LMFDB - Embedded newform 507.2.j.g.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-1.35234 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.g.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35234 + 0.780776i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.219224 - 0.379706i) q^{4} -3.56155i q^{5} +(1.35234 + 0.780776i) q^{6} +(0.486319 + 0.280776i) q^{7} -2.43845i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.35234 + 0.780776i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.219224 - 0.379706i) q^{4} -3.56155i q^{5} +(1.35234 + 0.780776i) q^{6} +(0.486319 + 0.280776i) q^{7} -2.43845i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.78078 + 4.81645i) q^{10} +(1.73205 - 1.00000i) q^{11} -0.438447 q^{12} -0.876894 q^{14} +(-3.08440 + 1.78078i) q^{15} +(2.34233 + 4.05703i) q^{16} +(-0.780776 + 1.35234i) q^{17} -1.56155i q^{18} +(-6.16879 - 3.56155i) q^{19} +(-1.35234 - 0.780776i) q^{20} -0.561553i q^{21} +(-1.56155 + 2.70469i) q^{22} +(1.00000 + 1.73205i) q^{23} +(-2.11176 + 1.21922i) q^{24} -7.68466 q^{25} +1.00000 q^{27} +(0.213225 - 0.123106i) q^{28} +(-3.34233 - 5.78908i) q^{29} +(2.78078 - 4.81645i) q^{30} +2.56155i q^{31} +(-2.11176 - 1.21922i) q^{32} +(-1.73205 - 1.00000i) q^{33} -2.43845i q^{34} +(1.00000 - 1.73205i) q^{35} +(0.219224 + 0.379706i) q^{36} +(-6.54850 + 3.78078i) q^{37} +11.1231 q^{38} -8.68466 q^{40} +(-1.35234 + 0.780776i) q^{41} +(0.438447 + 0.759413i) q^{42} +(2.28078 - 3.95042i) q^{43} -0.876894i q^{44} +(3.08440 + 1.78078i) q^{45} +(-2.70469 - 1.56155i) q^{46} -8.24621i q^{47} +(2.34233 - 4.05703i) q^{48} +(-3.34233 - 5.78908i) q^{49} +(10.3923 - 6.00000i) q^{50} +1.56155 q^{51} -0.684658 q^{53} +(-1.35234 + 0.780776i) q^{54} +(-3.56155 - 6.16879i) q^{55} +(0.684658 - 1.18586i) q^{56} +7.12311i q^{57} +(9.03996 + 5.21922i) q^{58} +(-2.49146 - 1.43845i) q^{59} +1.56155i q^{60} +(-1.93845 + 3.35749i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-0.486319 + 0.280776i) q^{63} -5.56155 q^{64} +3.12311 q^{66} +(3.95042 - 2.28078i) q^{67} +(0.342329 + 0.592932i) q^{68} +(1.00000 - 1.73205i) q^{69} +3.12311i q^{70} +(-12.1244 - 7.00000i) q^{71} +(2.11176 + 1.21922i) q^{72} +10.1231i q^{73} +(5.90388 - 10.2258i) q^{74} +(3.84233 + 6.65511i) q^{75} +(-2.70469 + 1.56155i) q^{76} +1.12311 q^{77} +5.43845 q^{79} +(14.4493 - 8.34233i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.21922 - 2.11176i) q^{82} -0.876894i q^{83} +(-0.213225 - 0.123106i) q^{84} +(4.81645 + 2.78078i) q^{85} +7.12311i q^{86} +(-3.34233 + 5.78908i) q^{87} +(-2.43845 - 4.22351i) q^{88} +(-4.22351 + 2.43845i) q^{89} -5.56155 q^{90} +0.876894 q^{92} +(2.21837 - 1.28078i) q^{93} +(6.43845 + 11.1517i) q^{94} +(-12.6847 + 21.9705i) q^{95} +2.43845i q^{96} +(7.41452 + 4.28078i) q^{97} +(9.03996 + 5.21922i) q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9} + 14 q^{10} - 20 q^{12} - 40 q^{14} - 6 q^{16} + 2 q^{17} + 4 q^{22} + 8 q^{23} - 12 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{30} + 8 q^{35} + 10 q^{36} + 56 q^{38} - 20 q^{40} + 20 q^{42} + 10 q^{43} - 6 q^{48} - 2 q^{49} - 4 q^{51} + 44 q^{53} - 12 q^{55} - 44 q^{56} - 32 q^{61} - 16 q^{62} - 28 q^{64} - 8 q^{66} - 22 q^{68} + 8 q^{69} + 6 q^{74} + 6 q^{75} - 24 q^{77} + 60 q^{79} - 4 q^{81} + 18 q^{82} - 2 q^{87} - 36 q^{88} - 28 q^{90} + 40 q^{92} + 68 q^{94} - 52 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9 + 14 * q^10 - 20 * q^12 - 40 * q^14 - 6 * q^16 + 2 * q^17 + 4 * q^22 + 8 * q^23 - 12 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^30 + 8 * q^35 + 10 * q^36 + 56 * q^38 - 20 * q^40 + 20 * q^42 + 10 * q^43 - 6 * q^48 - 2 * q^49 - 4 * q^51 + 44 * q^53 - 12 * q^55 - 44 * q^56 - 32 * q^61 - 16 * q^62 - 28 * q^64 - 8 * q^66 - 22 * q^68 + 8 * q^69 + 6 * q^74 + 6 * q^75 - 24 * q^77 + 60 * q^79 - 4 * q^81 + 18 * q^82 - 2 * q^87 - 36 * q^88 - 28 * q^90 + 40 * q^92 + 68 * q^94 - 52 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.35234	+	0.780776i	−0.956252	+	0.552092i	−0.895017	−	0.446031i	$-0.852837\pi$
$2$	−1.35234	+	0.780776i	−0.956252	+	0.552092i	−0.0612344	+	0.998123i	$0.519504\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.219224	−	0.379706i	0.109612	−	0.189853i
$5$		−	3.56155i		−	1.59277i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$		−	3.56155i		−	1.59277i	0.604787	−	0.796387i	$-0.293258\pi$
$6$	1.35234	+	0.780776i	0.552092	+	0.318751i
$7$	0.486319	+	0.280776i	0.183811	+	0.106124i	0.589082	−	0.808073i	$-0.299489\pi$
$7$	0.486319	+	0.280776i	0.183811	+	0.106124i	−0.405271	+	0.914197i	$0.632823\pi$
$8$		−	2.43845i		−	0.862121i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.78078	+	4.81645i	0.879359	+	1.52309i
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	−0.215615	−	0.976478i	$-0.569176\pi$
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	0.737848	+	0.674967i	$0.235842\pi$
$12$	−0.438447			−0.126569
$13$		0			0
$13$		0			0
$14$	−0.876894			−0.234360
$15$	−3.08440	+	1.78078i	−0.796387	+	0.459794i
$16$	2.34233	+	4.05703i	0.585582	+	1.01426i
$17$	−0.780776	+	1.35234i	−0.189366	+	0.327992i	−0.945039	−	0.326957i	$-0.893977\pi$
$17$	−0.780776	+	1.35234i	−0.189366	+	0.327992i	0.755673	+	0.654949i	$0.227310\pi$
$18$		−	1.56155i		−	0.368062i
$19$	−6.16879	−	3.56155i	−1.41522	−	0.817076i	−0.419344	−	0.907827i	$-0.637740\pi$
$19$	−6.16879	−	3.56155i	−1.41522	−	0.817076i	−0.995874	+	0.0907512i	$0.971073\pi$
$20$	−1.35234	−	0.780776i	−0.302393	−	0.174587i
$21$		−	0.561553i		−	0.122541i
$22$	−1.56155	+	2.70469i	−0.332924	+	0.576642i
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$	−2.11176	+	1.21922i	−0.431061	+	0.248873i
$25$	−7.68466			−1.53693
$26$		0			0
$27$	1.00000			0.192450
$28$	0.213225	−	0.123106i	0.0402958	−	0.0232648i
$29$	−3.34233	−	5.78908i	−0.620655	−	1.07501i	−0.989364	−	0.145461i	$-0.953533\pi$
$29$	−3.34233	−	5.78908i	−0.620655	−	1.07501i	0.368709	−	0.929545i	$-0.379800\pi$
$30$	2.78078	−	4.81645i	0.507698	−	0.879359i
$31$			2.56155i			0.460068i	0.973183	+	0.230034i	$0.0738838\pi$
$31$			2.56155i			0.460068i	−0.973183	+	0.230034i	$0.926116\pi$
$32$	−2.11176	−	1.21922i	−0.373309	−	0.215530i
$33$	−1.73205	−	1.00000i	−0.301511	−	0.174078i
$34$		−	2.43845i		−	0.418190i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	0.219224	+	0.379706i	0.0365373	+	0.0632844i
$37$	−6.54850	+	3.78078i	−1.07657	+	0.621556i	−0.929968	−	0.367640i	$-0.880166\pi$
$37$	−6.54850	+	3.78078i	−1.07657	+	0.621556i	−0.146598	+	0.989196i	$0.546832\pi$
$38$	11.1231			1.80441
$39$		0			0
$40$	−8.68466			−1.37317
$41$	−1.35234	+	0.780776i	−0.211201	+	0.121937i	−0.601869	−	0.798595i	$-0.705577\pi$
$41$	−1.35234	+	0.780776i	−0.211201	+	0.121937i	0.390669	+	0.920531i	$0.372244\pi$
$42$	0.438447	+	0.759413i	0.0676539	+	0.117180i
$43$	2.28078	−	3.95042i	0.347815	−	0.602433i	−0.638046	−	0.769998i	$-0.720257\pi$
$43$	2.28078	−	3.95042i	0.347815	−	0.602433i	0.985861	+	0.167565i	$0.0535903\pi$
$44$		−	0.876894i		−	0.132197i
$45$	3.08440	+	1.78078i	0.459794	+	0.265462i
$46$	−2.70469	−	1.56155i	−0.398785	−	0.230238i
$47$		−	8.24621i		−	1.20283i	−0.798935	−	0.601417i	$-0.794603\pi$
$47$		−	8.24621i		−	1.20283i	0.798935	−	0.601417i	$-0.205397\pi$
$48$	2.34233	−	4.05703i	0.338086	−	0.585582i
$49$	−3.34233	−	5.78908i	−0.477476	−	0.827012i
$50$	10.3923	−	6.00000i	1.46969	−	0.848528i
$51$	1.56155			0.218661
$52$		0			0
$53$	−0.684658			−0.0940451			−0.0470225	−	0.998894i	$-0.514973\pi$
$53$	−0.684658			−0.0940451			−0.0470225	+	0.998894i	$0.514973\pi$
$54$	−1.35234	+	0.780776i	−0.184031	+	0.106250i
$55$	−3.56155	−	6.16879i	−0.480240	−	0.831800i
$56$	0.684658	−	1.18586i	0.0914913	−	0.158468i
$57$			7.12311i			0.943478i
$58$	9.03996	+	5.21922i	1.18700	+	0.685318i
$59$	−2.49146	−	1.43845i	−0.324361	−	0.187270i	0.328974	−	0.944339i	$-0.393297\pi$
$59$	−2.49146	−	1.43845i	−0.324361	−	0.187270i	−0.653335	+	0.757069i	$0.726631\pi$
$60$			1.56155i			0.201596i
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	−0.963024	−	0.269414i	$-0.913170\pi$
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	0.714832	+	0.699297i	$0.246503\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−0.486319	+	0.280776i	−0.0612704	+	0.0353745i
$64$	−5.56155			−0.695194
$65$		0			0
$66$	3.12311			0.384428
$67$	3.95042	−	2.28078i	0.482621	−	0.278641i	−0.238887	−	0.971047i	$-0.576783\pi$
$67$	3.95042	−	2.28078i	0.482621	−	0.278641i	0.721508	+	0.692406i	$0.243449\pi$
$68$	0.342329	+	0.592932i	0.0415135	+	0.0719035i
