LMFDB - Embedded newform 312.2.h.c.155.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(155,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("312.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.h (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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.3
Character	$\chi$	$=$	312.155
Dual form			312.2.h.c.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38664 + 0.277882i) q^{2} +(-0.662918 - 1.60017i) q^{3} +(1.84556 - 0.770648i) q^{4} +2.38561i q^{5} +(1.36389 + 2.03465i) q^{6} +2.63829 q^{7} +(-2.34499 + 1.58146i) q^{8} +(-2.12108 + 2.12156i) q^{9} +O(q^{10})$	\(q+(-1.38664 + 0.277882i) q^{2} +(-0.662918 - 1.60017i) q^{3} +(1.84556 - 0.770648i) q^{4} +2.38561i q^{5} +(1.36389 + 2.03465i) q^{6} +2.63829 q^{7} +(-2.34499 + 1.58146i) q^{8} +(-2.12108 + 2.12156i) q^{9} +(-0.662918 - 3.30799i) q^{10} -0.764084 q^{11} +(-2.45662 - 2.44233i) q^{12} +(-1.05175 + 3.44874i) q^{13} +(-3.65836 + 0.733133i) q^{14} +(3.81737 - 1.58146i) q^{15} +(2.81220 - 2.84456i) q^{16} +0.584523i q^{17} +(2.35164 - 3.53126i) q^{18} +4.28969i q^{19} +(1.83846 + 4.40279i) q^{20} +(-1.74897 - 4.22170i) q^{21} +(1.05951 - 0.212325i) q^{22} +4.39993 q^{23} +(4.08514 + 2.70400i) q^{24} -0.691126 q^{25} +(0.500052 - 5.07444i) q^{26} +(4.80096 + 1.98766i) q^{27} +(4.86912 - 2.03319i) q^{28} +8.65308 q^{29} +(-4.85388 + 3.25371i) q^{30} +7.09996 q^{31} +(-3.10907 + 4.72585i) q^{32} +(0.506525 + 1.22266i) q^{33} +(-0.162429 - 0.810526i) q^{34} +6.29391i q^{35} +(-2.27961 + 5.55008i) q^{36} -7.63475 q^{37} +(-1.19203 - 5.94827i) q^{38} +(6.21579 - 0.603265i) q^{39} +(-3.77275 - 5.59422i) q^{40} -0.139556 q^{41} +(3.59833 + 5.36799i) q^{42} -6.17544 q^{43} +(-1.41016 + 0.588840i) q^{44} +(-5.06122 - 5.06006i) q^{45} +(-6.10114 + 1.22266i) q^{46} +0.889975i q^{47} +(-6.41603 - 2.61429i) q^{48} -0.0394518 q^{49} +(0.958345 - 0.192052i) q^{50} +(0.935336 - 0.387491i) q^{51} +(0.716703 + 7.17540i) q^{52} -0.803622 q^{53} +(-7.20956 - 1.42207i) q^{54} -1.82280i q^{55} +(-6.18675 + 4.17235i) q^{56} +(6.86423 - 2.84371i) q^{57} +(-11.9987 + 2.40454i) q^{58} +9.13099 q^{59} +(5.82645 - 5.86054i) q^{60} +9.47787i q^{61} +(-9.84511 + 1.97295i) q^{62} +(-5.59601 + 5.59729i) q^{63} +(2.99795 - 7.41703i) q^{64} +(-8.22735 - 2.50905i) q^{65} +(-1.04213 - 1.55464i) q^{66} -11.5441i q^{67} +(0.450462 + 1.07877i) q^{68} +(-2.91679 - 7.04063i) q^{69} +(-1.74897 - 8.72742i) q^{70} -2.56670i q^{71} +(1.61873 - 8.32945i) q^{72} -13.3885i q^{73} +(10.5867 - 2.12156i) q^{74} +(0.458160 + 1.10592i) q^{75} +(3.30584 + 7.91689i) q^{76} -2.01587 q^{77} +(-8.45145 + 2.56377i) q^{78} +10.9069i q^{79} +(6.78600 + 6.70882i) q^{80} +(-0.00205378 - 9.00000i) q^{81} +(0.193514 - 0.0387800i) q^{82} -14.6776 q^{83} +(-6.48127 - 6.44358i) q^{84} -1.39444 q^{85} +(8.56313 - 1.71605i) q^{86} +(-5.73629 - 13.8464i) q^{87} +(1.79177 - 1.20837i) q^{88} +5.68613 q^{89} +(8.42421 + 5.61008i) q^{90} +(-2.77481 + 9.09877i) q^{91} +(8.12035 - 3.39080i) q^{92} +(-4.70669 - 11.3611i) q^{93} +(-0.247308 - 1.23408i) q^{94} -10.2335 q^{95} +(9.62322 + 1.84219i) q^{96} +10.4965i q^{97} +(0.0547056 - 0.0109630i) q^{98} +(1.62068 - 1.62105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 20 q^{4} - 28 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 + 20 * q^4 - 28 * q^9	$ 32 q - 4 q^{3} + 20 q^{4} - 28 q^{9} - 4 q^{10} - 2 q^{12} - 28 q^{16} - 24 q^{22} + 56 q^{25} - 16 q^{27} + 34 q^{30} - 10 q^{36} - 12 q^{40} + 34 q^{42} + 40 q^{43} + 22 q^{48} + 8 q^{49} - 52 q^{51} - 72 q^{52} + 20 q^{64} + 4 q^{66} - 8 q^{75} + 26 q^{78} - 76 q^{81} - 40 q^{82} - 88 q^{88} - 14 q^{90} - 56 q^{91} - 68 q^{94}+O(q^{100}) $ 32 * q - 4 * q^3 + 20 * q^4 - 28 * q^9 - 4 * q^10 - 2 * q^12 - 28 * q^16 - 24 * q^22 + 56 * q^25 - 16 * q^27 + 34 * q^30 - 10 * q^36 - 12 * q^40 + 34 * q^42 + 40 * q^43 + 22 * q^48 + 8 * q^49 - 52 * q^51 - 72 * q^52 + 20 * q^64 + 4 * q^66 - 8 * q^75 + 26 * q^78 - 76 * q^81 - 40 * q^82 - 88 * q^88 - 14 * q^90 - 56 * q^91 - 68 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.38664	+	0.277882i	−0.980505	+	0.196493i
$2$	−1.38664	+	0.277882i	−0.980505	+	0.196493i
$3$	−0.662918	−	1.60017i	−0.382736	−	0.923858i
$3$	−0.662918	−	1.60017i	−0.382736	−	0.923858i
$4$	1.84556	−	0.770648i	0.922781	−	0.385324i
$5$			2.38561i			1.06688i	0.845839	+	0.533438i	$0.179100\pi$
$5$			2.38561i			1.06688i	−0.845839	+	0.533438i	$0.820900\pi$
$6$	1.36389	+	2.03465i	0.556806	+	0.830643i
$7$	2.63829			0.997178			0.498589	−	0.866839i	$-0.333852\pi$
$7$	2.63829			0.997178			0.498589	+	0.866839i	$0.333852\pi$
$8$	−2.34499	+	1.58146i	−0.829079	+	0.559132i
$9$	−2.12108	+	2.12156i	−0.707026	+	0.707187i
$10$	−0.662918	−	3.30799i	−0.209633	−	1.04608i
$11$	−0.764084			−0.230380			−0.115190	−	0.993343i	$-0.536748\pi$
$11$	−0.764084			−0.230380			−0.115190	+	0.993343i	$0.536748\pi$
$12$	−2.45662	−	2.44233i	−0.709166	−	0.705041i
$13$	−1.05175	+	3.44874i	−0.291702	+	0.956509i
$13$	−1.05175	+	3.44874i	−0.291702	+	0.956509i
$14$	−3.65836	+	0.733133i	−0.977738	+	0.195938i
$15$	3.81737	−	1.58146i	0.985642	−	0.408332i
$16$	2.81220	−	2.84456i	0.703051	−	0.711139i
$17$			0.584523i			0.141768i	0.997485	+	0.0708839i	$0.0225820\pi$
$17$			0.584523i			0.141768i	−0.997485	+	0.0708839i	$0.977418\pi$
$18$	2.35164	−	3.53126i	0.554286	−	0.832326i
$19$			4.28969i			0.984122i	0.870561	+	0.492061i	$0.163756\pi$
$19$			4.28969i			0.984122i	−0.870561	+	0.492061i	$0.836244\pi$
$20$	1.83846	+	4.40279i	0.411093	+	0.984494i
$21$	−1.74897	−	4.22170i	−0.381656	−	0.921251i
$22$	1.05951	−	0.212325i	0.225889	−	0.0452679i
$23$	4.39993			0.917449			0.458724	−	0.888579i	$-0.348307\pi$
$23$	4.39993			0.917449			0.458724	+	0.888579i	$0.348307\pi$
$24$	4.08514	+	2.70400i	0.833877	+	0.551951i
$25$	−0.691126			−0.138225
$26$	0.500052	−	5.07444i	0.0980683	−	0.995180i
$27$	4.80096	+	1.98766i	0.923945	+	0.382525i
$28$	4.86912	−	2.03319i	0.920177	−	0.384237i
$29$	8.65308			1.60684			0.803419	−	0.595415i	$-0.203012\pi$
$29$	8.65308			1.60684			0.803419	+	0.595415i	$0.203012\pi$
$30$	−4.85388	+	3.25371i	−0.886193	+	0.594043i
$31$	7.09996			1.27519			0.637595	−	0.770372i	$-0.279929\pi$
$31$	7.09996			1.27519			0.637595	+	0.770372i	$0.279929\pi$
$32$	−3.10907	+	4.72585i	−0.549612	+	0.835420i
$33$	0.506525	+	1.22266i	0.0881747	+	0.212838i
$34$	−0.162429	−	0.810526i	−0.0278563	−	0.139004i
$35$			6.29391i			1.06387i
$36$	−2.27961	+	5.55008i	−0.379934	+	0.925013i
$37$	−7.63475			−1.25515			−0.627573	−	0.778558i	$-0.715951\pi$
$37$	−7.63475			−1.25515			−0.627573	+	0.778558i	$0.715951\pi$
$38$	−1.19203	−	5.94827i	−0.193373	−	0.964937i
$39$	6.21579	−	0.603265i	0.995323	−	0.0965997i
$40$	−3.77275	−	5.59422i	−0.596524	−	0.884525i
$41$	−0.139556			−0.0217949			−0.0108975	−	0.999941i	$-0.503469\pi$
$41$	−0.139556			−0.0217949			−0.0108975	+	0.999941i	$0.503469\pi$
$42$	3.59833	+	5.36799i	0.555235	+	0.828299i
$43$	−6.17544			−0.941746			−0.470873	−	0.882201i	$-0.656061\pi$
$43$	−6.17544			−0.941746			−0.470873	+	0.882201i	$0.656061\pi$
$44$	−1.41016	+	0.588840i	−0.212590	+	0.0887709i
$45$	−5.06122	−	5.06006i	−0.754482	−	0.754309i
$46$	−6.10114	+	1.22266i	−0.899563	+	0.180272i
$47$			0.889975i			0.129816i	0.997891	+	0.0649081i	$0.0206754\pi$
$47$			0.889975i			0.129816i	−0.997891	+	0.0649081i	$0.979325\pi$
$48$	−6.41603	−	2.61429i	−0.926075	−	0.377340i
$49$	−0.0394518			−0.00563597
$50$	0.958345	−	0.192052i	0.135530	−	0.0271602i
$51$	0.935336	−	0.387491i	0.130973	−	0.0542596i
$52$	0.716703	+	7.17540i	0.0993889	+	0.995049i
$53$	−0.803622			−0.110386			−0.0551930	−	0.998476i	$-0.517577\pi$
$53$	−0.803622			−0.110386			−0.0551930	+	0.998476i	$0.517577\pi$
$54$	−7.20956	−	1.42207i	−0.981096	−	0.193520i
$55$		−	1.82280i		−	0.245787i
$56$	−6.18675	+	4.17235i	−0.826739	+	0.557554i
$57$	6.86423	−	2.84371i	0.909189	−	0.376659i
$58$	−11.9987	+	2.40454i	−1.57551	+	0.315731i
$59$	9.13099			1.18875			0.594377	−	0.804187i	$-0.297399\pi$
$59$	9.13099			1.18875			0.594377	+	0.804187i	$0.297399\pi$
$60$	5.82645	−	5.86054i	0.752192	−	0.756593i
$61$			9.47787i			1.21352i	0.794886	+	0.606758i	$0.207530\pi$
$61$			9.47787i			1.21352i	−0.794886	+	0.606758i	$0.792470\pi$
$62$	−9.84511	+	1.97295i	−1.25033	+	0.250565i
$63$	−5.59601	+	5.59729i	−0.705031	+	0.705192i
$64$	2.99795	−	7.41703i	0.374743	−	0.927129i
$65$	−8.22735	−	2.50905i	−1.02048	−	0.311210i
$66$	−1.04213	−	1.55464i	−0.128277	−	0.191363i
$67$		−	11.5441i		−	1.41034i	−0.709040	−	0.705168i	$-0.750872\pi$
