LMFDB - Embedded newform 585.2.i.h.196.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.4
Character	$\chi$	$=$	585.196
Dual form			585.2.i.h.391.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01209 + 1.75298i) q^{2} +(0.826646 - 1.52206i) q^{3} +(-1.04864 - 1.81629i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.83150 + 2.98955i) q^{6} +(-1.83320 + 3.17519i) q^{7} +0.196897 q^{8} +(-1.63331 - 2.51640i) q^{9} +O(q^{10})$	\(q+(-1.01209 + 1.75298i) q^{2} +(0.826646 - 1.52206i) q^{3} +(-1.04864 - 1.81629i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.83150 + 2.98955i) q^{6} +(-1.83320 + 3.17519i) q^{7} +0.196897 q^{8} +(-1.63331 - 2.51640i) q^{9} -2.02417 q^{10} +(-1.32427 + 2.29371i) q^{11} +(-3.63135 + 0.0946535i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-3.71071 - 6.42714i) q^{14} +(1.73146 - 0.0451317i) q^{15} +(1.89800 - 3.28743i) q^{16} -5.42866 q^{17} +(6.06427 - 0.316353i) q^{18} +2.77705 q^{19} +(1.04864 - 1.81629i) q^{20} +(3.31742 + 5.41499i) q^{21} +(-2.68056 - 4.64287i) q^{22} +(0.0274565 + 0.0475561i) q^{23} +(0.162764 - 0.299688i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.02417 q^{26} +(-5.18028 + 0.405818i) q^{27} +7.68943 q^{28} +(-4.85857 + 8.41529i) q^{29} +(-1.67327 + 3.08090i) q^{30} +(-3.73602 - 6.47098i) q^{31} +(4.03877 + 6.99535i) q^{32} +(2.39645 + 3.91171i) q^{33} +(5.49427 - 9.51636i) q^{34} -3.66640 q^{35} +(-2.85777 + 5.60536i) q^{36} -3.97871 q^{37} +(-2.81061 + 4.86812i) q^{38} +(-1.73146 + 0.0451317i) q^{39} +(0.0984484 + 0.170518i) q^{40} +(-1.46174 - 2.53181i) q^{41} +(-12.8499 + 0.334941i) q^{42} +(-3.38682 + 5.86614i) q^{43} +5.55473 q^{44} +(1.36261 - 2.67269i) q^{45} -0.111153 q^{46} +(-2.28240 + 3.95323i) q^{47} +(-3.43468 - 5.60640i) q^{48} +(-3.22123 - 5.57934i) q^{49} +(-1.01209 - 1.75298i) q^{50} +(-4.48758 + 8.26273i) q^{51} +(-1.04864 + 1.81629i) q^{52} -2.12951 q^{53} +(4.53150 - 9.49167i) q^{54} -2.64855 q^{55} +(-0.360951 + 0.625186i) q^{56} +(2.29564 - 4.22682i) q^{57} +(-9.83459 - 17.0340i) q^{58} +(5.28938 + 9.16148i) q^{59} +(-1.89765 - 3.09751i) q^{60} +(-1.30756 + 2.26477i) q^{61} +15.1247 q^{62} +(10.9843 - 0.573013i) q^{63} -8.75834 q^{64} +(0.500000 - 0.866025i) q^{65} +(-9.28258 + 0.241956i) q^{66} +(-0.219808 - 0.380718i) q^{67} +(5.69269 + 9.86003i) q^{68} +(0.0950799 - 0.00247832i) q^{69} +(3.71071 - 6.42714i) q^{70} +5.80046 q^{71} +(-0.321594 - 0.495472i) q^{72} +13.5941 q^{73} +(4.02680 - 6.97461i) q^{74} +(0.904817 + 1.47692i) q^{75} +(-2.91211 - 5.04393i) q^{76} +(-4.85532 - 8.40965i) q^{77} +(1.67327 - 3.08090i) q^{78} +(7.95257 - 13.7743i) q^{79} +3.79599 q^{80} +(-3.66458 + 8.22015i) q^{81} +5.91762 q^{82} +(-2.85290 + 4.94137i) q^{83} +(6.35644 - 11.7038i) q^{84} +(-2.71433 - 4.70136i) q^{85} +(-6.85550 - 11.8741i) q^{86} +(8.79223 + 14.3515i) q^{87} +(-0.260746 + 0.451625i) q^{88} -8.89674 q^{89} +(3.30611 + 5.09364i) q^{90} +3.66640 q^{91} +(0.0575838 - 0.0997381i) q^{92} +(-12.9376 + 0.337226i) q^{93} +(-4.61997 - 8.00202i) q^{94} +(1.38852 + 2.40499i) q^{95} +(13.9860 - 0.364553i) q^{96} +(-8.36562 + 14.4897i) q^{97} +13.0407 q^{98} +(7.93486 - 0.413936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−1.01209	+	1.75298i	−0.715653	+	1.23955i	0.247054	+	0.969002i	$0.420537\pi$
$2$	−1.01209	+	1.75298i	−0.715653	+	1.23955i	−0.962707	+	0.270546i	$0.912796\pi$
$3$	0.826646	−	1.52206i	0.477264	−	0.878760i
$3$	0.826646	−	1.52206i	0.477264	−	0.878760i
$4$	−1.04864	−	1.81629i	−0.524318	−	0.908146i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.83150	+	2.98955i	0.747709	+	1.22048i
$7$	−1.83320	+	3.17519i	−0.692884	+	1.20011i	0.278005	+	0.960580i	$0.410327\pi$
$7$	−1.83320	+	3.17519i	−0.692884	+	1.20011i	−0.970889	+	0.239530i	$0.923007\pi$
$8$	0.196897			0.0696136
$9$	−1.63331	−	2.51640i	−0.544437	−	0.838801i
$10$	−2.02417			−0.640099
$11$	−1.32427	+	2.29371i	−0.399284	+	0.691580i	−0.993638	−	0.112624i	$-0.964075\pi$
$11$	−1.32427	+	2.29371i	−0.399284	+	0.691580i	0.594354	+	0.804204i	$0.297408\pi$
$12$	−3.63135	+	0.0946535i	−1.04828	+	0.0273241i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−3.71071	−	6.42714i	−0.991729	−	1.71772i
$15$	1.73146	−	0.0451317i	0.447062	−	0.0116530i
$16$	1.89800	−	3.28743i	0.474499	−	0.821856i
$17$	−5.42866			−1.31664			−0.658322	−	0.752737i	$-0.728733\pi$
$17$	−5.42866			−1.31664			−0.658322	+	0.752737i	$0.728733\pi$
$18$	6.06427	−	0.316353i	1.42936	−	0.0745652i
$19$	2.77705			0.637098			0.318549	−	0.947906i	$-0.396804\pi$
$19$	2.77705			0.637098			0.318549	+	0.947906i	$0.396804\pi$
$20$	1.04864	−	1.81629i	0.234482	−	0.406135i
$21$	3.31742	+	5.41499i	0.723920	+	1.18165i
$22$	−2.68056	−	4.64287i	−0.571497	−	0.989862i
$23$	0.0274565	+	0.0475561i	0.00572508	+	0.00991613i	0.868874	−	0.495034i	$-0.164844\pi$
$23$	0.0274565	+	0.0475561i	0.00572508	+	0.00991613i	−0.863149	+	0.504950i	$0.831511\pi$
$24$	0.162764	−	0.299688i	0.0332241	−	0.0611736i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.02417			0.396973
$27$	−5.18028	+	0.405818i	−0.996946	+	0.0780996i
$28$	7.68943			1.45317
$29$	−4.85857	+	8.41529i	−0.902214	+	1.56268i	−0.0776003	+	0.996985i	$0.524726\pi$
$29$	−4.85857	+	8.41529i	−0.902214	+	1.56268i	−0.824614	+	0.565696i	$0.808608\pi$
$30$	−1.67327	+	3.08090i	−0.305497	+	0.562494i
$31$	−3.73602	−	6.47098i	−0.671009	−	1.16222i	−0.977618	−	0.210387i	$-0.932528\pi$
$31$	−3.73602	−	6.47098i	−0.671009	−	1.16222i	0.306609	−	0.951836i	$-0.400806\pi$
$32$	4.03877	+	6.99535i	0.713960	+	1.23662i
$33$	2.39645	+	3.91171i	0.417169	+	0.680941i
$34$	5.49427	−	9.51636i	0.942260	−	1.63204i
$35$	−3.66640			−0.619734
$36$	−2.85777	+	5.60536i	−0.476296	+	0.934227i
$37$	−3.97871			−0.654096			−0.327048	−	0.945008i	$-0.606054\pi$
$37$	−3.97871			−0.654096			−0.327048	+	0.945008i	$0.606054\pi$
$38$	−2.81061	+	4.86812i	−0.455941	+	0.789714i
$39$	−1.73146	+	0.0451317i	−0.277256	+	0.00722685i
$40$	0.0984484	+	0.170518i	0.0155661	+	0.0269612i
$41$	−1.46174	−	2.53181i	−0.228285	−	0.395402i	0.729015	−	0.684498i	$-0.239979\pi$
$41$	−1.46174	−	2.53181i	−0.228285	−	0.395402i	−0.957300	+	0.289096i	$0.906645\pi$
$42$	−12.8499	+	0.334941i	−1.98278	+	0.0516825i
$43$	−3.38682	+	5.86614i	−0.516485	+	0.894578i	0.483332	+	0.875437i	$0.339426\pi$
$43$	−3.38682	+	5.86614i	−0.516485	+	0.894578i	−0.999817	+	0.0191405i	$0.993907\pi$
$44$	5.55473			0.837407
$45$	1.36261	−	2.67269i	0.203127	−	0.398421i
$46$	−0.111153			−0.0163887
$47$	−2.28240	+	3.95323i	−0.332922	+	0.576638i	−0.983083	−	0.183158i	$-0.941368\pi$
$47$	−2.28240	+	3.95323i	−0.332922	+	0.576638i	0.650161	+	0.759796i	$0.274701\pi$
$48$	−3.43468	−	5.60640i	−0.495753	−	0.809213i
$49$	−3.22123	−	5.57934i	−0.460176	−	0.797049i
$50$	−1.01209	−	1.75298i	−0.143131	−	0.247909i
$51$	−4.48758	+	8.26273i	−0.628387	+	1.15701i
$52$	−1.04864	+	1.81629i	−0.145420	+	0.251874i
$53$	−2.12951			−0.292510			−0.146255	−	0.989247i	$-0.546722\pi$
$53$	−2.12951			−0.292510			−0.146255	+	0.989247i	$0.546722\pi$
$54$	4.53150	−	9.49167i	0.616659	−	1.29165i
$55$	−2.64855			−0.357130
$56$	−0.360951	+	0.625186i	−0.0482341	+	0.0835439i
$57$	2.29564	−	4.22682i	0.304064	−	0.559856i
$58$	−9.83459	−	17.0340i	−1.29134	−	2.23667i
$59$	5.28938	+	9.16148i	0.688619	+	1.19272i	0.972285	+	0.233800i	$0.0751160\pi$
$59$	5.28938	+	9.16148i	0.688619	+	1.19272i	−0.283666	+	0.958923i	$0.591551\pi$
$60$	−1.89765	−	3.09751i	−0.244985	−	0.399887i
$61$	−1.30756	+	2.26477i	−0.167416	+	0.289974i	−0.937511	−	0.347956i	$-0.886876\pi$
$61$	−1.30756	+	2.26477i	−0.167416	+	0.289974i	0.770094	+	0.637930i	$0.220209\pi$
$62$	15.1247			1.92084
$63$	10.9843	−	0.573013i	1.38389	−	0.0721928i
$64$	−8.75834			−1.09479
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	−9.28258	+	0.241956i	−1.14261	+	0.0297828i
$67$	−0.219808	−	0.380718i	−0.0268538	−	0.0465121i	0.852286	−	0.523076i	$-0.175216\pi$
$67$	−0.219808	−	0.380718i	−0.0268538	−	0.0465121i	−0.879140	+	0.476564i	$0.841882\pi$
$68$	5.69269	+	9.86003i	0.690340	+	1.19570i
$69$	0.0950799	−	0.00247832i	0.0114463	−	0.000298355i
$70$	3.71071	−	6.42714i	0.443515	−	0.768190i
$71$	5.80046			0.688388			0.344194	−	0.938899i	$-0.388152\pi$
$71$	5.80046			0.688388			0.344194	+	0.938899i	$0.388152\pi$
$72$	−0.321594	−	0.495472i	−0.0379002	−	0.0583920i
$73$	13.5941			1.59107			0.795536	−	0.605906i	$-0.207189\pi$
$73$	13.5941			1.59107			0.795536	+	0.605906i	$0.207189\pi$
$74$	4.02680	−	6.97461i	0.468105	−	0.810782i
$75$	0.904817	+	1.47692i	0.104479	+	0.170541i
$76$	−2.91211	−	5.04393i	−0.334042	−	0.578578i
$77$	−4.85532	−	8.40965i	−0.553315	−	0.958369i
$78$	1.67327	−	3.08090i	0.189461	−	0.348844i
