LMFDB - Embedded newform 252.2.bi.c.223.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(139,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.139"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,-6,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			223.28
Character	$\chi$	$=$	252.223
Dual form			252.2.bi.c.139.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.648812 + 1.25660i) q^{2} +(0.758625 - 1.55708i) q^{3} +(-1.15809 + 1.63059i) q^{4} +(2.66647 - 1.53948i) q^{5} +(2.44883 - 0.0569623i) q^{6} +(-1.15806 + 2.37885i) q^{7} +(-2.80038 - 0.397302i) q^{8} +(-1.84898 - 2.36247i) q^{9} +(3.66455 + 2.35184i) q^{10} +(3.64870 + 2.10658i) q^{11} +(1.66041 + 3.04024i) q^{12} +(2.97309 - 1.71651i) q^{13} +(-3.74062 + 0.0882086i) q^{14} +(-0.374249 - 5.31978i) q^{15} +(-1.31767 - 3.77674i) q^{16} -2.29127i q^{17} +(1.76905 - 3.85623i) q^{18} -1.70965 q^{19} +(-0.577723 + 6.13078i) q^{20} +(2.82551 + 3.60783i) q^{21} +(-0.279805 + 5.95173i) q^{22} +(-4.68317 + 2.70383i) q^{23} +(-2.74307 + 4.05901i) q^{24} +(2.24003 - 3.87984i) q^{25} +(4.08594 + 2.62229i) q^{26} +(-5.08123 + 1.08677i) q^{27} +(-2.53780 - 4.64323i) q^{28} +(-4.76517 + 8.25352i) q^{29} +(6.44202 - 3.92182i) q^{30} +(-3.22265 - 5.58179i) q^{31} +(3.89093 - 4.10618i) q^{32} +(6.04809 - 4.08320i) q^{33} +(2.87921 - 1.48660i) q^{34} +(0.574276 + 8.12592i) q^{35} +(5.99351 - 0.278982i) q^{36} -2.04135 q^{37} +(-1.10924 - 2.14835i) q^{38} +(-0.417285 - 5.93151i) q^{39} +(-8.07877 + 3.25176i) q^{40} +(-4.43693 + 2.56166i) q^{41} +(-2.70038 + 5.89135i) q^{42} +(-2.89849 - 1.67344i) q^{43} +(-7.66048 + 3.50995i) q^{44} +(-8.56723 - 3.45298i) q^{45} +(-6.43612 - 4.13059i) q^{46} +(-2.20674 + 3.82219i) q^{47} +(-6.88029 - 0.813409i) q^{48} +(-4.31781 - 5.50968i) q^{49} +(6.32876 + 0.297531i) q^{50} +(-3.56768 - 1.73821i) q^{51} +(-0.644156 + 6.83577i) q^{52} +10.5744 q^{53} +(-4.66240 - 5.67997i) q^{54} +12.9722 q^{55} +(4.18813 - 6.20158i) q^{56} +(-1.29698 + 2.66206i) q^{57} +(-13.4631 - 0.632933i) q^{58} +(-4.44595 - 7.70061i) q^{59} +(9.10782 + 5.55052i) q^{60} +(-3.57388 - 2.06338i) q^{61} +(4.92318 - 7.67111i) q^{62} +(7.76118 - 1.66255i) q^{63} +(7.68430 + 2.22520i) q^{64} +(5.28509 - 9.15404i) q^{65} +(9.05503 + 4.95080i) q^{66} +(9.53591 - 5.50556i) q^{67} +(3.73613 + 2.65349i) q^{68} +(0.657301 + 9.34324i) q^{69} +(-9.83843 + 5.99383i) q^{70} +2.48841i q^{71} +(4.23923 + 7.35044i) q^{72} +3.46980i q^{73} +(-1.32445 - 2.56517i) q^{74} +(-4.34187 - 6.43124i) q^{75} +(1.97992 - 2.78774i) q^{76} +(-9.23662 + 6.24015i) q^{77} +(7.18280 - 4.37280i) q^{78} +(8.87914 + 5.12638i) q^{79} +(-9.32776 - 8.04200i) q^{80} +(-2.16257 + 8.73632i) q^{81} +(-6.09771 - 3.91340i) q^{82} +(0.0572673 - 0.0991899i) q^{83} +(-9.15510 + 0.429082i) q^{84} +(-3.52738 - 6.10959i) q^{85} +(0.222275 - 4.72799i) q^{86} +(9.23639 + 13.6811i) q^{87} +(-9.38081 - 7.34886i) q^{88} -3.61933i q^{89} +(-1.21950 - 13.0059i) q^{90} +(0.640313 + 9.06033i) q^{91} +(1.01467 - 10.7676i) q^{92} +(-11.1361 + 0.783427i) q^{93} +(-6.23472 - 0.293110i) q^{94} +(-4.55872 + 2.63198i) q^{95} +(-3.44188 - 9.17352i) q^{96} +(-5.53677 - 3.19666i) q^{97} +(4.12201 - 9.00050i) q^{98} +(-1.76963 - 12.5150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44}+ \cdots + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	0.648812	+	1.25660i	0.458779	+	0.888550i
$2$	0.648812	+	1.25660i	0.458779	+	0.888550i
$3$	0.758625	−	1.55708i	0.437992	−	0.898979i
$3$	0.758625	−	1.55708i	0.437992	−	0.898979i
$4$	−1.15809	+	1.63059i	−0.579043	+	0.815297i
$5$	2.66647	−	1.53948i	1.19248	−	0.688479i	0.233612	−	0.972330i	$-0.424946\pi$
$5$	2.66647	−	1.53948i	1.19248	−	0.688479i	0.958868	+	0.283851i	$0.0916123\pi$
$6$	2.44883	−	0.0569623i	0.999730	−	0.0232548i
$7$	−1.15806	+	2.37885i	−0.437704	+	0.899119i
$7$	−1.15806	+	2.37885i	−0.437704	+	0.899119i
$8$	−2.80038	−	0.397302i	−0.990085	−	0.140468i
$9$	−1.84898	−	2.36247i	−0.616326	−	0.787491i
$10$	3.66455	+	2.35184i	1.15883	+	0.743719i
$11$	3.64870	+	2.10658i	1.10012	+	0.635157i	0.936254	−	0.351325i	$-0.114269\pi$
$11$	3.64870	+	2.10658i	1.10012	+	0.635157i	0.163870	+	0.986482i	$0.447602\pi$
$12$	1.66041	+	3.04024i	0.479318	+	0.877641i
$13$	2.97309	−	1.71651i	0.824586	−	0.476075i	−0.0274094	−	0.999624i	$-0.508726\pi$
$13$	2.97309	−	1.71651i	0.824586	−	0.476075i	0.851995	+	0.523549i	$0.175392\pi$
$14$	−3.74062	+	0.0882086i	−0.999722	+	0.0235747i
$15$	−0.374249	−	5.31978i	−0.0966308	−	1.37356i
$16$	−1.31767	−	3.77674i	−0.329418	−	0.944184i
$17$		−	2.29127i		−	0.555715i	−0.960622	−	0.277857i	$-0.910376\pi$
$17$		−	2.29127i		−	0.555715i	0.960622	−	0.277857i	$-0.0896242\pi$
$18$	1.76905	−	3.85623i	0.416968	−	0.908921i
$19$	−1.70965			−0.392221			−0.196110	−	0.980582i	$-0.562831\pi$
$19$	−1.70965			−0.392221			−0.196110	+	0.980582i	$0.562831\pi$
$20$	−0.577723	+	6.13078i	−0.129183	+	1.37088i
$21$	2.82551	+	3.60783i	0.616578	+	0.787294i
$22$	−0.279805	+	5.95173i	−0.0596547	+	1.26891i
$23$	−4.68317	+	2.70383i	−0.976507	+	0.563787i	−0.901214	−	0.433375i	$-0.857323\pi$
$23$	−4.68317	+	2.70383i	−0.976507	+	0.563787i	−0.0752935	+	0.997161i	$0.523989\pi$
$24$	−2.74307	+	4.05901i	−0.559927	+	0.828542i
$25$	2.24003	−	3.87984i	0.448005	−	0.775968i
$26$	4.08594	+	2.62229i	0.801319	+	0.514273i
$27$	−5.08123	+	1.08677i	−0.977884	+	0.209149i
$28$	−2.53780	−	4.64323i	−0.479599	−	0.877488i
$29$	−4.76517	+	8.25352i	−0.884870	+	1.53264i	−0.0390079	+	0.999239i	$0.512420\pi$
$29$	−4.76517	+	8.25352i	−0.884870	+	1.53264i	−0.845862	+	0.533401i	$0.820914\pi$
$30$	6.44202	−	3.92182i	1.17615	−	0.716023i
$31$	−3.22265	−	5.58179i	−0.578805	−	1.00252i	−0.995617	−	0.0935263i	$-0.970186\pi$
$31$	−3.22265	−	5.58179i	−0.578805	−	1.00252i	0.416812	−	0.908993i	$-0.363147\pi$
$32$	3.89093	−	4.10618i	0.687825	−	0.725877i
$33$	6.04809	−	4.08320i	1.05284	−	0.710794i
$34$	2.87921	−	1.48660i	0.493780	−	0.254950i
$35$	0.574276	+	8.12592i	0.0970704	+	1.37353i
$36$	5.99351	−	0.278982i	0.998918	−	0.0464970i
$37$	−2.04135			−0.335597			−0.167798	−	0.985821i	$-0.553666\pi$
$37$	−2.04135			−0.335597			−0.167798	+	0.985821i	$0.553666\pi$
$38$	−1.10924	−	2.14835i	−0.179943	−	0.348508i
$39$	−0.417285	−	5.93151i	−0.0668191	−	0.949802i
$40$	−8.07877	+	3.25176i	−1.27737	+	0.514148i
$41$	−4.43693	+	2.56166i	−0.692931	+	0.400064i	−0.804709	−	0.593669i	$-0.797679\pi$
$41$	−4.43693	+	2.56166i	−0.692931	+	0.400064i	0.111778	+	0.993733i	$0.464345\pi$
$42$	−2.70038	+	5.89135i	−0.416677	+	0.909054i
$43$	−2.89849	−	1.67344i	−0.442015	−	0.255198i	0.262437	−	0.964949i	$-0.415474\pi$
$43$	−2.89849	−	1.67344i	−0.442015	−	0.255198i	−0.704452	+	0.709752i	$0.748807\pi$
$44$	−7.66048	+	3.50995i	−1.15486	+	0.529144i
$45$	−8.56723	−	3.45298i	−1.27713	−	0.514741i
$46$	−6.43612	−	4.13059i	−0.948954	−	0.609022i
$47$	−2.20674	+	3.82219i	−0.321886	+	0.557524i	−0.980877	−	0.194627i	$-0.937650\pi$
$47$	−2.20674	+	3.82219i	−0.321886	+	0.557524i	0.658991	+	0.752151i	$0.270984\pi$
$48$	−6.88029	−	0.813409i	−0.993084	−	0.117405i
$49$	−4.31781	−	5.50968i	−0.616830	−	0.787097i
$50$	6.32876	+	0.297531i	0.895022	+	0.0420772i
$51$	−3.56768	−	1.73821i	−0.499576	−	0.243399i
$52$	−0.644156	+	6.83577i	−0.0893284	+	0.947950i
$53$	10.5744			1.45250			0.726250	−	0.687431i	$-0.241262\pi$
$53$	10.5744			1.45250			0.726250	+	0.687431i	$0.241262\pi$
$54$	−4.66240	−	5.67997i	−0.634472	−	0.772946i
$55$	12.9722			1.74917
$56$	4.18813	−	6.20158i	0.559662	−	0.828721i
$57$	−1.29698	+	2.66206i	−0.171790	+	0.352598i
$58$	−13.4631	−	0.632933i	−1.76779	−	0.0831081i
$59$	−4.44595	−	7.70061i	−0.578813	−	1.00253i	−0.995616	−	0.0935372i	$-0.970183\pi$
$59$	−4.44595	−	7.70061i	−0.578813	−	1.00253i	0.416802	−	0.908997i	$-0.363151\pi$
$60$	9.10782	+	5.55052i	1.17581	+	0.716569i
$61$	−3.57388	−	2.06338i	−0.457588	−	0.264189i	0.253441	−	0.967351i	$-0.418437\pi$
$61$	−3.57388	−	2.06338i	−0.457588	−	0.264189i	−0.711030	+	0.703162i	$0.751771\pi$
$62$	4.92318	−	7.67111i	0.625245	−	0.974232i
$63$	7.76118	−	1.66255i	0.977817	−	0.209462i
$64$	7.68430	+	2.22520i	0.960538	+	0.278150i
$65$	5.28509	−	9.15404i	0.655535	−	1.13542i
$66$	9.05503	+	4.95080i	1.11460	+	0.609402i
$67$	9.53591	−	5.50556i	1.16500	−	0.672611i	0.212500	−	0.977161i	$-0.431839\pi$
$67$	9.53591	−	5.50556i	1.16500	−	0.672611i	0.952496	+	0.304550i	$0.0985061\pi$
$68$	3.73613	+	2.65349i	0.453072	+	0.321783i
$69$	0.657301	+	9.34324i	0.0791298	+	1.12479i
$70$	−9.83843	+	5.99383i	−1.17592	+	0.716400i
$71$			2.48841i			0.295320i	0.989038	+	0.147660i	$0.0471741\pi$
$71$			2.48841i			0.295320i	−0.989038	+	0.147660i	$0.952826\pi$
$72$	4.23923	+	7.35044i	0.499598	+	0.866257i
$73$			3.46980i			0.406110i	0.979167	+	0.203055i	$0.0650870\pi$
$73$			3.46980i			0.406110i	−0.979167	+	0.203055i	$0.934913\pi$
$74$	−1.32445	−	2.56517i	−0.153965	−	0.298194i
$75$	−4.34187	−	6.43124i	−0.501356	−	0.742615i
$76$	1.97992	−	2.78774i	0.227113	−	0.319776i
$77$	−9.23662	+	6.24015i	−1.05261	+	0.711131i
$78$	7.18280	−	4.37280i	0.813292	−	0.495122i
$79$	8.87914	+	5.12638i	0.998982	+	0.576762i	0.907947	−	0.419085i	$-0.137649\pi$
