LMFDB - Embedded newform 588.2.o.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(19,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("588.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$-1.33790 - 0.458297i$ of defining polynomial
Character	$\chi$	$=$	588.19
Dual form			588.2.o.b.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.272050 + 1.38780i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.85198 - 0.755103i) q^{4} +(-2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(1.55176 - 2.36475i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.272050 + 1.38780i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.85198 - 0.755103i) q^{4} +(-2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(1.55176 - 2.36475i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.27971 - 2.61411i) q^{10} +(1.09586 - 0.632697i) q^{11} +(0.272050 + 1.98141i) q^{12} +2.99744i q^{13} +2.45262i q^{15} +(2.85964 + 2.79687i) q^{16} +(-1.58759 + 0.916595i) q^{17} +(-1.06584 - 0.929502i) q^{18} +(-2.07993 + 3.60254i) q^{19} +(3.00766 + 3.87495i) q^{20} +(0.579927 + 1.69296i) q^{22} +(5.83564 + 3.36921i) q^{23} +(-2.82381 - 0.161492i) q^{24} +(0.507662 + 0.879296i) q^{25} +(-4.15985 - 0.815456i) q^{26} +1.00000 q^{27} -9.42323 q^{29} +(-3.40374 - 0.667235i) q^{30} +(4.71989 + 8.17509i) q^{31} +(-4.65946 + 3.20772i) q^{32} +(-1.09586 - 0.632697i) q^{33} +(-0.840146 - 2.45262i) q^{34} +(1.57993 - 1.22631i) q^{36} +(-3.75572 + 6.50509i) q^{37} +(-4.43376 - 3.86659i) q^{38} +(2.59586 - 1.49872i) q^{39} +(-6.19590 + 3.11985i) q^{40} -1.08966i q^{41} +6.27176i q^{43} +(-2.50727 + 0.344251i) q^{44} +(2.12403 - 1.22631i) q^{45} +(-6.26338 + 7.18211i) q^{46} +(3.67579 - 6.36666i) q^{47} +(0.992338 - 3.87495i) q^{48} +(-1.35840 + 0.465320i) q^{50} +(1.58759 + 0.916595i) q^{51} +(2.26338 - 5.55120i) q^{52} +(0.0358262 + 0.0620528i) q^{53} +(-0.272050 + 1.38780i) q^{54} -3.10353 q^{55} +4.15985 q^{57} +(2.56359 - 13.0776i) q^{58} +(1.68345 + 2.91583i) q^{59} +(1.85198 - 4.54219i) q^{60} +(9.61496 + 5.55120i) q^{61} +(-12.6294 + 4.32623i) q^{62} +(-3.18406 - 7.33906i) q^{64} +(3.67579 - 6.36666i) q^{65} +(1.17619 - 1.34871i) q^{66} +(2.43151 - 1.40383i) q^{67} +(3.63230 - 0.498720i) q^{68} -6.73842i q^{69} +2.92285i q^{71} +(1.27205 + 2.52624i) q^{72} +(-7.01910 + 4.05248i) q^{73} +(-8.00602 - 6.98190i) q^{74} +(0.507662 - 0.879296i) q^{75} +(6.57226 - 5.10126i) q^{76} +(1.37372 + 4.01027i) q^{78} +(1.54471 + 0.891841i) q^{79} +(-2.64413 - 9.44742i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.51223 + 0.296442i) q^{82} -5.33626 q^{83} +4.49611 q^{85} +(-8.70395 - 1.70624i) q^{86} +(4.71162 + 8.16076i) q^{87} +(0.204351 - 3.57324i) q^{88} +(-7.42323 - 4.28581i) q^{89} +(1.12403 + 3.28134i) q^{90} +(-8.26338 - 10.6462i) q^{92} +(4.71989 - 8.17509i) q^{93} +(7.83564 + 6.83331i) q^{94} +(8.83564 - 5.10126i) q^{95} +(5.10769 + 2.43135i) q^{96} -7.10394i q^{97} +1.26539i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9} + 13 q^{10} - 6 q^{11} - q^{12} + 7 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 6 q^{22} - 11 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} - 16 q^{29} - 5 q^{30} + 6 q^{31} + 21 q^{32} + 6 q^{33} - 28 q^{34} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 6 q^{39} + 13 q^{40} + 19 q^{44} - 12 q^{46} + 4 q^{47} + 10 q^{48} + 2 q^{50} - 20 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 12 q^{57} - 23 q^{58} - 14 q^{59} + q^{60} - 12 q^{61} - 48 q^{62} + 2 q^{64} + 4 q^{65} + 21 q^{66} - 42 q^{67} + 10 q^{68} + 7 q^{72} + 18 q^{73} - 28 q^{74} + 2 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{79} + 33 q^{80} - 4 q^{81} + 14 q^{82} + 4 q^{83} - 32 q^{85} - 42 q^{86} + 8 q^{87} + 11 q^{88} - 8 q^{90} - 28 q^{92} + 6 q^{93} + 16 q^{94} + 24 q^{95} - 9 q^{96}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9 + 13 * q^10 - 6 * q^11 - q^12 + 7 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 6 * q^22 - 11 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 - 16 * q^29 - 5 * q^30 + 6 * q^31 + 21 * q^32 + 6 * q^33 - 28 * q^34 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 6 * q^39 + 13 * q^40 + 19 * q^44 - 12 * q^46 + 4 * q^47 + 10 * q^48 + 2 * q^50 - 20 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 12 * q^57 - 23 * q^58 - 14 * q^59 + q^60 - 12 * q^61 - 48 * q^62 + 2 * q^64 + 4 * q^65 + 21 * q^66 - 42 * q^67 + 10 * q^68 + 7 * q^72 + 18 * q^73 - 28 * q^74 + 2 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^79 + 33 * q^80 - 4 * q^81 + 14 * q^82 + 4 * q^83 - 32 * q^85 - 42 * q^86 + 8 * q^87 + 11 * q^88 - 8 * q^90 - 28 * q^92 + 6 * q^93 + 16 * q^94 + 24 * q^95 - 9 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.272050	+	1.38780i	−0.192369	+	0.981323i
$2$	−0.272050	+	1.38780i	−0.192369	+	0.981323i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.85198	−	0.755103i	−0.925989	−	0.377551i
$5$	−2.12403	−	1.22631i	−0.949894	−	0.548422i	−0.0568460	−	0.998383i	$-0.518104\pi$
$5$	−2.12403	−	1.22631i	−0.949894	−	0.548422i	−0.893048	+	0.449961i	$0.851438\pi$
$6$	1.33790	−	0.458297i	0.546193	−	0.187099i
$7$		0			0
$7$		0			0
$8$	1.55176	−	2.36475i	0.548631	−	0.836065i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.27971	−	2.61411i	0.720908	−	0.826653i
$11$	1.09586	−	0.632697i	0.330415	−	0.190765i	−0.325610	−	0.945504i	$-0.605570\pi$
$11$	1.09586	−	0.632697i	0.330415	−	0.190765i	0.656025	+	0.754739i	$0.272236\pi$
$12$	0.272050	+	1.98141i	0.0785342	+	0.571984i
$13$			2.99744i			0.831342i	0.909515	+	0.415671i	$0.136453\pi$
$13$			2.99744i			0.831342i	−0.909515	+	0.415671i	$0.863547\pi$
$14$		0			0
$15$			2.45262i			0.633263i
$16$	2.85964	+	2.79687i	0.714910	+	0.699217i
$17$	−1.58759	+	0.916595i	−0.385047	+	0.222307i	−0.680012	−	0.733201i	$-0.738025\pi$
$17$	−1.58759	+	0.916595i	−0.385047	+	0.222307i	0.294965	+	0.955508i	$0.404692\pi$
$18$	−1.06584	−	0.929502i	−0.251222	−	0.219086i
$19$	−2.07993	+	3.60254i	−0.477168	+	0.826479i	−0.999658	−	0.0261665i	$-0.991670\pi$
$19$	−2.07993	+	3.60254i	−0.477168	+	0.826479i	0.522490	+	0.852646i	$0.325003\pi$
$20$	3.00766	+	3.87495i	0.672534	+	0.866466i
$21$		0			0
$22$	0.579927	+	1.69296i	0.123641	+	0.360941i
$23$	5.83564	+	3.36921i	1.21682	+	0.702529i	0.964236	−	0.265047i	$-0.0853874\pi$
$23$	5.83564	+	3.36921i	1.21682	+	0.702529i	0.252580	+	0.967576i	$0.418721\pi$
$24$	−2.82381	−	0.161492i	−0.576408	−	0.0329644i
$25$	0.507662	+	0.879296i	0.101532	+	0.175859i
$26$	−4.15985	−	0.815456i	−0.815814	−	0.159924i
$27$	1.00000			0.192450
$28$		0			0
$29$	−9.42323			−1.74985			−0.874925	−	0.484258i	$-0.839090\pi$
$29$	−9.42323			−1.74985			−0.874925	+	0.484258i	$0.839090\pi$
$30$	−3.40374	−	0.667235i	−0.621435	−	0.121820i
$31$	4.71989	+	8.17509i	0.847717	+	1.46829i	0.883240	+	0.468921i	$0.155357\pi$
$31$	4.71989	+	8.17509i	0.847717	+	1.46829i	−0.0355228	+	0.999369i	$0.511310\pi$
$32$	−4.65946	+	3.20772i	−0.823683	+	0.567050i
$33$	−1.09586	−	0.632697i	−0.190765	−	0.110138i
$34$	−0.840146	−	2.45262i	−0.144084	−	0.420620i
$35$		0			0
$36$	1.57993	−	1.22631i	0.263321	−	0.204385i
$37$	−3.75572	+	6.50509i	−0.617436	+	1.06943i	0.372516	+	0.928026i	$0.378495\pi$
$37$	−3.75572	+	6.50509i	−0.617436	+	1.06943i	−0.989952	+	0.141405i	$0.954838\pi$
$38$	−4.43376	−	3.86659i	−0.719251	−	0.627244i
$39$	2.59586	−	1.49872i	0.415671	−	0.239988i
$40$	−6.19590	+	3.11985i	−0.979657	+	0.493292i
$41$		−	1.08966i		−	0.170176i	−0.996373	−	0.0850880i	$-0.972883\pi$
$41$		−	1.08966i		−	0.170176i	0.996373	−	0.0850880i	$-0.0271171\pi$
$42$		0			0
$43$			6.27176i			0.956435i	0.878241	+	0.478218i	$0.158717\pi$
$43$			6.27176i			0.956435i	−0.878241	+	0.478218i	$0.841283\pi$
$44$	−2.50727	+	0.344251i	−0.377984	+	0.0518978i
$45$	2.12403	−	1.22631i	0.316631	−	0.182807i
$46$	−6.26338	+	7.18211i	−0.923485	+	1.05894i
$47$	3.67579	−	6.36666i	0.536169	−	0.928672i	−0.462937	−	0.886391i	$-0.653204\pi$
$47$	3.67579	−	6.36666i	0.536169	−	0.928672i	0.999106	−	0.0422808i	$-0.0134624\pi$
$48$	0.992338	−	3.87495i	0.143232	−	0.559301i
$49$		0			0
$50$	−1.35840	+	0.465320i	−0.192106	+	0.0658063i
$51$	1.58759	+	0.916595i	0.222307	+	0.128349i
$52$	2.26338	−	5.55120i	0.313874	−	0.769813i
$53$	0.0358262	+	0.0620528i	0.00492111	+	0.00852361i	0.868475	−	0.495732i	$-0.165100\pi$
$53$	0.0358262	+	0.0620528i	0.00492111	+	0.00852361i	−0.863554	+	0.504256i	$0.831767\pi$
$54$	−0.272050	+	1.38780i	−0.0370214	+	0.188856i
$55$	−3.10353			−0.418479
$56$		0			0
$57$	4.15985			0.550986
$58$	2.56359	−	13.0776i	0.336616	−	1.71717i
$59$	1.68345	+	2.91583i	0.219167	+	0.379608i	0.954553	−	0.298040i	$-0.0963328\pi$
$59$	1.68345	+	2.91583i	0.219167	+	0.379608i	−0.735387	+	0.677648i	$0.762999\pi$
$60$	1.85198	−	4.54219i	0.239089	−	0.586394i