$79$	7.95257	−	13.7743i	0.894734	−	1.54972i	0.0606002	−	0.998162i	$-0.480699\pi$
$79$	7.95257	−	13.7743i	0.894734	−	1.54972i	0.834134	−	0.551562i	$-0.185968\pi$
$80$	3.79599			0.424405
$81$	−3.66458	+	8.22015i	−0.407176	+	0.913350i
$82$	5.91762			0.653492
$83$	−2.85290	+	4.94137i	−0.313147	+	0.542386i	−0.979042	−	0.203660i	$-0.934716\pi$
$83$	−2.85290	+	4.94137i	−0.313147	+	0.542386i	0.665895	+	0.746045i	$0.268050\pi$
$84$	6.35644	−	11.7038i	0.693545	−	1.27698i
$85$	−2.71433	−	4.70136i	−0.294410	−	0.509934i
$86$	−6.85550	−	11.8741i	−0.739247	−	1.28041i
$87$	8.79223	+	14.3515i	0.942626	+	1.53864i
$88$	−0.260746	+	0.451625i	−0.0277956	+	0.0481433i
$89$	−8.89674			−0.943052			−0.471526	−	0.881852i	$-0.656297\pi$
$89$	−8.89674			−0.943052			−0.471526	+	0.881852i	$0.656297\pi$
$90$	3.30611	+	5.09364i	0.348494	+	0.536916i
$91$	3.66640			0.384343
$92$	0.0575838	−	0.0997381i	0.00600353	−	0.0103984i
$93$	−12.9376	+	0.337226i	−1.34156	+	0.0349687i
$94$	−4.61997	−	8.00202i	−0.476513	−	0.825345i
$95$	1.38852	+	2.40499i	0.142460	+	0.246747i
$96$	13.9860	−	0.364553i	1.42744	−	0.0372070i
$97$	−8.36562	+	14.4897i	−0.849400	+	1.47120i	0.0323445	+	0.999477i	$0.489703\pi$
$97$	−8.36562	+	14.4897i	−0.849400	+	1.47120i	−0.881745	+	0.471727i	$0.843631\pi$
$98$	13.0407			1.31731
$99$	7.93486	−	0.413936i	0.797483	−	0.0416021i
$100$	2.09727			0.209727
$101$	7.82424	−	13.5520i	0.778541	−	1.34847i	−0.154241	−	0.988033i	$-0.549293\pi$
$101$	7.82424	−	13.5520i	0.778541	−	1.34847i	0.932783	−	0.360440i	$-0.117373\pi$
$102$	−9.94261	−	16.2293i	−0.984466	−	1.60694i
$103$	−5.49955	−	9.52551i	−0.541887	−	0.938576i	−0.998796	−	0.0490625i	$-0.984377\pi$
$103$	−5.49955	−	9.52551i	−0.541887	−	0.938576i	0.456908	−	0.889514i	$-0.348957\pi$
$104$	−0.0984484	−	0.170518i	−0.00965366	−	0.0167206i
$105$	−3.03081	+	5.58046i	−0.295777	+	0.544597i
$106$	2.15525	−	3.73300i	0.209336	−	0.362581i
$107$	−3.44694			−0.333228			−0.166614	−	0.986022i	$-0.553283\pi$
$107$	−3.44694			−0.333228			−0.166614	+	0.986022i	$0.553283\pi$
$108$	6.16931	+	8.98335i	0.593643	+	0.864423i
$109$	10.1391			0.971150			0.485575	−	0.874195i	$-0.338610\pi$
$109$	10.1391			0.971150			0.485575	+	0.874195i	$0.338610\pi$
$110$	2.68056	−	4.64287i	0.255581	−	0.442680i
$111$	−3.28898	+	6.05582i	−0.312177	+	0.574793i
$112$	6.95881	+	12.0530i	0.657546	+	1.13890i
$113$	2.78541	+	4.82448i	0.262030	+	0.453849i	0.966781	−	0.255605i	$-0.0822748\pi$
$113$	2.78541	+	4.82448i	0.262030	+	0.453849i	−0.704751	+	0.709454i	$0.748941\pi$
$114$	5.08617	+	8.30212i	0.476364	+	0.777565i
$115$	−0.0274565	+	0.0475561i	−0.00256033	+	0.00443463i
$116$	20.3795			1.89219
$117$	−1.36261	+	2.67269i	−0.125974	+	0.247090i
$118$	−21.4132			−1.97125
$119$	9.95181	−	17.2370i	0.912281	−	1.58012i
$120$	0.340920	−	0.00888629i	0.0311216	−	0.000811204i
$121$	1.99259	+	3.45127i	0.181145	+	0.313752i
$122$	−2.64674	−	4.58428i	−0.239624	−	0.415041i
$123$	−5.06189	+	0.131942i	−0.456416	+	0.0118968i
$124$	−7.83546	+	13.5714i	−0.703645	+	1.21875i
$125$	−1.00000			−0.0894427
$126$	−10.1125	+	19.8352i	−0.900896	+	1.76706i
$127$	18.3124			1.62496			0.812480	−	0.582989i	$-0.198117\pi$
$127$	18.3124			1.62496			0.812480	+	0.582989i	$0.198117\pi$
$128$	0.786656	−	1.36253i	0.0695312	−	0.120432i
$129$	6.12889	+	10.0041i	0.539619	+	0.880816i
$130$	1.01209	+	1.75298i	0.0887658	+	0.153747i
$131$	−6.19478	−	10.7297i	−0.541241	−	0.937456i	−0.998833	−	0.0482944i	$-0.984621\pi$
$131$	−6.19478	−	10.7297i	−0.541241	−	0.937456i	0.457592	−	0.889162i	$-0.348712\pi$
$132$	4.59180	−	8.45461i	0.399665	−	0.735880i
$133$	−5.09088	+	8.81766i	−0.441435	+	0.764588i
$134$	0.889858			0.0768720
$135$	−2.94159	−	4.28335i	−0.253172	−	0.368652i
$136$	−1.06889			−0.0916562
$137$	−5.94841	+	10.3029i	−0.508207	+	0.880240i	0.491748	+	0.870738i	$0.336358\pi$
$137$	−5.94841	+	10.3029i	−0.508207	+	0.880240i	−0.999955	+	0.00950252i	$0.996975\pi$
$138$	−0.0918846	+	0.169182i	−0.00782174	+	0.0144017i
$139$	3.63772	+	6.30072i	0.308547	+	0.534420i	0.978045	−	0.208395i	$-0.0668238\pi$
$139$	3.63772	+	6.30072i	0.308547	+	0.534420i	−0.669497	+	0.742814i	$0.733491\pi$
$140$	3.84472	+	6.65925i	0.324938	+	0.562809i
$141$	4.13030	+	6.74186i	0.347834	+	0.567767i
$142$	−5.87057	+	10.1681i	−0.492647	+	0.853290i
$143$	2.64855			0.221483
$144$	−11.3725	+	0.593267i	−0.947709	+	0.0494389i
$145$	−9.71714			−0.806965
$146$	−13.7584	+	23.8303i	−1.13866	+	1.97221i
$147$	−11.1549	+	0.290759i	−0.920040	+	0.0239814i
$148$	4.17222	+	7.22649i	0.342954	+	0.594014i
$149$	4.32917	+	7.49835i	0.354660	+	0.614289i	0.987060	−	0.160353i	$-0.0512634\pi$
$149$	4.32917	+	7.49835i	0.354660	+	0.614289i	−0.632400	+	0.774642i	$0.717930\pi$
$150$	−3.50478	+	0.0913543i	−0.286164	+	0.00745905i
$151$	−5.43779	+	9.41852i	−0.442521	+	0.766468i	−0.997876	−	0.0651450i	$-0.979249\pi$
$151$	−5.43779	+	9.41852i	−0.442521	+	0.766468i	0.555355	+	0.831613i	$0.312582\pi$
$152$	0.546792			0.0443507
$153$	8.86670	+	13.6607i	0.716830	+	1.10440i
$154$	19.6560			1.58392
$155$	3.73602	−	6.47098i	0.300084	−	0.519762i
$156$	1.89765	+	3.09751i	0.151933	+	0.248000i
$157$	5.94923	+	10.3044i	0.474800	+	0.822378i	0.999584	−	0.0288580i	$-0.00918707\pi$
$157$	5.94923	+	10.3044i	0.474800	+	0.822378i	−0.524784	+	0.851236i	$0.675854\pi$
$158$	16.0974	+	27.8815i	1.28064	+	2.21813i
$159$	−1.76035	+	3.24123i	−0.139605	+	0.257046i
$160$	−4.03877	+	6.99535i	−0.319293	+	0.553031i
$161$	−0.201333			−0.0158673
$162$	−10.7009	−	14.7435i	−0.840744	−	1.15836i
$163$	−15.6626			−1.22679			−0.613396	−	0.789776i	$-0.710197\pi$
$163$	−15.6626			−1.22679			−0.613396	+	0.789776i	$0.710197\pi$
$164$	−3.06567	+	5.30989i	−0.239388	+	0.414633i
$165$	−2.18941	+	4.03124i	−0.170446	+	0.313832i
$166$	−5.77476	−	10.0022i	−0.448208	−	0.776320i
$167$	−3.07077	−	5.31873i	−0.237623	−	0.411575i	0.722409	−	0.691466i	$-0.243035\pi$
$167$	−3.07077	−	5.31873i	−0.237623	−	0.411575i	−0.960032	+	0.279891i	$0.909702\pi$
$168$	0.653189	+	1.06620i	0.0503946	+	0.0822587i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	10.9885			0.842783
$171$	−4.53579	−	6.98817i	−0.346860	−	0.534399i
$172$	14.2062			1.08321
$173$	−4.18343	+	7.24592i	−0.318061	+	0.550897i	−0.980083	−	0.198587i	$-0.936365\pi$
$173$	−4.18343	+	7.24592i	−0.318061	+	0.550897i	0.662023	+	0.749484i	$0.269698\pi$
$174$	−34.0564	+	0.887703i	−2.58181	+	0.0672966i
$175$	−1.83320	−	3.17519i	−0.138577	−	0.240022i
$176$	5.02694	+	8.70691i	0.378920	+	0.656308i
$177$	18.3167	−	0.477438i	1.37677	−	0.0358864i
$178$	9.00427	−	15.5958i	0.674898	−	1.16896i
$179$	13.1418			0.982268			0.491134	−	0.871084i	$-0.336583\pi$
$179$	13.1418			0.982268			0.491134	+	0.871084i	$0.336583\pi$
$180$	−6.28327	+	0.327778i	−0.468328	+	0.0244311i
$181$	1.77975			0.132287			0.0661437	−	0.997810i	$-0.478930\pi$
$181$	1.77975			0.132287			0.0661437	+	0.997810i	$0.478930\pi$
$182$	−3.71071	+	6.42714i	−0.275056	+	0.476411i
$183$	2.36621	+	3.86235i	0.174915	+	0.285513i
$184$	0.00540611	+	0.00936365i	0.000398543	+	0.000690297i
$185$	−1.98935	−	3.44566i	−0.146260	−	0.253330i
$186$	12.5028	−	23.0207i	0.916748	−	1.68796i
$187$	7.18904	−	12.4518i	0.525714	−	0.910564i
$188$	9.57363			0.698229
$189$	8.20793	−	17.1923i	0.597039	−	1.25056i
$190$	−5.62122			−0.407806
$191$	10.2772	−	17.8007i	0.743635	−	1.28801i	−0.207195	−	0.978300i	$-0.566433\pi$
$191$	10.2772	−	17.8007i	0.743635	−	1.28801i	0.950830	−	0.309714i	$-0.100233\pi$
$192$	−7.24005	+	13.3307i	−0.522505	+	0.962059i
$193$	11.5305	+	19.9714i	0.829984	+	1.43757i	0.898050	+	0.439894i	$0.144984\pi$
$193$	11.5305	+	19.9714i	0.829984	+	1.43757i	−0.0680659	+	0.997681i	$0.521683\pi$
$194$	−16.9335	−	29.3296i	−1.21575	−	2.10574i
$195$	−0.904817	−	1.47692i	−0.0647953	−	0.105765i
$196$	−6.75580	+	11.7014i	−0.482557	+	0.835814i
$197$	20.5546			1.46446			0.732228	−	0.681059i	$-0.238480\pi$
$197$	20.5546			1.46446			0.732228	+	0.681059i	$0.238480\pi$
$198$	−7.30514	+	14.3286i	−0.519153	+	1.01829i
$199$	−12.9888			−0.920752			−0.460376	−	0.887724i	$-0.652285\pi$
$199$	−12.9888			−0.920752			−0.460376	+	0.887724i	$0.652285\pi$
$200$	−0.0984484	+	0.170518i	−0.00696136	+	0.0120574i
$201$	−0.761178	+	0.0198406i	−0.0536894	+	0.00139945i
$202$	15.8376	+	27.4315i	1.11433	+	1.93008i
$203$	−17.8135	−	30.8538i	−1.25026	−	2.16551i
$204$	19.7134	−	0.513841i	1.38021	−	0.0359761i
$205$	1.46174	−	2.53181i	0.102092	−	0.176829i
$206$	22.2641			1.55121
$207$	0.0748253	−	0.146766i	0.00520072	−	0.0102009i
$208$	−3.79599			−0.263205
$209$	−3.67757	+	6.36974i	−0.254383	+	0.440604i
$210$	−6.71502	−	10.9609i	−0.463381	−	0.756372i
$211$	0.547359	+	0.948054i	0.0376818	+	0.0652667i	0.884251	−	0.467012i	$-0.154669\pi$
