LMFDB - Embedded newform 552.2.j.d.323.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.19
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.218758 - 1.39719i) q^{2} +(0.262136 - 1.71210i) q^{3} +(-1.90429 + 0.611292i) q^{4} -0.130526 q^{5} +(-2.44948 + 0.00827965i) q^{6} +3.77863i q^{7} +(1.27067 + 2.52693i) q^{8} +(-2.86257 - 0.897607i) q^{9} +O(q^{10})$	\(q+(-0.218758 - 1.39719i) q^{2} +(0.262136 - 1.71210i) q^{3} +(-1.90429 + 0.611292i) q^{4} -0.130526 q^{5} +(-2.44948 + 0.00827965i) q^{6} +3.77863i q^{7} +(1.27067 + 2.52693i) q^{8} +(-2.86257 - 0.897607i) q^{9} +(0.0285535 + 0.182369i) q^{10} +4.36656i q^{11} +(0.547409 + 3.42058i) q^{12} +5.50350i q^{13} +(5.27947 - 0.826604i) q^{14} +(-0.0342155 + 0.223473i) q^{15} +(3.25264 - 2.32816i) q^{16} -0.402065i q^{17} +(-0.627921 + 4.19592i) q^{18} -2.08168 q^{19} +(0.248559 - 0.0797893i) q^{20} +(6.46939 + 0.990517i) q^{21} +(6.10092 - 0.955218i) q^{22} +1.00000 q^{23} +(4.65945 - 1.51311i) q^{24} -4.98296 q^{25} +(7.68945 - 1.20393i) q^{26} +(-2.28718 + 4.66571i) q^{27} +(-2.30985 - 7.19561i) q^{28} -8.77100 q^{29} +(0.319719 - 0.00108071i) q^{30} -7.75722i q^{31} +(-3.96442 - 4.03526i) q^{32} +(7.47599 + 1.14463i) q^{33} +(-0.561761 + 0.0879546i) q^{34} -0.493208i q^{35} +(5.99986 - 0.0405616i) q^{36} +10.1015i q^{37} +(0.455384 + 2.90851i) q^{38} +(9.42255 + 1.44267i) q^{39} +(-0.165855 - 0.329830i) q^{40} -2.80694i q^{41} +(-0.0312857 - 9.25566i) q^{42} +3.07905 q^{43} +(-2.66925 - 8.31520i) q^{44} +(0.373638 + 0.117161i) q^{45} +(-0.218758 - 1.39719i) q^{46} +3.41142 q^{47} +(-3.13340 - 6.17914i) q^{48} -7.27804 q^{49} +(1.09006 + 6.96216i) q^{50} +(-0.688374 - 0.105396i) q^{51} +(-3.36425 - 10.4803i) q^{52} -0.336698 q^{53} +(7.01923 + 2.17497i) q^{54} -0.569948i q^{55} +(-9.54835 + 4.80139i) q^{56} +(-0.545685 + 3.56405i) q^{57} +(1.91872 + 12.2548i) q^{58} -9.68031i q^{59} +(-0.0714509 - 0.446473i) q^{60} +2.78101i q^{61} +(-10.8383 + 1.69695i) q^{62} +(3.39173 - 10.8166i) q^{63} +(-4.77079 + 6.42180i) q^{64} -0.718348i q^{65} +(-0.0361536 - 10.6958i) q^{66} +12.8230 q^{67} +(0.245779 + 0.765648i) q^{68} +(0.262136 - 1.71210i) q^{69} +(-0.689106 + 0.107893i) q^{70} +8.19053 q^{71} +(-1.36919 - 8.37409i) q^{72} +0.417051 q^{73} +(14.1138 - 2.20979i) q^{74} +(-1.30622 + 8.53133i) q^{75} +(3.96413 - 1.27252i) q^{76} -16.4996 q^{77} +(-0.0455671 - 13.4807i) q^{78} +3.09607i q^{79} +(-0.424553 + 0.303884i) q^{80} +(7.38860 + 5.13893i) q^{81} +(-3.92184 + 0.614040i) q^{82} -3.59045i q^{83} +(-12.9251 + 2.06846i) q^{84} +0.0524797i q^{85} +(-0.673565 - 4.30202i) q^{86} +(-2.29920 + 15.0168i) q^{87} +(-11.0340 + 5.54846i) q^{88} +11.1036i q^{89} +(0.0819598 - 0.547674i) q^{90} -20.7957 q^{91} +(-1.90429 + 0.611292i) q^{92} +(-13.2811 - 2.03345i) q^{93} +(-0.746274 - 4.76641i) q^{94} +0.271713 q^{95} +(-7.94799 + 5.72969i) q^{96} +4.53325 q^{97} +(1.59213 + 10.1688i) q^{98} +(3.91946 - 12.4996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.218758	−	1.39719i	−0.154685	−	0.987964i
$2$	−0.218758	−	1.39719i	−0.154685	−	0.987964i
$3$	0.262136	−	1.71210i	0.151345	−	0.988481i
$3$	0.262136	−	1.71210i	0.151345	−	0.988481i
$4$	−1.90429	+	0.611292i	−0.952145	+	0.305646i
$5$	−0.130526			−0.0583728			−0.0291864	−	0.999574i	$-0.509292\pi$
$5$	−0.130526			−0.0583728			−0.0291864	+	0.999574i	$0.509292\pi$
$6$	−2.44948	+	0.00827965i	−0.999994	+	0.00338015i
$7$			3.77863i			1.42819i	0.700050	+	0.714094i	$0.253161\pi$
$7$			3.77863i			1.42819i	−0.700050	+	0.714094i	$0.746839\pi$
$8$	1.27067	+	2.52693i	0.449250	+	0.893406i
$9$	−2.86257	−	0.897607i	−0.954190	−	0.299202i
$10$	0.0285535	+	0.182369i	0.00902939	+	0.0576702i
$11$			4.36656i			1.31657i	0.752770	+	0.658284i	$0.228717\pi$
$11$			4.36656i			1.31657i	−0.752770	+	0.658284i	$0.771283\pi$
$12$	0.547409	+	3.42058i	0.158024	+	0.987435i
$13$			5.50350i			1.52640i	0.646164	+	0.763199i	$0.276372\pi$
$13$			5.50350i			1.52640i	−0.646164	+	0.763199i	$0.723628\pi$
$14$	5.27947	−	0.826604i	1.41100	−	0.220919i
$15$	−0.0342155	+	0.223473i	−0.00883441	+	0.0577004i
$16$	3.25264	−	2.32816i	0.813161	−	0.582039i
$17$		−	0.402065i		−	0.0975150i	−0.998811	−	0.0487575i	$-0.984474\pi$
$17$		−	0.402065i		−	0.0975150i	0.998811	−	0.0487575i	$-0.0155261\pi$
$18$	−0.627921	+	4.19592i	−0.148002	+	0.988987i
$19$	−2.08168			−0.477571			−0.238785	−	0.971072i	$-0.576749\pi$
$19$	−2.08168			−0.477571			−0.238785	+	0.971072i	$0.576749\pi$
$20$	0.248559	−	0.0797893i	0.0555794	−	0.0178414i
$21$	6.46939	+	0.990517i	1.41174	+	0.216148i
$22$	6.10092	−	0.955218i	1.30072	−	0.203653i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	4.65945	−	1.51311i	0.951107	−	0.308863i
$25$	−4.98296			−0.996593
$26$	7.68945	−	1.20393i	1.50803	−	0.236111i
$27$	−2.28718	+	4.66571i	−0.440167	+	0.897916i
$28$	−2.30985	−	7.19561i	−0.436520	−	1.35984i
$29$	−8.77100			−1.62873			−0.814367	−	0.580350i	$-0.802916\pi$
$29$	−8.77100			−1.62873			−0.814367	+	0.580350i	$0.802916\pi$
$30$	0.319719	−	0.00108071i	0.0583725	−	0.000197309i
$31$		−	7.75722i		−	1.39324i	−0.717442	−	0.696619i	$-0.754687\pi$
$31$		−	7.75722i		−	1.39324i	0.717442	−	0.696619i	$-0.245313\pi$
$32$	−3.96442	−	4.03526i	−0.700817	−	0.713341i
$33$	7.47599	+	1.14463i	1.30140	+	0.199255i
$34$	−0.561761	+	0.0879546i	−0.0963413	+	0.0150841i
$35$		−	0.493208i		−	0.0833673i
$36$	5.99986	−	0.0405616i	0.999977	−	0.00676026i
$37$			10.1015i			1.66068i	0.557254	+	0.830342i	$0.311855\pi$
$37$			10.1015i			1.66068i	−0.557254	+	0.830342i	$0.688145\pi$
$38$	0.455384	+	2.90851i	0.0738730	+	0.471823i
$39$	9.42255	+	1.44267i	1.50882	+	0.231012i
$40$	−0.165855	−	0.329830i	−0.0262240	−	0.0521506i
$41$		−	2.80694i		−	0.438371i	−0.975683	−	0.219185i	$-0.929660\pi$
$41$		−	2.80694i		−	0.438371i	0.975683	−	0.219185i	$-0.0703399\pi$
$42$	−0.0312857	−	9.25566i	−0.00482749	−	1.42818i
$43$	3.07905			0.469550			0.234775	−	0.972050i	$-0.424565\pi$
$43$	3.07905			0.469550			0.234775	+	0.972050i	$0.424565\pi$
$44$	−2.66925	−	8.31520i	−0.402404	−	1.25356i
$45$	0.373638	+	0.117161i	0.0556987	+	0.0174653i
$46$	−0.218758	−	1.39719i	−0.0322540	−	0.206005i
$47$	3.41142			0.497607			0.248803	−	0.968554i	$-0.419963\pi$
$47$	3.41142			0.497607			0.248803	+	0.968554i	$0.419963\pi$
$48$	−3.13340	−	6.17914i	−0.452267	−	0.891882i
$49$	−7.27804			−1.03972
$50$	1.09006	+	6.96216i	0.154158	+	0.984597i
$51$	−0.688374	−	0.105396i	−0.0963917	−	0.0147584i
$52$	−3.36425	−	10.4803i	−0.466538	−	1.45335i
$53$	−0.336698			−0.0462490			−0.0231245	−	0.999733i	$-0.507361\pi$
$53$	−0.336698			−0.0462490			−0.0231245	+	0.999733i	$0.507361\pi$
$54$	7.01923	+	2.17497i	0.955196	+	0.295975i
$55$		−	0.569948i		−	0.0768518i
$56$	−9.54835	+	4.80139i	−1.27595	+	0.641613i
$57$	−0.545685	+	3.56405i	−0.0722777	+	0.472070i
$58$	1.91872	+	12.2548i	0.251941	+	1.60913i
$59$		−	9.68031i		−	1.26027i	−0.776486	−	0.630134i	$-0.783000\pi$
$59$		−	9.68031i		−	1.26027i	0.776486	−	0.630134i	$-0.217000\pi$
$60$	−0.0714509	−	0.446473i	−0.00922428	−	0.0576394i
$61$			2.78101i			0.356072i	0.984024	+	0.178036i	$0.0569744\pi$
$61$			2.78101i			0.356072i	−0.984024	+	0.178036i	$0.943026\pi$
$62$	−10.8383	+	1.69695i	−1.37647	+	0.215513i
$63$	3.39173	−	10.8166i	0.427317	−	1.36276i
$64$	−4.77079	+	6.42180i	−0.596349	+	0.802725i
$65$		−	0.718348i		−	0.0891001i
$66$	−0.0361536	−	10.6958i	−0.00445020	−	1.31656i
$67$	12.8230			1.56658			0.783292	−	0.621654i	$-0.213539\pi$
$67$	12.8230			1.56658			0.783292	+	0.621654i	$0.213539\pi$
$68$	0.245779	+	0.765648i	0.0298051	+	0.0928484i
$69$	0.262136	−	1.71210i	0.0315575	−	0.206113i
$70$	−0.689106	+	0.107893i	−0.0823639	+	0.0128957i
$71$	8.19053			0.972037			0.486018	−	0.873949i	$-0.338449\pi$
$71$	8.19053			0.972037			0.486018	+	0.873949i	$0.338449\pi$
$72$	−1.36919	−	8.37409i	−0.161360	−	0.986896i
$73$	0.417051			0.0488121			0.0244061	−	0.999702i	$-0.492231\pi$
$73$	0.417051			0.0488121			0.0244061	+	0.999702i	$0.492231\pi$
$74$	14.1138	−	2.20979i	1.64070	−	0.256883i
$75$	−1.30622	+	8.53133i	−0.150829	+	0.985113i
$76$	3.96413	−	1.27252i	0.454717	−	0.145968i
$77$	−16.4996			−1.88031
$78$	−0.0455671	−	13.4807i	−0.00515945	−	1.52639i
$79$			3.09607i			0.348335i	0.984716	+	0.174168i	$0.0557235\pi$
