LMFDB - Embedded newform 882.2.f.p.589.1

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.1
Root			$-1.72286 + 0.178197i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.p.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.707107 - 1.58114i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.72286 + 2.98408i) q^{5} +(-1.01575 + 1.40294i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.707107 - 1.58114i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.72286 + 2.98408i) q^{5} +(-1.01575 + 1.40294i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +3.44572 q^{10} +(-2.00000 - 3.46410i) q^{11} +(1.72286 + 0.178197i) q^{12} +(-2.12132 + 3.67423i) q^{13} +(5.93649 + 0.614017i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.41421 q^{17} +(2.93649 + 0.614017i) q^{18} +6.27415 q^{19} +(-1.72286 - 2.98408i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(4.37298 - 7.57423i) q^{23} +(-0.707107 - 1.58114i) q^{24} +(-3.43649 - 5.95218i) q^{25} +4.24264 q^{26} +(4.94975 + 1.58114i) q^{27} +(-0.563508 - 0.976025i) q^{29} +(-2.43649 - 5.44816i) q^{30} +(2.73861 - 4.74342i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.06301 + 5.61177i) q^{33} +(0.707107 + 1.22474i) q^{34} +(-0.936492 - 2.85008i) q^{36} +5.74597 q^{37} +(-3.13707 - 5.43357i) q^{38} +(7.30948 + 0.756026i) q^{39} +(-1.72286 + 2.98408i) q^{40} +(2.82843 - 4.89898i) q^{41} +(-0.563508 - 0.976025i) q^{43} +4.00000 q^{44} +(-3.22689 - 9.82059i) q^{45} -8.74597 q^{46} +(-2.03151 - 3.51867i) q^{47} +(-1.01575 + 1.40294i) q^{48} +(-3.43649 + 5.95218i) q^{50} +(1.00000 + 2.23607i) q^{51} +(-2.12132 - 3.67423i) q^{52} +12.6190 q^{53} +(-1.10557 - 5.07718i) q^{54} +13.7829 q^{55} +(-4.43649 - 9.92030i) q^{57} +(-0.563508 + 0.976025i) q^{58} +(-4.15283 + 7.19291i) q^{59} +(-3.50000 + 4.83414i) q^{60} +(3.13707 + 5.43357i) q^{61} -5.47723 q^{62} +1.00000 q^{64} +(-7.30948 - 12.6604i) q^{65} +(6.89144 + 0.712788i) q^{66} +(3.43649 - 5.95218i) q^{67} +(0.707107 - 1.22474i) q^{68} +(-15.0681 - 1.55850i) q^{69} -9.87298 q^{71} +(-2.00000 + 2.23607i) q^{72} -4.42227 q^{73} +(-2.87298 - 4.97615i) q^{74} +(-6.98125 + 9.64240i) q^{75} +(-3.13707 + 5.43357i) q^{76} +(-3.00000 - 6.70820i) q^{78} +(0.936492 + 1.62205i) q^{79} +3.44572 q^{80} +(-1.00000 - 8.94427i) q^{81} -5.65685 q^{82} +(-1.32440 - 2.29393i) q^{83} +(2.43649 - 4.22013i) q^{85} +(-0.563508 + 0.976025i) q^{86} +(-1.14477 + 1.58114i) q^{87} +(-2.00000 - 3.46410i) q^{88} -7.07107 q^{89} +(-6.89144 + 7.70486i) q^{90} +(4.37298 + 7.57423i) q^{92} +(-9.43649 - 0.976025i) q^{93} +(-2.03151 + 3.51867i) q^{94} +(-10.8095 + 18.7226i) q^{95} +(1.72286 + 0.178197i) q^{96} +(7.50873 + 13.0055i) q^{97} +(11.7460 + 2.45607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^9	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9} - 16 q^{11} + 32 q^{15} - 4 q^{16} + 8 q^{18} - 16 q^{22} + 4 q^{23} - 12 q^{25} - 20 q^{29} - 4 q^{30} - 4 q^{32} + 8 q^{36} - 16 q^{37} + 12 q^{39} - 20 q^{43} + 32 q^{44} - 8 q^{46} - 12 q^{50} + 8 q^{51} + 8 q^{53} - 20 q^{57} - 20 q^{58} - 28 q^{60} + 8 q^{64} - 12 q^{65} + 12 q^{67} - 48 q^{71} - 16 q^{72} + 8 q^{74} - 24 q^{78} - 8 q^{79} - 8 q^{81} + 4 q^{85} - 20 q^{86} - 16 q^{88} + 4 q^{92} - 60 q^{93} - 40 q^{95} + 32 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^9 - 16 * q^11 + 32 * q^15 - 4 * q^16 + 8 * q^18 - 16 * q^22 + 4 * q^23 - 12 * q^25 - 20 * q^29 - 4 * q^30 - 4 * q^32 + 8 * q^36 - 16 * q^37 + 12 * q^39 - 20 * q^43 + 32 * q^44 - 8 * q^46 - 12 * q^50 + 8 * q^51 + 8 * q^53 - 20 * q^57 - 20 * q^58 - 28 * q^60 + 8 * q^64 - 12 * q^65 + 12 * q^67 - 48 * q^71 - 16 * q^72 + 8 * q^74 - 24 * q^78 - 8 * q^79 - 8 * q^81 + 4 * q^85 - 20 * q^86 - 16 * q^88 + 4 * q^92 - 60 * q^93 - 40 * q^95 + 32 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−0.707107	−	1.58114i	−0.408248	−	0.912871i
$3$	−0.707107	−	1.58114i	−0.408248	−	0.912871i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.72286	+	2.98408i	−0.770486	+	1.33452i	0.166810	+	0.985989i	$0.446653\pi$
$5$	−1.72286	+	2.98408i	−0.770486	+	1.33452i	−0.937297	+	0.348532i	$0.886680\pi$
$6$	−1.01575	+	1.40294i	−0.414679	+	0.572749i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−2.00000	+	2.23607i	−0.666667	+	0.745356i
$10$	3.44572			1.08963
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$	1.72286	+	0.178197i	0.497347	+	0.0514410i
$13$	−2.12132	+	3.67423i	−0.588348	+	1.01905i	0.406100	+	0.913828i	$0.366888\pi$
$13$	−2.12132	+	3.67423i	−0.588348	+	1.01905i	−0.994449	+	0.105221i	$0.966445\pi$
$14$		0			0
$15$	5.93649	+	0.614017i	1.53280	+	0.158538i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.41421			−0.342997			−0.171499	−	0.985184i	$-0.554861\pi$
$17$	−1.41421			−0.342997			−0.171499	+	0.985184i	$0.554861\pi$
$18$	2.93649	+	0.614017i	0.692138	+	0.144725i
$19$	6.27415			1.43939			0.719694	−	0.694291i	$-0.244282\pi$
$19$	6.27415			1.43939			0.719694	+	0.694291i	$0.244282\pi$
$20$	−1.72286	−	2.98408i	−0.385243	−	0.667261i
$21$		0			0
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$	4.37298	−	7.57423i	0.911830	−	1.57934i	0.100353	−	0.994952i	$-0.468003\pi$
$23$	4.37298	−	7.57423i	0.911830	−	1.57934i	0.811477	−	0.584384i	$-0.198664\pi$
$24$	−0.707107	−	1.58114i	−0.144338	−	0.322749i
$25$	−3.43649	−	5.95218i	−0.687298	−	1.19044i
$26$	4.24264			0.832050
$27$	4.94975	+	1.58114i	0.952579	+	0.304290i
$28$		0			0
$29$	−0.563508	−	0.976025i	−0.104641	−	0.181243i	0.808951	−	0.587877i	$-0.200036\pi$
$29$	−0.563508	−	0.976025i	−0.104641	−	0.181243i	−0.913591	+	0.406633i	$0.866703\pi$
$30$	−2.43649	−	5.44816i	−0.444840	−	0.994694i
$31$	2.73861	−	4.74342i	0.491869	−	0.851943i	−0.508087	−	0.861306i	$-0.669647\pi$
$31$	2.73861	−	4.74342i	0.491869	−	0.851943i	0.999956	+	0.00936313i	$0.00298042\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−4.06301	+	5.61177i	−0.707280	+	0.976883i
$34$	0.707107	+	1.22474i	0.121268	+	0.210042i
$35$		0			0
$36$	−0.936492	−	2.85008i	−0.156082	−	0.475014i
$37$	5.74597			0.944631			0.472316	−	0.881430i	$-0.343418\pi$
$37$	5.74597			0.944631			0.472316	+	0.881430i	$0.343418\pi$
$38$	−3.13707	−	5.43357i	−0.508900	−	0.881442i
$39$	7.30948	+	0.756026i	1.17045	+	0.121061i
$40$	−1.72286	+	2.98408i	−0.272408	+	0.471825i
$41$	2.82843	−	4.89898i	0.441726	−	0.765092i	−0.556092	−	0.831121i	$-0.687700\pi$
$41$	2.82843	−	4.89898i	0.441726	−	0.765092i	0.997818	+	0.0660290i	$0.0210330\pi$
$42$		0			0
$43$	−0.563508	−	0.976025i	−0.0859342	−	0.148842i	0.819855	−	0.572572i	$-0.194054\pi$
$43$	−0.563508	−	0.976025i	−0.0859342	−	0.148842i	−0.905789	+	0.423729i	$0.860721\pi$
$44$	4.00000			0.603023
$45$	−3.22689	−	9.82059i	−0.481036	−	1.46397i
$46$	−8.74597			−1.28952
$47$	−2.03151	−	3.51867i	−0.296326	−	0.513251i	0.678967	−	0.734169i	$-0.262428\pi$
$47$	−2.03151	−	3.51867i	−0.296326	−	0.513251i	−0.975292	+	0.220918i	$0.929095\pi$
$48$	−1.01575	+	1.40294i	−0.146611	+	0.202497i
$49$		0			0
$50$	−3.43649	+	5.95218i	−0.485993	+	0.841765i
$51$	1.00000	+	2.23607i	0.140028	+	0.313112i
$52$	−2.12132	−	3.67423i	−0.294174	−	0.509525i
$53$	12.6190			1.73335			0.866673	−	0.498877i	$-0.166254\pi$
$53$	12.6190			1.73335			0.866673	+	0.498877i	$0.166254\pi$
$54$	−1.10557	−	5.07718i	−0.150449	−	0.690916i
$55$	13.7829			1.85848
$56$		0			0
$57$	−4.43649	−	9.92030i	−0.587628	−	1.31398i
$58$	−0.563508	+	0.976025i	−0.0739923	+	0.128158i
$59$	−4.15283	+	7.19291i	−0.540652	+	0.936437i	0.458215	+	0.888842i	$0.348489\pi$
$59$	−4.15283	+	7.19291i	−0.540652	+	0.936437i	−0.998867	+	0.0475951i	$0.984844\pi$
$60$	−3.50000	+	4.83414i	−0.451848	+	0.624085i
$61$	3.13707	+	5.43357i	0.401661	+	0.695697i	0.993927	−	0.110045i	$-0.0350997\pi$
$61$	3.13707	+	5.43357i	0.401661	+	0.695697i	−0.592265	+	0.805743i	$0.701766\pi$
$62$	−5.47723			−0.695608
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.30948	−	12.6604i	−0.906629	−	1.57033i
$66$	6.89144	+	0.712788i	0.848278	+	0.0877381i
$67$	3.43649	−	5.95218i	0.419834	−	0.727174i	−0.576088	−	0.817388i	$-0.695422\pi$
$67$	3.43649	−	5.95218i	0.419834	−	0.727174i	0.995922	+	0.0902132i	$0.0287549\pi$
$68$	0.707107	−	1.22474i	0.0857493	−	0.148522i
$69$	−15.0681	−	1.55850i	−1.81398	−	0.187622i
$70$		0			0
$71$	−9.87298			−1.17171			−0.585854	−	0.810417i	$-0.699241\pi$
$71$	−9.87298			−1.17171			−0.585854	+	0.810417i	$0.699241\pi$
