LMFDB - Embedded newform 276.2.c.a.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37110 + 0.346521i) q^{2} +(1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} -2.20059i q^{5} +(-2.44214 + 0.189562i) q^{6} +3.71987i q^{7} +(-2.08365 + 1.91269i) q^{8} +(2.82810 + 1.00093i) q^{9} +O(q^{10})$	\(q+(-1.37110 + 0.346521i) q^{2} +(1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} -2.20059i q^{5} +(-2.44214 + 0.189562i) q^{6} +3.71987i q^{7} +(-2.08365 + 1.91269i) q^{8} +(2.82810 + 1.00093i) q^{9} +(0.762550 + 3.01723i) q^{10} +0.958233 q^{11} +(3.28274 - 1.10616i) q^{12} +2.52970 q^{13} +(-1.28901 - 5.10033i) q^{14} +(0.645153 - 3.75653i) q^{15} +(2.19412 - 3.34453i) q^{16} -2.72185i q^{17} +(-4.22446 - 0.392378i) q^{18} -0.627384i q^{19} +(-2.09107 - 3.87269i) q^{20} +(-1.09057 + 6.35004i) q^{21} +(-1.31384 + 0.332048i) q^{22} +1.00000 q^{23} +(-4.11767 + 2.65420i) q^{24} +0.157420 q^{25} +(-3.46848 + 0.876595i) q^{26} +(4.53429 + 2.53776i) q^{27} +(3.53474 + 6.54640i) q^{28} +6.59334i q^{29} +(0.417147 + 5.37415i) q^{30} -9.19216i q^{31} +(-1.84941 + 5.34600i) q^{32} +(1.63576 + 0.280928i) q^{33} +(0.943181 + 3.73194i) q^{34} +8.18590 q^{35} +(5.92813 - 0.925875i) q^{36} -8.67442 q^{37} +(0.217402 + 0.860208i) q^{38} +(4.31834 + 0.741640i) q^{39} +(4.20904 + 4.58526i) q^{40} -5.91840i q^{41} +(-0.705146 - 9.08446i) q^{42} +7.53264i q^{43} +(1.68634 - 0.910544i) q^{44} +(2.20263 - 6.22348i) q^{45} +(-1.37110 + 0.346521i) q^{46} -4.76344 q^{47} +(4.72601 - 5.06605i) q^{48} -6.83744 q^{49} +(-0.215840 + 0.0545495i) q^{50} +(0.797975 - 4.64637i) q^{51} +(4.45188 - 2.40380i) q^{52} +11.5826i q^{53} +(-7.09636 - 1.90831i) q^{54} -2.10867i q^{55} +(-7.11496 - 7.75092i) q^{56} +(0.183932 - 1.07098i) q^{57} +(-2.28473 - 9.04015i) q^{58} +0.0894257 q^{59} +(-2.43421 - 7.22396i) q^{60} -14.4467 q^{61} +(3.18528 + 12.6034i) q^{62} +(-3.72332 + 10.5202i) q^{63} +(0.683225 - 7.97077i) q^{64} -5.56682i q^{65} +(-2.34014 + 0.181644i) q^{66} -13.6616i q^{67} +(-2.58640 - 4.79004i) q^{68} +(1.70706 + 0.293173i) q^{69} +(-11.2237 + 2.83659i) q^{70} -12.6101 q^{71} +(-7.80724 + 3.32369i) q^{72} +4.66813 q^{73} +(11.8935 - 3.00587i) q^{74} +(0.268726 + 0.0461514i) q^{75} +(-0.596161 - 1.10410i) q^{76} +3.56450i q^{77} +(-6.17789 + 0.479534i) q^{78} -6.77610i q^{79} +(-7.35992 - 4.82834i) q^{80} +(6.99629 + 5.66144i) q^{81} +(2.05085 + 8.11473i) q^{82} -12.4401 q^{83} +(4.11479 + 12.2114i) q^{84} -5.98968 q^{85} +(-2.61022 - 10.3280i) q^{86} +(-1.93299 + 11.2552i) q^{87} +(-1.99663 + 1.83280i) q^{88} -0.323760i q^{89} +(-0.863461 + 9.29628i) q^{90} +9.41015i q^{91} +(1.75985 - 0.950233i) q^{92} +(2.69489 - 15.6916i) q^{93} +(6.53117 - 1.65064i) q^{94} -1.38061 q^{95} +(-4.72435 + 8.58374i) q^{96} +7.00161 q^{97} +(9.37483 - 2.36932i) q^{98} +(2.70998 + 0.959122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.37110	+	0.346521i	−0.969516	+	0.245028i
$2$	−1.37110	+	0.346521i	−0.969516	+	0.245028i
$3$	1.70706	+	0.293173i	0.985571	+	0.169264i
$3$	1.70706	+	0.293173i	0.985571	+	0.169264i
$4$	1.75985	−	0.950233i	0.879923	−	0.475116i
$5$		−	2.20059i		−	0.984132i	−0.870558	−	0.492066i	$-0.836242\pi$
$5$		−	2.20059i		−	0.984132i	0.870558	−	0.492066i	$-0.163758\pi$
$6$	−2.44214	+	0.189562i	−0.997001	+	0.0773883i
$7$			3.71987i			1.40598i	0.711200	+	0.702990i	$0.248152\pi$
$7$			3.71987i			1.40598i	−0.711200	+	0.702990i	$0.751848\pi$
$8$	−2.08365	+	1.91269i	−0.736683	+	0.676238i
$9$	2.82810	+	1.00093i	0.942700	+	0.333642i
$10$	0.762550	+	3.01723i	0.241140	+	0.954132i
$11$	0.958233			0.288918			0.144459	−	0.989511i	$-0.453856\pi$
$11$	0.958233			0.288918			0.144459	+	0.989511i	$0.453856\pi$
$12$	3.28274	−	1.10616i	0.947646	−	0.319322i
$13$	2.52970			0.701612			0.350806	−	0.936448i	$-0.385908\pi$
$13$	2.52970			0.701612			0.350806	+	0.936448i	$0.385908\pi$
$14$	−1.28901	−	5.10033i	−0.344504	−	1.36312i
$15$	0.645153	−	3.75653i	0.166578	−	0.969932i
$16$	2.19412	−	3.34453i	0.548529	−	0.836132i
$17$		−	2.72185i		−	0.660147i	−0.943955	−	0.330073i	$-0.892927\pi$
$17$		−	2.72185i		−	0.660147i	0.943955	−	0.330073i	$-0.107073\pi$
$18$	−4.22446	−	0.392378i	−0.995714	−	0.0924843i
$19$		−	0.627384i		−	0.143932i	−0.997407	−	0.0719659i	$-0.977073\pi$
$19$		−	0.627384i		−	0.143932i	0.997407	−	0.0719659i	$-0.0229273\pi$
$20$	−2.09107	−	3.87269i	−0.467577	−	0.865960i
$21$	−1.09057	+	6.35004i	−0.237981	+	1.38569i
$22$	−1.31384	+	0.332048i	−0.280111	+	0.0707929i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	−4.11767	+	2.65420i	−0.840516	+	0.541787i
$25$	0.157420			0.0314841
$26$	−3.46848	+	0.876595i	−0.680224	+	0.171914i
$27$	4.53429	+	2.53776i	0.872624	+	0.488393i
$28$	3.53474	+	6.54640i	0.668004	+	1.23715i
$29$			6.59334i			1.22435i	0.790721	+	0.612177i	$0.209706\pi$
$29$			6.59334i			1.22435i	−0.790721	+	0.612177i	$0.790294\pi$
$30$	0.417147	+	5.37415i	0.0761603	+	0.981181i
$31$		−	9.19216i		−	1.65096i	−0.564431	−	0.825480i	$-0.690904\pi$
$31$		−	9.19216i		−	1.65096i	0.564431	−	0.825480i	$-0.309096\pi$
$32$	−1.84941	+	5.34600i	−0.326932	+	0.945048i
$33$	1.63576	+	0.280928i	0.284749	+	0.0489033i
$34$	0.943181	+	3.73194i	0.161754	+	0.640023i
$35$	8.18590			1.38367
$36$	5.92813	−	0.925875i	0.988022	−	0.154312i
$37$	−8.67442			−1.42607			−0.713033	−	0.701130i	$-0.752679\pi$
$37$	−8.67442			−1.42607			−0.713033	+	0.701130i	$0.752679\pi$
$38$	0.217402	+	0.860208i	0.0352673	+	0.139544i
$39$	4.31834	+	0.741640i	0.691489	+	0.118757i
$40$	4.20904	+	4.58526i	0.665508	+	0.724993i
$41$		−	5.91840i		−	0.924298i	−0.886802	−	0.462149i	$-0.847079\pi$
$41$		−	5.91840i		−	0.924298i	0.886802	−	0.462149i	$-0.152921\pi$
$42$	−0.705146	−	9.08446i	−0.108806	−	1.40176i
$43$			7.53264i			1.14872i	0.818604	+	0.574358i	$0.194748\pi$
$43$			7.53264i			1.14872i	−0.818604	+	0.574358i	$0.805252\pi$
$44$	1.68634	−	0.910544i	0.254226	−	0.137270i
$45$	2.20263	−	6.22348i	0.328348	−	0.927741i
$46$	−1.37110	+	0.346521i	−0.202158	+	0.0510918i
$47$	−4.76344			−0.694820			−0.347410	−	0.937713i	$-0.612939\pi$
$47$	−4.76344			−0.694820			−0.347410	+	0.937713i	$0.612939\pi$
$48$	4.72601	−	5.06605i	0.682141	−	0.731221i
$49$	−6.83744			−0.976777
$50$	−0.215840	+	0.0545495i	−0.0305243	+	0.00771447i
$51$	0.797975	−	4.64637i	0.111739	−	0.650621i
$52$	4.45188	−	2.40380i	0.617365	−	0.333347i
$53$			11.5826i			1.59099i	0.605963	+	0.795493i	$0.292788\pi$
$53$			11.5826i			1.59099i	−0.605963	+	0.795493i	$0.707212\pi$
$54$	−7.09636	−	1.90831i	−0.965693	−	0.259688i
$55$		−	2.10867i		−	0.284334i
$56$	−7.11496	−	7.75092i	−0.950777	−	1.03576i
$57$	0.183932	−	1.07098i	0.0243624	−	0.141855i
$58$	−2.28473	−	9.04015i	−0.300000	−	1.18703i
$59$	0.0894257			0.0116422			0.00582112	−	0.999983i	$-0.498147\pi$
$59$	0.0894257			0.0116422			0.00582112	+	0.999983i	$0.498147\pi$
$60$	−2.43421	−	7.22396i	−0.314255	−	0.932609i
$61$	−14.4467			−1.84971			−0.924855	−	0.380320i	$-0.875814\pi$
$61$	−14.4467			−1.84971			−0.924855	+	0.380320i	$0.875814\pi$
$62$	3.18528	+	12.6034i	0.404531	+	1.60063i
$63$	−3.72332	+	10.5202i	−0.469094	+	1.32542i
$64$	0.683225	−	7.97077i	0.0854031	−	0.996346i
$65$		−	5.56682i		−	0.690479i
$66$	−2.34014	+	0.181644i	−0.288052	+	0.0223589i
$67$		−	13.6616i		−	1.66902i	−0.550989	−	0.834512i	$-0.685749\pi$
$67$		−	13.6616i		−	1.66902i	0.550989	−	0.834512i	$-0.314251\pi$
$68$	−2.58640	−	4.79004i	−0.313647	−	0.580878i
$69$	1.70706	+	0.293173i	0.205506	+	0.0352939i
$70$	−11.2237	+	2.83659i	−1.34149	+	0.339037i
$71$	−12.6101			−1.49654			−0.748271	−	0.663394i	$-0.769116\pi$
$71$	−12.6101			−1.49654			−0.748271	+	0.663394i	$0.769116\pi$
$72$	−7.80724	+	3.32369i	−0.920093	+	0.391701i
$73$	4.66813			0.546363			0.273181	−	0.961963i	$-0.411924\pi$
$73$	4.66813			0.546363			0.273181	+	0.961963i	$0.411924\pi$
$74$	11.8935	−	3.00587i	1.38259	−	0.349426i
$75$	0.268726	+	0.0461514i	0.0310298	+	0.00532911i
$76$	−0.596161	−	1.10410i	−0.0683843	−	0.126649i
$77$			3.56450i			0.406213i
$78$	−6.17789	+	0.479534i	−0.699508	+	0.0542966i
$79$		−	6.77610i		−	0.762371i	−0.924499	−	0.381185i	$-0.875516\pi$
