LMFDB - Embedded newform 567.2.h.j.352.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, degree $2$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$-1.54162 + 1.88572i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.j.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20800 q^{2} +2.87525 q^{4} +(-1.90389 - 3.29764i) q^{5} +(0.741726 - 2.53965i) q^{7} -1.93254 q^{8} +O(q^{10})$	\(q-2.20800 q^{2} +2.87525 q^{4} +(-1.90389 - 3.29764i) q^{5} +(0.741726 - 2.53965i) q^{7} -1.93254 q^{8} +(4.20379 + 7.28117i) q^{10} +(2.16217 - 3.74498i) q^{11} +(1.43762 - 2.49004i) q^{13} +(-1.63773 + 5.60755i) q^{14} -1.48345 q^{16} +(2.01297 + 3.48657i) q^{17} +(0.804103 - 1.39275i) q^{19} +(-5.47416 - 9.48152i) q^{20} +(-4.77406 + 8.26891i) q^{22} +(-1.33363 - 2.30991i) q^{23} +(-4.74962 + 8.22658i) q^{25} +(-3.17427 + 5.49799i) q^{26} +(2.13264 - 7.30213i) q^{28} +(0.375246 + 0.649945i) q^{29} +0.140536 q^{31} +7.14054 q^{32} +(-4.44464 - 7.69834i) q^{34} +(-9.78703 + 2.38928i) q^{35} +(4.14141 - 7.17313i) q^{37} +(-1.77546 + 3.07518i) q^{38} +(3.67935 + 6.37282i) q^{40} +(-5.18724 + 8.98456i) q^{41} +(-0.133520 - 0.231264i) q^{43} +(6.21676 - 10.7677i) q^{44} +(2.94464 + 5.10026i) q^{46} +7.93254 q^{47} +(-5.89969 - 3.76745i) q^{49} +(10.4871 - 18.1643i) q^{50} +(4.13352 - 7.15947i) q^{52} +(-5.61189 - 9.72008i) q^{53} -16.4661 q^{55} +(-1.43342 + 4.90798i) q^{56} +(-0.828542 - 1.43508i) q^{58} +0.693198 q^{59} +2.10744 q^{61} -0.310302 q^{62} -12.7994 q^{64} -10.9483 q^{65} -10.7663 q^{67} +(5.78780 + 10.0248i) q^{68} +(21.6097 - 5.27553i) q^{70} -3.62399 q^{71} +(1.78756 + 3.09614i) q^{73} +(-9.14422 + 15.8383i) q^{74} +(2.31199 - 4.00449i) q^{76} +(-7.90723 - 8.26891i) q^{77} -15.4234 q^{79} +(2.82433 + 4.89189i) q^{80} +(11.4534 - 19.8379i) q^{82} +(3.22034 + 5.57779i) q^{83} +(7.66497 - 13.2761i) q^{85} +(0.294812 + 0.510629i) q^{86} +(-4.17847 + 7.23733i) q^{88} +(0.128437 - 0.222459i) q^{89} +(-5.25751 - 5.49799i) q^{91} +(-3.83450 - 6.64155i) q^{92} -17.5150 q^{94} -6.12370 q^{95} +(-0.529281 - 0.916742i) q^{97} +(13.0265 + 8.31853i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8	$ 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} + 5 q^{13} - 16 q^{14} - 2 q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} - 36 q^{31} + 20 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} + 42 q^{47} - 19 q^{49} + 38 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} + 6 q^{56} + 7 q^{58} - 12 q^{59} - 40 q^{61} - 36 q^{62} - 46 q^{64} - 16 q^{65} - 10 q^{67} + 51 q^{68} + 29 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} - 53 q^{77} - 20 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} - 30 q^{94} + 32 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 + 5 * q^13 - 16 * q^14 - 2 * q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 - 10 * q^29 - 36 * q^31 + 20 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 + 42 * q^47 - 19 * q^49 + 38 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 + 6 * q^56 + 7 * q^58 - 12 * q^59 - 40 * q^61 - 36 * q^62 - 46 * q^64 - 16 * q^65 - 10 * q^67 + 51 * q^68 + 29 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 - 53 * q^77 - 20 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 - 30 * q^94 + 32 * q^95 + 9 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.20800			−1.56129			−0.780644	−	0.624975i	$-0.785109\pi$
$2$	−2.20800			−1.56129			−0.780644	+	0.624975i	$0.785109\pi$
$3$		0			0
$3$		0			0
$4$	2.87525			1.43762
$5$	−1.90389	−	3.29764i	−0.851447	−	1.47475i	−0.879903	−	0.475154i	$-0.842392\pi$
$5$	−1.90389	−	3.29764i	−0.851447	−	1.47475i	0.0284558	−	0.999595i	$-0.490941\pi$
$6$		0			0
$7$	0.741726	−	2.53965i	0.280346	−	0.959899i
$7$	0.741726	−	2.53965i	0.280346	−	0.959899i
$8$	−1.93254			−0.683256
$9$		0			0
$10$	4.20379	+	7.28117i	1.32935	+	2.30251i
$11$	2.16217	−	3.74498i	0.651918	−	1.12915i	−0.330739	−	0.943722i	$-0.607298\pi$
$11$	2.16217	−	3.74498i	0.651918	−	1.12915i	0.982657	−	0.185433i	$-0.0593687\pi$
$12$		0			0
$13$	1.43762	−	2.49004i	0.398725	−	0.690612i	−0.594844	−	0.803841i	$-0.702786\pi$
$13$	1.43762	−	2.49004i	0.398725	−	0.690612i	0.993569	+	0.113229i	$0.0361195\pi$
$14$	−1.63773	+	5.60755i	−0.437701	+	1.49868i
$15$		0			0
$16$	−1.48345			−0.370863
$17$	2.01297	+	3.48657i	0.488218	+	0.845618i	0.999908	−	0.0135517i	$-0.00431378\pi$
$17$	2.01297	+	3.48657i	0.488218	+	0.845618i	−0.511690	+	0.859170i	$0.670980\pi$
$18$		0			0
$19$	0.804103	−	1.39275i	0.184474	−	0.319518i	−0.758925	−	0.651178i	$-0.774275\pi$
$19$	0.804103	−	1.39275i	0.184474	−	0.319518i	0.943399	+	0.331660i	$0.107609\pi$
$20$	−5.47416	−	9.48152i	−1.22406	−	2.12013i
$21$		0			0
$22$	−4.77406	+	8.26891i	−1.01783	+	1.76294i
$23$	−1.33363	−	2.30991i	−0.278080	−	0.481649i	0.692828	−	0.721103i	$-0.256365\pi$
$23$	−1.33363	−	2.30991i	−0.278080	−	0.481649i	−0.970908	+	0.239455i	$0.923031\pi$
$24$		0			0
$25$	−4.74962	+	8.22658i	−0.949923	+	1.64532i
$26$	−3.17427	+	5.49799i	−0.622525	+	1.07824i
$27$		0			0
$28$	2.13264	−	7.30213i	0.403032	−	1.37997i
$29$	0.375246	+	0.649945i	0.0696815	+	0.120692i	0.898761	−	0.438439i	$-0.144468\pi$
$29$	0.375246	+	0.649945i	0.0696815	+	0.120692i	−0.829080	+	0.559131i	$0.811135\pi$
$30$		0			0
$31$	0.140536			0.0252410			0.0126205	−	0.999920i	$-0.495983\pi$
$31$	0.140536			0.0252410			0.0126205	+	0.999920i	$0.495983\pi$
$32$	7.14054			1.26228
$33$		0			0
$34$	−4.44464	−	7.69834i	−0.762249	−	1.32025i
$35$	−9.78703	+	2.38928i	−1.65431	+	0.403863i
$36$		0			0
$37$	4.14141	−	7.17313i	0.680844	−	1.17926i	−0.293880	−	0.955842i	$-0.594947\pi$
$37$	4.14141	−	7.17313i	0.680844	−	1.17926i	0.974724	−	0.223414i	$-0.0717201\pi$
$38$	−1.77546	+	3.07518i	−0.288017	+	0.498860i
$39$		0			0
$40$	3.67935	+	6.37282i	0.581756	+	1.00763i
$41$	−5.18724	+	8.98456i	−0.810111	+	1.40315i	0.102675	+	0.994715i	$0.467260\pi$
$41$	−5.18724	+	8.98456i	−0.810111	+	1.40315i	−0.912786	+	0.408438i	$0.866074\pi$
$42$		0			0
$43$	−0.133520	−	0.231264i	−0.0203616	−	0.0352674i	0.855665	−	0.517530i	$-0.173148\pi$
$43$	−0.133520	−	0.231264i	−0.0203616	−	0.0352674i	−0.876027	+	0.482263i	$0.839815\pi$
$44$	6.21676	−	10.7677i	0.937212	−	1.62330i
$45$		0			0
$46$	2.94464	+	5.10026i	0.434163	+	0.751993i
$47$	7.93254			1.15708			0.578540	−	0.815654i	$-0.303623\pi$
$47$	7.93254			1.15708			0.578540	+	0.815654i	$0.303623\pi$
$48$		0			0
$49$	−5.89969	−	3.76745i	−0.842812	−	0.538208i
$50$	10.4871	−	18.1643i	1.48310	−	2.56881i
$51$		0			0
$52$	4.13352	−	7.15947i	0.573216	−	0.992839i
$53$	−5.61189	−	9.72008i	−0.770852	−	1.33516i	−0.937096	−	0.349071i	$-0.886497\pi$
$53$	−5.61189	−	9.72008i	−0.770852	−	1.33516i	0.166244	−	0.986085i	$-0.446836\pi$
$54$		0			0
$55$	−16.4661			−2.22029
$56$	−1.43342	+	4.90798i	−0.191548	+	0.655857i
$57$		0			0
$58$	−0.828542	−	1.43508i	−0.108793	−	0.188435i
$59$	0.693198			0.0902468			0.0451234	−	0.998981i	$-0.485632\pi$
$59$	0.693198			0.0902468			0.0451234	+	0.998981i	$0.485632\pi$
$60$		0			0
$61$	2.10744			0.269830			0.134915	−	0.990857i	$-0.456924\pi$
$61$	2.10744			0.269830			0.134915	+	0.990857i	$0.456924\pi$
$62$	−0.310302			−0.0394085
$63$		0			0
$64$	−12.7994			−1.59992
$65$	−10.9483			−1.35797
$66$		0			0
$67$	−10.7663			−1.31531			−0.657655	−	0.753319i	$-0.728451\pi$
$67$	−10.7663			−1.31531			−0.657655	+	0.753319i	$0.728451\pi$
