LMFDB - Embedded newform 378.2.u.c.85.4

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			85.4
Character	$\chi$	$=$	378.85
Dual form			378.2.u.c.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(1.72892 - 0.104015i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.163613 + 0.927896i) q^{5} +(1.66023 + 0.493585i) q^{6} +(-0.766044 + 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.97836 - 0.359668i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(1.72892 - 0.104015i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.163613 + 0.927896i) q^{5} +(1.66023 + 0.493585i) q^{6} +(-0.766044 + 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.97836 - 0.359668i) q^{9} +(-0.471105 + 0.815978i) q^{10} +(-0.205406 - 1.16491i) q^{11} +(1.39129 + 1.03165i) q^{12} +(0.528086 - 0.192208i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.186360 + 1.62128i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.22588 + 2.12328i) q^{17} +(2.92176 + 0.680682i) q^{18} +(-2.07989 - 3.60248i) q^{19} +(-0.721775 + 0.605641i) q^{20} +(-1.25757 + 1.19101i) q^{21} +(0.205406 - 1.16491i) q^{22} +(0.572264 + 0.480187i) q^{23} +(0.954542 + 1.44529i) q^{24} +(3.86424 + 1.40647i) q^{25} +0.561977 q^{26} +(5.11195 - 0.931634i) q^{27} -1.00000 q^{28} +(-9.48124 - 3.45089i) q^{29} +(-0.729631 + 1.45977i) q^{30} +(-3.33687 - 2.79996i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.476300 - 1.99268i) q^{33} +(-1.87815 + 1.57596i) q^{34} +(-0.471105 - 0.815978i) q^{35} +(2.51275 + 1.63893i) q^{36} +(2.75815 - 4.77725i) q^{37} +(-0.722339 - 4.09659i) q^{38} +(0.893028 - 0.387241i) q^{39} +(-0.885388 + 0.322255i) q^{40} +(-0.559633 + 0.203690i) q^{41} +(-1.58908 + 0.689069i) q^{42} +(-0.948829 - 5.38108i) q^{43} +(0.591442 - 1.02441i) q^{44} +(-0.153564 + 2.82246i) q^{45} +(0.373519 + 0.646954i) q^{46} +(-5.74018 + 4.81658i) q^{47} +(0.402659 + 1.68460i) q^{48} +(0.173648 - 0.984808i) q^{49} +(3.15016 + 2.64330i) q^{50} +(-1.89859 + 3.79850i) q^{51} +(0.528086 + 0.192208i) q^{52} +4.38051 q^{53} +(5.12230 + 0.872941i) q^{54} +1.11453 q^{55} +(-0.939693 - 0.342020i) q^{56} +(-3.97069 - 6.01207i) q^{57} +(-7.72918 - 6.48555i) q^{58} +(-0.408115 + 2.31453i) q^{59} +(-1.18490 + 1.12218i) q^{60} +(-4.53619 + 3.80631i) q^{61} +(-2.17798 - 3.77238i) q^{62} +(-2.05037 + 2.18998i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0919469 + 0.521457i) q^{65} +(0.233963 - 2.03541i) q^{66} +(6.83985 - 2.48950i) q^{67} +(-2.30389 + 0.838548i) q^{68} +(1.03935 + 0.770682i) q^{69} +(-0.163613 - 0.927896i) q^{70} +(-3.42209 + 5.92723i) q^{71} +(1.80066 + 2.39950i) q^{72} +(0.138365 + 0.239655i) q^{73} +(4.22572 - 3.54580i) q^{74} +(6.82728 + 2.02974i) q^{75} +(0.722339 - 4.09659i) q^{76} +(0.906142 + 0.760344i) q^{77} +(0.971617 - 0.0584541i) q^{78} +(3.48781 + 1.26946i) q^{79} -0.942210 q^{80} +(8.74128 - 2.14245i) q^{81} -0.595549 q^{82} +(-12.9833 - 4.72555i) q^{83} +(-1.72892 + 0.104015i) q^{84} +(-1.76961 - 1.48488i) q^{85} +(0.948829 - 5.38108i) q^{86} +(-16.7513 - 4.98014i) q^{87} +(0.906142 - 0.760344i) q^{88} +(0.814931 + 1.41150i) q^{89} +(-1.10964 + 2.59972i) q^{90} +(-0.280989 + 0.486687i) q^{91} +(0.129722 + 0.735689i) q^{92} +(-6.06043 - 4.49384i) q^{93} +(-7.04137 + 2.56285i) q^{94} +(3.68302 - 1.34051i) q^{95} +(-0.197790 + 1.72072i) q^{96} +(0.961438 + 5.45259i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-1.03076 - 3.39566i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	1.72892	−	0.104015i	0.998195	−	0.0600531i
$3$	1.72892	−	0.104015i	0.998195	−	0.0600531i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.163613	+	0.927896i	−0.0731700	+	0.414968i	0.926118	+	0.377234i	$0.123125\pi$
$5$	−0.163613	+	0.927896i	−0.0731700	+	0.414968i	−0.999288	+	0.0377334i	$0.987986\pi$
$6$	1.66023	+	0.493585i	0.677787	+	0.201505i
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.97836	−	0.359668i	0.992787	−	0.119889i
$10$	−0.471105	+	0.815978i	−0.148977	+	0.258035i
$11$	−0.205406	−	1.16491i	−0.0619322	−	0.351235i	−0.999989	−	0.00475256i	$-0.998487\pi$
$11$	−0.205406	−	1.16491i	−0.0619322	−	0.351235i	0.938057	−	0.346482i	$-0.112624\pi$
$12$	1.39129	+	1.03165i	0.401632	+	0.297812i
$13$	0.528086	−	0.192208i	0.146465	−	0.0533088i	−0.267748	−	0.963489i	$-0.586279\pi$
$13$	0.528086	−	0.192208i	0.146465	−	0.0533088i	0.414212	+	0.910180i	$0.364057\pi$
$14$	−0.939693	+	0.342020i	−0.251143	+	0.0914087i
$15$	−0.186360	+	1.62128i	−0.0481178	+	0.418613i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.22588	+	2.12328i	−0.297318	+	0.514971i	−0.975522	−	0.219904i	$-0.929426\pi$
$17$	−1.22588	+	2.12328i	−0.297318	+	0.514971i	0.678203	+	0.734875i	$0.262759\pi$
$18$	2.92176	+	0.680682i	0.688665	+	0.160438i
$19$	−2.07989	−	3.60248i	−0.477160	−	0.826465i	0.522497	−	0.852641i	$-0.325000\pi$
$19$	−2.07989	−	3.60248i	−0.477160	−	0.826465i	−0.999657	+	0.0261756i	$0.991667\pi$
$20$	−0.721775	+	0.605641i	−0.161394	+	0.135425i
$21$	−1.25757	+	1.19101i	−0.274425	+	0.259900i
$22$	0.205406	−	1.16491i	0.0437927	−	0.248361i
$23$	0.572264	+	0.480187i	0.119325	+	0.100126i	0.700498	−	0.713655i	$-0.252961\pi$
$23$	0.572264	+	0.480187i	0.119325	+	0.100126i	−0.581172	+	0.813780i	$0.697406\pi$
$24$	0.954542	+	1.44529i	0.194845	+	0.295018i
$25$	3.86424	+	1.40647i	0.772848	+	0.281294i
$26$	0.561977			0.110213
$27$	5.11195	−	0.931634i	0.983796	−	0.179293i
$28$	−1.00000			−0.188982
$29$	−9.48124	−	3.45089i	−1.76062	−	0.640814i	−0.760657	−	0.649154i	$-0.775123\pi$
$29$	−9.48124	−	3.45089i	−1.76062	−	0.640814i	−0.999965	+	0.00834048i	$0.997345\pi$
$30$	−0.729631	+	1.45977i	−0.133212	+	0.266516i
$31$	−3.33687	−	2.79996i	−0.599319	−	0.502888i	0.291908	−	0.956446i	$-0.405710\pi$
$31$	−3.33687	−	2.79996i	−0.599319	−	0.502888i	−0.891227	+	0.453558i	$0.850154\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−0.476300	−	1.99268i	−0.0829131	−	0.346882i
$34$	−1.87815	+	1.57596i	−0.322100	+	0.270274i
$35$	−0.471105	−	0.815978i	−0.0796313	−	0.137925i
$36$	2.51275	+	1.63893i	0.418791	+	0.273155i
$37$	2.75815	−	4.77725i	0.453436	−	0.785375i	−0.545161	−	0.838332i	$-0.683531\pi$
$37$	2.75815	−	4.77725i	0.453436	−	0.785375i	0.998597	+	0.0529570i	$0.0168646\pi$
$38$	−0.722339	−	4.09659i	−0.117179	−	0.664554i
$39$	0.893028	−	0.387241i	0.142999	−	0.0620082i
$40$	−0.885388	+	0.322255i	−0.139992	+	0.0509530i
$41$	−0.559633	+	0.203690i	−0.0874000	+	0.0318110i	−0.385350	−	0.922770i	$-0.625919\pi$
$41$	−0.559633	+	0.203690i	−0.0874000	+	0.0318110i	0.297950	+	0.954581i	$0.403697\pi$
$42$	−1.58908	+	0.689069i	−0.245201	+	0.106326i
$43$	−0.948829	−	5.38108i	−0.144695	−	0.820607i	−0.967611	−	0.252444i	$-0.918766\pi$
$43$	−0.948829	−	5.38108i	−0.144695	−	0.820607i	0.822916	−	0.568163i	$-0.192346\pi$
$44$	0.591442	−	1.02441i	0.0891633	−	0.154435i
$45$	−0.153564	+	2.82246i	−0.0228920	+	0.420747i
$46$	0.373519	+	0.646954i	0.0550724	+	0.0953881i
$47$	−5.74018	+	4.81658i	−0.837291	+	0.702571i	−0.956953	−	0.290244i	$-0.906264\pi$
$47$	−5.74018	+	4.81658i	−0.837291	+	0.702571i	0.119661	+	0.992815i	$0.461819\pi$
$48$	0.402659	+	1.68460i	0.0581189	+	0.243151i
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$	3.15016	+	2.64330i	0.445500	+	0.373819i
$51$	−1.89859	+	3.79850i	−0.265856	+	0.531896i
$52$	0.528086	+	0.192208i	0.0732323	+	0.0266544i
$53$	4.38051			0.601709			0.300854	−	0.953670i	$-0.402728\pi$
$53$	4.38051			0.601709			0.300854	+	0.953670i	$0.402728\pi$
$54$	5.12230	+	0.872941i	0.697057	+	0.118792i
$55$	1.11453			0.150283
$56$	−0.939693	−	0.342020i	−0.125572	−	0.0457044i
$57$	−3.97069	−	6.01207i	−0.525931	−	0.796319i
$58$	−7.72918	−	6.48555i	−1.01489	−	0.851594i
$59$	−0.408115	+	2.31453i	−0.0531320	+	0.301327i	−0.999781	−	0.0209407i	$-0.993334\pi$
$59$	−0.408115	+	2.31453i	−0.0531320	+	0.301327i	0.946649	+	0.322267i	$0.104445\pi$
$60$	−1.18490	+	1.12218i	−0.152970	+	0.144873i
$61$	−4.53619	+	3.80631i	−0.580799	+	0.487348i	−0.885209	−	0.465193i	$-0.845985\pi$
$61$	−4.53619	+	3.80631i	−0.580799	+	0.487348i	0.304410	+	0.952541i	$0.401541\pi$
$62$	−2.17798	−	3.77238i	−0.276604	−	0.479093i
$63$	−2.05037	+	2.18998i	−0.258322	+	0.275911i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.0919469	+	0.521457i	0.0114046	+	0.0646787i
$66$	0.233963	−	2.03541i	0.0287988	−	0.250542i
$67$	6.83985	−	2.48950i	0.835621	−	0.304141i	0.111457	−	0.993769i	$-0.464448\pi$
$67$	6.83985	−	2.48950i	0.835621	−	0.304141i	0.724164	+	0.689628i	$0.242226\pi$
$68$	−2.30389	+	0.838548i	−0.279388	+	0.101689i
$69$	1.03935	+	0.770682i	0.125123	+	0.0927793i
$70$	−0.163613	−	0.927896i	−0.0195555	−	0.110905i
$71$	−3.42209	+	5.92723i	−0.406127	+	0.703433i	−0.994452	−	0.105192i	$-0.966454\pi$
$71$	−3.42209	+	5.92723i	−0.406127	+	0.703433i	0.588325	+	0.808625i	$0.299788\pi$
$72$	1.80066	+	2.39950i	0.212210	+	0.282784i
$73$	0.138365	+	0.239655i	0.0161944	+	0.0280495i	0.874009	−	0.485910i	$-0.161512\pi$
$73$	0.138365	+	0.239655i	0.0161944	+	0.0280495i	−0.857815	+	0.513959i	$0.828178\pi$
$74$	4.22572	−	3.54580i	0.491230	−	0.412191i
$75$	6.82728	+	2.02974i	0.788346	+	0.234374i
$76$	0.722339	−	4.09659i	0.0828580	−	0.469911i
$77$	0.906142	+	0.760344i	0.103264	+	0.0866492i
$78$	0.971617	−	0.0584541i	0.110014	−	0.00661862i