$61$	9.61496	+	5.55120i	1.23107	+	0.710758i	0.967253	−	0.253815i	$-0.0816853\pi$
$61$	9.61496	+	5.55120i	1.23107	+	0.710758i	0.263817	+	0.964573i	$0.415019\pi$
$62$	−12.6294	+	4.32623i	−1.60394	+	0.549432i
$63$		0			0
$64$	−3.18406	−	7.33906i	−0.398008	−	0.917382i
$65$	3.67579	−	6.36666i	0.455926	−	0.789686i
$66$	1.17619	−	1.34871i	0.144779	−	0.166015i
$67$	2.43151	−	1.40383i	0.297056	−	0.171505i	−0.344064	−	0.938946i	$-0.611804\pi$
$67$	2.43151	−	1.40383i	0.297056	−	0.171505i	0.641120	+	0.767441i	$0.278470\pi$
$68$	3.63230	−	0.498720i	0.440481	−	0.0604787i
$69$		−	6.73842i		−	0.811211i
$70$		0			0
$71$			2.92285i			0.346878i	0.984845	+	0.173439i	$0.0554880\pi$
$71$			2.92285i			0.346878i	−0.984845	+	0.173439i	$0.944512\pi$
$72$	1.27205	+	2.52624i	0.149913	+	0.297720i
$73$	−7.01910	+	4.05248i	−0.821523	+	0.474307i	−0.850941	−	0.525261i	$-0.823968\pi$
$73$	−7.01910	+	4.05248i	−0.821523	+	0.474307i	0.0294183	+	0.999567i	$0.490635\pi$
$74$	−8.00602	−	6.98190i	−0.930681	−	0.811629i
$75$	0.507662	−	0.879296i	0.0586198	−	0.101532i
$76$	6.57226	−	5.10126i	0.753890	−	0.585155i
$77$		0			0
$78$	1.37372	+	4.01027i	0.155543	+	0.454073i
$79$	1.54471	+	0.891841i	0.173794	+	0.100340i	0.584374	−	0.811485i	$-0.301340\pi$
$79$	1.54471	+	0.891841i	0.173794	+	0.100340i	−0.410580	+	0.911825i	$0.634674\pi$
$80$	−2.64413	−	9.44742i	−0.295623	−	1.05625i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.51223	+	0.296442i	0.166998	+	0.0327365i
$83$	−5.33626			−0.585730			−0.292865	−	0.956154i	$-0.594609\pi$
$83$	−5.33626			−0.585730			−0.292865	+	0.956154i	$0.594609\pi$
$84$		0			0
$85$	4.49611			0.487672
$86$	−8.70395	−	1.70624i	−0.938572	−	0.183988i
$87$	4.71162	+	8.16076i	0.505138	+	0.874925i
$88$	0.204351	−	3.57324i	0.0217839	−	0.380908i
$89$	−7.42323	−	4.28581i	−0.786861	−	0.454294i	0.0519952	−	0.998647i	$-0.483442\pi$
$89$	−7.42323	−	4.28581i	−0.786861	−	0.454294i	−0.838856	+	0.544353i	$0.816775\pi$
$90$	1.12403	+	3.28134i	0.118483	+	0.345884i
$91$		0			0
$92$	−8.26338	−	10.6462i	−0.861517	−	1.10994i
$93$	4.71989	−	8.17509i	0.489430	−	0.847717i
$94$	7.83564	+	6.83331i	0.808185	+	0.704802i
$95$	8.83564	−	5.10126i	0.906518	−	0.523378i
$96$	5.10769	+	2.43135i	0.521302	+	0.248149i
$97$		−	7.10394i		−	0.721296i	−0.932702	−	0.360648i	$-0.882556\pi$
$97$		−	7.10394i		−	0.721296i	0.932702	−	0.360648i	$-0.117444\pi$
$98$		0			0
$99$			1.26539i			0.127177i
$100$	−0.276219	−	2.01177i	−0.0276219	−	0.201177i
$101$	−0.808273	+	0.466657i	−0.0804262	+	0.0464341i	−0.539674	−	0.841874i	$-0.681452\pi$
$101$	−0.808273	+	0.466657i	−0.0804262	+	0.0464341i	0.459248	+	0.888308i	$0.348119\pi$
$102$	−1.70395	+	1.95390i	−0.168717	+	0.193465i
$103$	2.06460	−	3.57600i	0.203431	−	0.352353i	−0.746200	−	0.665721i	$-0.768124\pi$
$103$	2.06460	−	3.57600i	0.203431	−	0.352353i	0.949632	+	0.313368i	$0.101457\pi$
$104$	7.08820	+	4.65132i	0.695055	+	0.456100i
$105$		0			0
$106$	−0.0958634	+	0.0328381i	−0.00931108	+	0.00318952i
$107$	−11.9878	−	6.92118i	−1.15891	−	0.669096i	−0.207866	−	0.978157i	$-0.566652\pi$
$107$	−11.9878	−	6.92118i	−1.15891	−	0.669096i	−0.951042	+	0.309062i	$0.899985\pi$
$108$	−1.85198	−	0.755103i	−0.178207	−	0.0726598i
$109$	0.492338	+	0.852754i	0.0471574	+	0.0816791i	0.888641	−	0.458604i	$-0.151650\pi$
$109$	0.492338	+	0.852754i	0.0471574	+	0.0816791i	−0.841483	+	0.540283i	$0.818317\pi$
$110$	0.844315	−	4.30707i	0.0805023	−	0.410663i
$111$	7.51143			0.712954
$112$		0			0
$113$	5.03187			0.473359			0.236679	−	0.971588i	$-0.423941\pi$
$113$	5.03187			0.473359			0.236679	+	0.971588i	$0.423941\pi$
$114$	−1.13169	+	5.77304i	−0.105992	+	0.540695i
$115$	−8.26338	−	14.3126i	−0.770564	−	1.33466i
$116$	17.4516	+	7.11551i	1.62034	+	0.660659i
$117$	−2.59586	−	1.49872i	−0.239988	−	0.138557i
$118$	−4.50457	+	1.54304i	−0.414679	+	0.142049i
$119$		0			0
$120$	5.79982	+	3.80588i	0.529449	+	0.347428i
$121$	−4.69939	+	8.13958i	−0.427217	+	0.739962i
$122$	−10.3197	+	11.8334i	−0.934302	+	1.07135i
$123$	−0.943672	+	0.544829i	−0.0850880	+	0.0491256i
$124$	−2.56810	−	18.7041i	−0.230622	−	1.67968i
$125$			9.77288i			0.874113i
$126$		0			0
$127$			6.38337i			0.566433i	0.959056	+	0.283216i	$0.0914015\pi$
$127$			6.38337i			0.566433i	−0.959056	+	0.283216i	$0.908599\pi$
$128$	11.0514	−	2.42225i	0.976812	−	0.214099i
$129$	5.43151	−	3.13588i	0.478218	−	0.276099i
$130$	7.83564	+	6.83331i	0.687231	+	0.599321i
$131$	−1.93601	+	3.35327i	−0.169150	+	0.292976i	−0.938121	−	0.346307i	$-0.887436\pi$
$131$	−1.93601	+	3.35327i	−0.169150	+	0.292976i	0.768971	+	0.639283i	$0.220769\pi$
$132$	1.55176	+	1.99923i	0.135064	+	0.174011i
$133$		0			0
$134$	1.28674	+	3.75636i	0.111158	+	0.324500i
$135$	−2.12403	−	1.22631i	−0.182807	−	0.105544i
$136$	−0.296046	+	5.17659i	−0.0253857	+	0.443889i
$137$	7.35158	+	12.7333i	0.628088	+	1.08788i	0.987935	+	0.154869i	$0.0494955\pi$
$137$	7.35158	+	12.7333i	0.628088	+	1.08788i	−0.359847	+	0.933011i	$0.617171\pi$
$138$	9.35158	+	1.83319i	0.796059	+	0.156051i
$139$	2.01655			0.171041			0.0855207	−	0.996336i	$-0.472745\pi$
$139$	2.01655			0.171041			0.0855207	+	0.996336i	$0.472745\pi$
$140$		0			0
$141$	−7.35158			−0.619115
$142$	−4.05633	−	0.795162i	−0.340400	−	0.0667285i
$143$	1.89647	+	3.28479i	0.158591	+	0.274688i
$144$	−3.85198	+	1.07809i	−0.320998	+	0.0898406i
$145$	20.0152	+	11.5558i	1.66217	+	0.959656i
$146$	−3.71448	−	10.8436i	−0.307413	−	0.897421i
$147$		0			0
$148$	11.8675	−	9.21133i	0.975504	−	0.757167i
$149$	0.248055	−	0.429644i	0.0203215	−	0.0351978i	−0.855686	−	0.517496i	$-0.826864\pi$
$149$	0.248055	−	0.429644i	0.0203215	−	0.0351978i	0.876007	+	0.482298i	$0.160198\pi$
$150$	1.08218	+	0.943746i	0.0883595	+	0.0770566i
$151$	11.4636	−	6.61849i	0.932891	−	0.538605i	0.0451665	−	0.998979i	$-0.485618\pi$
$151$	11.4636	−	6.61849i	0.932891	−	0.538605i	0.887725	+	0.460374i	$0.152285\pi$
$152$	5.29154	+	10.5088i	0.429201	+	0.852375i
$153$		−	1.83319i		−	0.148205i
$154$		0			0
$155$		−	23.1522i		−	1.85963i
$156$	−5.93917	+	0.815456i	−0.475514	+	0.0652887i
$157$	−4.38345	+	2.53079i	−0.349838	+	0.201979i	−0.664614	−	0.747187i	$-0.731404\pi$
$157$	−4.38345	+	2.53079i	−0.349838	+	0.201979i	0.314776	+	0.949166i	$0.398071\pi$
$158$	−1.65794	+	1.90113i	−0.131898	+	0.151246i
$159$	0.0358262	−	0.0620528i	0.00284120	−	0.00492111i
$160$	13.8305	−	1.09935i	1.09339	−	0.0869115i
$161$		0			0
$162$	1.33790	−	0.458297i	0.105115	−	0.0360072i
$163$	−10.4232	−	6.01786i	−0.816411	−	0.471355i	0.0327665	−	0.999463i	$-0.489568\pi$
$163$	−10.4232	−	6.01786i	−0.816411	−	0.471355i	−0.849177	+	0.528108i	$0.822902\pi$
$164$	−0.822804	+	2.01802i	−0.0642502	+	0.157581i
$165$	1.55176	+	2.68773i	0.120805	+	0.209240i
$166$	1.45173	−	7.40566i	0.112676	−	0.574790i
$167$	−7.46424			−0.577600			−0.288800	−	0.957389i	$-0.593256\pi$
$167$	−7.46424			−0.577600			−0.288800	+	0.957389i	$0.593256\pi$
$168$		0			0
$169$	4.01532			0.308871
$170$	−1.22317	+	6.23970i	−0.0938127	+	0.478563i
$171$	−2.07993	−	3.60254i	−0.159056	−	0.275493i
$172$	4.73583	−	11.6152i	0.361103	−	0.885648i
$173$	−3.77932	−	2.18199i	−0.287336	−	0.165894i	0.349404	−	0.936972i	$-0.386384\pi$
$173$	−3.77932	−	2.18199i	−0.287336	−	0.165894i	−0.636740	+	0.771079i	$0.719717\pi$
$174$	−12.6073	+	4.31864i	−0.955757	+	0.327396i
$175$		0			0
$176$	4.90334	+	1.25570i	0.369603	+	0.0946518i
$177$	1.68345	−	2.91583i	0.126536	−	0.219167i
$178$	7.96733	−	9.13601i	0.597177	−	0.684773i
$179$	−21.2754	+	12.2834i	−1.59020	+	0.918102i	−0.596928	+	0.802295i	$0.703612\pi$
$179$	−21.2754	+	12.2834i	−1.59020	+	0.918102i	−0.993272	+	0.115808i	$0.963054\pi$
$180$	−4.85964	+	0.667235i	−0.362216	+	0.0497328i
$181$			11.7182i			0.871011i	0.900186	+	0.435505i	$0.143430\pi$
$181$			11.7182i			0.871011i	−0.900186	+	0.435505i	$0.856570\pi$
$182$		0			0
$183$		−	11.1024i		−	0.820713i
$184$	17.0229	−	8.57161i	1.25494	−	0.631908i
$185$	15.9545	−	9.21133i	1.17300	−	0.677231i
$186$	10.0613	+	8.77430i	0.737733	+	0.643363i
$187$	−1.15985	+	2.00893i	−0.0848169	+	0.146907i
$188$	−11.6150	+	9.01530i	−0.847108	+	0.657508i
$189$		0			0
$190$	4.67579	+	13.6499i	0.339217	+	0.990268i
$191$	13.7628	+	7.94594i	0.995839	+	0.574948i	0.907014	−	0.421099i	$-0.138356\pi$
$191$	13.7628	+	7.94594i	0.995839	+	0.574948i	0.0888244	+	0.996047i	$0.471689\pi$
$192$	−4.76378	+	6.42701i	−0.343796	+	0.463829i
$193$	−9.86690	−	17.0900i	−0.710235	−	1.23016i	−0.964769	−	0.263100i	$-0.915255\pi$
$193$	−9.86690	−	17.0900i	−0.710235	−	1.23016i	0.254533	−	0.967064i	$-0.418078\pi$
$194$	9.85885	+	1.93263i	0.707824	+	0.138755i
$195$	−7.35158			−0.526458
$196$		0			0
$197$	0.998775			0.0711598			0.0355799	−	0.999367i	$-0.488672\pi$
$197$	0.998775			0.0711598			0.0355799	+	0.999367i	$0.488672\pi$
$198$	−1.75611	−	0.344251i	−0.124802	−	0.0244648i
