LMFDB - Embedded newform 378.2.u.d.169.1

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			169.1
Character	$\chi$	$=$	378.169
Dual form			378.2.u.d.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-1.73005 - 0.0833302i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.111050 + 0.629795i) q^{5} +(1.65421 - 0.513405i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.98611 + 0.288330i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.73005 - 0.0833302i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.111050 + 0.629795i) q^{5} +(1.65421 - 0.513405i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.98611 + 0.288330i) q^{9} +(-0.319755 - 0.553832i) q^{10} +(0.0504445 - 0.286085i) q^{11} +(-1.37886 + 1.04822i) q^{12} +(-4.81453 - 1.75235i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-0.139640 - 1.09883i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.78750 + 4.82810i) q^{17} +(-2.90464 + 0.750369i) q^{18} +(3.87633 - 6.71400i) q^{19} +(0.489893 + 0.411069i) q^{20} +(1.27173 + 1.17589i) q^{21} +(0.0504445 + 0.286085i) q^{22} +(3.72896 - 3.12897i) q^{23} +(0.937189 - 1.45660i) q^{24} +(4.31415 - 1.57022i) q^{25} +5.12351 q^{26} +(-5.14208 - 0.747657i) q^{27} -1.00000 q^{28} +(4.43308 - 1.61351i) q^{29} +(0.507040 + 0.984800i) q^{30} +(5.53831 - 4.64720i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.111111 + 0.490736i) q^{33} +(-4.27070 - 3.58354i) q^{34} +(0.319755 - 0.553832i) q^{35} +(2.47283 - 1.69856i) q^{36} +(0.949111 + 1.64391i) q^{37} +(-1.34624 + 7.63488i) q^{38} +(8.18333 + 3.43283i) q^{39} +(-0.600943 - 0.218725i) q^{40} +(-7.68083 - 2.79559i) q^{41} +(-1.59721 - 0.670015i) q^{42} +(0.947438 - 5.37319i) q^{43} +(-0.145249 - 0.251579i) q^{44} +(0.150018 + 1.91266i) q^{45} +(-2.43391 + 4.21565i) q^{46} +(4.88703 + 4.10071i) q^{47} +(-0.382483 + 1.68929i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-3.51693 + 2.95105i) q^{50} +(-4.42018 - 8.58511i) q^{51} +(-4.81453 + 1.75235i) q^{52} +8.29396 q^{53} +(5.08769 - 1.05613i) q^{54} +0.185777 q^{55} +(0.939693 - 0.342020i) q^{56} +(-7.26570 + 11.2925i) q^{57} +(-3.61388 + 3.03241i) q^{58} +(-1.86840 - 10.5962i) q^{59} +(-0.813283 - 0.751991i) q^{60} +(3.92189 + 3.29085i) q^{61} +(-3.61488 + 6.26115i) q^{62} +(-2.10216 - 2.14031i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.568965 - 3.22676i) q^{65} +(-0.0634317 - 0.499144i) q^{66} +(-7.99409 - 2.90961i) q^{67} +(5.23879 + 1.90676i) q^{68} +(-6.71201 + 5.10252i) q^{69} +(-0.111050 + 0.629795i) q^{70} +(1.99996 + 3.46404i) q^{71} +(-1.74276 + 2.44188i) q^{72} +(-1.00849 + 1.74676i) q^{73} +(-1.45412 - 1.22015i) q^{74} +(-7.59453 + 2.35706i) q^{75} +(-1.34624 - 7.63488i) q^{76} +(-0.222535 + 0.186729i) q^{77} +(-8.86391 - 0.426944i) q^{78} +(-9.76214 + 3.55313i) q^{79} +0.639510 q^{80} +(8.83373 + 1.72197i) q^{81} +8.17377 q^{82} +(-9.78208 + 3.56039i) q^{83} +(1.73005 + 0.0833302i) q^{84} +(-2.73116 + 2.29171i) q^{85} +(0.947438 + 5.37319i) q^{86} +(-7.80388 + 2.42203i) q^{87} +(0.222535 + 0.186729i) q^{88} +(-8.78273 + 15.2121i) q^{89} +(-0.795138 - 1.74600i) q^{90} +(2.56176 + 4.43709i) q^{91} +(0.845287 - 4.79386i) q^{92} +(-9.96878 + 7.57835i) q^{93} +(-5.99483 - 2.18194i) q^{94} +(4.65891 + 1.69570i) q^{95} +(-0.218355 - 1.71823i) q^{96} +(2.49065 - 14.1252i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(0.233120 - 0.839737i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	−1.73005	−	0.0833302i	−0.998842	−	0.0481107i
$3$	−1.73005	−	0.0833302i	−0.998842	−	0.0481107i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.111050	+	0.629795i	0.0496630	+	0.281653i	0.999518	−	0.0310372i	$-0.00988103\pi$
$5$	0.111050	+	0.629795i	0.0496630	+	0.281653i	−0.949855	+	0.312690i	$0.898770\pi$
$6$	1.65421	−	0.513405i	0.675329	−	0.209597i
$7$	−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
$9$	2.98611	+	0.288330i	0.995371	+	0.0961100i
$10$	−0.319755	−	0.553832i	−0.101115	−	0.175137i
$11$	0.0504445	−	0.286085i	0.0152096	−	0.0862579i	−0.976258	−	0.216611i	$-0.930500\pi$
$11$	0.0504445	−	0.286085i	0.0152096	−	0.0862579i	0.991468	+	0.130353i	$0.0416109\pi$
$12$	−1.37886	+	1.04822i	−0.398041	+	0.302594i
$13$	−4.81453	−	1.75235i	−1.33531	−	0.486013i	−0.426978	−	0.904262i	$-0.640422\pi$
$13$	−4.81453	−	1.75235i	−1.33531	−	0.486013i	−0.908332	+	0.418249i	$0.862644\pi$
$14$	0.939693	+	0.342020i	0.251143	+	0.0914087i
$15$	−0.139640	−	1.09883i	−0.0360550	−	0.283716i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	2.78750	+	4.82810i	0.676069	+	1.17099i	0.976155	+	0.217073i	$0.0696511\pi$
$17$	2.78750	+	4.82810i	0.676069	+	1.17099i	−0.300087	+	0.953912i	$0.597016\pi$
$18$	−2.90464	+	0.750369i	−0.684631	+	0.176864i
$19$	3.87633	−	6.71400i	0.889291	−	1.54030i	0.0485761	−	0.998819i	$-0.484532\pi$
$19$	3.87633	−	6.71400i	0.889291	−	1.54030i	0.840715	−	0.541478i	$-0.182135\pi$
$20$	0.489893	+	0.411069i	0.109543	+	0.0919179i
$21$	1.27173	+	1.17589i	0.277514	+	0.256599i
$22$	0.0504445	+	0.286085i	0.0107548	+	0.0609935i
$23$	3.72896	−	3.12897i	0.777542	−	0.652435i	−0.165086	−	0.986279i	$-0.552790\pi$
$23$	3.72896	−	3.12897i	0.777542	−	0.652435i	0.942628	+	0.333844i	$0.108346\pi$
$24$	0.937189	−	1.45660i	0.191303	−	0.297327i
$25$	4.31415	−	1.57022i	0.862831	−	0.314045i
$26$	5.12351			1.00480
$27$	−5.14208	−	0.747657i	−0.989594	−	0.143887i
$28$	−1.00000			−0.188982
$29$	4.43308	−	1.61351i	0.823202	−	0.299621i	0.104137	−	0.994563i	$-0.466792\pi$
$29$	4.43308	−	1.61351i	0.823202	−	0.299621i	0.719066	+	0.694942i	$0.244570\pi$
$30$	0.507040	+	0.984800i	0.0925724	+	0.179799i
$31$	5.53831	−	4.64720i	0.994710	−	0.834661i	0.00846746	−	0.999964i	$-0.497305\pi$
$31$	5.53831	−	4.64720i	0.994710	−	0.834661i	0.986243	+	0.165303i	$0.0528602\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.111111	+	0.490736i	−0.0193419	+	0.0854262i
$34$	−4.27070	−	3.58354i	−0.732419	−	0.614573i
$35$	0.319755	−	0.553832i	0.0540485	−	0.0936147i
$36$	2.47283	−	1.69856i	0.412138	−	0.283094i
$37$	0.949111	+	1.64391i	0.156033	+	0.270257i	0.933435	−	0.358748i	$-0.116796\pi$
$37$	0.949111	+	1.64391i	0.156033	+	0.270257i	−0.777402	+	0.629004i	$0.783463\pi$
$38$	−1.34624	+	7.63488i	−0.218388	+	1.23854i
$39$	8.18333	+	3.43283i	1.31038	+	0.549693i
$40$	−0.600943	−	0.218725i	−0.0950175	−	0.0345835i
$41$	−7.68083	−	2.79559i	−1.19954	−	0.436598i	−0.336479	−	0.941691i	$-0.609236\pi$
$41$	−7.68083	−	2.79559i	−1.19954	−	0.436598i	−0.863065	+	0.505093i	$0.831458\pi$
$42$	−1.59721	−	0.670015i	−0.246455	−	0.103386i
$43$	0.947438	−	5.37319i	0.144483	−	0.819403i	−0.823298	−	0.567609i	$-0.807868\pi$
$43$	0.947438	−	5.37319i	0.144483	−	0.819403i	0.967781	−	0.251794i	$-0.0810205\pi$
$44$	−0.145249	−	0.251579i	−0.0218971	−	0.0379270i
$45$	0.150018	+	1.91266i	0.0223634	+	0.285122i
$46$	−2.43391	+	4.21565i	−0.358860	+	0.621563i
$47$	4.88703	+	4.10071i	0.712847	+	0.598149i	0.925396	−	0.379001i	$-0.123732\pi$
$47$	4.88703	+	4.10071i	0.712847	+	0.598149i	−0.212550	+	0.977150i	$0.568177\pi$
$48$	−0.382483	+	1.68929i	−0.0552067	+	0.243828i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	−3.51693	+	2.95105i	−0.497369	+	0.417342i
$51$	−4.42018	−	8.58511i	−0.618949	−	1.20216i
$52$	−4.81453	+	1.75235i	−0.667655	+	0.243007i
$53$	8.29396			1.13926			0.569632	−	0.821900i	$-0.307086\pi$
$53$	8.29396			1.13926			0.569632	+	0.821900i	$0.307086\pi$
$54$	5.08769	−	1.05613i	0.692347	−	0.143721i
$55$	0.185777			0.0250501
$56$	0.939693	−	0.342020i	0.125572	−	0.0457044i
$57$	−7.26570	+	11.2925i	−0.962366	+	1.49573i
$58$	−3.61388	+	3.03241i	−0.474526	+	0.398174i
$59$	−1.86840	−	10.5962i	−0.243244	−	1.37951i	−0.824535	−	0.565811i	$-0.808563\pi$
$59$	−1.86840	−	10.5962i	−0.243244	−	1.37951i	0.581290	−	0.813696i	$-0.302548\pi$
$60$	−0.813283	−	0.751991i	−0.104994	−	0.0970817i
$61$	3.92189	+	3.29085i	0.502146	+	0.421351i	0.858355	−	0.513056i	$-0.171487\pi$
$61$	3.92189	+	3.29085i	0.502146	+	0.421351i	−0.356209	+	0.934406i	$0.615931\pi$
$62$	−3.61488	+	6.26115i	−0.459090	+	0.795167i
$63$	−2.10216	−	2.14031i	−0.264847	−	0.269654i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.568965	−	3.22676i	0.0705715	−	0.400231i
$66$	−0.0634317	−	0.499144i	−0.00780791	−	0.0614403i
$67$	−7.99409	−	2.90961i	−0.976633	−	0.355465i	−0.196103	−	0.980583i	$-0.562829\pi$
$67$	−7.99409	−	2.90961i	−0.976633	−	0.355465i	−0.780530	+	0.625118i	$0.785051\pi$
$68$	5.23879	+	1.90676i	0.635297	+	0.231229i
$69$	−6.71201	+	5.10252i	−0.808031	+	0.614271i
$70$	−0.111050	+	0.629795i	−0.0132730	+	0.0752749i
$71$	1.99996	+	3.46404i	0.237352	+	0.411105i	0.959954	−	0.280159i	$-0.0903872\pi$
$71$	1.99996	+	3.46404i	0.237352	+	0.411105i	−0.722602	+	0.691265i	$0.757054\pi$
$72$	−1.74276	+	2.44188i	−0.205386	+	0.287779i
$73$	−1.00849	+	1.74676i	−0.118035	+	0.204442i	−0.918989	−	0.394283i	$-0.870993\pi$
$73$	−1.00849	+	1.74676i	−0.118035	+	0.204442i	0.800954	+	0.598726i	$0.204326\pi$
$74$	−1.45412	−	1.22015i	−0.169038	−	0.141840i
$75$	−7.59453	+	2.35706i	−0.876941	+	0.272170i
$76$	−1.34624	−	7.63488i	−0.154424	−	0.875781i
$77$	−0.222535	+	0.186729i	−0.0253602	+	0.0212797i
$78$	−8.86391	−	0.426944i	−1.00364	−	0.0483418i
