LMFDB - Embedded newform 546.2.bq.c.419.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(419,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("546.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.6
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.998793 - 1.41507i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.30549 q^{5} +(1.57251 + 0.726086i) q^{6} +(2.26007 + 1.37552i) q^{7} +1.00000i q^{8} +(-1.00482 + 2.82672i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.998793 - 1.41507i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.30549 q^{5} +(1.57251 + 0.726086i) q^{6} +(2.26007 + 1.37552i) q^{7} +1.00000i q^{8} +(-1.00482 + 2.82672i) q^{9} +(-1.13058 + 0.652743i) q^{10} +(-2.65606 + 1.53348i) q^{11} +(-1.72488 + 0.157447i) q^{12} +(-0.0981594 + 3.60421i) q^{13} +(-2.64504 - 0.0612007i) q^{14} +(-1.30391 - 1.84735i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.0434167 - 0.0752000i) q^{17} +(-0.543156 - 2.95042i) q^{18} +(4.99958 + 2.88651i) q^{19} +(0.652743 - 1.13058i) q^{20} +(-0.310892 - 4.57202i) q^{21} +(1.53348 - 2.65606i) q^{22} +(-1.49943 + 0.865695i) q^{23} +(1.41507 - 0.998793i) q^{24} -3.29570 q^{25} +(-1.71710 - 3.17042i) q^{26} +(5.00360 - 1.40141i) q^{27} +(2.32128 - 1.26952i) q^{28} +(0.290239 - 0.167569i) q^{29} +(2.05290 + 0.947896i) q^{30} -1.55145i q^{31} +(0.866025 + 0.500000i) q^{32} +(4.82283 + 2.22688i) q^{33} +0.0868334i q^{34} +(2.95050 + 1.79573i) q^{35} +(1.94560 + 2.28356i) q^{36} +(3.27525 + 5.67289i) q^{37} -5.77302 q^{38} +(5.19824 - 3.46096i) q^{39} +1.30549i q^{40} +(5.36006 + 9.28389i) q^{41} +(2.55525 + 3.80404i) q^{42} +(3.60795 - 6.24915i) q^{43} +3.06696i q^{44} +(-1.31178 + 3.69024i) q^{45} +(0.865695 - 1.49943i) q^{46} +3.29063 q^{47} +(-0.726086 + 1.57251i) q^{48} +(3.21587 + 6.21757i) q^{49} +(2.85416 - 1.64785i) q^{50} +(-0.149777 + 0.0136717i) q^{51} +(3.07226 + 1.88712i) q^{52} +9.11994i q^{53} +(-3.63254 + 3.71546i) q^{54} +(-3.46745 + 2.00194i) q^{55} +(-1.37552 + 2.26007i) q^{56} +(-0.908947 - 9.95776i) q^{57} +(-0.167569 + 0.290239i) q^{58} +(3.14371 - 5.44507i) q^{59} +(-2.25181 + 0.205546i) q^{60} +(-0.900957 - 0.520168i) q^{61} +(0.775724 + 1.34359i) q^{62} +(-6.15919 + 5.00643i) q^{63} -1.00000 q^{64} +(-0.128146 + 4.70526i) q^{65} +(-5.29013 + 0.482885i) q^{66} +(-6.48735 - 11.2364i) q^{67} +(-0.0434167 - 0.0752000i) q^{68} +(2.72263 + 1.25714i) q^{69} +(-3.45307 - 0.0798967i) q^{70} +(0.0353148 + 0.0203890i) q^{71} +(-2.82672 - 1.00482i) q^{72} -5.56752i q^{73} +(-5.67289 - 3.27525i) q^{74} +(3.29173 + 4.66364i) q^{75} +(4.99958 - 2.88651i) q^{76} +(-8.11223 - 0.187700i) q^{77} +(-2.77133 + 5.59640i) q^{78} +7.03754 q^{79} +(-0.652743 - 1.13058i) q^{80} +(-6.98066 - 5.68070i) q^{81} +(-9.28389 - 5.36006i) q^{82} +11.2537 q^{83} +(-4.11493 - 2.01677i) q^{84} +(0.0566800 - 0.0981726i) q^{85} +7.21590i q^{86} +(-0.527010 - 0.243340i) q^{87} +(-1.53348 - 2.65606i) q^{88} +(-2.25943 - 3.91345i) q^{89} +(-0.709083 - 3.85174i) q^{90} +(-5.17953 + 8.01077i) q^{91} +1.73139i q^{92} +(-2.19540 + 1.54958i) q^{93} +(-2.84977 + 1.64532i) q^{94} +(6.52688 + 3.76830i) q^{95} +(-0.157447 - 1.72488i) q^{96} +(-9.94312 - 5.74067i) q^{97} +(-5.89381 - 3.77664i) q^{98} +(-1.66584 - 9.04881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.998793	−	1.41507i	−0.576654	−	0.816989i
$3$	−0.998793	−	1.41507i	−0.576654	−	0.816989i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.30549			0.583832			0.291916	−	0.956444i	$-0.405707\pi$
$5$	1.30549			0.583832			0.291916	+	0.956444i	$0.405707\pi$
$6$	1.57251	+	0.726086i	0.641976	+	0.296424i
$7$	2.26007	+	1.37552i	0.854228	+	0.519899i
$7$	2.26007	+	1.37552i	0.854228	+	0.519899i
$8$			1.00000i			0.353553i
$9$	−1.00482	+	2.82672i	−0.334941	+	0.942239i
$10$	−1.13058	+	0.652743i	−0.357522	+	0.206416i
$11$	−2.65606	+	1.53348i	−0.800833	+	0.462361i	−0.843762	−	0.536717i	$-0.819664\pi$
$11$	−2.65606	+	1.53348i	−0.800833	+	0.462361i	0.0429294	+	0.999078i	$0.486331\pi$
$12$	−1.72488	+	0.157447i	−0.497930	+	0.0454512i
$13$	−0.0981594	+	3.60421i	−0.0272245	+	0.999629i
$13$	−0.0981594	+	3.60421i	−0.0272245	+	0.999629i
$14$	−2.64504	−	0.0612007i	−0.706918	−	0.0163566i
$15$	−1.30391	−	1.84735i	−0.336669	−	0.476984i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.0434167	−	0.0752000i	0.0105301	−	0.0182387i	−0.860712	−	0.509092i	$-0.829981\pi$
$17$	0.0434167	−	0.0752000i	0.0105301	−	0.0182387i	0.871242	+	0.490853i	$0.163315\pi$
$18$	−0.543156	−	2.95042i	−0.128023	−	0.695421i
$19$	4.99958	+	2.88651i	1.14698	+	0.662210i	0.948150	−	0.317823i	$-0.102952\pi$
$19$	4.99958	+	2.88651i	1.14698	+	0.662210i	0.198832	+	0.980034i	$0.436285\pi$
$20$	0.652743	−	1.13058i	0.145958	−	0.252806i
$21$	−0.310892	−	4.57202i	−0.0678421	−	0.997696i
$22$	1.53348	−	2.65606i	0.326939	−	0.566274i
$23$	−1.49943	+	0.865695i	−0.312652	+	0.180510i	−0.648113	−	0.761544i	$-0.724441\pi$
$23$	−1.49943	+	0.865695i	−0.312652	+	0.180510i	0.335460	+	0.942054i	$0.391108\pi$
$24$	1.41507	−	0.998793i	0.288849	−	0.203878i
$25$	−3.29570			−0.659141
$26$	−1.71710	−	3.17042i	−0.336751	−	0.621771i
$27$	5.00360	−	1.40141i	0.962944	−	0.269702i
$28$	2.32128	−	1.26952i	0.438680	−	0.239917i
$29$	0.290239	−	0.167569i	0.0538960	−	0.0311168i	−0.472810	−	0.881164i	$-0.656760\pi$
$29$	0.290239	−	0.167569i	0.0538960	−	0.0311168i	0.526706	+	0.850048i	$0.323427\pi$
$30$	2.05290	+	0.947896i	0.374806	+	0.173061i
$31$		−	1.55145i		−	0.278648i	−0.990247	−	0.139324i	$-0.955507\pi$
$31$		−	1.55145i		−	0.278648i	0.990247	−	0.139324i	$-0.0444930\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	4.82283	+	2.22688i	0.839547	+	0.387649i
$34$			0.0868334i			0.0148918i
$35$	2.95050	+	1.79573i	0.498725	+	0.303533i
$36$	1.94560	+	2.28356i	0.324266	+	0.380594i
$37$	3.27525	+	5.67289i	0.538447	+	0.932618i	0.998988	+	0.0449794i	$0.0143222\pi$
$37$	3.27525	+	5.67289i	0.538447	+	0.932618i	−0.460541	+	0.887639i	$0.652344\pi$
$38$	−5.77302			−0.936507
$39$	5.19824	−	3.46096i	0.832385	−	0.554198i
$40$			1.30549i			0.206416i
$41$	5.36006	+	9.28389i	0.837101	+	1.44990i	0.892309	+	0.451426i	$0.149084\pi$
$41$	5.36006	+	9.28389i	0.837101	+	1.44990i	−0.0552081	+	0.998475i	$0.517582\pi$
$42$	2.55525	+	3.80404i	0.394283	+	0.586976i
$43$	3.60795	−	6.24915i	0.550207	−	0.952987i	−0.448052	−	0.894008i	$-0.647882\pi$
$43$	3.60795	−	6.24915i	0.550207	−	0.952987i	0.998259	−	0.0589794i	$-0.0187846\pi$
$44$			3.06696i			0.462361i
$45$	−1.31178	+	3.69024i	−0.195549	+	0.550109i
$46$	0.865695	−	1.49943i	0.127640	−	0.221078i
$47$	3.29063			0.479988			0.239994	−	0.970774i	$-0.422855\pi$
$47$	3.29063			0.479988			0.239994	+	0.970774i	$0.422855\pi$
$48$	−0.726086	+	1.57251i	−0.104802	+	0.226973i
$49$	3.21587	+	6.21757i	0.459410	+	0.888224i
$50$	2.85416	−	1.64785i	0.403640	−	0.233041i
$51$	−0.149777	+	0.0136717i	−0.0209730	+	0.00191442i
$52$	3.07226	+	1.88712i	0.426046	+	0.261696i
$53$			9.11994i			1.25272i	0.779534	+	0.626360i	$0.215456\pi$
$53$			9.11994i			1.25272i	−0.779534	+	0.626360i	$0.784544\pi$
$54$	−3.63254	+	3.71546i	−0.494326	+	0.505610i
$55$	−3.46745	+	2.00194i	−0.467551	+	0.269941i
$56$	−1.37552	+	2.26007i	−0.183812	+	0.302015i
$57$	−0.908947	−	9.95776i	−0.120393	−	1.31894i
$58$	−0.167569	+	0.290239i	−0.0220029	+	0.0381102i
$59$	3.14371	−	5.44507i	0.409276	−	0.708887i	−0.585532	−	0.810649i	$-0.699115\pi$
$59$	3.14371	−	5.44507i	0.409276	−	0.708887i	0.994809	+	0.101762i	$0.0324479\pi$
$60$	−2.25181	+	0.205546i	−0.290707	+	0.0265358i
$61$	−0.900957	−	0.520168i	−0.115356	−	0.0666007i	0.441212	−	0.897403i	$-0.354549\pi$
$61$	−0.900957	−	0.520168i	−0.115356	−	0.0666007i	−0.556568	+	0.830802i	$0.687882\pi$
$62$	0.775724	+	1.34359i	0.0985171	+	0.170637i
$63$	−6.15919	+	5.00643i	−0.775985	+	0.630751i
$64$	−1.00000			−0.125000
$65$	−0.128146	+	4.70526i	−0.0158945	+	0.583615i
$66$	−5.29013	+	0.482885i	−0.651170	+	0.0594390i
$67$	−6.48735	−	11.2364i	−0.792556	−	1.37275i	−0.924379	−	0.381474i	$-0.875416\pi$
$67$	−6.48735	−	11.2364i	−0.792556	−	1.37275i	0.131823	−	0.991273i	$-0.457917\pi$
$68$	−0.0434167	−	0.0752000i	−0.00526505	−	0.00911934i
$69$	2.72263	+	1.25714i	0.327767	+	0.151342i
$70$	−3.45307	−	0.0798967i	−0.412721	−	0.00954948i
$71$	0.0353148	+	0.0203890i	0.00419110	+	0.00241973i	0.502094	−	0.864813i	$-0.332563\pi$
$71$	0.0353148	+	0.0203890i	0.00419110	+	0.00241973i	−0.497903	+	0.867233i	$0.665896\pi$
$72$	−2.82672	−	1.00482i	−0.333132	−	0.118420i
$73$		−	5.56752i		−	0.651629i	−0.945434	−	0.325815i	$-0.894362\pi$
$73$		−	5.56752i		−	0.651629i	0.945434	−	0.325815i	$-0.105638\pi$
$74$	−5.67289	−	3.27525i	−0.659460	−	0.380740i
$75$	3.29173	+	4.66364i	0.380096	+	0.538511i
$76$	4.99958	−	2.88651i	0.573491	−	0.331105i
$77$	−8.11223	−	0.187700i	−0.924475	−	0.0213904i
$78$	−2.77133	+	5.59640i	−0.313791	+	0.633668i
$79$	7.03754			0.791785			0.395892	−	0.918297i	$-0.370435\pi$
