LMFDB - Embedded newform 126.2.l.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(5,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("126.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.6
Root			$1.27866 - 1.16834i$ of defining polynomial
Character	$\chi$	$=$	126.5
Dual form			126.2.l.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.08509 - 1.35003i) q^{3} -1.00000 q^{4} +(1.77612 + 3.07634i) q^{5} +(1.35003 - 1.08509i) q^{6} +(2.63804 - 0.201867i) q^{7} -1.00000i q^{8} +(-0.645160 + 2.92981i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.08509 - 1.35003i) q^{3} -1.00000 q^{4} +(1.77612 + 3.07634i) q^{5} +(1.35003 - 1.08509i) q^{6} +(2.63804 - 0.201867i) q^{7} -1.00000i q^{8} +(-0.645160 + 2.92981i) q^{9} +(-3.07634 + 1.77612i) q^{10} +(2.61745 + 1.51119i) q^{11} +(1.08509 + 1.35003i) q^{12} +(-0.888944 - 0.513232i) q^{13} +(0.201867 + 2.63804i) q^{14} +(2.22589 - 5.73592i) q^{15} +1.00000 q^{16} +(-0.809204 - 1.40158i) q^{17} +(-2.92981 - 0.645160i) q^{18} +(-7.12643 - 4.11444i) q^{19} +(-1.77612 - 3.07634i) q^{20} +(-3.13504 - 3.34239i) q^{21} +(-1.51119 + 2.61745i) q^{22} +(2.90837 - 1.67915i) q^{23} +(-1.35003 + 1.08509i) q^{24} +(-3.80924 + 6.59779i) q^{25} +(0.513232 - 0.888944i) q^{26} +(4.65538 - 2.30812i) q^{27} +(-2.63804 + 0.201867i) q^{28} +(-3.70319 + 2.13804i) q^{29} +(5.73592 + 2.22589i) q^{30} -5.98576i q^{31} +1.00000i q^{32} +(-0.800023 - 5.17341i) q^{33} +(1.40158 - 0.809204i) q^{34} +(5.30650 + 7.75696i) q^{35} +(0.645160 - 2.92981i) q^{36} +(2.92323 - 5.06319i) q^{37} +(4.11444 - 7.12643i) q^{38} +(0.271706 + 1.75700i) q^{39} +(3.07634 - 1.77612i) q^{40} +(0.0472226 - 0.0817920i) q^{41} +(3.34239 - 3.13504i) q^{42} +(3.05899 + 5.29833i) q^{43} +(-2.61745 - 1.51119i) q^{44} +(-10.1590 + 3.21897i) q^{45} +(1.67915 + 2.90837i) q^{46} -5.14045 q^{47} +(-1.08509 - 1.35003i) q^{48} +(6.91850 - 1.06507i) q^{49} +(-6.59779 - 3.80924i) q^{50} +(-1.01412 + 2.61329i) q^{51} +(0.888944 + 0.513232i) q^{52} +(-2.76235 + 1.59484i) q^{53} +(2.30812 + 4.65538i) q^{54} +10.7362i q^{55} +(-0.201867 - 2.63804i) q^{56} +(2.17819 + 14.0854i) q^{57} +(-2.13804 - 3.70319i) q^{58} -8.84071 q^{59} +(-2.22589 + 5.73592i) q^{60} -4.69034i q^{61} +5.98576 q^{62} +(-1.11052 + 7.85918i) q^{63} -1.00000 q^{64} -3.64626i q^{65} +(5.17341 - 0.800023i) q^{66} -0.375675 q^{67} +(0.809204 + 1.40158i) q^{68} +(-5.42275 - 2.10436i) q^{69} +(-7.75696 + 5.30650i) q^{70} -13.9868i q^{71} +(2.92981 + 0.645160i) q^{72} +(1.13546 - 0.655556i) q^{73} +(5.06319 + 2.92323i) q^{74} +(13.0406 - 2.01662i) q^{75} +(7.12643 + 4.11444i) q^{76} +(7.20999 + 3.45819i) q^{77} +(-1.75700 + 0.271706i) q^{78} +0.924134 q^{79} +(1.77612 + 3.07634i) q^{80} +(-8.16754 - 3.78039i) q^{81} +(0.0817920 + 0.0472226i) q^{82} +(5.43209 + 9.40866i) q^{83} +(3.13504 + 3.34239i) q^{84} +(2.87450 - 4.97877i) q^{85} +(-5.29833 + 3.05899i) q^{86} +(6.90471 + 2.67945i) q^{87} +(1.51119 - 2.61745i) q^{88} +(-2.35495 + 4.07888i) q^{89} +(-3.21897 - 10.1590i) q^{90} +(-2.44867 - 1.17448i) q^{91} +(-2.90837 + 1.67915i) q^{92} +(-8.08095 + 6.49509i) q^{93} -5.14045i q^{94} -29.2311i q^{95} +(1.35003 - 1.08509i) q^{96} +(13.3330 - 7.69782i) q^{97} +(1.06507 + 6.91850i) q^{98} +(-6.11615 + 6.69367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 2 * q^7	$ 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 6 * q^97 - 24 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.08509	−	1.35003i	−0.626477	−	0.779440i
$3$	−1.08509	−	1.35003i	−0.626477	−	0.779440i
$4$	−1.00000			−0.500000
$5$	1.77612	+	3.07634i	0.794307	+	1.37578i	0.923278	+	0.384132i	$0.125499\pi$
$5$	1.77612	+	3.07634i	0.794307	+	1.37578i	−0.128971	+	0.991648i	$0.541167\pi$
$6$	1.35003	−	1.08509i	0.551147	−	0.442986i
$7$	2.63804	−	0.201867i	0.997085	−	0.0762987i
$7$	2.63804	−	0.201867i	0.997085	−	0.0762987i
$8$		−	1.00000i		−	0.353553i
$9$	−0.645160	+	2.92981i	−0.215053	+	0.976602i
$10$	−3.07634	+	1.77612i	−0.972824	+	0.561660i
$11$	2.61745	+	1.51119i	0.789191	+	0.455639i	0.839678	−	0.543085i	$-0.182744\pi$
$11$	2.61745	+	1.51119i	0.789191	+	0.455639i	−0.0504869	+	0.998725i	$0.516077\pi$
$12$	1.08509	+	1.35003i	0.313238	+	0.389720i
$13$	−0.888944	−	0.513232i	−0.246549	−	0.142345i	0.371634	−	0.928379i	$-0.378798\pi$
$13$	−0.888944	−	0.513232i	−0.246549	−	0.142345i	−0.618183	+	0.786034i	$0.712131\pi$
$14$	0.201867	+	2.63804i	0.0539513	+	0.705046i
$15$	2.22589	−	5.73592i	0.574723	−	1.48101i
$16$	1.00000			0.250000
$17$	−0.809204	−	1.40158i	−0.196261	−	0.339934i	0.751052	−	0.660243i	$-0.229547\pi$
$17$	−0.809204	−	1.40158i	−0.196261	−	0.339934i	−0.947313	+	0.320309i	$0.896213\pi$
$18$	−2.92981	−	0.645160i	−0.690562	−	0.152066i
$19$	−7.12643	−	4.11444i	−1.63491	−	0.943918i	−0.982547	−	0.186016i	$-0.940442\pi$
$19$	−7.12643	−	4.11444i	−1.63491	−	0.943918i	−0.652368	−	0.757903i	$-0.726224\pi$
$20$	−1.77612	−	3.07634i	−0.397154	−	0.687890i
$21$	−3.13504	−	3.34239i	−0.684121	−	0.729369i
$22$	−1.51119	+	2.61745i	−0.322186	+	0.558042i
$23$	2.90837	−	1.67915i	0.606438	−	0.350127i	−0.165132	−	0.986271i	$-0.552805\pi$
$23$	2.90837	−	1.67915i	0.606438	−	0.350127i	0.771570	+	0.636144i	$0.219472\pi$
$24$	−1.35003	+	1.08509i	−0.275574	+	0.221493i
$25$	−3.80924	+	6.59779i	−0.761848	+	1.31956i
$26$	0.513232	−	0.888944i	0.100653	−	0.174336i
$27$	4.65538	−	2.30812i	0.895929	−	0.444198i
$28$	−2.63804	+	0.201867i	−0.498543	+	0.0381493i
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	−0.802737	−	0.596333i	$-0.796624\pi$
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	0.115071	+	0.993357i	$0.463290\pi$
$30$	5.73592	+	2.22589i	1.04723	+	0.406391i
$31$		−	5.98576i		−	1.07507i	−0.843240	−	0.537537i	$-0.819355\pi$
$31$		−	5.98576i		−	1.07507i	0.843240	−	0.537537i	$-0.180645\pi$
$32$			1.00000i			0.176777i
$33$	−0.800023	−	5.17341i	−0.139266	−	0.900574i
$34$	1.40158	−	0.809204i	0.240369	−	0.138777i
$35$	5.30650	+	7.75696i	0.896962	+	1.31117i
$36$	0.645160	−	2.92981i	0.107527	−	0.488301i
$37$	2.92323	−	5.06319i	0.480577	−	0.832384i	−0.519175	−	0.854668i	$-0.673761\pi$
$37$	2.92323	−	5.06319i	0.480577	−	0.832384i	0.999752	+	0.0222846i	$0.00709398\pi$
$38$	4.11444	−	7.12643i	0.667451	−	1.15606i
$39$	0.271706	+	1.75700i	0.0435078	+	0.281346i
$40$	3.07634	−	1.77612i	0.486412	−	0.280830i
$41$	0.0472226	−	0.0817920i	0.00737493	−	0.0127738i	−0.862314	−	0.506373i	$-0.830986\pi$
$41$	0.0472226	−	0.0817920i	0.00737493	−	0.0127738i	0.869689	+	0.493600i	$0.164319\pi$
$42$	3.34239	−	3.13504i	0.515741	−	0.483747i
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	0.999267	−	0.0382684i	$-0.0121842\pi$
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	−0.532775	+	0.846257i	$0.678851\pi$
$44$	−2.61745	−	1.51119i	−0.394595	−	0.227820i
$45$	−10.1590	+	3.21897i	−1.51441	+	0.479856i
$46$	1.67915	+	2.90837i	0.247577	+	0.428816i
$47$	−5.14045			−0.749812			−0.374906	−	0.927063i	$-0.622325\pi$
$47$	−5.14045			−0.749812			−0.374906	+	0.927063i	$0.622325\pi$
$48$	−1.08509	−	1.35003i	−0.156619	−	0.194860i
$49$	6.91850	−	1.06507i	0.988357	−	0.152153i
$50$	−6.59779	−	3.80924i	−0.933069	−	0.538708i
$51$	−1.01412	+	2.61329i	−0.142005	+	0.365934i
$52$	0.888944	+	0.513232i	0.123274	+	0.0711725i
$53$	−2.76235	+	1.59484i	−0.379438	+	0.219068i	−0.677574	−	0.735455i	$-0.736968\pi$
$53$	−2.76235	+	1.59484i	−0.379438	+	0.219068i	0.298136	+	0.954523i	$0.403635\pi$
$54$	2.30812	+	4.65538i	0.314095	+	0.633517i
$55$			10.7362i			1.44767i
$56$	−0.201867	−	2.63804i	−0.0269757	−	0.352523i
$57$	2.17819	+	14.0854i	0.288509	+	1.86566i
$58$	−2.13804	−	3.70319i	−0.280738	−	0.486253i
$59$	−8.84071			−1.15096			−0.575481	−	0.817815i	$-0.695185\pi$
$59$	−8.84071			−1.15096			−0.575481	+	0.817815i	$0.695185\pi$
$60$	−2.22589	+	5.73592i	−0.287361	+	0.740505i
$61$		−	4.69034i		−	0.600537i	−0.953855	−	0.300268i	$-0.902924\pi$
$61$		−	4.69034i		−	0.600537i	0.953855	−	0.300268i	$-0.0970762\pi$
$62$	5.98576			0.760192
$63$	−1.11052	+	7.85918i	−0.139913	+	0.990164i
$64$	−1.00000			−0.125000
$65$		−	3.64626i		−	0.452263i
$66$	5.17341	−	0.800023i	0.636802	−	0.0984761i
$67$	−0.375675			−0.0458961			−0.0229480	−	0.999737i	$-0.507305\pi$
$67$	−0.375675			−0.0458961			−0.0229480	+	0.999737i	$0.507305\pi$
$68$	0.809204	+	1.40158i	0.0981304	+	0.169967i
$69$	−5.42275	−	2.10436i	−0.652822	−	0.253335i
$70$	−7.75696	+	5.30650i	−0.927134	+	0.634248i
$71$		−	13.9868i		−	1.65993i	−0.557815	−	0.829966i	$-0.688360\pi$
$71$		−	13.9868i		−	1.65993i	0.557815	−	0.829966i	$-0.311640\pi$
$72$	2.92981	+	0.645160i	0.345281	+	0.0760328i
$73$	1.13546	−	0.655556i	0.132895	−	0.0767270i	−0.432079	−	0.901836i	$-0.642220\pi$
$73$	1.13546	−	0.655556i	0.132895	−	0.0767270i	0.564974	+	0.825109i	$0.308886\pi$
$74$	5.06319	+	2.92323i	0.588584	+	0.339819i
$75$	13.0406	−	2.01662i	1.50580	−	0.232859i
$76$	7.12643	+	4.11444i	0.817457	+	0.471959i
$77$	7.20999	+	3.45819i	0.821655	+	0.394097i
$78$	−1.75700	+	0.271706i	−0.198942	+	0.0307646i
$79$	0.924134			0.103973			0.0519866	−	0.998648i	$-0.483445\pi$
$79$	0.924134			0.103973			0.0519866	+	0.998648i	$0.483445\pi$