$199$	−1.35158	−	2.34101i	−0.0958110	−	0.165950i	0.814136	−	0.580675i	$-0.197211\pi$
$199$	−1.35158	−	2.34101i	−0.0958110	−	0.165950i	−0.909947	+	0.414725i	$0.863878\pi$
$200$	2.86709	+	0.163967i	0.202734	+	0.0115942i
$201$	−2.43151	−	1.40383i	−0.171505	−	0.0990186i
$202$	−0.427735	−	1.24868i	−0.0300953	−	0.0878565i
$203$		0			0
$204$	−2.24806	−	2.89631i	−0.157395	−	0.202782i
$205$	−1.33626	+	2.31446i	−0.0933282	+	0.161649i
$206$	4.40109	+	3.83811i	0.306639	+	0.267414i
$207$	−5.83564	+	3.36921i	−0.405605	+	0.234176i
$208$	−8.38345	+	8.57161i	−0.581288	+	0.594334i
$209$			5.26385i			0.364108i
$210$		0			0
$211$		−	18.1798i		−	1.25155i	−0.780004	−	0.625774i	$-0.784783\pi$
$211$		−	18.1798i		−	1.25155i	0.780004	−	0.625774i	$-0.215217\pi$
$212$	−0.0194931	−	0.141973i	−0.00133879	−	0.00975074i
$213$	2.53126	−	1.46142i	0.173439	−	0.100135i
$214$	12.8665	−	14.7538i	0.879536	−	1.00855i
$215$	7.69111	−	13.3214i	0.524530	−	0.908512i
$216$	1.55176	−	2.36475i	0.105584	−	0.160901i
$217$		0			0
$218$	−1.31739	+	0.451274i	−0.0892251	+	0.0305642i
$219$	7.01910	+	4.05248i	0.474307	+	0.273841i
$220$	5.74766	+	2.34348i	0.387507	+	0.157997i
$221$	−2.74744	−	4.75871i	−0.184813	−	0.320106i
$222$	−2.04349	+	10.4244i	−0.137150	+	0.699638i
$223$	11.5996			0.776769			0.388385	−	0.921497i	$-0.373033\pi$
$223$	11.5996			0.776769			0.388385	+	0.921497i	$0.373033\pi$
$224$		0			0
$225$	−1.01532			−0.0676883
$226$	−1.36892	+	6.98323i	−0.0910594	+	0.464518i
$227$	−5.08054	−	8.79975i	−0.337207	−	0.584060i	0.646699	−	0.762745i	$-0.276149\pi$
$227$	−5.08054	−	8.79975i	−0.337207	−	0.584060i	−0.983906	+	0.178685i	$0.942816\pi$
$228$	−7.70395	−	3.14112i	−0.510207	−	0.208026i
$229$	−20.0025	−	11.5485i	−1.32181	−	0.763145i	−0.337789	−	0.941222i	$-0.609679\pi$
$229$	−20.0025	−	11.5485i	−1.32181	−	0.763145i	−0.984017	+	0.178077i	$0.943012\pi$
$230$	22.1111	−	7.57417i	1.45796	−	0.499426i
$231$		0			0
$232$	−14.6226	+	22.2836i	−0.960022	+	1.46299i
$233$	3.42774	−	5.93701i	0.224558	−	0.388947i	−0.731628	−	0.681704i	$-0.761239\pi$
$233$	3.42774	−	5.93701i	0.224558	−	0.388947i	0.956187	+	0.292757i	$0.0945727\pi$
$234$	2.78613	−	3.19481i	0.182135	−	0.208851i
$235$	−15.6150	+	9.01530i	−1.01861	+	0.588093i
$236$	−0.915968	−	6.67122i	−0.0596244	−	0.434260i
$237$		−	1.78368i		−	0.115863i
$238$		0			0
$239$			22.2257i			1.43766i	0.695184	+	0.718832i	$0.255323\pi$
$239$			22.2257i			1.43766i	−0.695184	+	0.718832i	$0.744677\pi$
$240$	−6.85964	+	7.01360i	−0.442788	+	0.452726i
$241$	−13.3605	+	7.71367i	−0.860623	+	0.496881i	−0.864221	−	0.503112i	$-0.832188\pi$
$241$	−13.3605	+	7.71367i	−0.860623	+	0.496881i	0.00359762	+	0.999994i	$0.498855\pi$
$242$	−10.0176	−	8.73619i	−0.643958	−	0.561583i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−13.6150	−	17.5410i	−0.871608	−	1.12295i
$245$		0			0
$246$	−0.499388	−	1.45785i	−0.0318398	−	0.0929490i
$247$	−10.7984	−	6.23447i	−0.687087	−	0.396690i
$248$	26.6562	+	1.52445i	1.69267	+	0.0968026i
$249$	2.66813	+	4.62133i	0.169086	+	0.292865i
$250$	−13.5628	−	2.65872i	−0.857787	−	0.168152i
$251$	22.2954			1.40727			0.703636	−	0.710561i	$-0.251559\pi$
$251$	22.2954			1.40727			0.703636	+	0.710561i	$0.251559\pi$
$252$		0			0
$253$	8.52676			0.536073
$254$	−8.85885	−	1.73660i	−0.555853	−	0.108964i
$255$	−2.24806	−	3.89375i	−0.140779	−	0.243836i
$256$	0.355074	+	15.9961i	0.0221921	+	0.999754i
$257$	−2.48529	−	1.43488i	−0.155028	−	0.0895055i	0.420479	−	0.907302i	$-0.361862\pi$
$257$	−2.48529	−	1.43488i	−0.155028	−	0.0895055i	−0.575507	+	0.817797i	$0.695195\pi$
$258$	2.87433	+	8.39096i	0.178948	+	0.522399i
$259$		0			0
$260$	−11.6150	+	9.01530i	−0.720329	+	0.559105i
$261$	4.71162	−	8.16076i	0.291642	−	0.505138i
$262$	−4.12697	−	3.59905i	−0.254965	−	0.222350i
$263$	−8.98186	+	5.18568i	−0.553845	+	0.319763i	−0.750672	−	0.660676i	$-0.770270\pi$
$263$	−8.98186	+	5.18568i	−0.553845	+	0.319763i	0.196826	+	0.980438i	$0.436937\pi$
$264$	−3.19669	+	1.60964i	−0.196743	+	0.0990668i
$265$		−	0.175736i		−	0.0107954i
$266$		0			0
$267$			8.57161i			0.524574i
$268$	−5.56313	+	0.763826i	−0.339822	+	0.0466581i
$269$	−4.48011	+	2.58659i	−0.273157	+	0.157707i	−0.630322	−	0.776334i	$-0.717077\pi$
$269$	−4.48011	+	2.58659i	−0.273157	+	0.157707i	0.357164	+	0.934042i	$0.383744\pi$
$270$	2.27971	−	2.61411i	0.138739	−	0.159090i
$271$	−12.1195	+	20.9916i	−0.736209	+	1.27515i	0.217982	+	0.975953i	$0.430053\pi$
$271$	−12.1195	+	20.9916i	−0.736209	+	1.27515i	−0.954191	+	0.299198i	$0.903281\pi$
$272$	−7.10353	−	1.81914i	−0.430714	−	0.110302i
$273$		0			0
$274$	−19.6713	+	6.73842i	−1.18839	+	0.407083i
$275$	1.11266	+	0.642393i	0.0670957	+	0.0387377i
$276$	−5.08820	+	12.4794i	−0.306274	+	0.751172i
$277$	1.50766	+	2.61135i	0.0905866	+	0.156901i	0.907758	−	0.419494i	$-0.137792\pi$
$277$	1.50766	+	2.61135i	0.0905866	+	0.156901i	−0.817171	+	0.576395i	$0.804459\pi$
$278$	−0.548603	+	2.79857i	−0.0329030	+	0.167847i
$279$	−9.43978			−0.565145
$280$		0			0
$281$	−6.91922			−0.412766			−0.206383	−	0.978471i	$-0.566169\pi$
$281$	−6.91922			−0.412766			−0.206383	+	0.978471i	$0.566169\pi$
$282$	2.00000	−	10.2025i	0.119098	−	0.607551i
$283$	−10.2870	−	17.8176i	−0.611497	−	1.05914i	−0.990988	−	0.133949i	$-0.957234\pi$
$283$	−10.2870	−	17.8176i	−0.611497	−	1.05914i	0.379491	−	0.925195i	$-0.376099\pi$
$284$	2.20705	−	5.41305i	0.130964	−	0.321205i
$285$	−8.83564	−	5.10126i	−0.523378	−	0.302173i
$286$	−5.07457	+	1.73830i	−0.300066	+	0.102788i
$287$		0			0
$288$	−0.448237	−	5.63907i	−0.0264126	−	0.332285i
$289$	−6.81971	+	11.8121i	−0.401159	+	0.694828i
$290$	−21.4823	+	24.6333i	−1.26148	+	1.44652i
$291$	−6.15219	+	3.55197i	−0.360648	+	0.208220i
$292$	16.0592	−	2.20496i	0.939796	−	0.129035i
$293$		−	28.3113i		−	1.65396i	−0.562229	−	0.826982i	$-0.690056\pi$
$293$		−	28.3113i		−	1.65396i	0.562229	−	0.826982i	$-0.309944\pi$
$294$		0			0
$295$		−	8.25772i		−	0.480783i
$296$	9.55492	+	18.9757i	0.555369	+	1.10294i
$297$	1.09586	−	0.632697i	0.0635884	−	0.0367128i
$298$	0.528777	+	0.461136i	0.0306312	+	0.0267129i
$299$	−10.0990	+	17.4920i	−0.584042	+	1.01159i
$300$	−1.60414	+	1.24510i	−0.0926149	+	0.0718859i
$301$		0			0
$302$	6.06647	+	17.7097i	0.349086	+	1.01908i
$303$	0.808273	+	0.466657i	0.0464341	+	0.0268087i
$304$	−16.0237	+	4.48468i	−0.919020	+	0.257214i
$305$	−13.6150	−	23.5818i	−0.779590	−	1.35029i
$306$	2.54410	+	0.498720i	0.145437	+	0.0285099i
$307$	−8.65596			−0.494022			−0.247011	−	0.969013i	$-0.579448\pi$
$307$	−8.65596			−0.494022			−0.247011	+	0.969013i	$0.579448\pi$
$308$		0			0
$309$	−4.12921			−0.234902
$310$	32.1306	+	6.29855i	1.82489	+	0.357734i
$311$	−4.67129	−	8.09091i	−0.264884	−	0.458793i	0.702649	−	0.711537i	$-0.252000\pi$
$311$	−4.67129	−	8.09091i	−0.264884	−	0.458793i	−0.967533	+	0.252743i	$0.918667\pi$
$312$	0.484063	−	8.46422i	0.0274047	−	0.479192i
$313$	6.38734	+	3.68773i	0.361034	+	0.208443i	0.669534	−	0.742781i	$-0.266494\pi$
$313$	6.38734	+	3.68773i	0.361034	+	0.208443i	−0.308500	+	0.951224i	$0.599827\pi$
$314$	−2.31971	−	6.77186i	−0.130909	−	0.382158i
$315$		0			0
$316$	−2.18734	−	2.81809i	−0.123048	−	0.158530i
$317$	1.81514	−	3.14392i	0.101949	−	0.176580i	−0.810539	−	0.585685i	$-0.800826\pi$
$317$	1.81514	−	3.14392i	0.101949	−	0.176580i	0.912487	+	0.409105i	$0.134159\pi$
$318$	0.0763704	+	0.0666011i	0.00428264	+	0.00373480i
$319$	−10.3266	+	5.96205i	−0.578177	+	0.333811i
$320$	−2.23690	+	19.4930i	−0.125047	+	1.08969i
$321$			13.8424i			0.772605i
$322$		0			0
$323$		−	7.62580i		−	0.424311i
$324$	0.272050	+	1.98141i	0.0151139	+	0.110078i
$325$	−2.63564	+	1.52169i	−0.146199	+	0.0844081i
$326$	11.1872	−	12.8282i	0.619603	−	0.710488i
$327$	0.492338	−	0.852754i	0.0272264	−	0.0471574i
$328$	−2.57677	−	1.69089i	−0.142278	−	0.0933638i
$329$		0			0
$330$	−4.15219	+	1.42234i	−0.228571	+	0.0782971i
$331$	0.544164	+	0.314173i	0.0299100	+	0.0172685i	0.514880	−	0.857262i	$-0.327836\pi$
$331$	0.544164	+	0.314173i	0.0299100	+	0.0172685i	−0.484970	+	0.874531i	$0.661170\pi$
$332$	9.88263	+	4.02942i	0.542380	+	0.221143i
$333$	−3.75572	−	6.50509i	−0.205812	−	0.356477i
$334$	2.03065	−	10.3589i	0.111112	−	0.566812i
$335$	−6.88612			−0.376229
$336$		0			0
$337$	−22.3119			−1.21541			−0.607704	−	0.794164i	$-0.707909\pi$
$337$	−22.3119			−1.21541			−0.607704	+	0.794164i	$0.707909\pi$
$338$	−1.09237	+	5.57247i	−0.0594171	+	0.303102i
$339$	−2.51594	−	4.35773i	−0.136647	−	0.236679i
$340$	−8.32669	−	3.39503i	−0.451578	−	0.184121i
$341$	10.3447	+	5.97252i	0.560198	+	0.323430i
$342$	5.56545	−	1.90645i	0.300945	−	0.103089i
$343$		0			0
$344$	14.8311	+	9.73229i	0.799642	+	0.524730i
$345$	−8.26338	+	14.3126i	−0.444885	+	0.770564i
$346$	4.05633	−	4.65132i	0.218070	−	0.250057i
$347$	5.97104	−	3.44738i	0.320542	−	0.185065i	−0.331092	−	0.943598i	$-0.607417\pi$