$79$	7.03754			0.791785			0.395892	+	0.918297i	$0.370435\pi$
$80$	−0.652743	−	1.13058i	−0.0729789	−	0.126403i
$81$	−6.98066	−	5.68070i	−0.775629	−	0.631189i
$82$	−9.28389	−	5.36006i	−1.02523	−	0.591919i
$83$	11.2537			1.23525			0.617627	−	0.786471i	$-0.288094\pi$
$83$	11.2537			1.23525			0.617627	+	0.786471i	$0.288094\pi$
$84$	−4.11493	−	2.01677i	−0.448976	−	0.220048i
$85$	0.0566800	−	0.0981726i	0.00614781	−	0.0106483i
$86$			7.21590i			0.778111i
$87$	−0.527010	−	0.243340i	−0.0565014	−	0.0260887i
$88$	−1.53348	−	2.65606i	−0.163469	−	0.283137i
$89$	−2.25943	−	3.91345i	−0.239499	−	0.414825i	0.721071	−	0.692861i	$-0.243650\pi$
$89$	−2.25943	−	3.91345i	−0.239499	−	0.414825i	−0.960571	+	0.278036i	$0.910317\pi$
$90$	−0.709083	−	3.85174i	−0.0747439	−	0.406009i
$91$	−5.17953	+	8.01077i	−0.542962	+	0.839757i
$92$			1.73139i			0.180510i
$93$	−2.19540	+	1.54958i	−0.227653	+	0.160684i
$94$	−2.84977	+	1.64532i	−0.293931	+	0.169701i
$95$	6.52688	+	3.76830i	0.669644	+	0.386619i
$96$	−0.157447	−	1.72488i	−0.0160694	−	0.176045i
$97$	−9.94312	−	5.74067i	−1.00957	−	0.582876i	−0.0985052	−	0.995137i	$-0.531406\pi$
$97$	−9.94312	−	5.74067i	−1.00957	−	0.582876i	−0.911066	+	0.412260i	$0.864739\pi$
$98$	−5.89381	−	3.77664i	−0.595365	−	0.381498i
$99$	−1.66584	−	9.04881i	−0.167423	−	0.909440i
$100$	−1.64785	+	2.85416i	−0.164785	+	0.285416i
$101$	4.92233	+	8.52573i	0.489790	+	0.848341i	0.999931	−	0.0117495i	$-0.00374006\pi$
$101$	4.92233	+	8.52573i	0.489790	+	0.848341i	−0.510141	+	0.860091i	$0.670407\pi$
$102$	0.122875	−	0.0867287i	0.0121664	−	0.00858742i
$103$		−	8.91151i		−	0.878077i	−0.898468	−	0.439039i	$-0.855319\pi$
$103$		−	8.91151i		−	0.878077i	0.898468	−	0.439039i	$-0.144681\pi$
$104$	−3.60421	−	0.0981594i	−0.353422	−	0.00962532i
$105$	−0.405865	−	5.96871i	−0.0396084	−	0.582486i
$106$	−4.55997	−	7.89810i	−0.442903	−	0.767131i
$107$	−11.8069	+	6.81672i	−1.14142	+	0.658997i	−0.946781	−	0.321878i	$-0.895686\pi$
$107$	−11.8069	+	6.81672i	−1.14142	+	0.658997i	−0.194636	+	0.980876i	$0.562352\pi$
$108$	1.28814	−	5.03395i	0.123951	−	0.484392i
$109$	12.2180			1.17027			0.585137	−	0.810935i	$-0.301041\pi$
$109$	12.2180			1.17027			0.585137	+	0.810935i	$0.301041\pi$
$110$	2.00194	−	3.46745i	0.190877	−	0.330609i
$111$	4.75622	−	10.3007i	0.451441	−	0.977703i
$112$	0.0612007	−	2.64504i	0.00578292	−	0.249933i
$113$	−9.47730	−	5.47172i	−0.891549	−	0.514736i	−0.0171002	−	0.999854i	$-0.505443\pi$
$113$	−9.47730	−	5.47172i	−0.891549	−	0.514736i	−0.874449	+	0.485118i	$0.838777\pi$
$114$	5.76605	+	8.16920i	0.540040	+	0.765115i
$115$	−1.95748	+	1.13015i	−0.182536	+	0.105387i
$116$		−	0.335139i		−	0.0311168i
$117$	−10.0895	−	3.89907i	−0.932771	−	0.360469i
$118$			6.28742i			0.578804i
$119$	0.201564	−	0.110237i	0.0184774	−	0.0101054i
$120$	1.84735	−	1.30391i	0.168639	−	0.119030i
$121$	−0.796889	+	1.38025i	−0.0724445	+	0.125478i
$122$	1.04034			0.0941876
$123$	7.78373	−	16.8575i	0.701835	−	1.51999i
$124$	−1.34359	−	0.775724i	−0.120658	−	0.0696621i
$125$	−10.8299			−0.968659
$126$	2.83080	−	7.41529i	0.252188	−	0.660607i
$127$	4.65076	+	8.05535i	0.412688	+	0.714797i	0.995183	−	0.0980380i	$-0.0312567\pi$
$127$	4.65076	+	8.05535i	0.412688	+	0.714797i	−0.582495	+	0.812834i	$0.697923\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−12.4466	+	1.13613i	−1.09586	+	0.100030i
$130$	−2.24165	−	4.13894i	−0.196606	−	0.363009i
$131$	4.60715			0.402529			0.201264	−	0.979537i	$-0.435495\pi$
$131$	4.60715			0.402529			0.201264	+	0.979537i	$0.435495\pi$
$132$	4.33995	−	3.06326i	0.377744	−	0.266622i
$133$	7.32896	+	13.4008i	0.635501	+	1.16199i
$134$	11.2364	+	6.48735i	0.970679	+	0.560422i
$135$	6.53214	−	1.82953i	0.562197	−	0.157461i
$136$	0.0752000	+	0.0434167i	0.00644834	+	0.00372295i
$137$	−1.00741	−	0.581627i	−0.0860687	−	0.0496918i	0.456348	−	0.889801i	$-0.349157\pi$
$137$	−1.00741	−	0.581627i	−0.0860687	−	0.0496918i	−0.542417	+	0.840110i	$0.682491\pi$
$138$	−2.98644	+	0.272603i	−0.254223	+	0.0232055i
$139$	−8.78134	−	5.06991i	−0.744824	−	0.430024i	0.0789968	−	0.996875i	$-0.474828\pi$
$139$	−8.78134	−	5.06991i	−0.744824	−	0.430024i	−0.823821	+	0.566851i	$0.808162\pi$
$140$	3.03039	−	1.65734i	0.256115	−	0.140071i
$141$	−3.28666	−	4.65646i	−0.276787	−	0.392145i
$142$	−0.0407780			−0.00342202
$143$	−5.26627	−	9.72354i	−0.440387	−	0.813124i
$144$	2.95042	−	0.543156i	0.245868	−	0.0452630i
$145$	0.378903	−	0.218760i	0.0314662	−	0.0181670i
$146$	2.78376	+	4.82161i	0.230386	+	0.399040i
$147$	5.58628	−	10.7607i	0.460748	−	0.887531i
$148$	6.55049			0.538447
$149$	15.6067	+	9.01055i	1.27855	+	0.738173i	0.976582	−	0.215144i	$-0.0690220\pi$
$149$	15.6067	+	9.01055i	1.27855	+	0.738173i	0.301971	+	0.953317i	$0.402355\pi$
$150$	−5.18254	−	2.39297i	−0.423152	−	0.195385i
$151$	−21.3112			−1.73428			−0.867142	−	0.498061i	$-0.834046\pi$
$151$	−21.3112			−1.73428			−0.867142	+	0.498061i	$0.834046\pi$
$152$	−2.88651	+	4.99958i	−0.234127	+	0.405519i
$153$	0.168943	+	0.198289i	0.0136582	+	0.0160308i
$154$	7.11925	−	3.89356i	0.573685	−	0.313752i
$155$		−	2.02540i		−	0.162684i
$156$	−0.398161	−	6.23229i	−0.0318784	−	0.498983i
$157$		−	11.6832i		−	0.932421i	−0.884674	−	0.466210i	$-0.845619\pi$
$157$		−	11.6832i		−	0.932421i	0.884674	−	0.466210i	$-0.154381\pi$
$158$	−6.09469	+	3.51877i	−0.484867	+	0.279938i
$159$	12.9053	−	9.10893i	1.02346	−	0.722386i
$160$	1.13058	+	0.652743i	0.0893806	+	0.0516039i
$161$	−4.57960	−	0.105962i	−0.360923	−	0.00835099i
$162$	8.88578	+	1.42930i	0.698133	+	0.112297i
$163$	−8.45727	+	14.6484i	−0.662425	+	1.14735i	0.317552	+	0.948241i	$0.397139\pi$
$163$	−8.45727	+	14.6484i	−0.662425	+	1.14735i	−0.979977	+	0.199112i	$0.936194\pi$
$164$	10.7201			0.837101
$165$	6.29614	+	2.90716i	0.490154	+	0.226322i
$166$	−9.74599	+	5.62685i	−0.756436	+	0.436728i
$167$	−10.3446	−	17.9173i	−0.800485	−	1.38648i	−0.919297	−	0.393565i	$-0.871242\pi$
$167$	−10.3446	−	17.9173i	−0.800485	−	1.38648i	0.118812	−	0.992917i	$-0.462092\pi$
$168$	4.57202	−	0.310892i	0.352739	−	0.0239858i
$169$	−12.9807	−	0.707575i	−0.998518	−	0.0544288i
$170$			0.113360i			0.00869431i
$171$	−13.1830	+	11.2320i	−1.00813	+	0.858930i
$172$	−3.60795	−	6.24915i	−0.275104	−	0.476493i
$173$	0.769009	−	1.33196i	0.0584667	−	0.101267i	−0.835311	−	0.549778i	$-0.814712\pi$
$173$	0.769009	−	1.33196i	0.0584667	−	0.101267i	0.893777	+	0.448511i	$0.148046\pi$
$174$	0.578074	−	0.0527667i	0.0438237	−	0.00400024i
$175$	−7.44854	−	4.53332i	−0.563056	−	0.342687i
$176$	2.65606	+	1.53348i	0.200208	+	0.115590i
$177$	−10.8450	+	0.989939i	−0.815164	+	0.0744084i
$178$	3.91345	+	2.25943i	0.293325	+	0.169352i
$179$	22.3395	−	12.8977i	1.66973	−	0.964021i	0.701953	−	0.712224i	$-0.252312\pi$
$179$	22.3395	−	12.8977i	1.66973	−	0.964021i	0.967780	−	0.251797i	$-0.0810216\pi$
$180$	2.53995	+	2.98116i	0.189317	+	0.222203i
$181$			11.2782i			0.838300i	0.907917	+	0.419150i	$0.137672\pi$
$181$			11.2782i			0.838300i	−0.907917	+	0.419150i	$0.862328\pi$
$182$	0.480216	−	9.52730i	0.0355960	−	0.706210i
$183$	0.163798	+	1.79445i	0.0121083	+	0.132650i
$184$	−0.865695	−	1.49943i	−0.0638199	−	0.110539i
$185$	4.27579	+	7.40589i	0.314362	+	0.544492i
$186$	1.12649	−	2.43967i	0.0825979	−	0.178886i
$187$			0.266314i			0.0194748i
$188$	1.64532	−	2.84977i	0.119997	−	0.207841i
$189$	13.2362	+	3.71527i	0.962791	+	0.270246i
$190$	−7.53660			−0.546762
$191$	−13.4257	−	7.75132i	−0.971448	−	0.560866i	−0.0717704	−	0.997421i	$-0.522865\pi$
$191$	−13.4257	−	7.75132i	−0.971448	−	0.560866i	−0.899677	+	0.436556i	$0.856198\pi$
$192$	0.998793	+	1.41507i	0.0720817	+	0.102124i
$193$	−4.79107	−	8.29837i	−0.344868	−	0.597330i	0.640461	−	0.767990i	$-0.278743\pi$
$193$	−4.79107	−	8.29837i	−0.344868	−	0.597330i	−0.985330	+	0.170661i	$0.945410\pi$
$194$	11.4813			0.824312
$195$	6.78624	−	4.51824i	0.485973	−	0.323558i
$196$	6.99251	+	0.323757i	0.499465	+	0.0231255i
$197$	−12.2378	+	7.06552i	−0.871910	+	0.503397i	−0.867982	−	0.496595i	$-0.834583\pi$
$197$	−12.2378	+	7.06552i	−0.871910	+	0.503397i	−0.00392733	+	0.999992i	$0.501250\pi$
$198$	5.96706	+	7.00358i	0.424061	+	0.497723i
$199$	21.3798	+	12.3436i	1.51557	+	0.875015i	0.999833	+	0.0182688i	$0.00581546\pi$
$199$	21.3798	+	12.3436i	1.51557	+	0.875015i	0.515738	+	0.856746i	$0.327518\pi$
$200$		−	3.29570i		−	0.233041i
$201$	−9.42076	+	20.4029i	−0.664489	+	1.43911i
$202$	−8.52573	−	4.92233i	−0.599868	−	0.346334i
$203$	0.886456	+	0.0205107i	0.0622170	+	0.00143957i
$204$	−0.0630486	+	0.136547i	−0.00441428	+	0.00956019i
$205$	6.99749	+	12.1200i	0.488726	+	0.846498i
$206$	4.45575	+	7.71759i	0.310447	+	0.537710i
$207$	−0.940414	−	5.10833i	−0.0653633	−	0.355053i
$208$	3.17042	−	1.71710i	0.219829	−	0.119059i
$209$	−17.7056			−1.22472
$210$	3.33584	+	4.96612i	0.230195	+	0.342695i
$211$	2.13971	+	3.70609i	0.147304	+	0.255138i	0.930230	−	0.366977i	$-0.119607\pi$
$211$	2.13971	+	3.70609i	0.147304	+	0.255138i	−0.782926	+	0.622115i	$0.786274\pi$