$79$	8.87914	+	5.12638i	0.998982	+	0.576762i	0.0910349	+	0.995848i	$0.470983\pi$
$80$	−9.32776	−	8.04200i	−1.04287	−	0.899123i
$81$	−2.16257	+	8.73632i	−0.240285	+	0.970702i
$82$	−6.09771	−	3.91340i	−0.673380	−	0.432163i
$83$	0.0572673	−	0.0991899i	0.00628591	−	0.0108875i	−0.862865	−	0.505434i	$-0.831332\pi$
$83$	0.0572673	−	0.0991899i	0.00628591	−	0.0108875i	0.869151	+	0.494546i	$0.164666\pi$
$84$	−9.15510	+	0.429082i	−0.998903	+	0.0468167i
$85$	−3.52738	−	6.10959i	−0.382598	−	0.662678i
$86$	0.222275	−	4.72799i	0.0239685	−	0.509832i
$87$	9.23639	+	13.6811i	0.990245	+	1.46676i
$88$	−9.38081	−	7.34886i	−0.999997	−	0.783391i
$89$		−	3.61933i		−	0.383648i	−0.981429	−	0.191824i	$-0.938560\pi$
$89$		−	3.61933i		−	0.383648i	0.981429	−	0.191824i	$-0.0614403\pi$
$90$	−1.21950	−	13.0059i	−0.128547	−	1.37094i
$91$	0.640313	+	9.06033i	0.0671230	+	0.949781i
$92$	1.01467	−	10.7676i	0.105786	−	1.12260i
$93$	−11.1361	+	0.783427i	−1.15476	+	0.0812376i
$94$	−6.23472	−	0.293110i	−0.643063	−	0.0302320i
$95$	−4.55872	+	2.63198i	−0.467715	+	0.270035i
$96$	−3.44188	−	9.17352i	−0.351286	−	0.936268i
$97$	−5.53677	−	3.19666i	−0.562174	−	0.324571i	0.191844	−	0.981426i	$-0.438553\pi$
$97$	−5.53677	−	3.19666i	−0.562174	−	0.324571i	−0.754018	+	0.656854i	$0.771887\pi$
$98$	4.12201	−	9.00050i	0.416386	−	0.909188i
$99$	−1.76963	−	12.5150i	−0.177854	−	1.25780i
$100$	3.73230	+	8.14576i	0.373230	+	0.814576i
$101$	14.8206	+	8.55666i	1.47470	+	0.851420i	0.999594	−	0.0285076i	$-0.00907547\pi$
$101$	14.8206	+	8.55666i	1.47470	+	0.851420i	0.475109	+	0.879927i	$0.342409\pi$
$102$	−0.130516	−	5.61092i	−0.0129230	−	0.555564i
$103$	0.807160	+	1.39804i	0.0795318	+	0.137753i	0.903048	−	0.429540i	$-0.141324\pi$
$103$	0.807160	+	1.39804i	0.0795318	+	0.137753i	−0.823516	+	0.567293i	$0.807991\pi$
$104$	−9.00776	+	3.62568i	−0.883283	+	0.355527i
$105$	13.0883	+	5.27033i	1.27729	+	0.514332i
$106$	6.86077	+	13.2877i	0.666377	+	1.29062i
$107$		−	1.84363i		−	0.178231i	−0.996021	−	0.0891153i	$-0.971596\pi$
$107$		−	1.84363i		−	0.178231i	0.996021	−	0.0891153i	$-0.0284040\pi$
$108$	4.11243	−	9.54400i	0.395719	−	0.918372i
$109$	−2.66853			−0.255599			−0.127800	−	0.991800i	$-0.540791\pi$
$109$	−2.66853			−0.255599			−0.127800	+	0.991800i	$0.540791\pi$
$110$	8.41650	+	16.3008i	0.802482	+	1.55422i
$111$	−1.54862	+	3.17855i	−0.146989	+	0.301694i
$112$	10.5102	+	1.23914i	0.993122	+	0.117088i
$113$	−0.626681	−	1.08544i	−0.0589532	−	0.102110i	0.835043	−	0.550185i	$-0.185443\pi$
$113$	−0.626681	−	1.08544i	−0.0589532	−	0.102110i	−0.893996	+	0.448075i	$0.852110\pi$
$114$	−4.18664	+	0.0973856i	−0.392115	+	0.00912100i
$115$	−8.32500	+	14.4193i	−0.776310	+	1.34461i
$116$	−7.93966	−	17.3283i	−0.737179	−	1.60890i
$117$	−9.55239	−	3.85005i	−0.883118	−	0.355937i
$118$	6.79200	−	10.5830i	0.625255	−	0.974247i
$119$	5.45058	+	2.65342i	0.499654	+	0.243239i
$120$	−1.06552	+	15.0461i	−0.0972683	+	1.37352i
$121$	3.37533	+	5.84625i	0.306848	+	0.531477i
$122$	0.274068	−	5.82968i	0.0248129	−	0.527794i
$123$	0.622741	+	8.85197i	0.0561506	+	0.798156i
$124$	12.8337	+	1.20936i	1.15250	+	0.108604i
$125$			1.60090i			0.143189i
$126$	7.12471	+	8.67402i	0.634719	+	0.772743i
$127$		−	10.6611i		−	0.946022i	−0.881056	−	0.473011i	$-0.843167\pi$
$127$		−	10.6611i		−	0.946022i	0.881056	−	0.473011i	$-0.156833\pi$
$128$	2.18948	+	11.0998i	0.193525	+	0.981095i
$129$	−4.80454	+	3.24365i	−0.423016	+	0.285588i
$130$	14.9320	+	0.701990i	1.30962	+	0.0615686i
$131$	4.50282	+	7.79911i	0.393413	+	0.681411i	0.992897	−	0.118975i	$-0.0379609\pi$
$131$	4.50282	+	7.79911i	0.393413	+	0.681411i	−0.599484	+	0.800387i	$0.704628\pi$
$132$	−0.346171	+	14.5907i	−0.0301303	+	1.26996i
$133$	1.97987	−	4.06699i	0.171677	−	0.352653i
$134$	13.1053	+	8.41075i	1.13213	+	0.726578i
$135$	−11.8759	+	10.7203i	−1.02211	+	0.922658i
$136$	−0.910327	+	6.41644i	−0.0780599	+	0.550205i
$137$	1.11722	−	1.93509i	0.0954509	−	0.165326i	−0.814346	−	0.580380i	$-0.802904\pi$
$137$	1.11722	−	1.93509i	0.0954509	−	0.165326i	0.909797	+	0.415054i	$0.136237\pi$
$138$	−11.3142	+	6.88797i	−0.963133	+	0.586343i
$139$	−5.09811	−	8.83019i	−0.432416	−	0.748967i	0.564665	−	0.825320i	$-0.309006\pi$
$139$	−5.09811	−	8.83019i	−0.432416	−	0.748967i	−0.997081	+	0.0763537i	$0.975672\pi$
$140$	−13.9151	−	8.47411i	−1.17604	−	0.716193i
$141$	4.27735	+	6.33567i	0.360218	+	0.533560i
$142$	−3.12693	+	1.61451i	−0.262406	+	0.135487i
$143$	14.4639			1.20953
$144$	−6.48610	+	10.0961i	−0.540508	+	0.841339i
$145$			29.3436i			2.43686i
$146$	−4.36016	+	2.25125i	−0.360849	+	0.186315i
$147$	−11.8546	+	2.54338i	−0.977750	+	0.209775i
$148$	2.36406	−	3.32862i	0.194325	−	0.273611i
$149$	6.16913	+	10.6853i	0.505395	+	0.875370i	0.999981	+	0.00624098i	$0.00198658\pi$
$149$	6.16913	+	10.6853i	0.505395	+	0.875370i	−0.494585	+	0.869129i	$0.664680\pi$
$150$	5.26443	−	9.62866i	0.429839	−	0.786176i
$151$	9.36053	+	5.40430i	0.761749	+	0.439796i	0.829923	−	0.557877i	$-0.188384\pi$
$151$	9.36053	+	5.40430i	0.761749	+	0.439796i	−0.0681743	+	0.997673i	$0.521717\pi$
$152$	4.78768	+	0.679248i	0.388332	+	0.0550943i
$153$	−5.41307	+	4.23651i	−0.437620	+	0.342501i
$154$	−13.8342	−	7.55805i	−1.11479	−	0.609045i
$155$	−17.1862	−	9.92243i	−1.38043	−	0.796989i
$156$	10.1551	+	6.18878i	0.813062	+	0.495499i
$157$	21.4858	−	12.4049i	1.71476	−	0.990015i	0.786896	−	0.617085i	$-0.211687\pi$
$157$	21.4858	−	12.4049i	1.71476	−	0.990015i	0.927860	−	0.372930i	$-0.121647\pi$
$158$	−0.680909	+	14.4836i	−0.0541702	+	1.15225i
$159$	8.02197	−	16.4651i	0.636183	−	1.30577i
$160$	4.05362	−	16.9390i	0.320467	−	1.33915i
$161$	−1.00861	−	14.2717i	−0.0794898	−	1.12477i
$162$	−12.3812	+	2.95075i	−0.972756	+	0.231833i
$163$		−	10.9277i		−	0.855920i	−0.903798	−	0.427960i	$-0.859232\pi$
$163$		−	10.9277i		−	0.855920i	0.903798	−	0.427960i	$-0.140768\pi$
$164$	0.961316	−	10.2014i	0.0750661	−	0.796599i
$165$	9.84101	−	20.1987i	0.766122	−	1.57246i
$166$	0.161798	+	0.00760652i	0.0125579	+	0.000590380i
$167$	8.50615	+	14.7331i	0.658226	+	1.14008i	0.981075	+	0.193630i	$0.0620261\pi$
$167$	8.50615	+	14.7331i	0.658226	+	1.14008i	−0.322849	+	0.946451i	$0.604641\pi$
$168$	−6.47912	−	11.2259i	−0.499875	−	0.866097i
$169$	−0.607170	+	1.05165i	−0.0467054	+	0.0808961i
$170$	5.38871	−	8.39648i	0.413295	−	0.643980i
$171$	3.16110	+	4.03900i	0.241736	+	0.308870i
$172$	6.08540	−	2.78827i	0.464008	−	0.212603i
$173$	4.06899	+	2.34923i	0.309360	+	0.178609i	0.646640	−	0.762795i	$-0.276174\pi$
$173$	4.06899	+	2.34923i	0.309360	+	0.178609i	−0.337280	+	0.941404i	$0.609507\pi$
$174$	−11.1989	+	20.4829i	−0.848990	+	1.55280i
$175$	6.63546	+	9.82175i	0.501594	+	0.742455i
$176$	3.14820	−	16.5559i	0.237304	−	1.24795i
$177$	−15.3633	+	1.08081i	−1.15477	+	0.0812388i
$178$	4.54805	−	2.34826i	0.340891	−	0.176010i
$179$		−	8.32224i		−	0.622034i	−0.950404	−	0.311017i	$-0.899330\pi$
$179$		−	8.32224i		−	0.622034i	0.950404	−	0.311017i	$-0.100670\pi$
$180$	15.5520	−	9.97081i	1.15918	−	0.743181i
$181$		−	9.07327i		−	0.674411i	−0.941431	−	0.337205i	$-0.890518\pi$
$181$		−	9.07327i		−	0.674411i	0.941431	−	0.337205i	$-0.109482\pi$
$182$	−10.9698	+	6.68307i	−0.813133	+	0.495382i
$183$	−5.92407	+	3.99947i	−0.437920	+	0.295649i
$184$	14.1889	−	5.71112i	1.04602	−	0.421029i
$185$	−5.44320	+	3.14263i	−0.400192	+	0.231051i
$186$	−8.20966	−	13.4853i	−0.601961	−	0.988788i
$187$	4.82674	−	8.36015i	0.352966	−	0.611355i
$188$	−3.67684	−	8.02473i	−0.268161	−	0.585263i
$189$	3.29910	−	13.3460i	0.239975	−	0.970779i
$190$	−6.26510	−	4.02083i	−0.454518	−	0.291702i
$191$	−10.1929	−	5.88490i	−0.737535	−	0.425816i	0.0836373	−	0.996496i	$-0.473346\pi$
$191$	−10.1929	−	5.88490i	−0.737535	−	0.425816i	−0.821172	+	0.570680i	$0.806680\pi$
$192$	9.29431	−	10.2770i	0.670759	−	0.741676i
$193$	10.6936	+	18.5218i	0.769742	+	1.33323i	0.937703	+	0.347438i	$0.112948\pi$
$193$	10.6936	+	18.5218i	0.769742	+	1.33323i	−0.167961	+	0.985794i	$0.553718\pi$
$194$	0.424595	−	9.03154i	0.0304841	−	0.648426i
$195$	−10.2442	−	15.1738i	−0.733599	−	1.08662i
$196$	13.9844	−	0.659909i	0.998888	−	0.0471364i
$197$	−10.7855			−0.768436			−0.384218	−	0.923242i	$-0.625529\pi$
$197$	−10.7855			−0.768436			−0.384218	+	0.923242i	$0.625529\pi$
$198$	14.5782	−	10.3436i	1.03602	−	0.735086i
$199$	−4.64957			−0.329599			−0.164800	−	0.986327i	$-0.552698\pi$
$199$	−4.64957			−0.329599			−0.164800	+	0.986327i	$0.552698\pi$
$200$	−7.81441	+	9.97507i	−0.552562	+	0.705344i
$201$	−1.33840	−	19.0248i	−0.0944037	−	1.34191i
$202$	−1.13654	+	24.1752i	−0.0799664	+	1.70096i
$203$	−14.1155	−	20.8937i	−0.990714	−	1.46645i
$204$	6.96601	−	3.80444i	0.487718	−	0.266364i
$205$	−7.88727	+	13.6612i	−0.550871	+	0.954137i
$206$	−1.23308	+	1.92134i	−0.0859130	+	0.133866i
$207$	15.0468	+	6.06454i	1.04582	+	0.421515i
$208$	−10.4004	−	8.96676i	−0.721136	−	0.621733i
$209$	−6.23800	−	3.60151i	−0.431491	−	0.249122i
$210$	1.86917	+	19.8663i	0.128985	+	1.37090i
$211$	2.23918	−	1.29279i	0.154151	−	0.0889993i	−0.420940	−	0.907088i	$-0.638300\pi$
$211$	2.23918	−	1.29279i	0.154151	−	0.0889993i	0.575092	+	0.818089i	$0.304966\pi$
$212$	−12.2460	+	17.2425i	−0.841060	+	1.18422i