$68$	5.78780	+	10.0248i	0.701873	+	1.21568i
$69$		0			0
$70$	21.6097	−	5.27553i	2.58286	−	0.630547i
$71$	−3.62399			−0.430088			−0.215044	−	0.976604i	$-0.568990\pi$
$71$	−3.62399			−0.430088			−0.215044	+	0.976604i	$0.568990\pi$
$72$		0			0
$73$	1.78756	+	3.09614i	0.209217	+	0.362375i	0.951468	−	0.307747i	$-0.0995750\pi$
$73$	1.78756	+	3.09614i	0.209217	+	0.362375i	−0.742251	+	0.670122i	$0.766242\pi$
$74$	−9.14422	+	15.8383i	−1.06299	+	1.84116i
$75$		0			0
$76$	2.31199	−	4.00449i	0.265204	−	0.459347i
$77$	−7.90723	−	8.26891i	−0.901112	−	0.942329i
$78$		0			0
$79$	−15.4234			−1.73526			−0.867632	−	0.497207i	$-0.834359\pi$
$79$	−15.4234			−1.73526			−0.867632	+	0.497207i	$0.834359\pi$
$80$	2.82433	+	4.89189i	0.315770	+	0.546930i
$81$		0			0
$82$	11.4534	−	19.8379i	1.26482	−	2.19073i
$83$	3.22034	+	5.57779i	0.353478	+	0.612241i	0.986856	−	0.161601i	$-0.0516657\pi$
$83$	3.22034	+	5.57779i	0.353478	+	0.612241i	−0.633378	+	0.773842i	$0.718332\pi$
$84$		0			0
$85$	7.66497	−	13.2761i	0.831383	−	1.44000i
$86$	0.294812	+	0.510629i	0.0317904	+	0.0550625i
$87$		0			0
$88$	−4.17847	+	7.23733i	−0.445427	+	0.771502i
$89$	0.128437	−	0.222459i	0.0136143	−	0.0235806i	−0.859138	−	0.511744i	$-0.829000\pi$
$89$	0.128437	−	0.222459i	0.0136143	−	0.0235806i	0.872752	+	0.488163i	$0.162333\pi$
$90$		0			0
$91$	−5.25751	−	5.49799i	−0.551137	−	0.576346i
$92$	−3.83450	−	6.64155i	−0.399774	−	0.692429i
$93$		0			0
$94$	−17.5150			−1.80654
$95$	−6.12370			−0.628279
$96$		0			0
$97$	−0.529281	−	0.916742i	−0.0537403	−	0.0930810i	0.837904	−	0.545818i	$-0.183781\pi$
$97$	−0.529281	−	0.916742i	−0.0537403	−	0.0930810i	−0.891644	+	0.452737i	$0.850448\pi$
$98$	13.0265	+	8.31853i	1.31587	+	0.840298i
$99$		0			0
$100$	−13.6563	+	23.6534i	−1.36563	+	2.36534i
$101$	−0.682923	+	1.18286i	−0.0679534	+	0.117699i	−0.898000	−	0.439995i	$-0.854980\pi$
$101$	−0.682923	+	1.18286i	−0.0679534	+	0.117699i	0.830047	+	0.557694i	$0.188314\pi$
$102$		0			0
$103$	7.48563	+	12.9655i	0.737581	+	1.27753i	0.953582	+	0.301134i	$0.0973651\pi$
$103$	7.48563	+	12.9655i	0.737581	+	1.27753i	−0.216001	+	0.976393i	$0.569302\pi$
$104$	−2.77826	+	4.81209i	−0.272431	+	0.471865i
$105$		0			0
$106$	12.3910	+	21.4619i	1.20352	+	2.08456i
$107$	4.04075	−	6.99878i	0.390634	−	0.676597i	−0.601900	−	0.798572i	$-0.705589\pi$
$107$	4.04075	−	6.99878i	0.390634	−	0.676597i	0.992533	+	0.121974i	$0.0389226\pi$
$108$		0			0
$109$	4.55460	+	7.88879i	0.436251	+	0.755609i	0.997397	−	0.0721080i	$-0.0229726\pi$
$109$	4.55460	+	7.88879i	0.436251	+	0.755609i	−0.561146	+	0.827717i	$0.689639\pi$
$110$	36.3572			3.46652
$111$		0			0
$112$	−1.10031	+	3.76745i	−0.103970	+	0.355991i
$113$	1.38303	−	2.39547i	0.130104	−	0.225347i	−0.793612	−	0.608424i	$-0.791802\pi$
$113$	1.38303	−	2.39547i	0.130104	−	0.225347i	0.923717	+	0.383077i	$0.125135\pi$
$114$		0			0
$115$	−5.07816	+	8.79563i	−0.473541	+	0.820197i
$116$	1.07892	+	1.86875i	0.100176	+	0.173509i
$117$		0			0
$118$	−1.53058			−0.140901
$119$	10.3478	−	2.52618i	0.948578	−	0.231574i
$120$		0			0
$121$	−3.84993	−	6.66828i	−0.349994	−	0.606207i
$122$	−4.65322			−0.421283
$123$		0			0
$124$	0.404075			0.0362870
$125$	17.1321			1.53234
$126$		0			0
$127$	13.6573			1.21189			0.605945	−	0.795507i	$-0.292795\pi$
$127$	13.6573			1.21189			0.605945	+	0.795507i	$0.292795\pi$
$128$	13.9799			1.23566
$129$		0			0
$130$	24.1739			2.12019
$131$	8.80691	+	15.2540i	0.769463	+	1.33275i	0.937854	+	0.347029i	$0.112810\pi$
$131$	8.80691	+	15.2540i	0.769463	+	1.33275i	−0.168391	+	0.985720i	$0.553857\pi$
$132$		0			0
$133$	−2.94067	−	3.07518i	−0.254989	−	0.266652i
$134$	23.7719			2.05358
$135$		0			0
$136$	−3.89015	−	6.73794i	−0.333578	−	0.577774i
$137$	4.33363	−	7.50606i	0.370247	−	0.641286i	−0.619357	−	0.785110i	$-0.712607\pi$
$137$	4.33363	−	7.50606i	0.370247	−	0.641286i	0.989603	+	0.143824i	$0.0459399\pi$
$138$		0			0
$139$	1.88303	−	3.26150i	0.159716	−	0.276637i	−0.775050	−	0.631900i	$-0.782275\pi$
$139$	1.88303	−	3.26150i	0.159716	−	0.276637i	0.934766	+	0.355263i	$0.115609\pi$
$140$	−28.1401	+	6.86978i	−2.37827	+	0.580602i
$141$		0			0
$142$	8.00175			0.671492
$143$	−6.21676	−	10.7677i	−0.519872	−	0.900444i
$144$		0			0
$145$	1.42886	−	2.47485i	0.118660	−	0.205525i
$146$	−3.94691	−	6.83626i	−0.326649	−	0.565773i
$147$		0			0
$148$	11.9076	−	20.6245i	0.978797	−	1.69533i
$149$	2.30561	+	3.99344i	0.188883	+	0.327155i	0.944878	−	0.327422i	$-0.106180\pi$
$149$	2.30561	+	3.99344i	0.188883	+	0.327155i	−0.755995	+	0.654577i	$0.772847\pi$
$150$		0			0
$151$	−3.89881	+	6.75294i	−0.317281	+	0.549546i	−0.979920	−	0.199393i	$-0.936103\pi$
$151$	−3.89881	+	6.75294i	−0.317281	+	0.549546i	0.662639	+	0.748939i	$0.269436\pi$
$152$	−1.55396	+	2.69154i	−0.126043	+	0.218313i
$153$		0			0
$154$	17.4591	+	18.2577i	1.40690	+	1.47125i
$155$	−0.267565	−	0.463436i	−0.0214913	−	0.0372241i
$156$		0			0
$157$	23.2655			1.85679			0.928395	−	0.371595i	$-0.121189\pi$
$157$	23.2655			1.85679			0.928395	+	0.371595i	$0.121189\pi$
$158$	34.0547			2.70925
$159$		0			0
$160$	−13.5948	−	23.5469i	−1.07476	−	1.86155i
$161$	−6.85555	+	1.67363i	−0.540293	+	0.131900i
$162$		0			0
$163$	−3.05547	+	5.29223i	−0.239323	+	0.414519i	−0.960520	−	0.278210i	$-0.910259\pi$
$163$	−3.05547	+	5.29223i	−0.239323	+	0.414519i	0.721197	+	0.692730i	$0.243592\pi$
$164$	−14.9146	+	25.8328i	−1.16463	+	2.01721i
$165$		0			0
$166$	−7.11049	−	12.3157i	−0.551881	−	0.955886i
$167$	5.82076	−	10.0819i	0.450424	−	0.780157i	−0.547988	−	0.836486i	$-0.684606\pi$
$167$	5.82076	−	10.0819i	0.450424	−	0.780157i	0.998412	+	0.0563288i	$0.0179395\pi$
$168$		0			0
$169$	2.36648	+	4.09886i	0.182037	+	0.315297i
$170$	−16.9242	+	29.3136i	−1.29803	+	2.24825i
$171$		0			0
$172$	−0.383903	−	0.664940i	−0.0292723	−	0.0507012i
$173$	−19.2571			−1.46409			−0.732045	−	0.681256i	$-0.761434\pi$
$173$	−19.2571			−1.46409			−0.732045	+	0.681256i	$0.761434\pi$
$174$		0			0
$175$	17.3697	+	18.1643i	1.31303	+	1.37309i
$176$	−3.20747	+	5.55550i	−0.241772	+	0.418762i
$177$		0			0
$178$	−0.283588	+	0.491189i	−0.0212558	+	0.0368162i
$179$	1.67093	+	2.89414i	0.124891	+	0.216318i	0.921690	−	0.387926i	$-0.126808\pi$
$179$	1.67093	+	2.89414i	0.124891	+	0.216318i	−0.796799	+	0.604244i	$0.793475\pi$
$180$		0			0
$181$	−19.7358			−1.46695			−0.733474	−	0.679717i	$-0.762103\pi$
$181$	−19.7358			−1.46695			−0.733474	+	0.679717i	$0.762103\pi$
$182$	11.6086	+	12.1395i	0.860483	+	0.899843i
$183$		0			0
$184$	2.57728	+	4.46399i	0.190000	+	0.329089i
$185$	−31.5392			−2.31881
$186$		0			0
$187$	17.4095			1.27311
$188$	22.8080			1.66344
$189$		0			0
$190$	13.5211			0.980925
$191$	−4.17490			−0.302085			−0.151043	−	0.988527i	$-0.548263\pi$
$191$	−4.17490			−0.302085			−0.151043	+	0.988527i	$0.548263\pi$
$192$		0			0
$193$	−13.8737			−0.998652			−0.499326	−	0.866414i	$-0.666419\pi$
$193$	−13.8737			−0.998652			−0.499326	+	0.866414i	$0.666419\pi$
$194$	1.16865	+	2.02416i	0.0839042	+	0.145326i
$195$		0			0
$196$	−16.9630	−	10.8324i	−1.21165	−	0.773740i
$197$	−7.48520			−0.533299			−0.266649	−	0.963794i	$-0.585917\pi$
$197$	−7.48520			−0.533299			−0.266649	+	0.963794i	$0.585917\pi$
$198$		0			0
$199$	6.32767	+	10.9598i	0.448556	+	0.776922i	0.998292	−	0.0584160i	$-0.0186050\pi$
$199$	6.32767	+	10.9598i	0.448556	+	0.776922i	−0.549736	+	0.835338i	$0.685272\pi$
$200$	9.17882	−	15.8982i	0.649041	−	1.12417i