$212$	7.89810	+	4.55997i	0.542444	+	0.313180i
$213$	−0.00642040	−	0.0703372i	−0.000439919	−	0.00481943i
$214$	6.81672	−	11.8069i	0.465981	−	0.807103i
$215$	4.71013	−	8.15819i	0.321228	−	0.556384i
$216$	1.40141	+	5.00360i	0.0953542	+	0.340452i
$217$	2.13405	−	3.50639i	0.144869	−	0.238029i
$218$	−10.5811	+	6.10901i	−0.716643	+	0.413754i
$219$	−7.87841	+	5.56080i	−0.532374	+	0.375764i
$220$			4.00387i			0.269941i
$221$	0.266775	+	0.163865i	0.0179452	+	0.0110227i
$222$	1.03136	+	11.2988i	0.0692203	+	0.758327i
$223$	3.99220	−	2.30490i	0.267337	−	0.154347i	−0.360340	−	0.932821i	$-0.617339\pi$
$223$	3.99220	−	2.30490i	0.267337	−	0.154347i	0.627677	+	0.778474i	$0.284006\pi$
$224$	1.26952	+	2.32128i	0.0848234	+	0.155097i
$225$	3.31160	−	9.31602i	0.220773	−	0.621068i
$226$	10.9434			0.727947
$227$	3.04171	−	5.26839i	0.201885	−	0.349675i	−0.747251	−	0.664542i	$-0.768627\pi$
$227$	3.04171	−	5.26839i	0.201885	−	0.349675i	0.949136	+	0.314867i	$0.101960\pi$
$228$	−9.07814	−	4.19171i	−0.601215	−	0.277603i
$229$			21.9563i			1.45092i	0.688267	+	0.725458i	$0.258372\pi$
$229$			21.9563i			1.45092i	−0.688267	+	0.725458i	$0.741628\pi$
$230$	1.13015	−	1.95748i	0.0745201	−	0.129073i
$231$	7.83684	+	11.6668i	0.515626	+	0.767620i
$232$	0.167569	+	0.290239i	0.0110015	+	0.0190551i
$233$		−	8.11714i		−	0.531771i	−0.964005	−	0.265886i	$-0.914336\pi$
$233$		−	8.11714i		−	0.531771i	0.964005	−	0.265886i	$-0.0856644\pi$
$234$	10.6873	−	1.66804i	0.698648	−	0.109043i
$235$	4.29588			0.280232
$236$	−3.14371	−	5.44507i	−0.204638	−	0.354444i
$237$	−7.02905	−	9.95858i	−0.456586	−	0.646879i
$238$	−0.119441	+	0.196250i	−0.00774224	+	0.0127210i
$239$		−	11.8387i		−	0.765785i	−0.923793	−	0.382892i	$-0.874928\pi$
$239$		−	11.8387i		−	0.765785i	0.923793	−	0.382892i	$-0.125072\pi$
$240$	−0.947896	+	2.05290i	−0.0611864	+	0.132514i
$241$	5.07035	+	2.92737i	0.326610	+	0.188569i	0.654335	−	0.756205i	$-0.272949\pi$
$241$	5.07035	+	2.92737i	0.326610	+	0.188569i	−0.327725	+	0.944773i	$0.606282\pi$
$242$		−	1.59378i		−	0.102452i
$243$	−1.06633	+	15.5519i	−0.0684053	+	0.997658i
$244$	−0.900957	+	0.520168i	−0.0576779	+	0.0333003i
$245$	4.19828	+	8.11696i	0.268218	+	0.518573i
$246$	1.68786	+	18.4909i	0.107614	+	1.17894i
$247$	−10.8943	+	17.7362i	−0.693191	+	1.12853i
$248$	1.55145			0.0985171
$249$	−11.2401	−	15.9247i	−0.712314	−	1.00919i
$250$	9.37900	−	5.41497i	0.593180	−	0.342473i
$251$	−12.8516	+	22.2596i	−0.811183	+	1.40501i	0.100853	+	0.994901i	$0.467843\pi$
$251$	−12.8516	+	22.2596i	−0.811183	+	1.40501i	−0.912036	+	0.410109i	$0.865491\pi$
$252$	1.25610	+	7.83723i	0.0791271	+	0.493699i
$253$	2.65505	−	4.59868i	0.166921	−	0.289116i
$254$	−8.05535	−	4.65076i	−0.505437	−	0.291814i
$255$	−0.195532	+	0.0178482i	−0.0122447	+	0.00111770i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.11327	−	7.12440i	−0.256579	−	0.444408i	0.708744	−	0.705465i	$-0.249262\pi$
$257$	−4.11327	−	7.12440i	−0.256579	−	0.444408i	−0.965323	+	0.261058i	$0.915929\pi$
$258$	10.2110	−	7.20719i	0.635708	−	0.448700i
$259$	−0.400895	+	17.3263i	−0.0249104	+	1.07661i
$260$	4.01080	+	2.46361i	0.248739	+	0.152786i
$261$	0.182033	+	0.988800i	0.0112675	+	0.0612052i
$262$	−3.98991	+	2.30358i	−0.246497	+	0.142315i
$263$	−18.5604	+	10.7159i	−1.14449	+	0.660769i	−0.947537	−	0.319645i	$-0.896436\pi$
$263$	−18.5604	+	10.7159i	−1.14449	+	0.660769i	−0.196948	+	0.980414i	$0.563103\pi$
$264$	−2.22688	+	4.82283i	−0.137055	+	0.296825i
$265$			11.9060i			0.731377i
$266$	−13.0474	−	7.94092i	−0.799990	−	0.486889i
$267$	−3.28108	+	7.10597i	−0.200799	+	0.434878i
$268$	−12.9747			−0.792556
$269$	−3.57221	+	6.18726i	−0.217802	+	0.377244i	−0.954136	−	0.299375i	$-0.903222\pi$
$269$	−3.57221	+	6.18726i	−0.217802	+	0.377244i	0.736334	+	0.676618i	$0.236555\pi$
$270$	−4.74223	+	4.85049i	−0.288603	+	0.295191i
$271$	−6.35101	+	3.66676i	−0.385797	+	0.222740i	−0.680337	−	0.732899i	$-0.738167\pi$
$271$	−6.35101	+	3.66676i	−0.385797	+	0.222740i	0.294541	+	0.955639i	$0.404833\pi$
$272$	−0.0868334			−0.00526505
$273$	16.5091	−	0.671734i	0.999173	−	0.0406552i
$274$	1.16325			0.0702748
$275$	8.75359	−	5.05389i	0.527862	−	0.304761i
$276$	2.45003	−	1.72930i	0.147475	−	0.104092i
$277$	13.7306	−	23.7821i	0.824990	−	1.42893i	−0.0769362	−	0.997036i	$-0.524514\pi$
$277$	13.7306	−	23.7821i	0.824990	−	1.42893i	0.901927	−	0.431889i	$-0.142153\pi$
$278$	10.1398			0.608146
$279$	4.38550	+	1.55893i	0.262553	+	0.0933308i
$280$	−1.79573	+	2.95050i	−0.107315	+	0.176326i
$281$		−	22.1642i		−	1.32220i	−0.750296	−	0.661102i	$-0.770089\pi$
$281$		−	22.1642i		−	1.32220i	0.750296	−	0.661102i	$-0.229911\pi$
$282$	5.17456	+	2.38928i	0.308141	+	0.142280i
$283$	24.3779	−	14.0746i	1.44912	−	0.836649i	0.450689	−	0.892681i	$-0.351178\pi$
$283$	24.3779	−	14.0746i	1.44912	−	0.836649i	0.998429	+	0.0560322i	$0.0178450\pi$
$284$	0.0353148	−	0.0203890i	0.00209555	−	0.00120987i
$285$	−1.18662	−	12.9997i	−0.0702892	−	0.770037i
$286$	9.42249	+	5.78770i	0.557164	+	0.342234i
$287$	−0.656078	+	28.3552i	−0.0387271	+	1.67375i
$288$	−2.28356	+	1.94560i	−0.134560	+	0.114645i
$289$	8.49623	+	14.7159i	0.499778	+	0.865641i
$290$	−0.218760	+	0.378903i	−0.0128460	+	0.0222499i
$291$	1.80771	+	19.8039i	0.105970	+	1.16093i
$292$	−4.82161	−	2.78376i	−0.282164	−	0.162907i
$293$	−12.3076	+	21.3174i	−0.719018	+	1.24538i	0.242371	+	0.970184i	$0.422075\pi$
$293$	−12.3076	+	21.3174i	−0.719018	+	1.24538i	−0.961389	+	0.275193i	$0.911258\pi$
$294$	0.542511	+	12.1122i	0.0316399	+	0.706399i
$295$	4.10407	−	7.10847i	0.238948	−	0.413871i
$296$	−5.67289	+	3.27525i	−0.329730	+	0.190370i
$297$	−11.1408	+	11.3952i	−0.646457	+	0.661214i
$298$	−18.0211			−1.04393
$299$	−2.97297	−	5.48923i	−0.171931	−	0.317451i
$300$	5.68469	−	0.518900i	0.328206	−	0.0299587i
$301$	16.7501	−	9.16073i	0.965459	−	0.528016i
$302$	18.4561	−	10.6556i	1.06203	−	0.613162i
$303$	7.14807	−	15.4809i	0.410646	−	0.889352i
$304$		−	5.77302i		−	0.331105i
$305$	−1.17619	−	0.679072i	−0.0673483	−	0.0388836i
$306$	−0.245454	−	0.0872523i	−0.0140316	−	0.00498788i
$307$		−	15.1308i		−	0.863559i	−0.901979	−	0.431780i	$-0.857886\pi$
$307$		−	15.1308i		−	0.863559i	0.901979	−	0.431780i	$-0.142114\pi$
$308$	−4.21867	+	6.93155i	−0.240381	+	0.394962i
$309$	−12.6104	+	8.90076i	−0.717379	+	0.506346i
$310$	1.01270	+	1.75404i	0.0575174	+	0.0996230i
$311$	20.4847			1.16158			0.580791	−	0.814053i	$-0.302743\pi$
$311$	20.4847			1.16158			0.580791	+	0.814053i	$0.302743\pi$
$312$	3.46096	+	5.19824i	0.195939	+	0.294293i
$313$		−	3.08704i		−	0.174490i	−0.996187	−	0.0872450i	$-0.972194\pi$
$313$		−	3.08704i		−	0.174490i	0.996187	−	0.0872450i	$-0.0278063\pi$
$314$	5.84160	+	10.1179i	0.329660	+	0.570989i
$315$	−8.04074	+	6.53583i	−0.453045	+	0.368252i
$316$	3.51877	−	6.09469i	0.197946	−	0.342853i
$317$		−	26.7046i		−	1.49988i	−0.661505	−	0.749941i	$-0.730082\pi$
$317$		−	26.7046i		−	1.49988i	0.661505	−	0.749941i	$-0.269918\pi$
$318$	−6.62186	+	14.3412i	−0.371336	+	0.804216i
$319$	−0.513928	+	0.890149i	−0.0287744	+	0.0498388i
$320$	−1.30549			−0.0729789
$321$	21.4388	+	9.89906i	1.19660	+	0.552511i
$322$	4.01903	−	2.19803i	0.223972	−	0.122492i
$323$	0.434131	−	0.250645i	0.0241557	−	0.0139463i
$324$	−8.40996	+	3.20508i	−0.467220	+	0.178060i
$325$	0.323504	−	11.8784i	0.0179448	−	0.658896i
$326$		−	16.9145i		−	0.936810i
$327$	−12.2033	−	17.2893i	−0.674842	−	0.956100i
$328$	−9.28389	+	5.36006i	−0.512617	+	0.295960i
$329$	7.43707	+	4.52634i	0.410019	+	0.249545i
$330$	−6.90620	+	0.630399i	−0.380174	+	0.0347023i
$331$	4.67409	−	8.09576i	0.256911	−	0.444983i	−0.708502	−	0.705709i	$-0.750628\pi$
$331$	4.67409	−	8.09576i	0.256911	−	0.444983i	0.965413	+	0.260726i	$0.0839618\pi$
$332$	5.62685	−	9.74599i	0.308814	−	0.534881i
$333$	−19.3267	+	3.55794i	−1.05910	+	0.194974i
$334$	17.9173	+	10.3446i	0.980390	+	0.566029i
$335$	−8.46915	−	14.6690i	−0.462719	−	0.801453i
$336$	−3.80404	+	2.55525i	−0.207527	+	0.139400i
$337$	−12.3019			−0.670127			−0.335064	−	0.942196i	$-0.608758\pi$
$337$	−12.3019			−0.670127			−0.335064	+	0.942196i	$0.608758\pi$
$338$	11.5954	−	5.87759i	0.630708	−	0.319699i
$339$	1.72302	+	18.8761i	0.0935814	+	1.02521i
$340$	−0.0566800	−	0.0981726i	−0.00307390	−	0.00532416i
$341$	2.37911	+	4.12074i	0.128836	+	0.223151i
$342$	5.80086	−	16.3187i	0.313675	−	0.882413i
$343$	−1.28430	+	18.4757i	−0.0693455	+	0.997593i
$344$	6.24915	+	3.60795i	0.336932	+	0.194528i
$345$	3.55436	+	1.64118i	0.191360	+	0.0883580i
$346$			1.53802i			0.0826844i
$347$	18.6834	+	10.7869i	1.00298	+	0.579069i	0.909128	−	0.416518i	$-0.136750\pi$
$347$	18.6834	+	10.7869i	1.00298	+	0.579069i	0.0938489	+	0.995586i	$0.470083\pi$
$348$	−0.474243	+	0.334734i	−0.0254221	+	0.0179436i
$349$	4.16977	−	2.40742i	0.223202	−	0.128866i	−0.384230	−	0.923237i	$-0.625533\pi$
$349$	4.16977	−	2.40742i	0.223202	−	0.128866i	0.607432	+	0.794372i	$0.292200\pi$
$350$	8.71728	+	0.201699i	0.465958	+	0.0107813i
$351$	4.55985	+	18.1716i	0.243387	+	0.969929i