$213$	3.87464	+	1.88777i	0.265486	+	0.129348i
$214$	2.31671	−	1.19617i	0.158367	−	0.0817685i
$215$	−10.3050			−0.702792
$216$	14.6612	−	1.02458i	0.997567	−	0.0697140i
$217$	17.0102	−	1.20215i	1.15473	−	0.0816072i
$218$	−1.73138	−	3.35328i	−0.117264	−	0.227113i
$219$	5.40275	+	2.63228i	0.365084	+	0.177873i
$220$	−15.0229	+	21.1523i	−1.01284	+	1.42609i
$221$	−3.93299	−	6.81214i	−0.264562	−	0.458234i
$222$	−4.99892	+	0.116280i	−0.335506	+	0.00780422i
$223$	−0.326746	+	0.565940i	−0.0218805	+	0.0378981i	−0.876758	−	0.480931i	$-0.840299\pi$
$223$	−0.326746	+	0.565940i	−0.0218805	+	0.0378981i	0.854878	+	0.518829i	$0.173632\pi$
$224$	5.26205	+	14.0111i	0.351585	+	0.936156i
$225$	−13.3078	+	1.88173i	−0.887185	+	0.125449i
$226$	0.957371	−	1.49174i	0.0636833	−	0.0992289i
$227$	2.88313	−	4.99372i	0.191360	−	0.331445i	−0.754341	−	0.656483i	$-0.772044\pi$
$227$	2.88313	−	4.99372i	0.191360	−	0.331445i	0.945701	+	0.325037i	$0.105377\pi$
$228$	−2.83872	−	5.19774i	−0.187999	−	0.344229i
$229$	−24.2527	+	14.0023i	−1.60267	+	0.925299i	−0.611714	+	0.791079i	$0.709520\pi$
$229$	−24.2527	+	14.0023i	−1.60267	+	0.925299i	−0.990951	+	0.134220i	$0.957147\pi$
$230$	−23.5207	−	1.10577i	−1.55091	−	0.0729120i
$231$	2.70927	+	19.1161i	0.178257	+	1.25774i
$232$	16.6235	−	21.2198i	1.09138	−	1.39315i
$233$	−8.45031			−0.553598			−0.276799	−	0.960928i	$-0.589274\pi$
$233$	−8.45031			−0.553598			−0.276799	+	0.960928i	$0.589274\pi$
$234$	−1.35973	−	14.5015i	−0.0888884	−	0.947992i
$235$			13.5890i			0.886448i
$236$	17.7054	+	1.66843i	1.15252	+	0.108606i
$237$	14.7181	−	9.93651i	0.956043	−	0.645446i
$238$	0.202110	+	8.57076i	0.0131008	+	0.555560i
$239$	18.5973	−	10.7371i	1.20296	−	0.694528i	0.241746	−	0.970339i	$-0.422280\pi$
$239$	18.5973	−	10.7371i	1.20296	−	0.694528i	0.961212	+	0.275811i	$0.0889465\pi$
$240$	−19.5983	+	8.42317i	−1.26506	+	0.543713i
$241$	−22.3544	−	12.9063i	−1.43998	−	0.831371i	−0.442129	−	0.896951i	$-0.645777\pi$
$241$	−22.3544	−	12.9063i	−1.43998	−	0.831371i	−0.997847	+	0.0655806i	$0.979110\pi$
$242$	−5.15644	+	8.03455i	−0.331468	+	0.516481i
$243$	11.9625	+	9.99487i	0.767398	+	0.641171i
$244$	7.50339	−	3.43797i	0.480355	−	0.220094i
$245$	−19.9954	−	8.04417i	−1.27746	−	0.513923i
$246$	−10.7193	+	6.52580i	−0.683441	+	0.416070i
$247$	−5.08294	+	2.93464i	−0.323420	+	0.186726i
$248$	6.80699	+	16.9115i	0.432244	+	1.07388i
$249$	−0.111002	−	0.164418i	−0.00703446	−	0.0104195i
$250$	−2.01169	+	1.03868i	−0.127230	+	0.0656920i
$251$	−14.3699			−0.907018			−0.453509	−	0.891252i	$-0.649828\pi$
$251$	−14.3699			−0.907018			−0.453509	+	0.891252i	$0.649828\pi$
$252$	−6.27717	+	14.5807i	−0.395425	+	0.918498i
$253$	−22.7833			−1.43237
$254$	13.3968	−	6.91707i	0.840588	−	0.434015i
$255$	−12.1891	+	0.857506i	−0.763309	+	0.0536991i
$256$	−12.5275	+	9.95300i	−0.782967	+	0.622063i
$257$	14.8202	−	8.55644i	0.924458	−	0.533736i	0.0394034	−	0.999223i	$-0.487454\pi$
$257$	14.8202	−	8.55644i	0.924458	−	0.533736i	0.885055	+	0.465487i	$0.154121\pi$
$258$	−7.19322	−	3.93287i	−0.447830	−	0.244850i
$259$	2.36400	−	4.85607i	0.146892	−	0.301741i
$260$	8.80594	+	19.2190i	0.546121	+	1.19191i
$261$	28.3094	−	4.00297i	1.75231	−	0.247778i
$262$	−6.87888	+	10.7184i	−0.424979	+	0.662185i
$263$	14.9410	+	8.62620i	0.921302	+	0.531914i	0.884050	−	0.467392i	$-0.154806\pi$
$263$	14.9410	+	8.62620i	0.921302	+	0.531914i	0.0372520	+	0.999306i	$0.488140\pi$
$264$	−18.5593	+	9.03161i	−1.14224	+	0.555857i
$265$	28.1962	−	16.2791i	1.73208	−	1.00001i
$266$	6.39515	−	0.150806i	0.392112	−	0.00924650i
$267$	−5.63557	−	2.74571i	−0.344891	−	0.168035i
$268$	−2.06607	+	21.9251i	−0.126206	+	1.33929i
$269$			21.5478i			1.31379i	0.753982	+	0.656895i	$0.228131\pi$
$269$			21.5478i			1.31379i	−0.753982	+	0.656895i	$0.771869\pi$
$270$	−21.1764	−	7.96775i	−1.28875	−	0.484902i
$271$	0.857294			0.0520769			0.0260384	−	0.999661i	$-0.491711\pi$
$271$	0.857294			0.0520769			0.0260384	+	0.999661i	$0.491711\pi$
$272$	−8.65352	+	3.01914i	−0.524697	+	0.183062i
$273$	14.5934	+	5.87638i	0.883232	+	0.355654i
$274$	3.15650	+	0.148395i	0.190691	+	0.00896487i
$275$	16.3464	−	9.43758i	0.985723	−	0.569107i
$276$	−15.9962	−	9.74848i	−0.962860	−	0.586790i
$277$	8.94703	−	15.4967i	0.537575	−	0.931107i	−0.461459	−	0.887162i	$-0.652674\pi$
$277$	8.94703	−	15.4967i	0.537575	−	0.931107i	0.999034	−	0.0439457i	$-0.0139928\pi$
$278$	7.78830	−	12.1354i	0.467111	−	0.727834i
$279$	−7.22823	+	17.9340i	−0.432743	+	1.07368i
$280$	1.62025	−	22.9839i	0.0968287	−	1.37355i
$281$	10.8543	−	18.8002i	0.647513	−	1.12153i	−0.336202	−	0.941790i	$-0.609143\pi$
$281$	10.8543	−	18.8002i	0.647513	−	1.12153i	0.983715	−	0.179735i	$-0.0575241\pi$
$282$	−5.18621	+	9.48558i	−0.308834	+	0.564858i
$283$	−11.7141	−	20.2894i	−0.696331	−	1.20608i	−0.969730	−	0.244180i	$-0.921481\pi$
$283$	−11.7141	−	20.2894i	−0.696331	−	1.20608i	0.273399	−	0.961901i	$-0.411852\pi$
$284$	−4.05758	−	2.88179i	−0.240773	−	0.171003i
$285$	0.639835	+	9.09497i	0.0379006	+	0.538739i
$286$	9.38432	+	18.1753i	0.554907	+	1.07473i
$287$	−0.955580	−	13.5213i	−0.0564061	−	0.798138i
$288$	−16.8950	−	1.59998i	−0.995546	−	0.0942797i
$289$	11.7501			0.691181
$290$	−36.8732	+	19.0385i	−2.16527	+	1.11798i
$291$	−9.17777	+	6.19612i	−0.538011	+	0.363223i
$292$	−5.65784	−	4.01833i	−0.331100	−	0.235155i
$293$	9.69068	−	5.59492i	0.566136	−	0.326859i	−0.189469	−	0.981887i	$-0.560677\pi$
$293$	9.69068	−	5.59492i	0.566136	−	0.326859i	0.755605	+	0.655028i	$0.227343\pi$
$294$	−10.8874	−	13.2463i	−0.634967	−	0.772540i
$295$	−23.7100	−	13.6889i	−1.38045	−	0.797001i
$296$	5.71658	+	0.811035i	0.332269	+	0.0471405i
$297$	−20.8292	−	6.73872i	−1.20864	−	0.391020i
$298$	−9.42448	+	14.6849i	−0.545945	+	0.850671i
$299$	−9.28230	+	16.0774i	−0.536809	+	0.929781i
$300$	15.5150	+	0.368101i	0.895759	+	0.0212523i
$301$	7.33748	−	4.95711i	0.422925	−	0.285723i
$302$	−0.717825	+	15.2688i	−0.0413062	+	0.878622i
$303$	24.5666	−	16.5855i	1.41132	−	0.952811i
$304$	2.25276	+	6.45690i	0.129205	+	0.370329i
$305$	−12.7062			−0.727553
$306$	−8.83565	−	4.05336i	−0.505101	−	0.231715i
$307$	−9.18388			−0.524152			−0.262076	−	0.965047i	$-0.584407\pi$
$307$	−9.18388			−0.524152			−0.262076	+	0.965047i	$0.584407\pi$
$308$	0.521652	−	22.2878i	0.0297239	−	1.26997i
$309$	2.78919	−	0.196221i	0.158671	−	0.0111626i
$310$	1.31794	−	28.0339i	0.0748542	−	1.59222i
$311$	−3.81067	−	6.60027i	−0.216083	−	0.374267i	0.737524	−	0.675321i	$-0.235995\pi$
$311$	−3.81067	−	6.60027i	−0.216083	−	0.374267i	−0.953607	+	0.301054i	$0.902662\pi$
$312$	−1.18805	+	16.7763i	−0.0672599	+	0.949771i
$313$	5.36993	+	3.10033i	0.303526	+	0.175241i	0.644026	−	0.765004i	$-0.277263\pi$
$313$	5.36993	+	3.10033i	0.303526	+	0.175241i	−0.340500	+	0.940245i	$0.610596\pi$
$314$	29.5282	+	18.9507i	1.66637	+	1.06945i
$315$	18.1355	−	16.3814i	1.02182	−	0.922985i
$316$	−18.6419	+	8.54149i	−1.04869	+	0.480496i
$317$	−4.84502	+	8.39183i	−0.272124	+	0.471332i	−0.969405	−	0.245465i	$-0.921059\pi$
$317$	−4.84502	+	8.39183i	−0.272124	+	0.471332i	0.697282	+	0.716797i	$0.254393\pi$
$318$	25.8948	−	0.602340i	1.45211	−	0.0337775i
$319$	−34.7733	+	20.0764i	−1.94693	+	1.12406i
$320$	23.9156	−	5.89645i	1.33692	−	0.329622i
$321$	−2.87068	−	1.39862i	−0.160226	−	0.0780636i
$322$	17.2794	−	10.5271i	0.962945	−	0.586651i
$323$			3.91727i			0.217963i
$324$	−11.7410	−	13.6437i	−0.652275	−	0.757982i
$325$		−	15.3801i		−	0.853136i
$326$	13.7317	−	7.08999i	0.760528	−	0.392678i
$327$	−2.02442	+	4.15511i	−0.111950	+	0.229778i
$328$	13.4429	−	5.41083i	0.742257	−	0.298763i
$329$	−6.53686	−	9.67581i	−0.360389	−	0.533445i
$330$	31.7666	−	0.738925i	1.74869	−	0.0406765i
$331$	−17.9174	−	10.3446i	−0.984827	−	0.568590i	−0.0811031	−	0.996706i	$-0.525844\pi$
$331$	−17.9174	−	10.3446i	−0.984827	−	0.568590i	−0.903724	+	0.428116i	$0.859178\pi$
$332$	0.0954180	+	0.208250i	0.00523674	+	0.0114292i
$333$	3.77442	+	4.82265i	0.206837	+	0.264279i
$334$	−12.9947	+	20.2478i	−0.711038	+	1.10791i
$335$	16.9514	−	29.3608i	0.926157	−	1.60415i
$336$	9.90274	−	15.4252i	0.540239	−	0.841512i
$337$	8.28764	+	14.3546i	0.451457	+	0.781946i	0.998477	−	0.0551737i	$-0.0175713\pi$
$337$	8.28764	+	14.3546i	0.451457	+	0.781946i	−0.547020	+	0.837119i	$0.684238\pi$
$338$	−1.71544	−	0.0806472i	−0.0933078	−	0.00438663i
$339$	−2.16554	+	0.152347i	−0.117616	+	0.00827433i
$340$	14.0473	+	1.32372i	0.761820	+	0.0717888i
$341$		−	27.1550i		−	1.47053i
$342$	−3.02445	+	6.59280i	−0.163544	+	0.356498i
$343$	18.1069	−	3.89087i	0.977683	−	0.210087i
$344$	7.45202	+	5.83786i	0.401786	+	0.314756i
$345$	16.1364	+	23.9015i	0.868757	+	1.28681i
$346$	−0.312036	+	6.63731i	−0.0167752	+	0.356824i
$347$	−8.93889	+	5.16087i	−0.479865	+	0.277050i	−0.720360	−	0.693600i	$-0.756023\pi$
$347$	−8.93889	+	5.16087i	−0.479865	+	0.277050i	0.240495	+	0.970650i	$0.422690\pi$
$348$	−33.0048	−	0.783055i	−1.76924	−	0.0419761i
$349$	−8.33414	−	4.81172i	−0.446116	−	0.257565i	0.260072	−	0.965589i	$-0.416254\pi$
$349$	−8.33414	−	4.81172i	−0.446116	−	0.257565i	−0.706189	+	0.708024i	$0.749587\pi$
$350$	−8.03685	+	14.7106i	−0.429588	+	0.786314i
