LMFDB - Embedded newform 882.2.f.n.589.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (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:	$7.04280545828$
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			589.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.n.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.59097 - 2.75564i) q^{5} +(-1.71053 + 0.272169i) q^{6} -1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +3.18194 q^{10} +(-1.59097 - 2.75564i) q^{11} +(-1.09097 - 1.34528i) q^{12} +(2.85185 - 4.93955i) q^{13} +(3.47141 + 4.28061i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.52175 q^{17} +(0.619562 - 2.93533i) q^{18} +1.28263 q^{19} +(1.59097 + 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +(-1.11956 + 1.93914i) q^{23} +(0.619562 - 1.61745i) q^{24} +(-2.56238 - 4.43818i) q^{25} +5.70370 q^{26} +(4.62476 - 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +(-1.97141 + 5.14663i) q^{30} +(4.71053 - 8.15888i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.44282 - 0.866025i) q^{33} +(0.760877 + 1.31788i) q^{34} +(2.85185 - 0.931107i) q^{36} -1.00000 q^{37} +(0.641315 + 1.11079i) q^{38} +(6.22257 + 7.67307i) q^{39} +(-1.59097 + 2.75564i) q^{40} +(-2.80150 + 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +3.18194 q^{44} +(-9.07442 + 2.96273i) q^{45} -2.23912 q^{46} +(2.91423 + 5.04759i) q^{47} +(1.71053 - 0.272169i) q^{48} +(2.56238 - 4.43818i) q^{50} +(-0.942820 + 2.46136i) q^{51} +(2.85185 + 4.93955i) q^{52} -2.05718 q^{53} +(4.36389 + 2.82073i) q^{54} -10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} +(3.54063 - 6.13255i) q^{58} +(0.562382 - 0.974074i) q^{59} +(-5.44282 + 0.866025i) q^{60} +(-1.56238 - 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(-9.07442 - 15.7174i) q^{65} +(3.47141 + 4.28061i) q^{66} +(-5.48345 + 9.49761i) q^{67} +(-0.760877 + 1.31788i) q^{68} +(-2.44282 - 3.01225i) q^{69} +8.69002 q^{71} +(2.23229 + 2.00422i) q^{72} +4.96690 q^{73} +(-0.500000 - 0.866025i) q^{74} +(8.76608 - 1.39480i) q^{75} +(-0.641315 + 1.11079i) q^{76} +(-3.53379 + 9.22544i) q^{78} +(2.06922 + 3.58399i) q^{79} -3.18194 q^{80} +(0.966208 + 8.94799i) q^{81} -5.60301 q^{82} +(-4.03379 - 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(-3.41423 + 5.91362i) q^{86} +(12.1127 - 1.92730i) q^{87} +(1.59097 + 2.75564i) q^{88} -0.225450 q^{89} +(-7.10301 - 6.37731i) q^{90} +(-1.11956 - 1.93914i) q^{92} +(10.2781 + 12.6740i) q^{93} +(-2.91423 + 5.04759i) q^{94} +(2.04063 - 3.53447i) q^{95} +(1.09097 + 1.34528i) 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} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} + 12 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + q^{20} + q^{22} - 7 q^{23}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 + q^5 - 2 * q^6 - 6 * q^8 - 4 * q^9 + 2 * q^10 - q^11 + 2 * q^12 + 8 * q^13 + 12 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + q^20 + q^22 - 7 * q^23 + 4 * q^24 + 2 * q^25 + 16 * q^26 - 7 * q^27 - 5 * q^29 - 3 * q^30 + 20 * q^31 + 3 * q^32 + 15 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - q^40 - 6 * q^43 + 2 * q^44 - 12 * q^45 - 14 * q^46 - 9 * q^47 + 2 * q^48 - 2 * q^50 + 12 * q^51 + 8 * q^52 - 30 * q^53 - 8 * q^54 - 26 * q^55 + 22 * q^57 + 5 * q^58 - 14 * q^59 - 15 * q^60 + 8 * q^61 + 40 * q^62 + 6 * q^64 - 12 * q^65 + 12 * q^66 + q^67 - 4 * q^68 + 3 * q^69 + 14 * q^71 + 4 * q^72 - 38 * q^73 - 3 * q^74 + 17 * q^75 - 3 * q^76 + 5 * q^78 + 5 * q^79 - 2 * q^80 + 32 * q^81 + 2 * q^83 - 2 * q^85 + 6 * q^86 + 63 * q^87 + q^88 + 18 * q^89 - 9 * q^90 - 7 * q^92 + q^93 + 9 * q^94 - 4 * q^95 - 2 * q^96 + 28 * q^97 - 3 * q^99

Character values

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

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

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
$3$	−0.619562	+	1.61745i	−0.357704	+	0.933835i
$3$	−0.619562	+	1.61745i	−0.357704	+	0.933835i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	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
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.23229	−	2.00422i	−0.744096	−	0.668073i
$10$	3.18194			1.00622
$11$	−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	$0.992586\pi$
$12$	−1.09097	−	1.34528i	−0.314936	−	0.388349i
$13$	2.85185	−	4.93955i	0.790960	−	1.36998i	−0.134412	−	0.990925i	$-0.542915\pi$
$13$	2.85185	−	4.93955i	0.790960	−	1.36998i	0.925373	−	0.379058i	$-0.123752\pi$
$14$		0			0
$15$	3.47141	+	4.28061i	0.896314	+	1.10525i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.52175			0.369079			0.184540	−	0.982825i	$-0.440921\pi$
$17$	1.52175			0.369079			0.184540	+	0.982825i	$0.440921\pi$
$18$	0.619562	−	2.93533i	0.146032	−	0.691863i
$19$	1.28263			0.294256			0.147128	−	0.989117i	$-0.452997\pi$
$19$	1.28263			0.294256			0.147128	+	0.989117i	$0.452997\pi$
$20$	1.59097	+	2.75564i	0.355752	+	0.616181i
$21$		0			0
$22$	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	$0.241666\pi$
$24$	0.619562	−	1.61745i	0.126467	−	0.330161i
$25$	−2.56238	−	4.43818i	−0.512476	−	0.887635i
$26$	5.70370			1.11859
$27$	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	$-0.395043\pi$
$30$	−1.97141	+	5.14663i	−0.359929	+	0.939642i
$31$	4.71053	−	8.15888i	0.846037	−	1.46538i	−0.0386810	−	0.999252i	$-0.512316\pi$
$31$	4.71053	−	8.15888i	0.846037	−	1.46538i	0.884718	−	0.466127i	$-0.154351\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	5.44282	−	0.866025i	0.947473	−	0.150756i
$34$	0.760877	+	1.31788i	0.130489	+	0.226014i
$35$		0			0
$36$	2.85185	−	0.931107i	0.475308	−	0.155185i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	0.641315	+	1.11079i	0.104035	+	0.180194i
$39$	6.22257	+	7.67307i	0.996409	+	1.22868i
$40$	−1.59097	+	2.75564i	−0.251555	+	0.435706i
$41$	−2.80150	+	4.85235i	−0.437522	+	0.757810i	−0.997498	−	0.0706992i	$-0.977477\pi$
$41$	−2.80150	+	4.85235i	−0.437522	+	0.757810i	0.559976	+	0.828509i	$0.310810\pi$
$42$		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	$0.659017\pi$
$44$	3.18194			0.479696
$45$	−9.07442	+	2.96273i	−1.35273	+	0.441658i
$46$	−2.23912			−0.330141
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	0.996428	−	0.0844432i	$-0.0269112\pi$
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	−0.571344	+	0.820711i	$0.693578\pi$
$48$	1.71053	−	0.272169i	0.246894	−	0.0392842i
$49$		0			0
$50$	2.56238	−	4.43818i	0.362375	−	0.627653i
$51$	−0.942820	+	2.46136i	−0.132021	+	0.344659i
$52$	2.85185	+	4.93955i	0.395480	+	0.684992i
$53$	−2.05718			−0.282575			−0.141288	−	0.989969i	$-0.545124\pi$
$53$	−2.05718			−0.282575			−0.141288	+	0.989969i	$0.545124\pi$
$54$	4.36389	+	2.82073i	0.593850	+	0.383852i
$55$	−10.1248			−1.36522
$56$		0			0
$57$	−0.794668	+	2.07459i	−0.105256	+	0.274786i
$58$	3.54063	−	6.13255i	0.464907	−	0.805243i
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	−0.827093	−	0.562065i	$-0.810007\pi$
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	0.900309	+	0.435251i	$0.143340\pi$
