LMFDB - Embedded newform 603.2.e.a.202.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(202,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("603.202");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.e (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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$33$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			202.3
Character	$\chi$	$=$	603.202
Dual form			603.2.e.a.403.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32675 - 2.29800i) q^{2} +(-1.72892 - 0.104057i) q^{3} +(-2.52055 + 4.36572i) q^{4} +(-1.11098 + 1.92427i) q^{5} +(2.05473 + 4.11113i) q^{6} +(-0.853017 - 1.47747i) q^{7} +8.06957 q^{8} +(2.97834 + 0.359812i) q^{9} +O(q^{10})$	\(q+(-1.32675 - 2.29800i) q^{2} +(-1.72892 - 0.104057i) q^{3} +(-2.52055 + 4.36572i) q^{4} +(-1.11098 + 1.92427i) q^{5} +(2.05473 + 4.11113i) q^{6} +(-0.853017 - 1.47747i) q^{7} +8.06957 q^{8} +(2.97834 + 0.359812i) q^{9} +5.89596 q^{10} +(0.744761 + 1.28996i) q^{11} +(4.81212 - 7.28571i) q^{12} +(2.18862 - 3.79080i) q^{13} +(-2.26349 + 3.92047i) q^{14} +(2.12102 - 3.21130i) q^{15} +(-5.66523 - 9.81247i) q^{16} -3.89554 q^{17} +(-3.12468 - 7.32163i) q^{18} +5.52922 q^{19} +(-5.60053 - 9.70041i) q^{20} +(1.32106 + 2.64319i) q^{21} +(1.97623 - 3.42293i) q^{22} +(-3.49756 + 6.05795i) q^{23} +(-13.9517 - 0.839694i) q^{24} +(0.0314685 + 0.0545050i) q^{25} -11.6150 q^{26} +(-5.11189 - 0.932004i) q^{27} +8.60028 q^{28} +(-0.0491591 - 0.0851461i) q^{29} +(-10.1937 - 0.613515i) q^{30} +(-1.27109 + 2.20159i) q^{31} +(-6.96317 + 12.0606i) q^{32} +(-1.15340 - 2.30775i) q^{33} +(5.16842 + 8.95196i) q^{34} +3.79072 q^{35} +(-9.07790 + 12.0957i) q^{36} -5.92075 q^{37} +(-7.33591 - 12.7062i) q^{38} +(-4.17841 + 6.32625i) q^{39} +(-8.96509 + 15.5280i) q^{40} +(2.48041 - 4.29620i) q^{41} +(4.32134 - 6.54266i) q^{42} +(-6.43372 - 11.1435i) q^{43} -7.50883 q^{44} +(-4.00124 + 5.33138i) q^{45} +18.5616 q^{46} +(-6.44911 - 11.1702i) q^{47} +(8.77370 + 17.5545i) q^{48} +(2.04472 - 3.54157i) q^{49} +(0.0835018 - 0.144629i) q^{50} +(6.73508 + 0.405357i) q^{51} +(11.0330 + 19.1098i) q^{52} +4.74157 q^{53} +(4.64046 + 12.9837i) q^{54} -3.30965 q^{55} +(-6.88348 - 11.9225i) q^{56} +(-9.55960 - 0.575353i) q^{57} +(-0.130444 + 0.225936i) q^{58} +(-1.98777 + 3.44292i) q^{59} +(8.67349 + 17.3540i) q^{60} +(-1.19568 - 2.07098i) q^{61} +6.74570 q^{62} +(-2.00897 - 4.70734i) q^{63} +14.2927 q^{64} +(4.86300 + 8.42296i) q^{65} +(-3.77293 + 5.71234i) q^{66} +(-0.500000 + 0.866025i) q^{67} +(9.81889 - 17.0068i) q^{68} +(6.67738 - 10.1098i) q^{69} +(-5.02935 - 8.71110i) q^{70} -14.0342 q^{71} +(24.0340 + 2.90353i) q^{72} +6.17855 q^{73} +(7.85537 + 13.6059i) q^{74} +(-0.0487350 - 0.0975095i) q^{75} +(-13.9367 + 24.1390i) q^{76} +(1.27059 - 2.20072i) q^{77} +(20.0815 + 1.20862i) q^{78} +(-1.52260 - 2.63722i) q^{79} +25.1757 q^{80} +(8.74107 + 2.14329i) q^{81} -13.1636 q^{82} +(-3.11342 - 5.39259i) q^{83} +(-14.8692 - 0.894918i) q^{84} +(4.32785 - 7.49605i) q^{85} +(-17.0719 + 29.5694i) q^{86} +(0.0761323 + 0.152326i) q^{87} +(6.00991 + 10.4095i) q^{88} -0.241076 q^{89} +(17.5602 + 2.12144i) q^{90} -7.46771 q^{91} +(-17.6315 - 30.5387i) q^{92} +(2.42671 - 3.67412i) q^{93} +(-17.1127 + 29.6401i) q^{94} +(-6.14283 + 10.6397i) q^{95} +(13.2938 - 20.1272i) q^{96} +(4.64461 + 8.04469i) q^{97} -10.8514 q^{98} +(1.75401 + 4.10993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9}+O(q^{10}) $ 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9	\( 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9} - 8 q^{11} + q^{12} - 7 q^{14} + 3 q^{15} - 33 q^{16} + 66 q^{17} - 11 q^{18} - 29 q^{20} + q^{21} - 17 q^{23} + 47 q^{24} - 33 q^{25} + 60 q^{26} - 21 q^{27} - 54 q^{28} - 39 q^{29} - 34 q^{30} - 53 q^{32} + 8 q^{33} - 6 q^{34} + 62 q^{35} - 35 q^{36} + 24 q^{37} - 30 q^{38} - 5 q^{39} - 6 q^{40} - 38 q^{41} + 65 q^{42} + 22 q^{44} - 9 q^{45} + 12 q^{46} - 58 q^{47} - 59 q^{48} - 33 q^{49} - 31 q^{50} + 26 q^{51} + 9 q^{52} + 128 q^{53} - 22 q^{54} - 36 q^{55} - 32 q^{56} - 34 q^{57} + 3 q^{58} - 39 q^{59} + 127 q^{60} + 138 q^{62} - 35 q^{63} + 132 q^{64} - 28 q^{65} - 94 q^{66} - 33 q^{67} - 62 q^{68} + 60 q^{69} - 6 q^{70} + 42 q^{71} - 34 q^{72} - 25 q^{74} + 55 q^{75} - 6 q^{76} - 91 q^{77} + 125 q^{78} + 116 q^{80} - 90 q^{82} - 61 q^{83} - 26 q^{84} + 15 q^{85} - 47 q^{86} - q^{87} - 12 q^{88} + 110 q^{89} - 91 q^{90} + 36 q^{91} - 41 q^{92} - 11 q^{93} - 21 q^{94} - 6 q^{95} + 80 q^{96} - 12 q^{97} + 80 q^{98} - 38 q^{99}+O(q^{100}) \) 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9 - 8 * q^11 + q^12 - 7 * q^14 + 3 * q^15 - 33 * q^16 + 66 * q^17 - 11 * q^18 - 29 * q^20 + q^21 - 17 * q^23 + 47 * q^24 - 33 * q^25 + 60 * q^26 - 21 * q^27 - 54 * q^28 - 39 * q^29 - 34 * q^30 - 53 * q^32 + 8 * q^33 - 6 * q^34 + 62 * q^35 - 35 * q^36 + 24 * q^37 - 30 * q^38 - 5 * q^39 - 6 * q^40 - 38 * q^41 + 65 * q^42 + 22 * q^44 - 9 * q^45 + 12 * q^46 - 58 * q^47 - 59 * q^48 - 33 * q^49 - 31 * q^50 + 26 * q^51 + 9 * q^52 + 128 * q^53 - 22 * q^54 - 36 * q^55 - 32 * q^56 - 34 * q^57 + 3 * q^58 - 39 * q^59 + 127 * q^60 + 138 * q^62 - 35 * q^63 + 132 * q^64 - 28 * q^65 - 94 * q^66 - 33 * q^67 - 62 * q^68 + 60 * q^69 - 6 * q^70 + 42 * q^71 - 34 * q^72 - 25 * q^74 + 55 * q^75 - 6 * q^76 - 91 * q^77 + 125 * q^78 + 116 * q^80 - 90 * q^82 - 61 * q^83 - 26 * q^84 + 15 * q^85 - 47 * q^86 - q^87 - 12 * q^88 + 110 * q^89 - 91 * q^90 + 36 * q^91 - 41 * q^92 - 11 * q^93 - 21 * q^94 - 6 * q^95 + 80 * q^96 - 12 * q^97 + 80 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.32675	−	2.29800i	−0.938156	−	1.62493i	−0.768907	−	0.639361i	$-0.779199\pi$
$2$	−1.32675	−	2.29800i	−0.938156	−	1.62493i	−0.169250	−	0.985573i	$-0.554134\pi$
$3$	−1.72892	−	0.104057i	−0.998194	−	0.0600772i
$3$	−1.72892	−	0.104057i	−0.998194	−	0.0600772i
$4$	−2.52055	+	4.36572i	−1.26027	+	2.18286i
$5$	−1.11098	+	1.92427i	−0.496843	+	0.860558i	−0.999993	−	0.00364135i	$-0.998841\pi$
$5$	−1.11098	+	1.92427i	−0.496843	+	0.860558i	0.503150	+	0.864199i	$0.332174\pi$
$6$	2.05473	+	4.11113i	0.838840	+	1.67836i
$7$	−0.853017	−	1.47747i	−0.322410	−	0.558431i	0.658575	−	0.752515i	$-0.271160\pi$
$7$	−0.853017	−	1.47747i	−0.322410	−	0.558431i	−0.980985	+	0.194085i	$0.937826\pi$
$8$	8.06957			2.85302
$9$	2.97834	+	0.359812i	0.992781	+	0.119937i
$10$	5.89596			1.86447
$11$	0.744761	+	1.28996i	0.224554	+	0.388939i	0.956186	−	0.292761i	$-0.0945742\pi$
$11$	0.744761	+	1.28996i	0.224554	+	0.388939i	−0.731632	+	0.681700i	$0.761241\pi$
$12$	4.81212	−	7.28571i	1.38914	−	2.10320i
$13$	2.18862	−	3.79080i	0.607013	−	1.05138i	−0.384717	−	0.923035i	$-0.625701\pi$
$13$	2.18862	−	3.79080i	0.607013	−	1.05138i	0.991730	−	0.128343i	$-0.0409658\pi$
$14$	−2.26349	+	3.92047i	−0.604942	+	1.04779i
$15$	2.12102	−	3.21130i	0.547646	−	0.829154i
$16$	−5.66523	−	9.81247i	−1.41631	−	2.45312i
$17$	−3.89554			−0.944807			−0.472403	−	0.881382i	$-0.656613\pi$
$17$	−3.89554			−0.944807			−0.472403	+	0.881382i	$0.656613\pi$
$18$	−3.12468	−	7.32163i	−0.736494	−	1.72572i
$19$	5.52922			1.26849			0.634245	−	0.773132i	$-0.281311\pi$
$19$	5.52922			1.26849			0.634245	+	0.773132i	$0.281311\pi$
$20$	−5.60053	−	9.70041i	−1.25232	−	2.16908i
$21$	1.32106	+	2.64319i	0.288279	+	0.576791i
$22$	1.97623	−	3.42293i	0.421333	−	0.729771i
$23$	−3.49756	+	6.05795i	−0.729292	+	1.26317i	0.227891	+	0.973687i	$0.426817\pi$
$23$	−3.49756	+	6.05795i	−0.729292	+	1.26317i	−0.957183	+	0.289484i	$0.906516\pi$
$24$	−13.9517	−	0.839694i	−2.84787	−	0.171402i
$25$	0.0314685	+	0.0545050i	0.00629370	+	0.0109010i
$26$	−11.6150			−2.27789
$27$	−5.11189	−	0.932004i	−0.983783	−	0.179364i
$28$	8.60028			1.62530
$29$	−0.0491591	−	0.0851461i	−0.00912862	−	0.0158112i	0.861425	−	0.507885i	$-0.169572\pi$
$29$	−0.0491591	−	0.0851461i	−0.00912862	−	0.0158112i	−0.870554	+	0.492074i	$0.836239\pi$
$30$	−10.1937	−	0.613515i	−1.86110	−	0.112012i
$31$	−1.27109	+	2.20159i	−0.228295	+	0.395418i	−0.957303	−	0.289087i	$-0.906648\pi$
$31$	−1.27109	+	2.20159i	−0.228295	+	0.395418i	0.729008	+	0.684505i	$0.239982\pi$
$32$	−6.96317	+	12.0606i	−1.23093	+	2.13203i
$33$	−1.15340	−	2.30775i	−0.200782	−	0.401727i
$34$	5.16842	+	8.95196i	0.886376	+	1.53525i
$35$	3.79072			0.640749
$36$	−9.07790	+	12.0957i	−1.51298	+	2.01595i
$37$	−5.92075			−0.973365			−0.486683	−	0.873579i	$-0.661793\pi$
$37$	−5.92075			−0.973365			−0.486683	+	0.873579i	$0.661793\pi$
$38$	−7.33591	−	12.7062i	−1.19004	−	2.06121i
$39$	−4.17841	+	6.32625i	−0.669080	+	1.01301i
$40$	−8.96509	+	15.5280i	−1.41751	+	2.45519i
$41$	2.48041	−	4.29620i	0.387375	−	0.670953i	−0.604721	−	0.796438i	$-0.706715\pi$
$41$	2.48041	−	4.29620i	0.387375	−	0.670953i	0.992096	+	0.125485i	$0.0400486\pi$
$42$	4.32134	−	6.54266i	0.666798	−	1.00955i
$43$	−6.43372	−	11.1435i	−0.981133	−	1.69937i	−0.657999	−	0.753019i	$-0.728597\pi$
$43$	−6.43372	−	11.1435i	−0.981133	−	1.69937i	−0.323134	−	0.946353i	$-0.604736\pi$
$44$	−7.50883			−1.13200
$45$	−4.00124	+	5.33138i	−0.596470	+	0.794756i
$46$	18.5616			2.73676
$47$	−6.44911	−	11.1702i	−0.940699	−	1.62934i	−0.764142	−	0.645047i	$-0.776838\pi$
