LMFDB - Embedded newform 48.2.k.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,2,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, 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:	$0.383281929702$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.2
Root			$1.27715 - 0.607364i$ of defining polynomial
Character	$\chi$	$=$	48.11
Dual form			48.2.k.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.607364 + 1.27715i) q^{2} +(1.73003 + 0.0835731i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(-0.431733 + 0.431733i) q^{5} +(-1.15749 + 2.15875i) q^{6} -3.10278 q^{7} +(2.74798 - 0.669785i) q^{8} +(2.98603 + 0.289169i) q^{9} +O(q^{10})$	\(q+(-0.607364 + 1.27715i) q^{2} +(1.73003 + 0.0835731i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(-0.431733 + 0.431733i) q^{5} +(-1.15749 + 2.15875i) q^{6} -3.10278 q^{7} +(2.74798 - 0.669785i) q^{8} +(2.98603 + 0.289169i) q^{9} +(-0.289169 - 0.813607i) q^{10} +(-2.98603 - 2.98603i) q^{11} +(-2.05403 - 2.78944i) q^{12} +(2.10278 - 2.10278i) q^{13} +(1.88451 - 3.96271i) q^{14} +(-0.782994 + 0.710831i) q^{15} +(-0.813607 + 3.91638i) q^{16} +2.42945i q^{17} +(-2.18292 + 3.63798i) q^{18} +(-0.710831 - 0.710831i) q^{19} +(1.21473 + 0.124844i) q^{20} +(-5.36790 - 0.259309i) q^{21} +(5.62721 - 2.00000i) q^{22} +5.97206i q^{23} +(4.81007 - 0.929094i) q^{24} +4.62721i q^{25} +(1.40841 + 3.96271i) q^{26} +(5.14177 + 0.749823i) q^{27} +(3.91638 + 4.81361i) q^{28} +(-2.86119 - 2.86119i) q^{29} +(-0.432276 - 1.43173i) q^{30} -0.524438i q^{31} +(-4.50765 - 3.41776i) q^{32} +(-4.91638 - 5.41549i) q^{33} +(-3.10278 - 1.47556i) q^{34} +(1.33957 - 1.33957i) q^{35} +(-3.32041 - 4.99749i) q^{36} +(1.52444 + 1.52444i) q^{37} +(1.33957 - 0.476105i) q^{38} +(3.81361 - 3.46214i) q^{39} +(-0.897225 + 1.47556i) q^{40} -1.81568 q^{41} +(3.59145 - 6.69812i) q^{42} +(0.710831 - 0.710831i) q^{43} +(-0.863466 + 8.40152i) q^{44} +(-1.41401 + 1.16432i) q^{45} +(-7.62721 - 3.62721i) q^{46} +7.53805 q^{47} +(-1.73487 + 6.70748i) q^{48} +2.62721 q^{49} +(-5.90964 - 2.81040i) q^{50} +(-0.203037 + 4.20304i) q^{51} +(-5.91638 - 0.608056i) q^{52} +(8.83325 - 8.83325i) q^{53} +(-4.08056 + 6.11139i) q^{54} +2.57834 q^{55} +(-8.52636 + 2.07819i) q^{56} +(-1.17036 - 1.28917i) q^{57} +(5.39194 - 1.91638i) q^{58} +(0.0804722 + 0.0804722i) q^{59} +(2.09108 + 0.317502i) q^{60} +(-5.72999 + 5.72999i) q^{61} +(0.669785 + 0.318525i) q^{62} +(-9.26498 - 0.897225i) q^{63} +(7.10278 - 3.68111i) q^{64} +1.81568i q^{65} +(9.90241 - 2.98978i) q^{66} +(-0.391944 - 0.391944i) q^{67} +(3.76903 - 3.06650i) q^{68} +(-0.499104 + 10.3319i) q^{69} +(0.897225 + 2.52444i) q^{70} -5.01985i q^{71} +(8.39923 - 1.20537i) q^{72} -13.4600i q^{73} +(-2.87282 + 1.02105i) q^{74} +(-0.386711 + 8.00523i) q^{75} +(-0.205550 + 2.00000i) q^{76} +(9.26498 + 9.26498i) q^{77} +(2.10542 + 6.97332i) q^{78} -3.47556i q^{79} +(-1.33957 - 2.04209i) q^{80} +(8.83276 + 1.72693i) q^{81} +(1.10278 - 2.31889i) q^{82} +(-4.55202 + 4.55202i) q^{83} +(6.37318 + 8.65500i) q^{84} +(-1.04888 - 1.04888i) q^{85} +(0.476105 + 1.33957i) q^{86} +(-4.71083 - 5.18907i) q^{87} +(-10.2056 - 6.20555i) q^{88} -12.5579 q^{89} +(-0.628197 - 2.51307i) q^{90} +(-6.52444 + 6.52444i) q^{91} +(9.26498 - 7.53805i) q^{92} +(0.0438289 - 0.907295i) q^{93} +(-4.57834 + 9.62721i) q^{94} +0.613779 q^{95} +(-7.51275 - 6.28956i) q^{96} -8.67609 q^{97} +(-1.59567 + 3.35534i) q^{98} +(-8.05292 - 9.77985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.607364	+	1.27715i	−0.429471	+	0.903081i
$2$	−0.607364	+	1.27715i	−0.429471	+	0.903081i
$3$	1.73003	+	0.0835731i	0.998835	+	0.0482510i
$3$	1.73003	+	0.0835731i	0.998835	+	0.0482510i
$4$	−1.26222	−	1.55139i	−0.631109	−	0.775694i
$5$	−0.431733	+	0.431733i	−0.193077	+	0.193077i	−0.797024	−	0.603947i	$-0.793594\pi$
$5$	−0.431733	+	0.431733i	−0.193077	+	0.193077i	0.603947	+	0.797024i	$0.293594\pi$
$6$	−1.15749	+	2.15875i	−0.472545	+	0.881306i
$7$	−3.10278			−1.17274			−0.586369	−	0.810044i	$-0.699443\pi$
$7$	−3.10278			−1.17274			−0.586369	+	0.810044i	$0.699443\pi$
$8$	2.74798	−	0.669785i	0.971557	−	0.236805i
$9$	2.98603	+	0.289169i	0.995344	+	0.0963895i
$10$	−0.289169	−	0.813607i	−0.0914431	−	0.257285i
$11$	−2.98603	−	2.98603i	−0.900322	−	0.900322i	0.0951415	−	0.995464i	$-0.469670\pi$
$11$	−2.98603	−	2.98603i	−0.900322	−	0.900322i	−0.995464	+	0.0951415i	$0.969670\pi$
$12$	−2.05403	−	2.78944i	−0.592946	−	0.805242i
$13$	2.10278	−	2.10278i	0.583205	−	0.583205i	−0.352578	−	0.935783i	$-0.614695\pi$
$13$	2.10278	−	2.10278i	0.583205	−	0.583205i	0.935783	+	0.352578i	$0.114695\pi$
$14$	1.88451	−	3.96271i	0.503657	−	1.05908i
$15$	−0.782994	+	0.710831i	−0.202168	+	0.183536i
$16$	−0.813607	+	3.91638i	−0.203402	+	0.979095i
$17$			2.42945i			0.589229i	0.955616	+	0.294615i	$0.0951913\pi$
$17$			2.42945i			0.589229i	−0.955616	+	0.294615i	$0.904809\pi$
$18$	−2.18292	+	3.63798i	−0.514519	+	0.857479i
$19$	−0.710831	−	0.710831i	−0.163076	−	0.163076i	0.620852	−	0.783928i	$-0.286787\pi$
$19$	−0.710831	−	0.710831i	−0.163076	−	0.163076i	−0.783928	+	0.620852i	$0.786787\pi$
$20$	1.21473	+	0.124844i	0.271621	+	0.0279159i
$21$	−5.36790	−	0.259309i	−1.17137	−	0.0565858i
$22$	5.62721	−	2.00000i	1.19973	−	0.426401i
$23$			5.97206i			1.24526i	0.782516	+	0.622631i	$0.213936\pi$
$23$			5.97206i			1.24526i	−0.782516	+	0.622631i	$0.786064\pi$
$24$	4.81007	−	0.929094i	0.981852	−	0.189651i
$25$			4.62721i			0.925443i
$26$	1.40841	+	3.96271i	0.276212	+	0.777151i
$27$	5.14177	+	0.749823i	0.989533	+	0.144304i
$28$	3.91638	+	4.81361i	0.740127	+	0.909686i
$29$	−2.86119	−	2.86119i	−0.531309	−	0.531309i	0.389653	−	0.920962i	$-0.372595\pi$
$29$	−2.86119	−	2.86119i	−0.531309	−	0.531309i	−0.920962	+	0.389653i	$0.872595\pi$
$30$	−0.432276	−	1.43173i	−0.0789224	−	0.261398i
$31$		−	0.524438i		−	0.0941918i	−0.998890	−	0.0470959i	$-0.985003\pi$
$31$		−	0.524438i		−	0.0941918i	0.998890	−	0.0470959i	$-0.0149966\pi$
$32$	−4.50765	−	3.41776i	−0.796847	−	0.604181i
$33$	−4.91638	−	5.41549i	−0.855832	−	0.942715i
$34$	−3.10278	−	1.47556i	−0.532122	−	0.253057i
$35$	1.33957	−	1.33957i	0.226429	−	0.226429i
$36$	−3.32041	−	4.99749i	−0.553402	−	0.832914i
$37$	1.52444	+	1.52444i	0.250616	+	0.250616i	0.821223	−	0.570607i	$-0.193292\pi$
$37$	1.52444	+	1.52444i	0.250616	+	0.250616i	−0.570607	+	0.821223i	$0.693292\pi$
$38$	1.33957	−	0.476105i	0.217307	−	0.0772344i
$39$	3.81361	−	3.46214i	0.610666	−	0.554385i
$40$	−0.897225	+	1.47556i	−0.141864	+	0.233307i
$41$	−1.81568			−0.283561			−0.141780	−	0.989898i	$-0.545283\pi$
$41$	−1.81568			−0.283561			−0.141780	+	0.989898i	$0.545283\pi$
$42$	3.59145	−	6.69812i	0.554172	−	1.03354i
$43$	0.710831	−	0.710831i	0.108401	−	0.108401i	−0.650826	−	0.759227i	$-0.725577\pi$
$43$	0.710831	−	0.710831i	0.108401	−	0.108401i	0.759227	+	0.650826i	$0.225577\pi$
$44$	−0.863466	+	8.40152i	−0.130172	+	1.26658i
$45$	−1.41401	+	1.16432i	−0.210788	+	0.173567i
$46$	−7.62721	−	3.62721i	−1.12457	−	0.534803i
$47$	7.53805			1.09954			0.549769	−	0.835317i	$-0.314716\pi$
$47$	7.53805			1.09954			0.549769	+	0.835317i	$0.314716\pi$
$48$	−1.73487	+	6.70748i	−0.250407	+	0.968141i
$49$	2.62721			0.375316
$50$	−5.90964	−	2.81040i	−0.835749	−	0.397451i
$51$	−0.203037	+	4.20304i	−0.0284309	+	0.588543i
$52$	−5.91638	−	0.608056i	−0.820455	−	0.0843223i
$53$	8.83325	−	8.83325i	1.21334	−	1.21334i	0.243419	−	0.969921i	$-0.421731\pi$
$53$	8.83325	−	8.83325i	1.21334	−	1.21334i	0.969921	−	0.243419i	$-0.0782690\pi$
$54$	−4.08056	+	6.11139i	−0.555294	+	0.831654i
$55$	2.57834			0.347663
$56$	−8.52636	+	2.07819i	−1.13938	+	0.277710i
$57$	−1.17036	−	1.28917i	−0.155017	−	0.170755i
$58$	5.39194	−	1.91638i	0.707997	−	0.251633i
$59$	0.0804722	+	0.0804722i	0.0104766	+	0.0104766i	0.712326	−	0.701849i	$-0.247642\pi$
$59$	0.0804722	+	0.0804722i	0.0104766	+	0.0104766i	−0.701849	+	0.712326i	$0.747642\pi$
$60$	2.09108	+	0.317502i	0.269958	+	0.0409894i
$61$	−5.72999	+	5.72999i	−0.733650	+	0.733650i	−0.971341	−	0.237691i	$-0.923609\pi$
$61$	−5.72999	+	5.72999i	−0.733650	+	0.733650i	0.237691	+	0.971341i	$0.423609\pi$
$62$	0.669785	+	0.318525i	0.0850628	+	0.0404527i
$63$	−9.26498	−	0.897225i	−1.16728	−	0.113040i
$64$	7.10278	−	3.68111i	0.887847	−	0.460139i
$65$			1.81568i			0.225207i
$66$	9.90241	−	2.98978i	1.21890	−	0.368017i
$67$	−0.391944	−	0.391944i	−0.0478835	−	0.0478835i	0.682760	−	0.730643i	$-0.260780\pi$
$67$	−0.391944	−	0.391944i	−0.0478835	−	0.0478835i	−0.730643	+	0.682760i	$0.760780\pi$
$68$	3.76903	−	3.06650i	0.457061	−	0.371868i
$69$	−0.499104	+	10.3319i	−0.0600850	+	1.24381i
$70$	0.897225	+	2.52444i	0.107239	+	0.301728i
$71$		−	5.01985i		−	0.595747i	−0.954605	−	0.297873i	$-0.903723\pi$
$71$		−	5.01985i		−	0.595747i	0.954605	−	0.297873i	$-0.0962774\pi$
$72$	8.39923	−	1.20537i	0.989859	−	0.142054i
$73$		−	13.4600i		−	1.57537i	−0.616078	−	0.787686i	$-0.711279\pi$
$73$		−	13.4600i		−	1.57537i	0.616078	−	0.787686i	$-0.288721\pi$