$67$		−	11.5441i		−	1.41034i	0.709040	−	0.705168i	$-0.249128\pi$
$68$	0.450462	+	1.07877i	0.0546265	+	0.130821i
$69$	−2.91679	−	7.04063i	−0.351141	−	0.847592i
$70$	−1.74897	−	8.72742i	−0.209042	−	1.04313i
$71$		−	2.56670i		−	0.304611i	−0.988333	−	0.152305i	$-0.951330\pi$
$71$		−	2.56670i		−	0.304611i	0.988333	−	0.152305i	$-0.0486697\pi$
$72$	1.61873	−	8.32945i	0.190769	−	0.981635i
$73$		−	13.3885i		−	1.56700i	−0.621391	−	0.783500i	$-0.713432\pi$
$73$		−	13.3885i		−	1.56700i	0.621391	−	0.783500i	$-0.286568\pi$
$74$	10.5867	−	2.12156i	1.23068	−	0.246627i
$75$	0.458160	+	1.10592i	0.0529037	+	0.127700i
$76$	3.30584	+	7.91689i	0.379206	+	0.908130i
$77$	−2.01587			−0.229730
$78$	−8.45145	+	2.56377i	−0.956939	+	0.290290i
$79$			10.9069i			1.22713i	0.789646	+	0.613563i	$0.210264\pi$
$79$			10.9069i			1.22713i	−0.789646	+	0.613563i	$0.789736\pi$
$80$	6.78600	+	6.70882i	0.758698	+	0.750068i
$81$	−0.00205378	−	9.00000i	−0.000228198	−	1.00000i
$82$	0.193514	−	0.0387800i	0.0213700	−	0.00428254i
$83$	−14.6776			−1.61107			−0.805536	−	0.592547i	$-0.798123\pi$
$83$	−14.6776			−1.61107			−0.805536	+	0.592547i	$0.798123\pi$
$84$	−6.48127	−	6.44358i	−0.707165	−	0.703052i
$85$	−1.39444			−0.151249
$86$	8.56313	−	1.71605i	0.923387	−	0.185046i
$87$	−5.73629	−	13.8464i	−0.614995	−	1.48449i
$88$	1.79177	−	1.20837i	0.191003	−	0.128813i
$89$	5.68613			0.602729			0.301364	−	0.953509i	$-0.402558\pi$
$89$	5.68613			0.602729			0.301364	+	0.953509i	$0.402558\pi$
$90$	8.42421	+	5.61008i	0.887989	+	0.591354i
$91$	−2.77481	+	9.09877i	−0.290879	+	0.953810i
$92$	8.12035	−	3.39080i	0.846605	−	0.353515i
$93$	−4.70669	−	11.3611i	−0.488061	−	1.17809i
$94$	−0.247308	−	1.23408i	−0.0255079	−	0.127286i
$95$	−10.2335			−1.04994
$96$	9.62322	+	1.84219i	0.982166	+	0.188017i
$97$			10.4965i			1.06576i	0.846191	+	0.532879i	$0.178890\pi$
$97$			10.4965i			1.06576i	−0.846191	+	0.532879i	$0.821110\pi$
$98$	0.0547056	−	0.0109630i	0.00552610	−	0.00110743i
$99$	1.62068	−	1.62105i	0.162885	−	0.162922i
$100$	−1.27552	+	0.532614i	−0.127552	+	0.0532614i
$101$	−15.4371			−1.53605			−0.768023	−	0.640422i	$-0.778759\pi$
$101$	−15.4371			−1.53605			−0.768023	+	0.640422i	$0.778759\pi$
$102$	−1.18930	+	0.797226i	−0.117758	+	0.0789371i
$103$			4.99712i			0.492381i	0.969221	+	0.246191i	$0.0791789\pi$
$103$			4.99712i			0.492381i	−0.969221	+	0.246191i	$0.920821\pi$
$104$	−2.98773	−	9.75056i	−0.292971	−	0.956121i
$105$	10.0713	−	4.17235i	0.982860	−	0.407180i
$106$	1.11434	−	0.223312i	0.108234	−	0.0216900i
$107$		−	19.1495i		−	1.85126i	−0.378434	−	0.925628i	$-0.623537\pi$
$107$		−	19.1495i		−	1.85126i	0.378434	−	0.925628i	$-0.376463\pi$
$108$	10.3923	−	0.0314979i	0.999995	−	0.00303088i
$109$	7.05520			0.675766			0.337883	−	0.941188i	$-0.390289\pi$
$109$	7.05520			0.675766			0.337883	+	0.941188i	$0.390289\pi$
$110$	0.506525	+	2.52758i	0.0482953	+	0.240995i
$111$	5.06122	+	12.2169i	0.480389	+	1.15958i
$112$	7.41940	−	7.50475i	0.701067	−	0.709133i
$113$			11.2283i			1.05627i	0.849160	+	0.528136i	$0.177109\pi$
$113$			11.2283i			1.05627i	−0.849160	+	0.528136i	$0.822891\pi$
$114$	−8.72802	+	5.85067i	−0.817454	+	0.547965i
$115$			10.4965i			0.978804i
$116$	15.9698	−	6.66848i	1.48276	−	0.619153i
$117$	−5.08589	−	9.54640i	−0.470191	−	0.882565i
$118$	−12.6614	+	2.53734i	−1.16558	+	0.233581i
$119$			1.54214i			0.141368i
$120$	−6.45067	+	9.74555i	−0.588863	+	0.889643i
$121$	−10.4162			−0.946925
$122$	−2.63373	−	13.1424i	−0.238447	−	1.18986i
$123$	0.0925140	+	0.223312i	0.00834170	+	0.0201354i
$124$	13.1034	−	5.47157i	1.17672	−	0.491361i
$125$			10.2793i			0.919407i
$126$	6.20428	−	9.31648i	0.552722	−	0.829978i
$127$		−	3.17432i		−	0.281675i	−0.990033	−	0.140838i	$-0.955020\pi$
$127$		−	3.17432i		−	0.281675i	0.990033	−	0.140838i	$-0.0449795\pi$
$128$	−2.09602	+	11.1179i	−0.185264	+	0.982689i
$129$	4.09381	+	9.88174i	0.360440	+	0.870039i
$130$	12.1056	+	1.19293i	1.06173	+	0.104627i
$131$		−	6.42017i		−	0.560933i	−0.959864	−	0.280467i	$-0.909511\pi$
$131$		−	6.42017i		−	0.560933i	0.959864	−	0.280467i	$-0.0904892\pi$
$132$	1.87707	+	1.86615i	0.163378	+	0.162427i
$133$			11.3174i			0.981345i
$134$	3.20790	+	16.0075i	0.277120	+	1.38284i
$135$	−4.74178	+	11.4532i	−0.408107	+	0.985735i
$136$	−0.924402	−	1.37070i	−0.0792669	−	0.117537i
$137$	−6.69918			−0.572350			−0.286175	−	0.958177i	$-0.592384\pi$
$137$	−6.69918			−0.572350			−0.286175	+	0.958177i	$0.592384\pi$
$138$	6.00102	+	8.95232i	0.510841	+	0.762072i
$139$	10.4217			0.883957			0.441979	−	0.897026i	$-0.354277\pi$
$139$	10.4217			0.883957			0.441979	+	0.897026i	$0.354277\pi$
$140$	4.85039	+	11.6158i	0.409933	+	0.981715i
$141$	1.42411	−	0.589981i	0.119932	−	0.0496854i
$142$	0.713240	+	3.55909i	0.0598538	+	0.298673i
$143$	0.803622	−	2.63513i	0.0672023	−	0.220361i
$144$	0.0700026	+	11.9998i	0.00583355	+	0.999983i
$145$			20.6429i			1.71430i
$146$	3.72042	+	18.5650i	0.307904	+	1.53645i
$147$	0.0261533	+	0.0631295i	0.00215709	+	0.00520683i
$148$	−14.0904	+	5.88370i	−1.15822	+	0.483637i
$149$			4.48086i			0.367086i	0.983012	+	0.183543i	$0.0587567\pi$
$149$			4.48086i			0.367086i	−0.983012	+	0.183543i	$0.941243\pi$
$150$	−0.942620	−	1.40620i	−0.0769646	−	0.114816i
$151$	5.12597			0.417145			0.208573	−	0.978007i	$-0.433118\pi$
$151$	5.12597			0.417145			0.208573	+	0.978007i	$0.433118\pi$
$152$	−6.78399	−	10.0593i	−0.550254	−	0.815915i
$153$	−1.24010	−	1.23982i	−0.100256	−	0.100233i
$154$	2.79530	−	0.560175i	0.225251	−	0.0451402i
$155$			16.9377i			1.36047i
$156$	11.0067	−	5.90355i	0.881244	−	0.472662i
$157$		−	7.23041i		−	0.577050i	−0.957472	−	0.288525i	$-0.906835\pi$
$157$		−	7.23041i		−	0.577050i	0.957472	−	0.288525i	$-0.0931648\pi$
$158$	−3.03085	−	15.1240i	−0.241121	−	1.20320i
$159$	0.532736	+	1.28593i	0.0422487	+	0.101981i
$160$	−11.2740	−	7.41703i	−0.891290	−	0.586368i
$161$	11.6083			0.914860
$162$	2.50379	+	12.4792i	0.196716	+	0.980460i
$163$		−	14.7862i		−	1.15814i	−0.815276	−	0.579072i	$-0.803415\pi$
$163$		−	14.7862i		−	1.15814i	0.815276	−	0.579072i	$-0.196585\pi$
$164$	−0.257559	+	0.107548i	−0.0201119	+	0.00839810i
$165$	−2.91679	+	1.20837i	−0.227072	+	0.0940715i
$166$	20.3526	−	4.07864i	1.57966	−	0.316564i
$167$		−	18.3295i		−	1.41838i	−0.705019	−	0.709189i	$-0.749062\pi$
$167$		−	18.3295i		−	1.41838i	0.705019	−	0.709189i	$-0.250938\pi$
$168$	10.7778	+	7.13391i	0.831523	+	0.550393i
$169$	−10.7877	−	7.25440i	−0.829820	−	0.558031i
$170$	1.93360	−	0.387491i	0.148300	−	0.0297192i
$171$	−9.10084	−	9.09877i	−0.695959	−	0.695800i
$172$	−11.3972	+	4.75909i	−0.869025	+	0.362877i
$173$	15.4371			1.17366			0.586829	−	0.809711i	$-0.300376\pi$
$173$	15.4371			1.17366			0.586829	+	0.809711i	$0.300376\pi$
$174$	11.8019	+	17.6060i	0.894696	+	1.33471i
$175$	−1.82339			−0.137835
$176$	−2.14876	+	2.17348i	−0.161969	+	0.163832i
$177$	−6.05310	−	14.6111i	−0.454979	−	1.09824i
$178$	−7.88464	+	1.58008i	−0.590979	+	0.118432i
$179$		−	2.31859i		−	0.173300i	−0.996239	−	0.0866499i	$-0.972384\pi$
$179$		−	2.31859i		−	0.173300i	0.996239	−	0.0866499i	$-0.0276162\pi$
$180$	−13.2403	−	5.43825i	−0.986875	−	0.405343i
$181$		−	20.4624i		−	1.52096i	−0.649364	−	0.760478i	$-0.724965\pi$
$181$		−	20.4624i		−	1.52096i	0.649364	−	0.760478i	$-0.275035\pi$
$182$	1.31928	−	13.3878i	0.0977916	−	0.992371i
$183$	15.1662	−	6.28305i	1.12112	−	0.464457i
$184$	−10.3178	+	6.95833i	−0.760637	+	0.512975i
$185$		−	18.2135i		−	1.33908i
$186$	9.68356	+	14.4459i	0.710033	+	1.05923i
$187$		−	0.446625i		−	0.0326604i
$188$	0.685858	+	1.64251i	0.0500213	+	0.119792i
$189$	12.6663	+	5.24401i	0.921338	+	0.381446i
$190$	14.1902	−	2.84371i	1.02947	−	0.206305i
$191$	−21.7061			−1.57060			−0.785299	−	0.619117i	$-0.787491\pi$
$191$	−21.7061			−1.57060			−0.785299	+	0.619117i	$0.787491\pi$
$192$	−13.8559	+	0.119666i	−0.999963	+	0.00863617i
$193$		−	4.36245i		−	0.314016i	−0.987597	−	0.157008i	$-0.949815\pi$
$193$		−	4.36245i		−	0.314016i	0.987597	−	0.157008i	$-0.0501849\pi$
$194$	−2.91679	−	14.5549i	−0.209414	−	1.04498i
$195$	1.43915	+	14.8284i	0.103060	+	1.06189i
$196$	−0.0728107	+	0.0304034i	−0.00520077	+	0.00217167i
$197$			23.5782i			1.67988i	0.542680	+	0.839939i	$0.317410\pi$
$197$			23.5782i			1.67988i	−0.542680	+	0.839939i	$0.682590\pi$
$198$	−1.79685	+	2.69818i	−0.127696	+	0.191751i
$199$		−	10.9069i		−	0.773172i	−0.922253	−	0.386586i	$-0.873654\pi$
$199$		−	10.9069i		−	0.773172i	0.922253	−	0.386586i	$-0.126346\pi$
$200$	1.62068	−	1.09299i	0.114600	−	0.0772861i
$201$	−18.4725	+	7.65279i	−1.30295	+	0.539786i
$202$	21.4057	−	4.28969i	1.50610	−	0.301822i
