LMFDB - Embedded newform 126.2.h.d.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(67,126)]

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([2, 4]))

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

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

chi := DirichletCharacter("126.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.h (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	126.79
Dual form			126.2.h.d.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.09097 + 1.34528i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +(-1.71053 - 0.272169i) q^{6} +(0.710533 + 2.54856i) q^{7} -1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +(-1.59097 - 2.75564i) q^{10} +3.18194 q^{11} +(-0.619562 - 1.61745i) q^{12} +(2.85185 + 4.93955i) q^{13} +(-1.85185 + 1.88962i) q^{14} +(3.47141 - 4.28061i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.760877 - 1.31788i) q^{17} +(2.23229 - 2.00422i) q^{18} +(-0.641315 + 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(-4.20370 - 1.82454i) q^{21} +(1.59097 + 2.75564i) q^{22} +2.23912 q^{23} +(1.09097 - 1.34528i) q^{24} +5.12476 q^{25} +(-2.85185 + 4.93955i) q^{26} +(4.62476 + 2.36887i) q^{27} +(-2.56238 - 0.658939i) q^{28} +(-3.54063 + 6.13255i) q^{29} +(5.44282 + 0.866025i) q^{30} +(4.71053 - 8.15888i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.47141 + 4.28061i) q^{33} +(0.760877 - 1.31788i) q^{34} +(-2.26088 - 8.10936i) q^{35} +(2.85185 + 0.931107i) q^{36} +(0.500000 - 0.866025i) q^{37} -1.28263 q^{38} +(-9.75636 - 1.55237i) q^{39} +3.18194 q^{40} +(-2.80150 - 4.85235i) q^{41} +(-0.521753 - 4.55278i) q^{42} +(3.41423 - 5.91362i) q^{43} +(-1.59097 + 2.75564i) q^{44} +(1.97141 + 9.34004i) q^{45} +(1.11956 + 1.93914i) q^{46} +(2.91423 + 5.04759i) q^{47} +(1.71053 + 0.272169i) q^{48} +(-5.99028 + 3.62167i) q^{49} +(2.56238 + 4.43818i) q^{50} +(2.60301 + 0.414174i) q^{51} -5.70370 q^{52} +(1.02859 + 1.78157i) q^{53} +(0.260877 + 5.18960i) q^{54} -10.1248 q^{55} +(-0.710533 - 2.54856i) q^{56} +(-0.794668 - 2.07459i) q^{57} -7.08126 q^{58} +(0.562382 - 0.974074i) q^{59} +(1.97141 + 5.14663i) q^{60} +(-1.56238 - 2.70612i) q^{61} +9.42107 q^{62} +(7.04063 - 3.66464i) q^{63} +1.00000 q^{64} +(-9.07442 - 15.7174i) q^{65} +(-5.44282 - 0.866025i) q^{66} +(-5.48345 + 9.49761i) q^{67} +1.52175 q^{68} +(-2.44282 + 3.01225i) q^{69} +(5.89248 - 6.01266i) q^{70} +8.69002 q^{71} +(0.619562 + 2.93533i) q^{72} +(-2.48345 - 4.30146i) q^{73} +1.00000 q^{74} +(-5.59097 + 6.89425i) q^{75} +(-0.641315 - 1.11079i) q^{76} +(2.26088 + 8.10936i) q^{77} +(-3.53379 - 9.22544i) q^{78} +(2.06922 + 3.58399i) q^{79} +(1.59097 + 2.75564i) q^{80} +(-8.23229 + 3.63723i) q^{81} +(2.80150 - 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(3.68194 - 2.72824i) q^{84} +(2.42107 + 4.19341i) q^{85} +6.82846 q^{86} +(-4.38727 - 11.4536i) q^{87} -3.18194 q^{88} +(0.112725 - 0.195246i) q^{89} +(-7.10301 + 6.37731i) q^{90} +(-10.5624 + 10.7778i) q^{91} +(-1.11956 + 1.93914i) q^{92} +(5.83693 + 15.2381i) q^{93} +(-2.91423 + 5.04759i) q^{94} +(2.04063 - 3.53447i) q^{95} +(0.619562 + 1.61745i) q^{96} +(7.42107 - 12.8537i) q^{97} +(-6.13160 - 3.37690i) q^{98} +(-1.97141 - 9.34004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} - 4 q^{9} - q^{10} + 2 q^{11} - 4 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} - 3 q^{16} - 4 q^{17} + 4 q^{18} - 3 q^{19} + q^{20}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 - 6 * q^8 - 4 * q^9 - q^10 + 2 * q^11 - 4 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 - 3 * q^16 - 4 * q^17 + 4 * q^18 - 3 * q^19 + q^20 - 7 * q^21 + q^22 + 14 * q^23 - 2 * q^24 - 4 * q^25 - 8 * q^26 - 7 * q^27 + 2 * q^28 - 5 * q^29 + 15 * q^30 + 20 * q^31 + 3 * q^32 - 12 * q^33 + 4 * q^34 - 13 * q^35 + 8 * q^36 + 3 * q^37 - 6 * q^38 + q^39 + 2 * q^40 - 2 * q^42 - 6 * q^43 - q^44 + 3 * q^45 + 7 * q^46 - 9 * q^47 + 2 * q^48 - 12 * q^49 - 2 * q^50 - 18 * q^51 - 16 * q^52 + 15 * q^53 + q^54 - 26 * q^55 + 4 * q^56 + 22 * q^57 - 10 * q^58 - 14 * q^59 + 3 * q^60 + 8 * q^61 + 40 * q^62 + 26 * q^63 + 6 * q^64 - 12 * q^65 - 15 * q^66 + q^67 + 8 * q^68 + 3 * q^69 + 10 * q^70 + 14 * q^71 + 4 * q^72 + 19 * q^73 + 6 * q^74 - 25 * q^75 - 3 * q^76 + 13 * q^77 + 5 * q^78 + 5 * q^79 + q^80 - 40 * q^81 + 2 * q^83 + 5 * q^84 - 2 * q^85 - 12 * q^86 - 36 * q^87 - 2 * q^88 - 9 * q^89 - 9 * q^90 - 46 * q^91 - 7 * q^92 + 37 * q^93 + 9 * q^94 - 4 * q^95 + 4 * q^96 + 28 * q^97 - 12 * q^98 - 3 * q^99

Character values

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

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.09097	+	1.34528i	−0.629873	+	0.776698i
$3$	−1.09097	+	1.34528i	−0.629873	+	0.776698i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.18194			−1.42301			−0.711504	−	0.702682i	$-0.751986\pi$
$5$	−3.18194			−1.42301			−0.711504	+	0.702682i	$0.751986\pi$
$6$	−1.71053	−	0.272169i	−0.698322	−	0.111112i
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$8$	−1.00000			−0.353553
$9$	−0.619562	−	2.93533i	−0.206521	−	0.978442i
$10$	−1.59097	−	2.75564i	−0.503109	−	0.871411i
$11$	3.18194			0.959392			0.479696	−	0.877435i	$-0.340747\pi$
$11$	3.18194			0.959392			0.479696	+	0.877435i	$0.340747\pi$
$12$	−0.619562	−	1.61745i	−0.178852	−	0.466917i
$13$	2.85185	+	4.93955i	0.790960	+	1.36998i	0.925373	+	0.379058i	$0.123752\pi$
$13$	2.85185	+	4.93955i	0.790960	+	1.36998i	−0.134412	+	0.990925i	$0.542915\pi$
$14$	−1.85185	+	1.88962i	−0.494927	+	0.505022i
$15$	3.47141	−	4.28061i	0.896314	−	1.10525i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.760877	−	1.31788i	−0.184540	−	0.319632i	0.758882	−	0.651229i	$-0.225746\pi$
$17$	−0.760877	−	1.31788i	−0.184540	−	0.319632i	−0.943421	+	0.331596i	$0.892413\pi$
$18$	2.23229	−	2.00422i	0.526155	−	0.472399i
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	−0.930165	−	0.367142i	$-0.880336\pi$
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	0.783037	+	0.621975i	$0.213670\pi$
$20$	1.59097	−	2.75564i	0.355752	−	0.616181i
$21$	−4.20370	−	1.82454i	−0.917322	−	0.398147i
$22$	1.59097	+	2.75564i	0.339196	+	0.587505i
$23$	2.23912			0.466889			0.233445	−	0.972370i	$-0.425000\pi$
$23$	2.23912			0.466889			0.233445	+	0.972370i	$0.425000\pi$
$24$	1.09097	−	1.34528i	0.222694	−	0.274604i
$25$	5.12476			1.02495
$26$	−2.85185	+	4.93955i	−0.559293	+	0.968725i
$27$	4.62476	+	2.36887i	0.890036	+	0.455890i
$28$	−2.56238	−	0.658939i	−0.484245	−	0.124528i
$29$	−3.54063	+	6.13255i	−0.657478	+	1.13879i	0.323788	+	0.946130i	$0.395043\pi$
$29$	−3.54063	+	6.13255i	−0.657478	+	1.13879i	−0.981266	+	0.192656i	$0.938290\pi$
$30$	5.44282	+	0.866025i	0.993718	+	0.158114i
$31$	4.71053	−	8.15888i	0.846037	−	1.46538i	−0.0386810	−	0.999252i	$-0.512316\pi$
$31$	4.71053	−	8.15888i	0.846037	−	1.46538i	0.884718	−	0.466127i	$-0.154351\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.47141	+	4.28061i	−0.604295	+	0.745158i
$34$	0.760877	−	1.31788i	0.130489	−	0.226014i
$35$	−2.26088	−	8.10936i	−0.382158	−	1.37073i
$36$	2.85185	+	0.931107i	0.475308	+	0.155185i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−1.28263			−0.208070
$39$	−9.75636	−	1.55237i	−1.56227	−	0.248578i
$40$	3.18194			0.503109
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	0.559976	−	0.828509i	$-0.310810\pi$
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	−0.997498	+	0.0706992i	$0.977477\pi$
$42$	−0.521753	−	4.55278i	−0.0805083	−	0.702509i
$43$	3.41423	−	5.91362i	0.520665	−	0.901819i	−0.479046	−	0.877790i	$-0.659017\pi$
$43$	3.41423	−	5.91362i	0.520665	−	0.901819i	0.999711	−	0.0240288i	$-0.00764935\pi$
$44$	−1.59097	+	2.75564i	−0.239848	+	0.415429i
$45$	1.97141	+	9.34004i	0.293880	+	1.39233i
$46$	1.11956	+	1.93914i	0.165070	+	0.285910i
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	0.996428	−	0.0844432i	$-0.0269112\pi$
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	−0.571344	+	0.820711i	$0.693578\pi$
$48$	1.71053	+	0.272169i	0.246894	+	0.0392842i
$49$	−5.99028	+	3.62167i	−0.855755	+	0.517381i
$50$	2.56238	+	4.43818i	0.362375	+	0.627653i
$51$	2.60301	+	0.414174i	0.364494	+	0.0579959i
$52$	−5.70370			−0.790960
$53$	1.02859	+	1.78157i	0.141288	+	0.244717i	0.927982	−	0.372626i	$-0.121542\pi$
$53$	1.02859	+	1.78157i	0.141288	+	0.244717i	−0.786694	+	0.617343i	$0.788209\pi$
$54$	0.260877	+	5.18960i	0.0355008	+	0.706215i
$55$	−10.1248			−1.36522
$56$	−0.710533	−	2.54856i	−0.0949490	−	0.340565i
$57$	−0.794668	−	2.07459i	−0.105256	−	0.274786i
$58$	−7.08126			−0.929815
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	−0.827093	−	0.562065i	$-0.810007\pi$
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	0.900309	+	0.435251i	$0.143340\pi$
$60$	1.97141	+	5.14663i	0.254508	+	0.664427i
$61$	−1.56238	−	2.70612i	−0.200042	−	0.346484i	0.748499	−	0.663135i	$-0.230775\pi$
$61$	−1.56238	−	2.70612i	−0.200042	−	0.346484i	−0.948542	+	0.316652i	$0.897441\pi$
$62$	9.42107			1.19648
$63$	7.04063	−	3.66464i	0.887036	−	0.461701i
$64$	1.00000			0.125000
$65$	−9.07442	−	15.7174i	−1.12554	−	1.94950i
$66$	−5.44282	−	0.866025i	−0.669965	−	0.106600i
$67$	−5.48345	+	9.49761i	−0.669910	+	1.16032i	0.308019	+	0.951380i	$0.400334\pi$
$67$	−5.48345	+	9.49761i	−0.669910	+	1.16032i	−0.977929	+	0.208938i	$0.932999\pi$
