LMFDB - Embedded newform 276.2.c.b.47.19

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			47.19
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37110 - 0.346521i) q^{2} +(-1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} +2.20059i q^{5} +(-2.23896 + 0.993503i) q^{6} +3.71987i q^{7} +(2.08365 - 1.91269i) q^{8} +(2.82810 - 1.00093i) q^{9} +O(q^{10})$	\(q+(1.37110 - 0.346521i) q^{2} +(-1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} +2.20059i q^{5} +(-2.23896 + 0.993503i) 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} +(-2.72558 + 2.13804i) 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} +(3.53077 - 2.35237i) 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} +(-2.99617 + 3.87595i) 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} +(-2.18629 - 4.92703i) 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} +(4.02590 - 4.44883i) 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} +(-3.69570 - 8.32865i) 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} +(-2.76496 + 6.35256i) 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} +(-5.33758 + 5.05076i) 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} +(-4.70495 - 5.99787i) 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} +(2.14545 - 0.952007i) 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} +(3.97831 - 7.49487i) 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} +(-5.66390 + 2.51326i) 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} +(-7.95324 - 10.1388i) 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} +(5.17660 + 7.76977i) 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} +(-1.58974 + 9.66813i) 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 + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * 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	$0.163758\pi$
$5$			2.20059i			0.984132i	−0.870558	+	0.492066i	$0.836242\pi$
$6$	−2.23896	+	0.993503i	−0.914053	+	0.405596i
$7$			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	$-0.546144\pi$
$11$	−0.958233			−0.288918			−0.144459	+	0.989511i	$0.546144\pi$
$12$	−2.72558	+	2.13804i	−0.786806	+	0.617200i
$13$	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	$0.107073\pi$
$17$			2.72185i			0.660147i	−0.943955	+	0.330073i	$0.892927\pi$
$18$	3.53077	−	2.35237i	0.832211	−	0.554459i
$19$		−	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
$24$	−2.99617	+	3.87595i	−0.611591	+	0.791174i
$25$	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	$-0.790294\pi$
$29$		−	6.59334i		−	1.22435i	0.790721	−	0.612177i	$-0.209706\pi$
$30$	−2.18629	−	4.92703i	−0.399160	−	0.899548i
$31$		−	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
$36$	4.02590	−	4.44883i	0.670984	−	0.741472i
$37$	−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	$0.152921\pi$
$41$			5.91840i			0.924298i	−0.886802	+	0.462149i	$0.847079\pi$
$42$	−3.69570	−	8.32865i	−0.570259	−	1.28514i
$43$			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	$-0.387061\pi$
$47$	4.76344			0.694820			0.347410	+	0.937713i	$0.387061\pi$
$48$	−2.76496	+	6.35256i	−0.399087	+	0.916913i
$49$	−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	$-0.707212\pi$
$53$		−	11.5826i		−	1.59099i	0.605963	−	0.795493i	$-0.292788\pi$
$54$	−5.33758	+	5.05076i	−0.726353	+	0.687322i
$55$		−	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	$-0.501853\pi$
$59$	−0.0894257			−0.0116422			−0.00582112	+	0.999983i	$0.501853\pi$
$60$	−4.70495	−	5.99787i	−0.607406	−	0.774321i
$61$	−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
$66$	2.14545	−	0.952007i	0.264086	−	0.117184i
$67$		−	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	$-0.230884\pi$
$71$	12.6101			1.49654			0.748271	+	0.663394i	$0.230884\pi$
$72$	3.97831	−	7.49487i	0.468849	−	0.883278i
$73$	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
$78$	−5.66390	+	2.51326i	−0.641310	+	0.284571i
$79$		−	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	$-0.260789\pi$
$83$	12.4401			1.36548			0.682738	+	0.730664i	$0.260789\pi$
$84$	−7.95324	−	10.1388i	−0.867770	−	1.10623i
