LMFDB - Embedded newform 126.2.e.c.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(25,126)]

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([4, 4]))

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

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

chi := DirichletCharacter("126.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.e (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			25.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	126.25
Dual form			126.2.e.c.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(1.71053 + 0.272169i) q^{3} +1.00000 q^{4} +(1.59097 - 2.75564i) q^{5} +(-1.71053 - 0.272169i) q^{6} +(-2.56238 + 0.658939i) q^{7} -1.00000 q^{8} +(2.85185 + 0.931107i) q^{9} +(-1.59097 + 2.75564i) q^{10} +(-1.59097 - 2.75564i) q^{11} +(1.71053 + 0.272169i) q^{12} +(2.85185 + 4.93955i) q^{13} +(2.56238 - 0.658939i) q^{14} +(3.47141 - 4.28061i) q^{15} +1.00000 q^{16} +(-0.760877 + 1.31788i) q^{17} +(-2.85185 - 0.931107i) q^{18} +(-0.641315 - 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(-4.56238 + 0.429736i) q^{21} +(1.59097 + 2.75564i) q^{22} +(-1.11956 + 1.93914i) q^{23} +(-1.71053 - 0.272169i) q^{24} +(-2.56238 - 4.43818i) 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} +(-3.47141 + 4.28061i) q^{30} -9.42107 q^{31} -1.00000 q^{32} +(-1.97141 - 5.14663i) 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} +(0.641315 + 1.11079i) q^{38} +(3.53379 + 9.22544i) q^{39} +(-1.59097 + 2.75564i) q^{40} +(-2.80150 - 4.85235i) q^{41} +(4.56238 - 0.429736i) q^{42} +(3.41423 - 5.91362i) q^{43} +(-1.59097 - 2.75564i) q^{44} +(7.10301 - 6.37731i) q^{45} +(1.11956 - 1.93914i) q^{46} -5.82846 q^{47} +(1.71053 + 0.272169i) q^{48} +(6.13160 - 3.37690i) q^{49} +(2.56238 + 4.43818i) q^{50} +(-1.66019 + 2.04719i) q^{51} +(2.85185 + 4.93955i) q^{52} +(1.02859 - 1.78157i) q^{53} +(-4.62476 - 2.36887i) q^{54} -10.1248 q^{55} +(2.56238 - 0.658939i) q^{56} +(-0.794668 - 2.07459i) q^{57} +(3.54063 - 6.13255i) q^{58} -1.12476 q^{59} +(3.47141 - 4.28061i) q^{60} +3.12476 q^{61} +9.42107 q^{62} +(-7.92107 - 0.506659i) q^{63} +1.00000 q^{64} +18.1488 q^{65} +(1.97141 + 5.14663i) q^{66} +10.9669 q^{67} +(-0.760877 + 1.31788i) q^{68} +(-2.44282 + 3.01225i) q^{69} +(2.26088 - 8.10936i) q^{70} +8.69002 q^{71} +(-2.85185 - 0.931107i) q^{72} +(-2.48345 + 4.30146i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(-3.17511 - 8.28905i) q^{75} +(-0.641315 - 1.11079i) q^{76} +(5.89248 + 6.01266i) q^{77} +(-3.53379 - 9.22544i) q^{78} -4.13844 q^{79} +(1.59097 - 2.75564i) q^{80} +(7.26608 + 5.31075i) q^{81} +(2.80150 + 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(-4.56238 + 0.429736i) q^{84} +(2.42107 + 4.19341i) q^{85} +(-3.41423 + 5.91362i) q^{86} +(-7.72545 + 9.52628i) q^{87} +(1.59097 + 2.75564i) 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} +(-16.1150 - 2.56412i) q^{93} +5.82846 q^{94} -4.08126 q^{95} +(-1.71053 - 0.272169i) 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 - 6 q^{2} + 2 q^{3} + 6 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} - q^{10} - q^{11} + 2 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} + 6 q^{16} - 4 q^{17} - 8 q^{18} - 3 q^{19} + q^{20}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 - q^10 - q^11 + 2 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 + 6 * q^16 - 4 * q^17 - 8 * q^18 - 3 * q^19 + q^20 - 10 * q^21 + q^22 - 7 * q^23 - 2 * q^24 + 2 * q^25 - 8 * q^26 - 7 * q^27 + 2 * q^28 - 5 * q^29 - 12 * q^30 - 40 * q^31 - 6 * q^32 - 3 * q^33 + 4 * q^34 - 13 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 5 * q^39 - q^40 + 10 * q^42 - 6 * q^43 - q^44 + 9 * q^45 + 7 * q^46 + 18 * q^47 + 2 * q^48 + 12 * q^49 - 2 * q^50 + 6 * q^51 + 8 * q^52 + 15 * q^53 + 7 * q^54 - 26 * q^55 - 2 * q^56 + 22 * q^57 + 5 * q^58 + 28 * q^59 + 12 * q^60 - 16 * q^61 + 40 * q^62 - 31 * q^63 + 6 * q^64 + 24 * q^65 + 3 * q^66 - 2 * q^67 - 4 * q^68 + 3 * q^69 + 13 * q^70 + 14 * q^71 - 8 * q^72 + 19 * q^73 - 3 * q^74 + 8 * q^75 - 3 * q^76 + 10 * q^77 + 5 * q^78 - 10 * q^79 + q^80 + 8 * q^81 + 2 * q^83 - 10 * q^84 - 2 * q^85 + 6 * q^86 - 27 * q^87 + q^88 - 9 * q^89 - 9 * q^90 - 46 * q^91 - 7 * q^92 - 38 * q^93 - 18 * q^94 + 8 * q^95 - 2 * q^96 + 28 * q^97 - 12 * q^98 - 3 * q^99

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.71053	+	0.272169i	0.987577	+	0.157137i
$3$	1.71053	+	0.272169i	0.987577	+	0.157137i
$4$	1.00000			0.500000
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	−0.252788	−	0.967522i	$-0.581348\pi$
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	0.964292	−	0.264840i	$-0.0853191\pi$
$6$	−1.71053	−	0.272169i	−0.698322	−	0.111112i
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$8$	−1.00000			−0.353553
$9$	2.85185	+	0.931107i	0.950616	+	0.310369i
$10$	−1.59097	+	2.75564i	−0.503109	+	0.871411i
$11$	−1.59097	−	2.75564i	−0.479696	−	0.830858i	0.520033	−	0.854146i	$-0.325920\pi$
$11$	−1.59097	−	2.75564i	−0.479696	−	0.830858i	−0.999729	+	0.0232884i	$0.992586\pi$
$12$	1.71053	+	0.272169i	0.493788	+	0.0785683i
$13$	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	$0.542915\pi$
$14$	2.56238	−	0.658939i	0.684825	−	0.176109i
$15$	3.47141	−	4.28061i	0.896314	−	1.10525i
$16$	1.00000			0.250000
$17$	−0.760877	+	1.31788i	−0.184540	+	0.319632i	−0.943421	−	0.331596i	$-0.892413\pi$
$17$	−0.760877	+	1.31788i	−0.184540	+	0.319632i	0.758882	+	0.651229i	$0.225746\pi$
$18$	−2.85185	−	0.931107i	−0.672187	−	0.219464i
$19$	−0.641315	−	1.11079i	−0.147128	−	0.254833i	0.783037	−	0.621975i	$-0.213670\pi$
$19$	−0.641315	−	1.11079i	−0.147128	−	0.254833i	−0.930165	+	0.367142i	$0.880336\pi$
$20$	1.59097	−	2.75564i	0.355752	−	0.616181i
$21$	−4.56238	+	0.429736i	−0.995593	+	0.0937761i
$22$	1.59097	+	2.75564i	0.339196	+	0.587505i
$23$	−1.11956	+	1.93914i	−0.233445	+	0.404338i	−0.958820	−	0.284016i	$-0.908333\pi$
$23$	−1.11956	+	1.93914i	−0.233445	+	0.404338i	0.725375	+	0.688354i	$0.241666\pi$
$24$	−1.71053	−	0.272169i	−0.349161	−	0.0555562i
$25$	−2.56238	−	4.43818i	−0.512476	−	0.887635i
$26$	−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	$0.938290\pi$
$30$	−3.47141	+	4.28061i	−0.633790	+	0.781528i
$31$	−9.42107			−1.69207			−0.846037	−	0.533125i	$-0.821018\pi$
$31$	−9.42107			−1.69207			−0.846037	+	0.533125i	$0.821018\pi$
