LMFDB - Embedded newform 588.2.o.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("588.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.432972864.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 $ x^8 - x^7 + x^6 + 4x^5 - 6x^4 + 8x^3 + 4x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-1.41156 - 0.0865986i$ of defining polynomial
Character	$\chi$	$=$	588.19
Dual form			588.2.o.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41156 + 0.0865986i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98500 - 0.244478i) q^{4} +(1.46890 + 0.848071i) q^{5} +(0.780776 + 1.17915i) q^{6} +(-2.78078 + 0.516994i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.41156 + 0.0865986i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98500 - 0.244478i) q^{4} +(1.46890 + 0.848071i) q^{5} +(0.780776 + 1.17915i) q^{6} +(-2.78078 + 0.516994i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.14688 - 1.06990i) q^{10} +(-2.61578 + 1.51022i) q^{11} +(-1.20422 - 1.59682i) q^{12} +6.04090i q^{13} -1.69614i q^{15} +(3.88046 - 0.970579i) q^{16} +(-3.76267 + 2.17238i) q^{17} +(0.630783 - 1.26575i) q^{18} +(-0.561553 + 0.972638i) q^{19} +(3.12311 + 1.32431i) q^{20} +(3.56155 - 2.35829i) q^{22} +(-2.61578 - 1.51022i) q^{23} +(1.83812 + 2.14973i) q^{24} +(-1.06155 - 1.83866i) q^{25} +(-0.523133 - 8.52708i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(0.146883 + 2.39420i) q^{30} +(-5.39345 + 1.70607i) q^{32} +(2.61578 + 1.51022i) q^{33} +(5.12311 - 3.39228i) q^{34} +(-0.780776 + 1.84130i) q^{36} +(3.56155 - 6.16879i) q^{37} +(0.708436 - 1.42157i) q^{38} +(5.23157 - 3.02045i) q^{39} +(-4.52313 - 1.59888i) q^{40} +7.73704i q^{41} +8.10887i q^{43} +(-4.82312 + 3.63730i) q^{44} +(-1.46890 + 0.848071i) q^{45} +(3.82312 + 1.90525i) q^{46} +(-5.12311 + 8.87348i) q^{47} +(-2.78078 - 2.87529i) q^{48} +(1.65767 + 2.50345i) q^{50} +(3.76267 + 2.17238i) q^{51} +(1.47687 + 11.9912i) q^{52} +(2.12311 + 3.67733i) q^{53} +(-1.41156 + 0.0865986i) q^{54} -5.12311 q^{55} +1.12311 q^{57} +(2.82312 - 0.173197i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-0.414669 - 3.36684i) q^{60} +(8.16937 + 4.71659i) q^{61} +(7.46543 - 2.87529i) q^{64} +(-5.12311 + 8.87348i) q^{65} +(-3.82312 - 1.90525i) q^{66} +(-1.79092 + 1.03399i) q^{67} +(-6.93780 + 5.23206i) q^{68} +3.02045i q^{69} -12.4536i q^{71} +(0.942658 - 2.66672i) q^{72} +(-2.93780 + 1.69614i) q^{73} +(-4.49314 + 9.01604i) q^{74} +(-1.06155 + 1.83866i) q^{75} +(-0.876894 + 2.06798i) q^{76} +(-7.12311 + 4.71659i) q^{78} +(4.08469 + 2.35829i) q^{79} +(6.52313 + 1.86522i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.670016 - 10.9213i) q^{82} -6.24621 q^{83} -7.36932 q^{85} +(-0.702217 - 11.4462i) q^{86} +(1.00000 + 1.73205i) q^{87} +(6.49314 - 5.55194i) q^{88} +(6.70047 + 3.86852i) q^{89} +(2.00000 - 1.32431i) q^{90} +(-5.56155 - 2.35829i) q^{92} +(6.46314 - 12.9691i) q^{94} +(-1.64973 + 0.952473i) q^{95} +(4.17423 + 3.81783i) q^{96} -8.68951i q^{97} -3.02045i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{16} + q^{18} + 12 q^{19} - 8 q^{20} + 12 q^{22} + 7 q^{24} + 8 q^{25} + 12 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 9 q^{32} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 20 q^{38} - 20 q^{40} - 14 q^{44} + 6 q^{46} - 8 q^{47} - 14 q^{48} + 38 q^{50} + 28 q^{52} - 16 q^{53} + q^{54} - 8 q^{55} - 24 q^{57} - 2 q^{58} + 16 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{65} - 6 q^{66} - 32 q^{68} + 7 q^{72} + 14 q^{74} + 8 q^{75} - 40 q^{76} - 24 q^{78} + 36 q^{80} - 4 q^{81} + 20 q^{82} + 16 q^{83} + 40 q^{85} + 30 q^{86} + 8 q^{87} + 2 q^{88} + 16 q^{90} - 28 q^{92} - 32 q^{94} - 9 q^{96}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9 - 8 * q^10 - q^12 + 7 * q^16 + q^18 + 12 * q^19 - 8 * q^20 + 12 * q^22 + 7 * q^24 + 8 * q^25 + 12 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 9 * q^32 + 8 * q^34 + 2 * q^36 + 12 * q^37 - 20 * q^38 - 20 * q^40 - 14 * q^44 + 6 * q^46 - 8 * q^47 - 14 * q^48 + 38 * q^50 + 28 * q^52 - 16 * q^53 + q^54 - 8 * q^55 - 24 * q^57 - 2 * q^58 + 16 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^65 - 6 * q^66 - 32 * q^68 + 7 * q^72 + 14 * q^74 + 8 * q^75 - 40 * q^76 - 24 * q^78 + 36 * q^80 - 4 * q^81 + 20 * q^82 + 16 * q^83 + 40 * q^85 + 30 * q^86 + 8 * q^87 + 2 * q^88 + 16 * q^90 - 28 * q^92 - 32 * q^94 - 9 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.41156	+	0.0865986i	−0.998123	+	0.0612344i
$2$	−1.41156	+	0.0865986i	−0.998123	+	0.0612344i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.98500	−	0.244478i	0.992501	−	0.122239i
$5$	1.46890	+	0.848071i	0.656913	+	0.379269i	0.791100	−	0.611687i	$-0.209509\pi$
$5$	1.46890	+	0.848071i	0.656913	+	0.379269i	−0.134187	+	0.990956i	$0.542842\pi$
$6$	0.780776	+	1.17915i	0.318751	+	0.481385i
$7$		0			0
$7$		0			0
$8$	−2.78078	+	0.516994i	−0.983153	+	0.182785i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.14688	−	1.06990i	−0.678904	−	0.338331i
$11$	−2.61578	+	1.51022i	−0.788689	+	0.455350i	−0.839501	−	0.543359i	$-0.817152\pi$
$11$	−2.61578	+	1.51022i	−0.788689	+	0.455350i	0.0508120	+	0.998708i	$0.483819\pi$
$12$	−1.20422	−	1.59682i	−0.347630	−	0.460963i
$13$			6.04090i			1.67544i	0.546098	+	0.837722i	$0.316113\pi$
$13$			6.04090i			1.67544i	−0.546098	+	0.837722i	$0.683887\pi$
$14$		0			0
$15$		−	1.69614i		−	0.437942i
$16$	3.88046	−	0.970579i	0.970115	−	0.242645i
$17$	−3.76267	+	2.17238i	−0.912581	+	0.526879i	−0.881261	−	0.472630i	$-0.843305\pi$
$17$	−3.76267	+	2.17238i	−0.912581	+	0.526879i	−0.0313203	+	0.999509i	$0.509971\pi$
$18$	0.630783	−	1.26575i	0.148677	−	0.298339i
$19$	−0.561553	+	0.972638i	−0.128829	+	0.223138i	−0.923223	−	0.384264i	$-0.874455\pi$
$19$	−0.561553	+	0.972638i	−0.128829	+	0.223138i	0.794394	+	0.607403i	$0.207789\pi$
$20$	3.12311	+	1.32431i	0.698348	+	0.296124i
$21$		0			0
$22$	3.56155	−	2.35829i	0.759326	−	0.502790i
$23$	−2.61578	−	1.51022i	−0.545429	−	0.314903i	0.201847	−	0.979417i	$-0.435305\pi$
$23$	−2.61578	−	1.51022i	−0.545429	−	0.314903i	−0.747276	+	0.664514i	$0.768639\pi$
$24$	1.83812	+	2.14973i	0.375204	+	0.438811i
$25$	−1.06155	−	1.83866i	−0.212311	−	0.367733i
$26$	−0.523133	−	8.52708i	−0.102595	−	1.67230i
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	0.146883	+	2.39420i	0.0268171	+	0.437120i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−5.39345	+	1.70607i	−0.953436	+	0.301594i
$33$	2.61578	+	1.51022i	0.455350	+	0.262896i
$34$	5.12311	−	3.39228i	0.878605	−	0.581772i
$35$		0			0
$36$	−0.780776	+	1.84130i	−0.130129	+	0.306883i
$37$	3.56155	−	6.16879i	0.585516	−	1.01414i	−0.409295	−	0.912402i	$-0.634225\pi$
$37$	3.56155	−	6.16879i	0.585516	−	1.01414i	0.994811	−	0.101741i	$-0.0324413\pi$
$38$	0.708436	−	1.42157i	0.114924	−	0.230608i
$39$	5.23157	−	3.02045i	0.837722	−	0.483659i
$40$	−4.52313	−	1.59888i	−0.715170	−	0.252805i
$41$			7.73704i			1.20832i	0.796862	+	0.604161i	$0.206492\pi$
$41$			7.73704i			1.20832i	−0.796862	+	0.604161i	$0.793508\pi$
$42$		0			0
$43$			8.10887i			1.23659i	0.785946	+	0.618296i	$0.212177\pi$
$43$			8.10887i			1.23659i	−0.785946	+	0.618296i	$0.787823\pi$
$44$	−4.82312	+	3.63730i	−0.727113	+	0.548343i
$45$	−1.46890	+	0.848071i	−0.218971	+	0.126423i
$46$	3.82312	+	1.90525i	0.563688	+	0.280913i
$47$	−5.12311	+	8.87348i	−0.747282	+	1.29433i	0.201839	+	0.979419i	$0.435308\pi$
$47$	−5.12311	+	8.87348i	−0.747282	+	1.29433i	−0.949121	+	0.314911i	$0.898025\pi$
$48$	−2.78078	−	2.87529i	−0.401371	−	0.415012i
$49$		0			0
$50$	1.65767	+	2.50345i	0.234430	+	0.354042i
$51$	3.76267	+	2.17238i	0.526879	+	0.304194i
$52$	1.47687	+	11.9912i	0.204805	+	1.66288i
$53$	2.12311	+	3.67733i	0.291631	+	0.505120i	0.974196	−	0.225706i	$-0.0724687\pi$
$53$	2.12311	+	3.67733i	0.291631	+	0.505120i	−0.682565	+	0.730825i	$0.739135\pi$
$54$	−1.41156	+	0.0865986i	−0.192089	+	0.0117846i
$55$	−5.12311			−0.690799
$56$		0			0
$57$	1.12311			0.148759
$58$	2.82312	−	0.173197i	0.370694	−	0.0227419i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−0.414669	−	3.36684i	−0.0535336	−	0.434657i
$61$	8.16937	+	4.71659i	1.04598	+	0.603897i	0.921521	−	0.388327i	$-0.126947\pi$
$61$	8.16937	+	4.71659i	1.04598	+	0.603897i	0.124459	+	0.992225i	$0.460280\pi$
$62$		0			0
$63$		0			0
$64$	7.46543	−	2.87529i	0.933179	−	0.359411i
$65$	−5.12311	+	8.87348i	−0.635443	+	1.10062i
