LMFDB - Embedded newform 252.2.bi.c.223.1

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			223.1
Character	$\chi$	$=$	252.223
Dual form			252.2.bi.c.139.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41265 + 0.0664123i) q^{2} +(-0.758625 + 1.55708i) q^{3} +(1.99118 - 0.187635i) q^{4} +(2.66647 - 1.53948i) q^{5} +(0.968265 - 2.24999i) 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} +(-1.21839 + 3.24276i) q^{12} +(2.97309 - 1.71651i) q^{13} +(-1.47795 + 3.43739i) q^{14} +(0.374249 + 5.31978i) q^{15} +(3.92959 - 0.747231i) q^{16} -2.29127i q^{17} +(2.76886 + 3.21456i) q^{18} +1.70965 q^{19} +(5.02055 - 3.56571i) q^{20} +(2.82551 + 3.60783i) q^{21} +(5.29425 + 2.73354i) q^{22} +(4.68317 - 2.70383i) q^{23} +(1.50581 - 4.66182i) 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} +(-0.881984 - 7.49016i) q^{30} +(3.22265 + 5.58179i) q^{31} +(-5.50152 + 1.31655i) q^{32} +(6.04809 - 4.08320i) q^{33} +(0.152169 + 3.23677i) q^{34} +(-0.574276 - 8.12592i) q^{35} +(-4.12493 - 4.35717i) q^{36} -2.04135 q^{37} +(-2.41514 + 0.113542i) q^{38} +(0.417285 + 5.93151i) q^{39} +(-6.85549 + 5.37054i) q^{40} +(-4.43693 + 2.56166i) q^{41} +(-4.23108 - 4.90897i) 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} +(-1.81759 + 6.68554i) q^{48} +(-4.31781 - 5.50968i) q^{49} +(-2.90671 + 5.62963i) q^{50} +(3.56768 + 1.73821i) q^{51} +(5.59787 - 3.97574i) q^{52} +10.5744 q^{53} +(-7.10585 + 1.87268i) q^{54} -12.9722 q^{55} +(-2.29788 + 7.12178i) q^{56} +(-1.29698 + 2.66206i) q^{57} +(6.18340 - 11.9758i) q^{58} +(4.44595 + 7.70061i) q^{59} +(1.74338 + 10.5224i) 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} +(-8.27269 + 6.16982i) q^{66} +(-9.53591 + 5.50556i) q^{67} +(-0.429923 - 4.56233i) q^{68} +(0.657301 + 9.34324i) q^{69} +(1.35091 + 11.4410i) q^{70} -2.48841i q^{71} +(6.11646 + 5.88123i) q^{72} +3.46980i q^{73} +(2.88373 - 0.135571i) q^{74} +(4.34187 + 6.43124i) q^{75} +(3.40422 - 0.320791i) q^{76} +(-9.23662 + 6.24015i) q^{77} +(-0.983405 - 8.35146i) 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} +(6.30306 + 6.65368i) q^{84} +(-3.52738 - 6.10959i) q^{85} +(-4.20570 - 2.17150i) q^{86} +(-9.23639 - 13.6811i) q^{87} +(11.0547 + 4.44959i) q^{88} -3.61933i q^{89} +(12.3318 + 4.30890i) q^{90} +(-0.640313 - 9.06033i) q^{91} +(8.81769 - 6.26253i) q^{92} +(-11.1361 + 0.783427i) q^{93} +(-2.86352 + 5.54598i) q^{94} +(4.55872 - 2.63198i) q^{95} +(2.12362 - 9.56505i) 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.41265	+	0.0664123i	−0.998897	+	0.0469606i
$2$	−1.41265	+	0.0664123i	−0.998897	+	0.0469606i
$3$	−0.758625	+	1.55708i	−0.437992	+	0.898979i
$3$	−0.758625	+	1.55708i	−0.437992	+	0.898979i
$4$	1.99118	−	0.187635i	0.995589	−	0.0938176i
$5$	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	$0.0916123\pi$
$6$	0.968265	−	2.24999i	0.395292	−	0.918555i
$7$	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	−0.163870	−	0.986482i	$-0.552398\pi$
$11$	−3.64870	−	2.10658i	−1.10012	−	0.635157i	−0.936254	+	0.351325i	$0.885731\pi$
$12$	−1.21839	+	3.24276i	−0.351720	+	0.936105i
$13$	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	$0.175392\pi$
$14$	−1.47795	+	3.43739i	−0.394998	+	0.918682i
$15$	0.374249	+	5.31978i	0.0966308	+	1.37356i
$16$	3.92959	−	0.747231i	0.982397	−	0.186808i
$17$		−	2.29127i		−	0.555715i	−0.960622	−	0.277857i	$-0.910376\pi$
$17$		−	2.29127i		−	0.555715i	0.960622	−	0.277857i	$-0.0896242\pi$
$18$	2.76886	+	3.21456i	0.652627	+	0.757680i
$19$	1.70965			0.392221			0.196110	−	0.980582i	$-0.437169\pi$
$19$	1.70965			0.392221			0.196110	+	0.980582i	$0.437169\pi$
$20$	5.02055	−	3.56571i	1.12263	−	0.797318i
$21$	2.82551	+	3.60783i	0.616578	+	0.787294i
$22$	5.29425	+	2.73354i	1.12874	+	0.582794i
$23$	4.68317	−	2.70383i	0.976507	−	0.563787i	0.0752935	−	0.997161i	$-0.476011\pi$
$23$	4.68317	−	2.70383i	0.976507	−	0.563787i	0.901214	+	0.433375i	$0.142677\pi$
$24$	1.50581	−	4.66182i	0.307372	−	0.951589i
$25$	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	−0.0390079	+	0.999239i	$0.512420\pi$
$29$	−4.76517	+	8.25352i	−0.884870	+	1.53264i	−0.845862	+	0.533401i	$0.820914\pi$
$30$	−0.881984	−	7.49016i	−0.161027	−	1.36751i
$31$	3.22265	+	5.58179i	0.578805	+	1.00252i	0.995617	+	0.0935263i	$0.0298139\pi$
$31$	3.22265	+	5.58179i	0.578805	+	1.00252i	−0.416812	+	0.908993i	$0.636853\pi$
$32$	−5.50152	+	1.31655i	−0.972540	+	0.232736i
$33$	6.04809	−	4.08320i	1.05284	−	0.710794i
$34$	0.152169	+	3.23677i	0.0260967	+	0.555102i
$35$	−0.574276	−	8.12592i	−0.0970704	−	1.37353i
$36$	−4.12493	−	4.35717i	−0.687488	−	0.726196i
$37$	−2.04135			−0.335597			−0.167798	−	0.985821i	$-0.553666\pi$
$37$	−2.04135			−0.335597			−0.167798	+	0.985821i	$0.553666\pi$
$38$	−2.41514	+	0.113542i	−0.391788	+	0.0184189i
$39$	0.417285	+	5.93151i	0.0668191	+	0.949802i
$40$	−6.85549	+	5.37054i	−1.08395	+	0.849157i
$41$	−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	$0.464345\pi$
$42$	−4.23108	−	4.90897i	−0.652869	−	0.757471i
$43$	2.89849	+	1.67344i	0.442015	+	0.255198i	0.704452	−	0.709752i	$-0.251193\pi$
$43$	2.89849	+	1.67344i	0.442015	+	0.255198i	−0.262437	+	0.964949i	$0.584526\pi$
$44$	−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	−0.658991	−	0.752151i	$-0.729016\pi$
$47$	2.20674	−	3.82219i	0.321886	−	0.557524i	0.980877	+	0.194627i	$0.0623497\pi$
$48$	−1.81759	+	6.68554i	−0.262346	+	0.964974i
$49$	−4.31781	−	5.50968i	−0.616830	−	0.787097i
$50$	−2.90671	+	5.62963i	−0.411071	+	0.796151i
$51$	3.56768	+	1.73821i	0.499576	+	0.243399i
$52$	5.59787	−	3.97574i	0.776285	−	0.551336i
$53$	10.5744			1.45250			0.726250	−	0.687431i	$-0.241262\pi$
$53$	10.5744			1.45250			0.726250	+	0.687431i	$0.241262\pi$
$54$	−7.10585	+	1.87268i	−0.966983	+	0.254840i
$55$	−12.9722			−1.74917
$56$	−2.29788	+	7.12178i	−0.307068	+	0.951688i
$57$	−1.29698	+	2.66206i	−0.171790	+	0.352598i
$58$	6.18340	−	11.9758i	0.811920	−	1.57250i
$59$	4.44595	+	7.70061i	0.578813	+	1.00253i	0.995616	+	0.0935372i	$0.0298174\pi$
$59$	4.44595	+	7.70061i	0.578813	+	1.00253i	−0.416802	+	0.908997i	$0.636849\pi$
$60$	1.74338	+	10.5224i	0.225069	+	1.35844i
$61$	−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
$66$	−8.27269	+	6.16982i	−1.01830	+	0.759452i
$67$	−9.53591	+	5.50556i	−1.16500	+	0.672611i	−0.952496	−	0.304550i	$-0.901494\pi$
$67$	−9.53591	+	5.50556i	−1.16500	+	0.672611i	−0.212500	+	0.977161i	$0.568161\pi$
$68$	−0.429923	−	4.56233i	−0.0521358	−	0.553264i
$69$	0.657301	+	9.34324i	0.0791298	+	1.12479i
$70$	1.35091	+	11.4410i	0.161465	+	1.36746i
$71$		−	2.48841i		−	0.295320i	−0.989038	−	0.147660i	$-0.952826\pi$
$71$		−	2.48841i		−	0.295320i	0.989038	−	0.147660i	$-0.0471741\pi$
$72$	6.11646	+	5.88123i	0.720832	+	0.693110i
$73$			3.46980i			0.406110i	0.979167	+	0.203055i	$0.0650870\pi$
$73$			3.46980i			0.406110i	−0.979167	+	0.203055i	$0.934913\pi$
$74$	2.88373	−	0.135571i	0.335226	−	0.0157598i
$75$	4.34187	+	6.43124i	0.501356	+	0.742615i
$76$	3.40422	−	0.320791i	0.390491	−	0.0367972i
$77$	−9.23662	+	6.24015i	−1.05261	+	0.711131i
$78$	−0.983405	−	8.35146i	−0.111349	−	0.945617i
$79$	−8.87914	−	5.12638i	−0.998982	−	0.576762i	−0.0910349	−	0.995848i	$-0.529017\pi$
