LMFDB - Embedded newform 1014.2.e.j.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.j.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.633975 + 1.09808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.633975 + 1.09808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.866025 + 1.50000i) q^{10} +(-0.633975 - 1.09808i) q^{11} -1.00000 q^{12} -1.26795 q^{14} +(0.866025 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 4.50000i) q^{17} -1.00000 q^{18} +(-2.36603 + 4.09808i) q^{19} +(-0.866025 + 1.50000i) q^{20} -1.26795 q^{21} +(0.633975 - 1.09808i) q^{22} +(4.09808 + 7.09808i) q^{23} +(-0.500000 - 0.866025i) q^{24} -2.00000 q^{25} -1.00000 q^{27} +(-0.633975 - 1.09808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.866025 + 1.50000i) q^{30} +9.46410 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.633975 - 1.09808i) q^{33} -5.19615 q^{34} +(-1.09808 + 1.90192i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.50000 - 2.59808i) q^{37} -4.73205 q^{38} -1.73205 q^{40} +(-3.23205 - 5.59808i) q^{41} +(-0.633975 - 1.09808i) q^{42} +(2.09808 - 3.63397i) q^{43} +1.26795 q^{44} +(-0.866025 + 1.50000i) q^{45} +(-4.09808 + 7.09808i) q^{46} -4.73205 q^{47} +(0.500000 - 0.866025i) q^{48} +(2.69615 + 4.66987i) q^{49} +(-1.00000 - 1.73205i) q^{50} -5.19615 q^{51} +3.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.09808 - 1.90192i) q^{55} +(0.633975 - 1.09808i) q^{56} -4.73205 q^{57} +(-1.50000 + 2.59808i) q^{58} +(6.92820 - 12.0000i) q^{59} -1.73205 q^{60} +(-7.59808 + 13.1603i) q^{61} +(4.73205 + 8.19615i) q^{62} +(-0.633975 - 1.09808i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-3.63397 - 6.29423i) q^{67} +(-2.59808 - 4.50000i) q^{68} +(-4.09808 + 7.09808i) q^{69} -2.19615 q^{70} +(1.09808 - 1.90192i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.1244 q^{73} +(1.50000 - 2.59808i) q^{74} +(-1.00000 - 1.73205i) q^{75} +(-2.36603 - 4.09808i) q^{76} +1.60770 q^{77} +8.39230 q^{79} +(-0.866025 - 1.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.23205 - 5.59808i) q^{82} +5.66025 q^{83} +(0.633975 - 1.09808i) q^{84} +(-4.50000 + 7.79423i) q^{85} +4.19615 q^{86} +(-1.50000 + 2.59808i) q^{87} +(0.633975 + 1.09808i) q^{88} +(-4.73205 - 8.19615i) q^{89} -1.73205 q^{90} -8.19615 q^{92} +(4.73205 + 8.19615i) q^{93} +(-2.36603 - 4.09808i) q^{94} +(-4.09808 + 7.09808i) q^{95} +1.00000 q^{96} +(-3.00000 + 5.19615i) q^{97} +(-2.69615 + 4.66987i) q^{98} +1.26795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 - 6 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9} - 6 q^{11} - 4 q^{12} - 12 q^{14} - 2 q^{16} - 4 q^{18} - 6 q^{19} - 12 q^{21} + 6 q^{22} + 6 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{27} - 6 q^{28} + 6 q^{29} + 24 q^{31} + 2 q^{32} + 6 q^{33} + 6 q^{35} - 2 q^{36} - 6 q^{37} - 12 q^{38} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 12 q^{44} - 6 q^{46} - 12 q^{47} + 2 q^{48} - 10 q^{49} - 4 q^{50} + 12 q^{53} - 2 q^{54} + 6 q^{55} + 6 q^{56} - 12 q^{57} - 6 q^{58} - 20 q^{61} + 12 q^{62} - 6 q^{63} + 4 q^{64} + 12 q^{66} - 18 q^{67} - 6 q^{69} + 12 q^{70} - 6 q^{71} + 2 q^{72} + 6 q^{74} - 4 q^{75} - 6 q^{76} + 48 q^{77} - 8 q^{79} - 2 q^{81} + 6 q^{82} - 12 q^{83} + 6 q^{84} - 18 q^{85} - 4 q^{86} - 6 q^{87} + 6 q^{88} - 12 q^{89} - 12 q^{92} + 12 q^{93} - 6 q^{94} - 6 q^{95} + 4 q^{96} - 12 q^{97} + 10 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 - 6 * q^7 - 4 * q^8 - 2 * q^9 - 6 * q^11 - 4 * q^12 - 12 * q^14 - 2 * q^16 - 4 * q^18 - 6 * q^19 - 12 * q^21 + 6 * q^22 + 6 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^27 - 6 * q^28 + 6 * q^29 + 24 * q^31 + 2 * q^32 + 6 * q^33 + 6 * q^35 - 2 * q^36 - 6 * q^37 - 12 * q^38 - 6 * q^41 - 6 * q^42 - 2 * q^43 + 12 * q^44 - 6 * q^46 - 12 * q^47 + 2 * q^48 - 10 * q^49 - 4 * q^50 + 12 * q^53 - 2 * q^54 + 6 * q^55 + 6 * q^56 - 12 * q^57 - 6 * q^58 - 20 * q^61 + 12 * q^62 - 6 * q^63 + 4 * q^64 + 12 * q^66 - 18 * q^67 - 6 * q^69 + 12 * q^70 - 6 * q^71 + 2 * q^72 + 6 * q^74 - 4 * q^75 - 6 * q^76 + 48 * q^77 - 8 * q^79 - 2 * q^81 + 6 * q^82 - 12 * q^83 + 6 * q^84 - 18 * q^85 - 4 * q^86 - 6 * q^87 + 6 * q^88 - 12 * q^89 - 12 * q^92 + 12 * q^93 - 6 * q^94 - 6 * q^95 + 4 * q^96 - 12 * q^97 + 10 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.73205			0.774597			0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205			0.774597			0.387298	+	0.921954i	$0.373408\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.633975	+	1.09808i	−0.239620	+	0.415034i	−0.960605	−	0.277916i	$-0.910356\pi$
$7$	−0.633975	+	1.09808i	−0.239620	+	0.415034i	0.720985	+	0.692950i	$0.243689\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.866025	+	1.50000i	0.273861	+	0.474342i
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	0.754481	−	0.656322i	$-0.227889\pi$
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	−0.945632	+	0.325239i	$0.894555\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−1.26795			−0.338874
$15$	0.866025	+	1.50000i	0.223607	+	0.387298i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	0.357400	+	0.933952i	$0.383663\pi$
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	−0.987526	+	0.157459i	$0.949670\pi$
$18$	−1.00000			−0.235702
$19$	−2.36603	+	4.09808i	−0.542803	+	0.940163i	0.455938	+	0.890011i	$0.349304\pi$
$19$	−2.36603	+	4.09808i	−0.542803	+	0.940163i	−0.998742	+	0.0501517i	$0.984030\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$	−1.26795			−0.276689
$22$	0.633975	−	1.09808i	0.135164	−	0.234111i
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	0.877101	+	0.480306i	$0.159475\pi$
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	−0.0225928	+	0.999745i	$0.507192\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−2.00000			−0.400000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−0.633975	−	1.09808i	−0.119810	−	0.207517i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	−0.866025	+	1.50000i	−0.158114	+	0.273861i
$31$	9.46410			1.69980			0.849901	−	0.526942i	$-0.176661\pi$
$31$	9.46410			1.69980			0.849901	+	0.526942i	$0.176661\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.633975	−	1.09808i	0.110361	−	0.191151i
$34$	−5.19615			−0.891133
$35$	−1.09808	+	1.90192i	−0.185609	+	0.321484i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−4.73205			−0.767640
$39$		0			0
$40$	−1.73205			−0.273861
$41$	−3.23205	−	5.59808i	−0.504762	−	0.874273i	−0.999985	−	0.00550690i	$-0.998247\pi$
$41$	−3.23205	−	5.59808i	−0.504762	−	0.874273i	0.495223	−	0.868766i	$-0.335086\pi$
$42$	−0.633975	−	1.09808i	−0.0978244	−	0.169437i
$43$	2.09808	−	3.63397i	0.319954	−	0.554176i	−0.660524	−	0.750805i	$-0.729666\pi$
$43$	2.09808	−	3.63397i	0.319954	−	0.554176i	0.980478	+	0.196629i	$0.0629993\pi$
$44$	1.26795			0.191151
$45$	−0.866025	+	1.50000i	−0.129099	+	0.223607i
$46$	−4.09808	+	7.09808i	−0.604228	+	1.04655i
$47$	−4.73205			−0.690241			−0.345120	−	0.938558i	$-0.612162\pi$
$47$	−4.73205			−0.690241			−0.345120	+	0.938558i	$0.612162\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	2.69615	+	4.66987i	0.385165	+	0.667125i
$50$	−1.00000	−	1.73205i	−0.141421	−	0.244949i
$51$	−5.19615			−0.727607
$52$		0			0
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−1.09808	−	1.90192i	−0.148065	−	0.256455i
$56$	0.633975	−	1.09808i	0.0847184	−	0.146737i
$57$	−4.73205			−0.626775
$58$	−1.50000	+	2.59808i	−0.196960	+	0.341144i
$59$	6.92820	−	12.0000i	0.901975	−	1.56227i	0.0770484	−	0.997027i	$-0.475450\pi$
$59$	6.92820	−	12.0000i	0.901975	−	1.56227i	0.824927	−	0.565240i	$-0.191216\pi$
$60$	−1.73205			−0.223607
$61$	−7.59808	+	13.1603i	−0.972834	+	1.68500i	−0.285929	+	0.958251i	$0.592302\pi$
$61$	−7.59808	+	13.1603i	−0.972834	+	1.68500i	−0.686905	+	0.726747i	$0.741031\pi$
$62$	4.73205	+	8.19615i	0.600971	+	1.04091i
$63$	−0.633975	−	1.09808i	−0.0798733	−	0.138345i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.26795			0.156074
$67$	−3.63397	−	6.29423i	−0.443961	−	0.768962i	0.554019	−	0.832504i	$-0.313094\pi$
$67$	−3.63397	−	6.29423i	−0.443961	−	0.768962i	−0.997979	+	0.0635419i	$0.979760\pi$
$68$	−2.59808	−	4.50000i	−0.315063	−	0.545705i
$69$	−4.09808	+	7.09808i	−0.493350	+	0.854508i
$70$	−2.19615			−0.262490
