LMFDB - Embedded newform 378.2.u.c.211.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.4
Character	$\chi$	$=$	378.211
Dual form			378.2.u.c.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.992383 - 1.41957i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.999746 - 0.363878i) q^{5} +(0.152272 + 1.72534i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.03035 - 2.81751i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.992383 - 1.41957i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.999746 - 0.363878i) q^{5} +(0.152272 + 1.72534i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.03035 - 2.81751i) q^{9} +(-0.531954 + 0.921371i) q^{10} +(4.14487 + 1.50861i) q^{11} +(-1.22568 - 1.22381i) q^{12} +(-2.35223 - 1.97375i) q^{13} +(0.766044 + 0.642788i) q^{14} +(0.475581 - 1.78032i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.333922 - 0.578370i) q^{17} +(2.60036 + 1.49604i) q^{18} +(0.367774 + 0.637002i) q^{19} +(-0.184746 - 1.04774i) q^{20} +(-1.57033 - 0.730800i) q^{21} +(-4.14487 + 1.50861i) q^{22} +(1.18685 - 6.73094i) q^{23} +(1.72557 + 0.149644i) q^{24} +(-2.96314 + 2.48637i) q^{25} +3.07061 q^{26} +(-5.02216 - 1.33339i) q^{27} -1.00000 q^{28} +(1.43546 - 1.20450i) q^{29} +(0.780049 + 1.66950i) q^{30} +(-0.0404103 + 0.229178i) q^{31} +(0.939693 - 0.342020i) q^{32} +(6.25488 - 4.38681i) q^{33} +(0.115970 + 0.657698i) q^{34} +(-0.531954 - 0.921371i) q^{35} +(-2.95363 + 0.525444i) q^{36} +(3.60010 - 6.23556i) q^{37} +(-0.691188 - 0.251572i) q^{38} +(-5.13619 + 1.38043i) q^{39} +(0.815001 + 0.683867i) q^{40} +(8.28814 + 6.95458i) q^{41} +(1.67269 - 0.449562i) q^{42} +(-7.07332 - 2.57448i) q^{43} +(2.20544 - 3.81993i) q^{44} +(-2.05532 - 2.44187i) q^{45} +(3.41739 + 5.91909i) q^{46} +(1.85542 + 10.5226i) q^{47} +(-1.41806 + 0.994544i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.671688 - 3.80933i) q^{50} +(-0.489658 - 1.04799i) q^{51} +(-2.35223 + 1.97375i) q^{52} +11.1071 q^{53} +(4.70428 - 2.20674i) q^{54} +4.69277 q^{55} +(0.766044 - 0.642788i) q^{56} +(1.26924 + 0.110070i) q^{57} +(-0.325393 + 1.84540i) q^{58} +(-7.20444 + 2.62220i) q^{59} +(-1.67068 - 0.777504i) q^{60} +(0.0669610 + 0.379755i) q^{61} +(-0.116357 - 0.201536i) q^{62} +(-2.59579 + 1.50396i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.06984 - 1.11733i) q^{65} +(-1.97172 + 7.38105i) q^{66} +(5.54826 + 4.65554i) q^{67} +(-0.511599 - 0.429282i) q^{68} +(-8.37723 - 8.36448i) q^{69} +(0.999746 + 0.363878i) q^{70} +(0.205419 - 0.355795i) q^{71} +(1.92486 - 2.30107i) q^{72} +(5.24172 + 9.07893i) q^{73} +(1.25030 + 7.09082i) q^{74} +(0.589005 + 6.67380i) q^{75} +(0.691188 - 0.251572i) q^{76} +(0.765941 - 4.34387i) q^{77} +(3.04722 - 4.35895i) q^{78} +(-8.60212 + 7.21804i) q^{79} -1.06391 q^{80} +(-6.87674 + 5.80607i) q^{81} -10.8194 q^{82} +(-9.01536 + 7.56478i) q^{83} +(-0.992383 + 1.41957i) q^{84} +(0.123381 - 0.699731i) q^{85} +(7.07332 - 2.57448i) q^{86} +(-0.285338 - 3.23306i) q^{87} +(0.765941 + 4.34387i) q^{88} +(-0.612505 - 1.06089i) q^{89} +(3.14408 + 0.549448i) q^{90} +(-1.53531 + 2.65923i) q^{91} +(-6.42259 - 2.33763i) q^{92} +(0.285232 + 0.284798i) q^{93} +(-8.18514 - 6.86814i) q^{94} +(0.599471 + 0.503016i) q^{95} +(0.447013 - 1.67337i) q^{96} +(-14.0822 - 5.12551i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-0.0201572 - 13.2326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.992383	−	1.41957i	0.572952	−	0.819589i
$3$	0.992383	−	1.41957i	0.572952	−	0.819589i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.999746	−	0.363878i	0.447100	−	0.162731i	−0.108651	−	0.994080i	$-0.534653\pi$
$5$	0.999746	−	0.363878i	0.447100	−	0.162731i	0.555751	+	0.831349i	$0.312431\pi$
$6$	0.152272	+	1.72534i	0.0621649	+	0.704369i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.03035	−	2.81751i	−0.343451	−	0.939171i
$10$	−0.531954	+	0.921371i	−0.168219	+	0.291363i
$11$	4.14487	+	1.50861i	1.24973	+	0.454863i	0.880309	−	0.474401i	$-0.157335\pi$
$11$	4.14487	+	1.50861i	1.24973	+	0.454863i	0.369417	+	0.929264i	$0.379557\pi$
$12$	−1.22568	−	1.22381i	−0.353823	−	0.353284i
$13$	−2.35223	−	1.97375i	−0.652390	−	0.547421i	0.255405	−	0.966834i	$-0.417791\pi$
$13$	−2.35223	−	1.97375i	−0.652390	−	0.547421i	−0.907795	+	0.419414i	$0.862236\pi$
$14$	0.766044	+	0.642788i	0.204734	+	0.171792i
$15$	0.475581	−	1.78032i	0.122795	−	0.459675i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.333922	−	0.578370i	0.0809880	−	0.140275i	−0.822687	−	0.568495i	$-0.807526\pi$
$17$	0.333922	−	0.578370i	0.0809880	−	0.140275i	0.903675	+	0.428220i	$0.140859\pi$
$18$	2.60036	+	1.49604i	0.612910	+	0.352620i
$19$	0.367774	+	0.637002i	0.0843730	+	0.146138i	0.905124	−	0.425148i	$-0.139778\pi$
$19$	0.367774	+	0.637002i	0.0843730	+	0.146138i	−0.820751	+	0.571286i	$0.806445\pi$
$20$	−0.184746	−	1.04774i	−0.0413104	−	0.234283i
$21$	−1.57033	−	0.730800i	−0.342674	−	0.159474i
$22$	−4.14487	+	1.50861i	−0.883690	+	0.321637i
$23$	1.18685	−	6.73094i	0.247475	−	1.40350i	−0.567200	−	0.823580i	$-0.691973\pi$
$23$	1.18685	−	6.73094i	0.247475	−	1.40350i	0.814675	−	0.579918i	$-0.196915\pi$
$24$	1.72557	+	0.149644i	0.352231	+	0.0305459i
$25$	−2.96314	+	2.48637i	−0.592627	+	0.497273i
$26$	3.07061			0.602197
$27$	−5.02216	−	1.33339i	−0.966515	−	0.256611i
$28$	−1.00000			−0.188982
$29$	1.43546	−	1.20450i	0.266559	−	0.223670i	−0.499705	−	0.866196i	$-0.666558\pi$
$29$	1.43546	−	1.20450i	0.266559	−	0.223670i	0.766264	+	0.642526i	$0.222114\pi$
$30$	0.780049	+	1.66950i	0.142417	+	0.304807i
$31$	−0.0404103	+	0.229178i	−0.00725790	+	0.0411616i	−0.988222	−	0.153029i	$-0.951097\pi$
$31$	−0.0404103	+	0.229178i	−0.00725790	+	0.0411616i	0.980964	+	0.194191i	$0.0622082\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	6.25488	−	4.38681i	1.08883	−	0.763646i
$34$	0.115970	+	0.657698i	0.0198887	+	0.112794i
$35$	−0.531954	−	0.921371i	−0.0899166	−	0.155740i
$36$	−2.95363	+	0.525444i	−0.492271	+	0.0875741i
$37$	3.60010	−	6.23556i	0.591854	−	1.02512i	−0.402129	−	0.915583i	$-0.631730\pi$
$37$	3.60010	−	6.23556i	0.591854	−	1.02512i	0.993983	−	0.109537i	$-0.0349370\pi$
$38$	−0.691188	−	0.251572i	−0.112126	−	0.0408104i
$39$	−5.13619	+	1.38043i	−0.822448	+	0.221046i
$40$	0.815001	+	0.683867i	0.128863	+	0.108129i
$41$	8.28814	+	6.95458i	1.29439	+	1.08612i	0.991085	+	0.133229i	$0.0425347\pi$
$41$	8.28814	+	6.95458i	1.29439	+	1.08612i	0.303305	+	0.952893i	$0.401910\pi$
$42$	1.67269	−	0.449562i	0.258102	−	0.0693689i
$43$	−7.07332	−	2.57448i	−1.07867	−	0.392604i	−0.259258	−	0.965808i	$-0.583478\pi$
$43$	−7.07332	−	2.57448i	−1.07867	−	0.392604i	−0.819413	+	0.573204i	$0.805700\pi$
$44$	2.20544	−	3.81993i	0.332483	−	0.575877i
$45$	−2.05532	−	2.44187i	−0.306389	−	0.364013i
$46$	3.41739	+	5.91909i	0.503866	+	0.872722i
$47$	1.85542	+	10.5226i	0.270641	+	1.53488i	0.752477	+	0.658619i	$0.228859\pi$
$47$	1.85542	+	10.5226i	0.270641	+	1.53488i	−0.481836	+	0.876261i	$0.660030\pi$
$48$	−1.41806	+	0.994544i	−0.204679	+	0.143550i
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	0.671688	−	3.80933i	0.0949911	−	0.538721i
$51$	−0.489658	−	1.04799i	−0.0685658	−	0.146748i
$52$	−2.35223	+	1.97375i	−0.326195	+	0.273710i
$53$	11.1071			1.52568			0.762839	−	0.646588i	$-0.223805\pi$
$53$	11.1071			1.52568			0.762839	+	0.646588i	$0.223805\pi$
$54$	4.70428	−	2.20674i	0.640172	−	0.300300i
$55$	4.69277			0.632773
$56$	0.766044	−	0.642788i	0.102367	−	0.0858961i
$57$	1.26924	+	0.110070i	0.168115	+	0.0145791i
$58$	−0.325393	+	1.84540i	−0.0427262	+	0.242312i
$59$	−7.20444	+	2.62220i	−0.937939	+	0.341382i	−0.765351	−	0.643613i	$-0.777435\pi$
$59$	−7.20444	+	2.62220i	−0.937939	+	0.341382i	−0.172587	+	0.984994i	$0.555213\pi$
$60$	−1.67068	−	0.777504i	−0.215684	−	0.100375i
$61$	0.0669610	+	0.379755i	0.00857348	+	0.0486226i	0.988794	−	0.149284i	$-0.0476968\pi$
$61$	0.0669610	+	0.379755i	0.00857348	+	0.0486226i	−0.980221	+	0.197907i	$0.936586\pi$
$62$	−0.116357	−	0.201536i	−0.0147773	−	0.0255951i
$63$	−2.59579	+	1.50396i	−0.327039	+	0.189481i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−3.06984	−	1.11733i	−0.380766	−	0.138588i
$66$	−1.97172	+	7.38105i	−0.242702	+	0.908545i
$67$	5.54826	+	4.65554i	0.677828	+	0.568765i	0.915371	−	0.402612i	$-0.131898\pi$
$67$	5.54826	+	4.65554i	0.677828	+	0.568765i	−0.237543	+	0.971377i	$0.576342\pi$
$68$	−0.511599	−	0.429282i	−0.0620404	−	0.0520581i
$69$	−8.37723	−	8.36448i	−1.00850	−	1.00696i
$70$	0.999746	+	0.363878i	0.119493	+	0.0434917i
$71$	0.205419	−	0.355795i	0.0243787	−	0.0422252i	−0.853579	−	0.520964i	$-0.825573\pi$
$71$	0.205419	−	0.355795i	0.0243787	−	0.0422252i	0.877957	+	0.478739i	$0.158906\pi$
$72$	1.92486	−	2.30107i	0.226847	−	0.271183i
$73$	5.24172	+	9.07893i	0.613497	+	1.06261i	0.990646	+	0.136455i	$0.0435711\pi$
$73$	5.24172	+	9.07893i	0.613497	+	1.06261i	−0.377149	+	0.926153i	$0.623096\pi$
$74$	1.25030	+	7.09082i	0.145345	+	0.824291i
$75$	0.589005	+	6.67380i	0.0680124	+	0.770625i
$76$	0.691188	−	0.251572i	0.0792847	−	0.0288573i
$77$	0.765941	−	4.34387i	0.0872871	−	0.495030i
$78$	3.04722	−	4.35895i	0.345030	−	0.493554i
$79$	−8.60212	+	7.21804i	−0.967814	+	0.812092i	−0.982207	−	0.187804i	$-0.939863\pi$
