
$852$	8.18283	+	0.745937i	0.280339	+	0.0255554i
$853$	−8.69480	+	7.29580i	−0.297704	+	0.249804i	−0.779388	−	0.626542i	$-0.784470\pi$
$853$	−8.69480	+	7.29580i	−0.297704	+	0.249804i	0.481684	+	0.876345i	$0.340025\pi$
$854$	−8.09878	+	25.8581i	−0.277135	+	0.884846i
$855$	−2.07222	+	50.2082i	−0.0708686	+	1.71708i
$856$	12.0963	−	22.2412i	0.413443	−	0.760190i
$857$	−21.4308	−	25.5403i	−0.732064	−	0.872440i	0.263679	−	0.964610i	$-0.415064\pi$
$857$	−21.4308	−	25.5403i	−0.732064	−	0.872440i	−0.995743	+	0.0921707i	$0.970619\pi$
$858$	−2.31158	−	2.36837i	−0.0789161	−	0.0808547i
$859$	49.9039	+	8.79940i	1.70270	+	0.300232i	0.938636	−	0.344910i	$-0.112090\pi$
$859$	49.9039	+	8.79940i	1.70270	+	0.300232i	0.764063	+	0.645141i	$0.223202\pi$
$860$	−9.49652	+	59.7769i	−0.323829	+	2.03838i
$861$	−15.5175	−	15.0159i	−0.528836	−	0.511742i
$862$	14.9332	−	12.7481i	0.508625	−	0.434201i
$863$	−23.2724	−	40.3089i	−0.792201	−	1.37213i	−0.924601	−	0.380936i	$-0.875602\pi$
$863$	−23.2724	−	40.3089i	−0.792201	−	1.37213i	0.132400	−	0.991196i	$-0.457732\pi$
$864$	−29.3262	+	1.99289i	−0.997699	+	0.0677994i
$865$	−26.5602	+	46.0036i	−0.903073	+	1.56417i
$866$	−29.1423	−	10.3275i	−0.990295	−	0.350944i
$867$	−17.4121	+	11.6644i	−0.591344	+	0.396144i
$868$	25.4855	+	39.1008i	0.865036	+	1.32717i
$869$	−11.3023	+	13.4696i	−0.383405	+	0.456924i
$870$	−26.5527	−	27.2049i	−0.900220	−	0.922334i
$871$	0.229559	+	0.273578i	0.00777831	+	0.00926982i
$872$	−20.6986	+	0.527417i	−0.700942	+	0.0178606i
$873$	−51.7130	−	11.3352i	−1.75022	−	0.383639i
$874$	0.473679	+	55.7795i	0.0160224	+	1.88677i
$875$	2.32000	+	1.80459i	0.0784303	+	0.0610061i
$876$	−22.4132	−	48.5259i	−0.757273	−	1.63954i
$877$	48.2995	−	17.5796i	1.63096	−	0.593621i	0.645534	−	0.763731i	$-0.276635\pi$
$877$	48.2995	−	17.5796i	1.63096	−	0.593621i	0.985425	+	0.170111i	$0.0544126\pi$
$878$	32.2687	+	5.40771i	1.08901	+	0.182501i
$879$	−0.235546	+	2.17470i	−0.00794476	+	0.0733509i
$880$	−40.2827	+	8.52280i	−1.35793	+	0.287304i
$881$	−3.39234	−	1.95857i	−0.114291	−	0.0659858i	0.441765	−	0.897131i	$-0.354353\pi$
$881$	−3.39234	−	1.95857i	−0.114291	−	0.0659858i	−0.556056	+	0.831145i	$0.687686\pi$
$882$	−1.22750	−	29.6731i	−0.0413319	−	0.999145i
$883$	−9.23099	+	5.32951i	−0.310648	+	0.179352i	−0.647216	−	0.762306i	$-0.724067\pi$
$883$	−9.23099	+	5.32951i	−0.310648	+	0.179352i	0.336569	+	0.941659i	$0.390734\pi$
$884$	1.43356	−	4.15701i	0.0482158	−	0.139815i
$885$	15.3146	+	4.44399i	0.514794	+	0.149383i
$886$	36.8638	+	30.4027i	1.23846	+	1.02140i
$887$	12.4773	+	10.4697i	0.418947	+	0.351538i	0.827762	−	0.561079i	$-0.189614\pi$
$887$	12.4773	+	10.4697i	0.418947	+	0.351538i	−0.408815	+	0.912617i	$0.634058\pi$
$888$	−0.393417	−	4.25874i	−0.0132022	−	0.142914i