$79$		−	6.77610i		−	0.762371i	0.924499	−	0.381185i	$-0.124484\pi$
$80$	−7.35992	−	4.82834i	−0.822864	−	0.539825i
$81$	6.99629	+	5.66144i	0.777365	+	0.629049i
$82$	2.05085	+	8.11473i	0.226479	+	0.896122i
$83$	−12.4401			−1.36548			−0.682738	−	0.730664i	$-0.739211\pi$
$83$	−12.4401			−1.36548			−0.682738	+	0.730664i	$0.739211\pi$
$84$	4.11479	+	12.2114i	0.448960	+	1.33237i
$85$	−5.98968			−0.649672
$86$	−2.61022	−	10.3280i	−0.281467	−	1.11370i
$87$	−1.93299	+	11.2552i	−0.207238	+	1.20669i
$88$	−1.99663	+	1.83280i	−0.212841	+	0.195378i
$89$		−	0.323760i		−	0.0343185i	−0.999853	−	0.0171592i	$-0.994538\pi$
$89$		−	0.323760i		−	0.0343185i	0.999853	−	0.0171592i	$-0.00546222\pi$
$90$	−0.863461	+	9.29628i	−0.0910168	+	0.979914i
$91$			9.41015i			0.986452i
$92$	1.75985	−	0.950233i	0.183477	−	0.0990686i
$93$	2.69489	−	15.6916i	0.279447	−	1.62714i
$94$	6.53117	−	1.65064i	0.673639	−	0.170250i
$95$	−1.38061			−0.141648
$96$	−4.72435	+	8.58374i	−0.482177	+	0.876074i
$97$	7.00161			0.710906			0.355453	−	0.934694i	$-0.384327\pi$
$97$	7.00161			0.710906			0.355453	+	0.934694i	$0.384327\pi$
$98$	9.37483	−	2.36932i	0.947001	−	0.239337i
$99$	2.70998	+	0.959122i	0.272363	+	0.0963953i
$100$	0.277036	−	0.149586i	0.0277036	−	0.0149586i
$101$		−	9.88362i		−	0.983457i	−0.870749	−	0.491728i	$-0.836365\pi$
$101$		−	9.88362i		−	0.983457i	0.870749	−	0.491728i	$-0.163635\pi$
$102$	0.515960	+	6.64716i	0.0510876	+	0.658167i
$103$			2.08595i			0.205535i	0.994705	+	0.102768i	$0.0327698\pi$
$103$			2.08595i			0.205535i	−0.994705	+	0.102768i	$0.967230\pi$
$104$	−5.27102	+	4.83853i	−0.516866	+	0.474457i
$105$	13.9738	+	2.39988i	1.36370	+	0.234205i
$106$	−4.01360	−	15.8809i	−0.389835	−	1.54249i
$107$	1.05445			0.101937			0.0509687	−	0.998700i	$-0.483769\pi$
$107$	1.05445			0.101937			0.0509687	+	0.998700i	$0.483769\pi$
$108$	10.3911	+	0.157447i	0.999885	+	0.0151503i
$109$	4.32641			0.414395			0.207198	−	0.978299i	$-0.433566\pi$
$109$	4.32641			0.414395			0.207198	+	0.978299i	$0.433566\pi$
$110$	0.730701	+	2.89121i	0.0696696	+	0.275666i
$111$	−14.8078	−	2.54311i	−1.40549	−	0.241381i
$112$	12.4412	+	8.16182i	1.17558	+	0.771220i
$113$		−	4.35577i		−	0.409756i	−0.978787	−	0.204878i	$-0.934320\pi$
$113$		−	4.35577i		−	0.409756i	0.978787	−	0.204878i	$-0.0656798\pi$
$114$	0.118928	+	1.53216i	0.0111386	+	0.143500i
$115$		−	2.20059i		−	0.205206i
$116$	6.26521	+	11.6033i	0.581710	+	1.07734i
$117$	7.15424	+	2.53205i	0.661410	+	0.234088i
$118$	−0.122612	+	0.0309879i	−0.0112873	+	0.00285267i
$119$	10.1249			0.928153
$120$	5.84081	+	9.06129i	0.533190	+	0.827178i
$121$	−10.0818			−0.916526
$122$	19.8079	−	5.00609i	1.79332	−	0.453230i
$123$	1.73511	−	10.1030i	0.156450	−	0.910961i
$124$	−8.73469	−	16.1768i	−0.784398	−	1.45272i
$125$		−	11.3493i		−	1.01512i
$126$	1.45959	−	15.7144i	0.130031	−	1.39995i
$127$			7.13737i			0.633339i	0.948536	+	0.316670i	$0.102565\pi$
$127$			7.13737i			0.633339i	−0.948536	+	0.316670i	$0.897435\pi$
$128$	1.82527	+	11.1655i	0.161333	+	0.986900i
$129$	−2.20837	+	12.8587i	−0.194436	+	1.13214i
$130$	1.92902	+	7.63268i	0.169186	+	0.669431i
$131$	1.02516			0.0895682			0.0447841	−	0.998997i	$-0.485740\pi$
$131$	1.02516			0.0895682			0.0447841	+	0.998997i	$0.485740\pi$
$132$	3.14563	−	1.05996i	0.273792	−	0.0922579i
$133$	2.33379			0.202365
$134$	4.73402	+	18.7314i	0.408957	+	1.61815i
$135$	5.58457	−	9.97809i	0.480643	−	0.858777i
$136$	5.20607	+	5.67140i	0.446417	+	0.486319i
$137$			1.11266i			0.0950611i	0.998870	+	0.0475306i	$0.0151352\pi$
$137$			1.11266i			0.0950611i	−0.998870	+	0.0475306i	$0.984865\pi$
$138$	−2.44214	+	0.189562i	−0.207889	+	0.0161366i
$139$		−	1.76757i		−	0.149923i	−0.997186	−	0.0749616i	$-0.976117\pi$
$139$		−	1.76757i		−	0.149923i	0.997186	−	0.0749616i	$-0.0238834\pi$
$140$	14.4059	−	7.77851i	1.21752	−	0.657404i
$141$	−8.13148	−	1.39651i	−0.684794	−	0.117608i
$142$	17.2897	−	4.36966i	1.45092	−	0.366694i
$143$	2.42404			0.202708
$144$	9.55280	−	7.26250i	0.796067	−	0.605209i
$145$	14.5092			1.20493
$146$	−6.40048	+	1.61761i	−0.529708	+	0.133874i
$147$	−11.6719	−	2.00455i	−0.962683	−	0.165333i
$148$	−15.2657	+	8.24272i	−1.25483	+	0.677548i
$149$			16.1678i			1.32452i	0.749274	+	0.662260i	$0.230402\pi$
$149$			16.1678i			1.32452i	−0.749274	+	0.662260i	$0.769598\pi$
$150$	−0.384443	+	0.0298409i	−0.0313897	+	0.00243650i
$151$			18.1394i			1.47616i	0.674712	+	0.738082i	$0.264268\pi$
$151$			18.1394i			1.47616i	−0.674712	+	0.738082i	$0.735732\pi$
$152$	1.19999	+	1.30725i	0.0973322	+	0.106032i
$153$	2.72438	−	7.69767i	0.220253	−	0.622320i
$154$	−1.23518	−	4.88730i	−0.0995333	−	0.393830i
$155$	−20.2281			−1.62476
$156$	8.30435	−	2.79826i	0.664880	−	0.224040i
$157$	−12.6703			−1.01120			−0.505600	−	0.862768i	$-0.668729\pi$
$157$	−12.6703			−1.01120			−0.505600	+	0.862768i	$0.668729\pi$
$158$	2.34806	+	9.29073i	0.186802	+	0.739131i
$159$	−3.39569	+	19.7721i	−0.269296	+	1.56803i
$160$	11.7643	+	4.06978i	0.930052	+	0.321744i
$161$			3.71987i			0.293167i
$162$	−11.5544	−	5.33806i	−0.907803	−	0.419397i
$163$			8.15381i			0.638656i	0.947644	+	0.319328i	$0.103457\pi$
$163$			8.15381i			0.638656i	−0.947644	+	0.319328i	$0.896543\pi$
$164$	−5.62385	−	10.4155i	−0.439149	−	0.813311i
$165$	0.618207	−	3.59963i	0.0481273	−	0.280231i
$166$	17.0566	−	4.31075i	1.32385	−	0.334579i
$167$	15.7788			1.22100			0.610501	−	0.792016i	$-0.290968\pi$
$167$	15.7788			1.22100			0.610501	+	0.792016i	$0.290968\pi$
$168$	−9.87330	−	15.3172i	−0.761742	−	1.18175i
$169$	−6.60062			−0.507740
$170$	8.21246	−	2.07555i	0.629867	−	0.159187i
$171$	0.627966	−	1.77430i	0.0480217	−	0.135684i
$172$	7.15776	+	13.2563i	0.545774	+	1.01078i
$173$			6.82180i			0.518652i	0.965790	+	0.259326i	$0.0835004\pi$
$173$			6.82180i			0.518652i	−0.965790	+	0.259326i	$0.916500\pi$
$174$	−1.24985	−	16.1019i	−0.0947506	−	1.22068i
$175$			0.585584i			0.0442660i
$176$	2.10247	−	3.20484i	0.158480	−	0.241574i
$177$	0.152655	+	0.0262172i	0.0114742	+	0.00197061i
$178$	0.112190	+	0.443908i	0.00840897	+	0.0332723i
$179$	23.6302			1.76620			0.883102	−	0.469182i	$-0.155451\pi$
$179$	23.6302			1.76620			0.883102	+	0.469182i	$0.155451\pi$
$180$	−2.03747	−	13.0454i	−0.151864	−	0.972344i
$181$	4.79466			0.356385			0.178192	−	0.983996i	$-0.442975\pi$
$181$	4.79466			0.356385			0.178192	+	0.983996i	$0.442975\pi$
$182$	−3.26082	−	12.9023i	−0.241708	−	0.956381i
$183$	−24.6614	−	4.23538i	−1.82302	−	0.313089i
$184$	−2.08365	+	1.91269i	−0.153609	+	0.141005i
$185$			19.0888i			1.40344i
$186$	1.74248	+	22.4486i	0.127765	+	1.64601i
$187$		−	2.60817i		−	0.190728i
$188$	−8.38293	+	4.52638i	−0.611388	+	0.330120i
$189$	−9.44016	+	16.8670i	−0.686670	+	1.22689i
$190$	1.89296	−	0.478412i	0.137330	−	0.0347076i
$191$	−9.33989			−0.675810			−0.337905	−	0.941180i	$-0.609718\pi$
$191$	−9.33989			−0.675810			−0.337905	+	0.941180i	$0.609718\pi$
$192$	3.50312	−	13.4063i	0.252816	−	0.967514i
$193$	6.46649			0.465468			0.232734	−	0.972540i	$-0.425233\pi$
$193$	6.46649			0.465468			0.232734	+	0.972540i	$0.425233\pi$
$194$	−9.59993	+	2.42621i	−0.689235	+	0.174192i
$195$	1.63204	−	9.50289i	0.116873	−	0.680516i
$196$	−12.0328	+	6.49716i	−0.859489	+	0.464083i
$197$		−	24.9756i		−	1.77944i	−0.456510	−	0.889718i	$-0.650901\pi$
$197$		−	24.9756i		−	1.77944i	0.456510	−	0.889718i	$-0.349099\pi$
$198$	−4.04801	−	0.375989i	−0.287680	−	0.0267204i
$199$		−	11.2235i		−	0.795615i	−0.917469	−	0.397807i	$-0.869771\pi$
$199$		−	11.2235i		−	0.795615i	0.917469	−	0.397807i	$-0.130229\pi$
$200$	−0.328010	+	0.301097i	−0.0231938	+	0.0212907i
$201$	4.00520	−	23.3211i	0.282505	−	1.64494i
$202$	3.42488	+	13.5515i	0.240974	+	0.953477i
$203$	−24.5264			−1.72141
$204$	−3.01082	−	8.93515i	−0.210799	−	0.625586i
$205$	−13.0239			−0.909631
$206$	−0.722828	−	2.86006i	−0.0503618	−	0.199270i
$207$	2.82810	+	1.00093i	0.196566	+	0.0695693i
$208$	5.55045	−	8.46065i	0.384854	−	0.586640i
$209$		−	0.601180i		−	0.0415845i
$210$	−19.9911	+	1.55173i	−1.37952	+	0.107080i
$211$		−	1.44381i		−	0.0993960i	−0.998764	−	0.0496980i	$-0.984174\pi$
$211$		−	1.44381i		−	0.0993960i	0.998764	−	0.0496980i	$-0.0158259\pi$