$72$	−2.00000	+	2.23607i	−0.235702	+	0.263523i
$73$	−4.42227			−0.517587			−0.258794	−	0.965933i	$-0.583325\pi$
$73$	−4.42227			−0.517587			−0.258794	+	0.965933i	$0.583325\pi$
$74$	−2.87298	−	4.97615i	−0.333978	−	0.578466i
$75$	−6.98125	+	9.64240i	−0.806126	+	1.11341i
$76$	−3.13707	+	5.43357i	−0.359847	+	0.623273i
$77$		0			0
$78$	−3.00000	−	6.70820i	−0.339683	−	0.759555i
$79$	0.936492	+	1.62205i	0.105364	+	0.182495i	0.913887	−	0.405969i	$-0.133066\pi$
$79$	0.936492	+	1.62205i	0.105364	+	0.182495i	−0.808523	+	0.588464i	$0.799733\pi$
$80$	3.44572			0.385243
$81$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$82$	−5.65685			−0.624695
$83$	−1.32440	−	2.29393i	−0.145372	−	0.251791i	0.784140	−	0.620584i	$-0.213104\pi$
$83$	−1.32440	−	2.29393i	−0.145372	−	0.251791i	−0.929512	+	0.368793i	$0.879771\pi$
$84$		0			0
$85$	2.43649	−	4.22013i	0.264275	−	0.457737i
$86$	−0.563508	+	0.976025i	−0.0607647	+	0.105247i
$87$	−1.14477	+	1.58114i	−0.122732	+	0.169516i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	−7.07107			−0.749532			−0.374766	−	0.927119i	$-0.622277\pi$
$89$	−7.07107			−0.749532			−0.374766	+	0.927119i	$0.622277\pi$
$90$	−6.89144	+	7.70486i	−0.726421	+	0.812164i
$91$		0			0
$92$	4.37298	+	7.57423i	0.455915	+	0.789668i
$93$	−9.43649	−	0.976025i	−0.978519	−	0.101209i
$94$	−2.03151	+	3.51867i	−0.209534	+	0.362923i
$95$	−10.8095	+	18.7226i	−1.10903	+	1.92089i
$96$	1.72286	+	0.178197i	0.175839	+	0.0181872i
$97$	7.50873	+	13.0055i	0.762396	+	1.32051i	0.941612	+	0.336699i	$0.109311\pi$
$97$	7.50873	+	13.0055i	0.762396	+	1.32051i	−0.179216	+	0.983810i	$0.557356\pi$
$98$		0			0
$99$	11.7460	+	2.45607i	1.18051	+	0.246844i
$100$	6.87298			0.687298
$101$	−6.67261	−	11.5573i	−0.663949	−	1.14999i	−0.979569	−	0.201108i	$-0.935546\pi$
$101$	−6.67261	−	11.5573i	−0.663949	−	1.14999i	0.315620	−	0.948886i	$-0.397788\pi$
$102$	1.43649	−	1.98406i	0.142234	−	0.196451i
$103$	1.94169	−	3.36311i	0.191321	−	0.331377i	−0.754368	−	0.656452i	$-0.772056\pi$
$103$	1.94169	−	3.36311i	0.191321	−	0.331377i	0.945688	+	0.325075i	$0.105390\pi$
$104$	−2.12132	+	3.67423i	−0.208013	+	0.360288i
$105$		0			0
$106$	−6.30948	−	10.9283i	−0.612830	−	1.06145i
$107$	0.254033			0.0245583			0.0122792	−	0.999925i	$-0.496091\pi$
$107$	0.254033			0.0245583			0.0122792	+	0.999925i	$0.496091\pi$
$108$	−3.84418	+	3.49604i	−0.369906	+	0.336406i
$109$	16.8730			1.61614			0.808069	−	0.589087i	$-0.200513\pi$
$109$	16.8730			1.61614			0.808069	+	0.589087i	$0.200513\pi$
$110$	−6.89144	−	11.9363i	−0.657073	−	1.13808i
$111$	−4.06301	−	9.08517i	−0.385644	−	0.862326i
$112$		0			0
$113$	−1.93649	+	3.35410i	−0.182170	+	0.315527i	−0.942619	−	0.333870i	$-0.891645\pi$
$113$	−1.93649	+	3.35410i	−0.182170	+	0.315527i	0.760449	+	0.649397i	$0.224979\pi$
$114$	−6.37298	+	8.80226i	−0.596885	+	0.824407i
$115$	15.0681	+	26.0987i	1.40511	+	2.43371i
$116$	1.12702			0.104641
$117$	−3.97320	−	12.0919i	−0.367322	−	1.11790i
$118$	8.30565			0.764597
$119$		0			0
$120$	5.93649	+	0.614017i	0.541925	+	0.0560518i
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	3.13707	−	5.43357i	0.284017	−	0.491932i
$123$	−9.74597	−	1.00803i	−0.878764	−	0.0908914i
$124$	2.73861	+	4.74342i	0.245935	+	0.425971i
$125$	6.45378			0.577243
$126$		0			0
$127$	−0.745967			−0.0661938			−0.0330969	−	0.999452i	$-0.510537\pi$
$127$	−0.745967			−0.0661938			−0.0330969	+	0.999452i	$0.510537\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.14477	+	1.58114i	−0.100791	+	0.139212i
$130$	−7.30948	+	12.6604i	−0.641083	+	1.11039i
$131$	6.67261	−	11.5573i	0.582988	−	1.00977i	−0.412135	−	0.911123i	$-0.635217\pi$
$131$	6.67261	−	11.5573i	0.582988	−	1.00977i	0.995123	−	0.0986425i	$-0.0314500\pi$
$132$	−2.82843	−	6.32456i	−0.246183	−	0.550482i
$133$		0			0
$134$	−6.87298			−0.593735
$135$	−13.2460	+	12.0464i	−1.14003	+	1.03679i
$136$	−1.41421			−0.121268
$137$	7.74597	+	13.4164i	0.661783	+	1.14624i	0.980147	+	0.198273i	$0.0635331\pi$
$137$	7.74597	+	13.4164i	0.661783	+	1.14624i	−0.318364	+	0.947968i	$0.603134\pi$
$138$	6.18433	+	13.8286i	0.526445	+	1.17717i
$139$	9.93870	−	17.2143i	0.842989	−	1.46010i	−0.0443665	−	0.999015i	$-0.514127\pi$
$139$	9.93870	−	17.2143i	0.842989	−	1.46010i	0.887356	−	0.461085i	$-0.152540\pi$
$140$		0			0
$141$	−4.12702	+	5.70017i	−0.347558	+	0.480041i
$142$	4.93649	+	8.55025i	0.414261	+	0.717521i
$143$	16.9706			1.41915
$144$	2.93649	+	0.614017i	0.244708	+	0.0511681i
$145$	3.88338			0.322497
$146$	2.21113	+	3.82980i	0.182995	+	0.316956i
$147$		0			0
$148$	−2.87298	+	4.97615i	−0.236158	+	0.409037i
$149$	7.87298	−	13.6364i	0.644980	−	1.11714i	−0.339326	−	0.940669i	$-0.610199\pi$
$149$	7.87298	−	13.6364i	0.644980	−	1.11714i	0.984306	−	0.176469i	$-0.0564676\pi$
$150$	11.8412	+	1.22474i	0.966829	+	0.100000i
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	6.27415			0.508900
$153$	2.82843	−	3.16228i	0.228665	−	0.255655i
$154$		0			0
$155$	9.43649	+	16.3445i	0.757957	+	1.31282i
$156$	−4.30948	+	5.95218i	−0.345034	+	0.476556i
$157$	5.96550	−	10.3325i	0.476099	−	0.824627i	−0.523526	−	0.852010i	$-0.675384\pi$
$157$	5.96550	−	10.3325i	0.476099	−	0.824627i	0.999625	+	0.0273823i	$0.00871714\pi$
$158$	0.936492	−	1.62205i	0.0745033	−	0.129043i
$159$	−8.92295	−	19.9523i	−0.707636	−	1.58232i
$160$	−1.72286	−	2.98408i	−0.136204	−	0.235912i
$161$		0			0
$162$	−7.24597	+	5.33816i	−0.569297	+	0.419406i
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$	2.82843	+	4.89898i	0.220863	+	0.382546i
$165$	−9.74597	−	21.7926i	−0.758722	−	1.69656i
$166$	−1.32440	+	2.29393i	−0.102793	+	0.178043i
$167$	4.77012	−	8.26209i	0.369123	−	0.639340i	−0.620306	−	0.784360i	$-0.712991\pi$
$167$	4.77012	−	8.26209i	0.369123	−	0.639340i	0.989429	+	0.145021i	$0.0463248\pi$
$168$		0			0
$169$	−2.50000	−	4.33013i	−0.192308	−	0.333087i
$170$	−4.87298			−0.373741
$171$	−12.5483	+	14.0294i	−0.959592	+	1.07286i
$172$	1.12702			0.0859342
$173$	6.36396	+	11.0227i	0.483843	+	0.838041i	0.999828	−	0.0185571i	$-0.00590724\pi$
$173$	6.36396	+	11.0227i	0.483843	+	0.838041i	−0.515985	+	0.856598i	$0.672574\pi$
$174$	1.94169	+	0.200831i	0.147199	+	0.0152250i
$175$		0			0
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$	14.3095	+	1.48004i	1.07557	+	0.111247i
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	−6.87298			−0.513711			−0.256855	−	0.966450i	$-0.582686\pi$
$179$	−6.87298			−0.513711			−0.256855	+	0.966450i	$0.582686\pi$
$180$	10.1183	+	2.11573i	0.754176	+	0.157697i
$181$	13.3452			0.991942			0.495971	−	0.868339i	$-0.334812\pi$
$181$	13.3452			0.991942			0.495971	+	0.868339i	$0.334812\pi$
$182$		0			0
$183$	6.37298	−	8.80226i	0.471104	−	0.650682i
$184$	4.37298	−	7.57423i	0.322381	−	0.558380i
$185$	−9.89949	+	17.1464i	−0.727825	+	1.26063i
$186$	3.87298	+	8.66025i	0.283981	+	0.635001i
$187$	2.82843	+	4.89898i	0.206835	+	0.358249i
$188$	4.06301			0.296326
$189$		0			0
$190$	21.6190			1.56840
$191$	3.06351	+	5.30615i	0.221668	+	0.383940i	0.955314	−	0.295591i	$-0.0955167\pi$
$191$	3.06351	+	5.30615i	0.221668	+	0.383940i	−0.733647	+	0.679531i	$0.762183\pi$
$192$	−0.707107	−	1.58114i	−0.0510310	−	0.114109i
$193$	−11.9365	+	20.6746i	−0.859207	+	1.48819i	0.0134785	+	0.999909i	$0.495710\pi$
$193$	−11.9365	+	20.6746i	−0.859207	+	1.48819i	−0.872686	+	0.488282i	$0.837624\pi$
$194$	7.50873	−	13.0055i	0.539096	−	0.933741i
$195$	−14.8492	+	20.5095i	−1.06338	+	1.46872i
$196$		0			0
$197$	16.6190			1.18405			0.592026	−	0.805919i	$-0.298328\pi$
$197$	16.6190			1.18405			0.592026	+	0.805919i	$0.298328\pi$
$198$	−3.74597	−	11.4003i	−0.266214	−	0.810187i
$199$	−12.1890			−0.864058			−0.432029	−	0.901860i	$-0.642202\pi$
$199$	−12.1890			−0.864058			−0.432029	+	0.901860i	$0.642202\pi$
$200$	−3.43649	−	5.95218i	−0.242997	−	0.420883i
$201$	−11.8412	−	1.22474i	−0.835213	−	0.0863868i
$202$	−6.67261	+	11.5573i	−0.469483	+	0.813168i
$203$		0			0
$204$	−2.43649	−	0.252009i	−0.170589	−	0.0176441i
$205$	9.74597	+	16.8805i	0.680688	+	1.17899i
$206$	−3.88338			−0.270568
$207$	8.19052	+	24.9267i	0.569281	+	1.73253i
$208$	4.24264			0.294174
$209$	−12.5483	−	21.7343i	−0.867984	−	1.50339i
$210$		0			0
$211$	−10.3095	+	17.8565i	−0.709734	+	1.22929i	0.255222	+	0.966882i	$0.417851\pi$
$211$	−10.3095	+	17.8565i	−0.709734	+	1.22929i	−0.964956	+	0.262412i	$0.915482\pi$
$212$	−6.30948	+	10.9283i	−0.433337	+	0.750561i