$79$	−8.87914	−	5.12638i	−0.998982	−	0.576762i	−0.907947	+	0.419085i	$0.862351\pi$
$80$	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	−0.869151	−	0.494546i	$-0.835334\pi$
$83$	−0.0572673	+	0.0991899i	−0.00628591	+	0.0108875i	0.862865	+	0.505434i	$0.168668\pi$
$84$	6.30306	+	6.65368i	0.687720	+	0.725976i
$85$	−3.52738	−	6.10959i	−0.382598	−	0.662678i
$86$	−4.20570	−	2.17150i	−0.453512	−	0.234159i
$87$	−9.23639	−	13.6811i	−0.990245	−	1.46676i
$88$	11.0547	+	4.44959i	1.17844	+	0.474328i
$89$		−	3.61933i		−	0.383648i	−0.981429	−	0.191824i	$-0.938560\pi$
$89$		−	3.61933i		−	0.383648i	0.981429	−	0.191824i	$-0.0614403\pi$
$90$	12.3318	+	4.30890i	1.29989	+	0.454198i
$91$	−0.640313	−	9.06033i	−0.0671230	−	0.949781i
$92$	8.81769	−	6.26253i	0.919307	−	0.652914i
$93$	−11.1361	+	0.783427i	−1.15476	+	0.0812376i
$94$	−2.86352	+	5.54598i	−0.295350	+	0.572025i
$95$	4.55872	−	2.63198i	0.467715	−	0.270035i
$96$	2.12362	−	9.56505i	0.216741	−	0.976229i
$97$	−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	$0.771887\pi$
$98$	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	$-0.00907547\pi$
$101$	14.8206	+	8.55666i	1.47470	+	0.851420i	0.475109	+	0.879927i	$0.342409\pi$
$102$	−5.15534	−	2.21856i	−0.510455	−	0.219670i
$103$	−0.807160	−	1.39804i	−0.0795318	−	0.137753i	0.823516	−	0.567293i	$-0.192009\pi$
$103$	−0.807160	−	1.39804i	−0.0795318	−	0.137753i	−0.903048	+	0.429540i	$0.858676\pi$
$104$	−7.64381	+	5.98811i	−0.749537	+	0.587182i
$105$	13.0883	+	5.27033i	1.27729	+	0.514332i
$106$	−14.9379	+	0.702268i	−1.45090	+	0.0682103i
$107$			1.84363i			0.178231i	0.996021	+	0.0891153i	$0.0284040\pi$
$107$			1.84363i			0.178231i	−0.996021	+	0.0891153i	$0.971596\pi$
$108$	9.91373	−	3.11737i	0.953949	−	0.299969i
$109$	−2.66853			−0.255599			−0.127800	−	0.991800i	$-0.540791\pi$
$109$	−2.66853			−0.255599			−0.127800	+	0.991800i	$0.540791\pi$
$110$	18.3252	−	0.861512i	1.74724	−	0.0821420i
$111$	1.54862	−	3.17855i	0.146989	−	0.301694i
$112$	2.77314	−	10.2132i	0.262037	−	0.965058i
$113$	−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	$0.852110\pi$
$114$	1.65539	−	3.84670i	0.155042	−	0.360276i
$115$	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
$120$	−3.16160	−	14.7487i	−0.288614	−	1.34637i
$121$	3.37533	+	5.84625i	0.306848	+	0.531477i
$122$	5.18568	+	2.67749i	0.469490	+	0.242409i
$123$	−0.622741	−	8.85197i	−0.0561506	−	0.798156i
$124$	7.46421	+	10.5097i	0.670306	+	0.943795i
$125$			1.60090i			0.143189i
$126$	10.8534	−	2.86405i	0.966902	−	0.255149i
$127$			10.6611i			0.946022i	0.881056	+	0.473011i	$0.156833\pi$
$127$			10.6611i			0.946022i	−0.881056	+	0.473011i	$0.843167\pi$
$128$	−10.7075	+	3.65377i	−0.946416	+	0.322950i
$129$	−4.80454	+	3.24365i	−0.423016	+	0.285588i
$130$	−6.85806	+	13.2825i	−0.601491	+	1.16495i
$131$	−4.50282	−	7.79911i	−0.393413	−	0.681411i	0.599484	−	0.800387i	$-0.295372\pi$
$131$	−4.50282	−	7.79911i	−0.393413	−	0.681411i	−0.992897	+	0.118975i	$0.962039\pi$
$132$	11.2767	−	9.26522i	0.981509	−	0.806434i
$133$	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	$0.136237\pi$
$138$	−1.54905	−	13.1551i	−0.131863	−	1.11984i
$139$	5.09811	+	8.83019i	0.432416	+	0.748967i	0.997081	−	0.0763537i	$-0.0243278\pi$
$139$	5.09811	+	8.83019i	0.432416	+	0.748967i	−0.564665	+	0.825320i	$0.690994\pi$
$140$	−2.66820	−	16.0724i	−0.225504	−	1.35837i
$141$	4.27735	+	6.33567i	0.360218	+	0.533560i
$142$	0.165261	+	3.51526i	0.0138684	+	0.294994i
$143$	−14.4639			−1.20953
$144$	−9.03103	−	7.90193i	−0.752586	−	0.658494i
$145$			29.3436i			2.43686i
$146$	−0.230438	−	4.90163i	−0.0190712	−	0.405662i
$147$	11.8546	−	2.54338i	0.977750	−	0.209775i
$148$	−4.06470	+	0.383030i	−0.334116	+	0.0314849i
$149$	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	$0.664680\pi$
$150$	−6.56067	−	8.79675i	−0.535677	−	0.718252i
$151$	−9.36053	−	5.40430i	−0.761749	−	0.439796i	0.0681743	−	0.997673i	$-0.478283\pi$
$151$	−9.36053	−	5.40430i	−0.761749	−	0.439796i	−0.829923	+	0.557877i	$0.811616\pi$
$152$	−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
$156$	1.94385	+	11.7324i	0.155633	+	0.939344i
$157$	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	$-0.121647\pi$
$158$	12.8836	+	6.65211i	1.02496	+	0.529213i
$159$	−8.02197	+	16.4651i	−0.636183	+	1.30577i
$160$	−12.6428	+	11.9800i	−0.999501	+	0.947105i
$161$	−1.00861	−	14.2717i	−0.0794898	−	1.12477i
$162$	2.47476	−	12.4850i	0.194435	−	0.980915i
$163$			10.9277i			0.855920i	0.903798	+	0.427960i	$0.140768\pi$
$163$			10.9277i			0.855920i	−0.903798	+	0.427960i	$0.859232\pi$
$164$	−8.35405	+	5.93325i	−0.652342	+	0.463309i
$165$	9.84101	−	20.1987i	0.766122	−	1.57246i
$166$	0.0743115	−	0.143924i	0.00576769	−	0.0111707i
$167$	−8.50615	−	14.7331i	−0.658226	−	1.14008i	−0.981075	−	0.193630i	$-0.937974\pi$
$167$	−8.50615	−	14.7331i	−0.658226	−	1.14008i	0.322849	−	0.946451i	$-0.395359\pi$
$168$	−9.34593	−	8.98074i	−0.721054	−	0.692879i
$169$	−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	$0.609507\pi$
$174$	13.9564	+	18.7132i	1.05803	+	1.41864i
$175$	−6.63546	−	9.82175i	−0.501594	−	0.742455i
$176$	−15.9120	−	5.55156i	−1.19941	−	0.418464i
$177$	−15.3633	+	1.08081i	−1.15477	+	0.0812388i
$178$	0.240368	+	5.11286i	0.0180163	+	0.383225i
$179$			8.32224i			0.622034i	0.950404	+	0.311017i	$0.100670\pi$
$179$			8.32224i			0.622034i	−0.950404	+	0.311017i	$0.899330\pi$
$180$	−17.7068	−	5.26800i	−1.31979	−	0.392653i
$181$		−	9.07327i		−	0.674411i	−0.941431	−	0.337205i	$-0.890518\pi$
$181$		−	9.07327i		−	0.674411i	0.941431	−	0.337205i	$-0.109482\pi$
$182$	1.50626	+	12.7566i	0.111651	+	0.945581i
$183$	5.92407	−	3.99947i	0.437920	−	0.295649i
$184$	−12.0404	+	9.43239i	−0.887632	+	0.695365i
$185$	−5.44320	+	3.14263i	−0.400192	+	0.231051i
$186$	15.6794	−	1.84628i	1.14967	−	0.135376i
$187$	−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	0.821172	−	0.570680i	$-0.193320\pi$
$191$	10.1929	+	5.88490i	0.737535	+	0.425816i	−0.0836373	+	0.996496i	$0.526654\pi$
$192$	−2.36470	+	13.6531i	−0.170657	+	0.985330i
$193$	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	$0.553718\pi$
$194$	8.03384	+	4.14806i	0.576796	+	0.297813i
$195$	10.2442	+	15.1738i	0.733599	+	1.08662i
$196$	−9.63134	−	10.1606i	−0.687953	−	0.725756i
$197$	−10.7855			−0.768436			−0.384218	−	0.923242i	$-0.625529\pi$
$197$	−10.7855			−0.768436			−0.384218	+	0.923242i	$0.625529\pi$
$198$	−3.33102	−	17.5618i	−0.236725	−	1.24806i
$199$	4.64957			0.329599			0.164800	−	0.986327i	$-0.447302\pi$
$199$	4.64957			0.329599			0.164800	+	0.986327i	$0.447302\pi$
$200$	−4.73147	+	11.7550i	−0.334565	+	0.831205i
$201$	−1.33840	−	19.0248i	−0.0944037	−	1.34191i
$202$	−21.5046	−	11.1033i	−1.51306	−	0.781227i
$203$	14.1155	+	20.8937i	0.990714	+	1.46645i
$204$	7.43005	+	2.79167i	0.520207	+	0.195456i
$205$	−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
$210$	−18.8393	−	6.57592i	−1.30004	−	0.453782i
$211$	−2.23918	+	1.29279i	−0.154151	+	0.0889993i	−0.575092	−	0.818089i	$-0.695034\pi$
$211$	−2.23918	+	1.29279i	−0.154151	+	0.0889993i	0.420940	+	0.907088i	$0.361700\pi$
$212$	21.0554	−	1.98412i	1.44609	−	0.136270i