$74$	−2.87282	+	1.02105i	−0.333959	+	0.118694i
$75$	−0.386711	+	8.00523i	−0.0446535	+	0.924365i
$76$	−0.205550	+	2.00000i	−0.0235782	+	0.229416i
$77$	9.26498	+	9.26498i	1.05584	+	1.05584i
$78$	2.10542	+	6.97332i	0.238392	+	0.789573i
$79$		−	3.47556i		−	0.391031i	−0.980701	−	0.195516i	$-0.937362\pi$
$79$		−	3.47556i		−	0.391031i	0.980701	−	0.195516i	$-0.0626380\pi$
$80$	−1.33957	−	2.04209i	−0.149769	−	0.228313i
$81$	8.83276	+	1.72693i	0.981418	+	0.191881i
$82$	1.10278	−	2.31889i	0.121781	−	0.256078i
$83$	−4.55202	+	4.55202i	−0.499649	+	0.499649i	−0.911329	−	0.411680i	$-0.864942\pi$
$83$	−4.55202	+	4.55202i	−0.499649	+	0.499649i	0.411680	+	0.911329i	$0.364942\pi$
$84$	6.37318	+	8.65500i	0.695371	+	0.944338i
$85$	−1.04888	−	1.04888i	−0.113767	−	0.113767i
$86$	0.476105	+	1.33957i	0.0513397	+	0.144450i
$87$	−4.71083	−	5.18907i	−0.505054	−	0.556326i
$88$	−10.2056	−	6.20555i	−1.08792	−	0.661514i
$89$	−12.5579			−1.33114			−0.665568	−	0.746338i	$-0.731810\pi$
$89$	−12.5579			−1.33114			−0.665568	+	0.746338i	$0.731810\pi$
$90$	−0.628197	−	2.51307i	−0.0662178	−	0.264901i
$91$	−6.52444	+	6.52444i	−0.683947	+	0.683947i
$92$	9.26498	−	7.53805i	0.965941	−	0.785896i
$93$	0.0438289	−	0.907295i	0.00454485	−	0.0940821i
$94$	−4.57834	+	9.62721i	−0.472219	+	0.992971i
$95$	0.613779			0.0629724
$96$	−7.51275	−	6.28956i	−0.766767	−	0.641926i
$97$	−8.67609			−0.880923			−0.440462	−	0.897771i	$-0.645185\pi$
$97$	−8.67609			−0.880923			−0.440462	+	0.897771i	$0.645185\pi$
$98$	−1.59567	+	3.35534i	−0.161187	+	0.338941i
$99$	−8.05292	−	9.77985i	−0.809348	−	0.982912i
$100$	7.17860	−	5.84056i	0.717860	−	0.584056i
$101$	−0.182046	+	0.182046i	−0.0181142	+	0.0181142i	−0.716106	−	0.697992i	$-0.754077\pi$
$101$	−0.182046	+	0.182046i	−0.0181142	+	0.0181142i	0.697992	+	0.716106i	$0.254077\pi$
$102$	−5.24459	−	2.81208i	−0.519292	−	0.278437i
$103$	6.35720			0.626394			0.313197	−	0.949688i	$-0.398600\pi$
$103$	6.35720			0.626394			0.313197	+	0.949688i	$0.398600\pi$
$104$	4.36997	−	7.18679i	0.428511	−	0.704723i
$105$	2.42945	−	2.20555i	0.237090	−	0.215240i
$106$	5.91638	+	16.6464i	0.574650	+	1.61684i
$107$	−1.64646	−	1.64646i	−0.159169	−	0.159169i	0.623029	−	0.782199i	$-0.285902\pi$
$107$	−1.64646	−	1.64646i	−0.159169	−	0.159169i	−0.782199	+	0.623029i	$0.785902\pi$
$108$	−5.32677	−	8.92331i	−0.512569	−	0.858646i
$109$	6.57331	−	6.57331i	0.629609	−	0.629609i	−0.318360	−	0.947970i	$-0.603132\pi$
$109$	6.57331	−	6.57331i	0.629609	−	0.629609i	0.947970	+	0.318360i	$0.103132\pi$
$110$	−1.56599	+	3.29292i	−0.149311	+	0.313968i
$111$	2.50993	+	2.76473i	0.238232	+	0.262417i
$112$	2.52444	−	12.1517i	0.238537	−	1.14822i
$113$			8.31277i			0.782000i	0.920391	+	0.391000i	$0.127871\pi$
$113$			8.31277i			0.782000i	−0.920391	+	0.391000i	$0.872129\pi$
$114$	2.35729	−	0.711725i	0.220781	−	0.0666591i
$115$	−2.57834	−	2.57834i	−0.240431	−	0.240431i
$116$	−0.827365	+	8.05026i	−0.0768189	+	0.747447i
$117$	6.88701	−	5.67090i	0.636704	−	0.524274i
$118$	−0.151651	+	0.0538991i	−0.0139606	+	0.00496182i
$119$		−	7.53805i		−	0.691012i
$120$	−1.67555	+	2.47779i	−0.152956	+	0.226190i
$121$			6.83276i			0.621160i
$122$	−3.83786	−	10.7982i	−0.347464	−	0.977626i
$123$	−3.14118	−	0.151742i	−0.283231	−	0.0136821i
$124$	−0.813607	+	0.661956i	−0.0730640	+	0.0594454i
$125$	−4.15639	−	4.15639i	−0.371759	−	0.371759i
$126$	6.77310	−	11.2878i	0.603396	−	1.00560i
$127$			15.7789i			1.40015i	0.714070	+	0.700074i	$0.246850\pi$
$127$			15.7789i			1.40015i	−0.714070	+	0.700074i	$0.753150\pi$
$128$	0.387362	+	11.3071i	0.0342383	+	0.999414i
$129$	1.28917	−	1.17036i	0.113505	−	0.103044i
$130$	−2.31889	−	1.10278i	−0.203380	−	0.0967198i
$131$	−0.0804722	+	0.0804722i	−0.00703089	+	0.00703089i	−0.710613	−	0.703583i	$-0.751583\pi$
$131$	−0.0804722	+	0.0804722i	−0.00703089	+	0.00703089i	0.703583	+	0.710613i	$0.251583\pi$
$132$	−2.19597	+	14.4627i	−0.191134	+	1.25882i
$133$	2.20555	+	2.20555i	0.191245	+	0.191245i
$134$	0.738623	−	0.262518i	0.0638073	−	0.0226781i
$135$	−2.54359	+	1.89615i	−0.218918	+	0.163194i
$136$	1.62721	+	6.67609i	0.139532	+	0.572470i
$137$	13.2604			1.13291			0.566457	−	0.824091i	$-0.308314\pi$
$137$	13.2604			1.13291			0.566457	+	0.824091i	$0.308314\pi$
$138$	−12.8922	−	6.91263i	−1.09746	−	0.588442i
$139$	8.39194	−	8.39194i	0.711795	−	0.711795i	−0.255115	−	0.966911i	$-0.582113\pi$
$139$	8.39194	−	8.39194i	0.711795	−	0.711795i	0.966911	+	0.255115i	$0.0821134\pi$
$140$	−3.76903	−	0.387362i	−0.318541	−	0.0327380i
$141$	13.0411	+	0.629978i	1.09826	+	0.0530537i
$142$	6.41110	+	3.04888i	0.538008	+	0.255856i
$143$	−12.5579			−1.05014
$144$	−3.56195	+	11.4592i	−0.296829	+	0.954931i
$145$	2.47054			0.205167
$146$	17.1904	+	8.17510i	1.42269	+	0.676576i
$147$	4.54517	+	0.219564i	0.374879	+	0.0181094i
$148$	0.440820	−	4.28917i	0.0362351	−	0.352567i
$149$	−5.79002	+	5.79002i	−0.474337	+	0.474337i	−0.903315	−	0.428978i	$-0.858874\pi$
$149$	−5.79002	+	5.79002i	−0.474337	+	0.474337i	0.428978	+	0.903315i	$0.358874\pi$
$150$	−9.98900	−	5.35597i	−0.815599	−	0.437313i
$151$	9.94610			0.809402			0.404701	−	0.914449i	$-0.367376\pi$
$151$	9.94610			0.809402			0.404701	+	0.914449i	$0.367376\pi$
$152$	−2.42945	−	1.47725i	−0.197055	−	0.119820i
$153$	−0.702522	+	7.25443i	−0.0567955	+	0.586486i
$154$	−17.4600	+	6.20555i	−1.40696	+	0.500057i
$155$	0.226417	+	0.226417i	0.0181863	+	0.0181863i
$156$	−10.1847	−	1.54641i	−0.815430	−	0.123812i
$157$	−9.15165	+	9.15165i	−0.730381	+	0.730381i	−0.970695	−	0.240314i	$-0.922750\pi$
$157$	−9.15165	+	9.15165i	−0.730381	+	0.730381i	0.240314	+	0.970695i	$0.422750\pi$
$158$	4.43881	+	2.11093i	0.353133	+	0.167937i
$159$	16.0200	−	14.5436i	1.27047	−	1.15338i
$160$	3.42166	−	0.470539i	0.270506	−	0.0371994i
$161$		−	18.5300i		−	1.46037i
$162$	−7.57025	+	10.2319i	−0.594775	+	0.803892i
$163$	15.7003	+	15.7003i	1.22974	+	1.22974i	0.964062	+	0.265678i	$0.0855959\pi$
$163$	15.7003	+	15.7003i	1.22974	+	1.22974i	0.265678	+	0.964062i	$0.414404\pi$
$164$	2.29178	+	2.81682i	0.178958	+	0.219956i
$165$	4.46061	+	0.215480i	0.347258	+	0.0167751i
$166$	−3.04888	−	8.57834i	−0.236639	−	0.665808i
$167$			19.1437i			1.48139i	0.671843	+	0.740694i	$0.265503\pi$
$167$			19.1437i			1.48139i	−0.671843	+	0.740694i	$0.734497\pi$
$168$	−14.9246	+	2.88277i	−1.15146	+	0.222410i
$169$			4.15667i			0.319744i
$170$	1.97662	−	0.702522i	0.151600	−	0.0538810i
$171$	−1.91701	−	2.32811i	−0.146598	−	0.178035i
$172$	−2.00000	−	0.205550i	−0.152499	−	0.0156730i
$173$	−13.3281	−	13.3281i	−1.01331	−	1.01331i	−0.999910	−	0.0134040i	$-0.995733\pi$
$173$	−13.3281	−	13.3281i	−1.01331	−	1.01331i	−0.0134040	−	0.999910i	$-0.504267\pi$
$174$	9.48840	−	2.86478i	0.719314	−	0.217179i
$175$		−	14.3572i		−	1.08530i
$176$	14.1239	−	9.26498i	1.06463	−	0.698374i
$177$	0.132494	+	0.145945i	0.00995889	+	0.0109699i
$178$	7.62721	−	16.0383i	0.571684	−	1.20212i
$179$	9.18451	−	9.18451i	0.686483	−	0.686483i	−0.274970	−	0.961453i	$-0.588668\pi$
$179$	9.18451	−	9.18451i	0.686483	−	0.686483i	0.961453	+	0.274970i	$0.0886680\pi$
$180$	3.59111	+	0.724048i	0.267666	+	0.0539673i
$181$	−16.5139	−	16.5139i	−1.22747	−	1.22747i	−0.964919	−	0.262548i	$-0.915437\pi$
$181$	−16.5139	−	16.5139i	−1.22747	−	1.22747i	−0.262548	−	0.964919i	$-0.584563\pi$
$182$	−4.36997	−	12.2954i	−0.323924	−	0.911395i
$183$	−10.3919	+	9.43420i	−0.768195	+	0.697396i
$184$	4.00000	+	16.4111i	0.294884	+	1.20984i
$185$	−1.31630			−0.0967764
$186$	1.13213	+	0.607034i	0.0830119	+	0.0445099i
$187$	7.25443	−	7.25443i	0.530496	−	0.530496i
$188$	−9.51467	−	11.6944i	−0.693929	−	0.852904i
$189$	−15.9537	−	2.32653i	−1.16046	−	0.169230i
$190$	−0.372787	+	0.783887i	−0.0270448	+	0.0568692i
$191$	3.17852			0.229989			0.114995	−	0.993366i	$-0.463315\pi$
$191$	3.17852			0.229989			0.114995	+	0.993366i	$0.463315\pi$
$192$	12.5957	−	5.77485i	0.909015	−	0.416764i
$193$	−11.4600			−0.824907			−0.412454	−	0.910979i	$-0.635328\pi$
$193$	−11.4600			−0.824907			−0.412454	+	0.910979i	$0.635328\pi$
$194$	5.26954	−	11.0807i	0.378331	−	0.795545i
$195$	−0.151742	+	3.14118i	−0.0108664	+	0.224944i
$196$	−3.31612	−	4.07583i	−0.236866	−	0.291130i
$197$	−14.8053	+	14.8053i	−1.05483	+	1.05483i	−0.0564281	+	0.998407i	$0.517971\pi$
$197$	−14.8053	+	14.8053i	−1.05483	+	1.05483i	−0.998407	+	0.0564281i	$0.982029\pi$
$198$	17.3814	−	4.34485i	1.23524	−	0.308775i
$199$	−24.4550			−1.73357			−0.866783	−	0.498686i	$-0.833816\pi$
$199$	−24.4550			−1.73357			−0.866783	+	0.498686i	$0.833816\pi$
$200$	3.09924	+	12.7155i	0.219149	+	0.899120i
$201$	−0.645320	−	0.710831i	−0.0455173	−	0.0501382i
$202$	−0.121932	−	0.343068i	−0.00857908	−	0.0241382i
$203$	8.87762	+	8.87762i	0.623087	+	0.623087i
$204$	6.77682	−	4.99016i	0.474472	−	0.349381i
$205$	0.783887	−	0.783887i	0.0547491	−	0.0547491i
$206$	−3.86113	+	8.11909i	−0.269018	+	0.565684i
$207$	−1.72693	+	17.8328i	−0.120030	+	1.23946i
$208$	6.52444	+	9.94610i	0.452388	+	0.689638i
$209$			4.24513i			0.293642i