$79$	−9.76214	+	3.55313i	−1.09833	+	0.399758i	−0.826699	−	0.562645i	$-0.809784\pi$
$79$	−9.76214	+	3.55313i	−1.09833	+	0.399758i	−0.271627	+	0.962403i	$0.587562\pi$
$80$	0.639510			0.0714994
$81$	8.83373	+	1.72197i	0.981526	+	0.191330i
$82$	8.17377			0.902642
$83$	−9.78208	+	3.56039i	−1.07372	+	0.390803i	−0.817568	−	0.575832i	$-0.804678\pi$
$83$	−9.78208	+	3.56039i	−1.07372	+	0.390803i	−0.256155	+	0.966636i	$0.582456\pi$
$84$	1.73005	+	0.0833302i	0.188763	+	0.00909207i
$85$	−2.73116	+	2.29171i	−0.296236	+	0.248571i
$86$	0.947438	+	5.37319i	0.102165	+	0.579406i
$87$	−7.80388	+	2.42203i	−0.836664	+	0.259669i
$88$	0.222535	+	0.186729i	0.0237223	+	0.0199053i
$89$	−8.78273	+	15.2121i	−0.930967	+	1.61248i	−0.149296	+	0.988793i	$0.547701\pi$
$89$	−8.78273	+	15.2121i	−0.930967	+	1.61248i	−0.781672	+	0.623690i	$0.785633\pi$
$90$	−0.795138	−	1.74600i	−0.0838149	−	0.184045i
$91$	2.56176	+	4.43709i	0.268545	+	0.465134i
$92$	0.845287	−	4.79386i	0.0881272	−	0.499794i
$93$	−9.96878	+	7.57835i	−1.03371	+	0.785838i
$94$	−5.99483	−	2.18194i	−0.618320	−	0.225050i
$95$	4.65891	+	1.69570i	0.477994	+	0.173976i
$96$	−0.218355	−	1.71823i	−0.0222858	−	0.175366i
$97$	2.49065	−	14.1252i	0.252887	−	1.43419i	−0.548552	−	0.836116i	$-0.684821\pi$
$97$	2.49065	−	14.1252i	0.252887	−	1.43419i	0.801439	−	0.598077i	$-0.204068\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	0.233120	−	0.839737i	0.0234294	−	0.0843968i
$100$	2.29551	−	3.97595i	0.229551	−	0.397595i
$101$	−8.80536	−	7.38858i	−0.876166	−	0.735191i	0.0892209	−	0.996012i	$-0.471562\pi$
$101$	−8.80536	−	7.38858i	−0.876166	−	0.735191i	−0.965387	+	0.260821i	$0.916007\pi$
$102$	7.08989	+	6.55557i	0.702004	+	0.649098i
$103$	0.928264	+	5.26445i	0.0914646	+	0.518721i	0.995774	+	0.0918428i	$0.0292757\pi$
$103$	0.928264	+	5.26445i	0.0914646	+	0.518721i	−0.904309	+	0.426879i	$0.859613\pi$
$104$	3.92484	−	3.29333i	0.384862	−	0.322938i
$105$	−0.599342	+	0.931510i	−0.0584898	+	0.0909060i
$106$	−7.79378	+	2.83670i	−0.756999	+	0.275525i
$107$	0.480399			0.0464420			0.0232210	−	0.999730i	$-0.492608\pi$
$107$	0.480399			0.0464420			0.0232210	+	0.999730i	$0.492608\pi$
$108$	−4.41965	+	2.73253i	−0.425281	+	0.262938i
$109$	16.2414			1.55564			0.777821	−	0.628486i	$-0.216325\pi$
$109$	16.2414			1.55564			0.777821	+	0.628486i	$0.216325\pi$
$110$	−0.174573	+	0.0635394i	−0.0166449	+	0.00605824i
$111$	−1.50502	−	2.92313i	−0.142850	−	0.277451i
$112$	−0.766044	+	0.642788i	−0.0723844	+	0.0607377i
$113$	−2.24774	−	12.7476i	−0.211450	−	1.19919i	−0.886962	−	0.461843i	$-0.847188\pi$
$113$	−2.24774	−	12.7476i	−0.211450	−	1.19919i	0.675512	−	0.737349i	$-0.263923\pi$
$114$	2.96526	−	13.0965i	0.277722	−	1.22660i
$115$	2.38471	+	2.00101i	0.222375	+	0.186595i
$116$	2.35879	−	4.08555i	0.219008	−	0.379334i
$117$	−13.8715	−	6.62087i	−1.28242	−	0.612100i
$118$	5.37983	+	9.31814i	0.495254	+	0.857804i
$119$	0.968089	−	5.49031i	0.0887446	−	0.503296i
$120$	1.02143	+	0.428482i	0.0932436	+	0.0391148i
$121$	10.2573	+	3.73336i	0.932484	+	0.339396i
$122$	−4.81091	−	1.75103i	−0.435559	−	0.158530i
$123$	13.0552	+	5.47655i	1.17715	+	0.493804i
$124$	1.25543	−	7.11992i	0.112741	−	0.639387i
$125$	3.06678	+	5.31182i	0.274301	+	0.475104i
$126$	2.70741	+	1.29225i	0.241196	+	0.115123i
$127$	2.11467	−	3.66271i	0.187646	−	0.325013i	−0.756819	−	0.653625i	$-0.773247\pi$
$127$	2.11467	−	3.66271i	0.187646	−	0.325013i	0.944465	+	0.328612i	$0.106581\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−2.08686	+	9.21691i	−0.183738	+	0.811503i
$130$	0.568965	+	3.22676i	0.0499016	+	0.283006i
$131$	11.8962	−	9.98213i	1.03938	−	0.872143i	0.0474421	−	0.998874i	$-0.484893\pi$
$131$	11.8962	−	9.98213i	1.03938	−	0.872143i	0.991937	+	0.126731i	$0.0404486\pi$
$132$	0.230323	+	0.447347i	0.0200471	+	0.0389365i
$133$	−7.28512	+	2.65157i	−0.631700	+	0.229920i
$134$	8.50713			0.734904
$135$	−0.100157	−	3.32148i	−0.00862010	−	0.285868i
$136$	−5.57500			−0.478053
$137$	−6.00262	+	2.18477i	−0.512838	+	0.186658i	−0.585459	−	0.810702i	$-0.699086\pi$
$137$	−6.00262	+	2.18477i	−0.512838	+	0.186658i	0.0726212	+	0.997360i	$0.476864\pi$
$138$	4.56206	−	7.09044i	0.388348	−	0.603579i
$139$	−9.05312	+	7.59647i	−0.767875	+	0.644324i	−0.940164	−	0.340723i	$-0.889328\pi$
$139$	−9.05312	+	7.59647i	−0.767875	+	0.644324i	0.172288	+	0.985047i	$0.444884\pi$
$140$	−0.111050	−	0.629795i	−0.00938542	−	0.0532274i
$141$	−8.11307	−	7.50164i	−0.683244	−	0.631752i
$142$	−3.06412	−	2.57110i	−0.257135	−	0.215762i
$143$	−0.744186	+	1.28897i	−0.0622320	+	0.107789i
$144$	0.802483	−	2.89068i	0.0668735	−	0.240890i
$145$	1.50847	+	2.61275i	0.125272	+	0.216977i
$146$	0.350245	−	1.98634i	0.0289865	−	0.164391i
$147$	−0.218355	−	1.71823i	−0.0180096	−	0.141717i
$148$	1.78375	+	0.649230i	0.146623	+	0.0533664i
$149$	−3.33889	−	1.21526i	−0.273532	−	0.0995576i	0.201612	−	0.979465i	$-0.435382\pi$
$149$	−3.33889	−	1.21526i	−0.273532	−	0.0995576i	−0.475144	+	0.879908i	$0.657604\pi$
$150$	6.33036	−	4.81239i	0.516872	−	0.392930i
$151$	−1.04034	+	5.90006i	−0.0846616	+	0.480140i	0.912768	+	0.408479i	$0.133941\pi$
$151$	−1.04034	+	5.90006i	−0.0846616	+	0.480140i	−0.997429	+	0.0716603i	$0.977170\pi$
$152$	3.87633	+	6.71400i	0.314412	+	0.544577i
$153$	6.93171	+	15.2210i	0.560396	+	1.23054i
$154$	0.145249	−	0.251579i	0.0117045	−	0.0202728i
$155$	3.54181	+	2.97193i	0.284485	+	0.238711i
$156$	8.47538	−	2.63044i	0.678573	−	0.210604i
$157$	2.30456	+	13.0698i	0.183924	+	1.04308i	0.927330	+	0.374244i	$0.122098\pi$
$157$	2.30456	+	13.0698i	0.183924	+	1.04308i	−0.743406	+	0.668840i	$0.766791\pi$
$158$	7.95817	−	6.67769i	0.633118	−	0.531249i
$159$	−14.3489	−	0.691138i	−1.13794	−	0.0548108i
$160$	−0.600943	+	0.218725i	−0.0475087	+	0.0172918i
$161$	−4.86781			−0.383637
$162$	−8.88994	+	1.40319i	−0.698460	+	0.110245i
$163$	11.4886			0.899854			0.449927	−	0.893065i	$-0.351450\pi$
$163$	11.4886			0.899854			0.449927	+	0.893065i	$0.351450\pi$
$164$	−7.68083	+	2.79559i	−0.599772	+	0.218299i
$165$	−0.321402	−	0.0154808i	−0.0250211	−	0.00120518i
$166$	7.97443	−	6.69134i	0.618936	−	0.519349i
$167$	0.386782	+	2.19355i	0.0299301	+	0.169742i	0.996109	−	0.0881311i	$-0.0280894\pi$
$167$	0.386782	+	2.19355i	0.0299301	+	0.169742i	−0.966179	+	0.257873i	$0.916978\pi$
$168$	−1.65421	+	0.513405i	−0.127625	+	0.0396101i
$169$	10.1504	+	8.51719i	0.780800	+	0.655169i
$170$	1.78264	−	3.08762i	0.136722	−	0.236809i
$171$	13.5110	−	18.9311i	1.03321	−	1.44770i
$172$	−2.72804	−	4.72510i	−0.208011	−	0.360286i
$173$	0.0859092	−	0.487215i	0.00653156	−	0.0370423i	−0.981368	−	0.192139i	$-0.938458\pi$
$173$	0.0859092	−	0.487215i	0.00653156	−	0.0370423i	0.987899	+	0.155096i	$0.0495688\pi$
$174$	6.50487	−	4.94505i	0.493133	−	0.374884i
$175$	−4.31415	−	1.57022i	−0.326119	−	0.118698i
$176$	−0.272979	−	0.0993563i	−0.0205766	−	0.00748926i
$177$	2.34943	+	18.4876i	0.176594	+	1.38961i
$178$	3.05021	−	17.2986i	0.228623	−	1.29658i
$179$	−1.64113	−	2.84252i	−0.122664	−	0.212460i	0.798154	−	0.602454i	$-0.205810\pi$
$179$	−1.64113	−	2.84252i	−0.122664	−	0.212460i	−0.920817	+	0.389994i	$0.872477\pi$
$180$	1.34435	+	1.36875i	0.100202	+	0.102021i
$181$	7.97787	−	13.8181i	0.592990	−	1.02709i	−0.400837	−	0.916149i	$-0.631281\pi$
$181$	7.97787	−	13.8181i	0.592990	−	1.02709i	0.993827	−	0.110940i	$-0.0353860\pi$
$182$	−3.92484	−	3.29333i	−0.290928	−	0.244118i
$183$	−6.51081	−	6.02014i	−0.481293	−	0.445021i
$184$	0.845287	+	4.79386i	0.0623154	+	0.353408i
$185$	−0.929926	+	0.780301i	−0.0683695	+	0.0573689i
$186$	6.77564	−	10.5308i	0.496814	−	0.772159i
$187$	1.52186	−	0.553912i	0.111289	−	0.0405060i
$188$	6.37957			0.465278
$189$	3.45848	+	3.87801i	0.251567	+	0.282083i
$190$	−4.95791			−0.359684
$191$	11.9764	−	4.35907i	0.866585	−	0.315411i	0.129801	−	0.991540i	$-0.458566\pi$
$191$	11.9764	−	4.35907i	0.866585	−	0.315411i	0.736783	+	0.676129i	$0.236344\pi$
$192$	0.792856	+	1.53993i	0.0572195	+	0.111135i
$193$	−6.52525	+	5.47533i	−0.469698	+	0.394123i	−0.846684	−	0.532096i	$-0.821405\pi$
$193$	−6.52525	+	5.47533i	−0.469698	+	0.394123i	0.376987	+	0.926219i	$0.376960\pi$
$194$	2.49065	+	14.1252i	0.178818	+	1.01413i
$195$	−1.25322	+	5.53503i	−0.0897451	+	0.396372i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	−2.83393	+	4.90851i	−0.201909	+	0.349717i	−0.949144	−	0.314844i	$-0.898048\pi$
$197$	−2.83393	+	4.90851i	−0.201909	+	0.349717i	0.747234	+	0.664561i	$0.231381\pi$
$198$	0.0681460	+	0.868827i	0.00484293	+	0.0617448i
$199$	7.57323	+	13.1172i	0.536852	+	0.929855i	0.999071	+	0.0430891i	$0.0137199\pi$
$199$	7.57323	+	13.1172i	0.536852	+	0.929855i	−0.462219	+	0.886766i	$0.652947\pi$
$200$	−0.797223	+	4.52128i	−0.0563722	+	0.319703i
$201$	13.5877	+	5.69990i	0.958400	+	0.402040i
$202$	10.8014	+	3.93138i	0.759982	+	0.276611i
$203$	−4.43308	−	1.61351i	−0.311141	−	0.113246i
$204$	−8.90445	−	3.73534i	−0.623436	−	0.261526i
$205$	0.907695	−	5.14780i	0.0633962	−	0.359538i
$206$	−2.67283	−	4.62948i	−0.186225	−	0.322551i
$207$	12.0373	−	8.26828i	0.836648	−	0.574685i
$208$	−2.56176	+	4.43709i	−0.177626	+	0.307657i
$209$	−1.72524	−	1.44764i	−0.119337	−	0.100136i
$210$	0.244602	−	1.08032i	0.0168792	−	0.0745491i
$211$	−1.31725	−	7.47048i	−0.0906830	−	0.514289i	−0.995985	−	0.0895204i	$-0.971467\pi$
