LMFDB - Embedded newform 73.2.h.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(3,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("73.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.h (of order $12$, degree $4$, 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:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 28 x^{18} + 326 x^{16} + 2044 x^{14} + 7471 x^{12} + 16090 x^{10} + 19590 x^{8} + 12030 x^{6} + \cdots + 1 $ x^20 + 28x^18 + 326x^16 + 2044x^14 + 7471x^12 + 16090x^10 + 19590x^8 + 12030x^6 + 2877x^4 + 230*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			3.4
Root			$0.0678852i$ of defining polynomial
Character	$\chi$	$=$	73.3
Dual form			73.2.h.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0339426 - 0.0587903i) q^{2} +1.73613i q^{3} +(0.997696 + 1.72806i) q^{4} +(-2.59207 - 0.694543i) q^{5} +(0.102067 + 0.0589286i) q^{6} +(0.823696 - 0.823696i) q^{7} +0.271228 q^{8} -0.0141334 q^{9} +O(q^{10})$	\(q+(0.0339426 - 0.0587903i) q^{2} +1.73613i q^{3} +(0.997696 + 1.72806i) q^{4} +(-2.59207 - 0.694543i) q^{5} +(0.102067 + 0.0589286i) q^{6} +(0.823696 - 0.823696i) q^{7} +0.271228 q^{8} -0.0141334 q^{9} +(-0.128814 + 0.128814i) q^{10} +(1.27209 - 4.74749i) q^{11} +(-3.00013 + 1.73213i) q^{12} +(4.09939 - 1.09843i) q^{13} +(-0.0204669 - 0.0763837i) q^{14} +(1.20581 - 4.50016i) q^{15} +(-1.98619 + 3.44017i) q^{16} +(-3.48348 + 3.48348i) q^{17} +(-0.000479724 + 0.000830906i) q^{18} +(-6.00388 - 3.46634i) q^{19} +(-1.38588 - 5.17219i) q^{20} +(1.43004 + 1.43004i) q^{21} +(-0.235928 - 0.235928i) q^{22} +(-0.846521 + 0.488739i) q^{23} +0.470886i q^{24} +(1.90630 + 1.10060i) q^{25} +(0.0745669 - 0.278287i) q^{26} +5.18384i q^{27} +(2.24519 + 0.601598i) q^{28} +(4.74401 - 1.27115i) q^{29} +(-0.223637 - 0.223637i) q^{30} +(-0.234430 + 0.0628153i) q^{31} +(0.406060 + 0.703317i) q^{32} +(8.24224 + 2.20850i) q^{33} +(0.0865564 + 0.323033i) q^{34} +(-2.70717 + 1.56298i) q^{35} +(-0.0141008 - 0.0244233i) q^{36} +(0.324066 + 0.561299i) q^{37} +(-0.407574 + 0.235313i) q^{38} +(1.90701 + 7.11705i) q^{39} +(-0.703041 - 0.188379i) q^{40} +(-3.76100 - 6.51424i) q^{41} +(0.132612 - 0.0355332i) q^{42} +(-3.45863 - 3.45863i) q^{43} +(9.47310 - 2.53831i) q^{44} +(0.0366347 + 0.00981624i) q^{45} +0.0663563i q^{46} +(-2.08759 + 7.79100i) q^{47} +(-5.97258 - 3.44827i) q^{48} +5.64305i q^{49} +(0.129410 - 0.0747146i) q^{50} +(-6.04775 - 6.04775i) q^{51} +(5.98809 + 5.98809i) q^{52} +(0.988907 + 3.69065i) q^{53} +(0.304759 + 0.175953i) q^{54} +(-6.59467 + 11.4223i) q^{55} +(0.223409 - 0.223409i) q^{56} +(6.01801 - 10.4235i) q^{57} +(0.0862925 - 0.322048i) q^{58} +(-1.75624 - 6.55437i) q^{59} +(8.97957 - 2.40607i) q^{60} +(9.03876 - 5.21853i) q^{61} +(-0.00426423 + 0.0159143i) q^{62} +(-0.0116416 + 0.0116416i) q^{63} -7.88961 q^{64} -11.3888 q^{65} +(0.409601 - 0.409601i) q^{66} +(-8.32687 - 4.80752i) q^{67} +(-9.49511 - 2.54421i) q^{68} +(-0.848513 - 1.46967i) q^{69} +0.212207i q^{70} +(2.40595 - 4.16722i) q^{71} -0.00383337 q^{72} +(5.64828 + 6.41069i) q^{73} +0.0439986 q^{74} +(-1.91079 + 3.30958i) q^{75} -13.8334i q^{76} +(-2.86267 - 4.95830i) q^{77} +(0.483142 + 0.129458i) q^{78} +(8.33547 + 4.81249i) q^{79} +(7.53767 - 7.53767i) q^{80} -9.04220 q^{81} -0.510632 q^{82} +(-5.35635 + 5.35635i) q^{83} +(-1.04445 + 3.89794i) q^{84} +(11.4488 - 6.60998i) q^{85} +(-0.320729 + 0.0859390i) q^{86} +(2.20688 + 8.23620i) q^{87} +(0.345025 - 1.28765i) q^{88} +(-6.08382 + 10.5375i) q^{89} +(0.00182058 - 0.00182058i) q^{90} +(2.47188 - 4.28142i) q^{91} +(-1.68914 - 0.975226i) q^{92} +(-0.109055 - 0.407000i) q^{93} +(0.387177 + 0.387177i) q^{94} +(13.1549 + 13.1549i) q^{95} +(-1.22105 + 0.704972i) q^{96} +7.81504i q^{97} +(0.331757 + 0.191540i) q^{98} +(-0.0179789 + 0.0670981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9	\( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9} - 12 q^{10} - 6 q^{11} + 30 q^{12} - 16 q^{13} - 8 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{18} - 12 q^{19} + 8 q^{20} + 24 q^{21} + 8 q^{22} - 6 q^{23} - 36 q^{25} - 36 q^{26} - 12 q^{28} - 6 q^{29} + 34 q^{30} + 20 q^{31} - 6 q^{32} + 34 q^{33} + 36 q^{34} + 18 q^{35} + 18 q^{36} - 8 q^{37} - 66 q^{38} + 28 q^{39} - 2 q^{40} + 10 q^{41} - 56 q^{42} + 12 q^{43} + 34 q^{44} - 4 q^{45} - 20 q^{47} - 48 q^{48} + 30 q^{50} - 36 q^{51} + 80 q^{52} + 24 q^{53} + 24 q^{54} + 10 q^{55} + 10 q^{57} + 54 q^{58} - 18 q^{59} + 50 q^{60} + 42 q^{61} - 12 q^{62} - 48 q^{63} - 56 q^{64} - 44 q^{65} - 10 q^{66} - 42 q^{67} - 44 q^{68} + 24 q^{69} + 4 q^{71} - 112 q^{72} - 16 q^{73} - 96 q^{74} - 52 q^{75} + 52 q^{77} - 12 q^{78} + 54 q^{79} - 2 q^{80} + 60 q^{81} + 32 q^{82} - 30 q^{83} - 16 q^{84} + 6 q^{85} + 16 q^{86} + 32 q^{87} + 2 q^{88} - 22 q^{89} - 110 q^{90} - 8 q^{91} - 78 q^{92} + 78 q^{93} + 38 q^{94} + 38 q^{95} + 72 q^{96} + 138 q^{98} - 32 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9 - 12 * q^10 - 6 * q^11 + 30 * q^12 - 16 * q^13 - 8 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^18 - 12 * q^19 + 8 * q^20 + 24 * q^21 + 8 * q^22 - 6 * q^23 - 36 * q^25 - 36 * q^26 - 12 * q^28 - 6 * q^29 + 34 * q^30 + 20 * q^31 - 6 * q^32 + 34 * q^33 + 36 * q^34 + 18 * q^35 + 18 * q^36 - 8 * q^37 - 66 * q^38 + 28 * q^39 - 2 * q^40 + 10 * q^41 - 56 * q^42 + 12 * q^43 + 34 * q^44 - 4 * q^45 - 20 * q^47 - 48 * q^48 + 30 * q^50 - 36 * q^51 + 80 * q^52 + 24 * q^53 + 24 * q^54 + 10 * q^55 + 10 * q^57 + 54 * q^58 - 18 * q^59 + 50 * q^60 + 42 * q^61 - 12 * q^62 - 48 * q^63 - 56 * q^64 - 44 * q^65 - 10 * q^66 - 42 * q^67 - 44 * q^68 + 24 * q^69 + 4 * q^71 - 112 * q^72 - 16 * q^73 - 96 * q^74 - 52 * q^75 + 52 * q^77 - 12 * q^78 + 54 * q^79 - 2 * q^80 + 60 * q^81 + 32 * q^82 - 30 * q^83 - 16 * q^84 + 6 * q^85 + 16 * q^86 + 32 * q^87 + 2 * q^88 - 22 * q^89 - 110 * q^90 - 8 * q^91 - 78 * q^92 + 78 * q^93 + 38 * q^94 + 38 * q^95 + 72 * q^96 + 138 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.0339426	−	0.0587903i	0.0240010	−	0.0415710i	−0.853775	−	0.520641i	$-0.825693\pi$
$2$	0.0339426	−	0.0587903i	0.0240010	−	0.0415710i	0.877776	+	0.479070i	$0.159026\pi$
$3$			1.73613i			1.00235i	0.865345	+	0.501176i	$0.167099\pi$
$3$			1.73613i			1.00235i	−0.865345	+	0.501176i	$0.832901\pi$
$4$	0.997696	+	1.72806i	0.498848	+	0.864030i
$5$	−2.59207	−	0.694543i	−1.15921	−	0.310609i	−0.372559	−	0.928009i	$-0.621519\pi$
$5$	−2.59207	−	0.694543i	−1.15921	−	0.310609i	−0.786650	+	0.617400i	$0.788186\pi$
$6$	0.102067	+	0.0589286i	0.0416688	+	0.0240575i
$7$	0.823696	−	0.823696i	0.311328	−	0.311328i	−0.534096	−	0.845424i	$-0.679348\pi$
$7$	0.823696	−	0.823696i	0.311328	−	0.311328i	0.845424	+	0.534096i	$0.179348\pi$
$8$	0.271228			0.0958935
$9$	−0.0141334			−0.00471113
$10$	−0.128814	+	0.128814i	−0.0407345	+	0.0407345i
$11$	1.27209	−	4.74749i	0.383548	−	1.43142i	−0.456894	−	0.889521i	$-0.651038\pi$
$11$	1.27209	−	4.74749i	0.383548	−	1.43142i	0.840443	−	0.541901i	$-0.182295\pi$
$12$	−3.00013	+	1.73213i	−0.866063	+	0.500022i
$13$	4.09939	−	1.09843i	1.13696	−	0.304649i	0.359235	−	0.933247i	$-0.383038\pi$
$13$	4.09939	−	1.09843i	1.13696	−	0.304649i	0.777730	+	0.628598i	$0.216371\pi$
$14$	−0.0204669	−	0.0763837i	−0.00547002	−	0.0204144i
$15$	1.20581	−	4.50016i	0.311340	−	1.16194i
$16$	−1.98619	+	3.44017i	−0.496546	+	0.860044i
$17$	−3.48348	+	3.48348i	−0.844867	+	0.844867i	−0.989487	−	0.144620i	$-0.953804\pi$
$17$	−3.48348	+	3.48348i	−0.844867	+	0.844867i	0.144620	+	0.989487i	$0.453804\pi$
$18$	−0.000479724	0	0.000830906i	−0.000113072	0	0.000195846i
$19$	−6.00388	−	3.46634i	−1.37738	−	0.795233i	−0.385541	−	0.922691i	$-0.625985\pi$
$19$	−6.00388	−	3.46634i	−1.37738	−	0.795233i	−0.991844	+	0.127457i	$0.959318\pi$
$20$	−1.38588	−	5.17219i	−0.309893	−	1.15654i
$21$	1.43004	+	1.43004i	0.312060	+	0.312060i
$22$	−0.235928	−	0.235928i	−0.0503001	−	0.0503001i
$23$	−0.846521	+	0.488739i	−0.176512	+	0.101909i	−0.585653	−	0.810562i	$-0.699162\pi$
$23$	−0.846521	+	0.488739i	−0.176512	+	0.101909i	0.409141	+	0.912471i	$0.365828\pi$
$24$			0.470886i			0.0961191i
$25$	1.90630	+	1.10060i	0.381260	+	0.220121i
$26$	0.0745669	−	0.278287i	0.0146238	−	0.0545767i
$27$			5.18384i			0.997631i
$28$	2.24519	+	0.601598i	0.424302	+	0.113691i
$29$	4.74401	−	1.27115i	0.880941	−	0.236047i	0.210128	−	0.977674i	$-0.432612\pi$
$29$	4.74401	−	1.27115i	0.880941	−	0.236047i	0.670813	+	0.741627i	$0.265945\pi$
$30$	−0.223637	−	0.223637i	−0.0408304	−	0.0408304i
$31$	−0.234430	+	0.0628153i	−0.0421048	+	0.0112820i	−0.279810	−	0.960055i	$-0.590271\pi$
$31$	−0.234430	+	0.0628153i	−0.0421048	+	0.0112820i	0.237705	+	0.971337i	$0.423605\pi$
$32$	0.406060	+	0.703317i	0.0717820	+	0.124330i
$33$	8.24224	+	2.20850i	1.43479	+	0.384451i
$34$	0.0865564	+	0.323033i	0.0148443	+	0.0553997i
$35$	−2.70717	+	1.56298i	−0.457595	+	0.264192i
$36$	−0.0141008	−	0.0244233i	−0.00235014	−	0.00407056i
$37$	0.324066	+	0.561299i	0.0532762	+	0.0922771i	0.891434	−	0.453151i	$-0.149700\pi$
$37$	0.324066	+	0.561299i	0.0532762	+	0.0922771i	−0.838157	+	0.545428i	$0.816367\pi$
$38$	−0.407574	+	0.235313i	−0.0661173	+	0.0381728i
$39$	1.90701	+	7.11705i	0.305366	+	1.13964i
$40$	−0.703041	−	0.188379i	−0.111161	−	0.0297854i
$41$	−3.76100	−	6.51424i	−0.587369	−	1.01735i	−0.994576	−	0.104017i	$-0.966830\pi$
$41$	−3.76100	−	6.51424i	−0.587369	−	1.01735i	0.407207	−	0.913336i	$-0.366503\pi$
$42$	0.132612	−	0.0355332i	0.0204624	−	0.00548289i
$43$	−3.45863	−	3.45863i	−0.527436	−	0.527436i	0.392371	−	0.919807i	$-0.371655\pi$
$43$	−3.45863	−	3.45863i	−0.527436	−	0.527436i	−0.919807	+	0.392371i	$0.871655\pi$
$44$	9.47310	−	2.53831i	1.42812	−	0.382665i
$45$	0.0366347	+	0.00981624i	0.00546118	+	0.00146332i
$46$			0.0663563i			0.00978370i