$210$	1.34125	+	4.44235i	0.0925553	+	0.306551i
$211$	−6.18639	−	6.18639i	−0.425889	−	0.425889i	0.461336	−	0.887225i	$-0.347370\pi$
$211$	−6.18639	−	6.18639i	−0.425889	−	0.425889i	−0.887225	+	0.461336i	$0.847370\pi$
$212$	−24.8533	−	2.55430i	−1.70693	−	0.175430i
$213$	0.419525	−	8.68451i	0.0287454	−	0.595053i
$214$	3.10278	−	1.10278i	0.212101	−	0.0753842i
$215$			0.613779i			0.0418594i
$216$	14.6317	−	1.38338i	0.995560	−	0.0941272i
$217$			1.62721i			0.110462i
$218$	4.40271	+	12.3875i	0.298189	+	0.838987i
$219$	1.12489	−	23.2862i	0.0760132	−	1.57354i
$220$	−3.25443	−	4.00000i	−0.219413	−	0.269680i
$221$	5.10860	+	5.10860i	0.343641	+	0.343641i
$222$	−5.05541	+	1.52635i	−0.339297	+	0.102442i
$223$		−	8.18996i		−	0.548441i	−0.961667	−	0.274220i	$-0.911580\pi$
$223$		−	8.18996i		−	0.548441i	0.961667	−	0.274220i	$-0.0884197\pi$
$224$	13.9862	+	10.6046i	0.934493	+	0.708547i
$225$	−1.33804	+	13.8170i	−0.0892030	+	0.921133i
$226$	−10.6167	−	5.04888i	−0.706209	−	0.335846i
$227$	−9.91030	+	9.91030i	−0.657770	+	0.657770i	−0.954852	−	0.297082i	$-0.903986\pi$
$227$	−9.91030	+	9.91030i	−0.657770	+	0.657770i	0.297082	+	0.954852i	$0.403986\pi$
$228$	−0.522755	+	3.44289i	−0.0346203	+	0.228011i
$229$	7.15165	+	7.15165i	0.472594	+	0.472594i	0.902753	−	0.430159i	$-0.141542\pi$
$229$	7.15165	+	7.15165i	0.472594	+	0.472594i	−0.430159	+	0.902753i	$0.641542\pi$
$230$	4.85891	−	1.72693i	0.320387	−	0.113871i
$231$	15.2544	+	16.8030i	1.00367	+	1.10556i
$232$	−9.77886	−	5.94610i	−0.642014	−	0.390381i
$233$	19.6431			1.28686			0.643432	−	0.765503i	$-0.277510\pi$
$233$	19.6431			1.28686			0.643432	+	0.765503i	$0.277510\pi$
$234$	3.05966	+	12.2400i	0.200016	+	0.800156i
$235$	−3.25443	+	3.25443i	−0.212295	+	0.212295i
$236$	0.0232700	−	0.226417i	0.00151475	−	0.0147385i
$237$	0.290464	−	6.01284i	0.0188676	−	0.390576i
$238$	9.62721	+	4.57834i	0.624040	+	0.296770i
$239$	−9.44247			−0.610782			−0.305391	−	0.952227i	$-0.598787\pi$
$239$	−9.44247			−0.610782			−0.305391	+	0.952227i	$0.598787\pi$
$240$	−2.14684	−	3.64484i	−0.138578	−	0.235273i
$241$	16.6167			1.07037			0.535186	−	0.844734i	$-0.320241\pi$
$241$	16.6167			1.07037			0.535186	+	0.844734i	$0.320241\pi$
$242$	−8.72646	−	4.14997i	−0.560958	−	0.266770i
$243$	15.1366	+	3.72583i	0.971017	+	0.239012i
$244$	16.1219	+	1.65693i	1.03210	+	0.106074i
$245$	−1.13425	+	1.13425i	−0.0724649	+	0.0724649i
$246$	2.10163	−	3.91959i	0.133995	−	0.249904i
$247$	−2.98944			−0.190213
$248$	−0.351261	−	1.44114i	−0.0223051	−	0.0915128i
$249$	−8.25557	+	7.49472i	−0.523176	+	0.474958i
$250$	7.83276	−	2.78389i	0.495387	−	0.176068i
$251$	−2.03382	−	2.03382i	−0.128374	−	0.128374i	0.640001	−	0.768374i	$-0.278934\pi$
$251$	−2.03382	−	2.03382i	−0.128374	−	0.128374i	−0.768374	+	0.640001i	$0.778934\pi$
$252$	10.3025	+	15.5061i	0.648996	+	0.976791i
$253$	17.8328	−	17.8328i	1.12114	−	1.12114i
$254$	−20.1520	−	9.58351i	−1.26445	−	0.601323i
$255$	−1.72693	−	1.90225i	−0.108145	−	0.119123i
$256$	−14.6761	−	6.37279i	−0.917256	−	0.398299i
$257$		−	15.0761i		−	0.940421i	−0.882554	−	0.470211i	$-0.844178\pi$
$257$		−	15.0761i		−	0.940421i	0.882554	−	0.470211i	$-0.155822\pi$
$258$	0.711725	+	2.35729i	0.0443100	+	0.146759i
$259$	−4.72999	−	4.72999i	−0.293907	−	0.293907i
$260$	2.81682	−	2.29178i	0.174692	−	0.142130i
$261$	−7.71623	−	9.37096i	−0.477623	−	0.580048i
$262$	−0.0538991	−	0.151651i	−0.00332990	−	0.00936903i
$263$		−	29.8138i		−	1.83840i	−0.393796	−	0.919198i	$-0.628838\pi$
$263$		−	29.8138i		−	1.83840i	0.393796	−	0.919198i	$-0.371162\pi$
$264$	−17.1373	−	11.5887i	−1.05473	−	0.713236i
$265$			7.62721i			0.468536i
$266$	−4.15639	+	1.47725i	−0.254844	+	0.0905757i
$267$	−21.7256	−	1.04950i	−1.32958	−	0.0642285i
$268$	−0.113338	+	1.10278i	−0.00692321	+	0.0673627i
$269$	16.3713	+	16.3713i	0.998176	+	0.998176i	0.999998	−	0.00182258i	$-0.000580145\pi$
$269$	16.3713	+	16.3713i	0.998176	+	0.998176i	−0.00182258	+	0.999998i	$0.500580\pi$
$270$	−0.876776	−	4.40020i	−0.0533589	−	0.267788i
$271$			13.3466i			0.810751i	0.914150	+	0.405375i	$0.132859\pi$
$271$			13.3466i			0.810751i	−0.914150	+	0.405375i	$0.867141\pi$
$272$	−9.51467	−	1.97662i	−0.576912	−	0.119850i
$273$	−11.8328	+	10.7422i	−0.716151	+	0.650149i
$274$	−8.05390	+	16.9355i	−0.486554	+	1.02311i
$275$	13.8170	−	13.8170i	0.833197	−	0.833197i
$276$	16.6587	−	12.2668i	1.00274	−	0.738373i
$277$	10.6811	+	10.6811i	0.641766	+	0.641766i	0.950989	−	0.309224i	$-0.100069\pi$
$277$	10.6811	+	10.6811i	0.641766	+	0.641766i	−0.309224	+	0.950989i	$0.600069\pi$
$278$	5.62080	+	15.8147i	0.337113	+	0.948504i
$279$	0.151651	−	1.56599i	0.00907911	−	0.0937533i
$280$	2.78389	−	4.57834i	0.166369	−	0.273608i
$281$	17.5943			1.04959			0.524794	−	0.851229i	$-0.324142\pi$
$281$	17.5943			1.04959			0.524794	+	0.851229i	$0.324142\pi$
$282$	−8.72525	+	16.2728i	−0.519581	+	0.969030i
$283$	−17.1758	+	17.1758i	−1.02100	+	1.02100i	−0.0212224	+	0.999775i	$0.506756\pi$
$283$	−17.1758	+	17.1758i	−1.02100	+	1.02100i	−0.999775	+	0.0212224i	$0.993244\pi$
$284$	−7.78774	+	6.33615i	−0.462117	+	0.375982i
$285$	1.06186	+	0.0512954i	0.0628990	+	0.00303848i
$286$	7.62721	−	16.0383i	0.451007	−	0.948365i
$287$	5.63363			0.332543
$288$	−12.4717	−	11.5090i	−0.734900	−	0.678176i
$289$	11.0978			0.652809
$290$	−1.50052	+	3.15525i	−0.0881133	+	0.185282i
$291$	−15.0099	−	0.725088i	−0.879897	−	0.0425054i
$292$	−20.8816	+	16.9894i	−1.22201	+	0.994232i
$293$	3.72465	−	3.72465i	0.217597	−	0.217597i	−0.589888	−	0.807485i	$-0.700828\pi$
$293$	3.72465	−	3.72465i	0.217597	−	0.217597i	0.807485	+	0.589888i	$0.200828\pi$
$294$	−3.04098	+	5.67150i	−0.177354	+	0.330769i
$295$	−0.0694851			−0.00404558
$296$	5.21017	+	3.16808i	0.302835	+	0.184141i
$297$	−13.1145	−	17.5925i	−0.760979	−	1.02082i
$298$	−3.87807	−	10.9114i	−0.224650	−	0.632078i
$299$	12.5579	+	12.5579i	0.726242	+	0.726242i
$300$	12.9073	−	9.50442i	0.745205	−	0.548738i
$301$	−2.20555	+	2.20555i	−0.127126	+	0.127126i
$302$	−6.04090	+	12.7027i	−0.347615	+	0.730956i
$303$	−0.330160	+	0.299731i	−0.0189672	+	0.0172191i
$304$	3.36222	−	2.20555i	0.192837	−	0.126497i
$305$		−	4.94765i		−	0.283302i
$306$	−8.83830	−	5.30330i	−0.505252	−	0.303169i
$307$	−13.4408	−	13.4408i	−0.767108	−	0.767108i	0.210488	−	0.977596i	$-0.432495\pi$
$307$	−13.4408	−	13.4408i	−0.767108	−	0.767108i	−0.977596	+	0.210488i	$0.932495\pi$
$308$	2.67914	−	26.0680i	0.152658	−	1.48536i
$309$	10.9982	+	0.531291i	0.625664	+	0.0302241i
$310$	−0.426686	+	0.151651i	−0.0242341	+	0.00861320i
$311$		−	13.8320i		−	0.784341i	−0.919893	−	0.392170i	$-0.871724\pi$
$311$		−	13.8320i		−	0.784341i	0.919893	−	0.392170i	$-0.128276\pi$
$312$	8.16082	−	12.0682i	0.462016	−	0.683226i
$313$		−	3.94056i		−	0.222734i	−0.993779	−	0.111367i	$-0.964477\pi$
$313$		−	3.94056i		−	0.222734i	0.993779	−	0.111367i	$-0.0355229\pi$
$314$	−6.12964	−	17.2464i	−0.345916	−	0.973271i
$315$	4.38736	−	3.61264i	0.247200	−	0.203549i
$316$	−5.39194	+	4.38692i	−0.303321	+	0.246784i
$317$	−8.92199	−	8.92199i	−0.501109	−	0.501109i	0.410673	−	0.911782i	$-0.365294\pi$
$317$	−8.92199	−	8.92199i	−0.501109	−	0.501109i	−0.911782	+	0.410673i	$0.865294\pi$
$318$	8.84435	+	29.2932i	0.495966	+	1.64268i
$319$			17.0872i			0.956699i
$320$	−1.47725	+	4.65576i	−0.0825805	+	0.260265i
$321$	−2.71083	−	2.98603i	−0.151304	−	0.166664i
$322$	23.6655	+	11.2544i	1.31883	+	0.627185i
$323$	1.72693	−	1.72693i	0.0960891	−	0.0960891i
$324$	−8.46974	−	15.8828i	−0.470541	−	0.882378i
$325$	9.72999	+	9.72999i	0.539723	+	0.539723i
$326$	−29.5874	+	10.5158i	−1.63869	+	0.582417i
$327$	11.9214	−	10.8227i	0.659255	−	0.598497i
$328$	−4.98944	+	1.21611i	−0.275496	+	0.0671486i
$329$	−23.3889			−1.28947
$330$	−2.98441	+	5.56599i	−0.164286	+	0.306398i
$331$	9.44082	−	9.44082i	0.518914	−	0.518914i	−0.398328	−	0.917243i	$-0.630410\pi$
$331$	9.44082	−	9.44082i	0.518914	−	0.518914i	0.917243	+	0.398328i	$0.130410\pi$
$332$	12.8076	+	1.31630i	0.702908	+	0.0722414i
$333$	4.11120	+	4.99284i	0.225292	+	0.273606i
$334$	−24.4494	−	11.6272i	−1.33781	−	0.636213i
$335$	0.338430			0.0184904
$336$	5.38291	−	20.8118i	0.293662	−	1.13538i
$337$	5.94056			0.323603			0.161801	−	0.986823i	$-0.448270\pi$
$337$	5.94056			0.323603			0.161801	+	0.986823i	$0.448270\pi$
$338$	−5.30869	−	2.52461i	−0.288755	−	0.137321i
$339$	−0.694724	+	14.3814i	−0.0377322	+	0.781089i
$340$	−0.303302	+	2.95112i	−0.0164489	+	0.160047i
$341$	−1.56599	+	1.56599i	−0.0848030	+	0.0848030i
$342$	4.13767	−	1.03430i	0.223740	−	0.0559286i
$343$	13.5678			0.732591
$344$	1.47725	−	2.42945i	0.0796477	−	0.130987i
$345$	−4.24513	−	4.67609i	−0.228550	−	0.251752i
$346$	25.1169	−	8.92694i	1.35029	−	0.479915i
$347$	4.09918	+	4.09918i	0.220056	+	0.220056i	0.808522	−	0.588466i	$-0.200268\pi$
$347$	4.09918	+	4.09918i	0.220056	+	0.220056i	−0.588466	+	0.808522i	$0.700268\pi$
$348$	−2.10415	+	13.8581i	−0.112795	+	0.742870i
$349$	−8.10278	+	8.10278i	−0.433732	+	0.433732i	−0.889896	−	0.456164i	$-0.849223\pi$