$85$	−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	$0.00546222\pi$
$89$			0.323760i			0.0343185i	−0.999853	+	0.0171592i	$0.994538\pi$
$90$	5.17660	+	7.76977i	0.545661	+	0.819005i
$91$			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
$96$	−1.58974	+	9.66813i	−0.162253	+	0.986749i
$97$	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	$0.163635\pi$
$101$			9.88362i			0.983457i	−0.870749	+	0.491728i	$0.836365\pi$
$102$	−2.70417	−	6.09413i	−0.267753	−	0.603409i
$103$			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	$-0.516231\pi$
$107$	−1.05445			−0.101937			−0.0509687	+	0.998700i	$0.516231\pi$
$108$	−5.56818	+	8.77470i	−0.535798	+	0.844346i
$109$	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	$0.0656798\pi$
$113$			4.35577i			0.409756i	−0.978787	+	0.204878i	$0.934320\pi$
$114$	0.623308	+	1.40469i	0.0583781	+	0.131561i
$115$		−	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
$120$	−8.52936	−	6.59333i	−0.778620	−	0.601886i
$121$	−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
$126$	8.75052	+	13.1340i	0.779558	+	1.17007i
$127$			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	$-0.514260\pi$
$131$	−1.02516			−0.0895682			−0.0447841	+	0.998997i	$0.514260\pi$
$132$	2.61174	−	2.04874i	0.227323	−	0.178320i
$133$	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	$-0.984865\pi$
$137$		−	1.11266i		−	0.0950611i	0.998870	−	0.0475306i	$-0.0151352\pi$
$138$	2.23896	−	0.993503i	0.190593	−	0.0845726i
$139$		−	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
$144$	2.85755	−	11.6548i	0.238129	−	0.971234i
$145$	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	$-0.769598\pi$
$149$		−	16.1678i		−	1.32452i	0.749274	−	0.662260i	$-0.230402\pi$
$150$	−0.352458	+	0.156398i	−0.0287781	+	0.0127698i
$151$			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
$156$	−6.89489	+	5.40860i	−0.552033	+	0.433035i
$157$	−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
$162$	7.63082	−	10.1868i	0.599534	−	0.800349i
$163$			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	$-0.709032\pi$
$167$	−15.7788			−1.22100			−0.610501	+	0.792016i	$0.709032\pi$
$168$	−14.4180	−	11.1454i	−1.11237	−	0.859884i
$169$	−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	$-0.916500\pi$
$173$		−	6.82180i		−	0.518652i	0.965790	−	0.259326i	$-0.0835004\pi$
$174$	6.55051	+	14.7622i	0.496593	+	1.11912i
$175$			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	$-0.844549\pi$
$179$	−23.6302			−1.76620			−0.883102	+	0.469182i	$0.844549\pi$
$180$	9.79004	+	8.85935i	0.729706	+	0.660337i
$181$	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
$186$	9.13244	+	20.5809i	0.669623	+	1.50906i
$187$		−	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	$-0.390282\pi$
$191$	9.33989			0.675810			0.337905	+	0.941180i	$0.390282\pi$
$192$	1.17051	+	13.8069i	0.0844743	+	0.996426i
$193$	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	$0.349099\pi$
$197$			24.9756i			1.77944i	−0.456510	+	0.889718i	$0.650901\pi$
$198$	−3.38330	+	2.25412i	−0.240441	+	0.160193i
$199$		−	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
$204$	−5.81944	−	7.41863i	−0.407442	−	0.519408i
$205$	−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
$210$	18.3279	−	8.13271i	1.26475	−	0.561210i
$211$		−	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
$216$	−4.59392	+	13.9605i	−0.312577	+	0.949892i
$217$	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
$222$	19.4217	−	8.61807i	1.30350	−	0.578407i
$223$		−	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	$-0.625318\pi$
$227$	−11.5592			−0.767210			−0.383605	+	0.923497i	$0.625318\pi$
$228$	1.34137	+	1.70998i	0.0888346	+	0.113246i
$229$	−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	$0.159696\pi$
$233$			14.6817i			0.961832i	−0.876767	+	0.480916i	$0.840304\pi$
$234$	8.93179	−	5.95079i	0.583889	−	0.389015i
$235$			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	$-0.658616\pi$
$239$	−14.7775			−0.955876			−0.477938	+	0.878393i	$0.658616\pi$
$240$	−13.9794	−	6.08453i	−0.902363	−	0.392755i
$241$	−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