$68$	1.52175			0.184540
$69$	−2.44282	+	3.01225i	−0.294081	+	0.362632i
$70$	5.89248	−	6.01266i	0.704286	−	0.718650i
$71$	8.69002			1.03132			0.515658	−	0.856794i	$-0.327548\pi$
$71$	8.69002			1.03132			0.515658	+	0.856794i	$0.327548\pi$
$72$	0.619562	+	2.93533i	0.0730160	+	0.345932i
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	0.683302	−	0.730136i	$-0.260543\pi$
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	−0.973967	+	0.226689i	$0.927210\pi$
$74$	1.00000			0.116248
$75$	−5.59097	+	6.89425i	−0.645590	+	0.796079i
$76$	−0.641315	−	1.11079i	−0.0735639	−	0.127416i
$77$	2.26088	+	8.10936i	0.257651	+	0.924148i
$78$	−3.53379	−	9.22544i	−0.400123	−	1.04458i
$79$	2.06922	+	3.58399i	0.232805	+	0.403231i	0.958633	−	0.284646i	$-0.0918762\pi$
$79$	2.06922	+	3.58399i	0.232805	+	0.403231i	−0.725827	+	0.687877i	$0.758543\pi$
$80$	1.59097	+	2.75564i	0.177876	+	0.308090i
$81$	−8.23229	+	3.63723i	−0.914699	+	0.404137i
$82$	2.80150	−	4.85235i	0.309374	−	0.535852i
$83$	−4.03379	+	6.98673i	−0.442766	+	0.766893i	−0.997894	−	0.0648718i	$-0.979336\pi$
$83$	−4.03379	+	6.98673i	−0.442766	+	0.766893i	0.555127	+	0.831765i	$0.312669\pi$
$84$	3.68194	−	2.72824i	0.401733	−	0.297675i
$85$	2.42107	+	4.19341i	0.262602	+	0.454839i
$86$	6.82846			0.736332
$87$	−4.38727	−	11.4536i	−0.470365	−	1.22795i
$88$	−3.18194			−0.339196
$89$	0.112725	−	0.195246i	0.0119488	−	0.0206960i	−0.859989	−	0.510312i	$-0.829530\pi$
$89$	0.112725	−	0.195246i	0.0119488	−	0.0206960i	0.871938	+	0.489616i	$0.162863\pi$
$90$	−7.10301	+	6.37731i	−0.748723	+	0.672228i
$91$	−10.5624	+	10.7778i	−1.10724	+	1.12982i
$92$	−1.11956	+	1.93914i	−0.116722	+	0.202169i
$93$	5.83693	+	15.2381i	0.605262	+	1.58012i
$94$	−2.91423	+	5.04759i	−0.300580	+	0.520620i
$95$	2.04063	−	3.53447i	0.209364	−	0.362629i
$96$	0.619562	+	1.61745i	0.0632337	+	0.165080i
$97$	7.42107	−	12.8537i	0.753495	−	1.30509i	−0.192624	−	0.981273i	$-0.561700\pi$
$97$	7.42107	−	12.8537i	0.753495	−	1.30509i	0.946119	−	0.323819i	$-0.104967\pi$
$98$	−6.13160	−	3.37690i	−0.619385	−	0.341119i
$99$	−1.97141	−	9.34004i	−0.198134	−	0.938710i
$100$	−2.56238	+	4.43818i	−0.256238	+	0.443818i
$101$	18.5893			1.84971			0.924854	−	0.380322i	$-0.124187\pi$
$101$	18.5893			1.84971			0.924854	+	0.380322i	$0.124187\pi$
$102$	0.942820	+	2.46136i	0.0933531	+	0.243711i
$103$	−0.282630			−0.0278484			−0.0139242	−	0.999903i	$-0.504432\pi$
$103$	−0.282630			−0.0278484			−0.0139242	+	0.999903i	$0.504432\pi$
$104$	−2.85185	−	4.93955i	−0.279647	−	0.484362i
$105$	13.3759	+	5.80557i	1.30536	+	0.566566i
$106$	−1.02859	+	1.78157i	−0.0999055	+	0.173041i
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	−0.448322	−	0.893872i	$-0.647978\pi$
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	0.998277	−	0.0586780i	$-0.0186885\pi$
$108$	−4.36389	+	2.82073i	−0.419915	+	0.271424i
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	0.740526	−	0.672028i	$-0.234577\pi$
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	−0.952256	+	0.305300i	$0.901243\pi$
$110$	−5.06238	−	8.76830i	−0.482679	−	0.836025i
$111$	0.619562	+	1.61745i	0.0588062	+	0.153522i
$112$	1.85185	−	1.88962i	0.174983	−	0.178552i
$113$	−1.60752	−	2.78431i	−0.151223	−	0.261926i	0.780454	−	0.625213i	$-0.214988\pi$
$113$	−1.60752	−	2.78431i	−0.151223	−	0.261926i	−0.931677	+	0.363287i	$0.881655\pi$
$114$	1.39931	−	1.72550i	0.131058	−	0.161608i
$115$	−7.12476			−0.664388
$116$	−3.54063	−	6.13255i	−0.328739	−	0.569393i
$117$	12.7323	−	11.4315i	1.17710	−	1.05684i
$118$	1.12476			0.103543
$119$	2.81806	−	2.87553i	0.258331	−	0.263600i
$120$	−3.47141	+	4.28061i	−0.316895	+	0.390764i
$121$	−0.875237			−0.0795670
$122$	1.56238	−	2.70612i	0.141451	−	0.245001i
$123$	9.58414	+	1.52496i	0.864172	+	0.137501i
$124$	4.71053	+	8.15888i	0.423018	+	0.732689i
$125$	−0.396990			−0.0355079
$126$	6.69398	+	4.26505i	0.596347	+	0.379960i
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	4.23065	+	11.0447i	0.372488	+	0.972431i
$130$	9.07442	−	15.7174i	0.795879	−	1.37850i
$131$	6.36389			0.556015			0.278008	−	0.960579i	$-0.410326\pi$
$131$	6.36389			0.556015			0.278008	+	0.960579i	$0.410326\pi$
$132$	−1.97141	−	5.14663i	−0.171589	−	0.447957i
$133$	−3.28659	−	0.845174i	−0.284983	−	0.0732859i
$134$	−10.9669			−0.947396
$135$	−14.7157	−	7.53762i	−1.26653	−	0.648735i
$136$	0.760877	+	1.31788i	0.0652446	+	0.113007i
$137$	2.74145			0.234218			0.117109	−	0.993119i	$-0.462637\pi$
$137$	2.74145			0.234218			0.117109	+	0.993119i	$0.462637\pi$
$138$	−3.83009	−	0.609419i	−0.326039	−	0.0518772i
$139$	−3.98345	−	6.89953i	−0.337872	−	0.585211i	0.646161	−	0.763202i	$-0.276374\pi$
$139$	−3.98345	−	6.89953i	−0.337872	−	0.585211i	−0.984032	+	0.177991i	$0.943040\pi$
$140$	8.15335	+	2.09671i	0.689084	+	0.177204i
$141$	−9.96978	−	1.58632i	−0.839607	−	0.133593i
$142$	4.34501	+	7.52578i	0.364625	+	0.631550i
$143$	9.07442	+	15.7174i	0.758841	+	1.31435i
$144$	−2.23229	+	2.00422i	−0.186024	+	0.167018i
$145$	11.2661	−	19.5134i	0.935597	−	1.62050i
$146$	2.48345	−	4.30146i	0.205532	−	0.355991i
$147$	1.66307	−	12.0098i	0.137168	−	0.990548i
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−23.2599			−1.90553			−0.952764	−	0.303712i	$-0.901774\pi$
$149$	−23.2599			−1.90553			−0.952764	+	0.303712i	$0.901774\pi$
$150$	−8.76608	−	1.39480i	−0.715747	−	0.113885i
$151$	−8.12476			−0.661184			−0.330592	−	0.943774i	$-0.607248\pi$
$151$	−8.12476			−0.661184			−0.330592	+	0.943774i	$0.607248\pi$
$152$	0.641315	−	1.11079i	0.0520175	−	0.0900970i
$153$	−3.39699	+	3.04993i	−0.274630	+	0.246572i
$154$	−5.89248	+	6.01266i	−0.474829	+	0.484514i
$155$	−14.9887	+	25.9611i	−1.20392	+	2.08525i
$156$	6.22257	−	7.67307i	0.498204	−	0.614338i
$157$	5.63160	−	9.75422i	0.449451	−	0.778471i	−0.548900	−	0.835888i	$-0.684953\pi$
$157$	5.63160	−	9.75422i	0.449451	−	0.778471i	0.998350	+	0.0574170i	$0.0182864\pi$
$158$	−2.06922	+	3.58399i	−0.164618	+	0.285127i
$159$	−3.51887	−	0.559900i	−0.279065	−	0.0444030i
$160$	−1.59097	+	2.75564i	−0.125777	+	0.217853i
$161$	1.59097	+	5.70653i	0.125386	+	0.449738i
$162$	−7.26608	−	5.31075i	−0.570877	−	0.417252i
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	−0.933383	−	0.358881i	$-0.883158\pi$
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	0.777492	+	0.628893i	$0.216492\pi$
$164$	5.60301			0.437522
$165$	11.0458	−	13.6207i	0.859917	−	1.06037i
$166$	−8.06758			−0.626166
$167$	2.61956	+	4.53721i	0.202708	+	0.351100i	0.949400	−	0.314070i	$-0.101693\pi$
$167$	2.61956	+	4.53721i	0.202708	+	0.351100i	−0.746692	+	0.665170i	$0.768359\pi$
$168$	4.20370	+	1.82454i	0.324322	+	0.140766i
$169$	−9.76608	+	16.9153i	−0.751237	+	1.30118i
$170$	−2.42107	+	4.19341i	−0.185687	+	0.321620i
$171$	3.65787	+	1.19427i	0.279724	+	0.0913278i
$172$	3.41423	+	5.91362i	0.260333	+	0.450909i
$173$	−1.27579	−	2.20974i	−0.0969968	−	0.168003i	0.813443	−	0.581644i	$-0.197590\pi$
$173$	−1.27579	−	2.20974i	−0.0969968	−	0.168003i	−0.910440	+	0.413641i	$0.864257\pi$
$174$	7.72545	−	9.52628i	0.585665	−	0.722185i
$175$	3.64132	+	13.0608i	0.275258	+	0.987300i
$176$	−1.59097	−	2.75564i	−0.119924	−	0.207714i
$177$	0.696860	+	1.81925i	0.0523792	+	0.136743i
$178$	0.225450			0.0168982
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	0.967041	−	0.254620i	$-0.0819504\pi$
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	−0.704028	+	0.710172i	$0.748617\pi$
$180$	−9.07442	−	2.96273i	−0.676367	−	0.220829i
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$	−14.6150	−	3.75839i	−1.08334	−	0.278590i
$183$	5.34501	+	0.850463i	0.395115	+	0.0628680i
$184$	−2.23912			−0.165070
$185$	−1.59097	+	2.75564i	−0.116971	+	0.202599i
$186$	−10.2781	+	12.6740i	−0.753628	+	0.929301i
$187$	−2.42107	−	4.19341i	−0.177046	−	0.306653i
$188$	−5.82846			−0.425084
$189$	−2.75116	+	13.4696i	−0.200118	+	0.979772i
$190$	4.08126			0.296085
$191$	−0.990285	−	1.71522i	−0.0716545	−	0.124109i	0.827972	−	0.560769i	$-0.189495\pi$
$191$	−0.990285	−	1.71522i	−0.0716545	−	0.124109i	−0.899627	+	0.436660i	$0.856161\pi$
$192$	−1.09097	+	1.34528i	−0.0787341	+	0.0970873i
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	−0.772552	−	0.634951i	$-0.781020\pi$
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	0.936160	+	0.351574i	$0.114353\pi$
$194$	14.8421			1.06560
$195$	31.0442	+	4.93955i	2.22312	+	0.353728i
$196$	−0.141315	−	6.99857i	−0.0100939	−	0.499898i
$197$	−21.8148			−1.55424			−0.777120	−	0.629353i	$-0.783320\pi$
$197$	−21.8148			−1.55424			−0.777120	+	0.629353i	$0.783320\pi$
$198$	7.10301	−	6.37731i	0.504789	−	0.453216i
$199$	6.14132	+	10.6371i	0.435346	+	0.754042i	0.997324	−	0.0731106i	$-0.0232926\pi$
$199$	6.14132	+	10.6371i	0.435346	+	0.754042i	−0.561978	+	0.827152i	$0.689959\pi$
$200$	−5.12476			−0.362375
$201$	−6.79467	−	17.7384i	−0.479259	−	1.25117i
$202$	9.29467	+	16.0988i	0.653971	+	1.13271i
$203$	−18.1449	−	4.66611i	−1.27352	−	0.327497i
$204$	−1.66019	+	2.04719i	−0.116237	+	0.143332i
$205$	8.91423	+	15.4399i	0.622597	+	1.07837i
$206$	−0.141315	−	0.244765i	−0.00984589	−	0.0170536i
$207$	−1.38727	−	6.57256i	−0.0964223	−	0.456824i
$208$	2.85185	−	4.93955i	0.197740	−	0.342496i
$209$	−2.04063	+	3.53447i	−0.141153	+	0.244485i
$210$	1.66019	+	14.4867i	0.114564	+	0.999676i