$80$	1.77612	+	3.07634i	0.198577	+	0.343945i
$81$	−8.16754	−	3.78039i	−0.907504	−	0.420043i
$82$	0.0817920	+	0.0472226i	0.00903241	+	0.00521487i
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	0.993369	+	0.114968i	$0.0366765\pi$
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	−0.397119	+	0.917767i	$0.629990\pi$
$84$	3.13504	+	3.34239i	0.342061	+	0.364684i
$85$	2.87450	−	4.97877i	0.311783	−	0.540024i
$86$	−5.29833	+	3.05899i	−0.571334	+	0.329860i
$87$	6.90471	+	2.67945i	0.740263	+	0.287268i
$88$	1.51119	−	2.61745i	0.161093	−	0.279021i
$89$	−2.35495	+	4.07888i	−0.249624	+	0.432361i	−0.963421	−	0.267991i	$-0.913640\pi$
$89$	−2.35495	+	4.07888i	−0.249624	+	0.432361i	0.713798	+	0.700352i	$0.246974\pi$
$90$	−3.21897	−	10.1590i	−0.339310	−	1.07085i
$91$	−2.44867	−	1.17448i	−0.256691	−	0.123119i
$92$	−2.90837	+	1.67915i	−0.303219	+	0.175063i
$93$	−8.08095	+	6.49509i	−0.837956	+	0.673509i
$94$		−	5.14045i		−	0.530197i
$95$		−	29.2311i		−	2.99904i
$96$	1.35003	−	1.08509i	0.137787	−	0.110747i
$97$	13.3330	−	7.69782i	1.35376	−	0.781595i	0.364988	−	0.931012i	$-0.381073\pi$
$97$	13.3330	−	7.69782i	1.35376	−	0.781595i	0.988774	+	0.149417i	$0.0477397\pi$
$98$	1.06507	+	6.91850i	0.107588	+	0.698874i
$99$	−6.11615	+	6.69367i	−0.614697	+	0.672739i
$100$	3.80924	−	6.59779i	0.380924	−	0.659779i
$101$	−6.85234	+	11.8686i	−0.681833	+	1.18097i	0.292588	+	0.956239i	$0.405484\pi$
$101$	−6.85234	+	11.8686i	−0.681833	+	1.18097i	−0.974421	+	0.224731i	$0.927850\pi$
$102$	−2.61329	−	1.01412i	−0.258755	−	0.100413i
$103$	2.64014	−	1.52429i	0.260141	−	0.150192i	−0.364258	−	0.931298i	$-0.618677\pi$
$103$	2.64014	−	1.52429i	0.260141	−	0.150192i	0.624399	+	0.781106i	$0.285344\pi$
$104$	−0.513232	+	0.888944i	−0.0503266	+	0.0871682i
$105$	4.71410	−	15.5809i	0.460049	−	1.52054i
$106$	−1.59484	−	2.76235i	−0.154905	−	0.268303i
$107$	−11.3681	−	6.56336i	−1.09899	−	0.634504i	−0.163037	−	0.986620i	$-0.552129\pi$
$107$	−11.3681	−	6.56336i	−1.09899	−	0.634504i	−0.935956	+	0.352116i	$0.885462\pi$
$108$	−4.65538	+	2.30812i	−0.447964	+	0.222099i
$109$	5.28574	+	9.15516i	0.506282	+	0.876906i	0.999974	+	0.00726875i	$0.00231373\pi$
$109$	5.28574	+	9.15516i	0.506282	+	0.876906i	−0.493692	+	0.869637i	$0.664353\pi$
$110$	−10.7362			−1.02366
$111$	−10.0074	+	1.54756i	−0.949863	+	0.146888i
$112$	2.63804	−	0.201867i	0.249271	−	0.0190747i
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.908856	−	0.417111i	$-0.136957\pi$
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.0931992	+	0.995647i	$0.470291\pi$
$114$	−14.0854	+	2.17819i	−1.31922	+	0.204006i
$115$	10.3313	+	5.96476i	0.963396	+	0.556217i
$116$	3.70319	−	2.13804i	0.343833	−	0.198512i
$117$	2.07718	−	2.27332i	0.192036	−	0.210168i
$118$		−	8.84071i		−	0.813853i
$119$	−2.41765	−	3.53408i	−0.221625	−	0.323968i
$120$	−5.73592	−	2.22589i	−0.523616	−	0.203195i
$121$	−0.932639	−	1.61538i	−0.0847854	−	0.146853i
$122$	4.69034			0.424644
$123$	−0.161662	+	0.0249997i	−0.0145766	+	0.00225415i
$124$			5.98576i			0.537537i
$125$	−9.30148			−0.831950
$126$	−7.85918	−	1.11052i	−0.700152	−	0.0989333i
$127$	0.287164			0.0254817			0.0127408	−	0.999919i	$-0.495944\pi$
$127$	0.287164			0.0254817			0.0127408	+	0.999919i	$0.495944\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.83362	−	9.87890i	0.337532	−	0.869789i
$130$	3.64626			0.319798
$131$	0.186474	+	0.322983i	0.0162923	+	0.0282192i	0.874057	−	0.485824i	$-0.161480\pi$
$131$	0.186474	+	0.322983i	0.0162923	+	0.0282192i	−0.857764	+	0.514043i	$0.828147\pi$
$132$	0.800023	+	5.17341i	0.0696331	+	0.450287i
$133$	−19.6304	−	9.41547i	−1.70217	−	0.816425i
$134$		−	0.375675i		−	0.0324534i
$135$	15.3691	+	10.2220i	1.32276	+	0.879772i
$136$	−1.40158	+	0.809204i	−0.120185	+	0.0693887i
$137$	6.11607	+	3.53111i	0.522531	+	0.301683i	0.737969	−	0.674834i	$-0.235785\pi$
$137$	6.11607	+	3.53111i	0.522531	+	0.301683i	−0.215439	+	0.976517i	$0.569118\pi$
$138$	2.10436	−	5.42275i	0.179135	−	0.461615i
$139$	−12.6320	−	7.29308i	−1.07143	−	0.618591i	−0.142858	−	0.989743i	$-0.545629\pi$
$139$	−12.6320	−	7.29308i	−1.07143	−	0.618591i	−0.928572	+	0.371152i	$0.878963\pi$
$140$	−5.30650	−	7.75696i	−0.448481	−	0.655583i
$141$	5.57785	+	6.93976i	0.469740	+	0.584434i
$142$	13.9868			1.17375
$143$	−1.55118	−	2.68672i	−0.129716	−	0.224675i
$144$	−0.645160	+	2.92981i	−0.0537633	+	0.244151i
$145$	−13.1547	−	7.59485i	−1.09244	−	0.630718i
$146$	0.655556	+	1.13546i	0.0542542	+	0.0939710i
$147$	−8.94507	−	8.18448i	−0.737777	−	0.675045i
$148$	−2.92323	+	5.06319i	−0.240288	+	0.416192i
$149$	−9.26832	+	5.35107i	−0.759290	+	0.438376i	−0.829041	−	0.559188i	$-0.811113\pi$
$149$	−9.26832	+	5.35107i	−0.759290	+	0.438376i	0.0697505	+	0.997564i	$0.477780\pi$
$150$	2.01662	+	13.0406i	0.164656	+	1.06476i
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	0.331777	+	0.943358i	$0.392352\pi$
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	−0.982860	+	0.184352i	$0.940981\pi$
$152$	−4.11444	+	7.12643i	−0.333726	+	0.578030i
$153$	4.62843	−	1.46657i	0.374187	−	0.118565i
$154$	−3.45819	+	7.20999i	−0.278669	+	0.580998i
$155$	18.4142	−	10.6315i	1.47907	−	0.853939i
$156$	−0.271706	−	1.75700i	−0.0217539	−	0.140673i
$157$			11.5267i			0.919928i	0.887937	+	0.459964i	$0.152138\pi$
$157$			11.5267i			0.919928i	−0.887937	+	0.459964i	$0.847862\pi$
$158$			0.924134i			0.0735202i
$159$	5.15048	+	1.99870i	0.408460	+	0.158508i
$160$	−3.07634	+	1.77612i	−0.243206	+	0.140415i
$161$	7.33344	−	5.01677i	0.577956	−	0.395377i
$162$	3.78039	−	8.16754i	0.297015	−	0.641702i
$163$	1.37386	−	2.37960i	0.107609	−	0.186385i	−0.807192	−	0.590289i	$-0.799014\pi$
$163$	1.37386	−	2.37960i	0.107609	−	0.186385i	0.914801	+	0.403904i	$0.132347\pi$
$164$	−0.0472226	+	0.0817920i	−0.00368747	+	0.00638688i
$165$	14.4942	−	11.6498i	1.12837	−	0.906932i
$166$	−9.40866	+	5.43209i	−0.730254	+	0.421612i
$167$	−2.76946	+	4.79685i	−0.214307	+	0.371191i	−0.953058	−	0.302788i	$-0.902083\pi$
$167$	−2.76946	+	4.79685i	−0.214307	+	0.371191i	0.738751	+	0.673979i	$0.235416\pi$
$168$	−3.34239	+	3.13504i	−0.257871	+	0.241873i
$169$	−5.97319	−	10.3459i	−0.459476	−	0.795835i
$170$	4.97877	+	2.87450i	0.381854	+	0.220464i
$171$	16.6522	−	18.2246i	1.27343	−	1.39367i
$172$	−3.05899	−	5.29833i	−0.233246	−	0.403994i
$173$	11.2051			0.851905			0.425953	−	0.904745i	$-0.359939\pi$
$173$	11.2051			0.851905			0.425953	+	0.904745i	$0.359939\pi$
$174$	−2.67945	+	6.90471i	−0.203129	+	0.523445i
$175$	−8.71704	+	18.1742i	−0.658946	+	1.37384i
$176$	2.61745	+	1.51119i	0.197298	+	0.113910i
$177$	9.59297	+	11.9352i	0.721052	+	0.897106i
$178$	−4.07888	−	2.35495i	−0.305725	−	0.176511i
$179$	−2.37445	+	1.37089i	−0.177475	+	0.102465i	−0.586106	−	0.810235i	$-0.699340\pi$
$179$	−2.37445	+	1.37089i	−0.177475	+	0.102465i	0.408631	+	0.912700i	$0.366006\pi$
$180$	10.1590	−	3.21897i	0.757204	−	0.239928i
$181$			22.2899i			1.65679i	0.560142	+	0.828397i	$0.310747\pi$
$181$			22.2899i			1.65679i	−0.560142	+	0.828397i	$0.689253\pi$
$182$	1.17448	−	2.44867i	0.0870581	−	0.181508i
$183$	−6.33210	+	5.08944i	−0.468082	+	0.376222i
$184$	−1.67915	−	2.90837i	−0.123789	−	0.214408i
$185$	20.7681			1.52690
$186$	−6.49509	−	8.08095i	−0.476243	−	0.592524i
$187$		−	4.89143i		−	0.357697i
$188$	5.14045			0.374906
$189$	11.8151	−	7.02868i	0.859425	−	0.511261i
$190$	29.2311			2.12064
$191$		−	5.13264i		−	0.371385i	−0.982608	−	0.185692i	$-0.940547\pi$
$191$		−	5.13264i		−	0.371385i	0.982608	−	0.185692i	$-0.0594528\pi$
$192$	1.08509	+	1.35003i	0.0783096	+	0.0974300i
$193$	15.9847			1.15060			0.575302	−	0.817941i	$-0.304884\pi$
$193$	15.9847			1.15060			0.575302	+	0.817941i	$0.304884\pi$
$194$	7.69782	+	13.3330i	0.552671	+	0.957254i
$195$	−4.92256	+	3.95652i	−0.352512	+	0.283332i
$196$	−6.91850	+	1.06507i	−0.494179	+	0.0760763i
$197$			4.72572i			0.336694i	0.985728	+	0.168347i	$0.0538428\pi$
$197$			4.72572i			0.336694i	−0.985728	+	0.168347i	$0.946157\pi$
$198$	−6.69367	−	6.11615i	−0.475698	−	0.434656i
$199$	1.83679	−	1.06047i	0.130207	−	0.0751749i	−0.433482	−	0.901162i	$-0.642715\pi$
$199$	1.83679	−	1.06047i	0.130207	−	0.0751749i	0.563689	+	0.825987i	$0.309382\pi$
$200$	6.59779	+	3.80924i	0.466534	+	0.269354i
$201$	0.407642	+	0.507173i	0.0287528	+	0.0357732i
$202$	−11.8686	−	6.85234i	−0.835072	−	0.482129i
$203$	−9.33756	+	6.38778i	−0.655369	+	0.448335i
$204$	1.01412	−	2.61329i	0.0710025	−	0.182967i
$205$	0.335493			0.0234319
$206$	1.52429	+	2.64014i	0.106202	+	0.183947i
$207$	3.04322	+	9.60429i	0.211518	+	0.667544i
$208$	−0.888944	−	0.513232i	−0.0616372	−	0.0355863i
$209$	−12.4354	−	21.5387i	−0.860173	−	1.48986i
$210$	15.5809	+	4.71410i	1.07519	+	0.325303i
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.206399	+	0.978468i	$0.566174\pi$
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.744179	+	0.667981i	$0.767159\pi$
$212$	2.76235	−	1.59484i	0.189719	−	0.109534i
$213$	−18.8826	+	15.1770i	−1.29382	+	1.03991i
$214$	6.56336	−	11.3681i	0.448662	−	0.777105i
$215$	−10.8663	+	18.8210i	−0.741076	+	1.28358i
$216$	−2.30812	−	4.65538i	−0.157048	−	0.316759i
$217$	−1.20833	−	15.7907i	−0.0820267	−	1.07194i
