LMFDB - Embedded newform 882.2.h.p.67.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(67,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,-2,-3,2,2,0,-6,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.04280545828$
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:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.p.79.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(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} -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} +(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} +(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} +(-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} +(2.85185 - 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} +(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} +(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} +(-0.794668 + 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} +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} +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} +(-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} +(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} +(-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} +(-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} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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	$-0.248014\pi$
$5$	3.18194			1.42301			0.711504	+	0.702682i	$0.248014\pi$
$6$	1.71053	−	0.272169i	0.698322	−	0.111112i
$7$		0			0
$7$		0			0
$8$	−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	0.134412	+	0.990925i	$0.457085\pi$
$13$	−2.85185	+	4.93955i	−0.790960	+	1.36998i	−0.925373	+	0.379058i	$0.876248\pi$
$14$		0			0
$15$	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	$-0.774254\pi$
$17$	0.760877	−	1.31788i	0.184540	−	0.319632i	0.943421	+	0.331596i	$0.107587\pi$
$18$	2.23229	+	2.00422i	0.526155	+	0.472399i
$19$	0.641315	+	1.11079i	0.147128	+	0.254833i	0.930165	−	0.367142i	$-0.119664\pi$
$19$	0.641315	+	1.11079i	0.147128	+	0.254833i	−0.783037	+	0.621975i	$0.786330\pi$
$20$	−1.59097	−	2.75564i	−0.355752	−	0.616181i
$21$		0			0
$22$	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
$28$		0			0
$29$	−3.54063	−	6.13255i	−0.657478	−	1.13879i	−0.981266	−	0.192656i	$-0.938290\pi$
$29$	−3.54063	−	6.13255i	−0.657478	−	1.13879i	0.323788	−	0.946130i	$-0.395043\pi$
$30$	5.44282	−	0.866025i	0.993718	−	0.158114i
$31$	−4.71053	−	8.15888i	−0.846037	−	1.46538i	−0.884718	−	0.466127i	$-0.845649\pi$
$31$	−4.71053	−	8.15888i	−0.846037	−	1.46538i	0.0386810	−	0.999252i	$-0.487684\pi$
$32$	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
$35$		0			0
$36$	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	$0.807139\pi$
$38$	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	$-0.689190\pi$
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	0.997498	+	0.0706992i	$0.0225230\pi$
$42$		0			0
$43$	3.41423	+	5.91362i	0.520665	+	0.901819i	0.999711	+	0.0240288i	$0.00764935\pi$
$43$	3.41423	+	5.91362i	0.520665	+	0.901819i	−0.479046	+	0.877790i	$0.659017\pi$
$44$	−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	$-0.973089\pi$
$47$	−2.91423	+	5.04759i	−0.425084	+	0.736267i	0.571344	+	0.820711i	$0.306422\pi$
$48$	−1.71053	+	0.272169i	−0.246894	+	0.0392842i
$49$		0			0
$50$	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	−0.786694	−	0.617343i	$-0.788209\pi$
$53$	1.02859	−	1.78157i	0.141288	−	0.244717i	0.927982	+	0.372626i	$0.121542\pi$
$54$	−0.260877	+	5.18960i	−0.0355008	+	0.706215i
$55$	10.1248			1.36522
$56$		0			0
$57$	−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	$-0.189993\pi$
$59$	−0.562382	−	0.974074i	−0.0732159	−	0.126814i	−0.900309	+	0.435251i	$0.856660\pi$
$60$	1.97141	−	5.14663i	0.254508	−	0.664427i
$61$	1.56238	−	2.70612i	0.200042	−	0.346484i	−0.748499	−	0.663135i	$-0.769225\pi$
$61$	1.56238	−	2.70612i	0.200042	−	0.346484i	0.948542	+	0.316652i	$0.102559\pi$
$62$	−9.42107			−1.19648
$63$		0			0
$64$	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	−0.977929	−	0.208938i	$-0.932999\pi$
$67$	−5.48345	−	9.49761i	−0.669910	−	1.16032i	0.308019	−	0.951380i	$-0.400334\pi$
$68$	−1.52175			−0.184540
$69$	2.44282	+	3.01225i	0.294081	+	0.362632i
$70$		0			0
$71$	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	$-0.739457\pi$
$73$	2.48345	−	4.30146i	0.290666	−	0.503448i	0.973967	+	0.226689i	$0.0727899\pi$
$74$	1.00000			0.116248
$75$	5.59097	+	6.89425i	0.645590	+	0.796079i
$76$	0.641315	−	1.11079i	0.0735639	−	0.127416i
$77$		0			0
$78$	−3.53379	+	9.22544i	−0.400123	+	1.04458i
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	−0.725827	−	0.687877i	$-0.758543\pi$
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	0.958633	+	0.284646i	$0.0918762\pi$