$889$	−15.2666	+	6.20621i	−0.512025	+	0.208149i
$890$	8.99581	+	15.2801i	0.301540	+	0.512189i
$891$	−29.7332	−	2.45852i	−0.996099	−	0.0823636i
$892$	−30.2269	+	18.1429i	−1.01207	+	0.607468i
$893$	−20.2470	+	55.6283i	−0.677541	+	1.86153i
$894$	−6.68895	+	13.9016i	−0.223712	+	0.464940i
$895$	−11.2419	−	30.8869i	−0.375776	−	1.03243i
$896$	−24.3604	+	17.3945i	−0.813825	+	0.581110i
$897$	−5.01247	+	1.23288i	−0.167361	+	0.0411646i
$898$	−11.4120	−	13.3681i	−0.380824	−	0.446100i
$899$	44.0840			1.47028
$900$	−10.1587	+	25.9348i	−0.338623	+	0.864494i
$901$	39.8351			1.32710
$902$	−7.37882	+	20.8216i	−0.245688	+	0.693283i
$903$	4.62280	+	44.4219i	0.153837	+	1.47827i
$904$	26.2399	+	3.94049i	0.872727	+	0.131059i
$905$	−13.8475	−	38.0456i	−0.460305	−	1.26468i
$906$	−0.631965	−	0.454032i	−0.0209956	−	0.0150842i
$907$	47.4880	−	8.37341i	1.57681	−	0.278035i	0.684349	−	0.729154i	$-0.260086\pi$
$907$	47.4880	−	8.37341i	1.57681	−	0.278035i	0.892463	+	0.451120i	$0.148975\pi$
$908$	2.71865	−	4.89914i	0.0902214	−	0.162584i
$909$	0.834865	−	3.80878i	0.0276907	−	0.126329i
$910$	−3.48519	+	3.20585i	−0.115533	+	0.106273i
$911$	−8.75733	−	3.18741i	−0.290143	−	0.105604i	0.192848	−	0.981229i	$-0.438228\pi$
$911$	−8.75733	−	3.18741i	−0.290143	−	0.105604i	−0.482991	+	0.875625i	$0.660450\pi$
$912$	26.0715	−	26.7767i	0.863315	−	0.886665i
$913$	−34.7378	+	12.6435i	−1.14965	+	0.418439i
$914$	−23.9434	+	8.94566i	−0.791978	+	0.295896i
$915$	17.1853	−	34.9533i	0.568128	−	1.15552i
$916$	37.5565	+	12.9515i	1.24090	+	0.427929i
$917$	−0.120142	−	0.132857i	−0.00396744	−	0.00438733i
$918$	−14.8122	−	36.7696i	−0.488875	−	1.21358i
$919$	−31.7138	+	18.3100i	−1.04614	+	0.603990i	−0.921566	−	0.388221i	$-0.873090\pi$
$919$	−31.7138	+	18.3100i	−1.04614	+	0.603990i	−0.124574	+	0.992210i	$0.539756\pi$
$920$	−20.4205	+	60.8877i	−0.673243	+	2.00741i
$921$	4.43033	+	6.61337i	0.145984	+	0.217918i
$922$	8.14831	+	1.36553i	0.268350	+	0.0449713i
$923$	−0.740573	−	0.621414i	−0.0243763	−	0.0204541i
$924$	−27.0913	+	13.7527i	−0.891238	+	0.452429i
$925$	−3.80833	−	1.38612i	−0.125217	−	0.0455753i
$926$	−0.124988	−	14.7184i	−0.00410737	−	0.483676i
$927$	−14.0767	−	26.8844i	−0.462339	−	0.882999i
$928$	1.20007	+	28.2472i	0.0393941	+	0.927261i
$929$	13.7106	−	37.6696i	0.449831	−	1.23590i	−0.483011	−	0.875614i	$-0.660457\pi$
$929$	13.7106	−	37.6696i	0.449831	−	1.23590i	0.932842	−	0.360286i	$-0.117321\pi$
$930$	−27.6134	−	61.1430i	−0.905478	−	2.00496i
$931$	26.3465	+	27.0495i	0.863472	+	0.886512i
$932$	11.0407	−	13.6211i	0.361651	−	0.446174i
$933$	11.5526	+	26.1706i	0.378215	+	0.856788i
$934$	−30.4096	+	25.9599i	−0.995031	+	0.849433i
$935$	−27.7642	−	48.0890i	−0.907986	−	1.57268i
$936$	2.96738	+	1.77621i	0.0969918	+	0.0580571i