$71$	1.09808	−	1.90192i	0.130318	−	0.225717i	−0.793481	−	0.608595i	$-0.791734\pi$
$71$	1.09808	−	1.90192i	0.130318	−	0.225717i	0.923799	+	0.382878i	$0.125067\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	12.1244			1.41905			0.709524	−	0.704681i	$-0.248910\pi$
$73$	12.1244			1.41905			0.709524	+	0.704681i	$0.248910\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$	−2.36603	−	4.09808i	−0.271402	−	0.470082i
$77$	1.60770			0.183214
$78$		0			0
$79$	8.39230			0.944208			0.472104	−	0.881543i	$-0.343495\pi$
$79$	8.39230			0.944208			0.472104	+	0.881543i	$0.343495\pi$
$80$	−0.866025	−	1.50000i	−0.0968246	−	0.167705i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.23205	−	5.59808i	0.356920	−	0.618204i
$83$	5.66025			0.621294			0.310647	−	0.950525i	$-0.399454\pi$
$83$	5.66025			0.621294			0.310647	+	0.950525i	$0.399454\pi$
$84$	0.633975	−	1.09808i	0.0691723	−	0.119810i
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	4.19615			0.452483
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	0.633975	+	1.09808i	0.0675819	+	0.117055i
$89$	−4.73205	−	8.19615i	−0.501596	−	0.868790i	−0.999998	−	0.00184433i	$-0.999413\pi$
$89$	−4.73205	−	8.19615i	−0.501596	−	0.868790i	0.498402	−	0.866946i	$-0.333920\pi$
$90$	−1.73205			−0.182574
$91$		0			0
$92$	−8.19615			−0.854508
$93$	4.73205	+	8.19615i	0.490691	+	0.849901i
$94$	−2.36603	−	4.09808i	−0.244037	−	0.422684i
$95$	−4.09808	+	7.09808i	−0.420454	+	0.728247i
$96$	1.00000			0.102062
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	−0.977173	−	0.212445i	$-0.931857\pi$
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	0.672569	+	0.740034i	$0.265191\pi$
$98$	−2.69615	+	4.66987i	−0.272353	+	0.471728i
$99$	1.26795			0.127434
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−9.69615	−	16.7942i	−0.964803	−	1.67109i	−0.710143	−	0.704058i	$-0.751370\pi$
$101$	−9.69615	−	16.7942i	−0.964803	−	1.67109i	−0.254660	−	0.967031i	$-0.581964\pi$
$102$	−2.59808	−	4.50000i	−0.257248	−	0.445566i
$103$	6.19615			0.610525			0.305263	−	0.952268i	$-0.401256\pi$
$103$	6.19615			0.610525			0.305263	+	0.952268i	$0.401256\pi$
$104$		0			0
$105$	−2.19615			−0.214323
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	1.09808	+	1.90192i	0.106155	+	0.183866i	0.914210	−	0.405242i	$-0.132813\pi$
$107$	1.09808	+	1.90192i	0.106155	+	0.183866i	−0.808054	+	0.589108i	$0.799479\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−4.39230			−0.420707			−0.210353	−	0.977625i	$-0.567461\pi$
$109$	−4.39230			−0.420707			−0.210353	+	0.977625i	$0.567461\pi$
$110$	1.09808	−	1.90192i	0.104697	−	0.181341i
$111$	1.50000	−	2.59808i	0.142374	−	0.246598i
$112$	1.26795			0.119810
$113$	−0.401924	+	0.696152i	−0.0378098	+	0.0654885i	−0.884311	−	0.466898i	$-0.845371\pi$
$113$	−0.401924	+	0.696152i	−0.0378098	+	0.0654885i	0.846501	+	0.532387i	$0.178705\pi$
$114$	−2.36603	−	4.09808i	−0.221599	−	0.383820i
$115$	7.09808	+	12.2942i	0.661899	+	1.14644i
$116$	−3.00000			−0.278543
$117$		0			0
$118$	13.8564			1.27559
$119$	−3.29423	−	5.70577i	−0.301981	−	0.523047i
$120$	−0.866025	−	1.50000i	−0.0790569	−	0.136931i
$121$	4.69615	−	8.13397i	0.426923	−	0.739452i
$122$	−15.1962			−1.37579
$123$	3.23205	−	5.59808i	0.291424	−	0.504762i
$124$	−4.73205	+	8.19615i	−0.424951	+	0.736036i
$125$	−12.1244			−1.08444
$126$	0.633975	−	1.09808i	0.0564789	−	0.0978244i
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	4.19615			0.369451
$130$		0			0
$131$	−4.39230			−0.383757			−0.191879	−	0.981419i	$-0.561458\pi$
$131$	−4.39230			−0.383757			−0.191879	+	0.981419i	$0.561458\pi$
$132$	0.633975	+	1.09808i	0.0551804	+	0.0955753i
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$	3.63397	−	6.29423i	0.313928	−	0.543739i
$135$	−1.73205			−0.149071
$136$	2.59808	−	4.50000i	0.222783	−	0.385872i
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$	−8.19615			−0.697703
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	−1.09808	−	1.90192i	−0.0928044	−	0.160742i
$141$	−2.36603	−	4.09808i	−0.199255	−	0.345120i
$142$	2.19615			0.184297
$143$		0			0
$144$	1.00000			0.0833333
$145$	2.59808	+	4.50000i	0.215758	+	0.373705i
$146$	6.06218	+	10.5000i	0.501709	+	0.868986i
$147$	−2.69615	+	4.66987i	−0.222375	+	0.385165i
$148$	3.00000			0.246598
$149$	−3.06218	+	5.30385i	−0.250863	+	0.434508i	−0.963764	−	0.266757i	$-0.914048\pi$
$149$	−3.06218	+	5.30385i	−0.250863	+	0.434508i	0.712900	+	0.701265i	$0.247381\pi$
$150$	1.00000	−	1.73205i	0.0816497	−	0.141421i
$151$	10.7321			0.873362			0.436681	−	0.899616i	$-0.356154\pi$
$151$	10.7321			0.873362			0.436681	+	0.899616i	$0.356154\pi$
$152$	2.36603	−	4.09808i	0.191910	−	0.332398i
$153$	−2.59808	−	4.50000i	−0.210042	−	0.363803i
$154$	0.803848	+	1.39230i	0.0647759	+	0.112195i
$155$	16.3923			1.31666
$156$		0			0
$157$	7.19615			0.574315			0.287158	−	0.957883i	$-0.407290\pi$
$157$	7.19615			0.574315			0.287158	+	0.957883i	$0.407290\pi$
$158$	4.19615	+	7.26795i	0.333828	+	0.578207i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$	0.866025	−	1.50000i	0.0684653	−	0.118585i
$161$	−10.3923			−0.819028
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−1.26795	+	2.19615i	−0.0993134	+	0.172016i	−0.911401	−	0.411520i	$-0.864998\pi$
$163$	−1.26795	+	2.19615i	−0.0993134	+	0.172016i	0.812087	+	0.583536i	$0.198331\pi$
$164$	6.46410			0.504762
$165$	1.09808	−	1.90192i	0.0854851	−	0.148065i
$166$	2.83013	+	4.90192i	0.219660	+	0.380463i
$167$	4.73205	+	8.19615i	0.366177	+	0.634237i	0.988964	−	0.148154i	$-0.0473331\pi$
$167$	4.73205	+	8.19615i	0.366177	+	0.634237i	−0.622787	+	0.782391i	$0.714000\pi$
$168$	1.26795			0.0978244
$169$		0			0
$170$	−9.00000			−0.690268
$171$	−2.36603	−	4.09808i	−0.180934	−	0.313388i
$172$	2.09808	+	3.63397i	0.159977	+	0.277088i
$173$	2.19615	−	3.80385i	0.166970	−	0.289201i	−0.770383	−	0.637582i	$-0.779935\pi$
$173$	2.19615	−	3.80385i	0.166970	−	0.289201i	0.937353	+	0.348380i	$0.113268\pi$
$174$	−3.00000			−0.227429
$175$	1.26795	−	2.19615i	0.0958479	−	0.166014i
$176$	−0.633975	+	1.09808i	−0.0477876	+	0.0827706i
$177$	13.8564			1.04151
$178$	4.73205	−	8.19615i	0.354682	−	0.614328i
$179$	−1.09808	−	1.90192i	−0.0820741	−	0.142156i	0.822067	−	0.569391i	$-0.192821\pi$
$179$	−1.09808	−	1.90192i	−0.0820741	−	0.142156i	−0.904141	+	0.427235i	$0.859488\pi$
$180$	−0.866025	−	1.50000i	−0.0645497	−	0.111803i
$181$	19.5885			1.45600			0.727999	−	0.685578i	$-0.240450\pi$
$181$	19.5885			1.45600			0.727999	+	0.685578i	$0.240450\pi$
$182$		0			0
$183$	−15.1962			−1.12333
$184$	−4.09808	−	7.09808i	−0.302114	−	0.523277i
$185$	−2.59808	−	4.50000i	−0.191014	−	0.330847i
$186$	−4.73205	+	8.19615i	−0.346971	+	0.600971i
$187$	6.58846			0.481796
$188$	2.36603	−	4.09808i	0.172560	−	0.298883i
$189$	0.633975	−	1.09808i	0.0461149	−	0.0798733i
$190$	−8.19615			−0.594611
$191$	10.3923	−	18.0000i	0.751961	−	1.30243i	−0.194910	−	0.980821i	$-0.562442\pi$
$191$	10.3923	−	18.0000i	0.751961	−	1.30243i	0.946871	−	0.321613i	$-0.104225\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	11.5981	+	20.0885i	0.834848	+	1.44600i	0.894154	+	0.447759i	$0.147778\pi$
$193$	11.5981	+	20.0885i	0.834848	+	1.44600i	−0.0593065	+	0.998240i	$0.518889\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	−5.39230			−0.385165
$197$	3.46410	+	6.00000i	0.246807	+	0.427482i	0.962638	−	0.270791i	$-0.0872853\pi$
$197$	3.46410	+	6.00000i	0.246807	+	0.427482i	−0.715831	+	0.698273i	$0.753952\pi$
$198$	0.633975	+	1.09808i	0.0450546	+	0.0780369i
$199$	11.2942	−	19.5622i	0.800627	−	1.38673i	−0.118578	−	0.992945i	$-0.537833\pi$
$199$	11.2942	−	19.5622i	0.800627	−	1.38673i	0.919204	−	0.393781i	$-0.128833\pi$
$200$	2.00000			0.141421
$201$	3.63397	−	6.29423i	0.256321	−	0.443961i
$202$	9.69615	−	16.7942i	0.682219	−	1.18164i
$203$	−3.80385			−0.266978
$204$	2.59808	−	4.50000i	0.181902	−	0.315063i
$205$	−5.59808	−	9.69615i	−0.390987	−	0.677209i
$206$	3.09808	+	5.36603i	0.215853	+	0.373869i
$207$	−8.19615			−0.569672
$208$		0			0
$209$	6.00000			0.415029
$210$	−1.09808	−	1.90192i	−0.0757745	−	0.131245i
$211$	12.1962	+	21.1244i	0.839618	+	1.45426i	0.890215	+	0.455541i	$0.150554\pi$
$211$	12.1962	+	21.1244i	0.839618	+	1.45426i	−0.0505968	+	0.998719i	$0.516112\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$	2.19615			0.150478