$203$	22.8293			1.60230
$204$	1.42760	−	1.43595i	0.0999521	−	0.100537i
$205$		−	0.332925i		−	0.0232525i
$206$	−1.38861	−	6.92923i	−0.0967492	−	0.482782i
$207$	−9.33260	+	9.33473i	−0.648660	+	0.648808i
$208$	6.85243	+	12.6903i	0.475130	+	0.879915i
$209$		−	3.27768i		−	0.226722i
$210$	−12.8059	+	8.58421i	−0.883692	+	0.592367i
$211$	19.5978			1.34917			0.674584	−	0.738198i	$-0.264323\pi$
$211$	19.5978			1.34917			0.674584	+	0.738198i	$0.264323\pi$
$212$	−1.48314	+	0.619310i	−0.101862	+	0.0425344i
$213$	−4.10715	+	1.70151i	−0.281417	+	0.116586i
$214$	5.32132	+	26.5536i	0.363758	+	1.81517i
$215$		−	14.7322i		−	1.00473i
$216$	−14.4016	+	2.93150i	−0.979905	+	0.199463i
$217$	18.7317			1.27159
$218$	−9.78306	+	1.96052i	−0.662592	+	0.132783i
$219$	−21.4238	+	8.87546i	−1.44769	+	0.599748i
$220$	−1.40474	−	3.36410i	−0.0947076	−	0.226808i
$221$	−2.01587	−	0.614770i	−0.135602	−	0.0413539i
$222$	−10.4130	−	15.5340i	−0.698872	−	1.04258i
$223$	−6.46108			−0.432666			−0.216333	−	0.976320i	$-0.569410\pi$
$223$	−6.46108			−0.432666			−0.216333	+	0.976320i	$0.569410\pi$
$224$	−8.20262	+	12.4681i	−0.548061	+	0.833063i
$225$	1.46593	−	1.46627i	0.0977288	−	0.0977511i
$226$	−3.12015	−	15.5697i	−0.207549	−	1.03568i
$227$	10.9383			0.725998			0.362999	−	0.931789i	$-0.381753\pi$
$227$	10.9383			0.725998			0.362999	+	0.931789i	$0.381753\pi$
$228$	10.4769	−	10.5382i	0.693847	−	0.697906i
$229$	22.2189			1.46826			0.734132	−	0.679007i	$-0.237590\pi$
$229$	22.2189			1.46826			0.734132	+	0.679007i	$0.237590\pi$
$230$	−2.91679	−	14.5549i	−0.192328	−	0.959723i
$231$	1.33636	+	3.22573i	0.0879259	+	0.212238i
$232$	−20.2914	+	13.6845i	−1.33219	+	0.898434i
$233$			16.4500i			1.07768i	0.842409	+	0.538839i	$0.181137\pi$
$233$			16.4500i			1.07768i	−0.842409	+	0.538839i	$0.818863\pi$
$234$	9.70509	+	11.8242i	0.634442	+	0.772971i
$235$	−2.12313			−0.138498
$236$	16.8518	−	7.03678i	1.09696	−	0.458055i
$237$	17.4529	−	7.23041i	1.13369	−	0.469666i
$238$	−0.428533	−	2.13840i	−0.0277777	−	0.138612i
$239$		−	28.2054i		−	1.82446i	−0.409681	−	0.912229i	$-0.634360\pi$
$239$		−	28.2054i		−	1.82446i	0.409681	−	0.912229i	$-0.365640\pi$
$240$	6.23667	−	15.3061i	0.402575	−	0.988007i
$241$		−	8.57938i		−	0.552646i	−0.961065	−	0.276323i	$-0.910884\pi$
$241$		−	8.57938i		−	0.552646i	0.961065	−	0.276323i	$-0.0891160\pi$
$242$	14.4435	−	2.89447i	0.928465	−	0.186064i
$243$	−14.4002	+	5.96955i	−0.923770	+	0.382947i
$244$	7.30410	+	17.4920i	0.467597	+	1.11981i
$245$		−	0.0941165i		−	0.00601288i
$246$	−0.190339	−	0.283947i	−0.0121355	−	0.0181038i
$247$	−14.7940	−	4.51166i	−0.941322	−	0.287070i
$248$	−16.6493	+	11.2283i	−1.05723	+	0.712999i
$249$	9.73003	+	23.4866i	0.616615	+	1.48840i
$250$	−2.85643	−	14.2537i	−0.180657	−	0.901484i
$251$		−	3.97532i		−	0.250920i	−0.992099	−	0.125460i	$-0.959959\pi$
$251$		−	3.97532i		−	0.250920i	0.992099	−	0.125460i	$-0.0400407\pi$
$252$	−6.01425	+	14.6427i	−0.378862	+	0.922403i
$253$	−3.36192			−0.211362
$254$	0.882087	+	4.40165i	0.0553471	+	0.276184i
$255$	0.924402	+	2.23134i	0.0578883	+	0.139732i
$256$	−0.183019	−	15.9990i	−0.0114387	−	0.999935i
$257$		−	13.5763i		−	0.846868i	−0.905927	−	0.423434i	$-0.860825\pi$
$257$		−	13.5763i		−	0.846868i	0.905927	−	0.423434i	$-0.139175\pi$
$258$	−8.42262	−	12.5649i	−0.524370	−	0.782254i
$259$	−20.1426			−1.25160
$260$	−17.1177	+	1.70977i	−1.06159	+	0.106036i
$261$	−18.3539	+	18.3581i	−1.13608	+	1.13633i
$262$	1.78405	+	8.90249i	0.110219	+	0.549998i
$263$	9.86533			0.608322			0.304161	−	0.952621i	$-0.401624\pi$
$263$	9.86533			0.608322			0.304161	+	0.952621i	$0.401624\pi$
$264$	−3.12139	−	2.06608i	−0.192108	−	0.127158i
$265$		−	1.91713i		−	0.117768i
$266$	−3.14491	−	15.6932i	−0.192827	−	0.962214i
$267$	−3.76944	−	9.09877i	−0.230686	−	0.556836i
$268$	−8.89643	−	21.3053i	−0.543436	−	1.30143i
$269$	13.4212			0.818305			0.409152	−	0.912466i	$-0.365824\pi$
$269$	13.4212			0.818305			0.409152	+	0.912466i	$0.365824\pi$
$270$	3.39251	−	17.1992i	0.206462	−	1.04671i
$271$	−10.7867			−0.655247			−0.327624	−	0.944808i	$-0.606248\pi$
$271$	−10.7867			−0.655247			−0.327624	+	0.944808i	$0.606248\pi$
$272$	1.66271	+	1.64380i	0.100817	+	0.0996699i
$273$	16.3990	−	1.59158i	0.992515	−	0.0963271i
$274$	9.28938	−	1.86158i	0.561192	−	0.112462i
$275$	0.528078			0.0318443
$276$	−10.8090	−	10.7461i	−0.650624	−	0.646839i
$277$			4.93632i			0.296594i	0.988943	+	0.148297i	$0.0473792\pi$
$277$			4.93632i			0.296594i	−0.988943	+	0.148297i	$0.952621\pi$
$278$	−14.4512	+	2.89601i	−0.866725	+	0.173691i
$279$	−15.0596	+	15.0630i	−0.901592	+	0.901798i
$280$	−9.95360	−	14.7592i	−0.594841	−	0.882028i
$281$	1.15261			0.0687587			0.0343794	−	0.999409i	$-0.489055\pi$
$281$	1.15261			0.0687587			0.0343794	+	0.999409i	$0.489055\pi$
$282$	−1.81079	+	1.21383i	−0.107831	+	0.0722824i
$283$	−5.16258			−0.306884			−0.153442	−	0.988158i	$-0.549036\pi$
$283$	−5.16258			−0.306884			−0.153442	+	0.988158i	$0.549036\pi$
$284$	−1.97802	−	4.73700i	−0.117374	−	0.281089i
$285$	6.78399	+	16.3754i	0.401849	+	0.969992i
$286$	−0.382082	+	3.87730i	−0.0225930	+	0.229269i
$287$	−0.368187			−0.0217334
$288$	−3.43160	−	16.6200i	−0.202209	−	0.979342i
$289$	16.6583			0.979902
$290$	−5.73629	−	28.6243i	−0.336846	−	1.68088i
$291$	16.7962	−	6.95833i	0.984610	−	0.407904i
$292$	−10.3178	−	24.7092i	−0.603803	−	1.44600i
$293$		−	5.96029i		−	0.348204i	−0.984728	−	0.174102i	$-0.944298\pi$
$293$		−	5.96029i		−	0.348204i	0.984728	−	0.174102i	$-0.0557022\pi$
$294$	−0.0538079	−	0.0802706i	−0.00313814	−	0.00468147i
$295$			21.7830i			1.26825i
$296$	17.9034	−	12.0741i	1.04061	−	0.701792i
$297$	−3.66834	−	1.51874i	−0.212858	−	0.0881262i
$298$	−1.24515	−	6.21335i	−0.0721297	−	0.359930i
$299$	−4.62761	+	15.1742i	−0.267622	+	0.877548i
$300$	1.69784	+	1.68796i	0.0980246	+	0.0974544i
$301$	−16.2926			−0.939088
$302$	−7.10789	+	1.42442i	−0.409013	+	0.0819659i
$303$	10.2335	+	24.7019i	0.587900	+	1.41909i
$304$	12.2023	+	12.0635i	0.699848	+	0.691888i
$305$	−22.6105			−1.29467
$306$	2.06411	+	1.37459i	0.117997	+	0.0785798i
$307$			8.30199i			0.473820i	0.971532	+	0.236910i	$0.0761346\pi$
$307$			8.30199i			0.473820i	−0.971532	+	0.236910i	$0.923865\pi$
$308$	−3.72042	+	1.55353i	−0.211990	+	0.0885204i
$309$	7.99624	−	3.31268i	0.454890	−	0.188452i
$310$	−4.70669	−	23.4866i	−0.267322	−	1.33395i
$311$	−5.46540			−0.309914			−0.154957	−	0.987921i	$-0.549524\pi$
$311$	−5.46540			−0.309914			−0.154957	+	0.987921i	$0.549524\pi$
$312$	−13.6219	+	11.2447i	−0.771190	+	0.636606i
$313$	5.46660			0.308991			0.154495	−	0.987994i	$-0.450625\pi$
$313$	5.46660			0.308991			0.154495	+	0.987994i	$0.450625\pi$
$314$	2.00920	+	10.0260i	0.113386	+	0.565800i
$315$	−13.3529	−	13.3499i	−0.752352	−	0.752181i
$316$	8.40541	+	20.1294i	0.472841	+	1.13237i
$317$		−	1.11720i		−	0.0627481i	−0.999508	−	0.0313741i	$-0.990012\pi$
$317$		−	1.11720i		−	0.0627481i	0.999508	−	0.0313741i	$-0.00998831\pi$
$318$	−1.09605	−	1.63509i	−0.0614636	−	0.0916913i
$319$	−6.61168			−0.370183
$320$	17.6941	+	7.15192i	0.989132	+	0.399805i
$321$	−30.6425	+	12.6946i	−1.71030	+	0.708543i
$322$	−16.0965	+	3.22573i	−0.897025	+	0.179763i
$323$	−2.50742			−0.139517
$324$	−6.93962	−	16.6085i	−0.385534	−	0.922693i
$325$	0.726889	−	2.38351i	0.0403205	−	0.132214i
$326$	4.10882	+	20.5032i	0.227567	+	1.13557i
$327$	−4.67703	−	11.2895i	−0.258640	−	0.624312i
$328$	0.327256	−	0.220702i	0.0180697	−	0.0121862i
$329$			2.34801i			0.129450i
$330$	3.70877	−	2.48611i	0.204161	−	0.136856i
$331$		−	21.5940i		−	1.18691i	−0.804866	−	0.593456i	$-0.797763\pi$
$331$		−	21.5940i		−	1.18691i	0.804866	−	0.593456i	$-0.202237\pi$
$332$	−27.0884	+	11.3112i	−1.48667	+	0.620785i
$333$	16.1939	−	16.1976i	0.887420	−	0.887623i
$334$	5.09344	+	25.4164i	0.278700	+	1.39073i
$335$	27.5397			1.50465
$336$	−16.9273	−	6.89724i	−0.923461	−	0.376275i
$337$	−23.6501			−1.28830			−0.644152	−	0.764898i	$-0.722790\pi$
$337$	−23.6501			−1.28830			−0.644152	+	0.764898i	$0.722790\pi$
$338$	16.9745	+	7.06157i	0.923292	+	0.384099i
$339$	17.9672	−	7.44346i	0.975845	−	0.404273i
$340$	−2.57353	+	1.07462i	−0.139569	+	0.0582797i
$341$	−5.42496			−0.293778
$342$	15.1480	+	10.0878i	0.819111	+	0.545485i
$343$	−18.5721			−1.00280
$344$	14.4813	−	9.76623i	0.780781	−	0.526560i
$345$	16.7962	−	6.95833i	0.904276	−	0.374624i
$346$	−21.4057	+	4.28969i	−1.15078	+	0.230615i
$347$			6.66848i			0.357983i	0.983851	+	0.178991i	$0.0572834\pi$
$347$			6.66848i			0.357983i	−0.983851	+	0.178991i	$0.942717\pi$
$348$	−21.2574	−	21.1337i	−1.13951	−	1.13289i
$349$	34.9112			1.86875			0.934376	−	0.356289i	$-0.115958\pi$