$201$		0			0
$202$	1.50789	−	2.61174i	0.106095	−	0.183762i
$203$	1.92897	−	0.470914i	0.135387	−	0.0330517i
$204$		0			0
$205$	39.5038			2.75907
$206$	−16.5282	−	28.6277i	−1.15158	−	1.99459i
$207$		0			0
$208$	−2.13264	+	3.69385i	−0.147872	+	0.256122i
$209$	−3.47721	−	6.02270i	−0.240524	−	0.416599i
$210$		0			0
$211$	2.57599	−	4.46174i	0.177338	−	0.307159i	−0.763630	−	0.645654i	$-0.776585\pi$
$211$	2.57599	−	4.46174i	0.177338	−	0.307159i	0.940968	+	0.338496i	$0.109918\pi$
$212$	−16.1356	−	27.9476i	−1.10819	−	1.91945i
$213$		0			0
$214$	−8.92195	+	15.4533i	−0.609892	+	1.05636i
$215$	−0.508416	+	0.880602i	−0.0346737	+	0.0600566i
$216$		0			0
$217$	0.104239	−	0.356912i	0.00707621	−	0.0242288i
$218$	−10.0565	−	17.4184i	−0.681114	−	1.17972i
$219$		0			0
$220$	−47.3442			−3.19195
$221$	11.5756			0.778659
$222$		0			0
$223$	7.60832	+	13.1780i	0.509490	+	0.882463i	0.999940	+	0.0109935i	$0.00349942\pi$
$223$	7.60832	+	13.1780i	0.509490	+	0.882463i	−0.490449	+	0.871470i	$0.663167\pi$
$224$	5.29632	−	18.1345i	0.353875	−	1.21166i
$225$		0			0
$226$	−3.05372	+	5.28920i	−0.203130	+	0.351832i
$227$	2.14474	−	3.71481i	0.142352	−	0.246560i	−0.786030	−	0.618188i	$-0.787867\pi$
$227$	2.14474	−	3.71481i	0.142352	−	0.246560i	0.928382	+	0.371628i	$0.121200\pi$
$228$		0			0
$229$	−0.485626	−	0.841128i	−0.0320910	−	0.0555833i	0.849534	−	0.527534i	$-0.176883\pi$
$229$	−0.485626	−	0.841128i	−0.0320910	−	0.0555833i	−0.881625	+	0.471951i	$0.843550\pi$
$230$	11.2126	−	19.4207i	0.739334	−	1.28056i
$231$		0			0
$232$	−0.725178	−	1.25605i	−0.0476103	−	0.0824634i
$233$	1.88671	−	3.26788i	0.123603	−	0.214086i	−0.797583	−	0.603209i	$-0.793889\pi$
$233$	1.88671	−	3.26788i	0.123603	−	0.214086i	0.921186	+	0.389123i	$0.127222\pi$
$234$		0			0
$235$	−15.1027	−	26.1587i	−0.985192	−	1.70640i
$236$	1.99312			0.129741
$237$		0			0
$238$	−22.8478	+	5.57779i	−1.48100	+	0.361554i
$239$	−3.34520	+	5.79405i	−0.216383	+	0.374786i	−0.953699	−	0.300761i	$-0.902759\pi$
$239$	−3.34520	+	5.79405i	−0.216383	+	0.374786i	0.737317	+	0.675547i	$0.236093\pi$
$240$		0			0
$241$	7.48563	−	12.9655i	0.482192	−	0.835180i	−0.517599	−	0.855623i	$-0.673174\pi$
$241$	7.48563	−	12.9655i	0.482192	−	0.835180i	0.999791	+	0.0204428i	$0.00650760\pi$
$242$	8.50063	+	14.7235i	0.546441	+	0.946464i
$243$		0			0
$244$	6.05941			0.387914
$245$	−1.19134	+	26.6279i	−0.0761118	+	1.70119i
$246$		0			0
$247$	−2.31199	−	4.00449i	−0.147109	−	0.254800i
$248$	−0.271591			−0.0172460
$249$		0			0
$250$	−37.8277			−2.39243
$251$	−17.0787			−1.07800			−0.538999	−	0.842307i	$-0.681197\pi$
$251$	−17.0787			−1.07800			−0.538999	+	0.842307i	$0.681197\pi$
$252$		0			0
$253$	−11.5341			−0.725141
$254$	−30.1553			−1.89211
$255$		0			0
$256$	−5.26879			−0.329299
$257$	−4.28615	−	7.42384i	−0.267363	−	0.463086i	0.700817	−	0.713341i	$-0.252819\pi$
$257$	−4.28615	−	7.42384i	−0.267363	−	0.463086i	−0.968180	+	0.250255i	$0.919486\pi$
$258$		0			0
$259$	−15.1455	−	15.8383i	−0.941095	−	0.984141i
$260$	−31.4791			−1.95225
$261$		0			0
$262$	−19.4456	−	33.6808i	−1.20135	−	2.08081i
$263$	2.84842	−	4.93361i	0.175641	−	0.304220i	−0.764742	−	0.644337i	$-0.777133\pi$
$263$	2.84842	−	4.93361i	0.175641	−	0.304220i	0.940383	+	0.340117i	$0.110467\pi$
$264$		0			0
$265$	−21.3689	+	37.0120i	−1.31268	+	2.27363i
$266$	6.49299	+	6.78999i	0.398111	+	0.416321i
$267$		0			0
$268$	−30.9557			−1.89092
$269$	−7.80077	−	13.5113i	−0.475621	−	0.823800i	0.523989	−	0.851725i	$-0.324443\pi$
$269$	−7.80077	−	13.5113i	−0.475621	−	0.823800i	−0.999610	+	0.0279249i	$0.991110\pi$
$270$		0			0
$271$	15.3688	−	26.6195i	0.933586	−	1.61702i	0.156449	−	0.987686i	$-0.449995\pi$
$271$	15.3688	−	26.6195i	0.933586	−	1.61702i	0.777136	−	0.629332i	$-0.216671\pi$
$272$	−2.98615	−	5.17216i	−0.181062	−	0.313609i
$273$		0			0
$274$	−9.56863	+	16.5733i	−0.578062	+	1.00123i
$275$	20.5389	+	35.5745i	1.23854	+	2.14522i
$276$		0			0
$277$	13.2963	−	23.0299i	0.798899	−	1.38373i	−0.121435	−	0.992599i	$-0.538750\pi$
$277$	13.2963	−	23.0299i	0.798899	−	1.38373i	0.920334	−	0.391133i	$-0.127917\pi$
$278$	−4.15772	+	7.20138i	−0.249363	+	0.431910i
$279$		0			0
$280$	18.9138	−	4.61739i	1.13032	−	0.275942i
$281$	−8.68065	−	15.0353i	−0.517844	−	0.896932i	−0.999785	−	0.0207285i	$-0.993401\pi$
$281$	−8.68065	−	15.0353i	−0.517844	−	0.896932i	0.481941	−	0.876204i	$-0.339932\pi$
$282$		0			0
$283$	18.3554			1.09112			0.545558	−	0.838073i	$-0.316318\pi$
$283$	18.3554			1.09112			0.545558	+	0.838073i	$0.316318\pi$
$284$	−10.4199			−0.618305
$285$		0			0
$286$	13.7266	+	23.7751i	0.811670	+	1.40585i
$287$	18.9702	+	19.8379i	1.11977	+	1.17099i
$288$		0			0
$289$	0.395870	−	0.685667i	0.0232865	−	0.0403334i
$290$	−3.15491	+	5.46446i	−0.185263	+	0.320884i
$291$		0			0
$292$	5.13966	+	8.90215i	0.300776	+	0.520959i
$293$	5.34906	−	9.26484i	0.312495	−	0.541258i	−0.666407	−	0.745588i	$-0.732169\pi$
$293$	5.34906	−	9.26484i	0.312495	−	0.541258i	0.978902	+	0.204331i	$0.0655018\pi$
$294$		0			0
$295$	−1.31978	−	2.28592i	−0.0768403	−	0.133091i
$296$	−8.00344	+	13.8624i	−0.465191	+	0.805734i
$297$		0			0
$298$	−5.09078	−	8.81749i	−0.294901	−	0.510784i
$299$	−7.66900			−0.443510
$300$		0			0
$301$	−0.686365	+	0.167561i	−0.0395614	+	0.00965803i
$302$	8.60856	−	14.9105i	0.495367	−	0.858000i
$303$		0			0
$304$	−1.19285	+	2.06607i	−0.0684145	+	0.118497i
$305$	−4.01234	−	6.94958i	−0.229746	−	0.397932i
$306$		0			0
$307$	31.3948			1.79180			0.895899	−	0.444258i	$-0.146533\pi$
$307$	31.3948			1.79180			0.895899	+	0.444258i	$0.146533\pi$
$308$	−22.7352	−	23.7751i	−1.29546	−	1.35471i
$309$		0			0
$310$	0.590783	+	1.02327i	0.0335542	+	0.0581176i
$311$	13.4891			0.764895			0.382447	−	0.923977i	$-0.375081\pi$
$311$	13.4891			0.764895			0.382447	+	0.923977i	$0.375081\pi$
$312$		0			0
$313$	−19.3414			−1.09324			−0.546620	−	0.837381i	$-0.684086\pi$
$313$	−19.3414			−1.09324			−0.546620	+	0.837381i	$0.684086\pi$
$314$	−51.3701			−2.89899
$315$		0			0
$316$	−44.3459			−2.49465
$317$	15.3576			0.862571			0.431286	−	0.902215i	$-0.358060\pi$
$317$	15.3576			0.862571			0.431286	+	0.902215i	$0.358060\pi$
$318$		0			0
$319$	3.24538			0.181706
$320$	24.3686	+	42.2077i	1.36225	+	2.35948i
$321$		0			0
$322$	15.1370	−	3.69537i	0.843553	−	0.205935i
$323$	6.47455			0.360254
$324$		0			0
$325$	13.6563	+	23.6534i	0.757516	+	1.31206i
$326$	6.74647	−	11.6852i	0.373652	−	0.647185i
$327$		0			0
$328$	10.0245	−	17.3630i	0.553513	−	0.958713i
$329$	5.88377	−	20.1459i	0.324383	−	1.11068i
$330$		0			0
$331$	−1.23829			−0.0680627			−0.0340313	−	0.999421i	$-0.510835\pi$
$331$	−1.23829			−0.0680627			−0.0340313	+	0.999421i	$0.510835\pi$
$332$	9.25926	+	16.0375i	0.508168	+	0.880172i
$333$		0			0
$334$	−12.8522	+	22.2607i	−0.703242	+	1.21805i
$335$	20.4978	+	35.5033i	1.11992	+	1.93975i
$336$		0			0
$337$	−5.95428	+	10.3131i	−0.324350	+	0.561791i	−0.981381	−	0.192073i	$-0.938479\pi$
$337$	−5.95428	+	10.3131i	−0.324350	+	0.561791i	0.657030	+	0.753864i	$0.271812\pi$
$338$	−5.22518	−	9.05027i	−0.284212	−	0.492270i
$339$		0			0
$340$	22.0387	−	38.1721i	1.19522	−	2.07017i
$341$	0.303862	−	0.526304i	0.0164550	−	0.0285010i
$342$		0			0
$343$	−13.9440	+	12.1887i	−0.752904	+	0.658130i
$344$	0.258033	+	0.446926i	0.0139122	+	0.0240966i
$345$		0			0
$346$	42.5196			2.28587
$347$	4.34678			0.233347			0.116674	−	0.993170i	$-0.462777\pi$