$213$	3.87464	+	1.88777i	0.265486	+	0.129348i
$214$	−0.122440	−	2.60441i	−0.00836982	−	0.178034i
$215$	10.3050			0.702792
$216$	−13.7976	+	5.06216i	−0.938810	+	0.344436i
$217$	17.0102	−	1.20215i	1.15473	−	0.0816072i
$218$	3.76971	−	0.177224i	0.255317	−	0.0120031i
$219$	−5.40275	−	2.63228i	−0.365084	−	0.177873i
$220$	−25.8299	+	2.43404i	−1.74145	+	0.164103i
$221$	−3.93299	−	6.81214i	−0.264562	−	0.458234i
$222$	−1.97657	+	4.59303i	−0.132659	+	0.308264i
$223$	0.326746	−	0.565940i	0.0218805	−	0.0378981i	−0.854878	−	0.518829i	$-0.826368\pi$
$223$	0.326746	−	0.565940i	0.0218805	−	0.0378981i	0.876758	+	0.480931i	$0.159701\pi$
$224$	−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	−0.945701	−	0.325037i	$-0.894623\pi$
$227$	−2.88313	+	4.99372i	−0.191360	+	0.331445i	0.754341	+	0.656483i	$0.227956\pi$
$228$	−2.08303	+	5.54399i	−0.137952	+	0.367160i
$229$	−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	$0.957147\pi$
$230$	−10.8027	+	20.9224i	−0.712310	+	1.37958i
$231$	−2.70927	−	19.1161i	−0.178257	−	1.25774i
$232$	10.0652	−	25.0062i	0.660811	−	1.64174i
$233$	−8.45031			−0.553598			−0.276799	−	0.960928i	$-0.589274\pi$
$233$	−8.45031			−0.553598			−0.276799	+	0.960928i	$0.589274\pi$
$234$	13.7499	+	4.80439i	0.898859	+	0.314073i
$235$		−	13.5890i		−	0.886448i
$236$	10.2976	+	14.4991i	0.670316	+	0.943810i
$237$	14.7181	−	9.93651i	0.956043	−	0.645446i
$238$	7.87599	+	3.38638i	0.510525	+	0.219506i
$239$	−18.5973	+	10.7371i	−1.20296	+	0.694528i	−0.961212	−	0.275811i	$-0.911054\pi$
$239$	−18.5973	+	10.7371i	−1.20296	+	0.694528i	−0.241746	+	0.970339i	$0.577720\pi$
$240$	5.44575	+	20.6249i	0.351522	+	1.33133i
$241$	−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
$246$	1.46760	+	12.4634i	0.0935706	+	0.794638i
$247$	5.08294	−	2.93464i	0.323420	−	0.186726i
$248$	−11.2423	−	14.3508i	−0.713887	−	0.911276i
$249$	−0.111002	−	0.164418i	−0.00703446	−	0.0104195i
$250$	−0.106319	−	2.26151i	−0.00672423	−	0.143031i
$251$	14.3699			0.907018			0.453509	−	0.891252i	$-0.350172\pi$
$251$	14.3699			0.907018			0.453509	+	0.891252i	$0.350172\pi$
$252$	−15.1419	+	4.76671i	−0.953853	+	0.300274i
$253$	−22.7833			−1.43237
$254$	−0.708031	−	15.0605i	−0.0444258	−	0.944979i
$255$	12.1891	−	0.857506i	0.763309	−	0.0536991i
$256$	14.8833	−	5.87261i	0.930206	−	0.367038i
$257$	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	$0.154121\pi$
$258$	6.57174	−	4.90124i	0.409138	−	0.305138i
$259$	−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	−0.0372520	−	0.999306i	$-0.511860\pi$
$263$	−14.9410	−	8.62620i	−0.921302	−	0.531914i	−0.884050	+	0.467392i	$0.845194\pi$
$264$	−15.3147	+	13.8375i	−0.942556	+	0.851637i
$265$	28.1962	−	16.2791i	1.73208	−	1.00001i
$266$	−2.52677	+	5.87674i	−0.154927	+	0.360326i
$267$	5.63557	+	2.74571i	0.344891	+	0.168035i
$268$	−17.9547	+	12.7518i	−1.09676	+	0.778942i
$269$			21.5478i			1.31379i	0.753982	+	0.656895i	$0.228131\pi$
$269$			21.5478i			1.31379i	−0.753982	+	0.656895i	$0.771869\pi$
$270$	−16.0645	+	15.9328i	−0.977656	+	0.969639i
$271$	−0.857294			−0.0520769			−0.0260384	−	0.999661i	$-0.508289\pi$
$271$	−0.857294			−0.0520769			−0.0260384	+	0.999661i	$0.508289\pi$
$272$	−1.71211	−	9.00374i	−0.103812	−	0.545932i
$273$	14.5934	+	5.87638i	0.883232	+	0.355654i
$274$	−1.44974	+	2.80781i	−0.0875818	+	0.169626i
$275$	−16.3464	+	9.43758i	−0.985723	+	0.569107i
$276$	3.06193	+	18.4807i	0.184306	+	1.11241i
$277$	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
$280$	4.83664	+	22.5275i	0.289045	+	1.34628i
$281$	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	$-0.0575241\pi$
$282$	−6.46319	−	8.66604i	−0.384877	−	0.516055i
$283$	11.7141	+	20.2894i	0.696331	+	1.20608i	0.969730	+	0.244180i	$0.0785186\pi$
$283$	11.7141	+	20.2894i	0.696331	+	1.20608i	−0.273399	+	0.961901i	$0.588148\pi$
$284$	−0.466913	−	4.95487i	−0.0277062	−	0.294017i
$285$	0.639835	+	9.09497i	0.0379006	+	0.538739i
$286$	20.4324	−	0.960579i	1.20819	−	0.0568002i
$287$	0.955580	+	13.5213i	0.0564061	+	0.798138i
$288$	13.2825	+	10.5629i	0.782679	+	0.622426i
$289$	11.7501			0.691181
$290$	−1.94878	−	41.4524i	−0.114436	−	2.43417i
$291$	9.17777	−	6.19612i	0.538011	−	0.363223i
$292$	0.651058	+	6.90900i	0.0381003	+	0.404319i
$293$	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	$0.227343\pi$
$294$	−16.5775	+	4.38021i	−0.966820	+	0.255459i
$295$	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
$300$	9.85217	+	11.9911i	0.568815	+	0.692304i
$301$	7.33748	−	4.95711i	0.422925	−	0.285723i
$302$	13.5821	+	7.01275i	0.781562	+	0.403539i
$303$	−24.5666	+	16.5855i	−1.41132	+	0.952811i
$304$	6.71822	−	1.27750i	0.385316	−	0.0732698i
$305$	−12.7062			−0.727553
$306$	7.36543	−	6.34421i	0.421054	−	0.362674i
$307$	9.18388			0.524152			0.262076	−	0.965047i	$-0.415593\pi$
$307$	9.18388			0.524152			0.262076	+	0.965047i	$0.415593\pi$
$308$	−17.2209	+	14.1584i	−0.981251	+	0.806748i
$309$	2.78919	−	0.196221i	0.158671	−	0.0111626i
$310$	−24.9371	−	12.8756i	−1.41633	−	0.731284i
$311$	3.81067	+	6.60027i	0.216083	+	0.374267i	0.953607	−	0.301054i	$-0.0973385\pi$
$311$	3.81067	+	6.60027i	0.216083	+	0.374267i	−0.737524	+	0.675321i	$0.764005\pi$
$312$	−3.52516	−	16.4447i	−0.199573	−	0.930999i
$313$	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	$0.254393\pi$
$318$	10.2388	−	23.7922i	0.574162	−	1.33420i
$319$	34.7733	−	20.0764i	1.94693	−	1.12406i
$320$	17.0643	−	17.7633i	0.953922	−	0.992998i
$321$	−2.87068	−	1.39862i	−0.160226	−	0.0780636i
$322$	2.37264	+	20.0940i	0.132222	+	1.11979i
$323$		−	3.91727i		−	0.217963i
$324$	−2.66682	+	17.8014i	−0.148156	+	0.988964i
$325$		−	15.3801i		−	0.853136i
$326$	−0.725731	−	15.4370i	−0.0401945	−	0.854975i
$327$	2.02442	−	4.15511i	0.111950	−	0.229778i
$328$	11.4073	−	8.93643i	0.629865	−	0.493432i
$329$	−6.53686	−	9.67581i	−0.360389	−	0.533445i
$330$	−12.5605	+	29.1873i	−0.691432	+	1.60671i
$331$	17.9174	+	10.3446i	0.984827	+	0.568590i	0.903724	−	0.428116i	$-0.140822\pi$
$331$	17.9174	+	10.3446i	0.984827	+	0.568590i	0.0811031	+	0.996706i	$0.474156\pi$
$332$	−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
$336$	13.7990	+	12.0660i	0.752796	+	0.658253i
$337$	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	$0.684238\pi$
$338$	0.787879	−	1.52594i	0.0428550	−	0.0830002i
$339$	2.16554	−	0.152347i	0.117616	−	0.00827433i
$340$	−8.17001	−	11.5034i	−0.443081	−	0.623861i
$341$		−	27.1550i		−	1.47053i
$342$	4.73378	+	5.49578i	0.255974	+	0.297178i
$343$	−18.1069	+	3.89087i	−0.977683	+	0.210087i
$344$	−8.78174	−	3.53471i	−0.473480	−	0.190579i
$345$	16.1364	+	23.9015i	0.868757	+	1.28681i
$346$	−5.90410	−	3.04842i	−0.317406	−	0.163884i
$347$	8.93889	−	5.16087i	0.479865	−	0.277050i	−0.240495	−	0.970650i	$-0.577310\pi$
$347$	8.93889	−	5.16087i	0.479865	−	0.277050i	0.720360	+	0.693600i	$0.243977\pi$
$348$	−20.9584	−	25.5084i	−1.12349	−	1.36739i
$349$	−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	$0.749587\pi$
$350$	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	$-0.118572\pi$
$353$	20.3278	+	11.7363i	1.08194	+	0.624658i	0.150520	+	0.988607i	$0.451905\pi$
$354$	21.6312	−	2.54712i	1.14968	−	0.135378i
