LMFDB - Embedded newform 567.2.h.k.352.4

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			352.4
Root			$-1.54162 + 1.88572i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.k.298.4

$q$-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	$-0.214891\pi$
$2$	2.20800			1.56129			0.780644	+	0.624975i	$0.214891\pi$
$3$		0			0
$3$		0			0
$4$	2.87525			1.43762
$5$	1.90389	+	3.29764i	0.851447	+	1.47475i	0.879903	+	0.475154i	$0.157608\pi$
$5$	1.90389	+	3.29764i	0.851447	+	1.47475i	−0.0284558	+	0.999595i	$0.509059\pi$
$6$		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	$0.392702\pi$
$11$	−2.16217	+	3.74498i	−0.651918	+	1.12915i	−0.982657	+	0.185433i	$0.940631\pi$
$12$		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	0.511690	−	0.859170i	$-0.329020\pi$
$17$	−2.01297	−	3.48657i	−0.488218	−	0.845618i	−0.999908	+	0.0135517i	$0.995686\pi$
$18$		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	0.970908	−	0.239455i	$-0.0769686\pi$
$23$	1.33363	+	2.30991i	0.278080	+	0.481649i	−0.692828	+	0.721103i	$0.743635\pi$
$24$		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	0.829080	−	0.559131i	$-0.188865\pi$
$29$	−0.375246	−	0.649945i	−0.0696815	−	0.120692i	−0.898761	+	0.438439i	$0.855532\pi$
$30$		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	$-0.532740\pi$
$41$	5.18724	−	8.98456i	0.810111	−	1.40315i	0.912786	−	0.408438i	$-0.133926\pi$
$42$		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	$-0.696377\pi$
$47$	−7.93254			−1.15708			−0.578540	+	0.815654i	$0.696377\pi$
$48$		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	$0.113503\pi$
$53$	5.61189	+	9.72008i	0.770852	+	1.33516i	−0.166244	+	0.986085i	$0.553164\pi$
$54$		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	$-0.514368\pi$
$59$	−0.693198			−0.0902468			−0.0451234	+	0.998981i	$0.514368\pi$
$60$		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	$-0.431010\pi$
$71$	3.62399			0.430088			0.215044	+	0.976604i	$0.431010\pi$
$72$		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	0.633378	−	0.773842i	$-0.281668\pi$
$83$	−3.22034	−	5.57779i	−0.353478	−	0.612241i	−0.986856	+	0.161601i	$0.948334\pi$
$84$		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	−0.872752	−	0.488163i	$-0.837667\pi$
$89$	−0.128437	+	0.222459i	−0.0136143	+	0.0235806i	0.859138	+	0.511744i	$0.171000\pi$
$90$		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	−0.830047	−	0.557694i	$-0.811686\pi$
$101$	0.682923	−	1.18286i	0.0679534	−	0.117699i	0.898000	+	0.439995i	$0.145020\pi$
$102$		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	−0.992533	−	0.121974i	$-0.961077\pi$
$107$	−4.04075	+	6.99878i	−0.390634	+	0.676597i	0.601900	+	0.798572i	$0.294411\pi$
$108$		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	−0.923717	−	0.383077i	$-0.874865\pi$
$113$	−1.38303	+	2.39547i	−0.130104	+	0.225347i	0.793612	+	0.608424i	$0.208198\pi$
$114$		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	$-0.887190\pi$
$131$	−8.80691	−	15.2540i	−0.769463	−	1.33275i	0.168391	−	0.985720i	$-0.446143\pi$
$132$		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	−0.989603	−	0.143824i	$-0.954060\pi$
$137$	−4.33363	+	7.50606i	−0.370247	+	0.641286i	0.619357	+	0.785110i	$0.287393\pi$
$138$		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	0.755995	−	0.654577i	$-0.227153\pi$
$149$	−2.30561	−	3.99344i	−0.188883	−	0.327155i	−0.944878	+	0.327422i	$0.893820\pi$
$150$		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	−0.998412	−	0.0563288i	$-0.982060\pi$
$167$	−5.82076	+	10.0819i	−0.450424	+	0.780157i	0.547988	+	0.836486i	$0.315394\pi$
$168$		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	$-0.238566\pi$
$173$	19.2571			1.46409			0.732045	+	0.681256i	$0.238566\pi$
$174$		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	0.796799	−	0.604244i	$-0.206525\pi$
$179$	−1.67093	−	2.89414i	−0.124891	−	0.216318i	−0.921690	+	0.387926i	$0.873192\pi$