$47$	−2.08759	+	7.79100i	−0.304507	+	1.13643i	0.628863	+	0.777516i	$0.283521\pi$
$47$	−2.08759	+	7.79100i	−0.304507	+	1.13643i	−0.933369	+	0.358917i	$0.883146\pi$
$48$	−5.97258	−	3.44827i	−0.862067	−	0.497715i
$49$			5.64305i			0.806150i
$50$	0.129410	−	0.0747146i	0.0183013	−	0.0105662i
$51$	−6.04775	−	6.04775i	−0.846855	−	0.846855i
$52$	5.98809	+	5.98809i	0.830398	+	0.830398i
$53$	0.988907	+	3.69065i	0.135837	+	0.506950i	0.999993	+	0.00372640i	$0.00118615\pi$
$53$	0.988907	+	3.69065i	0.135837	+	0.506950i	−0.864156	+	0.503224i	$0.832147\pi$
$54$	0.304759	+	0.175953i	0.0414725	+	0.0239442i
$55$	−6.59467	+	11.4223i	−0.889225	+	1.54018i
$56$	0.223409	−	0.223409i	0.0298543	−	0.0298543i
$57$	6.01801	−	10.4235i	0.797104	−	1.38063i
$58$	0.0862925	−	0.322048i	0.0113308	−	0.0422870i
$59$	−1.75624	−	6.55437i	−0.228643	−	0.853307i	−0.980912	−	0.194451i	$-0.937707\pi$
$59$	−1.75624	−	6.55437i	−0.228643	−	0.853307i	0.752269	−	0.658856i	$-0.228959\pi$
$60$	8.97957	−	2.40607i	1.15926	−	0.310622i
$61$	9.03876	−	5.21853i	1.15729	−	0.668164i	0.206640	−	0.978417i	$-0.433747\pi$
$61$	9.03876	−	5.21853i	1.15729	−	0.668164i	0.950654	+	0.310253i	$0.100414\pi$
$62$	−0.00426423	+	0.0159143i	−0.000541557	+	0.00202112i
$63$	−0.0116416	+	0.0116416i	−0.00146671	+	0.00146671i
$64$	−7.88961			−0.986201
$65$	−11.3888			−1.41261
$66$	0.409601	−	0.409601i	0.0504184	−	0.0504184i
$67$	−8.32687	−	4.80752i	−1.01729	−	0.587332i	−0.103971	−	0.994580i	$-0.533155\pi$
$67$	−8.32687	−	4.80752i	−1.01729	−	0.587332i	−0.913317	+	0.407248i	$0.866488\pi$
$68$	−9.49511	−	2.54421i	−1.15145	−	0.308530i
$69$	−0.848513	−	1.46967i	−0.102149	−	0.176927i
$70$			0.212207i			0.0253636i
$71$	2.40595	−	4.16722i	0.285533	−	0.494558i	−0.687205	−	0.726463i	$-0.741163\pi$
$71$	2.40595	−	4.16722i	0.285533	−	0.494558i	0.972738	+	0.231905i	$0.0744960\pi$
$72$	−0.00383337			−0.000451767
$73$	5.64828	+	6.41069i	0.661081	+	0.750315i
$73$	5.64828	+	6.41069i	0.661081	+	0.750315i
$74$	0.0439986			0.00511473
$75$	−1.91079	+	3.30958i	−0.220638	+	0.382157i
$76$		−	13.8334i		−	1.58680i
$77$	−2.86267	−	4.95830i	−0.326232	−	0.565050i
$78$	0.483142	+	0.129458i	0.0547051	+	0.0146582i
$79$	8.33547	+	4.81249i	0.937814	+	0.541447i	0.889274	−	0.457374i	$-0.151210\pi$
$79$	8.33547	+	4.81249i	0.937814	+	0.541447i	0.0485396	+	0.998821i	$0.484543\pi$
$80$	7.53767	−	7.53767i	0.842738	−	0.842738i
$81$	−9.04220			−1.00469
$82$	−0.510632			−0.0563898
$83$	−5.35635	+	5.35635i	−0.587935	+	0.587935i	−0.937072	−	0.349137i	$-0.886475\pi$
$83$	−5.35635	+	5.35635i	−0.587935	+	0.587935i	0.349137	+	0.937072i	$0.386475\pi$
$84$	−1.04445	+	3.89794i	−0.113959	+	0.425300i
$85$	11.4488	−	6.60998i	1.24180	−	0.716954i
$86$	−0.320729	+	0.0859390i	−0.0345850	+	0.00926704i
$87$	2.20688	+	8.23620i	0.236603	+	0.883014i
$88$	0.345025	−	1.28765i	0.0367798	−	0.137264i
$89$	−6.08382	+	10.5375i	−0.644884	+	1.11697i	0.339445	+	0.940626i	$0.389761\pi$
$89$	−6.08382	+	10.5375i	−0.644884	+	1.11697i	−0.984328	+	0.176345i	$0.943573\pi$
$90$	0.00182058	−	0.00182058i	0.000191906	−	0.000191906i
$91$	2.47188	−	4.28142i	0.259123	−	0.448814i
$92$	−1.68914	−	0.975226i	−0.176105	−	0.101674i
$93$	−0.109055	−	0.407000i	−0.0113085	−	0.0422039i
$94$	0.387177	+	0.387177i	0.0399342	+	0.0399342i
$95$	13.1549	+	13.1549i	1.34967	+	1.34967i
$96$	−1.22105	+	0.704972i	−0.124623	+	0.0719509i
$97$			7.81504i			0.793497i	0.917927	+	0.396748i	$0.129861\pi$
$97$			7.81504i			0.793497i	−0.917927	+	0.396748i	$0.870139\pi$
$98$	0.331757	+	0.191540i	0.0335125	+	0.0193484i
$99$	−0.0179789	+	0.0670981i	−0.00180695	+	0.00674361i
$100$			4.39227i			0.439227i
$101$	7.15774	+	1.91791i	0.712222	+	0.190839i	0.596698	−	0.802466i	$-0.296479\pi$
$101$	7.15774	+	1.91791i	0.712222	+	0.190839i	0.115523	+	0.993305i	$0.463146\pi$
$102$	−0.560826	+	0.150273i	−0.0555300	+	0.0148792i
$103$	−11.3429	−	11.3429i	−1.11765	−	1.11765i	−0.992086	−	0.125561i	$-0.959927\pi$
$103$	−11.3429	−	11.3429i	−1.11765	−	1.11765i	−0.125561	−	0.992086i	$-0.540073\pi$
$104$	1.11187	−	0.297924i	0.109028	−	0.0292139i
$105$	−2.71354	−	4.69998i	−0.264814	−	0.458671i
$106$	0.250541	+	0.0671321i	0.0243347	+	0.00652045i
$107$	1.45576	+	5.43296i	0.140733	+	0.525224i	0.999908	+	0.0135419i	$0.00431066\pi$
$107$	1.45576	+	5.43296i	0.140733	+	0.525224i	−0.859175	+	0.511682i	$0.829023\pi$
$108$	−8.95799	+	5.17190i	−0.861983	+	0.497666i
$109$	−4.52854	−	7.84365i	−0.433755	−	0.751286i	0.563438	−	0.826158i	$-0.309478\pi$
$109$	−4.52854	−	7.84365i	−0.433755	−	0.751286i	−0.997193	+	0.0748725i	$0.976145\pi$
$110$	0.447680	+	0.775405i	0.0426846	+	0.0739319i
$111$	−0.974487	+	0.562620i	−0.0924942	+	0.0534015i
$112$	1.19764	+	4.46967i	0.113167	+	0.422344i
$113$	9.55680	+	2.56074i	0.899028	+	0.240894i	0.678599	−	0.734509i	$-0.262587\pi$
$113$	9.55680	+	2.56074i	0.899028	+	0.240894i	0.220429	+	0.975403i	$0.429254\pi$
$114$	−0.408533	−	0.707601i	−0.0382627	−	0.0662729i
$115$	2.53369	−	0.678900i	0.236268	−	0.0633078i
$116$	6.92971	+	6.92971i	0.643408	+	0.643408i
$117$	−0.0579382	+	0.0155245i	−0.00535639	+	0.00143524i
$118$	−0.444945	−	0.119223i	−0.0409605	−	0.0109753i
$119$			5.73865i			0.526061i
$120$	0.327050	−	1.22057i	0.0298555	−	0.111422i
$121$	−11.3942	−	6.57843i	−1.03583	−	0.598039i
$122$		−	0.708522i		−	0.0641465i
$123$	11.3095	−	6.52956i	1.01975	−	0.588751i
$124$	−0.342438	−	0.342438i	−0.0307519	−	0.0307519i
$125$	5.31078	+	5.31078i	0.475011	+	0.475011i
$126$	0.000289267		0.00107956i	2.57700e−5		9.61749e-5i
$127$	12.3743	+	7.14432i	1.09804	+	0.633956i	0.935707	−	0.352779i	$-0.114763\pi$
$127$	12.3743	+	7.14432i	1.09804	+	0.633956i	0.162338	+	0.986735i	$0.448097\pi$
$128$	−1.07991	+	1.87047i	−0.0954519	+	0.165327i
$129$	6.00461	−	6.00461i	0.528677	−	0.528677i
$130$	−0.386565	+	0.669550i	−0.0339040	+	0.0587234i
$131$	2.75065	−	10.2656i	0.240325	−	0.896906i	−0.735351	−	0.677687i	$-0.762982\pi$
$131$	2.75065	−	10.2656i	0.240325	−	0.896906i	0.975676	−	0.219219i	$-0.0703509\pi$
$132$	4.40682	+	16.4465i	0.383565	+	1.43148i
$133$	−7.80058	+	2.09016i	−0.676396	+	0.181240i
$134$	−0.565271	+	0.326359i	−0.0488320	+	0.0281931i
$135$	3.60040	−	13.4369i	0.309873	−	1.15646i
$136$	−0.944816	+	0.944816i	−0.0810173	+	0.0810173i
$137$	11.3379			0.968666			0.484333	−	0.874884i	$-0.339062\pi$
$137$	11.3379			0.968666			0.484333	+	0.874884i	$0.339062\pi$
$138$	−0.115203			−0.00980672
$139$	−2.05738	+	2.05738i	−0.174505	+	0.174505i	−0.788955	−	0.614451i	$-0.789378\pi$
$139$	−2.05738	+	2.05738i	−0.174505	+	0.174505i	0.614451	+	0.788955i	$0.289378\pi$
$140$	−5.40186	−	3.11876i	−0.456540	−	0.263584i
$141$	−13.5262	−	3.62432i	−1.13911	−	0.305223i
$142$	−0.163328	−	0.282892i	−0.0137062	−	0.0237398i
$143$		−	20.8591i		−	1.74432i
$144$	0.0280715	−	0.0486213i	0.00233929	−	0.00405178i
$145$	−13.1797			−1.09451
$146$	0.568604	−	0.114468i	0.0470580	−	0.00947346i
$147$	−9.79705			−0.808047
$148$	−0.646639	+	1.12001i	−0.0531534	+	0.0920644i
$149$			24.2427i			1.98604i	0.117948	+	0.993020i	$0.462368\pi$
$149$			24.2427i			1.98604i	−0.117948	+	0.993020i	$0.537632\pi$
$150$	0.129714	+	0.224671i	0.0105911	+	0.0183443i
$151$	−15.4768	−	4.14699i	−1.25948	−	0.337477i	−0.433490	−	0.901158i	$-0.642718\pi$
$151$	−15.4768	−	4.14699i	−1.25948	−	0.337477i	−0.825993	+	0.563681i	$0.809385\pi$
$152$	−1.62842	−	0.940169i	−0.132082	−	0.0762577i
$153$	0.0492333	−	0.0492333i	0.00398028	−	0.00398028i
$154$	−0.388666			−0.0313196
$155$	0.651286			0.0523125
$156$	−10.3961	+	10.3961i	−0.832352	+	0.832352i
$157$	5.81557	−	21.7040i	0.464133	−	1.73217i	−0.195614	−	0.980681i	$-0.562670\pi$
$157$	5.81557	−	21.7040i	0.464133	−	1.73217i	0.659748	−	0.751487i	$-0.270663\pi$
$158$	0.565855	−	0.326697i	0.0450170	−	0.0259906i
$159$	−6.40744	+	1.71687i	−0.508143	+	0.136156i
$160$	−0.564052	−	2.10507i	−0.0445923	−	0.166421i
$161$	−0.294703	+	1.09985i	−0.0232259	+	0.0866802i
$162$	−0.306916	+	0.531594i	−0.0241136	+	0.0417659i
$163$	3.31654	−	3.31654i	0.259771	−	0.259771i	−0.565190	−	0.824961i	$-0.691197\pi$
$163$	3.31654	−	3.31654i	0.259771	−	0.259771i	0.824961	+	0.565190i	$0.191197\pi$
$164$	7.50466	−	12.9985i	0.586015	−	1.01501i
$165$	−19.8305	−	11.4492i	−1.54381	−	0.891317i
$166$	0.133093	+	0.496709i	0.0103300	+	0.0385521i
$167$	−0.992375	−	0.992375i	−0.0767923	−	0.0767923i	0.667667	−	0.744460i	$-0.267293\pi$
$167$	−0.992375	−	0.992375i	−0.0767923	−	0.0767923i	−0.744460	+	0.667667i	$0.767293\pi$
$168$	0.387866	+	0.387866i	0.0299245	+	0.0299245i
$169$	4.34009	−	2.50575i	0.333853	−	0.192750i
$170$		−	0.897440i		−	0.0688305i
$171$	0.0848552	+	0.0489912i	0.00648904	+	0.00374645i
$172$	2.52606	−	9.42738i	0.192610	−	0.718831i
$173$			3.22831i			0.245444i	0.992441	+	0.122722i	$0.0391624\pi$
$173$			3.22831i			0.245444i	−0.992441	+	0.122722i	$0.960838\pi$
$174$	0.559116	+	0.149815i	0.0423865	+	0.0113574i
$175$	2.47677	−	0.663649i	0.187226	−	0.0501672i
$176$	13.8056	+	13.8056i	1.04064	+	1.04064i
$177$	11.3792	−	3.04905i	0.855314	−	0.229181i
$178$	0.413001	+	0.715339i	0.0309557	+	0.0536169i
$179$	−6.59345	−	1.76671i	−0.492817	−	0.132050i	0.00384724	−	0.999993i	$-0.498775\pi$
$179$	−6.59345	−	1.76671i	−0.492817	−	0.132050i	−0.496664	+	0.867943i	$0.665442\pi$
$180$	0.0195872	+	0.0731006i	0.00145995	+	0.00544860i
$181$	4.70046	−	2.71381i	0.349382	−	0.201716i	−0.315031	−	0.949081i	$-0.602015\pi$
$181$	4.70046	−	2.71381i	0.349382	−	0.201716i	0.664413	+	0.747365i	$0.268682\pi$
$182$	−0.167804	−	0.290645i	−0.0124384	−	0.0215440i
$183$	9.06003	+	15.6924i	0.669736	+	1.16002i
$184$	−0.229600	+	0.132560i	−0.0169263	+	0.00977243i
$185$	−0.450156	−	1.68000i	−0.0330961	−	0.123516i
$186$	−0.0276292	−	0.00740323i	−0.00202587	−	0.000542831i
$187$	12.1065	+	20.9690i	0.885314	+	1.53341i
$188$	−15.5461	+	4.16556i	−1.13382	+	0.303805i
