LMFDB - Embedded newform 1014.2.e.h.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.h.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.36603 - 4.09808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(2.36603 - 4.09808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.866025 - 1.50000i) q^{10} +(2.36603 + 4.09808i) q^{11} -1.00000 q^{12} -4.73205 q^{14} +(0.866025 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.59808 - 4.50000i) q^{17} +1.00000 q^{18} +(0.633975 - 1.09808i) q^{19} +(-0.866025 + 1.50000i) q^{20} +4.73205 q^{21} +(2.36603 - 4.09808i) q^{22} +(-1.09808 - 1.90192i) q^{23} +(0.500000 + 0.866025i) q^{24} -2.00000 q^{25} -1.00000 q^{27} +(2.36603 + 4.09808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(0.866025 - 1.50000i) q^{30} -2.53590 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -5.19615 q^{34} +(4.09808 - 7.09808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} -1.26795 q^{38} +1.73205 q^{40} +(-0.232051 - 0.401924i) q^{41} +(-2.36603 - 4.09808i) q^{42} +(-3.09808 + 5.36603i) q^{43} -4.73205 q^{44} +(-0.866025 + 1.50000i) q^{45} +(-1.09808 + 1.90192i) q^{46} +1.26795 q^{47} +(0.500000 - 0.866025i) q^{48} +(-7.69615 - 13.3301i) q^{49} +(1.00000 + 1.73205i) q^{50} +5.19615 q^{51} +3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(4.09808 + 7.09808i) q^{55} +(2.36603 - 4.09808i) q^{56} +1.26795 q^{57} +(1.50000 - 2.59808i) q^{58} +(6.92820 - 12.0000i) q^{59} -1.73205 q^{60} +(-2.40192 + 4.16025i) q^{61} +(1.26795 + 2.19615i) q^{62} +(2.36603 + 4.09808i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.36603 + 9.29423i) q^{67} +(2.59808 + 4.50000i) q^{68} +(1.09808 - 1.90192i) q^{69} -8.19615 q^{70} +(4.09808 - 7.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} +12.1244 q^{73} +(1.50000 - 2.59808i) q^{74} +(-1.00000 - 1.73205i) q^{75} +(0.633975 + 1.09808i) q^{76} +22.3923 q^{77} -12.3923 q^{79} +(-0.866025 - 1.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.232051 + 0.401924i) q^{82} +11.6603 q^{83} +(-2.36603 + 4.09808i) q^{84} +(4.50000 - 7.79423i) q^{85} +6.19615 q^{86} +(-1.50000 + 2.59808i) q^{87} +(2.36603 + 4.09808i) q^{88} +(1.26795 + 2.19615i) q^{89} +1.73205 q^{90} +2.19615 q^{92} +(-1.26795 - 2.19615i) q^{93} +(-0.633975 - 1.09808i) q^{94} +(1.09808 - 1.90192i) q^{95} -1.00000 q^{96} +(3.00000 - 5.19615i) q^{97} +(-7.69615 + 13.3301i) q^{98} -4.73205 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
$7$	2.36603	−	4.09808i	0.894274	−	1.54893i	0.0595724	−	0.998224i	$-0.481026\pi$
$7$	2.36603	−	4.09808i	0.894274	−	1.54893i	0.834701	−	0.550703i	$-0.185640\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.866025	−	1.50000i	−0.273861	−	0.474342i
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	0.963580	+	0.267421i	$0.0861715\pi$
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	−0.250196	+	0.968195i	$0.580495\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−4.73205			−1.26469
$15$	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	$-0.616337\pi$
$17$	2.59808	−	4.50000i	0.630126	−	1.09141i	0.987526	−	0.157459i	$-0.0503301\pi$
$18$	1.00000			0.235702
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	−0.784095	−	0.620641i	$-0.786872\pi$
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	0.929538	+	0.368725i	$0.120206\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$	4.73205			1.03262
$22$	2.36603	−	4.09808i	0.504438	−	0.873713i
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	0.728537	−	0.685007i	$-0.240201\pi$
$23$	−1.09808	−	1.90192i	−0.228965	−	0.396579i	−0.957502	+	0.288428i	$0.906867\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−2.00000			−0.400000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	2.36603	+	4.09808i	0.447137	+	0.774464i
$29$	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
$31$	−2.53590			−0.455461			−0.227730	−	0.973724i	$-0.573130\pi$
$31$	−2.53590			−0.455461			−0.227730	+	0.973724i	$0.573130\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.36603	+	4.09808i	−0.411872	+	0.713384i
$34$	−5.19615			−0.891133
$35$	4.09808	−	7.09808i	0.692701	−	1.19979i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$	−1.26795			−0.205689
$39$		0			0
$40$	1.73205			0.273861
$41$	−0.232051	−	0.401924i	−0.0362402	−	0.0627700i	0.847336	−	0.531057i	$-0.178205\pi$
$41$	−0.232051	−	0.401924i	−0.0362402	−	0.0627700i	−0.883577	+	0.468287i	$0.844871\pi$
$42$	−2.36603	−	4.09808i	−0.365086	−	0.632347i
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	−0.999503	−	0.0315225i	$-0.989964\pi$
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	0.527051	+	0.849834i	$0.323298\pi$
$44$	−4.73205			−0.713384
$45$	−0.866025	+	1.50000i	−0.129099	+	0.223607i
$46$	−1.09808	+	1.90192i	−0.161903	+	0.280423i
$47$	1.26795			0.184949			0.0924747	−	0.995715i	$-0.470522\pi$
$47$	1.26795			0.184949			0.0924747	+	0.995715i	$0.470522\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−7.69615	−	13.3301i	−1.09945	−	1.90430i
$50$	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
$55$	4.09808	+	7.09808i	0.552584	+	0.957104i
$56$	2.36603	−	4.09808i	0.316173	−	0.547628i
$57$	1.26795			0.167944
$58$	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
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	−0.977822	−	0.209435i	$-0.932837\pi$
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	0.670288	+	0.742101i	$0.266171\pi$
$62$	1.26795	+	2.19615i	0.161030	+	0.278912i
$63$	2.36603	+	4.09808i	0.298091	+	0.516309i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.73205			0.582475
$67$	5.36603	+	9.29423i	0.655564	+	1.13547i	0.981752	+	0.190166i	$0.0609025\pi$
$67$	5.36603	+	9.29423i	0.655564	+	1.13547i	−0.326188	+	0.945305i	$0.605764\pi$
$68$	2.59808	+	4.50000i	0.315063	+	0.545705i
$69$	1.09808	−	1.90192i	0.132193	−	0.228965i
$70$	−8.19615			−0.979628
$71$	4.09808	−	7.09808i	0.486352	−	0.842387i	−0.513525	−	0.858075i	$-0.671661\pi$
$71$	4.09808	−	7.09808i	0.486352	−	0.842387i	0.999877	+	0.0156881i	$0.00499388\pi$
$72$	−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
$76$	0.633975	+	1.09808i	0.0727219	+	0.125958i
$77$	22.3923			2.55184
$78$		0			0
$79$	−12.3923			−1.39424			−0.697122	−	0.716953i	$-0.745536\pi$
$79$	−12.3923			−1.39424			−0.697122	+	0.716953i	$0.745536\pi$
$80$	−0.866025	−	1.50000i	−0.0968246	−	0.167705i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.232051	+	0.401924i	−0.0256257	+	0.0443851i
$83$	11.6603			1.27988			0.639940	−	0.768425i	$-0.278959\pi$
$83$	11.6603			1.27988			0.639940	+	0.768425i	$0.278959\pi$
$84$	−2.36603	+	4.09808i	−0.258155	+	0.447137i
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$	6.19615			0.668148
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	2.36603	+	4.09808i	0.252219	+	0.436856i
$89$	1.26795	+	2.19615i	0.134402	+	0.232792i	0.925369	−	0.379068i	$-0.123755\pi$
$89$	1.26795	+	2.19615i	0.134402	+	0.232792i	−0.790967	+	0.611859i	$0.790422\pi$
$90$	1.73205			0.182574
$91$		0			0
$92$	2.19615			0.228965
$93$	−1.26795	−	2.19615i	−0.131480	−	0.227730i
$94$	−0.633975	−	1.09808i	−0.0653895	−	0.113258i
$95$	1.09808	−	1.90192i	0.112660	−	0.195133i
$96$	−1.00000			−0.102062
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$	−7.69615	+	13.3301i	−0.777429	+	1.34655i
$99$	−4.73205			−0.475589
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	0.696152	+	1.20577i	0.0692698	+	0.119979i	0.898580	−	0.438810i	$-0.144600\pi$
$101$	0.696152	+	1.20577i	0.0692698	+	0.119979i	−0.829310	+	0.558788i	$0.811266\pi$