$355$	−3.83087	−	6.63526i	−0.203321	−	0.352163i
$356$	−0.679114	−	7.20673i	−0.0359929	−	0.381956i
$357$	8.26652	−	6.47402i	0.437511	−	0.342641i
$358$	−0.552700	−	11.7564i	−0.0292111	−	0.621347i
$359$			7.49888i			0.395776i	0.980225	+	0.197888i	$0.0634082\pi$
$359$			7.49888i			0.395776i	−0.980225	+	0.197888i	$0.936592\pi$
$360$	25.3634	+	6.26590i	1.33677	+	0.330242i
$361$	−16.0771			−0.846163
$362$	0.602577	+	12.8174i	0.0316708	+	0.673667i
$363$	−11.6637	+	0.820544i	−0.612184	+	0.0430674i
$364$	−2.97502	−	17.9206i	−0.155933	−	0.939294i
$365$	5.34171	+	9.25211i	0.279598	+	0.484278i
$366$	−8.10304	+	6.04330i	−0.423553	+	0.315888i
$367$	−2.39341	+	4.14551i	−0.124935	+	0.216394i	−0.921708	−	0.387885i	$-0.873206\pi$
$367$	−2.39341	+	4.14551i	−0.124935	+	0.216394i	0.796772	+	0.604279i	$0.206539\pi$
$368$	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
$372$	−22.0269	+	3.64946i	−1.14204	+	0.189216i
$373$	−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	$-0.422296\pi$
$374$	6.26329	−	12.1306i	0.323867	−	0.627256i
$375$	−2.49272	−	1.21448i	−0.128724	−	0.0627155i
$376$	−4.66116	+	11.5803i	−0.240381	+	0.597211i
$377$			32.7179i			1.68506i
$378$	−3.77415	+	19.0724i	−0.194121	+	0.980978i
$379$		−	27.3958i		−	1.40723i	−0.710583	−	0.703613i	$-0.751569\pi$
$379$		−	27.3958i		−	1.40723i	0.710583	−	0.703613i	$-0.248431\pi$
$380$	8.58338	−	6.09612i	0.440318	−	0.312724i
$381$	−16.6002	−	8.08780i	−0.850454	−	0.414350i
$382$	−14.7899	−	7.63638i	−0.756718	−	0.390711i
$383$	−7.36210	−	12.7515i	−0.376185	−	0.651572i	0.614318	−	0.789058i	$-0.289431\pi$
$383$	−7.36210	−	12.7515i	−0.376185	−	0.651572i	−0.990504	+	0.137486i	$0.956098\pi$
$384$	2.43376	−	19.4442i	0.124197	−	0.992258i
$385$	−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	$0.979304\pi$
$390$	−15.4792	−	20.7549i	−0.783818	−	1.05097i
$391$	−6.19520	−	10.7304i	−0.313305	−	0.542659i
$392$	14.2805	+	13.7137i	0.721276	+	0.692648i
$393$	15.5598	−	1.09464i	0.784886	−	0.0552171i
$394$	15.2362	−	0.716291i	0.767588	−	0.0360862i
$395$	−31.5679			−1.58835
$396$	5.87189	+	24.5875i	0.295074	+	1.23557i
$397$			34.9584i			1.75451i	0.480025	+	0.877255i	$0.340628\pi$
$397$			34.9584i			1.75451i	−0.480025	+	0.877255i	$0.659372\pi$
$398$	−6.56823	+	0.308789i	−0.329236	+	0.0154782i
$399$	4.83064	+	6.16813i	0.241834	+	0.308793i
$400$	5.90324	−	16.9200i	0.295162	−	0.845999i
$401$	−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	$0.995803\pi$
$402$	3.15418	+	26.7866i	0.157316	+	1.33599i
$403$	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
$408$	−10.6815	−	3.45022i	−0.528812	−	0.170811i
$409$	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	$0.306275\pi$
$410$	10.2347	−	19.8223i	0.505457	−	0.978953i
$411$	2.16553	+	3.20761i	0.106818	+	0.158220i
$412$	−1.86952	−	2.63230i	−0.0921047	−	0.129684i
$413$	23.4672	−	1.65848i	1.15475	−	0.0816084i
$414$	21.6587	+	7.56780i	1.06446	+	0.371937i
$415$			0.352649i			0.0173108i
$416$	−14.0966	+	13.3576i	−0.691143	+	0.654912i
$417$	−17.6168	+	1.23935i	−0.862700	+	0.0606914i
$418$	9.05131	+	4.67340i	0.442714	+	0.228584i
$419$	5.82364	+	10.0868i	0.284503	+	0.492774i	0.972489	−	0.232950i	$-0.0748380\pi$
$419$	5.82364	+	10.0868i	0.284503	+	0.492774i	−0.687985	+	0.725725i	$0.741505\pi$
$420$	27.0501	+	8.03834i	1.31991	+	0.392231i
$421$	−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
$426$	−5.59890	−	2.40944i	−0.271268	−	0.116738i
$427$	−9.04721	+	6.11219i	−0.437825	+	0.295790i
$428$	0.345930	+	3.67100i	0.0167212	+	0.177444i
$429$	10.9726	−	22.5213i	0.529764	−	1.08734i
$430$	−14.5573	+	0.684377i	−0.702017	+	0.0330036i
$431$		−	1.73760i		−	0.0836971i	−0.999124	−	0.0418485i	$-0.986675\pi$
$431$		−	1.73760i		−	0.0836971i	0.999124	−	0.0418485i	$-0.0133247\pi$
$432$	19.1551	−	8.06740i	0.921599	−	0.388143i
$433$		−	5.95764i		−	0.286306i	−0.989701	−	0.143153i	$-0.954276\pi$
$433$		−	5.95764i		−	0.286306i	0.989701	−	0.143153i	$-0.0457241\pi$
$434$	−23.9497	+	2.82791i	−1.14962	+	0.135744i
$435$	−45.6903	−	22.2608i	−2.19068	−	1.06732i
$436$	−5.31353	+	0.500711i	−0.254472	+	0.0239797i
$437$	8.00657	−	4.62260i	0.383006	−	0.221129i
$438$	7.80703	+	3.35969i	0.373034	+	0.160532i
$439$	10.6377	−	18.4250i	0.507708	−	0.879377i	−0.492252	−	0.870453i	$-0.663826\pi$
$439$	10.6377	−	18.4250i	0.507708	−	0.879377i	0.999960	−	0.00892391i	$-0.00284061\pi$
$440$	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	−0.434663	−	0.900593i	$-0.643132\pi$
$443$	−30.1387	−	17.4006i	−1.43193	−	0.826726i	−0.997268	+	0.0738675i	$0.976466\pi$
$444$	2.48718	−	6.61963i	0.118036	−	0.314154i
$445$	−5.57190	−	9.65081i	−0.264133	−	0.457492i
$446$	−0.423993	+	0.821177i	−0.0200766	+	0.0388838i
$447$	−21.3178	+	1.49972i	−1.00830	+	0.0709343i
$448$	3.60546	−	20.8567i	0.170342	−	0.985385i
$449$	0.109498			0.00516755			0.00258377	−	0.999997i	$-0.499178\pi$
$449$	0.109498			0.00516755			0.00258377	+	0.999997i	$0.499178\pi$
$450$	18.6743	−	3.54203i	0.880315	−	0.166973i
$451$	21.5853			1.01641
$452$	−1.45150	−	2.04373i	−0.0682729	−	0.0961288i
$453$	15.5160	−	10.4752i	0.729007	−	0.492169i
$454$	3.74122	−	7.24588i	0.175584	−	0.340066i
$455$	−15.6556	−	23.1733i	−0.733947	−	1.08638i
$456$	2.57441	−	7.97008i	0.120558	−	0.373233i
$457$	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	$0.949984\pi$
$462$	5.09680	+	26.8244i	0.237124	+	1.24799i
$463$	−8.98085	+	5.18510i	−0.417376	+	0.240972i	−0.693954	−	0.720019i	$-0.744133\pi$
$463$	−8.98085	+	5.18510i	−0.417376	+	0.240972i	0.276578	+	0.960991i	$0.410800\pi$
$464$	−12.5579	+	35.9936i	−0.582984	+	1.67096i
$465$	−28.4878	+	19.2328i	−1.32109	+	0.891898i
$466$	11.9374	−	0.561205i	0.552988	−	0.0259973i
$467$	7.81904			0.361822			0.180911	−	0.983499i	$-0.442095\pi$
$467$	7.81904			0.361822			0.180911	+	0.983499i	$0.442095\pi$
$468$	−19.7429	−	5.87377i	−0.912616	−	0.271515i
$469$	2.05375	+	29.0602i	0.0948332	+	1.34188i
$470$	0.902476	+	19.1965i	0.0416281	+	0.885470i
$471$	3.01562	+	42.8657i	0.138953	+	1.97515i
$472$	−15.5098	−	19.7983i	−0.713898	−	0.911290i
$473$	−7.05047	−	12.2118i	−0.324181	−	0.561498i
$474$	−20.1317	+	15.0143i	−0.924678	+	0.689630i
$475$	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	−0.922638	−	0.385668i	$-0.873971\pi$
$479$	−2.78654	+	4.82643i	−0.127320	+	0.220525i	0.795317	+	0.606193i	$0.207304\pi$
$480$	−9.06271	−	28.7742i	−0.413654	−	1.31335i
$481$	−6.06912	+	3.50401i	−0.276728	+	0.159769i
$482$	32.4362	+	16.7476i	1.47743	+	0.762831i
$483$	22.9873	+	9.25639i	1.04596	+	0.421180i
$484$	7.81785	+	11.0076i	0.355357	+	0.500345i
$485$	−19.6848			−0.893842
$486$	17.5627	+	13.3248i	0.796661	+	0.604427i
$487$			22.6868i			1.02804i	0.857780	+	0.514018i	$0.171843\pi$
$487$			22.6868i			1.02804i	−0.857780	+	0.514018i	$0.828157\pi$
$488$	10.8280	+	4.35834i	0.490161	+	0.197293i
$489$	−17.0152	−	8.28999i	−0.769454	−	0.374886i
$490$	28.7807	+	10.0357i	1.30018	+	0.453366i
$491$	−5.38821	+	3.11089i	−0.243167	+	0.140392i	−0.616631	−	0.787252i	$-0.711503\pi$
$491$	−5.38821	+	3.11089i	−0.243167	+	0.140392i	0.373465	+	0.927644i	$0.378170\pi$
$492$	−2.90093	−	17.5090i	−0.130784	−	0.789367i
