LMFDB - Embedded newform 378.2.u.d.211.5

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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.5
Character	$\chi$	$=$	378.211
Dual form			378.2.u.d.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(1.73061 + 0.0705192i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.918005 + 0.334126i) q^{5} +(1.37106 - 1.05840i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99005 + 0.244083i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(1.73061 + 0.0705192i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.918005 + 0.334126i) q^{5} +(1.37106 - 1.05840i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99005 + 0.244083i) q^{9} +(-0.488460 + 0.846038i) q^{10} +(3.68881 + 1.34262i) q^{11} +(0.369966 - 1.69208i) q^{12} +(0.336485 + 0.282345i) q^{13} +(-0.766044 - 0.642788i) q^{14} +(-1.61227 + 0.513507i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.75629 - 3.04198i) q^{17} +(2.44741 - 1.73499i) q^{18} +(-3.72506 - 6.45199i) q^{19} +(0.169640 + 0.962079i) q^{20} +(-0.231070 - 1.71657i) q^{21} +(3.68881 - 1.34262i) q^{22} +(-0.806925 + 4.57630i) q^{23} +(-0.804236 - 1.53402i) q^{24} +(-3.09913 + 2.60048i) q^{25} +0.439250 q^{26} +(5.15742 + 0.633270i) q^{27} -1.00000 q^{28} +(-3.40300 + 2.85546i) q^{29} +(-0.904998 + 1.42972i) q^{30} +(-0.888920 + 5.04131i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(6.28923 + 2.58368i) q^{33} +(-0.609953 - 3.45921i) q^{34} +(0.488460 + 0.846038i) q^{35} +(0.759593 - 2.90224i) q^{36} +(-4.10925 + 7.11742i) q^{37} +(-7.00082 - 2.54809i) q^{38} +(0.562416 + 0.512358i) q^{39} +(0.748364 + 0.627952i) q^{40} +(0.827470 + 0.694329i) q^{41} +(-1.28040 - 1.16644i) q^{42} +(-10.9554 - 3.98746i) q^{43} +(1.96277 - 3.39962i) q^{44} +(-2.82644 + 0.774986i) q^{45} +(2.32345 + 4.02433i) q^{46} +(0.138372 + 0.784746i) q^{47} +(-1.60213 - 0.658171i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(-0.702516 + 3.98416i) q^{50} +(3.25398 - 5.14065i) q^{51} +(0.336485 - 0.282345i) q^{52} +8.30175 q^{53} +(4.35787 - 2.83001i) q^{54} -3.83495 q^{55} +(-0.766044 + 0.642788i) q^{56} +(-5.99165 - 11.4286i) q^{57} +(-0.771398 + 4.37482i) q^{58} +(0.398471 - 0.145031i) q^{59} +(0.225737 + 1.67695i) q^{60} +(0.275687 + 1.56350i) q^{61} +(2.55954 + 4.43326i) q^{62} +(-0.278842 - 2.98701i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.403234 - 0.146765i) q^{65} +(6.47859 - 2.06342i) q^{66} +(5.61378 + 4.71052i) q^{67} +(-2.69079 - 2.25784i) q^{68} +(-1.71919 + 7.86291i) q^{69} +(0.918005 + 0.334126i) q^{70} +(-5.65742 + 9.79894i) q^{71} +(-1.28364 - 2.71150i) q^{72} +(-7.18605 - 12.4466i) q^{73} +(1.42713 + 8.09363i) q^{74} +(-5.54678 + 4.28188i) q^{75} +(-7.00082 + 2.54809i) q^{76} +(0.681664 - 3.86591i) q^{77} +(0.760173 + 0.0309756i) q^{78} +(8.48959 - 7.12361i) q^{79} +0.976920 q^{80} +(8.88085 + 1.45964i) q^{81} +1.08018 q^{82} +(6.15407 - 5.16388i) q^{83} +(-1.73061 - 0.0705192i) q^{84} +(-0.595875 + 3.37938i) q^{85} +(-10.9554 + 3.98746i) q^{86} +(-6.09065 + 4.70172i) q^{87} +(-0.681664 - 3.86591i) q^{88} +(1.02537 + 1.77599i) q^{89} +(-1.66703 + 2.41047i) q^{90} +(0.219625 - 0.380402i) q^{91} +(4.36666 + 1.58933i) q^{92} +(-1.89389 + 8.66189i) q^{93} +(0.610424 + 0.512207i) q^{94} +(5.57540 + 4.67832i) q^{95} +(-1.65036 + 0.525639i) q^{96} +(-13.7316 - 4.99789i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(10.7020 + 4.91487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9	$ 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 3 q^{12} - 9 q^{13} + 12 q^{15} - 12 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} + 9 q^{22} - 12 q^{23} - 3 q^{24} + 21 q^{25} + 18 q^{26} + 3 q^{27} - 30 q^{28} - 30 q^{29} - 15 q^{30} + 18 q^{31} + 9 q^{33} + 12 q^{34} + 3 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{38} + 72 q^{39} + 3 q^{40} + 36 q^{41} - 3 q^{42} - 9 q^{43} - 3 q^{44} - 48 q^{45} - 15 q^{46} + 3 q^{48} + 3 q^{50} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} + 66 q^{55} - 51 q^{57} - 3 q^{58} - 48 q^{59} + 24 q^{60} + 57 q^{61} - 18 q^{62} - 15 q^{63} - 15 q^{64} + 24 q^{65} + 54 q^{66} + 6 q^{67} - 15 q^{68} - 48 q^{69} - 3 q^{70} - 24 q^{71} - 6 q^{72} - 36 q^{73} - 48 q^{74} - 129 q^{75} - 3 q^{76} + 9 q^{77} + 24 q^{78} - 21 q^{79} + 6 q^{80} + 27 q^{81} - 15 q^{83} + 3 q^{84} - 72 q^{85} - 9 q^{86} + 42 q^{87} - 9 q^{88} - 30 q^{89} - 30 q^{90} + 9 q^{91} + 6 q^{92} + 111 q^{93} - 45 q^{94} + 81 q^{95} - 6 q^{96} - 15 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 3 * q^12 - 9 * q^13 + 12 * q^15 - 12 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 + 9 * q^22 - 12 * q^23 - 3 * q^24 + 21 * q^25 + 18 * q^26 + 3 * q^27 - 30 * q^28 - 30 * q^29 - 15 * q^30 + 18 * q^31 + 9 * q^33 + 12 * q^34 + 3 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^38 + 72 * q^39 + 3 * q^40 + 36 * q^41 - 3 * q^42 - 9 * q^43 - 3 * q^44 - 48 * q^45 - 15 * q^46 + 3 * q^48 + 3 * q^50 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 + 66 * q^55 - 51 * q^57 - 3 * q^58 - 48 * q^59 + 24 * q^60 + 57 * q^61 - 18 * q^62 - 15 * q^63 - 15 * q^64 + 24 * q^65 + 54 * q^66 + 6 * q^67 - 15 * q^68 - 48 * q^69 - 3 * q^70 - 24 * q^71 - 6 * q^72 - 36 * q^73 - 48 * q^74 - 129 * q^75 - 3 * q^76 + 9 * q^77 + 24 * q^78 - 21 * q^79 + 6 * q^80 + 27 * q^81 - 15 * q^83 + 3 * q^84 - 72 * q^85 - 9 * q^86 + 42 * q^87 - 9 * q^88 - 30 * q^89 - 30 * q^90 + 9 * q^91 + 6 * q^92 + 111 * q^93 - 45 * q^94 + 81 * q^95 - 6 * q^96 - 15 * q^97 - 15 * q^98 + 45 * 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
$3$	1.73061	+	0.0705192i	0.999171	+	0.0407143i
$3$	1.73061	+	0.0705192i	0.999171	+	0.0407143i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.918005	+	0.334126i	−0.410544	+	0.149426i	−0.539032	−	0.842285i	$-0.681210\pi$
$5$	−0.918005	+	0.334126i	−0.410544	+	0.149426i	0.128488	+	0.991711i	$0.458988\pi$
$6$	1.37106	−	1.05840i	0.559732	−	0.432089i
$7$	−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
$9$	2.99005	+	0.244083i	0.996685	+	0.0813611i
$10$	−0.488460	+	0.846038i	−0.154465	+	0.267541i
$11$	3.68881	+	1.34262i	1.11222	+	0.404814i	0.831806	−	0.555066i	$-0.187307\pi$
$11$	3.68881	+	1.34262i	1.11222	+	0.404814i	0.280411	+	0.959880i	$0.409529\pi$
$12$	0.369966	−	1.69208i	0.106800	−	0.488461i
$13$	0.336485	+	0.282345i	0.0933242	+	0.0783083i	0.688256	−	0.725468i	$-0.258377\pi$
$13$	0.336485	+	0.282345i	0.0933242	+	0.0783083i	−0.594932	+	0.803776i	$0.702821\pi$
$14$	−0.766044	−	0.642788i	−0.204734	−	0.171792i
$15$	−1.61227	+	0.513507i	−0.416288	+	0.132587i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.75629	−	3.04198i	0.425963	−	0.737789i	−0.570547	−	0.821265i	$-0.693269\pi$
$17$	1.75629	−	3.04198i	0.425963	−	0.737789i	0.996510	+	0.0834760i	$0.0266022\pi$
$18$	2.44741	−	1.73499i	0.576860	−	0.408941i
$19$	−3.72506	−	6.45199i	−0.854587	−	1.48019i	−0.877028	−	0.480440i	$-0.840477\pi$
$19$	−3.72506	−	6.45199i	−0.854587	−	1.48019i	0.0224409	−	0.999748i	$-0.492856\pi$
$20$	0.169640	+	0.962079i	0.0379328	+	0.215127i
$21$	−0.231070	−	1.71657i	−0.0504236	−	0.374586i
$22$	3.68881	−	1.34262i	0.786457	−	0.286247i
$23$	−0.806925	+	4.57630i	−0.168256	+	0.954225i	0.777388	+	0.629021i	$0.216544\pi$
$23$	−0.806925	+	4.57630i	−0.168256	+	0.954225i	−0.945644	+	0.325204i	$0.894567\pi$
$24$	−0.804236	−	1.53402i	−0.164164	−	0.313130i
$25$	−3.09913	+	2.60048i	−0.619826	+	0.520096i
$26$	0.439250			0.0861441
$27$	5.15742	+	0.633270i	0.992546	+	0.121873i
$28$	−1.00000			−0.188982
$29$	−3.40300	+	2.85546i	−0.631922	+	0.530246i	−0.901526	−	0.432726i	$-0.857552\pi$
$29$	−3.40300	+	2.85546i	−0.631922	+	0.530246i	0.269604	+	0.962971i	$0.413107\pi$
$30$	−0.904998	+	1.42972i	−0.165229	+	0.261030i
$31$	−0.888920	+	5.04131i	−0.159655	+	0.905447i	0.794751	+	0.606935i	$0.207601\pi$
$31$	−0.888920	+	5.04131i	−0.159655	+	0.905447i	−0.954406	+	0.298512i	$0.903510\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	6.28923	+	2.58368i	1.09481	+	0.449762i
$34$	−0.609953	−	3.45921i	−0.104606	−	0.593250i
$35$	0.488460	+	0.846038i	0.0825648	+	0.143006i
$36$	0.759593	−	2.90224i	0.126599	−	0.483707i
$37$	−4.10925	+	7.11742i	−0.675556	+	1.17010i	0.300750	+	0.953703i	$0.402763\pi$
$37$	−4.10925	+	7.11742i	−0.675556	+	1.17010i	−0.976306	+	0.216394i	$0.930570\pi$
$38$	−7.00082	−	2.54809i	−1.13568	−	0.413355i
$39$	0.562416	+	0.512358i	0.0900586	+	0.0820430i
$40$	0.748364	+	0.627952i	0.118327	+	0.0992880i
$41$	0.827470	+	0.694329i	0.129229	+	0.108436i	0.705111	−	0.709096i	$-0.250897\pi$
$41$	0.827470	+	0.694329i	0.129229	+	0.108436i	−0.575882	+	0.817533i	$0.695341\pi$
$42$	−1.28040	−	1.16644i	−0.197570	−	0.179985i
$43$	−10.9554	−	3.98746i	−1.67069	−	0.608081i	−0.678702	−	0.734414i	$-0.737457\pi$
$43$	−10.9554	−	3.98746i	−1.67069	−	0.608081i	−0.991988	+	0.126333i	$0.959679\pi$
$44$	1.96277	−	3.39962i	0.295899	−	0.512513i
$45$	−2.82644	+	0.774986i	−0.421341	+	0.115528i
$46$	2.32345	+	4.02433i	0.342574	+	0.593355i
$47$	0.138372	+	0.784746i	0.0201836	+	0.114467i	0.993235	−	0.116121i	$-0.0370461\pi$
$47$	0.138372	+	0.784746i	0.0201836	+	0.114467i	−0.973051	+	0.230588i	$0.925935\pi$
$48$	−1.60213	−	0.658171i	−0.231247	−	0.0949989i
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	−0.702516	+	3.98416i	−0.0993507	+	0.563446i
$51$	3.25398	−	5.14065i	0.455648	−	0.719834i
$52$	0.336485	−	0.282345i	0.0466621	−	0.0391542i
$53$	8.30175			1.14033			0.570167	−	0.821529i	$-0.306879\pi$
$53$	8.30175			1.14033			0.570167	+	0.821529i	$0.306879\pi$
$54$	4.35787	−	2.83001i	0.593031	−	0.385116i
$55$	−3.83495			−0.517104
$56$	−0.766044	+	0.642788i	−0.102367	+	0.0858961i
$57$	−5.99165	−	11.4286i	−0.793613	−	1.51375i