$180$		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	$-0.451737\pi$
$191$	4.17490			0.302085			0.151043	+	0.988527i	$0.451737\pi$
$192$		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	$-0.414083\pi$
$197$	7.48520			0.533299			0.266649	+	0.963794i	$0.414083\pi$
$198$		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	−0.928382	−	0.371628i	$-0.878800\pi$
$227$	−2.14474	+	3.71481i	−0.142352	+	0.246560i	0.786030	+	0.618188i	$0.212133\pi$
$228$		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	−0.921186	−	0.389123i	$-0.872778\pi$
$233$	−1.88671	+	3.26788i	−0.123603	+	0.214086i	0.797583	+	0.603209i	$0.206111\pi$
$234$		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	−0.737317	−	0.675547i	$-0.763907\pi$
$239$	3.34520	−	5.79405i	0.216383	−	0.374786i	0.953699	+	0.300761i	$0.0972407\pi$
$240$		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	$-0.318803\pi$
$251$	17.0787			1.07800			0.538999	+	0.842307i	$0.318803\pi$
$252$		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	0.968180	−	0.250255i	$-0.0805144\pi$
$257$	4.28615	+	7.42384i	0.267363	+	0.463086i	−0.700817	+	0.713341i	$0.747181\pi$
$258$		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	−0.940383	−	0.340117i	$-0.889533\pi$
$263$	−2.84842	+	4.93361i	−0.175641	+	0.304220i	0.764742	+	0.644337i	$0.222867\pi$
$264$		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	0.999610	−	0.0279249i	$-0.00888992\pi$
$269$	7.80077	+	13.5113i	0.475621	+	0.823800i	−0.523989	+	0.851725i	$0.675557\pi$
$270$		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	$0.00659857\pi$
$281$	8.68065	+	15.0353i	0.517844	+	0.896932i	−0.481941	+	0.876204i	$0.660068\pi$
$282$		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	−0.978902	−	0.204331i	$-0.934498\pi$
$293$	−5.34906	+	9.26484i	−0.312495	+	0.541258i	0.666407	+	0.745588i	$0.267831\pi$
$294$		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	$-0.624919\pi$
$311$	−13.4891			−0.764895			−0.382447	+	0.923977i	$0.624919\pi$
$312$		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	$-0.641940\pi$
$317$	−15.3576			−0.862571			−0.431286	+	0.902215i	$0.641940\pi$
$318$		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	$-0.537223\pi$
$347$	−4.34678			−0.233347			−0.116674	+	0.993170i	$0.537223\pi$
$348$		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	$0.399465\pi$
$353$	−12.5484	+	21.7344i	−0.667881	+	1.15680i	−0.978495	+	0.206268i	$0.933868\pi$
$354$		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	$0.486609\pi$
$359$	−15.9959	+	27.7057i	−0.844231	+	1.46225i	−0.886287	+	0.463136i	$0.846724\pi$
$360$		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	0.575052	−	0.818117i	$-0.304982\pi$
$383$	−8.23882	−	14.2700i	−0.420984	−	0.729165i	−0.996036	+	0.0889514i	$0.971648\pi$
$384$		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	$-0.532447\pi$
$389$	15.9885	−	27.6930i	0.810651	−	1.40409i	0.912409	−	0.409280i	$-0.134220\pi$
$390$		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	$0.0752163\pi$
$401$	13.7942	+	23.8922i	0.688847	+	1.19312i	−0.283364	+	0.959012i	$0.591450\pi$
$402$		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	−0.738023	−	0.674776i	$-0.764240\pi$
$419$	4.40834	−	7.63547i	0.215362	−	0.373017i	0.953384	+	0.301759i	$0.0975737\pi$
$420$		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	0.593493	−	0.804839i	$-0.297749\pi$
$431$	−8.30972	−	14.3929i	−0.400265	−	0.693279i	−0.993758	+	0.111560i	$0.964415\pi$
$432$		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	$-0.781447\pi$
$443$	−32.5565			−1.54681			−0.773404	+	0.633914i	$0.781447\pi$
$444$		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	$-0.498709\pi$
$449$	0.171881			0.00811158			0.00405579	+	0.999992i	$0.498709\pi$
$450$		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	0.735069	−	0.677993i	$-0.237150\pi$
$461$	−4.71554	−	8.16755i	−0.219624	−	0.380401i	−0.954693	+	0.297592i	$0.903817\pi$
