LMFDB - Embedded newform 570.2.bb.b.41.10

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			41.10
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.b.431.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.964794 + 1.43846i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(0.185551 - 1.72208i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.13835 + 2.77564i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.964794 + 1.43846i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(0.185551 - 1.72208i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.13835 + 2.77564i) q^{9} +(0.642788 + 0.766044i) q^{10} +(-3.98946 - 2.30332i) q^{11} +(-1.24907 + 1.19992i) q^{12} +(-2.05613 + 5.64918i) q^{13} +(-0.416874 + 2.36421i) q^{14} +(-0.700350 - 1.58414i) 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} +(1.83256 - 3.73250i) q^{21} +(1.57556 + 4.32882i) q^{22} +(-1.76390 + 0.311024i) q^{23} +(1.72814 - 0.116305i) q^{24} +(0.939693 + 0.342020i) q^{25} +(5.20631 - 3.00586i) q^{26} +(-5.09092 + 1.04045i) q^{27} +(1.83903 - 1.54313i) q^{28} +(-3.26368 + 2.73855i) q^{29} +(-0.481768 + 1.66370i) q^{30} +(-2.32175 + 1.34047i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.535774 - 7.96092i) q^{33} +(-0.950012 + 0.167513i) q^{34} +(0.821082 + 2.25590i) q^{35} +(-2.93114 - 0.639068i) 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} +(-3.80303 + 1.68132i) q^{42} +(1.80861 - 10.2571i) q^{43} +(1.57556 - 4.32882i) q^{44} +(1.60304 - 2.53580i) q^{45} +(1.55115 + 0.895558i) q^{46} +(-2.54962 - 3.03851i) q^{47} +(-1.39859 - 1.02173i) q^{48} +(0.618360 - 1.07103i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.66124 + 0.178995i) q^{51} +(-5.92040 - 1.04393i) q^{52} +(2.18971 + 12.4185i) q^{53} +(4.56866 + 2.47535i) q^{54} +(3.52889 + 2.96109i) q^{55} -2.40068 q^{56} +(-7.50410 + 0.829724i) q^{57} +4.26043 q^{58} +(-4.44196 - 3.72725i) q^{59} +(1.43846 - 0.964794i) q^{60} +(-0.204640 - 1.16057i) q^{61} +(2.64020 + 0.465539i) q^{62} +(7.13710 - 0.965032i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.00586 - 5.20631i) q^{65} +(-4.70675 + 6.44280i) q^{66} +(10.1322 + 12.0751i) q^{67} +(0.835427 + 0.482334i) q^{68} +(-2.14920 - 2.23724i) q^{69} +(0.821082 - 2.25590i) q^{70} +(0.344961 - 1.95637i) q^{71} +(1.83460 + 2.37366i) 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} +(9.34683 + 4.58904i) q^{78} +(5.29911 + 14.5592i) q^{79} +(0.984808 - 0.173648i) q^{80} +(-6.40834 - 6.31928i) q^{81} +(7.21865 + 2.62737i) q^{82} +(13.9171 - 8.03502i) q^{83} +(3.99402 + 1.15657i) q^{84} +(-0.738978 + 0.620076i) q^{85} +(-7.97864 + 6.69488i) q^{86} +(-7.08809 - 2.05254i) q^{87} +(-3.98946 + 2.30332i) q^{88} +(-14.0992 - 5.13168i) q^{89} +(-2.85798 + 0.912122i) q^{90} +(14.2130 - 2.50613i) q^{91} +(-0.612598 - 1.68310i) q^{92} +(-4.16822 - 2.04648i) 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} +(10.9346 - 8.45133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * 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
$3$	0.964794	+	1.43846i	0.557024	+	0.830496i
$3$	0.964794	+	1.43846i	0.557024	+	0.830496i
$4$	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
$6$	0.185551	−	1.72208i	0.0757508	−	0.703038i
$7$	−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
$9$	−1.13835	+	2.77564i	−0.379449	+	0.925213i
$10$	0.642788	+	0.766044i	0.203267	+	0.242245i
$11$	−3.98946	−	2.30332i	−1.20287	−	0.694476i	−0.241676	−	0.970357i	$-0.577697\pi$
$11$	−3.98946	−	2.30332i	−1.20287	−	0.694476i	−0.961192	+	0.275881i	$0.911031\pi$
$12$	−1.24907	+	1.19992i	−0.360577	+	0.346388i
$13$	−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
$15$	−0.700350	−	1.58414i	−0.180830	−	0.409024i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.620076	−	0.738978i	0.150391	−	0.179229i	−0.685589	−	0.727988i	$-0.740455\pi$
$17$	0.620076	−	0.738978i	0.150391	−	0.179229i	0.835980	+	0.548760i	$0.184900\pi$
$18$	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
$21$	1.83256	−	3.73250i	0.399897	−	0.814499i
$22$	1.57556	+	4.32882i	0.335911	+	0.922908i
$23$	−1.76390	+	0.311024i	−0.367800	+	0.0648530i	−0.354493	−	0.935058i	$-0.615347\pi$
$23$	−1.76390	+	0.311024i	−0.367800	+	0.0648530i	−0.0133061	+	0.999911i	$0.504236\pi$
$24$	1.72814	−	0.116305i	0.352755	−	0.0237406i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	5.20631	−	3.00586i	1.02104	−	0.589498i
$27$	−5.09092	+	1.04045i	−0.979748	+	0.200235i
$28$	1.83903	−	1.54313i	0.347544	−	0.291624i
$29$	−3.26368	+	2.73855i	−0.606051	+	0.508537i	−0.893384	−	0.449294i	$-0.851676\pi$
$29$	−3.26368	+	2.73855i	−0.606051	+	0.508537i	0.287333	+	0.957831i	$0.407231\pi$
$30$	−0.481768	+	1.66370i	−0.0879585	+	0.303749i
$31$	−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
$33$	−0.535774	−	7.96092i	−0.0932662	−	1.38582i
$34$	−0.950012	+	0.167513i	−0.162926	+	0.0287282i
$35$	0.821082	+	2.25590i	0.138788	+	0.381317i
$36$	−2.93114	−	0.639068i	−0.488524	−	0.106511i
$37$		−	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	−0.837334	−	0.546691i	$-0.815887\pi$
$41$	−7.21865	+	2.62737i	−1.12736	+	0.410327i	−0.290029	+	0.957018i	$0.593665\pi$
$42$	−3.80303	+	1.68132i	−0.586820	+	0.259433i
$43$	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
$45$	1.60304	−	2.53580i	0.238967	−	0.378014i
$46$	1.55115	+	0.895558i	0.228705	+	0.132043i
$47$	−2.54962	−	3.03851i	−0.371900	−	0.443213i	0.547340	−	0.836910i	$-0.315640\pi$
$47$	−2.54962	−	3.03851i	−0.371900	−	0.443213i	−0.919240	+	0.393697i	$0.871196\pi$
$48$	−1.39859	−	1.02173i	−0.201869	−	0.147475i
$49$	0.618360	−	1.07103i	0.0883372	−	0.153004i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	1.66124	+	0.178995i	0.232620	+	0.0250643i
$52$	−5.92040	−	1.04393i	−0.821011	−	0.144766i
$53$	2.18971	+	12.4185i	0.300780	+	1.70581i	0.642731	+	0.766092i	$0.277801\pi$
$53$	2.18971	+	12.4185i	0.300780	+	1.70581i	−0.341951	+	0.939718i	$0.611088\pi$
$54$	4.56866	+	2.47535i	0.621716	+	0.336852i
$55$	3.52889	+	2.96109i	0.475835	+	0.399273i
$56$	−2.40068			−0.320805
$57$	−7.50410	+	0.829724i	−0.993943	+	0.109900i
$58$	4.26043			0.559422
$59$	−4.44196	−	3.72725i	−0.578294	−	0.485246i	0.306092	−	0.952002i	$-0.400978\pi$
$59$	−4.44196	−	3.72725i	−0.578294	−	0.485246i	−0.884386	+	0.466756i	$0.845423\pi$
$60$	1.43846	−	0.964794i	0.185705	−	0.124554i
$61$	−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
$63$	7.13710	−	0.965032i	0.899190	−	0.121583i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.00586	−	5.20631i	0.372831	−	0.645763i
$66$	−4.70675	+	6.44280i	−0.579361	+	0.793054i
$67$	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
$69$	−2.14920	−	2.23724i	−0.258733	−	0.269332i
$70$	0.821082	−	2.25590i	0.0981381	−	0.269632i
$71$	0.344961	−	1.95637i	0.0409394	−	0.232179i	−0.957472	−	0.288527i	$-0.906835\pi$
$71$	0.344961	−	1.95637i	0.0409394	−	0.232179i	0.998411	+	0.0563481i	$0.0179457\pi$
$72$	1.83460	+	2.37366i	0.216210	+	0.279738i
$73$	−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