$32$	−1.00000			−0.176777
$33$	−1.97141	−	5.14663i	−0.343178	−	0.895914i
$34$	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	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	0.641315	+	1.11079i	0.104035	+	0.180194i
$39$	3.53379	+	9.22544i	0.565860	+	1.47725i
$40$	−1.59097	+	2.75564i	−0.251555	+	0.435706i
$41$	−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	$0.977477\pi$
$42$	4.56238	−	0.429736i	0.703991	−	0.0663097i
$43$	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
$45$	7.10301	−	6.37731i	1.05885	−	0.950674i
$46$	1.11956	−	1.93914i	0.165070	−	0.285910i
$47$	−5.82846			−0.850168			−0.425084	−	0.905154i	$-0.639755\pi$
$47$	−5.82846			−0.850168			−0.425084	+	0.905154i	$0.639755\pi$
$48$	1.71053	+	0.272169i	0.246894	+	0.0392842i
$49$	6.13160	−	3.37690i	0.875943	−	0.482415i
$50$	2.56238	+	4.43818i	0.362375	+	0.627653i
$51$	−1.66019	+	2.04719i	−0.232473	+	0.286663i
$52$	2.85185	+	4.93955i	0.395480	+	0.684992i
$53$	1.02859	−	1.78157i	0.141288	−	0.244717i	−0.786694	−	0.617343i	$-0.788209\pi$
$53$	1.02859	−	1.78157i	0.141288	−	0.244717i	0.927982	+	0.372626i	$0.121542\pi$
$54$	−4.62476	−	2.36887i	−0.629351	−	0.322363i
$55$	−10.1248			−1.36522
$56$	2.56238	−	0.658939i	0.342413	−	0.0880544i
$57$	−0.794668	−	2.07459i	−0.105256	−	0.274786i
$58$	3.54063	−	6.13255i	0.464907	−	0.805243i
$59$	−1.12476			−0.146432			−0.0732159	−	0.997316i	$-0.523326\pi$
$59$	−1.12476			−0.146432			−0.0732159	+	0.997316i	$0.523326\pi$
$60$	3.47141	−	4.28061i	0.448157	−	0.552624i
$61$	3.12476			0.400085			0.200042	−	0.979787i	$-0.435892\pi$
$61$	3.12476			0.400085			0.200042	+	0.979787i	$0.435892\pi$
$62$	9.42107			1.19648
$63$	−7.92107	−	0.506659i	−0.997961	−	0.0638331i
$64$	1.00000			0.125000
$65$	18.1488			2.25109
$66$	1.97141	+	5.14663i	0.242664	+	0.633507i
$67$	10.9669			1.33982			0.669910	−	0.742442i	$-0.266333\pi$
$67$	10.9669			1.33982			0.669910	+	0.742442i	$0.266333\pi$
$68$	−0.760877	+	1.31788i	−0.0922699	+	0.159816i
$69$	−2.44282	+	3.01225i	−0.294081	+	0.362632i
$70$	2.26088	−	8.10936i	0.270226	−	0.969254i
$71$	8.69002			1.03132			0.515658	−	0.856794i	$-0.327548\pi$
$71$	8.69002			1.03132			0.515658	+	0.856794i	$0.327548\pi$
$72$	−2.85185	−	0.931107i	−0.336094	−	0.109732i
$73$	−2.48345	+	4.30146i	−0.290666	+	0.503448i	−0.973967	−	0.226689i	$-0.927210\pi$
$73$	−2.48345	+	4.30146i	−0.290666	+	0.503448i	0.683302	+	0.730136i	$0.260543\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	−3.17511	−	8.28905i	−0.366630	−	0.957137i
$76$	−0.641315	−	1.11079i	−0.0735639	−	0.127416i
$77$	5.89248	+	6.01266i	0.671510	+	0.685206i
$78$	−3.53379	−	9.22544i	−0.400123	−	1.04458i
$79$	−4.13844			−0.465610			−0.232805	−	0.972523i	$-0.574790\pi$
$79$	−4.13844			−0.465610			−0.232805	+	0.972523i	$0.574790\pi$
$80$	1.59097	−	2.75564i	0.177876	−	0.308090i
$81$	7.26608	+	5.31075i	0.807342	+	0.590084i
$82$	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	$0.312669\pi$
$84$	−4.56238	+	0.429736i	−0.497797	+	0.0468881i
$85$	2.42107	+	4.19341i	0.262602	+	0.454839i
$86$	−3.41423	+	5.91362i	−0.368166	+	0.637682i
$87$	−7.72545	+	9.52628i	−0.828255	+	1.02132i
$88$	1.59097	+	2.75564i	0.169598	+	0.293753i
$89$	0.112725	+	0.195246i	0.0119488	+	0.0206960i	0.871938	−	0.489616i	$-0.162863\pi$
$89$	0.112725	+	0.195246i	0.0119488	+	0.0206960i	−0.859989	+	0.510312i	$0.829530\pi$
$90$	−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
$93$	−16.1150	−	2.56412i	−1.67105	−	0.265887i
$94$	5.82846			0.601160
$95$	−4.08126			−0.418728
$96$	−1.71053	−	0.272169i	−0.174581	−	0.0277781i
$97$	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
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.791796	−	0.610786i	$-0.790854\pi$
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.133058	−	0.991108i	$-0.542480\pi$
$102$	1.66019	−	2.04719i	0.164383	−	0.202702i
$103$	0.141315	−	0.244765i	0.0139242	−	0.0241174i	−0.858979	−	0.512010i	$-0.828901\pi$
$103$	0.141315	−	0.244765i	0.0139242	−	0.0241174i	0.872904	+	0.487893i	$0.162234\pi$
$104$	−2.85185	−	4.93955i	−0.279647	−	0.484362i
$105$	−6.07442	+	13.2560i	−0.592803	+	1.29365i
$106$	−1.02859	+	1.78157i	−0.0999055	+	0.173041i
$107$	5.68878	+	9.85326i	0.549955	+	0.952550i	0.998277	+	0.0586780i	$0.0186885\pi$
$107$	5.68878	+	9.85326i	0.549955	+	0.952550i	−0.448322	+	0.893872i	$0.647978\pi$
$108$	4.62476	+	2.36887i	0.445018	+	0.227945i
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	−0.952256	−	0.305300i	$-0.901243\pi$
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	0.740526	+	0.672028i	$0.234577\pi$
$110$	10.1248			0.965358
$111$	0.619562	+	1.61745i	0.0588062	+	0.153522i
$112$	−2.56238	+	0.658939i	−0.242122	+	0.0622638i
$113$	−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	$0.881655\pi$
$114$	0.794668	+	2.07459i	0.0744275	+	0.194303i
$115$	3.56238	+	6.17023i	0.332194	+	0.575377i
$116$	−3.54063	+	6.13255i	−0.328739	+	0.569393i
$117$	3.53379	+	16.7422i	0.326699	+	1.54782i
$118$	1.12476			0.103543
$119$	1.08126	−	3.87828i	0.0991186	−	0.355521i
$120$	−3.47141	+	4.28061i	−0.316895	+	0.390764i
$121$	0.437618	−	0.757977i	0.0397835	−	0.0689070i
$122$	−3.12476			−0.282903
$123$	−3.47141	−	9.06259i	−0.313007	−	0.817146i
$124$	−9.42107			−0.846037
$125$	−0.396990			−0.0355079
$126$	7.92107	+	0.506659i	0.705665	+	0.0451368i
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	−1.00000			−0.0883883
$129$	7.44966	−	9.18620i	0.655906	−	0.808800i
$130$	−18.1488			−1.59176
$131$	−3.18194	+	5.51129i	−0.278008	+	0.481523i	−0.970890	−	0.239528i	$-0.923007\pi$
$131$	−3.18194	+	5.51129i	−0.278008	+	0.481523i	0.692882	+	0.721051i	$0.256341\pi$
$132$	−1.97141	−	5.14663i	−0.171589	−	0.447957i
$133$	2.37524	+	2.42368i	0.205959	+	0.210160i
$134$	−10.9669			−0.947396
$135$	13.8856	−	8.97539i	1.19509	−	0.772479i
$136$	0.760877	−	1.31788i	0.0652446	−	0.113007i
$137$	−1.37072	−	2.37416i	−0.117109	−	0.202838i	0.801512	−	0.597979i	$-0.204029\pi$
$137$	−1.37072	−	2.37416i	−0.117109	−	0.202838i	−0.918621	+	0.395140i	$0.870696\pi$
$138$	2.44282	−	3.01225i	0.207947	−	0.256420i
$139$	−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	$0.943040\pi$
$140$	−2.26088	+	8.10936i	−0.191079	+	0.685366i
$141$	−9.96978	−	1.58632i	−0.839607	−	0.133593i
$142$	−8.69002			−0.729251
$143$	9.07442	−	15.7174i	0.758841	−	1.31435i