$47$	−6.44911	−	11.1702i	−0.940699	−	1.62934i	−0.176556	−	0.984291i	$-0.556496\pi$
$48$	8.77370	+	17.5545i	1.26637	+	2.53378i
$49$	2.04472	−	3.54157i	0.292103	−	0.505938i
$50$	0.0835018	−	0.144629i	0.0118089	−	0.0204537i
$51$	6.73508	+	0.405357i	0.943100	+	0.0567613i
$52$	11.0330	+	19.1098i	1.53001	+	2.65005i
$53$	4.74157			0.651305			0.325652	−	0.945490i	$-0.394416\pi$
$53$	4.74157			0.651305			0.325652	+	0.945490i	$0.394416\pi$
$54$	4.64046	+	12.9837i	0.631487	+	1.76685i
$55$	−3.30965			−0.446272
$56$	−6.88348	−	11.9225i	−0.919844	−	1.59322i
$57$	−9.55960	−	0.575353i	−1.26620	−	0.0762074i
$58$	−0.130444	+	0.225936i	−0.0171282	+	0.0296668i
$59$	−1.98777	+	3.44292i	−0.258785	+	0.448229i	−0.965917	−	0.258853i	$-0.916656\pi$
$59$	−1.98777	+	3.44292i	−0.258785	+	0.448229i	0.707131	+	0.707082i	$0.249989\pi$
$60$	8.67349	+	17.3540i	1.11974	+	2.24040i
$61$	−1.19568	−	2.07098i	−0.153091	−	0.265161i	0.779271	−	0.626687i	$-0.215589\pi$
$61$	−1.19568	−	2.07098i	−0.153091	−	0.265161i	−0.932362	+	0.361525i	$0.882256\pi$
$62$	6.74570			0.856704
$63$	−2.00897	−	4.70734i	−0.253106	−	0.593069i
$64$	14.2927			1.78658
$65$	4.86300	+	8.42296i	0.603181	+	1.04474i
$66$	−3.77293	+	5.71234i	−0.464415	+	0.703140i
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i
$68$	9.81889	−	17.0068i	1.19072	−	2.06238i
$69$	6.67738	−	10.1098i	0.803862	−	1.21708i
$70$	−5.02935	−	8.71110i	−0.601123	−	1.04118i
$71$	−14.0342			−1.66556			−0.832778	−	0.553608i	$-0.813251\pi$
$71$	−14.0342			−1.66556			−0.832778	+	0.553608i	$0.813251\pi$
$72$	24.0340	+	2.90353i	2.83243	+	0.342184i
$73$	6.17855			0.723144			0.361572	−	0.932344i	$-0.382240\pi$
$73$	6.17855			0.723144			0.361572	+	0.932344i	$0.382240\pi$
$74$	7.85537	+	13.6059i	0.913169	+	1.58165i
$75$	−0.0487350	−	0.0975095i	−0.00562743	−	0.0112594i
$76$	−13.9367	+	24.1390i	−1.59865	+	2.76894i
$77$	1.27059	−	2.20072i	0.144797	−	0.250796i
$78$	20.0815	+	1.20862i	2.27378	+	0.136849i
$79$	−1.52260	−	2.63722i	−0.171306	−	0.296711i	0.767571	−	0.640964i	$-0.221465\pi$
$79$	−1.52260	−	2.63722i	−0.171306	−	0.296711i	−0.938877	+	0.344253i	$0.888132\pi$
$80$	25.1757			2.81473
$81$	8.74107	+	2.14329i	0.971230	+	0.238143i
$82$	−13.1636			−1.45367
$83$	−3.11342	−	5.39259i	−0.341742	−	0.591914i	0.643014	−	0.765854i	$-0.277683\pi$
$83$	−3.11342	−	5.39259i	−0.341742	−	0.591914i	−0.984756	+	0.173940i	$0.944350\pi$
$84$	−14.8692	−	0.894918i	−1.62237	−	0.0976435i
$85$	4.32785	−	7.49605i	0.469421	−	0.813061i
$86$	−17.0719	+	29.5694i	−1.84091	+	3.18855i
$87$	0.0761323	+	0.152326i	0.00816224	+	0.0163311i
$88$	6.00991	+	10.4095i	0.640658	+	1.10965i
$89$	−0.241076			−0.0255540			−0.0127770	−	0.999918i	$-0.504067\pi$
$89$	−0.241076			−0.0255540			−0.0127770	+	0.999918i	$0.504067\pi$
$90$	17.5602	+	2.12144i	1.85101	+	0.223619i
$91$	−7.46771			−0.782828
$92$	−17.6315	−	30.5387i	−1.83822	−	3.18388i
$93$	2.42671	−	3.67412i	0.251638	−	0.380988i
$94$	−17.1127	+	29.6401i	−1.76504	+	3.05715i
$95$	−6.14283	+	10.6397i	−0.630241	+	1.09161i
$96$	13.2938	−	20.1272i	1.35679	−	2.05422i
$97$	4.64461	+	8.04469i	0.471588	+	0.816815i	0.999472	−	0.0325021i	$-0.0103476\pi$
$97$	4.64461	+	8.04469i	0.471588	+	0.816815i	−0.527883	+	0.849317i	$0.677014\pi$
$98$	−10.8514			−1.09615
$99$	1.75401	+	4.10993i	0.176285	+	0.413064i
$100$	−0.317271			−0.0317271
$101$	−1.90631	−	3.30183i	−0.189685	−	0.328544i	0.755460	−	0.655194i	$-0.227413\pi$
$101$	−1.90631	−	3.30183i	−0.189685	−	0.328544i	−0.945145	+	0.326651i	$0.894080\pi$
$102$	−8.00428	−	16.0151i	−0.792542	−	1.58573i
$103$	7.10371	−	12.3040i	0.699950	−	1.21235i	−0.268534	−	0.963270i	$-0.586539\pi$
$103$	7.10371	−	12.3040i	0.699950	−	1.21235i	0.968483	−	0.249078i	$-0.0801276\pi$
$104$	17.6612	−	30.5901i	1.73182	−	2.99961i
$105$	−6.55386	−	0.394450i	−0.639592	−	0.0384944i
$106$	−6.29089	−	10.8961i	−0.611025	−	1.05833i
$107$	−8.42090			−0.814079			−0.407039	−	0.913411i	$-0.633439\pi$
$107$	−8.42090			−0.814079			−0.407039	+	0.913411i	$0.633439\pi$
$108$	16.9536	−	19.9679i	1.63136	−	1.92141i
$109$	−7.78216			−0.745396			−0.372698	−	0.927953i	$-0.621567\pi$
$109$	−7.78216			−0.745396			−0.372698	+	0.927953i	$0.621567\pi$
$110$	4.39108	+	7.60558i	0.418673	+	0.725163i
$111$	10.2365	+	0.616094i	0.971607	+	0.0584770i
$112$	−9.66508	+	16.7404i	−0.913264	+	1.58182i
$113$	8.08614	−	14.0056i	0.760681	−	1.31754i	−0.181820	−	0.983332i	$-0.558199\pi$
$113$	8.08614	−	14.0056i	0.760681	−	1.31754i	0.942500	−	0.334205i	$-0.108468\pi$
$114$	11.3611	+	22.7313i	1.06406	+	2.12899i
$115$	−7.77141	−	13.4605i	−0.724687	−	1.25520i
$116$	0.495632			0.0460183
$117$	7.88243	−	10.5028i	0.728731	−	0.970984i
$118$	10.5491			0.971124
$119$	3.32296	+	5.75553i	0.304615	+	0.527609i
$120$	17.1157	−	25.9138i	1.56245	−	2.36560i
$121$	4.39066	−	7.60485i	0.399151	−	0.691350i
$122$	−3.17274	+	5.49535i	−0.287247	+	0.497526i
$123$	−4.73548	+	7.16969i	−0.426984	+	0.646469i
$124$	−6.40769	−	11.0985i	−0.575428	−	0.996670i
$125$	−11.2496			−1.00619
$126$	−8.15207	+	10.8621i	−0.726245	+	0.967672i
$127$	−8.70573			−0.772508			−0.386254	−	0.922392i	$-0.626231\pi$
$127$	−8.70573			−0.772508			−0.386254	+	0.922392i	$0.626231\pi$
$128$	−5.03652	−	8.72351i	−0.445170	−	0.771057i
$129$	9.96384	+	19.9358i	0.877267	+	1.75525i
$130$	12.9040	−	22.3504i	1.13176	−	1.96026i
$131$	−1.60465	+	2.77934i	−0.140199	+	0.242832i	−0.927571	−	0.373646i	$-0.878108\pi$
$131$	−1.60465	+	2.77934i	−0.140199	+	0.242832i	0.787373	+	0.616478i	$0.211441\pi$
$132$	12.9822	+	0.781344i	1.12995	+	0.0680073i
$133$	−4.71652	−	8.16925i	−0.408974	−	0.708364i
$134$	2.65351			0.229228
$135$	7.47260	−	8.80119i	0.643139	−	0.757486i
$136$	−31.4353			−2.69556
$137$	−0.963977	−	1.66966i	−0.0823581	−	0.142648i	0.821904	−	0.569626i	$-0.192912\pi$
$137$	−0.963977	−	1.66966i	−0.0823581	−	0.142648i	−0.904262	+	0.426977i	$0.859578\pi$
$138$	−32.0916	−	1.93146i	−2.73182	−	0.164417i
$139$	6.21821	−	10.7703i	0.527422	−	0.913522i	−0.472067	−	0.881563i	$-0.656492\pi$
$139$	6.21821	−	10.7703i	0.527422	−	0.913522i	0.999489	−	0.0319592i	$-0.0101747\pi$
$140$	−9.55470	+	16.5492i	−0.807520	+	1.39866i
$141$	9.98767	+	19.9834i	0.841114	+	1.68291i
$142$	18.6199	+	32.2507i	1.56255	+	2.70642i
$143$	6.51999			0.545229
$144$	−13.3424	−	31.2633i	−1.11186	−	2.60528i
$145$	0.218458			0.0181420
$146$	−8.19741	−	14.1983i	−0.678422	−	1.17506i
$147$	−3.90369	+	5.91033i	−0.321971	+	0.487475i
$148$	14.9235	−	25.8483i	1.22671	−	2.12472i
$149$	7.28259	−	12.6138i	0.596613	−	1.03336i	−0.396704	−	0.917947i	$-0.629846\pi$
$149$	7.28259	−	12.6138i	0.596613	−	1.03336i	0.993317	−	0.115417i	$-0.0368206\pi$
$150$	−0.159418	+	0.241364i	−0.0130164	+	0.0197073i
$151$	−5.36217	−	9.28755i	−0.436367	−	0.755810i	0.561039	−	0.827789i	$-0.310402\pi$
$151$	−5.36217	−	9.28755i	−0.436367	−	0.755810i	−0.997406	+	0.0719795i	$0.977068\pi$
$152$	44.6185			3.61904
$153$	−11.6023	−	1.40166i	−0.937987	−	0.113318i
$154$	−6.74303			−0.543369
$155$	−2.82430	−	4.89183i	−0.226853	−	0.392921i
$156$	−17.0867	−	34.1874i	−1.36803	−	2.73718i
$157$	−8.57492	+	14.8522i	−0.684353	+	1.18533i	0.289287	+	0.957243i	$0.406582\pi$
$157$	−8.57492	+	14.8522i	−0.684353	+	1.18533i	−0.973640	+	0.228092i	$0.926751\pi$
$158$	−4.04023	+	6.99789i	−0.321424	+	0.556722i
$159$	−8.19780	−	0.493392i	−0.650128	−	0.0391286i
$160$	−15.4718	−	26.7980i	−1.22315	−	2.11856i
$161$	11.9339			0.940524
$162$	−6.67196	−	22.9306i	−0.524198	−	1.80160i
$163$	−24.3705			−1.90885			−0.954424	−	0.298454i	$-0.903529\pi$
$163$	−24.3705			−1.90885			−0.954424	+	0.298454i	$0.903529\pi$
$164$	12.5040	+	21.6575i	0.976397	+	1.69117i
$165$	5.72212	+	0.344391i	0.445466	+	0.0268108i
$166$	−8.26147	+	14.3093i	−0.641214	+	1.11062i
$167$	0.234407	−	0.406006i	0.0181390	−	0.0314177i	−0.856813	−	0.515627i	$-0.827559\pi$
$167$	0.234407	−	0.406006i	0.0181390	−	0.0314177i	0.874952	+	0.484209i	$0.160893\pi$
$168$	10.6604	+	21.3294i	0.822467	+	1.64560i
$169$	−3.08008	−	5.33486i	−0.236930	−	0.410374i
$170$	−22.9679			−1.76156
$171$	16.4679	+	1.98948i	1.25933	+	0.152139i
$172$	64.8660			4.94599
$173$	12.0353	+	20.8458i	0.915029	+	1.58488i	0.806859	+	0.590744i	$0.201166\pi$
$173$	12.0353	+	20.8458i	0.915029	+	1.58488i	0.108170	+	0.994132i	$0.465501\pi$
$174$	0.249038	−	0.377052i	0.0188795	−	0.0285842i
$175$	0.0536863	−	0.0929874i	0.00405830	−	0.00702919i
$176$	8.43850	−	14.6159i	0.636076	−	1.10172i
$177$	3.79496	−	5.74569i	0.285246	−	0.431873i
$178$	0.319848	+	0.553993i	0.0239736	+	0.0415235i
$179$	−8.62015			−0.644300			−0.322150	−	0.946689i	$-0.604406\pi$
$179$	−8.62015			−0.644300			−0.322150	+	0.946689i	$0.604406\pi$
$180$	−13.1900	−	30.9063i	−0.983124	−	2.30362i
$181$	−24.6525			−1.83241			−0.916204	−	0.400713i	$-0.868763\pi$
$181$	−24.6525			−1.83241			−0.916204	+	0.400713i	$0.868763\pi$
$182$	9.90781	+	17.1608i	0.734415	+	1.27204i
$183$	1.85174	+	3.70498i	0.136884	+	0.273880i
$184$	−28.2238	+	48.8851i	−2.08069	+	3.60386i
$185$	6.57780	−	11.3931i	0.483610	−	0.837637i
$186$	−11.6628	−	0.701935i	−0.855157	−	0.0514684i
$187$	−2.90125	−	5.02510i	−0.212160	−	0.367472i
$188$	65.0211			4.74215
$189$	2.98352	+	8.34767i	0.217019	+	0.607203i