$78$	9.34683	+	4.58904i	1.05832	+	0.519606i
$79$	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
$81$	−6.40834	−	6.31928i	−0.712037	−	0.702142i
$82$	7.21865	+	2.62737i	0.797167	+	0.290145i
$83$	13.9171	−	8.03502i	1.52760	−	0.881958i	0.528134	−	0.849161i	$-0.322892\pi$
$83$	13.9171	−	8.03502i	1.52760	−	0.881958i	0.999462	−	0.0327971i	$-0.0104415\pi$
$84$	3.99402	+	1.15657i	0.435783	+	0.126193i
$85$	−0.738978	+	0.620076i	−0.0801534	+	0.0672567i
$86$	−7.97864	+	6.69488i	−0.860359	+	0.721927i
$87$	−7.08809	−	2.05254i	−0.759923	−	0.220056i
$88$	−3.98946	+	2.30332i	−0.425278	+	0.245534i
$89$	−14.0992	−	5.13168i	−1.49451	−	0.543957i	−0.539877	−	0.841744i	$-0.681529\pi$
$89$	−14.0992	−	5.13168i	−1.49451	−	0.543957i	−0.954632	+	0.297788i	$0.903751\pi$
$90$	−2.85798	+	0.912122i	−0.301257	+	0.0961461i
$91$	14.2130	−	2.50613i	1.48993	−	0.262714i
$92$	−0.612598	−	1.68310i	−0.0638677	−	0.175475i
$93$	−4.16822	−	2.04648i	−0.432225	−	0.212210i
$94$			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
$99$	10.9346	−	8.45133i	1.09897	−	0.849391i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−5.75439	+	15.8101i	−0.572583	+	1.57316i	0.227824	+	0.973702i	$0.426839\pi$
$101$	−5.75439	+	15.8101i	−0.572583	+	1.57316i	−0.800407	+	0.599457i	$0.795383\pi$
$102$	−1.15753	−	1.20494i	−0.114612	−	0.119307i
$103$	−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
$105$	−2.45286	+	3.35758i	−0.239374	+	0.327666i
$106$	6.30503	−	10.9206i	0.612398	−	1.06071i
$107$	5.86709	+	10.1621i	0.567193	+	0.982406i	0.996842	+	0.0794106i	$0.0253038\pi$
$107$	5.86709	+	10.1621i	0.567193	+	0.982406i	−0.429649	+	0.902996i	$0.641363\pi$
$108$	−1.90867	−	4.83290i	−0.183662	−	0.465046i
$109$	−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
$111$	7.71883	−	5.17711i	0.732639	−	0.491390i
$112$	1.83903	+	1.54313i	0.173772	+	0.145812i
$113$	6.61379			0.622173			0.311087	−	0.950382i	$-0.399307\pi$
$113$	6.61379			0.622173			0.311087	+	0.950382i	$0.399307\pi$
$114$	6.28181	+	4.18794i	0.588346	+	0.392236i
$115$	1.79112			0.167022
$116$	−3.26368	−	2.73855i	−0.303025	−	0.254268i
$117$	−13.3395	−	12.1378i	−1.23324	−	1.12214i
$118$	1.00691	+	5.71047i	0.0926936	+	0.525692i
$119$	−2.28068	−	0.402145i	−0.209069	−	0.0368646i
$120$	−1.72208	−	0.185551i	−0.157204	−	0.0169384i
$121$	5.11054	+	8.85171i	0.464594	+	0.804701i
$122$	−0.589237	+	1.02059i	−0.0533470	+	0.0923998i
$123$	−10.7439	−	7.84888i	−0.968743	−	0.707710i
$124$	−1.72327	−	2.05371i	−0.154754	−	0.184429i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	−6.08765	−	3.84838i	−0.542331	−	0.342841i
$127$	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
$129$	16.4995	−	7.29441i	1.45270	−	0.642237i
$130$	−5.64918	+	2.05613i	−0.495465	+	0.180335i
$131$	−2.40610	+	2.86747i	−0.210222	+	0.250532i	−0.860844	−	0.508869i	$-0.830064\pi$
$131$	−2.40610	+	2.86747i	−0.210222	+	0.250532i	0.650622	+	0.759402i	$0.274508\pi$
$132$	7.74694	−	1.91003i	0.674284	−	0.166247i
$133$	10.4547	−	0.449021i	0.906537	−	0.0389351i
$134$		−	15.7629i		−	1.36171i
$135$	5.19425	−	0.140614i	0.447050	−	0.0121022i
$136$	−0.329936	−	0.906491i	−0.0282918	−	0.0777310i
$137$	6.90086	−	1.21681i	0.589580	−	0.103959i	0.129104	−	0.991631i	$-0.458790\pi$
$137$	6.90086	−	1.21681i	0.589580	−	0.103959i	0.460476	+	0.887672i	$0.347679\pi$
$138$	0.208315	+	3.09530i	0.0177330	+	0.263490i
$139$	−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
$141$	1.91093	−	6.59907i	0.160930	−	0.555742i
$142$	−1.52179	+	1.27693i	−0.127706	+	0.107158i
$143$	21.2147	−	17.8012i	1.77406	−	1.48862i
$144$	0.120371	−	2.99758i	0.0100310	−	0.249799i
$145$	3.68964	−	2.13022i	0.306408	−	0.176905i
$146$	0.0140670	+	0.00511995i	0.00116419	+	0.000423730i
$147$	2.13723	−	0.143836i	0.176276	−	0.0118634i
$148$	5.28451	−	0.931801i	0.434384	−	0.0765936i
$149$	3.77873	+	10.3820i	0.309566	+	0.850525i	0.992741	+	0.120271i	$0.0383763\pi$
$149$	3.77873	+	10.3820i	0.309566	+	0.850525i	−0.683175	+	0.730254i	$0.739401\pi$
$150$	0.763348	−	1.55477i	0.0623271	−	0.126946i
$151$			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
$156$	−4.21031	−	9.52344i	−0.337095	−	0.762485i
$157$	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
$159$	−15.7509	+	15.1311i	−1.24913	+	1.19997i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	2.76392	+	3.29392i	0.217828	+	0.259597i
$162$	0.847118	+	8.96004i	0.0665558	+	0.703968i
$163$	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
$165$	−0.854765	+	7.93301i	−0.0665433	+	0.617584i
$166$	−15.8259	−	2.79053i	−1.22833	−	0.216587i
$167$	−3.05049	−	17.3002i	−0.236054	−	1.33873i	−0.840383	−	0.541993i	$-0.817670\pi$
$167$	−3.05049	−	17.3002i	−0.236054	−	1.33873i	0.604329	−	0.796735i	$-0.293441\pi$
$168$	−2.31616	−	3.45329i	−0.178696	−	0.266427i
$169$	−17.7269	−	14.8747i	−1.36361	−	1.14420i
$170$	0.964668			0.0739866
$171$	−8.43344	−	9.99386i	−0.644921	−	0.764249i
$172$	10.4154			0.794165
$173$	9.21180	+	7.72961i	0.700360	+	0.587672i	0.921876	−	0.387485i	$-0.126656\pi$
$173$	9.21180	+	7.72961i	0.700360	+	0.587672i	−0.221516	+	0.975157i	$0.571101\pi$
$174$	4.11044	+	6.12847i	0.311612	+	0.464598i
$175$	−0.416874	−	2.36421i	−0.0315127	−	0.178718i
$176$	4.53665	+	0.799934i	0.341963	+	0.0602973i
$177$	1.07593	−	9.98562i	0.0808718	−	0.750565i
$178$	7.50201	+	12.9939i	0.562299	+	0.973931i
$179$	7.69811	−	13.3335i	0.575384	−	0.996594i	−0.420616	−	0.907239i	$-0.638186\pi$
$179$	7.69811	−	13.3335i	0.575384	−	0.996594i	0.996000	−	0.0893555i	$-0.0284807\pi$
$180$	2.77564	+	1.13835i	0.206884	+	0.0848473i
$181$	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
$183$	1.47200	−	1.41408i	0.108813	−	0.104532i
$184$	−0.612598	+	1.68310i	−0.0451613	+	0.124080i
$185$	−0.931801	+	5.28451i	−0.0685074	+	0.388525i
$186$	1.87759	+	4.24698i	0.137672	+	0.311404i
$187$	−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	$0.327441\pi$
$191$			23.6775i			1.71324i	−0.515945	+	0.856622i	$0.672559\pi$
$192$	0.763348	−	1.55477i	0.0550899	−	0.112206i
$193$	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
$195$	10.3891	−	0.699193i	0.743980	−	0.0500702i
$196$	1.16214	+	0.422983i	0.0830098	+	0.0302131i
$197$	−13.0242	+	7.51952i	−0.927935	+	0.535743i	−0.886158	−	0.463384i	$-0.846635\pi$
$197$	−13.0242	+	7.51952i	−0.927935	+	0.535743i	−0.0417769	+	0.999127i	$0.513302\pi$
$198$	−13.8088	−	0.554507i	−0.981347	−	0.0394071i
$199$	−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
$201$	−7.59409	+	26.2248i	−0.535646	+	1.84976i
$202$	14.5706	−	8.41236i	1.02519	−	0.591891i
$203$	9.61113	+	3.49817i	0.674569	+	0.245523i
$204$	0.112195	+	1.66708i	0.00785525	+	0.116719i
$205$	7.56522	−	1.33395i	0.528378	−	0.0931673i
$206$	2.18393	+	6.00029i	0.152161	+	0.418060i
$207$	1.14464	−	5.25001i	0.0795583	−	0.364901i
$208$		−	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
$213$	3.14698	−	1.39128i	0.215628	−	0.0953291i
$214$	2.03762	−	11.5559i	0.139289	−	0.789945i
$215$	−3.56227	+	9.78726i	−0.242945	+	0.667485i