$214$	−1.09808	+	1.90192i	−0.0750629	+	0.130013i
$215$	3.63397	−	6.29423i	0.247835	−	0.429263i
$216$	1.00000			0.0680414
$217$	−6.00000	+	10.3923i	−0.407307	+	0.705476i
$218$	−2.19615	−	3.80385i	−0.148742	−	0.257629i
$219$	6.06218	+	10.5000i	0.409644	+	0.709524i
$220$	2.19615			0.148065
$221$		0			0
$222$	3.00000			0.201347
$223$	2.53590	+	4.39230i	0.169816	+	0.294130i	0.938355	−	0.345673i	$-0.112349\pi$
$223$	2.53590	+	4.39230i	0.169816	+	0.294130i	−0.768539	+	0.639803i	$0.779016\pi$
$224$	0.633975	+	1.09808i	0.0423592	+	0.0733683i
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$	−0.803848			−0.0534711
$227$	10.0981	−	17.4904i	0.670233	−	1.16088i	−0.307605	−	0.951514i	$-0.599528\pi$
$227$	10.0981	−	17.4904i	0.670233	−	1.16088i	0.977838	−	0.209363i	$-0.0671391\pi$
$228$	2.36603	−	4.09808i	0.156694	−	0.271402i
$229$	−7.85641			−0.519166			−0.259583	−	0.965721i	$-0.583585\pi$
$229$	−7.85641			−0.519166			−0.259583	+	0.965721i	$0.583585\pi$
$230$	−7.09808	+	12.2942i	−0.468033	+	0.810657i
$231$	0.803848	+	1.39230i	0.0528893	+	0.0916069i
$232$	−1.50000	−	2.59808i	−0.0984798	−	0.170572i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	−8.19615			−0.534658
$236$	6.92820	+	12.0000i	0.450988	+	0.781133i
$237$	4.19615	+	7.26795i	0.272569	+	0.472104i
$238$	3.29423	−	5.70577i	0.213533	−	0.369850i
$239$	6.58846			0.426172			0.213086	−	0.977033i	$-0.431649\pi$
$239$	6.58846			0.426172			0.213086	+	0.977033i	$0.431649\pi$
$240$	0.866025	−	1.50000i	0.0559017	−	0.0968246i
$241$	−5.59808	+	9.69615i	−0.360604	+	0.624584i	−0.988060	−	0.154068i	$-0.950763\pi$
$241$	−5.59808	+	9.69615i	−0.360604	+	0.624584i	0.627457	+	0.778652i	$0.284096\pi$
$242$	9.39230			0.603760
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−7.59808	−	13.1603i	−0.486417	−	0.842499i
$245$	4.66987	+	8.08846i	0.298347	+	0.516753i
$246$	6.46410			0.412136
$247$		0			0
$248$	−9.46410			−0.600971
$249$	2.83013	+	4.90192i	0.179352	+	0.310647i
$250$	−6.06218	−	10.5000i	−0.383406	−	0.664078i
$251$	−8.19615	+	14.1962i	−0.517337	+	0.896053i	0.482461	+	0.875918i	$0.339743\pi$
$251$	−8.19615	+	14.1962i	−0.517337	+	0.896053i	−0.999797	+	0.0201356i	$0.993590\pi$
$252$	1.26795			0.0798733
$253$	5.19615	−	9.00000i	0.326679	−	0.565825i
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$	−9.00000			−0.563602
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.5981	−	20.0885i	−0.723468	−	1.25308i	−0.959601	−	0.281363i	$-0.909214\pi$
$257$	−11.5981	−	20.0885i	−0.723468	−	1.25308i	0.236133	−	0.971721i	$-0.424120\pi$
$258$	2.09808	+	3.63397i	0.130621	+	0.226241i
$259$	3.80385			0.236360
$260$		0			0
$261$	−3.00000			−0.185695
$262$	−2.19615	−	3.80385i	−0.135679	−	0.235002i
$263$	−4.09808	−	7.09808i	−0.252698	−	0.437686i	0.711570	−	0.702616i	$-0.247985\pi$
$263$	−4.09808	−	7.09808i	−0.252698	−	0.437686i	−0.964268	+	0.264930i	$0.914651\pi$
$264$	−0.633975	+	1.09808i	−0.0390184	+	0.0675819i
$265$	5.19615			0.319197
$266$	3.00000	−	5.19615i	0.183942	−	0.318597i
$267$	4.73205	−	8.19615i	0.289597	−	0.501596i
$268$	7.26795			0.443961
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	−0.726450	−	0.687220i	$-0.758831\pi$
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	0.958374	+	0.285514i	$0.0921644\pi$
$270$	−0.866025	−	1.50000i	−0.0527046	−	0.0912871i
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	5.19615			0.315063
$273$		0			0
$274$	9.00000			0.543710
$275$	1.26795	+	2.19615i	0.0764602	+	0.132433i
$276$	−4.09808	−	7.09808i	−0.246675	−	0.427254i
$277$	−2.40192	+	4.16025i	−0.144318	+	0.249965i	−0.929118	−	0.369783i	$-0.879432\pi$
$277$	−2.40192	+	4.16025i	−0.144318	+	0.249965i	0.784801	+	0.619748i	$0.212765\pi$
$278$	4.00000			0.239904
$279$	−4.73205	+	8.19615i	−0.283300	+	0.490691i
$280$	1.09808	−	1.90192i	0.0656226	−	0.113662i
$281$	17.5359			1.04610			0.523052	−	0.852301i	$-0.324793\pi$
$281$	17.5359			1.04610			0.523052	+	0.852301i	$0.324793\pi$
$282$	2.36603	−	4.09808i	0.140895	−	0.244037i
$283$	9.90192	+	17.1506i	0.588608	+	1.01950i	0.994415	+	0.105541i	$0.0336573\pi$
$283$	9.90192	+	17.1506i	0.588608	+	1.01950i	−0.405807	+	0.913959i	$0.633009\pi$
$284$	1.09808	+	1.90192i	0.0651588	+	0.112858i
$285$	−8.19615			−0.485498
$286$		0			0
$287$	8.19615			0.483804
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−5.00000	−	8.66025i	−0.294118	−	0.509427i
$290$	−2.59808	+	4.50000i	−0.152564	+	0.264249i
$291$	−6.00000			−0.351726
$292$	−6.06218	+	10.5000i	−0.354762	+	0.614466i
$293$	−1.33013	+	2.30385i	−0.0777069	+	0.134592i	−0.902260	−	0.431192i	$-0.858093\pi$
$293$	−1.33013	+	2.30385i	−0.0777069	+	0.134592i	0.824553	+	0.565784i	$0.191426\pi$
$294$	−5.39230			−0.314486
$295$	12.0000	−	20.7846i	0.698667	−	1.21013i
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	0.633975	+	1.09808i	0.0367869	+	0.0637168i
$298$	−6.12436			−0.354774
$299$		0			0
$300$	2.00000			0.115470
$301$	2.66025	+	4.60770i	0.153334	+	0.265583i
$302$	5.36603	+	9.29423i	0.308780	+	0.534823i
$303$	9.69615	−	16.7942i	0.557029	−	0.964803i
$304$	4.73205			0.271402
$305$	−13.1603	+	22.7942i	−0.753554	+	1.30519i
$306$	2.59808	−	4.50000i	0.148522	−	0.257248i
$307$	7.26795			0.414804			0.207402	−	0.978256i	$-0.433499\pi$
$307$	7.26795			0.414804			0.207402	+	0.978256i	$0.433499\pi$
$308$	−0.803848	+	1.39230i	−0.0458035	+	0.0793339i
$309$	3.09808	+	5.36603i	0.176243	+	0.305263i
$310$	8.19615	+	14.1962i	0.465510	+	0.806287i
$311$	−8.19615			−0.464761			−0.232381	−	0.972625i	$-0.574651\pi$
$311$	−8.19615			−0.464761			−0.232381	+	0.972625i	$0.574651\pi$
$312$		0			0
$313$	−3.60770			−0.203919			−0.101959	−	0.994789i	$-0.532511\pi$
$313$	−3.60770			−0.203919			−0.101959	+	0.994789i	$0.532511\pi$
$314$	3.59808	+	6.23205i	0.203051	+	0.351695i
$315$	−1.09808	−	1.90192i	−0.0618696	−	0.107161i
$316$	−4.19615	+	7.26795i	−0.236052	+	0.408854i
$317$	−18.1244			−1.01797			−0.508983	−	0.860777i	$-0.669978\pi$
$317$	−18.1244			−1.01797			−0.508983	+	0.860777i	$0.669978\pi$
$318$	−1.50000	+	2.59808i	−0.0841158	+	0.145693i
$319$	1.90192	−	3.29423i	0.106487	−	0.184441i
$320$	1.73205			0.0968246
$321$	−1.09808	+	1.90192i	−0.0612886	+	0.106155i
$322$	−5.19615	−	9.00000i	−0.289570	−	0.501550i
$323$	−12.2942	−	21.2942i	−0.684069	−	1.18484i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−2.53590			−0.140450
$327$	−2.19615	−	3.80385i	−0.121448	−	0.210353i
$328$	3.23205	+	5.59808i	0.178460	+	0.309102i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$	2.19615			0.120894
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$	−2.83013	+	4.90192i	−0.155323	+	0.269028i
$333$	3.00000			0.164399
$334$	−4.73205	+	8.19615i	−0.258926	+	0.448474i
$335$	−6.29423	−	10.9019i	−0.343890	−	0.595636i
$336$	0.633975	+	1.09808i	0.0345861	+	0.0599050i
$337$	−31.0000			−1.68868			−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000			−1.68868			−0.844339	+	0.535810i	$0.820006\pi$
$338$		0			0
$339$	−0.803848			−0.0436590
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	2.36603	−	4.09808i	0.127940	−	0.221599i
$343$	−15.7128			−0.848412
$344$	−2.09808	+	3.63397i	−0.113121	+	0.195931i
$345$	−7.09808	+	12.2942i	−0.382148	+	0.661899i
$346$	4.39230			0.236132
$347$	−9.29423	+	16.0981i	−0.498940	+	0.864190i	−0.999999	−	0.00122316i	$-0.999611\pi$
$347$	−9.29423	+	16.0981i	−0.498940	+	0.864190i	0.501059	+	0.865413i	$0.332944\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−4.73205	−	8.19615i	−0.253301	−	0.438730i	0.711132	−	0.703059i	$-0.248183\pi$
$349$	−4.73205	−	8.19615i	−0.253301	−	0.438730i	−0.964433	+	0.264329i	$0.914850\pi$
$350$	2.53590			0.135549
$351$		0			0
$352$	−1.26795			−0.0675819
$353$	17.8923	+	30.9904i	0.952311	+	1.64945i	0.740404	+	0.672162i	$0.234634\pi$
$353$	17.8923	+	30.9904i	0.952311	+	1.64945i	0.211907	+	0.977290i	$0.432033\pi$
$354$	6.92820	+	12.0000i	0.368230	+	0.637793i
$355$	1.90192	−	3.29423i	0.100944	−	0.174840i
$356$	9.46410			0.501596
$357$	3.29423	−	5.70577i	0.174349	−	0.301981i
$358$	1.09808	−	1.90192i	0.0580351	−	0.100520i
$359$	−16.0526			−0.847222			−0.423611	−	0.905844i	$-0.639238\pi$
$359$	−16.0526			−0.847222			−0.423611	+	0.905844i	$0.639238\pi$
$360$	0.866025	−	1.50000i	0.0456435	−	0.0790569i
$361$	−1.69615	−	2.93782i	−0.0892712	−	0.154622i
$362$	9.79423	+	16.9641i	0.514773	+	0.891613i