$352$	−3.06696			−0.163469
$353$	−5.92052	−	10.2546i	−0.315117	−	0.545799i	0.664345	−	0.747426i	$-0.268711\pi$
$353$	−5.92052	−	10.2546i	−0.315117	−	0.545799i	−0.979462	+	0.201627i	$0.935377\pi$
$354$	8.89712	−	6.27984i	0.472876	−	0.333770i
$355$	0.0461030	+	0.0266176i	0.00244690	+	0.00141272i
$356$	−4.51886			−0.239499
$357$	−0.357314	−	0.175123i	−0.0189110	−	0.00926849i
$358$	−12.8977	+	22.3395i	−0.681666	+	1.18068i
$359$		−	6.72577i		−	0.354973i	−0.984123	−	0.177486i	$-0.943203\pi$
$359$		−	6.72577i		−	0.354973i	0.984123	−	0.177486i	$-0.0567966\pi$
$360$	−3.69024	−	1.31178i	−0.194493	−	0.0691371i
$361$	7.16385	+	12.4082i	0.377045	+	0.653061i
$362$	−5.63909	−	9.76719i	−0.296384	−	0.513352i
$363$	2.74908	−	0.250936i	0.144289	−	0.0131707i
$364$	4.34777	+	8.49099i	0.227885	+	0.445049i
$365$		−	7.26833i		−	0.380442i
$366$	−1.03908	−	1.47214i	−0.0543136	−	0.0769502i
$367$	−17.0478	+	9.84257i	−0.889890	+	0.513778i	−0.873907	−	0.486094i	$-0.838421\pi$
$367$	−17.0478	+	9.84257i	−0.889890	+	0.513778i	−0.0159835	+	0.999872i	$0.505088\pi$
$368$	1.49943	+	0.865695i	0.0781631	+	0.0451275i
$369$	−31.6289	+	5.82270i	−1.64653	+	0.303117i
$370$	−7.40589	−	4.27579i	−0.385014	−	0.222288i
$371$	−12.5447	+	20.6117i	−0.651288	+	1.07011i
$372$	0.244272	+	2.67606i	0.0126649	+	0.138747i
$373$	14.4920	−	25.1009i	0.750368	−	1.29967i	−0.197277	−	0.980348i	$-0.563210\pi$
$373$	14.4920	−	25.1009i	0.750368	−	1.29967i	0.947645	−	0.319327i	$-0.103457\pi$
$374$	−0.133157	−	0.230635i	−0.00688539	−	0.0119259i
$375$	10.8169	+	15.3251i	0.558581	+	0.791383i
$376$			3.29063i			0.169701i
$377$	0.575466	+	1.06253i	0.0296380	+	0.0547231i
$378$	−13.3205	+	3.40058i	−0.685133	+	0.174907i
$379$	−6.51133	−	11.2779i	−0.334464	−	0.579309i	0.648917	−	0.760859i	$-0.275222\pi$
$379$	−6.51133	−	11.2779i	−0.334464	−	0.579309i	−0.983382	+	0.181549i	$0.941889\pi$
$380$	6.52688	−	3.76830i	0.334822	−	0.193310i
$381$	6.75370	−	14.6268i	0.346003	−	0.749351i
$382$	15.5026			0.793184
$383$	16.9919	−	29.4308i	0.868243	−	1.50384i	0.00445320	−	0.999990i	$-0.498582\pi$
$383$	16.9919	−	29.4308i	0.868243	−	1.50384i	0.863790	−	0.503852i	$-0.168084\pi$
$384$	−1.57251	−	0.726086i	−0.0802470	−	0.0370529i
$385$	−10.5904	−	0.245040i	−0.539737	−	0.0124884i
$386$	8.29837	+	4.79107i	0.422376	+	0.243859i
$387$	14.0392	+	16.4780i	0.713654	+	0.837621i
$388$	−9.94312	+	5.74067i	−0.504786	+	0.291438i
$389$		−	17.7577i		−	0.900349i	−0.892941	−	0.450175i	$-0.851362\pi$
$389$		−	17.7577i		−	0.900349i	0.892941	−	0.450175i	$-0.148638\pi$
$390$	−3.61793	+	7.30603i	−0.183201	+	0.369955i
$391$			0.150343i			0.00760315i
$392$	−6.21757	+	3.21587i	−0.314035	+	0.162426i
$393$	−4.60159	−	6.51942i	−0.232120	−	0.328861i
$394$	7.06552	−	12.2378i	0.355956	−	0.616533i
$395$	9.18741			0.462269
$396$	−8.66942	−	3.08175i	−0.435655	−	0.154864i
$397$	0.617657	+	0.356605i	0.0309993	+	0.0178975i	0.515420	−	0.856938i	$-0.327636\pi$
$397$	0.617657	+	0.356605i	0.0309993	+	0.0178975i	−0.484420	+	0.874835i	$0.660969\pi$
$398$	−24.6872			−1.23746
$399$	11.6428	−	23.7556i	0.582871	−	1.18927i
$400$	1.64785	+	2.85416i	0.0823926	+	0.142708i
$401$	8.44690	−	4.87682i	0.421818	−	0.243537i	−0.274037	−	0.961719i	$-0.588359\pi$
$401$	8.44690	−	4.87682i	0.421818	−	0.243537i	0.695855	+	0.718182i	$0.255026\pi$
$402$	−2.04283	−	22.3798i	−0.101887	−	1.11620i
$403$	5.59175	+	0.152289i	0.278545	+	0.00758606i
$404$	9.84466			0.489790
$405$	−9.11316	−	7.41608i	−0.452837	−	0.368508i
$406$	−0.777949	+	0.425465i	−0.0386090	+	0.0211155i
$407$	−17.3985	−	10.0450i	−0.862412	−	0.497914i
$408$	−0.0136717	−	0.149777i	−0.000676850	−	0.00741508i
$409$	9.75977	+	5.63481i	0.482590	+	0.278623i	0.721495	−	0.692420i	$-0.243455\pi$
$409$	9.75977	+	5.63481i	0.482590	+	0.278623i	−0.238905	+	0.971043i	$0.576789\pi$
$410$	−12.1200	−	6.99749i	−0.598564	−	0.345581i
$411$	0.183152	+	2.00647i	0.00903420	+	0.0989721i
$412$	−7.71759	−	4.45575i	−0.380219	−	0.219519i
$413$	14.5948	−	7.98201i	0.718165	−	0.392769i
$414$	3.36859	+	3.95373i	0.165557	+	0.194315i
$415$	14.6916			0.721180
$416$	−1.88712	+	3.07226i	−0.0925235	+	0.150630i
$417$	1.59649	+	17.4900i	0.0781804	+	0.856488i
$418$	15.3335	−	8.85279i	0.749985	−	0.433004i
$419$	10.3268	+	17.8865i	0.504495	+	0.873811i	0.999986	+	0.00519813i	$0.00165462\pi$
$419$	10.3268	+	17.8865i	0.504495	+	0.873811i	−0.495492	+	0.868613i	$0.665012\pi$
$420$	−5.37199	−	2.63287i	−0.262126	−	0.128471i
$421$	32.6593			1.59172			0.795858	−	0.605484i	$-0.207020\pi$
$421$	32.6593			1.59172			0.795858	+	0.605484i	$0.207020\pi$
$422$	−3.70609	−	2.13971i	−0.180410	−	0.104160i
$423$	−3.30650	+	9.30169i	−0.160768	+	0.452263i
$424$	−9.11994			−0.442903
$425$	−0.143089	+	0.247837i	−0.00694082	+	0.0120219i
$426$	0.0407288	+	0.0577036i	0.00197332	+	0.00279575i
$427$	−1.32073	−	2.41491i	−0.0639145	−	0.116865i
$428$			13.6334i			0.658997i
$429$	−8.49954	+	17.1639i	−0.410362	+	0.828682i
$430$			9.42026i			0.454285i
$431$	31.4070	−	18.1328i	1.51282	−	0.873428i	0.512934	−	0.858428i	$-0.328559\pi$
$431$	31.4070	−	18.1328i	1.51282	−	0.873428i	0.999887	−	0.0149996i	$-0.00477471\pi$
$432$	−3.71546	−	3.63254i	−0.178760	−	0.174771i
$433$	−9.98533	−	5.76503i	−0.479864	−	0.277050i	0.240496	−	0.970650i	$-0.422690\pi$
$433$	−9.98533	−	5.76503i	−0.479864	−	0.277050i	−0.720360	+	0.693600i	$0.756023\pi$
$434$	−0.0949497	+	4.10365i	−0.00455773	+	0.196981i
$435$	−0.688005	−	0.317677i	−0.0329873	−	0.0152314i
$436$	6.10901	−	10.5811i	0.292568	−	0.506743i
$437$	−9.99534			−0.478142
$438$	4.04250	−	8.75500i	0.193158	−	0.418330i
$439$	2.29664	−	1.32597i	0.109613	−	0.0632849i	−0.444191	−	0.895932i	$-0.646509\pi$
$439$	2.29664	−	1.32597i	0.109613	−	0.0632849i	0.553804	+	0.832647i	$0.313176\pi$
$440$	−2.00194	−	3.46745i	−0.0954385	−	0.165304i
$441$	−20.8067	+	2.84280i	−0.990795	+	0.135372i
$442$	−0.312966	−	0.00852351i	−0.0148863	−	0.000405422i
$443$		−	30.2256i		−	1.43606i	−0.696010	−	0.718032i	$-0.745043\pi$
$443$		−	30.2256i		−	1.43606i	0.696010	−	0.718032i	$-0.254957\pi$
$444$	−6.54259	−	9.26938i	−0.310498	−	0.439905i
$445$	−2.94966	−	5.10896i	−0.139827	−	0.242188i
$446$	−2.30490	+	3.99220i	−0.109140	+	0.189036i
$447$	−2.83738	−	31.0842i	−0.134203	−	1.47023i
$448$	−2.26007	−	1.37552i	−0.106778	−	0.0649874i
$449$	23.6933	+	13.6793i	1.11815	+	0.645567i	0.940929	−	0.338603i	$-0.109954\pi$
$449$	23.6933	+	13.6793i	1.11815	+	0.645567i	0.177226	+	0.984170i	$0.443288\pi$
$450$	1.79008	+	9.72371i	0.0843852	+	0.458380i
$451$	−28.4733	−	16.4391i	−1.34076	−	0.774085i
$452$	−9.47730	+	5.47172i	−0.445775	+	0.257368i
$453$	21.2855	+	30.1568i	1.00008	+	1.41689i
$454$			6.08342i			0.285509i
$455$	−6.76181	+	10.4580i	−0.316998	+	0.490277i
$456$	9.95776	−	0.908947i	0.466315	−	0.0425653i
$457$	−11.8231	−	20.4782i	−0.553062	−	0.957931i	−0.998052	−	0.0623953i	$-0.980126\pi$
$457$	−11.8231	−	20.4782i	−0.553062	−	0.957931i	0.444990	−	0.895536i	$-0.353207\pi$
$458$	−10.9782	−	19.0147i	−0.512976	−	0.888500i
$459$	0.111854	−	0.437116i	0.00522088	−	0.0204028i
$460$			2.26031i			0.105387i
$461$	5.94413	−	10.2955i	0.276846	−	0.479511i	−0.693753	−	0.720213i	$-0.744044\pi$
$461$	5.94413	−	10.2955i	0.276846	−	0.479511i	0.970599	+	0.240702i	$0.0773776\pi$
$462$	−12.6203	−	6.18534i	−0.587150	−	0.287768i
$463$	−20.9008			−0.971345			−0.485672	−	0.874141i	$-0.661425\pi$
$463$	−20.9008			−0.971345			−0.485672	+	0.874141i	$0.661425\pi$
$464$	−0.290239	−	0.167569i	−0.0134740	−	0.00777921i
$465$	−2.86607	+	2.02295i	−0.132911	+	0.0938121i
$466$	4.05857	+	7.02965i	0.188010	+	0.325642i
$467$	28.4253			1.31536			0.657682	−	0.753296i	$-0.271537\pi$
$467$	28.4253			1.31536			0.657682	+	0.753296i	$0.271537\pi$
$468$	−8.42142	+	6.78820i	−0.389280	+	0.313785i
$469$	0.794061	−	34.3187i	0.0366663	−	1.58469i
$470$	−3.72034	+	2.14794i	−0.171606	+	0.0990770i
$471$	−16.5325	+	11.6691i	−0.761777	+	0.537684i
$472$	5.44507	+	3.14371i	0.250630	+	0.144701i
$473$			22.1309i			1.01758i
$474$	11.0666	+	5.10986i	0.508307	+	0.234704i
$475$	−16.4771	−	9.51307i	−0.756022	−	0.436490i
$476$	0.00531427	−	0.229678i	0.000243579	−	0.0105273i
$477$	−25.7795	−	9.16393i	−1.18036	−	0.419587i
$478$	5.91937	+	10.2527i	0.270746	+	0.468946i
$479$	−10.3099	−	17.8574i	−0.471073	−	0.815923i	0.528379	−	0.849009i	$-0.322800\pi$
$479$	−10.3099	−	17.8574i	−0.471073	−	0.815923i	−0.999453	+	0.0330854i	$0.989467\pi$
$480$	−0.205546	−	2.25181i	−0.00938183	−	0.102781i
$481$	−20.7678	+	11.2478i	−0.946931	+	0.512858i
$482$	−5.85474			−0.266676
$483$	4.42413	+	6.58627i	0.201305	+	0.299686i
$484$	0.796889	+	1.38025i	0.0362222	+	0.0627388i
$485$	−12.9806	−	7.49436i	−0.589420	−	0.340302i
$486$	−6.85250	−	14.0015i	−0.310836	−	0.635123i
$487$	0.476078	−	0.824591i	0.0215732	−	0.0373658i	−0.855037	−	0.518567i	$-0.826466\pi$
$487$	0.476078	−	0.824591i	0.0215732	−	0.0373658i	0.876610	+	0.481201i	$0.159799\pi$
$488$	0.520168	−	0.900957i	0.0235469	−	0.0407844i