$212$	11.0061	+	20.3835i	0.755903	+	1.39994i
$213$	−21.5262	−	3.69694i	−1.47495	−	0.253310i
$214$	−1.44576	+	0.365389i	−0.0988300	+	0.0249775i
$215$	16.5762			1.13049
$216$	−14.3018	+	3.38487i	−0.973117	+	0.230311i
$217$	34.1936			2.32122
$218$	−5.93196	+	1.49919i	−0.401763	+	0.101538i
$219$	7.96877	+	1.36857i	0.538479	+	0.0924794i
$220$	−2.00373	−	3.71094i	−0.135092	−	0.250192i
$221$		−	6.88547i		−	0.463167i
$222$	21.1842	−	1.64434i	1.42179	−	0.110361i
$223$		−	11.4471i		−	0.766556i	−0.923633	−	0.383278i	$-0.874795\pi$
$223$		−	11.4471i		−	0.766556i	0.923633	−	0.383278i	$-0.125205\pi$
$224$	−19.8864	−	6.87956i	−1.32872	−	0.459660i
$225$	0.445201	+	0.157566i	0.0296800	+	0.0105044i
$226$	1.50937	+	5.97221i	0.100402	+	0.397265i
$227$	11.5592			0.767210			0.383605	−	0.923497i	$-0.374682\pi$
$227$	11.5592			0.767210			0.383605	+	0.923497i	$0.374682\pi$
$228$	−0.693989	−	2.05954i	−0.0459606	−	0.136396i
$229$	−11.4270			−0.755115			−0.377558	−	0.925986i	$-0.623236\pi$
$229$	−11.4270			−0.755115			−0.377558	+	0.925986i	$0.623236\pi$
$230$	0.762550	+	3.01723i	0.0502811	+	0.198950i
$231$	−1.04502	+	6.08482i	−0.0687570	+	0.400351i
$232$	−12.6110	−	13.7382i	−0.827955	−	0.901960i
$233$		−	14.6817i		−	0.961832i	−0.876767	−	0.480916i	$-0.840304\pi$
$233$		−	14.6817i		−	0.961832i	0.876767	−	0.480916i	$-0.159696\pi$
$234$	−10.6866	−	0.992597i	−0.698605	−	0.0648881i
$235$			10.4824i			0.683794i
$236$	0.157375	−	0.0849752i	0.0102443	−	0.00553142i
$237$	1.98657	−	11.5672i	0.129042	−	0.751370i
$238$	−13.8823	+	3.50851i	−0.899859	+	0.227423i
$239$	14.7775			0.955876			0.477938	−	0.878393i	$-0.341384\pi$
$239$	14.7775			0.955876			0.477938	+	0.878393i	$0.341384\pi$
$240$	−11.1483	−	10.4000i	−0.719618	−	0.671316i
$241$	−17.3937			−1.12043			−0.560213	−	0.828349i	$-0.689281\pi$
$241$	−17.3937			−1.12043			−0.560213	+	0.828349i	$0.689281\pi$
$242$	13.8232	−	3.49356i	0.888587	−	0.224574i
$243$	10.2833	+	11.7155i	0.659673	+	0.751552i
$244$	−25.4240	+	13.7277i	−1.62760	+	0.878828i
$245$			15.0464i			0.961278i
$246$	1.12190	+	14.4536i	0.0715299	+	0.921526i
$247$		−	1.58709i		−	0.100984i
$248$	17.5818	+	19.1533i	1.11644	+	1.21623i
$249$	−21.2359	−	3.64709i	−1.34577	−	0.231125i
$250$	3.93279	+	15.5611i	0.248732	+	0.984172i
$251$	−12.7892			−0.807250			−0.403625	−	0.914925i	$-0.632250\pi$
$251$	−12.7892			−0.807250			−0.403625	+	0.914925i	$0.632250\pi$
$252$	3.44413	+	22.0519i	0.216960	+	1.38914i
$253$	0.958233			0.0602436
$254$	−2.47325	−	9.78607i	−0.155186	−	0.614033i
$255$	−10.2247	−	1.75601i	−0.640297	−	0.109966i
$256$	−6.37172	−	14.6766i	−0.398232	−	0.917285i
$257$			15.5053i			0.967196i	0.875290	+	0.483598i	$0.160670\pi$
$257$			15.5053i			0.967196i	−0.875290	+	0.483598i	$0.839330\pi$
$258$	−1.42790	−	18.3958i	−0.0888972	−	1.14527i
$259$		−	32.2677i		−	2.00502i
$260$	−5.28978	−	9.79675i	−0.328058	−	0.607568i
$261$	−6.59946	+	18.6466i	−0.408496	+	1.15420i
$262$	−1.40559	+	0.355238i	−0.0868378	+	0.0219467i
$263$	15.8314			0.976204			0.488102	−	0.872787i	$-0.337689\pi$
$263$	15.8314			0.976204			0.488102	+	0.872787i	$0.337689\pi$
$264$	−3.94569	+	2.54335i	−0.242840	+	0.156532i
$265$	25.4884			1.56574
$266$	−3.19986	+	0.808707i	−0.196196	+	0.0495850i
$267$	0.0949176	−	0.552677i	0.00580886	−	0.0338233i
$268$	−12.9817	−	24.0422i	−0.792981	−	1.46861i
$269$		−	3.60658i		−	0.219897i	−0.993937	−	0.109949i	$-0.964931\pi$
$269$		−	3.60658i		−	0.219897i	0.993937	−	0.109949i	$-0.0350686\pi$
$270$	−4.19940	+	15.6162i	−0.255567	+	0.950369i
$271$		−	21.4184i		−	1.30107i	−0.759474	−	0.650537i	$-0.774544\pi$
$271$		−	21.4184i		−	1.30107i	0.759474	−	0.650537i	$-0.225456\pi$
$272$	−9.10332	−	5.97206i	−0.551970	−	0.362109i
$273$	−2.75880	+	16.0637i	−0.166970	+	0.972218i
$274$	−0.385561	−	1.52557i	−0.0232926	−	0.0921633i
$275$	0.150845			0.00909632
$276$	3.28274	−	1.10616i	0.197598	−	0.0665832i
$277$	30.3603			1.82418			0.912088	−	0.409994i	$-0.134469\pi$
$277$	30.3603			1.82418			0.912088	+	0.409994i	$0.134469\pi$
$278$	0.612500	+	2.42352i	0.0367353	+	0.145353i
$279$	9.20068	−	25.9963i	0.550831	−	1.55636i
$280$	−17.0566	+	15.6571i	−1.01933	+	0.935690i
$281$		−	6.32399i		−	0.377257i	−0.982048	−	0.188629i	$-0.939596\pi$
$281$		−	6.32399i		−	0.377257i	0.982048	−	0.188629i	$-0.0604043\pi$
$282$	11.6330	−	0.902967i	0.692736	−	0.0537709i
$283$			12.0709i			0.717540i	0.933426	+	0.358770i	$0.116804\pi$
$283$			12.0709i			0.717540i	−0.933426	+	0.358770i	$0.883196\pi$
$284$	−22.1918	+	11.9825i	−1.31684	+	0.711031i
$285$	−2.35679	−	0.404758i	−0.139604	−	0.0239758i
$286$	−3.32361	+	0.839982i	−0.196529	+	0.0496692i
$287$	22.0157			1.29954
$288$	−10.5813	+	13.2679i	−0.623507	+	0.781818i
$289$	9.59151			0.564206
$290$	−19.8936	+	5.02776i	−1.16819	+	0.295240i
$291$	11.9522	+	2.05269i	0.700648	+	0.120331i
$292$	8.21518	−	4.43581i	0.480757	−	0.259586i
$293$			5.89202i			0.344216i	0.985078	+	0.172108i	$0.0550577\pi$
$293$			5.89202i			0.344216i	−0.985078	+	0.172108i	$0.944942\pi$
$294$	16.6980	−	1.29612i	0.973848	−	0.0755911i
$295$		−	0.196789i		−	0.0114575i
$296$	18.0745	−	16.5915i	1.05056	−	0.964361i
$297$	4.34490	+	2.43177i	0.252117	+	0.141106i
$298$	−5.60249	−	22.1677i	−0.324544	−	1.28414i
$299$	2.52970			0.146296
$300$	0.516771	−	0.174133i	0.0298358	−	0.0100536i
$301$	−28.0204			−1.61507
$302$	−6.28569	−	24.8710i	−0.361701	−	1.43116i
$303$	2.89761	−	16.8719i	0.166463	−	0.969266i
$304$	−2.09830	−	1.37655i	−0.120346	−	0.0789507i
$305$			31.7912i			1.82036i
$306$	−1.06800	+	11.4984i	−0.0610532	+	0.657317i
$307$			29.0210i			1.65632i	0.560494	+	0.828158i	$0.310611\pi$
$307$			29.0210i			1.65632i	−0.560494	+	0.828158i	$0.689389\pi$
$308$	3.38711	+	6.27298i	0.192998	+	0.357436i
$309$	−0.611546	+	3.56085i	−0.0347896	+	0.202570i
$310$	27.7349	−	7.00948i	1.57523	−	0.398112i
$311$	31.8428			1.80564			0.902820	−	0.430019i	$-0.141493\pi$
$311$	31.8428			1.80564			0.902820	+	0.430019i	$0.141493\pi$
$312$	−10.4165	+	6.71434i	−0.589716	+	0.380125i
$313$	32.8768			1.85831			0.929153	−	0.369694i	$-0.120538\pi$
$313$	32.8768			1.85831			0.929153	+	0.369694i	$0.120538\pi$
$314$	17.3723	−	4.39053i	0.980374	−	0.247772i
$315$	23.1505	+	8.19349i	1.30438	+	0.461651i
$316$	−6.43887	−	11.9249i	−0.362215	−	0.670828i
$317$			28.6626i			1.60985i	0.593375	+	0.804926i	$0.297795\pi$
$317$			28.6626i			1.60985i	−0.593375	+	0.804926i	$0.702205\pi$
$318$	−2.19561	−	28.2863i	−0.123124	−	1.58621i
$319$			6.31796i			0.353738i
$320$	−17.5404	−	1.50350i	−0.980537	−	0.0840480i
$321$	1.80001	+	0.309136i	0.100467	+	0.0172543i
$322$	−1.28901	−	5.10033i	−0.0718340	−	0.284230i
$323$	−1.70765			−0.0950161
$324$	17.6921	+	3.31517i	0.982893	+	0.184176i
$325$	0.398226			0.0220896
$326$	−2.82547	−	11.1797i	−0.156488	−	0.619187i
$327$	7.38544	+	1.26839i	0.408416	+	0.0701420i
$328$	11.3201	+	12.3319i	0.625046	+	0.680914i
$329$		−	17.7194i		−	0.976902i
$330$	0.399724	+	5.14968i	0.0220041	+	0.283481i
$331$			23.2121i			1.27585i	0.770098	+	0.637926i	$0.220207\pi$
$331$			23.2121i			1.27585i	−0.770098	+	0.637926i	$0.779793\pi$
$332$	−21.8926	+	11.8210i	−1.20151	+	0.648760i
$333$	−24.5321	−	8.68247i	−1.34435	−	0.475796i
$334$	−21.6344	+	5.46770i	−1.18378	+	0.299179i
$335$	−30.0634			−1.64254
$336$	18.8450	+	17.5801i	1.02808	+	0.959075i
$337$	−24.9496			−1.35909			−0.679546	−	0.733632i	$-0.737823\pi$
$337$	−24.9496			−1.35909			−0.679546	+	0.733632i	$0.737823\pi$
$338$	9.05013	−	2.28726i	0.492262	−	0.124410i
$339$	1.27699	−	7.43556i	0.0693568	−	0.403844i
$340$	−10.5409	+	5.69159i	−0.571661	+	0.308670i
$341$		−	8.80823i		−	0.476992i
$342$	−0.246171	+	2.65036i	−0.0133114	+	0.143315i
$343$			0.604700i			0.0326507i
$344$	−14.4076	−	15.6954i	−0.776806	−	0.846239i
$345$	0.645153	−	3.75653i	0.0347339	−	0.202245i
$346$	−2.36390	−	9.35340i	−0.127084	−	0.502842i
$347$	2.44357			0.131177			0.0655887	−	0.997847i	$-0.479107\pi$
$347$	2.44357			0.131177			0.0655887	+	0.997847i	$0.479107\pi$
$348$	7.29332	+	21.6443i	0.390963	+	1.16025i
$349$	−16.8631			−0.902663			−0.451331	−	0.892356i	$-0.649051\pi$
$349$	−16.8631			−0.902663			−0.451331	+	0.892356i	$0.649051\pi$