$80$	−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	$-0.0206639\pi$
$83$	4.03379	+	6.98673i	0.442766	+	0.766893i	−0.555127	+	0.831765i	$0.687331\pi$
$84$		0			0
$85$	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	$-0.170470\pi$
$89$	−0.112725	−	0.195246i	−0.0119488	−	0.0206960i	−0.871938	+	0.489616i	$0.837137\pi$
$90$	7.10301	+	6.37731i	0.748723	+	0.672228i
$91$		0			0
$92$	−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	−0.946119	−	0.323819i	$-0.895033\pi$
$97$	−7.42107	−	12.8537i	−0.753495	−	1.30509i	0.192624	−	0.981273i	$-0.438300\pi$
$98$		0			0
$99$	−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	$-0.875813\pi$
$101$	−18.5893			−1.84971			−0.924854	+	0.380322i	$0.875813\pi$
$102$	0.942820	−	2.46136i	0.0933531	−	0.243711i
$103$	0.282630			0.0278484			0.0139242	−	0.999903i	$-0.495568\pi$
$103$	0.282630			0.0278484			0.0139242	+	0.999903i	$0.495568\pi$
$104$	2.85185	−	4.93955i	0.279647	−	0.484362i
$105$		0			0
$106$	−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	$0.647978\pi$
$108$	4.36389	+	2.82073i	0.419915	+	0.271424i
$109$	−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	$0.234577\pi$
$110$	5.06238	−	8.76830i	0.482679	−	0.836025i
$111$	−0.619562	+	1.61745i	−0.0588062	+	0.153522i
$112$		0			0
$113$	−1.60752	+	2.78431i	−0.151223	+	0.261926i	−0.931677	−	0.363287i	$-0.881655\pi$
$113$	−1.60752	+	2.78431i	−0.151223	+	0.261926i	0.780454	+	0.625213i	$0.214988\pi$
$114$	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
$119$		0			0
$120$	−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
$126$		0			0
$127$	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	$-0.589674\pi$
$131$	−6.36389			−0.556015			−0.278008	+	0.960579i	$0.589674\pi$
$132$	1.97141	−	5.14663i	0.171589	−	0.447957i
$133$		0			0
$134$	−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	$-0.723626\pi$
$139$	3.98345	−	6.89953i	0.337872	−	0.585211i	0.984032	+	0.177991i	$0.0569597\pi$
$140$		0			0
$141$	−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
$147$		0			0
$148$	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
$154$		0			0
$155$	−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	$-0.315047\pi$
$157$	−5.63160	−	9.75422i	−0.449451	−	0.778471i	−0.998350	+	0.0574170i	$0.981714\pi$
$158$	−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
$161$		0			0
$162$	−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	$0.883158\pi$
$164$	−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	$-0.898307\pi$
$167$	−2.61956	+	4.53721i	−0.202708	+	0.351100i	0.746692	+	0.665170i	$0.231641\pi$
$168$		0			0
$169$	−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	$-0.802410\pi$
$173$	1.27579	−	2.20974i	0.0969968	−	0.168003i	0.910440	+	0.413641i	$0.135743\pi$
$174$	−7.72545	−	9.52628i	−0.585665	−	0.722185i
$175$		0			0
$176$	−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	−0.704028	−	0.710172i	$-0.748617\pi$
$179$	3.51887	−	6.09487i	0.263013	−	0.455552i	0.967041	+	0.254620i	$0.0819504\pi$
$180$	9.07442	−	2.96273i	0.676367	−	0.220829i
$181$	12.9669			0.963822			0.481911	−	0.876220i	$-0.339943\pi$
$181$	12.9669			0.963822			0.481911	+	0.876220i	$0.339943\pi$
$182$		0			0
$183$	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
$189$		0			0
$190$	4.08126			0.296085
$191$	−0.990285	+	1.71522i	−0.0716545	+	0.124109i	−0.899627	−	0.436660i	$-0.856161\pi$
$191$	−0.990285	+	1.71522i	−0.0716545	+	0.124109i	0.827972	+	0.560769i	$0.189495\pi$
$192$	1.09097	+	1.34528i	0.0787341	+	0.0970873i
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	0.936160	−	0.351574i	$-0.114353\pi$
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	−0.772552	+	0.634951i	$0.781020\pi$
$194$	−14.8421			−1.06560
$195$	−31.0442	+	4.93955i	−2.22312	+	0.353728i
$196$		0			0
$197$	−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	$-0.976707\pi$
$199$	−6.14132	+	10.6371i	−0.435346	+	0.754042i	0.561978	+	0.827152i	$0.310041\pi$
$200$	−5.12476			−0.362375
$201$	6.79467	−	17.7384i	0.479259	−	1.25117i
$202$	−9.29467	+	16.0988i	−0.653971	+	1.13271i
$203$		0			0
$204$	−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
$210$		0			0
$211$	−8.32846	+	14.4253i	−0.573355	+	0.993080i	0.422863	+	0.906193i	$0.361025\pi$
$211$	−8.32846	+	14.4253i	−0.573355	+	0.993080i	−0.996218	+	0.0868863i	$0.972308\pi$
$212$	−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
$217$		0			0
$218$	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	$-0.0505276\pi$
$223$	5.32846	+	9.22916i	0.356820	+	0.618031i	−0.630608	+	0.776102i	$0.717194\pi$
$224$		0			0
$225$	−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	$-0.340104\pi$
$227$	14.5081			0.962935			0.481468	+	0.876464i	$0.340104\pi$