$79$	−8.60212	+	7.21804i	−0.967814	+	0.812092i	0.0143925	+	0.999896i	$0.495419\pi$
$80$	−1.06391			−0.118949
$81$	−6.87674	+	5.80607i	−0.764083	+	0.645118i
$82$	−10.8194			−1.19480
$83$	−9.01536	+	7.56478i	−0.989564	+	0.830343i	−0.985505	−	0.169649i	$-0.945737\pi$
$83$	−9.01536	+	7.56478i	−0.989564	+	0.830343i	−0.00405960	+	0.999992i	$0.501292\pi$
$84$	−0.992383	+	1.41957i	−0.108278	+	0.154888i
$85$	0.123381	−	0.699731i	0.0133826	−	0.0758964i
$86$	7.07332	−	2.57448i	0.762735	−	0.277613i
$87$	−0.285338	−	3.23306i	−0.0305914	−	0.346621i
$88$	0.765941	+	4.34387i	0.0816496	+	0.463058i
$89$	−0.612505	−	1.06089i	−0.0649254	−	0.112454i	0.831735	−	0.555172i	$-0.187348\pi$
$89$	−0.612505	−	1.06089i	−0.0649254	−	0.112454i	−0.896661	+	0.442718i	$0.854014\pi$
$90$	3.14408	+	0.549448i	0.331415	+	0.0579169i
$91$	−1.53531	+	2.65923i	−0.160944	+	0.278763i
$92$	−6.42259	−	2.33763i	−0.669601	−	0.243715i
$93$	0.285232	+	0.284798i	0.0295772	+	0.0295321i
$94$	−8.18514	−	6.86814i	−0.844232	−	0.708395i
$95$	0.599471	+	0.503016i	0.0615045	+	0.0516084i
$96$	0.447013	−	1.67337i	0.0456231	−	0.170788i
$97$	−14.0822	−	5.12551i	−1.42983	−	0.520416i	−0.492949	−	0.870058i	$-0.664081\pi$
$97$	−14.0822	−	5.12551i	−1.42983	−	0.520416i	−0.936883	+	0.349642i	$0.886303\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−0.0201572	−	13.2326i	−0.00202587	−	1.32993i
$100$	1.93405	+	3.34987i	0.193405	+	0.334987i
$101$	0.747532	+	4.23947i	0.0743822	+	0.421843i	0.999147	+	0.0413026i	$0.0131508\pi$
$101$	0.747532	+	4.23947i	0.0743822	+	0.421843i	−0.924764	+	0.380540i	$0.875738\pi$
$102$	1.04874	+	0.488061i	0.103840	+	0.0483252i
$103$	−2.94863	+	1.07321i	−0.290537	+	0.105747i	−0.483177	−	0.875523i	$-0.660517\pi$
$103$	−2.94863	+	1.07321i	−0.290537	+	0.105747i	0.192640	+	0.981269i	$0.438295\pi$
$104$	0.533207	−	3.02396i	0.0522852	−	0.296524i
$105$	−1.83585	−	0.159207i	−0.179161	−	0.0155371i
$106$	−8.50854	+	7.13951i	−0.826422	+	0.693451i
$107$	−12.2844			−1.18758			−0.593788	−	0.804622i	$-0.702368\pi$
$107$	−12.2844			−1.18758			−0.593788	+	0.804622i	$0.702368\pi$
$108$	−2.18522	+	4.71432i	−0.210273	+	0.453636i
$109$	12.5809			1.20503			0.602515	−	0.798107i	$-0.294165\pi$
$109$	12.5809			1.20503			0.602515	+	0.798107i	$0.294165\pi$
$110$	−3.59487	+	3.01646i	−0.342758	+	0.287608i
$111$	−5.27913	−	11.2987i	−0.501073	−	1.07242i
$112$	−0.173648	+	0.984808i	−0.0164082	+	0.0930556i
$113$	2.16706	−	0.788745i	0.203860	−	0.0741989i	−0.238072	−	0.971247i	$-0.576515\pi$
$113$	2.16706	−	0.788745i	0.203860	−	0.0741989i	0.441932	+	0.897049i	$0.354293\pi$
$114$	−1.04305	+	0.731534i	−0.0976903	+	0.0685144i
$115$	−1.26270	−	7.16110i	−0.117747	−	0.667776i
$116$	−0.936933	−	1.62281i	−0.0869920	−	0.150675i
$117$	−3.13745	+	8.66109i	−0.290057	+	0.800718i
$118$	3.83340	−	6.63965i	0.352893	−	0.611229i
$119$	−0.627569	−	0.228416i	−0.0575291	−	0.0209389i
$120$	1.77959	−	0.478292i	0.162454	−	0.0436619i
$121$	6.47757	+	5.43533i	0.588870	+	0.494121i
$122$	−0.295397	−	0.247867i	−0.0267440	−	0.0224409i
$123$	18.0975	−	4.86399i	1.63180	−	0.438571i
$124$	0.218679	+	0.0795927i	0.0196380	+	0.00714764i
$125$	−4.71742	+	8.17081i	−0.421939	+	0.730820i
$126$	1.02176	−	2.82064i	0.0910261	−	0.251282i
$127$	5.52258	+	9.56539i	0.490050	+	0.848791i	0.999934	−	0.0114517i	$-0.00364528\pi$
$127$	5.52258	+	9.56539i	0.490050	+	0.848791i	−0.509885	+	0.860243i	$0.670312\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−10.6741	+	7.48620i	−0.939801	+	0.659123i
$130$	3.06984	−	1.11733i	0.269242	−	0.0979962i
$131$	−2.64328	+	14.9908i	−0.230945	+	1.30975i	0.620043	+	0.784567i	$0.287115\pi$
$131$	−2.64328	+	14.9908i	−0.230945	+	1.30975i	−0.850988	+	0.525185i	$0.823996\pi$
$132$	−3.23402	−	6.92161i	−0.281485	−	0.602449i
$133$	0.563462	−	0.472801i	0.0488583	−	0.0409970i
$134$	−7.24274			−0.625677
$135$	−5.50608	+	0.494399i	−0.473888	+	0.0425511i
$136$	0.667844			0.0572672
$137$	−1.82317	+	1.52982i	−0.155764	+	0.130702i	−0.717339	−	0.696724i	$-0.754640\pi$
$137$	−1.82317	+	1.52982i	−0.155764	+	0.130702i	0.561575	+	0.827426i	$0.310196\pi$
$138$	11.7939	+	1.02278i	1.00396	+	0.0870650i
$139$	0.157987	−	0.895989i	0.0134003	−	0.0759968i	−0.977374	−	0.211517i	$-0.932160\pi$
$139$	0.157987	−	0.895989i	0.0134003	−	0.0759968i	0.990775	+	0.135520i	$0.0432707\pi$
$140$	−0.999746	+	0.363878i	−0.0844940	+	0.0307533i
$141$	16.7789	+	7.80856i	1.41303	+	0.657599i
$142$	0.0713411	+	0.404596i	0.00598681	+	0.0339529i
$143$	−6.77206	−	11.7295i	−0.566308	−	0.980874i
$144$	0.00456987	+	3.00000i	0.000380823	+	0.250000i
$145$	0.996810	−	1.72653i	0.0827806	−	0.143380i
$146$	−9.85121	−	3.58555i	−0.815292	−	0.296742i
$147$	−0.447013	+	1.67337i	−0.0368690	+	0.138018i
$148$	−5.51568	−	4.62821i	−0.453386	−	0.380436i
$149$	12.1371	+	10.1842i	0.994311	+	0.834326i	0.986186	−	0.165641i	$-0.0529693\pi$
$149$	12.1371	+	10.1842i	0.994311	+	0.834326i	0.00812481	+	0.999967i	$0.497414\pi$
$150$	−4.74104	−	4.73383i	−0.387104	−	0.386515i
$151$	14.1760	+	5.15962i	1.15362	+	0.419884i	0.846815	−	0.531887i	$-0.178517\pi$
$151$	14.1760	+	5.15962i	1.15362	+	0.419884i	0.306807	+	0.951772i	$0.400739\pi$
$152$	−0.367774	+	0.637002i	−0.0298304	+	0.0516677i
$153$	−1.97362	−	0.344904i	−0.159558	−	0.0278838i
$154$	2.20544	+	3.81993i	0.177719	+	0.307819i
$155$	0.0429928	+	0.243824i	0.00345327	+	0.0195844i
$156$	0.467570	+	5.29787i	0.0374355	+	0.424169i
$157$	17.3674	−	6.32120i	1.38607	−	0.504487i	0.462054	−	0.886852i	$-0.347112\pi$
$157$	17.3674	−	6.32120i	1.38607	−	0.504487i	0.924011	+	0.382365i	$0.124890\pi$
$158$	1.94994	−	11.0587i	0.155129	−	0.879781i
$159$	11.0225	−	15.7673i	0.874141	−	1.25043i
$160$	0.815001	−	0.683867i	0.0644315	−	0.0540644i
$161$	−6.83478			−0.538656
$162$	1.53582	−	8.86799i	0.120666	−	0.696735i
$163$	−2.65571			−0.208011			−0.104006	−	0.994577i	$-0.533166\pi$
$163$	−2.65571			−0.208011			−0.104006	+	0.994577i	$0.533166\pi$
$164$	8.28814	−	6.95458i	0.647195	−	0.543061i
$165$	4.65702	−	6.66171i	0.362549	−	0.518614i
$166$	2.04362	−	11.5899i	0.158615	−	0.899552i
$167$	7.12245	−	2.59236i	0.551152	−	0.200603i	−0.0514062	−	0.998678i	$-0.516370\pi$
$167$	7.12245	−	2.59236i	0.551152	−	0.200603i	0.602558	+	0.798075i	$0.294148\pi$
$168$	−0.152272	−	1.72534i	−0.0117481	−	0.133113i
$169$	−0.620155	−	3.51707i	−0.0477042	−	0.270544i
$170$	0.355263	+	0.615333i	0.0272474	+	0.0471939i
$171$	1.41583	−	1.69254i	0.108271	−	0.129432i
$172$	−3.76363	+	6.51880i	−0.286974	+	0.497054i
$173$	1.15853	+	0.421672i	0.0880816	+	0.0320591i	0.385685	−	0.922630i	$-0.373965\pi$
$173$	1.15853	+	0.421672i	0.0880816	+	0.0320591i	−0.297603	+	0.954690i	$0.596187\pi$
$174$	2.29675	+	2.29326i	0.174116	+	0.173851i
$175$	2.96314	+	2.48637i	0.223992	+	0.187952i
$176$	−3.37893	−	2.83526i	−0.254696	−	0.213716i
$177$	−3.42717	+	12.8294i	−0.257602	+	0.964319i
$178$	1.15113	+	0.418978i	0.0862811	+	0.0314037i
$179$	2.98541	−	5.17087i	0.223140	−	0.386489i	−0.732620	−	0.680638i	$-0.761703\pi$
$179$	2.98541	−	5.17087i	0.223140	−	0.386489i	0.955760	+	0.294149i	$0.0950361\pi$
$180$	−2.76168	+	1.60007i	−0.205843	+	0.119262i
$181$	−0.971728	−	1.68308i	−0.0722279	−	0.125102i	0.827650	−	0.561245i	$-0.189678\pi$
$181$	−0.971728	−	1.68308i	−0.0722279	−	0.125102i	−0.899877	+	0.436143i	$0.856344\pi$
$182$	−0.533207	−	3.02396i	−0.0395239	−	0.224151i
$183$	0.605539	+	0.281806i	0.0447628	+	0.0208317i
$184$	6.42259	−	2.33763i	0.473479	−	0.172332i
$185$	1.33021	−	7.54398i	0.0977988	−	0.554645i
$186$	−0.401565	−	0.0348242i	−0.0294441	−	0.00255343i
$187$	2.25660	−	1.89351i	0.165019	−	0.138467i
$188$	10.6849			0.779279
$189$	−0.441046	+	5.17740i	−0.0320814	+	0.376600i
$190$	−0.782554			−0.0567725
$191$	−7.80553	+	6.54962i	−0.564788	+	0.473914i	−0.879912	−	0.475137i	$-0.842398\pi$
$191$	−7.80553	+	6.54962i	−0.564788	+	0.473914i	0.315124	+	0.949051i	$0.397954\pi$
$192$	0.733192	+	1.56921i	0.0529136	+	0.113248i
$193$	3.82928	−	21.7169i	0.275637	−	1.56322i	−0.461293	−	0.887248i	$-0.652614\pi$
$193$	3.82928	−	21.7169i	0.275637	−	1.56322i	0.736930	−	0.675969i	$-0.236275\pi$
$194$	14.0822	−	5.12551i	1.01104	−	0.367990i
$195$	−4.63258	+	3.24903i	−0.331746	+	0.232668i
$196$	0.173648	+	0.984808i	0.0124034	+	0.0703434i
$197$	1.93036	+	3.34348i	0.137532	+	0.238213i	0.926562	−	0.376142i	$-0.122750\pi$
$197$	1.93036	+	3.34348i	0.137532	+	0.238213i	−0.789030	+	0.614355i	$0.789416\pi$
$198$	8.52121	+	10.1238i	0.605576	+	0.719469i
$199$	8.39641	−	14.5430i	0.595206	−	1.03093i	−0.398312	−	0.917250i	$-0.630404\pi$
$199$	8.39641	−	14.5430i	0.595206	−	1.03093i	0.993518	−	0.113676i	$-0.0362627\pi$
$200$	−3.63482	−	1.32297i	−0.257021	−	0.0935480i
$201$	12.1149	−	3.25606i	0.854516	−	0.229665i
$202$	−3.29772	−	2.76711i	−0.232027	−	0.194694i
$203$	−1.43546	−	1.20450i	−0.100750	−	0.0845391i
$204$	−1.11710	+	0.300237i	−0.0782125	+	0.0210208i
$205$	10.8167	+	3.93694i	0.755468	+	0.274968i
$206$	1.56893	−	2.71747i	0.109313	−	0.189335i
$207$	−20.1874	+	3.59129i	−1.40312	+	0.249612i
$208$	1.53531	+	2.65923i	0.106454	+	0.184384i
$209$	0.563386	+	3.19512i	0.0389702	+	0.221011i
$210$	1.50868	−	1.05810i	0.104109	−	0.0730161i
$211$	−14.4386	+	5.25523i	−0.993996	+	0.361785i	−0.787266	−	0.616613i	$-0.788504\pi$