$211$	0.547359	+	0.948054i	0.0376818	+	0.0652667i	−0.846569	+	0.532278i	$0.821336\pi$
$212$	2.23308	+	3.86781i	0.153369	+	0.265642i
$213$	4.79493	−	8.82863i	0.328543	−	0.604928i
$214$	3.48860	−	6.04243i	0.238476	−	0.413052i
$215$	−6.77363			−0.461958
$216$	−1.01998	+	0.0799042i	−0.0694009	+	0.00543679i
$217$	27.3955			1.85973
$218$	−10.2616	+	17.7737i	−0.695007	+	1.20379i
$219$	11.2375	−	20.6910i	0.759362	−	1.39817i
$220$	2.77737	+	4.81054i	0.187250	+	0.324326i
$221$	2.71433	+	4.70136i	0.182586	+	0.316248i
$222$	−7.28702	−	11.8945i	−0.489073	−	0.798310i
$223$	12.5722	−	21.7757i	0.841897	−	1.45821i	−0.0463927	−	0.998923i	$-0.514773\pi$
$223$	12.5722	−	21.7757i	0.841897	−	1.45821i	0.888289	−	0.459284i	$-0.151894\pi$
$224$	−29.6155			−1.97877
$225$	2.99593	−	0.156288i	0.199728	−	0.0104192i
$226$	−11.2763			−0.750089
$227$	7.20185	−	12.4740i	0.478004	−	0.827927i	−0.521678	−	0.853142i	$-0.674694\pi$
$227$	7.20185	−	12.4740i	0.478004	−	0.827927i	0.999682	+	0.0252157i	$0.00802725\pi$
$228$	−10.0844	+	0.262857i	−0.667858	+	0.0174081i
$229$	−4.61630	−	7.99566i	−0.305054	−	0.528368i	0.672220	−	0.740352i	$-0.265341\pi$
$229$	−4.61630	−	7.99566i	−0.305054	−	0.528368i	−0.977273	+	0.211983i	$0.932008\pi$
$230$	−0.0555767	−	0.0962617i	−0.00366462	−	0.00634731i
$231$	−16.8136	+	0.438257i	−1.10625	+	0.0288352i
$232$	−0.956638	+	1.65694i	−0.0628063	+	0.108784i
$233$	−13.7604			−0.901472			−0.450736	−	0.892657i	$-0.648838\pi$
$233$	−13.7604			−0.901472			−0.450736	+	0.892657i	$0.648838\pi$
$234$	−3.30611	−	5.09364i	−0.216127	−	0.332981i
$235$	−4.56480			−0.297775
$236$	11.0933	−	19.2141i	0.722111	−	1.25073i
$237$	−14.3912	−	23.4907i	−0.934811	−	1.52588i
$238$	20.1442	+	34.8907i	1.30575	+	2.26163i
$239$	9.03642	+	15.6515i	0.584517	+	1.01241i	0.994935	+	0.100516i	$0.0320494\pi$
$239$	9.03642	+	15.6515i	0.584517	+	1.01241i	−0.410418	+	0.911897i	$0.634617\pi$
$240$	3.13794	−	5.77772i	0.202553	−	0.372950i
$241$	−9.86791	+	17.0917i	−0.635648	+	1.10097i	0.350730	+	0.936477i	$0.385934\pi$
$241$	−9.86791	+	17.0917i	−0.635648	+	1.10097i	−0.986377	+	0.164498i	$0.947400\pi$
$242$	−8.06671			−0.518547
$243$	9.48222	+	12.3729i	0.608285	+	0.793719i
$244$	5.48464			0.351118
$245$	3.22123	−	5.57934i	0.205797	−	0.356451i
$246$	4.89178	−	9.00696i	0.311889	−	0.574263i
$247$	−1.38852	−	2.40499i	−0.0883496	−	0.153026i
$248$	−0.735611	−	1.27412i	−0.0467113	−	0.0809064i
$249$	5.16270	+	8.42704i	0.327173	+	0.534042i
$250$	1.01209	−	1.75298i	0.0640099	−	0.110868i
$251$	3.06848			0.193681			0.0968405	−	0.995300i	$-0.469126\pi$
$251$	3.06848			0.193681			0.0968405	+	0.995300i	$0.469126\pi$
$252$	−12.5592	−	19.3497i	−0.791158	−	1.21892i
$253$	−0.145440			−0.00914373
$254$	−18.5337	+	32.1013i	−1.16291	+	2.01421i
$255$	−9.39952	+	0.245005i	−0.588621	+	0.0153428i
$256$	−7.16601	−	12.4119i	−0.447876	−	0.775743i
$257$	−9.10526	−	15.7708i	−0.567970	−	0.983754i	−0.996767	−	0.0803523i	$-0.974395\pi$
$257$	−9.10526	−	15.7708i	−0.567970	−	0.983754i	0.428796	−	0.903401i	$-0.358938\pi$
$258$	−23.7401	+	0.618800i	−1.47799	+	0.0385248i
$259$	7.29376	−	12.6332i	0.453212	−	0.784987i
$260$	−2.09727			−0.130067
$261$	29.1118	−	1.51867i	1.80198	−	0.0940033i
$262$	25.0786			1.54936
$263$	−0.0846846	+	0.146678i	−0.00522188	+	0.00904455i	−0.868625	−	0.495471i	$-0.834996\pi$
$263$	−0.0846846	+	0.146678i	−0.00522188	+	0.00904455i	0.863403	+	0.504515i	$0.168329\pi$
$264$	0.471854	+	0.770203i	0.0290406	+	0.0474027i
$265$	−1.06475	−	1.84421i	−0.0654073	−	0.113289i
$266$	−10.3048	−	17.8485i	−0.631829	−	1.09436i
$267$	−7.35446	+	13.5413i	−0.450085	+	0.828717i
$268$	−0.460997	+	0.798470i	−0.0281599	+	0.0487743i
$269$	−14.9029			−0.908644			−0.454322	−	0.890838i	$-0.650118\pi$
$269$	−14.9029			−0.908644			−0.454322	+	0.890838i	$0.650118\pi$
$270$	10.4858	−	0.821444i	0.638144	−	0.0499915i
$271$	5.80132			0.352405			0.176202	−	0.984354i	$-0.443619\pi$
$271$	5.80132			0.352405			0.176202	+	0.984354i	$0.443619\pi$
$272$	−10.3036	+	17.8463i	−0.624746	+	1.08209i
$273$	3.03081	−	5.58046i	0.183433	−	0.337745i
$274$	−12.0406	−	20.8549i	−0.727399	−	1.25989i
$275$	−1.32427	−	2.29371i	−0.0798568	−	0.138316i
$276$	−0.104206	−	0.170094i	−0.00627244	−	0.0102385i
$277$	−10.5646	+	18.2984i	−0.634764	+	1.09944i	0.351802	+	0.936075i	$0.385569\pi$
$277$	−10.5646	+	18.2984i	−0.634764	+	1.09944i	−0.986565	+	0.163368i	$0.947764\pi$
$278$	−14.7267			−0.883251
$279$	−10.1815	+	19.9705i	−0.609551	+	1.19560i
$280$	−0.721902			−0.0431419
$281$	−7.10687	+	12.3095i	−0.423960	+	0.734321i	−0.996323	−	0.0856802i	$-0.972694\pi$
$281$	−7.10687	+	12.3095i	−0.423960	+	0.734321i	0.572363	+	0.820001i	$0.306027\pi$
$282$	−15.9986	+	0.417014i	−0.952703	+	0.0248328i
$283$	0.583060	+	1.00989i	0.0346593	+	0.0600317i	0.882835	−	0.469684i	$-0.155632\pi$
$283$	0.583060	+	1.00989i	0.0346593	+	0.0600317i	−0.848175	+	0.529715i	$0.822299\pi$
$284$	−6.08258	−	10.5353i	−0.360934	−	0.625157i
$285$	4.80835	−	0.125333i	0.284822	−	0.00742408i
$286$	−2.68056	+	4.64287i	−0.158505	+	0.274538i
$287$	10.7186			0.632701
$288$	11.0066	−	21.5888i	0.648568	−	1.27213i
$289$	12.4703			0.733550
$290$	9.83459	−	17.0340i	0.577507	−	1.00027i
$291$	15.1387	+	24.7108i	0.887447	+	1.44857i
$292$	−14.2553	−	24.6909i	−0.834228	−	1.44493i
$293$	−10.1456	−	17.5728i	−0.592715	−	1.02661i	−0.993865	−	0.110600i	$-0.964723\pi$
$293$	−10.1456	−	17.5728i	−0.592715	−	1.02661i	0.401150	−	0.916012i	$-0.368611\pi$
$294$	10.7800	−	19.8486i	0.628703	−	1.15760i
$295$	−5.28938	+	9.16148i	−0.307960	+	0.533402i
$296$	−0.783395			−0.0455339
$297$	5.92929	−	12.4195i	0.344052	−	0.720651i
$298$	−17.5260			−1.01525
$299$	0.0274565	−	0.0475561i	0.00158785	−	0.00275024i
$300$	1.73370	−	3.19217i	0.100095	−	0.184300i
$301$	−12.4174	−	21.5076i	−0.715728	−	1.23968i
$302$	−11.0070	−	19.0647i	−0.633382	−	1.09705i
$303$	−14.1590	−	23.1116i	−0.813414	−	1.32773i
$304$	5.27083	−	9.12934i	0.302303	−	0.523603i
$305$	−2.61513			−0.149742
$306$	−32.9209	+	1.71737i	−1.88196	+	0.0981757i
$307$	3.84252			0.219304			0.109652	−	0.993970i	$-0.465026\pi$
$307$	3.84252			0.219304			0.109652	+	0.993970i	$0.465026\pi$
$308$	−10.1829	+	17.6373i	−0.580226	+	1.00498i
$309$	−19.0445	+	0.496408i	−1.08341	+	0.0282397i
$310$	7.56235	+	13.0984i	0.429513	+	0.743938i
$311$	10.1891	+	17.6481i	0.577774	+	1.00073i	0.995734	+	0.0922680i	$0.0294117\pi$
$311$	10.1891	+	17.6481i	0.577774	+	1.00073i	−0.417961	+	0.908465i	$0.637255\pi$
$312$	−0.340920	+	0.00888629i	−0.0193008	+	0.000503087i
$313$	−1.04346	+	1.80732i	−0.0589797	+	0.102156i	−0.894008	−	0.448052i	$-0.852118\pi$
$313$	−1.04346	+	1.80732i	−0.0589797	+	0.102156i	0.835028	+	0.550207i	$0.185451\pi$
$314$	−24.0845			−1.35917
$315$	5.98837	+	9.22614i	0.337406	+	0.519834i
$316$	−33.3574			−1.87650
$317$	15.3130	−	26.5229i	0.860064	−	1.48967i	−0.0118027	−	0.999930i	$-0.503757\pi$
$317$	15.3130	−	26.5229i	0.860064	−	1.48967i	0.871866	−	0.489744i	$-0.162910\pi$
$318$	−3.90020	−	6.36627i	−0.218713	−	0.357003i
$319$	−12.8682	−	22.2883i	−0.720479	−	1.24791i
$320$	−4.37917	−	7.58494i	−0.244803	−	0.424011i
$321$	−2.84940	+	5.24643i	−0.159038	+	0.292827i
$322$	0.203766	−	0.352934i	0.0113555	−	0.0196682i
$323$	−15.0756			−0.838831
$324$	18.7730	−	1.96400i	1.04294	−	0.109111i
$325$	1.00000			0.0554700
$326$	15.8519	−	27.4563i	0.877957	−	1.52067i
$327$	8.38145	−	15.4323i	0.463495	−	0.853408i
$328$	−0.287812	−	0.498505i	−0.0158918	−	0.0275253i
$329$	−8.36818	−	14.4941i	−0.461353	−	0.799086i
$330$	−4.85083	−	7.91797i	−0.267029	−	0.435870i
$331$	−11.6289	+	20.1418i	−0.639180	+	1.10709i	0.346433	+	0.938075i	$0.387393\pi$
$331$	−11.6289	+	20.1418i	−0.639180	+	1.10709i	−0.985613	+	0.169017i	$0.945941\pi$
$332$	11.9666			0.656754
$333$	6.49847	+	10.0120i	0.356114	+	0.548656i
$334$	12.4315			0.680223
$335$	0.219808	−	0.380718i	0.0120094	−	0.0208009i
$336$	24.0978	−	0.628125i	1.31464	−	0.0342671i
$337$	−1.73815	−	3.01056i	−0.0946828	−	0.163995i	0.814793	−	0.579751i	$-0.196850\pi$
$337$	−1.73815	−	3.01056i	−0.0946828	−	0.163995i	−0.909476	+	0.415756i	$0.863517\pi$
$338$	−1.01209	−	1.75298i	−0.0550502	−	0.0953498i
$339$	9.64568	−	0.251421i	0.523882	−	0.0136553i
$340$	−5.69269	+	9.86003i	−0.308729	+	0.534735i
$341$	19.7901			1.07169
$342$	16.8408	−	0.878528i	0.910644	−	0.0475053i
$343$	−2.04414			−0.110373
$344$	−0.666854	+	1.15502i	−0.0359543	+	0.0622747i
$345$	0.0496862	+	0.0811025i	0.00267502	+	0.00436641i
$346$	−8.46799	−	14.6670i	−0.455242	−	0.788502i
$347$	4.12822	+	7.15028i	0.221614	+	0.383847i	0.955298	−	0.295644i	$-0.0955341\pi$
$347$	4.12822	+	7.15028i	0.221614	+	0.383847i	−0.733684	+	0.679491i	$0.762201\pi$
$348$	16.8466	−	31.0188i	0.903074	−	1.66278i