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$			3.12311i			0.373283i
$71$	−12.1244	−	7.00000i	−1.43890	−	0.830747i	−0.441123	−	0.897447i	$-0.645420\pi$
$71$	−12.1244	−	7.00000i	−1.43890	−	0.830747i	−0.997773	+	0.0666994i	$0.978753\pi$
$72$	2.11176	+	1.21922i	0.248873	+	0.143687i
$73$			10.1231i			1.18482i	0.805637	+	0.592410i	$0.201823\pi$
$73$			10.1231i			1.18482i	−0.805637	+	0.592410i	$0.798177\pi$
$74$	5.90388	−	10.2258i	0.686312	−	1.18873i
$75$	3.84233	+	6.65511i	0.443674	+	0.768466i
$76$	−2.70469	+	1.56155i	−0.310249	+	0.179122i
$77$	1.12311			0.127990
$78$		0			0
$79$	5.43845			0.611873			0.305937	−	0.952052i	$-0.401030\pi$
$79$	5.43845			0.611873			0.305937	+	0.952052i	$0.401030\pi$
$80$	14.4493	−	8.34233i	1.61549	−	0.932701i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.21922	−	2.11176i	0.134641	−	0.233205i
$83$		−	0.876894i		−	0.0962517i	−0.998841	−	0.0481258i	$-0.984675\pi$
$83$		−	0.876894i		−	0.0962517i	0.998841	−	0.0481258i	$-0.0153248\pi$
$84$	−0.213225	−	0.123106i	−0.0232648	−	0.0134319i
$85$	4.81645	+	2.78078i	0.522417	+	0.301618i
$86$			7.12311i			0.768104i
$87$	−3.34233	+	5.78908i	−0.358335	+	0.620655i
$88$	−2.43845	−	4.22351i	−0.259939	−	0.450228i
$89$	−4.22351	+	2.43845i	−0.447692	+	0.258475i	−0.706855	−	0.707359i	$-0.749887\pi$
$89$	−4.22351	+	2.43845i	−0.447692	+	0.258475i	0.259163	+	0.965834i	$0.416553\pi$
$90$	−5.56155			−0.586239
$91$		0			0
$92$	0.876894			0.0914226
$93$	2.21837	−	1.28078i	0.230034	−	0.132810i
$94$	6.43845	+	11.1517i	0.664075	+	1.15021i
$95$	−12.6847	+	21.9705i	−1.30142	+	2.25412i
$96$			2.43845i			0.248873i
$97$	7.41452	+	4.28078i	0.752831	+	0.434647i	0.826716	−	0.562620i	$-0.190206\pi$
$97$	7.41452	+	4.28078i	0.752831	+	0.434647i	−0.0738851	+	0.997267i	$0.523540\pi$
$98$	9.03996	+	5.21922i	0.913174	+	0.527221i
$99$			2.00000i			0.201008i
$100$	−1.68466	+	2.91791i	−0.168466	+	0.291791i
$101$	−3.78078	−	6.54850i	−0.376201	−	0.651600i	0.614305	−	0.789069i	$-0.289437\pi$
$101$	−3.78078	−	6.54850i	−0.376201	−	0.651600i	−0.990506	+	0.137469i	$0.956103\pi$
$102$	−2.11176	+	1.21922i	−0.209095	+	0.120721i
$103$	3.43845			0.338800			0.169400	−	0.985547i	$-0.445817\pi$
$103$	3.43845			0.338800			0.169400	+	0.985547i	$0.445817\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$	0.925894	−	0.534565i	0.0899308	−	0.0519216i
$107$	4.12311	+	7.14143i	0.398596	+	0.690388i	0.993553	−	0.113369i	$-0.0361644\pi$
$107$	4.12311	+	7.14143i	0.398596	+	0.690388i	−0.594957	+	0.803757i	$0.702831\pi$
$108$	0.219224	−	0.379706i	0.0210948	−	0.0365373i
$109$		−	2.80776i		−	0.268935i	−0.990918	−	0.134468i	$-0.957068\pi$
$109$		−	2.80776i		−	0.268935i	0.990918	−	0.134468i	$-0.0429324\pi$
$110$	9.63289	+	5.56155i	0.918460	+	0.530273i
$111$	6.54850	+	3.78078i	0.621556	+	0.358855i
$112$			2.63068i			0.248576i
$113$	−2.90388	+	5.02967i	−0.273174	+	0.473152i	−0.969673	−	0.244406i	$-0.921407\pi$
$113$	−2.90388	+	5.02967i	−0.273174	+	0.473152i	0.696499	+	0.717558i	$0.254740\pi$
$114$	−5.56155	−	9.63289i	−0.520887	−	0.902203i
$115$	6.16879	−	3.56155i	0.575243	−	0.332117i
$116$	−2.93087			−0.272124
$117$		0			0
$118$	4.49242			0.413561
$119$	−0.759413	+	0.438447i	−0.0696153	+	0.0401924i
$120$	4.34233	+	7.52113i	0.396399	+	0.686583i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		−	6.05398i		−	0.548101i
$123$	1.35234	+	0.780776i	0.121937	+	0.0704002i
$124$	0.972638	+	0.561553i	0.0873455	+	0.0504289i
$125$			9.56155i			0.855211i
$126$	0.438447	−	0.759413i	0.0390600	−	0.0676539i
$127$	2.71922	+	4.70983i	0.241292	+	0.417930i	0.961083	−	0.276261i	$-0.0890955\pi$
$127$	2.71922	+	4.70983i	0.241292	+	0.417930i	−0.719791	+	0.694191i	$0.755762\pi$
$128$	11.7446	−	6.78078i	1.03809	−	0.599342i
$129$	−4.56155			−0.401622
$130$		0			0
$131$	7.36932			0.643860			0.321930	−	0.946763i	$-0.395668\pi$
$131$	7.36932			0.643860			0.321930	+	0.946763i	$0.395668\pi$
$132$	−0.759413	+	0.438447i	−0.0660984	+	0.0381619i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	−3.56155	+	6.16879i	−0.307671	+	0.532902i
$135$		−	3.56155i		−	0.306530i
$136$	3.29762	+	1.90388i	0.282769	+	0.163257i
$137$	−4.81645	−	2.78078i	−0.411497	−	0.237578i	0.279936	−	0.960019i	$-0.409687\pi$
$137$	−4.81645	−	2.78078i	−0.411497	−	0.237578i	−0.691433	+	0.722441i	$0.743020\pi$
$138$			3.12311i			0.265856i
$139$	8.96543	−	15.5286i	0.760438	−	1.31712i	−0.182187	−	0.983264i	$-0.558318\pi$
$139$	8.96543	−	15.5286i	0.760438	−	1.31712i	0.942625	−	0.333854i	$-0.108349\pi$
$140$	−0.438447	−	0.759413i	−0.0370556	−	0.0641821i
$141$	−7.14143	+	4.12311i	−0.601417	+	0.347228i
$142$	21.8617			1.83460
$143$		0			0
$144$	−4.68466			−0.390388
$145$	−20.6181	+	11.9039i	−1.71224	+	0.988564i
$146$	−7.90388	−	13.6899i	−0.654130	−	1.13299i
$147$	−3.34233	+	5.78908i	−0.275671	+	0.477476i
$148$			3.31534i			0.272519i
$149$	2.11176	+	1.21922i	0.173002	+	0.0998827i	0.584001	−	0.811753i	$-0.301487\pi$
$149$	2.11176	+	1.21922i	0.173002	+	0.0998827i	−0.410999	+	0.911636i	$0.634820\pi$
$150$	−10.3923	−	6.00000i	−0.848528	−	0.489898i
$151$			9.36932i			0.762464i	0.924479	+	0.381232i	$0.124500\pi$
$151$			9.36932i			0.762464i	−0.924479	+	0.381232i	$0.875500\pi$
$152$	−8.68466	+	15.0423i	−0.704419	+	1.22009i
$153$	−0.780776	−	1.35234i	−0.0631220	−	0.109331i
$154$	−1.51883	+	0.876894i	−0.122390	+	0.0706622i
$155$	9.12311			0.732785
$156$		0			0
$157$	20.3693			1.62565			0.812824	−	0.582509i	$-0.197929\pi$
$157$	20.3693			1.62565			0.812824	+	0.582509i	$0.197929\pi$
$158$	−7.35465	+	4.24621i	−0.585105	+	0.337810i
$159$	0.342329	+	0.592932i	0.0271485	+	0.0470225i
$160$	−4.34233	+	7.52113i	−0.343291	+	0.594598i
$161$			1.12311i			0.0885131i
$162$	1.35234	+	0.780776i	0.106250	+	0.0613436i
$163$	−4.16365	−	2.40388i	−0.326122	−	0.188287i	0.327996	−	0.944679i	$-0.393627\pi$
$163$	−4.16365	−	2.40388i	−0.326122	−	0.188287i	−0.654118	+	0.756393i	$0.726960\pi$
$164$			0.684658i			0.0534628i
$165$	−3.56155	+	6.16879i	−0.277267	+	0.480240i
$166$	0.684658	+	1.18586i	0.0531398	+	0.0920408i
$167$	−8.87348	+	5.12311i	−0.686650	+	0.396438i	−0.802356	−	0.596846i	$-0.796420\pi$
$167$	−8.87348	+	5.12311i	−0.686650	+	0.396438i	0.115706	+	0.993284i	$0.463087\pi$
$168$	−1.36932			−0.105645
$169$		0			0
$170$	−8.68466			−0.666083
$171$	6.16879	−	3.56155i	0.471739	−	0.272359i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	10.1231	−	17.5337i	0.769645	−	1.33307i	−0.168110	−	0.985768i	$-0.553766\pi$
$173$	10.1231	−	17.5337i	0.769645	−	1.33307i	0.937755	−	0.347297i	$-0.112900\pi$
$174$		−	10.4384i		−	0.791337i
$175$	−3.73720	−	2.15767i	−0.282505	−	0.163105i
$176$	8.11407	+	4.68466i	0.611621	+	0.353119i
$177$			2.87689i			0.216241i
$178$	3.80776	−	6.59524i	0.285404	−	0.494334i
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	0.760391	−	0.649466i	$-0.225007\pi$
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	−0.942649	+	0.333785i	$0.891674\pi$
$180$	1.35234	−	0.780776i	0.100798	−	0.0581956i
$181$	2.68466			0.199549			0.0997745	−	0.995010i	$-0.468188\pi$
$181$	2.68466			0.199549			0.0997745	+	0.995010i	$0.468188\pi$
$182$		0			0
$183$	3.87689			0.286588
$184$	4.22351	−	2.43845i	0.311362	−	0.179765i
$185$	13.4654	+	23.3228i	0.989998	+	1.71473i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$			3.12311i			0.228384i
$188$	−3.13114	−	1.80776i	−0.228362	−	0.131845i
$189$	0.486319	+	0.280776i	0.0353745	+	0.0204235i
$190$		−	39.6155i		−	2.87401i
$191$	4.56155	−	7.90084i	0.330062	−	0.571685i	−0.652461	−	0.757822i	$-0.726264\pi$
$191$	4.56155	−	7.90084i	0.330062	−	0.571685i	0.982524	+	0.186137i	$0.0595969\pi$
$192$	2.78078	+	4.81645i	0.200685	+	0.347597i
$193$	11.6848	−	6.74621i	0.841089	−	0.485603i	−0.0165453	−	0.999863i	$-0.505267\pi$
$193$	11.6848	−	6.74621i	0.841089	−	0.485603i	0.857634	+	0.514260i	$0.171933\pi$
$194$	−13.3693			−0.959861
$195$		0			0
$196$	−2.93087			−0.209348
$197$	11.5782	−	6.68466i	0.824910	−	0.476262i	−0.0271965	−	0.999630i	$-0.508658\pi$
$197$	11.5782	−	6.68466i	0.824910	−	0.476262i	0.852107	+	0.523368i	$0.175325\pi$
$198$	−1.56155	−	2.70469i	−0.110975	−	0.192214i
$199$	11.0885	−	19.2059i	0.786046	−	1.36147i	−0.142327	−	0.989820i	$-0.545458\pi$
$199$	11.0885	−	19.2059i	0.786046	−	1.36147i	0.928372	−	0.371651i	$-0.121208\pi$
$200$			18.7386i			1.32502i
$201$	−3.95042	−	2.28078i	−0.278641	−	0.160874i
$202$	10.2258	+	5.90388i	0.719486	+	0.415396i
$203$		−	3.75379i		−	0.263464i
$204$	0.342329	−	0.592932i	0.0239678	−	0.0415135i