$211$	−14.4386	+	5.25523i	−0.993996	+	0.361785i	−0.206730	+	0.978398i	$0.566282\pi$
$212$	1.92873	−	10.9384i	0.132466	−	0.751250i
$213$	−0.301222	−	0.644691i	−0.0206394	−	0.0441735i
$214$	9.41038	−	7.89624i	0.643280	−	0.539776i
$215$	−8.00832			−0.546163
$216$	−1.35633	−	5.01601i	−0.0922864	−	0.341296i
$217$	0.232714			0.0157976
$218$	−9.63752	+	8.08684i	−0.652735	+	0.547710i
$219$	18.0900	+	1.56878i	1.22241	+	0.106009i
$220$	0.814891	−	4.62148i	0.0549400	−	0.311580i
$221$	−1.92702	+	0.701378i	−0.129625	+	0.0471798i
$222$	11.3067	+	5.26192i	0.758855	+	0.353157i
$223$	−2.95541	−	16.7610i	−0.197909	−	1.12240i	−0.908215	−	0.418505i	$-0.862554\pi$
$223$	−2.95541	−	16.7610i	−0.197909	−	1.12240i	0.710305	−	0.703894i	$-0.248557\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	10.0584	+	5.78683i	0.670563	+	0.385789i
$226$	−1.15307	+	1.99717i	−0.0767009	+	0.132850i
$227$	3.09708	+	1.12725i	0.205561	+	0.0748179i	0.442748	−	0.896646i	$-0.354003\pi$
$227$	3.09708	+	1.12725i	0.205561	+	0.0748179i	−0.237188	+	0.971464i	$0.576226\pi$
$228$	0.328799	−	1.23085i	0.0217753	−	0.0815147i
$229$	−4.20096	−	3.52502i	−0.277607	−	0.232940i	0.493344	−	0.869834i	$-0.335774\pi$
$229$	−4.20096	−	3.52502i	−0.277607	−	0.232940i	−0.770951	+	0.636894i	$0.780219\pi$
$230$	5.57035	+	4.67408i	0.367298	+	0.308199i
$231$	−5.40632	−	5.39809i	−0.355710	−	0.355168i
$232$	1.76086	+	0.640900i	0.115606	+	0.0420771i
$233$	13.0803	−	22.6557i	0.856917	−	1.48422i	−0.0179391	−	0.999839i	$-0.505710\pi$
$233$	13.0803	−	22.6557i	0.856917	−	1.48422i	0.874856	−	0.484384i	$-0.160956\pi$
$234$	−3.16382	−	8.65149i	−0.206825	−	0.565566i
$235$	5.68389	+	9.84479i	0.370776	+	0.642204i
$236$	1.33133	+	7.55033i	0.0866620	+	0.491485i
$237$	1.70991	+	19.3744i	0.111070	+	1.25850i
$238$	0.627569	−	0.228416i	0.0406792	−	0.0148060i
$239$	−0.390571	+	2.21504i	−0.0252639	+	0.143279i	−0.994831	−	0.101549i	$-0.967620\pi$
$239$	−0.390571	+	2.21504i	−0.0252639	+	0.143279i	0.969567	+	0.244828i	$0.0787313\pi$
$240$	−1.05580	+	1.51029i	−0.0681518	+	0.0974889i
$241$	−15.1627	+	12.7230i	−0.976716	+	0.819562i	−0.983591	−	0.180415i	$-0.942256\pi$
$241$	−15.1627	+	12.7230i	−0.976716	+	0.819562i	0.00687501	+	0.999976i	$0.497812\pi$
$242$	−8.45587			−0.543564
$243$	1.41775	+	15.5239i	0.0909488	+	0.995856i
$244$	0.385613			0.0246864
$245$	−0.815001	+	0.683867i	−0.0520685	+	0.0436907i
$246$	−10.7370	+	15.3589i	−0.684565	+	0.979247i
$247$	0.392199	−	2.22427i	0.0249550	−	0.141527i
$248$	−0.218679	+	0.0795927i	−0.0138861	+	0.00505414i
$249$	1.79205	+	20.3051i	0.113567	+	1.28678i
$250$	−1.63834	−	9.29151i	−0.103618	−	0.587646i
$251$	−15.3601	−	26.6044i	−0.969519	−	1.67926i	−0.696950	−	0.717120i	$-0.745460\pi$
$251$	−15.3601	−	26.6044i	−0.969519	−	1.67926i	−0.272569	−	0.962136i	$-0.587873\pi$
$252$	1.03035	+	2.81751i	0.0649062	+	0.177487i
$253$	15.0737	−	26.1084i	0.947675	−	1.64142i
$254$	−10.3791	−	3.77767i	−0.651240	−	0.237032i
$255$	−0.870875	−	0.869549i	−0.0545363	−	0.0544533i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	2.65572	+	2.22841i	0.165659	+	0.139005i	0.721849	−	0.692051i	$-0.243293\pi$
$257$	2.65572	+	2.22841i	0.165659	+	0.139005i	−0.556189	+	0.831056i	$0.687737\pi$
$258$	3.36479	−	12.5959i	0.209483	−	0.784188i
$259$	−6.76598	−	2.46262i	−0.420418	−	0.153020i
$260$	−1.63343	+	2.82918i	−0.101301	+	0.175458i
$261$	−4.87272	−	2.80338i	−0.301614	−	0.173525i
$262$	−7.61103	−	13.1827i	−0.470211	−	0.814429i
$263$	−0.793933	−	4.50262i	−0.0489560	−	0.277643i	0.950496	−	0.310736i	$-0.100575\pi$
$263$	−0.793933	−	4.50262i	−0.0489560	−	0.277643i	−0.999452	+	0.0330926i	$0.989464\pi$
$264$	6.92653	+	3.22347i	0.426298	+	0.198391i
$265$	11.1043	−	4.04163i	0.682131	−	0.248275i
$266$	−0.127726	+	0.724372i	−0.00783141	+	0.0444141i
$267$	−2.11385	−	0.183315i	−0.129365	−	0.0112187i
$268$	5.54826	−	4.65554i	0.338914	−	0.284382i
$269$	−17.2815			−1.05367			−0.526835	−	0.849968i	$-0.676621\pi$
$269$	−17.2815			−1.05367			−0.526835	+	0.849968i	$0.676621\pi$
$270$	3.90011	−	3.91797i	0.237353	−	0.238440i
$271$	−31.1012			−1.88926			−0.944632	−	0.328132i	$-0.893581\pi$
$271$	−31.1012			−1.88926			−0.944632	+	0.328132i	$0.893581\pi$
$272$	−0.511599	+	0.429282i	−0.0310202	+	0.0260291i
$273$	2.25135	+	4.81845i	0.136258	+	0.291626i
$274$	0.413279	−	2.34382i	0.0249671	−	0.141596i
$275$	−16.0328	+	5.83545i	−0.966813	+	0.351891i
$276$	−9.69209	+	6.79748i	−0.583395	+	0.409160i
$277$	1.25229	+	7.10208i	0.0752427	+	0.426723i	0.999039	+	0.0438375i	$0.0139584\pi$
$277$	1.25229	+	7.10208i	0.0752427	+	0.426723i	−0.923796	+	0.382885i	$0.874930\pi$
$278$	0.454905	+	0.787919i	0.0272834	+	0.0472563i
$279$	0.687349	−	0.122278i	0.0411505	−	0.00732059i
$280$	0.531954	−	0.921371i	0.0317903	−	0.0550625i
$281$	21.0420	+	7.65866i	1.25526	+	0.456877i	0.882176	−	0.470920i	$-0.156078\pi$
$281$	21.0420	+	7.65866i	1.25526	+	0.456877i	0.373084	+	0.927797i	$0.378300\pi$
$282$	−17.8726	+	4.80354i	−1.06430	+	0.286047i
$283$	6.69105	+	5.61446i	0.397742	+	0.333745i	0.819620	−	0.572907i	$-0.194185\pi$
$283$	6.69105	+	5.61446i	0.397742	+	0.333745i	−0.421878	+	0.906653i	$0.638629\pi$
$284$	−0.314720	−	0.264081i	−0.0186752	−	0.0156703i
$285$	1.30897	−	0.351807i	0.0775368	−	0.0208392i
$286$	12.7273	+	4.63236i	0.752581	+	0.273917i
$287$	5.40970	−	9.36988i	0.319325	−	0.553086i
$288$	−1.93186	−	2.29519i	−0.113836	−	0.135246i
$289$	8.27699	+	14.3362i	0.486882	+	0.843304i
$290$	0.346188	+	1.96333i	0.0203289	+	0.115291i
$291$	−21.2510	+	14.9042i	−1.24575	+	0.873701i
$292$	9.85121	−	3.58555i	0.576499	−	0.209828i
$293$	−3.97423	+	22.5390i	−0.232177	+	1.31674i	0.616302	+	0.787510i	$0.288630\pi$
$293$	−3.97423	+	22.5390i	−0.232177	+	1.31674i	−0.848478	+	0.529230i	$0.822481\pi$
$294$	−0.733192	−	1.56921i	−0.0427606	−	0.0915184i
$295$	−6.24845	+	5.24308i	−0.363799	+	0.305264i
$296$	7.20021			0.418504
$297$	−18.8046	−	13.1032i	−1.09116	−	0.760326i
$298$	−15.8439			−0.917811
$299$	−16.0769	+	13.4902i	−0.929754	+	0.780156i
$300$	6.67469	+	0.578838i	0.385364	+	0.0334192i
$301$	−1.30710	+	7.41291i	−0.0753398	+	0.427273i
$302$	−14.1760	+	5.15962i	−0.815734	+	0.296903i
$303$	6.76005	+	3.14600i	0.388355	+	0.180733i
$304$	−0.127726	−	0.724372i	−0.00732561	−	0.0415456i
$305$	0.205128	+	0.355293i	0.0117456	+	0.0203440i
$306$	1.73358	−	1.00441i	0.0991023	−	0.0574182i
$307$	4.46320	−	7.73048i	0.254728	−	0.441202i	−0.710094	−	0.704107i	$-0.751347\pi$
$307$	4.46320	−	7.73048i	0.254728	−	0.441202i	0.964822	+	0.262905i	$0.0846807\pi$
$308$	−4.14487	−	1.50861i	−0.236176	−	0.0859610i
$309$	−1.40267	+	5.25082i	−0.0797950	+	0.298709i
$310$	−0.189662	−	0.159145i	−0.0107721	−	0.00903883i
$311$	−5.44574	−	4.56952i	−0.308799	−	0.259113i	0.475196	−	0.879880i	$-0.342377\pi$
$311$	−5.44574	−	4.56952i	−0.308799	−	0.259113i	−0.783996	+	0.620766i	$0.786822\pi$
$312$	−3.76358	−	3.75785i	−0.213071	−	0.212747i
$313$	−28.3895	−	10.3329i	−1.60467	−	0.584052i	−0.624294	−	0.781189i	$-0.714613\pi$
$313$	−28.3895	−	10.3329i	−1.60467	−	0.584052i	−0.980376	+	0.197137i	$0.936836\pi$
$314$	−9.24098	+	16.0058i	−0.521499	+	0.903262i
$315$	−2.04787	+	2.44812i	−0.115385	+	0.137936i
$316$	5.61463	+	9.72483i	0.315848	+	0.547065i
$317$	−1.69373	−	9.60560i	−0.0951291	−	0.539504i	−0.994708	−	0.102745i	$-0.967237\pi$
$317$	−1.69373	−	9.60560i	−0.0951291	−	0.539504i	0.899579	−	0.436759i	$-0.143874\pi$
$318$	1.69130	+	19.1636i	0.0948437	+	1.07464i
$319$	7.76693	−	2.82693i	0.434865	−	0.158278i
$320$	−0.184746	+	1.04774i	−0.0103276	+	0.0585707i
$321$	−12.1908	+	17.4385i	−0.680424	+	0.973323i
$322$	5.23574	−	4.39331i	0.291776	−	0.244830i
$323$	0.491231			0.0273328
$324$	4.52372	+	7.78048i	0.251318	+	0.432249i
$325$	11.8774			0.658842
$326$	2.03439	−	1.70706i	0.112675	−	0.0945452i
$327$	12.4851	−	17.8594i	0.690425	−	0.987629i
$328$	−1.87877	+	10.6550i	−0.103738	+	0.588326i
$329$	10.0406	−	3.65446i	0.553554	−	0.201477i
$330$	0.714579	+	8.09665i	0.0393363	+	0.445706i
$331$	5.53797	+	31.4074i	0.304394	+	1.72631i	0.626342	+	0.779548i	$0.284551\pi$
$331$	5.53797	+	31.4074i	0.304394	+	1.72631i	−0.321948	+	0.946757i	$0.604338\pi$
$332$	5.88436	+	10.1920i	0.322946	+	0.559359i
$333$	−21.2782	−	3.71850i	−1.16604	−	0.203773i
$334$	−3.78978	+	6.56409i	−0.207367	+	0.359171i
$335$	7.24090	+	2.63547i	0.395613	+	0.143991i
$336$	1.22568	+	1.22381i	0.0668662	+	0.0667644i
$337$	−24.2862	−	20.3785i	−1.32295	−	1.11009i	−0.985670	−	0.168687i	$-0.946047\pi$
$337$	−24.2862	−	20.3785i	−1.32295	−	1.11009i	−0.337284	−	0.941403i	$-0.609508\pi$
$338$	2.73580	+	2.29561i	0.148808	+	0.124864i
$339$	1.03087	−	3.85903i	0.0559893	−	0.209594i
$340$	−0.667675	−	0.243014i	−0.0362098	−	0.0131793i
$341$	−0.513236	+	0.888951i	−0.0277933	+	0.0481394i
$342$	0.00336135	+	2.20664i	0.000181761	+	0.119321i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	−1.30710	−	7.41291i	−0.0704739	−	0.399677i
$345$	−11.4188	−	5.31407i	−0.614765	−	0.286100i
$346$	−1.15853	+	0.421672i	−0.0622831	+	0.0226692i
$347$	3.95931	−	22.4544i	0.212547	−	1.20541i	−0.672566	−	0.740037i	$-0.734808\pi$
$347$	3.95931	−	22.4544i	0.212547	−	1.20541i	0.885113	−	0.465376i	$-0.154081\pi$
$348$	−3.23349	−	0.280413i	−0.173333	−	0.0150317i