$246$	−5.87994	−	13.2511i	−0.374891	−	0.844857i
$247$		−	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	$-0.367750\pi$
$251$	12.7892			0.807250			0.403625	+	0.914925i	$0.367750\pi$
$252$	16.5491	+	14.9758i	1.04249	+	0.943390i
$253$	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	$-0.839330\pi$
$257$		−	15.5053i		−	0.967196i	0.875290	−	0.483598i	$-0.160670\pi$
$258$	−7.48369	−	16.8653i	−0.465914	−	1.04999i
$259$		−	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	$-0.662311\pi$
$263$	−15.8314			−0.976204			−0.488102	+	0.872787i	$0.662311\pi$
$264$	2.87103	−	3.71406i	0.176700	−	0.228585i
$265$	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	$0.0350686\pi$
$269$			3.60658i			0.219897i	−0.993937	+	0.109949i	$0.964931\pi$
$270$	−11.1146	−	11.7458i	−0.676415	−	0.714827i
$271$		−	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
$276$	2.72558	−	2.13804i	0.164060	−	0.128695i
$277$	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	$0.0604043\pi$
$281$			6.32399i			0.377257i	−0.982048	+	0.188629i	$0.939596\pi$
$282$	−10.6652	+	4.73250i	−0.635102	+	0.281816i
$283$			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
$288$	−0.120649	−	16.9701i	−0.00710933	−	0.999975i
$289$	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	$-0.944942\pi$
$293$		−	5.89202i		−	0.344216i	0.985078	−	0.172108i	$-0.0550577\pi$
$294$	15.3088	−	6.79302i	0.892826	−	0.396177i
$295$		−	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
$300$	−0.429062	+	0.336572i	−0.0247719	+	0.0194320i
$301$	−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
$306$	6.40281	+	9.61025i	0.366024	+	0.549381i
$307$			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	$-0.858507\pi$
$311$	−31.8428			−1.80564			−0.902820	+	0.430019i	$0.858507\pi$
$312$	−7.57941	+	9.80498i	−0.429099	+	0.555098i
$313$	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	$-0.702205\pi$
$317$		−	28.6626i		−	1.60985i	0.593375	−	0.804926i	$-0.297795\pi$
$318$	11.5073	+	25.9329i	0.645297	+	1.45424i
$319$			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
$324$	6.93270	−	16.6114i	0.385150	−	0.922854i
$325$	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
$330$	2.09497	+	4.72124i	0.115324	+	0.259896i
$331$			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
$336$	−23.6307	−	10.2853i	−1.28916	−	0.561108i
$337$	−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
$342$	−1.47584	−	2.21515i	−0.0798043	−	0.119782i
$343$			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	$-0.520893\pi$
$347$	−2.44357			−0.131177			−0.0655887	+	0.997847i	$0.520893\pi$
$348$	14.0969	+	17.9707i	0.755671	+	0.963329i
$349$	−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	$0.386762\pi$
$353$			35.2238i			1.87477i	−0.348290	+	0.937387i	$0.613238\pi$
$354$	0.200221	−	0.0888447i	0.0106416	−	0.00472204i
$355$			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	$-0.415781\pi$
$359$	9.90967			0.523012			0.261506	+	0.965202i	$0.415781\pi$
$360$	16.4931	+	8.75462i	0.869263	+	0.461409i
$361$	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
$366$	32.3456	−	14.3528i	1.69073	−	0.750235i
$367$		−	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
$372$	19.6532	+	25.0539i	1.01897	+	1.29899i
$373$	−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
$378$	−18.7882	−	19.8551i	−0.966360	−	1.02124i
$379$		−	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	$-0.601690\pi$
$383$	−12.2927			−0.628126			−0.314063	+	0.949402i	$0.601690\pi$
$384$	6.38927	+	18.5250i	0.326051	+	0.945352i
$385$	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	$0.148373\pi$
$389$			17.7283i			0.898858i	−0.893316	+	0.449429i	$0.851627\pi$
$390$	−5.53065	−	12.4639i	−0.280055	−	0.631134i
$391$		−	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
$396$	−3.85775	+	4.26302i	−0.193859	+	0.214225i
$397$	−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	$-0.841578\pi$
$401$		−	19.1200i		−	0.954807i	0.878684	−	0.477404i	$-0.158422\pi$
$402$	13.5728	+	30.5877i	0.676950	+	1.52558i
$403$		−	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
$408$	−10.5498	−	8.15514i	−0.522291	−	0.403740i