$349$	−8.10278	+	8.10278i	−0.433732	+	0.433732i	0.456164	+	0.889896i	$0.349223\pi$
$350$	18.3363	+	8.72004i	0.980116	+	0.466106i
$351$	12.3887	−	9.23527i	0.661259	−	0.492942i
$352$	3.25443	+	23.6655i	0.173461	+	1.26138i
$353$			29.2465i			1.55664i	0.627870	+	0.778318i	$0.283927\pi$
$353$			29.2465i			1.55664i	−0.627870	+	0.778318i	$0.716073\pi$
$354$	−0.266866	+	0.0805734i	−0.0141838	+	0.00428243i
$355$	2.16724	+	2.16724i	0.115025	+	0.115025i
$356$	15.8508	+	19.4822i	0.840092	+	1.03255i
$357$	0.629978	−	13.0411i	0.0333420	−	0.690207i
$358$	6.15165	+	17.3083i	0.325125	+	0.914773i
$359$			21.3235i			1.12541i	0.826657	+	0.562706i	$0.190240\pi$
$359$			21.3235i			1.12541i	−0.826657	+	0.562706i	$0.809760\pi$
$360$	−3.10583	+	4.14662i	−0.163691	+	0.218546i
$361$		−	17.9894i		−	0.946812i
$362$	31.1206	−	11.0608i	1.63566	−	0.581340i
$363$	−0.571035	+	11.8209i	−0.0299716	+	0.620437i
$364$	18.3572	+	1.88666i	0.962179	+	0.0988880i
$365$	5.81112	+	5.81112i	0.304168	+	0.304168i
$366$	−5.73719	−	19.0020i	−0.299888	−	0.993253i
$367$		−	32.8277i		−	1.71359i	−0.515654	−	0.856797i	$-0.672451\pi$
$367$		−	32.8277i		−	1.71359i	0.515654	−	0.856797i	$-0.327549\pi$
$368$	−23.3889	−	4.85891i	−1.21923	−	0.253288i
$369$	−5.42166	−	0.525036i	−0.282240	−	0.0273323i
$370$	0.799473	−	1.68111i	0.0415626	−	0.0873969i
$371$	−27.4076	+	27.4076i	−1.42293	+	1.42293i
$372$	−1.46289	+	1.07721i	−0.0758472	+	0.0558507i
$373$	1.35720	+	1.35720i	0.0702732	+	0.0702732i	0.741370	−	0.671097i	$-0.234176\pi$
$373$	1.35720	+	1.35720i	0.0702732	+	0.0702732i	−0.671097	+	0.741370i	$0.734176\pi$
$374$	4.85891	+	13.6711i	0.251248	+	0.706914i
$375$	−6.84333	−	7.53805i	−0.353388	−	0.389263i
$376$	20.7144	−	5.04888i	1.06826	−	0.260376i
$377$	−12.0329			−0.619724
$378$	12.6611	−	18.9623i	0.651214	−	0.975313i
$379$	−17.3869	+	17.3869i	−0.893106	+	0.893106i	−0.994814	−	0.101708i	$-0.967569\pi$
$379$	−17.3869	+	17.3869i	−0.893106	+	0.893106i	0.101708	+	0.994814i	$0.467569\pi$
$380$	−0.774723	−	0.952209i	−0.0397425	−	0.0488473i
$381$	−1.31869	+	27.2980i	−0.0675585	+	1.39852i
$382$	−1.93051	+	4.05944i	−0.0987737	+	0.207699i
$383$	−32.9757			−1.68498			−0.842491	−	0.538711i	$-0.818912\pi$
$383$	−32.9757			−1.68498			−0.842491	+	0.538711i	$0.818912\pi$
$384$	−0.274819	+	19.5940i	−0.0140243	+	0.999902i
$385$	−8.00000			−0.407718
$386$	6.96037	−	14.6361i	0.354274	−	0.744958i
$387$	2.32811	−	1.91701i	0.118345	−	0.0974473i
$388$	10.9511	+	13.4600i	0.555959	+	0.683327i
$389$	3.97434	−	3.97434i	0.201507	−	0.201507i	−0.599138	−	0.800645i	$-0.704490\pi$
$389$	3.97434	−	3.97434i	0.201507	−	0.201507i	0.800645	+	0.599138i	$0.204490\pi$
$390$	−3.91959	−	2.10163i	−0.198476	−	0.106420i
$391$	−14.5089			−0.733744
$392$	7.21953	−	1.75967i	0.364641	−	0.0888767i
$393$	−0.145945	+	0.132494i	−0.00736195	+	0.00668346i
$394$	−9.91638	−	27.9008i	−0.499580	−	1.40562i
$395$	1.50052	+	1.50052i	0.0754991	+	0.0754991i
$396$	−5.00779	+	24.8375i	−0.251651	+	1.24813i
$397$	−15.9355	+	15.9355i	−0.799782	+	0.799782i	−0.983061	−	0.183279i	$-0.941329\pi$
$397$	−15.9355	+	15.9355i	−0.799782	+	0.799782i	0.183279	+	0.983061i	$0.441329\pi$
$398$	14.8530	−	31.2326i	0.744516	−	1.56555i
$399$	3.63135	+	4.00000i	0.181795	+	0.200250i
$400$	−18.1219	−	3.76473i	−0.906097	−	0.188237i
$401$		−	29.7716i		−	1.48672i	−0.668891	−	0.743361i	$-0.733231\pi$
$401$		−	29.7716i		−	1.48672i	0.668891	−	0.743361i	$-0.266769\pi$
$402$	1.29978	−	0.392436i	0.0648272	−	0.0195729i
$403$	−1.10278	−	1.10278i	−0.0549331	−	0.0549331i
$404$	0.512205	+	0.0526419i	0.0254832	+	0.00261903i
$405$	−4.55897	+	3.06782i	−0.226537	+	0.152441i
$406$	−16.7300	+	5.94610i	−0.830295	+	0.295100i
$407$		−	9.10404i		−	0.451270i
$408$	2.25719	+	11.6858i	0.111748	+	0.578536i
$409$		−	15.6655i		−	0.774610i	−0.921952	−	0.387305i	$-0.873406\pi$
$409$		−	15.6655i		−	0.774610i	0.921952	−	0.387305i	$-0.126594\pi$
$410$	0.525036	+	1.47725i	0.0259297	+	0.0729559i
$411$	22.9410	+	1.10821i	1.13159	+	0.0546642i
$412$	−8.02418	−	9.86248i	−0.395323	−	0.485890i
$413$	−0.249687	−	0.249687i	−0.0122863	−	0.0122863i
$414$	−21.7262	−	13.0365i	−1.06779	−	0.640710i
$415$		−	3.93051i		−	0.192941i
$416$	−16.6654	+	2.29178i	−0.817086	+	0.112364i
$417$	15.2197	−	13.8170i	0.745311	−	0.676621i
$418$	−5.42166	−	2.57834i	−0.265182	−	0.126111i
$419$	14.1554	−	14.1554i	0.691538	−	0.691538i	−0.271032	−	0.962570i	$-0.587365\pi$
$419$	14.1554	−	14.1554i	0.691538	−	0.691538i	0.962570	+	0.271032i	$0.0873650\pi$
$420$	−6.48817	−	0.985138i	−0.316590	−	0.0480698i
$421$	−7.35720	−	7.35720i	−0.358568	−	0.358568i	0.504717	−	0.863285i	$-0.331597\pi$
$421$	−7.35720	−	7.35720i	−0.358568	−	0.358568i	−0.863285	+	0.504717i	$0.831597\pi$
$422$	11.6583	−	4.14356i	0.567519	−	0.201705i
$423$	22.5089	+	2.17977i	1.09442	+	0.105984i
$424$	18.3572	−	30.1900i	0.891504	−	1.46615i
$425$	−11.2416			−0.545298
$426$	10.8366	+	5.81045i	0.525036	+	0.281517i
$427$	17.7789	−	17.7789i	0.860380	−	0.860380i
$428$	−0.476105	+	4.63249i	−0.0230134	+	0.223920i
$429$	−21.7256	−	1.04950i	−1.04892	−	0.0506705i
$430$	−0.783887	−	0.372787i	−0.0378024	−	0.0179774i
$431$	20.7097			0.997553			0.498776	−	0.866731i	$-0.333783\pi$
$431$	20.7097			0.997553			0.498776	+	0.866731i	$0.333783\pi$
$432$	−7.11997	+	19.5271i	−0.342560	+	0.939496i
$433$	−23.4005			−1.12456			−0.562279	−	0.826948i	$-0.690075\pi$
$433$	−23.4005			−1.12456			−0.562279	+	0.826948i	$0.690075\pi$
$434$	−2.07819	−	0.988310i	−0.0997565	−	0.0474404i
$435$	4.27411	+	0.206471i	0.204928	+	0.00989951i
$436$	−18.4947	−	1.90080i	−0.885736	−	0.0910316i
$437$	4.24513	−	4.24513i	0.203072	−	0.203072i
$438$	29.0567	+	15.5798i	1.38838	+	0.744434i
$439$	20.2594			0.966931			0.483465	−	0.875363i	$-0.339378\pi$
$439$	20.2594			0.966931			0.483465	+	0.875363i	$0.339378\pi$
$440$	7.08522	−	1.72693i	0.337774	−	0.0823283i
$441$	7.84494	+	0.759707i	0.373569	+	0.0361765i
$442$	−9.62721	+	3.42166i	−0.457920	+	0.162752i
$443$	4.05264	+	4.05264i	0.192547	+	0.192547i	0.796796	−	0.604249i	$-0.206527\pi$
$443$	4.05264	+	4.05264i	0.192547	+	0.192547i	−0.604249	+	0.796796i	$0.706527\pi$
$444$	1.12109	−	7.38356i	0.0532047	−	0.350408i
$445$	5.42166	−	5.42166i	0.257011	−	0.257011i
$446$	10.4598	+	4.97429i	0.495286	+	0.235539i
$447$	−10.5008	+	9.53303i	−0.496671	+	0.450897i
$448$	−22.0383	+	11.4217i	−1.04121	+	0.539623i
$449$			5.38394i			0.254084i	0.991897	+	0.127042i	$0.0405483\pi$
$449$			5.38394i			0.254084i	−0.991897	+	0.127042i	$0.959452\pi$
$450$	−16.8337	−	10.1008i	−0.793548	−	0.476157i
$451$	5.42166	+	5.42166i	0.255296	+	0.255296i
$452$	12.8963	−	10.4925i	0.606592	−	0.493528i
$453$	17.2071	+	0.831227i	0.808459	+	0.0390544i
$454$	−6.63778	−	18.6761i	−0.311526	−	0.876512i
$455$		−	5.63363i		−	0.264109i
$456$	−4.07958	−	2.75872i	−0.191044	−	0.129189i
$457$			28.0766i			1.31337i	0.754165	+	0.656685i	$0.228042\pi$
$457$			28.0766i			1.31337i	−0.754165	+	0.656685i	$0.771958\pi$
$458$	−13.4774	+	4.79007i	−0.629756	+	0.223825i
$459$	−1.82166	+	12.4917i	−0.0850279	+	0.583062i
$460$	−0.745574	+	7.25443i	−0.0347626	+	0.338239i
$461$	−22.7962	−	22.7962i	−1.06172	−	1.06172i	−0.997965	−	0.0637594i	$-0.979691\pi$
$461$	−22.7962	−	22.7962i	−1.06172	−	1.06172i	−0.0637594	−	0.997965i	$-0.520309\pi$
$462$	−30.7250	+	9.27662i	−1.42945	+	0.431588i
$463$		−	0.740035i		−	0.0343923i	−0.999852	−	0.0171962i	$-0.994526\pi$
$463$		−	0.740035i		−	0.0343923i	0.999852	−	0.0171962i	$-0.00547398\pi$
$464$	13.5334	−	8.87762i	0.628272	−	0.412133i
$465$	0.372787	+	0.410632i	0.0172876	+	0.0190426i
$466$	−11.9305	+	25.0872i	−0.552670	+	1.16214i
$467$	−9.73282	+	9.73282i	−0.450381	+	0.450381i	−0.895481	−	0.445100i	$-0.853168\pi$
$467$	−9.73282	+	9.73282i	−0.450381	+	0.450381i	0.445100	+	0.895481i	$0.353168\pi$
$468$	−17.4907	−	3.52651i	−0.808506	−	0.163013i
$469$	1.21611	+	1.21611i	0.0561549	+	0.0561549i
$470$	−2.17977	−	6.13301i	−0.100545	−	0.282895i
$471$	−16.5975	+	15.0678i	−0.764772	+	0.694289i
$472$	0.275035	+	0.167237i	0.0126595	+	0.00769770i
$473$	−4.24513			−0.195191
$474$	7.50287	+	4.02294i	0.344618	+	0.184780i
$475$	3.28917	−	3.28917i	0.150917	−	0.150917i
$476$	−11.6944	+	9.51467i	−0.536014	+	0.436104i
$477$	28.9307	−	23.8221i	1.32464	−	1.09074i
$478$	5.73501	−	12.0594i	0.262313	−	0.551586i
$479$	28.2478			1.29067			0.645337	−	0.763898i	$-0.276717\pi$
$479$	28.2478			1.29067			0.645337	+	0.763898i	$0.276717\pi$
$480$	5.95892	−	0.528089i	0.271986	−	0.0241038i
$481$	6.41110			0.292321
$482$	−10.0923	+	21.2219i	−0.459694	+	0.966633i
$483$	1.54861	−	32.0575i	0.0704641	−	1.45866i
$484$	10.6003	−	8.62444i	0.481830	−	0.392020i
$485$	3.74576	−	3.74576i	0.170086	−	0.170086i
$486$	−13.9519	+	17.0688i	−0.632871	+	0.774257i
$487$	19.7094			0.893117			0.446559	−	0.894754i	$-0.352649\pi$
$487$	19.7094			0.893117			0.446559	+	0.894754i	$0.352649\pi$
$488$	−11.9080	+	19.5837i	−0.539051	+	0.886515i
$489$	25.8499	+	28.4741i	1.16897	+	1.28764i
$490$	−0.759707	−	2.13752i	−0.0343201	−	0.0965632i