$350$	−0.202917	−	0.802895i	−0.0108464	−	0.0429166i
$351$	11.4704	+	6.41978i	0.612243	+	0.342663i
$352$	−1.77216	+	5.12271i	−0.0944566	+	0.273041i
$353$		−	35.2238i		−	1.87477i	−0.348290	−	0.937387i	$-0.613238\pi$
$353$		−	35.2238i		−	1.87477i	0.348290	−	0.937387i	$-0.386762\pi$
$354$	−0.218390	+	0.0169517i	−0.0116073	+	0.000900973i
$355$			27.7496i			1.47279i
$356$	−0.307647	−	0.569767i	−0.0163053	−	0.0301976i
$357$	17.2839	+	2.96836i	0.914760	+	0.157102i
$358$	−32.3994	+	8.18837i	−1.71236	+	0.432769i
$359$	−9.90967			−0.523012			−0.261506	−	0.965202i	$-0.584219\pi$
$359$	−9.90967			−0.523012			−0.261506	+	0.965202i	$0.584219\pi$
$360$	7.31407	+	17.1805i	0.385486	+	0.905493i
$361$	18.6064			0.979284
$362$	−6.57398	+	1.66145i	−0.345521	+	0.0873241i
$363$	−17.2102	−	2.95571i	−0.903302	−	0.155135i
$364$	8.94184	+	16.5604i	0.468680	+	0.868002i
$365$		−	10.2726i		−	0.537693i
$366$	35.2809	−	2.73854i	1.84416	−	0.143146i
$367$		−	2.74401i		−	0.143236i	−0.997432	−	0.0716180i	$-0.977184\pi$
$367$		−	2.74401i		−	0.143236i	0.997432	−	0.0716180i	$-0.0228162\pi$
$368$	2.19412	−	3.34453i	0.114376	−	0.174346i
$369$	5.92388	−	16.7378i	0.308385	−	0.871335i
$370$	−6.61468	−	26.1727i	−0.343881	−	1.36066i
$371$	−43.0856			−2.23689
$372$	−10.1680	−	30.1755i	−0.527188	−	1.56453i
$373$	−4.92429			−0.254970			−0.127485	−	0.991840i	$-0.540691\pi$
$373$	−4.92429			−0.254970			−0.127485	+	0.991840i	$0.540691\pi$
$374$	0.903787	+	3.57607i	0.0467337	+	0.184914i
$375$	3.32732	−	19.3740i	0.171822	−	1.00047i
$376$	9.92537	−	9.11100i	0.511862	−	0.469864i
$377$			16.6792i			0.859021i
$378$	7.09866	−	26.3976i	0.365116	−	1.35774i
$379$		−	5.86840i		−	0.301440i	−0.988577	−	0.150720i	$-0.951841\pi$
$379$		−	5.86840i		−	0.301440i	0.988577	−	0.150720i	$-0.0481591\pi$
$380$	−2.42967	+	1.31190i	−0.124639	+	0.0672992i
$381$	−2.09249	+	12.1839i	−0.107201	+	0.624201i
$382$	12.8059	−	3.23647i	0.655209	−	0.165592i
$383$	12.2927			0.628126			0.314063	−	0.949402i	$-0.398310\pi$
$383$	12.2927			0.628126			0.314063	+	0.949402i	$0.398310\pi$
$384$	−0.157579	+	19.5953i	−0.00804144	+	0.999968i
$385$	7.84400			0.399767
$386$	−8.86622	+	2.24078i	−0.451279	+	0.114053i
$387$	−7.53962	+	21.3030i	−0.383261	+	1.08289i
$388$	12.3218	−	6.65316i	0.625543	−	0.337763i
$389$		−	17.7283i		−	0.898858i	−0.893316	−	0.449429i	$-0.851627\pi$
$389$		−	17.7283i		−	0.898858i	0.893316	−	0.449429i	$-0.148373\pi$
$390$	1.05526	+	13.5950i	0.0534350	+	0.688408i
$391$		−	2.72185i		−	0.137650i
$392$	14.2469	−	13.0779i	0.719575	−	0.660534i
$393$	1.75000	+	0.300548i	0.0882758	+	0.0151606i
$394$	8.65457	+	34.2441i	0.436011	+	1.72519i
$395$	−14.9114			−0.750274
$396$	5.68053	−	0.887203i	0.285457	−	0.0445836i
$397$	−10.6156			−0.532781			−0.266391	−	0.963865i	$-0.585831\pi$
$397$	−10.6156			−0.532781			−0.266391	+	0.963865i	$0.585831\pi$
$398$	3.88919	+	15.3886i	0.194948	+	0.771361i
$399$	3.98391	+	0.684204i	0.199445	+	0.0342530i
$400$	0.345398	−	0.526497i	0.0172699	−	0.0263248i
$401$			19.1200i			0.954807i	0.878684	+	0.477404i	$0.158422\pi$
$401$			19.1200i			0.954807i	−0.878684	+	0.477404i	$0.841578\pi$
$402$	2.58971	+	33.3635i	0.129163	+	1.66402i
$403$		−	23.2534i		−	1.15833i
$404$	−9.39174	−	17.3936i	−0.467256	−	0.865366i
$405$	12.4585	−	15.3959i	0.619068	−	0.765030i
$406$	33.6282	−	8.49892i	1.66894	−	0.421794i
$407$	−8.31212			−0.412016
$408$	7.22436	+	11.2077i	0.357659	+	0.554864i
$409$	−22.4004			−1.10763			−0.553814	−	0.832641i	$-0.686828\pi$
$409$	−22.4004			−1.10763			−0.553814	+	0.832641i	$0.686828\pi$
$410$	17.8572	−	4.51307i	0.881902	−	0.222885i
$411$	−0.326203	+	1.89938i	−0.0160904	+	0.0936895i
$412$	1.98214	+	3.67096i	0.0976532	+	0.180855i
$413$			0.332652i			0.0163687i
$414$	−4.22446	−	0.392378i	−0.207621	−	0.0192843i
$415$			27.3754i			1.34381i
$416$	−4.67844	+	13.5238i	−0.229380	+	0.663057i
$417$	0.518204	−	3.01734i	0.0253765	−	0.147760i
$418$	0.208322	+	0.824279i	0.0101893	+	0.0403168i
$419$	9.56749			0.467402			0.233701	−	0.972308i	$-0.424916\pi$
$419$	9.56749			0.467402			0.233701	+	0.972308i	$0.424916\pi$
$420$	26.8722	−	9.05494i	1.31123	−	0.441836i
$421$	33.4727			1.63136			0.815681	−	0.578502i	$-0.196363\pi$
$421$	33.4727			1.63136			0.815681	+	0.578502i	$0.196363\pi$
$422$	0.500311	+	1.97961i	0.0243548	+	0.0963660i
$423$	−13.4715	−	4.76786i	−0.655006	−	0.231821i
$424$	−22.1538	−	24.1340i	−1.07589	−	1.17205i
$425$		−	0.428475i		−	0.0207841i
$426$	30.7956	−	2.39039i	1.49205	−	0.115815i
$427$		−	53.7399i		−	2.60065i
$428$	1.85567	−	1.00197i	0.0896971	−	0.0484321i
$429$	4.13798	+	0.710663i	0.199784	+	0.0343112i
$430$	−22.7277	+	5.74401i	−1.09603	+	0.277001i
$431$	−15.5475			−0.748897			−0.374449	−	0.927248i	$-0.622168\pi$
$431$	−15.5475			−0.748897			−0.374449	+	0.927248i	$0.622168\pi$
$432$	18.4364	−	9.59689i	0.887020	−	0.461731i
$433$	0.627720			0.0301663			0.0150832	−	0.999886i	$-0.495199\pi$
$433$	0.627720			0.0301663			0.0150832	+	0.999886i	$0.495199\pi$
$434$	−46.8830	+	11.8488i	−2.25046	+	0.568762i
$435$	24.7681	+	4.25371i	1.18754	+	0.203950i
$436$	7.61382	−	4.11110i	0.364636	−	0.196886i
$437$		−	0.627384i		−	0.0300118i
$438$	−11.4002	+	0.884899i	−0.544724	+	0.0422821i
$439$		−	5.07380i		−	0.242159i	−0.992643	−	0.121080i	$-0.961364\pi$
$439$		−	5.07380i		−	0.242159i	0.992643	−	0.121080i	$-0.0386356\pi$
$440$	4.03324	+	4.39375i	0.192277	+	0.209464i
$441$	−19.3370	−	6.84378i	−0.920808	−	0.325894i
$442$	2.38596	+	9.44069i	0.113489	+	0.449048i
$443$	−8.83365			−0.419700			−0.209850	−	0.977734i	$-0.567297\pi$
$443$	−8.83365			−0.419700			−0.209850	+	0.977734i	$0.567297\pi$
$444$	−28.4759	+	9.59533i	−1.35141	+	0.455374i
$445$	−0.712461			−0.0337739
$446$	3.96667	+	15.6952i	0.187827	+	0.743189i
$447$	−4.73997	+	27.5994i	−0.224193	+	1.30541i
$448$	29.6502	+	2.54151i	1.40084	+	0.120075i
$449$		−	16.0724i		−	0.758502i	−0.925294	−	0.379251i	$-0.876182\pi$
$449$		−	16.0724i		−	0.758502i	0.925294	−	0.379251i	$-0.123818\pi$
$450$	−0.665016	−	0.0617683i	−0.0313491	−	0.00291178i
$451$		−	5.67120i		−	0.267046i
$452$	−4.13900	−	7.66549i	−0.194682	−	0.360554i
$453$	−5.31798	+	30.9650i	−0.249861	+	1.45486i
$454$	−15.8488	+	4.00551i	−0.743823	+	0.187988i
$455$	20.7079			0.970799
$456$	1.66521	+	2.58336i	0.0779804	+	0.120977i
$457$	16.3723			0.765864			0.382932	−	0.923776i	$-0.374914\pi$
$457$	16.3723			0.765864			0.382932	+	0.923776i	$0.374914\pi$
$458$	15.6676	−	3.95969i	0.732097	−	0.185024i
$459$	6.90743	−	12.3417i	0.322411	−	0.576060i
$460$	−2.09107	−	3.87269i	−0.0974966	−	0.180565i
$461$		−	9.35232i		−	0.435581i	−0.975996	−	0.217790i	$-0.930115\pi$
$461$		−	9.35232i		−	0.435581i	0.975996	−	0.217790i	$-0.0698849\pi$
$462$	−0.675694	−	8.70503i	−0.0314361	−	0.404995i
$463$			10.2286i			0.475365i	0.971343	+	0.237682i	$0.0763877\pi$
$463$			10.2286i			0.475365i	−0.971343	+	0.237682i	$0.923612\pi$
$464$	22.0516	+	14.4666i	1.02372	+	0.671593i
$465$	−34.5306	−	5.93035i	−1.60132	−	0.275013i
$466$	5.08753	+	20.1302i	0.235675	+	0.932511i
$467$	−8.62755			−0.399236			−0.199618	−	0.979874i	$-0.563970\pi$
$467$	−8.62755			−0.399236			−0.199618	+	0.979874i	$0.563970\pi$
$468$	14.9964	−	2.34218i	0.693208	−	0.108267i
$469$	50.8192			2.34661
$470$	−3.63237	−	14.3724i	−0.167549	−	0.662950i
$471$	−21.6289	−	3.71459i	−0.996609	−	0.171159i
$472$	−0.186332	+	0.171044i	−0.00857663	+	0.00787293i
$473$			7.21802i			0.331885i
$474$	1.28449	+	16.5482i	0.0589986	+	0.760084i
$475$		−	0.0987630i		−	0.00453156i
$476$	17.8183	−	9.62106i	0.816703	−	0.440981i
$477$	−11.5933	+	32.7566i	−0.530820	+	1.49982i
$478$	−20.2615	+	5.12072i	−0.926737	+	0.234216i
$479$	6.82356			0.311776			0.155888	−	0.987775i	$-0.450176\pi$
$479$	6.82356			0.311776			0.155888	+	0.987775i	$0.450176\pi$
$480$	18.8893	+	10.3963i	0.862172	+	0.474526i
$481$	−21.9437			−1.00055
$482$	23.8485	−	6.02728i	1.08627	−	0.274535i
$483$	−1.09057	+	6.35004i	−0.0496225	+	0.288937i
$484$	−17.7424	+	9.58005i	−0.806473	+	0.435457i
$485$		−	15.4077i		−	0.699626i
$486$	−18.1591	−	12.4998i	−0.823715	−	0.567004i
$487$		−	6.28290i		−	0.284705i	−0.989816	−	0.142353i	$-0.954533\pi$