$211$	−8.32846	−	14.4253i	−0.573355	−	0.993080i	−0.996218	−	0.0868863i	$-0.972308\pi$
$211$	−8.32846	−	14.4253i	−0.573355	−	0.993080i	0.422863	−	0.906193i	$-0.361025\pi$
$212$	−2.05718			−0.141288
$213$	−9.48057	+	11.6905i	−0.649598	+	0.801021i
$214$	11.3776			0.777754
$215$	−10.8639	+	18.8168i	−0.740911	+	1.28330i
$216$	−4.62476	−	2.36887i	−0.314675	−	0.161181i
$217$	24.1404	+	6.20790i	1.63876	+	0.421420i
$218$	2.21053	−	3.82876i	0.149716	−	0.259316i
$219$	8.49604	+	1.35183i	0.574109	+	0.0913485i
$220$	5.06238	−	8.76830i	0.341306	−	0.591159i
$221$	4.33981	−	7.51677i	0.291927	−	0.505633i
$222$	−1.09097	+	1.34528i	−0.0732212	+	0.0902893i
$223$	−5.32846	+	9.22916i	−0.356820	+	0.618031i	−0.987428	−	0.158071i	$-0.949472\pi$
$223$	−5.32846	+	9.22916i	−0.356820	+	0.618031i	0.630608	+	0.776102i	$0.282806\pi$
$224$	2.56238	+	0.658939i	0.171206	+	0.0440272i
$225$	−3.17511	−	15.0429i	−0.211674	−	1.00286i
$226$	1.60752	−	2.78431i	0.106931	−	0.185210i
$227$	−14.5081			−0.962935			−0.481468	−	0.876464i	$-0.659896\pi$
$227$	−14.5081			−0.962935			−0.481468	+	0.876464i	$0.659896\pi$
$228$	2.19398	+	0.349092i	0.145300	+	0.0231192i
$229$	10.2495			0.677308			0.338654	−	0.940911i	$-0.390028\pi$
$229$	10.2495			0.677308			0.338654	+	0.940911i	$0.390028\pi$
$230$	−3.56238	−	6.17023i	−0.234896	−	0.406853i
$231$	−13.3759	−	5.80557i	−0.880071	−	0.381979i
$232$	3.54063	−	6.13255i	0.232454	−	0.402622i
$233$	0.540628	−	0.936396i	0.0354177	−	0.0613453i	−0.847773	−	0.530359i	$-0.822057\pi$
$233$	0.540628	−	0.936396i	0.0354177	−	0.0613453i	0.883191	+	0.469014i	$0.155390\pi$
$234$	16.2661	+	5.31075i	1.06335	+	0.347175i
$235$	−9.27292	−	16.0612i	−0.604898	−	1.04771i
$236$	0.562382	+	0.974074i	0.0366079	+	0.0634068i
$237$	−7.07893	−	1.12635i	−0.459826	−	0.0731645i
$238$	3.89931	+	1.00274i	0.252755	+	0.0649981i
$239$	−6.16019	−	10.6698i	−0.398470	−	0.690170i	0.595068	−	0.803676i	$-0.297125\pi$
$239$	−6.16019	−	10.6698i	−0.398470	−	0.690170i	−0.993537	+	0.113506i	$0.963792\pi$
$240$	−5.44282	−	0.866025i	−0.351333	−	0.0559017i
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$	−0.437618	−	0.757977i	−0.0281312	−	0.0487246i
$243$	4.08809	−	15.0429i	0.262251	−	0.965000i
$244$	3.12476			0.200042
$245$	19.0607	−	11.5239i	1.21775	−	0.736238i
$246$	3.47141	+	9.06259i	0.221329	+	0.577809i
$247$	−7.31573			−0.465489
$248$	−4.71053	+	8.15888i	−0.299119	+	0.518090i
$249$	−4.99837	−	13.0489i	−0.316759	−	0.826941i
$250$	−0.198495	−	0.343803i	−0.0125539	−	0.0217440i
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$	−0.346647	+	7.92968i	−0.0218367	+	0.499523i
$253$	7.12476			0.447930
$254$	10.0527	+	17.4117i	0.630760	+	1.09251i
$255$	−8.28263	−	1.31788i	−0.518678	−	0.0825287i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.66019			0.477830			0.238915	−	0.971041i	$-0.423208\pi$
$257$	7.66019			0.477830			0.238915	+	0.971041i	$0.423208\pi$
$258$	−7.44966	+	9.18620i	−0.463795	+	0.571908i
$259$	2.56238	+	0.658939i	0.159219	+	0.0409445i
$260$	18.1488			1.12554
$261$	20.1947	+	6.59341i	1.25002	+	0.408122i
$262$	3.18194	+	5.51129i	0.196581	+	0.340488i
$263$	−3.09493			−0.190842			−0.0954208	−	0.995437i	$-0.530420\pi$
$263$	−3.09493			−0.190842			−0.0954208	+	0.995437i	$0.530420\pi$
$264$	3.47141	−	4.28061i	0.213651	−	0.263453i
$265$	−3.27292	−	5.66886i	−0.201054	−	0.348235i
$266$	−0.911351	−	3.26886i	−0.0558785	−	0.200426i
$267$	0.139680	+	0.364654i	0.00854830	+	0.0223165i
$268$	−5.48345	−	9.49761i	−0.334955	−	0.580159i
$269$	−13.4451	−	23.2877i	−0.819765	−	1.41987i	−0.905855	−	0.423587i	$-0.860771\pi$
$269$	−13.4451	−	23.2877i	−0.819765	−	1.41987i	0.0860906	−	0.996287i	$-0.472563\pi$
$270$	−0.830095	−	16.5130i	−0.0505180	−	1.00495i
$271$	−11.1082	+	19.2400i	−0.674776	+	1.16875i	0.301759	+	0.953384i	$0.402426\pi$
$271$	−11.1082	+	19.2400i	−0.674776	+	1.16875i	−0.976534	+	0.215362i	$0.930907\pi$
$272$	−0.760877	+	1.31788i	−0.0461349	+	0.0799080i
$273$	−2.97592	−	25.9677i	−0.180111	−	1.57163i
$274$	1.37072	+	2.37416i	0.0828084	+	0.143428i
$275$	16.3067			0.983331
$276$	−1.38727	−	3.62167i	−0.0835041	−	0.217999i
$277$	−14.6375			−0.879482			−0.439741	−	0.898125i	$-0.644930\pi$
$277$	−14.6375			−0.879482			−0.439741	+	0.898125i	$0.644930\pi$
$278$	3.98345	−	6.89953i	0.238911	−	0.413807i
$279$	−26.8675	−	8.77202i	−1.60851	−	0.525167i
$280$	2.26088	+	8.10936i	0.135113	+	0.484627i
$281$	11.6992	−	20.2636i	0.697915	−	1.20882i	−0.271273	−	0.962502i	$-0.587445\pi$
$281$	11.6992	−	20.2636i	0.697915	−	1.20882i	0.969188	−	0.246322i	$-0.0792219\pi$
$282$	−3.61109	−	9.42724i	−0.215037	−	0.561384i
$283$	13.0624	−	22.6247i	0.776478	−	1.34490i	−0.157482	−	0.987522i	$-0.550338\pi$
$283$	13.0624	−	22.6247i	0.776478	−	1.34490i	0.933960	−	0.357377i	$-0.116329\pi$
$284$	−4.34501	+	7.52578i	−0.257829	+	0.446573i
$285$	2.52859	+	6.60123i	0.149781	+	0.391023i
$286$	−9.07442	+	15.7174i	−0.536582	+	0.929387i
$287$	10.3759	−	10.5876i	0.612471	−	0.624963i
$288$	−2.85185	−	0.931107i	−0.168047	−	0.0548660i
$289$	7.34213	−	12.7169i	0.431890	−	0.748056i
$290$	22.5322			1.32313
$291$	9.19562	+	24.0064i	0.539057	+	1.40728i
$292$	4.96690			0.290666
$293$	12.9315	+	22.3980i	0.755465	+	1.30850i	0.945143	+	0.326657i	$0.105922\pi$
$293$	12.9315	+	22.3980i	0.755465	+	1.30850i	−0.189678	+	0.981846i	$0.560745\pi$
$294$	11.2323	−	4.56462i	0.655080	−	0.266214i
$295$	−1.78947	+	3.09945i	−0.104187	+	0.180457i
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	14.7157	+	7.53762i	0.853894	+	0.437377i
$298$	−11.6300	−	20.1437i	−0.673706	−	1.16689i
$299$	6.38564	+	11.0603i	0.369291	+	0.639631i
$300$	−3.17511	−	8.28905i	−0.183315	−	0.478568i
$301$	17.4971	+	4.49954i	1.00852	+	0.259349i
$302$	−4.06238	−	7.03625i	−0.233764	−	0.404891i
$303$	−20.2804	+	25.0079i	−1.16508	+	1.43667i
$304$	1.28263			0.0735639
$305$	4.97141	+	8.61073i	0.284662	+	0.493049i
$306$	−4.33981	−	1.41692i	−0.248090	−	0.0809997i
$307$	3.53216			0.201591			0.100795	−	0.994907i	$-0.467861\pi$
$307$	3.53216			0.201591			0.100795	+	0.994907i	$0.467861\pi$
$308$	−8.15335	−	2.09671i	−0.464580	−	0.119471i
$309$	0.308342	−	0.380217i	0.0175409	−	0.0216298i
$310$	−29.9773			−1.70260
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	−0.889166	−	0.457584i	$-0.848715\pi$
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	0.840863	+	0.541249i	$0.182048\pi$
$312$	9.75636	+	1.55237i	0.552345	+	0.0878855i
$313$	1.42107	+	2.46136i	0.0803234	+	0.139124i	0.903389	−	0.428822i	$-0.141071\pi$
$313$	1.42107	+	2.46136i	0.0803234	+	0.139124i	−0.823065	+	0.567947i	$0.807738\pi$
$314$	11.2632			0.635619
$315$	−22.4029	+	11.6607i	−1.26226	+	0.657004i
$316$	−4.13844			−0.232805
$317$	12.4601	+	21.5815i	0.699827	+	1.21214i	0.968526	+	0.248911i	$0.0800728\pi$
$317$	12.4601	+	21.5815i	0.699827	+	1.21214i	−0.268700	+	0.963224i	$0.586594\pi$
$318$	−1.27455	−	3.32738i	−0.0714732	−	0.186590i
$319$	−11.2661	+	19.5134i	−0.630779	+	1.09254i
$320$	−3.18194			−0.177876
$321$	7.04910	+	18.4026i	0.393442	+	1.02713i
$322$	−4.14652	+	4.23109i	−0.231076	+	0.235789i
$323$	1.95185			0.108604
$324$	0.966208	−	8.94799i	0.0536782	−	0.497110i
$325$	14.6150	+	25.3140i	0.810697	+	1.40417i
$326$	−3.98057			−0.220463
$327$	7.56238	+	1.20328i	0.418201	+	0.0665413i
$328$	2.80150	+	4.85235i	0.154687	+	0.267926i
$329$	−10.7934	+	11.0136i	−0.595061	+	0.607198i
$330$	17.3187	+	2.75564i	0.953366	+	0.151693i
$331$	3.58577	+	6.21074i	0.197092	+	0.341373i	0.947584	−	0.319506i	$-0.103517\pi$
$331$	3.58577	+	6.21074i	0.197092	+	0.341373i	−0.750492	+	0.660879i	$0.770184\pi$
$332$	−4.03379	−	6.98673i	−0.221383	−	0.383447i
$333$	−2.85185	−	0.931107i	−0.156280	−	0.0510244i
$334$	−2.61956	+	4.53721i	−0.143336	+	0.248265i
$335$	17.4480	−	30.2209i	0.953287	−	1.65114i
$336$	0.521753	+	4.55278i	0.0284640	+	0.248374i
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	−0.993560	−	0.113309i	$-0.963855\pi$
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	0.398651	−	0.917103i	$-0.369478\pi$
$338$	−19.5322			−1.06241
$339$	5.49944	+	0.875035i	0.298689	+	0.0475254i
$340$	−4.84213			−0.262602
$341$	14.9887	−	25.9611i	0.811681	−	1.40587i
$342$	0.794668	+	3.76494i	0.0429707	+	0.203585i
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$	−3.41423	+	5.91362i	−0.184083	+	0.318841i
$345$	7.77292	−	9.58481i	0.418480	−	0.516029i
$346$	1.27579	−	2.20974i	0.0685871	−	0.118796i
$347$	1.05555	−	1.82826i	0.0566646	−	0.0981460i	−0.836302	−	0.548270i	$-0.815287\pi$
$347$	1.05555	−	1.82826i	0.0566646	−	0.0981460i	0.892966	+	0.450124i	$0.148620\pi$
$348$	12.1127	+	1.92730i	0.649310	+	0.103314i
$349$	18.1082	−	31.3643i	0.969310	−	1.67889i	0.271751	−	0.962368i	$-0.412397\pi$
$349$	18.1082	−	31.3643i	0.969310	−	1.67889i	0.697559	−	0.716527i	$-0.254269\pi$
$350$	−9.49028	+	9.68385i	−0.507277	+	0.517623i
$351$	1.48796	+	29.5999i	0.0794215	+	1.57993i
$352$	1.59097	−	2.75564i	0.0847991	−	0.146876i
$353$	−10.4887			−0.558255			−0.279127	−	0.960254i	$-0.590045\pi$
$353$	−10.4887			−0.558255			−0.279127	+	0.960254i	$0.590045\pi$
$354$	−1.22708	+	1.51312i	−0.0652188	+	0.0804216i
$355$	−27.6512			−1.46757
$356$	0.112725	+	0.195246i	0.00597442	+	0.0103480i
$357$	0.793980	+	6.92820i	0.0420219	+	0.366679i
$358$	−3.51887	+	6.09487i	−0.185978	+	0.322124i
