LMFDB - Embedded newform 570.2.bb.a.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.8
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.a.431.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.185551 + 1.72208i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.964794 + 1.43846i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.93114 + 0.639068i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.185551 + 1.72208i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.964794 + 1.43846i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.93114 + 0.639068i) q^{9} +(0.642788 + 0.766044i) q^{10} +(3.98946 + 2.30332i) q^{11} +(-1.66370 + 0.481768i) q^{12} +(-2.05613 + 5.64918i) q^{13} +(0.416874 - 2.36421i) q^{14} +(-0.116305 + 1.72814i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.620076 + 0.738978i) q^{17} +(-2.65617 - 1.39455i) q^{18} +(-2.01546 + 3.86496i) q^{19} +1.00000i q^{20} +(3.35758 - 2.45286i) q^{21} +(1.57556 + 4.32882i) q^{22} +(1.76390 - 0.311024i) q^{23} +(-1.58414 - 0.700350i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-5.20631 + 3.00586i) q^{26} +(-1.64440 - 4.92909i) q^{27} +(1.83903 - 1.54313i) q^{28} +(3.26368 - 2.73855i) q^{29} +(-1.19992 + 1.24907i) q^{30} +(-2.32175 + 1.34047i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-3.22626 + 7.29757i) q^{33} +(-0.950012 + 0.167513i) q^{34} +(-0.821082 - 2.25590i) q^{35} +(-1.13835 - 2.77564i) q^{36} -5.36603i q^{37} +(-4.02828 + 1.66522i) q^{38} +(-10.1099 - 2.49262i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(7.21865 - 2.62737i) q^{41} +(4.14872 + 0.279211i) q^{42} +(1.80861 - 10.2571i) q^{43} +(-1.57556 + 4.32882i) q^{44} +(-2.99758 + 0.120371i) q^{45} +(1.55115 + 0.895558i) q^{46} +(2.54962 + 3.03851i) q^{47} +(-0.763348 - 1.55477i) q^{48} +(0.618360 - 1.07103i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.38764 - 0.930705i) q^{51} +(-5.92040 - 1.04393i) q^{52} +(-2.18971 - 12.4185i) q^{53} +(1.90867 - 4.83290i) q^{54} +(3.52889 + 2.96109i) q^{55} +2.40068 q^{56} +(-7.02975 - 2.75365i) q^{57} +4.26043 q^{58} +(4.44196 + 3.72725i) q^{59} +(-1.72208 + 0.185551i) q^{60} +(-0.204640 - 1.16057i) q^{61} +(-2.64020 - 0.465539i) q^{62} +(4.84703 + 5.32690i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.00586 + 5.20631i) q^{65} +(-7.16224 + 3.51646i) q^{66} +(10.1322 + 12.0751i) q^{67} +(-0.835427 - 0.482334i) q^{68} +(0.862903 + 2.97988i) q^{69} +(0.821082 - 2.25590i) q^{70} +(-0.344961 + 1.95637i) q^{71} +(0.912122 - 2.85798i) q^{72} +(-0.0140670 + 0.00511995i) q^{73} +(3.44922 - 4.11062i) q^{74} +(-0.414626 + 1.68169i) q^{75} +(-4.15622 - 1.31370i) q^{76} -11.0591i q^{77} +(-6.14238 - 8.40796i) q^{78} +(5.29911 + 14.5592i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(8.18318 - 3.74640i) q^{81} +(7.21865 + 2.62737i) q^{82} +(-13.9171 + 8.03502i) q^{83} +(2.99863 + 2.88063i) q^{84} +(-0.738978 + 0.620076i) q^{85} +(7.97864 - 6.69488i) q^{86} +(5.32160 + 5.11219i) q^{87} +(-3.98946 + 2.30332i) q^{88} +(14.0992 + 5.13168i) q^{89} +(-2.37366 - 1.83460i) q^{90} +(14.2130 - 2.50613i) q^{91} +(0.612598 + 1.68310i) q^{92} +(-2.73920 - 3.74953i) q^{93} +3.96650i q^{94} +(-2.65599 + 3.45626i) q^{95} +(0.414626 - 1.68169i) q^{96} +(0.878623 - 1.04710i) q^{97} +(1.16214 - 0.422983i) q^{98} +(-13.1657 - 4.20181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.185551	+	1.72208i	0.107128	+	0.994245i
$3$	0.185551	+	1.72208i	0.107128	+	0.994245i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$6$	−0.964794	+	1.43846i	−0.393875	+	0.587250i
$7$	−1.20034	−	2.07905i	−0.453686	−	0.785808i	0.544925	−	0.838485i	$-0.316558\pi$
$7$	−1.20034	−	2.07905i	−0.453686	−	0.785808i	−0.998612	+	0.0526767i	$0.983225\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.93114	+	0.639068i	−0.977047	+	0.213023i
$10$	0.642788	+	0.766044i	0.203267	+	0.242245i
$11$	3.98946	+	2.30332i	1.20287	+	0.694476i	0.961192	−	0.275881i	$-0.0889695\pi$
$11$	3.98946	+	2.30332i	1.20287	+	0.694476i	0.241676	+	0.970357i	$0.422303\pi$
$12$	−1.66370	+	0.481768i	−0.480269	+	0.139075i
$13$	−2.05613	+	5.64918i	−0.570268	+	1.56680i	0.233814	+	0.972281i	$0.424879\pi$
$13$	−2.05613	+	5.64918i	−0.570268	+	1.56680i	−0.804082	+	0.594518i	$0.797343\pi$
$14$	0.416874	−	2.36421i	0.111414	−	0.631862i
$15$	−0.116305	+	1.72814i	−0.0300298	+	0.446204i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.620076	+	0.738978i	−0.150391	+	0.179229i	−0.835980	−	0.548760i	$-0.815100\pi$
$17$	−0.620076	+	0.738978i	−0.150391	+	0.179229i	0.685589	+	0.727988i	$0.259545\pi$
$18$	−2.65617	−	1.39455i	−0.626065	−	0.328698i
$19$	−2.01546	+	3.86496i	−0.462379	+	0.886683i
$19$	−2.01546	+	3.86496i	−0.462379	+	0.886683i
$20$			1.00000i			0.223607i
$21$	3.35758	−	2.45286i	0.732683	−	0.535258i
$22$	1.57556	+	4.32882i	0.335911	+	0.922908i
$23$	1.76390	−	0.311024i	0.367800	−	0.0648530i	0.0133061	−	0.999911i	$-0.495764\pi$
$23$	1.76390	−	0.311024i	0.367800	−	0.0648530i	0.354493	+	0.935058i	$0.384653\pi$
$24$	−1.58414	−	0.700350i	−0.323362	−	0.142958i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	−5.20631	+	3.00586i	−1.02104	+	0.589498i
$27$	−1.64440	−	4.92909i	−0.316466	−	0.948604i
$28$	1.83903	−	1.54313i	0.347544	−	0.291624i
$29$	3.26368	−	2.73855i	0.606051	−	0.508537i	−0.287333	−	0.957831i	$-0.592769\pi$
$29$	3.26368	−	2.73855i	0.606051	−	0.508537i	0.893384	+	0.449294i	$0.148324\pi$
$30$	−1.19992	+	1.24907i	−0.219075	+	0.228049i
$31$	−2.32175	+	1.34047i	−0.416999	+	0.240755i	−0.693793	−	0.720175i	$-0.744062\pi$
$31$	−2.32175	+	1.34047i	−0.416999	+	0.240755i	0.276793	+	0.960929i	$0.410728\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−3.22626	+	7.29757i	−0.561619	+	1.27034i
$34$	−0.950012	+	0.167513i	−0.162926	+	0.0287282i
$35$	−0.821082	−	2.25590i	−0.138788	−	0.381317i
$36$	−1.13835	−	2.77564i	−0.189724	−	0.462606i
$37$		−	5.36603i		−	0.882170i	−0.897465	−	0.441085i	$-0.854594\pi$
$37$		−	5.36603i		−	0.882170i	0.897465	−	0.441085i	$-0.145406\pi$
$38$	−4.02828	+	1.66522i	−0.653474	+	0.270134i
$39$	−10.1099	−	2.49262i	−1.61887	−	0.399139i
$40$	−0.642788	+	0.766044i	−0.101634	+	0.121122i
$41$	7.21865	−	2.62737i	1.12736	−	0.410327i	0.290029	−	0.957018i	$-0.406335\pi$
$41$	7.21865	−	2.62737i	1.12736	−	0.410327i	0.837334	+	0.546691i	$0.184113\pi$
$42$	4.14872	+	0.279211i	0.640161	+	0.0430832i
$43$	1.80861	−	10.2571i	0.275811	−	1.56420i	−0.460564	−	0.887626i	$-0.652353\pi$
$43$	1.80861	−	10.2571i	0.275811	−	1.56420i	0.736375	−	0.676574i	$-0.236536\pi$
$44$	−1.57556	+	4.32882i	−0.237525	+	0.652594i
$45$	−2.99758	+	0.120371i	−0.446853	+	0.0179439i
$46$	1.55115	+	0.895558i	0.228705	+	0.132043i
$47$	2.54962	+	3.03851i	0.371900	+	0.443213i	0.919240	−	0.393697i	$-0.128804\pi$
$47$	2.54962	+	3.03851i	0.371900	+	0.443213i	−0.547340	+	0.836910i	$0.684360\pi$
$48$	−0.763348	−	1.55477i	−0.110180	−	0.224411i
$49$	0.618360	−	1.07103i	0.0883372	−	0.153004i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−1.38764	−	0.930705i	−0.194308	−	0.130325i
$52$	−5.92040	−	1.04393i	−0.821011	−	0.144766i
$53$	−2.18971	−	12.4185i	−0.300780	−	1.70581i	−0.642731	−	0.766092i	$-0.722199\pi$
$53$	−2.18971	−	12.4185i	−0.300780	−	1.70581i	0.341951	−	0.939718i	$-0.388912\pi$
$54$	1.90867	−	4.83290i	0.259737	−	0.657675i
$55$	3.52889	+	2.96109i	0.475835	+	0.399273i
$56$	2.40068			0.320805
$57$	−7.02975	−	2.75365i	−0.931114	−	0.364729i
$58$	4.26043			0.559422
$59$	4.44196	+	3.72725i	0.578294	+	0.485246i	0.884386	−	0.466756i	$-0.154577\pi$
$59$	4.44196	+	3.72725i	0.578294	+	0.485246i	−0.306092	+	0.952002i	$0.599022\pi$
$60$	−1.72208	+	0.185551i	−0.222320	+	0.0239545i
$61$	−0.204640	−	1.16057i	−0.0262015	−	0.148596i	0.968900	−	0.247451i	$-0.0795930\pi$
$61$	−0.204640	−	1.16057i	−0.0262015	−	0.148596i	−0.995102	+	0.0988554i	$0.968482\pi$
$62$	−2.64020	−	0.465539i	−0.335306	−	0.0591235i
$63$	4.84703	+	5.32690i	0.610668	+	0.671126i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−3.00586	+	5.20631i	−0.372831	+	0.645763i
$66$	−7.16224	+	3.51646i	−0.881611	+	0.432847i
$67$	10.1322	+	12.0751i	1.23785	+	1.47521i	0.825715	+	0.564087i	$0.190772\pi$
$67$	10.1322	+	12.0751i	1.23785	+	1.47521i	0.412133	+	0.911124i	$0.364784\pi$
$68$	−0.835427	−	0.482334i	−0.101310	−	0.0584916i
$69$	0.862903	+	2.97988i	0.103881	+	0.358735i
$70$	0.821082	−	2.25590i	0.0981381	−	0.269632i
$71$	−0.344961	+	1.95637i	−0.0409394	+	0.232179i	−0.998411	−	0.0563481i	$-0.982054\pi$
$71$	−0.344961	+	1.95637i	−0.0409394	+	0.232179i	0.957472	+	0.288527i	$0.0931654\pi$
$72$	0.912122	−	2.85798i	0.107495	−	0.336816i
$73$	−0.0140670	+	0.00511995i	−0.00164641	+	0.000599245i	−0.342843	−	0.939393i	$-0.611390\pi$
$73$	−0.0140670	+	0.00511995i	−0.00164641	+	0.000599245i	0.341197	+	0.939992i	$0.389168\pi$
$74$	3.44922	−	4.11062i	0.400963	−	0.477850i
$75$	−0.414626	+	1.68169i	−0.0478769	+	0.194185i
$76$	−4.15622	−	1.31370i	−0.476752	−	0.150692i
$77$		−	11.0591i		−	1.26030i
$78$	−6.14238	−	8.40796i	−0.695488	−	0.952014i
$79$	5.29911	+	14.5592i	0.596196	+	1.63804i	0.758784	+	0.651342i	$0.225794\pi$
$79$	5.29911	+	14.5592i	0.596196	+	1.63804i	−0.162588	+	0.986694i	$0.551984\pi$
$80$	−0.984808	+	0.173648i	−0.110105	+	0.0194145i
