LMFDB - Embedded newform 588.2.o.a.19.3

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			19.3
Root			$0.630783 - 1.26575i$ of defining polynomial
Character	$\chi$	$=$	588.19
Dual form			588.2.o.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.630783 + 1.26575i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.20422 + 1.59682i) q^{4} +(-1.46890 - 0.848071i) q^{5} +(0.780776 - 1.17915i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.630783 + 1.26575i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.20422 + 1.59682i) 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} +(0.146883 - 2.39420i) q^{10} +(2.61578 - 1.51022i) q^{11} +(1.98500 + 0.244478i) q^{12} -6.04090i q^{13} +1.69614i q^{15} +(-1.09968 - 3.84587i) q^{16} +(3.76267 - 2.17238i) q^{17} +(-1.41156 - 0.0865986i) 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} +(0.942658 + 2.66672i) q^{24} +(-1.06155 - 1.83866i) q^{25} +(7.64624 - 3.81050i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-2.14688 + 1.06990i) q^{30} +(4.17423 - 3.81783i) 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} +(-1.58533 - 0.0972594i) q^{38} +(-5.23157 + 3.02045i) q^{39} +(3.64624 + 3.11771i) q^{40} -7.73704i q^{41} -8.10887i q^{43} +(-0.738433 + 5.99559i) q^{44} +(1.46890 - 0.848071i) q^{45} +(-0.261567 + 4.26354i) 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} +(9.64624 + 7.27460i) q^{52} +(2.12311 + 3.67733i) q^{53} +(0.630783 + 1.26575i) q^{54} -5.12311 q^{55} +1.12311 q^{57} +(-1.26157 - 2.53149i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-2.70844 - 2.04254i) q^{60} +(-8.16937 - 4.71659i) q^{61} +(7.46543 + 2.87529i) q^{64} +(-5.12311 + 8.87348i) q^{65} +(0.261567 - 4.26354i) q^{66} +(1.79092 - 1.03399i) q^{67} +(-1.06220 + 8.62434i) q^{68} -3.02045i q^{69} +12.4536i q^{71} +(1.83812 - 2.14973i) q^{72} +(2.93780 - 1.69614i) q^{73} +(10.0547 + 0.616851i) 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} +(-1.64624 + 6.58181i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.79312 - 4.88039i) q^{82} -6.24621 q^{83} -7.36932 q^{85} +(10.2638 - 5.11494i) q^{86} +(1.00000 + 1.73205i) q^{87} +(-8.05469 + 2.84725i) q^{88} +(-6.70047 - 3.86852i) q^{89} +(2.00000 + 1.32431i) q^{90} +(-5.56155 + 2.35829i) q^{92} +(-14.4631 - 0.887307i) q^{94} +(1.64973 - 0.952473i) q^{95} +(-5.39345 - 1.70607i) 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 $

$2$	0.630783	+	1.26575i	0.446031	+	0.895017i
$2$	0.630783	+	1.26575i	0.446031	+	0.895017i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.20422	+	1.59682i	−0.602112	+	0.798411i
$5$	−1.46890	−	0.848071i	−0.656913	−	0.379269i	0.134187	−	0.990956i	$-0.457158\pi$
$5$	−1.46890	−	0.848071i	−0.656913	−	0.379269i	−0.791100	+	0.611687i	$0.790491\pi$
$6$	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
$10$	0.146883	−	2.39420i	0.0464486	−	0.757114i
$11$	2.61578	−	1.51022i	0.788689	−	0.455350i	−0.0508120	−	0.998708i	$-0.516181\pi$
$11$	2.61578	−	1.51022i	0.788689	−	0.455350i	0.839501	+	0.543359i	$0.182848\pi$
$12$	1.98500	+	0.244478i	0.573021	+	0.0705748i
$13$		−	6.04090i		−	1.67544i	−0.546098	−	0.837722i	$-0.683887\pi$
$13$		−	6.04090i		−	1.67544i	0.546098	−	0.837722i	$-0.316113\pi$
$14$		0			0
$15$			1.69614i			0.437942i
$16$	−1.09968	−	3.84587i	−0.274921	−	0.961467i
$17$	3.76267	−	2.17238i	0.912581	−	0.526879i	0.0313203	−	0.999509i	$-0.490029\pi$
$17$	3.76267	−	2.17238i	0.912581	−	0.526879i	0.881261	+	0.472630i	$0.156695\pi$
$18$	−1.41156	−	0.0865986i	−0.332708	−	0.0204115i
$19$	−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	0.747276	−	0.664514i	$-0.231361\pi$
$23$	2.61578	+	1.51022i	0.545429	+	0.314903i	−0.201847	+	0.979417i	$0.564695\pi$
$24$	0.942658	+	2.66672i	0.192419	+	0.544342i
$25$	−1.06155	−	1.83866i	−0.212311	−	0.367733i
$26$	7.64624	−	3.81050i	1.49955	−	0.747300i
$27$	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	$0.559454\pi$
$30$	−2.14688	+	1.06990i	−0.391965	+	0.195336i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	4.17423	−	3.81783i	0.737906	−	0.674903i