$66$	−3.82312	−	1.90525i	−0.470593	−	0.234520i
$67$	−1.79092	+	1.03399i	−0.218796	+	0.126322i	−0.605392	−	0.795927i	$-0.706984\pi$
$67$	−1.79092	+	1.03399i	−0.218796	+	0.126322i	0.386597	+	0.922249i	$0.373650\pi$
$68$	−6.93780	+	5.23206i	−0.841332	+	0.634481i
$69$			3.02045i			0.363619i
$70$		0			0
$71$		−	12.4536i		−	1.47797i	−0.673720	−	0.738987i	$-0.735305\pi$
$71$		−	12.4536i		−	1.47797i	0.673720	−	0.738987i	$-0.264695\pi$
$72$	0.942658	−	2.66672i	0.111093	−	0.314276i
$73$	−2.93780	+	1.69614i	−0.343844	+	0.198518i	−0.661970	−	0.749530i	$-0.730280\pi$
$73$	−2.93780	+	1.69614i	−0.343844	+	0.198518i	0.318127	+	0.948048i	$0.396946\pi$
$74$	−4.49314	+	9.01604i	−0.522316	+	1.04809i
$75$	−1.06155	+	1.83866i	−0.122578	+	0.212311i
$76$	−0.876894	+	2.06798i	−0.100587	+	0.237213i
$77$		0			0
$78$	−7.12311	+	4.71659i	−0.806533	+	0.534049i
$79$	4.08469	+	2.35829i	0.459563	+	0.265329i	0.711861	−	0.702321i	$-0.247853\pi$
$79$	4.08469	+	2.35829i	0.459563	+	0.265329i	−0.252297	+	0.967650i	$0.581186\pi$
$80$	6.52313	+	1.86522i	0.729308	+	0.208538i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.670016	−	10.9213i	−0.0739909	−	1.20605i
$83$	−6.24621			−0.685611			−0.342805	−	0.939406i	$-0.611377\pi$
$83$	−6.24621			−0.685611			−0.342805	+	0.939406i	$0.611377\pi$
$84$		0			0
$85$	−7.36932			−0.799315
$86$	−0.702217	−	11.4462i	−0.0757220	−	1.23427i
$87$	1.00000	+	1.73205i	0.107211	+	0.185695i
$88$	6.49314	−	5.55194i	0.692171	−	0.591839i
$89$	6.70047	+	3.86852i	0.710248	+	0.410062i	0.811153	−	0.584834i	$-0.198840\pi$
$89$	6.70047	+	3.86852i	0.710248	+	0.410062i	−0.100905	+	0.994896i	$0.532174\pi$
$90$	2.00000	−	1.32431i	0.210819	−	0.139594i
$91$		0			0
$92$	−5.56155	−	2.35829i	−0.579832	−	0.245869i
$93$		0			0
$94$	6.46314	−	12.9691i	0.666622	−	1.33766i
$95$	−1.64973	+	0.952473i	−0.169259	+	0.0977216i
$96$	4.17423	+	3.81783i	0.426030	+	0.389656i
$97$		−	8.68951i		−	0.882286i	−0.897437	−	0.441143i	$-0.854573\pi$
$97$		−	8.68951i		−	0.882286i	0.897437	−	0.441143i	$-0.145427\pi$
$98$		0			0
$99$		−	3.02045i		−	0.303566i
$100$	−2.55670	−	3.39022i	−0.255670	−	0.339022i
$101$	6.05643	−	3.49668i	0.602638	−	0.347933i	−0.167441	−	0.985882i	$-0.553550\pi$
$101$	6.05643	−	3.49668i	0.602638	−	0.347933i	0.770079	+	0.637949i	$0.220217\pi$
$102$	−5.49936	−	2.74060i	−0.544517	−	0.271360i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	−3.12311	−	16.7984i	−0.306246	−	1.64722i
$105$		0			0
$106$	−3.31534	−	5.00691i	−0.322014	−	0.486314i
$107$	−4.90955	−	2.83453i	−0.474624	−	0.274024i	0.243549	−	0.969889i	$-0.421688\pi$
$107$	−4.90955	−	2.83453i	−0.474624	−	0.274024i	−0.718173	+	0.695864i	$0.755022\pi$
$108$	1.98500	−	0.244478i	0.191007	−	0.0235249i
$109$	−4.12311	−	7.14143i	−0.394922	−	0.684025i	0.598169	−	0.801370i	$-0.295895\pi$
$109$	−4.12311	−	7.14143i	−0.394922	−	0.684025i	−0.993091	+	0.117345i	$0.962562\pi$
$110$	7.23157	−	0.443654i	0.689503	−	0.0423007i
$111$	−7.12311			−0.676095
$112$		0			0
$113$	12.2462			1.15203			0.576013	−	0.817440i	$-0.304608\pi$
$113$	12.2462			1.15203			0.576013	+	0.817440i	$0.304608\pi$
$114$	−1.58533	+	0.0972594i	−0.148480	+	0.00910917i
$115$	−2.56155	−	4.43674i	−0.238866	−	0.413728i
$116$	−3.97000	+	0.488956i	−0.368606	+	0.0453985i
$117$	−5.23157	−	3.02045i	−0.483659	−	0.279241i
$118$	−3.12311	−	4.71659i	−0.287505	−	0.434197i
$119$		0			0
$120$	0.876894	+	4.71659i	0.0800491	+	0.430564i
$121$	−0.938447	+	1.62544i	−0.0853134	+	0.147767i
$122$	−11.9400	−	5.95029i	−1.08100	−	0.538714i
$123$	6.70047	−	3.86852i	0.604161	−	0.348813i
$124$		0			0
$125$		−	12.0818i		−	1.08063i
$126$		0			0
$127$			19.4470i			1.72564i	0.505510	+	0.862821i	$0.331304\pi$
$127$			19.4470i			1.72564i	−0.505510	+	0.862821i	$0.668696\pi$
$128$	−10.2889	+	4.70514i	−0.909420	+	0.415879i
$129$	7.02249	−	4.05444i	0.618296	−	0.356973i
$130$	6.46314	−	12.9691i	0.566855	−	1.13747i
$131$	11.1231	−	19.2658i	0.971830	−	1.68326i	0.281809	−	0.959471i	$-0.409066\pi$
$131$	11.1231	−	19.2658i	0.971830	−	1.68326i	0.690022	−	0.723789i	$-0.257601\pi$
$132$	5.56155	+	2.35829i	0.484071	+	0.205263i
$133$		0			0
$134$	2.43845	−	1.61463i	0.210650	−	0.139482i
$135$	1.46890	+	0.848071i	0.126423	+	0.0729903i
$136$	9.34003	−	7.98617i	0.800901	−	0.684809i
$137$	8.12311	+	14.0696i	0.694004	+	1.20205i	0.970515	+	0.241039i	$0.0774882\pi$
$137$	8.12311	+	14.0696i	0.694004	+	1.20205i	−0.276512	+	0.961011i	$0.589178\pi$
$138$	−0.261567	−	4.26354i	−0.0222660	−	0.362937i
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$	10.2462			0.862887
$142$	1.07847	+	17.5790i	0.0905029	+	1.47520i
$143$	−9.12311	−	15.8017i	−0.762912	−	1.32140i
$144$	−1.09968	+	3.84587i	−0.0916404	+	0.320489i
$145$	−2.93780	−	1.69614i	−0.243971	−	0.140857i
$146$	4.00000	−	2.64861i	0.331042	−	0.219201i
$147$		0			0
$148$	5.56155	−	13.1158i	0.457157	−	1.07811i
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	1.33922	−	2.68731i	0.109347	−	0.219418i
$151$	−7.02249	+	4.05444i	−0.571482	+	0.329945i	−0.757741	−	0.652555i	$-0.773697\pi$
$151$	−7.02249	+	4.05444i	−0.571482	+	0.329945i	0.186259	+	0.982501i	$0.440364\pi$
$152$	1.05871	−	2.99501i	0.0858723	−	0.242927i
$153$		−	4.34475i		−	0.351253i
$154$		0			0
$155$		0			0
$156$	9.64624	−	7.27460i	0.772317	−	0.582434i
$157$	3.58184	−	2.06798i	0.285862	−	0.165042i	−0.350212	−	0.936670i	$-0.613891\pi$
$157$	3.58184	−	2.06798i	0.285862	−	0.165042i	0.636074	+	0.771628i	$0.280557\pi$
$158$	−5.97000	−	2.97515i	−0.474948	−	0.236690i
$159$	2.12311	−	3.67733i	0.168373	−	0.291631i
$160$	−9.36932	−	2.06798i	−0.740710	−	0.163488i
$161$		0			0
$162$	0.780776	+	1.17915i	0.0613436	+	0.0926426i
$163$	−9.96029	−	5.75058i	−0.780150	−	0.450420i	0.0563333	−	0.998412i	$-0.482059\pi$
$163$	−9.96029	−	5.75058i	−0.780150	−	0.450420i	−0.836484	+	0.547992i	$0.815392\pi$
$164$	1.89154	+	15.3580i	0.147704	+	1.19926i
$165$	2.56155	+	4.43674i	0.199417	+	0.345400i
$166$	8.81690	−	0.540913i	0.684324	−	0.0419830i
$167$	2.24621			0.173817			0.0869085	−	0.996216i	$-0.472301\pi$
$167$	2.24621			0.173817			0.0869085	+	0.996216i	$0.472301\pi$
$168$		0			0
$169$	−23.4924			−1.80711
$170$	10.4022	−	0.638172i	0.797815	−	0.0489456i
$171$	−0.561553	−	0.972638i	−0.0429430	−	0.0743795i
$172$	1.98244	+	16.0961i	0.151160	+	1.22732i
$173$	−7.34451	−	4.24035i	−0.558392	−	0.322388i	0.194108	−	0.980980i	$-0.437819\pi$
$173$	−7.34451	−	4.24035i	−0.558392	−	0.322388i	−0.752500	+	0.658592i	$0.771152\pi$
$174$	−1.56155	−	2.35829i	−0.118381	−	0.178782i
$175$		0			0
$176$	−8.68466	+	8.39919i	−0.654631	+	0.633113i
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	−9.79312	−	4.88039i	−0.734026	−	0.365801i
$179$	1.97175	−	1.13839i	0.147375	−	0.0850873i	−0.424499	−	0.905428i	$-0.639550\pi$
$179$	1.97175	−	1.13839i	0.147375	−	0.0850873i	0.571874	+	0.820341i	$0.306216\pi$
$180$	−2.70844	+	2.04254i	−0.201875	+	0.152242i
$181$		−	6.04090i		−	0.449016i	−0.974472	−	0.224508i	$-0.927922\pi$
$181$		−	6.04090i		−	0.449016i	0.974472	−	0.224508i	$-0.0720775\pi$
$182$		0			0
$183$		−	9.43318i		−	0.697321i
$184$	8.05469	+	2.84725i	0.593800	+	0.209902i
$185$	10.4631	−	6.04090i	0.769265	−	0.444135i
$186$		0			0
$187$	6.56155	−	11.3649i	0.479828	−	0.831087i
$188$	−8.00000	+	18.8664i	−0.583460	+	1.37597i
$189$		0			0
$190$	2.24621	−	1.48734i	0.162957	−	0.107903i
$191$	7.84735	+	4.53067i	0.567815	+	0.327828i	0.756276	−	0.654253i	$-0.227017\pi$
$191$	7.84735	+	4.53067i	0.567815	+	0.327828i	−0.188461	+	0.982081i	$0.560350\pi$
$192$	−6.22279	−	5.02761i	−0.449091	−	0.362837i
$193$	−4.68466	−	8.11407i	−0.337209	−	0.584063i	0.646698	−	0.762747i	$-0.276150\pi$
$193$	−4.68466	−	8.11407i	−0.337209	−	0.584063i	−0.983907	+	0.178683i	$0.942816\pi$
$194$	0.752499	+	12.2658i	0.0540263	+	0.880630i
$195$	10.2462			0.733746
$196$		0			0
$197$	0.246211			0.0175418			0.00877091	−	0.999962i	$-0.497208\pi$
$197$	0.246211			0.0175418			0.00877091	+	0.999962i	$0.497208\pi$
$198$	0.261567	+	4.26354i	0.0185887	+	0.302997i
$199$	2.56155	+	4.43674i	0.181584	+	0.314512i	0.942420	−	0.334432i	$-0.108544\pi$
$199$	2.56155	+	4.43674i	0.181584	+	0.314512i	−0.760836	+	0.648944i	$0.775211\pi$
$200$	3.90252	+	4.56410i	0.275950	+	0.322730i
$201$	1.79092	+	1.03399i	0.126322	+	0.0729319i
$202$	−8.24621	+	5.46026i	−0.580201	+	0.384182i
$203$		0			0
$204$	8.00000	+	3.39228i	0.560112	+	0.237507i
$205$	−6.56155	+	11.3649i	−0.458279	+	0.793762i