$81$	8.18318	−	3.74640i	0.909243	−	0.416266i
$82$	7.21865	+	2.62737i	0.797167	+	0.290145i
$83$	−13.9171	+	8.03502i	−1.52760	+	0.881958i	−0.528134	+	0.849161i	$0.677108\pi$
$83$	−13.9171	+	8.03502i	−1.52760	+	0.881958i	−0.999462	+	0.0327971i	$0.989558\pi$
$84$	2.99863	+	2.88063i	0.327177	+	0.314303i
$85$	−0.738978	+	0.620076i	−0.0801534	+	0.0672567i
$86$	7.97864	−	6.69488i	0.860359	−	0.721927i
$87$	5.32160	+	5.11219i	0.570535	+	0.548085i
$88$	−3.98946	+	2.30332i	−0.425278	+	0.245534i
$89$	14.0992	+	5.13168i	1.49451	+	0.543957i	0.954632	−	0.297788i	$-0.0962487\pi$
$89$	14.0992	+	5.13168i	1.49451	+	0.543957i	0.539877	+	0.841744i	$0.318471\pi$
$90$	−2.37366	−	1.83460i	−0.250205	−	0.193384i
$91$	14.2130	−	2.50613i	1.48993	−	0.262714i
$92$	0.612598	+	1.68310i	0.0638677	+	0.175475i
$93$	−2.73920	−	3.74953i	−0.284042	−	0.388808i
$94$			3.96650i			0.409113i
$95$	−2.65599	+	3.45626i	−0.272498	+	0.354605i
$96$	0.414626	−	1.68169i	0.0423176	−	0.171637i
$97$	0.878623	−	1.04710i	0.0892106	−	0.106317i	−0.719592	−	0.694397i	$-0.755671\pi$
$97$	0.878623	−	1.04710i	0.0892106	−	0.106317i	0.808803	+	0.588080i	$0.200116\pi$
$98$	1.16214	−	0.422983i	0.117394	−	0.0427278i
$99$	−13.1657	−	4.20181i	−1.32320	−	0.422298i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	5.75439	−	15.8101i	0.572583	−	1.57316i	−0.227824	−	0.973702i	$-0.573161\pi$
$101$	5.75439	−	15.8101i	0.572583	−	1.57316i	0.800407	−	0.599457i	$-0.204617\pi$
$102$	−0.464746	−	1.60492i	−0.0460168	−	0.158911i
$103$	−5.52990	−	3.19269i	−0.544877	−	0.314585i	0.202176	−	0.979349i	$-0.435199\pi$
$103$	−5.52990	−	3.19269i	−0.544877	−	0.314585i	−0.747053	+	0.664764i	$0.768532\pi$
$104$	−3.86426	−	4.60525i	−0.378922	−	0.451582i
$105$	3.73250	−	1.83256i	0.364255	−	0.178839i
$106$	6.30503	−	10.9206i	0.612398	−	1.06071i
$107$	−5.86709	−	10.1621i	−0.567193	−	0.982406i	−0.996842	−	0.0794106i	$-0.974696\pi$
$107$	−5.86709	−	10.1621i	−0.567193	−	0.982406i	0.429649	−	0.902996i	$-0.358637\pi$
$108$	4.56866	−	2.47535i	0.439619	−	0.238191i
$109$	−0.193715	−	0.0341572i	−0.0185545	−	0.00327167i	0.164363	−	0.986400i	$-0.447443\pi$
$109$	−0.193715	−	0.0341572i	−0.0185545	−	0.00327167i	−0.182918	+	0.983128i	$0.558554\pi$
$110$	0.799934	+	4.53665i	0.0762707	+	0.432552i
$111$	9.24075	−	0.995671i	0.877093	−	0.0945049i
$112$	1.83903	+	1.54313i	0.173772	+	0.145812i
$113$	−6.61379			−0.622173			−0.311087	−	0.950382i	$-0.600693\pi$
$113$	−6.61379			−0.622173			−0.311087	+	0.950382i	$0.600693\pi$
$114$	−3.61509	−	6.62805i	−0.338585	−	0.620774i
$115$	1.79112			0.167022
$116$	3.26368	+	2.73855i	0.303025	+	0.254268i
$117$	2.41661	−	17.8725i	0.223415	−	1.65232i
$118$	1.00691	+	5.71047i	0.0926936	+	0.525692i
$119$	2.28068	+	0.402145i	0.209069	+	0.0368646i
$120$	−1.43846	−	0.964794i	−0.131313	−	0.0880732i
$121$	5.11054	+	8.85171i	0.464594	+	0.804701i
$122$	0.589237	−	1.02059i	0.0533470	−	0.0923998i
$123$	5.86398	+	11.9436i	0.528737	+	1.07692i
$124$	−1.72327	−	2.05371i	−0.154754	−	0.184429i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	0.288974	+	7.19625i	0.0257438	+	0.641093i
$127$	3.28399	−	9.02268i	0.291407	−	0.800634i	−0.704455	−	0.709749i	$-0.748808\pi$
$127$	3.28399	−	9.02268i	0.291407	−	0.800634i	0.995861	−	0.0908846i	$-0.0289694\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	17.9992	+	1.21136i	1.58475	+	0.106654i
$130$	−5.64918	+	2.05613i	−0.495465	+	0.180335i
$131$	2.40610	−	2.86747i	0.210222	−	0.250532i	−0.650622	−	0.759402i	$-0.725492\pi$
$131$	2.40610	−	2.86747i	0.210222	−	0.250532i	0.860844	+	0.508869i	$0.169936\pi$
$132$	−7.74694	−	1.91003i	−0.674284	−	0.166247i
$133$	10.4547	−	0.449021i	0.906537	−	0.0389351i
$134$			15.7629i			1.36171i
$135$	−0.763494	−	5.13975i	−0.0657111	−	0.442360i
$136$	−0.329936	−	0.906491i	−0.0282918	−	0.0777310i
$137$	−6.90086	+	1.21681i	−0.589580	+	0.103959i	−0.460476	−	0.887672i	$-0.652321\pi$
$137$	−6.90086	+	1.21681i	−0.589580	+	0.103959i	−0.129104	+	0.991631i	$0.541210\pi$
$138$	−1.25441	+	2.83738i	−0.106782	+	0.241534i
$139$	−6.97727	−	2.53952i	−0.591804	−	0.215399i	0.0287187	−	0.999588i	$-0.490857\pi$
$139$	−6.97727	−	2.53952i	−0.591804	−	0.215399i	−0.620523	+	0.784189i	$0.713080\pi$
$140$	2.07905	−	1.20034i	0.175712	−	0.101447i
$141$	−4.75949	+	4.95445i	−0.400822	+	0.417240i
$142$	−1.52179	+	1.27693i	−0.127706	+	0.107158i
$143$	−21.2147	+	17.8012i	−1.77406	+	1.48862i
$144$	2.53580	−	1.60304i	0.211317	−	0.133586i
$145$	3.68964	−	2.13022i	0.306408	−	0.176905i
$146$	−0.0140670	−	0.00511995i	−0.00116419	−	0.000423730i
$147$	1.95914	+	0.866137i	0.161587	+	0.0714378i
$148$	5.28451	−	0.931801i	0.434384	−	0.0765936i
$149$	−3.77873	−	10.3820i	−0.309566	−	0.850525i	−0.992741	−	0.120271i	$-0.961624\pi$
$149$	−3.77873	−	10.3820i	−0.309566	−	0.850525i	0.683175	−	0.730254i	$-0.260599\pi$
$150$	−1.39859	+	1.02173i	−0.114195	+	0.0834242i
$151$			1.38153i			0.112427i	0.998419	+	0.0562136i	$0.0179028\pi$
$151$			1.38153i			0.112427i	−0.998419	+	0.0562136i	$0.982097\pi$
$152$	−2.33942	−	3.67792i	−0.189752	−	0.298319i
$153$	1.34527	−	2.56232i	0.108759	−	0.207151i
$154$	7.10863	−	8.47174i	0.572830	−	0.682672i
$155$	−2.51925	+	0.916933i	−0.202351	+	0.0736498i
$156$	0.699193	−	10.3891i	0.0559802	−	0.831795i
$157$	1.58584	−	8.99376i	0.126564	−	0.717780i	−0.853803	−	0.520597i	$-0.825709\pi$
$157$	1.58584	−	8.99376i	0.126564	−	0.717780i	0.980367	−	0.197183i	$-0.0631794\pi$
$158$	−5.29911	+	14.5592i	−0.421575	+	1.15827i
$159$	20.9794	−	6.07513i	1.66377	−	0.481789i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−2.76392	−	3.29392i	−0.217828	−	0.259597i
$162$	8.67682	+	2.39014i	0.681715	+	0.187787i
$163$	2.41249	−	4.17855i	0.188961	−	0.327289i	−0.755943	−	0.654637i	$-0.772821\pi$
$163$	2.41249	−	4.17855i	0.188961	−	0.327289i	0.944904	+	0.327348i	$0.106155\pi$
$164$	3.84096	+	6.65274i	0.299929	+	0.519492i
$165$	−4.44445	+	6.62647i	−0.346000	+	0.515870i
$166$	−15.8259	−	2.79053i	−1.22833	−	0.216587i
$167$	3.05049	+	17.3002i	0.236054	+	1.33873i	0.840383	+	0.541993i	$0.182330\pi$
$167$	3.05049	+	17.3002i	0.236054	+	1.33873i	−0.604329	+	0.796735i	$0.706559\pi$
$168$	0.445449	+	4.13418i	0.0343671	+	0.318959i
$169$	−17.7269	−	14.8747i	−1.36361	−	1.14420i
$170$	−0.964668			−0.0739866
$171$	3.43763	−	12.6168i	0.262882	−	0.964828i
$172$	10.4154			0.794165
$173$	−9.21180	−	7.72961i	−0.700360	−	0.587672i	0.221516	−	0.975157i	$-0.428899\pi$
$173$	−9.21180	−	7.72961i	−0.700360	−	0.587672i	−0.921876	+	0.387485i	$0.873344\pi$
$174$	0.790527	+	7.33682i	0.0599297	+	0.556203i
$175$	−0.416874	−	2.36421i	−0.0315127	−	0.178718i
$176$	−4.53665	−	0.799934i	−0.341963	−	0.0602973i
$177$	−5.59442	+	8.34102i	−0.420502	+	0.626949i
$178$	7.50201	+	12.9939i	0.562299	+	0.973931i
$179$	−7.69811	+	13.3335i	−0.575384	+	0.996594i	0.420616	+	0.907239i	$0.361814\pi$
$179$	−7.69811	+	13.3335i	−0.575384	+	0.996594i	−0.996000	+	0.0893555i	$0.971519\pi$
$180$	−0.639068	−	2.93114i	−0.0476333	−	0.218474i
$181$	0.166642	+	0.198596i	0.0123864	+	0.0147615i	0.772202	−	0.635377i	$-0.219155\pi$
$181$	0.166642	+	0.198596i	0.0123864	+	0.0147615i	−0.759816	+	0.650139i	$0.774711\pi$
$182$	12.4987	+	7.21613i	0.926465	+	0.534895i
$183$	1.96063	−	0.567752i	0.144934	−	0.0419694i
$184$	−0.612598	+	1.68310i	−0.0451613	+	0.124080i
$185$	0.931801	−	5.28451i	0.0685074	−	0.388525i
$186$	0.311805	−	4.63303i	0.0228627	−	0.339710i
$187$	−4.17587	+	1.51989i	−0.305370	+	0.111146i
$188$	−2.54962	+	3.03851i	−0.185950	+	0.221606i
$189$	−8.27399	+	9.33539i	−0.601844	+	0.679050i
$190$	−4.25624	+	0.940415i	−0.308780	+	0.0682249i
$191$		−	23.6775i		−	1.71324i	−0.515945	−	0.856622i	$-0.672559\pi$
$191$		−	23.6775i		−	1.71324i	0.515945	−	0.856622i	$-0.327441\pi$
$192$	1.39859	−	1.02173i	0.100935	−	0.0737373i
$193$	7.04421	+	19.3538i	0.507053	+	1.39312i	0.884263	+	0.466989i	$0.154661\pi$
$193$	7.04421	+	19.3538i	0.507053	+	1.39312i	−0.377210	+	0.926128i	$0.623116\pi$
$194$	1.34613	−	0.237359i	0.0966464	−	0.0170414i
$195$	−9.52344	−	4.21031i	−0.681988	−	0.301507i
$196$	1.16214	+	0.422983i	0.0830098	+	0.0302131i
$197$	13.0242	−	7.51952i	0.927935	−	0.535743i	0.0417769	−	0.999127i	$-0.486698\pi$
$197$	13.0242	−	7.51952i	0.927935	−	0.535743i	0.886158	+	0.463384i	$0.153365\pi$
$198$	−7.38460	−	11.6815i	−0.524801	−	0.830168i
$199$	−0.287594	+	0.241320i	−0.0203870	+	0.0171067i	−0.652924	−	0.757423i	$-0.726458\pi$
$199$	−0.287594	+	0.241320i	−0.0203870	+	0.0171067i	0.632537	+	0.774530i	$0.282014\pi$
$200$	−0.766044	+	0.642788i	−0.0541675	+	0.0454519i
$201$	−18.9143	+	19.6891i	−1.33411	+	1.38876i
$202$	14.5706	−	8.41236i	1.02519	−	0.591891i
$203$	−9.61113	−	3.49817i	−0.674569	−	0.245523i
$204$	0.675605	−	1.52817i	0.0473018	−	0.106993i
$205$	7.56522	−	1.33395i	0.528378	−	0.0931673i
$206$	−2.18393	−	6.00029i	−0.152161	−	0.418060i
$207$	−4.97149	+	2.03891i	−0.345542	+	0.141714i
$208$		−	6.01173i		−	0.416838i
$209$	−16.9428	+	10.7769i	−1.17196	+	0.745451i
$210$	4.03721	+	0.995387i	0.278594	+	0.0686882i
$211$	−0.0393604	+	0.0469080i	−0.00270969	+	0.00322928i	−0.767398	−	0.641172i	$-0.778449\pi$
$211$	−0.0393604	+	0.0469080i	−0.00270969	+	0.00322928i	0.764688	+	0.644401i	$0.222893\pi$
$212$	11.8496	−	4.31289i	0.813832	−	0.296211i