$33$	−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	$-0.0324413\pi$
$38$	−1.58533	−	0.0972594i	−0.257175	−	0.0157776i
$39$	−5.23157	+	3.02045i	−0.837722	+	0.483659i
$40$	3.64624	+	3.11771i	0.576521	+	0.492953i
$41$		−	7.73704i		−	1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$41$		−	7.73704i		−	1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$42$		0			0
$43$		−	8.10887i		−	1.23659i	−0.785946	−	0.618296i	$-0.787823\pi$
$43$		−	8.10887i		−	1.23659i	0.785946	−	0.618296i	$-0.212177\pi$
$44$	−0.738433	+	5.99559i	−0.111323	+	0.903870i
$45$	1.46890	−	0.848071i	0.218971	−	0.126423i
$46$	−0.261567	+	4.26354i	−0.0385659	+	0.628625i
$47$	−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
$52$	9.64624	+	7.27460i	1.33769	+	1.00881i
$53$	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	$0.739135\pi$
$54$	0.630783	+	1.26575i	0.0858387	+	0.172246i
$55$	−5.12311			−0.690799
$56$		0			0
$57$	1.12311			0.148759
$58$	−1.26157	−	2.53149i	−0.165652	−	0.332401i
$59$	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	$0.749486\pi$
$60$	−2.70844	−	2.04254i	−0.349658	−	0.263690i
$61$	−8.16937	−	4.71659i	−1.04598	−	0.603897i	−0.124459	−	0.992225i	$-0.539720\pi$
$61$	−8.16937	−	4.71659i	−1.04598	−	0.603897i	−0.921521	+	0.388327i	$0.873053\pi$
$62$		0			0
$63$		0			0
$64$	7.46543	+	2.87529i	0.933179	+	0.359411i
$65$	−5.12311	+	8.87348i	−0.635443	+	1.10062i
$66$	0.261567	−	4.26354i	0.0321966	−	0.524806i
$67$	1.79092	−	1.03399i	0.218796	−	0.126322i	−0.386597	−	0.922249i	$-0.626350\pi$
$67$	1.79092	−	1.03399i	0.218796	−	0.126322i	0.605392	+	0.795927i	$0.293016\pi$
$68$	−1.06220	+	8.62434i	−0.128810	+	1.04586i
$69$		−	3.02045i		−	0.363619i
$70$		0			0
$71$			12.4536i			1.47797i	0.673720	+	0.738987i	$0.264695\pi$
$71$			12.4536i			1.47797i	−0.673720	+	0.738987i	$0.735305\pi$
$72$	1.83812	−	2.14973i	0.216624	−	0.253348i
$73$	2.93780	−	1.69614i	0.343844	−	0.198518i	−0.318127	−	0.948048i	$-0.603054\pi$
$73$	2.93780	−	1.69614i	0.343844	−	0.198518i	0.661970	+	0.749530i	$0.269720\pi$
$74$	10.0547	+	0.616851i	1.16883	+	0.0717075i
$75$	−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	0.252297	−	0.967650i	$-0.418814\pi$
$79$	−4.08469	−	2.35829i	−0.459563	−	0.265329i	−0.711861	+	0.702321i	$0.752147\pi$
$80$	−1.64624	+	6.58181i	−0.184055	+	0.735869i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	9.79312	−	4.88039i	1.08147	−	0.538949i
$83$	−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
$86$	10.2638	−	5.11494i	1.10677	−	0.551558i
$87$	1.00000	+	1.73205i	0.107211	+	0.185695i
$88$	−8.05469	+	2.84725i	−0.858633	+	0.303518i
$89$	−6.70047	−	3.86852i	−0.710248	−	0.410062i	0.100905	−	0.994896i	$-0.467826\pi$
$89$	−6.70047	−	3.86852i	−0.710248	−	0.410062i	−0.811153	+	0.584834i	$0.801160\pi$
$90$	2.00000	+	1.32431i	0.210819	+	0.139594i
$91$		0			0
$92$	−5.56155	+	2.35829i	−0.579832	+	0.245869i
$93$		0			0
$94$	−14.4631	−	0.887307i	−1.49176	−	0.0915188i
$95$	1.64973	−	0.952473i	0.169259	−	0.0977216i
$96$	−5.39345	−	1.70607i	−0.550467	−	0.174125i
$97$			8.68951i			0.882286i	0.897437	+	0.441143i	$0.145427\pi$
$97$			8.68951i			0.882286i	−0.897437	+	0.441143i	$0.854573\pi$
$98$		0			0
$99$			3.02045i			0.303566i
$100$	4.21437	+	0.519053i	0.421437	+	0.0519053i
$101$	−6.05643	+	3.49668i	−0.602638	+	0.347933i	−0.770079	−	0.637949i	$-0.779783\pi$
$101$	−6.05643	+	3.49668i	−0.602638	+	0.347933i	0.167441	+	0.985882i	$0.446450\pi$
$102$	0.376250	−	6.13288i	0.0372543	−	0.607246i
$103$	−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	0.718173	−	0.695864i	$-0.244978\pi$
$107$	4.90955	+	2.83453i	0.474624	+	0.274024i	−0.243549	+	0.969889i	$0.578312\pi$
$108$	−1.20422	+	1.59682i	−0.115877	+	0.153654i
$109$	−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	$0.962562\pi$
$110$	−3.23157	−	6.48455i	−0.308118	−	0.618278i
$111$	−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	$0.304608\pi$
$114$	0.708436	+	1.42157i	0.0663511	+	0.133142i
$115$	−2.56155	−	4.43674i	−0.238866	−	0.413728i