$206$	5.04627	−	10.1260i	0.351590	−	0.705510i
$207$	2.61578	−	1.51022i	0.181810	−	0.104968i
$208$	5.86317	+	23.4415i	0.406537	+	1.62537i
$209$		−	3.39228i		−	0.234649i
$210$		0			0
$211$		−	3.97292i		−	0.273507i	−0.990605	−	0.136754i	$-0.956333\pi$
$211$		−	3.97292i		−	0.273507i	0.990605	−	0.136754i	$-0.0436668\pi$
$212$	5.11339	+	6.78045i	0.351189	+	0.465683i
$213$	−10.7852	+	6.22681i	−0.738987	+	0.426654i
$214$	7.17559	+	3.57595i	0.490513	+	0.244447i
$215$	−6.87689	+	11.9111i	−0.469000	+	0.812332i
$216$	−2.78078	+	0.516994i	−0.189208	+	0.0351770i
$217$		0			0
$218$	6.43845	+	9.72350i	0.436067	+	0.658558i
$219$	2.93780	+	1.69614i	0.198518	+	0.114615i
$220$	−10.1694	+	1.25249i	−0.685619	+	0.0844427i
$221$	−13.1231	−	22.7299i	−0.882756	−	1.52898i
$222$	10.0547	−	0.616851i	0.674827	−	0.0414003i
$223$	−18.8769			−1.26409			−0.632045	−	0.774932i	$-0.717784\pi$
$223$	−18.8769			−1.26409			−0.632045	+	0.774932i	$0.717784\pi$
$224$		0			0
$225$	2.12311			0.141540
$226$	−17.2863	+	1.06050i	−1.14986	+	0.0705437i
$227$	8.24621	+	14.2829i	0.547320	+	0.947987i	0.998457	+	0.0555316i	$0.0176854\pi$
$227$	8.24621	+	14.2829i	0.547320	+	0.947987i	−0.451137	+	0.892455i	$0.648981\pi$
$228$	2.22937	−	0.274575i	0.147643	−	0.0181842i
$229$	−15.6947	−	9.06134i	−1.03714	−	0.598790i	−0.118115	−	0.993000i	$-0.537685\pi$
$229$	−15.6947	−	9.06134i	−1.03714	−	0.598790i	−0.919021	+	0.394209i	$0.871018\pi$
$230$	4.00000	+	6.04090i	0.263752	+	0.398325i
$231$		0			0
$232$	5.56155	−	1.03399i	0.365134	−	0.0678846i
$233$	5.24621	−	9.08670i	0.343691	−	0.595290i	−0.641424	−	0.767186i	$-0.721656\pi$
$233$	5.24621	−	9.08670i	0.343691	−	0.595290i	0.985115	+	0.171897i	$0.0549895\pi$
$234$	7.64624	+	3.81050i	0.499850	+	0.249100i
$235$	−15.0507	+	8.68951i	−0.981798	+	0.566841i
$236$	4.81690	+	6.38729i	0.313553	+	0.415777i
$237$		−	4.71659i		−	0.306375i
$238$		0			0
$239$		−	2.27678i		−	0.147273i	−0.997285	−	0.0736363i	$-0.976540\pi$
$239$		−	2.27678i		−	0.147273i	0.997285	−	0.0736363i	$-0.0234604\pi$
$240$	−1.64624	−	6.58181i	−0.106264	−	0.424854i
$241$	1.64973	−	0.952473i	0.106269	−	0.0613542i	−0.445924	−	0.895071i	$-0.647125\pi$
$241$	1.64973	−	0.952473i	0.106269	−	0.0613542i	0.552192	+	0.833717i	$0.313791\pi$
$242$	1.18391	−	2.37567i	0.0761048	−	0.152714i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	17.3693	+	7.36520i	1.11196	+	0.471509i
$245$		0			0
$246$	−9.12311	+	6.04090i	−0.581668	+	0.385153i
$247$	−5.87560	−	3.39228i	−0.373856	−	0.215846i
$248$		0			0
$249$	3.12311	+	5.40938i	0.197919	+	0.342805i
$250$	1.04627	+	17.0542i	0.0661717	+	1.07860i
$251$	22.2462			1.40417			0.702084	−	0.712094i	$-0.252253\pi$
$251$	22.2462			1.40417			0.702084	+	0.712094i	$0.252253\pi$
$252$		0			0
$253$	9.12311			0.573565
$254$	−1.68408	−	27.4506i	−0.105669	−	1.72240i
$255$	3.68466	+	6.38202i	0.230742	+	0.399657i
$256$	14.1160	−	7.53259i	0.882247	−	0.470787i
$257$	−17.1636	−	9.90941i	−1.07064	−	0.618132i	−0.142281	−	0.989826i	$-0.545444\pi$
$257$	−17.1636	−	9.90941i	−1.07064	−	0.618132i	−0.928355	+	0.371694i	$0.878777\pi$
$258$	−9.56155	+	6.33122i	−0.595276	+	0.394164i
$259$		0			0
$260$	−8.00000	+	18.8664i	−0.496139	+	1.17004i
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$	−14.0325	+	28.1580i	−0.866933	+	1.73961i
$263$	4.26552	−	2.46270i	0.263023	−	0.151856i	−0.362690	−	0.931910i	$-0.618142\pi$
$263$	4.26552	−	2.46270i	0.263023	−	0.151856i	0.625713	+	0.780054i	$0.284808\pi$
$264$	−8.05469	−	2.84725i	−0.495732	−	0.175236i
$265$			7.20217i			0.442426i
$266$		0			0
$267$		−	7.73704i		−	0.473499i
$268$	−3.30219	+	2.49031i	−0.201713	+	0.152120i
$269$	−19.4574	+	11.2337i	−1.18634	+	0.684932i	−0.957472	−	0.288526i	$-0.906835\pi$
$269$	−19.4574	+	11.2337i	−1.18634	+	0.684932i	−0.228865	+	0.973458i	$0.573501\pi$
$270$	−2.14688	−	1.06990i	−0.130655	−	0.0651119i
$271$	2.24621	−	3.89055i	0.136448	−	0.236334i	−0.789702	−	0.613491i	$-0.789765\pi$
$271$	2.24621	−	3.89055i	0.136448	−	0.236334i	0.926150	+	0.377157i	$0.123098\pi$
$272$	−12.4924	+	12.0818i	−0.757464	+	0.732566i
$273$		0			0
$274$	−12.6847	−	19.1567i	−0.766308	−	1.15730i
$275$	5.55359	+	3.20636i	0.334894	+	0.193351i
$276$	0.738433	+	5.99559i	0.0444485	+	0.360892i
$277$	−1.56155	−	2.70469i	−0.0938246	−	0.162509i	0.815293	−	0.579049i	$-0.196576\pi$
$277$	−1.56155	−	2.70469i	−0.0938246	−	0.162509i	−0.909117	+	0.416540i	$0.863243\pi$
$278$	−16.9387	+	1.03918i	−1.01592	+	0.0623261i
$279$		0			0
$280$		0			0
$281$	−0.246211			−0.0146877			−0.00734387	−	0.999973i	$-0.502338\pi$
$281$	−0.246211			−0.0146877			−0.00734387	+	0.999973i	$0.502338\pi$
$282$	−14.4631	+	0.887307i	−0.861267	+	0.0528384i
$283$	8.56155	+	14.8290i	0.508931	+	0.881495i	0.999946	+	0.0103441i	$0.00329268\pi$
$283$	8.56155	+	14.8290i	0.508931	+	0.881495i	−0.491015	+	0.871151i	$0.663374\pi$
$284$	−3.04464	−	24.7205i	−0.180666	−	1.46689i
$285$	1.64973	+	0.952473i	0.0977216	+	0.0564196i
$286$	14.2462	+	21.5150i	0.842396	+	1.27221i
$287$		0			0
$288$	1.21922	−	5.52390i	0.0718434	−	0.325499i
$289$	0.938447	−	1.62544i	0.0552028	−	0.0956140i
$290$	4.29377	+	2.13979i	0.252139	+	0.125653i
$291$	−7.52534	+	4.34475i	−0.441143	+	0.254694i
$292$	−5.41687	+	4.08507i	−0.316998	+	0.239061i
$293$			6.99337i			0.408557i	0.978913	+	0.204278i	$0.0654848\pi$
$293$			6.99337i			0.408557i	−0.978913	+	0.204278i	$0.934515\pi$
$294$		0			0
$295$			6.78456i			0.395013i
$296$	−6.71466	+	18.9953i	−0.390281	+	1.10408i
$297$	−2.61578	+	1.51022i	−0.151783	+	0.0876321i
$298$	−6.30783	+	12.6575i	−0.365403	+	0.733227i
$299$	9.12311	−	15.8017i	0.527603	−	0.913835i
$300$	−1.65767	+	3.90928i	−0.0957057	+	0.225702i
$301$		0			0
$302$	9.56155	−	6.33122i	0.550206	−	0.364320i
$303$	−6.05643	−	3.49668i	−0.347933	−	0.200879i
$304$	−1.23506	+	4.31932i	−0.0708357	+	0.247730i
$305$	8.00000	+	13.8564i	0.458079	+	0.793416i
$306$	0.376250	+	6.13288i	0.0215088	+	0.350593i
$307$	21.6155			1.23366			0.616832	−	0.787095i	$-0.288416\pi$
$307$	21.6155			1.23366			0.616832	+	0.787095i	$0.288416\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	0.956864	−	0.290537i	$-0.0938340\pi$
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	−0.730044	+	0.683400i	$0.760501\pi$
$312$	−12.9863	+	11.1039i	−0.735203	+	0.628633i
$313$	−22.2143	−	12.8255i	−1.25563	−	0.724938i	−0.283407	−	0.959000i	$-0.591465\pi$
$313$	−22.2143	−	12.8255i	−1.25563	−	0.724938i	−0.972222	+	0.234062i	$0.924798\pi$
$314$	−4.87689	+	3.22925i	−0.275219	+	0.182237i
$315$		0			0
$316$	8.68466	+	3.68260i	0.488550	+	0.207163i
$317$	−9.24621	+	16.0149i	−0.519319	+	0.899487i	0.480429	+	0.877034i	$0.340481\pi$
$317$	−9.24621	+	16.0149i	−0.519319	+	0.899487i	−0.999748	+	0.0224532i	$0.992852\pi$
$318$	−2.67844	+	5.37462i	−0.150199	+	0.301394i
$319$	5.23157	−	3.02045i	0.292912	−	0.169113i
$320$	13.4044	+	2.10770i	0.749331	+	0.117824i
$321$			5.66906i			0.316416i
$322$		0			0
$323$		−	4.87962i		−	0.271509i
$324$	−1.20422	−	1.59682i	−0.0669014	−	0.0887124i
$325$	11.1072	−	6.41273i	0.616115	−	0.355714i
$326$	14.5575	+	7.25473i	0.806267	+	0.401803i
$327$	−4.12311	+	7.14143i	−0.228008	+	0.394922i
$328$	−4.00000	−	21.5150i	−0.220863	−	1.18797i
$329$		0			0
$330$	−4.00000	−	6.04090i	−0.220193	−	0.332540i
$331$	4.72872	+	2.73013i	0.259914	+	0.150061i	0.624295	−	0.781188i	$-0.285386\pi$
$331$	4.72872	+	2.73013i	0.259914	+	0.150061i	−0.364381	+	0.931250i	$0.618720\pi$
$332$	−12.3987	+	1.52706i	−0.680469	+	0.0838084i
$333$	3.56155	+	6.16879i	0.195172	+	0.338048i
$334$	−3.17066	+	0.194519i	−0.173491	+	0.0106436i
$335$	−3.50758			−0.191639
$336$		0			0
$337$	−8.24621			−0.449200			−0.224600	−	0.974451i	$-0.572108\pi$
$337$	−8.24621			−0.449200			−0.224600	+	0.974451i	$0.572108\pi$
$338$	33.1610	−	2.03441i	1.80372	−	0.110657i
$339$	−6.12311	−	10.6055i	−0.332561	−	0.576013i
$340$	−14.6281	+	1.80164i	−0.793320	+	0.0977075i
$341$		0			0
$342$	0.876894	+	1.32431i	0.0474170	+	0.0716103i
$343$		0			0
$344$	−4.19224	−	22.5490i	−0.226030	−	1.21576i
$345$	−2.56155	+	4.43674i	−0.137909	+	0.238866i
$346$	10.7344	+	5.34949i	0.577086	+	0.287590i
$347$	30.0617	−	17.3561i	1.61380	−	0.931726i	0.625317	−	0.780371i	$-0.284970\pi$
$347$	30.0617	−	17.3561i	1.61380	−	0.931726i	0.988479	−	0.151355i	$-0.0483638\pi$
$348$	2.40845	+	3.19365i	0.129106	+	0.171197i
$349$			4.13595i			0.221392i	0.993854	+	0.110696i	$0.0353080\pi$
$349$			4.13595i			0.221392i	−0.993854	+	0.110696i	$0.964692\pi$