$937$	−10.5496	−	18.2724i	−0.344640	−	0.596935i	0.640648	−	0.767835i	$-0.278666\pi$
$937$	−10.5496	−	18.2724i	−0.344640	−	0.596935i	−0.985288	+	0.170900i	$0.945332\pi$
$938$	3.02662	−	1.26044i	0.0988226	−	0.0411549i
$939$	7.68435	+	8.00805i	0.250769	+	0.261333i
$940$	−42.9159	+	52.9459i	−1.39976	+	1.72691i
$941$	24.9216	+	4.39434i	0.812420	+	0.143251i	0.564398	−	0.825503i	$-0.309108\pi$
$941$	24.9216	+	4.39434i	0.812420	+	0.143251i	0.248022	+	0.968754i	$0.420220\pi$
$942$	6.13517	+	2.95202i	0.199895	+	0.0961820i
$943$	22.1472	+	26.3940i	0.721213	+	0.859508i
$944$	−6.27519	−	10.0634i	−0.204240	−	0.327537i
$945$	−4.77503	+	42.4215i	−0.155332	+	1.37997i
$946$	39.3732	−	23.1801i	1.28013	−	0.753651i
$947$	−34.1471	+	28.6528i	−1.10963	+	0.931092i	−0.998035	−	0.0626620i	$-0.980041\pi$
$947$	−34.1471	+	28.6528i	−1.10963	+	0.931092i	−0.111597	+	0.993754i	$0.535597\pi$
$948$	7.82592	−	16.6244i	0.254174	−	0.539937i
$949$	−1.09206	+	6.19339i	−0.0354498	+	0.201046i
$950$	−12.3945	−	33.1743i	−0.402130	−	1.07632i
$951$	−24.2224	−	7.02887i	−0.785465	−	0.227927i
$952$	−32.4849	−	23.9653i	−1.05284	−	0.776720i
$953$	−1.21826	+	0.703360i	−0.0394632	+	0.0227841i	−0.519602	−	0.854409i	$-0.673920\pi$
$953$	−1.21826	+	0.703360i	−0.0394632	+	0.0227841i	0.480139	+	0.877193i	$0.340586\pi$
$954$	−6.44791	+	30.6589i	−0.208759	+	0.992618i
$955$	38.2232	−	22.0682i	1.23687	−	0.714109i
$956$	29.1676	+	10.0585i	0.943347	+	0.325316i
$957$	−3.09011	+	28.5298i	−0.0998891	+	0.922238i
$958$	21.2372	−	7.93457i	0.686142	−	0.256354i
$959$	−19.5398	+	36.9399i	−0.630974	+	1.19285i
$960$	38.4263	−	19.3580i	1.24020	−	0.624776i
$961$	43.9772	+	16.0064i	1.41862	+	0.516335i
$962$	−0.247890	+	0.437904i	−0.00799229	+	0.0141186i
$963$	−10.2173	+	24.8339i	−0.329247	+	0.800263i
$964$	−16.4538	−	27.4129i	−0.529941	−	0.882909i
$965$	−11.4726	+	31.5208i	−0.369317	+	1.01469i
$966$	−2.95265	+	47.2957i	−0.0950001	+	1.52171i
$967$	26.9569	−	32.1260i	0.866875	−	1.03310i	−0.132248	−	0.991217i	$-0.542219\pi$
$967$	26.9569	−	32.1260i	0.866875	−	1.03310i	0.999122	−	0.0418844i	$-0.0133361\pi$
$968$	−0.0244058	−	0.0194413i	−0.000784431	−	0.000624868i
$969$	45.2301	+	22.2380i	1.45300	+	0.714388i
$970$	76.2005	−	14.1044i	2.44665	−	0.452866i
$971$	−2.40017	−	4.15722i	−0.0770252	−	0.133412i	0.824940	−	0.565220i	$-0.191209\pi$
$971$	−2.40017	−	4.15722i	−0.0770252	−	0.133412i	−0.901965	+	0.431809i	$0.857876\pi$
$972$	30.6971	−	5.44841i	0.984611	−	0.174758i
$973$	5.77621	+	26.8913i	0.185177	+	0.862095i
$974$	−3.03435	−	3.55446i	−0.0972268	−	0.113892i
$975$	2.72265	−	1.82392i	0.0871946	−	0.0584121i
$976$	−26.8685	+	10.8262i	−0.860039	+	0.346539i
$977$	−2.52502	−	6.93745i	−0.0807827	−	0.221949i	0.892725	−	0.450601i	$-0.148790\pi$