$213$	6.98125	+	15.6106i	0.478348	+	1.06962i
$214$	−0.127017	−	0.219999i	−0.00868268	−	0.0150388i
$215$	3.88338			0.264845
$216$	4.94975	+	1.58114i	0.336788	+	0.107583i
$217$		0			0
$218$	−8.43649	−	14.6124i	−0.571391	−	0.989679i
$219$	3.12702	+	6.99222i	0.211304	+	0.472491i
$220$	−6.89144	+	11.9363i	−0.464621	+	0.804747i
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$	−5.83648	+	8.06126i	−0.391719	+	0.541036i
$223$	−11.2239	−	19.4404i	−0.751608	−	1.30182i	−0.947043	−	0.321106i	$-0.895945\pi$
$223$	−11.2239	−	19.4404i	−0.751608	−	1.30182i	0.195436	−	0.980717i	$-0.437388\pi$
$224$		0			0
$225$	20.1825	+	4.22013i	1.34550	+	0.281342i
$226$	3.87298			0.257627
$227$	5.16858	+	8.95224i	0.343051	+	0.594181i	0.984998	−	0.172568i	$-0.0552064\pi$
$227$	5.16858	+	8.95224i	0.343051	+	0.594181i	−0.641947	+	0.766749i	$0.721873\pi$
$228$	10.8095	+	1.11803i	0.715875	+	0.0740436i
$229$	6.67261	−	11.5573i	0.440938	−	0.763728i	−0.556821	−	0.830632i	$-0.687979\pi$
$229$	6.67261	−	11.5573i	0.440938	−	0.763728i	0.997759	+	0.0669049i	$0.0213124\pi$
$230$	15.0681	−	26.0987i	0.993559	−	1.72090i
$231$		0			0
$232$	−0.563508	−	0.976025i	−0.0369961	−	0.0640792i
$233$	7.25403			0.475228			0.237614	−	0.971360i	$-0.423635\pi$
$233$	7.25403			0.475228			0.237614	+	0.971360i	$0.423635\pi$
$234$	−8.48528	+	9.48683i	−0.554700	+	0.620174i
$235$	14.0000			0.913259
$236$	−4.15283	−	7.19291i	−0.270326	−	0.468218i
$237$	1.90249	−	2.62769i	0.123580	−	0.170687i
$238$		0			0
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	−0.514719	−	0.857359i	$-0.672104\pi$
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	0.999854	+	0.0170808i	$0.00543724\pi$
$240$	−2.43649	−	5.44816i	−0.157275	−	0.351677i
$241$	−11.8412	−	20.5095i	−0.762758	−	1.32114i	−0.941424	−	0.337226i	$-0.890511\pi$
$241$	−11.8412	−	20.5095i	−0.762758	−	1.32114i	0.178666	−	0.983910i	$-0.442822\pi$
$242$	5.00000			0.321412
$243$	−13.4350	+	7.90569i	−0.861858	+	0.507151i
$244$	−6.27415			−0.401661
$245$		0			0
$246$	4.00000	+	8.94427i	0.255031	+	0.570266i
$247$	−13.3095	+	23.0527i	−0.846862	+	1.46681i
$248$	2.73861	−	4.74342i	0.173902	−	0.301207i
$249$	−2.69052	+	3.71611i	−0.170505	+	0.235499i
$250$	−3.22689	−	5.58913i	−0.204086	−	0.353488i
$251$	−9.46183			−0.597225			−0.298613	−	0.954374i	$-0.596524\pi$
$251$	−9.46183			−0.597225			−0.298613	+	0.954374i	$0.596524\pi$
$252$		0			0
$253$	−34.9839			−2.19942
$254$	0.372983	+	0.646026i	0.0234031	+	0.0405353i
$255$	−8.39547	−	0.868351i	−0.525745	−	0.0543782i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.50403	−	2.60505i	0.0938187	−	0.162499i	−0.815296	−	0.579044i	$-0.803426\pi$
$257$	1.50403	−	2.60505i	0.0938187	−	0.162499i	0.909115	+	0.416545i	$0.136759\pi$
$258$	1.94169	+	0.200831i	0.120884	+	0.0125032i
$259$		0			0
$260$	14.6190			0.906629
$261$	3.30948	+	0.692007i	0.204851	+	0.0428342i
$262$	−13.3452			−0.824470
$263$	8.80948	+	15.2585i	0.543216	+	0.940877i	0.998717	+	0.0506418i	$0.0161267\pi$
$263$	8.80948	+	15.2585i	0.543216	+	0.940877i	−0.455501	+	0.890235i	$0.650540\pi$
$264$	−4.06301	+	5.61177i	−0.250061	+	0.345380i
$265$	−21.7407	+	37.6560i	−1.33552	+	2.31319i
$266$		0			0
$267$	5.00000	+	11.1803i	0.305995	+	0.684226i
$268$	3.43649	+	5.95218i	0.209917	+	0.363587i
$269$	2.03151			0.123863			0.0619316	−	0.998080i	$-0.480274\pi$
$269$	2.03151			0.123863			0.0619316	+	0.998080i	$0.480274\pi$
$270$	17.0554	+	5.44816i	1.03796	+	0.331565i
$271$	−7.07107			−0.429537			−0.214768	−	0.976665i	$-0.568900\pi$
$271$	−7.07107			−0.429537			−0.214768	+	0.976665i	$0.568900\pi$
$272$	0.707107	+	1.22474i	0.0428746	+	0.0742611i
$273$		0			0
$274$	7.74597	−	13.4164i	0.467951	−	0.810515i
$275$	−13.7460	+	23.8087i	−0.828913	+	1.43572i
$276$	8.88374	−	12.2701i	0.534738	−	0.738572i
$277$	−7.18246	−	12.4404i	−0.431552	−	0.747470i	0.565455	−	0.824779i	$-0.308701\pi$
$277$	−7.18246	−	12.4404i	−0.431552	−	0.747470i	−0.997007	+	0.0773089i	$0.975367\pi$
$278$	−19.8774			−1.19217
$279$	5.12938	+	15.6106i	0.307088	+	0.934580i
$280$		0			0
$281$	−4.37298	−	7.57423i	−0.260870	−	0.451841i	0.705603	−	0.708607i	$-0.250676\pi$
$281$	−4.37298	−	7.57423i	−0.260870	−	0.451841i	−0.966473	+	0.256767i	$0.917343\pi$
$282$	7.00000	+	0.724016i	0.416844	+	0.0431146i
$283$	2.51978	−	4.36439i	0.149785	−	0.259436i	−0.781363	−	0.624077i	$-0.785475\pi$
$283$	2.51978	−	4.36439i	0.149785	−	0.259436i	0.931148	+	0.364641i	$0.118808\pi$
$284$	4.93649	−	8.55025i	0.292927	−	0.507364i
$285$	37.2464	+	3.85243i	2.20629	+	0.228198i
$286$	−8.48528	−	14.6969i	−0.501745	−	0.869048i
$287$		0			0
$288$	−0.936492	−	2.85008i	−0.0551833	−	0.167943i
$289$	−15.0000			−0.882353
$290$	−1.94169	−	3.36311i	−0.114020	−	0.197489i
$291$	15.2540	−	21.0686i	0.894207	−	1.23506i
$292$	2.21113	−	3.82980i	0.129397	−	0.224122i
$293$	−0.398461	+	0.690154i	−0.0232783	+	0.0403192i	−0.877430	−	0.479705i	$-0.840744\pi$
$293$	−0.398461	+	0.690154i	−0.0232783	+	0.0403192i	0.854152	+	0.520024i	$0.174077\pi$
$294$		0			0
$295$	−14.3095	−	24.7847i	−0.833130	−	1.44302i
$296$	5.74597			0.333978
$297$	−4.42227	−	20.3087i	−0.256606	−	1.17843i
$298$	−15.7460			−0.912139
$299$	18.5530	+	32.1347i	1.07295	+	1.85840i
$300$	−4.85993	−	10.8671i	−0.280588	−	0.627415i
$301$		0			0
$302$	−5.50000	+	9.52628i	−0.316489	+	0.548176i
$303$	−13.5554	+	18.7226i	−0.778740	+	1.07558i
$304$	−3.13707	−	5.43357i	−0.179923	−	0.311637i
$305$	−21.6190			−1.23790
$306$	−4.15283	−	0.868351i	−0.237401	−	0.0496403i
$307$	−14.2205			−0.811609			−0.405805	−	0.913960i	$-0.633009\pi$
$307$	−14.2205			−0.811609			−0.405805	+	0.913960i	$0.633009\pi$
$308$		0			0
$309$	−6.69052	−	0.692007i	−0.380611	−	0.0393669i
$310$	9.43649	−	16.3445i	0.535957	−	0.928304i
$311$	−0.707107	+	1.22474i	−0.0400963	+	0.0694489i	−0.885377	−	0.464873i	$-0.846100\pi$
$311$	−0.707107	+	1.22474i	−0.0400963	+	0.0694489i	0.845281	+	0.534322i	$0.179433\pi$
$312$	7.30948	+	0.756026i	0.413818	+	0.0428015i
$313$	7.86799	+	13.6278i	0.444725	+	0.770286i	0.998033	−	0.0626904i	$-0.0199681\pi$
$313$	7.86799	+	13.6278i	0.444725	+	0.770286i	−0.553308	+	0.832977i	$0.686635\pi$
$314$	−11.9310			−0.673305
$315$		0			0
$316$	−1.87298			−0.105364
$317$	−12.3095	−	21.3206i	−0.691369	−	1.19749i	−0.971389	−	0.237492i	$-0.923675\pi$
$317$	−12.3095	−	21.3206i	−0.691369	−	1.19749i	0.280020	−	0.959994i	$-0.409659\pi$
$318$	−12.8177	+	17.7037i	−0.718783	+	0.992772i
$319$	−2.25403	+	3.90410i	−0.126202	+	0.218588i
$320$	−1.72286	+	2.98408i	−0.0963108	+	0.166815i
$321$	−0.179629	−	0.401662i	−0.0100259	−	0.0224186i
$322$		0			0
$323$	−8.87298			−0.493706
$324$	8.24597	+	3.60611i	0.458109	+	0.200339i
$325$	29.1596			1.61748
$326$	−5.00000	−	8.66025i	−0.276924	−	0.479647i
$327$	−11.9310	−	26.6785i	−0.659786	−	1.47533i
$328$	2.82843	−	4.89898i	0.156174	−	0.270501i
$329$		0			0
$330$	−14.0000	+	19.3366i	−0.770675	+	1.06444i
$331$	−10.1825	−	17.6365i	−0.559679	−	0.969392i	−0.997523	−	0.0703409i	$-0.977591\pi$
$331$	−10.1825	−	17.6365i	−0.559679	−	0.969392i	0.437844	−	0.899051i	$-0.355742\pi$
$332$	2.64880			0.145372
$333$	−11.4919	+	12.8484i	−0.629754	+	0.704086i
$334$	−9.54024			−0.522019
$335$	11.8412	+	20.5095i	0.646953	+	1.12056i
$336$		0			0
$337$	−7.87298	+	13.6364i	−0.428869	+	0.742822i	−0.996773	−	0.0802722i	$-0.974421\pi$
$337$	−7.87298	+	13.6364i	−0.428869	+	0.742822i	0.567904	+	0.823095i	$0.307754\pi$
$338$	−2.50000	+	4.33013i	−0.135982	+	0.235528i
$339$	6.67261	+	0.690154i	0.362406	+	0.0374840i
$340$	2.43649	+	4.22013i	0.132137	+	0.228869i
$341$	−21.9089			−1.18643
$342$	18.4240	+	3.85243i	0.996255	+	0.208316i
$343$		0			0
$344$	−0.563508	−	0.976025i	−0.0303823	−	0.0526237i
$345$	30.6109	−	42.2793i	1.64803	−	2.27624i
$346$	6.36396	−	11.0227i	0.342129	−	0.592584i
$347$	−3.87298	+	6.70820i	−0.207913	+	0.360115i	−0.951057	−	0.309016i	$-0.900000\pi$
$347$	−3.87298	+	6.70820i	−0.207913	+	0.360115i	0.743144	+	0.669131i	$0.233334\pi$
$348$	−0.796921	−	1.78197i	−0.0427195	−	0.0955236i
$349$	−8.21584	−	14.2302i	−0.439784	−	0.761728i	0.557889	−	0.829916i	$-0.311612\pi$
$349$	−8.21584	−	14.2302i	−0.439784	−	0.761728i	−0.997672	+	0.0681880i	$0.978278\pi$
$350$		0			0
$351$	−16.3095	+	14.8324i	−0.870535	+	0.791697i
$352$	4.00000			0.213201
$353$	1.94169	+	3.36311i	0.103346	+	0.179000i	0.913061	−	0.407823i	$-0.133712\pi$
