LMFDB - Embedded newform 252.2.bi.c.139.27

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			139.27
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.27

$q$-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} +(1.48111 + 2.19233i) 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} +(3.71584 - 0.438755i) 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} +(2.29002 - 3.96936i) 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} +(1.85954 - 4.95400i) 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} +(-3.50211 - 5.45300i) 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} +(-2.61262 + 6.49417i) 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} +(-5.01870 - 5.55091i) 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} +(-7.91786 - 0.554479i) 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} +(-10.5836 - 4.55056i) 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} +(10.0224 + 4.87907i) 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} +(-9.12445 + 0.862773i) 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} +(6.46548 + 7.49651i) 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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	$-0.575054\pi$
$5$	−2.66647	−	1.53948i	−1.19248	−	0.688479i	−0.958868	+	0.283851i	$0.908388\pi$
$6$	−2.44883	−	0.0569623i	−0.999730	−	0.0232548i
$7$	1.48111	+	2.19233i	0.559808	+	0.828623i
$7$	1.48111	+	2.19233i	0.559808	+	0.828623i
$8$	−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	0.163870	−	0.986482i	$-0.447602\pi$
$11$	3.64870	−	2.10658i	1.10012	−	0.635157i	0.936254	+	0.351325i	$0.114269\pi$
$12$	−1.66041	+	3.04024i	−0.479318	+	0.877641i
$13$	−2.97309	−	1.71651i	−0.824586	−	0.476075i	0.0274094	−	0.999624i	$-0.491274\pi$
$13$	−2.97309	−	1.71651i	−0.824586	−	0.476075i	−0.851995	+	0.523549i	$0.824608\pi$
$14$	3.71584	−	0.438755i	0.993101	−	0.117262i
$15$	−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	$-0.437169\pi$
$19$	1.70965			0.392221			0.196110	+	0.980582i	$0.437169\pi$
$20$	0.577723	+	6.13078i	0.129183	+	1.37088i
$21$	2.29002	−	3.96936i	0.499723	−	0.866185i
$22$	−0.279805	−	5.95173i	−0.0596547	−	1.26891i
$23$	−4.68317	−	2.70383i	−0.976507	−	0.563787i	−0.0752935	−	0.997161i	$-0.523989\pi$
$23$	−4.68317	−	2.70383i	−0.976507	−	0.563787i	−0.901214	+	0.433375i	$0.857323\pi$
$24$	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
$28$	1.85954	−	4.95400i	0.351421	−	0.936218i
$29$	−4.76517	−	8.25352i	−0.884870	−	1.53264i	−0.845862	−	0.533401i	$-0.820914\pi$
$29$	−4.76517	−	8.25352i	−0.884870	−	1.53264i	−0.0390079	−	0.999239i	$-0.512420\pi$
$30$	6.44202	+	3.92182i	1.17615	+	0.716023i
$31$	3.22265	−	5.58179i	0.578805	−	1.00252i	−0.416812	−	0.908993i	$-0.636853\pi$
$31$	3.22265	−	5.58179i	0.578805	−	1.00252i	0.995617	−	0.0935263i	$-0.0298139\pi$
$32$	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	$-0.202321\pi$
$41$	4.43693	+	2.56166i	0.692931	+	0.400064i	−0.111778	+	0.993733i	$0.535655\pi$
$42$	−3.50211	−	5.45300i	−0.540387	−	0.841417i
$43$	−2.89849	+	1.67344i	−0.442015	+	0.255198i	−0.704452	−	0.709752i	$-0.748807\pi$
$43$	−2.89849	+	1.67344i	−0.442015	+	0.255198i	0.262437	+	0.964949i	$0.415474\pi$
$44$	−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	$-0.0623497\pi$
$47$	2.20674	+	3.82219i	0.321886	+	0.557524i	−0.658991	+	0.752151i	$0.729016\pi$
$48$	6.88029	−	0.813409i	0.993084	−	0.117405i
$49$	−2.61262	+	6.49417i	−0.373231	+	0.927738i
$50$	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
$56$	−5.01870	−	5.55091i	−0.670652	−	0.741772i
$57$	−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	−0.416802	−	0.908997i	$-0.636849\pi$
$59$	4.44595	−	7.70061i	0.578813	−	1.00253i	0.995616	−	0.0935372i	$-0.0298174\pi$
$60$	9.10782	−	5.55052i	1.17581	−	0.716569i
$61$	3.57388	−	2.06338i	0.457588	−	0.264189i	−0.253441	−	0.967351i	$-0.581563\pi$
$61$	3.57388	−	2.06338i	0.457588	−	0.264189i	0.711030	+	0.703162i	$0.248229\pi$
$62$	−4.92318	−	7.67111i	−0.625245	−	0.974232i
$63$	−7.91786	−	0.554479i	−0.997557	−	0.0698578i
$64$	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	0.952496	−	0.304550i	$-0.0985061\pi$
$67$	9.53591	+	5.50556i	1.16500	+	0.672611i	0.212500	+	0.977161i	$0.431839\pi$
$68$	−3.73613	+	2.65349i	−0.453072	+	0.321783i
$69$	−0.657301	+	9.34324i	−0.0791298	+	1.12479i
$70$	−10.5836	−	4.55056i	−1.26499	−	0.543896i
$71$		−	2.48841i		−	0.295320i	−0.989038	−	0.147660i	$-0.952826\pi$
$71$		−	2.48841i		−	0.295320i	0.989038	−	0.147660i	$-0.0471741\pi$
$72$	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
$77$	10.0224	+	4.87907i	1.14216	+	0.556022i
$78$	7.18280	+	4.37280i	0.813292	+	0.495122i
$79$	8.87914	−	5.12638i	0.998982	−	0.576762i	0.0910349	−	0.995848i	$-0.470983\pi$
$79$	8.87914	−	5.12638i	0.998982	−	0.576762i	0.907947	+	0.419085i	$0.137649\pi$
$80$	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	$-0.168668\pi$
$83$	−0.0572673	−	0.0991899i	−0.00628591	−	0.0108875i	−0.869151	+	0.494546i	$0.835334\pi$
$84$	−9.12445	+	0.862773i	−0.995559	+	0.0941363i