$349$	−15.9045	+	27.5474i	−0.851348	+	1.47458i	0.0286440	+	0.999590i	$0.490881\pi$
$349$	−15.9045	+	27.5474i	−0.851348	+	1.47458i	−0.879992	+	0.474988i	$0.842452\pi$
$350$	7.42142			0.396692
$351$	2.94159	+	4.28335i	0.157010	+	0.228628i
$352$	−21.3938			−1.14029
$353$	−8.29839	+	14.3732i	−0.441679	+	0.765010i	−0.997814	−	0.0660818i	$-0.978950\pi$
$353$	−8.29839	+	14.3732i	−0.441679	+	0.765010i	0.556136	+	0.831092i	$0.312284\pi$
$354$	−17.7012	+	32.5922i	−0.940807	+	1.73225i
$355$	2.90023	+	5.02335i	0.153928	+	0.266612i
$356$	9.32944	+	16.1591i	0.494460	+	0.856429i
$357$	−18.0091	−	29.3962i	−0.953144	−	1.55581i
$358$	−13.3007	+	23.0375i	−0.702963	+	1.21757i
$359$	−26.6831			−1.40828			−0.704140	−	0.710061i	$-0.748667\pi$
$359$	−26.6831			−1.40828			−0.704140	+	0.710061i	$0.748667\pi$
$360$	0.268294	−	0.526245i	0.0141404	−	0.0277355i
$361$	−11.2880			−0.594106
$362$	−1.80126	+	3.11987i	−0.0946719	+	0.163977i
$363$	6.90020	−	0.179858i	0.362167	−	0.00944011i
$364$	−3.84472	−	6.65925i	−0.201518	−	0.349039i
$365$	6.79707	+	11.7729i	0.355775	+	0.616220i
$366$	−9.16545	+	0.238903i	−0.479086	+	0.0124877i
$367$	16.9016	−	29.2744i	0.882256	−	1.52811i	0.0334294	−	0.999441i	$-0.489357\pi$
$367$	16.9016	−	29.2744i	0.882256	−	1.52811i	0.848827	−	0.528671i	$-0.177310\pi$
$368$	0.208450			0.0108662
$369$	−3.98357	+	7.81356i	−0.207377	+	0.406758i
$370$	8.05359			0.418686
$371$	3.90381	−	6.76160i	0.202676	−	0.351045i
$372$	14.1793	+	23.1448i	0.735163	+	1.20000i
$373$	12.8304	+	22.2229i	0.664333	+	1.15066i	0.979466	+	0.201610i	$0.0646175\pi$
$373$	12.8304	+	22.2229i	0.664333	+	1.15066i	−0.315133	+	0.949047i	$0.602049\pi$
$374$	14.5518	+	25.2045i	0.752458	+	1.30330i
$375$	−0.826646	+	1.52206i	−0.0426878	+	0.0785987i
$376$	−0.449397	+	0.778379i	−0.0231759	+	0.0401418i
$377$	9.71714			0.500458
$378$	21.8308	+	31.7885i	1.12285	+	1.63502i
$379$	−36.6761			−1.88392			−0.941961	−	0.335721i	$-0.891020\pi$
$379$	−36.6761			−1.88392			−0.941961	+	0.335721i	$0.891020\pi$
$380$	2.91211	−	5.04393i	0.149388	−	0.258748i
$381$	15.1378	−	27.8725i	0.775535	−	1.42795i
$382$	20.8029	+	36.0317i	1.06437	+	1.84354i
$383$	−11.2133	−	19.4220i	−0.572974	−	0.992420i	−0.996259	−	0.0864233i	$-0.972456\pi$
$383$	−11.2133	−	19.4220i	−0.572974	−	0.992420i	0.423284	−	0.905997i	$-0.360877\pi$
$384$	−1.42356	−	2.32366i	−0.0726457	−	0.118579i
$385$	4.85532	−	8.40965i	0.247450	−	0.428596i
$386$	−46.6795			−2.37592
$387$	20.2933	−	1.05864i	1.03157	−	0.0538135i
$388$	35.0900			1.78142
$389$	−2.93155	+	5.07759i	−0.148635	+	0.257444i	−0.930723	−	0.365724i	$-0.880821\pi$
$389$	−2.93155	+	5.07759i	−0.148635	+	0.257444i	0.782088	+	0.623168i	$0.214155\pi$
$390$	3.50478	−	0.0913543i	0.177471	−	0.00462591i
$391$	−0.149052	−	0.258166i	−0.00753789	−	0.0130560i
$392$	−0.634251	−	1.09855i	−0.0320345	−	0.0554854i
$393$	−21.4521	+	0.559162i	−1.08211	+	0.0282060i
$394$	−20.8030	+	36.0319i	−1.04804	+	1.81526i
$395$	15.9051			0.800274
$396$	−9.07261	−	13.9779i	−0.455916	−	0.702418i
$397$	−18.9594			−0.951545			−0.475772	−	0.879568i	$-0.657831\pi$
$397$	−18.9594			−0.951545			−0.475772	+	0.879568i	$0.657831\pi$
$398$	13.1458	−	22.7692i	0.658939	−	1.14132i
$399$	9.21262	+	15.0377i	0.461208	+	0.752826i
$400$	1.89800	+	3.28743i	0.0948998	+	0.164371i
$401$	4.69792	+	8.13704i	0.234603	+	0.406344i	0.959157	−	0.282873i	$-0.0912876\pi$
$401$	4.69792	+	8.13704i	0.234603	+	0.406344i	−0.724554	+	0.689218i	$0.757954\pi$
$402$	0.735598	−	1.35441i	0.0366883	−	0.0675520i
$403$	−3.73602	+	6.47098i	−0.186104	+	0.322342i
$404$	−32.8191			−1.63281
$405$	−8.95115	+	0.936453i	−0.444786	+	0.0465327i
$406$	72.1150			3.57901
$407$	5.26890	−	9.12601i	0.261170	−	0.452359i
$408$	−0.883591	+	1.62691i	−0.0437443	+	0.0805438i
$409$	7.20759	+	12.4839i	0.356392	+	0.617290i	0.987355	−	0.158523i	$-0.0506733\pi$
$409$	7.20759	+	12.4839i	0.356392	+	0.617290i	−0.630963	+	0.775813i	$0.717340\pi$
$410$	2.95881	+	5.12481i	0.146125	+	0.253096i
$411$	10.7644	+	17.5707i	0.530971	+	0.866699i
$412$	−11.5341	+	19.9776i	−0.568243	+	0.984225i
$413$	−38.7860			−1.90853
$414$	0.181548	+	0.279707i	0.00892262	+	0.0137469i
$415$	−5.70580			−0.280087
$416$	4.03877	−	6.99535i	0.198017	−	0.342975i
$417$	12.5972	−	0.328353i	0.616885	−	0.0160795i
$418$	−7.44404	−	12.8935i	−0.364100	−	0.630640i
$419$	3.10300	+	5.37455i	0.151591	+	0.262564i	0.931813	−	0.362940i	$-0.118227\pi$
$419$	3.10300	+	5.37455i	0.151591	+	0.262564i	−0.780221	+	0.625504i	$0.784894\pi$
$420$	13.3140	−	0.347037i	0.649655	−	0.0169337i
$421$	1.95624	−	3.38831i	0.0953414	−	0.165136i	−0.814410	−	0.580290i	$-0.802939\pi$
$421$	1.95624	−	3.38831i	0.0953414	−	0.165136i	0.909751	+	0.415154i	$0.136272\pi$
$422$	−2.21590			−0.107868
$423$	13.6758	−	0.713422i	0.664940	−	0.0346878i
$424$	−0.419294			−0.0203627
$425$	2.71433	−	4.70136i	0.131664	−	0.228049i
$426$	10.6236	+	17.3408i	0.514714	+	0.840163i
$427$	−4.79405	−	8.30354i	−0.232000	−	0.401836i
$428$	3.61458	+	6.26064i	0.174718	+	0.302620i
$429$	2.18941	−	4.03124i	0.105706	−	0.194630i
$430$	6.85550	−	11.8741i	0.330601	−	0.572619i
$431$	−18.8328			−0.907144			−0.453572	−	0.891220i	$-0.649851\pi$
$431$	−18.8328			−0.907144			−0.453572	+	0.891220i	$0.649851\pi$
$432$	−8.49806	+	17.8000i	−0.408863	+	0.856404i
$433$	−13.7109			−0.658903			−0.329452	−	0.944172i	$-0.606864\pi$
$433$	−13.7109			−0.658903			−0.329452	+	0.944172i	$0.606864\pi$
$434$	−27.7266	+	48.0238i	−1.33092	+	2.30522i
$435$	−8.03264	+	14.7900i	−0.385136	+	0.709128i
$436$	−10.6322	−	18.4156i	−0.509192	−	0.881946i
$437$	0.0762481	+	0.132066i	0.00364744	+	0.00631755i
$438$	24.8977	+	40.6403i	1.18966	+	1.94187i
$439$	0.164786	−	0.285418i	0.00786482	−	0.0136223i	−0.862066	−	0.506796i	$-0.830830\pi$
$439$	0.164786	−	0.285418i	0.00786482	−	0.0136223i	0.869931	+	0.493173i	$0.164163\pi$
$440$	−0.521491			−0.0248611
$441$	−8.77860	+	17.2187i	−0.418028	+	0.819939i
$442$	−10.9885			−0.522672
$443$	20.9237	−	36.2410i	0.994117	−	1.72186i	0.403260	−	0.915085i	$-0.367877\pi$
$443$	20.9237	−	36.2410i	0.994117	−	1.72186i	0.590857	−	0.806776i	$-0.298790\pi$
$444$	14.4481	−	0.376599i	0.685676	−	0.0178726i
$445$	−4.44837	−	7.70480i	−0.210873	−	0.365243i
$446$	25.4483	+	44.0777i	1.20501	+	2.08714i
$447$	14.9916	−	0.390766i	0.709079	−	0.0184826i
$448$	16.0558	−	27.8094i	0.758564	−	1.31387i
$449$	24.7987			1.17032			0.585161	−	0.810917i	$-0.301031\pi$
$449$	24.7987			1.17032			0.585161	+	0.810917i	$0.301031\pi$
$450$	−2.75817	+	5.40999i	−0.130021	+	0.255029i
$451$	7.74298			0.364603
$452$	5.84177	−	10.1182i	0.274774	−	0.475922i
$453$	9.84040	+	16.0624i	0.462342	+	0.754677i
$454$	14.5778	+	25.2495i	0.684169	+	1.18502i
$455$	1.83320	+	3.17519i	0.0859417	+	0.148855i
$456$	0.452003	−	0.832248i	0.0211670	−	0.0389736i
$457$	−9.73849	+	16.8676i	−0.455547	+	0.789031i	−0.998719	−	0.0505902i	$-0.983890\pi$
$457$	−9.73849	+	16.8676i	−0.455547	+	0.789031i	0.543172	+	0.839621i	$0.317223\pi$
$458$	18.6884			0.873250
$459$	28.1220	−	2.20305i	1.31262	−	0.102829i
$460$	0.115168			0.00536972
$461$	−9.16040	+	15.8663i	−0.426642	+	0.738966i	−0.996572	−	0.0827272i	$-0.973637\pi$
$461$	−9.16040	+	15.8663i	−0.426642	+	0.738966i	0.569930	+	0.821693i	$0.306970\pi$
$462$	16.2486	−	29.9175i	0.755951	−	1.39189i
$463$	−16.9429	−	29.3460i	−0.787405	−	1.36383i	−0.927552	−	0.373694i	$-0.878091\pi$
$463$	−16.9429	−	29.3460i	−0.787405	−	1.36383i	0.140147	−	0.990131i	$-0.455242\pi$
$464$	18.4431	+	31.9444i	0.856199	+	1.48298i
$465$	−6.76083	−	11.0356i	−0.313526	−	0.511766i
$466$	13.9267	−	24.1217i	0.645141	−	1.11742i
$467$	−15.2887			−0.707477			−0.353738	−	0.935344i	$-0.615090\pi$
$467$	−15.2887			−0.707477			−0.353738	+	0.935344i	$0.615090\pi$
$468$	6.28327	−	0.327778i	0.290444	−	0.0151515i
$469$	1.61181			0.0744263
$470$	4.61997	−	8.00202i	0.213103	−	0.369106i
$471$	20.6017	−	0.536997i	0.949278	−	0.0247435i
$472$	1.04146	+	1.80387i	0.0479372	+	0.0830297i
$473$	−8.97015	−	15.5368i	−0.412448	−	0.714381i
$474$	55.7440	−	1.45300i	2.56041	−	0.0667386i
$475$	−1.38852	+	2.40499i	−0.0637098	+	0.110349i
$476$	−41.7433			−1.91330
$477$	3.47815	+	5.35870i	0.159254	+	0.245358i
$478$	−36.5825			−1.67325
$479$	6.70373	−	11.6112i	0.306301	−	0.530530i	−0.671249	−	0.741232i	$-0.734242\pi$
$479$	6.70373	−	11.6112i	0.306301	−	0.530530i	0.977550	+	0.210702i	$0.0675751\pi$
$480$	7.30869	+	11.9299i	0.333594	+	0.544524i
$481$	1.98935	+	3.44566i	0.0907067	+	0.157109i
$482$	−19.9743	−	34.5966i	−0.909806	−	1.57583i
$483$	−0.166431	+	0.306440i	−0.00757288	+	0.0139435i
$484$	4.17901	−	7.23826i	0.189955	−	0.329012i
$485$	−16.7312			−0.759726
$486$	−31.2862	+	4.09979i	−1.41917	+	0.185970i
$487$	17.6850			0.801386			0.400693	−	0.916212i	$-0.368769\pi$