$79$			3.09607i			0.348335i	−0.984716	+	0.174168i	$0.944277\pi$
$80$	−0.424553	+	0.303884i	−0.0474665	+	0.0339753i
$81$	7.38860	+	5.13893i	0.820956	+	0.570992i
$82$	−3.92184	+	0.614040i	−0.433094	+	0.0678093i
$83$		−	3.59045i		−	0.394103i	−0.980393	−	0.197052i	$-0.936863\pi$
$83$		−	3.59045i		−	0.394103i	0.980393	−	0.197052i	$-0.0631367\pi$
$84$	−12.9251	+	2.06846i	−1.41024	+	0.225687i
$85$			0.0524797i			0.00569222i
$86$	−0.673565	−	4.30202i	−0.0726324	−	0.463899i
$87$	−2.29920	+	15.0168i	−0.246500	+	1.60997i
$88$	−11.0340	+	5.54846i	−1.17623	+	0.591468i
$89$			11.1036i			1.17698i	0.808506	+	0.588488i	$0.200276\pi$
$89$			11.1036i			1.17698i	−0.808506	+	0.588488i	$0.799724\pi$
$90$	0.0819598	−	0.547674i	0.00863932	−	0.0577300i
$91$	−20.7957			−2.17998
$92$	−1.90429	+	0.611292i	−0.198536	+	0.0637316i
$93$	−13.2811	−	2.03345i	−1.37719	−	0.210859i
$94$	−0.746274	−	4.76641i	−0.0769723	−	0.491618i
$95$	0.271713			0.0278772
$96$	−7.94799	+	5.72969i	−0.811189	+	0.584784i
$97$	4.53325			0.460281			0.230141	−	0.973157i	$-0.426081\pi$
$97$	4.53325			0.460281			0.230141	+	0.973157i	$0.426081\pi$
$98$	1.59213	+	10.1688i	0.160829	+	1.02721i
$99$	3.91946	−	12.4996i	0.393920	−	1.25626i
$100$	9.48901	−	3.04605i	0.948901	−	0.304605i
$101$	3.79039			0.377158			0.188579	−	0.982058i	$-0.439612\pi$
$101$	3.79039			0.377158			0.188579	+	0.982058i	$0.439612\pi$
$102$	0.00332895	+	0.984847i	0.000329615	+	0.0975144i
$103$			6.81074i			0.671082i	0.942026	+	0.335541i	$0.108919\pi$
$103$			6.81074i			0.671082i	−0.942026	+	0.335541i	$0.891081\pi$
$104$	−13.9070	+	6.99314i	−1.36369	+	0.685734i
$105$	−0.844421	−	0.129288i	−0.0824070	−	0.0126172i
$106$	0.0736551	+	0.470431i	0.00715402	+	0.0456923i
$107$		−	6.74888i		−	0.652439i	−0.945294	−	0.326219i	$-0.894225\pi$
$107$		−	6.74888i		−	0.652439i	0.945294	−	0.326219i	$-0.105775\pi$
$108$	1.50334	−	10.2830i	0.144659	−	0.989482i
$109$			18.3211i			1.75485i	0.479716	+	0.877424i	$0.340740\pi$
$109$			18.3211i			1.75485i	−0.479716	+	0.877424i	$0.659260\pi$
$110$	−0.796327	+	0.124680i	−0.0759268	+	0.0118878i
$111$	17.2948	+	2.64798i	1.64155	+	0.251335i
$112$	8.79724	+	12.2905i	0.831261	+	1.16135i
$113$		−	14.3459i		−	1.34955i	−0.738023	−	0.674775i	$-0.764241\pi$
$113$		−	14.3459i		−	1.34955i	0.738023	−	0.674775i	$-0.235759\pi$
$114$	5.09903	−	0.0172356i	0.477568	−	0.00161426i
$115$	−0.130526			−0.0121716
$116$	16.7025	−	5.36165i	1.55079	−	0.497816i
$117$	4.93999	−	15.7542i	0.456702	−	1.45647i
$118$	−13.5252	+	2.11764i	−1.24510	+	0.194945i
$119$	1.51925			0.139270
$120$	−0.608178	+	0.197500i	−0.0555188	+	0.0180292i
$121$	−8.06685			−0.733350
$122$	3.88561	−	0.608367i	0.351786	−	0.0550790i
$123$	−4.80576	−	0.735802i	−0.433321	−	0.0663450i
$124$	4.74193	+	14.7720i	0.425838	+	1.32656i
$125$	1.30303			0.116547
$126$	−15.8548	−	2.37268i	−1.41246	−	0.211375i
$127$			13.5190i			1.19962i	0.800143	+	0.599810i	$0.204757\pi$
$127$			13.5190i			1.19962i	−0.800143	+	0.599810i	$0.795243\pi$
$128$	10.0161	+	5.26089i	0.885310	+	0.465002i
$129$	0.807131	−	5.27164i	0.0710639	−	0.464142i
$130$	−1.00367	+	0.157144i	−0.0880277	+	0.0137824i
$131$			21.6396i			1.89066i	0.326114	+	0.945331i	$0.394261\pi$
$131$			21.6396i			1.89066i	−0.326114	+	0.945331i	$0.605739\pi$
$132$	−14.9362	+	2.39030i	−1.30003	+	0.208049i
$133$		−	7.86591i		−	0.682061i
$134$	−2.80514	−	17.9163i	−0.242327	−	1.54773i
$135$	0.298535	−	0.608994i	0.0256938	−	0.0524139i
$136$	1.01599	−	0.510892i	0.0871205	−	0.0438086i
$137$		−	14.9588i		−	1.27801i	−0.769201	−	0.639007i	$-0.779345\pi$
$137$		−	14.9588i		−	1.27801i	0.769201	−	0.639007i	$-0.220655\pi$
$138$	−2.44948	+	0.00827965i	−0.208513	+	0.000704810i
$139$	11.5627			0.980736			0.490368	−	0.871515i	$-0.336862\pi$
$139$	11.5627			0.980736			0.490368	+	0.871515i	$0.336862\pi$
$140$	0.301494	+	0.939211i	0.0254809	+	0.0793778i
$141$	0.894258	−	5.84069i	0.0753101	−	0.491875i
$142$	−1.79174	−	11.4437i	−0.150359	−	0.960337i
$143$	−24.0314			−2.00961
$144$	−11.4007	+	3.74491i	−0.950057	+	0.312076i
$145$	1.14484			0.0950738
$146$	−0.0912330	−	0.582700i	−0.00755050	−	0.0482246i
$147$	−1.90784	+	12.4607i	−0.157356	+	1.02774i
$148$	−6.17500	−	19.2363i	−0.507582	−	1.58121i
$149$	−13.1430			−1.07671			−0.538356	−	0.842717i	$-0.680955\pi$
$149$	−13.1430			−1.07671			−0.538356	+	0.842717i	$0.680955\pi$
$150$	12.2056	−	0.0412572i	0.996587	−	0.00336863i
$151$		−	1.10155i		−	0.0896425i	−0.998995	−	0.0448213i	$-0.985728\pi$
$151$		−	1.10155i		−	0.0896425i	0.998995	−	0.0448213i	$-0.0142718\pi$
$152$	−2.64513	−	5.26028i	−0.214549	−	0.426665i
$153$	−0.360896	+	1.15094i	−0.0291767	+	0.0930478i
$154$	3.60942	+	23.0531i	0.290855	+	1.85767i
$155$			1.01252i			0.0813272i
$156$	−18.8252	+	3.01267i	−1.50722	+	0.241207i
$157$		−	17.3372i		−	1.38366i	−0.722062	−	0.691828i	$-0.756805\pi$
$157$		−	17.3372i		−	1.38366i	0.722062	−	0.691828i	$-0.243195\pi$
$158$	4.32581	−	0.677289i	0.344143	−	0.0538822i
$159$	−0.0882607	+	0.576460i	−0.00699953	+	0.0457162i
$160$	0.517458	+	0.526705i	0.0409087	+	0.0416397i
$161$			3.77863i			0.297798i
$162$	5.56375	−	11.4475i	0.437130	−	0.899398i
$163$	−10.4421			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$163$	−10.4421			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$164$	1.71586	+	5.34523i	0.133986	+	0.417393i
$165$	−0.975807	−	0.149404i	−0.0759665	−	0.0116311i
$166$	−5.01655	+	0.785438i	−0.389360	+	0.0609618i
$167$	−1.67012			−0.129238			−0.0646188	−	0.997910i	$-0.520583\pi$
$167$	−1.67012			−0.129238			−0.0646188	+	0.997910i	$0.520583\pi$
$168$	5.71749	+	17.6063i	0.441114	+	1.35836i
$169$	−17.2886			−1.32989
$170$	0.0733242	−	0.0114803i	0.00562371	−	0.000880501i
$171$	5.95896	+	1.86853i	0.455693	+	0.142890i
$172$	−5.86340	+	1.88220i	−0.447080	+	0.143516i
$173$	−8.55215			−0.650208			−0.325104	−	0.945678i	$-0.605399\pi$
$173$	−8.55215			−0.650208			−0.325104	+	0.945678i	$0.605399\pi$
$174$	21.4844	−	0.0726208i	1.62872	−	0.00550537i
$175$		−	18.8288i		−	1.42332i
$176$	10.1660	+	14.2029i	0.766294	+	1.07058i
$177$	−16.5736	−	2.53756i	−1.24575	−	0.190735i
$178$	15.5138	−	2.42899i	1.16281	−	0.182060i
$179$			14.7284i			1.10085i	0.834885	+	0.550425i	$0.185534\pi$
$179$			14.7284i			1.10085i	−0.834885	+	0.550425i	$0.814466\pi$
$180$	−0.783136	+	0.00529432i	−0.0583715	+	0.000394616i
$181$			21.7258i			1.61487i	0.589959	+	0.807433i	$0.299144\pi$
$181$			21.7258i			1.61487i	−0.589959	+	0.807433i	$0.700856\pi$
$182$	4.54922	+	29.0556i	0.337210	+	2.15374i
$183$	4.76137	+	0.729005i	0.351971	+	0.0538896i
$184$	1.27067	+	2.52693i	0.0936751	+	0.186288i
$185$		−	1.31851i		−	0.0969388i
$186$	0.0642270	+	19.0011i	0.00470935	+	1.39323i
$187$	1.75564			0.128385
$188$	−6.49634	+	2.08538i	−0.473794	+	0.152092i
$189$	−17.6300	−	8.64240i	−1.28239	−	0.628642i
$190$	−0.0594392	−	0.379635i	−0.00431218	−	0.0275416i
$191$	10.7127			0.775145			0.387572	−	0.921839i	$-0.373314\pi$
$191$	10.7127			0.775145			0.387572	+	0.921839i	$0.373314\pi$
$192$	9.74416	+	9.85146i	0.703225	+	0.710968i
$193$	14.8172			1.06657			0.533283	−	0.845937i	$-0.320958\pi$
$193$	14.8172			1.06657			0.533283	+	0.845937i	$0.320958\pi$
$194$	−0.991682	−	6.33381i	−0.0711986	−	0.454741i
$195$	−1.22988	−	0.188305i	−0.0880738	−	0.0134848i
$196$	13.8595	−	4.44901i	0.989965	−	0.317787i
$197$	−17.5258			−1.24866			−0.624331	−	0.781160i	$-0.714628\pi$
$197$	−17.5258			−1.24866			−0.624331	+	0.781160i	$0.714628\pi$
$198$	−18.3217	−	2.74186i	−1.30207	−	0.194855i
$199$		−	23.3044i		−	1.65201i	−0.563666	−	0.826003i	$-0.690609\pi$
$199$		−	23.3044i		−	1.65201i	0.563666	−	0.826003i	$-0.309391\pi$
$200$	−6.33170	−	12.5916i	−0.447719	−	0.890362i
$201$	3.36139	−	21.9543i	0.237094	−	1.54854i
$202$	−0.829176	−	5.29590i	−0.0583406	−	0.372618i
$203$		−	33.1424i		−	2.32614i
$204$	1.37529	−	0.220094i	0.0962897	−	0.0154097i
$205$			0.366378i			0.0255889i
$206$	9.51591	−	1.48990i	0.663005	−	0.103806i
$207$	−2.86257	−	0.897607i	−0.198962	−	0.0623880i
$208$	12.8130	+	17.9009i	0.888423	+	1.24121i
$209$		−	9.08979i		−	0.628754i
$210$	0.00408359	+	1.20810i	0.000281794	+	0.0833669i
$211$	16.0748			1.10664			0.553319	−	0.832970i	$-0.313361\pi$
$211$	16.0748			1.10664			0.553319	+	0.832970i	$0.313361\pi$