$211$	−1.31725	−	7.47048i	−0.0906830	−	0.514289i	0.905302	−	0.424769i	$-0.139645\pi$
$212$	6.35355	−	5.33126i	0.436363	−	0.366152i
$213$	−3.17137	−	6.15960i	−0.217298	−	0.422049i
$214$	−0.451428	+	0.164306i	−0.0308590	+	0.0112317i
$215$	3.48922			0.237963
$216$	3.21853	−	4.07935i	0.218993	−	0.277564i
$217$	−7.22975			−0.490788
$218$	−15.2619	+	5.55488i	−1.03367	+	0.376224i
$219$	1.89029	−	2.93793i	0.127734	−	0.198527i
$220$	0.142313	−	0.119415i	0.00959475	−	0.00805096i
$221$	−4.96002	−	28.1297i	−0.333647	−	1.89221i
$222$	2.41402	+	2.23209i	0.162019	+	0.149808i
$223$	−8.79274	−	7.37799i	−0.588806	−	0.494067i	0.299020	−	0.954247i	$-0.403340\pi$
$223$	−8.79274	−	7.37799i	−0.588806	−	0.494067i	−0.887825	+	0.460180i	$0.847785\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	13.3353	−	3.44496i	0.889019	−	0.229664i
$226$	6.47212	+	11.2100i	0.430519	+	0.745681i
$227$	1.47481	−	8.36404i	0.0978863	−	0.555141i	−0.895938	−	0.444178i	$-0.853496\pi$
$227$	1.47481	−	8.36404i	0.0978863	−	0.555141i	0.993825	−	0.110962i	$-0.0353932\pi$
$228$	1.69283	+	13.3209i	0.112111	+	0.882196i
$229$	−6.87008	−	2.50051i	−0.453988	−	0.165238i	0.104897	−	0.994483i	$-0.466549\pi$
$229$	−6.87008	−	2.50051i	−0.453988	−	0.165238i	−0.558885	+	0.829245i	$0.688771\pi$
$230$	−2.92528	−	1.06471i	−0.192887	−	0.0702052i
$231$	0.400555	−	0.304505i	0.0263546	−	0.0200350i
$232$	−0.819200	+	4.64592i	−0.0537831	+	0.305019i
$233$	−12.3141	−	21.3287i	−0.806725	−	1.39729i	−0.915120	−	0.403181i	$-0.867904\pi$
$233$	−12.3141	−	21.3287i	−0.806725	−	1.39729i	0.108395	−	0.994108i	$-0.465429\pi$
$234$	15.2994	+	1.47726i	1.00015	+	0.0965717i
$235$	−2.03990	+	3.53321i	−0.133068	+	0.230481i
$236$	−8.24238	−	6.91618i	−0.536533	−	0.450205i
$237$	17.1850	−	5.33359i	1.11629	−	0.346454i
$238$	0.968089	+	5.49031i	0.0627519	+	0.355884i
$239$	−9.07755	+	7.61697i	−0.587178	+	0.492701i	−0.887296	−	0.461201i	$-0.847419\pi$
$239$	−9.07755	+	7.61697i	−0.587178	+	0.492701i	0.300117	+	0.953902i	$0.402974\pi$
$240$	−1.10638	−	0.0532905i	−0.0714166	−	0.00343989i
$241$	4.47068	−	1.62720i	0.287982	−	0.104817i	−0.193990	−	0.981004i	$-0.562143\pi$
$241$	4.47068	−	1.62720i	0.287982	−	0.104817i	0.481972	+	0.876187i	$0.339921\pi$
$242$	−10.9156			−0.701682
$243$	−15.1393	−	3.71521i	−0.971184	−	0.238331i
$244$	5.11966			0.327753
$245$	−0.600943	+	0.218725i	−0.0383929	+	0.0139739i
$246$	−14.1410	−	0.681122i	−0.901596	−	0.0434267i
$247$	−30.4280	+	25.5321i	−1.93608	+	1.62457i
$248$	1.25543	+	7.11992i	0.0797201	+	0.452115i
$249$	17.2201	−	5.34449i	1.09128	−	0.338693i
$250$	−4.69858	−	3.94258i	−0.297164	−	0.249350i
$251$	−9.01247	+	15.6101i	−0.568862	+	0.985298i	0.427817	+	0.903866i	$0.359283\pi$
$251$	−9.01247	+	15.6101i	−0.568862	+	0.985298i	−0.996679	+	0.0814328i	$0.974050\pi$
$252$	−2.98611	−	0.288330i	−0.188107	−	0.0181631i
$253$	−0.707046	−	1.22464i	−0.0444516	−	0.0769924i
$254$	−0.734417	+	4.16508i	−0.0460814	+	0.261341i
$255$	4.91600	−	3.73718i	0.307852	−	0.234031i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	15.6542	+	5.69768i	0.976485	+	0.355411i	0.780473	−	0.625190i	$-0.214979\pi$
$257$	15.6542	+	5.69768i	0.976485	+	0.355411i	0.196012	+	0.980601i	$0.437201\pi$
$258$	−1.19136	−	9.37481i	−0.0741709	−	0.583650i
$259$	0.329623	−	1.86938i	0.0204818	−	0.116158i
$260$	−1.63827	−	2.83757i	−0.101601	−	0.175978i
$261$	13.7029	−	3.53993i	0.848188	−	0.219116i
$262$	−7.76472	+	13.4489i	−0.479706	+	0.830875i
$263$	−6.56382	−	5.50770i	−0.404742	−	0.339619i	0.417581	−	0.908640i	$-0.362878\pi$
$263$	−6.56382	−	5.50770i	−0.404742	−	0.339619i	−0.822323	+	0.569021i	$0.807322\pi$
$264$	−0.369435	−	0.341593i	−0.0227371	−	0.0210236i
$265$	0.921043	+	5.22350i	0.0565792	+	0.320877i
$266$	5.93888	−	4.98331i	0.364136	−	0.305547i
$267$	16.4621	−	25.5858i	1.00747	−	1.56583i
$268$	−7.99409	+	2.90961i	−0.488316	+	0.177733i
$269$	0.571658			0.0348546			0.0174273	−	0.999848i	$-0.494452\pi$
$269$	0.571658			0.0348546			0.0174273	+	0.999848i	$0.494452\pi$
$270$	1.23013	+	3.08692i	0.0748634	+	0.187864i
$271$	22.3133			1.35544			0.677718	−	0.735322i	$-0.262969\pi$
$271$	22.3133			1.35544			0.677718	+	0.735322i	$0.262969\pi$
$272$	5.23879	−	1.90676i	0.317648	−	0.115615i
$273$	−4.06221	−	7.88984i	−0.245856	−	0.477515i
$274$	4.89338	−	4.10603i	0.295620	−	0.248054i
$275$	−0.231592	−	1.31342i	−0.0139655	−	0.0792024i
$276$	−1.86186	+	8.22315i	−0.112071	+	0.494976i
$277$	18.5761	+	15.5872i	1.11613	+	0.936544i	0.998402	−	0.0565019i	$-0.0179947\pi$
$277$	18.5761	+	15.5872i	1.11613	+	0.936544i	0.117727	+	0.993046i	$0.462439\pi$
$278$	5.90900	−	10.2347i	0.354398	−	0.613836i
$279$	17.8779	−	12.2802i	1.07032	−	0.735196i
$280$	0.319755	+	0.553832i	0.0191090	+	0.0330978i
$281$	−4.60026	+	26.0894i	−0.274428	+	1.55636i	0.466344	+	0.884604i	$0.345571\pi$
$281$	−4.60026	+	26.0894i	−0.274428	+	1.55636i	−0.740772	+	0.671757i	$0.765540\pi$
$282$	10.1895	+	4.27440i	0.606776	+	0.254537i
$283$	−17.3005	−	6.29688i	−1.02841	−	0.374311i	−0.227935	−	0.973676i	$-0.573197\pi$
$283$	−17.3005	−	6.29688i	−1.02841	−	0.374311i	−0.800475	+	0.599366i	$0.795419\pi$
$284$	3.75870	+	1.36805i	0.223038	+	0.0811791i
$285$	−7.91882	−	3.32187i	−0.469070	−	0.196771i
$286$	0.258453	−	1.46576i	0.0152827	−	0.0866722i
$287$	4.08688	+	7.07869i	0.241241	+	0.417842i
$288$	0.234583	+	2.99081i	0.0138230	+	0.176235i
$289$	−7.04034	+	12.1942i	−0.414138	+	0.717307i
$290$	−2.31111	−	1.93926i	−0.135713	−	0.113877i
$291$	−5.48599	+	24.2296i	−0.321594	+	1.42037i
$292$	0.350245	+	1.98634i	0.0204965	+	0.116242i
$293$	−13.2543	+	11.1217i	−0.774324	+	0.649735i	−0.941812	−	0.336139i	$-0.890879\pi$
$293$	−13.2543	+	11.1217i	−0.774324	+	0.649735i	0.167488	+	0.985874i	$0.446434\pi$
$294$	0.792856	+	1.53993i	0.0462403	+	0.0898104i
$295$	6.46594	−	2.35341i	0.376462	−	0.137021i
$296$	−1.89822			−0.110332
$297$	−0.473283	+	1.43336i	−0.0274627	+	0.0831718i
$298$	3.55317			0.205830
$299$	−23.4362	+	8.53009i	−1.35535	+	0.493308i
$300$	−4.30266	+	6.68728i	−0.248414	+	0.386090i
$301$	−4.17960	+	3.50710i	−0.240908	+	0.202146i
$302$	−1.04034	−	5.90006i	−0.0598648	−	0.339510i
$303$	14.6180	+	13.5163i	0.839781	+	0.776492i
$304$	−5.93888	−	4.98331i	−0.340618	−	0.285813i
$305$	−1.63704	+	2.83543i	−0.0937365	+	0.162356i
$306$	−11.7196	−	11.9322i	−0.669962	−	0.682121i
$307$	−5.49261	−	9.51348i	−0.313480	−	0.542963i	0.665633	−	0.746279i	$-0.268162\pi$
$307$	−5.49261	−	9.51348i	−0.313480	−	0.542963i	−0.979113	+	0.203316i	$0.934828\pi$
$308$	−0.0504445	+	0.286085i	−0.00287434	+	0.0163012i
$309$	−1.16725	−	9.18508i	−0.0664026	−	0.522521i
$310$	−4.34467	−	1.58133i	−0.246761	−	0.0898136i
$311$	−11.2095	−	4.07991i	−0.635630	−	0.231350i	0.00404978	−	0.999992i	$-0.498711\pi$
$311$	−11.2095	−	4.07991i	−0.635630	−	0.231350i	−0.639680	+	0.768641i	$0.720933\pi$
$312$	−7.06458	+	5.37055i	−0.399953	+	0.304048i
$313$	5.53095	−	31.3676i	0.312628	−	1.77300i	−0.272596	−	0.962129i	$-0.587882\pi$
$313$	5.53095	−	31.3676i	0.312628	−	1.77300i	0.585224	−	0.810872i	$-0.301007\pi$
$314$	−6.63572	−	11.4934i	−0.374475	−	0.648610i
$315$	1.11451	−	1.56161i	0.0627956	−	0.0879868i
$316$	−5.19432	+	8.99683i	−0.292204	+	0.506111i
$317$	−15.1170	−	12.6847i	−0.849057	−	0.712443i	0.110525	−	0.993873i	$-0.464747\pi$
$317$	−15.1170	−	12.6847i	−0.849057	−	0.712443i	−0.959582	+	0.281430i	$0.909191\pi$
$318$	13.7200	−	4.25817i	0.769378	−	0.238786i
$319$	−0.237976	−	1.34963i	−0.0133241	−	0.0755648i
$320$	0.489893	−	0.411069i	0.0273859	−	0.0229795i
$321$	−0.831113	−	0.0400318i	−0.0463882	−	0.00223436i
$322$	4.57425	−	1.66489i	0.254913	−	0.0927807i
$323$	43.2211			2.40489
$324$	7.87389	−	4.35911i	0.437439	−	0.242173i
$325$	−23.5222			−1.30478
$326$	−10.7957	+	3.92932i	−0.597920	+	0.217625i
$327$	−28.0983	−	1.35340i	−1.55384	−	0.0748431i
$328$	6.26147	−	5.25400i	0.345732	−	0.290103i
$329$	−1.10780	−	6.28265i	−0.0610750	−	0.346373i
$330$	0.307314	−	0.0953788i	0.0169171	−	0.00525043i
$331$	6.80762	+	5.71228i	0.374181	+	0.313975i	0.810413	−	0.585859i	$-0.199243\pi$
$331$	6.80762	+	5.71228i	0.374181	+	0.313975i	−0.436232	+	0.899834i	$0.643687\pi$
$332$	−5.20494	+	9.01522i	−0.285658	+	0.494774i
$333$	2.36016	+	5.18255i	0.129336	+	0.284002i
$334$	−1.11370	−	1.92898i	−0.0609387	−	0.105549i
$335$	0.944715	−	5.35775i	0.0516153	−	0.292725i
$336$	1.37886	−	1.04822i	0.0752227	−	0.0571849i
$337$	13.1086	+	4.77115i	0.714072	+	0.259901i	0.673407	−	0.739272i	$-0.264830\pi$
$337$	13.1086	+	4.77115i	0.714072	+	0.259901i	0.0406649	+	0.999173i	$0.487052\pi$
$338$	−12.4513	−	4.53190i	−0.677262	−	0.246503i
$339$	2.82644	+	22.2412i	0.153511	+	1.20798i
$340$	−0.619103	+	3.51111i	−0.0335756	+	0.190417i
$341$	−1.05012	−	1.81885i	−0.0568669	−	0.0984964i
$342$	−6.22137	+	22.4104i	−0.336413	+	1.21182i
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$	4.17960	+	3.50710i	0.225349	+	0.189090i
$345$	−3.95891	−	3.66055i	−0.213140	−	0.197078i
$346$	0.0859092	+	0.487215i	0.00461851	+	0.0261929i
$347$	−11.8977	+	9.98336i	−0.638702	+	0.535935i	−0.903619	−	0.428336i	$-0.859100\pi$
$347$	−11.8977	+	9.98336i	−0.638702	+	0.535935i	0.264917	+	0.964271i	$0.414655\pi$
$348$	−4.42127	+	6.87163i	−0.237005	+	0.368358i