$409$	−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
$414$	−3.53077	+	2.35237i	−0.173528	+	0.115613i
$415$			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	$-0.575084\pi$
$419$	−9.56749			−0.467402			−0.233701	+	0.972308i	$0.575084\pi$
$420$	22.3113	−	17.5018i	1.08868	−	0.854000i
$421$	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
$426$	−28.2335	+	12.5282i	−1.36792	+	0.606991i
$427$		−	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	$-0.377832\pi$
$431$	15.5475			0.748897			0.374449	+	0.927248i	$0.377832\pi$
$432$	−1.46112	+	20.7332i	−0.0702983	+	0.997526i
$433$	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
$438$	−10.4518	+	4.63780i	−0.499404	+	0.221603i
$439$		−	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	$-0.432703\pi$
$443$	8.83365			0.419700			0.209850	+	0.977734i	$0.432703\pi$
$444$	23.6428	−	18.5463i	1.12204	−	0.880168i
$445$	−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	$0.123818\pi$
$449$			16.0724i			0.758502i	−0.925294	+	0.379251i	$0.876182\pi$
$450$	0.555816	−	0.370311i	0.0262014	−	0.0174566i
$451$		−	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
$456$	2.43171	+	1.87975i	0.113875	+	0.0880273i
$457$	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	$0.0698849\pi$
$461$			9.35232i			0.435581i	−0.975996	+	0.217790i	$0.930115\pi$
$462$	3.54134	+	7.98079i	0.164758	+	0.371300i
$463$			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	$-0.436030\pi$
$467$	8.62755			0.399236			0.199618	+	0.979874i	$0.436030\pi$
$468$	10.1843	−	11.2542i	0.470771	−	0.520226i
$469$	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
$474$	6.73207	+	15.1714i	0.309214	+	0.696847i
$475$		−	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	$-0.549824\pi$
$479$	−6.82356			−0.311776			−0.155888	+	0.987775i	$0.549824\pi$
$480$	−21.2756	−	3.49837i	−0.971092	−	0.159678i
$481$	−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
$486$	−10.0398	+	19.6266i	−0.455413	+	0.890280i
$487$		−	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	$-0.333439\pi$
$491$	22.1458			0.999425			0.499713	+	0.866191i	$0.333439\pi$
$492$	−12.6538	−	16.1310i	−0.570477	−	0.727244i
$493$	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
$498$	−27.8529	+	12.3592i	−1.24812	+	0.553831i
$499$			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	$-0.444519\pi$
$503$	7.77873			0.346836			0.173418	+	0.984848i	$0.444519\pi$
$504$	27.8799	+	14.7988i	1.24187	+	0.659192i
$505$	−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	$-0.921696\pi$
$509$		−	10.9884i		−	0.487052i	0.969894	−	0.243526i	$-0.0783040\pi$
$510$	13.4107	−	5.95076i	0.593834	−	0.263504i
$511$			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
$516$	−16.1051	−	20.5308i	−0.708987	−	0.903817i
$517$	−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	$-0.666232\pi$
$521$		−	39.5660i		−	1.73342i	0.498816	−	0.866708i	$-0.333768\pi$
$522$	−15.5100	−	23.2796i	−0.678854	−	1.01892i
$523$		−	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
$528$	2.64947	−	6.08723i	0.115304	−	0.264913i
$529$	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
$534$	−0.321656	−	0.724886i	−0.0139194	−	0.0313689i
$535$		−	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
$540$	−19.3095	−	12.2533i	−0.830948	−	0.527296i
$541$	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
$546$	−9.34901	−	21.0690i	−0.400101	−	0.901669i
$547$		−	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
$552$	2.99617	−	3.87595i	0.127525	−	0.164971i
$553$	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	$-0.786901\pi$
$557$		−	29.2920i		−	1.24114i	0.784150	−	0.620571i	$-0.213099\pi$
$558$	−21.6234	−	32.4554i	−0.915390	−	1.37395i
$559$			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	$-0.416962\pi$
$563$	12.2397			0.515844			0.257922	+	0.966166i	$0.416962\pi$
$564$	−12.9831	+	10.1844i	−0.546689	+	0.428843i
$565$	−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	$0.205348\pi$
$569$			28.6863i			1.20259i	−0.799027	+	0.601295i	$0.794652\pi$
$570$	−3.09114	+	1.37164i	−0.129474	+	0.0574518i