$462$		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	−0.941272	−	0.337649i	$-0.890368\pi$
$467$	−3.85144	+	6.67089i	−0.178223	+	0.308692i	0.763049	+	0.646341i	$0.223702\pi$
$468$		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	$0.456613\pi$
$479$	−17.2911	+	29.9491i	−0.790051	+	1.36841i	−0.925935	+	0.377683i	$0.876721\pi$
$480$		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	−0.899411	−	0.437104i	$-0.856004\pi$
$491$	−1.57686	+	2.73120i	−0.0711627	+	0.123257i	0.828248	+	0.560361i	$0.189338\pi$
$492$		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	$-0.341092\pi$
$503$	21.4742			0.957487			0.478744	+	0.877955i	$0.341092\pi$
$504$		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	0.751520	−	0.659711i	$-0.229321\pi$
$509$	−4.41218	−	7.64211i	−0.195566	−	0.338731i	−0.947086	+	0.320980i	$0.895988\pi$
$510$		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	$-0.941461\pi$
$521$	−14.8351	−	25.6952i	−0.649939	−	1.12573i	0.333198	−	0.942857i	$-0.391872\pi$
$522$		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	0.961562	−	0.274587i	$-0.0885411\pi$
$557$	5.73458	+	9.93258i	0.242982	+	0.420857i	−0.718580	+	0.695444i	$0.755208\pi$
$558$		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	$-0.679633\pi$
$563$	−25.3816			−1.06971			−0.534854	+	0.844944i	$0.679633\pi$
$564$		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	$-0.441666\pi$
$569$	8.69404			0.364473			0.182237	+	0.983255i	$0.441666\pi$
$570$		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	$-0.948089\pi$
$587$	−15.3600	−	26.6043i	−0.633975	−	1.09808i	0.352756	−	0.935715i	$-0.385244\pi$
$588$		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	$-0.473278\pi$
$593$	22.0358	−	38.1671i	0.904901	−	1.56733i	0.821050	−	0.570856i	$-0.193388\pi$
$594$		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	$-0.688845\pi$
$599$	−27.3663			−1.11816			−0.559078	+	0.829115i	$0.688845\pi$
$600$		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	−0.550526	−	0.834818i	$-0.685573\pi$
$617$	11.1209	−	19.2620i	0.447710	−	0.775457i	0.998237	+	0.0593607i	$0.0189062\pi$
$618$		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	−0.767795	−	0.640696i	$-0.778646\pi$
$641$	4.32841	−	7.49703i	0.170962	−	0.296115i	0.938756	+	0.344581i	$0.111979\pi$
$642$		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	0.960108	−	0.279631i	$-0.0902121\pi$
$647$	6.05092	+	10.4805i	0.237886	+	0.412031i	−0.722221	+	0.691662i	$0.756879\pi$
$648$		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	$0.0839984\pi$
$653$	18.1070	+	31.3623i	0.708583	+	1.22730i	−0.256800	+	0.966464i	$0.582668\pi$
$654$		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	$-0.888781\pi$
$659$	−19.6707	−	34.0706i	−0.766261	−	1.32720i	0.173316	−	0.984866i	$-0.444552\pi$
$660$		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	$-0.854984\pi$
$677$	−46.7308			−1.79601			−0.898006	+	0.439984i	$0.854984\pi$
$678$		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	0.994278	−	0.106820i	$-0.0340669\pi$
$683$	10.5747	+	18.3159i	0.404630	+	0.700840i	−0.589648	+	0.807660i	$0.700734\pi$
$684$		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	$-0.792971\pi$
$701$	−42.1420			−1.59168			−0.795841	+	0.605505i	$0.792971\pi$
$702$		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	$-0.621974\pi$
$719$	16.5249	−	28.6220i	0.616275	−	1.06742i	0.990159	−	0.139944i	$-0.0446922\pi$
$720$		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	−0.848916	−	0.528527i	$-0.822745\pi$
$743$	0.906592	−	1.57026i	0.0332596	−	0.0576073i	0.882176	+	0.470920i	$0.156078\pi$
$744$		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	0.958729	−	0.284321i	$-0.0917683\pi$
$761$	6.43131	+	11.1394i	0.233135	+	0.403802i	−0.725594	+	0.688123i	$0.758435\pi$
$762$		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	0.944788	−	0.327681i	$-0.106267\pi$
$773$	5.24400	+	9.08288i	0.188614	+	0.326688i	−0.756175	+	0.654370i	$0.772934\pi$