$85$	−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	$-0.561447\pi$
$97$	5.53677	−	3.19666i	0.562174	−	0.324571i	0.754018	+	0.656854i	$0.228113\pi$
$98$	6.46548	+	7.49651i	0.653112	+	0.757262i
$99$	−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	$-0.990925\pi$
$101$	−14.8206	+	8.55666i	−1.47470	+	0.851420i	−0.475109	+	0.879927i	$0.657591\pi$
$102$	−0.130516	+	5.61092i	−0.0129230	+	0.555564i
$103$	−0.807160	+	1.39804i	−0.0795318	+	0.137753i	−0.903048	−	0.429540i	$-0.858676\pi$
$103$	−0.807160	+	1.39804i	−0.0795318	+	0.137753i	0.823516	+	0.567293i	$0.192009\pi$
$104$	9.00776	+	3.62568i	0.883283	+	0.355527i
$105$	−12.2170	+	7.05872i	−1.19226	+	0.688860i
$106$	6.86077	−	13.2877i	0.666377	−	1.29062i
$107$			1.84363i			0.178231i	0.996021	+	0.0891153i	$0.0284040\pi$
$107$			1.84363i			0.178231i	−0.996021	+	0.0891153i	$0.971596\pi$
$108$	−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
$112$	−10.2315	+	2.70500i	−0.966783	+	0.255598i
$113$	−0.626681	+	1.08544i	−0.0589532	+	0.102110i	−0.893996	−	0.448075i	$-0.852110\pi$
$113$	−0.626681	+	1.08544i	−0.0589532	+	0.102110i	0.835043	+	0.550185i	$0.185443\pi$
$114$	−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
$119$	5.02322	−	3.39363i	0.460478	−	0.311093i
$120$	−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
$126$	−5.83396	+	9.58983i	−0.519731	+	0.854330i
$127$			10.6611i			0.946022i	0.881056	+	0.473011i	$0.156833\pi$
$127$			10.6611i			0.946022i	−0.881056	+	0.473011i	$0.843167\pi$
$128$	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	$-0.962039\pi$
$131$	−4.50282	+	7.79911i	−0.393413	+	0.681411i	0.599484	+	0.800387i	$0.295372\pi$
$132$	0.346171	+	14.5907i	0.0301303	+	1.26996i
$133$	2.53218	+	3.74812i	0.219568	+	0.325003i
$134$	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	0.909797	−	0.415054i	$-0.136237\pi$
$137$	1.11722	+	1.93509i	0.0954509	+	0.165326i	−0.814346	+	0.580380i	$0.802904\pi$
$138$	11.3142	+	6.88797i	0.963133	+	0.586343i
$139$	5.09811	−	8.83019i	0.432416	−	0.748967i	−0.564665	−	0.825320i	$-0.690994\pi$
$139$	5.09811	−	8.83019i	0.432416	−	0.748967i	0.997081	+	0.0763537i	$0.0243278\pi$
$140$	−12.5850	+	10.3469i	−1.06363	+	0.874475i
$141$	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
$147$	12.0939	−	0.858593i	0.997489	−	0.0708155i
$148$	2.36406	+	3.32862i	0.194325	+	0.273611i
$149$	6.16913	−	10.6853i	0.505395	−	0.875370i	−0.494585	−	0.869129i	$-0.664680\pi$
$149$	6.16913	−	10.6853i	0.505395	−	0.875370i	0.999981	−	0.00624098i	$-0.00198658\pi$
$150$	−5.26443	−	9.62866i	−0.429839	−	0.786176i
$151$	9.36053	−	5.40430i	0.761749	−	0.439796i	−0.0681743	−	0.997673i	$-0.521717\pi$
$151$	9.36053	−	5.40430i	0.761749	−	0.439796i	0.829923	+	0.557877i	$0.188384\pi$
$152$	−4.78768	+	0.679248i	−0.388332	+	0.0550943i
$153$	5.41307	+	4.23651i	0.437620	+	0.342501i
$154$	12.6337	−	9.42860i	1.01805	−	0.759778i
$155$	−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	−0.927860	−	0.372930i	$-0.878353\pi$
$157$	−21.4858	−	12.4049i	−1.71476	−	0.990015i	−0.786896	−	0.617085i	$-0.788313\pi$
$158$	−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	$0.140768\pi$
$163$			10.9277i			0.855920i	−0.903798	+	0.427960i	$0.859232\pi$
$164$	−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	0.322849	+	0.946451i	$0.395359\pi$
$167$	−8.50615	+	14.7331i	−0.658226	+	1.14008i	−0.981075	+	0.193630i	$0.937974\pi$
$168$	−4.83589	+	12.0256i	−0.373097	+	0.927792i
$169$	−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	$-0.723826\pi$
$173$	−4.06899	+	2.34923i	−0.309360	+	0.178609i	0.337280	+	0.941404i	$0.390493\pi$
$174$	11.1989	+	20.4829i	0.848990	+	1.55280i
$175$	−5.18816	+	10.6574i	−0.392188	+	0.805620i
$176$	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	$0.100670\pi$
$179$			8.32224i			0.622034i	−0.950404	+	0.311017i	$0.899330\pi$
$180$	−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	$-0.109482\pi$
$182$	−11.8007	−	5.07383i	−0.874723	−	0.376098i
$183$	−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
$189$	5.14332	+	12.7494i	0.374121	+	0.927380i
$190$	−6.26510	+	4.02083i	−0.454518	+	0.291702i
$191$	−10.1929	+	5.88490i	−0.737535	+	0.425816i	−0.821172	−	0.570680i	$-0.806680\pi$
$191$	−10.1929	+	5.88490i	−0.737535	+	0.425816i	0.0836373	+	0.996496i	$0.473346\pi$
$192$	−9.29431	−	10.2770i	−0.670759	−	0.741676i
$193$	10.6936	−	18.5218i	0.769742	−	1.33323i	−0.167961	−	0.985794i	$-0.553718\pi$
$193$	10.6936	−	18.5218i	0.769742	−	1.33323i	0.937703	−	0.347438i	$-0.112948\pi$
$194$	−0.424595	−	9.03154i	−0.0304841	−	0.648426i
$195$	10.2442	−	15.1738i	0.733599	−	1.08662i
$196$	13.6150	−	3.26069i	0.972499	−	0.232907i
$197$	−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	$-0.447302\pi$
$199$	4.64957			0.329599			0.164800	+	0.986327i	$0.447302\pi$
$200$	−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
$203$	11.0367	−	22.6712i	0.774623	−	1.59121i
$204$	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
$210$	0.943432	+	19.9317i	0.0651030	+	1.37542i
$211$	2.23918	+	1.29279i	0.154151	+	0.0889993i	0.575092	−	0.818089i	$-0.304966\pi$