$351$	−13.2415	+	11.9531i	−0.706779	+	0.638007i
$352$	22.8468	−	6.78567i	1.21774	−	0.361678i
$353$	20.3278	+	11.7363i	1.08194	+	0.624658i	0.931419	−	0.363949i	$-0.118572\pi$
$353$	20.3278	+	11.7363i	1.08194	+	0.624658i	0.150520	+	0.988607i	$0.451905\pi$
$354$	−11.3260	−	18.6042i	−0.601971	−	0.988803i
$355$	3.83087	+	6.63526i	0.203321	+	0.352163i
$356$	5.90165	+	4.19149i	0.312787	+	0.222149i
$357$	8.26652	−	6.47402i	0.437511	−	0.342641i
$358$	10.4577	−	5.39957i	0.552708	−	0.285376i
$359$		−	7.49888i		−	0.395776i	−0.980225	−	0.197888i	$-0.936592\pi$
$359$		−	7.49888i		−	0.395776i	0.980225	−	0.197888i	$-0.0634082\pi$
$360$	22.6196	+	13.0735i	1.19216	+	0.689032i
$361$	−16.0771			−0.846163
$362$	11.4015	−	5.88685i	0.599248	−	0.309406i
$363$	11.6637	−	0.820544i	0.612184	−	0.0430674i
$364$	−15.5153	−	9.44856i	−0.813221	−	0.495239i
$365$	5.34171	+	9.25211i	0.279598	+	0.484278i
$366$	−8.86934	−	4.84928i	−0.463608	−	0.253476i
$367$	2.39341	−	4.14551i	0.124935	−	0.216394i	−0.796772	−	0.604279i	$-0.793461\pi$
$367$	2.39341	−	4.14551i	0.124935	−	0.216394i	0.921708	+	0.387885i	$0.126794\pi$
$368$	16.3825	+	14.1243i	0.853998	+	0.736281i
$369$	14.2556	+	5.74567i	0.742118	+	0.299108i
$370$	−7.48065	−	4.80095i	−0.388900	−	0.249589i
$371$	−12.2457	+	25.1548i	−0.635765	+	1.30597i
$372$	11.6191	−	19.0657i	0.602420	−	0.988508i
$373$	−13.8959	−	24.0683i	−0.719500	−	1.24621i	−0.961198	−	0.275859i	$-0.911038\pi$
$373$	−13.8959	−	24.0683i	−0.719500	−	1.24621i	0.241698	−	0.970352i	$-0.422296\pi$
$374$	13.6370	+	0.641110i	0.705153	+	0.0331510i
$375$	2.49272	+	1.21448i	0.128724	+	0.0627155i
$376$	7.69829	−	9.82685i	0.397009	−	0.506781i
$377$			32.7179i			1.68506i
$378$	18.9111	−	4.51339i	0.972681	−	0.232144i
$379$			27.3958i			1.40723i	0.710583	+	0.703613i	$0.248431\pi$
$379$			27.3958i			1.40723i	−0.710583	+	0.703613i	$0.751569\pi$
$380$	0.987705	−	10.4815i	0.0506682	−	0.537689i
$381$	−16.6002	−	8.08780i	−0.850454	−	0.414350i
$382$	0.781659	−	16.6266i	0.0399932	−	0.850693i
$383$	7.36210	+	12.7515i	0.376185	+	0.651572i	0.990504	−	0.137486i	$-0.0439022\pi$
$383$	7.36210	+	12.7515i	0.376185	+	0.651572i	−0.614318	+	0.789058i	$0.710569\pi$
$384$	18.9443	+	5.01141i	0.966746	+	0.255738i
$385$	−15.0225	+	30.8588i	−0.765618	+	1.57271i
$386$	−16.3364	+	25.4548i	−0.831502	+	1.29561i
$387$	1.40577	+	9.94176i	0.0714594	+	0.505368i
$388$	11.6245	−	5.32622i	0.590145	−	0.270398i
$389$	−10.9505	+	18.9668i	−0.555211	+	0.961653i	0.442676	+	0.896681i	$0.354029\pi$
$389$	−10.9505	+	18.9668i	−0.555211	+	0.961653i	−0.997887	+	0.0649717i	$0.979304\pi$
$390$	12.4208	−	22.7177i	0.628953	−	1.15036i
$391$	6.19520	+	10.7304i	0.313305	+	0.542659i
$392$	9.90251	+	17.1447i	0.500152	+	0.865937i
$393$	15.5598	−	1.09464i	0.784886	−	0.0552171i
$394$	−6.99777	−	13.5531i	−0.352542	−	0.682794i
$395$	31.5679			1.58835
$396$	22.4562	+	11.6079i	1.12847	+	0.583317i
$397$			34.9584i			1.75451i	0.480025	+	0.877255i	$0.340628\pi$
$397$			34.9584i			1.75451i	−0.480025	+	0.877255i	$0.659372\pi$
$398$	−3.01670	−	5.84265i	−0.151213	−	0.292865i
$399$	−4.83064	−	6.16813i	−0.241834	−	0.308793i
$400$	−17.6048	−	3.34763i	−0.880238	−	0.167382i
$401$	−9.78297	−	16.9446i	−0.488538	−	0.846173i	0.511375	−	0.859358i	$-0.329136\pi$
$401$	−9.78297	−	16.9446i	−0.488538	−	0.846173i	−0.999913	+	0.0131845i	$0.995803\pi$
$402$	23.0382	−	14.0254i	1.14904	−	0.699521i
$403$	−19.1624	−	11.0634i	−0.954548	−	0.551109i
$404$	−31.1159	+	14.2570i	−1.54808	+	0.709311i
$405$	7.68302	+	26.6243i	0.381772	+	1.32297i
$406$	17.0967	−	31.2936i	0.848493	−	1.55307i
$407$	−7.44829	−	4.30027i	−0.369198	−	0.213156i
$408$	9.30029	+	6.28512i	0.460433	+	0.311160i
$409$	2.97407	−	1.71708i	0.147058	−	0.0849042i	−0.424665	−	0.905350i	$-0.639608\pi$
$409$	2.97407	−	1.71708i	0.147058	−	0.0849042i	0.571724	+	0.820446i	$0.306275\pi$
$410$	−22.2840	−	1.04762i	−1.10053	−	0.0517385i
$411$	−2.16553	−	3.20761i	−0.106818	−	0.158220i
$412$	−3.21440	−	0.302903i	−0.158362	−	0.0149230i
$413$	23.4672	−	1.65848i	1.15475	−	0.0816084i
$414$	2.14183	+	22.8425i	0.105265	+	1.12265i
$415$		−	0.352649i		−	0.0173108i
$416$	4.51975	−	18.8868i	0.221599	−	0.926004i
$417$	−17.6168	+	1.23935i	−0.862700	+	0.0606914i
$418$	0.478369	−	10.1754i	0.0233978	−	0.497694i
$419$	−5.82364	−	10.0868i	−0.284503	−	0.492774i	0.687985	−	0.725725i	$-0.258495\pi$
$419$	−5.82364	−	10.0868i	−0.284503	−	0.492774i	−0.972489	+	0.232950i	$0.925162\pi$
$420$	−23.7512	+	15.2383i	−1.15894	+	0.743552i
$421$	−9.64312	+	16.7024i	−0.469977	+	0.814024i	−0.999411	−	0.0343274i	$-0.989071\pi$
$421$	−9.64312	+	16.7024i	−0.469977	+	0.814024i	0.529434	+	0.848351i	$0.322404\pi$
$422$	3.07732	+	1.97497i	0.149802	+	0.0961402i
$423$	13.1100	−	1.85377i	0.637432	−	0.0901334i
$424$	−29.6123	−	4.20122i	−1.43810	−	0.204029i
$425$	−8.88976	−	5.13251i	−0.431217	−	0.248963i
$426$	0.141746	+	6.09368i	0.00686759	+	0.295240i
$427$	9.04721	−	6.11219i	0.437825	−	0.295790i
$428$	3.00621	+	2.13508i	0.145311	+	0.103203i
$429$	10.9726	−	22.5213i	0.529764	−	1.08734i
$430$	−6.68598	−	12.9492i	−0.322427	−	0.624466i
$431$			1.73760i			0.0836971i	0.999124	+	0.0418485i	$0.0133247\pi$
$431$			1.73760i			0.0836971i	−0.999124	+	0.0418485i	$0.986675\pi$
$432$	10.7998	+	17.7585i	0.519607	+	0.854405i
$433$		−	5.95764i		−	0.286306i	−0.989701	−	0.143153i	$-0.954276\pi$
$433$		−	5.95764i		−	0.286306i	0.989701	−	0.143153i	$-0.0457241\pi$
$434$	12.5471	+	20.5951i	0.602278	+	0.988595i
$435$	45.6903	+	22.2608i	2.19068	+	1.06732i
$436$	3.09039	−	4.35130i	0.148003	−	0.208389i
$437$	8.00657	−	4.62260i	0.383006	−	0.221129i
$438$	0.197648	+	8.49695i	0.00944399	+	0.406000i
$439$	−10.6377	+	18.4250i	−0.507708	+	0.879377i	0.492252	+	0.870453i	$0.336174\pi$
$439$	−10.6377	+	18.4250i	−0.507708	+	0.879377i	−0.999960	+	0.00892391i	$0.997159\pi$
$440$	−36.3271	−	5.15388i	−1.73182	−	0.245701i
$441$	−5.03294	+	20.3880i	−0.239664	+	0.970856i
$442$	6.00837	−	9.36200i	0.285789	−	0.445305i
$443$	30.1387	+	17.4006i	1.43193	+	0.826726i	0.997268	−	0.0738675i	$-0.0235342\pi$
$443$	30.1387	+	17.4006i	1.43193	+	0.826726i	0.434663	+	0.900593i	$0.356868\pi$
$444$	−3.38948	−	6.20620i	−0.160858	−	0.294533i
$445$	−5.57190	−	9.65081i	−0.264133	−	0.457492i
$446$	−0.923156	−	0.0433999i	−0.0437127	−	0.00205504i
$447$	21.3178	−	1.49972i	1.00830	−	0.0709343i
$448$	−14.1923	+	15.7029i	−0.670521	+	0.741890i
$449$	0.109498			0.00516755			0.00258377	−	0.999997i	$-0.499178\pi$
$449$	0.109498			0.00516755			0.00258377	+	0.999997i	$0.499178\pi$
$450$	−10.9988	−	15.5017i	−0.518490	−	0.730756i
$451$	−21.5853			−1.01641
$452$	2.49567	+	0.235175i	0.117386	+	0.0110617i
$453$	15.5160	−	10.4752i	0.729007	−	0.492169i
$454$	8.14572	+	0.382951i	0.382298	+	0.0179728i
$455$	15.6556	+	23.1733i	0.733947	+	1.08638i
$456$	4.68969	−	6.93949i	0.219615	−	0.324971i
$457$	14.6591	−	25.3902i	0.685722	−	1.18770i	−0.287488	−	0.957784i	$-0.592820\pi$
$457$	14.6591	−	25.3902i	0.685722	−	1.18770i	0.973209	−	0.229920i	$-0.0738466\pi$
$458$	−33.3308	−	21.3911i	−1.55744	−	0.999541i
$459$	2.49008	+	11.6425i	0.116227	+	0.543424i
$460$	−13.8710	−	30.2735i	−0.646738	−	1.41151i
$461$	−28.8999	−	16.6853i	−1.34600	−	0.777114i	−0.358320	−	0.933599i	$-0.616650\pi$
$461$	−28.8999	−	16.6853i	−1.34600	−	0.777114i	−0.987680	+	0.156485i	$0.949984\pi$
$462$	−22.2634	+	15.8072i	−1.03579	+	0.735417i
$463$	8.98085	−	5.18510i	0.417376	−	0.240972i	−0.276578	−	0.960991i	$-0.589200\pi$
$463$	8.98085	−	5.18510i	0.417376	−	0.240972i	0.693954	+	0.720019i	$0.255867\pi$
$464$	37.4503	+	7.12137i	1.73859	+	0.330601i
$465$	−28.4878	+	19.2328i	−1.32109	+	0.891898i
$466$	−5.48266	−	10.6187i	−0.253979	−	0.491900i
$467$	−7.81904			−0.361822			−0.180911	−	0.983499i	$-0.557905\pi$
$467$	−7.81904			−0.361822			−0.180911	+	0.983499i	$0.557905\pi$
$468$	17.3404	−	11.1174i	0.801558	−	0.513901i
$469$	2.05375	+	29.0602i	0.0948332	+	1.34188i
$470$	−17.0759	+	8.81669i	−0.787653	+	0.406684i
$471$	−3.01562	−	42.8657i	−0.138953	−	1.97515i
$472$	9.39090	+	23.3311i	0.432251	+	1.07390i
$473$	−7.05047	−	12.2118i	−0.324181	−	0.561498i
$474$	22.0355	+	12.0478i	1.01212	+	0.553375i
$475$	−3.82966	+	6.63317i	−0.175717	+	0.304351i
$476$	−10.6389	+	5.81478i	−0.487633	+	0.266520i
$477$	−19.5517	−	24.9816i	−0.895213	−	1.14383i
$478$	25.5584	+	16.4030i	1.16902	+	0.750254i
$479$	2.78654	−	4.82643i	0.127320	−	0.220525i	−0.795317	−	0.606193i	$-0.792696\pi$
$479$	2.78654	−	4.82643i	0.127320	−	0.220525i	0.922638	+	0.385668i	$0.126029\pi$
$480$	−23.3002	−	19.1621i	−1.06350	−	0.874628i
$481$	−6.06912	+	3.50401i	−0.276728	+	0.159769i
$482$	1.71428	−	36.4644i	0.0780834	−	1.66091i
$483$	−22.9873	−	9.25639i	−1.04596	−	0.421180i
$484$	−13.4418	−	1.26666i	−0.610990	−	0.0575756i
$485$	−19.6848			−0.893842
$486$	−4.79811	+	21.5169i	−0.217647	+	0.976028i
$487$		−	22.6868i		−	1.02804i	−0.857780	−	0.514018i	$-0.828157\pi$
$487$		−	22.6868i		−	1.02804i	0.857780	−	0.514018i	$-0.171843\pi$
$488$	9.18844	+	7.19816i	0.415941	+	0.325846i
$489$	−17.0152	−	8.28999i	−0.769454	−	0.374886i
$490$	−2.86492	−	30.3453i	−0.129424	−	1.37086i