$349$	12.9435	−	10.8608i	0.692847	−	0.581368i	−0.226881	−	0.973922i	$-0.572853\pi$
$349$	12.9435	−	10.8608i	0.692847	−	0.581368i	0.919729	+	0.392554i	$0.128409\pi$
$350$	−3.86810			−0.206759
$351$	9.18147	+	13.0489i	0.490071	+	0.696501i
$352$	4.41088			0.235101
$353$	12.1621	−	10.2052i	0.647325	−	0.543170i	−0.258933	−	0.965895i	$-0.583371\pi$
$353$	12.1621	−	10.2052i	0.647325	−	0.543170i	0.906258	+	0.422725i	$0.138926\pi$
$354$	−5.62124	−	12.0309i	−0.298766	−	0.639433i
$355$	0.0759004	−	0.430453i	0.00402837	−	0.0228460i
$356$	−1.15113	+	0.418978i	−0.0610099	+	0.0222058i
$357$	−0.947041	+	0.664201i	−0.0501227	+	0.0351532i
$358$	1.03682	+	5.88010i	0.0547977	+	0.310773i
$359$	−14.5653	−	25.2279i	−0.768729	−	1.33148i	−0.938253	−	0.345951i	$-0.887556\pi$
$359$	−14.5653	−	25.2279i	−0.768729	−	1.33148i	0.169524	−	0.985526i	$-0.445777\pi$
$360$	1.08706	−	3.00090i	0.0572933	−	0.158161i
$361$	9.22949	−	15.9859i	0.485762	−	0.841365i
$362$	1.82625	+	0.664701i	0.0959856	+	0.0349359i
$363$	14.1441	−	3.80144i	0.742370	−	0.199524i
$364$	2.35223	+	1.97375i	0.123290	+	0.103453i
$365$	8.54401	+	7.16928i	0.447214	+	0.375257i
$366$	−0.645012	+	0.173357i	−0.0337153	+	0.00906152i
$367$	13.6228	+	4.95829i	0.711103	+	0.258820i	0.672144	−	0.740420i	$-0.265374\pi$
$367$	13.6228	+	4.95829i	0.711103	+	0.258820i	0.0389593	+	0.999241i	$0.487596\pi$
$368$	−3.41739	+	5.91909i	−0.178144	+	0.308554i
$369$	11.0549	−	30.5176i	0.575494	−	1.58868i
$370$	3.83018	+	6.63407i	0.199122	+	0.344889i
$371$	−1.92873	−	10.9384i	−0.100135	−	0.567892i
$372$	0.330001	−	0.231444i	0.0171097	−	0.0119998i
$373$	−5.08073	+	1.84924i	−0.263070	+	0.0957498i	−0.470188	−	0.882566i	$-0.655814\pi$
$373$	−5.08073	+	1.84924i	−0.263070	+	0.0957498i	0.207118	+	0.978316i	$0.433592\pi$
$374$	−0.511530	+	2.90103i	−0.0264506	+	0.150009i
$375$	6.91755	+	14.8053i	0.357221	+	0.764541i
$376$	−8.18514	+	6.86814i	−0.422116	+	0.354198i
$377$	−5.75392			−0.296342
$378$	−2.99011	−	4.24962i	−0.153795	−	0.218577i
$379$	13.9999			0.719127			0.359564	−	0.933121i	$-0.382926\pi$
$379$	13.9999			0.719127			0.359564	+	0.933121i	$0.382926\pi$
$380$	0.599471	−	0.503016i	0.0307522	−	0.0258042i
$381$	19.0592	+	1.65284i	0.976435	+	0.0846776i
$382$	1.76937	−	10.0346i	0.0905288	−	0.513415i
$383$	−25.9923	+	9.46043i	−1.32815	+	0.483406i	−0.906060	−	0.423150i	$-0.860924\pi$
$383$	−25.9923	+	9.46043i	−1.32815	+	0.483406i	−0.422086	+	0.906556i	$0.638702\pi$
$384$	−1.57033	−	0.730800i	−0.0801355	−	0.0372935i
$385$	−0.814891	−	4.62148i	−0.0415307	−	0.235532i
$386$	11.0260	+	19.0975i	0.561207	+	0.972038i
$387$	0.0343986	+	22.5818i	0.00174858	+	1.14790i
$388$	−7.49299	+	12.9782i	−0.380399	+	0.658870i
$389$	7.53614	+	2.74293i	0.382097	+	0.139072i	0.525926	−	0.850531i	$-0.323719\pi$
$389$	7.53614	+	2.74293i	0.382097	+	0.139072i	−0.143828	+	0.989603i	$0.545941\pi$
$390$	1.46033	−	5.46666i	0.0739465	−	0.276815i
$391$	−3.49666	−	2.93405i	−0.176834	−	0.148381i
$392$	−0.766044	−	0.642788i	−0.0386911	−	0.0324657i
$393$	18.6573	+	18.6289i	0.941138	+	0.939705i
$394$	−3.62789	−	1.32044i	−0.182770	−	0.0665230i
$395$	−5.97345	+	10.3463i	−0.300557	+	0.520580i
$396$	−13.0351	−	2.27797i	−0.655038	−	0.114472i
$397$	−7.98532	−	13.8310i	−0.400772	−	0.694157i	0.593047	−	0.805167i	$-0.297925\pi$
$397$	−7.98532	−	13.8310i	−0.400772	−	0.694157i	−0.993819	+	0.111010i	$0.964591\pi$
$398$	2.91604	+	16.5377i	0.146168	+	0.828960i
$399$	−0.112003	−	1.26907i	−0.00560719	−	0.0635331i
$400$	3.63482	−	1.32297i	0.181741	−	0.0661484i
$401$	−0.308113	+	1.74739i	−0.0153864	+	0.0872607i	−0.991534	−	0.129847i	$-0.958551\pi$
$401$	−0.308113	+	1.74739i	−0.0153864	+	0.0872607i	0.976148	+	0.217108i	$0.0696624\pi$
$402$	−7.18757	+	10.2816i	−0.358483	+	0.512798i
$403$	0.547395	−	0.459319i	0.0272677	−	0.0228803i
$404$	4.30487			0.214175
$405$	−4.76230	+	8.30689i	−0.236641	+	0.412773i
$406$	1.87387			0.0929984
$407$	24.3290	−	20.4145i	1.20594	−	1.01191i
$408$	0.662757	−	0.948051i	0.0328114	−	0.0469355i
$409$	−5.42484	+	30.7658i	−0.268241	+	1.52127i	0.491403	+	0.870932i	$0.336484\pi$
$409$	−5.42484	+	30.7658i	−0.268241	+	1.52127i	−0.759644	+	0.650339i	$0.774627\pi$
$410$	−10.8167	+	3.93694i	−0.534197	+	0.194432i
$411$	0.362405	+	4.10629i	0.0178761	+	0.202548i
$412$	0.544884	+	3.09019i	0.0268445	+	0.152243i
$413$	3.83340	+	6.63965i	0.188629	+	0.326716i
$414$	13.1560	−	15.7273i	0.646581	−	0.772954i
$415$	−6.26041	+	10.8434i	−0.307312	+	0.532279i
$416$	−2.88543	−	1.05021i	−0.141470	−	0.0514909i
$417$	−1.11513	−	1.11344i	−0.0546084	−	0.0545252i
$418$	−2.48536	−	2.08547i	−0.121563	−	0.102004i
$419$	19.0037	+	15.9460i	0.928389	+	0.779011i	0.975528	−	0.219877i	$-0.0705657\pi$
$419$	19.0037	+	15.9460i	0.928389	+	0.779011i	−0.0471384	+	0.998888i	$0.515010\pi$
$420$	−0.475581	+	1.78032i	−0.0232060	+	0.0868705i
$421$	−22.8604	−	8.32049i	−1.11415	−	0.405516i	−0.281633	−	0.959522i	$-0.590876\pi$
$421$	−22.8604	−	8.32049i	−1.11415	−	0.405516i	−0.832513	+	0.554006i	$0.813098\pi$
$422$	7.68264	−	13.3067i	0.373985	−	0.647761i
$423$	27.7358	−	16.0697i	1.34856	−	0.781334i
$424$	5.55355	+	9.61904i	0.269704	+	0.467142i
$425$	0.448583	+	2.54404i	0.0217595	+	0.123404i
$426$	0.645149	+	0.300240i	0.0312576	+	0.0145467i
$427$	0.362358	−	0.131887i	0.0175357	−	0.00638248i
$428$	−2.13316	+	12.0977i	−0.103110	+	0.584767i
$429$	−23.3714	−	2.02679i	−1.12838	−	0.0978546i
$430$	6.13473	−	5.14765i	0.295843	−	0.248242i
$431$	18.1157			0.872600			0.436300	−	0.899801i	$-0.356289\pi$
$431$	18.1157			0.872600			0.436300	+	0.899801i	$0.356289\pi$
$432$	4.26324	+	2.97066i	0.205115	+	0.142926i
$433$	−38.3644			−1.84367			−0.921837	−	0.387578i	$-0.873312\pi$
$433$	−38.3644			−1.84367			−0.921837	+	0.387578i	$0.873312\pi$
$434$	−0.178269	+	0.149585i	−0.00855718	+	0.00718033i
$435$	−1.46171	−	3.12841i	−0.0700834	−	0.149996i
$436$	2.18465	−	12.3898i	0.104626	−	0.593362i
$437$	4.72412	−	1.71944i	0.225985	−	0.0822519i
$438$	−14.8661	+	10.4262i	−0.710330	+	0.498185i
$439$	−2.33028	−	13.2157i	−0.111218	−	0.630749i	−0.988553	−	0.150871i	$-0.951792\pi$
$439$	−2.33028	−	13.2157i	−0.111218	−	0.630749i	0.877335	−	0.479878i	$-0.159319\pi$
$440$	2.34639	+	4.06406i	0.111860	+	0.193746i
$441$	1.93186	+	2.29519i	0.0919934	+	0.109295i
$442$	1.02535	−	1.77595i	0.0487708	−	0.0844734i
$443$	14.8639	+	5.41002i	0.706206	+	0.257038i	0.670058	−	0.742309i	$-0.266269\pi$
$443$	14.8639	+	5.41002i	0.706206	+	0.257038i	0.0361476	+	0.999346i	$0.488491\pi$
$444$	−12.0437	+	3.23694i	−0.571570	+	0.153618i
$445$	−0.998384	−	0.837744i	−0.0473280	−	0.0397129i
$446$	13.0377	+	10.9400i	0.617354	+	0.518022i
$447$	26.5019	−	7.12280i	1.25350	−	0.336897i
$448$	0.939693	+	0.342020i	0.0443963	+	0.0161589i
$449$	−17.4219	+	30.1756i	−0.822190	+	1.42407i	0.0818586	+	0.996644i	$0.473914\pi$
$449$	−17.4219	+	30.1756i	−0.822190	+	1.42407i	−0.904048	+	0.427430i	$0.859419\pi$
$450$	−11.4249	+	2.03247i	−0.538576	+	0.0958116i
$451$	23.8615	+	41.3294i	1.12360	+	1.94613i
$452$	−0.400456	−	2.27110i	−0.0188359	−	0.106824i
$453$	21.3924	−	15.0034i	1.00510	−	0.704922i
$454$	−3.09708	+	1.12725i	−0.145353	+	0.0529043i
$455$	−0.567283	+	3.21722i	−0.0265946	+	0.150826i
$456$	0.539297	+	1.15423i	0.0252549	+	0.0540518i
$457$	11.0480	−	9.27041i	0.516806	−	0.433652i	−0.346711	−	0.937972i	$-0.612701\pi$
$457$	11.0480	−	9.27041i	0.516806	−	0.433652i	0.863517	+	0.504321i	$0.168257\pi$
$458$	5.48396			0.256249
$459$	−2.44820	+	2.45942i	−0.114272	+	0.114796i
$460$	−7.27157			−0.339039
$461$	0.603830	−	0.506673i	0.0281231	−	0.0235981i	−0.628618	−	0.777714i	$-0.716379\pi$
$461$	0.603830	−	0.506673i	0.0281231	−	0.0235981i	0.656741	+	0.754116i	$0.271935\pi$
$462$	7.61130	+	0.660062i	0.354110	+	0.0307088i
$463$	7.22116	−	40.9532i	0.335596	−	1.90326i	−0.0856762	−	0.996323i	$-0.527305\pi$
$463$	7.22116	−	40.9532i	0.335596	−	1.90326i	0.421272	−	0.906934i	$-0.361584\pi$
$464$	−1.76086	+	0.640900i	−0.0817457	+	0.0297530i
$465$	0.388791	+	0.180936i	0.0180297	+	0.00839070i
$466$	4.54273	+	25.7631i	0.210438	+	1.19345i
$467$	−1.65616	−	2.86855i	−0.0766377	−	0.132740i	0.825160	−	0.564900i	$-0.191085\pi$
$467$	−1.65616	−	2.86855i	−0.0766377	−	0.132740i	−0.901797	+	0.432159i	$0.857752\pi$
$468$	7.98470	+	4.59376i	0.369093	+	0.212347i
$469$	3.62137	−	6.27239i	0.167219	−	0.289632i
$470$	−10.6822	−	3.88801i	−0.492734	−	0.179341i
$471$	8.26168	−	30.9272i	0.380678	−	1.42505i
$472$	−5.87312	−	4.92813i	−0.270332	−	0.226836i
$473$	−25.4341	−	21.3418i	−1.16946	−	0.981295i
$474$	−13.7635	−	13.7425i	−0.632177	−	0.631214i
$475$	−2.67358	−	0.973105i	−0.122672	−	0.0446491i
$476$	−0.333922	+	0.578370i	−0.0153053	+	0.0265096i
$477$	−11.4442	−	31.2944i	−0.523996	−	1.43287i
$478$	−1.12460	−	1.94787i	−0.0514382	−	0.0890935i
$479$	−6.44033	−	36.5249i	−0.294266	−	1.66887i	−0.670170	−	0.742207i	$-0.733779\pi$
$479$	−6.44033	−	36.5249i	−0.294266	−	1.66887i	0.375904	−	0.926659i	$-0.377332\pi$
$480$	−0.162004	−	1.83561i	−0.00739443	−	0.0837836i
$481$	−20.7757	+	7.56175i	−0.947292	+	0.344786i
$482$	3.43711	−	19.4928i	0.156556	−	0.887873i
$483$	−6.78271	+	9.70244i	−0.308624	+	0.441476i
$484$	6.47757	−	5.43533i	0.294435	−	0.247060i
$485$	−15.9437			−0.723966
$486$	−11.0646	−	10.9806i	−0.501900	−	0.498092i