$347$	4.34678			0.233347			0.116674	+	0.993170i	$0.462777\pi$
$348$		0			0
$349$	−3.58780	−	6.21425i	−0.192051	−	0.332641i	0.753879	−	0.657013i	$-0.228180\pi$
$349$	−3.58780	−	6.21425i	−0.192051	−	0.332641i	−0.945930	+	0.324372i	$0.894847\pi$
$350$	−38.3523	−	40.1066i	−2.05002	−	2.14379i
$351$		0			0
$352$	15.4390	−	26.7412i	0.822903	−	1.42531i
$353$	12.5484	−	21.7344i	0.667881	−	1.15680i	−0.310614	−	0.950536i	$-0.600535\pi$
$353$	12.5484	−	21.7344i	0.667881	−	1.15680i	0.978495	−	0.206268i	$-0.0661320\pi$
$354$		0			0
$355$	6.89969	+	11.9506i	0.366197	+	0.634272i
$356$	0.369288	−	0.639625i	0.0195722	−	0.0339001i
$357$		0			0
$358$	−3.68941	−	6.39025i	−0.194992	−	0.337735i
$359$	15.9959	−	27.7057i	0.844231	−	1.46225i	−0.0420557	−	0.999115i	$-0.513391\pi$
$359$	15.9959	−	27.7057i	0.844231	−	1.46225i	0.886287	−	0.463136i	$-0.153276\pi$
$360$		0			0
$361$	8.20684	+	14.2147i	0.431939	+	0.748140i
$362$	43.5765			2.29033
$363$		0			0
$364$	−15.1166	−	15.8081i	−0.792327	−	0.828568i
$365$	6.80663	−	11.7894i	0.356275	−	0.617087i
$366$		0			0
$367$	5.56238	−	9.63432i	0.290354	−	0.502907i	−0.683540	−	0.729913i	$-0.739560\pi$
$367$	5.56238	−	9.63432i	0.290354	−	0.502907i	0.973893	+	0.227006i	$0.0728937\pi$
$368$	1.97837	+	3.42664i	0.103130	+	0.178626i
$369$		0			0
$370$	69.6385			3.62033
$371$	−28.8481	+	7.04262i	−1.49772	+	0.365635i
$372$		0			0
$373$	−8.07728	−	13.9903i	−0.418226	−	0.724388i	0.577535	−	0.816366i	$-0.304015\pi$
$373$	−8.07728	−	13.9903i	−0.418226	−	0.724388i	−0.995761	+	0.0919773i	$0.970681\pi$
$374$	−38.4402			−1.98770
$375$		0			0
$376$	−15.3299			−0.790582
$377$	2.15785			0.111135
$378$		0			0
$379$	3.18485			0.163595			0.0817973	−	0.996649i	$-0.473934\pi$
$379$	3.18485			0.163595			0.0817973	+	0.996649i	$0.473934\pi$
$380$	−17.6072			−0.903228
$381$		0			0
$382$	9.21816			0.471642
$383$	8.23882	+	14.2700i	0.420984	+	0.729165i	0.996036	−	0.0889514i	$-0.0283516\pi$
$383$	8.23882	+	14.2700i	0.420984	+	0.729165i	−0.575052	+	0.818117i	$0.695018\pi$
$384$		0			0
$385$	−12.2134	+	41.8183i	−0.622451	+	2.13126i
$386$	30.6331			1.55918
$387$		0			0
$388$	−1.52181	−	2.63586i	−0.0772584	−	0.133815i
$389$	−15.9885	+	27.6930i	−0.810651	+	1.40409i	0.101758	+	0.994809i	$0.467553\pi$
$389$	−15.9885	+	27.6930i	−0.810651	+	1.40409i	−0.912409	+	0.409280i	$0.865780\pi$
$390$		0			0
$391$	5.36911	−	9.29956i	0.271527	−	0.470299i
$392$	11.4014	+	7.28076i	0.575856	+	0.367734i
$393$		0			0
$394$	16.5273			0.832633
$395$	29.3644	+	50.8607i	1.47748	+	2.55908i
$396$		0			0
$397$	−13.9059	+	24.0858i	−0.697919	+	1.20883i	0.271268	+	0.962504i	$0.412557\pi$
$397$	−13.9059	+	24.0858i	−0.697919	+	1.20883i	−0.969187	+	0.246327i	$0.920776\pi$
$398$	−13.9715	−	24.1993i	−0.700326	−	1.21300i
$399$		0			0
$400$	7.04583	−	12.2037i	0.352291	−	0.610187i
$401$	−13.7942	−	23.8922i	−0.688847	−	1.19312i	−0.972211	−	0.234106i	$-0.924784\pi$
$401$	−13.7942	−	23.8922i	−0.688847	−	1.19312i	0.283364	−	0.959012i	$-0.408550\pi$
$402$		0			0
$403$	0.202038	−	0.349939i	0.0100642	−	0.0174317i
$404$	−1.96357	+	3.40101i	−0.0976913	+	0.169206i
$405$		0			0
$406$	−4.25915	+	1.03978i	−0.211378	+	0.0516032i
$407$	−17.9088	−	31.0190i	−0.887708	−	1.53756i
$408$		0			0
$409$	−11.8246			−0.584690			−0.292345	−	0.956313i	$-0.594436\pi$
$409$	−11.8246			−0.584690			−0.292345	+	0.956313i	$0.594436\pi$
$410$	−87.2242			−4.30770
$411$		0			0
$412$	21.5230	+	37.2790i	1.06036	+	1.83660i
$413$	0.514163	−	1.76048i	0.0253003	−	0.0866278i
$414$		0			0
$415$	12.2624	−	21.2390i	0.601935	−	1.04258i
$416$	10.2654	−	17.7802i	0.503303	−	0.871746i
$417$		0			0
$418$	7.67767	+	13.2981i	0.375527	+	0.650432i
$419$	−4.40834	+	7.63547i	−0.215362	+	0.373017i	−0.953384	−	0.301759i	$-0.902426\pi$
$419$	−4.40834	+	7.63547i	−0.215362	+	0.373017i	0.738023	+	0.674776i	$0.235760\pi$
$420$		0			0
$421$	−9.35004	−	16.1947i	−0.455693	−	0.789284i	0.543035	−	0.839710i	$-0.317275\pi$
$421$	−9.35004	−	16.1947i	−0.455693	−	0.789284i	−0.998728	+	0.0504267i	$0.983942\pi$
$422$	−5.68776	+	9.85150i	−0.276876	+	0.479563i
$423$		0			0
$424$	10.8452	+	18.7844i	0.526689	+	0.912253i
$425$	−38.2434			−1.85508
$426$		0			0
$427$	1.56314	−	5.35217i	0.0756458	−	0.259010i
$428$	11.6181	−	20.1232i	0.561584	−	0.972692i
$429$		0			0
$430$	1.12258	−	1.94437i	0.0541356	−	0.0937657i
$431$	8.30972	+	14.3929i	0.400265	+	0.693279i	0.993758	−	0.111560i	$-0.0355847\pi$
$431$	8.30972	+	14.3929i	0.400265	+	0.693279i	−0.593493	+	0.804839i	$0.702251\pi$
$432$		0			0
$433$	−25.3004			−1.21586			−0.607929	−	0.793992i	$-0.707999\pi$
$433$	−25.3004			−1.21586			−0.607929	+	0.793992i	$0.707999\pi$
$434$	−0.230159	+	0.788061i	−0.0110480	+	0.0378281i
$435$		0			0
$436$	13.0956	+	22.6822i	0.627165	+	1.08628i
$437$	−4.28949			−0.205194
$438$		0			0
$439$	−29.4523			−1.40568			−0.702841	−	0.711347i	$-0.748086\pi$
$439$	−29.4523			−1.40568			−0.702841	+	0.711347i	$0.748086\pi$
$440$	31.8215			1.51703
$441$		0			0
$442$	−25.5589			−1.21571
$443$	32.5565			1.54681			0.773404	−	0.633914i	$-0.218553\pi$
$443$	32.5565			1.54681			0.773404	+	0.633914i	$0.218553\pi$
$444$		0			0
$445$	−0.978120			−0.0463674
$446$	−16.7991	−	29.0969i	−0.795462	−	1.37778i
$447$		0			0
$448$	−9.49363	+	32.5060i	−0.448532	+	1.53576i
$449$	−0.171881			−0.00811158			−0.00405579	−	0.999992i	$-0.501291\pi$
$449$	−0.171881			−0.00811158			−0.00405579	+	0.999992i	$0.501291\pi$
$450$		0			0
$451$	22.4314	+	38.8523i	1.05625	+	1.82948i
$452$	3.97655	−	6.88758i	0.187041	−	0.323964i
$453$		0			0
$454$	−4.73559	+	8.20227i	−0.222252	+	0.384952i
$455$	−8.12066	+	27.8049i	−0.380702	+	1.30352i
$456$		0			0
$457$	24.5020			1.14616			0.573079	−	0.819500i	$-0.305749\pi$
$457$	24.5020			1.14616			0.573079	+	0.819500i	$0.305749\pi$
$458$	1.07226	+	1.85721i	0.0501034	+	0.0867816i
$459$		0			0
$460$	−14.6010	+	25.2896i	−0.680773	+	1.17913i
$461$	4.71554	+	8.16755i	0.219624	+	0.380401i	0.954693	−	0.297592i	$-0.0961835\pi$
$461$	4.71554	+	8.16755i	0.219624	+	0.380401i	−0.735069	+	0.677993i	$0.762850\pi$
$462$		0			0
$463$	−1.43061	+	2.47788i	−0.0664860	+	0.115157i	−0.897352	−	0.441315i	$-0.854512\pi$
$463$	−1.43061	+	2.47788i	−0.0664860	+	0.115157i	0.830866	+	0.556472i	$0.187845\pi$
$464$	−0.556660	−	0.964163i	−0.0258423	−	0.0447601i
$465$		0			0
$466$	−4.16585	+	7.21546i	−0.192979	+	0.334250i
$467$	3.85144	−	6.67089i	0.178223	−	0.308692i	−0.763049	−	0.646341i	$-0.776298\pi$
$467$	3.85144	−	6.67089i	0.178223	−	0.308692i	0.941272	+	0.337649i	$0.109632\pi$
$468$		0			0
$469$	−7.98563	+	27.3426i	−0.368742	+	1.26256i
$470$	33.3467	+	57.7582i	1.53817	+	2.66419i
$471$		0			0
$472$	−1.33963			−0.0616616
$473$	−1.15477			−0.0530964
$474$		0			0
$475$	7.63836	+	13.2300i	0.350472	+	0.607035i
$476$	29.7524	−	7.26338i	1.36370	−	0.332916i
$477$		0			0
$478$	7.38619	−	12.7932i	0.337836	−	0.585150i
$479$	17.2911	−	29.9491i	0.790051	−	1.36841i	−0.135884	−	0.990725i	$-0.543387\pi$
$479$	17.2911	−	29.9491i	0.790051	−	1.36841i	0.925935	−	0.377683i	$-0.123279\pi$
$480$		0			0
$481$	−11.9076	−	20.6245i	−0.542939	−	0.940397i
$482$	−16.5282	+	28.6277i	−0.752840	+	1.30396i
$483$		0			0
$484$	−11.0695	−	19.1729i	−0.503159	−	0.871497i
$485$	−2.01539	+	3.49076i	−0.0915141	+	0.158507i
$486$		0			0
$487$	−9.21782	−	15.9657i	−0.417699	−	0.723476i	0.578008	−	0.816031i	$-0.303830\pi$
$487$	−9.21782	−	15.9657i	−0.417699	−	0.723476i	−0.995708	+	0.0925545i	$0.970497\pi$