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	−0.0195047	−	0.999810i	$-0.506209\pi$
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	0.875613	−	0.483013i	$-0.160458\pi$
$360$	−1.97141	−	9.34004i	−0.103902	−	0.492264i
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$	−6.48345	−	11.2297i	−0.340762	−	0.590218i
$363$	0.954858	−	1.17744i	0.0501171	−	0.0617995i
$364$	−4.05267	−	14.5362i	−0.212417	−	0.761904i
$365$	7.90219	+	13.6870i	0.413620	+	0.716410i
$366$	1.93598	+	5.05415i	0.101195	+	0.264185i
$367$	−18.1111			−0.945391			−0.472696	−	0.881226i	$-0.656719\pi$
$367$	−18.1111			−0.945391			−0.472696	+	0.881226i	$0.656719\pi$
$368$	−1.11956	−	1.93914i	−0.0583612	−	0.101085i
$369$	−12.5075	+	11.2297i	−0.651116	+	0.584593i
$370$	−3.18194			−0.165421
$371$	−3.80959	+	3.88728i	−0.197784	+	0.201818i
$372$	−16.1150	−	2.56412i	−0.835526	−	0.132943i
$373$	−11.6706			−0.604280			−0.302140	−	0.953263i	$-0.597701\pi$
$373$	−11.6706			−0.604280			−0.302140	+	0.953263i	$0.597701\pi$
$374$	2.42107	−	4.19341i	0.125190	−	0.216836i
$375$	0.433105	−	0.534063i	0.0223654	−	0.0275789i
$376$	−2.91423	−	5.04759i	−0.150290	−	0.260310i
$377$	−40.3893			−2.08016
$378$	−13.0406	+	4.35224i	−0.670738	+	0.223855i
$379$	14.2690			0.732947			0.366474	−	0.930428i	$-0.380565\pi$
$379$	14.2690			0.732947			0.366474	+	0.930428i	$0.380565\pi$
$380$	2.04063	+	3.53447i	0.104682	+	0.181315i
$381$	−21.9343	+	27.0473i	−1.12373	+	1.38568i
$382$	0.990285	−	1.71522i	0.0506674	−	0.0877585i
$383$	−1.64979			−0.0843001			−0.0421501	−	0.999111i	$-0.513421\pi$
$383$	−1.64979			−0.0843001			−0.0421501	+	0.999111i	$0.513421\pi$
$384$	−1.71053	−	0.272169i	−0.0872903	−	0.0138891i
$385$	−7.19398	−	25.8035i	−0.366639	−	1.31507i
$386$	4.54583			0.231377
$387$	−19.4737	−	6.35803i	−0.989905	−	0.323197i
$388$	7.42107	+	12.8537i	0.376748	+	0.652546i
$389$	−32.0676			−1.62589			−0.812946	−	0.582340i	$-0.802137\pi$
$389$	−32.0676			−1.62589			−0.812946	+	0.582340i	$0.802137\pi$
$390$	11.2443	+	29.3548i	0.569379	+	1.48644i
$391$	−1.70370	−	2.95089i	−0.0861596	−	0.149233i
$392$	5.99028	−	3.62167i	0.302555	−	0.182922i
$393$	−6.94282	+	8.56122i	−0.350219	+	0.431856i
$394$	−10.9074	−	18.8922i	−0.549507	−	0.951773i
$395$	−6.58414	−	11.4041i	−0.331284	−	0.573800i
$396$	9.07442	+	2.96273i	0.456007	+	0.148883i
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.210660	+	0.977559i	$0.567561\pi$
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.741261	+	0.671217i	$0.765772\pi$
$398$	−6.14132	+	10.6371i	−0.307836	+	0.533188i
$399$	4.72257	−	3.49932i	0.236424	−	0.175185i
$400$	−2.56238	−	4.43818i	−0.128119	−	0.221909i
$401$	10.6192			0.530296			0.265148	−	0.964208i	$-0.414579\pi$
$401$	10.6192			0.530296			0.265148	+	0.964208i	$0.414579\pi$
$402$	11.9646	−	14.7536i	0.596739	−	0.735841i
$403$	53.7349			2.67673
$404$	−9.29467	+	16.0988i	−0.462427	+	0.800947i
$405$	26.1947	−	11.5735i	1.30162	−	0.575090i
$406$	−5.03147	−	18.0470i	−0.249708	−	0.895657i
$407$	1.59097	−	2.75564i	0.0788615	−	0.136592i
$408$	−2.60301	−	0.414174i	−0.128868	−	0.0205047i
$409$	−2.77292	+	4.80283i	−0.137112	+	0.237485i	−0.926402	−	0.376535i	$-0.877115\pi$
$409$	−2.77292	+	4.80283i	−0.137112	+	0.237485i	0.789290	+	0.614020i	$0.210449\pi$
$410$	−8.91423	+	15.4399i	−0.440242	+	0.762522i
$411$	−2.99084	+	3.68802i	−0.147527	+	0.181916i
$412$	0.141315	−	0.244765i	0.00696209	−	0.0120587i
$413$	2.88207	+	0.741150i	0.141818	+	0.0364696i
$414$	4.99837	−	4.48769i	0.245656	−	0.220558i
$415$	12.8353	−	22.2314i	0.630060	−	1.09130i
$416$	5.70370			0.279647
$417$	13.6276	+	2.16834i	0.667349	+	0.106184i
$418$	−4.08126			−0.199621
$419$	2.77455	+	4.80566i	0.135546	+	0.234772i	0.925806	−	0.378000i	$-0.123388\pi$
$419$	2.77455	+	4.80566i	0.135546	+	0.234772i	−0.790260	+	0.612772i	$0.790055\pi$
$420$	−11.7157	+	8.68110i	−0.571669	+	0.423595i
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	−0.937269	−	0.348606i	$-0.886655\pi$
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	0.770537	+	0.637396i	$0.219988\pi$
$422$	8.32846	−	14.4253i	0.405423	−	0.702213i
$423$	13.0108	−	11.6815i	0.632606	−	0.567975i
$424$	−1.02859	−	1.78157i	−0.0499527	−	0.0865207i
$425$	−3.89931	−	6.75381i	−0.189144	−	0.327608i
$426$	−14.8646	−	2.36515i	−0.720191	−	0.114592i
$427$	5.78659	−	5.90461i	0.280033	−	0.285744i
$428$	5.68878	+	9.85326i	0.274978	+	0.476275i
$429$	−31.0442	−	4.93955i	−1.49883	−	0.238484i
$430$	−21.7278			−1.04781
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	0.921321	+	0.388803i	$0.127111\pi$
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	−0.123947	+	0.992289i	$0.539555\pi$
$432$	−0.260877	−	5.18960i	−0.0125514	−	0.249685i
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$	6.69398	+	24.0101i	0.321321	+	1.15252i
$435$	13.9601	+	36.4446i	0.669334	+	1.74739i
$436$	4.42107			0.211731
$437$	−1.43598	+	2.48720i	−0.0686924	+	0.118979i
$438$	3.07730	+	8.03371i	0.147039	+	0.383865i
$439$	4.41711	+	7.65066i	0.210817	+	0.365146i	0.951970	−	0.306190i	$-0.0990542\pi$
$439$	4.41711	+	7.65066i	0.210817	+	0.365146i	−0.741153	+	0.671336i	$0.765721\pi$
$440$	10.1248			0.482679
$441$	14.3421	+	15.3396i	0.682959	+	0.730457i
$442$	8.67962			0.412847
$443$	−8.75924	−	15.1715i	−0.416164	−	0.720817i	0.579386	−	0.815053i	$-0.303292\pi$
$443$	−8.75924	−	15.1715i	−0.416164	−	0.720817i	−0.995550	+	0.0942360i	$0.969959\pi$
$444$	−1.71053	−	0.272169i	−0.0811783	−	0.0129166i
$445$	−0.358685	+	0.621261i	−0.0170033	+	0.0294506i
$446$	−10.6569			−0.504620
$447$	25.3759	−	31.2911i	1.20024	−	1.48002i
$448$	0.710533	+	2.54856i	0.0335695	+	0.120408i
$449$	31.2301			1.47384			0.736920	−	0.675980i	$-0.236280\pi$
$449$	31.2301			1.47384			0.736920	+	0.675980i	$0.236280\pi$
$450$	11.4399	−	10.2712i	0.539284	−	0.484187i
$451$	−8.91423	−	15.4399i	−0.419755	−	0.727036i
$452$	3.21505			0.151223
$453$	8.86389	−	10.9301i	0.416462	−	0.513540i
$454$	−7.25404	−	12.5644i	−0.340449	−	0.589675i
$455$	33.6089	−	34.2944i	1.57561	−	1.60775i
$456$	0.794668	+	2.07459i	0.0372138	+	0.0971516i
$457$	16.0624	+	27.8209i	0.751367	+	1.30140i	0.947161	+	0.320760i	$0.103938\pi$
$457$	16.0624	+	27.8209i	0.751367	+	1.30140i	−0.195794	+	0.980645i	$0.562728\pi$
$458$	5.12476	+	8.87635i	0.239464	+	0.414765i
$459$	−0.396990	−	7.89729i	−0.0185299	−	0.368614i
$460$	3.56238	−	6.17023i	0.166097	−	0.287688i
$461$	1.23229	−	2.13438i	0.0573933	−	0.0994081i	−0.835901	−	0.548880i	$-0.815054\pi$
$461$	1.23229	−	2.13438i	0.0573933	−	0.0994081i	0.893295	+	0.449472i	$0.148388\pi$
$462$	−1.66019	−	14.4867i	−0.0772390	−	0.673981i
$463$	15.1735	+	26.2812i	0.705171	+	1.22139i	0.966630	+	0.256177i	$0.0824631\pi$
$463$	15.1735	+	26.2812i	0.705171	+	1.22139i	−0.261459	+	0.965215i	$0.584204\pi$
$464$	7.08126			0.328739
$465$	−18.5728	−	48.4868i	−0.861292	−	2.24852i
$466$	1.08126			0.0500882
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	−0.989465	−	0.144774i	$-0.953754\pi$
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	0.620110	+	0.784515i	$0.287088\pi$
$468$	3.53379	+	16.7422i	0.163350	+	0.773909i
$469$	−28.1014	−	7.22651i	−1.29760	−	0.333689i
$470$	9.27292	−	16.0612i	0.427728	−	0.740846i
$471$	6.97825	+	18.2177i	0.321541	+	0.839425i
$472$	−0.562382	+	0.974074i	−0.0258857	+	0.0448354i
$473$	10.8639	−	18.8168i	0.499522	−	0.865198i
$474$	−2.56402	−	6.69371i	−0.117769	−	0.307452i
$475$	−3.28659	+	5.69254i	−0.150799	+	0.261192i
$476$	1.08126	+	3.87828i	0.0495593	+	0.177760i
$477$	4.59222	−	4.12304i	0.210263	−	0.188781i
$478$	6.16019	−	10.6698i	0.281761	−	0.488024i
$479$	−23.1729			−1.05880			−0.529399	−	0.848373i	$-0.677582\pi$
$479$	−23.1729			−1.05880			−0.529399	+	0.848373i	$0.677582\pi$
$480$	−1.97141	−	5.14663i	−0.0899821	−	0.234911i
$481$	5.70370			0.260066
$482$	−6.50000	−	11.2583i	−0.296067	−	0.512803i
$483$	−9.41260	−	4.08536i	−0.428288	−	0.185890i
$484$	0.437618	−	0.757977i	0.0198917	−	0.0344535i
$485$	−23.6134	+	40.8996i	−1.07223	+	1.85716i
$486$	15.0715	−	3.98104i	0.683659	−	0.180583i
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	0.902098	−	0.431531i	$-0.142026\pi$
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	−0.824766	+	0.565474i	$0.808693\pi$
$488$	1.56238	+	2.70612i	0.0707257	+	0.122500i
$489$	−2.46621	−	6.43837i	−0.111526	−	0.291153i
$490$	19.5104	+	10.7451i	0.881390	+	0.485415i
$491$	−9.58414	−	16.6002i	−0.432526	−	0.749157i	0.564564	−	0.825389i	$-0.309044\pi$
$491$	−9.58414	−	16.6002i	−0.432526	−	0.749157i	−0.997090	+	0.0762323i	$0.975711\pi$
$492$	−6.11273	+	7.53762i	−0.275583	+	0.339822i
$493$	10.7759			0.485323
$494$	−3.65787	−	6.33561i	−0.164575	−	0.285053i
$495$	6.27292	+	29.7195i	0.281947	+	1.33579i
$496$	−9.42107			−0.423018
$497$	6.17455	+	22.1470i	0.276966	+	0.993430i
$498$	8.80150	−	10.8532i	0.394405	−	0.486342i
$499$	41.1696			1.84301			0.921503	−	0.388371i	$-0.126962\pi$
$499$	41.1696			1.84301			0.921503	+	0.388371i	$0.126962\pi$
$500$	0.198495	−	0.343803i	0.00887697	−	0.0153754i
$501$	−8.96169	−	1.42593i	−0.400379	−	0.0637056i
$502$	2.55555	+	4.42633i	0.114060	+	0.197557i
$503$	−26.4542			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$503$	−26.4542			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$504$	−7.04063	+	3.66464i	−0.313615	+	0.163236i