$228$	2.19398	−	0.349092i	0.145300	−	0.0231192i
$229$	−10.2495			−0.677308			−0.338654	−	0.940911i	$-0.609972\pi$
$229$	−10.2495			−0.677308			−0.338654	+	0.940911i	$0.609972\pi$
$230$	3.56238	−	6.17023i	0.234896	−	0.406853i
$231$		0			0
$232$	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	$0.822057\pi$
$234$	−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
$238$		0			0
$239$	−6.16019	+	10.6698i	−0.398470	+	0.690170i	−0.993537	−	0.113506i	$-0.963792\pi$
$239$	−6.16019	+	10.6698i	−0.398470	+	0.690170i	0.595068	+	0.803676i	$0.297125\pi$
$240$	−5.44282	+	0.866025i	−0.351333	+	0.0559017i
$241$	13.0000			0.837404			0.418702	−	0.908124i	$-0.362485\pi$
$241$	13.0000			0.837404			0.418702	+	0.908124i	$0.362485\pi$
$242$	−0.437618	+	0.757977i	−0.0281312	+	0.0487246i
$243$	−4.08809	−	15.0429i	−0.262251	−	0.965000i
$244$	−3.12476			−0.200042
$245$		0			0
$246$	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	$-0.551570\pi$
$251$	−5.11109			−0.322609			−0.161305	+	0.986905i	$0.551570\pi$
$252$		0			0
$253$	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	$-0.576792\pi$
$257$	−7.66019			−0.477830			−0.238915	+	0.971041i	$0.576792\pi$
$258$	7.44966	+	9.18620i	0.463795	+	0.571908i
$259$		0			0
$260$	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			0
$267$	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	−0.0860906	−	0.996287i	$-0.527437\pi$
$269$	13.4451	−	23.2877i	0.819765	−	1.41987i	0.905855	−	0.423587i	$-0.139229\pi$
$270$	−0.830095	+	16.5130i	−0.0505180	+	1.00495i
$271$	11.1082	+	19.2400i	0.674776	+	1.16875i	0.976534	+	0.215362i	$0.0690930\pi$
$271$	11.1082	+	19.2400i	0.674776	+	1.16875i	−0.301759	+	0.953384i	$0.597574\pi$
$272$	0.760877	+	1.31788i	0.0461349	+	0.0799080i
$273$		0			0
$274$	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
$280$		0			0
$281$	11.6992	+	20.2636i	0.697915	+	1.20882i	0.969188	+	0.246322i	$0.0792219\pi$
$281$	11.6992	+	20.2636i	0.697915	+	1.20882i	−0.271273	+	0.962502i	$0.587445\pi$
$282$	−3.61109	+	9.42724i	−0.215037	+	0.561384i
$283$	−13.0624	−	22.6247i	−0.776478	−	1.34490i	−0.933960	−	0.357377i	$-0.883671\pi$
$283$	−13.0624	−	22.6247i	−0.776478	−	1.34490i	0.157482	−	0.987522i	$-0.449662\pi$
$284$	−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
$287$		0			0
$288$	−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	0.189678	+	0.981846i	$0.439255\pi$
$293$	−12.9315	+	22.3980i	−0.755465	+	1.30850i	−0.945143	+	0.326657i	$0.894078\pi$
$294$		0			0
$295$	−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
$301$		0			0
$302$	−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	$-0.532139\pi$
$307$	−3.53216			−0.201591			−0.100795	+	0.994907i	$0.532139\pi$
$308$		0			0
$309$	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	$-0.151285\pi$
$311$	0.851848	+	1.47544i	0.0483039	+	0.0836648i	−0.840863	+	0.541249i	$0.817952\pi$
$312$	9.75636	−	1.55237i	0.552345	−	0.0878855i
$313$	−1.42107	+	2.46136i	−0.0803234	+	0.139124i	−0.903389	−	0.428822i	$-0.858929\pi$
$313$	−1.42107	+	2.46136i	−0.0803234	+	0.139124i	0.823065	+	0.567947i	$0.192262\pi$
$314$	−11.2632			−0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	12.4601	−	21.5815i	0.699827	−	1.21214i	−0.268700	−	0.963224i	$-0.586594\pi$
$317$	12.4601	−	21.5815i	0.699827	−	1.21214i	0.968526	−	0.248911i	$-0.0800728\pi$
$318$	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
$322$		0			0
$323$	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
$329$		0			0
$330$	17.3187	−	2.75564i	0.953366	−	0.151693i
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	−0.750492	−	0.660879i	$-0.770184\pi$
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	0.947584	+	0.319506i	$0.103517\pi$
$332$	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			0
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	0.398651	+	0.917103i	$0.369478\pi$
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	−0.993560	+	0.113309i	$0.963855\pi$
$338$	−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
$343$		0			0
$344$	−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	0.892966	−	0.450124i	$-0.148620\pi$
$347$	1.05555	+	1.82826i	0.0566646	+	0.0981460i	−0.836302	+	0.548270i	$0.815287\pi$
$348$	−12.1127	+	1.92730i	−0.649310	+	0.103314i
$349$	−18.1082	−	31.3643i	−0.969310	−	1.67889i	−0.697559	−	0.716527i	$-0.745731\pi$
$349$	−18.1082	−	31.3643i	−0.969310	−	1.67889i	−0.271751	−	0.962368i	$-0.587603\pi$
$350$		0			0
$351$	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	$-0.409955\pi$
$353$	10.4887			0.558255			0.279127	+	0.960254i	$0.409955\pi$
$354$	−1.22708	−	1.51312i	−0.0652188	−	0.0804216i
$355$	27.6512			1.46757
$356$	−0.112725	+	0.195246i	−0.00597442	+	0.0103480i
$357$		0			0