$213$	−3.43304	−	0.231046i	−0.235228	−	0.0158310i
$214$	2.03762	−	11.5559i	0.139289	−	0.789945i
$215$	3.56227	−	9.78726i	0.242945	−	0.667485i
$216$	5.09092	+	1.04045i	0.346393	+	0.0707937i
$217$	5.57380	+	3.21803i	0.378374	+	0.218454i
$218$	−0.126439	−	0.150684i	−0.00856350	−	0.0102056i
$219$	−0.0114271	−	0.0232745i	−0.000772173	−	0.00157274i
$220$	−2.30332	+	3.98946i	−0.155290	+	0.268969i
$221$	−2.89966	−	5.02236i	−0.195052	−	0.337840i
$222$	7.71883	+	5.17711i	0.518054	+	0.347465i
$223$	−20.2364	−	3.56823i	−1.35513	−	0.238946i	−0.551550	−	0.834142i	$-0.685963\pi$
$223$	−20.2364	−	3.56823i	−1.35513	−	0.238946i	−0.803581	+	0.595196i	$0.797075\pi$
$224$	0.416874	+	2.36421i	0.0278536	+	0.157966i
$225$	−2.97295	−	0.401982i	−0.198196	−	0.0267988i
$226$	−5.06646	−	4.25126i	−0.337016	−	0.282790i
$227$	13.4718			0.894157			0.447078	−	0.894495i	$-0.352465\pi$
$227$	13.4718			0.894157			0.447078	+	0.894495i	$0.352465\pi$
$228$	1.49111	−	7.40112i	0.0987511	−	0.490151i
$229$	−2.84712			−0.188143			−0.0940714	−	0.995565i	$-0.529988\pi$
$229$	−2.84712			−0.188143			−0.0940714	+	0.995565i	$0.529988\pi$
$230$	1.37207	+	1.15131i	0.0904719	+	0.0759149i
$231$	19.0446	−	2.05202i	1.25305	−	0.135013i
$232$	0.739817	+	4.19571i	0.0485713	+	0.275462i
$233$	8.97563	+	1.58265i	0.588013	+	0.103683i	0.459736	−	0.888056i	$-0.347944\pi$
$233$	8.97563	+	1.58265i	0.588013	+	0.103683i	0.128277	+	0.991738i	$0.459055\pi$
$234$	13.3395	−	12.1378i	0.872029	−	0.793473i
$235$	1.98325	+	3.43509i	0.129373	+	0.224081i
$236$	−2.89928	+	5.02171i	−0.188727	+	0.326885i
$237$	−24.0889	+	11.8270i	−1.56474	+	0.768245i
$238$	1.48861	+	1.77405i	0.0964921	+	0.114995i
$239$	6.72533	+	3.88287i	0.435026	+	0.251162i	0.701485	−	0.712684i	$-0.252521\pi$
$239$	6.72533	+	3.88287i	0.435026	+	0.251162i	−0.266460	+	0.963846i	$0.585854\pi$
$240$	−0.481768	−	1.66370i	−0.0310980	−	0.107391i
$241$	2.77014	−	7.61089i	0.178440	−	0.490261i	−0.817937	−	0.575308i	$-0.804882\pi$
$241$	2.77014	−	7.61089i	0.178440	−	0.490261i	0.996377	+	0.0850477i	$0.0271043\pi$
$242$	−1.77487	+	10.0658i	−0.114093	+	0.647054i
$243$	7.97000	+	13.3970i	0.511276	+	0.859417i
$244$	1.10740	−	0.403062i	0.0708943	−	0.0258034i
$245$	0.794949	−	0.947383i	0.0507874	−	0.0605261i
$246$	−3.18513	+	12.9186i	−0.203076	+	0.823662i
$247$	−17.6898	−	19.3326i	−1.12557	−	1.23010i
$248$		−	2.68093i		−	0.170239i
$249$	−16.4193	−	22.4754i	−1.04053	−	1.42432i
$250$	0.342020	+	0.939693i	0.0216313	+	0.0594314i
$251$	1.68837	−	0.297704i	0.106569	−	0.0187909i	−0.120109	−	0.992761i	$-0.538325\pi$
$251$	1.68837	−	0.297704i	0.106569	−	0.0187909i	0.226678	+	0.973970i	$0.427213\pi$
$252$	−4.40429	+	5.69840i	−0.277444	+	0.358965i
$253$	7.75342	+	2.82201i	0.487453	+	0.177418i
$254$	8.31535	−	4.80087i	0.521751	−	0.301233i
$255$	−1.20494	−	1.15753i	−0.0754563	−	0.0724871i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−14.2297	+	11.9401i	−0.887624	+	0.744805i	−0.967732	−	0.251981i	$-0.918918\pi$
$257$	−14.2297	+	11.9401i	−0.887624	+	0.744805i	0.0801083	+	0.996786i	$0.474473\pi$
$258$	13.0096	+	12.4976i	0.809941	+	0.778070i
$259$	−11.1563	+	6.44107i	−0.693216	+	0.400229i
$260$	−5.64918	−	2.05613i	−0.350347	−	0.127516i
$261$	−7.81619	+	10.1128i	−0.483810	+	0.625967i
$262$	3.68635	−	0.650004i	0.227744	−	0.0401574i
$263$	−1.72478	−	4.73879i	−0.106354	−	0.292206i	0.875088	−	0.483964i	$-0.160803\pi$
$263$	−1.72478	−	4.73879i	−0.106354	−	0.292206i	−0.981442	+	0.191758i	$0.938581\pi$
$264$	−4.70675	−	6.44280i	−0.289681	−	0.396527i
$265$		−	12.6101i		−	0.774629i
$266$	8.29739	+	6.37618i	0.508745	+	0.390949i
$267$	−6.22106	+	25.2321i	−0.380723	+	1.54418i
$268$	−10.1322	+	12.0751i	−0.618924	+	0.737605i
$269$	22.7475	−	8.27943i	1.38694	−	0.504806i	0.462667	−	0.886532i	$-0.346893\pi$
$269$	22.7475	−	8.27943i	1.38694	−	0.504806i	0.924275	+	0.381726i	$0.124670\pi$
$270$	2.71890	−	4.42804i	0.165467	−	0.269482i
$271$	−1.61641	+	9.16710i	−0.0981898	+	0.556862i	0.895533	+	0.444994i	$0.146794\pi$
$271$	−1.61641	+	9.16710i	−0.0981898	+	0.556862i	−0.993723	+	0.111867i	$0.964317\pi$
$272$	0.329936	−	0.906491i	0.0200053	−	0.0549641i
$273$	6.95300	+	24.0109i	0.420815	+	1.45321i
$274$	−6.06851	−	3.50366i	−0.366612	−	0.211664i
$275$	2.96109	+	3.52889i	0.178560	+	0.212800i
$276$	−2.78477	+	1.36724i	−0.167623	+	0.0822984i
$277$	−14.8454	+	25.7130i	−0.891975	+	1.54495i	−0.0544710	+	0.998515i	$0.517347\pi$
$277$	−14.8454	+	25.7130i	−0.891975	+	1.54495i	−0.837504	+	0.546431i	$0.815986\pi$
$278$	−3.71253	−	6.43028i	−0.222662	−	0.385663i
$279$	5.94874	−	5.41285i	0.356142	−	0.324059i
$280$	2.36421	+	0.416874i	0.141289	+	0.0249130i
$281$	−1.65593	−	9.39127i	−0.0987848	−	0.560236i	−0.993522	−	0.113643i	$-0.963748\pi$
$281$	−1.65593	−	9.39127i	−0.0987848	−	0.560236i	0.894737	−	0.446594i	$-0.147363\pi$
$282$	−6.83064	+	0.735987i	−0.406759	+	0.0438274i
$283$	−10.6360	−	8.92466i	−0.632244	−	0.530516i	0.269381	−	0.963034i	$-0.413181\pi$
$283$	−10.6360	−	8.92466i	−0.632244	−	0.530516i	−0.901626	+	0.432518i	$0.857625\pi$
$284$	−1.98655			−0.117880
$285$	−6.44479	−	3.93252i	−0.381756	−	0.232942i
$286$	−27.6938			−1.63757
$287$	−14.1273	−	11.8542i	−0.833908	−	0.699732i
$288$	2.97295	+	0.401982i	0.175183	+	0.0236870i
$289$	2.79042	+	15.8253i	0.164143	+	0.930899i
$290$	4.19571	+	0.739817i	0.246381	+	0.0434435i
$291$	1.96623	+	1.31877i	0.115262	+	0.0773077i
$292$	−0.00748487	−	0.0129642i	−0.000438019	−	0.000758671i
$293$	5.72607	−	9.91785i	0.334521	−	0.579407i	−0.648872	−	0.760898i	$-0.724759\pi$
$293$	5.72607	−	9.91785i	0.334521	−	0.579407i	0.983393	+	0.181491i	$0.0580922\pi$
$294$	0.944048	+	1.92281i	0.0550580	+	0.112141i
$295$	3.72725	+	4.44196i	0.217009	+	0.258621i
$296$	4.64712	+	2.68302i	0.270108	+	0.155947i
$297$	4.79297	−	23.4520i	0.278116	−	1.36082i
$298$	3.77873	−	10.3820i	0.218896	−	0.601412i
$299$	−1.86979	+	10.6041i	−0.108133	+	0.613252i
$300$	−1.72814	−	0.116305i	−0.0997743	−	0.00671486i
$301$	−23.4961	+	8.55188i	−1.35429	+	0.492922i
$302$	−0.888030	+	1.05831i	−0.0511004	+	0.0608991i
$303$	28.2940	+	6.97597i	1.62545	+	0.400759i
$304$	0.572020	−	4.32120i	0.0328076	−	0.247838i
$305$		−	1.17847i		−	0.0674792i
$306$	2.67757	−	1.09813i	0.153066	−	0.0627757i
$307$	9.29783	+	25.5456i	0.530655	+	1.45796i	0.858293	+	0.513159i	$0.171525\pi$
$307$	9.29783	+	25.5456i	0.530655	+	1.45796i	−0.327638	+	0.944803i	$0.606253\pi$
$308$	10.8911	−	1.92039i	0.620576	−	0.109424i
$309$	4.47200	−	10.1154i	0.254403	−	0.575442i
$310$	−2.51925	−	0.916933i	−0.143084	−	0.0520783i
$311$	−6.73107	+	3.88618i	−0.381684	+	0.220365i	−0.678551	−	0.734554i	$-0.737392\pi$
$311$	−6.73107	+	3.88618i	−0.381684	+	0.220365i	0.296867	+	0.954919i	$0.404058\pi$
$312$	7.21361	−	7.50909i	0.408390	−	0.425119i
$313$	1.63130	−	1.36882i	0.0922063	−	0.0773703i	−0.595519	−	0.803341i	$-0.703054\pi$
$313$	1.63130	−	1.36882i	0.0922063	−	0.0773703i	0.687726	+	0.725971i	$0.258609\pi$
$314$	6.99590	−	5.87026i	0.394802	−	0.331278i
$315$	3.84838	+	6.08765i	0.216832	+	0.343000i
$316$	−13.4178	+	7.74678i	−0.754811	+	0.435790i
$317$	−4.39112	−	1.59824i	−0.246630	−	0.0897659i	0.215747	−	0.976449i	$-0.430781\pi$
$317$	−4.39112	−	1.59824i	−0.246630	−	0.0897659i	−0.462377	+	0.886683i	$0.653003\pi$
$318$	19.9761	+	8.83145i	1.12021	+	0.495243i
$319$	19.3281	−	3.40806i	1.08217	−	0.190815i
$320$	−0.342020	−	0.939693i	−0.0191195	−	0.0525304i
$321$	16.4113	−	11.9892i	0.915991	−	0.669172i
$322$		−	4.29990i		−	0.239624i
$323$	−1.60638	−	3.88595i	−0.0893814	−	0.216220i
$324$	5.11048	+	7.40831i	0.283915	+	0.411573i
$325$	−3.86426	+	4.60525i	−0.214351	+	0.255453i
$326$	4.53399	−	1.65024i	0.251115	−	0.0913982i
$327$	0.0228775	−	0.339931i	0.00126513	−	0.0187982i
$328$	−1.33395	+	7.56522i	−0.0736552	+	0.417719i
$329$	3.25682	−	8.94804i	0.179554	−	0.493322i
$330$	−7.66406	+	2.21933i	−0.421893	+	0.122170i
$331$	26.5493	+	15.3282i	1.45928	+	0.842515i	0.998976	−	0.0452468i	$-0.0144074\pi$
$331$	26.5493	+	15.3282i	1.45928	+	0.842515i	0.460303	+	0.887762i	$0.347741\pi$
$332$	−10.3296	−	12.3104i	−0.566912	−	0.675619i
$333$	3.42926	+	15.7286i	0.187922	+	0.861922i
$334$	−8.78353	+	15.2135i	−0.480613	+	0.832446i
$335$	7.88147	+	13.6511i	0.430611	+	0.745840i
$336$	−2.31616	+	3.45329i	−0.126357	+	0.188393i
$337$	−14.0856	−	2.48367i	−0.767291	−	0.135294i	−0.223715	−	0.974655i	$-0.571819\pi$
$337$	−14.0856	−	2.48367i	−0.767291	−	0.135294i	−0.543575	+	0.839360i	$0.682930\pi$
$338$	−4.01837	−	22.7893i	−0.218570	−	1.23957i
$339$	−1.22719	−	11.3895i	−0.0666521	−	0.618593i
$340$	−0.738978	−	0.620076i	−0.0400767	−	0.0336284i
$341$	−12.3501			−0.668794
$342$	10.7433	−	7.45533i	0.580930	−	0.403138i
$343$	−19.7738			−1.06768
$344$	7.97864	+	6.69488i	0.430180	+	0.360964i
$345$	0.332343	+	3.08445i	0.0178927	+	0.166061i
$346$	−2.08814	−	11.8425i	−0.112259	−	0.636654i
$347$	−2.13762	−	0.376919i	−0.114753	−	0.0202341i	0.115977	−	0.993252i	$-0.463000\pi$
$347$	−2.13762	−	0.376919i	−0.114753	−	0.0202341i	−0.230730	+	0.973018i	$0.574111\pi$
$348$	−4.11044	+	6.12847i	−0.220343	+	0.328521i
$349$	−12.8240	−	22.2118i	−0.686452	−	1.18897i	−0.972978	−	0.230897i	$-0.925834\pi$
$349$	−12.8240	−	22.2118i	−0.686452	−	1.18897i	0.286527	−	0.958072i	$-0.407499\pi$