$349$	−18.5960	+	6.76839i	−0.995421	+	0.362303i	−0.787817	−	0.615910i	$-0.788789\pi$
$349$	−18.5960	+	6.76839i	−0.995421	+	0.362303i	−0.207604	+	0.978213i	$0.566566\pi$
$350$	4.59103			0.245401
$351$	23.4465	+	12.6103i	1.25148	+	0.673089i
$352$	0.290498			0.0154836
$353$	17.9499	−	6.53322i	0.955376	−	0.347728i	0.183156	−	0.983084i	$-0.441369\pi$
$353$	17.9499	−	6.53322i	0.955376	−	0.347728i	0.772220	+	0.635355i	$0.219146\pi$
$354$	−8.53087	−	16.5691i	−0.453410	−	0.880638i
$355$	−1.95954	+	1.64425i	−0.104001	+	0.0872675i
$356$	3.05021	+	17.2986i	0.161661	+	0.916824i
$357$	−2.13235	+	9.41781i	−0.112856	+	0.498443i
$358$	2.51436	+	2.10979i	0.132888	+	0.111506i
$359$	−0.389456	+	0.674557i	−0.0205547	+	0.0356018i	−0.876120	−	0.482093i	$-0.839877\pi$
$359$	−0.389456	+	0.674557i	−0.0205547	+	0.0356018i	0.855565	+	0.517695i	$0.173210\pi$
$360$	−1.73142	−	0.826409i	−0.0912538	−	0.0435556i
$361$	−20.5519	−	35.5969i	−1.08168	−	1.87352i
$362$	−2.77068	+	15.7133i	−0.145624	+	0.825874i
$363$	−17.4345	−	7.31362i	−0.915075	−	0.383866i
$364$	4.81453	+	1.75235i	0.252350	+	0.0918478i
$365$	−1.21209	−	0.441165i	−0.0634438	−	0.0230916i
$366$	8.17717	+	3.43025i	0.427428	+	0.179302i
$367$	−2.70797	+	15.3577i	−0.141355	+	0.801664i	0.828867	+	0.559446i	$0.188986\pi$
$367$	−2.70797	+	15.3577i	−0.141355	+	0.801664i	−0.970222	+	0.242218i	$0.922125\pi$
$368$	−2.43391	−	4.21565i	−0.126876	−	0.219756i
$369$	−22.1298	−	10.5626i	−1.15203	−	0.549865i
$370$	0.606966	−	1.05130i	0.0315547	−	0.0546543i
$371$	−6.35355	−	5.33126i	−0.329860	−	0.276785i
$372$	−2.76526	+	12.2132i	−0.143372	+	0.633223i
$373$	5.37689	+	30.4939i	0.278405	+	1.57891i	0.727934	+	0.685648i	$0.240481\pi$
$373$	5.37689	+	30.4939i	0.278405	+	1.57891i	−0.449529	+	0.893266i	$0.648408\pi$
$374$	−1.24063	+	1.04101i	−0.0641515	+	0.0538295i
$375$	−4.86303	−	9.44524i	−0.251126	−	0.487750i
$376$	−5.99483	+	2.18194i	−0.309160	+	0.112525i
$377$	−24.1706			−1.24485
$378$	−4.57626	−	2.46126i	−0.235378	−	0.126594i
$379$	−28.7995			−1.47933			−0.739665	−	0.672975i	$-0.765016\pi$
$379$	−28.7995			−1.47933			−0.739665	+	0.672975i	$0.765016\pi$
$380$	4.65891	−	1.69570i	0.238997	−	0.0869878i
$381$	−3.96369	+	6.16044i	−0.203066	+	0.315609i
$382$	−9.76328	+	8.19237i	−0.499533	+	0.419158i
$383$	4.02303	+	22.8157i	0.205567	+	1.16583i	0.896545	+	0.442953i	$0.146069\pi$
$383$	4.02303	+	22.8157i	0.205567	+	1.16583i	−0.690978	+	0.722876i	$0.742820\pi$
$384$	−1.27173	−	1.17589i	−0.0648976	−	0.0600067i
$385$	−0.142313	−	0.119415i	−0.00725295	−	0.00608595i
$386$	4.25905	−	7.37690i	0.216780	−	0.375474i
$387$	4.37841	−	15.7718i	0.222567	−	0.801724i
$388$	−7.17153	−	12.4215i	−0.364079	−	0.630604i
$389$	−2.76259	+	15.6675i	−0.140069	+	0.794371i	0.831126	+	0.556085i	$0.187697\pi$
$389$	−2.76259	+	15.6675i	−0.140069	+	0.794371i	−0.971195	+	0.238287i	$0.923414\pi$
$390$	−0.715449	−	5.62986i	−0.0362282	−	0.285079i
$391$	25.5014	+	9.28177i	1.28966	+	0.469399i
$392$	−0.939693	−	0.342020i	−0.0474616	−	0.0172746i
$393$	−21.4128	+	16.2782i	−1.08013	+	0.821127i
$394$	0.984213	−	5.58175i	0.0495839	−	0.281205i
$395$	−3.32182	−	5.75357i	−0.167139	−	0.289493i
$396$	−0.361193	−	0.793123i	−0.0181506	−	0.0398559i
$397$	7.87435	−	13.6388i	0.395202	−	0.684511i	−0.597925	−	0.801552i	$-0.704008\pi$
$397$	7.87435	−	13.6388i	0.395202	−	0.684511i	0.993127	+	0.117042i	$0.0373411\pi$
$398$	−11.6029	−	9.73595i	−0.581599	−	0.488019i
$399$	12.8245	−	3.98026i	0.642030	−	0.199262i
$400$	−0.797223	−	4.52128i	−0.0398612	−	0.226064i
$401$	7.91728	−	6.64338i	0.395370	−	0.331755i	−0.423331	−	0.905975i	$-0.639139\pi$
$401$	7.91728	−	6.64338i	0.395370	−	0.331755i	0.818701	+	0.574220i	$0.194695\pi$
$402$	−14.7177	−	0.708901i	−0.734053	−	0.0353568i
$403$	−34.8079	+	12.6690i	−1.73390	+	0.631089i
$404$	−11.4946			−0.571877
$405$	−0.103505	+	5.75466i	−0.00514318	+	0.285951i
$406$	4.71759			0.234130
$407$	0.518175	−	0.188600i	0.0256850	−	0.00934857i
$408$	9.64501	+	0.464566i	0.477499	+	0.0229995i
$409$	15.7345	−	13.2028i	0.778019	−	0.652835i	−0.164730	−	0.986339i	$-0.552675\pi$
$409$	15.7345	−	13.2028i	0.778019	−	0.652835i	0.942749	+	0.333503i	$0.108231\pi$
$410$	0.907695	+	5.14780i	0.0448279	+	0.254232i
$411$	10.5669	−	3.27956i	0.521225	−	0.161769i
$412$	4.09501	+	3.43612i	0.201747	+	0.169286i
$413$	−5.37983	+	9.31814i	−0.264724	+	0.458516i
$414$	−8.48341	+	11.8866i	−0.416937	+	0.584196i
$415$	−3.32861	−	5.76533i	−0.163395	−	0.283009i
$416$	0.889689	−	5.04568i	0.0436206	−	0.247385i
$417$	16.2953	−	12.3878i	0.797985	−	0.606635i
$418$	2.11631	+	0.770275i	0.103512	+	0.0376754i
$419$	23.6119	+	8.59402i	1.15352	+	0.419845i	0.846777	−	0.531948i	$-0.178540\pi$
$419$	23.6119	+	8.59402i	1.15352	+	0.419845i	0.306739	+	0.951794i	$0.400762\pi$
$420$	0.139640	+	1.09883i	0.00681375	+	0.0536173i
$421$	2.71915	−	15.4210i	0.132523	−	0.751576i	−0.844029	−	0.536297i	$-0.819823\pi$
$421$	2.71915	−	15.4210i	0.132523	−	0.751576i	0.976553	−	0.215279i	$-0.0690661\pi$
$422$	3.79286	+	6.56943i	0.184634	+	0.319795i
$423$	13.4109	+	13.6542i	0.652059	+	0.663892i
$424$	−4.14698	+	7.18278i	−0.201395	+	0.348827i
$425$	19.6069	+	16.4521i	0.951075	+	0.798046i
$426$	5.08681	+	4.70346i	0.246457	+	0.227883i
$427$	−0.889019	−	5.04188i	−0.0430227	−	0.243994i
$428$	0.368007	−	0.308795i	0.0177883	−	0.0149262i
$429$	1.39489	−	2.16796i	0.0673457	−	0.104670i
$430$	−3.27879	+	1.19338i	−0.158117	+	0.0575500i
$431$	−8.96617			−0.431885			−0.215943	−	0.976406i	$-0.569282\pi$
$431$	−8.96617			−0.431885			−0.215943	+	0.976406i	$0.569282\pi$
$432$	−1.62921	+	4.93413i	−0.0783855	+	0.237394i
$433$	17.8307			0.856889			0.428445	−	0.903568i	$-0.359062\pi$
$433$	17.8307			0.856889			0.428445	+	0.903568i	$0.359062\pi$
$434$	6.79375	−	2.47272i	0.326110	−	0.118694i
$435$	−2.39200	−	4.64588i	−0.114688	−	0.222753i
$436$	12.4416	−	10.4398i	0.595846	−	0.499974i
$437$	−6.55322	−	37.1652i	−0.313483	−	1.77785i
$438$	−0.771462	+	3.40727i	−0.0368619	+	0.162806i
$439$	14.3266	+	12.0215i	0.683773	+	0.573753i	0.917106	−	0.398643i	$-0.130519\pi$
$439$	14.3266	+	12.0215i	0.683773	+	0.573753i	−0.233333	+	0.972397i	$0.574963\pi$
$440$	−0.0928884	+	0.160887i	−0.00442828	+	0.00767000i
$441$	0.234583	+	2.99081i	0.0111706	+	0.142420i
$442$	14.2818	+	24.7368i	0.679316	+	1.17661i
$443$	−0.122009	+	0.691947i	−0.00579682	+	0.0328754i	−0.987569	−	0.157186i	$-0.949758\pi$
$443$	−0.122009	+	0.691947i	−0.00579682	+	0.0328754i	0.981772	+	0.190062i	$0.0608688\pi$
$444$	−3.03186	−	1.27184i	−0.143886	−	0.0603587i
$445$	−10.5558	−	3.84201i	−0.500395	−	0.182129i
$446$	10.7859	+	3.92575i	0.510727	+	0.185889i
$447$	5.67516	+	2.38068i	0.268426	+	0.112602i
$448$	−0.173648	+	0.984808i	−0.00820411	+	0.0465278i
$449$	10.5637	+	18.2969i	0.498532	+	0.863482i	0.999999	−	0.00169448i	$-0.000539371\pi$
$449$	10.5637	+	18.2969i	0.498532	+	0.863482i	−0.501467	+	0.865177i	$0.667206\pi$
$450$	−11.3528	+	7.79814i	−0.535177	+	0.367608i
$451$	−1.18723	+	2.05635i	−0.0559046	+	0.0968296i
$452$	−9.91586	−	8.32039i	−0.466403	−	0.391358i
$453$	2.29149	−	10.1207i	0.107663	−	0.475511i
$454$	1.47481	+	8.36404i	0.0692160	+	0.392544i
$455$	−2.50998	+	2.10612i	−0.117669	+	0.0987364i
$456$	−6.14675	−	11.9385i	−0.287848	−	0.559073i
$457$	12.6051	−	4.58789i	0.589643	−	0.214613i	−0.0299292	−	0.999552i	$-0.509528\pi$
$457$	12.6051	−	4.58789i	0.589643	−	0.214613i	0.619573	+	0.784939i	$0.287306\pi$
$458$	7.31099			0.341620
$459$	−10.7238	−	26.9106i	−0.500544	−	1.25608i
$460$	3.11302			0.145145
$461$	28.3541	−	10.3201i	1.32058	−	0.480653i	0.416939	−	0.908935i	$-0.363103\pi$
$461$	28.3541	−	10.3201i	1.32058	−	0.480653i	0.903645	+	0.428281i	$0.140881\pi$
$462$	−0.272252	+	0.423139i	−0.0126663	+	0.0196862i
$463$	31.2502	−	26.2220i	1.45232	−	1.21864i	0.521455	−	0.853279i	$-0.325389\pi$
$463$	31.2502	−	26.2220i	1.45232	−	1.21864i	0.930865	−	0.365362i	$-0.119055\pi$
$464$	−0.819200	−	4.64592i	−0.0380304	−	0.215681i
$465$	−5.87984	−	5.43671i	−0.272671	−	0.252122i
$466$	18.8663	+	15.8307i	0.873966	+	0.733345i
$467$	−5.88341	+	10.1904i	−0.272252	+	0.471554i	−0.969438	−	0.245336i	$-0.921102\pi$
$467$	−5.88341	+	10.1904i	−0.272252	+	0.471554i	0.697186	+	0.716890i	$0.254435\pi$
$468$	−14.8820	+	3.84453i	−0.687920	+	0.177713i
$469$	4.25356	+	7.36739i	0.196411	+	0.340194i
$470$	0.708450	−	4.01782i	0.0326783	−	0.185328i
$471$	−2.89788	−	22.8034i	−0.133527	−	1.05073i
$472$	10.1108	+	3.68002i	0.465386	+	0.169387i
$473$	−1.48940	−	0.542096i	−0.0684825	−	0.0249256i
$474$	−14.3244	+	10.8896i	−0.657943	+	0.500174i
$475$	6.18060	−	35.0519i	0.283585	−	1.60829i
$476$	−2.78750	−	4.82810i	−0.127765	−	0.221295i
$477$	24.7667	+	2.39140i	1.13399	+	0.109495i
$478$	5.92495	−	10.2623i	0.271001	−	0.469388i
$479$	23.3778	+	19.6163i	1.06816	+	0.896293i	0.994885	−	0.101018i	$-0.0322101\pi$
$479$	23.3778	+	19.6163i	1.06816	+	0.896293i	0.0732763	+	0.997312i	$0.476654\pi$
$480$	1.05789	−	0.328328i	0.0482856	−	0.0149861i
$481$	−1.68883	−	9.57781i	−0.0770039	−	0.436711i
$482$	−3.64453	+	3.05813i	−0.166004	+	0.139294i
$483$	8.42153	+	0.405636i	0.383193	+	0.0184571i
$484$	10.2573	−	3.73336i	0.466242	−	0.169698i
$485$	9.17254			0.416504
$486$	15.4969	−	1.68678i	0.702955	−	0.0765140i