$571$		−	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
$576$	−6.04594	−	23.2260i	−0.251914	−	0.967750i
$577$	−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
$582$	−15.6764	+	6.95612i	−0.649806	+	0.288341i
$583$			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	$-0.391401\pi$
$587$	16.2131			0.669187			0.334594	+	0.942362i	$0.391401\pi$
$588$	18.6360	−	14.6187i	0.768535	−	0.602867i
$589$	−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	$-0.942202\pi$
$593$		−	8.79493i		−	0.361165i	0.983560	−	0.180582i	$-0.0577982\pi$
$594$	5.11465	−	4.83981i	0.209857	−	0.198580i
$595$		−	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	$-0.576966\pi$
$599$	−11.7207			−0.478896			−0.239448	+	0.970909i	$0.576966\pi$
$600$	−0.471658	+	0.610153i	−0.0192554	+	0.0249094i
$601$	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
$606$	−9.81940	−	22.1290i	−0.398886	−	0.898931i
$607$			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
$612$	12.1091	+	10.9579i	0.489480	+	0.442948i
$613$	−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	$-0.876263\pi$
$617$		−	18.8290i		−	0.758028i	0.925391	−	0.379014i	$-0.123737\pi$
$618$	−2.07240	−	4.67037i	−0.0833642	−	0.187870i
$619$		−	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
$624$	−6.99451	+	16.0701i	−0.280005	+	0.643317i
$625$	−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
$630$	−28.9025	+	19.2563i	−1.15150	+	0.767188i
$631$		−	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
$636$	24.7640	+	31.5691i	0.981956	+	1.25180i
$637$	−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	$-0.895372\pi$
$641$		−	16.3458i		−	0.645620i	0.946464	−	0.322810i	$-0.104628\pi$
$642$	2.36087	−	1.04760i	0.0931762	−	0.0413454i
$643$		−	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	$-0.483963\pi$
$647$	2.56200			0.100723			0.0503614	+	0.998731i	$0.483963\pi$
$648$	3.74925	−	25.1782i	0.147284	−	0.989094i
$649$	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	$0.0468382\pi$
$653$			7.49322i			0.293232i	−0.989193	+	0.146616i	$0.953162\pi$
$654$	−9.68668	+	4.29830i	−0.378779	+	0.168077i
$655$		−	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	$-0.566129\pi$
$659$	−10.5898			−0.412518			−0.206259	+	0.978497i	$0.566129\pi$
$660$	4.50844	+	5.74735i	0.175491	+	0.223715i
$661$	−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
$666$	−30.6274	+	20.4055i	−1.18679	+	0.790696i
$667$			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
$672$	−35.9642	−	5.91364i	−1.38735	−	0.228124i
$673$	−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	$0.0842200\pi$
$677$			13.6085i			0.523018i	−0.965201	+	0.261509i	$0.915780\pi$
$678$	−4.32747	−	9.75241i	−0.166196	−	0.374539i
$679$			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	$-0.346246\pi$
$683$	24.2770			0.928932			0.464466	+	0.885591i	$0.346246\pi$
$684$	−2.79112	−	2.52579i	−0.106721	−	0.0965759i
$685$	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
$690$	2.18629	+	4.92703i	0.0832306	+	0.187569i
$691$			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
$696$	25.5555	+	19.7548i	0.968677	+	0.748803i
$697$	−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	$0.0320520\pi$
$701$			5.32303i			0.201048i	−0.994935	+	0.100524i	$0.967948\pi$
$702$	−13.5025	+	12.7769i	−0.509618	+	0.482233i
$703$			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
$708$	0.243737	−	0.191196i	0.00916018	−	0.00718558i
$709$	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
$714$	22.6694	−	10.0592i	0.848380	−	0.376455i
$715$		−	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	$-0.762974\pi$
$719$	−39.4347			−1.47067			−0.735333	+	0.677706i	$0.762974\pi$
$720$	25.6474	+	6.28828i	0.955822	+	0.234350i
$721$	−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
$726$	22.5727	−	10.0163i	0.837753	−	0.371739i
$727$			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
$732$	39.3756	−	30.8877i	1.45536	−	1.14164i
$733$	−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
$738$	13.9223	+	20.8965i	0.512486	+	0.769211i
$739$		−	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	$-0.507948\pi$