$363$	9.39230			0.492968
$364$		0			0
$365$	21.0000			1.09919
$366$	−7.59808	−	13.1603i	−0.397158	−	0.687897i
$367$	6.90192	+	11.9545i	0.360277	+	0.624019i	0.988006	−	0.154413i	$-0.0493487\pi$
$367$	6.90192	+	11.9545i	0.360277	+	0.624019i	−0.627729	+	0.778432i	$0.716015\pi$
$368$	4.09808	−	7.09808i	0.213627	−	0.370013i
$369$	6.46410			0.336508
$370$	2.59808	−	4.50000i	0.135068	−	0.233944i
$371$	−1.90192	+	3.29423i	−0.0987430	+	0.171028i
$372$	−9.46410			−0.490691
$373$	13.9904	−	24.2321i	0.724394	−	1.25469i	−0.234828	−	0.972037i	$-0.575453\pi$
$373$	13.9904	−	24.2321i	0.724394	−	1.25469i	0.959223	−	0.282651i	$-0.0912139\pi$
$374$	3.29423	+	5.70577i	0.170341	+	0.295038i
$375$	−6.06218	−	10.5000i	−0.313050	−	0.542218i
$376$	4.73205			0.244037
$377$		0			0
$378$	1.26795			0.0652163
$379$	−15.1244	−	26.1962i	−0.776886	−	1.34561i	−0.933728	−	0.357982i	$-0.883465\pi$
$379$	−15.1244	−	26.1962i	−0.776886	−	1.34561i	0.156842	−	0.987624i	$-0.449869\pi$
$380$	−4.09808	−	7.09808i	−0.210227	−	0.364124i
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$	20.7846			1.06343
$383$	11.6603	−	20.1962i	0.595811	−	1.03198i	−0.397621	−	0.917550i	$-0.630164\pi$
$383$	11.6603	−	20.1962i	0.595811	−	1.03198i	0.993432	−	0.114425i	$-0.0365027\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	2.78461			0.141917
$386$	−11.5981	+	20.0885i	−0.590327	+	1.02248i
$387$	2.09808	+	3.63397i	0.106651	+	0.184725i
$388$	−3.00000	−	5.19615i	−0.152302	−	0.263795i
$389$	7.39230			0.374805			0.187402	−	0.982283i	$-0.439993\pi$
$389$	7.39230			0.374805			0.187402	+	0.982283i	$0.439993\pi$
$390$		0			0
$391$	−42.5885			−2.15379
$392$	−2.69615	−	4.66987i	−0.136176	−	0.235864i
$393$	−2.19615	−	3.80385i	−0.110781	−	0.191879i
$394$	−3.46410	+	6.00000i	−0.174519	+	0.302276i
$395$	14.5359			0.731380
$396$	−0.633975	+	1.09808i	−0.0318584	+	0.0551804i
$397$	−2.19615	+	3.80385i	−0.110222	+	0.190910i	−0.915860	−	0.401499i	$-0.868489\pi$
$397$	−2.19615	+	3.80385i	−0.110222	+	0.190910i	0.805638	+	0.592408i	$0.201823\pi$
$398$	22.5885			1.13226
$399$	3.00000	−	5.19615i	0.150188	−	0.260133i
$400$	1.00000	+	1.73205i	0.0500000	+	0.0866025i
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$	7.26795			0.362492
$403$		0			0
$404$	19.3923			0.964803
$405$	−0.866025	−	1.50000i	−0.0430331	−	0.0745356i
$406$	−1.90192	−	3.29423i	−0.0943909	−	0.163490i
$407$	−1.90192	+	3.29423i	−0.0942749	+	0.163289i
$408$	5.19615			0.257248
$409$	10.3301	−	17.8923i	0.510792	−	0.884718i	−0.489130	−	0.872211i	$-0.662686\pi$
$409$	10.3301	−	17.8923i	0.510792	−	0.884718i	0.999922	−	0.0125066i	$-0.00398107\pi$
$410$	5.59808	−	9.69615i	0.276469	−	0.478859i
$411$	9.00000			0.443937
$412$	−3.09808	+	5.36603i	−0.152631	+	0.264365i
$413$	8.78461	+	15.2154i	0.432262	+	0.748700i
$414$	−4.09808	−	7.09808i	−0.201409	−	0.348851i
$415$	9.80385			0.481252
$416$		0			0
$417$	4.00000			0.195881
$418$	3.00000	+	5.19615i	0.146735	+	0.254152i
$419$	2.19615	+	3.80385i	0.107289	+	0.185830i	0.914671	−	0.404199i	$-0.132450\pi$
$419$	2.19615	+	3.80385i	0.107289	+	0.185830i	−0.807382	+	0.590029i	$0.799116\pi$
$420$	1.09808	−	1.90192i	0.0535806	−	0.0928044i
$421$	−6.46410			−0.315041			−0.157521	−	0.987516i	$-0.550350\pi$
$421$	−6.46410			−0.315041			−0.157521	+	0.987516i	$0.550350\pi$
$422$	−12.1962	+	21.1244i	−0.593699	+	1.02832i
$423$	2.36603	−	4.09808i	0.115040	−	0.199255i
$424$	−3.00000			−0.145693
$425$	5.19615	−	9.00000i	0.252050	−	0.436564i
$426$	1.09808	+	1.90192i	0.0532020	+	0.0921485i
$427$	−9.63397	−	16.6865i	−0.466221	−	0.807518i
$428$	−2.19615			−0.106155
$429$		0			0
$430$	7.26795			0.350492
$431$	−19.0981	−	33.0788i	−0.919922	−	1.59335i	−0.799531	−	0.600625i	$-0.794918\pi$
$431$	−19.0981	−	33.0788i	−0.919922	−	1.59335i	−0.120391	−	0.992727i	$-0.538415\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−3.89230	+	6.74167i	−0.187052	+	0.323984i	−0.944266	−	0.329183i	$-0.893227\pi$
$433$	−3.89230	+	6.74167i	−0.187052	+	0.323984i	0.757214	+	0.653167i	$0.226560\pi$
$434$	−12.0000			−0.576018
$435$	−2.59808	+	4.50000i	−0.124568	+	0.215758i
$436$	2.19615	−	3.80385i	0.105177	−	0.182171i
$437$	−38.7846			−1.85532
$438$	−6.06218	+	10.5000i	−0.289662	+	0.501709i
$439$	7.29423	+	12.6340i	0.348135	+	0.602987i	0.985918	−	0.167229i	$-0.0534819\pi$
$439$	7.29423	+	12.6340i	0.348135	+	0.602987i	−0.637784	+	0.770216i	$0.720149\pi$
$440$	1.09808	+	1.90192i	0.0523487	+	0.0906707i
$441$	−5.39230			−0.256776
$442$		0			0
$443$	16.3923			0.778822			0.389411	−	0.921064i	$-0.372679\pi$
$443$	16.3923			0.778822			0.389411	+	0.921064i	$0.372679\pi$
$444$	1.50000	+	2.59808i	0.0711868	+	0.123299i
$445$	−8.19615	−	14.1962i	−0.388535	−	0.672962i
$446$	−2.53590	+	4.39230i	−0.120078	+	0.207982i
$447$	−6.12436			−0.289672
$448$	−0.633975	+	1.09808i	−0.0299525	+	0.0518792i
$449$	−13.2679	+	22.9808i	−0.626153	+	1.08453i	0.362163	+	0.932115i	$0.382038\pi$
$449$	−13.2679	+	22.9808i	−0.626153	+	1.08453i	−0.988317	+	0.152415i	$0.951295\pi$
$450$	2.00000			0.0942809
$451$	−4.09808	+	7.09808i	−0.192971	+	0.334235i
$452$	−0.401924	−	0.696152i	−0.0189049	−	0.0327443i
$453$	5.36603	+	9.29423i	0.252118	+	0.436681i
$454$	20.1962			0.947852
$455$		0			0
$456$	4.73205			0.221599
$457$	15.9904	+	27.6962i	0.747998	+	1.29557i	0.948781	+	0.315935i	$0.102318\pi$
$457$	15.9904	+	27.6962i	0.747998	+	1.29557i	−0.200782	+	0.979636i	$0.564348\pi$
$458$	−3.92820	−	6.80385i	−0.183553	−	0.317923i
$459$	2.59808	−	4.50000i	0.121268	−	0.210042i
$460$	−14.1962			−0.661899
$461$	−15.9904	+	27.6962i	−0.744746	+	1.28994i	0.205567	+	0.978643i	$0.434096\pi$
$461$	−15.9904	+	27.6962i	−0.744746	+	1.28994i	−0.950313	+	0.311295i	$0.899237\pi$
$462$	−0.803848	+	1.39230i	−0.0373984	+	0.0647759i
$463$	−15.8038			−0.734467			−0.367234	−	0.930129i	$-0.619695\pi$
$463$	−15.8038			−0.734467			−0.367234	+	0.930129i	$0.619695\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	8.19615	+	14.1962i	0.380087	+	0.658331i
$466$	−9.00000	−	15.5885i	−0.416917	−	0.722121i
$467$	5.41154			0.250416			0.125208	−	0.992130i	$-0.460040\pi$
$467$	5.41154			0.250416			0.125208	+	0.992130i	$0.460040\pi$
$468$		0			0
$469$	9.21539			0.425527
$470$	−4.09808	−	7.09808i	−0.189030	−	0.327410i
$471$	3.59808	+	6.23205i	0.165791	+	0.287158i
$472$	−6.92820	+	12.0000i	−0.318896	+	0.552345i
$473$	−5.32051			−0.244637
$474$	−4.19615	+	7.26795i	−0.192736	+	0.333828i
$475$	4.73205	−	8.19615i	0.217121	−	0.376065i
$476$	6.58846			0.301981
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	3.29423	+	5.70577i	0.150675	+	0.260976i
$479$	0.339746	+	0.588457i	0.0155234	+	0.0268873i	0.873683	−	0.486496i	$-0.161725\pi$
$479$	0.339746	+	0.588457i	0.0155234	+	0.0268873i	−0.858159	+	0.513383i	$0.828392\pi$
$480$	1.73205			0.0790569
$481$		0			0
$482$	−11.1962			−0.509971
$483$	−5.19615	−	9.00000i	−0.236433	−	0.409514i
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	−5.19615	+	9.00000i	−0.235945	+	0.408669i
$486$	1.00000			0.0453609
$487$	7.56218	−	13.0981i	0.342675	−	0.593530i	−0.642254	−	0.766492i	$-0.722000\pi$
$487$	7.56218	−	13.0981i	0.342675	−	0.593530i	0.984929	+	0.172962i	$0.0553337\pi$
$488$	7.59808	−	13.1603i	0.343949	−	0.595737i
$489$	−2.53590			−0.114677
$490$	−4.66987	+	8.08846i	−0.210963	+	0.365399i
$491$	15.2942	+	26.4904i	0.690219	+	1.19549i	0.971766	+	0.235947i	$0.0758191\pi$
$491$	15.2942	+	26.4904i	0.690219	+	1.19549i	−0.281547	+	0.959547i	$0.590848\pi$
$492$	3.23205	+	5.59808i	0.145712	+	0.252381i
$493$	−15.5885			−0.702069
$494$		0			0
$495$	2.19615			0.0987097
$496$	−4.73205	−	8.19615i	−0.212475	−	0.368018i
$497$	1.39230	+	2.41154i	0.0624534	+	0.108172i
$498$	−2.83013	+	4.90192i	−0.126821	+	0.219660i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$	−4.73205	+	8.19615i	−0.211412	+	0.366177i
$502$	−16.3923			−0.731624
$503$	−6.29423	+	10.9019i	−0.280646	+	0.486093i	−0.971544	−	0.236859i	$-0.923882\pi$
$503$	−6.29423	+	10.9019i	−0.280646	+	0.486093i	0.690898	+	0.722952i	$0.257215\pi$
$504$	0.633975	+	1.09808i	0.0282395	+	0.0489122i
$505$	−16.7942	−	29.0885i	−0.747333	−	1.29442i
$506$	10.3923			0.461994
$507$		0			0
$508$	−4.00000			−0.177471
$509$	−13.3301	−	23.0885i	−0.590847	−	1.02338i	−0.994119	−	0.108297i	$-0.965460\pi$