$205$	2.78078	+	4.81645i	0.194218	+	0.336395i
$206$	−4.64996	+	2.68466i	−0.323978	+	0.187049i
$207$	−2.00000			−0.139010
$208$		0			0
$209$	−14.2462			−0.985431
$210$	2.70469	−	1.56155i	0.186641	−	0.107757i
$211$	−9.84233	−	17.0474i	−0.677574	−	1.17359i	−0.975709	−	0.219069i	$-0.929698\pi$
$211$	−9.84233	−	17.0474i	−0.677574	−	1.17359i	0.298136	−	0.954524i	$-0.403635\pi$
$212$	−0.150093	+	0.259969i	−0.0103084	+	0.0178548i
$213$			14.0000i			0.959264i
$214$	−11.1517	−	6.43845i	−0.762316	−	0.440123i
$215$	−14.0696	−	8.12311i	−0.959541	−	0.553991i
$216$		−	2.43845i		−	0.165915i
$217$	−0.719224	+	1.24573i	−0.0488241	+	0.0845658i
$218$	2.19224	+	3.79706i	0.148477	+	0.257170i
$219$	8.76687	−	5.06155i	0.592410	−	0.342028i
$220$	−3.12311			−0.210560
$221$		0			0
$222$	−11.8078			−0.792485
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	−0.249756	−	0.968309i	$-0.580350\pi$
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	0.713702	+	0.700449i	$0.247017\pi$
$224$	−0.684658	−	1.18586i	−0.0457457	−	0.0792338i
$225$	3.84233	−	6.65511i	0.256155	−	0.443674i
$226$		−	9.06913i		−	0.603270i
$227$	−6.16879	−	3.56155i	−0.409437	−	0.236389i	0.281111	−	0.959675i	$-0.409297\pi$
$227$	−6.16879	−	3.56155i	−0.409437	−	0.236389i	−0.690548	+	0.723287i	$0.742630\pi$
$228$	2.70469	+	1.56155i	0.179122	+	0.103416i
$229$			16.2462i			1.07358i	0.843716	+	0.536790i	$0.180363\pi$
$229$			16.2462i			1.07358i	−0.843716	+	0.536790i	$0.819637\pi$
$230$	−5.56155	+	9.63289i	−0.366718	+	0.635174i
$231$	−0.561553	−	0.972638i	−0.0369475	−	0.0639949i
$232$	−14.1164	+	8.15009i	−0.926785	+	0.535080i
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	−29.3693			−1.91584
$236$	−1.09238	+	0.630683i	−0.0711076	+	0.0410540i
$237$	−2.71922	−	4.70983i	−0.176633	−	0.305937i
$238$	0.684658	−	1.18586i	0.0443798	−	0.0768681i
$239$		−	25.3693i		−	1.64100i	−0.571643	−	0.820502i	$-0.693694\pi$
$239$		−	25.3693i		−	1.64100i	0.571643	−	0.820502i	$-0.306306\pi$
$240$	−14.4493	−	8.34233i	−0.932701	−	0.538495i
$241$	−15.4220	−	8.90388i	−0.993417	−	0.573549i	−0.0871229	−	0.996198i	$-0.527767\pi$
$241$	−15.4220	−	8.90388i	−0.993417	−	0.573549i	−0.906294	+	0.422648i	$0.861101\pi$
$242$		−	10.9309i		−	0.702663i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.849907	+	1.47208i	0.0544097	+	0.0942404i
$245$	−20.6181	+	11.9039i	−1.31724	+	0.760511i
$246$	−2.43845			−0.155470
$247$		0			0
$248$	6.24621			0.396635
$249$	−0.759413	+	0.438447i	−0.0481258	+	0.0277855i
$250$	−7.46543	−	12.9305i	−0.472156	−	0.817797i
$251$	9.36932	−	16.2281i	0.591386	−	1.02431i	−0.402660	−	0.915350i	$-0.631914\pi$
$251$	9.36932	−	16.2281i	0.591386	−	1.02431i	0.994046	−	0.108961i	$-0.0347524\pi$
$252$			0.246211i			0.0155099i
$253$	3.46410	+	2.00000i	0.217786	+	0.125739i
$254$	−7.35465	−	4.24621i	−0.461472	−	0.266431i
$255$		−	5.56155i		−	0.348278i
$256$	−5.02699	+	8.70700i	−0.314187	+	0.544187i
$257$	14.5885	+	25.2681i	0.910008	+	1.57618i	0.814050	+	0.580795i	$0.197258\pi$
$257$	14.5885	+	25.2681i	0.910008	+	1.57618i	0.0959583	+	0.995385i	$0.469408\pi$
$258$	6.16879	−	3.56155i	0.384052	−	0.221733i
$259$	−4.24621			−0.263847
$260$		0			0
$261$	6.68466			0.413770
$262$	−9.96585	+	5.75379i	−0.615693	+	0.355470i
$263$	−4.68466	−	8.11407i	−0.288868	−	0.500335i	0.684672	−	0.728852i	$-0.259946\pi$
$263$	−4.68466	−	8.11407i	−0.288868	−	0.500335i	−0.973540	+	0.228517i	$0.926612\pi$
$264$	−2.43845	+	4.22351i	−0.150076	+	0.259939i
$265$			2.43845i			0.149793i
$266$	5.40938	+	3.12311i	0.331670	+	0.191490i
$267$	4.22351	+	2.43845i	0.258475	+	0.149231i
$268$		−	2.00000i		−	0.122169i
$269$	10.6847	−	18.5064i	0.651455	−	1.12835i	−0.331315	−	0.943520i	$-0.607492\pi$
$269$	10.6847	−	18.5064i	0.651455	−	1.12835i	0.982770	−	0.184833i	$-0.0591745\pi$
$270$	2.78078	+	4.81645i	0.169233	+	0.293120i
$271$	25.9209	−	14.9654i	1.57458	−	0.909085i	0.578986	−	0.815337i	$-0.303449\pi$
$271$	25.9209	−	14.9654i	1.57458	−	0.909085i	0.995596	−	0.0937481i	$-0.0298848\pi$
$272$	−7.31534			−0.443558
$273$		0			0
$274$	8.68466			0.524659
$275$	−13.3102	+	7.68466i	−0.802636	+	0.463402i
$276$	−0.438447	−	0.759413i	−0.0263914	−	0.0457113i
$277$	2.65767	−	4.60322i	0.159684	−	0.276581i	−0.775071	−	0.631874i	$-0.782286\pi$
$277$	2.65767	−	4.60322i	0.159684	−	0.276581i	0.934755	+	0.355294i	$0.115619\pi$
$278$			28.0000i			1.67933i
$279$	−2.21837	−	1.28078i	−0.132810	−	0.0766781i
$280$	−4.22351	−	2.43845i	−0.252403	−	0.145725i
$281$		−	17.8078i		−	1.06232i	−0.847271	−	0.531161i	$-0.821756\pi$
$281$		−	17.8078i		−	1.06232i	0.847271	−	0.531161i	$-0.178244\pi$
$282$	6.43845	−	11.1517i	0.383404	−	0.664075i
$283$	−6.84233	−	11.8513i	−0.406734	−	0.704484i	0.587787	−	0.809015i	$-0.299999\pi$
$283$	−6.84233	−	11.8513i	−0.406734	−	0.704484i	−0.994522	+	0.104531i	$0.966666\pi$
$284$	−5.31589	+	3.06913i	−0.315440	+	0.182119i
$285$	25.3693			1.50275
$286$		0			0
$287$	−0.876894			−0.0517614
$288$	2.11176	−	1.21922i	0.124436	−	0.0718434i
$289$	7.28078	+	12.6107i	0.428281	+	0.741804i
$290$	18.5885	−	32.1963i	1.09156	−	1.89063i
$291$		−	8.56155i		−	0.501887i
$292$	3.84381	+	2.21922i	0.224942	+	0.129870i
$293$	17.7002	+	10.2192i	1.03406	+	0.597013i	0.918144	−	0.396246i	$-0.129687\pi$
$293$	17.7002	+	10.2192i	1.03406	+	0.597013i	0.115913	+	0.993259i	$0.463021\pi$
$294$		−	10.4384i		−	0.608783i
$295$	−5.12311	+	8.87348i	−0.298279	+	0.516634i
$296$	9.21922	+	15.9682i	0.535856	+	0.928131i
$297$	1.73205	−	1.00000i	0.100504	−	0.0580259i
$298$	−3.80776			−0.220578
$299$		0			0
$300$	3.36932			0.194528
$301$	2.21837	−	1.28078i	0.127865	−	0.0738227i
$302$	−7.31534	−	12.6705i	−0.420951	−	0.729108i
$303$	−3.78078	+	6.54850i	−0.217200	+	0.376201i
$304$		−	33.3693i		−	1.91386i
$305$	11.9579	+	6.90388i	0.684706	+	0.395315i
$306$	2.11176	+	1.21922i	0.120721	+	0.0696984i
$307$		−	30.8078i		−	1.75829i	−0.476553	−	0.879146i	$-0.658114\pi$
$307$		−	30.8078i		−	1.75829i	0.476553	−	0.879146i	$-0.341886\pi$
$308$	0.246211	−	0.426450i	0.0140292	−	0.0242993i
$309$	−1.71922	−	2.97778i	−0.0978032	−	0.169400i
$310$	−12.3376	+	7.12311i	−0.700728	+	0.404565i
$311$	19.1231			1.08437			0.542186	−	0.840259i	$-0.317597\pi$
$311$	19.1231			1.08437			0.542186	+	0.840259i	$0.317597\pi$
$312$		0			0
$313$	−13.6847			−0.773503			−0.386751	−	0.922184i	$-0.626403\pi$
$313$	−13.6847			−0.773503			−0.386751	+	0.922184i	$0.626403\pi$
$314$	−27.5463	+	15.9039i	−1.55453	+	0.897508i
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$	1.19224	−	2.06501i	0.0670685	−	0.116166i
$317$			14.0540i			0.789350i	0.918821	+	0.394675i	$0.129143\pi$
$317$			14.0540i			0.789350i	−0.918821	+	0.394675i	$0.870857\pi$
$318$	−0.925894	−	0.534565i	−0.0519216	−	0.0299769i
$319$	−11.5782	−	6.68466i	−0.648253	−	0.374269i
$320$			19.8078i			1.10729i
$321$	4.12311	−	7.14143i	0.230129	−	0.398596i
$322$	−0.876894	−	1.51883i	−0.0488674	−	0.0846408i
$323$	9.63289	−	5.56155i	0.535988	−	0.309453i
$324$	−0.438447			−0.0243582
$325$		0			0
$326$	7.50758			0.415806
$327$	−2.43160	+	1.40388i	−0.134468	+	0.0776349i
$328$	1.90388	+	3.29762i	0.105124	+	0.182081i
$329$	2.31534	−	4.01029i	0.127649	−	0.221094i
$330$		−	11.1231i		−	0.612307i
$331$	2.76456	+	1.59612i	0.151954	+	0.0877306i	0.574049	−	0.818821i	$-0.305372\pi$
$331$	2.76456	+	1.59612i	0.151954	+	0.0877306i	−0.422095	+	0.906552i	$0.638705\pi$
$332$	−0.332962	−	0.192236i	−0.0182737	−	0.0105503i
$333$		−	7.56155i		−	0.414371i
$334$	8.00000	−	13.8564i	0.437741	−	0.758189i
$335$	−8.12311	−	14.0696i	−0.443813	−	0.768706i
$336$	2.27824	−	1.31534i	0.124288	−	0.0717578i
$337$	6.12311			0.333547			0.166773	−	0.985995i	$-0.446665\pi$
$337$	6.12311			0.333547			0.166773	+	0.985995i	$0.446665\pi$
$338$		0			0
$339$	5.80776			0.315434
$340$	2.11176	−	1.21922i	0.114526	−	0.0661217i
$341$	2.56155	+	4.43674i	0.138716	+	0.240263i
$342$	−5.56155	+	9.63289i	−0.300734	+	0.520887i
$343$		−	7.68466i		−	0.414933i
$344$	−9.63289	−	5.56155i	−0.519371	−	0.299859i
$345$	−6.16879	−	3.56155i	−0.332117	−	0.191748i
$346$			31.6155i			1.69966i
$347$	−13.8078	+	23.9157i	−0.741240	+	1.28386i	0.210692	+	0.977553i	$0.432428\pi$
$347$	−13.8078	+	23.9157i	−0.741240	+	1.28386i	−0.951931	+	0.306312i	$0.900905\pi$
$348$	1.46543	+	2.53821i	0.0785556	+	0.136062i
$349$	−5.89570	+	3.40388i	−0.315589	+	0.182206i	−0.649425	−	0.760426i	$-0.724990\pi$
$349$	−5.89570	+	3.40388i	−0.315589	+	0.182206i	0.333836	+	0.942631i	$0.391657\pi$
$350$	6.73863			0.360195
$351$		0			0
$352$	−4.87689			−0.259939
