LMFDB - Embedded newform 507.2.j.h.361.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.5
Root			$1.07992 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.h.316.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07992 - 0.623490i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.222521 + 0.385418i) q^{4} -2.80194i q^{5} +(-1.07992 - 0.623490i) q^{6} +(-4.15860 - 2.40097i) q^{7} +3.04892i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.07992 - 0.623490i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.222521 + 0.385418i) q^{4} -2.80194i q^{5} +(-1.07992 - 0.623490i) q^{6} +(-4.15860 - 2.40097i) q^{7} +3.04892i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.74698 - 3.02586i) q^{10} +(-1.27030 + 0.733406i) q^{11} +0.445042 q^{12} -5.98792 q^{14} +(-2.42655 + 1.40097i) q^{15} +(1.45593 + 2.52174i) q^{16} +(-1.22252 + 2.11747i) q^{17} +1.24698i q^{18} +(-2.20220 - 1.27144i) q^{19} +(1.07992 + 0.623490i) q^{20} +4.80194i q^{21} +(-0.914542 + 1.58403i) q^{22} +(-1.75786 - 3.04471i) q^{23} +(2.64044 - 1.52446i) q^{24} -2.85086 q^{25} +1.00000 q^{27} +(1.85075 - 1.06853i) q^{28} +(-0.925428 - 1.60289i) q^{29} +(-1.74698 + 3.02586i) q^{30} -7.63102i q^{31} +(-2.13632 - 1.23341i) q^{32} +(1.27030 + 0.733406i) q^{33} +3.04892i q^{34} +(-6.72737 + 11.6521i) q^{35} +(-0.222521 - 0.385418i) q^{36} +(3.94471 - 2.27748i) q^{37} -3.17092 q^{38} +8.54288 q^{40} +(1.07992 - 0.623490i) q^{41} +(2.99396 + 5.18569i) q^{42} +(1.19202 - 2.06464i) q^{43} -0.652793i q^{44} +(2.42655 + 1.40097i) q^{45} +(-3.79669 - 2.19202i) q^{46} -12.8170i q^{47} +(1.45593 - 2.52174i) q^{48} +(8.02930 + 13.9072i) q^{49} +(-3.07868 + 1.77748i) q^{50} +2.44504 q^{51} -8.85086 q^{53} +(1.07992 - 0.623490i) q^{54} +(2.05496 + 3.55929i) q^{55} +(7.32036 - 12.6792i) q^{56} +2.54288i q^{57} +(-1.99877 - 1.15399i) q^{58} +(1.88472 + 1.08815i) q^{59} -1.24698i q^{60} +(3.91454 - 6.78019i) q^{61} +(-4.75786 - 8.24086i) q^{62} +(4.15860 - 2.40097i) q^{63} -8.89977 q^{64} +1.82908 q^{66} +(-3.10219 + 1.79105i) q^{67} +(-0.544073 - 0.942362i) q^{68} +(-1.75786 + 3.04471i) q^{69} +16.7778i q^{70} +(7.65460 + 4.41939i) q^{71} +(-2.64044 - 1.52446i) q^{72} +7.69202i q^{73} +(2.83997 - 4.91897i) q^{74} +(1.42543 + 2.46891i) q^{75} +(0.980069 - 0.565843i) q^{76} +7.04354 q^{77} -4.02177 q^{79} +(7.06576 - 4.07942i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.777479 - 1.34663i) q^{82} -0.652793i q^{83} +(-1.85075 - 1.06853i) q^{84} +(5.93301 + 3.42543i) q^{85} -2.97285i q^{86} +(-0.925428 + 1.60289i) q^{87} +(-2.23609 - 3.87303i) q^{88} +(-5.45241 + 3.14795i) q^{89} +3.49396 q^{90} +1.56465 q^{92} +(-6.60866 + 3.81551i) q^{93} +(-7.99127 - 13.8413i) q^{94} +(-3.56249 + 6.17042i) q^{95} +2.46681i q^{96} +(8.68750 + 5.01573i) q^{97} +(17.3419 + 10.0124i) q^{98} -1.46681i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9	$ 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9} - 2 q^{10} + 4 q^{12} + 4 q^{14} + 10 q^{16} - 14 q^{17} + 10 q^{22} + 4 q^{23} + 20 q^{25} + 12 q^{27} + 16 q^{29} - 2 q^{30} - 36 q^{35} - 2 q^{36} - 80 q^{38} + 28 q^{40} - 2 q^{42} - 6 q^{43} + 10 q^{48} + 34 q^{49} + 28 q^{51} - 52 q^{53} + 26 q^{55} + 14 q^{56} + 26 q^{61} - 32 q^{62} - 16 q^{64} - 20 q^{66} - 14 q^{68} + 4 q^{69} - 14 q^{74} - 10 q^{75} + 60 q^{77} - 36 q^{79} - 6 q^{81} + 10 q^{82} + 16 q^{87} - 14 q^{88} + 4 q^{90} - 68 q^{92} - 64 q^{94} + 6 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9 - 2 * q^10 + 4 * q^12 + 4 * q^14 + 10 * q^16 - 14 * q^17 + 10 * q^22 + 4 * q^23 + 20 * q^25 + 12 * q^27 + 16 * q^29 - 2 * q^30 - 36 * q^35 - 2 * q^36 - 80 * q^38 + 28 * q^40 - 2 * q^42 - 6 * q^43 + 10 * q^48 + 34 * q^49 + 28 * q^51 - 52 * q^53 + 26 * q^55 + 14 * q^56 + 26 * q^61 - 32 * q^62 - 16 * q^64 - 20 * q^66 - 14 * q^68 + 4 * q^69 - 14 * q^74 - 10 * q^75 + 60 * q^77 - 36 * q^79 - 6 * q^81 + 10 * q^82 + 16 * q^87 - 14 * q^88 + 4 * q^90 - 68 * q^92 - 64 * q^94 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.07992	−	0.623490i	0.763616	−	0.440874i	−0.0669766	−	0.997755i	$-0.521335\pi$
$2$	1.07992	−	0.623490i	0.763616	−	0.440874i	0.830593	+	0.556881i	$0.188002\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.222521	+	0.385418i	−0.111260	+	0.192709i
$5$		−	2.80194i		−	1.25306i	−0.779395	−	0.626532i	$-0.784474\pi$
$5$		−	2.80194i		−	1.25306i	0.779395	−	0.626532i	$-0.215526\pi$
$6$	−1.07992	−	0.623490i	−0.440874	−	0.254539i
$7$	−4.15860	−	2.40097i	−1.57180	−	0.907481i	−0.995948	−	0.0899290i	$-0.971336\pi$
$7$	−4.15860	−	2.40097i	−1.57180	−	0.907481i	−0.575855	−	0.817552i	$-0.695331\pi$
$8$			3.04892i			1.07796i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.74698	−	3.02586i	−0.552443	−	0.956860i
$11$	−1.27030	+	0.733406i	−0.383009	+	0.221130i	−0.679127	−	0.734021i	$-0.737641\pi$
$11$	−1.27030	+	0.733406i	−0.383009	+	0.221130i	0.296118	+	0.955151i	$0.404308\pi$
$12$	0.445042			0.128473
$13$		0			0
$13$		0			0
$14$	−5.98792			−1.60034
$15$	−2.42655	+	1.40097i	−0.626532	+	0.361729i
$16$	1.45593	+	2.52174i	0.363982	+	0.630435i
$17$	−1.22252	+	2.11747i	−0.296505	+	0.513562i	−0.975334	−	0.220735i	$-0.929154\pi$
$17$	−1.22252	+	2.11747i	−0.296505	+	0.513562i	0.678829	+	0.734296i	$0.262488\pi$
$18$			1.24698i			0.293916i
$19$	−2.20220	−	1.27144i	−0.505218	−	0.291688i	0.225648	−	0.974209i	$-0.427550\pi$
$19$	−2.20220	−	1.27144i	−0.505218	−	0.291688i	−0.730866	+	0.682521i	$0.760884\pi$
$20$	1.07992	+	0.623490i	0.241477	+	0.139417i
$21$			4.80194i			1.04787i
$22$	−0.914542	+	1.58403i	−0.194981	+	0.337717i
$23$	−1.75786	−	3.04471i	−0.366540	−	0.634866i	0.622482	−	0.782634i	$-0.286124\pi$
$23$	−1.75786	−	3.04471i	−0.366540	−	0.634866i	−0.989022	+	0.147768i	$0.952791\pi$
$24$	2.64044	−	1.52446i	0.538978	−	0.311179i
$25$	−2.85086			−0.570171
$26$		0			0
$27$	1.00000			0.192450
$28$	1.85075	−	1.06853i	0.349759	−	0.201934i
$29$	−0.925428	−	1.60289i	−0.171848	−	0.297649i	0.767218	−	0.641386i	$-0.221640\pi$
$29$	−0.925428	−	1.60289i	−0.171848	−	0.297649i	−0.939066	+	0.343737i	$0.888307\pi$
$30$	−1.74698	+	3.02586i	−0.318953	+	0.552443i
$31$		−	7.63102i		−	1.37057i	−0.728274	−	0.685286i	$-0.759677\pi$
$31$		−	7.63102i		−	1.37057i	0.728274	−	0.685286i	$-0.240323\pi$
$32$	−2.13632	−	1.23341i	−0.377652	−	0.218037i
$33$	1.27030	+	0.733406i	0.221130	+	0.127670i
$34$			3.04892i			0.522885i
$35$	−6.72737	+	11.6521i	−1.13713	+	1.96957i
$36$	−0.222521	−	0.385418i	−0.0370868	−	0.0642363i
$37$	3.94471	−	2.27748i	0.648506	−	0.374415i	−0.139377	−	0.990239i	$-0.544510\pi$
$37$	3.94471	−	2.27748i	0.648506	−	0.374415i	0.787884	+	0.615824i	$0.211177\pi$
$38$	−3.17092			−0.514390
$39$		0			0
$40$	8.54288			1.35075