$58$	−0.771398	+	4.37482i	−0.101290	+	0.574442i
$59$	0.398471	−	0.145031i	0.0518765	−	0.0188815i	−0.315952	−	0.948775i	$-0.602324\pi$
$59$	0.398471	−	0.145031i	0.0518765	−	0.0188815i	0.367828	+	0.929894i	$0.380101\pi$
$60$	0.225737	+	1.67695i	0.0291425	+	0.216493i
$61$	0.275687	+	1.56350i	0.0352981	+	0.200186i	0.997357	−	0.0726561i	$-0.0231476\pi$
$61$	0.275687	+	1.56350i	0.0352981	+	0.200186i	−0.962059	+	0.272842i	$0.912036\pi$
$62$	2.55954	+	4.43326i	0.325062	+	0.563024i
$63$	−0.278842	−	2.98701i	−0.0351308	−	0.376328i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.403234	−	0.146765i	−0.0500150	−	0.0182040i
$66$	6.47859	−	2.06342i	0.797459	−	0.253989i
$67$	5.61378	+	4.71052i	0.685833	+	0.575482i	0.917704	−	0.397264i	$-0.130040\pi$
$67$	5.61378	+	4.71052i	0.685833	+	0.575482i	−0.231871	+	0.972746i	$0.574485\pi$
$68$	−2.69079	−	2.25784i	−0.326306	−	0.273803i
$69$	−1.71919	+	7.86291i	−0.206967	+	0.946583i
$70$	0.918005	+	0.334126i	0.109723	+	0.0399357i
$71$	−5.65742	+	9.79894i	−0.671412	+	1.16292i	0.306091	+	0.952002i	$0.400979\pi$
$71$	−5.65742	+	9.79894i	−0.671412	+	1.16292i	−0.977504	+	0.210918i	$0.932355\pi$
$72$	−1.28364	−	2.71150i	−0.151279	−	0.319554i
$73$	−7.18605	−	12.4466i	−0.841064	−	1.45676i	−0.888996	−	0.457914i	$-0.848597\pi$
$73$	−7.18605	−	12.4466i	−0.841064	−	1.45676i	0.0479328	−	0.998851i	$-0.484737\pi$
$74$	1.42713	+	8.09363i	0.165900	+	0.940866i
$75$	−5.54678	+	4.28188i	−0.640487	+	0.494429i
$76$	−7.00082	+	2.54809i	−0.803049	+	0.292286i
$77$	0.681664	−	3.86591i	0.0776829	−	0.440561i
$78$	0.760173	+	0.0309756i	0.0860726	+	0.00350730i
$79$	8.48959	−	7.12361i	0.955153	−	0.801469i	−0.0250044	−	0.999687i	$-0.507960\pi$
$79$	8.48959	−	7.12361i	0.955153	−	0.801469i	0.980158	+	0.198218i	$0.0635155\pi$
$80$	0.976920			0.109223
$81$	8.88085	+	1.45964i	0.986761	+	0.162183i
$82$	1.08018			0.119286
$83$	6.15407	−	5.16388i	0.675497	−	0.566810i	−0.239190	−	0.970973i	$-0.576882\pi$
$83$	6.15407	−	5.16388i	0.675497	−	0.566810i	0.914687	+	0.404163i	$0.132437\pi$
$84$	−1.73061	−	0.0705192i	−0.188826	−	0.00769428i
$85$	−0.595875	+	3.37938i	−0.0646317	+	0.366545i
$86$	−10.9554	+	3.98746i	−1.18136	+	0.429978i
$87$	−6.09065	+	4.70172i	−0.652987	+	0.504078i
$88$	−0.681664	−	3.86591i	−0.0726657	−	0.412107i
$89$	1.02537	+	1.77599i	0.108689	+	0.188254i	0.915239	−	0.402911i	$-0.132002\pi$
$89$	1.02537	+	1.77599i	0.108689	+	0.188254i	−0.806551	+	0.591165i	$0.798668\pi$
$90$	−1.66703	+	2.41047i	−0.175720	+	0.254086i
$91$	0.219625	−	0.380402i	0.0230230	−	0.0398770i
$92$	4.36666	+	1.58933i	0.455255	+	0.165699i
$93$	−1.89389	+	8.66189i	−0.196387	+	0.898196i
$94$	0.610424	+	0.512207i	0.0629605	+	0.0528301i
$95$	5.57540	+	4.67832i	0.572024	+	0.479985i
$96$	−1.65036	+	0.525639i	−0.168440	+	0.0536478i
$97$	−13.7316	−	4.99789i	−1.39423	−	0.507459i	−0.467772	−	0.883849i	$-0.654943\pi$
$97$	−13.7316	−	4.99789i	−1.39423	−	0.507459i	−0.926461	+	0.376390i	$0.877165\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	10.7020	+	4.91487i	1.07559	+	0.493963i
$100$	2.02281	+	3.50362i	0.202281	+	0.350362i
$101$	−0.537387	−	3.04767i	−0.0534720	−	0.303255i	0.946329	−	0.323205i	$-0.104760\pi$
$101$	−0.537387	−	3.04767i	−0.0534720	−	0.303255i	−0.999801	+	0.0199502i	$0.993649\pi$
$102$	−0.811652	−	6.02958i	−0.0803655	−	0.597017i
$103$	8.15570	−	2.96843i	0.803605	−	0.292488i	0.0926258	−	0.995701i	$-0.470474\pi$
$103$	8.15570	−	2.96843i	0.803605	−	0.292488i	0.710980	+	0.703213i	$0.248252\pi$
$104$	0.0762750	−	0.432577i	0.00747938	−	0.0424177i
$105$	0.785674	+	1.49861i	0.0766740	+	0.146249i
$106$	6.35951	−	5.33626i	0.617690	−	0.518304i
$107$	8.20871			0.793566			0.396783	−	0.917913i	$-0.370127\pi$
$107$	8.20871			0.793566			0.396783	+	0.917913i	$0.370127\pi$
$108$	1.51923	−	4.96910i	0.146188	−	0.478152i
$109$	−10.0224			−0.959968			−0.479984	−	0.877277i	$-0.659358\pi$
$109$	−10.0224			−0.959968			−0.479984	+	0.877277i	$0.659358\pi$
$110$	−2.93774	+	2.46506i	−0.280103	+	0.235034i
$111$	−7.61344	+	12.0277i	−0.722635	+	1.14162i
$112$	−0.173648	+	0.984808i	−0.0164082	+	0.0930556i
$113$	−9.77163	+	3.55658i	−0.919237	+	0.334575i	−0.757935	−	0.652330i	$-0.773792\pi$
$113$	−9.77163	+	3.55658i	−0.919237	+	0.334575i	−0.161302	+	0.986905i	$0.551569\pi$
$114$	−11.9360	−	4.90345i	−1.11791	−	0.459251i
$115$	−0.788302	−	4.47068i	−0.0735095	−	0.416893i
$116$	2.22115	+	3.84715i	0.206229	+	0.357199i
$117$	0.937193	+	0.926356i	0.0866436	+	0.0856417i
$118$	0.212022	−	0.367233i	0.0195182	−	0.0338065i
$119$	−3.30074	−	1.20137i	−0.302579	−	0.110130i
$120$	1.25085	+	1.13952i	0.114186	+	0.104023i
$121$	3.37820	+	2.83465i	0.307109	+	0.257695i
$122$	1.21619	+	1.02050i	0.110108	+	0.0923919i
$123$	1.38307	+	1.25997i	0.124707	+	0.113608i
$124$	4.81037	+	1.75083i	0.431984	+	0.157229i
$125$	4.41843	−	7.65294i	0.395196	−	0.684500i
$126$	−2.13362	−	2.10895i	−0.190078	−	0.187880i
$127$	−2.00712	−	3.47643i	−0.178103	−	0.308483i	0.763128	−	0.646248i	$-0.223663\pi$
$127$	−2.00712	−	3.47643i	−0.178103	−	0.308483i	−0.941231	+	0.337764i	$0.890329\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−18.6785	−	7.67332i	−1.64455	−	0.675598i
$130$	−0.403234	+	0.146765i	−0.0353659	+	0.0128722i
$131$	−2.68188	+	15.2097i	−0.234317	+	1.32888i	0.609730	+	0.792609i	$0.291278\pi$
$131$	−2.68188	+	15.2097i	−0.234317	+	1.32888i	−0.844047	+	0.536269i	$0.819833\pi$
$132$	3.63654	−	5.74503i	0.316521	−	0.500040i
$133$	−5.70712	+	4.78884i	−0.494870	+	0.415245i
$134$	7.32827			0.633066
$135$	−4.94613	+	1.14188i	−0.425695	+	0.0982778i
$136$	−3.51258			−0.301201
$137$	0.0237297	−	0.0199115i	0.00202736	−	0.00170116i	−0.641773	−	0.766894i	$-0.721801\pi$
$137$	0.0237297	−	0.0199115i	0.00202736	−	0.00170116i	0.643801	+	0.765193i	$0.277357\pi$
$138$	3.73720	+	7.12842i	0.318132	+	0.606811i
$139$	0.926206	−	5.25277i	0.0785597	−	0.445534i	−0.920002	−	0.391914i	$-0.871813\pi$
$139$	0.926206	−	5.25277i	0.0785597	−	0.445534i	0.998561	−	0.0536200i	$-0.0170759\pi$
$140$	0.918005	−	0.334126i	0.0775856	−	0.0282388i
$141$	0.184129	+	1.36785i	0.0155064	+	0.115194i
$142$	1.96480	+	11.1429i	0.164883	+	0.935095i
$143$	0.862149	+	1.49329i	0.0720965	+	0.124875i
$144$	−2.72625	−	1.25202i	−0.227188	−	0.104335i
$145$	2.16989	−	3.75836i	0.180200	−	0.312115i
$146$	−13.5054	−	4.91555i	−1.11771	−	0.406814i
$147$	−1.65036	+	0.525639i	−0.136120	+	0.0433539i
$148$	6.29573	+	5.28274i	0.517506	+	0.434239i
$149$	11.9762	+	10.0492i	0.981127	+	0.823263i	0.984259	−	0.176732i	$-0.0565526\pi$
$149$	11.9762	+	10.0492i	0.981127	+	0.823263i	−0.00313222	+	0.999995i	$0.500997\pi$
$150$	−1.49674	+	6.84551i	−0.122209	+	0.558934i
$151$	11.8729	+	4.32137i	0.966201	+	0.351668i	0.776460	−	0.630166i	$-0.217013\pi$
$151$	11.8729	+	4.32137i	0.966201	+	0.351668i	0.189740	+	0.981834i	$0.439235\pi$
$152$	−3.72506	+	6.45199i	−0.302142	+	0.523325i
$153$	5.99389	−	8.66701i	0.484578	−	0.700686i
$154$	−1.96277	−	3.39962i	−0.158165	−	0.273950i
$155$	−0.868404	−	4.92496i	−0.0697519	−	0.395582i
$156$	0.602237	−	0.464901i	0.0482175	−	0.0372219i
$157$	14.9404	−	5.43786i	1.19237	−	0.433989i	0.331817	−	0.943344i	$-0.392338\pi$
$157$	14.9404	−	5.43786i	1.19237	−	0.433989i	0.860556	+	0.509355i	$0.170116\pi$
$158$	1.92443	−	10.9140i	0.153100	−	0.868272i
$159$	14.3671	+	0.585433i	1.13939	+	0.0464279i
$160$	0.748364	−	0.627952i	0.0591634	−	0.0496440i
$161$	4.64690			0.366227
$162$	7.74136	−	4.59035i	0.608219	−	0.360652i
$163$	10.6112			0.831135			0.415567	−	0.909562i	$-0.363583\pi$
$163$	10.6112			0.831135			0.415567	+	0.909562i	$0.363583\pi$
$164$	0.827470	−	0.694329i	0.0646145	−	0.0542180i
$165$	−6.63682	−	0.270438i	−0.516675	−	0.0210535i
$166$	1.39502	−	7.91152i	0.108274	−	0.614053i
$167$	−11.9952	+	4.36590i	−0.928217	+	0.337843i	−0.761502	−	0.648162i	$-0.775538\pi$
$167$	−11.9952	+	4.36590i	−0.928217	+	0.337843i	−0.166714	+	0.986005i	$0.553316\pi$
$168$	−1.37106	+	1.05840i	−0.105779	+	0.0816571i
$169$	−2.22392	−	12.6125i	−0.171071	−	0.970192i
$170$	1.71575	+	2.97177i	0.131592	+	0.227925i
$171$	−9.56330	−	20.2010i	−0.731324	−	1.54481i
$172$	−5.82927	+	10.0966i	−0.444478	+	0.769858i
$173$	−14.9112	−	5.42722i	−1.13367	−	0.412624i	−0.294049	−	0.955790i	$-0.595003\pi$
$173$	−14.9112	−	5.42722i	−1.13367	−	0.412624i	−0.839625	+	0.543166i	$0.817225\pi$
$174$	−1.64350	+	7.51673i	−0.124594	+	0.569841i
$175$	3.09913	+	2.60048i	0.234272	+	0.196578i
$176$	−3.00714	−	2.52329i	−0.226672	−	0.190200i
$177$	0.699827	−	0.222894i	0.0526022	−	0.0167537i
$178$	1.92706	+	0.701392i	0.144439	+	0.0525715i
$179$	13.0385	−	22.5833i	0.974543	−	1.68796i	0.293108	−	0.956079i	$-0.405311\pi$
$179$	13.0385	−	22.5833i	0.974543	−	1.68796i	0.681435	−	0.731878i	$-0.261356\pi$
$180$	0.272407	+	2.91807i	0.0203040	+	0.217500i
$181$	−8.08074	−	13.9962i	−0.600637	−	1.04033i	−0.992725	−	0.120405i	$-0.961581\pi$
$181$	−8.08074	−	13.9962i	−0.600637	−	1.04033i	0.392088	−	0.919928i	$-0.371753\pi$
$182$	−0.0762750	−	0.432577i	−0.00565388	−	0.0320647i
$183$	0.366852	+	2.72526i	0.0271184	+	0.201457i
$184$	4.36666	−	1.58933i	0.321914	−	0.117167i
$185$	1.39419	−	7.90683i	0.102503	−	0.581322i
$186$	4.11695	+	7.85276i	0.301870	+	0.575792i
$187$	10.5628	−	8.86326i	0.772430	−	0.648146i
$188$	0.796852			0.0581164
$189$	−0.271927	−	5.18903i	−0.0197798	−	0.377447i
$190$	7.27817			0.528014
$191$	15.3257	−	12.8598i	1.10893	−	0.930503i	0.110937	−	0.993827i	$-0.464615\pi$
$191$	15.3257	−	12.8598i	1.10893	−	0.930503i	0.997993	+	0.0633249i	$0.0201704\pi$
$192$	−0.926379	+	1.46350i	−0.0668556	+	0.105619i
$193$	−2.44378	+	13.8593i	−0.175907	+	0.997617i	0.761185	+	0.648535i	$0.224618\pi$
$193$	−2.44378	+	13.8593i	−0.175907	+	0.997617i	−0.937092	+	0.349083i	$0.886493\pi$
$194$	−13.7316	+	4.99789i	−0.985872	+	0.358828i