$509$	−13.3301	−	23.0885i	−0.590847	−	1.02338i	0.403271	−	0.915081i	$-0.367873\pi$
$510$	−4.50000	−	7.79423i	−0.199263	−	0.345134i
$511$	−7.68653	+	13.3135i	−0.340032	+	0.588953i
$512$	−1.00000			−0.0441942
$513$	2.36603	−	4.09808i	0.104463	−	0.180934i
$514$	11.5981	−	20.0885i	0.511569	−	0.886064i
$515$	10.7321			0.472911
$516$	−2.09808	+	3.63397i	−0.0923627	+	0.159977i
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$	1.90192	+	3.29423i	0.0835657	+	0.144740i
$519$	4.39230			0.192801
$520$		0			0
$521$	−29.1962			−1.27911			−0.639553	−	0.768747i	$-0.720881\pi$
$521$	−29.1962			−1.27911			−0.639553	+	0.768747i	$0.720881\pi$
$522$	−1.50000	−	2.59808i	−0.0656532	−	0.113715i
$523$	−16.2942	−	28.2224i	−0.712497	−	1.23408i	−0.963917	−	0.266203i	$-0.914231\pi$
$523$	−16.2942	−	28.2224i	−0.712497	−	1.23408i	0.251420	−	0.967878i	$-0.419102\pi$
$524$	2.19615	−	3.80385i	0.0959394	−	0.166172i
$525$	2.53590			0.110676
$526$	4.09808	−	7.09808i	0.178685	−	0.309491i
$527$	−24.5885	+	42.5885i	−1.07109	+	1.85518i
$528$	−1.26795			−0.0551804
$529$	−22.0885	+	38.2583i	−0.960368	+	1.66341i
$530$	2.59808	+	4.50000i	0.112853	+	0.195468i
$531$	6.92820	+	12.0000i	0.300658	+	0.520756i
$532$	6.00000			0.260133
$533$		0			0
$534$	9.46410			0.409552
$535$	1.90192	+	3.29423i	0.0822273	+	0.142422i
$536$	3.63397	+	6.29423i	0.156964	+	0.271869i
$537$	1.09808	−	1.90192i	0.0473855	−	0.0820741i
$538$	7.60770			0.327991
$539$	3.41858	−	5.92116i	0.147249	−	0.255042i
$540$	0.866025	−	1.50000i	0.0372678	−	0.0645497i
$541$	−10.8564			−0.466753			−0.233377	−	0.972386i	$-0.574978\pi$
$541$	−10.8564			−0.466753			−0.233377	+	0.972386i	$0.574978\pi$
$542$		0			0
$543$	9.79423	+	16.9641i	0.420311	+	0.727999i
$544$	2.59808	+	4.50000i	0.111392	+	0.192936i
$545$	−7.60770			−0.325878
$546$		0			0
$547$	4.19615			0.179415			0.0897073	−	0.995968i	$-0.471407\pi$
$547$	4.19615			0.179415			0.0897073	+	0.995968i	$0.471407\pi$
$548$	4.50000	+	7.79423i	0.192230	+	0.332953i
$549$	−7.59808	−	13.1603i	−0.324278	−	0.561666i
$550$	−1.26795	+	2.19615i	−0.0540655	+	0.0936443i
$551$	−14.1962			−0.604776
$552$	4.09808	−	7.09808i	0.174426	−	0.302114i
$553$	−5.32051	+	9.21539i	−0.226251	+	0.391878i
$554$	−4.80385			−0.204096
$555$	2.59808	−	4.50000i	0.110282	−	0.191014i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−12.8660	−	22.2846i	−0.545151	−	0.944229i	−0.998597	−	0.0529457i	$-0.983139\pi$
$557$	−12.8660	−	22.2846i	−0.545151	−	0.944229i	0.453446	−	0.891284i	$-0.350194\pi$
$558$	−9.46410			−0.400647
$559$		0			0
$560$	2.19615			0.0928044
$561$	3.29423	+	5.70577i	0.139082	+	0.240898i
$562$	8.76795	+	15.1865i	0.369854	+	0.640605i
$563$	16.3923	−	28.3923i	0.690853	−	1.19659i	−0.280705	−	0.959794i	$-0.590568\pi$
$563$	16.3923	−	28.3923i	0.690853	−	1.19659i	0.971559	−	0.236799i	$-0.0760983\pi$
$564$	4.73205			0.199255
$565$	−0.696152	+	1.20577i	−0.0292874	+	0.0507272i
$566$	−9.90192	+	17.1506i	−0.416209	+	0.720895i
$567$	1.26795			0.0532489
$568$	−1.09808	+	1.90192i	−0.0460743	+	0.0798029i
$569$	−4.39230	−	7.60770i	−0.184135	−	0.318931i	0.759150	−	0.650916i	$-0.225615\pi$
$569$	−4.39230	−	7.60770i	−0.184135	−	0.318931i	−0.943285	+	0.331985i	$0.892282\pi$
$570$	−4.09808	−	7.09808i	−0.171650	−	0.297306i
$571$	−24.1962			−1.01258			−0.506289	−	0.862364i	$-0.668983\pi$
$571$	−24.1962			−1.01258			−0.506289	+	0.862364i	$0.668983\pi$
$572$		0			0
$573$	20.7846			0.868290
$574$	4.09808	+	7.09808i	0.171050	+	0.296268i
$575$	−8.19615	−	14.1962i	−0.341803	−	0.592020i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−19.7321			−0.821456			−0.410728	−	0.911758i	$-0.634725\pi$
$577$	−19.7321			−0.821456			−0.410728	+	0.911758i	$0.634725\pi$
$578$	5.00000	−	8.66025i	0.207973	−	0.360219i
$579$	−11.5981	+	20.0885i	−0.482000	+	0.834848i
$580$	−5.19615			−0.215758
$581$	−3.58846	+	6.21539i	−0.148874	+	0.257858i
$582$	−3.00000	−	5.19615i	−0.124354	−	0.215387i
$583$	−1.90192	−	3.29423i	−0.0787696	−	0.136433i
$584$	−12.1244			−0.501709
$585$		0			0
$586$	−2.66025			−0.109894
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$	−2.69615	−	4.66987i	−0.111187	−	0.192582i
$589$	−22.3923	+	38.7846i	−0.922659	+	1.59809i
$590$	24.0000			0.988064
$591$	−3.46410	+	6.00000i	−0.142494	+	0.246807i
$592$	−1.50000	+	2.59808i	−0.0616496	+	0.106780i
$593$	−19.1436			−0.786133			−0.393067	−	0.919510i	$-0.628586\pi$
$593$	−19.1436			−0.786133			−0.393067	+	0.919510i	$0.628586\pi$
$594$	−0.633975	+	1.09808i	−0.0260123	+	0.0450546i
$595$	−5.70577	−	9.88269i	−0.233914	−	0.405151i
$596$	−3.06218	−	5.30385i	−0.125432	−	0.217254i
$597$	22.5885			0.924484
$598$		0			0
$599$	16.3923			0.669771			0.334886	−	0.942259i	$-0.391302\pi$
$599$	16.3923			0.669771			0.334886	+	0.942259i	$0.391302\pi$
$600$	1.00000	+	1.73205i	0.0408248	+	0.0707107i
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	0.994147	−	0.108032i	$-0.0344548\pi$
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	−0.590632	+	0.806941i	$0.701121\pi$
$602$	−2.66025	+	4.60770i	−0.108424	+	0.187796i
$603$	7.26795			0.295974
$604$	−5.36603	+	9.29423i	−0.218340	+	0.378177i
$605$	8.13397	−	14.0885i	0.330693	−	0.572777i
$606$	19.3923			0.787759
$607$	3.60770	−	6.24871i	0.146432	−	0.253627i	−0.783474	−	0.621424i	$-0.786554\pi$
$607$	3.60770	−	6.24871i	0.146432	−	0.253627i	0.929906	+	0.367797i	$0.119888\pi$
$608$	2.36603	+	4.09808i	0.0959550	+	0.166199i
$609$	−1.90192	−	3.29423i	−0.0770698	−	0.133489i
$610$	−26.3205			−1.06569
$611$		0			0
$612$	5.19615			0.210042
$613$	6.57180	+	11.3827i	0.265432	+	0.459742i	0.967677	−	0.252194i	$-0.0811520\pi$
$613$	6.57180	+	11.3827i	0.265432	+	0.459742i	−0.702244	+	0.711936i	$0.747819\pi$
$614$	3.63397	+	6.29423i	0.146655	+	0.254014i
$615$	5.59808	−	9.69615i	0.225736	−	0.390987i
$616$	−1.60770			−0.0647759
$617$	−15.6962	+	27.1865i	−0.631903	+	1.09449i	0.355259	+	0.934768i	$0.384393\pi$
$617$	−15.6962	+	27.1865i	−0.631903	+	1.09449i	−0.987162	+	0.159721i	$0.948941\pi$
$618$	−3.09808	+	5.36603i	−0.124623	+	0.215853i
$619$	−28.3923			−1.14118			−0.570592	−	0.821234i	$-0.693286\pi$
$619$	−28.3923			−1.14118			−0.570592	+	0.821234i	$0.693286\pi$
$620$	−8.19615	+	14.1962i	−0.329165	+	0.570131i
$621$	−4.09808	−	7.09808i	−0.164450	−	0.284836i
$622$	−4.09808	−	7.09808i	−0.164318	−	0.284607i
$623$	12.0000			0.480770
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−1.80385	−	3.12436i	−0.0720962	−	0.124874i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	−3.59808	+	6.23205i	−0.143579	+	0.248686i
$629$	15.5885			0.621552
$630$	1.09808	−	1.90192i	0.0437484	−	0.0757745i
$631$	0.928203	−	1.60770i	0.0369512	−	0.0640013i	−0.846958	−	0.531659i	$-0.821569\pi$
$631$	0.928203	−	1.60770i	0.0369512	−	0.0640013i	0.883910	+	0.467658i	$0.154902\pi$
$632$	−8.39230			−0.333828
$633$	−12.1962	+	21.1244i	−0.484754	+	0.839618i
$634$	−9.06218	−	15.6962i	−0.359905	−	0.623374i
$635$	3.46410	+	6.00000i	0.137469	+	0.238103i
$636$	−3.00000			−0.118958
$637$		0			0
$638$	3.80385			0.150596
$639$	1.09808	+	1.90192i	0.0434392	+	0.0752389i
$640$	0.866025	+	1.50000i	0.0342327	+	0.0592927i
$641$	20.5981	−	35.6769i	0.813575	−	1.40915i	−0.0967715	−	0.995307i	$-0.530852\pi$
$641$	20.5981	−	35.6769i	0.813575	−	1.40915i	0.910347	−	0.413847i	$-0.135815\pi$
$642$	−2.19615			−0.0866752
$643$	−13.8564	+	24.0000i	−0.546443	+	0.946468i	0.452071	+	0.891982i	$0.350685\pi$
$643$	−13.8564	+	24.0000i	−0.546443	+	0.946468i	−0.998515	+	0.0544858i	$0.982648\pi$
$644$	5.19615	−	9.00000i	0.204757	−	0.354650i
$645$	7.26795			0.286175
$646$	12.2942	−	21.2942i	0.483710	−	0.837810i
$647$	24.5885	+	42.5885i	0.966672	+	1.67433i	0.705054	+	0.709153i	$0.250923\pi$
$647$	24.5885	+	42.5885i	0.966672	+	1.67433i	0.261618	+	0.965172i	$0.415744\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−17.5692			−0.689652
$650$		0			0
$651$	−12.0000			−0.470317
$652$	−1.26795	−	2.19615i	−0.0496567	−	0.0860080i
$653$	−6.58846	−	11.4115i	−0.257826	−	0.446568i	0.707833	−	0.706380i	$-0.249673\pi$
$653$	−6.58846	−	11.4115i	−0.257826	−	0.446568i	−0.965659	+	0.259812i	$0.916340\pi$
$654$	2.19615	−	3.80385i	0.0858764	−	0.148742i
$655$	−7.60770			−0.297257
$656$	−3.23205	+	5.59808i	−0.126190	+	0.218568i
$657$	−6.06218	+	10.5000i	−0.236508	+	0.409644i
$658$	6.00000			0.233904