$216$	−1.64440	+	4.92909i	−0.111887	+	0.335382i
$217$	5.57380	+	3.21803i	0.378374	+	0.218454i
$218$	0.126439	+	0.150684i	0.00856350	+	0.0102056i
$219$	−0.0209366	−	0.0152951i	−0.00141476	−	0.00103355i
$220$	−2.30332	+	3.98946i	−0.155290	+	0.268969i
$221$	2.89966	+	5.02236i	0.195052	+	0.337840i
$222$	−9.24075	−	0.995671i	−0.620199	−	0.0668251i
$223$	−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
$225$	−2.01902	+	2.21891i	−0.134601	+	0.147927i
$226$	−5.06646	−	4.25126i	−0.337016	−	0.282790i
$227$	−13.4718			−0.894157			−0.447078	−	0.894495i	$-0.647535\pi$
$227$	−13.4718			−0.894157			−0.447078	+	0.894495i	$0.647535\pi$
$228$	−2.12019	−	7.24602i	−0.140413	−	0.479879i
$229$	−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
$231$	−15.9081	+	10.6697i	−1.04667	+	0.702016i
$232$	0.739817	+	4.19571i	0.0485713	+	0.275462i
$233$	−8.97563	−	1.58265i	−0.588013	−	0.103683i	−0.128277	−	0.991738i	$-0.540945\pi$
$233$	−8.97563	−	1.58265i	−0.588013	−	0.103683i	−0.459736	+	0.888056i	$0.652056\pi$
$234$	2.41661	+	17.8725i	0.157979	+	1.16836i
$235$	1.98325	+	3.43509i	0.129373	+	0.224081i
$236$	2.89928	−	5.02171i	0.188727	−	0.326885i
$237$	−15.8303	+	21.6692i	−1.02829	+	1.40756i
$238$	1.48861	+	1.77405i	0.0964921	+	0.114995i
$239$	−6.72533	−	3.88287i	−0.435026	−	0.251162i	0.266460	−	0.963846i	$-0.414146\pi$
$239$	−6.72533	−	3.88287i	−0.435026	−	0.251162i	−0.701485	+	0.712684i	$0.747479\pi$
$240$	1.19992	+	1.24907i	0.0774547	+	0.0806274i
$241$	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
$243$	2.90732	−	15.3149i	0.186504	−	0.982454i
$244$	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
$249$	24.9852	+	12.2670i	1.58337	+	0.777392i
$250$	0.342020	+	0.939693i	0.0216313	+	0.0594314i
$251$	−1.68837	+	0.297704i	−0.106569	+	0.0187909i	−0.226678	−	0.973970i	$-0.572787\pi$
$251$	−1.68837	+	0.297704i	−0.106569	+	0.0187909i	0.120109	+	0.992761i	$0.461675\pi$
$252$	2.18972	+	6.86110i	0.137939	+	0.432209i
$253$	7.75342	+	2.82201i	0.487453	+	0.177418i
$254$	−8.31535	+	4.80087i	−0.521751	+	0.301233i
$255$	−1.60492	−	0.464746i	−0.100504	−	0.0291035i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	14.2297	−	11.9401i	0.887624	−	0.744805i	−0.0801083	−	0.996786i	$-0.525527\pi$
$257$	14.2297	−	11.9401i	0.887624	−	0.744805i	0.967732	+	0.251981i	$0.0810822\pi$
$258$	−17.3281	−	5.01780i	−1.07880	−	0.312395i
$259$	−11.1563	+	6.44107i	−0.693216	+	0.400229i
$260$	5.64918	+	2.05613i	0.350347	+	0.127516i
$261$	−3.88604	−	12.1762i	−0.240540	−	0.753689i
$262$	3.68635	−	0.650004i	0.227744	−	0.0401574i
$263$	1.72478	+	4.73879i	0.106354	+	0.292206i	0.981442	−	0.191758i	$-0.0614188\pi$
$263$	1.72478	+	4.73879i	0.106354	+	0.292206i	−0.875088	+	0.483964i	$0.839197\pi$
$264$	−7.16224	−	3.51646i	−0.440806	−	0.216423i
$265$		−	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	−0.924275	−	0.381726i	$-0.875330\pi$
$269$	−22.7475	+	8.27943i	−1.38694	+	0.504806i	−0.462667	+	0.886532i	$0.653107\pi$
$270$	−4.06941	−	3.23108i	−0.247656	−	0.196637i
$271$	−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
$273$	17.3176	+	18.0270i	1.04811	+	1.09104i
$274$	−6.06851	−	3.50366i	−0.366612	−	0.211664i
$275$	−2.96109	−	3.52889i	−0.178560	−	0.212800i
$276$	1.83004	−	2.50504i	0.110156	−	0.150786i
$277$	−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
$279$	−1.07769	−	7.97027i	−0.0645194	−	0.477167i
$280$	2.36421	+	0.416874i	0.141289	+	0.0249130i
$281$	1.65593	+	9.39127i	0.0987848	+	0.560236i	0.993522	+	0.113643i	$0.0362519\pi$
$281$	1.65593	+	9.39127i	0.0987848	+	0.560236i	−0.894737	+	0.446594i	$0.852637\pi$
$282$	−5.70566	+	3.82685i	−0.339767	+	0.227886i
$283$	−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
$285$	7.53418	+	0.485956i	0.446286	+	0.0287855i
$286$	−27.6938			−1.63757
$287$	14.1273	+	11.8542i	0.833908	+	0.699732i
$288$	−2.01902	+	2.21891i	−0.118972	+	0.130750i
$289$	2.79042	+	15.8253i	0.164143	+	0.930899i
$290$	−4.19571	−	0.739817i	−0.246381	−	0.0434435i
$291$	2.35391	+	0.253628i	0.137988	+	0.0148680i
$292$	−0.00748487	−	0.0129642i	−0.000438019	−	0.000758671i
$293$	−5.72607	+	9.91785i	−0.334521	+	0.579407i	−0.983393	−	0.181491i	$-0.941908\pi$
$293$	−5.72607	+	9.91785i	−0.334521	+	0.579407i	0.648872	+	0.760898i	$0.275241\pi$
$294$	−1.72967	−	1.26360i	−0.100876	−	0.0736946i
$295$	3.72725	+	4.44196i	0.217009	+	0.258621i
$296$	−4.64712	−	2.68302i	−0.270108	−	0.155947i
$297$	22.7065	+	7.57517i	1.31757	+	0.439556i
$298$	3.77873	−	10.3820i	0.218896	−	0.601412i
$299$	1.86979	−	10.6041i	0.108133	−	0.613252i
$300$	−1.58414	+	0.700350i	−0.0914606	+	0.0404347i
$301$	−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
$306$	0.616488	−	2.82758i	0.0352423	−	0.161642i
$307$	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
$309$	−0.742650	−	11.0348i	−0.0422479	−	0.627750i
$310$	−2.51925	−	0.916933i	−0.143084	−	0.0520783i
$311$	6.73107	−	3.88618i	0.381684	−	0.220365i	−0.296867	−	0.954919i	$-0.595942\pi$
$311$	6.73107	−	3.88618i	0.381684	−	0.220365i	0.678551	+	0.734554i	$0.262608\pi$
$312$	−2.89626	+	10.0017i	−0.163968	+	0.566236i
$313$	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
$315$	−7.19625	−	0.288974i	−0.405463	−	0.0162818i
$316$	−13.4178	+	7.74678i	−0.754811	+	0.435790i
$317$	4.39112	+	1.59824i	0.246630	+	0.0897659i	0.462377	−	0.886683i	$-0.346997\pi$
$317$	4.39112	+	1.59824i	0.246630	+	0.0897659i	−0.215747	+	0.976449i	$0.569219\pi$
$318$	21.7920	−	1.46661i	1.22203	−	0.0822434i
$319$	19.3281	−	3.40806i	1.08217	−	0.190815i
$320$	0.342020	+	0.939693i	0.0191195	+	0.0525304i
$321$	−8.95725	+	18.2439i	−0.499945	+	1.01828i
$322$		−	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
$327$	−0.137761	−	0.311606i	−0.00761821	−	0.0172319i
$328$	−1.33395	+	7.56522i	−0.0736552	+	0.417719i
$329$	−3.25682	+	8.94804i	−0.179554	+	0.493322i
$330$	5.75403	−	5.52760i	0.316749	−	0.304285i
$331$	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
$333$	14.8942	+	6.10840i	0.816195	+	0.334738i
$334$	−8.78353	+	15.2135i	−0.480613	+	0.832446i
$335$	−7.88147	−	13.6511i	−0.430611	−	0.745840i
$336$	−0.445449	+	4.13418i	−0.0243012	+	0.225538i
$337$	−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
$339$	6.38095	+	9.51369i	0.346565	+	0.516713i
$340$	−0.738978	−	0.620076i	−0.0400767	−	0.0336284i
$341$	12.3501			0.668794
$342$	0.0364611	+	13.0766i	0.00197159	+	0.707104i
$343$	−19.7738			−1.06768
$344$	−7.97864	−	6.69488i	−0.430180	−	0.360964i
$345$	1.72806	+	2.57645i	0.0930355	+	0.138712i
$346$	−2.08814	−	11.8425i	−0.112259	−	0.636654i
$347$	2.13762	+	0.376919i	0.114753	+	0.0202341i	0.230730	−	0.973018i	$-0.425889\pi$
$347$	2.13762	+	0.376919i	0.114753	+	0.0202341i	−0.115977	+	0.993252i	$0.537000\pi$
$348$	0.790527	−	7.33682i	0.0423767	−	0.393295i
$349$	−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
$351$	4.58992	−	30.8988i	0.244992	−	1.64926i
$352$	−2.96109	−	3.52889i	−0.157826	−	0.188090i
$353$	12.2148	+	7.05224i	0.650130	+	0.375353i	0.788506	−	0.615027i	$-0.210855\pi$