$212$	0.641170	−	0.205821i	0.0440357	−	0.0141358i
$213$	2.14704	−	14.0230i	0.147112	−	0.960840i
$214$	−9.42948	+	1.47637i	−0.644586	+	0.100922i
$215$	−0.401894			−0.0274090
$216$	−14.6962	+	0.149031i	−0.999949	+	0.0101403i
$217$	29.3117			1.98980
$218$	25.5982	−	4.00789i	1.73373	−	0.271448i
$219$	0.109324	−	0.714033i	0.00738745	−	0.0482499i
$220$	0.348405	+	1.08535i	0.0234894	+	0.0731740i
$221$	2.21276			0.148847
$222$	−0.0836372	−	24.7435i	−0.00561336	−	1.66067i
$223$		−	16.7322i		−	1.12047i	−0.828333	−	0.560237i	$-0.810710\pi$
$223$		−	16.7322i		−	1.12047i	0.828333	−	0.560237i	$-0.189290\pi$
$224$	15.2478	−	14.9801i	1.01878	−	1.00090i
$225$	14.2641	+	4.47274i	0.950938	+	0.298183i
$226$	−20.0440	+	3.13828i	−1.33331	+	0.208755i
$227$			5.60178i			0.371803i	0.982568	+	0.185902i	$0.0595206\pi$
$227$			5.60178i			0.371803i	−0.982568	+	0.185902i	$0.940479\pi$
$228$	−1.13953	−	7.12056i	−0.0754674	−	0.471570i
$229$		−	17.9554i		−	1.18653i	−0.805008	−	0.593264i	$-0.797839\pi$
$229$		−	17.9554i		−	1.18653i	0.805008	−	0.593264i	$-0.202161\pi$
$230$	0.0285535	+	0.182369i	0.00188276	+	0.0120251i
$231$	−4.32515	+	28.2490i	−0.284574	+	1.85865i
$232$	−11.1451	−	22.1637i	−0.731709	−	1.45512i
$233$			24.5310i			1.60708i	0.595252	+	0.803539i	$0.297052\pi$
$233$			24.5310i			1.60708i	−0.595252	+	0.803539i	$0.702948\pi$
$234$	−23.0922	−	3.45577i	−1.50959	−	0.225911i
$235$	−0.445278			−0.0290467
$236$	5.91750	+	18.4341i	0.385196	+	1.19996i
$237$	5.30078	+	0.811594i	0.344323	+	0.0527187i
$238$	−0.332348	−	2.12269i	−0.0215429	−	0.137593i
$239$	−3.73158			−0.241376			−0.120688	−	0.992691i	$-0.538510\pi$
$239$	−3.73158			−0.241376			−0.120688	+	0.992691i	$0.538510\pi$
$240$	0.408989	+	0.806536i	0.0264001	+	0.0520617i
$241$	8.92696			0.575036			0.287518	−	0.957775i	$-0.407170\pi$
$241$	8.92696			0.575036			0.287518	+	0.957775i	$0.407170\pi$
$242$	1.76468	+	11.2709i	0.113438	+	0.724524i
$243$	10.7352	−	11.3029i	0.688662	−	0.725083i
$244$	−1.70001	−	5.29585i	−0.108832	−	0.339032i
$245$	0.949971			0.0606914
$246$	0.0232405	+	6.87554i	0.00148176	+	0.438368i
$247$		−	11.4566i		−	0.728963i
$248$	19.6020	−	9.85687i	1.24473	−	0.625912i
$249$	−6.14721	−	0.941188i	−0.389564	−	0.0596454i
$250$	−0.285048	−	1.82059i	−0.0180280	−	0.115144i
$251$			15.0476i			0.949798i	0.880040	+	0.474899i	$0.157515\pi$
$251$			15.0476i			0.949798i	−0.880040	+	0.474899i	$0.842485\pi$
$252$	0.153267	+	22.6713i	0.00965493	+	1.42816i
$253$			4.36656i			0.274523i
$254$	18.8887	−	2.95739i	1.18518	−	0.185563i
$255$	0.0898505	+	0.0137568i	0.00562666	+	0.000861487i
$256$	5.15937	−	15.1453i	0.322461	−	0.946583i
$257$		−	7.84239i		−	0.489195i	−0.969625	−	0.244597i	$-0.921344\pi$
$257$		−	7.84239i		−	0.489195i	0.969625	−	0.244597i	$-0.0786558\pi$
$258$	−7.54205	+	0.0254934i	−0.469548	+	0.00158715i
$259$	−38.1700			−2.37177
$260$	0.439121	+	1.36794i	0.0272331	+	0.0848362i
$261$	25.1076	+	7.87292i	1.55412	+	0.487321i
$262$	30.2347	−	4.73383i	1.86790	−	0.292457i
$263$	18.6358			1.14913			0.574566	−	0.818458i	$-0.305171\pi$
$263$	18.6358			1.14913			0.574566	+	0.818458i	$0.305171\pi$
$264$	6.60710	+	20.3458i	0.406639	+	1.25220i
$265$	0.0439477			0.00269968
$266$	−10.9902	+	1.72073i	−0.673851	+	0.105505i
$267$	19.0104	+	2.91065i	1.16342	+	0.178129i
$268$	−24.4188	+	7.83863i	−1.49162	+	0.478821i
$269$	5.72570			0.349102			0.174551	−	0.984648i	$-0.444153\pi$
$269$	5.72570			0.349102			0.174551	+	0.984648i	$0.444153\pi$
$270$	−0.916188	−	0.283889i	−0.0557575	−	0.0172769i
$271$		−	10.0447i		−	0.610173i	−0.952325	−	0.305086i	$-0.901315\pi$
$271$		−	10.0447i		−	0.610173i	0.952325	−	0.305086i	$-0.0986853\pi$
$272$	−0.936069	−	1.30777i	−0.0567575	−	0.0792954i
$273$	−5.45131	+	35.6043i	−0.329928	+	2.15487i
$274$	−20.9003	+	3.27235i	−1.26263	+	0.197690i
$275$		−	21.7584i		−	1.31208i
$276$	0.547409	+	3.42058i	0.0329502	+	0.205895i
$277$		−	12.6894i		−	0.762431i	−0.924486	−	0.381215i	$-0.875506\pi$
$277$		−	12.6894i		−	0.762431i	0.924486	−	0.381215i	$-0.124494\pi$
$278$	−2.52943	−	16.1553i	−0.151705	−	0.968932i
$279$	−6.96294	+	22.2056i	−0.416860	+	1.32941i
$280$	1.24630	−	0.626705i	0.0744809	−	0.0374528i
$281$			25.8591i			1.54262i	0.636458	+	0.771311i	$0.280399\pi$
$281$			25.8591i			1.54262i	−0.636458	+	0.771311i	$0.719601\pi$
$282$	−8.35619	+	0.0282454i	−0.497604	+	0.00168199i
$283$	21.0898			1.25366			0.626828	−	0.779158i	$-0.284353\pi$
$283$	21.0898			1.25366			0.626828	+	0.779158i	$0.284353\pi$
$284$	−15.5971	+	5.00681i	−0.925520	+	0.297099i
$285$	0.0712259	−	0.465199i	0.00421906	−	0.0275560i
$286$	5.25705	+	33.5765i	0.310856	+	1.98542i
$287$	10.6064			0.626076
$288$	7.72635	+	15.1097i	0.455279	+	0.890349i
$289$	16.8383			0.990491
$290$	−0.250442	−	1.59956i	−0.0147065	−	0.0939295i
$291$	1.18833	−	7.76137i	0.0696611	−	0.454979i
$292$	−0.794186	+	0.254940i	−0.0464762	+	0.0149192i
$293$	17.5822			1.02717			0.513583	−	0.858040i	$-0.328318\pi$
$293$	17.5822			1.02717			0.513583	+	0.858040i	$0.328318\pi$
$294$	17.8274	−	0.0602596i	1.03971	−	0.00351441i
$295$			1.26353i			0.0735654i
$296$	−25.5259	+	12.8357i	−1.48367	+	0.746062i
$297$	−20.3731	−	9.98710i	−1.18217	−	0.579510i
$298$	2.87512	+	18.3632i	0.166551	+	1.06375i
$299$			5.50350i			0.318276i
$300$	−2.72772	−	17.0446i	−0.157485	−	0.984071i
$301$			11.6346i			0.670606i
$302$	−1.53907	+	0.240971i	−0.0885636	+	0.0138663i
$303$	0.993599	−	6.48952i	0.0570808	−	0.372813i
$304$	−6.77097	+	4.84648i	−0.388342	+	0.277965i
$305$		−	0.362993i		−	0.0207849i
$306$	1.68703	+	0.252465i	0.0964410	+	0.0144325i
$307$	−12.0490			−0.687674			−0.343837	−	0.939029i	$-0.611727\pi$
$307$	−12.0490			−0.687674			−0.343837	+	0.939029i	$0.611727\pi$
$308$	31.4201	−	10.0861i	1.79032	−	0.574708i
$309$	11.6607	+	1.78534i	0.663352	+	0.101565i
$310$	1.41468	−	0.221495i	0.0803483	−	0.0125801i
$311$	−8.92121			−0.505876			−0.252938	−	0.967483i	$-0.581397\pi$
$311$	−8.92121			−0.505876			−0.252938	+	0.967483i	$0.581397\pi$
$312$	8.32742	+	25.6433i	0.471448	+	1.45177i
$313$	0.481564			0.0272196			0.0136098	−	0.999907i	$-0.495668\pi$
$313$	0.481564			0.0272196			0.0136098	+	0.999907i	$0.495668\pi$
$314$	−24.2234	+	3.79264i	−1.36700	+	0.214031i
$315$	−0.442707	+	1.41184i	−0.0249437	+	0.0795483i
$316$	−1.89261	−	5.89582i	−0.106467	−	0.331666i
$317$	−6.46721			−0.363235			−0.181617	−	0.983369i	$-0.558133\pi$
$317$	−6.46721			−0.363235			−0.181617	+	0.983369i	$0.558133\pi$
$318$	0.824733	−	0.00278774i	0.0462487	−	0.000156329i
$319$		−	38.2991i		−	2.14434i
$320$	0.622710	−	0.838209i	0.0348106	−	0.0468573i
$321$	−11.5548	−	1.76913i	−0.644923	−	0.0987431i
$322$	5.27947	−	0.826604i	0.294213	−	0.0460648i
$323$			0.836971i			0.0465703i
$324$	−17.2114	−	5.26941i	−0.956191	−	0.292745i
$325$		−	27.4238i		−	1.52120i
$326$	2.28429	+	14.5896i	0.126515	+	0.808045i
$327$	31.3676	+	4.80264i	1.73463	+	0.265587i
$328$	7.09296	−	3.56670i	0.391643	−	0.196938i
$329$			12.8905i			0.710676i
$330$	0.00471897	+	1.39607i	0.000259771	+	0.0768513i
$331$	25.1117			1.38026			0.690132	−	0.723683i	$-0.257552\pi$
$331$	25.1117			1.38026			0.690132	+	0.723683i	$0.257552\pi$
$332$	2.19482	+	6.83726i	0.120456	+	0.375243i
$333$	9.06722	−	28.9164i	0.496881	−	1.58461i
$334$	0.365351	+	2.33347i	0.0199911	+	0.127682i
$335$	−1.67374			−0.0914459
$336$	23.3487	−	11.8400i	1.27378	−	0.645923i
$337$	−10.0318			−0.546465			−0.273232	−	0.961948i	$-0.588093\pi$
$337$	−10.0318			−0.546465			−0.273232	+	0.961948i	$0.588093\pi$
$338$	3.78200	+	24.1554i	0.205714	+	1.31388i
$339$	−24.5616	−	3.76059i	−1.33401	−	0.204247i
$340$	−0.0320804	−	0.0999366i	−0.00173981	−	0.00541982i
$341$	33.8724			1.83429
$342$	1.30713	−	8.73457i	0.0706817	−	0.472311i
$343$		−	1.05062i		−	0.0567283i
$344$	3.91246	+	7.78055i	0.210945	+	0.419499i
$345$	−0.0342155	+	0.223473i	−0.00184210	+	0.0120314i
$346$	1.87085	+	11.9490i	0.100577	+	0.642382i
$347$			12.4062i			0.665998i	0.942927	+	0.332999i	$0.108061\pi$
$347$			12.4062i			0.665998i	−0.942927	+	0.332999i	$0.891939\pi$
$348$	−4.80133	−	30.0019i	−0.257378	−	1.60827i
$349$			17.9711i			0.961969i	0.876729	+	0.480985i	$0.159721\pi$
$349$			17.9711i			0.961969i	−0.876729	+	0.480985i	$0.840279\pi$
$350$	−26.3074	+	4.11894i	−1.40619	+	0.220166i