$489$	29.1756	−	2.66315i	1.31936	−	0.120432i
$490$	−7.69429	−	4.93035i	−0.347593	−	0.222730i
$491$	−18.1739	+	10.4927i	−0.820179	+	0.473530i	−0.850478	−	0.526011i	$-0.823687\pi$
$491$	−18.1739	+	10.4927i	−0.820179	+	0.473530i	0.0302994	+	0.999541i	$0.490354\pi$
$492$	−10.7072	−	15.1697i	−0.482717	−	0.683902i
$493$		−	0.0291012i		−	0.00131065i
$494$	0.566675	−	20.8072i	0.0254959	−	0.936160i
$495$	−2.17473	−	11.8131i	−0.0977467	−	0.530960i
$496$	−1.34359	+	0.775724i	−0.0603291	+	0.0348310i
$497$	0.0517686	+	0.0946571i	0.00232214	+	0.00424595i
$498$	17.6966	+	8.17116i	0.793004	+	0.366158i
$499$	−30.8180			−1.37960			−0.689802	−	0.723998i	$-0.742303\pi$
$499$	−30.8180			−1.37960			−0.689802	+	0.723998i	$0.742303\pi$
$500$	−5.41497	+	9.37900i	−0.242165	+	0.419442i
$501$	−15.0221	+	32.5339i	−0.671137	+	1.45351i
$502$		−	25.7031i		−	1.14719i
$503$	6.86671	−	11.8935i	0.306171	−	0.530304i	−0.671350	−	0.741140i	$-0.734285\pi$
$503$	6.86671	−	11.8935i	0.306171	−	0.530304i	0.977521	+	0.210836i	$0.0676186\pi$
$504$	−5.00643	−	6.15919i	−0.223004	−	0.274352i
$505$	6.42604	+	11.1302i	0.285955	+	0.495288i
$506$			5.31010i			0.236063i
$507$	11.9638	+	19.0753i	0.531331	+	0.847164i
$508$	9.30151			0.412688
$509$	−13.3327	−	23.0929i	−0.590962	−	1.02358i	−0.994103	−	0.108438i	$-0.965415\pi$
$509$	−13.3327	−	23.0929i	−0.590962	−	1.02358i	0.403142	−	0.915138i	$-0.367918\pi$
$510$	0.160412	−	0.113223i	0.00710315	−	0.00501361i
$511$	7.65825	−	12.5830i	0.338781	−	0.556640i
$512$		−	1.00000i		−	0.0441942i
$513$	29.0611	+	7.43645i	1.28308	+	0.328327i
$514$	7.12440	+	4.11327i	0.314244	+	0.181429i
$515$		−	11.6339i		−	0.512649i
$516$	−5.23937	+	11.3471i	−0.230650	+	0.499528i
$517$	−8.74012	+	5.04611i	−0.384390	+	0.221928i
$518$	−8.31598	−	15.2055i	−0.365383	−	0.668091i
$519$	−2.65290	+	0.242157i	−0.116449	+	0.0106295i
$520$	−4.70526	−	0.128146i	−0.206339	−	0.00561956i
$521$	14.2304			0.623443			0.311721	−	0.950174i	$-0.399094\pi$
$521$	14.2304			0.623443			0.311721	+	0.950174i	$0.399094\pi$
$522$	−0.652045	−	0.765310i	−0.0285392	−	0.0334967i
$523$	−6.99225	+	4.03698i	−0.305750	+	0.176525i	−0.645023	−	0.764163i	$-0.723152\pi$
$523$	−6.99225	+	4.03698i	−0.305750	+	0.176525i	0.339273	+	0.940688i	$0.389819\pi$
$524$	2.30358	−	3.98991i	0.100632	−	0.174300i
$525$	1.02461	+	15.0680i	0.0447175	+	0.657622i
$526$	10.7159	−	18.5604i	0.467234	−	0.809274i
$527$	−0.116669	−	0.0673588i	−0.00508217	−	0.00293420i
$528$	−0.482885	−	5.29013i	−0.0210149	−	0.230223i
$529$	−10.0011	+	17.3225i	−0.434832	+	0.753152i
$530$	−5.95298	−	10.3109i	−0.258581	−	0.447875i
$531$	12.2328	+	14.3577i	0.530858	+	0.623072i
$532$	15.2699	+	0.353312i	0.662033	+	0.0153180i
$533$	−33.9873	+	18.4075i	−1.47215	+	0.797317i
$534$	−0.711483	−	7.79450i	−0.0307889	−	0.337301i
$535$	−15.4138	+	8.89914i	−0.666395	+	0.384743i
$536$	11.2364	−	6.48735i	0.485340	−	0.280211i
$537$	−40.5637	−	18.7297i	−1.75045	−	0.808247i
$538$		−	7.14443i		−	0.308018i
$539$	−18.0761	−	11.5828i	−0.778591	−	0.498906i
$540$	1.68165	−	6.57176i	0.0723667	−	0.282804i
$541$	4.68178			0.201285			0.100643	−	0.994923i	$-0.467910\pi$
$541$	4.68178			0.201285			0.100643	+	0.994923i	$0.467910\pi$
$542$	3.66676	−	6.35101i	0.157501	−	0.272799i
$543$	15.9594	−	11.2646i	0.684882	−	0.483409i
$544$	0.0752000	−	0.0434167i	0.00322417	−	0.00186148i
$545$	15.9505			0.683242
$546$	−13.9614	+	8.83626i	−0.597492	+	0.378157i
$547$	−8.48191			−0.362660			−0.181330	−	0.983422i	$-0.558040\pi$
$547$	−8.48191			−0.362660			−0.181330	+	0.983422i	$0.558040\pi$
$548$	−1.00741	+	0.581627i	−0.0430343	+	0.0248459i
$549$	2.37567	−	2.02407i	0.101391	−	0.0863854i
$550$	−5.05389	+	8.75359i	−0.215499	+	0.373254i
$551$	1.93476			0.0824236
$552$	−1.25714	+	2.72263i	−0.0535074	+	0.115883i
$553$	15.9054	+	9.68029i	0.676365	+	0.411648i
$554$			27.4612i			1.16671i
$555$	6.20919	−	13.4475i	0.263565	−	0.570814i
$556$	−8.78134	+	5.06991i	−0.372412	+	0.215012i
$557$	−23.2556	+	13.4266i	−0.985369	+	0.568903i	−0.903887	−	0.427772i	$-0.859299\pi$
$557$	−23.2556	+	13.4266i	−0.985369	+	0.568903i	−0.0814824	+	0.996675i	$0.525965\pi$
$558$	−4.57742	+	0.842678i	−0.193778	+	0.0356734i
$559$	22.1691	+	13.6172i	0.937655	+	0.575948i
$560$	0.0798967	−	3.45307i	0.00337625	−	0.145919i
$561$	0.376852	−	0.265993i	0.0159107	−	0.0112302i
$562$	11.0821	+	19.1948i	0.467470	+	0.809682i
$563$	−18.1895	+	31.5051i	−0.766596	+	1.32778i	0.172803	+	0.984956i	$0.444718\pi$
$563$	−18.1895	+	31.5051i	−0.766596	+	1.32778i	−0.939399	+	0.342827i	$0.888616\pi$
$564$	−5.67594	+	0.518102i	−0.239000	+	0.0218160i
$565$	−12.3725	−	7.14326i	−0.520514	−	0.300519i
$566$	−14.0746	+	24.3779i	−0.591600	+	1.02468i
$567$	−7.96287	−	22.4409i	−0.334409	−	0.942428i
$568$	−0.0203890	+	0.0353148i	−0.000855504	+	0.00148178i
$569$	−11.3724	+	6.56585i	−0.476755	+	0.275255i	−0.719063	−	0.694945i	$-0.755429\pi$
$569$	−11.3724	+	6.56585i	−0.476755	+	0.275255i	0.242308	+	0.970199i	$0.422096\pi$
$570$	7.52750	+	10.6648i	0.315292	+	0.446699i
$571$	−7.37225			−0.308519			−0.154260	−	0.988030i	$-0.549299\pi$
$571$	−7.37225			−0.308519			−0.154260	+	0.988030i	$0.549299\pi$
$572$	−11.0540	−	0.301050i	−0.462190	−	0.0125876i
$573$	2.44085	+	26.7402i	0.101968	+	1.11709i
$574$	−13.6094	−	24.8843i	−0.568046	−	1.03865i
$575$	4.94167	−	2.85307i	0.206082	−	0.118981i
$576$	1.00482	−	2.82672i	0.0418676	−	0.117780i
$577$		−	42.9694i		−	1.78884i	−0.447230	−	0.894419i	$-0.647590\pi$
$577$		−	42.9694i		−	1.78884i	0.447230	−	0.894419i	$-0.352410\pi$
$578$	−14.7159	−	8.49623i	−0.612101	−	0.353397i
$579$	−6.95745	+	15.0680i	−0.289142	+	0.626206i
$580$		−	0.437519i		−	0.0181670i
$581$	25.4342	+	15.4797i	1.05519	+	0.642207i
$582$	−11.4675	−	16.2468i	−0.475342	−	0.673453i
$583$	−13.9852	−	24.2231i	−0.579209	−	1.00322i
$584$	5.56752			0.230386
$585$	−13.1717	−	5.09018i	−0.544581	−	0.210453i
$586$		−	24.6152i		−	1.01685i
$587$	19.5638	+	33.8856i	0.807486	+	1.39861i	0.914600	+	0.404360i	$0.132506\pi$
$587$	19.5638	+	33.8856i	0.807486	+	1.39861i	−0.107114	+	0.994247i	$0.534161\pi$
$588$	−6.52593	−	10.2182i	−0.269125	−	0.421393i
$589$	4.47827	−	7.75659i	0.184524	−	0.319605i
$590$			8.20815i			0.337924i
$591$	22.2212	+	10.2604i	0.914060	+	0.422055i
$592$	3.27525	−	5.67289i	0.134612	−	0.233154i
$593$	33.7897			1.38758			0.693788	−	0.720180i	$-0.255941\pi$
$593$	33.7897			1.38758			0.693788	+	0.720180i	$0.255941\pi$
$594$	3.95067	−	15.4389i	0.162098	−	0.633466i
$595$	0.263140	−	0.143913i	0.0107877	−	0.00589985i
$596$	15.6067	−	9.01055i	0.639277	−	0.369087i
$597$	−3.88694	−	42.5825i	−0.159082	−	1.74279i
$598$	5.31928	+	3.26733i	0.217522	+	0.133611i
$599$			16.4094i			0.670470i	0.942135	+	0.335235i	$0.108816\pi$
$599$			16.4094i			0.670470i	−0.942135	+	0.335235i	$0.891184\pi$
$600$	−4.66364	+	3.29173i	−0.190392	+	0.134384i
$601$	3.44272	−	1.98765i	0.140431	−	0.0810780i	−0.428138	−	0.903713i	$-0.640830\pi$
$601$	3.44272	−	1.98765i	0.140431	−	0.0810780i	0.568570	+	0.822635i	$0.307497\pi$
$602$	−9.92564	+	16.3085i	−0.404539	+	0.664684i
$603$	38.2808	−	7.04729i	1.55892	−	0.286988i
$604$	−10.6556	+	18.4561i	−0.433571	+	0.750967i
$605$	−1.04033	+	1.80190i	−0.0422954	+	0.0732577i
$606$	1.55002	+	16.9809i	0.0629651	+	0.689800i
$607$	−21.1314	−	12.2002i	−0.857699	−	0.495193i	0.00554203	−	0.999985i	$-0.498236\pi$
$607$	−21.1314	−	12.2002i	−0.857699	−	0.495193i	−0.863241	+	0.504792i	$0.831569\pi$
$608$	2.88651	+	4.99958i	0.117063	+	0.202760i
$609$	−0.856363	−	1.27488i	−0.0347016	−	0.0516607i
$610$	1.35814			0.0549897
$611$	−0.323006	+	11.8601i	−0.0130674	+	0.479810i
$612$	0.256195	−	0.0471641i	0.0103561	−	0.00190650i
$613$	13.4919	+	23.3686i	0.544932	+	0.943849i	0.998611	+	0.0526844i	$0.0167777\pi$
$613$	13.4919	+	23.3686i	0.544932	+	0.943849i	−0.453680	+	0.891165i	$0.649889\pi$
$614$	7.56539	+	13.1036i	0.305314	+	0.528820i
$615$	10.1616	−	22.0073i	0.409754	−	0.887419i
$616$	0.187700	−	8.11223i	0.00756264	−	0.326851i
$617$	30.7157	+	17.7337i	1.23657	+	0.713933i	0.968391	−	0.249437i	$-0.0802455\pi$
$617$	30.7157	+	17.7337i	1.23657	+	0.713933i	0.268177	+	0.963370i	$0.413579\pi$
$618$	6.47053	−	14.0135i	0.260283	−	0.563704i
$619$		−	10.3406i		−	0.415625i	−0.978169	−	0.207813i	$-0.933366\pi$
$619$		−	10.3406i		−	0.415625i	0.978169	−	0.207813i	$-0.0666344\pi$
$620$	−1.75404	−	1.01270i	−0.0704441	−	0.0406709i
$621$	−6.28934	+	6.43291i	−0.252383	+	0.258144i
$622$	−17.7403	+	10.2424i	−0.711321	+	0.410681i
$623$	0.276557	−	11.9526i	0.0110800	−	0.478870i
$624$	−5.59640	−	2.77133i	−0.224035	−	0.110942i
$625$	2.34018			0.0936073
$626$	1.54352	+	2.67346i	0.0616915	+	0.106853i
$627$	17.6842	+	25.0546i	0.706240	+	1.00058i
$628$	−10.1179	−	5.84160i	−0.403750	−	0.233105i
$629$	0.568802			0.0226796
$630$	3.69557	−	9.68057i	0.147235	−	0.385683i
$631$	−2.49594	+	4.32310i	−0.0993620	+	0.172100i	−0.911421	−	0.411476i	$-0.865014\pi$
$631$	−2.49594	+	4.32310i	−0.0993620	+	0.172100i	0.812059	+	0.583576i	$0.198347\pi$