$79$	3.48781	+	1.26946i	0.392409	+	0.142825i	0.530686	−	0.847568i	$-0.321934\pi$
$79$	3.48781	+	1.26946i	0.392409	+	0.142825i	−0.138277	+	0.990394i	$0.544156\pi$
$80$	−0.942210			−0.105342
$81$	8.74128	−	2.14245i	0.971253	−	0.238049i
$82$	−0.595549			−0.0657674
$83$	−12.9833	−	4.72555i	−1.42511	−	0.518696i	−0.489581	−	0.871958i	$-0.662850\pi$
$83$	−12.9833	−	4.72555i	−1.42511	−	0.518696i	−0.935524	+	0.353262i	$0.885072\pi$
$84$	−1.72892	+	0.104015i	−0.188641	+	0.0113490i
$85$	−1.76961	−	1.48488i	−0.191941	−	0.161058i
$86$	0.948829	−	5.38108i	0.102315	−	0.580257i
$87$	−16.7513	−	4.98014i	−1.79593	−	0.533927i
$88$	0.906142	−	0.760344i	0.0965951	−	0.0810529i
$89$	0.814931	+	1.41150i	0.0863825	+	0.149619i	0.905979	−	0.423322i	$-0.139136\pi$
$89$	0.814931	+	1.41150i	0.0863825	+	0.149619i	−0.819597	+	0.572940i	$0.805803\pi$
$90$	−1.10964	+	2.59972i	−0.116966	+	0.274035i
$91$	−0.280989	+	0.486687i	−0.0294556	+	0.0510186i
$92$	0.129722	+	0.735689i	0.0135244	+	0.0767008i
$93$	−6.06043	−	4.49384i	−0.628437	−	0.465990i
$94$	−7.04137	+	2.56285i	−0.726262	+	0.264338i
$95$	3.68302	−	1.34051i	0.377870	−	0.137534i
$96$	−0.197790	+	1.72072i	−0.0201868	+	0.175620i
$97$	0.961438	+	5.45259i	0.0976192	+	0.553626i	0.993913	+	0.110166i	$0.0351382\pi$
$97$	0.961438	+	5.45259i	0.0976192	+	0.553626i	−0.896294	+	0.443460i	$0.853751\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−1.03076	−	3.39566i	−0.103595	−	0.341276i
$100$	2.05612	+	3.56130i	0.205612	+	0.356130i
$101$	−10.7886	+	9.05273i	−1.07351	+	0.900781i	−0.995366	−	0.0961614i	$-0.969344\pi$
$101$	−10.7886	+	9.05273i	−1.07351	+	0.900781i	−0.0781430	+	0.996942i	$0.524899\pi$
$102$	−3.08326	+	2.92006i	−0.305288	+	0.289129i
$103$	2.86972	−	16.2750i	0.282762	−	1.60362i	−0.430409	−	0.902634i	$-0.641631\pi$
$103$	2.86972	−	16.2750i	0.282762	−	1.60362i	0.713171	−	0.700990i	$-0.247258\pi$
$104$	0.430500	+	0.361232i	0.0422140	+	0.0354217i
$105$	−0.899379	−	1.36176i	−0.0877705	−	0.132894i
$106$	4.11633	+	1.49822i	0.399813	+	0.145520i
$107$	11.4023			1.10230			0.551149	−	0.834407i	$-0.314190\pi$
$107$	11.4023			1.10230			0.551149	+	0.834407i	$0.314190\pi$
$108$	4.51483	+	2.57223i	0.434439	+	0.247513i
$109$	4.97065			0.476102			0.238051	−	0.971253i	$-0.423491\pi$
$109$	4.97065			0.476102			0.238051	+	0.971253i	$0.423491\pi$
$110$	1.04731	+	0.381190i	0.0998573	+	0.0363451i
$111$	4.27172	−	8.54639i	0.405454	−	0.811187i
$112$	−0.766044	−	0.642788i	−0.0723844	−	0.0607377i
$113$	−1.98966	+	11.2839i	−0.187172	+	1.06150i	0.735962	+	0.677023i	$0.236730\pi$
$113$	−1.98966	+	11.2839i	−0.187172	+	1.06150i	−0.923133	+	0.384480i	$0.874381\pi$
$114$	−1.67498	−	7.00756i	−0.156876	−	0.656318i
$115$	−0.539193	+	0.452437i	−0.0502800	+	0.0421900i
$116$	−5.04486	−	8.73796i	−0.468404	−	0.811299i
$117$	1.50370	−	0.762400i	0.139017	−	0.0704839i
$118$	−1.17512	+	2.03537i	−0.108179	+	0.187371i
$119$	−0.425742	−	2.41450i	−0.0390277	−	0.221337i
$120$	−1.49725	+	0.649248i	−0.136680	+	0.0592680i
$121$	9.02179	−	3.28366i	0.820162	−	0.298515i
$122$	−5.56445	+	2.02530i	−0.503782	+	0.183362i
$123$	−0.946377	+	0.410375i	−0.0853320	+	0.0370022i
$124$	−0.756406	−	4.28979i	−0.0679273	−	0.385235i
$125$	−4.29282	+	7.43539i	−0.383962	+	0.665041i
$126$	−2.67573	+	1.35664i	−0.238373	+	0.120859i
$127$	−7.01035	−	12.1423i	−0.622068	−	1.07745i	−0.989100	−	0.147245i	$-0.952959\pi$
$127$	−7.01035	−	12.1423i	−0.622068	−	1.07745i	0.367032	−	0.930208i	$-0.380374\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−2.20017	−	9.20479i	−0.193714	−	0.810436i
$130$	−0.0919469	+	0.521457i	−0.00806427	+	0.0457348i
$131$	13.4910	+	11.3203i	1.17872	+	0.989060i	0.999987	+	0.00516216i	$0.00164317\pi$
$131$	13.4910	+	11.3203i	1.17872	+	0.989060i	0.178730	+	0.983898i	$0.442801\pi$
$132$	0.916005	−	1.83264i	0.0797280	−	0.159511i
$133$	3.90892	+	1.42273i	0.338946	+	0.123366i
$134$	7.27882			0.628794
$135$	0.0280771	+	4.89579i	0.00241649	+	0.421362i
$136$	−2.45175			−0.210236
$137$	−8.07989	−	2.94084i	−0.690311	−	0.251253i	−0.0270428	−	0.999634i	$-0.508609\pi$
$137$	−8.07989	−	2.94084i	−0.690311	−	0.251253i	−0.663268	+	0.748382i	$0.730831\pi$
$138$	0.713079	+	1.07968i	0.0607013	+	0.0919087i
$139$	−11.7020	−	9.81914i	−0.992551	−	0.832849i	−0.00661566	−	0.999978i	$-0.502106\pi$
$139$	−11.7020	−	9.81914i	−0.992551	−	0.832849i	−0.985935	+	0.167129i	$0.946550\pi$
$140$	0.163613	−	0.927896i	0.0138278	−	0.0784215i
$141$	−9.42334	+	8.92457i	−0.793589	+	0.751585i
$142$	−5.24295	+	4.39935i	−0.439978	+	0.369186i
$143$	−0.332377	−	0.575694i	−0.0277948	−	0.0481420i
$144$	0.871391	+	2.87066i	0.0726159	+	0.239221i
$145$	4.75332	−	8.23299i	0.394742	−	0.683713i
$146$	0.0480537	+	0.272526i	0.00397695	+	0.0225544i
$147$	0.197790	−	1.72072i	0.0163134	−	0.141923i
$148$	5.18362	−	1.88668i	0.426091	−	0.155084i
$149$	5.08843	−	1.85204i	0.416860	−	0.151725i	−0.125071	−	0.992148i	$-0.539916\pi$
$149$	5.08843	−	1.85204i	0.416860	−	0.151725i	0.541931	+	0.840423i	$0.317693\pi$
$150$	5.72133	+	4.24240i	0.467145	+	0.346390i
$151$	3.07186	+	17.4214i	0.249984	+	1.41773i	0.808626	+	0.588323i	$0.200211\pi$
$151$	3.07186	+	17.4214i	0.249984	+	1.41773i	−0.558642	+	0.829409i	$0.688677\pi$
$152$	2.07989	−	3.60248i	0.168702	−	0.292200i
$153$	−2.88742	+	6.76480i	−0.233434	+	0.546902i
$154$	0.591442	+	1.02441i	0.0476598	+	0.0825492i
$155$	3.14403	−	2.63815i	0.252535	−	0.211902i
$156$	0.933013	+	0.277384i	0.0747009	+	0.0222085i
$157$	−1.84368	+	10.4560i	−0.147142	+	0.834483i	0.818481	+	0.574534i	$0.194817\pi$
$157$	−1.84368	+	10.4560i	−0.147142	+	0.834483i	−0.965622	+	0.259949i	$0.916294\pi$
$158$	2.84329	+	2.38580i	0.226200	+	0.189804i
$159$	7.57357	−	0.455639i	0.600623	−	0.0361345i
$160$	−0.885388	−	0.322255i	−0.0699961	−	0.0254765i
$161$	−0.747038			−0.0588748
$162$	8.94687	+	0.976453i	0.702933	+	0.0767174i
$163$	19.4040			1.51984			0.759918	−	0.650019i	$-0.225239\pi$
$163$	19.4040			1.51984			0.759918	+	0.650019i	$0.225239\pi$
$164$	−0.559633	−	0.203690i	−0.0437000	−	0.0159055i
$165$	1.92693	−	0.115928i	0.150011	−	0.00902494i
$166$	−10.5841	−	8.88112i	−0.821486	−	0.689309i
$167$	0.876865	−	4.97295i	0.0678539	−	0.384818i	−0.931902	−	0.362711i	$-0.881851\pi$
$167$	0.876865	−	4.97295i	0.0678539	−	0.384818i	0.999756	−	0.0221075i	$-0.00703762\pi$
$168$	−1.66023	−	0.493585i	−0.128090	−	0.0380809i
$169$	−9.71665	+	8.15323i	−0.747434	+	0.627172i
$170$	−1.15503	−	2.00058i	−0.0885870	−	0.153437i
$171$	−7.49037	−	9.98141i	−0.572803	−	0.763298i
$172$	2.73205	−	4.73204i	0.208317	−	0.360815i
$173$	3.48685	+	19.7749i	0.265100	+	1.50346i	0.768750	+	0.639550i	$0.220879\pi$
$173$	3.48685	+	19.7749i	0.265100	+	1.50346i	−0.503649	+	0.863908i	$0.668010\pi$
$174$	−14.0378	−	10.4091i	−1.06420	−	0.789110i
$175$	−3.86424	+	1.40647i	−0.292109	+	0.106319i
$176$	1.11155	−	0.404570i	0.0837861	−	0.0304956i
$177$	−0.464853	+	4.04411i	−0.0349405	+	0.303974i
$178$	0.283022	+	1.60510i	0.0212134	+	0.120307i
$179$	10.4210	−	18.0497i	0.778904	−	1.34910i	−0.153671	−	0.988122i	$-0.549109\pi$
$179$	10.4210	−	18.0497i	0.778904	−	1.34910i	0.932574	−	0.360979i	$-0.117557\pi$
$180$	−1.93188	+	2.06342i	−0.143994	+	0.153798i
$181$	10.6287	+	18.4095i	0.790027	+	1.36837i	0.925950	+	0.377647i	$0.123267\pi$
$181$	10.6287	+	18.4095i	0.790027	+	1.36837i	−0.135923	+	0.990719i	$0.543400\pi$
$182$	−0.430500	+	0.361232i	−0.0319108	+	0.0267763i
$183$	−7.44681	+	7.05266i	−0.550484	+	0.521347i
$184$	−0.129722	+	0.735689i	−0.00956321	+	0.0542357i
$185$	3.98152	+	3.34089i	0.292727	+	0.245627i
$186$	−4.15795	−	6.29562i	−0.304876	−	0.461617i
$187$	2.72524	+	0.991906i	0.199289	+	0.0725353i
$188$	−7.49327			−0.546503
$189$	−3.31714	+	3.99957i	−0.241286	+	0.290926i
$190$	3.91939			0.284343
$191$	14.4533	+	5.26059i	1.04581	+	0.380643i	0.807079	−	0.590444i	$-0.201047\pi$
$191$	14.4533	+	5.26059i	1.04581	+	0.380643i	0.238728	+	0.971086i	$0.423270\pi$
$192$	−0.774383	+	1.54930i	−0.0558863	+	0.111811i
$193$	15.8994	+	13.3412i	1.14447	+	0.960322i	0.999576	−	0.0291255i	$-0.00927223\pi$
$193$	15.8994	+	13.3412i	1.14447	+	0.960322i	0.144892	+	0.989448i	$0.453717\pi$
$194$	−0.961438	+	5.45259i	−0.0690272	+	0.391473i
$195$	0.213209	+	0.891995i	0.0152682	+	0.0638771i
$196$	0.766044	−	0.642788i	0.0547175	−	0.0459134i
$197$	3.28016	+	5.68141i	0.233702	+	0.404784i	0.958895	−	0.283762i	$-0.0915827\pi$
$197$	3.28016	+	5.68141i	0.233702	+	0.404784i	−0.725193	+	0.688546i	$0.758249\pi$
$198$	0.192790	−	3.54341i	0.0137010	−	0.251819i
$199$	−1.16826	+	2.02348i	−0.0828156	+	0.143441i	−0.904458	−	0.426562i	$-0.859725\pi$
$199$	−1.16826	+	2.02348i	−0.0828156	+	0.143441i	0.821643	+	0.570003i	$0.193058\pi$
$200$	0.714083	+	4.04977i	0.0504933	+	0.286362i
$201$	11.5666	−	5.01561i	0.815848	−	0.353774i
$202$	−13.2342	+	4.81686i	−0.931156	+	0.338913i
$203$	9.48124	−	3.45089i	0.665453	−	0.242205i
$204$	−3.89603	+	1.68943i	−0.272777	+	0.118283i
$205$	−0.0974397	−	0.552608i	−0.00680548	−	0.0385958i
$206$	8.26303	−	14.3120i	0.575713	−	0.997164i
$207$	1.87712	+	1.22434i	0.130469	+	0.0850978i
$208$	0.280989	+	0.486687i	0.0194831	+	0.0337456i
$209$	−3.76936	+	3.16287i	−0.260732	+	0.218780i
$210$	−0.379390	−	1.58724i	−0.0261804	−	0.109530i