$358$	−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	$0.506209\pi$
$360$	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
$364$		0			0
$365$	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	$-0.343281\pi$
$367$	18.1111			0.945391			0.472696	+	0.881226i	$0.343281\pi$
$368$	−1.11956	+	1.93914i	−0.0583612	+	0.101085i
$369$	12.5075	+	11.2297i	0.651116	+	0.584593i
$370$	3.18194			0.165421
$371$		0			0
$372$	−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
$378$		0			0
$379$	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	$-0.486579\pi$
$383$	1.64979			0.0843001			0.0421501	+	0.999111i	$0.486579\pi$
$384$	1.71053	−	0.272169i	0.0872903	−	0.0138891i
$385$		0			0
$386$	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
$392$		0			0
$393$	−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	0.741261	+	0.671217i	$0.234228\pi$
$397$	18.9669	+	32.8516i	0.951921	+	1.64878i	0.210660	+	0.977559i	$0.432439\pi$
$398$	6.14132	+	10.6371i	0.307836	+	0.533188i
$399$		0			0
$400$	−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
$406$		0			0
$407$	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	$-0.122885\pi$
$409$	2.77292	+	4.80283i	0.137112	+	0.237485i	−0.789290	+	0.614020i	$0.789551\pi$
$410$	−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
$413$		0			0
$414$	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	$-0.876612\pi$
$419$	−2.77455	+	4.80566i	−0.135546	+	0.234772i	0.790260	+	0.612772i	$0.209945\pi$
$420$		0			0
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	0.770537	−	0.637396i	$-0.219988\pi$
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	−0.937269	+	0.348606i	$0.886655\pi$
$422$	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
$427$		0			0
$428$	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	−0.123947	−	0.992289i	$-0.539555\pi$
$431$	16.5539	−	28.6722i	0.797374	−	1.38109i	0.921321	−	0.388803i	$-0.127111\pi$
$432$	0.260877	−	5.18960i	0.0125514	−	0.249685i
$433$	12.1111			0.582022			0.291011	−	0.956720i	$-0.406008\pi$
$433$	12.1111			0.582022			0.291011	+	0.956720i	$0.406008\pi$
$434$		0			0
$435$	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	$-0.900946\pi$
$439$	−4.41711	+	7.65066i	−0.210817	+	0.365146i	0.741153	+	0.671336i	$0.234279\pi$
$440$	−10.1248			−0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	−8.75924	+	15.1715i	−0.416164	+	0.720817i	−0.995550	−	0.0942360i	$-0.969959\pi$
$443$	−8.75924	+	15.1715i	−0.416164	+	0.720817i	0.579386	+	0.815053i	$0.303292\pi$
$444$	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			0
$449$	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
$455$		0			0
$456$	0.794668	−	2.07459i	0.0372138	−	0.0971516i
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	−0.195794	−	0.980645i	$-0.562728\pi$
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	0.947161	−	0.320760i	$-0.103938\pi$
$458$	−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	$-0.184946\pi$
$461$	−1.23229	−	2.13438i	−0.0573933	−	0.0994081i	−0.893295	+	0.449472i	$0.851612\pi$
$462$		0			0
$463$	15.1735	−	26.2812i	0.705171	−	1.22139i	−0.261459	−	0.965215i	$-0.584204\pi$
$463$	15.1735	−	26.2812i	0.705171	−	1.22139i	0.966630	−	0.256177i	$-0.0824631\pi$
$464$	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	$-0.0462456\pi$
$467$	7.98181	+	13.8249i	0.369354	+	0.639740i	−0.620110	+	0.784515i	$0.712912\pi$
$468$	−3.53379	+	16.7422i	−0.163350	+	0.773909i
$469$		0			0
$470$	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
$476$		0			0
$477$	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	$-0.322418\pi$
$479$	23.1729			1.05880			0.529399	+	0.848373i	$0.322418\pi$
$480$	−1.97141	+	5.14663i	−0.0899821	+	0.234911i
$481$	−5.70370			−0.260066
$482$	6.50000	−	11.2583i	0.296067	−	0.512803i
$483$		0			0
$484$	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	−0.824766	−	0.565474i	$-0.808693\pi$
$487$	1.70658	−	2.95588i	0.0773323	−	0.133943i	0.902098	+	0.431531i	$0.142026\pi$
$488$	−1.56238	+	2.70612i	−0.0707257	+	0.122500i
$489$	2.46621	−	6.43837i	0.111526	−	0.291153i
$490$		0			0
$491$	−9.58414	+	16.6002i	−0.432526	+	0.749157i	−0.997090	−	0.0762323i	$-0.975711\pi$
$491$	−9.58414	+	16.6002i	−0.432526	+	0.749157i	0.564564	+	0.825389i	$0.309044\pi$
$492$	−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
$497$		0			0
$498$	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	$-0.299220\pi$
$503$	26.4542			1.17953			0.589767	+	0.807574i	$0.299220\pi$
$504$		0			0
$505$	−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	$-0.591342\pi$
$509$	−12.7713			−0.566077			−0.283039	+	0.959109i	$0.591342\pi$
$510$	3.00000	−	7.83191i	0.132842	−	0.346803i
$511$		0			0
$512$	−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			0