$144$	2.85185	+	0.931107i	0.237654	+	0.0775923i
$145$	11.2661	+	19.5134i	0.935597	+	1.62050i
$146$	2.48345	−	4.30146i	0.205532	−	0.355991i
$147$	11.4074	−	4.10748i	0.940866	−	0.338779i
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	11.6300	−	20.1437i	0.952764	−	1.65024i	0.213360	−	0.976974i	$-0.431559\pi$
$149$	11.6300	−	20.1437i	0.952764	−	1.65024i	0.739404	−	0.673262i	$-0.235107\pi$
$150$	3.17511	+	8.28905i	0.259246	+	0.676798i
$151$	4.06238	+	7.03625i	0.330592	+	0.572602i	0.982628	−	0.185586i	$-0.0594183\pi$
$151$	4.06238	+	7.03625i	0.330592	+	0.572602i	−0.652036	+	0.758188i	$0.726085\pi$
$152$	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
$156$	3.53379	+	9.22544i	0.282930	+	0.738627i
$157$	−11.2632			−0.898901			−0.449451	−	0.893305i	$-0.648380\pi$
$157$	−11.2632			−0.898901			−0.449451	+	0.893305i	$0.648380\pi$
$158$	4.13844			0.329236
$159$	2.24433	−	2.76748i	0.177987	−	0.219476i
$160$	−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	0.777492	−	0.628893i	$-0.216492\pi$
$163$	−1.99028	−	3.44727i	−0.155891	−	0.270011i	−0.933383	+	0.358881i	$0.883158\pi$
$164$	−2.80150	−	4.85235i	−0.218761	−	0.378905i
$165$	−17.3187	−	2.75564i	−1.34826	−	0.214527i
$166$	4.03379	−	6.98673i	0.313083	−	0.542276i
$167$	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	$0.768359\pi$
$168$	4.56238	−	0.429736i	0.351995	−	0.0331549i
$169$	−9.76608	+	16.9153i	−0.751237	+	1.30118i
$170$	−2.42107	−	4.19341i	−0.185687	−	0.321620i
$171$	−0.794668	−	3.76494i	−0.0607698	−	0.287912i
$172$	3.41423	−	5.91362i	0.260333	−	0.450909i
$173$	2.55159			0.193994			0.0969968	−	0.995285i	$-0.469076\pi$
$173$	2.55159			0.193994			0.0969968	+	0.995285i	$0.469076\pi$
$174$	7.72545	−	9.52628i	0.585665	−	0.722185i
$175$	9.49028	+	9.68385i	0.717398	+	0.732030i
$176$	−1.59097	−	2.75564i	−0.119924	−	0.207714i
$177$	−1.92395	−	0.306125i	−0.144613	−	0.0230098i
$178$	−0.112725	−	0.195246i	−0.00844910	−	0.0146343i
$179$	3.51887	−	6.09487i	0.263013	−	0.455552i	−0.704028	−	0.710172i	$-0.748617\pi$
$179$	3.51887	−	6.09487i	0.263013	−	0.455552i	0.967041	+	0.254620i	$0.0819504\pi$
$180$	7.10301	−	6.37731i	0.529427	−	0.475337i
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$	10.5624	+	10.7778i	0.782936	+	0.798904i
$183$	5.34501	+	0.850463i	0.395115	+	0.0628680i
$184$	1.11956	−	1.93914i	0.0825352	−	0.142955i
$185$	3.18194			0.233941
$186$	16.1150	+	2.56412i	1.18161	+	0.188010i
$187$	4.84213			0.354092
$188$	−5.82846			−0.425084
$189$	−13.4114	−	3.02252i	−0.975532	−	0.219856i
$190$	4.08126			0.296085
$191$	1.98057			0.143309			0.0716545	−	0.997430i	$-0.477172\pi$
$191$	1.98057			0.143309			0.0716545	+	0.997430i	$0.477172\pi$
$192$	1.71053	+	0.272169i	0.123447	+	0.0196421i
$193$	−4.54583			−0.327216			−0.163608	−	0.986525i	$-0.552313\pi$
$193$	−4.54583			−0.327216			−0.163608	+	0.986525i	$0.552313\pi$
$194$	−7.42107	+	12.8537i	−0.532802	+	0.922839i
$195$	31.0442	+	4.93955i	2.22312	+	0.353728i
$196$	6.13160	−	3.37690i	0.437971	−	0.241207i
$197$	−21.8148			−1.55424			−0.777120	−	0.629353i	$-0.783320\pi$
$197$	−21.8148			−1.55424			−0.777120	+	0.629353i	$0.783320\pi$
$198$	1.97141	+	9.34004i	0.140102	+	0.663768i
$199$	6.14132	−	10.6371i	0.435346	−	0.754042i	−0.561978	−	0.827152i	$-0.689959\pi$
$199$	6.14132	−	10.6371i	0.435346	−	0.754042i	0.997324	+	0.0731106i	$0.0232926\pi$
$200$	2.56238	+	4.43818i	0.181188	+	0.313826i
$201$	18.7592	+	2.98485i	1.32317	+	0.210535i
$202$	9.29467	+	16.0988i	0.653971	+	1.13271i
$203$	5.03147	−	18.0470i	0.353140	−	1.26665i
$204$	−1.66019	+	2.04719i	−0.116237	+	0.143332i
$205$	−17.8285			−1.24519
$206$	−0.141315	+	0.244765i	−0.00984589	+	0.0170536i
$207$	−4.99837	+	4.48769i	−0.347410	+	0.311916i
$208$	2.85185	+	4.93955i	0.197740	+	0.342496i
$209$	−2.04063	+	3.53447i	−0.141153	+	0.244485i
$210$	6.07442	−	13.2560i	0.419175	−	0.914751i
$211$	−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	$-0.361025\pi$
$212$	1.02859	−	1.78157i	0.0706438	−	0.122359i
$213$	14.8646	+	2.36515i	1.01850	+	0.162058i
$214$	−5.68878	−	9.85326i	−0.388877	−	0.673555i
$215$	−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
$219$	−5.41874	+	6.68187i	−0.366165	+	0.451519i
$220$	−10.1248			−0.682611
$221$	−8.67962			−0.583854
$222$	−0.619562	−	1.61745i	−0.0415823	−	0.108556i
$223$	−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
$227$	7.25404	+	12.5644i	0.481468	+	0.833926i	0.999774	−	0.0212688i	$-0.00677059\pi$
$227$	7.25404	+	12.5644i	0.481468	+	0.833926i	−0.518306	+	0.855195i	$0.673437\pi$
$228$	−0.794668	−	2.07459i	−0.0526282	−	0.137393i
$229$	−5.12476	+	8.87635i	−0.338654	+	0.586566i	−0.984180	−	0.177173i	$-0.943305\pi$
$229$	−5.12476	+	8.87635i	−0.338654	+	0.586566i	0.645526	+	0.763738i	$0.276638\pi$
$230$	−3.56238	−	6.17023i	−0.234896	−	0.406853i
$231$	8.44282	+	11.8886i	0.555497	+	0.782212i
$232$	3.54063	−	6.13255i	0.232454	−	0.402622i
$233$	0.540628	+	0.936396i	0.0354177	+	0.0613453i	0.883191	−	0.469014i	$-0.155390\pi$
$233$	0.540628	+	0.936396i	0.0354177	+	0.0613453i	−0.847773	+	0.530359i	$0.822057\pi$
$234$	−3.53379	−	16.7422i	−0.231011	−	1.09447i
$235$	−9.27292	+	16.0612i	−0.604898	+	1.04771i
$236$	−1.12476			−0.0732159
$237$	−7.07893	−	1.12635i	−0.459826	−	0.0731645i
$238$	−1.08126	+	3.87828i	−0.0700874	+	0.251391i
$239$	−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	$0.963792\pi$
$240$	3.47141	−	4.28061i	0.224079	−	0.276312i
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$	−0.437618	+	0.757977i	−0.0281312	+	0.0487246i
$243$	10.9834	+	11.0618i	0.704589	+	0.709616i
$244$	3.12476			0.200042
$245$	0.449657	−	22.2691i	0.0287275	−	1.42272i
$246$	3.47141	+	9.06259i	0.221329	+	0.577809i
$247$	3.65787	−	6.33561i	0.232744	−	0.403125i
$248$	9.42107			0.598238
$249$	−8.80150	+	10.8532i	−0.557773	+	0.687791i
$250$	0.396990			0.0251079
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$	−7.92107	−	0.506659i	−0.498980	−	0.0319165i
$253$	7.12476			0.447930
$254$	−20.1053			−1.26152
$255$	3.00000	+	7.83191i	0.187867	+	0.490453i
$256$	1.00000			0.0625000
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	−0.960403	−	0.278614i	$-0.910125\pi$
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	0.721488	+	0.692427i	$0.243458\pi$
$258$	−7.44966	+	9.18620i	−0.463795	+	0.571908i