$116$	2.40845	−	3.19365i	0.223619	−	0.296523i
$117$	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
$122$	0.816900	−	13.3155i	0.0739586	−	1.20553i
$123$	−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	$-0.668696\pi$
$127$		−	19.4470i		−	1.72564i	0.505510	−	0.862821i	$-0.331304\pi$
$128$	1.06969	+	11.2630i	0.0945479	+	0.995520i
$129$	−7.02249	+	4.05444i	−0.618296	+	0.356973i
$130$	−14.4631	−	0.887307i	−1.26850	−	0.0778220i
$131$	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
$136$	−11.5862	+	4.09562i	−0.993512	+	0.351197i
$137$	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	$0.589178\pi$
$138$	3.82312	−	1.90525i	0.325446	−	0.162185i
$139$	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
$142$	−15.7631	+	7.85554i	−1.32281	+	0.659222i
$143$	−9.12311	−	15.8017i	−0.762912	−	1.32140i
$144$	3.88046	+	0.970579i	0.323372	+	0.0808816i
$145$	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	$0.0323294\pi$
$150$	−2.99689	−	0.183858i	−0.244695	−	0.0150119i
$151$	7.02249	−	4.05444i	0.571482	−	0.329945i	−0.186259	−	0.982501i	$-0.559636\pi$
$151$	7.02249	−	4.05444i	0.571482	−	0.329945i	0.757741	+	0.652555i	$0.226303\pi$
$152$	2.06440	−	2.41437i	0.167445	−	0.195831i
$153$			4.34475i			0.351253i
$154$		0			0
$155$		0			0
$156$	1.47687	−	11.9912i	0.118244	−	0.960063i
$157$	−3.58184	+	2.06798i	−0.285862	+	0.165042i	−0.636074	−	0.771628i	$-0.719443\pi$
$157$	−3.58184	+	2.06798i	−0.285862	+	0.165042i	0.350212	+	0.936670i	$0.386109\pi$
$158$	0.408450	−	6.65775i	0.0324945	−	0.529662i
$159$	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	0.836484	−	0.547992i	$-0.184608\pi$
$163$	9.96029	+	5.75058i	0.780150	+	0.450420i	−0.0563333	+	0.998412i	$0.517941\pi$
$164$	12.3547	+	9.31713i	0.964738	+	0.727546i
$165$	2.56155	+	4.43674i	0.199417	+	0.345400i
$166$	−3.94001	−	7.90612i	−0.305804	−	0.613634i
$167$	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
$170$	−4.64844	−	9.32768i	−0.356519	−	0.715401i
$171$	−0.561553	−	0.972638i	−0.0429430	−	0.0743795i
$172$	12.9484	+	9.76490i	0.987308	+	0.744567i
$173$	7.34451	+	4.24035i	0.558392	+	0.322388i	0.752500	−	0.658592i	$-0.228848\pi$
$173$	7.34451	+	4.24035i	0.558392	+	0.322388i	−0.194108	+	0.980980i	$0.562181\pi$
$174$	−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
$178$	0.670016	−	10.9213i	0.0502199	−	0.818585i
$179$	−1.97175	+	1.13839i	−0.147375	+	0.0850873i	−0.571874	−	0.820341i	$-0.693784\pi$
$179$	−1.97175	+	1.13839i	−0.147375	+	0.0850873i	0.424499	+	0.905428i	$0.360450\pi$
$180$	−0.414669	+	3.36684i	−0.0309076	+	0.250950i
$181$			6.04090i			0.449016i	0.974472	+	0.224508i	$0.0720775\pi$
$181$			6.04090i			0.449016i	−0.974472	+	0.224508i	$0.927922\pi$
$182$		0			0
$183$			9.43318i			0.697321i
$184$	−6.49314	−	5.55194i	−0.478680	−	0.409294i
$185$	−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	0.188461	−	0.982081i	$-0.439650\pi$
$191$	−7.84735	−	4.53067i	−0.567815	−	0.327828i	−0.756276	+	0.654253i	$0.772983\pi$
$192$	−1.24264	−	7.90290i	−0.0896802	−	0.570343i
$193$	−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	$0.942816\pi$
$194$	−10.9987	+	5.48120i	−0.789661	+	0.393527i
$195$	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	$0.497208\pi$
$198$	−3.82312	+	1.90525i	−0.271697	+	0.135400i
$199$	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	$0.775211\pi$
$200$	2.00136	+	5.66173i	0.141518	+	0.400345i
$201$	−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
$206$	−11.2925	−	0.692789i	−0.786784	−	0.0482689i
$207$	−2.61578	+	1.51022i	−0.181810	+	0.104968i
$208$	−23.2325	+	6.64308i	−1.61088	+	0.460615i
$209$			3.39228i			0.234649i
$210$		0			0
$211$			3.97292i			0.273507i	0.990605	+	0.136754i	$0.0436668\pi$
$211$			3.97292i			0.273507i	−0.990605	+	0.136754i	$0.956333\pi$
$212$	−8.42874	−	1.03811i	−0.578888	−	0.0712974i
$213$	10.7852	−	6.22681i	0.738987	−	0.426654i
$214$	−0.490933	+	8.00222i	−0.0335595	+	0.547020i
$215$	−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
$220$	6.16937	−	8.18069i	0.415939	−	0.551542i