$487$		−	6.28290i		−	0.284705i	0.989816	−	0.142353i	$-0.0454667\pi$
$488$	30.1019	−	27.6321i	1.36265	−	1.25085i
$489$	−2.39048	+	13.9190i	−0.108101	+	0.629441i
$490$	−5.21389	−	20.6301i	−0.235540	−	0.931974i
$491$	−22.1458			−0.999425			−0.499713	−	0.866191i	$-0.666561\pi$
$491$	−22.1458			−0.999425			−0.499713	+	0.866191i	$0.666561\pi$
$492$	−6.54671	−	19.4286i	−0.295149	−	0.875908i
$493$	17.9461			0.808253
$494$	0.549961	+	2.17607i	0.0247439	+	0.0979059i
$495$	2.11063	−	5.96354i	0.0948657	−	0.268041i
$496$	−30.7434	−	20.1687i	−1.38042	−	0.905599i
$497$		−	46.9079i		−	2.10411i
$498$	30.3804	−	2.35816i	1.36138	−	0.105672i
$499$			29.0340i			1.29974i	0.760045	+	0.649871i	$0.225177\pi$
$499$			29.0340i			1.29974i	−0.760045	+	0.649871i	$0.774823\pi$
$500$	−10.7845	−	19.9731i	−0.482299	−	0.893224i
$501$	26.9354	+	4.62592i	1.20338	+	0.206671i
$502$	17.5354	−	4.43175i	0.782642	−	0.197799i
$503$	−7.77873			−0.346836			−0.173418	−	0.984848i	$-0.555481\pi$
$503$	−7.77873			−0.346836			−0.173418	+	0.984848i	$0.555481\pi$
$504$	−12.3637	−	29.0419i	−0.550724	−	1.29363i
$505$	−21.7498			−0.967851
$506$	−1.31384	+	0.332048i	−0.0584071	+	0.0147613i
$507$	−11.2677	−	1.93513i	−0.500414	−	0.0859419i
$508$	6.78217	+	12.5607i	0.300910	+	0.557290i
$509$			10.9884i			0.487052i	0.969894	+	0.243526i	$0.0783040\pi$
$509$			10.9884i			0.487052i	−0.969894	+	0.243526i	$0.921696\pi$
$510$	14.6277	−	1.13541i	0.647723	−	0.0502770i
$511$			17.3648i			0.768175i
$512$	13.8220	+	17.9151i	0.610853	+	0.791744i
$513$	1.59215	−	2.84474i	0.0702953	−	0.125598i
$514$	−5.37293	−	21.2594i	−0.236990	−	0.937712i
$515$	4.59032			0.202274
$516$	8.33233	+	24.7277i	0.366810	+	1.08858i
$517$	−4.56449			−0.200746
$518$	11.1815	+	44.2424i	0.491285	+	1.94390i
$519$	−1.99997	+	11.6452i	−0.0877889	+	0.511168i
$520$	10.6476	+	11.5993i	0.466928	+	0.508664i
$521$			39.5660i			1.73342i	0.498816	+	0.866708i	$0.333768\pi$
$521$			39.5660i			1.73342i	−0.498816	+	0.866708i	$0.666232\pi$
$522$	2.58708	−	27.8533i	0.113233	−	1.21911i
$523$		−	2.37731i		−	0.103952i	−0.998648	−	0.0519762i	$-0.983448\pi$
$523$		−	2.37731i		−	0.103952i	0.998648	−	0.0519762i	$-0.0165520\pi$
$524$	1.80412	−	0.974136i	0.0788131	−	0.0425553i
$525$	−0.171677	+	0.999626i	−0.00749262	+	0.0436272i
$526$	−21.7064	+	5.48591i	−0.946446	+	0.239197i
$527$	−25.0197			−1.08988
$528$	4.52862	−	4.85445i	0.197083	−	0.211263i
$529$	1.00000			0.0434783
$530$	−34.9472	+	8.83228i	−1.51801	+	0.383650i
$531$	0.252905	+	0.0895086i	0.0109751	+	0.00388434i
$532$	4.10711	−	2.21764i	0.178066	−	0.0961469i
$533$		−	14.9718i		−	0.648499i
$534$	0.0613725	+	0.790668i	0.00265585	+	0.0342155i
$535$		−	2.32041i		−	0.100320i
$536$	26.1303	+	28.4660i	1.12866	+	1.22954i
$537$	40.3381	+	6.92774i	1.74072	+	0.298954i
$538$	1.24976	+	4.94500i	0.0538809	+	0.213194i
$539$	−6.55186			−0.282209
$540$	0.346475	−	22.8665i	0.0149099	−	0.984019i
$541$	29.0791			1.25021			0.625103	−	0.780542i	$-0.285057\pi$
$541$	29.0791			1.25021			0.625103	+	0.780542i	$0.285057\pi$
$542$	7.42193	+	29.3668i	0.318799	+	1.26141i
$543$	8.18477	+	1.40567i	0.351242	+	0.0603229i
$544$	14.5510	+	5.03382i	0.623870	+	0.215823i
$545$		−	9.52065i		−	0.407820i
$546$	−1.78381	−	22.9809i	−0.0763398	−	0.983494i
$547$		−	10.0489i		−	0.429658i	−0.976652	−	0.214829i	$-0.931081\pi$
$547$		−	10.0489i		−	0.429658i	0.976652	−	0.214829i	$-0.0689194\pi$
$548$	1.05729	+	1.95811i	0.0451651	+	0.0836465i
$549$	−40.8567	−	14.4601i	−1.74372	−	0.617142i
$550$	−0.206825	+	0.0522712i	−0.00881903	+	0.00222885i
$551$	4.13656			0.176223
$552$	−4.11767	+	2.65420i	−0.175260	+	0.112970i
$553$	25.2062			1.07188
$554$	−41.6272	+	10.5205i	−1.76857	+	0.446974i
$555$	−5.59633	+	32.5857i	−0.237551	+	1.38319i
$556$	−1.67960	−	3.11065i	−0.0712310	−	0.131921i
$557$			29.2920i			1.24114i	0.784150	+	0.620571i	$0.213099\pi$
$557$			29.2920i			1.24114i	−0.784150	+	0.620571i	$0.786901\pi$
$558$	−3.60680	+	38.8319i	−0.152688	+	1.64388i
$559$			19.0553i			0.805953i
$560$	17.9608	−	27.3780i	0.758982	−	1.15693i
$561$	0.764646	−	4.45230i	0.0322834	−	0.187976i
$562$	2.19140	+	8.67084i	0.0924385	+	0.365757i
$563$	−12.2397			−0.515844			−0.257922	−	0.966166i	$-0.583038\pi$
$563$	−12.2397			−0.515844			−0.257922	+	0.966166i	$0.583038\pi$
$564$	−15.6372	+	5.26915i	−0.658443	+	0.221871i
$565$	−9.58525			−0.403254
$566$	−4.18282	−	16.5504i	−0.175817	−	0.695666i
$567$	−21.0598	+	26.0253i	−0.884430	+	1.09296i
$568$	26.2750	−	24.1192i	1.10248	−	1.01202i
$569$		−	28.6863i		−	1.20259i	−0.799027	−	0.601295i	$-0.794652\pi$
$569$		−	28.6863i		−	1.20259i	0.799027	−	0.601295i	$-0.205348\pi$
$570$	3.37165	−	0.261711i	0.141223	−	0.0109619i
$571$		−	8.12001i		−	0.339812i	−0.985460	−	0.169906i	$-0.945654\pi$
$571$		−	8.12001i		−	0.339812i	0.985460	−	0.169906i	$-0.0543464\pi$
$572$	4.26594	−	2.30340i	0.178368	−	0.0963101i
$573$	−15.9437	−	2.73820i	−0.666059	−	0.114390i
$574$	−30.1857	+	7.62890i	−1.25993	+	0.318424i
$575$	0.157420			0.00656488
$576$	9.91039	−	21.8583i	0.412933	−	0.910761i
$577$	−34.8648			−1.45144			−0.725719	−	0.687991i	$-0.758493\pi$
$577$	−34.8648			−1.45144			−0.725719	+	0.687991i	$0.758493\pi$
$578$	−13.1509	+	3.32366i	−0.547007	+	0.138246i
$579$	11.0387	+	1.89580i	0.458752	+	0.0787868i
$580$	25.5340	−	13.7871i	1.06024	−	0.572480i
$581$		−	46.2755i		−	1.91983i
$582$	−17.0989	+	1.32724i	−0.708774	+	0.0550158i
$583$			11.0988i			0.459665i
$584$	−9.72676	+	8.92869i	−0.402496	+	0.369472i
$585$	5.57198	−	15.7435i	0.230373	−	0.650914i
$586$	−2.04171	−	8.07857i	−0.0843423	−	0.333723i
$587$	−16.2131			−0.669187			−0.334594	−	0.942362i	$-0.608599\pi$
$587$	−16.2131			−0.669187			−0.334594	+	0.942362i	$0.608599\pi$
$588$	−22.4456	+	7.56333i	−0.925639	+	0.311906i
$589$	−5.76701			−0.237626
$590$	0.0681916	+	0.269818i	0.00280740	+	0.0111082i
$591$	7.32217	−	42.6348i	0.301194	−	1.75376i
$592$	−19.0327	+	29.0118i	−0.782239	+	1.19238i
$593$			8.79493i			0.361165i	0.983560	+	0.180582i	$0.0577982\pi$
$593$			8.79493i			0.361165i	−0.983560	+	0.180582i	$0.942202\pi$
$594$	−6.79997	−	1.82860i	−0.279006	−	0.0750286i
$595$		−	22.2808i		−	0.913425i
$596$	15.3632	+	28.4529i	0.629301	+	1.16547i
$597$	3.29044	−	19.1592i	0.134669	−	0.784135i
$598$	−3.46848	+	0.876595i	−0.141837	+	0.0358466i
$599$	11.7207			0.478896			0.239448	−	0.970909i	$-0.423034\pi$
$599$	11.7207			0.478896			0.239448	+	0.970909i	$0.423034\pi$
$600$	−0.648205	+	0.417826i	−0.0264629	+	0.0170577i
$601$	4.64820			0.189604			0.0948021	−	0.995496i	$-0.469778\pi$
$601$	4.64820			0.189604			0.0948021	+	0.995496i	$0.469778\pi$
$602$	38.4189	−	9.70968i	1.56584	−	0.395737i
$603$	13.6742	−	38.6362i	0.556858	−	1.57339i
$604$	17.2366	+	31.9225i	0.701349	+	1.29891i
$605$			22.1858i			0.901983i
$606$	1.87356	+	24.1372i	0.0761080	+	0.980507i
$607$			19.8336i			0.805020i	0.915416	+	0.402510i	$0.131862\pi$
$607$			19.8336i			0.805020i	−0.915416	+	0.402510i	$0.868138\pi$
$608$	3.35399	+	1.16029i	0.136022	+	0.0470559i
$609$	−41.8680	−	7.19048i	−1.69658	−	0.291373i
$610$	−11.0163	−	43.5890i	−0.446038	−	1.76487i
$611$	−12.0501			−0.487494
$612$	−2.52010	−	16.1355i	−0.101869	−	0.652240i
$613$	−19.6394			−0.793229			−0.396615	−	0.917985i	$-0.629815\pi$
$613$	−19.6394			−0.793229			−0.396615	+	0.917985i	$0.629815\pi$
$614$	−10.0564	−	39.7908i	−0.405843	−	1.60583i
$615$	−22.2326	−	3.81827i	−0.896506	−	0.153967i
$616$	−6.81779	−	7.42719i	−0.274697	−	0.299250i
$617$			18.8290i			0.758028i	0.925391	+	0.379014i	$0.123737\pi$
$617$			18.8290i			0.758028i	−0.925391	+	0.379014i	$0.876263\pi$
$618$	−0.395417	−	5.09420i	−0.0159060	−	0.204919i
$619$		−	1.87158i		−	0.0752251i	−0.999292	−	0.0376125i	$-0.988025\pi$
$619$		−	1.87158i		−	0.0752251i	0.999292	−	0.0376125i	$-0.0119753\pi$
$620$	−35.5984	+	19.2214i	−1.42967	+	0.771952i
$621$	4.53429	+	2.53776i	0.181955	+	0.101837i
$622$	−43.6598	+	11.0342i	−1.75060	+	0.442432i
$623$	1.20434			0.0482510
$624$	11.9554	−	12.8156i	0.478598	−	0.513034i
$625$	−24.1881			−0.967525
$626$	−45.0775	+	11.3925i	−1.80166	+	0.455336i
$627$	0.176250	−	1.02625i	0.00703874	−	0.0409845i
$628$	−22.2978	+	12.0397i	−0.889778	+	0.480438i