$659$	18.5885	−	32.1962i	0.724103	−	1.25418i	−0.235238	−	0.971938i	$-0.575587\pi$
$659$	18.5885	−	32.1962i	0.724103	−	1.25418i	0.959342	−	0.282246i	$-0.0910796\pi$
$660$	1.09808	+	1.90192i	0.0427426	+	0.0740323i
$661$	−4.50000	−	7.79423i	−0.175030	−	0.303160i	0.765142	−	0.643862i	$-0.222669\pi$
$661$	−4.50000	−	7.79423i	−0.175030	−	0.303160i	−0.940172	+	0.340701i	$0.889335\pi$
$662$	−12.0000			−0.466393
$663$		0			0
$664$	−5.66025			−0.219660
$665$	−5.19615	−	9.00000i	−0.201498	−	0.349005i
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	−12.2942	+	21.2942i	−0.476034	+	0.824516i
$668$	−9.46410			−0.366177
$669$	−2.53590	+	4.39230i	−0.0980435	+	0.169816i
$670$	6.29423	−	10.9019i	0.243167	−	0.421178i
$671$	19.2679			0.743831
$672$	−0.633975	+	1.09808i	−0.0244561	+	0.0423592i
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	0.856228	−	0.516599i	$-0.172802\pi$
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	−0.875501	+	0.483216i	$0.839469\pi$
$674$	−15.5000	−	26.8468i	−0.597038	−	1.03410i
$675$	2.00000			0.0769800
$676$		0			0
$677$	−16.3923			−0.630007			−0.315004	−	0.949090i	$-0.602006\pi$
$677$	−16.3923			−0.630007			−0.315004	+	0.949090i	$0.602006\pi$
$678$	−0.401924	−	0.696152i	−0.0154358	−	0.0267356i
$679$	−3.80385	−	6.58846i	−0.145978	−	0.252842i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	20.1962			0.773918
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	13.8564	−	24.0000i	0.530201	−	0.918334i	−0.469179	−	0.883103i	$-0.655450\pi$
$683$	13.8564	−	24.0000i	0.530201	−	0.918334i	0.999379	−	0.0352311i	$-0.0112167\pi$
$684$	4.73205			0.180934
$685$	7.79423	−	13.5000i	0.297802	−	0.515808i
$686$	−7.85641	−	13.6077i	−0.299959	−	0.519544i
$687$	−3.92820	−	6.80385i	−0.149870	−	0.259583i
$688$	−4.19615			−0.159977
$689$		0			0
$690$	−14.1962			−0.540438
$691$	−12.7583	−	22.0981i	−0.485350	−	0.840650i	0.514509	−	0.857485i	$-0.327974\pi$
$691$	−12.7583	−	22.0981i	−0.485350	−	0.840650i	−0.999858	+	0.0168348i	$0.994641\pi$
$692$	2.19615	+	3.80385i	0.0834852	+	0.144601i
$693$	−0.803848	+	1.39230i	−0.0305356	+	0.0528893i
$694$	−18.5885			−0.705608
$695$	3.46410	−	6.00000i	0.131401	−	0.227593i
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	33.5885			1.27225
$698$	4.73205	−	8.19615i	0.179111	−	0.310229i
$699$	−9.00000	−	15.5885i	−0.340411	−	0.589610i
$700$	1.26795	+	2.19615i	0.0479240	+	0.0830068i
$701$	−16.3923			−0.619129			−0.309564	−	0.950878i	$-0.600183\pi$
$701$	−16.3923			−0.619129			−0.309564	+	0.950878i	$0.600183\pi$
$702$		0			0
$703$	14.1962			0.535418
$704$	−0.633975	−	1.09808i	−0.0238938	−	0.0413853i
$705$	−4.09808	−	7.09808i	−0.154342	−	0.267329i
$706$	−17.8923	+	30.9904i	−0.673386	+	1.16634i
$707$	24.5885			0.924744
$708$	−6.92820	+	12.0000i	−0.260378	+	0.450988i
$709$	22.6244	−	39.1865i	0.849676	−	1.47168i	−0.0318226	−	0.999494i	$-0.510131\pi$
$709$	22.6244	−	39.1865i	0.849676	−	1.47168i	0.881498	−	0.472188i	$-0.156536\pi$
$710$	3.80385			0.142756
$711$	−4.19615	+	7.26795i	−0.157368	+	0.272569i
$712$	4.73205	+	8.19615i	0.177341	+	0.307164i
$713$	38.7846	+	67.1769i	1.45250	+	2.51580i
$714$	6.58846			0.246567
$715$		0			0
$716$	2.19615			0.0820741
$717$	3.29423	+	5.70577i	0.123025	+	0.213086i
$718$	−8.02628	−	13.9019i	−0.299538	−	0.518815i
$719$	−15.8038	+	27.3731i	−0.589384	+	1.02084i	0.404929	+	0.914348i	$0.367296\pi$
$719$	−15.8038	+	27.3731i	−0.589384	+	1.02084i	−0.994313	+	0.106495i	$0.966037\pi$
$720$	1.73205			0.0645497
$721$	−3.92820	+	6.80385i	−0.146294	+	0.253389i
$722$	1.69615	−	2.93782i	0.0631243	−	0.109334i
$723$	−11.1962			−0.416389
$724$	−9.79423	+	16.9641i	−0.364000	+	0.630466i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	4.69615	+	8.13397i	0.174291	+	0.301880i
$727$	−13.8038			−0.511956			−0.255978	−	0.966683i	$-0.582398\pi$
$727$	−13.8038			−0.511956			−0.255978	+	0.966683i	$0.582398\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	10.5000	+	18.1865i	0.388622	+	0.673114i
$731$	10.9019	+	18.8827i	0.403222	+	0.698401i
$732$	7.59808	−	13.1603i	0.280833	−	0.486417i
$733$	20.3205			0.750555			0.375278	−	0.926912i	$-0.377547\pi$
$733$	20.3205			0.750555			0.375278	+	0.926912i	$0.377547\pi$
$734$	−6.90192	+	11.9545i	−0.254755	+	0.441248i
$735$	−4.66987	+	8.08846i	−0.172251	+	0.298347i
$736$	8.19615			0.302114
$737$	−4.60770	+	7.98076i	−0.169727	+	0.293975i
$738$	3.23205	+	5.59808i	0.118973	+	0.206068i
$739$	2.53590	+	4.39230i	0.0932845	+	0.161574i	0.908891	−	0.417033i	$-0.136930\pi$
$739$	2.53590	+	4.39230i	0.0932845	+	0.161574i	−0.815607	+	0.578607i	$0.803597\pi$
$740$	5.19615			0.191014
$741$		0			0
$742$	−3.80385			−0.139644
$743$	8.19615	+	14.1962i	0.300688	+	0.520806i	0.976292	−	0.216458i	$-0.0694505\pi$
$743$	8.19615	+	14.1962i	0.300688	+	0.520806i	−0.675604	+	0.737264i	$0.736117\pi$
$744$	−4.73205	−	8.19615i	−0.173485	−	0.300486i
$745$	−5.30385	+	9.18653i	−0.194318	+	0.336569i
$746$	27.9808			1.02445
$747$	−2.83013	+	4.90192i	−0.103549	+	0.179352i
$748$	−3.29423	+	5.70577i	−0.120449	+	0.208624i
$749$	−2.78461			−0.101747
$750$	6.06218	−	10.5000i	0.221359	−	0.383406i
$751$	−13.4904	−	23.3660i	−0.492271	−	0.852638i	0.507689	−	0.861540i	$-0.330500\pi$
$751$	−13.4904	−	23.3660i	−0.492271	−	0.852638i	−0.999960	+	0.00890181i	$0.997166\pi$
$752$	2.36603	+	4.09808i	0.0862801	+	0.149441i
$753$	−16.3923			−0.597369
$754$		0			0
$755$	18.5885			0.676503
$756$	0.633975	+	1.09808i	0.0230574	+	0.0399366i
$757$	11.3923	+	19.7321i	0.414060	+	0.717174i	0.995329	−	0.0965379i	$-0.0307769\pi$
$757$	11.3923	+	19.7321i	0.414060	+	0.717174i	−0.581269	+	0.813712i	$0.697444\pi$
$758$	15.1244	−	26.1962i	0.549341	−	0.951487i
$759$	10.3923			0.377217
$760$	4.09808	−	7.09808i	0.148653	−	0.257474i
$761$	−8.19615	+	14.1962i	−0.297110	+	0.514610i	−0.975474	−	0.220117i	$-0.929356\pi$
$761$	−8.19615	+	14.1962i	−0.297110	+	0.514610i	0.678363	+	0.734727i	$0.262690\pi$
$762$	−4.00000			−0.144905
$763$	2.78461	−	4.82309i	0.100810	−	0.174607i
$764$	10.3923	+	18.0000i	0.375980	+	0.651217i
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	23.3205			0.842604
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	10.8564	+	18.8038i	0.391492	+	0.678084i	0.992647	−	0.121049i	$-0.0386257\pi$
$769$	10.8564	+	18.8038i	0.391492	+	0.678084i	−0.601155	+	0.799133i	$0.705292\pi$
$770$	1.39230	+	2.41154i	0.0501752	+	0.0869060i
$771$	11.5981	−	20.0885i	0.417695	−	0.723468i
$772$	−23.1962			−0.834848
$773$	4.60770	−	7.98076i	0.165727	−	0.287048i	−0.771186	−	0.636610i	$-0.780336\pi$
$773$	4.60770	−	7.98076i	0.165727	−	0.287048i	0.936913	+	0.349562i	$0.113670\pi$
$774$	−2.09808	+	3.63397i	−0.0754138	+	0.130621i
$775$	−18.9282			−0.679921
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	1.90192	+	3.29423i	0.0682311	+	0.118180i
$778$	3.69615	+	6.40192i	0.132513	+	0.229520i
$779$	30.5885			1.09595
$780$		0			0
$781$	−2.78461			−0.0996412
$782$	−21.2942	−	36.8827i	−0.761480	−	1.31892i
$783$	−1.50000	−	2.59808i	−0.0536056	−	0.0928477i
$784$	2.69615	−	4.66987i	0.0962912	−	0.166781i
$785$	12.4641			0.444863
$786$	2.19615	−	3.80385i	0.0783342	−	0.135679i
$787$	10.7321	−	18.5885i	0.382556	−	0.662607i	−0.608871	−	0.793270i	$-0.708377\pi$
$787$	10.7321	−	18.5885i	0.382556	−	0.662607i	0.991427	+	0.130663i	$0.0417105\pi$
$788$	−6.92820			−0.246807
$789$	4.09808	−	7.09808i	0.145895	−	0.252698i
$790$	7.26795	+	12.5885i	0.258582	+	0.447877i
$791$	−0.509619	−	0.882686i	−0.0181200	−	0.0313847i
$792$	−1.26795			−0.0450546
$793$		0			0
$794$	−4.39230			−0.155877
$795$	2.59808	+	4.50000i	0.0921443	+	0.159599i
$796$	11.2942	+	19.5622i	0.400313	+	0.693363i
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	−0.914255	−	0.405140i	$-0.867223\pi$
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	0.807989	+	0.589197i	$0.200556\pi$
$798$	6.00000			0.212398
$799$	12.2942	−	21.2942i	0.434939	−	0.753336i
$800$	−1.00000	+	1.73205i	−0.0353553	+	0.0612372i
$801$	9.46410			0.334398
$802$	10.5000	−	18.1865i	0.370768	−	0.642189i
$803$	−7.68653	−	13.3135i	−0.271252	−	0.469822i
$804$	3.63397	+	6.29423i	0.128160	+	0.221980i
$805$	−18.0000			−0.634417
$806$		0			0
$807$	7.60770			0.267804
$808$	9.69615	+	16.7942i	0.341109	+	0.590819i
$809$	18.4019	+	31.8731i	0.646977	+	1.12060i	0.983841	+	0.179044i	$0.0573004\pi$