$221$	−13.1231	−	22.7299i	−0.882756	−	1.52898i
$222$	−4.49314	−	9.01604i	−0.301560	−	0.605117i
$223$	−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
$226$	7.72471	+	15.5006i	0.513840	+	1.03108i
$227$	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	$0.648981\pi$
$228$	−1.35247	+	1.79340i	−0.0895696	+	0.118771i
$229$	15.6947	+	9.06134i	1.03714	+	0.598790i	0.919021	−	0.394209i	$-0.128982\pi$
$229$	15.6947	+	9.06134i	1.03714	+	0.598790i	0.118115	+	0.993000i	$0.462315\pi$
$230$	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	$0.0549895\pi$
$234$	−0.523133	+	8.52708i	−0.0341983	+	0.557433i
$235$	15.0507	−	8.68951i	0.981798	−	0.566841i
$236$	−7.94001	−	0.977913i	−0.516850	−	0.0636567i
$237$			4.71659i			0.306375i
$238$		0			0
$239$			2.27678i			0.147273i	0.997285	+	0.0736363i	$0.0234604\pi$
$239$			2.27678i			0.147273i	−0.997285	+	0.0736363i	$0.976540\pi$
$240$	6.52313	−	1.86522i	0.421066	−	0.120399i
$241$	−1.64973	+	0.952473i	−0.106269	+	0.0613542i	−0.552192	−	0.833717i	$-0.686209\pi$
$241$	−1.64973	+	0.952473i	−0.106269	+	0.0613542i	0.445924	+	0.895071i	$0.352875\pi$
$242$	−2.64935	−	0.162536i	−0.170307	−	0.0104482i
$243$	−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
$250$	−15.2925	+	7.62099i	−0.967181	+	0.481994i
$251$	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
$254$	24.6150	−	12.2668i	1.54448	−	0.769690i
$255$	3.68466	+	6.38202i	0.230742	+	0.399657i
$256$	−13.5814	+	8.45848i	−0.848837	+	0.528655i
$257$	17.1636	+	9.90941i	1.07064	+	0.618132i	0.928355	−	0.371694i	$-0.121223\pi$
$257$	17.1636	+	9.90941i	1.07064	+	0.618132i	0.142281	+	0.989826i	$0.454556\pi$
$258$	−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
$262$	31.4019	+	1.92649i	1.94001	+	0.119019i
$263$	−4.26552	+	2.46270i	−0.263023	+	0.151856i	−0.625713	−	0.780054i	$-0.715192\pi$
$263$	−4.26552	+	2.46270i	−0.263023	+	0.151856i	0.362690	+	0.931910i	$0.381858\pi$
$264$	6.49314	+	5.55194i	0.399625	+	0.341698i
$265$		−	7.20217i		−	0.442426i
$266$		0			0
$267$			7.73704i			0.473499i
$268$	−0.505575	+	4.10493i	−0.0308829	+	0.250749i
$269$	19.4574	−	11.2337i	1.18634	−	0.684932i	0.228865	−	0.973458i	$-0.426499\pi$
$269$	19.4574	−	11.2337i	1.18634	−	0.684932i	0.957472	+	0.288526i	$0.0931652\pi$
$270$	0.146883	−	2.39420i	0.00893904	−	0.145707i
$271$	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
$276$	4.82312	+	3.63730i	0.290318	+	0.218940i
$277$	−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	$0.863243\pi$
$278$	7.56940	+	15.1889i	0.453982	+	0.910973i
$279$		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	$0.502338\pi$
$282$	6.46314	+	12.9691i	0.384874	+	0.772299i
$283$	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	$0.663374\pi$
$284$	−19.8862	−	14.9970i	−1.18003	−	0.889906i
$285$	−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
$290$	−0.293767	+	4.78841i	−0.0172506	+	0.281185i
$291$	7.52534	−	4.34475i	0.441143	−	0.254694i
$292$	−0.829339	+	6.73368i	−0.0485334	+	0.394059i
$293$		−	6.99337i		−	0.408557i	−0.978913	−	0.204278i	$-0.934515\pi$
$293$		−	6.99337i		−	0.408557i	0.978913	−	0.204278i	$-0.0654848\pi$
$294$		0			0
$295$		−	6.78456i		−	0.395013i
$296$	−13.0931	+	15.3127i	−0.761021	+	0.890034i
$297$	2.61578	−	1.51022i	0.151783	−	0.0876321i
$298$	14.1156	+	0.865986i	0.817695	+	0.0501652i
$299$	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
$304$	4.35817	+	1.09006i	0.249958	+	0.0625194i
$305$	8.00000	+	13.8564i	0.458079	+	0.793416i
$306$	−5.49936	+	2.74060i	−0.314377	+	0.156670i
$307$	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	$0.760501\pi$
$312$	16.1094	−	5.69450i	0.912014	−	0.322388i
$313$	22.2143	+	12.8255i	1.25563	+	0.724938i	0.972222	−	0.234062i	$-0.0752018\pi$
$313$	22.2143	+	12.8255i	1.25563	+	0.724938i	0.283407	+	0.959000i	$0.408535\pi$
$314$	−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	$0.992852\pi$
$318$	5.99378	+	0.367716i	0.336115	+	0.0206205i
$319$	−5.23157	+	3.02045i	−0.292912	+	0.169113i
$320$	−8.52754	−	10.5547i	−0.476704	−	0.590027i
$321$		−	5.66906i		−	0.316416i