$211$	2.23918	+	1.29279i	0.154151	+	0.0889993i	−0.420940	+	0.907088i	$0.638300\pi$
$212$	−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	$-0.159701\pi$
$223$	0.326746	+	0.565940i	0.0218805	+	0.0378981i	−0.854878	+	0.518829i	$0.826368\pi$
$224$	−3.23920	+	14.6119i	−0.216428	+	0.976299i
$225$	−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	$-0.227956\pi$
$227$	−2.88313	−	4.99372i	−0.191360	−	0.331445i	−0.945701	+	0.325037i	$0.894623\pi$
$228$	−2.83872	+	5.19774i	−0.187999	+	0.344229i
$229$	24.2527	+	14.0023i	1.60267	+	0.925299i	0.990951	+	0.134220i	$0.0428530\pi$
$229$	24.2527	+	14.0023i	1.60267	+	0.925299i	0.611714	+	0.791079i	$0.290480\pi$
$230$	23.5207	−	1.10577i	1.55091	−	0.0729120i
$231$	−0.00617924	−	19.3071i	−0.000406564	−	1.27031i
$232$	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
$238$	−1.00531	−	8.51400i	−0.0651644	−	0.551881i
$239$	18.5973	+	10.7371i	1.20296	+	0.694528i	0.961212	−	0.275811i	$-0.0889465\pi$
$239$	18.5973	+	10.7371i	1.20296	+	0.694528i	0.241746	+	0.970339i	$0.422280\pi$
$240$	−19.5983	−	8.42317i	−1.26506	−	0.543713i
$241$	22.3544	−	12.9063i	1.43998	−	0.831371i	0.442129	−	0.896951i	$-0.354223\pi$
$241$	22.3544	−	12.9063i	1.43998	−	0.831371i	0.997847	+	0.0655806i	$0.0208899\pi$
$242$	−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
$245$	16.9641	−	13.2944i	1.08380	−	0.849348i
$246$	−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	$-0.350172\pi$
$251$	14.3699			0.907018			0.453509	+	0.891252i	$0.350172\pi$
$252$	8.26544	+	13.5530i	0.520674	+	0.853756i
$253$	−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	$-0.512546\pi$
$257$	−14.8202	−	8.55644i	−0.924458	−	0.533736i	−0.885055	+	0.465487i	$0.845879\pi$
$258$	7.19322	−	3.93287i	0.447830	−	0.244850i
$259$	−3.02347	−	4.47532i	−0.187870	−	0.278083i
$260$	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	0.0372520	−	0.999306i	$-0.488140\pi$
$263$	14.9410	−	8.62620i	0.921302	−	0.531914i	0.884050	+	0.467392i	$0.154806\pi$
$264$	18.5593	+	9.03161i	1.14224	+	0.555857i
$265$	−28.1962	−	16.2791i	−1.73208	−	1.00001i
$266$	6.35279	−	0.750118i	0.389515	−	0.0459927i
$267$	−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	$-0.508289\pi$
$271$	−0.857294			−0.0520769			−0.0260384	+	0.999661i	$0.508289\pi$
$272$	8.65352	+	3.01914i	0.524697	+	0.183062i
$273$	−13.6219	+	7.87041i	−0.824433	+	0.476339i
$274$	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	0.999034	+	0.0439457i	$0.0139928\pi$
$277$	8.94703	+	15.4967i	0.537575	+	0.931107i	−0.461459	+	0.887162i	$0.652674\pi$
$278$	−7.78830	−	12.1354i	−0.467111	−	0.727834i
$279$	7.22823	+	17.9340i	0.432743	+	1.07368i
$280$	4.83664	+	22.5275i	0.289045	+	1.34628i
$281$	10.8543	+	18.8002i	0.647513	+	1.12153i	0.983715	+	0.179735i	$0.0575241\pi$
$281$	10.8543	+	18.8002i	0.647513	+	1.12153i	−0.336202	+	0.941790i	$0.609143\pi$
$282$	−5.18621	−	9.48558i	−0.308834	−	0.564858i
$283$	11.7141	−	20.2894i	0.696331	−	1.20608i	−0.273399	−	0.961901i	$-0.588148\pi$
$283$	11.7141	−	20.2894i	0.696331	−	1.20608i	0.969730	−	0.244180i	$-0.0785186\pi$
$284$	−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	$-0.439323\pi$
$293$	−9.69068	−	5.59492i	−0.566136	−	0.326859i	−0.755605	+	0.655028i	$0.772657\pi$
$294$	6.76777	−	15.7543i	0.394704	−	0.918808i
$295$	−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
$301$	−7.96172	−	3.87588i	−0.458906	−	0.223402i
$302$	−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	$-0.415593\pi$
$307$	9.18388			0.524152			0.262076	+	0.965047i	$0.415593\pi$
$308$	−3.65106	−	21.9929i	−0.208039	−	1.25316i
$309$	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	$-0.764005\pi$
$311$	3.81067	−	6.60027i	0.216083	−	0.374267i	0.953607	+	0.301054i	$0.0973385\pi$
$312$	−1.18805	−	16.7763i	−0.0672599	−	0.949771i
$313$	−5.36993	+	3.10033i	−0.303526	+	0.175241i	−0.644026	−	0.765004i	$-0.722737\pi$
$313$	−5.36993	+	3.10033i	−0.303526	+	0.175241i	0.340500	+	0.940245i	$0.389404\pi$
$314$	−29.5282	+	18.9507i	−1.66637	+	1.06945i
$315$	20.2591	+	13.6679i	1.14147	+	0.770101i
$316$	−18.6419	−	8.54149i	−1.04869	−	0.480496i
$317$	−4.84502	−	8.39183i	−0.272124	−	0.471332i	0.697282	−	0.716797i	$-0.254393\pi$
$317$	−4.84502	−	8.39183i	−0.272124	−	0.471332i	−0.969405	+	0.245465i	$0.921059\pi$
$318$	−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
$322$	−18.5882	−	7.99223i	−1.03588	−	0.445390i
$323$		−	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
$329$	−5.11107	+	10.4990i	−0.281782	+	0.578828i
$330$	31.7666	+	0.738925i	1.74869	+	0.0406765i
$331$	−17.9174	+	10.3446i	−0.984827	+	0.568590i	−0.903724	−	0.428116i	$-0.859178\pi$
$331$	−17.9174	+	10.3446i	−0.984827	+	0.568590i	−0.0811031	+	0.996706i	$0.525844\pi$
$332$	−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
$336$	11.9737	+	13.8791i	0.653221	+	0.757167i
$337$	8.28764	−	14.3546i	0.451457	−	0.781946i	−0.547020	−	0.837119i	$-0.684238\pi$
$337$	8.28764	−	14.3546i	0.451457	−	0.781946i	0.998477	+	0.0551737i	$0.0175713\pi$
$338$	−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	0.240495	−	0.970650i	$-0.422690\pi$