$211$	−0.472019	+	2.67695i	−0.0324951	+	0.184289i	−0.996735	−	0.0807418i	$-0.974271\pi$
$211$	−0.472019	+	2.67695i	−0.0324951	+	0.184289i	0.964240	+	0.265031i	$0.0853822\pi$
$212$	3.35566	+	2.81574i	0.230468	+	0.193385i
$213$	−5.30001	+	10.6037i	−0.363151	+	0.726553i
$214$	10.7146	+	3.89980i	0.732436	+	0.266585i
$215$	5.14832			0.351113
$216$	3.36279	+	3.96126i	0.228809	+	0.269530i
$217$	4.35597			0.295702
$218$	4.67088	+	1.70006i	0.316352	+	0.115143i
$219$	0.264151	+	0.399954i	0.0178496	+	0.0270264i
$220$	0.853777	+	0.716404i	0.0575616	+	0.0482999i
$221$	−0.239257	+	1.35690i	−0.0160942	+	0.0912747i
$222$	6.93714	−	6.56997i	0.465590	−	0.440947i
$223$	−18.7784	+	15.7570i	−1.25750	+	1.05516i	−0.261551	+	0.965190i	$0.584234\pi$
$223$	−18.7784	+	15.7570i	−1.25750	+	1.05516i	−0.995944	+	0.0899739i	$0.971322\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	12.0150	+	2.79913i	0.800998	+	0.186608i
$226$	−5.72900	+	9.92293i	−0.381088	+	0.660063i
$227$	−3.03892	−	17.2346i	−0.201700	−	1.14390i	−0.902548	−	0.430588i	$-0.858306\pi$
$227$	−3.03892	−	17.2346i	−0.201700	−	1.14390i	0.700848	−	0.713310i	$-0.252805\pi$
$228$	0.822763	−	7.15783i	0.0544888	−	0.474039i
$229$	−3.28822	+	1.19681i	−0.217292	+	0.0790877i	−0.448372	−	0.893847i	$-0.647996\pi$
$229$	−3.28822	+	1.19681i	−0.217292	+	0.0790877i	0.231081	+	0.972935i	$0.425774\pi$
$230$	−0.661418	+	0.240737i	−0.0436126	+	0.0158737i
$231$	1.64574	+	1.22032i	0.108282	+	0.0802915i
$232$	−1.75206	−	9.93644i	−0.115029	−	0.652359i
$233$	−0.907697	+	1.57218i	−0.0594652	+	0.102997i	−0.894225	−	0.447617i	$-0.852273\pi$
$233$	−0.907697	+	1.57218i	−0.0594652	+	0.102997i	0.834760	+	0.550614i	$0.185606\pi$
$234$	1.67377	−	0.202125i	0.109418	−	0.0132134i
$235$	−3.53012	−	6.11435i	−0.230280	−	0.398856i
$236$	−1.80039	+	1.51070i	−0.117195	+	0.0983385i
$237$	6.16220	+	1.83201i	0.400278	+	0.119002i
$238$	0.425742	−	2.41450i	0.0275968	−	0.156509i
$239$	−6.89294	−	5.78387i	−0.445867	−	0.374127i	0.392032	−	0.919951i	$-0.371772\pi$
$239$	−6.89294	−	5.78387i	−0.445867	−	0.374127i	−0.837900	+	0.545824i	$0.816217\pi$
$240$	−1.62901	+	0.0980041i	−0.105152	+	0.00632614i
$241$	13.9384	+	5.07318i	0.897854	+	0.326792i	0.749393	−	0.662126i	$-0.230346\pi$
$241$	13.9384	+	5.07318i	0.897854	+	0.326792i	0.148462	+	0.988918i	$0.452568\pi$
$242$	9.60078			0.617162
$243$	14.8902	−	4.61335i	0.955204	−	0.295947i
$244$	−5.92157			−0.379090
$245$	0.885388	+	0.322255i	0.0565654	+	0.0205881i
$246$	−1.02966	+	0.0619461i	−0.0656487	+	0.00394954i
$247$	−1.79079	−	1.50265i	−0.113945	−	0.0956112i
$248$	0.756406	−	4.28979i	0.0480318	−	0.272402i
$249$	−22.9387	−	6.81965i	−1.45368	−	0.432178i
$250$	−6.57699	+	5.51875i	−0.415965	+	0.349036i
$251$	−4.80697	−	8.32592i	−0.303413	−	0.525527i	0.673493	−	0.739193i	$-0.264793\pi$
$251$	−4.80697	−	8.32592i	−0.303413	−	0.525527i	−0.976907	+	0.213666i	$0.931460\pi$
$252$	−2.97836	+	0.359668i	−0.187619	+	0.0226570i
$253$	0.441830	−	0.765272i	0.0277776	−	0.0481122i
$254$	−2.43467	−	13.8077i	−0.152765	−	0.866372i
$255$	−3.21398	−	2.38318i	−0.201267	−	0.149241i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	2.44748	−	0.890809i	0.152669	−	0.0555671i	−0.264555	−	0.964371i	$-0.585225\pi$
$257$	2.44748	−	0.890809i	0.152669	−	0.0555671i	0.417224	+	0.908803i	$0.363003\pi$
$258$	1.08074	−	9.40217i	0.0672840	−	0.585354i
$259$	0.957894	+	5.43249i	0.0595206	+	0.337558i
$260$	−0.264750	+	0.458561i	−0.0164191	+	0.0284388i
$261$	−29.4797	−	6.86789i	−1.82475	−	0.425112i
$262$	8.80564	+	15.2518i	0.544014	+	0.942260i
$263$	7.36421	−	6.17930i	0.454097	−	0.381032i	−0.386857	−	0.922140i	$-0.626439\pi$
$263$	7.36421	−	6.17930i	0.454097	−	0.381032i	0.840953	+	0.541108i	$0.181995\pi$
$264$	1.48756	−	1.40883i	0.0915533	−	0.0867075i
$265$	−0.716708	+	4.06466i	−0.0440270	+	0.249690i
$266$	3.18658	+	2.67386i	0.195382	+	0.163945i
$267$	1.55577	+	2.35561i	0.0952116	+	0.144161i
$268$	6.83985	+	2.48950i	0.417810	+	0.152071i
$269$	23.2038			1.41476			0.707382	−	0.706832i	$-0.249876\pi$
$269$	23.2038			1.41476			0.707382	+	0.706832i	$0.249876\pi$
$270$	−1.64807	+	4.61014i	−0.100299	+	0.280564i
$271$	3.66854			0.222848			0.111424	−	0.993773i	$-0.464459\pi$
$271$	3.66854			0.222848			0.111424	+	0.993773i	$0.464459\pi$
$272$	−2.30389	−	0.838548i	−0.139694	−	0.0508445i
$273$	−0.435186	+	0.870672i	−0.0263386	+	0.0526954i
$274$	−6.58678	−	5.52697i	−0.397922	−	0.333896i
$275$	0.844678	−	4.79041i	0.0509360	−	0.288872i
$276$	0.300802	+	1.25846i	0.0181061	+	0.0757502i
$277$	−19.6685	+	16.5038i	−1.18176	+	0.991617i	−0.181798	+	0.983336i	$0.558192\pi$
$277$	−19.6685	+	16.5038i	−1.18176	+	0.991617i	−0.999966	+	0.00828141i	$0.997364\pi$
$278$	−7.63794	−	13.2293i	−0.458093	−	0.793440i
$279$	−10.9455	−	7.13914i	−0.655287	−	0.427409i
$280$	0.471105	−	0.815978i	0.0281539	−	0.0487640i
$281$	−3.12938	−	17.7476i	−0.186683	−	1.05873i	−0.923774	−	0.382938i	$-0.874912\pi$
$281$	−3.12938	−	17.7476i	−0.186683	−	1.05873i	0.737091	−	0.675793i	$-0.236199\pi$
$282$	−11.9074	+	5.16338i	−0.709077	+	0.307475i
$283$	6.61159	−	2.40642i	0.393018	−	0.143047i	−0.137949	−	0.990439i	$-0.544051\pi$
$283$	6.61159	−	2.40642i	0.393018	−	0.143047i	0.530967	+	0.847392i	$0.321829\pi$
$284$	−6.43143	+	2.34085i	−0.381635	+	0.138904i
$285$	6.22824	−	2.70073i	0.368929	−	0.159978i
$286$	−0.115433	−	0.654655i	−0.00682572	−	0.0387106i
$287$	0.297775	−	0.515761i	0.0175771	−	0.0304444i
$288$	−0.162983	+	2.99557i	−0.00960386	+	0.176516i
$289$	5.49446	+	9.51668i	0.323203	+	0.559805i
$290$	7.28251	−	6.11075i	0.427644	−	0.358836i
$291$	2.22941	+	9.32711i	0.130690	+	0.546765i
$292$	−0.0480537	+	0.272526i	−0.00281213	+	0.0159484i
$293$	−1.65587	−	1.38944i	−0.0967371	−	0.0811721i	0.593136	−	0.805102i	$-0.297889\pi$
$293$	−1.65587	−	1.38944i	−0.0967371	−	0.0811721i	−0.689874	+	0.723930i	$0.742334\pi$
$294$	0.774383	−	1.54930i	0.0451629	−	0.0903570i
$295$	−2.08087	−	0.757376i	−0.121153	−	0.0440962i
$296$	5.51629			0.320628
$297$	−2.13530	−	5.76362i	−0.123903	−	0.334439i
$298$	5.41499			0.313682
$299$	0.394500	+	0.143586i	0.0228145	+	0.00830381i
$300$	3.92531	+	5.94336i	0.226628	+	0.343140i
$301$	4.18574	+	3.51225i	0.241262	+	0.202443i
$302$	−3.07186	+	17.4214i	−0.176766	+	1.00249i
$303$	−17.7111	+	16.7737i	−1.01748	+	0.963623i
$304$	3.18658	−	2.67386i	0.182763	−	0.153356i
$305$	−2.78968	−	4.83187i	−0.159737	−	0.276672i
$306$	−5.02699	+	5.36928i	−0.287374	+	0.306941i
$307$	6.37520	−	11.0422i	0.363852	−	0.630210i	−0.624739	−	0.780834i	$-0.714795\pi$
$307$	6.37520	−	11.0422i	0.363852	−	0.630210i	0.988591	+	0.150623i	$0.0481280\pi$
$308$	0.205406	+	1.16491i	0.0117041	+	0.0663771i
$309$	3.26869	−	28.4367i	0.185949	−	1.61771i
$310$	3.85672	−	1.40373i	0.219047	−	0.0797266i
$311$	9.85505	−	3.58695i	0.558829	−	0.203397i	−0.0471360	−	0.998888i	$-0.515009\pi$
$311$	9.85505	−	3.58695i	0.558829	−	0.203397i	0.605965	+	0.795491i	$0.292787\pi$
$312$	0.781875	+	0.579765i	0.0442650	+	0.0328227i
$313$	−2.79267	−	15.8380i	−0.157851	−	0.895219i	−0.956133	−	0.292934i	$-0.905368\pi$
$313$	−2.79267	−	15.8380i	−0.157851	−	0.895219i	0.798281	−	0.602285i	$-0.205743\pi$
$314$	−5.30867	+	9.19489i	−0.299586	+	0.518898i
$315$	−1.69660	−	2.26084i	−0.0955928	−	0.127384i
$316$	1.85582	+	3.21438i	0.104398	+	0.180823i
$317$	−2.42349	+	2.03355i	−0.136117	+	0.114215i	−0.708304	−	0.705907i	$-0.750539\pi$
$317$	−2.42349	+	2.03355i	−0.136117	+	0.114215i	0.572187	+	0.820123i	$0.306095\pi$
$318$	7.27266	+	2.16215i	0.407831	+	0.121247i
$319$	−2.07249	+	11.7537i	−0.116037	+	0.658079i
$320$	−0.721775	−	0.605641i	−0.0403485	−	0.0338564i
$321$	19.7136	−	1.18601i	1.10031	−	0.0661964i
$322$	−0.701986	−	0.255502i	−0.0391201	−	0.0142386i
$323$	10.1988			0.567474
$324$	8.07334	+	3.97758i	0.448519	+	0.220976i
$325$	2.31099			0.128190
$326$	18.2338	+	6.63654i	1.00987	+	0.367564i
$327$	8.59388	−	0.517022i	0.475243	−	0.0285914i
$328$	−0.456217	−	0.382812i	−0.0251904	−	0.0211372i
$329$	1.30119	−	7.37943i	0.0717371	−	0.406841i
$330$	1.85037	+	0.550113i	0.101860	+	0.0302827i
$331$	−24.6144	+	20.6539i	−1.35293	+	1.13524i	−0.374831	+	0.927093i	$0.622299\pi$
$331$	−24.6144	+	20.6539i	−1.35293	+	1.13524i	−0.978097	+	0.208148i	$0.933256\pi$
$332$	−6.90828	−	11.9655i	−0.379141	−	0.656692i
$333$	6.49653	−	15.2204i	0.356008	−	0.834072i
$334$	2.52483	−	4.37314i	0.138153	−	0.239287i
$335$	1.19091	+	6.75399i	0.0650664	+	0.369010i
$336$	−1.39129	−	1.03165i	−0.0759012	−	0.0562812i
$337$	−23.6495	+	8.60772i	−1.28827	+	0.468892i	−0.893159	−	0.449741i	$-0.851516\pi$
$337$	−23.6495	+	8.60772i	−1.28827	+	0.468892i	−0.395112	+	0.918633i	$0.629294\pi$
$338$	−11.9192	+	4.33825i	−0.648321	+	0.235969i
$339$	−2.26628	+	19.7160i	−0.123087	+	1.07083i
$340$	−0.401139	−	2.27497i	−0.0217548	−	0.123378i
$341$	−2.57630	+	4.46229i	−0.139515	+	0.241647i
$342$	−3.62480	−	11.9413i	−0.196007	−	0.645713i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	4.18574	−	3.51225i	0.225680	−	0.189368i
$345$	−0.885164	+	0.838313i	−0.0476556	+	0.0451333i
$346$	−3.48685	+	19.7749i	−0.187454	+	1.06311i
$347$	−17.4843	−	14.6711i	−0.938609	−	0.787586i	0.0387340	−	0.999250i	$-0.487667\pi$
$347$	−17.4843	−	14.6711i	−0.938609	−	0.787586i	−0.977343	+	0.211663i	$0.932112\pi$
$348$	−9.63107	−	14.5825i	−0.516279	−	0.781706i