$218$	−9.15516	+	5.28574i	−0.620066	+	0.357995i
$219$	−2.11709	−	0.821562i	−0.143060	−	0.0555160i
$220$		−	10.7362i		−	0.723835i
$221$			1.66124i			0.111747i
$222$	−1.54756	−	10.0074i	−0.103866	−	0.671655i
$223$	−17.6209	+	10.1734i	−1.17998	+	0.681264i	−0.956011	−	0.293331i	$-0.905236\pi$
$223$	−17.6209	+	10.1734i	−1.17998	+	0.681264i	−0.223973	+	0.974595i	$0.571903\pi$
$224$	0.201867	+	2.63804i	0.0134878	+	0.176261i
$225$	−16.8727	−	15.4170i	−1.12485	−	1.02780i
$226$	−6.14993	+	10.6520i	−0.409087	+	0.708560i
$227$	−2.08000	+	3.60266i	−0.138054	+	0.239117i	−0.926760	−	0.375654i	$-0.877418\pi$
$227$	−2.08000	+	3.60266i	−0.138054	+	0.239117i	0.788706	+	0.614771i	$0.210752\pi$
$228$	−2.17819	−	14.0854i	−0.144254	−	0.932830i
$229$	−5.16986	+	2.98482i	−0.341634	+	0.197242i	−0.660994	−	0.750391i	$-0.729865\pi$
$229$	−5.16986	+	2.98482i	−0.341634	+	0.197242i	0.319361	+	0.947633i	$0.396532\pi$
$230$	−5.96476	+	10.3313i	−0.393305	+	0.681224i
$231$	−3.15483	−	13.4861i	−0.207573	−	0.887323i
$232$	2.13804	+	3.70319i	0.140369	+	0.243126i
$233$	−3.88603	−	2.24360i	−0.254582	−	0.146983i	0.367278	−	0.930111i	$-0.380290\pi$
$233$	−3.88603	−	2.24360i	−0.254582	−	0.146983i	−0.621861	+	0.783128i	$0.713623\pi$
$234$	2.27332	+	2.07718i	0.148611	+	0.135790i
$235$	−9.13009	−	15.8138i	−0.595581	−	1.03158i
$236$	8.84071			0.575481
$237$	−1.00277	−	1.24761i	−0.0651368	−	0.0810409i
$238$	3.53408	−	2.41765i	0.229080	−	0.156713i
$239$	−3.02944	−	1.74905i	−0.195958	−	0.113136i	0.398811	−	0.917033i	$-0.369423\pi$
$239$	−3.02944	−	1.74905i	−0.195958	−	0.113136i	−0.594769	+	0.803897i	$0.702756\pi$
$240$	2.22589	−	5.73592i	0.143681	−	0.370252i
$241$	10.0170	+	5.78332i	0.645252	+	0.372537i	0.786635	−	0.617419i	$-0.211821\pi$
$241$	10.0170	+	5.78332i	0.645252	+	0.372537i	−0.141383	+	0.989955i	$0.545155\pi$
$242$	1.61538	−	0.932639i	0.103840	−	0.0599523i
$243$	3.75888	+	15.1285i	0.241132	+	0.970492i
$244$			4.69034i			0.300268i
$245$	15.5646	+	19.3920i	0.994387	+	1.23891i
$246$	−0.0249997	−	0.161662i	−0.00159392	−	0.0103072i
$247$	4.22333	+	7.31502i	0.268724	+	0.465444i
$248$	−5.98576			−0.380096
$249$	6.80766	−	17.5427i	0.431418	−	1.11173i
$250$		−	9.30148i		−	0.588277i
$251$	26.7426			1.68798			0.843988	−	0.536361i	$-0.180202\pi$
$251$	26.7426			1.68798			0.843988	+	0.536361i	$0.180202\pi$
$252$	1.11052	−	7.85918i	0.0699564	−	0.495082i
$253$	10.1500			0.638127
$254$			0.287164i			0.0180183i
$255$	−9.84057	+	1.52176i	−0.616241	+	0.0952964i
$256$	1.00000			0.0625000
$257$	2.60614	+	4.51396i	0.162566	+	0.281573i	0.935788	−	0.352562i	$-0.114690\pi$
$257$	2.60614	+	4.51396i	0.162566	+	0.281573i	−0.773222	+	0.634135i	$0.781356\pi$
$258$	9.87890	+	3.83362i	0.615034	+	0.238671i
$259$	6.68951	−	13.9470i	0.415666	−	0.866624i
$260$			3.64626i			0.226131i
$261$	−3.87489	−	12.2290i	−0.239850	−	0.756957i
$262$	−0.322983	+	0.186474i	−0.0199540	+	0.0115204i
$263$	−13.0228	−	7.51869i	−0.803018	−	0.463622i	0.0415076	−	0.999138i	$-0.486784\pi$
$263$	−13.0228	−	7.51869i	−0.803018	−	0.463622i	−0.844525	+	0.535516i	$0.820117\pi$
$264$	−5.17341	+	0.800023i	−0.318401	+	0.0492380i
$265$	−9.81255	−	5.66528i	−0.602780	−	0.348015i
$266$	9.41547	−	19.6304i	0.577300	−	1.20361i
$267$	8.06194	−	1.24671i	0.493383	−	0.0762975i
$268$	0.375675			0.0229480
$269$	−11.5657	−	20.0323i	−0.705170	−	1.22139i	−0.966630	−	0.256177i	$-0.917537\pi$
$269$	−11.5657	−	20.0323i	−0.705170	−	1.22139i	0.261460	−	0.965214i	$-0.415796\pi$
$270$	−10.2220	+	15.3691i	−0.622092	+	0.935333i
$271$	8.58661	+	4.95748i	0.521599	+	0.301146i	0.737589	−	0.675250i	$-0.235964\pi$
$271$	8.58661	+	4.95748i	0.521599	+	0.301146i	−0.215989	+	0.976396i	$0.569298\pi$
$272$	−0.809204	−	1.40158i	−0.0490652	−	0.0849834i
$273$	1.07145	+	4.58020i	0.0648472	+	0.277206i
$274$	−3.53111	+	6.11607i	−0.213322	+	0.369485i
$275$	−19.9410	+	11.5129i	−1.20249	+	0.694256i
$276$	5.42275	+	2.10436i	0.326411	+	0.126668i
$277$	4.29721	−	7.44299i	0.258195	−	0.447206i	−0.707564	−	0.706650i	$-0.750206\pi$
$277$	4.29721	−	7.44299i	0.258195	−	0.447206i	0.965758	+	0.259443i	$0.0835391\pi$
$278$	7.29308	−	12.6320i	0.437410	−	0.757616i
$279$	17.5371	+	3.86177i	1.04992	+	0.231198i
$280$	7.75696	−	5.30650i	0.463567	−	0.317124i
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.928415	−	0.371545i	$-0.878828\pi$
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.142440	+	0.989803i	$0.545495\pi$
$282$	−6.93976	+	5.57785i	−0.413257	+	0.332156i
$283$			2.36710i			0.140709i	0.997522	+	0.0703547i	$0.0224131\pi$
$283$			2.36710i			0.140709i	−0.997522	+	0.0703547i	$0.977587\pi$
$284$			13.9868i			0.829966i
$285$	−39.4628	+	31.7183i	−2.33757	+	1.87883i
$286$	2.68672	−	1.55118i	0.158869	−	0.0917231i
$287$	0.108064	−	0.225303i	0.00637882	−	0.0132992i
$288$	−2.92981	−	0.645160i	−0.172641	−	0.0380164i
$289$	7.19038	−	12.4541i	0.422963	−	0.732594i
$290$	7.59485	−	13.1547i	0.445985	−	0.772468i
$291$	−24.8598	−	9.64714i	−1.45731	−	0.565525i
$292$	−1.13546	+	0.655556i	−0.0664475	+	0.0383635i
$293$	8.83774	−	15.3074i	0.516306	−	0.894268i	−0.483515	−	0.875336i	$-0.660640\pi$
$293$	8.83774	−	15.3074i	0.516306	−	0.894268i	0.999821	−	0.0189321i	$-0.00602664\pi$
$294$	8.18448	−	8.94507i	0.477329	−	0.521687i
$295$	−15.7022	−	27.1970i	−0.914218	−	1.58347i
$296$	−5.06319	−	2.92323i	−0.294292	−	0.169910i
$297$	15.6732	+	0.993759i	0.909453	+	0.0576637i
$298$	−5.35107	−	9.26832i	−0.309979	−	0.536899i
$299$	−3.44718			−0.199355
$300$	−13.0406	+	2.01662i	−0.752898	+	0.116429i
$301$	9.13931	+	13.3597i	0.526781	+	0.770040i
$302$	−13.8575	−	8.00065i	−0.797411	−	0.460386i
$303$	23.4584	−	3.62764i	1.34765	−	0.208402i
$304$	−7.12643	−	4.11444i	−0.408729	−	0.235980i
$305$	14.4291	−	8.33063i	0.826206	−	0.477011i
$306$	1.46657	+	4.62843i	0.0838381	+	0.264590i
$307$		−	1.28155i		−	0.0731422i	−0.999331	−	0.0365711i	$-0.988356\pi$
$307$		−	1.28155i		−	0.0731422i	0.999331	−	0.0365711i	$-0.0116435\pi$
$308$	−7.20999	−	3.45819i	−0.410827	−	0.197049i
$309$	−4.92262	−	1.91028i	−0.280038	−	0.108672i
$310$	10.6315	+	18.4142i	0.603826	+	1.04586i
$311$	12.5329			0.710673			0.355336	−	0.934738i	$-0.384366\pi$
$311$	12.5329			0.710673			0.355336	+	0.934738i	$0.384366\pi$
$312$	1.75700	−	0.271706i	0.0994708	−	0.0153823i
$313$			8.75385i			0.494797i	0.968914	+	0.247398i	$0.0795756\pi$
$313$			8.75385i			0.494797i	−0.968914	+	0.247398i	$0.920424\pi$
$314$	−11.5267			−0.650488
$315$	−26.1499	+	10.5425i	−1.47338	+	0.594005i
$316$	−0.924134			−0.0519866
$317$		−	13.6784i		−	0.768256i	−0.923280	−	0.384128i	$-0.874502\pi$
$317$		−	13.6784i		−	0.768256i	0.923280	−	0.384128i	$-0.125498\pi$
$318$	−1.99870	+	5.15048i	−0.112082	+	0.288825i
$319$	−12.9239			−0.723599
$320$	−1.77612	−	3.07634i	−0.0992884	−	0.171973i
$321$	3.47465	+	22.4691i	0.193936	+	1.25410i
$322$	5.01677	+	7.33344i	0.279574	+	0.408676i
$323$			13.3177i			0.741017i
$324$	8.16754	+	3.78039i	0.453752	+	0.210021i
$325$	6.77240	−	3.91005i	0.375665	−	0.216890i
$326$	2.37960	+	1.37386i	0.131794	+	0.0760912i
$327$	6.62424	−	17.0701i	0.366321	−	0.943977i
$328$	−0.0817920	−	0.0472226i	−0.00451621	−	0.00260743i
$329$	−13.5607	+	1.03769i	−0.747626	+	0.0572097i
$330$	11.6498	+	14.4942i	0.641298	+	0.797880i
$331$	−10.8972			−0.598962			−0.299481	−	0.954102i	$-0.596813\pi$
$331$	−10.8972			−0.598962			−0.299481	+	0.954102i	$0.596813\pi$
$332$	−5.43209	−	9.40866i	−0.298125	−	0.516367i
$333$	12.9482	+	11.8311i	0.709558	+	0.648339i
$334$	−4.79685	−	2.76946i	−0.262472	−	0.151538i
$335$	−0.667247	−	1.15570i	−0.0364556	−	0.0631429i
$336$	−3.13504	−	3.34239i	−0.171030	−	0.182342i
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	−0.271496	−	0.962440i	$-0.587518\pi$
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	0.969245	−	0.246098i	$-0.0791484\pi$
$338$	10.3459	−	5.97319i	0.562741	−	0.324898i
$339$	−3.25578	−	21.0537i	−0.176830	−	1.14348i
$340$	−2.87450	+	4.97877i	−0.155891	+	0.270012i
$341$	9.04559	−	15.6674i	0.489846	−	0.848438i
$342$	18.2246	+	16.6522i	0.985473	+	0.900448i
$343$	18.0363	−	4.20631i	0.973867	−	0.227119i
$344$	5.29833	−	3.05899i	0.285667	−	0.164930i
$345$	−3.15775	−	20.4198i	−0.170008	−	1.09937i
$346$			11.2051i			0.602388i
$347$			16.7623i			0.899848i	0.893067	+	0.449924i	$0.148549\pi$
$347$			16.7623i			0.899848i	−0.893067	+	0.449924i	$0.851451\pi$
$348$	−6.90471	−	2.67945i	−0.370131	−	0.143634i
$349$	14.4455	−	8.34010i	0.773249	−	0.446435i	−0.0607835	−	0.998151i	$-0.519360\pi$
$349$	14.4455	−	8.34010i	0.773249	−	0.446435i	0.834032	+	0.551716i	$0.186027\pi$
$350$	−18.1742	−	8.71704i	−0.971452	−	0.465945i
$351$	−5.32298	−	0.337503i	−0.284119	−	0.0180146i
$352$	−1.51119	+	2.61745i	−0.0805464	+	0.139511i
$353$	−17.9568	+	31.1021i	−0.955746	+	1.65540i	−0.223093	+	0.974797i	$0.571615\pi$
$353$	−17.9568	+	31.1021i	−0.955746	+	1.65540i	−0.732653	+	0.680603i	$0.761718\pi$
$354$	−11.9352	+	9.59297i	−0.634350	+	0.509860i
$355$	43.0282	−	24.8424i	2.28370	−	1.31850i
$356$	2.35495	−	4.07888i	0.124812	−	0.216180i
$357$	−2.14775	+	7.09869i	−0.113671	+	0.375702i
$358$	−1.37089	−	2.37445i	−0.0724538	−	0.125494i