$488$	−4.07271			−0.184363
$489$		0			0
$490$	2.63047	−	58.7942i	0.118833	−	2.65605i
$491$	1.57686	−	2.73120i	0.0711627	−	0.123257i	−0.828248	−	0.560361i	$-0.810662\pi$
$491$	1.57686	−	2.73120i	0.0711627	−	0.123257i	0.899411	+	0.437104i	$0.143996\pi$
$492$		0			0
$493$	−1.51072	+	2.61665i	−0.0680395	+	0.117848i
$494$	5.10487	+	8.84190i	0.229679	+	0.397816i
$495$		0			0
$496$	−0.208478			−0.00936094
$497$	−2.68801	+	9.20368i	−0.120574	+	0.412841i
$498$		0			0
$499$	−14.4399	−	25.0107i	−0.646419	−	1.11963i	−0.983972	−	0.178324i	$-0.942933\pi$
$499$	−14.4399	−	25.0107i	−0.646419	−	1.11963i	0.337553	−	0.941307i	$-0.390401\pi$
$500$	49.2591			2.20293
$501$		0			0
$502$	37.7097			1.68307
$503$	−21.4742			−0.957487			−0.478744	−	0.877955i	$-0.658908\pi$
$503$	−21.4742			−0.957487			−0.478744	+	0.877955i	$0.658908\pi$
$504$		0			0
$505$	5.20085			0.231435
$506$	25.4672			1.13216
$507$		0			0
$508$	39.2681			1.74224
$509$	4.41218	+	7.64211i	0.195566	+	0.338731i	0.947086	−	0.320980i	$-0.104012\pi$
$509$	4.41218	+	7.64211i	0.195566	+	0.338731i	−0.751520	+	0.659711i	$0.770679\pi$
$510$		0			0
$511$	9.18899	−	2.24329i	0.406497	−	0.0992372i
$512$	−16.3263			−0.721527
$513$		0			0
$514$	9.46381	+	16.3918i	0.417431	+	0.723011i
$515$	28.5037	−	49.3698i	1.25602	−	2.17549i
$516$		0			0
$517$	17.1515	−	29.7072i	0.754321	−	1.30652i
$518$	33.4412	+	34.9708i	1.46932	+	1.53653i
$519$		0			0
$520$	21.1581			0.927843
$521$	14.8351	+	25.6952i	0.649939	+	1.12573i	0.983137	+	0.182871i	$0.0585391\pi$
$521$	14.8351	+	25.6952i	0.649939	+	1.12573i	−0.333198	+	0.942857i	$0.608128\pi$
$522$		0			0
$523$	3.46995	−	6.01013i	0.151730	−	0.262805i	−0.780133	−	0.625613i	$-0.784849\pi$
$523$	3.46995	−	6.01013i	0.151730	−	0.262805i	0.931864	+	0.362809i	$0.118182\pi$
$524$	25.3220	+	43.8591i	1.10620	+	1.91599i
$525$		0			0
$526$	−6.28931	+	10.8934i	−0.274227	+	0.474975i
$527$	0.282895	+	0.489988i	0.0123231	+	0.0213442i
$528$		0			0
$529$	7.94289	−	13.7575i	0.345343	−	0.598152i
$530$	47.1824	−	81.7223i	2.04947	−	3.54979i
$531$		0			0
$532$	−8.45516	−	8.84190i	−0.366577	−	0.383345i
$533$	14.9146	+	25.8328i	0.646023	+	1.11894i
$534$		0			0
$535$	−30.7726			−1.33042
$536$	20.8063			0.898693
$537$		0			0
$538$	17.2241	+	29.8330i	0.742582	+	1.28619i
$539$	−26.8652	+	13.9484i	−1.15716	+	0.600798i
$540$		0			0
$541$	8.34520	−	14.4543i	0.358788	−	0.621439i	−0.628971	−	0.777429i	$-0.716523\pi$
$541$	8.34520	−	14.4543i	0.358788	−	0.621439i	0.987759	+	0.155990i	$0.0498567\pi$
$542$	−33.9342	+	58.7757i	−1.45760	+	2.52463i
$543$		0			0
$544$	14.3737	+	24.8960i	0.616268	+	1.06741i
$545$	17.3429	−	30.0388i	0.742889	−	1.28672i
$546$		0			0
$547$	−1.88962	−	3.27292i	−0.0807943	−	0.139940i	0.822797	−	0.568335i	$-0.192412\pi$
$547$	−1.88962	−	3.27292i	−0.0807943	−	0.139940i	−0.903591	+	0.428395i	$0.859079\pi$
$548$	12.4602	−	21.5818i	0.532275	−	0.921927i
$549$		0			0
$550$	−45.3499	−	78.5483i	−1.93373	−	3.34931i
$551$	1.20695			0.0514176
$552$		0			0
$553$	−11.4399	+	39.1700i	−0.486474	+	1.66568i
$554$	−29.3582	+	50.8499i	−1.24731	+	2.16041i
$555$		0			0
$556$	5.41417	−	9.37762i	0.229612	−	0.397699i
$557$	−5.73458	−	9.93258i	−0.242982	−	0.420857i	0.718580	−	0.695444i	$-0.244792\pi$
$557$	−5.73458	−	9.93258i	−0.242982	−	0.420857i	−0.961562	+	0.274587i	$0.911459\pi$
$558$		0			0
$559$	−0.767806			−0.0324747
$560$	14.5186	−	3.54439i	0.613522	−	0.149778i
$561$		0			0
$562$	19.1668	+	33.1979i	0.808504	+	1.40037i
$563$	25.3816			1.06971			0.534854	−	0.844944i	$-0.320367\pi$
$563$	25.3816			1.06971			0.534854	+	0.844944i	$0.320367\pi$
$564$		0			0
$565$	−10.5325			−0.443108
$566$	−40.5287			−1.70355
$567$		0			0
$568$	7.00350			0.293860
$569$	−8.69404			−0.364473			−0.182237	−	0.983255i	$-0.558334\pi$
$569$	−8.69404			−0.364473			−0.182237	+	0.983255i	$0.558334\pi$
$570$		0			0
$571$	8.12757			0.340128			0.170064	−	0.985433i	$-0.445603\pi$
$571$	8.12757			0.340128			0.170064	+	0.985433i	$0.445603\pi$
$572$	−17.8747	−	30.9599i	−0.747380	−	1.29450i
$573$		0			0
$574$	−41.8861	−	43.8020i	−1.74829	−	1.82826i
$575$	25.3368			1.05662
$576$		0			0
$577$	−11.0420	−	19.1253i	−0.459683	−	0.796195i	0.539261	−	0.842139i	$-0.318704\pi$
$577$	−11.0420	−	19.1253i	−0.459683	−	0.796195i	−0.998944	+	0.0459441i	$0.985370\pi$
$578$	−0.874080	+	1.51395i	−0.0363569	+	0.0629720i
$579$		0			0
$580$	4.10832	−	7.11581i	0.170589	−	0.295468i
$581$	16.5543	−	4.04135i	0.686786	−	0.167663i
$582$		0			0
$583$	−48.5354			−2.01013
$584$	−3.45452	−	5.98341i	−0.142949	−	0.247595i
$585$		0			0
$586$	−11.8107	+	20.4567i	−0.487895	+	0.845060i
$587$	15.3600	+	26.6043i	0.633975	+	1.09808i	0.986731	+	0.162362i	$0.0519111\pi$
$587$	15.3600	+	26.6043i	0.633975	+	1.09808i	−0.352756	+	0.935715i	$0.614756\pi$
$588$		0			0
$589$	0.113005	−	0.195731i	0.00465630	−	0.00806495i
$590$	2.91406	+	5.04730i	0.119970	+	0.207794i
$591$		0			0
$592$	−6.14358	+	10.6410i	−0.252500	+	0.437342i
$593$	−22.0358	+	38.1671i	−0.904901	+	1.56733i	−0.0838502	+	0.996478i	$0.526722\pi$
$593$	−22.0358	+	38.1671i	−0.904901	+	1.56733i	−0.821050	+	0.570856i	$0.806612\pi$
$594$		0			0
$595$	−28.0315	−	29.3136i	−1.14918	−	1.20174i
$596$	6.62920	+	11.4821i	0.271543	+	0.470326i
$597$		0			0
$598$	16.9331			0.692447
$599$	27.3663			1.11816			0.559078	−	0.829115i	$-0.311155\pi$
$599$	27.3663			1.11816			0.559078	+	0.829115i	$0.311155\pi$
$600$		0			0
$601$	3.60908	+	6.25111i	0.147217	+	0.254988i	0.930198	−	0.367058i	$-0.119635\pi$
$601$	3.60908	+	6.25111i	0.147217	+	0.254988i	−0.782981	+	0.622046i	$0.786302\pi$
$602$	1.51549	−	0.369973i	0.0617668	−	0.0150790i
$603$		0			0
$604$	−11.2100	+	19.4164i	−0.456130	+	0.790040i
$605$	−14.6597	+	25.3914i	−0.596002	+	1.03231i
$606$		0			0
$607$	−18.5024	−	32.0471i	−0.750989	−	1.30075i	−0.947344	−	0.320218i	$-0.896244\pi$
$607$	−18.5024	−	32.0471i	−0.750989	−	1.30075i	0.196355	−	0.980533i	$-0.437090\pi$
$608$	5.74173	−	9.94496i	0.232858	−	0.403321i
$609$		0			0
$610$	8.85923	+	15.3446i	0.358700	+	0.621286i
$611$	11.4040	−	19.7523i	0.461357	−	0.799093i
$612$		0			0
$613$	−0.830292	−	1.43811i	−0.0335352	−	0.0580847i	0.848771	−	0.528761i	$-0.177343\pi$
$613$	−0.830292	−	1.43811i	−0.0335352	−	0.0580847i	−0.882306	+	0.470676i	$0.844010\pi$
$614$	−69.3197			−2.79751
$615$		0			0
$616$	15.2810	+	15.9800i	0.615690	+	0.643852i
$617$	−11.1209	+	19.2620i	−0.447710	+	0.775457i	−0.998237	−	0.0593607i	$-0.981094\pi$
$617$	−11.1209	+	19.2620i	−0.447710	+	0.775457i	0.550526	+	0.834818i	$0.314427\pi$
$618$		0			0
$619$	−9.89026	+	17.1304i	−0.397523	+	0.688530i	−0.993420	−	0.114531i	$-0.963464\pi$
$619$	−9.89026	+	17.1304i	−0.397523	+	0.688530i	0.595896	+	0.803061i	$0.296797\pi$
$620$	−0.769316	−	1.33249i	−0.0308965	−	0.0535142i
$621$		0			0
$622$	−29.7838			−1.19422
$623$	−0.469704	−	0.491189i	−0.0188183	−	0.0196791i
$624$		0			0
$625$	−8.86964	−	15.3627i	−0.354786	−	0.614507i
$626$	42.7057			1.70686
$627$		0			0
$628$	66.8941			2.66936
$629$	33.3462			1.32960
$630$		0			0
$631$	49.2569			1.96089			0.980443	−	0.196804i	$-0.0630562\pi$
$631$	49.2569			1.96089			0.980443	+	0.196804i	$0.0630562\pi$
$632$	29.8063			1.18563
$633$		0			0
$634$	−33.9096			−1.34672
$635$	−26.0020	−	45.0369i	−1.03186	−	1.78723i
$636$		0			0
$637$	−17.8626	+	9.27425i	−0.707743	+	0.367459i
$638$	−7.16578			−0.283696