$487$	17.6850			0.801386			0.400693	+	0.916212i	$0.368769\pi$
$488$	−0.257455	+	0.445926i	−0.0116545	+	0.0201861i
$489$	−12.9475	+	23.8394i	−0.585504	+	1.07806i
$490$	6.52033	+	11.2935i	0.294559	+	0.510190i
$491$	7.29617	+	12.6373i	0.329272	+	0.570315i	0.982368	−	0.186960i	$-0.0598635\pi$
$491$	7.29617	+	12.6373i	0.329272	+	0.570315i	−0.653096	+	0.757275i	$0.726530\pi$
$492$	5.54773	+	9.05552i	0.250111	+	0.408254i
$493$	26.3755	−	45.6838i	1.18789	−	2.05749i
$494$	5.62122			0.252911
$495$	4.32591	+	6.66482i	0.194435	+	0.299561i
$496$	−28.3638			−1.27357
$497$	−10.6334	+	18.4176i	−0.476973	+	0.826142i
$498$	−19.9976	+	0.521250i	−0.896113	+	0.0233578i
$499$	9.18047	+	15.9010i	0.410974	+	0.711829i	0.994997	−	0.0999091i	$-0.0318552\pi$
$499$	9.18047	+	15.9010i	0.410974	+	0.711829i	−0.584022	+	0.811738i	$0.698522\pi$
$500$	1.04864	+	1.81629i	0.0468964	+	0.0812270i
$501$	−10.6338	+	0.277178i	−0.475085	+	0.0123834i
$502$	−3.10557	+	5.37900i	−0.138608	+	0.240077i
$503$	−38.5376			−1.71831			−0.859154	−	0.511718i	$-0.829009\pi$
$503$	−38.5376			−1.71831			−0.859154	+	0.511718i	$0.829009\pi$
$504$	2.16277	−	0.112824i	0.0963372	−	0.00502560i
$505$	15.6485			0.696348
$506$	0.147198	−	0.254954i	0.00654374	−	0.0113341i
$507$	0.904817	+	1.47692i	0.0401843	+	0.0655925i
$508$	−19.2030	−	33.2606i	−0.851996	−	1.47570i
$509$	−1.45900	−	2.52707i	−0.0646691	−	0.112010i	0.831878	−	0.554958i	$-0.187266\pi$
$509$	−1.45900	−	2.52707i	−0.0646691	−	0.112010i	−0.896547	+	0.442948i	$0.853933\pi$
$510$	9.08364	−	16.7252i	0.402230	−	0.740604i
$511$	−24.9207	+	43.1640i	−1.10243	+	1.90946i
$512$	32.1571			1.42116
$513$	−14.3859	+	1.12697i	−0.635152	+	0.0497571i
$514$	36.8612			1.62588
$515$	5.49955	−	9.52551i	0.242339	−	0.419744i
$516$	11.7435	−	21.6226i	0.516977	−	0.951881i
$517$	−6.04505	−	10.4703i	−0.265861	−	0.460484i
$518$	14.7638	+	25.5717i	0.648685	+	1.12356i
$519$	7.57048	+	12.3572i	0.332307	+	0.542422i
$520$	0.0984484	−	0.170518i	0.00431725	−	0.00747770i
$521$	−40.3124			−1.76612			−0.883058	−	0.469264i	$-0.844519\pi$
$521$	−40.3124			−1.76612			−0.883058	+	0.469264i	$0.844519\pi$
$522$	−26.8015	+	52.5696i	−1.17307	+	2.30091i
$523$	21.1309			0.923989			0.461994	−	0.886883i	$-0.347134\pi$
$523$	21.1309			0.923989			0.461994	+	0.886883i	$0.347134\pi$
$524$	−12.9922	+	22.5031i	−0.567565	+	0.983051i
$525$	−6.34823	+	0.165471i	−0.277059	+	0.00722173i
$526$	−0.171416	−	0.296902i	−0.00747410	−	0.0129455i
$527$	20.2816	+	35.1287i	0.883480	+	1.53023i
$528$	17.4079	−	0.453748i	0.757582	−	0.0197469i
$529$	11.4985	−	19.9160i	0.499934	−	0.865912i
$530$	4.31049			0.187236
$531$	14.4148	−	28.2738i	0.625548	−	1.22698i
$532$	21.3539			0.925810
$533$	−1.46174	+	2.53181i	−0.0633150	+	0.109665i
$534$	−16.2944	−	26.5972i	−0.705128	−	1.15098i
$535$	−1.72347	−	2.98514i	−0.0745121	−	0.129059i
$536$	−0.0432795	−	0.0749623i	−0.00186939	−	0.00323788i
$537$	10.8637	−	20.0026i	0.468801	−	0.863177i
$538$	15.0830	−	26.1245i	0.650274	−	1.12631i
$539$	17.0632			0.734964
$540$	−4.69515	+	9.83446i	−0.202047	+	0.423208i
$541$	−4.28845			−0.184375			−0.0921874	−	0.995742i	$-0.529386\pi$
$541$	−4.28845			−0.184375			−0.0921874	+	0.995742i	$0.529386\pi$
$542$	−5.87143	+	10.1696i	−0.252200	+	0.436822i
$543$	1.47122	−	2.70887i	0.0631361	−	0.116249i
$544$	−21.9251	−	37.9754i	−0.940031	−	1.62818i
$545$	5.06955	+	8.78072i	0.217156	+	0.376125i
$546$	6.71502	+	10.9609i	0.287376	+	0.469082i
$547$	−12.4735	+	21.6047i	−0.533328	+	0.923751i	0.465915	+	0.884830i	$0.345725\pi$
$547$	−12.4735	+	21.6047i	−0.533328	+	0.923751i	−0.999242	+	0.0389209i	$0.987608\pi$
$548$	24.9509			1.06585
$549$	7.83473	−	0.408712i	0.334378	−	0.0174434i
$550$	5.36112			0.228599
$551$	−13.4925	+	23.3697i	−0.574799	+	0.995581i
$552$	0.0187209		0.000487973i	0.000796816		2.07695e-5i
$553$	29.1573	+	50.5019i	1.23989	+	2.14756i
$554$	−21.3845	−	37.0391i	−0.908541	−	1.57364i
$555$	−6.88898	+	0.179566i	−0.292421	+	0.00762214i
$556$	7.62929	−	13.2143i	0.323554	−	0.560412i
$557$	−45.7105			−1.93681			−0.968407	−	0.249374i	$-0.919775\pi$
$557$	−45.7105			−1.93681			−0.968407	+	0.249374i	$0.919775\pi$
$558$	−24.7034	−	38.0599i	−1.04578	−	1.61120i
$559$	6.77363			0.286494
$560$	−6.95881	+	12.0530i	−0.294063	+	0.509333i
$561$	−13.0095	−	21.2353i	−0.549262	−	0.896556i
$562$	−14.3855	−	24.9165i	−0.606817	−	1.05104i
$563$	−17.1230	−	29.6579i	−0.721649	−	1.24993i	−0.960339	−	0.278836i	$-0.910051\pi$
$563$	−17.1230	−	29.6579i	−0.721649	−	1.24993i	0.238690	−	0.971096i	$-0.423282\pi$
$564$	7.91400	−	14.5716i	0.333240	−	0.613575i
$565$	−2.78541	+	4.82448i	−0.117183	+	0.202967i
$566$	−2.36043			−0.0992161
$567$	−19.3826	−	26.7049i	−0.813995	−	1.12150i
$568$	1.14209			0.0479212
$569$	10.5107	−	18.2051i	0.440633	−	0.763198i	−0.557104	−	0.830443i	$-0.688087\pi$
$569$	10.5107	−	18.2051i	0.440633	−	0.763198i	0.997737	+	0.0672445i	$0.0214207\pi$
$570$	−4.64676	+	8.55582i	−0.194631	+	0.358364i
$571$	5.37045	+	9.30190i	0.224746	+	0.389272i	0.956243	−	0.292573i	$-0.0945113\pi$
$571$	5.37045	+	9.30190i	0.224746	+	0.389272i	−0.731497	+	0.681845i	$0.761178\pi$
$572$	−2.77737	−	4.81054i	−0.116127	−	0.201139i
$573$	−18.5980	−	30.3574i	−0.776944	−	1.26820i
$574$	−10.8482	+	18.7896i	−0.452794	+	0.784263i
$575$	−0.0549131			−0.00229003
$576$	14.3051	+	22.0395i	0.596046	+	0.918313i
$577$	5.54522			0.230851			0.115425	−	0.993316i	$-0.463177\pi$
$577$	5.54522			0.230851			0.115425	+	0.993316i	$0.463177\pi$
$578$	−12.6211	+	21.8603i	−0.524967	+	0.909270i
$579$	39.9293	−	1.04078i	1.65940	−	0.0432534i
$580$	10.1897	+	17.6492i	0.423106	+	0.732842i
$581$	−10.4599	−	18.1170i	−0.433948	−	0.751621i
$582$	−58.6393	+	1.52847i	−2.43068	+	0.0633572i
$583$	2.82005	−	4.88448i	0.116795	−	0.202294i
$584$	2.67664			0.110760
$585$	−2.99593	+	0.156288i	−0.123866	+	0.00646170i
$586$	41.0731			1.69671
$587$	6.17105	−	10.6886i	0.254707	−	0.441165i	−0.710109	−	0.704092i	$-0.751354\pi$
$587$	6.17105	−	10.6886i	0.254707	−	0.441165i	0.964816	+	0.262927i	$0.0846878\pi$
$588$	12.2255	+	19.9556i	0.504172	+	0.822956i
$589$	−10.3751	−	17.9702i	−0.427499	−	0.740450i
$590$	−10.7066	−	18.5444i	−0.440785	−	0.763461i
$591$	16.9914	−	31.2853i	0.698933	−	1.28691i
$592$	−7.55157	+	13.0797i	−0.310368	+	0.537573i
$593$	−1.64053			−0.0673685			−0.0336842	−	0.999433i	$-0.510724\pi$
$593$	−1.64053			−0.0673685			−0.0336842	+	0.999433i	$0.510724\pi$
$594$	15.7702	+	22.9635i	0.647059	+	0.942205i
$595$	19.9036			0.815969
$596$	9.07946	−	15.7261i	0.371909	−	0.644165i
$597$	−10.7371	+	19.7697i	−0.439442	+	0.809120i
$598$	0.0555767	+	0.0962617i	0.00227270	+	0.00393644i
$599$	19.1926	+	33.2425i	0.784188	+	1.35825i	0.929483	+	0.368865i	$0.120253\pi$
$599$	19.1926	+	33.2425i	0.784188	+	1.35825i	−0.145295	+	0.989388i	$0.546413\pi$
$600$	0.178156	+	0.290802i	0.00727317	+	0.0118719i
$601$	−4.94658	+	8.56773i	−0.201775	+	0.349485i	−0.949100	−	0.314973i	$-0.898004\pi$
$601$	−4.94658	+	8.56773i	−0.201775	+	0.349485i	0.747325	+	0.664458i	$0.231338\pi$
$602$	50.2700			2.04885
$603$	−0.599026	+	1.17496i	−0.0243942	+	0.0478480i
$604$	22.8090			0.928087
$605$	−1.99259	+	3.45127i	−0.0810105	+	0.140314i
$606$	54.8445	−	1.42956i	2.22790	−	0.0580718i
$607$	0.490426	+	0.849442i	0.0199058	+	0.0344778i	0.875807	−	0.482662i	$-0.160330\pi$
$607$	0.490426	+	0.849442i	0.0199058	+	0.0344778i	−0.855901	+	0.517140i	$0.826997\pi$
$608$	11.2159	+	19.4264i	0.454863	+	0.787845i
$609$	−61.6867	+	1.60790i	−2.49967	+	0.0651555i
$610$	2.64674	−	4.58428i	0.107163	−	0.185612i
$611$	4.56480			0.184672
$612$	15.5139	−	30.4296i	0.627111	−	1.23004i
$613$	−19.6352			−0.793060			−0.396530	−	0.918022i	$-0.629786\pi$
$613$	−19.6352			−0.793060			−0.396530	+	0.918022i	$0.629786\pi$
$614$	−3.88896	+	6.73587i	−0.156946	+	0.271838i
$615$	−2.64521	−	4.31776i	−0.106665	−	0.174109i
$616$	−0.955997	−	1.65583i	−0.0385182	−	0.0667155i
$617$	1.69153	+	2.92981i	0.0680984	+	0.117950i	0.898064	−	0.439864i	$-0.144973\pi$
$617$	1.69153	+	2.92981i	0.0680984	+	0.117950i	−0.829966	+	0.557814i	$0.811640\pi$
$618$	18.4045	−	33.8872i	0.740339	−	1.36314i
$619$	5.19745	−	9.00224i	0.208903	−	0.361831i	−0.742466	−	0.669883i	$-0.766344\pi$
$619$	5.19745	−	9.00224i	0.208903	−	0.361831i	0.951369	+	0.308053i	$0.0996774\pi$
$620$	−15.6709			−0.629359
$621$	−0.161532	−	0.235212i	−0.00648204	−	0.00943872i
$622$	−41.2492			−1.65394
$623$	16.3095	−	28.2489i	0.653426	−	1.13177i
$624$	−3.13794	+	5.77772i	−0.125618	+	0.231294i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.11214	−	3.65833i	−0.0844179	−	0.146216i
$627$	6.65506	+	10.8630i	0.265777	+	0.433826i
$628$	12.4772	−	21.6111i	0.497893	−	0.862375i