$491$	−29.4414	−	29.4414i	−1.32867	−	1.32867i	−0.906529	−	0.422143i	$-0.861278\pi$
$491$	−29.4414	−	29.4414i	−1.32867	−	1.32867i	−0.422143	−	0.906529i	$-0.638722\pi$
$492$	3.72945	+	5.06472i	0.168136	+	0.228335i
$493$	6.95112	−	6.95112i	0.313063	−	0.313063i
$494$	1.81568	−	3.81796i	0.0816911	−	0.171778i
$495$	7.69899	+	0.745574i	0.346044	+	0.0335111i
$496$	2.05390	+	0.426686i	0.0922228	+	0.0191588i
$497$			15.5755i			0.698656i
$498$	−4.55774	−	15.0956i	−0.204237	−	0.676451i
$499$	4.43026	+	4.43026i	0.198326	+	0.198326i	0.799282	−	0.600956i	$-0.205213\pi$
$499$	4.43026	+	4.43026i	0.198326	+	0.198326i	−0.600956	+	0.799282i	$0.705213\pi$
$500$	−1.20190	+	11.6944i	−0.0537504	+	0.522991i
$501$	−1.59990	+	33.1193i	−0.0714784	+	1.47966i
$502$	3.83276	−	1.36222i	0.171065	−	0.0607990i
$503$			27.6805i			1.23421i	0.786879	+	0.617107i	$0.211696\pi$
$503$			27.6805i			1.23421i	−0.786879	+	0.617107i	$0.788304\pi$
$504$	−26.0609	+	3.73999i	−1.16085	+	0.166593i
$505$		−	0.157190i		−	0.00699488i
$506$	11.9441	+	33.6061i	0.530981	+	1.49397i
$507$	−0.347386	+	7.19119i	−0.0154280	+	0.319372i
$508$	24.4791	−	19.9164i	1.08609	−	0.883647i
$509$	17.3235	+	17.3235i	0.767851	+	0.767851i	0.977728	−	0.209877i	$-0.0673063\pi$
$509$	17.3235	+	17.3235i	0.767851	+	0.767851i	−0.209877	+	0.977728i	$0.567306\pi$
$510$	3.47833	−	1.05019i	0.154023	−	0.0465034i
$511$			41.7633i			1.84750i
$512$	17.0527	−	14.8730i	0.753631	−	0.657298i
$513$	−3.12193	−	4.18793i	−0.137837	−	0.184902i
$514$	19.2544	+	9.15667i	0.849276	+	0.403884i
$515$	−2.74461	+	2.74461i	−0.120942	+	0.120942i
$516$	−3.44289	−	0.522755i	−0.151565	−	0.0230130i
$517$	−22.5089	−	22.5089i	−0.989938	−	0.989938i
$518$	8.91372	−	3.16808i	0.391646	−	0.139197i
$519$	−21.9441	−	24.1719i	−0.963240	−	1.06103i
$520$	1.21611	+	4.98944i	0.0533301	+	0.218801i
$521$	−10.1284			−0.443735			−0.221868	−	0.975077i	$-0.571215\pi$
$521$	−10.1284			−0.443735			−0.221868	+	0.975077i	$0.571215\pi$
$522$	16.6547	−	4.16319i	0.728955	−	0.182218i
$523$	1.45641	−	1.45641i	0.0636842	−	0.0636842i	−0.674547	−	0.738232i	$-0.735661\pi$
$523$	1.45641	−	1.45641i	0.0636842	−	0.0636842i	0.738232	+	0.674547i	$0.235661\pi$
$524$	0.226417	+	0.0232700i	0.00989108	+	0.00101656i
$525$	1.19988	−	24.8384i	0.0523669	−	1.08404i
$526$	38.0766	+	18.1078i	1.66022	+	0.789538i
$527$	1.27410			0.0555006
$528$	25.2091	−	14.8484i	1.09709	−	0.646192i
$529$	−12.6655			−0.550675
$530$	−9.74109	−	4.63249i	−0.423126	−	0.201223i
$531$	0.217023	+	0.263563i	0.00941798	+	0.0114376i
$532$	0.637776	−	6.20555i	0.0276511	−	0.269045i
$533$	−3.81796	+	3.81796i	−0.165374	+	0.165374i
$534$	14.5357	−	27.1094i	0.629021	−	1.17314i
$535$	1.42166			0.0614638
$536$	−1.33957	−	0.814535i	−0.0578606	−	0.0351825i
$537$	16.6571	−	15.1219i	0.718806	−	0.652560i
$538$	−30.8519	+	10.9653i	−1.33012	+	0.472746i
$539$	−7.84494	−	7.84494i	−0.337905	−	0.337905i
$540$	6.15223	+	1.55275i	0.264750	+	0.0668196i
$541$	5.18996	−	5.18996i	0.223134	−	0.223134i	−0.586683	−	0.809817i	$-0.699566\pi$
$541$	5.18996	−	5.18996i	0.223134	−	0.223134i	0.809817	+	0.586683i	$0.199566\pi$
$542$	−17.0456	−	8.10626i	−0.732173	−	0.348194i
$543$	−27.1894	−	29.9497i	−1.16681	−	1.28526i
$544$	8.30330	−	10.9511i	0.356001	−	0.469526i
$545$			5.67583i			0.243126i
$546$	−6.53264	−	21.6366i	−0.279571	−	0.925963i
$547$	12.6413	+	12.6413i	0.540505	+	0.540505i	0.923677	−	0.383172i	$-0.125168\pi$
$547$	12.6413	+	12.6413i	0.540505	+	0.540505i	−0.383172	+	0.923677i	$0.625168\pi$
$548$	−16.7376	−	20.5721i	−0.714993	−	0.878795i
$549$	−18.7669	+	15.4530i	−0.800950	+	0.659518i
$550$	9.25443	+	26.0383i	0.394610	+	1.11028i
$551$			4.06764i			0.173287i
$552$	5.54861	+	28.7260i	0.236164	+	1.22266i
$553$			10.7839i			0.458578i
$554$	−20.1287	+	7.15405i	−0.855186	+	0.303947i
$555$	−2.27724	−	0.110007i	−0.0966636	−	0.00466955i
$556$	−23.6116	−	2.42669i	−1.00136	−	0.102914i
$557$	6.90317	+	6.90317i	0.292497	+	0.292497i	0.838066	−	0.545569i	$-0.183686\pi$
$557$	6.90317	+	6.90317i	0.292497	+	0.292497i	−0.545569	+	0.838066i	$0.683686\pi$
$558$	1.90789	+	1.14480i	0.0807675	+	0.0484635i
$559$		−	2.98944i		−	0.126440i
$560$	4.15639	+	6.33615i	0.175639	+	0.267751i
$561$	13.1567	−	11.9441i	0.555475	−	0.504281i
$562$	−10.6861	+	22.4705i	−0.450767	+	0.947862i
$563$	18.3840	−	18.3840i	0.774794	−	0.774794i	−0.204146	−	0.978940i	$-0.565442\pi$
$563$	18.3840	−	18.3840i	0.774794	−	0.774794i	0.978940	+	0.204146i	$0.0654418\pi$
$564$	−15.4834	−	21.0269i	−0.651967	−	0.885394i
$565$	−3.58890	−	3.58890i	−0.150986	−	0.150986i
$566$	−11.5041	−	32.3681i	−0.483554	−	1.36053i
$567$	−27.4061	−	5.35828i	−1.15095	−	0.225027i
$568$	−3.36222	−	13.7944i	−0.141076	−	0.578802i
$569$	43.5570			1.82601			0.913003	−	0.407953i	$-0.133757\pi$
$569$	43.5570			1.82601			0.913003	+	0.407953i	$0.133757\pi$
$570$	−0.710446	+	1.32500i	−0.0297573	+	0.0554980i
$571$	7.00859	−	7.00859i	0.293301	−	0.293301i	−0.545082	−	0.838383i	$-0.683502\pi$
$571$	7.00859	−	7.00859i	0.293301	−	0.293301i	0.838383	+	0.545082i	$0.183502\pi$
$572$	15.8508	+	19.4822i	0.662756	+	0.814591i
$573$	5.49894	+	0.265638i	0.229721	+	0.0110972i
$574$	−3.42166	+	7.19499i	−0.142817	+	0.300313i
$575$	−27.6340			−1.15242
$576$	22.2736	−	8.93802i	0.928065	−	0.372417i
$577$	28.4494			1.18436			0.592182	−	0.805804i	$-0.298267\pi$
$577$	28.4494			1.18436			0.592182	+	0.805804i	$0.298267\pi$
$578$	−6.74037	+	14.1735i	−0.280362	+	0.589539i
$579$	−19.8261	−	0.957746i	−0.823946	−	0.0398026i
$580$	−3.11836	−	3.83276i	−0.129483	−	0.159147i
$581$	14.1239	−	14.1239i	0.585958	−	0.585958i
$582$	10.0425	−	18.7295i	0.416276	−	0.776363i
$583$	−52.7527			−2.18479
$584$	−9.01530	−	36.9877i	−0.373056	−	1.53056i
$585$	−0.525036	+	5.42166i	−0.0217076	+	0.224158i
$586$	2.49472	+	7.01916i	0.103056	+	0.289959i
$587$	−19.9011	−	19.9011i	−0.821405	−	0.821405i	0.164904	−	0.986310i	$-0.447268\pi$
$587$	−19.9011	−	19.9011i	−0.821405	−	0.821405i	−0.986310	+	0.164904i	$0.947268\pi$
$588$	−5.39637	−	7.32845i	−0.222542	−	0.302220i
$589$	−0.372787	+	0.372787i	−0.0153604	+	0.0153604i
$590$	0.0422027	−	0.0887428i	0.00173746	−	0.00365348i
$591$	−26.8510	+	24.3764i	−1.10450	+	1.00271i
$592$	−7.21057	+	4.72999i	−0.296353	+	0.194401i
$593$			20.4344i			0.839140i	0.907723	+	0.419570i	$0.137819\pi$
$593$			20.4344i			0.839140i	−0.907723	+	0.419570i	$0.862181\pi$
$594$	30.4335	−	6.06412i	1.24870	−	0.248814i
$595$	3.25443	+	3.25443i	0.133418	+	0.133418i
$596$	16.2908	+	1.67429i	0.667298	+	0.0685816i
$597$	−42.3079	−	2.04378i	−1.73155	−	0.0836462i
$598$	−23.6655	+	8.41110i	−0.967755	+	0.343955i
$599$			32.6704i			1.33488i	0.744665	+	0.667438i	$0.232609\pi$
$599$			32.6704i			1.33488i	−0.744665	+	0.667438i	$0.767391\pi$
$600$	4.29912	+	22.2572i	0.175511	+	0.908647i
$601$		−	6.73553i		−	0.274748i	−0.990519	−	0.137374i	$-0.956134\pi$
$601$		−	6.73553i		−	0.274748i	0.990519	−	0.137374i	$-0.0438662\pi$
$602$	−1.47725	−	4.15639i	−0.0602080	−	0.169402i
$603$	−1.05702	−	1.28369i	−0.0430451	−	0.0522760i
$604$	−12.5542	−	15.4303i	−0.510821	−	0.627848i
$605$	−2.94993	−	2.94993i	−0.119932	−	0.119932i
$606$	−0.182275	−	0.603709i	−0.00740440	−	0.0245240i
$607$		−	21.2388i		−	0.862058i	−0.902338	−	0.431029i	$-0.858151\pi$
$607$		−	21.2388i		−	0.862058i	0.902338	−	0.431029i	$-0.141849\pi$
$608$	0.774723	+	5.63363i	0.0314192	+	0.228474i
$609$	14.6167	+	16.1005i	0.592297	+	0.652426i
$610$	6.31889	+	3.00502i	0.255844	+	0.121670i
$611$	15.8508	−	15.8508i	0.641256	−	0.641256i
$612$	12.1412	−	8.06679i	0.490777	−	0.326081i
$613$	−9.62219	−	9.62219i	−0.388637	−	0.388637i	0.485564	−	0.874201i	$-0.338614\pi$
$613$	−9.62219	−	9.62219i	−0.388637	−	0.388637i	−0.874201	+	0.485564i	$0.838614\pi$
$614$	25.3294	−	9.00246i	1.02221	−	0.363310i
$615$	1.42166	−	1.29064i	0.0573270	−	0.0520436i
$616$	31.6655	+	19.2544i	1.27584	+	0.775783i
$617$	−3.74576			−0.150798			−0.0753992	−	0.997153i	$-0.524023\pi$
$617$	−3.74576			−0.150798			−0.0753992	+	0.997153i	$0.524023\pi$
$618$	−7.35843	+	13.7236i	−0.295999	+	0.552045i
$619$	−13.0680	+	13.0680i	−0.525249	+	0.525249i	−0.919152	−	0.393903i	$-0.871124\pi$
$619$	−13.0680	+	13.0680i	−0.525249	+	0.525249i	0.393903	+	0.919152i	$0.371124\pi$
$620$	0.0654727	−	0.637049i	0.00262945	−	0.0255845i
$621$	−4.47799	+	30.7070i	−0.179696	+	1.23223i
$622$	17.6655	+	8.40105i	0.708323	+	0.336852i
$623$	38.9643			1.56107
$624$	10.4563	+	17.7524i	0.418586	+	0.710663i
$625$	−19.5472			−0.781887
$626$	5.03268	+	2.39335i	0.201147	+	0.0956576i
$627$	−0.354779	+	7.34422i	−0.0141685	+	0.293300i
$628$	25.7491	+	2.64637i	1.02750	+	0.105602i
$629$	−3.70355	+	3.70355i	−0.147670	+	0.147670i
$630$	1.94915	+	7.79750i	0.0776561	+	0.310660i
$631$	−7.51388			−0.299123			−0.149561	−	0.988752i	$-0.547786\pi$
$631$	−7.51388			−0.299123			−0.149561	+	0.988752i	$0.547786\pi$
$632$	−2.32788	−	9.55077i	−0.0925981	−	0.379909i
$633$	−10.1857	−	11.2197i	−0.404843	−	0.445942i
$634$	16.8136	−	5.97582i	0.667754	−	0.237330i