$189$	4.26991	+	4.26991i	0.310590	+	0.310590i
$190$	1.21990	−	0.326870i	0.0885005	−	0.0237136i
$191$	13.4214	+	3.59624i	0.971136	+	0.260215i	0.709307	−	0.704899i	$-0.249008\pi$
$191$	13.4214	+	3.59624i	0.971136	+	0.260215i	0.261829	+	0.965114i	$0.415674\pi$
$192$		−	13.6974i		−	0.988522i
$193$	−2.76355	+	10.3137i	−0.198924	+	0.742396i	0.792292	+	0.610143i	$0.208888\pi$
$193$	−2.76355	+	10.3137i	−0.198924	+	0.742396i	−0.991216	+	0.132253i	$0.957779\pi$
$194$	0.459448	+	0.265263i	0.0329865	+	0.0190447i
$195$		−	19.7724i		−	1.41593i
$196$	−9.75153	+	5.63005i	−0.696538	+	0.402146i
$197$	−0.587489	−	0.587489i	−0.0418569	−	0.0418569i	0.685869	−	0.727725i	$-0.259422\pi$
$197$	−0.587489	−	0.587489i	−0.0418569	−	0.0418569i	−0.727725	+	0.685869i	$0.759422\pi$
$198$	0.00333447	+	0.00333447i	0.000236970	+	0.000236970i
$199$	−6.28620	−	23.4604i	−0.445617	−	1.66306i	−0.714303	−	0.699836i	$-0.753256\pi$
$199$	−6.28620	−	23.4604i	−0.445617	−	1.66306i	0.268687	−	0.963228i	$-0.413410\pi$
$200$	0.517042	+	0.298514i	0.0365604	+	0.0211081i
$201$	8.34646	−	14.4565i	0.588714	−	1.01968i
$202$	0.355707	−	0.355707i	0.0250274	−	0.0250274i
$203$	2.86058	−	4.95467i	0.200773	−	0.347749i
$204$	4.41706	−	16.4847i	0.309256	−	1.15416i
$205$	5.22434	+	19.4975i	0.364884	+	1.36177i
$206$	−1.05186	+	0.281844i	−0.0732864	+	0.0196370i
$207$	0.0119642	−	0.00690754i	0.000831570	−	0.000480107i
$208$	−4.36336	+	16.2843i	−0.302545	+	1.12911i
$209$	−24.0939	+	24.0939i	−1.66661	+	1.66661i
$210$	−0.368418			−0.0254232
$211$	14.6840			1.01089			0.505446	−	0.862858i	$-0.331328\pi$
$211$	14.6840			1.01089			0.505446	+	0.862858i	$0.331328\pi$
$212$	−5.39104	+	5.39104i	−0.370258	+	0.370258i
$213$	7.23482	+	4.17703i	0.495722	+	0.286205i
$214$	0.368817	+	0.0988243i	0.0252118	+	0.00675549i
$215$	6.56284	+	11.3672i	0.447582	+	0.775234i
$216$			1.40600i			0.0956663i
$217$	−0.141358	+	0.244839i	−0.00959601	+	0.0166208i
$218$	−0.614841			−0.0416423
$219$	−11.1298	+	9.80612i	−0.752080	+	0.662636i
$220$	−26.3179			−1.77435
$221$	−10.4538	+	18.1065i	−0.703196	+	1.21797i
$222$			0.0763871i			0.00512677i
$223$	10.6020	+	18.3632i	0.709963	+	1.22969i	0.964870	+	0.262726i	$0.0846216\pi$
$223$	10.6020	+	18.3632i	0.709963	+	1.22969i	−0.254908	+	0.966965i	$0.582045\pi$
$224$	0.913789	+	0.244849i	0.0610551	+	0.0163597i
$225$	−0.0269425	−	0.0155553i	−0.00179617	−	0.00103702i
$226$	0.474929	−	0.474929i	0.0315918	−	0.0315918i
$227$	−5.10954			−0.339132			−0.169566	−	0.985519i	$-0.554237\pi$
$227$	−5.10954			−0.339132			−0.169566	+	0.985519i	$0.554237\pi$
$228$	24.0166			1.59054
$229$	2.08710	−	2.08710i	0.137919	−	0.137919i	−0.634776	−	0.772696i	$-0.718908\pi$
$229$	2.08710	−	2.08710i	0.137919	−	0.137919i	0.772696	+	0.634776i	$0.218908\pi$
$230$	0.0460873	−	0.172000i	0.00303890	−	0.0113413i
$231$	8.60823	−	4.96996i	0.566380	−	0.327000i
$232$	1.28671	−	0.344772i	0.0844765	−	0.0226354i
$233$	−6.30140	−	23.5172i	−0.412819	−	1.54066i	−0.789165	−	0.614181i	$-0.789486\pi$
$233$	−6.30140	−	23.5172i	−0.412819	−	1.54066i	0.376347	−	0.926479i	$-0.377180\pi$
$234$	−0.00105388	+	0.00393315i	−6.88945e−5	+	0.000257118i
$235$	10.8224	−	18.7449i	0.705973	−	1.22278i
$236$	9.57416	−	9.57416i	0.623225	−	0.623225i
$237$	−8.35508	+	14.4714i	−0.542721	+	0.940020i
$238$	0.337377	+	0.194785i	0.0218689	+	0.0126260i
$239$	−2.47547	−	9.23857i	−0.160125	−	0.597594i	−0.998612	−	0.0526722i	$-0.983226\pi$
$239$	−2.47547	−	9.23857i	−0.160125	−	0.597594i	0.838487	−	0.544921i	$-0.183441\pi$
$240$	13.0864	+	13.0864i	0.844720	+	0.844720i
$241$	12.3733	+	12.3733i	0.797036	+	0.797036i	0.982627	−	0.185591i	$-0.0594200\pi$
$241$	12.3733	+	12.3733i	0.797036	+	0.797036i	−0.185591	+	0.982627i	$0.559420\pi$
$242$	−0.773495	+	0.446578i	−0.0497221	+	0.0287071i
$243$		−	0.146877i		−	0.00942218i
$244$	18.0359	+	10.4130i	1.15463	+	0.666625i
$245$	3.91934	−	14.6272i	0.250397	−	0.934496i
$246$		−	0.886521i		−	0.0565225i
$247$	−28.4197	−	7.61505i	−1.80831	−	0.484534i
$248$	−0.0635839	+	0.0170373i	−0.00403758	+	0.00108187i
$249$	−9.29929	−	9.29929i	−0.589319	−	0.589319i
$250$	0.492484	−	0.131961i	0.0311474	−	0.00834593i
$251$	6.03319	+	10.4498i	0.380812	+	0.659585i	0.991178	−	0.132534i	$-0.0423113\pi$
$251$	6.03319	+	10.4498i	0.380812	+	0.659585i	−0.610367	+	0.792119i	$0.708978\pi$
$252$	−0.0317322	−	0.00850262i	−0.00199894	−	0.000535614i
$253$	1.24344	+	4.64057i	0.0781742	+	0.291750i
$254$	0.840034	−	0.484994i	0.0527084	−	0.0304312i
$255$	11.4758	+	19.8766i	0.718640	+	1.24472i
$256$	−7.81630	−	13.5382i	−0.488519	−	0.846139i
$257$	6.79577	−	3.92354i	0.423908	−	0.244744i	−0.272840	−	0.962060i	$-0.587963\pi$
$257$	6.79577	−	3.92354i	0.423908	−	0.244744i	0.696748	+	0.717316i	$0.254630\pi$
$258$	−0.149201	−	0.556825i	−0.00928884	−	0.0346664i
$259$	0.729272	+	0.195408i	0.0453148	+	0.0121421i
$260$	−11.3625	−	19.6805i	−0.704675	−	1.22053i
$261$	−0.0670490	+	0.0179657i	−0.00415023	+	0.00111205i
$262$	−0.510151	−	0.510151i	−0.0315172	−	0.0315172i
$263$	2.11083	−	0.565594i	0.130159	−	0.0348760i	−0.193151	−	0.981169i	$-0.561871\pi$
$263$	2.11083	−	0.565594i	0.130159	−	0.0348760i	0.323310	+	0.946293i	$0.395204\pi$
$264$	2.23552	+	0.599007i	0.137587	+	0.0368663i
$265$		−	10.2533i		−	0.629853i
$266$	−0.141891	+	0.529544i	−0.00869989	+	0.0324684i
$267$	−18.2944	−	10.5623i	−1.11960	−	0.646401i
$268$		−	19.1858i		−	1.17196i
$269$	−16.8194	+	9.71070i	−1.02550	+	0.592072i	−0.915692	−	0.401881i	$-0.868357\pi$
$269$	−16.8194	+	9.71070i	−1.02550	+	0.592072i	−0.109807	+	0.993953i	$0.535023\pi$
$270$	−0.667750	−	0.667750i	−0.0406380	−	0.0406380i
$271$	4.72438	+	4.72438i	0.286986	+	0.286986i	0.835887	−	0.548901i	$-0.184954\pi$
$271$	4.72438	+	4.72438i	0.286986	+	0.286986i	−0.548901	+	0.835887i	$0.684954\pi$
$272$	−5.06493	−	18.9026i	−0.307107	−	1.14614i
$273$	7.43308	+	4.29149i	0.449870	+	0.259733i
$274$	0.384839	−	0.666561i	0.0232490	−	0.0402684i
$275$	7.65008	−	7.65008i	0.461317	−	0.461317i
$276$	1.69312	−	2.93256i	0.101914	−	0.176519i
$277$	0.0121521	−	0.0453523i	0.000730149	−	0.00272495i	−0.965560	−	0.260181i	$-0.916218\pi$
$277$	0.0121521	−	0.0453523i	0.000730149	−	0.00272495i	0.966290	+	0.257456i	$0.0828843\pi$
$278$	0.0511211	+	0.190787i	0.00306604	+	0.0114426i
$279$	0.00331329		0.000887793i	0.000198361		5.31508e-5i
$280$	−0.734259	+	0.423925i	−0.0438804	+	0.0253343i
$281$	1.70030	−	6.34560i	0.101431	−	0.378547i	−0.896485	−	0.443075i	$-0.853888\pi$
$281$	1.70030	−	6.34560i	0.101431	−	0.378547i	0.997916	+	0.0645281i	$0.0205542\pi$
$282$	−0.672188	+	0.672188i	−0.0400282	+	0.0400282i
$283$	−14.8899			−0.885111			−0.442556	−	0.896741i	$-0.645928\pi$
$283$	−14.8899			−0.885111			−0.442556	+	0.896741i	$0.645928\pi$
$284$	9.60161			0.569751
$285$	−22.8386	+	22.8386i	−1.35284	+	1.35284i
$286$	−1.22631	−	0.708011i	−0.0725133	−	0.0418656i
$287$	−8.46366	−	2.26783i	−0.499594	−	0.133866i
$288$	−0.00573901	−	0.00994026i	−0.000338174	−	0.000585735i
$289$		−	7.26921i		−	0.427601i
$290$	−0.447352	+	0.774837i	−0.0262694	+	0.0455000i
$291$	−13.5679			−0.795364
$292$	−5.44280	+	16.1565i	−0.318516	+	0.945486i
$293$	−18.3491			−1.07196			−0.535982	−	0.844229i	$-0.680059\pi$
$293$	−18.3491			−1.07196			−0.535982	+	0.844229i	$0.680059\pi$
$294$	−0.332537	+	0.575971i	−0.0193940	+	0.0335913i
$295$			18.2092i			1.06018i
$296$	0.0878958	+	0.152240i	0.00510884	+	0.00884877i
$297$	24.6102	+	6.59429i	1.42803	+	0.382640i
$298$	1.42524	+	0.822860i	0.0825617	+	0.0476670i
$299$	−2.93337	+	2.93337i	−0.169641	+	0.169641i
$300$	−7.62553			−0.440260
$301$	−5.69771			−0.328411
$302$	−0.769125	+	0.769125i	−0.0442582	+	0.0442582i
$303$	−3.32973	+	12.4267i	−0.191288	+	0.713897i
$304$	23.8496	−	13.7696i	1.36787	−	0.789741i
$305$	−27.0536	+	7.24898i	−1.54908	+	0.415076i
$306$	−0.00122334	−	0.00456555i	−6.99334e−5	−	0.000260995i
$307$	3.40947	−	12.7243i	0.194588	−	0.726214i	−0.797785	−	0.602943i	$-0.793995\pi$
$307$	3.40947	−	12.7243i	0.194588	−	0.726214i	0.992373	−	0.123271i	$-0.0393386\pi$
$308$	5.71216	−	9.89374i	0.325480	−	0.563748i
$309$	19.6927	−	19.6927i	1.12028	−	1.12028i
$310$	0.0221063	−	0.0382893i	0.00125555	−	0.00217468i
$311$	10.8432	+	6.26034i	0.614863	+	0.354991i	0.774866	−	0.632125i	$-0.217817\pi$
$311$	10.8432	+	6.26034i	0.614863	+	0.354991i	−0.160004	+	0.987116i	$0.551151\pi$
$312$	0.517234	+	1.93034i	0.0292826	+	0.109284i
$313$	−17.4969	−	17.4969i	−0.988984	−	0.988984i	0.0109555	−	0.999940i	$-0.496513\pi$
$313$	−17.4969	−	17.4969i	−0.988984	−	0.988984i	−0.999940	+	0.0109555i	$0.996513\pi$
$314$	−1.07859	−	1.07859i	−0.0608683	−	0.0608683i
$315$	0.0382614	−	0.0220903i	0.00215579	−	0.00124464i
$316$			19.2056i			1.08040i
$317$	−23.5040	−	13.5701i	−1.32012	−	0.762170i	−0.336370	−	0.941730i	$-0.609199\pi$
$317$	−23.5040	−	13.5701i	−1.32012	−	0.762170i	−0.983747	+	0.179560i	$0.942533\pi$
$318$	−0.116550	+	0.434970i	−0.00653579	+	0.0243919i
$319$		−	24.1392i		−	1.35153i
$320$	20.4504	+	5.47967i	1.14321	+	0.306323i
$321$	−9.43230	+	2.52738i	−0.526459	+	0.141064i
$322$	0.0546574	+	0.0546574i	0.00304594	+	0.00304594i
$323$	32.9893	−	8.83946i	1.83557	−	0.491840i
$324$	−9.02137	−	15.6255i	−0.501187	−	0.868081i
$325$	9.02359	+	2.41786i	0.500539	+	0.134119i
$326$	−0.0824083	−	0.307552i	−0.00456418	−	0.0170337i
$327$	13.6176	−	7.86211i	0.753054	−	0.434776i
$328$	−1.02009	−	1.76684i	−0.0563249	−	0.0975575i
$329$	4.69787	+	8.13695i	0.259002	+	0.448605i
$330$	−1.34620	+	0.777229i	−0.0741059	+	0.0427850i
$331$	3.60692	+	13.4612i	0.198254	+	0.739895i	0.991400	+	0.130864i	$0.0417750\pi$
$331$	3.60692	+	13.4612i	0.198254	+	0.739895i	−0.793146	+	0.609031i	$0.791558\pi$
$332$	−14.6001	−	3.91208i	−0.801284	−	0.214703i
$333$	−0.00458016	−	0.00793307i	−0.000250991	−	0.000434729i
$334$	−0.0920258	+	0.0246582i	−0.00503543	+	0.00134924i