$491$	5.38821	−	3.11089i	0.243167	−	0.140392i	−0.373465	−	0.927644i	$-0.621830\pi$
$491$	5.38821	−	3.11089i	0.243167	−	0.140392i	0.616631	+	0.787252i	$0.288497\pi$
$492$	−15.1552	−	9.23591i	−0.683247	−	0.416387i
$493$	18.9110	+	10.9183i	0.851711	+	0.491735i
$494$	−6.98553	−	4.48319i	−0.314294	−	0.201708i
$495$	−23.9852	−	30.6464i	−1.07806	−	1.37745i
$496$	−16.8346	+	19.5261i	−0.755894	+	0.876746i
$497$	−5.91954	−	2.88172i	−0.265528	−	0.129263i
$498$	0.134588	−	0.246161i	0.00603102	−	0.0110307i
$499$	−35.4214	+	20.4505i	−1.58568	+	0.915491i	−0.591670	+	0.806180i	$0.701531\pi$
$499$	−35.4214	+	20.4505i	−1.58568	+	0.915491i	−0.994008	+	0.109311i	$0.965135\pi$
$500$	−2.61042	−	1.85398i	−0.116741	−	0.0829125i
$501$	29.3935	−	2.06785i	1.31321	−	0.0923847i
$502$	−9.32334	−	18.0572i	−0.416121	−	0.805931i
$503$	−8.58006			−0.382566			−0.191283	−	0.981535i	$-0.561265\pi$
$503$	−8.58006			−0.382566			−0.191283	+	0.981535i	$0.561265\pi$
$504$	−22.3948	+	1.57224i	−0.997545	+	0.0700333i
$505$	52.6914			2.34474
$506$	−14.7821	−	28.6295i	−0.657143	−	1.27273i
$507$	1.17689	+	1.74322i	0.0522673	+	0.0774191i
$508$	17.3840	+	12.3465i	0.771289	+	0.547788i
$509$	−5.48332	+	3.16579i	−0.243044	+	0.140321i	−0.616575	−	0.787296i	$-0.711480\pi$
$509$	−5.48332	+	3.16579i	−0.243044	+	0.140321i	0.373531	+	0.927618i	$0.378147\pi$
$510$	−8.98595	−	14.7604i	−0.397905	−	0.653602i
$511$	−8.25413	−	4.01823i	−0.365141	−	0.177756i
$512$	−20.6349	−	9.28440i	−0.911943	−	0.410317i
$513$	8.68713	−	1.85799i	0.383546	−	0.0820324i
$514$	20.3675	+	13.0715i	0.898373	+	0.576560i
$515$	4.30453	+	2.48522i	0.189680	+	0.109512i
$516$	0.274995	−	11.5907i	0.0121060	−	0.510252i
$517$	−16.1035	+	9.29734i	−0.708230	+	0.408897i
$518$	7.63593	−	0.180065i	0.335503	−	0.00791160i
$519$	6.74478	−	4.55355i	0.296063	−	0.199879i
$520$	−18.4372	+	23.5351i	−0.808525	+	1.03208i
$521$			19.8412i			0.869261i	0.900609	+	0.434630i	$0.143121\pi$
$521$			19.8412i			0.869261i	−0.900609	+	0.434630i	$0.856879\pi$
$522$	23.3976	+	32.9764i	1.02409	+	1.44334i
$523$	39.5715			1.73034			0.865171	−	0.501476i	$-0.167210\pi$
$523$	39.5715			1.73034			0.865171	+	0.501476i	$0.167210\pi$
$524$	−17.9318	−	1.68977i	−0.783356	−	0.0738182i
$525$	20.3270	−	2.88090i	0.887145	−	0.125733i
$526$	−1.14577	+	24.3717i	−0.0499580	+	1.06265i
$527$	−12.7894	+	7.38396i	−0.557114	+	0.321650i
$528$	−23.3906	−	17.4617i	−1.01794	−	0.759925i
$529$	3.12136	−	5.40635i	0.135711	−	0.235059i
$530$	38.7503	+	24.8692i	1.68320	+	1.08025i
$531$	−9.97204	+	24.7417i	−0.432749	+	1.07370i
$532$	4.33875	+	7.93830i	0.188109	+	0.344169i
$533$	−8.79424	+	15.2321i	−0.380921	+	0.659774i
$534$	−0.206165	−	8.86311i	−0.00892165	−	0.383544i
$535$	−2.83824	−	4.91598i	−0.122708	−	0.212536i
$536$	−28.8916	+	11.6290i	−1.24793	+	0.502298i
$537$	−12.9584	−	6.31346i	−0.559195	−	0.272446i
$538$	−27.0769	+	13.9805i	−1.16737	+	0.602740i
$539$	−4.14782	−	29.1989i	−0.178659	−	1.25769i
$540$	−3.72719	−	31.7798i	−0.160393	−	1.36758i
$541$	−14.8643			−0.639068			−0.319534	−	0.947575i	$-0.603526\pi$
$541$	−14.8643			−0.639068			−0.319534	+	0.947575i	$0.603526\pi$
$542$	0.556222	+	1.07727i	0.0238918	+	0.0462729i
$543$	−14.1278	−	6.88321i	−0.606281	−	0.295387i
$544$	−9.40836	−	8.91516i	−0.403380	−	0.382234i
$545$	−7.11556	+	4.10817i	−0.304797	+	0.175975i
$546$	2.08411	+	22.1507i	0.0891918	+	0.947963i
$547$	17.5001	+	10.1037i	0.748252	+	0.432003i	0.825062	−	0.565042i	$-0.191140\pi$
$547$	17.5001	+	10.1037i	0.748252	+	0.432003i	−0.0768102	+	0.997046i	$0.524474\pi$
$548$	1.86150	+	4.06274i	0.0795194	+	0.173552i
$549$	1.73334	+	12.2583i	0.0739771	+	0.523173i
$550$	22.4650	+	14.4176i	0.957910	+	0.614770i
$551$	8.14678	−	14.1106i	0.347064	−	0.601133i
$552$	1.87139	−	26.4258i	0.0796519	−	1.12476i
$553$	−22.4774	+	15.1855i	−0.955837	+	0.645752i
$554$	25.2781	+	1.18839i	1.07396	+	0.0504897i
$555$	0.763976	+	10.8596i	0.0324290	+	0.460963i
$556$	20.3025	+	1.91317i	0.861018	+	0.0811365i
$557$	12.0437			0.510308			0.255154	−	0.966900i	$-0.417874\pi$
$557$	12.0437			0.510308			0.255154	+	0.966900i	$0.417874\pi$
$558$	−27.2257	+	2.55281i	−1.15255	+	0.108069i
$559$	−11.4899			−0.485973
$560$	29.9328	−	12.8762i	1.26489	−	0.544118i
$561$	−9.35572	−	13.8578i	−0.394999	−	0.585078i
$562$	30.6667	+	1.44172i	1.29360	+	0.0608152i
$563$	19.3253	+	33.4724i	0.814463	+	1.41069i	0.909713	+	0.415238i	$0.136302\pi$
$563$	19.3253	+	33.4724i	0.814463	+	1.41069i	−0.0952496	+	0.995453i	$0.530365\pi$
$564$	−15.2845	−	0.362631i	−0.643592	−	0.0152695i
$565$	−3.34205	−	1.92953i	−0.140601	−	0.0811761i
$566$	17.8954	−	27.8839i	0.752201	−	1.17205i
$567$	−18.2780	−	15.2616i	−0.767603	−	0.640926i
$568$	0.988651	−	6.96850i	0.0414829	−	0.292392i
$569$	−6.96304	+	12.0603i	−0.291906	+	0.505596i	−0.974260	−	0.225426i	$-0.927623\pi$
$569$	−6.96304	+	12.0603i	−0.291906	+	0.505596i	0.682355	+	0.731021i	$0.260956\pi$
$570$	−11.0136	+	6.70494i	−0.461309	+	0.280839i
$571$	21.6359	−	12.4915i	0.905436	−	0.522754i	0.0264762	−	0.999649i	$-0.491571\pi$
$571$	21.6359	−	12.4915i	0.905436	−	0.522754i	0.878960	+	0.476896i	$0.158238\pi$
$572$	−16.7504	+	23.5847i	−0.700369	+	0.986125i
$573$	−16.8958	+	11.4068i	−0.705834	+	0.476524i
$574$	16.3709	−	9.97357i	0.683307	−	0.416289i
$575$			24.2266i			1.01032i
$576$	−8.95112	−	22.2683i	−0.372963	−	0.927846i
$577$		−	41.9153i		−	1.74495i	−0.488654	−	0.872477i	$-0.662512\pi$
$577$		−	41.9153i		−	1.74495i	0.488654	−	0.872477i	$-0.337488\pi$
$578$	7.62359	+	14.7652i	0.317100	+	0.614149i
$579$	36.9524	−	2.59962i	1.53569	−	0.108036i
$580$	−47.8476	−	33.9825i	−1.98676	−	1.41105i
$581$	0.169639	+	0.251098i	0.00703780	+	0.0104173i
$582$	−13.7407	−	7.51267i	−0.569570	−	0.311410i
$583$	38.5826	+	22.2757i	1.59793	+	0.922565i
$584$	1.37856	−	9.71678i	0.0570453	−	0.402083i
$585$	−31.3982	+	4.43973i	−1.29816	+	0.183560i
$586$	13.3180	+	8.54726i	0.550162	+	0.353084i
$587$	13.1495	−	22.7757i	0.542740	−	0.940053i	−0.456006	−	0.889977i	$-0.650720\pi$
$587$	13.1495	−	22.7757i	0.542740	−	0.940053i	0.998745	−	0.0500760i	$-0.0159464\pi$
$588$	9.58141	−	22.2755i	0.395131	−	0.918625i
$589$	5.50960	+	9.54291i	0.227019	+	0.393209i
$590$	1.81823	−	38.6755i	0.0748554	−	1.59224i
$591$	−8.18215	+	16.7939i	−0.336569	+	0.690807i
$592$	2.68984	+	7.70966i	0.110552	+	0.316865i
$593$			14.9954i			0.615786i	0.951421	+	0.307893i	$0.0996239\pi$
$593$			14.9954i			0.615786i	−0.951421	+	0.307893i	$0.900376\pi$
$594$	−5.04639	−	30.5462i	−0.207056	−	1.25333i
$595$	18.6187	−	1.31582i	0.763291	−	0.0539434i
$596$	−24.5677	−	2.31509i	−1.00633	−	0.0948299i
$597$	−3.52728	+	7.23974i	−0.144362	+	0.296303i
$598$	−26.2254	−	1.23292i	−1.07243	−	0.0504178i
$599$	−11.6301	+	6.71463i	−0.475192	+	0.274352i	−0.718411	−	0.695619i	$-0.755130\pi$
$599$	−11.6301	+	6.71463i	−0.475192	+	0.274352i	0.243219	+	0.969972i	$0.421797\pi$
$600$	9.60376	+	19.7350i	0.392072	+	0.805677i
$601$	11.6714	+	6.73847i	0.476086	+	0.274868i	0.718784	−	0.695234i	$-0.244699\pi$
$601$	11.6714	+	6.73847i	0.476086	+	0.274868i	−0.242698	+	0.970102i	$0.578032\pi$
$602$	10.9897	+	6.00404i	0.447909	+	0.244706i
$603$	−30.6384	−	12.3487i	−1.24769	−	0.502877i
$604$	−19.6525	+	9.00457i	−0.799650	+	0.366391i
$605$	18.0004	+	10.3925i	0.731821	+	0.422517i
$606$	36.7804	+	20.1096i	1.49410	+	0.816896i
$607$	−17.3550	−	30.0598i	−0.704419	−	1.22009i	−0.966901	−	0.255153i	$-0.917874\pi$
$607$	−17.3550	−	30.0598i	−0.704419	−	1.22009i	0.262482	−	0.964937i	$-0.415459\pi$
$608$	−6.65212	+	7.02013i	−0.269779	+	0.284704i
$609$	−43.2414	+	6.12848i	−1.75223	+	0.248339i
$610$	−8.24391	−	15.9666i	−0.333786	−	0.646467i
$611$			15.1516i			0.612968i
$612$	−0.639223	−	13.7328i	−0.0258390	−	0.555114i
$613$	−27.2426			−1.10032			−0.550159	−	0.835060i	$-0.685433\pi$
$613$	−27.2426			−1.10032			−0.550159	+	0.835060i	$0.685433\pi$
$614$	−5.95861	−	11.5405i	−0.240470	−	0.465735i
$615$	15.2880	+	22.6448i	0.616471	+	0.913126i
$616$	28.3453	−	13.8051i	1.14207	−	0.556223i
$617$	−3.19357	−	5.53142i	−0.128568	−	0.222687i	0.794554	−	0.607194i	$-0.207705\pi$
$617$	−3.19357	−	5.53142i	−0.128568	−	0.222687i	−0.923122	+	0.384507i	$0.874371\pi$
$618$	2.05623	+	3.37759i	0.0827137	+	0.135866i
$619$	13.4240	−	23.2510i	0.539554	−	0.934536i	−0.459374	−	0.888243i	$-0.651926\pi$
$619$	13.4240	−	23.2510i	0.539554	−	0.934536i	0.998928	−	0.0462924i	$-0.0147406\pi$
$620$	36.0825	−	16.5326i	1.44911	−	0.663966i
$621$	20.8578	−	18.8283i	0.836996	−	0.755553i
$622$	5.82149	−	9.07082i	0.233421	−	0.363707i
$623$	8.60982	+	4.19139i	0.344945	+	0.167924i
$624$	−21.8519	+	9.39177i	−0.874777	+	0.375972i
$625$	13.6647	+	23.6679i	0.546588	+	0.946718i
$626$	−0.411800	+	8.75938i	−0.0164588	+	0.350095i
$627$	−10.3401	+	6.98085i	−0.412945	+	0.278788i
$628$	−4.65517	+	49.4005i	−0.185762	+	1.97130i
$629$			4.67729i			0.186496i
$630$	32.3513	+	12.1606i	1.28891	+	0.484490i
$631$			24.9328i			0.992557i	0.868163	+	0.496279i	$0.165301\pi$
$631$			24.9328i			0.992557i	−0.868163	+	0.496279i	$0.834699\pi$
$632$	−22.8283	−	17.8835i	−0.908061	−	0.711369i
$633$	−0.314278	−	4.46731i	−0.0124914	−	0.177560i
$634$	−13.6887	−	0.643539i	−0.543647	−	0.0255582i