$322$		0			0
$323$			4.87962i			0.271509i
$324$	1.98500	+	0.244478i	0.110278	+	0.0135821i
$325$	−11.1072	+	6.41273i	−0.616115	+	0.355714i
$326$	−0.995984	+	16.2346i	−0.0551624	+	0.899149i
$327$	−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	0.364381	−	0.931250i	$-0.381280\pi$
$331$	−4.72872	−	2.73013i	−0.259914	−	0.150061i	−0.624295	+	0.781188i	$0.714614\pi$
$332$	7.52184	−	9.97409i	0.412815	−	0.547399i
$333$	3.56155	+	6.16879i	0.195172	+	0.338048i
$334$	1.41687	+	2.84313i	0.0775278	+	0.155569i
$335$	−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	$0.572108\pi$
$338$	−14.8186	−	29.7354i	−0.806027	−	1.61739i
$339$	−6.12311	−	10.6055i	−0.332561	−	0.576013i
$340$	8.87432	−	11.7675i	0.481277	−	0.638182i
$341$		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
$346$	−0.734417	+	11.9710i	−0.0394825	+	0.643566i
$347$	−30.0617	+	17.3561i	−1.61380	+	0.931726i	−0.625317	+	0.780371i	$0.715030\pi$
$347$	−30.0617	+	17.3561i	−1.61380	+	0.931726i	−0.988479	+	0.151355i	$0.951636\pi$
$348$	−3.97000	−	0.488956i	−0.212814	−	0.0262108i
$349$		−	4.13595i		−	0.221392i	−0.993854	−	0.110696i	$-0.964692\pi$
$349$		−	4.13595i		−	0.221392i	0.993854	−	0.110696i	$-0.0353080\pi$
$350$		0			0
$351$		−	6.04090i		−	0.322439i
$352$	5.15310	−	16.2906i	0.274661	−	0.868294i
$353$	5.41240	−	3.12485i	0.288073	−	0.166319i	−0.349000	−	0.937123i	$-0.613479\pi$
$353$	5.41240	−	3.12485i	0.288073	−	0.166319i	0.637072	+	0.770804i	$0.280145\pi$
$354$	5.64624	+	0.346394i	0.300094	+	0.0184107i
$355$	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	0.525276	−	0.850932i	$-0.323962\pi$
$359$	0.966053	+	0.557751i	0.0509863	+	0.0294370i	−0.474290	+	0.880369i	$0.657295\pi$
$360$	−4.52313	+	1.59888i	−0.238390	+	0.0842685i
$361$	8.86932	+	15.3621i	0.466806	+	0.808532i
$362$	−7.64624	+	3.81050i	−0.401877	+	0.200275i
$363$	1.87689			0.0985114
$364$		0			0
$365$	−5.75379			−0.301167
$366$	−11.9400	+	5.95029i	−0.624114	+	0.311027i
$367$	−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	$0.905656\pi$
$368$	2.93158	−	11.7207i	0.152819	−	0.610985i
$369$	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	$0.0833099\pi$
$374$	18.5240	+	1.13644i	0.957856	+	0.0587640i
$375$	10.4631	−	6.04090i	0.540314	−	0.311951i
$376$	18.8337	−	22.0265i	0.971276	−	1.13593i
$377$			12.0818i			0.622244i
$378$		0			0
$379$		−	18.7033i		−	0.960725i	−0.877070	−	0.480363i	$-0.840505\pi$
$379$		−	18.7033i		−	0.960725i	0.877070	−	0.480363i	$-0.159495\pi$
$380$	−0.465718	+	3.78132i	−0.0238908	+	0.193978i
$381$	−16.8416	+	9.72350i	−0.862821	+	0.498150i
$382$	0.784700	−	12.7906i	0.0401487	−	0.654425i
$383$	−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
$388$	−13.8756	−	10.4641i	−0.704427	−	0.531235i
$389$	−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	$0.835320\pi$
$390$	6.46314	+	12.9691i	0.327274	+	0.656716i
$391$	13.1231			0.663664
$392$		0			0
$393$	−22.2462			−1.12217
$394$	0.155306	+	0.311641i	0.00782420	+	0.0157002i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	−4.82312	−	3.63730i	−0.242371	−	0.182781i
$397$	−14.0450	−	8.10887i	−0.704897	−	0.406973i	0.104272	−	0.994549i	$-0.466749\pi$
$397$	−14.0450	−	8.10887i	−0.704897	−	0.406973i	−0.809169	+	0.587576i	$0.800082\pi$
$398$	−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	$0.100655\pi$
$402$	0.179084	−	2.91907i	0.00893188	−	0.145590i
$403$		0			0
$404$	1.70973	−	13.8818i	0.0850620	−	0.690648i
$405$			1.69614i			0.0842819i
$406$		0			0
$407$		−	21.5150i		−	1.06646i
$408$	9.34003	+	7.98617i	0.462401	+	0.395374i
$409$	23.8641	−	13.7779i	1.18000	−	0.681275i	0.223988	−	0.974592i	$-0.428092\pi$
$409$	23.8641	−	13.7779i	1.18000	−	0.681275i	0.956015	+	0.293317i	$0.0947592\pi$
$410$	−18.5240	−	1.13644i	−0.914837	−	0.0561249i
$411$	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
$416$	−23.0631	−	25.2161i	−1.13076	−	1.23632i
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$	−4.29377	+	2.13979i	−0.210015	+	0.104661i
$419$	−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	$0.345694\pi$