$60$	−5.44282	+	0.866025i	−0.702665	+	0.111803i
$61$	−1.56238	−	2.70612i	−0.200042	−	0.346484i	0.748499	−	0.663135i	$-0.230775\pi$
$61$	−1.56238	−	2.70612i	−0.200042	−	0.346484i	−0.948542	+	0.316652i	$0.897441\pi$
$62$	9.42107			1.19648
$63$		0			0
$64$	1.00000			0.125000
$65$	−9.07442	−	15.7174i	−1.12554	−	1.94950i
$66$	3.47141	+	4.28061i	0.427301	+	0.526906i
$67$	−5.48345	+	9.49761i	−0.669910	+	1.16032i	0.308019	+	0.951380i	$0.400334\pi$
$67$	−5.48345	+	9.49761i	−0.669910	+	1.16032i	−0.977929	+	0.208938i	$0.932999\pi$
$68$	−0.760877	+	1.31788i	−0.0922699	+	0.159816i
$69$	−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	$0.327548\pi$
$72$	2.23229	+	2.00422i	0.263078	+	0.236200i
$73$	4.96690			0.581331			0.290666	−	0.956825i	$-0.406123\pi$
$73$	4.96690			0.581331			0.290666	+	0.956825i	$0.406123\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	8.76608	−	1.39480i	1.01222	−	0.161058i
$76$	−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	0.958633	−	0.284646i	$-0.0918762\pi$
$79$	2.06922	+	3.58399i	0.232805	+	0.403231i	−0.725827	+	0.687877i	$0.758543\pi$
$80$	−3.18194			−0.355752
$81$	0.966208	+	8.94799i	0.107356	+	0.994221i
$82$	−5.60301			−0.618749
$83$	−4.03379	−	6.98673i	−0.442766	−	0.766893i	0.555127	−	0.831765i	$-0.312669\pi$
$83$	−4.03379	−	6.98673i	−0.442766	−	0.766893i	−0.997894	+	0.0648718i	$0.979336\pi$
$84$		0			0
$85$	2.42107	−	4.19341i	0.262602	−	0.454839i
$86$	−3.41423	+	5.91362i	−0.368166	+	0.637682i
$87$	12.1127	−	1.92730i	1.29862	−	0.206628i
$88$	1.59097	+	2.75564i	0.169598	+	0.293753i
$89$	−0.225450			−0.0238977			−0.0119488	−	0.999929i	$-0.503804\pi$
$89$	−0.225450			−0.0238977			−0.0119488	+	0.999929i	$0.503804\pi$
$90$	−7.10301	−	6.37731i	−0.748723	−	0.672228i
$91$		0			0
$92$	−1.11956	−	1.93914i	−0.116722	−	0.202169i
$93$	10.2781	+	12.6740i	1.06579	+	1.31423i
$94$	−2.91423	+	5.04759i	−0.300580	+	0.520620i
$95$	2.04063	−	3.53447i	0.209364	−	0.362629i
$96$	1.09097	+	1.34528i	0.111347	+	0.137302i
$97$	7.42107	+	12.8537i	0.753495	+	1.30509i	0.946119	+	0.323819i	$0.104967\pi$
$97$	7.42107	+	12.8537i	0.753495	+	1.30509i	−0.192624	+	0.981273i	$0.561700\pi$
$98$		0			0
$99$	−1.97141	+	9.34004i	−0.198134	+	0.938710i
$100$	5.12476			0.512476
$101$	−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	$-0.542480\pi$
$102$	−2.60301	+	0.414174i	−0.257736	+	0.0410093i
$103$	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
$105$		0			0
$106$	−1.02859	−	1.78157i	−0.0999055	−	0.173041i
$107$	−11.3776			−1.09991			−0.549955	−	0.835194i	$-0.685355\pi$
$107$	−11.3776			−1.09991			−0.549955	+	0.835194i	$0.685355\pi$
$108$	−0.260877	+	5.18960i	−0.0251029	+	0.499369i
$109$	4.42107			0.423461			0.211731	−	0.977328i	$-0.432090\pi$
$109$	4.42107			0.423461			0.211731	+	0.977328i	$0.432090\pi$
$110$	−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	$0.214988\pi$
$114$	−2.19398	+	0.349092i	−0.205485	+	0.0326954i
$115$	3.56238	+	6.17023i	0.332194	+	0.575377i
$116$	7.08126			0.657478
$117$	−16.2661	+	5.31075i	−1.50380	+	0.490979i
$118$	1.12476			0.103543
$119$		0			0
$120$	−3.47141	−	4.28061i	−0.316895	−	0.390764i
$121$	0.437618	−	0.757977i	0.0397835	−	0.0689070i
$122$	1.56238	−	2.70612i	0.141451	−	0.245001i
$123$	−6.11273	−	7.53762i	−0.551166	−	0.679645i
$124$	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
$129$	−11.6803	+	1.85849i	−1.02839	+	0.163631i
$130$	9.07442	−	15.7174i	0.795879	−	1.37850i
$131$	−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
$133$		0			0
$134$	−10.9669			−0.947396
$135$	0.830095	−	16.5130i	0.0714432	−	1.42121i
$136$	−1.52175			−0.130489
$137$	−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	$0.870696\pi$
$138$	1.38727	−	3.62167i	0.118093	−	0.308297i
$139$	−3.98345	+	6.89953i	−0.337872	+	0.585211i	−0.984032	−	0.177991i	$-0.943040\pi$
$139$	−3.98345	+	6.89953i	−0.337872	+	0.585211i	0.646161	+	0.763202i	$0.276374\pi$
$140$		0			0
$141$	−9.96978	+	1.58632i	−0.839607	+	0.133593i
$142$	4.34501	+	7.52578i	0.364625	+	0.631550i
$143$	−18.1488			−1.51768
$144$	−0.619562	+	2.93533i	−0.0516301	+	0.244611i
$145$	−22.5322			−1.87119
$146$	2.48345	+	4.30146i	0.205532	+	0.355991i
$147$		0			0
$148$	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	$-0.235107\pi$
$150$	5.59097	+	6.89425i	0.456501	+	0.562913i
$151$	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	$0.726085\pi$
$152$	−1.28263			−0.104035
$153$	−3.39699	−	3.04993i	−0.274630	−	0.246572i
$154$		0			0
$155$	−14.9887	−	25.9611i	−1.20392	−	2.08525i
$156$	−9.75636	+	1.55237i	−0.781134	+	0.124289i
$157$	5.63160	−	9.75422i	0.449451	−	0.778471i	−0.548900	−	0.835888i	$-0.684953\pi$
$157$	5.63160	−	9.75422i	0.449451	−	0.778471i	0.998350	+	0.0574170i	$0.0182864\pi$
$158$	−2.06922	+	3.58399i	−0.164618	+	0.285127i
$159$	1.27455	−	3.32738i	0.101078	−	0.263879i
$160$	−1.59097	−	2.75564i	−0.125777	−	0.217853i
$161$		0			0
$162$	−7.26608	+	5.31075i	−0.570877	+	0.417252i
$163$	3.98057			0.311782			0.155891	−	0.987774i	$-0.450175\pi$
$163$	3.98057			0.311782			0.155891	+	0.987774i	$0.450175\pi$
$164$	−2.80150	−	4.85235i	−0.218761	−	0.378905i
$165$	6.27292	−	16.3763i	0.488346	−	1.27489i
$166$	4.03379	−	6.98673i	0.313083	−	0.542276i
$167$	2.61956	−	4.53721i	0.202708	−	0.351100i	−0.746692	−	0.665170i	$-0.768359\pi$
$167$	2.61956	−	4.53721i	0.202708	−	0.351100i	0.949400	+	0.314070i	$0.101693\pi$
$168$		0			0
$169$	−9.76608	−	16.9153i	−0.751237	−	1.30118i
$170$	4.84213			0.371375
$171$	−2.86320	−	2.57067i	−0.218954	−	0.196584i
$172$	−6.82846			−0.520665
$173$	−1.27579	−	2.20974i	−0.0969968	−	0.168003i	0.813443	−	0.581644i	$-0.197590\pi$
$173$	−1.27579	−	2.20974i	−0.0969968	−	0.168003i	−0.910440	+	0.413641i	$0.864257\pi$
$174$	7.72545	+	9.52628i	0.585665	+	0.722185i
$175$		0			0
$176$	−1.59097	+	2.75564i	−0.119924	+	0.207714i
$177$	1.22708	+	1.51312i	0.0922334	+	0.113733i
$178$	−0.112725	−	0.195246i	−0.00844910	−	0.0146343i
$179$	−7.03775			−0.526026			−0.263013	−	0.964792i	$-0.584716\pi$
$179$	−7.03775			−0.526026			−0.263013	+	0.964792i	$0.584716\pi$
$180$	1.97141	−	9.34004i	0.146940	−	0.696166i
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$		0			0
$183$	5.34501	−	0.850463i	0.395115	−	0.0628680i
$184$	1.11956	−	1.93914i	0.0825352	−	0.142955i
$185$	−1.59097	+	2.75564i	−0.116971	+	0.202599i
$186$	−5.83693	+	15.2381i	−0.427985	+	1.11731i
$187$	−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	0.827972	−	0.560769i	$-0.189495\pi$
$191$	−0.990285	−	1.71522i	−0.0716545	−	0.124109i	−0.899627	+	0.436660i	$0.856161\pi$
$192$	−0.619562	+	1.61745i	−0.0447130	+	0.116729i
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	−0.772552	−	0.634951i	$-0.781020\pi$
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	0.936160	+	0.351574i	$0.114353\pi$
$194$	−7.42107	+	12.8537i	−0.532802	+	0.922839i
$195$	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	$0.783320\pi$
$198$	−9.07442	+	2.96273i	−0.644891	+	0.210552i