$505$	−59.1502			−2.63215
$506$	3.56238	+	6.17023i	0.158367	+	0.274300i
$507$	−12.1014	−	31.5923i	−0.537441	−	1.40306i
$508$	−10.0527	+	17.4117i	−0.446015	+	0.772521i
$509$	12.7713			0.566077			0.283039	−	0.959109i	$-0.408658\pi$
$509$	12.7713			0.566077			0.283039	+	0.959109i	$0.408658\pi$
$510$	−3.00000	−	7.83191i	−0.132842	−	0.346803i
$511$	9.19794	−	9.38554i	0.406893	−	0.415192i
$512$	−1.00000			−0.0441942
$513$	−5.59725	+	3.61795i	−0.247125	+	0.159736i
$514$	3.83009	+	6.63392i	0.168938	+	0.292610i
$515$	0.899313			0.0396285
$516$	−11.6803	−	1.85849i	−0.514197	−	0.0818156i
$517$	9.27292	+	16.0612i	0.407822	+	0.706369i
$518$	0.710533	+	2.54856i	0.0312190	+	0.111977i
$519$	4.36458	+	0.694462i	0.191584	+	0.0304835i
$520$	9.07442	+	15.7174i	0.397940	+	0.689252i
$521$	−3.40615	−	5.89962i	−0.149226	−	0.258467i	0.781716	−	0.623635i	$-0.214345\pi$
$521$	−3.40615	−	5.89962i	−0.149226	−	0.258467i	−0.930942	+	0.365168i	$0.881012\pi$
$522$	4.38727	+	20.7858i	0.192026	+	0.909770i
$523$	14.7535	−	25.5538i	0.645125	−	1.11739i	−0.339148	−	0.940733i	$-0.610139\pi$
$523$	14.7535	−	25.5538i	0.645125	−	1.11739i	0.984273	−	0.176656i	$-0.0565280\pi$
$524$	−3.18194	+	5.51129i	−0.139004	+	0.240762i
$525$	−21.5430	−	9.35032i	−0.940211	−	0.408081i
$526$	−1.54746	−	2.68029i	−0.0674727	−	0.116866i
$527$	−14.3365			−0.624510
$528$	5.44282	+	0.866025i	0.236868	+	0.0376889i
$529$	−17.9863			−0.782014
$530$	3.27292	−	5.66886i	0.142166	−	0.246239i
$531$	−3.20765	−	1.04728i	−0.139200	−	0.0454479i
$532$	2.37524	−	2.42368i	0.102980	−	0.105080i
$533$	15.9789	−	27.6763i	0.692125	−	1.19879i
$534$	−0.245960	+	0.303294i	−0.0106437	+	0.0131248i
$535$	−18.1014	+	31.3525i	−0.782591	+	1.35549i
$536$	5.48345	−	9.49761i	0.236849	−	0.410234i
$537$	−12.0383	−	1.91546i	−0.519491	−	0.0826580i
$538$	13.4451	−	23.2877i	0.579661	−	1.00400i
$539$	−19.0607	+	11.5239i	−0.821004	+	0.496371i
$540$	13.8856	−	8.97539i	0.597543	−	0.386239i
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	−0.355097	−	0.934829i	$-0.615552\pi$
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	0.987135	−	0.159892i	$-0.0511145\pi$
$542$	−22.2164			−0.954277
$543$	14.1465	−	17.4441i	0.607085	−	0.748599i
$544$	−1.52175			−0.0652446
$545$	7.03379	+	12.1829i	0.301295	+	0.521857i
$546$	21.0007	−	15.5611i	0.898746	−	0.665952i
$547$	17.6150	−	30.5102i	0.753165	−	1.30452i	−0.193116	−	0.981176i	$-0.561859\pi$
$547$	17.6150	−	30.5102i	0.753165	−	1.30452i	0.946281	−	0.323344i	$-0.104807\pi$
$548$	−1.37072	+	2.37416i	−0.0585544	+	0.101419i
$549$	−6.97537	+	6.26271i	−0.297701	+	0.267286i
$550$	8.15335	+	14.1220i	0.347660	+	0.602165i
$551$	−4.54132	−	7.86579i	−0.193467	−	0.335094i
$552$	2.44282	−	3.01225i	0.103973	−	0.128210i
$553$	−7.66376	+	7.82007i	−0.325896	+	0.332543i
$554$	−7.31875	−	12.6764i	−0.310944	−	0.538570i
$555$	−1.97141	−	5.14663i	−0.0836817	−	0.218462i
$556$	7.96690			0.337872
$557$	−3.36909	−	5.83543i	−0.142753	−	0.247255i	0.785779	−	0.618507i	$-0.212262\pi$
$557$	−3.36909	−	5.83543i	−0.142753	−	0.247255i	−0.928532	+	0.371252i	$0.878929\pi$
$558$	−5.83693	−	27.6539i	−0.247097	−	1.17068i
$559$	38.9475			1.64730
$560$	−5.89248	+	6.01266i	−0.249003	+	0.254081i
$561$	8.28263	+	1.31788i	0.349693	+	0.0556408i
$562$	23.3984			0.987001
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	−0.850233	−	0.526406i	$-0.823539\pi$
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	0.880998	+	0.473121i	$0.156873\pi$
$564$	6.35868	−	7.84092i	0.267749	−	0.330162i
$565$	5.11505	+	8.85952i	0.215192	+	0.372723i
$566$	26.1248			1.09811
$567$	−15.1190	−	18.3961i	−0.634939	−	0.772563i
$568$	−8.69002			−0.364625
$569$	−9.78263	−	16.9440i	−0.410109	−	0.710330i	0.584792	−	0.811183i	$-0.301176\pi$
$569$	−9.78263	−	16.9440i	−0.410109	−	0.710330i	−0.994901	+	0.100853i	$0.967843\pi$
$570$	−4.45254	+	5.49044i	−0.186496	+	0.229969i
$571$	10.9629	−	18.9884i	0.458785	−	0.794638i	−0.540112	−	0.841593i	$-0.681618\pi$
$571$	10.9629	−	18.9884i	0.458785	−	0.794638i	0.998897	+	0.0469545i	$0.0149516\pi$
$572$	−18.1488			−0.758841
$573$	3.38783	+	0.539049i	0.141529	+	0.0225191i
$574$	14.3571	+	3.69204i	0.599252	+	0.154103i
$575$	11.4750			0.478540
$576$	−0.619562	−	2.93533i	−0.0258151	−	0.122305i
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	0.999853	+	0.0171554i	$0.00546099\pi$
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	−0.485069	+	0.874476i	$0.661206\pi$
$578$	14.6843			0.610785
$579$	2.81642	+	7.35265i	0.117046	+	0.305566i
$580$	11.2661	+	19.5134i	0.467798	+	0.810251i
$581$	−20.6722	−	5.31604i	−0.857629	−	0.220547i
$582$	−16.1923	+	19.9668i	−0.671194	+	0.827652i
$583$	3.27292	+	5.66886i	0.135550	+	0.234780i
$584$	2.48345	+	4.30146i	0.102766	+	0.177996i
$585$	−40.5134	+	36.3743i	−1.67502	+	1.50389i
$586$	−12.9315	+	22.3980i	−0.534194	+	0.925251i
$587$	−18.0796	+	31.3148i	−0.746226	+	1.29250i	0.203394	+	0.979097i	$0.434803\pi$
$587$	−18.0796	+	31.3148i	−0.746226	+	1.29250i	−0.949620	+	0.313404i	$0.898531\pi$
$588$	9.56922	+	7.44514i	0.394628	+	0.307032i
$589$	6.04187	+	10.4648i	0.248951	+	0.431196i
$590$	−3.57893			−0.147342
$591$	23.7993	−	29.3470i	0.978973	−	1.20717i
$592$	−1.00000			−0.0410997
$593$	−7.55391	+	13.0838i	−0.310202	+	0.537285i	−0.978406	−	0.206693i	$-0.933730\pi$
$593$	−7.55391	+	13.0838i	−0.310202	+	0.537285i	0.668204	+	0.743978i	$0.267063\pi$
$594$	0.830095	+	16.5130i	0.0340592	+	0.677537i
$595$	−8.96690	+	9.14978i	−0.367607	+	0.375105i
$596$	11.6300	−	20.1437i	0.476382	−	0.825118i
$597$	−21.0098	−	3.34295i	−0.859876	−	0.136818i
$598$	−6.38564	+	11.0603i	−0.261128	+	0.452287i
$599$	2.72708	−	4.72345i	0.111426	−	0.192995i	−0.804920	−	0.593384i	$-0.797792\pi$
$599$	2.72708	−	4.72345i	0.111426	−	0.192995i	0.916345	+	0.400389i	$0.131125\pi$
$600$	5.59097	−	6.89425i	0.228250	−	0.281456i
$601$	−3.36840	+	5.83424i	−0.137400	+	0.237984i	−0.926512	−	0.376266i	$-0.877208\pi$
$601$	−3.36840	+	5.83424i	−0.137400	+	0.237984i	0.789112	+	0.614250i	$0.210541\pi$
$602$	4.85185	+	17.4027i	0.197747	+	0.709282i
$603$	31.2759	+	10.2114i	1.27365	+	0.415839i
$604$	4.06238	−	7.03625i	0.165296	−	0.286301i
$605$	2.78495			0.113224
$606$	−31.7977	−	5.05944i	−1.29169	−	0.205526i
$607$	6.67059			0.270751			0.135376	−	0.990794i	$-0.456776\pi$
$607$	6.67059			0.270751			0.135376	+	0.990794i	$0.456776\pi$
$608$	0.641315	+	1.11079i	0.0260088	+	0.0450485i
$609$	26.0728	−	19.3194i	1.05652	−	0.782860i
$610$	−4.97141	+	8.61073i	−0.201287	+	0.348638i
$611$	−16.6219	+	28.7899i	−0.672449	+	1.16472i
$612$	−0.942820	−	4.46684i	−0.0381112	−	0.180561i
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	0.878950	−	0.476915i	$-0.158245\pi$
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	−0.852495	+	0.522735i	$0.824912\pi$
$614$	1.76608	+	3.05894i	0.0712731	+	0.123449i
$615$	−30.4962	−	4.85235i	−1.22972	−	0.195666i
$616$	−2.26088	−	8.10936i	−0.0910933	−	0.326736i
$617$	17.2483	+	29.8749i	0.694390	+	1.20272i	0.970386	+	0.241560i	$0.0776589\pi$
$617$	17.2483	+	29.8749i	0.694390	+	1.20272i	−0.275996	+	0.961159i	$0.589008\pi$
$618$	0.483448	+	0.0769231i	0.0194471	+	0.00309430i
$619$	−16.4484			−0.661118			−0.330559	−	0.943785i	$-0.607237\pi$
$619$	−16.4484			−0.661118			−0.330559	+	0.943785i	$0.607237\pi$
$620$	−14.9887	−	25.9611i	−0.601959	−	1.04262i
$621$	10.3554	+	5.30420i	0.415549	+	0.212850i
$622$	−1.70370			−0.0683120
$623$	0.577690	+	0.148558i	0.0231446	+	0.00595184i
$624$	3.53379	+	9.22544i	0.141465	+	0.369313i
$625$	−24.3606			−0.974425
$626$	−1.42107	+	2.46136i	−0.0567972	+	0.0983757i
$627$	−2.52859	−	6.60123i	−0.100982	−	0.263628i
$628$	5.63160	+	9.75422i	0.224725	+	0.389236i
$629$	−1.52175			−0.0606763
$630$	−21.2999	−	13.5711i	−0.848607	−	0.540687i
$631$	−30.0118			−1.19475			−0.597375	−	0.801962i	$-0.703790\pi$
$631$	−30.0118			−1.19475			−0.597375	+	0.801962i	$0.703790\pi$
$632$	−2.06922	−	3.58399i	−0.0823091	−	0.142564i
$633$	28.4922	+	4.53349i	1.13246	+	0.180190i
$634$	−12.4601	+	21.5815i	−0.494852	+	0.857109i
$635$	−63.9740			−2.53873
$636$	2.24433	−	2.76748i	0.0889933	−	0.109738i
$637$	−34.9728	−	19.2608i	−1.38567	−	0.763142i
$638$	−22.5322			−0.892057
$639$	−5.38401	−	25.5081i	−0.212988	−	1.00908i
$640$	−1.59097	−	2.75564i	−0.0628887	−	0.108926i
$641$	27.8993			1.10196			0.550978	−	0.834520i	$-0.314255\pi$
$641$	27.8993			1.10196			0.550978	+	0.834520i	$0.314255\pi$
$642$	−12.4126	+	15.3060i	−0.489886	+	0.604080i
$643$	14.2524	+	24.6859i	0.562060	+	0.973516i	0.997317	+	0.0732100i	$0.0233243\pi$
$643$	14.2524	+	24.6859i	0.562060	+	0.973516i	−0.435257	+	0.900306i	$0.643342\pi$
$644$	−5.73749	−	1.47544i	−0.226089	−	0.0581407i
$645$	−13.4617	−	35.1436i	−0.530054	−	1.38378i
$646$	0.975923	+	1.69035i	0.0383972	+	0.0665059i
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	0.982224	−	0.187711i	$-0.0601069\pi$
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	−0.653675	+	0.756776i	$0.726774\pi$
$648$	8.23229	−	3.63723i	0.323395	−	0.142884i
$649$	1.78947	−	3.09945i	0.0702427	−	0.121664i
$650$	−14.6150	+	25.3140i	−0.573249	+	0.992897i
$651$	−34.6878	+	25.7029i	−1.35952	+	1.00738i
$652$	−1.99028	−	3.44727i	−0.0779456	−	0.135006i
$653$	38.1650			1.49351			0.746756	−	0.665098i	$-0.231610\pi$
$653$	38.1650			1.49351			0.746756	+	0.665098i	$0.231610\pi$