$350$	1.20034	−	2.07905i	0.0641610	−	0.111130i
$351$	31.2264	+	0.845335i	1.66674	+	0.0451207i
$352$	−2.96109	−	3.52889i	−0.157826	−	0.188090i
$353$	−12.2148	−	7.05224i	−0.650130	−	0.375353i	0.138376	−	0.990380i	$-0.455812\pi$
$353$	−12.2148	−	7.05224i	−0.650130	−	0.375353i	−0.788506	+	0.615027i	$0.789145\pi$
$354$	−9.64708	+	2.79357i	−0.512737	+	0.148476i
$355$	−0.679441	+	1.86675i	−0.0360610	+	0.0990767i
$356$	−2.60542	+	14.7761i	−0.138087	+	0.783130i
$357$	−0.269346	+	4.00214i	−0.0142553	+	0.211815i
$358$	−14.4677	+	5.26582i	−0.764643	+	0.278307i
$359$	−16.5538	+	19.7281i	−0.873676	+	1.04121i	0.125119	+	0.992142i	$0.460069\pi$
$359$	−16.5538	+	19.7281i	−0.873676	+	1.04121i	−0.998796	+	0.0490651i	$0.984376\pi$
$360$	1.39455	−	2.65617i	0.0734991	−	0.139992i
$361$	−10.8758	−	15.5794i	−0.572412	−	0.819966i
$362$			0.259249i			0.0136258i
$363$	−14.2951	+	10.4432i	−0.750299	+	0.548127i
$364$	4.93612	+	13.5619i	0.258723	+	0.710836i
$365$	−0.0147423	+	0.00259947i	−0.000771648	+	0.000136062i
$366$	1.86687	+	0.825345i	0.0975830	+	0.0431414i
$367$	−5.45809	−	1.98658i	−0.284910	−	0.103699i	0.195612	−	0.980681i	$-0.437331\pi$
$367$	−5.45809	−	1.98658i	−0.284910	−	0.103699i	−0.480522	+	0.876983i	$0.659553\pi$
$368$	−1.55115	+	0.895558i	−0.0808594	+	0.0466842i
$369$	−19.4798	+	12.3144i	−1.01408	+	0.641063i
$370$	4.11062	−	3.44922i	0.213701	−	0.179316i
$371$	−23.1903	+	19.4589i	−1.20398	+	1.01026i
$372$	3.21691	−	3.34868i	0.166789	−	0.173621i
$373$	−28.9835	+	16.7336i	−1.50071	+	0.866433i	−0.500707	+	0.865617i	$0.666926\pi$
$373$	−28.9835	+	16.7336i	−1.50071	+	0.866433i	−1.00000		0.000816151i	$0.999740\pi$
$374$	−4.17587	−	1.51989i	−0.215929	−	0.0785918i
$375$	−0.700350	+	1.58414i	−0.0361659	+	0.0818048i
$376$	−3.90624	+	0.688775i	−0.201449	+	0.0355209i
$377$	8.76002	+	24.0679i	0.451164	+	1.23956i
$378$	−12.3389	+	1.83291i	−0.634646	+	0.0942746i
$379$		−	34.8838i		−	1.79186i	−0.444194	−	0.895931i	$-0.646510\pi$
$379$		−	34.8838i		−	1.79186i	0.444194	−	0.895931i	$-0.353490\pi$
$380$	−3.86496	−	2.01546i	−0.198268	−	0.103391i
$381$	16.1472	+	3.98113i	0.827244	+	0.203960i
$382$	15.2196	−	18.1380i	0.778703	−	0.928022i
$383$	8.55456	−	3.11361i	0.437118	−	0.159098i	−0.114082	−	0.993471i	$-0.536393\pi$
$383$	8.55456	−	3.11361i	0.437118	−	0.159098i	0.551199	+	0.834374i	$0.314170\pi$
$384$	1.72814	+	0.116305i	0.0881889	+	0.00593515i
$385$	1.92039	−	10.8911i	0.0978720	−	0.555060i
$386$	−7.04421	+	19.3538i	−0.358541	+	0.985083i
$387$	1.25371	+	31.2210i	0.0637299	+	1.58705i
$388$	1.18377	+	0.683447i	0.0600966	+	0.0346968i
$389$	−9.49330	−	11.3137i	−0.481330	−	0.573626i	0.469661	−	0.882847i	$-0.344376\pi$
$389$	−9.49330	−	11.3137i	−0.481330	−	0.573626i	−0.950990	+	0.309221i	$0.899932\pi$
$390$	−4.58904	−	9.34683i	−0.232375	−	0.473295i
$391$	−0.863916	+	1.49635i	−0.0436901	+	0.0756735i
$392$	0.618360	+	1.07103i	0.0312319	+	0.0540952i
$393$	5.38448	+	3.61144i	0.271611	+	0.182173i
$394$	14.8106	+	2.61150i	0.746145	+	0.131565i
$395$	2.69043	+	15.2582i	0.135370	+	0.767722i
$396$	1.85179	−	13.6953i	0.0930557	−	0.688213i
$397$	−5.20196	−	4.36497i	−0.261079	−	0.219071i	0.502846	−	0.864376i	$-0.332286\pi$
$397$	−5.20196	−	4.36497i	−0.261079	−	0.219071i	−0.763926	+	0.645304i	$0.776731\pi$
$398$	−0.375427			−0.0188185
$399$	2.71313	+	17.9205i	0.135826	+	0.897149i
$400$	−1.00000			−0.0500000
$401$	23.8812	+	20.0387i	1.19257	+	1.00069i	0.999811	+	0.0194400i	$0.00618835\pi$
$401$	23.8812	+	20.0387i	1.19257	+	1.00069i	0.192760	+	0.981246i	$0.438256\pi$
$402$	−27.1451	+	2.92483i	−1.35388	+	0.145877i
$403$	−2.79869	−	15.8722i	−0.139413	−	0.790649i
$404$	16.5691	+	2.92158i	0.824344	+	0.145354i
$405$	8.70942	−	2.26849i	0.432774	−	0.112722i
$406$	−5.11398	−	8.85767i	−0.253802	−	0.439599i
$407$	12.3597	−	21.4076i	0.612646	−	1.06113i
$408$	1.49983	−	0.736377i	0.0742528	−	0.0364561i
$409$	−10.8867	−	12.9743i	−0.538314	−	0.641538i	0.426495	−	0.904490i	$-0.359748\pi$
$409$	−10.8867	−	12.9743i	−0.538314	−	0.641538i	−0.964809	+	0.262952i	$0.915304\pi$
$410$	6.65274	+	3.84096i	0.328556	+	0.189692i
$411$	−3.37590	−	11.6581i	−0.166521	−	0.575050i
$412$	2.18393	−	6.00029i	0.107594	−	0.295613i
$413$	2.41727	−	13.7090i	0.118946	−	0.674578i
$414$	−5.11897	−	1.63372i	−0.251584	−	0.0802928i
$415$	−15.1009	+	5.49628i	−0.741274	+	0.269802i
$416$	3.86426	−	4.60525i	0.189461	−	0.225791i
$417$	3.07862	−	12.4866i	0.150761	−	0.611473i
$418$	−19.9062	−	2.63509i	−0.973644	−	0.128886i
$419$			15.3605i			0.750412i	0.926942	+	0.375206i	$0.122428\pi$
$419$			15.3605i			0.750412i	−0.926942	+	0.375206i	$0.877572\pi$
$420$	2.45286	+	3.35758i	0.119687	+	0.163833i
$421$	1.45662	+	4.00204i	0.0709914	+	0.195047i	0.970114	−	0.242650i	$-0.0780165\pi$
$421$	1.45662	+	4.00204i	0.0709914	+	0.195047i	−0.899123	+	0.437697i	$0.855794\pi$
$422$	−0.0603037	+	0.0106332i	−0.00293554	+	0.000517615i
$423$	−9.41510	−	7.27694i	−0.457778	−	0.353817i
$424$	11.8496	+	4.31289i	0.575466	+	0.209453i
$425$	−0.835427	+	0.482334i	−0.0405241	+	0.0233966i
$426$	−2.48135	−	2.38371i	−0.120222	−	0.115491i
$427$	−2.16725	+	1.81854i	−0.104881	+	0.0880052i
$428$	8.98890	−	7.54258i	0.434495	−	0.364584i
$429$	−34.5916	−	33.2304i	−1.67010	−	1.60438i
$430$	9.01998	−	5.20769i	0.434982	−	0.251137i
$431$	−7.28825	−	2.65271i	−0.351063	−	0.127776i	0.160469	−	0.987041i	$-0.448699\pi$
$431$	−7.28825	−	2.65271i	−0.351063	−	0.127776i	−0.511532	+	0.859265i	$0.670922\pi$
$432$	3.23108	+	4.06941i	0.155456	+	0.195790i
$433$	16.3089	−	2.87570i	0.783755	−	0.138197i	0.232569	−	0.972580i	$-0.425287\pi$
$433$	16.3089	−	2.87570i	0.783755	−	0.138197i	0.551186	+	0.834383i	$0.314176\pi$
$434$	2.20126	+	6.04792i	0.105664	+	0.290310i
$435$	4.35303	+	5.95861i	0.208712	+	0.285694i
$436$		−	0.196703i		−	0.00942039i
$437$	−2.35299	+	7.44428i	−0.112559	+	0.356108i
$438$	0.00620685	−	0.0251745i	0.000296575	−	0.00120288i
$439$	−12.7205	+	15.1597i	−0.607115	+	0.723531i	−0.978798	−	0.204828i	$-0.934336\pi$
$439$	−12.7205	+	15.1597i	−0.607115	+	0.723531i	0.371683	+	0.928360i	$0.378781\pi$
$440$	−4.32882	+	1.57556i	−0.206368	+	0.0751120i
$441$	−1.12804	+	3.53452i	−0.0537162	+	0.168310i
$442$	1.00704	−	5.71121i	0.0479001	−	0.271655i
$443$	0.884933	−	2.43133i	0.0420444	−	0.115516i	−0.916894	−	0.399132i	$-0.869312\pi$
$443$	0.884933	−	2.43133i	0.0420444	−	0.115516i	0.958938	+	0.283615i	$0.0915339\pi$
$444$	2.58518	+	8.92747i	0.122687	+	0.423679i
$445$	12.9939	+	7.50201i	0.615968	+	0.355629i
$446$	−13.2084	−	15.7411i	−0.625435	−	0.745365i
$447$	17.1775	−	8.43368i	0.812468	−	0.398899i
$448$	−1.20034	+	2.07905i	−0.0567108	+	0.0982260i
$449$	6.28439	+	10.8849i	0.296579	+	0.513689i	0.975351	−	0.220659i	$-0.0708209\pi$
$449$	6.28439	+	10.8849i	0.296579	+	0.513689i	−0.678772	+	0.734349i	$0.737488\pi$
$450$	−2.01902	−	2.21891i	−0.0951775	−	0.104600i
$451$	34.8502	+	6.14503i	1.64103	+	0.289358i
$452$	−1.14847	−	6.51331i	−0.0540196	−	0.306361i
$453$	−2.37911	+	0.256344i	−0.111780	+	0.0120441i
$454$	10.3200	+	8.65952i	0.484342	+	0.406412i
$455$	14.4323			0.676594
$456$	5.89960	−	4.71112i	0.276274	−	0.220618i
$457$	−19.6053			−0.917096			−0.458548	−	0.888670i	$-0.651630\pi$
$457$	−19.6053			−0.917096			−0.458548	+	0.888670i	$0.651630\pi$
$458$	−2.18102	−	1.83009i	−0.101912	−	0.0855145i
$459$	4.66215	+	1.84123i	0.217610	+	0.0859415i
$460$	0.311024	+	1.76390i	0.0145016	+	0.0822425i
$461$	−32.3687	−	5.70748i	−1.50756	−	0.265824i	−0.642030	−	0.766679i	$-0.721908\pi$
$461$	−32.3687	−	5.70748i	−1.50756	−	0.265824i	−0.865531	+	0.500855i	$0.833019\pi$
$462$	15.9081	+	10.6697i	0.740110	+	0.496400i
$463$	−18.3561	−	31.7937i	−0.853081	−	1.47758i	−0.878414	−	0.477901i	$-0.841398\pi$
$463$	−18.3561	−	31.7937i	−0.853081	−	1.47758i	0.0253328	−	0.999679i	$-0.491935\pi$
$464$	−2.13022	+	3.68964i	−0.0988929	+	0.171287i
$465$	−2.04648	−	4.16822i	−0.0949034	−	0.193297i
$466$	5.85842	+	6.98180i	0.271386	+	0.323426i
$467$	15.9054	+	9.18297i	0.736013	+	0.424937i	0.820618	−	0.571477i	$-0.193630\pi$
$467$	15.9054	+	9.18297i	0.736013	+	0.424937i	−0.0846051	+	0.996415i	$0.526963\pi$
$468$	18.0207	−	0.723641i	0.833005	−	0.0334503i
$469$	12.9427	−	35.5597i	0.597637	−	1.64199i
$470$	−0.688775	+	3.90624i	−0.0317708	+	0.180181i
$471$	15.7823	+	1.06215i	0.727208	+	0.0489415i
$472$	−5.44887	+	1.98323i	−0.250805	+	0.0912854i
$473$	30.8408	−	36.7547i	1.41806	−	1.68998i
$474$	−26.0554	−	6.42404i	−1.19676	−	0.295066i
$475$	−3.21581	+	2.94255i	−0.147551	+	0.135013i
$476$			2.31586i			0.106147i
$477$	14.3546	+	35.0009i	0.657252	+	1.60258i
$478$	2.65604	+	7.29741i	0.121484	+	0.333776i
$479$	35.3168	−	6.22730i	1.61367	−	0.284533i	0.707264	−	0.706950i	$-0.249929\pi$
$479$	35.3168	−	6.22730i	1.61367	−	0.284533i	0.906402	+	0.422417i	$0.138818\pi$
$480$	0.700350	−	1.58414i	0.0319665	−	0.0723059i
$481$	30.3136	+	11.0333i	1.38218	+	0.503074i
$482$	7.01424	−	4.04967i	0.319490	−	0.184457i
$483$	5.15955	−	5.37089i	0.234768	−	0.244384i
$484$	−7.82980	+	6.56998i	−0.355900	+	0.298635i
$485$	1.04710	−	0.878623i	0.0475464	−	0.0398962i
$486$	−2.50604	+	15.3857i	−0.113676	+	0.697910i
$487$	27.5931	−	15.9309i	1.25036	−	0.721898i	0.279182	−	0.960238i	$-0.409937\pi$
$487$	27.5931	−	15.9309i	1.25036	−	0.721898i	0.971182	+	0.238340i	$0.0766033\pi$