$493$	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
$498$	0.167727	+	0.224893i	0.00751601	+	0.0100777i
$499$	35.4214	−	20.4505i	1.58568	−	0.915491i	0.591670	−	0.806180i	$-0.298469\pi$
$499$	35.4214	−	20.4505i	1.58568	−	0.915491i	0.994008	−	0.109311i	$-0.0348645\pi$
$500$	0.300385	+	3.18768i	0.0134336	+	0.142557i
$501$	29.3935	−	2.06785i	1.31321	−	0.0923847i
$502$	−20.2996	+	0.954337i	−0.906017	+	0.0425941i
$503$	8.58006			0.382566			0.191283	−	0.981535i	$-0.438735\pi$
$503$	8.58006			0.382566			0.191283	+	0.981535i	$0.438735\pi$
$504$	21.0738	−	7.73932i	0.938699	−	0.344736i
$505$	52.6914			2.34474
$506$	32.1849	−	1.51309i	1.43079	−	0.0672651i
$507$	−1.17689	−	1.74322i	−0.0522673	−	0.0774191i
$508$	2.00040	+	21.2282i	0.0887536	+	0.941850i
$509$	−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	$0.378147\pi$
$510$	−17.1620	+	2.02086i	−0.759945	+	0.0894853i
$511$	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
$516$	−8.95808	+	7.36020i	−0.394358	+	0.324015i
$517$	−16.1035	+	9.29734i	−0.708230	+	0.408897i
$518$	3.01702	−	7.01694i	0.132560	−	0.308306i
$519$	−6.74478	+	4.55355i	−0.296063	+	0.199879i
$520$	−11.1634	+	27.7346i	−0.489546	+	1.21624i
$521$			19.8412i			0.869261i	0.900609	+	0.434630i	$0.143121\pi$
$521$			19.8412i			0.869261i	−0.900609	+	0.434630i	$0.856879\pi$
$522$	−39.7256	+	7.53491i	−1.73874	+	0.329794i
$523$	−39.5715			−1.73034			−0.865171	−	0.501476i	$-0.832790\pi$
$523$	−39.5715			−1.73034			−0.865171	+	0.501476i	$0.832790\pi$
$524$	−10.4293	−	14.6845i	−0.455606	−	0.641497i
$525$	20.3270	−	2.88090i	0.887145	−	0.125733i
$526$	21.6794	+	11.1936i	0.945265	+	0.488062i
$527$	12.7894	−	7.38396i	0.557114	−	0.321650i
$528$	20.7154	−	20.5646i	0.901523	−	0.894960i
$529$	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
$534$	−8.14346	−	3.50447i	−0.352402	−	0.151653i
$535$	2.83824	+	4.91598i	0.122708	+	0.212536i
$536$	24.5168	−	19.2063i	1.05897	−	0.829587i
$537$	−12.9584	−	6.31346i	−0.559195	−	0.272446i
$538$	−1.43104	−	30.4395i	−0.0616964	−	1.31234i
$539$	4.14782	+	29.1989i	0.178659	+	1.25769i
$540$	21.6355	−	23.5744i	0.931043	−	1.01448i
$541$	−14.8643			−0.639068			−0.319534	−	0.947575i	$-0.603526\pi$
$541$	−14.8643			−0.639068			−0.319534	+	0.947575i	$0.603526\pi$
$542$	1.21106	−	0.0569349i	0.0520194	−	0.00244556i
$543$	14.1278	+	6.88321i	0.606281	+	0.295387i
$544$	3.01657	+	12.6055i	0.129335	+	0.540455i
$545$	−7.11556	+	4.10817i	−0.304797	+	0.175975i
$546$	−21.0057	−	7.33210i	−0.898960	−	0.313785i
$547$	−17.5001	−	10.1037i	−0.748252	−	0.432003i	0.0768102	−	0.997046i	$-0.475526\pi$
$547$	−17.5001	−	10.1037i	−0.748252	−	0.432003i	−0.825062	+	0.565042i	$0.808860\pi$
$548$	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
$552$	−5.55279	−	25.9035i	−0.236342	−	1.10253i
$553$	−22.4774	+	15.1855i	−0.955837	+	0.645752i
$554$	−11.6099	+	22.4857i	−0.493257	+	0.955325i
$555$	−0.763976	−	10.8596i	−0.0324290	−	0.460963i
$556$	11.8081	+	16.6259i	0.500775	+	0.705095i
$557$	12.0437			0.510308			0.255154	−	0.966900i	$-0.417874\pi$
$557$	12.0437			0.510308			0.255154	+	0.966900i	$0.417874\pi$
$558$	−9.01994	+	25.8146i	−0.381845	+	1.09282i
$559$	11.4899			0.485973
$560$	−8.32860	−	31.5024i	−0.351948	−	1.33122i
$561$	−9.35572	−	13.8578i	−0.394999	−	0.585078i
$562$	−14.0848	+	27.2790i	−0.594131	+	1.15070i
$563$	−19.3253	−	33.4724i	−0.814463	−	1.41069i	−0.909713	−	0.415238i	$-0.863698\pi$
$563$	−19.3253	−	33.4724i	−0.814463	−	1.41069i	0.0952496	−	0.995453i	$-0.469635\pi$
$564$	9.70577	+	11.8129i	0.408687	+	0.497412i
$565$	−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	$0.260956\pi$
$570$	−1.50788	−	12.8055i	−0.0631583	−	0.536365i
$571$	−21.6359	+	12.4915i	−0.905436	+	0.522754i	−0.878960	−	0.476896i	$-0.841762\pi$
$571$	−21.6359	+	12.4915i	−0.905436	+	0.522754i	−0.0264762	+	0.999649i	$0.508429\pi$
$572$	−28.8001	+	2.71393i	−1.20419	+	0.113475i
$573$	−16.8958	+	11.4068i	−0.705834	+	0.476524i
$574$	−2.24788	−	19.0375i	−0.0938249	−	0.794608i
$575$		−	24.2266i		−	1.01032i
$576$	−19.4651	−	14.0396i	−0.811045	−	0.584984i
$577$		−	41.9153i		−	1.74495i	−0.488654	−	0.872477i	$-0.662512\pi$
$577$		−	41.9153i		−	1.74495i	0.488654	−	0.872477i	$-0.337488\pi$
$578$	−16.5988	+	0.780351i	−0.690419	+	0.0324583i
$579$	−36.9524	+	2.59962i	−1.53569	+	0.108036i
$580$	5.50590	+	58.4284i	0.228620	+	2.42611i
$581$	0.169639	+	0.251098i	0.00703780	+	0.0104173i
$582$	−12.5535	+	9.36248i	−0.520360	+	0.388087i
$583$	−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	$0.349280\pi$
$587$	−13.1495	+	22.7757i	−0.542740	+	0.940053i	−0.998745	+	0.0500760i	$0.984054\pi$
$588$	23.1274	−	7.28867i	0.953757	−	0.300580i
$589$	5.50960	+	9.54291i	0.227019	+	0.393209i
$590$	−34.4031	−	17.7631i	−1.41635	−	0.731295i
$591$	8.18215	−	16.7939i	0.336569	−	0.690807i
$592$	−8.02168	+	1.52536i	−0.329689	+	0.0626920i
$593$			14.9954i			0.615786i	0.951421	+	0.307893i	$0.0996239\pi$
$593$			14.9954i			0.615786i	−0.951421	+	0.307893i	$0.900376\pi$
$594$	29.8720	+	8.13615i	1.22566	+	0.333830i
$595$	−18.6187	+	1.31582i	−0.763291	+	0.0539434i
$596$	14.2888	+	20.1187i	0.585291	+	0.824094i
$597$	−3.52728	+	7.23974i	−0.144362	+	0.296303i
$598$	−12.0449	+	23.3283i	−0.492554	+	0.953964i
$599$	11.6301	−	6.71463i	0.475192	−	0.274352i	−0.243219	−	0.969972i	$-0.578203\pi$
$599$	11.6301	−	6.71463i	0.475192	−	0.274352i	0.718411	+	0.695619i	$0.244870\pi$
$600$	−14.7140	−	16.2849i	−0.600699	−	0.664828i
$601$	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	$0.578032\pi$
$602$	−10.0361	+	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
$606$	33.6027	−	25.0611i	1.36501	−	1.01804i
$607$	17.3550	+	30.0598i	0.704419	+	1.22009i	0.966901	+	0.255153i	$0.0821257\pi$
$607$	17.3550	+	30.0598i	0.704419	+	1.22009i	−0.262482	+	0.964937i	$0.584541\pi$
$608$	−9.40567	+	2.25084i	−0.381450	+	0.0912837i
$609$	−43.2414	+	6.12848i	−1.75223	+	0.248339i
$610$	17.9494	−	0.843846i	0.726750	−	0.0341663i
$611$		−	15.1516i		−	0.612968i
$612$	−9.98346	+	9.45132i	−0.403558	+	0.382047i
$613$	−27.2426			−1.10032			−0.550159	−	0.835060i	$-0.685433\pi$
$613$	−27.2426			−1.10032			−0.550159	+	0.835060i	$0.685433\pi$
$614$	−12.9736	+	0.609923i	−0.523573	+	0.0246145i
$615$	−15.2880	−	22.6448i	−0.616471	−	0.913126i
$616$	23.3869	−	21.1446i	0.942283	−	0.851938i
$617$	−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	$0.874371\pi$
$618$	−3.92713	+	0.462429i	−0.157972	+	0.0186016i
$619$	−13.4240	+	23.2510i	−0.539554	+	0.934536i	0.459374	+	0.888243i	$0.348074\pi$
$619$	−13.4240	+	23.2510i	−0.539554	+	0.934536i	−0.998928	+	0.0462924i	$0.985259\pi$
$620$	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
$624$	6.07197	+	22.9966i	0.243073	+	0.920600i
$625$	13.6647	+	23.6679i	0.546588	+	0.946718i
$626$	−7.79175	−	4.02306i	−0.311421	−	0.160794i
$627$	10.3401	−	6.98085i	0.412945	−	0.278788i
$628$	40.4545	−	28.7318i	1.61431	−	1.14652i
$629$			4.67729i			0.186496i
$630$	24.5312	−	24.3456i	0.977346	−	0.969952i
$631$		−	24.9328i		−	0.992557i	−0.868163	−	0.496279i	$-0.834699\pi$
$631$		−	24.9328i		−	0.992557i	0.868163	−	0.496279i	$-0.165301\pi$
$632$	26.9017	+	10.8281i	1.07009	+	0.430719i