$102$	−2.59808	−	4.50000i	−0.257248	−	0.445566i
$103$	−4.19615			−0.413459			−0.206730	−	0.978398i	$-0.566282\pi$
$103$	−4.19615			−0.413459			−0.206730	+	0.978398i	$0.566282\pi$
$104$		0			0
$105$	8.19615			0.799863
$106$	−1.50000	−	2.59808i	−0.145693	−	0.252347i
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	0.597075	−	0.802186i	$-0.296330\pi$
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	−0.993251	+	0.115989i	$0.962996\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−16.3923			−1.57010			−0.785049	−	0.619434i	$-0.787362\pi$
$109$	−16.3923			−1.57010			−0.785049	+	0.619434i	$0.787362\pi$
$110$	4.09808	−	7.09808i	0.390736	−	0.676775i
$111$	−1.50000	+	2.59808i	−0.142374	+	0.246598i
$112$	−4.73205			−0.447137
$113$	−5.59808	+	9.69615i	−0.526623	+	0.912137i	0.472896	+	0.881118i	$0.343209\pi$
$113$	−5.59808	+	9.69615i	−0.526623	+	0.912137i	−0.999519	+	0.0310191i	$0.990125\pi$
$114$	−0.633975	−	1.09808i	−0.0593772	−	0.102844i
$115$	−1.90192	−	3.29423i	−0.177355	−	0.307188i
$116$	−3.00000			−0.278543
$117$		0			0
$118$	−13.8564			−1.27559
$119$	−12.2942	−	21.2942i	−1.12701	−	1.95204i
$120$	0.866025	+	1.50000i	0.0790569	+	0.136931i
$121$	−5.69615	+	9.86603i	−0.517832	+	0.896911i
$122$	4.80385			0.434920
$123$	0.232051	−	0.401924i	0.0209233	−	0.0362402i
$124$	1.26795	−	2.19615i	0.113865	−	0.197220i
$125$	−12.1244			−1.08444
$126$	2.36603	−	4.09808i	0.210782	−	0.365086i
$127$	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
$129$	−6.19615			−0.545541
$130$		0			0
$131$	16.3923			1.43220			0.716101	−	0.697997i	$-0.245925\pi$
$131$	16.3923			1.43220			0.716101	+	0.697997i	$0.245925\pi$
$132$	−2.36603	−	4.09808i	−0.205936	−	0.356692i
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$	5.36603	−	9.29423i	0.463554	−	0.802899i
$135$	−1.73205			−0.149071
$136$	2.59808	−	4.50000i	0.222783	−	0.385872i
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$	−2.19615			−0.186949
$139$	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	$0.112407\pi$
$140$	4.09808	+	7.09808i	0.346351	+	0.599897i
$141$	0.633975	+	1.09808i	0.0533903	+	0.0924747i
$142$	−8.19615			−0.687806
$143$		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
$147$	7.69615	−	13.3301i	0.634768	−	1.09945i
$148$	−3.00000			−0.246598
$149$	−9.06218	+	15.6962i	−0.742403	+	1.28588i	0.208996	+	0.977916i	$0.432980\pi$
$149$	−9.06218	+	15.6962i	−0.742403	+	1.28588i	−0.951399	+	0.307962i	$0.900353\pi$
$150$	−1.00000	+	1.73205i	−0.0816497	+	0.141421i
$151$	−7.26795			−0.591457			−0.295729	−	0.955272i	$-0.595562\pi$
$151$	−7.26795			−0.591457			−0.295729	+	0.955272i	$0.595562\pi$
$152$	0.633975	−	1.09808i	0.0514221	−	0.0890657i
$153$	2.59808	+	4.50000i	0.210042	+	0.363803i
$154$	−11.1962	−	19.3923i	−0.902212	−	1.56268i
$155$	−4.39230			−0.352798
$156$		0			0
$157$	−3.19615			−0.255081			−0.127540	−	0.991833i	$-0.540708\pi$
$157$	−3.19615			−0.255081			−0.127540	+	0.991833i	$0.540708\pi$
$158$	6.19615	+	10.7321i	0.492939	+	0.853796i
$159$	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
$163$	4.73205	−	8.19615i	0.370643	−	0.641972i	−0.619022	−	0.785374i	$-0.712471\pi$
$163$	4.73205	−	8.19615i	0.370643	−	0.641972i	0.989665	+	0.143402i	$0.0458041\pi$
$164$	0.464102			0.0362402
$165$	−4.09808	+	7.09808i	−0.319035	+	0.552584i
$166$	−5.83013	−	10.0981i	−0.452506	−	0.783763i
$167$	−1.26795	−	2.19615i	−0.0981169	−	0.169943i	0.812788	−	0.582559i	$-0.197949\pi$
$167$	−1.26795	−	2.19615i	−0.0981169	−	0.169943i	−0.910905	+	0.412616i	$0.864615\pi$
$168$	4.73205			0.365086
$169$		0			0
$170$	−9.00000			−0.690268
$171$	0.633975	+	1.09808i	0.0484812	+	0.0839720i
$172$	−3.09808	−	5.36603i	−0.236226	−	0.409156i
$173$	−8.19615	+	14.1962i	−0.623142	+	1.07931i	0.365755	+	0.930711i	$0.380811\pi$
$173$	−8.19615	+	14.1962i	−0.623142	+	1.07931i	−0.988897	+	0.148602i	$0.952523\pi$
$174$	3.00000			0.227429
$175$	−4.73205	+	8.19615i	−0.357709	+	0.619571i
$176$	2.36603	−	4.09808i	0.178346	−	0.308904i
$177$	13.8564			1.04151
$178$	1.26795	−	2.19615i	0.0950368	−	0.164609i
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	0.977551	−	0.210699i	$-0.0675741\pi$
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	−0.671246	+	0.741234i	$0.734241\pi$
$180$	−0.866025	−	1.50000i	−0.0645497	−	0.111803i
$181$	−11.5885			−0.861363			−0.430682	−	0.902504i	$-0.641727\pi$
$181$	−11.5885			−0.861363			−0.430682	+	0.902504i	$0.641727\pi$
$182$		0			0
$183$	−4.80385			−0.355111
$184$	−1.09808	−	1.90192i	−0.0809513	−	0.140212i
$185$	2.59808	+	4.50000i	0.191014	+	0.330847i
$186$	−1.26795	+	2.19615i	−0.0929705	+	0.161030i
$187$	24.5885			1.79809
$188$	−0.633975	+	1.09808i	−0.0462373	+	0.0800854i
$189$	−2.36603	+	4.09808i	−0.172103	+	0.298091i
$190$	−2.19615			−0.159326
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	0.194910	+	0.980821i	$0.437558\pi$
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	−0.946871	+	0.321613i	$0.895775\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−6.40192	−	11.0885i	−0.460821	−	0.798165i	0.538181	−	0.842829i	$-0.319111\pi$
$193$	−6.40192	−	11.0885i	−0.460821	−	0.798165i	−0.999002	+	0.0446644i	$0.985778\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	15.3923			1.09945
$197$	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	$0.753952\pi$
$198$	2.36603	+	4.09808i	0.168146	+	0.291238i
$199$	−4.29423	+	7.43782i	−0.304410	+	0.527253i	−0.977130	−	0.212644i	$-0.931793\pi$
$199$	−4.29423	+	7.43782i	−0.304410	+	0.527253i	0.672720	+	0.739897i	$0.265126\pi$
$200$	−2.00000			−0.141421
$201$	−5.36603	+	9.29423i	−0.378490	+	0.655564i
$202$	0.696152	−	1.20577i	0.0489811	−	0.0848378i
$203$	14.1962			0.996375
$204$	−2.59808	+	4.50000i	−0.181902	+	0.315063i
$205$	−0.401924	−	0.696152i	−0.0280716	−	0.0486214i
$206$	2.09808	+	3.63397i	0.146180	+	0.253191i
$207$	2.19615			0.152643
$208$		0			0
$209$	6.00000			0.415029
$210$	−4.09808	−	7.09808i	−0.282794	−	0.489814i
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	0.921413	−	0.388585i	$-0.127036\pi$
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	−0.797231	+	0.603674i	$0.793703\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$	8.19615			0.561591
$214$	−4.09808	+	7.09808i	−0.280139	+	0.485215i
$215$	−5.36603	+	9.29423i	−0.365960	+	0.633861i
$216$	−1.00000			−0.0680414
$217$	−6.00000	+	10.3923i	−0.407307	+	0.705476i
$218$	8.19615	+	14.1962i	0.555113	+	0.961485i
$219$	6.06218	+	10.5000i	0.409644	+	0.709524i
$220$	−8.19615			−0.552584
$221$		0			0
$222$	3.00000			0.201347
$223$	−9.46410	−	16.3923i	−0.633763	−	1.09771i	−0.986776	−	0.162091i	$-0.948176\pi$
$223$	−9.46410	−	16.3923i	−0.633763	−	1.09771i	0.353013	−	0.935619i	$-0.385157\pi$
$224$	2.36603	+	4.09808i	0.158087	+	0.273814i
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$	11.1962			0.744757
$227$	−4.90192	+	8.49038i	−0.325352	+	0.563526i	−0.981584	−	0.191033i	$-0.938816\pi$
$227$	−4.90192	+	8.49038i	−0.325352	+	0.563526i	0.656231	+	0.754560i	$0.272149\pi$
$228$	−0.633975	+	1.09808i	−0.0419860	+	0.0727219i
$229$	−19.8564			−1.31215			−0.656074	−	0.754696i	$-0.727784\pi$
$229$	−19.8564			−1.31215			−0.656074	+	0.754696i	$0.727784\pi$
$230$	−1.90192	+	3.29423i	−0.125409	+	0.217215i
$231$	11.1962	+	19.3923i	0.736653	+	1.27592i
$232$	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
$235$	2.19615			0.143261
$236$	6.92820	+	12.0000i	0.450988	+	0.781133i
$237$	−6.19615	−	10.7321i	−0.402483	−	0.697122i
$238$	−12.2942	+	21.2942i	−0.796916	+	1.38030i