$347$	5.97104	−	3.44738i	0.320542	−	0.185065i	0.651634	+	0.758533i	$0.274084\pi$
$348$	−2.56359	−	18.6713i	−0.137423	−	1.00089i
$349$			13.4768i			0.721399i	0.932682	+	0.360699i	$0.117462\pi$
$349$			13.4768i			0.721399i	−0.932682	+	0.360699i	$0.882538\pi$
$350$		0			0
$351$			2.99744i			0.159992i
$352$	−3.07661	+	6.46325i	−0.163984	+	0.344492i
$353$	24.7550	−	14.2923i	1.31758	−	0.760702i	0.334237	−	0.942489i	$-0.391521\pi$
$353$	24.7550	−	14.2923i	1.31758	−	0.760702i	0.983338	+	0.181787i	$0.0581881\pi$
$354$	3.58860	+	3.12955i	0.190732	+	0.166334i
$355$	3.58431	−	6.20821i	0.190236	−	0.329498i
$356$	10.5114	+	13.5425i	0.557105	+	0.717752i
$357$		0			0
$358$	−11.2589	−	32.8677i	−0.595050	−	1.73711i
$359$	−6.00000	−	3.46410i	−0.316668	−	0.182828i	0.333238	−	0.942843i	$-0.391859\pi$
$359$	−6.00000	−	3.46410i	−0.316668	−	0.182828i	−0.649906	+	0.760014i	$0.725192\pi$
$360$	0.396078	−	6.92573i	0.0208751	−	0.365018i
$361$	0.847808	+	1.46845i	0.0446215	+	0.0772867i
$362$	−16.2626	−	3.18795i	−0.854743	−	0.167555i
$363$	9.39878			0.493308
$364$		0			0
$365$	19.8783			1.04048
$366$	15.4079	+	3.02041i	0.805384	+	0.157879i
$367$	6.47184	+	11.2095i	0.337827	+	0.585134i	0.984024	−	0.178037i	$-0.0569748\pi$
$367$	6.47184	+	11.2095i	0.337827	+	0.585134i	−0.646197	+	0.763171i	$0.723641\pi$
$368$	7.26460	+	25.9562i	0.378694	+	1.35306i
$369$	0.943672	+	0.544829i	0.0491256	+	0.0283627i
$370$	8.44306	+	24.6476i	0.438934	+	1.28137i
$371$		0			0
$372$	−14.9142	+	11.5761i	−0.773263	+	0.600192i
$373$	−1.53954	+	2.66655i	−0.0797141	+	0.138069i	−0.903127	−	0.429374i	$-0.858734\pi$
$373$	−1.53954	+	2.66655i	−0.0797141	+	0.138069i	0.823412	+	0.567443i	$0.192067\pi$
$374$	−2.47245	−	2.15617i	−0.127847	−	0.111493i
$375$	8.46356	−	4.88644i	0.437056	−	0.252335i
$376$	−9.35158	−	18.5719i	−0.482271	−	0.957770i
$377$		−	28.2456i		−	1.45472i
$378$		0			0
$379$		−	5.21020i		−	0.267630i	−0.991006	−	0.133815i	$-0.957277\pi$
$379$		−	5.21020i		−	0.267630i	0.991006	−	0.133815i	$-0.0427228\pi$
$380$	−20.2154	+	2.77560i	−1.03703	+	0.142385i
$381$	5.52816	−	3.19169i	0.283216	−	0.163515i
$382$	−14.7715	+	16.9383i	−0.755778	+	0.866637i
$383$	−19.4353	+	33.6629i	−0.993096	+	1.72009i	−0.394963	+	0.918697i	$0.629242\pi$
$383$	−19.4353	+	33.6629i	−0.993096	+	1.72009i	−0.598134	+	0.801396i	$0.704091\pi$
$384$	−7.62342	−	8.35964i	−0.389031	−	0.426601i
$385$		0			0
$386$	26.4018	−	9.04395i	1.34381	−	0.460325i
$387$	−5.43151	−	3.13588i	−0.276099	−	0.159406i
$388$	−5.36420	+	13.1563i	−0.272326	+	0.667912i
$389$	1.86752	+	3.23463i	0.0946869	+	0.164002i	0.909478	−	0.415752i	$-0.136482\pi$
$389$	1.86752	+	3.23463i	0.0946869	+	0.164002i	−0.814791	+	0.579755i	$0.803148\pi$
$390$	2.00000	−	10.2025i	0.101274	−	0.516625i
$391$	−12.3528			−0.624708
$392$		0			0
$393$	3.87202			0.195318
$394$	−0.271717	+	1.38610i	−0.0136889	+	0.0698307i
$395$	−2.18734	−	3.78859i	−0.110057	−	0.190625i
$396$	0.955503	−	2.34348i	0.0480158	−	0.117764i
$397$	5.81082	+	3.35488i	0.291637	+	0.168377i	0.638680	−	0.769473i	$-0.279481\pi$
$397$	5.81082	+	3.35488i	0.291637	+	0.168377i	−0.347043	+	0.937849i	$0.612814\pi$
$398$	3.61655	−	1.23885i	0.181281	−	0.0620980i
$399$		0			0
$400$	−1.00754	+	3.93433i	−0.0503772	+	0.196717i
$401$	−2.92385	+	5.06425i	−0.146010	+	0.252897i	−0.929749	−	0.368193i	$-0.879976\pi$
$401$	−2.92385	+	5.06425i	−0.146010	+	0.252897i	0.783739	+	0.621090i	$0.213310\pi$
$402$	2.60973	−	2.99253i	0.130161	−	0.149254i
$403$	−24.5044	+	14.1476i	−1.22065	+	0.704743i
$404$	1.84928	−	0.253908i	0.0920050	−	0.0126324i
$405$			2.45262i			0.121871i
$406$		0			0
$407$			9.50492i			0.471142i
$408$	4.63108	−	2.33191i	0.229272	−	0.115447i
$409$	26.7299	−	15.4325i	1.32171	−	0.763089i	0.337708	−	0.941251i	$-0.390348\pi$
$409$	26.7299	−	15.4325i	1.32171	−	0.763089i	0.984001	+	0.178162i	$0.0570150\pi$
$410$	−2.84848	−	2.48411i	−0.140677	−	0.122681i
$411$	7.35158	−	12.7333i	0.362627	−	0.628088i
$412$	−6.52384	+	5.06368i	−0.321407	+	0.249469i
$413$		0			0
$414$	−3.08820	−	9.01530i	−0.151777	−	0.443078i
$415$	11.3344	+	6.54389i	0.556382	+	0.321227i
$416$	−9.61496	−	13.9665i	−0.471412	−	0.684762i
$417$	−1.00827	−	1.74638i	−0.0493754	−	0.0855207i
$418$	−7.30518	−	1.43203i	−0.357308	−	0.0700430i
$419$	29.0866			1.42097			0.710487	−	0.703710i	$-0.248475\pi$
$419$	29.0866			1.42097			0.710487	+	0.703710i	$0.248475\pi$
$420$		0			0
$421$	13.8642			0.675702			0.337851	−	0.941200i	$-0.390300\pi$
$421$	13.8642			0.675702			0.337851	+	0.941200i	$0.390300\pi$
$422$	25.2299	+	4.94582i	1.22817	+	0.240759i
$423$	3.67579	+	6.36666i	0.178723	+	0.309557i
$424$	0.202333	+	0.0115713i	0.00982616	+	0.000561952i
$425$	−1.61192	−	0.930641i	−0.0781895	−	0.0451427i
$426$	1.33953	+	3.91046i	0.0649006	+	0.189463i
$427$		0			0
$428$	16.9750	+	21.8699i	0.820517	+	1.05712i
$429$	1.89647	−	3.28479i	0.0915627	−	0.158591i
$430$	16.3951	+	14.2978i	0.790640	+	0.689502i
$431$	27.6258	−	15.9498i	1.33069	−	0.768273i	0.345282	−	0.938499i	$-0.387783\pi$
$431$	27.6258	−	15.9498i	1.33069	−	0.768273i	0.985405	+	0.170226i	$0.0544499\pi$
$432$	2.85964	+	2.79687i	0.137584	+	0.134564i
$433$			9.82239i			0.472034i	0.971749	+	0.236017i	$0.0758421\pi$
$433$			9.82239i			0.472034i	−0.971749	+	0.236017i	$0.924158\pi$
$434$		0			0
$435$		−	23.1116i		−	1.10811i
$436$	−0.267881	−	1.95105i	−0.0128292	−	0.0934382i
$437$	−24.2754	+	14.0154i	−1.16125	+	0.670449i
$438$	−7.53358	+	8.63862i	−0.359968	+	0.412769i
$439$	8.51989	−	14.7569i	0.406632	−	0.704308i	−0.587878	−	0.808950i	$-0.700036\pi$
$439$	8.51989	−	14.7569i	0.406632	−	0.704308i	0.994510	+	0.104642i	$0.0333697\pi$
$440$	−4.81594	+	7.33906i	−0.229591	+	0.349876i
$441$		0			0
$442$	7.35158	−	2.51829i	0.349679	−	0.119783i
$443$	−7.30000	−	4.21466i	−0.346833	−	0.200244i	0.316456	−	0.948607i	$-0.397507\pi$
$443$	−7.30000	−	4.21466i	−0.346833	−	0.200244i	−0.663290	+	0.748363i	$0.730840\pi$
$444$	−13.9110	−	5.67191i	−0.660187	−	0.269177i
$445$	10.5114	+	18.2063i	0.498290	+	0.863063i
$446$	−3.15568	+	16.0980i	−0.149426	+	0.762261i
$447$	−0.496110			−0.0234652
$448$		0			0
$449$	9.64064			0.454970			0.227485	−	0.973782i	$-0.426950\pi$
$449$	9.64064			0.454970			0.227485	+	0.973782i	$0.426950\pi$
$450$	0.276219	−	1.40907i	0.0130211	−	0.0664240i
$451$	−0.689424	−	1.19412i	−0.0324637	−	0.0562288i
$452$	−9.31891	−	3.79958i	−0.438325	−	0.178717i
$453$	−11.4636	−	6.61849i	−0.538605	−	0.310964i
$454$	13.5945	−	4.65680i	0.638020	−	0.218554i
$455$		0			0
$456$	6.45511	−	9.83701i	0.302288	−	0.460660i
$457$	14.5229	−	25.1543i	0.679351	−	1.17667i	−0.295825	−	0.955242i	$-0.595595\pi$
$457$	14.5229	−	25.1543i	0.679351	−	1.17667i	0.975177	−	0.221429i	$-0.0710720\pi$
$458$	21.4687	−	24.6178i	1.00317	−	1.15031i
$459$	−1.58759	+	0.916595i	−0.0741023	+	0.0427830i
$460$	4.49611	+	32.7463i	0.209632	+	1.52680i
$461$			23.9796i			1.11684i	0.829559	+	0.558420i	$0.188592\pi$
$461$			23.9796i			1.11684i	−0.829559	+	0.558420i	$0.811408\pi$
$462$		0			0
$463$			28.4975i			1.32439i	0.749331	+	0.662196i	$0.230375\pi$
$463$			28.4975i			1.32439i	−0.749331	+	0.662196i	$0.769625\pi$
$464$	−26.9470	−	26.3555i	−1.25099	−	1.22352i
$465$	−20.0504	+	11.5761i	−0.929813	+	0.536828i
$466$	7.30687	+	6.37218i	0.338484	+	0.295185i
$467$	9.29075	−	16.0921i	0.429925	−	0.744651i	−0.566942	−	0.823758i	$-0.691873\pi$
$467$	9.29075	−	16.0921i	0.429925	−	0.744651i	0.996866	+	0.0791067i	$0.0252068\pi$
$468$	3.67579	+	4.73574i	0.169913	+	0.218910i
$469$		0			0
$470$	−8.26338	−	24.1231i	−0.381161	−	1.11271i
$471$	4.38345	+	2.53079i	0.201979	+	0.116613i
$472$	9.50751	+	0.543728i	0.437619	+	0.0250271i
$473$	3.96813	+	6.87300i	0.182455	+	0.316021i
$474$	2.47539	+	0.485251i	0.113699	+	0.0222883i
$475$	−4.22360			−0.193792
$476$		0			0
$477$	−0.0716524			−0.00328074
$478$	−30.8449	−	6.04652i	−1.41081	−	0.276561i
$479$	14.1707	+	24.5443i	0.647475	+	1.12146i	0.983724	+	0.179686i	$0.0575082\pi$
$479$	14.1707	+	24.5443i	0.647475	+	1.12146i	−0.336249	+	0.941773i	$0.609158\pi$
$480$	−7.86730	−	11.4279i	−0.359092	−	0.521608i
$481$	−19.4987	−	11.2576i	−0.889062	−	0.513300i
$482$	−7.07031	−	20.6402i	−0.322044	−	0.940134i
$483$		0			0
$484$	14.8494	−	11.5258i	0.674972	−	0.523900i
$485$	−8.71162	+	15.0890i	−0.395574	+	0.685154i
$486$	−1.06584	−	0.929502i	−0.0483477	−	0.0421631i
$487$	35.9498	−	20.7556i	1.62904	−	0.940528i	0.644662	−	0.764468i	$-0.276998\pi$
$487$	35.9498	−	20.7556i	1.62904	−	0.940528i	0.984379	−	0.176060i	$-0.0563352\pi$
$488$	28.0473	−	14.1228i	1.26964	−	0.639310i
$489$			12.0357i			0.544274i
$490$		0			0
$491$			1.72728i			0.0779509i	0.999240	+	0.0389755i	$0.0124094\pi$
$491$			1.72728i			0.0779509i	−0.999240	+	0.0389755i	$0.987591\pi$
$492$	2.15906	−	0.296442i	0.0973380	−	0.0133646i
$493$	14.9602	−	8.63729i	0.673774	−	0.389004i
$494$	11.5899	−	13.2899i	0.521454	−	0.597943i