$635$	−6.81226	−	6.81226i	−0.270336	−	0.270336i
$636$	−42.7835	−	6.49609i	−1.69648	−	0.257587i
$637$	5.52444	−	5.52444i	0.218886	−	0.218886i
$638$	−21.8229	−	10.3781i	−0.863976	−	0.410874i
$639$	1.45158	−	14.9894i	0.0574238	−	0.592973i
$640$	−5.04888	−	4.71440i	−0.199574	−	0.186353i
$641$			27.7227i			1.09498i	0.836811	+	0.547491i	$0.184417\pi$
$641$			27.7227i			1.09498i	−0.836811	+	0.547491i	$0.815583\pi$
$642$	5.46007	−	1.64853i	0.215492	−	0.0650623i
$643$	19.7003	+	19.7003i	0.776903	+	0.776903i	0.979303	−	0.202400i	$-0.0648742\pi$
$643$	19.7003	+	19.7003i	0.776903	+	0.776903i	−0.202400	+	0.979303i	$0.564874\pi$
$644$	−28.7472	+	23.3889i	−1.13280	+	0.921651i
$645$	−0.0512954	+	1.06186i	−0.00201976	+	0.0418106i
$646$	1.15667	+	3.25443i	0.0455087	+	0.128044i
$647$		−	5.29520i		−	0.208176i	−0.994568	−	0.104088i	$-0.966808\pi$
$647$		−	5.29520i		−	0.208176i	0.994568	−	0.104088i	$-0.0331923\pi$
$648$	25.4289	−	1.17048i	0.998942	−	0.0459809i
$649$		−	0.480585i		−	0.0188646i
$650$	−18.3363	+	6.51700i	−0.719208	+	0.255618i
$651$	−0.135991	+	2.81513i	−0.00532992	+	0.110334i
$652$	4.54002	−	44.1744i	0.177801	−	1.73000i
$653$	−29.7039	−	29.7039i	−1.16240	−	1.16240i	−0.983948	−	0.178457i	$-0.942890\pi$
$653$	−29.7039	−	29.7039i	−1.16240	−	1.16240i	−0.178457	−	0.983948i	$-0.557110\pi$
$654$	6.58157	+	21.7987i	0.257360	+	0.852398i
$655$		−	0.0694851i		−	0.00271501i
$656$	1.47725	−	7.11088i	0.0576767	−	0.277633i
$657$	3.89220	−	40.1919i	0.151849	−	1.56804i
$658$	14.2056	−	29.8711i	0.553790	−	1.16450i
$659$	−1.03268	+	1.03268i	−0.0402276	+	0.0402276i	−0.726934	−	0.686707i	$-0.759056\pi$
$659$	−1.03268	+	1.03268i	−0.0402276	+	0.0402276i	0.686707	+	0.726934i	$0.259056\pi$
$660$	−5.29597	−	7.19212i	−0.206145	−	0.279953i
$661$	29.8277	+	29.8277i	1.16016	+	1.16016i	0.984439	+	0.175725i	$0.0562271\pi$
$661$	29.8277	+	29.8277i	1.16016	+	1.16016i	0.175725	+	0.984439i	$0.443773\pi$
$662$	6.32332	+	17.7913i	0.245763	+	0.691480i
$663$	8.41110	+	9.26498i	0.326660	+	0.359822i
$664$	−9.45998	+	15.5577i	−0.367118	+	0.603757i
$665$	−1.90442			−0.0738502
$666$	−8.87359	+	2.21815i	−0.343845	+	0.0859514i
$667$	17.0872	−	17.0872i	0.661619	−	0.661619i
$668$	29.6994	−	24.1636i	1.14910	−	0.934918i
$669$	0.684461	−	14.1689i	0.0264628	−	0.547802i
$670$	−0.205550	+	0.432226i	−0.00794109	+	0.0166983i
$671$	34.2198			1.32104
$672$	23.3104	+	19.5151i	0.899217	+	0.752811i
$673$	−0.891685			−0.0343719			−0.0171860	−	0.999852i	$-0.505471\pi$
$673$	−0.891685			−0.0343719			−0.0171860	+	0.999852i	$0.505471\pi$
$674$	−3.60808	+	7.58698i	−0.138978	+	0.292240i
$675$	−3.46959	+	23.7920i	−0.133545	+	0.915756i
$676$	6.44861	−	5.24663i	0.248024	−	0.201794i
$677$	8.13073	−	8.13073i	0.312489	−	0.312489i	−0.533384	−	0.845873i	$-0.679080\pi$
$677$	8.13073	−	8.13073i	0.312489	−	0.312489i	0.845873	+	0.533384i	$0.179080\pi$
$678$	−17.9452	−	9.62199i	−0.689182	−	0.369530i
$679$	26.9200			1.03309
$680$	−3.58481	−	2.17977i	−0.137471	−	0.0835902i
$681$	−17.9734	+	16.3169i	−0.688742	+	0.625266i
$682$	−1.04888	−	2.95112i	−0.0401635	−	0.113004i
$683$	14.5917	+	14.5917i	0.558337	+	0.558337i	0.928834	−	0.370497i	$-0.120813\pi$
$683$	14.5917	+	14.5917i	0.558337	+	0.558337i	−0.370497	+	0.928834i	$0.620813\pi$
$684$	−1.19212	+	5.91262i	−0.0455817	+	0.226075i
$685$	−5.72496	+	5.72496i	−0.218740	+	0.218740i
$686$	−8.24057	+	17.3281i	−0.314626	+	0.661589i
$687$	11.7749	+	12.9703i	0.449241	+	0.494847i
$688$	2.20555	+	3.36222i	0.0840858	+	0.128184i
$689$		−	37.1487i		−	1.41525i
$690$	8.55040	−	2.58158i	0.325508	−	0.0982790i
$691$	−11.2197	−	11.2197i	−0.426817	−	0.426817i	0.460726	−	0.887543i	$-0.347589\pi$
$691$	−11.2197	−	11.2197i	−0.426817	−	0.426817i	−0.887543	+	0.460726i	$0.847589\pi$
$692$	−3.85406	+	37.4999i	−0.146509	+	1.42553i
$693$	24.9864	+	30.3447i	0.949154	+	1.15270i
$694$	−7.72496	+	2.74557i	−0.293236	+	0.104221i
$695$			7.24616i			0.274863i
$696$	−16.4208	−	11.1042i	−0.622430	−	0.420904i
$697$		−	4.41110i		−	0.167082i
$698$	−5.42712	−	15.2698i	−0.205420	−	0.577970i
$699$	33.9833	+	1.64164i	1.28536	+	0.0620924i
$700$	−22.2736	+	18.1219i	−0.841862	+	0.684945i
$701$	14.7166	+	14.7166i	0.555837	+	0.555837i	0.928120	−	0.372282i	$-0.121425\pi$
$701$	14.7166	+	14.7166i	0.555837	+	0.555837i	−0.372282	+	0.928120i	$0.621425\pi$
$702$	4.27038	+	21.4314i	0.161175	+	0.808875i
$703$		−	2.16724i		−	0.0817389i
$704$	−32.2010	−	10.2172i	−1.21362	−	0.385075i
$705$	−5.90225	+	5.35828i	−0.222292	+	0.201805i
$706$	−37.3522	−	17.7633i	−1.40577	−	0.668530i
$707$	0.564847	−	0.564847i	0.0212433	−	0.0212433i
$708$	0.0591803	−	0.389765i	0.00222413	−	0.0146483i
$709$	−23.2978	−	23.2978i	−0.874966	−	0.874966i	0.118043	−	0.993009i	$-0.462338\pi$
$709$	−23.2978	−	23.2978i	−0.874966	−	0.874966i	−0.993009	+	0.118043i	$0.962338\pi$
$710$	−4.08419	+	1.45158i	−0.153277	+	0.0544770i
$711$	1.00502	−	10.3781i	0.0376913	−	0.389211i
$712$	−34.5089	+	8.41110i	−1.29327	+	0.315219i
$713$	3.13198			0.117293
$714$	16.2728	+	8.72525i	0.608993	+	0.326534i
$715$	5.42166	−	5.42166i	0.202759	−	0.202759i
$716$	−25.8416	−	2.65587i	−0.965746	−	0.0992546i
$717$	−16.3358	−	0.789136i	−0.610071	−	0.0294708i
$718$	−27.2333	−	12.9511i	−1.01634	−	0.483332i
$719$	−27.3421			−1.01969			−0.509844	−	0.860267i	$-0.670297\pi$
$719$	−27.3421			−1.01969			−0.509844	+	0.860267i	$0.670297\pi$
$720$	−3.40949	−	6.48511i	−0.127064	−	0.241686i
$721$	−19.7250			−0.734596
$722$	22.9752	+	10.9261i	0.855048	+	0.406628i
$723$	28.7474	+	1.38871i	1.06913	+	0.0516465i
$724$	−4.77529	+	46.4635i	−0.177472	+	1.72680i
$725$	13.2393	−	13.2393i	0.491696	−	0.491696i
$726$	−14.7502	−	7.90889i	−0.547433	−	0.293526i
$727$	24.1517			0.895735			0.447868	−	0.894100i	$-0.352184\pi$
$727$	24.1517			0.895735			0.447868	+	0.894100i	$0.352184\pi$
$728$	−13.5590	+	22.2990i	−0.502532	+	0.826456i
$729$	25.8755	+	7.71083i	0.958353	+	0.285586i
$730$	−10.9511	+	3.89220i	−0.405319	+	0.144057i
$731$	1.72693	+	1.72693i	0.0638729	+	0.0638729i
$732$	27.7530	+	4.21391i	1.02578	+	0.155751i
$733$	−6.00502	+	6.00502i	−0.221801	+	0.221801i	−0.809256	−	0.587456i	$-0.800130\pi$
$733$	−6.00502	+	6.00502i	−0.221801	+	0.221801i	0.587456	+	0.809256i	$0.300130\pi$
$734$	41.9259	+	19.9384i	1.54751	+	0.735939i
$735$	−2.05709	+	1.86751i	−0.0758770	+	0.0688840i
$736$	20.4111	−	26.9200i	0.752363	−	0.992283i
$737$			2.34071i			0.0862212i
$738$	3.96347	−	6.60538i	0.145897	−	0.243148i
$739$	−10.9008	−	10.9008i	−0.400992	−	0.400992i	0.477590	−	0.878583i	$-0.341510\pi$
$739$	−10.9008	−	10.9008i	−0.400992	−	0.400992i	−0.878583	+	0.477590i	$0.841510\pi$
$740$	1.66146	+	2.04209i	0.0610765	+	0.0750688i
$741$	−5.17183	−	0.249837i	−0.189992	−	0.00917798i
$742$	−18.3572	−	51.6499i	−0.673914	−	1.89613i
$743$		−	1.29064i		−	0.0473490i	−0.999720	−	0.0236745i	$-0.992463\pi$
$743$		−	1.29064i		−	0.0473490i	0.999720	−	0.0236745i	$-0.00753652\pi$
$744$	−0.487252	−	2.52258i	−0.0178635	−	0.0924824i
$745$		−	4.99948i		−	0.183167i
$746$	−2.55766	+	0.909033i	−0.0936427	+	0.0332821i
$747$	−14.9088	+	12.2762i	−0.545483	+	0.449162i
$748$	−20.4111	−	2.09775i	−0.746304	−	0.0767014i
$749$	5.10860	+	5.10860i	0.186664	+	0.186664i
$750$	13.7836	−	4.16161i	0.503306	−	0.151960i
$751$		−	1.46552i		−	0.0534774i	−0.999642	−	0.0267387i	$-0.991488\pi$
$751$		−	1.46552i		−	0.0534774i	0.999642	−	0.0267387i	$-0.00851221\pi$
$752$	−6.13301	+	29.5219i	−0.223648	+	1.07655i
$753$	−3.34861	−	3.68855i	−0.122030	−	0.134418i
$754$	7.30833	−	15.3678i	0.266154	−	0.559661i
$755$	−4.29406	+	4.29406i	−0.156277	+	0.156277i
$756$	16.5278	+	27.6870i	0.601109	+	1.00697i
$757$	4.71943	+	4.71943i	0.171530	+	0.171530i	0.787651	−	0.616121i	$-0.211297\pi$
$757$	4.71943	+	4.71943i	0.171530	+	0.171530i	−0.616121	+	0.787651i	$0.711297\pi$
$758$	−11.6455	−	32.7659i	−0.422984	−	1.19011i
$759$	32.3416	−	29.3609i	1.17393	−	1.06573i
$760$	1.68665	−	0.411100i	0.0611813	−	0.0149122i
$761$	−29.1578			−1.05697			−0.528485	−	0.848943i	$-0.677240\pi$
$761$	−29.1578			−1.05697			−0.528485	+	0.848943i	$0.677240\pi$
$762$	−34.0626	−	18.2639i	−1.23396	−	0.661633i
$763$	−20.3955	+	20.3955i	−0.738367	+	0.738367i
$764$	−4.01198	−	4.93111i	−0.145148	−	0.178401i
$765$	−2.82867	−	3.43528i	−0.102271	−	0.124203i
$766$	20.0283	−	42.1149i	0.723651	−	1.52167i
$767$	0.338430			0.0122200
$768$	−24.8575	−	12.2517i	−0.896969	−	0.442094i
$769$	20.8122			0.750505			0.375253	−	0.926923i	$-0.377556\pi$
$769$	20.8122			0.750505			0.375253	+	0.926923i	$0.377556\pi$
$770$	4.85891	−	10.2172i	0.175103	−	0.368202i
$771$	1.25996	−	26.0822i	0.0453762	−	0.939326i
$772$	14.4650	+	17.7789i	0.520607	+	0.639875i
$773$	26.6607	−	26.6607i	0.958918	−	0.958918i	−0.0402703	−	0.999189i	$-0.512822\pi$
$773$	26.6607	−	26.6607i	0.958918	−	0.958918i	0.999189	+	0.0402703i	$0.0128219\pi$
$774$	1.03430	+	4.13767i	0.0371772	+	0.148726i
$775$	2.42669			0.0871691
$776$	−23.8417	+	5.81112i	−0.855867	+	0.208607i