$199$	−12.2826			−0.870693			−0.435346	−	0.900263i	$-0.643374\pi$
$199$	−12.2826			−0.870693			−0.435346	+	0.900263i	$0.643374\pi$
$200$	2.56238	+	4.43818i	0.181188	+	0.313826i
$201$	−11.9646	−	14.7536i	−0.843916	−	1.04064i
$202$	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
$206$	0.282630			0.0196918
$207$	6.38564	−	2.08486i	0.443833	−	0.144908i
$208$	−5.70370			−0.395480
$209$	−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	$0.972308\pi$
$212$	1.02859	−	1.78157i	0.0706438	−	0.122359i
$213$	−5.38401	+	14.0557i	−0.368906	+	0.963079i
$214$	−5.68878	−	9.85326i	−0.388877	−	0.673555i
$215$	21.7278			1.48182
$216$	−4.62476	+	2.36887i	−0.314675	+	0.161181i
$217$		0			0
$218$	2.21053	+	3.82876i	0.149716	+	0.259316i
$219$	−3.07730	+	8.03371i	−0.207945	+	0.542867i
$220$	5.06238	−	8.76830i	0.341306	−	0.591159i
$221$	4.33981	−	7.51677i	0.291927	−	0.505633i
$222$	1.71053	−	0.272169i	0.114803	−	0.0182668i
$223$	−5.32846	−	9.22916i	−0.356820	−	0.618031i	0.630608	−	0.776102i	$-0.282806\pi$
$223$	−5.32846	−	9.22916i	−0.356820	−	0.618031i	−0.987428	+	0.158071i	$0.949472\pi$
$224$		0			0
$225$	−3.17511	+	15.0429i	−0.211674	+	1.00286i
$226$	−3.21505			−0.213862
$227$	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	$0.673437\pi$
$228$	−1.39931	−	1.72550i	−0.0926718	−	0.114274i
$229$	−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
$231$		0			0
$232$	3.54063	+	6.13255i	0.232454	+	0.402622i
$233$	−1.08126			−0.0708355			−0.0354177	−	0.999373i	$-0.511276\pi$
$233$	−1.08126			−0.0708355			−0.0354177	+	0.999373i	$0.511276\pi$
$234$	−12.7323	−	11.4315i	−0.832336	−	0.747298i
$235$	18.5458			1.20980
$236$	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	$0.297125\pi$
$240$	1.97141	−	5.14663i	0.127254	−	0.332214i
$241$	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	$0.695819\pi$
$242$	0.875237			0.0562623
$243$	−15.0715	−	3.98104i	−0.966840	−	0.255384i
$244$	3.12476			0.200042
$245$		0			0
$246$	3.47141	−	9.06259i	0.221329	−	0.577809i
$247$	3.65787	−	6.33561i	0.232744	−	0.403125i
$248$	−4.71053	+	8.15888i	−0.299119	+	0.518090i
$249$	13.7999	−	2.19574i	0.874531	−	0.139150i
$250$	−0.198495	−	0.343803i	−0.0125539	−	0.0217440i
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$	10.0527	+	17.4117i	0.630760	+	1.09251i
$255$	5.28263	+	6.51403i	0.330811	+	0.407924i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−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
$259$		0			0
$260$	18.1488			1.12554
$261$	−4.38727	+	20.7858i	−0.271565	+	1.28661i
$262$	−6.36389			−0.393162
$263$	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	$0.802914\pi$
$264$	−5.44282	+	0.866025i	−0.334982	+	0.0533002i
$265$	−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
$269$	26.8903			1.63953			0.819765	−	0.572700i	$-0.194104\pi$
$269$	26.8903			1.63953			0.819765	+	0.572700i	$0.194104\pi$
$270$	14.7157	−	7.53762i	0.895571	−	0.458725i
$271$	22.2164			1.34955			0.674776	−	0.738023i	$-0.264240\pi$
$271$	22.2164			1.34955			0.674776	+	0.738023i	$0.264240\pi$
$272$	−0.760877	−	1.31788i	−0.0461349	−	0.0799080i
$273$		0			0
$274$	1.37072	−	2.37416i	0.0828084	−	0.143428i
$275$	−8.15335	+	14.1220i	−0.491666	+	0.851590i
$276$	3.83009	−	0.609419i	0.230545	−	0.0366827i
$277$	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	$0.688404\pi$
$278$	−7.96690			−0.477823
$279$	−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	$0.587445\pi$
$282$	−6.35868	−	7.84092i	−0.378654	−	0.466920i
$283$	13.0624	−	22.6247i	0.776478	−	1.34490i	−0.157482	−	0.987522i	$-0.550338\pi$
$283$	13.0624	−	22.6247i	0.776478	−	1.34490i	0.933960	−	0.357377i	$-0.116329\pi$
$284$	−4.34501	+	7.52578i	−0.257829	+	0.446573i
$285$	4.45254	+	5.49044i	0.263745	+	0.325225i
$286$	−9.07442	−	15.7174i	−0.536582	−	0.929387i
$287$		0			0
$288$	−2.85185	+	0.931107i	−0.168047	+	0.0548660i
$289$	−14.6843			−0.863780
$290$	−11.2661	−	19.5134i	−0.661567	−	1.14587i
$291$	−25.3880	+	4.03956i	−1.48827	+	0.236803i
$292$	−2.48345	+	4.30146i	−0.145333	+	0.251724i
$293$	12.9315	−	22.3980i	0.755465	−	1.30850i	−0.189678	−	0.981846i	$-0.560745\pi$
$293$	12.9315	−	22.3980i	0.755465	−	1.30850i	0.945143	−	0.326657i	$-0.105922\pi$
$294$		0			0
$295$	−1.78947	−	3.09945i	−0.104187	−	0.180457i
$296$	1.00000			0.0581238
$297$	−13.8856	−	8.97539i	−0.805727	−	0.520805i
$298$	23.2599			1.34741
$299$	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
$303$	31.7977	−	5.05944i	1.82673	−	0.290657i
$304$	−0.641315	−	1.11079i	−0.0367819	−	0.0637082i
$305$	−9.94282			−0.569324
$306$	0.942820	−	4.46684i	0.0538974	−	0.255352i
$307$	3.53216			0.201591			0.100795	−	0.994907i	$-0.467861\pi$
$307$	3.53216			0.201591			0.100795	+	0.994907i	$0.467861\pi$
$308$		0			0
$309$	0.308342	+	0.380217i	0.0175409	+	0.0216298i
$310$	14.9887	−	25.9611i	0.851298	−	1.47449i
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	−0.889166	−	0.457584i	$-0.848715\pi$
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	0.840863	+	0.541249i	$0.182048\pi$
$312$	−6.22257	−	7.67307i	−0.352284	−	0.434402i
$313$	1.42107	+	2.46136i	0.0803234	+	0.139124i	0.903389	−	0.428822i	$-0.141071\pi$
$313$	1.42107	+	2.46136i	0.0803234	+	0.139124i	−0.823065	+	0.567947i	$0.807738\pi$
$314$	11.2632			0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	12.4601	+	21.5815i	0.699827	+	1.21214i	0.968526	+	0.248911i	$0.0800728\pi$
$317$	12.4601	+	21.5815i	0.699827	+	1.21214i	−0.268700	+	0.963224i	$0.586594\pi$
$318$	3.51887	−	0.559900i	0.197329	−	0.0313976i
$319$	−11.2661	+	19.5134i	−0.630779	+	1.09254i
$320$	1.59097	−	2.75564i	0.0889380	−	0.154045i
$321$	7.04910	−	18.4026i	0.393442	−	1.02713i
$322$		0			0
$323$	1.95185			0.108604
$324$	−8.23229	−	3.63723i	−0.457349	−	0.202068i
$325$	−29.2301			−1.62139
$326$	1.99028	+	3.44727i	0.110232	+	0.190927i
$327$	−2.73912	+	7.15085i	−0.151474	+	0.395443i
$328$	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	0.947584	−	0.319506i	$-0.103517\pi$
$331$	3.58577	+	6.21074i	0.197092	+	0.341373i	−0.750492	+	0.660879i	$0.770184\pi$
$332$	8.06758			0.442766
$333$	2.23229	+	2.00422i	0.122329	+	0.109831i
$334$	5.23912			0.286672
$335$	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	$0.963855\pi$
$338$	9.76608	−	16.9153i	0.531205	−	0.920073i
$339$	−3.50752	−	4.32514i	−0.190503	−	0.234909i
$340$	2.42107	+	4.19341i	0.131301	+	0.227420i
$341$	−29.9773			−1.62336
$342$	0.794668	−	3.76494i	0.0429707	−	0.203585i
$343$		0			0
$344$	−3.41423	−	5.91362i	−0.184083	−	0.318841i
$345$	−12.1871	+	1.93914i	−0.656134	+	0.104400i
$346$	1.27579	−	2.20974i	0.0685871	−	0.118796i
$347$	1.05555	−	1.82826i	0.0566646	−	0.0981460i	−0.836302	−	0.548270i	$-0.815287\pi$
$347$	1.05555	−	1.82826i	0.0566646	−	0.0981460i	0.892966	+	0.450124i	$0.148620\pi$
$348$	−4.38727	+	11.4536i	−0.235183	+	0.613976i
$349$	18.1082	+	31.3643i	0.969310	+	1.67889i	0.697559	+	0.716527i	$0.254269\pi$
$349$	18.1082	+	31.3643i	0.969310	+	1.67889i	0.271751	+	0.962368i	$0.412397\pi$