$635$	−16.4126	−	28.4275i	−0.651316	−	1.12811i
$636$	17.5577	+	32.1486i	0.696210	+	1.27477i
$637$	−22.2946	−	8.96918i	−0.883346	−	0.355372i
$638$	−47.7894	−	30.6704i	−1.89200	−	1.21425i
$639$	5.87880	−	4.60101i	0.232562	−	0.182013i
$640$	22.9262	+	26.2266i	0.906237	+	1.03670i
$641$	12.1458	−	21.0372i	0.479732	−	0.830920i	−0.519998	−	0.854168i	$-0.674067\pi$
$641$	12.1458	−	21.0372i	0.479732	−	0.830920i	0.999730	+	0.0232475i	$0.00740057\pi$
$642$	−0.105018	−	4.51473i	−0.00414471	−	0.178182i
$643$	5.13144	+	8.88791i	0.202364	+	0.350505i	0.949290	−	0.314403i	$-0.101804\pi$
$643$	5.13144	+	8.88791i	0.202364	+	0.350505i	−0.746926	+	0.664908i	$0.768471\pi$
$644$	24.4394	+	14.8832i	0.963048	+	0.586482i
$645$	−7.81760	+	16.0456i	−0.307818	+	0.631795i
$646$	−4.92244	+	2.54157i	−0.193671	+	0.0999968i
$647$	−44.3871			−1.74504			−0.872518	−	0.488581i	$-0.837515\pi$
$647$	−44.3871			−1.74504			−0.872518	+	0.488581i	$0.837515\pi$
$648$	9.52698	−	23.6059i	0.374255	−	0.927326i
$649$		−	37.4629i		−	1.47055i
$650$	19.3267	−	9.97881i	0.758055	−	0.391401i
$651$	11.0325	−	27.3982i	0.432399	−	1.07382i
$652$	17.8186	+	12.6552i	0.697829	+	0.495614i
$653$	11.3840	+	19.7176i	0.445489	+	0.771610i	0.998086	−	0.0618385i	$-0.0196964\pi$
$653$	11.3840	+	19.7176i	0.445489	+	0.771610i	−0.552597	+	0.833449i	$0.686363\pi$
$654$	−6.53478	+	0.152006i	−0.255530	+	0.00594390i
$655$	24.0132	+	13.8640i	0.938274	+	0.541713i
$656$	15.5211	+	13.3817i	0.605998	+	0.522466i
$657$	8.19732	−	6.41559i	0.319808	−	0.250296i
$658$	7.91743	−	14.4920i	0.308654	−	0.564957i
$659$	−20.9713	−	12.1078i	−0.816927	−	0.471653i	0.0324284	−	0.999474i	$-0.489676\pi$
$659$	−20.9713	−	12.1078i	−0.816927	−	0.471653i	−0.849356	+	0.527821i	$0.823009\pi$
$660$	21.5391	+	39.4385i	0.838408	+	1.53514i
$661$	9.97746	−	5.76049i	0.388078	−	0.224057i	−0.293249	−	0.956036i	$-0.594736\pi$
$661$	9.97746	−	5.76049i	0.388078	−	0.224057i	0.681327	+	0.731979i	$0.261403\pi$
$662$	1.37402	−	29.2266i	0.0534027	−	1.13593i
$663$	−13.5907	+	0.956112i	−0.527819	+	0.0371323i
$664$	−0.199779	+	0.255017i	−0.00775293	+	0.00989660i
$665$	−0.981811	−	13.8925i	−0.0380730	−	0.538727i
$666$	−3.61125	+	7.87192i	−0.139933	+	0.305031i
$667$		−	51.5368i		−	1.99551i
$668$	−33.8745	−	3.19211i	−1.31065	−	0.123506i
$669$	0.633335	+	0.938104i	0.0244861	+	0.0362692i
$670$	47.8930	+	2.25157i	1.85027	+	0.0869858i
$671$	−8.69333	−	15.0573i	−0.335602	−	0.581280i
$672$	25.8083	+	2.43575i	0.995576	+	0.0939611i
$673$	10.9799	−	19.0178i	0.423245	−	0.733083i	−0.573009	−	0.819549i	$-0.694224\pi$
$673$	10.9799	−	19.0178i	0.423245	−	0.733083i	0.996255	+	0.0864662i	$0.0275575\pi$
$674$	−12.6609	+	19.7277i	−0.487679	+	0.759882i
$675$	−7.16561	+	22.1488i	−0.275805	+	0.852506i
$676$	−1.01166	−	2.20795i	−0.0389099	−	0.0849211i
$677$	−38.3056	−	22.1157i	−1.47220	−	0.849977i	−0.472692	−	0.881228i	$-0.656718\pi$
$677$	−38.3056	−	22.1157i	−1.47220	−	0.849977i	−0.999512	+	0.0312511i	$0.990051\pi$
$678$	−1.59646	−	2.62237i	−0.0613118	−	0.100711i
$679$	14.0162	−	9.46921i	0.537894	−	0.363395i
$680$	7.45065	+	18.5106i	0.285719	+	0.709851i
$681$	−5.58840	−	8.27762i	−0.214148	−	0.317199i
$682$	34.1230	−	17.6185i	1.30664	−	0.674647i
$683$		−	15.0761i		−	0.576872i	−0.957499	−	0.288436i	$-0.906865\pi$
$683$		−	15.0761i		−	0.576872i	0.957499	−	0.288436i	$-0.0931352\pi$
$684$	−10.2468	+	0.476961i	−0.391796	+	0.0182371i
$685$		−	6.87980i		−	0.262864i
$686$	16.6373	+	20.2287i	0.635214	+	0.772336i
$687$	3.40397	+	48.3859i	0.129870	+	1.84604i
$688$	−2.50090	+	13.1519i	−0.0953458	+	0.501411i
$689$	31.4385	−	18.1510i	1.19771	−	0.691499i
$690$	−19.5651	+	35.7846i	−0.744832	+	1.36230i
$691$	−11.3171	+	19.6017i	−0.430522	+	0.745686i	−0.996918	−	0.0784473i	$-0.975004\pi$
$691$	−11.3171	+	19.6017i	−0.430522	+	0.745686i	0.566396	+	0.824133i	$0.308337\pi$
$692$	−8.54289	+	3.91426i	−0.324752	+	0.148798i
$693$	31.8205	+	10.2834i	1.20876	+	0.390633i
$694$	−12.2848	−	7.88418i	−0.466325	−	0.299279i
$695$	−27.1879	−	15.6969i	−1.03130	−	0.595418i
$696$	−20.4299	−	41.9819i	−0.774394	−	1.59132i
$697$	5.86946	+	10.1662i	0.222321	+	0.385072i
$698$	0.639115	−	13.5946i	0.0241909	−	0.514563i
$699$	−6.41062	+	13.1578i	−0.242472	+	0.497673i
$700$	−23.6997	−	0.554698i	−0.895765	−	0.0209656i
$701$	8.62984			0.325945			0.162972	−	0.986631i	$-0.447892\pi$
$701$	8.62984			0.325945			0.162972	+	0.986631i	$0.447892\pi$
$702$	−23.6114	−	8.88398i	−0.891157	−	0.335304i
$703$	3.49000			0.131628
$704$	23.3501	+	24.3066i	0.880042	+	0.916091i
$705$	21.1591	+	10.3089i	0.796898	+	0.388257i
$706$	−1.55886	+	33.1585i	−0.0586686	+	1.24794i
$707$	−37.5180	+	25.3467i	−1.41101	+	0.953262i
$708$	16.0296	−	26.3029i	0.602430	−	0.988524i
$709$	11.8717	−	20.5624i	0.445851	−	0.772237i	−0.552260	−	0.833672i	$-0.686234\pi$
$709$	11.8717	−	20.5624i	0.445851	−	0.772237i	0.998111	+	0.0614349i	$0.0195677\pi$
$710$	−5.85235	+	9.11890i	−0.219635	+	0.342226i
$711$	−4.30640	−	30.4553i	−0.161503	−	1.14216i
$712$	−1.43797	+	10.1355i	−0.0538901	+	0.379844i
$713$	30.1844	+	17.4270i	1.13041	+	0.652645i
$714$	13.4987	+	6.18729i	0.505175	+	0.231554i
$715$	38.5674	−	22.2669i	1.44234	−	0.832735i
$716$	13.5702	+	9.63788i	0.507142	+	0.360184i
$717$	−2.61020	−	37.1029i	−0.0974799	−	1.38563i
$718$	9.42309	−	4.86536i	0.351667	−	0.181574i
$719$	−25.3519			−0.945467			−0.472734	−	0.881205i	$-0.656733\pi$
$719$	−25.3519			−0.945467			−0.472734	+	0.881205i	$0.656733\pi$
$720$	−1.75221	+	36.9061i	−0.0653012	+	1.37541i
$721$	−4.26046	+	0.301096i	−0.158668	+	0.0112134i
$722$	−10.4310	−	20.2025i	−0.388202	−	0.751858i
$723$	−37.0548	+	25.0165i	−1.37808	+	0.930374i
$724$	14.7948	+	10.5076i	0.549845	+	0.390513i
$725$	21.3482	+	36.9762i	0.792853	+	1.37326i
$726$	8.59862	+	14.1242i	0.319125	+	0.524197i
$727$	−5.16319	+	8.94291i	−0.191492	+	0.331674i	−0.945745	−	0.324910i	$-0.894666\pi$
$727$	−5.16319	+	8.94291i	−0.191492	+	0.331674i	0.754253	+	0.656584i	$0.227999\pi$
$728$	1.80657	−	25.6268i	0.0669559	−	0.949793i
$729$	24.6379	−	11.0442i	0.912514	−	0.409046i
$730$	−8.16044	+	12.7153i	−0.302031	+	0.470613i
$731$	−3.83431	+	6.64122i	−0.141817	+	0.245634i
$732$	0.339072	−	14.2915i	0.0125325	−	0.528229i
$733$	10.1555	−	5.86329i	0.375102	−	0.216565i	−0.300583	−	0.953756i	$-0.597181\pi$
$733$	10.1555	−	5.86329i	0.375102	−	0.216565i	0.675685	+	0.737190i	$0.263848\pi$
$734$	6.76212	+	0.317904i	0.249595	+	0.0117341i
$735$	−27.6944	+	25.0318i	−1.02152	+	0.923312i
$736$	−7.11945	+	29.7503i	−0.262426	+	1.09661i
$737$	46.3915			1.70885
$738$	2.02921	+	21.6415i	0.0746964	+	0.796634i
$739$			0.463561i			0.0170524i	0.999964	+	0.00852618i	$0.00271400\pi$
$739$			0.463561i			0.0170524i	−0.999964	+	0.00852618i	$0.997286\pi$
$740$	1.17934	−	12.5151i	0.0433533	−	0.460064i
$741$	0.713411	+	10.1408i	0.0262078	+	0.372532i
$742$	−39.5546	+	0.932749i	−1.45210	+	0.0342423i
$743$	11.4461	−	6.60840i	0.419916	−	0.242439i	−0.275125	−	0.961408i	$-0.588719\pi$
$743$	11.4461	−	6.60840i	0.419916	−	0.242439i	0.695041	+	0.718970i	$0.255386\pi$
$744$	31.4965	+	2.23049i	1.15472	+	0.0817736i
$745$	32.8996	+	18.9946i	1.20535	+	0.695907i
$746$	21.2285	−	33.0773i	0.777229	−	1.21105i
$747$	−0.340220	+	0.0481073i	−0.0124480	+	0.00176016i
$748$	8.04224	+	17.5522i	0.294053	+	0.641773i
$749$	4.38571	+	2.13503i	0.160250	+	0.0780123i
$750$	0.0911909	+	3.92032i	0.00332982	+	0.143150i
$751$	9.82352	−	5.67161i	0.358465	−	0.206960i	−0.309942	−	0.950755i	$-0.600310\pi$
$751$	9.82352	−	5.67161i	0.358465	−	0.206960i	0.668407	+	0.743795i	$0.266976\pi$
$752$	17.3432	+	3.29789i	0.632440	+	0.120262i
$753$	−10.9013	+	22.3750i	−0.397267	+	0.815390i
$754$	−41.1133	+	21.2278i	−1.49726	+	0.773070i
$755$	33.2794			1.21116
$756$	17.9413	+	20.8353i	0.652518	+	0.757774i
$757$	−21.1566			−0.768950			−0.384475	−	0.923135i	$-0.625618\pi$
$757$	−21.1566			−0.768950			−0.384475	+	0.923135i	$0.625618\pi$
$758$	−34.4255	+	17.7747i	−1.25039	+	0.645606i
$759$	−17.2840	+	35.4753i	−0.627368	+	1.28767i
$760$	13.8119	−	5.55936i	0.501009	−	0.201659i
$761$	7.75469	−	4.47717i	0.281107	−	0.162297i	−0.352817	−	0.935692i	$-0.614776\pi$
$761$	7.75469	−	4.47717i	0.281107	−	0.162297i	0.633925	+	0.773395i	$0.281443\pi$
$762$	−0.607283	−	26.1073i	−0.0219995	−	0.945766i
$763$	3.09032	−	6.34803i	0.111877	−	0.229814i
$764$	21.4002	−	9.80532i	0.774231	−	0.354744i
$765$	−7.91172	+	19.6298i	−0.286049	+	0.709718i
$766$	−11.2469	+	17.5245i	−0.406369	+	0.633188i
$767$	−26.4364	−	15.2631i	−0.954563	−	0.551117i
$768$	5.99393	+	27.0568i	0.216287	+	0.976330i
$769$	−7.27639	+	4.20103i	−0.262393	+	0.151493i	−0.625426	−	0.780284i	$-0.715075\pi$
$769$	−7.27639	+	4.20103i	−0.262393	+	0.151493i	0.363033	+	0.931776i	$0.381741\pi$
$770$	−48.5239	+	1.14426i	−1.74868	+	0.0412362i
$771$	−2.08007	−	29.5673i	−0.0749120	−	1.06484i
$772$	−42.5857	−	4.01299i	−1.53269	−	0.144431i
$773$		−	5.75834i		−	0.207113i	−0.994624	−	0.103556i	$-0.966978\pi$
$773$		−	5.75834i		−	0.207113i	0.994624	−	0.103556i	$-0.0330223\pi$
$774$	−11.5807	+	8.21683i	−0.416261	+	0.295348i
$775$	−28.8753			−1.03723
$776$	14.2350	+	11.1516i	0.511008	+	0.400321i