$633$	−0.314278	−	4.46731i	−0.0124914	−	0.177560i
$634$	6.28702	−	12.1765i	0.249689	−	0.483591i
$635$	16.4126	+	28.4275i	0.651316	+	1.12811i
$636$	−12.8837	+	34.2901i	−0.510874	+	1.35969i
$637$	−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	$0.00740057\pi$
$642$	4.14816	+	1.78512i	0.163715	+	0.0704532i
$643$	−5.13144	−	8.88791i	−0.202364	−	0.350505i	0.746926	−	0.664908i	$-0.231529\pi$
$643$	−5.13144	−	8.88791i	−0.202364	−	0.350505i	−0.949290	+	0.314403i	$0.898196\pi$
$644$	−4.68620	−	28.2283i	−0.184662	−	1.11235i
$645$	−7.81760	+	16.0456i	−0.307818	+	0.631795i
$646$	0.260155	+	5.53374i	0.0102357	+	0.217722i
$647$	44.3871			1.74504			0.872518	−	0.488581i	$-0.162485\pi$
$647$	44.3871			1.74504			0.872518	+	0.488581i	$0.162485\pi$
$648$	2.58506	−	25.3242i	0.101551	−	0.994830i
$649$		−	37.4629i		−	1.47055i
$650$	1.02143	+	21.7268i	0.0400638	+	0.852195i
$651$	−11.0325	+	27.3982i	−0.432399	+	1.07382i
$652$	2.05041	+	21.7589i	0.0803004	+	0.852145i
$653$	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	$0.686363\pi$
$654$	−2.58385	+	6.00418i	−0.101036	+	0.234782i
$655$	−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	$-0.176991\pi$
$659$	20.9713	+	12.1078i	0.816927	+	0.471653i	−0.0324284	+	0.999474i	$0.510324\pi$
$660$	15.8052	−	42.0657i	0.615218	−	1.63740i
$661$	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	$0.261403\pi$
$662$	−25.9980	−	13.4234i	−1.01044	−	0.521715i
$663$	13.5907	−	0.956112i	0.527819	−	0.0371323i
$664$	0.120962	−	0.300522i	0.00469424	−	0.0116625i
$665$	−0.981811	−	13.8925i	−0.0380730	−	0.538727i
$666$	−5.65223	−	6.56206i	−0.219019	−	0.254275i
$667$			51.5368i			1.99551i
$668$	−19.7017	−	27.7402i	−0.762282	−	1.07330i
$669$	0.633335	+	0.938104i	0.0244861	+	0.0362692i
$670$	21.9966	−	42.6024i	0.849803	−	1.64587i
$671$	8.69333	+	15.0573i	0.335602	+	0.581280i
$672$	−20.2945	−	16.1286i	−0.782878	−	0.622175i
$673$	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	$0.990051\pi$
$678$	−3.04903	+	0.359031i	−0.117097	+	0.0137885i
$679$	−14.0162	+	9.46921i	−0.537894	+	0.363395i
$680$	12.3054	+	15.7078i	0.471889	+	0.602366i
$681$	−5.58840	−	8.27762i	−0.214148	−	0.317199i
$682$	1.80343	+	38.3606i	0.0690568	+	1.46890i
$683$			15.0761i			0.576872i	0.957499	+	0.288436i	$0.0931352\pi$
$683$			15.0761i			0.576872i	−0.957499	+	0.288436i	$0.906865\pi$
$684$	−7.05218	−	7.44924i	−0.269647	−	0.284829i
$685$		−	6.87980i		−	0.262864i
$686$	25.3204	−	6.69898i	0.966738	−	0.255768i
$687$	−3.40397	−	48.3859i	−0.129870	−	1.84604i
$688$	12.6403	+	4.41010i	0.481907	+	0.168133i
$689$	31.4385	−	18.1510i	1.19771	−	0.691499i
$690$	−24.3826	−	32.6929i	−0.928228	−	1.24460i
$691$	11.3171	−	19.6017i	0.430522	−	0.745686i	−0.566396	−	0.824133i	$-0.691663\pi$
$691$	11.3171	−	19.6017i	0.430522	−	0.745686i	0.996918	+	0.0784473i	$0.0249962\pi$
$692$	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
$696$	31.3010	+	34.6426i	1.18646	+	1.31312i
$697$	5.86946	+	10.1662i	0.222321	+	0.385072i
$698$	12.0928	+	6.24380i	0.457720	+	0.236331i
$699$	6.41062	−	13.1578i	0.242472	−	0.497673i
$700$	−15.0553	−	18.3118i	−0.569037	−	0.692122i
$701$	8.62984			0.325945			0.162972	−	0.986631i	$-0.447892\pi$
$701$	8.62984			0.325945			0.162972	+	0.986631i	$0.447892\pi$
$702$	−17.9118	+	17.7649i	−0.676038	+	0.670494i
$703$	−3.49000			−0.131628
$704$	−32.7252	−	8.06849i	−1.23338	−	0.304093i
$705$	21.1591	+	10.3089i	0.796898	+	0.388257i
$706$	−29.4955	−	15.2292i	−1.11008	−	0.573160i
$707$	37.5180	−	25.3467i	1.41101	−	0.953262i
$708$	−30.3882	+	5.03478i	−1.14206	+	0.189219i
$709$	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
$714$	−11.2478	+	9.69454i	−0.420937	+	0.362809i
$715$	−38.5674	+	22.2669i	−1.44234	+	0.832735i
$716$	1.56155	+	16.5711i	0.0583577	+	0.619290i
$717$	−2.61020	−	37.1029i	−0.0974799	−	1.38563i
$718$	−0.498018	−	10.5933i	−0.0185859	−	0.395339i
$719$	25.3519			0.945467			0.472734	−	0.881205i	$-0.343267\pi$
$719$	25.3519			0.945467			0.472734	+	0.881205i	$0.343267\pi$
$720$	−36.2458	−	7.16710i	−1.35080	−	0.267102i
$721$	−4.26046	+	0.301096i	−0.158668	+	0.0112134i
$722$	22.7114	−	1.06772i	0.845229	−	0.0397363i
$723$	37.0548	−	25.0165i	1.37808	−	0.930374i
$724$	−1.70247	−	18.0665i	−0.0632716	−	0.671436i
$725$	21.3482	+	36.9762i	0.792853	+	1.37326i
$726$	16.4222	−	1.93376i	0.609486	−	0.0717684i
$727$	5.16319	−	8.94291i	0.191492	−	0.331674i	−0.754253	−	0.656584i	$-0.772001\pi$
$727$	5.16319	−	8.94291i	0.191492	−	0.331674i	0.945745	+	0.324910i	$0.105334\pi$
$728$	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
$732$	11.0454	−	9.07523i	0.408251	−	0.335430i
$733$	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	$0.263848\pi$
$734$	3.10575	−	6.01512i	0.114635	−	0.222022i
$735$	27.6944	−	25.0318i	1.02152	−	0.923312i
$736$	−22.2048	+	21.0408i	−0.818479	+	0.775573i
$737$	46.3915			1.70885
$738$	−20.5198	−	7.16989i	−0.755346	−	0.263927i
$739$		−	0.463561i		−	0.0170524i	−0.999964	−	0.00852618i	$-0.997286\pi$
$739$		−	0.463561i		−	0.0170524i	0.999964	−	0.00852618i	$-0.00271400\pi$
$740$	−10.2487	+	7.27888i	−0.376750	+	0.267577i
$741$	0.713411	+	10.1408i	0.0262078	+	0.372532i
$742$	−15.6284	+	36.3482i	−0.573735	+	1.33438i
$743$	−11.4461	+	6.60840i	−0.419916	+	0.242439i	−0.695041	−	0.718970i	$-0.744614\pi$
$743$	−11.4461	+	6.60840i	−0.419916	+	0.242439i	0.275125	+	0.961408i	$0.411281\pi$
$744$	30.8740	−	6.61828i	1.13189	−	0.242638i
$745$	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
$750$	3.60201	+	1.55009i	0.131527	+	0.0566014i
$751$	−9.82352	+	5.67161i	−0.358465	+	0.206960i	−0.668407	−	0.743795i	$-0.733024\pi$
$751$	−9.82352	+	5.67161i	−0.358465	+	0.206960i	0.309942	+	0.950755i	$0.399690\pi$
$752$	5.81553	−	16.6686i	0.212070	−	0.607840i
$753$	−10.9013	+	22.3750i	−0.397267	+	0.815390i
$754$	−2.17287	−	46.2191i	−0.0791314	−	1.68320i
$755$	−33.2794			−1.21116
$756$	4.06493	−	27.1933i	0.147840	−	0.989011i
$757$	−21.1566			−0.768950			−0.384475	−	0.923135i	$-0.625618\pi$
$757$	−21.1566			−0.768950			−0.384475	+	0.923135i	$0.625618\pi$
$758$	1.81942	+	38.7007i	0.0660842	+	1.40567i
$759$	17.2840	−	35.4753i	0.627368	−	1.28767i
$760$	−11.7205	+	9.18175i	−0.425147	+	0.333057i
$761$	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	$0.281443\pi$
$762$	23.9875	+	10.3228i	0.868974	+	0.373955i
$763$	−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
$768$	−2.14672	+	27.6295i	−0.0774631	+	0.996995i
$769$	−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	$0.381741\pi$
$770$	19.1722	−	44.5904i	0.690918	−	1.60693i
$771$	2.08007	+	29.5673i	0.0749120	+	1.06484i
$772$	24.7682	+	34.8738i	0.891427	+	1.25514i
$773$		−	5.75834i		−	0.207113i	−0.994624	−	0.103556i	$-0.966978\pi$
$773$		−	5.75834i		−	0.207113i	0.994624	−	0.103556i	$-0.0330223\pi$
$774$	2.64613	+	13.9509i	0.0951130	+	0.501455i
$775$	28.8753			1.03723
$776$	16.7751	+	6.75209i	0.602192	+	0.242386i
$777$	−5.76788	−	7.36487i	−0.206921	−	0.264213i
$778$	14.2096	−	27.5207i	0.509438	−	0.986665i
$779$	−7.58559	+	4.37954i	−0.271782	+	0.156913i
$780$	23.2451	+	28.2915i	0.832307	+	1.01300i
$781$	−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