$195$	−0.687493	−	0.282430i	−0.0492324	−	0.0202252i
$196$	0.173648	+	0.984808i	0.0124034	+	0.0703434i
$197$	−9.99059	−	17.3042i	−0.711800	−	1.23287i	−0.964181	−	0.265246i	$-0.914547\pi$
$197$	−9.99059	−	17.3042i	−0.711800	−	1.23287i	0.252381	−	0.967628i	$-0.418787\pi$
$198$	11.3574	−	3.11412i	0.807139	−	0.221311i
$199$	−5.83872	+	10.1130i	−0.413896	+	0.716889i	−0.995312	−	0.0967177i	$-0.969166\pi$
$199$	−5.83872	+	10.1130i	−0.413896	+	0.716889i	0.581416	+	0.813606i	$0.302499\pi$
$200$	3.80165	+	1.38369i	0.268817	+	0.0978414i
$201$	9.38311	+	8.54798i	0.661834	+	0.602928i
$202$	−2.37067	−	1.98923i	−0.166800	−	0.139962i
$203$	3.40300	+	2.85546i	0.238844	+	0.200414i
$204$	−4.49750	−	4.09721i	−0.314888	−	0.286862i
$205$	−0.991615	−	0.360918i	−0.0692574	−	0.0252076i
$206$	4.33956	−	7.51634i	0.302351	−	0.523688i
$207$	−3.52975	+	13.4864i	−0.245335	+	0.937372i
$208$	−0.219625	−	0.380402i	−0.0152283	−	0.0263761i
$209$	−5.07848	−	28.8015i	−0.351286	−	1.99224i
$210$	1.56515	+	0.642981i	0.108006	+	0.0443699i
$211$	11.0688	−	4.02872i	0.762009	−	0.277349i	0.0683591	−	0.997661i	$-0.478224\pi$
$211$	11.0688	−	4.02872i	0.762009	−	0.277349i	0.693650	+	0.720312i	$0.256001\pi$
$212$	1.44158	−	8.17563i	0.0990084	−	0.561504i
$213$	−10.4818	+	16.5592i	−0.718203	+	1.13462i
$214$	6.28823	−	5.27645i	0.429855	−	0.360691i
$215$	11.3895			0.776755
$216$	−2.03028	−	4.78309i	−0.138143	−	0.325448i
$217$	5.11908			0.347506
$218$	−7.67757	+	6.44225i	−0.519991	+	0.436324i
$219$	−11.5586	−	22.0470i	−0.781055	−	1.48980i
$220$	−0.665932	+	3.77669i	−0.0448971	+	0.254624i
$221$	1.44985	−	0.527703i	0.0975276	−	0.0354971i
$222$	1.89905	+	14.1076i	0.127456	+	0.946840i
$223$	0.270495	+	1.53405i	0.0181137	+	0.102728i	0.992524	−	0.122048i	$-0.0389462\pi$
$223$	0.270495	+	1.53405i	0.0181137	+	0.102728i	−0.974411	+	0.224776i	$0.927835\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	−9.90130	+	7.01913i	−0.660087	+	0.467942i
$226$	−5.19937	+	9.00558i	−0.345857	+	0.599042i
$227$	15.8102	+	5.75445i	1.04936	+	0.381936i	0.808422	−	0.588604i	$-0.200322\pi$
$227$	15.8102	+	5.75445i	1.04936	+	0.381936i	0.240940	+	0.970540i	$0.422544\pi$
$228$	−12.2954	+	3.91607i	−0.814283	+	0.259348i
$229$	−4.76314	−	3.99675i	−0.314757	−	0.264113i	0.471698	−	0.881760i	$-0.343641\pi$
$229$	−4.76314	−	3.99675i	−0.314757	−	0.264113i	−0.786455	+	0.617648i	$0.788086\pi$
$230$	−3.47757	−	2.91803i	−0.229304	−	0.192409i
$231$	1.45232	−	6.64233i	0.0955556	−	0.437033i
$232$	4.17440	+	1.51936i	0.274063	+	0.0997508i
$233$	−4.21509	+	7.30075i	−0.276140	+	0.478288i	−0.970422	−	0.241415i	$-0.922389\pi$
$233$	−4.21509	+	7.30075i	−0.276140	+	0.478288i	0.694282	+	0.719703i	$0.255722\pi$
$234$	1.31338	+	0.107214i	0.0858585	+	0.00700877i
$235$	−0.389231	−	0.674167i	−0.0253906	−	0.0439778i
$236$	−0.0736344	−	0.417601i	−0.00479319	−	0.0271835i
$237$	15.1946	−	11.7295i	0.986993	−	0.761916i
$238$	−3.30074	+	1.20137i	−0.213955	+	0.0778734i
$239$	2.07919	−	11.7917i	0.134492	−	0.762742i	−0.840720	−	0.541470i	$-0.817868\pi$
$239$	2.07919	−	11.7917i	0.134492	−	0.762742i	0.975212	−	0.221272i	$-0.0710208\pi$
$240$	1.69067	+	0.0688917i	0.109132	+	0.00444694i
$241$	−6.34822	+	5.32679i	−0.408925	+	0.343129i	−0.823931	−	0.566690i	$-0.808224\pi$
$241$	−6.34822	+	5.32679i	−0.408925	+	0.343129i	0.415006	+	0.909819i	$0.363779\pi$
$242$	4.40993			0.283481
$243$	15.2664	+	3.15235i	0.979339	+	0.202223i
$244$	1.58762			0.101637
$245$	0.748364	−	0.627952i	0.0478112	−	0.0401184i
$246$	1.86938	+	0.0761738i	0.119188	+	0.00485666i
$247$	0.568258	−	3.22275i	0.0361574	−	0.205059i
$248$	4.81037	−	1.75083i	0.305459	−	0.111178i
$249$	11.0145	−	8.50271i	0.698014	−	0.538837i
$250$	−1.53450	−	8.70260i	−0.0970506	−	0.550401i
$251$	10.2624	+	17.7749i	0.647755	+	1.12194i	0.983658	+	0.180048i	$0.0576252\pi$
$251$	10.2624	+	17.7749i	0.647755	+	1.12194i	−0.335903	+	0.941897i	$0.609042\pi$
$252$	−2.99005	−	0.244083i	−0.188356	−	0.0153758i
$253$	−9.12081	+	15.7977i	−0.573421	+	0.993194i
$254$	−3.77215	−	1.37295i	−0.236686	−	0.0861465i
$255$	−1.26954	+	5.80638i	−0.0795018	+	0.363609i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−7.20416	−	6.04501i	−0.449383	−	0.377077i	0.389824	−	0.920889i	$-0.372536\pi$
$257$	−7.20416	−	6.04501i	−0.449383	−	0.377077i	−0.839207	+	0.543812i	$0.816980\pi$
$258$	−19.2408	+	6.12818i	−1.19788	+	0.381524i
$259$	7.72286	+	2.81089i	0.479875	+	0.174660i
$260$	−0.214556	+	0.371622i	−0.0133062	+	0.0230470i
$261$	−10.8721	+	7.70736i	−0.672968	+	0.477074i
$262$	7.72217	+	13.3752i	0.477077	+	0.826322i
$263$	−2.47013	−	14.0088i	−0.152315	−	0.863820i	−0.961200	−	0.275853i	$-0.911040\pi$
$263$	−2.47013	−	14.0088i	−0.152315	−	0.863820i	0.808885	−	0.587967i	$-0.200071\pi$
$264$	−0.907077	−	6.73847i	−0.0558267	−	0.414724i
$265$	−7.62105	+	2.77383i	−0.468157	+	0.170395i
$266$	−1.29370	+	7.33693i	−0.0793218	+	0.449856i
$267$	1.64927	+	3.14586i	0.100934	+	0.192523i
$268$	5.61378	−	4.71052i	0.342916	−	0.287741i
$269$	−24.9316			−1.52011			−0.760054	−	0.649859i	$-0.774828\pi$
$269$	−24.9316			−1.52011			−0.760054	+	0.649859i	$0.774828\pi$
$270$	−3.05496	+	4.05404i	−0.185919	+	0.246721i
$271$	19.8520			1.20593			0.602963	−	0.797769i	$-0.293987\pi$
$271$	19.8520			1.20593			0.602963	+	0.797769i	$0.293987\pi$
$272$	−2.69079	+	2.25784i	−0.163153	+	0.136902i
$273$	0.406912	−	0.642841i	0.0246274	−	0.0389065i
$274$	0.00537908	−	0.0305063i	0.000324962	−	0.00184295i
$275$	−14.9235	+	5.43173i	−0.899924	+	0.327545i
$276$	7.44492	+	3.05846i	0.448132	+	0.184097i
$277$	0.382310	+	2.16819i	0.0229708	+	0.130274i	0.994137	−	0.108131i	$-0.0344866\pi$
$277$	0.382310	+	2.16819i	0.0229708	+	0.130274i	−0.971166	+	0.238405i	$0.923375\pi$
$278$	−2.66690	−	4.61921i	−0.159950	−	0.277042i
$279$	−3.88842	+	14.8568i	−0.232794	+	0.889455i
$280$	0.488460	−	0.846038i	0.0291911	−	0.0505604i
$281$	−10.4277	−	3.79535i	−0.622062	−	0.226412i	0.0117109	−	0.999931i	$-0.496272\pi$
$281$	−10.4277	−	3.79535i	−0.622062	−	0.226412i	−0.633772	+	0.773520i	$0.718494\pi$
$282$	1.02029	+	0.929479i	0.0607573	+	0.0553497i
$283$	9.94689	+	8.34643i	0.591281	+	0.496144i	0.888630	−	0.458625i	$-0.151658\pi$
$283$	9.94689	+	8.34643i	0.591281	+	0.496144i	−0.297349	+	0.954769i	$0.596102\pi$
$284$	8.66767	+	7.27304i	0.514332	+	0.431576i
$285$	9.31896	+	8.48954i	0.552007	+	0.502877i
$286$	1.62031	+	0.589745i	0.0958110	+	0.0348723i
$287$	0.540092	−	0.935468i	0.0318806	−	0.0552189i
$288$	−2.89321	+	0.793295i	−0.170484	+	0.0467454i
$289$	2.33090	+	4.03724i	0.137112	+	0.237485i
$290$	−0.753595	−	4.27385i	−0.0442526	−	0.250969i
$291$	−23.4117	−	9.61777i	−1.37242	−	0.563804i
$292$	−13.5054	+	4.91555i	−0.790341	+	0.287661i
$293$	1.44373	−	8.18782i	0.0843438	−	0.478337i	−0.913152	−	0.407618i	$-0.866359\pi$
$293$	1.44373	−	8.18782i	0.0843438	−	0.478337i	0.997496	−	0.0707192i	$-0.0225294\pi$
$294$	−0.926379	+	1.46350i	−0.0540275	+	0.0853529i
$295$	−0.317339	+	0.266279i	−0.0184762	+	0.0155034i
$296$	8.21849			0.477690
$297$	18.1745	+	9.26045i	1.05459	+	0.537346i
$298$	15.6338			0.905641
$299$	−1.56361	+	1.31203i	−0.0904261	+	0.0758765i
$300$	3.25364	+	6.20606i	0.187849	+	0.358307i
$301$	−2.02448	+	11.4814i	−0.116689	+	0.661778i
$302$	11.8729	−	4.32137i	0.683207	−	0.248667i
$303$	−0.715090	−	5.31224i	−0.0410809	−	0.305180i
$304$	1.29370	+	7.33693i	0.0741987	+	0.420802i
$305$	−0.775489	−	1.34319i	−0.0444044	−	0.0769106i
$306$	−0.979455	−	10.4921i	−0.0559917	−	0.599794i
$307$	2.95070	−	5.11077i	0.168406	−	0.291687i	−0.769454	−	0.638702i	$-0.779472\pi$
$307$	2.95070	−	5.11077i	0.168406	−	0.291687i	0.937859	+	0.347015i	$0.112805\pi$
$308$	−3.68881	−	1.34262i	−0.210189	−	0.0765027i
$309$	14.3237	−	4.56208i	0.814848	−	0.259528i
$310$	−3.83094	−	3.21454i	−0.217583	−	0.182574i
$311$	18.2228	+	15.2908i	1.03332	+	0.867060i	0.991243	−	0.132054i	$-0.0421572\pi$
$311$	18.2228	+	15.2908i	1.03332	+	0.867060i	0.0420796	+	0.999114i	$0.486602\pi$
$312$	0.162508	−	0.743245i	0.00920018	−	0.0420780i
$313$	23.5361	+	8.56646i	1.33034	+	0.484205i	0.906758	−	0.421652i	$-0.138550\pi$
$313$	23.5361	+	8.56646i	1.33034	+	0.484205i	0.423584	+	0.905857i	$0.360772\pi$
$314$	7.94962	−	13.7691i	0.448623	−	0.777038i
$315$	1.25402	+	2.64892i	0.0706559	+	0.149250i
$316$	−5.54119	−	9.59762i	−0.311716	−	0.539908i
$317$	−4.52271	−	25.6496i	−0.254021	−	1.44062i	−0.798574	−	0.601896i	$-0.794412\pi$
$317$	−4.52271	−	25.6496i	−0.254021	−	1.44062i	0.544554	−	0.838726i	$-0.316699\pi$
$318$	11.3822	−	8.78655i	0.638280	−	0.492725i
$319$	−16.3868	+	5.96431i	−0.917486	+	0.333938i
$320$	0.169640	−	0.962079i	0.00948319	−	0.0537818i
$321$	14.2061	+	0.578872i	0.792908	+	0.0323095i
$322$	3.55973	−	2.98697i	0.198376	−	0.166457i
$323$	−26.1691			−1.45609
$324$	2.97961	−	8.49246i	0.165534	−	0.471803i
$325$	−1.77704			−0.0985726
$326$	8.12867	−	6.82076i	0.450205	−	0.377767i
$327$	−17.3448	−	0.706769i	−0.959172	−	0.0390844i
$328$	0.187572	−	1.06377i	0.0103569	−	0.0587371i
$329$	0.748796	−	0.272540i	0.0412825	−	0.0150256i
$330$	−5.25793	+	4.05890i	−0.289440	+	0.223435i
$331$	3.17760	+	18.0211i	0.174657	+	0.990527i	0.938539	+	0.345172i	$0.112179\pi$
$331$	3.17760	+	18.0211i	0.174657	+	0.990527i	−0.763883	+	0.645355i	$0.776709\pi$
$332$	−4.01679	−	6.95728i	−0.220450	−	0.381830i
$333$	−14.0241	+	20.2785i	−0.768516	+	1.11125i
$334$	−6.38251	+	11.0548i	−0.349236	+	0.604894i
$335$	−6.72739	−	2.44857i	−0.367557	−	0.133780i
$336$	−0.369966	+	1.69208i	−0.0201833	+	0.0923104i
$337$	16.2702	+	13.6523i	0.886296	+	0.743691i	0.967464	−	0.253010i	$-0.0814205\pi$
$337$	16.2702	+	13.6523i	0.886296	+	0.743691i	−0.0811677	+	0.996700i	$0.525865\pi$
$338$	−9.81078	−	8.23222i	−0.533636	−	0.447774i
$339$	−17.1617	+	5.46598i	−0.932097	+	0.296872i