$259$	−1.85185	−	1.88962i	−0.115068	−	0.117415i
$260$	18.1488			1.12554
$261$	−15.8074	+	14.1924i	−0.978453	+	0.878487i
$262$	3.18194	−	5.51129i	0.196581	−	0.340488i
$263$	1.54746	+	2.68029i	0.0954208	+	0.165274i	0.909784	−	0.415082i	$-0.136247\pi$
$263$	1.54746	+	2.68029i	0.0954208	+	0.165274i	−0.814363	+	0.580355i	$0.802914\pi$
$264$	1.97141	+	5.14663i	0.121332	+	0.316753i
$265$	−3.27292	−	5.66886i	−0.201054	−	0.348235i
$266$	−2.37524	−	2.42368i	−0.145635	−	0.148605i
$267$	0.139680	+	0.364654i	0.00854830	+	0.0223165i
$268$	10.9669			0.669910
$269$	−13.4451	+	23.2877i	−0.819765	+	1.41987i	0.0860906	+	0.996287i	$0.472563\pi$
$269$	−13.4451	+	23.2877i	−0.819765	+	1.41987i	−0.905855	+	0.423587i	$0.860771\pi$
$270$	−13.8856	+	8.97539i	−0.845053	+	0.546225i
$271$	−11.1082	−	19.2400i	−0.674776	−	1.16875i	−0.976534	−	0.215362i	$-0.930907\pi$
$271$	−11.1082	−	19.2400i	−0.674776	−	1.16875i	0.301759	−	0.953384i	$-0.402426\pi$
$272$	−0.760877	+	1.31788i	−0.0461349	+	0.0799080i
$273$	−15.1339	−	21.3106i	−0.915947	−	1.28977i
$274$	1.37072	+	2.37416i	0.0828084	+	0.143428i
$275$	−8.15335	+	14.1220i	−0.491666	+	0.851590i
$276$	−2.44282	+	3.01225i	−0.147040	+	0.181316i
$277$	7.31875	+	12.6764i	0.439741	+	0.761653i	0.997669	−	0.0682357i	$-0.0217370\pi$
$277$	7.31875	+	12.6764i	0.439741	+	0.761653i	−0.557928	+	0.829889i	$0.688404\pi$
$278$	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	$-0.0792219\pi$
$282$	9.96978	+	1.58632i	0.593691	+	0.0944642i
$283$	−26.1248			−1.55296			−0.776478	−	0.630144i	$-0.782996\pi$
$283$	−26.1248			−1.55296			−0.776478	+	0.630144i	$0.782996\pi$
$284$	8.69002			0.515658
$285$	−6.98113	−	1.11079i	−0.413526	−	0.0657975i
$286$	−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
$290$	−11.2661	−	19.5134i	−0.661567	−	1.14587i
$291$	16.1923	−	19.9668i	0.949212	−	1.17048i
$292$	−2.48345	+	4.30146i	−0.145333	+	0.251724i
$293$	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	$0.560745\pi$
$294$	−11.4074	+	4.10748i	−0.665293	+	0.239553i
$295$	−1.78947	+	3.09945i	−0.104187	+	0.180457i
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	−0.830095	−	16.5130i	−0.0481670	−	0.958182i
$298$	−11.6300	+	20.1437i	−0.673706	+	1.16689i
$299$	−12.7713			−0.738582
$300$	−3.17511	−	8.28905i	−0.183315	−	0.478568i
$301$	−4.85185	+	17.4027i	−0.279656	+	1.00308i
$302$	−4.06238	−	7.03625i	−0.233764	−	0.404891i
$303$	−11.5172	−	30.0673i	−0.661648	−	1.72732i
$304$	−0.641315	−	1.11079i	−0.0367819	−	0.0637082i
$305$	4.97141	−	8.61073i	0.284662	−	0.493049i
$306$	3.39699	−	3.04993i	0.194193	−	0.174353i
$307$	3.53216			0.201591			0.100795	−	0.994907i	$-0.467861\pi$
$307$	3.53216			0.201591			0.100795	+	0.994907i	$0.467861\pi$
$308$	5.89248	+	6.01266i	0.335755	+	0.342603i
$309$	0.308342	−	0.380217i	0.0175409	−	0.0216298i
$310$	14.9887	−	25.9611i	0.851298	−	1.47449i
$311$	1.70370			0.0966078			0.0483039	−	0.998833i	$-0.484618\pi$
$311$	1.70370			0.0966078			0.0483039	+	0.998833i	$0.484618\pi$
$312$	−3.53379	−	9.22544i	−0.200062	−	0.522288i
$313$	−2.84213			−0.160647			−0.0803234	−	0.996769i	$-0.525595\pi$
$313$	−2.84213			−0.160647			−0.0803234	+	0.996769i	$0.525595\pi$
$314$	11.2632			0.635619
$315$	−13.9984	+	21.0216i	−0.788719	+	1.18443i
$316$	−4.13844			−0.232805
$317$	−24.9201			−1.39965			−0.699827	−	0.714313i	$-0.746739\pi$
$317$	−24.9201			−1.39965			−0.699827	+	0.714313i	$0.746739\pi$
$318$	−2.24433	+	2.76748i	−0.125855	+	0.155193i
$319$	22.5322			1.26156
$320$	1.59097	−	2.75564i	0.0889380	−	0.154045i
$321$	7.04910	+	18.4026i	0.393442	+	1.02713i
$322$	−1.59097	+	5.70653i	−0.0886614	+	0.318013i
$323$	1.95185			0.108604
$324$	7.26608	+	5.31075i	0.403671	+	0.295042i
$325$	14.6150	−	25.3140i	0.810697	−	1.40417i
$326$	1.99028	+	3.44727i	0.110232	+	0.190927i
$327$	−4.82326	+	5.94758i	−0.266727	+	0.328902i
$328$	2.80150	+	4.85235i	0.154687	+	0.267926i
$329$	14.9347	−	3.84060i	0.823379	−	0.211739i
$330$	17.3187	+	2.75564i	0.953366	+	0.151693i
$331$	−7.17154			−0.394183			−0.197092	−	0.980385i	$-0.563150\pi$
$331$	−7.17154			−0.394183			−0.197092	+	0.980385i	$0.563150\pi$
$332$	−4.03379	+	6.98673i	−0.221383	+	0.383447i
$333$	0.619562	+	2.93533i	0.0339518	+	0.160855i
$334$	−2.61956	−	4.53721i	−0.143336	−	0.248265i
$335$	17.4480	−	30.2209i	0.953287	−	1.65114i
$336$	−4.56238	+	0.429736i	−0.248898	+	0.0234440i
$337$	−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	$-0.369478\pi$
$338$	9.76608	−	16.9153i	0.531205	−	0.920073i
$339$	−1.99192	−	5.20018i	−0.108186	−	0.282435i
$340$	2.42107	+	4.19341i	0.131301	+	0.227420i
$341$	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
$345$	4.41423	+	11.5239i	0.237654	+	0.620428i
$346$	−2.55159			−0.137174
$347$	−2.11109			−0.113329			−0.0566646	−	0.998393i	$-0.518047\pi$
$347$	−2.11109			−0.113329			−0.0566646	+	0.998393i	$0.518047\pi$
$348$	−7.72545	+	9.52628i	−0.414128	+	0.510662i
$349$	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
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	0.971168	−	0.238396i	$-0.0766215\pi$
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	−0.692041	+	0.721858i	$0.743288\pi$
$354$	1.92395	+	0.306125i	0.102257	+	0.0162704i
$355$	13.8256	−	23.9466i	0.733786	−	1.27095i
$356$	0.112725	+	0.195246i	0.00597442	+	0.0103480i
$357$	2.90507	−	6.33963i	0.153753	−	0.335529i
$358$	−3.51887	+	6.09487i	−0.185978	+	0.322124i
$359$	16.2209	+	28.0955i	0.856108	+	1.48282i	0.875613	+	0.483013i	$0.160458\pi$
$359$	16.2209	+	28.0955i	0.856108	+	1.48282i	−0.0195047	+	0.999810i	$0.506209\pi$
$360$	−7.10301	+	6.37731i	−0.374361	+	0.336114i
$361$	8.67743	−	15.0297i	0.456707	−	0.791039i
$362$	12.9669			0.681525
$363$	0.954858	−	1.17744i	0.0501171	−	0.0617995i
$364$	−10.5624	−	10.7778i	−0.553619	−	0.564911i
$365$	7.90219	+	13.6870i	0.413620	+	0.716410i
$366$	−5.34501	−	0.850463i	−0.279388	−	0.0444544i
$367$	9.05555	+	15.6847i	0.472696	+	0.818733i	0.999512	−	0.0312465i	$-0.00994768\pi$
$367$	9.05555	+	15.6847i	0.472696	+	0.818733i	−0.526816	+	0.849979i	$0.676614\pi$
$368$	−1.11956	+	1.93914i	−0.0583612	+	0.101085i
$369$	−3.47141	−	16.4467i	−0.180714	−	0.856179i
$370$	−3.18194			−0.165421
$371$	−1.46169	+	5.24284i	−0.0758874	+	0.272195i
$372$	−16.1150	−	2.56412i	−0.835526	−	0.132943i
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	−0.674480	−	0.738293i	$-0.735632\pi$