$349$	2.63313	+	0.958382i	0.140948	+	0.0513010i	0.411531	−	0.911396i	$-0.364994\pi$
$349$	2.63313	+	0.958382i	0.140948	+	0.0513010i	−0.270583	+	0.962697i	$0.587216\pi$
$350$	−4.11224			−0.219808
$351$	2.52048	−	1.47454i	0.134533	−	0.0787051i
$352$	1.18288			0.0630480
$353$	−22.7661	−	8.28618i	−1.21172	−	0.441029i	−0.344418	−	0.938817i	$-0.611924\pi$
$353$	−22.7661	−	8.28618i	−1.21172	−	0.441029i	−0.867299	+	0.497788i	$0.834146\pi$
$354$	−1.81998	+	3.64123i	−0.0967311	+	0.193529i
$355$	−4.93996	−	4.14512i	−0.262186	−	0.220000i
$356$	−0.283022	+	1.60510i	−0.0150002	+	0.0850701i
$357$	−0.987221	−	4.13021i	−0.0522493	−	0.218594i
$358$	15.9659	−	13.3970i	0.843826	−	0.708054i
$359$	−14.1766	−	24.5546i	−0.748213	−	1.29594i	−0.948679	−	0.316242i	$-0.897579\pi$
$359$	−14.1766	−	24.5546i	−0.748213	−	1.29594i	0.200466	−	0.979701i	$-0.435754\pi$
$360$	−2.52110	+	1.27824i	−0.132874	+	0.0673691i
$361$	0.848098	−	1.46895i	0.0446367	−	0.0773131i
$362$	3.69132	+	20.9345i	0.194011	+	1.10029i
$363$	15.2564	−	6.61561i	0.800755	−	0.347229i
$364$	−0.528086	+	0.192208i	−0.0276792	+	0.0100744i
$365$	−0.245014	+	0.0891776i	−0.0128246	+	0.00466777i
$366$	−9.40986	+	4.08037i	−0.491861	+	0.213284i
$367$	−5.58574	−	31.6783i	−0.291573	−	1.65359i	−0.680813	−	0.732457i	$-0.738373\pi$
$367$	−5.58574	−	31.6783i	−0.291573	−	1.65359i	0.389240	−	0.921136i	$-0.372738\pi$
$368$	−0.373519	+	0.646954i	−0.0194710	+	0.0337248i
$369$	−1.59353	+	0.807945i	−0.0829558	+	0.0420599i
$370$	2.59875	+	4.50117i	0.135103	+	0.234005i
$371$	−3.35566	+	2.81574i	−0.174217	+	0.146186i
$372$	−1.75397	−	7.33805i	−0.0909392	−	0.380460i
$373$	−0.137640	+	0.780593i	−0.00712671	+	0.0404176i	−0.988164	−	0.153403i	$-0.950977\pi$
$373$	−0.137640	+	0.780593i	−0.00712671	+	0.0404176i	0.981037	+	0.193820i	$0.0620879\pi$
$374$	2.22164	+	1.86417i	0.114878	+	0.0963941i
$375$	−6.64858	+	13.3017i	−0.343331	+	0.686899i
$376$	−7.04137	−	2.56285i	−0.363131	−	0.132169i
$377$	−5.67020			−0.292030
$378$	−4.48503	+	2.62384i	−0.230685	+	0.134956i
$379$	−35.0603			−1.80093			−0.900463	−	0.434932i	$-0.856772\pi$
$379$	−35.0603			−1.80093			−0.900463	+	0.434932i	$0.856772\pi$
$380$	3.68302	+	1.34051i	0.188935	+	0.0687668i
$381$	−13.3833	−	20.2639i	−0.685650	−	1.03815i
$382$	11.7825	+	9.88667i	0.602844	+	0.505846i
$383$	−3.04361	+	17.2611i	−0.155521	+	0.882003i	0.802787	+	0.596266i	$0.203350\pi$
$383$	−3.04361	+	17.2611i	−0.155521	+	0.882003i	−0.958308	+	0.285737i	$0.907762\pi$
$384$	−1.25757	+	1.19101i	−0.0641753	+	0.0607786i
$385$	−0.853777	+	0.716404i	−0.0435125	+	0.0365113i
$386$	10.3776	+	17.9746i	0.528207	+	0.914882i
$387$	−4.76136	−	15.6855i	−0.242034	−	0.797341i
$388$	−2.76835	+	4.79492i	−0.140542	+	0.243425i
$389$	−4.78623	−	27.1441i	−0.242672	−	1.37626i	−0.825839	−	0.563907i	$-0.809298\pi$
$389$	−4.78623	−	27.1441i	−0.242672	−	1.37626i	0.583167	−	0.812352i	$-0.301813\pi$
$390$	−0.104730	+	0.911123i	−0.00530320	+	0.0461365i
$391$	−1.72109	+	0.626427i	−0.0870395	+	0.0316798i
$392$	0.939693	−	0.342020i	0.0474616	−	0.0172746i
$393$	24.5024	+	18.1687i	1.23599	+	0.916490i
$394$	1.13919	+	6.46066i	0.0573915	+	0.325483i
$395$	−1.74858	+	3.02862i	−0.0879805	+	0.152387i
$396$	1.39308	−	3.26378i	0.0700050	−	0.164011i
$397$	−13.4080	−	23.2234i	−0.672930	−	1.16555i	−0.977069	−	0.212921i	$-0.931702\pi$
$397$	−13.4080	−	23.2234i	−0.672930	−	1.16555i	0.304140	−	0.952627i	$-0.401631\pi$
$398$	−1.78987	+	1.50188i	−0.0897183	+	0.0752826i
$399$	6.90621	+	2.05321i	0.345743	+	0.102789i
$400$	−0.714083	+	4.04977i	−0.0357041	+	0.202488i
$401$	−12.9829	−	10.8939i	−0.648333	−	0.544016i	0.258232	−	0.966083i	$-0.416860\pi$
$401$	−12.9829	−	10.8939i	−0.648333	−	0.544016i	−0.906565	+	0.422067i	$0.861305\pi$
$402$	12.5845	−	0.757107i	0.627659	−	0.0377610i
$403$	−2.30033	−	0.837250i	−0.114587	−	0.0417064i
$404$	−14.0836			−0.700683
$405$	0.557779	+	8.46153i	0.0277163	+	0.420457i
$406$	10.0897			0.500745
$407$	−6.13162	−	2.23173i	−0.303933	−	0.110623i
$408$	−4.23889	+	0.255019i	−0.209856	+	0.0126253i
$409$	5.70523	+	4.78726i	0.282105	+	0.236715i	0.772850	−	0.634589i	$-0.218831\pi$
$409$	5.70523	+	4.78726i	0.282105	+	0.236715i	−0.490744	+	0.871304i	$0.663275\pi$
$410$	0.0974397	−	0.552608i	0.00481220	−	0.0272914i
$411$	−14.2754	−	4.24406i	−0.704154	−	0.209344i
$412$	12.6597	−	10.6228i	0.623699	−	0.523345i
$413$	−1.17512	−	2.03537i	−0.0578239	−	0.100154i
$414$	1.34516	+	1.79252i	0.0661112	+	0.0880975i
$415$	6.50906	−	11.2740i	0.319517	−	0.553420i
$416$	0.0975863	+	0.553440i	0.00478456	+	0.0271346i
$417$	−21.2532	−	15.7594i	−1.04077	−	0.771740i
$418$	−4.62380	+	1.68293i	−0.226157	+	0.0823146i
$419$	18.3401	−	6.67525i	0.895973	−	0.326107i	0.147335	−	0.989087i	$-0.452930\pi$
$419$	18.3401	−	6.67525i	0.895973	−	0.326107i	0.748638	+	0.662979i	$0.230708\pi$
$420$	0.186360	−	1.62128i	0.00909342	−	0.0791104i
$421$	−5.71592	−	32.4166i	−0.278577	−	1.57989i	−0.727365	−	0.686251i	$-0.759255\pi$
$421$	−5.71592	−	32.4166i	−0.278577	−	1.57989i	0.448788	−	0.893638i	$-0.351856\pi$
$422$	−1.35913	+	2.35407i	−0.0661612	+	0.114595i
$423$	−15.3640	+	16.4101i	−0.747021	+	0.797886i
$424$	2.19025	+	3.79363i	0.106368	+	0.184235i
$425$	−7.72340	+	6.48070i	−0.374640	+	0.314360i
$426$	−8.60706	+	8.15150i	−0.417013	+	0.394941i
$427$	1.02827	−	5.83161i	0.0497615	−	0.282211i
$428$	8.73463	+	7.32923i	0.422204	+	0.354272i
$429$	−0.634536	−	0.960760i	−0.0306357	−	0.0463859i
$430$	4.83784	+	1.76083i	0.233301	+	0.0849148i
$431$	−0.674649			−0.0324967			−0.0162483	−	0.999868i	$-0.505172\pi$
$431$	−0.674649			−0.0324967			−0.0162483	+	0.999868i	$0.505172\pi$
$432$	1.80516	+	4.87251i	0.0868509	+	0.234429i
$433$	19.0705			0.916468			0.458234	−	0.888832i	$-0.348482\pi$
$433$	19.0705			0.916468			0.458234	+	0.888832i	$0.348482\pi$
$434$	4.09327	+	1.48983i	0.196483	+	0.0715141i
$435$	7.36178	−	14.7286i	0.352970	−	0.706184i
$436$	3.80774	+	3.19507i	0.182358	+	0.153016i
$437$	0.539614	−	3.06031i	0.0258133	−	0.146394i
$438$	0.111428	+	0.466179i	0.00532424	+	0.0222749i
$439$	−15.9183	+	13.3570i	−0.759740	+	0.637497i	−0.938059	−	0.346475i	$-0.887378\pi$
$439$	−15.9183	+	13.3570i	−0.759740	+	0.637497i	0.178319	+	0.983973i	$0.442934\pi$
$440$	0.557263	+	0.965208i	0.0265665	+	0.0460145i
$441$	0.162983	−	2.99557i	0.00776109	−	0.142646i
$442$	−0.688914	+	1.19323i	−0.0327683	+	0.0567564i
$443$	2.87332	+	16.2954i	0.136516	+	0.774219i	0.973792	+	0.227440i	$0.0730354\pi$
$443$	2.87332	+	16.2954i	0.136516	+	0.774219i	−0.837276	+	0.546780i	$0.815853\pi$
$444$	8.76584	−	3.80111i	0.416008	−	0.180393i
$445$	−1.44306	+	0.525231i	−0.0684076	+	0.0248983i
$446$	−23.0351	+	8.38410i	−1.09074	+	0.396999i
$447$	8.60487	−	3.73130i	0.406996	−	0.176485i
$448$	−0.173648	−	0.984808i	−0.00820411	−	0.0465278i
$449$	−10.3569	+	17.9387i	−0.488773	+	0.846580i	−0.999917	−	0.0129153i	$-0.995889\pi$
$449$	−10.3569	+	17.9387i	−0.488773	+	0.846580i	0.511143	+	0.859496i	$0.329222\pi$
$450$	10.3330	+	6.73968i	0.487103	+	0.317712i
$451$	0.352233	+	0.610086i	0.0165860	+	0.0287278i
$452$	−8.77734	+	7.36507i	−0.412852	+	0.346424i
$453$	7.12310	+	29.8007i	0.334672	+	1.40016i
$454$	3.03892	−	17.2346i	0.142624	−	0.808859i
$455$	−0.405621	−	0.340357i	−0.0190158	−	0.0159562i
$456$	3.22126	−	6.44475i	0.150850	−	0.301803i
$457$	−3.68983	−	1.34299i	−0.172603	−	0.0628223i	0.254273	−	0.967132i	$-0.418164\pi$
$457$	−3.68983	−	1.34299i	−0.172603	−	0.0628223i	−0.426876	+	0.904310i	$0.640386\pi$
$458$	−3.49925			−0.163509
$459$	−4.28850	+	11.9962i	−0.200170	+	0.559933i
$460$	−0.703867			−0.0328180
$461$	14.7319	+	5.36199i	0.686135	+	0.249733i	0.661479	−	0.749963i	$-0.269929\pi$
$461$	14.7319	+	5.36199i	0.686135	+	0.249733i	0.0246555	+	0.999696i	$0.492151\pi$
$462$	1.12911	+	1.70961i	0.0525311	+	0.0795381i
$463$	15.8009	+	13.2585i	0.734331	+	0.616176i	0.931308	−	0.364231i	$-0.118668\pi$
$463$	15.8009	+	13.2585i	0.734331	+	0.616176i	−0.196978	+	0.980408i	$0.563113\pi$
$464$	1.75206	−	9.93644i	0.0813374	−	0.461288i
$465$	5.16138	−	4.88820i	0.239353	−	0.226685i
$466$	−1.39067	+	1.16691i	−0.0644216	+	0.0540562i
$467$	4.75342	+	8.23316i	0.219962	+	0.380985i	0.954796	−	0.297262i	$-0.0960733\pi$
$467$	4.75342	+	8.23316i	0.219962	+	0.380985i	−0.734834	+	0.678247i	$0.762740\pi$
$468$	1.64196	+	0.382528i	0.0758997	+	0.0176824i
$469$	−3.63941	+	6.30364i	−0.168052	+	0.291075i
$470$	−1.22600	−	6.95298i	−0.0565511	−	0.320717i
$471$	−2.10000	+	18.2695i	−0.0967630	+	0.841813i
$472$	−2.20850	+	0.803829i	−0.101655	+	0.0369992i
$473$	−6.07360	+	2.21061i	−0.279264	+	0.101644i
$474$	5.16399	+	3.82913i	0.237190	+	0.175878i
$475$	−2.97043	−	16.8461i	−0.136293	−	0.772954i
$476$	1.22588	−	2.12328i	0.0561879	−	0.0973203i
$477$	13.0467	−	1.57553i	0.597369	−	0.0721386i
$478$	−4.49905	−	7.79258i	−0.205782	−	0.356424i
$479$	21.9937	−	18.4549i	1.00492	−	0.843227i	0.0172603	−	0.999851i	$-0.494506\pi$
$479$	21.9937	−	18.4549i	1.00492	−	0.843227i	0.987658	+	0.156624i	$0.0500612\pi$
$480$	−1.56429	−	0.465061i	−0.0713997	−	0.0212270i
$481$	0.538315	−	3.05293i	0.0245450	−	0.139202i
$482$	11.3627	+	9.53446i	0.517558	+	0.434283i
$483$	−1.29157	+	0.0777032i	−0.0587686	+	0.00353562i
$484$	9.02179	+	3.28366i	0.410081	+	0.149257i