$353$	1.94169	+	3.36311i	0.103346	+	0.179000i	−0.809715	+	0.586823i	$0.800378\pi$
$354$	−5.87298	−	13.1324i	−0.312146	−	0.697979i
$355$	17.0098	−	29.4618i	0.902785	−	1.56367i
$356$	3.53553	−	6.12372i	0.187383	−	0.324557i
$357$		0			0
$358$	3.43649	+	5.95218i	0.181624	+	0.314582i
$359$	18.2379			0.962560			0.481280	−	0.876567i	$-0.340172\pi$
$359$	18.2379			0.962560			0.481280	+	0.876567i	$0.340172\pi$
$360$	−3.22689	−	9.82059i	−0.170072	−	0.517591i
$361$	20.3649			1.07184
$362$	−6.67261	−	11.5573i	−0.350704	−	0.607438i
$363$	8.61430	+	0.890985i	0.452133	+	0.0467646i
$364$		0			0
$365$	7.61895	−	13.1964i	0.398794	−	0.690732i
$366$	−10.8095	−	1.11803i	−0.565020	−	0.0584406i
$367$	3.44572	+	5.96816i	0.179865	+	0.311535i	0.941834	−	0.336078i	$-0.109101\pi$
$367$	3.44572	+	5.96816i	0.179865	+	0.311535i	−0.761969	+	0.647613i	$0.775767\pi$
$368$	−8.74597			−0.455915
$369$	5.29760	+	16.1225i	0.275782	+	0.839305i
$370$	19.7990			1.02930
$371$		0			0
$372$	5.56351	−	7.68423i	0.288454	−	0.398409i
$373$	0.563508	−	0.976025i	0.0291774	−	0.0505367i	−0.851068	−	0.525055i	$-0.824045\pi$
$373$	0.563508	−	0.976025i	0.0291774	−	0.0505367i	0.880245	+	0.474519i	$0.157378\pi$
$374$	2.82843	−	4.89898i	0.146254	−	0.253320i
$375$	−4.56351	−	10.2043i	−0.235659	−	0.526949i
$376$	−2.03151	−	3.51867i	−0.104767	−	0.181462i
$377$	4.78153			0.246261
$378$		0			0
$379$	26.3649			1.35427			0.677137	−	0.735857i	$-0.263220\pi$
$379$	26.3649			1.35427			0.677137	+	0.735857i	$0.263220\pi$
$380$	−10.8095	−	18.7226i	−0.554514	−	0.960447i
$381$	0.527478	+	1.17948i	0.0270235	+	0.0604264i
$382$	3.06351	−	5.30615i	0.156743	−	0.271486i
$383$	−6.45378	+	11.1783i	−0.329773	+	0.571183i	−0.982467	−	0.186439i	$-0.940305\pi$
$383$	−6.45378	+	11.1783i	−0.329773	+	0.571183i	0.652694	+	0.757622i	$0.273639\pi$
$384$	−1.01575	+	1.40294i	−0.0518349	+	0.0715936i
$385$		0			0
$386$	23.8730			1.21510
$387$	3.30948	+	0.692007i	0.168230	+	0.0351767i
$388$	−15.0175			−0.762396
$389$	−6.56351	−	11.3683i	−0.332783	−	0.576397i	0.650273	−	0.759700i	$-0.274654\pi$
$389$	−6.56351	−	11.3683i	−0.332783	−	0.576397i	−0.983056	+	0.183303i	$0.941321\pi$
$390$	25.1864	+	2.60505i	1.27536	+	0.131912i
$391$	−6.18433	+	10.7116i	−0.312755	+	0.541708i
$392$		0			0
$393$	−22.9919	−	2.37808i	−1.15979	−	0.119958i
$394$	−8.30948	−	14.3924i	−0.418625	−	0.725080i
$395$	−6.45378			−0.324725
$396$	−8.00000	+	8.94427i	−0.402015	+	0.449467i
$397$	−7.07107			−0.354887			−0.177443	−	0.984131i	$-0.556783\pi$
$397$	−7.07107			−0.354887			−0.177443	+	0.984131i	$0.556783\pi$
$398$	6.09452	+	10.5560i	0.305491	+	0.529125i
$399$		0			0
$400$	−3.43649	+	5.95218i	−0.171825	+	0.297609i
$401$	1.93649	−	3.35410i	0.0967038	−	0.167496i	−0.813615	−	0.581405i	$-0.802503\pi$
$401$	1.93649	−	3.35410i	0.0967038	−	0.167496i	0.910318	+	0.413909i	$0.135837\pi$
$402$	4.85993	+	10.8671i	0.242391	+	0.542004i
$403$	11.6190	+	20.1246i	0.578781	+	1.00248i
$404$	13.3452			0.663949
$405$	28.4133	+	12.4256i	1.41187	+	0.617435i
$406$		0			0
$407$	−11.4919	−	19.9046i	−0.569634	−	0.986635i
$408$	1.00000	+	2.23607i	0.0495074	+	0.110702i
$409$	11.5717	−	20.0428i	0.572186	−	0.991055i	−0.424155	−	0.905589i	$-0.639429\pi$
$409$	11.5717	−	20.0428i	0.572186	−	0.991055i	0.996341	−	0.0854655i	$-0.0272378\pi$
$410$	9.74597	−	16.8805i	0.481319	−	0.833669i
$411$	15.7360	−	21.7343i	0.776199	−	1.07207i
$412$	1.94169	+	3.36311i	0.0956603	+	0.165688i
$413$		0			0
$414$	17.4919	−	19.5566i	0.859682	−	0.961153i
$415$	9.12702			0.448028
$416$	−2.12132	−	3.67423i	−0.104006	−	0.180144i
$417$	−34.2460	−	3.54209i	−1.67703	−	0.173457i
$418$	−12.5483	+	21.7343i	−0.613757	+	1.06306i
$419$	−15.6854	+	27.1679i	−0.766280	+	1.32724i	0.173287	+	0.984871i	$0.444561\pi$
$419$	−15.6854	+	27.1679i	−0.766280	+	1.32724i	−0.939567	+	0.342365i	$0.888772\pi$
$420$		0			0
$421$	6.43649	+	11.1483i	0.313695	+	0.543336i	0.979159	−	0.203094i	$-0.0650996\pi$
$421$	6.43649	+	11.1483i	0.313695	+	0.543336i	−0.665464	+	0.746430i	$0.731766\pi$
$422$	20.6190			1.00371
$423$	11.9310	+	2.49476i	0.580105	+	0.121299i
$424$	12.6190			0.612830
$425$	4.85993	+	8.41765i	0.235741	+	0.408316i
$426$	10.0285	−	13.8512i	0.485883	−	0.671094i
$427$		0			0
$428$	−0.127017	+	0.219999i	−0.00613958	+	0.0106341i
$429$	−12.0000	−	26.8328i	−0.579365	−	1.29550i
$430$	−1.94169	−	3.36311i	−0.0936367	−	0.162183i
$431$	−21.4919			−1.03523			−0.517615	−	0.855614i	$-0.673180\pi$
$431$	−21.4919			−1.03523			−0.517615	+	0.855614i	$0.673180\pi$
$432$	−1.10557	−	5.07718i	−0.0531916	−	0.244276i
$433$	29.6985			1.42722			0.713609	−	0.700544i	$-0.247059\pi$
$433$	29.6985			1.42722			0.713609	+	0.700544i	$0.247059\pi$
$434$		0			0
$435$	−2.74597	−	6.14017i	−0.131659	−	0.294399i
$436$	−8.43649	+	14.6124i	−0.404035	+	0.699809i
$437$	27.4367	−	47.5218i	1.31248	−	2.27328i
$438$	4.49193	−	6.20419i	0.214633	−	0.296448i
$439$	−5.47723	−	9.48683i	−0.261414	−	0.452782i	0.705204	−	0.709004i	$-0.250855\pi$
$439$	−5.47723	−	9.48683i	−0.261414	−	0.452782i	−0.966618	+	0.256223i	$0.917522\pi$
$440$	13.7829			0.657073
$441$		0			0
$442$	−6.00000			−0.285391
$443$	7.18246	+	12.4404i	0.341249	+	0.591060i	0.984665	−	0.174456i	$-0.0558168\pi$
$443$	7.18246	+	12.4404i	0.341249	+	0.591060i	−0.643416	+	0.765517i	$0.722483\pi$
$444$	9.89949	+	1.02391i	0.469809	+	0.0485928i
$445$	12.1825	−	21.1006i	0.577504	−	1.00027i
$446$	−11.2239	+	19.4404i	−0.531467	+	0.920527i
$447$	−27.1281	−	2.80588i	−1.28311	−	0.132714i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	−6.43649	−	19.5886i	−0.303419	−	0.923415i
$451$	−22.6274			−1.06548
$452$	−1.93649	−	3.35410i	−0.0910849	−	0.157764i
$453$	−11.1733	+	15.4324i	−0.524967	+	0.725076i
$454$	5.16858	−	8.95224i	0.242573	−	0.420150i
$455$		0			0
$456$	−4.43649	−	9.92030i	−0.207758	−	0.464560i
$457$	−13.0635	−	22.6267i	−0.611085	−	1.05843i	−0.991058	−	0.133433i	$-0.957400\pi$
$457$	−13.0635	−	22.6267i	−0.611085	−	1.05843i	0.379973	−	0.924998i	$-0.375933\pi$
$458$	−13.3452			−0.623581
$459$	−7.00000	−	2.23607i	−0.326732	−	0.104371i
$460$	−30.1361			−1.40511
$461$	14.1813	+	24.5628i	0.660491	+	1.14400i	0.980487	+	0.196585i	$0.0629851\pi$
$461$	14.1813	+	24.5628i	0.660491	+	1.14400i	−0.319996	+	0.947419i	$0.603682\pi$
$462$		0			0
$463$	0.809475	−	1.40205i	0.0376195	−	0.0651589i	−0.846603	−	0.532226i	$-0.821356\pi$
$463$	0.809475	−	1.40205i	0.0376195	−	0.0651589i	0.884222	+	0.467067i	$0.154689\pi$
$464$	−0.563508	+	0.976025i	−0.0261602	+	0.0453108i
$465$	19.1703	−	26.4777i	0.889001	−	1.22787i
$466$	−3.62702	−	6.28218i	−0.168018	−	0.291016i
$467$	−6.19574			−0.286705			−0.143352	−	0.989672i	$-0.545788\pi$
$467$	−6.19574			−0.286705			−0.143352	+	0.989672i	$0.545788\pi$
$468$	12.4585	+	2.60505i	0.575893	+	0.120419i
$469$		0			0
$470$	−7.00000	−	12.1244i	−0.322886	−	0.559255i
$471$	−20.5554	−	2.12607i	−0.947145	−	0.0979641i
$472$	−4.15283	+	7.19291i	−0.191149	+	0.331080i
$473$	−2.25403	+	3.90410i	−0.103641	+	0.179511i
$474$	−3.22689	−	0.333760i	−0.148216	−	0.0153301i
$475$	−21.5611	−	37.3448i	−0.989289	−	1.71350i
$476$		0			0
$477$	−25.2379	+	28.2168i	−1.15556	+	1.29196i
$478$	−15.0000			−0.686084
$479$	1.94169	+	3.36311i	0.0887182	+	0.153664i	0.906970	−	0.421196i	$-0.138390\pi$
$479$	1.94169	+	3.36311i	0.0887182	+	0.153664i	−0.818251	+	0.574861i	$0.805056\pi$
$480$	−3.50000	+	4.83414i	−0.159752	+	0.220647i
$481$	−12.1890	+	21.1120i	−0.555772	+	0.962626i
$482$	−11.8412	+	20.5095i	−0.539351	+	0.934184i
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−51.7460			−2.34966
$486$	13.5640	+	7.68223i	0.615278	+	0.348473i
$487$	−0.491933			−0.0222916			−0.0111458	−	0.999938i	$-0.503548\pi$
$487$	−0.491933			−0.0222916			−0.0111458	+	0.999938i	$0.503548\pi$
$488$	3.13707	+	5.43357i	0.142009	+	0.245966i
$489$	−7.07107	−	15.8114i	−0.319765	−	0.715016i
$490$		0			0
$491$	−0.872983	+	1.51205i	−0.0393972	+	0.0682379i	−0.885052	−	0.465493i	$-0.845877\pi$
$491$	−0.872983	+	1.51205i	−0.0393972	+	0.0682379i	0.845654	+	0.533731i	$0.179210\pi$
$492$	5.74597	−	7.93624i	0.259048	−	0.357793i
$493$	0.796921	+	1.38031i	0.0358915	+	0.0621659i
$494$	26.6190			1.19764
$495$	−27.5658	+	30.8195i	−1.23899	+	1.38523i
$496$	−5.47723			−0.245935
$497$		0			0
$498$	4.56351	+	0.472008i	0.204496	+	0.0211512i
$499$	14.8730	−	25.7608i	0.665806	−	1.15321i	−0.313260	−	0.949667i	$-0.601421\pi$