$347$	−8.93889	−	5.16087i	−0.479865	−	0.277050i	−0.720360	+	0.693600i	$0.756023\pi$
$348$	33.0048	−	0.783055i	1.76924	−	0.0419761i
$349$	8.33414	−	4.81172i	0.446116	−	0.257565i	−0.260072	−	0.965589i	$-0.583746\pi$
$349$	8.33414	−	4.81172i	0.446116	−	0.257565i	0.706189	+	0.708024i	$0.250413\pi$
$350$	10.0259	+	13.4341i	0.535906	+	0.718081i
$351$	−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	$-0.881428\pi$
$353$	−20.3278	+	11.7363i	−1.08194	+	0.624658i	−0.150520	+	0.988607i	$0.548095\pi$
$354$	−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
$357$	−9.09488	−	5.24705i	−0.481352	−	0.277703i
$358$	10.4577	+	5.39957i	0.552708	+	0.285376i
$359$			7.49888i			0.395776i	0.980225	+	0.197888i	$0.0634082\pi$
$359$			7.49888i			0.395776i	−0.980225	+	0.197888i	$0.936592\pi$
$360$	−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
$364$	−14.0322	+	11.5367i	−0.735486	+	0.604689i
$365$	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	$-0.206539\pi$
$367$	−2.39341	−	4.14551i	−0.124935	−	0.216394i	−0.921708	+	0.387885i	$0.873206\pi$
$368$	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
$371$	15.6618	+	23.1825i	0.813120	+	1.20357i
$372$	11.6191	+	19.0657i	0.602420	+	0.988508i
$373$	−13.8959	+	24.0683i	−0.719500	+	1.24621i	0.241698	+	0.970352i	$0.422296\pi$
$373$	−13.8959	+	24.0683i	−0.719500	+	1.24621i	−0.961198	+	0.275859i	$0.911038\pi$
$374$	−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
$378$	19.3579	+	1.80884i	0.995663	+	0.0930368i
$379$		−	27.3958i		−	1.40723i	−0.710583	−	0.703613i	$-0.751569\pi$
$379$		−	27.3958i		−	1.40723i	0.710583	−	0.703613i	$-0.248431\pi$
$380$	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	$-0.956098\pi$
$383$	−7.36210	+	12.7515i	−0.376185	+	0.651572i	0.614318	+	0.789058i	$0.289431\pi$
$384$	−18.9443	+	5.01141i	−0.966746	+	0.255738i
$385$	−19.2132	−	28.4393i	−0.979197	−	1.44940i
$386$	−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	−0.997887	−	0.0649717i	$-0.979304\pi$
$389$	−10.9505	−	18.9668i	−0.555211	−	0.961653i	0.442676	−	0.896681i	$-0.354029\pi$
$390$	−12.4208	−	22.7177i	−0.628953	−	1.15036i
$391$	−6.19520	+	10.7304i	−0.313305	+	0.542659i
$392$	4.73618	−	19.2242i	0.239213	−	0.970967i
$393$	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
$399$	3.91513	−	6.78622i	0.196002	−	0.339736i
$400$	−17.6048	+	3.34763i	−0.880238	+	0.167382i
$401$	−9.78297	+	16.9446i	−0.488538	+	0.846173i	−0.999913	−	0.0131845i	$-0.995803\pi$
$401$	−9.78297	+	16.9446i	−0.488538	+	0.846173i	0.511375	+	0.859358i	$0.329136\pi$
$402$	−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
$406$	−21.3279	−	28.5780i	−1.05849	−	1.41830i
$407$	−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	$-0.360392\pi$
$409$	−2.97407	−	1.71708i	−0.147058	−	0.0849042i	−0.571724	+	0.820446i	$0.693725\pi$
$410$	−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	$-0.741505\pi$
$419$	5.82364	−	10.0868i	0.284503	−	0.492774i	0.972489	+	0.232950i	$0.0748380\pi$
$420$	25.6583	+	11.7464i	1.25200	+	0.573166i
$421$	−9.64312	−	16.7024i	−0.469977	−	0.814024i	0.529434	−	0.848351i	$-0.322404\pi$
$421$	−9.64312	−	16.7024i	−0.469977	−	0.814024i	−0.999411	+	0.0343274i	$0.989071\pi$
$422$	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
$427$	9.81692	+	4.77902i	0.475074	+	0.231273i
$428$	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	$-0.986675\pi$
$431$		−	1.73760i		−	0.0836971i	0.999124	−	0.0418485i	$-0.0133247\pi$
$432$	−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	$-0.0457241\pi$
$434$	9.52581	−	22.1550i	0.457254	−	1.06347i
$435$	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	0.999960	+	0.00892391i	$0.00284061\pi$
$439$	10.6377	+	18.4250i	0.507708	+	0.879377i	−0.492252	+	0.870453i	$0.663826\pi$
$440$	36.3271	−	5.15388i	1.73182	−	0.245701i
$441$	−10.5116	−	18.1798i	−0.500554	−	0.865705i
$442$	6.00837	+	9.36200i	0.285789	+	0.445305i
$443$	30.1387	−	17.4006i	1.43193	−	0.826726i	0.434663	−	0.900593i	$-0.356868\pi$
$443$	30.1387	−	17.4006i	1.43193	−	0.826726i	0.997268	+	0.0738675i	$0.0235342\pi$
$444$	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
$448$	16.2597	+	13.5508i	0.768198	+	0.640213i
$449$	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
$455$	−12.2409	+	25.1448i	−0.573861	+	1.17881i
$456$	4.68969	+	6.93949i	0.219615	+	0.324971i
$457$	14.6591	+	25.3902i	0.685722	+	1.18770i	0.973209	+	0.229920i	$0.0738466\pi$
$457$	14.6591	+	25.3902i	0.685722	+	1.18770i	−0.287488	+	0.957784i	$0.592820\pi$
$458$	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	$-0.383350\pi$
$461$	28.8999	−	16.6853i	1.34600	−	0.777114i	0.987680	+	0.156485i	$0.0500163\pi$
$462$	−24.2653	−	12.5189i	−1.12892	−	0.582432i
$463$	8.98085	+	5.18510i	0.417376	+	0.240972i	0.693954	−	0.720019i	$-0.255867\pi$
$463$	8.98085	+	5.18510i	0.417376	+	0.240972i	−0.276578	+	0.960991i	$0.589200\pi$
$464$	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	$-0.442095\pi$
$467$	7.81904			0.361822			0.180911	+	0.983499i	$0.442095\pi$
$468$	−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