$485$	−5.21674			−0.236880
$486$	15.5700	+	0.757604i	0.706271	+	0.0343656i
$487$	−40.7770			−1.84778			−0.923892	−	0.382654i	$-0.875010\pi$
$487$	−40.7770			−1.84778			−0.923892	+	0.382654i	$0.875010\pi$
$488$	−5.56445	−	2.02530i	−0.251891	−	0.0916808i
$489$	33.5480	−	2.01830i	1.51709	−	0.0912708i
$490$	0.721775	+	0.605641i	0.0326065	+	0.0273601i
$491$	−1.69368	+	9.60532i	−0.0764346	+	0.433482i	0.922444	+	0.386131i	$0.126189\pi$
$491$	−1.69368	+	9.60532i	−0.0764346	+	0.433482i	−0.998878	+	0.0473505i	$0.984922\pi$
$492$	−0.988751	−	0.293954i	−0.0445763	−	0.0132525i
$493$	18.9500	−	15.9010i	0.853466	−	0.716143i
$494$	−1.16885	−	2.02451i	−0.0525891	−	0.0910871i
$495$	3.31946	−	0.400860i	0.149199	−	0.0180173i
$496$	2.17798	−	3.77238i	0.0977944	−	0.169385i
$497$	−1.18848	−	6.74020i	−0.0533106	−	0.302339i
$498$	−19.2229	−	14.2539i	−0.861398	−	0.638732i
$499$	−3.07925	+	1.12076i	−0.137846	+	0.0501719i	−0.410022	−	0.912076i	$-0.634479\pi$
$499$	−3.07925	+	1.12076i	−0.137846	+	0.0501719i	0.272176	+	0.962248i	$0.412257\pi$
$500$	−8.06787	+	2.93646i	−0.360806	+	0.131323i
$501$	0.998772	−	8.68906i	0.0446219	−	0.388199i
$502$	−1.66944	−	9.46789i	−0.0745109	−	0.422572i
$503$	−2.65726	+	4.60251i	−0.118481	+	0.205216i	−0.919166	−	0.393870i	$-0.871136\pi$
$503$	−2.65726	+	4.60251i	−0.118481	+	0.205216i	0.800685	+	0.599086i	$0.204469\pi$
$504$	−2.92176	−	0.680682i	−0.130145	−	0.0303200i
$505$	−6.63484	−	11.4919i	−0.295246	−	0.511382i
$506$	0.676922	−	0.568005i	0.0300929	−	0.0252509i
$507$	−15.9513	+	15.1070i	−0.708422	+	0.670926i
$508$	2.43467	−	13.8077i	0.108021	−	0.612617i
$509$	−15.2042	−	12.7578i	−0.673915	−	0.565482i	0.240306	−	0.970697i	$-0.422752\pi$
$509$	−15.2042	−	12.7578i	−0.673915	−	0.565482i	−0.914221	+	0.405215i	$0.867197\pi$
$510$	−2.20505	−	3.33870i	−0.0976415	−	0.147840i
$511$	−0.260041	−	0.0946473i	−0.0115035	−	0.00418695i
$512$	−1.00000			−0.0441942
$513$	−13.9885	−	16.4780i	−0.617607	−	0.727522i
$514$	2.60455			0.114882
$515$	14.6320	+	5.32561i	0.644762	+	0.234674i
$516$	4.23130	−	8.46552i	0.186272	−	0.372674i
$517$	6.78997	+	5.69746i	0.298623	+	0.250574i
$518$	−0.957894	+	5.43249i	−0.0420874	+	0.238690i
$519$	8.08539	+	33.8266i	0.354909	+	1.48482i
$520$	−0.405621	+	0.340357i	−0.0177877	+	0.0149256i
$521$	21.3109	+	36.9116i	0.933649	+	1.61713i	0.777025	+	0.629470i	$0.216728\pi$
$521$	21.3109	+	36.9116i	0.933649	+	1.61713i	0.156625	+	0.987658i	$0.449939\pi$
$522$	−25.3529	−	16.5364i	−1.10967	−	0.723777i
$523$	−0.102819	+	0.178087i	−0.00449595	+	0.00778722i	−0.868265	−	0.496101i	$-0.834764\pi$
$523$	−0.102819	+	0.178087i	−0.00449595	+	0.00778722i	0.863769	+	0.503889i	$0.168098\pi$
$524$	3.05817	+	17.3437i	0.133597	+	0.757664i
$525$	−6.53469	+	2.83362i	−0.285197	+	0.123669i
$526$	9.03354	−	3.28794i	0.393881	−	0.143361i
$527$	10.0357	−	3.65269i	0.437161	−	0.159114i
$528$	1.87970	−	0.815089i	0.0818035	−	0.0354722i
$529$	−3.89700	−	22.1010i	−0.169435	−	0.960913i
$530$	−2.06368	+	3.57440i	−0.0896405	+	0.155262i
$531$	−0.383049	+	7.04031i	−0.0166229	+	0.305523i
$532$	2.07989	+	3.60248i	0.0901748	+	0.156187i
$533$	−0.256384	+	0.215132i	−0.0111052	+	0.00931838i
$534$	0.656279	+	2.74566i	0.0284000	+	0.118816i
$535$	−1.86556	+	10.5801i	−0.0806551	+	0.457418i
$536$	5.57590	+	4.67873i	0.240842	+	0.202091i
$537$	16.1397	−	32.2906i	0.696480	−	1.39344i
$538$	21.8045	+	7.93618i	0.940058	+	0.342153i
$539$	−1.18288			−0.0509505
$540$	−3.12544	+	3.76844i	−0.134498	+	0.162168i
$541$	19.4984			0.838301			0.419151	−	0.907917i	$-0.362328\pi$
$541$	19.4984			0.838301			0.419151	+	0.907917i	$0.362328\pi$
$542$	3.44730	+	1.25471i	0.148074	+	0.0538946i
$543$	20.2911	+	30.7231i	0.870775	+	1.31845i
$544$	−1.87815	−	1.57596i	−0.0805250	−	0.0675685i
$545$	−0.813264	+	4.61225i	−0.0348364	+	0.197567i
$546$	−0.706728	+	0.669322i	−0.0302452	+	0.0286443i
$547$	25.9620	−	21.7847i	1.11005	−	0.931446i	0.111994	−	0.993709i	$-0.464276\pi$
$547$	25.9620	−	21.7847i	1.11005	−	0.931446i	0.998060	+	0.0622632i	$0.0198318\pi$
$548$	−4.29922	−	7.44646i	−0.183653	−	0.318097i
$549$	−12.1414	+	12.9681i	−0.518182	+	0.553465i
$550$	2.43215	−	4.21261i	0.103707	−	0.179626i
$551$	7.28820	+	41.3334i	0.310488	+	1.76086i
$552$	−0.147756	+	1.28544i	−0.00628893	+	0.0547121i
$553$	−3.48781	+	1.26946i	−0.148317	+	0.0539829i
$554$	−24.1269	+	8.78149i	−1.02506	+	0.373090i
$555$	7.23125	+	5.36201i	0.306950	+	0.227605i
$556$	−2.65263	−	15.0438i	−0.112496	−	0.637999i
$557$	8.81145	−	15.2619i	0.373353	−	0.646667i	−0.616726	−	0.787178i	$-0.711541\pi$
$557$	8.81145	−	15.2619i	0.373353	−	0.646667i	0.990079	+	0.140511i	$0.0448747\pi$
$558$	−7.84363	−	10.4522i	−0.332047	−	0.442475i
$559$	−1.53535	−	2.65930i	−0.0649383	−	0.112476i
$560$	0.721775	−	0.605641i	0.0305006	−	0.0255930i
$561$	4.81491	+	1.43146i	0.203285	+	0.0604365i
$562$	3.12938	−	17.7476i	0.132005	−	0.748636i
$563$	−9.14782	−	7.67593i	−0.385534	−	0.323502i	0.429336	−	0.903145i	$-0.358748\pi$
$563$	−9.14782	−	7.67593i	−0.385534	−	0.323502i	−0.814871	+	0.579643i	$0.803192\pi$
$564$	−12.9553	+	0.779413i	−0.545517	+	0.0328192i
$565$	−10.1448	−	3.69240i	−0.426794	−	0.155340i
$566$	7.03590			0.295741
$567$	−5.31907	+	7.25999i	−0.223380	+	0.304891i
$568$	−6.84418			−0.287175
$569$	17.4032	+	6.33425i	0.729580	+	0.265545i	0.679987	−	0.733224i	$-0.261985\pi$
$569$	17.4032	+	6.33425i	0.729580	+	0.265545i	0.0495930	+	0.998770i	$0.484208\pi$
$570$	6.77633	−	0.407676i	0.283829	−	0.0170757i
$571$	16.4220	+	13.7797i	0.687240	+	0.576663i	0.918112	−	0.396321i	$-0.129713\pi$
$571$	16.4220	+	13.7797i	0.687240	+	0.576663i	−0.230872	+	0.972984i	$0.574158\pi$
$572$	0.115433	−	0.654655i	0.00482651	−	0.0273725i
$573$	25.5359	+	7.59179i	1.06678	+	0.317152i
$574$	0.456217	−	0.382812i	0.0190421	−	0.0159783i
$575$	1.53600	+	2.66043i	0.0640556	+	0.110948i
$576$	−1.17770	+	2.75917i	−0.0490708	+	0.114965i
$577$	4.34906	−	7.53279i	0.181054	−	0.313594i	−0.761186	−	0.648534i	$-0.775383\pi$
$577$	4.34906	−	7.53279i	0.181054	−	0.313594i	0.942240	+	0.334940i	$0.108716\pi$
$578$	1.90821	+	10.8220i	0.0793709	+	0.450135i
$579$	28.8766	+	21.4122i	1.20007	+	0.889860i
$580$	8.93332	−	3.25146i	0.370936	−	0.135010i
$581$	12.9833	−	4.72555i	0.538639	−	0.196049i
$582$	−1.09510	+	9.52712i	−0.0453935	+	0.394912i
$583$	−0.899781	−	5.10291i	−0.0372651	−	0.211341i
$584$	−0.138365	+	0.239655i	−0.00572559	+	0.00991701i
$585$	0.461402	+	1.52002i	0.0190766	+	0.0628449i
$586$	−1.08079	−	1.87199i	−0.0446472	−	0.0773312i
$587$	14.8959	−	12.4991i	0.614819	−	0.515895i	−0.281351	−	0.959605i	$-0.590783\pi$
$587$	14.8959	−	12.4991i	0.614819	−	0.515895i	0.896170	+	0.443710i	$0.146338\pi$
$588$	1.25757	−	1.19101i	0.0518615	−	0.0491165i
$589$	−3.14649	+	17.8446i	−0.129649	+	0.735274i
$590$	−1.69634	−	1.42340i	−0.0698374	−	0.0586005i
$591$	6.26211	+	9.48154i	0.257589	+	0.390018i
$592$	5.18362	+	1.88668i	0.213045	+	0.0775422i
$593$	−36.9797			−1.51858			−0.759288	−	0.650755i	$-0.774453\pi$
$593$	−36.9797			−1.51858			−0.759288	+	0.650755i	$0.774453\pi$
$594$	−0.0352490	−	6.14635i	−0.00144628	−	0.252188i
$595$	2.31007			0.0947034
$596$	5.08843	+	1.85204i	0.208430	+	0.0758624i
$597$	−1.80936	+	3.61996i	−0.0740520	+	0.148155i
$598$	0.321599	+	0.269854i	0.0131512	+	0.0110352i
$599$	−3.20214	+	18.1602i	−0.130836	+	0.742007i	0.846833	+	0.531858i	$0.178506\pi$
$599$	−3.20214	+	18.1602i	−0.130836	+	0.742007i	−0.977669	+	0.210149i	$0.932605\pi$
$600$	1.65583	+	6.92746i	0.0675991	+	0.282813i
$601$	−10.5538	+	8.85572i	−0.430500	+	0.361232i	−0.832140	−	0.554565i	$-0.812885\pi$
$601$	−10.5538	+	8.85572i	−0.430500	+	0.361232i	0.401640	+	0.915798i	$0.368440\pi$
$602$	2.73205	+	4.73204i	0.111350	+	0.192864i
$603$	19.4762	−	9.87472i	0.793130	−	0.402130i
$604$	−8.84506	+	15.3201i	−0.359901	+	0.623366i
$605$	1.57081	+	8.90853i	0.0638627	+	0.362183i
$606$	−22.3799	+	9.70455i	−0.909123	+	0.394220i
$607$	18.5065	−	6.73581i	0.751155	−	0.273398i	0.0620632	−	0.998072i	$-0.480232\pi$
$607$	18.5065	−	6.73581i	0.751155	−	0.273398i	0.689092	+	0.724674i	$0.258010\pi$
$608$	3.90892	−	1.42273i	0.158528	−	0.0576993i
$609$	16.0334	−	6.95252i	0.649706	−	0.281730i
$610$	−0.968846	−	5.49460i	−0.0392274	−	0.222470i
$611$	−2.10552	+	3.64688i	−0.0851804	+	0.147537i
$612$	−6.56023	+	3.32614i	−0.265181	+	0.134451i
$613$	−5.15674	−	8.93173i	−0.208279	−	0.360749i	0.742894	−	0.669409i	$-0.233453\pi$
$613$	−5.15674	−	8.93173i	−0.208279	−	0.360749i	−0.951172	+	0.308660i	$0.900119\pi$
$614$	9.76738	−	8.19580i	0.394179	−	0.330756i
$615$	−0.225945	−	0.945282i	−0.00911100	−	0.0381175i
$616$	−0.205406	+	1.16491i	−0.00827603	+	0.0469357i
$617$	−20.6316	−	17.3120i	−0.830597	−	0.696953i	0.124831	−	0.992178i	$-0.460161\pi$
$617$	−20.6316	−	17.3120i	−0.830597	−	0.696953i	−0.955428	+	0.295225i	$0.904606\pi$
$618$	12.7975	−	25.6038i	0.514791	−	1.02994i
$619$	38.5991	+	14.0489i	1.55143	+	0.564674i	0.968752	−	0.248031i	$-0.0797835\pi$
$619$	38.5991	+	14.0489i	1.55143	+	0.564674i	0.582676	+	0.812705i	$0.302006\pi$
$620$	4.10424			0.164830
$621$	3.37275	+	1.92155i	0.135344	+	0.0771092i
$622$	10.4875			0.420512
$623$	−1.53157	−	0.557445i	−0.0613610	−	0.0223336i
$624$	0.536431	+	0.812218i	0.0214744	+	0.0325147i
$625$	9.55388	+	8.01666i	0.382155	+	0.320666i