$629$	21.5991			0.861211
$630$	−22.2340	+	1.15988i	−0.885825	+	0.0462106i
$631$	−12.0594			−0.480077			−0.240038	−	0.970763i	$-0.577160\pi$
$631$	−12.0594			−0.480077			−0.240038	+	0.970763i	$0.577160\pi$
$632$	1.56584	−	2.71211i	0.0622856	−	0.107882i
$633$	1.89546	−	0.0494065i	0.0753380	−	0.00196373i
$634$	30.9961	+	53.6869i	1.23101	+	2.13218i
$635$	9.15618	+	15.8590i	0.363352	+	0.629344i
$636$	7.73299	−	0.201565i	0.306633	−	0.00799259i
$637$	−3.22123	+	5.57934i	−0.127630	+	0.221061i
$638$	52.0948			2.06245
$639$	−9.47397	−	14.5963i	−0.374784	−	0.577421i
$640$	1.57331			0.0621906
$641$	−8.34116	+	14.4473i	−0.329456	+	0.570634i	−0.982404	−	0.186768i	$-0.940199\pi$
$641$	−8.34116	+	14.4473i	−0.329456	+	0.570634i	0.652948	+	0.757403i	$0.273532\pi$
$642$	−6.31308	−	10.3048i	−0.249157	−	0.406698i
$643$	0.206134	+	0.357035i	0.00812914	+	0.0140801i	0.870061	−	0.492943i	$-0.164079\pi$
$643$	0.206134	+	0.357035i	0.00812914	+	0.0140801i	−0.861932	+	0.507024i	$0.830746\pi$
$644$	0.211125	+	0.365680i	0.00831950	+	0.0144098i
$645$	−5.59940	+	10.3099i	−0.220476	+	0.405950i
$646$	15.2579	−	26.4274i	0.600312	−	1.03977i
$647$	−2.14833			−0.0844595			−0.0422298	−	0.999108i	$-0.513446\pi$
$647$	−2.14833			−0.0844595			−0.0422298	+	0.999108i	$0.513446\pi$
$648$	−0.721545	+	1.61852i	−0.0283450	+	0.0635815i
$649$	−28.0184			−1.09982
$650$	−1.01209	+	1.75298i	−0.0396973	+	0.0687577i
$651$	22.6464	−	41.6975i	0.887581	−	1.63425i
$652$	16.4244	+	28.4479i	0.643229	+	1.11411i
$653$	10.5402	+	18.2562i	0.412471	+	0.714421i	0.995159	−	0.0982748i	$-0.0313324\pi$
$653$	10.5402	+	18.2562i	0.412471	+	0.714421i	−0.582688	+	0.812696i	$0.697999\pi$
$654$	18.5698	+	30.3114i	0.726137	+	1.18527i
$655$	6.19478	−	10.7297i	0.242050	−	0.419243i
$656$	−11.0975			−0.433285
$657$	−22.2035	−	34.2083i	−0.866240	−	1.33459i
$658$	33.8773			1.32067
$659$	10.0627	−	17.4291i	0.391986	−	0.678940i	−0.600725	−	0.799455i	$-0.705121\pi$
$659$	10.0627	−	17.4291i	0.391986	−	0.678940i	0.992711	+	0.120516i	$0.0384548\pi$
$660$	9.61781	−	0.250694i	0.374373	−	0.00975826i
$661$	−15.1113	−	26.1736i	−0.587762	−	1.01803i	−0.994525	−	0.104500i	$-0.966676\pi$
$661$	−15.1113	−	26.1736i	−0.587762	−	1.01803i	0.406763	−	0.913534i	$-0.366658\pi$
$662$	−23.5388	−	40.7704i	−0.914862	−	1.58459i
$663$	9.39952	−	0.245005i	0.365047	−	0.00951519i
$664$	−0.561727	+	0.972940i	−0.0217992	+	0.0377574i
$665$	−10.1818			−0.394832
$666$	−24.1280	+	1.25868i	−0.934940	+	0.0487727i
$667$	−0.533598			−0.0206610
$668$	−6.44024	+	11.1548i	−0.249180	+	0.431593i
$669$	−22.7511	−	37.1364i	−0.879607	−	1.43578i
$670$	0.444929	+	0.770639i	0.0171891	+	0.0297724i
$671$	−3.46315	−	5.99835i	−0.133693	−	0.231564i
$672$	−24.4815	+	45.0764i	−0.944394	+	1.73886i
$673$	0.148506	−	0.257219i	0.00572447	−	0.00991508i	−0.863149	−	0.504949i	$-0.831511\pi$
$673$	0.148506	−	0.257219i	0.00572447	−	0.00991508i	0.868873	+	0.495034i	$0.164845\pi$
$674$	7.03661			0.271040
$675$	2.23869	−	4.68916i	0.0861673	−	0.180486i
$676$	2.09727			0.0806643
$677$	15.8788	−	27.5029i	0.610273	−	1.05702i	−0.380921	−	0.924608i	$-0.624393\pi$
$677$	15.8788	−	27.5029i	0.610273	−	1.05702i	0.991194	−	0.132416i	$-0.0422736\pi$
$678$	−9.32152	+	17.1632i	−0.357991	+	0.659148i
$679$	−30.6717	−	53.1249i	−1.17707	−	2.03875i
$680$	−0.534443	−	0.925683i	−0.0204950	−	0.0354983i
$681$	−13.0327	−	21.2732i	−0.499414	−	0.815190i
$682$	−20.0293	+	34.6917i	−0.766960	+	1.32841i
$683$	34.6077			1.32423			0.662114	−	0.749403i	$-0.269659\pi$
$683$	34.6077			1.32423			0.662114	+	0.749403i	$0.269659\pi$
$684$	−7.93617	+	15.5664i	−0.303447	+	0.595195i
$685$	−11.8968			−0.454554
$686$	2.06884	−	3.58334i	0.0789889	−	0.136813i
$687$	−15.9859	+	0.416683i	−0.609900	+	0.0158974i
$688$	12.8563	+	22.2678i	0.490143	+	0.848952i
$689$	1.06475	+	1.84421i	0.0405639	+	0.0702587i
$690$	−0.192458	+	0.00501655i	−0.00732676	+	0.000190977i
$691$	−12.6224	+	21.8627i	−0.480180	+	0.831696i	−0.999741	−	0.0227372i	$-0.992762\pi$
$691$	−12.6224	+	21.8627i	−0.480180	+	0.831696i	0.519562	+	0.854433i	$0.326095\pi$
$692$	17.5476			0.667060
$693$	−13.2318	+	25.9535i	−0.502636	+	0.985893i
$694$	−16.7124			−0.634395
$695$	−3.63772	+	6.30072i	−0.137987	+	0.239000i
$696$	1.73116	+	2.82576i	0.0656196	+	0.107110i
$697$	7.93529	+	13.7443i	0.300570	+	0.520603i
$698$	−32.1934	−	55.7607i	−1.21854	−	2.11057i
$699$	−11.3750	+	20.9441i	−0.430241	+	0.792178i
$700$	−3.84472	+	6.65925i	−0.145317	+	0.251696i
$701$	−5.25839			−0.198607			−0.0993033	−	0.995057i	$-0.531661\pi$
$701$	−5.25839			−0.198607			−0.0993033	+	0.995057i	$0.531661\pi$
$702$	−10.4858	+	0.821444i	−0.395760	+	0.0310034i
$703$	−11.0491			−0.416723
$704$	11.5984	−	20.0891i	0.437133	−	0.757136i
$705$	−3.77347	+	6.94788i	−0.142117	+	0.261672i
$706$	−16.7974	−	29.0939i	−0.632177	−	1.09496i
$707$	28.6868	+	49.6870i	1.07888	+	1.86867i
$708$	−20.0748	−	32.7679i	−0.754456	−	1.23149i
$709$	25.0649	−	43.4136i	0.941331	−	1.63043i	0.178396	−	0.983959i	$-0.442909\pi$
$709$	25.0649	−	43.4136i	0.941331	−	1.63043i	0.762935	−	0.646475i	$-0.223757\pi$
$710$	−11.7411			−0.440637
$711$	−47.6506	+	2.48578i	−1.78704	+	0.0932239i
$712$	−1.75174			−0.0656492
$713$	0.205156	−	0.355341i	0.00768317	−	0.0133076i
$714$	69.7578	−	1.81828i	2.61062	−	0.0680475i
$715$	1.32427	+	2.29371i	0.0495251	+	0.0857799i
$716$	−13.7810	−	23.8694i	−0.515021	−	0.892042i
$717$	31.2924	−	0.815658i	1.16864	−	0.0304613i
$718$	27.0056	−	46.7751i	1.00784	−	1.74563i
$719$	6.50605			0.242635			0.121317	−	0.992614i	$-0.461288\pi$
$719$	6.50605			0.242635			0.121317	+	0.992614i	$0.461288\pi$
$720$	−6.20004	−	9.55225i	−0.231062	−	0.355991i
$721$	40.3271			1.50186
$722$	11.4244	−	19.7877i	0.425173	−	0.736422i
$723$	17.8573	+	29.1483i	0.664120	+	1.08404i
$724$	−1.86631	−	3.23254i	−0.0693607	−	0.120136i
$725$	−4.85857	−	8.41529i	−0.180443	−	0.312536i
$726$	−6.66831	+	12.2780i	−0.247484	+	0.455679i
$727$	−17.5395	+	30.3792i	−0.650502	+	1.12670i	0.332499	+	0.943104i	$0.392108\pi$
$727$	−17.5395	+	30.3792i	−0.650502	+	1.12670i	−0.983001	+	0.183600i	$0.941225\pi$
$728$	0.721902			0.0267555
$729$	26.6706	−	4.20450i	0.987801	−	0.155722i
$730$	−27.5169			−1.01844
$731$	18.3859	−	31.8453i	0.680026	−	1.17784i
$732$	4.53386	−	8.34793i	0.167576	−	0.308548i
$733$	8.04314	+	13.9311i	0.297080	+	0.514558i	0.975467	−	0.220147i	$-0.0706538\pi$
$733$	8.04314	+	13.9311i	0.297080	+	0.514558i	−0.678387	+	0.734705i	$0.737320\pi$
$734$	34.2117	+	59.2565i	1.26278	+	2.18720i
$735$	−5.82925	−	9.51504i	−0.215015	−	0.350967i
$736$	−0.221781	+	0.384136i	−0.00817496	+	0.0141594i
$737$	1.16434			0.0428892
$738$	−9.66533	−	14.8911i	−0.355786	−	0.548150i
$739$	−27.0932			−0.996638			−0.498319	−	0.866994i	$-0.666049\pi$
$739$	−27.0932			−0.996638			−0.498319	+	0.866994i	$0.666049\pi$
$740$	−4.17222	+	7.22649i	−0.153374	+	0.265651i
$741$	−4.80835	+	0.125333i	−0.176639	+	0.00460422i
$742$	7.90199	+	13.6866i	0.290091	+	0.502452i
$743$	13.4638	+	23.3200i	0.493938	+	0.855526i	0.999976	−	0.00698531i	$-0.00222351\pi$
$743$	13.4638	+	23.3200i	0.493938	+	0.855526i	−0.506037	+	0.862512i	$0.668890\pi$
$744$	−2.54737	+	0.0663987i	−0.0933910	+	0.00243430i
$745$	−4.32917	+	7.49835i	−0.158609	+	0.274718i
$746$	−51.9418			−1.90173
$747$	17.0942	−	0.891747i	0.625443	−	0.0326273i
$748$	−30.1547			−1.10257
$749$	6.31892	−	10.9447i	0.230888	−	0.399910i
$750$	−1.83150	−	2.98955i	−0.0668771	−	0.109163i
$751$	16.9769	+	29.4048i	0.619495	+	1.07300i	0.989578	+	0.143999i	$0.0459961\pi$
$751$	16.9769	+	29.4048i	0.619495	+	1.07300i	−0.370082	+	0.928999i	$0.620671\pi$
$752$	8.66397	+	15.0064i	0.315942	+	0.547228i
$753$	2.53655	−	4.67041i	0.0924370	−	0.170199i
$754$	−9.83459	+	17.0340i	−0.358154	+	0.620342i
$755$	−10.8756			−0.395803
$756$	−39.8334	+	3.12051i	−1.44873	+	0.113492i
$757$	−14.7996			−0.537902			−0.268951	−	0.963154i	$-0.586677\pi$
$757$	−14.7996			−0.537902			−0.268951	+	0.963154i	$0.586677\pi$
$758$	37.1193	−	64.2926i	1.34823	−	2.33521i
$759$	−0.120227	+	0.221368i	−0.00436398	+	0.00803514i
$760$	0.273396	+	0.473536i	0.00991711	+	0.0171769i
$761$	12.0732	+	20.9114i	0.437652	+	0.758036i	0.997508	−	0.0705540i	$-0.0224767\pi$
$761$	12.0732	+	20.9114i	0.437652	+	0.758036i	−0.559856	+	0.828590i	$0.689143\pi$
$762$	33.5392	+	54.7457i	1.21500	+	1.98323i
$763$	−18.5870	+	32.1936i	−0.672894	+	1.16549i
$764$	−43.1084			−1.55961
$765$	−7.39717	+	14.5091i	−0.267445	+	0.524579i
$766$	45.3954			1.64020
$767$	5.28938	−	9.16148i	0.190989	−	0.330802i
$768$	−24.8154	+	0.646828i	−0.895447	+	0.0233404i
$769$	3.30884	+	5.73108i	0.119320	+	0.206668i	0.919498	−	0.393094i	$-0.128595\pi$
$769$	3.30884	+	5.73108i	0.119320	+	0.206668i	−0.800179	+	0.599762i	$0.795262\pi$