$639$		0			0
$640$	−26.6162	−	46.1006i	−1.05210	−	1.82229i
$641$	−4.32841	+	7.49703i	−0.170962	+	0.296115i	−0.938756	−	0.344581i	$-0.888021\pi$
$641$	−4.32841	+	7.49703i	−0.170962	+	0.296115i	0.767795	+	0.640696i	$0.221354\pi$
$642$		0			0
$643$	−8.85782	+	15.3422i	−0.349318	+	0.605037i	−0.986129	−	0.165983i	$-0.946920\pi$
$643$	−8.85782	+	15.3422i	−0.349318	+	0.605037i	0.636810	+	0.771021i	$0.280254\pi$
$644$	−19.7114	+	4.81209i	−0.776737	+	0.189623i
$645$		0			0
$646$	−14.2958			−0.562460
$647$	−6.05092	−	10.4805i	−0.237886	−	0.412031i	0.722221	−	0.691662i	$-0.243121\pi$
$647$	−6.05092	−	10.4805i	−0.237886	−	0.412031i	−0.960108	+	0.279631i	$0.909788\pi$
$648$		0			0
$649$	1.49881	−	2.59602i	0.0588335	−	0.101903i
$650$	−30.1531	−	52.2267i	−1.18270	−	2.04850i
$651$		0			0
$652$	−8.78523	+	15.2165i	−0.344056	+	0.595923i
$653$	−18.1070	−	31.3623i	−0.708583	−	1.22730i	−0.965383	−	0.260837i	$-0.916002\pi$
$653$	−18.1070	−	31.3623i	−0.708583	−	1.22730i	0.256800	−	0.966464i	$-0.417332\pi$
$654$		0			0
$655$	33.5348	−	58.0840i	1.31031	−	2.26953i
$656$	7.69502	−	13.3282i	0.300440	−	0.520378i
$657$		0			0
$658$	−12.9913	+	44.4821i	−0.506455	+	1.73409i
$659$	19.6707	+	34.0706i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111219\pi$
$659$	19.6707	+	34.0706i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$660$		0			0
$661$	−1.66080			−0.0645978			−0.0322989	−	0.999478i	$-0.510283\pi$
$661$	−1.66080			−0.0645978			−0.0322989	+	0.999478i	$0.510283\pi$
$662$	2.73414			0.106265
$663$		0			0
$664$	−6.22343	−	10.7793i	−0.241516	−	0.418318i
$665$	−4.54211	+	15.5521i	−0.176135	+	0.603084i
$666$		0			0
$667$	1.00088	−	1.73357i	0.0387540	−	0.0671240i
$668$	16.7361	−	28.9878i	0.647540	−	1.12157i
$669$		0			0
$670$	−45.2591	−	78.3911i	−1.74851	−	3.02851i
$671$	4.55664	−	7.89233i	0.175907	−	0.304680i
$672$		0			0
$673$	−10.4154	−	18.0399i	−0.401483	−	0.695388i	0.592423	−	0.805627i	$-0.298172\pi$
$673$	−10.4154	−	18.0399i	−0.401483	−	0.695388i	−0.993905	+	0.110239i	$0.964838\pi$
$674$	13.1470	−	22.7713i	0.506405	−	0.877118i
$675$		0			0
$676$	6.80421	+	11.7852i	0.261700	+	0.453279i
$677$	46.7308			1.79601			0.898006	−	0.439984i	$-0.145016\pi$
$677$	46.7308			1.79601			0.898006	+	0.439984i	$0.145016\pi$
$678$		0			0
$679$	−2.72079	+	0.664220i	−0.104414	+	0.0254904i
$680$	−14.8129	+	25.6566i	−0.568048	+	0.983887i
$681$		0			0
$682$	−0.670926	+	1.16208i	−0.0256911	+	0.0444982i
$683$	−10.5747	−	18.3159i	−0.404630	−	0.700840i	0.589648	−	0.807660i	$-0.299266\pi$
$683$	−10.5747	−	18.3159i	−0.404630	−	0.700840i	−0.994278	+	0.106820i	$0.965933\pi$
$684$		0			0
$685$	−33.0030			−1.26098
$686$	30.7883	−	26.9127i	1.17550	−	1.02753i
$687$		0			0
$688$	0.198071	+	0.343068i	0.00755137	+	0.0130794i
$689$	−32.2711			−1.22943
$690$		0			0
$691$	−23.5970			−0.897672			−0.448836	−	0.893614i	$-0.648161\pi$
$691$	−23.5970			−0.897672			−0.448836	+	0.893614i	$0.648161\pi$
$692$	−55.3689			−2.10481
$693$		0			0
$694$	−9.59768			−0.364323
$695$	−14.3403			−0.543960
$696$		0			0
$697$	−41.7671			−1.58204
$698$	7.92185	+	13.7210i	0.299846	+	0.519349i
$699$		0			0
$700$	49.9423	+	52.2267i	1.88764	+	1.97398i
$701$	42.1420			1.59168			0.795841	−	0.605505i	$-0.207029\pi$
$701$	42.1420			1.59168			0.795841	+	0.605505i	$0.207029\pi$
$702$		0			0
$703$	−6.66024	−	11.5359i	−0.251196	−	0.435084i
$704$	−27.6744	+	47.9334i	−1.04302	+	1.80656i
$705$		0			0
$706$	−27.7067	+	47.9894i	−1.04276	+	1.80611i
$707$	2.49751	+	2.61174i	0.0939284	+	0.0982247i
$708$		0			0
$709$	45.9838			1.72696			0.863478	−	0.504386i	$-0.168281\pi$
$709$	45.9838			1.72696			0.863478	+	0.504386i	$0.168281\pi$
$710$	−15.2345	−	26.3869i	−0.571740	−	0.990282i
$711$		0			0
$712$	−0.248209	+	0.429911i	−0.00930204	+	0.0161116i
$713$	−0.187422	−	0.324625i	−0.00701901	−	0.0121573i
$714$		0			0
$715$	−23.6721	+	41.0013i	−0.885286	+	1.53336i
$716$	4.80434	+	8.32137i	0.179547	+	0.310984i
$717$		0			0
$718$	−35.3189	+	61.1741i	−1.31809	+	2.28300i
$719$	−16.5249	+	28.6220i	−0.616275	+	1.06742i	0.373885	+	0.927475i	$0.378026\pi$
$719$	−16.5249	+	28.6220i	−0.616275	+	1.06742i	−0.990159	+	0.139944i	$0.955308\pi$
$720$		0			0
$721$	38.4801	−	9.39406i	1.43307	−	0.349853i
$722$	−18.1207	−	31.3859i	−0.674381	−	1.16806i
$723$		0			0
$724$	−56.7452			−2.10892
$725$	−7.12910			−0.264768
$726$		0			0
$727$	12.5275	+	21.6982i	0.464619	+	0.804743i	0.999184	−	0.0403837i	$-0.0128580\pi$
$727$	12.5275	+	21.6982i	0.464619	+	0.804743i	−0.534565	+	0.845127i	$0.679525\pi$
$728$	10.1603	+	10.6251i	0.376567	+	0.393792i
$729$		0			0
$730$	−15.0290	+	26.0310i	−0.556248	+	0.963451i
$731$	0.537545	−	0.931055i	0.0198818	−	0.0344363i
$732$		0			0
$733$	−7.00625	−	12.1352i	−0.258782	−	0.448223i	0.707134	−	0.707079i	$-0.249988\pi$
$733$	−7.00625	−	12.1352i	−0.258782	−	0.448223i	−0.965916	+	0.258856i	$0.916654\pi$
$734$	−12.2817	+	21.2725i	−0.453326	+	0.785184i
$735$		0			0
$736$	−9.52280	−	16.4940i	−0.351015	−	0.607976i
$737$	−23.2785	+	40.3195i	−0.857474	+	1.48519i
$738$		0			0
$739$	19.3007	+	33.4297i	0.709987	+	1.22973i	0.964862	+	0.262759i	$0.0846323\pi$
$739$	19.3007	+	33.4297i	0.709987	+	1.22973i	−0.254875	+	0.966974i	$0.582034\pi$
$740$	−90.6830			−3.33357
$741$		0			0
$742$	63.6965	−	15.5501i	2.33837	−	0.570861i
$743$	−0.906592	+	1.57026i	−0.0332596	+	0.0576073i	−0.882176	−	0.470920i	$-0.843922\pi$
$743$	−0.906592	+	1.57026i	−0.0332596	+	0.0576073i	0.848916	+	0.528527i	$0.177255\pi$
$744$		0			0
$745$	8.77928	−	15.2062i	0.321648	−	0.557110i
$746$	17.8346	+	30.8904i	0.652971	+	1.13098i
$747$		0			0
$748$	50.0567			1.83026
$749$	−14.7773	−	15.4533i	−0.539952	−	0.564650i
$750$		0			0
$751$	14.7131	+	25.4838i	0.536888	+	0.929918i	0.999069	+	0.0431321i	$0.0137336\pi$
$751$	14.7131	+	25.4838i	0.536888	+	0.929918i	−0.462181	+	0.886785i	$0.652933\pi$
$752$	−11.7675			−0.429118
$753$		0			0
$754$	−4.76452			−0.173514
$755$	29.6917			1.08059
$756$		0			0
$757$	22.5455			0.819431			0.409715	−	0.912213i	$-0.365628\pi$
$757$	22.5455			0.819431			0.409715	+	0.912213i	$0.365628\pi$
$758$	−7.03213			−0.255419
$759$		0			0
$760$	11.8343			0.429275
$761$	−6.43131	−	11.1394i	−0.233135	−	0.403802i	0.725594	−	0.688123i	$-0.241565\pi$
$761$	−6.43131	−	11.1394i	−0.233135	−	0.403802i	−0.958729	+	0.284321i	$0.908232\pi$
$762$		0			0
$763$	23.4131	−	5.71577i	0.847610	−	0.206925i
$764$	−12.0039			−0.434285
$765$		0			0
$766$	−18.1913	−	31.5082i	−0.657277	−	1.13844i
$767$	0.996558	−	1.72609i	0.0359836	−	0.0623255i
$768$		0			0
$769$	22.3611	−	38.7305i	0.806362	−	1.39666i	−0.109007	−	0.994041i	$-0.534767\pi$
$769$	22.3611	−	38.7305i	0.806362	−	1.39666i	0.915368	−	0.402618i	$-0.131900\pi$
$770$	26.9671	−	92.3346i	0.971825	−	3.32751i
$771$		0			0
$772$	−39.8903			−1.43568
$773$	−5.24400	−	9.08288i	−0.188614	−	0.326688i	0.756175	−	0.654370i	$-0.227066\pi$
$773$	−5.24400	−	9.08288i	−0.188614	−	0.326688i	−0.944788	+	0.327681i	$0.893733\pi$
$774$		0			0
$775$	−0.667491	+	1.15613i	−0.0239770	+	0.0415294i
$776$	1.02286	+	1.77164i	0.0367184	+	0.0635982i
$777$		0			0
$778$	35.3026	−	61.1460i	1.26566	−	2.19219i
$779$	8.34215	+	14.4490i	0.298889	+	0.517690i
$780$		0			0
$781$	−7.83567	+	13.5718i	−0.280382	+	0.485636i
$782$	−11.8550	+	20.5334i	−0.423933	+	0.734273i
$783$		0			0
$784$	8.75190	+	5.58884i	0.312568	+	0.199601i
$785$	−44.2950	−	76.7213i	−1.58096	−	2.73830i