$350$		0			0
$351$			6.04090i			0.322439i
$352$	11.5316	−	12.6080i	0.614634	−	0.672011i
$353$	−5.41240	+	3.12485i	−0.288073	+	0.166319i	−0.637072	−	0.770804i	$-0.719855\pi$
$353$	−5.41240	+	3.12485i	−0.288073	+	0.166319i	0.349000	+	0.937123i	$0.386521\pi$
$354$	−2.52313	+	5.06298i	−0.134103	+	0.269095i
$355$	10.5616	−	18.2931i	0.560549	−	0.970899i
$356$	14.2462	+	6.04090i	0.755048	+	0.320167i
$357$		0			0
$358$	−2.68466	+	1.77766i	−0.141889	+	0.0939520i
$359$	−0.966053	−	0.557751i	−0.0509863	−	0.0294370i	0.474290	−	0.880369i	$-0.342705\pi$
$359$	−0.966053	−	0.557751i	−0.0509863	−	0.0294370i	−0.525276	+	0.850932i	$0.676038\pi$
$360$	3.64624	−	3.11771i	0.192174	−	0.164318i
$361$	8.86932	+	15.3621i	0.466806	+	0.808532i
$362$	0.523133	+	8.52708i	0.0274953	+	0.448174i
$363$	1.87689			0.0985114
$364$		0			0
$365$	−5.75379			−0.301167
$366$	0.816900	+	13.3155i	0.0427000	+	0.696012i
$367$	−4.31534	−	7.47439i	−0.225259	−	0.390160i	0.731138	−	0.682229i	$-0.238989\pi$
$367$	−4.31534	−	7.47439i	−0.225259	−	0.390160i	−0.956397	+	0.292069i	$0.905656\pi$
$368$	−11.6162	−	3.32154i	−0.605538	−	0.173147i
$369$	−6.70047	−	3.86852i	−0.348813	−	0.201387i
$370$	−14.2462	+	9.43318i	−0.740625	+	0.490408i
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−8.27784	+	16.6105i	−0.428037	+	0.858909i
$375$	−10.4631	+	6.04090i	−0.540314	+	0.311951i
$376$	9.65868	−	27.3238i	0.498108	−	1.40912i
$377$		−	12.0818i		−	0.622244i
$378$		0			0
$379$			18.7033i			0.960725i	0.877070	+	0.480363i	$0.159495\pi$
$379$			18.7033i			0.960725i	−0.877070	+	0.480363i	$0.840505\pi$
$380$	−3.04186	+	2.29398i	−0.156044	+	0.117679i
$381$	16.8416	−	9.72350i	0.862821	−	0.498150i
$382$	−11.4694	−	5.71574i	−0.586823	−	0.292443i
$383$	−13.1231	+	22.7299i	−0.670559	+	1.16144i	0.307186	+	0.951649i	$0.400613\pi$
$383$	−13.1231	+	22.7299i	−0.670559	+	1.16144i	−0.977746	+	0.209794i	$0.932721\pi$
$384$	9.21922	+	6.55789i	0.470467	+	0.334656i
$385$		0			0
$386$	7.31534	+	11.0478i	0.372341	+	0.562318i
$387$	−7.02249	−	4.05444i	−0.356973	−	0.206099i
$388$	−2.12440	−	17.2487i	−0.107850	−	0.875669i
$389$	−0.123106	−	0.213225i	−0.00624170	−	0.0108109i	0.862888	−	0.505396i	$-0.168653\pi$
$389$	−0.123106	−	0.213225i	−0.00624170	−	0.0108109i	−0.869129	+	0.494585i	$0.835320\pi$
$390$	−14.4631	+	0.887307i	−0.732369	+	0.0449306i
$391$	13.1231			0.663664
$392$		0			0
$393$	−22.2462			−1.12217
$394$	−0.347542	+	0.0213215i	−0.0175089	+	0.00107416i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	−0.738433	−	5.99559i	−0.0371077	−	0.301290i
$397$	14.0450	+	8.10887i	0.704897	+	0.406973i	0.809169	−	0.587576i	$-0.199918\pi$
$397$	14.0450	+	8.10887i	0.704897	+	0.406973i	−0.104272	+	0.994549i	$0.533251\pi$
$398$	−4.00000	−	6.04090i	−0.200502	−	0.302803i
$399$		0			0
$400$	−5.90388	−	6.10454i	−0.295194	−	0.305227i
$401$	4.12311	−	7.14143i	0.205898	−	0.356626i	−0.744520	−	0.667600i	$-0.767322\pi$
$401$	4.12311	−	7.14143i	0.205898	−	0.356626i	0.950418	+	0.310974i	$0.100655\pi$
$402$	−2.61753	−	1.30444i	−0.130551	−	0.0650598i
$403$		0			0
$404$	11.1672	−	8.42159i	0.555587	−	0.418990i
$405$		−	1.69614i		−	0.0842819i
$406$		0			0
$407$			21.5150i			1.06646i
$408$	−11.5862	−	4.09562i	−0.573605	−	0.202763i
$409$	−23.8641	+	13.7779i	−1.18000	+	0.681275i	−0.956015	−	0.293317i	$-0.905241\pi$
$409$	−23.8641	+	13.7779i	−1.18000	+	0.681275i	−0.223988	+	0.974592i	$0.571908\pi$
$410$	8.27784	−	16.6105i	0.408813	−	0.820335i
$411$	8.12311	−	14.0696i	0.400683	−	0.694004i
$412$	−6.24621	+	14.7304i	−0.307729	+	0.725715i
$413$		0			0
$414$	−3.56155	+	2.35829i	−0.175041	+	0.115904i
$415$	−9.17507	−	5.29723i	−0.450386	−	0.260031i
$416$	−10.3062	−	32.5813i	−0.505303	−	1.59743i
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$	0.293767	+	4.78841i	0.0143686	+	0.234209i
$419$	−16.4924			−0.805708			−0.402854	−	0.915264i	$-0.631982\pi$
$419$	−16.4924			−0.805708			−0.402854	+	0.915264i	$0.631982\pi$
$420$		0			0
$421$	19.1231			0.932003			0.466002	−	0.884784i	$-0.345694\pi$
$421$	19.1231			0.932003			0.466002	+	0.884784i	$0.345694\pi$
$422$	0.344049	+	5.60801i	0.0167481	+	0.272994i
$423$	−5.12311	−	8.87348i	−0.249094	−	0.431443i
$424$	−7.80504	−	9.12819i	−0.379046	−	0.443304i
$425$	7.98854	+	4.61219i	0.387501	+	0.223724i
$426$	14.6847	−	9.72350i	0.711474	−	0.471105i
$427$		0			0
$428$	−10.4384	−	4.42627i	−0.504561	−	0.213952i
$429$	−9.12311	+	15.8017i	−0.440468	+	0.762912i
$430$	8.67566	−	17.4088i	0.418377	−	0.839527i
$431$	13.0789	−	7.55112i	0.629990	−	0.363725i	−0.150758	−	0.988571i	$-0.548172\pi$
$431$	13.0789	−	7.55112i	0.629990	−	0.363725i	0.780748	+	0.624846i	$0.214838\pi$
$432$	3.88046	−	0.970579i	0.186699	−	0.0466970i
$433$			6.78456i			0.326045i	0.986622	+	0.163023i	$0.0521244\pi$
$433$			6.78456i			0.326045i	−0.986622	+	0.163023i	$0.947876\pi$
$434$		0			0
$435$			3.39228i			0.162647i
$436$	−9.93029	−	13.1677i	−0.475575	−	0.630620i
$437$	2.93780	−	1.69614i	0.140534	−	0.0811374i
$438$	−4.29377	−	2.13979i	−0.205164	−	0.102243i
$439$	−15.6847	+	27.1666i	−0.748588	+	1.29659i	0.199912	+	0.979814i	$0.435934\pi$
$439$	−15.6847	+	27.1666i	−0.748588	+	1.29659i	−0.948500	+	0.316778i	$0.897399\pi$
$440$	14.2462	−	2.64861i	0.679161	−	0.126268i
$441$		0			0
$442$	20.4924	+	30.9481i	0.974725	+	1.47205i
$443$	31.0674	+	17.9368i	1.47606	+	0.852202i	0.999635	−	0.0270153i	$-0.00860028\pi$
$443$	31.0674	+	17.9368i	1.47606	+	0.852202i	0.476422	+	0.879217i	$0.341934\pi$
$444$	−14.1394	+	1.74144i	−0.671025	+	0.0826453i
$445$	6.56155	+	11.3649i	0.311047	+	0.538750i
$446$	26.6459	−	1.63471i	1.26172	−	0.0774059i
$447$	−10.0000			−0.472984
$448$		0			0
$449$	28.2462			1.33302			0.666511	−	0.745496i	$-0.267787\pi$
$449$	28.2462			1.33302			0.666511	+	0.745496i	$0.267787\pi$
$450$	−2.99689	+	0.183858i	−0.141275	+	0.00866715i
$451$	−11.6847	−	20.2384i	−0.550209	−	0.952990i
$452$	24.3087	−	2.99393i	1.14339	−	0.140823i
$453$	7.02249	+	4.05444i	0.329945	+	0.190494i
$454$	−12.8769	−	19.4470i	−0.604343	−	0.912693i
$455$		0			0
$456$	−3.12311	+	0.580639i	−0.146253	+	0.0271909i
$457$	8.12311	−	14.0696i	0.379983	−	0.658150i	−0.611076	−	0.791572i	$-0.709263\pi$
$457$	8.12311	−	14.0696i	0.379983	−	0.658150i	0.991059	+	0.133422i	$0.0425966\pi$
$458$	22.9387	+	11.4315i	1.07186	+	0.534158i
$459$	−3.76267	+	2.17238i	−0.175626	+	0.101398i
$460$	−6.16937	−	8.18069i	−0.287648	−	0.381427i
$461$			17.1702i			0.799697i	0.916581	+	0.399848i	$0.130937\pi$
$461$			17.1702i			0.799697i	−0.916581	+	0.399848i	$0.869063\pi$
$462$		0			0
$463$		−	39.4746i		−	1.83454i	−0.398264	−	0.917271i	$-0.630387\pi$
$463$		−	39.4746i		−	1.83454i	0.398264	−	0.917271i	$-0.369613\pi$
$464$	−7.76092	+	1.94116i	−0.360292	+	0.0901160i
$465$		0			0
$466$	−6.61844	+	13.2807i	−0.306594	+	0.615218i
$467$	8.87689	−	15.3752i	0.410774	−	0.711481i	−0.584201	−	0.811609i	$-0.698592\pi$
$467$	8.87689	−	15.3752i	0.410774	−	0.711481i	0.994975	+	0.100128i	$0.0319253\pi$
$468$	−11.1231	−	4.71659i	−0.514166	−	0.218024i
$469$		0			0
$470$	20.4924	−	13.5691i	0.945245	−	0.625897i
$471$	−3.58184	−	2.06798i	−0.165042	−	0.0952873i
$472$	−7.35247	−	8.59890i	−0.338425	−	0.395797i
$473$	−12.2462	−	21.2111i	−0.563081	−	0.975286i
$474$	0.408450	+	6.65775i	0.0187607	+	0.305800i
$475$	2.38447			0.109407
$476$		0			0
$477$	−4.24621			−0.194421
$478$	0.197166	+	3.21381i	0.00901816	+	0.146996i
$479$	−10.2462	−	17.7470i	−0.468161	−	0.810879i	0.531177	−	0.847261i	$-0.321750\pi$
$479$	−10.2462	−	17.7470i	−0.468161	−	0.810879i	−0.999338	+	0.0363819i	$0.988417\pi$
$480$	2.89374	+	9.14805i	0.132081	+	0.417550i
$481$	37.2650	+	21.5150i	1.69914	+	0.980998i
$482$	−2.24621	+	1.48734i	−0.102312	+	0.0677463i
$483$		0			0
$484$	−1.46543	+	3.45593i	−0.0666107	+	0.157088i
$485$	7.36932	−	12.7640i	0.334623	−	0.579585i
$486$	0.630783	−	1.26575i	0.0286129	−	0.0574154i
$487$	−27.9488	+	16.1362i	−1.26648	+	0.731202i	−0.974320	−	0.225167i	$-0.927707\pi$
$487$	−27.9488	+	16.1362i	−1.26648	+	0.731202i	−0.292159	+	0.956370i	$0.594374\pi$
$488$	−25.1556	−	8.89226i	−1.13874	−	0.402534i
$489$			11.5012i			0.520100i
$490$		0			0
$491$		−	11.7100i		−	0.528463i	−0.964459	−	0.264231i	$-0.914882\pi$
$491$		−	11.7100i		−	0.528463i	0.964459	−	0.264231i	$-0.0851183\pi$
$492$	12.3547	−	9.31713i	0.556992	−	0.420049i
$493$	7.52534	−	4.34475i	0.338924	−	0.195678i
$494$	8.58753	+	4.27959i	0.386371	+	0.192548i