$495$	1.55176	−	2.68773i	0.0697465	−	0.120805i
$496$	−9.36745	+	36.5787i	−0.420611	+	1.64243i
$497$		0			0
$498$	−7.13935	+	2.44559i	−0.319922	+	0.109590i
$499$	36.6216	+	21.1435i	1.63941	+	0.946514i	0.981037	+	0.193822i	$0.0620886\pi$
$499$	36.6216	+	21.1435i	1.63941	+	0.946514i	0.658373	+	0.752691i	$0.271245\pi$
$500$	7.37953	−	18.0991i	0.330023	−	0.809419i
$501$	3.73212	+	6.46422i	0.166739	+	0.288800i
$502$	−6.06547	+	30.9415i	−0.270715	+	1.38099i
$503$	4.23770			0.188950			0.0944748	−	0.995527i	$-0.469883\pi$
$503$	4.23770			0.188950			0.0944748	+	0.995527i	$0.469883\pi$
$504$		0			0
$505$	2.28906			0.101862
$506$	−2.31971	+	11.8334i	−0.103124	+	0.526060i
$507$	−2.00766	−	3.47737i	−0.0891634	−	0.154436i
$508$	4.82010	−	11.8219i	0.213858	−	0.524510i
$509$	36.1788	+	20.8878i	1.60360	+	0.925836i	0.990760	+	0.135626i	$0.0433046\pi$
$509$	36.1788	+	20.8878i	1.60360	+	0.925836i	0.612836	+	0.790210i	$0.290029\pi$
$510$	6.01532	−	2.06056i	0.266363	−	0.0912429i
$511$		0			0
$512$	−22.2959	−	3.85896i	−0.985350	−	0.170544i
$513$	−2.07993	+	3.60254i	−0.0918310	+	0.159056i
$514$	2.66745	−	3.05872i	0.117656	−	0.134914i
$515$	−8.77055	+	5.06368i	−0.386476	+	0.223132i
$516$	−12.4269	+	1.70624i	−0.547066	+	0.0751128i
$517$		−	9.30265i		−	0.409130i
$518$		0			0
$519$			4.36398i			0.191557i
$520$	−9.35158	−	18.5719i	−0.410094	−	0.814430i
$521$	−30.2681	+	17.4753i	−1.32607	+	0.765607i	−0.984689	−	0.174318i	$-0.944228\pi$
$521$	−30.2681	+	17.4753i	−1.32607	+	0.765607i	−0.341381	+	0.939925i	$0.610895\pi$
$522$	10.0437	+	8.75892i	0.439601	+	0.383367i
$523$	6.13503	−	10.6262i	0.268266	−	0.464651i	−0.700148	−	0.713998i	$-0.746883\pi$
$523$	6.13503	−	10.6262i	0.268266	−	0.464651i	0.968414	+	0.249347i	$0.0802160\pi$
$524$	6.11751	−	4.74829i	0.267245	−	0.207430i
$525$		0			0
$526$	−4.75317	−	13.8758i	−0.207248	−	0.605014i
$527$	−14.9865	−	8.65246i	−0.652822	−	0.376907i
$528$	−1.36420	−	4.87427i	−0.0593694	−	0.212125i
$529$	11.2032	+	19.4044i	0.487094	+	0.843671i
$530$	0.243886	+	0.0478090i	0.0105937	+	0.00207669i
$531$	−3.36690			−0.146111
$532$		0			0
$533$	3.26619			0.141474
$534$	−11.8957	−	2.33191i	−0.514776	−	0.100912i
$535$	16.9750	+	29.4016i	0.733893	+	1.27114i
$536$	0.453415	−	7.92832i	0.0195846	−	0.342451i
$537$	21.2754	+	12.2834i	0.918102	+	0.530067i
$538$	−2.37086	−	6.92118i	−0.102215	−	0.298393i
$539$		0			0
$540$	3.00766	+	3.87495i	0.129429	+	0.166751i
$541$	0.467883	−	0.810397i	0.0201158	−	0.0348417i	−0.855792	−	0.517320i	$-0.826930\pi$
$541$	0.467883	−	0.810397i	0.0201158	−	0.0348417i	0.875908	+	0.482478i	$0.160263\pi$
$542$	−25.8351	−	22.5303i	−1.10971	−	0.967757i
$543$	10.1483	−	5.85912i	0.435505	−	0.251439i
$544$	4.45712	−	9.36337i	0.191098	−	0.401451i
$545$		−	2.41503i		−	0.103449i
$546$		0			0
$547$		−	7.13048i		−	0.304877i	−0.988313	−	0.152439i	$-0.951287\pi$
$547$		−	7.13048i		−	0.304877i	0.988313	−	0.152439i	$-0.0487127\pi$
$548$	−4.00000	−	29.1330i	−0.170872	−	1.24450i
$549$	−9.61496	+	5.55120i	−0.410356	+	0.236919i
$550$	−1.19421	+	1.36938i	−0.0509213	+	0.0583906i
$551$	19.5996	−	33.9476i	0.834973	−	1.44621i
$552$	−15.9347	−	10.4564i	−0.678224	−	0.445055i
$553$		0			0
$554$	−4.03419	+	1.38192i	−0.171396	+	0.0587120i
$555$	−15.9545	−	9.21133i	−0.677231	−	0.390999i
$556$	−3.73460	−	1.52270i	−0.158382	−	0.0645769i
$557$	−4.97622	−	8.61907i	−0.210849	−	0.365202i	0.741131	−	0.671360i	$-0.234290\pi$
$557$	−4.97622	−	8.61907i	−0.210849	−	0.365202i	−0.951981	+	0.306159i	$0.900956\pi$
$558$	2.56810	−	13.1005i	0.108716	−	0.554590i
$559$	−18.7993			−0.795124
$560$		0			0
$561$	2.31971			0.0979381
$562$	1.88238	−	9.60249i	0.0794032	−	0.405057i
$563$	0.844531	+	1.46277i	0.0355927	+	0.0616484i	0.883273	−	0.468859i	$-0.155335\pi$
$563$	0.844531	+	1.46277i	0.0355927	+	0.0616484i	−0.847680	+	0.530507i	$0.822001\pi$
$564$	13.6150	+	5.55120i	0.573293	+	0.233748i
$565$	−10.6878	−	6.17063i	−0.449641	−	0.259600i
$566$	27.5258	−	9.42899i	1.15700	−	0.396330i
$567$		0			0
$568$	6.91180	+	4.53557i	0.290013	+	0.190308i
$569$	6.96935	−	12.0713i	0.292170	−	0.506054i	−0.682152	−	0.731210i	$-0.738956\pi$
$569$	6.96935	−	12.0713i	0.292170	−	0.506054i	0.974323	+	0.225156i	$0.0722892\pi$
$570$	9.48327	−	10.8743i	0.397210	−	0.455475i
$571$	16.1591	−	9.32947i	0.676238	−	0.390426i	−0.122198	−	0.992506i	$-0.538994\pi$
$571$	16.1591	−	9.32947i	0.676238	−	0.390426i	0.798436	+	0.602079i	$0.205661\pi$
$572$	−1.03187	−	7.51539i	−0.0431448	−	0.314234i
$573$		−	15.8919i		−	0.663893i
$574$		0			0
$575$			6.84168i			0.285318i
$576$	7.94784	+	0.912047i	0.331160	+	0.0380019i
$577$	−29.4591	+	17.0082i	−1.22640	+	0.708062i	−0.966275	−	0.257513i	$-0.917097\pi$
$577$	−29.4591	+	17.0082i	−1.22640	+	0.708062i	−0.260125	+	0.965575i	$0.583764\pi$
$578$	−14.5375	−	12.6779i	−0.604680	−	0.527330i
$579$	−9.86690	+	17.0900i	−0.410055	+	0.710235i
$580$	−28.3419	−	36.5146i	−1.17683	−	1.51619i
$581$		0			0
$582$	−3.25572	−	9.50433i	−0.134954	−	0.393967i
$583$	0.0785213	+	0.0453343i	0.00325202	+	0.00187755i
$584$	−1.30889	+	22.8869i	−0.0541621	+	0.947066i
$585$	3.67579	+	6.36666i	0.151975	+	0.263229i
$586$	39.2904	+	7.70210i	1.62307	+	0.318171i
$587$	−41.9153			−1.73003			−0.865015	−	0.501746i	$-0.832691\pi$
$587$	−41.9153			−1.73003			−0.865015	+	0.501746i	$0.832691\pi$
$588$		0			0
$589$	−39.2681			−1.61801
$590$	11.4601	+	2.24652i	0.471804	+	0.0924876i
$591$	−0.499388	−	0.864965i	−0.0205421	−	0.0355799i
$592$	−28.9339	+	8.09798i	−1.18917	+	0.332825i
$593$	−21.1354	−	12.2025i	−0.867927	−	0.501098i	−0.00126806	−	0.999999i	$-0.500404\pi$
$593$	−21.1354	−	12.2025i	−0.867927	−	0.501098i	−0.866659	+	0.498901i	$0.833737\pi$
$594$	0.579927	+	1.69296i	0.0237947	+	0.0694632i
$595$		0			0
$596$	−0.783818	+	0.608384i	−0.0321064	+	0.0249204i
$597$	−1.35158	+	2.34101i	−0.0553165	+	0.0958110i
$598$	−21.5280	−	18.7741i	−0.880345	−	0.767731i
$599$	18.0000	−	10.3923i	0.735460	−	0.424618i	−0.0849563	−	0.996385i	$-0.527075\pi$
$599$	18.0000	−	10.3923i	0.735460	−	0.424618i	0.820416	+	0.571767i	$0.193742\pi$
$600$	−1.29154	−	2.56495i	−0.0527270	−	0.104714i
$601$		−	10.6623i		−	0.434924i	−0.976069	−	0.217462i	$-0.930222\pi$
$601$		−	10.6623i		−	0.434924i	0.976069	−	0.217462i	$-0.0697778\pi$
$602$		0			0
$603$			2.80766i			0.114337i
$604$	−26.2279	+	3.60113i	−1.06720	+	0.146528i
$605$	19.9633	−	11.5258i	0.811622	−	0.468590i
$606$	−0.867517	+	0.994767i	−0.0352405	+	0.0404097i
$607$	20.0215	−	34.6782i	0.812646	−	1.40754i	−0.0983597	−	0.995151i	$-0.531360\pi$
$607$	20.0215	−	34.6782i	0.812646	−	1.40754i	0.911006	−	0.412393i	$-0.135307\pi$
$608$	−1.86460	−	23.4577i	−0.0756196	−	0.951335i
$609$		0			0
$610$	36.4308	−	12.4794i	1.47504	−	0.505276i
$611$	19.0837	+	11.0180i	0.772044	+	0.445740i
$612$	−1.38425	+	3.39503i	−0.0559549	+	0.137236i
$613$	−11.2481	−	19.4822i	−0.454305	−	0.786879i	0.544343	−	0.838863i	$-0.316779\pi$
$613$	−11.2481	−	19.4822i	−0.454305	−	0.786879i	−0.998648	+	0.0519838i	$0.983446\pi$
$614$	2.35486	−	12.0127i	0.0950343	−	0.484795i
$615$	2.67251			0.107766
$616$		0			0
$617$	−18.0820			−0.727954			−0.363977	−	0.931408i	$-0.618581\pi$
$617$	−18.0820			−0.727954			−0.363977	+	0.931408i	$0.618581\pi$
$618$	1.12335	−	5.73051i	0.0451878	−	0.230515i
$619$	16.0465	+	27.7933i	0.644962	+	1.11711i	0.984310	+	0.176446i	$0.0564601\pi$
$619$	16.0465	+	27.7933i	0.644962	+	1.11711i	−0.339348	+	0.940661i	$0.610207\pi$
$620$	−17.4823	+	42.8773i	−0.702105	+	1.72199i
$621$	5.83564	+	3.36921i	0.234176	+	0.135202i
$622$	12.4994	−	4.28168i	0.501180	−	0.171680i
$623$		0			0
$624$	11.6150	+	2.97448i	0.464971	+	0.119074i
$625$	14.5229	−	25.1543i	0.580915	−	1.00617i
$626$	−6.85552	+	7.86111i	−0.274002	+	0.314193i
$627$	4.55863	−	2.63193i	0.182054	−	0.105109i
$628$	10.0291	−	1.37700i	0.400203	−	0.0549484i
$629$		−	13.7699i		−	0.549041i
$630$		0			0
$631$			2.95509i			0.117640i	0.998269	+	0.0588201i	$0.0187338\pi$
$631$			2.95509i			0.117640i	−0.998269	+	0.0588201i	$0.981266\pi$
$632$	4.50601	−	2.26893i	0.179239	−	0.0902533i
$633$	−15.7442	+	9.08990i	−0.625774	+	0.361291i
$634$	3.86932	+	3.37436i	0.153670	+	0.134013i
$635$	7.82798	−	13.5585i	0.310644	−	0.538051i
$636$	−0.113206	+	0.0878679i	−0.00448889	+	0.00348419i
$637$		0			0
$638$	−5.46479	−	15.9532i	−0.216353	−	0.631593i
$639$	−2.53126	−	1.46142i	−0.100135	−	0.0578130i
$640$	−26.4438	−	8.40745i	−1.04528	−	0.332334i
$641$	20.7459	+	35.9329i	0.819412	+	1.41926i	0.906116	+	0.423029i	$0.139033\pi$
$641$	20.7459	+	35.9329i	0.819412	+	1.41926i	−0.0867040	+	0.996234i	$0.527633\pi$
$642$	−19.2104	−	3.76582i	−0.758175	−	0.148625i
$643$	16.7686			0.661290			0.330645	−	0.943755i	$-0.392734\pi$
$643$	16.7686			0.661290			0.330645	+	0.943755i	$0.392734\pi$
$644$		0			0
$645$	−15.3822			−0.605675
$646$	10.5831	+	2.07460i	0.416386	+	0.0816241i