$626$	2.79267	−	15.8380i	0.111618	−	0.633015i
$627$	−6.18795	+	5.86043i	−0.247123	+	0.234043i
$628$	−8.13336	+	6.82470i	−0.324556	+	0.272335i
$629$	6.76228	+	11.7126i	0.269630	+	0.467013i
$630$	−0.821034	−	2.70476i	−0.0327108	−	0.107760i
$631$	−18.0295	+	31.2280i	−0.717742	+	1.24317i	0.244150	+	0.969737i	$0.421491\pi$
$631$	−18.0295	+	31.2280i	−0.717742	+	1.24317i	−0.961892	+	0.273428i	$0.911842\pi$
$632$	0.644521	+	3.65526i	0.0256377	+	0.145398i
$633$	−0.537642	+	4.67735i	−0.0213694	+	0.185908i
$634$	−2.97285	+	1.08203i	−0.118067	+	0.0429728i
$635$	12.4138	−	4.51824i	0.492625	−	0.179301i
$636$	6.09457	+	4.51916i	0.241665	+	0.179196i
$637$	−0.0975863	−	0.553440i	−0.00386651	−	0.0219281i
$638$	−5.96749	+	10.3360i	−0.236255	+	0.409206i
$639$	−8.06038	+	18.8843i	−0.318864	+	0.747050i
$640$	−0.471105	−	0.815978i	−0.0186221	−	0.0322544i
$641$	−27.1777	+	22.8048i	−1.07345	+	0.900734i	−0.995361	−	0.0962118i	$-0.969327\pi$
$641$	−27.1777	+	22.8048i	−1.07345	+	0.900734i	−0.0780925	+	0.996946i	$0.524883\pi$
$642$	18.9304	+	5.62798i	0.747123	+	0.222119i
$643$	6.60951	−	37.4844i	0.260654	−	1.47824i	−0.520478	−	0.853875i	$-0.674246\pi$
$643$	6.60951	−	37.4844i	0.260654	−	1.47824i	0.781132	−	0.624366i	$-0.214642\pi$
$644$	−0.572264	−	0.480187i	−0.0225504	−	0.0189220i
$645$	8.90106	−	0.535503i	0.350479	−	0.0210854i
$646$	9.58369	+	3.48818i	0.377065	+	0.137241i
$647$	−15.7470			−0.619079			−0.309540	−	0.950887i	$-0.600175\pi$
$647$	−15.7470			−0.619079			−0.309540	+	0.950887i	$0.600175\pi$
$648$	6.22605	+	6.49895i	0.244582	+	0.255303i
$649$	2.78006			0.109127
$650$	2.17162	+	0.790404i	0.0851778	+	0.0310022i
$651$	7.53114	−	0.453086i	0.295169	−	0.0177579i
$652$	14.8643	+	12.4726i	0.582131	+	0.488466i
$653$	0.291364	−	1.65241i	0.0114020	−	0.0646638i	−0.978576	−	0.205886i	$-0.933992\pi$
$653$	0.291364	−	1.65241i	0.0114020	−	0.0646638i	0.989978	+	0.141223i	$0.0451034\pi$
$654$	8.25244	+	2.45344i	0.322696	+	0.0959370i
$655$	−12.7114	+	10.6661i	−0.496675	+	0.416760i
$656$	−0.297775	−	0.515761i	−0.0116261	−	0.0201371i
$657$	0.498298	+	0.664015i	0.0194404	+	0.0259057i
$658$	3.74664	−	6.48936i	0.146059	−	0.252982i
$659$	−2.80820	−	15.9261i	−0.109392	−	0.620392i	−0.989375	−	0.145387i	$-0.953557\pi$
$659$	−2.80820	−	15.9261i	−0.109392	−	0.620392i	0.879983	−	0.475005i	$-0.157554\pi$
$660$	1.55063	+	1.14980i	0.0603583	+	0.0447560i
$661$	42.2615	−	15.3819i	1.64378	−	0.598288i	0.656087	−	0.754685i	$-0.272210\pi$
$661$	42.2615	−	15.3819i	1.64378	−	0.598288i	0.987694	+	0.156397i	$0.0499880\pi$
$662$	−30.1940	+	10.9897i	−1.17352	+	0.427127i
$663$	−0.272520	+	2.37086i	−0.0105838	+	0.0920765i
$664$	−2.39922	−	13.6067i	−0.0931079	−	0.528041i
$665$	−1.95970	+	3.39429i	−0.0759938	+	0.131625i
$666$	11.3104	−	12.0805i	0.438270	−	0.468112i
$667$	−3.76870	−	6.52758i	−0.145925	−	0.252749i
$668$	3.86827	−	3.24586i	0.149668	−	0.125586i
$669$	−30.8275	+	29.1958i	−1.19186	+	1.12878i
$670$	−1.19091	+	6.75399i	−0.0460089	+	0.260929i
$671$	5.36578	+	4.50243i	0.207144	+	0.173814i
$672$	−0.954542	−	1.44529i	−0.0368223	−	0.0557531i
$673$	14.3109	+	5.20875i	0.551646	+	0.200783i	0.602778	−	0.797909i	$-0.294061\pi$
$673$	14.3109	+	5.20875i	0.551646	+	0.200783i	−0.0511318	+	0.998692i	$0.516283\pi$
$674$	−25.1673			−0.969407
$675$	21.0641	+	3.58974i	0.810759	+	0.138169i
$676$	−12.6842			−0.487853
$677$	−20.6334	−	7.50993i	−0.793005	−	0.288630i	−0.0864204	−	0.996259i	$-0.527543\pi$
$677$	−20.6334	−	7.50993i	−0.793005	−	0.288630i	−0.706585	+	0.707629i	$0.749765\pi$
$678$	−8.87288	+	17.7519i	−0.340761	+	0.681758i
$679$	−4.24136	−	3.55892i	−0.162768	−	0.136579i
$680$	0.401139	−	2.27497i	0.0153830	−	0.0872411i
$681$	−7.04672	−	29.4812i	−0.270031	−	1.12972i
$682$	−3.94713	+	3.31203i	−0.151143	+	0.126824i
$683$	−1.68722	−	2.92235i	−0.0645597	−	0.111821i	0.831939	−	0.554867i	$-0.187231\pi$
$683$	−1.68722	−	2.92235i	−0.0645597	−	0.111821i	−0.896499	+	0.443047i	$0.853898\pi$
$684$	0.677974	−	12.4609i	0.0259230	−	0.476455i
$685$	4.05077	−	7.01614i	0.154772	−	0.268073i
$686$	0.173648	+	0.984808i	0.00662992	+	0.0376001i
$687$	−5.56060	+	2.41123i	−0.212150	+	0.0919940i
$688$	5.13457	−	1.86883i	0.195753	−	0.0712484i
$689$	2.31328	−	0.841967i	0.0881291	−	0.0320764i
$690$	−1.11850	+	0.485013i	−0.0425807	+	0.0184641i
$691$	2.90523	+	16.4764i	0.110520	+	0.626790i	0.988871	+	0.148774i	$0.0475328\pi$
$691$	2.90523	+	16.4764i	0.110520	+	0.626790i	−0.878351	+	0.478016i	$0.841356\pi$
$692$	−10.0400	+	17.3898i	−0.381663	+	0.661059i
$693$	2.97229	+	1.93867i	0.112908	+	0.0736439i
$694$	−11.4121	−	19.7663i	−0.433197	−	0.750319i
$695$	11.0257	−	9.25170i	0.418230	−	0.350937i
$696$	−4.06272	−	16.9971i	−0.153997	−	0.644274i
$697$	0.253550	−	1.43796i	0.00960391	−	0.0544665i
$698$	2.14655	+	1.80117i	0.0812481	+	0.0681753i
$699$	−1.40581	+	2.81259i	−0.0531726	+	0.106382i
$700$	−3.86424	−	1.40647i	−0.146055	−	0.0531595i
$701$	44.4077			1.67725			0.838627	−	0.544706i	$-0.183359\pi$
$701$	44.4077			1.67725			0.838627	+	0.544706i	$0.183359\pi$
$702$	2.87280	−	0.523557i	0.108427	−	0.0197604i
$703$	−22.9466			−0.865447
$704$	1.11155	+	0.404570i	0.0418930	+	0.0152478i
$705$	−6.73930	−	10.2041i	−0.253817	−	0.384307i
$706$	−18.5591	−	15.5729i	−0.698480	−	0.586095i
$707$	2.44558	−	13.8696i	0.0919756	−	0.521620i
$708$	−2.95560	+	2.79916i	−0.111078	+	0.105199i
$709$	14.7733	−	12.3962i	0.554822	−	0.465551i	−0.321748	−	0.946825i	$-0.604270\pi$
$709$	14.7733	−	12.3962i	0.554822	−	0.465551i	0.876570	+	0.481275i	$0.159826\pi$
$710$	−3.22433	−	5.58470i	−0.121007	−	0.209590i
$711$	10.8445	+	2.52645i	0.406702	+	0.0947494i
$712$	−0.814931	+	1.41150i	−0.0305408	+	0.0528982i
$713$	−0.565064	−	3.20464i	−0.0211618	−	0.120015i
$714$	0.484931	−	4.21878i	0.0181481	−	0.157884i
$715$	0.588566	−	0.214220i	0.0220111	−	0.00801139i
$716$	19.5851	−	7.12840i	0.731930	−	0.266401i
$717$	−12.5190	−	9.28290i	−0.467530	−	0.346676i
$718$	−4.92348	−	27.9225i	−0.183743	−	1.04206i
$719$	−20.7932	+	36.0148i	−0.775454	+	1.34313i	0.159085	+	0.987265i	$0.449146\pi$
$719$	−20.7932	+	36.0148i	−0.775454	+	1.34313i	−0.934539	+	0.355861i	$0.884188\pi$
$720$	−2.80624	+	0.338883i	−0.104583	+	0.0126294i
$721$	8.26303	+	14.3120i	0.307731	+	0.533007i
$722$	1.29936	−	1.09029i	0.0483572	−	0.0405765i
$723$	24.6262	+	7.32134i	0.915859	+	0.272284i
$724$	−3.69132	+	20.9345i	−0.137187	+	0.778024i
$725$	−31.7842	−	26.6701i	−1.18044	−	0.990504i
$726$	16.5990	−	0.998626i	0.616048	−	0.0370625i
$727$	−8.60989	−	3.13374i	−0.319323	−	0.116224i	0.177386	−	0.984141i	$-0.443236\pi$
$727$	−8.60989	−	3.13374i	−0.319323	−	0.116224i	−0.496709	+	0.867917i	$0.665458\pi$
$728$	−0.561977			−0.0208283
$729$	25.2641	−	9.52494i	0.935708	−	0.352775i
$730$	−0.260738			−0.00965035
$731$	12.5887	+	4.58190i	0.465609	+	0.169468i
$732$	−10.2379	+	0.615932i	−0.378405	+	0.0227655i
$733$	−29.6348	−	24.8665i	−1.09459	−	0.918466i	−0.0975362	−	0.995232i	$-0.531096\pi$
$733$	−29.6348	−	24.8665i	−1.09459	−	0.918466i	−0.997049	+	0.0767658i	$0.975541\pi$
$734$	5.58574	−	31.6783i	0.206173	−	1.16927i
$735$	1.56429	+	0.465061i	0.0576997	+	0.0171540i
$736$	−0.572264	+	0.480187i	−0.0210939	+	0.0176999i
$737$	−4.30500	−	7.45648i	−0.158577	−	0.274663i
$738$	−1.77376	+	0.214200i	−0.0652931	+	0.00788482i
$739$	−8.20720	+	14.2153i	−0.301907	+	0.522918i	−0.976568	−	0.215210i	$-0.930956\pi$
$739$	−8.20720	+	14.2153i	−0.301907	+	0.522918i	0.674661	+	0.738128i	$0.264290\pi$
$740$	0.902538	+	5.11854i	0.0331779	+	0.188161i
$741$	−3.25243	−	2.41170i	−0.119481	−	0.0885959i
$742$	−4.11633	+	1.49822i	−0.151115	+	0.0550014i
$743$	−44.0700	+	16.0402i	−1.61677	+	0.588457i	−0.982763	−	0.184868i	$-0.940814\pi$
$743$	−44.0700	+	16.0402i	−1.61677	+	0.588457i	−0.634009	+	0.773325i	$0.718592\pi$
$744$	0.861566	−	7.49540i	0.0315865	−	0.274795i
$745$	0.885964	+	5.02455i	0.0324592	+	0.184085i
$746$	−0.396318	+	0.686442i	−0.0145102	+	0.0251324i
$747$	−40.3687	−	9.40469i	−1.47701	−	0.344100i
$748$	1.45007	+	2.51159i	0.0530198	+	0.0918330i
$749$	−8.73463	+	7.32923i	−0.319157	+	0.267804i
$750$	−10.7971	+	10.2256i	−0.394254	+	0.373386i
$751$	−2.93043	+	16.6193i	−0.106933	+	0.606446i	0.883498	+	0.468435i	$0.155182\pi$
$751$	−2.93043	+	16.6193i	−0.106933	+	0.606446i	−0.990431	+	0.138011i	$0.955929\pi$
$752$	−5.74018	−	4.81658i	−0.209323	−	0.175643i
$753$	−9.17691	−	13.8949i	−0.334425	−	0.506358i
$754$	−5.32824	−	1.93932i	−0.194043	−	0.0706259i
$755$	−16.6678			−0.606604
$756$	−5.11195	+	0.931634i	−0.185920	+	0.0338832i
$757$	−20.6314			−0.749860			−0.374930	−	0.927053i	$-0.622333\pi$
$757$	−20.6314			−0.749860			−0.374930	+	0.927053i	$0.622333\pi$
$758$	−32.9459	−	11.9913i	−1.19665	−	0.435545i
$759$	0.684291	−	1.36905i	0.0248382	−	0.0496935i
$760$	3.00243	+	2.51934i	0.108910	+	0.0913859i
$761$	7.49845	−	42.5258i	0.271819	−	1.54156i	−0.477071	−	0.878865i	$-0.658301\pi$
$761$	7.49845	−	42.5258i	0.271819	−	1.54156i	0.748889	−	0.662695i	$-0.230588\pi$
$762$	−5.64557	−	23.6192i	−0.204517	−	0.855634i
$763$	−3.80774	+	3.19507i	−0.137849	+	0.115669i
$764$	7.69046	+	13.3203i	0.278231	+	0.481910i
$765$	−5.80461	−	3.78604i	−0.209866	−	0.136885i
$766$	−8.76371	+	15.1792i	−0.316646	+	0.548447i
$767$	0.229351	+	1.30072i	0.00828139	+	0.0469661i