$190$	32.6001			2.36506
$191$	−9.07601	−	15.7201i	−0.656717	−	1.13747i	−0.981460	−	0.191665i	$-0.938611\pi$
$191$	−9.07601	−	15.7201i	−0.656717	−	1.13747i	0.324744	−	0.945802i	$-0.394722\pi$
$192$	−24.7109	−	1.48725i	−1.78336	−	0.107333i
$193$	3.10732	−	5.38204i	0.223670	−	0.387408i	−0.732250	−	0.681036i	$-0.761530\pi$
$193$	3.10732	−	5.38204i	0.223670	−	0.387408i	0.955920	+	0.293629i	$0.0948629\pi$
$194$	12.3245	−	21.3466i	0.884847	−	1.53260i
$195$	−7.53128	−	15.0687i	−0.539326	−	1.07909i
$196$	10.3077	+	17.8534i	0.736261	+	1.27524i
$197$	9.19198			0.654901			0.327451	−	0.944868i	$-0.393810\pi$
$197$	9.19198			0.654901			0.327451	+	0.944868i	$0.393810\pi$
$198$	7.11750	−	9.48359i	0.505819	−	0.673969i
$199$	25.8112			1.82971			0.914853	−	0.403786i	$-0.132306\pi$
$199$	25.8112			1.82971			0.914853	+	0.403786i	$0.132306\pi$
$200$	0.253937	+	0.439832i	0.0179561	+	0.0311008i
$201$	0.954577	−	1.44526i	0.0673307	−	0.101941i
$202$	−5.05841	+	8.76142i	−0.355908	+	0.616451i
$203$	−0.0838672	+	0.145262i	−0.00588632	+	0.0101954i
$204$	−18.7458	+	28.3817i	−1.31247	+	1.98712i
$205$	5.51135	+	9.54593i	0.384929	+	0.666717i
$206$	−37.6995			−2.62665
$207$	−12.5967	+	16.7842i	−0.875529	+	1.16658i
$208$	−49.5961			−3.43887
$209$	4.11795	+	7.13250i	0.284845	+	0.493365i
$210$	7.78891	+	15.5841i	0.537486	+	1.07541i
$211$	1.07847	−	1.86797i	0.0742451	−	0.128596i	−0.826513	−	0.562918i	$-0.809679\pi$
$211$	1.07847	−	1.86797i	0.0742451	−	0.128596i	0.900758	+	0.434322i	$0.143012\pi$
$212$	−11.9514	+	20.7004i	−0.820822	+	1.42171i
$213$	24.2641	+	1.46036i	1.66255	+	0.100062i
$214$	11.1725	+	19.3513i	0.763733	+	1.32282i
$215$	28.5908			1.94988
$216$	−41.2507	−	7.52087i	−2.80676	−	0.511731i
$217$	4.33705			0.294418
$218$	10.3250	+	17.8834i	0.699298	+	1.21122i
$219$	−10.6822	−	0.642919i	−0.721838	−	0.0434445i
$220$	8.34212	−	14.4490i	0.562426	−	0.974150i
$221$	−8.52584	+	14.7672i	−0.573510	+	0.993348i
$222$	−12.1655	−	24.3410i	−0.816498	−	1.63366i
$223$	11.5877	+	20.0704i	0.775967	+	1.34401i	0.934249	+	0.356621i	$0.116071\pi$
$223$	11.5877	+	20.0704i	0.775967	+	1.34401i	−0.158282	+	0.987394i	$0.550595\pi$
$224$	23.7588			1.58745
$225$	0.0741124	+	0.173657i	0.00494083	+	0.0115772i
$226$	−42.9133			−2.85455
$227$	−4.55861	−	7.89574i	−0.302565	−	0.524059i	0.674151	−	0.738594i	$-0.264510\pi$
$227$	−4.55861	−	7.89574i	−0.302565	−	0.524059i	−0.976716	+	0.214535i	$0.931176\pi$
$228$	26.6073	−	40.2843i	1.76211	−	2.66789i
$229$	7.54613	−	13.0703i	0.498662	−	0.863708i	−0.501337	−	0.865252i	$-0.667158\pi$
$229$	7.54613	−	13.0703i	0.498662	−	0.863708i	0.999999	+	0.00154425i	$0.000491551\pi$
$230$	−20.6215	+	35.7175i	−1.35974	+	2.35514i
$231$	−2.42575	+	3.67267i	−0.159602	+	0.241644i
$232$	−0.396693	−	0.687093i	−0.0260442	−	0.0451099i
$233$	6.59402			0.431989			0.215994	−	0.976395i	$-0.430701\pi$
$233$	6.59402			0.431989			0.215994	+	0.976395i	$0.430701\pi$
$234$	−34.5935	−	4.17922i	−2.26145	−	0.273204i
$235$	28.6592			1.86952
$236$	−10.0205	−	17.3561i	−0.652281	−	1.12978i
$237$	2.35804	+	4.71799i	0.153171	+	0.306467i
$238$	8.81750	−	15.2724i	0.571553	−	0.989959i
$239$	0.813439	−	1.40892i	0.0526170	−	0.0911354i	−0.838517	−	0.544875i	$-0.816577\pi$
$239$	0.813439	−	1.40892i	0.0526170	−	0.0911354i	0.891134	+	0.453740i	$0.149910\pi$
$240$	−43.5269	−	2.61971i	−2.80965	−	0.169101i
$241$	−6.31647	−	10.9404i	−0.406880	−	0.704736i	0.587659	−	0.809109i	$-0.300050\pi$
$241$	−6.31647	−	10.9404i	−0.406880	−	0.704736i	−0.994538	+	0.104373i	$0.966716\pi$
$242$	−23.3013			−1.49786
$243$	−14.8896	−	4.61515i	−0.955169	−	0.296062i
$244$	12.0551			0.771747
$245$	4.54328	+	7.86918i	0.290259	+	0.502744i
$246$	22.7588	+	1.36976i	1.45105	+	0.0873326i
$247$	12.1013	−	20.9601i	0.769990	−	1.33366i
$248$	−10.2572	+	17.7659i	−0.651330	+	1.12814i
$249$	4.82172	+	9.64735i	0.305564	+	0.611376i
$250$	14.9254	+	25.8516i	0.943967	+	1.63500i
$251$	14.3316			0.904605			0.452302	−	0.891865i	$-0.350603\pi$
$251$	14.3316			0.904605			0.452302	+	0.891865i	$0.350603\pi$
$252$	25.6146	+	3.09449i	1.61357	+	0.194934i
$253$	−10.4194			−0.655062
$254$	11.5504	+	20.0058i	0.724734	+	1.25528i
$255$	−8.26252	+	12.5097i	−0.517419	+	0.783391i
$256$	0.928230	−	1.60774i	0.0580144	−	0.100484i
$257$	3.14849	−	5.45334i	0.196397	−	0.340170i	−0.750960	−	0.660347i	$-0.770409\pi$
$257$	3.14849	−	5.45334i	0.196397	−	0.340170i	0.947358	+	0.320177i	$0.103742\pi$
$258$	32.5929	−	49.3468i	2.02915	−	3.07220i
$259$	5.05050	+	8.74772i	0.313823	+	0.543557i
$260$	−49.0297			−3.04069
$261$	−0.115776	−	0.271283i	−0.00716637	−	0.0167920i
$262$	8.51590			0.526114
$263$	3.76245	+	6.51675i	0.232002	+	0.401840i	0.958397	−	0.285438i	$-0.0921389\pi$
$263$	3.76245	+	6.51675i	0.232002	+	0.401840i	−0.726395	+	0.687278i	$0.758806\pi$
$264$	−9.30748	−	18.6225i	−0.572836	−	1.14614i
$265$	−5.26776	+	9.12404i	−0.323596	+	0.560485i
$266$	−12.5153	+	21.6772i	−0.767363	+	1.32911i
$267$	0.416801	+	0.0250856i	0.0255078	+	0.00153521i
$268$	−2.52055	−	4.36572i	−0.153967	−	0.266679i
$269$	−13.4606			−0.820706			−0.410353	−	0.911927i	$-0.634594\pi$
$269$	−13.4606			−0.820706			−0.410353	+	0.911927i	$0.634594\pi$
$270$	−30.1395	−	5.49506i	−1.83423	−	0.334419i
$271$	24.2763			1.47468			0.737342	−	0.675520i	$-0.236081\pi$
$271$	24.2763			1.47468			0.737342	+	0.675520i	$0.236081\pi$
$272$	22.0691	+	38.2249i	1.33814	+	2.31772i
$273$	12.9111	+	0.777066i	0.781414	+	0.0470301i
$274$	−2.55792	+	4.43045i	−0.154530	+	0.267653i
$275$	−0.0468730	+	0.0811865i	−0.00282655	+	0.00489573i
$276$	27.3058	+	54.6338i	1.64362	+	3.28857i
$277$	11.4073	+	19.7581i	0.685399	+	1.18715i	0.973311	+	0.229490i	$0.0737057\pi$
$277$	11.4073	+	19.7581i	0.685399	+	1.18715i	−0.287912	+	0.957657i	$0.592961\pi$
$278$	−33.0001			−1.97922
$279$	−4.57791	+	6.09975i	−0.274072	+	0.365183i
$280$	30.5895			1.82807
$281$	−0.538744	−	0.933132i	−0.0321388	−	0.0556660i	0.849509	−	0.527575i	$-0.176899\pi$
$281$	−0.538744	−	0.933132i	−0.0321388	−	0.0556660i	−0.881647	+	0.471909i	$0.843565\pi$
$282$	32.6709	−	49.4648i	1.94552	−	2.94559i
$283$	−8.07343	+	13.9836i	−0.479916	+	0.831238i	−0.999735	−	0.0230383i	$-0.992666\pi$
$283$	−8.07343	+	13.9836i	−0.479916	+	0.831238i	0.519819	+	0.854276i	$0.325999\pi$
$284$	35.3739	−	61.2694i	2.09906	−	3.63567i
$285$	11.7276	−	17.7560i	0.694683	−	1.05177i
$286$	−8.65041	−	14.9830i	−0.511510	−	0.885961i
$287$	−8.46333			−0.499574
$288$	−25.0782	+	33.4151i	−1.47775	+	1.96900i
$289$	−1.82479			−0.107340
$290$	−0.289840	−	0.502018i	−0.0170200	−	0.0294795i
$291$	−7.19306	−	14.3920i	−0.421664	−	0.843671i
$292$	−15.5733	+	26.9738i	−0.911360	+	1.57852i
$293$	7.89333	−	13.6717i	0.461134	−	0.798707i	−0.537884	−	0.843019i	$-0.680776\pi$
$293$	7.89333	−	13.6717i	0.461134	−	0.798707i	0.999018	+	0.0443120i	$0.0141096\pi$
$294$	18.7612	+	1.12916i	1.09417	+	0.0658539i
$295$	−4.41672	−	7.64999i	−0.257151	−	0.445399i
$296$	−47.7779			−2.77703
$297$	−2.60488	−	7.28827i	−0.151151	−	0.422908i
$298$	−38.6488			−2.23886
$299$	15.3096	+	26.5171i	0.885379	+	1.53352i
$300$	0.548538	+	0.0330142i	0.0316698	+	0.00190608i
$301$	−10.9761	+	19.0112i	−0.632654	+	1.09579i
$302$	−14.2285	+	24.6446i	−0.818761	+	1.41814i
$303$	2.95228	+	5.90696i	0.169604	+	0.339346i
$304$	−31.3243	−	54.2554i	−1.79657	−	3.11176i
$305$	5.31348			0.304249
$306$	12.1723	+	28.5217i	0.695844	+	1.63048i
$307$	−7.14312			−0.407679			−0.203840	−	0.979004i	$-0.565342\pi$
$307$	−7.14312			−0.407679			−0.203840	+	0.979004i	$0.565342\pi$
$308$	6.40516	+	11.0941i	0.364968	+	0.632143i
$309$	−13.5621	+	20.5335i	−0.771520	+	1.16811i
$310$	−7.49430	+	12.9805i	−0.425648	+	0.737243i
$311$	−7.08691	+	12.2749i	−0.401862	+	0.696045i	−0.993951	−	0.109828i	$-0.964970\pi$
$311$	−7.08691	+	12.2749i	−0.401862	+	0.696045i	0.592089	+	0.805873i	$0.298303\pi$
$312$	−33.7179	+	51.0501i	−1.90890	+	2.89014i
$313$	−8.77934	−	15.2063i	−0.496238	−	0.859509i	0.503753	−	0.863848i	$-0.331952\pi$
$313$	−8.77934	−	15.2063i	−0.496238	−	0.859509i	−0.999991	+	0.00433876i	$0.998619\pi$
$314$	45.5072			2.56812
$315$	11.2901	+	1.36395i	0.636124	+	0.0768498i
$316$	15.3512			0.863571
$317$	−8.98731	−	15.5665i	−0.504778	−	0.874301i	−0.999985	−	0.00552562i	$-0.998241\pi$
$317$	−8.98731	−	15.5665i	−0.504778	−	0.874301i	0.495207	−	0.868775i	$-0.335092\pi$
$318$	9.74265	+	19.4932i	0.546340	+	1.09312i
$319$	0.0732237	−	0.126827i	0.00409974	−	0.00710095i
$320$	−15.8788	+	27.5029i	−0.887652	+	1.53746i
$321$	14.5591	+	0.876251i	0.812609	+	0.0489076i
$322$	−15.8334	−	27.4242i	−0.882359	−	1.52829i
$323$	−21.5393			−1.19848
$324$	−31.3893	+	32.7588i	−1.74385	+	1.81993i
$325$	0.275490			0.0152814
$326$	32.3337	+	56.0036i	1.79080	+	3.10175i
$327$	13.4547	+	0.809786i	0.744049	+	0.0447813i
$328$	20.0158	−	34.6685i	1.10519	−	1.91425i
$329$	−11.0024	+	19.0567i	−0.606582	+	1.05063i
$330$	−6.80043	−	13.6064i	−0.374351	−	0.749006i
$331$	−9.66082	−	16.7330i	−0.531007	−	0.919731i	−0.999345	−	0.0361815i	$-0.988481\pi$
$331$	−9.66082	−	16.7330i	−0.531007	−	0.919731i	0.468339	−	0.883549i	$-0.344853\pi$
$332$	31.3901			1.72275
$333$	−17.6340	−	2.13036i	−0.966339	−	0.116743i