$349$	34.9112			1.86875			0.934376	+	0.356289i	$0.115958\pi$
$350$	2.52839	−	0.506687i	0.135148	−	0.0270836i
$351$	−11.9043	+	14.4668i	−0.635405	+	0.772179i
$352$	2.37559	−	3.61095i	0.126619	−	0.192464i
$353$	4.70688			0.250522			0.125261	−	0.992124i	$-0.460023\pi$
$353$	4.70688			0.250522			0.125261	+	0.992124i	$0.460023\pi$
$354$	12.4537	+	18.5784i	0.661905	+	0.987429i
$355$	6.12313			0.324982
$356$	10.4941	−	4.38200i	0.556187	−	0.232246i
$357$	2.46768	−	1.02231i	0.130604	−	0.0541065i
$358$	0.644297	+	3.21506i	0.0340521	+	0.169921i
$359$			17.1329i			0.904242i	0.891957	+	0.452121i	$0.149332\pi$
$359$			17.1329i			0.904242i	−0.891957	+	0.452121i	$0.850668\pi$
$360$	19.8708	+	3.86166i	1.04728	+	0.203527i
$361$	0.598561			0.0315032
$362$	5.68613	+	28.3740i	0.298856	+	1.49131i
$363$	6.90508	+	16.6676i	0.362422	+	0.874824i
$364$	1.89087	+	18.9307i	0.0991084	+	0.992241i
$365$	31.9396			1.67180
$366$	−19.2841	+	12.9268i	−1.00800	+	0.675693i
$367$		−	3.48197i		−	0.181757i	−0.995862	−	0.0908787i	$-0.971032\pi$
$367$		−	3.48197i		−	0.181757i	0.995862	−	0.0908787i	$-0.0289676\pi$
$368$	12.3735	−	12.5159i	0.645013	−	0.652434i
$369$	0.296008	−	0.296076i	0.0154096	−	0.0154131i
$370$	5.06122	+	25.2557i	0.263120	+	1.31298i
$371$	−2.12018			−0.110074
$372$	−17.4419	−	17.3405i	−0.904322	−	0.899061i
$373$		−	22.5462i		−	1.16740i	−0.811970	−	0.583699i	$-0.801605\pi$
$373$		−	22.5462i		−	1.16740i	0.811970	−	0.583699i	$-0.198395\pi$
$374$	0.124109	+	0.619310i	0.00641753	+	0.0320237i
$375$	16.4486	−	6.81433i	0.849401	−	0.351890i
$376$	−1.40746	−	2.08698i	−0.0725844	−	0.107628i
$377$	−9.10084	+	29.8423i	−0.468717	+	1.53695i
$378$	−19.0209	−	3.75184i	−0.978328	−	0.192974i
$379$		−	24.4044i		−	1.25357i	−0.779193	−	0.626784i	$-0.784371\pi$
$379$		−	24.4044i		−	1.25357i	0.779193	−	0.626784i	$-0.215629\pi$
$380$	−18.8866	+	7.88644i	−0.968862	+	0.404566i
$381$	−5.07944	+	2.10431i	−0.260228	+	0.107807i
$382$	30.0986	−	6.03174i	1.53998	−	0.308611i
$383$		−	10.6604i		−	0.544722i	−0.962195	−	0.272361i	$-0.912196\pi$
$383$		−	10.6604i		−	0.544722i	0.962195	−	0.272361i	$-0.0878045\pi$
$384$	19.1799	−	4.01624i	0.978772	−	0.204953i
$385$		−	4.80908i		−	0.245093i
$386$	1.21225	+	6.04917i	0.0617018	+	0.307895i
$387$	13.0986	−	13.1016i	0.665839	−	0.665991i
$388$	8.08911	+	19.3720i	0.410662	+	0.983462i
$389$	−29.1201			−1.47645			−0.738224	−	0.674555i	$-0.764335\pi$
$389$	−29.1201			−1.47645			−0.738224	+	0.674555i	$0.764335\pi$
$390$	−6.11616	−	20.1619i	−0.309704	−	1.02094i
$391$			2.57186i			0.130065i
$392$	0.0925140	−	0.0623915i	0.00467266	−	0.00315125i
$393$	−10.2734	+	4.25605i	−0.518222	+	0.214689i
$394$	−6.55197	−	32.6946i	−0.330084	−	1.64713i
$395$	−26.0197			−1.30919
$396$	1.74181	−	4.24073i	0.0875292	−	0.213105i
$397$	6.54151			0.328309			0.164154	−	0.986435i	$-0.447510\pi$
$397$	6.54151			0.328309			0.164154	+	0.986435i	$0.447510\pi$
$398$	3.03085	+	15.1240i	0.151923	+	0.758100i
$399$	18.1098	−	7.50253i	0.906623	−	0.375596i
$400$	−1.94359	+	1.96595i	−0.0971793	+	0.0982973i
$401$	28.2966			1.41307			0.706533	−	0.707681i	$-0.250258\pi$
$401$	28.2966			1.41307			0.706533	+	0.707681i	$0.250258\pi$
$402$	23.4882	−	15.7449i	1.17148	−	0.785283i
$403$	−7.46735	+	24.4859i	−0.371975	+	1.21973i
$404$	−28.4901	+	11.8965i	−1.41743	+	0.591875i
$405$	21.4705	−	0.00489951i	1.06688	−	0.000243459i
$406$	−31.6561	+	6.34386i	−1.57107	+	0.314840i
$407$	5.83359			0.289160
$408$	−1.58055	+	2.38786i	−0.0782488	+	0.118217i
$409$			30.6927i			1.51766i	0.651290	+	0.758829i	$0.274228\pi$
$409$			30.6927i			1.51766i	−0.651290	+	0.758829i	$0.725772\pi$
$410$	0.0925140	+	0.461648i	0.00456894	+	0.0227992i
$411$	4.44101	+	10.7198i	0.219059	+	0.528770i
$412$	3.85102	+	9.22250i	0.189726	+	0.454360i
$413$	24.0902			1.18540
$414$	10.3470	−	15.5373i	0.508529	−	0.763617i
$415$		−	35.0149i		−	1.71881i
$416$	−13.0283	−	15.6928i	−0.638765	−	0.769402i
$417$	−6.90874	−	16.6765i	−0.338322	−	0.816651i
$418$	0.910810	+	4.54498i	0.0445492	+	0.222302i
$419$			4.78509i			0.233767i	0.993146	+	0.116883i	$0.0372904\pi$
$419$			4.78509i			0.233767i	−0.993146	+	0.116883i	$0.962710\pi$
$420$	15.3718	−	15.4618i	0.750069	−	0.754458i
$421$	−4.18333			−0.203883			−0.101942	−	0.994790i	$-0.532505\pi$
$421$	−4.18333			−0.203883			−0.101942	+	0.994790i	$0.532505\pi$
$422$	−27.1752	+	5.44589i	−1.32287	+	0.265102i
$423$	−1.88814	−	1.88771i	−0.0918044	−	0.0917835i
$424$	1.88449	−	1.27090i	0.0915187	−	0.0617203i
$425$		−	0.403979i		−	0.0195959i
$426$	5.22233	−	3.50069i	0.253023	−	0.169609i
$427$			25.0053i			1.21009i
$428$	−14.7576	−	35.3417i	−0.713333	−	1.70831i
$429$	−4.74939	+	0.460945i	−0.229303	+	0.0222546i
$430$	4.09381	+	20.4283i	0.197421	+	0.985139i
$431$			19.8528i			0.956274i	0.878285	+	0.478137i	$0.158688\pi$
$431$			19.8528i			0.956274i	−0.878285	+	0.478137i	$0.841312\pi$
$432$	19.1553	−	8.06690i	0.921609	−	0.388119i
$433$	24.3561			1.17048			0.585240	−	0.810860i	$-0.301000\pi$
$433$	24.3561			1.17048			0.585240	+	0.810860i	$0.301000\pi$
$434$	−25.9742	+	5.20521i	−1.24680	+	0.249858i
$435$	33.0321	−	13.6845i	1.58377	−	0.656123i
$436$	13.0208	−	5.43708i	0.623584	−	0.260389i
$437$			18.8743i			0.902882i
$438$	27.2408	−	18.2604i	1.30162	−	0.872515i
$439$			16.7139i			0.797712i	0.917014	+	0.398856i	$0.130593\pi$
$439$			16.7139i			0.797712i	−0.917014	+	0.398856i	$0.869407\pi$
$440$	2.88270	+	4.27446i	0.137427	+	0.203777i
$441$	0.0836803	−	0.0836994i	0.00398478	−	0.00398569i
$442$	2.96613	+	0.292292i	0.141084	+	0.0139029i
$443$		−	27.4553i		−	1.30444i	−0.758030	−	0.652219i	$-0.773838\pi$
$443$		−	27.4553i		−	1.30444i	0.758030	−	0.652219i	$-0.226162\pi$
$444$	18.7557	+	18.6466i	0.890107	+	0.884929i
$445$			13.5649i			0.643037i
$446$	8.95921	−	1.79542i	0.424231	−	0.0850156i
$447$	7.17013	−	2.97044i	0.339135	−	0.140497i
$448$	7.90944	−	19.5682i	0.373686	−	0.924512i
$449$	−19.3205			−0.911791			−0.455895	−	0.890033i	$-0.650681\pi$
$449$	−19.3205			−0.911791			−0.455895	+	0.890033i	$0.650681\pi$
$450$	−1.62528	+	2.44055i	−0.0766162	+	0.115048i
$451$	0.106632			0.00502111
$452$	8.65308	+	20.7226i	0.407007	+	0.974708i
$453$	−3.39810	−	8.20241i	−0.159657	−	0.385383i
$454$	−15.1675	+	3.03955i	−0.711845	+	0.142653i
$455$	−21.7061	−	6.61960i	−1.01760	−	0.310332i
$456$	−11.5993	+	17.5240i	−0.543187	+	0.820637i
$457$			22.5600i			1.05531i	0.849458	+	0.527656i	$0.176929\pi$
$457$			22.5600i			1.05531i	−0.849458	+	0.527656i	$0.823071\pi$
$458$	−30.8096	+	6.17423i	−1.43964	+	0.288503i
$459$	−1.16183	+	2.80627i	−0.0542297	+	0.130986i
$460$	8.08911	+	19.3720i	0.377157	+	0.903222i
$461$		−	17.8735i		−	0.832451i	−0.909261	−	0.416226i	$-0.863353\pi$
$461$		−	17.8735i		−	0.832451i	0.909261	−	0.416226i	$-0.136647\pi$
$462$	−2.74943	−	4.10159i	−0.127915	−	0.190823i
$463$	−4.69526			−0.218207			−0.109104	−	0.994030i	$-0.534798\pi$
$463$	−4.69526			−0.218207			−0.109104	+	0.994030i	$0.534798\pi$
$464$	24.3342	−	24.6142i	1.12969	−	1.14269i
$465$	27.1032	−	11.2283i	1.25688	−	0.520701i
$466$	−4.57117	−	22.8103i	−0.211756	−	1.05667i
$467$			11.7976i			0.545926i	0.962025	+	0.272963i	$0.0880036\pi$
$467$			11.7976i			0.545926i	−0.962025	+	0.272963i	$0.911996\pi$
$468$	−16.7432	−	13.6991i	−0.773956	−	0.633239i
$469$		−	30.4566i		−	1.40636i
$470$	2.94403	−	0.589981i	0.135798	−	0.0272138i
$471$	−11.5699	+	4.79317i	−0.533112	+	0.220858i
$472$	−21.4121	+	14.4403i	−0.985570	+	0.664670i
$473$	4.71855			0.216959
$474$	−22.1918	+	14.8759i	−1.01930	+	0.683271i
$475$		−	2.96471i		−	0.136030i
$476$	1.18845	+	2.84611i	0.0544723	+	0.130451i
$477$	1.70455	−	1.70493i	0.0780458	−	0.0780636i
$478$	7.83779	+	39.1109i	0.358492	+	1.78889i
$479$			33.8258i			1.54554i	0.634687	+	0.772770i	$0.281129\pi$
$479$			33.8258i			1.54554i	−0.634687	+	0.772770i	$0.718871\pi$
$480$	−4.39474	+	22.9572i	−0.200591	+	1.04785i
$481$	8.02982	−	26.3303i	0.366128	−	1.20056i
$482$	2.38406	+	11.8965i	0.108591	+	0.541873i
$483$	−7.69534	−	18.5752i	−0.350150	−	0.845200i
$484$	−19.2237	+	8.02720i	−0.873805	+	0.364873i
$485$	−25.0406			−1.13703
$486$	18.3091	−	12.2792i	0.830516	−	0.556995i
$487$	12.4952			0.566211			0.283106	−	0.959089i	$-0.408635\pi$
$487$	12.4952			0.566211			0.283106	+	0.959089i	$0.408635\pi$
$488$	−14.9889	−	22.2255i	−0.678516	−	1.00610i
$489$	−23.6604	+	9.80204i	−1.06996	+	0.443264i
$490$	0.0261533	+	0.130506i	0.00118149	+	0.00589566i
$491$		−	11.0921i		−	0.500582i	−0.968171	−	0.250291i	$-0.919474\pi$
$491$		−	11.0921i		−	0.500582i	0.968171	−	0.250291i	$-0.0805262\pi$