$809$	18.4019	+	31.8731i	0.646977	+	1.12060i	−0.336864	+	0.941553i	$0.609366\pi$
$810$	0.866025	−	1.50000i	0.0304290	−	0.0527046i
$811$	−16.3923			−0.575612			−0.287806	−	0.957689i	$-0.592926\pi$
$811$	−16.3923			−0.575612			−0.287806	+	0.957689i	$0.592926\pi$
$812$	1.90192	−	3.29423i	0.0667444	−	0.115605i
$813$		0			0
$814$	−3.80385			−0.133325
$815$	−2.19615	+	3.80385i	−0.0769279	+	0.133243i
$816$	2.59808	+	4.50000i	0.0909509	+	0.157532i
$817$	9.92820	+	17.1962i	0.347344	+	0.601617i
$818$	20.6603			0.722369
$819$		0			0
$820$	11.1962			0.390987
$821$	−14.3205	−	24.8038i	−0.499789	−	0.865660i	0.500211	−	0.865904i	$-0.333256\pi$
$821$	−14.3205	−	24.8038i	−0.499789	−	0.865660i	−1.00000		0.000243419i	$0.999923\pi$
$822$	4.50000	+	7.79423i	0.156956	+	0.271855i
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$	−6.19615			−0.215853
$825$	−1.26795	+	2.19615i	−0.0441443	+	0.0764602i
$826$	−8.78461	+	15.2154i	−0.305656	+	0.529411i
$827$	44.1051			1.53369			0.766843	−	0.641835i	$-0.221827\pi$
$827$	44.1051			1.53369			0.766843	+	0.641835i	$0.221827\pi$
$828$	4.09808	−	7.09808i	0.142418	−	0.246675i
$829$	−19.9904	−	34.6244i	−0.694295	−	1.20255i	−0.970418	−	0.241431i	$-0.922383\pi$
$829$	−19.9904	−	34.6244i	−0.694295	−	1.20255i	0.276123	−	0.961122i	$-0.410950\pi$
$830$	4.90192	+	8.49038i	0.170148	+	0.294705i
$831$	−4.80385			−0.166644
$832$		0			0
$833$	−28.0192			−0.970809
$834$	2.00000	+	3.46410i	0.0692543	+	0.119952i
$835$	8.19615	+	14.1962i	0.283640	+	0.491278i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$	−9.46410			−0.327127
$838$	−2.19615	+	3.80385i	−0.0758648	+	0.131402i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$	2.19615			0.0757745
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−3.23205	−	5.59808i	−0.111384	−	0.192922i
$843$	8.76795	+	15.1865i	0.301984	+	0.523052i
$844$	−24.3923			−0.839618
$845$		0			0
$846$	4.73205			0.162691
$847$	5.95448	+	10.3135i	0.204598	+	0.354375i
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$	−9.90192	+	17.1506i	−0.339833	+	0.588608i
$850$	10.3923			0.356453
$851$	12.2942	−	21.2942i	0.421441	−	0.729957i
$852$	−1.09808	+	1.90192i	−0.0376195	+	0.0651588i
$853$	9.00000			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$854$	9.63397	−	16.6865i	0.329668	−	0.571001i
$855$	−4.09808	−	7.09808i	−0.140151	−	0.242749i
$856$	−1.09808	−	1.90192i	−0.0375315	−	0.0650064i
$857$	18.3731			0.627612			0.313806	−	0.949487i	$-0.398396\pi$
$857$	18.3731			0.627612			0.313806	+	0.949487i	$0.398396\pi$
$858$		0			0
$859$	−20.5885			−0.702469			−0.351235	−	0.936288i	$-0.614238\pi$
$859$	−20.5885			−0.702469			−0.351235	+	0.936288i	$0.614238\pi$
$860$	3.63397	+	6.29423i	0.123918	+	0.214631i
$861$	4.09808	+	7.09808i	0.139662	+	0.241902i
$862$	19.0981	−	33.0788i	0.650483	−	1.12667i
$863$	49.5167			1.68557			0.842783	−	0.538253i	$-0.180915\pi$
$863$	49.5167			1.68557			0.842783	+	0.538253i	$0.180915\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	3.80385	−	6.58846i	0.129335	−	0.224014i
$866$	−7.78461			−0.264532
$867$	5.00000	−	8.66025i	0.169809	−	0.294118i
$868$	−6.00000	−	10.3923i	−0.203653	−	0.352738i
$869$	−5.32051	−	9.21539i	−0.180486	−	0.312611i
$870$	−5.19615			−0.176166
$871$		0			0
$872$	4.39230			0.148742
$873$	−3.00000	−	5.19615i	−0.101535	−	0.175863i
$874$	−19.3923	−	33.5885i	−0.655954	−	1.13615i
$875$	7.68653	−	13.3135i	0.259852	−	0.450077i
$876$	−12.1244			−0.409644
$877$	−11.3038	+	19.5788i	−0.381704	+	0.661130i	−0.991306	−	0.131577i	$-0.957996\pi$
$877$	−11.3038	+	19.5788i	−0.381704	+	0.661130i	0.609602	+	0.792708i	$0.291329\pi$
$878$	−7.29423	+	12.6340i	−0.246168	+	0.426376i
$879$	−2.66025			−0.0897281
$880$	−1.09808	+	1.90192i	−0.0370161	+	0.0641138i
$881$	6.99038	+	12.1077i	0.235512	+	0.407919i	0.959421	−	0.281976i	$-0.0909900\pi$
$881$	6.99038	+	12.1077i	0.235512	+	0.407919i	−0.723909	+	0.689895i	$0.757657\pi$
$882$	−2.69615	−	4.66987i	−0.0907842	−	0.157243i
$883$	16.7846			0.564847			0.282424	−	0.959290i	$-0.408862\pi$
$883$	16.7846			0.564847			0.282424	+	0.959290i	$0.408862\pi$
$884$		0			0
$885$	24.0000			0.806751
$886$	8.19615	+	14.1962i	0.275355	+	0.476929i
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$	−1.50000	+	2.59808i	−0.0503367	+	0.0871857i
$889$	−5.07180			−0.170103
$890$	8.19615	−	14.1962i	0.274736	−	0.475856i
$891$	−0.633975	+	1.09808i	−0.0212389	+	0.0367869i
$892$	−5.07180			−0.169816
$893$	11.1962	−	19.3923i	0.374665	−	0.648939i
$894$	−3.06218	−	5.30385i	−0.102415	−	0.177387i
$895$	−1.90192	−	3.29423i	−0.0635743	−	0.110114i
$896$	−1.26795			−0.0423592
$897$		0			0
$898$	−26.5359			−0.885514
$899$	14.1962	+	24.5885i	0.473468	+	0.820071i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	−7.79423	+	13.5000i	−0.259663	+	0.449750i
$902$	−8.19615			−0.272902
$903$	−2.66025	+	4.60770i	−0.0885277	+	0.153334i
$904$	0.401924	−	0.696152i	0.0133678	−	0.0231537i
$905$	33.9282			1.12781
$906$	−5.36603	+	9.29423i	−0.178274	+	0.308780i
$907$	−10.5885	−	18.3397i	−0.351584	−	0.608961i	0.634943	−	0.772559i	$-0.281023\pi$
$907$	−10.5885	−	18.3397i	−0.351584	−	0.608961i	−0.986527	+	0.163598i	$0.947690\pi$
$908$	10.0981	+	17.4904i	0.335116	+	0.580439i
$909$	19.3923			0.643202
$910$		0			0
$911$	−25.1769			−0.834148			−0.417074	−	0.908872i	$-0.636944\pi$
$911$	−25.1769			−0.834148			−0.417074	+	0.908872i	$0.636944\pi$
$912$	2.36603	+	4.09808i	0.0783469	+	0.135701i
$913$	−3.58846	−	6.21539i	−0.118761	−	0.205699i
$914$	−15.9904	+	27.6962i	−0.528915	+	0.916107i
$915$	−26.3205			−0.870129
$916$	3.92820	−	6.80385i	0.129791	−	0.224805i
$917$	2.78461	−	4.82309i	0.0919559	−	0.159272i
$918$	5.19615			0.171499
$919$	−5.80385	+	10.0526i	−0.191451	+	0.331603i	−0.945731	−	0.324949i	$-0.894653\pi$
$919$	−5.80385	+	10.0526i	−0.191451	+	0.331603i	0.754280	+	0.656553i	$0.227986\pi$
$920$	−7.09808	−	12.2942i	−0.234017	−	0.405329i
$921$	3.63397	+	6.29423i	0.119744	+	0.207402i
$922$	−31.9808			−1.05323
$923$		0			0
$924$	−1.60770			−0.0528893
$925$	3.00000	+	5.19615i	0.0986394	+	0.170848i
$926$	−7.90192	−	13.6865i	−0.259673	−	0.449767i
$927$	−3.09808	+	5.36603i	−0.101754	+	0.176243i
$928$	3.00000			0.0984798
$929$	27.6962	−	47.9711i	0.908681	−	1.57388i	0.0927833	−	0.995686i	$-0.470424\pi$
$929$	27.6962	−	47.9711i	0.908681	−	1.57388i	0.815898	−	0.578196i	$-0.196243\pi$
$930$	−8.19615	+	14.1962i	−0.268762	+	0.465510i
$931$	−25.5167			−0.836275
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$	−4.09808	−	7.09808i	−0.134165	−	0.232381i
$934$	2.70577	+	4.68653i	0.0885355	+	0.153348i
$935$	11.4115			0.373197
$936$		0			0
$937$	−15.3923			−0.502845			−0.251422	−	0.967877i	$-0.580898\pi$
$937$	−15.3923			−0.502845			−0.251422	+	0.967877i	$0.580898\pi$
$938$	4.60770	+	7.98076i	0.150447	+	0.260581i
$939$	−1.80385	−	3.12436i	−0.0588663	−	0.101959i
$940$	4.09808	−	7.09808i	0.133665	−	0.231514i
$941$	−38.7846			−1.26434			−0.632171	−	0.774829i	$-0.717836\pi$
$941$	−38.7846			−1.26434			−0.632171	+	0.774829i	$0.717836\pi$
$942$	−3.59808	+	6.23205i	−0.117232	+	0.203051i
$943$	26.4904	−	45.8827i	0.862645	−	1.49415i
$944$	−13.8564			−0.450988
$945$	1.09808	−	1.90192i	0.0357204	−	0.0618696i
$946$	−2.66025	−	4.60770i	−0.0864923	−	0.149809i
$947$	14.5359	+	25.1769i	0.472353	+	0.818140i	0.999499	−	0.0316348i	$-0.0100713\pi$
$947$	14.5359	+	25.1769i	0.472353	+	0.818140i	−0.527146	+	0.849775i	$0.676738\pi$
$948$	−8.39230			−0.272569
$949$		0			0
$950$	9.46410			0.307056
$951$	−9.06218	−	15.6962i	−0.293861	−	0.508983i
$952$	3.29423	+	5.70577i	0.106767	+	0.184925i
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	−0.603559	−	0.797318i	$-0.706251\pi$
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	0.992277	+	0.124039i	$0.0395847\pi$
$954$	−3.00000			−0.0971286
$955$	18.0000	−	31.1769i	0.582466	−	1.00886i
$956$	−3.29423	+	5.70577i	−0.106543	+	0.184538i
$957$	3.80385			0.122961
$958$	−0.339746	+	0.588457i	−0.0109767	+	0.0190122i
$959$	5.70577	+	9.88269i	0.184249	+	0.319129i
$960$	0.866025	+	1.50000i	0.0279508	+	0.0484123i
$961$	58.5692			1.88933
$962$		0			0
$963$	−2.19615			−0.0707700
$964$	−5.59808	−	9.69615i	−0.180302	−	0.312292i
$965$	20.0885	+	34.7942i	0.646670	+	1.12007i
$966$	5.19615	−	9.00000i	0.167183	−	0.289570i