$340$	3.22456	+	1.17364i	0.174876	+	0.0636498i
$341$	−10.0476	+	17.4030i	−0.544108	+	0.942423i
$342$	−20.3109	−	9.32771i	−1.09829	−	0.504385i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	2.02448	+	11.4814i	0.109153	+	0.619037i
$345$	−1.04898	−	7.79262i	−0.0564751	−	0.419540i
$346$	−14.9112	+	5.42722i	−0.801629	+	0.291769i
$347$	−2.77456	+	15.7353i	−0.148946	+	0.844716i	0.815167	+	0.579226i	$0.196645\pi$
$347$	−2.77456	+	15.7353i	−0.148946	+	0.844716i	−0.964113	+	0.265490i	$0.914466\pi$
$348$	3.57266	+	6.81457i	0.191515	+	0.365299i
$349$	−0.687968	+	0.577273i	−0.0368261	+	0.0309007i	−0.661015	−	0.750373i	$-0.729874\pi$
$349$	−0.687968	+	0.577273i	−0.0368261	+	0.0309007i	0.624189	+	0.781273i	$0.285430\pi$
$350$	4.04563			0.216248
$351$	1.55659	+	1.66926i	0.0830849	+	0.0890983i
$352$	−3.92555			−0.209232
$353$	4.83241	−	4.05487i	0.257203	−	0.215819i	−0.505063	−	0.863082i	$-0.668531\pi$
$353$	4.83241	−	4.05487i	0.257203	−	0.215819i	0.762267	+	0.647263i	$0.224086\pi$
$354$	0.392825	−	0.620586i	0.0208784	−	0.0329838i
$355$	1.91945	−	10.8858i	0.101874	−	0.577757i
$356$	1.92706	−	0.701392i	0.102134	−	0.0371737i
$357$	−5.62759	−	2.31188i	−0.297844	−	0.122358i
$358$	−4.52822	−	25.6808i	−0.239324	−	1.35727i
$359$	2.18977	+	3.79279i	0.115571	+	0.200176i	0.918008	−	0.396562i	$-0.129797\pi$
$359$	2.18977	+	3.79279i	0.115571	+	0.200176i	−0.802437	+	0.596737i	$0.796463\pi$
$360$	2.08438	+	2.06027i	0.109856	+	0.108586i
$361$	−18.2521	+	31.6136i	−0.960637	+	1.66387i
$362$	−15.1868	−	5.52755i	−0.798202	−	0.290522i
$363$	5.64647	+	5.14391i	0.296363	+	0.269985i
$364$	−0.336485	−	0.282345i	−0.0176366	−	0.0147989i
$365$	10.7556	+	9.02499i	0.562972	+	0.472390i
$366$	2.03279	+	1.85186i	0.106255	+	0.0967983i
$367$	−28.1200	−	10.2348i	−1.46785	−	0.534254i	−0.520336	−	0.853962i	$-0.674193\pi$
$367$	−28.1200	−	10.2348i	−1.46785	−	0.534254i	−0.947516	+	0.319707i	$0.896415\pi$
$368$	2.32345	−	4.02433i	0.121118	−	0.209783i
$369$	2.30470	+	2.27805i	0.119978	+	0.118591i
$370$	−4.01441	−	6.95315i	−0.208699	−	0.361477i
$371$	−1.44158	−	8.17563i	−0.0748433	−	0.424457i
$372$	8.20142	+	3.36924i	0.425224	+	0.174687i
$373$	12.3358	−	4.48985i	0.638721	−	0.232476i	−0.00230146	−	0.999997i	$-0.500733\pi$
$373$	12.3358	−	4.48985i	0.638721	−	0.232476i	0.641023	+	0.767522i	$0.278510\pi$
$374$	2.39440	−	13.5793i	0.123811	−	0.702169i
$375$	8.18628	−	12.9327i	0.422737	−	0.667842i
$376$	0.610424	−	0.512207i	0.0314802	−	0.0264151i
$377$	−1.95128			−0.100496
$378$	−3.54375	−	3.80024i	−0.182271	−	0.195463i
$379$	−1.87232			−0.0961745			−0.0480872	−	0.998843i	$-0.515313\pi$
$379$	−1.87232			−0.0961745			−0.0480872	+	0.998843i	$0.515313\pi$
$380$	5.57540	−	4.67832i	0.286012	−	0.239993i
$381$	−3.22839	−	6.15790i	−0.165395	−	0.315479i
$382$	3.47406	−	19.7024i	0.177748	−	1.00806i
$383$	−25.1840	+	9.16621i	−1.28684	+	0.468372i	−0.892689	−	0.450674i	$-0.851184\pi$
$383$	−25.1840	+	9.16621i	−1.28684	+	0.468372i	−0.394152	+	0.919045i	$0.628962\pi$
$384$	0.231070	+	1.71657i	0.0117918	+	0.0875983i
$385$	0.665932	+	3.77669i	0.0339390	+	0.192478i
$386$	7.03657	+	12.1877i	0.358152	+	0.620338i
$387$	−31.7841	−	14.5967i	−1.61568	−	0.741994i
$388$	−7.30643	+	12.6551i	−0.370928	+	0.642466i
$389$	29.2650	+	10.6516i	1.48379	+	0.540057i	0.951808	−	0.306696i	$-0.0992234\pi$
$389$	29.2650	+	10.6516i	1.48379	+	0.540057i	0.531987	+	0.846753i	$0.321446\pi$
$390$	−0.708192	+	0.225558i	−0.0358607	+	0.0114216i
$391$	12.5038	+	10.4920i	0.632346	+	0.530601i
$392$	0.766044	+	0.642788i	0.0386911	+	0.0324657i
$393$	−5.71388	+	26.1330i	−0.288227	+	1.31824i
$394$	−18.7762	−	6.83397i	−0.945930	−	0.344290i
$395$	−5.41330	+	9.37611i	−0.272373	+	0.471763i
$396$	6.69859	−	9.68598i	0.336617	−	0.486739i
$397$	−15.1504	−	26.2412i	−0.760374	−	1.31701i	−0.942658	−	0.333761i	$-0.891682\pi$
$397$	−15.1504	−	26.2412i	−0.760374	−	1.31701i	0.182283	−	0.983246i	$-0.441651\pi$
$398$	2.02777	+	11.5000i	0.101643	+	0.576445i
$399$	−10.2145	+	7.88518i	−0.511366	+	0.394753i
$400$	3.80165	−	1.38369i	0.190082	−	0.0691843i
$401$	0.274112	−	1.55456i	0.0136885	−	0.0776313i	−0.977198	−	0.212329i	$-0.931895\pi$
$401$	0.274112	−	1.55456i	0.0136885	−	0.0776313i	0.990887	+	0.134698i	$0.0430063\pi$
$402$	12.6824	+	0.516784i	0.632541	+	0.0257749i
$403$	−1.72250	+	1.44535i	−0.0858036	+	0.0719978i
$404$	−3.09469			−0.153967
$405$	−8.64037	+	1.62737i	−0.429343	+	0.0808644i
$406$	4.44231			0.220468
$407$	−24.7142	+	20.7377i	−1.22504	+	1.02793i
$408$	−6.07892	−	0.247704i	−0.300951	−	0.0122632i
$409$	0.108822	−	0.617159i	0.00538089	−	0.0305166i	−0.981999	−	0.188886i	$-0.939512\pi$
$409$	0.108822	−	0.617159i	0.00538089	−	0.0305166i	0.987380	+	0.158369i	$0.0506236\pi$
$410$	−0.991615	+	0.360918i	−0.0489724	+	0.0178245i
$411$	0.0424710	−	0.0327858i	0.00209494	−	0.00161721i
$412$	−1.50711	−	8.54726i	−0.0742501	−	0.421093i
$413$	−0.212022	−	0.367233i	−0.0104329	−	0.0180703i
$414$	5.96497	+	12.6001i	0.293162	+	0.619260i
$415$	−3.92408	+	6.79671i	−0.192625	+	0.333637i
$416$	−0.412760	−	0.150232i	−0.0202372	−	0.00736575i
$417$	1.97333	−	9.02521i	0.0966342	−	0.441966i
$418$	−22.4036	−	18.7988i	−1.09579	−	0.919481i
$419$	13.7383	+	11.5278i	0.671159	+	0.563169i	0.913408	−	0.407045i	$-0.133441\pi$
$419$	13.7383	+	11.5278i	0.671159	+	0.563169i	−0.242250	+	0.970214i	$0.577885\pi$
$420$	1.61227	−	0.513507i	0.0786710	−	0.0250566i
$421$	−17.8710	−	6.50452i	−0.870980	−	0.317011i	−0.132416	−	0.991194i	$-0.542274\pi$
$421$	−17.8710	−	6.50452i	−0.870980	−	0.317011i	−0.738564	+	0.674183i	$0.764496\pi$
$422$	5.88960	−	10.2011i	0.286701	−	0.496581i
$423$	0.222196	+	2.38021i	0.0108035	+	0.115730i
$424$	−4.15087	−	7.18953i	−0.201584	−	0.349154i
$425$	2.46764	+	13.9947i	0.119698	+	0.678842i
$426$	2.61452	+	19.4227i	0.126674	+	0.941033i
$427$	1.49187	−	0.542998i	0.0721969	−	0.0262775i
$428$	1.42543	−	8.08400i	0.0689006	−	0.390755i
$429$	1.38674	+	2.64510i	0.0669526	+	0.127707i
$430$	8.72484	−	7.32101i	0.420749	−	0.353050i
$431$	−32.4225			−1.56174			−0.780869	−	0.624695i	$-0.785224\pi$
$431$	−32.4225			−1.56174			−0.780869	+	0.624695i	$0.785224\pi$
$432$	−4.62980	−	2.35902i	−0.222751	−	0.113498i
$433$	34.4240			1.65431			0.827157	−	0.561971i	$-0.189957\pi$
$433$	34.4240			1.65431			0.827157	+	0.561971i	$0.189957\pi$
$434$	3.92145	−	3.29048i	0.188235	−	0.157948i
$435$	4.02028	−	6.35125i	0.192758	−	0.304519i
$436$	−1.74036	+	9.87010i	−0.0833483	+	0.472692i
$437$	32.5321	−	11.8407i	1.55622	−	0.566418i
$438$	−23.0259	−	9.45931i	−1.10022	−	0.451983i
$439$	−1.69593	−	9.61811i	−0.0809424	−	0.459047i	−0.998159	−	0.0606575i	$-0.980680\pi$
$439$	−1.69593	−	9.61811i	−0.0809424	−	0.459047i	0.917216	−	0.398390i	$-0.130431\pi$
$440$	1.91747	+	3.32116i	0.0914120	+	0.158330i
$441$	−2.89321	+	0.793295i	−0.137772	+	0.0377760i
$442$	0.771450	−	1.33619i	0.0366941	−	0.0635561i
$443$	3.74337	+	1.36248i	0.177853	+	0.0647332i	0.429412	−	0.903109i	$-0.358721\pi$
$443$	3.74337	+	1.36248i	0.177853	+	0.0647332i	−0.251559	+	0.967842i	$0.580943\pi$
$444$	10.5229	+	9.58636i	0.499397	+	0.454949i
$445$	−1.53469	−	1.28776i	−0.0727515	−	0.0610458i
$446$	1.19328	+	1.00128i	0.0565034	+	0.0474120i
$447$	20.0175	+	18.2359i	0.946795	+	0.862526i
$448$	0.939693	+	0.342020i	0.0443963	+	0.0161589i
$449$	−6.94343	+	12.0264i	−0.327681	+	0.567560i	−0.982051	−	0.188614i	$-0.939600\pi$
$449$	−6.94343	+	12.0264i	−0.327681	+	0.567560i	0.654370	+	0.756174i	$0.272934\pi$
$450$	−3.07303	+	11.7414i	−0.144864	+	0.553495i
$451$	2.12016	+	3.67222i	0.0998344	+	0.172918i
$452$	1.80572	+	10.2408i	0.0849341	+	0.481685i
$453$	20.2426	+	8.31589i	0.951081	+	0.390715i
$454$	15.8102	−	5.75445i	0.742011	−	0.270070i
$455$	−0.0745146	+	0.422593i	−0.00349330	+	0.0198115i
$456$	−6.90163	+	10.9032i	−0.323198	+	0.510590i
$457$	−20.0862	+	16.8543i	−0.939592	+	0.788411i	−0.977514	−	0.210870i	$-0.932370\pi$
$457$	−20.0862	+	16.8543i	−0.939592	+	0.788411i	0.0379224	+	0.999281i	$0.487926\pi$
$458$	−6.21784			−0.290540
$459$	10.9843	−	14.5766i	0.512704	−	0.680376i
$460$	−4.53965			−0.211662
$461$	−6.55853	+	5.50326i	−0.305461	+	0.256312i	−0.782613	−	0.622509i	$-0.786114\pi$
$461$	−6.55853	+	5.50326i	−0.305461	+	0.256312i	0.477152	+	0.878821i	$0.341669\pi$
$462$	−3.15707	−	6.02185i	−0.146880	−	0.280162i
$463$	1.66845	−	9.46225i	0.0775394	−	0.439748i	−0.921179	−	0.389139i	$-0.872773\pi$
$463$	1.66845	−	9.46225i	0.0775394	−	0.439748i	0.998719	−	0.0506090i	$-0.0161162\pi$
$464$	4.17440	−	1.51936i	0.193792	−	0.0705344i
$465$	−1.15557	−	8.58445i	−0.0535882	−	0.398094i
$466$	1.46388	+	8.30210i	0.0678132	+	0.384587i
$467$	−21.3828	−	37.0361i	−0.989477	−	1.71383i	−0.620041	−	0.784569i	$-0.712884\pi$
$467$	−21.3828	−	37.0361i	−0.989477	−	1.71383i	−0.369436	−	0.929256i	$-0.620449\pi$
$468$	1.07502	−	0.762095i	0.0496930	−	0.0352279i
$469$	3.66414	−	6.34647i	0.169194	−	0.293053i
$470$	−0.731514	−	0.266249i	−0.0337422	−	0.0122812i
$471$	26.2396	−	8.35726i	1.20905	−	0.385082i
$472$	−0.324836	−	0.272570i	−0.0149518	−	0.0125461i
$473$	−35.0589	−	29.4179i	−1.61201	−	1.35264i
$474$	4.10010	−	18.7522i	0.188324	−	0.861318i
$475$	28.3227	+	10.3086i	1.29953	+	0.472992i
$476$	−1.75629	+	3.04198i	−0.0804994	+	0.139429i
$477$	24.8227	+	2.02632i	1.13655	+	0.0927787i
$478$	−5.98680	−	10.3694i	−0.273830	−	0.474287i
$479$	3.69301	+	20.9441i	0.168738	+	0.956960i	0.945126	+	0.326705i	$0.105938\pi$
$479$	3.69301	+	20.9441i	0.168738	+	0.956960i	−0.776389	+	0.630255i	$0.782951\pi$
$480$	1.33941	−	1.03397i	0.0611356	−	0.0471940i
$481$	−3.39227	+	1.23468i	−0.154674	+	0.0562967i
$482$	−1.43903	+	8.16112i	−0.0655458	+	0.371729i
$483$	8.04199	+	0.327696i	0.365923	+	0.0149107i
$484$	3.37820	−	2.83465i	0.153555	−	0.128848i
$485$	14.2756			0.648222