$476$	−11.3509	−	4.26072i	−0.520270	−	0.195290i
$477$	−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	$-0.207304\pi$
$479$	−2.78654	−	4.82643i	−0.127320	−	0.220525i	−0.922638	+	0.385668i	$0.873971\pi$
$480$	−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
$483$	−21.4570	+	12.3974i	−0.976327	+	0.564099i
$484$	−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	$0.171843\pi$
$487$			22.6868i			1.02804i	−0.857780	+	0.514018i	$0.828157\pi$
$488$	−9.18844	+	7.19816i	−0.415941	+	0.325846i
$489$	17.0152	−	8.28999i	0.769454	−	0.374886i
$490$	−5.69921	−	29.9427i	−0.257464	−	1.35267i
$491$	5.38821	+	3.11089i	0.243167	+	0.140392i	0.616631	−	0.787252i	$-0.288497\pi$
$491$	5.38821	+	3.11089i	0.243167	+	0.140392i	−0.373465	+	0.927644i	$0.621830\pi$
$492$	−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
$497$	5.45541	−	3.68561i	0.244709	−	0.165322i
$498$	0.134588	+	0.246161i	0.00603102	+	0.0110307i
$499$	−35.4214	−	20.4505i	−1.58568	−	0.915491i	−0.994008	−	0.109311i	$-0.965135\pi$
$499$	−35.4214	−	20.4505i	−1.58568	−	0.915491i	−0.591670	−	0.806180i	$-0.701531\pi$
$500$	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	$-0.438735\pi$
$503$	8.58006			0.382566			0.191283	+	0.981535i	$0.438735\pi$
$504$	22.3934	−	1.59303i	0.997479	−	0.0709593i
$505$	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	$-0.288520\pi$
$509$	5.48332	+	3.16579i	0.243044	+	0.140321i	−0.373531	+	0.927618i	$0.621853\pi$
$510$	8.98595	−	14.7604i	0.397905	−	0.653602i
$511$	−7.60695	+	5.13917i	−0.336512	+	0.227343i
$512$	−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
$518$	−7.58535	+	0.895655i	−0.333281	+	0.0393528i
$519$	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	$-0.832790\pi$
$523$	−39.5715			−1.73034			−0.865171	+	0.501476i	$0.832790\pi$
$524$	17.9318	−	1.68977i	0.783356	−	0.0738182i
$525$	20.5302	−	0.00657069i	0.896011	−	0.000286769i
$526$	−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
$532$	3.17917	−	8.46960i	0.137834	−	0.367204i
$533$	−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
$546$	1.05192	+	22.2237i	0.0450179	+	0.951085i
$547$	17.5001	−	10.1037i	0.748252	−	0.432003i	−0.0768102	−	0.997046i	$-0.524474\pi$
$547$	17.5001	−	10.1037i	0.748252	−	0.432003i	0.825062	+	0.565042i	$0.191140\pi$
$548$	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
$553$	24.3897	+	11.8733i	1.03716	+	0.504903i
$554$	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
$560$	31.4462	+	8.53841i	1.32884	+	0.360814i
$561$	−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	0.0952496	+	0.995453i	$0.469635\pi$
$563$	−19.3253	+	33.4724i	−0.814463	+	1.41069i	−0.909713	+	0.415238i	$0.863698\pi$
$564$	−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
$567$	15.9499	−	17.6805i	0.669832	−	0.742512i
$568$	0.988651	+	6.96850i	0.0414829	+	0.292392i
$569$	−6.96304	−	12.0603i	−0.291906	−	0.505596i	0.682355	−	0.731021i	$-0.260956\pi$
$569$	−6.96304	−	12.0603i	−0.291906	−	0.505596i	−0.974260	+	0.225426i	$0.927623\pi$
$570$	11.0136	+	6.70494i	0.461309	+	0.280839i
$571$	21.6359	+	12.4915i	0.905436	+	0.522754i	0.878960	−	0.476896i	$-0.158238\pi$
$571$	21.6359	+	12.4915i	0.905436	+	0.522754i	0.0264762	+	0.999649i	$0.491571\pi$
$572$	16.7504	+	23.5847i	0.700369	+	0.986125i
$573$	16.8958	+	11.4068i	0.705834	+	0.476524i
$574$	17.6109	+	7.57200i	0.735063	+	0.316049i
$575$		−	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
$581$	0.132638	−	0.272460i	0.00550274	−	0.0113036i
$582$	−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	−0.998745	−	0.0500760i	$-0.984054\pi$
$587$	−13.1495	−	22.7757i	−0.542740	−	0.940053i	0.456006	−	0.889977i	$-0.349280\pi$
$588$	−15.4058	−	18.7259i	−0.635325	−	0.772245i
$589$	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	0.243219	−	0.969972i	$-0.421797\pi$
$599$	−11.6301	−	6.71463i	−0.475192	−	0.274352i	−0.718411	+	0.695619i	$0.755130\pi$
$600$	−9.60376	+	19.7350i	−0.392072	+	0.805677i
$601$	−11.6714	+	6.73847i	−0.476086	+	0.274868i	−0.718784	−	0.695234i	$-0.755301\pi$
$601$	−11.6714	+	6.73847i	−0.476086	+	0.274868i	0.242698	+	0.970102i	$0.421968\pi$
$602$	−10.0361	+	7.48998i	−0.409041	+	0.305269i
$603$	−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	−0.262482	−	0.964937i	$-0.584541\pi$
$607$	17.3550	−	30.0598i	0.704419	−	1.22009i	0.966901	−	0.255153i	$-0.0821257\pi$
$608$	6.65212	+	7.02013i	0.269779	+	0.284704i
$609$	−43.6735	+	0.0139777i	−1.76974	+	0.000566406i
$610$	−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
$616$	−30.0051	−	9.68134i	−1.20894	−	0.390072i
$617$	−3.19357	+	5.53142i	−0.128568	+	0.222687i	−0.923122	−	0.384507i	$-0.874371\pi$
$617$	−3.19357	+	5.53142i	−0.128568	+	0.222687i	0.794554	+	0.607194i	$0.207705\pi$
$618$	2.05623	−	3.37759i	0.0827137	−	0.135866i
$619$	−13.4240	−	23.2510i	−0.539554	−	0.934536i	−0.998928	−	0.0462924i	$-0.985259\pi$
$619$	−13.4240	−	23.2510i	−0.539554	−	0.934536i	0.459374	−	0.888243i	$-0.348074\pi$
$620$	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
$623$	7.93476	−	5.36063i	0.317899	−	0.214769i