$334$	−1.24400			−0.0680688
$335$	−1.11098	−	1.92427i	−0.0606991	−	0.105134i
$336$	18.4521	−	27.9372i	1.00665	−	1.52410i
$337$	−2.17307	+	3.76388i	−0.118375	+	0.205031i	−0.919124	−	0.393969i	$-0.871102\pi$
$337$	−2.17307	+	3.76388i	−0.118375	+	0.205031i	0.800749	+	0.599000i	$0.204435\pi$
$338$	−8.17303	+	14.1561i	−0.444554	+	0.769990i
$339$	−15.4377	+	23.3732i	−0.838460	+	1.26946i
$340$	21.8171	+	37.7883i	1.18320	+	2.04936i
$341$	−3.78664			−0.205058
$342$	−17.2770	−	40.4829i	−0.934236	−	2.18907i
$343$	−18.9190			−1.02153
$344$	−51.9174	−	89.9235i	−2.79920	−	4.84835i
$345$	12.0355	+	24.0808i	0.647970	+	1.29647i
$346$	31.9358	−	55.3145i	1.71688	−	2.97372i
$347$	16.9930	−	29.4327i	0.912232	−	1.58003i	0.101328	−	0.994853i	$-0.467691\pi$
$347$	16.9930	−	29.4327i	0.912232	−	1.58003i	0.810904	−	0.585179i	$-0.198976\pi$
$348$	−0.856909	−	0.0515739i	−0.0459352	−	0.00276465i
$349$	−1.95001	−	3.37752i	−0.104382	−	0.180795i	0.809104	−	0.587666i	$-0.199953\pi$
$349$	−1.95001	−	3.37752i	−0.104382	−	0.180795i	−0.913485	+	0.406871i	$0.866620\pi$
$350$	−0.284914			−0.0152293
$351$	−14.7210	+	17.3383i	−0.785748	+	0.925450i
$352$	−20.7436			−1.10564
$353$	8.52171	+	14.7600i	0.453565	+	0.785597i	0.998604	−	0.0528130i	$-0.0168187\pi$
$353$	8.52171	+	14.7600i	0.453565	+	0.785597i	−0.545040	+	0.838410i	$0.683485\pi$
$354$	−18.2386	−	1.09771i	−0.969370	−	0.0583424i
$355$	15.5917	−	27.0056i	0.827520	−	1.43331i
$356$	0.607643	−	1.05247i	0.0322050	−	0.0557807i
$357$	−5.14624	−	10.2966i	−0.272368	−	0.544956i
$358$	11.4368	+	19.8091i	0.604454	+	1.04695i
$359$	−21.3515			−1.12689			−0.563443	−	0.826155i	$-0.690524\pi$
$359$	−21.3515			−1.12689			−0.563443	+	0.826155i	$0.690524\pi$
$360$	−32.2883	+	43.0220i	−1.70174	+	2.26746i
$361$	11.5723			0.609069
$362$	32.7078	+	56.6516i	1.71908	+	2.97754i
$363$	−8.38245	+	12.6913i	−0.439964	+	0.666121i
$364$	18.8227	−	32.6019i	0.986579	−	1.70880i
$365$	−6.86421	+	11.8892i	−0.359289	+	0.622307i
$366$	6.05725	−	9.17089i	0.316618	−	0.479370i
$367$	2.67093	+	4.62618i	0.139421	+	0.241485i	0.927278	−	0.374374i	$-0.122142\pi$
$367$	2.67093	+	4.62618i	0.139421	+	0.241485i	−0.787856	+	0.615859i	$0.788809\pi$
$368$	79.2580			4.13161
$369$	8.93334	−	11.9031i	0.465051	−	0.619649i
$370$	−34.9085			−1.81481
$371$	−4.04464	−	7.00552i	−0.209987	−	0.363708i
$372$	9.92354	+	19.8551i	0.514511	+	1.02944i
$373$	−10.3910	+	17.9977i	−0.538025	+	0.931887i	0.460985	+	0.887408i	$0.347496\pi$
$373$	−10.3910	+	17.9977i	−0.538025	+	0.931887i	−0.999010	+	0.0444791i	$0.985837\pi$
$374$	−7.69847	+	13.3341i	−0.398079	+	0.689492i
$375$	19.4497	+	1.17060i	1.00438	+	0.0604493i
$376$	−52.0415	−	90.1386i	−2.68384	−	4.64854i
$377$	−0.430362			−0.0221648
$378$	15.2246	−	17.9314i	0.783068	−	0.922293i
$379$	−24.6715			−1.26729			−0.633645	−	0.773624i	$-0.718442\pi$
$379$	−24.6715			−1.26729			−0.633645	+	0.773624i	$0.718442\pi$
$380$	−30.9666	−	53.6357i	−1.58855	−	2.75145i
$381$	15.0515	+	0.905890i	0.771113	+	0.0464101i
$382$	−24.0832	+	41.7134i	−1.23221	+	2.13424i
$383$	−10.2265	+	17.7128i	−0.522550	+	0.905084i	0.477105	+	0.878846i	$0.341686\pi$
$383$	−10.2265	+	17.7128i	−0.522550	+	0.905084i	−0.999656	+	0.0262376i	$0.991647\pi$
$384$	7.80001	+	15.6064i	0.398043	+	0.796409i
$385$	2.82318	+	4.88990i	0.143883	+	0.249212i
$386$	−16.4906			−0.839350
$387$	−15.1523	−	35.5042i	−0.770232	−	1.80478i
$388$	−46.8278			−2.37732
$389$	−13.5395	−	23.4511i	−0.686481	−	1.18902i	−0.972969	−	0.230936i	$-0.925821\pi$
$389$	−13.5395	−	23.4511i	−0.686481	−	1.18902i	0.286488	−	0.958084i	$-0.407512\pi$
$390$	−24.6357	+	37.2993i	−1.24748	+	1.88872i
$391$	13.6249	−	23.5990i	0.689040	−	1.19345i
$392$	16.5001	−	28.5789i	0.833378	−	1.44345i
$393$	3.06352	−	4.63828i	0.154534	−	0.233970i
$394$	−12.1955	−	21.1232i	−0.614400	−	1.06417i
$395$	6.76629			0.340449
$396$	−22.3639	−	2.70177i	−1.12383	−	0.135769i
$397$	−9.73033			−0.488351			−0.244176	−	0.969731i	$-0.578517\pi$
$397$	−9.73033			−0.488351			−0.244176	+	0.969731i	$0.578517\pi$
$398$	−34.2451	−	59.3142i	−1.71655	−	2.97315i
$399$	7.30443	+	14.6148i	0.365679	+	0.731655i
$400$	0.356553	−	0.617567i	0.0178276	−	0.0308784i
$401$	5.09881	−	8.83140i	0.254623	−	0.441019i	−0.710170	−	0.704030i	$-0.751382\pi$
$401$	5.09881	−	8.83140i	0.254623	−	0.441019i	0.964793	+	0.263011i	$0.0847154\pi$
$402$	−4.58771	−	0.276115i	−0.228814	−	0.0137714i
$403$	5.56386	+	9.63689i	0.277156	+	0.480048i
$404$	19.2198			0.956220
$405$	−13.8354	+	14.4390i	−0.687485	+	0.717480i
$406$	0.445084			0.0220892
$407$	−4.40954	−	7.63755i	−0.218573	−	0.378580i
$408$	54.3492	+	3.27106i	2.69069	+	0.161942i
$409$	−18.3665	+	31.8117i	−0.908165	+	1.57299i	−0.0915540	+	0.995800i	$0.529183\pi$
$409$	−18.3665	+	31.8117i	−0.908165	+	1.57299i	−0.816611	+	0.577188i	$0.804150\pi$
$410$	14.6244	−	25.3302i	0.722248	−	1.25097i
$411$	1.49290	+	2.98702i	0.0736394	+	0.147339i
$412$	35.8105	+	62.0256i	1.76426	+	3.05578i
$413$	6.78240			0.333740
$414$	55.2828	+	6.67869i	2.71700	+	0.328240i
$415$	13.8357			0.679168
$416$	30.4794	+	52.7919i	1.49438	+	2.58833i
$417$	−11.8715	+	17.9739i	−0.581351	+	0.880186i
$418$	10.9270	−	18.9261i	0.534458	−	0.925708i
$419$	−0.773505	+	1.33975i	−0.0377882	+	0.0654510i	−0.884301	−	0.466917i	$-0.845365\pi$
$419$	−0.773505	+	1.33975i	−0.0377882	+	0.0654510i	0.846513	+	0.532368i	$0.178698\pi$
$420$	18.2414	−	27.6181i	0.890089	−	1.34763i
$421$	9.08176	+	15.7301i	0.442618	+	0.766637i	0.997883	−	0.0650367i	$-0.0207164\pi$
$421$	9.08176	+	15.7301i	0.442618	+	0.766637i	−0.555265	+	0.831674i	$0.687383\pi$
$422$	−5.72346			−0.278614
$423$	−15.1885	−	35.5891i	−0.738490	−	1.73040i
$424$	38.2624			1.85819
$425$	−0.122587	−	0.212326i	−0.00594633	−	0.0102993i
$426$	−28.8365	−	57.6965i	−1.39713	−	2.79540i
$427$	−2.03987	+	3.53316i	−0.0987162	+	0.170981i
$428$	21.2253	−	36.7633i	1.02596	−	1.77702i
$429$	−11.2726	−	0.678449i	−0.544244	−	0.0327558i
$430$	−37.9329	−	65.7018i	−1.82929	−	3.16842i
$431$	22.6688			1.09192			0.545960	−	0.837811i	$-0.316165\pi$
$431$	22.6688			1.09192			0.545960	+	0.837811i	$0.316165\pi$
$432$	19.8148	+	55.4403i	0.953338	+	2.66737i
$433$	29.4783			1.41664			0.708318	−	0.705894i	$-0.249455\pi$
$433$	29.4783			1.41664			0.708318	+	0.705894i	$0.249455\pi$
$434$	−5.75419	−	9.96656i	−0.276210	−	0.478410i
$435$	−0.377698	−	0.0227321i	−0.0181092	−	0.00108992i
$436$	19.6153	−	33.9747i	0.939403	−	1.62709i
$437$	−19.3388	+	33.4958i	−0.925100	+	1.60232i
$438$	12.6952	+	25.4008i	0.606602	+	1.21370i
$439$	7.35154	+	12.7332i	0.350870	+	0.607724i	0.986402	−	0.164350i	$-0.0525526\pi$
$439$	7.35154	+	12.7332i	0.350870	+	0.607724i	−0.635532	+	0.772074i	$0.719219\pi$
$440$	−26.7074			−1.27323
$441$	7.36419	−	9.81229i	0.350676	−	0.467252i
$442$	45.2467			2.15217
$443$	−16.9563	−	29.3692i	−0.805620	−	1.39537i	−0.915872	−	0.401470i	$-0.868499\pi$
$443$	−16.9563	−	29.3692i	−0.805620	−	1.39537i	0.110252	−	0.993904i	$-0.464834\pi$
$444$	−28.4913	+	43.1368i	−1.35214	+	2.04718i
$445$	0.267829	−	0.463894i	0.0126963	−	0.0219907i
$446$	30.7479	−	53.2570i	1.45596	−	2.52179i
$447$	−13.9036	+	21.0505i	−0.657617	+	0.995655i
$448$	−12.1919	−	21.1170i	−0.576013	−	0.997683i
$449$	25.6459			1.21030			0.605152	−	0.796110i	$-0.293112\pi$
$449$	25.6459			1.21030			0.605152	+	0.796110i	$0.293112\pi$
$450$	0.300737	−	0.400711i	0.0141769	−	0.0188897i
$451$	7.38925			0.347946
$452$	40.7630	+	70.6037i	1.91733	+	3.32092i
$453$	8.30434	+	16.6154i	0.390172	+	0.780660i
$454$	−12.0963	+	20.9514i	−0.567707	+	0.983298i
$455$	8.29644	−	14.3699i	0.388943	−	0.673669i
$456$	−77.1419	−	4.64285i	−3.61250	−	0.217422i
$457$	8.00811	+	13.8704i	0.374603	+	0.648832i	0.990268	−	0.139176i	$-0.0444455\pi$
$457$	8.00811	+	13.8704i	0.374603	+	0.648832i	−0.615664	+	0.788009i	$0.711112\pi$
$458$	−40.0474			−1.87129
$459$	19.9135	+	3.63066i	0.929484	+	0.169465i
$460$	78.3528			3.65322
$461$	−20.6610	−	35.7860i	−0.962280	−	1.66672i	−0.716752	−	0.697328i	$-0.754372\pi$
$461$	−20.6610	−	35.7860i	−0.962280	−	1.66672i	−0.245528	−	0.969389i	$-0.578961\pi$
$462$	11.6582	+	0.701658i	0.542387	+	0.0326441i
$463$	5.06260	−	8.76868i	0.235279	−	0.407515i	−0.724075	−	0.689722i	$-0.757733\pi$
$463$	5.06260	−	8.76868i	0.235279	−	0.407515i	0.959354	+	0.282206i	$0.0910663\pi$
$464$	−0.556996	+	0.964746i	−0.0258579	+	0.0447872i
$465$	4.37397	+	8.75149i	0.202838	+	0.405840i
$466$	−8.74864	−	15.1531i	−0.405273	−	0.701953i
$467$	27.1318			1.25551			0.627755	−	0.778411i	$-0.283974\pi$
$467$	27.1318			1.25551			0.627755	+	0.778411i	$0.283974\pi$
$468$	25.9842	+	60.8853i	1.20112	+	2.81442i
$469$	1.70603			0.0787773
$470$	−38.0237	−	65.8589i	−1.75390	−	3.03785i
$471$	16.3708	−	24.7860i	0.754329	−	1.14208i
$472$	−16.0404	+	27.7829i	−0.738321	+	1.27881i
$473$	9.58317	−	16.5985i	0.440635	−	0.763201i
$474$	7.71343	−	11.6784i	0.354290	−	0.536407i
$475$	0.173996	+	0.301370i	0.00798350	+	0.0138278i
$476$	−33.5027			−1.53559
$477$	14.1220	+	1.70607i	0.646603	+	0.0781158i
$478$	−4.31693			−0.197452
$479$	−15.7549	−	27.2884i	−0.719861	−	1.24684i	−0.961054	−	0.276359i	$-0.910872\pi$
$479$	−15.7549	−	27.2884i	−0.719861	−	1.24684i	0.241193	−	0.970477i	$-0.422461\pi$