$335$	18.2448	+	18.2448i	0.996819	+	0.996819i
$336$	−7.75991	+	2.07926i	−0.423338	+	0.113433i
$337$	−3.19533	−	0.856187i	−0.174061	−	0.0466395i	0.170736	−	0.985317i	$-0.445386\pi$
$337$	−3.19533	−	0.856187i	−0.174061	−	0.0466395i	−0.344797	+	0.938677i	$0.612052\pi$
$338$		−	0.340207i		−	0.0185048i
$339$	−4.44576	+	16.5918i	−0.241461	+	0.901144i
$340$	22.8449	+	13.1895i	1.23894	+	0.715302i
$341$			1.19286i			0.0645969i
$342$	0.00576041	−	0.00332577i	0.000311487	−	0.000179837i
$343$	10.4140	+	10.4140i	0.562305	+	0.562305i
$344$	−0.938076	−	0.938076i	−0.0505777	−	0.0505777i
$345$	1.17866	+	4.39881i	0.0634567	+	0.236824i
$346$	0.189793	+	0.109577i	0.0102034	+	0.00589091i
$347$	11.8006	−	20.4392i	0.633490	−	1.09724i	−0.353343	−	0.935494i	$-0.614955\pi$
$347$	11.8006	−	20.4392i	0.633490	−	1.09724i	0.986833	−	0.161742i	$-0.0517114\pi$
$348$	−12.0309	+	12.0309i	−0.644921	+	0.644921i
$349$	3.34960	−	5.80168i	0.179300	−	0.310557i	−0.762341	−	0.647176i	$-0.775950\pi$
$349$	3.34960	−	5.80168i	0.179300	−	0.310557i	0.941641	+	0.336619i	$0.109283\pi$
$350$	0.0450519	−	0.168136i	0.00240813	−	0.00898726i
$351$	5.69407	+	21.2506i	0.303927	+	1.13427i
$352$	3.85553	−	1.03309i	0.205501	−	0.0550637i
$353$	13.8082	−	7.97219i	0.734938	−	0.424317i	−0.0852879	−	0.996356i	$-0.527181\pi$
$353$	13.8082	−	7.97219i	0.734938	−	0.424317i	0.820226	+	0.572040i	$0.193848\pi$
$354$	0.206985	−	0.772480i	0.0110012	−	0.0410569i
$355$	−9.13069	+	9.13069i	−0.484607	+	0.484607i
$356$	−24.2792			−1.28680
$357$	−9.96302			−0.527299
$358$	−0.327664	+	0.327664i	−0.0173176	+	0.0173176i
$359$	8.24908	+	4.76261i	0.435370	+	0.251361i	0.701632	−	0.712540i	$-0.252455\pi$
$359$	8.24908	+	4.76261i	0.435370	+	0.251361i	−0.266262	+	0.963901i	$0.585789\pi$
$360$	0.00993635	+	0.00266244i	0.000523692	+	0.000140323i
$361$	14.5311	+	25.1685i	0.764793	+	1.32466i
$362$		−	0.368455i		−	0.0193656i
$363$	11.4210	−	19.7817i	0.599446	−	1.03827i
$364$	9.86472			0.517052
$365$	−10.1882	−	20.5399i	−0.533276	−	1.07511i
$366$	1.23008			0.0642975
$367$	−7.45781	+	12.9173i	−0.389295	+	0.674278i	−0.992355	−	0.123418i	$-0.960615\pi$
$367$	−7.45781	+	12.9173i	−0.389295	+	0.674278i	0.603060	+	0.797696i	$0.293948\pi$
$368$		−	3.88291i		−	0.202411i
$369$	0.0531556	+	0.0920683i	0.00276717	+	0.00479288i
$370$	−0.114047	−	0.0305589i	−0.00592904	−	0.00158868i
$371$	3.85453	+	2.22542i	0.200117	+	0.115538i
$372$	0.594516	−	0.594516i	0.0308242	−	0.0308242i
$373$	−17.9497			−0.929400			−0.464700	−	0.885468i	$-0.653838\pi$
$373$	−17.9497			−0.929400			−0.464700	+	0.885468i	$0.653838\pi$
$374$	1.64370			0.0849938
$375$	−9.22019	+	9.22019i	−0.476128	+	0.476128i
$376$	−0.566213	+	2.11314i	−0.0292002	+	0.108977i
$377$	18.0513	−	10.4219i	0.929687	−	0.536755i
$378$	0.395961	−	0.106097i	0.0203660	−	0.00545706i
$379$	4.38416	+	16.3619i	0.225199	+	0.840454i	0.982325	+	0.187185i	$0.0599364\pi$
$379$	4.38416	+	16.3619i	0.225199	+	0.840454i	−0.757126	+	0.653269i	$0.773397\pi$
$380$	−9.60790	+	35.8572i	−0.492875	+	1.83943i
$381$	−12.4034	+	21.4834i	−0.635448	+	1.10063i
$382$	0.666980	−	0.666980i	0.0341257	−	0.0341257i
$383$	8.68209	−	15.0378i	0.443634	−	0.768396i	−0.554322	−	0.832302i	$-0.687022\pi$
$383$	8.68209	−	15.0378i	0.443634	−	0.768396i	0.997956	+	0.0639059i	$0.0203557\pi$
$384$	−3.24737	−	1.87487i	−0.165716	−	0.0956764i
$385$	3.97650	+	14.8405i	0.202661	+	0.756342i
$386$	0.512543	+	0.512543i	0.0260878	+	0.0260878i
$387$	0.0488822	+	0.0488822i	0.00248482	+	0.00248482i
$388$	−13.5048	+	7.79703i	−0.685605	+	0.395834i
$389$		−	9.07519i		−	0.460131i	−0.973175	−	0.230065i	$-0.926106\pi$
$389$		−	9.07519i		−	0.460131i	0.973175	−	0.230065i	$-0.0738940\pi$
$390$	−1.16242	−	0.671125i	−0.0588616	−	0.0339838i
$391$	1.24632	−	4.65135i	0.0630294	−	0.235229i
$392$			1.53055i			0.0773046i
$393$	17.8223	+	4.77547i	0.899016	+	0.240891i
$394$	−0.0544796	+	0.0145978i	−0.00274464	+	0.000735424i
$395$	−18.2636	−	18.2636i	−0.918943	−	0.918943i
$396$	−0.133887	+	0.0358749i	−0.00672808	+	0.00180278i
$397$	−3.07886	−	5.33275i	−0.154524	−	0.267643i	0.778362	−	0.627816i	$-0.216051\pi$
$397$	−3.07886	−	5.33275i	−0.154524	−	0.267643i	−0.932886	+	0.360173i	$0.882718\pi$
$398$	−1.59261	−	0.426740i	−0.0798305	−	0.0213905i
$399$	−3.62878	−	13.5428i	−0.181666	−	0.677988i
$400$	−7.57253	+	4.37200i	−0.378627	+	0.218600i
$401$	−19.3367	−	33.4921i	−0.965629	−	1.67252i	−0.707917	−	0.706296i	$-0.750365\pi$
$401$	−19.3367	−	33.4921i	−0.965629	−	1.67252i	−0.257712	−	0.966222i	$-0.582969\pi$
$402$	−0.566601	−	0.981381i	−0.0282595	−	0.0489469i
$403$	−0.892020	+	0.515008i	−0.0444347	+	0.0256544i
$404$	3.82698	+	14.2825i	0.190400	+	0.710581i
$405$	23.4380	+	6.28019i	1.16464	+	0.312065i
$406$	−0.194191	−	0.336348i	−0.00963753	−	0.0166927i
$407$	3.07700	−	0.824480i	0.152521	−	0.0408680i
$408$	−1.64032	−	1.64032i	−0.0812079	−	0.0812079i
$409$	−7.75532	+	2.07803i	−0.383476	+	0.102752i	−0.445407	−	0.895328i	$-0.646941\pi$
$409$	−7.75532	+	2.07803i	−0.383476	+	0.102752i	0.0619307	+	0.998080i	$0.480274\pi$
$410$	1.32359	+	0.354655i	0.0653676	+	0.0175152i
$411$			19.6841i			0.970945i
$412$	8.28443	−	30.9179i	0.408144	−	1.52322i
$413$	−6.84542	−	3.95220i	−0.336841	−	0.194475i
$414$		0	0.000937840i		0	4.60923e-5i
$415$	17.6042	−	10.1638i	0.864157	−	0.498921i
$416$	2.43714	+	2.43714i	0.119491	+	0.119491i
$417$	−3.57187	−	3.57187i	−0.174915	−	0.174915i
$418$	0.598677	+	2.23429i	0.0292823	+	0.109283i
$419$	−2.94854	−	1.70234i	−0.144045	−	0.0831647i	0.426245	−	0.904608i	$-0.359836\pi$
$419$	−2.94854	−	1.70234i	−0.144045	−	0.0831647i	−0.570291	+	0.821443i	$0.693169\pi$
$420$	5.41457	−	9.37831i	0.264204	−	0.457614i
$421$	−9.14260	+	9.14260i	−0.445583	+	0.445583i	−0.893883	−	0.448300i	$-0.852030\pi$
$421$	−9.14260	+	9.14260i	−0.445583	+	0.445583i	0.448300	+	0.893883i	$0.352030\pi$
$422$	0.498414	−	0.863279i	0.0242624	−	0.0420238i
$423$	0.0295047	−	0.110113i	0.00143457	−	0.00535389i
$424$	0.268219	+	1.00101i	0.0130259	+	0.0486132i
$425$	−10.4745	+	2.80663i	−0.508087	+	0.136141i
$426$	0.491137	−	0.283558i	0.0237957	−	0.0137384i
$427$	3.14671	−	11.7437i	0.152280	−	0.568316i
$428$	−7.93607	+	7.93607i	−0.383604	+	0.383604i
$429$	36.2140			1.74843
$430$	0.891038			0.0429697
$431$	1.42230	−	1.42230i	0.0685097	−	0.0685097i	−0.672022	−	0.740531i	$-0.734574\pi$
$431$	1.42230	−	1.42230i	0.0685097	−	0.0685097i	0.740531	+	0.672022i	$0.234574\pi$
$432$	−17.8333	−	10.2961i	−0.858006	−	0.495370i
$433$	30.4802	+	8.16715i	1.46479	+	0.392488i	0.901140	−	0.433528i	$-0.142731\pi$
$433$	30.4802	+	8.16715i	1.46479	+	0.392488i	0.563646	+	0.826016i	$0.309398\pi$
$434$	0.00959612	+	0.0166210i	0.000460629	+	0.000797832i
$435$		−	22.8816i		−	1.09709i
$436$	9.03620	−	15.6512i	0.432756	−	0.749555i
$437$	6.77655			0.324166
$438$	0.198731	+	0.987167i	0.00949575	+	0.0471687i
$439$	13.7315			0.655370			0.327685	−	0.944787i	$-0.393731\pi$
$439$	13.7315			0.655370			0.327685	+	0.944787i	$0.393731\pi$
$440$	−1.78866	+	3.09804i	−0.0852709	+	0.147693i
$441$		−	0.0797555i		−	0.00379788i
$442$	0.709656	+	1.22916i	0.0337549	+	0.0584652i
$443$	−39.4586	−	10.5729i	−1.87474	−	0.502334i	−0.999838	−	0.0180264i	$-0.994262\pi$
$443$	−39.4586	−	10.5729i	−1.87474	−	0.502334i	−0.874898	−	0.484307i	$-0.839072\pi$
$444$	−1.94448	−	1.12265i	−0.0922810	−	0.0532785i
$445$	23.0884	−	23.0884i	1.09450	−	1.09450i
$446$	1.43944			0.0681594
$447$	−42.0884			−1.99071
$448$	−6.49864	+	6.49864i	−0.307032	+	0.307032i
$449$	−4.17761	+	15.5911i	−0.197154	+	0.735787i	0.794545	+	0.607205i	$0.207709\pi$
$449$	−4.17761	+	15.5911i	−0.197154	+	0.735787i	−0.991699	+	0.128582i	$0.958957\pi$
$450$	−0.00182900	+	0.00105597i	−8.62197e−5	+	4.97789e-5i
$451$	−35.7106	+	9.56862i	−1.68155	+	0.450569i
$452$	5.10967	+	19.0696i	0.240339	+	0.896957i
$453$	7.19970	−	26.8696i	0.338271	−	1.26245i
$454$	−0.173431	+	0.300391i	−0.00813951	+	0.0140981i
$455$	−9.38090	+	9.38090i	−0.439783	+	0.439783i
$456$	1.63225	−	2.82714i	0.0764372	−	0.132393i
$457$	−12.1287	−	7.00252i	−0.567358	−	0.327564i	0.188736	−	0.982028i	$-0.439561\pi$
$457$	−12.1287	−	7.00252i	−0.567358	−	0.327564i	−0.756093	+	0.654464i	$0.772894\pi$
$458$	−0.0518596	−	0.193543i	−0.00242324	−	0.00904365i
$459$	−18.0578	−	18.0578i	−0.842865	−	0.842865i
$460$	3.70103	+	3.70103i	0.172562	+	0.172562i
$461$	21.7721	−	12.5701i	1.01403	−	0.585450i	0.101660	−	0.994819i	$-0.467585\pi$
$461$	21.7721	−	12.5701i	1.01403	−	0.585450i	0.912369	+	0.409369i	$0.134251\pi$
$462$		−	0.674774i		−	0.0313933i
$463$	−17.8658	−	10.3148i	−0.830293	−	0.479370i	0.0236598	−	0.999720i	$-0.492468\pi$
$463$	−17.8658	−	10.3148i	−0.830293	−	0.479370i	−0.853953	+	0.520350i	$0.825801\pi$
$464$	−5.04950	+	18.8450i	−0.234417	+	0.874856i
$465$			1.13071i			0.0524356i
$466$	−1.59647	−	0.427772i	−0.0739549	−	0.0198161i
$467$	7.10274	−	1.90317i	0.328676	−	0.0880684i	−0.0907079	−	0.995878i	$-0.528913\pi$
$467$	7.10274	−	1.90317i	0.328676	−	0.0880684i	0.419383	+	0.907809i	$0.362246\pi$
$468$	−0.0846320	−	0.0846320i	−0.00391211	−	0.00391211i
$469$	−10.8187	+	2.89887i	−0.499563	+	0.133857i
$470$	−0.734678	−	1.27250i	−0.0338882	−	0.0586960i
$471$	37.6809	+	10.0966i	1.73624	+	0.465225i
$472$	−0.476341	−	1.77773i	−0.0219254	−	0.0818266i
$473$	−20.8195	+	12.0201i	−0.957280	+	0.552686i
$474$	0.567186	+	0.982396i	0.0260517	+	0.0451229i
$475$	−7.63013	−	13.2158i	−0.350095	−	0.606381i
$476$	−9.91673	+	5.72543i	−0.454532	+	0.262424i
$477$	−0.0139766	−	0.0521614i	−0.000639945	−	0.00238831i
$478$	−0.627162	−	0.168048i	−0.0286857	−	0.00768632i
$479$	−0.0885703	−	0.153408i	−0.00404688	−	0.00700940i	0.863995	−	0.503501i	$-0.167955\pi$
$479$	−0.0885703	−	0.153408i	−0.00404688	−	0.00700940i	−0.868042	+	0.496491i	$0.834621\pi$
$480$	3.65467	−	0.979266i	0.166812	−	0.0446972i