$786$		0			0
$787$	32.2074			1.14807			0.574035	−	0.818831i	$-0.305377\pi$
$787$	32.2074			1.14807			0.574035	+	0.818831i	$0.305377\pi$
$788$	−21.5218			−0.766682
$789$		0			0
$790$	−64.8365	−	112.300i	−2.30678	−	3.99546i
$791$	−5.05785	−	5.28920i	−0.179836	−	0.188062i
$792$		0			0
$793$	3.02970	−	5.24760i	0.107588	−	0.186348i
$794$	30.7042	−	53.1813i	1.08965	−	1.88733i
$795$		0			0
$796$	18.1936	+	31.5122i	0.644855	+	1.11692i
$797$	−16.1389	+	27.9534i	−0.571669	+	0.990160i	0.424726	+	0.905322i	$0.360371\pi$
$797$	−16.1389	+	27.9534i	−0.571669	+	0.990160i	−0.996395	+	0.0848377i	$0.972963\pi$
$798$		0			0
$799$	15.9680	+	27.6574i	0.564907	+	0.978448i
$800$	−33.9148	+	58.7422i	−1.19907	+	2.07685i
$801$		0			0
$802$	30.4574	+	52.7538i	1.07549	+	1.86280i
$803$	15.4600			0.545570
$804$		0			0
$805$	18.5713	+	19.4207i	0.654551	+	0.684490i
$806$	−0.446098	+	0.772664i	−0.0157131	+	0.0272159i
$807$		0			0
$808$	1.31978	−	2.28592i	0.0464295	−	0.0804183i
$809$	−14.9820	−	25.9495i	−0.526737	−	0.912336i	−0.999515	−	0.0311538i	$-0.990082\pi$
$809$	−14.9820	−	25.9495i	−0.526737	−	0.912336i	0.472777	−	0.881182i	$-0.343252\pi$
$810$		0			0
$811$	−13.1971			−0.463414			−0.231707	−	0.972786i	$-0.574431\pi$
$811$	−13.1971			−0.463414			−0.231707	+	0.972786i	$0.574431\pi$
$812$	5.54625	−	1.35399i	0.194635	−	0.0475159i
$813$		0			0
$814$	39.5427	+	68.4899i	1.38597	+	2.40057i
$815$	23.2692			0.815083
$816$		0			0
$817$	−0.429456			−0.0150247
$818$	26.1087			0.912870
$819$		0			0
$820$	113.583			3.96650
$821$	−8.03611			−0.280462			−0.140231	−	0.990119i	$-0.544785\pi$
$821$	−8.03611			−0.280462			−0.140231	+	0.990119i	$0.544785\pi$
$822$		0			0
$823$	19.5656			0.682015			0.341008	−	0.940060i	$-0.389232\pi$
$823$	19.5656			0.682015			0.341008	+	0.940060i	$0.389232\pi$
$824$	−14.4663	−	25.0563i	−0.503956	−	0.872878i
$825$		0			0
$826$	−1.13527	+	3.88714i	−0.0395011	+	0.135251i
$827$	−45.8218			−1.59338			−0.796690	−	0.604389i	$-0.793417\pi$
$827$	−45.8218			−1.59338			−0.796690	+	0.604389i	$0.793417\pi$
$828$		0			0
$829$	−17.0773	−	29.5787i	−0.593119	−	1.02731i	−0.993809	−	0.111098i	$-0.964563\pi$
$829$	−17.0773	−	29.5787i	−0.593119	−	1.02731i	0.400691	−	0.916213i	$-0.368770\pi$
$830$	−27.0752	+	46.8957i	−0.939795	+	1.62777i
$831$		0			0
$832$	−18.4007	+	31.8709i	−0.637928	+	1.10492i
$833$	1.25960	−	28.1535i	0.0436424	−	0.975460i
$834$		0			0
$835$	−44.3284			−1.53405
$836$	−9.99783	−	17.3168i	−0.345782	−	0.598913i
$837$		0			0
$838$	9.73360	−	16.8591i	0.336242	−	0.582388i
$839$	17.7986	+	30.8281i	0.614476	+	1.06430i	0.990476	+	0.137684i	$0.0439659\pi$
$839$	17.7986	+	30.8281i	0.614476	+	1.06430i	−0.376000	+	0.926620i	$0.622701\pi$
$840$		0			0
$841$	14.2184	−	24.6270i	0.490289	−	0.849205i
$842$	20.6449	+	35.7579i	0.711469	+	1.23230i
$843$		0			0
$844$	7.40659	−	12.8286i	0.254945	−	0.441578i
$845$	9.01105	−	15.6076i	0.309990	−	0.536918i
$846$		0			0
$847$	−19.7907	+	4.83146i	−0.680017	+	0.166011i
$848$	8.32497	+	14.4193i	0.285881	+	0.495160i
$849$		0			0
$850$	84.4413			2.89631
$851$	−22.0924			−0.757316
$852$		0			0
$853$	−16.6973	−	28.9206i	−0.571705	−	0.990222i	−0.996391	−	0.0848812i	$-0.972949\pi$
$853$	−16.6973	−	28.9206i	−0.571705	−	0.990222i	0.424686	−	0.905341i	$-0.360384\pi$
$854$	−3.45141	+	11.8176i	−0.118105	+	0.404389i
$855$		0			0
$856$	−7.80890	+	13.5254i	−0.266903	+	0.462289i
$857$	12.9074	−	22.3562i	0.440907	−	0.763674i	−0.556850	−	0.830613i	$-0.687990\pi$
$857$	12.9074	−	22.3562i	0.440907	−	0.763674i	0.997757	+	0.0669395i	$0.0213235\pi$
$858$		0			0
$859$	21.5003	+	37.2397i	0.733582	+	1.27060i	0.955343	+	0.295500i	$0.0954862\pi$
$859$	21.5003	+	37.2397i	0.733582	+	1.27060i	−0.221761	+	0.975101i	$0.571181\pi$
$860$	−1.46182	+	2.53195i	−0.0498477	+	0.0863387i
$861$		0			0
$862$	−18.3478	−	31.7794i	−0.624929	−	1.08241i
$863$	−10.7483	+	18.6166i	−0.365877	+	0.633718i	−0.988917	−	0.148473i	$-0.952564\pi$
$863$	−10.7483	+	18.6166i	−0.365877	+	0.633718i	0.623039	+	0.782191i	$0.285898\pi$
$864$		0			0
$865$	36.6634	+	63.5029i	1.24659	+	2.15916i
$866$	55.8631			1.89830
$867$		0			0
$868$	0.299713	−	1.02621i	0.0101729	−	0.0348319i
$869$	−33.3479	+	57.7602i	−1.13125	+	1.95938i
$870$		0			0
$871$	−15.4778	+	26.8084i	−0.524447	+	0.908368i
$872$	−8.80194	−	15.2454i	−0.298071	−	0.516274i
$873$		0			0
$874$	9.47117			0.320367
$875$	12.7073	−	43.5097i	0.429586	−	1.47089i
$876$		0			0
$877$	−7.34204	−	12.7168i	−0.247923	−	0.429415i	0.715026	−	0.699098i	$-0.246415\pi$
$877$	−7.34204	−	12.7168i	−0.247923	−	0.429415i	−0.962949	+	0.269682i	$0.913081\pi$
$878$	65.0306			2.19468
$879$		0			0
$880$	24.4267			0.823425
$881$	37.6060			1.26698			0.633490	−	0.773751i	$-0.281622\pi$
$881$	37.6060			1.26698			0.633490	+	0.773751i	$0.281622\pi$
$882$		0			0
$883$	−46.9989			−1.58164			−0.790820	−	0.612049i	$-0.790345\pi$
$883$	−46.9989			−1.58164			−0.790820	+	0.612049i	$0.790345\pi$
$884$	33.2827			1.11942
$885$		0			0
$886$	−71.8847			−2.41501
$887$	13.2124	+	22.8846i	0.443630	+	0.768389i	0.997956	−	0.0639105i	$-0.0203572\pi$
$887$	13.2124	+	22.8846i	0.443630	+	0.768389i	−0.554326	+	0.832300i	$0.687024\pi$
$888$		0			0
$889$	10.1300	−	34.6848i	0.339749	−	1.16329i
$890$	2.15969			0.0723928
$891$		0			0
$892$	21.8758	+	37.8900i	0.732455	+	1.26865i
$893$	6.37858	−	11.0480i	0.213451	−	0.369708i
$894$		0			0
$895$	6.36256	−	11.0203i	0.212677	−	0.368367i
$896$	10.3692	−	35.5041i	0.346412	−	1.18611i
$897$		0			0
$898$	0.379513			0.0126645
$899$	0.0527355	+	0.0913406i	0.00175883	+	0.00304638i
$900$		0			0
$901$	22.5932	−	39.1325i	0.752688	−	1.30369i
$902$	−49.5283	−	85.7856i	−1.64911	−	2.85635i
$903$		0			0
$904$	−2.67276	+	4.62935i	−0.0888946	+	0.153970i
$905$	37.5748	+	65.0815i	1.24903	+	2.16338i
$906$		0			0
$907$	0.225026	−	0.389757i	0.00747187	−	0.0129417i	−0.862265	−	0.506457i	$-0.830955\pi$
$907$	0.225026	−	0.389757i	0.00747187	−	0.0129417i	0.869737	+	0.493515i	$0.164288\pi$
$908$	6.16667	−	10.6810i	0.204648	−	0.354461i
$909$		0			0
$910$	17.9304	−	61.3932i	0.594386	−	2.03517i
$911$	2.37220	+	4.10877i	0.0785944	+	0.136129i	0.902644	−	0.430389i	$-0.141623\pi$
$911$	2.37220	+	4.10877i	0.0785944	+	0.136129i	−0.824049	+	0.566518i	$0.808290\pi$
$912$		0			0
$913$	27.8516			0.921754
$914$	−54.1004			−1.78948
$915$		0			0
$916$	−1.39629	−	2.41845i	−0.0461348	−	0.0799079i
$917$	45.2722	−	11.0522i	1.49502	−	0.364976i
$918$		0			0
$919$	−21.2103	+	36.7372i	−0.699662	+	1.21185i	0.268922	+	0.963162i	$0.413333\pi$
$919$	−21.2103	+	36.7372i	−0.699662	+	1.21185i	−0.968584	+	0.248688i	$0.920001\pi$
$920$	9.81374	−	16.9979i	0.323550	−	0.560404i
$921$		0			0
$922$	−10.4119	−	18.0339i	−0.342897	−	0.593915i
$923$	−5.20993	+	9.02386i	−0.171487	+	0.297024i
$924$		0			0
$925$	39.3402	+	68.1393i	1.29350	+	2.24041i
$926$	3.15878	−	5.47116i	0.103804	−	0.179793i
$927$		0			0
$928$	2.67946	+	4.64096i	0.0879575	+	0.152347i
$929$	−45.0817			−1.47908			−0.739541	−	0.673111i	$-0.764958\pi$
$929$	−45.0817			−1.47908			−0.739541	+	0.673111i	$0.764958\pi$
$930$		0			0
$931$	−9.99107	+	5.18735i	−0.327444	+	0.170008i
$932$	5.42476	−	9.39596i	0.177694	−	0.307775i
$933$		0			0
$934$	−8.50397	+	14.7293i	−0.278258	+	0.481958i
$935$	−33.1459	−	57.4104i	−1.08399	−	1.87752i
$936$		0			0
$937$	19.3045			0.630650			0.315325	−	0.948984i	$-0.397886\pi$