$495$	2.56155	−	4.43674i	0.115133	−	0.199417i
$496$		0			0
$497$		0			0
$498$	−4.87689	−	7.36520i	−0.218539	−	0.330043i
$499$	15.1919	+	8.77102i	0.680081	+	0.392645i	0.799886	−	0.600153i	$-0.204893\pi$
$499$	15.1919	+	8.77102i	0.680081	+	0.392645i	−0.119805	+	0.992797i	$0.538227\pi$
$500$	−2.95373	−	23.9824i	−0.132095	−	1.07252i
$501$	−1.12311	−	1.94528i	−0.0501767	−	0.0869085i
$502$	−31.4019	+	1.92649i	−1.40153	+	0.0859835i
$503$	−22.7386			−1.01387			−0.506933	−	0.861986i	$-0.669221\pi$
$503$	−22.7386			−1.01387			−0.506933	+	0.861986i	$0.669221\pi$
$504$		0			0
$505$	11.8617			0.527840
$506$	−12.8778	+	0.790048i	−0.572488	+	0.0351219i
$507$	11.7462	+	20.3450i	0.521668	+	0.903555i
$508$	4.75436	+	38.6023i	0.210941	+	1.71270i
$509$	−1.46890	−	0.848071i	−0.0651079	−	0.0375901i	0.467093	−	0.884208i	$-0.345301\pi$
$509$	−1.46890	−	0.848071i	−0.0651079	−	0.0375901i	−0.532201	+	0.846618i	$0.678635\pi$
$510$	−5.75379	−	8.68951i	−0.254782	−	0.384778i
$511$		0			0
$512$	−19.2732	+	11.8551i	−0.851763	+	0.523927i
$513$	−0.561553	+	0.972638i	−0.0247932	+	0.0429430i
$514$	25.0856	+	12.5014i	1.10648	+	0.551412i
$515$	−11.7512	+	6.78456i	−0.517820	+	0.298964i
$516$	12.9484	−	9.76490i	0.570023	−	0.429876i
$517$		−	30.9481i		−	1.36110i
$518$		0			0
$519$			8.48071i			0.372262i
$520$	9.65868	−	27.3238i	0.423561	−	1.19823i
$521$	29.2765	−	16.9028i	1.28263	−	0.740524i	0.305298	−	0.952257i	$-0.401244\pi$
$521$	29.2765	−	16.9028i	1.28263	−	0.740524i	0.977328	+	0.211732i	$0.0679105\pi$
$522$	−1.26157	+	2.53149i	−0.0552173	+	0.110800i
$523$	−0.246211	+	0.426450i	−0.0107661	+	0.0186474i	−0.871358	−	0.490647i	$-0.836760\pi$
$523$	−0.246211	+	0.426450i	−0.0107661	+	0.0186474i	0.860592	+	0.509295i	$0.170094\pi$
$524$	17.3693	−	40.9620i	0.758782	−	1.78943i
$525$		0			0
$526$	−5.80776	+	3.84563i	−0.253231	+	0.167677i
$527$		0			0
$528$	11.6162	+	3.32154i	0.505532	+	0.144551i
$529$	−6.93845	−	12.0177i	−0.301672	−	0.522511i
$530$	−0.623698	−	10.1663i	−0.0270917	−	0.441596i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−46.7386			−2.02447
$534$	0.670016	+	10.9213i	0.0289944	+	0.472610i
$535$	−4.80776	−	8.32729i	−0.207858	−	0.360020i
$536$	4.44558	−	3.80118i	0.192020	−	0.164186i
$537$	−1.97175	−	1.13839i	−0.0850873	−	0.0491251i
$538$	26.4924	−	17.5420i	1.14217	−	0.756291i
$539$		0			0
$540$	3.12311	+	1.32431i	0.134397	+	0.0569891i
$541$	−5.56155	+	9.63289i	−0.239110	+	0.414150i	−0.960459	−	0.278421i	$-0.910189\pi$
$541$	−5.56155	+	9.63289i	−0.239110	+	0.414150i	0.721349	+	0.692571i	$0.243522\pi$
$542$	−2.83374	+	5.68627i	−0.121720	+	0.244246i
$543$	−5.23157	+	3.02045i	−0.224508	+	0.129620i
$544$	16.5875	−	18.1360i	0.711185	−	0.777574i
$545$		−	13.9867i		−	0.599126i
$546$		0			0
$547$		−	33.0161i		−	1.41167i	−0.708378	−	0.705834i	$-0.750573\pi$
$547$		−	33.0161i		−	1.41167i	0.708378	−	0.705834i	$-0.249427\pi$
$548$	19.5641	+	25.9423i	0.835737	+	1.10820i
$549$	−8.16937	+	4.71659i	−0.348660	+	0.201299i
$550$	−8.11689	−	4.04504i	−0.346105	−	0.172481i
$551$	1.12311	−	1.94528i	0.0478459	−	0.0828715i
$552$	−1.56155	−	8.39919i	−0.0664641	−	0.357493i
$553$		0			0
$554$	2.43845	+	3.68260i	0.103600	+	0.156459i
$555$	−10.4631	−	6.04090i	−0.444135	−	0.256422i
$556$	23.8200	−	2.93374i	1.01019	−	0.124418i
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	0.678756	−	0.734364i	$-0.262519\pi$
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	−0.975356	+	0.220638i	$0.929186\pi$
$558$		0			0
$559$	−48.9848			−2.07184
$560$		0			0
$561$	−13.1231			−0.554058
$562$	0.347542	−	0.0213215i	0.0146602	−	0.000899395i
$563$	−7.12311	−	12.3376i	−0.300203	−	0.519967i	0.675979	−	0.736921i	$-0.263721\pi$
$563$	−7.12311	−	12.3376i	−0.300203	−	0.519967i	−0.976182	+	0.216954i	$0.930388\pi$
$564$	20.3387	−	2.50497i	0.856416	−	0.105478i
$565$	17.9885	+	10.3857i	0.756781	+	0.436928i
$566$	−13.3693	−	20.1907i	−0.561954	−	0.848677i
$567$		0			0
$568$	6.43845	+	34.6307i	0.270151	+	1.45307i
$569$	−17.4924	+	30.2978i	−0.733320	+	1.27015i	0.222136	+	0.975016i	$0.428697\pi$
$569$	−17.4924	+	30.2978i	−0.733320	+	1.27015i	−0.955456	+	0.295133i	$0.904636\pi$
$570$	−2.41118	−	1.20161i	−0.100993	−	0.0503298i
$571$	35.4741	−	20.4810i	1.48454	−	0.857102i	0.484699	−	0.874681i	$-0.338929\pi$
$571$	35.4741	−	20.4810i	1.48454	−	0.857102i	0.999845	+	0.0175783i	$0.00559565\pi$
$572$	−21.9725	−	29.1360i	−0.918718	−	1.21824i
$573$		−	9.06134i		−	0.378543i
$574$		0			0
$575$			6.41273i			0.267429i
$576$	−1.24264	+	7.90290i	−0.0517769	+	0.329288i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−1.18391	+	2.37567i	−0.0492443	+	0.0988149i
$579$	−4.68466	+	8.11407i	−0.194688	+	0.337209i
$580$	−6.24621	−	2.64861i	−0.259360	−	0.109978i
$581$		0			0
$582$	10.2462	−	6.78456i	0.424719	−	0.281229i
$583$	−11.1072	−	6.41273i	−0.460012	−	0.265588i
$584$	7.29248	−	6.23541i	0.301765	−	0.258023i
$585$	−5.12311	−	8.87348i	−0.211814	−	0.366873i
$586$	−0.605616	−	9.87156i	−0.0250178	−	0.407790i
$587$	38.2462			1.57859			0.789295	−	0.614014i	$-0.210446\pi$
$587$	38.2462			1.57859			0.789295	+	0.614014i	$0.210446\pi$
$588$		0			0
$589$		0			0
$590$	−0.587534	−	9.57682i	−0.0241884	−	0.394271i
$591$	−0.123106	−	0.213225i	−0.00506389	−	0.00877091i
$592$	7.83317	−	27.3945i	0.321941	−	1.12591i
$593$	18.8133	+	10.8619i	0.772571	+	0.446044i	0.833791	−	0.552080i	$-0.186166\pi$
$593$	18.8133	+	10.8619i	0.772571	+	0.446044i	−0.0612198	+	0.998124i	$0.519499\pi$
$594$	3.56155	−	2.35829i	0.146132	−	0.0967620i
$595$		0			0
$596$	7.80776	−	18.4130i	0.319818	−	0.754226i
$597$	2.56155	−	4.43674i	0.104837	−	0.181584i
$598$	−11.5094	+	23.0951i	−0.470655	+	0.944427i
$599$	−16.6608	+	9.61909i	−0.680740	+	0.393026i	−0.800134	−	0.599821i	$-0.795238\pi$
$599$	−16.6608	+	9.61909i	−0.680740	+	0.393026i	0.119394	+	0.992847i	$0.461905\pi$
$600$	2.00136	−	5.66173i	0.0817053	−	0.231139i
$601$		−	5.29723i		−	0.216078i	−0.994147	−	0.108039i	$-0.965543\pi$
$601$		−	5.29723i		−	0.216078i	0.994147	−	0.108039i	$-0.0344572\pi$
$602$		0			0
$603$		−	2.06798i		−	0.0842145i
$604$	−12.9484	+	9.76490i	−0.526864	+	0.397328i
$605$	−2.75697	+	1.59174i	−0.112087	+	0.0647134i
$606$	8.85183	+	4.41130i	0.359581	+	0.179197i
$607$	−16.8078	+	29.1119i	−0.682206	+	1.18162i	0.292100	+	0.956388i	$0.405646\pi$
$607$	−16.8078	+	29.1119i	−0.682206	+	1.18162i	−0.974306	+	0.225228i	$0.927687\pi$
$608$	1.36932	−	6.20393i	0.0555331	−	0.251602i
$609$		0			0
$610$	−12.4924	−	18.8664i	−0.505803	−	0.763876i
$611$	−53.6038	−	30.9481i	−2.16858	−	1.25203i
$612$	−1.06220	−	8.62434i	−0.0429368	−	0.348618i
$613$	20.3693	+	35.2807i	0.822709	+	1.42497i	0.903658	+	0.428255i	$0.140872\pi$
$613$	20.3693	+	35.2807i	0.822709	+	1.42497i	−0.0809488	+	0.996718i	$0.525795\pi$
$614$	−30.5116	+	1.87187i	−1.23135	+	0.0755427i
$615$	13.1231			0.529175
$616$		0			0
$617$	15.7538			0.634224			0.317112	−	0.948388i	$-0.397287\pi$
$617$	15.7538			0.634224			0.317112	+	0.948388i	$0.397287\pi$
$618$	−11.2925	+	0.692789i	−0.454250	+	0.0278680i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$		0			0
$621$	−2.61578	−	1.51022i	−0.104968	−	0.0606032i
$622$	−6.24621	−	9.43318i	−0.250450	−	0.378236i
$623$		0			0
$624$	17.3693	−	16.7984i	0.695329	−	0.672473i
$625$	4.93845	−	8.55364i	0.197538	−	0.342146i
$626$	32.4675	+	16.1802i	1.29766	+	0.646690i
$627$	−2.93780	+	1.69614i	−0.117325	+	0.0677373i
$628$	6.60438	−	4.98061i	0.263543	−	0.198748i
$629$			30.9481i			1.23398i
$630$		0			0
$631$			17.9597i			0.714963i	0.933920	+	0.357481i	$0.116364\pi$
$631$			17.9597i			0.714963i	−0.933920	+	0.357481i	$0.883636\pi$
$632$	−12.5778	−	4.44613i	−0.500319	−	0.176858i
$633$	−3.44065	+	1.98646i	−0.136754	+	0.0789547i
$634$	11.6647	−	23.4067i	0.463265	−	0.929599i
$635$	−16.4924	+	28.5657i	−0.654482	+	1.13360i
$636$	3.31534	−	7.81855i	0.131462	−	0.310026i
$637$		0			0
$638$	−7.12311	+	4.71659i	−0.282006	+	0.186732i
$639$	10.7852	+	6.22681i	0.426654	+	0.246329i
$640$	−19.1037	−	1.81434i	−0.755139	−	0.0717181i
$641$	4.75379	+	8.23380i	0.187763	+	0.325216i	0.944504	−	0.328499i	$-0.106543\pi$
$641$	4.75379	+	8.23380i	0.187763	+	0.325216i	−0.756741	+	0.653715i	$0.773210\pi$
$642$	−0.490933	−	8.00222i	−0.0193756	−	0.315822i
$643$	−29.6155			−1.16792			−0.583961	−	0.811782i	$-0.698498\pi$
$643$	−29.6155			−1.16792			−0.583961	+	0.811782i	$0.698498\pi$
$644$		0			0