$654$	2.73912	+	7.15085i	0.107108	+	0.279620i
$655$	−20.2495			−0.791214
$656$	−2.80150	+	4.85235i	−0.109380	+	0.189452i
$657$	−11.0875	+	9.95475i	−0.432566	+	0.388372i
$658$	−14.9347	−	3.84060i	−0.582217	−	0.149722i
$659$	4.37072	−	7.57031i	0.170259	−	0.294898i	−0.768251	−	0.640148i	$-0.778873\pi$
$659$	4.37072	−	7.57031i	0.170259	−	0.294898i	0.938510	+	0.345251i	$0.112206\pi$
$660$	6.27292	+	16.3763i	0.244173	+	0.637446i
$661$	10.0419	−	17.3930i	0.390584	−	0.676511i	−0.601943	−	0.798539i	$-0.705607\pi$
$661$	10.0419	−	17.3930i	0.390584	−	0.676511i	0.992527	+	0.122028i	$0.0389399\pi$
$662$	−3.58577	+	6.21074i	−0.139365	+	0.241387i
$663$	5.37756	+	14.0388i	0.208847	+	0.545224i
$664$	4.03379	−	6.98673i	0.156541	−	0.271138i
$665$	10.4577	+	2.68930i	0.405534	+	0.104286i
$666$	−0.619562	−	2.93533i	−0.0240075	−	0.113742i
$667$	−7.92790	+	13.7315i	−0.306970	+	0.531687i
$668$	−5.23912			−0.202708
$669$	−6.60262	−	17.2370i	−0.255272	−	0.666422i
$670$	34.8960			1.34815
$671$	−4.97141	−	8.61073i	−0.191919	−	0.332414i
$672$	−3.68194	+	2.72824i	−0.142034	+	0.105244i
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	0.325242	+	0.945631i	$0.394554\pi$
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	−0.981561	+	0.191148i	$0.938779\pi$
$674$	10.9211	−	18.9158i	0.420664	−	0.728611i
$675$	23.7008	+	12.1399i	0.912245	+	0.467266i
$676$	−9.76608	−	16.9153i	−0.375618	−	0.650590i
$677$	0.358685	+	0.621261i	0.0137854	+	0.0238770i	0.872836	−	0.488014i	$-0.162279\pi$
$677$	0.358685	+	0.621261i	0.0137854	+	0.0238770i	−0.859050	+	0.511891i	$0.828945\pi$
$678$	1.99192	+	5.20018i	0.0764992	+	0.199712i
$679$	38.0312	+	9.78005i	1.45950	+	0.375324i
$680$	−2.42107	−	4.19341i	−0.0928437	−	0.160810i
$681$	15.8279	−	19.5174i	0.606527	−	0.747910i
$682$	29.9773			1.14789
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	0.591260	−	0.806481i	$-0.298631\pi$
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	−0.994063	+	0.108806i	$0.965297\pi$
$684$	−2.86320	+	2.57067i	−0.109477	+	0.0982921i
$685$	−8.72313			−0.333294
$686$	4.24953	−	18.0261i	0.162248	−	0.688241i
$687$	−11.1819	+	13.7885i	−0.426618	+	0.526064i
$688$	−6.82846			−0.260333
$689$	−5.86677	+	10.1615i	−0.223506	+	0.387124i
$690$	12.1871	+	1.93914i	0.463957	+	0.0738217i
$691$	−2.92395	−	5.06442i	−0.111232	−	0.192660i	0.805035	−	0.593227i	$-0.202146\pi$
$691$	−2.92395	−	5.06442i	−0.111232	−	0.192660i	−0.916267	+	0.400567i	$0.868813\pi$
$692$	2.55159			0.0969968
$693$	22.4029	−	11.6607i	0.851015	−	0.442952i
$694$	2.11109			0.0801359
$695$	12.6751	+	21.9539i	0.480794	+	0.832760i
$696$	4.38727	+	11.4536i	0.166299	+	0.434147i
$697$	−4.26320	+	7.38408i	−0.161480	+	0.279692i
$698$	36.2164			1.37081
$699$	0.669905	+	1.74888i	0.0253381	+	0.0661486i
$700$	−13.1316	−	3.37690i	−0.496328	−	0.127635i
$701$	10.2711			0.387935			0.193967	−	0.981008i	$-0.437864\pi$
$701$	10.2711			0.387935			0.193967	+	0.981008i	$0.437864\pi$
$702$	−24.8903	+	16.0886i	−0.939423	+	0.607224i
$703$	0.641315	+	1.11079i	0.0241877	+	0.0418942i
$704$	3.18194			0.119924
$705$	31.7233	+	5.04759i	1.19477	+	0.190103i
$706$	−5.24433	−	9.08344i	−0.197373	−	0.341860i
$707$	13.2083	+	47.3760i	0.496751	+	1.78176i
$708$	−1.92395	−	0.306125i	−0.0723063	−	0.0115049i
$709$	−21.7427	−	37.6594i	−0.816564	−	1.41433i	−0.908200	−	0.418538i	$-0.862543\pi$
$709$	−21.7427	−	37.6594i	−0.816564	−	1.41433i	0.0916356	−	0.995793i	$-0.470790\pi$
$710$	−13.8256	−	23.9466i	−0.518865	−	0.898700i
$711$	9.23818	−	8.29434i	0.346459	−	0.311062i
$712$	−0.112725	+	0.195246i	−0.00422455	+	0.00731714i
$713$	10.5475	−	18.2687i	0.395006	−	0.684170i
$714$	−5.60301	+	4.15171i	−0.209687	+	0.155374i
$715$	−28.8743	−	50.0117i	−1.07984	−	1.87033i
$716$	−7.03775			−0.263013
$717$	21.0744	+	3.35322i	0.787039	+	0.125228i
$718$	32.4419			1.21072
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.200830	−	0.979626i	$-0.435636\pi$
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.747966	−	0.663737i	$-0.231031\pi$
$720$	7.10301	−	6.37731i	0.264714	−	0.237668i
$721$	−0.200818	−	0.720299i	−0.00747886	−	0.0268253i
$722$	−8.67743	+	15.0297i	−0.322941	+	0.559349i
$723$	14.1826	−	17.4887i	0.527458	−	0.650410i
$724$	6.48345	−	11.2297i	0.240955	−	0.417347i
$725$	−18.1449	+	31.4279i	−0.673884	+	1.16720i
$726$	1.49712	+	0.238212i	0.0555634	+	0.00884088i
$727$	6.07210	−	10.5172i	0.225202	−	0.390061i	−0.731178	−	0.682186i	$-0.761029\pi$
$727$	6.07210	−	10.5172i	0.225202	−	0.390061i	0.956380	+	0.292126i	$0.0943626\pi$
$728$	10.5624	−	10.7778i	0.391468	−	0.399452i
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$	−7.90219	+	13.6870i	−0.292473	+	0.506579i
$731$	−10.3912			−0.384334
$732$	−3.40903	+	4.20368i	−0.126001	+	0.155373i
$733$	−46.1696			−1.70531			−0.852657	−	0.522470i	$-0.825011\pi$
$733$	−46.1696			−1.70531			−0.852657	+	0.522470i	$0.825011\pi$
$734$	−9.05555	−	15.6847i	−0.334246	−	0.578932i
$735$	−5.29179	+	38.2144i	−0.195191	+	1.40956i
$736$	1.11956	−	1.93914i	0.0412676	−	0.0714776i
$737$	−17.4480	+	30.2209i	−0.642706	+	1.11320i
$738$	−15.9789	−	5.21700i	−0.588193	−	0.192041i
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	0.816458	−	0.577405i	$-0.195935\pi$
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	−0.908276	+	0.418371i	$0.862601\pi$
$740$	−1.59097	−	2.75564i	−0.0584853	−	0.101299i
$741$	7.98126	−	9.84172i	0.293199	−	0.361545i
$742$	−5.27128	−	1.35556i	−0.193515	−	0.0497640i
$743$	−15.7060	−	27.2036i	−0.576198	−	0.998004i	−0.995910	−	0.0903470i	$-0.971202\pi$
$743$	−15.7060	−	27.2036i	−0.576198	−	0.998004i	0.419712	−	0.907657i	$-0.362131\pi$
$744$	−5.83693	−	15.2381i	−0.213992	−	0.558656i
$745$	74.0118			2.71158
$746$	−5.83530	−	10.1070i	−0.213645	−	0.370045i
$747$	23.0075	+	7.51179i	0.841801	+	0.274842i
$748$	4.84213			0.177046
$749$	29.1537	+	7.49711i	1.06525	+	0.273939i
$750$	0.679065	+	0.108048i	0.0247959	+	0.00394536i
$751$	3.29630			0.120284			0.0601419	−	0.998190i	$-0.480845\pi$
$751$	3.29630			0.120284			0.0601419	+	0.998190i	$0.480845\pi$
$752$	2.91423	−	5.04759i	0.106271	−	0.184067i
$753$	−5.57605	+	6.87585i	−0.203203	+	0.250570i
$754$	−20.1947	−	34.9782i	−0.735447	−	1.27383i
$755$	25.8525			0.940870
$756$	−10.2895	−	9.11739i	−0.374224	−	0.331596i
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$	7.13448	+	12.3573i	0.259136	+	0.448837i
$759$	−7.77292	+	9.58481i	−0.282139	+	0.347907i
$760$	−2.04063	+	3.53447i	−0.0740214	+	0.128209i
$761$	14.0676			0.509950			0.254975	−	0.966948i	$-0.417933\pi$
$761$	14.0676			0.509950			0.254975	+	0.966948i	$0.417933\pi$
$762$	−34.3908	−	5.47204i	−1.24585	−	0.198231i
$763$	8.18715	−	8.35413i	0.296395	−	0.302440i
$764$	1.98057			0.0716545
$765$	10.8090	−	9.70470i	0.390801	−	0.350874i
$766$	−0.824893	−	1.42876i	−0.0298046	−	0.0516231i
$767$	6.41531			0.231643
$768$	−0.619562	−	1.61745i	−0.0223565	−	0.0583647i
$769$	11.3461	+	19.6520i	0.409151	+	0.708669i	0.994795	−	0.101899i	$-0.0324918\pi$
$769$	11.3461	+	19.6520i	0.409151	+	0.708669i	−0.585644	+	0.810568i	$0.699158\pi$
$770$	18.7495	−	19.1319i	0.675686	−	0.689467i
$771$	−8.35705	+	10.3051i	−0.300972	+	0.371129i
$772$	2.27292	+	3.93680i	0.0818040	+	0.141689i
$773$	0.327772	+	0.567717i	0.0117891	+	0.0204194i	0.871860	−	0.489756i	$-0.162914\pi$
$773$	0.327772	+	0.567717i	0.0117891	+	0.0204194i	−0.860071	+	0.510175i	$0.829581\pi$
$774$	−4.23065	−	20.0438i	−0.152068	−	0.720458i
$775$	24.1404	−	41.8123i	0.867148	−	1.50194i
$776$	−7.42107	+	12.8537i	−0.266401	+	0.461420i
$777$	−3.68194	+	2.72824i	−0.132089	+	0.0978751i
$778$	−16.0338	−	27.7713i	−0.574839	−	0.995651i
$779$	7.18659			0.257486
$780$	−19.7999	+	24.4153i	−0.708949	+	0.874208i
$781$	27.6512			0.989436
$782$	1.70370	−	2.95089i	0.0609241	−	0.105524i
$783$	−30.9018	+	19.9743i	−1.10434	+	0.713823i
$784$	6.13160	+	3.37690i	0.218986	+	0.120604i
$785$	−17.9194	+	31.0374i	−0.639572	+	1.10777i
$786$	−10.8856	−	1.73205i	−0.388278	−	0.0617802i
$787$	−0.270036	+	0.467717i	−0.00962576	+	0.0166723i	−0.870798	−	0.491641i	$-0.836397\pi$
$787$	−0.270036	+	0.467717i	−0.00962576	+	0.0166723i	0.861172	+	0.508313i	$0.169731\pi$
$788$	10.9074	−	18.8922i	0.388560	−	0.673005i
$789$	3.37648	−	4.16355i	0.120206	−	0.148226i
$790$	6.58414	−	11.4041i	0.234253	−	0.405738i
$791$	5.95378	−	6.07521i	0.211692	−	0.216010i
$792$	1.97141	+	9.34004i	0.0700510	+	0.331884i
$793$	8.91135	−	15.4349i	0.316451	−	0.548110i
$794$	−37.9338			−1.34622
$795$	11.1969	+	1.78157i	0.397112	+	0.0631858i
$796$	−12.2826			−0.435346
$797$	−12.5550	−	21.7459i	−0.444721	−	0.770279i	0.553312	−	0.832974i	$-0.313364\pi$
$797$	−12.5550	−	21.7459i	−0.444721	−	0.770279i	−0.998033	+	0.0626954i	$0.980030\pi$
$798$	5.39179	+	2.34021i	0.190867	+	0.0828424i
$799$	4.43474	−	7.68119i	0.156890	−	0.271741i
$800$	2.56238	−	4.43818i	0.0905939	−	0.156913i
$801$	−0.642950	−	0.209918i	−0.0227175	−	0.00741710i
$802$	5.30959	+	9.19647i	0.187488	+	0.324739i
$803$	−7.90219	−	13.6870i	−0.278862	−	0.483004i
$804$	18.7592	+	2.98485i	0.661587	+	0.105267i
$805$	−5.06238	−	18.1579i	−0.178426	−	0.639981i
$806$	26.8675	+	46.5358i	0.946366	+	1.63915i
$807$	45.9967	+	7.31869i	1.61916	+	0.257630i
$808$	−18.5893			−0.653971
$809$	−14.5865	−	25.2645i	−0.512833	−	0.888252i	−0.999889	−	0.0148817i	$-0.995263\pi$