$422$	−5.02871	+	2.50605i	−0.244794	+	0.121993i
$423$	−5.12311	−	8.87348i	−0.249094	−	0.431443i
$424$	−4.00273	−	11.3235i	−0.194390	−	0.549916i
$425$	−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
$430$	−19.4143	−	1.19106i	−0.936240	−	0.0574379i
$431$	−13.0789	+	7.55112i	−0.629990	+	0.363725i	−0.780748	−	0.624846i	$-0.785162\pi$
$431$	−13.0789	+	7.55112i	−0.629990	+	0.363725i	0.150758	+	0.988571i	$0.451828\pi$
$432$	−1.09968	−	3.84587i	−0.0529086	−	0.185034i
$433$		−	6.78456i		−	0.326045i	−0.986622	−	0.163023i	$-0.947876\pi$
$433$		−	6.78456i		−	0.326045i	0.986622	−	0.163023i	$-0.0521244\pi$
$434$		0			0
$435$		−	3.39228i		−	0.162647i
$436$	16.3687	+	2.01602i	0.783921	+	0.0965498i
$437$	−2.93780	+	1.69614i	−0.140534	+	0.0811374i
$438$	0.293767	−	4.78841i	0.0140367	−	0.228799i
$439$	−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	−0.476422	−	0.879217i	$-0.658066\pi$
$443$	−31.0674	−	17.9368i	−1.47606	−	0.852202i	−0.999635	+	0.0270153i	$0.991400\pi$
$444$	8.57782	−	11.3743i	0.407085	−	0.539802i
$445$	6.56155	+	11.3649i	0.311047	+	0.538750i
$446$	−11.9072	−	23.8934i	−0.563824	−	1.13138i
$447$	−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	$0.267787\pi$
$450$	1.33922	+	2.68731i	0.0631314	+	0.126681i
$451$	−11.6847	−	20.2384i	−0.550209	−	0.952990i
$452$	−14.7472	+	19.5550i	−0.693650	+	0.919791i
$453$	−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	$0.0425966\pi$
$458$	−1.56940	+	25.5813i	−0.0733332	+	1.19533i
$459$	3.76267	−	2.17238i	0.175626	−	0.101398i
$460$	10.1694	+	1.25249i	0.474149	+	0.0583975i
$461$		−	17.1702i		−	0.799697i	−0.916581	−	0.399848i	$-0.869063\pi$
$461$		−	17.1702i		−	0.799697i	0.916581	−	0.399848i	$-0.130937\pi$
$462$		0			0
$463$			39.4746i			1.83454i	0.398264	+	0.917271i	$0.369613\pi$
$463$			39.4746i			1.83454i	−0.398264	+	0.917271i	$0.630387\pi$
$464$	2.19937	+	7.69173i	0.102103	+	0.357080i
$465$		0			0
$466$	14.8107	+	0.908629i	0.686092	+	0.0420914i
$467$	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
$472$	−3.77063	−	10.6669i	−0.173557	−	0.490983i
$473$	−12.2462	−	21.2111i	−0.563081	−	0.975286i
$474$	−5.97000	+	2.97515i	−0.274211	+	0.136653i
$475$	2.38447			0.109407
$476$		0			0
$477$	−4.24621			−0.194421
$478$	−2.88182	+	1.43615i	−0.131812	+	0.0656882i
$479$	−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	$0.988417\pi$
$480$	6.47558	+	7.08008i	0.295568	+	0.323160i
$481$	−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
$486$	−1.41156	−	0.0865986i	−0.0640296	−	0.00392819i
$487$	27.9488	−	16.1362i	1.26648	−	0.731202i	0.292159	−	0.956370i	$-0.405626\pi$
$487$	27.9488	−	16.1362i	1.26648	−	0.731202i	0.974320	+	0.225167i	$0.0722929\pi$
$488$	20.2787	+	17.3393i	0.917976	+	0.784913i
$489$		−	11.5012i		−	0.520100i
$490$		0			0
$491$			11.7100i			0.528463i	0.964459	+	0.264231i	$0.0851183\pi$
$491$			11.7100i			0.528463i	−0.964459	+	0.264231i	$0.914882\pi$
$492$	1.89154	−	15.3580i	0.0852770	−	0.692393i
$493$	−7.52534	+	4.34475i	−0.338924	+	0.195678i
$494$	−0.587534	+	9.57682i	−0.0264344	+	0.430881i
$495$	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	0.119805	−	0.992797i	$-0.461773\pi$
$499$	−15.1919	−	8.77102i	−0.680081	−	0.392645i	−0.799886	+	0.600153i	$0.795107\pi$
$500$	−19.2925	−	14.5492i	−0.862786	−	0.650660i
$501$	−1.12311	−	1.94528i	−0.0501767	−	0.0869085i
$502$	14.0325	+	28.1580i	0.626303	+	1.25676i
$503$	−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
$506$	5.75470	+	11.5475i	0.255828	+	0.513350i
$507$	11.7462	+	20.3450i	0.521668	+	0.903555i
$508$	31.0534	+	23.4186i	1.37777	+	1.03903i
$509$	1.46890	+	0.848071i	0.0651079	+	0.0375901i	0.532201	−	0.846618i	$-0.321365\pi$
$509$	1.46890	+	0.848071i	0.0651079	+	0.0375901i	−0.467093	+	0.884208i	$0.654699\pi$
$510$	−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
$514$	−1.71628	+	27.9755i	−0.0757020	+	1.23394i
$515$	11.7512	−	6.78456i	0.517820	−	0.298964i
$516$	1.98244	−	16.0961i	0.0872721	−	0.708592i
$517$			30.9481i			1.36110i
$518$		0			0
$519$		−	8.48071i		−	0.372262i