$359$	24.7248	+	14.2749i	1.30493	+	0.753399i	0.981245	−	0.192767i	$-0.0617461\pi$
$359$	24.7248	+	14.2749i	1.30493	+	0.753399i	0.323681	+	0.946166i	$0.395079\pi$
$360$	3.21897	+	10.1590i	0.169655	+	0.535424i
$361$	24.3573	+	42.1881i	1.28196	+	2.22043i
$362$	−22.2899			−1.17153
$363$	−1.16881	+	3.01192i	−0.0613467	+	0.158085i
$364$	2.44867	+	1.17448i	0.128345	+	0.0615594i
$365$	4.03342	+	2.32870i	0.211119	+	0.121890i
$366$	−5.08944	−	6.33210i	−0.266029	−	0.330984i
$367$	0.310665	+	0.179362i	0.0162166	+	0.00936264i	0.508086	−	0.861306i	$-0.330353\pi$
$367$	0.310665	+	0.179362i	0.0162166	+	0.00936264i	−0.491870	+	0.870669i	$0.663686\pi$
$368$	2.90837	−	1.67915i	0.151609	−	0.0875317i
$369$	0.209169	+	0.191122i	0.0108889	+	0.00994942i
$370$			20.7681i			1.07968i
$371$	−6.96523	+	4.76488i	−0.361617	+	0.247380i
$372$	8.08095	−	6.49509i	0.418978	−	0.336755i
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	−0.981433	−	0.191807i	$-0.938565\pi$
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	0.324606	−	0.945849i	$-0.394768\pi$
$374$	4.89143			0.252930
$375$	10.0929	+	12.5573i	0.521197	+	0.648455i
$376$			5.14045i			0.265099i
$377$	4.38924			0.226057
$378$	7.02868	+	11.8151i	0.361516	+	0.607706i
$379$	26.9063			1.38209			0.691043	−	0.722814i	$-0.257152\pi$
$379$	26.9063			1.38209			0.691043	+	0.722814i	$0.257152\pi$
$380$			29.2311i			1.49952i
$381$	−0.311599	−	0.387680i	−0.0159637	−	0.0198614i
$382$	5.13264			0.262609
$383$	−6.28586	−	10.8874i	−0.321192	−	0.556322i	0.659542	−	0.751668i	$-0.270750\pi$
$383$	−6.28586	−	10.8874i	−0.321192	−	0.556322i	−0.980734	+	0.195346i	$0.937417\pi$
$384$	−1.35003	+	1.08509i	−0.0688934	+	0.0553733i
$385$	2.16729	+	28.3225i	0.110455	+	1.44345i
$386$			15.9847i			0.813600i
$387$	−17.4966	+	5.54399i	−0.889404	+	0.281817i
$388$	−13.3330	+	7.69782i	−0.676881	+	0.390798i
$389$	−14.0805	−	8.12937i	−0.713909	−	0.412175i	0.0985980	−	0.995127i	$-0.468564\pi$
$389$	−14.0805	−	8.12937i	−0.713909	−	0.412175i	−0.812507	+	0.582952i	$0.801898\pi$
$390$	−3.95652	−	4.92256i	−0.200346	−	0.249263i
$391$	−4.70694	−	2.71755i	−0.238040	−	0.137432i
$392$	−1.06507	−	6.91850i	−0.0537940	−	0.349437i
$393$	0.233695	−	0.602212i	0.0117884	−	0.0303776i
$394$	−4.72572			−0.238078
$395$	1.64138	+	2.84295i	0.0825866	+	0.143044i
$396$	6.11615	−	6.69367i	0.307348	−	0.336369i
$397$	−12.7252	−	7.34692i	−0.638662	−	0.368732i	0.145437	−	0.989368i	$-0.453541\pi$
$397$	−12.7252	−	7.34692i	−0.638662	−	0.368732i	−0.784099	+	0.620636i	$0.786875\pi$
$398$	1.06047	+	1.83679i	0.0531567	+	0.0920701i
$399$	8.58954	+	36.7182i	0.430015	+	1.83821i
$400$	−3.80924	+	6.59779i	−0.190462	+	0.329890i
$401$	14.4162	−	8.32318i	0.719909	−	0.415640i	−0.0948099	−	0.995495i	$-0.530224\pi$
$401$	14.4162	−	8.32318i	0.719909	−	0.415640i	0.814719	+	0.579855i	$0.196891\pi$
$402$	−0.507173	+	0.407642i	−0.0252955	+	0.0203313i
$403$	−3.07208	+	5.32101i	−0.153031	+	0.265058i
$404$	6.85234	−	11.8686i	0.340917	−	0.590485i
$405$	−2.87682	−	31.8405i	−0.142950	−	1.58217i
$406$	−6.38778	−	9.33756i	−0.317020	−	0.463416i
$407$	15.3028	−	8.83510i	0.758534	−	0.437940i
$408$	2.61329	+	1.01412i	0.129377	+	0.0502064i
$409$			2.80886i			0.138889i	0.997586	+	0.0694446i	$0.0221227\pi$
$409$			2.80886i			0.138889i	−0.997586	+	0.0694446i	$0.977877\pi$
$410$			0.335493i			0.0165688i
$411$	−1.86938	−	12.0884i	−0.0922095	−	0.596279i
$412$	−2.64014	+	1.52429i	−0.130070	+	0.0750962i
$413$	−23.3221	+	1.78465i	−1.14761	+	0.0878169i
$414$	−9.60429	+	3.04322i	−0.472025	+	0.149566i
$415$	−19.2962	+	33.4219i	−0.947211	+	1.64062i
$416$	0.513232	−	0.888944i	0.0251633	−	0.0435841i
$417$	3.86096	+	24.9672i	0.189072	+	1.22265i
$418$	21.5387	−	12.4354i	1.05349	−	0.608234i
$419$	7.47362	−	12.9447i	0.365110	−	0.632390i	−0.623684	−	0.781677i	$-0.714365\pi$
$419$	7.47362	−	12.9447i	0.365110	−	0.632390i	0.988794	+	0.149287i	$0.0476980\pi$
$420$	−4.71410	+	15.5809i	−0.230024	+	0.760271i
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	0.610794	−	0.791789i	$-0.290850\pi$
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	−0.991107	+	0.133069i	$0.957517\pi$
$422$	−23.9160	−	13.8079i	−1.16421	−	0.672160i
$423$	3.31641	−	15.0605i	0.161250	−	0.732268i
$424$	1.59484	+	2.76235i	0.0774524	+	0.134151i
$425$	12.3298			0.598083
$426$	−15.1770	−	18.8826i	−0.735326	−	0.914867i
$427$	−0.946827	−	12.3733i	−0.0458201	−	0.598786i
$428$	11.3681	+	6.56336i	0.549496	+	0.317252i
$429$	−1.94398	+	5.00947i	−0.0938563	+	0.241859i
$430$	−18.8210	−	10.8663i	−0.907629	−	0.524020i
$431$	−14.0087	+	8.08792i	−0.674775	+	0.389581i	−0.797883	−	0.602812i	$-0.794047\pi$
$431$	−14.0087	+	8.08792i	−0.674775	+	0.389581i	0.123109	+	0.992393i	$0.460714\pi$
$432$	4.65538	−	2.30812i	0.223982	−	0.111049i
$433$		−	27.2499i		−	1.30955i	−0.755824	−	0.654774i	$-0.772764\pi$
$433$		−	27.2499i		−	1.30955i	0.755824	−	0.654774i	$-0.227236\pi$
$434$	15.7907	−	1.20833i	0.757976	−	0.0580017i
$435$	4.02072	+	26.0003i	0.192779	+	1.24662i
$436$	−5.28574	−	9.15516i	−0.253141	−	0.438453i
$437$	−27.6351			−1.32197
$438$	0.821562	−	2.11709i	0.0392557	−	0.101159i
$439$			33.1347i			1.58143i	0.612182	+	0.790717i	$0.290292\pi$
$439$			33.1347i			1.58143i	−0.612182	+	0.790717i	$0.709708\pi$
$440$	10.7362			0.511829
$441$	−1.34309	+	20.9570i	−0.0639568	+	0.997953i
$442$	−1.66124			−0.0790171
$443$		−	22.2636i		−	1.05777i	−0.848692	−	0.528887i	$-0.822609\pi$
$443$		−	22.2636i		−	1.05777i	0.848692	−	0.528887i	$-0.177391\pi$
$444$	10.0074	−	1.54756i	0.474932	−	0.0734442i
$445$	−16.7307			−0.793111
$446$	−10.1734	−	17.6209i	−0.481727	−	0.834375i
$447$	17.2811	+	6.70612i	0.817366	+	0.317188i
$448$	−2.63804	+	0.201867i	−0.124636	+	0.00953733i
$449$		−	6.80819i		−	0.321298i	−0.987012	−	0.160649i	$-0.948641\pi$
$449$		−	6.80819i		−	0.321298i	0.987012	−	0.160649i	$-0.0513588\pi$
$450$	15.4170	−	16.8727i	0.726763	−	0.795386i
$451$	0.247206	−	0.142724i	0.0116405	−	0.00672062i
$452$	−10.6520	−	6.14993i	−0.501027	−	0.289268i
$453$	27.3895	−	4.23555i	1.28687	−	0.199004i
$454$	−3.60266	−	2.08000i	−0.169081	−	0.0976192i
$455$	−0.736060	−	9.61897i	−0.0345070	−	0.450944i
$456$	14.0854	−	2.17819i	0.659611	−	0.102003i
$457$	15.2260			0.712240			0.356120	−	0.934440i	$-0.384099\pi$
$457$	15.2260			0.712240			0.356120	+	0.934440i	$0.384099\pi$
$458$	−2.98482	−	5.16986i	−0.139471	−	0.241572i
$459$	−7.00218	−	4.65716i	−0.326834	−	0.217378i
$460$	−10.3313	−	5.96476i	−0.481698	−	0.278108i
$461$	0.103381	+	0.179060i	0.00481492	+	0.00833968i	0.868423	−	0.495824i	$-0.165134\pi$
$461$	0.103381	+	0.179060i	0.00481492	+	0.00833968i	−0.863608	+	0.504164i	$0.831801\pi$
$462$	13.4861	−	3.15483i	0.627432	−	0.146776i
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	−0.986826	−	0.161785i	$-0.948275\pi$
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	0.633523	+	0.773724i	$0.281608\pi$
$464$	−3.70319	+	2.13804i	−0.171916	+	0.0992560i
$465$	−34.3339	−	13.3237i	−1.59219	−	0.617870i
$466$	2.24360	−	3.88603i	0.103933	−	0.180017i
$467$	1.15424	−	1.99921i	0.0534120	−	0.0925123i	−0.838083	−	0.545542i	$-0.816324\pi$
$467$	1.15424	−	1.99921i	0.0534120	−	0.0925123i	0.891495	+	0.453030i	$0.149657\pi$
$468$	−2.07718	+	2.27332i	−0.0960178	+	0.105084i
$469$	−0.991047	+	0.0758366i	−0.0457623	+	0.00350181i
$470$	15.8138	−	9.13009i	0.729435	−	0.421139i
$471$	15.5613	−	12.5075i	0.717029	−	0.576314i
$472$			8.84071i			0.406927i
$473$			18.4908i			0.850209i
$474$	1.24761	−	1.00277i	0.0573045	−	0.0460587i
$475$	54.2925	−	31.3458i	2.49111	−	1.43824i
$476$	2.41765	+	3.53408i	0.110813	+	0.161984i
$477$	−2.89042	−	9.12207i	−0.132343	−	0.417671i
$478$	1.74905	−	3.02944i	0.0799996	−	0.138563i
$479$	6.21659	−	10.7674i	0.284043	−	0.491977i	−0.688334	−	0.725394i	$-0.741657\pi$
$479$	6.21659	−	10.7674i	0.284043	−	0.491977i	0.972377	+	0.233417i	$0.0749908\pi$
$480$	5.73592	+	2.22589i	0.261808	+	0.101598i
$481$	−5.19719	+	3.00060i	−0.236971	+	0.136815i
$482$	−5.78332	+	10.0170i	−0.263423	+	0.456262i
$483$	−14.7302	−	4.45671i	−0.670248	−	0.202787i
$484$	0.932639	+	1.61538i	0.0423927	+	0.0734263i
$485$	47.3622	+	27.3446i	2.15061	+	1.24165i
$486$	−15.1285	+	3.75888i	−0.686242	+	0.170506i
$487$	−18.6503	−	32.3033i	−0.845128	−	1.46380i	−0.885510	−	0.464620i	$-0.846191\pi$
$487$	−18.6503	−	32.3033i	−0.845128	−	1.46380i	0.0403829	−	0.999184i	$-0.487142\pi$
$488$	−4.69034			−0.212322
$489$	−4.70330	+	0.727325i	−0.212690	+	0.0328908i
$490$	−19.3920	+	15.5646i	−0.876039	+	0.703138i
$491$	−11.8191	−	6.82377i	−0.533389	−	0.307952i	0.209006	−	0.977914i	$-0.432977\pi$
$491$	−11.8191	−	6.82377i	−0.533389	−	0.307952i	−0.742396	+	0.669962i	$0.766310\pi$
$492$	0.161662	−	0.0249997i	0.00728830	−	0.00112707i
$493$	5.99328	+	3.46022i	0.269924	+	0.155840i
$494$	−7.31502	+	4.22333i	−0.329118	+	0.190017i
$495$	−31.4550	−	6.92657i	−1.41380	−	0.311326i
$496$		−	5.98576i		−	0.268768i
$497$	−2.82348	−	36.8978i	−0.126651	−	1.65509i
$498$	17.5427	+	6.80766i	0.786109	+	0.305059i
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	0.999415	−	0.0342021i	$-0.0108890\pi$
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	−0.529327	+	0.848418i	$0.677556\pi$