$519$	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	$-0.785655\pi$
$521$	3.40615	−	5.89962i	0.149226	−	0.258467i	0.930942	+	0.365168i	$0.118988\pi$
$522$	4.38727	−	20.7858i	0.192026	−	0.909770i
$523$	−14.7535	−	25.5538i	−0.645125	−	1.11739i	−0.984273	−	0.176656i	$-0.943472\pi$
$523$	−14.7535	−	25.5538i	−0.645125	−	1.11739i	0.339148	−	0.940733i	$-0.389861\pi$
$524$	3.18194	+	5.51129i	0.139004	+	0.240762i
$525$		0			0
$526$	−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
$532$		0			0
$533$	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
$539$		0			0
$540$	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	$0.615552\pi$
$542$	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
$546$		0			0
$547$	17.6150	+	30.5102i	0.753165	+	1.30452i	0.946281	+	0.323344i	$0.104807\pi$
$547$	17.6150	+	30.5102i	0.753165	+	1.30452i	−0.193116	+	0.981176i	$0.561859\pi$
$548$	−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
$553$		0			0
$554$	−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	−0.928532	−	0.371252i	$-0.878929\pi$
$557$	−3.36909	+	5.83543i	−0.142753	+	0.247255i	0.785779	+	0.618507i	$0.212262\pi$
$558$	5.83693	−	27.6539i	0.247097	−	1.17068i
$559$	−38.9475			−1.64730
$560$		0			0
$561$	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	$-0.176461\pi$
$563$	−0.729964	−	1.26433i	−0.0307643	−	0.0532853i	−0.880998	+	0.473121i	$0.843127\pi$
$564$	6.35868	+	7.84092i	0.267749	+	0.330162i
$565$	−5.11505	+	8.85952i	−0.215192	+	0.372723i
$566$	−26.1248			−1.09811
$567$		0			0
$568$	−8.69002			−0.364625
$569$	−9.78263	+	16.9440i	−0.410109	+	0.710330i	−0.994901	−	0.100853i	$-0.967843\pi$
$569$	−9.78263	+	16.9440i	−0.410109	+	0.710330i	0.584792	+	0.811183i	$0.301176\pi$
$570$	4.45254	+	5.49044i	0.186496	+	0.229969i
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	0.998897	−	0.0469545i	$-0.0149516\pi$
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	−0.540112	+	0.841593i	$0.681618\pi$
$572$	18.1488			0.758841
$573$	−3.38783	+	0.539049i	−0.141529	+	0.0225191i
$574$		0			0
$575$	11.4750			0.478540
$576$	−0.619562	+	2.93533i	−0.0258151	+	0.122305i
$577$	−12.3655	+	21.4177i	−0.514783	+	0.891631i	0.485069	+	0.874476i	$0.338794\pi$
$577$	−12.3655	+	21.4177i	−0.514783	+	0.891631i	−0.999853	+	0.0171554i	$0.994539\pi$
$578$	14.6843			0.610785
$579$	−2.81642	+	7.35265i	−0.117046	+	0.305566i
$580$	−11.2661	+	19.5134i	−0.467798	+	0.810251i
$581$		0			0
$582$	−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	0.949620	+	0.313404i	$0.101469\pi$
$587$	18.0796	+	31.3148i	0.746226	+	1.29250i	−0.203394	+	0.979097i	$0.565197\pi$
$588$		0			0
$589$	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	$-0.0662700\pi$
$593$	7.55391	+	13.0838i	0.310202	+	0.537285i	−0.668204	+	0.743978i	$0.732937\pi$
$594$	−0.830095	+	16.5130i	−0.0340592	+	0.677537i
$595$		0			0
$596$	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	0.916345	−	0.400389i	$-0.131125\pi$
$599$	2.72708	+	4.72345i	0.111426	+	0.192995i	−0.804920	+	0.593384i	$0.797792\pi$
$600$	−5.59097	−	6.89425i	−0.228250	−	0.281456i
$601$	3.36840	+	5.83424i	0.137400	+	0.237984i	0.926512	−	0.376266i	$-0.122792\pi$
$601$	3.36840	+	5.83424i	0.137400	+	0.237984i	−0.789112	+	0.614250i	$0.789459\pi$
$602$		0			0
$603$	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	$-0.543224\pi$
$607$	−6.67059			−0.270751			−0.135376	+	0.990794i	$0.543224\pi$
$608$	−0.641315	+	1.11079i	−0.0260088	+	0.0450485i
$609$		0			0
$610$	−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	−0.852495	−	0.522735i	$-0.824912\pi$
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	0.878950	+	0.476915i	$0.158245\pi$
$614$	−1.76608	+	3.05894i	−0.0712731	+	0.123449i
$615$	30.4962	−	4.85235i	1.22972	−	0.195666i
$616$		0			0
$617$	17.2483	−	29.8749i	0.694390	−	1.20272i	−0.275996	−	0.961159i	$-0.589008\pi$
$617$	17.2483	−	29.8749i	0.694390	−	1.20272i	0.970386	−	0.241560i	$-0.0776589\pi$
$618$	0.483448	−	0.0769231i	0.0194471	−	0.00309430i
$619$	16.4484			0.661118			0.330559	−	0.943785i	$-0.392763\pi$
$619$	16.4484			0.661118			0.330559	+	0.943785i	$0.392763\pi$
$620$	−14.9887	+	25.9611i	−0.601959	+	1.04262i
$621$	−10.3554	+	5.30420i	−0.415549	+	0.212850i
$622$	1.70370			0.0683120
$623$		0			0
$624$	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
$630$		0			0
$631$	−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
$637$		0			0
$638$	−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	0.435257	+	0.900306i	$0.356658\pi$
$643$	−14.2524	+	24.6859i	−0.562060	+	0.973516i	−0.997317	+	0.0732100i	$0.976676\pi$
$644$		0			0
$645$	−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	$-0.939893\pi$
$647$	−8.35705	+	14.4748i	−0.328550	+	0.569065i	0.653675	+	0.756776i	$0.273226\pi$