$492$	0.342836	+	0.340841i	0.0154562	+	0.0153663i
$493$			5.05793i			0.227798i
$494$	21.7678	+	2.14507i	0.979379	+	0.0965112i
$495$	3.86719	+	3.86631i	0.173817	+	0.173778i
$496$	19.9665	−	20.1962i	0.896523	−	0.906838i
$497$		−	6.77168i		−	0.303751i
$498$	−20.0186	−	29.8637i	−0.897054	−	1.33823i
$499$			8.57057i			0.383671i	0.981427	+	0.191836i	$0.0614441\pi$
$499$			8.57057i			0.383671i	−0.981427	+	0.191836i	$0.938556\pi$
$500$	7.92171	+	18.9711i	0.354270	+	0.848412i
$501$	−29.3302	+	12.1509i	−1.31038	+	0.542864i
$502$	1.10467	+	5.51235i	0.0493039	+	0.246028i
$503$	18.9134			0.843307			0.421654	−	0.906757i	$-0.361450\pi$
$503$	18.9134			0.843307			0.421654	+	0.906757i	$0.361450\pi$
$504$	4.27068	−	21.9755i	0.190231	−	0.978865i
$505$		−	36.8268i		−	1.63877i
$506$	4.66178	−	0.934217i	0.207241	−	0.0415310i
$507$	−4.45693	+	22.0712i	−0.197939	+	0.980214i
$508$	−2.44628	−	5.85840i	−0.108536	−	0.259925i
$509$		−	21.7567i		−	0.964349i	−0.876075	−	0.482174i	$-0.839847\pi$
$509$		−	21.7567i		−	0.964349i	0.876075	−	0.482174i	$-0.160153\pi$
$510$	−1.90187	−	2.83721i	−0.0842161	−	0.125634i
$511$		−	35.3226i		−	1.56258i
$512$	4.69961	+	22.1340i	0.207695	+	0.978194i
$513$	−8.52644	+	20.5946i	−0.376452	+	0.909275i
$514$	3.77262	+	18.8255i	0.166403	+	0.830359i
$515$	−11.9212			−0.525310
$516$	15.1707	+	15.0825i	0.667854	+	0.663970i
$517$		−	0.680016i		−	0.0299071i
$518$	27.9307	−	5.59729i	1.22720	−	0.245931i
$519$	−10.2335	−	24.7019i	−0.449202	−	1.08429i
$520$	23.2610	−	7.12755i	1.02006	−	0.312564i
$521$		−	35.7964i		−	1.56827i	−0.620591	−	0.784134i	$-0.713107\pi$
$521$		−	35.7964i		−	1.56827i	0.620591	−	0.784134i	$-0.286893\pi$
$522$	20.3489	−	30.5563i	0.890647	−	1.33741i
$523$	10.4148			0.455406			0.227703	−	0.973731i	$-0.426879\pi$
$523$	10.4148			0.455406			0.227703	+	0.973731i	$0.426879\pi$
$524$	−4.94769	−	11.8488i	−0.216141	−	0.517619i
$525$	1.20876	+	2.91773i	0.0527545	+	0.127340i
$526$	−13.6797	+	2.74140i	−0.596463	+	0.119531i
$527$			4.15009i			0.180781i
$528$	4.90239	+	1.99754i	0.213349	+	0.0869316i
$529$	−3.64062			−0.158288
$530$	0.532736	+	2.65837i	0.0231406	+	0.115472i
$531$	−19.3675	+	19.3720i	−0.840480	+	0.840672i
$532$	8.72175	+	20.8870i	0.378136	+	0.905567i
$533$	0.146777	−	0.481291i	0.00635762	−	0.0208470i
$534$	7.75526	+	11.5693i	0.335603	+	0.500652i
$535$	45.6833			1.97506
$536$	18.2566	+	27.0708i	0.788563	+	1.16928i
$537$	−3.71014	+	1.53704i	−0.160104	+	0.0663281i
$538$	−18.6104	+	3.72951i	−0.802352	+	0.160791i
$539$	0.0301445			0.00129841
$540$	0.0751416	+	24.7919i	0.00323358	+	1.06687i
$541$	−42.8351			−1.84162			−0.920812	−	0.390006i	$-0.872473\pi$
$541$	−42.8351			−1.84162			−0.920812	+	0.390006i	$0.872473\pi$
$542$	14.9574	−	2.99744i	0.642473	−	0.128751i
$543$	−32.7432	+	13.5649i	−1.40515	+	0.582125i
$544$	−2.76237	−	1.81733i	−0.118436	−	0.0779172i
$545$			16.8310i			0.720959i
$546$	−22.2973	+	6.76396i	−0.954238	+	0.289471i
$547$	−6.86925			−0.293708			−0.146854	−	0.989158i	$-0.546915\pi$
$547$	−6.86925			−0.293708			−0.146854	+	0.989158i	$0.546915\pi$
$548$	−12.3638	+	5.16271i	−0.528154	+	0.220540i
$549$	−20.1079	−	20.1033i	−0.858184	−	0.857988i
$550$	−0.732256	+	0.146744i	−0.0312235	+	0.00625717i
$551$			37.1190i			1.58132i
$552$	17.9743	+	11.8974i	0.765039	+	0.506387i
$553$			28.7756i			1.22366i
$554$	−1.37172	−	6.84491i	−0.0582786	−	0.290812i
$555$	−29.1447	+	12.0741i	−1.23712	+	0.512516i
$556$	19.2339	−	8.03146i	0.815699	−	0.340610i
$557$			31.9362i			1.35318i	0.736360	+	0.676590i	$0.236543\pi$
$557$			31.9362i			1.35318i	−0.736360	+	0.676590i	$0.763457\pi$
$558$	16.6965	−	25.0718i	0.706820	−	1.06137i
$559$	6.49499	−	21.2975i	0.274709	−	0.900788i
$560$	17.9034	+	17.6998i	0.756557	+	0.747952i
$561$	−0.714675	+	0.296076i	−0.0301736	+	0.0125003i
$562$	−1.59825	+	0.320289i	−0.0674183	+	0.0135106i
$563$			6.16766i			0.259936i	0.991518	+	0.129968i	$0.0414874\pi$
$563$			6.16766i			0.259936i	−0.991518	+	0.129968i	$0.958513\pi$
$564$	2.17362	−	2.18633i	0.0915258	−	0.0920613i
$565$	−26.7864			−1.12691
$566$	7.15867	−	1.43459i	0.300901	−	0.0603004i
$567$	−0.00541845	−	23.7446i	−0.000227554	−	0.997178i
$568$	4.05914	+	6.01888i	0.170318	+	0.252546i
$569$		−	0.180544i		−	0.00756881i	−0.999993	−	0.00378441i	$-0.998795\pi$
$569$		−	0.180544i		−	0.00756881i	0.999993	−	0.00378441i	$-0.00120462\pi$
$570$	−13.9574	−	20.8216i	−0.584611	−	0.872122i
$571$	0.551781			0.0230913			0.0115457	−	0.999933i	$-0.496325\pi$
$571$	0.551781			0.0230913			0.0115457	+	0.999933i	$0.496325\pi$
$572$	−0.547621	−	5.48261i	−0.0228972	−	0.229239i
$573$	14.3894	+	34.7334i	0.601125	+	1.45101i
$574$	0.510545	−	0.102313i	0.0213097	−	0.00427045i
$575$	−3.04090			−0.126814
$576$	9.37681	+	22.0924i	0.390700	+	0.920518i
$577$		−	32.0177i		−	1.33292i	−0.745543	−	0.666458i	$-0.767810\pi$
$577$		−	32.0177i		−	1.33292i	0.745543	−	0.666458i	$-0.232190\pi$
$578$	−23.0992	+	4.62906i	−0.960799	+	0.192543i
$579$	−6.98066	+	2.89195i	−0.290106	+	0.120185i
$580$	15.9084	+	38.0977i	0.660559	+	1.58192i
$581$	−38.7236			−1.60653
$582$	−21.3567	+	14.3161i	−0.885265	+	0.593421i
$583$	0.614035			0.0254307
$584$	21.1734	+	31.3958i	0.876160	+	1.29917i
$585$	22.7740	−	12.1329i	0.941588	−	0.501635i
$586$	1.65626	+	8.26480i	0.0684195	+	0.341416i
$587$	22.7316			0.938232			0.469116	−	0.883137i	$-0.344573\pi$
$587$	22.7316			0.938232			0.469116	+	0.883137i	$0.344573\pi$
$588$	0.0969182	+	0.0963544i	0.00399684	+	0.00397359i
$589$			30.4566i			1.25494i
$590$	−6.05310	−	30.2052i	−0.249202	−	1.24353i
$591$	37.7291	−	15.6304i	1.55197	−	0.642950i
$592$	−21.4705	+	21.7175i	−0.882431	+	0.892583i
$593$	13.2588			0.544474			0.272237	−	0.962230i	$-0.412237\pi$
$593$	13.2588			0.544474			0.272237	+	0.962230i	$0.412237\pi$
$594$	5.50871	+	1.08658i	0.226025	+	0.0445831i
$595$	−3.67894			−0.150822
$596$	3.45316	+	8.26970i	0.141447	+	0.338740i
$597$	−17.4529	+	7.23041i	−0.714301	+	0.295921i
$598$	2.20019	−	22.3272i	0.0899726	−	0.913026i
$599$	−14.6334			−0.597906			−0.298953	−	0.954268i	$-0.596637\pi$
$599$	−14.6334			−0.597906			−0.298953	+	0.954268i	$0.596637\pi$
$600$	−2.82335	−	1.86880i	−0.115263	−	0.0762935i
$601$	23.6583			0.965044			0.482522	−	0.875884i	$-0.339721\pi$
$601$	23.6583			0.965044			0.482522	+	0.875884i	$0.339721\pi$
$602$	22.5920	−	4.52742i	0.920781	−	0.184524i
$603$	24.4915	+	24.4859i	0.997372	+	0.997144i
$604$	9.46030	−	3.95032i	0.384934	−	0.160736i
$605$		−	24.8489i		−	1.01025i
$606$	−21.0545	−	31.4090i	−0.855279	−	1.27591i
$607$			15.9152i			0.645977i	0.946403	+	0.322988i	$0.104687\pi$
$607$			15.9152i			0.645977i	−0.946403	+	0.322988i	$0.895313\pi$
$608$	−20.2724	−	13.3370i	−0.822156	−	0.540885i
$609$	−15.1340	−	36.5307i	−0.613259	−	1.48030i
$610$	31.3527	−	6.28305i	1.26943	−	0.254393i
$611$	−3.06930	−	0.936028i	−0.124170	−	0.0378676i
$612$	−3.24415	−	1.33248i	−0.131137	−	0.0538624i
$613$	8.36313			0.337784			0.168892	−	0.985635i	$-0.445981\pi$
$613$	8.36313			0.337784			0.168892	+	0.985635i	$0.445981\pi$
$614$	−2.30698	−	11.5119i	−0.0931020	−	0.464583i
$615$	−0.532736	+	0.220702i	−0.0214820	+	0.00889957i
$616$	4.72720	−	3.18803i	0.190464	−	0.128449i
$617$	4.84880			0.195205			0.0976026	−	0.995225i	$-0.468883\pi$
$617$	4.84880			0.195205			0.0976026	+	0.995225i	$0.468883\pi$
$618$	−10.1674	+	6.81553i	−0.408993	+	0.274161i
$619$			9.89555i			0.397736i	0.980026	+	0.198868i	$0.0637264\pi$
$619$			9.89555i			0.397736i	−0.980026	+	0.198868i	$0.936274\pi$
$620$	13.0530	+	31.2596i	0.524222	+	1.25542i
$621$	21.1239	+	8.74556i	0.847672	+	0.350947i
$622$	7.57857	−	1.51874i	0.303873	−	0.0608959i
$623$	15.0016			0.601028
$624$	15.7641	−	19.3777i	0.631067	−	0.775728i
$625$	−27.9780			−1.11912
$626$	−7.58023	+	1.51907i	−0.302967	+	0.0607143i
$627$	−5.24484	+	2.17284i	−0.209459	+	0.0867747i
$628$	−5.57210	−	13.3442i	−0.222351	−	0.532491i
$629$		−	4.46269i		−	0.177939i
$630$	22.2255	+	14.8010i	0.885483	+	0.589686i
$631$	13.4569			0.535713			0.267856	−	0.963459i	$-0.413685\pi$
$631$	13.4569			0.535713			0.267856	+	0.963459i	$0.413685\pi$
$632$	−17.2489	−	25.5767i	−0.686125	−	1.01738i
$633$	−12.9918	−	31.3598i	−0.516376	−	1.24644i
$634$	0.310450	+	1.54916i	0.0123295	+	0.0615249i
$635$	7.57268			0.300513
$636$	1.97420	+	1.96271i	0.0782820	+	0.0778267i
$637$	0.0414932	−	0.136059i	0.00164402	−	0.00539086i
$638$	9.16805	−	1.83727i	0.362966	−	0.0727382i
$639$	5.44541	+	5.44416i	0.215417	+	0.215368i
$640$	−26.5228	−	5.00029i	−1.04841	−	0.197654i
$641$			0.939589i			0.0371115i	0.999828	+	0.0185558i	$0.00590683\pi$