$41$	1.07992	−	0.623490i	0.168655	−	0.0973727i	−0.413297	−	0.910596i	$-0.635623\pi$
$41$	1.07992	−	0.623490i	0.168655	−	0.0973727i	0.581951	+	0.813224i	$0.302289\pi$
$42$	2.99396	+	5.18569i	0.461978	+	0.800169i
$43$	1.19202	−	2.06464i	0.181782	−	0.314855i	−0.760706	−	0.649097i	$-0.775147\pi$
$43$	1.19202	−	2.06464i	0.181782	−	0.314855i	0.942487	+	0.334242i	$0.108480\pi$
$44$		−	0.652793i		−	0.0984122i
$45$	2.42655	+	1.40097i	0.361729	+	0.208844i
$46$	−3.79669	−	2.19202i	−0.559792	−	0.323196i
$47$		−	12.8170i		−	1.86955i	−0.355238	−	0.934776i	$-0.615600\pi$
$47$		−	12.8170i		−	1.86955i	0.355238	−	0.934776i	$-0.384400\pi$
$48$	1.45593	−	2.52174i	0.210145	−	0.363982i
$49$	8.02930	+	13.9072i	1.14704	+	1.98674i
$50$	−3.07868	+	1.77748i	−0.435392	+	0.251374i
$51$	2.44504			0.342374
$52$		0			0
$53$	−8.85086			−1.21576			−0.607879	−	0.794030i	$-0.707980\pi$
$53$	−8.85086			−1.21576			−0.607879	+	0.794030i	$0.707980\pi$
$54$	1.07992	−	0.623490i	0.146958	−	0.0848462i
$55$	2.05496	+	3.55929i	0.277090	+	0.479935i
$56$	7.32036	−	12.6792i	0.978224	−	1.69433i
$57$			2.54288i			0.336812i
$58$	−1.99877	−	1.15399i	−0.262451	−	0.151526i
$59$	1.88472	+	1.08815i	0.245370	+	0.141665i	0.617642	−	0.786459i	$-0.288088\pi$
$59$	1.88472	+	1.08815i	0.245370	+	0.141665i	−0.372272	+	0.928124i	$0.621421\pi$
$60$		−	1.24698i		−	0.160984i
$61$	3.91454	−	6.78019i	0.501206	−	0.868114i	−0.498793	−	0.866721i	$-0.666223\pi$
$61$	3.91454	−	6.78019i	0.501206	−	0.868114i	0.999999	−	0.00139289i	$-0.000443372\pi$
$62$	−4.75786	−	8.24086i	−0.604249	−	1.04659i
$63$	4.15860	−	2.40097i	0.523934	−	0.302494i
$64$	−8.89977			−1.11247
$65$		0			0
$66$	1.82908			0.225145
$67$	−3.10219	+	1.79105i	−0.378993	+	0.218812i	−0.677380	−	0.735633i	$-0.736885\pi$
$67$	−3.10219	+	1.79105i	−0.378993	+	0.218812i	0.298387	+	0.954445i	$0.403551\pi$
$68$	−0.544073	−	0.942362i	−0.0659785	−	0.114278i
$69$	−1.75786	+	3.04471i	−0.211622	+	0.366540i
$70$			16.7778i			2.00533i
$71$	7.65460	+	4.41939i	0.908434	+	0.524485i	0.879927	−	0.475109i	$-0.157591\pi$
$71$	7.65460	+	4.41939i	0.908434	+	0.524485i	0.0285072	+	0.999594i	$0.490925\pi$
$72$	−2.64044	−	1.52446i	−0.311179	−	0.179659i
$73$			7.69202i			0.900283i	0.892957	+	0.450142i	$0.148626\pi$
$73$			7.69202i			0.900283i	−0.892957	+	0.450142i	$0.851374\pi$
$74$	2.83997	−	4.91897i	0.330140	−	0.571819i
$75$	1.42543	+	2.46891i	0.164594	+	0.285086i
$76$	0.980069	−	0.565843i	0.112422	−	0.0649067i
$77$	7.04354			0.802686
$78$		0			0
$79$	−4.02177			−0.452485			−0.226242	−	0.974071i	$-0.572644\pi$
$79$	−4.02177			−0.452485			−0.226242	+	0.974071i	$0.572644\pi$
$80$	7.06576	−	4.07942i	0.789976	−	0.456093i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.777479	−	1.34663i	0.0858582	−	0.148711i
$83$		−	0.652793i		−	0.0716533i	−0.999358	−	0.0358267i	$-0.988594\pi$
$83$		−	0.652793i		−	0.0716533i	0.999358	−	0.0358267i	$-0.0114064\pi$
$84$	−1.85075	−	1.06853i	−0.201934	−	0.116586i
$85$	5.93301	+	3.42543i	0.643526	+	0.371540i
$86$		−	2.97285i		−	0.320571i
$87$	−0.925428	+	1.60289i	−0.0992162	+	0.171848i
$88$	−2.23609	−	3.87303i	−0.238368	−	0.412866i
$89$	−5.45241	+	3.14795i	−0.577954	+	0.333682i	−0.760320	−	0.649549i	$-0.774958\pi$
$89$	−5.45241	+	3.14795i	−0.577954	+	0.333682i	0.182366	+	0.983231i	$0.441624\pi$
$90$	3.49396			0.368296
$91$		0			0
$92$	1.56465			0.163126
$93$	−6.60866	+	3.81551i	−0.685286	+	0.395650i
$94$	−7.99127	−	13.8413i	−0.824237	−	1.42762i
$95$	−3.56249	+	6.17042i	−0.365504	+	0.633071i
$96$			2.46681i			0.251768i
$97$	8.68750	+	5.01573i	0.882082	+	0.509270i	0.871344	−	0.490672i	$-0.163249\pi$
$97$	8.68750	+	5.01573i	0.882082	+	0.509270i	0.0107376	+	0.999942i	$0.496582\pi$
$98$	17.3419	+	10.0124i	1.75180	+	1.01140i
$99$		−	1.46681i		−	0.147420i
$100$	0.634375	−	1.09877i	0.0634375	−	0.109877i
$101$	6.94385	+	12.0271i	0.690938	+	1.19674i	0.971531	+	0.236913i	$0.0761358\pi$
$101$	6.94385	+	12.0271i	0.690938	+	1.19674i	−0.280592	+	0.959827i	$0.590531\pi$
$102$	2.64044	−	1.52446i	0.261443	−	0.150944i
$103$	17.4034			1.71481			0.857405	−	0.514642i	$-0.172075\pi$
$103$	17.4034			1.71481			0.857405	+	0.514642i	$0.172075\pi$
$104$		0			0
$105$	13.4547			1.31305
$106$	−9.55818	+	5.51842i	−0.928373	+	0.535996i
$107$	−5.27628	−	9.13879i	−0.510077	−	0.883480i	−0.999932	−	0.0116758i	$-0.996283\pi$
$107$	−5.27628	−	9.13879i	−0.510077	−	0.883480i	0.489854	−	0.871804i	$-0.337050\pi$
$108$	−0.222521	+	0.385418i	−0.0214121	+	0.0370868i
$109$			1.07069i			0.102553i	0.998684	+	0.0512766i	$0.0163290\pi$
$109$			1.07069i			0.102553i	−0.998684	+	0.0512766i	$0.983671\pi$
$110$	4.43836	+	2.56249i	0.423181	+	0.244324i
$111$	−3.94471	−	2.27748i	−0.374415	−	0.216169i
$112$		−	13.9825i		−	1.32123i
$113$	8.26540	−	14.3161i	0.777543	−	1.34674i	−0.155811	−	0.987787i	$-0.549799\pi$
$113$	8.26540	−	14.3161i	0.777543	−	1.34674i	0.933354	−	0.358957i	$-0.116868\pi$
$114$	1.58546	+	2.74609i	0.148492	+	0.257195i
$115$	−8.53109	+	4.92543i	−0.795528	+	0.459298i
$116$	0.823708			0.0764794
$117$		0			0
$118$	2.71379			0.249825
$119$	10.1680	−	5.87047i	0.932095	−	0.538145i
$120$	−4.27144	−	7.39835i	−0.389927	−	0.675374i
$121$	−4.42423	+	7.66299i	−0.402203	+	0.696636i
$122$		−	9.76271i		−	0.883874i
$123$	−1.07992	−	0.623490i	−0.0973727	−	0.0562182i
$124$	2.94113	+	1.69806i	0.264121	+	0.152490i
$125$		−	6.02177i		−	0.538604i
$126$	2.99396	−	5.18569i	0.266723	−	0.461978i
$127$	−4.76875	−	8.25972i	−0.423158	−	0.732931i	0.573088	−	0.819494i	$-0.305745\pi$
$127$	−4.76875	−	8.25972i	−0.423158	−	0.732931i	−0.996246	+	0.0865622i	$0.972412\pi$
$128$	−5.33836	+	3.08211i	−0.471849	+	0.272422i
$129$	−2.38404			−0.209903
$130$		0			0
$131$	−5.50902			−0.481326			−0.240663	−	0.970609i	$-0.577365\pi$
$131$	−5.50902			−0.481326			−0.240663	+	0.970609i	$0.577365\pi$
$132$	−0.565335	+	0.326396i	−0.0492061	+	0.0284092i
$133$	6.10537	+	10.5748i	0.529402	+	0.916952i
$134$	−2.23341	+	3.86837i	−0.192937	+	0.334177i
$135$		−	2.80194i		−	0.241152i
$136$	−6.45599	−	3.72737i	−0.553596	−	0.319619i
$137$	−14.0154	−	8.09179i	−1.19742	−	0.691329i	−0.237438	−	0.971403i	$-0.576308\pi$
$137$	−14.0154	−	8.09179i	−1.19742	−	0.691329i	−0.959978	+	0.280074i	$0.909641\pi$
$138$			4.38404i			0.373195i
$139$	5.25451	−	9.10108i	0.445682	−	0.771944i	−0.552418	−	0.833568i	$-0.686295\pi$
$139$	5.25451	−	9.10108i	0.445682	−	0.771944i	0.998099	+	0.0616238i	$0.0196279\pi$
$140$	−2.99396	−	5.18569i	−0.253036	−	0.438271i
$141$	−11.0999	+	6.40850i	−0.934776	+	0.539693i
$142$	11.0218			0.924926
$143$		0			0
$144$	−2.91185			−0.242654
$145$	−4.49119	+	2.59299i	−0.372973	+	0.215336i
$146$	4.79590	+	8.30674i	0.396911	+	0.687470i
$147$	8.02930	−	13.9072i	0.662246	−	1.14704i
$148$			2.02715i			0.166630i