$809$	−14.5865	−	25.2645i	−0.512833	−	0.888252i	0.487057	−	0.873370i	$-0.338071\pi$
$810$	23.1202	+	16.8985i	0.812363	+	0.593753i
$811$	−15.4290			−0.541785			−0.270892	−	0.962610i	$-0.587319\pi$
$811$	−15.4290			−0.541785			−0.270892	+	0.962610i	$0.587319\pi$
$812$	13.1134	−	13.3809i	0.460191	−	0.469577i
$813$	−13.7644	−	35.9339i	−0.482740	−	1.26026i
$814$	3.18194			0.111527
$815$	6.33297	−	10.9690i	0.221834	−	0.384228i
$816$	−0.942820	−	2.46136i	−0.0330053	−	0.0861648i
$817$	4.37919	+	7.58499i	0.153209	+	0.265365i
$818$	−5.54583			−0.193905
$819$	38.1804	+	24.3265i	1.33413	+	0.850038i
$820$	−17.8285			−0.622597
$821$	−4.24364	−	7.35019i	−0.148104	−	0.256524i	0.782423	−	0.622748i	$-0.213984\pi$
$821$	−4.24364	−	7.35019i	−0.148104	−	0.256524i	−0.930527	+	0.366224i	$0.880650\pi$
$822$	−4.68934	−	0.746136i	−0.163559	−	0.0260245i
$823$	−14.5487	+	25.1991i	−0.507136	+	0.878385i	0.492830	+	0.870126i	$0.335963\pi$
$823$	−14.5487	+	25.1991i	−0.507136	+	0.878385i	−0.999966	+	0.00825976i	$0.997371\pi$
$824$	0.282630			0.00984589
$825$	−17.7902	+	21.9371i	−0.619374	+	0.763752i
$826$	0.799182	+	2.86652i	0.0278071	+	0.0997391i
$827$	−25.9396			−0.902007			−0.451003	−	0.892522i	$-0.648934\pi$
$827$	−25.9396			−0.902007			−0.451003	+	0.892522i	$0.648934\pi$
$828$	6.38564	+	2.08486i	0.221916	+	0.0724540i
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	0.914941	−	0.403588i	$-0.132237\pi$
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	−0.806988	+	0.590568i	$0.798904\pi$
$830$	25.6706			0.891039
$831$	15.9691	−	19.6915i	0.553961	−	0.683092i
$832$	2.85185	+	4.93955i	0.0988701	+	0.171248i
$833$	9.33078	+	5.13882i	0.323292	+	0.178049i
$834$	4.93598	+	12.8861i	0.170919	+	0.446208i
$835$	−8.33530	−	14.4372i	−0.288455	−	0.499618i
$836$	−2.04063	−	3.53447i	−0.0705766	−	0.122242i
$837$	41.1125	−	26.5742i	1.42105	−	0.918540i
$838$	−2.77455	+	4.80566i	−0.0958452	+	0.166009i
$839$	21.2947	−	36.8834i	0.735174	−	1.27336i	−0.219474	−	0.975618i	$-0.570434\pi$
$839$	21.2947	−	36.8834i	0.735174	−	1.27336i	0.954647	−	0.297740i	$-0.0962327\pi$
$840$	−13.3759	−	5.80557i	−0.461513	−	0.200311i
$841$	−10.5721	−	18.3114i	−0.364555	−	0.631428i
$842$	−6.84213			−0.235795
$843$	14.4967	+	37.8457i	0.499294	+	1.30347i
$844$	16.6569			0.573355
$845$	31.0751	−	53.8237i	1.06902	−	1.85159i
$846$	16.6219	+	5.42692i	0.571472	+	0.186581i
$847$	−0.621885	−	2.23059i	−0.0213682	−	0.0766440i
$848$	1.02859	−	1.78157i	0.0353219	−	0.0611794i
$849$	16.1859	+	42.2555i	0.555499	+	1.45020i
$850$	3.89931	−	6.75381i	0.133745	−	0.231654i
$851$	1.11956	−	1.93914i	0.0383781	−	0.0664728i
$852$	−5.38401	−	14.0557i	−0.184453	−	0.481540i
$853$	−10.6969	+	18.5275i	−0.366254	+	0.634370i	−0.988976	−	0.148073i	$-0.952693\pi$
$853$	−10.6969	+	18.5275i	−0.366254	+	0.634370i	0.622723	+	0.782442i	$0.286026\pi$
$854$	8.00684	+	2.05903i	0.273988	+	0.0704585i
$855$	−11.6391	−	3.80009i	−0.398050	−	0.129960i
$856$	−5.68878	+	9.85326i	−0.194438	+	0.336777i
$857$	−36.8435			−1.25855			−0.629275	−	0.777183i	$-0.716648\pi$
$857$	−36.8435			−1.25855			−0.629275	+	0.777183i	$0.716648\pi$
$858$	−11.2443	−	29.3548i	−0.383875	−	1.00216i
$859$	−17.6375			−0.601783			−0.300892	−	0.953658i	$-0.597284\pi$
$859$	−17.6375			−0.601783			−0.300892	+	0.953658i	$0.597284\pi$
$860$	−10.8639	−	18.8168i	−0.370455	−	0.641648i
$861$	2.92339	+	25.5093i	0.0996289	+	0.869353i
$862$	−16.5539	+	28.6722i	−0.563828	+	0.976579i
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	−0.872428	−	0.488743i	$-0.837456\pi$
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	0.859478	+	0.511173i	$0.170789\pi$
$864$	4.36389	−	2.82073i	0.148462	−	0.0959630i
$865$	4.05950	+	7.03127i	0.138027	+	0.239070i
$866$	−6.05555	−	10.4885i	−0.205776	−	0.356414i
$867$	9.09781	+	23.7511i	0.308978	+	0.806628i
$868$	−17.4464	+	17.8022i	−0.592169	+	0.604247i
$869$	6.58414	+	11.4041i	0.223351	+	0.386856i
$870$	−24.5819	+	30.3121i	−0.833406	+	1.02768i
$871$	−62.5519			−2.11949
$872$	2.21053	+	3.82876i	0.0748581	+	0.129658i
$873$	−42.3275	−	13.8196i	−1.43257	−	0.467723i
$874$	−2.87197			−0.0971457
$875$	−0.282075	−	1.01175i	−0.00953586	−	0.0342035i
$876$	−5.41874	+	6.68187i	−0.183082	+	0.225760i
$877$	−41.4991			−1.40132			−0.700662	−	0.713494i	$-0.747112\pi$
$877$	−41.4991			−1.40132			−0.700662	+	0.713494i	$0.747112\pi$
$878$	−4.41711	+	7.65066i	−0.149070	+	0.258197i
$879$	−44.2394	−	7.03908i	−1.49216	−	0.237422i
$880$	5.06238	+	8.76830i	0.170653	+	0.295579i
$881$	8.35486			0.281482			0.140741	−	0.990046i	$-0.455051\pi$
$881$	8.35486			0.281482			0.140741	+	0.990046i	$0.455051\pi$
$882$	−6.11341	+	20.0904i	−0.205849	+	0.676481i
$883$	35.6181			1.19864			0.599322	−	0.800508i	$-0.295437\pi$
$883$	35.6181			1.19864			0.599322	+	0.800508i	$0.295437\pi$
$884$	4.33981	+	7.51677i	0.145964	+	0.252816i
$885$	−2.21737	−	5.78874i	−0.0745361	−	0.194587i
$886$	8.75924	−	15.1715i	0.294272	−	0.509695i
$887$	−37.1100			−1.24603			−0.623016	−	0.782209i	$-0.714093\pi$
$887$	−37.1100			−1.24603			−0.623016	+	0.782209i	$0.714093\pi$
$888$	−0.619562	−	1.61745i	−0.0207911	−	0.0542781i
$889$	14.2855	+	51.2396i	0.479121	+	1.71852i
$890$	−0.717370			−0.0240463
$891$	−26.1947	+	11.5735i	−0.877554	+	0.387726i
$892$	−5.32846	−	9.22916i	−0.178410	−	0.309015i
$893$	−7.47576			−0.250167
$894$	39.7869	+	6.33063i	1.33067	+	0.211728i
$895$	−11.1969	−	19.3935i	−0.374270	−	0.648254i
$896$	−1.85185	+	1.88962i	−0.0618659	+	0.0631277i
$897$	−21.8457	−	3.47594i	−0.729407	−	0.116058i
$898$	15.6150	+	27.0461i	0.521081	+	0.902539i
$899$	33.3565	+	57.7751i	1.11250	+	1.92691i
$900$	14.6150	+	4.77170i	0.487168	+	0.159057i
$901$	1.56526	−	2.71111i	0.0521464	−	0.0903202i
$902$	8.91423	−	15.4399i	0.296811	−	0.514092i
$903$	−25.1420	+	18.6297i	−0.836673	+	0.619957i
$904$	1.60752	+	2.78431i	0.0534654	+	0.0926048i
$905$	41.2599			1.37153
$906$	13.8977	+	2.21131i	0.461719	+	0.0734657i
$907$	−48.1502			−1.59880			−0.799401	−	0.600798i	$-0.794850\pi$
$907$	−48.1502			−1.59880			−0.799401	+	0.600798i	$0.794850\pi$
$908$	7.25404	−	12.5644i	0.240734	−	0.416963i
$909$	−11.5172	−	54.5658i	−0.382003	−	1.80983i
$910$	46.5043	+	11.9590i	1.54160	+	0.396436i
$911$	17.4428	−	30.2119i	0.577906	−	1.00096i	−0.417813	−	0.908533i	$-0.637203\pi$
$911$	17.4428	−	30.2119i	0.577906	−	1.00096i	0.995719	−	0.0924301i	$-0.0294635\pi$
$912$	−1.39931	+	1.72550i	−0.0463359	+	0.0571369i
$913$	−12.8353	+	22.2314i	−0.424786	+	0.735751i
$914$	−16.0624	+	27.8209i	−0.531296	+	0.920232i
$915$	−17.0075	−	2.70612i	−0.562251	−	0.0894617i
$916$	−5.12476	+	8.87635i	−0.169327	+	0.293283i
$917$	4.52175	+	16.2187i	0.149321	+	0.535590i
$918$	6.64076	−	4.29245i	0.219178	−	0.141672i
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	0.0249351	+	0.999689i	$0.492062\pi$
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	−0.878224	+	0.478250i	$0.841271\pi$
$920$	7.12476			0.234896
$921$	−3.85348	+	4.75174i	−0.126977	+	0.156575i
$922$	2.46457			0.0811664
$923$	24.7826	+	42.9248i	0.815730	+	1.41289i
$924$	11.7157	−	8.68110i	0.385419	−	0.285587i
$925$	2.56238	−	4.43818i	0.0842506	−	0.145926i
$926$	−15.1735	+	26.2812i	−0.498631	+	0.863655i
$927$	0.175107	+	0.829612i	0.00575126	+	0.0272480i
$928$	3.54063	+	6.13255i	0.116227	+	0.201311i
$929$	25.4142	+	44.0187i	0.833814	+	1.44421i	0.894993	+	0.446081i	$0.147181\pi$
$929$	25.4142	+	44.0187i	0.833814	+	1.44421i	−0.0611787	+	0.998127i	$0.519486\pi$
$930$	32.7044	−	40.3279i	1.07242	−	1.32240i
$931$	−0.181255	−	8.97658i	−0.00594039	−	0.294196i
$932$	0.540628	+	0.936396i	0.0177089	+	0.0306727i
$933$	−1.05555	−	2.75564i	−0.0345570	−	0.0902157i
$934$	−15.9636			−0.522346
$935$	7.70370	+	13.3432i	0.251938	+	0.436369i
$936$	−12.7323	+	11.4315i	−0.416168	+	0.373649i
$937$	2.54583			0.0831686			0.0415843	−	0.999135i	$-0.486759\pi$
$937$	2.54583			0.0831686			0.0415843	+	0.999135i	$0.486759\pi$
$938$	−7.79235	−	27.9498i	−0.254429	−	0.912592i
$939$	−4.86156	−	0.773540i	−0.158651	−	0.0252435i
$940$	18.5458			0.604898
$941$	−0.578933	+	1.00274i	−0.0188727	+	0.0326885i	−0.875308	−	0.483567i	$-0.839341\pi$
$941$	−0.578933	+	1.00274i	−0.0188727	+	0.0326885i	0.856435	+	0.516255i	$0.172674\pi$
$942$	−12.2878	+	15.1522i	−0.400359	+	0.493684i
$943$	−6.27292	−	10.8650i	−0.204274	−	0.353813i
$944$	−1.12476			−0.0366079
$945$	8.75404	−	42.8596i	0.284769	−	1.39422i
$946$	21.7278			0.706431
$947$	−4.90739	−	8.49985i	−0.159469	−	0.276208i	0.775208	−	0.631706i	$-0.217645\pi$
$947$	−4.90739	−	8.49985i	−0.159469	−	0.276208i	−0.934677	+	0.355497i	$0.884311\pi$
$948$	4.51492	−	5.56736i	0.146638	−	0.180819i
$949$	14.1648	−	24.5342i	0.459810	−	0.796414i
$950$	−6.57318			−0.213262
$951$	−42.6267	−	6.78248i	−1.38227	−	0.219937i
$952$	−2.81806	+	2.87553i	−0.0913337	+	0.0931966i
$953$	6.53791			0.211784			0.105892	−	0.994378i	$-0.466230\pi$
$953$	6.53791			0.211784			0.105892	+	0.994378i	$0.466230\pi$
$954$	5.86677	+	1.91546i	0.189944	+	0.0620152i
$955$	3.15103	+	5.45774i	0.101965	+	0.176608i
$956$	12.3204			0.398470
$957$	−13.9601	−	36.4446i	−0.451265	−	1.17809i
$958$	−11.5865	−	20.0683i	−0.374341	−	0.648378i
$959$	1.94789	+	6.98673i	0.0629006	+	0.225613i
$960$	3.47141	−	4.28061i	0.112039	−	0.138156i