$629$			23.6105i			0.941413i
$630$	−34.5810	−	3.21196i	−1.37774	−	0.127968i
$631$		−	36.3862i		−	1.44851i	−0.689532	−	0.724255i	$-0.742184\pi$
$631$		−	36.3862i		−	1.44851i	0.689532	−	0.724255i	$-0.257816\pi$
$632$	12.9606	+	14.1190i	0.515544	+	0.561625i
$633$	0.423286	−	2.46467i	0.0168241	−	0.0979618i
$634$	−9.93221	−	39.2994i	−0.394458	−	1.56078i
$635$	15.7064			0.623290
$636$	12.8122	+	38.0225i	0.508037	+	1.50769i
$637$	−17.2967			−0.685319
$638$	−2.18931	−	8.66257i	−0.0866755	−	0.342954i
$639$	−35.6626	−	12.6218i	−1.41079	−	0.499310i
$640$	24.5706	−	4.01667i	0.971240	−	0.158773i
$641$			16.3458i			0.645620i	0.946464	+	0.322810i	$0.104628\pi$
$641$			16.3458i			0.645620i	−0.946464	+	0.322810i	$0.895372\pi$
$642$	−2.57512	+	0.199883i	−0.101632	+	0.00788876i
$643$		−	11.5323i		−	0.454791i	−0.973803	−	0.227395i	$-0.926979\pi$
$643$		−	11.5323i		−	0.454791i	0.973803	−	0.227395i	$-0.0730210\pi$
$644$	3.53474	+	6.54640i	0.139288	+	0.257964i
$645$	28.2966	+	4.85970i	1.11418	+	0.191351i
$646$	2.34136	−	0.591737i	0.0921196	−	0.0232816i
$647$	−2.56200			−0.100723			−0.0503614	−	0.998731i	$-0.516037\pi$
$647$	−2.56200			−0.100723			−0.0503614	+	0.998731i	$0.516037\pi$
$648$	−25.4064	+	1.58525i	−0.998059	+	0.0622745i
$649$	0.0856906			0.00336365
$650$	−0.546009	+	0.137994i	−0.0214162	+	0.00541257i
$651$	58.3706	+	10.0247i	2.28772	+	0.392897i
$652$	7.74802	+	14.3495i	0.303436	+	0.561968i
$653$		−	7.49322i		−	0.293232i	−0.989193	−	0.146616i	$-0.953162\pi$
$653$		−	7.49322i		−	0.293232i	0.989193	−	0.146616i	$-0.0468382\pi$
$654$	−10.5657	+	0.820123i	−0.413153	+	0.0320693i
$655$		−	2.25594i		−	0.0881470i
$656$	−19.7942	−	12.9856i	−0.772835	−	0.507004i
$657$	13.2019	+	4.67246i	0.515056	+	0.182290i
$658$	6.14015	+	24.2951i	0.239368	+	0.947122i
$659$	10.5898			0.412518			0.206259	−	0.978497i	$-0.433871\pi$
$659$	10.5898			0.412518			0.206259	+	0.978497i	$0.433871\pi$
$660$	−2.33254	−	6.92223i	−0.0907939	−	0.269448i
$661$	−11.5819			−0.450482			−0.225241	−	0.974303i	$-0.572317\pi$
$661$	−11.5819			−0.450482			−0.225241	+	0.974303i	$0.572317\pi$
$662$	−8.04348	−	31.8262i	−0.312619	−	1.23696i
$663$	2.01864	−	11.7539i	0.0783973	−	0.456484i
$664$	25.9208	−	23.7940i	1.00592	−	0.923387i
$665$		−	5.13570i		−	0.199154i
$666$	36.6447	+	3.40365i	1.41995	+	0.131889i
$667$			6.59334i			0.255295i
$668$	27.7683	−	14.9935i	1.07439	−	0.580118i
$669$	3.35599	−	19.5409i	0.129750	−	0.755495i
$670$	41.2201	−	10.4176i	1.59247	−	0.402468i
$671$	−13.8433			−0.534415
$672$	−31.9304	−	17.5740i	−1.23174	−	0.677931i
$673$	−28.1359			−1.08456			−0.542279	−	0.840199i	$-0.682438\pi$
$673$	−28.1359			−1.08456			−0.542279	+	0.840199i	$0.682438\pi$
$674$	34.2085	−	8.64558i	1.31766	−	0.333015i
$675$	0.713789	+	0.399496i	0.0274738	+	0.0153766i
$676$	−11.6161	+	6.27213i	−0.446772	+	0.241236i
$677$		−	13.6085i		−	0.523018i	−0.965201	−	0.261509i	$-0.915780\pi$
$677$		−	13.6085i		−	0.523018i	0.965201	−	0.261509i	$-0.0842200\pi$
$678$	0.825688	+	10.6374i	0.0317104	+	0.408528i
$679$			26.0451i			0.999519i
$680$	12.4804	−	11.4564i	0.478602	−	0.439333i
$681$	19.7322	+	3.38884i	0.756140	+	0.129861i
$682$	3.05224	+	12.0770i	0.116876	+	0.462452i
$683$	−24.2770			−0.928932			−0.464466	−	0.885591i	$-0.653754\pi$
$683$	−24.2770			−0.928932			−0.464466	+	0.885591i	$0.653754\pi$
$684$	−0.580879	−	3.71922i	−0.0222105	−	0.142208i
$685$	2.44851			0.0935527
$686$	−0.209541	−	0.829106i	−0.00800033	−	0.0316554i
$687$	−19.5065	−	3.35008i	−0.744220	−	0.127814i
$688$	25.1931	+	16.5275i	0.960478	+	0.630104i
$689$			29.3004i			1.11626i
$690$	0.417147	+	5.37415i	0.0158805	+	0.204590i
$691$			3.51437i			0.133693i	0.997763	+	0.0668466i	$0.0212938\pi$
$691$			3.51437i			0.133693i	−0.997763	+	0.0668466i	$0.978706\pi$
$692$	6.48230	+	12.0053i	0.246420	+	0.456374i
$693$	−3.56781	+	10.0808i	−0.135530	+	0.382937i
$694$	−3.35038	+	0.846748i	−0.127179	+	0.0321421i
$695$	−3.88969			−0.147544
$696$	−17.5001	−	27.1492i	−0.663339	−	1.02909i
$697$	−16.1090			−0.610172
$698$	23.1211	−	5.84344i	0.875146	−	0.221177i
$699$	4.30429	−	25.0626i	0.162803	−	0.947953i
$700$	0.556441	+	1.03054i	0.0210315	+	0.0389506i
$701$		−	5.32303i		−	0.201048i	−0.994935	−	0.100524i	$-0.967948\pi$
$701$		−	5.32303i		−	0.201048i	0.994935	−	0.100524i	$-0.0320520\pi$
$702$	−17.9517	−	4.82745i	−0.677542	−	0.182200i
$703$			5.44219i			0.205256i
$704$	0.654689	−	7.63786i	0.0246745	−	0.287862i
$705$	−3.07315	+	17.8940i	−0.115741	+	0.673928i
$706$	12.2058	+	48.2955i	0.459371	+	1.81762i
$707$	36.7658			1.38272
$708$	0.293562	−	0.0989195i	0.0110327	−	0.00371762i
$709$	48.1004			1.80645			0.903225	−	0.429167i	$-0.141193\pi$
$709$	48.1004			1.80645			0.903225	+	0.429167i	$0.141193\pi$
$710$	−9.61582	−	38.0475i	−0.360875	−	1.42790i
$711$	6.78238	−	19.1635i	0.254359	−	0.718687i
$712$	0.619252	+	0.674603i	0.0232075	+	0.0252818i
$713$		−	9.19216i		−	0.344249i
$714$	−24.7266	+	1.91930i	−0.925369	+	0.0718281i
$715$		−	5.33431i		−	0.199492i
$716$	41.5855	−	22.4542i	1.55412	−	0.839152i
$717$	25.2260	+	4.33236i	0.942084	+	0.161795i
$718$	13.5872	−	3.43391i	0.507069	−	0.128152i
$719$	39.4347			1.47067			0.735333	−	0.677706i	$-0.237026\pi$
$719$	39.4347			1.47067			0.735333	+	0.677706i	$0.237026\pi$
$720$	−15.9818	−	21.0218i	−0.595605	−	0.783435i
$721$	−7.75948			−0.288978
$722$	−25.5113	+	6.44751i	−0.949431	+	0.239952i
$723$	−29.6920	−	5.09936i	−1.10426	−	0.189647i
$724$	8.43787	−	4.55605i	0.313591	−	0.169324i
$725$			1.03793i			0.0385476i
$726$	24.6212	−	1.91112i	0.913778	−	0.0709284i
$727$			30.8119i			1.14275i	0.820689	+	0.571374i	$0.193590\pi$
$727$			30.8119i			1.14275i	−0.820689	+	0.571374i	$0.806410\pi$
$728$	−17.9987	−	19.6075i	−0.667077	−	0.726702i
$729$	14.1195	+	23.0139i	0.522944	+	0.852367i
$730$	3.55968	+	14.0848i	0.131750	+	0.521302i
$731$	20.5027			0.758321
$732$	−47.4248	+	15.9804i	−1.75287	+	0.590653i
$733$	−25.7605			−0.951486			−0.475743	−	0.879584i	$-0.657821\pi$
$733$	−25.7605			−0.951486			−0.475743	+	0.879584i	$0.657821\pi$
$734$	0.950857	+	3.76231i	0.0350968	+	0.138870i
$735$	−4.41119	+	25.6850i	−0.162709	+	0.947407i
$736$	−1.84941	+	5.34600i	−0.0681701	+	0.197056i
$737$		−	13.0910i		−	0.482211i
$738$	−2.32225	+	25.0020i	−0.0854831	+	0.920337i
$739$		−	4.15414i		−	0.152813i	−0.997077	−	0.0764063i	$-0.975655\pi$
$739$		−	4.15414i		−	0.152813i	0.997077	−	0.0764063i	$-0.0243446\pi$
$740$	18.1388	+	33.5934i	0.666796	+	1.23492i
$741$	0.465293	−	2.70926i	0.0170930	−	0.0995271i
$742$	59.0748	−	14.9301i	2.16870	−	0.548100i
$743$	1.36108			0.0499332			0.0249666	−	0.999688i	$-0.492052\pi$
$743$	1.36108			0.0499332			0.0249666	+	0.999688i	$0.492052\pi$
$744$	24.3979	+	37.8503i	0.894469	+	1.38766i
$745$	35.5787			1.30350
$746$	6.75171	−	1.70637i	0.247198	−	0.0624748i
$747$	−35.1818	−	12.4516i	−1.28723	−	0.455581i
$748$	−2.47837	−	4.58998i	−0.0906182	−	0.167826i
$749$			3.92241i			0.143322i
$750$	2.15140	+	27.7167i	0.0785581	+	1.01207i
$751$		−	15.2763i		−	0.557439i	−0.960373	−	0.278720i	$-0.910090\pi$
$751$		−	15.2763i		−	0.557439i	0.960373	−	0.278720i	$-0.0899100\pi$
$752$	−10.4515	+	15.9315i	−0.381129	+	0.580961i
$753$	−21.8320	−	3.74946i	−0.795602	−	0.136638i
$754$	−5.77969	−	22.8689i	−0.210484	−	0.832835i
$755$	39.9173			1.45274
$756$	−0.585682	+	38.6536i	−0.0213011	+	1.40582i
$757$	−33.9871			−1.23528			−0.617641	−	0.786460i	$-0.711911\pi$
$757$	−33.9871			−1.23528			−0.617641	+	0.786460i	$0.711911\pi$
$758$	2.03353	+	8.04619i	0.0738610	+	0.292251i
$759$	1.63576	+	0.280928i	0.0593743	+	0.0101970i
$760$	2.87672	−	2.64069i	0.104350	−	0.0957877i
$761$			7.51143i			0.272289i	0.990689	+	0.136145i	$0.0434712\pi$
$761$			7.51143i			0.272289i	−0.990689	+	0.136145i	$0.956529\pi$
$762$	−1.35297	−	17.4305i	−0.0490131	−	0.631440i
$763$			16.0937i			0.582631i
$764$	−16.4368	+	8.87507i	−0.594661	+	0.321089i
$765$	−16.9394	−	5.99523i	−0.612445	−	0.216758i
$766$	−16.8545	+	4.25967i	−0.608978	+	0.153908i
$767$	0.226220			0.00816833
$768$	−6.57413	−	26.9218i	−0.237223	−	0.971455i
$769$	19.6743			0.709474			0.354737	−	0.934966i	$-0.384570\pi$