$239$	24.5885			1.59050			0.795248	−	0.606285i	$-0.207341\pi$
$239$	24.5885			1.59050			0.795248	+	0.606285i	$0.207341\pi$
$240$	0.866025	−	1.50000i	0.0559017	−	0.0968246i
$241$	0.401924	−	0.696152i	0.0258902	−	0.0448431i	−0.852790	−	0.522254i	$-0.825091\pi$
$241$	0.401924	−	0.696152i	0.0258902	−	0.0448431i	0.878680	+	0.477411i	$0.158425\pi$
$242$	11.3923			0.732325
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.40192	−	4.16025i	−0.153767	−	0.266333i
$245$	−13.3301	−	23.0885i	−0.851631	−	1.47507i
$246$	−0.464102			−0.0295900
$247$		0			0
$248$	−2.53590			−0.161030
$249$	5.83013	+	10.0981i	0.369469	+	0.639940i
$250$	6.06218	+	10.5000i	0.383406	+	0.664078i
$251$	2.19615	−	3.80385i	0.138620	−	0.240097i	−0.788355	−	0.615221i	$-0.789067\pi$
$251$	2.19615	−	3.80385i	0.138620	−	0.240097i	0.926974	+	0.375124i	$0.122400\pi$
$252$	−4.73205			−0.298091
$253$	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
$257$	−6.40192	−	11.0885i	−0.399341	−	0.691679i	0.594304	−	0.804241i	$-0.297428\pi$
$257$	−6.40192	−	11.0885i	−0.399341	−	0.691679i	−0.993645	+	0.112562i	$0.964094\pi$
$258$	3.09808	+	5.36603i	0.192878	+	0.334074i
$259$	14.1962			0.882106
$260$		0			0
$261$	−3.00000			−0.185695
$262$	−8.19615	−	14.1962i	−0.506360	−	0.877041i
$263$	1.09808	+	1.90192i	0.0677103	+	0.117278i	0.897893	−	0.440214i	$-0.145097\pi$
$263$	1.09808	+	1.90192i	0.0677103	+	0.117278i	−0.830183	+	0.557491i	$0.811764\pi$
$264$	−2.36603	+	4.09808i	−0.145619	+	0.252219i
$265$	5.19615			0.319197
$266$	−3.00000	+	5.19615i	−0.183942	+	0.318597i
$267$	−1.26795	+	2.19615i	−0.0775972	+	0.134402i
$268$	−10.7321			−0.655564
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	−0.000940662	−	1.00000i	$-0.500299\pi$
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	0.866495	−	0.499185i	$-0.166367\pi$
$270$	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
$275$	−4.73205	−	8.19615i	−0.285353	−	0.494247i
$276$	1.09808	+	1.90192i	0.0660964	+	0.114482i
$277$	−7.59808	+	13.1603i	−0.456524	+	0.790723i	−0.998774	−	0.0494940i	$-0.984239\pi$
$277$	−7.59808	+	13.1603i	−0.456524	+	0.790723i	0.542250	+	0.840217i	$0.317572\pi$
$278$	−4.00000			−0.239904
$279$	1.26795	−	2.19615i	0.0759101	−	0.131480i
$280$	4.09808	−	7.09808i	0.244907	−	0.424191i
$281$	−24.4641			−1.45941			−0.729703	−	0.683764i	$-0.760342\pi$
$281$	−24.4641			−1.45941			−0.729703	+	0.683764i	$0.760342\pi$
$282$	0.633975	−	1.09808i	0.0377526	−	0.0653895i
$283$	15.0981	+	26.1506i	0.897487	+	1.55449i	0.830696	+	0.556727i	$0.187943\pi$
$283$	15.0981	+	26.1506i	0.897487	+	1.55449i	0.0667919	+	0.997767i	$0.478724\pi$
$284$	4.09808	+	7.09808i	0.243176	+	0.421193i
$285$	2.19615			0.130089
$286$		0			0
$287$	−2.19615			−0.129635
$288$	−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
$293$	−7.33013	+	12.6962i	−0.428231	+	0.741717i	−0.996716	−	0.0809762i	$-0.974196\pi$
$293$	−7.33013	+	12.6962i	−0.428231	+	0.741717i	0.568485	+	0.822693i	$0.307530\pi$
$294$	−15.3923			−0.897697
$295$	12.0000	−	20.7846i	0.698667	−	1.21013i
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	−2.36603	−	4.09808i	−0.137291	−	0.237795i
$298$	18.1244			1.04992
$299$		0			0
$300$	2.00000			0.115470
$301$	14.6603	+	25.3923i	0.845003	+	1.46359i
$302$	3.63397	+	6.29423i	0.209112	+	0.362192i
$303$	−0.696152	+	1.20577i	−0.0399929	+	0.0692698i
$304$	−1.26795			−0.0727219
$305$	−4.16025	+	7.20577i	−0.238215	+	0.412601i
$306$	2.59808	−	4.50000i	0.148522	−	0.257248i
$307$	−10.7321			−0.612510			−0.306255	−	0.951949i	$-0.599076\pi$
$307$	−10.7321			−0.612510			−0.306255	+	0.951949i	$0.599076\pi$
$308$	−11.1962	+	19.3923i	−0.637960	+	1.10498i
$309$	−2.09808	−	3.63397i	−0.119355	−	0.206730i
$310$	2.19615	+	3.80385i	0.124733	+	0.216044i
$311$	2.19615			0.124532			0.0622662	−	0.998060i	$-0.480167\pi$
$311$	2.19615			0.124532			0.0622662	+	0.998060i	$0.480167\pi$
$312$		0			0
$313$	−24.3923			−1.37873			−0.689367	−	0.724412i	$-0.742111\pi$
$313$	−24.3923			−1.37873			−0.689367	+	0.724412i	$0.742111\pi$
$314$	1.59808	+	2.76795i	0.0901847	+	0.156204i
$315$	4.09808	+	7.09808i	0.230900	+	0.399931i
$316$	6.19615	−	10.7321i	0.348561	−	0.603725i
$317$	−6.12436			−0.343978			−0.171989	−	0.985099i	$-0.555019\pi$
$317$	−6.12436			−0.343978			−0.171989	+	0.985099i	$0.555019\pi$
$318$	1.50000	−	2.59808i	0.0841158	−	0.145693i
$319$	−7.09808	+	12.2942i	−0.397416	+	0.688345i
$320$	1.73205			0.0968246
$321$	4.09808	−	7.09808i	0.228732	−	0.396176i
$322$	5.19615	+	9.00000i	0.289570	+	0.501550i
$323$	−3.29423	−	5.70577i	−0.183296	−	0.317478i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−9.46410			−0.524168
$327$	−8.19615	−	14.1962i	−0.453248	−	0.785049i
$328$	−0.232051	−	0.401924i	−0.0128129	−	0.0221925i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$	8.19615			0.451183
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$	−5.83013	+	10.0981i	−0.319970	+	0.554204i
$333$	−3.00000			−0.164399
$334$	−1.26795	+	2.19615i	−0.0693791	+	0.120168i
$335$	9.29423	+	16.0981i	0.507798	+	0.879532i
$336$	−2.36603	−	4.09808i	−0.129077	−	0.223568i
$337$	−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
$339$	−11.1962			−0.608092
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	0.633975	−	1.09808i	0.0342814	−	0.0593772i
$343$	−39.7128			−2.14429
$344$	−3.09808	+	5.36603i	−0.167037	+	0.289317i
$345$	1.90192	−	3.29423i	0.102396	−	0.177355i
$346$	16.3923			0.881256
$347$	6.29423	−	10.9019i	0.337892	−	0.585246i	−0.646144	−	0.763215i	$-0.723620\pi$
$347$	6.29423	−	10.9019i	0.337892	−	0.585246i	0.984036	+	0.177969i	$0.0569528\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	1.26795	+	2.19615i	0.0678718	+	0.117557i	0.897964	−	0.440068i	$-0.145046\pi$
$349$	1.26795	+	2.19615i	0.0678718	+	0.117557i	−0.830093	+	0.557626i	$0.811712\pi$
$350$	9.46410			0.505878
$351$		0			0
$352$	−4.73205			−0.252219
$353$	2.89230	+	5.00962i	0.153942	+	0.266635i	0.932673	−	0.360722i	$-0.117470\pi$
$353$	2.89230	+	5.00962i	0.153942	+	0.266635i	−0.778731	+	0.627358i	$0.784136\pi$
$354$	−6.92820	−	12.0000i	−0.368230	−	0.637793i
$355$	7.09808	−	12.2942i	0.376727	−	0.652510i
$356$	−2.53590			−0.134402
$357$	12.2942	−	21.2942i	0.650680	−	1.12701i
$358$	4.09808	−	7.09808i	0.216590	−	0.375145i
$359$	−22.0526			−1.16389			−0.581945	−	0.813228i	$-0.697708\pi$
$359$	−22.0526			−1.16389			−0.581945	+	0.813228i	$0.697708\pi$
$360$	−0.866025	+	1.50000i	−0.0456435	+	0.0790569i
$361$	8.69615	+	15.0622i	0.457692	+	0.792746i
$362$	5.79423	+	10.0359i	0.304538	+	0.527475i
$363$	−11.3923			−0.597941
$364$		0			0
$365$	21.0000			1.09919
$366$	2.40192	+	4.16025i	0.125551	+	0.217460i
$367$	12.0981	+	20.9545i	0.631514	+	1.09382i	0.987242	+	0.159225i	$0.0508997\pi$
$367$	12.0981	+	20.9545i	0.631514	+	1.09382i	−0.355728	+	0.934590i	$0.615767\pi$
$368$	−1.09808	+	1.90192i	−0.0572412	+	0.0991446i
$369$	0.464102			0.0241602
$370$	2.59808	−	4.50000i	0.135068	−	0.233944i
$371$	7.09808	−	12.2942i	0.368514	−	0.638285i
$372$	2.53590			0.131480
$373$	−11.9904	+	20.7679i	−0.620838	+	1.07532i	0.368492	+	0.929631i	$0.379874\pi$
$373$	−11.9904	+	20.7679i	−0.620838	+	1.07532i	−0.989330	+	0.145693i	$0.953459\pi$
$374$	−12.2942	−	21.2942i	−0.635719	−	1.10110i
$375$	−6.06218	−	10.5000i	−0.313050	−	0.542218i
$376$	1.26795			0.0653895
$377$		0			0
$378$	4.73205			0.243390
$379$	−9.12436	−	15.8038i	−0.468687	−	0.811789i	0.530673	−	0.847577i	$-0.321939\pi$
$379$	−9.12436	−	15.8038i	−0.468687	−	0.811789i	−0.999359	+	0.0357877i	$0.988606\pi$
$380$	1.09808	+	1.90192i	0.0563301	+	0.0975666i