$624$	−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
$630$	30.3195	−	16.5897i	1.20796	−	0.660948i
$631$		−	24.9328i		−	0.992557i	−0.868163	−	0.496279i	$-0.834699\pi$
$631$		−	24.9328i		−	0.992557i	0.868163	−	0.496279i	$-0.165301\pi$
$632$	−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
$637$	18.9149	−	14.8231i	0.749434	−	0.587314i
$638$	−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	0.999730	−	0.0232475i	$-0.00740057\pi$
$641$	12.1458	+	21.0372i	0.479732	+	0.830920i	−0.519998	+	0.854168i	$0.674067\pi$
$642$	0.105018	−	4.51473i	0.00414471	−	0.178182i
$643$	−5.13144	+	8.88791i	−0.202364	+	0.350505i	−0.949290	−	0.314403i	$-0.898196\pi$
$643$	−5.13144	+	8.88791i	−0.202364	+	0.350505i	0.746926	+	0.664908i	$0.231529\pi$
$644$	−22.1033	+	18.1725i	−0.870992	+	0.716097i
$645$	−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	$-0.162485\pi$
$647$	44.3871			1.74504			0.872518	+	0.488581i	$0.162485\pi$
$648$	9.52698	+	23.6059i	0.374255	+	0.927326i
$649$		−	37.4629i		−	1.47055i
$650$	−19.3267	−	9.97881i	−0.758055	−	0.391401i
$651$	−14.7762	−	25.5742i	−0.579125	−	1.00233i
$652$	17.8186	−	12.6552i	0.697829	−	0.495614i
$653$	11.3840	−	19.7176i	0.445489	−	0.771610i	−0.552597	−	0.833449i	$-0.686363\pi$
$653$	11.3840	−	19.7176i	0.445489	−	0.771610i	0.998086	+	0.0618385i	$0.0196964\pi$
$654$	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
$658$	9.87692	+	13.2344i	0.385042	+	0.515932i
$659$	−20.9713	+	12.1078i	−0.816927	+	0.471653i	−0.849356	−	0.527821i	$-0.823009\pi$
$659$	−20.9713	+	12.1078i	−0.816927	+	0.471653i	0.0324284	+	0.999474i	$0.489676\pi$
$660$	21.5391	−	39.4385i	0.838408	−	1.53514i
$661$	−9.97746	−	5.76049i	−0.388078	−	0.224057i	0.293249	−	0.956036i	$-0.405264\pi$
$661$	−9.97746	−	5.76049i	−0.388078	−	0.224057i	−0.681327	+	0.731979i	$0.738597\pi$
$662$	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
$672$	25.2092	−	6.04126i	0.972466	−	0.233047i
$673$	10.9799	+	19.0178i	0.423245	+	0.733083i	0.996255	−	0.0864662i	$-0.0275575\pi$
$673$	10.9799	+	19.0178i	0.423245	+	0.733083i	−0.573009	+	0.819549i	$0.694224\pi$
$674$	−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	$-0.343282\pi$
$677$	38.3056	−	22.1157i	1.47220	−	0.849977i	0.999512	+	0.0312511i	$0.00994916\pi$
$678$	1.59646	−	2.62237i	0.0613118	−	0.100711i
$679$	15.2087	+	7.40382i	0.583656	+	0.284133i
$680$	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	$0.0931352\pi$
$683$			15.0761i			0.576872i	−0.957499	+	0.288436i	$0.906865\pi$
$684$	10.2468	+	0.476961i	0.391796	+	0.0182371i
$685$		−	6.87980i		−	0.262864i
$686$	−6.85872	+	25.2776i	−0.261867	+	0.965104i
$687$	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	$-0.0249962\pi$
$691$	11.3171	+	19.6017i	0.430522	+	0.745686i	−0.566396	+	0.824133i	$0.691663\pi$
$692$	8.54289	+	3.91426i	0.324752	+	0.148798i
$693$	−30.0579	+	14.6565i	−1.14181	+	0.556753i
$694$	−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
$700$	23.3861	−	3.88236i	0.883913	−	0.146739i
$701$	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
$707$	−40.7099	−	19.8182i	−1.53106	−	0.745340i
$708$	16.0296	+	26.3029i	0.602430	+	0.988524i
$709$	11.8717	+	20.5624i	0.445851	+	0.772237i	0.998111	−	0.0614349i	$-0.0195677\pi$
$709$	11.8717	+	20.5624i	0.445851	+	0.772237i	−0.552260	+	0.833672i	$0.686234\pi$
$710$	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
$714$	−12.4943	+	8.02427i	−0.467588	+	0.300301i
$715$	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	$-0.343267\pi$
$719$	25.3519			0.945467			0.472734	+	0.881205i	$0.343267\pi$
$720$	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	$-0.105334\pi$
$727$	5.16319	+	8.94291i	0.191492	+	0.331674i	−0.754253	+	0.656584i	$0.772001\pi$
$728$	5.39281	+	25.1180i	0.199871	+	0.930935i
$729$	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	$-0.402819\pi$
$733$	−10.1555	−	5.86329i	−0.375102	−	0.216565i	−0.675685	+	0.737190i	$0.736152\pi$
$734$	−6.76212	+	0.317904i	−0.249595	+	0.0117341i
$735$	−33.5698	−	16.3290i	−1.23824	−	0.602304i
$736$	−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	$-0.997286\pi$
$739$		−	0.463561i		−	0.0170524i	0.999964	−	0.00852618i	$-0.00271400\pi$
$740$	−1.17934	−	12.5151i	−0.0433533	−	0.460064i
$741$	−0.713411	+	10.1408i	−0.0262078	+	0.372532i
$742$	39.2927	−	4.63956i	1.44248	−	0.170323i
$743$	11.4461	+	6.60840i	0.419916	+	0.242439i	0.695041	−	0.718970i	$-0.255386\pi$
$743$	11.4461	+	6.60840i	0.419916	+	0.242439i	−0.275125	+	0.961408i	$0.588719\pi$
$744$	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
$749$	−4.04185	+	2.73062i	−0.147686	+	0.0997748i
$750$	0.0911909	−	3.92032i	0.00332982	−	0.143150i
$751$	9.82352	+	5.67161i	0.358465	+	0.206960i	0.668407	−	0.743795i	$-0.266976\pi$
$751$	9.82352	+	5.67161i	0.358465	+	0.206960i	−0.309942	+	0.950755i	$0.600310\pi$
$752$	−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
$756$	14.8326	−	23.1515i	0.539457	−	0.842013i
$757$	−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	$-0.385224\pi$
$761$	−7.75469	−	4.47717i	−0.281107	−	0.162297i	−0.633925	+	0.773395i	$0.718557\pi$