$350$		0			0
$351$	1.48796	−	29.5999i	0.0794215	−	1.57993i
$352$	−3.18194			−0.169598
$353$	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	$0.743288\pi$
$354$	−0.696860	+	1.81925i	−0.0370377	+	0.0966919i
$355$	13.8256	−	23.9466i	0.733786	−	1.27095i
$356$	0.112725	−	0.195246i	0.00597442	−	0.0103480i
$357$		0			0
$358$	−3.51887	−	6.09487i	−0.185978	−	0.322124i
$359$	−32.4419			−1.71222			−0.856108	−	0.516796i	$-0.827124\pi$
$359$	−32.4419			−1.71222			−0.856108	+	0.516796i	$0.827124\pi$
$360$	9.07442	−	2.96273i	0.478264	−	0.156150i
$361$	−17.3549			−0.913414
$362$	−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
$366$	3.40903	+	4.20368i	0.178193	+	0.219730i
$367$	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	$0.676614\pi$
$368$	2.23912			0.116722
$369$	15.9789	−	5.21700i	0.831830	−	0.271586i
$370$	−3.18194			−0.165421
$371$		0			0
$372$	−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	$0.0689656\pi$
$374$	2.42107	−	4.19341i	0.125190	−	0.216836i
$375$	0.245960	−	0.642111i	0.0127013	−	0.0331585i
$376$	−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
$381$	−12.4565	+	32.5194i	−0.638165	+	1.66602i
$382$	0.990285	−	1.71522i	0.0506674	−	0.0877585i
$383$	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
$385$		0			0
$386$	4.54583			0.231377
$387$	4.23065	−	20.0438i	0.215056	−	1.01888i
$388$	−14.8421			−0.753495
$389$	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	$0.531196\pi$
$390$	19.7999	+	24.4153i	1.00261	+	1.23632i
$391$	−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
$395$	13.1683			0.662568
$396$	−7.10301	−	6.37731i	−0.356940	−	0.320472i
$397$	37.9338			1.90384			0.951921	−	0.306343i	$-0.0991054\pi$
$397$	37.9338			1.90384			0.951921	+	0.306343i	$0.0991054\pi$
$398$	−6.14132	−	10.6371i	−0.307836	−	0.533188i
$399$		0			0
$400$	−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	$0.252087\pi$
$402$	6.79467	−	17.7384i	0.338887	−	0.884711i
$403$	−26.8675	−	46.5358i	−1.33836	−	2.31811i
$404$	18.5893			0.924854
$405$	26.1947	+	11.5735i	1.30162	+	0.575090i
$406$		0			0
$407$	1.59097	+	2.75564i	0.0788615	+	0.136592i
$408$	0.942820	−	2.46136i	0.0466765	−	0.121855i
$409$	−2.77292	+	4.80283i	−0.137112	+	0.237485i	−0.926402	−	0.376535i	$-0.877115\pi$
$409$	−2.77292	+	4.80283i	−0.137112	+	0.237485i	0.789290	+	0.614020i	$0.210449\pi$
$410$	−8.91423	+	15.4399i	−0.440242	+	0.762522i
$411$	4.68934	−	0.746136i	0.231308	−	0.0368042i
$412$	0.141315	+	0.244765i	0.00696209	+	0.0120587i
$413$		0			0
$414$	4.99837	+	4.48769i	0.245656	+	0.220558i
$415$	−25.6706			−1.26012
$416$	−2.85185	−	4.93955i	−0.139823	−	0.242181i
$417$	−8.69166	−	10.7177i	−0.425632	−	0.524849i
$418$	2.04063	−	3.53447i	0.0998104	−	0.172877i
$419$	2.77455	−	4.80566i	0.135546	−	0.234772i	−0.790260	−	0.612772i	$-0.790055\pi$
$419$	2.77455	−	4.80566i	0.135546	−	0.234772i	0.925806	+	0.378000i	$0.123388\pi$
$420$		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	$0.886655\pi$
$422$	−16.6569			−0.810846
$423$	3.61109	−	17.1084i	0.175577	−	0.831841i
$424$	2.05718			0.0999055
$425$	−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
$429$	11.2443	−	29.3548i	0.542881	−	1.41726i
$430$	10.8639	+	18.8168i	0.523903	+	0.907427i
$431$	−33.1078			−1.59475			−0.797374	−	0.603486i	$-0.793778\pi$
$431$	−33.1078			−1.59475			−0.797374	+	0.603486i	$0.793778\pi$
$432$	−4.36389	−	2.82073i	−0.209958	−	0.135712i
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$		0			0
$435$	13.9601	−	36.4446i	0.669334	−	1.74739i
$436$	−2.21053	+	3.82876i	−0.105865	+	0.183364i
$437$	−1.43598	+	2.48720i	−0.0686924	+	0.118979i
$438$	−8.49604	+	1.35183i	−0.405957	+	0.0645931i
$439$	4.41711	+	7.65066i	0.210817	+	0.365146i	0.951970	−	0.306190i	$-0.0990542\pi$
$439$	4.41711	+	7.65066i	0.210817	+	0.365146i	−0.741153	+	0.671336i	$0.765721\pi$
$440$	10.1248			0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	−8.75924	−	15.1715i	−0.416164	−	0.720817i	0.579386	−	0.815053i	$-0.303292\pi$
$443$	−8.75924	−	15.1715i	−0.416164	−	0.720817i	−0.995550	+	0.0942360i	$0.969959\pi$
$444$	1.09097	+	1.34528i	0.0517752	+	0.0638442i
$445$	−0.358685	+	0.621261i	−0.0170033	+	0.0294506i
$446$	5.32846	−	9.22916i	0.252310	−	0.437014i
$447$	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	$0.236280\pi$
$450$	−14.6150	+	4.77170i	−0.688960	+	0.224940i
$451$	17.8285			0.839509
$452$	−1.60752	−	2.78431i	−0.0756115	−	0.130963i
$453$	−13.8977	+	2.21131i	−0.652970	+	0.103896i
$454$	−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	0.947161	+	0.320760i	$0.103938\pi$
$457$	16.0624	+	27.8209i	0.751367	+	1.30140i	−0.195794	+	0.980645i	$0.562728\pi$
$458$	−10.2495			−0.478929
$459$	7.03775	−	3.60484i	0.328494	−	0.168260i
$460$	−7.12476			−0.332194
$461$	1.23229	+	2.13438i	0.0573933	+	0.0994081i	0.893295	−	0.449472i	$-0.148388\pi$
$461$	1.23229	+	2.13438i	0.0573933	+	0.0994081i	−0.835901	+	0.548880i	$0.815054\pi$
$462$		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	$-0.0824631\pi$
$464$	−3.54063	+	6.13255i	−0.164370	+	0.284696i
$465$	51.2772	−	8.15888i	2.37792	−	0.378359i
$466$	−0.540628	−	0.936396i	−0.0250441	−	0.0433777i
$467$	15.9636			0.738709			0.369354	−	0.929289i	$-0.379579\pi$
$467$	15.9636			0.738709			0.369354	+	0.929289i	$0.379579\pi$
$468$	3.53379	−	16.7422i	0.163350	−	0.773909i
$469$		0			0
$470$	9.27292	+	16.0612i	0.427728	+	0.740846i
$471$	12.2878	+	15.1522i	0.566193	+	0.698175i
$472$	−0.562382	+	0.974074i	−0.0258857	+	0.0448354i
$473$	10.8639	−	18.8168i	0.499522	−	0.865198i
$474$	−4.51492	−	5.56736i	−0.207377	−	0.255717i
$475$	−3.28659	−	5.69254i	−0.150799	−	0.261192i
$476$		0			0
$477$	4.59222	+	4.12304i	0.210263	+	0.188781i
$478$	−12.3204			−0.563521
$479$	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	$0.655751\pi$
$480$	5.44282	−	0.866025i	0.248430	−	0.0395285i
$481$	−2.85185	+	4.93955i	−0.130033	+	0.225224i
$482$	−6.50000	+	11.2583i	−0.296067	+	0.512803i
$483$		0			0
$484$	0.437618	+	0.757977i	0.0198917	+	0.0344535i
$485$	47.2268			2.14446
$486$	−4.08809	−	15.0429i	−0.185440	−	0.682358i
$487$	−3.41315			−0.154665			−0.0773323	−	0.997005i	$-0.524640\pi$
$487$	−3.41315			−0.154665			−0.0773323	+	0.997005i	$0.524640\pi$
$488$	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	$0.309044\pi$
$492$	9.58414	−	1.52496i	0.432086	−	0.0687507i
$493$	−5.38796	−	9.33223i	−0.242662	−	0.420302i
$494$	7.31573			0.329150
$495$	22.6014	+	20.2922i	1.01586	+	0.912069i
$496$	−9.42107			−0.423018
$497$		0			0
$498$	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	$0.793629\pi$
$500$	0.198495	−	0.343803i	0.00887697	−	0.0153754i
$501$	5.71574	+	7.04809i	0.255360	+	0.314886i
$502$	2.55555	+	4.42633i	0.114060	+	0.197557i
$503$	−26.4542			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$503$	−26.4542			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$	3.56238	+	6.17023i	0.158367	+	0.274300i
$507$	33.4104	−	5.31604i	1.48381	−	0.236094i
$508$	−10.0527	+	17.4117i	−0.446015	+	0.772521i