$500$	9.30148			0.415975
$501$	9.48100	−	1.46616i	0.423580	−	0.0655030i
$502$			26.7426i			1.19358i
$503$	−22.3018			−0.994388			−0.497194	−	0.867639i	$-0.665636\pi$
$503$	−22.3018			−0.994388			−0.497194	+	0.867639i	$0.665636\pi$
$504$	7.85918	+	1.11052i	0.350076	+	0.0494667i
$505$	−48.6824			−2.16634
$506$			10.1500i			0.451224i
$507$	−7.48577	+	19.2902i	−0.332455	+	0.856706i
$508$	−0.287164			−0.0127408
$509$	−10.9589	−	18.9814i	−0.485746	−	0.841337i	0.514120	−	0.857719i	$-0.328119\pi$
$509$	−10.9589	−	18.9814i	−0.485746	−	0.841337i	−0.999866	+	0.0163813i	$0.994785\pi$
$510$	−1.52176	−	9.84057i	−0.0673847	−	0.435748i
$511$	2.86304	−	1.95859i	0.126653	−	0.0866430i
$512$			1.00000i			0.0441942i
$513$	−42.6729	−	2.70567i	−1.88405	−	0.119458i
$514$	−4.51396	+	2.60614i	−0.199102	+	0.114952i
$515$	9.37844	+	5.41465i	0.413264	+	0.238598i
$516$	−3.83362	+	9.87890i	−0.168766	+	0.434894i
$517$	−13.4549	−	7.76818i	−0.591745	−	0.341644i
$518$	13.9470	+	6.68951i	0.612796	+	0.293920i
$519$	−12.1585	−	15.1272i	−0.533699	−	0.664009i
$520$	−3.64626			−0.159899
$521$	13.3839	+	23.1816i	0.586358	+	1.01560i	0.994705	+	0.102775i	$0.0327723\pi$
$521$	13.3839	+	23.1816i	0.586358	+	1.01560i	−0.408346	+	0.912827i	$0.633894\pi$
$522$	12.2290	−	3.87489i	0.535249	−	0.169599i
$523$	14.8576	+	8.57805i	0.649678	+	0.375092i	0.788333	−	0.615249i	$-0.210945\pi$
$523$	14.8576	+	8.57805i	0.649678	+	0.375092i	−0.138655	+	0.990341i	$0.544278\pi$
$524$	−0.186474	−	0.322983i	−0.00814617	−	0.0141096i
$525$	33.9945	−	7.95238i	1.48364	−	0.347070i
$526$	7.51869	−	13.0228i	0.327831	−	0.567819i
$527$	−8.38954	+	4.84370i	−0.365454	+	0.210995i
$528$	−0.800023	−	5.17341i	−0.0348165	−	0.225144i
$529$	−5.86091	+	10.1514i	−0.254822	+	0.441365i
$530$	5.66528	−	9.81255i	0.246084	−	0.426230i
$531$	5.70367	−	25.9016i	0.247518	−	1.12403i
$532$	19.6304	+	9.41547i	0.851084	+	0.408212i
$533$	−0.0839566	+	0.0484723i	−0.00363656	+	0.00209957i
$534$	1.24671	+	8.06194i	0.0539505	+	0.348874i
$535$		−	46.6294i		−	2.01596i
$536$			0.375675i			0.0162267i
$537$	4.42724	+	1.71804i	0.191049	+	0.0741390i
$538$	20.0323	−	11.5657i	0.863654	−	0.498631i
$539$	19.7183	+	7.66737i	0.849329	+	0.330257i
$540$	−15.3691	−	10.2220i	−0.661381	−	0.439886i
$541$	−14.4091	+	24.9573i	−0.619496	+	1.07300i	0.370081	+	0.928999i	$0.379330\pi$
$541$	−14.4091	+	24.9573i	−0.619496	+	1.07300i	−0.989578	+	0.144000i	$0.954004\pi$
$542$	−4.95748	+	8.58661i	−0.212942	+	0.368827i
$543$	30.0920	−	24.1865i	1.29137	−	1.03794i
$544$	1.40158	−	0.809204i	0.0600924	−	0.0346943i
$545$	−18.7763	+	32.5214i	−0.804286	+	1.39306i
$546$	−4.58020	+	1.07145i	−0.196014	+	0.0458539i
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	−0.967972	−	0.251056i	$-0.919222\pi$
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	0.266565	−	0.963817i	$-0.414111\pi$
$548$	−6.11607	−	3.53111i	−0.261265	−	0.150842i
$549$	13.7418	+	3.02602i	0.586485	+	0.129147i
$550$	−11.5129	−	19.9410i	−0.490913	−	0.850286i
$551$	35.1874			1.49903
$552$	−2.10436	+	5.42275i	−0.0895676	+	0.230808i
$553$	2.43790	−	0.186552i	0.103670	−	0.00793302i
$554$	7.44299	+	4.29721i	0.316223	+	0.182571i
$555$	−22.5353	−	28.0376i	−0.956569	−	1.19013i
$556$	12.6320	+	7.29308i	0.535715	+	0.309295i
$557$	−40.0544	+	23.1254i	−1.69716	+	0.979855i	−0.748725	+	0.662880i	$0.769334\pi$
$557$	−40.0544	+	23.1254i	−1.69716	+	0.979855i	−0.948434	+	0.316975i	$0.897333\pi$
$558$	−3.86177	+	17.5371i	−0.163482	+	0.742405i
$559$		−	6.27990i		−	0.265611i
$560$	5.30650	+	7.75696i	0.224240	+	0.327791i
$561$	−6.60357	+	5.30764i	−0.278803	+	0.224089i
$562$	−10.3639	−	17.9508i	−0.437174	−	0.757208i
$563$	1.97727			0.0833322			0.0416661	−	0.999132i	$-0.486733\pi$
$563$	1.97727			0.0833322			0.0416661	+	0.999132i	$0.486733\pi$
$564$	−5.57785	−	6.93976i	−0.234870	−	0.292217i
$565$			43.6922i			1.83814i
$566$	−2.36710			−0.0994966
$567$	−22.3094	−	8.32405i	−0.936908	−	0.349577i
$568$	−13.9868			−0.586874
$569$			32.9901i			1.38302i	0.722369	+	0.691508i	$0.243053\pi$
$569$			32.9901i			1.38302i	−0.722369	+	0.691508i	$0.756947\pi$
$570$	−31.7183	−	39.4628i	−1.32853	−	1.65291i
$571$	14.8065			0.619634			0.309817	−	0.950796i	$-0.399732\pi$
$571$	14.8065			0.619634			0.309817	+	0.950796i	$0.399732\pi$
$572$	1.55118	+	2.68672i	0.0648580	+	0.112337i
$573$	−6.92921	+	5.56937i	−0.289472	+	0.232664i
$574$	0.225303	+	0.108064i	0.00940397	+	0.00451050i
$575$			25.5851i			1.06697i
$576$	0.645160	−	2.92981i	0.0268817	−	0.122075i
$577$	−15.9505	+	9.20901i	−0.664027	+	0.383376i	−0.793810	−	0.608166i	$-0.791905\pi$
$577$	−15.9505	+	9.20901i	−0.664027	+	0.383376i	0.129783	+	0.991542i	$0.458572\pi$
$578$	12.4541	+	7.19038i	0.518022	+	0.299080i
$579$	−17.3448	−	21.5798i	−0.720827	−	0.896827i
$580$	13.1547	+	7.59485i	0.546218	+	0.315359i
$581$	16.2294	+	23.7239i	0.673308	+	0.984231i
$582$	9.64714	−	24.8598i	0.399887	−	1.03047i
$583$	−9.64041			−0.399265
$584$	−0.655556	−	1.13546i	−0.0271271	−	0.0469855i
$585$	10.6828	+	2.35242i	0.441681	+	0.0972605i
$586$	15.3074	+	8.83774i	0.632343	+	0.365084i
$587$	23.1065	+	40.0216i	0.953707	+	1.65187i	0.737301	+	0.675565i	$0.236100\pi$
$587$	23.1065	+	40.0216i	0.953707	+	1.65187i	0.216406	+	0.976304i	$0.430567\pi$
$588$	8.94507	+	8.18448i	0.368888	+	0.337522i
$589$	−24.6281	+	42.6571i	−1.01478	+	1.75765i
$590$	27.1970	−	15.7022i	1.11968	−	0.646450i
$591$	6.37986	−	5.12783i	0.262432	−	0.210931i
$592$	2.92323	−	5.06319i	0.120144	−	0.208096i
$593$	6.80465	−	11.7860i	0.279434	−	0.483993i	−0.691810	−	0.722079i	$-0.743187\pi$
$593$	6.80465	−	11.7860i	0.279434	−	0.483993i	0.971244	+	0.238086i	$0.0765200\pi$
$594$	−0.993759	+	15.6732i	−0.0407744	+	0.643080i
$595$	6.57798	−	13.7145i	0.269671	−	0.562238i
$596$	9.26832	−	5.35107i	0.379645	−	0.219188i
$597$	−3.42476	−	1.32902i	−0.140166	−	0.0543930i
$598$		−	3.44718i		−	0.140965i
$599$			23.5806i			0.963477i	0.876315	+	0.481739i	$0.159995\pi$
$599$			23.5806i			0.963477i	−0.876315	+	0.481739i	$0.840005\pi$
$600$	−2.01662	−	13.0406i	−0.0823280	−	0.532380i
$601$	−31.0765	+	17.9420i	−1.26764	+	0.731871i	−0.974540	−	0.224212i	$-0.928019\pi$
$601$	−31.0765	+	17.9420i	−1.26764	+	0.731871i	−0.293097	+	0.956083i	$0.594686\pi$
$602$	−13.3597	+	9.13931i	−0.544501	+	0.372490i
$603$	0.242371	−	1.10066i	0.00987010	−	0.0448222i
$604$	8.00065	−	13.8575i	0.325542	−	0.563855i
$605$	3.31297	−	5.73823i	0.134691	−	0.233292i
$606$	3.62764	+	23.4584i	0.147363	+	0.952931i
$607$	−16.8502	+	9.72845i	−0.683928	+	0.394866i	−0.801333	−	0.598218i	$-0.795876\pi$
$607$	−16.8502	+	9.72845i	−0.683928	+	0.394866i	0.117406	+	0.993084i	$0.462542\pi$
$608$	4.11444	−	7.12643i	0.166863	−	0.289015i
$609$	18.7558	+	5.67467i	0.760023	+	0.229949i
$610$	8.33063	+	14.4291i	0.337297	+	0.584216i
$611$	4.56958	+	2.63825i	0.184865	+	0.106732i
$612$	−4.62843	+	1.46657i	−0.187093	+	0.0592825i
$613$	−21.1210	−	36.5827i	−0.853071	−	1.47756i	−0.878423	−	0.477883i	$-0.841404\pi$
$613$	−21.1210	−	36.5827i	−0.853071	−	1.47756i	0.0253526	−	0.999679i	$-0.491929\pi$
$614$	1.28155			0.0517193
$615$	−0.364040	−	0.452926i	−0.0146795	−	0.0182637i
$616$	3.45819	−	7.20999i	0.139334	−	0.290499i
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	0.681274	−	0.732029i	$-0.261426\pi$
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	−0.293319	+	0.956015i	$0.594760\pi$
$618$	1.91028	−	4.92262i	0.0768428	−	0.198017i
$619$	8.71387	+	5.03096i	0.350240	+	0.202211i	0.664791	−	0.747029i	$-0.268521\pi$
$619$	8.71387	+	5.03096i	0.350240	+	0.202211i	−0.314551	+	0.949241i	$0.601854\pi$
$620$	−18.4142	+	10.6315i	−0.739533	+	0.426969i
$621$	9.66391	−	14.5300i	0.387799	−	0.583067i
$622$			12.5329i			0.502522i
$623$	−5.38904	+	11.2356i	−0.215907	+	0.450147i
$624$	0.271706	+	1.75700i	0.0108769	+	0.0703365i
$625$	2.52560	+	4.37447i	0.101024	+	0.174979i
$626$	−8.75385			−0.349874
$627$	−15.5844	+	40.1595i	−0.622380	+	1.60382i
$628$		−	11.5267i		−	0.459964i
$629$	−9.46198			−0.377274
$630$	−10.5425	−	26.1499i	−0.420025	−	1.04184i
$631$	10.3528			0.412139			0.206070	−	0.978537i	$-0.433933\pi$
$631$	10.3528			0.412139			0.206070	+	0.978537i	$0.433933\pi$
$632$		−	0.924134i		−	0.0367601i
$633$	47.2702	−	7.30994i	1.87882	−	0.290544i
$634$	13.6784			0.543239
$635$	0.510039	+	0.883413i	0.0202403	+	0.0350572i
$636$	−5.15048	−	1.99870i	−0.204230	−	0.0792538i
$637$	−6.69679	−	2.60401i	−0.265336	−	0.103175i
$638$		−	12.9239i		−	0.511662i
$639$	40.9787	+	9.02374i	1.62109	+	0.356974i
$640$	3.07634	−	1.77612i	0.121603	−	0.0702075i
$641$	−23.0678	−	13.3182i	−0.911123	−	0.526037i	−0.0303310	−	0.999540i	$-0.509656\pi$
$641$	−23.0678	−	13.3182i	−0.911123	−	0.526037i	−0.880792	+	0.473503i	$0.842989\pi$
$642$	−22.4691	+	3.47465i	−0.886783	+	0.137134i
$643$	40.0493	+	23.1225i	1.57939	+	0.911861i	0.994944	+	0.100429i	$0.0320214\pi$
$643$	40.0493	+	23.1225i	1.57939	+	0.911861i	0.584446	+	0.811433i	$0.301312\pi$
$644$	−7.33344	+	5.01677i	−0.288978	+	0.197688i
$645$	37.1998	−	5.75264i	1.46474	−	0.226510i
$646$	−13.3177			−0.523978
$647$	−15.7032	−	27.1987i	−0.617355	−	1.06929i	−0.989966	−	0.141303i	$-0.954871\pi$