$641$			0.939589i			0.0371115i	−0.999828	+	0.0185558i	$0.994093\pi$
$642$	38.9626	−	26.1179i	1.53773	−	1.03079i
$643$		−	42.1553i		−	1.66244i	−0.555943	−	0.831221i	$-0.687643\pi$
$643$		−	42.1553i		−	1.66244i	0.555943	−	0.831221i	$-0.312357\pi$
$644$	21.4238	−	8.94589i	0.844216	−	0.352517i
$645$	−23.5740	+	9.76623i	−0.928224	+	0.384545i
$646$	3.47690	−	0.696769i	0.136797	−	0.0274140i
$647$	−33.5469			−1.31886			−0.659432	−	0.751765i	$-0.729203\pi$
$647$	−33.5469			−1.31886			−0.659432	+	0.751765i	$0.729203\pi$
$648$	14.2380	+	21.1017i	0.559321	+	0.828951i
$649$	−6.97684			−0.273865
$650$	−0.345599	+	3.50708i	−0.0135555	+	0.137559i
$651$	−12.4176	−	29.9739i	−0.486684	−	1.17477i
$652$	−11.3950	−	27.2889i	−0.446261	−	1.06871i
$653$	−11.6194			−0.454700			−0.227350	−	0.973813i	$-0.573006\pi$
$653$	−11.6194			−0.454700			−0.227350	+	0.973813i	$0.573006\pi$
$654$	9.62253	+	14.3549i	0.376271	+	0.561320i
$655$	15.3160			0.598446
$656$	−0.392459	+	0.396974i	−0.0153229	+	0.0154992i
$657$	28.4044	+	28.3980i	1.10816	+	1.10791i
$658$	−0.652470	−	3.25585i	−0.0254359	−	0.126926i
$659$		−	17.4797i		−	0.680912i	−0.940261	−	0.340456i	$-0.889419\pi$
$659$		−	17.4797i		−	0.680912i	0.940261	−	0.340456i	$-0.110581\pi$
$660$	−4.45190	+	4.47795i	−0.173290	+	0.174304i
$661$	−41.5530			−1.61623			−0.808113	−	0.589028i	$-0.799511\pi$
$661$	−41.5530			−1.61623			−0.808113	+	0.589028i	$0.799511\pi$
$662$	6.00059	+	29.9432i	0.233219	+	1.16377i
$663$	0.352622	+	3.63328i	0.0136947	+	0.141105i
$664$	34.4187	−	23.2120i	1.33571	−	0.900802i
$665$	−26.9989			−1.04697
$666$	−17.9541	+	26.9603i	−0.695709	+	1.04469i
$667$	38.0730			1.47419
$668$	−14.1256	−	33.8282i	−0.546535	−	1.30885i
$669$	4.28317	+	10.3388i	0.165597	+	0.399722i
$670$	−38.1877	+	7.65279i	−1.47532	+	0.295653i
$671$		−	7.24189i		−	0.279570i
$672$	25.3888	+	4.86021i	0.979394	+	0.187487i
$673$	−23.7494			−0.915473			−0.457736	−	0.889088i	$-0.651340\pi$
$673$	−23.7494			−0.915473			−0.457736	+	0.889088i	$0.651340\pi$
$674$	32.7943	−	6.57195i	1.26319	−	0.253142i
$675$	−3.31807	−	1.37372i	−0.127712	−	0.0528746i
$676$	−25.4999	−	5.07497i	−0.980765	−	0.195191i
$677$	−0.998225			−0.0383649			−0.0191824	−	0.999816i	$-0.506106\pi$
$677$	−0.998225			−0.0383649			−0.0191824	+	0.999816i	$0.506106\pi$
$678$	−22.8457	+	15.3142i	−0.877384	+	0.588138i
$679$			27.6928i			1.06275i
$680$	3.26995	−	2.20526i	0.125397	−	0.0845679i
$681$	−7.25118	−	17.5031i	−0.277866	−	0.670719i
$682$	7.52249	−	1.50750i	0.288051	−	0.0577252i
$683$	20.6883			0.791615			0.395808	−	0.918333i	$-0.370465\pi$
$683$	20.6883			0.791615			0.395808	+	0.918333i	$0.370465\pi$
$684$	−23.8081	−	9.77880i	−0.910326	−	0.373902i
$685$		−	15.9816i		−	0.610626i
$686$	25.7529	−	5.16085i	0.983249	−	0.197042i
$687$	−14.7293	−	35.5539i	−0.561957	−	1.35647i
$688$	−17.3666	+	17.5664i	−0.662095	+	0.669712i
$689$	0.845206	−	2.77149i	0.0321998	−	0.105585i
$690$	−21.3567	+	14.3161i	−0.813037	+	0.545004i
$691$		−	28.8484i		−	1.09744i	−0.836005	−	0.548722i	$-0.815115\pi$
$691$		−	28.8484i		−	1.09744i	0.836005	−	0.548722i	$-0.184885\pi$
$692$	28.4901	−	11.8965i	1.08303	−	0.452239i
$693$	4.27582	−	4.27680i	0.162425	−	0.162462i
$694$	−1.85305	−	9.24681i	−0.0703409	−	0.351004i
$695$			24.8621i			0.943073i
$696$	35.3491	+	23.3979i	1.33990	+	0.886895i
$697$		−	0.0815735i		−	0.00308982i
$698$	−48.4094	+	9.70120i	−1.83232	+	0.367196i
$699$	26.3228	−	10.9050i	0.995621	−	0.412466i
$700$	−3.36517	+	1.40519i	−0.127192	+	0.0531111i
$701$	1.46047			0.0551611			0.0275805	−	0.999620i	$-0.491220\pi$
$701$	1.46047			0.0551611			0.0275805	+	0.999620i	$0.491220\pi$
$702$	12.4870	−	23.3682i	0.471291	−	0.881978i
$703$		−	32.7507i		−	1.23522i
$704$	−2.29068	+	5.66723i	−0.0863333	+	0.213592i
$705$	1.40746	+	3.39737i	0.0530081	+	0.127952i
$706$	−6.52676	+	1.30796i	−0.245638	+	0.0492256i
$707$	−40.7274			−1.53171
$708$	−22.4314	−	22.3009i	−0.843024	−	0.838120i
$709$	−21.9297			−0.823586			−0.411793	−	0.911277i	$-0.635097\pi$
$709$	−21.9297			−0.823586			−0.411793	+	0.911277i	$0.635097\pi$
$710$	−8.49060	+	1.70151i	−0.318647	+	0.0638566i
$711$	−23.1398	−	23.1345i	−0.867809	−	0.867611i
$712$	−13.3339	+	8.99241i	−0.499710	+	0.337005i
$713$	31.2393			1.16992
$714$	−3.13771	+	2.10331i	−0.117426	+	0.0787144i
$715$	6.28639	+	1.91713i	0.235097	+	0.0716965i
$716$	−1.78682	−	4.27911i	−0.0667766	−	0.159918i
$717$	−45.1334	+	18.6979i	−1.68554	+	0.698286i
$718$	−4.76094	−	23.7573i	−0.177677	−	0.886614i
$719$	15.0016			0.559467			0.279733	−	0.960078i	$-0.409754\pi$
$719$	15.0016			0.559467			0.279733	+	0.960078i	$0.409754\pi$
$720$	−28.6268	+	0.166999i	−1.06686	+	0.00622367i
$721$			13.1838i			0.490992i
$722$	−0.829991	+	0.166330i	−0.0308891	+	0.00619014i
$723$	−13.7285	+	5.68743i	−0.510567	+	0.211518i
$724$	−15.7693	−	37.7646i	−0.586061	−	1.40351i
$725$	−5.98037			−0.222105
$726$	−14.2065	−	21.1933i	−0.527254	−	0.786556i
$727$			24.4156i			0.905526i	0.891631	+	0.452763i	$0.149562\pi$
$727$			24.4156i			0.905526i	−0.891631	+	0.452763i	$0.850438\pi$
$728$	−7.88248	−	25.7248i	−0.292144	−	0.953423i
$729$	19.0984	+	19.0853i	0.707349	+	0.706865i
$730$	−44.2889	+	8.87546i	−1.63920	+	0.328495i
$731$		−	3.60969i		−	0.133509i
$732$	23.1481	−	23.2836i	0.855579	−	0.860585i
$733$	−12.6996			−0.469071			−0.234536	−	0.972108i	$-0.575357\pi$
$733$	−12.6996			−0.469071			−0.234536	+	0.972108i	$0.575357\pi$
$734$	0.967578	+	4.82825i	0.0357140	+	0.178214i
$735$	−0.150602	+	0.0623915i	−0.00555505	+	0.00230135i
$736$	−13.6797	+	20.7934i	−0.504240	+	0.766455i
$737$			8.82066i			0.324913i
$738$	−0.328184	+	0.492807i	−0.0120806	+	0.0181405i
$739$			20.7156i			0.762037i	0.924567	+	0.381018i	$0.124427\pi$
$739$			20.7156i			0.762037i	−0.924567	+	0.381018i	$0.875573\pi$
$740$	−14.0362	−	33.6142i	−0.515981	−	1.23568i
$741$	2.58782	+	26.6638i	0.0950659	+	0.979520i
$742$	2.93994	−	0.589162i	0.107929	−	0.0216288i
$743$		−	31.3626i		−	1.15058i	−0.817948	−	0.575292i	$-0.804889\pi$
$743$		−	31.3626i		−	1.15058i	0.817948	−	0.575292i	$-0.195111\pi$
$744$	29.0043	+	19.1983i	1.06335	+	0.703842i
$745$	−10.6896			−0.391636
$746$	6.26519	+	31.2635i	0.229385	+	1.14464i
$747$	31.1323	−	31.1394i	1.13907	−	1.13933i
$748$	−0.344191	−	0.824274i	−0.0125849	−	0.0301385i
$749$		−	50.5220i		−	1.84603i
$750$	−20.9148	+	14.0198i	−0.763699	+	0.511931i
$751$		−	37.1565i		−	1.35586i	−0.735127	−	0.677930i	$-0.762877\pi$
$751$		−	37.1565i		−	1.35586i	0.735127	−	0.677930i	$-0.237123\pi$
$752$	2.53159	+	2.50279i	0.0923174	+	0.0912674i
$753$	−6.36118	+	2.63531i	−0.231814	+	0.0960361i
$754$	4.32699	−	43.9096i	0.157580	−	1.59909i
$755$			12.2286i			0.445043i
$756$	27.4177	−	0.0831004i	0.997173	−	0.00302233i
$757$		−	10.7590i		−	0.391043i	−0.980699	−	0.195522i	$-0.937360\pi$
$757$		−	10.7590i		−	0.391043i	0.980699	−	0.195522i	$-0.0626400\pi$
$758$	6.78154	+	33.8401i	0.246317	+	1.22913i
$759$	2.22868	+	5.37963i	0.0808958	+	0.195268i
$760$	23.9975	−	16.1839i	0.870480	−	0.587053i
$761$	−36.7545			−1.33235			−0.666174	−	0.745796i	$-0.732069\pi$
$761$	−36.7545			−1.33235			−0.666174	+	0.745796i	$0.732069\pi$
$762$	6.45863	−	4.32942i	0.233971	−	0.156838i
$763$	18.6136			0.673859
$764$	−40.0600	+	16.7278i	−1.44932	+	0.605189i
$765$	2.95772	−	2.95840i	0.106937	−	0.106961i
$766$	2.96234	+	14.7822i	0.107034	+	0.534103i
$767$	−9.60348	+	31.4904i	−0.346762	+	1.13705i
$768$	−25.4797	+	10.8989i	−0.919419	+	0.393279i
$769$			15.7373i			0.567502i	0.958898	+	0.283751i	$0.0915789\pi$
$769$			15.7373i			0.567502i	−0.958898	+	0.283751i	$0.908421\pi$
$770$	1.33636	+	6.66848i	0.0481590	+	0.240315i
$771$	−21.7244	+	9.00000i	−0.782386	+	0.324127i
$772$	−3.36192	−	8.05118i	−0.120998	−	0.289768i
$773$		−	11.9057i		−	0.428220i	−0.976810	−	0.214110i	$-0.931315\pi$
$773$		−	11.9057i		−	0.428220i	0.976810	−	0.214110i	$-0.0686851\pi$
$774$	−14.5224	+	21.8071i	−0.521996	+	0.783840i
$775$	−4.90696			−0.176263
$776$	−16.5998	−	24.6142i	−0.595900	−	0.883598i
$777$	13.3529	+	32.2316i	0.479034	+	1.15630i
$778$	40.3792	−	8.09197i	1.44767	−	0.290111i
$779$		−	0.598650i		−	0.0214489i
$780$	14.0836	+	26.2577i	0.504272	+	0.940178i
$781$			1.96117i			0.0701762i
$782$	−0.714675	−	3.56626i	−0.0255567	−	0.127529i
$783$	41.5431	+	17.1994i	1.48463	+	0.614656i
$784$	−0.110946	+	0.112223i	−0.00396237	+	0.00400796i
$785$	17.2489			0.615641
$786$	13.0628	−	8.75641i	0.465935	−	0.312331i
$787$			16.1112i			0.574301i	0.957885	+	0.287151i	$0.0927080\pi$
$787$			16.1112i			0.574301i	−0.957885	+	0.287151i	$0.907292\pi$
$788$	18.1705	+	43.5151i	0.647297	+	1.55016i