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	0.976621	+	0.214971i	$0.0689656\pi$
$374$	−4.84213			−0.250381
$375$	−0.679065	−	0.108048i	−0.0350668	−	0.00557959i
$376$	5.82846			0.300580
$377$	−40.3893			−2.08016
$378$	13.4114	+	3.02252i	0.689805	+	0.155462i
$379$	14.2690			0.732947			0.366474	−	0.930428i	$-0.380565\pi$
$379$	14.2690			0.732947			0.366474	+	0.930428i	$0.380565\pi$
$380$	−4.08126			−0.209364
$381$	34.3908	+	5.47204i	1.76190	+	0.280341i
$382$	−1.98057			−0.101335
$383$	0.824893	−	1.42876i	0.0421501	−	0.0730061i	−0.844181	−	0.536059i	$-0.819913\pi$
$383$	0.824893	−	1.42876i	0.0421501	−	0.0730061i	0.886331	+	0.463053i	$0.153246\pi$
$384$	−1.71053	−	0.272169i	−0.0872903	−	0.0138891i
$385$	25.9435	−	6.67160i	1.32220	−	0.340016i
$386$	4.54583			0.231377
$387$	15.2431	−	13.6857i	0.774849	−	0.695685i
$388$	7.42107	−	12.8537i	0.376748	−	0.652546i
$389$	16.0338	+	27.7713i	0.812946	+	1.40806i	0.910794	+	0.412862i	$0.135471\pi$
$389$	16.0338	+	27.7713i	0.812946	+	1.40806i	−0.0978483	+	0.995201i	$0.531196\pi$
$390$	−31.0442	−	4.93955i	−1.57198	−	0.250124i
$391$	−1.70370	−	2.95089i	−0.0861596	−	0.149233i
$392$	−6.13160	+	3.37690i	−0.309693	+	0.170559i
$393$	−6.94282	+	8.56122i	−0.350219	+	0.431856i
$394$	21.8148			1.09901
$395$	−6.58414	+	11.4041i	−0.331284	+	0.573800i
$396$	−1.97141	−	9.34004i	−0.0990671	−	0.469355i
$397$	−18.9669	−	32.8516i	−0.951921	−	1.64878i	−0.741261	−	0.671217i	$-0.765772\pi$
$397$	−18.9669	−	32.8516i	−0.951921	−	1.64878i	−0.210660	−	0.977559i	$-0.567561\pi$
$398$	−6.14132	+	10.6371i	−0.307836	+	0.533188i
$399$	3.40327	+	4.79225i	0.170377	+	0.239913i
$400$	−2.56238	−	4.43818i	−0.128119	−	0.221909i
$401$	−5.30959	+	9.19647i	−0.265148	+	0.459250i	−0.967602	−	0.252479i	$-0.918754\pi$
$401$	−5.30959	+	9.19647i	−0.265148	+	0.459250i	0.702454	+	0.711729i	$0.252087\pi$
$402$	−18.7592	−	2.98485i	−0.935626	−	0.148871i
$403$	−26.8675	−	46.5358i	−1.33836	−	2.31811i
$404$	−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
$408$	1.66019	−	2.04719i	0.0821916	−	0.101351i
$409$	5.54583			0.274224			0.137112	−	0.990556i	$-0.456218\pi$
$409$	5.54583			0.274224			0.137112	+	0.990556i	$0.456218\pi$
$410$	17.8285			0.880485
$411$	−1.69850	−	4.43415i	−0.0837806	−	0.218721i
$412$	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
$416$	−2.85185	−	4.93955i	−0.139823	−	0.242181i
$417$	−4.93598	−	12.8861i	−0.241716	−	0.631033i
$418$	2.04063	−	3.53447i	0.0998104	−	0.172877i
$419$	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	$0.790055\pi$
$420$	−6.07442	+	13.2560i	−0.296401	+	0.646826i
$421$	−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
$423$	−16.6219	−	5.42692i	−0.808184	−	0.263866i
$424$	−1.02859	+	1.78157i	−0.0499527	+	0.0865207i
$425$	7.79863			0.378289
$426$	−14.8646	−	2.36515i	−0.720191	−	0.114592i
$427$	−8.00684	+	2.05903i	−0.387478	+	0.0996433i
$428$	5.68878	+	9.85326i	0.274978	+	0.476275i
$429$	19.7999	−	24.4153i	0.955947	−	1.17878i
$430$	10.8639	+	18.8168i	0.523903	+	0.907427i
$431$	16.5539	−	28.6722i	0.797374	−	1.38109i	−0.123947	−	0.992289i	$-0.539555\pi$
$431$	16.5539	−	28.6722i	0.797374	−	1.38109i	0.921321	−	0.388803i	$-0.127111\pi$
$432$	4.62476	+	2.36887i	0.222509	+	0.113972i
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$	−24.1404	+	6.20790i	−1.15877	+	0.297989i
$435$	13.9601	+	36.4446i	0.669334	+	1.74739i
$436$	−2.21053	+	3.82876i	−0.105865	+	0.183364i
$437$	2.87197			0.137385
$438$	5.41874	−	6.68187i	0.258918	−	0.319272i
$439$	−8.83422			−0.421634			−0.210817	−	0.977526i	$-0.567612\pi$
$439$	−8.83422			−0.421634			−0.210817	+	0.977526i	$0.567612\pi$
$440$	10.1248			0.482679
$441$	20.6307	−	3.92124i	0.982412	−	0.186726i
$442$	8.67962			0.412847
$443$	17.5185			0.832328			0.416164	−	0.909290i	$-0.363374\pi$
$443$	17.5185			0.832328			0.416164	+	0.909290i	$0.363374\pi$
$444$	0.619562	+	1.61745i	0.0294031	+	0.0767608i
$445$	0.717370			0.0340066
$446$	5.32846	−	9.22916i	0.252310	−	0.437014i
$447$	25.3759	−	31.2911i	1.20024	−	1.48002i
$448$	−2.56238	+	0.658939i	−0.121061	+	0.0311319i
$449$	31.2301			1.47384			0.736920	−	0.675980i	$-0.236280\pi$
$449$	31.2301			1.47384			0.736920	+	0.675980i	$0.236280\pi$
$450$	3.17511	+	15.0429i	0.149676	+	0.709127i
$451$	−8.91423	+	15.4399i	−0.419755	+	0.727036i
$452$	−1.60752	−	2.78431i	−0.0756115	−	0.130963i
$453$	5.03379	+	13.1414i	0.236508	+	0.617437i
$454$	−7.25404	−	12.5644i	−0.340449	−	0.589675i
$455$	−46.5043	+	11.9590i	−2.18015	+	0.560645i
$456$	0.794668	+	2.07459i	0.0372138	+	0.0971516i
$457$	−32.1248			−1.50273			−0.751367	−	0.659885i	$-0.770605\pi$
$457$	−32.1248			−1.50273			−0.751367	+	0.659885i	$0.770605\pi$
$458$	5.12476	−	8.87635i	0.239464	−	0.414765i
$459$	−6.64076	+	4.29245i	−0.309964	+	0.200354i
$460$	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	$0.148388\pi$
$462$	−8.44282	−	11.8886i	−0.392796	−	0.553108i
$463$	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	$0.584204\pi$
$464$	−3.54063	+	6.13255i	−0.164370	+	0.284696i
$465$	−32.7044	+	40.3279i	−1.51663	+	1.87016i
$466$	−0.540628	−	0.936396i	−0.0250441	−	0.0433777i
$467$	−7.98181	−	13.8249i	−0.369354	−	0.639740i	0.620110	−	0.784515i	$-0.287088\pi$
$467$	−7.98181	−	13.8249i	−0.369354	−	0.639740i	−0.989465	+	0.144774i	$0.953754\pi$
$468$	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
$471$	−19.2661	−	3.06549i	−0.887734	−	0.141250i
$472$	1.12476			0.0517714
$473$	−21.7278			−0.999044
$474$	7.07893	+	1.12635i	0.325146	+	0.0517351i
$475$	−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
$479$	11.5865	+	20.0683i	0.529399	+	0.916946i	0.999412	+	0.0342863i	$0.0109158\pi$
$479$	11.5865	+	20.0683i	0.529399	+	0.916946i	−0.470013	+	0.882659i	$0.655751\pi$
$480$	−3.47141	+	4.28061i	−0.158447	+	0.195382i
$481$	−2.85185	+	4.93955i	−0.130033	+	0.225224i
$482$	−6.50000	−	11.2583i	−0.296067	−	0.512803i
$483$	4.27455	−	9.32820i	0.194499	−	0.424448i
$484$	0.437618	−	0.757977i	0.0198917	−	0.0344535i
$485$	−23.6134	−	40.8996i	−1.07223	−	1.85716i
$486$	−10.9834	−	11.0618i	−0.498219	−	0.501774i
$487$	1.70658	−	2.95588i	0.0773323	−	0.133943i	−0.824766	−	0.565474i	$-0.808693\pi$
$487$	1.70658	−	2.95588i	0.0773323	−	0.133943i	0.902098	+	0.431531i	$0.142026\pi$
$488$	−3.12476			−0.141451
$489$	−2.46621	−	6.43837i	−0.111526	−	0.291153i