$647$	−15.7032	−	27.1987i	−0.617355	−	1.06929i	0.372611	−	0.927988i	$-0.378463\pi$
$648$	−3.78039	+	8.16754i	−0.148508	+	0.320851i
$649$	−23.1401	−	13.3600i	−0.908329	−	0.524424i
$650$	3.91005	+	6.77240i	0.153365	+	0.265635i
$651$	−20.0067	+	18.7656i	−0.784125	+	0.735481i
$652$	−1.37386	+	2.37960i	−0.0538046	+	0.0931923i
$653$	39.9639	−	23.0732i	1.56391	−	0.902924i	0.567054	−	0.823681i	$-0.308083\pi$
$653$	39.9639	−	23.0732i	1.56391	−	0.902924i	0.996855	−	0.0792429i	$-0.0252503\pi$
$654$	17.0701	+	6.62424i	0.667493	+	0.259028i
$655$	−0.662404	+	1.14732i	−0.0258823	+	0.0448294i
$656$	0.0472226	−	0.0817920i	0.00184373	−	0.00319344i
$657$	1.18810	+	3.74960i	0.0463522	+	0.146286i
$658$	−1.03769	−	13.5607i	−0.0404534	−	0.528652i
$659$	1.18052	−	0.681575i	0.0459867	−	0.0265504i	−0.476830	−	0.878995i	$-0.658214\pi$
$659$	1.18052	−	0.681575i	0.0459867	−	0.0265504i	0.522817	+	0.852445i	$0.324881\pi$
$660$	−14.4942	+	11.6498i	−0.564186	+	0.453466i
$661$		−	7.20404i		−	0.280205i	−0.990137	−	0.140102i	$-0.955257\pi$
$661$		−	7.20404i		−	0.280205i	0.990137	−	0.140102i	$-0.0447431\pi$
$662$		−	10.8972i		−	0.423530i
$663$	2.24272	−	1.80259i	0.0871001	−	0.0700069i
$664$	9.40866	−	5.43209i	0.365127	−	0.210806i
$665$	−5.90080	−	77.1127i	−0.228823	−	2.99030i
$666$	−11.8311	+	12.9482i	−0.458445	+	0.501733i
$667$	−7.18018	+	12.4364i	−0.278018	+	0.481541i
$668$	2.76946	−	4.79685i	0.107154	−	0.185596i
$669$	32.8547	+	12.7497i	1.27024	+	0.492931i
$670$	1.15570	−	0.667247i	0.0446488	−	0.0257780i
$671$	7.08797	−	12.2767i	0.273628	−	0.473938i
$672$	3.34239	−	3.13504i	0.128935	−	0.120937i
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	0.947558	+	0.319585i	$0.103544\pi$
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	−0.197010	+	0.980402i	$0.563123\pi$
$674$	22.1858	+	12.8090i	0.854565	+	0.493383i
$675$	−2.50496	+	39.5074i	−0.0964161	+	1.52064i
$676$	5.97319	+	10.3459i	0.229738	+	0.397918i
$677$	2.41011			0.0926280			0.0463140	−	0.998927i	$-0.485253\pi$
$677$	2.41011			0.0926280			0.0463140	+	0.998927i	$0.485253\pi$
$678$	21.0537	−	3.25578i	0.808563	−	0.125037i
$679$	33.6191	−	22.9986i	1.29018	−	0.882607i
$680$	−4.97877	−	2.87450i	−0.190927	−	0.110232i
$681$	7.12069	−	1.10115i	0.272865	−	0.0421963i
$682$	15.6674	+	9.04559i	0.599937	+	0.346374i
$683$	24.5302	−	14.1625i	0.938624	−	0.541915i	0.0490952	−	0.998794i	$-0.484366\pi$
$683$	24.5302	−	14.1625i	0.938624	−	0.541915i	0.889529	+	0.456879i	$0.151033\pi$
$684$	−16.6522	+	18.2246i	−0.636713	+	0.696834i
$685$			25.0868i			0.958517i
$686$	4.20631	+	18.0363i	0.160598	+	0.688628i
$687$	9.63935	+	3.74066i	0.367764	+	0.142715i
$688$	3.05899	+	5.29833i	0.116623	+	0.201997i
$689$	3.27410			0.124733
$690$	20.4198	−	3.15775i	0.777369	−	0.120214i
$691$		−	3.41022i		−	0.129731i	−0.997894	−	0.0648655i	$-0.979338\pi$
$691$		−	3.41022i		−	0.129731i	0.997894	−	0.0648655i	$-0.0206618\pi$
$692$	−11.2051			−0.425953
$693$	−14.7834	+	18.8928i	−0.561576	+	0.717678i
$694$	−16.7623			−0.636289
$695$		−	51.8136i		−	1.96540i
$696$	2.67945	−	6.90471i	0.101564	−	0.261722i
$697$	−0.152851			−0.00578964
$698$	8.34010	+	14.4455i	0.315678	+	0.546769i
$699$	1.18776	+	7.68076i	0.0449254	+	0.290513i
$700$	8.71704	−	18.1742i	0.329473	−	0.686920i
$701$		−	51.4943i		−	1.94491i	−0.233087	−	0.972456i	$-0.574883\pi$
$701$		−	51.4943i		−	1.94491i	0.233087	−	0.972456i	$-0.425117\pi$
$702$	0.337503	−	5.32298i	0.0127382	−	0.200903i
$703$	−41.6644	+	24.0550i	−1.57140	+	0.907251i
$704$	−2.61745	−	1.51119i	−0.0986488	−	0.0569549i
$705$	−11.4421	+	29.4853i	−0.430934	+	1.11048i
$706$	−31.1021	−	17.9568i	−1.17054	−	0.675814i
$707$	−15.6809	+	32.6931i	−0.589739	+	1.22955i
$708$	−9.59297	−	11.9352i	−0.360526	−	0.448553i
$709$	10.0844			0.378726			0.189363	−	0.981907i	$-0.439358\pi$
$709$	10.0844			0.378726			0.189363	+	0.981907i	$0.439358\pi$
$710$	24.8424	+	43.0282i	0.932317	+	1.61482i
$711$	−0.596214	+	2.70753i	−0.0223598	+	0.101540i
$712$	4.07888	+	2.35495i	0.152863	+	0.0882553i
$713$	−10.0510	−	17.4088i	−0.376412	−	0.651965i
$714$	−7.09869	−	2.14775i	−0.265662	−	0.0803774i
$715$	5.51017	−	9.54389i	0.206069	−	0.356921i
$716$	2.37445	−	1.37089i	0.0887375	−	0.0512326i
$717$	0.925948	+	5.98770i	0.0345802	+	0.223615i
$718$	−14.2749	+	24.7248i	−0.532734	+	0.922722i
$719$	−15.9584	+	27.6408i	−0.595148	+	1.03083i	0.398378	+	0.917221i	$0.369573\pi$
$719$	−15.9584	+	27.6408i	−0.595148	+	1.03083i	−0.993526	+	0.113605i	$0.963760\pi$
$720$	−10.1590	+	3.21897i	−0.378602	+	0.119964i
$721$	6.65709	−	4.55409i	0.247923	−	0.169603i
$722$	−42.1881	+	24.3573i	−1.57008	+	0.906485i
$723$	−3.06170	−	19.7987i	−0.113866	−	0.736321i
$724$		−	22.2899i		−	0.828397i
$725$		−	32.5772i		−	1.20989i
$726$	−3.01192	−	1.16881i	−0.111783	−	0.0433787i
$727$	−17.9336	+	10.3540i	−0.665120	+	0.384007i	−0.794225	−	0.607624i	$-0.792123\pi$
$727$	−17.9336	+	10.3540i	−0.665120	+	0.384007i	0.129105	+	0.991631i	$0.458790\pi$
$728$	−1.17448	+	2.44867i	−0.0435290	+	0.0907539i
$729$	16.3452	−	21.4904i	0.605377	−	0.795939i
$730$	−2.32870	+	4.03342i	−0.0861889	+	0.149284i
$731$	4.95070	−	8.57487i	0.183108	−	0.317153i
$732$	6.33210	−	5.08944i	0.234041	−	0.188111i
$733$	7.69996	−	4.44558i	0.284405	−	0.164201i	−0.351011	−	0.936371i	$-0.614162\pi$
$733$	7.69996	−	4.44558i	0.284405	−	0.164201i	0.635416	+	0.772170i	$0.280829\pi$
$734$	−0.179362	+	0.310665i	−0.00662038	+	0.0114668i
$735$	9.29069	−	42.0547i	0.342692	−	1.55121i
$736$	1.67915	+	2.90837i	0.0618943	+	0.107204i
$737$	−0.983312	−	0.567715i	−0.0362207	−	0.0209121i
$738$	−0.191122	+	0.209169i	−0.00703530	+	0.00769960i
$739$	−16.3882	−	28.3851i	−0.602848	−	1.04416i	−0.992388	−	0.123154i	$-0.960699\pi$
$739$	−16.3882	−	28.3851i	−0.602848	−	1.04416i	0.389539	−	0.921010i	$-0.372634\pi$
$740$	−20.7681			−0.763451
$741$	5.29280	−	13.6391i	0.194436	−	0.501044i
$742$	−4.76488	−	6.96523i	−0.174924	−	0.255702i
$743$	−6.68055	−	3.85702i	−0.245086	−	0.141500i	0.372426	−	0.928062i	$-0.378526\pi$
$743$	−6.68055	−	3.85702i	−0.245086	−	0.141500i	−0.617512	+	0.786562i	$0.711859\pi$
$744$	6.49509	+	8.08095i	0.238121	+	0.296262i
$745$	−32.9234	−	19.0083i	−1.20622	−	0.696411i
$746$	21.9718	−	12.6854i	0.804445	−	0.464446i
$747$	−31.0701	+	9.84490i	−1.13680	+	0.360206i
$748$			4.89143i			0.178848i
$749$	−31.3143	−	15.0196i	−1.14420	−	0.548803i
$750$	−12.5573	+	10.0929i	−0.458527	+	0.368542i
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	−0.997389	−	0.0722207i	$-0.976991\pi$
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	0.436149	−	0.899874i	$-0.356342\pi$
$752$	−5.14045			−0.187453
$753$	−29.0181	−	36.1033i	−1.05748	−	1.31568i
$754$			4.38924i			0.159847i
$755$	−56.8406			−2.06864
$756$	−11.8151	+	7.02868i	−0.429713	+	0.255631i
$757$	46.4611			1.68866			0.844328	−	0.535827i	$-0.180000\pi$
$757$	46.4611			1.68866			0.844328	+	0.535827i	$0.180000\pi$
$758$			26.9063i			0.977282i
$759$	−11.0137	−	13.7028i	−0.399772	−	0.497381i
$760$	−29.2311			−1.06032
$761$	−18.5959	−	32.2090i	−0.674099	−	1.16757i	−0.976731	−	0.214467i	$-0.931199\pi$
$761$	−18.5959	−	32.2090i	−0.674099	−	1.16757i	0.302632	−	0.953107i	$-0.402135\pi$
$762$	0.387680	−	0.311599i	0.0140442	−	0.0112880i
$763$	15.7921	+	23.0847i	0.571713	+	0.835721i
$764$			5.13264i			0.185692i
$765$	12.7323	+	11.6338i	0.460338	+	0.420622i
$766$	10.8874	−	6.28586i	0.393379	−	0.227117i
$767$	7.85890	+	4.53734i	0.283768	+	0.163834i
$768$	−1.08509	−	1.35003i	−0.0391548	−	0.0487150i
$769$	−12.2312	−	7.06166i	−0.441067	−	0.254650i	0.262983	−	0.964800i	$-0.415294\pi$
$769$	−12.2312	−	7.06166i	−0.441067	−	0.254650i	−0.704050	+	0.710150i	$0.748627\pi$
$770$	−28.3225	+	2.16729i	−1.02067	+	0.0781037i
$771$	3.26609	−	8.41642i	0.117625	−	0.303110i
$772$	−15.9847			−0.575302
$773$	15.4728	+	26.7996i	0.556517	+	0.963915i	0.997784	+	0.0665393i	$0.0211958\pi$
$773$	15.4728	+	26.7996i	0.556517	+	0.963915i	−0.441267	+	0.897376i	$0.645471\pi$
$774$	−5.54399	−	17.4966i	−0.199275	−	0.628904i
$775$	39.4928	+	22.8012i	1.41862	+	0.819043i
$776$	−7.69782	−	13.3330i	−0.276336	−	0.478627i
$777$	−26.0876	+	6.10271i	−0.935887	+	0.218933i
$778$	8.12937	−	14.0805i	0.291452	−	0.504810i
$779$	−0.673057	+	0.388590i	−0.0241148	+	0.0139227i
$780$	4.92256	−	3.95652i	0.176256	−	0.141666i
$781$	21.1367	−	36.6098i	0.756330	−	1.31000i
$782$	2.71755	−	4.70694i	0.0971794	−	0.168320i
$783$	−12.3049	+	18.5008i	−0.439742	+	0.661165i
$784$	6.91850	−	1.06507i	0.247089	−	0.0380381i
$785$	−35.4599	+	20.4728i	−1.26562	+	0.730706i
$786$	0.602212	+	0.233695i	0.0214802	+	0.00833564i
$787$			18.3256i			0.653237i	0.945156	+	0.326619i	$0.105909\pi$
$787$			18.3256i			0.653237i	−0.945156	+	0.326619i	$0.894091\pi$
$788$		−	4.72572i		−	0.168347i
$789$	3.98041	+	25.7396i	0.141706	+	0.916353i
$790$	−2.84295	+	1.64138i	−0.101148	+	0.0583976i
$791$	29.3418	+	14.0735i	1.04328	+	0.500395i
$792$	6.69367	+	6.11615i	0.237849	+	0.217328i
$793$	−2.40723	+	4.16945i	−0.0854834	+	0.148062i
$794$	7.34692	−	12.7252i	0.260733	−	0.451602i
$795$	2.99921	+	19.3946i	0.106371	+	0.687854i
$796$	−1.83679	+	1.06047i	−0.0651034	+	0.0375875i