$499$	14.8730	−	25.7608i	0.665806	−	1.15321i	0.979066	−	0.203543i	$-0.0652456\pi$
$500$	−3.22689	+	5.58913i	−0.144311	+	0.249954i
$501$	−16.4365	−	1.70004i	−0.734328	−	0.0759523i
$502$	4.73092	+	8.19419i	0.211151	+	0.365724i
$503$	3.88338			0.173152			0.0865758	−	0.996245i	$-0.472408\pi$
$503$	3.88338			0.173152			0.0865758	+	0.996245i	$0.472408\pi$
$504$		0			0
$505$	45.9839			2.04626
$506$	17.4919	+	30.2969i	0.777611	+	1.34686i
$507$	−5.07877	+	7.01471i	−0.225556	+	0.311534i
$508$	0.372983	−	0.646026i	0.0165485	−	0.0286628i
$509$	11.4035	−	19.7515i	0.505452	−	0.875469i	−0.494528	−	0.869162i	$-0.664659\pi$
$509$	11.4035	−	19.7515i	0.505452	−	0.875469i	0.999980	−	0.00630722i	$-0.00200766\pi$
$510$	3.44572	+	7.70486i	0.152579	+	0.341177i
$511$		0			0
$512$	1.00000			0.0441942
$513$	31.0554	+	9.92030i	1.37113	+	0.437992i
$514$	−3.00806			−0.132680
$515$	6.69052	+	11.5883i	0.294820	+	0.510643i
$516$	−0.796921	−	1.78197i	−0.0350825	−	0.0784468i
$517$	−8.12602	+	14.0747i	−0.357382	+	0.619004i
$518$		0			0
$519$	12.9284	−	17.8565i	0.567495	−	0.783815i
$520$	−7.30948	−	12.6604i	−0.320542	−	0.555194i
$521$	−1.41421			−0.0619578			−0.0309789	−	0.999520i	$-0.509862\pi$
$521$	−1.41421			−0.0619578			−0.0309789	+	0.999520i	$0.509862\pi$
$522$	−1.05544	−	3.21209i	−0.0461954	−	0.140589i
$523$	−18.2836			−0.799484			−0.399742	−	0.916628i	$-0.630900\pi$
$523$	−18.2836			−0.799484			−0.399742	+	0.916628i	$0.630900\pi$
$524$	6.67261	+	11.5573i	0.291494	+	0.504883i
$525$		0			0
$526$	8.80948	−	15.2585i	0.384111	−	0.665300i
$527$	−3.87298	+	6.70820i	−0.168710	+	0.292214i
$528$	6.89144	+	0.712788i	0.299911	+	0.0310201i
$529$	−26.7460	−	46.3254i	−1.16287	−	2.01415i
$530$	43.4814			1.88871
$531$	−7.77817	−	23.6718i	−0.337544	−	1.02727i
$532$		0			0
$533$	12.0000	+	20.7846i	0.519778	+	0.900281i
$534$	7.18246	−	9.92030i	0.310815	−	0.429293i
$535$	−0.437664	+	0.758056i	−0.0189219	+	0.0327736i
$536$	3.43649	−	5.95218i	0.148434	−	0.257095i
$537$	4.85993	+	10.8671i	0.209722	+	0.468952i
$538$	−1.01575	−	1.75934i	−0.0437922	−	0.0758504i
$539$		0			0
$540$	−3.80948	−	17.4945i	−0.163934	−	0.752845i
$541$	−38.1109			−1.63851			−0.819257	−	0.573426i	$-0.805614\pi$
$541$	−38.1109			−1.63851			−0.819257	+	0.573426i	$0.805614\pi$
$542$	3.53553	+	6.12372i	0.151864	+	0.263036i
$543$	−9.43649	−	21.1006i	−0.404959	−	0.905515i
$544$	0.707107	−	1.22474i	0.0303170	−	0.0525105i
$545$	−29.0698	+	50.3503i	−1.24521	+	2.15677i
$546$		0			0
$547$	16.4919	+	28.5649i	0.705144	+	1.22135i	0.966639	+	0.256141i	$0.0824511\pi$
$547$	16.4919	+	28.5649i	0.705144	+	1.22135i	−0.261495	+	0.965205i	$0.584216\pi$
$548$	−15.4919			−0.661783
$549$	−18.4240	−	3.85243i	−0.786316	−	0.164418i
$550$	27.4919			1.17226
$551$	−3.53553	−	6.12372i	−0.150619	−	0.260879i
$552$	−15.0681	−	1.55850i	−0.641340	−	0.0663344i
$553$		0			0
$554$	−7.18246	+	12.4404i	−0.305153	+	0.528541i
$555$	34.1109	+	3.52812i	1.44793	+	0.149760i
$556$	9.93870	+	17.2143i	0.421495	+	0.730050i
$557$	26.6190			1.12788			0.563941	−	0.825815i	$-0.309285\pi$
$557$	26.6190			1.12788			0.563941	+	0.825815i	$0.309285\pi$
$558$	10.9545	−	12.2474i	0.463739	−	0.518476i
$559$	4.78153			0.202237
$560$		0			0
$561$	5.74597	−	7.93624i	0.242595	−	0.335068i
$562$	−4.37298	+	7.57423i	−0.184463	+	0.319500i
$563$	−10.8254	+	18.7502i	−0.456238	+	0.790227i	−0.998758	−	0.0498156i	$-0.984137\pi$
$563$	−10.8254	+	18.7502i	−0.456238	+	0.790227i	0.542521	+	0.840042i	$0.317470\pi$
$564$	−2.87298	−	6.42419i	−0.120974	−	0.270507i
$565$	−6.67261	−	11.5573i	−0.280719	−	0.486219i
$566$	−5.03956			−0.211829
$567$		0			0
$568$	−9.87298			−0.414261
$569$	11.7460	+	20.3446i	0.492417	+	0.852890i	0.999962	−	0.00873460i	$-0.00278035\pi$
$569$	11.7460	+	20.3446i	0.492417	+	0.852890i	−0.507545	+	0.861625i	$0.669447\pi$
$570$	−15.2869	−	34.1826i	−0.640298	−	1.43175i
$571$	−15.7460	+	27.2728i	−0.658948	+	1.14133i	0.321940	+	0.946760i	$0.395665\pi$
$571$	−15.7460	+	27.2728i	−0.658948	+	1.14133i	−0.980888	+	0.194572i	$0.937668\pi$
$572$	−8.48528	+	14.6969i	−0.354787	+	0.614510i
$573$	6.22354	−	8.59585i	0.259992	−	0.359097i
$574$		0			0
$575$	−60.1109			−2.50680
$576$	−2.00000	+	2.23607i	−0.0833333	+	0.0931695i
$577$	−24.2213			−1.00834			−0.504172	−	0.863603i	$-0.668202\pi$
$577$	−24.2213			−1.00834			−0.504172	+	0.863603i	$0.668202\pi$
$578$	7.50000	+	12.9904i	0.311959	+	0.540329i
$579$	41.1298	+	4.25409i	1.70930	+	0.176794i
$580$	−1.94169	+	3.36311i	−0.0806244	+	0.139645i
$581$		0			0
$582$	−25.8730	−	2.67607i	−1.07247	−	0.110927i
$583$	−25.2379	−	43.7133i	−1.04525	−	1.81042i
$584$	−4.42227			−0.182995
$585$	42.9284	+	8.97628i	1.77487	+	0.371124i
$586$	0.796921			0.0329205
$587$	4.28184	+	7.41637i	0.176731	+	0.306106i	0.940759	−	0.339076i	$-0.110115\pi$
$587$	4.28184	+	7.41637i	0.176731	+	0.306106i	−0.764028	+	0.645183i	$0.776781\pi$
$588$		0			0
$589$	17.1825	−	29.7609i	0.707991	−	1.22628i
$590$	−14.3095	+	24.7847i	−0.589112	+	1.02037i
$591$	−11.7514	−	26.2769i	−0.483387	−	1.08089i
$592$	−2.87298	−	4.97615i	−0.118079	−	0.204519i
$593$	−33.7615			−1.38642			−0.693209	−	0.720736i	$-0.743804\pi$
$593$	−33.7615			−1.38642			−0.693209	+	0.720736i	$0.743804\pi$
$594$	−15.3767	+	13.9842i	−0.630914	+	0.573777i
$595$		0			0
$596$	7.87298	+	13.6364i	0.322490	+	0.558569i
$597$	8.61895	+	19.2726i	0.352750	+	0.788773i
$598$	18.5530	−	32.1347i	0.758688	−	1.31409i
$599$	22.6190	−	39.1772i	0.924185	−	1.60074i	0.131319	−	0.991340i	$-0.458079\pi$
$599$	22.6190	−	39.1772i	0.924185	−	1.60074i	0.792866	−	0.609396i	$-0.208588\pi$
$600$	−6.98125	+	9.64240i	−0.285008	+	0.393649i
$601$	−2.39076	−	4.14092i	−0.0975213	−	0.168912i	0.813137	−	0.582073i	$-0.197758\pi$
$601$	−2.39076	−	4.14092i	−0.0975213	−	0.168912i	−0.910658	+	0.413161i	$0.864425\pi$
$602$		0			0
$603$	6.43649	+	19.5886i	0.262114	+	0.797709i
$604$	11.0000			0.447584
$605$	−8.61430	−	14.9204i	−0.350221	−	0.606601i
$606$	22.9919	+	2.37808i	0.933983	+	0.0966028i
$607$	13.3452	−	23.1146i	0.541666	−	0.938192i	−0.457143	−	0.889393i	$-0.651127\pi$
$607$	13.3452	−	23.1146i	0.541666	−	0.938192i	0.998809	−	0.0487991i	$-0.0155394\pi$
$608$	−3.13707	+	5.43357i	−0.127225	+	0.220360i
$609$		0			0
$610$	10.8095	+	18.7226i	0.437663	+	0.758054i
$611$	17.2379			0.697371
$612$	1.32440	+	4.03063i	0.0535357	+	0.162929i
$613$	26.6190			1.07513			0.537565	−	0.843223i	$-0.319344\pi$
$613$	26.6190			1.07513			0.537565	+	0.843223i	$0.319344\pi$
$614$	7.11027	+	12.3154i	0.286947	+	0.497007i
$615$	19.7990	−	27.3460i	0.798372	−	1.10270i
$616$		0			0
$617$	6.12702	−	10.6123i	0.246664	−	0.427235i	−0.715934	−	0.698168i	$-0.753999\pi$
$617$	6.12702	−	10.6123i	0.246664	−	0.427235i	0.962598	+	0.270933i	$0.0873321\pi$
$618$	2.74597	+	6.14017i	0.110459	+	0.246994i
$619$	−18.9515	−	32.8249i	−0.761723	−	1.31934i	−0.941962	−	0.335721i	$-0.891020\pi$
$619$	−18.9515	−	32.8249i	−0.761723	−	1.31934i	0.180238	−	0.983623i	$-0.442313\pi$
$620$	−18.8730			−0.757957
$621$	33.6211	−	30.5762i	1.34917	−	1.22698i
$622$	1.41421			0.0567048
$623$		0			0
$624$	−3.00000	−	6.70820i	−0.120096	−	0.268543i
$625$	6.06351	−	10.5023i	0.242540	−	0.420092i
$626$	7.86799	−	13.6278i	0.314468	−	0.544675i
$627$	−25.4919	+	35.2091i	−1.01805	+	1.40611i
$628$	5.96550	+	10.3325i	0.238049	+	0.412314i
$629$	−8.12602			−0.324006
$630$		0			0
$631$	−4.38105			−0.174407			−0.0872034	−	0.996191i	$-0.527793\pi$
$631$	−4.38105			−0.174407			−0.0872034	+	0.996191i	$0.527793\pi$
$632$	0.936492	+	1.62205i	0.0372516	+	0.0645217i
$633$	35.5236	+	3.67423i	1.41193	+	0.146038i
$634$	−12.3095	+	21.3206i	−0.488872	+	0.846751i
$635$	1.28520	−	2.22602i	0.0510014	−	0.0883371i
$636$	21.7407	+	2.24866i	0.862074	+	0.0891651i
$637$		0			0
$638$	4.50807			0.178476
$639$	19.7460	−	22.0767i	0.781138	−	0.873339i
$640$	3.44572			0.136204
$641$	−8.55544	−	14.8185i	−0.337920	−	0.585294i	0.646122	−	0.763234i	$-0.276390\pi$
$641$	−8.55544	−	14.8185i	−0.337920	−	0.585294i	−0.984041	+	0.177941i	$0.943057\pi$
$642$	−0.258035	+	0.356394i	−0.0101838	+	0.0140657i
$643$	1.76206	−	3.05198i	0.0694890	−	0.120358i	−0.829187	−	0.558971i	$-0.811196\pi$
$643$	1.76206	−	3.05198i	0.0694890	−	0.120358i	0.898676	+	0.438612i	$0.144530\pi$
$644$		0			0
$645$	−2.74597	−	6.14017i	−0.108122	−	0.241769i
$646$	4.43649	+	7.68423i	0.174551	+	0.302332i
$647$	5.47723			0.215332			0.107666	−	0.994187i	$-0.465662\pi$