$743$	−1.36108			−0.0499332			−0.0249666	+	0.999688i	$0.507948\pi$
$744$	35.6283	+	27.5413i	1.30620	+	1.00971i
$745$	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
$750$	−11.2756	−	25.4108i	−0.411727	−	0.927870i
$751$		−	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
$756$	−32.6408	−	20.7129i	−1.18713	−	0.753321i
$757$	−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	$-0.956529\pi$
$761$		−	7.51143i		−	0.272289i	0.990689	−	0.136145i	$-0.0434712\pi$
$762$	−7.09100	−	15.9803i	−0.256880	−	0.578905i
$763$			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
$768$	15.1797	+	23.1857i	0.547749	+	0.836643i
$769$	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	$-0.744517\pi$
$773$		−	39.9906i		−	1.43836i	0.694822	−	0.719182i	$-0.255483\pi$
$774$	17.7196	+	26.5960i	0.636916	+	0.955974i
$775$		−	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
$780$	−11.9021	−	15.1728i	−0.426164	−	0.543273i
$781$	−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
$786$	2.29528	−	1.01849i	0.0818701	−	0.0363285i
$787$		−	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
$792$	−3.81215	+	7.18183i	−0.135459	+	0.255195i
$793$	−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	$0.228977\pi$
$797$			37.2029i			1.31780i	−0.752233	+	0.658898i	$0.771023\pi$
$798$	−5.22526	+	2.31862i	−0.184972	+	0.0820784i
$799$			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
$804$	29.2090	+	37.2356i	1.03012	+	1.31320i
$805$	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	$-0.759360\pi$
$809$		−	39.0244i		−	1.37202i	0.727590	−	0.686012i	$-0.240640\pi$
$810$	22.4169	+	16.7923i	0.787650	+	0.590020i
$811$			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
$816$	−17.2907	−	7.52581i	−0.605297	−	0.263456i
$817$	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	$-0.926584\pi$
$821$		−	13.1005i		−	0.457209i	0.973519	−	0.228605i	$-0.0734163\pi$
$822$	1.10543	+	2.49121i	0.0385564	+	0.0868909i
$823$			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	$-0.619932\pi$
$827$	−21.1614			−0.735853			−0.367927	+	0.929855i	$0.619932\pi$
$828$	−4.02590	+	4.44883i	−0.139910	+	0.154608i
$829$	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
$834$	1.75608	+	3.95752i	0.0608082	+	0.137038i
$835$		−	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	$-0.593464\pi$
$839$	−16.7666			−0.578847			−0.289424	+	0.957201i	$0.593464\pi$
$840$	24.5263	−	31.7281i	0.846239	−	1.09472i
$841$	−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
$846$	16.8186	−	11.2054i	0.578237	−	0.385249i
$847$		−	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
$852$	−34.3698	+	26.9609i	−1.17749	+	0.923665i
$853$	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	$-0.949206\pi$
$857$		−	9.30340i		−	0.317798i	0.987295	−	0.158899i	$-0.0507945\pi$
$858$	5.42734	−	2.40829i	0.185286	−	0.0822177i
$859$		−	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	$-0.356245\pi$
$863$	25.6415			0.872847			0.436423	+	0.899741i	$0.356245\pi$
$864$	5.18114	+	28.9336i	0.176266	+	0.984343i
$865$	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
$870$	−32.4856	+	14.4150i	−1.10136	+	0.488713i
$871$		−	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
$876$	−12.7233	+	9.98066i	−0.429882	+	0.337215i
$877$	−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	$0.398271\pi$
$881$			56.3574i			1.89873i	−0.314178	+	0.949364i	$0.601729\pi$
$882$	−24.1414	+	16.0842i	−0.812885	+	0.541583i
$883$			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	$-0.573702\pi$
$887$	−13.6688			−0.458954			−0.229477	+	0.973314i	$0.573702\pi$
$888$	25.9900	−	33.6216i	0.872169	−	1.12827i
$889$	−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
$894$	16.0628	+	36.1991i	0.537219	+	1.21068i
$895$		−	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
$900$	0.633759	−	0.700337i	0.0211253	−	0.0233446i
$901$	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
$906$	−18.0215	−	40.6134i	−0.598726	−	1.34929i
$907$			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	$-0.678015\pi$
$911$	−32.0270			−1.06110			−0.530551	+	0.847653i	$0.678015\pi$
$912$	3.98549	+	1.73469i	0.131973	+	0.0574413i