$353$	4.60322	−	2.65767i	0.245005	−	0.141454i	−0.372470	−	0.928044i	$-0.621489\pi$
$353$	4.60322	−	2.65767i	0.245005	−	0.141454i	0.617475	+	0.786591i	$0.288156\pi$
$354$	−2.24621	−	3.89055i	−0.119385	−	0.206781i
$355$	−24.9309	+	43.1815i	−1.32319	+	2.29184i
$356$			2.13826i			0.113328i
$357$	0.759413	+	0.438447i	0.0401924	+	0.0232051i
$358$	6.59524	+	3.80776i	0.348569	+	0.201247i
$359$			9.36932i			0.494494i	0.968953	+	0.247247i	$0.0795258\pi$
$359$			9.36932i			0.494494i	−0.968953	+	0.247247i	$0.920474\pi$
$360$	4.34233	−	7.52113i	0.228861	−	0.396399i
$361$	15.8693	+	27.4865i	0.835227	+	1.44666i
$362$	−3.63058	+	2.09612i	−0.190819	+	0.110170i
$363$	7.00000			0.367405
$364$		0			0
$365$	36.0540			1.88715
$366$	−5.24290	+	3.02699i	−0.274051	+	0.158223i
$367$	8.52699	+	14.7692i	0.445105	+	0.770945i	0.998060	−	0.0622668i	$-0.0198330\pi$
$367$	8.52699	+	14.7692i	0.445105	+	0.770945i	−0.552954	+	0.833212i	$0.686500\pi$
$368$	−4.68466	+	8.11407i	−0.244205	+	0.422975i
$369$		−	1.56155i		−	0.0812912i
$370$	−36.4198	−	21.0270i	−1.89338	−	1.09314i
$371$	−0.332962	−	0.192236i	−0.0172865	−	0.00998039i
$372$		−	1.12311i		−	0.0582303i
$373$	−14.1847	+	24.5685i	−0.734454	+	1.27211i	0.220509	+	0.975385i	$0.429228\pi$
$373$	−14.1847	+	24.5685i	−0.734454	+	1.27211i	−0.954963	+	0.296726i	$0.904105\pi$
$374$	−2.43845	−	4.22351i	−0.126089	−	0.218393i
$375$	8.28055	−	4.78078i	0.427606	−	0.246878i
$376$	−20.1080			−1.03699
$377$		0			0
$378$	−0.876894			−0.0451026
$379$	20.5115	−	11.8423i	1.05361	−	0.608300i	0.129949	−	0.991521i	$-0.458519\pi$
$379$	20.5115	−	11.8423i	1.05361	−	0.608300i	0.923657	+	0.383221i	$0.125185\pi$
$380$	5.56155	+	9.63289i	0.285302	+	0.494157i
$381$	2.71922	−	4.70983i	0.139310	−	0.241292i
$382$			14.2462i			0.728900i
$383$	19.6922	+	11.3693i	1.00623	+	0.580945i	0.910085	−	0.414423i	$-0.136016\pi$
$383$	19.6922	+	11.3693i	1.00623	+	0.580945i	0.0961417	+	0.995368i	$0.469350\pi$
$384$	−11.7446	−	6.78078i	−0.599342	−	0.346030i
$385$		−	4.00000i		−	0.203859i
$386$	−10.5346	+	18.2464i	−0.536195	+	0.928717i
$387$	2.28078	+	3.95042i	0.115938	+	0.200811i
$388$	3.25088	−	1.87689i	0.165038	−	0.0952849i
$389$	−34.0540			−1.72661			−0.863303	−	0.504687i	$-0.831608\pi$
$389$	−34.0540			−1.72661			−0.863303	+	0.504687i	$0.831608\pi$
$390$		0			0
$391$	−3.12311			−0.157942
$392$	−14.1164	+	8.15009i	−0.712985	+	0.411642i
$393$	−3.68466	−	6.38202i	−0.185866	−	0.321930i
$394$	−10.4384	+	18.0799i	−0.525881	+	0.910853i
$395$		−	19.3693i		−	0.974576i
$396$	0.759413	+	0.438447i	0.0381619	+	0.0220328i
$397$	21.6974	+	12.5270i	1.08896	+	0.628711i	0.933299	−	0.359099i	$-0.116916\pi$
$397$	21.6974	+	12.5270i	1.08896	+	0.628711i	0.155661	+	0.987811i	$0.450249\pi$
$398$			34.6307i			1.73588i
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$	−18.0000	−	31.1769i	−0.900000	−	1.55885i
$401$	−12.5041	+	7.21922i	−0.624423	+	0.360511i	−0.778589	−	0.627534i	$-0.784064\pi$
$401$	−12.5041	+	7.21922i	−0.624423	+	0.360511i	0.154166	+	0.988045i	$0.450731\pi$
$402$	7.12311			0.355268
$403$		0			0
$404$	−3.31534			−0.164944
$405$	−3.08440	+	1.78078i	−0.153265	+	0.0884875i
$406$	2.93087	+	5.07642i	0.145457	+	0.251938i
$407$	−7.56155	+	13.0970i	−0.374812	+	0.649194i
$408$		−	3.80776i		−	0.188512i
$409$	−5.51599	−	3.18466i	−0.272748	−	0.157471i	0.357388	−	0.933956i	$-0.383667\pi$
$409$	−5.51599	−	3.18466i	−0.272748	−	0.157471i	−0.630136	+	0.776485i	$0.717001\pi$
$410$	−7.52113	−	4.34233i	−0.371442	−	0.214452i
$411$			5.56155i			0.274331i
$412$	0.753789	−	1.30560i	0.0371365	−	0.0643223i
$413$	−0.807764	−	1.39909i	−0.0397475	−	0.0688446i
$414$	2.70469	−	1.56155i	0.132928	−	0.0767461i
$415$	−3.12311			−0.153307
$416$		0			0
$417$	−17.9309			−0.878078
$418$	19.2658	−	11.1231i	0.942320	−	0.544049i
$419$	17.1231	+	29.6581i	0.836518	+	1.44889i	0.892788	+	0.450477i	$0.148746\pi$
$419$	17.1231	+	29.6581i	0.836518	+	1.44889i	−0.0562697	+	0.998416i	$0.517921\pi$
$420$	−0.438447	+	0.759413i	−0.0213940	+	0.0370556i
$421$			31.2462i			1.52285i	0.648255	+	0.761424i	$0.275499\pi$
$421$			31.2462i			1.52285i	−0.648255	+	0.761424i	$0.724501\pi$
$422$	26.6204	+	15.3693i	1.29586	+	0.748167i
$423$	7.14143	+	4.12311i	0.347228	+	0.200472i
$424$			1.66950i			0.0810783i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	−10.9309	−	18.9328i	−0.529602	−	0.917298i
$427$	−1.88541	+	1.08854i	−0.0912413	+	0.0526782i
$428$	3.61553			0.174763
$429$		0			0
$430$	25.3693			1.22342
$431$	−9.63289	+	5.56155i	−0.464000	+	0.267891i	−0.713725	−	0.700426i	$-0.752993\pi$
$431$	−9.63289	+	5.56155i	−0.464000	+	0.267891i	0.249725	+	0.968317i	$0.419660\pi$
$432$	2.34233	+	4.05703i	0.112695	+	0.195194i
$433$	4.37689	−	7.58100i	0.210340	−	0.364320i	−0.741481	−	0.670974i	$-0.765876\pi$
$433$	4.37689	−	7.58100i	0.210340	−	0.364320i	0.951821	+	0.306654i	$0.0992095\pi$
$434$		−	2.24621i		−	0.107822i
$435$	20.6181	+	11.9039i	0.988564	+	0.570747i
$436$	−1.06613	−	0.615528i	−0.0510582	−	0.0294785i
$437$		−	14.2462i		−	0.681489i
$438$	−7.90388	+	13.6899i	−0.377662	+	0.654130i
$439$	−6.84233	−	11.8513i	−0.326567	−	0.565630i	0.655262	−	0.755402i	$-0.272558\pi$
$439$	−6.84233	−	11.8513i	−0.326567	−	0.565630i	−0.981828	+	0.189772i	$0.939225\pi$
$440$	−15.0423	+	8.68466i	−0.717112	+	0.414025i
$441$	6.68466			0.318317
$442$		0			0
$443$	−34.7386			−1.65048			−0.825241	−	0.564781i	$-0.808961\pi$
$443$	−34.7386			−1.65048			−0.825241	+	0.564781i	$0.808961\pi$
$444$	2.87117	−	1.65767i	0.136260	−	0.0786696i
$445$	8.68466	+	15.0423i	0.411692	+	0.713072i
$446$	−6.24621	+	10.8188i	−0.295767	+	0.512283i
$447$		−	2.43845i		−	0.115335i
$448$	−2.70469	−	1.56155i	−0.127785	−	0.0737764i
$449$	−7.14143	−	4.12311i	−0.337025	−	0.194581i	0.321931	−	0.946763i	$-0.395668\pi$
$449$	−7.14143	−	4.12311i	−0.337025	−	0.194581i	−0.658956	+	0.752182i	$0.729002\pi$
$450$			12.0000i			0.565685i
$451$	−1.56155	+	2.70469i	−0.0735307	+	0.127359i
$452$	1.27320	+	2.20525i	0.0598862	+	0.103726i
$453$	8.11407	−	4.68466i	0.381232	−	0.220104i
$454$	11.1231			0.522033
$455$		0			0
$456$	17.3693			0.813393
$457$	10.9254	−	6.30776i	0.511067	−	0.295065i	−0.222205	−	0.975000i	$-0.571325\pi$
$457$	10.9254	−	6.30776i	0.511067	−	0.295065i	0.733272	+	0.679935i	$0.237992\pi$
$458$	−12.6847	−	21.9705i	−0.592715	−	1.02661i
$459$	−0.780776	+	1.35234i	−0.0364435	+	0.0631220i
$460$		−	3.12311i		−	0.145616i
$461$	14.0229	+	8.09612i	0.653111	+	0.377074i	0.789647	−	0.613561i	$-0.210264\pi$
$461$	14.0229	+	8.09612i	0.653111	+	0.377074i	−0.136536	+	0.990635i	$0.543597\pi$
$462$	1.51883	+	0.876894i	0.0706622	+	0.0407968i
$463$			14.3153i			0.665290i	0.943052	+	0.332645i	$0.107941\pi$
$463$			14.3153i			0.665290i	−0.943052	+	0.332645i	$0.892059\pi$
$464$	15.6577	−	27.1199i	0.726889	−	1.25901i
$465$	−4.56155	−	7.90084i	−0.211537	−	0.366393i
$466$	35.1610	−	20.3002i	1.62880	−	0.940388i
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$		0			0
$469$	2.56155			0.118282
$470$	39.7174	−	22.9309i	1.83203	−	1.05772i
$471$	−10.1847	−	17.6403i	−0.469284	−	0.812824i
$472$	−3.50758	+	6.07530i	−0.161449	+	0.279638i
$473$		−	9.12311i		−	0.419481i
$474$	7.35465	+	4.24621i	0.337810	+	0.195035i
$475$	47.4050	+	27.3693i	2.17509	+	1.25579i
$476$			0.384472i			0.0176222i
$477$	0.342329	−	0.592932i	0.0156742	−	0.0271485i
$478$	19.8078	+	34.3081i	0.905986	+	1.56921i
$479$	−8.87348	+	5.12311i	−0.405440	+	0.234081i	−0.688828	−	0.724924i	$-0.741875\pi$
$479$	−8.87348	+	5.12311i	−0.405440	+	0.234081i	0.283389	+	0.959005i	$0.408541\pi$
$480$	8.68466			0.396399
$481$		0			0
$482$	27.8078			1.26661
$483$	0.972638	−	0.561553i	0.0442566	−	0.0255515i
$484$	1.53457	+	2.65794i	0.0697530	+	0.120816i
$485$	15.2462	−	26.4072i	0.692295	−	1.19909i
$486$		−	1.56155i		−	0.0708335i
$487$	−6.16879	−	3.56155i	−0.279535	−	0.161389i	0.353678	−	0.935367i	$-0.384931\pi$
$487$	−6.16879	−	3.56155i	−0.279535	−	0.161389i	−0.633213	+	0.773978i	$0.718264\pi$
$488$	8.18706	+	4.72680i	0.370611	+	0.213972i
$489$			4.80776i			0.217415i
$490$	18.5885	−	32.1963i	0.839745	−	1.45448i
$491$	−18.1231	−	31.3901i	−0.817884	−	1.41662i	−0.907238	−	0.420617i	$-0.861814\pi$
$491$	−18.1231	−	31.3901i	−0.817884	−	1.41662i	0.0893539	−	0.996000i	$-0.471520\pi$
$492$	0.592932	−	0.342329i	0.0267314	−	0.0154334i
$493$	10.4384			0.470124
$494$		0			0
$495$	7.12311			0.320160
$496$	−10.3923	+	6.00000i	−0.466628	+	0.269408i
$497$	−3.93087	−	6.80847i	−0.176324	−	0.305401i
$498$	0.684658	−	1.18586i	0.0306803	−	0.0531398i