$647$	5.47723			0.215332			0.107666	+	0.994187i	$0.465662\pi$
$648$	−1.00000	−	8.94427i	−0.0392837	−	0.351364i
$649$	33.2226			1.30410
$650$	−14.5798	−	25.2530i	−0.571867	−	0.990502i
$651$		0			0
$652$	−5.00000	+	8.66025i	−0.195815	+	0.339162i
$653$	7.25403	−	12.5644i	0.283872	−	0.491681i	−0.688463	−	0.725272i	$-0.741714\pi$
$653$	7.25403	−	12.5644i	0.283872	−	0.491681i	0.972335	+	0.233590i	$0.0750475\pi$
$654$	−17.1388	+	23.6718i	−0.670179	+	0.925641i
$655$	22.9919	+	39.8232i	0.898369	+	1.55602i
$656$	−5.65685			−0.220863
$657$	8.84454	−	9.88849i	0.345058	−	0.385787i
$658$		0			0
$659$	−14.5635	−	25.2247i	−0.567314	−	0.982616i	−0.996830	−	0.0795572i	$-0.974649\pi$
$659$	−14.5635	−	25.2247i	−0.567314	−	0.982616i	0.429517	−	0.903059i	$-0.358684\pi$
$660$	23.7460	+	2.45607i	0.924310	+	0.0956023i
$661$	−23.1043	+	40.0178i	−0.898652	+	1.55651i	−0.0694345	+	0.997587i	$0.522119\pi$
$661$	−23.1043	+	40.0178i	−0.898652	+	1.55651i	−0.829218	+	0.558925i	$0.811214\pi$
$662$	−10.1825	+	17.6365i	−0.395752	+	0.685463i
$663$	−10.3372	−	1.06918i	−0.401462	−	0.0415236i
$664$	−1.32440	−	2.29393i	−0.0513967	−	0.0890216i
$665$		0			0
$666$	16.8730	+	3.52812i	0.653815	+	0.136712i
$667$	−9.85685			−0.381659
$668$	4.77012	+	8.26209i	0.184561	+	0.319670i
$669$	−22.8014	+	31.4929i	−0.881553	+	1.21759i
$670$	11.8412	−	20.5095i	0.457465	−	0.792353i
$671$	12.5483	−	21.7343i	0.484421	−	0.839043i
$672$		0			0
$673$	−7.11895	−	12.3304i	−0.274415	−	0.475301i	0.695572	−	0.718456i	$-0.255151\pi$
$673$	−7.11895	−	12.3304i	−0.274415	−	0.475301i	−0.969987	+	0.243155i	$0.921818\pi$
$674$	15.7460			0.606512
$675$	−7.59855	−	34.8953i	−0.292468	−	1.34312i
$676$	5.00000			0.192308
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	0.962015	−	0.272995i	$-0.0880143\pi$
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	−0.717428	+	0.696632i	$0.754681\pi$
$678$	−2.73861	−	6.12372i	−0.105176	−	0.235180i
$679$		0			0
$680$	2.43649	−	4.22013i	0.0934352	−	0.161834i
$681$	10.5000	−	14.5024i	0.402361	−	0.555734i
$682$	10.9545	+	18.9737i	0.419468	+	0.726539i
$683$	7.74597			0.296391			0.148196	−	0.988958i	$-0.452653\pi$
$683$	7.74597			0.296391			0.148196	+	0.988958i	$0.452653\pi$
$684$	−5.87569	−	17.8819i	−0.224662	−	0.683730i
$685$	−53.3809			−2.03958
$686$		0			0
$687$	−22.9919	−	2.37808i	−0.877197	−	0.0907293i
$688$	−0.563508	+	0.976025i	−0.0214836	+	0.0372106i
$689$	−26.7688	+	46.3650i	−1.01981	+	1.76637i
$690$	−51.9204	−	5.37017i	−1.97657	−	0.204439i
$691$	8.52448	+	14.7648i	0.324287	+	0.561681i	0.981368	−	0.192139i	$-0.0615424\pi$
$691$	8.52448	+	14.7648i	0.324287	+	0.561681i	−0.657081	+	0.753820i	$0.728209\pi$
$692$	−12.7279			−0.483843
$693$		0			0
$694$	7.74597			0.294033
$695$	34.2460	+	59.3158i	1.29902	+	2.24997i
$696$	−1.14477	+	1.58114i	−0.0433924	+	0.0599329i
$697$	−4.00000	+	6.92820i	−0.151511	+	0.262424i
$698$	−8.21584	+	14.2302i	−0.310974	+	0.538623i
$699$	−5.12938	−	11.4696i	−0.194011	−	0.433821i
$700$		0			0
$701$	−16.2540			−0.613906			−0.306953	−	0.951725i	$-0.599310\pi$
$701$	−16.2540			−0.613906			−0.306953	+	0.951725i	$0.599310\pi$
$702$	21.0000	+	6.70820i	0.792594	+	0.253185i
$703$	36.0510			1.35969
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$	−9.89949	−	22.1359i	−0.372837	−	0.833688i
$706$	1.94169	−	3.36311i	0.0730765	−	0.126572i
$707$		0			0
$708$	−8.43649	+	11.6523i	−0.317063	+	0.437922i
$709$	26.3649	+	45.6654i	0.990155	+	1.71500i	0.616298	+	0.787513i	$0.288632\pi$
$709$	26.3649	+	45.6654i	0.990155	+	1.71500i	0.373857	+	0.927486i	$0.378035\pi$
$710$	−34.0195			−1.27673
$711$	−5.50000	−	1.15004i	−0.206266	−	0.0431300i
$712$	−7.07107			−0.264999
$713$	−23.9518	−	41.4858i	−0.897003	−	1.55365i
$714$		0			0
$715$	−29.2379	+	50.6415i	−1.09344	+	1.89389i
$716$	3.43649	−	5.95218i	0.128428	−	0.222443i
$717$	−25.8429	−	2.67295i	−0.965121	−	0.0998233i
$718$	−9.11895	−	15.7945i	−0.340316	−	0.589445i
$719$	23.5027			0.876504			0.438252	−	0.898852i	$-0.355598\pi$
$719$	23.5027			0.876504			0.438252	+	0.898852i	$0.355598\pi$
$720$	−6.89144	+	7.70486i	−0.256829	+	0.287143i
$721$		0			0
$722$	−10.1825	−	17.6365i	−0.378952	−	0.656364i
$723$	−24.0554	+	33.2250i	−0.894632	+	1.23565i
$724$	−6.67261	+	11.5573i	−0.247985	+	0.429523i
$725$	−3.87298	+	6.70820i	−0.143839	+	0.249136i
$726$	−3.53553	−	7.90569i	−0.131216	−	0.293408i
$727$	1.68366	+	2.91618i	0.0624434	+	0.108155i	0.895557	−	0.444947i	$-0.146777\pi$
$727$	1.68366	+	2.91618i	0.0624434	+	0.108155i	−0.833114	+	0.553102i	$0.813444\pi$
$728$		0			0
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	−15.2379			−0.563980
$731$	0.796921	+	1.38031i	0.0294752	+	0.0510525i
$732$	4.43649	+	9.92030i	0.163977	+	0.366665i
$733$	−18.5138	+	32.0668i	−0.683823	+	1.18442i	0.289983	+	0.957032i	$0.406350\pi$
$733$	−18.5138	+	32.0668i	−0.683823	+	1.18442i	−0.973805	+	0.227384i	$0.926983\pi$
$734$	3.44572	−	5.96816i	0.127184	−	0.220289i
$735$		0			0
$736$	4.37298	+	7.57423i	0.161190	+	0.279190i
$737$	−27.4919			−1.01268
$738$	11.3137	−	12.6491i	0.416463	−	0.465620i
$739$	−30.0000			−1.10357			−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000			−1.10357			−0.551784	+	0.833987i	$0.686053\pi$
$740$	−9.89949	−	17.1464i	−0.363913	−	0.630315i
$741$	45.8607	+	4.74342i	1.68474	+	0.174254i
$742$		0			0
$743$	6.12702	−	10.6123i	0.224778	−	0.389328i	−0.731475	−	0.681869i	$-0.761167\pi$
$743$	6.12702	−	10.6123i	0.224778	−	0.389328i	0.956253	+	0.292541i	$0.0945008\pi$
$744$	−9.43649	−	0.976025i	−0.345959	−	0.0357828i
$745$	27.1281	+	46.9872i	0.993896	+	1.72148i
$746$	−1.12702			−0.0412630
$747$	7.77817	+	1.62641i	0.284589	+	0.0595071i
$748$	−5.65685			−0.206835
$749$		0			0
$750$	−6.55544	+	9.05427i	−0.239371	+	0.330615i
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$	−2.03151	+	3.51867i	−0.0740814	+	0.128313i
$753$	6.69052	+	14.9605i	0.243816	+	0.545190i
$754$	−2.39076	−	4.14092i	−0.0870665	−	0.150804i
$755$	37.9029			1.37943
$756$		0			0
$757$	31.2379			1.13536			0.567680	−	0.823249i	$-0.307841\pi$
$757$	31.2379			1.13536			0.567680	+	0.823249i	$0.307841\pi$
$758$	−13.1825	−	22.8327i	−0.478808	−	0.829321i
$759$	24.7373	+	55.3144i	0.897908	+	2.00778i
$760$	−10.8095	+	18.7226i	−0.392101	+	0.679139i
$761$	−15.2869	+	26.4777i	−0.554150	+	0.959816i	0.443819	+	0.896116i	$0.353623\pi$
$761$	−15.2869	+	26.4777i	−0.554150	+	0.959816i	−0.997969	+	0.0636995i	$0.979710\pi$
$762$	0.757718	−	1.04655i	0.0274492	−	0.0379124i
$763$		0			0
$764$	−6.12702			−0.221668
$765$	4.56351	+	13.8884i	0.164994	+	0.502137i
$766$	12.9076			0.466369
$767$	−17.6190	−	30.5169i	−0.636183	−	1.10190i
$768$	1.72286	+	0.178197i	0.0621683	+	0.00643013i
$769$	−0.617292	+	1.06918i	−0.0222601	+	0.0385557i	−0.876941	−	0.480598i	$-0.840420\pi$
$769$	−0.617292	+	1.06918i	−0.0222601	+	0.0385557i	0.854681	+	0.519154i	$0.173753\pi$
$770$		0			0
$771$	−5.18246	−	0.536026i	−0.186642	−	0.0193045i
$772$	−11.9365	−	20.6746i	−0.429604	−	0.744095i
$773$	2.03151			0.0730682			0.0365341	−	0.999332i	$-0.488368\pi$
$773$	2.03151			0.0730682			0.0365341	+	0.999332i	$0.488368\pi$
$774$	−1.05544	−	3.21209i	−0.0379371	−	0.115456i
$775$	−37.6449			−1.35224
$776$	7.50873	+	13.0055i	0.269548	+	0.466870i
$777$		0			0
$778$	−6.56351	+	11.3683i	−0.235313	+	0.407574i
$779$	17.7460	−	30.7369i	0.635815	−	1.10126i
$780$	−10.3372	−	23.1146i	−0.370130	−	0.827635i
$781$	19.7460	+	34.2010i	0.706566	+	1.22381i
$782$	12.3687			0.442303
$783$	−1.24599	−	5.72206i	−0.0445282	−	0.204490i
$784$		0			0
$785$	20.5554	+	35.6031i	0.733655	+	1.27073i
$786$	9.43649	+	21.1006i	0.336589	+	0.752635i
$787$	6.18433	−	10.7116i	0.220448	−	0.381827i	−0.734496	−	0.678613i	$-0.762582\pi$
$787$	6.18433	−	10.7116i	0.220448	−	0.381827i	0.954944	+	0.296786i	$0.0959149\pi$
$788$	−8.30948	+	14.3924i	−0.296013	+	0.512709i
$789$	17.8965	−	24.7184i	0.637132	−	0.879997i
$790$	3.22689	+	5.58913i	0.114808	+	0.198852i
$791$		0			0
$792$	11.7460	+	2.45607i	0.417375	+	0.0872726i
$793$	−26.6190			−0.945267
$794$	3.53553	+	6.12372i	0.125471	+	0.217323i
$795$	74.9123	+	7.74825i	2.65687	+	0.274802i
$796$	6.09452	−	10.5560i	0.216014	−	0.374148i
$797$	−10.2980	+	17.8366i	−0.364772	+	0.631804i	−0.988740	−	0.149646i	$-0.952187\pi$
$797$	−10.2980	+	17.8366i	−0.364772	+	0.631804i	0.623967	+	0.781450i	$0.285520\pi$
$798$		0			0
$799$	2.87298	+	4.97615i	0.101639	+	0.176044i