$149$	−12.4276	−	7.17510i	−1.01811	−	0.587807i	−0.104555	−	0.994519i	$-0.533342\pi$
$149$	−12.4276	−	7.17510i	−1.01811	−	0.587807i	−0.913556	+	0.406712i	$0.866675\pi$
$150$	3.07868	+	1.77748i	0.251374	+	0.145131i
$151$		−	1.96615i		−	0.160003i	−0.996795	−	0.0800014i	$-0.974508\pi$
$151$		−	1.96615i		−	0.160003i	0.996795	−	0.0800014i	$-0.0254925\pi$
$152$	3.87651	−	6.71431i	0.314426	−	0.544603i
$153$	−1.22252	−	2.11747i	−0.0988350	−	0.171187i
$154$	7.60643	−	4.39158i	0.612944	−	0.353883i
$155$	−21.3817			−1.71742
$156$		0			0
$157$	10.7017			0.854089			0.427045	−	0.904231i	$-0.359555\pi$
$157$	10.7017			0.854089			0.427045	+	0.904231i	$0.359555\pi$
$158$	−4.34317	+	2.50753i	−0.345524	+	0.199489i
$159$	4.42543	+	7.66507i	0.350959	+	0.607879i
$160$	−3.45593	+	5.98584i	−0.273215	+	0.473222i
$161$			16.8823i			1.33051i
$162$	−1.07992	−	0.623490i	−0.0848462	−	0.0489860i
$163$	3.37730	+	1.94989i	0.264531	+	0.152727i	0.626400	−	0.779502i	$-0.284528\pi$
$163$	3.37730	+	1.94989i	0.264531	+	0.152727i	−0.361869	+	0.932229i	$0.617861\pi$
$164$			0.554958i			0.0433349i
$165$	2.05496	−	3.55929i	0.159978	−	0.277090i
$166$	−0.407010	−	0.704961i	−0.0315901	−	0.0547156i
$167$	−18.2033	+	10.5097i	−1.40861	+	0.813264i	−0.995255	−	0.0973035i	$-0.968978\pi$
$167$	−18.2033	+	10.5097i	−1.40861	+	0.813264i	−0.413360	+	0.910568i	$0.635645\pi$
$168$	−14.6407			−1.12956
$169$		0			0
$170$	8.54288			0.655209
$171$	2.20220	−	1.27144i	0.168406	−	0.0972293i
$172$	0.530499	+	0.918852i	0.0404502	+	0.0700618i
$173$	6.61745	−	11.4618i	0.503115	−	0.871421i	−0.496878	−	0.867820i	$-0.665520\pi$
$173$	6.61745	−	11.4618i	0.503115	−	0.871421i	0.999994	−	0.00360102i	$-0.00114624\pi$
$174$			2.30798i			0.174967i
$175$	11.8556	+	6.84481i	0.896197	+	0.517419i
$176$	−3.69892	−	2.13557i	−0.278816	−	0.160975i
$177$		−	2.17629i		−	0.163580i
$178$	−3.92543	+	6.79904i	−0.294223	+	0.509610i
$179$	4.26391	+	7.38530i	0.318699	+	0.552003i	0.980217	−	0.197926i	$-0.0634207\pi$
$179$	4.26391	+	7.38530i	0.318699	+	0.552003i	−0.661518	+	0.749930i	$0.730087\pi$
$180$	−1.07992	+	0.623490i	−0.0804922	+	0.0464722i
$181$	3.63640			0.270291			0.135146	−	0.990826i	$-0.456850\pi$
$181$	3.63640			0.270291			0.135146	+	0.990826i	$0.456850\pi$
$182$		0			0
$183$	−7.82908			−0.578743
$184$	9.28307	−	5.35958i	0.684357	−	0.395114i
$185$	−6.38135	−	11.0528i	−0.469167	−	0.812620i
$186$	−4.75786	+	8.24086i	−0.348864	+	0.604249i
$187$		−	3.58642i		−	0.262265i
$188$	4.93990	+	2.85205i	0.360279	+	0.208007i
$189$	−4.15860	−	2.40097i	−0.302494	−	0.174645i
$190$			8.88471i			0.644564i
$191$	−10.6908	+	18.5171i	−0.773561	+	1.33985i	0.162039	+	0.986784i	$0.448193\pi$
$191$	−10.6908	+	18.5171i	−0.773561	+	1.33985i	−0.935600	+	0.353062i	$0.885140\pi$
$192$	4.44989	+	7.70743i	0.321143	+	0.556236i
$193$	7.29850	−	4.21379i	0.525358	−	0.303315i	−0.213766	−	0.976885i	$-0.568573\pi$
$193$	7.29850	−	4.21379i	0.525358	−	0.303315i	0.739124	+	0.673569i	$0.235240\pi$
$194$	12.5090			0.898096
$195$		0			0
$196$	−7.14675			−0.510482
$197$	−22.9293	+	13.2383i	−1.63365	+	0.943186i	−0.650691	+	0.759343i	$0.725521\pi$
$197$	−22.9293	+	13.2383i	−1.63365	+	0.943186i	−0.982955	+	0.183844i	$0.941146\pi$
$198$	−0.914542	−	1.58403i	−0.0649937	−	0.112572i
$199$	−7.12618	+	12.3429i	−0.505161	+	0.874965i	0.494821	+	0.868995i	$0.335234\pi$
$199$	−7.12618	+	12.3429i	−0.505161	+	0.874965i	−0.999982	+	0.00597014i	$0.998100\pi$
$200$		−	8.69202i		−	0.614619i
$201$	3.10219	+	1.79105i	0.218812	+	0.126331i
$202$	14.9975	+	8.65883i	1.05522	+	0.609233i
$203$			8.88769i			0.623794i
$204$	−0.544073	+	0.942362i	−0.0380927	+	0.0659785i
$205$	−1.74698	−	3.02586i	−0.122014	−	0.211335i
$206$	18.7942	−	10.8509i	1.30946	−	0.756015i
$207$	3.51573			0.244360
$208$		0			0
$209$	3.72992			0.258004
$210$	14.5300	−	8.38889i	1.00266	−	0.578888i
$211$	−0.925428	−	1.60289i	−0.0637091	−	0.110347i	0.832412	−	0.554158i	$-0.186960\pi$
$211$	−0.925428	−	1.60289i	−0.0637091	−	0.110347i	−0.896121	+	0.443811i	$0.853626\pi$
$212$	1.96950	−	3.41127i	0.135266	−	0.234287i
$213$		−	8.83877i		−	0.605623i
$214$	−11.3959	−	6.57942i	−0.779007	−	0.449760i
$215$	−5.78500	−	3.33997i	−0.394534	−	0.227784i
$216$			3.04892i			0.207453i
$217$	−18.3218	+	31.7344i	−1.24377	+	2.15427i
$218$	0.667563	+	1.15625i	0.0452131	+	0.0783113i
$219$	6.66149	−	3.84601i	0.450142	−	0.259889i
$220$	−1.82908			−0.123317
$221$		0			0
$222$	−5.67994			−0.381213
$223$	16.1517	−	9.32520i	1.08160	−	0.624462i	0.150272	−	0.988645i	$-0.451985\pi$
$223$	16.1517	−	9.32520i	1.08160	−	0.624462i	0.931327	+	0.364183i	$0.118652\pi$
$224$	5.92274	+	10.2585i	0.395730	+	0.685424i
$225$	1.42543	−	2.46891i	0.0950285	−	0.164594i
$226$		−	20.6136i		−	1.37119i
$227$	−8.45010	−	4.87867i	−0.560853	−	0.323808i	0.192635	−	0.981270i	$-0.438297\pi$
$227$	−8.45010	−	4.87867i	−0.560853	−	0.323808i	−0.753488	+	0.657462i	$0.771630\pi$
$228$	−0.980069	−	0.565843i	−0.0649067	−	0.0374739i
$229$			2.86294i			0.189188i	0.995516	+	0.0945941i	$0.0301553\pi$
$229$			2.86294i			0.189188i	−0.995516	+	0.0945941i	$0.969845\pi$
$230$	−6.14191	+	10.6381i	−0.404985	+	0.701455i
$231$	−3.52177	−	6.09989i	−0.231715	−	0.401343i
$232$	4.88707	−	2.82155i	0.320852	−	0.185244i
$233$	5.78554			0.379024			0.189512	−	0.981878i	$-0.439309\pi$
$233$	5.78554			0.379024			0.189512	+	0.981878i	$0.439309\pi$
$234$		0			0
$235$	−35.9124			−2.34267
$236$	−0.838781	+	0.484271i	−0.0546000	+	0.0315233i
$237$	2.01089	+	3.48296i	0.130621	+	0.226242i
$238$	7.32036	−	12.6792i	0.474508	−	0.821872i
$239$			7.09246i			0.458773i	0.973335	+	0.229386i	$0.0736720\pi$
$239$			7.09246i			0.458773i	−0.973335	+	0.229386i	$0.926328\pi$
$240$	−7.06576	−	4.07942i	−0.456093	−	0.263325i
$241$	3.37730	+	1.94989i	0.217551	+	0.125603i	0.604816	−	0.796365i	$-0.293247\pi$
$241$	3.37730	+	1.94989i	0.217551	+	0.125603i	−0.387265	+	0.921969i	$0.626580\pi$
$242$			11.0339i			0.709283i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.74214	+	3.01747i	0.111529	+	0.193174i
$245$	38.9670	−	22.4976i	2.48951	−	1.43732i
$246$	−1.55496			−0.0991405
$247$		0			0
$248$	23.2664			1.47742
$249$	−0.565335	+	0.326396i	−0.0358267	+	0.0206845i
$250$	−3.75451	−	6.50301i	−0.237456	−	0.411286i
$251$	−1.22252	+	2.11747i	−0.0771648	+	0.133653i	−0.902026	−	0.431682i	$-0.857920\pi$
$251$	−1.22252	+	2.11747i	−0.0771648	+	0.133653i	0.824861	+	0.565336i	$0.191253\pi$
$252$			2.13706i			0.134622i
$253$	4.46602	+	2.57846i	0.280776	+	0.162106i
$254$	−10.2997	−	5.94653i	−0.646261	−	0.373119i
$255$		−	6.85086i		−	0.429017i
$256$	5.05645	−	8.75803i	0.316028	−	0.547377i
$257$	−7.06518	−	12.2372i	−0.440714	−	0.763339i	0.557029	−	0.830493i	$-0.311941\pi$
$257$	−7.06518	−	12.2372i	−0.440714	−	0.763339i	−0.997743	+	0.0671545i	$0.978608\pi$