$937$	19.3045			0.630650			0.315325	+	0.948984i	$0.397886\pi$
$938$	17.6322	−	60.3724i	0.575713	−	1.97123i
$939$		0			0
$940$	−43.4240	−	75.2126i	−1.41633	−	2.45316i
$941$	−10.5539			−0.344048			−0.172024	−	0.985093i	$-0.555031\pi$
$941$	−10.5539			−0.344048			−0.172024	+	0.985093i	$0.555031\pi$
$942$		0			0
$943$	27.6713			0.901103
$944$	−1.02833			−0.0334692
$945$		0			0
$946$	2.54973			0.0828989
$947$	−47.7600			−1.55199			−0.775996	−	0.630737i	$-0.782753\pi$
$947$	−47.7600			−1.55199			−0.775996	+	0.630737i	$0.782753\pi$
$948$		0			0
$949$	10.2793			0.333681
$950$	−16.8655	−	29.2119i	−0.547188	−	0.947758i
$951$		0			0
$952$	−19.9975	+	4.88194i	−0.648122	+	0.158224i
$953$	−53.8101			−1.74308			−0.871540	−	0.490324i	$-0.836879\pi$
$953$	−53.8101			−1.74308			−0.871540	+	0.490324i	$0.836879\pi$
$954$		0			0
$955$	7.94856	+	13.7673i	0.257209	+	0.445500i
$956$	−9.61827	+	16.6593i	−0.311077	+	0.538801i
$957$		0			0
$958$	−38.1787	+	66.1274i	−1.23350	+	2.13648i
$959$	−15.8484	−	16.5733i	−0.511772	−	0.535181i
$960$		0			0
$961$	−30.9802			−0.999363
$962$	26.2919	+	45.5389i	0.847684	+	1.46823i
$963$		0			0
$964$	21.5230	−	37.2790i	0.693210	−	1.20067i
$965$	26.4141	+	45.7505i	0.850299	+	1.47276i
$966$		0			0
$967$	4.90887	−	8.50242i	0.157859	−	0.273419i	−0.776238	−	0.630441i	$-0.782874\pi$
$967$	4.90887	−	8.50242i	0.157859	−	0.273419i	0.934096	+	0.357021i	$0.116208\pi$
$968$	7.44015	+	12.8867i	0.239135	+	0.414195i
$969$		0			0
$970$	4.44997	−	7.70757i	0.142880	−	0.247475i
$971$	−11.8993	+	20.6102i	−0.381867	+	0.661413i	−0.991329	−	0.131402i	$-0.958052\pi$
$971$	−11.8993	+	20.6102i	−0.381867	+	0.661413i	0.609462	+	0.792815i	$0.291385\pi$
$972$		0			0
$973$	−6.88639	−	7.20138i	−0.220768	−	0.230866i
$974$	20.3529	+	35.2523i	0.652149	+	1.12956i
$975$		0			0
$976$	−3.12629			−0.100070
$977$	39.9903			1.27940			0.639701	−	0.768624i	$-0.279058\pi$
$977$	39.9903			1.27940			0.639701	+	0.768624i	$0.279058\pi$
$978$		0			0
$979$	−0.555404	−	0.961988i	−0.0177508	−	0.0307453i
$980$	−3.42539	+	76.5617i	−0.109420	+	2.44567i
$981$		0			0
$982$	−3.48170	+	6.03048i	−0.111106	+	0.192440i
$983$	−23.1143	+	40.0351i	−0.737231	+	1.27692i	0.216506	+	0.976281i	$0.430534\pi$
$983$	−23.1143	+	40.0351i	−0.737231	+	1.27692i	−0.953738	+	0.300640i	$0.902800\pi$
$984$		0			0
$985$	14.2510	+	24.6835i	0.454075	+	0.786482i
$986$	3.33567	−	5.77754i	0.106229	−	0.183994i
$987$		0			0
$988$	−6.64755	−	11.5139i	−0.211487	−	0.366306i
$989$	−0.356131	+	0.616838i	−0.0113243	+	0.0196143i
$990$		0			0
$991$	−7.19818	−	12.4676i	−0.228658	−	0.396047i	0.728753	−	0.684777i	$-0.240100\pi$
$991$	−7.19818	−	12.4676i	−0.228658	−	0.396047i	−0.957411	+	0.288730i	$0.906767\pi$
$992$	1.00350			0.0318612
$993$		0			0
$994$	5.93511	−	20.3217i	0.188250	−	0.644564i
$995$	24.0944	−	41.7327i	0.763844	−	1.32302i
$996$		0			0
$997$	−21.9273	+	37.9792i	−0.694444	+	1.20281i	0.275924	+	0.961180i	$0.411016\pi$
$997$	−21.9273	+	37.9792i	−0.694444	+	1.20281i	−0.970368	+	0.241633i	$0.922317\pi$
$998$	31.8833	+	55.2234i	1.00925	+	1.74807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.j.352.1		8
3.2	odd	2		567.2.h.k.352.4		8
7.4	even	3		567.2.g.k.109.4		8
9.2	odd	6		567.2.g.j.541.1		8
9.4	even	3		567.2.e.d.163.4	yes	8
9.5	odd	6		567.2.e.c.163.1	✓	8
9.7	even	3		567.2.g.k.541.4		8
21.11	odd	6		567.2.g.j.109.1		8
63.4	even	3		567.2.e.d.487.4	yes	8
63.5	even	6		3969.2.a.w.1.4		4
63.11	odd	6		567.2.h.k.298.4		8
63.23	odd	6		3969.2.a.x.1.4		4
63.25	even	3	inner	567.2.h.j.298.1		8
63.32	odd	6		567.2.e.c.487.1	yes	8
63.40	odd	6		3969.2.a.t.1.1		4
63.58	even	3		3969.2.a.s.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.1	✓	8	9.5	odd	6
567.2.e.c.487.1	yes	8	63.32	odd	6
567.2.e.d.163.4	yes	8	9.4	even	3
567.2.e.d.487.4	yes	8	63.4	even	3
567.2.g.j.109.1		8	21.11	odd	6
567.2.g.j.541.1		8	9.2	odd	6
567.2.g.k.109.4		8	7.4	even	3
567.2.g.k.541.4		8	9.7	even	3
567.2.h.j.298.1		8	63.25	even	3	inner
567.2.h.j.352.1		8	1.1	even	1	trivial
567.2.h.k.298.4		8	63.11	odd	6
567.2.h.k.352.4		8	3.2	odd	2
3969.2.a.s.1.1		4	63.58	even	3
3969.2.a.t.1.1		4	63.40	odd	6
3969.2.a.w.1.4		4	63.5	even	6
3969.2.a.x.1.4		4	63.23	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.20800 q^{2} +2.87525 q^{4} +(-1.90389 - 3.29764i) q^{5} +(0.741726 - 2.53965i) q^{7} -1.93254 q^{8} +O(q^{10})\)	\(q-2.20800 q^{2} +2.87525 q^{4} +(-1.90389 - 3.29764i) q^{5} +(0.741726 - 2.53965i) q^{7} -1.93254 q^{8} +(4.20379 + 7.28117i) q^{10} +(2.16217 - 3.74498i) q^{11} +(1.43762 - 2.49004i) q^{13} +(-1.63773 + 5.60755i) q^{14} -1.48345 q^{16} +(2.01297 + 3.48657i) q^{17} +(0.804103 - 1.39275i) q^{19} +(-5.47416 - 9.48152i) q^{20} +(-4.77406 + 8.26891i) q^{22} +(-1.33363 - 2.30991i) q^{23} +(-4.74962 + 8.22658i) q^{25} +(-3.17427 + 5.49799i) q^{26} +(2.13264 - 7.30213i) q^{28} +(0.375246 + 0.649945i) q^{29} +0.140536 q^{31} +7.14054 q^{32} +(-4.44464 - 7.69834i) q^{34} +(-9.78703 + 2.38928i) q^{35} +(4.14141 - 7.17313i) q^{37} +(-1.77546 + 3.07518i) q^{38} +(3.67935 + 6.37282i) q^{40} +(-5.18724 + 8.98456i) q^{41} +(-0.133520 - 0.231264i) q^{43} +(6.21676 - 10.7677i) q^{44} +(2.94464 + 5.10026i) q^{46} +7.93254 q^{47} +(-5.89969 - 3.76745i) q^{49} +(10.4871 - 18.1643i) q^{50} +(4.13352 - 7.15947i) q^{52} +(-5.61189 - 9.72008i) q^{53} -16.4661 q^{55} +(-1.43342 + 4.90798i) q^{56} +(-0.828542 - 1.43508i) q^{58} +0.693198 q^{59} +2.10744 q^{61} -0.310302 q^{62} -12.7994 q^{64} -10.9483 q^{65} -10.7663 q^{67} +(5.78780 + 10.0248i) q^{68} +(21.6097 - 5.27553i) q^{70} -3.62399 q^{71} +(1.78756 + 3.09614i) q^{73} +(-9.14422 + 15.8383i) q^{74} +(2.31199 - 4.00449i) q^{76} +(-7.90723 - 8.26891i) q^{77} -15.4234 q^{79} +(2.82433 + 4.89189i) q^{80} +(11.4534 - 19.8379i) q^{82} +(3.22034 + 5.57779i) q^{83} +(7.66497 - 13.2761i) q^{85} +(0.294812 + 0.510629i) q^{86} +(-4.17847 + 7.23733i) q^{88} +(0.128437 - 0.222459i) q^{89} +(-5.25751 - 5.49799i) q^{91} +(-3.83450 - 6.64155i) q^{92} -17.5150 q^{94} -6.12370 q^{95} +(-0.529281 - 0.916742i) q^{97} +(13.0265 + 8.31853i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8	\( 8 q - 2 q^{2} + 10 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} + 5 q^{13} - 16 q^{14} - 2 q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} - 36 q^{31} + 20 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} + 42 q^{47} - 19 q^{49} + 38 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} + 6 q^{56} + 7 q^{58} - 12 q^{59} - 40 q^{61} - 36 q^{62} - 46 q^{64} - 16 q^{65} - 10 q^{67} + 51 q^{68} + 29 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} - 53 q^{77} - 20 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} - 30 q^{94} + 32 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 10 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 + 5 * q^13 - 16 * q^14 - 2 * q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 - 10 * q^29 - 36 * q^31 + 20 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 + 42 * q^47 - 19 * q^49 + 38 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 + 6 * q^56 + 7 * q^58 - 12 * q^59 - 40 * q^61 - 36 * q^62 - 46 * q^64 - 16 * q^65 - 10 * q^67 + 51 * q^68 + 29 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 - 53 * q^77 - 20 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 - 30 * q^94 + 32 * q^95 + 9 * q^97 - 11 * q^98

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