$353$	12.2148	+	7.05224i	0.650130	+	0.375353i	−0.138376	+	0.990380i	$0.544188\pi$
$354$	−7.24284	+	6.95783i	−0.384953	+	0.369805i
$355$	−0.679441	+	1.86675i	−0.0360610	+	0.0990767i
$356$	2.60542	−	14.7761i	0.138087	−	0.783130i
$357$	−1.62191	−	3.66866i	−0.0858408	−	0.194166i
$358$	−14.4677	+	5.26582i	−0.764643	+	0.278307i
$359$	16.5538	−	19.7281i	0.873676	−	1.04121i	−0.125119	−	0.992142i	$-0.539931\pi$
$359$	16.5538	−	19.7281i	0.873676	−	1.04121i	0.998796	−	0.0490651i	$-0.0156242\pi$
$360$	−1.39455	−	2.65617i	−0.0734991	−	0.139992i
$361$	−10.8758	−	15.5794i	−0.572412	−	0.819966i
$362$		−	0.259249i		−	0.0136258i
$363$	−7.80224	+	15.8914i	−0.409511	+	0.834082i
$364$	4.93612	+	13.5619i	0.258723	+	0.710836i
$365$	0.0147423	−	0.00259947i	0.000771648	−	0.000136062i
$366$	−2.03657	+	0.137062i	−0.106453	+	0.00716436i
$367$	−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
$369$	0.924685	−	23.0272i	0.0481372	−	1.19875i
$370$	4.11062	−	3.44922i	0.213701	−	0.179316i
$371$	23.1903	−	19.4589i	1.20398	−	1.01026i
$372$	1.29159	−	4.46027i	0.0669657	−	0.231254i
$373$	−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
$375$	−0.116305	−	1.72814i	−0.00600595	−	0.0892408i
$376$	−3.90624	+	0.688775i	−0.201449	+	0.0355209i
$377$	−8.76002	−	24.0679i	−0.451164	−	1.23956i
$378$	−0.337571	−	12.4697i	−0.0173628	−	0.641375i
$379$		−	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	−0.551199	−	0.834374i	$-0.685830\pi$
$383$	−8.55456	+	3.11361i	−0.437118	+	0.159098i	0.114082	+	0.993471i	$0.463607\pi$
$384$	−1.58414	+	0.700350i	−0.0808405	+	0.0357396i
$385$	1.92039	−	10.8911i	0.0978720	−	0.555060i
$386$	7.04421	−	19.3538i	0.358541	−	0.985083i
$387$	26.4113	+	16.6962i	1.34256	+	0.848717i
$388$	1.18377	+	0.683447i	0.0600966	+	0.0346968i
$389$	9.49330	+	11.3137i	0.481330	+	0.573626i	0.950990	−	0.309221i	$-0.100068\pi$
$389$	9.49330	+	11.3137i	0.481330	+	0.573626i	−0.469661	+	0.882847i	$0.655624\pi$
$390$	−8.40796	−	6.14238i	−0.425753	−	0.311032i
$391$	−0.863916	+	1.49635i	−0.0436901	+	0.0756735i
$392$	−0.618360	−	1.07103i	−0.0312319	−	0.0540952i
$393$	−6.44614	−	0.694558i	−0.325165	−	0.0350358i
$394$	14.8106	+	2.61150i	0.746145	+	0.131565i
$395$	−2.69043	−	15.2582i	−0.135370	−	0.767722i
$396$	10.2217	+	9.30089i	0.513660	+	0.467387i
$397$	−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
$399$	10.7325	+	14.6055i	0.537298	+	0.731188i
$400$	−1.00000			−0.0500000
$401$	−23.8812	−	20.0387i	−1.19257	−	1.00069i	−0.999811	−	0.0194400i	$-0.993812\pi$
$401$	−23.8812	−	20.0387i	−1.19257	−	1.00069i	−0.192760	−	0.981246i	$-0.561744\pi$
$402$	22.6744	−	15.2080i	1.13090	−	0.758506i
$403$	−2.79869	−	15.8722i	−0.139413	−	0.790649i
$404$	−16.5691	−	2.92158i	−0.824344	−	0.145354i
$405$	5.21365	+	7.33607i	0.259068	+	0.364532i
$406$	−5.11398	−	8.85767i	−0.253802	−	0.439599i
$407$	−12.3597	+	21.4076i	−0.612646	+	1.06113i
$408$	0.985633	−	1.34918i	0.0487961	−	0.0667942i
$409$	−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
$411$	8.40824	+	8.75266i	0.414748	+	0.431737i
$412$	2.18393	−	6.00029i	0.107594	−	0.295613i
$413$	−2.41727	+	13.7090i	−0.118946	+	0.674578i
$414$	−4.25149	+	3.28598i	−0.208949	+	0.161497i
$415$	−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	$-0.877572\pi$
$419$		−	15.3605i		−	0.750412i	0.926942	−	0.375206i	$-0.122428\pi$
$420$	−3.73250	−	1.83256i	−0.182127	−	0.0894196i
$421$	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
$423$	11.3362	−	3.61793i	0.551183	−	0.175910i
$424$	11.8496	+	4.31289i	0.575466	+	0.209453i
$425$	0.835427	−	0.482334i	0.0405241	−	0.0233966i
$426$	−3.30503	−	0.957058i	−0.160129	−	0.0463696i
$427$	−2.16725	+	1.81854i	−0.104881	+	0.0880052i
$428$	−8.98890	+	7.54258i	−0.434495	+	0.364584i
$429$	46.0742	+	13.3420i	2.22448	+	0.644158i
$430$	9.01998	−	5.20769i	0.434982	−	0.251137i
$431$	7.28825	+	2.65271i	0.351063	+	0.127776i	0.511532	−	0.859265i	$-0.329078\pi$
$431$	7.28825	+	2.65271i	0.351063	+	0.127776i	−0.160469	+	0.987041i	$0.551301\pi$
$432$	4.42804	−	2.71890i	0.213044	−	0.130813i
$433$	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
$435$	6.62398	+	3.25219i	0.317596	+	0.155931i
$436$		−	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
$441$	2.26889	+	2.93555i	0.108042	+	0.139788i
$442$	1.00704	−	5.71121i	0.0479001	−	0.271655i
$443$	−0.884933	+	2.43133i	−0.0420444	+	0.115516i	−0.958938	−	0.283615i	$-0.908466\pi$
$443$	−0.884933	+	2.43133i	−0.0420444	+	0.115516i	0.916894	+	0.399132i	$0.130688\pi$
$444$	6.43882	+	6.70257i	0.305573	+	0.318090i
$445$	12.9939	+	7.50201i	0.615968	+	0.355629i
$446$	13.2084	+	15.7411i	0.625435	+	0.745365i
$447$	−11.2884	+	15.4520i	−0.533923	+	0.730856i
$448$	−1.20034	+	2.07905i	−0.0567108	+	0.0982260i
$449$	−6.28439	−	10.8849i	−0.296579	−	0.513689i	0.678772	−	0.734349i	$-0.262512\pi$
$449$	−6.28439	−	10.8849i	−0.296579	−	0.513689i	−0.975351	+	0.220659i	$0.929179\pi$
$450$	2.97295	−	0.401982i	0.140146	−	0.0189496i
$451$	34.8502	+	6.14503i	1.64103	+	0.289358i
$452$	1.14847	+	6.51331i	0.0540196	+	0.306361i
$453$	−1.98728	+	1.33289i	−0.0933705	+	0.0626247i
$454$	10.3200	+	8.65952i	0.484342	+	0.406412i
$455$	−14.4323			−0.676594
$456$	−3.03349	+	6.91361i	−0.142056	+	0.323759i
$457$	−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
$459$	−2.38789	+	4.40724i	−0.111457	+	0.205712i
$460$	0.311024	+	1.76390i	0.0145016	+	0.0822425i
$461$	32.3687	+	5.70748i	1.50756	+	0.265824i	0.865531	−	0.500855i	$-0.166981\pi$
$461$	32.3687	+	5.70748i	1.50756	+	0.265824i	0.642030	+	0.766679i	$0.278092\pi$
$462$	19.0446	+	2.05202i	0.886037	+	0.0954686i
$463$	−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
$465$	3.74953	+	2.73920i	0.173880	+	0.127027i
$466$	5.85842	+	6.98180i	0.271386	+	0.323426i
$467$	−15.9054	−	9.18297i	−0.736013	−	0.424937i	0.0846051	−	0.996415i	$-0.473037\pi$
$467$	−15.9054	−	9.18297i	−0.736013	−	0.424937i	−0.820618	+	0.571477i	$0.806370\pi$
$468$	9.63702	−	15.2445i	0.445471	−	0.704679i
$469$	12.9427	−	35.5597i	0.597637	−	1.64199i
$470$	0.688775	−	3.90624i	0.0317708	−	0.180181i
$471$	14.4672	−	6.39595i	0.666613	−	0.294710i
$472$	−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
$477$	−36.9619	−	8.05868i	−1.69237	−	0.368982i
$478$	2.65604	+	7.29741i	0.121484	+	0.333776i
$479$	−35.3168	+	6.22730i	−1.61367	+	0.284533i	−0.906402	−	0.422417i	$-0.861182\pi$
$479$	−35.3168	+	6.22730i	−1.61367	+	0.284533i	−0.707264	+	0.706950i	$0.750071\pi$
$480$	−0.116305	−	1.72814i	−0.00530856	−	0.0788785i
$481$	30.3136	+	11.0333i	1.38218	+	0.503074i
$482$	−7.01424	+	4.04967i	−0.319490	+	0.184457i
$483$	−2.07156	+	7.15375i	−0.0942591	+	0.325507i
$484$	−7.82980	+	6.56998i	−0.355900	+	0.298635i
$485$	−1.04710	+	0.878623i	−0.0475464	+	0.0398962i
$486$	−12.0714	+	9.86314i	−0.547569	+	0.447401i
$487$	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
$489$	8.33824	−	0.561168i	0.377068	−	0.0253769i
$490$	1.21793	−	0.214754i	0.0550205	−	0.00970161i