$786$	−21.9079	+	2.57970i	−0.781427	+	0.0920150i
$787$	−18.4924	−	32.0297i	−0.659181	−	1.14174i	−0.980828	−	0.194876i	$-0.937570\pi$
$787$	−18.4924	−	32.0297i	−0.659181	−	1.14174i	0.321647	−	0.946860i	$-0.395764\pi$
$788$	−21.4759	+	2.02374i	−0.765047	+	0.0720928i
$789$	24.7663	−	16.7203i	0.881703	−	0.595257i
$790$	44.5945	−	2.09650i	1.58660	−	0.0745901i
$791$	−3.30784	+	0.233772i	−0.117613	+	0.00831197i
$792$	−9.92786	−	34.3436i	−0.352771	−	1.22035i
$793$	−14.1673			−0.503094
$794$	−2.32167	−	49.3841i	−0.0823929	−	1.75257i
$795$	3.95745	+	56.2533i	0.140356	+	1.99510i
$796$	9.25812	−	0.872423i	0.328145	−	0.0309222i
$797$	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	$0.199188\pi$
$798$	−7.23366	−	8.39262i	−0.256069	−	0.297096i
$799$	−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
$804$	−6.23472	−	37.6306i	−0.219882	−	1.32713i
$805$	−24.6605	−	36.5023i	−0.869169	−	1.28654i
$806$	−27.8046	−	14.3562i	−0.979375	−	0.505674i
$807$	−33.5515	−	16.3467i	−1.18107	−	0.575430i
$808$	−44.9029	−	18.0737i	−1.57968	−	0.635830i
$809$	−22.9976			−0.808553			−0.404277	−	0.914637i	$-0.632477\pi$
$809$	−22.9976			−0.808553			−0.404277	+	0.914637i	$0.632477\pi$
$810$	−12.6216	−	37.1007i	−0.443479	−	1.30359i
$811$	27.1173			0.952216			0.476108	−	0.879387i	$-0.342047\pi$
$811$	27.1173			0.952216			0.476108	+	0.879387i	$0.342047\pi$
$812$	32.0269	+	38.9544i	1.12392	+	1.36703i
$813$	0.650364	−	1.33487i	0.0228093	−	0.0468160i
$814$	−10.8074	−	5.58013i	−0.378800	−	0.195584i
$815$	16.8230	+	29.1382i	0.589282	+	1.02067i
$816$	15.3184	+	4.16458i	0.536250	+	0.145789i
$817$	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	$0.191957\pi$
$822$	−3.27217	−	4.38742i	−0.114130	−	0.153029i
$823$	−20.0197	+	11.5584i	−0.697844	+	0.402900i	−0.806544	−	0.591174i	$-0.798665\pi$
$823$	−20.0197	+	11.5584i	−0.697844	+	0.402900i	0.108700	+	0.994075i	$0.465331\pi$
$824$	2.81580	+	3.59437i	0.0980931	+	0.125216i
$825$	−2.29428	−	32.6121i	−0.0798765	−	1.13541i
$826$	−33.0409	+	3.90137i	−1.14964	+	0.135746i
$827$		−	51.8058i		−	1.80146i	−0.434376	−	0.900732i	$-0.643031\pi$
$827$		−	51.8058i		−	1.80146i	0.434376	−	0.900732i	$-0.356969\pi$
$828$	−31.0988	−	9.25228i	−1.08076	−	0.321539i
$829$		−	13.9412i		−	0.484197i	−0.970252	−	0.242098i	$-0.922164\pi$
$829$		−	13.9412i		−	0.484197i	0.970252	−	0.242098i	$-0.0778357\pi$
$830$	−0.0234202	−	0.498170i	−0.000812928	−	0.0172917i
$831$	17.3421	+	25.6874i	0.601592	+	0.891086i
$832$	19.0265	−	19.8059i	0.659626	−	0.686646i
$833$	−12.6242	+	9.89326i	−0.437401	+	0.342781i
$834$	24.8042	−	2.92075i	0.858898	−	0.101137i
$835$	−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	$-0.508759\pi$
$839$	24.6769	−	42.7416i	0.851941	−	1.47561i	0.879454	−	0.475984i	$-0.157908\pi$
$840$	−38.7463	−	9.55892i	−1.33687	−	0.329814i
$841$	−30.9137	−	53.5441i	−1.06599	−	1.84635i
$842$	12.5131	−	24.2351i	0.431231	−	0.835196i
$843$	21.0390	+	31.1633i	0.724622	+	1.07332i
$844$	−4.21603	+	2.99432i	−0.145122	+	0.103069i
$845$			3.73892i			0.128623i
$846$	18.3968	−	3.48940i	0.632496	−	0.119968i
$847$	17.8161	−	1.25910i	0.612170	−	0.0432633i
$848$	41.5528	−	7.90148i	1.42693	−	0.271338i
$849$	−40.4788	+	2.84770i	−1.38923	+	0.0977329i
$850$	12.8990	+	6.66006i	0.442433	+	0.228438i
$851$	−9.56000	+	5.51947i	−0.327713	+	0.189205i
$852$	8.06932	+	3.03186i	0.276450	+	0.103870i
$853$	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	$0.507397\pi$
$854$	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	$-0.395739\pi$
$857$	−9.87736	−	5.70269i	−0.337404	−	0.194800i	−0.659123	+	0.752035i	$0.729073\pi$
$858$	−14.0048	+	32.5436i	−0.478117	+	1.11102i
$859$	−20.0438	−	34.7168i	−0.683884	−	1.18452i	−0.973786	−	0.227466i	$-0.926956\pi$
$859$	−20.0438	−	34.7168i	−0.683884	−	1.18452i	0.289902	−	0.957056i	$-0.406377\pi$
$860$	20.5190	−	1.93357i	0.699693	−	0.0659343i
$861$	−21.7786	−	8.76969i	−0.742214	−	0.298870i
$862$	0.115398	+	2.45462i	0.00393047	+	0.0836047i
$863$		−	45.2430i		−	1.54009i	−0.637989	−	0.770045i	$-0.720234\pi$
$863$		−	45.2430i		−	1.54009i	0.637989	−	0.770045i	$-0.279766\pi$
$864$	−26.5237	+	12.6686i	−0.902355	+	0.430994i
$865$	14.4664			0.491874
$866$	0.395661	+	8.41609i	0.0134451	+	0.285990i
$867$	−8.91390	+	18.2958i	−0.302732	+	0.621357i
$868$	33.6448	−	5.58541i	1.14198	−	0.189581i
$869$	21.5982	+	37.4092i	0.732669	+	1.26902i
$870$	66.0230	+	28.4124i	2.23839	+	0.963271i
$871$	−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
$876$	−11.2518	−	4.22759i	−0.380162	−	0.142837i
$877$	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	$0.758519\pi$
$878$	−13.8037	+	26.7346i	−0.465852	+	0.902249i
$879$	1.36013	+	19.3336i	0.0458759	+	0.652106i
$880$	−50.9753	+	9.69320i	−1.71838	+	0.326758i
$881$		−	46.4443i		−	1.56475i	−0.622808	−	0.782375i	$-0.714008\pi$
$881$		−	46.4443i		−	1.56475i	0.622808	−	0.782375i	$-0.285992\pi$
$882$	5.75579	−	29.1354i	0.193807	−	0.981040i
$883$		−	22.9737i		−	0.773127i	−0.922263	−	0.386564i	$-0.873662\pi$
$883$		−	22.9737i		−	0.773127i	0.922263	−	0.386564i	$-0.126338\pi$
$884$	−9.10949	−	12.8262i	−0.306385	−	0.431393i
$885$	−39.3017	+	26.5334i	−1.32111	+	0.891912i
$886$	43.7311	+	22.5794i	1.46917	+	0.758569i
$887$	−10.6026	−	18.3642i	−0.356000	−	0.616610i	0.631289	−	0.775548i	$-0.282526\pi$
$887$	−10.6026	−	18.3642i	−0.356000	−	0.616610i	−0.987289	+	0.158938i	$0.949193\pi$
$888$	−3.07389	+	9.51642i	−0.103153	+	0.319350i
$889$	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
$894$	30.0151	−	3.53435i	1.00385	−	0.118206i
$895$	12.8120	+	22.1910i	0.428257	+	0.741763i
$896$	−3.70812	+	29.7027i	−0.123880	+	0.992297i
$897$	17.9920	+	26.6500i	0.600735	+	0.889817i
$898$	−0.154683	+	0.00727204i	−0.00516184	+	0.000242671i
$899$	−61.4259			−2.04867
$900$	−26.1451	+	6.24387i	−0.871503	+	0.208129i
$901$		−	24.2287i		−	0.807175i
$902$	−30.4926	+	1.43353i	−1.01529	+	0.0477314i
$903$	2.15221	+	15.1856i	0.0716212	+	0.505345i
$904$	2.18620	+	2.79068i	0.0727119	+	0.0928166i
$905$	−13.9682	−	24.1936i	−0.464317	−	0.804221i
$906$	−21.2231	+	15.8283i	−0.705091	+	0.525861i
$907$	18.6114	+	10.7453i	0.617981	+	0.356791i	0.776082	−	0.630632i	$-0.217204\pi$
$907$	18.6114	+	10.7453i	0.617981	+	0.356791i	−0.158102	+	0.987423i	$0.550537\pi$
$908$	−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	$-0.657513\pi$
$911$	−44.5039	−	25.6943i	−1.47448	−	0.851291i	−0.999587	+	0.0287535i	$0.990846\pi$
$912$	−3.10744	+	11.4299i	−0.102897	+	0.378483i
$913$	0.417902	−	0.241276i	0.0138306	−	0.00798507i
$914$	−19.0219	+	36.8411i	−0.629190	+	1.21860i
$915$	9.63921	−	19.7845i	0.318662	−	0.654054i
$916$	−45.6642	+	32.4318i	−1.50879	+	1.07158i
$917$	−23.7674	+	1.67969i	−0.784869	+	0.0554683i
$918$	4.29082	+	16.2814i	0.141618	+	0.537367i
$919$		−	33.2245i		−	1.09597i	−0.836487	−	0.547987i	$-0.815394\pi$
$919$		−	33.2245i		−	1.09597i	0.836487	−	0.547987i	$-0.184606\pi$
$920$	−17.5844	+	43.6872i	−0.579739	+	1.44032i
$921$	−6.96712	+	14.3000i	−0.229574	+	0.471201i
$922$	41.9336	+	21.6513i	1.38101	+	0.713047i
$923$	−4.27138	−	7.39825i	−0.140594	−	0.243516i
$924$	−8.98148	−	37.5551i	−0.295469	−	1.23547i