$499$			4.49242i			0.201108i	0.994932	+	0.100554i	$0.0320616\pi$
$499$			4.49242i			0.201108i	−0.994932	+	0.100554i	$0.967938\pi$
$500$	3.63058	+	2.09612i	0.162365	+	0.0937412i
$501$	8.87348	+	5.12311i	0.396438	+	0.228883i
$502$			29.2614i			1.30600i
$503$	14.1231	−	24.4619i	0.629718	−	1.09070i	−0.357890	−	0.933764i	$-0.616504\pi$
$503$	14.1231	−	24.4619i	0.629718	−	1.09070i	0.987608	−	0.156940i	$-0.0501630\pi$
$504$	0.684658	+	1.18586i	0.0304971	+	0.0528225i
$505$	−23.3228	+	13.4654i	−1.03785	+	0.599204i
$506$	−6.24621			−0.277678
$507$		0			0
$508$	2.38447			0.105794
$509$	−11.9579	+	6.90388i	−0.530023	+	0.306009i	−0.741026	−	0.671476i	$-0.765660\pi$
$509$	−11.9579	+	6.90388i	−0.530023	+	0.306009i	0.211003	+	0.977486i	$0.432327\pi$
$510$	4.34233	+	7.52113i	0.192282	+	0.333041i
$511$	−2.84233	+	4.92306i	−0.125737	+	0.217783i
$512$			11.4233i			0.504843i
$513$	−6.16879	−	3.56155i	−0.272359	−	0.157246i
$514$	−39.4575	−	22.7808i	−1.74039	−	1.00482i
$515$		−	12.2462i		−	0.539633i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	−8.24621	−	14.2829i	−0.362668	−	0.628159i
$518$	5.74234	−	3.31534i	0.252304	−	0.145668i
$519$	−20.2462			−0.888710
$520$		0			0
$521$	−9.06913			−0.397326			−0.198663	−	0.980068i	$-0.563660\pi$
$521$	−9.06913			−0.397326			−0.198663	+	0.980068i	$0.563660\pi$
$522$	−9.03996	+	5.21922i	−0.395668	+	0.228439i
$523$	−16.9309	−	29.3251i	−0.740335	−	1.28230i	−0.952343	−	0.305030i	$-0.901333\pi$
$523$	−16.9309	−	29.3251i	−0.740335	−	1.28230i	0.212007	−	0.977268i	$-0.432000\pi$
$524$	1.61553	−	2.79818i	0.0705747	−	0.122239i
$525$			4.31534i			0.188337i
$526$	12.6705	+	7.31534i	0.552462	+	0.318964i
$527$	−3.46410	−	2.00000i	−0.150899	−	0.0871214i
$528$		−	9.36932i		−	0.407747i
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	−1.90388	−	3.29762i	−0.0826994	−	0.143239i
$531$	2.49146	−	1.43845i	0.108120	−	0.0624233i
$532$	−1.75379			−0.0760364
$533$		0			0
$534$	−7.61553			−0.329556
$535$	25.4346	−	14.6847i	1.09963	−	0.634873i
$536$	−5.56155	−	9.63289i	−0.240222	−	0.416078i
$537$	−2.43845	+	4.22351i	−0.105227	+	0.182258i
$538$			33.3693i			1.43865i
$539$	−11.5782	−	6.68466i	−0.498707	−	0.287929i
$540$	−1.35234	−	0.780776i	−0.0581956	−	0.0335993i
$541$		−	19.7386i		−	0.848630i	−0.905515	−	0.424315i	$-0.860515\pi$
$541$		−	19.7386i		−	0.848630i	0.905515	−	0.424315i	$-0.139485\pi$
$542$	−23.3693	+	40.4768i	−1.00380	+	1.73863i
$543$	−1.34233	−	2.32498i	−0.0576049	−	0.0997745i
$544$	3.29762	−	1.90388i	0.141384	−	0.0816283i
$545$	−10.0000			−0.428353
$546$		0			0
$547$	3.93087			0.168072			0.0840359	−	0.996463i	$-0.473219\pi$
$547$	3.93087			0.168072			0.0840359	+	0.996463i	$0.473219\pi$
$548$	−2.11176	+	1.21922i	−0.0902098	+	0.0520827i
$549$	−1.93845	−	3.35749i	−0.0827309	−	0.143294i
$550$	12.0000	−	20.7846i	0.511682	−	0.886259i
$551$			47.6155i			2.02849i
$552$	−4.22351	−	2.43845i	−0.179765	−	0.103787i
$553$	2.64482	+	1.52699i	0.112469	+	0.0649341i
$554$			8.30019i			0.352641i
$555$	13.4654	−	23.3228i	0.571576	−	0.989998i
$556$	−3.93087	−	6.80847i	−0.166706	−	0.288743i
$557$	37.1792	−	21.4654i	1.57533	−	0.909520i	0.579837	−	0.814733i	$-0.303116\pi$
$557$	37.1792	−	21.4654i	1.57533	−	0.909520i	0.995498	−	0.0947869i	$-0.0302170\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	9.36932			0.395926
$561$	2.70469	−	1.56155i	0.114192	−	0.0659288i
$562$	13.9039	+	24.0822i	0.586500	+	1.01585i
$563$	−11.6847	+	20.2384i	−0.492450	+	0.852948i	−0.999962	−	0.00869657i	$-0.997232\pi$
$563$	−11.6847	+	20.2384i	−0.492450	+	0.852948i	0.507513	+	0.861644i	$0.330565\pi$
$564$			3.61553i			0.152241i
$565$	17.9134	+	10.3423i	0.753624	+	0.435105i
$566$	18.5064	+	10.6847i	0.777881	+	0.449110i
$567$		−	0.561553i		−	0.0235830i
$568$	−17.0691	+	29.5646i	−0.716205	+	1.24050i
$569$	−4.36932	−	7.56788i	−0.183171	−	0.317262i	0.759787	−	0.650171i	$-0.225303\pi$
$569$	−4.36932	−	7.56788i	−0.183171	−	0.317262i	−0.942959	+	0.332910i	$0.891970\pi$
$570$	−34.3081	+	19.8078i	−1.43701	+	0.829656i
$571$	5.36932			0.224699			0.112349	−	0.993669i	$-0.464162\pi$
$571$	5.36932			0.224699			0.112349	+	0.993669i	$0.464162\pi$
$572$		0			0
$573$	−9.12311			−0.381123
$574$	1.18586	−	0.684658i	0.0494970	−	0.0285771i
$575$	−7.68466	−	13.3102i	−0.320472	−	0.555074i
$576$	2.78078	−	4.81645i	0.115866	−	0.200685i
$577$		−	17.3153i		−	0.720847i	−0.932789	−	0.360424i	$-0.882632\pi$
$577$		−	17.3153i		−	0.720847i	0.932789	−	0.360424i	$-0.117368\pi$
$578$	−19.6922	−	11.3693i	−0.819089	−	0.472901i
$579$	−11.6848	−	6.74621i	−0.485603	−	0.280363i
$580$			10.4384i			0.433433i
$581$	0.246211	−	0.426450i	0.0102146	−	0.0176921i
$582$	6.68466	+	11.5782i	0.277088	+	0.479931i
$583$	−1.18586	+	0.684658i	−0.0491134	+	0.0283557i
$584$	24.6847			1.02146
$585$		0			0
$586$	−31.9157			−1.31843
$587$	34.0948	−	19.6847i	1.40724	−	0.812473i	0.412123	−	0.911128i	$-0.364788\pi$
$587$	34.0948	−	19.6847i	1.40724	−	0.812473i	0.995122	+	0.0986556i	$0.0314542\pi$
$588$	1.46543	+	2.53821i	0.0604335	+	0.104674i
$589$	9.12311	−	15.8017i	0.375911	−	0.651097i
$590$		−	16.0000i		−	0.658710i
$591$	−11.5782	−	6.68466i	−0.476262	−	0.274970i
$592$	−30.6775	−	17.7116i	−1.26084	−	0.727944i
$593$			17.4233i			0.715489i	0.933820	+	0.357744i	$0.116454\pi$
$593$			17.4233i			0.715489i	−0.933820	+	0.357744i	$0.883546\pi$
$594$	−1.56155	+	2.70469i	−0.0640713	+	0.110975i
$595$	1.56155	+	2.70469i	0.0640174	+	0.110881i
$596$	0.925894	−	0.534565i	0.0379261	−	0.0218966i
$597$	−22.1771			−0.907648
$598$		0			0
$599$	−41.6155			−1.70036			−0.850182	−	0.526489i	$-0.823508\pi$
$599$	−41.6155			−1.70036			−0.850182	+	0.526489i	$0.823508\pi$
$600$	16.2281	−	9.36932i	0.662511	−	0.382501i
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	0.929066	−	0.369914i	$-0.120613\pi$
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	−0.784888	+	0.619638i	$0.787280\pi$
$602$	−2.00000	+	3.46410i	−0.0815139	+	0.141186i
$603$			4.56155i			0.185761i
$604$	3.55759	+	2.05398i	0.144756	+	0.0835751i
$605$	21.5908	+	12.4654i	0.877789	+	0.506792i
$606$		−	11.8078i		−	0.479658i
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	8.68466	+	15.0423i	0.352209	+	0.610045i
$609$	−3.25088	+	1.87689i	−0.131732	+	0.0760556i
$610$	−21.5616			−0.873002
$611$		0			0
$612$	−0.684658			−0.0276757
$613$	−30.1912	+	17.4309i	−1.21941	+	0.704026i	−0.964792	−	0.263016i	$-0.915283\pi$
$613$	−30.1912	+	17.4309i	−1.21941	+	0.704026i	−0.254618	+	0.967042i	$0.581950\pi$
$614$	24.0540	+	41.6627i	0.970739	+	1.68137i
$615$	2.78078	−	4.81645i	0.112132	−	0.194218i
$616$		−	2.73863i		−	0.110343i
$617$	−8.49377	−	4.90388i	−0.341946	−	0.197423i	0.319186	−	0.947692i	$-0.396591\pi$
$617$	−8.49377	−	4.90388i	−0.341946	−	0.197423i	−0.661132	+	0.750269i	$0.729924\pi$
$618$	4.64996	+	2.68466i	0.187049	+	0.107993i
$619$		−	29.3002i		−	1.17767i	−0.808252	−	0.588837i	$-0.799586\pi$
$619$		−	29.3002i		−	1.17767i	0.808252	−	0.588837i	$-0.200414\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$	1.00000	+	1.73205i	0.0401286	+	0.0695048i
$622$	−25.8610	+	14.9309i	−1.03693	+	0.598673i
$623$	−2.73863			−0.109721
$624$		0			0
$625$	−4.36932			−0.174773
$626$	18.5064	−	10.6847i	0.739663	−	0.427045i
$627$	7.12311	+	12.3376i	0.284469	+	0.492716i
$628$	4.46543	−	7.73436i	0.178190	−	0.308635i
$629$		−	11.8078i		−	0.470806i
$630$	−2.70469	−	1.56155i	−0.107757	−	0.0622138i
$631$	−16.0748	−	9.28078i	−0.639927	−	0.369462i	0.144660	−	0.989481i	$-0.453791\pi$
$631$	−16.0748	−	9.28078i	−0.639927	−	0.369462i	−0.784586	+	0.620020i	$0.787125\pi$
$632$		−	13.2614i		−	0.527509i
$633$	−9.84233	+	17.0474i	−0.391197	+	0.677574i
$634$	−10.9730	−	19.0058i	−0.435794	−	0.754817i
$635$	16.7743	−	9.68466i	0.665669	−	0.384324i
$636$	0.300187			0.0119032
$637$		0			0
$638$	20.8769			0.826524
$639$	12.1244	−	7.00000i	0.479632	−	0.276916i
$640$	−24.1501	−	41.8292i	−0.954616	−	1.65344i
$641$	−9.58854	+	16.6078i	−0.378725	+	0.655970i	−0.990877	−	0.134770i	$-0.956971\pi$
$641$	−9.58854	+	16.6078i	−0.378725	+	0.655970i	0.612152	+	0.790740i	$0.290304\pi$
$642$			12.8769i			0.508210i
$643$	27.3200	+	15.7732i	1.07739	+	0.622034i	0.930192	−	0.367072i	$-0.119640\pi$
$643$	27.3200	+	15.7732i	1.07739	+	0.622034i	0.147202	+	0.989106i	$0.452973\pi$
$644$	0.426450	+	0.246211i	0.0168045	+	0.00970208i
$645$			16.2462i			0.639694i
$646$	−8.68466	+	15.0423i	−0.341693	+	0.591830i
$647$	−3.19224	−	5.52911i	−0.125500	−	0.217372i	0.796428	−	0.604733i	$-0.206720\pi$