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$	20.7846			1.06343
$383$	5.66025	−	9.80385i	0.289225	−	0.500953i	−0.684400	−	0.729107i	$-0.739936\pi$
$383$	5.66025	−	9.80385i	0.289225	−	0.500953i	0.973625	+	0.228154i	$0.0732689\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	38.7846			1.97665
$386$	−6.40192	+	11.0885i	−0.325849	+	0.564388i
$387$	−3.09808	−	5.36603i	−0.157484	−	0.272770i
$388$	3.00000	+	5.19615i	0.152302	+	0.263795i
$389$	−13.3923			−0.679017			−0.339508	−	0.940603i	$-0.610261\pi$
$389$	−13.3923			−0.679017			−0.339508	+	0.940603i	$0.610261\pi$
$390$		0			0
$391$	−11.4115			−0.577107
$392$	−7.69615	−	13.3301i	−0.388714	−	0.673273i
$393$	8.19615	+	14.1962i	0.413441	+	0.716101i
$394$	3.46410	−	6.00000i	0.174519	−	0.302276i
$395$	−21.4641			−1.07998
$396$	2.36603	−	4.09808i	0.118897	−	0.205936i
$397$	−8.19615	+	14.1962i	−0.411353	+	0.712484i	−0.995038	−	0.0994958i	$-0.968277\pi$
$397$	−8.19615	+	14.1962i	−0.411353	+	0.712484i	0.583685	+	0.811980i	$0.301610\pi$
$398$	8.58846			0.430500
$399$	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	$0.00902310\pi$
$401$	10.5000	+	18.1865i	0.524345	+	0.908192i	−0.475253	+	0.879849i	$0.657644\pi$
$402$	10.7321			0.535266
$403$		0			0
$404$	−1.39230			−0.0692698
$405$	−0.866025	−	1.50000i	−0.0430331	−	0.0745356i
$406$	−7.09808	−	12.2942i	−0.352272	−	0.610152i
$407$	−7.09808	+	12.2942i	−0.351839	+	0.609402i
$408$	5.19615			0.257248
$409$	−1.66987	+	2.89230i	−0.0825699	+	0.143015i	−0.904353	−	0.426785i	$-0.859646\pi$
$409$	−1.66987	+	2.89230i	−0.0825699	+	0.143015i	0.821783	+	0.569800i	$0.192979\pi$
$410$	−0.401924	+	0.696152i	−0.0198496	+	0.0343805i
$411$	−9.00000			−0.443937
$412$	2.09808	−	3.63397i	0.103365	−	0.179033i
$413$	−32.7846	−	56.7846i	−1.61323	−	2.79419i
$414$	−1.09808	−	1.90192i	−0.0539675	−	0.0934745i
$415$	20.1962			0.991390
$416$		0			0
$417$	4.00000			0.195881
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	−8.19615	−	14.1962i	−0.400408	−	0.693527i	0.593367	−	0.804932i	$-0.297798\pi$
$419$	−8.19615	−	14.1962i	−0.400408	−	0.693527i	−0.993775	+	0.111405i	$0.964465\pi$
$420$	−4.09808	+	7.09808i	−0.199966	+	0.346351i
$421$	−0.464102			−0.0226189			−0.0113095	−	0.999936i	$-0.503600\pi$
$421$	−0.464102			−0.0226189			−0.0113095	+	0.999936i	$0.503600\pi$
$422$	1.80385	−	3.12436i	0.0878099	−	0.152091i
$423$	−0.633975	+	1.09808i	−0.0308249	+	0.0533903i
$424$	3.00000			0.145693
$425$	−5.19615	+	9.00000i	−0.252050	+	0.436564i
$426$	−4.09808	−	7.09808i	−0.198552	−	0.343903i
$427$	11.3660	+	19.6865i	0.550041	+	0.952698i
$428$	8.19615			0.396176
$429$		0			0
$430$	10.7321			0.517545
$431$	13.9019	+	24.0788i	0.669632	+	1.15984i	0.978007	+	0.208572i	$0.0668815\pi$
$431$	13.9019	+	24.0788i	0.669632	+	1.15984i	−0.308375	+	0.951265i	$0.599785\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	16.8923	−	29.2583i	0.811792	−	1.40607i	−0.0998161	−	0.995006i	$-0.531825\pi$
$433$	16.8923	−	29.2583i	0.811792	−	1.40607i	0.911608	−	0.411060i	$-0.134841\pi$
$434$	12.0000			0.576018
$435$	−2.59808	+	4.50000i	−0.124568	+	0.215758i
$436$	8.19615	−	14.1962i	0.392525	−	0.679872i
$437$	−2.78461			−0.133206
$438$	6.06218	−	10.5000i	0.289662	−	0.501709i
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	0.597349	−	0.801982i	$-0.296221\pi$
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	−0.993211	+	0.116329i	$0.962887\pi$
$440$	4.09808	+	7.09808i	0.195368	+	0.338388i
$441$	15.3923			0.732967
$442$		0			0
$443$	−4.39230			−0.208685			−0.104342	−	0.994541i	$-0.533274\pi$
$443$	−4.39230			−0.208685			−0.104342	+	0.994541i	$0.533274\pi$
$444$	−1.50000	−	2.59808i	−0.0711868	−	0.123299i
$445$	2.19615	+	3.80385i	0.104108	+	0.180320i
$446$	−9.46410	+	16.3923i	−0.448138	+	0.776198i
$447$	−18.1244			−0.857253
$448$	2.36603	−	4.09808i	0.111784	−	0.193616i
$449$	16.7321	−	28.9808i	0.789634	−	1.36769i	−0.136557	−	0.990632i	$-0.543604\pi$
$449$	16.7321	−	28.9808i	0.789634	−	1.36769i	0.926191	−	0.377054i	$-0.123063\pi$
$450$	−2.00000			−0.0942809
$451$	1.09808	−	1.90192i	0.0517064	−	0.0895581i
$452$	−5.59808	−	9.69615i	−0.263311	−	0.456069i
$453$	−3.63397	−	6.29423i	−0.170739	−	0.295729i
$454$	9.80385			0.460117
$455$		0			0
$456$	1.26795			0.0593772
$457$	9.99038	+	17.3038i	0.467330	+	0.809440i	0.999303	−	0.0373215i	$-0.0118826\pi$
$457$	9.99038	+	17.3038i	0.467330	+	0.809440i	−0.531973	+	0.846761i	$0.678549\pi$
$458$	9.92820	+	17.1962i	0.463914	+	0.803523i
$459$	−2.59808	+	4.50000i	−0.121268	+	0.210042i
$460$	3.80385			0.177355
$461$	−9.99038	+	17.3038i	−0.465298	+	0.805921i	−0.999215	−	0.0396167i	$-0.987386\pi$
$461$	−9.99038	+	17.3038i	−0.465298	+	0.805921i	0.533917	+	0.845537i	$0.320720\pi$
$462$	11.1962	−	19.3923i	0.520892	−	0.902212i
$463$	26.1962			1.21744			0.608719	−	0.793386i	$-0.291684\pi$
$463$	26.1962			1.21744			0.608719	+	0.793386i	$0.291684\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	−2.19615	−	3.80385i	−0.101844	−	0.176399i
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$	36.5885			1.69311			0.846556	−	0.532300i	$-0.178672\pi$
$467$	36.5885			1.69311			0.846556	+	0.532300i	$0.178672\pi$
$468$		0			0
$469$	50.7846			2.34502
$470$	−1.09808	−	1.90192i	−0.0506505	−	0.0877292i
$471$	−1.59808	−	2.76795i	−0.0736355	−	0.127540i
$472$	6.92820	−	12.0000i	0.318896	−	0.552345i
$473$	−29.3205			−1.34816
$474$	−6.19615	+	10.7321i	−0.284599	+	0.492939i
$475$	−1.26795	+	2.19615i	−0.0581775	+	0.100766i
$476$	24.5885			1.12701
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	−12.2942	−	21.2942i	−0.562325	−	0.973975i
$479$	−17.6603	−	30.5885i	−0.806918	−	1.39762i	−0.914989	−	0.403479i	$-0.867801\pi$
$479$	−17.6603	−	30.5885i	−0.806918	−	1.39762i	0.108071	−	0.994143i	$-0.465533\pi$
$480$	−1.73205			−0.0790569
$481$		0			0
$482$	−0.803848			−0.0366143
$483$	−5.19615	−	9.00000i	−0.236433	−	0.409514i
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	5.19615	−	9.00000i	0.235945	−	0.408669i
$486$	−1.00000			−0.0453609
$487$	4.56218	−	7.90192i	0.206732	−	0.358070i	−0.743951	−	0.668234i	$-0.767051\pi$
$487$	4.56218	−	7.90192i	0.206732	−	0.358070i	0.950683	+	0.310164i	$0.100384\pi$
$488$	−2.40192	+	4.16025i	−0.108730	+	0.188326i
$489$	9.46410			0.427981
$490$	−13.3301	+	23.0885i	−0.602194	+	1.04303i
$491$	−0.294229	−	0.509619i	−0.0132784	−	0.0229988i	0.859310	−	0.511455i	$-0.170893\pi$
$491$	−0.294229	−	0.509619i	−0.0132784	−	0.0229988i	−0.872588	+	0.488457i	$0.837560\pi$
$492$	0.232051	+	0.401924i	0.0104617	+	0.0181201i
$493$	15.5885			0.702069
$494$		0			0
$495$	−8.19615			−0.368390
$496$	1.26795	+	2.19615i	0.0569326	+	0.0986102i
$497$	−19.3923	−	33.5885i	−0.869864	−	1.50665i
$498$	5.83013	−	10.0981i	0.261254	−	0.452506i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$	1.26795	−	2.19615i	0.0566478	−	0.0981169i
$502$	−4.39230			−0.196038
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	−0.580957	−	0.813934i	$-0.697322\pi$
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	0.995366	+	0.0961565i	$0.0306549\pi$
$504$	2.36603	+	4.09808i	0.105391	+	0.182543i
$505$	1.20577	+	2.08846i	0.0536561	+	0.0929351i
$506$	−10.3923			−0.461994
$507$		0			0
$508$	−4.00000			−0.177471
$509$	4.66987	+	8.08846i	0.206988	+	0.358515i	0.950764	−	0.309914i	$-0.100300\pi$
$509$	4.66987	+	8.08846i	0.206988	+	0.358515i	−0.743776	+	0.668429i	$0.766967\pi$
$510$	−4.50000	−	7.79423i	−0.199263	−	0.345134i
$511$	28.6865	−	49.6865i	1.26902	−	2.19800i
$512$	1.00000			0.0441942
$513$	−0.633975	+	1.09808i	−0.0279907	+	0.0484812i