$487$	−33.0410			−1.49723			−0.748615	−	0.663005i	$-0.769281\pi$
$487$	−33.0410			−1.49723			−0.748615	+	0.663005i	$0.769281\pi$
$488$	−0.295397	+	0.247867i	−0.0133720	+	0.0112204i
$489$	−2.63548	+	3.76997i	−0.119181	+	0.170484i
$490$	0.184746	−	1.04774i	0.00834596	−	0.0473323i
$491$	−19.9880	+	7.27502i	−0.902044	+	0.328317i	−0.751072	−	0.660221i	$-0.770463\pi$
$491$	−19.9880	+	7.27502i	−0.902044	+	0.328317i	−0.150973	+	0.988538i	$0.548241\pi$
$492$	−1.64750	−	18.6672i	−0.0742748	−	0.841582i
$493$	−0.217312	−	1.23244i	−0.00978724	−	0.0555062i
$494$	1.12929	+	1.95599i	0.0508092	+	0.0880041i
$495$	−4.83521	−	13.2219i	−0.217327	−	0.594282i
$496$	0.116357	−	0.201536i	0.00522457	−	0.00904923i
$497$	−0.386061	−	0.140515i	−0.0173172	−	0.00630294i
$498$	−14.4246	−	14.4027i	−0.646384	−	0.645400i
$499$	1.70800	+	1.43318i	0.0764606	+	0.0641581i	0.680217	−	0.733011i	$-0.261886\pi$
$499$	1.70800	+	1.43318i	0.0764606	+	0.0641581i	−0.603756	+	0.797169i	$0.706330\pi$
$500$	7.22751	+	6.06460i	0.323224	+	0.271217i
$501$	3.38816	−	12.6834i	0.151372	−	0.566654i
$502$	28.8675	+	10.5069i	1.28842	+	0.468946i
$503$	−0.602828	+	1.04413i	−0.0268788	+	0.0465554i	−0.879152	−	0.476542i	$-0.841890\pi$
$503$	−0.602828	+	1.04413i	−0.0268788	+	0.0465554i	0.852273	+	0.523097i	$0.175223\pi$
$504$	−2.60036	−	1.49604i	−0.115829	−	0.0666389i
$505$	2.28999	+	3.96638i	0.101903	+	0.176502i
$506$	5.23504	+	29.6894i	0.232726	+	1.31985i
$507$	−5.60816	−	2.60993i	−0.249067	−	0.115911i
$508$	10.3791	−	3.77767i	0.460496	−	0.167607i
$509$	3.28416	−	18.6254i	0.145568	−	0.825557i	−0.821341	−	0.570437i	$-0.806774\pi$
$509$	3.28416	−	18.6254i	0.145568	−	0.825557i	0.966909	−	0.255120i	$-0.0821150\pi$
$510$	1.22606	+	0.106326i	0.0542910	+	0.00470818i
$511$	8.03078	−	6.73863i	0.355261	−	0.298099i
$512$	−1.00000			−0.0441942
$513$	−0.997643	−	3.68951i	−0.0440470	−	0.162896i
$514$	−3.46680			−0.152914
$515$	−2.55736	+	2.14588i	−0.112691	+	0.0945588i
$516$	5.51893	+	11.8119i	0.242957	+	0.519989i
$517$	−8.18404	+	46.4140i	−0.359933	+	2.04128i
$518$	6.76598	−	2.46262i	0.297280	−	0.108201i
$519$	1.74830	−	1.22616i	0.0767419	−	0.0538224i
$520$	−0.567283	−	3.21722i	−0.0248770	−	0.141084i
$521$	15.7611	+	27.2990i	0.690505	+	1.19599i	0.971673	+	0.236331i	$0.0759450\pi$
$521$	15.7611	+	27.2990i	0.690505	+	1.19599i	−0.281168	+	0.959659i	$0.590722\pi$
$522$	5.53470	−	0.984612i	0.242247	−	0.0430953i
$523$	2.10564	−	3.64708i	0.0920733	−	0.159476i	−0.816310	−	0.577614i	$-0.803984\pi$
$523$	2.10564	−	3.64708i	0.0920733	−	0.159476i	0.908383	+	0.418138i	$0.137317\pi$
$524$	14.3041	+	5.20625i	0.624876	+	0.227436i
$525$	6.47013	−	1.73895i	0.282380	−	0.0758940i
$526$	3.50242	+	2.93888i	0.152713	+	0.128141i
$527$	0.119056	+	0.0998998i	0.00518616	+	0.00435170i
$528$	−7.37804	+	1.98296i	−0.321088	+	0.0862974i
$529$	−22.2840	−	8.11072i	−0.968870	−	0.352640i
$530$	−5.90847	+	10.2338i	−0.256648	+	0.444527i
$531$	14.8112	+	17.5968i	0.642752	+	0.763636i
$532$	−0.367774	−	0.637002i	−0.0159450	−	0.0276176i
$533$	−5.76898	−	32.7175i	−0.249882	−	1.41715i
$534$	1.73713	−	1.21833i	0.0751731	−	0.0527221i
$535$	−12.2813	+	4.47001i	−0.530965	+	0.193255i
$536$	−1.25769	+	7.13270i	−0.0543239	+	0.308086i
$537$	−4.37775	−	9.36947i	−0.188914	−	0.404323i
$538$	13.2384	−	11.1083i	0.570747	−	0.478913i
$539$	−4.41088			−0.189990
$540$	−0.469232	+	5.50828i	−0.0201925	+	0.237039i
$541$	−36.0951			−1.55185			−0.775924	−	0.630826i	$-0.782716\pi$
$541$	−36.0951			−1.55185			−0.775924	+	0.630826i	$0.782716\pi$
$542$	23.8249	−	19.9915i	1.02337	−	0.858707i
$543$	−3.35358	−	0.290826i	−0.143916	−	0.0124806i
$544$	0.115970	−	0.657698i	0.00497217	−	0.0281986i
$545$	12.5777	−	4.57791i	0.538769	−	0.196096i
$546$	−4.82187	−	2.24401i	−0.206357	−	0.0960346i
$547$	6.41873	+	36.4024i	0.274445	+	1.55645i	0.740719	+	0.671815i	$0.234485\pi$
$547$	6.41873	+	36.4024i	0.274445	+	1.55645i	−0.466274	+	0.884640i	$0.654404\pi$
$548$	1.18999	+	2.06112i	0.0508339	+	0.0880469i
$549$	1.00097	−	0.579945i	0.0427204	−	0.0247515i
$550$	8.53086	−	14.7759i	0.363757	−	0.630046i
$551$	1.29519	+	0.471412i	0.0551771	+	0.0200828i
$552$	3.05524	−	11.4371i	0.130039	−	0.486797i
$553$	8.60212	+	7.21804i	0.365799	+	0.306942i
$554$	−5.52444	−	4.63555i	−0.234711	−	0.196946i
$555$	−9.38913	−	9.37484i	−0.398546	−	0.397940i
$556$	−0.854942	−	0.311174i	−0.0362576	−	0.0131967i
$557$	15.5077	−	26.8601i	0.657081	−	1.13810i	−0.324287	−	0.945959i	$-0.605124\pi$
$557$	15.5077	−	26.8601i	0.657081	−	1.13810i	0.981368	−	0.192138i	$-0.0615422\pi$
$558$	−0.447941	+	0.535490i	−0.0189629	+	0.0226691i
$559$	11.5567	+	20.0167i	0.488795	+	0.846618i
$560$	0.184746	+	1.04774i	0.00780693	+	0.0442753i
$561$	−0.448561	−	5.08249i	−0.0189383	−	0.214583i
$562$	−21.0420	+	7.65866i	−0.887603	+	0.323061i
$563$	−3.49506	+	19.8215i	−0.147299	+	0.835376i	0.818193	+	0.574944i	$0.194976\pi$
$563$	−3.49506	+	19.8215i	−0.147299	+	0.835376i	−0.965492	+	0.260432i	$0.916135\pi$
$564$	10.6035	−	15.1680i	0.446490	−	0.638688i
$565$	1.87950	−	1.57709i	0.0790712	−	0.0663487i
$566$	−8.73455			−0.367141
$567$	6.91199	+	5.76406i	0.290276	+	0.242068i
$568$	0.410837			0.0172383
$569$	14.9108	−	12.5116i	0.625093	−	0.524515i	−0.274307	−	0.961642i	$-0.588448\pi$
$569$	14.9108	−	12.5116i	0.625093	−	0.524515i	0.899400	+	0.437127i	$0.144004\pi$
$570$	−0.776593	+	1.11089i	−0.0325279	+	0.0465301i
$571$	−6.26351	+	35.5221i	−0.262120	+	1.48656i	0.514993	+	0.857194i	$0.327794\pi$
$571$	−6.26351	+	35.5221i	−0.262120	+	1.48656i	−0.777113	+	0.629361i	$0.783317\pi$
$572$	−12.7273	+	4.63236i	−0.532155	+	0.193689i
$573$	1.55156	+	17.5802i	0.0648175	+	0.734424i
$574$	1.87877	+	10.6550i	0.0784183	+	0.444732i
$575$	13.2188	+	22.8956i	0.551262	+	0.954814i
$576$	2.95521	+	0.516443i	0.123134	+	0.0215185i
$577$	14.3736	−	24.8958i	0.598382	−	1.03643i	−0.394678	−	0.918819i	$-0.629144\pi$
$577$	14.3736	−	24.8958i	0.598382	−	1.03643i	0.993060	−	0.117608i	$-0.0375227\pi$
$578$	−15.5557	−	5.66180i	−0.647030	−	0.235500i
$579$	−27.0285	−	26.9874i	−1.12327	−	1.12156i
$580$	−1.52720	−	1.28147i	−0.0634136	−	0.0532103i
$581$	9.01536	+	7.56478i	0.374020	+	0.313840i
$582$	6.69893	−	25.0771i	0.277680	−	1.03948i
$583$	46.0375	+	16.7563i	1.90668	+	0.693975i
$584$	−5.24172	+	9.07893i	−0.216904	+	0.375689i
$585$	0.0149291	+	9.80054i	0.000617242	+	0.405203i
$586$	−11.4433	−	19.8204i	−0.472720	−	0.818774i
$587$	−2.57681	−	14.6138i	−0.106357	−	0.603178i	−0.990670	−	0.136284i	$-0.956484\pi$
$587$	−2.57681	−	14.6138i	−0.106357	−	0.603178i	0.884313	−	0.466894i	$-0.154627\pi$
$588$	1.57033	+	0.730800i	0.0647592	+	0.0301377i
$589$	−0.160849	+	0.0585442i	−0.00662766	+	0.00241227i
$590$	1.41641	−	8.03286i	0.0583127	−	0.330708i
$591$	6.66196	+	0.577733i	0.274036	+	0.0237648i
$592$	−5.51568	+	4.62821i	−0.226693	+	0.190218i
$593$	24.0429			0.987322			0.493661	−	0.869654i	$-0.335658\pi$
$593$	24.0429			0.987322			0.493661	+	0.869654i	$0.335658\pi$
$594$	22.8278	−	2.04974i	0.936635	−	0.0841019i
$595$	−0.710525			−0.0291287
$596$	12.1371	−	10.1842i	0.497155	−	0.417163i
$597$	−12.3124	−	26.3515i	−0.503911	−	1.07850i
$598$	3.64435	−	20.6681i	0.149028	−	0.845182i
$599$	−15.4949	+	5.63967i	−0.633103	+	0.230431i	−0.638581	−	0.769554i	$-0.720478\pi$
$599$	−15.4949	+	5.63967i	−0.633103	+	0.230431i	0.00547836	+	0.999985i	$0.498256\pi$
$600$	−5.48518	+	3.84699i	−0.223932	+	0.157053i
$601$	0.858984	+	4.87154i	0.0350387	+	0.198714i	0.997302	−	0.0734051i	$-0.0233866\pi$
$601$	0.858984	+	4.87154i	0.0350387	+	0.198714i	−0.962264	+	0.272119i	$0.912275\pi$
$602$	−3.76363	−	6.51880i	−0.153394	−	0.265687i
$603$	7.40037	−	20.4291i	0.301367	−	0.831939i
$604$	7.54287	−	13.0646i	0.306915	−	0.531592i
$605$	8.45373	+	3.07690i	0.343693	+	0.125094i
$606$	−7.20071	+	1.93530i	−0.292509	+	0.0786163i
$607$	33.3503	+	27.9842i	1.35364	+	1.13584i	0.977889	+	0.209124i	$0.0670613\pi$
$607$	33.3503	+	27.9842i	1.35364	+	1.13584i	0.375756	+	0.926719i	$0.377383\pi$
$608$	0.563462	+	0.472801i	0.0228514	+	0.0191746i
$609$	−3.13440	+	0.842418i	−0.127012	+	0.0341365i
$610$	−0.385515	−	0.140316i	−0.0156091	−	0.00568124i
$611$	16.4047	−	28.4137i	0.663661	−	1.14950i
$612$	−0.682380	+	1.88375i	−0.0275836	+	0.0761460i
$613$	−16.7112	−	28.9447i	−0.674959	−	1.16906i	−0.976481	−	0.215604i	$-0.930828\pi$
$613$	−16.7112	−	28.9447i	−0.674959	−	1.16906i	0.301522	−	0.953459i	$-0.402505\pi$
$614$	1.55005	+	8.79078i	0.0625550	+	0.354767i
$615$	16.3230	−	11.4480i	0.658208	−	0.461630i
$616$	4.14487	−	1.50861i	0.167002	−	0.0607836i
$617$	1.53741	−	8.71909i	0.0618938	−	0.351017i	−0.938095	−	0.346377i	$-0.887412\pi$
$617$	1.53741	−	8.71909i	0.0618938	−	0.351017i	0.999989	−	0.00464039i	$-0.00147709\pi$
$618$	−2.30066	−	4.92398i	−0.0925460	−	0.198071i
$619$	−22.4608	+	18.8469i	−0.902777	+	0.757520i	−0.970731	−	0.240169i	$-0.922797\pi$
$619$	−22.4608	+	18.8469i	−0.902777	+	0.757520i	0.0679541	+	0.997688i	$0.478353\pi$
$620$	0.247586			0.00994329
$621$	−14.9355	+	32.2213i	−0.599341	+	1.29300i
$622$	7.10890			0.285041
$623$	−0.938412	+	0.787421i	−0.0375967	+	0.0315474i
$624$	5.29857	+	0.459499i	0.212113	+	0.0183947i
$625$	1.61540	−	9.16137i	0.0646158	−	0.366455i