$509$	−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
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	5.93186	−	3.03839i	0.261898	−	0.134148i
$514$	−7.66019			−0.337876
$515$	−0.449657	−	0.778828i	−0.0198142	−	0.0343193i
$516$	4.23065	−	11.0447i	0.186244	−	0.486215i
$517$	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
$521$	6.81230			0.298452			0.149226	−	0.988803i	$-0.452322\pi$
$521$	6.81230			0.298452			0.149226	+	0.988803i	$0.452322\pi$
$522$	−20.1947	+	6.59341i	−0.883897	+	0.288586i
$523$	−29.5070			−1.29025			−0.645125	−	0.764077i	$-0.723195\pi$
$523$	−29.5070			−1.29025			−0.645125	+	0.764077i	$0.723195\pi$
$524$	−3.18194	−	5.51129i	−0.139004	−	0.240762i
$525$		0			0
$526$	−1.54746	+	2.68029i	−0.0674727	+	0.116866i
$527$	7.16827	−	12.4158i	0.312255	−	0.540841i
$528$	−3.47141	−	4.28061i	−0.151074	−	0.186290i
$529$	8.99316	+	15.5766i	0.391007	+	0.677244i
$530$	−6.54583			−0.284333
$531$	−3.20765	+	1.04728i	−0.139200	+	0.0454479i
$532$		0			0
$533$	15.9789	+	27.6763i	0.692125	+	1.19879i
$534$	0.385640	−	0.0613605i	0.0166883	−	0.00265533i
$535$	−18.1014	+	31.3525i	−0.782591	+	1.35549i
$536$	5.48345	−	9.49761i	0.236849	−	0.410234i
$537$	4.36032	−	11.3832i	0.188162	−	0.491222i
$538$	13.4451	+	23.2877i	0.579661	+	1.00400i
$539$		0			0
$540$	13.8856	+	8.97539i	0.597543	+	0.386239i
$541$	−29.4016			−1.26408			−0.632038	−	0.774938i	$-0.717781\pi$
$541$	−29.4016			−1.26408			−0.632038	+	0.774938i	$0.717781\pi$
$542$	11.1082	+	19.2400i	0.477139	+	0.826428i
$543$	8.03379	−	20.9733i	0.344763	−	0.900051i
$544$	0.760877	−	1.31788i	0.0326223	−	0.0565035i
$545$	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	$0.561859\pi$
$548$	2.74145			0.117109
$549$	−1.93598	+	9.17220i	−0.0826258	+	0.391460i
$550$	−16.3067			−0.695320
$551$	−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
$555$	−3.47141	−	4.28061i	−0.147353	−	0.181702i
$556$	−3.98345	−	6.89953i	−0.168936	−	0.292605i
$557$	6.73818			0.285506			0.142753	−	0.989758i	$-0.454405\pi$
$557$	6.73818			0.285506			0.142753	+	0.989758i	$0.454405\pi$
$558$	−21.0305	−	18.8819i	−0.890293	−	0.799334i
$559$	38.9475			1.64730
$560$		0			0
$561$	8.28263	−	1.31788i	0.349693	−	0.0556408i
$562$	−11.6992	+	20.2636i	−0.493500	+	0.854768i
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	−0.850233	−	0.526406i	$-0.823539\pi$
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	0.880998	+	0.473121i	$0.156873\pi$
$564$	3.61109	−	9.42724i	0.152054	−	0.396958i
$565$	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	0.584792	−	0.811183i	$-0.301176\pi$
$569$	−9.78263	−	16.9440i	−0.410109	−	0.710330i	−0.994901	+	0.100853i	$0.967843\pi$
$570$	−2.52859	+	6.60123i	−0.105911	+	0.276495i
$571$	10.9629	−	18.9884i	0.458785	−	0.794638i	−0.540112	−	0.841593i	$-0.681618\pi$
$571$	10.9629	−	18.9884i	0.458785	−	0.794638i	0.998897	+	0.0469545i	$0.0149516\pi$
$572$	9.07442	−	15.7174i	0.379421	−	0.657176i
$573$	3.38783	−	0.539049i	0.141529	−	0.0225191i
$574$		0			0
$575$	11.4750			0.478540
$576$	−2.23229	−	2.00422i	−0.0930119	−	0.0835091i
$577$	−24.7310			−1.02957			−0.514783	−	0.857320i	$-0.672128\pi$
$577$	−24.7310			−1.02957			−0.514783	+	0.857320i	$0.672128\pi$
$578$	−7.34213	−	12.7169i	−0.305392	−	0.528955i
$579$	4.95937	+	6.11542i	0.206104	+	0.254148i
$580$	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
$584$	−4.96690			−0.205532
$585$	−11.2443	+	53.2728i	−0.464896	+	2.20256i
$586$	25.8629			1.06839
$587$	−18.0796	−	31.3148i	−0.746226	−	1.29250i	−0.949620	−	0.313404i	$-0.898531\pi$
$587$	−18.0796	−	31.3148i	−0.746226	−	1.29250i	0.203394	−	0.979097i	$-0.434803\pi$
$588$		0			0
$589$	6.04187	−	10.4648i	0.248951	−	0.431196i
$590$	1.78947	−	3.09945i	0.0736712	−	0.127602i
$591$	13.5156	−	35.2843i	0.555958	−	1.45140i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	15.1078			0.620404			0.310202	−	0.950671i	$-0.399603\pi$
$593$	15.1078			0.620404			0.310202	+	0.950671i	$0.399603\pi$
$594$	0.830095	−	16.5130i	0.0340592	−	0.677537i
$595$		0			0
$596$	11.6300	+	20.1437i	0.476382	+	0.825118i
$597$	7.60985	−	19.8665i	0.311450	−	0.813083i
$598$	−6.38564	+	11.0603i	−0.261128	+	0.452287i
$599$	2.72708	−	4.72345i	0.111426	−	0.192995i	−0.804920	−	0.593384i	$-0.797792\pi$
$599$	2.72708	−	4.72345i	0.111426	−	0.192995i	0.916345	+	0.400389i	$0.131125\pi$
$600$	−8.76608	+	1.39480i	−0.357874	+	0.0569425i
$601$	−3.36840	−	5.83424i	−0.137400	−	0.237984i	0.789112	−	0.614250i	$-0.210541\pi$
$601$	−3.36840	−	5.83424i	−0.137400	−	0.237984i	−0.926512	+	0.376266i	$0.877208\pi$
$602$		0			0
$603$	31.2759	−	10.2114i	1.27365	−	0.415839i
$604$	−8.12476			−0.330592
$605$	−1.39248	−	2.41184i	−0.0566122	−	0.0980553i
$606$	20.2804	+	25.0079i	0.823837	+	1.01588i
$607$	−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
$609$		0			0
$610$	−4.97141	−	8.61073i	−0.201287	−	0.348638i
$611$	33.2438			1.34490
$612$	4.33981	−	1.41692i	0.175426	−	0.0572754i
$613$	−1.30998			−0.0529094			−0.0264547	−	0.999650i	$-0.508422\pi$
$613$	−1.30998			−0.0529094			−0.0264547	+	0.999650i	$0.508422\pi$
$614$	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	$-0.0776589\pi$
$618$	−0.175107	+	0.457140i	−0.00704383	+	0.0183889i
$619$	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	$0.726096\pi$
$620$	29.9773			1.20392
$621$	−0.584135	+	11.6202i	−0.0234405	+	0.466301i
$622$	−1.70370			−0.0683120
$623$		0			0
$624$	3.53379	−	9.22544i	0.141465	−	0.369313i
$625$	12.1803	−	21.0969i	0.487212	−	0.843877i
$626$	−1.42107	+	2.46136i	−0.0567972	+	0.0983757i
$627$	6.98113	−	1.11079i	0.278799	−	0.0443607i
$628$	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
$633$	−18.1722	−	22.4082i	−0.722281	−	0.890647i
$634$	−12.4601	+	21.5815i	−0.494852	+	0.857109i
$635$	31.9870	−	55.4031i	1.26937	−	2.19861i
$636$	2.24433	+	2.76748i	0.0889933	+	0.109738i
$637$		0			0
$638$	−22.5322			−0.892057
$639$	−19.3986	−	17.4167i	−0.767398	−	0.688995i
$640$	3.18194			0.125777
$641$	−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	$-0.352412\pi$
$642$	19.4617	−	3.09662i	0.768092	−	0.122214i
$643$	14.2524	−	24.6859i	0.562060	−	0.973516i	−0.435257	−	0.900306i	$-0.643342\pi$
$643$	14.2524	−	24.6859i	0.562060	−	0.973516i	0.997317	−	0.0732100i	$-0.0233243\pi$
$644$		0			0
$645$	−13.4617	+	35.1436i	−0.530054	+	1.38378i
$646$	0.975923	+	1.69035i	0.0383972	+	0.0665059i
$647$	−16.7141			−0.657099			−0.328550	−	0.944487i	$-0.606560\pi$
$647$	−16.7141			−0.657099			−0.328550	+	0.944487i	$0.606560\pi$
$648$	−0.966208	−	8.94799i	−0.0379562	−	0.351510i
$649$	−3.57893			−0.140485
$650$	−14.6150	−	25.3140i	−0.573249	−	0.992897i
$651$		0			0
$652$	−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	$0.898277\pi$
$654$	−7.56238	+	1.20328i	−0.295713	+	0.0470518i
$655$	10.1248	+	17.5366i	0.395607	+	0.685212i
$656$	5.60301			0.218761
$657$	−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	$0.778873\pi$
$660$	11.0458	+	13.6207i	0.429958	+	0.530183i