$258$	−2.57457	+	1.48643i	−0.160285	+	0.0925409i
$259$	−21.8726			−1.35910
$260$		0			0
$261$	1.85086			0.114565
$262$	−5.94928	+	3.43482i	−0.367548	+	0.212204i
$263$	11.8617	+	20.5451i	0.731426	+	1.26687i	0.956274	+	0.292473i	$0.0944783\pi$
$263$	11.8617	+	20.5451i	0.731426	+	1.26687i	−0.224847	+	0.974394i	$0.572188\pi$
$264$	−2.23609	+	3.87303i	−0.137622	+	0.238368i
$265$			24.7995i			1.52342i
$266$	13.1866	+	7.61327i	0.808520	+	0.466799i
$267$	5.45241	+	3.14795i	0.333682	+	0.192651i
$268$		−	1.59419i		−	0.0973805i
$269$	2.95808	−	5.12355i	0.180357	−	0.312388i	−0.761645	−	0.647995i	$-0.775608\pi$
$269$	2.95808	−	5.12355i	0.180357	−	0.312388i	0.942002	+	0.335606i	$0.108941\pi$
$270$	−1.74698	−	3.02586i	−0.106318	−	0.184148i
$271$	−2.76287	+	1.59515i	−0.167833	+	0.0968982i	−0.581563	−	0.813501i	$-0.697559\pi$
$271$	−2.76287	+	1.59515i	−0.167833	+	0.0968982i	0.413731	+	0.910399i	$0.364225\pi$
$272$	−7.11960			−0.431689
$273$		0			0
$274$	−20.1806			−1.21915
$275$	3.62143	−	2.09083i	0.218381	−	0.126082i
$276$	−0.782323	−	1.35502i	−0.0470903	−	0.0815629i
$277$	10.9683	−	18.9977i	0.659022	−	1.14146i	−0.321848	−	0.946791i	$-0.604304\pi$
$277$	10.9683	−	18.9977i	0.659022	−	1.14146i	0.980869	−	0.194667i	$-0.0623627\pi$
$278$		−	13.1045i		−	0.785958i
$279$	6.60866	+	3.81551i	0.395650	+	0.228429i
$280$	−35.5264	−	20.5112i	−2.12311	−	1.22578i
$281$			11.9903i			0.715282i	0.933859	+	0.357641i	$0.116419\pi$
$281$			11.9903i			0.715282i	−0.933859	+	0.357641i	$0.883581\pi$
$282$	−7.99127	+	13.8413i	−0.475873	+	0.824237i
$283$	−7.18329	−	12.4418i	−0.427002	−	0.739590i	0.569603	−	0.821920i	$-0.307097\pi$
$283$	−7.18329	−	12.4418i	−0.427002	−	0.739590i	−0.996605	+	0.0823303i	$0.973764\pi$
$284$	−3.40662	+	1.96681i	−0.202146	+	0.116709i
$285$	7.12498			0.422047
$286$		0			0
$287$	−5.98792			−0.353456
$288$	2.13632	−	1.23341i	0.125884	−	0.0726791i
$289$	5.51089	+	9.54513i	0.324170	+	0.561478i
$290$	−3.23341	+	5.60042i	−0.189872	+	0.328868i
$291$		−	10.0315i		−	0.588055i
$292$	−2.96464	−	1.71164i	−0.173492	−	0.100166i
$293$	−16.2452	−	9.37920i	−0.949058	−	0.547939i	−0.0562695	−	0.998416i	$-0.517921\pi$
$293$	−16.2452	−	9.37920i	−0.949058	−	0.547939i	−0.892788	+	0.450477i	$0.851254\pi$
$294$		−	20.0248i		−	1.16787i
$295$	3.04892	−	5.28088i	0.177515	−	0.307465i
$296$	6.94385	+	12.0271i	0.403603	+	0.699061i
$297$	−1.27030	+	0.733406i	−0.0737101	+	0.0425565i
$298$	−17.8944			−1.03659
$299$		0			0
$300$	−1.26875			−0.0732513
$301$	−9.91428	+	5.72401i	−0.571450	+	0.329927i
$302$	−1.22587	−	2.12327i	−0.0705411	−	0.122181i
$303$	6.94385	−	12.0271i	0.398913	−	0.690938i
$304$		−	7.40449i		−	0.424676i
$305$	−18.9977	−	10.9683i	−1.08780	−	0.628043i
$306$	−2.64044	−	1.52446i	−0.150944	−	0.0871475i
$307$			25.6262i			1.46257i	0.682074	+	0.731283i	$0.261078\pi$
$307$			25.6262i			1.46257i	−0.682074	+	0.731283i	$0.738922\pi$
$308$	−1.56734	+	2.71470i	−0.0893072	+	0.154685i
$309$	−8.70171	−	15.0718i	−0.495023	−	0.857405i
$310$	−23.0904	+	13.3312i	−1.31145	+	0.757164i
$311$	−11.3817			−0.645394			−0.322697	−	0.946502i	$-0.604590\pi$
$311$	−11.3817			−0.645394			−0.322697	+	0.946502i	$0.604590\pi$
$312$		0			0
$313$	27.5743			1.55859			0.779297	−	0.626655i	$-0.215576\pi$
$313$	27.5743			1.55859			0.779297	+	0.626655i	$0.215576\pi$
$314$	11.5569	−	6.67241i	0.652196	−	0.376546i
$315$	−6.72737	−	11.6521i	−0.379044	−	0.656524i
$316$	0.894928	−	1.55006i	0.0503436	−	0.0871977i
$317$			11.2597i			0.632405i	0.948692	+	0.316203i	$0.102408\pi$
$317$			11.2597i			0.632405i	−0.948692	+	0.316203i	$0.897592\pi$
$318$	9.55818	+	5.51842i	0.535996	+	0.309458i
$319$	2.35113	+	1.35743i	0.131638	+	0.0760014i
$320$			24.9366i			1.39400i
$321$	−5.27628	+	9.13879i	−0.294493	+	0.510077i
$322$	10.5260	+	18.2315i	0.586588	+	1.01600i
$323$	5.38446	−	3.10872i	0.299599	−	0.172974i
$324$	0.445042			0.0247245
$325$		0			0
$326$	4.86294			0.269333
$327$	0.927243	−	0.535344i	0.0512766	−	0.0296046i
$328$	1.90097	+	3.29257i	0.104963	+	0.181802i
$329$	−30.7732	+	53.3008i	−1.69658	+	2.93857i
$330$		−	5.12498i		−	0.282121i
$331$	−10.3113	−	5.95324i	−0.566761	−	0.327220i	0.189094	−	0.981959i	$-0.439445\pi$
$331$	−10.3113	−	5.95324i	−0.566761	−	0.327220i	−0.755855	+	0.654739i	$0.772778\pi$
$332$	0.251598	+	0.145260i	0.0138082	+	0.00797218i
$333$			4.55496i			0.249610i
$334$	−13.1054	+	22.6992i	−0.717094	+	1.24204i
$335$	5.01842	+	8.69215i	0.274185	+	0.474903i
$336$	−12.1092	+	6.99127i	−0.660613	+	0.381405i
$337$	−17.1672			−0.935157			−0.467578	−	0.883952i	$-0.654873\pi$
$337$	−17.1672			−0.935157			−0.467578	+	0.883952i	$0.654873\pi$
$338$		0			0
$339$	−16.5308			−0.897830
$340$	−2.64044	+	1.52446i	−0.143198	+	0.0826754i
$341$	5.59664	+	9.69366i	0.303075	+	0.524941i
$342$	1.58546	−	2.74609i	0.0857317	−	0.148492i
$343$		−	43.4989i		−	2.34872i
$344$	6.29492	+	3.63437i	0.339399	+	0.195952i
$345$	8.53109	+	4.92543i	0.459298	+	0.265176i
$346$		−	16.5036i		−	0.887242i
$347$	12.1380	−	21.0237i	0.651603	−	1.12861i	−0.331131	−	0.943585i	$-0.607430\pi$
$347$	12.1380	−	21.0237i	0.651603	−	1.12861i	0.982734	−	0.185025i	$-0.0592366\pi$
$348$	−0.411854	−	0.713352i	−0.0220777	−	0.0382397i
$349$	−3.95983	+	2.28621i	−0.211965	+	0.122378i	−0.602224	−	0.798327i	$-0.705719\pi$
$349$	−3.95983	+	2.28621i	−0.211965	+	0.122378i	0.390259	+	0.920705i	$0.372385\pi$
$350$	17.0707			0.912467
$351$		0			0
$352$	3.61835			0.192859
$353$	5.26203	−	3.03803i	0.280069	−	0.161698i	−0.353385	−	0.935478i	$-0.614970\pi$
$353$	5.26203	−	3.03803i	0.280069	−	0.161698i	0.633455	+	0.773780i	$0.281636\pi$
$354$	−1.35690	−	2.35021i	−0.0721182	−	0.124912i
$355$	12.3828	−	21.4477i	0.657213	−	1.13833i
$356$		−	2.80194i		−	0.148502i
$357$	−10.1680	−	5.87047i	−0.538145	−	0.310698i
$358$	9.20932	+	5.31700i	0.486728	+	0.281012i
$359$		−	14.9661i		−	0.789883i	−0.918706	−	0.394942i	$-0.870765\pi$
$359$		−	14.9661i		−	0.789883i	0.918706	−	0.394942i	$-0.129235\pi$
$360$	−4.27144	+	7.39835i	−0.225125	+	0.389927i
$361$	−6.26689	−	10.8546i	−0.329836	−	0.571293i
$362$	3.92701	−	2.26726i	0.206399	−	0.119164i
$363$	8.84846			0.464424
$364$		0			0
$365$	21.5526			1.12811
$366$	−8.45475	+	4.88135i	−0.441937	+	0.255152i
$367$	−18.5417	−	32.1151i	−0.967868	−	1.67640i	−0.701704	−	0.712468i	$-0.747577\pi$
$367$	−18.5417	−	32.1151i	−0.967868	−	1.67640i	−0.266164	−	0.963928i	$-0.585756\pi$
$368$	5.11865	−	8.86575i	0.266828	−	0.462159i
$369$			1.24698i			0.0649152i
$370$	−13.7827	−	7.95742i	−0.716526	−	0.413687i
$371$	36.8072	+	21.2506i	1.91093	+	1.10328i
$372$		−	3.39612i		−	0.176081i
$373$	18.2545	−	31.6177i	0.945183	−	1.63710i	0.189798	−	0.981823i	$-0.439217\pi$
$373$	18.2545	−	31.6177i	0.945183	−	1.63710i	0.755385	−	0.655282i	$-0.227450\pi$