$647$	−3.19224	−	5.52911i	−0.125500	−	0.217372i	−0.921928	+	0.387361i	$0.873387\pi$
$648$	−2.11176	+	1.21922i	−0.0829577	+	0.0478956i
$649$	−5.75379			−0.225856
$650$		0			0
$651$	1.43845			0.0563772
$652$	−1.82554	+	1.05398i	−0.0714936	+	0.0412769i
$653$	−11.5616	−	20.0252i	−0.452439	−	0.783647i	0.546098	−	0.837721i	$-0.316112\pi$
$653$	−11.5616	−	20.0252i	−0.452439	−	0.783647i	−0.998537	+	0.0540745i	$0.982779\pi$
$654$	2.19224	−	3.79706i	0.0857232	−	0.148477i
$655$		−	26.2462i		−	1.02552i
$656$	−6.33527	−	3.65767i	−0.247351	−	0.142808i
$657$	−8.76687	−	5.06155i	−0.342028	−	0.197470i
$658$			7.23106i			0.281896i
$659$	1.12311	−	1.94528i	0.0437500	−	0.0757772i	−0.843321	−	0.537410i	$-0.819403\pi$
$659$	1.12311	−	1.94528i	0.0437500	−	0.0757772i	0.887071	+	0.461633i	$0.152736\pi$
$660$	1.56155	+	2.70469i	0.0607834	+	0.105280i
$661$	−4.87631	+	2.81534i	−0.189667	+	0.109504i	−0.591827	−	0.806065i	$-0.701593\pi$
$661$	−4.87631	+	2.81534i	−0.189667	+	0.109504i	0.402160	+	0.915569i	$0.368260\pi$
$662$	−4.98485			−0.193742
$663$		0			0
$664$	−2.13826			−0.0829806
$665$	−12.3376	+	7.12311i	−0.478431	+	0.276222i
$666$	5.90388	+	10.2258i	0.228771	+	0.396243i
$667$	6.68466	−	11.5782i	0.258831	−	0.448308i
$668$			4.49242i			0.173817i
$669$	−6.92820	−	4.00000i	−0.267860	−	0.154649i
$670$	21.9705	+	12.6847i	0.848793	+	0.490051i
$671$			7.75379i			0.299332i
$672$	−0.684658	+	1.18586i	−0.0264113	+	0.0457457i
$673$	−11.6231	−	20.1318i	−0.448038	−	0.776024i	0.550220	−	0.835019i	$-0.314544\pi$
$673$	−11.6231	−	20.1318i	−0.448038	−	0.776024i	−0.998258	+	0.0589952i	$0.981210\pi$
$674$	−8.28055	+	4.78078i	−0.318955	+	0.184149i
$675$	−7.68466			−0.295783
$676$		0			0
$677$	−15.6155			−0.600153			−0.300077	−	0.953915i	$-0.597012\pi$
$677$	−15.6155			−0.600153			−0.300077	+	0.953915i	$0.597012\pi$
$678$	−7.85410	+	4.53457i	−0.301635	+	0.174149i
$679$	2.40388	+	4.16365i	0.0922525	+	0.159786i
$680$	6.78078	−	11.7446i	0.260031	−	0.450387i
$681$			7.12311i			0.272958i
$682$	−6.92820	−	4.00000i	−0.265295	−	0.153168i
$683$	−33.0025	−	19.0540i	−1.26280	−	0.729080i	−0.289188	−	0.957272i	$-0.593385\pi$
$683$	−33.0025	−	19.0540i	−1.26280	−	0.729080i	−0.973616	+	0.228192i	$0.926719\pi$
$684$		−	3.12311i		−	0.119415i
$685$	−9.90388	+	17.1540i	−0.378408	+	0.655422i
$686$	6.00000	+	10.3923i	0.229081	+	0.396780i
$687$	14.0696	−	8.12311i	0.536790	−	0.309916i
$688$	21.3693			0.814698
$689$		0			0
$690$	11.1231			0.423449
$691$	−44.4273	+	25.6501i	−1.69009	+	0.975776i	−0.735659	+	0.677352i	$0.763128\pi$
$691$	−44.4273	+	25.6501i	−1.69009	+	0.975776i	−0.954433	+	0.298424i	$0.903539\pi$
$692$	−4.43845	−	7.68762i	−0.168724	−	0.292239i
$693$	−0.561553	+	0.972638i	−0.0213316	+	0.0369475i
$694$		−	43.1231i		−	1.63693i
$695$	−55.3059	−	31.9309i	−2.09787	−	1.21121i
$696$	14.1164	+	8.15009i	0.535080	+	0.308928i
$697$		−	2.43845i		−	0.0923628i
$698$	5.31534	−	9.20644i	0.201189	−	0.348469i
$699$	13.0000	+	22.5167i	0.491705	+	0.851658i
$700$	−1.63856	+	0.946025i	−0.0619319	+	0.0357564i
$701$	5.36932			0.202796			0.101398	−	0.994846i	$-0.467668\pi$
$701$	5.36932			0.202796			0.101398	+	0.994846i	$0.467668\pi$
$702$		0			0
$703$	53.8617			2.03143
$704$	−9.63289	+	5.56155i	−0.363053	+	0.209609i
$705$	14.6847	+	25.4346i	0.553056	+	0.957921i
$706$	−4.15009	+	7.18817i	−0.156191	+	0.270530i
$707$		−	4.24621i		−	0.159695i
$708$	1.09238	+	0.630683i	0.0410540	+	0.0237025i
$709$	−6.48863	−	3.74621i	−0.243686	−	0.140692i	0.373184	−	0.927757i	$-0.378266\pi$
$709$	−6.48863	−	3.74621i	−0.243686	−	0.140692i	−0.616869	+	0.787065i	$0.711599\pi$
$710$		−	77.8617i		−	2.92210i
$711$	−2.71922	+	4.70983i	−0.101979	+	0.176633i
$712$	5.94602	+	10.2988i	0.222837	+	0.385964i
$713$	−4.43674	+	2.56155i	−0.166157	+	0.0959309i
$714$	−1.36932			−0.0512454
$715$		0			0
$716$	−2.13826			−0.0799106
$717$	−21.9705	+	12.6847i	−0.820502	+	0.473717i
$718$	−7.31534	−	12.6705i	−0.273006	−	0.472860i
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	−0.997358	−	0.0726475i	$-0.976855\pi$
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	0.561593	+	0.827413i	$0.310189\pi$
$720$			16.6847i			0.621801i
$721$	1.67218	+	0.965435i	0.0622753	+	0.0359547i
$722$	−42.9216	−	24.7808i	−1.59738	−	0.922245i
$723$			17.8078i			0.662278i
$724$	0.588540	−	1.01938i	0.0218729	−	0.0378850i
$725$	25.6847	+	44.4871i	0.953904	+	1.65221i
$726$	−9.46641	+	5.46543i	−0.351331	+	0.202841i
$727$	38.6695			1.43417			0.717086	−	0.696984i	$-0.245475\pi$
$727$	38.6695			1.43417			0.717086	+	0.696984i	$0.245475\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−48.7574	+	28.1501i	−1.80459	+	1.04188i
$731$	3.56155	+	6.16879i	0.131729	+	0.228161i
$732$	0.849907	−	1.47208i	0.0314135	−	0.0544097i
$733$			20.5076i			0.757465i	0.925506	+	0.378732i	$0.123640\pi$
$733$			20.5076i			0.757465i	−0.925506	+	0.378732i	$0.876360\pi$
$734$	−23.0628	−	13.3153i	−0.851265	−	0.491478i
$735$	20.6181	+	11.9039i	0.760511	+	0.439081i
$736$		−	4.87689i		−	0.179765i
$737$	4.56155	−	7.90084i	0.168027	−	0.291031i
$738$	1.21922	+	2.11176i	0.0448802	+	0.0777349i
$739$	−8.87348	+	5.12311i	−0.326416	+	0.188456i	−0.654249	−	0.756279i	$-0.727015\pi$
$739$	−8.87348	+	5.12311i	−0.326416	+	0.188456i	0.327833	+	0.944736i	$0.393682\pi$
$740$	11.8078			0.434062
$741$		0			0
$742$	0.600373			0.0220404
$743$	−10.9385	+	6.31534i	−0.401294	+	0.231687i	−0.687042	−	0.726617i	$-0.741091\pi$
$743$	−10.9385	+	6.31534i	−0.401294	+	0.231687i	0.285748	+	0.958305i	$0.407758\pi$
$744$	−3.12311	−	5.40938i	−0.114499	−	0.198317i
$745$	4.34233	−	7.52113i	0.159091	−	0.275553i
$746$		−	44.3002i		−	1.62195i
$747$	0.759413	+	0.438447i	0.0277855	+	0.0160419i
$748$	1.18586	+	0.684658i	0.0433595	+	0.0250336i
$749$			4.63068i			0.169201i
$750$	−7.46543	+	12.9305i	−0.272599	+	0.472156i
$751$	22.0540	+	38.1986i	0.804761	+	1.39389i	0.916452	+	0.400144i	$0.131040\pi$
$751$	22.0540	+	38.1986i	0.804761	+	1.39389i	−0.111691	+	0.993743i	$0.535627\pi$
$752$	33.4552	−	19.3153i	1.21998	−	0.704358i
$753$	−18.7386			−0.682874
$754$		0			0
$755$	33.3693			1.21443
$756$	0.213225	−	0.123106i	0.00775493	−	0.00447731i
$757$	−15.0000	−	25.9808i	−0.545184	−	0.944287i	−0.998595	−	0.0529853i	$-0.983126\pi$
$757$	−15.0000	−	25.9808i	−0.545184	−	0.944287i	0.453411	−	0.891302i	$-0.350207\pi$
$758$	−18.4924	+	32.0298i	−0.671675	+	1.16338i
$759$		−	4.00000i		−	0.145191i
$760$	53.5738	+	30.9309i	1.94333	+	1.12198i
$761$	8.11407	+	4.68466i	0.294135	+	0.169819i	0.639805	−	0.768537i	$-0.279015\pi$
$761$	8.11407	+	4.68466i	0.294135	+	0.169819i	−0.345670	+	0.938356i	$0.612348\pi$
$762$			8.49242i			0.307648i
$763$	0.788354	−	1.36547i	0.0285403	−	0.0494333i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$	−4.81645	+	2.78078i	−0.174139	+	0.100539i
$766$	−35.5076			−1.28294
$767$		0			0
$768$	10.0540			0.362792
$769$	−15.5885	+	9.00000i	−0.562134	+	0.324548i	−0.754002	−	0.656873i	$-0.771879\pi$
$769$	−15.5885	+	9.00000i	−0.562134	+	0.324548i	0.191867	+	0.981421i	$0.438546\pi$
$770$	3.12311	+	5.40938i	0.112549	+	0.194940i
$771$	14.5885	−	25.2681i	0.525393	−	0.910008i
$772$		−	5.91571i		−	0.212911i
$773$	20.9978	+	12.1231i	0.755240	+	0.436038i	0.827584	−	0.561342i	$-0.189715\pi$
$773$	20.9978	+	12.1231i	0.755240	+	0.436038i	−0.0723444	+	0.997380i	$0.523048\pi$
$774$	−6.16879	−	3.56155i	−0.221733	−	0.128017i
$775$		−	19.6847i		−	0.707094i
$776$	10.4384	−	18.0799i	0.374718	−	0.649031i
$777$	2.12311	+	3.67733i	0.0761660	+	0.131923i
$778$	46.0527	−	26.5885i	1.65107	−	0.953245i
$779$	11.1231			0.398527
$780$		0			0
$781$	−28.0000			−1.00192
$782$	4.22351	−	2.43845i	0.151033	−	0.0871987i
$783$	−3.34233	−	5.78908i	−0.119445	−	0.206885i
$784$	15.6577	−	27.1199i	0.559203	−	0.968567i
$785$		−	72.5464i		−	2.58929i
$786$	9.96585	+	5.75379i	0.355470	+	0.205231i
$787$	38.2585	+	22.0885i	1.36377	+	0.787371i	0.990123	−	0.140201i	$-0.0447748\pi$
$787$	38.2585	+	22.0885i	1.36377	+	0.787371i	0.373644	+	0.927572i	$0.378108\pi$
$788$		−	5.86174i		−	0.208816i
$789$	−4.68466	+	8.11407i	−0.166778	+	0.288868i
$790$	15.1231	+	26.1940i	0.538056	+	0.931940i
$791$	−2.82443	+	1.63068i	−0.100425	+	0.0579804i
$792$	4.87689			0.173293
$793$		0			0
$794$	−39.1231			−1.38843
$795$	2.11176	−	1.21922i	0.0748963	−	0.0432414i
$796$	−4.86174	−	8.42078i	−0.172320	−	0.298467i
$797$	−0.192236	+	0.332962i	−0.00680935	+	0.0117941i	−0.869410	−	0.494091i	$-0.835501\pi$
$797$	−0.192236	+	0.332962i	−0.00680935	+	0.0117941i	0.862601	+	0.505885i	$0.168834\pi$
$798$		−	6.24621i		−	0.221113i