$490$	−0.449657	+	22.2691i	−0.0203134	+	1.00601i
$491$	−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	$0.975711\pi$
$492$	−3.47141	−	9.06259i	−0.156503	−	0.408573i
$493$	−5.38796	−	9.33223i	−0.242662	−	0.420302i
$494$	−3.65787	+	6.33561i	−0.164575	+	0.285053i
$495$	−28.8743	−	9.42724i	−1.29780	−	0.423723i
$496$	−9.42107			−0.423018
$497$	−22.2672	+	5.72619i	−0.998819	+	0.256855i
$498$	8.80150	−	10.8532i	0.394405	−	0.486342i
$499$	−20.5848	+	35.6540i	−0.921503	+	1.59609i	−0.124413	+	0.992231i	$0.539705\pi$
$499$	−20.5848	+	35.6540i	−0.921503	+	1.59609i	−0.797090	+	0.603860i	$0.793629\pi$
$500$	−0.396990			−0.0177539
$501$	3.24596	+	8.47402i	0.145019	+	0.378591i
$502$	−5.11109			−0.228119
$503$	−26.4542			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$503$	−26.4542			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$504$	7.92107	+	0.506659i	0.352832	+	0.0225684i
$505$	−59.1502			−2.63215
$506$	−7.12476			−0.316734
$507$	−21.3090	+	26.2762i	−0.946367	+	1.16697i
$508$	20.1053			0.892030
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	−0.972132	−	0.234436i	$-0.924676\pi$
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	0.689093	+	0.724673i	$0.258009\pi$
$510$	−3.00000	−	7.83191i	−0.132842	−	0.346803i
$511$	3.52915	−	12.6584i	0.156120	−	0.559975i
$512$	−1.00000			−0.0441942
$513$	−0.334608	−	6.65634i	−0.0147733	−	0.293884i
$514$	3.83009	−	6.63392i	0.168938	−	0.292610i
$515$	−0.449657	−	0.778828i	−0.0198142	−	0.0343193i
$516$	7.44966	−	9.18620i	0.327953	−	0.404400i
$517$	9.27292	+	16.0612i	0.407822	+	0.706369i
$518$	1.85185	+	1.88962i	0.0813655	+	0.0830251i
$519$	4.36458	+	0.694462i	0.191584	+	0.0304835i
$520$	−18.1488			−0.795879
$521$	−3.40615	+	5.89962i	−0.149226	+	0.258467i	−0.930942	−	0.365168i	$-0.881012\pi$
$521$	−3.40615	+	5.89962i	−0.149226	+	0.258467i	0.781716	+	0.623635i	$0.214345\pi$
$522$	15.8074	−	14.1924i	0.691871	−	0.621184i
$523$	14.7535	+	25.5538i	0.645125	+	1.11739i	0.984273	+	0.176656i	$0.0565280\pi$
$523$	14.7535	+	25.5538i	0.645125	+	1.11739i	−0.339148	+	0.940733i	$0.610139\pi$
$524$	−3.18194	+	5.51129i	−0.139004	+	0.240762i
$525$	13.5978	+	19.1475i	0.593457	+	0.835665i
$526$	−1.54746	−	2.68029i	−0.0674727	−	0.116866i
$527$	7.16827	−	12.4158i	0.312255	−	0.540841i
$528$	−1.97141	−	5.14663i	−0.0857946	−	0.223978i
$529$	8.99316	+	15.5766i	0.391007	+	0.677244i
$530$	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
$534$	−0.139680	−	0.364654i	−0.00604456	−	0.0157801i
$535$	36.2028			1.56518
$536$	−10.9669			−0.473698
$537$	7.67799	−	9.46775i	0.331330	−	0.408564i
$538$	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	0.987135	+	0.159892i	$0.0511145\pi$
$541$	14.7008	+	25.4626i	0.632038	+	1.09472i	−0.355097	+	0.934829i	$0.615552\pi$
$542$	11.1082	+	19.2400i	0.477139	+	0.826428i
$543$	−22.1803	−	3.52918i	−0.951848	−	0.151452i
$544$	0.760877	−	1.31788i	0.0326223	−	0.0565035i
$545$	7.03379	+	12.1829i	0.301295	+	0.521857i
$546$	15.1339	+	21.3106i	0.647672	+	0.912007i
$547$	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
$549$	8.91135	+	2.90949i	0.380327	+	0.124174i
$550$	8.15335	−	14.1220i	0.347660	−	0.602165i
$551$	9.08263			0.386933
$552$	2.44282	−	3.01225i	0.103973	−	0.128210i
$553$	10.6043	−	2.72698i	0.450939	−	0.115963i
$554$	−7.31875	−	12.6764i	−0.310944	−	0.538570i
$555$	5.44282	+	0.866025i	0.231035	+	0.0367607i
$556$	−3.98345	−	6.89953i	−0.168936	−	0.292605i
$557$	−3.36909	+	5.83543i	−0.142753	+	0.247255i	−0.928532	−	0.371252i	$-0.878929\pi$
$557$	−3.36909	+	5.83543i	−0.142753	+	0.247255i	0.785779	+	0.618507i	$0.212262\pi$
$558$	26.8675	+	8.77202i	1.13739	+	0.371349i
$559$	38.9475			1.64730
$560$	−2.26088	+	8.10936i	−0.0955395	+	0.342683i
$561$	8.28263	+	1.31788i	0.349693	+	0.0556408i
$562$	−11.6992	+	20.2636i	−0.493500	+	0.854768i
$563$	−1.45993			−0.0615286			−0.0307643	−	0.999527i	$-0.509794\pi$
$563$	−1.45993			−0.0615286			−0.0307643	+	0.999527i	$0.509794\pi$
$564$	−9.96978	−	1.58632i	−0.419803	−	0.0667963i
$565$	−10.2301			−0.430383
$566$	26.1248			1.09811
$567$	−22.1179	−	8.82028i	−0.928866	−	0.370417i
$568$	−8.69002			−0.364625
$569$	19.5653			0.820218			0.410109	−	0.912036i	$-0.365491\pi$
$569$	19.5653			0.820218			0.410109	+	0.912036i	$0.365491\pi$
$570$	6.98113	+	1.11079i	0.292407	+	0.0465259i
$571$	−21.9259			−0.917569			−0.458785	−	0.888547i	$-0.651715\pi$
$571$	−21.9259			−0.917569			−0.458785	+	0.888547i	$0.651715\pi$
$572$	9.07442	−	15.7174i	0.379421	−	0.657176i
$573$	3.38783	+	0.539049i	0.141529	+	0.0225191i
$574$	−10.3759	−	10.5876i	−0.433083	−	0.441916i
$575$	11.4750			0.478540
$576$	2.85185	+	0.931107i	0.118827	+	0.0387961i
$577$	12.3655	−	21.4177i	0.514783	−	0.891631i	−0.485069	−	0.874476i	$-0.661206\pi$
$577$	12.3655	−	21.4177i	0.514783	−	0.891631i	0.999853	−	0.0171554i	$-0.00546099\pi$
$578$	−7.34213	−	12.7169i	−0.305392	−	0.528955i
$579$	−7.77579	−	1.23723i	−0.323151	−	0.0514176i
$580$	11.2661	+	19.5134i	0.467798	+	0.810251i
$581$	5.73229	−	20.5607i	0.237815	−	0.853001i
$582$	−16.1923	+	19.9668i	−0.671194	+	0.827652i
$583$	−6.54583			−0.271101
$584$	2.48345	−	4.30146i	0.102766	−	0.177996i
$585$	51.7577	+	16.8985i	2.13992	+	0.698668i
$586$	−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	$0.898531\pi$
$588$	11.4074	−	4.10748i	0.470433	−	0.169390i
$589$	6.04187	+	10.4648i	0.248951	+	0.431196i
$590$	1.78947	−	3.09945i	0.0736712	−	0.127602i
$591$	−37.3149	−	5.93730i	−1.53493	−	0.244228i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−7.55391	−	13.0838i	−0.310202	−	0.537285i	0.668204	−	0.743978i	$-0.267063\pi$
$593$	−7.55391	−	13.0838i	−0.310202	−	0.537285i	−0.978406	+	0.206693i	$0.933730\pi$
$594$	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
$597$	13.4000	−	16.5236i	0.548426	−	0.676265i
$598$	12.7713			0.522256
$599$	−5.45417			−0.222851			−0.111426	−	0.993773i	$-0.535542\pi$
$599$	−5.45417			−0.222851			−0.111426	+	0.993773i	$0.535542\pi$
$600$	3.17511	+	8.28905i	0.129623	+	0.338399i
$601$	−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
$605$	−1.39248	−	2.41184i	−0.0566122	−	0.0980553i
$606$	11.5172	+	30.0673i	0.467856	+	1.22140i
$607$	−3.33530	+	5.77690i	−0.135376	+	0.234477i	−0.925741	−	0.378159i	$-0.876557\pi$
$607$	−3.33530	+	5.77690i	−0.135376	+	0.234477i	0.790365	+	0.612636i	$0.209891\pi$