$487$	−31.1017			−1.40935			−0.704676	−	0.709530i	$-0.748907\pi$
$487$	−31.1017			−1.40935			−0.704676	+	0.709530i	$0.748907\pi$
$488$	−4.81091	+	1.75103i	−0.217779	+	0.0792652i
$489$	−19.8757	−	0.957345i	−0.898812	−	0.0432926i
$490$	0.489893	−	0.411069i	0.0221311	−	0.0185702i
$491$	−0.257010	−	1.45757i	−0.0115987	−	0.0657794i	0.978459	−	0.206441i	$-0.0661882\pi$
$491$	−0.257010	−	1.45757i	−0.0115987	−	0.0657794i	−0.990058	+	0.140662i	$0.955077\pi$
$492$	13.5211	−	4.19646i	0.609580	−	0.189191i
$493$	20.1474	+	16.9057i	0.907393	+	0.761393i
$494$	19.8604	−	34.3993i	0.893563	−	1.54770i
$495$	0.554750	+	0.0535650i	0.0249342	+	0.00240757i
$496$	−3.61488	−	6.26115i	−0.162313	−	0.281134i
$497$	0.694580	−	3.93916i	0.0311562	−	0.176695i
$498$	−14.3537	+	10.9118i	−0.643205	+	0.488970i
$499$	−33.5180	−	12.1996i	−1.50047	−	0.546127i	−0.544290	−	0.838897i	$-0.683201\pi$
$499$	−33.5180	−	12.1996i	−1.50047	−	0.546127i	−0.956183	+	0.292770i	$0.905423\pi$
$500$	5.76366	+	2.09780i	0.257759	+	0.0938165i
$501$	−0.486362	−	3.82717i	−0.0217290	−	0.170985i
$502$	3.13000	−	17.7511i	0.139699	−	0.792271i
$503$	4.56445	+	7.90586i	0.203519	+	0.352505i	0.949660	−	0.313283i	$-0.101429\pi$
$503$	4.56445	+	7.90586i	0.203519	+	0.352505i	−0.746141	+	0.665788i	$0.768096\pi$
$504$	2.90464	−	0.750369i	0.129383	−	0.0334241i
$505$	3.67545	−	6.36607i	0.163556	−	0.283286i
$506$	1.08326	+	0.908960i	0.0481566	+	0.0404082i
$507$	−16.8509	−	15.5810i	−0.748375	−	0.691975i
$508$	−0.734417	−	4.16508i	−0.0325845	−	0.184796i
$509$	−11.1364	+	9.34456i	−0.493613	+	0.414191i	−0.855319	−	0.518102i	$-0.826639\pi$
$509$	−11.1364	+	9.34456i	−0.493613	+	0.414191i	0.361706	+	0.932292i	$0.382194\pi$
$510$	−3.34133	+	5.19317i	−0.147957	+	0.229957i
$511$	1.89534	−	0.689848i	0.0838450	−	0.0305171i
$512$	1.00000			0.0441942
$513$	−24.9522	+	31.6258i	−1.10167	+	1.39631i
$514$	−16.6589			−0.734793
$515$	−3.21244	+	1.16923i	−0.141557	+	0.0515225i
$516$	4.32589	+	8.40197i	0.190437	+	0.369876i
$517$	1.41967	−	1.19125i	0.0624372	−	0.0523910i
$518$	0.329623	+	1.86938i	0.0144828	+	0.0821360i
$519$	−0.189227	+	0.835746i	−0.00830612	+	0.0366852i
$520$	2.50998	+	2.10612i	0.110070	+	0.0923595i
$521$	13.2546	−	22.9577i	0.580696	−	1.00579i	−0.414702	−	0.909957i	$-0.636114\pi$
$521$	13.2546	−	22.9577i	0.580696	−	1.00579i	0.995397	−	0.0958367i	$-0.0305526\pi$
$522$	−11.6658	+	8.01311i	−0.510598	+	0.350724i
$523$	−9.15938	−	15.8645i	−0.400512	−	0.693707i	0.593276	−	0.804999i	$-0.297834\pi$
$523$	−9.15938	−	15.8645i	−0.400512	−	0.693707i	−0.993788	+	0.111292i	$0.964501\pi$
$524$	2.69666	−	15.2935i	0.117804	−	0.668100i
$525$	7.33283	+	3.07606i	0.320031	+	0.134250i
$526$	8.05172	+	2.93058i	0.351071	+	0.127780i
$527$	37.8752	+	13.7854i	1.64987	+	0.600503i
$528$	0.463987	+	0.194638i	0.0201924	+	0.00847054i
$529$	0.120788	−	0.685020i	0.00525163	−	0.0297835i
$530$	−2.65204	−	4.59346i	−0.115197	−	0.199527i
$531$	−2.52404	−	32.1801i	−0.109534	−	1.39650i
$532$	−3.87633	+	6.71400i	−0.168060	+	0.291089i
$533$	32.0807	+	26.9189i	1.38957	+	1.16599i
$534$	−6.71850	+	29.6732i	−0.290738	+	1.28408i
$535$	0.0533483	+	0.302553i	0.00230645	+	0.0130805i
$536$	6.51684	−	5.46828i	0.281485	−	0.236194i
$537$	2.60236	+	5.05444i	0.112300	+	0.218115i
$538$	−0.537182	+	0.195518i	−0.0231596	+	0.00842940i
$539$	0.290498			0.0125126
$540$	−2.21173	−	2.48002i	−0.0951778	−	0.106723i
$541$	−12.9684			−0.557557			−0.278779	−	0.960355i	$-0.589930\pi$
$541$	−12.9684			−0.557557			−0.278779	+	0.960355i	$0.589930\pi$
$542$	−20.9676	+	7.63160i	−0.900637	+	0.327805i
$543$	−14.9535	+	23.2411i	−0.641717	+	0.997370i
$544$	−4.27070	+	3.58354i	−0.183105	+	0.153643i
$545$	1.80360	+	10.2287i	0.0772578	+	0.438151i
$546$	6.51572	+	6.02467i	0.278847	+	0.257832i
$547$	28.7276	+	24.1053i	1.22830	+	1.03067i	0.998347	+	0.0574691i	$0.0183031\pi$
$547$	28.7276	+	24.1053i	1.22830	+	1.03067i	0.229957	+	0.973201i	$0.426141\pi$
$548$	−3.19393	+	5.53204i	−0.136438	+	0.236317i
$549$	10.7623	+	10.9577i	0.459326	+	0.467661i
$550$	0.666843	+	1.15501i	0.0284343	+	0.0492496i
$551$	6.35098	−	36.0182i	0.270561	−	1.53443i
$552$	−1.06291	−	8.36403i	−0.0452405	−	0.355997i
$553$	9.76214	+	3.55313i	0.415128	+	0.151094i
$554$	−22.7870	−	8.29378i	−0.968125	−	0.352369i
$555$	1.67384	−	1.27246i	0.0710504	−	0.0540131i
$556$	−2.05218	+	11.6385i	−0.0870316	+	0.493581i
$557$	−16.2874	−	28.2106i	−0.690119	−	1.19532i	−0.971798	−	0.235813i	$-0.924225\pi$
$557$	−16.2874	−	28.2106i	−0.690119	−	1.19532i	0.281679	−	0.959509i	$-0.409109\pi$
$558$	−12.5997	+	17.6542i	−0.533388	+	0.747363i
$559$	−13.9771	+	24.2091i	−0.591170	+	1.02394i
$560$	−0.489893	−	0.411069i	−0.0207018	−	0.0173709i
$561$	−2.67904	+	0.831475i	−0.113109	+	0.0351049i
$562$	−4.60026	−	26.0894i	−0.194050	−	1.10051i
$563$	18.1384	−	15.2199i	0.764443	−	0.641444i	−0.174836	−	0.984597i	$-0.555940\pi$
$563$	18.1384	−	15.2199i	0.764443	−	0.641444i	0.939279	+	0.343154i	$0.111495\pi$
$564$	−11.0369	−	0.531611i	−0.464739	−	0.0223848i
$565$	7.77875	−	2.83123i	0.327254	−	0.119111i
$566$	18.4108			0.773865
$567$	−5.66017	−	6.99732i	−0.237705	−	0.293860i
$568$	−3.99992			−0.167833
$569$	−16.3576	+	5.95369i	−0.685747	+	0.249592i	−0.661313	−	0.750110i	$-0.730001\pi$
$569$	−16.3576	+	5.95369i	−0.685747	+	0.249592i	−0.0244340	+	0.999701i	$0.507778\pi$
$570$	8.57740	+	0.413143i	0.359268	+	0.0173047i
$571$	−23.1026	+	19.3854i	−0.966812	+	0.811252i	−0.982048	−	0.188632i	$-0.939595\pi$
$571$	−23.1026	+	19.3854i	−0.966812	+	0.811252i	0.0152357	+	0.999884i	$0.495150\pi$
$572$	0.258453	+	1.46576i	0.0108065	+	0.0612865i
$573$	−21.0830	+	6.54338i	−0.880756	+	0.273354i
$574$	−6.26147	−	5.25400i	−0.261349	−	0.219298i
$575$	11.1741	−	19.3542i	0.465993	−	0.807124i
$576$	−1.24335	−	2.73021i	−0.0518065	−	0.113759i
$577$	6.40578	+	11.0951i	0.266676	+	0.461897i	0.968001	−	0.250945i	$-0.0807412\pi$
$577$	6.40578	+	11.0951i	0.266676	+	0.461897i	−0.701325	+	0.712842i	$0.747408\pi$
$578$	2.44508	−	13.8668i	0.101702	−	0.576781i
$579$	11.7452	−	8.92882i	0.488115	−	0.371069i
$580$	2.83500	+	1.03186i	0.117717	+	0.0428455i
$581$	9.78208	+	3.56039i	0.405829	+	0.147710i
$582$	−3.13188	−	24.6447i	−0.129821	−	1.02156i
$583$	0.418385	−	2.37278i	0.0173277	−	0.0982705i
$584$	−1.00849	−	1.74676i	−0.0417316	−	0.0722813i
$585$	2.62937	−	9.47143i	0.108711	−	0.391595i
$586$	8.65113	−	14.9842i	0.357375	−	0.618991i
$587$	23.2198	+	19.4837i	0.958382	+	0.804178i	0.980689	−	0.195573i	$-0.0626567\pi$
$587$	23.2198	+	19.4837i	0.958382	+	0.804178i	−0.0223069	+	0.999751i	$0.507101\pi$
$588$	−1.27173	−	1.17589i	−0.0524452	−	0.0484927i
$589$	−9.73295	−	55.1983i	−0.401039	−	2.27441i
$590$	−5.27109	+	4.42297i	−0.217007	+	0.182091i
$591$	5.31185	−	8.25579i	0.218500	−	0.339598i
$592$	1.78375	−	0.649230i	0.0733115	−	0.0266832i
$593$	−13.5852			−0.557877			−0.278938	−	0.960309i	$-0.589983\pi$
$593$	−13.5852			−0.557877			−0.278938	+	0.960309i	$0.589983\pi$
$594$	−0.0454962	−	1.50879i	−0.00186673	−	0.0619063i
$595$	3.56527			0.146162
$596$	−3.33889	+	1.21526i	−0.136766	+	0.0497788i
$597$	−12.0090	−	23.3245i	−0.491494	−	0.954606i
$598$	19.1054	−	16.0313i	0.781277	−	0.655569i
$599$	6.69476	+	37.9679i	0.273540	+	1.55132i	0.743560	+	0.668669i	$0.233136\pi$
$599$	6.69476	+	37.9679i	0.273540	+	1.55132i	−0.470020	+	0.882656i	$0.655753\pi$
$600$	1.75599	−	7.75558i	0.0716881	−	0.316620i
$601$	0.143680	+	0.120562i	0.00586085	+	0.00491784i	0.645713	−	0.763580i	$-0.276560\pi$
$601$	0.143680	+	0.120562i	0.00586085	+	0.00491784i	−0.639852	+	0.768498i	$0.721005\pi$
$602$	2.72804	−	4.72510i	0.111187	−	0.192581i
$603$	−23.0323	−	10.9934i	−0.937948	−	0.447684i
$604$	2.99554	+	5.18842i	0.121887	+	0.211114i
$605$	−1.21218	+	6.87459i	−0.0492820	+	0.279492i
$606$	−18.3593	−	7.70154i	−0.745794	−	0.312854i
$607$	−8.16164	−	2.97059i	−0.331271	−	0.120573i	0.171030	−	0.985266i	$-0.445291\pi$
$607$	−8.16164	−	2.97059i	−0.331271	−	0.120573i	−0.502300	+	0.864693i	$0.667513\pi$
$608$	7.28512	+	2.65157i	0.295451	+	0.107535i
$609$	7.53498	+	3.16085i	0.305333	+	0.128084i
$610$	0.568537	−	3.22433i	0.0230194	−	0.130549i
$611$	−16.3429	−	28.3067i	−0.661163	−	1.14517i
$612$	15.0938	+	7.20431i	0.610132	+	0.291217i
$613$	3.20349	−	5.54861i	0.129388	−	0.224106i	−0.794052	−	0.607850i	$-0.792032\pi$
$613$	3.20349	−	5.54861i	0.129388	−	0.224106i	0.923440	+	0.383744i	$0.125365\pi$
$614$	8.41517	+	7.06117i	0.339609	+	0.284966i
$615$	−1.99932	+	8.83028i	−0.0806204	+	0.356071i
$616$	−0.0504445	−	0.286085i	−0.00203247	−	0.0115267i
$617$	−29.1095	+	24.4258i	−1.17190	+	0.983345i	−0.999998	−	0.00176830i	$-0.999437\pi$
$617$	−29.1095	+	24.4258i	−1.17190	+	0.983345i	−0.171906	+	0.985113i	$0.554993\pi$
$618$	4.23834	+	8.23193i	0.170491	+	0.331137i
$619$	−36.6541	+	13.3410i	−1.47325	+	0.536220i	−0.948981	−	0.315332i	$-0.897884\pi$
$619$	−36.6541	+	13.3410i	−1.47325	+	0.536220i	−0.524271	+	0.851552i	$0.675662\pi$
$620$	4.62350			0.185684
$621$	−21.5140	+	13.3014i	−0.863328	+	0.533768i
$622$	11.9289			0.478304
$623$	16.5061	−	6.00774i	0.661304	−	0.240695i
$624$	4.80170	−	7.46290i	0.192222	−	0.298755i
$625$	14.5799	−	12.2340i	0.583194	−	0.489358i
$626$	5.53095	+	31.3676i	0.221061	+	1.25370i