$488$	1.10740	+	0.403062i	0.0501298	+	0.0182458i
$489$	7.64345	+	3.37917i	0.345649	+	0.152811i
$490$	1.21793	−	0.214754i	0.0550205	−	0.00970161i
$491$	−5.71475	−	15.7012i	−0.257903	−	0.708583i	−0.999296	−	0.0375121i	$-0.988057\pi$
$491$	−5.71475	−	15.7012i	−0.257903	−	0.708583i	0.741393	−	0.671071i	$-0.234165\pi$
$492$	−10.7439	+	7.84888i	−0.484372	+	0.353855i
$493$			4.10990i			0.185101i
$494$	−1.12443	−	26.1804i	−0.0505904	−	1.17791i
$495$	−12.2360	−	6.42417i	−0.549967	−	0.288745i
$496$	1.72327	−	2.05371i	0.0773771	−	0.0922144i
$497$	4.48147	−	1.63112i	0.201021	−	0.0731658i
$498$	1.86902	−	27.7713i	0.0837529	−	1.24446i
$499$	−0.459049	+	2.60340i	−0.0205499	+	0.116544i	−0.993357	−	0.115072i	$-0.963290\pi$
$499$	−0.459049	+	2.60340i	−0.0205499	+	0.116544i	0.972807	+	0.231616i	$0.0744013\pi$
$500$	−0.342020	+	0.939693i	−0.0152956	+	0.0420243i
$501$	−29.2263	+	8.46325i	−1.30574	+	0.378110i
$502$	1.48472	+	0.857206i	0.0662665	+	0.0382590i
$503$	23.4914	+	27.9959i	1.04743	+	1.24828i	0.967871	+	0.251447i	$0.0809065\pi$
$503$	23.4914	+	27.9959i	1.04743	+	1.24828i	0.0795583	+	0.996830i	$0.474649\pi$
$504$	−7.03674	+	1.53420i	−0.313441	+	0.0683387i
$505$	8.41236	−	14.5706i	0.374345	−	0.648384i
$506$	4.12551	+	7.14559i	0.183401	+	0.317660i
$507$	22.3262	−	33.2873i	0.991540	−	1.47834i
$508$	9.45587	+	1.66732i	0.419536	+	0.0739756i
$509$	−0.977817	−	5.54548i	−0.0433410	−	0.245799i	0.955439	−	0.295190i	$-0.0953830\pi$
$509$	−0.977817	−	5.54548i	−0.0433410	−	0.245799i	−0.998780	+	0.0493912i	$0.984272\pi$
$510$	−0.178995	−	1.66124i	−0.00792602	−	0.0735609i
$511$	0.0275298	+	0.0231003i	0.00121785	+	0.00102190i
$512$	1.00000			0.0441942
$513$	22.3650	+	3.57884i	0.987438	+	0.158010i
$514$	−18.5755			−0.819332
$515$	−4.89148	−	4.10444i	−0.215545	−	0.180863i
$516$	1.93258	+	17.9362i	0.0850772	+	0.789595i
$517$	3.17294	+	17.9946i	0.139546	+	0.791402i
$518$	−12.6864	−	2.23696i	−0.557410	−	0.0982864i
$519$	11.6018	−	17.2977i	0.509262	−	0.759285i
$520$	−3.00586	−	5.20631i	−0.131816	−	0.228312i
$521$	−13.8842	+	24.0482i	−0.608280	+	1.05357i	0.383244	+	0.923647i	$0.374807\pi$
$521$	−13.8842	+	24.0482i	−0.608280	+	1.05357i	−0.991524	+	0.129924i	$0.958527\pi$
$522$	−12.4879	+	2.72271i	−0.546582	+	0.119170i
$523$	7.50579	+	8.94505i	0.328205	+	0.391140i	0.904762	−	0.425917i	$-0.140049\pi$
$523$	7.50579	+	8.94505i	0.328205	+	0.391140i	−0.576557	+	0.817057i	$0.695604\pi$
$524$	3.24173	+	1.87161i	0.141615	+	0.0817617i
$525$	3.99402	−	1.15657i	0.174313	−	0.0504770i
$526$	1.72478	−	4.73879i	0.0752039	−	0.206621i
$527$	0.449090	−	2.54692i	0.0195627	−	0.110945i
$528$	0.535774	−	7.96092i	0.0233166	−	0.346454i
$529$	−18.5983	+	6.76923i	−0.808622	+	0.294314i
$530$	8.10559	−	9.65986i	0.352084	−	0.419598i
$531$	−15.4020	−	8.08638i	−0.668389	−	0.350919i
$532$	2.25764	+	10.2179i	0.0978811	+	0.443002i
$533$			46.1816i			2.00035i
$534$	−20.9845	+	15.3301i	−0.908089	+	0.663399i
$535$	−4.01332	−	11.0265i	−0.173511	−	0.476718i
$536$	−15.5235	+	2.73721i	−0.670512	+	0.118229i
$537$	−24.3898	−	10.7827i	−1.05250	−	0.465310i
$538$	22.7475	+	8.27943i	0.980716	+	0.356952i
$539$	4.93385	−	2.84856i	0.212516	−	0.122696i
$540$	4.92909	−	1.64440i	0.212114	−	0.0707639i
$541$	−2.40855	+	2.02101i	−0.103552	+	0.0868902i	−0.693094	−	0.720848i	$-0.743753\pi$
$541$	−2.40855	+	2.02101i	−0.103552	+	0.0868902i	0.589542	+	0.807738i	$0.299308\pi$
$542$	−7.13074	+	5.98340i	−0.306292	+	0.257009i
$543$	−0.311078	+	0.323821i	−0.0133497	+	0.0138965i
$544$	0.835427	−	0.482334i	0.0358186	−	0.0206799i
$545$	−0.184841	−	0.0672765i	−0.00791771	−	0.00288181i
$546$	−10.1076	+	22.8628i	−0.432567	+	0.978436i
$547$	−35.4366	+	6.24843i	−1.51516	+	0.267164i	−0.868529	−	0.495639i	$-0.834934\pi$
$547$	−35.4366	+	6.24843i	−1.51516	+	0.267164i	−0.646632	+	0.762802i	$0.723823\pi$
$548$	−2.39664	−	6.58472i	−0.102380	−	0.281285i
$549$	1.34151	+	3.27102i	0.0572543	+	0.139604i
$550$			4.60663i			0.196428i
$551$	4.00658	+	18.1335i	0.170686	+	0.772511i
$552$	−3.01210	−	0.742644i	−0.128204	−	0.0316090i
$553$	23.9086	−	28.4931i	1.01670	−	1.21165i
$554$	−27.9003	+	10.1549i	−1.18537	+	0.431439i
$555$	9.27326	+	0.624095i	0.393628	+	0.0264914i
$556$	1.28935	−	7.31225i	0.0546805	−	0.310108i
$557$	12.6403	−	34.7290i	0.535588	−	1.47152i	−0.316742	−	0.948512i	$-0.602589\pi$
$557$	12.6403	−	34.7290i	0.535588	−	1.47152i	0.852330	−	0.523004i	$-0.175189\pi$
$558$	8.03632	−	0.322708i	0.340204	−	0.0136613i
$559$	54.2257	+	31.3072i	2.29350	+	1.32415i
$560$	1.54313	+	1.83903i	0.0652091	+	0.0777132i
$561$	−3.39222	−	6.90918i	−0.143220	−	0.291706i
$562$	4.76807	−	8.25854i	0.201129	−	0.348366i
$563$	−17.0578	−	29.5451i	−0.718903	−	1.24518i	−0.961435	−	0.275032i	$-0.911311\pi$
$563$	−17.0578	−	29.5451i	−0.718903	−	1.24518i	0.242532	−	0.970143i	$-0.422022\pi$
$564$	−5.70566	−	3.82685i	−0.240252	−	0.161140i
$565$	−6.51331	−	1.14847i	−0.274017	−	0.0483166i
$566$	−2.41099	−	13.6734i	−0.101341	−	0.574735i
$567$	−17.6116	−	12.5163i	−0.739617	−	0.525636i
$568$	−1.52179	−	1.27693i	−0.0638528	−	0.0535788i
$569$	11.9907			0.502677			0.251339	−	0.967899i	$-0.419129\pi$
$569$	11.9907			0.502677			0.251339	+	0.967899i	$0.419129\pi$
$570$	−2.40922	−	7.15511i	−0.100911	−	0.299695i
$571$	−15.5868			−0.652286			−0.326143	−	0.945320i	$-0.605749\pi$
$571$	−15.5868			−0.652286			−0.326143	+	0.945320i	$0.605749\pi$
$572$	−21.2147	−	17.8012i	−0.887031	−	0.744308i
$573$	40.7746	−	4.39338i	1.70338	−	0.183536i
$574$	−3.20240	−	18.1617i	−0.133665	−	0.758055i
$575$	1.76390	+	0.311024i	0.0735599	+	0.0129706i
$576$	2.01902	+	2.21891i	0.0841258	+	0.0924546i
$577$	5.36051	+	9.28467i	0.223161	+	0.386526i	0.955766	−	0.294128i	$-0.0950292\pi$
$577$	5.36051	+	9.28467i	0.223161	+	0.386526i	−0.732605	+	0.680654i	$0.761696\pi$
$578$	−8.03471	+	13.9165i	−0.334200	+	0.578851i
$579$	−32.0218	+	15.7218i	−1.33078	+	0.653377i
$580$	2.73855	+	3.26368i	0.113712	+	0.135517i
$581$	33.4105	+	19.2895i	1.38610	+	0.800265i
$582$	0.658527	+	2.27410i	0.0272968	+	0.0942646i
$583$	19.8679	−	54.5867i	0.822845	−	2.26075i
$584$	0.00259947	−	0.0147423i	0.000107567	−	0.000610042i
$585$	5.48343	−	17.1814i	0.226712	−	0.710363i
$586$	10.7615	−	3.91686i	0.444553	−	0.161804i
$587$	−14.8177	+	17.6590i	−0.611592	+	0.728867i	−0.979600	−	0.200956i	$-0.935595\pi$
$587$	−14.8177	+	17.6590i	−0.611592	+	0.728867i	0.368008	+	0.929822i	$0.380040\pi$
$588$	−0.512777	+	2.07978i	−0.0211466	+	0.0857687i
$589$	−0.501439	−	11.6751i	−0.0206614	−	0.481066i
$590$			5.79857i			0.238723i
$591$	15.3659	+	21.0335i	0.632068	+	0.865202i
$592$	1.83529	+	5.04242i	0.0754300	+	0.207242i
$593$	15.3435	−	2.70547i	0.630081	−	0.111100i	0.150517	−	0.988607i	$-0.451906\pi$
$593$	15.3435	−	2.70547i	0.630081	−	0.111100i	0.479563	+	0.877507i	$0.340795\pi$
$594$	18.7463	−	14.8844i	0.769169	−	0.610715i
$595$	2.17620	+	0.792071i	0.0892154	+	0.0324718i
$596$	9.56809	−	5.52414i	0.391924	−	0.226278i
$597$	−0.468936	−	0.450484i	−0.0191923	−	0.0184371i
$598$	−8.24854	+	6.92134i	−0.337308	+	0.283035i
$599$	19.1658	−	16.0820i	0.783091	−	0.657092i	−0.160934	−	0.986965i	$-0.551451\pi$
$599$	19.1658	−	16.0820i	0.783091	−	0.657092i	0.944025	+	0.329873i	$0.107006\pi$
$600$	−1.24907	−	1.19992i	−0.0509932	−	0.0489866i
$601$	−19.9730	+	11.5314i	−0.814715	+	0.470376i	−0.848591	−	0.529050i	$-0.822548\pi$
$601$	−19.9730	+	11.5314i	−0.814715	+	0.470376i	0.0338753	+	0.999426i	$0.489215\pi$
$602$	−23.4961	−	8.55188i	−0.957629	−	0.348549i
$603$	−37.4158	−	28.9187i	−1.52369	−	1.17766i
$604$	−1.36054	+	0.239900i	−0.0553596	+	0.00976140i
$605$	3.49581	+	9.60467i	0.142125	+	0.390485i
$606$	17.1904	+	23.5309i	0.698311	+	0.955878i
$607$		−	12.7911i		−	0.519175i	−0.965720	−	0.259587i	$-0.916413\pi$
$607$		−	12.7911i		−	0.519175i	0.965720	−	0.259587i	$-0.0835865\pi$
$608$	3.21581	−	2.94255i	0.130418	−	0.119336i
$609$	4.24078	−	17.2003i	0.171845	−	0.696990i
$610$	0.757509	−	0.902764i	0.0306706	−	0.0365518i
$611$	−22.4075	+	8.15565i	−0.906508	+	0.329942i
$612$	2.75700	+	0.879894i	0.111445	+	0.0355676i
$613$	1.28491	−	7.28707i	0.0518969	−	0.294322i	−0.947802	−	0.318859i	$-0.896700\pi$
$613$	1.28491	−	7.28707i	0.0518969	−	0.294322i	0.999699	+	0.0245376i	$0.00781134\pi$
$614$	−9.29783	+	25.5456i	−0.375230	+	1.03094i
$615$	3.70091	+	12.7804i	0.149235	+	0.515356i
$616$	9.57743	+	5.52953i	0.385886	+	0.222791i
$617$	−26.9526	−	32.1209i	−1.08507	−	1.29314i	−0.953355	−	0.301850i	$-0.902396\pi$
$617$	−26.9526	−	32.1209i	−1.08507	−	1.29314i	−0.131716	−	0.991287i	$-0.542049\pi$
$618$	9.92778	−	4.87427i	0.399354	−	0.196072i
$619$	−15.9906	+	27.6965i	−0.642716	+	1.11322i	0.342108	+	0.939661i	$0.388859\pi$
$619$	−15.9906	+	27.6965i	−0.642716	+	1.11322i	−0.984824	+	0.173556i	$0.944474\pi$
$620$	−1.34047	−	2.32175i	−0.0538344	−	0.0932439i
$621$	−4.43364	−	8.18300i	−0.177916	−	0.328372i
$622$	−7.65429	−	1.34966i	−0.306909	−	0.0541163i
$623$	−6.25479	−	35.4727i	−0.250593	−	1.42118i
$624$	10.3527	−	1.11548i	0.414439	−	0.0446550i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	2.12951			0.0851122
$627$	−21.7024	−	27.1773i	−0.866711	−	1.08536i
$628$	9.13250			0.364427
$629$	3.96538	+	3.32735i	0.158110	+	0.132670i