$514$	−6.40192	+	11.0885i	−0.282377	+	0.489091i
$515$	−7.26795			−0.320264
$516$	3.09808	−	5.36603i	0.136385	−	0.236226i
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$	−7.09808	−	12.2942i	−0.311872	−	0.540177i
$519$	−16.3923			−0.719542
$520$		0			0
$521$	−18.8038			−0.823812			−0.411906	−	0.911226i	$-0.635137\pi$
$521$	−18.8038			−0.823812			−0.411906	+	0.911226i	$0.635137\pi$
$522$	1.50000	+	2.59808i	0.0656532	+	0.113715i
$523$	−0.705771	−	1.22243i	−0.0308612	−	0.0534532i	0.850182	−	0.526488i	$-0.176492\pi$
$523$	−0.705771	−	1.22243i	−0.0308612	−	0.0534532i	−0.881044	+	0.473035i	$0.843158\pi$
$524$	−8.19615	+	14.1962i	−0.358051	+	0.620162i
$525$	−9.46410			−0.413047
$526$	1.09808	−	1.90192i	0.0478784	−	0.0829278i
$527$	−6.58846	+	11.4115i	−0.286998	+	0.497095i
$528$	4.73205			0.205936
$529$	9.08846	−	15.7417i	0.395150	−	0.684420i
$530$	−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
$534$	2.53590			0.109739
$535$	−7.09808	−	12.2942i	−0.306877	−	0.531526i
$536$	5.36603	+	9.29423i	0.231777	+	0.401450i
$537$	−4.09808	+	7.09808i	−0.176845	+	0.306305i
$538$	−28.3923			−1.22408
$539$	36.4186	−	63.0788i	1.56866	−	2.71700i
$540$	0.866025	−	1.50000i	0.0372678	−	0.0645497i
$541$	−16.8564			−0.724714			−0.362357	−	0.932039i	$-0.618028\pi$
$541$	−16.8564			−0.724714			−0.362357	+	0.932039i	$0.618028\pi$
$542$		0			0
$543$	−5.79423	−	10.0359i	−0.248654	−	0.430682i
$544$	2.59808	+	4.50000i	0.111392	+	0.192936i
$545$	−28.3923			−1.21619
$546$		0			0
$547$	−6.19615			−0.264928			−0.132464	−	0.991188i	$-0.542289\pi$
$547$	−6.19615			−0.264928			−0.132464	+	0.991188i	$0.542289\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$	−2.40192	−	4.16025i	−0.102512	−	0.177555i
$550$	−4.73205	+	8.19615i	−0.201775	+	0.349485i
$551$	3.80385			0.162049
$552$	1.09808	−	1.90192i	0.0467372	−	0.0809513i
$553$	−29.3205	+	50.7846i	−1.24683	+	2.15958i
$554$	15.1962			0.645623
$555$	−2.59808	+	4.50000i	−0.110282	+	0.191014i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	11.1340	+	19.2846i	0.471762	+	0.817115i	0.999478	−	0.0323055i	$-0.0102849\pi$
$557$	11.1340	+	19.2846i	0.471762	+	0.817115i	−0.527716	+	0.849421i	$0.676952\pi$
$558$	−2.53590			−0.107353
$559$		0			0
$560$	−8.19615			−0.346351
$561$	12.2942	+	21.2942i	0.519063	+	0.899043i
$562$	12.2321	+	21.1865i	0.515978	+	0.893700i
$563$	−4.39230	+	7.60770i	−0.185114	+	0.320626i	−0.943615	−	0.331046i	$-0.892599\pi$
$563$	−4.39230	+	7.60770i	−0.185114	+	0.320626i	0.758501	+	0.651672i	$0.225932\pi$
$564$	−1.26795			−0.0533903
$565$	−9.69615	+	16.7942i	−0.407920	+	0.706539i
$566$	15.0981	−	26.1506i	0.634619	−	1.09919i
$567$	−4.73205			−0.198727
$568$	4.09808	−	7.09808i	0.171951	−	0.297829i
$569$	16.3923	+	28.3923i	0.687201	+	1.19027i	0.972740	+	0.231900i	$0.0744942\pi$
$569$	16.3923	+	28.3923i	0.687201	+	1.19027i	−0.285538	+	0.958367i	$0.592172\pi$
$570$	−1.09808	−	1.90192i	−0.0459934	−	0.0796628i
$571$	−13.8038			−0.577673			−0.288837	−	0.957378i	$-0.593268\pi$
$571$	−13.8038			−0.577673			−0.288837	+	0.957378i	$0.593268\pi$
$572$		0			0
$573$	−20.7846			−0.868290
$574$	1.09808	+	1.90192i	0.0458328	+	0.0793848i
$575$	2.19615	+	3.80385i	0.0915859	+	0.158631i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	16.2679			0.677244			0.338622	−	0.940923i	$-0.390039\pi$
$577$	16.2679			0.677244			0.338622	+	0.940923i	$0.390039\pi$
$578$	−5.00000	+	8.66025i	−0.207973	+	0.360219i
$579$	6.40192	−	11.0885i	0.266055	−	0.460821i
$580$	−5.19615			−0.215758
$581$	27.5885	−	47.7846i	1.14456	−	1.98244i
$582$	−3.00000	−	5.19615i	−0.124354	−	0.215387i
$583$	7.09808	+	12.2942i	0.293972	+	0.509175i
$584$	12.1244			0.501709
$585$		0			0
$586$	14.6603			0.605610
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$	7.69615	+	13.3301i	0.317384	+	0.549725i
$589$	−1.60770	+	2.78461i	−0.0662439	+	0.114738i
$590$	−24.0000			−0.988064
$591$	−3.46410	+	6.00000i	−0.142494	+	0.246807i
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$	46.8564			1.92416			0.962081	−	0.272764i	$-0.0879378\pi$
$593$	46.8564			1.92416			0.962081	+	0.272764i	$0.0879378\pi$
$594$	−2.36603	+	4.09808i	−0.0970792	+	0.168146i
$595$	−21.2942	−	36.8827i	−0.872978	−	1.51204i
$596$	−9.06218	−	15.6962i	−0.371201	−	0.642939i
$597$	−8.58846			−0.351502
$598$		0			0
$599$	−4.39230			−0.179465			−0.0897324	−	0.995966i	$-0.528601\pi$
$599$	−4.39230			−0.179465			−0.0897324	+	0.995966i	$0.528601\pi$
$600$	−1.00000	−	1.73205i	−0.0408248	−	0.0707107i
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	0.553697	−	0.832718i	$-0.313216\pi$
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	−0.998004	+	0.0631568i	$0.979883\pi$
$602$	14.6603	−	25.3923i	0.597507	−	1.03491i
$603$	−10.7321			−0.437043
$604$	3.63397	−	6.29423i	0.147864	−	0.256109i
$605$	−9.86603	+	17.0885i	−0.401111	+	0.694745i
$606$	1.39230			0.0565585
$607$	24.3923	−	42.2487i	0.990053	−	1.71482i	0.373182	−	0.927758i	$-0.378267\pi$
$607$	24.3923	−	42.2487i	0.990053	−	1.71482i	0.616871	−	0.787064i	$-0.288400\pi$
$608$	0.633975	+	1.09808i	0.0257111	+	0.0445329i
$609$	7.09808	+	12.2942i	0.287629	+	0.498187i
$610$	8.32051			0.336888
$611$		0			0
$612$	−5.19615			−0.210042
$613$	−20.4282	−	35.3827i	−0.825087	−	1.42909i	−0.901853	−	0.432044i	$-0.857793\pi$
$613$	−20.4282	−	35.3827i	−0.825087	−	1.42909i	0.0767652	−	0.997049i	$-0.475541\pi$
$614$	5.36603	+	9.29423i	0.216555	+	0.375085i
$615$	0.401924	−	0.696152i	0.0162071	−	0.0280716i
$616$	22.3923			0.902212
$617$	5.30385	−	9.18653i	0.213525	−	0.369836i	−0.739290	−	0.673387i	$-0.764839\pi$
$617$	5.30385	−	9.18653i	0.213525	−	0.369836i	0.952815	+	0.303551i	$0.0981722\pi$
$618$	−2.09808	+	3.63397i	−0.0843970	+	0.146180i
$619$	7.60770			0.305779			0.152890	−	0.988243i	$-0.451142\pi$
$619$	7.60770			0.305779			0.152890	+	0.988243i	$0.451142\pi$
$620$	2.19615	−	3.80385i	0.0881996	−	0.152766i
$621$	1.09808	+	1.90192i	0.0440643	+	0.0763216i
$622$	−1.09808	−	1.90192i	−0.0440288	−	0.0762602i
$623$	12.0000			0.480770
$624$		0			0
$625$	−11.0000			−0.440000
$626$	12.1962	+	21.1244i	0.487456	+	0.844299i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	1.59808	−	2.76795i	0.0637702	−	0.110453i
$629$	15.5885			0.621552
$630$	4.09808	−	7.09808i	0.163271	−	0.282794i
$631$	12.9282	−	22.3923i	0.514664	−	0.891424i	−0.485192	−	0.874408i	$-0.661250\pi$
$631$	12.9282	−	22.3923i	0.514664	−	0.891424i	0.999855	−	0.0170157i	$-0.00541653\pi$
$632$	−12.3923			−0.492939
$633$	−1.80385	+	3.12436i	−0.0716965	+	0.124182i
$634$	3.06218	+	5.30385i	0.121615	+	0.210643i
$635$	3.46410	+	6.00000i	0.137469	+	0.238103i
$636$	−3.00000			−0.118958
$637$		0			0
$638$	14.1962			0.562031
$639$	4.09808	+	7.09808i	0.162117	+	0.280796i
$640$	−0.866025	−	1.50000i	−0.0342327	−	0.0592927i
$641$	15.4019	−	26.6769i	0.608339	−	1.05367i	−0.383175	−	0.923676i	$-0.625169\pi$
$641$	15.4019	−	26.6769i	0.608339	−	1.05367i	0.991514	−	0.129999i	$-0.0414974\pi$
$642$	−8.19615			−0.323476
$643$	−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
$645$	−10.7321			−0.422574
$646$	−3.29423	+	5.70577i	−0.129610	+	0.224491i
$647$	−6.58846	−	11.4115i	−0.259019	−	0.448634i	0.706960	−	0.707253i	$-0.250066\pi$
$647$	−6.58846	−	11.4115i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916733\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	65.5692			2.57382
$650$		0			0
$651$	−12.0000			−0.470317
$652$	4.73205	+	8.19615i	0.185321	+	0.320986i
$653$	24.5885	+	42.5885i	0.962221	+	1.66662i	0.716904	+	0.697172i	$0.245559\pi$