$491$	5.71475	+	15.7012i	0.257903	+	0.708583i	0.999296	+	0.0375121i	$0.0119433\pi$
$491$	5.71475	+	15.7012i	0.257903	+	0.708583i	−0.741393	+	0.671071i	$0.765835\pi$
$492$	5.86398	−	11.9436i	0.264369	−	0.538459i
$493$			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
$498$	−11.2547	−	25.4572i	−0.504333	−	1.14077i
$499$	−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
$501$	21.9425	−	21.0791i	0.980321	−	0.941745i
$502$	1.48472	+	0.857206i	0.0662665	+	0.0382590i
$503$	−23.4914	−	27.9959i	−1.04743	−	1.24828i	−0.967871	−	0.251447i	$-0.919093\pi$
$503$	−23.4914	−	27.9959i	−1.04743	−	1.24828i	−0.0795583	−	0.996830i	$-0.525351\pi$
$504$	2.73281	−	6.66343i	0.121729	−	0.296813i
$505$	8.41236	−	14.5706i	0.374345	−	0.648384i
$506$	−4.12551	−	7.14559i	−0.183401	−	0.317660i
$507$	4.29381	−	39.8505i	0.190695	−	1.76982i
$508$	9.45587	+	1.66732i	0.419536	+	0.0739756i
$509$	0.977817	+	5.54548i	0.0433410	+	0.245799i	0.998780	−	0.0493912i	$-0.0157281\pi$
$509$	0.977817	+	5.54548i	0.0433410	+	0.245799i	−0.955439	+	0.295190i	$0.904617\pi$
$510$	0.930705	+	1.38764i	0.0412123	+	0.0614456i
$511$	0.0275298	+	0.0231003i	0.00121785	+	0.00102190i
$512$	−1.00000			−0.0441942
$513$	6.23926	−	21.7732i	0.275470	−	0.961310i
$514$	−18.5755			−0.819332
$515$	4.89148	+	4.10444i	0.215545	+	0.180863i
$516$	10.0487	+	14.9821i	0.442369	+	0.659551i
$517$	3.17294	+	17.9946i	0.139546	+	0.791402i
$518$	12.6864	+	2.23696i	0.557410	+	0.0982864i
$519$	−2.23128	+	20.7083i	−0.0979421	+	0.908994i
$520$	−3.00586	−	5.20631i	−0.131816	−	0.228312i
$521$	13.8842	−	24.0482i	0.608280	−	1.05357i	−0.383244	−	0.923647i	$-0.625193\pi$
$521$	13.8842	−	24.0482i	0.608280	−	1.05357i	0.991524	−	0.129924i	$-0.0414735\pi$
$522$	−4.84985	+	11.8254i	−0.212272	+	0.517585i
$523$	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
$525$	2.99863	−	2.88063i	0.130871	−	0.125721i
$526$	1.72478	−	4.73879i	0.0752039	−	0.206621i
$527$	−0.449090	+	2.54692i	−0.0195627	+	0.110945i
$528$	3.22626	+	7.29757i	0.140405	+	0.317586i
$529$	−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
$534$	−11.4533	+	23.3278i	−0.495632	+	1.00949i
$535$	−4.01332	−	11.0265i	−0.173511	−	0.476718i
$536$	15.5235	−	2.73721i	0.670512	−	0.118229i
$537$	26.6069	−	1.79065i	1.14817	−	0.0772725i
$538$	22.7475	+	8.27943i	0.980716	+	0.356952i
$539$	−4.93385	+	2.84856i	−0.212516	+	0.122696i
$540$	1.04045	+	5.09092i	0.0447738	+	0.219078i
$541$	−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
$543$	−0.124898	+	0.431312i	−0.00535988	+	0.0185094i
$544$	0.835427	−	0.482334i	0.0358186	−	0.0206799i
$545$	0.184841	+	0.0672765i	0.00791771	+	0.00288181i
$546$	−1.67854	−	24.9410i	−0.0718349	−	1.06738i
$547$	−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
$549$	3.45428	+	0.753125i	0.147425	+	0.0321426i
$550$			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
$555$	−8.50056	+	3.75810i	−0.360829	+	0.159522i
$556$	1.28935	−	7.31225i	0.0546805	−	0.310108i
$557$	−12.6403	+	34.7290i	−0.535588	+	1.47152i	0.316742	+	0.948512i	$0.397411\pi$
$557$	−12.6403	+	34.7290i	−0.535588	+	1.47152i	−0.852330	+	0.523004i	$0.824811\pi$
$558$	−4.29763	+	6.79830i	−0.181933	+	0.287795i
$559$	54.2257	+	31.3072i	2.29350	+	1.32415i
$560$	−1.54313	−	1.83903i	−0.0652091	−	0.0777132i
$561$	−6.21516	−	4.54045i	−0.262404	−	0.191698i
$562$	4.76807	−	8.25854i	0.201129	−	0.348366i
$563$	17.0578	+	29.5451i	0.718903	+	1.24518i	0.961435	+	0.275032i	$0.0886886\pi$
$563$	17.0578	+	29.5451i	0.718903	+	1.24518i	−0.242532	+	0.970143i	$0.577978\pi$
$564$	6.83064	+	0.735987i	0.287622	+	0.0309906i
$565$	−6.51331	−	1.14847i	−0.274017	−	0.0483166i
$566$	2.41099	+	13.6734i	0.101341	+	0.574735i
$567$	−5.44591	+	20.9086i	−0.228707	+	0.878077i
$568$	−1.52179	−	1.27693i	−0.0638528	−	0.0535788i
$569$	−11.9907			−0.502677			−0.251339	−	0.967899i	$-0.580871\pi$
$569$	−11.9907			−0.502677			−0.251339	+	0.967899i	$0.580871\pi$
$570$	−5.45915	−	5.21514i	−0.228659	−	0.218438i
$571$	−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
$573$	−34.0592	+	22.8439i	−1.42284	+	0.954318i
$574$	−3.20240	−	18.1617i	−0.133665	−	0.758055i
$575$	−1.76390	−	0.311024i	−0.0735599	−	0.0129706i
$576$	2.97295	−	0.401982i	0.123873	−	0.0167493i
$577$	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
$579$	−21.0435	+	28.8053i	−0.874538	+	1.19711i
$580$	2.73855	+	3.26368i	0.113712	+	0.135517i
$581$	−33.4105	−	19.2895i	−1.38610	−	0.800265i
$582$	−1.64017	−	1.70735i	−0.0679871	−	0.0707720i
$583$	19.8679	−	54.5867i	0.822845	−	2.26075i
$584$	−0.00259947	+	0.0147423i	−0.000107567	+	0.000610042i
$585$	11.0291	+	14.2698i	0.455998	+	0.589982i
$586$	10.7615	−	3.91686i	0.444553	−	0.161804i
$587$	14.8177	−	17.6590i	0.611592	−	0.728867i	−0.368008	−	0.929822i	$-0.619960\pi$
$587$	14.8177	−	17.6590i	0.611592	−	0.728867i	0.979600	+	0.200956i	$0.0644047\pi$
$588$	0.512777	+	2.07978i	0.0211466	+	0.0857687i
$589$	−0.501439	−	11.6751i	−0.0206614	−	0.481066i
$590$		−	5.79857i		−	0.238723i
$591$	−23.3822	−	11.4800i	−0.961815	−	0.472225i
$592$	1.83529	+	5.04242i	0.0754300	+	0.207242i
$593$	−15.3435	+	2.70547i	−0.630081	+	0.111100i	−0.479563	−	0.877507i	$-0.659205\pi$
$593$	−15.3435	+	2.70547i	−0.630081	+	0.111100i	−0.150517	+	0.988607i	$0.548094\pi$
$594$	−12.5250	−	20.3984i	−0.513906	−	0.836956i
$595$	2.17620	+	0.792071i	0.0892154	+	0.0324718i
$596$	−9.56809	+	5.52414i	−0.391924	+	0.226278i
$597$	−0.624598	−	0.180869i	−0.0255631	−	0.00740248i
$598$	−8.24854	+	6.92134i	−0.337308	+	0.283035i
$599$	−19.1658	+	16.0820i	−0.783091	+	0.657092i	−0.944025	−	0.329873i	$-0.892994\pi$
$599$	−19.1658	+	16.0820i	−0.783091	+	0.657092i	0.160934	+	0.986965i	$0.448549\pi$
$600$	1.66370	+	0.481768i	0.0679203	+	0.0196681i
$601$	−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
$603$	−45.0501	+	14.3777i	−1.83458	+	0.585506i
$604$	−1.36054	+	0.239900i	−0.0553596	+	0.00976140i
$605$	−3.49581	−	9.60467i	−0.142125	−	0.390485i
$606$	26.1585	+	12.8431i	1.06262	+	0.521716i
$607$		−	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
$612$	−2.28979	+	1.76978i	−0.0925592	+	0.0715391i
$613$	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
$615$	9.21772	+	9.59529i	0.371694	+	0.386920i
$616$	9.57743	+	5.52953i	0.385886	+	0.222791i
$617$	26.9526	+	32.1209i	1.08507	+	1.29314i	0.953355	+	0.301850i	$0.0976042\pi$
$617$	26.9526	+	32.1209i	1.08507	+	1.29314i	0.131716	+	0.991287i	$0.457951\pi$
$618$	−6.52415	+	8.93054i	−0.262440	+	0.359239i
$619$	−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
$621$	8.65629	−	3.41865i	0.347365	−	0.137186i
$622$	−7.65429	−	1.34966i	−0.306909	−	0.0541163i
$623$	6.25479	+	35.4727i	0.250593	+	1.42118i
$624$	8.64764	−	5.80008i	0.346183	−	0.232189i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−2.12951			−0.0851122
$627$	31.8484	+	13.9742i	1.27190	+	0.558075i
$628$	9.13250			0.364427
$629$	−3.96538	−	3.32735i	−0.158110	−	0.132670i
$630$	5.32690	+	4.84703i	0.212229	+	0.193110i
$631$	−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