$632$			7.03754i			0.279938i
$633$	3.10723	−	6.72946i	0.123501	−	0.267472i
$634$	13.3523	+	23.1269i	0.530288	+	0.918487i
$635$	6.07150	+	10.5162i	0.240940	+	0.417321i
$636$	−1.43591	−	15.7308i	−0.0569376	−	0.623767i
$637$	−22.7251	+	10.9804i	−0.900402	+	0.435059i
$638$		−	1.02786i		−	0.0406932i
$639$	−0.0931192	+	0.0793376i	−0.00368374	+	0.00313855i
$640$	1.13058	−	0.652743i	0.0446903	−	0.0258020i
$641$	−40.0718	−	23.1355i	−1.58274	−	0.913795i	−0.994457	−	0.105140i	$-0.966471\pi$
$641$	−40.0718	−	23.1355i	−1.58274	−	0.913795i	−0.588283	−	0.808655i	$-0.700196\pi$
$642$	−23.5160	+	2.14655i	−0.928104	+	0.0847176i
$643$	18.3928	+	10.6191i	0.725340	+	0.418775i	0.816715	−	0.577042i	$-0.195793\pi$
$643$	18.3928	+	10.6191i	0.725340	+	0.418775i	−0.0913752	+	0.995817i	$0.529126\pi$
$644$	−2.38157	+	3.91307i	−0.0938469	+	0.154197i
$645$	−16.2488	+	1.48320i	−0.639797	+	0.0584008i
$646$	−0.250645	+	0.434131i	−0.00986151	+	0.0170806i
$647$	−9.17136	−	15.8853i	−0.360563	−	0.624514i	0.627490	−	0.778624i	$-0.284082\pi$
$647$	−9.17136	−	15.8853i	−0.360563	−	0.624514i	−0.988054	+	0.154110i	$0.950749\pi$
$648$	5.68070	−	6.98066i	0.223159	−	0.274226i
$649$			19.2833i			0.756934i
$650$	5.65905	+	10.4488i	0.221966	+	0.409834i
$651$	−7.09325	+	0.482332i	−0.278006	+	0.0189041i
$652$	8.45727	+	14.6484i	0.331212	+	0.573677i
$653$	4.70386	−	2.71577i	0.184076	−	0.106276i	−0.405130	−	0.914259i	$-0.632774\pi$
$653$	4.70386	−	2.71577i	0.184076	−	0.106276i	0.589206	+	0.807983i	$0.299440\pi$
$654$	19.2130	+	8.87133i	0.751287	+	0.346897i
$655$	6.01457			0.235009
$656$	5.36006	−	9.28389i	0.209275	−	0.362475i
$657$	15.7378	+	5.59438i	0.613990	+	0.218257i
$658$	−8.70386	−	0.201389i	−0.339312	−	0.00785096i
$659$	−21.6345	−	12.4907i	−0.842761	−	0.486568i	0.0154407	−	0.999881i	$-0.495085\pi$
$659$	−21.6345	−	12.4907i	−0.842761	−	0.486568i	−0.858202	+	0.513312i	$0.828418\pi$
$660$	5.66574	−	3.99904i	0.220539	−	0.155662i
$661$	24.7077	−	14.2650i	0.961019	−	0.554845i	0.0645326	−	0.997916i	$-0.479444\pi$
$661$	24.7077	−	14.2650i	0.961019	−	0.554845i	0.896487	+	0.443071i	$0.146111\pi$
$662$			9.34818i			0.363327i
$663$	−0.0345737	−	0.541171i	−0.00134273	−	0.0210174i
$664$			11.2537i			0.436728i
$665$	9.56786	+	17.4945i	0.371026	+	0.678408i
$666$	14.9585	−	12.7446i	0.579628	−	0.493844i
$667$	−0.290128	+	0.502516i	−0.0112338	+	0.0194575i
$668$	−20.6891			−0.800485
$669$	−7.24896	−	3.34711i	−0.280261	−	0.129407i
$670$	14.6690	+	8.46915i	0.566713	+	0.327192i
$671$	3.19066			0.123174
$672$	2.01677	−	4.11493i	0.0777985	−	0.158737i
$673$	12.9068	+	22.3552i	0.497520	+	0.861730i	0.999996	−	0.00286101i	$-0.000910689\pi$
$673$	12.9068	+	22.3552i	0.497520	+	0.861730i	−0.502476	+	0.864591i	$0.667577\pi$
$674$	10.6538	−	6.15095i	0.410367	−	0.236926i
$675$	−16.4904	+	4.61865i	−0.634715	+	0.177772i
$676$	−7.10314	+	10.8879i	−0.273198	+	0.418764i
$677$	43.2801			1.66339			0.831694	−	0.555234i	$-0.187371\pi$
$677$	43.2801			1.66339			0.831694	+	0.555234i	$0.187371\pi$
$678$	−10.9302	−	15.4857i	−0.419773	−	0.594724i
$679$	−14.5758	−	26.6513i	−0.559367	−	1.02278i
$680$	0.0981726	+	0.0566800i	0.00376475	+	0.00217358i
$681$	−10.4932	+	0.957818i	−0.402099	+	0.0367037i
$682$	−4.12074	−	2.37911i	−0.157791	−	0.0911009i
$683$	29.3919	+	16.9694i	1.12465	+	0.649317i	0.942584	−	0.333969i	$-0.108388\pi$
$683$	29.3919	+	16.9694i	1.12465	+	0.649317i	0.182067	+	0.983286i	$0.441721\pi$
$684$	3.13565	+	17.0328i	0.119894	+	0.651266i
$685$	−1.31516	−	0.759307i	−0.0502496	−	0.0290116i
$686$	−8.12560	−	16.6426i	−0.310237	−	0.635416i
$687$	31.0697	−	21.9298i	1.18538	−	0.836675i
$688$	−7.21590			−0.275104
$689$	−32.8702	−	0.895207i	−1.25226	−	0.0341047i
$690$	−3.89876	+	0.355880i	−0.148423	+	0.0135481i
$691$	15.0195	−	8.67148i	0.571367	−	0.329879i	−0.186328	−	0.982488i	$-0.559659\pi$
$691$	15.0195	−	8.67148i	0.571367	−	0.329879i	0.757695	+	0.652609i	$0.226325\pi$
$692$	−0.769009	−	1.33196i	−0.0292333	−	0.0506336i
$693$	8.68194	−	22.7424i	0.329799	−	0.863912i
$694$	−21.5737			−0.818927
$695$	−11.4639	−	6.61870i	−0.434852	−	0.251062i
$696$	0.243340	−	0.527010i	0.00922376	−	0.0199763i
$697$	0.930865			0.0352590
$698$	−2.40742	+	4.16977i	−0.0911220	+	0.157828i
$699$	−11.4863	+	8.10735i	−0.434451	+	0.306648i
$700$	−7.65024	+	4.18396i	−0.289152	+	0.158139i
$701$		−	0.520176i		−	0.0196468i	−0.999952	−	0.00982338i	$-0.996873\pi$
$701$		−	0.520176i		−	0.0196468i	0.999952	−	0.00982338i	$-0.00312693\pi$
$702$	−13.0348	−	13.4572i	−0.491965	−	0.507908i
$703$			37.8161i			1.42626i
$704$	2.65606	−	1.53348i	0.100104	−	0.0577951i
$705$	−4.29069	−	6.07895i	−0.161597	−	0.228946i
$706$	10.2546	+	5.92052i	0.385938	+	0.222822i
$707$	−0.602500	+	26.0396i	−0.0226593	+	0.979318i
$708$	−4.56521	+	9.88706i	−0.171571	+	0.371578i
$709$	1.22741	−	2.12594i	0.0460963	−	0.0798412i	−0.842057	−	0.539389i	$-0.818655\pi$
$709$	1.22741	−	2.12594i	0.0460963	−	0.0798412i	0.888153	+	0.459548i	$0.151989\pi$
$710$	−0.0532352			−0.00199788
$711$	−7.07148	+	19.8931i	−0.265201	+	0.746051i
$712$	3.91345	−	2.25943i	0.146663	−	0.0846758i
$713$	1.34308	+	2.32628i	0.0502988	+	0.0871200i
$714$	0.397004	−	0.0269958i	0.0148575	−	0.00101029i
$715$	−6.87504	−	12.6940i	−0.257112	−	0.474727i
$716$		−	25.7954i		−	0.964021i
$717$	−16.7526	+	11.8245i	−0.625638	+	0.441593i
$718$	3.36289	+	5.82469i	0.125502	+	0.217376i
$719$	−10.6686	+	18.4786i	−0.397872	+	0.689135i	−0.993463	−	0.114153i	$-0.963585\pi$
$719$	−10.6686	+	18.4786i	−0.397872	+	0.689135i	0.595591	+	0.803288i	$0.296918\pi$
$720$	3.85174	−	0.709083i	0.143546	−	0.0264260i
$721$	12.2580	−	20.1407i	0.456511	−	0.750078i
$722$	−12.4082	−	7.16385i	−0.461784	−	0.266611i
$723$	−0.921814	−	10.0987i	−0.0342826	−	0.375576i
$724$	9.76719	+	5.63909i	0.362995	+	0.209575i
$725$	−0.956540	+	0.552259i	−0.0355250	+	0.0205104i
$726$	−2.25530	+	1.59186i	−0.0837021	+	0.0590793i
$727$		−	14.7058i		−	0.545408i	−0.962098	−	0.272704i	$-0.912082\pi$
$727$		−	14.7058i		−	0.545408i	0.962098	−	0.272704i	$-0.0879180\pi$
$728$	−8.01077	−	5.17953i	−0.296899	−	0.191966i
$729$	23.0721	−	14.0242i	0.854521	−	0.519417i
$730$	3.63416	+	6.29456i	0.134506	+	0.232972i
$731$	−0.313291	−	0.542636i	−0.0115875	−	0.0200701i
$732$	1.63594	+	0.755374i	0.0604662	+	0.0279194i
$733$			52.0642i			1.92303i	0.274744	+	0.961517i	$0.411407\pi$
$733$			52.0642i			1.92303i	−0.274744	+	0.961517i	$0.588593\pi$
$734$	9.84257	−	17.0478i	0.363296	−	0.629247i
$735$	7.29281	−	14.0480i	0.268999	−	0.518168i
$736$	−1.73139			−0.0638199
$737$	34.4616	+	19.8964i	1.26941	+	0.732894i
$738$	24.4800	−	20.8570i	0.901123	−	0.767758i
$739$	7.73023	+	13.3891i	0.284361	+	0.492528i	0.972454	−	0.233095i	$-0.0748852\pi$
$739$	7.73023	+	13.3891i	0.284361	+	0.492528i	−0.688093	+	0.725623i	$0.741552\pi$
$740$	8.55158			0.314362
$741$	35.9791	−	2.29859i	1.32173	−	0.0844409i
$742$	0.558146	−	24.1226i	0.0204902	−	0.885570i
$743$	13.2405	−	7.64443i	0.485748	−	0.280447i	−0.237061	−	0.971495i	$-0.576184\pi$
$743$	13.2405	−	7.64443i	0.485748	−	0.280447i	0.722809	+	0.691048i	$0.242851\pi$
$744$	−1.54958	−	2.19540i	−0.0568102	−	0.0804873i
$745$	20.3744	+	11.7632i	0.746460	+	0.430969i
$746$			28.9840i			1.06118i
$747$	−11.3080	+	31.8110i	−0.413738	+	1.16390i
$748$	0.230635	+	0.133157i	0.00843285	+	0.00486871i
$749$	−36.0610	−	0.834376i	−1.31764	−	0.0304874i
$750$	−17.0302	−	7.86347i	−0.621856	−	0.287133i
$751$	−25.2310	−	43.7013i	−0.920691	−	1.59468i	−0.798348	−	0.602196i	$-0.794292\pi$
$751$	−25.2310	−	43.7013i	−0.920691	−	1.59468i	−0.122343	−	0.992488i	$-0.539041\pi$
$752$	−1.64532	−	2.84977i	−0.0599985	−	0.103920i
$753$	44.3348	−	4.04689i	1.61565	−	0.147477i
$754$	−1.02963	−	0.632445i	−0.0374970	−	0.0230323i
$755$	−27.8216			−1.01253
$756$	9.83561	−	9.60524i	0.357718	−	0.349339i
$757$	6.68024	+	11.5705i	0.242797	+	0.420537i	0.961510	−	0.274770i	$-0.0886017\pi$
$757$	6.68024	+	11.5705i	0.242797	+	0.420537i	−0.718713	+	0.695307i	$0.755268\pi$
$758$	11.2779	+	6.51133i	0.409634	+	0.236502i
$759$	−9.15928	+	0.836061i	−0.332461	+	0.0303471i
$760$	−3.76830	+	6.52688i	−0.136691	+	0.236755i
$761$	21.0008	−	36.3745i	0.761279	−	1.31857i	−0.180912	−	0.983499i	$-0.557905\pi$
$761$	21.0008	−	36.3745i	0.761279	−	1.31857i	0.942192	−	0.335075i	$-0.108762\pi$
$762$	1.46450	+	16.0440i	0.0530532	+	0.581213i
$763$	27.6136	+	16.8062i	0.999680	+	0.608424i
$764$	−13.4257	+	7.75132i	−0.485724	+	0.280433i
$765$	0.220553	+	0.258864i	0.00797410	+	0.00935926i
$766$			33.9837i			1.22788i
$767$	19.3166	+	11.8651i	0.697482	+	0.428424i
$768$	1.72488	−	0.157447i	0.0622412	−	0.00568140i
$769$	19.7922	−	11.4271i	0.713726	−	0.412070i	−0.0987129	−	0.995116i	$-0.531473\pi$
$769$	19.7922	−	11.4271i	0.713726	−	0.412070i	0.812439	+	0.583046i	$0.198139\pi$
$770$	9.29409	−	5.08300i	0.334936	−	0.183178i
$771$	−5.97318	+	12.9364i	−0.215119	+	0.465891i
$772$	−9.58213			−0.344868