$608$	0.641315	+	1.11079i	0.0260088	+	0.0450485i
$609$	13.5183	−	29.5006i	0.547790	−	1.19542i
$610$	−4.97141	+	8.61073i	−0.201287	+	0.348638i
$611$	−16.6219	−	28.7899i	−0.672449	−	1.16472i
$612$	−3.39699	+	3.04993i	−0.137315	+	0.123286i
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	−0.852495	−	0.522735i	$-0.824912\pi$
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	0.878950	+	0.476915i	$0.158245\pi$
$614$	−3.53216			−0.142546
$615$	−30.4962	−	4.85235i	−1.22972	−	0.195666i
$616$	−5.89248	−	6.01266i	−0.237415	−	0.242257i
$617$	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	$0.589008\pi$
$618$	−0.308342	+	0.380217i	−0.0124033	+	0.0152946i
$619$	8.22421	+	14.2447i	0.330559	+	0.572545i	0.982622	−	0.185620i	$-0.0594295\pi$
$619$	8.22421	+	14.2447i	0.330559	+	0.572545i	−0.652063	+	0.758165i	$0.726096\pi$
$620$	−14.9887	+	25.9611i	−0.601959	+	1.04262i
$621$	−9.77128	+	6.31595i	−0.392108	+	0.253450i
$622$	−1.70370			−0.0683120
$623$	−0.417500	−	0.426015i	−0.0167268	−	0.0170679i
$624$	3.53379	+	9.22544i	0.141465	+	0.369313i
$625$	12.1803	−	21.0969i	0.487212	−	0.843877i
$626$	2.84213			0.113594
$627$	−4.45254	+	5.49044i	−0.177817	+	0.219267i
$628$	−11.2632			−0.449451
$629$	−1.52175			−0.0606763
$630$	13.9984	−	21.0216i	0.557708	−	0.837519i
$631$	−30.0118			−1.19475			−0.597375	−	0.801962i	$-0.703790\pi$
$631$	−30.0118			−1.19475			−0.597375	+	0.801962i	$0.703790\pi$
$632$	4.13844			0.164618
$633$	−10.3200	−	26.9417i	−0.410183	−	1.07084i
$634$	24.9201			0.989704
$635$	31.9870	−	55.4031i	1.26937	−	2.19861i
$636$	2.24433	−	2.76748i	0.0889933	−	0.109738i
$637$	34.1668	+	20.6569i	1.35374	+	0.818456i
$638$	−22.5322			−0.892057
$639$	24.7826	+	8.09134i	0.980386	+	0.320089i
$640$	−1.59097	+	2.75564i	−0.0628887	+	0.108926i
$641$	−13.9497	−	24.1615i	−0.550978	−	0.954322i	−0.998204	−	0.0599014i	$-0.980921\pi$
$641$	−13.9497	−	24.1615i	−0.550978	−	0.954322i	0.447226	−	0.894421i	$-0.352412\pi$
$642$	−7.04910	−	18.4026i	−0.278206	−	0.726294i
$643$	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	$0.643342\pi$
$644$	1.59097	−	5.70653i	0.0626931	−	0.224869i
$645$	−13.4617	−	35.1436i	−0.530054	−	1.38378i
$646$	−1.95185			−0.0767944
$647$	8.35705	−	14.4748i	0.328550	−	0.569065i	−0.653675	−	0.756776i	$-0.726774\pi$
$647$	8.35705	−	14.4748i	0.328550	−	0.569065i	0.982224	+	0.187711i	$0.0601069\pi$
$648$	−7.26608	−	5.31075i	−0.285439	−	0.208626i
$649$	1.78947	+	3.09945i	0.0702427	+	0.121664i
$650$	−14.6150	+	25.3140i	−0.573249	+	0.992897i
$651$	42.9825	−	4.04857i	1.68462	−	0.158676i
$652$	−1.99028	−	3.44727i	−0.0779456	−	0.135006i
$653$	−19.0825	+	33.0519i	−0.746756	+	1.29342i	0.202614	+	0.979259i	$0.435056\pi$
$653$	−19.0825	+	33.0519i	−0.746756	+	1.29342i	−0.949370	+	0.314161i	$0.898277\pi$
$654$	4.82326	−	5.94758i	0.188604	−	0.232569i
$655$	10.1248	+	17.5366i	0.395607	+	0.685212i
$656$	−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	$0.112206\pi$
$660$	−17.3187	−	2.75564i	−0.674131	−	0.107263i
$661$	−20.0837			−0.781167			−0.390584	−	0.920567i	$-0.627727\pi$
$661$	−20.0837			−0.781167			−0.390584	+	0.920567i	$0.627727\pi$
$662$	7.17154			0.278730
$663$	−14.8468	−	2.36232i	−0.576601	−	0.0917449i
$664$	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
$668$	2.61956	+	4.53721i	0.101354	+	0.175550i
$669$	−11.6264	+	14.3366i	−0.449503	+	0.554283i
$670$	−17.4480	+	30.2209i	−0.674076	+	1.16753i
$671$	−4.97141	−	8.61073i	−0.191919	−	0.332414i
$672$	4.56238	−	0.429736i	0.175998	−	0.0165774i
$673$	−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
$675$	−1.33693	−	26.5955i	−0.0514585	−	1.02366i
$676$	−9.76608	+	16.9153i	−0.375618	+	0.650590i
$677$	−0.717370			−0.0275708			−0.0137854	−	0.999905i	$-0.504388\pi$
$677$	−0.717370			−0.0275708			−0.0137854	+	0.999905i	$0.504388\pi$
$678$	1.99192	+	5.20018i	0.0764992	+	0.199712i
$679$	−10.5458	+	37.8260i	−0.404712	+	1.45163i
$680$	−2.42107	−	4.19341i	−0.0928437	−	0.160810i
$681$	8.98865	+	23.4661i	0.344446	+	0.899223i
$682$	−14.9887	−	25.9611i	−0.573945	−	0.994102i
$683$	−10.5270	+	18.2332i	−0.402803	+	0.697675i	−0.994063	−	0.108806i	$-0.965297\pi$
$683$	−10.5270	+	18.2332i	−0.402803	+	0.697675i	0.591260	+	0.806481i	$0.298631\pi$
$684$	−0.794668	−	3.76494i	−0.0303849	−	0.143956i
$685$	−8.72313			−0.333294
$686$	13.4863	−	12.6933i	0.514910	−	0.484631i
$687$	−11.1819	+	13.7885i	−0.426618	+	0.526064i
$688$	3.41423	−	5.91362i	0.130166	−	0.225455i
$689$	11.7335			0.447012
$690$	−4.41423	−	11.5239i	−0.168047	−	0.438709i
$691$	5.84789			0.222464			0.111232	−	0.993794i	$-0.464520\pi$
$691$	5.84789			0.222464			0.111232	+	0.993794i	$0.464520\pi$
$692$	2.55159			0.0969968
$693$	11.2060	+	22.6337i	0.425681	+	0.859784i
$694$	2.11109			0.0801359
$695$	−25.3502			−0.961588
$696$	7.72545	−	9.52628i	0.292832	−	0.361093i
$697$	8.52640			0.322960
$698$	−18.1082	+	31.3643i	−0.685406	+	1.18716i
$699$	0.669905	+	1.74888i	0.0253381	+	0.0661486i
$700$	9.49028	+	9.68385i	0.358699	+	0.366015i
$701$	10.2711			0.387935			0.193967	−	0.981008i	$-0.437864\pi$
$701$	10.2711			0.387935			0.193967	+	0.981008i	$0.437864\pi$
$702$	−1.48796	−	29.5999i	−0.0561595	−	1.11718i
$703$	0.641315	−	1.11079i	0.0241877	−	0.0418942i
$704$	−1.59097	−	2.75564i	−0.0599620	−	0.103857i
$705$	−20.2330	+	24.9494i	−0.762018	+	0.939647i
$706$	−5.24433	−	9.08344i	−0.197373	−	0.341860i
$707$	34.4246	+	35.1268i	1.29467	+	1.32108i
$708$	−1.92395	−	0.306125i	−0.0723063	−	0.0115049i
$709$	43.4854			1.63313			0.816564	−	0.577255i	$-0.195876\pi$
$709$	43.4854			1.63313			0.816564	+	0.577255i	$0.195876\pi$
$710$	−13.8256	+	23.9466i	−0.518865	+	0.898700i
$711$	−11.8022	−	3.85333i	−0.442617	−	0.144511i
$712$	−0.112725	−	0.195246i	−0.00422455	−	0.00731714i
$713$	10.5475	−	18.2687i	0.395006	−	0.684170i
$714$	−2.90507	+	6.33963i	−0.108720	+	0.237255i
$715$	−28.8743	−	50.0117i	−1.07984	−	1.87033i
$716$	3.51887	−	6.09487i	0.131507	−	0.227776i
$717$	−7.63323	−	19.9276i	−0.285068	−	0.744210i
$718$	−16.2209	−	28.0955i	−0.605360	−	1.04851i
$719$	25.4412	+	44.0654i	0.948796	+	1.64336i	0.747966	+	0.663737i	$0.231031\pi$
$719$	25.4412	+	44.0654i	0.948796	+	1.64336i	0.200830	+	0.979626i	$0.435636\pi$
$720$	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
$723$	8.05430	+	21.0268i	0.299543	+	0.781997i