$913$	−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
$918$	−13.7474	−	14.5281i	−0.453733	−	0.479500i
$919$		−	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
$924$	7.62106	+	9.71533i	0.250714	+	0.319611i
$925$	−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	$-0.922284\pi$
$929$		−	14.7359i		−	0.483468i	0.970343	−	0.241734i	$-0.0777161\pi$
$930$	−45.2900	+	20.0967i	−1.48512	+	0.658997i
$931$			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
$936$	10.0639	−	18.9598i	0.328950	−	0.619719i
$937$	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	$-0.759046\pi$
$941$		−	42.1318i		−	1.37346i	0.726913	−	0.686729i	$-0.240954\pi$
$942$	28.3683	−	12.5880i	0.924290	−	0.410138i
$943$		−	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	$-0.215494\pi$
$947$	47.9731			1.55892			0.779458	+	0.626454i	$0.215494\pi$
$948$	14.4876	+	18.4688i	0.470535	+	0.599838i
$949$	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	$0.230481\pi$
$953$			40.9003i			1.32489i	−0.749111	+	0.662445i	$0.769519\pi$
$954$	−27.2465	−	40.8953i	−0.882137	−	1.32404i
$955$			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
$960$	−30.3832	+	2.57581i	−0.980614	+	0.0831339i
$961$	−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
$966$	3.69570	+	8.32865i	0.118907	+	0.267970i
$967$		−	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	$-0.480691\pi$
$971$	3.77813			0.121246			0.0606229	+	0.998161i	$0.480691\pi$
$972$	−6.96452	+	30.3891i	−0.223387	+	0.974730i
$973$	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	$0.199285\pi$
$977$			36.6311i			1.17193i	−0.810335	+	0.585967i	$0.800715\pi$
$978$	−8.10084	−	18.2561i	−0.259036	−	0.583765i
$979$		−	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	$-0.698493\pi$
$983$	−36.6169			−1.16790			−0.583949	+	0.811791i	$0.698493\pi$
$984$	−22.9394	−	17.7325i	−0.731281	−	0.565292i
$985$	−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
$990$	−4.96038	−	7.44525i	−0.157651	−	0.236625i
$991$		−	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
$996$	−33.9064	+	26.5974i	−1.07436	+	0.842771i
$997$	−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.b.47.19	yes	22
3.2	odd	2		276.2.c.a.47.4	yes	22
4.3	odd	2		276.2.c.a.47.3	✓	22
12.11	even	2	inner	276.2.c.b.47.20	yes	22

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37110 - 0.346521i) q^{2} +(-1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} +2.20059i q^{5} +(-2.23896 + 0.993503i) q^{6} +3.71987i q^{7} +(2.08365 - 1.91269i) q^{8} +(2.82810 - 1.00093i) q^{9} +O(q^{10})\)	\(q+(1.37110 - 0.346521i) q^{2} +(-1.70706 + 0.293173i) q^{3} +(1.75985 - 0.950233i) q^{4} +2.20059i q^{5} +(-2.23896 + 0.993503i) 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} +(-2.72558 + 2.13804i) 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} +(3.53077 - 2.35237i) 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} +(-2.99617 + 3.87595i) 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} +(-2.18629 - 4.92703i) 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} +(4.02590 - 4.44883i) 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} +(-3.69570 - 8.32865i) 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} +(-2.76496 + 6.35256i) 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} +(-5.33758 + 5.05076i) 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} +(-4.70495 - 5.99787i) 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} +(2.14545 - 0.952007i) 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} +(3.97831 - 7.49487i) 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} +(-5.66390 + 2.51326i) 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} +(-7.95324 - 10.1388i) 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} +(5.17660 + 7.76977i) 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} +(-1.58974 + 9.66813i) q^{96} +7.00161 q^{97} +(-9.37483 + 2.36932i) q^{98} +(-2.70998 + 0.959122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * 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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