$627$	2.86410	+	2.64825i	0.114381	+	0.105761i
$628$	10.1665	+	8.53071i	0.405688	+	0.340412i
$629$	−5.29130	+	9.16480i	−0.210978	+	0.365424i
$630$	−0.513196	+	1.84862i	−0.0204462	+	0.0736507i
$631$	−9.11242	−	15.7832i	−0.362760	−	0.628318i	0.625654	−	0.780101i	$-0.284832\pi$
$631$	−9.11242	−	15.7832i	−0.362760	−	0.628318i	−0.988414	+	0.151782i	$0.951499\pi$
$632$	1.80397	−	10.2308i	0.0717581	−	0.406960i
$633$	1.65638	+	13.0340i	0.0658352	+	0.518056i
$634$	18.5438	+	6.74938i	0.736468	+	0.268052i
$635$	2.54159	+	0.925063i	0.100860	+	0.0367100i
$636$	−11.4362	+	8.69387i	−0.453474	+	0.344735i
$637$	0.889689	−	5.04568i	0.0352508	−	0.199917i
$638$	0.685225	+	1.18685i	0.0271283	+	0.0469877i
$639$	4.97333	+	10.9206i	0.196742	+	0.432014i
$640$	−0.319755	+	0.553832i	−0.0126394	+	0.0218921i
$641$	−12.0883	−	10.1433i	−0.477459	−	0.400636i	0.372048	−	0.928214i	$-0.378656\pi$
$641$	−12.0883	−	10.1433i	−0.477459	−	0.400636i	−0.849507	+	0.527578i	$0.823100\pi$
$642$	0.794682	−	0.246640i	0.0313636	−	0.00973409i
$643$	−0.349777	−	1.98368i	−0.0137939	−	0.0782289i	0.977134	−	0.212626i	$-0.0682015\pi$
$643$	−0.349777	−	1.98368i	−0.0137939	−	0.0782289i	−0.990928	+	0.134397i	$0.957090\pi$
$644$	−3.72896	+	3.12897i	−0.146942	+	0.123299i
$645$	−6.03650	−	0.290757i	−0.237687	−	0.0114486i
$646$	−40.6146	+	14.7825i	−1.59796	+	0.581609i
$647$	28.9218			1.13703			0.568516	−	0.822672i	$-0.307518\pi$
$647$	28.9218			1.13703			0.568516	+	0.822672i	$0.307518\pi$
$648$	−5.90814	+	6.78925i	−0.232094	+	0.266707i
$649$	−3.12566			−0.122693
$650$	22.1036	−	8.04506i	0.866976	−	0.315553i
$651$	12.5078	+	0.602457i	0.490219	+	0.0236121i
$652$	8.80075	−	7.38471i	0.344664	−	0.289208i
$653$	−1.21090	−	6.86736i	−0.0473862	−	0.268740i	0.951905	−	0.306394i	$-0.0991226\pi$
$653$	−1.21090	−	6.86736i	−0.0473862	−	0.268740i	−0.999291	+	0.0376540i	$0.988012\pi$
$654$	26.8667	−	8.33842i	1.05057	−	0.326058i
$655$	7.60777	+	6.38368i	0.297260	+	0.249431i
$656$	−4.08688	+	7.07869i	−0.159566	+	0.276376i
$657$	−3.51511	+	4.92523i	−0.137137	+	0.192152i
$658$	3.18978	+	5.52487i	0.124351	+	0.215382i
$659$	−4.42336	+	25.0861i	−0.172310	+	0.977217i	0.768894	+	0.639377i	$0.220807\pi$
$659$	−4.42336	+	25.0861i	−0.172310	+	0.977217i	−0.941203	+	0.337840i	$0.890304\pi$
$660$	−0.256159	+	0.194734i	−0.00997098	+	0.00758002i
$661$	35.4184	+	12.8912i	1.37762	+	0.501411i	0.921455	−	0.388486i	$-0.127002\pi$
$661$	35.4184	+	12.8912i	1.37762	+	0.501411i	0.456161	+	0.889897i	$0.349224\pi$
$662$	−8.35079	−	3.03944i	−0.324563	−	0.118131i
$663$	6.23701	+	49.0789i	0.242225	+	1.90607i
$664$	1.80766	−	10.2517i	0.0701507	−	0.397844i
$665$	−2.47895	−	4.29367i	−0.0961297	−	0.166502i
$666$	−3.99037	−	4.06278i	−0.154624	−	0.157430i
$667$	11.4822	−	19.8877i	0.444591	−	0.770054i
$668$	1.70628	+	1.43174i	0.0660180	+	0.0553956i
$669$	14.5970	+	13.4970i	0.564354	+	0.521822i
$670$	0.944715	+	5.35775i	0.0364975	+	0.206988i
$671$	1.13930	−	0.955987i	0.0439822	−	0.0369055i
$672$	−0.937189	+	1.45660i	−0.0361528	+	0.0561895i
$673$	−2.10809	+	0.767283i	−0.0812610	+	0.0295766i	−0.382331	−	0.924026i	$-0.624879\pi$
$673$	−2.10809	+	0.767283i	−0.0812610	+	0.0295766i	0.301070	+	0.953602i	$0.402656\pi$
$674$	−13.9499			−0.537330
$675$	−23.3577	+	4.84871i	−0.899039	+	0.186627i
$676$	13.2504			0.509631
$677$	20.7982	−	7.56991i	0.799338	−	0.290935i	0.0901259	−	0.995930i	$-0.471273\pi$
$677$	20.7982	−	7.56991i	0.799338	−	0.290935i	0.709212	+	0.704995i	$0.249051\pi$
$678$	−10.2629	−	19.9332i	−0.394145	−	0.765530i
$679$	−10.9874	+	9.21955i	−0.421659	+	0.353814i
$680$	−0.619103	−	3.51111i	−0.0237415	−	0.134645i
$681$	−3.24846	+	14.3473i	−0.124481	+	0.549788i
$682$	1.60887	+	1.35000i	0.0616068	+	0.0516943i
$683$	−0.658894	+	1.14124i	−0.0252119	+	0.0436682i	−0.878356	−	0.478007i	$-0.841359\pi$
$683$	−0.658894	+	1.14124i	−0.0252119	+	0.0436682i	0.853144	+	0.521675i	$0.174693\pi$
$684$	−1.81864	−	23.1868i	−0.0695376	−	0.886568i
$685$	−2.04255	−	3.53780i	−0.0780418	−	0.135172i
$686$	−0.173648	+	0.984808i	−0.00662992	+	0.0376001i
$687$	11.6772	+	4.89847i	0.445512	+	0.186888i
$688$	−5.12704	−	1.86609i	−0.195466	−	0.0711439i
$689$	−39.9315	−	14.5339i	−1.52127	−	0.553697i
$690$	4.97214	+	2.08577i	0.189286	+	0.0794038i
$691$	−5.17511	+	29.3495i	−0.196870	+	1.11651i	0.712860	+	0.701307i	$0.247400\pi$
$691$	−5.17511	+	29.3495i	−0.196870	+	1.11651i	−0.909730	+	0.415201i	$0.863711\pi$
$692$	−0.247366	−	0.428450i	−0.00940343	−	0.0162872i
$693$	−0.718353	+	0.493429i	−0.0272880	+	0.0187438i
$694$	7.76568	−	13.4505i	0.294781	−	0.510576i
$695$	−5.78956	−	4.85802i	−0.219611	−	0.184275i
$696$	1.80440	−	7.96938i	0.0683955	−	0.302079i
$697$	−7.91294	−	44.8765i	−0.299724	−	1.69982i
$698$	15.1596	−	12.7204i	0.573799	−	0.481475i
$699$	19.5267	+	37.9257i	0.738567	+	1.43448i
$700$	−4.31415	+	1.57022i	−0.163060	+	0.0593489i
$701$	−41.8031			−1.57888			−0.789440	−	0.613828i	$-0.789629\pi$
$701$	−41.8031			−1.57888			−0.789440	+	0.613828i	$0.789629\pi$
$702$	−26.3455	−	3.83063i	−0.994348	−	0.144578i
$703$	14.7163			0.555035
$704$	−0.272979	+	0.0993563i	−0.0102883	+	0.00374463i
$705$	3.82354	−	5.94263i	0.144003	−	0.223812i
$706$	−14.6329	+	12.2784i	−0.550716	+	0.462105i
$707$	1.99601	+	11.3200i	0.0750678	+	0.425731i
$708$	13.6834	+	12.6521i	0.514252	+	0.475496i
$709$	−10.4326	−	8.75396i	−0.391803	−	0.328762i	0.425512	−	0.904953i	$-0.360094\pi$
$709$	−10.4326	−	8.75396i	−0.391803	−	0.328762i	−0.817315	+	0.576191i	$0.804538\pi$
$710$	1.27900	−	2.21529i	0.0479999	−	0.0831382i
$711$	−30.1753	+	7.79532i	−1.13166	+	0.292347i
$712$	−8.78273	−	15.2121i	−0.329147	−	0.570099i
$713$	6.11121	−	34.6584i	0.228867	−	1.29797i
$714$	−1.21733	−	9.57915i	−0.0455574	−	0.358491i
$715$	−0.894427	−	0.325545i	−0.0334497	−	0.0121747i
$716$	−3.08431	−	1.12260i	−0.115266	−	0.0419535i
$717$	16.3393	−	12.4213i	0.610202	−	0.463881i
$718$	0.135257	−	0.767078i	0.00504773	−	0.0286271i
$719$	21.8991	+	37.9304i	0.816699	+	1.41456i	0.908102	+	0.418750i	$0.137531\pi$
$719$	21.8991	+	37.9304i	0.816699	+	1.41456i	−0.0914031	+	0.995814i	$0.529135\pi$
$720$	1.90965	+	0.184390i	0.0711684	+	0.00687181i
$721$	2.67283	−	4.62948i	0.0995414	−	0.172411i
$722$	31.4873	+	26.4210i	1.17184	+	0.983287i
$723$	−7.87008	+	2.44258i	−0.292691	+	0.0908405i
$724$	−2.77068	−	15.7133i	−0.102972	−	0.583981i
$725$	16.5914	−	13.9219i	0.616190	−	0.517045i
$726$	18.8845	+	0.909600i	0.700869	+	0.0337584i
$727$	−6.97453	+	2.53852i	−0.258671	+	0.0941486i	−0.468101	−	0.883675i	$-0.655062\pi$
$727$	−6.97453	+	2.53852i	−0.258671	+	0.0941486i	0.209430	+	0.977824i	$0.432839\pi$
$728$	−5.12351			−0.189890
$729$	25.8820	+	7.68903i	0.958593	+	0.284779i
$730$	1.28988			0.0477406
$731$	28.5832	−	10.4035i	1.05719	−	0.384786i
$732$	−8.85724	−	0.426622i	−0.327373	−	0.0157684i
$733$	−8.73089	+	7.32609i	−0.322483	+	0.270595i	−0.789629	−	0.613585i	$-0.789727\pi$
$733$	−8.73089	+	7.32609i	−0.322483	+	0.270595i	0.467146	+	0.884180i	$0.345282\pi$
$734$	−2.70797	−	15.3577i	−0.0999531	−	0.566862i
$735$	1.05789	−	0.328328i	0.0390207	−	0.0121106i
$736$	3.72896	+	3.12897i	0.137451	+	0.115335i
$737$	−1.23565	+	2.14021i	−0.0455159	+	0.0788358i
$738$	24.4078	+	2.35674i	0.898463	+	0.0867529i
$739$	9.88025	+	17.1131i	0.363451	+	0.629515i	0.988526	−	0.151049i	$-0.0482651\pi$
$739$	9.88025	+	17.1131i	0.363451	+	0.629515i	−0.625075	+	0.780564i	$0.714932\pi$
$740$	−0.210797	+	1.19549i	−0.00774906	+	0.0439471i
$741$	54.7693	−	41.6361i	2.01200	−	1.52954i
$742$	7.79378	+	2.83670i	0.286119	+	0.104139i
$743$	−13.1861	−	4.79934i	−0.483750	−	0.176071i	0.0886208	−	0.996065i	$-0.471754\pi$
$743$	−13.1861	−	4.79934i	−0.483750	−	0.176071i	−0.572371	+	0.819995i	$0.693976\pi$
$744$	−1.57865	−	12.4224i	−0.0578762	−	0.455427i
$745$	0.394579	−	2.23777i	0.0144562	−	0.0819855i
$746$	−15.4822	−	26.8159i	−0.566842	−	0.981799i
$747$	−30.2370	+	7.81125i	−1.10631	+	0.285799i
$748$	0.809765	−	1.40255i	0.0296079	−	0.0512824i
$749$	−0.368007	−	0.308795i	−0.0134467	−	0.0112831i
$750$	7.80022	+	7.21237i	0.284824	+	0.263359i
$751$	6.47375	+	36.7145i	0.236231	+	1.33973i	0.840007	+	0.542576i	$0.182551\pi$
$751$	6.47375	+	36.7145i	0.236231	+	1.33973i	−0.603776	+	0.797154i	$0.706338\pi$
$752$	4.88703	−	4.10071i	0.178212	−	0.149537i
$753$	16.8928	−	26.2551i	0.615607	−	0.956789i
$754$	22.7130	−	8.26684i	0.827157	−	0.301061i
$755$	−3.83135			−0.139437
$756$	5.14208	+	0.747657i	0.187016	+	0.0271920i
$757$	−49.0623			−1.78320			−0.891600	−	0.452825i	$-0.850416\pi$
$757$	−49.0623			−1.78320			−0.891600	+	0.452825i	$0.850416\pi$
$758$	27.0627	−	9.85001i	0.982960	−	0.357768i
$759$	1.12117	+	2.17760i	0.0406959	+	0.0790418i
$760$	−3.79798	+	3.18688i	−0.137767	+	0.115600i
$761$	0.657365	+	3.72810i	0.0238295	+	0.135144i	0.994402	−	0.105667i	$-0.0336978\pi$
$761$	0.657365	+	3.72810i	0.0238295	+	0.135144i	−0.970572	+	0.240811i	$0.922587\pi$
$762$	1.61765	−	7.14458i	0.0586013	−	0.258821i
$763$	−12.4416	−	10.4398i	−0.450417	−	0.377945i
$764$	6.37253	−	11.0375i	0.230550	−	0.399324i
$765$	−8.81631	+	6.05584i	−0.318755	+	0.218949i
$766$	−11.5838	−	20.0638i	−0.418541	−	0.724935i
$767$	−9.57275	+	54.2898i	−0.345652	+	1.96029i
$768$	1.59721	+	0.670015i	0.0576344	+	0.0241771i