$773$	19.2142	−	33.2800i	0.691088	−	1.19700i	−0.280394	−	0.959885i	$-0.590465\pi$
$773$	19.2142	−	33.2800i	0.691088	−	1.19700i	0.971482	−	0.237114i	$-0.0762016\pi$
$774$	−20.3973	−	7.25071i	−0.733166	−	0.260621i
$775$			5.11311i			0.183668i
$776$	5.74067	−	9.94312i	0.206078	−	0.356937i
$777$	24.9183	−	16.7381i	0.893940	−	0.600477i
$778$	8.87883	+	15.3786i	0.318321	+	0.551349i
$779$			61.8874i			2.21735i
$780$	−0.519795	−	8.13618i	−0.0186116	−	0.291322i
$781$	−0.125064			−0.00447516
$782$	−0.0751713	−	0.130200i	−0.00268812	−	0.00465596i
$783$	1.21740	−	1.24519i	0.0435065	−	0.0444996i
$784$	3.77664	−	5.89381i	0.134880	−	0.210493i
$785$		−	15.2523i		−	0.544377i
$786$	7.24481	+	3.34519i	0.258414	+	0.119319i
$787$	−25.1011	−	14.4922i	−0.894759	−	0.516590i	−0.0192631	−	0.999814i	$-0.506132\pi$
$787$	−25.1011	−	14.4922i	−0.894759	−	0.516590i	−0.875496	+	0.483225i	$0.839465\pi$
$788$			14.1310i			0.503397i
$789$	33.7017	+	15.5613i	1.19981	+	0.553997i
$790$	−7.95653	+	4.59371i	−0.283081	+	0.163437i
$791$	−13.8929	−	25.4027i	−0.493975	−	0.903217i
$792$	9.04881	−	1.66584i	0.321536	−	0.0591929i
$793$	1.96323	−	3.19618i	0.0697165	−	0.113500i
$794$	−0.713209			−0.0253109
$795$	16.8477	−	11.8916i	0.597527	−	0.421751i
$796$	21.3798	−	12.3436i	0.757785	−	0.437508i
$797$	−7.35493	+	12.7391i	−0.260525	+	0.451242i	−0.966381	−	0.257112i	$-0.917229\pi$
$797$	−7.35493	+	12.7391i	−0.260525	+	0.451242i	0.705857	+	0.708355i	$0.250562\pi$
$798$	1.79478	+	26.3943i	0.0635346	+	0.934349i
$799$	0.142868	−	0.247455i	0.00505432	−	0.00875434i
$800$	−2.85416	−	1.64785i	−0.100910	−	0.0582604i
$801$	13.3325	−	2.45445i	0.471082	−	0.0867236i
$802$	−4.87682	+	8.44690i	−0.172207	+	0.298271i
$803$	8.53767	+	14.7877i	0.301288	+	0.521846i
$804$	12.9590	+	18.3601i	0.457030	+	0.647509i
$805$	−5.97861	−	0.138332i	−0.210718	−	0.00487557i
$806$	−4.91874	+	2.66399i	−0.173255	+	0.0938350i
$807$	12.3233	−	1.12487i	0.433800	−	0.0395974i
$808$	−8.52573	+	4.92233i	−0.299934	+	0.173167i
$809$	−28.3477	+	16.3666i	−0.996652	+	0.575418i	−0.907256	−	0.420579i	$-0.861827\pi$
$809$	−28.3477	+	16.3666i	−0.996652	+	0.575418i	−0.0893963	+	0.995996i	$0.528494\pi$
$810$	11.6003	+	1.86594i	0.407592	+	0.0655624i
$811$		−	16.4407i		−	0.577310i	−0.957433	−	0.288655i	$-0.906792\pi$
$811$		−	16.4407i		−	0.577310i	0.957433	−	0.288655i	$-0.0932081\pi$
$812$	0.460991	−	0.757438i	0.0161776	−	0.0265809i
$813$	11.5321	+	5.32477i	0.404447	+	0.186748i
$814$	20.0901			0.704157
$815$	−11.0409	+	19.1233i	−0.386744	+	0.669861i
$816$	0.0867287	+	0.122875i	0.00303611	+	0.00430149i
$817$	36.0765	−	20.8288i	1.26216	−	0.728706i
$818$	−11.2696			−0.394033
$819$	−17.4397	−	22.6905i	−0.609392	−	0.792869i
$820$	13.9950			0.488726
$821$	13.9784	−	8.07041i	0.487848	−	0.281659i	−0.235833	−	0.971794i	$-0.575782\pi$
$821$	13.9784	−	8.07041i	0.487848	−	0.281659i	0.723681	+	0.690134i	$0.242449\pi$
$822$	−1.16185	−	1.64608i	−0.0405242	−	0.0574137i
$823$	−11.2699	+	19.5200i	−0.392844	+	0.680426i	−0.992823	−	0.119590i	$-0.961842\pi$
$823$	−11.2699	+	19.5200i	−0.392844	+	0.680426i	0.599979	+	0.800015i	$0.295175\pi$
$824$	8.91151			0.310447
$825$	−15.8946	−	7.33912i	−0.553380	−	0.255515i
$826$	−8.64849	+	14.2100i	−0.300920	+	0.494431i
$827$		−	33.2767i		−	1.15714i	−0.815632	−	0.578572i	$-0.803610\pi$
$827$		−	33.2767i		−	1.15714i	0.815632	−	0.578572i	$-0.196390\pi$
$828$	−4.89415	−	1.73974i	−0.170083	−	0.0604602i
$829$	6.67718	−	3.85507i	0.231908	−	0.133892i	−0.379544	−	0.925174i	$-0.623919\pi$
$829$	6.67718	−	3.85507i	0.231908	−	0.133892i	0.611452	+	0.791282i	$0.290586\pi$
$830$	−12.7233	+	7.34578i	−0.441631	+	0.254976i
$831$	−47.3672	+	4.32369i	−1.64315	+	0.149987i
$832$	0.0981594	−	3.60421i	0.00340306	−	0.124954i
$833$	0.607184	+	0.0281129i	0.0210377	+	0.000974055i
$834$	−10.1276	−	14.3485i	−0.350690	−	0.496848i
$835$	−13.5047	−	23.3908i	−0.467349	−	0.809472i
$836$	−8.85279	+	15.3335i	−0.306180	+	0.530320i
$837$	−2.17422	−	7.76283i	−0.0751521	−	0.268323i
$838$	−17.8865	−	10.3268i	−0.617878	−	0.356732i
$839$	−1.67127	+	2.89473i	−0.0576987	+	0.0999371i	−0.893432	−	0.449198i	$-0.851710\pi$
$839$	−1.67127	+	2.89473i	−0.0576987	+	0.0999371i	0.835733	+	0.549136i	$0.185043\pi$
$840$	5.96871	−	0.405865i	0.205940	−	0.0140037i
$841$	−14.4438	+	25.0175i	−0.498063	+	0.862671i
$842$	−28.2838	+	16.3296i	−0.974723	+	0.562756i
$843$	−31.3638	+	22.1374i	−1.08023	+	0.762454i
$844$	4.27943			0.147304
$845$	−16.9462	−	0.923730i	−0.582966	−	0.0317773i
$846$	−1.78733	−	9.70875i	−0.0614495	−	0.333794i
$847$	−3.69960	+	2.02333i	−0.127120	+	0.0695226i
$848$	7.89810	−	4.55997i	0.271222	−	0.156590i
$849$	−44.2650	−	20.4388i	−1.51917	−	0.701457i
$850$		−	0.286177i		−	0.00981580i
$851$	−9.82199	−	5.67073i	−0.336693	−	0.194390i
$852$	−0.0641240	−	0.0296084i	−0.00219685	−	0.00101437i
$853$			33.0674i			1.13221i	0.824335	+	0.566103i	$0.191549\pi$
$853$			33.0674i			1.13221i	−0.824335	+	0.566103i	$0.808451\pi$
$854$	2.35124	+	1.43101i	0.0804577	+	0.0489680i
$855$	−17.2103	+	14.6632i	−0.588579	+	0.501470i
$856$	−6.81672	−	11.8069i	−0.232991	−	0.403552i
$857$	29.8857			1.02087			0.510437	−	0.859915i	$-0.329483\pi$
$857$	29.8857			1.02087			0.510437	+	0.859915i	$0.329483\pi$
$858$	−1.22114	−	19.1142i	−0.0416892	−	0.652547i
$859$			15.6359i			0.533490i	0.963767	+	0.266745i	$0.0859481\pi$
$859$			15.6359i			0.533490i	−0.963767	+	0.266745i	$0.914052\pi$
$860$	−4.71013	−	8.15819i	−0.160614	−	0.278192i
$861$	40.7797	−	27.3926i	1.38977	−	0.933536i
$862$	−18.1328	+	31.4070i	−0.617607	+	1.06973i
$863$			32.3986i			1.10286i	0.834221	+	0.551430i	$0.185918\pi$
$863$			32.3986i			1.10286i	−0.834221	+	0.551430i	$0.814082\pi$
$864$	5.03395	+	1.28814i	0.171259	+	0.0438234i
$865$	1.00393	−	1.73886i	0.0341347	−	0.0591230i
$866$	11.5301			0.391808
$867$	12.3380	−	26.7209i	0.419020	−	0.907488i
$868$	−1.96959	−	3.60134i	−0.0668524	−	0.122237i
$869$	−18.6921	+	10.7919i	−0.634087	+	0.366090i
$870$	0.754668	−	0.0688863i	0.0255856	−	0.00233546i
$871$	41.1353	−	22.2789i	1.39382	−	0.754890i
$872$			12.2180i			0.413754i
$873$	26.2183	−	22.3380i	0.887356	−	0.756028i
$874$	8.65622	−	4.99767i	0.292801	−	0.169049i
$875$	−24.4765	−	14.8968i	−0.827455	−	0.503605i
$876$	0.876592	+	9.60330i	0.0296173	+	0.324466i
$877$	12.8318	−	22.2253i	0.433298	−	0.750494i	−0.563857	−	0.825872i	$-0.690683\pi$
$877$	12.8318	−	22.2253i	0.433298	−	0.750494i	0.997155	+	0.0753785i	$0.0240165\pi$
$878$	−1.32597	+	2.29664i	−0.0447492	+	0.0775079i
$879$	42.4583	−	3.87560i	1.43208	−	0.130721i
$880$	3.46745	+	2.00194i	0.116888	+	0.0674852i
$881$	−13.9927	−	24.2361i	−0.471426	−	0.816534i	0.528039	−	0.849220i	$-0.322927\pi$
$881$	−13.9927	−	24.2361i	−0.471426	−	0.816534i	−0.999466	+	0.0326855i	$0.989594\pi$
$882$	16.5977	−	12.8653i	0.558874	−	0.433197i
$883$	−23.0476			−0.775613			−0.387807	−	0.921741i	$-0.626767\pi$
$883$	−23.0476			−0.775613			−0.387807	+	0.921741i	$0.626767\pi$
$884$	0.275299	−	0.149102i	0.00925929	−	0.00501483i
$885$	−14.1581	+	1.29235i	−0.475918	+	0.0434419i
$886$	15.1128	+	26.1762i	0.507725	+	0.879406i
$887$	−25.8382	−	44.7531i	−0.867562	−	1.50266i	−0.864481	−	0.502666i	$-0.832353\pi$
$887$	−25.8382	−	44.7531i	−0.867562	−	1.50266i	−0.00308090	−	0.999995i	$-0.500981\pi$
$888$	10.3007	+	4.75622i	0.345670	+	0.159608i
$889$	−0.569259	+	24.6029i	−0.0190923	+	0.825155i
$890$	5.10896	+	2.94966i	0.171253	+	0.0988728i
$891$	27.2523	+	4.38361i	0.912986	+	0.146857i
$892$		−	4.60979i		−	0.154347i
$893$	16.4518	+	9.49843i	0.550538	+	0.317853i
$894$	17.9994	+	25.5011i	0.601989	+	0.852883i
$895$	29.1639	−	16.8378i	0.974843	−	0.562826i
$896$	2.64504	+	0.0612007i	0.0883647	+	0.00204457i
$897$	−4.79825	+	9.68956i	−0.160209	+	0.323525i
$898$	−27.3586			−0.912970
$899$	−0.259975	−	0.450290i	−0.00867065	−	0.0150180i
$900$	−6.41211	−	7.52594i	−0.213737	−	0.250865i
$901$	0.685819	+	0.395958i	0.0228479	+	0.0131913i
$902$	32.8781			1.09472
$903$	−29.6929	−	14.5528i	−0.988119	−	0.484287i
$904$	5.47172	−	9.47730i	0.181987	−	0.315210i
$905$			14.7235i			0.489426i
$906$	−33.5122	−	15.4738i	−1.11337	−	0.514083i
$907$	10.6253	+	18.4036i	0.352809	+	0.611082i	0.986740	−	0.162307i	$-0.0518934\pi$
$907$	10.6253	+	18.4036i	0.352809	+	0.611082i	−0.633932	+	0.773389i	$0.718560\pi$
$908$	−3.04171	−	5.26839i	−0.100943	−	0.174838i
$909$	−29.0459	+	5.34719i	−0.963391	+	0.177355i
$910$	0.626916	−	12.4378i	0.0207821	−	0.412308i
$911$		−	16.1905i		−	0.536416i	−0.963361	−	0.268208i	$-0.913569\pi$
$911$		−	16.1905i		−	0.536416i	0.963361	−	0.268208i	$-0.0864315\pi$
$912$	−8.16920	+	5.76605i	−0.270509	+	0.190933i
$913$	−29.8905	+	17.2573i	−0.989232	+	0.571134i
$914$	20.4782	+	11.8231i	0.677359	+	0.391074i
$915$	0.213836	+	2.34264i	0.00706922	+	0.0774452i
$916$	19.0147	+	10.9782i	0.628265	+	0.362729i
$917$	10.4125	+	6.33724i	0.343851	+	0.209274i
$918$	0.121690	+	0.434480i	0.00401636	+	0.0143400i
$919$	−2.88259	+	4.99280i	−0.0950880	+	0.164697i	−0.909645	−	0.415386i	$-0.863647\pi$