$770$	9.82800	+	17.0226i	0.354176	+	0.613451i
$771$	−31.5308	+	0.821871i	−1.13556	+	0.0295990i
$772$	24.1826	−	41.8855i	0.870351	−	1.50749i
$773$	45.0193			1.61923			0.809615	−	0.586961i	$-0.199676\pi$
$773$	45.0193			1.61923			0.809615	+	0.586961i	$0.199676\pi$
$774$	−18.6828	+	36.6453i	−0.671539	+	1.31719i
$775$	7.47204			0.268404
$776$	−1.64716	+	2.85297i	−0.0591298	+	0.102416i
$777$	−13.1990	−	21.5447i	−0.473513	−	0.772911i
$778$	−5.93395	−	10.2779i	−0.212743	−	0.368481i
$779$	−4.05932	−	7.03095i	−0.145440	−	0.251910i
$780$	−1.73370	+	3.19217i	−0.0620765	+	0.114298i
$781$	−7.68140	+	13.3046i	−0.274862	+	0.476075i
$782$	0.603415			0.0215781
$783$	21.7537	−	45.5653i	0.777414	−	1.62837i
$784$	−24.4556			−0.873413
$785$	−5.94923	+	10.3044i	−0.212337	+	0.367778i
$786$	20.7311	−	38.1711i	0.739455	−	1.36152i
$787$	−3.04183	−	5.26860i	−0.108429	−	0.187805i	0.806705	−	0.590955i	$-0.201249\pi$
$787$	−3.04183	−	5.26860i	−0.108429	−	0.187805i	−0.915134	+	0.403149i	$0.867915\pi$
$788$	−21.5543	−	37.3332i	−0.767841	−	1.32994i
$789$	0.153248	+	0.250146i	0.00545577	+	0.00890542i
$790$	−16.0974	+	27.8815i	−0.572719	+	0.991978i
$791$	−20.4249			−0.726225
$792$	1.56235	−	0.0815026i	0.0555156	−	0.00289607i
$793$	2.61513			0.0928659
$794$	19.1885	−	33.2355i	0.680976	−	1.17948i
$795$	−3.68716	+	0.0961083i	−0.130770	+	0.00340861i
$796$	13.6205	+	23.5915i	0.482767	+	0.836177i
$797$	16.5495	+	28.6645i	0.586212	+	1.01535i	0.994723	+	0.102596i	$0.0327149\pi$
$797$	16.5495	+	28.6645i	0.586212	+	1.01535i	−0.408511	+	0.912753i	$0.633952\pi$
$798$	−35.6848	+	0.930148i	−1.26323	+	0.0329269i
$799$	12.3904	−	21.4607i	0.438340	−	0.759227i
$800$	−8.07754			−0.285584
$801$	14.5312	+	22.3878i	0.513433	+	0.791034i
$802$	−19.0188			−0.671577
$803$	−18.0024	+	31.1810i	−0.635290	+	1.10035i
$804$	0.834235	+	1.36172i	0.0294212	+	0.0480240i
$805$	−0.100667	−	0.174360i	−0.00354803	−	0.00614537i
$806$	−7.56235	−	13.0984i	−0.266372	−	0.461371i
$807$	−12.3194	+	22.6830i	−0.433663	+	0.798480i
$808$	1.54057	−	2.66834i	0.0541970	−	0.0938720i
$809$	−36.4711			−1.28226			−0.641128	−	0.767434i	$-0.721533\pi$
$809$	−36.4711			−1.28226			−0.641128	+	0.767434i	$0.721533\pi$
$810$	7.41775	−	16.6390i	0.260633	−	0.584635i
$811$	−21.7978			−0.765425			−0.382713	−	0.923867i	$-0.625010\pi$
$811$	−21.7978			−0.765425			−0.382713	+	0.923867i	$0.625010\pi$
$812$	−37.3597	+	64.7088i	−1.31107	+	2.27084i
$813$	4.79564	−	8.82993i	0.168190	−	0.309679i
$814$	10.6652	+	18.4726i	0.373814	+	0.647465i
$815$	−7.83132	−	13.5642i	−0.274319	−	0.475134i
$816$	18.6457	+	30.4352i	0.652730	+	1.06545i
$817$	−9.40535	+	16.2905i	−0.329051	+	0.569934i
$818$	−29.1788			−1.02021
$819$	−5.98837	−	9.22614i	−0.209251	−	0.322387i
$820$	−6.13133			−0.214115
$821$	−22.1014	+	38.2808i	−0.771344	+	1.33601i	0.165482	+	0.986213i	$0.447082\pi$
$821$	−22.1014	+	38.2808i	−0.771344	+	1.33601i	−0.936826	+	0.349795i	$0.886251\pi$
$822$	−41.6957	+	1.08683i	−1.45430	+	0.0379074i
$823$	10.4675	+	18.1303i	0.364874	+	0.631981i	0.988756	−	0.149538i	$-0.0477786\pi$
$823$	10.4675	+	18.1303i	0.364874	+	0.631981i	−0.623882	+	0.781519i	$0.714445\pi$
$824$	−1.08285	−	1.87554i	−0.0377227	−	0.0653376i
$825$	−4.58586	+	0.119534i	−0.159659	+	0.00416162i
$826$	39.2547	−	67.9912i	1.36585	−	2.36572i
$827$	47.8839			1.66509			0.832544	−	0.553960i	$-0.186884\pi$
$827$	47.8839			1.66509			0.832544	+	0.553960i	$0.186884\pi$
$828$	−0.345034	+	0.0179993i	−0.0119908	+	0.000625519i
$829$	7.10603			0.246803			0.123401	−	0.992357i	$-0.460620\pi$
$829$	7.10603			0.246803			0.123401	+	0.992357i	$0.460620\pi$
$830$	5.77476	−	10.0022i	0.200445	−	0.347181i
$831$	19.1180	+	31.2062i	0.663196	+	1.08253i
$832$	4.37917	+	7.58494i	0.151820	+	0.262961i
$833$	17.4870	+	30.2883i	0.605888	+	1.04943i
$834$	−12.1738	+	22.4149i	−0.421544	+	0.776166i
$835$	3.07077	−	5.31873i	0.106268	−	0.184062i
$836$	15.4257			0.533511
$837$	21.9797	+	32.0053i	0.759729	+	1.10627i
$838$	−12.5620			−0.433947
$839$	1.20286	−	2.08341i	0.0415272	−	0.0719272i	−0.844515	−	0.535532i	$-0.820111\pi$
$839$	1.20286	−	2.08341i	0.0415272	−	0.0719272i	0.886042	+	0.463605i	$0.153444\pi$
$840$	−0.596758	+	1.09878i	−0.0205901	+	0.0379114i
$841$	−32.7114	−	56.6579i	−1.12798	−	1.95372i
$842$	3.95977	+	6.85852i	0.136463	+	0.236360i
$843$	12.8608	+	20.9926i	0.442950	+	0.723024i
$844$	1.14796	−	1.98833i	0.0395145	−	0.0684411i
$845$	−1.00000			−0.0344010
$846$	−12.5905	+	24.6955i	−0.432869	+	0.849049i
$847$	−14.6113			−0.502049
$848$	−4.04180	+	7.00060i	−0.138796	+	0.240402i
$849$	2.01909	−	0.0526290i	0.0692951	−	0.00180622i
$850$	5.49427	+	9.51636i	0.188452	+	0.326408i
$851$	−0.109242	−	0.189212i	−0.00374475	−	0.00648610i
$852$	−21.0635	+	0.549034i	−0.721624	+	0.0188096i
$853$	−6.04250	+	10.4659i	−0.206891	+	0.358346i	−0.950734	−	0.310009i	$-0.899668\pi$
$853$	−6.04250	+	10.4659i	−0.206891	+	0.358346i	0.743842	+	0.668355i	$0.233001\pi$
$854$	19.4080			0.664127
$855$	3.78404	−	7.42219i	0.129412	−	0.253834i
$856$	−0.678691			−0.0231972
$857$	15.2783	−	26.4627i	0.521896	−	0.903950i	−0.477780	−	0.878480i	$-0.658558\pi$
$857$	15.2783	−	26.4627i	0.521896	−	0.903950i	0.999676	−	0.0254702i	$-0.00810828\pi$
$858$	4.85083	+	7.91797i	0.165605	+	0.270315i
$859$	19.2275	+	33.3030i	0.656035	+	1.13629i	0.981633	+	0.190777i	$0.0611008\pi$
$859$	19.2275	+	33.3030i	0.656035	+	1.13629i	−0.325599	+	0.945508i	$0.605566\pi$
$860$	7.10308	+	12.3029i	0.242213	+	0.419525i
$861$	8.86052	−	16.3144i	0.301966	−	0.555992i
$862$	19.0604	−	33.0136i	0.649200	−	1.12445i
$863$	15.5487			0.529284			0.264642	−	0.964347i	$-0.414746\pi$
$863$	15.5487			0.529284			0.264642	+	0.964347i	$0.414746\pi$
$864$	−23.7608	−	34.5989i	−0.808358	−	1.17708i
$865$	−8.36687			−0.284482
$866$	13.8766	−	24.0350i	0.471546	−	0.816742i
$867$	10.3086	−	18.9806i	0.350097	−	0.644614i
$868$	−28.7279	−	49.7582i	−0.975088	−	1.68890i
$869$	21.0628	+	36.4818i	0.714505	+	1.23756i
$870$	−17.7970	−	29.0499i	−0.603374	−	0.984883i
$871$	−0.219808	+	0.380718i	−0.00744790	+	0.0129001i
$872$	1.99636			0.0676052
$873$	50.1256	−	2.61489i	1.69649	−	0.0885005i
$874$	−0.308679			−0.0104412
$875$	1.83320	−	3.17519i	0.0619734	−	0.107341i
$876$	−49.3650	+	1.28673i	−1.66789	+	0.0434746i
$877$	−11.6846	−	20.2384i	−0.394562	−	0.683402i	0.598483	−	0.801135i	$-0.295770\pi$
$877$	−11.6846	−	20.2384i	−0.394562	−	0.683402i	−0.993045	+	0.117734i	$0.962437\pi$
$878$	0.333556	+	0.577736i	0.0112570	+	0.0194976i
$879$	−35.1336	+	0.915780i	−1.18503	+	0.0308885i
$880$	−5.02694	+	8.70691i	−0.169458	+	0.293510i
$881$	−9.62251			−0.324191			−0.162095	−	0.986775i	$-0.551825\pi$
$881$	−9.62251			−0.324191			−0.162095	+	0.986775i	$0.551825\pi$
$882$	−21.2995	−	32.8156i	−0.717191	−	1.10496i
$883$	6.05028			0.203608			0.101804	−	0.994804i	$-0.467539\pi$
$883$	6.05028			0.203608			0.101804	+	0.994804i	$0.467539\pi$
$884$	5.69269	−	9.86003i	0.191466	−	0.331629i
$885$	9.57184	+	15.6240i	0.321754	+	0.525196i
$886$	42.3533	+	73.3580i	1.42289	+	2.46451i
$887$	−3.02407	−	5.23784i	−0.101538	−	0.175869i	0.810780	−	0.585351i	$-0.199043\pi$
$887$	−3.02407	−	5.23784i	−0.101538	−	0.175869i	−0.912319	+	0.409481i	$0.865710\pi$
$888$	−0.647591	+	1.19237i	−0.0217317	+	0.0400134i
$889$	−33.5702	+	58.1453i	−1.12591	+	1.95013i
$890$	18.0085			0.603647
$891$	−14.0017	−	19.2912i	−0.469076	−	0.646280i
$892$	−52.7347			−1.76569
$893$	−6.33833	+	10.9783i	−0.212104	+	0.367375i
$894$	−14.4878	+	26.6755i	−0.484544	+	0.892163i
$895$	6.57092	+	11.3812i	0.219642	+	0.380431i
$896$	2.88419	+	4.99557i	0.0963541	+	0.166890i
$897$	−0.0496862	−	0.0811025i	−0.00165898	−	0.00270793i
$898$	−25.0984	+	43.4717i	−0.837545	+	1.45067i
$899$	72.6069			2.42158
$900$	−3.42550	−	5.27759i	−0.114183	−	0.175920i
$901$	11.5604			0.385132
$902$	−7.83656	+	13.5733i	−0.260929	+	0.451942i
$903$	−43.0006	+	1.12084i	−1.43097	+	0.0372991i
$904$	0.548439	+	0.949925i	0.0182408	+	0.0315940i
$905$	0.889873	+	1.54131i	0.0295804	+	0.0512347i
$906$	−38.1165	+	0.993530i	−1.26633	+	0.0330078i
$907$	−14.8461	+	25.7143i	−0.492958	+	0.853828i	−0.999967	−	0.00811270i	$-0.997418\pi$
$907$	−14.8461	+	25.7143i	−0.492958	+	0.853828i	0.507009	+	0.861941i	$0.330751\pi$
$908$	−30.2085			−1.00250
$909$	−46.8817	+	2.44567i	−1.55497	+	0.0811176i
$910$	−7.42142			−0.246018
$911$	28.5350	−	49.4241i	0.945408	−	1.63749i	0.190475	−	0.981692i	$-0.438997\pi$
$911$	28.5350	−	49.4241i	0.945408	−	1.63749i	0.754933	−	0.655802i	$-0.227670\pi$
$912$	−9.53826	−	15.5692i	−0.315843	−	0.515549i
$913$	−7.55605	−	13.0875i	−0.250069	−	0.433132i
$914$	−19.7124	−	34.1428i	−0.652028	−	1.12934i
$915$	−2.16179	+	3.98037i	−0.0714664	+	0.131587i