$647$	9.31180	+	16.1285i	0.366085	+	0.634077i	0.988950	−	0.148252i	$-0.0473647\pi$
$647$	9.31180	+	16.1285i	0.366085	+	0.634077i	−0.622865	+	0.782329i	$0.714031\pi$
$648$	−2.82381	−	0.161492i	−0.110930	−	0.00634401i
$649$	3.68967	+	2.13023i	0.144832	+	0.0836189i
$650$	−1.39477	−	4.07172i	−0.0547075	−	0.159706i
$651$		0			0
$652$	14.7595	+	19.0155i	0.578026	+	0.744706i
$653$	−12.8305	+	22.2230i	−0.502095	+	0.869654i	0.497902	+	0.867233i	$0.334104\pi$
$653$	−12.8305	+	22.2230i	−0.502095	+	0.869654i	−0.999997	+	0.00242072i	$0.999229\pi$
$654$	1.04951	+	0.915259i	0.0410392	+	0.0357894i
$655$	8.22428	−	4.74829i	0.321349	−	0.185531i
$656$	3.04763	−	3.11603i	0.118990	−	0.121661i
$657$		−	8.10495i		−	0.316204i
$658$		0			0
$659$			27.7044i			1.07921i	0.841919	+	0.539604i	$0.181426\pi$
$659$			27.7044i			1.07921i	−0.841919	+	0.539604i	$0.818574\pi$
$660$	−0.844315	−	6.14936i	−0.0328649	−	0.239363i
$661$	29.5472	−	17.0591i	1.14925	−	0.663522i	0.200548	−	0.979684i	$-0.435728\pi$
$661$	29.5472	−	17.0591i	1.14925	−	0.663522i	0.948705	+	0.316162i	$0.102394\pi$
$662$	−0.584050	+	0.669720i	−0.0226997	+	0.0260294i
$663$	−2.74744	+	4.75871i	−0.106702	+	0.184813i
$664$	−8.28060	+	12.6189i	−0.321350	+	0.489708i
$665$		0			0
$666$	10.0495	−	3.44247i	0.389411	−	0.133393i
$667$	−54.9906	−	31.7489i	−2.12925	−	1.22932i
$668$	13.8236	+	5.63627i	0.534851	+	0.218074i
$669$	−5.79982	−	10.0456i	−0.224234	−	0.388385i
$670$	1.87337	−	9.55655i	0.0723746	−	0.369202i
$671$	14.0489			0.542352
$672$		0			0
$673$	−17.7032			−0.682407			−0.341203	−	0.939990i	$-0.610834\pi$
$673$	−17.7032			−0.682407			−0.341203	+	0.939990i	$0.610834\pi$
$674$	6.06997	−	30.9645i	0.233806	−	1.19271i
$675$	0.507662	+	0.879296i	0.0195399	+	0.0338441i
$676$	−7.43629	−	3.03198i	−0.286011	−	0.116615i
$677$	35.5808	+	20.5426i	1.36748	+	0.789516i	0.990606	−	0.136747i	$-0.0436649\pi$
$677$	35.5808	+	20.5426i	1.36748	+	0.789516i	0.376876	+	0.926264i	$0.376998\pi$
$678$	6.73212	−	2.30609i	0.258545	−	0.0885650i
$679$		0			0
$680$	6.97690	−	10.6322i	0.267552	−	0.407725i
$681$	−5.08054	+	8.79975i	−0.194687	+	0.337207i
$682$	−11.1029	+	12.7316i	−0.425154	+	0.487517i
$683$	18.3842	−	10.6141i	0.703450	−	0.406137i	−0.105181	−	0.994453i	$-0.533542\pi$
$683$	18.3842	−	10.6141i	0.703450	−	0.406137i	0.808631	+	0.588316i	$0.200209\pi$
$684$	1.13169	+	8.24238i	0.0432712	+	0.315155i
$685$		−	36.0612i		−	1.37783i
$686$		0			0
$687$			23.0970i			0.881204i
$688$	−17.5413	+	17.9350i	−0.668755	+	0.683765i
$689$	−0.186000	+	0.107387i	−0.00708603	+	0.00409112i
$690$	−17.6150	−	15.3617i	−0.670590	−	0.584809i
$691$	−19.4878	+	33.7539i	−0.741352	+	1.28406i	0.210528	+	0.977588i	$0.432482\pi$
$691$	−19.4878	+	33.7539i	−0.741352	+	1.28406i	−0.951880	+	0.306472i	$0.900851\pi$
$692$	5.35158	+	6.89477i	0.203437	+	0.262100i
$693$		0			0
$694$	3.15985	+	9.22447i	0.119946	+	0.350156i
$695$	−4.28321	−	2.47291i	−0.162471	−	0.0938028i
$696$	26.6094	+	1.52178i	1.00863	+	0.0576828i
$697$	0.998775	+	1.72993i	0.0378313	+	0.0655257i
$698$	−18.7032	−	3.66638i	−0.707925	−	0.138775i
$699$	−6.85547			−0.259298
$700$		0			0
$701$	4.28115			0.161697			0.0808485	−	0.996726i	$-0.474237\pi$
$701$	4.28115			0.161697			0.0808485	+	0.996726i	$0.474237\pi$
$702$	−4.15985	−	0.815456i	−0.157004	−	0.0307774i
$703$	−15.6232	−	27.0602i	−0.589241	−	1.02060i
$704$	−8.13270	−	6.02805i	−0.306513	−	0.227191i
$705$	15.6150	+	9.01530i	0.588093	+	0.339536i
$706$	13.1002	+	38.2432i	0.493034	+	1.43930i
$707$		0			0
$708$	−5.31946	+	4.12886i	−0.199918	+	0.155172i
$709$	21.8796	−	37.8965i	0.821704	−	1.42323i	−0.0827080	−	0.996574i	$-0.526357\pi$
$709$	21.8796	−	37.8965i	0.821704	−	1.42323i	0.904412	−	0.426660i	$-0.140310\pi$
$710$	7.64064	+	6.66325i	0.286748	+	0.250067i
$711$	−1.54471	+	0.891841i	−0.0579313	+	0.0334466i
$712$	−21.6539	+	10.9035i	−0.811516	+	0.408627i
$713$			63.6092i			2.38218i
$714$		0			0
$715$		−	9.30265i		−	0.347899i
$716$	48.6768	−	6.68339i	1.81914	−	0.249770i
$717$	19.2481	−	11.1129i	0.718832	−	0.415018i
$718$	6.43978	−	7.38439i	0.240331	−	0.275583i
$719$	−20.7657	+	35.9672i	−0.774429	+	1.34135i	0.160685	+	0.987006i	$0.448630\pi$
$719$	−20.7657	+	35.9672i	−0.774429	+	1.34135i	−0.935115	+	0.354345i	$0.884704\pi$
$720$	9.50377	+	2.43382i	0.354185	+	0.0907033i
$721$		0			0
$722$	−2.26856	+	0.777097i	−0.0844270	+	0.0289205i
$723$	13.3605	+	7.71367i	0.496881	+	0.286874i
$724$	8.84848	−	21.7019i	0.328851	−	0.806546i
$725$	−4.78382	−	8.28582i	−0.177667	−	0.307727i
$726$	−2.55694	+	13.0436i	−0.0948970	+	0.484094i
$727$	−7.19963			−0.267020			−0.133510	−	0.991047i	$-0.542625\pi$
$727$	−7.19963			−0.267020			−0.133510	+	0.991047i	$0.542625\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.40791	+	27.5872i	−0.200156	+	1.02105i
$731$	−5.74867	−	9.95698i	−0.212622	−	0.368272i
$732$	−8.38345	+	20.5614i	−0.309861	+	0.759971i
$733$	−20.9219	−	12.0793i	−0.772768	−	0.446158i	0.0610934	−	0.998132i	$-0.480541\pi$
$733$	−20.9219	−	12.0793i	−0.772768	−	0.446158i	−0.833861	+	0.551974i	$0.813875\pi$
$734$	−17.3173	+	5.93205i	−0.639192	+	0.218956i
$735$		0			0
$736$	−37.9984	+	3.02041i	−1.40064	+	0.111334i
$737$	1.77640	−	3.07682i	0.0654345	−	0.113336i
$738$	−1.01284	+	1.16141i	−0.0372832	+	0.0427520i
$739$	−8.16690	+	4.71516i	−0.300424	+	0.173450i	−0.642634	−	0.766174i	$-0.722158\pi$
$739$	−8.16690	+	4.71516i	−0.300424	+	0.173450i	0.342209	+	0.939624i	$0.388825\pi$
$740$	−36.5029	+	5.01189i	−1.34187	+	0.184241i
$741$			12.4689i			0.458058i
$742$		0			0
$743$		−	2.32851i		−	0.0854248i	−0.999087	−	0.0427124i	$-0.986400\pi$
$743$		−	2.32851i		−	0.0854248i	0.999087	−	0.0427124i	$-0.0135999\pi$
$744$	−12.0079	−	23.8472i	−0.440230	−	0.874279i
$745$	−1.05375	+	0.608384i	−0.0386065	+	0.0222895i
$746$	−3.28181	−	2.86200i	−0.120156	−	0.104785i
$747$	2.66813	−	4.62133i	0.0976217	−	0.169086i
$748$	3.66497	−	2.84468i	0.134005	−	0.104012i
$749$		0			0
$750$	4.47889	+	13.0751i	0.163546	+	0.477435i
$751$	26.9834	+	15.5789i	0.984638	+	0.568481i	0.903667	−	0.428235i	$-0.140865\pi$
$751$	26.9834	+	15.5789i	0.984638	+	0.568481i	0.0809709	+	0.996716i	$0.474198\pi$
$752$	28.3181	−	7.92564i	1.03266	−	0.289018i
$753$	−11.1477	−	19.3084i	−0.406244	−	0.703636i
$754$	39.1993	+	7.68423i	1.42755	+	0.279843i
$755$	−32.4652			−1.18153
$756$		0			0
$757$	−0.559856			−0.0203483			−0.0101742	−	0.999948i	$-0.503239\pi$
$757$	−0.559856			−0.0203483			−0.0101742	+	0.999948i	$0.503239\pi$
$758$	7.23071	+	1.41744i	0.262631	+	0.0514836i
$759$	−4.26338	−	7.38439i	−0.154751	−	0.268036i
$760$	1.64763	−	28.8100i	0.0597657	−	1.04505i
$761$	−39.6196	−	22.8744i	−1.43621	−	0.829196i	−0.438625	−	0.898670i	$-0.644534\pi$
$761$	−39.6196	−	22.8744i	−1.43621	−	0.829196i	−0.997584	+	0.0694744i	$0.977868\pi$
$762$	2.92548	+	8.54029i	0.105979	+	0.309382i
$763$		0			0
$764$	−19.4883	−	25.1080i	−0.705063	−	0.908376i
$765$	−2.24806	+	3.89375i	−0.0812786	+	0.140779i
$766$	−41.4300	−	36.1303i	−1.49693	−	1.30544i
$767$	−8.74002	+	5.04606i	−0.315584	+	0.182203i
$768$	13.6755	−	8.30553i	0.493471	−	0.299700i
$769$		−	8.33377i		−	0.300524i	−0.988646	−	0.150262i	$-0.951988\pi$
$769$		−	8.33377i		−	0.300524i	0.988646	−	0.150262i	$-0.0480117\pi$
$770$		0			0
$771$			2.86976i			0.103352i
$772$	5.36859	+	39.1008i	0.193220	+	1.40727i
$773$	−26.5674	+	15.3387i	−0.955563	+	0.551695i	−0.894805	−	0.446458i	$-0.852685\pi$
$773$	−26.5674	+	15.3387i	−0.955563	+	0.551695i	−0.0607584	+	0.998153i	$0.519352\pi$
$774$	5.82962	−	6.68473i	0.209541	−	0.240278i
$775$	−4.79222	+	8.30037i	−0.172142	+	0.298158i
$776$	−16.7990	−	11.0236i	−0.603050	−	0.395725i
$777$		0			0
$778$	−4.99708	+	1.71176i	−0.179154	+	0.0613695i
$779$	3.92554	+	2.26641i	0.140647	+	0.0812025i
$780$	13.6150	+	5.55120i	0.487494	+	0.198765i
$781$	1.84928	+	3.20304i	0.0661723	+	0.114614i
$782$	3.36058	−	17.1432i	0.120174	−	0.613040i
$783$	−9.42323			−0.336759
$784$		0			0
$785$	12.4141			0.443078
$786$	−1.05338	+	5.37359i	−0.0375730	+	0.191670i
$787$	11.0792	+	19.1897i	0.394931	+	0.684040i	0.993092	−	0.117335i	$-0.0374353\pi$
$787$	11.0792	+	19.1897i	0.394931	+	0.684040i	−0.598162	+	0.801375i	$0.704102\pi$
$788$	−1.84971	−	0.754178i	−0.0658932	−	0.0268665i
$789$	8.98186	+	5.18568i	0.319763	+	0.184615i
$790$	5.85287	−	2.00491i	0.208236	−	0.0713314i
$791$		0			0
$792$	2.99234	+	1.96359i	0.106328	+	0.0697732i
$793$	−16.6394	+	28.8203i	−0.590883	+	1.02344i
$794$	−6.23674	+	7.15156i	−0.221333	+	0.253799i
$795$	−0.152192	+	0.0878679i	−0.00539768	+	0.00311635i
$796$	0.735396	+	5.35607i	0.0260654	+	0.189841i
$797$			24.1705i			0.856164i	0.903740	+	0.428082i	$0.140811\pi$
$797$			24.1705i			0.856164i	−0.903740	+	0.428082i	$0.859189\pi$
$798$		0			0
$799$			13.4768i			0.476776i
$800$	−5.18597	−	2.46861i	−0.183352	−	0.0872784i