$645$	13.7538			0.541555
$646$	0.422568	+	6.88787i	0.0166257	+	0.271000i
$647$	16.4924	+	28.5657i	0.648384	+	1.12303i	0.983509	+	0.180860i	$0.0578882\pi$
$647$	16.4924	+	28.5657i	0.648384	+	1.12303i	−0.335125	+	0.942174i	$0.608778\pi$
$648$	1.83812	+	2.14973i	0.0722081	+	0.0844492i
$649$	−10.4631	−	6.04090i	−0.410714	−	0.237126i
$650$	−15.1231	+	10.0138i	−0.593177	+	0.392774i
$651$		0			0
$652$	−21.1771	−	8.97983i	−0.829358	−	0.351677i
$653$	16.3693	−	28.3525i	0.640581	−	1.10952i	−0.344722	−	0.938705i	$-0.612027\pi$
$653$	16.3693	−	28.3525i	0.640581	−	1.10952i	0.985303	−	0.170814i	$-0.0546397\pi$
$654$	5.20157	−	10.4376i	0.203398	−	0.408143i
$655$	32.6775	−	18.8664i	1.27682	−	0.737170i
$656$	7.50940	+	30.0233i	0.293193	+	1.17221i
$657$		−	3.39228i		−	0.132346i
$658$		0			0
$659$			38.1045i			1.48434i	0.670210	+	0.742171i	$0.266204\pi$
$659$			38.1045i			1.48434i	−0.670210	+	0.742171i	$0.733796\pi$
$660$	6.16937	+	8.18069i	0.240142	+	0.318433i
$661$	2.29377	−	1.32431i	0.0892172	−	0.0515096i	−0.454728	−	0.890631i	$-0.650263\pi$
$661$	2.29377	−	1.32431i	0.0892172	−	0.0515096i	0.543945	+	0.839121i	$0.316930\pi$
$662$	−6.91130	−	3.44424i	−0.268615	−	0.133864i
$663$	−13.1231	+	22.7299i	−0.509659	+	0.882756i
$664$	17.3693	−	3.22925i	0.674060	−	0.125319i
$665$		0			0
$666$	−5.56155	−	8.39919i	−0.215506	−	0.325462i
$667$	5.23157	+	3.02045i	0.202567	+	0.116952i
$668$	4.45873	−	0.549150i	0.172514	−	0.0212472i
$669$	9.43845	+	16.3479i	0.364911	+	0.632045i
$670$	4.95115	−	0.303751i	0.191280	−	0.0117349i
$671$	−28.4924			−1.09994
$672$		0			0
$673$	29.8617			1.15109			0.575543	−	0.817772i	$-0.304791\pi$
$673$	29.8617			1.15109			0.575543	+	0.817772i	$0.304791\pi$
$674$	11.6400	−	0.714110i	0.448357	−	0.0275065i
$675$	−1.06155	−	1.83866i	−0.0408592	−	0.0707702i
$676$	−46.6325	+	5.74338i	−1.79356	+	0.220899i
$677$	28.2708	+	16.3221i	1.08653	+	0.627311i	0.932652	−	0.360778i	$-0.117489\pi$
$677$	28.2708	+	16.3221i	1.08653	+	0.627311i	0.153883	+	0.988089i	$0.450822\pi$
$678$	9.56155	+	14.4401i	0.367209	+	0.554568i
$679$		0			0
$680$	20.4924	−	3.80989i	0.785849	−	0.146103i
$681$	8.24621	−	14.2829i	0.315996	−	0.547320i
$682$		0			0
$683$	−25.1918	+	14.5445i	−0.963937	+	0.556529i	−0.897383	−	0.441253i	$-0.854534\pi$
$683$	−25.1918	+	14.5445i	−0.963937	+	0.556529i	−0.0665546	+	0.997783i	$0.521201\pi$
$684$	−1.35247	−	1.79340i	−0.0517131	−	0.0685724i
$685$			27.5559i			1.05286i
$686$		0			0
$687$			18.1227i			0.691424i
$688$	7.87030	+	31.4662i	0.300052	+	1.19964i
$689$	−22.2143	+	12.8255i	−0.846299	+	0.488611i
$690$	3.23157	−	6.48455i	0.123024	−	0.246863i
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$	−15.6155	−	6.62153i	−0.593613	−	0.251713i
$693$		0			0
$694$	−40.9309	+	27.1025i	−1.55371	+	1.02880i
$695$	17.6268	+	10.1768i	0.668623	+	0.386030i
$696$	−3.67624	−	4.29945i	−0.139347	−	0.162970i
$697$	−16.8078	−	29.1119i	−0.636639	−	1.10269i
$698$	−0.358167	−	5.83814i	−0.0135568	−	0.220977i
$699$	−10.4924			−0.396860
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	−0.523133	−	8.52708i	−0.0197444	−	0.321834i
$703$	4.00000	+	6.92820i	0.150863	+	0.261302i
$704$	−15.1856	+	18.7956i	−0.572330	+	0.708386i
$705$	15.0507	+	8.68951i	0.566841	+	0.327266i
$706$	7.36932	−	4.87962i	0.277348	−	0.183647i
$707$		0			0
$708$	3.12311	−	7.36520i	0.117373	−	0.276801i
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$	−13.3241	+	26.7365i	−0.500045	+	1.00340i
$711$	−4.08469	+	2.35829i	−0.153188	+	0.0884430i
$712$	−20.6325	−	7.29338i	−0.773236	−	0.273331i
$713$		0			0
$714$		0			0
$715$		−	30.9481i		−	1.15740i
$716$	3.63561	−	2.74175i	0.135869	−	0.102464i
$717$	−1.97175	+	1.13839i	−0.0736363	+	0.0425139i
$718$	1.41194	+	0.703640i	0.0526932	+	0.0262596i
$719$	−2.24621	+	3.89055i	−0.0837695	+	0.145093i	−0.904866	−	0.425696i	$-0.860029\pi$
$719$	−2.24621	+	3.89055i	−0.0837695	+	0.145093i	0.821097	+	0.570789i	$0.193363\pi$
$720$	−4.87689	+	4.71659i	−0.181751	+	0.175777i
$721$		0			0
$722$	−13.8499	−	20.9165i	−0.515440	−	0.778430i
$723$	−1.64973	−	0.952473i	−0.0613542	−	0.0354228i
$724$	−1.47687	−	11.9912i	−0.0548873	−	0.445649i
$725$	2.12311	+	3.67733i	0.0788502	+	0.136572i
$726$	−2.64935	+	0.162536i	−0.0983265	+	0.00603229i
$727$	32.9848			1.22334			0.611670	−	0.791113i	$-0.290498\pi$
$727$	32.9848			1.22334			0.611670	+	0.791113i	$0.290498\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	8.12182	−	0.498270i	0.300602	−	0.0184418i
$731$	−17.6155	−	30.5110i	−0.651534	−	1.12849i
$732$	−2.30621	−	18.7249i	−0.0852398	−	0.692091i
$733$	−14.4066	−	8.31768i	−0.532121	−	0.307220i	0.209759	−	0.977753i	$-0.432732\pi$
$733$	−14.4066	−	8.31768i	−0.532121	−	0.307220i	−0.741880	+	0.670533i	$0.766066\pi$
$734$	6.73863	+	10.1768i	0.248728	+	0.375634i
$735$		0			0
$736$	16.6847	+	3.68260i	0.615005	+	0.135742i
$737$	3.12311	−	5.40938i	0.115041	−	0.199257i
$738$	9.79312	+	4.88039i	0.360490	+	0.179650i
$739$	−5.09038	+	2.93893i	−0.187253	+	0.108110i	−0.590696	−	0.806894i	$-0.701147\pi$
$739$	−5.09038	+	2.93893i	−0.187253	+	0.108110i	0.403443	+	0.915005i	$0.367813\pi$
$740$	19.2925	−	14.5492i	0.709206	−	0.534839i
$741$			6.78456i			0.249237i
$742$		0			0
$743$			13.6149i			0.499482i	0.968313	+	0.249741i	$0.0803455\pi$
$743$			13.6149i			0.499482i	−0.968313	+	0.249741i	$0.919654\pi$
$744$		0			0
$745$	14.6890	−	8.48071i	0.538164	−	0.310709i
$746$	−6.30783	+	12.6575i	−0.230946	+	0.463422i
$747$	3.12311	−	5.40938i	0.114268	−	0.197919i
$748$	10.2462	−	24.1636i	0.374639	−	0.883508i
$749$		0			0
$750$	14.2462	−	9.43318i	0.520198	−	0.344451i
$751$	26.6607	+	15.3926i	0.972863	+	0.561682i	0.900108	−	0.435667i	$-0.143488\pi$
$751$	26.6607	+	15.3926i	0.972863	+	0.561682i	0.0727548	+	0.997350i	$0.476821\pi$
$752$	−11.2676	+	39.4056i	−0.410887	+	1.43697i
$753$	−11.1231	−	19.2658i	−0.405349	−	0.702084i
$754$	1.04627	+	17.0542i	0.0381028	+	0.621076i
$755$	−13.7538			−0.500552
$756$		0			0
$757$	30.9848			1.12616			0.563082	−	0.826401i	$-0.309616\pi$
$757$	30.9848			1.12616			0.563082	+	0.826401i	$0.309616\pi$
$758$	−1.61968	−	26.4009i	−0.0588295	−	0.958922i
$759$	−4.56155	−	7.90084i	−0.165574	−	0.286782i
$760$	4.09511	−	3.50151i	0.148545	−	0.127013i
$761$	29.2765	+	16.9028i	1.06127	+	0.612725i	0.925784	−	0.378054i	$-0.123407\pi$
$761$	29.2765	+	16.9028i	1.06127	+	0.612725i	0.135488	+	0.990779i	$0.456740\pi$
$762$	−22.9309	+	15.1838i	−0.830698	+	0.550049i
$763$		0			0
$764$	16.6847	+	7.07488i	0.603630	+	0.255960i
$765$	3.68466	−	6.38202i	0.133219	−	0.230742i
$766$	16.5557	−	33.2210i	0.598181	−	1.20032i
$767$	−20.9263	+	12.0818i	−0.755604	+	0.436248i
$768$	−13.5814	−	8.45848i	−0.490076	−	0.305219i
$769$			44.5173i			1.60533i	0.596427	+	0.802667i	$0.296586\pi$
$769$			44.5173i			1.60533i	−0.596427	+	0.802667i	$0.703414\pi$
$770$		0			0
$771$			19.8188i			0.713758i
$772$	−11.2828	−	14.9611i	−0.406076	−	0.538463i
$773$	−1.46890	+	0.848071i	−0.0528327	+	0.0305030i	−0.526184	−	0.850371i	$-0.676378\pi$
$773$	−1.46890	+	0.848071i	−0.0528327	+	0.0305030i	0.473351	+	0.880874i	$0.343044\pi$
$774$	10.2638	+	5.11494i	0.368924	+	0.183853i
$775$		0			0
$776$	4.49242	+	24.1636i	0.161269	+	0.867422i
$777$		0			0
$778$	0.192236	+	0.290319i	0.00689199	+	0.0104085i
$779$	−7.52534	−	4.34475i	−0.269623	−	0.155667i
$780$	20.3387	−	2.50497i	0.728244	−	0.0896925i
$781$	18.8078	+	32.5760i	0.672995	+	1.16566i
$782$	−18.5240	+	1.13644i	−0.662419	+	0.0406391i
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	7.01515			0.250382
$786$	31.4019	−	1.92649i	1.12007	−	0.0687156i
$787$	10.4924	+	18.1734i	0.374014	+	0.647812i	0.990179	−	0.139805i	$-0.0446477\pi$
$787$	10.4924	+	18.1734i	0.374014	+	0.647812i	−0.616165	+	0.787617i	$0.711314\pi$
$788$	0.488730	−	0.0601933i	0.0174103	−	0.00214430i
$789$	−4.26552	−	2.46270i	−0.151856	−	0.0876743i
$790$	−6.24621	−	9.43318i	−0.222230	−	0.335617i
$791$		0			0
$792$	1.56155	+	8.39919i	0.0554874	+	0.298452i
$793$	−28.4924	+	49.3503i	−1.01180	+	1.75248i
$794$	−20.5275	−	10.2299i	−0.728495	−	0.363045i
$795$	6.23726	−	3.60109i	0.221213	−	0.127717i
$796$	6.16937	+	8.18069i	0.218668	+	0.289957i
$797$		−	34.1316i		−	1.20900i	−0.796604	−	0.604502i	$-0.793372\pi$
$797$		−	34.1316i		−	1.20900i	0.796604	−	0.604502i	$-0.206628\pi$
$798$		0			0
$799$		−	44.5173i		−	1.57491i
$800$	8.86233	+	8.10566i	0.313331	+	0.286578i
$801$	−6.70047	+	3.86852i	−0.236749	+	0.136687i