$797$	−1.07681	+	1.86508i	−0.0381424	+	0.0660646i	−0.884466	−	0.466604i	$-0.845477\pi$
$797$	−1.07681	+	1.86508i	−0.0381424	+	0.0660646i	0.846324	+	0.532668i	$0.178811\pi$
$798$	−36.7182	+	8.58954i	−1.29981	+	0.304067i
$799$	4.15968	+	7.20477i	0.147159	+	0.254886i
$800$	−6.59779	−	3.80924i	−0.233267	−	0.134677i
$801$	−10.4310	−	9.53107i	−0.368562	−	0.336764i
$802$	8.32318	+	14.4162i	0.293902	+	0.509053i
$803$	3.96266			0.139839
$804$	−0.407642	−	0.507173i	−0.0143764	−	0.0178866i
$805$	28.4584	+	13.6497i	1.00303	+	0.481090i
$806$	−5.32101	−	3.07208i	−0.187424	−	0.108210i
$807$	−14.4944	+	37.3508i	−0.510228	+	1.31481i
$808$	11.8686	+	6.85234i	0.417536	+	0.241064i
$809$	17.0147	−	9.82342i	0.598204	−	0.345373i	−0.170131	−	0.985421i	$-0.554419\pi$
$809$	17.0147	−	9.82342i	0.598204	−	0.345373i	0.768335	+	0.640048i	$0.221086\pi$
$810$	31.8405	−	2.87682i	1.11876	−	0.101081i
$811$			12.3340i			0.433105i	0.976271	+	0.216552i	$0.0694812\pi$
$811$			12.3340i			0.433105i	−0.976271	+	0.216552i	$0.930519\pi$
$812$	9.33756	−	6.38778i	0.327684	−	0.224167i
$813$	−2.62450	−	16.9715i	−0.0920452	−	0.595216i
$814$	8.83510	+	15.3028i	0.309670	+	0.536364i
$815$	9.76061			0.341899
$816$	−1.01412	+	2.61329i	−0.0355013	+	0.0914836i
$817$		−	50.3443i		−	1.76132i
$818$	−2.80886			−0.0982095
$819$	5.02078	−	6.41642i	0.175440	−	0.224208i
$820$	−0.335493			−0.0117159
$821$			22.3738i			0.780853i	0.920634	+	0.390426i	$0.127672\pi$
$821$			22.3738i			0.780853i	−0.920634	+	0.390426i	$0.872328\pi$
$822$	12.0884	−	1.86938i	0.421633	−	0.0652020i
$823$	27.0065			0.941388			0.470694	−	0.882297i	$-0.344004\pi$
$823$	27.0065			0.941388			0.470694	+	0.882297i	$0.344004\pi$
$824$	−1.52429	−	2.64014i	−0.0531010	−	0.0919737i
$825$	37.1805	+	14.4283i	1.29446	+	0.502330i
$826$	−1.78465	−	23.3221i	−0.0620959	−	0.811481i
$827$			26.3189i			0.915196i	0.889159	+	0.457598i	$0.151290\pi$
$827$			26.3189i			0.915196i	−0.889159	+	0.457598i	$0.848710\pi$
$828$	−3.04322	−	9.60429i	−0.105759	−	0.333772i
$829$	28.8691	−	16.6676i	1.00266	−	0.578888i	0.0936287	−	0.995607i	$-0.470153\pi$
$829$	28.8691	−	16.6676i	1.00266	−	0.578888i	0.909035	+	0.416719i	$0.136820\pi$
$830$	−33.4219	−	19.2962i	−1.16009	−	0.669779i
$831$	−14.7111	+	2.27495i	−0.510323	+	0.0789172i
$832$	0.888944	+	0.513232i	0.0308186	+	0.0177931i
$833$	−7.09126	−	8.83499i	−0.245698	−	0.306114i
$834$	−24.9672	+	3.86096i	−0.864543	+	0.133694i
$835$	−19.6756			−0.680903
$836$	12.4354	+	21.5387i	0.430086	+	0.744932i
$837$	−13.8158	−	27.8660i	−0.477545	−	0.963190i
$838$	12.9447	+	7.47362i	0.447167	+	0.258172i
$839$	−18.6896	−	32.3713i	−0.645236	−	1.11758i	−0.984247	−	0.176799i	$-0.943426\pi$
$839$	−18.6896	−	32.3713i	−0.645236	−	1.11758i	0.339011	−	0.940782i	$-0.389908\pi$
$840$	−15.5809	−	4.71410i	−0.537593	−	0.162652i
$841$	−5.35758	+	9.27960i	−0.184744	+	0.319986i
$842$	13.5158	−	7.80336i	0.465786	−	0.268922i
$843$	33.4698	+	12.9883i	1.15276	+	0.447342i
$844$	13.8079	−	23.9160i	0.475289	−	0.823224i
$845$	21.2182	−	36.7511i	0.729930	−	1.26428i
$846$	15.0605	+	3.31641i	0.517792	+	0.114021i
$847$	−2.78643	−	4.07316i	−0.0957429	−	0.139956i
$848$	−2.76235	+	1.59484i	−0.0948594	+	0.0547671i
$849$	3.19565	−	2.56852i	0.109675	−	0.0881512i
$850$			12.3298i			0.422909i
$851$		−	19.6342i		−	0.673052i
$852$	18.8826	−	15.1770i	0.646908	−	0.519954i
$853$	−4.65798	+	2.68929i	−0.159486	+	0.0920795i	−0.577619	−	0.816306i	$-0.696018\pi$
$853$	−4.65798	+	2.68929i	−0.159486	+	0.0920795i	0.418133	+	0.908386i	$0.362685\pi$
$854$	12.3733	−	0.946827i	0.423406	−	0.0323997i
$855$	85.6414	+	18.8587i	2.92887	+	0.644954i
$856$	−6.56336	+	11.3681i	−0.224331	+	0.388553i
$857$	22.7000	−	39.3176i	0.775418	−	1.34306i	−0.159142	−	0.987256i	$-0.550873\pi$
$857$	22.7000	−	39.3176i	0.775418	−	1.34306i	0.934559	−	0.355807i	$-0.115794\pi$
$858$	−5.00947	−	1.94398i	−0.171020	−	0.0663665i
$859$	3.36261	−	1.94141i	0.114731	−	0.0662399i	−0.441536	−	0.897243i	$-0.645566\pi$
$859$	3.36261	−	1.94141i	0.114731	−	0.0662399i	0.556267	+	0.831003i	$0.312233\pi$
$860$	10.8663	−	18.8210i	0.370538	−	0.641791i
$861$	−0.421425	+	0.0985846i	−0.0143621	+	0.00335975i
$862$	−8.08792	−	14.0087i	−0.275476	−	0.477138i
$863$	−20.3332	−	11.7394i	−0.692152	−	0.399614i	0.112266	−	0.993678i	$-0.464189\pi$
$863$	−20.3332	−	11.7394i	−0.692152	−	0.399614i	−0.804418	+	0.594064i	$0.797522\pi$
$864$	2.30812	+	4.65538i	0.0785238	+	0.158379i
$865$	19.9016	+	34.4706i	0.676674	+	1.17203i
$866$	27.2499			0.925991
$867$	−24.6156	+	3.80660i	−0.835990	+	0.129279i
$868$	1.20833	+	15.7907i	0.0410134	+	0.535970i
$869$	2.41887	+	1.39654i	0.0820547	+	0.0473743i
$870$	−26.0003	+	4.02072i	−0.881492	+	0.136315i
$871$	0.333955	+	0.192809i	0.0113156	+	0.00653308i
$872$	9.15516	−	5.28574i	0.310033	−	0.178998i
$873$	13.9512	+	44.0295i	0.472177	+	1.49017i
$874$		−	27.6351i		−	0.934770i
$875$	−24.5377	+	1.87766i	−0.829524	+	0.0634767i
$876$	2.11709	+	0.821562i	0.0715299	+	0.0277580i
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	−0.997787	−	0.0664896i	$-0.978820\pi$
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	0.441312	−	0.897354i	$-0.354513\pi$
$878$	−33.1347			−1.11824
$879$	−30.2552	+	4.67871i	−1.02048	+	0.157809i
$880$			10.7362i			0.361918i
$881$	7.44403			0.250796			0.125398	−	0.992107i	$-0.459979\pi$
$881$	7.44403			0.250796			0.125398	+	0.992107i	$0.459979\pi$
$882$	−20.9570	−	1.34309i	−0.705659	−	0.0452243i
$883$	−28.2839			−0.951828			−0.475914	−	0.879492i	$-0.657883\pi$
$883$	−28.2839			−0.951828			−0.475914	+	0.879492i	$0.657883\pi$
$884$		−	1.66124i		−	0.0558735i
$885$	−19.6785	+	50.7097i	−0.661485	+	1.70459i
$886$	22.2636			0.747960
$887$	6.06377	+	10.5028i	0.203602	+	0.352648i	0.949686	−	0.313203i	$-0.101402\pi$
$887$	6.06377	+	10.5028i	0.203602	+	0.352648i	−0.746085	+	0.665851i	$0.768069\pi$
$888$	1.54756	+	10.0074i	0.0519329	+	0.335827i
$889$	0.757550	−	0.0579690i	0.0254074	−	0.00194422i
$890$		−	16.7307i		−	0.560814i
$891$	−15.6653	−	22.2376i	−0.524806	−	0.744989i
$892$	17.6209	−	10.1734i	0.589992	−	0.340632i
$893$	36.6331	+	21.1501i	1.22588	+	0.707761i
$894$	−6.70612	+	17.2811i	−0.224286	+	0.577965i
$895$	−8.43465	−	4.86975i	−0.281939	−	0.162778i
$896$	−0.201867	−	2.63804i	−0.00674391	−	0.0881307i
$897$	3.74050	+	4.65379i	0.124892	+	0.155385i
$898$	6.80819			0.227192
$899$	12.7978	+	22.1664i	0.426830	+	0.739291i
$900$	16.8727	+	15.4170i	0.562423	+	0.513899i
$901$	4.47061	+	2.58111i	0.148938	+	0.0859891i
$902$	0.142724	+	0.247206i	0.00475220	+	0.00823105i
$903$	8.11902	−	26.8348i	0.270184	−	0.893007i
$904$	6.14993	−	10.6520i	0.204544	−	0.354280i
$905$	−68.5712	+	39.5896i	−2.27938	+	1.31600i
$906$	4.23555	+	27.3895i	0.140717	+	0.909955i
$907$	23.0890	−	39.9913i	0.766657	−	1.32789i	−0.172709	−	0.984973i	$-0.555252\pi$
$907$	23.0890	−	39.9913i	0.766657	−	1.32789i	0.939366	−	0.342916i	$-0.111415\pi$
$908$	2.08000	−	3.60266i	0.0690272	−	0.119559i
$909$	−30.3518	−	27.7332i	−1.00671	−	0.919851i
$910$	9.61897	−	0.736060i	0.318866	−	0.0244002i
$911$	−12.7284	+	7.34874i	−0.421710	+	0.243475i	−0.695809	−	0.718227i	$-0.744954\pi$
$911$	−12.7284	+	7.34874i	−0.421710	+	0.243475i	0.274098	+	0.961702i	$0.411621\pi$
$912$	2.17819	+	14.0854i	0.0721272	+	0.466415i
$913$			32.8356i			1.08670i
$914$			15.2260i			0.503630i
$915$	−26.9034	−	10.4402i	−0.889400	−	0.345142i
$916$	5.16986	−	2.98482i	0.170817	−	0.0986212i
$917$	0.557126	+	0.814399i	0.0183979	+	0.0268938i
$918$	4.65716	−	7.00218i	0.153709	−	0.231106i
$919$	−12.9345	+	22.4033i	−0.426671	+	0.739015i	−0.996575	−	0.0826958i	$-0.973647\pi$
$919$	−12.9345	+	22.4033i	−0.426671	+	0.739015i	0.569904	+	0.821711i	$0.306980\pi$
$920$	5.96476	−	10.3313i	0.196652	−	0.340612i
$921$	−1.73014	+	1.39060i	−0.0570099	+	0.0458219i
$922$	−0.179060	+	0.103381i	−0.00589704	+	0.00340466i
$923$	−7.17849	+	12.4335i	−0.236283	+	0.409254i
$924$	3.15483	+	13.4861i	0.103786	+	0.443662i
$925$	22.2706	+	38.5738i	0.732253	+	1.26830i
$926$	−13.1673	−	7.60217i	−0.432706	−	0.249823i
$927$	2.76255	+	8.71852i	0.0907341	+	0.286354i
$928$	−2.13804	−	3.70319i	−0.0701846	−	0.121563i
$929$	13.1935			0.432863			0.216432	−	0.976298i	$-0.430558\pi$
$929$	13.1935			0.432863			0.216432	+	0.976298i	$0.430558\pi$
$930$	13.3237	−	34.3339i	0.436900	−	1.12585i
$931$	−53.6863	−	20.8757i	−1.75950	−	0.684172i
$932$	3.88603	+	2.24360i	0.127291	+	0.0734915i
$933$	−13.5993	−	16.9197i	−0.445220	−	0.553927i
$934$	1.99921	+	1.15424i	0.0654161	+	0.0377680i
$935$	15.0477	−	8.68779i	0.492112	−	0.284121i
$936$	−2.27332	−	2.07718i	−0.0743057	−	0.0678948i
$937$			8.86021i			0.289451i	0.989472	+	0.144725i	$0.0462298\pi$
$937$			8.86021i			0.289451i	−0.989472	+	0.144725i	$0.953770\pi$
$938$	−0.0758366	−	0.991047i	−0.00247615	−	0.0323588i
$939$	11.8180	−	9.49871i	0.385664	−	0.309979i
$940$	9.13009	+	15.8138i	0.297791	+	0.515788i
$941$	−4.11839			−0.134256			−0.0671278	−	0.997744i	$-0.521384\pi$
$941$	−4.11839			−0.134256			−0.0671278	+	0.997744i	$0.521384\pi$
$942$	12.5075	+	15.5613i	0.407516	+	0.507016i
$943$		−	0.317175i		−	0.0103287i
$944$	−8.84071			−0.287741