$630$	−0.965032	+	7.13710i	−0.0384478	+	0.284349i
$631$	−1.32141	−	7.49406i	−0.0526043	−	0.298334i	0.947143	−	0.320812i	$-0.103956\pi$
$631$	−1.32141	−	7.49406i	−0.0526043	−	0.298334i	−0.999747	+	0.0224776i	$0.992845\pi$
$632$	−15.2582	−	2.69043i	−0.606938	−	0.107019i
$633$	−0.0880828	−	0.0590782i	−0.00350098	−	0.00234815i
$634$	−2.33647	−	4.04688i	−0.0927929	−	0.160722i
$635$	4.80087	−	8.31535i	0.190517	−	0.329985i
$636$	9.62586	+	19.6057i	0.381690	+	0.777416i
$637$	4.77901	+	5.69541i	0.189351	+	0.225660i
$638$	16.9968	+	9.81313i	0.672911	+	0.388506i
$639$	−0.239124	−	5.95486i	−0.00945961	−	0.235571i
$640$	0.342020	−	0.939693i	0.0135195	−	0.0371446i
$641$	6.13415	−	34.7885i	0.242284	−	1.37406i	−0.584432	−	0.811443i	$-0.698683\pi$
$641$	6.13415	−	34.7885i	0.242284	−	1.37406i	0.826716	−	0.562619i	$-0.190206\pi$
$642$	20.2783	+	1.36474i	0.800321	+	0.0538620i
$643$	20.7333	−	7.54630i	0.817641	−	0.297597i	0.100864	−	0.994900i	$-0.467839\pi$
$643$	20.7333	−	7.54630i	0.817641	−	0.297597i	0.716776	+	0.697303i	$0.245617\pi$
$644$	2.76392	−	3.29392i	0.108914	−	0.129798i
$645$	17.5155	+	4.31849i	0.689670	+	0.170040i
$646$	1.26728	−	4.00937i	0.0498606	−	0.157747i
$647$		−	20.5151i		−	0.806530i	−0.915083	−	0.403265i	$-0.867875\pi$
$647$		−	20.5151i		−	0.806530i	0.915083	−	0.403265i	$-0.132125\pi$
$648$	−0.847118	+	8.96004i	−0.0332779	+	0.351984i
$649$	9.13600	+	25.1010i	0.358619	+	0.985299i
$650$	−5.92040	+	1.04393i	−0.232217	+	0.0409461i
$651$	−4.50750	+	10.1957i	−0.176663	+	0.399599i
$652$	4.53399	+	1.65024i	0.177565	+	0.0646283i
$653$	28.0157	−	16.1749i	1.09634	−	0.632971i	0.161081	−	0.986941i	$-0.448502\pi$
$653$	28.0157	−	16.1749i	1.09634	−	0.632971i	0.935257	+	0.353970i	$0.115169\pi$
$654$	0.236029	−	0.245697i	0.00922946	−	0.00960752i
$655$	2.86747	−	2.40610i	0.112041	−	0.0940140i
$656$	−5.88470	+	4.93785i	−0.229759	+	0.192791i
$657$	0.0379603	−	0.0239971i	0.00148097	−	0.000936214i
$658$	8.24656	−	4.76115i	0.321484	−	0.185609i
$659$	−21.4135	−	7.79388i	−0.834152	−	0.303606i	−0.110590	−	0.993866i	$-0.535274\pi$
$659$	−21.4135	−	7.79388i	−0.834152	−	0.303606i	−0.723562	+	0.690260i	$0.757496\pi$
$660$	−7.29757	−	3.22626i	−0.284057	−	0.125582i
$661$	37.3039	−	6.57769i	1.45096	−	0.255843i	0.608047	−	0.793901i	$-0.291953\pi$
$661$	37.3039	−	6.57769i	1.45096	−	0.255843i	0.842908	+	0.538058i	$0.180842\pi$
$662$	10.4851	+	28.8076i	0.407516	+	1.11964i
$663$	8.11088	−	5.92536i	0.315001	−	0.230122i
$664$		−	16.0700i		−	0.623639i
$665$	10.3738	+	1.37324i	0.402280	+	0.0532519i
$666$	−7.48318	+	14.2531i	−0.289967	+	0.552296i
$667$	4.90507	−	5.84563i	0.189925	−	0.226344i
$668$	−16.5076	+	6.00829i	−0.638699	+	0.232468i
$669$	2.38990	−	35.5109i	0.0923989	−	1.37293i
$670$	−2.73721	+	15.5235i	−0.105748	+	0.599724i
$671$	1.85676	−	5.10140i	0.0716794	−	0.196937i
$672$	−3.99402	+	1.15657i	−0.154073	+	0.0446158i
$673$	−11.1486	−	6.43663i	−0.429746	−	0.248114i	0.269492	−	0.963003i	$-0.413144\pi$
$673$	−11.1486	−	6.43663i	−0.429746	−	0.248114i	−0.699238	+	0.714889i	$0.746477\pi$
$674$	−9.19371	−	10.9566i	−0.354128	−	0.422034i
$675$	0.140614	−	5.19425i	0.00541225	−	0.199927i
$676$	11.5704	−	20.0406i	0.445017	−	0.770791i
$677$	5.51909	+	9.55934i	0.212116	+	0.367395i	0.952376	−	0.304925i	$-0.0986313\pi$
$677$	5.51909	+	9.55934i	0.212116	+	0.367395i	−0.740261	+	0.672320i	$0.765298\pi$
$678$	6.38095	−	9.51369i	0.245059	−	0.365371i
$679$	−3.23163	−	0.569823i	−0.124018	−	0.0218678i
$680$	−0.167513	−	0.950012i	−0.00642382	−	0.0364313i
$681$	2.49971	+	23.1996i	0.0957890	+	0.889011i
$682$	−9.46070	−	7.93847i	−0.362269	−	0.303980i
$683$	−36.4486			−1.39467			−0.697333	−	0.716748i	$-0.745630\pi$
$683$	−36.4486			−1.39467			−0.697333	+	0.716748i	$0.745630\pi$
$684$	13.0220	+	1.19453i	0.497910	+	0.0456740i
$685$	−7.00732			−0.267736
$686$	−15.1476	−	12.7103i	−0.578337	−	0.485282i
$687$	−0.528285	−	4.90297i	−0.0201553	−	0.187060i
$688$	1.80861	+	10.2571i	0.0689527	+	0.391050i
$689$	74.6565	+	13.1640i	2.84419	+	0.501507i
$690$	−1.72806	+	2.57645i	−0.0657860	+	0.0980838i
$691$	−9.54021	−	16.5241i	−0.362927	−	0.628607i	0.625514	−	0.780213i	$-0.284889\pi$
$691$	−9.54021	−	16.5241i	−0.362927	−	0.628607i	−0.988441	+	0.151605i	$0.951556\pi$
$692$	6.01257	−	10.4141i	0.228564	−	0.395884i
$693$	7.06749	+	32.4157i	0.268472	+	1.23137i
$694$	−1.39523	−	1.66277i	−0.0529622	−	0.0631179i
$695$	−6.43028	−	3.71253i	−0.243915	−	0.140824i
$696$	−7.08809	+	2.05254i	−0.268673	+	0.0778014i
$697$	−2.53454	+	6.96360i	−0.0960026	+	0.263765i
$698$	4.45372	−	25.2583i	0.168576	−	0.956041i
$699$	−1.06001	+	15.7504i	−0.0400933	+	0.595736i
$700$	2.25590	−	0.821082i	0.0852652	−	0.0310340i
$701$	−12.1630	+	14.4953i	−0.459391	+	0.547481i	−0.945161	−	0.326606i	$-0.894095\pi$
$701$	−12.1630	+	14.4953i	−0.459391	+	0.547481i	0.485770	+	0.874087i	$0.338539\pi$
$702$	23.3774	+	20.7195i	0.882325	+	0.782008i
$703$	20.7395	+	10.8150i	0.782205	+	0.407896i
$704$		−	4.60663i		−	0.173619i
$705$	−5.54752	+	4.05270i	−0.208932	+	0.152634i
$706$	−4.82401	−	13.2539i	−0.181554	−	0.498816i
$707$	−39.7772	+	7.01379i	−1.49597	+	0.263781i
$708$	−9.18576	−	4.06103i	−0.345222	−	0.152623i
$709$	−1.55167	−	0.564763i	−0.0582744	−	0.0212101i	0.312719	−	0.949846i	$-0.398760\pi$
$709$	−1.55167	−	0.564763i	−0.0582744	−	0.0212101i	−0.370993	+	0.928636i	$0.620983\pi$
$710$	−1.72040	+	0.993276i	−0.0645656	+	0.0372770i
$711$	−24.8367	−	39.2885i	−0.931451	−	1.47344i
$712$	−11.4937	+	9.64440i	−0.430746	+	0.361439i
$713$	−3.67844	+	3.08657i	−0.137759	+	0.115593i
$714$	−2.77885	+	2.89268i	−0.103996	+	0.108256i
$715$	−23.9836	+	13.8469i	−0.896934	+	0.517845i
$716$	−14.4677	−	5.26582i	−0.540684	−	0.196793i
$717$	−5.43874	+	12.3021i	−0.203113	+	0.459429i
$718$	−25.3619	+	4.47199i	−0.946498	+	0.166893i
$719$	0.456613	+	1.25453i	0.0170288	+	0.0467862i	0.947916	−	0.318521i	$-0.103186\pi$
$719$	0.456613	+	1.25453i	0.0170288	+	0.0467862i	−0.930887	+	0.365307i	$0.880964\pi$
$720$	2.77564	−	1.13835i	0.103442	−	0.0424237i
$721$			15.3293i			0.570892i
$722$	1.68285	−	18.9253i	0.0626292	−	0.704328i
$723$	13.6206	+	3.35820i	0.506555	+	0.124893i
$724$	−0.166642	+	0.198596i	−0.00619320	+	0.00738077i
$725$	4.00350	−	1.45715i	0.148686	−	0.0541174i
$726$	−17.6635	−	1.18876i	−0.655553	−	0.0441190i
$727$	−2.32140	+	13.1653i	−0.0860959	+	0.488274i	0.911019	+	0.412365i	$0.135297\pi$
$727$	−2.32140	+	13.1653i	−0.0860959	+	0.488274i	−0.997115	+	0.0759093i	$0.975814\pi$
$728$	−4.93612	+	13.5619i	−0.182945	+	0.502637i
$729$	−21.5919	+	16.2108i	−0.799699	+	0.600401i
$730$	−0.0129642	−	0.00748487i	−0.000479826	−	0.000277028i
$731$	6.45833	+	7.69674i	0.238870	+	0.284674i
$732$	0.899586	+	1.83225i	0.0332497	+	0.0677220i
$733$	−12.7170	+	22.0265i	−0.469713	+	0.813567i	−0.999400	−	0.0346264i	$-0.988976\pi$
$733$	−12.7170	+	22.0265i	−0.469713	+	0.813567i	0.529687	+	0.848193i	$0.322309\pi$
$734$	−2.90419	−	5.03020i	−0.107196	−	0.185668i
$735$	1.77898	+	1.19318i	0.0656185	+	0.0440111i
$736$	−1.76390	−	0.311024i	−0.0650184	−	0.0114645i
$737$	12.6093	+	71.5110i	0.464470	+	2.63414i
$738$	−22.8380	−	3.08800i	−0.840677	−	0.113671i
$739$	11.4510	+	9.60854i	0.421232	+	0.353456i	0.828632	−	0.559794i	$-0.189120\pi$
$739$	11.4510	+	9.60854i	0.421232	+	0.353456i	−0.407399	+	0.913250i	$0.633564\pi$
$740$	5.36603			0.197259
$741$	30.0099	−	34.0505i	1.10244	−	1.25087i
$742$	−30.2727			−1.11135
$743$	33.9317	+	28.4721i	1.24483	+	1.04454i	0.997130	+	0.0757035i	$0.0241203\pi$
$743$	33.9317	+	28.4721i	1.24483	+	1.04454i	0.247703	+	0.968836i	$0.420324\pi$
$744$	4.61679	−	0.497449i	0.169260	−	0.0182374i
$745$	−1.91851	−	10.8804i	−0.0702889	−	0.398628i
$746$	−32.9588	−	5.81152i	−1.20671	−	0.212775i
$747$	35.6580	−	32.4457i	1.30466	−	1.18713i
$748$	−2.22194	−	3.84850i	−0.0812420	−	0.140715i
$749$	−14.0850	+	24.3960i	−0.514655	+	0.891409i
$750$	−1.55477	+	0.763348i	−0.0567721	+	0.0278735i
$751$	2.39009	+	2.84840i	0.0872156	+	0.103939i	0.807887	−	0.589337i	$-0.200611\pi$
$751$	2.39009	+	2.84840i	0.0872156	+	0.103939i	−0.720672	+	0.693276i	$0.756167\pi$
$752$	−3.43509	−	1.98325i	−0.125265	−	0.0723217i
$753$	0.825950	+	2.85227i	0.0300993	+	0.103942i
$754$	−8.76002	+	24.0679i	−0.319021	+	0.876503i
$755$	−0.239900	+	1.36054i	−0.00873086	+	0.0495152i
$756$	−10.6303	−	6.52722i	−0.386621	−	0.237393i
$757$	44.1896	−	16.0837i	1.60610	−	0.584571i	0.625434	−	0.780277i	$-0.284922\pi$
$757$	44.1896	−	16.0837i	1.60610	−	0.584571i	0.980663	+	0.195705i	$0.0626996\pi$
$758$	22.4229	−	26.7226i	0.814436	−	0.970607i
$759$	−3.42109	+	13.8757i	−0.124178	+	0.503654i
$760$	−1.66522	−	4.02828i	−0.0604038	−	0.146121i
$761$			6.31602i			0.228956i	0.993426	+	0.114478i	$0.0365195\pi$
$761$			6.31602i			0.228956i	−0.993426	+	0.114478i	$0.963481\pi$
$762$	9.81042	+	13.4289i	0.355394	+	0.486478i
$763$	0.161510	+	0.443744i	0.00584704	+	0.0160646i
$764$	23.3178	−	4.11155i	0.843608	−	0.148751i
$765$	1.76978	−	2.28979i	0.0639865	−	0.0827875i
$766$	8.55456	+	3.11361i	0.309089	+	0.112499i
$767$	−30.1891	+	17.4297i	−1.09007	+	0.629350i
$768$	1.24907	+	1.19992i	0.0450721	+	0.0432985i
$769$	−28.8816	+	24.2345i	−1.04150	+	0.873920i	−0.992174	−	0.124863i	$-0.960151\pi$
$769$	−28.8816	+	24.2345i	−1.04150	+	0.873920i	−0.0493232	+	0.998783i	$0.515706\pi$