$768$	−1.58908	+	0.689069i	−0.0573411	+	0.0248646i
$769$	−45.4554	+	16.5444i	−1.63916	+	0.596606i	−0.986892	−	0.161380i	$-0.948405\pi$
$769$	−45.4554	+	16.5444i	−1.63916	+	0.596606i	−0.652270	+	0.757987i	$0.726183\pi$
$770$	−1.04731	+	0.381190i	−0.0377425	+	0.0137372i
$771$	4.13885	−	1.79472i	0.149057	−	0.0646351i
$772$	3.60411	+	20.4399i	0.129715	+	0.735649i
$773$	−7.94149	+	13.7551i	−0.285635	+	0.494735i	−0.972763	−	0.231802i	$-0.925538\pi$
$773$	−7.94149	+	13.7551i	−0.285635	+	0.494735i	0.687128	+	0.726537i	$0.258871\pi$
$774$	0.890553	−	16.3681i	0.0320103	−	0.588338i
$775$	−8.95639	−	15.5129i	−0.321723	−	0.557241i
$776$	−4.24136	+	3.55892i	−0.152256	+	0.127758i
$777$	2.22119	+	9.29272i	0.0796846	+	0.333375i
$778$	4.78623	−	27.1441i	0.171595	−	0.973162i
$779$	1.89777	+	1.59241i	0.0679945	+	0.0570542i
$780$	−0.410036	+	0.820356i	−0.0146817	+	0.0293735i
$781$	7.60763	+	2.76895i	0.272223	+	0.0990809i
$782$	−1.83155			−0.0654961
$783$	−51.6826	−	8.80773i	−1.84699	−	0.314763i
$784$	1.00000			0.0357143
$785$	−9.40047	−	3.42149i	−0.335517	−	0.122118i
$786$	16.8107	+	25.4533i	0.599618	+	0.907890i
$787$	−30.0119	−	25.1830i	−1.06981	−	0.897676i	−0.0747740	−	0.997201i	$-0.523824\pi$
$787$	−30.0119	−	25.1830i	−1.06981	−	0.897676i	−0.995035	+	0.0995240i	$0.968268\pi$
$788$	−1.13919	+	6.46066i	−0.0405819	+	0.230151i
$789$	12.0894	−	11.4495i	0.430395	−	0.407614i
$790$	−2.67898	+	2.24793i	−0.0953137	+	0.0799777i
$791$	−5.72900	−	9.92293i	−0.203700	−	0.352819i
$792$	2.42535	−	2.59049i	0.0861810	−	0.0920490i
$793$	−1.66389	+	2.88195i	−0.0590866	+	0.102341i
$794$	−4.65656	−	26.4087i	−0.165255	−	0.937209i
$795$	−0.816350	+	7.10203i	−0.0289529	+	0.251883i
$796$	−2.19561	+	0.799135i	−0.0778212	+	0.0283246i
$797$	49.7527	−	18.1085i	1.76233	−	0.641436i	0.762347	−	0.647169i	$-0.224047\pi$
$797$	49.7527	−	18.1085i	1.76233	−	0.641436i	0.999984	+	0.00573336i	$0.00182500\pi$
$798$	5.78748	+	4.29145i	0.204874	+	0.151916i
$799$	−3.19020	−	18.0925i	−0.112861	−	0.640068i
$800$	−2.05612	+	3.56130i	−0.0726948	+	0.125911i
$801$	2.93483	+	3.91086i	0.103697	+	0.138183i
$802$	−8.47396	−	14.6773i	−0.299226	−	0.518274i
$803$	0.250757	−	0.210410i	0.00884902	−	0.00742521i
$804$	12.0845	+	3.59271i	0.426189	+	0.126705i
$805$	0.122225	−	0.693173i	0.00430787	−	0.0244312i
$806$	−1.87524	−	1.57352i	−0.0660526	−	0.0554247i
$807$	40.1177	−	2.41355i	1.41221	−	0.0849609i
$808$	−13.2342	−	4.81686i	−0.465578	−	0.169457i
$809$	−23.9703			−0.842751			−0.421376	−	0.906886i	$-0.638453\pi$
$809$	−23.9703			−0.842751			−0.421376	+	0.906886i	$0.638453\pi$
$810$	−2.36987	+	8.14201i	−0.0832688	+	0.286081i
$811$	−22.1285			−0.777037			−0.388519	−	0.921441i	$-0.627013\pi$
$811$	−22.1285			−0.777037			−0.388519	+	0.921441i	$0.627013\pi$
$812$	9.48124	+	3.45089i	0.332726	+	0.121102i
$813$	6.34262	−	0.381583i	0.222446	−	0.0133827i
$814$	−4.99854	−	4.19428i	−0.175199	−	0.147009i
$815$	−3.17474	+	18.0049i	−0.111206	+	0.630683i
$816$	−4.07048	−	1.21015i	−0.142495	−	0.0423636i
$817$	−17.4118	+	14.6102i	−0.609160	+	0.511146i
$818$	3.72382	+	6.44985i	0.130200	+	0.225514i
$819$	−0.661840	+	1.55059i	−0.0231266	+	0.0541821i
$820$	0.280566	−	0.485955i	0.00979780	−	0.0169703i
$821$	−0.310667	−	1.76188i	−0.0108424	−	0.0614901i	0.978907	−	0.204309i	$-0.0654946\pi$
$821$	−0.310667	−	1.76188i	−0.0108424	−	0.0614901i	−0.989749	+	0.142818i	$0.954383\pi$
$822$	−11.9629	−	8.87059i	−0.417255	−	0.309397i
$823$	8.38264	−	3.05103i	0.292200	−	0.106352i	−0.191761	−	0.981442i	$-0.561420\pi$
$823$	8.38264	−	3.05103i	0.292200	−	0.106352i	0.483961	+	0.875089i	$0.339198\pi$
$824$	15.5294	−	5.65225i	0.540993	−	0.196905i
$825$	0.962110	−	8.37011i	0.0334964	−	0.291410i
$826$	−0.408115	−	2.31453i	−0.0142001	−	0.0805329i
$827$	12.2186	−	21.1632i	0.424882	−	0.735917i	−0.571527	−	0.820583i	$-0.693649\pi$
$827$	12.2186	−	21.1632i	0.424882	−	0.735917i	0.996409	+	0.0846656i	$0.0269822\pi$
$828$	0.650962	+	2.14449i	0.0226225	+	0.0745262i
$829$	−5.29535	−	9.17182i	−0.183915	−	0.318550i	0.759295	−	0.650746i	$-0.225544\pi$
$829$	−5.29535	−	9.17182i	−0.183915	−	0.318550i	−0.943210	+	0.332196i	$0.892210\pi$
$830$	9.97246	−	8.36788i	0.346149	−	0.290453i
$831$	−32.2887	+	30.5796i	−1.12008	+	1.06080i
$832$	−0.0975863	+	0.553440i	−0.00338320	+	0.0191871i
$833$	1.87815	+	1.57596i	0.0650740	+	0.0546036i
$834$	−14.5815	−	22.0780i	−0.504915	−	0.764499i
$835$	4.47091	+	1.62728i	0.154722	+	0.0563143i
$836$	−4.92055			−0.170181
$837$	−19.6664	−	11.2045i	−0.679772	−	0.387285i
$838$	19.5171			0.674208
$839$	−5.18183	−	1.88603i	−0.178897	−	0.0651130i	0.251019	−	0.967982i	$-0.419234\pi$
$839$	−5.18183	−	1.88603i	−0.178897	−	0.0651130i	−0.429915	+	0.902869i	$0.641457\pi$
$840$	0.729631	−	1.45977i	0.0251747	−	0.0503667i
$841$	55.7700	+	46.7966i	1.92310	+	1.61367i
$842$	5.71592	−	32.4166i	0.196984	−	1.11715i
$843$	−7.25647	−	30.3587i	−0.249926	−	1.04561i
$844$	−2.08230	+	1.74726i	−0.0716758	+	0.0601431i
$845$	−5.97558	−	10.3500i	−0.205566	−	0.356051i
$846$	−20.0500	+	10.1657i	−0.689333	+	0.349502i
$847$	−4.80039	+	8.31452i	−0.164943	+	0.285690i
$848$	0.760667	+	4.31396i	0.0261214	+	0.148142i
$849$	11.1806	−	4.84823i	0.383718	−	0.166391i
$850$	−9.47416	+	3.44831i	−0.324961	+	0.118276i
$851$	3.87236	−	1.40942i	0.132743	−	0.0483144i
$852$	−10.8760	+	4.71611i	−0.372604	+	0.161571i
$853$	−8.43257	−	47.8235i	−0.288726	−	1.63744i	−0.691665	−	0.722218i	$-0.743123\pi$
$853$	−8.43257	−	47.8235i	−0.288726	−	1.63744i	0.402940	−	0.915227i	$-0.367988\pi$
$854$	2.96078	−	5.12823i	0.101316	−	0.175484i
$855$	10.4872	−	5.31719i	0.358656	−	0.181844i
$856$	5.70113	+	9.87464i	0.194860	+	0.337508i
$857$	−10.4321	+	8.75355i	−0.356353	+	0.299015i	−0.803335	−	0.595527i	$-0.796943\pi$
$857$	−10.4321	+	8.75355i	−0.356353	+	0.299015i	0.446982	+	0.894543i	$0.352499\pi$
$858$	−0.267670	−	1.11984i	−0.00913809	−	0.0382308i
$859$	2.71671	−	15.4072i	0.0926929	−	0.525688i	−0.902737	−	0.430193i	$-0.858446\pi$
$859$	2.71671	−	15.4072i	0.0926929	−	0.525688i	0.995430	−	0.0954948i	$-0.0304433\pi$
$860$	3.94384	+	3.30928i	0.134484	+	0.112845i
$861$	0.461183	−	0.922685i	0.0157171	−	0.0314450i
$862$	−0.633962	−	0.230743i	−0.0215928	−	0.00785915i
$863$	−7.82043			−0.266211			−0.133105	−	0.991102i	$-0.542495\pi$
$863$	−7.82043			−0.266211			−0.133105	+	0.991102i	$0.542495\pi$
$864$	0.0297992	+	5.19607i	0.00101379	+	0.176774i
$865$	−18.9196			−0.643284
$866$	17.9204	+	6.52248i	0.608959	+	0.221643i
$867$	10.4894	+	15.8821i	0.356238	+	0.539385i
$868$	3.33687	+	2.79996i	0.113261	+	0.0950369i
$869$	0.762394	−	4.32375i	0.0258625	−	0.146673i
$870$	11.9553	−	11.3225i	0.405323	−	0.383869i
$871$	3.13353	−	2.62934i	0.106176	−	0.0890919i
$872$	2.48532	+	4.30471i	0.0841637	+	0.145776i
$873$	4.82463	+	15.8940i	0.163289	+	0.537930i
$874$	1.55376	−	2.69119i	0.0525566	−	0.0910308i
$875$	−1.49088	−	8.45521i	−0.0504010	−	0.285838i
$876$	−0.0547344	+	0.476175i	−0.00184930	+	0.0160885i
$877$	8.51491	−	3.09917i	0.287528	−	0.104652i	−0.194230	−	0.980956i	$-0.562221\pi$
$877$	8.51491	−	3.09917i	0.287528	−	0.104652i	0.481758	+	0.876304i	$0.339999\pi$
$878$	−19.5267	+	7.10714i	−0.658994	+	0.239854i
$879$	−3.00740	−	2.23001i	−0.101437	−	0.0752162i
$880$	0.193535	+	1.09759i	0.00652408	+	0.0369999i
$881$	2.67621	−	4.63533i	0.0901638	−	0.156168i	−0.817416	−	0.576048i	$-0.804594\pi$
$881$	2.67621	−	4.63533i	0.0901638	−	0.156168i	0.907580	+	0.419879i	$0.137928\pi$
$882$	1.17770	−	2.75917i	0.0396552	−	0.0929061i
$883$	0.374484	+	0.648625i	0.0126024	+	0.0218280i	0.872258	−	0.489046i	$-0.162655\pi$
$883$	0.374484	+	0.648625i	0.0126024	+	0.0218280i	−0.859655	+	0.510874i	$0.829322\pi$
$884$	−1.05548	+	0.885651i	−0.0354996	+	0.0297877i
$885$	−3.67645	−	1.09300i	−0.123583	−	0.0367409i
$886$	−2.87332	+	16.2954i	−0.0965312	+	0.547456i
$887$	−8.54143	−	7.16711i	−0.286793	−	0.240648i	0.488029	−	0.872828i	$-0.337716\pi$
$887$	−8.54143	−	7.16711i	−0.286793	−	0.240648i	−0.774822	+	0.632179i	$0.782161\pi$
$888$	9.53725	−	0.573777i	0.320049	−	0.0192547i
$889$	13.1751	+	4.79536i	0.441880	+	0.160831i
$890$	−1.53567			−0.0514759
$891$	−4.29127	−	9.74277i	−0.143763	−	0.326395i
$892$	−24.5135			−0.820772
$893$	29.2906	+	10.6609i	0.980172	+	0.356754i
$894$	9.36211	−	0.563241i	0.313116	−	0.0188376i
$895$	15.0433	+	12.6228i	0.502841	+	0.421934i
$896$	0.173648	−	0.984808i	0.00580118	−	0.0329001i
$897$	0.696996	+	0.207216i	0.0232720	+	0.00691874i
$898$	−15.8677	+	13.3146i	−0.529513	+	0.444314i
$899$	21.9753	+	38.0623i	0.732916	+	1.26945i
$900$	7.40476	+	9.86733i	0.246825	+	0.328911i
$901$	−5.36996	+	9.30104i	−0.178899	+	0.309862i
$902$	0.122329	+	0.693764i	0.00407312	+	0.0230998i
$903$	7.60215	+	5.63704i	0.252984	+	0.187589i
$904$	−10.7670	+	3.91887i	−0.358105	+	0.130340i
$905$	−18.8211	+	6.85032i	−0.625634	+	0.227712i
$906$	−3.49893	+	30.4398i	−0.116244	+	1.01129i
$907$	5.31161	+	30.1236i	0.176369	+	1.00024i	0.936552	+	0.350529i	$0.113998\pi$
$907$	5.31161	+	30.1236i	0.176369	+	1.00024i	−0.760183	+	0.649709i	$0.774891\pi$
$908$	8.75022	−	15.1558i	0.290386	−	0.502964i
$909$	−28.8765	+	30.8426i	−0.957772	+	1.02299i
$910$	−0.264750	−	0.458561i	−0.00877639	−	0.0152012i
$911$	44.4336	−	37.2842i	1.47215	−	1.23528i	0.558040	−	0.829814i	$-0.311554\pi$