$916$	−9.68164	+	16.7691i	−0.319890	+	0.554066i
$917$	45.4251			1.50007
$918$	−24.6000	+	51.5271i	−0.811920	+	1.70065i
$919$	14.7095			0.485223			0.242611	−	0.970124i	$-0.421996\pi$
$919$	14.7095			0.485223			0.242611	+	0.970124i	$0.421996\pi$
$920$	−0.00540611	+	0.00936365i	−0.000178234	+	0.000308710i
$921$	3.17640	−	5.84853i	0.104666	−	0.192716i
$922$	−18.5422	−	32.1161i	−0.610656	−	1.05769i
$923$	−2.90023	−	5.02335i	−0.0954623	−	0.165346i
$924$	18.4274	+	30.0788i	0.606215	+	0.989521i
$925$	1.98935	−	3.44566i	0.0654096	−	0.113293i
$926$	68.5908			2.25403
$927$	−14.9875	+	29.3972i	−0.492255	+	0.965532i
$928$	−78.4906			−2.57658
$929$	15.0654	−	26.0940i	0.494279	−	0.856116i	−0.505699	−	0.862710i	$-0.668765\pi$
$929$	15.0654	−	26.0940i	0.494279	−	0.856116i	0.999978	+	0.00659356i	$0.00209881\pi$
$930$	26.1879	−	0.682603i	0.858734	−	0.0223834i
$931$	−8.94552	−	15.4941i	−0.293177	−	0.507798i
$932$	14.4296	+	24.9929i	0.472658	+	0.818668i
$933$	35.2843	−	0.919707i	1.15515	−	0.0301099i
$934$	15.4735	−	26.8009i	0.506308	−	0.876951i
$935$	14.3781			0.470213
$936$	−0.268294	+	0.526245i	−0.00876948	+	0.0172008i
$937$	36.6824			1.19836			0.599181	−	0.800614i	$-0.295493\pi$
$937$	36.6824			1.19836			0.599181	+	0.800614i	$0.295493\pi$
$938$	−1.63129	+	2.82547i	−0.0532634	+	0.0922549i
$939$	1.88827	+	3.08221i	0.0616215	+	0.100584i
$940$	4.78681	+	8.29100i	0.156129	+	0.270423i
$941$	−2.89540	−	5.01499i	−0.0943875	−	0.163484i	0.814965	−	0.579510i	$-0.196756\pi$
$941$	−2.89540	−	5.01499i	−0.0943875	−	0.163484i	−0.909353	+	0.416026i	$0.863423\pi$
$942$	−19.9094	+	36.6580i	−0.648682	+	1.19438i
$943$	0.0802686	−	0.139029i	0.00261390	−	0.00452742i
$944$	40.1569			1.30700
$945$	18.9930	−	1.48789i	0.617841	−	0.0484010i
$946$	36.3142			1.18068
$947$	12.8257	−	22.2148i	0.416780	−	0.721884i	−0.578834	−	0.815446i	$-0.696492\pi$
$947$	12.8257	−	22.2148i	0.416780	−	0.721884i	0.995613	+	0.0935617i	$0.0298252\pi$
$948$	−27.5748	+	50.7719i	−0.895587	+	1.64899i
$949$	−6.79707	−	11.7729i	−0.220642	−	0.382163i
$950$	−2.81061	−	4.86812i	−0.0911883	−	0.157943i
$951$	−27.7109	−	45.2323i	−0.898588	−	1.46676i
$952$	1.95948	−	3.39392i	0.0635071	−	0.109998i
$953$	−6.21920			−0.201460			−0.100730	−	0.994914i	$-0.532118\pi$
$953$	−6.21920			−0.201460			−0.100730	+	0.994914i	$0.532118\pi$
$954$	−12.9139	+	0.673677i	−0.418103	+	0.0218111i
$955$	20.5545			0.665127
$956$	18.9518	−	32.8255i	0.612946	−	1.06165i
$957$	−44.5615	+	1.16152i	−1.44047	+	0.0375467i
$958$	13.5695	+	23.5031i	0.438411	+	0.759350i
$959$	−21.8092	−	37.7747i	−0.704257	−	1.21981i
$960$	−15.1647	+	0.395279i	−0.489440	+	0.0127576i
$961$	−12.4157	+	21.5046i	−0.400507	+	0.693698i
$962$	−8.05359			−0.259658
$963$	5.62993	+	8.67389i	0.181422	+	0.279512i
$964$	41.3914			1.33313
$965$	−11.5305	+	19.9714i	−0.371180	+	0.642903i
$966$	−0.368742	−	0.601895i	−0.0118641	−	0.0193657i
$967$	−19.0519	−	32.9989i	−0.612668	−	1.06117i	−0.990789	−	0.135416i	$-0.956763\pi$
$967$	−19.0519	−	32.9989i	−0.612668	−	1.06117i	0.378120	−	0.925756i	$-0.376571\pi$
$968$	0.392335	+	0.679545i	0.0126101	+	0.0218414i
$969$	−12.4622	+	22.9460i	−0.400344	+	0.737131i
$970$	16.9335	−	29.3296i	0.543700	−	0.941717i
$971$	−0.262219			−0.00841500			−0.00420750	−	0.999991i	$-0.501339\pi$
$971$	−0.262219			−0.00841500			−0.00420750	+	0.999991i	$0.501339\pi$
$972$	12.5293	−	30.1971i	0.401878	−	0.968572i
$973$	−26.6746			−0.855150
$974$	−17.8988	+	31.0016i	−0.573514	+	0.993356i
$975$	0.826646	−	1.52206i	0.0264739	−	0.0487448i
$976$	4.96350	+	8.59704i	0.158878	+	0.275185i
$977$	−18.0107	−	31.1955i	−0.576215	−	0.998033i	−0.995909	−	0.0903673i	$-0.971196\pi$
$977$	−18.0107	−	31.1955i	−0.576215	−	0.998033i	0.419694	−	0.907666i	$-0.362137\pi$
$978$	−28.6862	−	46.8242i	−0.917283	−	1.49727i
$979$	11.7817	−	20.4065i	0.376546	−	0.652196i
$980$	−13.5116			−0.431613
$981$	−16.5603	−	25.5141i	−0.528731	−	0.814602i
$982$	−29.5374			−0.942577
$983$	−21.8048	+	37.7670i	−0.695464	+	1.20458i	0.274560	+	0.961570i	$0.411468\pi$
$983$	−21.8048	+	37.7670i	−0.695464	+	1.20458i	−0.970024	+	0.243009i	$0.921865\pi$
$984$	−0.996671	+	0.0259789i	−0.0317727	+	0.000828176i
$985$	10.2773	+	17.8008i	0.327462	+	0.567182i
$986$	53.3886	+	92.4718i	1.70024	+	2.94490i
$987$	−28.9784	+	0.755340i	−0.922392	+	0.0240427i
$988$	−2.91211	+	5.04393i	−0.0926467	+	0.160469i
$989$	−0.371961			−0.0118277
$990$	−16.0615	+	0.837877i	−0.510469	+	0.0266295i
$991$	17.0413			0.541335			0.270667	−	0.962673i	$-0.412756\pi$
$991$	17.0413			0.541335			0.270667	+	0.962673i	$0.412756\pi$
$992$	30.1778	−	52.2696i	0.958148	−	1.65956i
$993$	21.0440	+	34.3499i	0.667810	+	1.09006i
$994$	−21.5238	−	37.2804i	−0.682694	−	1.18246i
$995$	−6.49440	−	11.2486i	−0.205886	−	0.356606i
$996$	9.89216	−	18.2139i	0.313445	−	0.577129i
$997$	7.06691	−	12.2403i	0.223811	−	0.387653i	−0.732151	−	0.681143i	$-0.761483\pi$
$997$	7.06691	−	12.2403i	0.223811	−	0.387653i	0.955962	+	0.293490i	$0.0948167\pi$
$998$	−37.1657			−1.17646
$999$	20.6108	−	1.61463i	0.652098	−	0.0510846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.196.4	✓	30
3.2	odd	2		1755.2.i.h.586.12		30
9.2	odd	6		5265.2.a.bl.1.4		15
9.4	even	3	inner	585.2.i.h.391.4	yes	30
9.5	odd	6		1755.2.i.h.1171.12		30
9.7	even	3		5265.2.a.bk.1.12		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.4	✓	30	1.1	even	1	trivial
585.2.i.h.391.4	yes	30	9.4	even	3	inner
1755.2.i.h.586.12		30	3.2	odd	2
1755.2.i.h.1171.12		30	9.5	odd	6
5265.2.a.bk.1.12		15	9.7	even	3
5265.2.a.bl.1.4		15	9.2	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01209 + 1.75298i) q^{2} +(0.826646 - 1.52206i) q^{3} +(-1.04864 - 1.81629i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.83150 + 2.98955i) q^{6} +(-1.83320 + 3.17519i) q^{7} +0.196897 q^{8} +(-1.63331 - 2.51640i) q^{9} +O(q^{10})\)	\(q+(-1.01209 + 1.75298i) q^{2} +(0.826646 - 1.52206i) q^{3} +(-1.04864 - 1.81629i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.83150 + 2.98955i) q^{6} +(-1.83320 + 3.17519i) q^{7} +0.196897 q^{8} +(-1.63331 - 2.51640i) q^{9} -2.02417 q^{10} +(-1.32427 + 2.29371i) q^{11} +(-3.63135 + 0.0946535i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-3.71071 - 6.42714i) q^{14} +(1.73146 - 0.0451317i) q^{15} +(1.89800 - 3.28743i) q^{16} -5.42866 q^{17} +(6.06427 - 0.316353i) q^{18} +2.77705 q^{19} +(1.04864 - 1.81629i) q^{20} +(3.31742 + 5.41499i) q^{21} +(-2.68056 - 4.64287i) q^{22} +(0.0274565 + 0.0475561i) q^{23} +(0.162764 - 0.299688i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.02417 q^{26} +(-5.18028 + 0.405818i) q^{27} +7.68943 q^{28} +(-4.85857 + 8.41529i) q^{29} +(-1.67327 + 3.08090i) q^{30} +(-3.73602 - 6.47098i) q^{31} +(4.03877 + 6.99535i) q^{32} +(2.39645 + 3.91171i) q^{33} +(5.49427 - 9.51636i) q^{34} -3.66640 q^{35} +(-2.85777 + 5.60536i) q^{36} -3.97871 q^{37} +(-2.81061 + 4.86812i) q^{38} +(-1.73146 + 0.0451317i) q^{39} +(0.0984484 + 0.170518i) q^{40} +(-1.46174 - 2.53181i) q^{41} +(-12.8499 + 0.334941i) q^{42} +(-3.38682 + 5.86614i) q^{43} +5.55473 q^{44} +(1.36261 - 2.67269i) q^{45} -0.111153 q^{46} +(-2.28240 + 3.95323i) q^{47} +(-3.43468 - 5.60640i) q^{48} +(-3.22123 - 5.57934i) q^{49} +(-1.01209 - 1.75298i) q^{50} +(-4.48758 + 8.26273i) q^{51} +(-1.04864 + 1.81629i) q^{52} -2.12951 q^{53} +(4.53150 - 9.49167i) q^{54} -2.64855 q^{55} +(-0.360951 + 0.625186i) q^{56} +(2.29564 - 4.22682i) q^{57} +(-9.83459 - 17.0340i) q^{58} +(5.28938 + 9.16148i) q^{59} +(-1.89765 - 3.09751i) q^{60} +(-1.30756 + 2.26477i) q^{61} +15.1247 q^{62} +(10.9843 - 0.573013i) q^{63} -8.75834 q^{64} +(0.500000 - 0.866025i) q^{65} +(-9.28258 + 0.241956i) q^{66} +(-0.219808 - 0.380718i) q^{67} +(5.69269 + 9.86003i) q^{68} +(0.0950799 - 0.00247832i) q^{69} +(3.71071 - 6.42714i) q^{70} +5.80046 q^{71} +(-0.321594 - 0.495472i) q^{72} +13.5941 q^{73} +(4.02680 - 6.97461i) q^{74} +(0.904817 + 1.47692i) q^{75} +(-2.91211 - 5.04393i) q^{76} +(-4.85532 - 8.40965i) q^{77} +(1.67327 - 3.08090i) q^{78} +(7.95257 - 13.7743i) q^{79} +3.79599 q^{80} +(-3.66458 + 8.22015i) q^{81} +5.91762 q^{82} +(-2.85290 + 4.94137i) q^{83} +(6.35644 - 11.7038i) q^{84} +(-2.71433 - 4.70136i) q^{85} +(-6.85550 - 11.8741i) q^{86} +(8.79223 + 14.3515i) q^{87} +(-0.260746 + 0.451625i) q^{88} -8.89674 q^{89} +(3.30611 + 5.09364i) q^{90} +3.66640 q^{91} +(0.0575838 - 0.0997381i) q^{92} +(-12.9376 + 0.337226i) q^{93} +(-4.61997 - 8.00202i) q^{94} +(1.38852 + 2.40499i) q^{95} +(13.9860 - 0.364553i) q^{96} +(-8.36562 + 14.4897i) q^{97} +13.0407 q^{98} +(7.93486 - 0.413936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Introduction

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