$777$	−5.76788	−	7.36487i	−0.206921	−	0.264213i
$778$	−30.9384	−	1.45449i	−1.10920	−	0.0521461i
$779$	7.58559	−	4.37954i	0.271782	−	0.156913i
$780$	36.6059	+	0.868492i	1.31070	+	0.0310970i
$781$	−5.24202	+	9.07945i	−0.187574	+	0.324888i
$782$	−9.46430	+	14.7469i	−0.338443	+	0.527348i
$783$	15.2433	−	47.1167i	0.544751	−	1.68381i
$784$	−15.1191	+	23.5672i	−0.539969	+	0.841685i
$785$	38.1942	−	66.1542i	1.36321	−	2.36115i
$786$	11.4709	+	18.8422i	0.409153	+	0.672078i
$787$	18.4924	+	32.0297i	0.659181	+	1.14174i	0.980828	+	0.194876i	$0.0624303\pi$
$787$	18.4924	+	32.0297i	0.659181	+	1.14174i	−0.321647	+	0.946860i	$0.604236\pi$
$788$	12.4906	−	17.5868i	0.444957	−	0.626503i
$789$	24.7663	−	16.7203i	0.881703	−	0.595257i
$790$	20.4816	+	39.6682i	0.728704	+	1.41133i
$791$	3.30784	−	0.233772i	0.117613	−	0.00831197i
$792$	−0.0165938	+	35.7498i	−0.000589634	+	1.27031i
$793$	−14.1673			−0.503094
$794$	−43.9287	+	22.6814i	−1.55897	+	0.804933i
$795$	−3.95745	−	56.2533i	−0.140356	−	1.99510i
$796$	5.38460	−	7.58156i	0.190852	−	0.268721i
$797$	20.0024	−	11.5484i	0.708522	−	0.409065i	−0.101992	−	0.994785i	$-0.532522\pi$
$797$	20.0024	−	11.5484i	0.708522	−	0.409065i	0.810513	+	0.585720i	$0.199188\pi$
$798$	4.61670	−	10.0721i	0.163429	−	0.356550i
$799$	8.75767	+	5.05624i	0.309824	+	0.178877i
$800$	−7.21554	−	24.2941i	−0.255108	−	0.858927i
$801$	−8.55057	+	6.69205i	−0.302119	+	0.236452i
$802$	14.9453	−	23.2871i	0.527736	−	0.822298i
$803$	−7.30941	+	12.6603i	−0.257943	+	0.446771i
$804$	32.5717	+	19.8500i	1.14872	+	0.700054i
$805$	−24.6605	−	36.5023i	−0.869169	−	1.28654i
$806$	1.46950	−	31.2576i	0.0517608	−	1.10100i
$807$	33.5515	+	16.3467i	1.18107	+	0.575430i
$808$	−38.1037	−	29.8502i	−1.34048	−	1.05013i
$809$	−22.9976			−0.808553			−0.404277	−	0.914637i	$-0.632477\pi$
$809$	−22.9976			−0.808553			−0.404277	+	0.914637i	$0.632477\pi$
$810$	−28.4713	+	26.9287i	−1.00038	+	0.946177i
$811$	−27.1173			−0.952216			−0.476108	−	0.879387i	$-0.657953\pi$
$811$	−27.1173			−0.952216			−0.476108	+	0.879387i	$0.657953\pi$
$812$	50.4160	+	1.18000i	1.76926	+	0.0414099i
$813$	0.650364	−	1.33487i	0.0228093	−	0.0468160i
$814$	0.571182	−	12.1496i	0.0200199	−	0.425843i
$815$	−16.8230	−	29.1382i	−0.589282	−	1.02067i
$816$	−1.86374	+	15.7646i	−0.0652439	+	0.551871i
$817$	4.95540	+	2.86100i	0.173368	+	0.100094i
$818$	4.08730	+	2.62315i	0.142909	+	0.0917165i
$819$	20.2209	−	18.2651i	0.706575	−	0.638233i
$820$	−13.1417	−	28.6817i	−0.458927	−	1.00161i
$821$	−2.27415	+	3.93894i	−0.0793682	+	0.137470i	−0.902978	−	0.429688i	$-0.858624\pi$
$821$	−2.27415	+	3.93894i	−0.0793682	+	0.137470i	0.823609	+	0.567158i	$0.191957\pi$
$822$	2.62566	−	4.80234i	0.0915805	−	0.167501i
$823$	20.0197	−	11.5584i	0.697844	−	0.402900i	−0.108700	−	0.994075i	$-0.534669\pi$
$823$	20.0197	−	11.5584i	0.697844	−	0.402900i	0.806544	+	0.591174i	$0.201335\pi$
$824$	−1.70491	−	4.23574i	−0.0593934	−	0.147559i
$825$	−2.29428	−	32.6121i	−0.0798765	−	1.13541i
$826$	17.3099	+	28.4129i	0.602287	+	0.988610i
$827$			51.8058i			1.80146i	0.434376	+	0.900732i	$0.356969\pi$
$827$			51.8058i			1.80146i	−0.434376	+	0.900732i	$0.643031\pi$
$828$	−27.3143	+	17.5119i	−0.949237	+	0.608582i
$829$		−	13.9412i		−	0.484197i	−0.970252	−	0.242098i	$-0.922164\pi$
$829$		−	13.9412i		−	0.484197i	0.970252	−	0.242098i	$-0.0778357\pi$
$830$	0.443138	−	0.228803i	0.0153816	−	0.00794186i
$831$	−17.3421	−	25.6874i	−0.601592	−	0.891086i
$832$	26.6657	−	6.57449i	0.924466	−	0.227929i
$833$	−12.6242	+	9.89326i	−0.437401	+	0.342781i
$834$	−12.9874	−	21.3332i	−0.449716	−	0.738708i
$835$	45.3627	+	26.1902i	1.56984	+	0.906349i
$836$	13.0967	−	6.00078i	0.452960	−	0.207541i
$837$	22.4411	+	24.8601i	0.775679	+	0.859291i
$838$	8.89667	−	13.8624i	0.307330	−	0.478870i
$839$	−24.6769	+	42.7416i	−0.851941	+	1.47561i	0.0275127	+	0.999621i	$0.491241\pi$
$839$	−24.6769	+	42.7416i	−0.851941	+	1.47561i	−0.879454	+	0.475984i	$0.842092\pi$
$840$	−34.5585	−	19.9590i	−1.19238	−	0.688650i
$841$	−30.9137	−	53.5441i	−1.06599	−	1.84635i
$842$	−27.2448	−	1.28084i	−0.938917	−	0.0441408i
$843$	−21.0390	−	31.1633i	−0.724622	−	1.07332i
$844$	−0.485146	+	5.14835i	−0.0166994	+	0.177214i
$845$			3.73892i			0.128623i
$846$	10.8354	+	15.2713i	0.372529	+	0.525039i
$847$	−17.8161	+	1.25910i	−0.612170	+	0.0432633i
$848$	−13.9335	−	39.9366i	−0.478480	−	1.37143i
$849$	−40.4788	+	2.84770i	−1.38923	+	0.0977329i
$850$	0.681724	−	14.5009i	0.0233829	−	0.497377i
$851$	9.56000	−	5.51947i	0.327713	−	0.189205i
$852$	−7.56535	+	4.13177i	−0.259185	+	0.141552i
$853$	24.2685	+	14.0114i	0.830939	+	0.479743i	0.854174	−	0.519987i	$-0.174063\pi$
$853$	24.2685	+	14.0114i	0.830939	+	0.479743i	−0.0232350	+	0.999730i	$0.507397\pi$
$854$	13.5505	+	7.40306i	0.463689	+	0.253328i
$855$	14.6470	+	5.90339i	0.500915	+	0.201892i
$856$	−0.732479	+	5.16288i	−0.0250356	+	0.176463i
$857$	−9.87736	−	5.70269i	−0.337404	−	0.194800i	0.321719	−	0.946835i	$-0.395739\pi$
$857$	−9.87736	−	5.70269i	−0.337404	−	0.194800i	−0.659123	+	0.752035i	$0.729073\pi$
$858$	35.4195	−	0.823895i	1.20920	−	0.0281273i
$859$	20.0438	+	34.7168i	0.683884	+	1.18452i	0.973786	+	0.227466i	$0.0730440\pi$
$859$	20.0438	+	34.7168i	0.683884	+	1.18452i	−0.289902	+	0.957056i	$0.593623\pi$
$860$	11.9340	−	16.8032i	0.406947	−	0.572984i
$861$	−21.7786	−	8.76969i	−0.742214	−	0.298870i
$862$	−2.18346	+	1.12737i	−0.0743691	+	0.0383985i
$863$			45.2430i			1.54009i	0.637989	+	0.770045i	$0.279766\pi$
$863$			45.2430i			1.54009i	−0.637989	+	0.770045i	$0.720234\pi$
$864$	−15.3082	+	25.0930i	−0.520797	+	0.853681i
$865$	14.4664			0.491874
$866$	7.48638	−	3.86539i	0.254397	−	0.131351i
$867$	8.91390	−	18.2958i	0.302732	−	0.621357i
$868$	−17.7391	+	29.1290i	−0.602104	+	0.988701i
$869$	21.5982	+	37.4092i	0.732669	+	1.26902i
$870$	1.67148	+	71.8575i	0.0566685	+	2.43620i
$871$	18.9007	−	32.7370i	0.640426	−	1.10925i
$872$	7.47292	+	1.06022i	0.253065	+	0.0359034i
$873$	2.68535	+	18.9910i	0.0908852	+	0.642749i
$874$	11.0035	+	7.06186i	0.372199	+	0.238871i
$875$	−3.80829	−	1.85393i	−0.128744	−	0.0626743i
$876$	−10.5490	+	5.76129i	−0.356419	+	0.194656i
$877$	6.89651	+	11.9451i	0.232878	+	0.403357i	0.958654	−	0.284574i	$-0.0918522\pi$
$877$	6.89651	+	11.9451i	0.232878	+	0.403357i	−0.725776	+	0.687932i	$0.758519\pi$
$878$	−30.0547	−	1.41295i	−1.01430	−	0.0476846i
$879$	−1.36013	−	19.3336i	−0.0458759	−	0.652106i
$880$	−17.0931	−	48.9925i	−0.576207	−	1.65154i
$881$		−	46.4443i		−	1.56475i	−0.622808	−	0.782375i	$-0.714008\pi$
$881$		−	46.4443i		−	1.56475i	0.622808	−	0.782375i	$-0.285992\pi$
$882$	−28.8850	+	6.90357i	−0.972607	+	0.232455i
$883$			22.9737i			0.773127i	0.922263	+	0.386564i	$0.126338\pi$
$883$			22.9737i			0.773127i	−0.922263	+	0.386564i	$0.873662\pi$
$884$	15.6626	+	1.47594i	0.526790	+	0.0496411i
$885$	−39.3017	+	26.5334i	−1.32111	+	0.891912i
$886$	−2.31122	+	49.1619i	−0.0776471	+	1.65163i
$887$	10.6026	+	18.3642i	0.356000	+	0.616610i	0.987289	−	0.158938i	$-0.0508071\pi$
$887$	10.6026	+	18.3642i	0.356000	+	0.616610i	−0.631289	+	0.775548i	$0.717474\pi$
$888$	5.59958	−	8.28588i	0.187910	−	0.278056i
$889$	25.3612	+	12.3462i	0.850586	+	0.414078i
$890$	8.51210	−	13.2632i	0.285326	−	0.444584i
$891$	−26.2943	+	27.3206i	−0.880892	+	0.915274i
$892$	−0.544418	−	1.18820i	−0.0182285	−	0.0397838i
$893$	3.77276	−	6.53461i	0.126251	−	0.218672i
$894$	15.7158	+	25.8149i	0.525615	+	0.863380i
$895$	−12.8120	−	22.1910i	−0.428257	−	0.741763i
$896$	−28.9403	−	7.64580i	−0.966828	−	0.255428i
$897$	17.9920	+	26.6500i	0.600735	+	0.889817i
$898$	0.0710438	+	0.137596i	0.00237076	+	0.00459162i
$899$	61.4259			2.04867
$900$	12.3432	−	23.8788i	0.411441	−	0.795960i
$901$		−	24.2287i		−	0.807175i
$902$	−14.0048	−	27.1241i	−0.466310	−	0.903135i
$903$	−2.15221	−	15.1856i	−0.0716212	−	0.505345i
$904$	1.32370	+	3.28864i	0.0440256	+	0.109379i
$905$	−13.9682	−	24.1936i	−0.464317	−	0.804221i
$906$	23.2302	+	12.7010i	0.771770	+	0.421963i
$907$	−18.6114	−	10.7453i	−0.617981	−	0.356791i	0.158102	−	0.987423i	$-0.449463\pi$
$907$	−18.6114	−	10.7453i	−0.617981	−	0.356791i	−0.776082	+	0.630632i	$0.782796\pi$
$908$	4.80383	+	10.4844i	0.159421	+	0.347936i
$909$	−7.18801	−	50.8343i	−0.238411	−	1.68607i
$910$	−18.9620	+	34.7080i	−0.628585	+	1.15056i
$911$	44.5039	+	25.6943i	1.47448	+	0.851291i	0.999587	−	0.0287535i	$-0.00915379\pi$
$911$	44.5039	+	25.6943i	1.47448	+	0.851291i	0.474892	+	0.880044i	$0.342487\pi$
$912$	11.7629	+	1.39064i	0.389508	+	0.0460488i
$913$	0.417902	−	0.241276i	0.0138306	−	0.00798507i
$914$	41.4163	+	1.94708i	1.36993	+	0.0644038i
$915$	−9.63921	+	19.7845i	−0.318662	+	0.654054i
$916$	5.25466	−	55.7622i	0.173619	−	1.84244i
$917$	−23.7674	+	1.67969i	−0.784869	+	0.0554683i
$918$	−13.0143	+	10.6828i	−0.429537	+	0.352585i
$919$			33.2245i			1.09597i	0.836487	+	0.547987i	$0.184606\pi$
$919$			33.2245i			1.09597i	−0.836487	+	0.547987i	$0.815394\pi$
$920$	29.0420	−	37.0721i	0.957487	−	1.22223i
$921$	−6.96712	+	14.3000i	−0.229574	+	0.471201i
$922$	2.21623	−	47.1412i	0.0729875	−	1.55251i
$923$	4.27138	+	7.39825i	0.140594	+	0.243516i
$924$	−34.3081	−	17.7203i	−1.12865	−	0.582956i