$762$	0.607283	−	26.1073i	0.0219995	−	0.945766i
$763$	−3.95240	−	5.85031i	−0.143086	−	0.211795i
$764$	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	$-0.284925\pi$
$769$	7.27639	+	4.20103i	0.262393	+	0.151493i	−0.363033	+	0.931776i	$0.618259\pi$
$770$	−48.2026	+	5.69161i	−1.73710	+	0.205111i
$771$	−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
$777$	−4.67474	+	8.10287i	−0.167705	+	0.290689i
$778$	−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
$784$	−21.0842	−	18.4244i	−0.753007	−	0.658013i
$785$	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	0.321647	+	0.946860i	$0.395764\pi$
$787$	−18.4924	+	32.0297i	−0.659181	+	1.14174i	−0.980828	+	0.194876i	$0.937570\pi$
$788$	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	$-0.467478\pi$
$797$	−20.0024	−	11.5484i	−0.708522	−	0.409065i	−0.810513	+	0.585720i	$0.800812\pi$
$798$	−5.98738	−	9.32273i	−0.211951	−	0.330021i
$799$	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
$805$	−19.2817	+	39.6078i	−0.679589	+	1.39599i
$806$	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	$-0.342047\pi$
$811$	27.1173			0.952216			0.476108	+	0.879387i	$0.342047\pi$
$812$	−49.7490	+	8.25887i	−1.74585	+	0.289830i
$813$	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
$819$	22.5887	+	15.2396i	0.789314	+	0.532516i
$820$	−13.1417	+	28.6817i	−0.458927	+	1.00161i
$821$	−2.27415	−	3.93894i	−0.0793682	−	0.137470i	0.823609	−	0.567158i	$-0.191957\pi$
$821$	−2.27415	−	3.93894i	−0.0793682	−	0.137470i	−0.902978	+	0.429688i	$0.858624\pi$
$822$	−2.62566	−	4.80234i	−0.0915805	−	0.167501i
$823$	20.0197	+	11.5584i	0.697844	+	0.402900i	0.806544	−	0.591174i	$-0.201335\pi$
$823$	20.0197	+	11.5584i	0.697844	+	0.402900i	−0.108700	+	0.994075i	$0.534669\pi$
$824$	1.70491	−	4.23574i	0.0593934	−	0.147559i
$825$	2.29428	−	32.6121i	0.0798765	−	1.13541i
$826$	13.1418	−	30.5650i	0.457261	−	1.06349i
$827$		−	51.8058i		−	1.80146i	−0.434376	−	0.900732i	$-0.643031\pi$
$827$		−	51.8058i		−	1.80146i	0.434376	−	0.900732i	$-0.356969\pi$
$828$	−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
$833$	14.8799	+	5.98621i	0.515558	+	0.207410i
$834$	−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	0.879454	+	0.475984i	$0.157908\pi$
$839$	24.6769	+	42.7416i	0.851941	+	1.47561i	−0.0275127	+	0.999621i	$0.508759\pi$
$840$	31.4079	−	24.6210i	1.08368	−	0.849504i
$841$	−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	$-0.825937\pi$
$853$	−24.2685	+	14.0114i	−0.830939	+	0.479743i	0.0232350	+	0.999730i	$0.492603\pi$
$854$	12.3746	−	9.23525i	0.423452	−	0.316024i
$855$	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	$-0.604261\pi$
$857$	9.87736	−	5.70269i	0.337404	−	0.194800i	0.659123	+	0.752035i	$0.270927\pi$
$858$	35.4195	+	0.823895i	1.20920	+	0.0281273i
$859$	−20.0438	+	34.7168i	−0.683884	+	1.18452i	0.289902	+	0.957056i	$0.406377\pi$
$859$	−20.0438	+	34.7168i	−0.683884	+	1.18452i	−0.973786	+	0.227466i	$0.926956\pi$
$860$	−11.9340	−	16.8032i	−0.406947	−	0.572984i
$861$	20.3288	−	11.7455i	0.692803	−	0.400286i
$862$	−2.18346	−	1.12737i	−0.0743691	−	0.0383985i
$863$		−	45.2430i		−	1.54009i	−0.637989	−	0.770045i	$-0.720234\pi$
$863$		−	45.2430i		−	1.54009i	0.637989	−	0.770045i	$-0.279766\pi$
$864$	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
$868$	−21.6595	−	26.3446i	−0.735172	−	0.894193i
$869$	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
$875$	−3.50970	+	2.37111i	−0.118649	+	0.0801581i
$876$	−10.5490	−	5.76129i	−0.356419	−	0.194656i
$877$	6.89651	−	11.9451i	0.232878	−	0.403357i	−0.725776	−	0.687932i	$-0.758519\pi$
$877$	6.89651	−	11.9451i	0.232878	−	0.403357i	0.958654	+	0.284574i	$0.0918522\pi$
$878$	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	$-0.285992\pi$
$882$	−29.6648	+	1.41365i	−0.998866	+	0.0476000i
$883$		−	22.9737i		−	0.773127i	−0.922263	−	0.386564i	$-0.873662\pi$
$883$		−	22.9737i		−	0.773127i	0.922263	−	0.386564i	$-0.126338\pi$
$884$	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	$-0.949193\pi$
$887$	−10.6026	+	18.3642i	−0.356000	+	0.616610i	0.631289	+	0.775548i	$0.282526\pi$
$888$	−5.59958	−	8.28588i	−0.187910	−	0.278056i
$889$	−23.3727	+	15.7903i	−0.783895	+	0.529590i
$890$	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
$896$	27.5773	−	11.6400i	0.921294	−	0.388866i
$897$	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
$903$	0.00490873	+	15.3374i	0.000163352	+	0.510395i
$904$	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	−0.776082	−	0.630632i	$-0.782796\pi$
$907$	−18.6114	+	10.7453i	−0.617981	+	0.356791i	0.158102	+	0.987423i	$0.449463\pi$
$908$	−4.80383	+	10.4844i	−0.159421	+	0.347936i
$909$	7.18801	−	50.8343i	0.238411	−	1.68607i
$910$	23.6550	+	31.6961i	0.784154	+	1.05072i
$911$	44.5039	−	25.6943i	1.47448	−	0.851291i	0.474892	−	0.880044i	$-0.342487\pi$
$911$	44.5039	−	25.6943i	1.47448	−	0.851291i	0.999587	+	0.0287535i	$0.00915379\pi$
$912$	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	$-0.815394\pi$
$919$		−	33.2245i		−	1.09597i	0.836487	−	0.547987i	$-0.184606\pi$