$961$	−28.8782	−	50.0186i	−0.931556	−	1.61350i
$962$	2.85185	+	4.93955i	0.0919473	+	0.159257i
$963$	−32.4471	−	10.5937i	−1.04559	−	0.341378i
$964$	6.50000	−	11.2583i	0.209351	−	0.362606i
$965$	−7.23229	+	12.5267i	−0.232816	+	0.403248i
$966$	−1.16827	−	10.1942i	−0.0375885	−	0.327994i
$967$	14.4445	+	25.0185i	0.464502	+	0.804542i	0.999179	−	0.0405151i	$-0.0128999\pi$
$967$	14.4445	+	25.0185i	0.464502	+	0.804542i	−0.534677	+	0.845057i	$0.679567\pi$
$968$	0.875237			0.0281312
$969$	−2.12941	+	2.62578i	−0.0684065	+	0.0843523i
$970$	−47.2268			−1.51636
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	−0.820030	−	0.572320i	$-0.806043\pi$
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	0.905659	+	0.424007i	$0.139377\pi$
$972$	10.9834	+	11.0618i	0.352294	+	0.354808i
$973$	14.7535	−	15.0544i	0.472975	−	0.482622i
$974$	−1.70658	+	2.95588i	−0.0546822	+	0.0947124i
$975$	−49.9991	−	7.95552i	−1.60125	−	0.254780i
$976$	−1.56238	+	2.70612i	−0.0500106	+	0.0866209i
$977$	24.0361	−	41.6318i	0.768983	−	1.33192i	−0.169131	−	0.985594i	$-0.554096\pi$
$977$	24.0361	−	41.6318i	0.768983	−	1.33192i	0.938115	−	0.346325i	$-0.112571\pi$
$978$	4.34269	−	5.35498i	0.138864	−	0.171234i
$979$	0.358685	−	0.621261i	0.0114636	−	0.0198556i
$980$	0.449657	+	22.2691i	0.0143638	+	0.711359i
$981$	−9.86909	+	8.86079i	−0.315096	+	0.282903i
$982$	9.58414	−	16.6002i	0.305842	−	0.529734i
$983$	29.4627			0.939714			0.469857	−	0.882743i	$-0.344306\pi$
$983$	29.4627			0.939714			0.469857	+	0.882743i	$0.344306\pi$
$984$	−9.58414	−	1.52496i	−0.305531	−	0.0486141i
$985$	69.4134			2.21170
$986$	5.38796	+	9.33223i	0.171588	+	0.297199i
$987$	−3.04102	−	26.5357i	−0.0967967	−	0.844640i
$988$	3.65787	−	6.33561i	0.116372	−	0.201563i
$989$	7.64488	−	13.2413i	0.243093	−	0.421050i
$990$	−22.6014	+	20.2922i	−0.718319	+	0.644930i
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	0.999929	−	0.0119112i	$-0.00379153\pi$
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	−0.510280	+	0.860008i	$0.670458\pi$
$992$	−4.71053	−	8.15888i	−0.149560	−	0.259045i
$993$	−12.2672	−	1.95187i	−0.389286	−	0.0619407i
$994$	−16.0926	+	16.4208i	−0.510426	+	0.520837i
$995$	−19.5413	−	33.8466i	−0.619501	−	1.07301i
$996$	13.7999	+	2.19574i	0.437266	+	0.0695748i
$997$	5.54583			0.175638			0.0878191	−	0.996136i	$-0.472010\pi$
$997$	5.54583			0.175638			0.0878191	+	0.996136i	$0.472010\pi$
$998$	20.5848	+	35.6540i	0.651601	+	1.12861i
$999$	4.36389	−	2.82073i	0.138067	−	0.0892438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.h.d.79.1	yes	6
3.2	odd	2		378.2.h.c.289.3		6
4.3	odd	2		1008.2.t.h.961.3		6
7.2	even	3		882.2.f.n.295.2		6
7.3	odd	6		882.2.e.o.655.1		6
7.4	even	3		126.2.e.c.25.3	✓	6
7.5	odd	6		882.2.f.o.295.2		6
7.6	odd	2		882.2.h.p.79.3		6
9.2	odd	6		1134.2.g.l.163.1		6
9.4	even	3		126.2.e.c.121.3	yes	6
9.5	odd	6		378.2.e.d.37.1		6
9.7	even	3		1134.2.g.m.163.3		6
12.11	even	2		3024.2.t.h.289.3		6
21.2	odd	6		2646.2.f.l.883.1		6
21.5	even	6		2646.2.f.m.883.3		6
21.11	odd	6		378.2.e.d.235.1		6
21.17	even	6		2646.2.e.p.2125.3		6
21.20	even	2		2646.2.h.o.667.1		6
28.11	odd	6		1008.2.q.g.529.1		6
36.23	even	6		3024.2.q.g.2305.1		6
36.31	odd	6		1008.2.q.g.625.1		6
63.2	odd	6		7938.2.a.ca.1.3		3
63.4	even	3	inner	126.2.h.d.67.1	yes	6
63.5	even	6		2646.2.f.m.1765.3		6
63.11	odd	6		1134.2.g.l.487.1		6
63.13	odd	6		882.2.e.o.373.1		6
63.16	even	3		7938.2.a.bv.1.1		3
63.23	odd	6		2646.2.f.l.1765.1		6
63.25	even	3		1134.2.g.m.487.3		6
63.31	odd	6		882.2.h.p.67.3		6
63.32	odd	6		378.2.h.c.361.3		6
63.40	odd	6		882.2.f.o.589.2		6
63.41	even	6		2646.2.e.p.1549.3		6
63.47	even	6		7938.2.a.bz.1.1		3
63.58	even	3		882.2.f.n.589.2		6
63.59	even	6		2646.2.h.o.361.1		6
63.61	odd	6		7938.2.a.bw.1.3		3
84.11	even	6		3024.2.q.g.2881.1		6
252.67	odd	6		1008.2.t.h.193.3		6
252.95	even	6		3024.2.t.h.1873.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	7.4	even	3
126.2.e.c.121.3	yes	6	9.4	even	3
126.2.h.d.67.1	yes	6	63.4	even	3	inner
126.2.h.d.79.1	yes	6	1.1	even	1	trivial
378.2.e.d.37.1		6	9.5	odd	6
378.2.e.d.235.1		6	21.11	odd	6
378.2.h.c.289.3		6	3.2	odd	2
378.2.h.c.361.3		6	63.32	odd	6
882.2.e.o.373.1		6	63.13	odd	6
882.2.e.o.655.1		6	7.3	odd	6
882.2.f.n.295.2		6	7.2	even	3
882.2.f.n.589.2		6	63.58	even	3
882.2.f.o.295.2		6	7.5	odd	6
882.2.f.o.589.2		6	63.40	odd	6
882.2.h.p.67.3		6	63.31	odd	6
882.2.h.p.79.3		6	7.6	odd	2
1008.2.q.g.529.1		6	28.11	odd	6
1008.2.q.g.625.1		6	36.31	odd	6
1008.2.t.h.193.3		6	252.67	odd	6
1008.2.t.h.961.3		6	4.3	odd	2
1134.2.g.l.163.1		6	9.2	odd	6
1134.2.g.l.487.1		6	63.11	odd	6
1134.2.g.m.163.3		6	9.7	even	3
1134.2.g.m.487.3		6	63.25	even	3
2646.2.e.p.1549.3		6	63.41	even	6
2646.2.e.p.2125.3		6	21.17	even	6
2646.2.f.l.883.1		6	21.2	odd	6
2646.2.f.l.1765.1		6	63.23	odd	6
2646.2.f.m.883.3		6	21.5	even	6
2646.2.f.m.1765.3		6	63.5	even	6
2646.2.h.o.361.1		6	63.59	even	6
2646.2.h.o.667.1		6	21.20	even	2
3024.2.q.g.2305.1		6	36.23	even	6
3024.2.q.g.2881.1		6	84.11	even	6
3024.2.t.h.289.3		6	12.11	even	2
3024.2.t.h.1873.3		6	252.95	even	6
7938.2.a.bv.1.1		3	63.16	even	3
7938.2.a.bw.1.3		3	63.61	odd	6
7938.2.a.bz.1.1		3	63.47	even	6
7938.2.a.ca.1.3		3	63.2	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.09097 + 1.34528i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +(-1.71053 - 0.272169i) q^{6} +(0.710533 + 2.54856i) q^{7} -1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +(-1.59097 - 2.75564i) q^{10} +3.18194 q^{11} +(-0.619562 - 1.61745i) q^{12} +(2.85185 + 4.93955i) q^{13} +(-1.85185 + 1.88962i) q^{14} +(3.47141 - 4.28061i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.760877 - 1.31788i) q^{17} +(2.23229 - 2.00422i) q^{18} +(-0.641315 + 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(-4.20370 - 1.82454i) q^{21} +(1.59097 + 2.75564i) q^{22} +2.23912 q^{23} +(1.09097 - 1.34528i) q^{24} +5.12476 q^{25} +(-2.85185 + 4.93955i) q^{26} +(4.62476 + 2.36887i) q^{27} +(-2.56238 - 0.658939i) q^{28} +(-3.54063 + 6.13255i) q^{29} +(5.44282 + 0.866025i) q^{30} +(4.71053 - 8.15888i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.47141 + 4.28061i) q^{33} +(0.760877 - 1.31788i) q^{34} +(-2.26088 - 8.10936i) q^{35} +(2.85185 + 0.931107i) q^{36} +(0.500000 - 0.866025i) q^{37} -1.28263 q^{38} +(-9.75636 - 1.55237i) q^{39} +3.18194 q^{40} +(-2.80150 - 4.85235i) q^{41} +(-0.521753 - 4.55278i) q^{42} +(3.41423 - 5.91362i) q^{43} +(-1.59097 + 2.75564i) q^{44} +(1.97141 + 9.34004i) q^{45} +(1.11956 + 1.93914i) q^{46} +(2.91423 + 5.04759i) q^{47} +(1.71053 + 0.272169i) q^{48} +(-5.99028 + 3.62167i) q^{49} +(2.56238 + 4.43818i) q^{50} +(2.60301 + 0.414174i) q^{51} -5.70370 q^{52} +(1.02859 + 1.78157i) q^{53} +(0.260877 + 5.18960i) q^{54} -10.1248 q^{55} +(-0.710533 - 2.54856i) q^{56} +(-0.794668 - 2.07459i) q^{57} -7.08126 q^{58} +(0.562382 - 0.974074i) q^{59} +(1.97141 + 5.14663i) q^{60} +(-1.56238 - 2.70612i) q^{61} +9.42107 q^{62} +(7.04063 - 3.66464i) q^{63} +1.00000 q^{64} +(-9.07442 - 15.7174i) q^{65} +(-5.44282 - 0.866025i) q^{66} +(-5.48345 + 9.49761i) q^{67} +1.52175 q^{68} +(-2.44282 + 3.01225i) q^{69} +(5.89248 - 6.01266i) q^{70} +8.69002 q^{71} +(0.619562 + 2.93533i) q^{72} +(-2.48345 - 4.30146i) q^{73} +1.00000 q^{74} +(-5.59097 + 6.89425i) q^{75} +(-0.641315 - 1.11079i) q^{76} +(2.26088 + 8.10936i) q^{77} +(-3.53379 - 9.22544i) q^{78} +(2.06922 + 3.58399i) q^{79} +(1.59097 + 2.75564i) q^{80} +(-8.23229 + 3.63723i) q^{81} +(2.80150 - 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(3.68194 - 2.72824i) q^{84} +(2.42107 + 4.19341i) q^{85} +6.82846 q^{86} +(-4.38727 - 11.4536i) q^{87} -3.18194 q^{88} +(0.112725 - 0.195246i) q^{89} +(-7.10301 + 6.37731i) q^{90} +(-10.5624 + 10.7778i) q^{91} +(-1.11956 + 1.93914i) q^{92} +(5.83693 + 15.2381i) q^{93} +(-2.91423 + 5.04759i) q^{94} +(2.04063 - 3.53447i) q^{95} +(0.619562 + 1.61745i) q^{96} +(7.42107 - 12.8537i) q^{97} +(-6.13160 - 3.37690i) q^{98} +(-1.97141 - 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} - 4 q^{9} - q^{10} + 2 q^{11} - 4 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} - 3 q^{16} - 4 q^{17} + 4 q^{18} - 3 q^{19} + q^{20}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 - 6 * q^8 - 4 * q^9 - q^10 + 2 * q^11 - 4 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 - 3 * q^16 - 4 * q^17 + 4 * q^18 - 3 * q^19 + q^20 - 7 * q^21 + q^22 + 14 * q^23 - 2 * q^24 - 4 * q^25 - 8 * q^26 - 7 * q^27 + 2 * q^28 - 5 * q^29 + 15 * q^30 + 20 * q^31 + 3 * q^32 - 12 * q^33 + 4 * q^34 - 13 * q^35 + 8 * q^36 + 3 * q^37 - 6 * q^38 + q^39 + 2 * q^40 - 2 * q^42 - 6 * q^43 - q^44 + 3 * q^45 + 7 * q^46 - 9 * q^47 + 2 * q^48 - 12 * q^49 - 2 * q^50 - 18 * q^51 - 16 * q^52 + 15 * q^53 + q^54 - 26 * q^55 + 4 * q^56 + 22 * q^57 - 10 * q^58 - 14 * q^59 + 3 * q^60 + 8 * q^61 + 40 * q^62 + 26 * q^63 + 6 * q^64 - 12 * q^65 - 15 * q^66 + q^67 + 8 * q^68 + 3 * q^69 + 10 * q^70 + 14 * q^71 + 4 * q^72 + 19 * q^73 + 6 * q^74 - 25 * q^75 - 3 * q^76 + 13 * q^77 + 5 * q^78 + 5 * q^79 + q^80 - 40 * q^81 + 2 * q^83 + 5 * q^84 - 2 * q^85 - 12 * q^86 - 36 * q^87 - 2 * q^88 - 9 * q^89 - 9 * q^90 - 46 * q^91 - 7 * q^92 + 37 * q^93 + 9 * q^94 - 4 * q^95 + 4 * q^96 + 28 * q^97 - 12 * q^98 - 3 * q^99

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