$801$	7.42323	−	4.28581i	0.262287	−	0.151431i
$802$	−6.23273	−	5.43544i	−0.220085	−	0.191932i
$803$	−5.12798	+	8.88192i	−0.180963	+	0.313436i
$804$	3.44306	+	4.43590i	0.121427	+	0.156442i
$805$		0			0
$806$	−12.9676	−	37.8560i	−0.456765	−	1.33342i
$807$	4.48011	+	2.58659i	0.157707	+	0.0910524i
$808$	−0.150723	+	2.63550i	−0.00530241	+	0.0927167i
$809$	−7.61046	−	13.1817i	−0.267569	−	0.463444i	0.700664	−	0.713491i	$-0.252887\pi$
$809$	−7.61046	−	13.1817i	−0.267569	−	0.463444i	−0.968234	+	0.250047i	$0.919554\pi$
$810$	−3.40374	−	0.667235i	−0.119595	−	0.0234442i
$811$	48.4574			1.70157			0.850785	−	0.525515i	$-0.176127\pi$
$811$	48.4574			1.70157			0.850785	+	0.525515i	$0.176127\pi$
$812$		0			0
$813$	24.2391			0.850101
$814$	−13.1909	−	2.58582i	−0.462342	−	0.0906329i
$815$	14.7595	+	25.5642i	0.517002	+	0.895474i
$816$	1.97634	+	7.06141i	0.0691857	+	0.247199i
$817$	−22.5943	−	13.0448i	−0.790474	−	0.456380i
$818$	14.1454	+	41.2942i	0.494581	+	1.44382i
$819$		0			0
$820$	4.22238	−	3.27732i	0.147452	−	0.114449i
$821$	−25.7647	+	44.6257i	−0.899193	+	1.55745i	−0.0706654	+	0.997500i	$0.522512\pi$
$821$	−25.7647	+	44.6257i	−0.899193	+	1.55745i	−0.828528	+	0.559948i	$0.810821\pi$
$822$	15.6713	+	13.6666i	0.546599	+	0.476678i
$823$	−1.90279	+	1.09858i	−0.0663272	+	0.0382941i	−0.532797	−	0.846243i	$-0.678859\pi$
$823$	−1.90279	+	1.09858i	−0.0663272	+	0.0382941i	0.466470	+	0.884537i	$0.345526\pi$
$824$	−5.25256	−	10.4314i	−0.182982	−	0.363394i
$825$		−	1.28479i		−	0.0447305i
$826$		0			0
$827$		−	10.2864i		−	0.357693i	−0.983877	−	0.178846i	$-0.942763\pi$
$827$		−	10.2864i		−	0.357693i	0.983877	−	0.178846i	$-0.0572365\pi$
$828$	13.3516	−	1.83319i	0.464000	−	0.0637078i
$829$	−0.662548	+	0.382522i	−0.0230112	+	0.0132855i	−0.511461	−	0.859306i	$-0.670896\pi$
$829$	−0.662548	+	0.382522i	−0.0230112	+	0.0132855i	0.488450	+	0.872592i	$0.337562\pi$
$830$	−12.1651	+	13.9495i	−0.422258	+	0.484196i
$831$	1.50766	−	2.61135i	0.0523002	−	0.0905866i
$832$	21.9984	−	9.54406i	0.762658	−	0.330881i
$833$		0			0
$834$	2.69793	−	0.924179i	0.0934217	−	0.0320017i
$835$	15.8542	+	9.15345i	0.548659	+	0.316768i
$836$	3.97475	−	9.74854i	0.137470	−	0.337160i
$837$	4.71989	+	8.17509i	0.163143	+	0.282572i
$838$	−7.91302	+	40.3664i	−0.273351	+	1.39443i
$839$	−3.50389			−0.120968			−0.0604839	−	0.998169i	$-0.519264\pi$
$839$	−3.50389			−0.120968			−0.0604839	+	0.998169i	$0.519264\pi$
$840$		0			0
$841$	59.7973			2.06198
$842$	−3.77177	+	19.2408i	−0.129984	+	0.663081i
$843$	3.45961	+	5.99222i	0.119155	+	0.206383i
$844$	−13.7276	+	33.6686i	−0.472524	+	1.15892i
$845$	−8.52866	−	4.92402i	−0.293395	−	0.169392i
$846$	−9.83564	+	3.36921i	−0.338156	+	0.115836i
$847$		0			0
$848$	−0.0711034	+	0.277650i	−0.00244170	+	0.00953453i
$849$	−10.2870	+	17.8176i	−0.353048	+	0.611497i
$850$	1.73007	−	1.98384i	0.0593408	−	0.0680451i
$851$	−43.8341	+	25.3076i	−1.50261	+	0.867534i
$852$	−5.79136	+	0.795162i	−0.198409	+	0.0272418i
$853$		−	25.3974i		−	0.869589i	−0.900530	−	0.434795i	$-0.856821\pi$
$853$		−	25.3974i		−	0.869589i	0.900530	−	0.434795i	$-0.143179\pi$
$854$		0			0
$855$			10.2025i			0.348919i
$856$	−34.9691	+	17.6082i	−1.19522	+	0.601835i
$857$	25.0609	−	14.4689i	0.856065	−	0.494249i	−0.00662744	−	0.999978i	$-0.502110\pi$
$857$	25.0609	−	14.4689i	0.856065	−	0.494249i	0.862693	+	0.505729i	$0.168776\pi$
$858$	4.04270	+	3.52556i	0.138015	+	0.120360i
$859$	2.34404	−	4.05999i	0.0799775	−	0.138525i	−0.823263	−	0.567661i	$-0.807848\pi$
$859$	2.34404	−	4.05999i	0.0799775	−	0.138525i	0.903240	+	0.429136i	$0.141182\pi$
$860$	−24.3028	+	18.8633i	−0.828718	+	0.643235i
$861$		0			0
$862$	14.6195	+	42.6782i	0.497941	+	1.45363i
$863$	37.6419	+	21.7325i	1.28134	+	0.739784i	0.977094	−	0.212808i	$-0.0682609\pi$
$863$	37.6419	+	21.7325i	1.28134	+	0.739784i	0.304250	+	0.952592i	$0.401594\pi$
$864$	−4.65946	+	3.20772i	−0.158518	+	0.109129i
$865$	5.35158	+	9.26921i	0.181959	+	0.315163i
$866$	−13.6315	−	2.67218i	−0.463218	−	0.0908045i
$867$	13.6394			0.463219
$868$		0			0
$869$	2.25706			0.0765655
$870$	32.0742	+	6.28751i	1.08742	+	0.213167i
$871$	4.20791	+	7.28831i	0.142580	+	0.246955i
$872$	2.78054	+	0.159017i	0.0941610	+	0.00538501i
$873$	6.15219	+	3.55197i	0.208220	+	0.120216i
$874$	−12.8465	−	37.5023i	−0.434538	−	1.26854i
$875$		0			0
$876$	−9.93917	−	12.8052i	−0.335813	−	0.432649i
$877$	23.0063	−	39.8481i	0.776868	−	1.34558i	−0.156870	−	0.987619i	$-0.550140\pi$
$877$	23.0063	−	39.8481i	0.776868	−	1.34558i	0.933738	−	0.357956i	$-0.116526\pi$
$878$	18.1618	+	15.8385i	0.612930	+	0.534524i
$879$	−24.5183	+	14.1556i	−0.826982	+	0.477458i
$880$	−8.87496	−	8.68015i	−0.299175	−	0.292608i
$881$		−	40.8047i		−	1.37475i	−0.726304	−	0.687373i	$-0.758764\pi$
$881$		−	40.8047i		−	1.37475i	0.726304	−	0.687373i	$-0.241236\pi$
$882$		0			0
$883$			6.06234i			0.204014i	0.994784	+	0.102007i	$0.0325264\pi$
$883$			6.06234i			0.204014i	−0.994784	+	0.102007i	$0.967474\pi$
$884$	1.49489	+	10.8876i	0.0502784	+	0.366190i
$885$	−7.15140	+	4.12886i	−0.240392	+	0.138790i
$886$	7.83507	−	8.98434i	0.263224	−	0.301835i
$887$	22.1276	−	38.3262i	0.742973	−	1.28687i	−0.208163	−	0.978094i	$-0.566749\pi$
$887$	22.1276	−	38.3262i	0.742973	−	1.28687i	0.951136	−	0.308772i	$-0.0999181\pi$
$888$	11.6560	−	17.7626i	0.391149	−	0.596075i
$889$		0			0
$890$	−28.1264	+	9.63473i	−0.942799	+	0.322957i
$891$	−1.09586	−	0.632697i	−0.0367128	−	0.0211961i
$892$	−21.4823	−	8.75892i	−0.719279	−	0.293270i
$893$	15.2908	+	26.4844i	0.511685	+	0.886265i
$894$	0.134967	−	0.688502i	0.00451397	−	0.0230269i
$895$	60.2528			2.01403
$896$		0			0
$897$	20.1980			0.674393
$898$	−2.62274	+	13.3793i	−0.0875219	+	0.446472i
$899$	−44.4766	−	77.0358i	−1.48338	−	2.56929i
$900$	1.88036	+	0.766674i	0.0626786	+	0.0255558i
$901$	−0.113755	−	0.0656762i	−0.00378971	−	0.00218799i
$902$	1.84475	−	0.631922i	0.0614236	−	0.0210407i
$903$		0			0
$904$	7.80827	−	11.8991i	0.259699	−	0.395759i
$905$	14.3702	−	24.8899i	0.477681	−	0.827368i
$906$	12.3038	−	14.1086i	0.408767	−	0.468726i
$907$	5.54526	−	3.20156i	0.184127	−	0.106306i	−0.405103	−	0.914271i	$-0.632764\pi$
$907$	5.54526	−	3.20156i	0.184127	−	0.106306i	0.589230	+	0.807965i	$0.299431\pi$
$908$	2.76432	+	20.1333i	0.0917373	+	0.668146i
$909$		−	0.933313i		−	0.0309561i
$910$		0			0
$911$		−	48.9687i		−	1.62241i	−0.584765	−	0.811203i	$-0.698813\pi$
$911$		−	48.9687i		−	1.62241i	0.584765	−	0.811203i	$-0.301187\pi$
$912$	11.8957	+	11.6346i	0.393905	+	0.385259i
$913$	−5.84781	+	3.37623i	−0.193534	+	0.111737i
$914$	30.9582	+	26.9981i	1.02401	+	0.893017i
$915$	−13.6150	+	23.5818i	−0.450097	+	0.779590i
$916$	28.3240	+	36.4915i	0.935850	+	1.20571i
$917$		0			0
$918$	−0.840146	−	2.45262i	−0.0277290	−	0.0809484i
$919$	21.2676	+	12.2789i	0.701554	+	0.405042i	0.807926	−	0.589284i	$-0.200590\pi$
$919$	21.2676	+	12.2789i	0.701554	+	0.405042i	−0.106372	+	0.994326i	$0.533923\pi$
$920$	−46.6685	−	2.66894i	−1.53861	−	0.0879923i
$921$	4.32798	+	7.49628i	0.142612	+	0.247011i
$922$	−33.2788	−	6.52365i	−1.09598	−	0.214845i
$923$	−8.76108			−0.288374
$924$		0			0
$925$	−7.62654			−0.250759
$926$	−39.5488	−	7.75276i	−1.29966	−	0.254771i
$927$	2.06460	+	3.57600i	0.0678105	+	0.117451i
$928$	43.9072	−	30.2271i	1.44132	−	0.992253i
$929$	8.51680	+	4.91718i	0.279427	+	0.161327i	0.633164	−	0.774018i	$-0.281756\pi$
$929$	8.51680	+	4.91718i	0.279427	+	0.161327i	−0.353737	+	0.935345i	$0.615089\pi$
$930$	−10.6106	−	30.9752i	−0.347934	−	1.01572i
$931$		0			0
$932$	−10.8311	+	8.40692i	−0.354786	+	0.275378i
$933$	−4.67129	+	8.09091i	−0.152931	+	0.264884i
$934$	19.8050	+	17.2716i	0.648039	+	0.565142i
$935$	4.92712	−	2.84468i	0.161134	−	0.0930308i
$936$	−7.57226	+	3.81290i	−0.247507	+	0.124629i
$937$			38.1447i			1.24613i	0.782168	+	0.623067i	$0.214114\pi$
$937$			38.1447i			1.24613i	−0.782168	+	0.623067i	$0.785886\pi$
$938$		0			0
$939$		−	7.37547i		−	0.240689i
$940$	35.7260	−	4.90523i	1.16525	−	0.159991i
$941$	−29.7788	+	17.1928i	−0.970760	+	0.560469i	−0.899468	−	0.436987i	$-0.856046\pi$
$941$	−29.7788	+	17.1928i	−0.970760	+	0.560469i	−0.0712922	+	0.997455i	$0.522712\pi$
$942$	−4.70475	+	5.39485i	−0.153289	+	0.175774i
$943$	3.67129	−	6.35886i	0.119554	−	0.207073i
$944$	−3.34111	+	13.0466i	−0.108744	+	0.424631i
$945$		0			0
$946$	−10.6179	+	3.63716i	−0.345217	+	0.118254i
$947$	−14.2630	−	8.23476i	−0.463486	−	0.267594i	0.250023	−	0.968240i	$-0.419562\pi$
$947$	−14.2630	−	8.23476i	−0.463486	−	0.267594i	−0.713509	+	0.700646i	$0.752895\pi$
$948$	−1.34686	+	3.30334i	−0.0437441	+	0.107287i
$949$	−12.1471	−	21.0394i	−0.394311	−	0.682966i
$950$	1.14903	−	5.86151i	0.0372795	−	0.190173i
$951$	−3.63028			−0.117720
$952$		0			0
$953$	−52.4540			−1.69915			−0.849576	−	0.527466i	$-0.823142\pi$