$661$	10.0419	−	17.3930i	0.390584	−	0.676511i	−0.601943	−	0.798539i	$-0.705607\pi$
$661$	10.0419	−	17.3930i	0.390584	−	0.676511i	0.992527	+	0.122028i	$0.0389399\pi$
$662$	−3.58577	+	6.21074i	−0.139365	+	0.241387i
$663$	9.46922	+	11.6765i	0.367754	+	0.453479i
$664$	4.03379	+	6.98673i	0.156541	+	0.271138i
$665$		0			0
$666$	−0.619562	+	2.93533i	−0.0240075	+	0.113742i
$667$	15.8558			0.613939
$668$	2.61956	+	4.53721i	0.101354	+	0.175550i
$669$	18.2290	−	2.90048i	0.704775	−	0.112139i
$670$	−17.4480	+	30.2209i	−0.674076	+	1.16753i
$671$	−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	$-0.394554\pi$
$674$	−21.8421			−0.841328
$675$	−22.3639	−	14.4556i	−0.860786	−	0.556394i
$676$	19.5322			0.751237
$677$	0.358685	+	0.621261i	0.0137854	+	0.0238770i	0.872836	−	0.488014i	$-0.162279\pi$
$677$	0.358685	+	0.621261i	0.0137854	+	0.0238770i	−0.859050	+	0.511891i	$0.828945\pi$
$678$	1.99192	−	5.20018i	0.0764992	−	0.199712i
$679$		0			0
$680$	−2.42107	+	4.19341i	−0.0928437	+	0.160810i
$681$	−24.8166	+	3.94865i	−0.950972	+	0.151312i
$682$	−14.9887	−	25.9611i	−0.573945	−	0.994102i
$683$	21.0539			0.805605			0.402803	−	0.915287i	$-0.368036\pi$
$683$	21.0539			0.805605			0.402803	+	0.915287i	$0.368036\pi$
$684$	3.65787	−	1.19427i	0.139862	−	0.0456639i
$685$	−8.72313			−0.333294
$686$		0			0
$687$	−11.1819	−	13.7885i	−0.426618	−	0.526064i
$688$	3.41423	−	5.91362i	0.130166	−	0.225455i
$689$	−5.86677	+	10.1615i	−0.223506	+	0.387124i
$690$	−7.77292	−	9.58481i	−0.295910	−	0.364887i
$691$	−2.92395	−	5.06442i	−0.111232	−	0.192660i	0.805035	−	0.593227i	$-0.202146\pi$
$691$	−2.92395	−	5.06442i	−0.111232	−	0.192660i	−0.916267	+	0.400567i	$0.868813\pi$
$692$	2.55159			0.0969968
$693$		0			0
$694$	2.11109			0.0801359
$695$	12.6751	+	21.9539i	0.480794	+	0.832760i
$696$	−12.1127	+	1.92730i	−0.459132	+	0.0730540i
$697$	−4.26320	+	7.38408i	−0.161480	+	0.279692i
$698$	−18.1082	+	31.3643i	−0.685406	+	1.18716i
$699$	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	$0.437864\pi$
$702$	26.3782	−	13.5113i	0.995583	−	0.509953i
$703$	−1.28263			−0.0483753
$704$	−1.59097	−	2.75564i	−0.0599620	−	0.103857i
$705$	−11.4903	+	29.9969i	−0.432749	+	1.12975i
$706$	−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	−0.908200	−	0.418538i	$-0.862543\pi$
$709$	−21.7427	−	37.6594i	−0.816564	−	1.41433i	0.0916356	−	0.995793i	$-0.470790\pi$
$710$	27.6512			1.03773
$711$	2.56402	−	12.1477i	0.0961581	−	0.455573i
$712$	0.225450			0.00844910
$713$	10.5475	+	18.2687i	0.395006	+	0.684170i
$714$		0			0
$715$	−28.8743	+	50.0117i	−1.07984	+	1.87033i
$716$	3.51887	−	6.09487i	0.131507	−	0.227776i
$717$	−13.4412	−	16.5744i	−0.501970	−	0.618981i
$718$	−16.2209	−	28.0955i	−0.605360	−	1.04851i
$719$	−50.8824			−1.89759			−0.948796	−	0.315889i	$-0.897697\pi$
$719$	−50.8824			−1.89759			−0.948796	+	0.315889i	$0.897697\pi$
$720$	7.10301	+	6.37731i	0.264714	+	0.237668i
$721$		0			0
$722$	−8.67743	−	15.0297i	−0.322941	−	0.559349i
$723$	−22.2369	+	3.53819i	−0.827000	+	0.131587i
$724$	6.48345	−	11.2297i	0.240955	−	0.417347i
$725$	−18.1449	+	31.4279i	−0.673884	+	1.16720i
$726$	−0.542263	+	1.41565i	−0.0201253	+	0.0525397i
$727$	6.07210	+	10.5172i	0.225202	+	0.390061i	0.956380	−	0.292126i	$-0.0943626\pi$
$727$	6.07210	+	10.5172i	0.225202	+	0.390061i	−0.731178	+	0.682186i	$0.761029\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$	15.8044			0.584946
$731$	5.19562	+	8.99907i	0.192167	+	0.332843i
$732$	−1.93598	+	5.05415i	−0.0715560	+	0.186807i
$733$	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
$735$		0			0
$736$	1.11956	+	1.93914i	0.0412676	+	0.0714776i
$737$	34.8960			1.28541
$738$	12.5075	+	11.2297i	0.460408	+	0.413370i
$739$	4.99208			0.183637			0.0918184	−	0.995776i	$-0.470732\pi$
$739$	4.99208			0.183637			0.0918184	+	0.995776i	$0.470732\pi$
$740$	−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	$0.971202\pi$
$744$	−10.2781	−	12.6740i	−0.376814	−	0.464651i
$745$	−37.0059	−	64.0961i	−1.35579	−	2.34830i
$746$	11.6706			0.427291
$747$	−4.99837	+	23.6810i	−0.182881	+	0.866442i
$748$	4.84213			0.177046
$749$		0			0
$750$	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	$0.185822\pi$
$752$	2.91423	−	5.04759i	0.106271	−	0.184067i
$753$	−3.16664	+	8.26693i	−0.115399	+	0.301264i
$754$	−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
$759$	−4.41423	+	11.5239i	−0.160226	+	0.418293i
$760$	−2.04063	+	3.53447i	−0.0740214	+	0.128209i
$761$	−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
$763$		0			0
$764$	1.98057			0.0716545
$765$	−13.8090	+	4.50855i	−0.499267	+	0.163007i
$766$	1.64979			0.0596092
$767$	−3.20765	−	5.55582i	−0.115822	−	0.200609i
$768$	−1.09097	−	1.34528i	−0.0393670	−	0.0485436i
$769$	11.3461	−	19.6520i	0.409151	−	0.708669i	−0.585644	−	0.810568i	$-0.699158\pi$
$769$	11.3461	−	19.6520i	0.409151	−	0.708669i	0.994795	+	0.101899i	$0.0324918\pi$
$770$		0			0
$771$	−8.35705	−	10.3051i	−0.300972	−	0.371129i
$772$	2.27292	+	3.93680i	0.0818040	+	0.141689i
$773$	−0.655544			−0.0235783			−0.0117891	−	0.999931i	$-0.503753\pi$
$773$	−0.655544			−0.0235783			−0.0117891	+	0.999931i	$0.503753\pi$
$774$	19.4737	−	6.35803i	0.699969	−	0.228535i
$775$	−48.2807			−1.73430
$776$	−7.42107	−	12.8537i	−0.266401	−	0.461420i
$777$		0			0
$778$	−16.0338	+	27.7713i	−0.574839	+	0.995651i
$779$	−3.59329	+	6.22377i	−0.128743	+	0.222990i
$780$	−11.2443	+	29.3548i	−0.402611	+	1.05107i
$781$	−13.8256	−	23.9466i	−0.494718	−	0.856877i
$782$	−3.40739			−0.121848
$783$	−30.9018	−	19.9743i	−1.10434	−	0.713823i
$784$		0			0
$785$	−17.9194	−	31.0374i	−0.639572	−	1.10777i
$786$	3.94282	−	10.2933i	0.140636	−	0.367149i
$787$	−0.270036	+	0.467717i	−0.00962576	+	0.0166723i	−0.870798	−	0.491641i	$-0.836397\pi$
$787$	−0.270036	+	0.467717i	−0.00962576	+	0.0166723i	0.861172	+	0.508313i	$0.169731\pi$
$788$	10.9074	−	18.8922i	0.388560	−	0.673005i
$789$	−5.29398	+	0.842343i	−0.188471	+	0.0299882i
$790$	6.58414	+	11.4041i	0.234253	+	0.405738i
$791$		0			0
$792$	1.97141	−	9.34004i	0.0700510	−	0.331884i
$793$	−17.8227			−0.632903
$794$	18.9669	+	32.8516i	0.673110	+	1.16586i
$795$	−7.14132	−	8.80598i	−0.253276	−	0.312316i
$796$	6.14132	−	10.6371i	0.217673	−	0.377021i
$797$	−12.5550	+	21.7459i	−0.444721	+	0.770279i	−0.998033	−	0.0626954i	$-0.980030\pi$
$797$	−12.5550	+	21.7459i	−0.444721	+	0.770279i	0.553312	+	0.832974i	$0.313364\pi$
$798$		0			0
$799$	4.43474	+	7.68119i	0.156890	+	0.271741i
$800$	−5.12476			−0.181188
$801$	0.503270	+	0.451852i	0.0177822	+	0.0159654i
$802$	−10.6192			−0.374976
$803$	−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
$807$	−16.6602	+	43.4937i	−0.586466	+	1.53105i
$808$	9.29467	+	16.0988i	0.326985	+	0.566355i
$809$	29.1729			1.02567			0.512833	−	0.858489i	$-0.328596\pi$
$809$	29.1729			1.02567			0.512833	+	0.858489i	$0.328596\pi$
$810$	3.07442	+	28.4720i	0.108024	+	1.00040i
$811$	−15.4290			−0.541785			−0.270892	−	0.962610i	$-0.587319\pi$
$811$	−15.4290			−0.541785			−0.270892	+	0.962610i	$0.587319\pi$