$626$	28.3895	−	10.3329i	1.13467	−	0.412987i
$627$	5.09479	+	2.37102i	0.203466	+	0.0946893i
$628$	−3.20936	−	18.2012i	−0.128067	−	0.726306i
$629$	−2.40431	−	4.16439i	−0.0958661	−	0.166045i
$630$	−0.00486192	−	3.19172i	−0.000193704	−	0.127161i
$631$	0.763181	−	1.32187i	0.0303818	−	0.0526227i	−0.850435	−	0.526081i	$-0.823661\pi$
$631$	0.763181	−	1.32187i	0.0303818	−	0.0526227i	0.880816	+	0.473458i	$0.156994\pi$
$632$	−10.5521	−	3.84064i	−0.419738	−	0.152772i
$633$	−6.86848	+	25.7118i	−0.272998	+	1.02195i
$634$	7.47183	+	6.26961i	0.296744	+	0.248998i
$635$	9.00181	+	7.55342i	0.357226	+	0.299748i
$636$	−13.6137	−	13.5930i	−0.539819	−	0.538998i
$637$	2.88543	+	1.05021i	0.114325	+	0.0416109i
$638$	−4.13270	+	7.15804i	−0.163615	+	0.283390i
$639$	−1.21411	−	0.212174i	−0.0480295	−	0.00839348i
$640$	−0.531954	−	0.921371i	−0.0210273	−	0.0364204i
$641$	−3.43516	−	19.4818i	−0.135681	−	0.769484i	−0.974383	−	0.224894i	$-0.927796\pi$
$641$	−3.43516	−	19.4818i	−0.135681	−	0.769484i	0.838703	−	0.544590i	$-0.183315\pi$
$642$	−1.87057	−	21.1948i	−0.0738255	−	0.836491i
$643$	−9.97170	+	3.62940i	−0.393245	+	0.143130i	−0.531072	−	0.847327i	$-0.678211\pi$
$643$	−9.97170	+	3.62940i	−0.393245	+	0.143130i	0.137826	+	0.990456i	$0.455988\pi$
$644$	−1.18685	+	6.73094i	−0.0467683	+	0.265236i
$645$	−7.94732	+	11.3684i	−0.312925	+	0.447629i
$646$	−0.376305	+	0.315757i	−0.0148055	+	0.0124233i
$647$	29.2682			1.15065			0.575326	−	0.817924i	$-0.304875\pi$
$647$	29.2682			1.15065			0.575326	+	0.817924i	$0.304875\pi$
$648$	−8.46657	−	3.05240i	−0.332598	−	0.119910i
$649$	−33.8174			−1.32745
$650$	−9.09865	+	7.63467i	−0.356878	+	0.299457i
$651$	0.230941	−	0.330353i	0.00905129	−	0.0129476i
$652$	−0.461159	+	2.61536i	−0.0180604	+	0.102426i
$653$	−8.28507	+	3.01552i	−0.324220	+	0.118006i	−0.499002	−	0.866601i	$-0.666300\pi$
$653$	−8.28507	+	3.01552i	−0.324220	+	0.118006i	0.174782	+	0.984607i	$0.444078\pi$
$654$	1.91572	+	21.7064i	0.0749106	+	0.848786i
$655$	2.81221	+	15.9488i	0.109882	+	0.623172i
$656$	−5.40970	−	9.36988i	−0.211213	−	0.365832i
$657$	20.1792	−	24.1231i	0.787264	−	0.941132i
$658$	−5.34247	+	9.25343i	−0.208271	+	0.360736i
$659$	35.4918	+	12.9180i	1.38256	+	0.503212i	0.922955	−	0.384909i	$-0.125767\pi$
$659$	35.4918	+	12.9180i	1.38256	+	0.503212i	0.459609	+	0.888121i	$0.347989\pi$
$660$	−5.75182	−	5.74307i	−0.223889	−	0.223549i
$661$	22.2427	+	18.6638i	0.865141	+	0.725939i	0.963069	−	0.269254i	$-0.0867772\pi$
$661$	22.2427	+	18.6638i	0.865141	+	0.725939i	−0.0979284	+	0.995193i	$0.531222\pi$
$662$	−24.4306	−	20.4997i	−0.949522	−	0.796744i
$663$	−0.916687	+	3.43158i	−0.0356012	+	0.133271i
$664$	−11.0590	−	4.02514i	−0.429171	−	0.156206i
$665$	0.391277	−	0.677712i	0.0151731	−	0.0262805i
$666$	18.6902	−	10.8288i	0.724231	−	0.419607i
$667$	−6.40372	−	11.0916i	−0.247953	−	0.429467i
$668$	−1.31618	−	7.46441i	−0.0509244	−	0.288807i
$669$	−26.7263	−	12.4379i	−1.03330	−	0.480877i
$670$	−7.24090	+	2.63547i	−0.279740	+	0.101817i
$671$	−0.295357	+	1.67505i	−0.0114021	+	0.0646647i
$672$	−1.72557	−	0.149644i	−0.0665655	−	0.00577264i
$673$	−13.6184	+	11.4272i	−0.524950	+	0.440485i	−0.866353	−	0.499432i	$-0.833542\pi$
$673$	−13.6184	+	11.4272i	−0.524950	+	0.440485i	0.341403	+	0.939917i	$0.389098\pi$
$674$	31.7034			1.22117
$675$	18.1966	−	8.53590i	0.700389	−	0.328547i
$676$	−3.57133			−0.137359
$677$	−34.6806	+	29.1005i	−1.33289	+	1.11842i	−0.349492	+	0.936939i	$0.613646\pi$
$677$	−34.6806	+	29.1005i	−1.33289	+	1.11842i	−0.983394	+	0.181484i	$0.941910\pi$
$678$	1.69084	+	3.61882i	0.0649363	+	0.138980i
$679$	−2.60229	+	14.7583i	−0.0998667	+	0.566372i
$680$	0.667675	−	0.243014i	0.0256042	−	0.00931916i
$681$	4.67369	−	3.27786i	0.179096	−	0.125608i
$682$	−0.178245	−	1.01088i	−0.00682535	−	0.0387085i
$683$	5.83934	+	10.1140i	0.223436	+	0.387003i	0.955849	−	0.293858i	$-0.0949392\pi$
$683$	5.83934	+	10.1140i	0.223436	+	0.387003i	−0.732413	+	0.680861i	$0.761606\pi$
$684$	−1.42097	−	1.68822i	−0.0543323	−	0.0645508i
$685$	−1.26604	+	2.19285i	−0.0483729	+	0.0837843i
$686$	−0.939693	−	0.342020i	−0.0358776	−	0.0130584i
$687$	−9.17297	+	2.46538i	−0.349971	+	0.0940601i
$688$	5.76622	+	4.83843i	0.219835	+	0.184464i
$689$	−26.1264	−	21.9227i	−0.995338	−	0.835188i
$690$	12.1631	−	3.26902i	0.463041	−	0.124450i
$691$	−9.92598	−	3.61276i	−0.377602	−	0.137436i	0.146245	−	0.989248i	$-0.453281\pi$
$691$	−9.92598	−	3.61276i	−0.377602	−	0.137436i	−0.523847	+	0.851813i	$0.675504\pi$
$692$	0.616443	−	1.06771i	0.0234336	−	0.0405882i
$693$	−13.0281	+	2.31767i	−0.494896	+	0.0880411i
$694$	11.4004	+	19.7460i	0.432752	+	0.749549i
$695$	−0.168084	−	0.953249i	−0.00637577	−	0.0361588i
$696$	2.65725	−	1.86364i	0.100723	−	0.0706411i
$697$	6.78992	−	2.47133i	0.257186	−	0.0936082i
$698$	−2.93404	+	16.6398i	−0.111055	+	0.629825i
$699$	−19.1807	−	41.0514i	−0.725480	−	1.55271i
$700$	2.96314	−	2.48637i	0.111996	−	0.0939758i
$701$	22.4593			0.848276			0.424138	−	0.905598i	$-0.360577\pi$
$701$	22.4593			0.848276			0.424138	+	0.905598i	$0.360577\pi$
$702$	−15.4211	−	4.09433i	−0.582032	−	0.154531i
$703$	5.29609			0.199746
$704$	−3.37893	+	2.83526i	−0.127348	+	0.106858i
$705$	19.6160	+	1.70112i	0.738780	+	0.0640679i
$706$	−2.75693	+	15.6353i	−0.103758	+	0.588443i
$707$	4.04525	−	1.47235i	0.152137	−	0.0553735i
$708$	12.0394	+	5.60291i	0.452469	+	0.210570i
$709$	−9.08917	−	51.5473i	−0.341351	−	1.93590i	−0.352117	−	0.935956i	$-0.614538\pi$
$709$	−9.08917	−	51.5473i	−0.341351	−	1.93590i	0.0107661	−	0.999942i	$-0.496573\pi$
$710$	0.218546	+	0.378534i	0.00820190	+	0.0142061i
$711$	29.2001	+	16.7994i	1.09509	+	0.630028i
$712$	0.612505	−	1.06089i	0.0229546	−	0.0397585i
$713$	1.49462	+	0.543998i	0.0559741	+	0.0203729i
$714$	0.298535	−	1.11755i	0.0111724	−	0.0418234i
$715$	−11.0385	−	9.26237i	−0.412815	−	0.346393i
$716$	−4.57391	−	3.83796i	−0.170935	−	0.143431i
$717$	2.75680	+	2.75261i	0.102955	+	0.102798i
$718$	27.3739	+	9.96327i	1.02158	+	0.371826i
$719$	−9.55183	+	16.5443i	−0.356223	+	0.616997i	−0.987327	−	0.158702i	$-0.949269\pi$
$719$	−9.55183	+	16.5443i	−0.356223	+	0.616997i	0.631103	+	0.775699i	$0.282602\pi$
$720$	1.09620	+	2.99757i	0.0408530	+	0.111713i
$721$	1.56893	+	2.71747i	0.0584301	+	0.101204i
$722$	3.20537	+	18.1785i	0.119291	+	0.676535i
$723$	3.01400	+	34.1506i	0.112092	+	1.27007i
$724$	−1.82625	+	0.664701i	−0.0678721	+	0.0247034i
$725$	−1.25865	+	7.13818i	−0.0467452	+	0.265105i
$726$	−8.39146	+	12.0037i	−0.311436	+	0.445499i
$727$	21.1086	−	17.7122i	0.782873	−	0.656908i	−0.161097	−	0.986939i	$-0.551503\pi$
$727$	21.1086	−	17.7122i	0.782873	−	0.656908i	0.943970	+	0.330030i	$0.107059\pi$
$728$	−3.07061			−0.113805
$729$	23.4441	+	13.3930i	0.868301	+	0.496037i
$730$	−11.1534			−0.412806
$731$	−3.85094	+	3.23132i	−0.142432	+	0.119515i
$732$	0.382676	−	0.547405i	0.0141441	−	0.0202327i
$733$	−2.66739	+	15.1275i	−0.0985223	+	0.558748i	0.895089	+	0.445888i	$0.147112\pi$
$733$	−2.66739	+	15.1275i	−0.0985223	+	0.558748i	−0.993611	+	0.112860i	$0.963999\pi$
$734$	−13.6228	+	4.95829i	−0.502826	+	0.183014i
$735$	0.162004	+	1.83561i	0.00597560	+	0.0677074i
$736$	−1.18685	−	6.73094i	−0.0437477	−	0.248106i
$737$	15.9734	+	27.6668i	0.588389	+	1.01912i
$738$	11.1478	+	30.4838i	0.410357	+	1.12212i
$739$	−16.3684	+	28.3509i	−0.602122	+	1.04291i	0.390377	+	0.920655i	$0.372345\pi$
$739$	−16.3684	+	28.3509i	−0.602122	+	1.04291i	−0.992499	+	0.122251i	$0.960989\pi$
$740$	−7.19838	−	2.62000i	−0.264618	−	0.0963130i
$741$	−2.76829	−	2.76408i	−0.101696	−	0.101541i
$742$	8.50854	+	7.13951i	0.312358	+	0.262100i
$743$	−17.5618	−	14.7361i	−0.644282	−	0.540617i	0.261048	−	0.965326i	$-0.415932\pi$
$743$	−17.5618	−	14.7361i	−0.644282	−	0.540617i	−0.905330	+	0.424709i	$0.860376\pi$
$744$	−0.104026	+	0.389417i	−0.00381378	+	0.0142767i
$745$	15.8399	+	5.76524i	0.580327	+	0.211222i
$746$	2.70340	−	4.68243i	0.0989786	−	0.171436i
$747$	30.6029	+	17.6065i	1.11970	+	0.644187i
$748$	−1.47289	−	2.55112i	−0.0538542	−	0.0932783i
$749$	2.13316	+	12.0977i	0.0779439	+	0.442042i
$750$	−14.8158	−	6.89499i	−0.540996	−	0.251769i
$751$	−1.37562	+	0.500687i	−0.0501973	+	0.0182703i	−0.366997	−	0.930222i	$-0.619614\pi$
$751$	−1.37562	+	0.500687i	−0.0501973	+	0.0182703i	0.316799	+	0.948493i	$0.397392\pi$
$752$	1.85542	−	10.5226i	0.0676602	−	0.383720i
$753$	−53.0099	−	4.59708i	−1.93179	−	0.167527i
$754$	4.40776	−	3.69855i	0.160521	−	0.134693i
$755$	16.0498			0.584113
$756$	5.02216	+	1.33339i	0.182654	+	0.0484950i
$757$	14.0745			0.511545			0.255773	−	0.966737i	$-0.417670\pi$
$757$	14.0745			0.511545			0.255773	+	0.966737i	$0.417670\pi$
$758$	−10.7246	+	8.99897i	−0.389533	+	0.326857i
$759$	−22.1038	−	47.3077i	−0.802317	−	1.71716i
$760$	−0.135889	+	0.770666i	−0.00492922	+	0.0279550i
$761$	39.6207	−	14.4208i	1.43625	−	0.522752i	0.497534	−	0.867444i	$-0.334239\pi$
$761$	39.6207	−	14.4208i	1.43625	−	0.522752i	0.938716	+	0.344692i	$0.112017\pi$
$762$	−15.6627	+	10.9849i	−0.567398	+	0.397941i
$763$	−2.18465	−	12.3898i	−0.0790896	−	0.448539i
$764$	5.09470	+	8.82428i	0.184320	+	0.319251i
$765$	−2.09863	+	0.373341i	−0.0758760	+	0.0134982i
$766$	13.8302	−	23.9547i	0.499706	−	0.865517i
$767$	22.1221	+	8.05177i	0.798781	+	0.290733i