$633$	−0.105450	−	0.0113620i	−0.00419126	−	0.000451600i
$634$	−2.33647	−	4.04688i	−0.0927929	−	0.160722i
$635$	−4.80087	+	8.31535i	−0.190517	+	0.329985i
$636$	−17.6363	−	12.8841i	−0.699326	−	0.510888i
$637$	4.77901	+	5.69541i	0.189351	+	0.225660i
$638$	−16.9968	−	9.81313i	−0.672911	−	0.388506i
$639$	5.03750	+	3.18452i	0.199280	+	0.125978i
$640$	0.342020	−	0.939693i	0.0135195	−	0.0371446i
$641$	−6.13415	+	34.7885i	−0.242284	+	1.37406i	0.584432	+	0.811443i	$0.301317\pi$
$641$	−6.13415	+	34.7885i	−0.242284	+	1.37406i	−0.826716	+	0.562619i	$0.809794\pi$
$642$	18.5886	−	8.21803i	0.733634	−	0.324340i
$643$	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	$0.132125\pi$
$647$			20.5151i			0.806530i	−0.915083	+	0.403265i	$0.867875\pi$
$648$	−8.67682	+	2.39014i	−0.340858	+	0.0938937i
$649$	9.13600	+	25.1010i	0.358619	+	0.985299i
$650$	5.92040	−	1.04393i	0.232217	−	0.0409461i
$651$	0.748545	+	11.1224i	0.0293378	+	0.435923i
$652$	4.53399	+	1.65024i	0.177565	+	0.0646283i
$653$	−28.0157	+	16.1749i	−1.09634	+	0.632971i	−0.935257	−	0.353970i	$-0.884831\pi$
$653$	−28.0157	+	16.1749i	−1.09634	+	0.632971i	−0.161081	+	0.986941i	$0.551498\pi$
$654$	−0.0947655	+	0.327256i	−0.00370562	+	0.0127967i
$655$	2.86747	−	2.40610i	0.112041	−	0.0940140i
$656$	5.88470	−	4.93785i	0.229759	−	0.192791i
$657$	0.00180193	−	0.0448731i	7.03000e−5	−	0.00175067i
$658$	8.24656	−	4.76115i	0.321484	−	0.185609i
$659$	21.4135	+	7.79388i	0.834152	+	0.303606i	0.723562	−	0.690260i	$-0.242504\pi$
$659$	21.4135	+	7.79388i	0.834152	+	0.303606i	0.110590	+	0.993866i	$0.464726\pi$
$660$	−7.96092	+	0.535774i	−0.309878	+	0.0208550i
$661$	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
$663$	−4.42690	+	9.01659i	−0.171926	+	0.350175i
$664$		−	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
$669$	−14.3912	−	32.5519i	−0.556396	−	1.25853i
$670$	−2.73721	+	15.5235i	−0.105748	+	0.599724i
$671$	−1.85676	+	5.10140i	−0.0716794	+	0.196937i
$672$	2.99863	−	2.88063i	0.115675	−	0.111123i
$673$	−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
$675$	−5.13975	−	0.763494i	−0.197829	−	0.0293869i
$676$	11.5704	−	20.0406i	0.445017	−	0.770791i
$677$	−5.51909	−	9.55934i	−0.212116	−	0.367395i	0.740261	−	0.672320i	$-0.234702\pi$
$677$	−5.51909	−	9.55934i	−0.212116	−	0.367395i	−0.952376	+	0.304925i	$0.901369\pi$
$678$	1.22719	−	11.3895i	0.0471301	−	0.437411i
$679$	−3.23163	−	0.569823i	−0.124018	−	0.0218678i
$680$	0.167513	+	0.950012i	0.00642382	+	0.0364313i
$681$	−12.9975	−	19.3787i	−0.498067	−	0.742594i
$682$	−9.46070	−	7.93847i	−0.362269	−	0.303980i
$683$	36.4486			1.39467			0.697333	−	0.716748i	$-0.254370\pi$
$683$	36.4486			1.39467			0.697333	+	0.716748i	$0.254370\pi$
$684$	8.37758	−	10.0407i	0.320325	−	0.383917i
$685$	−7.00732			−0.267736
$686$	15.1476	+	12.7103i	0.578337	+	0.485282i
$687$	−2.74688	−	4.09547i	−0.104800	−	0.156252i
$688$	1.80861	+	10.2571i	0.0689527	+	0.391050i
$689$	−74.6565	−	13.1640i	−2.84419	−	0.501507i
$690$	0.332343	−	3.08445i	0.0126521	−	0.117423i
$691$	−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
$693$	−30.6960	−	12.5891i	−1.16604	−	0.478218i
$694$	−1.39523	−	1.66277i	−0.0529622	−	0.0631179i
$695$	6.43028	+	3.71253i	0.243915	+	0.140824i
$696$	−5.32160	+	5.11219i	−0.201715	+	0.193777i
$697$	−2.53454	+	6.96360i	−0.0960026	+	0.263765i
$698$	−4.45372	+	25.2583i	−0.168576	+	0.956041i
$699$	−6.38305	−	14.4380i	−0.241429	−	0.546096i
$700$	2.25590	−	0.821082i	0.0852652	−	0.0310340i
$701$	12.1630	−	14.4953i	0.459391	−	0.547481i	−0.485770	−	0.874087i	$-0.661461\pi$
$701$	12.1630	−	14.4953i	0.459391	−	0.547481i	0.945161	+	0.326606i	$0.105905\pi$
$702$	−23.3774	+	20.7195i	−0.882325	+	0.782008i
$703$	20.7395	+	10.8150i	0.782205	+	0.407896i
$704$			4.60663i			0.173619i
$705$	−3.02782	+	6.16698i	−0.114034	+	0.232262i
$706$	−4.82401	−	13.2539i	−0.181554	−	0.498816i
$707$	39.7772	−	7.01379i	1.49597	−	0.263781i
$708$	10.0207	−	0.674401i	0.376603	−	0.0253455i
$709$	−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
$711$	−46.4432	−	1.86498i	−1.74176	−	0.0699423i
$712$	−11.4937	+	9.64440i	−0.430746	+	0.361439i
$713$	3.67844	−	3.08657i	0.137759	−	0.115593i
$714$	−1.11571	+	3.85290i	−0.0417544	+	0.144191i
$715$	−23.9836	+	13.8469i	−0.896934	+	0.517845i
$716$	14.4677	+	5.26582i	0.540684	+	0.196793i
$717$	−0.903193	−	13.4203i	−0.0337304	−	0.501190i
$718$	−25.3619	+	4.47199i	−0.946498	+	0.166893i
$719$	−0.456613	−	1.25453i	−0.0170288	−	0.0467862i	0.930887	−	0.365307i	$-0.119036\pi$
$719$	−0.456613	−	1.25453i	−0.0170288	−	0.0467862i	−0.947916	+	0.318521i	$0.896814\pi$
$720$	−0.639068	+	2.93114i	−0.0238167	+	0.109237i
$721$			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
$726$	16.1916	−	7.15833i	0.600928	−	0.265671i
$727$	−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
$729$	24.8349	−	10.5937i	0.919812	−	0.392359i
$730$	−0.0129642	−	0.00748487i	−0.000479826	−	0.000277028i
$731$	−6.45833	−	7.69674i	−0.238870	−	0.284674i
$732$	1.64821	+	1.20409i	0.0609194	+	0.0445043i
$733$	−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
$735$	−2.12974	−	0.229474i	−0.0785565	−	0.00846429i
$736$	−1.76390	−	0.311024i	−0.0650184	−	0.0114645i
$737$	−12.6093	−	71.5110i	−0.464470	−	2.63414i
$738$	−15.5100	+	17.0455i	−0.570930	+	0.627453i
$739$	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
$741$	10.7422	−	44.0980i	0.394623	−	1.61998i
$742$	−30.2727			−1.11135
$743$	−33.9317	−	28.4721i	−1.24483	−	1.04454i	−0.997130	−	0.0757035i	$-0.975880\pi$
$743$	−33.9317	−	28.4721i	−1.24483	−	1.04454i	−0.247703	−	0.968836i	$-0.579676\pi$
$744$	−3.85642	+	2.58655i	−0.141383	+	0.0948274i
$745$	−1.91851	−	10.8804i	−0.0702889	−	0.398628i
$746$	32.9588	+	5.81152i	1.20671	+	0.212775i
$747$	6.45987	+	47.7754i	0.236354	+	1.74801i
$748$	−2.22194	−	3.84850i	−0.0812420	−	0.140715i
$749$	14.0850	−	24.3960i	0.514655	−	0.891409i
$750$	−1.02173	+	1.39859i	−0.0373084	+	0.0510694i
$751$	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
$753$	−2.05716	−	2.14143i	−0.0749671	−	0.0780379i
$754$	−8.76002	+	24.0679i	−0.319021	+	0.876503i
$755$	0.239900	−	1.36054i	0.00873086	−	0.0495152i
$756$	−7.75680	+	9.76937i	−0.282112	+	0.355308i
$757$	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	$-0.963481\pi$
$761$		−	6.31602i		−	0.228956i	0.993426	−	0.114478i	$-0.0365195\pi$
$762$	−14.9285	−	7.32947i	−0.540801	−	0.265519i
$763$	0.161510	+	0.443744i	0.00584704	+	0.0160646i
$764$	−23.3178	+	4.11155i	−0.843608	+	0.148751i
$765$	−0.879894	−	2.75700i	−0.0318127	−	0.0996795i
$766$	8.55456	+	3.11361i	0.309089	+	0.112499i
$767$	30.1891	−	17.4297i	1.09007	−	0.629350i
$768$	1.66370	+	0.481768i	0.0600336	+	0.0173843i
$769$	−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
$771$	30.9041	+	8.94911i	1.11299	+	0.322294i
$772$	−17.8366	+	10.2979i	−0.641952	+	0.370631i
$773$	−17.4953	−	6.36775i	−0.629261	−	0.229032i	0.00764878	−	0.999971i	$-0.497565\pi$
$773$	−17.4953	−	6.36775i	−0.629261	−	0.229032i	−0.636909	+	0.770939i	$0.719788\pi$