$802$	−5.20157	+	10.4376i	−0.183674	+	0.368565i
$803$	5.12311	−	8.87348i	0.180790	−	0.313138i
$804$	3.80776	+	1.61463i	0.134289	+	0.0569435i
$805$		0			0
$806$		0			0
$807$	19.4574	+	11.2337i	0.684932	+	0.395446i
$808$	−15.0338	+	12.8546i	−0.528888	+	0.452225i
$809$	5.24621	+	9.08670i	0.184447	+	0.319472i	0.943390	−	0.331685i	$-0.107617\pi$
$809$	5.24621	+	9.08670i	0.184447	+	0.319472i	−0.758943	+	0.651157i	$0.774284\pi$
$810$	0.146883	+	2.39420i	0.00516096	+	0.0841238i
$811$	32.4924			1.14096			0.570482	−	0.821310i	$-0.306757\pi$
$811$	32.4924			1.14096			0.570482	+	0.821310i	$0.306757\pi$
$812$		0			0
$813$	−4.49242			−0.157556
$814$	−1.86317	−	30.3697i	−0.0653039	−	1.06446i
$815$	−9.75379	−	16.8941i	−0.341660	−	0.591773i
$816$	16.7093	+	4.77786i	0.584944	+	0.167259i
$817$	−7.88700	−	4.55356i	−0.275931	−	0.159309i
$818$	32.4924	−	21.5150i	1.13607	−	0.752253i
$819$		0			0
$820$	−10.2462	+	24.1636i	−0.357813	+	0.843829i
$821$	−12.6155	+	21.8507i	−0.440285	+	0.762596i	−0.997710	−	0.0676311i	$-0.978456\pi$
$821$	−12.6155	+	21.8507i	−0.440285	+	0.762596i	0.557425	+	0.830227i	$0.311789\pi$
$822$	−10.2478	+	20.5636i	−0.357434	+	0.717237i
$823$	39.0559	−	22.5490i	1.36140	−	0.786007i	0.371594	−	0.928396i	$-0.378811\pi$
$823$	39.0559	−	22.5490i	1.36140	−	0.786007i	0.989811	+	0.142388i	$0.0454782\pi$
$824$	7.54127	−	21.3338i	0.262713	−	0.743197i
$825$		−	6.41273i		−	0.223263i
$826$		0			0
$827$		−	30.9939i		−	1.07776i	−0.842381	−	0.538882i	$-0.818847\pi$
$827$		−	30.9939i		−	1.07776i	0.842381	−	0.538882i	$-0.181153\pi$
$828$	4.82312	−	3.63730i	0.167615	−	0.126405i
$829$	−27.4459	+	15.8459i	−0.953236	+	0.550351i	−0.894085	−	0.447898i	$-0.852173\pi$
$829$	−27.4459	+	15.8459i	−0.953236	+	0.550351i	−0.0591514	+	0.998249i	$0.518839\pi$
$830$	13.4099	+	6.68280i	0.465464	+	0.231964i
$831$	−1.56155	+	2.70469i	−0.0541697	+	0.0938246i
$832$	17.3693	+	45.0979i	0.602173	+	1.56349i
$833$		0			0
$834$	9.36932	+	14.1498i	0.324433	+	0.489966i
$835$	3.29946	+	1.90495i	0.114183	+	0.0659234i
$836$	−0.829339	−	6.73368i	−0.0286833	−	0.232889i
$837$		0			0
$838$	23.2800	−	1.42822i	0.804196	−	0.0493371i
$839$	−6.73863			−0.232643			−0.116322	−	0.993212i	$-0.537110\pi$
$839$	−6.73863			−0.232643			−0.116322	+	0.993212i	$0.537110\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−26.9934	+	1.65603i	−0.930254	+	0.0570707i
$843$	0.123106	+	0.213225i	0.00423998	+	0.00734387i
$844$	−0.971292	−	7.88625i	−0.0334333	−	0.271456i
$845$	−34.5080	−	19.9232i	−1.18711	−	0.685380i
$846$	8.00000	+	12.0818i	0.275046	+	0.415381i
$847$		0			0
$848$	11.8078	+	12.2091i	0.405480	+	0.419262i
$849$	8.56155	−	14.8290i	0.293832	−	0.508931i
$850$	−11.6757	−	5.81858i	−0.400474	−	0.199576i
$851$	−18.6325	+	10.7575i	−0.638714	+	0.368762i
$852$	−19.8862	+	14.9970i	−0.681291	+	0.513788i
$853$			37.4067i			1.28078i	0.768050	+	0.640390i	$0.221227\pi$
$853$			37.4067i			1.28078i	−0.768050	+	0.640390i	$0.778773\pi$
$854$		0			0
$855$		−	1.90495i		−	0.0651478i
$856$	15.1178	+	5.34399i	0.516716	+	0.182654i
$857$	−17.5253	+	10.1182i	−0.598652	+	0.345632i	−0.768511	−	0.639837i	$-0.779002\pi$
$857$	−17.5253	+	10.1182i	−0.598652	+	0.345632i	0.169859	+	0.985468i	$0.445669\pi$
$858$	11.5094	−	23.0951i	0.392925	−	0.788453i
$859$	15.9309	−	27.5931i	0.543554	−	0.941464i	−0.455142	−	0.890419i	$-0.650412\pi$
$859$	15.9309	−	27.5931i	0.543554	−	0.941464i	0.998696	−	0.0510448i	$-0.0162551\pi$
$860$	−10.7386	+	25.3249i	−0.366184	+	0.863571i
$861$		0			0
$862$	−17.8078	+	11.7915i	−0.606535	+	0.401619i
$863$	−18.9545	−	10.9434i	−0.645220	−	0.372518i	0.141403	−	0.989952i	$-0.454839\pi$
$863$	−18.9545	−	10.9434i	−0.645220	−	0.372518i	−0.786622	+	0.617434i	$0.788172\pi$
$864$	−5.39345	+	1.70607i	−0.183489	+	0.0580418i
$865$	−7.19224	−	12.4573i	−0.244543	−	0.423562i
$866$	−0.587534	−	9.57682i	−0.0199652	−	0.325433i
$867$	−1.87689			−0.0637427
$868$		0			0
$869$	−14.2462			−0.483270
$870$	−0.293767	−	4.78841i	−0.00995963	−	0.162342i
$871$	−6.24621	−	10.8188i	−0.211645	−	0.366580i
$872$	15.1575	+	17.7271i	0.513298	+	0.600315i
$873$	7.52534	+	4.34475i	0.254694	+	0.147048i
$874$	−4.00000	+	2.64861i	−0.135302	+	0.0895907i
$875$		0			0
$876$	6.24621	+	2.64861i	0.211040	+	0.0894884i
$877$	−9.87689	+	17.1073i	−0.333519	+	0.577672i	−0.983199	−	0.182536i	$-0.941569\pi$
$877$	−9.87689	+	17.1073i	−0.333519	+	0.577672i	0.649680	+	0.760208i	$0.274903\pi$
$878$	19.7872	−	39.7056i	0.667787	−	1.34000i
$879$	6.05643	−	3.49668i	0.204278	−	0.117940i
$880$	−19.8800	+	4.97238i	−0.670155	+	0.167619i
$881$			39.1028i			1.31741i	0.752403	+	0.658703i	$0.228895\pi$
$881$			39.1028i			1.31741i	−0.752403	+	0.658703i	$0.771105\pi$
$882$		0			0
$883$			26.9752i			0.907789i	0.891056	+	0.453894i	$0.149966\pi$
$883$			26.9752i			0.907789i	−0.891056	+	0.453894i	$0.850034\pi$
$884$	−31.6063	−	41.9105i	−1.06304	−	1.40960i
$885$	5.87560	−	3.39228i	0.197506	−	0.114030i
$886$	−45.4068	−	22.6284i	−1.52547	−	0.760217i
$887$	11.3693	−	19.6922i	0.381744	−	0.661201i	−0.609567	−	0.792734i	$-0.708657\pi$
$887$	11.3693	−	19.6922i	0.381744	−	0.661201i	0.991312	+	0.131534i	$0.0419902\pi$
$888$	19.8078	−	3.68260i	0.664705	−	0.123580i
$889$		0			0
$890$	−10.2462	−	15.4741i	−0.343454	−	0.518692i
$891$	2.61578	+	1.51022i	0.0876321	+	0.0505944i
$892$	−37.4707	+	4.61499i	−1.25461	+	0.154521i
$893$	−5.75379	−	9.96585i	−0.192543	−	0.333495i
$894$	14.1156	−	0.865986i	0.472096	−	0.0289629i
$895$	3.86174			0.129084
$896$		0			0
$897$	−18.2462			−0.609223
$898$	−39.8712	+	2.44608i	−1.33052	+	0.0816268i
$899$		0			0
$900$	4.21437	−	0.519053i	0.140479	−	0.0173018i
$901$	−15.9771	−	9.22437i	−0.532274	−	0.307308i
$902$	18.2462	+	27.5559i	0.607532	+	0.917510i
$903$		0			0
$904$	−34.0540	+	6.33122i	−1.13262	+	0.210573i
$905$	5.12311	−	8.87348i	0.170298	−	0.294964i
$906$	−10.2638	−	5.11494i	−0.340991	−	0.169933i
$907$	10.3220	−	5.95938i	0.342735	−	0.197878i	−0.318746	−	0.947840i	$-0.603262\pi$
$907$	10.3220	−	5.95938i	0.342735	−	0.197878i	0.661481	+	0.749962i	$0.269928\pi$
$908$	19.8606	+	26.3355i	0.659097	+	0.873973i
$909$			6.99337i			0.231955i
$910$		0			0
$911$			6.41273i			0.212463i	0.994341	+	0.106232i	$0.0338785\pi$
$911$			6.41273i			0.212463i	−0.994341	+	0.106232i	$0.966122\pi$
$912$	4.35817	−	1.09006i	0.144313	−	0.0360956i
$913$	16.3387	−	9.43318i	0.540733	−	0.312193i
$914$	−10.2478	+	20.5636i	−0.338968	+	0.680183i
$915$	8.00000	−	13.8564i	0.264472	−	0.458079i
$916$	−33.3693	−	14.1498i	−1.10255	−	0.467521i
$917$		0			0
$918$	5.12311	−	3.39228i	0.169088	−	0.111962i
$919$	7.02249	+	4.05444i	0.231651	+	0.133743i	0.611333	−	0.791373i	$-0.290634\pi$
$919$	7.02249	+	4.05444i	0.231651	+	0.133743i	−0.379683	+	0.925117i	$0.623967\pi$
$920$	9.41687	+	11.0133i	0.310465	+	0.363097i
$921$	−10.8078	−	18.7196i	−0.356128	−	0.616832i
$922$	−1.48692	−	24.2368i	−0.0489690	−	0.798196i
$923$	75.2311			2.47626
$924$		0			0
$925$	−15.1231			−0.497245
$926$	3.41845	+	55.7208i	0.112337	+	1.83110i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	10.7869	−	3.41214i	0.354097	−	0.112009i
$929$	−43.9655	−	25.3835i	−1.44246	−	0.832805i	−0.444447	−	0.895805i	$-0.646600\pi$
$929$	−43.9655	−	25.3835i	−1.44246	−	0.832805i	−0.998014	+	0.0629997i	$0.979933\pi$
$930$		0			0
$931$		0			0
$932$	8.19224	−	19.3197i	0.268346	−	0.632838i
$933$	4.00000	−	6.92820i	0.130954	−	0.226819i
$934$	−11.1988	+	22.4718i	−0.366436	+	0.735299i
$935$	19.2765	−	11.1293i	0.630410	−	0.363968i
$936$	16.1094	+	5.69450i	0.526551	+	0.186131i
$937$		−	56.5991i		−	1.84901i	−0.381169	−	0.924505i	$-0.624478\pi$
$937$		−	56.5991i		−	1.84901i	0.381169	−	0.924505i	$-0.375522\pi$
$938$		0			0
$939$			25.6509i			0.837086i
$940$	−27.7512	+	20.9282i	−0.905145	+	0.682604i
$941$	11.5704	−	6.68016i	0.377184	−	0.217767i	−0.299409	−	0.954125i	$-0.596789\pi$
$941$	11.5704	−	6.68016i	0.377184	−	0.217767i	0.676592	+	0.736358i	$0.263456\pi$
$942$	5.23506	+	2.60889i	0.170568	+	0.0850022i
$943$	11.6847	−	20.2384i	0.380505	−	0.659054i
$944$	11.1231	+	11.5012i	0.362026	+	0.374331i
$945$		0			0
$946$	19.1231	+	28.8802i	0.621746	+	0.938975i
$947$	36.5813	+	21.1202i	1.18873	+	0.686316i	0.958019	−	0.286705i	$-0.0925601\pi$
$947$	36.5813	+	21.1202i	1.18873	+	0.686316i	0.230715	+	0.973021i	$0.425893\pi$
$948$	−1.15310	−	9.36244i	−0.0374510	−	0.304078i
$949$	−10.2462	−	17.7470i	−0.332606	−	0.576091i