$486$	13.7210	−	7.39820i	0.622398	−	0.335589i
$487$	−1.17650			−0.0533124			−0.0266562	−	0.999645i	$-0.508486\pi$
$487$	−1.17650			−0.0533124			−0.0266562	+	0.999645i	$0.508486\pi$
$488$	1.21619	−	1.02050i	0.0550542	−	0.0461960i
$489$	18.3639	+	0.748295i	0.830446	+	0.0338391i
$490$	0.169640	−	0.962079i	0.00766357	−	0.0434623i
$491$	22.9122	−	8.33934i	1.03401	−	0.376349i	0.231404	−	0.972858i	$-0.425668\pi$
$491$	22.9122	−	8.33934i	1.03401	−	0.376349i	0.802607	+	0.596508i	$0.203446\pi$
$492$	1.48099	−	1.14326i	0.0667684	−	0.0515423i
$493$	2.70960	+	15.3669i	0.122034	+	0.692090i
$494$	−1.63623	−	2.83404i	−0.0736176	−	0.127509i
$495$	−11.4667	−	0.936046i	−0.515390	−	0.0420722i
$496$	2.55954	−	4.43326i	0.114927	−	0.199059i
$497$	10.6325	+	3.86990i	0.476932	+	0.173589i
$498$	2.97215	−	13.5934i	0.133185	−	0.609136i
$499$	−16.4854	−	13.8329i	−0.737989	−	0.619246i	0.194308	−	0.980941i	$-0.437754\pi$
$499$	−16.4854	−	13.8329i	−0.737989	−	0.619246i	−0.932297	+	0.361695i	$0.882198\pi$
$500$	−6.76942	−	5.68022i	−0.302738	−	0.254027i
$501$	−21.0670	+	6.70979i	−0.941202	+	0.299771i
$502$	19.2869	+	7.01987i	0.860818	+	0.313312i
$503$	−20.9491	+	36.2850i	−0.934075	+	1.61787i	−0.157801	+	0.987471i	$0.550440\pi$
$503$	−20.9491	+	36.2850i	−0.934075	+	1.61787i	−0.776275	+	0.630395i	$0.782893\pi$
$504$	−2.44741	+	1.73499i	−0.109016	+	0.0772826i
$505$	1.51163	+	2.61822i	0.0672667	+	0.116509i
$506$	3.16762	+	17.9645i	0.140818	+	0.798619i
$507$	−2.95933	−	21.9842i	−0.131428	−	0.976352i
$508$	−3.77215	+	1.37295i	−0.167362	+	0.0609148i
$509$	−4.86503	+	27.5910i	−0.215639	+	1.22295i	0.664156	+	0.747594i	$0.268791\pi$
$509$	−4.86503	+	27.5910i	−0.215639	+	1.22295i	−0.879795	+	0.475354i	$0.842320\pi$
$510$	2.75974	+	5.26399i	0.122203	+	0.233093i
$511$	−11.0097	+	9.23821i	−0.487039	+	0.408674i
$512$	1.00000			0.0441942
$513$	−15.1258	−	35.6346i	−0.667822	−	1.57331i
$514$	−9.40436			−0.414809
$515$	−6.49514	+	5.45007i	−0.286210	+	0.240159i
$516$	−10.8002	+	17.0622i	−0.475453	+	0.751123i
$517$	−0.543186	+	3.08056i	−0.0238893	+	0.135483i
$518$	7.72286	−	2.81089i	0.339323	−	0.123503i
$519$	−25.4227	−	10.4439i	−1.11593	−	0.458438i
$520$	0.0745146	+	0.422593i	0.00326768	+	0.0185319i
$521$	11.5495	+	20.0044i	0.505994	+	0.876407i	0.999976	+	0.00693463i	$0.00220738\pi$
$521$	11.5495	+	20.0044i	0.505994	+	0.876407i	−0.493982	+	0.869472i	$0.664459\pi$
$522$	−3.37434	+	12.8927i	−0.147691	+	0.564296i
$523$	15.2873	−	26.4784i	0.668469	−	1.15782i	−0.309864	−	0.950781i	$-0.600283\pi$
$523$	15.2873	−	26.4784i	0.668469	−	1.15782i	0.978332	−	0.207041i	$-0.0663833\pi$
$524$	14.5129	+	5.28228i	0.634000	+	0.230757i
$525$	5.18002	+	4.71897i	0.226074	+	0.205953i
$526$	−10.8969	−	9.14360i	−0.475128	−	0.398680i
$527$	13.7744	+	11.5581i	0.600022	+	0.503478i
$528$	−5.02627	−	4.57891i	−0.218740	−	0.199272i
$529$	1.32152	+	0.480995i	0.0574575	+	0.0209128i
$530$	−4.05507	+	7.02359i	−0.176141	+	0.305085i
$531$	1.22685	−	0.336392i	0.0532407	−	0.0145982i
$532$	3.72506	+	6.45199i	0.161502	+	0.279729i
$533$	0.0823911	+	0.467263i	0.00356875	+	0.0202394i
$534$	3.28553	+	1.34973i	0.142179	+	0.0584087i
$535$	−7.53563	+	2.74275i	−0.325794	+	0.118579i
$536$	1.27254	−	7.21694i	0.0549654	−	0.311724i
$537$	24.1572	−	38.1636i	1.04246	−	1.64688i
$538$	−19.0987	+	16.0257i	−0.823405	+	0.690919i
$539$	−3.92555			−0.169085
$540$	0.265651	+	5.06927i	0.0114318	+	0.218147i
$541$	−8.64945			−0.371869			−0.185934	−	0.982562i	$-0.559531\pi$
$541$	−8.64945			−0.371869			−0.185934	+	0.982562i	$0.559531\pi$
$542$	15.2075	−	12.7606i	0.653220	−	0.548117i
$543$	−12.9976	−	24.7920i	−0.557782	−	1.06392i
$544$	−0.609953	+	3.45921i	−0.0261515	+	0.148313i
$545$	9.20057	−	3.34874i	0.394109	−	0.143444i
$546$	−0.101498	−	0.754003i	−0.00434370	−	0.0322684i
$547$	−2.56872	−	14.5680i	−0.109831	−	0.622881i	−0.989180	−	0.146704i	$-0.953133\pi$
$547$	−2.56872	−	14.5680i	−0.109831	−	0.622881i	0.879350	−	0.476177i	$-0.157978\pi$
$548$	−0.0154884	−	0.0268268i	−0.000661633	−	0.00114598i
$549$	0.442696	+	4.74224i	0.0188938	+	0.202394i
$550$	−7.94065	+	13.7536i	−0.338591	+	0.586456i
$551$	31.0998	+	11.3194i	1.32490	+	0.482222i
$552$	7.66908	−	2.44259i	0.326418	−	0.103964i
$553$	−8.48959	−	7.12361i	−0.361014	−	0.302927i
$554$	1.68655	+	1.41519i	0.0716548	+	0.0601255i
$555$	2.97039	−	13.5854i	0.126086	−	0.576667i
$556$	−5.01214	−	1.82427i	−0.212562	−	0.0773662i
$557$	12.2527	−	21.2223i	0.519163	−	0.899217i	−0.480589	−	0.876946i	$-0.659577\pi$
$557$	12.2527	−	21.2223i	0.519163	−	0.899217i	0.999752	−	0.0222707i	$-0.00708955\pi$
$558$	6.57109	+	13.8804i	0.278176	+	0.587605i
$559$	−2.56051	−	4.43493i	−0.108298	−	0.187578i
$560$	−0.169640	−	0.962079i	−0.00716862	−	0.0406552i
$561$	18.9052	−	14.5940i	0.798179	−	0.616160i
$562$	−10.4277	+	3.79535i	−0.439864	+	0.160097i
$563$	−4.86427	+	27.5866i	−0.205004	+	1.16264i	0.692429	+	0.721486i	$0.256541\pi$
$563$	−4.86427	+	27.5866i	−0.205004	+	1.16264i	−0.897433	+	0.441151i	$0.854570\pi$
$564$	1.37904	+	0.0561934i	0.0580682	+	0.00236617i
$565$	7.78205	−	6.52992i	0.327393	−	0.274716i
$566$	12.9847			0.545789
$567$	−0.104674	−	8.99939i	−0.00439589	−	0.377939i
$568$	11.3148			0.474760
$569$	−16.6543	+	13.9746i	−0.698183	+	0.585845i	−0.921256	−	0.388957i	$-0.872836\pi$
$569$	−16.6543	+	13.9746i	−0.698183	+	0.585845i	0.223073	+	0.974802i	$0.428391\pi$
$570$	12.5957	+	0.513251i	0.527576	+	0.0214977i
$571$	3.17437	−	18.0028i	0.132843	−	0.753392i	−0.843494	−	0.537139i	$-0.819505\pi$
$571$	3.17437	−	18.0028i	0.132843	−	0.753392i	0.976337	−	0.216253i	$-0.0693838\pi$
$572$	1.62031	−	0.589745i	0.0677486	−	0.0246585i
$573$	27.4298	−	21.1746i	1.14590	−	0.884582i
$574$	−0.187572	−	1.06377i	−0.00782911	−	0.0444011i
$575$	−9.39981	−	16.2809i	−0.391999	−	0.678962i
$576$	−1.70641	+	2.46742i	−0.0711004	+	0.102809i
$577$	9.06356	−	15.6985i	0.377321	−	0.653539i	−0.613351	−	0.789811i	$-0.710179\pi$
$577$	9.06356	−	15.6985i	0.377321	−	0.653539i	0.990671	+	0.136272i	$0.0435120\pi$
$578$	4.38066	+	1.59443i	0.182211	+	0.0663195i
$579$	−5.20659	+	23.8128i	−0.216378	+	0.989628i
$580$	−3.32446	−	2.78956i	−0.138041	−	0.115830i
$581$	−6.15407	−	5.16388i	−0.255314	−	0.214234i
$582$	−24.1166	+	7.68109i	−0.999663	+	0.318391i
$583$	30.6236	+	11.1461i	1.26830	+	0.461623i
$584$	−7.18605	+	12.4466i	−0.297361	+	0.515044i
$585$	−1.16987	−	0.537258i	−0.0483681	−	0.0222129i
$586$	−4.15706	−	7.20025i	−0.171727	−	0.297439i
$587$	−2.95599	−	16.7643i	−0.122007	−	0.691936i	−0.983041	−	0.183388i	$-0.941294\pi$
$587$	−2.95599	−	16.7643i	−0.122007	−	0.691936i	0.861034	−	0.508548i	$-0.169818\pi$
$588$	0.231070	+	1.71657i	0.00952917	+	0.0707901i
$589$	35.8378	−	13.0439i	1.47667	−	0.537464i
$590$	−0.0719349	+	0.407963i	−0.00296151	+	0.0167956i
$591$	−16.0696	−	30.6515i	−0.661014	−	1.26083i
$592$	6.29573	−	5.28274i	0.258753	−	0.217119i
$593$	3.04371			0.124990			0.0624952	−	0.998045i	$-0.480094\pi$
$593$	3.04371			0.124990			0.0624952	+	0.998045i	$0.480094\pi$
$594$	19.8750	−	4.58842i	0.815480	−	0.188265i
$595$	3.43151			0.140678
$596$	11.9762	−	10.0492i	0.490563	−	0.411632i
$597$	−10.8177	+	17.0899i	−0.442740	+	0.699443i
$598$	−0.354442	+	2.01014i	−0.0144942	+	0.0822008i
$599$	13.5197	−	4.92076i	0.552399	−	0.201057i	−0.0507130	−	0.998713i	$-0.516149\pi$
$599$	13.5197	−	4.92076i	0.552399	−	0.201057i	0.603112	+	0.797656i	$0.293927\pi$
$600$	6.48161	+	2.66272i	0.264611	+	0.108705i
$601$	1.24466	+	7.05880i	0.0507706	+	0.287935i	0.999613	−	0.0278153i	$-0.00885504\pi$
$601$	1.24466	+	7.05880i	0.0507706	+	0.287935i	−0.948842	+	0.315750i	$0.897744\pi$
$602$	5.82927	+	10.0966i	0.237583	+	0.411506i
$603$	15.6358	+	15.4550i	0.636737	+	0.629374i
$604$	6.31742	−	10.9421i	0.257052	−	0.445228i
$605$	−4.04834	−	1.47347i	−0.164588	−	0.0599052i
$606$	−3.96244	−	3.60976i	−0.160963	−	0.146637i
$607$	−34.9196	−	29.3010i	−1.41734	−	1.18929i	−0.952745	−	0.303770i	$-0.901754\pi$
$607$	−34.9196	−	29.3010i	−1.41734	−	1.18929i	−0.464598	−	0.885522i	$-0.653801\pi$
$608$	5.70712	+	4.78884i	0.231454	+	0.194213i
$609$	5.68792	+	5.18168i	0.230486	+	0.209972i
$610$	−1.45744	−	0.530466i	−0.0590101	−	0.0214779i
$611$	−0.175009	+	0.303124i	−0.00708010	+	0.0122631i
$612$	−7.49451	−	7.40784i	−0.302948	−	0.299444i
$613$	2.02373	+	3.50521i	0.0817379	+	0.141574i	0.903996	−	0.427540i	$-0.140620\pi$
$613$	2.02373	+	3.50521i	0.0817379	+	0.141574i	−0.822259	+	0.569114i	$0.807286\pi$
$614$	−1.02477	−	5.81175i	−0.0413563	−	0.234543i
$615$	−1.69065	−	0.694538i	−0.0681736	−	0.0280065i
$616$	−3.68881	+	1.34262i	−0.148626	+	0.0540956i
$617$	7.75944	−	44.0060i	0.312383	−	1.77161i	−0.274148	−	0.961687i	$-0.588396\pi$
$617$	7.75944	−	44.0060i	0.312383	−	1.77161i	0.586531	−	0.809926i	$-0.300493\pi$
$618$	8.04015	−	12.7019i	0.323422	−	0.510944i
$619$	31.0152	−	26.0248i	1.24661	−	1.04603i	0.249627	−	0.968342i	$-0.419692\pi$
$619$	31.0152	−	26.0248i	1.24661	−	1.04603i	0.996978	−	0.0776838i	$-0.0247525\pi$
$620$	−5.00094			−0.200842
$621$	−7.05969	+	23.0909i	−0.283296	+	0.926606i
$622$	23.7882			0.953821
$623$	1.57095	−	1.31819i	0.0629389	−	0.0528120i
$624$	−0.353261	−	0.673817i	−0.0141418	−	0.0269743i
$625$	2.01349	−	11.4191i	0.0805396	−	0.456763i
$626$	23.5361	−	8.56646i	0.940693	−	0.342384i
$627$	−6.75783	−	50.2024i	−0.269882	−	2.00489i
$628$	−2.76087	−	15.6577i	−0.110171	−	0.624810i
$629$	14.4340	+	25.0005i	0.575523	+	0.996835i
$630$	2.66333	+	1.22313i	0.106110	+	0.0487305i
$631$	−16.7712	+	29.0486i	−0.667652	+	1.15641i	0.310907	+	0.950440i	$0.399367\pi$
$631$	−16.7712	+	29.0486i	−0.667652	+	1.15641i	−0.978559	+	0.205966i	$0.933966\pi$
$632$	−10.4140	−	3.79039i	−0.414248	−	0.150774i
$633$	19.4400	−	6.19160i	0.772669	−	0.246094i