$481$	1.94502	+	1.94502i	0.0886853	+	0.0886853i
$482$	1.14741	−	0.307449i	0.0522633	−	0.0140039i
$483$	−1.90947	−	0.511642i	−0.0868841	−	0.0232805i
$484$		−	26.2531i		−	1.19332i
$485$	5.42787	−	20.2571i	0.246467	−	0.919828i
$486$	−0.00863496	−	0.00498540i	−0.000391690	−	0.000226142i
$487$		−	8.57006i		−	0.388346i	−0.980967	−	0.194173i	$-0.937798\pi$
$487$		−	8.57006i		−	0.388346i	0.980967	−	0.194173i	$-0.0622024\pi$
$488$	2.45156	−	1.41541i	0.110977	−	0.0640726i
$489$	5.75793	+	5.75793i	0.260383	+	0.260383i
$490$	−0.726903	−	0.726903i	−0.0328381	−	0.0328381i
$491$	3.80705	+	14.2081i	0.171810	+	0.641203i	0.997073	+	0.0764546i	$0.0243600\pi$
$491$	3.80705	+	14.2081i	0.171810	+	0.641203i	−0.825263	+	0.564748i	$0.808973\pi$
$492$	22.5670	+	13.0290i	1.01740	+	0.587394i
$493$	−12.0976	+	20.9537i	−0.544849	+	0.943707i
$494$	−1.41233	+	1.41233i	−0.0635438	+	0.0635438i
$495$	0.0932050	−	0.161436i	0.00418925	−	0.00725600i
$496$	0.249526	−	0.931242i	0.0112040	−	0.0418140i
$497$	−1.45075	−	5.41429i	−0.0650752	−	0.242864i
$498$	−0.862350	+	0.231066i	−0.0386428	+	0.0103543i
$499$	−29.7346	+	17.1673i	−1.33111	+	0.768514i	−0.985469	−	0.169855i	$-0.945670\pi$
$499$	−29.7346	+	17.1673i	−1.33111	+	0.768514i	−0.345636	+	0.938369i	$0.612337\pi$
$500$	−3.87880	+	14.4759i	−0.173465	+	0.647382i
$501$	1.72289	−	1.72289i	0.0769730	−	0.0769730i
$502$	0.819128			0.0365595
$503$	0.390962			0.0174321			0.00871606	−	0.999962i	$-0.497226\pi$
$503$	0.390962			0.0174321			0.00871606	+	0.999962i	$0.497226\pi$
$504$	−0.00315753	+	0.00315753i	−0.000140648	+	0.000140648i
$505$	−17.2213	−	9.94271i	−0.766337	−	0.442445i
$506$	0.315026	+	0.0844109i	0.0140046	+	0.00375252i
$507$	4.35030	+	7.53494i	0.193204	+	0.334638i
$508$			28.5114i			1.26499i
$509$	2.09332	−	3.62573i	0.0927846	−	0.160708i	−0.815897	−	0.578197i	$-0.803757\pi$
$509$	2.09332	−	3.62573i	0.0927846	−	0.160708i	0.908682	+	0.417489i	$0.137090\pi$
$510$	1.55807			0.0689924
$511$	9.93292	+	0.627999i	0.439406	+	0.0277810i
$512$	−5.38088			−0.237804
$513$	17.9690	−	31.1232i	0.793349	−	1.37412i
$514$		−	0.532700i		−	0.0234964i
$515$	21.5234	+	37.2796i	0.948434	+	1.64274i
$516$	16.3671	+	4.38555i	0.720522	+	0.193063i
$517$	34.3321	+	19.8216i	1.50992	+	0.871754i
$518$	0.0362415	−	0.0362415i	0.00159236	−	0.00159236i
$519$	−5.60476			−0.246022
$520$	−3.08896			−0.135460
$521$	25.2821	−	25.2821i	1.10763	−	1.10763i	0.114167	−	0.993462i	$-0.463580\pi$
$521$	25.2821	−	25.2821i	1.10763	−	1.10763i	0.993462	−	0.114167i	$-0.0364199\pi$
$522$	−0.00121961	+	0.00455163i	−5.33807e−5	+	0.000199219i
$523$	5.89561	−	3.40383i	0.257797	−	0.148839i	−0.365532	−	0.930799i	$-0.619113\pi$
$523$	5.89561	−	3.40383i	0.257797	−	0.148839i	0.623329	+	0.781959i	$0.285780\pi$
$524$	20.4838	−	5.48862i	0.894839	−	0.239771i
$525$	1.15218	+	4.29999i	0.0502852	+	0.187667i
$526$	0.0383954	−	0.143294i	0.00167412	−	0.00624791i
$527$	0.597815	−	1.03545i	0.0260412	−	0.0451047i
$528$	−23.9682	+	23.9682i	−1.04308	+	1.04308i
$529$	−11.0223	+	19.0911i	−0.479229	+	0.830049i
$530$	−0.602792	−	0.348022i	−0.0261836	−	0.0151171i
$531$	0.0248216	+	0.0926355i	0.00107717	+	0.00402004i
$532$	−11.3945	−	11.3945i	−0.494015	−	0.494015i
$533$	−22.5732	−	22.5732i	−0.977753	−	0.977753i
$534$	−1.24192	+	0.717022i	−0.0537431	+	0.0310286i
$535$		−	15.0937i		−	0.652557i
$536$	−2.25848	−	1.30393i	−0.0975514	−	0.0563213i
$537$	3.06723	−	11.4471i	0.132361	−	0.493977i
$538$			1.31843i			0.0568414i
$539$	26.7903	+	7.17845i	1.15394	+	0.309198i
$540$	26.8118	−	7.18420i	1.15380	−	0.309159i
$541$	22.0324	+	22.0324i	0.947247	+	0.947247i	0.998677	−	0.0514300i	$-0.0163779\pi$
$541$	22.0324	+	22.0324i	0.947247	+	0.947247i	−0.0514300	+	0.998677i	$0.516378\pi$
$542$	0.438106	−	0.117390i	0.0188183	−	0.00504234i
$543$	4.71152	+	8.16059i	0.202191	+	0.350204i
$544$	−3.86449	−	1.03549i	−0.165689	−	0.0443961i
$545$	6.29052	+	23.4765i	0.269456	+	1.00562i
$546$	0.504596	−	0.291328i	0.0215947	−	0.0124677i
$547$	4.22370	+	7.31566i	0.180592	+	0.312795i	0.942082	−	0.335382i	$-0.108865\pi$
$547$	4.22370	+	7.31566i	0.180592	+	0.312795i	−0.761490	+	0.648176i	$0.775532\pi$
$548$	11.3118	+	19.5927i	0.483217	+	0.836957i
$549$	−0.127748	+	0.0737555i	−0.00545217	+	0.00314781i
$550$	−0.190087	−	0.709414i	−0.00810533	−	0.0302495i
$551$	−32.8887	−	8.81251i	−1.40111	−	0.375426i
$552$	−0.230140	−	0.398615i	−0.00979542	−	0.0169662i
$553$	10.8299	−	2.90187i	0.460535	−	0.123400i
$554$	−0.00225380	−	0.00225380i	−9.57548e−5	−	9.57548e-5i
$555$	2.91670	−	0.781527i	0.123807	−	0.0331740i
$556$	−5.60791	−	1.50264i	−0.237829	−	0.0637260i
$557$			35.0915i			1.48687i	0.668806	+	0.743437i	$0.266806\pi$
$557$			35.0915i			1.48687i	−0.668806	+	0.743437i	$0.733194\pi$
$558$	6.02680e−5	0	0.000224923i	2.55135e−6	0	9.52176e-6i
$559$	−17.9773	−	10.3792i	−0.760359	−	0.438993i
$560$		−	12.4175i		−	0.524735i
$561$	−36.4049	+	21.0184i	−1.53702	+	0.887397i
$562$	−0.315347	−	0.315347i	−0.0133021	−	0.0133021i
$563$	−3.53281	−	3.53281i	−0.148890	−	0.148890i	0.628732	−	0.777622i	$-0.283574\pi$
$563$	−3.53281	−	3.53281i	−0.148890	−	0.148890i	−0.777622	+	0.628732i	$0.783574\pi$
$564$	−7.23194	−	26.9900i	−0.304520	−	1.13648i
$565$	−22.9933	−	13.2752i	−0.967337	−	0.558492i
$566$	−0.505401	+	0.875380i	−0.0212436	+	0.0367950i
$567$	−7.44802	+	7.44802i	−0.312787	+	0.312787i
$568$	0.652560	−	1.13027i	0.0273808	−	0.0474249i
$569$	−0.994096	+	3.71002i	−0.0416747	+	0.155532i	−0.983628	−	0.180213i	$-0.942321\pi$
$569$	−0.994096	+	3.71002i	−0.0416747	+	0.155532i	0.941953	+	0.335745i	$0.108988\pi$
$570$	0.567488	+	2.11789i	0.0237694	+	0.0887088i
$571$	25.6435	−	6.87115i	1.07315	−	0.287549i	0.321361	−	0.946957i	$-0.395860\pi$
$571$	25.6435	−	6.87115i	1.07315	−	0.287549i	0.751785	+	0.659408i	$0.229193\pi$
$572$	36.0457	−	20.8110i	1.50715	−	0.870152i
$573$	−6.24353	+	23.3012i	−0.260827	+	0.973421i
$574$	−0.420605	+	0.420605i	−0.0175557	+	0.0175557i
$575$	−2.15163			−0.0897292
$576$	0.111507			0.00464612
$577$	12.6989	−	12.6989i	0.528661	−	0.528661i	−0.391512	−	0.920173i	$-0.628048\pi$
$577$	12.6989	−	12.6989i	0.528661	−	0.528661i	0.920173	+	0.391512i	$0.128048\pi$
$578$	−0.427359	−	0.246736i	−0.0177758	−	0.0102629i
$579$	−17.9059	−	4.79786i	−0.744143	−	0.199392i
$580$	−13.1493	−	22.7753i	−0.545995	−	0.945691i
$581$			8.82400i			0.366081i
$582$	−0.460529	+	0.797660i	−0.0190895	+	0.0330641i
$583$	18.7793			0.777759
$584$	1.53197	+	1.73876i	0.0633934	+	0.0719503i
$585$	0.160962			0.00665497
$586$	−0.622815	+	1.07875i	−0.0257282	+	0.0445626i
$587$			16.5000i			0.681029i	0.940239	+	0.340514i	$0.110601\pi$
$587$			16.5000i			0.681029i	−0.940239	+	0.340514i	$0.889399\pi$
$588$	−9.77447	−	16.9299i	−0.403092	−	0.698177i
$589$	1.62523	+	0.435478i	0.0669663	+	0.0179436i
$590$	1.07052	+	0.618066i	0.0440727	+	0.0254454i
$591$	1.01996	−	1.01996i	0.0419554	−	0.0419554i
$592$	−2.57462			−0.105816
$593$	37.9912			1.56011			0.780055	−	0.625710i	$-0.215191\pi$
$593$	37.9912			1.56011			0.780055	+	0.625710i	$0.215191\pi$
$594$	1.22301	−	1.22301i	0.0501809	−	0.0501809i
$595$	3.98574	−	14.8750i	0.163399	−	0.609814i
$596$	−41.8928	+	24.1868i	−1.71600	+	0.990732i
$597$	40.7302	−	10.9136i	1.66698	−	0.446665i
$598$	0.0728875	+	0.272020i	0.00298059	+	0.0111237i
$599$	−2.33275	+	8.70596i	−0.0953137	+	0.355716i	−0.997067	−	0.0765358i	$-0.975614\pi$
$599$	−2.33275	+	8.70596i	−0.0953137	+	0.355716i	0.901753	+	0.432252i	$0.142281\pi$
$600$	−0.518258	+	0.897649i	−0.0211578	+	0.0366464i
$601$	−5.98344	+	5.98344i	−0.244070	+	0.244070i	−0.818531	−	0.574462i	$-0.805211\pi$
$601$	−5.98344	+	5.98344i	−0.244070	+	0.244070i	0.574462	+	0.818531i	$0.305211\pi$
$602$	−0.193395	+	0.334970i	−0.00788220	+	0.0136524i
$603$	0.117687	+	0.0679466i	0.00479258	+	0.00276700i
$604$	−8.27487	−	30.8822i	−0.336700	−	1.25658i
$605$	24.9655	+	24.9655i	1.01499	+	1.01499i
$606$	0.617552	+	0.617552i	0.0250863	+	0.0250863i
$607$	−22.9251	+	13.2358i	−0.930501	+	0.537225i	−0.886970	−	0.461827i	$-0.847194\pi$
$607$	−22.9251	+	13.2358i	−0.930501	+	0.537225i	−0.0435311	+	0.999052i	$0.513861\pi$
$608$		−	5.63018i		−	0.228334i
$609$	8.60192	+	4.96632i	0.348568	+	0.201246i
$610$	−0.492098	+	1.83654i	−0.0199245	+	0.0743592i
$611$			34.2314i			1.38485i
$612$	0.134198	+	0.0359583i	0.00542463	+	0.00145353i
$613$	−3.51743	+	0.942493i	−0.142068	+	0.0380669i	−0.329152	−	0.944277i	$-0.606763\pi$
$613$	−3.51743	+	0.942493i	−0.142068	+	0.0380669i	0.187084	+	0.982344i	$0.440096\pi$
$614$	−0.632339	−	0.632339i	−0.0255191	−	0.0255191i
$615$	−33.8501	+	9.07012i	−1.36497	+	0.365742i
$616$	−0.776437	−	1.34483i	−0.0312835	−	0.0541847i
$617$	16.8950	+	4.52700i	0.680166	+	0.182250i	0.582330	−	0.812953i	$-0.302141\pi$
$617$	16.8950	+	4.52700i	0.680166	+	0.182250i	0.0978363	+	0.995203i	$0.468808\pi$
$618$	−0.489317	−	1.82616i	−0.0196832	−	0.0734588i
$619$	7.78318	−	4.49362i	0.312833	−	0.180614i	−0.335361	−	0.942090i	$-0.608858\pi$
$619$	7.78318	−	4.49362i	0.312833	−	0.180614i	0.648193	+	0.761476i	$0.275525\pi$
$620$	0.649785	+	1.12546i	0.0260960	+	0.0451996i
$621$	−2.53355	−	4.38823i	−0.101668	−	0.176094i
$622$	0.736094	−	0.424984i	0.0295147	−	0.0170403i
$623$	3.66846	+	13.6909i	0.146974	+	0.548514i
$624$	−28.2716	−	7.57534i	−1.13177	−	0.303256i
$625$	−15.5804	−	26.9860i	−0.623214	−	1.07944i
$626$	−1.62254	+	0.434758i	−0.0648497	+	0.0173764i
$627$	−41.8300	−	41.8300i	−1.67053	−	1.67053i
$628$	43.3080	−	11.6043i	1.72818	−	0.463064i
$629$	−3.08415	−	0.826396i	−0.122973	−	0.0329506i
$630$		−	0.00299920i		−	0.000119491i
$631$	−2.86485	+	10.6918i	−0.114048	+	0.425632i	−0.999214	−	0.0396431i	$-0.987378\pi$
$631$	−2.86485	+	10.6918i	−0.114048	+	0.425632i	0.885166	+	0.465275i	$0.154045\pi$
$632$	2.26081	+	1.30528i	0.0899303	+	0.0519213i