$777$	−7.78774	−	8.57834i	−0.279384	−	0.307746i
$778$	2.66196	+	7.48970i	0.0954357	+	0.268519i
$779$	1.29064	+	1.29064i	0.0462419	+	0.0462419i
$780$	5.06472	−	3.72945i	0.181346	−	0.133536i
$781$	−14.9894	+	14.9894i	−0.536364	+	0.536364i
$782$	8.81215	−	18.5300i	0.315122	−	0.662630i
$783$	−12.5662	−	16.8569i	−0.449078	−	0.602418i
$784$	−2.13752	+	10.2892i	−0.0763399	+	0.367470i
$785$		−	7.90214i		−	0.282040i
$786$	−0.0805734	−	0.266866i	−0.00287396	−	0.00951879i
$787$	−32.7875	−	32.7875i	−1.16875	−	1.16875i	−0.982504	−	0.186243i	$-0.940369\pi$
$787$	−32.7875	−	32.7875i	−1.16875	−	1.16875i	−0.186243	−	0.982504i	$-0.559631\pi$
$788$	41.6563	+	4.28123i	1.48395	+	0.152513i
$789$	2.49163	−	51.5788i	0.0887044	−	1.83625i
$790$	−2.82774	+	1.00502i	−0.100606	+	0.0357571i
$791$		−	25.7927i		−	0.917082i
$792$	−28.6796	−	21.4811i	−1.01909	−	0.763297i
$793$			24.0978i			0.855736i
$794$	−10.6734	−	30.0307i	−0.378784	−	1.06575i
$795$	−0.637430	+	13.1953i	−0.0226073	+	0.467990i
$796$	30.8675	+	37.9391i	1.09407	+	1.34472i
$797$	11.2627	+	11.2627i	0.398945	+	0.398945i	0.877861	−	0.478916i	$-0.158970\pi$
$797$	11.2627	+	11.2627i	0.398945	+	0.398945i	−0.478916	+	0.877861i	$0.658970\pi$
$798$	−7.31415	+	2.20832i	−0.258918	+	0.0781737i
$799$			18.3133i			0.647880i
$800$	15.8147	−	20.8578i	0.559135	−	0.737436i
$801$	−37.4983	−	3.63135i	−1.32494	−	0.128307i
$802$	38.0227	+	18.0822i	1.34263	+	0.638503i
$803$	−40.1919	+	40.1919i	−1.41834	+	1.41834i
$804$	−0.288240	+	1.89837i	−0.0101655	+	0.0669502i
$805$	8.00000	+	8.00000i	0.281963	+	0.281963i
$806$	2.07819	−	0.738623i	0.0732012	−	0.0260169i
$807$	26.9547	+	29.6911i	0.948850	+	1.04518i
$808$	−0.378326	+	0.622190i	−0.0133095	+	0.0218886i
$809$	−48.5934			−1.70845			−0.854227	−	0.519900i	$-0.825969\pi$
$809$	−48.5934			−1.70845			−0.854227	+	0.519900i	$0.825969\pi$
$810$	−1.14911	−	7.68577i	−0.0403757	−	0.270050i
$811$	19.2197	−	19.2197i	0.674894	−	0.674894i	−0.283946	−	0.958840i	$-0.591644\pi$
$811$	19.2197	−	19.2197i	0.674894	−	0.674894i	0.958840	+	0.283946i	$0.0916436\pi$
$812$	2.56713	−	24.9781i	0.0900886	−	0.876561i
$813$	−1.11542	+	23.0901i	−0.0391195	+	0.809806i
$814$	11.6272	+	5.52946i	0.407534	+	0.193808i
$815$	−13.5567			−0.474869
$816$	−16.2955	−	4.21479i	−0.570457	−	0.147547i
$817$	−1.01056			−0.0353551
$818$	20.0072	+	9.51467i	0.699536	+	0.332673i
$819$	−21.3688	+	17.5955i	−0.746688	+	0.614837i
$820$	−2.20555	−	0.226676i	−0.0770212	−	0.00791585i
$821$	−33.7881	+	33.7881i	−1.17921	+	1.17921i	−0.199268	+	0.979945i	$0.563857\pi$
$821$	−33.7881	+	33.7881i	−1.17921	+	1.17921i	−0.979945	+	0.199268i	$0.936143\pi$
$822$	−15.3489	+	28.6260i	−0.535353	+	0.998445i
$823$	−4.37833			−0.152619			−0.0763094	−	0.997084i	$-0.524314\pi$
$823$	−4.37833			−0.152619			−0.0763094	+	0.997084i	$0.524314\pi$
$824$	17.4695	−	4.25796i	0.608577	−	0.148333i
$825$	25.0586	−	22.7491i	0.872429	−	0.792024i
$826$	0.470539	−	0.167237i	0.0163721	−	0.00581892i
$827$	14.2044	+	14.2044i	0.493934	+	0.493934i	0.909543	−	0.415609i	$-0.136432\pi$
$827$	14.2044	+	14.2044i	0.493934	+	0.493934i	−0.415609	+	0.909543i	$0.636432\pi$
$828$	29.8453	−	19.8297i	1.03720	−	0.689130i
$829$	14.8483	−	14.8483i	0.515704	−	0.515704i	−0.400564	−	0.916269i	$-0.631186\pi$
$829$	14.8483	−	14.8483i	0.515704	−	0.515704i	0.916269	+	0.400564i	$0.131186\pi$
$830$	5.01985	+	2.38725i	0.174242	+	0.0828627i
$831$	17.5860	+	19.3713i	0.610053	+	0.671984i
$832$	7.19499	−	22.6761i	0.249441	−	0.786152i
$833$			6.38269i			0.221147i
$834$	8.40249	+	27.8297i	0.290954	+	0.963665i
$835$	−8.26499	−	8.26499i	−0.286022	−	0.286022i
$836$	6.58584	−	5.35828i	0.227776	−	0.185320i
$837$	0.393236	−	2.69654i	0.0135922	−	0.0932060i
$838$	9.48110	+	26.6761i	0.327519	+	0.921510i
$839$		−	3.11543i		−	0.107557i	−0.998553	−	0.0537784i	$-0.982874\pi$
$839$		−	3.11543i		−	0.107557i	0.998553	−	0.0537784i	$-0.0171265\pi$
$840$	5.19884	−	7.68802i	0.179377	−	0.265262i
$841$		−	12.6272i		−	0.435421i
$842$	13.8647	−	4.92775i	0.477810	−	0.169821i
$843$	30.4387	+	1.47041i	1.04837	+	0.0506436i
$844$	−1.78891	+	17.4061i	−0.0615768	+	0.599142i
$845$	−1.79457	−	1.79457i	−0.0617352	−	0.0617352i
$846$	−16.4549	+	27.4232i	−0.565733	+	0.942831i
$847$		−	21.2005i		−	0.728459i
$848$	27.4076	+	41.7812i	0.941180	+	1.43477i
$849$	−31.1502	+	28.2793i	−1.06907	+	0.970544i
$850$	6.82774	−	14.3572i	0.234190	−	0.492448i
$851$	−9.10404	+	9.10404i	−0.312082	+	0.312082i
$852$	−14.0026	+	10.3109i	−0.479720	+	0.353246i
$853$	35.4550	+	35.4550i	1.21395	+	1.21395i	0.969715	+	0.244240i	$0.0785383\pi$
$853$	35.4550	+	35.4550i	1.21395	+	1.21395i	0.244240	+	0.969715i	$0.421462\pi$
$854$	11.9080	+	33.5045i	0.407484	+	1.14650i
$855$	1.83276	+	0.177486i	0.0626792	+	0.00606988i
$856$	−5.62721	−	3.42166i	−0.192334	−	0.116950i
$857$	−14.0817			−0.481021			−0.240511	−	0.970646i	$-0.577315\pi$
$857$	−14.0817			−0.481021			−0.240511	+	0.970646i	$0.577315\pi$
$858$	14.5357	−	27.1094i	0.496241	−	0.925499i
$859$	−30.9547	+	30.9547i	−1.05616	+	1.05616i	−0.0578344	+	0.998326i	$0.518420\pi$
$859$	−30.9547	+	30.9547i	−1.05616	+	1.05616i	−0.998326	+	0.0578344i	$0.981580\pi$
$860$	0.952209	−	0.774723i	0.0324701	−	0.0264179i
$861$	9.74637	+	0.470820i	0.332155	+	0.0160455i
$862$	−12.5783	+	26.4494i	−0.428420	+	0.900871i
$863$	14.4458			0.491740			0.245870	−	0.969303i	$-0.420926\pi$
$863$	14.4458			0.491740			0.245870	+	0.969303i	$0.420926\pi$
$864$	−20.6146	−	20.9533i	−0.701321	−	0.712845i
$865$	11.5083			0.391295
$866$	14.2126	−	29.8860i	0.482965	−	1.01557i
$867$	19.1995	+	0.927474i	0.652049	+	0.0314987i
$868$	2.52444	−	2.05390i	0.0856850	−	0.0697139i
$869$	−10.3781	+	10.3781i	−0.352054	+	0.352054i
$870$	−2.85964	+	5.33328i	−0.0969507	+	0.180815i
$871$	−1.64834			−0.0558518
$872$	13.6606	−	22.4660i	0.462607	−	0.760796i
$873$	−25.9071	−	2.50885i	−0.876822	−	0.0849118i
$874$	2.84333	+	8.00000i	0.0961769	+	0.270604i
$875$	12.8963	+	12.8963i	0.435976	+	0.435976i
$876$	−37.5458	+	27.6472i	−1.26855	+	0.934111i
$877$	11.3672	−	11.3672i	0.383845	−	0.383845i	−0.488641	−	0.872485i	$-0.662507\pi$
$877$	11.3672	−	11.3672i	0.383845	−	0.383845i	0.872485	+	0.488641i	$0.162507\pi$
$878$	−12.3049	+	25.8743i	−0.415269	+	0.873217i
$879$	6.75506	−	6.13249i	0.227842	−	0.206844i
$880$	−2.09775	+	10.0978i	−0.0707152	+	0.340395i
$881$			10.2172i			0.344226i	0.985077	+	0.172113i	$0.0550594\pi$
$881$			10.2172i			0.344226i	−0.985077	+	0.172113i	$0.944941\pi$
$882$	−5.73499	+	9.55774i	−0.193107	+	0.321826i
$883$	0.230246	+	0.230246i	0.00774840	+	0.00774840i	0.710970	−	0.703222i	$-0.248256\pi$
$883$	0.230246	+	0.230246i	0.00774840	+	0.00774840i	−0.703222	+	0.710970i	$0.748256\pi$
$884$	1.47725	−	14.3736i	0.0496851	−	0.483436i
$885$	−0.120211	−	0.00580708i	−0.00404087	−	0.000195203i
$886$	−7.63726	+	2.71440i	−0.256579	+	0.0911921i
$887$		−	34.2664i		−	1.15055i	−0.817959	−	0.575276i	$-0.804895\pi$
$887$		−	34.2664i		−	1.15055i	0.817959	−	0.575276i	$-0.195105\pi$
$888$	8.74900	+	5.91631i	0.293597	+	0.198538i
$889$		−	48.9583i		−	1.64201i
$890$	3.63135	+	10.2172i	0.121723	+	0.342481i
$891$	−21.2182	−	31.5316i	−0.710837	−	1.05635i
$892$	−12.7058	+	10.3375i	−0.425422	+	0.346126i
$893$	−5.35828	−	5.35828i	−0.179308	−	0.179308i
$894$	−5.79729	−	19.2011i	−0.193890	−	0.642181i
$895$			7.93051i			0.265088i
$896$	−1.20190	−	35.0833i	−0.0401525	−	1.17205i
$897$	20.6761	+	22.7751i	0.690355	+	0.760438i
$898$	−6.87610	−	3.27001i	−0.229458	−	0.109122i
$899$	−1.50052	+	1.50052i	−0.0500450	+	0.0500450i
$900$	23.1244	−	15.3643i	0.770814	−	0.512142i
$901$	21.4600	+	21.4600i	0.714935	+	0.714935i
$902$	−10.2172	+	3.63135i	−0.340195	+	0.120911i
$903$	−4.00000	+	3.63135i	−0.133112	+	0.120844i
$904$	5.56777	+	22.8433i	0.185181	+	0.759758i
$905$	14.2592			0.473991
$906$	−11.5126	+	21.4712i	−0.382479	+	0.713331i
$907$	−26.5436	+	26.5436i	−0.881366	+	0.881366i	−0.993673	−	0.112308i	$-0.964176\pi$
$907$	−26.5436	+	26.5436i	−0.881366	+	0.881366i	0.112308	+	0.993673i	$0.464176\pi$
$908$	27.8837	+	2.86575i	0.925353	+	0.0951032i
$909$	−0.596236	+	0.490953i	−0.0197759	+	0.0162839i
$910$	7.19499	+	3.42166i	0.238512	+	0.113427i
$911$	−24.1636			−0.800576			−0.400288	−	0.916389i	$-0.631090\pi$
$911$	−24.1636			−0.800576			−0.400288	+	0.916389i	$0.631090\pi$
$912$	6.00108	−	3.53468i	0.198716	−	0.117045i
$913$	27.1849			0.899690
$914$	−35.8580	−	17.0527i	−1.18608	−	0.564054i
$915$	0.413491	−	8.55960i	0.0136696	−	0.282972i
$916$	2.06803	−	20.1219i	0.0683297	−	0.664847i
$917$	0.249687	−	0.249687i	0.00824540	−	0.00824540i
$918$	−14.8473	−	9.91353i	−0.490035	−	0.327195i
$919$	−25.8272			−0.851961			−0.425981	−	0.904732i	$-0.640071\pi$
$919$	−25.8272			−0.851961			−0.425981	+	0.904732i	$0.640071\pi$
$920$	−8.81215	−	5.35828i	−0.290528	−	0.176657i
$921$	−22.1298	−	24.3764i	−0.729201	−	0.803228i
$922$	42.9597	−	15.2686i	1.41480	−	0.502843i
$923$	−10.5556	−	10.5556i	−0.347443	−	0.347443i
$924$	6.81359	−	44.8746i	0.224151	−	1.47627i