$653$	24.5885	+	42.5885i	0.962221	+	1.66662i	0.245317	+	0.969443i	$0.421108\pi$
$654$	−8.19615	+	14.1962i	−0.320495	+	0.555113i
$655$	28.3923			1.10938
$656$	−0.232051	+	0.401924i	−0.00906006	+	0.0156925i
$657$	−6.06218	+	10.5000i	−0.236508	+	0.409644i
$658$	−6.00000			−0.233904
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	−0.999939	−	0.0110766i	$-0.996474\pi$
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	0.509562	+	0.860434i	$0.329807\pi$
$660$	−4.09808	−	7.09808i	−0.159517	−	0.276292i
$661$	4.50000	+	7.79423i	0.175030	+	0.303160i	0.940172	−	0.340701i	$-0.110665\pi$
$661$	4.50000	+	7.79423i	0.175030	+	0.303160i	−0.765142	+	0.643862i	$0.777331\pi$
$662$	−12.0000			−0.466393
$663$		0			0
$664$	11.6603			0.452506
$665$	−5.19615	−	9.00000i	−0.201498	−	0.349005i
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	3.29423	−	5.70577i	0.127553	−	0.220928i
$668$	2.53590			0.0981169
$669$	9.46410	−	16.3923i	0.365903	−	0.633763i
$670$	9.29423	−	16.0981i	0.359067	−	0.621923i
$671$	−22.7321			−0.877561
$672$	−2.36603	+	4.09808i	−0.0912714	+	0.158087i
$673$	−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
$677$	4.39230			0.168810			0.0844050	−	0.996432i	$-0.473101\pi$
$677$	4.39230			0.168810			0.0844050	+	0.996432i	$0.473101\pi$
$678$	5.59808	+	9.69615i	0.214993	+	0.372378i
$679$	−14.1962	−	24.5885i	−0.544798	−	0.943618i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	−9.80385			−0.375684
$682$	−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	$-0.0112167\pi$
$684$	−1.26795			−0.0484812
$685$	−7.79423	+	13.5000i	−0.297802	+	0.515808i
$686$	19.8564	+	34.3923i	0.758121	+	1.31310i
$687$	−9.92820	−	17.1962i	−0.378785	−	0.656074i
$688$	6.19615			0.236226
$689$		0			0
$690$	−3.80385			−0.144810
$691$	−9.75833	−	16.9019i	−0.371224	−	0.642979i	0.618530	−	0.785761i	$-0.287729\pi$
$691$	−9.75833	−	16.9019i	−0.371224	−	0.642979i	−0.989754	+	0.142782i	$0.954395\pi$
$692$	−8.19615	−	14.1962i	−0.311571	−	0.539657i
$693$	−11.1962	+	19.3923i	−0.425307	+	0.736653i
$694$	−12.5885			−0.477851
$695$	3.46410	−	6.00000i	0.131401	−	0.227593i
$696$	−1.50000	+	2.59808i	−0.0568574	+	0.0984798i
$697$	−2.41154			−0.0913437
$698$	1.26795	−	2.19615i	0.0479926	−	0.0831256i
$699$	−9.00000	−	15.5885i	−0.340411	−	0.589610i
$700$	−4.73205	−	8.19615i	−0.178855	−	0.309785i
$701$	4.39230			0.165895			0.0829475	−	0.996554i	$-0.473567\pi$
$701$	4.39230			0.165895			0.0829475	+	0.996554i	$0.473567\pi$
$702$		0			0
$703$	3.80385			0.143465
$704$	2.36603	+	4.09808i	0.0891729	+	0.154452i
$705$	1.09808	+	1.90192i	0.0413559	+	0.0716306i
$706$	2.89230	−	5.00962i	0.108853	−	0.188539i
$707$	6.58846			0.247784
$708$	−6.92820	+	12.0000i	−0.260378	+	0.450988i
$709$	1.62436	−	2.81347i	0.0610040	−	0.105662i	−0.833910	−	0.551900i	$-0.813903\pi$
$709$	1.62436	−	2.81347i	0.0610040	−	0.105662i	0.894914	+	0.446238i	$0.147236\pi$
$710$	−14.1962			−0.532772
$711$	6.19615	−	10.7321i	0.232374	−	0.402483i
$712$	1.26795	+	2.19615i	0.0475184	+	0.0823043i
$713$	2.78461	+	4.82309i	0.104284	+	0.180626i
$714$	−24.5885			−0.920200
$715$		0			0
$716$	−8.19615			−0.306305
$717$	12.2942	+	21.2942i	0.459136	+	0.795248i
$718$	11.0263	+	19.0981i	0.411497	+	0.712734i
$719$	−26.1962	+	45.3731i	−0.976952	+	1.69213i	−0.303613	+	0.952795i	$0.598193\pi$
$719$	−26.1962	+	45.3731i	−0.976952	+	1.69213i	−0.673338	+	0.739335i	$0.735140\pi$
$720$	1.73205			0.0645497
$721$	−9.92820	+	17.1962i	−0.369746	+	0.640418i
$722$	8.69615	−	15.0622i	0.323637	−	0.560556i
$723$	0.803848			0.0298954
$724$	5.79423	−	10.0359i	0.215341	−	0.372981i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	5.69615	+	9.86603i	0.211404	+	0.366163i
$727$	−24.1962			−0.897386			−0.448693	−	0.893686i	$-0.648110\pi$
$727$	−24.1962			−0.897386			−0.448693	+	0.893686i	$0.648110\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−10.5000	−	18.1865i	−0.388622	−	0.673114i
$731$	16.0981	+	27.8827i	0.595409	+	1.03128i
$732$	2.40192	−	4.16025i	0.0887777	−	0.153767i
$733$	14.3205			0.528940			0.264470	−	0.964394i	$-0.414803\pi$
$733$	14.3205			0.528940			0.264470	+	0.964394i	$0.414803\pi$
$734$	12.0981	−	20.9545i	0.446548	−	0.773444i
$735$	13.3301	−	23.0885i	0.491689	−	0.851631i
$736$	2.19615			0.0809513
$737$	−25.3923	+	43.9808i	−0.935338	+	1.62005i
$738$	−0.232051	−	0.401924i	−0.00854191	−	0.0147950i
$739$	−9.46410	−	16.3923i	−0.348143	−	0.603001i	0.637777	−	0.770221i	$-0.279854\pi$
$739$	−9.46410	−	16.3923i	−0.348143	−	0.603001i	−0.985920	+	0.167220i	$0.946521\pi$
$740$	−5.19615			−0.191014
$741$		0			0
$742$	−14.1962			−0.521157
$743$	2.19615	+	3.80385i	0.0805690	+	0.139550i	0.903494	−	0.428600i	$-0.140993\pi$
$743$	2.19615	+	3.80385i	0.0805690	+	0.139550i	−0.822925	+	0.568149i	$0.807660\pi$
$744$	−1.26795	−	2.19615i	−0.0464853	−	0.0805149i
$745$	−15.6962	+	27.1865i	−0.575063	+	0.996038i
$746$	23.9808			0.877998
$747$	−5.83013	+	10.0981i	−0.213313	+	0.369469i
$748$	−12.2942	+	21.2942i	−0.449522	+	0.778594i
$749$	−38.7846			−1.41716
$750$	−6.06218	+	10.5000i	−0.221359	+	0.383406i
$751$	12.4904	+	21.6340i	0.455780	+	0.789435i	0.998733	−	0.0503286i	$-0.0160269\pi$
$751$	12.4904	+	21.6340i	0.455780	+	0.789435i	−0.542952	+	0.839764i	$0.682694\pi$
$752$	−0.633975	−	1.09808i	−0.0231187	−	0.0400427i
$753$	4.39230			0.160064
$754$		0			0
$755$	−12.5885			−0.458141
$756$	−2.36603	−	4.09808i	−0.0860515	−	0.149046i
$757$	−9.39230	−	16.2679i	−0.341369	−	0.591269i	0.643318	−	0.765599i	$-0.277557\pi$
$757$	−9.39230	−	16.2679i	−0.341369	−	0.591269i	−0.984687	+	0.174330i	$0.944224\pi$
$758$	−9.12436	+	15.8038i	−0.331412	+	0.574022i
$759$	10.3923			0.377217
$760$	1.09808	−	1.90192i	0.0398314	−	0.0689900i
$761$	−2.19615	+	3.80385i	−0.0796105	+	0.137889i	−0.903082	−	0.429468i	$-0.858701\pi$
$761$	−2.19615	+	3.80385i	−0.0796105	+	0.137889i	0.823471	+	0.567358i	$0.192034\pi$
$762$	4.00000			0.144905
$763$	−38.7846	+	67.1769i	−1.40410	+	2.43197i
$764$	−10.3923	−	18.0000i	−0.375980	−	0.651217i
$765$	4.50000	+	7.79423i	0.162698	+	0.281801i
$766$	−11.3205			−0.409027
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	16.8564	+	29.1962i	0.607858	+	1.05284i	0.991593	+	0.129397i	$0.0413042\pi$
$769$	16.8564	+	29.1962i	0.607858	+	1.05284i	−0.383735	+	0.923443i	$0.625362\pi$
$770$	−19.3923	−	33.5885i	−0.698850	−	1.21044i
$771$	6.40192	−	11.0885i	0.230560	−	0.399341i
$772$	12.8038			0.460821
$773$	−25.3923	+	43.9808i	−0.913298	+	1.58188i	−0.103923	+	0.994585i	$0.533140\pi$
$773$	−25.3923	+	43.9808i	−0.913298	+	1.58188i	−0.809375	+	0.587293i	$0.800194\pi$
$774$	−3.09808	+	5.36603i	−0.111358	+	0.192878i
$775$	5.07180			0.182184
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	7.09808	+	12.2942i	0.254642	+	0.441053i
$778$	6.69615	+	11.5981i	0.240069	+	0.415811i
$779$	−0.588457			−0.0210837
$780$		0			0
$781$	38.7846			1.38782
$782$	5.70577	+	9.88269i	0.204038	+	0.353404i
$783$	−1.50000	−	2.59808i	−0.0536056	−	0.0928477i
$784$	−7.69615	+	13.3301i	−0.274863	+	0.476076i
$785$	−5.53590			−0.197585
$786$	8.19615	−	14.1962i	0.292347	−	0.506360i
$787$	−7.26795	+	12.5885i	−0.259074	+	0.448730i	−0.965994	−	0.258564i	$-0.916751\pi$
$787$	−7.26795	+	12.5885i	−0.259074	+	0.448730i	0.706920	+	0.707294i	$0.250084\pi$
$788$	−6.92820			−0.246807
$789$	−1.09808	+	1.90192i	−0.0390925	+	0.0677103i
$790$	10.7321	+	18.5885i	0.381829	+	0.661348i
$791$	26.4904	+	45.8827i	0.941890	+	1.63140i
$792$	−4.73205			−0.168146
$793$		0			0
$794$	16.3923			0.581741
$795$	2.59808	+	4.50000i	0.0921443	+	0.159599i