$977$	−2.52502	−	6.93745i	−0.0807827	−	0.221949i	−0.973508	+	0.228652i	$0.926568\pi$
$978$	6.64021	+	1.86587i	0.212330	+	0.0596640i
$979$	4.57795	−	12.5778i	0.146312	−	0.401988i
$980$	18.5227	+	39.3292i	0.591685	+	1.25633i
$981$	21.7665	−	2.91842i	0.694951	−	0.0931780i
$982$	−18.2220	−	30.9515i	−0.581488	−	0.987701i
$983$	6.57097	+	37.2658i	0.209581	+	1.18859i	0.890066	+	0.455832i	$0.150658\pi$
$983$	6.57097	+	37.2658i	0.209581	+	1.18859i	−0.680484	+	0.732763i	$0.738231\pi$
$984$	1.90035	−	23.0059i	0.0605810	−	0.733401i
$985$	−46.8888	+	17.0661i	−1.49400	+	0.543772i
$986$	−35.7175	+	13.3446i	−1.13748	+	0.424980i
$987$	−20.5022	+	45.9216i	−0.652591	+	1.46170i
$988$	−4.31672	+	0.836981i	−0.137333	+	0.0266279i
$989$		−	71.2637i		−	2.26606i
$990$	41.5055	−	13.5846i	1.31913	−	0.431748i
$991$		−	24.8374i		−	0.788986i	−0.918899	−	0.394493i	$-0.870920\pi$
$991$		−	24.8374i		−	0.788986i	0.918899	−	0.394493i	$-0.129080\pi$
$992$	−15.0598	+	47.5688i	−0.478149	+	1.51031i
$993$	−30.5771	−	8.87289i	−0.970336	−	0.281573i
$994$	−7.47608	+	4.78288i	−0.237127	+	0.151704i
$995$	24.7697	−	9.01542i	0.785251	−	0.285808i
$996$	31.7246	−	22.0421i	1.00523	−	0.698430i
$997$	34.1096	+	12.4149i	1.08026	+	0.393183i	0.820005	−	0.572356i	$-0.193970\pi$
$997$	34.1096	+	12.4149i	1.08026	+	0.393183i	0.260257	+	0.965539i	$0.416193\pi$
$998$	0.218489	+	25.7289i	0.00691615	+	0.814433i
$999$	0.900895	+	4.44595i	0.0285030	+	0.140664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.17	yes	840
4.3	odd	2	inner	756.2.ci.a.95.63	yes	840
7.2	even	3		756.2.bs.a.527.78	yes	840
27.2	odd	18		756.2.bs.a.515.32	✓	840
28.23	odd	6		756.2.bs.a.527.32	yes	840
108.83	even	18		756.2.bs.a.515.78	yes	840
189.2	odd	18	inner	756.2.ci.a.191.63	yes	840
756.191	even	18	inner	756.2.ci.a.191.17	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.32	✓	840	27.2	odd	18
756.2.bs.a.515.78	yes	840	108.83	even	18
756.2.bs.a.527.32	yes	840	28.23	odd	6
756.2.bs.a.527.78	yes	840	7.2	even	3
756.2.ci.a.95.17	yes	840	1.1	even	1	trivial
756.2.ci.a.95.63	yes	840	4.3	odd	2	inner
756.2.ci.a.191.17	yes	840	756.191	even	18	inner
756.2.ci.a.191.63	yes	840	189.2	odd	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33299 - 0.472387i) q^{2} +(-1.55434 - 0.764214i) q^{3} +(1.55370 + 1.25937i) q^{4} +(3.05802 + 0.539212i) q^{5} +(1.71091 + 1.75294i) q^{6} +(-2.62079 - 0.362599i) q^{7} +(-1.47615 - 2.41267i) q^{8} +(1.83195 + 2.37570i) q^{9} +O(q^{10})\)	\(q+(-1.33299 - 0.472387i) q^{2} +(-1.55434 - 0.764214i) q^{3} +(1.55370 + 1.25937i) q^{4} +(3.05802 + 0.539212i) q^{5} +(1.71091 + 1.75294i) q^{6} +(-2.62079 - 0.362599i) q^{7} +(-1.47615 - 2.41267i) q^{8} +(1.83195 + 2.37570i) q^{9} +(-3.82158 - 2.16333i) q^{10} +(0.575637 + 