$911$	44.4336	−	37.2842i	1.47215	−	1.23528i	0.914110	−	0.405466i	$-0.132891\pi$
$912$	5.23123	−	4.95435i	0.173223	−	0.164055i
$913$	−2.83800	+	16.0951i	−0.0939242	+	0.532671i
$914$	−3.00797	−	2.52399i	−0.0994949	−	0.0834862i
$915$	−5.32574	−	8.06377i	−0.176063	−	0.266580i
$916$	−3.28822	−	1.19681i	−0.108646	−	0.0395439i
$917$	−17.6113			−0.581576
$918$	−8.13280	+	9.80596i	−0.268422	+	0.323645i
$919$	−14.0872			−0.464694			−0.232347	−	0.972633i	$-0.574641\pi$
$919$	−14.0872			−0.464694			−0.232347	+	0.972633i	$0.574641\pi$
$920$	−0.661418	−	0.240737i	−0.0218063	−	0.00793685i
$921$	9.87370	−	19.7542i	0.325349	−	0.650923i
$922$	12.0096	+	10.0772i	0.395515	+	0.331876i
$923$	−0.667898	+	3.78784i	−0.0219841	+	0.124678i
$924$	0.476300	+	1.99268i	0.0156691	+	0.0655545i
$925$	17.3772	−	14.5812i	0.571358	−	0.479427i
$926$	10.3133	+	17.8632i	0.338916	+	0.587020i
$927$	2.69347	−	49.5050i	0.0884650	−	1.62596i
$928$	5.04486	−	8.73796i	0.165606	−	0.286837i
$929$	0.728887	+	4.13373i	0.0239140	+	0.135623i	0.994427	−	0.105424i	$-0.0336201\pi$
$929$	0.728887	+	4.13373i	0.0239140	+	0.135623i	−0.970513	+	0.241048i	$0.922509\pi$
$930$	6.52197	−	2.82810i	0.213864	−	0.0927372i
$931$	−3.90892	+	1.42273i	−0.128110	+	0.0466281i
$932$	−1.70591	+	0.620901i	−0.0558790	+	0.0203383i
$933$	16.6656	−	7.22663i	0.545606	−	0.236589i
$934$	1.65085	+	9.36241i	0.0540173	+	0.306347i
$935$	−1.36627	+	2.36645i	−0.0446818	+	0.0773912i
$936$	1.41211	+	0.921043i	0.0461562	+	0.0301052i
$937$	26.8151	+	46.4452i	0.876012	+	1.51730i	0.855681	+	0.517504i	$0.173139\pi$
$937$	26.8151	+	46.4452i	0.876012	+	1.51730i	0.0203317	+	0.999793i	$0.493528\pi$
$938$	−5.57590	+	4.67873i	−0.182060	+	0.152766i
$939$	−6.47572	−	27.0923i	−0.211327	−	0.884124i
$940$	1.22600	−	6.95298i	0.0399876	−	0.226781i
$941$	36.2414	+	30.4102i	1.18144	+	0.991343i	0.999968	+	0.00794577i	$0.00252924\pi$
$941$	36.2414	+	30.4102i	1.18144	+	0.991343i	0.181468	+	0.983397i	$0.441915\pi$
$942$	−8.22189	+	16.4495i	−0.267884	+	0.535952i
$943$	−0.418067	−	0.152164i	−0.0136141	−	0.00495514i
$944$	−2.35024			−0.0764938
$945$	−3.16846	−	3.73234i	−0.103070	−	0.121413i
$946$	−6.46339			−0.210143
$947$	40.2774	+	14.6598i	1.30884	+	0.476379i	0.899865	−	0.436168i	$-0.143665\pi$
$947$	40.2774	+	14.6598i	1.30884	+	0.476379i	0.408974	+	0.912546i	$0.365887\pi$
$948$	3.54293	+	5.36439i	0.115069	+	0.174227i
$949$	0.119132	+	0.0999638i	0.00386719	+	0.00324496i
$950$	2.97043	−	16.8461i	0.0963735	−	0.546561i
$951$	−3.97851	+	3.76793i	−0.129012	+	0.122184i
$952$	1.87815	−	1.57596i	0.0608712	−	0.0510770i
$953$	15.2738	+	26.4551i	0.494768	+	0.856964i	0.999982	−	0.00603039i	$-0.00191955\pi$
$953$	15.2738	+	26.4551i	0.494768	+	0.856964i	−0.505213	+	0.862994i	$0.668586\pi$
$954$	12.7988	+	2.98173i	0.414376	+	0.0965371i
$955$	−7.24603	+	12.5505i	−0.234476	+	0.406125i
$956$	−1.56250	−	8.86140i	−0.0505350	−	0.286598i
$957$	−2.36062	+	20.5368i	−0.0763079	+	0.663859i
$958$	26.9793	−	9.81966i	0.871661	−	0.317259i
$959$	8.07989	−	2.94084i	0.260913	−	0.0949646i
$960$	−1.31089	−	0.972033i	−0.0423088	−	0.0313722i
$961$	−2.08821	−	11.8428i	−0.0673617	−	0.382027i
$962$	1.55002	−	2.68470i	0.0499745	−	0.0865584i
$963$	33.9600	−	4.10103i	1.09435	−	0.132154i
$964$	7.41649	+	12.8457i	0.238869	+	0.413734i
$965$	−14.9806	+	12.5702i	−0.482243	+	0.404650i
$966$	−1.24026	−	0.368727i	−0.0399046	−	0.0118636i
$967$	−5.12468	+	29.0635i	−0.164799	+	0.934620i	0.784473	+	0.620163i	$0.212933\pi$
$967$	−5.12468	+	29.0635i	−0.164799	+	0.934620i	−0.949272	+	0.314457i	$0.898178\pi$
$968$	7.35463	+	6.17126i	0.236387	+	0.198352i
$969$	17.6329	−	1.06082i	0.566450	−	0.0340786i
$970$	−4.90213	−	1.78423i	−0.157398	−	0.0572882i
$971$	−33.9468			−1.08940			−0.544702	−	0.838630i	$-0.683357\pi$
$971$	−33.9468			−1.08940			−0.544702	+	0.838630i	$0.683357\pi$
$972$	14.3719	+	6.03718i	0.460980	+	0.193643i
$973$	15.2759			0.489722
$974$	−38.3179	−	13.9466i	−1.22778	−	0.446877i
$975$	3.99552	−	0.240377i	0.127959	−	0.00769823i
$976$	−4.53619	−	3.80631i	−0.145200	−	0.121837i
$977$	5.00262	−	28.3713i	0.160048	−	0.907677i	−0.793977	−	0.607948i	$-0.791993\pi$
$977$	5.00262	−	28.3713i	0.160048	−	0.907677i	0.954024	−	0.299729i	$-0.0968962\pi$
$978$	32.2151	+	9.57750i	1.03012	+	0.306255i
$979$	1.47689	−	1.23925i	0.0472015	−	0.0396067i
$980$	0.471105	+	0.815978i	0.0150489	+	0.0260655i
$981$	14.8044	−	1.78779i	0.472668	−	0.0570796i
$982$	−4.87675	+	8.44678i	−0.155623	+	0.269547i
$983$	−5.22221	−	29.6166i	−0.166563	−	0.944624i	−0.947439	−	0.319938i	$-0.896338\pi$
$983$	−5.22221	−	29.6166i	−0.166563	−	0.944624i	0.780876	−	0.624686i	$-0.214773\pi$
$984$	−0.828584	−	0.614399i	−0.0264143	−	0.0195863i
$985$	−5.80843	+	2.11410i	−0.185072	+	0.0673607i
$986$	23.2456	−	8.46072i	0.740292	−	0.269444i
$987$	1.48209	−	12.8938i	0.0471755	−	0.410415i
$988$	−0.405938	−	2.30219i	−0.0129146	−	0.0732424i
$989$	2.04094	−	3.53501i	0.0648982	−	0.112407i
$990$	3.25638	+	0.758638i	0.103494	+	0.0241111i
$991$	3.45119	+	5.97764i	0.109631	+	0.189886i	0.915621	−	0.402043i	$-0.131700\pi$
$991$	3.45119	+	5.97764i	0.109631	+	0.189886i	−0.805990	+	0.591929i	$0.798367\pi$
$992$	3.33687	−	2.79996i	0.105946	−	0.0888989i
$993$	−40.4081	+	38.2693i	−1.28231	+	1.21444i
$994$	1.18848	−	6.74020i	0.0376963	−	0.213786i
$995$	−1.68644	−	1.41509i	−0.0534637	−	0.0448614i
$996$	−13.1885	−	19.9689i	−0.417894	−	0.632738i
$997$	−6.70968	−	2.44213i	−0.212498	−	0.0773429i	0.233578	−	0.972338i	$-0.424957\pi$
$997$	−6.70968	−	2.44213i	−0.212498	−	0.0773429i	−0.446076	+	0.894995i	$0.647179\pi$
$998$	−3.27687			−0.103728
$999$	9.64886	−	26.9906i	0.305276	−	0.853946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.85.4	✓	24
27.7	even	9	inner	378.2.u.c.169.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.85.4	✓	24	1.1	even	1	trivial
378.2.u.c.169.4	yes	24	27.7	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.72892 - 0.104015i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.163613 + 0.927896i) q^{5} +(1.66023 + 0.493585i) q^{6} +(-0.766044 + 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.97836 - 0.359668i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.72892 - 0.104015i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.163613 + 0.927896i) q^{5} +(1.66023 + 0.493585i) q^{6} +(-0.766044 + 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.97836 - 0.359668i) q^{9} +(-0.471105 + 0.815978i) q^{10} +(-0.205406 - 1.16491i) q^{11} +(1.39129 + 1.03165i) q^{12} +(0.528086 - 0.192208i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.186360 + 1.62128i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.22588 + 2.12328i) q^{17} +(2.92176 + 0.680682i) q^{18} +(-2.07989 - 3.60248i) q^{19} +(-0.721775 + 0.605641i) q^{20} +(-1.25757 + 1.19101i) q^{21} +(0.205406 - 1.16491i) q^{22} +(0.572264 + 0.480187i) q^{23} +(0.954542 + 1.44529i) q^{24} +(3.86424 + 1.40647i) q^{25} +0.561977 q^{26} +(5.11195 - 0.931634i) q^{27} -1.00000 q^{28} +(-9.48124 - 3.45089i) q^{29} +(-0.729631 + 1.45977i) q^{30} +(-3.33687 - 2.79996i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.476300 - 1.99268i) q^{33} +(-1.87815 + 1.57596i) q^{34} +(-0.471105 - 0.815978i) q^{35} +(2.51275 + 1.63893i) q^{36} +(2.75815 - 4.77725i) q^{37} +(-0.722339 - 4.09659i) q^{38} +(0.893028 - 0.387241i) q^{39} +(-0.885388 + 0.322255i) q^{40} +(-0.559633 + 0.203690i) q^{41} +(-1.58908 + 0.689069i) q^{42} +(-0.948829 - 5.38108i) q^{43} +(0.591442 - 1.02441i) q^{44} +(-0.153564 + 2.82246i) q^{45} +(0.373519 + 0.646954i) q^{46} +(-5.74018 + 4.81658i) q^{47} +(0.402659 + 1.68460i) q^{48} +(0.173648 - 0.984808i) q^{49} +(3.15016 + 2.64330i) q^{50} +(-1.89859 + 3.79850i) q^{51} +(0.528086 + 0.192208i) q^{52} +4.38051 q^{53} +(5.12230 + 0.872941i) q^{54} +1.11453 q^{55} +(-0.939693 - 0.342020i) q^{56} +(-3.97069 - 6.01207i) q^{57} +(-7.72918 - 6.48555i) q^{58} +(-0.408115 + 2.31453i) q^{59} +(-1.18490 + 1.12218i) q^{60} +(-4.53619 + 3.80631i) q^{61} +(-2.17798 - 3.77238i) q^{62} +(-2.05037 + 2.18998i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0919469 + 0.521457i) q^{65} +(0.233963 - 2.03541i) q^{66} +(6.83985 - 2.48950i) q^{67} +(-2.30389 + 0.838548i) q^{68} +(1.03935 + 0.770682i) q^{69} +(-0.163613 - 0.927896i) q^{70} +(-3.42209 + 5.92723i) q^{71} +(1.80066 + 2.39950i) q^{72} +(0.138365 + 0.239655i) q^{73} +(4.22572 - 3.54580i) q^{74} +(6.82728 + 2.02974i) q^{75} +(0.722339 - 4.09659i) q^{76} +(0.906142 + 0.760344i) q^{77} +(0.971617 - 0.0584541i) q^{78} +(3.48781 + 1.26946i) q^{79} -0.942210 q^{80} +(8.74128 - 2.14245i) q^{81} -0.595549 q^{82} +(-12.9833 - 4.72555i) q^{83} +(-1.72892 + 0.104015i) q^{84} +(-1.76961 - 1.48488i) q^{85} +(0.948829 - 5.38108i) q^{86} +(-16.7513 - 4.98014i) q^{87} +(0.906142 - 0.760344i) q^{88} +(0.814931 + 1.41150i) q^{89} +(-1.10964 + 2.59972i) q^{90} +(-0.280989 + 0.486687i) q^{91} +(0.129722 + 0.735689i) q^{92} +(-6.06043 - 4.49384i) q^{93} +(-7.04137 + 2.56285i) q^{94} +(3.68302 - 1.34051i) q^{95} +(-0.197790 + 1.72072i) q^{96} +(0.961438 + 5.45259i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-1.03076 - 3.39566i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more