$480$	23.9610	+	47.9415i	1.09367	+	2.18822i
$481$	−12.9582	+	22.4443i	−0.590845	+	1.02337i
$482$	−16.7608	+	29.0305i	−0.763433	+	1.32231i
$483$	−20.6328	−	1.24180i	−0.938825	−	0.0565041i
$484$	22.1338	+	38.3368i	1.00608	+	1.74258i
$485$	−20.6402			−0.937222
$486$	9.14921	+	40.3395i	0.415017	+	1.82984i
$487$	10.7668			0.487891			0.243946	−	0.969789i	$-0.421558\pi$
$487$	10.7668			0.487891			0.243946	+	0.969789i	$0.421558\pi$
$488$	−9.64862	−	16.7119i	−0.436773	−	0.756512i
$489$	42.1348	+	2.53592i	1.90540	+	0.114678i
$490$	12.0556	−	20.8809i	0.544617	−	0.943304i
$491$	−13.0917	+	22.6754i	−0.590819	+	1.02333i	0.403304	+	0.915066i	$0.367862\pi$
$491$	−13.0917	+	22.6754i	−0.590819	+	1.02333i	−0.994122	+	0.108262i	$0.965471\pi$
$492$	−19.3648	−	38.7453i	−0.873033	−	1.74677i
$493$	0.191501	+	0.331690i	0.00862479	+	0.0149386i
$494$	−64.2220			−2.88949
$495$	−9.85726	−	1.19085i	−0.443051	−	0.0535247i
$496$	28.8041			1.29334
$497$	11.9714	+	20.7351i	0.536992	+	0.930097i
$498$	15.7724	−	23.8800i	0.706779	−	1.07009i
$499$	−12.1313	+	21.0121i	−0.543072	+	0.940629i	0.455653	+	0.890157i	$0.349406\pi$
$499$	−12.1313	+	21.0121i	−0.543072	+	0.940629i	−0.998726	+	0.0504715i	$0.983928\pi$
$500$	28.3552	−	49.1126i	1.26808	−	2.19638i
$501$	−0.447520	+	0.677560i	−0.0199937	+	0.0302712i
$502$	−19.0145	−	32.9342i	−0.848661	−	1.46992i
$503$	13.0741			0.582943			0.291472	−	0.956579i	$-0.405855\pi$
$503$	13.0741			0.582943			0.291472	+	0.956579i	$0.405855\pi$
$504$	−16.2115	−	37.9862i	−0.722118	−	1.69204i
$505$	8.47145			0.376975
$506$	13.8240	+	23.9438i	0.614550	+	1.06443i
$507$	4.77010	+	9.54407i	0.211848	+	0.423867i
$508$	21.9432	−	38.0068i	0.973573	−	1.68628i
$509$	−10.8079	+	18.7198i	−0.479051	+	0.829741i	−0.999711	−	0.0240231i	$-0.992352\pi$
$509$	−10.8079	+	18.7198i	−0.479051	+	0.829741i	0.520660	+	0.853764i	$0.325686\pi$
$510$	39.7098	+	2.38997i	1.75838	+	0.105830i
$511$	−5.27040	−	9.12861i	−0.233149	−	0.403826i
$512$	−25.0722			−1.10805
$513$	−28.2648	−	5.15326i	−1.24792	−	0.227522i
$514$	−16.7091			−0.737005
$515$	15.7841	+	27.3389i	0.695530	+	1.20469i
$516$	−112.148	−	6.74975i	−4.93705	−	0.297141i
$517$	9.60609	−	16.6382i	0.422475	−	0.731749i
$518$	13.4015	−	23.2121i	0.588830	−	1.01988i
$519$	−18.6390	−	37.2931i	−0.818161	−	1.63699i
$520$	39.2423	+	67.9697i	1.72089	+	2.98067i
$521$	27.3504			1.19824			0.599121	−	0.800659i	$-0.295517\pi$
$521$	27.3504			1.19824			0.599121	+	0.800659i	$0.295517\pi$
$522$	−0.469802	+	0.625979i	−0.0205627	+	0.0273984i
$523$	−30.8330			−1.34823			−0.674116	−	0.738626i	$-0.735475\pi$
$523$	−30.8330			−1.34823			−0.674116	+	0.738626i	$0.735475\pi$
$524$	−8.08920	−	14.0109i	−0.353378	−	0.612069i
$525$	−0.102495	+	0.155182i	−0.00447327	+	0.00677268i
$526$	9.98368	−	17.2922i	0.435309	−	0.753977i
$527$	4.95158	−	8.57639i	0.215694	−	0.373594i
$528$	−16.1104	+	24.3917i	−0.701115	+	1.06151i
$529$	−12.9659	−	22.4575i	−0.563733	−	0.976415i
$530$	27.9561			1.21434
$531$	−7.15906	+	9.53896i	−0.310677	+	0.413956i
$532$	47.5529			2.06168
$533$	−10.8573	−	18.8055i	−0.470283	−	0.814555i
$534$	−0.495345	−	0.991093i	−0.0214357	−	0.0428888i
$535$	9.35541	−	16.2040i	0.404470	−	0.700562i
$536$	−4.03479	+	6.98846i	−0.174276	+	0.301855i
$537$	14.9036	+	0.896985i	0.643136	+	0.0387077i
$538$	17.8589	+	30.9325i	0.769950	+	1.33359i
$539$	6.09133			0.262372
$540$	19.5885	+	54.8071i	0.842953	+	2.35852i
$541$	−15.0981			−0.649117			−0.324558	−	0.945866i	$-0.605216\pi$
$541$	−15.0981			−0.649117			−0.324558	+	0.945866i	$0.605216\pi$
$542$	−32.2087	−	55.7872i	−1.38348	−	2.39626i
$543$	42.6223	+	2.56526i	1.82910	+	0.110086i
$544$	27.1253	−	46.9824i	1.16299	−	2.01435i
$545$	8.64579	−	14.9749i	0.370345	−	0.641456i
$546$	−15.3441	−	30.7007i	−0.656668	−	1.31387i
$547$	1.72167	+	2.98203i	0.0736135	+	0.127502i	0.900482	−	0.434892i	$-0.143214\pi$
$547$	1.72167	+	2.98203i	0.0736135	+	0.127502i	−0.826869	+	0.562395i	$0.809880\pi$
$548$	9.71900			0.415175
$549$	−2.81598	−	6.59830i	−0.120183	−	0.281609i
$550$	0.248756			0.0106070
$551$	−0.271812	−	0.470792i	−0.0115796	−	0.0200564i
$552$	53.8836	−	81.5817i	2.29344	−	3.47235i
$553$	−2.59761	+	4.49919i	−0.110462	+	0.191325i
$554$	30.2694	−	52.4281i	1.28602	−	2.22746i
$555$	−12.5580	+	19.0133i	−0.533059	+	0.807070i
$556$	31.3466	+	54.2939i	1.32939	+	2.30258i
$557$	−12.1868			−0.516371			−0.258186	−	0.966095i	$-0.583125\pi$
$557$	−12.1868			−0.516371			−0.258186	+	0.966095i	$0.583125\pi$
$558$	20.0910	+	2.42718i	0.850520	+	0.102751i
$559$	−56.3238			−2.38224
$560$	−21.4753	−	37.1964i	−0.907498	−	1.57183i
$561$	4.49313	+	8.98991i	0.189700	+	0.379554i
$562$	−1.42956	+	2.47607i	−0.0603024	+	0.104447i
$563$	−2.45414	+	4.25069i	−0.103429	+	0.179145i	−0.913095	−	0.407746i	$-0.866315\pi$
$563$	−2.45414	+	4.25069i	−0.103429	+	0.179145i	0.809666	+	0.586891i	$0.199648\pi$
$564$	−112.417	−	6.76589i	−4.73359	−	0.284895i
$565$	17.9670	+	31.1198i	0.755878	+	1.30922i
$566$	42.8458			1.80094
$567$	−4.28964	−	14.7429i	−0.180148	−	0.619144i
$568$	−113.250			−4.75187
$569$	19.0738	+	33.0367i	0.799614	+	1.38497i	0.919868	+	0.392229i	$0.128296\pi$
$569$	19.0738	+	33.0367i	0.799614	+	1.38497i	−0.120254	+	0.992743i	$0.538371\pi$
$570$	−56.3630	−	3.39226i	−2.36079	−	0.142086i
$571$	2.16189	−	3.74451i	0.0904723	−	0.156703i	−0.817238	−	0.576301i	$-0.804496\pi$
$571$	2.16189	−	3.74451i	0.0904723	−	0.156703i	0.907710	+	0.419598i	$0.137829\pi$
$572$	−16.4339	+	28.4644i	−0.687138	+	1.19016i
$573$	14.0559	+	28.1233i	0.587195	+	1.17487i
$574$	11.2287	+	19.4488i	0.468679	+	0.811776i
$575$	−0.440252			−0.0183598
$576$	42.5685	+	5.14268i	1.77369	+	0.214278i
$577$	−12.8484			−0.534886			−0.267443	−	0.963574i	$-0.586179\pi$
$577$	−12.8484			−0.534886			−0.267443	+	0.963574i	$0.586179\pi$
$578$	2.42104	+	4.19337i	0.100702	+	0.174421i
$579$	−5.93236	+	8.98179i	−0.246540	+	0.373271i
$580$	−0.550635	+	0.953728i	−0.0228639	+	0.0396014i
$581$	−5.31159	+	9.19995i	−0.220362	+	0.381678i
$582$	−23.5293	+	35.6242i	−0.975323	+	1.47667i
$583$	3.53134	+	6.11645i	0.146253	+	0.253318i
$584$	49.8582			2.06315
$585$	11.4530	+	26.8362i	0.473523	+	1.10954i
$586$	−41.8900			−1.73046
$587$	−3.91280	−	6.77717i	−0.161499	−	0.279724i	0.773908	−	0.633298i	$-0.218299\pi$
$587$	−3.91280	−	6.77717i	−0.161499	−	0.279724i	−0.935406	+	0.353575i	$0.884966\pi$
$588$	−15.9634	−	31.9397i	−0.658318	−	1.31717i
$589$	−7.02814	+	12.1731i	−0.289590	+	0.501584i
$590$	−11.7198	+	20.2993i	−0.482497	+	0.835709i
$591$	−15.8922	−	0.956487i	−0.653718	−	0.0393446i
$592$	33.5424	+	58.0972i	1.37859	+	2.38778i
$593$	42.6137			1.74993			0.874967	−	0.484182i	$-0.160883\pi$
$593$	42.6137			1.74993			0.874967	+	0.484182i	$0.160883\pi$
$594$	−13.2924	+	15.6558i	−0.545395	+	0.642364i
$595$	−14.7669			−0.605384
$596$	36.7122	+	63.5875i	1.50379	+	2.60464i
$597$	−44.6255	−	2.68583i	−1.82640	−	0.109924i
$598$	40.6242	−	70.3632i	1.66125	−	2.87737i
$599$	−12.9993	+	22.5154i	−0.531136	+	0.919955i	0.468204	+	0.883621i	$0.344901\pi$
$599$	−12.9993	+	22.5154i	−0.531136	+	0.919955i	−0.999340	+	0.0363342i	$0.988432\pi$
$600$	−0.393270	−	0.786860i	−0.0160552	−	0.0321234i
$601$	−3.40157	−	5.89170i	−0.138753	−	0.240327i	0.788272	−	0.615327i	$-0.210976\pi$
$601$	−3.40157	−	5.89170i	−0.138753	−	0.240327i	−0.927025	+	0.375000i	$0.877643\pi$
$602$	58.2505			2.37411
$603$	−1.80078	+	2.39942i	−0.0733334	+	0.0977118i
$604$	54.0624			2.19977
$605$	9.75583	+	16.8976i	0.396631	+	0.686985i
$606$	9.65728	−	14.6214i	0.392300	−	0.593956i
$607$	16.6426	−	28.8257i	0.675500	−	1.17000i	−0.300822	−	0.953680i	$-0.597261\pi$
$607$	16.6426	−	28.8257i	0.675500	−	1.17000i	0.976322	−	0.216321i	$-0.0694057\pi$
$608$	−38.5009	+	66.6855i	−1.56142	+	2.70445i
$609$	0.160115	−	0.242420i	0.00648820	−	0.00982336i
$610$	−7.04968	−	12.2104i	−0.285433	−	0.494385i
$611$	−56.4585			−2.28407
$612$	35.3633	−	47.1192i	1.42948	−	1.90468i
$613$	−20.7583			−0.838421			−0.419210	−	0.907889i	$-0.637693\pi$
$613$	−20.7583			−0.838421			−0.419210	+	0.907889i	$0.637693\pi$
$614$	9.47716	+	16.4149i	0.382467	+	0.662452i
$615$	−8.53537	−	17.0777i	−0.344179	−	0.688638i
$616$	10.2531	−	17.7589i	0.413109	−	0.715526i
$617$	1.29271	−	2.23904i	0.0520426	−	0.0901404i	−0.838831	−	0.544393i	$-0.816760\pi$
$617$	1.29271	−	2.23904i	0.0520426	−	0.0901404i	0.890873	+	0.454252i	$0.150094\pi$
$618$	65.1795	+	3.92289i	2.62190	+	0.157802i
$619$	2.49932	+	4.32895i	0.100456	+	0.173995i	0.911873	−	0.410473i	$-0.134636\pi$
$619$	2.49932	+	4.32895i	0.100456	+	0.173995i	−0.811416	+	0.584468i	$0.801303\pi$
$620$	28.4752			1.14359
$621$	23.5252	−	27.7078i	0.944032	−	1.11188i
$622$	37.6103			1.50804
$623$	0.205642	+	0.356182i	0.00823886	+	0.0142701i
$624$	85.7478	+	5.16081i	3.43266	+	0.206598i
$625$	12.3407	−	21.3747i	0.493627	−	0.854987i
$626$	−23.2960	+	40.3499i	−0.931097	+	1.61271i
$627$	−6.37743	−	12.7600i	−0.254690	−	0.509587i
$628$	−43.2270	−	74.8714i	−1.72495	−	2.98769i
$629$	23.0645			0.919642
$630$	−11.8448	−	27.7543i	−0.471908	−	1.10576i
$631$	−3.84642			−0.153124			−0.0765618	−	0.997065i	$-0.524394\pi$
$631$	−3.84642			−0.153124			−0.0765618	+	0.997065i	$0.524394\pi$