$724$	−12.9669			−0.481911
$725$	36.2898			1.34777
$726$	−0.954858	+	1.17744i	−0.0354381	+	0.0436989i
$727$	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
$731$	5.19562	+	8.99907i	0.192167	+	0.332843i
$732$	5.34501	+	0.850463i	0.197557	+	0.0314340i
$733$	23.0848	−	39.9841i	0.852657	−	1.47685i	−0.0261440	−	0.999658i	$-0.508323\pi$
$733$	23.0848	−	39.9841i	0.852657	−	1.47685i	0.878801	−	0.477188i	$-0.158344\pi$
$734$	−9.05555	−	15.6847i	−0.334246	−	0.578932i
$735$	6.83009	−	37.9696i	0.251932	−	1.40053i
$736$	1.11956	−	1.93914i	0.0412676	−	0.0714776i
$737$	−17.4480	−	30.2209i	−0.642706	−	1.11320i
$738$	3.47141	+	16.4467i	0.127784	+	0.605410i
$739$	−2.49604	+	4.32327i	−0.0918184	+	0.159034i	−0.908276	−	0.418371i	$-0.862601\pi$
$739$	−2.49604	+	4.32327i	−0.0918184	+	0.159034i	0.816458	+	0.577405i	$0.195935\pi$
$740$	3.18194			0.116971
$741$	7.98126	−	9.84172i	0.293199	−	0.361545i
$742$	1.46169	−	5.24284i	0.0536605	−	0.192471i
$743$	−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	$-0.362131\pi$
$744$	16.1150	+	2.56412i	0.590806	+	0.0940052i
$745$	−37.0059	−	64.0961i	−1.35579	−	2.34830i
$746$	−5.83530	+	10.1070i	−0.213645	+	0.370045i
$747$	−18.0092	+	16.1692i	−0.658921	+	0.591600i
$748$	4.84213			0.177046
$749$	−21.0695	−	21.4992i	−0.769863	−	0.785565i
$750$	0.679065	+	0.108048i	0.0247959	+	0.00394536i
$751$	−1.64815	+	2.85468i	−0.0601419	+	0.104169i	−0.894529	−	0.447010i	$-0.852489\pi$
$751$	−1.64815	+	2.85468i	−0.0601419	+	0.104169i	0.834387	+	0.551179i	$0.185822\pi$
$752$	−5.82846			−0.212542
$753$	8.74269	+	1.39108i	0.318601	+	0.0506937i
$754$	40.3893			1.47089
$755$	25.8525			0.940870
$756$	−13.4114	−	3.02252i	−0.487766	−	0.109928i
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$	−14.2690			−0.518272
$759$	12.1871	+	1.93914i	0.442365	+	0.0703862i
$760$	4.08126			0.148043
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	−0.964889	−	0.262659i	$-0.915400\pi$
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	0.709914	+	0.704288i	$0.248734\pi$
$762$	−34.3908	−	5.47204i	−1.24585	−	0.198231i
$763$	3.14132	−	11.2673i	0.113723	−	0.407905i
$764$	1.98057			0.0716545
$765$	3.00000	+	14.2132i	0.108465	+	0.513881i
$766$	−0.824893	+	1.42876i	−0.0298046	+	0.0516231i
$767$	−3.20765	−	5.55582i	−0.115822	−	0.200609i
$768$	1.71053	+	0.272169i	0.0617236	+	0.00982104i
$769$	11.3461	+	19.6520i	0.409151	+	0.708669i	0.994795	−	0.101899i	$-0.0324918\pi$

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.71053 + 0.272169i) q^{3} +1.00000 q^{4} +(1.59097 - 2.75564i) q^{5} +(-1.71053 - 0.272169i) q^{6} +(-2.56238 + 0.658939i) q^{7} -1.00000 q^{8} +(2.85185 + 0.931107i) q^{9} +(-1.59097 + 2.75564i) q^{10} +(-1.59097 - 2.75564i) q^{11} +(1.71053 + 0.272169i) q^{12} +(2.85185 + 4.93955i) q^{13} +(2.56238 - 0.658939i) q^{14} +(3.47141 - 4.28061i) q^{15} +1.00000 q^{16} +(-0.760877 + 1.31788i) q^{17} +(-2.85185 - 0.931107i) q^{18} +(-0.641315 - 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(-4.56238 + 0.429736i) q^{21} +(1.59097 + 2.75564i) q^{22} +(-1.11956 + 1.93914i) q^{23} +(-1.71053 - 0.272169i) q^{24} +(-2.56238 - 4.43818i) 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} +(-3.47141 + 4.28061i) q^{30} -9.42107 q^{31} -1.00000 q^{32} +(-1.97141 - 5.14663i) 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} +(0.641315 + 1.11079i) q^{38} +(3.53379 + 9.22544i) q^{39} +(-1.59097 + 2.75564i) q^{40} +(-2.80150 - 4.85235i) q^{41} +(4.56238 - 0.429736i) q^{42} +(3.41423 - 5.91362i) q^{43} +(-1.59097 - 2.75564i) q^{44} +(7.10301 - 6.37731i) q^{45} +(1.11956 - 1.93914i) q^{46} -5.82846 q^{47} +(1.71053 + 0.272169i) q^{48} +(6.13160 - 3.37690i) q^{49} +(2.56238 + 4.43818i) q^{50} +(-1.66019 + 2.04719i) q^{51} +(2.85185 + 4.93955i) q^{52} +(1.02859 - 1.78157i) q^{53} +(-4.62476 - 2.36887i) q^{54} -10.1248 q^{55} +(2.56238 - 0.658939i) q^{56} +(-0.794668 - 2.07459i) q^{57} +(3.54063 - 6.13255i) q^{58} -1.12476 q^{59} +(3.47141 - 4.28061i) q^{60} +3.12476 q^{61} +9.42107 q^{62} +(-7.92107 - 0.506659i) q^{63} +1.00000 q^{64} +18.1488 q^{65} +(1.97141 + 5.14663i) q^{66} +10.9669 q^{67} +(-0.760877 + 1.31788i) q^{68} +(-2.44282 + 3.01225i) q^{69} +(2.26088 - 8.10936i) q^{70} +8.69002 q^{71} +(-2.85185 - 0.931107i) q^{72} +(-2.48345 + 4.30146i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(-3.17511 - 8.28905i) q^{75} +(-0.641315 - 1.11079i) q^{76} +(5.89248 + 6.01266i) q^{77} +(-3.53379 - 9.22544i) q^{78} -4.13844 q^{79} +(1.59097 - 2.75564i) q^{80} +(7.26608 + 5.31075i) q^{81} +(2.80150 + 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(-4.56238 + 0.429736i) q^{84} +(2.42107 + 4.19341i) q^{85} +(-3.41423 + 5.91362i) q^{86} +(-7.72545 + 9.52628i) q^{87} +(1.59097 + 2.75564i) 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} +(-16.1150 - 2.56412i) q^{93} +5.82846 q^{94} -4.08126 q^{95} +(-1.71053 - 0.272169i) q^{96} +(7.42107 - 12.8537i) q^{97} +(-6.13160 + 3.37690i) q^{98} +(-1.97141 - 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} - q^{10} - q^{11} + 2 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} + 6 q^{16} - 4 q^{17} - 8 q^{18} - 3 q^{19} + q^{20}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 - q^10 - q^11 + 2 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 + 6 * q^16 - 4 * q^17 - 8 * q^18 - 3 * q^19 + q^20 - 10 * q^21 + q^22 - 7 * q^23 - 2 * q^24 + 2 * q^25 - 8 * q^26 - 7 * q^27 + 2 * q^28 - 5 * q^29 - 12 * q^30 - 40 * q^31 - 6 * q^32 - 3 * q^33 + 4 * q^34 - 13 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 5 * q^39 - q^40 + 10 * q^42 - 6 * q^43 - q^44 + 9 * q^45 + 7 * q^46 + 18 * q^47 + 2 * q^48 + 12 * q^49 - 2 * q^50 + 6 * q^51 + 8 * q^52 + 15 * q^53 + 7 * q^54 - 26 * q^55 - 2 * q^56 + 22 * q^57 + 5 * q^58 + 28 * q^59 + 12 * q^60 - 16 * q^61 + 40 * q^62 - 31 * q^63 + 6 * q^64 + 24 * q^65 + 3 * q^66 - 2 * q^67 - 4 * q^68 + 3 * q^69 + 13 * q^70 + 14 * q^71 - 8 * q^72 + 19 * q^73 - 3 * q^74 + 8 * q^75 - 3 * q^76 + 10 * q^77 + 5 * q^78 - 10 * q^79 + q^80 + 8 * q^81 + 2 * q^83 - 10 * q^84 - 2 * q^85 + 6 * q^86 - 27 * q^87 + q^88 - 9 * q^89 - 9 * q^90 - 46 * q^91 - 7 * q^92 - 38 * q^93 - 18 * q^94 + 8 * q^95 - 2 * q^96 + 28 * q^97 - 12 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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