$520$	18.8337	−	22.0265i	0.825914	−	0.965928i
$521$	−29.2765	+	16.9028i	−1.28263	+	0.740524i	−0.977328	−	0.211732i	$-0.932089\pi$
$521$	−29.2765	+	16.9028i	−1.28263	+	0.740524i	−0.305298	+	0.952257i	$0.598756\pi$
$522$	2.82312	+	0.173197i	0.123565	+	0.00758063i
$523$	−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
$528$	−2.93158	+	11.7207i	−0.127581	+	0.510079i
$529$	−6.93845	−	12.0177i	−0.301672	−	0.522511i
$530$	9.11612	−	4.54301i	0.395979	−	0.197336i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−46.7386			−2.02447
$534$	−9.79312	+	4.88039i	−0.423790	+	0.211195i
$535$	−4.80776	−	8.32729i	−0.207858	−	0.360020i
$536$	−5.51471	+	1.94939i	−0.238199	+	0.0842010i
$537$	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	$0.243522\pi$
$542$	6.34132	+	0.389037i	0.272383	+	0.0167106i
$543$	5.23157	−	3.02045i	0.224508	−	0.129620i
$544$	7.41247	−	23.4332i	0.317807	−	1.00469i
$545$			13.9867i			0.599126i
$546$		0			0
$547$			33.0161i			1.41167i	0.708378	+	0.705834i	$0.249427\pi$
$547$			33.0161i			1.41167i	−0.708378	+	0.705834i	$0.750573\pi$
$548$	−32.2488	−	3.97184i	−1.37760	−	0.169669i
$549$	8.16937	−	4.71659i	0.348660	−	0.201299i
$550$	0.555333	−	9.05195i	0.0236795	−	0.385976i
$551$	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
$556$	−14.4507	+	19.1619i	−0.612846	+	0.812644i
$557$	−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
$562$	−0.155306	−	0.311641i	−0.00655119	−	0.0131458i
$563$	−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	$0.930388\pi$
$564$	−12.3387	+	16.3614i	−0.519555	+	0.688938i
$565$	−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	$0.904636\pi$
$570$	0.164966	−	2.68894i	0.00690965	−	0.112627i
$571$	−35.4741	+	20.4810i	−1.48454	+	0.857102i	−0.999845	−	0.0175783i	$-0.994404\pi$
$571$	−35.4741	+	20.4810i	−1.48454	+	0.857102i	−0.484699	+	0.874681i	$0.661071\pi$
$572$	36.2188	+	4.46080i	1.51438	+	0.186515i
$573$			9.06134i			0.378543i
$574$		0			0
$575$		−	6.41273i		−	0.267429i
$576$	−6.22279	+	5.02761i	−0.259283	+	0.209484i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	2.64935	+	0.162536i	0.110198	+	0.00676062i
$579$	−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
$584$	−9.04627	+	3.19776i	−0.374337	+	0.132324i
$585$	−5.12311	−	8.87348i	−0.211814	−	0.366873i
$586$	8.85183	−	4.41130i	0.365666	−	0.182229i
$587$	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
$590$	8.58753	−	4.27959i	0.353543	−	0.176188i
$591$	−0.123106	−	0.213225i	−0.00506389	−	0.00877091i
$592$	−27.6409	−	6.91354i	−1.13604	−	0.284145i
$593$	−18.8133	−	10.8619i	−0.772571	−	0.446044i	0.0612198	−	0.998124i	$-0.480501\pi$
$593$	−18.8133	−	10.8619i	−0.772571	−	0.446044i	−0.833791	+	0.552080i	$0.813834\pi$
$594$	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
$598$	25.7556	+	1.58010i	1.05323	+	0.0646149i
$599$	16.6608	−	9.61909i	0.680740	−	0.393026i	−0.119394	−	0.992847i	$-0.538095\pi$
$599$	16.6608	−	9.61909i	0.680740	−	0.393026i	0.800134	+	0.599821i	$0.204762\pi$
$600$	3.90252	−	4.56410i	0.159320	−	0.186328i
$601$			5.29723i			0.216078i	0.994147	+	0.108039i	$0.0344572\pi$
$601$			5.29723i			0.216078i	−0.994147	+	0.108039i	$0.965543\pi$
$602$		0			0
$603$			2.06798i			0.0842145i
$604$	−1.98244	+	16.0961i	−0.0806644	+	0.654942i
$605$	2.75697	−	1.59174i	0.112087	−	0.0647134i
$606$	−0.605616	+	9.87156i	−0.0246015	+	0.401005i
$607$	−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
$612$	−6.93780	−	5.23206i	−0.280444	−	0.211494i
$613$	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	$0.525795\pi$
$614$	13.6347	+	27.3598i	0.550252	+	1.10415i
$615$	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	$0.397287\pi$
$618$	5.04627	+	10.1260i	0.202991	+	0.407326i
$619$	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
$626$	−2.22133	+	36.2078i	−0.0887823	+	1.44715i
$627$	2.93780	−	1.69614i	0.117325	−	0.0677373i
$628$	1.01115	−	8.20987i	0.0403493	−	0.327609i
$629$		−	30.9481i		−	1.23398i
$630$		0			0
$631$		−	17.9597i		−	0.714963i	−0.933920	−	0.357481i	$-0.883636\pi$