$768$	1.67269	−	0.449562i	0.0603580	−	0.0162222i
$769$	7.01523	+	5.88648i	0.252976	+	0.212272i	0.760452	−	0.649394i	$-0.224977\pi$
$769$	7.01523	+	5.88648i	0.252976	+	0.212272i	−0.507477	+	0.861665i	$0.669422\pi$
$770$	3.59487	+	3.01646i	0.129550	+	0.108706i
$771$	5.79888	−	1.55854i	0.208842	−	0.0561295i
$772$	−20.7220	−	7.54220i	−0.745802	−	0.271450i
$773$	−16.9158	+	29.2989i	−0.608417	+	1.05381i	0.383084	+	0.923713i	$0.374862\pi$
$773$	−16.9158	+	29.2989i	−0.608417	+	1.05381i	−0.991501	+	0.130096i	$0.958471\pi$
$774$	−14.5416	−	17.2765i	−0.522688	−	0.620992i
$775$	−0.450080	−	0.779561i	−0.0161673	−	0.0280026i
$776$	−2.60229	−	14.7583i	−0.0934167	−	0.529793i
$777$	−10.2103	+	7.16092i	−0.366292	+	0.256897i
$778$	−7.53614	+	2.74293i	−0.270184	+	0.0983388i
$779$	−1.38192	+	7.83728i	−0.0495126	+	0.280800i
$780$	2.39523	+	5.12639i	0.0857629	+	0.183554i
$781$	1.38819	−	1.16483i	0.0496734	−	0.0416809i
$782$	4.56457			0.163229
$783$	−8.81519	+	4.13514i	−0.315029	+	0.147778i
$784$	1.00000			0.0357143
$785$	15.0628	−	12.6392i	0.537615	−	0.451112i
$786$	−26.2668	−	2.27789i	−0.936905	−	0.0812496i
$787$	−1.36056	+	7.71611i	−0.0484987	+	0.275050i	−0.999407	−	0.0344218i	$-0.989041\pi$
$787$	−1.36056	+	7.71611i	−0.0484987	+	0.275050i	0.950909	+	0.309472i	$0.100152\pi$
$788$	3.62789	−	1.32044i	0.129238	−	0.0470389i
$789$	−7.17967	−	3.34128i	−0.255603	−	0.118953i
$790$	−2.07456	−	11.7654i	−0.0738095	−	0.418594i
$791$	−1.15307	−	1.99717i	−0.0409984	−	0.0710113i
$792$	11.4497	−	6.63377i	0.406848	−	0.235721i
$793$	0.592035	−	1.02543i	0.0210238	−	0.0364142i
$794$	15.0075	+	5.46228i	0.532596	+	0.193849i
$795$	5.28233	−	19.7742i	0.187345	−	0.701317i
$796$	−12.8640	−	10.7942i	−0.455954	−	0.382591i
$797$	15.2138	+	12.7659i	0.538901	+	0.452191i	0.871162	−	0.490996i	$-0.163367\pi$
$797$	15.2138	+	12.7659i	0.538901	+	0.452191i	−0.332261	+	0.943187i	$0.607812\pi$
$798$	0.901543	+	0.900171i	0.0319143	+	0.0318657i
$799$	6.70553	+	2.44061i	0.237225	+	0.0863427i
$800$	−1.93405	+	3.34987i	−0.0683790	+	0.118436i
$801$	−2.35797	+	2.81883i	−0.0833149	+	0.0995985i
$802$	−0.887176	−	1.53663i	−0.0313273	−	0.0542604i
$803$	8.02970	+	45.5387i	0.283362	+	1.60703i
$804$	−1.10287	−	12.4962i	−0.0388952	−	0.440708i
$805$	−6.83304	+	2.48702i	−0.240833	+	0.0876561i
$806$	−0.124084	+	0.703718i	−0.00437069	+	0.0247874i
$807$	−17.1498	+	24.5322i	−0.603703	+	0.863576i
$808$	−3.29772	+	2.76711i	−0.116013	+	0.0973468i
$809$	−21.8638			−0.768690			−0.384345	−	0.923189i	$-0.625573\pi$
$809$	−21.8638			−0.768690			−0.384345	+	0.923189i	$0.625573\pi$
$810$	−1.69143	−	9.42459i	−0.0594309	−	0.331146i
$811$	−27.9995			−0.983197			−0.491598	−	0.870822i	$-0.663587\pi$
$811$	−27.9995			−0.983197			−0.491598	+	0.870822i	$0.663587\pi$
$812$	−1.43546	+	1.20450i	−0.0503749	+	0.0422696i
$813$	−30.8643	+	44.1503i	−1.08246	+	1.54842i
$814$	−5.51494	+	31.2768i	−0.193298	+	1.09625i
$815$	−2.65504	+	0.966355i	−0.0930019	+	0.0338499i
$816$	0.101694	+	1.15226i	0.00356001	+	0.0403372i
$817$	−0.961431	−	5.45255i	−0.0336362	−	0.190760i
$818$	−15.6202	−	27.0550i	−0.546148	−	0.945956i
$819$	9.07432	+	1.58580i	0.317082	+	0.0554123i
$820$	5.75542	−	9.96869i	0.200988	−	0.348122i
$821$	−25.1763	−	9.16343i	−0.878660	−	0.319806i	−0.136991	−	0.990572i	$-0.543743\pi$
$821$	−25.1763	−	9.16343i	−0.878660	−	0.319806i	−0.741669	+	0.670766i	$0.765965\pi$
$822$	−2.91709	−	2.91265i	−0.101745	−	0.101590i
$823$	−42.1725	−	35.3869i	−1.47004	−	1.23351i	−0.916097	−	0.400957i	$-0.868678\pi$
$823$	−42.1725	−	35.3869i	−1.47004	−	1.23351i	−0.553944	−	0.832554i	$-0.686878\pi$
$824$	−2.40374	−	2.01698i	−0.0837384	−	0.0702648i
$825$	−7.62682	+	28.5506i	−0.265532	+	0.994006i
$826$	−7.20444	−	2.62220i	−0.250675	−	0.0912381i
$827$	−19.4563	+	33.6994i	−0.676563	+	1.17184i	0.299446	+	0.954113i	$0.403198\pi$
$827$	−19.4563	+	33.6994i	−0.676563	+	1.17184i	−0.976009	+	0.217729i	$0.930135\pi$
$828$	0.0312340	+	20.5043i	0.00108546	+	0.712574i
$829$	−1.28335	−	2.22282i	−0.0445725	−	0.0772018i	0.842878	−	0.538104i	$-0.180859\pi$
$829$	−1.28335	−	2.22282i	−0.0445725	−	0.0772018i	−0.887451	+	0.460902i	$0.847526\pi$
$830$	−2.17422	−	12.3306i	−0.0754683	−	0.428002i
$831$	11.3246	+	5.27027i	0.392848	+	0.182824i
$832$	2.88543	−	1.05021i	0.100034	−	0.0364095i
$833$	−0.115970	+	0.657698i	−0.00401812	+	0.0227879i
$834$	1.56995	+	0.136148i	0.0543628	+	0.00471441i
$835$	6.17735	−	5.18341i	0.213776	−	0.179379i
$836$	3.24441			0.112210
$837$	0.508531	−	1.09709i	0.0175774	−	0.0379208i
$838$	−24.8075			−0.856961
$839$	14.7610	−	12.3859i	0.509606	−	0.427610i	−0.351384	−	0.936231i	$-0.614289\pi$
$839$	14.7610	−	12.3859i	0.509606	−	0.427610i	0.860991	+	0.508621i	$0.169845\pi$
$840$	−0.780049	−	1.66950i	−0.0269142	−	0.0576032i
$841$	−4.42605	+	25.1014i	−0.152623	+	0.865566i
$842$	22.8604	−	8.32049i	0.787820	−	0.286743i
$843$	31.7537	−	22.2702i	1.09366	−	0.767028i
$844$	2.66815	+	15.1318i	0.0918416	+	0.520859i
$845$	−1.89978	−	3.29052i	−0.0653545	−	0.113197i
$846$	−10.9175	+	30.1383i	−0.375351	+	1.03618i
$847$	4.22793	−	7.32300i	0.145274	−	0.251621i
$848$	−10.4373	−	3.79885i	−0.358417	−	0.130453i
$849$	14.6102	−	3.92672i	0.501421	−	0.134765i
$850$	−1.97891	−	1.66051i	−0.0678762	−	0.0569549i
$851$	−37.6984	−	31.6327i	−1.29229	−	1.08436i
$852$	−0.687204	+	0.184697i	−0.0235432	+	0.00632761i
$853$	−18.7102	−	6.80997i	−0.640626	−	0.233169i	0.00122365	−	0.999999i	$-0.499611\pi$
$853$	−18.7102	−	6.80997i	−0.640626	−	0.233169i	−0.641850	+	0.766830i	$0.721833\pi$
$854$	−0.192807	+	0.333951i	−0.00659771	+	0.0114276i
$855$	0.799587	−	2.20730i	0.0273453	−	0.0754882i
$856$	−6.14219	−	10.6386i	−0.209936	−	0.363619i
$857$	−0.843781	−	4.78532i	−0.0288230	−	0.163464i	0.966999	−	0.254781i	$-0.0820033\pi$
$857$	−0.843781	−	4.78532i	−0.0288230	−	0.163464i	−0.995822	+	0.0913174i	$0.970892\pi$
$858$	19.2063	−	13.4702i	0.655693	−	0.459866i
$859$	15.7744	−	5.74140i	0.538214	−	0.195894i	−0.0585882	−	0.998282i	$-0.518660\pi$
$859$	15.7744	−	5.74140i	0.538214	−	0.195894i	0.596802	+	0.802388i	$0.296438\pi$
$860$	−1.39063	+	7.88666i	−0.0474201	+	0.268933i
$861$	−7.93270	−	16.9780i	−0.270346	−	0.578607i
$862$	−13.8774	+	11.6445i	−0.472666	+	0.396614i
$863$	−45.5230			−1.54962			−0.774810	−	0.632194i	$-0.782155\pi$
$863$	−45.5230			−1.54962			−0.774810	+	0.632194i	$0.782155\pi$
$864$	−5.17533	+	0.464701i	−0.176068	+	0.0158094i
$865$	1.31168			0.0445983
$866$	29.3888	−	24.6601i	0.998672	−	0.837986i
$867$	28.5651	+	2.47720i	0.970123	+	0.0841302i
$868$	0.0404103	−	0.229178i	0.00137161	−	0.00777881i
$869$	−46.5439	+	16.9406i	−1.57889	+	0.574670i
$870$	3.13064	+	1.45694i	0.106139	+	0.0493948i
$871$	−3.86188	−	21.9018i	−0.130855	−	0.742114i
$872$	6.29044	+	10.8954i	0.213021	+	0.368964i
$873$	0.0684840	+	44.9579i	0.00231783	+	1.52159i
$874$	−2.51365	+	4.35377i	−0.0850255	+	0.147268i
$875$	8.86585	+	3.22691i	0.299720	+	0.109089i
$876$	4.68624	−	17.5427i	0.158333	−	0.592713i
$877$	36.8610	+	30.9300i	1.24471	+	1.04443i	0.997141	+	0.0755610i	$0.0240748\pi$
$877$	36.8610	+	30.9300i	1.24471	+	1.04443i	0.247565	+	0.968871i	$0.420370\pi$
$878$	10.2800	+	8.62592i	0.346932	+	0.291111i
$879$	28.0517	+	28.0090i	0.946159	+	0.944719i
$880$	−4.40976	−	1.60502i	−0.148653	−	0.0541053i
$881$	23.6462	−	40.9564i	0.796660	−	1.37986i	−0.125120	−	0.992142i	$-0.539932\pi$
$881$	23.6462	−	40.9564i	0.796660	−	1.37986i	0.921780	−	0.387713i	$-0.126735\pi$
$882$	−2.95521	−	0.516443i	−0.0995072	−	0.0173896i
$883$	−19.1759	−	33.2136i	−0.645321	−	1.11773i	−0.984227	−	0.176908i	$-0.943390\pi$
$883$	−19.1759	−	33.2136i	−0.645321	−	1.11773i	0.338907	−	0.940820i	$-0.389943\pi$
$884$	0.356099	+	2.01954i	0.0119769	+	0.0679244i
$885$	1.24205	+	14.0733i	0.0417511	+	0.473067i
$886$	−14.8639	+	5.41002i	−0.499363	+	0.181753i
$887$	−2.12529	+	12.0531i	−0.0713603	+	0.404705i	0.928114	+	0.372295i	$0.121429\pi$
$887$	−2.12529	+	12.0531i	−0.0713603	+	0.404705i	−0.999475	+	0.0324093i	$0.989682\pi$
$888$	7.14536	−	10.2212i	0.239783	−	0.343001i
$889$	8.46108	−	7.09969i	0.283776	−	0.238116i
$890$	1.30330			0.0436867
$891$	−37.2623	+	13.6911i	−1.24833	+	0.458668i
$892$	−17.0195			−0.569857
$893$	−6.02055	+	5.05184i	−0.201470	+	0.169054i
$894$	−15.7232	+	22.4915i	−0.525862	+	0.752227i
$895$	1.10308	−	6.25589i	0.0368719	−	0.209111i
$896$	−0.939693	+	0.342020i	−0.0313929	+	0.0114261i
$897$	3.19573	+	36.2097i	0.106702	+	1.20901i
$898$	−6.05056	−	34.3144i	−0.201910	−	1.14509i
$899$	0.218037	+	0.377651i	0.00727194	+	0.0125954i
$900$	7.44555	−	8.90076i	0.248185	−	0.296692i
$901$	3.70891	−	6.42402i	0.123562	−	0.214015i
$902$	−44.8450	−	16.3223i	−1.49318	−	0.543472i
$903$	9.22600	+	9.21196i	0.307022	+	0.306555i
$904$	1.76660	+	1.48236i	0.0587563	+	0.0493024i
$905$	−1.58392	−	1.32906i	−0.0526512	−	0.0441796i
$906$	−6.74352	+	25.2441i	−0.224039	+	0.838678i
$907$	−15.3830	−	5.59897i	−0.510785	−	0.185911i	0.0737533	−	0.997277i	$-0.476502\pi$
$907$	−15.3830	−	5.59897i	−0.510785	−	0.185911i	−0.584539	+	0.811366i	$0.698724\pi$
$908$	1.64792	−	2.85429i	0.0546883	−	0.0947228i
$909$	11.1745	−	6.47433i	0.370635	−	0.214740i
$910$	−1.63343	−	2.82918i	−0.0541475	−	0.0937863i
$911$	−2.91082	−	16.5081i	−0.0964397	−	0.546937i	−0.994297	−	0.106650i	$-0.965988\pi$