$770$	8.47174	−	7.10863i	0.305300	−	0.256177i
$771$	−23.2022	−	22.2892i	−0.835608	−	0.802726i
$772$	−17.8366	+	10.2979i	−0.641952	+	0.370631i
$773$	17.4953	+	6.36775i	0.629261	+	0.229032i	0.636909	−	0.770939i	$-0.280212\pi$
$773$	17.4953	+	6.36775i	0.629261	+	0.229032i	−0.00764878	+	0.999971i	$0.502435\pi$
$774$	−19.1081	+	24.7225i	−0.686825	+	0.888633i
$775$	−2.64020	+	0.465539i	−0.0948389	+	0.0167226i
$776$	0.467505	+	1.28446i	0.0167825	+	0.0461094i
$777$	−13.1621	−	18.0169i	−0.472188	−	0.646351i
$778$		−	14.7690i		−	0.529493i
$779$	−4.39422	+	33.1952i	−0.157439	+	1.18934i
$780$	2.49262	−	10.1099i	0.0892502	−	0.361991i
$781$	−5.88235	+	7.01032i	−0.210487	+	0.250849i
$782$	−1.62363	+	0.590953i	−0.0580609	+	0.0211324i
$783$	−18.8654	−	11.5837i	−0.674194	−	0.413968i
$784$	−0.214754	+	1.21793i	−0.00766979	+	0.0434976i
$785$	3.12350	−	8.58175i	0.111483	−	0.306296i
$786$	1.80337	+	6.22760i	0.0643239	+	0.222131i
$787$	−34.9085	−	20.1544i	−1.24435	−	0.718428i	−0.274376	−	0.961623i	$-0.588471\pi$
$787$	−34.9085	−	20.1544i	−1.24435	−	0.718428i	−0.969977	+	0.243195i	$0.921805\pi$
$788$	9.66690	+	11.5206i	0.344369	+	0.410403i
$789$	7.84056	−	3.84950i	0.279131	−	0.137046i
$790$	−7.74678	+	13.4178i	−0.275618	+	0.477384i
$791$	7.93881	+	13.7504i	0.282272	+	0.488909i
$792$	10.2217	−	9.30089i	0.363212	−	0.330493i
$793$	6.97703	+	1.23024i	0.247762	+	0.0436871i
$794$	−1.17919	−	6.68752i	−0.0418479	−	0.237331i
$795$	21.7156	−	2.33981i	0.770172	−	0.0829843i
$796$	−0.287594	−	0.241320i	−0.0101935	−	0.00855336i
$797$	15.3456			0.543570			0.271785	−	0.962358i	$-0.412386\pi$
$797$	15.3456			0.543570			0.271785	+	0.962358i	$0.412386\pi$
$798$	−9.44073	+	15.4719i	−0.334198	+	0.547699i
$799$	−3.82635			−0.135367
$800$	−0.766044	−	0.642788i	−0.0270838	−	0.0227260i
$801$	−44.6061	−	6.03135i	−1.57608	−	0.213107i
$802$	5.41343	+	30.7011i	0.191155	+	1.08409i
$803$	−0.0679125	−	0.0119748i	−0.00239658	−	0.000422582i
$804$	−22.6744	−	15.2080i	−0.799665	−	0.536345i
$805$	−2.14995	−	3.72382i	−0.0757758	−	0.131248i
$806$	8.05851	−	13.9578i	0.283849	−	0.491641i
$807$	18.4787	+	37.6369i	0.650481	+	1.32488i
$808$	10.8147	+	12.8885i	0.380460	+	0.453415i
$809$	−32.6236	−	18.8352i	−1.14698	−	0.662212i	−0.198834	−	0.980033i	$-0.563715\pi$
$809$	−32.6236	−	18.8352i	−1.14698	−	0.662212i	−0.948151	+	0.317821i	$0.897049\pi$
$810$	8.12996	+	3.86055i	0.285658	+	0.135646i
$811$	−8.83785	+	24.2818i	−0.310339	+	0.852649i	0.682249	+	0.731120i	$0.261002\pi$
$811$	−8.83785	+	24.2818i	−0.310339	+	0.852649i	−0.992588	+	0.121529i	$0.961220\pi$
$812$	1.77607	−	10.0726i	0.0623277	−	0.353478i
$813$	−16.0864	−	1.08263i	−0.564176	−	0.0379693i
$814$	23.2286	−	8.45451i	0.814161	−	0.296330i
$815$	3.10143	−	3.69614i	0.108638	−	0.129470i
$816$	1.62227	+	0.399977i	0.0567909	+	0.0140020i
$817$	35.9983	+	27.6631i	1.25942	+	0.967809i
$818$		−	16.9367i		−	0.592179i
$819$	−40.0587	+	16.4289i	−1.39976	+	0.574072i
$820$	2.62737	+	7.21865i	0.0917519	+	0.252086i
$821$	−42.6639	+	7.52280i	−1.48898	+	0.262547i	−0.858160	−	0.513382i	$-0.828393\pi$
$821$	−42.6639	+	7.52280i	−1.48898	+	0.262547i	−0.630820	+	0.775929i	$0.717281\pi$
$822$	4.90757	−	11.1006i	0.171171	−	0.387178i
$823$	36.1355	+	13.1522i	1.25960	+	0.458458i	0.883636	−	0.468175i	$-0.155088\pi$
$823$	36.1355	+	13.1522i	1.25960	+	0.458458i	0.375967	+	0.926633i	$0.377310\pi$
$824$	5.52990	−	3.19269i	0.192643	−	0.111223i
$825$	−5.52760	+	5.75403i	−0.192446	+	0.200329i
$826$	10.6637	−	8.94794i	0.371039	−	0.311339i
$827$	−32.0393	+	26.8842i	−1.11412	+	0.934854i	−0.998292	−	0.0584156i	$-0.981395\pi$
$827$	−32.0393	+	26.8842i	−1.11412	+	0.934854i	−0.115823	+	0.993270i	$0.536951\pi$
$828$	−2.87122	−	4.54191i	−0.0997819	−	0.157842i
$829$	20.1094	−	11.6101i	0.698427	−	0.403237i	−0.108334	−	0.994115i	$-0.534552\pi$
$829$	20.1094	−	11.6101i	0.698427	−	0.403237i	0.806761	+	0.590878i	$0.201218\pi$
$830$	−15.1009	−	5.49628i	−0.524160	−	0.190779i
$831$	−47.0346	−	20.7940i	−1.63161	−	0.721335i
$832$	5.92040	−	1.04393i	0.205253	−	0.0361916i
$833$	0.408038	+	1.12108i	0.0141377	+	0.0388430i
$834$	10.3846	−	7.58642i	0.359590	−	0.262696i
$835$			17.5671i			0.607933i
$836$	−13.5552	−	14.8141i	−0.468817	−	0.512355i
$837$	10.4252	+	9.23987i	0.360347	+	0.319377i
$838$	−9.87357	+	11.7669i	−0.341077	+	0.406479i
$839$	5.60378	−	2.03961i	0.193464	−	0.0704151i	−0.243471	−	0.969908i	$-0.578286\pi$
$839$	5.60378	−	2.03961i	0.193464	−	0.0704151i	0.436935	+	0.899493i	$0.356064\pi$
$840$	−0.279211	+	4.14872i	−0.00963369	+	0.143144i
$841$	−1.88386	+	10.6839i	−0.0649606	+	0.368410i
$842$	−1.45662	+	4.00204i	−0.0501985	+	0.137919i
$843$	15.8653	−	4.59421i	0.546430	−	0.158233i
$844$	−0.0530302	−	0.0306170i	−0.00182537	−	0.00105388i
$845$	−14.8747	−	17.7269i	−0.511704	−	0.609825i
$846$	−2.53486	−	11.6264i	−0.0871503	−	0.399723i
$847$	12.2688	−	21.2502i	0.421560	−	0.730164i
$848$	6.30503	+	10.9206i	0.216516	+	0.375016i
$849$	13.3955	−	19.9721i	0.459732	−	0.685439i
$850$	−0.950012	−	0.167513i	−0.0325851	−	0.00574564i
$851$	−1.66896	−	9.46516i	−0.0572113	−	0.324462i
$852$	−0.368606	−	3.42101i	−0.0126282	−	0.117202i
$853$	7.58980	+	6.36860i	0.259870	+	0.218057i	0.763408	−	0.645916i	$-0.223524\pi$
$853$	7.58980	+	6.36860i	0.259870	+	0.218057i	−0.503539	+	0.863973i	$0.667969\pi$
$854$	−2.82914			−0.0968113
$855$	5.57628	−	11.8281i	0.190705	−	0.404514i
$856$	11.7342			0.401066
$857$	27.8267	+	23.3494i	0.950543	+	0.797600i	0.979389	−	0.201984i	$-0.0647388\pi$
$857$	27.8267	+	23.3494i	0.950543	+	0.797600i	−0.0288460	+	0.999584i	$0.509183\pi$
$858$	−5.13861	−	47.6911i	−0.175429	−	1.62815i
$859$	−0.589755	−	3.34466i	−0.0201222	−	0.114118i	0.973092	−	0.230416i	$-0.0740086\pi$
$859$	−0.589755	−	3.34466i	−0.0201222	−	0.114118i	−0.993214	+	0.116297i	$0.962897\pi$
$860$	10.2571	+	1.80861i	0.349766	+	0.0616731i
$861$	17.7926	−	26.5279i	0.606370	−	0.904070i
$862$	−3.87800	−	6.71689i	−0.132085	−	0.228778i
$863$	6.55287	−	11.3499i	0.223062	−	0.386355i	−0.732674	−	0.680580i	$-0.761728\pi$
$863$	6.55287	−	11.3499i	0.223062	−	0.386355i	0.955736	+	0.294224i	$0.0950613\pi$
$864$	−0.140614	+	5.19425i	−0.00478380	+	0.176712i
$865$	−7.72961	−	9.21180i	−0.262815	−	0.313210i
$866$	14.3418	+	8.28024i	0.487354	+	0.281374i
$867$	−26.7347	+	7.74174i	−0.907958	+	0.262923i
$868$	−2.20126	+	6.04792i	−0.0747158	+	0.205280i
$869$	−12.3938	+	70.2888i	−0.420431	+	2.38439i
$870$	−0.495509	+	7.36263i	−0.0167993	+	0.249617i
$871$	−89.0477	+	32.4107i	−3.01727	+	1.09819i
$872$	0.126439	−	0.150684i	0.00428175	−	0.00510279i
$873$	−1.90620	+	3.63070i	−0.0645150	+	0.122881i
$874$	−6.58758	+	4.19018i	−0.222828	+	0.141735i
$875$		−	2.40068i		−	0.0811579i
$876$	0.0209366	−	0.0152951i	0.000707381	−	0.000516773i
$877$	4.07938	+	11.2080i	0.137751	+	0.378467i	0.989317	−	0.145780i	$-0.0465690\pi$
$877$	4.07938	+	11.2080i	0.137751	+	0.378467i	−0.851566	+	0.524247i	$0.824347\pi$
$878$	−19.4889	+	3.43642i	−0.657718	+	0.115973i
$879$	18.1418	+	8.02051i	0.611909	+	0.270525i
$880$	−4.32882	−	1.57556i	−0.145924	−	0.0531122i
$881$	10.5449	−	6.08808i	0.355265	−	0.205113i	−0.311737	−	0.950169i	$-0.600911\pi$
$881$	10.5449	−	6.08808i	0.355265	−	0.205113i	0.667002	+	0.745056i	$0.267577\pi$
$882$	−3.13607	+	1.98251i	−0.105597	+	0.0667545i
$883$	22.1958	−	18.6245i	0.746948	−	0.626764i	−0.187746	−	0.982218i	$-0.560118\pi$
$883$	22.1958	−	18.6245i	0.746948	−	0.626764i	0.934694	+	0.355454i	$0.115674\pi$
$884$	4.44254	−	3.72773i	0.149419	−	0.125377i
$885$	−6.95783	+	7.24284i	−0.233885	+	0.243465i
$886$	2.24073	−	1.29369i	0.0752788	−	0.0434622i
$887$	−20.1576	−	7.33676i	−0.676826	−	0.246344i	−0.0193417	−	0.999813i	$-0.506157\pi$
$887$	−20.1576	−	7.33676i	−0.676826	−	0.246344i	−0.657484	+	0.753469i	$0.728379\pi$
$888$	−3.75810	+	8.50056i	−0.126114	+	0.285260i
$889$	−22.7005	+	4.00272i	−0.761352	+	0.134247i
$890$	5.13168	+	14.0992i	0.172014	+	0.472605i
$891$	41.2756	+	3.90236i	1.38279	+	0.130734i
$892$		−	20.5486i		−	0.688018i
$893$	−16.8824	+	3.73016i	−0.564948	+	0.124825i
$894$	18.5798	+	4.58091i	0.621401	+	0.153208i
$895$	−9.89650	+	11.7942i	−0.330804	+	0.394236i
$896$	−2.25590	+	0.821082i	−0.0753645	+	0.0274304i
$897$	−18.6081	−	1.25233i	−0.621307	−	0.0418142i
$898$	−2.18255	+	12.3778i	−0.0728325	+	0.413054i
$899$	−3.90653	+	10.7331i	−0.130290	+	0.357969i
$900$	−0.120371	−	2.99758i	−0.00401238	−	0.0999195i
$901$	10.5348	+	6.08226i	0.350964	+	0.202629i
$902$	22.7469	+	27.1086i	0.757387	+	0.902619i
$903$	−19.0868	−	38.8754i	−0.635168	−	1.29369i
$904$	3.30690	−	5.72771i	0.109986	−	0.190501i
$905$	0.129624	+	0.224516i	0.00430886	+	0.00746317i
$906$	−1.98728	−	1.33289i	−0.0660229	−	0.0442823i
$907$	9.65555	+	1.70253i	0.320607	+	0.0565317i	0.331636	−	0.943407i	$-0.392399\pi$
$907$	9.65555	+	1.70253i	0.320607	+	0.0565317i	−0.0110286	+	0.999939i	$0.503511\pi$
$908$	2.33936	+	13.2672i	0.0776343	+	0.440286i
$909$	−6.76323	+	50.0190i	−0.224322	+	1.65902i
$910$	11.0557	+	9.27687i	0.366494	+	0.307525i
$911$	−51.2887			−1.69927			−0.849636	−	0.527370i	$-0.823178\pi$
$911$	−51.2887			−1.69927			−0.849636	+	0.527370i	$0.823178\pi$
$912$	7.54761	+	0.183264i	0.249926	+	0.00606848i
$913$	−74.0288			−2.45000