$634$	−19.9518	−	16.7416i	−0.792388	−	0.664892i
$635$	3.00411	+	2.52075i	0.119214	+	0.100033i
$636$	3.07136	−	14.0472i	0.121788	−	0.557008i
$637$	−0.412760	−	0.150232i	−0.0163542	−	0.00595243i
$638$	−8.71924	+	15.1022i	−0.345198	+	0.597901i
$639$	−19.3078	+	27.9185i	−0.763803	+	1.10444i
$640$	−0.488460	−	0.846038i	−0.0193081	−	0.0334426i
$641$	3.98082	+	22.5764i	0.157233	+	0.891712i	0.956716	+	0.291024i	$0.0939958\pi$
$641$	3.98082	+	22.5764i	0.157233	+	0.891712i	−0.799483	+	0.600689i	$0.794893\pi$
$642$	11.2546	−	8.68807i	0.444184	−	0.342891i
$643$	−30.2255	+	11.0012i	−1.19198	+	0.433844i	−0.860417	−	0.509590i	$-0.829797\pi$
$643$	−30.2255	+	11.0012i	−1.19198	+	0.433844i	−0.331559	+	0.943434i	$0.607575\pi$
$644$	0.806925	−	4.57630i	0.0317973	−	0.180332i
$645$	19.7108	+	0.803176i	0.776111	+	0.0316250i
$646$	−20.0467	+	16.8212i	−0.788727	+	0.661820i
$647$	29.3439			1.15363			0.576813	−	0.816876i	$-0.304296\pi$
$647$	29.3439			1.15363			0.576813	+	0.816876i	$0.304296\pi$
$648$	−3.17633	−	8.42086i	−0.124778	−	0.330803i
$649$	1.66460			0.0653414
$650$	−1.36129	+	1.14226i	−0.0533943	+	0.0448032i
$651$	8.85916	+	0.360994i	0.347218	+	0.0141485i
$652$	1.84262	−	10.4500i	0.0721625	−	0.409254i
$653$	14.1846	−	5.16277i	0.555086	−	0.202035i	−0.0492190	−	0.998788i	$-0.515673\pi$
$653$	14.1846	−	5.16277i	0.555086	−	0.202035i	0.604305	+	0.796753i	$0.293451\pi$
$654$	−13.7412	+	10.6076i	−0.537324	+	0.414791i
$655$	−2.61998	−	14.8587i	−0.102371	−	0.580576i
$656$	−0.540092	−	0.935468i	−0.0210871	−	0.0365239i
$657$	−18.4487	−	38.9700i	−0.719751	−	1.52037i
$658$	0.398426	−	0.690094i	0.0155323	−	0.0269027i
$659$	36.3930	+	13.2460i	1.41767	+	0.515989i	0.933371	−	0.358914i	$-0.116853\pi$
$659$	36.3930	+	13.2460i	1.41767	+	0.515989i	0.484298	+	0.874903i	$0.339075\pi$
$660$	−1.41880	+	6.48903i	−0.0552267	+	0.252585i
$661$	15.2199	+	12.7710i	0.591987	+	0.496736i	0.888859	−	0.458181i	$-0.151499\pi$
$661$	15.2199	+	12.7710i	0.591987	+	0.496736i	−0.296872	+	0.954917i	$0.595943\pi$
$662$	14.0179	+	11.7624i	0.544821	+	0.457159i
$663$	2.54635	−	0.811008i	0.0988920	−	0.0314969i
$664$	−7.54909	−	2.74764i	−0.292961	−	0.106629i
$665$	3.63908	−	6.30308i	0.141118	−	0.244423i
$666$	2.29166	+	24.5487i	0.0888002	+	0.951244i
$667$	−10.3215	−	17.8773i	−0.399649	−	0.692212i
$668$	2.21662	+	12.5711i	0.0857637	+	0.486390i
$669$	0.359942	+	2.67393i	0.0139162	+	0.103380i
$670$	−6.72739	+	2.44857i	−0.259902	+	0.0945965i
$671$	−1.08222	+	6.13760i	−0.0417788	+	0.236939i
$672$	0.804236	+	1.53402i	0.0310241	+	0.0591759i
$673$	−28.4082	+	23.8373i	−1.09506	+	0.918860i	−0.997083	−	0.0763287i	$-0.975680\pi$
$673$	−28.4082	+	23.8373i	−1.09506	+	0.918860i	−0.0979725	+	0.995189i	$0.531236\pi$
$674$	21.2393			0.818107
$675$	−17.6303	+	11.4492i	−0.678591	+	0.440679i
$676$	−12.8071			−0.492579
$677$	−12.9018	+	10.8259i	−0.495856	+	0.416073i	−0.856119	−	0.516778i	$-0.827131\pi$
$677$	−12.9018	+	10.8259i	−0.495856	+	0.416073i	0.360263	+	0.932851i	$0.382687\pi$
$678$	−9.63318	+	15.2185i	−0.369960	+	0.584464i
$679$	−2.53750	+	14.3909i	−0.0973802	+	0.552271i
$680$	3.22456	−	1.17364i	0.123656	−	0.0450072i
$681$	26.9556	+	11.0737i	1.03294	+	0.424344i
$682$	3.48950	+	19.7899i	0.133620	+	0.757795i
$683$	−14.9176	−	25.8380i	−0.570806	−	0.988665i	−0.996483	−	0.0837901i	$-0.973297\pi$
$683$	−14.9176	−	25.8380i	−0.570806	−	0.988665i	0.425677	−	0.904875i	$-0.360036\pi$
$684$	−21.5548	+	5.91014i	−0.824167	+	0.225980i
$685$	−0.0151310	+	0.0262076i	−0.000578124	+	0.00100134i
$686$	0.939693	+	0.342020i	0.0358776	+	0.0130584i
$687$	−7.96131	−	7.25272i	−0.303743	−	0.276709i
$688$	8.93096	+	7.49397i	0.340490	+	0.285705i
$689$	2.79342	+	2.34395i	0.106421	+	0.0892976i
$690$	−5.81256	−	5.29522i	−0.221280	−	0.201586i
$691$	−48.2986	−	17.5793i	−1.83737	−	0.668746i	−0.990602	−	0.136776i	$-0.956326\pi$
$691$	−48.2986	−	17.5793i	−1.83737	−	0.668746i	−0.846763	−	0.531970i	$-0.821452\pi$
$692$	−7.93406	+	13.7422i	−0.301608	+	0.522400i
$693$	2.98182	−	11.3929i	0.113270	−	0.432780i
$694$	7.98903	+	13.8374i	0.303259	+	0.525261i
$695$	0.904829	+	5.13154i	0.0343221	+	0.194650i
$696$	7.11714	+	2.92380i	0.269774	+	0.110826i
$697$	3.56541	−	1.29770i	0.135050	−	0.0491540i
$698$	−0.155950	+	0.884434i	−0.00590278	+	0.0334763i
$699$	−7.80954	+	12.3375i	−0.295384	+	0.466648i
$700$	3.09913	−	2.60048i	0.117136	−	0.0982889i
$701$	−29.6379			−1.11941			−0.559703	−	0.828693i	$-0.689085\pi$
$701$	−29.6379			−1.11941			−0.559703	+	0.828693i	$0.689085\pi$
$702$	2.26540	+	0.278164i	0.0855019	+	0.0104986i
$703$	61.2287			2.30928
$704$	−3.00714	+	2.52329i	−0.113336	+	0.0951002i
$705$	−0.626066	−	1.19417i	−0.0235790	−	0.0449751i
$706$	1.09542	−	6.21243i	0.0412266	−	0.233808i
$707$	−2.90806	+	1.05845i	−0.109369	+	0.0398070i
$708$	−0.0979838	−	0.727900i	−0.00368246	−	0.0273562i
$709$	1.12889	+	6.40228i	0.0423965	+	0.240443i	0.998640	−	0.0521281i	$-0.0166004\pi$
$709$	1.12889	+	6.40228i	0.0423965	+	0.240443i	−0.956244	+	0.292571i	$0.905489\pi$
$710$	−5.52685	−	9.57278i	−0.207419	−	0.359260i
$711$	27.1231	−	19.2278i	1.01720	−	0.721099i
$712$	1.02537	−	1.77599i	0.0384272	−	0.0665579i
$713$	−22.3533	−	8.13593i	−0.837137	−	0.304693i
$714$	−5.79703	+	1.84635i	−0.216949	+	0.0690978i
$715$	−1.29040	−	1.08278i	−0.0482583	−	0.0404936i
$716$	−19.9761	−	16.7620i	−0.746543	−	0.626424i
$717$	4.42983	−	20.2603i	0.165435	−	0.756633i
$718$	4.11542	+	1.49789i	0.153586	+	0.0559007i
$719$	−2.62324	+	4.54359i	−0.0978305	+	0.169447i	−0.910786	−	0.412878i	$-0.864524\pi$
$719$	−2.62324	+	4.54359i	−0.0978305	+	0.169447i	0.812956	+	0.582325i	$0.197857\pi$
$720$	2.92104	+	0.238450i	0.108861	+	0.00888650i
$721$	−4.33956	−	7.51634i	−0.161614	−	0.279923i
$722$	6.33889	+	35.9496i	0.235909	+	1.33791i
$723$	−11.3620	+	8.77095i	−0.422556	+	0.326195i
$724$	−15.1868	+	5.52755i	−0.564414	+	0.205430i
$725$	3.12079	−	17.6989i	0.115903	−	0.657320i
$726$	7.63189	+	0.310985i	0.283246	+	0.0115417i
$727$	−24.2418	+	20.3413i	−0.899079	+	0.754417i	−0.970010	−	0.243064i	$-0.921847\pi$
$727$	−24.2418	+	20.3413i	−0.899079	+	0.754417i	0.0709310	+	0.997481i	$0.477403\pi$
$728$	−0.439250			−0.0162797
$729$	26.1979	+	6.53208i	0.970294	+	0.241929i
$730$	14.0404			0.519658
$731$	−31.3707	+	26.3231i	−1.16029	+	0.973596i
$732$	2.74756	+	0.111958i	0.101553	+	0.00413808i
$733$	0.00356696	−	0.0202292i	0.000131749	−	0.000747184i	−0.984742	−	0.174022i	$-0.944324\pi$
$733$	0.00356696	−	0.0202292i	0.000131749	−	0.000747184i	0.984874	+	0.173275i	$0.0554348\pi$
$734$	−28.1200	+	10.2348i	−1.03793	+	0.377775i
$735$	1.33941	−	1.03397i	0.0494050	−	0.0381385i
$736$	−0.806925	−	4.57630i	−0.0297437	−	0.168685i
$737$	14.3837	+	24.9134i	0.529832	+	0.917696i
$738$	3.22981	+	0.263655i	0.118891	+	0.00970528i
$739$	−4.93681	+	8.55080i	−0.181603	+	0.314546i	−0.942427	−	0.334413i	$-0.891462\pi$
$739$	−4.93681	+	8.55080i	−0.181603	+	0.314546i	0.760823	+	0.648959i	$0.224795\pi$
$740$	−7.54461	−	2.74601i	−0.277346	−	0.100946i
$741$	1.21070	−	5.53726i	0.0444762	−	0.203416i
$742$	−6.35951	−	5.33626i	−0.233465	−	0.195900i
$743$	6.68722	+	5.61124i	0.245330	+	0.205856i	0.757158	−	0.653231i	$-0.226587\pi$
$743$	6.68722	+	5.61124i	0.245330	+	0.205856i	−0.511828	+	0.859088i	$0.671032\pi$
$744$	8.44836	−	2.69079i	0.309732	−	0.0986491i
$745$	−14.3519	−	5.22366i	−0.525813	−	0.191380i
$746$	6.56372	−	11.3687i	0.240315	−	0.416238i
$747$	19.6614	−	13.9382i	0.719374	−	0.509971i
$748$	−6.89440	−	11.9414i	−0.252084	−	0.436622i
$749$	−1.42543	−	8.08400i	−0.0520840	−	0.295383i
$750$	−2.04193	−	15.1691i	−0.0745609	−	0.553896i
$751$	−36.1457	+	13.1560i	−1.31897	+	0.480068i	−0.903130	−	0.429368i	$-0.858736\pi$
$751$	−36.1457	+	13.1560i	−1.31897	+	0.480068i	−0.415845	+	0.909435i	$0.636514\pi$
$752$	0.138372	−	0.784746i	0.00504591	−	0.0286168i
$753$	16.5067	+	31.4853i	0.601538	+	1.14739i
$754$	−1.49477	+	1.25426i	−0.0544363	+	0.0456775i
$755$	−12.3432			−0.449216
$756$	−5.15742	−	0.633270i	−0.187574	−	0.0230318i
$757$	−9.13898			−0.332162			−0.166081	−	0.986112i	$-0.553111\pi$
$757$	−9.13898			−0.332162			−0.166081	+	0.986112i	$0.553111\pi$
$758$	−1.43428	+	1.20350i	−0.0520953	+	0.0437132i
$759$	−16.8987	+	26.6966i	−0.613382	+	0.969024i
$760$	1.26384	−	7.16760i	0.0458443	−	0.259996i
$761$	−39.3933	+	14.3380i	−1.42801	+	0.519752i	−0.936359	−	0.351043i	$-0.885827\pi$
$761$	−39.3933	+	14.3380i	−1.42801	+	0.519752i	−0.491647	+	0.870795i	$0.663605\pi$
$762$	−6.43131	−	2.64205i	−0.232982	−	0.0957115i
$763$	1.74036	+	9.87010i	0.0630054	+	0.357322i
$764$	−10.0031	−	17.3260i	−0.361901	−	0.626831i
$765$	−2.60655	+	9.95907i	−0.0942399	+	0.360071i
$766$	−13.4001	+	23.2097i	−0.484165	+	0.838599i
$767$	0.175028	+	0.0637051i	0.00631991	+	0.00230026i
$768$	1.28040	+	1.16644i	0.0462024	+	0.0420902i
$769$	2.90712	+	2.43936i	0.104833	+	0.0879657i	0.693698	−	0.720266i	$-0.255980\pi$
$769$	2.90712	+	2.43936i	0.104833	+	0.0879657i	−0.588864	+	0.808232i	$0.700425\pi$
$770$	2.93774	+	2.46506i	0.105869	+	0.0888345i
$771$	−12.0413	−	10.9696i	−0.433658	−	0.395061i
$772$	13.2244	+	4.81330i	0.475958	+	0.173234i
$773$	8.12754	−	14.0773i	0.292327	−	0.506326i	−0.682032	−	0.731322i	$-0.738904\pi$
$773$	8.12754	−	14.0773i	0.292327	−	0.506326i	0.974360	+	0.224996i	$0.0722370\pi$
$774$	−33.7306	+	9.24867i	−1.21242	+	0.332437i
$775$	−10.3550	−	17.9353i	−0.371961	−	0.644255i
$776$	2.53750	+	14.3909i	0.0910908	+	0.516602i
$777$	13.1671	+	5.40918i	0.472366	+	0.194053i
$778$	29.2650	−	10.6516i	1.04920	−	0.381878i
$779$	1.39743	−	7.92524i	0.0500683	−	0.283951i
$780$	−0.397521	+	0.628005i	−0.0142335	+	0.0224862i
$781$	−34.0254	+	28.5507i	−1.21752	+	1.02162i
$782$	16.3226			0.583695
$783$	−19.3590	+	12.5718i	−0.691834	+	0.449279i
$784$	1.00000			0.0357143