$799$	11.1517	+	6.43845i	0.394519	+	0.227776i
$800$	16.2281	+	9.36932i	0.573751	+	0.331255i
$801$		−	4.87689i		−	0.172317i
$802$	11.2732	−	19.5258i	0.398070	−	0.689478i
$803$	10.1231	+	17.5337i	0.357237	+	0.618752i
$804$	−1.73205	+	1.00000i	−0.0610847	+	0.0352673i
$805$	4.00000			0.140981
$806$		0			0
$807$	−21.3693			−0.752236
$808$	−15.9682	+	9.21922i	−0.561758	+	0.324331i
$809$	8.15009	+	14.1164i	0.286542	+	0.496305i	0.972982	−	0.230881i	$-0.0741609\pi$
$809$	8.15009	+	14.1164i	0.286542	+	0.496305i	−0.686440	+	0.727187i	$0.740828\pi$
$810$	2.78078	−	4.81645i	0.0977065	−	0.169233i
$811$			2.56155i			0.0899483i	0.998988	+	0.0449741i	$0.0143205\pi$
$811$			2.56155i			0.0899483i	−0.998988	+	0.0449741i	$0.985679\pi$
$812$	−1.42534	−	0.822919i	−0.0500195	−	0.0288788i
$813$	−25.9209	−	14.9654i	−0.909085	−	0.524861i
$814$		−	23.6155i		−	0.827724i
$815$	−8.56155	+	14.8290i	−0.299898	+	0.519439i
$816$	3.65767	+	6.33527i	0.128044	+	0.221779i
$817$	−28.1393	+	16.2462i	−0.984468	+	0.568383i
$818$	9.94602			0.347755
$819$		0			0
$820$	2.43845			0.0851543
$821$	5.62260	−	3.24621i	0.196230	−	0.113294i	−0.398666	−	0.917096i	$-0.630527\pi$
$821$	5.62260	−	3.24621i	0.196230	−	0.113294i	0.594896	+	0.803803i	$0.297193\pi$
$822$	−4.34233	−	7.52113i	−0.151456	−	0.262330i
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		−	8.38447i		−	0.292087i
$825$	13.3102	+	7.68466i	0.463402	+	0.267545i
$826$	2.18475	+	1.26137i	0.0760172	+	0.0438885i
$827$			14.7386i			0.512513i	0.966609	+	0.256256i	$0.0824891\pi$
$827$			14.7386i			0.512513i	−0.966609	+	0.256256i	$0.917511\pi$
$828$	−0.438447	+	0.759413i	−0.0152371	+	0.0263914i
$829$	6.74621	+	11.6848i	0.234306	+	0.405829i	0.959071	−	0.283167i	$-0.0913850\pi$
$829$	6.74621	+	11.6848i	0.234306	+	0.405829i	−0.724765	+	0.688996i	$0.758052\pi$
$830$	4.22351	−	2.43845i	0.146600	−	0.0846397i
$831$	−5.31534			−0.184387
$832$		0			0
$833$	10.4384			0.361671
$834$	24.2487	−	14.0000i	0.839664	−	0.484780i
$835$	18.2462	+	31.6034i	0.631436	+	1.09368i
$836$	−3.12311	+	5.40938i	−0.108015	+	0.187087i
$837$			2.56155i			0.0885402i
$838$	−46.3127	−	26.7386i	−1.59984	−	0.923671i
$839$	18.7196	+	10.8078i	0.646272	+	0.373125i	0.787027	−	0.616919i	$-0.211619\pi$
$839$	18.7196	+	10.8078i	0.646272	+	0.373125i	−0.140754	+	0.990045i	$0.544953\pi$
$840$			4.87689i			0.168269i
$841$	−7.84233	+	13.5833i	−0.270425	+	0.468390i
$842$	−24.3963	−	42.2556i	−0.840752	−	1.45623i
$843$	−15.4220	+	8.90388i	−0.531161	+	0.306666i
$844$	−8.63068			−0.297080
$845$		0			0
$846$	−12.8769			−0.442717
$847$	−3.40423	+	1.96543i	−0.116971	+	0.0675331i
$848$	−1.60370	−	2.77768i	−0.0550711	−	0.0953860i
$849$	−6.84233	+	11.8513i	−0.234828	+	0.406734i
$850$			18.7386i			0.642730i
$851$	−13.0970	−	7.56155i	−0.448959	−	0.259207i
$852$	5.31589	+	3.06913i	0.182119	+	0.105147i
$853$		−	2.12311i		−	0.0726938i	−0.999339	−	0.0363469i	$-0.988428\pi$
$853$		−	2.12311i		−	0.0726938i	0.999339	−	0.0363469i	$-0.0115721\pi$
$854$	1.69981	−	2.94416i	0.0581664	−	0.100747i
$855$	−12.6847	−	21.9705i	−0.433806	−	0.751374i
$856$	17.4140	−	10.0540i	0.595198	−	0.343638i
$857$	−35.5616			−1.21476			−0.607380	−	0.794412i	$-0.707779\pi$
$857$	−35.5616			−1.21476			−0.607380	+	0.794412i	$0.707779\pi$
$858$		0			0
$859$	24.5616			0.838029			0.419015	−	0.907979i	$-0.362376\pi$
$859$	24.5616			0.838029			0.419015	+	0.907979i	$0.362376\pi$
$860$	−6.16879	+	3.56155i	−0.210354	+	0.121448i
$861$	0.438447	+	0.759413i	0.0149422	+	0.0258807i
$862$	8.68466	−	15.0423i	0.295801	−	0.512342i
$863$			30.4924i			1.03797i	0.854782	+	0.518987i	$0.173691\pi$
$863$			30.4924i			1.03797i	−0.854782	+	0.518987i	$0.826309\pi$
$864$	−2.11176	−	1.21922i	−0.0718434	−	0.0414788i
$865$	−62.4473	−	36.0540i	−2.12327	−	1.22587i
$866$			13.6695i			0.464509i
$867$	7.28078	−	12.6107i	0.247268	−	0.428281i
$868$	0.315342	+	0.546188i	0.0107034	+	0.0185388i
$869$	9.41967	−	5.43845i	0.319540	−	0.184487i
$870$	−37.1771			−1.26042
$871$		0			0
$872$	−6.84658			−0.231855
$873$	−7.41452	+	4.28078i	−0.250944	+	0.144882i
$874$	11.1231	+	19.2658i	0.376245	+	0.651675i
$875$	−2.68466	+	4.64996i	−0.0907580	+	0.157198i
$876$		−	4.43845i		−	0.149961i
$877$	−20.4049	−	11.7808i	−0.689025	−	0.397809i	0.114222	−	0.993455i	$-0.463563\pi$
$877$	−20.4049	−	11.7808i	−0.689025	−	0.397809i	−0.803247	+	0.595647i	$0.796896\pi$
$878$	18.5064	+	10.6847i	0.624560	+	0.360590i
$879$		−	20.4384i		−	0.689372i
$880$	16.6847	−	28.8987i	0.562440	−	0.974174i
$881$	−4.53457	−	7.85410i	−0.152773	−	0.264611i	0.779473	−	0.626436i	$-0.215487\pi$
$881$	−4.53457	−	7.85410i	−0.152773	−	0.264611i	−0.932246	+	0.361825i	$0.882154\pi$
$882$	−9.03996	+	5.21922i	−0.304391	+	0.175740i
$883$	−8.80776			−0.296405			−0.148202	−	0.988957i	$-0.547349\pi$
$883$	−8.80776			−0.296405			−0.148202	+	0.988957i	$0.547349\pi$
$884$		0			0
$885$	10.2462			0.344423
$886$	46.9786	−	27.1231i	1.57828	−	0.911219i
$887$	−12.3153	−	21.3308i	−0.413509	−	0.716218i	0.581762	−	0.813359i	$-0.302364\pi$
$887$	−12.3153	−	21.3308i	−0.413509	−	0.716218i	−0.995271	+	0.0971410i	$0.969030\pi$
$888$	9.21922	−	15.9682i	0.309377	−	0.535856i
$889$			3.05398i			0.102427i
$890$	−23.4893	−	13.5616i	−0.787363	−	0.454584i
$891$	−1.73205	−	1.00000i	−0.0580259	−	0.0335013i
$892$		−	3.50758i		−	0.117442i
$893$	−29.3693	+	50.8691i	−0.982807	+	1.70227i
$894$	1.90388	+	3.29762i	0.0636753	+	0.110289i
$895$	−15.0423	+	8.68466i	−0.502808	+	0.290296i
$896$	7.61553			0.254417
$897$		0			0
$898$	12.8769			0.429708
$899$	14.8290	−	8.56155i	0.494576	−	0.285544i
$900$	−1.68466	−	2.91791i	−0.0561553	−	0.0972638i
$901$	0.534565	−	0.925894i	0.0178089	−	0.0308460i
$902$		−	4.87689i		−	0.162383i
$903$	−2.21837	−	1.28078i	−0.0738227	−	0.0426216i
$904$	12.2646	+	7.08096i	0.407914	+	0.235509i
$905$		−	9.56155i		−	0.317837i
$906$	−7.31534	+	12.6705i	−0.243036	+	0.420951i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	−2.70469	+	1.56155i	−0.0897583	+	0.0518220i
$909$	7.56155			0.250801
$910$		0			0
$911$	38.7386			1.28347			0.641734	−	0.766927i	$-0.278215\pi$
$911$	38.7386			1.28347			0.641734	+	0.766927i	$0.278215\pi$
$912$	−28.8987	+	16.6847i	−0.956931	+	0.552484i
$913$	−0.876894	−	1.51883i	−0.0290210	−	0.0502658i
$914$	−9.84991	+	17.0605i	−0.325806	+	0.564312i
$915$		−	13.8078i		−	0.456471i
$916$	6.16879	+	3.56155i	0.203823	+	0.117677i
$917$	3.58384	+	2.06913i	0.118349	+	0.0683287i
$918$		−	2.43845i		−	0.0804807i
$919$	−5.75379	+	9.96585i	−0.189800	+	0.328743i	−0.945183	−	0.326540i	$-0.894117\pi$
$919$	−5.75379	+	9.96585i	−0.189800	+	0.328743i	0.755383	+	0.655283i	$0.227451\pi$
$920$	−8.68466	−	15.0423i	−0.286325	−	0.495929i
$921$	−26.6803	+	15.4039i	−0.879146	+	0.507575i
$922$	−25.2850			−0.832718
$923$		0			0
$924$	−0.492423			−0.0161995
$925$	50.3230	−	29.0540i	1.65461	−	0.955289i
$926$	−11.1771	−	19.3593i	−0.367302	−	0.636185i
$927$	−1.71922	+	2.97778i	−0.0564667	+	0.0978032i
$928$			16.3002i			0.535080i
$929$	6.76172	+	3.90388i	0.221845	+	0.128082i	0.606804	−	0.794851i	$-0.292451\pi$
$929$	6.76172	+	3.90388i	0.221845	+	0.128082i	−0.384959	+	0.922934i	$0.625785\pi$
$930$	12.3376	+	7.12311i	0.404565	+	0.233576i
$931$			47.6155i			1.56054i
$932$	−5.69981	+	9.87237i	−0.186704	+	0.323380i
$933$	−9.56155	−	16.5611i	−0.313031	−	0.542186i
$934$	−35.1610	+	20.3002i	−1.15050	+	0.664242i
$935$	11.1231			0.363764
$936$		0			0
$937$	−7.56155			−0.247025			−0.123513	−	0.992343i	$-0.539416\pi$
$937$	−7.56155			−0.247025			−0.123513	+	0.992343i	$0.539416\pi$
$938$	−3.46410	+	2.00000i	−0.113107	+	0.0653023i
$939$	6.84233	+	11.8513i	0.223291	+	0.386751i
$940$	−6.43845	+	11.1517i	−0.209999	+	0.363729i
$941$			30.4924i			0.994025i	0.867744	+	0.497012i	$0.165570\pi$
$941$			30.4924i			0.994025i	−0.867744	+	0.497012i	$0.834430\pi$
$942$	27.5463	+	15.9039i	0.897508	+	0.518176i
$943$	−2.70469	−	1.56155i	−0.0880768	−	0.0508512i
$944$		−	13.4773i		−	0.438648i
$945$	1.00000	−	1.73205i	0.0325300	−	0.0563436i
$946$	7.12311	+	12.3376i	0.231592	+	0.401129i
$947$	33.5486	−	19.3693i	1.09018	−	0.629418i	0.156559	−	0.987669i	$-0.449960\pi$
$947$	33.5486	−	19.3693i	1.09018	−	0.629418i	0.933626	+	0.358250i	$0.116627\pi$
$948$	−2.38447			−0.0774440
$949$		0			0
$950$	−85.4773			−2.77325
$951$	12.1711	−	7.02699i	0.394675	−	0.227866i
$952$	1.06913	+	1.85179i	0.0346507	+	0.0600168i
$953$	15.4924	−	26.8337i	0.501849	−	0.869228i	−0.498149	−	0.867091i	$-0.665987\pi$
$953$	15.4924	−	26.8337i	0.501849	−	0.869228i	0.999998	−	0.00213612i	$-0.000679948\pi$