$351$	−25.6777	−	12.5875i	−1.37058	−	0.671870i
$352$	17.6202	−	17.3109i	0.939161	−	0.922673i
$353$			25.5729i			1.36111i	0.732698	+	0.680554i	$0.238261\pi$
$353$			25.5729i			1.36111i	−0.732698	+	0.680554i	$0.761739\pi$
$354$	0.0801495	+	23.7117i	0.00425990	+	1.26026i
$355$	−1.06907			−0.0567405
$356$	−6.78752	−	21.1444i	−0.359738	−	1.12065i
$357$	0.398252	−	2.60111i	0.0210777	−	0.137665i
$358$	20.5784	−	3.22194i	1.08760	−	0.170285i
$359$	−20.5959			−1.08701			−0.543506	−	0.839405i	$-0.682904\pi$
$359$	−20.5959			−1.08701			−0.543506	+	0.839405i	$0.682904\pi$
$360$	0.178714	+	1.09303i	0.00941905	+	0.0576079i
$361$	−14.6666			−0.771926
$362$	30.3551	−	4.75268i	1.59543	−	0.249796i
$363$	−2.11462	+	13.8113i	−0.110989	+	0.724903i
$364$	39.6011	−	12.7123i	2.07566	−	0.666303i
$365$	−0.0544358			−0.00284930
$366$	−0.0230258	−	6.81202i	−0.00120358	−	0.356070i
$367$		−	0.995463i		−	0.0519628i	−0.999662	−	0.0259814i	$-0.991729\pi$
$367$		−	0.995463i		−	0.0519628i	0.999662	−	0.0259814i	$-0.00827106\pi$
$368$	3.25264	−	2.32816i	0.169556	−	0.121364i
$369$	−2.51953	+	8.03507i	−0.131162	+	0.418289i
$370$	−1.84221	+	0.288434i	−0.0957720	+	0.0149950i
$371$		−	1.27226i		−	0.0660522i
$372$	26.5342	−	4.24637i	1.37573	−	0.220164i
$373$			19.8991i			1.03034i	0.857089	+	0.515168i	$0.172271\pi$
$373$			19.8991i			1.03034i	−0.857089	+	0.515168i	$0.827729\pi$
$374$	−0.384059	−	2.45296i	−0.0198592	−	0.126840i
$375$	0.341572	−	2.23092i	0.0176387	−	0.115204i
$376$	4.33479	+	8.62044i	0.223550	+	0.444565i
$377$		−	48.2713i		−	2.48610i
$378$	−8.21839	+	26.5231i	−0.422709	+	1.36420i
$379$	−13.7477			−0.706172			−0.353086	−	0.935591i	$-0.614868\pi$
$379$	−13.7477			−0.706172			−0.353086	+	0.935591i	$0.614868\pi$
$380$	−0.517420	+	0.166096i	−0.0265431	+	0.00852055i
$381$	23.1459	+	3.54383i	1.18580	+	0.181556i
$382$	−2.34349	−	14.9677i	−0.119903	−	0.765815i
$383$	5.57295			0.284764			0.142382	−	0.989812i	$-0.454524\pi$
$383$	5.57295			0.284764			0.142382	+	0.989812i	$0.454524\pi$
$384$	11.6328	−	15.7695i	0.593632	−	0.804736i
$385$	2.15362			0.109759
$386$	−3.24138	−	20.7025i	−0.164982	−	1.05373i
$387$	−8.81399	−	2.76378i	−0.448040	−	0.140491i
$388$	−8.63262	+	2.77114i	−0.438255	+	0.140683i
$389$	−14.5658			−0.738516			−0.369258	−	0.929327i	$-0.620388\pi$
$389$	−14.5658			−0.738516			−0.369258	+	0.929327i	$0.620388\pi$
$390$	0.00594767	+	1.75958i	0.000301172	+	0.0890996i
$391$		−	0.402065i		−	0.0203333i
$392$	−9.24800	−	18.3911i	−0.467094	−	0.928893i
$393$	37.0492	+	5.67253i	1.86888	+	0.286141i
$394$	3.83390	+	24.4869i	0.193149	+	1.23363i
$395$		−	0.404117i		−	0.0203333i
$396$	0.177115	+	26.1988i	0.00890035	+	1.31654i
$397$		−	1.50196i		−	0.0753812i	−0.999289	−	0.0376906i	$-0.988000\pi$
$397$		−	1.50196i		−	0.0753812i	0.999289	−	0.0376906i	$-0.0120001\pi$
$398$	−32.5607	+	5.09802i	−1.63212	+	0.255540i
$399$	−13.4672	−	2.06194i	−0.674204	−	0.103226i
$400$	−16.2078	+	11.6011i	−0.810390	+	0.580056i
$401$		−	21.6674i		−	1.08202i	−0.841016	−	0.541010i	$-0.818042\pi$
$401$		−	21.6674i		−	1.08202i	0.841016	−	0.541010i	$-0.181958\pi$
$402$	−31.4097	+	0.106170i	−1.56658	+	0.00529529i
$403$	42.6919			2.12663
$404$	−7.21800	+	2.31703i	−0.359109	+	0.115277i
$405$	−0.964402	−	0.670761i	−0.0479215	−	0.0333304i
$406$	−46.3063	+	7.25014i	−2.29814	+	0.359819i
$407$	−44.1090			−2.18640
$408$	−0.608369	−	1.87340i	−0.0301188	−	0.0927471i
$409$	7.53712			0.372687			0.186343	−	0.982485i	$-0.440336\pi$
$409$	7.53712			0.372687			0.186343	+	0.982485i	$0.440336\pi$
$410$	0.511900	−	0.0801479i	0.0252809	−	0.00395822i
$411$	−25.6109	−	3.92124i	−1.26329	−	0.193421i
$412$	−4.16335	−	12.9696i	−0.205114	−	0.638968i
$413$	36.5783			1.79990
$414$	−0.627921	+	4.19592i	−0.0308607	+	0.206218i
$415$			0.468646i			0.0230049i
$416$	22.2081	−	21.8182i	1.08884	−	1.06973i
$417$	3.03101	−	19.7965i	0.148429	−	0.969439i
$418$	−12.7002	+	1.98846i	−0.621186	+	0.0972588i
$419$			4.47808i			0.218768i	0.994000	+	0.109384i	$0.0348879\pi$
$419$			4.47808i			0.218768i	−0.994000	+	0.109384i	$0.965112\pi$
$420$	1.68706	−	0.269987i	0.0823199	−	0.0131740i
$421$			8.65241i			0.421693i	0.977519	+	0.210846i	$0.0676220\pi$
$421$			8.65241i			0.421693i	−0.977519	+	0.210846i	$0.932378\pi$
$422$	−3.51649	−	22.4596i	−0.171180	−	1.09332i
$423$	−9.76543	−	3.06212i	−0.474811	−	0.148885i
$424$	−0.427832	−	0.850813i	−0.0207774	−	0.0413191i
$425$			2.00347i			0.0971827i
$426$	−20.0625	+	0.0678147i	−0.972031	+	0.00328563i
$427$	−10.5084			−0.508538
$428$	4.12554	+	12.8518i	0.199415	+	0.621216i
$429$	−6.29950	+	41.1441i	−0.304143	+	1.98646i
$430$	0.0879174	+	0.561524i	0.00423976	+	0.0270791i
$431$	−12.6268			−0.608214			−0.304107	−	0.952638i	$-0.598358\pi$
$431$	−12.6268			−0.608214			−0.304107	+	0.952638i	$0.598358\pi$
$432$	3.42313	+	20.5008i	0.164695	+	0.986345i
$433$	−30.6380			−1.47237			−0.736185	−	0.676781i	$-0.763375\pi$
$433$	−30.6380			−1.47237			−0.736185	+	0.676781i	$0.763375\pi$
$434$	−6.41214	−	40.9540i	−0.307793	−	1.96586i
$435$	0.300104	−	1.96008i	0.0143889	−	0.0939787i
$436$	−11.1996	−	34.8888i	−0.536362	−	1.67087i
$437$	−2.08168			−0.0995804
$438$	−1.02156	+	0.00345303i	−0.0488118	+	0.000164992i
$439$			30.6982i			1.46514i	0.680689	+	0.732572i	$0.261681\pi$
$439$			30.6982i			1.46514i	−0.680689	+	0.732572i	$0.738319\pi$
$440$	1.44022	−	0.724216i	0.0686598	−	0.0345256i
$441$	20.8339	+	6.53283i	0.992091	+	0.311087i
$442$	−0.484059	−	3.09166i	−0.0230243	−	0.147055i
$443$			1.20435i			0.0572206i	0.999591	+	0.0286103i	$0.00910818\pi$
$443$			1.20435i			0.0572206i	−0.999591	+	0.0286103i	$0.990892\pi$
$444$	−34.5531	+	5.52968i	−1.63982	+	0.262427i
$445$		−	1.44930i		−	0.0687034i
$446$	−23.3781	+	3.66030i	−1.10699	+	0.173320i
$447$	−3.44525	+	22.5020i	−0.162955	+	1.06431i
$448$	−24.2656	−	18.0271i	−1.14644	−	0.851698i
$449$		−	30.8882i		−	1.45771i	−0.684670	−	0.728853i	$-0.740054\pi$
$449$		−	30.8882i		−	1.45771i	0.684670	−	0.728853i	$-0.259946\pi$
$450$	3.12891	−	20.9081i	0.147498	−	0.985617i
$451$	12.2567			0.577145
$452$	8.76955	+	27.3188i	0.412485	+	1.28497i
$453$	−1.88596	−	0.288755i	−0.0886099	−	0.0135669i
$454$	7.82676	−	1.22543i	0.367328	−	0.0575124i
$455$	2.71437			0.127252
$456$	−9.69950	+	3.14982i	−0.454221	+	0.147504i
$457$	−2.41262			−0.112858			−0.0564289	−	0.998407i	$-0.517971\pi$
$457$	−2.41262			−0.112858			−0.0564289	+	0.998407i	$0.517971\pi$
$458$	−25.0872	+	3.92789i	−1.17225	+	0.183538i
$459$	1.87592	+	0.919593i	0.0875602	+	0.0429229i
$460$	0.248559	−	0.0797893i	0.0115891	−	0.00372020i
$461$	26.7626			1.24646			0.623230	−	0.782039i	$-0.285820\pi$
$461$	26.7626			1.24646			0.623230	+	0.782039i	$0.285820\pi$
$462$	40.4154	−	0.136611i	1.88030	−	0.00635572i
$463$		−	4.03126i		−	0.187349i	−0.995603	−	0.0936743i	$-0.970139\pi$
$463$		−	4.03126i		−	0.187349i	0.995603	−	0.0936743i	$-0.0298613\pi$
$464$	−28.5289	+	20.4203i	−1.32442	+	0.947987i
$465$	1.73353	+	0.265417i	0.0803904	+	0.0123084i
$466$	34.2745	−	5.36633i	1.58773	−	0.248591i
$467$		−	19.4906i		−	0.901918i	−0.892545	−	0.450959i	$-0.851082\pi$
$467$		−	19.4906i		−	0.901918i	0.892545	−	0.450959i	$-0.148918\pi$
$468$	0.223231	+	33.0203i	0.0103189	+	1.52636i
$469$			48.4535i			2.23738i
$470$	0.0974078	+	0.622138i	0.00449309	+	0.0286971i
$471$	−29.6830	−	4.54470i	−1.36772	−	0.209409i
$472$	24.4615	−	12.3005i	1.12593	−	0.566176i
$473$			13.4448i			0.618195i
$474$	−0.0256344	−	7.58375i	−0.00117743	−	0.348333i
$475$	10.3729			0.475944
$476$	−2.89310	+	0.928708i	−0.132605	+	0.0425673i
$477$	0.963820	+	0.302222i	0.0441303	+	0.0138378i
$478$	0.816310	+	5.21373i	0.0373372	+	0.238470i
$479$	−11.7760			−0.538061			−0.269030	−	0.963132i	$-0.586703\pi$
$479$	−11.7760			−0.538061			−0.269030	+	0.963132i	$0.586703\pi$
$480$	1.03742	−	0.747872i	0.0473514	−	0.0341355i
$481$	−55.5939			−2.53486
$482$	−1.95284	−	12.4727i	−0.0889494	−	0.568115i
$483$	6.46939	+	0.990517i	0.294367	+	0.0450701i
$484$	15.3616	−	4.93121i	0.698256	−	0.224146i
$485$	−0.591705			−0.0268679
$486$	−18.1407	−	12.5265i	−0.822881	−	0.568214i
$487$		−	7.24525i		−	0.328314i	−0.986434	−	0.164157i	$-0.947510\pi$
$487$		−	7.24525i		−	0.328314i	0.986434	−	0.164157i	$-0.0524903\pi$
$488$	−7.02743	+	3.53375i	−0.318117	+	0.159965i