$769$	19.6743			0.709474			0.354737	+	0.934966i	$0.384570\pi$
$770$	−10.7549	+	2.71811i	−0.387581	+	0.0979540i
$771$	−4.54575	+	26.4685i	−0.163711	+	0.953240i
$772$	11.3800	−	6.14467i	0.409576	−	0.221152i
$773$			39.9906i			1.43836i	0.694822	+	0.719182i	$0.255483\pi$
$773$			39.9906i			1.43836i	−0.694822	+	0.719182i	$0.744517\pi$
$774$	2.95564	−	31.8213i	0.106238	−	1.14379i
$775$		−	1.44703i		−	0.0519790i
$776$	−14.5889	+	13.3919i	−0.523712	+	0.480742i
$777$	9.46003	−	55.0829i	0.339377	−	1.97609i
$778$	6.14322	+	24.3073i	0.220245	+	0.871458i
$779$	−3.71311			−0.133036
$780$	−6.15782	−	18.2744i	−0.220485	−	0.654330i
$781$	−12.0834			−0.432378
$782$	0.943181	+	3.73194i	0.0337281	+	0.133454i
$783$	−16.7324	+	29.8961i	−0.597966	+	1.06840i
$784$	−15.0021	+	22.8680i	−0.535790	+	0.816714i
$785$			27.8821i			0.995154i
$786$	−2.50358	+	0.194330i	−0.0892996	+	0.00693153i
$787$		−	41.2555i		−	1.47060i	−0.677742	−	0.735300i	$-0.737041\pi$
$787$		−	41.2555i		−	1.47060i	0.677742	−	0.735300i	$-0.262959\pi$
$788$	−23.7326	−	43.9532i	−0.845439	−	1.56577i
$789$	27.0251	+	4.64133i	0.962118	+	0.165236i
$790$	20.4451	−	5.16712i	0.727402	−	0.183838i
$791$	16.2029			0.576109
$792$	−7.48116	+	3.18487i	−0.265831	+	0.113170i
$793$	−36.5458			−1.29778
$794$	14.5551	−	3.67853i	0.516540	−	0.130546i
$795$	43.5102	+	7.47251i	1.54315	+	0.265023i
$796$	−10.6650	−	19.7517i	−0.378010	−	0.700080i
$797$		−	37.2029i		−	1.31780i	−0.752233	−	0.658898i	$-0.771023\pi$
$797$		−	37.2029i		−	1.31780i	0.752233	−	0.658898i	$-0.228977\pi$
$798$	−5.69944	+	0.442397i	−0.201758	+	0.0156607i
$799$			12.9654i			0.458683i
$800$	−0.291134	+	0.841569i	−0.0102932	+	0.0297540i
$801$	0.324060	−	0.915624i	0.0114501	−	0.0323520i
$802$	−6.62549	−	26.2155i	−0.233954	−	0.925701i
$803$	4.47315			0.157854
$804$	−15.1119	−	44.8474i	−0.532956	−	1.58165i
$805$	8.18590			0.288515
$806$	8.05780	+	31.8828i	0.283824	+	1.12302i
$807$	1.05735	−	6.15665i	0.0372206	−	0.216724i
$808$	18.9043	+	20.5940i	0.665051	+	0.724496i
$809$			39.0244i			1.37202i	0.727590	+	0.686012i	$0.240640\pi$
$809$			39.0244i			1.37202i	−0.727590	+	0.686012i	$0.759360\pi$
$810$	−11.7469	+	25.4265i	−0.412743	+	0.893398i
$811$			46.5108i			1.63321i	0.577194	+	0.816607i	$0.304147\pi$
$811$			46.5108i			1.63321i	−0.577194	+	0.816607i	$0.695853\pi$
$812$	−43.1627	+	23.3058i	−1.51471	+	0.817873i
$813$	6.27930	−	36.5624i	0.220224	−	1.28230i
$814$	11.3968	−	2.88033i	0.399457	−	0.100955i
$815$	17.9432			0.628522
$816$	−13.7890	−	12.8635i	−0.482713	−	0.450313i
$817$	4.72585			0.165337
$818$	30.7132	−	7.76221i	1.07386	−	0.271399i
$819$	−9.41888	+	26.6128i	−0.329122	+	0.929928i
$820$	−22.9201	+	12.3758i	−0.800405	+	0.432181i
$821$			13.1005i			0.457209i	0.973519	+	0.228605i	$0.0734163\pi$
$821$			13.1005i			0.457209i	−0.973519	+	0.228605i	$0.926584\pi$
$822$	−0.210918	−	2.71728i	−0.00735662	−	0.0947760i
$823$			38.5602i			1.34412i	0.740495	+	0.672062i	$0.234591\pi$
$823$			38.5602i			1.34412i	−0.740495	+	0.672062i	$0.765409\pi$
$824$	−3.98979	−	4.34641i	−0.138991	−	0.151414i
$825$	0.257502	+	0.0442238i	0.00896507	+	0.00153968i
$826$	−0.115271	−	0.456100i	−0.00401079	−	0.0158698i
$827$	21.1614			0.735853			0.367927	−	0.929855i	$-0.380068\pi$
$827$	21.1614			0.735853			0.367927	+	0.929855i	$0.380068\pi$
$828$	5.92813	−	0.925875i	0.206017	−	0.0321764i
$829$	10.5121			0.365099			0.182550	−	0.983197i	$-0.441565\pi$
$829$	10.5121			0.365099			0.182550	+	0.983197i	$0.441565\pi$
$830$	−9.48618	−	37.5346i	−0.329270	−	1.30284i
$831$	51.8269	+	8.90084i	1.79786	+	0.308767i
$832$	1.72835	−	20.1637i	0.0599199	−	0.699049i
$833$			18.6105i			0.644816i
$834$	0.335064	+	4.31666i	0.0116023	+	0.149474i
$835$		−	34.7226i		−	1.20163i
$836$	−0.571261	−	1.05798i	−0.0197575	−	0.0365911i
$837$	23.3275	−	41.6799i	0.806318	−	1.44067i
$838$	−13.1180	+	3.31534i	−0.453154	+	0.114526i
$839$	16.7666			0.578847			0.289424	−	0.957201i	$-0.406536\pi$
$839$	16.7666			0.578847			0.289424	+	0.957201i	$0.406536\pi$
$840$	−33.7068	+	21.7270i	−1.16300	+	0.749654i
$841$	−14.4722			−0.499041
$842$	−45.8946	+	11.5990i	−1.58163	+	0.399729i
$843$	1.85402	−	10.7954i	0.0638559	−	0.371814i
$844$	−1.37196	−	2.54088i	−0.0472247	−	0.0874608i
$845$			14.5252i			0.499684i
$846$	20.1230	+	1.86907i	0.691842	+	0.0642599i
$847$		−	37.5030i		−	1.28862i
$848$	38.7382	+	25.4134i	1.33027	+	0.872701i
$849$	−3.53886	+	20.6057i	−0.121453	+	0.707186i
$850$	0.148476	+	0.587484i	0.00509268	+	0.0201505i
$851$	−8.67442			−0.297355
$852$	−41.3957	+	13.9488i	−1.41819	+	0.477879i
$853$	16.3383			0.559414			0.279707	−	0.960085i	$-0.409763\pi$
$853$	16.3383			0.559414			0.279707	+	0.960085i	$0.409763\pi$
$854$	18.6220	+	73.6829i	0.637232	+	2.52138i
$855$	−3.90451	−	1.38189i	−0.133531	−	0.0472597i
$856$	−2.19711	+	2.01684i	−0.0750955	+	0.0689340i
$857$			9.30340i			0.317798i	0.987295	+	0.158899i	$0.0507945\pi$
$857$			9.30340i			0.317798i	−0.987295	+	0.158899i	$0.949206\pi$
$858$	−5.91986	+	0.459506i	−0.202101	+	0.0156873i
$859$		−	51.5860i		−	1.76009i	−0.474889	−	0.880046i	$-0.657512\pi$
$859$		−	51.5860i		−	1.76009i	0.474889	−	0.880046i	$-0.342488\pi$
$860$	29.1716	−	15.7513i	0.994743	−	0.537114i
$861$	37.5820	+	6.45440i	1.28079	+	0.219965i
$862$	21.3172	−	5.38754i	0.726068	−	0.183501i
$863$	−25.6415			−0.872847			−0.436423	−	0.899741i	$-0.643755\pi$
$863$	−25.6415			−0.872847			−0.436423	+	0.899741i	$0.643755\pi$
$864$	−21.9526	+	19.5469i	−0.746843	+	0.665000i
$865$	15.0120			0.510422
$866$	−0.860669	+	0.217518i	−0.0292467	+	0.00739158i
$867$	16.3733	+	2.81197i	0.556065	+	0.0954996i
$868$	60.1755	−	32.4919i	2.04249	−	1.10285i
$869$		−	6.49308i		−	0.220263i
$870$	−35.4336	+	2.75039i	−1.20131	+	0.0932471i
$871$		−	34.5596i		−	1.17101i
$872$	−9.01475	+	8.27509i	−0.305278	+	0.280230i
$873$	19.8013	+	7.00811i	0.670171	+	0.237189i
$874$	0.217402	+	0.860208i	0.00735373	+	0.0290970i
$875$	42.2181			1.42723
$876$	15.3243	−	5.16371i	0.517759	−	0.174466i
$877$	−5.45955			−0.184356			−0.0921779	−	0.995743i	$-0.529383\pi$
$877$	−5.45955			−0.184356			−0.0921779	+	0.995743i	$0.529383\pi$
$878$	1.75818	+	6.95670i	0.0593357	+	0.234777i
$879$	−1.72738	+	10.0580i	−0.0582632	+	0.339249i
$880$	−7.05252	−	4.62667i	−0.237740	−	0.155965i
$881$		−	56.3574i		−	1.89873i	−0.314178	−	0.949364i	$-0.601729\pi$
$881$		−	56.3574i		−	1.89873i	0.314178	−	0.949364i	$-0.398271\pi$
$882$	28.8845	+	2.68286i	0.972591	+	0.0903366i
$883$			21.4218i			0.720902i	0.932778	+	0.360451i	$0.117377\pi$
$883$			21.4218i			0.720902i	−0.932778	+	0.360451i	$0.882623\pi$
$884$	−6.54280	−	12.1174i	−0.220058	−	0.407551i
$885$	0.0576932	−	0.335930i	0.00193934	−	0.0112922i
$886$	12.1118	−	3.06105i	0.406905	−	0.102838i
$887$	13.6688			0.458954			0.229477	−	0.973314i	$-0.426298\pi$
$887$	13.6688			0.458954			0.229477	+	0.973314i	$0.426298\pi$
$888$	35.7184	−	23.0237i	1.19863	−	0.772625i
$889$	−26.5501			−0.890462
$890$	0.976857	−	0.246883i	0.0327443	−	0.00827554i
$891$	6.70407	+	5.42498i	0.224595	+	0.181744i
$892$	−10.8774	−	20.1452i	−0.364203	−	0.674510i
$893$			2.98851i			0.100007i
$894$	−3.06480	−	39.4841i	−0.102502	−	1.32055i
$895$		−	52.0003i		−	1.73818i
$896$	−41.5342	+	6.78977i	−1.38756	+	0.226830i
$897$	4.31834	+	0.741640i	0.144185	+	0.0247626i
$898$	5.56942	+	22.0369i	0.185854	+	0.735380i
$899$	60.6071			2.02136
$900$	0.933209	−	0.145752i	0.0311070	−	0.00485839i
$901$	31.5260			1.05028
$902$	1.96519	+	7.77580i	0.0654337	+	0.258906i
$903$	−47.8325	−	8.21484i	−1.59177	−	0.273373i
$904$	8.33124	+	9.07592i	0.277093	+	0.301861i
$905$		−	10.5511i		−	0.350730i
$906$	−3.43854	−	44.2990i	−0.114238	−	1.47174i
$907$			43.0069i			1.42802i	0.700135	+	0.714010i	$0.253123\pi$
$907$			43.0069i			1.42802i	−0.700135	+	0.714010i	$0.746877\pi$
$908$	20.3424	−	10.9839i	0.675086	−	0.364514i
$909$	9.89278	−	27.9518i	0.328123	−	0.927104i
$910$	−28.3926	+	7.17571i	−0.941205	+	0.237873i
$911$	32.0270			1.06110			0.530551	−	0.847653i	$-0.321985\pi$
$911$	32.0270			1.06110			0.530551	+	0.847653i	$0.321985\pi$
$912$	−3.17836	−	2.96502i	−0.105246	−	0.0981817i
$913$	−11.9205			−0.394510