$774$		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	$-0.639629\pi$
$797$	16.1389	−	27.9534i	0.571669	−	0.990160i	0.996395	−	0.0848377i	$-0.0270372\pi$
$798$		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	$0.00991818\pi$
$809$	14.9820	+	25.9495i	0.526737	+	0.912336i	−0.472777	+	0.881182i	$0.656748\pi$
$810$		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	$-0.455215\pi$
$821$	8.03611			0.280462			0.140231	+	0.990119i	$0.455215\pi$
$822$		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	$-0.206583\pi$
$827$	45.8218			1.59338			0.796690	+	0.604389i	$0.206583\pi$
$828$		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	$-0.956034\pi$
$839$	−17.7986	−	30.8281i	−0.614476	−	1.06430i	0.376000	−	0.926620i	$-0.377299\pi$
$840$		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	−0.997757	−	0.0669395i	$-0.978677\pi$
$857$	−12.9074	+	22.3562i	−0.440907	+	0.763674i	0.556850	+	0.830613i	$0.312010\pi$
$858$		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	−0.623039	−	0.782191i	$-0.714102\pi$
$863$	10.7483	−	18.6166i	0.365877	−	0.633718i	0.988917	+	0.148473i	$0.0474357\pi$
$864$		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	$-0.718378\pi$
$881$	−37.6060			−1.26698			−0.633490	+	0.773751i	$0.718378\pi$
$882$		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	0.554326	−	0.832300i	$-0.312976\pi$
$887$	−13.2124	−	22.8846i	−0.443630	−	0.768389i	−0.997956	+	0.0639105i	$0.979643\pi$
$888$		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	0.824049	−	0.566518i	$-0.191710\pi$
$911$	−2.37220	−	4.10877i	−0.0785944	−	0.136129i	−0.902644	+	0.430389i	$0.858377\pi$
$912$		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	$-0.235042\pi$
$929$	45.0817			1.47908			0.739541	+	0.673111i	$0.235042\pi$
$930$		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	$-0.444969\pi$
$941$	10.5539			0.344048			0.172024	+	0.985093i	$0.444969\pi$
$942$		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	$-0.217247\pi$
$947$	47.7600			1.55199			0.775996	+	0.630737i	$0.217247\pi$
$948$		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	$-0.163121\pi$
$953$	53.8101			1.74308			0.871540	+	0.490324i	$0.163121\pi$
$954$		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	−0.609462	−	0.792815i	$-0.708615\pi$
$971$	11.8993	−	20.6102i	0.381867	−	0.661413i	0.991329	+	0.131402i	$0.0419479\pi$
$972$		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	$-0.720942\pi$
$977$	−39.9903			−1.27940			−0.639701	+	0.768624i	$0.720942\pi$
$978$		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	$-0.569466\pi$
$983$	23.1143	−	40.0351i	0.737231	−	1.27692i	0.953738	−	0.300640i	$-0.0972004\pi$
$984$		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.k.352.4		8
3.2	odd	2		567.2.h.j.352.1		8
7.4	even	3		567.2.g.j.109.1		8
9.2	odd	6		567.2.g.k.541.4		8
9.4	even	3		567.2.e.c.163.1	✓	8
9.5	odd	6		567.2.e.d.163.4	yes	8
9.7	even	3		567.2.g.j.541.1		8
21.11	odd	6		567.2.g.k.109.4		8
63.4	even	3		567.2.e.c.487.1	yes	8
63.5	even	6		3969.2.a.t.1.1		4
63.11	odd	6		567.2.h.j.298.1		8
63.23	odd	6		3969.2.a.s.1.1		4
63.25	even	3	inner	567.2.h.k.298.4		8
63.32	odd	6		567.2.e.d.487.4	yes	8
63.40	odd	6		3969.2.a.w.1.4		4
63.58	even	3		3969.2.a.x.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.1	✓	8	9.4	even	3
567.2.e.c.487.1	yes	8	63.4	even	3
567.2.e.d.163.4	yes	8	9.5	odd	6
567.2.e.d.487.4	yes	8	63.32	odd	6
567.2.g.j.109.1		8	7.4	even	3
567.2.g.j.541.1		8	9.7	even	3
567.2.g.k.109.4		8	21.11	odd	6
567.2.g.k.541.4		8	9.2	odd	6
567.2.h.j.298.1		8	63.11	odd	6
567.2.h.j.352.1		8	3.2	odd	2
567.2.h.k.298.4		8	63.25	even	3	inner
567.2.h.k.352.4		8	1.1	even	1	trivial
3969.2.a.s.1.1		4	63.23	odd	6
3969.2.a.t.1.1		4	63.5	even	6
3969.2.a.w.1.4		4	63.40	odd	6
3969.2.a.x.1.4		4	63.58	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
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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