$785$	−11.8984	+	9.98397i	−0.424673	+	0.356343i
$786$	12.4209	+	23.6919i	0.443039	+	0.845061i
$787$	2.01705	−	11.4393i	0.0719000	−	0.407765i	−0.927522	−	0.373769i	$-0.878065\pi$
$787$	2.01705	−	11.4393i	0.0719000	−	0.407765i	0.999422	−	0.0339965i	$-0.0108235\pi$
$788$	−18.7762	+	6.83397i	−0.668873	+	0.243450i
$789$	−3.28695	−	24.4180i	−0.117019	−	0.869305i
$790$	1.88002	+	10.6621i	0.0668880	+	0.379341i
$791$	5.19937	+	9.00558i	0.184868	+	0.320202i
$792$	−1.09461	−	11.7257i	−0.0388952	−	0.416653i
$793$	−0.348681	+	0.603933i	−0.0123820	+	0.0214463i
$794$	−28.4733	−	10.3635i	−1.01048	−	0.367785i
$795$	−13.3847	+	4.26301i	−0.474706	+	0.151193i
$796$	8.94544	+	7.50611i	0.317063	+	0.266047i
$797$	−21.1534	−	17.7498i	−0.749292	−	0.628731i	0.186024	−	0.982545i	$-0.440440\pi$
$797$	−21.1534	−	17.7498i	−0.749292	−	0.628731i	−0.935316	+	0.353815i	$0.884884\pi$
$798$	−2.75629	+	12.6062i	−0.0975716	+	0.446254i
$799$	2.63020	+	0.957316i	0.0930500	+	0.0338674i
$800$	2.02281	−	3.50362i	0.0715173	−	0.123872i
$801$	2.63241	+	5.56057i	0.0930117	+	0.196473i
$802$	−0.789273	−	1.36706i	−0.0278702	−	0.0482726i
$803$	−9.79695	−	55.5613i	−0.345727	−	1.96071i
$804$	10.0475	−	7.75622i	0.354347	−	0.273541i
$805$	−4.26587	+	1.55265i	−0.150352	+	0.0547238i
$806$	−0.390458	+	2.21440i	−0.0137533	+	0.0779989i
$807$	−43.1471	−	1.75816i	−1.51885	−	0.0618902i
$808$	−2.37067	+	1.98923i	−0.0833999	+	0.0699808i
$809$	−29.6836			−1.04362			−0.521810	−	0.853062i	$-0.674743\pi$
$809$	−29.6836			−1.04362			−0.521810	+	0.853062i	$0.674743\pi$
$810$	−5.57285	+	6.80055i	−0.195810	+	0.238947i
$811$	20.3436			0.714360			0.357180	−	0.934036i	$-0.383738\pi$
$811$	20.3436			0.714360			0.357180	+	0.934036i	$0.383738\pi$
$812$	3.40300	−	2.85546i	0.119422	−	0.100207i
$813$	34.3562	+	1.39995i	1.20493	+	0.0490984i
$814$	−5.60225	+	31.7720i	−0.196359	+	1.11361i
$815$	−9.74115	+	3.54549i	−0.341218	+	0.124193i
$816$	−4.81594	+	3.71770i	−0.168592	+	0.130146i
$817$	15.0826	+	85.5379i	0.527675	+	2.99259i
$818$	−0.313340	−	0.542721i	−0.0109557	−	0.0189758i
$819$	0.749541	−	1.08382i	0.0261911	−	0.0378716i
$820$	−0.527627	+	0.913877i	−0.0184255	+	0.0319140i
$821$	39.0662	+	14.2189i	1.36342	+	0.496244i	0.917110	−	0.398635i	$-0.130516\pi$
$821$	39.0662	+	14.2189i	1.36342	+	0.496244i	0.446310	+	0.894879i	$0.352738\pi$
$822$	0.0114604	−	0.0524152i	0.000399727	−	0.00182819i
$823$	−18.9944	−	15.9382i	−0.662102	−	0.555569i	0.248614	−	0.968603i	$-0.420025\pi$
$823$	−18.9944	−	15.9382i	−0.662102	−	0.555569i	−0.910716	+	0.413033i	$0.864469\pi$
$824$	−6.64859	−	5.57883i	−0.231615	−	0.194348i
$825$	−26.2099	+	8.34783i	−0.912513	+	0.290634i
$826$	−0.398471	−	0.145031i	−0.0138646	−	0.00504629i
$827$	−8.49652	+	14.7164i	−0.295453	+	0.511739i	−0.975090	−	0.221809i	$-0.928804\pi$
$827$	−8.49652	+	14.7164i	−0.295453	+	0.511739i	0.679637	+	0.733548i	$0.262137\pi$
$828$	12.6686	+	5.81802i	0.440265	+	0.202190i
$829$	−26.9708	−	46.7148i	−0.936734	−	1.62247i	−0.771512	−	0.636215i	$-0.780499\pi$
$829$	−26.9708	−	46.7148i	−0.936734	−	1.62247i	−0.165222	−	0.986256i	$-0.552834\pi$
$830$	1.36282	+	7.72893i	0.0473041	+	0.268275i
$831$	0.508733	+	3.77926i	0.0176477	+	0.131101i
$832$	−0.412760	+	0.150232i	−0.0143099	+	0.00520837i
$833$	−0.609953	+	3.45921i	−0.0211336	+	0.119855i
$834$	−4.28964	−	8.18214i	−0.148538	−	0.283324i
$835$	9.55289	−	8.01583i	0.330591	−	0.277399i
$836$	−29.2458			−1.01149
$837$	−7.77705	+	25.4372i	−0.268814	+	0.879240i
$838$	17.9340			0.619521
$839$	16.9339	−	14.2092i	0.584623	−	0.490557i	−0.301839	−	0.953359i	$-0.597600\pi$
$839$	16.9339	−	14.2092i	0.584623	−	0.490557i	0.886462	+	0.462802i	$0.153156\pi$
$840$	0.904998	−	1.42972i	0.0312254	−	0.0493300i
$841$	−1.60901	+	9.12514i	−0.0554831	+	0.314660i
$842$	−17.8710	+	6.50452i	−0.615876	+	0.224161i
$843$	−17.7786	−	7.30365i	−0.612328	−	0.251551i
$844$	−2.04544	−	11.6002i	−0.0704068	−	0.399297i
$845$	6.25574	+	10.8353i	0.215204	+	0.372744i
$846$	1.70018	+	1.68052i	0.0584534	+	0.0577775i
$847$	2.20497	−	3.81911i	0.0757635	−	0.131226i
$848$	−7.80109	−	2.83937i	−0.267891	−	0.0975042i
$849$	16.6256	+	15.1459i	0.570591	+	0.519806i
$850$	10.8859	+	9.13438i	0.373384	+	0.313307i
$851$	−29.2556	−	24.5484i	−1.00287	−	0.841508i
$852$	14.4875	+	13.1981i	0.496334	+	0.452158i
$853$	35.5454	+	12.9375i	1.21705	+	0.442970i	0.869144	−	0.494559i	$-0.164670\pi$
$853$	35.5454	+	12.9375i	1.21705	+	0.442970i	0.347907	+	0.937529i	$0.386893\pi$
$854$	0.793810	−	1.37492i	0.0271636	−	0.0470488i
$855$	15.5289	+	15.3493i	0.531075	+	0.524934i
$856$	−4.10435	−	7.10895i	−0.140284	−	0.242979i
$857$	6.78279	+	38.4671i	0.231696	+	1.31401i	0.849462	+	0.527649i	$0.176927\pi$
$857$	6.78279	+	38.4671i	0.231696	+	1.31401i	−0.617767	+	0.786361i	$0.711962\pi$
$858$	2.76254	+	1.13488i	0.0943117	+	0.0387443i
$859$	−11.6276	+	4.23211i	−0.396730	+	0.144398i	−0.532678	−	0.846318i	$-0.678814\pi$
$859$	−11.6276	+	4.23211i	−0.396730	+	0.144398i	0.135948	+	0.990716i	$0.456592\pi$
$860$	1.97776	−	11.2164i	0.0674411	−	0.382477i
$861$	1.00066	−	1.58085i	0.0341024	−	0.0538751i
$862$	−24.8371	+	20.8408i	−0.845955	+	0.709841i
$863$	−39.4935			−1.34437			−0.672187	−	0.740382i	$-0.734645\pi$
$863$	−39.4935			−1.34437			−0.672187	+	0.740382i	$0.734645\pi$
$864$	−5.06298	+	1.16886i	−0.172246	+	0.0397655i
$865$	15.5019			0.527080
$866$	26.3704	−	22.1274i	0.896101	−	0.751918i
$867$	3.74919	+	7.15128i	0.127329	+	0.242870i
$868$	0.888920	−	5.04131i	0.0301719	−	0.171113i
$869$	40.8808	−	14.8794i	1.38678	−	0.504748i
$870$	−1.00279	−	7.44953i	−0.0339979	−	0.252563i
$871$	0.558964	+	3.17004i	0.0189398	+	0.107413i
$872$	5.01118	+	8.67962i	0.169700	+	0.293929i
$873$	−39.8383	−	18.2956i	−1.34832	−	0.619213i
$874$	17.3100	−	29.9817i	0.585518	−	1.01415i
$875$	−8.30393	−	3.02238i	−0.280724	−	0.102175i
$876$	−23.7192	+	7.55453i	−0.801398	+	0.255244i
$877$	−35.6904	−	29.9478i	−1.20518	−	1.01127i	−0.999467	−	0.0326528i	$-0.989604\pi$
$877$	−35.6904	−	29.9478i	−1.20518	−	1.01127i	−0.205712	−	0.978613i	$-0.565951\pi$
$878$	−7.48156	−	6.27777i	−0.252490	−	0.211865i
$879$	3.07594	−	14.0681i	0.103749	−	0.474507i
$880$	3.60367	+	1.31163i	0.121480	+	0.0442150i
$881$	6.94703	−	12.0326i	0.234051	−	0.405389i	−0.724945	−	0.688807i	$-0.758135\pi$
$881$	6.94703	−	12.0326i	0.234051	−	0.405389i	0.958997	+	0.283418i	$0.0914683\pi$
$882$	−1.70641	+	2.46742i	−0.0574578	+	0.0830824i
$883$	8.67681	+	15.0287i	0.291998	+	0.505755i	0.974282	−	0.225332i	$-0.0723466\pi$
$883$	8.67681	+	15.0287i	0.291998	+	0.505755i	−0.682284	+	0.731087i	$0.739013\pi$
$884$	−0.267922	−	1.51946i	−0.00901119	−	0.0511050i
$885$	−0.567970	+	0.438448i	−0.0190921	+	0.0147383i
$886$	3.74337	−	1.36248i	0.125761	−	0.0457733i
$887$	4.02319	−	22.8166i	0.135085	−	0.766107i	−0.839715	−	0.543028i	$-0.817278\pi$
$887$	4.02319	−	22.8166i	0.135085	−	0.766107i	0.974800	−	0.223080i	$-0.0716110\pi$
$888$	14.2230	+	0.579562i	0.477294	+	0.0194488i
$889$	−3.07508	+	2.58030i	−0.103135	+	0.0865405i
$890$	−2.00340			−0.0671542
$891$	30.8000	+	17.3079i	1.03184	+	0.579837i
$892$	1.55772			0.0521562
$893$	4.54773	−	3.81600i	0.152184	−	0.127698i
$894$	27.0561	+	1.10248i	0.904890	+	0.0368725i
$895$	−4.42371	+	25.0881i	−0.147868	+	0.838603i
$896$	0.939693	−	0.342020i	0.0313929	−	0.0114261i
$897$	−2.79853	+	2.16035i	−0.0934403	+	0.0721319i
$898$	2.41143	+	13.6759i	0.0804704	+	0.456370i
$899$	−11.3703	−	19.6939i	−0.379220	−	0.656828i
$900$	5.19315	+	10.9697i	0.173105	+	0.365658i
$901$	14.5803	−	25.2538i	0.485739	−	0.841325i
$902$	3.98460	+	1.45027i	0.132673	+	0.0482888i
$903$	−4.31326	+	19.7272i	−0.143536	+	0.656479i
$904$	7.96590	+	6.68419i	0.264942	+	0.222313i
$905$	12.0947	+	10.1486i	0.402041	+	0.337352i
$906$	20.8521	−	6.64136i	0.692765	−	0.220645i
$907$	29.2638	+	10.6511i	0.971688	+	0.353666i	0.778603	−	0.627517i	$-0.215929\pi$
$907$	29.2638	+	10.6511i	0.971688	+	0.353666i	0.193085	+	0.981182i	$0.438151\pi$
$908$	8.41245	−	14.5708i	0.279177	−	0.483548i
$909$	−0.862930	−	9.24388i	−0.0286216	−	0.306600i
$910$	0.214556	+	0.371622i	0.00711247	+	0.0123192i
$911$	9.46880	+	53.7002i	0.313715	+	1.77917i	0.579334	+	0.815090i	$0.303313\pi$
$911$	9.46880	+	53.7002i	0.313715	+	1.77917i	−0.265619	+	0.964078i	$0.585576\pi$
$912$	1.72150	+	12.7886i	0.0570045	+	0.423474i
$913$	29.6343	−	10.7860i	0.980753	−	0.356965i
$914$	−4.55317	+	25.8223i	−0.150605	+	0.854126i
$915$	−1.24735	−	2.37922i	−0.0412362	−	0.0786547i
$916$	−4.76314	+	3.99675i	−0.157379	+	0.132056i
$917$	15.4443			0.510017
$918$	−0.955164	−	18.2269i	−0.0315251	−	0.601577i
$919$	50.5944			1.66896			0.834478	−	0.551042i	$-0.185769\pi$
$919$	50.5944			1.66896			0.834478	+	0.551042i	$0.185769\pi$
$920$	−3.47757	+	2.91803i	−0.114652	+	0.0962046i
$921$	5.46694	−	8.63669i	0.180142	−	0.284589i
$922$	−1.48670	+	8.43148i	−0.0489618	+	0.277676i
$923$	−4.67032	+	1.69986i	−0.153725	+	0.0559515i
$924$	−6.28923	−	2.58368i	−0.206900	−	0.0849970i
$925$	−5.77362	−	32.7438i	−0.189835	−	1.07661i
$926$	−4.80411	−	8.32096i	−0.157873	−	0.273444i
$927$	25.1105	−	6.88511i	0.824738	−	0.226137i
$928$	2.22115	−	3.84715i	0.0729129	−	0.126289i
$929$	−9.01425	−	3.28092i	−0.295748	−	0.107643i	0.189885	−	0.981806i	$-0.439189\pi$
$929$	−9.01425	−	3.28092i	−0.295748	−	0.107643i	−0.485633	+	0.874163i	$0.661411\pi$
$930$	−6.40319	−	5.83329i	−0.209969	−	0.191281i
$931$	5.70712	+	4.78884i	0.187043	+	0.156948i
$932$	6.45789	+	5.41881i	0.211535	+	0.177499i
$933$	30.4584	+	27.7475i	0.997164	+	0.908412i
$934$	−40.1865	−	14.6267i	−1.31494	−	0.478600i
$935$	−6.73528	+	11.6658i	−0.220267	+	0.381514i
$936$	0.333651	−	1.27481i	0.0109057	−	0.0416685i
$937$	−9.75555	−	16.8971i	−0.318700	−	0.552005i	0.661517	−	0.749930i	$-0.269913\pi$