$812$		0			0
$813$	−13.7644	+	35.9339i	−0.482740	+	1.26026i
$814$	−1.59097	+	2.75564i	−0.0557635	+	0.0965853i
$815$	6.33297	−	10.9690i	0.221834	−	0.384228i
$816$	2.60301	−	0.414174i	0.0911236	−	0.0144990i
$817$	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	0.782423	−	0.622748i	$-0.213984\pi$
$821$	−4.24364	−	7.35019i	−0.148104	−	0.256524i	−0.930527	+	0.366224i	$0.880650\pi$
$822$	2.99084	+	3.68802i	0.104318	+	0.128634i
$823$	−14.5487	+	25.1991i	−0.507136	+	0.878385i	0.492830	+	0.870126i	$0.335963\pi$
$823$	−14.5487	+	25.1991i	−0.507136	+	0.878385i	−0.999966	+	0.00825976i	$0.997371\pi$
$824$	−0.141315	+	0.244765i	−0.00492294	+	0.00852679i
$825$	−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	$0.648934\pi$
$828$	−1.38727	+	6.57256i	−0.0482111	+	0.228412i
$829$	−6.21642			−0.215905			−0.107953	−	0.994156i	$-0.534429\pi$
$829$	−6.21642			−0.215905			−0.107953	+	0.994156i	$0.534429\pi$
$830$	−12.8353	−	22.2314i	−0.445520	−	0.771663i
$831$	−25.0379	+	3.98387i	−0.868556	+	0.138199i
$832$	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
$836$	4.08126			0.141153
$837$	2.45774	−	48.8916i	0.0849518	−	1.68994i
$838$	5.54910			0.191690
$839$	21.2947	+	36.8834i	0.735174	+	1.27336i	0.954647	+	0.297740i	$0.0962327\pi$
$839$	21.2947	+	36.8834i	0.735174	+	1.27336i	−0.219474	+	0.975618i	$0.570434\pi$
$840$		0			0
$841$	−10.5721	+	18.3114i	−0.364555	+	0.631428i
$842$	3.42107	−	5.92546i	0.117898	−	0.204205i
$843$	−40.0237	+	6.36830i	−1.37849	+	0.219336i
$844$	−8.32846	−	14.4253i	−0.286677	−	0.496540i
$845$	−62.1502			−2.13803
$846$	16.6219	−	5.42692i	0.571472	−	0.186581i
$847$		0			0
$848$	1.02859	+	1.78157i	0.0353219	+	0.0611794i
$849$	28.5014	+	35.1451i	0.978165	+	1.20618i
$850$	3.89931	−	6.75381i	0.133745	−	0.231654i
$851$	1.11956	−	1.93914i	0.0383781	−	0.0664728i
$852$	−9.48057	−	11.6905i	−0.324799	−	0.400511i
$853$	−10.6969	−	18.5275i	−0.366254	−	0.634370i	0.622723	−	0.782442i	$-0.286026\pi$
$853$	−10.6969	−	18.5275i	−0.366254	−	0.634370i	−0.988976	+	0.148073i	$0.952693\pi$
$854$		0			0
$855$	−11.6391	+	3.80009i	−0.398050	+	0.129960i
$856$	11.3776			0.388877
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	0.987697	+	0.156377i	$0.0499815\pi$
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	−0.358422	+	0.933560i	$0.616685\pi$
$858$	31.0442	−	4.93955i	1.05983	−	0.168633i
$859$	8.81875	−	15.2745i	0.300892	−	0.521160i	−0.675446	−	0.737409i	$-0.736049\pi$
$859$	8.81875	−	15.2745i	0.300892	−	0.521160i	0.976338	+	0.216249i	$0.0693824\pi$
$860$	−10.8639	+	18.8168i	−0.370455	+	0.641648i
$861$		0			0
$862$	−16.5539	−	28.6722i	−0.563828	−	0.976579i
$863$	0.760877			0.0259005			0.0129503	−	0.999916i	$-0.495878\pi$
$863$	0.760877			0.0259005			0.0129503	+	0.999916i	$0.495878\pi$
$864$	0.260877	−	5.18960i	0.00887521	−	0.176554i
$865$	−8.11901			−0.276054
$866$	−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
$870$	38.5420	−	6.13255i	1.30670	−	0.207913i
$871$	31.2759	+	54.1715i	1.05974	+	1.83553i
$872$	−4.42107			−0.149716
$873$	9.19562	−	43.5665i	0.311224	−	1.47450i
$874$	−2.87197			−0.0971457
$875$		0			0
$876$	−5.41874	−	6.68187i	−0.183082	−	0.225760i
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	−0.267573	−	0.963538i	$-0.586222\pi$
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	0.968234	−	0.250044i	$-0.0804451\pi$
$878$	−4.41711	+	7.65066i	−0.149070	+	0.258197i
$879$	28.2157	+	34.7929i	0.951693	+	1.17354i
$880$	5.06238	+	8.76830i	0.170653	+	0.295579i
$881$	8.35486			0.281482			0.140741	−	0.990046i	$-0.455051\pi$
$881$	8.35486			0.281482			0.140741	+	0.990046i	$0.455051\pi$
$882$		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
$885$	6.12188	−	0.974074i	0.205785	−	0.0327431i
$886$	8.75924	−	15.1715i	0.294272	−	0.509695i
$887$	18.5550	−	32.1382i	0.623016	−	1.07909i	−0.365905	−	0.930652i	$-0.619241\pi$
$887$	18.5550	−	32.1382i	0.623016	−	1.07909i	0.988921	−	0.148443i	$-0.0474260\pi$
$888$	−0.619562	+	1.61745i	−0.0207911	+	0.0542781i
$889$		0			0
$890$	−0.717370			−0.0240463
$891$	23.1202	−	16.8985i	0.774558	−	0.566122i
$892$	10.6569			0.356820
$893$	3.73788	+	6.47420i	0.125083	+	0.216651i
$894$	−14.4110	+	37.6218i	−0.481975	+	1.25826i
$895$	−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
$899$	−66.7130			−2.22500
$900$	−11.4399	−	10.2712i	−0.381331	−	0.342372i
$901$	−3.13052			−0.104293
$902$	8.91423	+	15.4399i	0.296811	+	0.514092i
$903$		0			0
$904$	1.60752	−	2.78431i	0.0534654	−	0.0926048i
$905$	−20.6300	+	35.7321i	−0.685763	+	1.18778i
$906$	−8.86389	−	10.9301i	−0.294483	−	0.363128i
$907$	24.0751	+	41.6993i	0.799401	+	1.38460i	0.920007	+	0.391902i	$0.128183\pi$
$907$	24.0751	+	41.6993i	0.799401	+	1.38460i	−0.120606	+	0.992700i	$0.538484\pi$
$908$	−14.5081			−0.481468
$909$	−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	$0.637203\pi$
$912$	2.19398	−	0.349092i	0.0726500	−	0.0115596i
$913$	−12.8353	+	22.2314i	−0.424786	+	0.735751i
$914$	−16.0624	+	27.8209i	−0.531296	+	0.920232i
$915$	6.16019	−	16.0820i	0.203650	−	0.531655i
$916$	−5.12476	−	8.87635i	−0.169327	−	0.293283i
$917$		0			0
$918$	6.64076	+	4.29245i	0.219178	+	0.141672i
$919$	51.7349			1.70658			0.853289	−	0.521439i	$-0.174605\pi$
$919$	51.7349			1.70658			0.853289	+	0.521439i	$0.174605\pi$
$920$	−3.56238	−	6.17023i	−0.117448	−	0.203426i
$921$	−2.18839	+	5.71309i	−0.0721099	+	0.188253i
$922$	−1.23229	+	2.13438i	−0.0405832	+	0.0702922i
$923$	24.7826	−	42.9248i	0.815730	−	1.41289i
$924$		0			0
$925$	2.56238	+	4.43818i	0.0842506	+	0.145926i
$926$	30.3469			0.997262
$927$	−0.806018	+	0.263159i	−0.0264731	+	0.00864328i
$928$	−7.08126			−0.232454
$929$	25.4142	+	44.0187i	0.833814	+	1.44421i	0.894993	+	0.446081i	$0.147181\pi$
$929$	25.4142	+	44.0187i	0.833814	+	1.44421i	−0.0611787	+	0.998127i	$0.519486\pi$
$930$	32.7044	+	40.3279i	1.07242	+	1.32240i
$931$		0			0
$932$	0.540628	−	0.936396i	0.0177089	−	0.0306727i
$933$	−1.85868	−	2.29195i	−0.0608506	−	0.0750351i
$934$	7.98181	+	13.8249i	0.261173	+	0.452365i
$935$	−15.4074			−0.503876
$936$	16.2661	−	5.31075i	0.531673	−	0.173587i
$937$	2.54583			0.0831686			0.0415843	−	0.999135i	$-0.486759\pi$
$937$	2.54583			0.0831686			0.0415843	+	0.999135i	$0.486759\pi$
$938$		0			0
$939$	−4.86156	+	0.773540i	−0.158651	+	0.0252435i
$940$	−9.27292	+	16.0612i	−0.302449	+	0.523857i
$941$	−0.578933	+	1.00274i	−0.0188727	+	0.0326885i	−0.875308	−	0.483567i	$-0.839341\pi$
$941$	−0.578933	+	1.00274i	−0.0188727	+	0.0326885i	0.856435	+	0.516255i	$0.172674\pi$
$942$	−6.97825	+	18.2177i	−0.227364	+	0.593563i
$943$	−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	0.775208	−	0.631706i	$-0.217645\pi$
$947$	−4.90739	−	8.49985i	−0.159469	−	0.276208i	−0.934677	+	0.355497i	$0.884311\pi$
$948$	2.56402	−	6.69371i	0.0832754	−	0.217402i
$949$	14.1648	−	24.5342i	0.459810	−	0.796414i
$950$	3.28659	−	5.69254i	0.106631	−	0.184690i
$951$	−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	$0.466230\pi$