$925$	−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	$0.813265\pi$
$930$	38.9661	−	29.0612i	1.27775	−	0.952954i
$931$	−7.38194	−	9.41962i	−0.241933	−	0.308716i
$932$	−16.8261	+	1.58558i	−0.551157	+	0.0519373i
$933$	−13.1680	+	0.926375i	−0.431101	+	0.0303281i
$934$	−11.0456	+	0.519281i	−0.361423	+	0.0169914i
$935$			29.7227i			0.972038i
$936$	28.2800	+	6.98643i	0.924360	+	0.228359i
$937$			34.2337i			1.11837i	0.829044	+	0.559183i	$0.188885\pi$
$937$			34.2337i			1.11837i	−0.829044	+	0.559183i	$0.811115\pi$
$938$	−4.83119	−	40.9156i	−0.157744	−	1.33594i
$939$	−8.90121	+	6.00940i	−0.290480	+	0.196109i
$940$	−2.54977	−	27.0581i	−0.0831644	−	0.882538i
$941$	−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	$0.978027\pi$
$942$	−7.10684	−	60.3541i	−0.231553	−	1.96644i
$943$	−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	0.699378	−	0.714752i	$-0.253460\pi$
$947$	13.2348	+	7.64112i	0.430073	+	0.248303i	−0.269305	+	0.963055i	$0.586794\pi$
$948$	27.4419	−	22.5470i	0.891272	−	0.732293i
$949$	5.95596	+	10.3160i	0.193339	+	0.334872i
$950$	−4.96946	+	9.62471i	−0.161231	+	0.312267i
$951$	−9.39116	−	13.9103i	−0.304529	−	0.451073i
$952$	16.3179	+	5.26507i	0.528867	+	0.170642i
$953$	7.58109			0.245576			0.122788	−	0.992433i	$-0.460817\pi$
$953$	7.58109			0.245576			0.122788	+	0.992433i	$0.460817\pi$
$954$	29.2789	+	33.9919i	0.947940	+	1.10053i
$955$	36.2388			1.17266
$956$	−35.0158	+	24.8691i	−1.13249	+	0.804324i
$957$	4.88058	+	69.3752i	0.157767	+	2.24258i
$958$	3.61588	−	7.00313i	0.116824	−	0.226261i
$959$	−3.30947	−	4.89865i	−0.106868	−	0.158186i
$960$	14.7134	+	40.0460i	0.474874	+	1.29248i
$961$	−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
$966$	−33.0878	−	11.5494i	−1.06458	−	0.371597i
$967$	−4.06638	+	2.34772i	−0.130766	+	0.0754977i	−0.563956	−	0.825805i	$-0.690721\pi$
$967$	−4.06638	+	2.34772i	−0.130766	+	0.0754977i	0.433190	+	0.901303i	$0.357388\pi$
$968$	−11.7750	−	15.0307i	−0.378461	−	0.483105i
$969$	6.09949	+	2.97174i	0.195944	+	0.0954660i
$970$	27.8078	−	1.30732i	0.892855	−	0.0419754i
$971$	−44.5685			−1.43027			−0.715135	−	0.698986i	$-0.753635\pi$
$971$	−44.5685			−1.43027			−0.715135	+	0.698986i	$0.753635\pi$
$972$	−25.6950	−	17.6570i	−0.824166	−	0.566348i
$973$	26.9096	−	1.90176i	0.862681	−	0.0609675i
$974$	−1.50668	−	32.0485i	−0.0482772	−	1.02690i
$975$	23.9481	+	11.6678i	0.766952	+	0.373667i
$976$	−15.5857	−	5.43771i	−0.498885	−	0.174057i
$977$	−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	$0.882227\pi$
$978$	24.5871	+	10.5809i	0.786210	+	0.338339i
$979$	−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	0.0650157	+	0.997884i	$0.479290\pi$
$983$	−26.0757	+	45.1644i	−0.831685	+	1.44052i	−0.896701	+	0.442637i	$0.854043\pi$
$984$	5.26082	+	24.5415i	0.167709	+	0.782355i
$985$	−28.7592	+	16.6041i	−0.916344	+	0.529052i
$986$	−27.4399	−	14.1678i	−0.873863	−	0.451196i
$987$	20.0250	−	2.83809i	0.637403	−	0.0903374i
$988$	9.57040	−	6.79712i	0.304475	−	0.216245i
$989$	18.0988			0.575508
$990$	−35.9181	−	41.6998i	−1.14155	−	1.32531i
$991$			41.3545i			1.31367i	0.754034	+	0.656835i	$0.228105\pi$
$991$			41.3545i			1.31367i	−0.754034	+	0.656835i	$0.771895\pi$
$992$	−25.0782	−	26.4655i	−0.796232	−	0.840281i
$993$	−29.6999	+	20.0510i	−0.942497	+	0.636301i
$994$	8.55364	+	3.67774i	0.271305	+	0.116651i
$995$	12.3979	−	7.15794i	0.393040	−	0.226922i
$996$	−0.251875	−	0.306557i	−0.00798097	−	0.00971363i
$997$	−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.223.1	yes	80
3.2	odd	2		756.2.bi.c.559.39		80
4.3	odd	2	inner	252.2.bi.c.223.28	yes	80
7.6	odd	2	inner	252.2.bi.c.223.2	yes	80
9.4	even	3	inner	252.2.bi.c.139.27	yes	80
9.5	odd	6		756.2.bi.c.307.14		80
12.11	even	2		756.2.bi.c.559.13		80
21.20	even	2		756.2.bi.c.559.40		80
28.27	even	2	inner	252.2.bi.c.223.27	yes	80
36.23	even	6		756.2.bi.c.307.40		80
36.31	odd	6	inner	252.2.bi.c.139.2	yes	80
63.13	odd	6	inner	252.2.bi.c.139.28	yes	80
63.41	even	6		756.2.bi.c.307.13		80
84.83	odd	2		756.2.bi.c.559.14		80
252.139	even	6	inner	252.2.bi.c.139.1	✓	80
252.167	odd	6		756.2.bi.c.307.39		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.1	✓	80	252.139	even	6	inner
252.2.bi.c.139.2	yes	80	36.31	odd	6	inner
252.2.bi.c.139.27	yes	80	9.4	even	3	inner
252.2.bi.c.139.28	yes	80	63.13	odd	6	inner
252.2.bi.c.223.1	yes	80	1.1	even	1	trivial
252.2.bi.c.223.2	yes	80	7.6	odd	2	inner
252.2.bi.c.223.27	yes	80	28.27	even	2	inner
252.2.bi.c.223.28	yes	80	4.3	odd	2	inner
756.2.bi.c.307.13		80	63.41	even	6
756.2.bi.c.307.14		80	9.5	odd	6
756.2.bi.c.307.39		80	252.167	odd	6
756.2.bi.c.307.40		80	36.23	even	6
756.2.bi.c.559.13		80	12.11	even	2
756.2.bi.c.559.14		80	84.83	odd	2
756.2.bi.c.559.39		80	3.2	odd	2
756.2.bi.c.559.40		80	21.20	even	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+(-1.41265 + 0.0664123i) q^{2} +(-0.758625 + 1.55708i) q^{3} +(1.99118 - 0.187635i) q^{4} +(2.66647 - 1.53948i) q^{5} +(0.968265 - 2.24999i) 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} +(-1.21839 + 3.24276i) q^{12} +(2.97309 - 1.71651i) q^{13} +(-1.47795 + 3.43739i) q^{14} +(0.374249 + 5.31978i) q^{15} +(3.92959 - 0.747231i) q^{16} -2.29127i q^{17} +(2.76886 + 3.21456i) q^{18} +1.70965 q^{19} +(5.02055 - 3.56571i) q^{20} +(2.82551 + 3.60783i) q^{21} +(5.29425 + 2.73354i) q^{22} +(4.68317 - 2.70383i) q^{23} +(1.50581 - 4.66182i) 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} +(-0.881984 - 7.49016i) q^{30} +(3.22265 + 5.58179i) q^{31} +(-5.50152 + 1.31655i) q^{32} +(6.04809 - 4.08320i) q^{33} +(0.152169 + 3.23677i) q^{34} +(-0.574276 - 8.12592i) q^{35} +(-4.12493 - 4.35717i) q^{36} -2.04135 q^{37} +(-2.41514 + 0.113542i) q^{38} +(0.417285 + 5.93151i) q^{39} +(-6.85549 + 5.37054i) q^{40} +(-4.43693 + 2.56166i) q^{41} +(-4.23108 - 4.90897i) 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} +(-1.81759 + 6.68554i) q^{48} +(-4.31781 - 5.50968i) q^{49} +(-2.90671 + 5.62963i) q^{50} +(3.56768 + 1.73821i) q^{51} +(5.59787 - 3.97574i) q^{52} +10.5744 q^{53} +(-7.10585 + 1.87268i) q^{54} -12.9722 q^{55} +(-2.29788 + 7.12178i) q^{56} +(-1.29698 + 2.66206i) q^{57} +(6.18340 - 11.9758i) q^{58} +(4.44595 + 7.70061i) q^{59} +(1.74338 + 10.5224i) 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} +(-8.27269 + 6.16982i) q^{66} +(-9.53591 + 5.50556i) q^{67} +(-0.429923 - 4.56233i) q^{68} +(0.657301 + 9.34324i) q^{69} +(1.35091 + 11.4410i) q^{70} -2.48841i q^{71} +(6.11646 + 5.88123i) q^{72} +3.46980i q^{73} +(2.88373 - 0.135571i) q^{74} +(4.34187 + 6.43124i) q^{75} +(3.40422 - 0.320791i) q^{76} +(-9.23662 + 6.24015i) q^{77} +(-0.983405 - 8.35146i) 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} +(6.30306 + 6.65368i) q^{84} +(-3.52738 - 6.10959i) q^{85} +(-4.20570 - 2.17150i) q^{86} +(-9.23639 - 13.6811i) q^{87} +(11.0547 + 4.44959i) q^{88} -3.61933i q^{89} +(12.3318 + 4.30890i) q^{90} +(-0.640313 - 9.06033i) q^{91} +(8.81769 - 6.26253i) q^{92} +(-11.1361 + 0.783427i) q^{93} +(-2.86352 + 5.54598i) q^{94} +(4.55872 - 2.63198i) q^{95} +(2.12362 - 9.56505i) 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

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