$633$			25.4934i			1.01327i
$634$	−1.59557	+	0.921205i	−0.0633684	+	0.0365857i
$635$	−27.1131	−	27.1131i	−1.07595	−	1.07595i
$636$	−9.35952	−	9.35952i	−0.371129	−	0.371129i
$637$	6.19848	+	23.1330i	0.245593	+	0.916564i
$638$	−1.41915	−	0.819346i	−0.0561846	−	0.0324382i
$639$	−0.0340042	+	0.0588970i	−0.00134518	+	0.00232993i
$640$	4.09833	−	4.09833i	0.162001	−	0.162001i
$641$	17.2076	−	29.8045i	0.679660	−	1.17721i	−0.295423	−	0.955367i	$-0.595460\pi$
$641$	17.2076	−	29.8045i	0.679660	−	1.17721i	0.975083	−	0.221840i	$-0.0712062\pi$
$642$	−0.171571	+	0.640313i	−0.00677138	+	0.0252711i
$643$	−7.87286	−	29.3819i	−0.310475	−	1.15871i	−0.928129	−	0.372259i	$-0.878583\pi$
$643$	−7.87286	−	29.3819i	−0.310475	−	1.15871i	0.617653	−	0.786450i	$-0.288083\pi$
$644$	−2.19463	+	0.588049i	−0.0864804	+	0.0231724i
$645$	−19.7348	+	11.3939i	−0.777058	+	0.448635i
$646$	0.600068	−	2.23948i	0.0236094	−	0.0881113i
$647$	24.0883	−	24.0883i	0.947007	−	0.947007i	−0.0516579	−	0.998665i	$-0.516451\pi$
$647$	24.0883	−	24.0883i	0.947007	−	0.947007i	0.998665	+	0.0516579i	$0.0164505\pi$
$648$	−2.45250			−0.0963432
$649$	−33.3509			−1.30914
$650$	0.448431	−	0.448431i	0.0175889	−	0.0175889i
$651$	−0.425072	−	0.245416i	−0.0166599	−	0.00961859i
$652$	9.04007	+	2.42228i	0.354037	+	0.0948638i
$653$	−0.197265	−	0.341673i	−0.00771957	−	0.0133707i	0.862140	−	0.506670i	$-0.169124\pi$
$653$	−0.197265	−	0.341673i	−0.00771957	−	0.0133707i	−0.869859	+	0.493300i	$0.835791\pi$
$654$		−	1.06744i		−	0.0417403i
$655$	−14.2597	+	24.6986i	−0.557174	+	0.965053i
$656$	29.8801			1.16662
$657$	−0.0798293	−	0.0906048i	−0.00311444	−	0.00353483i
$658$	0.637832			0.0248653
$659$	3.49855	−	6.05967i	0.136284	−	0.236051i	−0.789803	−	0.613361i	$-0.789817\pi$
$659$	3.49855	−	6.05967i	0.136284	−	0.236051i	0.926087	+	0.377309i	$0.123151\pi$
$660$		−	45.6912i		−	1.77853i
$661$	3.53720	+	6.12661i	0.137581	+	0.238297i	0.926580	−	0.376097i	$-0.122734\pi$
$661$	3.53720	+	6.12661i	0.137581	+	0.238297i	−0.788999	+	0.614394i	$0.789401\pi$
$662$	0.913817	+	0.244856i	0.0355165	+	0.00951661i
$663$	−31.4351	−	18.1491i	−1.22084	−	0.704851i
$664$	−1.45279	+	1.45279i	−0.0563792	+	0.0563792i
$665$	21.6713			0.840379
$666$	−0.000621850	0		−2.40962e−5	0
$667$	−3.39464	+	3.39464i	−0.131441	+	0.131441i
$668$	0.724795	−	2.70497i	0.0280432	−	0.104659i
$669$	−31.8809	+	18.4064i	−1.23258	+	0.711633i
$670$	1.69189	−	0.453341i	0.0653634	−	0.0175141i
$671$	−13.2768	−	49.5498i	−0.512547	−	1.91285i
$672$	−0.425089	+	1.58645i	−0.0163982	+	0.0611988i
$673$	3.09080	−	5.35343i	0.119142	−	0.206359i	−0.800286	−	0.599618i	$-0.795319\pi$
$673$	3.09080	−	5.35343i	0.119142	−	0.206359i	0.919428	+	0.393259i	$0.128652\pi$
$674$	−0.158793	+	0.158793i	−0.00611649	+	0.00611649i
$675$	−5.70535	+	9.88196i	−0.219599	+	0.380357i
$676$	8.66018	+	4.99995i	0.333084	+	0.192306i
$677$	−2.43095	−	9.07242i	−0.0934289	−	0.348682i	0.903348	−	0.428909i	$-0.141102\pi$
$677$	−2.43095	−	9.07242i	−0.0934289	−	0.348682i	−0.996777	+	0.0802276i	$0.974435\pi$
$678$	0.824537	+	0.824537i	0.0316661	+	0.0316661i
$679$	6.43721	+	6.43721i	0.247037	+	0.247037i
$680$	3.10524	−	1.79281i	0.119081	−	0.0687512i
$681$		−	8.87080i		−	0.339930i
$682$	0.0701285	+	0.0404887i	0.00268536	+	0.00155039i
$683$	−1.69603	+	6.32969i	−0.0648969	+	0.242199i	−0.990753	−	0.135678i	$-0.956679\pi$
$683$	−1.69603	+	6.32969i	−0.0648969	+	0.242199i	0.925856	+	0.377876i	$0.123346\pi$
$684$			0.195513i			0.00747563i
$685$	−29.3887	−	7.87469i	−1.12289	−	0.300876i
$686$	0.965722	−	0.258765i	0.0368715	−	0.00987968i
$687$	3.62347	+	3.62347i	0.138244	+	0.138244i
$688$	18.7678	−	5.02881i	0.715514	−	0.191721i
$689$	8.10782	+	14.0432i	0.308884	+	0.535002i
$690$	0.298614	+	0.0800133i	0.0113680	+	0.00304605i
$691$	−2.21603	−	8.27032i	−0.0843016	−	0.314618i	0.910879	−	0.412673i	$-0.135405\pi$
$691$	−2.21603	−	8.27032i	−0.0843016	−	0.314618i	−0.995181	+	0.0980547i	$0.968738\pi$
$692$	−5.57872	+	3.22087i	−0.212071	+	0.122439i
$693$	0.0404593	+	0.0700776i	0.00153692	+	0.00266203i
$694$	−0.801086	−	1.38752i	−0.0304088	−	0.0526696i
$695$	6.76181	−	3.90393i	0.256490	−	0.148085i
$696$	0.598568	+	2.23389i	0.0226887	+	0.0846753i
$697$	35.7935	+	9.59085i	1.35578	+	0.363279i
$698$	−0.227388	−	0.393848i	−0.00860678	−	0.0149074i
$699$	40.8287	−	10.9400i	1.54428	−	0.413790i
$700$	3.61789	+	3.61789i	0.136743	+	0.136743i
$701$	−31.7054	+	8.49544i	−1.19750	+	0.320868i	−0.801845	−	0.597532i	$-0.796148\pi$
$701$	−31.7054	+	8.49544i	−1.19750	+	0.320868i	−0.395652	+	0.918401i	$0.629481\pi$
$702$	1.44260	+	0.386543i	0.0544473	+	0.0145891i
$703$		−	4.49330i		−	0.169468i
$704$	−10.0363	+	37.4558i	−0.378256	+	1.41167i
$705$	32.5435	+	18.7890i	1.22566	+	0.707634i
$706$		−	1.08239i		−	0.0407362i
$707$	7.47557	−	4.31602i	0.281148	−	0.162321i
$708$	16.6219	+	16.6219i	0.624691	+	0.624691i
$709$	13.5610	+	13.5610i	0.509294	+	0.509294i	0.914310	−	0.405016i	$-0.132734\pi$
$709$	13.5610	+	13.5610i	0.509294	+	0.509294i	−0.405016	+	0.914310i	$0.632734\pi$
$710$	0.226877	+	0.846715i	0.00851453	+	0.0317766i
$711$	−0.117808	−	0.0680168i	−0.00441816	−	0.00255083i
$712$	−1.65010	+	2.85806i	−0.0618402	+	0.107110i
$713$	0.167749	−	0.167749i	0.00628227	−	0.00628227i
$714$	−0.338171	+	0.585729i	−0.0126557	+	0.0219203i
$715$	−14.4875	+	54.0682i	−0.541802	+	2.02203i
$716$	−3.52528	−	13.1565i	−0.131746	−	0.491682i
$717$	16.0393	−	4.29772i	0.599000	−	0.160501i
$718$	0.559990	−	0.323310i	0.0208986	−	0.0120658i
$719$	8.43708	−	31.4876i	0.314650	−	1.17429i	−0.609665	−	0.792659i	$-0.708696\pi$
$719$	8.43708	−	31.4876i	0.314650	−	1.17429i	0.924315	−	0.381630i	$-0.124637\pi$
$720$	−0.106533	+	0.106533i	−0.00397025	+	0.00397025i
$721$	−18.6862			−0.695909
$722$	1.97289			0.0734232
$723$	−21.4817	+	21.4817i	−0.798911	+	0.798911i
$724$	9.37925	+	5.41511i	0.348577	+	0.201251i
$725$	10.4425	+	2.79807i	0.387826	+	0.103918i
$726$	−0.775315	−	1.34288i	−0.0287746	−	0.0498391i
$727$			0.0876925i			0.00325234i	0.999999	+	0.00162617i	$0.000517625\pi$
$727$			0.0876925i			0.00325234i	−0.999999	+	0.00162617i	$0.999482\pi$
$728$	0.670442	−	1.16124i	0.0248482	−	0.0430384i
$729$	−26.8716			−0.995245
$730$	−1.55336	−	0.0982098i	−0.0574925	−	0.00363491i
$731$	24.0961			0.891227
$732$	−18.0783	+	31.3125i	−0.668193	+	1.15734i
$733$			1.01752i			0.0375831i	0.999823	+	0.0187916i	$0.00598189\pi$
$733$			1.01752i			0.0375831i	−0.999823	+	0.0187916i	$0.994018\pi$
$734$	0.506275	+	0.876894i	0.0186869	+	0.0323667i
$735$	25.3946	+	6.80447i	0.936694	+	0.250987i
$736$	−0.687477	−	0.396915i	−0.0253408	−	0.0146305i
$737$	−33.4161	+	33.4161i	−1.23090	+	1.23090i
$738$	0.00721696			0.000265660
$739$	−2.68830			−0.0988908			−0.0494454	−	0.998777i	$-0.515745\pi$
$739$	−2.68830			−0.0988908			−0.0494454	+	0.998777i	$0.515745\pi$
$740$	2.45403	−	2.45403i	0.0902119	−	0.0902119i
$741$	13.2207	−	49.3403i	0.485674	−	1.81256i
$742$	0.261666	−	0.151073i	0.00960605	−	0.00554605i
$743$	−8.56343	+	2.29456i	−0.314162	+	0.0841794i	−0.412455	−	0.910978i	$-0.635328\pi$
$743$	−8.56343	+	2.29456i	−0.314162	+	0.0841794i	0.0982929	+	0.995158i	$0.468662\pi$
$744$	−0.0295788	−	0.110390i	−0.00108441	−	0.00404708i
$745$	16.8376	−	62.8387i	0.616881	−	2.30223i
$746$	−0.609259	+	1.05527i	−0.0223066	+	0.0386361i
$747$	0.0757033	−	0.0757033i	0.00276984	−	0.00276984i
$748$	−24.1572	+	41.8415i	−0.883274	+	1.52988i
$749$	5.67420	+	3.27600i	0.207331	+	0.119703i
$750$	0.229100	+	0.855015i	0.00836557	+	0.0312207i
$751$	19.8398	+	19.8398i	0.723966	+	0.723966i	0.969411	−	0.245445i	$-0.0789341\pi$
$751$	19.8398	+	19.8398i	0.723966	+	0.723966i	−0.245445	+	0.969411i	$0.578934\pi$
$752$	−22.6560	−	22.6560i	−0.826181	−	0.826181i
$753$	−18.1422	+	10.4744i	−0.661137	+	0.381708i
$754$		−	1.41499i		−	0.0515307i
$755$	37.2366	+	21.4986i	1.35518	+	0.782413i
$756$	−3.11859	+	11.6387i	−0.113422	+	0.423296i
$757$		−	29.6904i		−	1.07912i	−0.841948	−	0.539558i	$-0.818591\pi$
$757$		−	29.6904i		−	1.07912i	0.841948	−	0.539558i	$-0.181409\pi$
$758$	1.11073	+	0.297619i	0.0403435	+	0.0108100i
$759$	−8.05661	+	2.15876i	−0.292436	+	0.0783581i
$760$	3.56799	+	3.56799i	0.129425	+	0.129425i
$761$	−16.7475	+	4.48748i	−0.607097	+	0.162671i	−0.549255	−	0.835655i	$-0.685089\pi$
$761$	−16.7475	+	4.48748i	−0.607097	+	0.162671i	−0.0578417	+	0.998326i	$0.518422\pi$
$762$	0.842010	+	1.45840i	0.0305028	+	0.0528324i
$763$	−10.1909	−	2.73065i	−0.368936	−	0.0988561i
$764$	7.17592	+	26.7809i	0.259616	+	0.968898i
$765$	−0.161811	+	0.0934215i	−0.00585028	+	0.00337766i
$766$	−0.589385	−	1.02084i	−0.0212953	−	0.0368846i
$767$	−14.3990	−	24.9398i	−0.519918	−	0.900524i
$768$	23.5041	−	13.5701i	0.848130	−	0.489668i
$769$	−2.64260	−	9.86232i	−0.0952946	−	0.355644i	0.901769	−	0.432218i	$-0.142269\pi$
$769$	−2.64260	−	9.86232i	−0.0952946	−	0.355644i	−0.997064	+	0.0765733i	$0.975602\pi$
$770$	1.00745	+	0.269945i	0.0363060	+	0.00972815i
$771$	6.81176	+	11.7983i	0.245319	+	0.424906i
$772$	−20.5799	+	5.51436i	−0.740685	+	0.198466i
$773$	−2.90236	−	2.90236i	−0.104391	−	0.104391i	0.652982	−	0.757373i	$-0.273518\pi$
$773$	−2.90236	−	2.90236i	−0.104391	−	0.104391i	−0.757373	+	0.652982i	$0.773518\pi$
$774$	0.00453298	−	0.00121461i	0.000162935	−	4.36582e-5i
$775$	−0.516028	−	0.138269i	−0.0185363	−	0.00496678i
$776$			2.11966i			0.0760912i
$777$	−0.339253	+	1.26611i	−0.0121706	+	0.0454214i
$778$	−0.533533	−	0.308036i	−0.0191281	−	0.0110436i
$779$			52.1476i			1.86838i
$780$	34.1678	−	19.7268i	1.22341	−	0.706333i
$781$	−16.7233	−	16.7233i	−0.598405	−	0.598405i
$782$	−0.231151	−	0.231151i	−0.00826593	−	0.00826593i
$783$	6.58946	+	24.5922i	0.235488	+	0.878854i
$784$	−19.4131	−	11.2081i	−0.693324	−	0.400291i
$785$	−30.1487	+	52.2191i	−1.07605	+	1.86378i
$786$	0.885686	−	0.885686i	0.0315914	−	0.0315914i