$954$	−1.27455	+	6.03850i	−0.0412651	+	0.195504i
$955$	−6.30206			−0.203930
$956$	−6.16019	−	10.6698i	−0.199235	−	0.345085i
$957$	−24.5819	−	30.3121i	−0.794621	−	0.979850i
$958$	−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
$962$	−5.70370			−0.183895
$963$	25.3980	+	22.8031i	0.818438	+	0.734821i
$964$	−13.0000			−0.418702
$965$	−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	$0.0128999\pi$
$968$	−0.437618	+	0.757977i	−0.0140656	+	0.0243623i
$969$	−1.20929	+	3.15701i	−0.0388480	+	0.101418i
$970$	23.6134	+	40.8996i	0.758181	+	1.31321i
$971$	−5.33654			−0.171258			−0.0856289	−	0.996327i	$-0.527290\pi$
$971$	−5.33654			−0.171258			−0.0856289	+	0.996327i	$0.527290\pi$
$972$	10.9834	−	11.0618i	0.352294	−	0.354808i
$973$		0			0
$974$	−1.70658	−	2.95588i	−0.0546822	−	0.0947124i
$975$	18.1098	−	47.2782i	0.579979	−	1.51411i
$976$	−1.56238	+	2.70612i	−0.0500106	+	0.0866209i
$977$	24.0361	−	41.6318i	0.768983	−	1.33192i	−0.169131	−	0.985594i	$-0.554096\pi$
$977$	24.0361	−	41.6318i	0.768983	−	1.33192i	0.938115	−	0.346325i	$-0.112571\pi$
$978$	−6.80890	+	1.08339i	−0.217725	+	0.0346429i
$979$	0.358685	+	0.621261i	0.0114636	+	0.0198556i
$980$		0			0
$981$	−9.86909	−	8.86079i	−0.315096	−	0.282903i
$982$	−19.1683			−0.611684
$983$	−14.7313	−	25.5154i	−0.469857	−	0.813816i	0.529549	−	0.848279i	$-0.322361\pi$
$983$	−14.7313	−	25.5154i	−0.469857	−	0.813816i	−0.999406	+	0.0344634i	$0.989028\pi$
$984$	6.11273	+	7.53762i	0.194867	+	0.240291i
$985$	−34.7067	+	60.1138i	−1.10585	+	1.91538i
$986$	5.38796	−	9.33223i	0.171588	−	0.297199i
$987$		0			0
$988$	3.65787	+	6.33561i	0.116372	+	0.201563i
$989$	−15.2898			−0.486186
$990$	−6.27292	+	29.7195i	−0.199366	+	0.944547i
$991$	−30.8285			−0.979298			−0.489649	−	0.871920i	$-0.662875\pi$
$991$	−30.8285			−0.979298			−0.489649	+	0.871920i	$0.662875\pi$
$992$	−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
$996$	−4.99837	+	13.0489i	−0.158379	+	0.413471i
$997$	−2.77292	−	4.80283i	−0.0878191	−	0.152107i	0.818770	−	0.574122i	$-0.194656\pi$
$997$	−2.77292	−	4.80283i	−0.0878191	−	0.152107i	−0.906589	+	0.422015i	$0.861323\pi$
$998$	−41.1696			−1.30320
$999$	−4.62476	+	2.36887i	−0.146321	+	0.0749479i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	63.16	even	3
126.2.e.c.121.3	yes	6	7.4	even	3
126.2.h.d.67.1	yes	6	7.2	even	3
126.2.h.d.79.1	yes	6	63.25	even	3
378.2.e.d.37.1		6	21.11	odd	6
378.2.e.d.235.1		6	63.2	odd	6
378.2.h.c.289.3		6	63.11	odd	6
378.2.h.c.361.3		6	21.2	odd	6
882.2.e.o.373.1		6	7.3	odd	6
882.2.e.o.655.1		6	63.61	odd	6
882.2.f.n.295.2		6	9.7	even	3	inner
882.2.f.n.589.2		6	1.1	even	1	trivial
882.2.f.o.295.2		6	63.34	odd	6
882.2.f.o.589.2		6	7.6	odd	2
882.2.h.p.67.3		6	7.5	odd	6
882.2.h.p.79.3		6	63.52	odd	6
1008.2.q.g.529.1		6	252.79	odd	6
1008.2.q.g.625.1		6	28.11	odd	6
1008.2.t.h.193.3		6	28.23	odd	6
1008.2.t.h.961.3		6	252.151	odd	6
1134.2.g.l.163.1		6	63.32	odd	6
1134.2.g.l.487.1		6	63.23	odd	6
1134.2.g.m.163.3		6	63.4	even	3
1134.2.g.m.487.3		6	63.58	even	3
2646.2.e.p.1549.3		6	21.17	even	6
2646.2.e.p.2125.3		6	63.47	even	6
2646.2.f.l.883.1		6	9.2	odd	6
2646.2.f.l.1765.1		6	3.2	odd	2
2646.2.f.m.883.3		6	63.20	even	6
2646.2.f.m.1765.3		6	21.20	even	2
2646.2.h.o.361.1		6	21.5	even	6
2646.2.h.o.667.1		6	63.38	even	6
3024.2.q.g.2305.1		6	84.11	even	6
3024.2.q.g.2881.1		6	252.191	even	6
3024.2.t.h.289.3		6	252.11	even	6
3024.2.t.h.1873.3		6	84.23	even	6
7938.2.a.bv.1.1		3	9.4	even	3
7938.2.a.bw.1.3		3	63.13	odd	6
7938.2.a.bz.1.1		3	63.41	even	6
7938.2.a.ca.1.3		3	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.59097 - 2.75564i) q^{5} +(-1.71053 + 0.272169i) q^{6} -1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +3.18194 q^{10} +(-1.59097 - 2.75564i) q^{11} +(-1.09097 - 1.34528i) q^{12} +(2.85185 - 4.93955i) q^{13} +(3.47141 + 4.28061i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.52175 q^{17} +(0.619562 - 2.93533i) q^{18} +1.28263 q^{19} +(1.59097 + 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +(-1.11956 + 1.93914i) q^{23} +(0.619562 - 1.61745i) q^{24} +(-2.56238 - 4.43818i) q^{25} +5.70370 q^{26} +(4.62476 - 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +(-1.97141 + 5.14663i) q^{30} +(4.71053 - 8.15888i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.44282 - 0.866025i) q^{33} +(0.760877 + 1.31788i) q^{34} +(2.85185 - 0.931107i) q^{36} -1.00000 q^{37} +(0.641315 + 1.11079i) q^{38} +(6.22257 + 7.67307i) q^{39} +(-1.59097 + 2.75564i) q^{40} +(-2.80150 + 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +3.18194 q^{44} +(-9.07442 + 2.96273i) q^{45} -2.23912 q^{46} +(2.91423 + 5.04759i) q^{47} +(1.71053 - 0.272169i) q^{48} +(2.56238 - 4.43818i) q^{50} +(-0.942820 + 2.46136i) q^{51} +(2.85185 + 4.93955i) q^{52} -2.05718 q^{53} +(4.36389 + 2.82073i) q^{54} -10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} +(3.54063 - 6.13255i) q^{58} +(0.562382 - 0.974074i) q^{59} +(-5.44282 + 0.866025i) q^{60} +(-1.56238 - 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(-9.07442 - 15.7174i) q^{65} +(3.47141 + 4.28061i) q^{66} +(-5.48345 + 9.49761i) q^{67} +(-0.760877 + 1.31788i) q^{68} +(-2.44282 - 3.01225i) q^{69} +8.69002 q^{71} +(2.23229 + 2.00422i) q^{72} +4.96690 q^{73} +(-0.500000 - 0.866025i) q^{74} +(8.76608 - 1.39480i) q^{75} +(-0.641315 + 1.11079i) q^{76} +(-3.53379 + 9.22544i) q^{78} +(2.06922 + 3.58399i) q^{79} -3.18194 q^{80} +(0.966208 + 8.94799i) q^{81} -5.60301 q^{82} +(-4.03379 - 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(-3.41423 + 5.91362i) q^{86} +(12.1127 - 1.92730i) q^{87} +(1.59097 + 2.75564i) q^{88} -0.225450 q^{89} +(-7.10301 - 6.37731i) q^{90} +(-1.11956 - 1.93914i) q^{92} +(10.2781 + 12.6740i) q^{93} +(-2.91423 + 5.04759i) q^{94} +(2.04063 - 3.53447i) q^{95} +(1.09097 + 1.34528i) q^{96} +(7.42107 + 12.8537i) q^{97} +(-1.97141 + 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} + 12 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + q^{20} + q^{22} - 7 q^{23}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 + q^5 - 2 * q^6 - 6 * q^8 - 4 * q^9 + 2 * q^10 - q^11 + 2 * q^12 + 8 * q^13 + 12 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + q^20 + q^22 - 7 * q^23 + 4 * q^24 + 2 * q^25 + 16 * q^26 - 7 * q^27 - 5 * q^29 - 3 * q^30 + 20 * q^31 + 3 * q^32 + 15 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - q^40 - 6 * q^43 + 2 * q^44 - 12 * q^45 - 14 * q^46 - 9 * q^47 + 2 * q^48 - 2 * q^50 + 12 * q^51 + 8 * q^52 - 30 * q^53 - 8 * q^54 - 26 * q^55 + 22 * q^57 + 5 * q^58 - 14 * q^59 - 15 * q^60 + 8 * q^61 + 40 * q^62 + 6 * q^64 - 12 * q^65 + 12 * q^66 + q^67 - 4 * q^68 + 3 * q^69 + 14 * q^71 + 4 * q^72 - 38 * q^73 - 3 * q^74 + 17 * q^75 - 3 * q^76 + 5 * q^78 + 5 * q^79 - 2 * q^80 + 32 * q^81 + 2 * q^83 - 2 * q^85 + 6 * q^86 + 63 * q^87 + q^88 + 18 * q^89 - 9 * q^90 - 7 * q^92 + q^93 + 9 * q^94 - 4 * q^95 - 2 * q^96 + 28 * q^97 - 3 * q^99

Introduction

L-functions

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