$789$	−6.53991	−	15.7862i	−0.232827	−	0.562003i
$790$	36.0800	−	7.23041i	1.28367	−	0.257246i
$791$			29.6235i			1.05329i
$792$	−1.23685	+	6.36440i	−0.0439494	+	0.226149i
$793$	−32.6867	−	9.96831i	−1.16074	−	0.353985i
$794$	−9.07075	+	1.81777i	−0.321909	+	0.0645103i
$795$	−3.06773	+	1.27090i	−0.108801	+	0.0450741i
$796$	−8.40541	−	20.1294i	−0.297922	−	0.713469i
$797$	14.7802			0.523542			0.261771	−	0.965130i	$-0.415693\pi$
$797$	14.7802			0.523542			0.261771	+	0.965130i	$0.415693\pi$
$798$	−23.0270	+	15.4357i	−0.815147	+	0.546419i
$799$	−0.520211			−0.0184038
$800$	2.14876	−	3.26616i	0.0759701	−	0.115476i
$801$	−12.0607	+	12.0635i	−0.426145	+	0.426242i
$802$	−39.2373	+	7.86313i	−1.38552	+	0.277657i
$803$			10.2299i			0.361005i
$804$	−28.1945	+	28.3595i	−0.994345	+	1.00016i
$805$			27.6928i			0.976042i
$806$	3.55035	−	36.0283i	0.125056	−	1.26904i
$807$	−8.89716	−	21.4762i	−0.313195	−	0.755997i
$808$	36.1998	−	24.4132i	1.27350	−	0.858852i
$809$		−	18.0231i		−	0.633657i	−0.948483	−	0.316829i	$-0.897382\pi$
$809$		−	18.0231i		−	0.633657i	0.948483	−	0.316829i	$-0.102618\pi$
$810$	−29.7705	+	5.97306i	−1.04603	+	0.209872i
$811$			45.5754i			1.60037i	0.599754	+	0.800185i	$0.295265\pi$
$811$			45.5754i			1.60037i	−0.599754	+	0.800185i	$0.704735\pi$
$812$	42.1329	−	17.5933i	1.47857	−	0.617406i
$813$	7.15072	+	17.2606i	0.250787	+	0.605355i
$814$	−8.08911	+	1.62105i	−0.283523	+	0.0568178i
$815$	35.2741			1.23560
$816$	1.52811	−	3.75032i	0.0534947	−	0.131288i
$817$		−	26.4907i		−	0.926793i
$818$	−8.52897	−	42.5599i	−0.298209	−	1.48807i
$819$	−13.4180	−	25.1861i	−0.468864	−	0.880074i
$820$	−0.256568	−	0.614434i	−0.00895974	−	0.0214570i
$821$		−	43.8260i		−	1.52954i	−0.644305	−	0.764769i	$-0.722853\pi$
$821$		−	43.8260i		−	1.52954i	0.644305	−	0.764769i	$-0.277147\pi$
$822$	−9.13695	−	13.6305i	−0.318688	−	0.475418i
$823$			41.8348i			1.45827i	0.684369	+	0.729135i	$0.260078\pi$
$823$			41.8348i			1.45827i	−0.684369	+	0.729135i	$0.739922\pi$
$824$	−7.90277	−	11.7182i	−0.275306	−	0.408223i
$825$	−0.350073	−	0.845014i	−0.0121880	−	0.0294196i
$826$	−33.4045	+	6.69423i	−1.16229	+	0.232922i
$827$	−32.1625			−1.11840			−0.559200	−	0.829033i	$-0.688892\pi$
$827$	−32.1625			−1.11840			−0.559200	+	0.829033i	$0.688892\pi$
$828$	−10.0301	+	24.4200i	−0.348570	+	0.848652i
$829$			11.0453i			0.383619i	0.981432	+	0.191810i	$0.0614356\pi$
$829$			11.0453i			0.383619i	−0.981432	+	0.191810i	$0.938564\pi$
$830$	9.73003	+	48.5532i	0.337734	+	1.68531i
$831$	7.89894	−	3.27237i	0.274011	−	0.113517i
$832$	22.4264	+	18.1400i	0.777494	+	0.628891i
$833$		−	0.0230605i		−	0.000798998i
$834$	14.2141	+	21.2045i	0.492193	+	0.734253i
$835$	43.7269			1.51323
$836$	−2.52594	−	6.04917i	−0.0873614	−	0.209215i
$837$	34.0866	+	14.1123i	1.17821	+	0.487792i
$838$	−1.32969	−	6.63521i	−0.0459334	−	0.229210i
$839$			32.2336i			1.11283i	0.830905	+	0.556415i	$0.187823\pi$
$839$			32.2336i			1.11283i	−0.830905	+	0.556415i	$0.812177\pi$
$840$	−17.0187	+	25.7115i	−0.587202	+	0.887133i
$841$	45.8758			1.58193
$842$	5.80079	−	1.16247i	0.199908	−	0.0400615i
$843$	−0.764084	−	1.84436i	−0.0263164	−	0.0635233i
$844$	36.1690	−	15.1030i	1.24499	−	0.519867i
$845$	17.3062	−	25.7351i	0.595350	−	0.885315i
$846$	3.14274	+	2.09290i	0.108049	+	0.0719553i
$847$	−27.4808			−0.944253
$848$	−2.25995	+	2.28595i	−0.0776070	+	0.0784998i
$849$	3.42237	+	8.26100i	0.117456	+	0.283517i
$850$	0.112259	+	0.560175i	0.00385044	+	0.0192138i
$851$	−33.5924			−1.15153
$852$	−6.26873	+	6.30541i	−0.214763	+	0.216020i
$853$	22.1165			0.757256			0.378628	−	0.925549i	$-0.376396\pi$
$853$	22.1165			0.757256			0.378628	+	0.925549i	$0.376396\pi$
$854$	−6.94854	−	34.6735i	−0.237774	−	1.18650i
$855$	21.7061	−	21.7110i	0.742333	−	0.742502i
$856$	30.2843	+	44.9055i	1.03510	+	1.53484i
$857$		−	2.33809i		−	0.0798678i	−0.999202	−	0.0399339i	$-0.987285\pi$
$857$		−	2.33809i		−	0.0798678i	0.999202	−	0.0399339i	$-0.0127147\pi$
$858$	6.45762	−	1.95894i	0.220459	−	0.0668770i
$859$	−43.4057			−1.48098			−0.740492	−	0.672065i	$-0.765408\pi$
$859$	−43.4057			−1.48098			−0.740492	+	0.672065i	$0.765408\pi$
$860$	−11.3533	−	27.1892i	−0.387145	−	0.927142i
$861$	0.244078	+	0.589162i	0.00831816	+	0.0200786i
$862$	−5.51673	−	27.5287i	−0.187901	−	0.937631i
$863$		−	42.1353i		−	1.43430i	−0.696917	−	0.717152i	$-0.745445\pi$
$863$		−	42.1353i		−	1.43430i	0.696917	−	0.717152i	$-0.254555\pi$
$864$	−24.3199	+	16.5088i	−0.827380	+	0.561642i
$865$			36.8268i			1.25215i
$866$	−33.7733	+	6.76814i	−1.14766	+	0.229991i
$867$	−11.0431	−	26.6561i	−0.375044	−	0.905290i
$868$	34.5705	−	14.4356i	1.17340	−	0.489975i
$869$		−	8.33382i		−	0.282705i
$870$	−42.0010	+	28.1546i	−1.42397	+	0.954530i
$871$	39.8126	+	12.1415i	1.34900	+	0.411397i
$872$	−16.5444	+	11.1575i	−0.560263	+	0.377842i
$873$	−22.2690	−	22.2639i	−0.753691	−	0.753519i
$874$	−5.24484	−	26.1720i	−0.177410	−	0.885280i
$875$			27.1197i			0.916813i
$876$	−32.6991	+	32.8904i	−1.10480	+	1.11126i
$877$	38.5223			1.30080			0.650402	−	0.759590i	$-0.274600\pi$
$877$	38.5223			1.30080			0.650402	+	0.759590i	$0.274600\pi$
$878$	−4.64451	−	23.1763i	−0.156744	−	0.782161i
$879$	−9.53747	+	3.95119i	−0.321691	+	0.133270i
$880$	−5.18507	−	5.12610i	−0.174789	−	0.172801i
$881$		−	3.54012i		−	0.119270i	−0.998220	−	0.0596348i	$-0.981006\pi$
$881$		−	3.54012i		−	0.119270i	0.998220	−	0.0596348i	$-0.0189936\pi$
$882$	−0.0927762	+	0.139315i	−0.00312394	+	0.00469096i
$883$	−24.1271			−0.811942			−0.405971	−	0.913886i	$-0.633067\pi$
$883$	−24.1271			−0.811942			−0.405971	+	0.913886i	$0.633067\pi$
$884$	−4.19419	+	0.418930i	−0.141066	+	0.0140901i
$885$	34.8564	−	14.4403i	1.17169	−	0.485406i
$886$	7.62933	+	38.0707i	0.256312	+	1.27901i
$887$	34.9805			1.17453			0.587265	−	0.809394i	$-0.300204\pi$
$887$	34.9805			1.17453			0.587265	+	0.809394i	$0.300204\pi$
$888$	−31.1891	−	20.6443i	−1.04664	−	0.692778i
$889$		−	8.37475i		−	0.280880i
$890$	−3.76944	−	18.8097i	−0.126352	−	0.630501i
$891$	0.00156926	+	6.87675i	5.25721e−5	+	0.230380i
$892$	−11.9243	+	4.97922i	−0.399256	+	0.166716i
$893$	−3.81772			−0.127755
$894$	−9.11698	+	6.11140i	−0.304917	+	0.204396i
$895$	5.53126			0.184890
$896$	−5.52990	+	29.3321i	−0.184741	+	0.979916i
$897$	27.3490	−	2.65432i	0.913158	−	0.0886252i
$898$	26.7907	−	5.36883i	0.894016	−	0.179160i
$899$	61.4365			2.04902
$900$	1.57549	−	3.83580i	0.0525165	−	0.127860i
$901$		−	0.469736i		−	0.0156492i
$902$	−0.147861	+	0.0296312i	−0.00492323	+	0.000986611i
$903$	10.8006	+	26.0709i	0.359423	+	0.867584i
$904$	−17.7572	−	26.3303i	−0.590595	−	0.875732i
$905$	48.8152			1.62267
$906$	6.99126	+	10.4296i	0.232269	+	0.346499i
$907$	−49.1062			−1.63054			−0.815272	−	0.579078i	$-0.803413\pi$
$907$	−49.1062			−1.63054			−0.815272	+	0.579078i	$0.803413\pi$
$908$	20.1873	−	8.42955i	0.669938	−	0.279745i
$909$	32.7432	−	32.7507i	1.08602	−	1.08627i
$910$	31.9381	+	3.14729i	1.05874	+	0.104332i
$911$	29.3415			0.972128			0.486064	−	0.873923i	$-0.338432\pi$
$911$	29.3415			0.972128			0.486064	+	0.873923i	$0.338432\pi$
$912$	11.2145	−	27.5228i	0.371349	−	0.911371i
$913$	11.2149			0.371159
$914$	−6.26902	−	31.2827i	−0.207361	−	1.03474i
$915$	14.9889	+	36.1806i	0.495518	+	1.19609i
$916$	41.0063	−	17.1229i	1.35489	−	0.565757i
$917$		−	16.9382i		−	0.559350i
$918$	0.831236	−	4.21415i	0.0274349	−	0.139088i
$919$			30.8671i			1.01821i	0.860704	+	0.509106i	$0.170024\pi$
$919$			30.8671i			1.01821i	−0.860704	+	0.509106i	$0.829976\pi$
$920$	−16.5998	−	24.6142i	−0.547281	−	0.811506i
$921$	13.2846	−	5.50354i	0.437742	−	0.181348i
$922$	4.96673	+	24.7842i	0.163570	+	0.816223i
$923$	8.85188	+	2.69951i	0.291363	+	0.0888556i
$924$	4.95224	+	4.92343i	0.162917	+	0.161969i
$925$	5.27657			0.173493
$926$	6.51065	−	1.30473i	0.213953	−	0.0428761i
$927$	−10.6017	−	10.5993i	−0.348206	−	0.348126i
$928$	−26.9031	+	40.8932i	−0.883136	+	1.34238i
$929$	56.3252			1.84797			0.923985	−	0.382429i	$-0.124912\pi$
$929$	56.3252			1.84797			0.923985	+	0.382429i	$0.124912\pi$
$930$	−34.4623	+	23.1012i	−1.13006	+	0.757518i
$931$		−	0.169236i		−	0.00554648i
$932$	12.6772	+	30.3596i	0.415255	+	0.994461i
$933$	3.62312	+	8.74556i	0.118615	+	0.286317i
$934$	−3.27833	−	16.3590i	−0.107270	−	0.535283i
$935$	1.06547			0.0348447
$936$	27.0236	+	14.3431i	0.883295	+	0.468817i
$937$	−1.08988			−0.0356047			−0.0178024	−	0.999842i	$-0.505667\pi$
$937$	−1.08988			−0.0356047			−0.0178024	+	0.999842i	$0.505667\pi$
$938$	8.46336	+	42.2325i	0.276338	+	1.37894i
$939$	−3.62391	−	8.74748i	−0.118262	−	0.285463i
$940$	−3.91837	+	1.63619i	−0.127803	+	0.0533665i