$769$	0.262062	+	0.0953829i	0.00945021	+	0.00343959i	0.346741	−	0.937961i	$-0.387288\pi$
$769$	0.262062	+	0.0953829i	0.00945021	+	0.00343959i	−0.337291	+	0.941401i	$0.609511\pi$
$770$	0.174573	+	0.0635394i	0.00629117	+	0.00228980i
$771$	−26.6078	−	11.1617i	−0.958255	−	0.401979i
$772$	−1.47915	+	8.38870i	−0.0532359	+	0.301916i
$773$	23.7909	+	41.2070i	0.855698	+	1.48211i	0.875996	+	0.482319i	$0.160205\pi$
$773$	23.7909	+	41.2070i	0.855698	+	1.48211i	−0.0202975	+	0.999794i	$0.506461\pi$
$774$	1.27990	+	16.3181i	0.0460052	+	0.586543i
$775$	16.5960	−	28.7451i	0.596146	−	1.03255i
$776$	10.9874	+	9.21955i	0.394426	+	0.330962i
$777$	−0.726038	+	3.20665i	−0.0260465	+	0.115038i
$778$	−2.76259	−	15.6675i	−0.0990438	−	0.561705i
$779$	−48.5430	+	40.7324i	−1.73924	+	1.45939i
$780$	2.59783	+	5.04564i	0.0930171	+	0.180663i
$781$	1.09190	−	0.397418i	0.0390711	−	0.0142207i
$782$	−27.1381			−0.970456
$783$	−24.0016	+	4.98237i	−0.857748	+	0.178055i
$784$	1.00000			0.0357143
$785$	−7.97538	+	2.90280i	−0.284653	+	0.103605i
$786$	14.5540	−	22.6201i	0.519124	−	0.806834i
$787$	24.4799	−	20.5410i	0.872613	−	0.732209i	−0.0920338	−	0.995756i	$-0.529337\pi$
$787$	24.4799	−	20.5410i	0.872613	−	0.732209i	0.964647	+	0.263547i	$0.0848923\pi$
$788$	0.984213	+	5.58175i	0.0350611	+	0.198842i
$789$	10.8967	+	10.0755i	0.387934	+	0.358698i
$790$	5.08933	+	4.27045i	0.181070	+	0.151936i
$791$	−6.47212	+	11.2100i	−0.230122	+	0.398583i
$792$	0.610674	+	0.621756i	0.0216994	+	0.0220931i
$793$	−13.1153	−	22.7164i	−0.465739	−	0.806683i
$794$	−2.73473	+	15.5094i	−0.0970521	+	0.550410i
$795$	−1.15817	−	9.11363i	−0.0410761	−	0.323227i
$796$	14.2330	+	5.18039i	0.504476	+	0.183614i
$797$	16.5210	+	6.01315i	0.585204	+	0.212997i	0.617619	−	0.786478i	$-0.288097\pi$
$797$	16.5210	+	6.01315i	0.585204	+	0.212997i	−0.0324147	+	0.999475i	$0.510320\pi$
$798$	−10.6898	+	8.12647i	−0.378415	+	0.287674i
$799$	−6.17599	+	35.0258i	−0.218491	+	1.23912i
$800$	2.29551	+	3.97595i	0.0811586	+	0.140571i
$801$	−30.6123	+	42.8928i	−1.08163	+	1.51554i
$802$	−5.16764	+	8.95061i	−0.182476	+	0.316057i
$803$	0.448848	+	0.376628i	0.0158395	+	0.0132909i
$804$	14.0726	−	4.36761i	0.496302	−	0.154034i
$805$	−0.540570	−	3.06572i	−0.0190526	−	0.108053i
$806$	28.3756	−	23.8100i	0.999489	−	0.838671i
$807$	−0.988993	−	0.0476363i	−0.0348142	−	0.00167688i
$808$	10.8014	−	3.93138i	0.379991	−	0.138305i
$809$	−12.0719			−0.424426			−0.212213	−	0.977223i	$-0.568067\pi$
$809$	−12.0719			−0.424426			−0.212213	+	0.977223i	$0.568067\pi$
$810$	−1.87095	−	5.44301i	−0.0657384	−	0.191248i
$811$	30.8293			1.08256			0.541282	−	0.840841i	$-0.317939\pi$
$811$	30.8293			1.08256			0.541282	+	0.840841i	$0.317939\pi$
$812$	−4.43308	+	1.61351i	−0.155571	+	0.0566231i
$813$	−38.6030	−	1.85937i	−1.35387	−	0.0652110i
$814$	−0.422420	+	0.354453i	−0.0148058	+	0.0124236i
$815$	1.27580	+	7.23544i	0.0446894	+	0.253446i
$816$	−9.22224	+	2.86224i	−0.322843	+	0.100198i
$817$	−32.4030	−	27.1893i	−1.13364	−	0.951235i
$818$	−10.2699	+	17.7881i	−0.359080	+	0.621945i
$819$	6.37035	+	13.9883i	0.222598	+	0.488790i
$820$	−2.61360	−	4.52690i	−0.0912710	−	0.158086i
$821$	1.94515	−	11.0315i	0.0678861	−	0.385001i	−0.931867	−	0.362799i	$-0.881821\pi$
$821$	1.94515	−	11.0315i	0.0678861	−	0.385001i	0.999754	−	0.0222022i	$-0.00706777\pi$
$822$	−8.80792	+	6.69585i	−0.307212	+	0.233545i
$823$	−10.9583	−	3.98848i	−0.381981	−	0.139030i	0.143891	−	0.989594i	$-0.454039\pi$
$823$	−10.9583	−	3.98848i	−0.381981	−	0.139030i	−0.525872	+	0.850564i	$0.676261\pi$
$824$	−5.02328	−	1.82832i	−0.174994	−	0.0636927i
$825$	0.291217	+	2.29158i	0.0101389	+	0.0797826i
$826$	1.86840	−	10.5962i	0.0650098	−	0.368689i
$827$	−11.7755	−	20.3957i	−0.409473	−	0.709228i	0.585358	−	0.810775i	$-0.300954\pi$
$827$	−11.7755	−	20.3957i	−0.409473	−	0.709228i	−0.994831	+	0.101547i	$0.967621\pi$
$828$	3.90633	−	14.0713i	0.135754	−	0.489011i
$829$	−17.4147	+	30.1631i	−0.604837	+	1.04761i	0.387241	+	0.921979i	$0.373428\pi$
$829$	−17.4147	+	30.1631i	−0.604837	+	1.04761i	−0.992077	+	0.125629i	$0.959905\pi$
$830$	5.09973	+	4.27918i	0.177014	+	0.148533i
$831$	−30.8386	−	28.5145i	−1.06978	−	0.989157i
$832$	0.889689	+	5.04568i	0.0308444	+	0.174927i
$833$	−4.27070	+	3.58354i	−0.147971	+	0.124162i
$834$	−11.0757	+	17.2141i	−0.383520	+	0.596075i
$835$	−1.33854	+	0.487187i	−0.0463219	+	0.0168598i
$836$	−2.25213			−0.0778917
$837$	−31.9530	+	19.7555i	−1.10446	+	0.682850i
$838$	−25.1272			−0.868006
$839$	−15.4178	+	5.61160i	−0.532280	+	0.193734i	−0.594156	−	0.804350i	$-0.702514\pi$
$839$	−15.4178	+	5.61160i	−0.532280	+	0.193734i	0.0618760	+	0.998084i	$0.480292\pi$
$840$	−0.507040	−	0.984800i	−0.0174945	−	0.0339788i
$841$	−5.16649	+	4.33520i	−0.178155	+	0.149490i
$842$	2.71915	+	15.4210i	0.0937080	+	0.531444i
$843$	10.1327	−	44.7524i	0.348988	−	1.54136i
$844$	−5.81100	−	4.87601i	−0.200023	−	0.167839i
$845$	−4.23689	+	7.33850i	−0.145753	+	0.252452i
$846$	−17.2721	−	8.24401i	−0.593828	−	0.283435i
$847$	−5.45781	−	9.45320i	−0.187532	−	0.324816i
$848$	1.44023	−	8.16796i	0.0494578	−	0.280489i
$849$	29.4060	+	12.3355i	1.00921	+	0.423355i
$850$	−24.0514	−	8.75400i	−0.824957	−	0.300260i
$851$	8.68293	+	3.16033i	0.297647	+	0.108335i
$852$	−6.38872	−	2.68001i	−0.218874	−	0.0918156i
$853$	−1.90258	+	10.7901i	−0.0651431	+	0.369445i	0.934757	+	0.355289i	$0.115617\pi$
$853$	−1.90258	+	10.7901i	−0.0651431	+	0.369445i	−0.999900	+	0.0141565i	$0.995494\pi$
$854$	2.55983	+	4.43375i	0.0875956	+	0.151720i
$855$	13.4231	+	6.40687i	0.459060	+	0.219110i
$856$	−0.240200	+	0.416038i	−0.00820986	+	0.0142199i
$857$	−21.6782	−	18.1901i	−0.740512	−	0.621364i	0.192463	−	0.981304i	$-0.438352\pi$
$857$	−21.6782	−	18.1901i	−0.740512	−	0.621364i	−0.932975	+	0.359941i	$0.882797\pi$
$858$	−0.569278	+	2.51430i	−0.0194348	+	0.0858366i
$859$	−2.80152	−	15.8882i	−0.0955865	−	0.542098i	−0.994566	−	0.104107i	$-0.966801\pi$
$859$	−2.80152	−	15.8882i	−0.0955865	−	0.542098i	0.898980	−	0.437991i	$-0.144310\pi$
$860$	2.67290	−	2.24283i	0.0911450	−	0.0764797i
$861$	−6.48062	−	12.5870i	−0.220859	−	0.428964i
$862$	8.42545	−	3.06661i	0.286972	−	0.104449i
$863$	−21.4492			−0.730138			−0.365069	−	0.930980i	$-0.618955\pi$
$863$	−21.4492			−0.730138			−0.365069	+	0.930980i	$0.618955\pi$
$864$	−0.156614	−	5.19379i	−0.00532813	−	0.176696i
$865$	0.316386			0.0107574
$866$	−16.7554	+	6.09846i	−0.569371	+	0.207234i
$867$	13.1963	−	20.5099i	0.448168	−	0.696552i
$868$	−5.53831	+	4.64720i	−0.187983	+	0.157736i
$869$	0.524050	+	2.97204i	0.0177772	+	0.100819i
$870$	3.83673	+	3.54758i	0.130077	+	0.120274i
$871$	33.3891	+	28.0168i	1.13135	+	0.949313i
$872$	−8.12069	+	14.0655i	−0.275001	+	0.476316i
$873$	11.5101	−	41.4612i	0.389557	−	1.40325i
$874$	18.8692	+	32.6825i	0.638262	+	1.10550i
$875$	1.06508	−	6.04038i	0.0360063	−	0.204202i
$876$	−0.440418	−	3.46564i	−0.0148803	−	0.117093i
$877$	11.5437	+	4.20155i	0.389802	+	0.141876i	0.529484	−	0.848320i	$-0.322386\pi$
$877$	11.5437	+	4.20155i	0.389802	+	0.141876i	−0.139682	+	0.990196i	$0.544608\pi$
$878$	−17.5742	−	6.39649i	−0.593101	−	0.215871i
$879$	23.8573	−	18.1365i	0.804687	−	0.611730i
$880$	0.0322598	−	0.182954i	0.00108748	−	0.00616739i
$881$	19.4880	+	33.7541i	0.656566	+	1.13721i	0.981499	+	0.191469i	$0.0613251\pi$
$881$	19.4880	+	33.7541i	0.656566	+	1.13721i	−0.324932	+	0.945737i	$0.605342\pi$
$882$	−1.24335	−	2.73021i	−0.0418659	−	0.0919311i
$883$	−17.5921	+	30.4703i	−0.592020	+	1.02541i	0.401940	+	0.915666i	$0.368336\pi$
$883$	−17.5921	+	30.4703i	−0.592020	+	1.02541i	−0.993960	+	0.109742i	$0.964997\pi$
$884$	−21.8810	−	18.3603i	−0.735938	−	0.617525i
$885$	−11.3825	+	3.53270i	−0.382618	+	0.118750i
$886$	−0.122009	−	0.691947i	−0.00409897	−	0.0232464i
$887$	−32.5586	+	27.3199i	−1.09321	+	0.917312i	−0.996950	−	0.0780440i	$-0.975133\pi$
$887$	−32.5586	+	27.3199i	−1.09321	+	0.917312i	−0.0962602	+	0.995356i	$0.530688\pi$
$888$	3.28401	+	0.158179i	0.110204	+	0.00530815i
$889$	−3.97428	+	1.44652i	−0.133293	+	0.0485147i
$890$	11.2333			0.376541
$891$	0.938244	−	2.44033i	0.0314323	−	0.0817543i
$892$	−11.4781			−0.384316
$893$	46.4759	−	16.9158i	1.55526	−	0.566067i
$894$	−6.14714	−	0.296086i	−0.205591	−	0.00990261i
$895$	1.60796	−	1.34924i	0.0537481	−	0.0451000i
$896$	−0.173648	−	0.984808i	−0.00580118	−	0.0329001i
$897$	41.2565	−	12.8045i	1.37752	−	0.427529i
$898$	−16.1845	−	13.5804i	−0.540085	−	0.453185i
$899$	17.0535	−	29.5375i	0.568766	−	0.985131i
$900$	8.00104	−	11.2108i	0.266701	−	0.373692i
$901$	23.1194	+	40.0441i	0.770220	+	1.33406i
$902$	0.412322	−	2.33839i	0.0137288	−	0.0778599i
$903$	7.52314	−	5.71915i	0.250354	−	0.190321i
$904$	12.1636	+	4.42719i	0.404555	+	0.147246i
$905$	9.58849	+	3.48992i	0.318732	+	0.116009i
$906$	1.30818	+	10.2941i	0.0434614	+	0.341997i
$907$	−5.99020	+	33.9721i	−0.198901	+	1.12803i	0.707851	+	0.706362i	$0.249665\pi$
$907$	−5.99020	+	33.9721i	−0.198901	+	1.12803i	−0.906752	+	0.421663i	$0.861446\pi$
$908$	−4.24653	−	7.35521i	−0.140926	−	0.244091i
$909$	−24.1634	−	24.6020i	−0.801451	−	0.815996i
$910$	1.63827	−	2.83757i	0.0543081	−	0.0940645i
$911$	−34.2714	−	28.7571i	−1.13546	−	0.952765i	−0.136181	−	0.990684i	$-0.543483\pi$