$796$	−4.29423	−	7.43782i	−0.152205	−	0.263627i
$797$	−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
$799$	3.29423	−	5.70577i	0.116541	−	0.201856i
$800$	1.00000	−	1.73205i	0.0353553	−	0.0612372i
$801$	−2.53590			−0.0896016
$802$	10.5000	−	18.1865i	0.370768	−	0.642189i
$803$	28.6865	+	49.6865i	1.01233	+	1.75340i
$804$	−5.36603	−	9.29423i	−0.189245	−	0.327782i
$805$	−18.0000			−0.634417
$806$		0			0
$807$	28.3923			0.999456
$808$	0.696152	+	1.20577i	0.0244906	+	0.0424189i
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	0.898302	+	0.439379i	$0.144801\pi$
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	−0.0686377	+	0.997642i	$0.521865\pi$
$810$	−0.866025	+	1.50000i	−0.0304290	+	0.0527046i
$811$	−4.39230			−0.154235			−0.0771173	−	0.997022i	$-0.524572\pi$
$811$	−4.39230			−0.154235			−0.0771173	+	0.997022i	$0.524572\pi$
$812$	−7.09808	+	12.2942i	−0.249094	+	0.431443i
$813$		0			0
$814$	14.1962			0.497575
$815$	8.19615	−	14.1962i	0.287099	−	0.497270i
$816$	−2.59808	−	4.50000i	−0.0909509	−	0.157532i
$817$	3.92820	+	6.80385i	0.137430	+	0.238036i
$818$	3.33975			0.116771
$819$		0			0
$820$	0.803848			0.0280716
$821$	−20.3205	−	35.1962i	−0.709191	−	1.22835i	−0.965158	−	0.261669i	$-0.915727\pi$
$821$	−20.3205	−	35.1962i	−0.709191	−	1.22835i	0.255967	−	0.966685i	$-0.417606\pi$
$822$	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	$-0.0216589\pi$
$824$	−4.19615			−0.146180
$825$	4.73205	−	8.19615i	0.164749	−	0.285353i
$826$	−32.7846	+	56.7846i	−1.14072	+	1.97579i
$827$	32.1051			1.11640			0.558202	−	0.829705i	$-0.311491\pi$
$827$	32.1051			1.11640			0.558202	+	0.829705i	$0.311491\pi$
$828$	−1.09808	+	1.90192i	−0.0381608	+	0.0660964i
$829$	5.99038	+	10.3756i	0.208055	+	0.360361i	0.951102	−	0.308878i	$-0.0999535\pi$
$829$	5.99038	+	10.3756i	0.208055	+	0.360361i	−0.743047	+	0.669239i	$0.766620\pi$
$830$	−10.0981	−	17.4904i	−0.350509	−	0.607100i
$831$	−15.1962			−0.527149
$832$		0			0
$833$	−79.9808			−2.77117
$834$	−2.00000	−	3.46410i	−0.0692543	−	0.119952i
$835$	−2.19615	−	3.80385i	−0.0760010	−	0.131638i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$	2.53590			0.0876535
$838$	−8.19615	+	14.1962i	−0.283131	+	0.490398i
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$	8.19615			0.282794
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	0.232051	+	0.401924i	0.00799700	+	0.0138512i
$843$	−12.2321	−	21.1865i	−0.421294	−	0.729703i
$844$	−3.60770			−0.124182
$845$		0			0
$846$	1.26795			0.0435930
$847$	26.9545	+	46.6865i	0.926167	+	1.60417i
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$	−15.0981	+	26.1506i	−0.518165	+	0.897487i
$850$	10.3923			0.356453
$851$	3.29423	−	5.70577i	0.112925	−	0.195591i
$852$	−4.09808	+	7.09808i	−0.140398	+	0.243176i
$853$	−9.00000			−0.308154			−0.154077	−	0.988059i	$-0.549240\pi$
$853$	−9.00000			−0.308154			−0.154077	+	0.988059i	$0.549240\pi$
$854$	11.3660	−	19.6865i	0.388937	−	0.673659i
$855$	1.09808	+	1.90192i	0.0375534	+	0.0650444i
$856$	−4.09808	−	7.09808i	−0.140069	−	0.242607i
$857$	−54.3731			−1.85735			−0.928674	−	0.370896i	$-0.879051\pi$
$857$	−54.3731			−1.85735			−0.928674	+	0.370896i	$0.879051\pi$
$858$		0			0
$859$	10.5885			0.361273			0.180637	−	0.983550i	$-0.442184\pi$
$859$	10.5885			0.361273			0.180637	+	0.983550i	$0.442184\pi$
$860$	−5.36603	−	9.29423i	−0.182980	−	0.316931i
$861$	−1.09808	−	1.90192i	−0.0374223	−	0.0648174i
$862$	13.9019	−	24.0788i	0.473501	−	0.820128i
$863$	−4.48334			−0.152615			−0.0763073	−	0.997084i	$-0.524313\pi$
$863$	−4.48334			−0.152615			−0.0763073	+	0.997084i	$0.524313\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−14.1962	+	24.5885i	−0.482684	+	0.836033i
$866$	−33.7846			−1.14805
$867$	5.00000	−	8.66025i	0.169809	−	0.294118i
$868$	−6.00000	−	10.3923i	−0.203653	−	0.352738i
$869$	−29.3205	−	50.7846i	−0.994630	−	1.72275i
$870$	5.19615			0.176166
$871$		0			0
$872$	−16.3923			−0.555113
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$	1.39230	+	2.41154i	0.0470954	+	0.0815716i
$875$	−28.6865	+	49.6865i	−0.969782	+	1.67971i
$876$	−12.1244			−0.409644
$877$	21.6962	−	37.5788i	0.732627	−	1.26895i	−0.223130	−	0.974789i	$-0.571627\pi$
$877$	21.6962	−	37.5788i	0.732627	−	1.26895i	0.955757	−	0.294158i	$-0.0950393\pi$
$878$	−8.29423	+	14.3660i	−0.279917	+	0.484830i
$879$	−14.6603			−0.494478
$880$	4.09808	−	7.09808i	0.138146	−	0.239276i
$881$	−18.9904	−	32.8923i	−0.639802	−	1.10817i	−0.985476	−	0.169815i	$-0.945683\pi$
$881$	−18.9904	−	32.8923i	−0.639802	−	1.10817i	0.345674	−	0.938355i	$-0.387650\pi$
$882$	−7.69615	−	13.3301i	−0.259143	−	0.448849i
$883$	−24.7846			−0.834069			−0.417034	−	0.908891i	$-0.636930\pi$
$883$	−24.7846			−0.834069			−0.417034	+	0.908891i	$0.636930\pi$
$884$		0			0
$885$	24.0000			0.806751
$886$	2.19615	+	3.80385i	0.0737812	+	0.127793i
$887$	−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
$889$	18.9282			0.634832
$890$	2.19615	−	3.80385i	0.0736152	−	0.127505i
$891$	2.36603	−	4.09808i	0.0792648	−	0.137291i
$892$	18.9282			0.633763
$893$	0.803848	−	1.39230i	0.0268997	−	0.0465917i
$894$	9.06218	+	15.6962i	0.303085	+	0.524958i
$895$	7.09808	+	12.2942i	0.237263	+	0.410951i
$896$	−4.73205			−0.158087
$897$		0			0
$898$	−33.4641			−1.11671
$899$	−3.80385	−	6.58846i	−0.126865	−	0.219737i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	7.79423	−	13.5000i	0.259663	−	0.449750i
$902$	−2.19615			−0.0731239
$903$	−14.6603	+	25.3923i	−0.487863	+	0.845003i
$904$	−5.59808	+	9.69615i	−0.186189	+	0.322489i
$905$	−20.0718			−0.667209
$906$	−3.63397	+	6.29423i	−0.120731	+	0.209112i
$907$	20.5885	+	35.6603i	0.683629	+	1.18408i	0.973866	+	0.227125i	$0.0729325\pi$
$907$	20.5885	+	35.6603i	0.683629	+	1.18408i	−0.290237	+	0.956955i	$0.593734\pi$
$908$	−4.90192	−	8.49038i	−0.162676	−	0.281763i
$909$	−1.39230			−0.0461798
$910$		0			0
$911$	37.1769			1.23173			0.615863	−	0.787853i	$-0.288807\pi$
$911$	37.1769			1.23173			0.615863	+	0.787853i	$0.288807\pi$
$912$	−0.633975	−	1.09808i	−0.0209930	−	0.0363609i
$913$	27.5885	+	47.7846i	0.913045	+	1.58144i
$914$	9.99038	−	17.3038i	0.330452	−	0.572360i
$915$	−8.32051			−0.275068
$916$	9.92820	−	17.1962i	0.328037	−	0.568177i
$917$	38.7846	−	67.1769i	1.28078	−	2.21838i
$918$	5.19615			0.171499
$919$	−16.1962	+	28.0526i	−0.534262	+	0.925369i	0.464937	+	0.885344i	$0.346077\pi$
$919$	−16.1962	+	28.0526i	−0.534262	+	0.925369i	−0.999199	+	0.0400247i	$0.987256\pi$
$920$	−1.90192	−	3.29423i	−0.0627046	−	0.108608i
$921$	−5.36603	−	9.29423i	−0.176817	−	0.306255i
$922$	19.9808			0.658031
$923$		0			0
$924$	−22.3923			−0.736653
$925$	−3.00000	−	5.19615i	−0.0986394	−	0.170848i
$926$	−13.0981	−	22.6865i	−0.430429	−	0.745526i
$927$	2.09808	−	3.63397i	0.0689099	−	0.119355i
$928$	−3.00000			−0.0984798
$929$	−17.3038	+	29.9711i	−0.567721	+	0.983321i	0.429070	+	0.903271i	$0.358841\pi$
$929$	−17.3038	+	29.9711i	−0.567721	+	0.983321i	−0.996791	+	0.0800501i	$0.974492\pi$
$930$	−2.19615	+	3.80385i	−0.0720147	+	0.124733i
$931$	−19.5167			−0.639633
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$	1.09808	+	1.90192i	0.0359494	+	0.0622662i
$934$	−18.2942	−	31.6865i	−0.598605	−	1.03682i
$935$	42.5885			1.39279
$936$		0			0
$937$	5.39230			0.176159			0.0880795	−	0.996113i	$-0.471927\pi$
$937$	5.39230			0.176159			0.0880795	+	0.996113i	$0.471927\pi$
$938$	−25.3923	−	43.9808i	−0.829088	−	1.43602i
$939$	−12.1962	−	21.1244i	−0.398006	−	0.689367i
$940$	−1.09808	+	1.90192i	−0.0358153	+	0.0620339i
$941$	−2.78461			−0.0907757			−0.0453878	−	0.998969i	$-0.514452\pi$