$925$	−4.57269	+	7.92013i	−0.150349	+	0.260412i
$926$	12.3425	+	7.92118i	0.405599	+	0.260306i
$927$	1.81042	−	4.49184i	0.0594619	−	0.147531i
$928$	15.3495	+	51.6805i	0.503872	+	1.69649i
$929$	−23.4631	−	13.5464i	−0.769800	−	0.444444i	0.0630034	−	0.998013i	$-0.479932\pi$
$929$	−23.4631	−	13.5464i	−0.769800	−	0.444444i	−0.832803	+	0.553569i	$0.813265\pi$
$930$	−42.6511	−	23.3194i	−1.39859	−	0.764672i
$931$	7.38194	+	9.41962i	0.241933	+	0.308716i
$932$	9.78619	−	13.7790i	0.320557	−	0.451347i
$933$	−13.1680	+	0.926375i	−0.431101	+	0.0303281i
$934$	−5.07309	−	9.82540i	−0.165996	−	0.321497i
$935$		−	29.7227i		−	0.972038i
$936$	25.2207	+	14.5768i	0.824365	+	0.476458i
$937$			34.2337i			1.11837i	0.829044	+	0.559183i	$0.188885\pi$
$937$			34.2337i			1.11837i	−0.829044	+	0.559183i	$0.811115\pi$
$938$	−35.1845	+	21.4353i	−1.14882	+	0.699889i
$939$	8.90121	−	6.00940i	0.290480	−	0.196109i
$940$	−22.1581	−	15.7372i	−0.722718	−	0.513291i
$941$	−47.7364	+	27.5606i	−1.55616	+	0.898450i	−0.558543	+	0.829476i	$0.688639\pi$
$941$	−47.7364	+	27.5606i	−1.55616	+	0.898450i	−0.997618	+	0.0689741i	$0.978027\pi$
$942$	51.9085	−	31.6012i	1.69127	−	1.02962i
$943$	13.8526	−	23.9934i	0.451102	−	0.781331i
$944$	−23.2249	+	26.9381i	−0.755905	+	0.876759i
$945$	−11.7490	−	40.6656i	−0.382196	−	1.32285i
$946$	10.7709	−	16.7828i	0.350192	−	0.545655i
$947$	−13.2348	−	7.64112i	−0.430073	−	0.248303i	0.269305	−	0.963055i	$-0.413206\pi$
$947$	−13.2348	−	7.64112i	−0.430073	−	0.248303i	−0.699378	+	0.714752i	$0.746540\pi$
$948$	−0.842411	+	35.5066i	−0.0273602	+	1.15320i
$949$	5.95596	+	10.3160i	0.193339	+	0.334872i
$950$	−10.8200	−	0.508674i	−0.351046	−	0.0165036i
$951$	9.39116	+	13.9103i	0.304529	+	0.451073i
$952$	−14.2095	−	9.59613i	−0.460532	−	0.311012i
$953$	7.58109			0.245576			0.122788	−	0.992433i	$-0.460817\pi$
$953$	7.58109			0.245576			0.122788	+	0.992433i	$0.460817\pi$
$954$	18.7065	−	40.7771i	0.605646	−	1.32021i
$955$	−36.2388			−1.17266
$956$	−4.02933	+	42.7592i	−0.130318	+	1.38293i
$957$	4.88058	+	69.3752i	0.157767	+	2.24258i
$958$	7.87283	+	0.370121i	0.254360	+	0.0119581i
$959$	3.30947	+	4.89865i	0.106868	+	0.158186i
$960$	8.96173	−	41.7116i	0.289239	−	1.34624i
$961$	−5.27092	+	9.12949i	−0.170030	+	0.294500i
$962$	−8.34086	−	5.35302i	−0.268920	−	0.172588i
$963$	−4.35553	+	3.40883i	−0.140355	+	0.109848i
$964$	46.9334	−	21.5044i	1.51162	−	0.692609i
$965$	57.0282	+	32.9253i	1.83580	+	1.05990i
$966$	−3.28287	−	34.8915i	−0.105624	−	1.12262i
$967$	4.06638	−	2.34772i	0.130766	−	0.0754977i	−0.433190	−	0.901303i	$-0.642612\pi$
$967$	4.06638	−	2.34772i	0.130766	−	0.0754977i	0.563956	+	0.825805i	$0.309279\pi$
$968$	−7.12950	−	17.7128i	−0.229151	−	0.569310i
$969$	6.09949	+	2.97174i	0.195944	+	0.0954660i
$970$	−12.7717	−	24.7359i	−0.410076	−	0.794223i
$971$	44.5685			1.43027			0.715135	−	0.698986i	$-0.246365\pi$
$971$	44.5685			1.43027			0.715135	+	0.698986i	$0.246365\pi$
$972$	−30.1512	+	7.93113i	−0.967101	+	0.254391i
$973$	26.9096	−	1.90176i	0.862681	−	0.0609675i
$974$	28.5082	−	14.7194i	0.913461	−	0.471641i
$975$	−23.9481	−	11.6678i	−0.766952	−	0.373667i
$976$	−3.08364	+	16.2164i	−0.0987049	+	0.519076i
$977$	−4.78233	−	8.28324i	−0.153000	−	0.265004i	0.779329	−	0.626615i	$-0.215560\pi$
$977$	−4.78233	−	8.28324i	−0.153000	−	0.265004i	−0.932329	+	0.361611i	$0.882227\pi$
$978$	−0.622464	−	26.7599i	−0.0199042	−	0.855688i
$979$	7.62439	−	13.2058i	0.243677	−	0.422060i
$980$	36.2731	−	23.2885i	1.15870	−	0.743922i
$981$	4.93406	+	6.30434i	0.157532	+	0.201282i
$982$	7.40507	+	4.75245i	0.236305	+	0.151657i
$983$	26.0757	−	45.1644i	0.831685	−	1.44052i	−0.0650157	−	0.997884i	$-0.520710\pi$
$983$	26.0757	−	45.1644i	0.831685	−	1.44052i	0.896701	−	0.442637i	$-0.145957\pi$
$984$	1.77300	−	25.0363i	0.0565211	−	0.798129i
$985$	−28.7592	+	16.6041i	−0.916344	+	0.529052i
$986$	−1.45022	+	30.8475i	−0.0461844	+	0.982386i
$987$	−20.0250	+	2.83809i	−0.637403	+	0.0903374i
$988$	1.10128	−	11.6868i	0.0350365	−	0.371806i
$989$	18.0988			0.575508
$990$	22.9484	−	50.0236i	0.729347	−	1.58985i
$991$		−	41.3545i		−	1.31367i	−0.754034	−	0.656835i	$-0.771895\pi$
$991$		−	41.3545i		−	1.31367i	0.754034	−	0.656835i	$-0.228105\pi$
$992$	−35.4589	−	8.48556i	−1.12582	−	0.269417i
$993$	−29.6999	+	20.0510i	−0.942497	+	0.636301i
$994$	−0.219499	−	9.30818i	−0.00696208	−	0.295238i
$995$	−12.3979	+	7.15794i	−0.393040	+	0.226922i
$996$	0.396648	+	0.00941067i	0.0125683	+	0.000298188i
$997$	−45.7292	−	26.4017i	−1.44826	−	0.836152i	−0.449879	−	0.893089i	$-0.648533\pi$
$997$	−45.7292	−	26.4017i	−1.44826	−	0.836152i	−0.998378	+	0.0569376i	$0.981866\pi$
$998$	−48.6799	−	31.2419i	−1.54094	−	0.988946i
$999$	10.3726	−	2.21848i	0.328174	−	0.0701896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.223.28	yes	80
3.2	odd	2		756.2.bi.c.559.13		80
4.3	odd	2	inner	252.2.bi.c.223.1	yes	80
7.6	odd	2	inner	252.2.bi.c.223.27	yes	80
9.4	even	3	inner	252.2.bi.c.139.2	yes	80
9.5	odd	6		756.2.bi.c.307.40		80
12.11	even	2		756.2.bi.c.559.39		80
21.20	even	2		756.2.bi.c.559.14		80
28.27	even	2	inner	252.2.bi.c.223.2	yes	80
36.23	even	6		756.2.bi.c.307.14		80
36.31	odd	6	inner	252.2.bi.c.139.27	yes	80
63.13	odd	6	inner	252.2.bi.c.139.1	✓	80
63.41	even	6		756.2.bi.c.307.39		80
84.83	odd	2		756.2.bi.c.559.40		80
252.139	even	6	inner	252.2.bi.c.139.28	yes	80
252.167	odd	6		756.2.bi.c.307.13		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.1	✓	80	63.13	odd	6	inner
252.2.bi.c.139.2	yes	80	9.4	even	3	inner
252.2.bi.c.139.27	yes	80	36.31	odd	6	inner
252.2.bi.c.139.28	yes	80	252.139	even	6	inner
252.2.bi.c.223.1	yes	80	4.3	odd	2	inner
252.2.bi.c.223.2	yes	80	28.27	even	2	inner
252.2.bi.c.223.27	yes	80	7.6	odd	2	inner
252.2.bi.c.223.28	yes	80	1.1	even	1	trivial
756.2.bi.c.307.13		80	252.167	odd	6
756.2.bi.c.307.14		80	36.23	even	6
756.2.bi.c.307.39		80	63.41	even	6
756.2.bi.c.307.40		80	9.5	odd	6
756.2.bi.c.559.13		80	3.2	odd	2
756.2.bi.c.559.14		80	21.20	even	2
756.2.bi.c.559.39		80	12.11	even	2
756.2.bi.c.559.40		80	84.83	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.648812 + 1.25660i) q^{2} +(0.758625 - 1.55708i) q^{3} +(-1.15809 + 1.63059i) q^{4} +(2.66647 - 1.53948i) q^{5} +(2.44883 - 0.0569623i) q^{6} +(-1.15806 + 2.37885i) q^{7} +(-2.80038 - 0.397302i) q^{8} +(-1.84898 - 2.36247i) q^{9} +(3.66455 + 2.35184i) q^{10} +(3.64870 + 2.10658i) q^{11} +(1.66041 + 3.04024i) q^{12} +(2.97309 - 1.71651i) q^{13} +(-3.74062 + 0.0882086i) q^{14} +(-0.374249 - 5.31978i) q^{15} +(-1.31767 - 3.77674i) q^{16} -2.29127i q^{17} +(1.76905 - 3.85623i) q^{18} -1.70965 q^{19} +(-0.577723 + 6.13078i) q^{20} +(2.82551 + 3.60783i) q^{21} +(-0.279805 + 5.95173i) q^{22} +(-4.68317 + 2.70383i) q^{23} +(-2.74307 + 4.05901i) q^{24} +(2.24003 - 3.87984i) q^{25} +(4.08594 + 2.62229i) q^{26} +(-5.08123 + 1.08677i) q^{27} +(-2.53780 - 4.64323i) q^{28} +(-4.76517 + 8.25352i) q^{29} +(6.44202 - 3.92182i) q^{30} +(-3.22265 - 5.58179i) q^{31} +(3.89093 - 4.10618i) q^{32} +(6.04809 - 4.08320i) q^{33} +(2.87921 - 1.48660i) q^{34} +(0.574276 + 8.12592i) q^{35} +(5.99351 - 0.278982i) q^{36} -2.04135 q^{37} +(-1.10924 - 2.14835i) q^{38} +(-0.417285 - 5.93151i) q^{39} +(-8.07877 + 3.25176i) q^{40} +(-4.43693 + 2.56166i) q^{41} +(-2.70038 + 5.89135i) q^{42} +(-2.89849 - 1.67344i) q^{43} +(-7.66048 + 3.50995i) q^{44} +(-8.56723 - 3.45298i) q^{45} +(-6.43612 - 4.13059i) q^{46} +(-2.20674 + 3.82219i) q^{47} +(-6.88029 - 0.813409i) q^{48} +(-4.31781 - 5.50968i) q^{49} +(6.32876 + 0.297531i) q^{50} +(-3.56768 - 1.73821i) q^{51} +(-0.644156 + 6.83577i) q^{52} +10.5744 q^{53} +(-4.66240 - 5.67997i) q^{54} +12.9722 q^{55} +(4.18813 - 6.20158i) q^{56} +(-1.29698 + 2.66206i) q^{57} +(-13.4631 - 0.632933i) q^{58} +(-4.44595 - 7.70061i) q^{59} +(9.10782 + 5.55052i) q^{60} +(-3.57388 - 2.06338i) q^{61} +(4.92318 - 7.67111i) q^{62} +(7.76118 - 1.66255i) q^{63} +(7.68430 + 2.22520i) q^{64} +(5.28509 - 9.15404i) q^{65} +(9.05503 + 4.95080i) q^{66} +(9.53591 - 5.50556i) q^{67} +(3.73613 + 2.65349i) q^{68} +(0.657301 + 9.34324i) q^{69} +(-9.83843 + 5.99383i) q^{70} +2.48841i q^{71} +(4.23923 + 7.35044i) q^{72} +3.46980i q^{73} +(-1.32445 - 2.56517i) q^{74} +(-4.34187 - 6.43124i) q^{75} +(1.97992 - 2.78774i) q^{76} +(-9.23662 + 6.24015i) q^{77} +(7.18280 - 4.37280i) q^{78} +(8.87914 + 5.12638i) q^{79} +(-9.32776 - 8.04200i) q^{80} +(-2.16257 + 8.73632i) q^{81} +(-6.09771 - 3.91340i) q^{82} +(0.0572673 - 0.0991899i) q^{83} +(-9.15510 + 0.429082i) q^{84} +(-3.52738 - 6.10959i) q^{85} +(0.222275 - 4.72799i) q^{86} +(9.23639 + 13.6811i) q^{87} +(-9.38081 - 7.34886i) q^{88} -3.61933i q^{89} +(-1.21950 - 13.0059i) q^{90} +(0.640313 + 9.06033i) q^{91} +(1.01467 - 10.7676i) q^{92} +(-11.1361 + 0.783427i) q^{93} +(-6.23472 - 0.293110i) q^{94} +(-4.55872 + 2.63198i) q^{95} +(-3.44188 - 9.17352i) q^{96} +(-5.53677 - 3.19666i) q^{97} +(4.12201 - 9.00050i) q^{98} +(-1.76963 - 12.5150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44}+ \cdots + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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