$787$	−23.3067	+	40.3685i	−0.830796	+	1.43898i	0.0666125	+	0.997779i	$0.478781\pi$
$787$	−23.3067	+	40.3685i	−0.830796	+	1.43898i	−0.897408	+	0.441201i	$0.854552\pi$
$788$	0.429081	−	1.60135i	0.0152854	−	0.0570458i
$789$	0.981943	+	3.66466i	0.0349581	+	0.130465i
$790$	−1.69364	+	0.453809i	−0.0602570	+	0.0161458i
$791$	9.98116	−	5.76263i	0.354889	−	0.204895i
$792$	−0.00487637	+	0.0181989i	−0.000173274	+	0.000646669i
$793$	31.3212	−	31.3212i	1.11225	−	1.11225i
$794$	−0.418018			−0.0148349
$795$	17.8010			0.631335
$796$	34.2693	−	34.2693i	1.21464	−	1.21464i
$797$	25.7996	+	14.8954i	0.913869	+	0.527623i	0.881674	−	0.471859i	$-0.156417\pi$
$797$	25.7996	+	14.8954i	0.913869	+	0.527623i	0.0321951	+	0.999482i	$0.489750\pi$
$798$	−0.919355	−	0.246340i	−0.0325448	−	0.00872035i
$799$	−19.8677	−	34.4118i	−0.702868	−	1.21740i
$800$			1.78764i			0.0632028i
$801$	0.0859850	−	0.148930i	0.00303813	−	0.00526220i
$802$	−2.62535			−0.0927043
$803$	37.6198	−	18.6602i	1.32757	−	0.658503i
$804$	33.3089			1.17471
$805$	1.52778	−	2.64620i	0.0538473	−	0.0932662i
$806$			0.0699228i			0.00246293i
$807$	−16.8590	−	29.2007i	−0.593465	−	1.02791i
$808$	1.94138	+	0.520191i	0.0682975	+	0.0183002i
$809$	−9.73232	−	5.61896i	−0.342170	−	0.197552i	0.319061	−	0.947734i	$-0.396632\pi$
$809$	−9.73232	−	5.61896i	−0.342170	−	0.197552i	−0.661231	+	0.750182i	$0.729966\pi$
$810$	1.16476	−	1.16476i	0.0409255	−	0.0409255i
$811$	50.1731			1.76182			0.880909	−	0.473286i	$-0.156932\pi$
$811$	50.1731			1.76182			0.880909	+	0.473286i	$0.156932\pi$
$812$	11.4159			0.400621
$813$	−8.20213	+	8.20213i	−0.287661	+	0.287661i
$814$	0.0559700	−	0.208883i	0.00196175	−	0.00732134i
$815$	−10.9002	+	6.29322i	−0.381816	+	0.220442i
$816$	32.8173	−	8.79337i	1.14883	−	0.307829i
$817$	8.77640	+	32.7540i	0.307048	+	1.14592i
$818$	−0.141068	+	0.526471i	−0.00493231	+	0.0184076i
$819$	−0.0349360	+	0.0605109i	−0.00122076	+	0.00211442i
$820$	−28.4806	+	28.4806i	−0.994585	+	0.994585i
$821$	26.8381	−	46.4850i	0.936657	−	1.62234i	0.165006	−	0.986293i	$-0.447236\pi$
$821$	26.8381	−	46.4850i	0.936657	−	1.62234i	0.771651	−	0.636046i	$-0.219431\pi$
$822$	1.15723	+	0.668129i	0.0403632	+	0.0233037i
$823$	3.81120	+	14.2236i	0.132850	+	0.495804i	0.999997	−	0.00224816i	$-0.000715611\pi$
$823$	3.81120	+	14.2236i	0.132850	+	0.495804i	−0.867147	+	0.498052i	$0.834049\pi$
$824$	−3.07650	−	3.07650i	−0.107175	−	0.107175i
$825$	13.2815	+	13.2815i	0.462402	+	0.462402i
$826$	−0.464702	+	0.268296i	−0.0161691	+	0.00933521i
$827$			32.4358i			1.12790i	0.825808	+	0.563952i	$0.190720\pi$
$827$			32.4358i			1.12790i	−0.825808	+	0.563952i	$0.809280\pi$
$828$	0.0238733	+	0.0137833i	0.000829654	+	0.000479001i
$829$	4.52848	−	16.9005i	0.157281	−	0.586980i	−0.841619	−	0.540072i	$-0.818397\pi$
$829$	4.52848	−	16.9005i	0.157281	−	0.586980i	0.998899	−	0.0469072i	$-0.0149365\pi$
$830$		−	1.37994i		−	0.0478985i
$831$	0.0787373	+	0.0210976i	0.00273137	+	0.000731867i
$832$	−32.3426	+	8.66616i	−1.12128	+	0.300445i
$833$	−19.6574	−	19.6574i	−0.681090	−	0.681090i
$834$	−0.331230	+	0.0887527i	−0.0114695	+	0.00307326i
$835$	1.88306	+	3.26155i	0.0651659	+	0.112871i
$836$	−65.6740	−	17.5973i	−2.27138	−	0.608615i
$837$	−0.325624	−	1.21525i	−0.0112552	−	0.0420051i
$838$	−0.200162	+	0.115564i	−0.00691448	+	0.00399208i
$839$	−7.89537	−	13.6752i	−0.272578	−	0.472120i	0.696943	−	0.717127i	$-0.254543\pi$
$839$	−7.89537	−	13.6752i	−0.272578	−	0.472120i	−0.969521	+	0.245007i	$0.921210\pi$
$840$	−0.735987	−	1.27477i	−0.0253939	−	0.0439836i
$841$	−4.22492	+	2.43926i	−0.145687	+	0.0841124i
$842$	0.227173	+	0.847820i	0.00782889	+	0.0292178i
$843$	11.0168	+	2.95193i	0.379437	+	0.101670i
$844$	14.6502	+	25.3749i	0.504281	+	0.873440i
$845$	−12.9902	+	3.48070i	−0.446875	+	0.119740i
$846$	−0.00547212	−	0.00547212i	−0.000188135	−	0.000188135i
$847$	−14.8039	+	3.96671i	−0.508670	+	0.136298i
$848$	−14.6606	−	3.92831i	−0.503448	−	0.134899i
$849$		−	25.8507i		−	0.887194i
$850$	−0.190528	+	0.711062i	−0.00653507	+	0.0243892i
$851$	−0.548658	−	0.316768i	−0.0188078	−	0.0108587i
$852$			16.6696i			0.571091i
$853$	18.4792	−	10.6690i	0.632716	−	0.365299i	−0.149087	−	0.988824i	$-0.547633\pi$
$853$	18.4792	−	10.6690i	0.632716	−	0.365299i	0.781803	+	0.623525i	$0.214300\pi$
$854$	−0.583606	−	0.583606i	−0.0199706	−	0.0199706i
$855$	−0.185924	−	0.185924i	−0.00635847	−	0.00635847i
$856$	0.394842	+	1.47357i	0.0134954	+	0.0503656i
$857$	−28.3780	−	16.3841i	−0.969375	−	0.559669i	−0.0703294	−	0.997524i	$-0.522405\pi$
$857$	−28.3780	−	16.3841i	−0.969375	−	0.559669i	−0.899046	+	0.437855i	$0.855738\pi$
$858$	1.22920	−	2.12903i	0.0419641	−	0.0726839i
$859$	14.8137	−	14.8137i	0.505437	−	0.505437i	−0.407685	−	0.913123i	$-0.633664\pi$
$859$	14.8137	−	14.8137i	0.505437	−	0.505437i	0.913123	+	0.407685i	$0.133664\pi$
$860$	−13.0954	+	22.6819i	−0.446550	+	0.773448i
$861$	3.93724	−	14.6940i	0.134181	−	0.500770i
$862$	−0.0353408	−	0.131894i	−0.00120371	−	0.00449232i
$863$	−40.8399	+	10.9430i	−1.39020	+	0.372504i	−0.874817	−	0.484453i	$-0.839019\pi$
$863$	−40.8399	+	10.9430i	−1.39020	+	0.372504i	−0.515387	+	0.856957i	$0.672352\pi$
$864$	−3.64588	+	2.10495i	−0.124036	+	0.0716119i
$865$	2.24220	−	8.36801i	0.0762371	−	0.284521i
$866$	1.51473	−	1.51473i	0.0514725	−	0.0514725i
$867$	12.6203			0.428607
$868$	−0.564130			−0.0191478
$869$	33.4507	−	33.4507i	1.13474	−	1.13474i
$870$	−1.34521	−	0.776660i	−0.0456070	−	0.0263312i
$871$	−39.4157	−	10.5614i	−1.33555	−	0.357860i
$872$	−1.22827	−	2.12742i	−0.0415943	−	0.0720435i
$873$		−	0.110453i		−	0.00373827i
$874$	0.230014	−	0.398395i	0.00778033	−	0.0134759i
$875$	8.74894			0.295768
$876$	−28.0497	−	9.44938i	−0.947711	−	0.319265i
$877$	36.7816			1.24203			0.621014	−	0.783800i	$-0.286721\pi$
$877$	36.7816			1.24203			0.621014	+	0.783800i	$0.286721\pi$
$878$	0.466084	−	0.807281i	0.0157296	−	0.0272444i
$879$		−	31.8563i		−	1.07449i
$880$	−26.1965	−	45.3736i	−0.883082	−	1.52954i
$881$	−51.6580	−	13.8417i	−1.74040	−	0.466340i	−0.757867	−	0.652409i	$-0.773758\pi$
$881$	−51.6580	−	13.8417i	−1.74040	−	0.466340i	−0.982537	+	0.186069i	$0.940425\pi$
$882$	−0.00468885	−	0.00270711i	−0.000157882	−	9.11530e-5i
$883$	−6.23372	+	6.23372i	−0.209781	+	0.209781i	−0.804175	−	0.594393i	$-0.797392\pi$
$883$	−6.23372	+	6.23372i	−0.209781	+	0.209781i	0.594393	+	0.804175i	$0.297392\pi$
$884$	−41.7187			−1.40315
$885$	−31.6134			−1.06267
$886$	−1.96091	+	1.96091i	−0.0658781	+	0.0658781i
$887$	−7.38381	+	27.5567i	−0.247924	+	0.925265i	0.723967	+	0.689834i	$0.242317\pi$
$887$	−7.38381	+	27.5567i	−0.247924	+	0.925265i	−0.971891	+	0.235430i	$0.924350\pi$
$888$	−0.264308	+	0.152598i	−0.00886959	+	0.00512086i
$889$	16.0774	−	4.30793i	0.539220	−	0.144483i
$890$	−0.573694	−	2.14105i	−0.0192303	−	0.0717683i
$891$	−11.5025	+	42.9277i	−0.385347	+	1.43813i
$892$	−21.1552	+	36.6418i	−0.708327	+	1.22686i
$893$	39.5399	−	39.5399i	1.32315	−	1.32315i
$894$	−1.42859	+	2.47439i	−0.0477792	+	0.0827559i
$895$	15.8636	+	9.15886i	0.530262	+	0.306147i
$896$	0.651174	+	2.43022i	0.0217542	+	0.0811878i
$897$	−5.09270	−	5.09270i	−0.170040	−	0.170040i
$898$	0.774803	+	0.774803i	0.0258555	+	0.0258555i
$899$	−1.03229	+	0.595993i	−0.0344288	+	0.0198775i
$900$		−	0.0620776i		−	0.00206925i
$901$	−16.3011	−	9.41146i	−0.543070	−	0.313541i
$902$	−0.649567	+	2.42422i	−0.0216282	+	0.0807176i
$903$		−	9.89195i		−	0.329183i
$904$	2.59207	+	0.694543i	0.0862110	+	0.0231002i
$905$	−14.0688	+	3.76971i	−0.467661	+	0.125310i
$906$	−1.33530	−	1.33530i	−0.0443623	−	0.0443623i
$907$	−35.9556	+	9.63428i	−1.19389	+	0.319901i	−0.800421	−	0.599438i	$-0.795391\pi$
$907$	−35.9556	+	9.63428i	−1.19389	+	0.319901i	−0.393466	+	0.919339i	$0.628724\pi$
$908$	−5.09776	−	8.82958i	−0.169175	−	0.293020i
$909$	−0.101163	−	0.0271066i	−0.00335537	−	0.000899069i
$910$	0.233094	+	0.869917i	0.00772698	+	0.0288375i
$911$	18.4573	−	10.6563i	0.611518	−	0.353060i	−0.162041	−	0.986784i	$-0.551808\pi$
$911$	18.4573	−	10.6563i	0.611518	−	0.353060i	0.773559	+	0.633724i	$0.218474\pi$
$912$	23.9058	+	41.4060i	0.791599	+	1.37109i
$913$	18.6155	+	32.2429i	0.616082	+	1.06708i
$914$	−0.823360	+	0.475367i	−0.0272343	+	0.0157238i
$915$	−12.5851	−	46.9684i	−0.416052	−	1.55273i
$916$	5.68892	+	1.52434i	0.187967	+	0.0503657i
$917$	−6.19000	−	10.7214i	−0.204412	−	0.354051i
$918$	−1.67455	+	0.448694i	−0.0552684	+	0.0148091i
$919$	18.8289	+	18.8289i	0.621109	+	0.621109i	0.945815	−	0.324706i	$-0.105265\pi$
$919$	18.8289	+	18.8289i	0.621109	+	0.621109i	−0.324706	+	0.945815i	$0.605265\pi$
$920$	0.687207	−	0.184137i	0.0226566	−	0.00607081i
$921$	22.0910	+	5.91926i	0.727923	+	0.195046i
$922$		−	1.70665i		−	0.0562056i
$923$	5.28551	−	19.7258i	0.173975	−	0.649283i
$924$	17.1768	+	9.91702i	0.565075	+	0.326246i
$925$			1.42667i			0.0469087i
$926$	−1.21282	+	0.700223i	−0.0398558	+	0.0230108i
$927$	0.160313	+	0.160313i	0.00526538	+	0.00526538i
$928$	2.82038	+	2.82038i	0.0925835	+	0.0925835i
$929$	13.5796	+	50.6799i	0.445534	+	1.66275i	0.714523	+	0.699612i	$0.246644\pi$
$929$	13.5796	+	50.6799i	0.445534	+	1.66275i	−0.268989	+	0.963143i	$0.586690\pi$
$930$	0.0664750	+	0.0383794i	0.00217980	+	0.00125851i
$931$	19.5607	−	33.8802i	0.641078	−	1.11038i
$932$	34.3522	−	34.3522i	1.12524	−	1.12524i
$933$	−10.8687	+	18.8252i	−0.355826	+	0.616309i
$934$	0.129197	−	0.482171i	0.00422746	−	0.0157771i
$935$	−16.8169	−	62.7617i	−0.549973	−	2.05253i
$936$	−0.0157145	+	0.00421068i	−0.000513643	+	0.000137630i
$937$	−12.5538	+	7.24792i	−0.410114	+	0.236779i	−0.690839	−	0.723009i	$-0.742758\pi$
$937$	−12.5538	+	7.24792i	−0.410114	+	0.236779i	0.280725	+	0.959788i	$0.409425\pi$
$938$	−0.196790	+	0.734432i	−0.00642543	+	0.0239800i
$939$	30.3769	−	30.3769i	0.991311	−	0.991311i
$940$	43.1897			1.40869