$911$	−2.91082	−	16.5081i	−0.0964397	−	0.546937i	0.897857	−	0.440287i	$-0.145123\pi$
$912$	−1.15505	−	0.537538i	−0.0382475	−	0.0177997i
$913$	−48.7798	+	17.7544i	−1.61438	+	0.587585i
$914$	−2.50439	+	14.2031i	−0.0828378	+	0.469797i
$915$	0.707929	+	0.0613925i	0.0234034	+	0.00202957i
$916$	−4.20096	+	3.52502i	−0.138804	+	0.116470i
$917$	15.2221			0.502677
$918$	0.294550	−	3.45770i	0.00972160	−	0.114121i
$919$	7.27053			0.239833			0.119916	−	0.992784i	$-0.461737\pi$
$919$	7.27053			0.239833			0.119916	+	0.992784i	$0.461737\pi$
$920$	5.57035	−	4.67408i	0.183649	−	0.154100i
$921$	−6.54476	−	14.0074i	−0.215657	−	0.461560i
$922$	−0.136877	+	0.776268i	−0.00450781	+	0.0255650i
$923$	−1.18544	+	0.431466i	−0.0390193	+	0.0142019i
$924$	−6.25488	+	4.38681i	−0.205770	+	0.144316i
$925$	4.83630	+	27.4280i	0.159016	+	0.901827i
$926$	20.7925	+	36.0137i	0.683284	+	1.18348i
$927$	6.06192	+	7.20201i	0.199100	+	0.236545i
$928$	0.936933	−	1.62281i	0.0307563	−	0.0532715i
$929$	−8.36823	−	3.04579i	−0.274553	−	0.0999290i	0.201075	−	0.979576i	$-0.435557\pi$
$929$	−8.36823	−	3.04579i	−0.274553	−	0.0999290i	−0.475627	+	0.879647i	$0.657779\pi$
$930$	−0.414134	+	0.111305i	−0.0135800	+	0.00364984i
$931$	−0.563462	−	0.472801i	−0.0184667	−	0.0154954i
$932$	−20.0401	−	16.8157i	−0.656436	−	0.550815i
$933$	−11.8910	+	3.19589i	−0.389294	+	0.104629i
$934$	3.11255	+	1.13288i	0.101846	+	0.0370689i
$935$	1.56702	−	2.71416i	0.0512471	−	0.0887625i
$936$	−9.06945	+	1.61344i	−0.296444	+	0.0527368i
$937$	−10.7329	−	18.5899i	−0.350628	−	0.607305i	0.635732	−	0.771910i	$-0.280698\pi$
$937$	−10.7329	−	18.5899i	−0.350628	−	0.607305i	−0.986360	+	0.164605i	$0.947365\pi$
$938$	1.25769	+	7.13270i	0.0410650	+	0.232891i
$939$	−42.8416	+	30.0466i	−1.39808	+	0.980535i
$940$	10.6822	−	3.88801i	0.348416	−	0.126813i
$941$	−2.75079	+	15.6005i	−0.0896733	+	0.508562i	0.906577	+	0.422041i	$0.138686\pi$
$941$	−2.75079	+	15.6005i	−0.0896733	+	0.508562i	−0.996250	+	0.0865213i	$0.972425\pi$
$942$	13.5508	+	29.0021i	0.441509	+	0.944940i
$943$	56.6476	−	47.5330i	1.84470	−	1.54789i
$944$	7.66681			0.249533
$945$	1.44301	+	5.33658i	0.0469411	+	0.173599i
$946$	33.2019			1.07949
$947$	−7.20035	+	6.04181i	−0.233980	+	0.196333i	−0.752237	−	0.658892i	$-0.771025\pi$
$947$	−7.20035	+	6.04181i	−0.233980	+	0.196333i	0.518257	+	0.855225i	$0.326581\pi$
$948$	19.3769	+	1.68039i	0.629334	+	0.0545766i
$949$	5.58984	−	31.7016i	0.181454	−	1.02908i
$950$	2.67358	−	0.973105i	0.0867425	−	0.0315717i
$951$	−15.3166	−	7.12807i	−0.496676	−	0.231143i
$952$	−0.115970	−	0.657698i	−0.00375861	−	0.0213161i
$953$	11.4928	+	19.9062i	0.372290	+	0.644824i	0.989917	−	0.141646i	$-0.0452395\pi$
$953$	11.4928	+	19.9062i	0.372290	+	0.644824i	−0.617628	+	0.786470i	$0.711906\pi$
$954$	28.8825	+	16.6167i	0.935104	+	0.537985i
$955$	−5.42029	+	9.38822i	−0.175396	+	0.303796i
$956$	2.11356	+	0.769274i	0.0683575	+	0.0248801i
$957$	3.69474	−	13.8311i	0.119434	−	0.447096i
$958$	28.4113	+	23.8399i	0.917929	+	0.770234i
$959$	1.82317	+	1.52982i	0.0588733	+	0.0494005i
$960$	1.30401	+	1.30202i	0.0420867	+	0.0420226i
$961$	29.0796	+	10.5841i	0.938051	+	0.341423i
$962$	11.0545	−	19.1470i	0.356412	−	0.617324i
$963$	12.6572	+	34.6114i	0.407874	+	1.11534i
$964$	9.89675	+	17.1417i	0.318753	+	0.552096i
$965$	−4.07400	−	23.1048i	−0.131147	−	0.743769i
$966$	−1.04075	−	11.7923i	−0.0334855	−	0.379412i
$967$	−17.1456	+	6.24050i	−0.551367	+	0.200681i	−0.602654	−	0.798003i	$-0.705890\pi$
$967$	−17.1456	+	6.24050i	−0.551367	+	0.200681i	0.0512870	+	0.998684i	$0.483668\pi$
$968$	−1.46835	+	8.32741i	−0.0471944	+	0.267653i
$969$	0.487489	−	0.697337i	0.0156604	−	0.0224017i
$970$	12.2136	−	10.2484i	0.392155	−	0.329057i
$971$	44.0605			1.41397			0.706985	−	0.707229i	$-0.250055\pi$
$971$	44.0605			1.41397			0.706985	+	0.707229i	$0.250055\pi$
$972$	15.5342	+	1.29948i	0.498260	+	0.0416807i
$973$	−0.909811			−0.0291672
$974$	25.3109	−	21.2383i	0.811013	−	0.680520i
$975$	11.7870	−	16.8609i	0.377485	−	0.539979i
$976$	0.0669610	−	0.379755i	0.00214337	−	0.0121557i
$977$	56.7627	−	20.6599i	1.81600	−	0.660970i	0.819924	−	0.572472i	$-0.194015\pi$
$977$	56.7627	−	20.6599i	1.81600	−	0.660970i	0.996076	−	0.0884984i	$-0.0282068\pi$
$978$	−0.404391	−	4.58202i	−0.0129310	−	0.146517i
$979$	−0.938286	−	5.32128i	−0.0299878	−	0.170069i
$980$	0.531954	+	0.921371i	0.0169926	+	0.0294321i
$981$	−12.9628	−	35.4468i	−0.413869	−	1.13173i
$982$	10.6354	−	18.4210i	0.339388	−	0.587838i
$983$	−48.3457	−	17.5964i	−1.54199	−	0.561238i	−0.575467	−	0.817825i	$-0.695180\pi$
$983$	−48.3457	−	17.5964i	−1.54199	−	0.561238i	−0.966521	+	0.256588i	$0.917402\pi$
$984$	13.2611	+	13.2409i	0.422748	+	0.422105i
$985$	3.14649	+	2.64022i	0.100256	+	0.0841244i
$986$	0.958667	+	0.804417i	0.0305302	+	0.0256179i
$987$	4.77631	−	17.8799i	0.152032	−	0.569123i
$988$	−2.12237	−	0.772480i	−0.0675217	−	0.0245759i
$989$	−25.7236	+	44.5546i	−0.817963	+	1.41675i
$990$	12.2029	+	7.02058i	0.387833	+	0.223129i
$991$	15.3462	+	26.5804i	0.487487	+	0.844353i	0.999896	−	0.0143885i	$-0.00458016\pi$
$991$	15.3462	+	26.5804i	0.487487	+	0.844353i	−0.512409	+	0.858742i	$0.671247\pi$
$992$	0.0404103	+	0.229178i	0.00128303	+	0.00727641i
$993$	50.0807	+	23.3066i	1.58926	+	0.739613i
$994$	0.386061	−	0.140515i	0.0122451	−	0.00445685i
$995$	3.10240	−	17.5946i	0.0983527	−	0.557786i
$996$	20.3078	+	1.76112i	0.643477	+	0.0558031i
$997$	−17.2620	+	14.4845i	−0.546692	+	0.458729i	−0.873819	−	0.486252i	$-0.838364\pi$
$997$	−17.2620	+	14.4845i	−0.546692	+	0.458729i	0.327127	+	0.944980i	$0.393919\pi$
$998$	−2.22964			−0.0705779
$999$	−26.3947	+	26.5156i	−0.835093	+	0.838918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.211.4	yes	24
27.16	even	9	inner	378.2.u.c.43.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.43.4	✓	24	27.16	even	9	inner
378.2.u.c.211.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.992383 - 1.41957i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.999746 - 0.363878i) q^{5} +(0.152272 + 1.72534i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.03035 - 2.81751i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.992383 - 1.41957i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.999746 - 0.363878i) q^{5} +(0.152272 + 1.72534i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.03035 - 2.81751i) q^{9} +(-0.531954 + 0.921371i) q^{10} +(4.14487 + 1.50861i) q^{11} +(-1.22568 - 1.22381i) q^{12} +(-2.35223 - 1.97375i) q^{13} +(0.766044 + 0.642788i) q^{14} +(0.475581 - 1.78032i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.333922 - 0.578370i) q^{17} +(2.60036 + 1.49604i) q^{18} +(0.367774 + 0.637002i) q^{19} +(-0.184746 - 1.04774i) q^{20} +(-1.57033 - 0.730800i) q^{21} +(-4.14487 + 1.50861i) q^{22} +(1.18685 - 6.73094i) q^{23} +(1.72557 + 0.149644i) q^{24} +(-2.96314 + 2.48637i) q^{25} +3.07061 q^{26} +(-5.02216 - 1.33339i) q^{27} -1.00000 q^{28} +(1.43546 - 1.20450i) q^{29} +(0.780049 + 1.66950i) q^{30} +(-0.0404103 + 0.229178i) q^{31} +(0.939693 - 0.342020i) q^{32} +(6.25488 - 4.38681i) q^{33} +(0.115970 + 0.657698i) q^{34} +(-0.531954 - 0.921371i) q^{35} +(-2.95363 + 0.525444i) q^{36} +(3.60010 - 6.23556i) q^{37} +(-0.691188 - 0.251572i) q^{38} +(-5.13619 + 1.38043i) q^{39} +(0.815001 + 0.683867i) q^{40} +(8.28814 + 6.95458i) q^{41} +(1.67269 - 0.449562i) q^{42} +(-7.07332 - 2.57448i) q^{43} +(2.20544 - 3.81993i) q^{44} +(-2.05532 - 2.44187i) q^{45} +(3.41739 + 5.91909i) q^{46} +(1.85542 + 10.5226i) q^{47} +(-1.41806 + 0.994544i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.671688 - 3.80933i) q^{50} +(-0.489658 - 1.04799i) q^{51} +(-2.35223 + 1.97375i) q^{52} +11.1071 q^{53} +(4.70428 - 2.20674i) q^{54} +4.69277 q^{55} +(0.766044 - 0.642788i) q^{56} +(1.26924 + 0.110070i) q^{57} +(-0.325393 + 1.84540i) q^{58} +(-7.20444 + 2.62220i) q^{59} +(-1.67068 - 0.777504i) q^{60} +(0.0669610 + 0.379755i) q^{61} +(-0.116357 - 0.201536i) q^{62} +(-2.59579 + 1.50396i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.06984 - 1.11733i) q^{65} +(-1.97172 + 7.38105i) q^{66} +(5.54826 + 4.65554i) q^{67} +(-0.511599 - 0.429282i) q^{68} +(-8.37723 - 8.36448i) q^{69} +(0.999746 + 0.363878i) q^{70} +(0.205419 - 0.355795i) q^{71} +(1.92486 - 2.30107i) q^{72} +(5.24172 + 9.07893i) q^{73} +(1.25030 + 7.09082i) q^{74} +(0.589005 + 6.67380i) q^{75} +(0.691188 - 0.251572i) q^{76} +(0.765941 - 4.34387i) q^{77} +(3.04722 - 4.35895i) q^{78} +(-8.60212 + 7.21804i) q^{79} -1.06391 q^{80} +(-6.87674 + 5.80607i) q^{81} -10.8194 q^{82} +(-9.01536 + 7.56478i) q^{83} +(-0.992383 + 1.41957i) q^{84} +(0.123381 - 0.699731i) q^{85} +(7.07332 - 2.57448i) q^{86} +(-0.285338 - 3.23306i) q^{87} +(0.765941 + 4.34387i) q^{88} +(-0.612505 - 1.06089i) q^{89} +(3.14408 + 0.549448i) q^{90} +(-1.53531 + 2.65923i) q^{91} +(-6.42259 - 2.33763i) q^{92} +(0.285232 + 0.284798i) q^{93} +(-8.18514 - 6.86814i) q^{94} +(0.599471 + 0.503016i) q^{95} +(0.447013 - 1.67337i) q^{96} +(-14.0822 - 5.12551i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-0.0201572 - 13.2326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

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