$489$	−2.73726	+	17.8779i	−0.123783	+	0.808468i
$490$	−0.207813	−	1.32729i	−0.00938805	−	0.0599609i
$491$		−	16.2051i		−	0.731328i	−0.930747	−	0.365664i	$-0.880842\pi$
$491$		−	16.2051i		−	0.731328i	0.930747	−	0.365664i	$-0.119158\pi$
$492$	9.60136	−	1.53655i	0.432863	−	0.0692729i
$493$			3.52651i			0.158826i
$494$	−16.0070	+	2.50621i	−0.720189	+	0.112760i
$495$	−0.511589	+	1.63152i	−0.0229942	+	0.0733312i
$496$	−18.0600	−	25.2315i	−0.810919	−	1.13293i
$497$			30.9490i			1.38825i
$498$	0.0297277	+	8.79472i	0.00133213	+	0.394101i
$499$	5.30706			0.237576			0.118788	−	0.992920i	$-0.462099\pi$
$499$	5.30706			0.237576			0.118788	+	0.992920i	$0.462099\pi$
$500$	−2.48135	+	0.796534i	−0.110969	+	0.0356221i
$501$	−0.437799	+	2.85941i	−0.0195594	+	0.127749i
$502$	21.0244	−	3.29178i	0.938366	−	0.146919i
$503$	0.131455			0.00586131			0.00293065	−	0.999996i	$-0.499067\pi$
$503$	0.131455			0.00586131			0.00293065	+	0.999996i	$0.499067\pi$
$504$	31.6426	−	5.17365i	1.40947	−	0.230453i
$505$	−0.494742			−0.0220157
$506$	6.10092	−	0.955218i	0.271219	−	0.0424646i
$507$	−4.53196	+	29.5997i	−0.201272	+	1.31457i
$508$	−8.26408	−	25.7442i	−0.366659	−	1.14221i
$509$	−35.3633			−1.56745			−0.783725	−	0.621108i	$-0.786683\pi$
$509$	−35.3633			−1.56745			−0.783725	+	0.621108i	$0.786683\pi$
$510$	−0.000434513	−	0.128548i	−1.92406e−5	−	0.00569219i
$511$			1.57588i			0.0697129i
$512$	−22.2896	−	3.89548i	−0.985069	−	0.172158i
$513$	4.76118	−	9.71252i	0.210211	−	0.428818i
$514$	−10.9573	+	1.71558i	−0.483307	+	0.0756711i
$515$		−	0.888976i		−	0.0391730i
$516$	1.68550	+	10.5321i	0.0742000	+	0.463651i
$517$			14.8962i			0.655133i
$518$	8.34997	+	53.3308i	0.366877	+	2.34322i
$519$	−2.24183	+	14.6421i	−0.0984055	+	0.642719i
$520$	1.81522	−	0.912784i	0.0796026	−	0.0400282i
$521$			0.362476i			0.0158804i	0.999968	+	0.00794019i	$0.00252747\pi$
$521$			0.362476i			0.0158804i	−0.999968	+	0.00794019i	$0.997473\pi$
$522$	5.50750	−	36.8024i	0.241057	−	1.61080i
$523$	−0.701562			−0.0306772			−0.0153386	−	0.999882i	$-0.504883\pi$
$523$	−0.701562			−0.0306772			−0.0153386	+	0.999882i	$0.504883\pi$
$524$	−13.2281	−	41.2081i	−0.577873	−	1.80018i
$525$	−32.2367	−	4.93571i	−1.40693	−	0.215412i
$526$	−4.07672	−	26.0378i	−0.177754	−	1.13530i
$527$	−3.11890			−0.135862
$528$	26.9816	−	13.6822i	1.17422	−	0.595440i
$529$	1.00000			0.0434783
$530$	−0.00961388	−	0.0614033i	−0.000417600	−	0.00266719i
$531$	−8.68912	+	27.7105i	−0.377076	+	1.20254i
$532$	4.80837	+	14.9790i	0.208469	+	0.649421i
$533$	15.4480			0.669128
$534$	−0.0919336	−	27.1979i	−0.00397836	−	1.17697i
$535$			0.880901i			0.0380847i
$536$	16.2939	+	32.4030i	0.703788	+	1.39960i
$537$	25.2164	+	3.86084i	1.08817	+	0.166608i
$538$	−1.25254	−	7.99990i	−0.0540008	−	0.344900i
$539$		−	31.7800i		−	1.36886i
$540$	−0.196224	+	1.34219i	−0.00844414	+	0.0577588i
$541$		−	8.62101i		−	0.370646i	−0.982678	−	0.185323i	$-0.940667\pi$
$541$		−	8.62101i		−	0.370646i	0.982678	−	0.185323i	$-0.0593332\pi$
$542$	−14.0344	+	2.19736i	−0.602828	+	0.0943845i
$543$	37.1967	+	5.69513i	1.59627	+	0.244401i
$544$	−1.62244	+	1.59395i	−0.0695614	+	0.0683402i
$545$		−	2.39138i		−	0.102435i
$546$	50.9386	−	0.172181i	2.17997	−	0.00736867i
$547$	−7.45918			−0.318931			−0.159466	−	0.987203i	$-0.550977\pi$
$547$	−7.45918			−0.318931			−0.159466	+	0.987203i	$0.550977\pi$
$548$	9.14419	+	28.4859i	0.390620	+	1.21686i
$549$	2.49626	−	7.96084i	0.106538	−	0.339760i
$550$	−30.4007	+	4.75982i	−1.29629	+	0.202959i
$551$	18.2584			0.777836
$552$	4.65945	−	1.51311i	0.198319	−	0.0644024i
$553$	−11.6989			−0.497488
$554$	−17.7295	+	2.77590i	−0.753254	+	0.117937i
$555$	−2.25742	−	0.345630i	−0.0958222	−	0.0146712i
$556$	−22.0187	+	7.06819i	−0.933803	+	0.299758i
$557$	24.0703			1.01989			0.509945	−	0.860207i	$-0.329666\pi$
$557$	24.0703			1.01989			0.509945	+	0.860207i	$0.329666\pi$
$558$	32.5486	+	4.87092i	1.37789	+	0.206203i
$559$			16.9456i			0.716720i
$560$	−1.14827	−	1.60423i	−0.0485231	−	0.0677911i
$561$	0.460217	−	3.00583i	0.0194304	−	0.126906i
$562$	36.1301	−	5.65687i	1.52406	−	0.238620i
$563$			3.51983i			0.148343i	0.997246	+	0.0741715i	$0.0236312\pi$
$563$			3.51983i			0.148343i	−0.997246	+	0.0741715i	$0.976369\pi$
$564$	1.86744	+	11.6690i	0.0786336	+	0.491355i
$565$			1.87251i			0.0787771i
$566$	−4.61354	−	29.4664i	−0.193922	−	1.23857i
$567$	−19.4181	+	27.9188i	−0.815484	+	1.17248i
$568$	10.4075	+	20.6969i	0.436687	+	0.868424i
$569$		−	34.0590i		−	1.42783i	−0.700233	−	0.713914i	$-0.746921\pi$
$569$		−	34.0590i		−	1.42783i	0.700233	−	0.713914i	$-0.253079\pi$
$570$	−0.665554	+	0.00224969i	−0.0278770	+	9.42290e-5i
$571$	−9.16056			−0.383357			−0.191679	−	0.981458i	$-0.561393\pi$
$571$	−9.16056			−0.383357			−0.191679	+	0.981458i	$0.561393\pi$
$572$	45.7627	−	14.6902i	1.91344	−	0.614228i
$573$	2.80819	−	18.3412i	0.117314	−	0.766216i
$574$	−2.32023	−	14.8192i	−0.0968445	−	0.618540i
$575$	−4.98296			−0.207804
$576$	19.4210	−	14.1006i	0.809207	−	0.587523i
$577$	14.7661			0.614720			0.307360	−	0.951593i	$-0.400554\pi$
$577$	14.7661			0.614720			0.307360	+	0.951593i	$0.400554\pi$
$578$	−3.68351	−	23.5264i	−0.153214	−	0.978569i
$579$	3.88413	−	25.3686i	0.161419	−	1.05428i
$580$	−2.18011	+	0.699832i	−0.0905241	+	0.0290589i
$581$	13.5670			0.562853
$582$	−11.1041	+	0.0375337i	−0.460279	+	0.00155582i
$583$		−	1.47021i		−	0.0608899i
$584$	0.529934	+	1.05386i	0.0219288	+	0.0436090i
$585$	−0.644795	+	2.05632i	−0.0266590	+	0.0850184i
$586$	−3.84625	−	24.5658i	−0.158887	−	1.01480i
$587$			0.974726i			0.0402313i	0.999798	+	0.0201156i	$0.00640344\pi$
$587$			0.974726i			0.0402313i	−0.999798	+	0.0201156i	$0.993597\pi$
$588$	−3.98407	−	24.8951i	−0.164300	−	1.02666i
$589$			16.1481i			0.665370i
$590$	1.76539	−	0.276406i	0.0726800	−	0.0113795i
$591$	−4.59415	+	30.0059i	−0.188978	+	1.23428i
$592$	23.5180	+	32.8567i	0.966583	+	1.35040i
$593$			20.2807i			0.832828i	0.909175	+	0.416414i	$0.136713\pi$
$593$			20.2807i			0.832828i	−0.909175	+	0.416414i	$0.863287\pi$
$594$	−9.49712	+	30.6499i	−0.389672	+	1.25758i
$595$	−0.198301			−0.00812956
$596$	25.0280	−	8.03419i	1.02519	−	0.329093i
$597$	−39.8995	−	6.10894i	−1.63298	−	0.250022i
$598$	7.68945	−	1.20393i	0.314445	−	0.0492325i
$599$	−31.5805			−1.29034			−0.645172	−	0.764037i	$-0.723214\pi$
$599$	−31.5805			−1.29034			−0.645172	+	0.764037i	$0.723214\pi$
$600$	−23.2179	+	7.53979i	−0.947866	+	0.307810i
$601$	7.95503			0.324492			0.162246	−	0.986750i	$-0.448126\pi$
$601$	7.95503			0.324492			0.162246	+	0.986750i	$0.448126\pi$
$602$	16.2557	−	2.54515i	0.662535	−	0.103733i
$603$	−36.7069	−	11.5101i	−1.49482	−	0.468726i
$604$	0.673367	+	2.09766i	0.0273989	+	0.0853527i
$605$	1.05293			0.0428077
$606$	−9.28446	+	0.0313831i	−0.377155	+	0.00127485i
$607$		−	5.15628i		−	0.209287i	−0.994510	−	0.104643i	$-0.966630\pi$
$607$		−	5.15628i		−	0.209287i	0.994510	−	0.104643i	$-0.0333701\pi$
$608$	8.25267	+	8.40014i	0.334690	+	0.340671i
$609$	−56.7430	−	8.68782i	−2.29934	−	0.352048i
$610$	−0.507171	+	0.0794075i	−0.0205348	+	0.00321512i
$611$			18.7748i			0.759546i
$612$	−0.0163084	−	2.41233i	−0.000659227	−	0.0975127i
$613$		−	34.3625i		−	1.38789i	−0.720029	−	0.693944i	$-0.755871\pi$
$613$		−	34.3625i		−	1.38789i	0.720029	−	0.693944i	$-0.244129\pi$
$614$	2.63582	+	16.8348i	0.106373	+	0.679398i
$615$	0.627275	+	0.0960410i	0.0252942	+	0.00387275i
$616$	−20.9656	−	41.6934i	−0.844727	−	1.67988i
$617$			0.319112i			0.0128470i	0.999979	+	0.00642349i	$0.00204467\pi$
$617$			0.319112i			0.0128470i	−0.999979	+	0.00642349i	$0.997955\pi$
$618$	−0.0563905	−	16.6827i	−0.00226836	−	0.671078i
$619$	1.90822			0.0766978			0.0383489	−	0.999264i	$-0.487790\pi$
$619$	1.90822			0.0766978			0.0383489	+	0.999264i	$0.487790\pi$
$620$	−0.618943	−	1.92812i	−0.0248573	−	0.0774353i
$621$	−2.28718	+	4.66571i	−0.0917812	+	0.187228i
$622$	1.95158	+	12.4646i	0.0782513	+	0.499787i
$623$	−41.9563			−1.68094
$624$	34.0069	−	17.2447i	1.36137	−	0.690340i
$625$	24.7447			0.989789
$626$	−0.105346	−	0.672837i	−0.00421046	−	0.0268920i
$627$	−15.5626	−	2.38277i	−0.621512	−	0.0951585i
$628$	10.5981	+	33.0150i	0.422909	+	1.31744i
$629$	4.06147			0.161942
$630$	2.06946	+	0.309696i	0.0824492	+	0.0123386i