$800$	6.87298			0.242997
$801$	14.1421	−	15.8114i	0.499688	−	0.558668i
$802$	−3.87298			−0.136760
$803$	8.84454	+	15.3192i	0.312117	+	0.540602i
$804$	6.98125	−	9.64240i	0.246210	−	0.340061i
$805$		0			0
$806$	11.6190	−	20.1246i	0.409260	−	0.708859i
$807$	−1.43649	−	3.21209i	−0.0505669	−	0.113071i
$808$	−6.67261	−	11.5573i	−0.234742	−	0.406584i
$809$	46.7298			1.64293			0.821467	−	0.570256i	$-0.193156\pi$
$809$	46.7298			1.64293			0.821467	+	0.570256i	$0.193156\pi$
$810$	−3.44572	−	30.8195i	−0.121070	−	1.08289i
$811$	3.00806			0.105627			0.0528136	−	0.998604i	$-0.483181\pi$
$811$	3.00806			0.105627			0.0528136	+	0.998604i	$0.483181\pi$
$812$		0			0
$813$	5.00000	+	11.1803i	0.175358	+	0.392112i
$814$	−11.4919	+	19.9046i	−0.402792	+	0.697656i
$815$	−17.2286	+	29.8408i	−0.603491	+	1.04528i
$816$	1.43649	−	1.98406i	0.0502873	−	0.0694560i
$817$	−3.53553	−	6.12372i	−0.123693	−	0.214242i
$818$	−23.1435			−0.809193
$819$		0			0
$820$	−19.4919			−0.680688
$821$	4.74597	+	8.22026i	0.165635	+	0.286889i	0.936881	−	0.349649i	$-0.113699\pi$
$821$	4.74597	+	8.22026i	0.165635	+	0.286889i	−0.771245	+	0.636538i	$0.780366\pi$
$822$	−26.6904	−	2.76062i	−0.930936	−	0.0962875i
$823$	3.12702	−	5.41615i	0.109001	−	0.188795i	−0.806365	−	0.591418i	$-0.798568\pi$
$823$	3.12702	−	5.41615i	0.109001	−	0.188795i	0.915366	+	0.402623i	$0.131902\pi$
$824$	1.94169	−	3.36311i	0.0676420	−	0.117159i
$825$	47.3647	+	4.89898i	1.64903	+	0.170561i
$826$		0			0
$827$	48.8730			1.69948			0.849740	−	0.527202i	$-0.176759\pi$
$827$	48.8730			1.69948			0.849740	+	0.527202i	$0.176759\pi$
$828$	−25.6825	−	5.37017i	−0.892527	−	0.186626i
$829$	10.6180			0.368779			0.184389	−	0.982853i	$-0.440969\pi$
$829$	10.6180			0.368779			0.184389	+	0.982853i	$0.440969\pi$
$830$	−4.56351	−	7.90423i	−0.158402	−	0.274360i
$831$	−14.5912	+	20.1531i	−0.506163	+	0.699105i
$832$	−2.12132	+	3.67423i	−0.0735436	+	0.127381i
$833$		0			0
$834$	14.0554	+	31.4289i	0.486700	+	1.08829i
$835$	16.4365	+	28.4688i	0.568808	+	0.985205i
$836$	25.0966			0.867984
$837$	21.0554	−	19.1486i	0.727783	−	0.661872i
$838$	31.3707			1.08368
$839$	12.8961	+	22.3368i	0.445224	+	0.771151i	0.998068	−	0.0621340i	$-0.0197906\pi$
$839$	12.8961	+	22.3368i	0.445224	+	0.771151i	−0.552844	+	0.833285i	$0.686457\pi$
$840$		0			0
$841$	13.8649	−	24.0147i	0.478101	−	0.828094i
$842$	6.43649	−	11.1483i	0.221816	−	0.384197i
$843$	−8.88374	+	12.2701i	−0.305972	+	0.422604i
$844$	−10.3095	−	17.8565i	−0.354867	−	0.614647i
$845$	17.2286			0.592682
$846$	−3.80498	−	11.5799i	−0.130818	−	0.398126i
$847$		0			0
$848$	−6.30948	−	10.9283i	−0.216668	−	0.375280i
$849$	−8.68246	−	0.898035i	−0.297981	−	0.0308205i
$850$	4.85993	−	8.41765i	0.166694	−	0.288723i
$851$	25.1270	−	43.5213i	0.861343	−	1.49189i
$852$	−17.0098	−	1.75934i	−0.582745	−	0.0602739i
$853$	−9.06337	−	15.6982i	−0.310324	−	0.537497i	0.668109	−	0.744064i	$-0.267104\pi$
$853$	−9.06337	−	15.6982i	−0.310324	−	0.537497i	−0.978432	+	0.206567i	$0.933771\pi$
$854$		0			0
$855$	−20.2460	−	61.6158i	−0.692397	−	2.10722i
$856$	0.254033			0.00868268
$857$	12.9076	+	22.3565i	0.440914	+	0.763685i	0.997758	−	0.0669325i	$-0.0213212\pi$
$857$	12.9076	+	22.3565i	0.440914	+	0.763685i	−0.556844	+	0.830617i	$0.687988\pi$
$858$	−17.2379	+	23.8087i	−0.588492	+	0.812816i
$859$	15.2869	−	26.4777i	0.521583	−	0.903407i	−0.478102	−	0.878304i	$-0.658675\pi$
$859$	15.2869	−	26.4777i	0.521583	−	0.903407i	0.999685	−	0.0251033i	$-0.00799146\pi$
$860$	−1.94169	+	3.36311i	−0.0662111	+	0.114681i
$861$		0			0
$862$	10.7460	+	18.6126i	0.366009	+	0.633946i
$863$	−43.8730			−1.49345			−0.746727	−	0.665131i	$-0.768376\pi$
$863$	−43.8730			−1.49345			−0.746727	+	0.665131i	$0.768376\pi$
$864$	−3.84418	+	3.49604i	−0.130782	+	0.118938i
$865$	−43.8569			−1.49118
$866$	−14.8492	−	25.7196i	−0.504598	−	0.873989i
$867$	10.6066	+	23.7171i	0.360219	+	0.805474i
$868$		0			0
$869$	3.74597	−	6.48820i	0.127073	−	0.220097i
$870$	−3.94456	+	5.44816i	−0.133733	+	0.184710i
$871$	14.5798	+	25.2530i	0.494018	+	0.855664i
$872$	16.8730			0.571391
$873$	−44.0987	−	9.22097i	−1.49251	−	0.312083i
$874$	−54.8735			−1.85612
$875$		0			0
$876$	−7.61895	−	0.788035i	−0.257420	−	0.0266252i
$877$	−15.5635	+	26.9568i	−0.525542	+	0.910266i	0.474015	+	0.880517i	$0.342804\pi$
$877$	−15.5635	+	26.9568i	−0.525542	+	0.910266i	−0.999557	+	0.0297493i	$0.990529\pi$
$878$	−5.47723	+	9.48683i	−0.184847	+	0.320165i
$879$	1.37298	+	0.142009i	0.0463096	+	0.00478984i
$880$	−6.89144	−	11.9363i	−0.232310	−	0.402373i
$881$	−26.6904			−0.899223			−0.449612	−	0.893224i	$-0.648438\pi$
$881$	−26.6904			−0.899223			−0.449612	+	0.893224i	$0.648438\pi$
$882$		0			0
$883$	35.4919			1.19440			0.597199	−	0.802093i	$-0.296280\pi$
$883$	35.4919			1.19440			0.597199	+	0.802093i	$0.296280\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$	−29.0698	+	40.1507i	−0.977170	+	1.34965i
$886$	7.18246	−	12.4404i	0.241299	−	0.417943i
$887$	3.88338	−	6.72622i	0.130391	−	0.225844i	−0.793436	−	0.608653i	$-0.791710\pi$
$887$	3.88338	−	6.72622i	0.130391	−	0.225844i	0.923827	+	0.382809i	$0.125043\pi$
$888$	−4.06301	−	9.08517i	−0.136346	−	0.304878i
$889$		0			0
$890$	−24.3649			−0.816714
$891$	−28.9839	+	21.3526i	−0.970996	+	0.715341i
$892$	22.4478			0.751608
$893$	−12.7460	−	22.0767i	−0.426528	−	0.738767i
$894$	11.1341	+	24.8966i	0.372379	+	0.832666i
$895$	11.8412	−	20.5095i	0.395807	−	0.685558i
$896$		0			0
$897$	37.6905	−	52.0576i	1.25845	−	1.73815i
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	−6.17292			−0.205879
$900$	−13.7460	+	15.3685i	−0.458199	+	0.512282i
$901$	−17.8459			−0.594533
$902$	11.3137	+	19.5959i	0.376705	+	0.652473i
$903$		0			0
$904$	−1.93649	+	3.35410i	−0.0644068	+	0.111556i
$905$	−22.9919	+	39.8232i	−0.764278	+	1.32377i
$906$	18.9515	+	1.96017i	0.629620	+	0.0651222i
$907$	−9.30948	−	16.1245i	−0.309116	−	0.535405i	0.669053	−	0.743215i	$-0.266700\pi$
$907$	−9.30948	−	16.1245i	−0.309116	−	0.535405i	−0.978169	+	0.207810i	$0.933366\pi$
$908$	−10.3372			−0.343051
$909$	39.1881	+	8.19419i	1.29979	+	0.271784i
$910$		0			0
$911$	19.3730	+	33.5550i	0.641856	+	1.11173i	0.985018	+	0.172450i	$0.0551685\pi$
$911$	19.3730	+	33.5550i	0.641856	+	1.11173i	−0.343163	+	0.939276i	$0.611498\pi$
$912$	−6.37298	+	8.80226i	−0.211031	+	0.291472i
$913$	−5.29760	+	9.17571i	−0.175325	+	0.303672i
$914$	−13.0635	+	22.6267i	−0.432102	+	0.748423i
$915$	15.2869	+	34.1826i	0.505370	+	1.13004i
$916$	6.67261	+	11.5573i	0.220469	+	0.381864i
$917$		0			0
$918$	1.56351	+	7.18021i	0.0516035	+	0.236982i
$919$	−0.635083			−0.0209495			−0.0104747	−	0.999945i	$-0.503334\pi$
$919$	−0.635083			−0.0209495			−0.0104747	+	0.999945i	$0.503334\pi$
$920$	15.0681	+	26.0987i	0.496780	+	0.860448i
$921$	10.0554	+	22.4847i	0.331338	+	0.740894i
$922$	14.1813	−	24.5628i	0.467038	−	0.808933i
$923$	20.9438	−	36.2757i	0.689372	−	1.19403i
$924$		0			0
$925$	−19.7460	−	34.2010i	−0.649243	−	1.12452i
$926$	−1.61895			−0.0532020
$927$	3.63676	+	11.0680i	0.119447	+	0.363520i
$928$	1.12702			0.0369961
$929$	−27.2179	−	47.1428i	−0.892991	−	1.54671i	−0.836272	−	0.548315i	$-0.815270\pi$
$929$	−27.2179	−	47.1428i	−0.892991	−	1.54671i	−0.0567186	−	0.998390i	$-0.518064\pi$
$930$	−32.5155	−	3.36311i	−1.06623	−	0.110281i
$931$		0			0
$932$	−3.62702	+	6.28218i	−0.118807	+	0.205780i
$933$	2.43649	+	0.252009i	0.0797672	+	0.00825039i
$934$	3.09787	+	5.36567i	0.101365	+	0.175570i
$935$	−19.4919			−0.637454
$936$	−3.97320	−	12.0919i	−0.129868	−	0.395236i
$937$	45.2320			1.47767			0.738833	−	0.673889i	$-0.235377\pi$
$937$	45.2320			1.47767			0.738833	+	0.673889i	$0.235377\pi$
$938$		0			0
$939$	15.9839	−	22.0767i	0.521614	−	0.720445i
$940$	−7.00000	+	12.1244i	−0.228315	+	0.395453i
$941$	12.8569	−	22.2689i	0.419124	−	0.725945i	−0.576727	−	0.816937i	$-0.695670\pi$
$941$	12.8569	−	22.2689i	0.419124	−	0.725945i	0.995852	+	0.0909922i	$0.0290038\pi$
$942$	8.43649	+	18.8646i	0.274876	+	0.614641i
$943$	−24.7373	−	42.8463i	−0.805558	−	1.39527i
$944$	8.30565			0.270326
$945$		0			0
$946$	4.50807			0.146570
$947$	28.8014	+	49.8855i	0.935920	+	1.62106i	0.772985	+	0.634424i	$0.218763\pi$
$947$	28.8014	+	49.8855i	0.935920	+	1.62106i	0.162935	+	0.986637i	$0.447904\pi$
$948$	1.32440	+	2.96145i	0.0430145	+	0.0961833i
$949$	9.38105	−	16.2485i	0.304522	−	0.527447i
$950$	−21.5611	+	37.3448i	−0.699533	+	1.21163i