$774$	−9.50010	−	29.7669i	−0.341474	−	1.06995i
$775$	−2.64020	+	0.465539i	−0.0948389	+	0.0167226i
$776$	−0.467505	−	1.28446i	−0.0167825	−	0.0461094i
$777$	−20.0287	−	9.83355i	−0.718526	−	0.352777i
$778$		−	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
$783$	13.7658	−	17.3375i	0.491950	−	0.619590i
$784$	−0.214754	+	1.21793i	−0.00766979	+	0.0434976i
$785$	−3.12350	+	8.58175i	−0.111483	+	0.306296i
$786$	4.49158	+	4.67556i	0.160209	+	0.166772i
$787$	−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
$789$	−5.15251	+	7.05298i	−0.183434	+	0.251093i
$790$	−7.74678	+	13.4178i	−0.275618	+	0.477384i
$791$	−7.93881	−	13.7504i	−0.282272	−	0.488909i
$792$	−1.85179	−	13.6953i	−0.0658003	−	0.486640i
$793$	6.97703	+	1.23024i	0.247762	+	0.0436871i
$794$	1.17919	+	6.68752i	0.0418479	+	0.237331i
$795$	18.1391	−	12.1661i	0.643327	−	0.431487i
$796$	−0.287594	−	0.241320i	−0.0101935	−	0.00855336i
$797$	−15.3456			−0.543570			−0.271785	−	0.962358i	$-0.587614\pi$
$797$	−15.3456			−0.543570			−0.271785	+	0.962358i	$0.587614\pi$
$798$	1.16663	−	18.0872i	0.0412981	−	0.640279i
$799$	−3.82635			−0.135367
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	30.2934	−	33.2926i	1.07037	−	1.17633i
$802$	5.41343	+	30.7011i	0.191155	+	1.08409i
$803$	0.0679125	+	0.0119748i	0.00239658	+	0.000422582i
$804$	−27.1451	−	2.92483i	−0.957334	−	0.103151i
$805$	−2.14995	−	3.72382i	−0.0757758	−	0.131248i
$806$	−8.05851	+	13.9578i	−0.283849	+	0.491641i
$807$	−33.8563	−	24.7335i	−1.19180	−	0.870662i
$808$	10.8147	+	12.8885i	0.380460	+	0.453415i
$809$	32.6236	+	18.8352i	1.14698	+	0.662212i	0.948151	−	0.317821i	$-0.102951\pi$
$809$	32.6236	+	18.8352i	1.14698	+	0.662212i	0.198834	+	0.980033i	$0.436285\pi$
$810$	0.721647	−	8.97102i	0.0253561	−	0.315210i
$811$	−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
$813$	−14.7460	+	6.51922i	−0.517166	+	0.228639i
$814$	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
$819$	−9.22319	+	42.3030i	−0.322284	+	1.47819i
$820$	2.62737	+	7.21865i	0.0917519	+	0.252086i
$821$	42.6639	−	7.52280i	1.48898	−	0.262547i	0.630820	−	0.775929i	$-0.282719\pi$
$821$	42.6639	−	7.52280i	1.48898	−	0.262547i	0.858160	+	0.513382i	$0.171607\pi$
$822$	−0.814984	−	12.1096i	−0.0284258	−	0.422372i
$823$	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
$825$	2.21933	−	7.66406i	0.0772672	−	0.266828i
$826$	10.6637	−	8.94794i	0.371039	−	0.311339i
$827$	32.0393	−	26.8842i	1.11412	−	0.934854i	0.115823	−	0.993270i	$-0.463049\pi$
$827$	32.0393	−	26.8842i	1.11412	−	0.934854i	0.998292	+	0.0584156i	$0.0186049\pi$
$828$	5.36902	+	0.215599i	0.186586	+	0.00749259i
$829$	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
$831$	−51.3100	+	3.45319i	−1.77992	+	0.119790i
$832$	5.92040	−	1.04393i	0.205253	−	0.0361916i
$833$	−0.408038	−	1.12108i	−0.0141377	−	0.0388430i
$834$	−5.66790	+	11.5442i	−0.196263	+	0.399744i
$835$			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	−0.436935	−	0.899493i	$-0.643936\pi$
$839$	−5.60378	+	2.03961i	−0.193464	+	0.0704151i	0.243471	+	0.969908i	$0.421714\pi$
$840$	1.68132	+	3.80303i	0.0580110	+	0.131217i
$841$	−1.88386	+	10.6839i	−0.0649606	+	0.368410i
$842$	1.45662	−	4.00204i	0.0501985	−	0.137919i
$843$	−11.9114	+	11.4426i	−0.410249	+	0.394105i
$844$	−0.0530302	−	0.0306170i	−0.00182537	−	0.00105388i
$845$	14.8747	+	17.7269i	0.511704	+	0.609825i
$846$	−11.0096	−	4.51525i	−0.378517	−	0.155237i
$847$	12.2688	−	21.2502i	0.421560	−	0.730164i
$848$	−6.30503	−	10.9206i	−0.216516	−	0.375016i
$849$	2.57624	−	23.9099i	0.0884165	−	0.820587i
$850$	−0.950012	−	0.167513i	−0.0325851	−	0.00574564i
$851$	1.66896	+	9.46516i	0.0572113	+	0.324462i
$852$	1.91661	+	2.85758i	0.0656621	+	0.0978991i
$853$	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
$855$	6.56990	+	11.3065i	0.224686	+	0.386673i
$856$	11.7342			0.401066
$857$	−27.8267	−	23.3494i	−0.950543	−	0.797600i	0.0288460	−	0.999584i	$-0.490817\pi$
$857$	−27.8267	−	23.3494i	−0.950543	−	0.797600i	−0.979389	+	0.201984i	$0.935261\pi$
$858$	−26.7188	−	39.8365i	−0.912166	−	1.36000i
$859$	−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
$861$	−3.42190	+	31.7584i	−0.116618	+	1.08232i
$862$	−3.87800	−	6.71689i	−0.132085	−	0.228778i
$863$	−6.55287	+	11.3499i	−0.223062	+	0.386355i	−0.955736	−	0.294224i	$-0.904939\pi$
$863$	−6.55287	+	11.3499i	−0.223062	+	0.386355i	0.732674	+	0.680580i	$0.238272\pi$
$864$	−5.13975	−	0.763494i	−0.174858	−	0.0259746i
$865$	−7.72961	−	9.21180i	−0.262815	−	0.313210i
$866$	−14.3418	−	8.28024i	−0.487354	−	0.281374i
$867$	−20.0719	+	19.2821i	−0.681677	+	0.654853i
$868$	−2.20126	+	6.04792i	−0.0747158	+	0.205280i
$869$	12.3938	−	70.2888i	0.420431	−	2.38439i
$870$	−2.98380	−	6.74914i	−0.101160	−	0.228817i
$871$	−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
$876$	0.0114271	−	0.0232745i	0.000386087	−	0.000786371i
$877$	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
$879$	−19.7909	+	1.33194i	−0.667531	+	0.0449252i
$880$	−4.32882	−	1.57556i	−0.145924	−	0.0531122i
$881$	−10.5449	+	6.08808i	−0.355265	+	0.205113i	−0.667002	−	0.745056i	$-0.732423\pi$
$881$	−10.5449	+	6.08808i	−0.355265	+	0.205113i	0.311737	+	0.950169i	$0.399089\pi$
$882$	0.148866	−	3.70717i	0.00501257	−	0.124827i
$883$	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
$885$	−2.79357	+	9.64708i	−0.0939047	+	0.324283i
$886$	2.24073	−	1.29369i	0.0752788	−	0.0434622i
$887$	20.1576	+	7.33676i	0.676826	+	0.246344i	0.657484	−	0.753469i	$-0.271621\pi$
$887$	20.1576	+	7.33676i	0.676826	+	0.246344i	0.0193417	+	0.999813i	$0.493843\pi$
$888$	−0.624095	−	9.27326i	−0.0209433	−	0.311190i
$889$	−22.7005	+	4.00272i	−0.761352	+	0.134247i
$890$	−5.13168	−	14.0992i	−0.172014	−	0.472605i
$891$	11.0105	+	39.9709i	0.368866	+	1.33908i
$892$		−	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
$897$	17.0576	−	7.54116i	0.569536	−	0.251792i
$898$	−2.18255	+	12.3778i	−0.0728325	+	0.413054i
$899$	3.90653	−	10.7331i	0.130290	−	0.357969i
$900$	−2.53580	−	1.60304i	−0.0845266	−	0.0534346i
$901$	10.5348	+	6.08226i	0.350964	+	0.202629i
$902$	−22.7469	−	27.1086i	−0.757387	−	0.902619i
$903$	−34.9704	−	25.5474i	−1.16374	−	0.850166i
$904$	3.30690	−	5.72771i	0.109986	−	0.190501i
$905$	−0.129624	−	0.224516i	−0.00430886	−	0.00746317i
$906$	2.37911	+	0.256344i	0.0790406	+	0.00851646i
$907$	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
$909$	−37.3325	−	33.9694i	−1.23824	−	1.12669i
$910$	11.0557	+	9.27687i	0.366494	+	0.307525i
$911$	51.2887			1.69927			0.849636	−	0.527370i	$-0.176822\pi$
$911$	51.2887			1.69927			0.849636	+	0.527370i	$0.176822\pi$
$912$	6.76777	−	3.34624i	0.224103	−	0.110805i
$913$	−74.0288			−2.45000
$914$	15.0185	+	12.6020i	0.496768	+	0.416838i
$915$	−1.69519	+	1.13698i	−0.0560413	+	0.0375876i
$916$	−0.494397	−	2.80386i	−0.0163353	−	0.0926422i
$917$	8.84977	+	1.56045i	0.292245	+	0.0515307i
$918$	4.66215	−	1.84123i	0.153874	−	0.0607698i
$919$	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
$921$	−27.7758	+	38.0208i	−0.915245	+	1.25283i