$945$	42.6078	+	23.8636i	1.38603	+	0.776282i
$946$	−18.4908			−0.601189
$947$			24.7681i			0.804854i	0.915452	+	0.402427i	$0.131833\pi$
$947$			24.7681i			0.804854i	−0.915452	+	0.402427i	$0.868167\pi$
$948$	1.00277	+	1.24761i	0.0325684	+	0.0405204i
$949$	−1.34581			−0.0436868
$950$	31.3458	+	54.2925i	1.01699	+	1.76148i
$951$	−18.4662	+	14.8423i	−0.598809	+	0.481294i
$952$	−3.53408	+	2.41765i	−0.114540	+	0.0783564i
$953$		−	9.62625i		−	0.311825i	−0.987771	−	0.155912i	$-0.950168\pi$
$953$		−	9.62625i		−	0.311825i	0.987771	−	0.155912i	$-0.0498317\pi$
$954$	9.12207	−	2.89042i	0.295338	−	0.0935810i
$955$	15.7897	−	9.11620i	0.510944	−	0.294993i
$956$	3.02944	+	1.74905i	0.0979790	+	0.0565682i
$957$	14.0236	+	17.4476i	0.453318	+	0.564002i
$958$	10.7674	+	6.21659i	0.347880	+	0.200849i
$959$	16.8472	+	8.08058i	0.544026	+	0.260935i
$960$	−2.22589	+	5.73592i	−0.0718404	+	0.185126i
$961$	−4.82931			−0.155784
$962$	−3.00060	−	5.19719i	−0.0967431	−	0.167564i
$963$	26.5636	−	29.0718i	0.856000	−	0.936827i
$964$	−10.0170	−	5.78332i	−0.322626	−	0.186268i
$965$	28.3908	+	49.1744i	0.913933	+	1.58298i
$966$	4.45671	−	14.7302i	0.143392	−	0.473937i
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	−0.773216	−	0.634143i	$-0.781353\pi$
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	0.935792	+	0.352553i	$0.114686\pi$
$968$	−1.61538	+	0.932639i	−0.0519202	+	0.0299762i
$969$	17.9793	−	14.4509i	0.577578	−	0.464230i
$970$	−27.3446	+	47.3622i	−0.877981	+	1.52071i
$971$	−12.6574	+	21.9233i	−0.406196	+	0.703552i	−0.994460	−	0.105117i	$-0.966478\pi$
$971$	−12.6574	+	21.9233i	−0.406196	+	0.703552i	0.588264	+	0.808669i	$0.299812\pi$
$972$	−3.75888	−	15.1285i	−0.120566	−	0.485246i
$973$	−34.7959	−	16.6894i	−1.11550	−	0.535039i
$974$	32.3033	−	18.6503i	1.03507	−	0.597595i
$975$	−12.6273	−	4.90019i	−0.404399	−	0.156932i
$976$		−	4.69034i		−	0.150134i
$977$			9.05294i			0.289629i	0.989459	+	0.144815i	$0.0462586\pi$
$977$			9.05294i			0.289629i	−0.989459	+	0.144815i	$0.953741\pi$
$978$	−0.727325	−	4.70330i	−0.0232573	−	0.150395i
$979$	−12.3279	+	7.11752i	−0.394001	+	0.227477i
$980$	−15.5646	−	19.3920i	−0.497194	−	0.619453i
$981$	−30.2330	+	9.57964i	−0.965266	+	0.305855i
$982$	6.82377	−	11.8191i	0.217755	−	0.377163i
$983$	−3.19651	+	5.53653i	−0.101953	+	0.176588i	−0.912489	−	0.409101i	$-0.865842\pi$
$983$	−3.19651	+	5.53653i	−0.101953	+	0.176588i	0.810536	+	0.585688i	$0.199176\pi$
$984$	0.0249997	+	0.161662i	0.000796962	+	0.00515361i
$985$	−14.5379	+	8.39347i	−0.463216	+	0.267438i
$986$	−3.46022	+	5.99328i	−0.110196	+	0.190865i
$987$	16.1155	+	17.1814i	0.512962	+	0.546889i
$988$	−4.22333	−	7.31502i	−0.134362	−	0.232722i
$989$	17.7934	+	10.2730i	0.565797	+	0.326663i
$990$	6.92657	−	31.4550i	0.220141	−	0.999706i
$991$	6.92230	+	11.9898i	0.219894	+	0.380868i	0.954775	−	0.297328i	$-0.0960954\pi$
$991$	6.92230	+	11.9898i	0.219894	+	0.380868i	−0.734881	+	0.678196i	$0.762762\pi$
$992$	5.98576			0.190048
$993$	11.8244	+	14.7115i	0.375236	+	0.466855i
$994$	36.8978	−	2.82348i	1.17033	−	0.0895555i
$995$	6.52475	+	3.76706i	0.206848	+	0.119424i
$996$	−6.80766	+	17.5427i	−0.215709	+	0.555863i
$997$	−5.99391	−	3.46059i	−0.189829	−	0.109598i	0.402073	−	0.915607i	$-0.368290\pi$
$997$	−5.99391	−	3.46059i	−0.189829	−	0.109598i	−0.591903	+	0.806010i	$0.701623\pi$
$998$	−18.1882	+	10.5010i	−0.575737	+	0.332402i
$999$	1.92233	−	30.3183i	0.0608197	−	0.959227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.l.a.5.6	✓	16
3.2	odd	2		378.2.l.a.341.1		16
4.3	odd	2		1008.2.ca.c.257.7		16
7.2	even	3		882.2.m.b.293.8		16
7.3	odd	6		126.2.t.a.59.4	yes	16
7.4	even	3		882.2.t.a.815.1		16
7.5	odd	6		882.2.m.a.293.5		16
7.6	odd	2		882.2.l.b.509.7		16
9.2	odd	6		126.2.t.a.47.4	yes	16
9.4	even	3		1134.2.k.a.971.4		16
9.5	odd	6		1134.2.k.b.971.5		16
9.7	even	3		378.2.t.a.89.5		16
12.11	even	2		3024.2.ca.c.2609.1		16
21.2	odd	6		2646.2.m.b.881.1		16
21.5	even	6		2646.2.m.a.881.4		16
21.11	odd	6		2646.2.t.b.2285.8		16
21.17	even	6		378.2.t.a.17.5		16
21.20	even	2		2646.2.l.a.1097.4		16
28.3	even	6		1008.2.df.c.689.3		16
36.7	odd	6		3024.2.df.c.1601.1		16
36.11	even	6		1008.2.df.c.929.3		16
63.2	odd	6		882.2.m.a.587.5		16
63.11	odd	6		882.2.l.b.227.3		16
63.16	even	3		2646.2.m.a.1763.4		16
63.20	even	6		882.2.t.a.803.1		16
63.25	even	3		2646.2.l.a.521.8		16
63.31	odd	6		1134.2.k.b.647.5		16
63.34	odd	6		2646.2.t.b.1979.8		16
63.38	even	6	inner	126.2.l.a.101.2	yes	16
63.47	even	6		882.2.m.b.587.8		16
63.52	odd	6		378.2.l.a.143.5		16
63.59	even	6		1134.2.k.a.647.4		16
63.61	odd	6		2646.2.m.b.1763.1		16
84.59	odd	6		3024.2.df.c.17.1		16
252.115	even	6		3024.2.ca.c.2033.1		16
252.227	odd	6		1008.2.ca.c.353.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	1.1	even	1	trivial
126.2.l.a.101.2	yes	16	63.38	even	6	inner
126.2.t.a.47.4	yes	16	9.2	odd	6
126.2.t.a.59.4	yes	16	7.3	odd	6
378.2.l.a.143.5		16	63.52	odd	6
378.2.l.a.341.1		16	3.2	odd	2
378.2.t.a.17.5		16	21.17	even	6
378.2.t.a.89.5		16	9.7	even	3
882.2.l.b.227.3		16	63.11	odd	6
882.2.l.b.509.7		16	7.6	odd	2
882.2.m.a.293.5		16	7.5	odd	6
882.2.m.a.587.5		16	63.2	odd	6
882.2.m.b.293.8		16	7.2	even	3
882.2.m.b.587.8		16	63.47	even	6
882.2.t.a.803.1		16	63.20	even	6
882.2.t.a.815.1		16	7.4	even	3
1008.2.ca.c.257.7		16	4.3	odd	2
1008.2.ca.c.353.7		16	252.227	odd	6
1008.2.df.c.689.3		16	28.3	even	6
1008.2.df.c.929.3		16	36.11	even	6
1134.2.k.a.647.4		16	63.59	even	6
1134.2.k.a.971.4		16	9.4	even	3
1134.2.k.b.647.5		16	63.31	odd	6
1134.2.k.b.971.5		16	9.5	odd	6
2646.2.l.a.521.8		16	63.25	even	3
2646.2.l.a.1097.4		16	21.20	even	2
2646.2.m.a.881.4		16	21.5	even	6
2646.2.m.a.1763.4		16	63.16	even	3
2646.2.m.b.881.1		16	21.2	odd	6
2646.2.m.b.1763.1		16	63.61	odd	6
2646.2.t.b.1979.8		16	63.34	odd	6
2646.2.t.b.2285.8		16	21.11	odd	6
3024.2.ca.c.2033.1		16	252.115	even	6
3024.2.ca.c.2609.1		16	12.11	even	2
3024.2.df.c.17.1		16	84.59	odd	6
3024.2.df.c.1601.1		16	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.08509 - 1.35003i) q^{3} -1.00000 q^{4} +(1.77612 + 3.07634i) q^{5} +(1.35003 - 1.08509i) q^{6} +(2.63804 - 0.201867i) q^{7} -1.00000i q^{8} +(-0.645160 + 2.92981i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.08509 - 1.35003i) q^{3} -1.00000 q^{4} +(1.77612 + 3.07634i) q^{5} +(1.35003 - 1.08509i) q^{6} +(2.63804 - 0.201867i) q^{7} -1.00000i q^{8} +(-0.645160 + 2.92981i) q^{9} +(-3.07634 + 1.77612i) q^{10} +(2.61745 + 1.51119i) q^{11} +(1.08509 + 1.35003i) q^{12} +(-0.888944 - 0.513232i) q^{13} +(0.201867 + 2.63804i) q^{14} +(2.22589 - 5.73592i) q^{15} +1.00000 q^{16} +(-0.809204 - 1.40158i) q^{17} +(-2.92981 - 0.645160i) q^{18} +(-7.12643 - 4.11444i) q^{19} +(-1.77612 - 3.07634i) q^{20} +(-3.13504 - 3.34239i) q^{21} +(-1.51119 + 2.61745i) q^{22} +(2.90837 - 1.67915i) q^{23} +(-1.35003 + 1.08509i) q^{24} +(-3.80924 + 6.59779i) q^{25} +(0.513232 - 0.888944i) q^{26} +(4.65538 - 2.30812i) q^{27} +(-2.63804 + 0.201867i) q^{28} +(-3.70319 + 2.13804i) q^{29} +(5.73592 + 2.22589i) q^{30} -5.98576i q^{31} +1.00000i q^{32} +(-0.800023 - 5.17341i) q^{33} +(1.40158 - 0.809204i) q^{34} +(5.30650 + 7.75696i) q^{35} +(0.645160 - 2.92981i) q^{36} +(2.92323 - 5.06319i) q^{37} +(4.11444 - 7.12643i) q^{38} +(0.271706 + 1.75700i) q^{39} +(3.07634 - 1.77612i) q^{40} +(0.0472226 - 0.0817920i) q^{41} +(3.34239 - 3.13504i) q^{42} +(3.05899 + 5.29833i) q^{43} +(-2.61745 - 1.51119i) q^{44} +(-10.1590 + 3.21897i) q^{45} +(1.67915 + 2.90837i) q^{46} -5.14045 q^{47} +(-1.08509 - 1.35003i) q^{48} +(6.91850 - 1.06507i) q^{49} +(-6.59779 - 3.80924i) q^{50} +(-1.01412 + 2.61329i) q^{51} +(0.888944 + 0.513232i) q^{52} +(-2.76235 + 1.59484i) q^{53} +(2.30812 + 4.65538i) q^{54} +10.7362i q^{55} +(-0.201867 - 2.63804i) q^{56} +(2.17819 + 14.0854i) q^{57} +(-2.13804 - 3.70319i) q^{58} -8.84071 q^{59} +(-2.22589 + 5.73592i) q^{60} -4.69034i q^{61} +5.98576 q^{62} +(-1.11052 + 7.85918i) q^{63} -1.00000 q^{64} -3.64626i q^{65} +(5.17341 - 0.800023i) q^{66} -0.375675 q^{67} +(0.809204 + 1.40158i) q^{68} +(-5.42275 - 2.10436i) q^{69} +(-7.75696 + 5.30650i) q^{70} -13.9868i q^{71} +(2.92981 + 0.645160i) q^{72} +(1.13546 - 0.655556i) q^{73} +(5.06319 + 2.92323i) q^{74} +(13.0406 - 2.01662i) q^{75} +(7.12643 + 4.11444i) q^{76} +(7.20999 + 3.45819i) q^{77} +(-1.75700 + 0.271706i) q^{78} +0.924134 q^{79} +(1.77612 + 3.07634i) q^{80} +(-8.16754 - 3.78039i) q^{81} +(0.0817920 + 0.0472226i) q^{82} +(5.43209 + 9.40866i) q^{83} +(3.13504 + 3.34239i) q^{84} +(2.87450 - 4.97877i) q^{85} +(-5.29833 + 3.05899i) q^{86} +(6.90471 + 2.67945i) q^{87} +(1.51119 - 2.61745i) q^{88} +(-2.35495 + 4.07888i) q^{89} +(-3.21897 - 10.1590i) q^{90} +(-2.44867 - 1.17448i) q^{91} +(-2.90837 + 1.67915i) q^{92} +(-8.08095 + 6.49509i) q^{93} -5.14045i q^{94} -29.2311i q^{95} +(1.35003 - 1.08509i) q^{96} +(13.3330 - 7.69782i) q^{97} +(1.06507 + 6.91850i) q^{98} +(-6.11615 + 6.69367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 2 * q^7	\( 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 6 * q^97 - 24 * q^98 + 18 * q^99

Introduction

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