$632$	−12.2867	−	21.2813i	−0.488741	−	0.846524i
$633$	−2.05897	+	3.11735i	−0.0818367	+	0.123903i
$634$	−23.8479	+	41.3058i	−0.947121	+	1.64046i
$635$	9.67185	−	16.7521i	0.383816	−	0.664788i
$636$	22.8170	−	34.5457i	0.904752	−	1.36983i
$637$	−8.95023	−	15.5023i	−0.354621	−	0.614222i
$638$	−0.388599			−0.0153848
$639$	−41.7987	−	5.04968i	−1.65353	−	0.199762i
$640$	22.3818			0.884718
$641$	−8.50469	−	14.7306i	−0.335915	−	0.581822i	0.647745	−	0.761857i	$-0.275712\pi$
$641$	−8.50469	−	14.7306i	−0.335915	−	0.581822i	−0.983660	+	0.180035i	$0.942379\pi$
$642$	−17.3027	−	34.6194i	−0.682882	−	1.36632i
$643$	−18.1310	+	31.4039i	−0.715018	+	1.23845i	0.247934	+	0.968777i	$0.420248\pi$
$643$	−18.1310	+	31.4039i	−0.715018	+	1.23845i	−0.962953	+	0.269671i	$0.913085\pi$
$644$	−30.0800	+	52.1001i	−1.18532	+	2.05303i
$645$	−49.4313	−	2.97507i	−1.94635	−	0.117143i
$646$	28.5773	+	49.4974i	1.12436	+	1.94745i
$647$	−19.1960			−0.754672			−0.377336	−	0.926076i	$-0.623160\pi$
$647$	−19.1960			−0.754672			−0.377336	+	0.926076i	$0.623160\pi$
$648$	70.5367	+	17.2954i	2.77094	+	0.679428i
$649$	−5.92165			−0.232445
$650$	−0.365507	−	0.633077i	−0.0143364	−	0.0248313i
$651$	−7.49842	−	0.451299i	−0.293886	−	0.0176878i
$652$	61.4271	−	106.395i	2.40567	−	4.16675i
$653$	−0.333367	+	0.577409i	−0.0130457	+	0.0225958i	−0.872475	−	0.488660i	$-0.837486\pi$
$653$	−0.333367	+	0.577409i	−0.0130457	+	0.0225958i	0.859429	+	0.511255i	$0.170819\pi$
$654$	−15.9902	−	31.9935i	−0.625268	−	1.25104i
$655$	−3.56545	−	6.17555i	−0.139314	−	0.241299i
$656$	−56.2084			−2.19457
$657$	18.4018	+	2.22312i	0.717924	+	0.0867320i
$658$	58.3898			2.27627
$659$	−3.84282	−	6.65595i	−0.149695	−	0.259279i	0.781420	−	0.624006i	$-0.214496\pi$
$659$	−3.84282	−	6.65595i	−0.149695	−	0.259279i	−0.931115	+	0.364727i	$0.881162\pi$
$660$	−15.9264	+	24.1131i	−0.619934	+	0.938601i
$661$	17.1973	−	29.7866i	0.668898	−	1.15857i	−0.309314	−	0.950960i	$-0.600100\pi$
$661$	17.1973	−	29.7866i	0.668898	−	1.15857i	0.978213	−	0.207606i	$-0.0665671\pi$
$662$	−25.6350	+	44.4012i	−0.996335	+	1.72570i
$663$	16.2771	−	24.6441i	0.632152	−	0.957099i
$664$	−25.1239	−	43.5159i	−0.974998	−	1.68875i
$665$	20.9597			0.812784
$666$	18.5004	+	43.3495i	0.716877	+	1.67976i
$667$	0.687748			0.0266297
$668$	1.18167	+	2.04671i	0.0457202	+	0.0791897i
$669$	−17.9457	−	35.9060i	−0.693821	−	1.38821i
$670$	−2.94798	+	5.10605i	−0.113890	+	0.197264i
$671$	1.78099	−	3.08477i	0.0687544	−	0.119086i
$672$	−41.0771	−	2.47226i	−1.58458	−	0.0953696i
$673$	1.39680	+	2.41932i	0.0538425	+	0.0932580i	0.891690	−	0.452646i	$-0.149520\pi$
$673$	1.39680	+	2.41932i	0.0538425	+	0.0932580i	−0.837848	+	0.545904i	$0.816186\pi$
$674$	11.5325			0.444217
$675$	−0.110064	−	0.307952i	−0.00423638	−	0.0118531i
$676$	31.0540			1.19439
$677$	1.20487	+	2.08690i	0.0463070	+	0.0802062i	0.888250	−	0.459361i	$-0.151921\pi$
$677$	1.20487	+	2.08690i	0.0463070	+	0.0802062i	−0.841943	+	0.539567i	$0.818588\pi$
$678$	74.1937	+	4.46542i	2.84939	+	0.171493i
$679$	7.92385	−	13.7245i	0.304090	−	0.526699i
$680$	34.9239	−	60.4899i	1.33927	−	2.31968i
$681$	7.05987	+	14.1255i	0.270535	+	0.541289i
$682$	5.02393	+	8.70171i	0.192376	+	0.333206i
$683$	16.8394			0.644340			0.322170	−	0.946682i	$-0.395588\pi$
$683$	16.8394			0.644340			0.322170	+	0.946682i	$0.395588\pi$
$684$	−50.1937	+	66.8798i	−1.91921	+	2.55721i
$685$	4.28382			0.163676
$686$	25.1008	+	43.4759i	0.958353	+	1.65992i
$687$	−14.4067	+	21.8123i	−0.549650	+	0.832190i
$688$	−72.8971	+	126.261i	−2.77917	+	4.81367i
$689$	10.3775	−	17.9743i	0.395350	−	0.684767i
$690$	39.3696	−	59.6069i	1.49877	−	2.26920i
$691$	24.8047	+	42.9630i	0.943615	+	1.63439i	0.758500	+	0.651673i	$0.225932\pi$
$691$	24.8047	+	42.9630i	0.943615	+	1.63439i	0.185115	+	0.982717i	$0.440734\pi$
$692$	−121.343			−4.61275
$693$	4.57610	−	6.09734i	0.173831	−	0.231619i
$694$	−90.1821			−3.42326
$695$	13.8166	+	23.9310i	0.524092	+	0.907754i
$696$	0.614355	+	1.22921i	0.0232871	+	0.0465930i
$697$	−9.66253	+	16.7360i	−0.365994	+	0.633921i
$698$	−5.17437	+	8.96228i	−0.195853	+	0.339227i
$699$	−11.4006	−	0.686153i	−0.431209	−	0.0259527i
$700$	0.270638	+	0.468759i	0.0102292	+	0.0177174i
$701$	−6.78148			−0.256133			−0.128067	−	0.991766i	$-0.540877\pi$
$701$	−6.78148			−0.256133			−0.128067	+	0.991766i	$0.540877\pi$
$702$	59.3746	+	10.8252i	2.24095	+	0.408572i
$703$	−32.7371			−1.23470
$704$	10.6446	+	18.4370i	0.401185	+	0.694872i
$705$	−49.5495	−	2.98218i	−1.86614	−	0.112315i
$706$	22.6124	−	39.1658i	0.851029	−	1.47403i
$707$	−3.25223	+	5.63303i	−0.122313	+	0.211852i
$708$	15.5187	+	31.0500i	0.583229	+	1.16693i
$709$	0.793670	+	1.37468i	0.0298069	+	0.0516271i	0.880544	−	0.473964i	$-0.157177\pi$
$709$	0.793670	+	1.37468i	0.0298069	+	0.0516271i	−0.850737	+	0.525591i	$0.823844\pi$
$710$	−82.7452			−3.10537
$711$	−3.58593	−	8.40241i	−0.134483	−	0.315115i
$712$	−1.94538			−0.0729061
$713$	−8.89144	−	15.4004i	−0.332987	−	0.576750i
$714$	−16.8340	+	25.4872i	−0.629995	+	0.953834i
$715$	−7.24354	+	12.5462i	−0.270893	+	0.469201i
$716$	21.7275	−	37.6331i	0.811995	−	1.40642i
$717$	−1.55298	+	2.35127i	−0.0579971	+	0.0878097i
$718$	28.3281	+	49.0657i	1.05720	+	1.83112i
$719$	35.5901			1.32729			0.663644	−	0.748049i	$-0.269009\pi$
$719$	35.5901			1.32729			0.663644	+	0.748049i	$0.269009\pi$
$720$	74.9820	+	9.05854i	2.79442	+	0.337592i
$721$	−24.2383			−0.902683
$722$	−15.3536	−	26.5932i	−0.571402	−	0.989697i
$723$	9.78226	+	19.5725i	0.363806	+	0.727907i
$724$	62.1379	−	107.626i	2.30934	−	3.99989i
$725$	0.00309393	−	0.00535884i	0.000114906	−	0.000199022i
$726$	40.2861	+	2.42466i	1.49516	+	0.0899875i
$727$	14.3394	+	24.8366i	0.531819	+	0.921138i	0.999310	+	0.0371400i	$0.0118248\pi$
$727$	14.3394	+	24.8366i	0.531819	+	0.921138i	−0.467491	+	0.883998i	$0.654842\pi$
$728$	−60.2612			−2.23343
$729$	25.2627	+	9.52860i	0.935657	+	0.352911i
$730$	36.4285			1.34828
$731$	25.0628	+	43.4100i	0.926981	+	1.60558i
$732$	−20.8423	−	1.25441i	−0.770353	−	0.0463644i
$733$	−7.87355	+	13.6374i	−0.290816	+	0.503708i	−0.974003	−	0.226535i	$-0.927260\pi$
$733$	−7.87355	+	13.6374i	−0.290816	+	0.503708i	0.683187	+	0.730244i	$0.260593\pi$
$734$	7.08732	−	12.2756i	0.261598	−	0.453101i
$735$	−7.03613	−	14.0780i	−0.259532	−	0.519274i
$736$	−48.7082	−	84.3651i	−1.79541	−	3.10974i
$737$	−1.48952			−0.0548673
$738$	−39.2056	−	4.73641i	−1.44318	−	0.174350i
$739$	−35.9515			−1.32250			−0.661248	−	0.750167i	$-0.729973\pi$
$739$	−35.9515			−1.32250			−0.661248	+	0.750167i	$0.729973\pi$
$740$	33.1594	+	57.4337i	1.21896	+	2.11130i
$741$	−23.1033	+	34.9792i	−0.848722	+	1.28499i
$742$	−10.7325	+	18.5892i	−0.394002	+	0.682431i
$743$	−23.7921	+	41.2091i	−0.872848	+	1.51182i	−0.0138102	+	0.999905i	$0.504396\pi$
$743$	−23.7921	+	41.2091i	−0.872848	+	1.51182i	−0.859038	+	0.511912i	$0.828937\pi$
$744$	19.5825	−	29.6486i	0.717929	−	1.08697i
$745$	16.1816	+	28.0273i	0.592846	+	1.02684i
$746$	55.1451			2.01901
$747$	−7.33250	−	17.1812i	−0.268282	−	0.628629i
$748$	29.2509			1.06952
$749$	7.18317	+	12.4416i	0.262467	+	0.454607i
$750$	−23.1149	−	46.2485i	−0.844036	−	1.68876i
$751$	−7.63308	+	13.2209i	−0.278535	+	0.482437i	−0.971021	−	0.238995i	$-0.923182\pi$
$751$	−7.63308	+	13.2209i	−0.278535	+	0.482437i	0.692486	+	0.721431i	$0.256515\pi$
$752$	−73.0714	+	126.563i	−2.66464	+	4.61529i
$753$	−24.7783	−	1.49130i	−0.902971	−	0.0543461i
$754$	0.570984	+	0.988974i	0.0207940	+	0.0360163i
$755$	23.8289			0.867224
$756$	−43.9637	−	8.01550i	−1.59894	−	0.291521i
$757$	19.8223			0.720452			0.360226	−	0.932865i	$-0.382700\pi$
$757$	19.8223			0.720452			0.360226	+	0.932865i	$0.382700\pi$
$758$	32.7330	+	56.6952i	1.18892	+	2.05926i
$759$	18.0143	+	1.08421i	0.653878	+	0.0393543i
$760$	−49.5700	+	85.8578i	−1.79809	+	3.11439i
$761$	4.14496	−	7.17929i	0.150255	−	0.260249i	−0.781066	−	0.624448i	$-0.785324\pi$
$761$	4.14496	−	7.17929i	0.150255	−	0.260249i	0.931321	+	0.364199i	$0.118657\pi$
$762$	−17.8879	−	35.7904i	−0.648011	−	1.29655i
$763$	6.63831	+	11.4979i	0.240323	+	0.416252i
$764$	91.5061			3.31057
$765$	15.5870	−	20.7686i	0.563549	−	0.750890i
$766$	54.2722			1.96094
$767$	8.70092	+	15.0704i	0.314172	+	0.544162i
$768$	−1.77213	+	2.68307i	−0.0639464	+	0.0968170i
$769$	11.7836	−	20.4098i	0.424928	−	0.735996i	−0.571486	−	0.820612i	$-0.693633\pi$
$769$	11.7836	−	20.4098i	0.424928	−	0.735996i	0.996414	+	0.0846157i	$0.0269663\pi$
$770$	7.49134	−	12.9754i	0.269969	−	0.467600i
$771$	−6.01095	+	9.10078i	−0.216479	+	0.327756i
$772$	15.6643	+	27.1314i	0.563771	+	0.976480i
$773$	28.3725			1.02049			0.510244	−	0.860030i	$-0.329555\pi$
$773$	28.3725			1.02049			0.510244	+	0.860030i	$0.329555\pi$
$774$	−61.4855	+	81.9252i	−2.21005	+	2.94474i
$775$	−0.159997			−0.00574727
$776$	37.4800	+	64.9172i	1.34545	+	2.33039i
$777$	−7.82166	−	15.6497i	−0.280600	−	0.561429i
$778$	−35.9272	+	62.2277i	−1.28805	+	2.23097i
$779$	13.7147	−	23.7546i	0.491382	−	0.851098i
$780$	84.7685	+	5.10187i	3.03520	+	0.182676i
$781$	−10.4521	−	18.1036i	−0.374007	−	0.647799i
$782$	−72.3074			−2.58571
$783$	0.171939	+	0.481074i	0.00614461	+	0.0171922i
$784$	−46.3354			−1.65483