$954$			1.06913i			0.0346144i
$955$	−28.1393	−	16.2462i	−0.910565	−	0.525715i
$956$	−9.63289	−	5.56155i	−0.311550	−	0.179873i
$957$			13.3693i			0.432169i
$958$	8.00000	−	13.8564i	0.258468	−	0.447680i
$959$	−1.56155	−	2.70469i	−0.0504252	−	0.0873390i
$960$	17.1540	−	9.90388i	0.553644	−	0.319646i
$961$	24.4384			0.788337
$962$		0			0
$963$	−8.24621			−0.265730
$964$	−6.76172	+	3.90388i	−0.217780	+	0.125736i
$965$	−24.0270	−	41.6160i	−0.773456	−	1.33967i
$966$	−0.876894	+	1.51883i	−0.0282136	+	0.0488674i
$967$		−	0.876894i		−	0.0281990i	−0.999901	−	0.0140995i	$-0.995512\pi$
$967$		−	0.876894i		−	0.0281990i	0.999901	−	0.0140995i	$-0.00448816\pi$
$968$	14.7823	+	8.53457i	0.475121	+	0.274311i
$969$	−9.63289	−	5.56155i	−0.309453	−	0.178663i
$970$			47.6155i			1.52884i
$971$	6.49242	−	11.2452i	0.208352	−	0.360876i	−0.742844	−	0.669465i	$-0.766523\pi$
$971$	6.49242	−	11.2452i	0.208352	−	0.360876i	0.951195	+	0.308589i	$0.0998568\pi$
$972$	0.219224	+	0.379706i	0.00703160	+	0.0121791i
$973$	8.72012	−	5.03457i	0.279554	−	0.161401i
$974$	11.1231			0.356407
$975$		0			0
$976$	−18.1619			−0.581349
$977$	52.9809	−	30.5885i	1.69501	−	0.978614i	0.744652	−	0.667453i	$-0.232615\pi$
$977$	52.9809	−	30.5885i	1.69501	−	0.978614i	0.950357	−	0.311162i	$-0.100718\pi$
$978$	−3.75379	−	6.50175i	−0.120033	−	0.207903i
$979$	−4.87689	+	8.44703i	−0.155866	+	0.269968i
$980$			10.4384i			0.333444i
$981$	2.43160	+	1.40388i	0.0776349	+	0.0448225i
$982$	49.0174	+	28.3002i	1.56421	+	0.903095i
$983$		−	13.6155i		−	0.434268i	−0.976142	−	0.217134i	$-0.930329\pi$
$983$		−	13.6155i		−	0.434268i	0.976142	−	0.217134i	$-0.0696708\pi$
$984$	1.90388	−	3.29762i	0.0606935	−	0.105124i
$985$	−23.8078	−	41.2363i	−0.758578	−	1.31390i
$986$	−14.1164	+	8.15009i	−0.449557	+	0.259552i
$987$	−4.63068			−0.147396
$988$		0			0
$989$	9.12311			0.290098
$990$	−9.63289	+	5.56155i	−0.306153	+	0.176758i
$991$	25.1771	+	43.6080i	0.799776	+	1.38525i	0.919762	+	0.392478i	$0.128382\pi$
$991$	25.1771	+	43.6080i	0.799776	+	1.38525i	−0.119985	+	0.992776i	$0.538285\pi$
$992$	3.12311	−	5.40938i	0.0991587	−	0.171748i
$993$		−	3.19224i		−	0.101303i
$994$	10.6318	+	6.13826i	0.337220	+	0.194694i
$995$	−68.4029	−	39.4924i	−2.16852	−	1.25199i
$996$			0.384472i			0.0121825i
$997$	10.3078	−	17.8536i	0.326450	−	0.565428i	−0.655355	−	0.755321i	$-0.727481\pi$
$997$	10.3078	−	17.8536i	0.326450	−	0.565428i	0.981805	+	0.189893i	$0.0608141\pi$
$998$	−3.50758	−	6.07530i	−0.111030	−	0.192310i
$999$	−6.54850	+	3.78078i	−0.207185	+	0.119618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.g.361.2		8
13.2	odd	12		507.2.a.g.1.1		2
13.3	even	3		507.2.b.d.337.2		4
13.4	even	6	inner	507.2.j.g.316.2		8
13.5	odd	4		39.2.e.b.16.2	✓	4
13.6	odd	12		39.2.e.b.22.2	yes	4
13.7	odd	12		507.2.e.g.22.1		4
13.8	odd	4		507.2.e.g.484.1		4
13.9	even	3	inner	507.2.j.g.316.3		8
13.10	even	6		507.2.b.d.337.3		4
13.11	odd	12		507.2.a.d.1.2		2
13.12	even	2	inner	507.2.j.g.361.3		8
39.2	even	12		1521.2.a.g.1.2		2
39.5	even	4		117.2.g.c.55.1		4
39.11	even	12		1521.2.a.m.1.1		2
39.23	odd	6		1521.2.b.h.1351.2		4
39.29	odd	6		1521.2.b.h.1351.3		4
39.32	even	12		117.2.g.c.100.1		4
52.11	even	12		8112.2.a.bo.1.2		2
52.15	even	12		8112.2.a.bk.1.1		2
52.19	even	12		624.2.q.h.529.1		4
52.31	even	4		624.2.q.h.289.1		4
65.18	even	4		975.2.bb.i.874.3		8
65.19	odd	12		975.2.i.k.451.1		4
65.32	even	12		975.2.bb.i.724.3		8
65.44	odd	4		975.2.i.k.601.1		4
65.57	even	4		975.2.bb.i.874.2		8
65.58	even	12		975.2.bb.i.724.2		8
156.71	odd	12		1872.2.t.r.1153.2		4
156.83	odd	4		1872.2.t.r.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.2	✓	4	13.5	odd	4
39.2.e.b.22.2	yes	4	13.6	odd	12
117.2.g.c.55.1		4	39.5	even	4
117.2.g.c.100.1		4	39.32	even	12
507.2.a.d.1.2		2	13.11	odd	12
507.2.a.g.1.1		2	13.2	odd	12
507.2.b.d.337.2		4	13.3	even	3
507.2.b.d.337.3		4	13.10	even	6
507.2.e.g.22.1		4	13.7	odd	12
507.2.e.g.484.1		4	13.8	odd	4
507.2.j.g.316.2		8	13.4	even	6	inner
507.2.j.g.316.3		8	13.9	even	3	inner
507.2.j.g.361.2		8	1.1	even	1	trivial
507.2.j.g.361.3		8	13.12	even	2	inner
624.2.q.h.289.1		4	52.31	even	4
624.2.q.h.529.1		4	52.19	even	12
975.2.i.k.451.1		4	65.19	odd	12
975.2.i.k.601.1		4	65.44	odd	4
975.2.bb.i.724.2		8	65.58	even	12
975.2.bb.i.724.3		8	65.32	even	12
975.2.bb.i.874.2		8	65.57	even	4
975.2.bb.i.874.3		8	65.18	even	4
1521.2.a.g.1.2		2	39.2	even	12
1521.2.a.m.1.1		2	39.11	even	12
1521.2.b.h.1351.2		4	39.23	odd	6
1521.2.b.h.1351.3		4	39.29	odd	6
1872.2.t.r.289.2		4	156.83	odd	4
1872.2.t.r.1153.2		4	156.71	odd	12
8112.2.a.bk.1.1		2	52.15	even	12
8112.2.a.bo.1.2		2	52.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.35234 + 0.780776i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.219224 - 0.379706i) q^{4} -3.56155i q^{5} +(1.35234 + 0.780776i) q^{6} +(0.486319 + 0.280776i) q^{7} -2.43845i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.35234 + 0.780776i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.219224 - 0.379706i) q^{4} -3.56155i q^{5} +(1.35234 + 0.780776i) q^{6} +(0.486319 + 0.280776i) q^{7} -2.43845i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.78078 + 4.81645i) q^{10} +(1.73205 - 1.00000i) q^{11} -0.438447 q^{12} -0.876894 q^{14} +(-3.08440 + 1.78078i) q^{15} +(2.34233 + 4.05703i) q^{16} +(-0.780776 + 1.35234i) q^{17} -1.56155i q^{18} +(-6.16879 - 3.56155i) q^{19} +(-1.35234 - 0.780776i) q^{20} -0.561553i q^{21} +(-1.56155 + 2.70469i) q^{22} +(1.00000 + 1.73205i) q^{23} +(-2.11176 + 1.21922i) q^{24} -7.68466 q^{25} +1.00000 q^{27} +(0.213225 - 0.123106i) q^{28} +(-3.34233 - 5.78908i) q^{29} +(2.78078 - 4.81645i) q^{30} +2.56155i q^{31} +(-2.11176 - 1.21922i) q^{32} +(-1.73205 - 1.00000i) q^{33} -2.43845i q^{34} +(1.00000 - 1.73205i) q^{35} +(0.219224 + 0.379706i) q^{36} +(-6.54850 + 3.78078i) q^{37} +11.1231 q^{38} -8.68466 q^{40} +(-1.35234 + 0.780776i) q^{41} +(0.438447 + 0.759413i) q^{42} +(2.28078 - 3.95042i) q^{43} -0.876894i q^{44} +(3.08440 + 1.78078i) q^{45} +(-2.70469 - 1.56155i) q^{46} -8.24621i q^{47} +(2.34233 - 4.05703i) q^{48} +(-3.34233 - 5.78908i) q^{49} +(10.3923 - 6.00000i) q^{50} +1.56155 q^{51} -0.684658 q^{53} +(-1.35234 + 0.780776i) q^{54} +(-3.56155 - 6.16879i) q^{55} +(0.684658 - 1.18586i) q^{56} +7.12311i q^{57} +(9.03996 + 5.21922i) q^{58} +(-2.49146 - 1.43845i) q^{59} +1.56155i q^{60} +(-1.93845 + 3.35749i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-0.486319 + 0.280776i) q^{63} -5.56155 q^{64} +3.12311 q^{66} +(3.95042 - 2.28078i) q^{67} +(0.342329 + 0.592932i) q^{68} +(1.00000 - 1.73205i) q^{69} +3.12311i q^{70} +(-12.1244 - 7.00000i) q^{71} +(2.11176 + 1.21922i) q^{72} +10.1231i q^{73} +(5.90388 - 10.2258i) q^{74} +(3.84233 + 6.65511i) q^{75} +(-2.70469 + 1.56155i) q^{76} +1.12311 q^{77} +5.43845 q^{79} +(14.4493 - 8.34233i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.21922 - 2.11176i) q^{82} -0.876894i q^{83} +(-0.213225 - 0.123106i) q^{84} +(4.81645 + 2.78078i) q^{85} +7.12311i q^{86} +(-3.34233 + 5.78908i) q^{87} +(-2.43845 - 4.22351i) q^{88} +(-4.22351 + 2.43845i) q^{89} -5.56155 q^{90} +0.876894 q^{92} +(2.21837 - 1.28078i) q^{93} +(6.43845 + 11.1517i) q^{94} +(-12.6847 + 21.9705i) q^{95} +2.43845i q^{96} +(7.41452 + 4.28078i) q^{97} +(9.03996 + 5.21922i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9} + 14 q^{10} - 20 q^{12} - 40 q^{14} - 6 q^{16} + 2 q^{17} + 4 q^{22} + 8 q^{23} - 12 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{30} + 8 q^{35} + 10 q^{36} + 56 q^{38} - 20 q^{40} + 20 q^{42} + 10 q^{43} - 6 q^{48} - 2 q^{49} - 4 q^{51} + 44 q^{53} - 12 q^{55} - 44 q^{56} - 32 q^{61} - 16 q^{62} - 28 q^{64} - 8 q^{66} - 22 q^{68} + 8 q^{69} + 6 q^{74} + 6 q^{75} - 24 q^{77} + 60 q^{79} - 4 q^{81} + 18 q^{82} - 2 q^{87} - 36 q^{88} - 28 q^{90} + 40 q^{92} + 68 q^{94} - 52 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9 + 14 * q^10 - 20 * q^12 - 40 * q^14 - 6 * q^16 + 2 * q^17 + 4 * q^22 + 8 * q^23 - 12 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^30 + 8 * q^35 + 10 * q^36 + 56 * q^38 - 20 * q^40 + 20 * q^42 + 10 * q^43 - 6 * q^48 - 2 * q^49 - 4 * q^51 + 44 * q^53 - 12 * q^55 - 44 * q^56 - 32 * q^61 - 16 * q^62 - 28 * q^64 - 8 * q^66 - 22 * q^68 + 8 * q^69 + 6 * q^74 + 6 * q^75 - 24 * q^77 + 60 * q^79 - 4 * q^81 + 18 * q^82 - 2 * q^87 - 36 * q^88 - 28 * q^90 + 40 * q^92 + 68 * q^94 - 52 * q^95

Introduction

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