$950$	−3.36582	+	0.206492i	−0.109202	+	0.00669948i
$951$	18.4924			0.599658
$952$		0			0
$953$	61.2311			1.98347			0.991734	−	0.128309i	$-0.0409549\pi$
$953$	61.2311			1.98347			0.991734	+	0.128309i	$0.0409549\pi$
$954$	5.99378	−	0.367716i	0.194056	−	0.0119052i
$955$	7.68466	+	13.3102i	0.248670	+	0.430709i
$956$	−0.556623	−	4.51941i	−0.0180025	−	0.146168i
$957$	−5.23157	−	3.02045i	−0.169113	−	0.0976372i
$958$	16.0000	+	24.1636i	0.516937	+	0.780690i
$959$		0			0
$960$	−4.87689	−	12.6624i	−0.157401	−	0.408678i
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−54.4650	−	27.1426i	−1.75602	−	0.875111i
$963$	4.90955	−	2.83453i	0.158208	−	0.0913415i
$964$	3.04186	−	2.29398i	0.0979717	−	0.0738842i
$965$		−	15.8917i		−	0.511571i
$966$		0			0
$967$		−	40.9620i		−	1.31725i	−0.752472	−	0.658624i	$-0.771139\pi$
$967$		−	40.9620i		−	1.31725i	0.752472	−	0.658624i	$-0.228861\pi$
$968$	1.76927	−	5.00515i	0.0568665	−	0.160872i
$969$	−4.22587	+	2.43981i	−0.135755	+	0.0783780i
$970$	−9.29688	+	18.6554i	−0.298505	+	0.598988i
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$	−0.780776	+	1.84130i	−0.0250434	+	0.0590597i
$973$		0			0
$974$	38.0540	−	25.1976i	1.21933	−	0.807382i
$975$	−11.1072	−	6.41273i	−0.355714	−	0.205372i
$976$	36.2787	+	10.3735i	1.16125	+	0.332048i
$977$	30.3693	+	52.6012i	0.971601	+	1.68286i	0.690725	+	0.723117i	$0.257291\pi$
$977$	30.3693	+	52.6012i	0.971601	+	1.68286i	0.280875	+	0.959744i	$0.409375\pi$
$978$	−0.995984	−	16.2346i	−0.0318480	−	0.519124i
$979$	−23.3693			−0.746887
$980$		0			0
$981$	8.24621			0.263281
$982$	1.01407	+	16.5293i	0.0323601	+	0.527471i
$983$	27.3693	+	47.4050i	0.872946	+	1.51199i	0.858935	+	0.512084i	$0.171126\pi$
$983$	27.3693	+	47.4050i	0.872946	+	1.51199i	0.0140105	+	0.999902i	$0.495540\pi$
$984$	−16.6325	+	14.2216i	−0.530225	+	0.453368i
$985$	0.361660	+	0.208805i	0.0115234	+	0.00665306i
$986$	−10.2462	+	6.78456i	−0.326306	+	0.216065i
$987$		0			0
$988$	−12.4924	−	5.29723i	−0.397437	−	0.168527i
$989$	12.2462	−	21.2111i	0.389407	−	0.674472i
$990$	−3.23157	+	6.48455i	−0.102706	+	0.206093i
$991$	9.31626	−	5.37874i	0.295941	−	0.170861i	−0.344677	−	0.938721i	$-0.612012\pi$
$991$	9.31626	−	5.37874i	0.295941	−	0.170861i	0.640618	+	0.767860i	$0.278678\pi$
$992$		0			0
$993$		−	5.46026i		−	0.173276i
$994$		0			0
$995$			8.68951i			0.275476i
$996$	7.52184	+	9.97409i	0.238339	+	0.316041i
$997$	−33.6832	+	19.4470i	−1.06676	+	0.615892i	−0.927294	−	0.374335i	$-0.877871\pi$
$997$	−33.6832	+	19.4470i	−1.06676	+	0.615892i	−0.139463	+	0.990227i	$0.544538\pi$
$998$	−22.2038	−	11.0652i	−0.702848	−	0.350264i
$999$	3.56155	−	6.16879i	0.112683	−	0.195172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.a.19.1		8
4.3	odd	2		588.2.o.c.19.3		8
7.2	even	3		84.2.b.b.55.4	yes	4
7.3	odd	6		588.2.o.c.31.3		8
7.4	even	3	inner	588.2.o.a.31.3		8
7.5	odd	6		84.2.b.a.55.4	yes	4
7.6	odd	2		588.2.o.c.19.1		8
21.2	odd	6		252.2.b.d.55.1		4
21.5	even	6		252.2.b.e.55.1		4
28.3	even	6	inner	588.2.o.a.31.1		8
28.11	odd	6		588.2.o.c.31.1		8
28.19	even	6		84.2.b.b.55.3	yes	4
28.23	odd	6		84.2.b.a.55.3	✓	4
28.27	even	2	inner	588.2.o.a.19.3		8
56.5	odd	6		1344.2.b.f.895.2		4
56.19	even	6		1344.2.b.e.895.2		4
56.37	even	6		1344.2.b.e.895.3		4
56.51	odd	6		1344.2.b.f.895.3		4
84.23	even	6		252.2.b.e.55.2		4
84.47	odd	6		252.2.b.d.55.2		4
168.5	even	6		4032.2.b.n.3583.3		4
168.107	even	6		4032.2.b.n.3583.2		4
168.131	odd	6		4032.2.b.j.3583.3		4
168.149	odd	6		4032.2.b.j.3583.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.b.a.55.3	✓	4	28.23	odd	6
84.2.b.a.55.4	yes	4	7.5	odd	6
84.2.b.b.55.3	yes	4	28.19	even	6
84.2.b.b.55.4	yes	4	7.2	even	3
252.2.b.d.55.1		4	21.2	odd	6
252.2.b.d.55.2		4	84.47	odd	6
252.2.b.e.55.1		4	21.5	even	6
252.2.b.e.55.2		4	84.23	even	6
588.2.o.a.19.1		8	1.1	even	1	trivial
588.2.o.a.19.3		8	28.27	even	2	inner
588.2.o.a.31.1		8	28.3	even	6	inner
588.2.o.a.31.3		8	7.4	even	3	inner
588.2.o.c.19.1		8	7.6	odd	2
588.2.o.c.19.3		8	4.3	odd	2
588.2.o.c.31.1		8	28.11	odd	6
588.2.o.c.31.3		8	7.3	odd	6
1344.2.b.e.895.2		4	56.19	even	6
1344.2.b.e.895.3		4	56.37	even	6
1344.2.b.f.895.2		4	56.5	odd	6
1344.2.b.f.895.3		4	56.51	odd	6
4032.2.b.j.3583.2		4	168.149	odd	6
4032.2.b.j.3583.3		4	168.131	odd	6
4032.2.b.n.3583.2		4	168.107	even	6
4032.2.b.n.3583.3		4	168.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41156 + 0.0865986i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98500 - 0.244478i) q^{4} +(1.46890 + 0.848071i) q^{5} +(0.780776 + 1.17915i) q^{6} +(-2.78078 + 0.516994i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.41156 + 0.0865986i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98500 - 0.244478i) q^{4} +(1.46890 + 0.848071i) q^{5} +(0.780776 + 1.17915i) q^{6} +(-2.78078 + 0.516994i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.14688 - 1.06990i) q^{10} +(-2.61578 + 1.51022i) q^{11} +(-1.20422 - 1.59682i) q^{12} +6.04090i q^{13} -1.69614i q^{15} +(3.88046 - 0.970579i) q^{16} +(-3.76267 + 2.17238i) q^{17} +(0.630783 - 1.26575i) q^{18} +(-0.561553 + 0.972638i) q^{19} +(3.12311 + 1.32431i) q^{20} +(3.56155 - 2.35829i) q^{22} +(-2.61578 - 1.51022i) q^{23} +(1.83812 + 2.14973i) q^{24} +(-1.06155 - 1.83866i) q^{25} +(-0.523133 - 8.52708i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(0.146883 + 2.39420i) q^{30} +(-5.39345 + 1.70607i) q^{32} +(2.61578 + 1.51022i) q^{33} +(5.12311 - 3.39228i) q^{34} +(-0.780776 + 1.84130i) q^{36} +(3.56155 - 6.16879i) q^{37} +(0.708436 - 1.42157i) q^{38} +(5.23157 - 3.02045i) q^{39} +(-4.52313 - 1.59888i) q^{40} +7.73704i q^{41} +8.10887i q^{43} +(-4.82312 + 3.63730i) q^{44} +(-1.46890 + 0.848071i) q^{45} +(3.82312 + 1.90525i) q^{46} +(-5.12311 + 8.87348i) q^{47} +(-2.78078 - 2.87529i) q^{48} +(1.65767 + 2.50345i) q^{50} +(3.76267 + 2.17238i) q^{51} +(1.47687 + 11.9912i) q^{52} +(2.12311 + 3.67733i) q^{53} +(-1.41156 + 0.0865986i) q^{54} -5.12311 q^{55} +1.12311 q^{57} +(2.82312 - 0.173197i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-0.414669 - 3.36684i) q^{60} +(8.16937 + 4.71659i) q^{61} +(7.46543 - 2.87529i) q^{64} +(-5.12311 + 8.87348i) q^{65} +(-3.82312 - 1.90525i) q^{66} +(-1.79092 + 1.03399i) q^{67} +(-6.93780 + 5.23206i) q^{68} +3.02045i q^{69} -12.4536i q^{71} +(0.942658 - 2.66672i) q^{72} +(-2.93780 + 1.69614i) q^{73} +(-4.49314 + 9.01604i) q^{74} +(-1.06155 + 1.83866i) q^{75} +(-0.876894 + 2.06798i) q^{76} +(-7.12311 + 4.71659i) q^{78} +(4.08469 + 2.35829i) q^{79} +(6.52313 + 1.86522i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.670016 - 10.9213i) q^{82} -6.24621 q^{83} -7.36932 q^{85} +(-0.702217 - 11.4462i) q^{86} +(1.00000 + 1.73205i) q^{87} +(6.49314 - 5.55194i) q^{88} +(6.70047 + 3.86852i) q^{89} +(2.00000 - 1.32431i) q^{90} +(-5.56155 - 2.35829i) q^{92} +(6.46314 - 12.9691i) q^{94} +(-1.64973 + 0.952473i) q^{95} +(4.17423 + 3.81783i) q^{96} -8.68951i q^{97} -3.02045i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{16} + q^{18} + 12 q^{19} - 8 q^{20} + 12 q^{22} + 7 q^{24} + 8 q^{25} + 12 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 9 q^{32} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 20 q^{38} - 20 q^{40} - 14 q^{44} + 6 q^{46} - 8 q^{47} - 14 q^{48} + 38 q^{50} + 28 q^{52} - 16 q^{53} + q^{54} - 8 q^{55} - 24 q^{57} - 2 q^{58} + 16 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{65} - 6 q^{66} - 32 q^{68} + 7 q^{72} + 14 q^{74} + 8 q^{75} - 40 q^{76} - 24 q^{78} + 36 q^{80} - 4 q^{81} + 20 q^{82} + 16 q^{83} + 40 q^{85} + 30 q^{86} + 8 q^{87} + 2 q^{88} + 16 q^{90} - 28 q^{92} - 32 q^{94} - 9 q^{96}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9 - 8 * q^10 - q^12 + 7 * q^16 + q^18 + 12 * q^19 - 8 * q^20 + 12 * q^22 + 7 * q^24 + 8 * q^25 + 12 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 9 * q^32 + 8 * q^34 + 2 * q^36 + 12 * q^37 - 20 * q^38 - 20 * q^40 - 14 * q^44 + 6 * q^46 - 8 * q^47 - 14 * q^48 + 38 * q^50 + 28 * q^52 - 16 * q^53 + q^54 - 8 * q^55 - 24 * q^57 - 2 * q^58 + 16 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^65 - 6 * q^66 - 32 * q^68 + 7 * q^72 + 14 * q^74 + 8 * q^75 - 40 * q^76 - 24 * q^78 + 36 * q^80 - 4 * q^81 + 20 * q^82 + 16 * q^83 + 40 * q^85 + 30 * q^86 + 8 * q^87 + 2 * q^88 + 16 * q^90 - 28 * q^92 - 32 * q^94 - 9 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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