$374$	−2.23609	−	3.87303i	−0.115626	−	0.200270i
$375$	−5.21501	+	3.01089i	−0.269302	+	0.155481i
$376$	39.0780			2.01529
$377$		0			0
$378$	−5.98792			−0.307985
$379$	23.0234	−	13.2925i	1.18263	−	0.682792i	0.226009	−	0.974125i	$-0.427432\pi$
$379$	23.0234	−	13.2925i	1.18263	−	0.682792i	0.956622	+	0.291333i	$0.0940988\pi$
$380$	−1.58546	−	2.74609i	−0.0813323	−	0.140872i
$381$	−4.76875	+	8.25972i	−0.244310	+	0.423158i
$382$			26.6625i			1.36417i
$383$	−12.4276	−	7.17510i	−0.635022	−	0.366630i	0.147672	−	0.989036i	$-0.452822\pi$
$383$	−12.4276	−	7.17510i	−0.635022	−	0.366630i	−0.782694	+	0.622406i	$0.786155\pi$
$384$	5.33836	+	3.08211i	0.272422	+	0.157283i
$385$		−	19.7356i		−	1.00582i
$386$	5.25451	−	9.10108i	0.267448	−	0.463233i
$387$	1.19202	+	2.06464i	0.0605939	+	0.104952i
$388$	−3.86630	+	2.23221i	−0.196282	+	0.113323i
$389$	22.6582			1.14881			0.574407	−	0.818570i	$-0.305233\pi$
$389$	22.6582			1.14881			0.574407	+	0.818570i	$0.305233\pi$
$390$		0			0
$391$	8.59611			0.434724
$392$	−42.4018	+	24.4807i	−2.14161	+	1.23646i
$393$	2.75451	+	4.77096i	0.138947	+	0.240663i
$394$	−16.5078	+	28.5924i	−0.831652	+	1.44046i
$395$			11.2687i			0.566992i
$396$	0.565335	+	0.326396i	0.0284092	+	0.0164020i
$397$	−6.84813	−	3.95377i	−0.343698	−	0.198434i	0.318208	−	0.948021i	$-0.396919\pi$
$397$	−6.84813	−	3.95377i	−0.343698	−	0.198434i	−0.661906	+	0.749587i	$0.730252\pi$
$398$			17.7724i			0.890850i
$399$	6.10537	−	10.5748i	0.305651	−	0.529402i
$400$	−4.15064	−	7.18911i	−0.207532	−	0.359456i
$401$	2.54318	−	1.46830i	0.127000	−	0.0733236i	−0.435154	−	0.900356i	$-0.643306\pi$
$401$	2.54318	−	1.46830i	0.127000	−	0.0733236i	0.562154	+	0.827032i	$0.309973\pi$
$402$	4.46681			0.222784
$403$		0			0
$404$	−6.18060			−0.307497
$405$	−2.42655	+	1.40097i	−0.120576	+	0.0696147i
$406$	5.54138	+	9.59796i	0.275014	+	0.476339i
$407$	−3.34063	+	5.78615i	−0.165589	+	0.286809i
$408$			7.45473i			0.369064i
$409$	10.1801	+	5.87747i	0.503372	+	0.290622i	0.730105	−	0.683335i	$-0.239471\pi$
$409$	10.1801	+	5.87747i	0.503372	+	0.290622i	−0.226733	+	0.973957i	$0.572804\pi$
$410$	−3.77318	−	2.17845i	−0.186344	−	0.107586i
$411$			16.1836i			0.798278i
$412$	−3.87263	+	6.70758i	−0.190791	+	0.330459i
$413$	−5.22521	−	9.05033i	−0.257116	−	0.445338i
$414$	3.79669	−	2.19202i	0.186597	−	0.107732i
$415$	−1.82908			−0.0897862
$416$		0			0
$417$	−10.5090			−0.514629
$418$	4.02800	−	2.32557i	0.197016	−	0.113747i
$419$	−3.67092	−	6.35821i	−0.179336	−	0.310619i	0.762317	−	0.647203i	$-0.224062\pi$
$419$	−3.67092	−	6.35821i	−0.179336	−	0.310619i	−0.941653	+	0.336584i	$0.890728\pi$
$420$	−2.99396	+	5.18569i	−0.146090	+	0.253036i
$421$		−	25.6963i		−	1.25236i	−0.779677	−	0.626181i	$-0.784617\pi$
$421$		−	25.6963i		−	1.25236i	0.779677	−	0.626181i	$-0.215383\pi$
$422$	−1.99877	−	1.15399i	−0.0972985	−	0.0561753i
$423$	11.0999	+	6.40850i	0.539693	+	0.311592i
$424$		−	26.9855i		−	1.31053i
$425$	3.48523	−	6.03660i	0.169058	−	0.292818i
$426$	−5.51089	−	9.54513i	−0.267003	−	0.462463i
$427$	−32.5580	+	18.7974i	−1.57559	+	0.909669i
$428$	4.69633			0.227006
$429$		0			0
$430$	−8.32975			−0.401696
$431$	−7.74399	+	4.47099i	−0.373015	+	0.215360i	−0.674775	−	0.738024i	$-0.735759\pi$
$431$	−7.74399	+	4.47099i	−0.373015	+	0.215360i	0.301760	+	0.953384i	$0.402426\pi$
$432$	1.45593	+	2.52174i	0.0700483	+	0.121327i
$433$	1.45742	−	2.52432i	0.0700391	−	0.121311i	−0.828879	−	0.559428i	$-0.811021\pi$
$433$	1.45742	−	2.52432i	0.0700391	−	0.121311i	0.898918	+	0.438116i	$0.144354\pi$
$434$			45.6939i			2.19338i
$435$	4.49119	+	2.59299i	0.215336	+	0.124324i
$436$	−0.412662	−	0.238250i	−0.0197629	−	0.0114101i
$437$			8.94007i			0.427661i
$438$	4.79590	−	8.30674i	0.229157	−	0.396911i
$439$	4.52930	+	7.84498i	0.216172	+	0.374421i	0.953634	−	0.300967i	$-0.0973095\pi$
$439$	4.52930	+	7.84498i	0.216172	+	0.374421i	−0.737463	+	0.675388i	$0.763976\pi$
$440$	−10.8520	+	6.26540i	−0.517348	+	0.298691i
$441$	−16.0586			−0.764696
$442$		0			0
$443$	11.2325			0.533672			0.266836	−	0.963742i	$-0.414022\pi$
$443$	11.2325			0.533672			0.266836	+	0.963742i	$0.414022\pi$
$444$	1.75556	−	1.01357i	0.0833152	−	0.0481021i
$445$	8.82036	+	15.2773i	0.418125	+	0.724214i
$446$	11.6283	−	20.1409i	0.550618	−	0.953698i
$447$			14.3502i			0.678741i
$448$	37.0106	+	21.3681i	1.74859	+	1.00955i
$449$	−24.9051	−	14.3790i	−1.17534	−	0.678585i	−0.220411	−	0.975407i	$-0.570740\pi$
$449$	−24.9051	−	14.3790i	−1.17534	−	0.678585i	−0.954933	+	0.296822i	$0.904073\pi$
$450$		−	3.55496i		−	0.167582i
$451$	−0.914542	+	1.58403i	−0.0430641	+	0.0745892i
$452$	3.67845	+	6.37126i	0.173020	+	0.299679i
$453$	−1.70273	+	0.983074i	−0.0800014	+	0.0461888i
$454$	−12.1672			−0.571035
$455$		0			0
$456$	−7.75302			−0.363068
$457$	16.5204	−	9.53803i	0.772790	−	0.446170i	−0.0610792	−	0.998133i	$-0.519454\pi$
$457$	16.5204	−	9.53803i	0.772790	−	0.446170i	0.833869	+	0.551963i	$0.186121\pi$
$458$	1.78501	+	3.09173i	0.0834081	+	0.144467i
$459$	−1.22252	+	2.11747i	−0.0570624	+	0.0988350i
$460$		−	4.38404i		−	0.204407i
$461$	27.4817	+	15.8666i	1.27995	+	0.738981i	0.976839	−	0.213974i	$-0.0686409\pi$
$461$	27.4817	+	15.8666i	1.27995	+	0.738981i	0.303113	+	0.952955i	$0.401974\pi$
$462$	−7.60643	−	4.39158i	−0.353883	−	0.204315i
$463$		−	36.4784i		−	1.69530i	−0.530559	−	0.847648i	$-0.678018\pi$
$463$		−	36.4784i		−	1.69530i	0.530559	−	0.847648i	$-0.321982\pi$
$464$	2.69471	−	4.66737i	0.125099	−	0.216677i
$465$	10.6908	+	18.5171i	0.495775	+	0.858708i
$466$	6.24790	−	3.60723i	0.289428	−	0.167102i
$467$	−13.0000			−0.601568			−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000			−0.601568			−0.300784	+	0.953692i	$0.597248\pi$
$468$		0			0
$469$	17.2010			0.794271
$470$	−38.7824	+	22.3910i	−1.78890	+	1.03282i
$471$	−5.35086	−	9.26795i	−0.246554	−	0.427045i
$472$	−3.31767	+	5.74637i	−0.152708	+	0.264498i
$473$			3.49694i			0.160790i
$474$	4.34317	+	2.50753i	0.199489	+	0.115175i
$475$	6.27814	+	3.62469i	0.288061	+	0.166312i
$476$			5.22521i			0.239497i
$477$	4.42543	−	7.66507i	0.202626	−	0.350959i
$478$	4.42208	+	7.65926i	0.202261	+	0.350326i
$479$	4.86407	−	2.80827i	0.222245	−	0.128313i	−0.384744	−	0.923023i	$-0.625710\pi$
$479$	4.86407	−	2.80827i	0.222245	−	0.128313i	0.606989	+	0.794710i	$0.292377\pi$
$480$	6.91185			0.315482
$481$		0			0
$482$	4.86294			0.221501
$483$	14.6205	−	8.44116i	0.665256	−	0.384086i
$484$	−1.96897	−	3.41035i	−0.0894985	−	0.155016i
$485$	14.0538	−	24.3418i	0.638148	−	1.10531i
$486$			1.24698i			0.0565641i
$487$	−8.45010	−	4.87867i	−0.382910	−	0.221073i	0.296173	−	0.955134i	$-0.404289\pi$
$487$	−8.45010	−	4.87867i	−0.382910	−	0.221073i	−0.679084	+	0.734061i	$0.737623\pi$
$488$	20.6722	+	11.9351i	0.935788	+	0.540277i