$937$	−9.75555	−	16.8971i	−0.318700	−	0.552005i	−0.980217	+	0.197926i	$0.936580\pi$
$938$	−1.27254	−	7.21694i	−0.0415499	−	0.235641i
$939$	40.1279	+	16.4850i	1.30952	+	0.537967i
$940$	−0.731514	+	0.266249i	−0.0238594	+	0.00868410i
$941$	9.03922	−	51.2640i	0.294670	−	1.67116i	−0.373870	−	0.927481i	$-0.621969\pi$
$941$	9.03922	−	51.2640i	0.294670	−	1.67116i	0.668540	−	0.743676i	$-0.266919\pi$
$942$	14.7287	−	23.2685i	0.479888	−	0.758128i
$943$	−3.84517	+	3.22648i	−0.125216	+	0.105069i
$944$	−0.424044			−0.0138014
$945$	1.98342	+	4.67270i	0.0645207	+	0.152003i
$946$	−45.7662			−1.48799
$947$	26.2655	−	22.0394i	0.853514	−	0.716184i	−0.107046	−	0.994254i	$-0.534139\pi$
$947$	26.2655	−	22.0394i	0.853514	−	0.716184i	0.960561	+	0.278070i	$0.0896949\pi$
$948$	−8.91284	−	17.0005i	−0.289476	−	0.552152i
$949$	1.09623	−	6.21704i	0.0355852	−	0.201814i
$950$	28.3227	−	10.3086i	0.918910	−	0.334456i
$951$	−6.01828	−	44.7084i	−0.195156	−	1.44977i
$952$	0.609953	+	3.45921i	0.0197687	+	0.112114i
$953$	−19.8339	−	34.3533i	−0.642482	−	1.11281i	−0.984877	−	0.173256i	$-0.944571\pi$
$953$	−19.8339	−	34.3533i	−0.642482	−	1.11281i	0.342394	−	0.939556i	$-0.388762\pi$
$954$	20.3178	−	14.4035i	0.657812	−	0.466329i
$955$	−9.77228	+	16.9261i	−0.316224	+	0.547715i
$956$	−11.2515	−	4.09521i	−0.363900	−	0.132449i
$957$	−28.7799	+	9.16634i	−0.930321	+	0.296306i
$958$	16.2916	+	13.6703i	0.526358	+	0.441667i
$959$	−0.0237297	−	0.0199115i	−0.000766271	−	0.000642977i
$960$	0.361427	−	1.65302i	0.0116650	−	0.0533511i
$961$	4.50580	+	1.63998i	0.145348	+	0.0529025i
$962$	−1.80499	+	3.12633i	−0.0581951	+	0.100797i
$963$	24.5445	+	2.00361i	0.790935	+	0.0645653i
$964$	4.14351	+	7.17677i	0.133453	+	0.231148i
$965$	−2.38737	−	13.5395i	−0.0768523	−	0.435851i
$966$	6.37116	−	4.91826i	0.204989	−	0.158242i
$967$	−8.36818	+	3.04577i	−0.269103	+	0.0979453i	−0.473047	−	0.881037i	$-0.656846\pi$
$967$	−8.36818	+	3.04577i	−0.269103	+	0.0979453i	0.203945	+	0.978982i	$0.434624\pi$
$968$	0.765776	−	4.34293i	0.0246130	−	0.139587i
$969$	−45.2886	−	1.84543i	−1.45488	−	0.0592836i
$970$	10.9357	−	9.17618i	0.351126	−	0.294629i
$971$	51.2642			1.64515			0.822573	−	0.568659i	$-0.192538\pi$
$971$	51.2642			1.64515			0.822573	+	0.568659i	$0.192538\pi$
$972$	5.75544	−	14.4871i	0.184606	−	0.464673i
$973$	−5.33380			−0.170994
$974$	−0.901254	+	0.756242i	−0.0288780	+	0.0242315i
$975$	−3.07538	−	0.125316i	−0.0984909	−	0.00401331i
$976$	0.275687	−	1.56350i	0.00882453	−	0.0500464i
$977$	5.59087	−	2.03491i	0.178868	−	0.0651026i	−0.251034	−	0.967978i	$-0.580770\pi$
$977$	5.59087	−	2.03491i	0.178868	−	0.0651026i	0.429902	+	0.902876i	$0.358548\pi$
$978$	14.5486	−	11.2309i	0.465212	−	0.359124i
$979$	1.39791	+	7.92795i	0.0446774	+	0.253378i
$980$	−0.488460	−	0.846038i	−0.0156033	−	0.0270257i
$981$	−29.9674	−	2.44629i	−0.956785	−	0.0781040i
$982$	12.1913	−	21.1160i	0.389040	−	0.673837i
$983$	27.3903	+	9.96924i	0.873614	+	0.317969i	0.739630	−	0.673014i	$-0.235001\pi$
$983$	27.3903	+	9.96924i	0.873614	+	0.317969i	0.133984	+	0.990983i	$0.457223\pi$
$984$	0.399632	−	1.82776i	0.0127398	−	0.0582667i
$985$	14.9532	+	12.5472i	0.476449	+	0.399788i
$986$	11.9533	+	10.0300i	0.380671	+	0.319421i
$987$	1.31510	−	0.418856i	0.0418600	−	0.0133323i
$988$	−3.07511	−	1.11925i	−0.0978323	−	0.0356081i
$989$	27.0880	−	46.9178i	0.861349	−	1.49190i
$990$	−9.38568	+	6.65360i	−0.298297	+	0.211465i
$991$	17.3065	+	29.9758i	0.549760	+	0.952212i	0.998291	+	0.0584449i	$0.0186142\pi$
$991$	17.3065	+	29.9758i	0.549760	+	0.952212i	−0.448531	+	0.893768i	$0.648052\pi$
$992$	−0.888920	−	5.04131i	−0.0282232	−	0.160062i
$993$	4.22837	+	31.4116i	0.134183	+	0.996817i
$994$	10.6325	−	3.86990i	0.337242	−	0.122746i
$995$	1.98097	−	11.2346i	0.0628008	−	0.356161i
$996$	−6.46089	−	12.3236i	−0.204721	−	0.390489i
$997$	3.89809	−	3.27089i	0.123454	−	0.103590i	−0.578971	−	0.815348i	$-0.696545\pi$
$997$	3.89809	−	3.27089i	0.123454	−	0.103590i	0.702424	+	0.711758i	$0.252101\pi$
$998$	−21.5202			−0.681209
$999$	−25.7004	+	34.1053i	−0.813123	+	1.07904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.d.211.5	yes	30
27.16	even	9	inner	378.2.u.d.43.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.d.43.5	✓	30	27.16	even	9	inner
378.2.u.d.211.5	yes	30	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)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.73061 + 0.0705192i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.918005 + 0.334126i) q^{5} +(1.37106 - 1.05840i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99005 + 0.244083i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.73061 + 0.0705192i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.918005 + 0.334126i) q^{5} +(1.37106 - 1.05840i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99005 + 0.244083i) q^{9} +(-0.488460 + 0.846038i) q^{10} +(3.68881 + 1.34262i) q^{11} +(0.369966 - 1.69208i) q^{12} +(0.336485 + 0.282345i) q^{13} +(-0.766044 - 0.642788i) q^{14} +(-1.61227 + 0.513507i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.75629 - 3.04198i) q^{17} +(2.44741 - 1.73499i) q^{18} +(-3.72506 - 6.45199i) q^{19} +(0.169640 + 0.962079i) q^{20} +(-0.231070 - 1.71657i) q^{21} +(3.68881 - 1.34262i) q^{22} +(-0.806925 + 4.57630i) q^{23} +(-0.804236 - 1.53402i) q^{24} +(-3.09913 + 2.60048i) q^{25} +0.439250 q^{26} +(5.15742 + 0.633270i) q^{27} -1.00000 q^{28} +(-3.40300 + 2.85546i) q^{29} +(-0.904998 + 1.42972i) q^{30} +(-0.888920 + 5.04131i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(6.28923 + 2.58368i) q^{33} +(-0.609953 - 3.45921i) q^{34} +(0.488460 + 0.846038i) q^{35} +(0.759593 - 2.90224i) q^{36} +(-4.10925 + 7.11742i) q^{37} +(-7.00082 - 2.54809i) q^{38} +(0.562416 + 0.512358i) q^{39} +(0.748364 + 0.627952i) q^{40} +(0.827470 + 0.694329i) q^{41} +(-1.28040 - 1.16644i) q^{42} +(-10.9554 - 3.98746i) q^{43} +(1.96277 - 3.39962i) q^{44} +(-2.82644 + 0.774986i) q^{45} +(2.32345 + 4.02433i) q^{46} +(0.138372 + 0.784746i) q^{47} +(-1.60213 - 0.658171i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(-0.702516 + 3.98416i) q^{50} +(3.25398 - 5.14065i) q^{51} +(0.336485 - 0.282345i) q^{52} +8.30175 q^{53} +(4.35787 - 2.83001i) q^{54} -3.83495 q^{55} +(-0.766044 + 0.642788i) q^{56} +(-5.99165 - 11.4286i) q^{57} +(-0.771398 + 4.37482i) q^{58} +(0.398471 - 0.145031i) q^{59} +(0.225737 + 1.67695i) q^{60} +(0.275687 + 1.56350i) q^{61} +(2.55954 + 4.43326i) q^{62} +(-0.278842 - 2.98701i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.403234 - 0.146765i) q^{65} +(6.47859 - 2.06342i) q^{66} +(5.61378 + 4.71052i) q^{67} +(-2.69079 - 2.25784i) q^{68} +(-1.71919 + 7.86291i) q^{69} +(0.918005 + 0.334126i) q^{70} +(-5.65742 + 9.79894i) q^{71} +(-1.28364 - 2.71150i) q^{72} +(-7.18605 - 12.4466i) q^{73} +(1.42713 + 8.09363i) q^{74} +(-5.54678 + 4.28188i) q^{75} +(-7.00082 + 2.54809i) q^{76} +(0.681664 - 3.86591i) q^{77} +(0.760173 + 0.0309756i) q^{78} +(8.48959 - 7.12361i) q^{79} +0.976920 q^{80} +(8.88085 + 1.45964i) q^{81} +1.08018 q^{82} +(6.15407 - 5.16388i) q^{83} +(-1.73061 - 0.0705192i) q^{84} +(-0.595875 + 3.37938i) q^{85} +(-10.9554 + 3.98746i) q^{86} +(-6.09065 + 4.70172i) q^{87} +(-0.681664 - 3.86591i) q^{88} +(1.02537 + 1.77599i) q^{89} +(-1.66703 + 2.41047i) q^{90} +(0.219625 - 0.380402i) q^{91} +(4.36666 + 1.58933i) q^{92} +(-1.89389 + 8.66189i) q^{93} +(0.610424 + 0.512207i) q^{94} +(5.57540 + 4.67832i) q^{95} +(-1.65036 + 0.525639i) q^{96} +(-13.7316 - 4.99789i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(10.7020 + 4.91487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9	\( 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 3 q^{12} - 9 q^{13} + 12 q^{15} - 12 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} + 9 q^{22} - 12 q^{23} - 3 q^{24} + 21 q^{25} + 18 q^{26} + 3 q^{27} - 30 q^{28} - 30 q^{29} - 15 q^{30} + 18 q^{31} + 9 q^{33} + 12 q^{34} + 3 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{38} + 72 q^{39} + 3 q^{40} + 36 q^{41} - 3 q^{42} - 9 q^{43} - 3 q^{44} - 48 q^{45} - 15 q^{46} + 3 q^{48} + 3 q^{50} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} + 66 q^{55} - 51 q^{57} - 3 q^{58} - 48 q^{59} + 24 q^{60} + 57 q^{61} - 18 q^{62} - 15 q^{63} - 15 q^{64} + 24 q^{65} + 54 q^{66} + 6 q^{67} - 15 q^{68} - 48 q^{69} - 3 q^{70} - 24 q^{71} - 6 q^{72} - 36 q^{73} - 48 q^{74} - 129 q^{75} - 3 q^{76} + 9 q^{77} + 24 q^{78} - 21 q^{79} + 6 q^{80} + 27 q^{81} - 15 q^{83} + 3 q^{84} - 72 q^{85} - 9 q^{86} + 42 q^{87} - 9 q^{88} - 30 q^{89} - 30 q^{90} + 9 q^{91} + 6 q^{92} + 111 q^{93} - 45 q^{94} + 81 q^{95} - 6 q^{96} - 15 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 3 * q^12 - 9 * q^13 + 12 * q^15 - 12 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 + 9 * q^22 - 12 * q^23 - 3 * q^24 + 21 * q^25 + 18 * q^26 + 3 * q^27 - 30 * q^28 - 30 * q^29 - 15 * q^30 + 18 * q^31 + 9 * q^33 + 12 * q^34 + 3 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^38 + 72 * q^39 + 3 * q^40 + 36 * q^41 - 3 * q^42 - 9 * q^43 - 3 * q^44 - 48 * q^45 - 15 * q^46 + 3 * q^48 + 3 * q^50 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 + 66 * q^55 - 51 * q^57 - 3 * q^58 - 48 * q^59 + 24 * q^60 + 57 * q^61 - 18 * q^62 - 15 * q^63 - 15 * q^64 + 24 * q^65 + 54 * q^66 + 6 * q^67 - 15 * q^68 - 48 * q^69 - 3 * q^70 - 24 * q^71 - 6 * q^72 - 36 * q^73 - 48 * q^74 - 129 * q^75 - 3 * q^76 + 9 * q^77 + 24 * q^78 - 21 * q^79 + 6 * q^80 + 27 * q^81 - 15 * q^83 + 3 * q^84 - 72 * q^85 - 9 * q^86 + 42 * q^87 - 9 * q^88 - 30 * q^89 - 30 * q^90 + 9 * q^91 + 6 * q^92 + 111 * q^93 - 45 * q^94 + 81 * q^95 - 6 * q^96 - 15 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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