$919$	−2.88259	+	4.99280i	−0.0950880	+	0.164697i	0.814557	+	0.580083i	$0.196980\pi$
$920$	−1.13015	−	1.95748i	−0.0372600	−	0.0645363i
$921$	−21.4111	+	15.1125i	−0.705518	+	0.497975i
$922$			11.8883i			0.391519i
$923$	−0.0769529	+	0.125281i	−0.00253294	+	0.00412367i
$924$	14.0222	−	0.953491i	0.461296	−	0.0313675i
$925$	−10.7942	−	18.6962i	−0.354913	−	0.614726i
$926$	18.1007	−	10.4504i	0.594825	−	0.343422i
$927$	25.1903	+	8.95449i	0.827358	+	0.294104i
$928$	0.335139			0.0110015
$929$	1.41023	−	2.44259i	0.0462682	−	0.0801388i	−0.841964	−	0.539534i	$-0.818600\pi$
$929$	1.41023	−	2.44259i	0.0462682	−	0.0801388i	0.888232	+	0.459395i	$0.151934\pi$
$930$	1.47061	−	3.18496i	0.0482233	−	0.104439i
$931$	−1.86905	+	40.3679i	−0.0612558	+	1.32300i
$932$	−7.02965	−	4.05857i	−0.230264	−	0.132943i
$933$	−20.4600	−	28.9872i	−0.669830	−	0.948999i
$934$	−24.6170	+	14.2126i	−0.805493	+	0.465052i
$935$			0.347670i			0.0113700i
$936$	3.89907	−	10.0895i	0.127445	−	0.329784i
$937$			11.2844i			0.368645i	0.982866	+	0.184322i	$0.0590090\pi$
$937$			11.2844i			0.368645i	−0.982866	+	0.184322i	$0.940991\pi$
$938$	16.4717	+	30.1179i	0.537818	+	0.983383i
$939$	−4.36837	+	3.08332i	−0.142556	+	0.100620i
$940$	2.14794	−	3.72034i	0.0700580	−	0.121344i
$941$	39.0236			1.27213			0.636066	−	0.771634i	$-0.280561\pi$
$941$	39.0236			1.27213			0.636066	+	0.771634i	$0.280561\pi$
$942$	8.48301	−	18.3720i	0.276391	−	0.598592i
$943$	−16.0740	−	9.28035i	−0.523443	−	0.302210i
$944$	−6.28742			−0.204638
$945$	17.2797	+	4.85023i	0.562108	+	0.157778i
$946$	−11.0654	−	19.1659i	−0.359768	−	0.623136i
$947$	−43.0226	+	24.8391i	−1.39805	+	0.807163i	−0.994188	−	0.107658i	$-0.965665\pi$
$947$	−43.0226	+	24.8391i	−1.39805	+	0.807163i	−0.403859	+	0.914821i	$0.632331\pi$
$948$	−12.1389	+	1.10804i	−0.394253	+	0.0359875i
$949$	20.0665	+	0.546504i	0.651388	+	0.0177403i
$950$	19.0261			0.617290
$951$	−37.7888	+	26.6724i	−1.22539	+	0.864913i
$952$	0.110237	+	0.201564i	0.00357280	+	0.00653274i
$953$	−10.7703	−	6.21825i	−0.348885	−	0.201429i	0.315309	−	0.948989i	$-0.397892\pi$
$953$	−10.7703	−	6.21825i	−0.348885	−	0.201429i	−0.664194	+	0.747560i	$0.731225\pi$
$954$	26.9077	−	4.95355i	0.871168	−	0.160377i
$955$	−17.5270	−	10.1192i	−0.567162	−	0.327451i
$956$	−10.2527	−	5.91937i	−0.331595	−	0.191446i
$957$	1.77293	−	0.161833i	0.0573106	−	0.00523133i
$958$	17.8574	+	10.3099i	0.576945	+	0.333099i
$959$	−1.47678	−	2.70023i	−0.0476876	−	0.0871951i
$960$	1.30391	+	1.84735i	0.0420836	+	0.0596230i
$961$	28.5930			0.922355
$962$	12.3615	−	20.1248i	0.398552	−	0.648851i
$963$	−7.40508	−	40.2244i	−0.238625	−	1.29621i
$964$	5.07035	−	2.92737i	0.163305	−	0.0942843i
$965$	−6.25467	−	10.8334i	−0.201345	−	0.348740i
$966$	−7.12455	−	3.49181i	−0.229228	−	0.112347i
$967$	−16.2824			−0.523606			−0.261803	−	0.965121i	$-0.584317\pi$
$967$	−16.2824			−0.523606			−0.261803	+	0.965121i	$0.584317\pi$
$968$	−1.38025	−	0.796889i	−0.0443630	−	0.0256130i
$969$	−0.788287	−	0.363980i	−0.0253234	−	0.0116927i
$970$	14.9887			0.481259
$971$	−28.6052	+	49.5456i	−0.917984	+	1.59000i	−0.115512	+	0.993306i	$0.536851\pi$
$971$	−28.6052	+	49.5456i	−0.917984	+	1.59000i	−0.802472	+	0.596689i	$0.796482\pi$
$972$	12.9352	+	8.69944i	0.414897	+	0.279035i
$973$	−12.8727	−	23.5373i	−0.412680	−	0.754572i
$974$			0.952156i			0.0305090i
$975$	−17.1319	+	11.4063i	−0.548659	+	0.365294i
$976$			1.04034i			0.0333003i
$977$	−31.9500	+	18.4463i	−1.02217	+	0.590151i	−0.914732	−	0.404061i	$-0.867598\pi$
$977$	−31.9500	+	18.4463i	−1.02217	+	0.590151i	−0.107439	+	0.994212i	$0.534265\pi$
$978$	−23.9352	+	16.8941i	−0.765363	+	0.540215i
$979$	12.0024	+	6.92958i	0.383598	+	0.221470i
$980$	9.12863	+	0.422660i	0.291603	+	0.0135014i
$981$	−12.2769	+	34.5369i	−0.391973	+	1.10268i
$982$	10.4927	−	18.1739i	0.334837	−	0.579954i
$983$	−46.8524			−1.49436			−0.747180	−	0.664622i	$-0.768593\pi$
$983$	−46.8524			−1.49436			−0.747180	+	0.664622i	$0.768593\pi$
$984$	16.8575	+	7.78373i	0.537398	+	0.248136i
$985$	−15.9763	+	9.22394i	−0.509048	+	0.293899i
$986$	0.0145506	+	0.0252024i	0.000463386	+	0.000802608i
$987$	−1.02303	−	15.0448i	−0.0325634	−	0.478882i
$988$	9.91284	+	18.3029i	0.315369	+	0.582293i
$989$			12.4935i			0.397271i
$990$	7.78992	+	9.14309i	0.247580	+	0.290586i
$991$	−4.64312	−	8.04211i	−0.147493	−	0.255466i	0.782807	−	0.622265i	$-0.213787\pi$
$991$	−4.64312	−	8.04211i	−0.147493	−	0.255466i	−0.930300	+	0.366798i	$0.880454\pi$
$992$	0.775724	−	1.34359i	0.0246293	−	0.0426591i
$993$	−16.1245	+	1.47185i	−0.511695	+	0.0467077i
$994$	−0.0921614	−	0.0560911i	−0.00292318	−	0.00177910i
$995$	27.9110	+	16.1144i	0.884838	+	0.510861i
$996$	−19.4113	+	1.77187i	−0.615070	+	0.0561438i
$997$	−32.6850	−	18.8707i	−1.03515	−	0.597641i	−0.116691	−	0.993168i	$-0.537229\pi$
$997$	−32.6850	−	18.8707i	−1.03515	−	0.597641i	−0.918454	+	0.395527i	$0.870562\pi$
$998$	26.6892	−	15.4090i	0.844832	−	0.487764i
$999$	24.3381	+	23.7949i	0.770024	+	0.752838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.c.419.6	✓	64
3.2	odd	2	inner	546.2.bq.c.419.26	yes	64
7.6	odd	2	inner	546.2.bq.c.419.11	yes	64
13.9	even	3	inner	546.2.bq.c.503.23	yes	64
21.20	even	2	inner	546.2.bq.c.419.23	yes	64
39.35	odd	6	inner	546.2.bq.c.503.11	yes	64
91.48	odd	6	inner	546.2.bq.c.503.26	yes	64
273.230	even	6	inner	546.2.bq.c.503.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.c.419.6	✓	64	1.1	even	1	trivial
546.2.bq.c.419.11	yes	64	7.6	odd	2	inner
546.2.bq.c.419.23	yes	64	21.20	even	2	inner
546.2.bq.c.419.26	yes	64	3.2	odd	2	inner
546.2.bq.c.503.6	yes	64	273.230	even	6	inner
546.2.bq.c.503.11	yes	64	39.35	odd	6	inner
546.2.bq.c.503.23	yes	64	13.9	even	3	inner
546.2.bq.c.503.26	yes	64	91.48	odd	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.998793 - 1.41507i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.30549 q^{5} +(1.57251 + 0.726086i) q^{6} +(2.26007 + 1.37552i) q^{7} +1.00000i q^{8} +(-1.00482 + 2.82672i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.998793 - 1.41507i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.30549 q^{5} +(1.57251 + 0.726086i) q^{6} +(2.26007 + 1.37552i) q^{7} +1.00000i q^{8} +(-1.00482 + 2.82672i) q^{9} +(-1.13058 + 0.652743i) q^{10} +(-2.65606 + 1.53348i) q^{11} +(-1.72488 + 0.157447i) q^{12} +(-0.0981594 + 3.60421i) q^{13} +(-2.64504 - 0.0612007i) q^{14} +(-1.30391 - 1.84735i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.0434167 - 0.0752000i) q^{17} +(-0.543156 - 2.95042i) q^{18} +(4.99958 + 2.88651i) q^{19} +(0.652743 - 1.13058i) q^{20} +(-0.310892 - 4.57202i) q^{21} +(1.53348 - 2.65606i) q^{22} +(-1.49943 + 0.865695i) q^{23} +(1.41507 - 0.998793i) q^{24} -3.29570 q^{25} +(-1.71710 - 3.17042i) q^{26} +(5.00360 - 1.40141i) q^{27} +(2.32128 - 1.26952i) q^{28} +(0.290239 - 0.167569i) q^{29} +(2.05290 + 0.947896i) q^{30} -1.55145i q^{31} +(0.866025 + 0.500000i) q^{32} +(4.82283 + 2.22688i) q^{33} +0.0868334i q^{34} +(2.95050 + 1.79573i) q^{35} +(1.94560 + 2.28356i) q^{36} +(3.27525 + 5.67289i) q^{37} -5.77302 q^{38} +(5.19824 - 3.46096i) q^{39} +1.30549i q^{40} +(5.36006 + 9.28389i) q^{41} +(2.55525 + 3.80404i) q^{42} +(3.60795 - 6.24915i) q^{43} +3.06696i q^{44} +(-1.31178 + 3.69024i) q^{45} +(0.865695 - 1.49943i) q^{46} +3.29063 q^{47} +(-0.726086 + 1.57251i) q^{48} +(3.21587 + 6.21757i) q^{49} +(2.85416 - 1.64785i) q^{50} +(-0.149777 + 0.0136717i) q^{51} +(3.07226 + 1.88712i) q^{52} +9.11994i q^{53} +(-3.63254 + 3.71546i) q^{54} +(-3.46745 + 2.00194i) q^{55} +(-1.37552 + 2.26007i) q^{56} +(-0.908947 - 9.95776i) q^{57} +(-0.167569 + 0.290239i) q^{58} +(3.14371 - 5.44507i) q^{59} +(-2.25181 + 0.205546i) q^{60} +(-0.900957 - 0.520168i) q^{61} +(0.775724 + 1.34359i) q^{62} +(-6.15919 + 5.00643i) q^{63} -1.00000 q^{64} +(-0.128146 + 4.70526i) q^{65} +(-5.29013 + 0.482885i) q^{66} +(-6.48735 - 11.2364i) q^{67} +(-0.0434167 - 0.0752000i) q^{68} +(2.72263 + 1.25714i) q^{69} +(-3.45307 - 0.0798967i) q^{70} +(0.0353148 + 0.0203890i) q^{71} +(-2.82672 - 1.00482i) q^{72} -5.56752i q^{73} +(-5.67289 - 3.27525i) q^{74} +(3.29173 + 4.66364i) q^{75} +(4.99958 - 2.88651i) q^{76} +(-8.11223 - 0.187700i) q^{77} +(-2.77133 + 5.59640i) q^{78} +7.03754 q^{79} +(-0.652743 - 1.13058i) q^{80} +(-6.98066 - 5.68070i) q^{81} +(-9.28389 - 5.36006i) q^{82} +11.2537 q^{83} +(-4.11493 - 2.01677i) q^{84} +(0.0566800 - 0.0981726i) q^{85} +7.21590i q^{86} +(-0.527010 - 0.243340i) q^{87} +(-1.53348 - 2.65606i) q^{88} +(-2.25943 - 3.91345i) q^{89} +(-0.709083 - 3.85174i) q^{90} +(-5.17953 + 8.01077i) q^{91} +1.73139i q^{92} +(-2.19540 + 1.54958i) q^{93} +(-2.84977 + 1.64532i) q^{94} +(6.52688 + 3.76830i) q^{95} +(-0.157447 - 1.72488i) q^{96} +(-9.94312 - 5.74067i) q^{97} +(-5.89381 - 3.77664i) q^{98} +(-1.66584 - 9.04881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

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