$489$		−	3.89977i		−	0.176354i
$490$	28.0541	−	48.5911i	1.26735	−	2.19512i
$491$	−3.69418	−	6.39850i	−0.166716	−	0.288760i	0.770547	−	0.637383i	$-0.219983\pi$
$491$	−3.69418	−	6.39850i	−0.166716	−	0.288760i	−0.937263	+	0.348622i	$0.886650\pi$
$492$	0.480608	−	0.277479i	0.0216675	−	0.0125097i
$493$	4.52542			0.203815
$494$		0			0
$495$	−4.10992			−0.184727
$496$	19.2435	−	11.1102i	0.864056	−	0.498863i
$497$	−21.2216	−	36.7569i	−0.951920	−	1.64877i
$498$	−0.407010	+	0.704961i	−0.0182385	+	0.0315901i
$499$			43.2814i			1.93754i	0.247956	+	0.968771i	$0.420241\pi$
$499$			43.2814i			1.93754i	−0.247956	+	0.968771i	$0.579759\pi$
$500$	2.32090	+	1.33997i	0.103794	+	0.0599253i
$501$	18.2033	+	10.5097i	0.813264	+	0.469538i
$502$			3.04892i			0.136080i
$503$	−5.38351	+	9.32451i	−0.240039	+	0.415760i	−0.960725	−	0.277502i	$-0.910494\pi$
$503$	−5.38351	+	9.32451i	−0.240039	+	0.415760i	0.720686	+	0.693261i	$0.243827\pi$
$504$	7.32036	+	12.6792i	0.326075	+	0.564778i
$505$	33.6992	−	19.4562i	1.49959	−	0.865791i
$506$	6.43057			0.285874
$507$		0			0
$508$	4.24459			0.188323
$509$	35.9788	−	20.7724i	1.59473	−	0.920720i	0.602256	−	0.798303i	$-0.294269\pi$
$509$	35.9788	−	20.7724i	1.59473	−	0.920720i	0.992479	−	0.122417i	$-0.0390646\pi$
$510$	−4.27144	−	7.39835i	−0.189142	−	0.327604i
$511$	18.4683	−	31.9880i	0.816990	−	1.41507i
$512$		−	24.9390i		−	1.10216i
$513$	−2.20220	−	1.27144i	−0.0972293	−	0.0561354i
$514$	−15.2596	−	8.81013i	−0.673072	−	0.388598i
$515$		−	48.7633i		−	2.14877i
$516$	0.530499	−	0.918852i	0.0233539	−	0.0404502i
$517$	9.40007	+	16.2814i	0.413415	+	0.716055i
$518$	−23.6206	+	13.6374i	−1.03783	+	0.599191i
$519$	−13.2349			−0.580948
$520$		0			0
$521$	25.7198			1.12680			0.563402	−	0.826183i	$-0.309492\pi$
$521$	25.7198			1.12680			0.563402	+	0.826183i	$0.309492\pi$
$522$	1.99877	−	1.15399i	0.0874837	−	0.0505087i
$523$	−4.29643	−	7.44163i	−0.187870	−	0.325400i	0.756670	−	0.653797i	$-0.226825\pi$
$523$	−4.29643	−	7.44163i	−0.187870	−	0.325400i	−0.944540	+	0.328397i	$0.893492\pi$
$524$	1.22587	−	2.12327i	0.0535525	−	0.0927557i
$525$		−	13.6896i		−	0.597464i
$526$	25.6194	+	14.7913i	1.11706	+	0.644933i
$527$	16.1584	+	9.32908i	0.703873	+	0.406381i
$528$			4.27114i			0.185878i
$529$	5.31982	−	9.21420i	0.231297	−	0.400618i
$530$	15.4623	+	26.7814i	0.671638	+	1.16331i
$531$	−1.88472	+	1.08815i	−0.0817901	+	0.0472215i
$532$	−5.43429			−0.235606
$533$		0			0
$534$	7.85086			0.339740
$535$	−25.6063	+	14.7838i	−1.10706	+	0.639160i
$536$	−5.46077	−	9.45833i	−0.235869	−	0.408538i
$537$	4.26391	−	7.38530i	0.184001	−	0.318699i
$538$		−	7.37734i		−	0.318060i
$539$	−20.3992	−	11.7775i	−0.878655	−	0.507292i
$540$	1.07992	+	0.623490i	0.0464722	+	0.0268307i
$541$			31.3534i			1.34799i	0.738736	+	0.673995i	$0.235423\pi$
$541$			31.3534i			1.34799i	−0.738736	+	0.673995i	$0.764577\pi$
$542$	−1.98911	+	3.44525i	−0.0854398	+	0.147986i
$543$	−1.81820	−	3.14921i	−0.0780264	−	0.135146i
$544$	5.22340	−	3.01573i	0.223951	−	0.129298i
$545$	3.00000			0.128506
$546$		0			0
$547$	19.9342			0.852325			0.426163	−	0.904647i	$-0.359865\pi$
$547$	19.9342			0.852325			0.426163	+	0.904647i	$0.359865\pi$
$548$	6.23744	−	3.60119i	0.266450	−	0.153835i
$549$	3.91454	+	6.78019i	0.167069	+	0.289371i
$550$	2.60723	−	4.51585i	0.111173	−	0.192557i
$551$			4.70650i			0.200503i
$552$	−9.28307	−	5.35958i	−0.395114	−	0.228119i
$553$	16.7249	+	9.65615i	0.711217	+	0.410621i
$554$		−	27.3545i		−	1.16218i
$555$	−6.38135	+	11.0528i	−0.270873	+	0.469167i
$556$	2.33848	+	4.05036i	0.0991736	+	0.171774i
$557$	28.7823	−	16.6174i	1.21954	−	0.704104i	0.254723	−	0.967014i	$-0.418016\pi$
$557$	28.7823	−	16.6174i	1.21954	−	0.704104i	0.964820	+	0.262910i	$0.0846822\pi$
$558$	9.51573			0.402833
$559$		0			0
$560$	−39.1782			−1.65558
$561$	−3.10593	+	1.79321i	−0.131132	+	0.0757093i
$562$	7.47584	+	12.9485i	0.315349	+	0.546201i
$563$	1.93565	−	3.35264i	0.0815779	−	0.141297i	−0.822350	−	0.568982i	$-0.807337\pi$
$563$	1.93565	−	3.35264i	0.0815779	−	0.141297i	0.903928	+	0.427685i	$0.140671\pi$
$564$		−	5.70410i		−	0.240186i
$565$	−40.1128	−	23.1591i	−1.68756	−	0.974312i
$566$	−15.5147	−	8.95742i	−0.652132	−	0.376508i
$567$			4.80194i			0.201662i
$568$	−13.4743	+	23.3382i	−0.565371	+	0.979251i
$569$	10.0728	+	17.4467i	0.422276	+	0.731403i	0.996162	−	0.0875324i	$-0.0278981\pi$
$569$	10.0728	+	17.4467i	0.422276	+	0.731403i	−0.573886	+	0.818935i	$0.694565\pi$
$570$	7.69438	−	4.44235i	0.322282	−	0.186070i
$571$	32.1269			1.34447			0.672234	−	0.740338i	$-0.265335\pi$
$571$	32.1269			1.34447			0.672234	+	0.740338i	$0.265335\pi$
$572$		0			0
$573$	21.3817			0.893231
$574$	−6.46645	+	3.73341i	−0.269904	+	0.155829i
$575$	5.01142	+	8.68003i	0.208991	+	0.361982i
$576$	4.44989	−	7.70743i	0.185412	−	0.321143i
$577$			16.7506i			0.697338i	0.937246	+	0.348669i	$0.113366\pi$
$577$			16.7506i			0.697338i	−0.937246	+	0.348669i	$0.886634\pi$
$578$	11.9026	+	6.87196i	0.495082	+	0.285836i
$579$	−7.29850	−	4.21379i	−0.303315	−	0.175119i
$580$		−	2.30798i		−	0.0958336i
$581$	−1.56734	+	2.71470i	−0.0650240	+	0.112625i
$582$	−6.25451	−	10.8331i	−0.259258	−	0.449048i
$583$	11.2432	−	6.49127i	0.465646	−	0.268841i
$584$	−23.4523			−0.970465
$585$		0			0
$586$	−23.3913			−0.966287
$587$	5.83524	−	3.36898i	0.240846	−	0.139053i	−0.374719	−	0.927138i	$-0.622261\pi$
$587$	5.83524	−	3.36898i	0.240846	−	0.139053i	0.615566	+	0.788086i	$0.288928\pi$
$588$	3.57338	+	6.18927i	0.147364	+	0.255241i
$589$	−9.70237	+	16.8050i	−0.399779	+	0.692438i
$590$		−	7.60388i		−	0.313047i
$591$	22.9293	+	13.2383i	0.943186	+	0.544549i
$592$	11.4864	+	6.63169i	0.472089	+	0.272561i
$593$			18.1172i			0.743985i	0.928236	+	0.371992i	$0.121325\pi$
$593$			18.1172i			0.743985i	−0.928236	+	0.371992i	$0.878675\pi$
$594$	−0.914542	+	1.58403i	−0.0375241	+	0.0649937i
$595$	−16.4487	−	28.4900i	−0.674331	−	1.16797i
$596$	5.53082	−	3.19322i	0.226551	−	0.130799i
$597$	14.2524			0.583310
$598$		0			0
$599$	−26.7851			−1.09441			−0.547204	−	0.836999i	$-0.684308\pi$
$599$	−26.7851			−1.09441			−0.547204	+	0.836999i	$0.684308\pi$
$600$	−7.52751	+	4.34601i	−0.307309	+	0.177425i
$601$	2.35086	+	4.07180i	0.0958934	+	0.166092i	0.909981	−	0.414650i	$-0.136096\pi$
$601$	2.35086	+	4.07180i	0.0958934	+	0.166092i	−0.814088	+	0.580742i	$0.802763\pi$
$602$	−7.13773	+	12.3629i	−0.290912	+	0.503874i
$603$		−	3.58211i		−	0.145875i
$604$	0.757788	+	0.437509i	0.0308340	+	0.0178020i
$605$	21.4712	+	12.3964i	0.872930	+	0.503986i
$606$		−	17.3177i		−	0.703482i
$607$	−13.8198	+	23.9366i	−0.560929	+	0.971558i	0.436486	+	0.899711i	$0.356223\pi$
$607$	−13.8198	+	23.9366i	−0.560929	+	0.971558i	−0.997416	+	0.0718472i	$0.977111\pi$
$608$	3.13640	+	5.43240i	0.127198	+	0.220313i