$631$			37.3783i			1.48801i	0.668175	+	0.744004i	$0.267076\pi$
$631$			37.3783i			1.48801i	−0.668175	+	0.744004i	$0.732924\pi$
$632$	−7.82357	+	3.93409i	−0.311205	+	0.156490i
$633$	4.21380	−	27.5217i	0.167484	−	1.09389i
$634$	1.41475	+	9.03593i	0.0561869	+	0.358863i
$635$		−	1.76458i		−	0.0700252i
$636$	−0.184312	−	1.15170i	−0.00730843	−	0.0456679i
$637$		−	40.0547i		−	1.58703i
$638$	−53.5112	+	8.37822i	−2.11853	+	0.331697i
$639$	−23.4459	−	7.35188i	−0.927507	−	0.290836i
$640$	−1.30736	−	0.686681i	−0.0516780	−	0.0271435i
$641$			20.2501i			0.799831i	0.916552	+	0.399915i	$0.130961\pi$
$641$			20.2501i			0.799831i	−0.916552	+	0.399915i	$0.869039\pi$
$642$	0.0558783	+	16.5312i	0.00220534	+	0.652435i
$643$	−28.2916			−1.11571			−0.557856	−	0.829938i	$-0.688376\pi$
$643$	−28.2916			−1.11571			−0.557856	+	0.829938i	$0.688376\pi$
$644$	−2.30985	−	7.19561i	−0.0910208	−	0.283547i
$645$	−0.105351	+	0.688083i	−0.00414820	+	0.0270933i
$646$	1.16941	−	0.183094i	0.0460098	−	0.00720372i
$647$	47.8762			1.88221			0.941104	−	0.338118i	$-0.109790\pi$
$647$	47.8762			1.88221			0.941104	+	0.338118i	$0.109790\pi$
$648$	−3.59725	+	25.2004i	−0.141313	+	0.989965i
$649$	42.2696			1.65923
$650$	−38.3163	+	5.99915i	−1.50289	+	0.235306i
$651$	7.68365	−	50.1845i	0.301146	−	1.96688i
$652$	19.8848	−	6.38318i	0.778749	−	0.249985i
$653$	−9.67576			−0.378642			−0.189321	−	0.981915i	$-0.560629\pi$
$653$	−9.67576			−0.378642			−0.189321	+	0.981915i	$0.560629\pi$
$654$	−0.151693	−	44.8772i	−0.00593165	−	1.75484i
$655$		−	2.82452i		−	0.110363i
$656$	−6.53500	−	9.12998i	−0.255149	−	0.356466i
$657$	−1.19384	−	0.374348i	−0.0465760	−	0.0146047i
$658$	18.0105	−	2.81989i	0.702122	−	0.109931i
$659$			18.2791i			0.712052i	0.934476	+	0.356026i	$0.115869\pi$
$659$			18.2791i			0.712052i	−0.934476	+	0.356026i	$0.884131\pi$
$660$	1.94955	−	0.311995i	0.0758861	−	0.0121444i
$661$		−	1.38156i		−	0.0537364i	−0.999639	−	0.0268682i	$-0.991447\pi$
$661$		−	1.38156i		−	0.0537364i	0.999639	−	0.0268682i	$-0.00855344\pi$
$662$	−5.49337	−	35.0859i	−0.213506	−	1.36365i
$663$	0.580046	−	3.78847i	0.0225271	−	0.147132i
$664$	9.07283	−	4.56228i	0.352094	−	0.177051i
$665$			1.02670i			0.0398138i
$666$	−42.3852	−	6.34298i	−1.64239	−	0.245785i
$667$	−8.77100			−0.339615
$668$	3.18039	−	1.02093i	0.123053	−	0.0395010i
$669$	−28.6472	−	4.38613i	−1.10757	−	0.169578i
$670$	0.366142	+	2.33853i	0.0141453	+	0.0903453i
$671$	−12.1435			−0.468793
$672$	−21.6504	−	30.0325i	−0.835182	−	1.15853i
$673$	−21.5643			−0.831243			−0.415621	−	0.909538i	$-0.636436\pi$
$673$	−21.5643			−0.831243			−0.415621	+	0.909538i	$0.636436\pi$
$674$	2.19452	+	14.0163i	0.0845299	+	0.539887i
$675$	11.3969	−	23.2490i	0.438668	−	0.894856i
$676$	32.9224	−	10.5684i	1.26625	−	0.406476i
$677$	−24.7287			−0.950401			−0.475201	−	0.879878i	$-0.657624\pi$
$677$	−24.7287			−0.950401			−0.475201	+	0.879878i	$0.657624\pi$
$678$	0.118779	+	35.1400i	0.00456169	+	1.34954i
$679$			17.1295i			0.657368i
$680$	−0.132613	+	0.0666844i	−0.00508547	+	0.00255723i
$681$	9.59081	+	1.46843i	0.367520	+	0.0562704i
$682$	−7.40983	−	47.3262i	−0.283737	−	1.81221i
$683$			35.4360i			1.35592i	0.735098	+	0.677961i	$0.237136\pi$
$683$			35.4360i			1.35592i	−0.735098	+	0.677961i	$0.762864\pi$
$684$	−12.4898	+	0.0844364i	−0.477560	+	0.00322851i
$685$			1.95250i			0.0746013i
$686$	−1.46792	+	0.229832i	−0.0560455	+	0.00877502i
$687$	−30.7415	−	4.70677i	−1.17286	−	0.179575i
$688$	10.0150	−	7.16850i	0.381820	−	0.273297i
$689$		−	1.85302i		−	0.0705943i
$690$	0.319719	−	0.00108071i	0.0121715	−	4.11418e-5i
$691$	47.3180			1.80006			0.900032	−	0.435824i	$-0.143543\pi$
$691$	47.3180			1.80006			0.900032	+	0.435824i	$0.143543\pi$
$692$	16.2858	−	5.22787i	0.619093	−	0.198734i
$693$	47.2313	+	14.8102i	1.79417	+	0.562592i
$694$	17.3338	−	2.71394i	0.657982	−	0.103020i
$695$	−1.50923			−0.0572483
$696$	−40.8681	+	13.2715i	−1.54910	+	0.503056i
$697$	−1.12857			−0.0427477
$698$	25.1090	−	3.93131i	0.950391	−	0.148802i
$699$	41.9995	+	6.43046i	1.58857	+	0.243222i
$700$	11.5099	+	35.8554i	0.435033	+	1.35521i
$701$	30.6619			1.15808			0.579042	−	0.815298i	$-0.303427\pi$
$701$	30.6619			1.15808			0.579042	+	0.815298i	$0.303427\pi$
$702$	−11.9699	+	38.6303i	−0.451776	+	1.45801i
$703$		−	21.0282i		−	0.793094i
$704$	−28.0412	−	20.8320i	−1.05684	−	0.785134i
$705$	−0.116724	+	0.762360i	−0.00439606	+	0.0287121i
$706$	35.7302	−	5.59426i	1.34473	−	0.210543i
$707$			14.3225i			0.538652i
$708$	33.1122	−	5.29909i	1.24443	−	0.199152i
$709$			19.6131i			0.736586i	0.929710	+	0.368293i	$0.120058\pi$
$709$			19.6131i			0.736586i	−0.929710	+	0.368293i	$0.879942\pi$
$710$	0.233868	+	1.49370i	0.00877690	+	0.0560576i
$711$	2.77906	−	8.86272i	0.104223	−	0.332378i
$712$	−28.0580	+	14.1090i	−1.05152	+	0.528756i
$713$		−	7.75722i		−	0.290510i
$714$	−3.72137	+	0.0125789i	−0.139269	+	0.000470753i
$715$	3.13671			0.117306
$716$	−9.00334	−	28.0471i	−0.336471	−	1.04817i
$717$	−0.978182	+	6.38883i	−0.0365309	+	0.238595i
$718$	4.50552	+	28.7765i	0.168144	+	1.07393i
$719$	42.9444			1.60156			0.800778	−	0.598961i	$-0.204420\pi$
$719$	42.9444			1.60156			0.800778	+	0.598961i	$0.204420\pi$
$720$	1.48808	−	0.488807i	0.0554575	−	0.0182168i
$721$	−25.7353			−0.958432
$722$	3.20843	+	20.4920i	0.119405	+	0.762635i
$723$	2.34008	−	15.2838i	0.0870285	−	0.568412i
$724$	−13.2808	−	41.3722i	−0.493578	−	1.53759i
$725$	43.7056			1.62318
$726$	19.7596	−	0.0667907i	0.733346	−	0.00247884i
$727$			51.8477i			1.92292i	0.274937	+	0.961462i	$0.411343\pi$
$727$			51.8477i			1.92292i	−0.274937	+	0.961462i	$0.588657\pi$
$728$	−26.4245	−	52.5494i	−0.979357	−	1.94761i
$729$	−16.5376	−	21.3426i	−0.612505	−	0.790466i
$730$	0.0119082	+	0.0760573i	0.000440744	+	0.00281501i
$731$		−	1.23798i		−	0.0457882i
$732$	−9.51266	+	1.52235i	−0.351598	+	0.0562678i
$733$		−	25.2940i		−	0.934254i	−0.884190	−	0.467127i	$-0.845289\pi$
$733$		−	25.2940i		−	0.934254i	0.884190	−	0.467127i	$-0.154711\pi$
$734$	−1.39085	+	0.217765i	−0.0513373	+	0.00803786i
$735$	0.249022	−	1.62644i	0.00918532	−	0.0599923i
$736$	−3.96442	−	4.03526i	−0.146131	−	0.148742i
$737$			55.9926i			2.06251i
$738$	11.7777	+	1.76254i	0.433543	+	0.0648800i
$739$	2.11141			0.0776696			0.0388348	−	0.999246i	$-0.487635\pi$
$739$	2.11141			0.0776696			0.0388348	+	0.999246i	$0.487635\pi$
$740$	0.805995	+	2.51083i	0.0296290	+	0.0922998i
$741$	−19.6148	−	3.00318i	−0.720566	−	0.110325i
$742$	−1.77759	+	0.278316i	−0.0652572	+	0.0102173i
$743$	−6.40799			−0.235087			−0.117543	−	0.993068i	$-0.537502\pi$
$743$	−6.40799			−0.235087			−0.117543	+	0.993068i	$0.537502\pi$
$744$	−11.7375	−	36.1444i	−0.430319	−	1.32512i
$745$	1.71549			0.0628508
$746$	27.8029	−	4.35308i	1.01793	−	0.159377i
$747$	−3.22282	+	10.2779i	−0.117917	+	0.376049i
$748$	−3.34325	+	1.07321i	−0.122241	+	0.0392404i
$749$	25.5015			0.931805
$750$	−3.19175	+	0.0107886i	−0.116546	+	0.000393946i
$751$		−	24.3046i		−	0.886888i	−0.896302	−	0.443444i	$-0.853756\pi$
$751$		−	24.3046i		−	0.886888i	0.896302	−	0.443444i	$-0.146244\pi$
$752$	11.0961	−	7.94232i	0.404634	−	0.289627i
$753$	25.7630	+	3.94453i	0.938857	+	0.143747i
$754$	−67.4442	+	10.5597i	−2.45617	+	0.384562i
$755$			0.143780i			0.00523269i
$756$	38.8556	+	5.68056i	1.41317	+	0.206600i
$757$		−	18.6833i		−	0.679054i	−0.940596	−	0.339527i	$-0.889733\pi$
$757$		−	18.6833i		−	0.679054i	0.940596	−	0.339527i	$-0.110267\pi$
$758$	3.00741	+	19.2082i	0.109234	+	0.697673i
$759$	7.47599	+	1.14463i	0.271361	+	0.0415476i
$760$	0.345258	+	0.686601i	0.0125238	+	0.0249056i
$761$			30.2497i			1.09655i	0.836297	+	0.548276i	$0.184716\pi$
$761$			30.2497i			1.09655i	−0.836297	+	0.548276i	$0.815284\pi$
$762$	−0.111933	−	33.1145i	−0.00405490	−	1.19961i
$763$	−69.2288			−2.50625
$764$	−20.4001	+	6.54860i	−0.738050	+	0.236920i
$765$	0.0471062	−	0.150227i	0.00170313	−	0.00543146i
$766$	−1.21912	−	7.78648i	−0.0440488	−	0.281337i
$767$	53.2756			1.92367
$768$	−24.5778	−	12.8035i	−0.886876	−	0.462007i
$769$	47.4784			1.71211			0.856057	−	0.516882i	$-0.172907\pi$
$769$	47.4784			1.71211			0.856057	+	0.516882i	$0.172907\pi$
$770$	−0.471121	−	3.00902i	−0.0169780	−	0.108438i
$771$	−13.4270	−	2.05578i	−0.483560	−	0.0740370i
$772$	−28.2163	+	9.05765i	−1.01553	+	0.325992i