$648$	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
$651$		0			0
$652$	−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
$658$		0			0
$659$	4.37072	+	7.57031i	0.170259	+	0.294898i	0.938510	−	0.345251i	$-0.112206\pi$
$659$	4.37072	+	7.57031i	0.170259	+	0.294898i	−0.768251	+	0.640148i	$0.778873\pi$
$660$	6.27292	−	16.3763i	0.244173	−	0.637446i
$661$	−10.0419	−	17.3930i	−0.390584	−	0.676511i	0.601943	−	0.798539i	$-0.294393\pi$
$661$	−10.0419	−	17.3930i	−0.390584	−	0.676511i	−0.992527	+	0.122028i	$0.961060\pi$
$662$	−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
$665$		0			0
$666$	−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
$672$		0			0
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	−0.981561	−	0.191148i	$-0.938779\pi$
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	0.325242	−	0.945631i	$-0.394554\pi$
$674$	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	$-0.837721\pi$
$677$	−0.358685	+	0.621261i	−0.0137854	+	0.0238770i	0.859050	+	0.511891i	$0.171055\pi$
$678$	−1.99192	+	5.20018i	−0.0764992	+	0.199712i
$679$		0			0
$680$	−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	−0.994063	−	0.108806i	$-0.965297\pi$
$683$	−10.5270	+	18.2332i	−0.402803	+	0.697675i	0.591260	+	0.806481i	$0.298631\pi$
$684$	2.86320	+	2.57067i	0.109477	+	0.0982921i
$685$	8.72313			0.333294
$686$		0			0
$687$	−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	$-0.797854\pi$
$691$	2.92395	−	5.06442i	0.111232	−	0.192660i	0.916267	+	0.400567i	$0.131187\pi$
$692$	−2.55159			−0.0969968
$693$		0			0
$694$	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
$700$		0			0
$701$	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
$707$		0			0
$708$	−1.92395	+	0.306125i	−0.0723063	+	0.0115049i
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	0.0916356	+	0.995793i	$0.470790\pi$
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	−0.908200	+	0.418538i	$0.862543\pi$
$710$	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
$714$		0			0
$715$	−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	−0.747966	−	0.663737i	$-0.768969\pi$
$719$	−25.4412	−	44.0654i	−0.948796	−	1.64336i	−0.200830	−	0.979626i	$-0.564364\pi$
$720$	−7.10301	−	6.37731i	−0.264714	−	0.237668i
$721$		0			0
$722$	−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	$-0.238971\pi$
$727$	−6.07210	−	10.5172i	−0.225202	−	0.390061i	−0.956380	+	0.292126i	$0.905637\pi$
$728$		0			0
$729$	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	$-0.174989\pi$
$733$	46.1696			1.70531			0.852657	+	0.522470i	$0.174989\pi$
$734$	9.05555	−	15.6847i	0.334246	−	0.578932i
$735$		0			0
$736$	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	−0.908276	−	0.418371i	$-0.862601\pi$
$739$	−2.49604	+	4.32327i	−0.0918184	+	0.159034i	0.816458	+	0.577405i	$0.195935\pi$
$740$	1.59097	−	2.75564i	0.0584853	−	0.101299i
$741$	−7.98126	−	9.84172i	−0.293199	−	0.361545i
$742$		0			0
$743$	−15.7060	+	27.2036i	−0.576198	+	0.998004i	0.419712	+	0.907657i	$0.362131\pi$
$743$	−15.7060	+	27.2036i	−0.576198	+	0.998004i	−0.995910	+	0.0903470i	$0.971202\pi$
$744$	−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
$749$		0			0
$750$	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
$756$		0			0
$757$	−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	$-0.582067\pi$
$761$	−14.0676			−0.509950			−0.254975	+	0.966948i	$0.582067\pi$
$762$	34.3908	−	5.47204i	1.24585	−	0.198231i
$763$		0			0
$764$	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	$-0.967508\pi$
$769$	−11.3461	+	19.6520i	−0.409151	+	0.708669i	0.585644	+	0.810568i	$0.300842\pi$
$770$		0			0
$771$	−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	$-0.837086\pi$
$773$	−0.327772	+	0.567717i	−0.0117891	+	0.0204194i	0.860071	+	0.510175i	$0.170419\pi$
$774$	−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
$777$		0			0
$778$	−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
$784$		0			0
$785$	−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	$-0.163603\pi$
$787$	0.270036	+	0.467717i	0.00962576	+	0.0166723i	−0.861172	+	0.508313i	$0.830269\pi$
$788$	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
$791$		0			0
$792$	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	$-0.686636\pi$
$797$	12.5550	−	21.7459i	0.444721	−	0.770279i	0.998033	+	0.0626954i	$0.0199697\pi$
$798$		0			0
$799$	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
$805$		0			0
$806$	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	0.487057	+	0.873370i	$0.338071\pi$
$809$	−14.5865	+	25.2645i	−0.512833	+	0.888252i	−0.999889	+	0.0148817i	$0.995263\pi$
$810$	−23.1202	+	16.8985i	−0.812363	+	0.593753i
$811$	15.4290			0.541785			0.270892	−	0.962610i	$-0.412681\pi$