3.26460i) q^{11} +(-1.45255 - 3.14485i) q^{12} +(-0.0707741 + 0.401380i) q^{13} +(3.32218 + 1.72137i) q^{14} +(-4.34113 - 3.17510i) q^{15} +(0.827971 + 3.91337i) q^{16} +(-4.67173 + 2.69723i) q^{17} +(-1.31972 - 4.03216i) q^{18} +(4.67159 + 2.69714i) q^{19} +(4.07218 + 4.68896i) q^{20} +(3.79649 + 2.56645i) q^{21} +(0.774840 - 4.62359i) q^{22} +(-5.60139 - 4.70012i) q^{23} +(0.450642 + 4.87821i) q^{24} +(4.36228 + 1.58774i) q^{25} +(0.283947 - 0.501600i) q^{26} +(-1.03194 - 5.09265i) q^{27} +(-3.61527 - 3.86391i) q^{28} +(-4.92203 + 0.867886i) q^{29} +(4.28679 + 6.28306i) q^{30} +(-8.68640 - 1.53165i) q^{31} +(0.744953 - 5.60759i) q^{32} +(1.60012 - 5.51421i) q^{33} +(7.50149 - 1.38850i) q^{34} +(-7.81890 - 2.52199i) q^{35} +(-0.145580 + 5.99823i) q^{36} -0.873013 q^{37} +(-4.95306 - 5.80205i) q^{38} +(0.416747 - 0.569794i) q^{39} +(-3.21316 - 8.17396i) q^{40} +(-4.64047 - 0.818240i) q^{41} +(-3.84831 - 5.21445i) q^{42} +(6.26462 + 7.46588i) q^{43} +(-3.21697 + 5.79715i) q^{44} +(4.32115 + 8.25275i) q^{45} +(5.24629 + 8.91122i) q^{46} +(1.90566 + 10.8076i) q^{47} +(1.70370 - 6.71546i) q^{48} +(6.73704 + 1.90059i) q^{49} +(-5.06483 - 4.17712i) q^{50} +(9.32272 - 0.622205i) q^{51} +(-0.615447 + 0.534493i) q^{52} +(-6.39512 - 3.69223i) q^{53} +(-1.03015 + 7.27591i) q^{54} +10.2936i q^{55} +(2.99384 + 6.85835i) q^{56} +(-5.20004 - 7.76237i) q^{57} +(6.97097 + 1.16822i) q^{58} +(-2.78610 + 1.01406i) q^{59} +(-2.74619 - 10.4003i) q^{60} +(1.25754 + 7.13188i) q^{61} +(10.8553 + 6.14501i) q^{62} +(-3.93973 - 6.89047i) q^{63} +(-3.64197 + 7.12293i) q^{64} +(-0.432857 + 1.18927i) q^{65} +(-4.73778 + 6.59449i) q^{66} +(0.563236 - 0.671238i) q^{67} +(-10.6553 - 1.69276i) q^{68} +(5.11457 + 11.5863i) q^{69} +(9.23112 + 7.05533i) q^{70} +(-1.18599 + 2.05419i) q^{71} +(3.02755 - 7.92679i) q^{72} +15.4303 q^{73} +(1.16371 + 0.412400i) q^{74} +(-5.56710 - 5.80160i) q^{75} +(3.86154 + 10.0738i) q^{76} +(-0.324880 - 8.76454i) q^{77} +(-0.824681 + 0.562662i) q^{78} +(3.40949 + 4.06327i) q^{79} +(0.421817 + 12.4136i) q^{80} +(-2.28790 + 8.70434i) q^{81} +(5.79915 + 3.28280i) q^{82} +(1.93646 + 10.9822i) q^{83} +(2.66651 + 8.76868i) q^{84} +(-15.7406 + 5.72912i) q^{85} +(-4.82386 - 12.9112i) q^{86} +(8.31376 + 2.41249i) q^{87} +(7.02668 - 6.20786i) q^{88} +(-3.49680 - 2.01888i) q^{89} +(-1.86153 - 13.0420i) q^{90} +(0.331024 - 1.02627i) q^{91} +(-2.78368 - 14.3568i) q^{92} +(12.3311 + 9.01897i) q^{93} +(2.56513 - 15.3065i) q^{94} +(12.8315 + 10.7669i) q^{95} +(-5.44331 + 8.14680i) q^{96} +(-13.5183 + 11.3432i) q^{97} +(-8.08257 - 5.71595i) q^{98} +(-6.70117 + 7.34813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

L-functions

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