$773$	30.2729			1.08884			0.544421	−	0.838812i	$-0.316750\pi$
$773$	30.2729			1.08884			0.544421	+	0.838812i	$0.316750\pi$
$774$	−1.93340	+	12.9194i	−0.0694946	+	0.464379i
$775$			38.6539i			1.38849i
$776$	5.76026	+	11.4552i	0.206781	+	0.411218i
$777$	−10.0057	+	65.3508i	−0.358954	+	2.34445i
$778$	3.18638	+	20.3512i	0.114237	+	0.729627i
$779$			5.84316i			0.209353i
$780$	2.45716	−	0.393231i	0.0879806	−	0.0140799i
$781$			35.7644i			1.27975i
$782$	−0.561761	+	0.0879546i	−0.0200885	+	0.00314525i
$783$	20.0608	−	40.9229i	0.716916	−	1.46247i
$784$	−23.6729	+	16.9444i	−0.845460	+	0.605158i
$785$			2.26294i			0.0807679i
$786$	−0.179168	−	53.0057i	−0.00639072	−	1.89065i
$787$	−11.7940			−0.420411			−0.210205	−	0.977657i	$-0.567413\pi$
$787$	−11.7940			−0.420411			−0.210205	+	0.977657i	$0.567413\pi$
$788$	33.3742	−	10.7134i	1.18891	−	0.381649i
$789$	4.88512	−	31.9064i	0.173915	−	1.13590i
$790$	−0.564629	+	0.0884036i	−0.0200886	+	0.00314526i
$791$	54.2079			1.92741
$792$	36.5660	−	5.97864i	1.29931	−	0.212442i
$793$	−15.3053			−0.543508
$794$	−2.09853	+	0.328565i	−0.0744739	+	0.0116603i
$795$	0.0115203	−	0.0752428i	0.000408582	−	0.00266859i
$796$	14.2458	+	44.3784i	0.504929	+	1.57295i
$797$	13.6252			0.482629			0.241314	−	0.970447i	$-0.422421\pi$
$797$	13.6252			0.482629			0.241314	+	0.970447i	$0.422421\pi$
$798$	0.0651269	+	19.2674i	0.00230547	+	0.682057i
$799$		−	1.37161i		−	0.0485241i
$800$	19.7546	+	20.1076i	0.698429	+	0.710910i
$801$	9.96664	−	31.7847i	0.352154	−	1.12306i
$802$	−30.2735	+	4.73991i	−1.06900	+	0.167372i
$803$			1.82108i			0.0642645i
$804$	7.01946	+	43.8622i	0.247557	+	1.54690i
$805$		−	0.493208i		−	0.0173833i
$806$	−9.33917	−	59.6488i	−0.328958	−	2.10104i
$807$	1.50091	−	9.80297i	0.0528347	−	0.345081i
$808$	4.81633	+	9.57806i	0.169438	+	0.336955i
$809$			5.37668i			0.189034i	0.995523	+	0.0945170i	$0.0301307\pi$
$809$			5.37668i			0.189034i	−0.995523	+	0.0945170i	$0.969869\pi$
$810$	−0.726212	+	1.49419i	−0.0255165	+	0.0525004i
$811$	−20.2058			−0.709521			−0.354761	−	0.934957i	$-0.615438\pi$
$811$	−20.2058			−0.709521			−0.354761	+	0.934957i	$0.615438\pi$
$812$	20.2597	+	63.1127i	0.710975	+	2.21482i
$813$	−17.1975	−	2.63308i	−0.603144	−	0.0923463i
$814$	9.64918	+	61.6288i	0.338203	+	2.16009i
$815$	1.36296			0.0477425
$816$	−2.48441	+	1.25983i	−0.0869719	+	0.0441028i
$817$	−6.40960			−0.224244
$818$	−1.64880	−	10.5308i	−0.0576490	−	0.368201i
$819$	59.5291	+	18.6664i	2.08012	+	0.652256i
$820$	−0.223964	−	0.697690i	−0.00782116	−	0.0243644i
$821$	−26.7962			−0.935193			−0.467596	−	0.883942i	$-0.654880\pi$
$821$	−26.7962			−0.935193			−0.467596	+	0.883942i	$0.654880\pi$
$822$	0.123853	+	36.6412i	0.00431988	+	1.27801i
$823$		−	1.87513i		−	0.0653629i	−0.999466	−	0.0326815i	$-0.989595\pi$
$823$		−	1.87513i		−	0.0653629i	0.999466	−	0.0326815i	$-0.0104047\pi$
$824$	−17.2103	+	8.65421i	−0.599549	+	0.301484i
$825$	−37.2526	−	5.70367i	−1.29697	−	0.198576i
$826$	−8.00178	−	51.1069i	−0.278417	−	1.77824i
$827$		−	53.8718i		−	1.87331i	−0.350260	−	0.936653i	$-0.613907\pi$
$827$		−	53.8718i		−	1.87331i	0.350260	−	0.936653i	$-0.386093\pi$
$828$	5.99986	−	0.0405616i	0.208510	−	0.00140961i
$829$			36.9767i			1.28425i	0.766599	+	0.642127i	$0.221948\pi$
$829$			36.9767i			1.28425i	−0.766599	+	0.642127i	$0.778052\pi$
$830$	0.654788	−	0.102520i	0.0227280	−	0.00355851i
$831$	−21.7255	−	3.32635i	−0.753648	−	0.115390i
$832$	−35.3424	−	26.2561i	−1.22528	−	0.910266i
$833$			2.92624i			0.101388i
$834$	−28.3226	+	0.0957351i	−0.980730	+	0.00331504i
$835$	0.217993			0.00754396
$836$	5.55652	+	17.3096i	0.192176	+	0.598665i
$837$	36.1929	+	17.7421i	1.25101	+	0.613258i
$838$	6.25673	−	0.979613i	0.216135	−	0.0338402i
$839$	12.1566			0.419693			0.209847	−	0.977734i	$-0.432704\pi$
$839$	12.1566			0.419693			0.209847	+	0.977734i	$0.432704\pi$
$840$	−0.746279	−	2.29808i	−0.0257491	−	0.0792912i
$841$	47.9305			1.65278
$842$	12.0891	−	1.89278i	0.416617	−	0.0652295i
$843$	44.2733	+	6.77860i	1.52485	+	0.233468i
$844$	−30.6111	+	9.82642i	−1.05368	+	0.338239i
$845$	2.25660			0.0776294
$846$	−2.14210	+	14.3140i	−0.0736471	+	0.492127i
$847$		−	30.4817i		−	1.04736i
$848$	−1.09516	+	0.783885i	−0.0376079	+	0.0269187i
$849$	5.52840	−	36.1078i	0.189734	−	1.23922i
$850$	2.79924	−	0.438275i	0.0960130	−	0.0150327i
$851$			10.1015i			0.346277i
$852$	4.48357	+	28.0163i	0.153605	+	0.959823i
$853$		−	19.4838i		−	0.667114i	−0.942730	−	0.333557i	$-0.891751\pi$
$853$		−	19.4838i		−	0.667114i	0.942730	−	0.333557i	$-0.108249\pi$
$854$	2.29879	+	14.6823i	0.0786631	+	0.502417i
$855$	−0.777797	−	0.243891i	−0.0266001	−	0.00834091i
$856$	17.0540	−	8.57560i	0.582893	−	0.293108i
$857$		−	23.9656i		−	0.818649i	−0.912389	−	0.409324i	$-0.865764\pi$
$857$		−	23.9656i		−	0.818649i	0.912389	−	0.409324i	$-0.134236\pi$
$858$	58.8643	−	0.198971i	2.00959	−	0.00679277i
$859$	−3.22143			−0.109914			−0.0549568	−	0.998489i	$-0.517502\pi$
$859$	−3.22143			−0.109914			−0.0549568	+	0.998489i	$0.517502\pi$
$860$	0.765324	−	0.245675i	0.0260973	−	0.00837745i
$861$	2.78032	−	18.1592i	0.0947532	−	0.618864i
$862$	2.76222	+	17.6421i	0.0940815	+	0.600893i
$863$	28.5105			0.970509			0.485255	−	0.874373i	$-0.338727\pi$
$863$	28.5105			0.970509			0.485255	+	0.874373i	$0.338727\pi$
$864$	27.8947	−	9.26746i	0.948997	−	0.315286i
$865$	1.11627			0.0379545
$866$	6.70230	+	42.8072i	0.227753	+	1.45465i
$867$	4.41394	−	28.8289i	0.149905	−	0.979081i
$868$	−55.8179	+	17.9180i	−1.89458	+	0.608176i
$869$	−13.5192			−0.458607
$870$	−2.80426	+	0.00947887i	−0.0950733	+	0.000321364i
$871$			70.5717i			2.39123i
$872$	−46.2963	+	23.2801i	−1.56779	+	0.788365i
$873$	−12.9767	−	4.06908i	−0.439196	−	0.137717i
$874$	0.455384	+	2.90851i	0.0154036	+	0.0983818i
$875$			4.92368i			0.166451i
$876$	0.228298	+	1.42655i	0.00771346	+	0.0481988i
$877$			26.6860i			0.901123i	0.892746	+	0.450561i	$0.148776\pi$
$877$			26.6860i			0.901123i	−0.892746	+	0.450561i	$0.851224\pi$
$878$	42.8913	−	6.71546i	1.44751	−	0.226636i
$879$	4.60894	−	30.1025i	0.155456	−	1.01533i
$880$	−1.32693	−	1.85384i	−0.0447307	−	0.0624928i
$881$			7.40195i			0.249378i	0.992196	+	0.124689i	$0.0397933\pi$
$881$			7.40195i			0.249378i	−0.992196	+	0.124689i	$0.960207\pi$
$882$	4.57004	−	30.5381i	0.153881	−	1.02827i
$883$	−7.09453			−0.238750			−0.119375	−	0.992849i	$-0.538089\pi$
$883$	−7.09453			−0.238750			−0.119375	+	0.992849i	$0.538089\pi$
$884$	−4.21375	+	1.35265i	−0.141724	+	0.0454944i
$885$	2.16329	+	0.331217i	0.0727180	+	0.0111337i
$886$	1.68271	−	0.263461i	0.0565319	−	0.00885116i
$887$	27.4157			0.920529			0.460264	−	0.887782i	$-0.347755\pi$
$887$	27.4157			0.920529			0.460264	+	0.887782i	$0.347755\pi$
$888$	15.2848	+	47.0677i	0.512924	+	1.57949i
$889$	−51.0834			−1.71328
$890$	−2.02495	+	0.317045i	−0.0678764	+	0.0106274i
$891$	−22.4394	+	32.2628i	−0.751749	+	1.08084i
$892$	10.2283	+	31.8630i	0.342468	+	1.06685i
$893$	−7.10150			−0.237643
$894$	32.1933	−	0.108819i	1.07671	−	0.00363945i
$895$		−	1.92243i		−	0.0642597i
$896$	−19.8790	+	37.8473i	−0.664110	+	1.26439i
$897$	9.42255	+	1.44267i	0.314610	+	0.0481693i
$898$	−43.1568	+	6.75703i	−1.44016	+	0.225485i
$899$			68.0386i			2.26921i
$900$	−29.8971	+	0.202117i	−0.996570	+	0.00673723i
$901$			0.135374i			0.00450997i
$902$	−2.68124	−	17.1249i	−0.0892756	−	0.570198i
$903$	19.9196	+	3.04985i	0.662881	+	0.101493i
$904$	36.2512	−	18.2289i	1.20570	−	0.606285i
$905$		−	2.83577i		−	0.0942643i
$906$	0.00912041	+	2.69821i	0.000303005	+	0.0896420i
$907$	17.7447			0.589203			0.294601	−	0.955620i	$-0.404813\pi$
$907$	17.7447			0.589203			0.294601	+	0.955620i	$0.404813\pi$
$908$	−3.42433	−	10.6674i	−0.113640	−	0.354011i
$909$	−10.8502	−	3.40228i	−0.359880	−	0.112846i
$910$	−0.593789	−	3.79250i	−0.0196839	−	0.125720i
$911$	−40.5517			−1.34354			−0.671769	−	0.740761i	$-0.734465\pi$
$911$	−40.5517			−1.34354			−0.671769	+	0.740761i	$0.734465\pi$
$912$	6.52274	+	12.8630i	0.215990	+	0.425937i
$913$	15.6779			0.518864
$914$	0.527779	+	3.37090i	0.0174574	+	0.111499i
$915$	−0.621481	−	0.0951538i	−0.0205455	−	0.00314569i
$916$	10.9760	+	34.1924i	0.362658	+	1.12975i
$917$	−81.7681			−2.70022
$918$	0.874477	−	2.82218i	0.0288620	−	0.0931459i