$609$	7.69697	−	4.44385i	0.311897	−	0.180074i
$610$	−27.3545			−1.10755
$611$		0			0
$612$	1.08815			0.0439857
$613$	−41.7236	+	24.0891i	−1.68520	+	0.972950i	−0.727091	+	0.686541i	$0.759128\pi$
$613$	−41.7236	+	24.0891i	−1.68520	+	0.972950i	−0.958108	+	0.286409i	$0.907539\pi$
$614$	15.9777	+	27.6742i	0.644807	+	1.11684i
$615$	−1.74698	+	3.02586i	−0.0704450	+	0.122014i
$616$			21.4752i			0.865259i
$617$	26.2443	+	15.1521i	1.05655	+	0.610002i	0.924477	−	0.381238i	$-0.124502\pi$
$617$	26.2443	+	15.1521i	1.05655	+	0.610002i	0.132077	+	0.991239i	$0.457835\pi$
$618$	−18.7942	−	10.8509i	−0.756015	−	0.436485i
$619$		−	10.9041i		−	0.438272i	−0.975694	−	0.219136i	$-0.929676\pi$
$619$		−	10.9041i		−	0.438272i	0.975694	−	0.219136i	$-0.0703239\pi$
$620$	4.75786	−	8.24086i	0.191080	−	0.330961i
$621$	−1.75786	−	3.04471i	−0.0705407	−	0.122180i
$622$	−12.2912	+	7.09634i	−0.492833	+	0.284537i
$623$	30.2325			1.21124
$624$		0			0
$625$	−31.1269			−1.24508
$626$	29.7780	−	17.1923i	1.19017	−	0.687143i
$627$	−1.86496	−	3.23021i	−0.0744794	−	0.129002i
$628$	−2.38135	+	4.12463i	−0.0950264	+	0.164591i
$629$			11.1371i			0.444064i
$630$	−14.5300	−	8.38889i	−0.578888	−	0.334221i
$631$	9.05199	+	5.22617i	0.360354	+	0.208050i	0.669236	−	0.743050i	$-0.266621\pi$
$631$	9.05199	+	5.22617i	0.360354	+	0.208050i	−0.308882	+	0.951100i	$0.599955\pi$
$632$		−	12.2620i		−	0.487758i
$633$	−0.925428	+	1.60289i	−0.0367824	+	0.0637091i
$634$	7.02028	+	12.1595i	0.278811	+	0.482915i
$635$	−23.1432	+	13.3617i	−0.918410	+	0.530244i
$636$	−3.93900			−0.156192
$637$		0			0
$638$	3.38537			0.134028
$639$	−7.65460	+	4.41939i	−0.302811	+	0.174828i
$640$	8.63587	+	14.9578i	0.341363	+	0.591257i
$641$	−8.79709	+	15.2370i	−0.347464	+	0.601826i	−0.985798	−	0.167934i	$-0.946291\pi$
$641$	−8.79709	+	15.2370i	−0.347464	+	0.601826i	0.638334	+	0.769760i	$0.279624\pi$
$642$			13.1588i			0.519338i
$643$	19.5772	+	11.3029i	0.772049	+	0.445743i	0.833605	−	0.552361i	$-0.186273\pi$
$643$	19.5772	+	11.3029i	0.772049	+	0.445743i	−0.0615560	+	0.998104i	$0.519606\pi$
$644$	−6.50674	−	3.75667i	−0.256401	−	0.148033i
$645$			6.67994i			0.263022i
$646$	3.87651	−	6.71431i	0.152519	−	0.264171i
$647$	−12.3959	−	21.4703i	−0.487333	−	0.844085i	0.512561	−	0.858651i	$-0.328697\pi$
$647$	−12.3959	−	21.4703i	−0.487333	−	0.844085i	−0.999894	+	0.0145658i	$0.995363\pi$
$648$	2.64044	−	1.52446i	0.103726	−	0.0598864i
$649$	−3.19221			−0.125305
$650$		0			0
$651$	36.6437			1.43618
$652$	−1.50304	+	0.867781i	−0.0588636	+	0.0339849i
$653$	10.9053	+	18.8885i	0.426757	+	0.739164i	0.996583	−	0.0826012i	$-0.0263228\pi$
$653$	10.9053	+	18.8885i	0.426757	+	0.739164i	−0.569826	+	0.821765i	$0.692989\pi$
$654$	0.667563	−	1.15625i	0.0261038	−	0.0452131i
$655$			15.4359i			0.603132i
$656$	3.14456	+	1.81551i	0.122774	+	0.0708838i
$657$	−6.66149	−	3.84601i	−0.259889	−	0.150047i
$658$			76.7472i			2.99192i
$659$	−8.27628	+	14.3349i	−0.322398	+	0.558410i	−0.980982	−	0.194097i	$-0.937822\pi$
$659$	−8.27628	+	14.3349i	−0.322398	+	0.558410i	0.658584	+	0.752507i	$0.271156\pi$
$660$	0.914542	+	1.58403i	0.0355985	+	0.0616584i
$661$	−13.8166	+	7.97703i	−0.537405	+	0.310271i	−0.744026	−	0.668150i	$-0.767086\pi$
$661$	−13.8166	+	7.97703i	−0.537405	+	0.310271i	0.206622	+	0.978421i	$0.433753\pi$
$662$	−14.8471			−0.577050
$663$		0			0
$664$	1.99031			0.0772391
$665$	29.6299	−	17.1069i	1.14900	−	0.663376i
$666$	2.83997	+	4.91897i	0.110047	+	0.190606i
$667$	−3.25355	+	5.63532i	−0.125978	+	0.218200i
$668$		−	9.35450i		−	0.361937i
$669$	−16.1517	−	9.32520i	−0.624462	−	0.360533i
$670$	10.8389	+	6.25786i	0.418745	+	0.241762i
$671$			11.4838i			0.443327i
$672$	5.92274	−	10.2585i	0.228475	−	0.395730i
$673$	−3.69418	−	6.39850i	−0.142400	−	0.246644i	0.786000	−	0.618227i	$-0.212149\pi$
$673$	−3.69418	−	6.39850i	−0.142400	−	0.246644i	−0.928400	+	0.371583i	$0.878815\pi$
$674$	−18.5391	+	10.7036i	−0.714101	+	0.412286i
$675$	−2.85086			−0.109729
$676$		0			0
$677$	−22.1454			−0.851118			−0.425559	−	0.904931i	$-0.639922\pi$
$677$	−22.1454			−0.851118			−0.425559	+	0.904931i	$0.639922\pi$
$678$	−17.8519	+	10.3068i	−0.685597	+	0.395830i
$679$	−24.0852	−	41.7168i	−0.924306	−	1.60094i
$680$	−10.4438	+	18.0893i	−0.400503	+	0.693692i
$681$			9.75733i			0.373902i
$682$	12.0878	+	6.97889i	0.462866	+	0.267236i
$683$	−7.88103	−	4.55011i	−0.301559	−	0.174105i	0.341584	−	0.939851i	$-0.389037\pi$
$683$	−7.88103	−	4.55011i	−0.301559	−	0.174105i	−0.643143	+	0.765746i	$0.722370\pi$
$684$			1.13169i			0.0432711i
$685$	−22.6727	+	39.2703i	−0.866279	+	1.50044i
$686$	−27.1211	−	46.9751i	−1.03549	−	1.79352i
$687$	2.47938	−	1.43147i	0.0945941	−	0.0546139i
$688$	6.94198			0.264661
$689$		0			0
$690$	12.2838			0.467637
$691$	−11.9261	+	6.88553i	−0.453690	+	0.261938i	−0.709387	−	0.704819i	$-0.751028\pi$
$691$	−11.9261	+	6.88553i	−0.453690	+	0.261938i	0.255697	+	0.966757i	$0.417695\pi$
$692$	2.94504	+	5.10096i	0.111954	+	0.193909i
$693$	−3.52177	+	6.09989i	−0.133781	+	0.231715i
$694$		−	30.2717i		−	1.14910i
$695$	−25.5007	−	14.7228i	−0.967295	−	0.558468i
$696$	−4.88707	−	2.82155i	−0.185244	−	0.106951i
$697$			3.04892i			0.115486i
$698$	−2.85086	+	4.93783i	−0.107906	+	0.186899i
$699$	−2.89277	−	5.01043i	−0.109415	−	0.189512i
$700$	−5.27622	+	3.04623i	−0.199422	+	0.115137i
$701$	−46.5090			−1.75662			−0.878311	−	0.478090i	$-0.841329\pi$
$701$	−46.5090			−1.75662			−0.878311	+	0.478090i	$0.841329\pi$
$702$		0			0
$703$	−11.5827			−0.436850
$704$	11.3054	−	6.52715i	0.426086	−	0.246001i
$705$	17.9562	+	31.1011i	0.676270	+	1.17133i
$706$	3.78836	−	6.56164i	0.142577	−	0.246951i
$707$		−	66.6878i		−	2.50805i
$708$	0.838781	+	0.484271i	0.0315233	+	0.0182000i
$709$	−6.27492	−	3.62283i	−0.235660	−	0.136058i	0.377521	−	0.926001i	$-0.376777\pi$
$709$	−6.27492	−	3.62283i	−0.235660	−	0.136058i	−0.613180	+	0.789943i	$0.710110\pi$
$710$		−	30.8823i		−	1.15899i
$711$	2.01089	−	3.48296i	0.0754141	−	0.130621i
$712$	−9.59783	−	16.6239i	−0.359694	−	0.623008i
$713$	−23.2343	+	13.4143i	−0.870130	+	0.502370i
$714$	−14.6407			−0.547915
$715$		0			0
$716$	−3.79523			−0.141835
$717$	6.14225	−	3.54623i	0.229386	−	0.132436i
$718$	−9.33124	−	16.1622i	−0.348239	−	0.603167i
$719$	12.7573	−	22.0963i	0.475768	−	0.824055i	−0.523846	−	0.851813i	$-0.675503\pi$
$719$	12.7573	−	22.0963i	0.475768	−	0.824055i	0.999615	+	0.0277580i	$0.00883678\pi$
$720$			8.15883i			0.304062i
$721$	−72.3739	−	41.7851i	−2.69534	−	1.55616i
$722$	−13.5354	−	7.81468i	−0.503736	−	0.290832i
$723$		−	3.89977i		−	0.145034i
$724$	−0.809175	+	1.40153i	−0.0300728	+	0.0520875i
$725$	2.63826	+	4.56960i	0.0979825	+	0.169711i
$726$	9.55560	−	5.51693i	0.354641	−	0.204752i
$727$	14.4873			0.537303			0.268651	−	0.963238i	$-0.413422\pi$