$785$	−19.0530	−	33.0008i	−0.680032	−	1.17785i
$786$	−14.7233	−	0.886137i	−0.525164	−	0.0316075i
$787$	11.1214	−	19.2628i	0.396434	−	0.686644i	−0.596849	−	0.802354i	$-0.703581\pi$
$787$	11.1214	−	19.2628i	0.396434	−	0.686644i	0.993283	+	0.115710i	$0.0369142\pi$
$788$	−23.1688	+	40.1296i	−0.825355	+	1.42956i
$789$	−5.82687	−	11.6585i	−0.207442	−	0.415052i
$790$	−8.97720	−	15.5490i	−0.319394	−	0.553207i
$791$	−27.5905			−0.981004
$792$	14.1541	+	33.1654i	0.502945	+	1.17848i
$793$	−10.4675			−0.371713
$794$	12.9097	+	22.3603i	0.458150	+	0.793539i
$795$	10.0570	−	15.2266i	0.356684	−	0.540032i
$796$	−65.0584	+	112.684i	−2.30593	+	3.99399i
$797$	−13.5576	+	23.4825i	−0.480236	+	0.831793i	−0.999743	−	0.0226733i	$-0.992782\pi$
$797$	−13.5576	+	23.4825i	−0.480236	+	0.831793i	0.519507	+	0.854466i	$0.326116\pi$
$798$	23.8937	−	36.1758i	0.845827	−	1.28061i
$799$	25.1227	+	43.5139i	0.888778	+	1.53941i
$800$	−0.876481			−0.0309883
$801$	−0.718006	−	0.0867419i	−0.0253695	−	0.00306488i
$802$	−27.0595			−0.955503
$803$	4.60154	+	7.97010i	0.162385	+	0.281259i
$804$	3.90355	+	7.81027i	0.137668	+	0.275447i
$805$	−13.2583	+	22.9640i	−0.467293	+	0.809375i
$806$	14.7637	−	25.5716i	0.520031	−	0.900720i
$807$	23.2723	+	1.40066i	0.819223	+	0.0493057i
$808$	−15.3831	−	26.6443i	−0.541176	−	0.937344i
$809$	−26.4253			−0.929065			−0.464532	−	0.885556i	$-0.653778\pi$
$809$	−26.4253			−0.929065			−0.464532	+	0.885556i	$0.653778\pi$
$810$	51.5370	+	12.6367i	1.81083	+	0.444010i
$811$	−3.90359			−0.137073			−0.0685367	−	0.997649i	$-0.521833\pi$
$811$	−3.90359			−0.137073			−0.0685367	+	0.997649i	$0.521833\pi$
$812$	−0.422783	−	0.732281i	−0.0148368	−	0.0256980i
$813$	−41.9719	−	2.52612i	−1.47202	−	0.0885948i
$814$	−11.7008	+	20.2663i	−0.410111	+	0.710334i
$815$	27.0751	−	46.8954i	0.948398	−	1.64267i
$816$	−34.1783	−	68.3843i	−1.19648	−	2.39393i
$817$	−35.5735	−	61.6150i	−1.24456	−	2.15564i
$818$	97.4713			3.40800
$819$	−22.2414	−	2.68697i	−0.777178	−	0.0938904i
$820$	−55.5665			−1.94047
$821$	−18.6730	−	32.3426i	−0.651693	−	1.12876i	−0.982712	−	0.185141i	$-0.940726\pi$
$821$	−18.6730	−	32.3426i	−0.651693	−	1.12876i	0.331019	−	0.943624i	$-0.392607\pi$
$822$	4.88346	−	7.39373i	0.170330	−	0.257886i
$823$	26.0736	−	45.1608i	0.908868	−	1.57421i	0.0932281	−	0.995645i	$-0.470281\pi$
$823$	26.0736	−	45.1608i	0.908868	−	1.57421i	0.815640	−	0.578560i	$-0.196385\pi$
$824$	57.3239	−	99.2880i	1.99697	−	3.45886i
$825$	0.0894878	−	0.135488i	0.00311557	−	0.00471707i
$826$	−8.99857	−	15.5860i	−0.313100	−	0.542306i
$827$	54.7825			1.90497			0.952487	−	0.304579i	$-0.0985159\pi$
$827$	54.7825			1.90497			0.952487	+	0.304579i	$0.0985159\pi$
$828$	−41.5246	−	97.2989i	−1.44308	−	3.38137i
$829$	13.9139			0.483248			0.241624	−	0.970370i	$-0.422320\pi$
$829$	13.9139			0.483248			0.241624	+	0.970370i	$0.422320\pi$
$830$	−18.3566	−	31.7945i	−0.637166	−	1.10360i
$831$	−17.6664	−	35.3472i	−0.612841	−	1.22618i
$832$	31.2812	−	54.1806i	1.08448	−	1.87837i
$833$	−7.96530	+	13.7963i	−0.275981	+	0.478014i
$834$	57.0547	+	3.43389i	1.97564	+	0.118906i
$835$	0.520842	+	0.902124i	0.0180245	+	0.0312193i
$836$	−41.5180			−1.43593
$837$	8.54957	−	10.0696i	0.295516	−	0.348057i
$838$	4.10500			0.141805
$839$	−4.73275	−	8.19736i	−0.163393	−	0.283004i	0.772691	−	0.634783i	$-0.218910\pi$
$839$	−4.73275	−	8.19736i	−0.163393	−	0.283004i	−0.936083	+	0.351778i	$0.885577\pi$
$840$	−52.8869	−	3.18305i	−1.82477	−	0.109826i
$841$	14.4952	−	25.1064i	0.499833	−	0.865737i
$842$	24.0985	−	41.7399i	0.830490	−	1.43845i
$843$	0.834348	+	1.66937i	0.0287365	+	0.0574962i
$844$	5.43668	+	9.41661i	0.187138	+	0.324133i
$845$	13.6876			0.470867
$846$	−61.6325	+	82.1212i	−2.11897	+	2.82338i
$847$	−14.9812			−0.514761
$848$	−26.8621	−	46.5265i	−0.922448	−	1.59773i
$849$	15.4134	−	23.3364i	0.528987	−	0.800905i
$850$	−0.325285	+	0.563409i	−0.0111572	+	0.0193248i
$851$	20.7082	−	35.8676i	0.709867	−	1.22953i
$852$	−67.5343	+	102.249i	−2.31369	+	3.50300i
$853$	9.31783	+	16.1389i	0.319036	+	0.552587i	0.980287	−	0.197578i	$-0.0633075\pi$
$853$	9.31783	+	16.1389i	0.319036	+	0.552587i	−0.661251	+	0.750165i	$0.729974\pi$
$854$	10.8256			0.370445
$855$	−22.1238	+	29.4784i	−0.756616	+	1.00814i
$856$	−67.9531			−2.32259
$857$	−11.1382	−	19.2918i	−0.380472	−	0.658997i	0.610658	−	0.791895i	$-0.290905\pi$
$857$	−11.1382	−	19.2918i	−0.380472	−	0.658997i	−0.991130	+	0.132898i	$0.957572\pi$
$858$	13.3968	+	26.8045i	0.457360	+	0.915091i
$859$	−12.1030	+	20.9630i	−0.412949	+	0.715249i	−0.995211	−	0.0977524i	$-0.968835\pi$
$859$	−12.1030	+	20.9630i	−0.412949	+	0.715249i	0.582261	+	0.813002i	$0.302168\pi$
$860$	−72.0645	+	124.819i	−2.45738	+	4.25631i
$861$	14.6324	+	0.880666i	0.498672	+	0.0300130i
$862$	−30.0760	−	52.0931i	−1.02439	−	1.77430i
$863$	−31.3463			−1.06704			−0.533519	−	0.845788i	$-0.679131\pi$
$863$	−31.3463			−1.06704			−0.533519	+	0.845788i	$0.679131\pi$
$864$	46.8354	−	55.1625i	1.59337	−	1.87667i
$865$	−53.4838			−1.81850
$866$	−39.1104	−	67.7412i	−1.32903	−	2.30194i
$867$	3.15491	+	0.189881i	0.107146	+	0.00644871i
$868$	−10.9317	+	18.9343i	−0.371048	+	0.642673i
$869$	2.26795	−	3.92820i	0.0769349	−	0.133255i
$870$	0.448873	+	0.898110i	0.0152182	+	0.0304488i
$871$	2.18862	+	3.79080i	0.0741584	+	0.128446i
$872$	−62.7987			−2.12663
$873$	10.9387	+	25.6310i	0.370217	+	0.867480i
$874$	102.631			3.47155
$875$	9.59609	+	16.6209i	0.324407	+	0.561890i
$876$	29.7319	−	45.0151i	1.00455	−	1.52092i
$877$	10.2985	−	17.8375i	0.347756	−	0.602331i	−0.638094	−	0.769958i	$-0.720277\pi$
$877$	10.2985	−	17.8375i	0.347756	−	0.602331i	0.985851	+	0.167627i	$0.0536104\pi$
$878$	19.5074	−	33.7877i	0.658342	−	1.14028i
$879$	−15.0696	+	22.8159i	−0.508285	+	0.769560i
$880$	18.7499	+	32.4758i	0.632060	+	1.09476i
$881$	−7.01153			−0.236224			−0.118112	−	0.993000i	$-0.537684\pi$
$881$	−7.01153			−0.236224			−0.118112	+	0.993000i	$0.537684\pi$
$882$	−32.3191	−	3.90446i	−1.08824	−	0.131470i
$883$	19.1283			0.643717			0.321859	−	0.946788i	$-0.395692\pi$
$883$	19.1283			0.643717			0.321859	+	0.946788i	$0.395692\pi$
$884$	−42.9796	−	74.4428i	−1.44556	−	2.50378i
$885$	6.84014	+	13.6858i	0.229929	+	0.460044i
$886$	−44.9937	+	77.9314i	−1.51159	+	2.61816i
$887$	1.68335	−	2.91564i	0.0565213	−	0.0978977i	−0.836380	−	0.548150i	$-0.815332\pi$
$887$	1.68335	−	2.91564i	0.0565213	−	0.0978977i	0.892902	+	0.450252i	$0.148666\pi$
$888$	82.6043	+	4.97161i	2.77202	+	0.166836i
$889$	7.42613	+	12.8624i	0.249065	+	0.431392i
$890$	−1.42137			−0.0476445
$891$	3.74524	+	12.8719i	0.125470	+	0.431225i
$892$	−116.829			−3.91173
$893$	−35.6585	−	61.7624i	−1.19327	−	2.06680i
$894$	66.8208	+	4.02167i	2.23482	+	0.134505i
$895$	9.57677	−	16.5875i	0.320116	−	0.554457i
$896$	−8.59248	+	14.8826i	−0.287055	+	0.497193i
$897$	−23.7099	−	47.4390i	−0.791650	−	1.58394i
$898$	−34.0257	−	58.9343i	−1.13545	−	1.96666i
$899$	0.249943			0.00833607
$900$	−0.944944	−	0.114158i	−0.0314981	−	0.00380527i
$901$	−18.4710			−0.615357
$902$	−9.80372	−	16.9805i	−0.326428	−	0.565390i
$903$	20.9551	−	31.7268i	0.697344	−	1.05580i
$904$	65.2517	−	113.019i	2.17024	−	3.75897i
$905$	27.3883	−	47.4380i	0.910419	−	1.57689i
$906$	27.1645	−	41.1280i	0.902479	−	1.36638i
$907$	−5.54647	−	9.60677i	−0.184168	−	0.318988i	0.759128	−	0.650941i	$-0.225626\pi$
$907$	−5.54647	−	9.60677i	−0.184168	−	0.318988i	−0.943296	+	0.331954i	$0.892292\pi$
$908$	45.9608			1.52526
$909$	−4.48961	−	10.5199i	−0.148911	−	0.348923i
$910$	−44.0293			−1.45956
$911$	−4.48921	−	7.77554i	−0.148734	−	0.257615i	0.782026	−	0.623246i	$-0.214187\pi$
$911$	−4.48921	−	7.77554i	−0.148734	−	0.257615i	−0.930760	+	0.365631i	$0.880853\pi$
$912$	48.5117	+	97.0628i	1.60638	+	3.21407i
$913$	4.63750	−	8.03239i	0.153479	−	0.265833i
$914$	21.2496	−	36.8053i	0.702873	−	1.21741i
$915$	−9.18659	−	0.552903i	−0.303699	−	0.0182784i
$916$	38.0408	+	65.8885i	1.25690	+	2.17702i
$917$	5.47518			0.180806
$918$	−18.0771	−	50.5784i	−0.596633	−	1.66934i
$919$	56.2919			1.85690			0.928449	−	0.371459i	$-0.121142\pi$
$919$	56.2919			1.85690			0.928449	+	0.371459i	$0.121142\pi$
$920$	−62.7119	−	108.620i	−2.06755	−	3.58110i
$921$	12.3499	+	0.743290i	0.406943	+	0.0244922i
$922$	−54.8242	+	94.9583i	−1.80554	+	3.12728i
$923$	−30.7155	+	53.2008i	−1.01101	+	1.75113i
$924$	−9.91961	−	19.8473i	−0.326331	−	0.652927i
$925$	−0.186317	−	0.322711i	−0.00612607	−	0.0106107i
$926$	−26.8673			−0.882914
$927$	25.5844	−	34.0895i	0.840303	−	1.11965i
$928$	1.36921			0.0449466
$929$	4.02378	+	6.96940i	0.132016	+	0.228658i	0.924454	−	0.381295i	$-0.124522\pi$
$929$	4.02378	+	6.96940i	0.132016	+	0.228658i	−0.792438	+	0.609953i	$0.791188\pi$
$930$	14.3078	−	21.6625i	0.469170	−	0.710340i
$931$	11.3057	−	19.5821i	0.370531	−	0.641778i
$932$	−16.6206	+	28.7876i	−0.544424	+	0.942971i
$933$	13.5300	−	20.4849i	0.442952	−	0.670645i
$934$	−35.9972	−	62.3490i	−1.17786	−	2.04012i
$935$	12.8928			0.421641
$936$	63.6078	−	84.7531i	2.07909	−	2.77024i
$937$	9.28064			0.303185			0.151593	−	0.988443i	$-0.451560\pi$
$937$	9.28064			0.303185			0.151593	+	0.988443i	$0.451560\pi$
$938$	−2.26349	−	3.92047i	−0.0739054	−	0.128008i
$939$	13.5965	+	27.2040i	0.443705	+	0.887769i