$811$	15.4290			0.541785			0.270892	+	0.962610i	$0.412681\pi$
$812$		0			0
$813$	−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
$819$		0			0
$820$	−17.8285			−0.622597
$821$	−4.24364	+	7.35019i	−0.148104	+	0.256524i	−0.930527	−	0.366224i	$-0.880650\pi$
$821$	−4.24364	+	7.35019i	−0.148104	+	0.256524i	0.782423	+	0.622748i	$0.213984\pi$
$822$	4.68934	−	0.746136i	0.163559	−	0.0260245i
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	−0.999966	−	0.00825976i	$-0.997371\pi$
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	0.492830	−	0.870126i	$-0.335963\pi$
$824$	−0.282630			−0.00984589
$825$	17.7902	+	21.9371i	0.619374	+	0.763752i
$826$		0			0
$827$	−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	$-0.867763\pi$
$829$	−3.10821	+	5.38358i	−0.107953	+	0.186979i	0.806988	+	0.590568i	$0.201096\pi$
$830$	25.6706			0.891039
$831$	−15.9691	−	19.6915i	−0.553961	−	0.683092i
$832$	−2.85185	+	4.93955i	−0.0988701	+	0.171248i
$833$		0			0
$834$	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	−0.954647	−	0.297740i	$-0.903767\pi$
$839$	−21.2947	−	36.8834i	−0.735174	−	1.27336i	0.219474	−	0.975618i	$-0.429566\pi$
$840$		0			0
$841$	−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			0
$848$	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	$-0.0473070\pi$
$853$	10.6969	+	18.5275i	0.366254	+	0.634370i	−0.622723	+	0.782442i	$0.713974\pi$
$854$		0			0
$855$	−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	$-0.283352\pi$
$857$	36.8435			1.25855			0.629275	+	0.777183i	$0.283352\pi$
$858$	−11.2443	+	29.3548i	−0.383875	+	1.00216i
$859$	17.6375			0.601783			0.300892	−	0.953658i	$-0.402716\pi$
$859$	17.6375			0.601783			0.300892	+	0.953658i	$0.402716\pi$
$860$	10.8639	−	18.8168i	0.370455	−	0.641648i
$861$		0			0
$862$	−16.5539	−	28.6722i	−0.563828	−	0.976579i
$863$	−0.380438	−	0.658939i	−0.0129503	−	0.0224305i	0.859478	−	0.511173i	$-0.170789\pi$
$863$	−0.380438	−	0.658939i	−0.0129503	−	0.0224305i	−0.872428	+	0.488743i	$0.837456\pi$
$864$	−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
$868$		0			0
$869$	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			0
$876$	−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	$-0.544949\pi$
$881$	−8.35486			−0.281482			−0.140741	+	0.990046i	$0.544949\pi$
$882$		0			0
$883$	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	$-0.285907\pi$
$887$	37.1100			1.24603			0.623016	+	0.782209i	$0.285907\pi$
$888$	0.619562	−	1.61745i	0.0207911	−	0.0542781i
$889$		0			0
$890$	−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
$896$		0			0
$897$	−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
$903$		0			0
$904$	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
$910$		0			0
$911$	17.4428	+	30.2119i	0.577906	+	1.00096i	0.995719	+	0.0924301i	$0.0294635\pi$
$911$	17.4428	+	30.2119i	0.577906	+	1.00096i	−0.417813	+	0.908533i	$0.637203\pi$
$912$	−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
$917$		0			0
$918$	6.64076	+	4.29245i	0.219178	+	0.141672i
$919$	−25.8675	−	44.8037i	−0.853289	−	1.47794i	−0.878224	−	0.478250i	$-0.841271\pi$
$919$	−25.8675	−	44.8037i	−0.853289	−	1.47794i	0.0249351	−	0.999689i	$-0.492062\pi$
$920$	−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
$924$		0			0
$925$	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	0.0611787	+	0.998127i	$0.480514\pi$
$929$	−25.4142	+	44.0187i	−0.833814	+	1.44421i	−0.894993	+	0.446081i	$0.852819\pi$
$930$	−32.7044	−	40.3279i	−1.07242	−	1.32240i
$931$		0			0
$932$	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	$-0.513241\pi$
$937$	−2.54583			−0.0831686			−0.0415843	+	0.999135i	$0.513241\pi$
$938$		0			0
$939$	−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	$-0.160659\pi$
$941$	0.578933	+	1.00274i	0.0188727	+	0.0326885i	−0.856435	+	0.516255i	$0.827326\pi$
$942$	−12.2878	−	15.1522i	−0.400359	−	0.493684i
$943$	6.27292	−	10.8650i	0.204274	−	0.353813i
$944$	1.12476			0.0366079
$945$		0			0
$946$	21.7278			0.706431
$947$	−4.90739	+	8.49985i	−0.159469	+	0.276208i	−0.934677	−	0.355497i	$-0.884311\pi$
$947$	−4.90739	+	8.49985i	−0.159469	+	0.276208i	0.775208	+	0.631706i	$0.217645\pi$
$948$	−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
$952$		0			0
$953$	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
$959$		0			0
$960$	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
$966$		0			0
$967$	14.4445	−	25.0185i	0.464502	−	0.804542i	−0.534677	−	0.845057i	$-0.679567\pi$
$967$	14.4445	−	25.0185i	0.464502	−	0.804542i	0.999179	+	0.0405151i	$0.0128999\pi$
$968$	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	$-0.193957\pi$
$971$	−2.66827	−	4.62158i	−0.0856289	−	0.148314i	−0.905659	+	0.424007i	$0.860623\pi$
$972$	−10.9834	+	11.0618i	−0.352294	+	0.354808i