$727$	14.4873			0.537303			0.268651	+	0.963238i	$0.413422\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	23.2750	−	13.4378i	0.861445	−	0.497355i
$731$	2.91454	+	5.04814i	0.107798	+	0.186712i
$732$	1.74214	−	3.01747i	0.0643912	−	0.111529i
$733$		−	37.5036i		−	1.38523i	−0.721308	−	0.692614i	$-0.756459\pi$
$733$		−	37.5036i		−	1.38523i	0.721308	−	0.692614i	$-0.243541\pi$
$734$	−40.0469	−	23.1211i	−1.47816	−	0.853415i
$735$	−38.9670	−	22.4976i	−1.43732	−	0.829837i
$736$			8.67264i			0.319678i
$737$	2.62714	−	4.55034i	0.0967719	−	0.167614i
$738$	0.777479	+	1.34663i	0.0286194	+	0.0495703i
$739$	37.4016	−	21.5938i	1.37584	−	0.794341i	0.384184	−	0.923257i	$-0.374483\pi$
$739$	37.4016	−	21.5938i	1.37584	−	0.794341i	0.991656	+	0.128915i	$0.0411495\pi$
$740$	5.67994			0.208799
$741$		0			0
$742$	52.9982			1.94563
$743$	−11.6710	+	6.73825i	−0.428167	+	0.247202i	−0.698566	−	0.715546i	$-0.746178\pi$
$743$	−11.6710	+	6.73825i	−0.428167	+	0.247202i	0.270398	+	0.962749i	$0.412845\pi$
$744$	−11.6332	−	20.1493i	−0.426493	−	0.738708i
$745$	−20.1042	+	34.8214i	−0.736560	+	1.27576i
$746$		−	45.5260i		−	1.66683i
$747$	0.565335	+	0.326396i	0.0206845	+	0.0119422i
$748$	1.38227	+	0.798053i	0.0505407	+	0.0291797i
$749$			50.6728i			1.85154i
$750$	−3.75451	+	6.50301i	−0.137095	+	0.237456i
$751$	17.7947	+	30.8213i	0.649338	+	1.12469i	0.983281	+	0.182093i	$0.0582872\pi$
$751$	17.7947	+	30.8213i	0.649338	+	1.12469i	−0.333943	+	0.942593i	$0.608379\pi$
$752$	32.3211	−	18.6606i	1.17863	−	0.680483i
$753$	2.44504			0.0891023
$754$		0			0
$755$	−5.50902			−0.200494
$756$	1.85075	−	1.06853i	0.0673112	−	0.0388621i
$757$	6.10537	+	10.5748i	0.221903	+	0.384348i	0.955386	−	0.295360i	$-0.0954397\pi$
$757$	6.10537	+	10.5748i	0.221903	+	0.384348i	−0.733483	+	0.679708i	$0.762106\pi$
$758$	16.5755	−	28.7097i	0.602050	−	1.04278i
$759$		−	5.15691i		−	0.187184i
$760$	−18.8131	−	10.8617i	−0.682422	−	0.393997i
$761$	−26.7663	−	15.4535i	−0.970278	−	0.560190i	−0.0709569	−	0.997479i	$-0.522605\pi$
$761$	−26.7663	−	15.4535i	−0.970278	−	0.560190i	−0.899321	+	0.437289i	$0.855939\pi$
$762$			11.8931i			0.430840i
$763$	2.57069	−	4.45256i	0.0930651	−	0.161194i
$764$	−4.75786	−	8.24086i	−0.172134	−	0.298144i
$765$	−5.93301	+	3.42543i	−0.214509	+	0.123847i
$766$	−17.8944			−0.646551
$767$		0			0
$768$	−10.1129			−0.364918
$769$	−10.3830	+	5.99462i	−0.374420	+	0.216172i	−0.675388	−	0.737463i	$-0.736024\pi$
$769$	−10.3830	+	5.99462i	−0.374420	+	0.216172i	0.300968	+	0.953634i	$0.402690\pi$
$770$	−12.3049	−	21.3127i	−0.443439	−	0.768058i
$771$	−7.06518	+	12.2372i	−0.254446	+	0.440714i
$772$			3.75063i			0.134988i
$773$	38.0758	+	21.9831i	1.36949	+	0.790676i	0.990863	−	0.134873i	$-0.0430625\pi$
$773$	38.0758	+	21.9831i	1.36949	+	0.790676i	0.378628	+	0.925549i	$0.376396\pi$
$774$	2.57457	+	1.48643i	0.0925409	+	0.0534285i

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.07992 - 0.623490i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.222521 + 0.385418i) q^{4} -2.80194i q^{5} +(-1.07992 - 0.623490i) q^{6} +(-4.15860 - 2.40097i) q^{7} +3.04892i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.07992 - 0.623490i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.222521 + 0.385418i) q^{4} -2.80194i q^{5} +(-1.07992 - 0.623490i) q^{6} +(-4.15860 - 2.40097i) q^{7} +3.04892i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.74698 - 3.02586i) q^{10} +(-1.27030 + 0.733406i) q^{11} +0.445042 q^{12} -5.98792 q^{14} +(-2.42655 + 1.40097i) q^{15} +(1.45593 + 2.52174i) q^{16} +(-1.22252 + 2.11747i) q^{17} +1.24698i q^{18} +(-2.20220 - 1.27144i) q^{19} +(1.07992 + 0.623490i) q^{20} +4.80194i q^{21} +(-0.914542 + 1.58403i) q^{22} +(-1.75786 - 3.04471i) q^{23} +(2.64044 - 1.52446i) q^{24} -2.85086 q^{25} +1.00000 q^{27} +(1.85075 - 1.06853i) q^{28} +(-0.925428 - 1.60289i) q^{29} +(-1.74698 + 3.02586i) q^{30} -7.63102i q^{31} +(-2.13632 - 1.23341i) q^{32} +(1.27030 + 0.733406i) q^{33} +3.04892i q^{34} +(-6.72737 + 11.6521i) q^{35} +(-0.222521 - 0.385418i) q^{36} +(3.94471 - 2.27748i) q^{37} -3.17092 q^{38} +8.54288 q^{40} +(1.07992 - 0.623490i) q^{41} +(2.99396 + 5.18569i) q^{42} +(1.19202 - 2.06464i) q^{43} -0.652793i q^{44} +(2.42655 + 1.40097i) q^{45} +(-3.79669 - 2.19202i) q^{46} -12.8170i q^{47} +(1.45593 - 2.52174i) q^{48} +(8.02930 + 13.9072i) q^{49} +(-3.07868 + 1.77748i) q^{50} +2.44504 q^{51} -8.85086 q^{53} +(1.07992 - 0.623490i) q^{54} +(2.05496 + 3.55929i) q^{55} +(7.32036 - 12.6792i) q^{56} +2.54288i q^{57} +(-1.99877 - 1.15399i) q^{58} +(1.88472 + 1.08815i) q^{59} -1.24698i q^{60} +(3.91454 - 6.78019i) q^{61} +(-4.75786 - 8.24086i) q^{62} +(4.15860 - 2.40097i) q^{63} -8.89977 q^{64} +1.82908 q^{66} +(-3.10219 + 1.79105i) q^{67} +(-0.544073 - 0.942362i) q^{68} +(-1.75786 + 3.04471i) q^{69} +16.7778i q^{70} +(7.65460 + 4.41939i) q^{71} +(-2.64044 - 1.52446i) q^{72} +7.69202i q^{73} +(2.83997 - 4.91897i) q^{74} +(1.42543 + 2.46891i) q^{75} +(0.980069 - 0.565843i) q^{76} +7.04354 q^{77} -4.02177 q^{79} +(7.06576 - 4.07942i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.777479 - 1.34663i) q^{82} -0.652793i q^{83} +(-1.85075 - 1.06853i) q^{84} +(5.93301 + 3.42543i) q^{85} -2.97285i q^{86} +(-0.925428 + 1.60289i) q^{87} +(-2.23609 - 3.87303i) q^{88} +(-5.45241 + 3.14795i) q^{89} +3.49396 q^{90} +1.56465 q^{92} +(-6.60866 + 3.81551i) q^{93} +(-7.99127 - 13.8413i) q^{94} +(-3.56249 + 6.17042i) q^{95} +2.46681i q^{96} +(8.68750 + 5.01573i) q^{97} +(17.3419 + 10.0124i) q^{98} -1.46681i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9	\( 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9} - 2 q^{10} + 4 q^{12} + 4 q^{14} + 10 q^{16} - 14 q^{17} + 10 q^{22} + 4 q^{23} + 20 q^{25} + 12 q^{27} + 16 q^{29} - 2 q^{30} - 36 q^{35} - 2 q^{36} - 80 q^{38} + 28 q^{40} - 2 q^{42} - 6 q^{43} + 10 q^{48} + 34 q^{49} + 28 q^{51} - 52 q^{53} + 26 q^{55} + 14 q^{56} + 26 q^{61} - 32 q^{62} - 16 q^{64} - 20 q^{66} - 14 q^{68} + 4 q^{69} - 14 q^{74} - 10 q^{75} + 60 q^{77} - 36 q^{79} - 6 q^{81} + 10 q^{82} + 16 q^{87} - 14 q^{88} + 4 q^{90} - 68 q^{92} - 64 q^{94} + 6 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9 - 2 * q^10 + 4 * q^12 + 4 * q^14 + 10 * q^16 - 14 * q^17 + 10 * q^22 + 4 * q^23 + 20 * q^25 + 12 * q^27 + 16 * q^29 - 2 * q^30 - 36 * q^35 - 2 * q^36 - 80 * q^38 + 28 * q^40 - 2 * q^42 - 6 * q^43 + 10 * q^48 + 34 * q^49 + 28 * q^51 - 52 * q^53 + 26 * q^55 + 14 * q^56 + 26 * q^61 - 32 * q^62 - 16 * q^64 - 20 * q^66 - 14 * q^68 + 4 * q^69 - 14 * q^74 - 10 * q^75 + 60 * q^77 - 36 * q^79 - 6 * q^81 + 10 * q^82 + 16 * q^87 - 14 * q^88 + 4 * q^90 - 68 * q^92 - 64 * q^94 + 6 * q^95

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