$967$	−39.1244			−1.25815			−0.629077	−	0.777343i	$-0.716567\pi$
$967$	−39.1244			−1.25815			−0.629077	+	0.777343i	$0.716567\pi$
$968$	−4.69615	+	8.13397i	−0.150940	+	0.261436i
$969$	12.2942	−	21.2942i	0.394948	−	0.684069i
$970$	−10.3923			−0.333677
$971$	−24.5885	+	42.5885i	−0.789081	+	1.36673i	0.137449	+	0.990509i	$0.456110\pi$
$971$	−24.5885	+	42.5885i	−0.789081	+	1.36673i	−0.926530	+	0.376220i	$0.877224\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	2.53590	+	4.39230i	0.0812972	+	0.140811i
$974$	15.1244			0.484616
$975$		0			0
$976$	15.1962			0.486417
$977$	−5.42820	−	9.40192i	−0.173664	−	0.300794i	0.766034	−	0.642800i	$-0.222227\pi$
$977$	−5.42820	−	9.40192i	−0.173664	−	0.300794i	−0.939698	+	0.342005i	$0.888894\pi$
$978$	−1.26795	−	2.19615i	−0.0405445	−	0.0702252i
$979$	−6.00000	+	10.3923i	−0.191761	+	0.332140i
$980$	−9.33975			−0.298347
$981$	2.19615	−	3.80385i	0.0701178	−	0.121448i
$982$	−15.2942	+	26.4904i	−0.488058	+	0.845342i
$983$	20.7846			0.662926			0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846			0.662926			0.331463	+	0.943468i	$0.392458\pi$
$984$	−3.23205	+	5.59808i	−0.103034	+	0.178460i
$985$	6.00000	+	10.3923i	0.191176	+	0.331126i
$986$	−7.79423	−	13.5000i	−0.248219	−	0.429928i
$987$	6.00000			0.190982
$988$		0			0
$989$	34.3923			1.09361
$990$	1.09808	+	1.90192i	0.0348992	+	0.0604471i
$991$	21.6865	+	37.5622i	0.688895	+	1.19320i	0.972196	+	0.234171i	$0.0752374\pi$
$991$	21.6865	+	37.5622i	0.688895	+	1.19320i	−0.283300	+	0.959031i	$0.591429\pi$
$992$	4.73205	−	8.19615i	0.150243	−	0.260228i
$993$	−12.0000			−0.380808
$994$	−1.39230	+	2.41154i	−0.0441612	+	0.0764895i
$995$	19.5622	−	33.8827i	0.620163	−	1.07415i
$996$	−5.66025			−0.179352
$997$	−1.40192	+	2.42820i	−0.0443994	+	0.0769020i	−0.887371	−	0.461056i	$-0.847471\pi$
$997$	−1.40192	+	2.42820i	−0.0443994	+	0.0769020i	0.842972	+	0.537958i	$0.180804\pi$
$998$		0			0
$999$	1.50000	+	2.59808i	0.0474579	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.j.991.2		4
13.2	odd	12		1014.2.b.d.337.3		4
13.3	even	3		1014.2.a.h.1.2		2
13.4	even	6		1014.2.e.h.529.1		4
13.5	odd	4		1014.2.i.f.361.2		4
13.6	odd	12		78.2.i.b.43.1	✓	4
13.7	odd	12		1014.2.i.f.823.2		4
13.8	odd	4		78.2.i.b.49.1	yes	4
13.9	even	3	inner	1014.2.e.j.529.2		4
13.10	even	6		1014.2.a.j.1.1		2
13.11	odd	12		1014.2.b.d.337.2		4
13.12	even	2		1014.2.e.h.991.1		4
39.2	even	12		3042.2.b.l.1351.2		4
39.8	even	4		234.2.l.a.127.2		4
39.11	even	12		3042.2.b.l.1351.3		4
39.23	odd	6		3042.2.a.s.1.2		2
39.29	odd	6		3042.2.a.v.1.1		2
39.32	even	12		234.2.l.a.199.2		4
52.3	odd	6		8112.2.a.bq.1.2		2
52.19	even	12		624.2.bv.d.433.1		4
52.23	odd	6		8112.2.a.bx.1.1		2
52.47	even	4		624.2.bv.d.49.1		4
65.8	even	4		1950.2.y.h.49.1		4
65.19	odd	12		1950.2.bc.c.901.2		4
65.32	even	12		1950.2.y.h.199.1		4
65.34	odd	4		1950.2.bc.c.751.2		4
65.47	even	4		1950.2.y.a.49.2		4
65.58	even	12		1950.2.y.a.199.2		4
156.47	odd	4		1872.2.by.k.1297.1		4
156.71	odd	12		1872.2.by.k.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.1	✓	4	13.6	odd	12
78.2.i.b.49.1	yes	4	13.8	odd	4
234.2.l.a.127.2		4	39.8	even	4
234.2.l.a.199.2		4	39.32	even	12
624.2.bv.d.49.1		4	52.47	even	4
624.2.bv.d.433.1		4	52.19	even	12
1014.2.a.h.1.2		2	13.3	even	3
1014.2.a.j.1.1		2	13.10	even	6
1014.2.b.d.337.2		4	13.11	odd	12
1014.2.b.d.337.3		4	13.2	odd	12
1014.2.e.h.529.1		4	13.4	even	6
1014.2.e.h.991.1		4	13.12	even	2
1014.2.e.j.529.2		4	13.9	even	3	inner
1014.2.e.j.991.2		4	1.1	even	1	trivial
1014.2.i.f.361.2		4	13.5	odd	4
1014.2.i.f.823.2		4	13.7	odd	12
1872.2.by.k.433.1		4	156.71	odd	12
1872.2.by.k.1297.1		4	156.47	odd	4
1950.2.y.a.49.2		4	65.47	even	4
1950.2.y.a.199.2		4	65.58	even	12
1950.2.y.h.49.1		4	65.8	even	4
1950.2.y.h.199.1		4	65.32	even	12
1950.2.bc.c.751.2		4	65.34	odd	4
1950.2.bc.c.901.2		4	65.19	odd	12
3042.2.a.s.1.2		2	39.23	odd	6
3042.2.a.v.1.1		2	39.29	odd	6
3042.2.b.l.1351.2		4	39.2	even	12
3042.2.b.l.1351.3		4	39.11	even	12
8112.2.a.bq.1.2		2	52.3	odd	6
8112.2.a.bx.1.1		2	52.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.633975 + 1.09808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.633975 + 1.09808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.866025 + 1.50000i) q^{10} +(-0.633975 - 1.09808i) q^{11} -1.00000 q^{12} -1.26795 q^{14} +(0.866025 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 4.50000i) q^{17} -1.00000 q^{18} +(-2.36603 + 4.09808i) q^{19} +(-0.866025 + 1.50000i) q^{20} -1.26795 q^{21} +(0.633975 - 1.09808i) q^{22} +(4.09808 + 7.09808i) q^{23} +(-0.500000 - 0.866025i) q^{24} -2.00000 q^{25} -1.00000 q^{27} +(-0.633975 - 1.09808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.866025 + 1.50000i) q^{30} +9.46410 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.633975 - 1.09808i) q^{33} -5.19615 q^{34} +(-1.09808 + 1.90192i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.50000 - 2.59808i) q^{37} -4.73205 q^{38} -1.73205 q^{40} +(-3.23205 - 5.59808i) q^{41} +(-0.633975 - 1.09808i) q^{42} +(2.09808 - 3.63397i) q^{43} +1.26795 q^{44} +(-0.866025 + 1.50000i) q^{45} +(-4.09808 + 7.09808i) q^{46} -4.73205 q^{47} +(0.500000 - 0.866025i) q^{48} +(2.69615 + 4.66987i) q^{49} +(-1.00000 - 1.73205i) q^{50} -5.19615 q^{51} +3.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.09808 - 1.90192i) q^{55} +(0.633975 - 1.09808i) q^{56} -4.73205 q^{57} +(-1.50000 + 2.59808i) q^{58} +(6.92820 - 12.0000i) q^{59} -1.73205 q^{60} +(-7.59808 + 13.1603i) q^{61} +(4.73205 + 8.19615i) q^{62} +(-0.633975 - 1.09808i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-3.63397 - 6.29423i) q^{67} +(-2.59808 - 4.50000i) q^{68} +(-4.09808 + 7.09808i) q^{69} -2.19615 q^{70} +(1.09808 - 1.90192i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.1244 q^{73} +(1.50000 - 2.59808i) q^{74} +(-1.00000 - 1.73205i) q^{75} +(-2.36603 - 4.09808i) q^{76} +1.60770 q^{77} +8.39230 q^{79} +(-0.866025 - 1.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.23205 - 5.59808i) q^{82} +5.66025 q^{83} +(0.633975 - 1.09808i) q^{84} +(-4.50000 + 7.79423i) q^{85} +4.19615 q^{86} +(-1.50000 + 2.59808i) q^{87} +(0.633975 + 1.09808i) q^{88} +(-4.73205 - 8.19615i) q^{89} -1.73205 q^{90} -8.19615 q^{92} +(4.73205 + 8.19615i) q^{93} +(-2.36603 - 4.09808i) q^{94} +(-4.09808 + 7.09808i) q^{95} +1.00000 q^{96} +(-3.00000 + 5.19615i) q^{97} +(-2.69615 + 4.66987i) q^{98} +1.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 - 6 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9} - 6 q^{11} - 4 q^{12} - 12 q^{14} - 2 q^{16} - 4 q^{18} - 6 q^{19} - 12 q^{21} + 6 q^{22} + 6 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{27} - 6 q^{28} + 6 q^{29} + 24 q^{31} + 2 q^{32} + 6 q^{33} + 6 q^{35} - 2 q^{36} - 6 q^{37} - 12 q^{38} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 12 q^{44} - 6 q^{46} - 12 q^{47} + 2 q^{48} - 10 q^{49} - 4 q^{50} + 12 q^{53} - 2 q^{54} + 6 q^{55} + 6 q^{56} - 12 q^{57} - 6 q^{58} - 20 q^{61} + 12 q^{62} - 6 q^{63} + 4 q^{64} + 12 q^{66} - 18 q^{67} - 6 q^{69} + 12 q^{70} - 6 q^{71} + 2 q^{72} + 6 q^{74} - 4 q^{75} - 6 q^{76} + 48 q^{77} - 8 q^{79} - 2 q^{81} + 6 q^{82} - 12 q^{83} + 6 q^{84} - 18 q^{85} - 4 q^{86} - 6 q^{87} + 6 q^{88} - 12 q^{89} - 12 q^{92} + 12 q^{93} - 6 q^{94} - 6 q^{95} + 4 q^{96} - 12 q^{97} + 10 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 - 6 * q^7 - 4 * q^8 - 2 * q^9 - 6 * q^11 - 4 * q^12 - 12 * q^14 - 2 * q^16 - 4 * q^18 - 6 * q^19 - 12 * q^21 + 6 * q^22 + 6 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^27 - 6 * q^28 + 6 * q^29 + 24 * q^31 + 2 * q^32 + 6 * q^33 + 6 * q^35 - 2 * q^36 - 6 * q^37 - 12 * q^38 - 6 * q^41 - 6 * q^42 - 2 * q^43 + 12 * q^44 - 6 * q^46 - 12 * q^47 + 2 * q^48 - 10 * q^49 - 4 * q^50 + 12 * q^53 - 2 * q^54 + 6 * q^55 + 6 * q^56 - 12 * q^57 - 6 * q^58 - 20 * q^61 + 12 * q^62 - 6 * q^63 + 4 * q^64 + 12 * q^66 - 18 * q^67 - 6 * q^69 + 12 * q^70 - 6 * q^71 + 2 * q^72 + 6 * q^74 - 4 * q^75 - 6 * q^76 + 48 * q^77 - 8 * q^79 - 2 * q^81 + 6 * q^82 - 12 * q^83 + 6 * q^84 - 18 * q^85 - 4 * q^86 - 6 * q^87 + 6 * q^88 - 12 * q^89 - 12 * q^92 + 12 * q^93 - 6 * q^94 - 6 * q^95 + 4 * q^96 - 12 * q^97 + 10 * q^98 + 12 * q^99

Introduction

L-functions

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