$941$		−	11.8789i		−	0.387240i	−0.981077	−	0.193620i	$-0.937977\pi$
$941$		−	11.8789i		−	0.387240i	0.981077	−	0.193620i	$-0.0620229\pi$
$942$	14.7114	−	9.86149i	0.479322	−	0.321305i
$943$	−0.614035			−0.0199957
$944$	25.6782	−	25.9736i	0.835754	−	0.845370i
$945$	−12.5102	+	30.2168i	−0.406956	+	0.982953i
$946$	−6.54295	+	1.31120i	−0.212730	+	0.0426309i
$947$	26.2255			0.852216			0.426108	−	0.904672i	$-0.359884\pi$
$947$	26.2255			0.852216			0.426108	+	0.904672i	$0.359884\pi$
$948$	26.6384	−	26.7942i	0.865175	−	0.870237i
$949$	46.1734	+	14.0813i	1.49885	+	0.457097i
$950$	0.823842	+	4.11100i	0.0267290	+	0.133379i
$951$	−1.78771	+	0.740612i	−0.0579703	+	0.0240160i
$952$	−2.43884	−	3.61630i	−0.0790432	−	0.117205i
$953$			16.4039i			0.531375i	0.964059	+	0.265687i	$0.0855989\pi$
$953$			16.4039i			0.531375i	−0.964059	+	0.265687i	$0.914401\pi$
$954$	−1.88983	+	2.83780i	−0.0611854	+	0.0918772i
$955$		−	51.7822i		−	1.67563i
$956$	−21.7365	−	52.0549i	−0.703007	−	1.68358i
$957$	4.38300	+	10.5798i	0.141682	+	0.341996i
$958$	−9.39959	−	46.9043i	−0.303687	−	1.51541i
$959$	−17.6744			−0.570735
$960$	−0.285477	−	33.0547i	−0.00921372	−	1.06684i
$961$	19.4094			0.626109
$962$	−3.81777	+	38.7421i	−0.123090	+	1.24909i
$963$	40.6270	+	40.6177i	1.30919	+	1.30889i
$964$	−6.61168	−	15.8338i	−0.212948	−	0.509972i
$965$	10.4071			0.335017
$966$	15.8324	+	23.6188i	0.509399	+	0.759921i
$967$	−23.4856			−0.755245			−0.377622	−	0.925960i	$-0.623258\pi$
$967$	−23.4856			−0.755245			−0.377622	+	0.925960i	$0.623258\pi$
$968$	24.4258	−	16.4728i	0.785075	−	0.529456i
$969$	1.66222	+	4.01230i	0.0533981	+	0.128894i
$970$	34.7223	−	6.95833i	1.11487	−	0.223418i
$971$			38.7343i			1.24304i	0.783397	+	0.621521i	$0.213485\pi$
$971$			38.7343i			1.24304i	−0.783397	+	0.621521i	$0.786515\pi$
$972$	−21.9760	+	22.1146i	−0.704879	+	0.709327i
$973$	27.4954			0.881463
$974$	−17.3264	+	3.47219i	−0.555173	+	0.111256i
$975$	−4.29589	+	0.416932i	−0.137579	+	0.0133525i
$976$	26.9603	+	26.6537i	0.862980	+	0.853164i
$977$	−61.1629			−1.95677			−0.978387	−	0.206781i	$-0.933701\pi$
$977$	−61.1629			−1.95677			−0.978387	+	0.206781i	$0.933701\pi$
$978$	30.0847	−	20.1668i	0.962004	−	0.644862i
$979$	−4.34468			−0.138857
$980$	−0.0725306	−	0.173698i	−0.00231691	−	0.00554857i
$981$	−14.9646	+	14.9681i	−0.477784	+	0.477893i
$982$	3.08231	+	15.3809i	0.0983605	+	0.490823i
$983$			3.87323i			0.123537i	0.998091	+	0.0617684i	$0.0196740\pi$
$983$			3.87323i			0.123537i	−0.998091	+	0.0617684i	$0.980326\pi$
$984$	−0.570105	−	0.377358i	−0.0181743	−	0.0120297i
$985$	−56.2484			−1.79222
$986$	−1.40551	−	7.01355i	−0.0447605	−	0.223357i
$987$	3.75721	−	1.55654i	0.119593	−	0.0495452i
$988$	−30.7802	+	3.07443i	−0.979250	+	0.0978108i
$989$	−27.1715			−0.864003
$990$	−6.43680	−	4.28657i	−0.204575	−	0.136236i
$991$		−	20.9226i		−	0.664627i	−0.943169	−	0.332313i	$-0.892171\pi$
$991$		−	20.9226i		−	0.664627i	0.943169	−	0.332313i	$-0.107829\pi$
$992$	−22.0743	+	33.5533i	−0.700859	+	1.06532i
$993$	−34.5540	+	14.3150i	−1.09654	+	0.454274i
$994$	1.88173	+	9.38991i	0.0596848	+	0.297830i
$995$	26.0197			0.824879
$996$	36.0573	+	35.8475i	1.14252	+	1.13587i
$997$			46.7104i			1.47933i	0.672974	+	0.739666i	$0.265016\pi$
$997$			46.7104i			1.47933i	−0.672974	+	0.739666i	$0.734984\pi$
$998$	−2.38161	−	11.8843i	−0.0753886	−	0.376192i
$999$	−36.6541	−	15.1753i	−1.15969	−	0.480125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.h.c.155.3	yes	32
3.2	odd	2	inner	312.2.h.c.155.30	yes	32
4.3	odd	2		1248.2.h.c.623.24		32
8.3	odd	2	inner	312.2.h.c.155.1	✓	32
8.5	even	2		1248.2.h.c.623.23		32
12.11	even	2		1248.2.h.c.623.18		32
13.12	even	2	inner	312.2.h.c.155.29	yes	32
24.5	odd	2		1248.2.h.c.623.17		32
24.11	even	2	inner	312.2.h.c.155.32	yes	32
39.38	odd	2	inner	312.2.h.c.155.4	yes	32
52.51	odd	2		1248.2.h.c.623.21		32
104.51	odd	2	inner	312.2.h.c.155.31	yes	32
104.77	even	2		1248.2.h.c.623.22		32
156.155	even	2		1248.2.h.c.623.19		32
312.77	odd	2		1248.2.h.c.623.20		32
312.155	even	2	inner	312.2.h.c.155.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.h.c.155.1	✓	32	8.3	odd	2	inner
312.2.h.c.155.2	yes	32	312.155	even	2	inner
312.2.h.c.155.3	yes	32	1.1	even	1	trivial
312.2.h.c.155.4	yes	32	39.38	odd	2	inner
312.2.h.c.155.29	yes	32	13.12	even	2	inner
312.2.h.c.155.30	yes	32	3.2	odd	2	inner
312.2.h.c.155.31	yes	32	104.51	odd	2	inner
312.2.h.c.155.32	yes	32	24.11	even	2	inner
1248.2.h.c.623.17		32	24.5	odd	2
1248.2.h.c.623.18		32	12.11	even	2
1248.2.h.c.623.19		32	156.155	even	2
1248.2.h.c.623.20		32	312.77	odd	2
1248.2.h.c.623.21		32	52.51	odd	2
1248.2.h.c.623.22		32	104.77	even	2
1248.2.h.c.623.23		32	8.5	even	2
1248.2.h.c.623.24		32	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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38664 + 0.277882i) q^{2} +(-0.662918 - 1.60017i) q^{3} +(1.84556 - 0.770648i) q^{4} +2.38561i q^{5} +(1.36389 + 2.03465i) q^{6} +2.63829 q^{7} +(-2.34499 + 1.58146i) q^{8} +(-2.12108 + 2.12156i) q^{9} +O(q^{10})\)	\(q+(-1.38664 + 0.277882i) q^{2} +(-0.662918 - 1.60017i) q^{3} +(1.84556 - 0.770648i) q^{4} +2.38561i q^{5} +(1.36389 + 2.03465i) q^{6} +2.63829 q^{7} +(-2.34499 + 1.58146i) q^{8} +(-2.12108 + 2.12156i) q^{9} +(-0.662918 - 3.30799i) q^{10} -0.764084 q^{11} +(-2.45662 - 2.44233i) q^{12} +(-1.05175 + 3.44874i) q^{13} +(-3.65836 + 0.733133i) q^{14} +(3.81737 - 1.58146i) q^{15} +(2.81220 - 2.84456i) q^{16} +0.584523i q^{17} +(2.35164 - 3.53126i) q^{18} +4.28969i q^{19} +(1.83846 + 4.40279i) q^{20} +(-1.74897 - 4.22170i) q^{21} +(1.05951 - 0.212325i) q^{22} +4.39993 q^{23} +(4.08514 + 2.70400i) q^{24} -0.691126 q^{25} +(0.500052 - 5.07444i) q^{26} +(4.80096 + 1.98766i) q^{27} +(4.86912 - 2.03319i) q^{28} +8.65308 q^{29} +(-4.85388 + 3.25371i) q^{30} +7.09996 q^{31} +(-3.10907 + 4.72585i) q^{32} +(0.506525 + 1.22266i) q^{33} +(-0.162429 - 0.810526i) q^{34} +6.29391i q^{35} +(-2.27961 + 5.55008i) q^{36} -7.63475 q^{37} +(-1.19203 - 5.94827i) q^{38} +(6.21579 - 0.603265i) q^{39} +(-3.77275 - 5.59422i) q^{40} -0.139556 q^{41} +(3.59833 + 5.36799i) q^{42} -6.17544 q^{43} +(-1.41016 + 0.588840i) q^{44} +(-5.06122 - 5.06006i) q^{45} +(-6.10114 + 1.22266i) q^{46} +0.889975i q^{47} +(-6.41603 - 2.61429i) q^{48} -0.0394518 q^{49} +(0.958345 - 0.192052i) q^{50} +(0.935336 - 0.387491i) q^{51} +(0.716703 + 7.17540i) q^{52} -0.803622 q^{53} +(-7.20956 - 1.42207i) q^{54} -1.82280i q^{55} +(-6.18675 + 4.17235i) q^{56} +(6.86423 - 2.84371i) q^{57} +(-11.9987 + 2.40454i) q^{58} +9.13099 q^{59} +(5.82645 - 5.86054i) q^{60} +9.47787i q^{61} +(-9.84511 + 1.97295i) q^{62} +(-5.59601 + 5.59729i) q^{63} +(2.99795 - 7.41703i) q^{64} +(-8.22735 - 2.50905i) q^{65} +(-1.04213 - 1.55464i) q^{66} -11.5441i q^{67} +(0.450462 + 1.07877i) q^{68} +(-2.91679 - 7.04063i) q^{69} +(-1.74897 - 8.72742i) q^{70} -2.56670i q^{71} +(1.61873 - 8.32945i) q^{72} -13.3885i q^{73} +(10.5867 - 2.12156i) q^{74} +(0.458160 + 1.10592i) q^{75} +(3.30584 + 7.91689i) q^{76} -2.01587 q^{77} +(-8.45145 + 2.56377i) q^{78} +10.9069i q^{79} +(6.78600 + 6.70882i) q^{80} +(-0.00205378 - 9.00000i) q^{81} +(0.193514 - 0.0387800i) q^{82} -14.6776 q^{83} +(-6.48127 - 6.44358i) q^{84} -1.39444 q^{85} +(8.56313 - 1.71605i) q^{86} +(-5.73629 - 13.8464i) q^{87} +(1.79177 - 1.20837i) q^{88} +5.68613 q^{89} +(8.42421 + 5.61008i) q^{90} +(-2.77481 + 9.09877i) q^{91} +(8.12035 - 3.39080i) q^{92} +(-4.70669 - 11.3611i) q^{93} +(-0.247308 - 1.23408i) q^{94} -10.2335 q^{95} +(9.62322 + 1.84219i) q^{96} +10.4965i q^{97} +(0.0547056 - 0.0109630i) q^{98} +(1.62068 - 1.62105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 20 q^{4} - 28 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 + 20 * q^4 - 28 * q^9	\( 32 q - 4 q^{3} + 20 q^{4} - 28 q^{9} - 4 q^{10} - 2 q^{12} - 28 q^{16} - 24 q^{22} + 56 q^{25} - 16 q^{27} + 34 q^{30} - 10 q^{36} - 12 q^{40} + 34 q^{42} + 40 q^{43} + 22 q^{48} + 8 q^{49} - 52 q^{51} - 72 q^{52} + 20 q^{64} + 4 q^{66} - 8 q^{75} + 26 q^{78} - 76 q^{81} - 40 q^{82} - 88 q^{88} - 14 q^{90} - 56 q^{91} - 68 q^{94}+O(q^{100}) \) 32 * q - 4 * q^3 + 20 * q^4 - 28 * q^9 - 4 * q^10 - 2 * q^12 - 28 * q^16 - 24 * q^22 + 56 * q^25 - 16 * q^27 + 34 * q^30 - 10 * q^36 - 12 * q^40 + 34 * q^42 + 40 * q^43 + 22 * q^48 + 8 * q^49 - 52 * q^51 - 72 * q^52 + 20 * q^64 + 4 * q^66 - 8 * q^75 + 26 * q^78 - 76 * q^81 - 40 * q^82 - 88 * q^88 - 14 * q^90 - 56 * q^91 - 68 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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