$914$	−15.0185	−	12.6020i	−0.496768	−	0.416838i
$915$	2.02943	−	0.218667i	0.0670909	−	0.00722890i
$916$	−0.494397	−	2.80386i	−0.0163353	−	0.0926422i
$917$	−8.84977	−	1.56045i	−0.292245	−	0.0515307i
$918$	2.38789	+	4.40724i	0.0788121	+	0.145461i
$919$	8.82926	+	15.2927i	0.291250	+	0.504460i	0.974106	−	0.226093i	$-0.0725954\pi$
$919$	8.82926	+	15.2927i	0.291250	+	0.504460i	−0.682855	+	0.730554i	$0.739262\pi$
$920$	−0.895558	+	1.55115i	−0.0295257	+	0.0511400i
$921$	−42.2664	+	20.7516i	−1.39272	+	0.683790i
$922$	−21.1272	−	25.1784i	−0.695787	−	0.829206i
$923$	−10.3426	−	5.97131i	−0.340431	−	0.196548i
$924$	5.32791	+	18.3990i	0.175275	+	0.605282i
$925$	1.83529	−	5.04242i	0.0603440	−	0.165794i
$926$	6.37501	−	36.1545i	0.209496	−	1.18811i
$927$	18.2493	+	5.82424i	0.599385	+	0.191293i
$928$	−4.00350	+	1.45715i	−0.131421	+	0.0478334i
$929$	−21.7978	+	25.9777i	−0.715164	+	0.852300i	−0.994151	−	0.107995i	$-0.965557\pi$
$929$	−21.7978	+	25.9777i	−0.715164	+	0.852300i	0.278987	+	0.960295i	$0.410001\pi$
$930$	1.11159	−	4.50850i	0.0364503	−	0.147839i
$931$	2.89321	+	4.54856i	0.0948212	+	0.149073i
$932$			9.11409i			0.298542i
$933$	−7.94129	−	10.8704i	−0.259986	−	0.355880i
$934$	6.28152	+	17.2583i	0.205538	+	0.564710i
$935$	−4.37636	+	0.771670i	−0.143122	+	0.0252363i
$936$	14.2698	+	11.0291i	0.466422	+	0.360498i
$937$	19.4813	+	7.09061i	0.636426	+	0.231640i	0.640026	−	0.768353i	$-0.278924\pi$
$937$	19.4813	+	7.09061i	0.636426	+	0.231640i	−0.00359971	+	0.999994i	$0.501146\pi$
$938$	32.7720	−	18.9209i	1.07004	−	0.617790i
$939$	2.65991	+	2.55524i	0.0868029	+	0.0833872i
$940$	−3.03851	+	2.54962i	−0.0991054	+	0.0831593i
$941$	18.5680	−	15.5804i	0.605300	−	0.507907i	−0.287844	−	0.957677i	$-0.592939\pi$
$941$	18.5680	−	15.5804i	0.605300	−	0.507907i	0.893144	+	0.449770i	$0.148494\pi$
$942$	11.4072	+	10.9583i	0.371666	+	0.357041i
$943$	11.9158	−	6.87961i	0.388033	−	0.224031i
$944$	−5.44887	−	1.98323i	−0.177346	−	0.0645485i
$945$	−9.76937	+	7.75680i	−0.317798	+	0.252329i
$946$	47.2509	−	8.33161i	1.53626	−	0.270884i
$947$	−5.59422	−	15.3700i	−0.181788	−	0.499457i	0.815008	−	0.579450i	$-0.196733\pi$
$947$	−5.59422	−	15.3700i	−0.181788	−	0.499457i	−0.996795	+	0.0799925i	$0.974510\pi$
$948$	−15.8303	−	21.6692i	−0.514144	−	0.703782i
$949$		−	0.0899940i		−	0.00292133i
$950$	−4.35488	+	0.187039i	−0.141291	+	0.00606834i
$951$	1.93752	−	7.85843i	0.0628284	−	0.254827i
$952$	−1.48861	+	1.77405i	−0.0482460	+	0.0574974i
$953$	−12.1638	+	4.42727i	−0.394025	+	0.143413i	−0.531431	−	0.847101i	$-0.678346\pi$
$953$	−12.1638	+	4.42727i	−0.394025	+	0.143413i	0.137406	+	0.990515i	$0.456123\pi$
$954$	−11.5019	+	36.0392i	−0.372388	+	1.16681i
$955$	4.11155	−	23.3178i	0.133047	−	0.754546i
$956$	−2.65604	+	7.29741i	−0.0859025	+	0.236015i
$957$	9.45531	+	32.6522i	0.305647	+	1.05550i
$958$	31.0571	+	17.9308i	1.00341	+	0.579318i
$959$	10.8132	+	12.8867i	0.349176	+	0.416132i
$960$	1.55477	−	0.763348i	0.0501799	−	0.0246369i
$961$	−11.9063	+	20.6223i	−0.384074	+	0.665236i
$962$	16.1296	+	27.9372i	0.520038	+	0.900732i
$963$	23.6915	+	26.0371i	0.763449	+	0.839033i
$964$	7.97629	+	1.40644i	0.256899	+	0.0452983i
$965$	3.57644	+	20.2830i	0.115130	+	0.652932i
$966$	7.40479	−	0.797850i	0.238245	−	0.0256704i
$967$	34.1902	+	28.6890i	1.09948	+	0.922576i	0.997390	−	0.0721986i	$-0.0230015\pi$
$967$	34.1902	+	28.6890i	1.09948	+	0.922576i	0.102093	+	0.994775i	$0.467446\pi$
$968$	−10.2211			−0.328518
$969$	6.39387	−	3.48736i	0.205401	−	0.112030i
$970$	1.36689			0.0438883
$971$	−0.722485	−	0.606237i	−0.0231856	−	0.0194551i	0.631121	−	0.775684i	$-0.282595\pi$
$971$	−0.722485	−	0.606237i	−0.0231856	−	0.0194551i	−0.654307	+	0.756229i	$0.727040\pi$
$972$	−11.8095	+	10.1753i	−0.378789	+	0.326372i
$973$	3.09531	+	17.5544i	0.0992312	+	0.562768i
$974$	31.3778	+	5.53274i	1.00541	+	0.177281i
$975$	−8.64764	−	5.80008i	−0.276946	−	0.185751i
$976$	0.589237	+	1.02059i	0.0188610	+	0.0326683i
$977$	27.0137	−	46.7892i	0.864246	−	1.49692i	−0.00354719	−	0.999994i	$-0.501129\pi$
$977$	27.0137	−	46.7892i	0.864246	−	1.49692i	0.867794	−	0.496925i	$-0.165538\pi$
$978$	3.68313	+	7.50171i	0.117774	+	0.239878i
$979$	44.4282	+	52.9475i	1.41993	+	1.69221i
$980$	1.07103	+	0.618360i	0.0342128	+	0.0197528i
$981$	0.589635	−	0.0236775i	0.0188256	−	0.000755964i
$982$	5.71475	−	15.7012i	0.182365	−	0.501044i
$983$	8.48579	−	48.1253i	0.270655	−	1.53496i	−0.481780	−	0.876292i	$-0.660009\pi$
$983$	8.48579	−	48.1253i	0.270655	−	1.53496i	0.752435	−	0.658667i	$-0.228879\pi$
$984$	−13.2755	−	0.893445i	−0.423206	−	0.0284820i
$985$	14.1321	−	5.14365i	0.450285	−	0.163890i
$986$	−2.64179	+	3.14837i	−0.0841319	+	0.100264i
$987$	16.0136	+	3.94820i	0.509718	+	0.125673i
$988$	15.9671	−	20.7781i	0.507980	−	0.661039i
$989$		−	18.6551i		−	0.593199i
$990$	−5.24394	−	12.7863i	−0.166664	−	0.406377i
$991$	−0.531214	−	1.45950i	−0.0168746	−	0.0463625i	0.930969	−	0.365097i	$-0.118964\pi$
$991$	−0.531214	−	1.45950i	−0.0168746	−	0.0463625i	−0.947844	+	0.318735i	$0.896742\pi$
$992$	2.64020	−	0.465539i	0.0838265	−	0.0147809i
$993$	−21.4702	+	48.5642i	−0.681337	+	1.54114i
$994$	4.48147	+	1.63112i	0.142144	+	0.0517361i
$995$	−0.325130	+	0.187714i	−0.0103073	+	0.00595092i
$996$	19.2828	−	20.0727i	0.610999	−	0.636027i
$997$	23.8176	−	19.9854i	0.754312	−	0.632943i	−0.182327	−	0.983238i	$-0.558363\pi$
$997$	23.8176	−	19.9854i	0.754312	−	0.632943i	0.936640	+	0.350295i	$0.113919\pi$
$998$	−2.02508	+	1.69925i	−0.0641029	+	0.0537887i
$999$	−26.4496	+	8.82392i	−0.836830	+	0.279176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.a.41.8	✓	84
3.2	odd	2		570.2.bb.b.41.10	yes	84
19.13	odd	18		570.2.bb.b.431.10	yes	84
57.32	even	18	inner	570.2.bb.a.431.8	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.8	✓	84	1.1	even	1	trivial
570.2.bb.a.431.8	yes	84	57.32	even	18	inner
570.2.bb.b.41.10	yes	84	3.2	odd	2
570.2.bb.b.431.10	yes	84	19.13	odd	18

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.185551 + 1.72208i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.964794 + 1.43846i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.93114 + 0.639068i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.185551 + 1.72208i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.964794 + 1.43846i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.93114 + 0.639068i) q^{9} +(0.642788 + 0.766044i) q^{10} +(3.98946 + 2.30332i) q^{11} +(-1.66370 + 0.481768i) q^{12} +(-2.05613 + 5.64918i) q^{13} +(0.416874 - 2.36421i) q^{14} +(-0.116305 + 1.72814i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.620076 + 0.738978i) q^{17} +(-2.65617 - 1.39455i) q^{18} +(-2.01546 + 3.86496i) q^{19} +1.00000i q^{20} +(3.35758 - 2.45286i) q^{21} +(1.57556 + 4.32882i) q^{22} +(1.76390 - 0.311024i) q^{23} +(-1.58414 - 0.700350i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-5.20631 + 3.00586i) q^{26} +(-1.64440 - 4.92909i) q^{27} +(1.83903 - 1.54313i) q^{28} +(3.26368 - 2.73855i) q^{29} +(-1.19992 + 1.24907i) q^{30} +(-2.32175 + 1.34047i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-3.22626 + 7.29757i) q^{33} +(-0.950012 + 0.167513i) q^{34} +(-0.821082 - 2.25590i) q^{35} +(-1.13835 - 2.77564i) q^{36} -5.36603i q^{37} +(-4.02828 + 1.66522i) q^{38} +(-10.1099 - 2.49262i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(7.21865 - 2.62737i) q^{41} +(4.14872 + 0.279211i) q^{42} +(1.80861 - 10.2571i) q^{43} +(-1.57556 + 4.32882i) q^{44} +(-2.99758 + 0.120371i) q^{45} +(1.55115 + 0.895558i) q^{46} +(2.54962 + 3.03851i) q^{47} +(-0.763348 - 1.55477i) q^{48} +(0.618360 - 1.07103i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.38764 - 0.930705i) q^{51} +(-5.92040 - 1.04393i) q^{52} +(-2.18971 - 12.4185i) q^{53} +(1.90867 - 4.83290i) q^{54} +(3.52889 + 2.96109i) q^{55} +2.40068 q^{56} +(-7.02975 - 2.75365i) q^{57} +4.26043 q^{58} +(4.44196 + 3.72725i) q^{59} +(-1.72208 + 0.185551i) q^{60} +(-0.204640 - 1.16057i) q^{61} +(-2.64020 - 0.465539i) q^{62} +(4.84703 + 5.32690i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.00586 + 5.20631i) q^{65} +(-7.16224 + 3.51646i) q^{66} +(10.1322 + 12.0751i) q^{67} +(-0.835427 - 0.482334i) q^{68} +(0.862903 + 2.97988i) q^{69} +(0.821082 - 2.25590i) q^{70} +(-0.344961 + 1.95637i) q^{71} +(0.912122 - 2.85798i) q^{72} +(-0.0140670 + 0.00511995i) q^{73} +(3.44922 - 4.11062i) q^{74} +(-0.414626 + 1.68169i) q^{75} +(-4.15622 - 1.31370i) q^{76} -11.0591i q^{77} +(-6.14238 - 8.40796i) q^{78} +(5.29911 + 14.5592i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(8.18318 - 3.74640i) q^{81} +(7.21865 + 2.62737i) q^{82} +(-13.9171 + 8.03502i) q^{83} +(2.99863 + 2.88063i) q^{84} +(-0.738978 + 0.620076i) q^{85} +(7.97864 - 6.69488i) q^{86} +(5.32160 + 5.11219i) q^{87} +(-3.98946 + 2.30332i) q^{88} +(14.0992 + 5.13168i) q^{89} +(-2.37366 - 1.83460i) q^{90} +(14.2130 - 2.50613i) q^{91} +(0.612598 + 1.68310i) q^{92} +(-2.73920 - 3.74953i) q^{93} +3.96650i q^{94} +(-2.65599 + 3.45626i) q^{95} +(0.414626 - 1.68169i) q^{96} +(0.878623 - 1.04710i) q^{97} +(1.16214 - 0.422983i) q^{98} +(-13.1657 - 4.20181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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