$925$	−7.05390	+	7.05390i	−0.231931	+	0.231931i
$926$	0.945134	+	0.449470i	0.0310590	+	0.0147705i
$927$	18.9828	+	1.83830i	0.623477	+	0.0603778i
$928$	3.11836	+	22.6761i	0.102365	+	0.744379i
$929$		−	29.6272i		−	0.972036i	−0.873949	−	0.486018i	$-0.838449\pi$
$929$		−	29.6272i		−	0.972036i	0.873949	−	0.486018i	$-0.161551\pi$
$930$	−0.750855	+	0.226702i	−0.0246215	+	0.00743384i
$931$	−1.86751	−	1.86751i	−0.0612050	−	0.0612050i
$932$	−24.7939	−	30.4741i	−0.812152	−	0.998212i
$933$	1.15598	−	23.9298i	0.0378452	−	0.783427i
$934$	−6.51890	−	18.3416i	−0.213305	−	0.600156i
$935$			6.26395i			0.204853i
$936$	15.1271	−	20.1963i	0.494444	−	0.660137i
$937$			33.4005i			1.09115i	0.838063	+	0.545574i	$0.183688\pi$
$937$			33.4005i			1.09115i	−0.838063	+	0.545574i	$0.816312\pi$
$938$	−2.29178	+	0.814535i	−0.0748293	+	0.0265955i
$939$	0.329325	−	6.81730i	0.0107471	−	0.222474i
$940$	9.15667	+	0.941078i	0.298658	+	0.0306946i
$941$	15.6688	+	15.6688i	0.510788	+	0.510788i	0.914768	−	0.403980i	$-0.132374\pi$
$941$	15.6688	+	15.6688i	0.510788	+	0.510788i	−0.403980	+	0.914768i	$0.632374\pi$
$942$	−9.16315	−	30.3491i	−0.298552	−	0.988828i
$943$		−	10.8433i		−	0.353107i
$944$	−0.380633	+	0.249687i	−0.0123885	+	0.00812663i
$945$	7.89220	−	5.88332i	0.256733	−	0.191384i
$946$	2.57834	−	5.42166i	0.0838290	−	0.176273i
$947$	21.4040	−	21.4040i	0.695536	−	0.695536i	−0.267908	−	0.963444i	$-0.586332\pi$
$947$	21.4040	−	21.4040i	0.695536	−	0.695536i	0.963444	+	0.267908i	$0.0863325\pi$
$948$	−9.69487	+	7.13890i	−0.314875	+	0.231861i
$949$	−28.3033	−	28.3033i	−0.918764	−	0.918764i
$950$	2.20304	+	6.19848i	0.0714760	+	0.201105i
$951$	−14.6897	−	16.1810i	−0.476346	−	0.524704i
$952$	−5.04888	−	20.7144i	−0.163635	−	0.671358i
$953$	30.7403			0.995777			0.497888	−	0.867241i	$-0.334109\pi$
$953$	30.7403			0.995777			0.497888	+	0.867241i	$0.334109\pi$
$954$	12.8529	+	51.4174i	0.416128	+	1.66470i
$955$	−1.37227	+	1.37227i	−0.0444056	+	0.0444056i
$956$	11.9185	+	14.6489i	0.385471	+	0.473780i
$957$	−1.42803	+	29.5614i	−0.0461616	+	0.955585i
$958$	−17.1567	+	36.0766i	−0.554307	+	1.16558i
$959$	−41.1441			−1.32861
$960$	−2.94478	+	7.93116i	−0.0950424	+	0.255977i
$961$	30.7250			0.991128
$962$	−3.89387	+	8.18793i	−0.125543	+	0.263989i
$963$	−4.44028	−	5.39249i	−0.143086	−	0.173770i
$964$	−20.9739	−	25.7789i	−0.675522	−	0.830281i
$965$	4.94765	−	4.94765i	0.159271	−	0.159271i
$966$	40.0016	+	21.4483i	1.28703	+	0.690089i
$967$	−15.8172			−0.508646			−0.254323	−	0.967119i	$-0.581853\pi$
$967$	−15.8172			−0.508646			−0.254323	+	0.967119i	$0.581853\pi$
$968$	4.57648	+	18.7763i	0.147094	+	0.603493i
$969$	3.13198	−	2.84333i	0.100614	−	0.0913408i
$970$	2.50885	+	7.05892i	0.0805544	+	0.226648i
$971$	13.8170	+	13.8170i	0.443409	+	0.443409i	0.893156	−	0.449747i	$-0.148486\pi$
$971$	13.8170	+	13.8170i	0.443409	+	0.443409i	−0.449747	+	0.893156i	$0.648486\pi$
$972$	−13.3256	−	28.1856i	−0.427417	−	0.904054i
$973$	−26.0383	+	26.0383i	−0.834750	+	0.834750i
$974$	−11.9708	+	25.1718i	−0.383568	+	0.806557i
$975$	16.0200	+	17.6464i	0.513052	+	0.565136i
$976$	−17.7789	−	27.1028i	−0.569088	−	0.867539i
$977$			16.1005i			0.515101i	0.966265	+	0.257550i	$0.0829154\pi$
$977$			16.1005i			0.515101i	−0.966265	+	0.257550i	$0.917085\pi$
$978$	−52.0659	+	15.7200i	−1.66489	+	0.502670i
$979$	37.4983	+	37.4983i	1.19845	+	1.19845i
$980$	3.19135	+	0.327991i	0.101944	+	0.0104773i
$981$	21.5289	−	17.7273i	0.687365	−	0.565990i
$982$	55.4827	−	19.7194i	1.77052	−	0.629272i
$983$		−	37.0765i		−	1.18256i	−0.806468	−	0.591278i	$-0.798624\pi$
$983$		−	37.0765i		−	1.18256i	0.806468	−	0.591278i	$-0.201376\pi$
$984$	−8.73353	+	1.68693i	−0.278415	+	0.0537775i
$985$		−	12.7839i		−	0.407329i
$986$	4.65576	+	13.0995i	0.148270	+	0.417172i
$987$	−40.4635	−	1.95468i	−1.28797	−	0.0622182i
$988$	3.77332	+	4.63778i	0.120045	+	0.147547i
$989$	4.24513	+	4.24513i	0.134987	+	0.134987i
$990$	−5.62830	+	9.37993i	−0.178879	+	0.298114i
$991$		−	40.7089i		−	1.29316i	−0.762846	−	0.646580i	$-0.776199\pi$
$991$		−	40.7089i		−	1.29316i	0.762846	−	0.646580i	$-0.223801\pi$
$992$	−1.79241	+	2.36398i	−0.0569089	+	0.0750565i
$993$	17.1219	−	15.5439i	0.543348	−	0.493272i
$994$	−19.8922	−	9.45998i	−0.630942	−	0.300052i
$995$	10.5580	−	10.5580i	0.334712	−	0.334712i
$996$	22.0476	+	3.34761i	0.698603	+	0.106073i
$997$	9.52444	+	9.52444i	0.301642	+	0.301642i	0.841656	−	0.540014i	$-0.181581\pi$
$997$	9.52444	+	9.52444i	0.301642	+	0.301642i	−0.540014	+	0.841656i	$0.681581\pi$
$998$	−8.34887	+	2.96732i	−0.264279	+	0.0939289i
$999$	6.69525	+	8.98136i	0.211828	+	0.284158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.2.k.a.11.2	✓	12
3.2	odd	2	inner	48.2.k.a.11.5	yes	12
4.3	odd	2		192.2.k.a.143.1		12
8.3	odd	2		384.2.k.a.287.6		12
8.5	even	2		384.2.k.b.287.1		12
12.11	even	2		192.2.k.a.143.3		12
16.3	odd	4	inner	48.2.k.a.35.5	yes	12
16.5	even	4		384.2.k.a.95.4		12
16.11	odd	4		384.2.k.b.95.3		12
16.13	even	4		192.2.k.a.47.3		12
24.5	odd	2		384.2.k.b.287.3		12
24.11	even	2		384.2.k.a.287.4		12
48.5	odd	4		384.2.k.a.95.6		12
48.11	even	4		384.2.k.b.95.1		12
48.29	odd	4		192.2.k.a.47.1		12
48.35	even	4	inner	48.2.k.a.35.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.k.a.11.2	✓	12	1.1	even	1	trivial
48.2.k.a.11.5	yes	12	3.2	odd	2	inner
48.2.k.a.35.2	yes	12	48.35	even	4	inner
48.2.k.a.35.5	yes	12	16.3	odd	4	inner
192.2.k.a.47.1		12	48.29	odd	4
192.2.k.a.47.3		12	16.13	even	4
192.2.k.a.143.1		12	4.3	odd	2
192.2.k.a.143.3		12	12.11	even	2
384.2.k.a.95.4		12	16.5	even	4
384.2.k.a.95.6		12	48.5	odd	4
384.2.k.a.287.4		12	24.11	even	2
384.2.k.a.287.6		12	8.3	odd	2
384.2.k.b.95.1		12	48.11	even	4
384.2.k.b.95.3		12	16.11	odd	4
384.2.k.b.287.1		12	8.5	even	2
384.2.k.b.287.3		12	24.5	odd	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.607364 + 1.27715i) q^{2} +(1.73003 + 0.0835731i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(-0.431733 + 0.431733i) q^{5} +(-1.15749 + 2.15875i) q^{6} -3.10278 q^{7} +(2.74798 - 0.669785i) q^{8} +(2.98603 + 0.289169i) q^{9} +O(q^{10})\)	\(q+(-0.607364 + 1.27715i) q^{2} +(1.73003 + 0.0835731i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(-0.431733 + 0.431733i) q^{5} +(-1.15749 + 2.15875i) q^{6} -3.10278 q^{7} +(2.74798 - 0.669785i) q^{8} +(2.98603 + 0.289169i) q^{9} +(-0.289169 - 0.813607i) q^{10} +(-2.98603 - 2.98603i) q^{11} +(-2.05403 - 2.78944i) q^{12} +(2.10278 - 2.10278i) q^{13} +(1.88451 - 3.96271i) q^{14} +(-0.782994 + 0.710831i) q^{15} +(-0.813607 + 3.91638i) q^{16} +2.42945i q^{17} +(-2.18292 + 3.63798i) q^{18} +(-0.710831 - 0.710831i) q^{19} +(1.21473 + 0.124844i) q^{20} +(-5.36790 - 0.259309i) q^{21} +(5.62721 - 2.00000i) q^{22} +5.97206i q^{23} +(4.81007 - 0.929094i) q^{24} +4.62721i q^{25} +(1.40841 + 3.96271i) q^{26} +(5.14177 + 0.749823i) q^{27} +(3.91638 + 4.81361i) q^{28} +(-2.86119 - 2.86119i) q^{29} +(-0.432276 - 1.43173i) q^{30} -0.524438i q^{31} +(-4.50765 - 3.41776i) q^{32} +(-4.91638 - 5.41549i) q^{33} +(-3.10278 - 1.47556i) q^{34} +(1.33957 - 1.33957i) q^{35} +(-3.32041 - 4.99749i) q^{36} +(1.52444 + 1.52444i) q^{37} +(1.33957 - 0.476105i) q^{38} +(3.81361 - 3.46214i) q^{39} +(-0.897225 + 1.47556i) q^{40} -1.81568 q^{41} +(3.59145 - 6.69812i) q^{42} +(0.710831 - 0.710831i) q^{43} +(-0.863466 + 8.40152i) q^{44} +(-1.41401 + 1.16432i) q^{45} +(-7.62721 - 3.62721i) q^{46} +7.53805 q^{47} +(-1.73487 + 6.70748i) q^{48} +2.62721 q^{49} +(-5.90964 - 2.81040i) q^{50} +(-0.203037 + 4.20304i) q^{51} +(-5.91638 - 0.608056i) q^{52} +(8.83325 - 8.83325i) q^{53} +(-4.08056 + 6.11139i) q^{54} +2.57834 q^{55} +(-8.52636 + 2.07819i) q^{56} +(-1.17036 - 1.28917i) q^{57} +(5.39194 - 1.91638i) q^{58} +(0.0804722 + 0.0804722i) q^{59} +(2.09108 + 0.317502i) q^{60} +(-5.72999 + 5.72999i) q^{61} +(0.669785 + 0.318525i) q^{62} +(-9.26498 - 0.897225i) q^{63} +(7.10278 - 3.68111i) q^{64} +1.81568i q^{65} +(9.90241 - 2.98978i) q^{66} +(-0.391944 - 0.391944i) q^{67} +(3.76903 - 3.06650i) q^{68} +(-0.499104 + 10.3319i) q^{69} +(0.897225 + 2.52444i) q^{70} -5.01985i q^{71} +(8.39923 - 1.20537i) q^{72} -13.4600i q^{73} +(-2.87282 + 1.02105i) q^{74} +(-0.386711 + 8.00523i) q^{75} +(-0.205550 + 2.00000i) q^{76} +(9.26498 + 9.26498i) q^{77} +(2.10542 + 6.97332i) q^{78} -3.47556i q^{79} +(-1.33957 - 2.04209i) q^{80} +(8.83276 + 1.72693i) q^{81} +(1.10278 - 2.31889i) q^{82} +(-4.55202 + 4.55202i) q^{83} +(6.37318 + 8.65500i) q^{84} +(-1.04888 - 1.04888i) q^{85} +(0.476105 + 1.33957i) q^{86} +(-4.71083 - 5.18907i) q^{87} +(-10.2056 - 6.20555i) q^{88} -12.5579 q^{89} +(-0.628197 - 2.51307i) q^{90} +(-6.52444 + 6.52444i) q^{91} +(9.26498 - 7.53805i) q^{92} +(0.0438289 - 0.907295i) q^{93} +(-4.57834 + 9.62721i) q^{94} +0.613779 q^{95} +(-7.51275 - 6.28956i) q^{96} -8.67609 q^{97} +(-1.59567 + 3.35534i) q^{98} +(-8.05292 - 9.77985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

Introduction

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