$953$	−52.4540			−1.69915			−0.849576	+	0.527466i	$0.823142\pi$
$954$	0.0194931	−	0.0994392i	0.000631111	−	0.00321946i
$955$	−19.4883	−	33.7548i	−0.630628	−	1.09228i
$956$	16.7827	−	41.1616i	0.542792	−	1.33126i
$957$	10.3266	+	5.96205i	0.333811	+	0.192726i
$958$	−37.9178	+	12.9888i	−1.22507	+	0.419648i
$959$		0			0
$960$	17.9999	−	7.80929i	0.580944	−	0.252044i
$961$	−29.0547	+	50.3243i	−0.937250	+	1.62336i
$962$	20.9279	−	23.9976i	0.674741	−	0.773714i
$963$	11.9878	−	6.92118i	0.386303	−	0.223032i
$964$	30.5679	−	4.19701i	0.984526	−	0.135177i
$965$			48.3995i			1.55803i
$966$		0			0
$967$		−	16.3573i		−	0.526016i	−0.964794	−	0.263008i	$-0.915285\pi$
$967$		−	16.3573i		−	0.526016i	0.964794	−	0.263008i	$-0.0847146\pi$
$968$	11.9557	+	23.7436i	0.384271	+	0.763147i
$969$	−6.60414	+	3.81290i	−0.212155	+	0.122488i
$970$	−18.5705	−	16.1949i	−0.596262	−	0.519988i
$971$	−11.6591	+	20.1942i	−0.374159	+	0.648063i	−0.990201	−	0.139651i	$-0.955402\pi$
$971$	−11.6591	+	20.1942i	−0.374159	+	0.648063i	0.616042	+	0.787714i	$0.288735\pi$
$972$	1.57993	−	1.22631i	0.0506762	−	0.0393338i
$973$		0			0
$974$	19.0245	+	55.5377i	0.609585	+	1.77954i
$975$	2.63564	+	1.52169i	0.0844081	+	0.0487331i
$976$	11.9694	+	42.7662i	0.383130	+	1.36891i
$977$	−19.9922	−	34.6275i	−0.639608	−	1.10783i	−0.985519	−	0.169566i	$-0.945763\pi$
$977$	−19.9922	−	34.6275i	−0.639608	−	1.10783i	0.345911	−	0.938267i	$-0.387570\pi$
$978$	−16.7032	−	3.27432i	−0.534108	−	0.104701i
$979$	−10.8465			−0.346655
$980$		0			0
$981$	−0.984676			−0.0314383
$982$	−2.39712	−	0.469906i	−0.0764950	−	0.0149953i
$983$	10.7628	+	18.6417i	0.343279	+	0.594577i	0.985040	−	0.172328i	$-0.0551290\pi$
$983$	10.7628	+	18.6417i	0.343279	+	0.594577i	−0.641761	+	0.766905i	$0.721796\pi$
$984$	−0.175971	+	3.07699i	−0.00560975	+	0.0980909i
$985$	−2.12143	−	1.22481i	−0.0675943	−	0.0390256i
$986$	7.91689	+	23.1116i	0.252125	+	0.736022i
$987$		0			0
$988$	15.2908	+	19.7000i	0.486464	+	0.626741i
$989$	−21.1309	+	36.5998i	−0.671923	+	1.16381i
$990$	3.30788	+	2.88473i	0.105131	+	0.0916829i
$991$	−9.69666	+	5.59837i	−0.308025	+	0.177838i	−0.646042	−	0.763302i	$-0.723577\pi$
$991$	−9.69666	+	5.59837i	−0.308025	+	0.177838i	0.338018	+	0.941140i	$0.390244\pi$
$992$	−48.2155	−	22.9514i	−1.53084	−	0.728708i
$993$		−	0.628347i		−	0.0199400i
$994$		0			0
$995$			6.62982i			0.210179i
$996$	−1.45173	−	10.5733i	−0.0459998	−	0.335028i
$997$	49.1699	−	28.3883i	1.55723	−	0.899066i	0.559707	−	0.828690i	$-0.310914\pi$
$997$	49.1699	−	28.3883i	1.55723	−	0.899066i	0.997521	−	0.0703755i	$-0.0224197\pi$
$998$	−39.3059	+	45.0714i	−1.24421	+	1.42671i
$999$	−3.75572	+	6.50509i	−0.118826	+	0.205812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.b.19.2		8
4.3	odd	2		588.2.o.d.19.1		8
7.2	even	3		588.2.b.b.391.7		8
7.3	odd	6		588.2.o.d.31.1		8
7.4	even	3		84.2.o.a.31.1	yes	8
7.5	odd	6		588.2.b.a.391.7		8
7.6	odd	2		84.2.o.b.19.2	yes	8
21.2	odd	6		1764.2.b.i.1567.2		8
21.5	even	6		1764.2.b.j.1567.2		8
21.11	odd	6		252.2.bf.g.199.4		8
21.20	even	2		252.2.bf.f.19.3		8
28.3	even	6	inner	588.2.o.b.31.2		8
28.11	odd	6		84.2.o.b.31.2	yes	8
28.19	even	6		588.2.b.b.391.8		8
28.23	odd	6		588.2.b.a.391.8		8
28.27	even	2		84.2.o.a.19.1	✓	8
56.11	odd	6		1344.2.bl.i.703.1		8
56.13	odd	2		1344.2.bl.i.1279.1		8
56.27	even	2		1344.2.bl.j.1279.1		8
56.53	even	6		1344.2.bl.j.703.1		8
84.11	even	6		252.2.bf.f.199.3		8
84.23	even	6		1764.2.b.j.1567.1		8
84.47	odd	6		1764.2.b.i.1567.1		8
84.83	odd	2		252.2.bf.g.19.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.1	✓	8	28.27	even	2
84.2.o.a.31.1	yes	8	7.4	even	3
84.2.o.b.19.2	yes	8	7.6	odd	2
84.2.o.b.31.2	yes	8	28.11	odd	6
252.2.bf.f.19.3		8	21.20	even	2
252.2.bf.f.199.3		8	84.11	even	6
252.2.bf.g.19.4		8	84.83	odd	2
252.2.bf.g.199.4		8	21.11	odd	6
588.2.b.a.391.7		8	7.5	odd	6
588.2.b.a.391.8		8	28.23	odd	6
588.2.b.b.391.7		8	7.2	even	3
588.2.b.b.391.8		8	28.19	even	6
588.2.o.b.19.2		8	1.1	even	1	trivial
588.2.o.b.31.2		8	28.3	even	6	inner
588.2.o.d.19.1		8	4.3	odd	2
588.2.o.d.31.1		8	7.3	odd	6
1344.2.bl.i.703.1		8	56.11	odd	6
1344.2.bl.i.1279.1		8	56.13	odd	2
1344.2.bl.j.703.1		8	56.53	even	6
1344.2.bl.j.1279.1		8	56.27	even	2
1764.2.b.i.1567.1		8	84.47	odd	6
1764.2.b.i.1567.2		8	21.2	odd	6
1764.2.b.j.1567.1		8	84.23	even	6
1764.2.b.j.1567.2		8	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.272050 + 1.38780i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.85198 - 0.755103i) q^{4} +(-2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(1.55176 - 2.36475i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.272050 + 1.38780i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.85198 - 0.755103i) q^{4} +(-2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(1.55176 - 2.36475i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.27971 - 2.61411i) q^{10} +(1.09586 - 0.632697i) q^{11} +(0.272050 + 1.98141i) q^{12} +2.99744i q^{13} +2.45262i q^{15} +(2.85964 + 2.79687i) q^{16} +(-1.58759 + 0.916595i) q^{17} +(-1.06584 - 0.929502i) q^{18} +(-2.07993 + 3.60254i) q^{19} +(3.00766 + 3.87495i) q^{20} +(0.579927 + 1.69296i) q^{22} +(5.83564 + 3.36921i) q^{23} +(-2.82381 - 0.161492i) q^{24} +(0.507662 + 0.879296i) q^{25} +(-4.15985 - 0.815456i) q^{26} +1.00000 q^{27} -9.42323 q^{29} +(-3.40374 - 0.667235i) q^{30} +(4.71989 + 8.17509i) q^{31} +(-4.65946 + 3.20772i) q^{32} +(-1.09586 - 0.632697i) q^{33} +(-0.840146 - 2.45262i) q^{34} +(1.57993 - 1.22631i) q^{36} +(-3.75572 + 6.50509i) q^{37} +(-4.43376 - 3.86659i) q^{38} +(2.59586 - 1.49872i) q^{39} +(-6.19590 + 3.11985i) q^{40} -1.08966i q^{41} +6.27176i q^{43} +(-2.50727 + 0.344251i) q^{44} +(2.12403 - 1.22631i) q^{45} +(-6.26338 + 7.18211i) q^{46} +(3.67579 - 6.36666i) q^{47} +(0.992338 - 3.87495i) q^{48} +(-1.35840 + 0.465320i) q^{50} +(1.58759 + 0.916595i) q^{51} +(2.26338 - 5.55120i) q^{52} +(0.0358262 + 0.0620528i) q^{53} +(-0.272050 + 1.38780i) q^{54} -3.10353 q^{55} +4.15985 q^{57} +(2.56359 - 13.0776i) q^{58} +(1.68345 + 2.91583i) q^{59} +(1.85198 - 4.54219i) q^{60} +(9.61496 + 5.55120i) q^{61} +(-12.6294 + 4.32623i) q^{62} +(-3.18406 - 7.33906i) q^{64} +(3.67579 - 6.36666i) q^{65} +(1.17619 - 1.34871i) q^{66} +(2.43151 - 1.40383i) q^{67} +(3.63230 - 0.498720i) q^{68} -6.73842i q^{69} +2.92285i q^{71} +(1.27205 + 2.52624i) q^{72} +(-7.01910 + 4.05248i) q^{73} +(-8.00602 - 6.98190i) q^{74} +(0.507662 - 0.879296i) q^{75} +(6.57226 - 5.10126i) q^{76} +(1.37372 + 4.01027i) q^{78} +(1.54471 + 0.891841i) q^{79} +(-2.64413 - 9.44742i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.51223 + 0.296442i) q^{82} -5.33626 q^{83} +4.49611 q^{85} +(-8.70395 - 1.70624i) q^{86} +(4.71162 + 8.16076i) q^{87} +(0.204351 - 3.57324i) q^{88} +(-7.42323 - 4.28581i) q^{89} +(1.12403 + 3.28134i) q^{90} +(-8.26338 - 10.6462i) q^{92} +(4.71989 - 8.17509i) q^{93} +(7.83564 + 6.83331i) q^{94} +(8.83564 - 5.10126i) q^{95} +(5.10769 + 2.43135i) q^{96} -7.10394i q^{97} +1.26539i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9} + 13 q^{10} - 6 q^{11} - q^{12} + 7 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 6 q^{22} - 11 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} - 16 q^{29} - 5 q^{30} + 6 q^{31} + 21 q^{32} + 6 q^{33} - 28 q^{34} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 6 q^{39} + 13 q^{40} + 19 q^{44} - 12 q^{46} + 4 q^{47} + 10 q^{48} + 2 q^{50} - 20 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 12 q^{57} - 23 q^{58} - 14 q^{59} + q^{60} - 12 q^{61} - 48 q^{62} + 2 q^{64} + 4 q^{65} + 21 q^{66} - 42 q^{67} + 10 q^{68} + 7 q^{72} + 18 q^{73} - 28 q^{74} + 2 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{79} + 33 q^{80} - 4 q^{81} + 14 q^{82} + 4 q^{83} - 32 q^{85} - 42 q^{86} + 8 q^{87} + 11 q^{88} - 8 q^{90} - 28 q^{92} + 6 q^{93} + 16 q^{94} + 24 q^{95} - 9 q^{96}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9 + 13 * q^10 - 6 * q^11 - q^12 + 7 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 6 * q^22 - 11 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 - 16 * q^29 - 5 * q^30 + 6 * q^31 + 21 * q^32 + 6 * q^33 - 28 * q^34 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 6 * q^39 + 13 * q^40 + 19 * q^44 - 12 * q^46 + 4 * q^47 + 10 * q^48 + 2 * q^50 - 20 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 12 * q^57 - 23 * q^58 - 14 * q^59 + q^60 - 12 * q^61 - 48 * q^62 + 2 * q^64 + 4 * q^65 + 21 * q^66 - 42 * q^67 + 10 * q^68 + 7 * q^72 + 18 * q^73 - 28 * q^74 + 2 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^79 + 33 * q^80 - 4 * q^81 + 14 * q^82 + 4 * q^83 - 32 * q^85 - 42 * q^86 + 8 * q^87 + 11 * q^88 - 8 * q^90 - 28 * q^92 + 6 * q^93 + 16 * q^94 + 24 * q^95 - 9 * q^96

Introduction

L-functions

Modular forms

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