$911$	−34.2714	−	28.7571i	−1.13546	−	0.952765i	−0.999281	+	0.0379188i	$0.987927\pi$
$912$	9.85927	+	9.11625i	0.326473	+	0.301869i
$913$	0.525121	+	2.97811i	0.0173790	+	0.0985610i
$914$	−10.2758	+	8.62242i	−0.339893	+	0.285204i
$915$	3.06843	−	4.76901i	0.101439	−	0.157659i
$916$	−6.87008	+	2.50051i	−0.226994	+	0.0826190i
$917$	−15.5294			−0.512827
$918$	19.2810	+	21.6199i	0.636369	+	0.713563i
$919$	−27.9154			−0.920844			−0.460422	−	0.887700i	$-0.652302\pi$
$919$	−27.9154			−0.920844			−0.460422	+	0.887700i	$0.652302\pi$
$920$	−2.92528	+	1.06471i	−0.0964436	+	0.0351026i
$921$	8.70971	+	16.9165i	0.286995	+	0.557416i
$922$	−23.1145	+	19.3954i	−0.761236	+	0.638753i
$923$	−3.55869	−	20.1823i	−0.117136	−	0.664309i
$924$	0.111111	−	0.490736i	0.00365528	−	0.0161440i
$925$	6.67591	+	5.60176i	0.219503	+	0.184185i
$926$	−20.3971	+	35.3289i	−0.670291	+	1.16098i
$927$	1.25400	+	15.9879i	0.0411868	+	0.525111i
$928$	2.35879	+	4.08555i	0.0774312	+	0.134115i
$929$	7.97115	−	45.2067i	0.261525	−	1.48318i	−0.517226	−	0.855849i	$-0.673035\pi$
$929$	7.97115	−	45.2067i	0.261525	−	1.48318i	0.778751	−	0.627333i	$-0.215854\pi$
$930$	7.38470	+	3.09782i	0.242154	+	0.101581i
$931$	7.28512	+	2.65157i	0.238760	+	0.0869016i
$932$	−23.1430	−	8.42336i	−0.758074	−	0.275916i
$933$	19.0529	+	7.99252i	0.623764	+	0.261663i
$934$	2.04329	−	11.5880i	0.0668583	−	0.379173i
$935$	0.517853	+	0.896948i	0.0169356	+	0.0293333i
$936$	12.6696	−	8.70261i	0.414118	−	0.284454i
$937$	−16.9310	+	29.3254i	−0.553113	+	0.958019i	0.444935	+	0.895563i	$0.353227\pi$
$937$	−16.9310	+	29.3254i	−0.553113	+	0.958019i	−0.998048	+	0.0624562i	$0.980107\pi$
$938$	−6.51684	−	5.46828i	−0.212782	−	0.178546i
$939$	−12.1827	+	53.8064i	−0.397566	+	1.75591i
$940$	0.708450	+	4.01782i	0.0231071	+	0.131047i
$941$	−29.0004	+	24.3342i	−0.945385	+	0.793272i	−0.978514	−	0.206179i	$-0.933897\pi$
$941$	−29.0004	+	24.3342i	−0.945385	+	0.793272i	0.0331294	+	0.999451i	$0.489453\pi$
$942$	10.5223	+	20.4371i	0.342836	+	0.665875i
$943$	−37.3888	+	13.6084i	−1.21755	+	0.443151i
$944$	−10.7597			−0.350197
$945$	−2.05828	+	2.60878i	−0.0669560	+	0.0848637i
$946$	1.58498			0.0515322
$947$	−11.2446	+	4.09270i	−0.365400	+	0.132995i	−0.518194	−	0.855263i	$-0.673395\pi$
$947$	−11.2446	+	4.09270i	−0.365400	+	0.132995i	0.152793	+	0.988258i	$0.451173\pi$
$948$	9.73612	−	15.1321i	0.316215	−	0.491467i
$949$	7.91633	−	6.64259i	0.256975	−	0.215628i
$950$	6.18060	+	35.0519i	0.200525	+	1.13723i
$951$	25.0961	+	23.2048i	0.813798	+	0.752467i
$952$	4.27070	+	3.58354i	0.138414	+	0.116143i
$953$	1.94487	−	3.36861i	0.0630005	−	0.109120i	−0.832805	−	0.553567i	$-0.813266\pi$
$953$	1.94487	−	3.36861i	0.0630005	−	0.109120i	0.895805	+	0.444447i	$0.146600\pi$
$954$	−24.0910	+	6.22353i	−0.779975	+	0.201494i
$955$	4.07530	+	7.05863i	0.131874	+	0.228412i
$956$	−2.05771	+	11.6699i	−0.0665512	+	0.377431i
$957$	0.299245	+	2.35475i	0.00967321	+	0.0761183i
$958$	−28.6772	−	10.4376i	−0.926517	−	0.337225i
$959$	6.00262	+	2.18477i	0.193835	+	0.0705500i
$960$	−0.881792	+	0.670346i	−0.0284597	+	0.0216353i
$961$	3.69338	−	20.9462i	0.119141	−	0.675684i
$962$	4.86278	+	8.42259i	0.156782	+	0.271555i
$963$	1.43453	+	0.138514i	0.0462270	+	0.00446354i
$964$	2.37880	−	4.12020i	0.0766160	−	0.132703i
$965$	−4.17296	−	3.50153i	−0.134332	−	0.112718i
$966$	−8.05239	+	2.49916i	−0.259081	+	0.0804092i
$967$	−6.10536	−	34.6252i	−0.196335	−	1.11347i	−0.910505	−	0.413499i	$-0.864307\pi$
$967$	−6.10536	−	34.6252i	−0.196335	−	1.11347i	0.714169	−	0.699973i	$-0.246805\pi$
$968$	−8.36184	+	7.01642i	−0.268760	+	0.225516i
$969$	−74.7745	−	3.60162i	−2.40210	−	0.115701i
$970$	−8.61937	+	3.13719i	−0.276751	+	0.100729i
$971$	−53.1442			−1.70548			−0.852740	−	0.522336i	$-0.825061\pi$
$971$	−53.1442			−1.70548			−0.852740	+	0.522336i	$0.825061\pi$
$972$	−13.9854	+	6.88532i	−0.448583	+	0.220847i
$973$	11.8180			0.378868
$974$	29.2260	−	10.6374i	0.936462	−	0.340844i
$975$	40.6945	+	1.96011i	1.30327	+	0.0627737i
$976$	3.92189	−	3.29085i	0.125537	−	0.105338i
$977$	−9.47966	−	53.7618i	−0.303281	−	1.71999i	−0.631486	−	0.775387i	$-0.717555\pi$
$977$	−9.47966	−	53.7618i	−0.303281	−	1.71999i	0.328205	−	0.944607i	$-0.393556\pi$
$978$	19.0045	−	5.89829i	0.607698	−	0.188607i
$979$	3.90892	+	3.27998i	0.124930	+	0.104828i
$980$	−0.319755	+	0.553832i	−0.0102142	+	0.0176915i
$981$	48.4986	+	4.68288i	1.54844	+	0.149513i
$982$	0.740030	+	1.28177i	0.0236153	+	0.0409029i
$983$	−1.21196	+	6.87334i	−0.0386554	+	0.219226i	−0.998016	−	0.0629564i	$-0.979947\pi$
$983$	−1.21196	+	6.87334i	−0.0386554	+	0.219226i	0.959361	+	0.282182i	$0.0910582\pi$
$984$	−11.2704	+	8.56788i	−0.359289	+	0.273134i
$985$	−3.40606	−	1.23970i	−0.108526	−	0.0395003i
$986$	−24.7144	−	8.99532i	−0.787068	−	0.286469i
$987$	1.39301	+	10.9616i	0.0443400	+	0.348911i
$988$	−6.89746	+	39.1174i	−0.219437	+	1.24449i
$989$	−13.2796	−	23.0009i	−0.422266	−	0.731386i
$990$	−0.539615	+	0.139401i	−0.0171501	+	0.00443046i
$991$	4.60856	−	7.98226i	0.146396	−	0.253565i	−0.783497	−	0.621395i	$-0.786566\pi$
$991$	4.60856	−	7.98226i	0.146396	−	0.253565i	0.929893	+	0.367831i	$0.119899\pi$
$992$	5.53831	+	4.64720i	0.175842	+	0.147549i
$993$	−11.3015	−	10.4498i	−0.358642	−	0.331614i
$994$	0.694580	+	3.93916i	0.0220307	+	0.124942i
$995$	−7.42015	+	6.22624i	−0.235235	+	0.197385i
$996$	9.75602	−	15.1630i	0.309131	−	0.480458i
$997$	6.87431	−	2.50204i	0.217712	−	0.0792405i	−0.230862	−	0.972987i	$-0.574155\pi$
$997$	6.87431	−	2.50204i	0.217712	−	0.0792405i	0.448573	+	0.893746i	$0.351932\pi$
$998$	35.6691			1.12909
$999$	−3.65133	−	9.16272i	−0.115523	−	0.289896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.d.169.1	yes	30
27.4	even	9	inner	378.2.u.d.85.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.d.85.1	✓	30	27.4	even	9	inner
378.2.u.d.169.1	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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.73005 - 0.0833302i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.111050 + 0.629795i) q^{5} +(1.65421 - 0.513405i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.98611 + 0.288330i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.73005 - 0.0833302i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.111050 + 0.629795i) q^{5} +(1.65421 - 0.513405i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.98611 + 0.288330i) q^{9} +(-0.319755 - 0.553832i) q^{10} +(0.0504445 - 0.286085i) q^{11} +(-1.37886 + 1.04822i) q^{12} +(-4.81453 - 1.75235i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-0.139640 - 1.09883i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.78750 + 4.82810i) q^{17} +(-2.90464 + 0.750369i) q^{18} +(3.87633 - 6.71400i) q^{19} +(0.489893 + 0.411069i) q^{20} +(1.27173 + 1.17589i) q^{21} +(0.0504445 + 0.286085i) q^{22} +(3.72896 - 3.12897i) q^{23} +(0.937189 - 1.45660i) q^{24} +(4.31415 - 1.57022i) q^{25} +5.12351 q^{26} +(-5.14208 - 0.747657i) q^{27} -1.00000 q^{28} +(4.43308 - 1.61351i) q^{29} +(0.507040 + 0.984800i) q^{30} +(5.53831 - 4.64720i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.111111 + 0.490736i) q^{33} +(-4.27070 - 3.58354i) q^{34} +(0.319755 - 0.553832i) q^{35} +(2.47283 - 1.69856i) q^{36} +(0.949111 + 1.64391i) q^{37} +(-1.34624 + 7.63488i) q^{38} +(8.18333 + 3.43283i) q^{39} +(-0.600943 - 0.218725i) q^{40} +(-7.68083 - 2.79559i) q^{41} +(-1.59721 - 0.670015i) q^{42} +(0.947438 - 5.37319i) q^{43} +(-0.145249 - 0.251579i) q^{44} +(0.150018 + 1.91266i) q^{45} +(-2.43391 + 4.21565i) q^{46} +(4.88703 + 4.10071i) q^{47} +(-0.382483 + 1.68929i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-3.51693 + 2.95105i) q^{50} +(-4.42018 - 8.58511i) q^{51} +(-4.81453 + 1.75235i) q^{52} +8.29396 q^{53} +(5.08769 - 1.05613i) q^{54} +0.185777 q^{55} +(0.939693 - 0.342020i) q^{56} +(-7.26570 + 11.2925i) q^{57} +(-3.61388 + 3.03241i) q^{58} +(-1.86840 - 10.5962i) q^{59} +(-0.813283 - 0.751991i) q^{60} +(3.92189 + 3.29085i) q^{61} +(-3.61488 + 6.26115i) q^{62} +(-2.10216 - 2.14031i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.568965 - 3.22676i) q^{65} +(-0.0634317 - 0.499144i) q^{66} +(-7.99409 - 2.90961i) q^{67} +(5.23879 + 1.90676i) q^{68} +(-6.71201 + 5.10252i) q^{69} +(-0.111050 + 0.629795i) q^{70} +(1.99996 + 3.46404i) q^{71} +(-1.74276 + 2.44188i) q^{72} +(-1.00849 + 1.74676i) q^{73} +(-1.45412 - 1.22015i) q^{74} +(-7.59453 + 2.35706i) q^{75} +(-1.34624 - 7.63488i) q^{76} +(-0.222535 + 0.186729i) q^{77} +(-8.86391 - 0.426944i) q^{78} +(-9.76214 + 3.55313i) q^{79} +0.639510 q^{80} +(8.83373 + 1.72197i) q^{81} +8.17377 q^{82} +(-9.78208 + 3.56039i) q^{83} +(1.73005 + 0.0833302i) q^{84} +(-2.73116 + 2.29171i) q^{85} +(0.947438 + 5.37319i) q^{86} +(-7.80388 + 2.42203i) q^{87} +(0.222535 + 0.186729i) q^{88} +(-8.78273 + 15.2121i) q^{89} +(-0.795138 - 1.74600i) q^{90} +(2.56176 + 4.43709i) q^{91} +(0.845287 - 4.79386i) q^{92} +(-9.96878 + 7.57835i) q^{93} +(-5.99483 - 2.18194i) q^{94} +(4.65891 + 1.69570i) q^{95} +(-0.218355 - 1.71823i) q^{96} +(2.49065 - 14.1252i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(0.233120 - 0.839737i) 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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