$922$	−21.1272	−	25.1784i	−0.695787	−	0.829206i
$923$	10.3426	+	5.97131i	0.340431	+	0.196548i
$924$	−13.2700	−	13.8136i	−0.436552	−	0.454434i
$925$	1.83529	−	5.04242i	0.0603440	−	0.165794i
$926$	−6.37501	+	36.1545i	−0.209496	+	1.18811i
$927$	15.1567	−	11.7146i	0.497811	−	0.384758i
$928$	−4.00350	+	1.45715i	−0.131421	+	0.0478334i
$929$	21.7978	−	25.9777i	0.715164	−	0.852300i	−0.278987	−	0.960295i	$-0.589999\pi$
$929$	21.7978	−	25.9777i	0.715164	−	0.852300i	0.994151	+	0.107995i	$0.0344432\pi$
$930$	−1.11159	−	4.50850i	−0.0364503	−	0.147839i
$931$	2.89321	+	4.54856i	0.0948212	+	0.149073i
$932$		−	9.11409i		−	0.298542i
$933$	12.0842	+	5.93302i	0.395620	+	0.194238i
$934$	6.28152	+	17.2583i	0.205538	+	0.564710i
$935$	4.37636	−	0.771670i	0.143122	−	0.0252363i
$936$	−17.1814	+	5.48343i	−0.561591	+	0.179231i
$937$	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
$939$	3.54286	+	1.02593i	0.115617	+	0.0334799i
$940$	−3.03851	+	2.54962i	−0.0991054	+	0.0831593i
$941$	−18.5680	+	15.5804i	−0.605300	+	0.507907i	−0.893144	−	0.449770i	$-0.851506\pi$
$941$	−18.5680	+	15.5804i	−0.605300	+	0.507907i	0.287844	+	0.957677i	$0.407061\pi$
$942$	−15.1938	−	4.39975i	−0.495039	−	0.143352i
$943$	11.9158	−	6.87961i	0.388033	−	0.224031i
$944$	5.44887	+	1.98323i	0.177346	+	0.0645485i
$945$	−6.52722	−	10.6303i	−0.212330	−	0.345805i
$946$	47.2509	−	8.33161i	1.53626	−	0.270884i
$947$	5.59422	+	15.3700i	0.181788	+	0.499457i	0.996795	−	0.0799925i	$-0.0254896\pi$
$947$	5.59422	+	15.3700i	0.181788	+	0.499457i	−0.815008	+	0.579450i	$0.803267\pi$
$948$	−24.0889	−	11.8270i	−0.782370	−	0.384122i
$949$		−	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	−0.137406	−	0.990515i	$-0.543877\pi$
$953$	12.1638	−	4.42727i	0.394025	−	0.143413i	0.531431	+	0.847101i	$0.321654\pi$
$954$	23.1344	+	29.9319i	0.749004	+	0.969082i
$955$	4.11155	−	23.3178i	0.133047	−	0.754546i
$956$	2.65604	−	7.29741i	0.0859025	−	0.236015i
$957$	23.5500	+	24.5147i	0.761263	+	0.792446i
$958$	31.0571	+	17.9308i	1.00341	+	0.579318i
$959$	−10.8132	−	12.8867i	−0.349176	−	0.416132i
$960$	−1.02173	+	1.39859i	−0.0329763	+	0.0451394i
$961$	−11.9063	+	20.6223i	−0.384074	+	0.665236i
$962$	−16.1296	−	27.9372i	−0.520038	−	0.900732i
$963$	−34.8851	+	4.71693i	−1.12416	+	0.152001i
$964$	7.97629	+	1.40644i	0.256899	+	0.0452983i
$965$	−3.57644	−	20.2830i	−0.115130	−	0.652932i
$966$	6.18524	−	4.14852i	0.199007	−	0.133476i
$967$	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
$969$	−4.03997	+	6.05986i	−0.129783	+	0.194671i
$970$	1.36689			0.0438883
$971$	0.722485	+	0.606237i	0.0231856	+	0.0194551i	0.654307	−	0.756229i	$-0.272960\pi$
$971$	0.722485	+	0.606237i	0.0231856	+	0.0194551i	−0.631121	+	0.775684i	$0.717405\pi$
$972$	15.5871	+	0.203736i	0.499957	+	0.00653484i
$973$	3.09531	+	17.5544i	0.0992312	+	0.562768i
$974$	−31.3778	−	5.53274i	−1.00541	−	0.177281i
$975$	−10.3527	−	1.11548i	−0.331552	−	0.0357240i
$976$	0.589237	+	1.02059i	0.0188610	+	0.0326683i
$977$	−27.0137	+	46.7892i	−0.864246	+	1.49692i	0.00354719	+	0.999994i	$0.498871\pi$
$977$	−27.0137	+	46.7892i	−0.864246	+	1.49692i	−0.867794	+	0.496925i	$0.834462\pi$
$978$	−6.74817	−	4.92984i	−0.215783	−	0.157639i
$979$	44.4282	+	52.9475i	1.41993	+	1.69221i
$980$	−1.07103	−	0.618360i	−0.0342128	−	0.0197528i
$981$	0.315323	−	0.498800i	0.0100675	−	0.0159255i
$982$	5.71475	−	15.7012i	0.182365	−	0.501044i
$983$	−8.48579	+	48.1253i	−0.270655	+	1.53496i	0.481780	+	0.876292i	$0.339991\pi$
$983$	−8.48579	+	48.1253i	−0.270655	+	1.53496i	−0.752435	+	0.658667i	$0.771121\pi$
$984$	−12.1693	+	5.38004i	−0.387942	+	0.171509i
$985$	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
$990$	13.5027	+	2.94395i	0.429144	+	0.0935649i
$991$	−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
$993$	3.56549	+	52.9787i	0.113147	+	1.68123i
$994$	4.48147	+	1.63112i	0.142144	+	0.0517361i
$995$	0.325130	−	0.187714i	0.0103073	−	0.00595092i
$996$	−7.74204	+	26.7357i	−0.245316	+	0.847154i
$997$	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
$999$	5.58309	+	27.3180i	0.176641	+	0.864304i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.964794 + 1.43846i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(0.185551 - 1.72208i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.13835 + 2.77564i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.964794 + 1.43846i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(0.185551 - 1.72208i) q^{6} +(-1.20034 - 2.07905i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.13835 + 2.77564i) q^{9} +(0.642788 + 0.766044i) q^{10} +(-3.98946 - 2.30332i) q^{11} +(-1.24907 + 1.19992i) q^{12} +(-2.05613 + 5.64918i) q^{13} +(-0.416874 + 2.36421i) q^{14} +(-0.700350 - 1.58414i) 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} +(1.83256 - 3.73250i) q^{21} +(1.57556 + 4.32882i) q^{22} +(-1.76390 + 0.311024i) q^{23} +(1.72814 - 0.116305i) q^{24} +(0.939693 + 0.342020i) q^{25} +(5.20631 - 3.00586i) q^{26} +(-5.09092 + 1.04045i) q^{27} +(1.83903 - 1.54313i) q^{28} +(-3.26368 + 2.73855i) q^{29} +(-0.481768 + 1.66370i) q^{30} +(-2.32175 + 1.34047i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.535774 - 7.96092i) q^{33} +(-0.950012 + 0.167513i) q^{34} +(0.821082 + 2.25590i) q^{35} +(-2.93114 - 0.639068i) 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} +(-3.80303 + 1.68132i) q^{42} +(1.80861 - 10.2571i) q^{43} +(1.57556 - 4.32882i) q^{44} +(1.60304 - 2.53580i) q^{45} +(1.55115 + 0.895558i) q^{46} +(-2.54962 - 3.03851i) q^{47} +(-1.39859 - 1.02173i) q^{48} +(0.618360 - 1.07103i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.66124 + 0.178995i) q^{51} +(-5.92040 - 1.04393i) q^{52} +(2.18971 + 12.4185i) q^{53} +(4.56866 + 2.47535i) q^{54} +(3.52889 + 2.96109i) q^{55} -2.40068 q^{56} +(-7.50410 + 0.829724i) q^{57} +4.26043 q^{58} +(-4.44196 - 3.72725i) q^{59} +(1.43846 - 0.964794i) q^{60} +(-0.204640 - 1.16057i) q^{61} +(2.64020 + 0.465539i) q^{62} +(7.13710 - 0.965032i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.00586 - 5.20631i) q^{65} +(-4.70675 + 6.44280i) q^{66} +(10.1322 + 12.0751i) q^{67} +(0.835427 + 0.482334i) q^{68} +(-2.14920 - 2.23724i) q^{69} +(0.821082 - 2.25590i) q^{70} +(0.344961 - 1.95637i) q^{71} +(1.83460 + 2.37366i) 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} +(9.34683 + 4.58904i) q^{78} +(5.29911 + 14.5592i) q^{79} +(0.984808 - 0.173648i) q^{80} +(-6.40834 - 6.31928i) q^{81} +(7.21865 + 2.62737i) q^{82} +(13.9171 - 8.03502i) q^{83} +(3.99402 + 1.15657i) q^{84} +(-0.738978 + 0.620076i) q^{85} +(-7.97864 + 6.69488i) q^{86} +(-7.08809 - 2.05254i) q^{87} +(-3.98946 + 2.30332i) q^{88} +(-14.0992 - 5.13168i) q^{89} +(-2.85798 + 0.912122i) q^{90} +(14.2130 - 2.50613i) q^{91} +(-0.612598 - 1.68310i) q^{92} +(-4.16822 - 2.04648i) 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} +(10.9346 - 8.45133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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