$941$	−2.78461			−0.0907757			−0.0453878	+	0.998969i	$0.514452\pi$
$942$	−1.59808	+	2.76795i	−0.0520681	+	0.0901847i
$943$	−0.509619	+	0.882686i	−0.0165955	+	0.0287442i
$944$	−13.8564			−0.450988
$945$	−4.09808	+	7.09808i	−0.133310	+	0.230900i
$946$	14.6603	+	25.3923i	0.476646	+	0.825575i
$947$	−21.4641	−	37.1769i	−0.697490	−	1.20809i	−0.969334	−	0.245746i	$-0.920967\pi$
$947$	−21.4641	−	37.1769i	−0.697490	−	1.20809i	0.271845	−	0.962341i	$-0.412366\pi$
$948$	12.3923			0.402483
$949$		0			0
$950$	2.53590			0.0822754
$951$	−3.06218	−	5.30385i	−0.0992979	−	0.171989i
$952$	−12.2942	−	21.2942i	−0.398458	−	0.690150i
$953$	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
$956$	−12.2942	+	21.2942i	−0.397624	+	0.688705i
$957$	−14.1962			−0.458896
$958$	−17.6603	+	30.5885i	−0.570577	+	0.988268i
$959$	21.2942	+	36.8827i	0.687627	+	1.19100i
$960$	0.866025	+	1.50000i	0.0279508	+	0.0484123i
$961$	−24.5692			−0.792555
$962$		0			0
$963$	8.19615			0.264117
$964$	0.401924	+	0.696152i	0.0129451	+	0.0224216i
$965$	−11.0885	−	19.2058i	−0.356950	−	0.618256i
$966$	−5.19615	+	9.00000i	−0.167183	+	0.289570i
$967$	14.8756			0.478368			0.239184	−	0.970974i	$-0.423120\pi$
$967$	14.8756			0.478368			0.239184	+	0.970974i	$0.423120\pi$
$968$	−5.69615	+	9.86603i	−0.183081	+	0.317106i
$969$	3.29423	−	5.70577i	0.105826	−	0.183296i
$970$	−10.3923			−0.333677
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	−0.740730	−	0.671803i	$-0.765520\pi$
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	0.952163	+	0.305589i	$0.0988534\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−9.46410	−	16.3923i	−0.303405	−	0.525513i
$974$	−9.12436			−0.292363
$975$		0			0
$976$	4.80385			0.153767
$977$	−8.42820	−	14.5981i	−0.269642	−	0.467034i	0.699127	−	0.714997i	$-0.253572\pi$
$977$	−8.42820	−	14.5981i	−0.269642	−	0.467034i	−0.968769	+	0.247963i	$0.920239\pi$
$978$	−4.73205	−	8.19615i	−0.151314	−	0.262084i
$979$	−6.00000	+	10.3923i	−0.191761	+	0.332140i
$980$	26.6603			0.851631
$981$	8.19615	−	14.1962i	0.261683	−	0.453248i
$982$	−0.294229	+	0.509619i	−0.00938921	+	0.0162626i
$983$	20.7846			0.662926			0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846			0.662926			0.331463	+	0.943468i	$0.392458\pi$
$984$	0.232051	−	0.401924i	0.00739751	−	0.0128129i
$985$	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
$989$	13.6077			0.432700
$990$	4.09808	+	7.09808i	0.130245	+	0.225592i
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	0.532736	−	0.846281i	$-0.321164\pi$
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	−0.999269	+	0.0382223i	$0.987830\pi$
$992$	1.26795	−	2.19615i	0.0402574	−	0.0697279i
$993$	12.0000			0.380808
$994$	−19.3923	+	33.5885i	−0.615087	+	1.06536i
$995$	−7.43782	+	12.8827i	−0.235795	+	0.408409i
$996$	−11.6603			−0.369469
$997$	−6.59808	+	11.4282i	−0.208963	+	0.361935i	−0.951388	−	0.307994i	$-0.900342\pi$
$997$	−6.59808	+	11.4282i	−0.208963	+	0.361935i	0.742425	+	0.669929i	$0.233676\pi$
$998$		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.h.991.2		4
13.2	odd	12		1014.2.b.d.337.1		4
13.3	even	3		1014.2.a.j.1.2		2
13.4	even	6		1014.2.e.j.529.1		4
13.5	odd	4		1014.2.i.f.361.1		4
13.6	odd	12		78.2.i.b.43.2	✓	4
13.7	odd	12		1014.2.i.f.823.1		4
13.8	odd	4		78.2.i.b.49.2	yes	4
13.9	even	3	inner	1014.2.e.h.529.2		4
13.10	even	6		1014.2.a.h.1.1		2
13.11	odd	12		1014.2.b.d.337.4		4
13.12	even	2		1014.2.e.j.991.1		4
39.2	even	12		3042.2.b.l.1351.4		4
39.8	even	4		234.2.l.a.127.1		4
39.11	even	12		3042.2.b.l.1351.1		4
39.23	odd	6		3042.2.a.v.1.2		2
39.29	odd	6		3042.2.a.s.1.1		2
39.32	even	12		234.2.l.a.199.1		4
52.3	odd	6		8112.2.a.bx.1.2		2
52.19	even	12		624.2.bv.d.433.2		4
52.23	odd	6		8112.2.a.bq.1.1		2
52.47	even	4		624.2.bv.d.49.2		4
65.8	even	4		1950.2.y.a.49.1		4
65.19	odd	12		1950.2.bc.c.901.1		4
65.32	even	12		1950.2.y.a.199.1		4
65.34	odd	4		1950.2.bc.c.751.1		4
65.47	even	4		1950.2.y.h.49.2		4
65.58	even	12		1950.2.y.h.199.2		4
156.47	odd	4		1872.2.by.k.1297.2		4
156.71	odd	12		1872.2.by.k.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.2	✓	4	13.6	odd	12
78.2.i.b.49.2	yes	4	13.8	odd	4
234.2.l.a.127.1		4	39.8	even	4
234.2.l.a.199.1		4	39.32	even	12
624.2.bv.d.49.2		4	52.47	even	4
624.2.bv.d.433.2		4	52.19	even	12
1014.2.a.h.1.1		2	13.10	even	6
1014.2.a.j.1.2		2	13.3	even	3
1014.2.b.d.337.1		4	13.2	odd	12
1014.2.b.d.337.4		4	13.11	odd	12
1014.2.e.h.529.2		4	13.9	even	3	inner
1014.2.e.h.991.2		4	1.1	even	1	trivial
1014.2.e.j.529.1		4	13.4	even	6
1014.2.e.j.991.1		4	13.12	even	2
1014.2.i.f.361.1		4	13.5	odd	4
1014.2.i.f.823.1		4	13.7	odd	12
1872.2.by.k.433.2		4	156.71	odd	12
1872.2.by.k.1297.2		4	156.47	odd	4
1950.2.y.a.49.1		4	65.8	even	4
1950.2.y.a.199.1		4	65.32	even	12
1950.2.y.h.49.2		4	65.47	even	4
1950.2.y.h.199.2		4	65.58	even	12
1950.2.bc.c.751.1		4	65.34	odd	4
1950.2.bc.c.901.1		4	65.19	odd	12
3042.2.a.s.1.1		2	39.29	odd	6
3042.2.a.v.1.2		2	39.23	odd	6
3042.2.b.l.1351.1		4	39.11	even	12
3042.2.b.l.1351.4		4	39.2	even	12
8112.2.a.bq.1.1		2	52.23	odd	6
8112.2.a.bx.1.2		2	52.3	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.36603 - 4.09808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(2.36603 - 4.09808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.866025 - 1.50000i) q^{10} +(2.36603 + 4.09808i) q^{11} -1.00000 q^{12} -4.73205 q^{14} +(0.866025 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.59808 - 4.50000i) q^{17} +1.00000 q^{18} +(0.633975 - 1.09808i) q^{19} +(-0.866025 + 1.50000i) q^{20} +4.73205 q^{21} +(2.36603 - 4.09808i) q^{22} +(-1.09808 - 1.90192i) q^{23} +(0.500000 + 0.866025i) q^{24} -2.00000 q^{25} -1.00000 q^{27} +(2.36603 + 4.09808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(0.866025 - 1.50000i) q^{30} -2.53590 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -5.19615 q^{34} +(4.09808 - 7.09808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} -1.26795 q^{38} +1.73205 q^{40} +(-0.232051 - 0.401924i) q^{41} +(-2.36603 - 4.09808i) q^{42} +(-3.09808 + 5.36603i) q^{43} -4.73205 q^{44} +(-0.866025 + 1.50000i) q^{45} +(-1.09808 + 1.90192i) q^{46} +1.26795 q^{47} +(0.500000 - 0.866025i) q^{48} +(-7.69615 - 13.3301i) q^{49} +(1.00000 + 1.73205i) q^{50} +5.19615 q^{51} +3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(4.09808 + 7.09808i) q^{55} +(2.36603 - 4.09808i) q^{56} +1.26795 q^{57} +(1.50000 - 2.59808i) q^{58} +(6.92820 - 12.0000i) q^{59} -1.73205 q^{60} +(-2.40192 + 4.16025i) q^{61} +(1.26795 + 2.19615i) q^{62} +(2.36603 + 4.09808i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.36603 + 9.29423i) q^{67} +(2.59808 + 4.50000i) q^{68} +(1.09808 - 1.90192i) q^{69} -8.19615 q^{70} +(4.09808 - 7.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} +12.1244 q^{73} +(1.50000 - 2.59808i) q^{74} +(-1.00000 - 1.73205i) q^{75} +(0.633975 + 1.09808i) q^{76} +22.3923 q^{77} -12.3923 q^{79} +(-0.866025 - 1.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.232051 + 0.401924i) q^{82} +11.6603 q^{83} +(-2.36603 + 4.09808i) q^{84} +(4.50000 - 7.79423i) q^{85} +6.19615 q^{86} +(-1.50000 + 2.59808i) q^{87} +(2.36603 + 4.09808i) q^{88} +(1.26795 + 2.19615i) q^{89} +1.73205 q^{90} +2.19615 q^{92} +(-1.26795 - 2.19615i) q^{93} +(-0.633975 - 1.09808i) q^{94} +(1.09808 - 1.90192i) q^{95} -1.00000 q^{96} +(3.00000 - 5.19615i) q^{97} +(-7.69615 + 13.3301i) q^{98} -4.73205 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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