$919$		−	42.2700i		−	1.39436i	−0.716896	−	0.697180i	$-0.754438\pi$
$919$		−	42.2700i		−	1.39436i	0.716896	−	0.697180i	$-0.245562\pi$
$920$	−0.165855	−	0.329830i	−0.00546808	−	0.0108742i
$921$	−3.15849	+	20.6291i	−0.104076	+	0.679753i
$922$	−5.85452	−	37.3925i	−0.192808	−	1.23146i
$923$			45.0766i			1.48371i
$924$	−9.03205	−	56.4382i	−0.297133	−	1.85668i
$925$		−	50.3356i		−	1.65503i
$926$	−5.63245	+	0.881869i	−0.185094	+	0.0289800i
$927$	6.11337	−	19.4962i	0.200789	−	0.640340i
$928$	34.7720	+	35.3933i	1.14145	+	1.16184i
$929$			28.1066i			0.922147i	0.887362	+	0.461073i	$0.152536\pi$
$929$			28.1066i			0.922147i	−0.887362	+	0.461073i	$0.847464\pi$
$930$	−0.00838327	−	2.48013i	−0.000274898	−	0.0813267i
$931$	15.1506			0.496540
$932$	−14.9956	−	46.7141i	−0.491197	−	1.53017i
$933$	−2.33858	+	15.2740i	−0.0765615	+	0.500049i
$934$	−27.2321	+	4.26372i	−0.891062	+	0.139513i
$935$	−0.229156			−0.00749420
$936$	46.0868	−	7.53533i	1.50639	−	0.246300i
$937$	19.6450			0.641773			0.320887	−	0.947118i	$-0.396019\pi$
$937$	19.6450			0.641773			0.320887	+	0.947118i	$0.396019\pi$
$938$	67.6989	−	10.5996i	2.21045	−	0.346088i
$939$	0.126235	−	0.824485i	0.00411954	−	0.0269061i
$940$	0.847938	−	0.272195i	0.0276567	−	0.00887802i
$941$	39.9096			1.30101			0.650507	−	0.759500i	$-0.274556\pi$
$941$	39.9096			1.30101			0.650507	+	0.759500i	$0.274556\pi$
$942$	0.143546	+	42.4670i	0.00467697	+	1.38365i
$943$		−	2.80694i		−	0.0914066i
$944$	−22.5373	−	31.4866i	−0.733526	−	1.02480i
$945$	2.30116	+	1.12805i	0.0748568	+	0.0366956i
$946$	18.7850	−	2.94116i	0.610754	−	0.0956254i
$947$		−	40.6728i		−	1.32169i	−0.750523	−	0.660845i	$-0.770198\pi$
$947$		−	40.6728i		−	1.32169i	0.750523	−	0.660845i	$-0.229802\pi$
$948$	−10.5904	+	1.69482i	−0.343959	+	0.0550452i
$949$			2.29524i			0.0745067i
$950$	−2.26916	−	14.4930i	−0.0736213	−	0.470215i
$951$	−1.69529	+	11.0725i	−0.0549736	+	0.359051i
$952$	1.93047	+	3.83905i	0.0625669	+	0.124424i
$953$		−	10.4493i		−	0.338484i	−0.985574	−	0.169242i	$-0.945868\pi$
$953$		−	10.4493i		−	0.338484i	0.985574	−	0.169242i	$-0.0541320\pi$
$954$	0.211420	−	1.41276i	0.00684496	−	0.0457396i
$955$	−1.39828			−0.0452474
$956$	7.10600	−	2.28108i	0.229825	−	0.0737755i
$957$	−65.5719	−	10.0396i	−2.11964	−	0.324534i
$958$	2.57610	+	16.4534i	0.0832299	+	0.531585i
$959$	56.5237			1.82525
$960$	−1.27186	−	1.28587i	−0.0410492	−	0.0415012i
$961$	−29.1744			−0.941111
$962$	12.1616	+	77.6753i	0.392105	+	2.50435i
$963$	−6.05784	+	19.3191i	−0.195211	+	0.622550i
$964$	−16.9995	+	5.45698i	−0.547517	+	0.175758i
$965$	−1.93403			−0.0622585
$966$	−0.0312857	−	9.25566i	−0.00100660	−	0.297796i
$967$			10.6501i			0.342484i	0.985229	+	0.171242i	$0.0547779\pi$
$967$			10.6501i			0.342484i	−0.985229	+	0.171242i	$0.945222\pi$
$968$	−10.2503	−	20.3844i	−0.329458	−	0.655180i
$969$	1.43298	+	0.219401i	0.0460339	+	0.00704816i
$970$	0.129440	+	0.826725i	0.00415606	+	0.0265445i
$971$			27.4861i			0.882070i	0.897490	+	0.441035i	$0.145389\pi$
$971$			27.4861i			0.882070i	−0.897490	+	0.441035i	$0.854611\pi$
$972$	−13.5335	+	28.0864i	−0.434087	+	0.900871i
$973$			43.6912i			1.40068i
$974$	−10.1230	+	1.58495i	−0.324362	+	0.0507852i
$975$	−46.9522	−	7.18877i	−1.50367	−	0.230225i
$976$	6.47463	+	9.04564i	0.207248	+	0.289544i
$977$		−	49.0762i		−	1.57009i	−0.619441	−	0.785043i	$-0.712641\pi$
$977$		−	49.0762i		−	1.57009i	0.619441	−	0.785043i	$-0.287359\pi$
$978$	25.5777	−	0.0864569i	0.817884	−	0.00276459i
$979$	−48.4844			−1.54957
$980$	−1.80902	+	0.580710i	−0.0577870	+	0.0185501i
$981$	16.4452	−	52.4455i	0.525055	−	1.67446i
$982$	−22.6417	+	3.54500i	−0.722525	+	0.113125i
$983$	26.9525			0.859651			0.429825	−	0.902912i	$-0.358575\pi$
$983$	26.9525			0.859651			0.429825	+	0.902912i	$0.358575\pi$
$984$	−4.24722	−	13.0788i	−0.135396	−	0.416937i
$985$	2.28756			0.0728879
$986$	4.92721	−	0.771450i	0.156914	−	0.0245680i
$987$	22.0698	+	3.37907i	0.702490	+	0.107557i
$988$	7.00330	+	21.8166i	0.222805	+	0.694078i
$989$	3.07905			0.0979080
$990$	2.39145	+	0.357882i	0.0760054	+	0.0113743i
$991$		−	44.4537i		−	1.41212i	−0.708153	−	0.706059i	$-0.750471\pi$
$991$		−	44.4537i		−	1.41212i	0.708153	−	0.706059i	$-0.249529\pi$
$992$	−31.3024	+	30.7529i	−0.993853	+	0.976405i
$993$	6.58269	−	42.9937i	0.208895	−	1.36437i
$994$	43.2416	−	6.77032i	1.37154	−	0.214741i
$995$			3.04182i			0.0964323i
$996$	12.2814	−	1.96545i	0.389151	−	0.0622776i
$997$		−	10.5458i		−	0.333989i	−0.985958	−	0.166994i	$-0.946594\pi$
$997$		−	10.5458i		−	0.333989i	0.985958	−	0.166994i	$-0.0534062\pi$
$998$	−1.16096	−	7.41498i	−0.0367495	−	0.234717i
$999$	−47.1308	−	23.1040i	−1.49115	−	0.730979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.19	yes	42
3.2	odd	2		552.2.j.c.323.24	yes	42
4.3	odd	2		2208.2.j.d.47.20		42
8.3	odd	2		552.2.j.c.323.23	✓	42
8.5	even	2		2208.2.j.c.47.20		42
12.11	even	2		2208.2.j.c.47.19		42
24.5	odd	2		2208.2.j.d.47.19		42
24.11	even	2	inner	552.2.j.d.323.20	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.23	✓	42	8.3	odd	2
552.2.j.c.323.24	yes	42	3.2	odd	2
552.2.j.d.323.19	yes	42	1.1	even	1	trivial
552.2.j.d.323.20	yes	42	24.11	even	2	inner
2208.2.j.c.47.19		42	12.11	even	2
2208.2.j.c.47.20		42	8.5	even	2
2208.2.j.d.47.19		42	24.5	odd	2
2208.2.j.d.47.20		42	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.218758 - 1.39719i) q^{2} +(0.262136 - 1.71210i) q^{3} +(-1.90429 + 0.611292i) q^{4} -0.130526 q^{5} +(-2.44948 + 0.00827965i) q^{6} +3.77863i q^{7} +(1.27067 + 2.52693i) q^{8} +(-2.86257 - 0.897607i) q^{9} +O(q^{10})\)	\(q+(-0.218758 - 1.39719i) q^{2} +(0.262136 - 1.71210i) q^{3} +(-1.90429 + 0.611292i) q^{4} -0.130526 q^{5} +(-2.44948 + 0.00827965i) q^{6} +3.77863i q^{7} +(1.27067 + 2.52693i) q^{8} +(-2.86257 - 0.897607i) q^{9} +(0.0285535 + 0.182369i) q^{10} +4.36656i q^{11} +(0.547409 + 3.42058i) q^{12} +5.50350i q^{13} +(5.27947 - 0.826604i) q^{14} +(-0.0342155 + 0.223473i) q^{15} +(3.25264 - 2.32816i) q^{16} -0.402065i q^{17} +(-0.627921 + 4.19592i) q^{18} -2.08168 q^{19} +(0.248559 - 0.0797893i) q^{20} +(6.46939 + 0.990517i) q^{21} +(6.10092 - 0.955218i) q^{22} +1.00000 q^{23} +(4.65945 - 1.51311i) q^{24} -4.98296 q^{25} +(7.68945 - 1.20393i) q^{26} +(-2.28718 + 4.66571i) q^{27} +(-2.30985 - 7.19561i) q^{28} -8.77100 q^{29} +(0.319719 - 0.00108071i) q^{30} -7.75722i q^{31} +(-3.96442 - 4.03526i) q^{32} +(7.47599 + 1.14463i) q^{33} +(-0.561761 + 0.0879546i) q^{34} -0.493208i q^{35} +(5.99986 - 0.0405616i) q^{36} +10.1015i q^{37} +(0.455384 + 2.90851i) q^{38} +(9.42255 + 1.44267i) q^{39} +(-0.165855 - 0.329830i) q^{40} -2.80694i q^{41} +(-0.0312857 - 9.25566i) q^{42} +3.07905 q^{43} +(-2.66925 - 8.31520i) q^{44} +(0.373638 + 0.117161i) q^{45} +(-0.218758 - 1.39719i) q^{46} +3.41142 q^{47} +(-3.13340 - 6.17914i) q^{48} -7.27804 q^{49} +(1.09006 + 6.96216i) q^{50} +(-0.688374 - 0.105396i) q^{51} +(-3.36425 - 10.4803i) q^{52} -0.336698 q^{53} +(7.01923 + 2.17497i) q^{54} -0.569948i q^{55} +(-9.54835 + 4.80139i) q^{56} +(-0.545685 + 3.56405i) q^{57} +(1.91872 + 12.2548i) q^{58} -9.68031i q^{59} +(-0.0714509 - 0.446473i) q^{60} +2.78101i q^{61} +(-10.8383 + 1.69695i) q^{62} +(3.39173 - 10.8166i) q^{63} +(-4.77079 + 6.42180i) q^{64} -0.718348i q^{65} +(-0.0361536 - 10.6958i) q^{66} +12.8230 q^{67} +(0.245779 + 0.765648i) q^{68} +(0.262136 - 1.71210i) q^{69} +(-0.689106 + 0.107893i) q^{70} +8.19053 q^{71} +(-1.36919 - 8.37409i) q^{72} +0.417051 q^{73} +(14.1138 - 2.20979i) q^{74} +(-1.30622 + 8.53133i) q^{75} +(3.96413 - 1.27252i) q^{76} -16.4996 q^{77} +(-0.0455671 - 13.4807i) q^{78} +3.09607i q^{79} +(-0.424553 + 0.303884i) q^{80} +(7.38860 + 5.13893i) q^{81} +(-3.92184 + 0.614040i) q^{82} -3.59045i q^{83} +(-12.9251 + 2.06846i) q^{84} +0.0524797i q^{85} +(-0.673565 - 4.30202i) q^{86} +(-2.29920 + 15.0168i) q^{87} +(-11.0340 + 5.54846i) q^{88} +11.1036i q^{89} +(0.0819598 - 0.547674i) q^{90} -20.7957 q^{91} +(-1.90429 + 0.611292i) q^{92} +(-13.2811 - 2.03345i) q^{93} +(-0.746274 - 4.76641i) q^{94} +0.271713 q^{95} +(-7.94799 + 5.72969i) q^{96} +4.53325 q^{97} +(1.59213 + 10.1688i) q^{98} +(3.91946 - 12.4996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

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