$951$	−25.0068	+	34.5390i	−0.810900	+	1.12000i
$952$		0			0
$953$	−59.4919			−1.92713			−0.963566	−	0.267469i	$-0.913813\pi$
$953$	−59.4919			−1.92713			−0.963566	+	0.267469i	$0.913813\pi$
$954$	37.0554	+	7.74825i	1.19971	+	0.250859i
$955$	−21.1120			−0.683168
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$	7.76677	+	0.803324i	0.251064	+	0.0259678i
$958$	1.94169	−	3.36311i	0.0627332	−	0.108657i
$959$		0			0
$960$	5.93649	+	0.614017i	0.191599	+	0.0198173i
$961$	0.500000	+	0.866025i	0.0161290	+	0.0279363i
$962$	24.3781			0.785981
$963$	−0.508067	+	0.568036i	−0.0163722	+	0.0183047i
$964$	23.6824			0.762758
$965$	−41.1298	−	71.2389i	−1.32402	−	2.29326i
$966$		0			0
$967$	−30.2460	+	52.3876i	−0.972645	+	1.68467i	−0.285147	+	0.958484i	$0.592042\pi$
$967$	−30.2460	+	52.3876i	−0.972645	+	1.68467i	−0.687498	+	0.726186i	$0.741291\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	6.27415	+	14.0294i	0.201555	+	0.450690i
$970$	25.8730	+	44.8133i	0.830731	+	1.43887i
$971$	−1.49262			−0.0479005			−0.0239502	−	0.999713i	$-0.507624\pi$
$971$	−1.49262			−0.0479005			−0.0239502	+	0.999713i	$0.507624\pi$
$972$	−0.129018	−	15.5879i	−0.00413824	−	0.499983i
$973$		0			0
$974$	0.245967	+	0.426027i	0.00788128	+	0.0136508i
$975$	−20.6190	−	46.1054i	−0.660335	−	1.47655i
$976$	3.13707	−	5.43357i	0.100415	−	0.173924i
$977$	−22.7460	+	39.3972i	−0.727708	+	1.26043i	0.230142	+	0.973157i	$0.426081\pi$
$977$	−22.7460	+	39.3972i	−0.727708	+	1.26043i	−0.957850	+	0.287270i	$0.907252\pi$
$978$	−10.1575	+	14.0294i	−0.324802	+	0.448611i
$979$	14.1421	+	24.4949i	0.451985	+	0.782860i
$980$		0			0
$981$	−33.7460	+	37.7291i	−1.07743	+	1.20460i
$982$	1.74597			0.0557160
$983$	−4.94975	−	8.57321i	−0.157872	−	0.273443i	0.776229	−	0.630451i	$-0.217130\pi$
$983$	−4.94975	−	8.57321i	−0.157872	−	0.273443i	−0.934101	+	0.357008i	$0.883797\pi$
$984$	−9.74597	−	1.00803i	−0.310690	−	0.0321350i
$985$	−28.6321	+	49.5923i	−0.912295	+	1.58014i
$986$	0.796921	−	1.38031i	0.0253791	−	0.0439580i
$987$		0			0
$988$	−13.3095	−	23.0527i	−0.423431	−	0.733404i
$989$	−9.85685			−0.313430
$990$	40.4733	+	8.46292i	1.28633	+	0.268969i
$991$	−11.7460			−0.373123			−0.186561	−	0.982443i	$-0.559734\pi$
$991$	−11.7460			−0.373123			−0.186561	+	0.982443i	$0.559734\pi$
$992$	2.73861	+	4.74342i	0.0869510	+	0.150604i
$993$	−20.6857	+	28.5708i	−0.656442	+	0.906667i
$994$		0			0
$995$	21.0000	−	36.3731i	0.665745	−	1.15310i
$996$	−1.87298	−	4.18812i	−0.0593477	−	0.132706i
$997$	−13.5640	−	23.4936i	−0.429578	−	0.744050i	0.567258	−	0.823540i	$-0.308004\pi$
$997$	−13.5640	−	23.4936i	−0.429578	−	0.744050i	−0.996836	+	0.0794898i	$0.974671\pi$
$998$	−29.7460			−0.941592
$999$	28.4411	+	9.08517i	0.899836	+	0.287442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.p.589.1	yes	8
3.2	odd	2		2646.2.f.s.1765.4		8
7.2	even	3		882.2.h.r.67.4		8
7.3	odd	6		882.2.e.t.373.3		8
7.4	even	3		882.2.e.t.373.2		8
7.5	odd	6		882.2.h.r.67.1		8
7.6	odd	2	inner	882.2.f.p.589.4	yes	8
9.2	odd	6		2646.2.f.s.883.4		8
9.4	even	3		7938.2.a.cu.1.4		4
9.5	odd	6		7938.2.a.cd.1.1		4
9.7	even	3	inner	882.2.f.p.295.2	✓	8
21.2	odd	6		2646.2.h.s.361.1		8
21.5	even	6		2646.2.h.s.361.4		8
21.11	odd	6		2646.2.e.r.1549.4		8
21.17	even	6		2646.2.e.r.1549.1		8
21.20	even	2		2646.2.f.s.1765.1		8
63.2	odd	6		2646.2.e.r.2125.4		8
63.11	odd	6		2646.2.h.s.667.1		8
63.13	odd	6		7938.2.a.cu.1.1		4
63.16	even	3		882.2.e.t.655.2		8
63.20	even	6		2646.2.f.s.883.1		8
63.25	even	3		882.2.h.r.79.4		8
63.34	odd	6	inner	882.2.f.p.295.3	yes	8
63.38	even	6		2646.2.h.s.667.4		8
63.41	even	6		7938.2.a.cd.1.4		4
63.47	even	6		2646.2.e.r.2125.1		8
63.52	odd	6		882.2.h.r.79.1		8
63.61	odd	6		882.2.e.t.655.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.t.373.2		8	7.4	even	3
882.2.e.t.373.3		8	7.3	odd	6
882.2.e.t.655.2		8	63.16	even	3
882.2.e.t.655.3		8	63.61	odd	6
882.2.f.p.295.2	✓	8	9.7	even	3	inner
882.2.f.p.295.3	yes	8	63.34	odd	6	inner
882.2.f.p.589.1	yes	8	1.1	even	1	trivial
882.2.f.p.589.4	yes	8	7.6	odd	2	inner
882.2.h.r.67.1		8	7.5	odd	6
882.2.h.r.67.4		8	7.2	even	3
882.2.h.r.79.1		8	63.52	odd	6
882.2.h.r.79.4		8	63.25	even	3
2646.2.e.r.1549.1		8	21.17	even	6
2646.2.e.r.1549.4		8	21.11	odd	6
2646.2.e.r.2125.1		8	63.47	even	6
2646.2.e.r.2125.4		8	63.2	odd	6
2646.2.f.s.883.1		8	63.20	even	6
2646.2.f.s.883.4		8	9.2	odd	6
2646.2.f.s.1765.1		8	21.20	even	2
2646.2.f.s.1765.4		8	3.2	odd	2
2646.2.h.s.361.1		8	21.2	odd	6
2646.2.h.s.361.4		8	21.5	even	6
2646.2.h.s.667.1		8	63.11	odd	6
2646.2.h.s.667.4		8	63.38	even	6
7938.2.a.cd.1.1		4	9.5	odd	6
7938.2.a.cd.1.4		4	63.41	even	6
7938.2.a.cu.1.1		4	63.13	odd	6
7938.2.a.cu.1.4		4	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.707107 - 1.58114i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.72286 + 2.98408i) q^{5} +(-1.01575 + 1.40294i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.707107 - 1.58114i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.72286 + 2.98408i) q^{5} +(-1.01575 + 1.40294i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +3.44572 q^{10} +(-2.00000 - 3.46410i) q^{11} +(1.72286 + 0.178197i) q^{12} +(-2.12132 + 3.67423i) q^{13} +(5.93649 + 0.614017i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.41421 q^{17} +(2.93649 + 0.614017i) q^{18} +6.27415 q^{19} +(-1.72286 - 2.98408i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(4.37298 - 7.57423i) q^{23} +(-0.707107 - 1.58114i) q^{24} +(-3.43649 - 5.95218i) q^{25} +4.24264 q^{26} +(4.94975 + 1.58114i) q^{27} +(-0.563508 - 0.976025i) q^{29} +(-2.43649 - 5.44816i) q^{30} +(2.73861 - 4.74342i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.06301 + 5.61177i) q^{33} +(0.707107 + 1.22474i) q^{34} +(-0.936492 - 2.85008i) q^{36} +5.74597 q^{37} +(-3.13707 - 5.43357i) q^{38} +(7.30948 + 0.756026i) q^{39} +(-1.72286 + 2.98408i) q^{40} +(2.82843 - 4.89898i) q^{41} +(-0.563508 - 0.976025i) q^{43} +4.00000 q^{44} +(-3.22689 - 9.82059i) q^{45} -8.74597 q^{46} +(-2.03151 - 3.51867i) q^{47} +(-1.01575 + 1.40294i) q^{48} +(-3.43649 + 5.95218i) q^{50} +(1.00000 + 2.23607i) q^{51} +(-2.12132 - 3.67423i) q^{52} +12.6190 q^{53} +(-1.10557 - 5.07718i) q^{54} +13.7829 q^{55} +(-4.43649 - 9.92030i) q^{57} +(-0.563508 + 0.976025i) q^{58} +(-4.15283 + 7.19291i) q^{59} +(-3.50000 + 4.83414i) q^{60} +(3.13707 + 5.43357i) q^{61} -5.47723 q^{62} +1.00000 q^{64} +(-7.30948 - 12.6604i) q^{65} +(6.89144 + 0.712788i) q^{66} +(3.43649 - 5.95218i) q^{67} +(0.707107 - 1.22474i) q^{68} +(-15.0681 - 1.55850i) q^{69} -9.87298 q^{71} +(-2.00000 + 2.23607i) q^{72} -4.42227 q^{73} +(-2.87298 - 4.97615i) q^{74} +(-6.98125 + 9.64240i) q^{75} +(-3.13707 + 5.43357i) q^{76} +(-3.00000 - 6.70820i) q^{78} +(0.936492 + 1.62205i) q^{79} +3.44572 q^{80} +(-1.00000 - 8.94427i) q^{81} -5.65685 q^{82} +(-1.32440 - 2.29393i) q^{83} +(2.43649 - 4.22013i) q^{85} +(-0.563508 + 0.976025i) q^{86} +(-1.14477 + 1.58114i) q^{87} +(-2.00000 - 3.46410i) q^{88} -7.07107 q^{89} +(-6.89144 + 7.70486i) q^{90} +(4.37298 + 7.57423i) q^{92} +(-9.43649 - 0.976025i) q^{93} +(-2.03151 + 3.51867i) q^{94} +(-10.8095 + 18.7226i) q^{95} +(1.72286 + 0.178197i) q^{96} +(7.50873 + 13.0055i) q^{97} +(11.7460 + 2.45607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^9	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9} - 16 q^{11} + 32 q^{15} - 4 q^{16} + 8 q^{18} - 16 q^{22} + 4 q^{23} - 12 q^{25} - 20 q^{29} - 4 q^{30} - 4 q^{32} + 8 q^{36} - 16 q^{37} + 12 q^{39} - 20 q^{43} + 32 q^{44} - 8 q^{46} - 12 q^{50} + 8 q^{51} + 8 q^{53} - 20 q^{57} - 20 q^{58} - 28 q^{60} + 8 q^{64} - 12 q^{65} + 12 q^{67} - 48 q^{71} - 16 q^{72} + 8 q^{74} - 24 q^{78} - 8 q^{79} - 8 q^{81} + 4 q^{85} - 20 q^{86} - 16 q^{88} + 4 q^{92} - 60 q^{93} - 40 q^{95} + 32 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^9 - 16 * q^11 + 32 * q^15 - 4 * q^16 + 8 * q^18 - 16 * q^22 + 4 * q^23 - 12 * q^25 - 20 * q^29 - 4 * q^30 - 4 * q^32 + 8 * q^36 - 16 * q^37 + 12 * q^39 - 20 * q^43 + 32 * q^44 - 8 * q^46 - 12 * q^50 + 8 * q^51 + 8 * q^53 - 20 * q^57 - 20 * q^58 - 28 * q^60 + 8 * q^64 - 12 * q^65 + 12 * q^67 - 48 * q^71 - 16 * q^72 + 8 * q^74 - 24 * q^78 - 8 * q^79 - 8 * q^81 + 4 * q^85 - 20 * q^86 - 16 * q^88 + 4 * q^92 - 60 * q^93 - 40 * q^95 + 32 * q^99

Introduction

L-functions

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