$920$	−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
$924$	−31.4749	+	22.3694i	−1.03545	+	0.735898i
$925$	−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	$-0.520068\pi$
$929$	23.4631	−	13.5464i	0.769800	−	0.444444i	0.832803	+	0.553569i	$0.186735\pi$
$930$	42.6511	−	23.3194i	1.39859	−	0.764672i
$931$	−4.46666	+	11.1028i	−0.146389	+	0.363878i
$932$	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	$0.811115\pi$
$938$	37.8495	+	16.2739i	1.23583	+	0.531361i
$939$	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	0.997618	+	0.0689741i	$0.0219726\pi$
$941$	47.7364	+	27.5606i	1.55616	+	0.898450i	0.558543	+	0.829476i	$0.311361\pi$
$942$	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
$945$	5.91296	−	41.9138i	0.192349	−	1.36346i
$946$	10.7709	+	16.7828i	0.350192	+	0.545655i
$947$	−13.2348	+	7.64112i	−0.430073	+	0.248303i	−0.699378	−	0.714752i	$-0.746540\pi$
$947$	−13.2348	+	7.64112i	−0.430073	+	0.248303i	0.269305	+	0.963055i	$0.413206\pi$
$948$	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
$952$	−12.7186	+	11.4992i	−0.412214	+	0.372691i
$953$	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
$959$	−2.58762	+	5.31541i	−0.0835586	+	0.171643i
$960$	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
$966$	1.65697	+	35.0064i	0.0533120	+	1.12631i
$967$	4.06638	+	2.34772i	0.130766	+	0.0754977i	0.563956	−	0.825805i	$-0.309279\pi$
$967$	4.06638	+	2.34772i	0.130766	+	0.0754977i	−0.433190	+	0.901303i	$0.642612\pi$
$968$	−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	$-0.753635\pi$
$971$	−44.5685			−1.43027			−0.715135	+	0.698986i	$0.753635\pi$
$972$	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	−0.932329	−	0.361611i	$-0.882227\pi$
$977$	−4.78233	+	8.28324i	−0.153000	+	0.265004i	0.779329	+	0.626615i	$0.215560\pi$
$978$	0.622464	−	26.7599i	0.0199042	−	0.855688i
$979$	−7.62439	−	13.2058i	−0.243677	−	0.422060i
$980$	−41.3237	−	12.2655i	−1.32004	−	0.391808i
$981$	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	−0.896701	−	0.442637i	$-0.854043\pi$
$983$	−26.0757	−	45.1644i	−0.831685	−	1.44052i	0.0650157	−	0.997884i	$-0.479290\pi$
$984$	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
$987$	20.2251	−	0.00647306i	0.643773	−	0.000206040i
$988$	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	$0.228105\pi$
$991$			41.3545i			1.31367i	−0.754034	+	0.656835i	$0.771895\pi$
$992$	35.4589	−	8.48556i	1.12582	−	0.269417i
$993$	29.6999	+	20.0510i	0.942497	+	0.636301i
$994$	−1.09180	−	9.24654i	−0.0346299	−	0.293282i
$995$	−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	$-0.351467\pi$
$997$	45.7292	−	26.4017i	1.44826	−	0.836152i	0.998378	+	0.0569376i	$0.0181336\pi$
$998$	−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.139.27	yes	80
3.2	odd	2		756.2.bi.c.307.14		80
4.3	odd	2	inner	252.2.bi.c.139.2	yes	80
7.6	odd	2	inner	252.2.bi.c.139.28	yes	80
9.2	odd	6		756.2.bi.c.559.39		80
9.7	even	3	inner	252.2.bi.c.223.1	yes	80
12.11	even	2		756.2.bi.c.307.40		80
21.20	even	2		756.2.bi.c.307.13		80
28.27	even	2	inner	252.2.bi.c.139.1	✓	80
36.7	odd	6	inner	252.2.bi.c.223.28	yes	80
36.11	even	6		756.2.bi.c.559.13		80
63.20	even	6		756.2.bi.c.559.40		80
63.34	odd	6	inner	252.2.bi.c.223.2	yes	80
84.83	odd	2		756.2.bi.c.307.39		80
252.83	odd	6		756.2.bi.c.559.14		80
252.223	even	6	inner	252.2.bi.c.223.27	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.1	✓	80	28.27	even	2	inner
252.2.bi.c.139.2	yes	80	4.3	odd	2	inner
252.2.bi.c.139.27	yes	80	1.1	even	1	trivial
252.2.bi.c.139.28	yes	80	7.6	odd	2	inner
252.2.bi.c.223.1	yes	80	9.7	even	3	inner
252.2.bi.c.223.2	yes	80	63.34	odd	6	inner
252.2.bi.c.223.27	yes	80	252.223	even	6	inner
252.2.bi.c.223.28	yes	80	36.7	odd	6	inner
756.2.bi.c.307.13		80	21.20	even	2
756.2.bi.c.307.14		80	3.2	odd	2
756.2.bi.c.307.39		80	84.83	odd	2
756.2.bi.c.307.40		80	12.11	even	2
756.2.bi.c.559.13		80	36.11	even	6
756.2.bi.c.559.14		80	252.83	odd	6
756.2.bi.c.559.39		80	9.2	odd	6
756.2.bi.c.559.40		80	63.20	even	6

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} +(1.48111 + 2.19233i) 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} +(3.71584 - 0.438755i) 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} +(2.29002 - 3.96936i) 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} +(1.85954 - 4.95400i) 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} +(-3.50211 - 5.45300i) 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} +(-2.61262 + 6.49417i) 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} +(-5.01870 - 5.55091i) 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} +(-7.91786 - 0.554479i) 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} +(-10.5836 - 4.55056i) 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} +(10.0224 + 4.87907i) 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} +(-9.12445 + 0.862773i) 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} +(6.46548 + 7.49651i) 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

Introduction

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