$941$	6.33171			0.206408			0.103204	−	0.994660i	$-0.467091\pi$
$941$	6.33171			0.206408			0.103204	+	0.994660i	$0.467091\pi$
$942$	1.87257	−	1.87257i	0.0610115	−	0.0610115i
$943$	6.36753	+	3.67629i	0.207355	+	0.119717i
$944$	26.0364	+	6.97643i	0.847413	+	0.227064i
$945$	−8.10226	−	14.0335i	−0.263566	−	0.456510i
$946$			1.63198i			0.0530601i
$947$	−17.0649	+	29.5573i	−0.554535	+	0.960483i	0.443404	+	0.896322i	$0.353771\pi$
$947$	−17.0649	+	29.5573i	−0.554535	+	0.960483i	−0.997940	+	0.0641614i	$0.979563\pi$
$948$	−33.3433			−1.08294
$949$	30.1961	+	20.0757i	0.980208	+	0.651684i
$950$	−1.03595			−0.0336105
$951$	23.5593	−	40.8059i	0.763963	−	1.32322i
$952$			1.55648i			0.0504458i
$953$	−7.28582	−	12.6194i	−0.236011	−	0.408783i	0.723555	−	0.690267i	$-0.242507\pi$
$953$	−7.28582	−	12.6194i	−0.236011	−	0.408783i	−0.959566	+	0.281484i	$0.909173\pi$
$954$	−0.00354099		0.000948805i	−0.000114644		3.07187e-5i
$955$	−32.2914	−	18.6434i	−1.04492	−	0.603287i
$956$	13.4950	−	13.4950i	0.436461	−	0.436461i
$957$	41.9086			1.35471
$958$	−0.0120252			−0.000388517
$959$	9.33902	−	9.33902i	0.301573	−	0.301573i
$960$	−9.51340	+	35.5045i	−0.307044	+	1.14590i
$961$	−26.7958	+	15.4705i	−0.864380	+	0.499050i
$962$	0.180367	−	0.0483293i	0.00581527	−	0.00155820i
$963$	−0.0205748	−	0.0767861i	−0.000663013	−	0.00247440i
$964$	−9.03703	+	33.7267i	−0.291063	+	1.08626i
$965$	14.3266	−	24.8144i	0.461190	−	0.798804i
$966$	−0.0948921	+	0.0948921i	−0.00305310	+	0.00305310i
$967$	5.22036	−	9.04193i	0.167876	−	0.290769i	−0.769797	−	0.638289i	$-0.779643\pi$
$967$	5.22036	−	9.04193i	0.167876	−	0.290769i	0.937673	+	0.347520i	$0.112976\pi$
$968$	−3.09042	−	1.78425i	−0.0993297	−	0.0573480i
$969$	15.3464	+	57.2736i	0.492998	+	1.83989i
$970$	−1.00668	−	1.00668i	−0.0323227	−	0.0323227i
$971$	10.7584	+	10.7584i	0.345254	+	0.345254i	0.858338	−	0.513084i	$-0.171497\pi$
$971$	10.7584	+	10.7584i	0.345254	+	0.345254i	−0.513084	+	0.858338i	$0.671497\pi$
$972$	0.253813	−	0.146539i	0.00814105	−	0.00470024i
$973$			3.38931i			0.108656i
$974$	−0.503836	−	0.290890i	−0.0161439	−	0.00932071i
$975$	−4.19772	+	15.6661i	−0.134435	+	0.501716i
$976$			41.4599i			1.32710i
$977$	−43.7545	−	11.7240i	−1.39983	−	0.375084i	−0.521548	−	0.853222i	$-0.674645\pi$
$977$	−43.7545	−	11.7240i	−1.39983	−	0.375084i	−0.878285	+	0.478138i	$0.841312\pi$
$978$	0.533949	−	0.143071i	0.0170738	−	0.00457491i
$979$	42.2874	+	42.2874i	1.35151	+	1.35151i
$980$	29.1869	−	7.82062i	0.932342	−	0.249820i
$981$	0.0640036	+	0.110857i	0.00204348	+	0.00353941i
$982$	0.964520	+	0.258442i	0.0307791	+	0.00824722i
$983$	−10.0281	−	37.4255i	−0.319847	−	1.19369i	−0.919391	−	0.393345i	$-0.871318\pi$
$983$	−10.0281	−	37.4255i	−0.319847	−	1.19369i	0.599543	−	0.800342i	$-0.295349\pi$
$984$	3.06746	−	1.77100i	0.0977871	−	0.0564574i
$985$	1.11478	+	1.93085i	0.0355197	+	0.0615219i
$986$	0.821249	+	1.42244i	0.0261539	+	0.0452999i
$987$	−14.1268	+	8.15610i	−0.449660	+	0.259611i
$988$	−15.1950	−	56.7085i	−0.483417	−	1.80414i
$989$	4.61817	+	1.23743i	0.146849	+	0.0393481i
$990$	−0.00632724	−	0.0109591i	−0.000201093	−	0.000348303i
$991$	−20.5181	+	5.49781i	−0.651779	+	0.174644i	−0.569533	−	0.821968i	$-0.692876\pi$
$991$	−20.5181	+	5.49781i	−0.651779	+	0.174644i	−0.0822458	+	0.996612i	$0.526209\pi$
$992$	−0.139372	−	0.139372i	−0.00442506	−	0.00442506i
$993$	−23.3704	+	6.26207i	−0.741636	+	0.198721i
$994$	−0.367550	−	0.0984847i	−0.0116580	−	0.00312374i
$995$			65.1770i			2.06625i
$996$	6.79187	−	25.3476i	0.215209	−	0.803169i
$997$	−21.6549	−	12.5024i	−0.685816	−	0.395956i	0.116226	−	0.993223i	$-0.462920\pi$
$997$	−21.6549	−	12.5024i	−0.685816	−	0.395956i	−0.802043	+	0.597266i	$0.796254\pi$
$998$			2.33081i			0.0737805i
$999$	−2.90969	+	1.67991i	−0.0920584	+	0.0531500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.h.a.3.4	✓	20
3.2	odd	2		657.2.be.c.514.2		20
73.7	odd	24		5329.2.a.m.1.8		20
73.49	even	12	inner	73.2.h.a.49.4	yes	20
73.66	odd	24		5329.2.a.m.1.7		20
219.122	odd	12		657.2.be.c.487.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.h.a.3.4	✓	20	1.1	even	1	trivial
73.2.h.a.49.4	yes	20	73.49	even	12	inner
657.2.be.c.487.2		20	219.122	odd	12
657.2.be.c.514.2		20	3.2	odd	2
5329.2.a.m.1.7		20	73.66	odd	24
5329.2.a.m.1.8		20	73.7	odd	24

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:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.h (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0339426 - 0.0587903i) q^{2} +1.73613i q^{3} +(0.997696 + 1.72806i) q^{4} +(-2.59207 - 0.694543i) q^{5} +(0.102067 + 0.0589286i) q^{6} +(0.823696 - 0.823696i) q^{7} +0.271228 q^{8} -0.0141334 q^{9} +O(q^{10})\)	\(q+(0.0339426 - 0.0587903i) q^{2} +1.73613i q^{3} +(0.997696 + 1.72806i) q^{4} +(-2.59207 - 0.694543i) q^{5} +(0.102067 + 0.0589286i) q^{6} +(0.823696 - 0.823696i) q^{7} +0.271228 q^{8} -0.0141334 q^{9} +(-0.128814 + 0.128814i) q^{10} +(1.27209 - 4.74749i) q^{11} +(-3.00013 + 1.73213i) q^{12} +(4.09939 - 1.09843i) q^{13} +(-0.0204669 - 0.0763837i) q^{14} +(1.20581 - 4.50016i) q^{15} +(-1.98619 + 3.44017i) q^{16} +(-3.48348 + 3.48348i) q^{17} +(-0.000479724 + 0.000830906i) q^{18} +(-6.00388 - 3.46634i) q^{19} +(-1.38588 - 5.17219i) q^{20} +(1.43004 + 1.43004i) q^{21} +(-0.235928 - 0.235928i) q^{22} +(-0.846521 + 0.488739i) q^{23} +0.470886i q^{24} +(1.90630 + 1.10060i) q^{25} +(0.0745669 - 0.278287i) q^{26} +5.18384i q^{27} +(2.24519 + 0.601598i) q^{28} +(4.74401 - 1.27115i) q^{29} +(-0.223637 - 0.223637i) q^{30} +(-0.234430 + 0.0628153i) q^{31} +(0.406060 + 0.703317i) q^{32} +(8.24224 + 2.20850i) q^{33} +(0.0865564 + 0.323033i) q^{34} +(-2.70717 + 1.56298i) q^{35} +(-0.0141008 - 0.0244233i) q^{36} +(0.324066 + 0.561299i) q^{37} +(-0.407574 + 0.235313i) q^{38} +(1.90701 + 7.11705i) q^{39} +(-0.703041 - 0.188379i) q^{40} +(-3.76100 - 6.51424i) q^{41} +(0.132612 - 0.0355332i) q^{42} +(-3.45863 - 3.45863i) q^{43} +(9.47310 - 2.53831i) q^{44} +(0.0366347 + 0.00981624i) q^{45} +0.0663563i q^{46} +(-2.08759 + 7.79100i) q^{47} +(-5.97258 - 3.44827i) q^{48} +5.64305i q^{49} +(0.129410 - 0.0747146i) q^{50} +(-6.04775 - 6.04775i) q^{51} +(5.98809 + 5.98809i) q^{52} +(0.988907 + 3.69065i) q^{53} +(0.304759 + 0.175953i) q^{54} +(-6.59467 + 11.4223i) q^{55} +(0.223409 - 0.223409i) q^{56} +(6.01801 - 10.4235i) q^{57} +(0.0862925 - 0.322048i) q^{58} +(-1.75624 - 6.55437i) q^{59} +(8.97957 - 2.40607i) q^{60} +(9.03876 - 5.21853i) q^{61} +(-0.00426423 + 0.0159143i) q^{62} +(-0.0116416 + 0.0116416i) q^{63} -7.88961 q^{64} -11.3888 q^{65} +(0.409601 - 0.409601i) q^{66} +(-8.32687 - 4.80752i) q^{67} +(-9.49511 - 2.54421i) q^{68} +(-0.848513 - 1.46967i) q^{69} +0.212207i q^{70} +(2.40595 - 4.16722i) q^{71} -0.00383337 q^{72} +(5.64828 + 6.41069i) q^{73} +0.0439986 q^{74} +(-1.91079 + 3.30958i) q^{75} -13.8334i q^{76} +(-2.86267 - 4.95830i) q^{77} +(0.483142 + 0.129458i) q^{78} +(8.33547 + 4.81249i) q^{79} +(7.53767 - 7.53767i) q^{80} -9.04220 q^{81} -0.510632 q^{82} +(-5.35635 + 5.35635i) q^{83} +(-1.04445 + 3.89794i) q^{84} +(11.4488 - 6.60998i) q^{85} +(-0.320729 + 0.0859390i) q^{86} +(2.20688 + 8.23620i) q^{87} +(0.345025 - 1.28765i) q^{88} +(-6.08382 + 10.5375i) q^{89} +(0.00182058 - 0.00182058i) q^{90} +(2.47188 - 4.28142i) q^{91} +(-1.68914 - 0.975226i) q^{92} +(-0.109055 - 0.407000i) q^{93} +(0.387177 + 0.387177i) q^{94} +(13.1549 + 13.1549i) q^{95} +(-1.22105 + 0.704972i) q^{96} +7.81504i q^{97} +(0.331757 + 0.191540i) q^{98} +(-0.0179789 + 0.0670981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9	\( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9} - 12 q^{10} - 6 q^{11} + 30 q^{12} - 16 q^{13} - 8 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{18} - 12 q^{19} + 8 q^{20} + 24 q^{21} + 8 q^{22} - 6 q^{23} - 36 q^{25} - 36 q^{26} - 12 q^{28} - 6 q^{29} + 34 q^{30} + 20 q^{31} - 6 q^{32} + 34 q^{33} + 36 q^{34} + 18 q^{35} + 18 q^{36} - 8 q^{37} - 66 q^{38} + 28 q^{39} - 2 q^{40} + 10 q^{41} - 56 q^{42} + 12 q^{43} + 34 q^{44} - 4 q^{45} - 20 q^{47} - 48 q^{48} + 30 q^{50} - 36 q^{51} + 80 q^{52} + 24 q^{53} + 24 q^{54} + 10 q^{55} + 10 q^{57} + 54 q^{58} - 18 q^{59} + 50 q^{60} + 42 q^{61} - 12 q^{62} - 48 q^{63} - 56 q^{64} - 44 q^{65} - 10 q^{66} - 42 q^{67} - 44 q^{68} + 24 q^{69} + 4 q^{71} - 112 q^{72} - 16 q^{73} - 96 q^{74} - 52 q^{75} + 52 q^{77} - 12 q^{78} + 54 q^{79} - 2 q^{80} + 60 q^{81} + 32 q^{82} - 30 q^{83} - 16 q^{84} + 6 q^{85} + 16 q^{86} + 32 q^{87} + 2 q^{88} - 22 q^{89} - 110 q^{90} - 8 q^{91} - 78 q^{92} + 78 q^{93} + 38 q^{94} + 38 q^{95} + 72 q^{96} + 138 q^{98} - 32 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 + 6 * q^6 - 2 * q^7 + 12 * q^8 - 32 * q^9 - 12 * q^10 - 6 * q^11 + 30 * q^12 - 16 * q^13 - 8 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^18 - 12 * q^19 + 8 * q^20 + 24 * q^21 + 8 * q^22 - 6 * q^23 - 36 * q^25 - 36 * q^26 - 12 * q^28 - 6 * q^29 + 34 * q^30 + 20 * q^31 - 6 * q^32 + 34 * q^33 + 36 * q^34 + 18 * q^35 + 18 * q^36 - 8 * q^37 - 66 * q^38 + 28 * q^39 - 2 * q^40 + 10 * q^41 - 56 * q^42 + 12 * q^43 + 34 * q^44 - 4 * q^45 - 20 * q^47 - 48 * q^48 + 30 * q^50 - 36 * q^51 + 80 * q^52 + 24 * q^53 + 24 * q^54 + 10 * q^55 + 10 * q^57 + 54 * q^58 - 18 * q^59 + 50 * q^60 + 42 * q^61 - 12 * q^62 - 48 * q^63 - 56 * q^64 - 44 * q^65 - 10 * q^66 - 42 * q^67 - 44 * q^68 + 24 * q^69 + 4 * q^71 - 112 * q^72 - 16 * q^73 - 96 * q^74 - 52 * q^75 + 52 * q^77 - 12 * q^78 + 54 * q^79 - 2 * q^80 + 60 * q^81 + 32 * q^82 - 30 * q^83 - 16 * q^84 + 6 * q^85 + 16 * q^86 + 32 * q^87 + 2 * q^88 - 22 * q^89 - 110 * q^90 - 8 * q^91 - 78 * q^92 + 78 * q^93 + 38 * q^94 + 38 * q^95 + 72 * q^96 + 138 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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