$914$	−22.4481	+	5.67336i	−0.742518	+	0.187658i
$915$	−9.32033	+	54.2694i	−0.308120	+	1.79409i
$916$	−20.1097	+	10.8583i	−0.664443	+	0.358768i
$917$			3.81345i			0.125931i
$918$	−5.19414	+	19.3153i	−0.171432	+	0.637499i
$919$		−	2.94437i		−	0.0971259i	−0.998820	−	0.0485629i	$-0.984536\pi$
$919$		−	2.94437i		−	0.0971259i	0.998820	−	0.0485629i	$-0.0154641\pi$
$920$	4.20904	+	4.58526i	0.138768	+	0.151172i
$921$	−8.50818	+	49.5406i	−0.280354	+	1.63242i
$922$	3.24078	+	12.8230i	0.106729	+	0.422303i
$923$	−31.8997			−1.04999
$924$	3.94292	+	11.7013i	0.129713	+	0.384946i
$925$	−1.36553			−0.0448984
$926$	−3.54444	−	14.0245i	−0.116477	−	0.460874i
$927$	−2.08789	+	5.89929i	−0.0685753	+	0.193758i
$928$	−35.2480	−	12.1938i	−1.15707	−	0.400280i
$929$			14.7359i			0.483468i	0.970343	+	0.241734i	$0.0777161\pi$
$929$			14.7359i			0.483468i	−0.970343	+	0.241734i	$0.922284\pi$
$930$	49.4000	−	3.83448i	1.61989	−	0.125738i
$931$			4.28970i			0.140589i
$932$	−13.9511	−	25.8376i	−0.456982	−	0.846338i
$933$	54.3575	+	9.33545i	1.77959	+	0.305629i
$934$	11.8293	−	2.98963i	0.387065	−	0.0978237i
$935$	−5.73950			−0.187702
$936$	−19.7500	+	8.40794i	−0.645548	+	0.274822i
$937$	33.9922			1.11048			0.555238	−	0.831692i	$-0.312627\pi$
$937$	33.9922			1.11048			0.555238	+	0.831692i	$0.312627\pi$
$938$	−69.6784	+	17.6099i	−2.27508	+	0.574985i
$939$	56.1226	+	9.63859i	1.83149	+	0.314544i
$940$	9.96069	+	18.4474i	0.324882	+	0.601686i
$941$			42.1318i			1.37346i	0.726913	+	0.686729i	$0.240954\pi$
$941$			42.1318i			1.37346i	−0.726913	+	0.686729i	$0.759046\pi$
$942$	30.9427	−	2.40180i	1.00817	−	0.0782550i
$943$		−	5.91840i		−	0.192729i
$944$	0.196210	−	0.299087i	0.00638610	−	0.00973444i
$945$	37.1172	+	20.7739i	1.20742	+	0.675774i
$946$	−2.50120	−	9.89665i	−0.0813209	−	0.321768i
$947$	−47.9731			−1.55892			−0.779458	−	0.626454i	$-0.784506\pi$
$947$	−47.9731			−1.55892			−0.779458	+	0.626454i	$0.784506\pi$
$948$	−7.49548	−	22.2442i	−0.243442	−	0.722458i
$949$	11.8090			0.383335
$950$	0.0342235	+	0.135414i	0.00111036	+	0.00439342i
$951$	−8.40311	+	48.9288i	−0.272489	+	1.58662i
$952$	−21.0969	+	19.3659i	−0.683754	+	0.627652i
$953$		−	40.9003i		−	1.32489i	−0.749111	−	0.662445i	$-0.769519\pi$
$953$		−	40.9003i		−	1.32489i	0.749111	−	0.662445i	$-0.230481\pi$
$954$	4.54473	−	48.9300i	0.147141	−	1.58417i
$955$			20.5532i			0.665087i
$956$	26.0061	−	14.0421i	0.841097	−	0.454153i
$957$	−1.85226	+	10.7851i	−0.0598749	+	0.348634i
$958$	−9.35580	+	2.36451i	−0.302272	+	0.0763938i
$959$	−4.13896			−0.133654
$960$	−29.5017	−	7.70892i	−0.952162	−	0.248804i
$961$	−53.4958			−1.72567
$962$	30.0870	−	7.60395i	0.970045	−	0.245161i
$963$	2.98209	+	1.05543i	0.0960964	+	0.0340107i
$964$	−30.6102	+	16.5280i	−0.985888	+	0.532332i
$965$		−	14.2301i		−	0.458082i
$966$	−0.705146	−	9.08446i	−0.0226877	−	0.292288i
$967$		−	51.7116i		−	1.66293i	−0.555574	−	0.831467i	$-0.687502\pi$
$967$		−	51.7116i		−	1.66293i	0.555574	−	0.831467i	$-0.312498\pi$
$968$	21.0070	−	19.2834i	0.675189	−	0.619790i
$969$	−2.91506	−	0.500636i	−0.0936451	−	0.0160828i
$970$	5.33908	+	21.1255i	0.171428	+	0.678298i
$971$	−3.77813			−0.121246			−0.0606229	−	0.998161i	$-0.519309\pi$
$971$	−3.77813			−0.121246			−0.0606229	+	0.998161i	$0.519309\pi$
$972$	29.2295	+	10.8460i	0.937537	+	0.347886i
$973$	6.57513			0.210789
$974$	2.17716	+	8.61450i	0.0697607	+	0.276027i
$975$	0.679796	+	0.116749i	0.0217709	+	0.00373897i
$976$	−31.6977	+	48.3174i	−1.01462	+	1.54660i
$977$		−	36.6311i		−	1.17193i	−0.810335	−	0.585967i	$-0.800715\pi$
$977$		−	36.6311i		−	1.17193i	0.810335	−	0.585967i	$-0.199285\pi$
$978$	−1.54565	−	19.9128i	−0.0494245	−	0.636741i
$979$		−	0.310237i		−	0.00991522i
$980$	14.2976	+	26.4793i	0.456719	+	0.845850i
$981$	12.2355	+	4.33043i	0.390650	+	0.138260i
$982$	30.3641	−	7.67399i	0.968959	−	0.244887i
$983$	36.6169			1.16790			0.583949	−	0.811791i	$-0.301507\pi$
$983$	36.6169			1.16790			0.583949	+	0.811791i	$0.301507\pi$
$984$	15.7086	+	24.3700i	0.500773	+	0.776887i
$985$	−54.9609			−1.75120
$986$	−24.6060	+	6.21872i	−0.783614	+	0.198044i
$987$	5.19485	−	30.2481i	0.165354	−	0.962806i
$988$	−1.50811	−	2.79304i	−0.0479793	−	0.0888584i
$989$			7.53264i			0.239524i
$990$	−0.827397	+	8.90800i	−0.0262964	+	0.283115i
$991$		−	46.5569i		−	1.47893i	−0.673196	−	0.739464i	$-0.735079\pi$
$991$		−	46.5569i		−	1.47893i	0.673196	−	0.739464i	$-0.264921\pi$
$992$	49.1413	+	17.0000i	1.56024	+	0.539752i
$993$	−6.80516	+	39.6244i	−0.215955	+	1.25744i
$994$	16.2546	+	64.3155i	0.515564	+	2.03996i
$995$	−24.6983			−0.782990
$996$	−40.8376	+	13.7608i	−1.29399	+	0.436026i
$997$	−8.99973			−0.285024			−0.142512	−	0.989793i	$-0.545518\pi$
$997$	−8.99973			−0.285024			−0.142512	+	0.989793i	$0.545518\pi$
$998$	−10.0609	−	39.8086i	−0.318473	−	1.26012i
$999$	−39.3323	−	22.0136i	−1.24442	−	0.696481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.a.47.4	yes	22
3.2	odd	2		276.2.c.b.47.19	yes	22
4.3	odd	2		276.2.c.b.47.20	yes	22
12.11	even	2	inner	276.2.c.a.47.3	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.3	✓	22	12.11	even	2	inner
276.2.c.a.47.4	yes	22	1.1	even	1	trivial
276.2.c.b.47.19	yes	22	3.2	odd	2
276.2.c.b.47.20	yes	22	4.3	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37110 + 0.346521i) q^{2} +(1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} -2.20059i q^{5} +(-2.44214 + 0.189562i) q^{6} +3.71987i q^{7} +(-2.08365 + 1.91269i) q^{8} +(2.82810 + 1.00093i) q^{9} +O(q^{10})\)	\(q+(-1.37110 + 0.346521i) q^{2} +(1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} -2.20059i q^{5} +(-2.44214 + 0.189562i) q^{6} +3.71987i q^{7} +(-2.08365 + 1.91269i) q^{8} +(2.82810 + 1.00093i) q^{9} +(0.762550 + 3.01723i) q^{10} +0.958233 q^{11} +(3.28274 - 1.10616i) q^{12} +2.52970 q^{13} +(-1.28901 - 5.10033i) q^{14} +(0.645153 - 3.75653i) q^{15} +(2.19412 - 3.34453i) q^{16} -2.72185i q^{17} +(-4.22446 - 0.392378i) q^{18} -0.627384i q^{19} +(-2.09107 - 3.87269i) q^{20} +(-1.09057 + 6.35004i) q^{21} +(-1.31384 + 0.332048i) q^{22} +1.00000 q^{23} +(-4.11767 + 2.65420i) q^{24} +0.157420 q^{25} +(-3.46848 + 0.876595i) q^{26} +(4.53429 + 2.53776i) q^{27} +(3.53474 + 6.54640i) q^{28} +6.59334i q^{29} +(0.417147 + 5.37415i) q^{30} -9.19216i q^{31} +(-1.84941 + 5.34600i) q^{32} +(1.63576 + 0.280928i) q^{33} +(0.943181 + 3.73194i) q^{34} +8.18590 q^{35} +(5.92813 - 0.925875i) q^{36} -8.67442 q^{37} +(0.217402 + 0.860208i) q^{38} +(4.31834 + 0.741640i) q^{39} +(4.20904 + 4.58526i) q^{40} -5.91840i q^{41} +(-0.705146 - 9.08446i) q^{42} +7.53264i q^{43} +(1.68634 - 0.910544i) q^{44} +(2.20263 - 6.22348i) q^{45} +(-1.37110 + 0.346521i) q^{46} -4.76344 q^{47} +(4.72601 - 5.06605i) q^{48} -6.83744 q^{49} +(-0.215840 + 0.0545495i) q^{50} +(0.797975 - 4.64637i) q^{51} +(4.45188 - 2.40380i) q^{52} +11.5826i q^{53} +(-7.09636 - 1.90831i) q^{54} -2.10867i q^{55} +(-7.11496 - 7.75092i) q^{56} +(0.183932 - 1.07098i) q^{57} +(-2.28473 - 9.04015i) q^{58} +0.0894257 q^{59} +(-2.43421 - 7.22396i) q^{60} -14.4467 q^{61} +(3.18528 + 12.6034i) q^{62} +(-3.72332 + 10.5202i) q^{63} +(0.683225 - 7.97077i) q^{64} -5.56682i q^{65} +(-2.34014 + 0.181644i) q^{66} -13.6616i q^{67} +(-2.58640 - 4.79004i) q^{68} +(1.70706 + 0.293173i) q^{69} +(-11.2237 + 2.83659i) q^{70} -12.6101 q^{71} +(-7.80724 + 3.32369i) q^{72} +4.66813 q^{73} +(11.8935 - 3.00587i) q^{74} +(0.268726 + 0.0461514i) q^{75} +(-0.596161 - 1.10410i) q^{76} +3.56450i q^{77} +(-6.17789 + 0.479534i) q^{78} -6.77610i q^{79} +(-7.35992 - 4.82834i) q^{80} +(6.99629 + 5.66144i) q^{81} +(2.05085 + 8.11473i) q^{82} -12.4401 q^{83} +(4.11479 + 12.2114i) q^{84} -5.98968 q^{85} +(-2.61022 - 10.3280i) q^{86} +(-1.93299 + 11.2552i) q^{87} +(-1.99663 + 1.83280i) q^{88} -0.323760i q^{89} +(-0.863461 + 9.29628i) q^{90} +9.41015i q^{91} +(1.75985 - 0.950233i) q^{92} +(2.69489 - 15.6916i) q^{93} +(6.53117 - 1.65064i) q^{94} -1.38061 q^{95} +(-4.72435 + 8.58374i) q^{96} +7.00161 q^{97} +(9.37483 - 2.36932i) q^{98} +(2.70998 + 0.959122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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