$973$		0			0
$974$	−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	0.938115	+	0.346325i	$0.112571\pi$
$977$	24.0361	+	41.6318i	0.768983	+	1.33192i	−0.169131	+	0.985594i	$0.554096\pi$
$978$	−4.34269	−	5.35498i	−0.138864	−	0.171234i
$979$	−0.358685	−	0.621261i	−0.0114636	−	0.0198556i
$980$		0			0
$981$	−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	$-0.655694\pi$
$983$	−29.4627			−0.939714			−0.469857	+	0.882743i	$0.655694\pi$
$984$	−9.58414	+	1.52496i	−0.305531	+	0.0486141i
$985$	−69.4134			−2.21170
$986$	−5.38796	+	9.33223i	−0.171588	+	0.297199i
$987$		0			0
$988$	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	−0.510280	−	0.860008i	$-0.670458\pi$
$991$	15.4142	−	26.6982i	0.489649	−	0.848097i	0.999929	+	0.0119112i	$0.00379153\pi$
$992$	4.71053	−	8.15888i	0.149560	−	0.259045i
$993$	12.2672	−	1.95187i	0.389286	−	0.0619407i
$994$		0			0
$995$	−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	$-0.527990\pi$
$997$	−5.54583			−0.175638			−0.0878191	+	0.996136i	$0.527990\pi$
$998$	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	882.2.h.p.67.3		6
3.2	odd	2		2646.2.h.o.361.1		6
7.2	even	3		882.2.e.o.373.1		6
7.3	odd	6		882.2.f.n.589.2		6
7.4	even	3		882.2.f.o.589.2		6
7.5	odd	6		126.2.e.c.121.3	yes	6
7.6	odd	2		126.2.h.d.67.1	yes	6
9.2	odd	6		2646.2.e.p.2125.3		6
9.7	even	3		882.2.e.o.655.1		6
21.2	odd	6		2646.2.e.p.1549.3		6
21.5	even	6		378.2.e.d.37.1		6
21.11	odd	6		2646.2.f.m.1765.3		6
21.17	even	6		2646.2.f.l.1765.1		6
21.20	even	2		378.2.h.c.361.3		6
28.19	even	6		1008.2.q.g.625.1		6
28.27	even	2		1008.2.t.h.193.3		6
63.2	odd	6		2646.2.h.o.667.1		6
63.4	even	3		7938.2.a.bw.1.3		3
63.5	even	6		1134.2.g.l.163.1		6
63.11	odd	6		2646.2.f.m.883.3		6
63.13	odd	6		1134.2.g.m.487.3		6
63.16	even	3	inner	882.2.h.p.79.3		6
63.20	even	6		378.2.e.d.235.1		6
63.25	even	3		882.2.f.o.295.2		6
63.31	odd	6		7938.2.a.bv.1.1		3
63.32	odd	6		7938.2.a.bz.1.1		3
63.34	odd	6		126.2.e.c.25.3	✓	6
63.38	even	6		2646.2.f.l.883.1		6
63.40	odd	6		1134.2.g.m.163.3		6
63.41	even	6		1134.2.g.l.487.1		6
63.47	even	6		378.2.h.c.289.3		6
63.52	odd	6		882.2.f.n.295.2		6
63.59	even	6		7938.2.a.ca.1.3		3
63.61	odd	6		126.2.h.d.79.1	yes	6
84.47	odd	6		3024.2.q.g.2305.1		6
84.83	odd	2		3024.2.t.h.1873.3		6
252.47	odd	6		3024.2.t.h.289.3		6
252.83	odd	6		3024.2.q.g.2881.1		6
252.187	even	6		1008.2.t.h.961.3		6
252.223	even	6		1008.2.q.g.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	63.34	odd	6
126.2.e.c.121.3	yes	6	7.5	odd	6
126.2.h.d.67.1	yes	6	7.6	odd	2
126.2.h.d.79.1	yes	6	63.61	odd	6
378.2.e.d.37.1		6	21.5	even	6
378.2.e.d.235.1		6	63.20	even	6
378.2.h.c.289.3		6	63.47	even	6
378.2.h.c.361.3		6	21.20	even	2
882.2.e.o.373.1		6	7.2	even	3
882.2.e.o.655.1		6	9.7	even	3
882.2.f.n.295.2		6	63.52	odd	6
882.2.f.n.589.2		6	7.3	odd	6
882.2.f.o.295.2		6	63.25	even	3
882.2.f.o.589.2		6	7.4	even	3
882.2.h.p.67.3		6	1.1	even	1	trivial
882.2.h.p.79.3		6	63.16	even	3	inner
1008.2.q.g.529.1		6	252.223	even	6
1008.2.q.g.625.1		6	28.19	even	6
1008.2.t.h.193.3		6	28.27	even	2
1008.2.t.h.961.3		6	252.187	even	6
1134.2.g.l.163.1		6	63.5	even	6
1134.2.g.l.487.1		6	63.41	even	6
1134.2.g.m.163.3		6	63.40	odd	6
1134.2.g.m.487.3		6	63.13	odd	6
2646.2.e.p.1549.3		6	21.2	odd	6
2646.2.e.p.2125.3		6	9.2	odd	6
2646.2.f.l.883.1		6	63.38	even	6
2646.2.f.l.1765.1		6	21.17	even	6
2646.2.f.m.883.3		6	63.11	odd	6
2646.2.f.m.1765.3		6	21.11	odd	6
2646.2.h.o.361.1		6	3.2	odd	2
2646.2.h.o.667.1		6	63.2	odd	6
3024.2.q.g.2305.1		6	84.47	odd	6
3024.2.q.g.2881.1		6	252.83	odd	6
3024.2.t.h.289.3		6	252.47	odd	6
3024.2.t.h.1873.3		6	84.83	odd	2
7938.2.a.bv.1.1		3	63.31	odd	6
7938.2.a.bw.1.3		3	63.4	even	3
7938.2.a.bz.1.1		3	63.32	odd	6
7938.2.a.ca.1.3		3	63.59	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not 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} -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} +(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} +(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} +(-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} +(2.85185 - 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} +(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} +(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} +(-0.794668 + 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} +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} +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} +(-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} +(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} +(-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} +(-1.97141 + 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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