$940$	−72.2369	+	125.118i	−2.35611	+	4.08090i
$941$	7.93729	−	13.7478i	0.258748	−	0.448165i	−0.707159	−	0.707055i	$-0.750023\pi$
$941$	7.93729	−	13.7478i	0.258748	−	0.448165i	0.965907	+	0.258890i	$0.0833567\pi$
$942$	−78.6784	−	4.73533i	−2.56348	−	0.154286i
$943$	17.3508	+	30.0524i	0.565019	+	0.978641i
$944$	45.0447			1.46608
$945$	−19.3777	−	3.53297i	−0.630358	−	0.114927i
$946$	−50.8580			−1.65354
$947$	−20.7114	−	35.8731i	−0.673029	−	1.16572i	−0.977041	−	0.213052i	$-0.931660\pi$
$947$	−20.7114	−	35.8731i	−0.673029	−	1.16572i	0.304012	−	0.952668i	$-0.401674\pi$
$948$	−26.5410	−	1.59739i	−0.862011	−	0.0518809i
$949$	13.5225	−	23.4216i	0.438958	−	0.760297i
$950$	0.461700	−	0.799688i	0.0149795	−	0.0259453i
$951$	13.9186	+	27.8484i	0.451340	+	0.903047i
$952$	26.8149	+	46.4447i	0.869075	+	1.50528i
$953$	−52.5956			−1.70374			−0.851870	−	0.523754i	$-0.824531\pi$
$953$	−52.5956			−1.70374			−0.851870	+	0.523754i	$0.824531\pi$
$954$	−14.8159	−	34.7160i	−0.479682	−	1.12397i
$955$	40.3329			1.30514
$956$	4.10063	+	7.10250i	0.132624	+	0.229711i
$957$	−0.139795	+	0.211655i	−0.00451894	+	0.00684183i
$958$	−41.8058	+	72.4098i	−1.35069	+	2.33946i
$959$	−1.64458	+	2.84849i	−0.0531062	+	0.0919826i
$960$	30.3151	−	45.8981i	0.978415	−	1.48135i
$961$	12.2687	+	21.2499i	0.395763	+	0.685482i
$962$	68.7696			2.21722
$963$	−25.0803	−	3.02994i	−0.808202	−	0.0976385i
$964$	63.6839			2.05112
$965$	6.90432	+	11.9586i	0.222258	+	0.384962i
$966$	24.5210	+	49.0619i	0.788950	+	1.57854i
$967$	−6.76995	+	11.7259i	−0.217707	+	0.377079i	−0.954107	−	0.299467i	$-0.903191\pi$
$967$	−6.76995	+	11.7259i	−0.217707	+	0.377079i	0.736400	+	0.676547i	$0.236524\pi$
$968$	35.4308	−	61.3679i	1.13879	−	1.97244i
$969$	37.2398	+	2.24131i	1.19631	+	0.0720012i
$970$	27.3844	+	47.4312i	0.879260	+	1.52292i
$971$	−12.1584			−0.390181			−0.195091	−	0.980785i	$-0.562500\pi$
$971$	−12.1584			−0.390181			−0.195091	+	0.980785i	$0.562500\pi$
$972$	57.6784	−	53.3711i	1.85004	−	1.71188i
$973$	−21.2170			−0.680185
$974$	−14.2849	−	24.7422i	−0.457718	−	0.792791i
$975$	−0.476300	−	0.0286666i	−0.0152538	−	0.000918065i
$976$	−13.5476	+	23.4651i	−0.433648	+	0.751101i
$977$	13.3002	−	23.0367i	0.425512	−	0.737008i	−0.570956	−	0.820980i	$-0.693427\pi$
$977$	13.3002	−	23.0367i	0.425512	−	0.737008i	0.996468	+	0.0839724i	$0.0267608\pi$
$978$	−50.0749	−	100.190i	−1.60122	−	3.20374i
$979$	−0.179544	−	0.310979i	−0.00573825	−	0.00993893i
$980$	−45.8062			−1.46323
$981$	−23.1780	−	2.80012i	−0.740015	−	0.0894008i
$982$	69.4777			2.21712
$983$	10.9945	+	19.0431i	0.350671	+	0.607379i	0.986367	−	0.164560i	$-0.0526204\pi$
$983$	10.9945	+	19.0431i	0.350671	+	0.607379i	−0.635697	+	0.771939i	$0.719287\pi$
$984$	−38.2133	+	57.8563i	−1.21820	+	1.84439i
$985$	−10.2121	+	17.6878i	−0.325383	+	0.563580i
$986$	0.508150	−	0.880142i	0.0161828	−	0.0280294i
$987$	21.0053	−	31.8027i	0.668605	−	1.01229i
$988$	61.0041	+	105.662i	1.94080	+	3.36156i
$989$	90.0093			2.86213
$990$	10.3416	+	24.2320i	0.328677	+	0.770143i
$991$	−54.1490			−1.72010			−0.860050	−	0.510209i	$-0.829568\pi$
$991$	−54.1490			−1.72010			−0.860050	+	0.510209i	$0.829568\pi$
$992$	−17.7016	−	30.6601i	−0.562027	−	0.973460i
$993$	14.9616	+	29.9354i	0.474793	+	0.949971i
$994$	31.7663	−	55.0208i	1.00756	−	1.74515i
$995$	−28.6756	+	49.6676i	−0.909077	+	1.57457i
$996$	−54.2710	−	3.26635i	−1.71964	−	0.103498i
$997$	−14.1173	−	24.4519i	−0.447099	−	0.774398i	0.551097	−	0.834441i	$-0.314210\pi$
$997$	−14.1173	−	24.4519i	−0.447099	−	0.774398i	−0.998196	+	0.0600431i	$0.980876\pi$
$998$	64.3811			2.03795
$999$	30.2662	+	5.51816i	0.957580	+	0.174587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.e.a.202.3	✓	66
9.4	even	3		5427.2.a.p.1.31		33
9.5	odd	6		5427.2.a.o.1.3		33
9.7	even	3	inner	603.2.e.a.403.3	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.e.a.202.3	✓	66	1.1	even	1	trivial
603.2.e.a.403.3	yes	66	9.7	even	3	inner
5427.2.a.o.1.3		33	9.5	odd	6
5427.2.a.p.1.31		33	9.4	even	3

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32675 - 2.29800i) q^{2} +(-1.72892 - 0.104057i) q^{3} +(-2.52055 + 4.36572i) q^{4} +(-1.11098 + 1.92427i) q^{5} +(2.05473 + 4.11113i) q^{6} +(-0.853017 - 1.47747i) q^{7} +8.06957 q^{8} +(2.97834 + 0.359812i) q^{9} +O(q^{10})\)	\(q+(-1.32675 - 2.29800i) q^{2} +(-1.72892 - 0.104057i) q^{3} +(-2.52055 + 4.36572i) q^{4} +(-1.11098 + 1.92427i) q^{5} +(2.05473 + 4.11113i) q^{6} +(-0.853017 - 1.47747i) q^{7} +8.06957 q^{8} +(2.97834 + 0.359812i) q^{9} +5.89596 q^{10} +(0.744761 + 1.28996i) q^{11} +(4.81212 - 7.28571i) q^{12} +(2.18862 - 3.79080i) q^{13} +(-2.26349 + 3.92047i) q^{14} +(2.12102 - 3.21130i) q^{15} +(-5.66523 - 9.81247i) q^{16} -3.89554 q^{17} +(-3.12468 - 7.32163i) q^{18} +5.52922 q^{19} +(-5.60053 - 9.70041i) q^{20} +(1.32106 + 2.64319i) q^{21} +(1.97623 - 3.42293i) q^{22} +(-3.49756 + 6.05795i) q^{23} +(-13.9517 - 0.839694i) q^{24} +(0.0314685 + 0.0545050i) q^{25} -11.6150 q^{26} +(-5.11189 - 0.932004i) q^{27} +8.60028 q^{28} +(-0.0491591 - 0.0851461i) q^{29} +(-10.1937 - 0.613515i) q^{30} +(-1.27109 + 2.20159i) q^{31} +(-6.96317 + 12.0606i) q^{32} +(-1.15340 - 2.30775i) q^{33} +(5.16842 + 8.95196i) q^{34} +3.79072 q^{35} +(-9.07790 + 12.0957i) q^{36} -5.92075 q^{37} +(-7.33591 - 12.7062i) q^{38} +(-4.17841 + 6.32625i) q^{39} +(-8.96509 + 15.5280i) q^{40} +(2.48041 - 4.29620i) q^{41} +(4.32134 - 6.54266i) q^{42} +(-6.43372 - 11.1435i) q^{43} -7.50883 q^{44} +(-4.00124 + 5.33138i) q^{45} +18.5616 q^{46} +(-6.44911 - 11.1702i) q^{47} +(8.77370 + 17.5545i) q^{48} +(2.04472 - 3.54157i) q^{49} +(0.0835018 - 0.144629i) q^{50} +(6.73508 + 0.405357i) q^{51} +(11.0330 + 19.1098i) q^{52} +4.74157 q^{53} +(4.64046 + 12.9837i) q^{54} -3.30965 q^{55} +(-6.88348 - 11.9225i) q^{56} +(-9.55960 - 0.575353i) q^{57} +(-0.130444 + 0.225936i) q^{58} +(-1.98777 + 3.44292i) q^{59} +(8.67349 + 17.3540i) q^{60} +(-1.19568 - 2.07098i) q^{61} +6.74570 q^{62} +(-2.00897 - 4.70734i) q^{63} +14.2927 q^{64} +(4.86300 + 8.42296i) q^{65} +(-3.77293 + 5.71234i) q^{66} +(-0.500000 + 0.866025i) q^{67} +(9.81889 - 17.0068i) q^{68} +(6.67738 - 10.1098i) q^{69} +(-5.02935 - 8.71110i) q^{70} -14.0342 q^{71} +(24.0340 + 2.90353i) q^{72} +6.17855 q^{73} +(7.85537 + 13.6059i) q^{74} +(-0.0487350 - 0.0975095i) q^{75} +(-13.9367 + 24.1390i) q^{76} +(1.27059 - 2.20072i) q^{77} +(20.0815 + 1.20862i) q^{78} +(-1.52260 - 2.63722i) q^{79} +25.1757 q^{80} +(8.74107 + 2.14329i) q^{81} -13.1636 q^{82} +(-3.11342 - 5.39259i) q^{83} +(-14.8692 - 0.894918i) q^{84} +(4.32785 - 7.49605i) q^{85} +(-17.0719 + 29.5694i) q^{86} +(0.0761323 + 0.152326i) q^{87} +(6.00991 + 10.4095i) q^{88} -0.241076 q^{89} +(17.5602 + 2.12144i) q^{90} -7.46771 q^{91} +(-17.6315 - 30.5387i) q^{92} +(2.42671 - 3.67412i) q^{93} +(-17.1127 + 29.6401i) q^{94} +(-6.14283 + 10.6397i) q^{95} +(13.2938 - 20.1272i) q^{96} +(4.64461 + 8.04469i) q^{97} -10.8514 q^{98} +(1.75401 + 4.10993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9	\( 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9} - 8 q^{11} + q^{12} - 7 q^{14} + 3 q^{15} - 33 q^{16} + 66 q^{17} - 11 q^{18} - 29 q^{20} + q^{21} - 17 q^{23} + 47 q^{24} - 33 q^{25} + 60 q^{26} - 21 q^{27} - 54 q^{28} - 39 q^{29} - 34 q^{30} - 53 q^{32} + 8 q^{33} - 6 q^{34} + 62 q^{35} - 35 q^{36} + 24 q^{37} - 30 q^{38} - 5 q^{39} - 6 q^{40} - 38 q^{41} + 65 q^{42} + 22 q^{44} - 9 q^{45} + 12 q^{46} - 58 q^{47} - 59 q^{48} - 33 q^{49} - 31 q^{50} + 26 q^{51} + 9 q^{52} + 128 q^{53} - 22 q^{54} - 36 q^{55} - 32 q^{56} - 34 q^{57} + 3 q^{58} - 39 q^{59} + 127 q^{60} + 138 q^{62} - 35 q^{63} + 132 q^{64} - 28 q^{65} - 94 q^{66} - 33 q^{67} - 62 q^{68} + 60 q^{69} - 6 q^{70} + 42 q^{71} - 34 q^{72} - 25 q^{74} + 55 q^{75} - 6 q^{76} - 91 q^{77} + 125 q^{78} + 116 q^{80} - 90 q^{82} - 61 q^{83} - 26 q^{84} + 15 q^{85} - 47 q^{86} - q^{87} - 12 q^{88} + 110 q^{89} - 91 q^{90} + 36 q^{91} - 41 q^{92} - 11 q^{93} - 21 q^{94} - 6 q^{95} + 80 q^{96} - 12 q^{97} + 80 q^{98} - 38 q^{99}+O(q^{100}) \) 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9 - 8 * q^11 + q^12 - 7 * q^14 + 3 * q^15 - 33 * q^16 + 66 * q^17 - 11 * q^18 - 29 * q^20 + q^21 - 17 * q^23 + 47 * q^24 - 33 * q^25 + 60 * q^26 - 21 * q^27 - 54 * q^28 - 39 * q^29 - 34 * q^30 - 53 * q^32 + 8 * q^33 - 6 * q^34 + 62 * q^35 - 35 * q^36 + 24 * q^37 - 30 * q^38 - 5 * q^39 - 6 * q^40 - 38 * q^41 + 65 * q^42 + 22 * q^44 - 9 * q^45 + 12 * q^46 - 58 * q^47 - 59 * q^48 - 33 * q^49 - 31 * q^50 + 26 * q^51 + 9 * q^52 + 128 * q^53 - 22 * q^54 - 36 * q^55 - 32 * q^56 - 34 * q^57 + 3 * q^58 - 39 * q^59 + 127 * q^60 + 138 * q^62 - 35 * q^63 + 132 * q^64 - 28 * q^65 - 94 * q^66 - 33 * q^67 - 62 * q^68 + 60 * q^69 - 6 * q^70 + 42 * q^71 - 34 * q^72 - 25 * q^74 + 55 * q^75 - 6 * q^76 - 91 * q^77 + 125 * q^78 + 116 * q^80 - 90 * q^82 - 61 * q^83 - 26 * q^84 + 15 * q^85 - 47 * q^86 - q^87 - 12 * q^88 + 110 * q^89 - 91 * q^90 + 36 * q^91 - 41 * q^92 - 11 * q^93 - 21 * q^94 - 6 * q^95 + 80 * q^96 - 12 * q^97 + 80 * q^98 - 38 * q^99

Introduction

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