$631$		−	17.9597i		−	0.714963i	0.933920	−	0.357481i	$-0.116364\pi$
$632$	10.1394	+	8.66965i	0.403323	+	0.344860i
$633$	3.44065	−	1.98646i	0.136754	−	0.0789547i
$634$	−26.1032	−	1.60142i	−1.03669	−	0.0636004i
$635$	−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
$640$	7.98058	−	17.4514i	0.315460	−	0.689829i
$641$	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	$0.773210\pi$
$642$	7.17559	−	3.57595i	0.283198	−	0.141131i
$643$	−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
$646$	−6.17636	+	3.07798i	−0.243006	+	0.121102i
$647$	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	$0.608778\pi$
$648$	0.942658	+	2.66672i	0.0370311	+	0.104759i
$649$	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	$-0.0546397\pi$
$654$	−11.6400	−	0.714110i	−0.455161	−	0.0279239i
$655$	−32.6775	+	18.8664i	−1.27682	+	0.737170i
$656$	−29.7556	+	8.50830i	−1.16176	+	0.332193i
$657$			3.39228i			0.132346i
$658$		0			0
$659$		−	38.1045i		−	1.48434i	−0.670210	−	0.742171i	$-0.733796\pi$
$659$		−	38.1045i		−	1.48434i	0.670210	−	0.742171i	$-0.266204\pi$
$660$	−10.1694	−	1.25249i	−0.395842	−	0.0487530i
$661$	−2.29377	+	1.32431i	−0.0892172	+	0.0515096i	−0.543945	−	0.839121i	$-0.683070\pi$
$661$	−2.29377	+	1.32431i	−0.0892172	+	0.0515096i	0.454728	+	0.890631i	$0.349737\pi$
$662$	0.472851	−	7.70748i	0.0183779	−	0.299560i
$663$	−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
$668$	−2.70494	+	3.58680i	−0.104657	+	0.138777i
$669$	9.43845	+	16.3479i	0.364911	+	0.632045i
$670$	−2.21252	−	4.43970i	−0.0854771	−	0.171521i
$671$	−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	$0.304791\pi$
$674$	−5.20157	−	10.4376i	−0.200357	−	0.402042i
$675$	−1.06155	−	1.83866i	−0.0408592	−	0.0707702i
$676$	28.2902	−	37.5132i	1.08808	−	1.44282i
$677$	−28.2708	−	16.3221i	−1.08653	−	0.627311i	−0.153883	−	0.988089i	$-0.549178\pi$
$677$	−28.2708	−	16.3221i	−1.08653	−	0.627311i	−0.932652	+	0.360778i	$0.882511\pi$
$678$	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	0.0665546	−	0.997783i	$-0.478799\pi$
$683$	25.1918	−	14.5445i	0.963937	−	0.556529i	0.897383	+	0.441253i	$0.145466\pi$
$684$	2.22937	+	0.274575i	0.0852419	+	0.0104986i
$685$		−	27.5559i		−	1.05286i
$686$		0			0
$687$		−	18.1227i		−	0.691424i
$688$	−31.1856	+	8.91720i	−1.18894	+	0.339965i
$689$	22.2143	−	12.8255i	0.846299	−	0.488611i
$690$	−7.23157	−	0.443654i	−0.275301	−	0.0168896i
$691$	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
$696$	−1.88532	−	5.33344i	−0.0714628	−	0.202164i
$697$	−16.8078	−	29.1119i	−0.636639	−	1.10269i
$698$	5.23506	−	2.60889i	0.198150	−	0.0987479i
$699$	−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	$0.721929\pi$
$702$	7.64624	−	3.81050i	0.288589	−	0.143818i
$703$	4.00000	+	6.92820i	0.150863	+	0.261302i
$704$	23.8703	−	3.75334i	0.899646	−	0.141459i
$705$	−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	$0.202606\pi$
$710$	29.8165	+	1.82923i	1.11899	+	0.0686498i
$711$	4.08469	−	2.35829i	0.153188	−	0.0884430i
$712$	16.6325	+	14.2216i	0.623330	+	0.532976i
$713$		0			0
$714$		0			0
$715$			30.9481i			1.15740i
$716$	0.556623	−	4.51941i	0.0208020	−	0.168898i
$717$	1.97175	−	1.13839i	0.0736363	−	0.0425139i
$718$	−0.0966009	+	1.57460i	−0.00360511	+	0.0587635i
$719$	−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
$724$	−9.64624	−	7.27460i	−0.358500	−	0.270358i
$725$	2.12311	+	3.67733i	0.0788502	+	0.136572i
$726$	1.18391	+	2.37567i	0.0439392	+	0.0881694i
$727$	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
$730$	−3.62939	−	7.28283i	−0.134330	−	0.269550i
$731$	−17.6155	−	30.5110i	−0.651534	−	1.12849i
$732$	−15.0631	−	11.3597i	−0.556749	−	0.419865i
$733$	14.4066	+	8.31768i	0.532121	+	0.307220i	0.741880	−	0.670533i	$-0.233934\pi$
$733$	14.4066	+	8.31768i	0.532121	+	0.307220i	−0.209759	+	0.977753i	$0.567268\pi$
$734$	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
$738$	−0.670016	+	10.9213i	−0.0246636	+	0.402018i
$739$	5.09038	−	2.93893i	0.187253	−	0.108110i	−0.403443	−	0.915005i	$-0.632187\pi$
$739$	5.09038	−	2.93893i	0.187253	−	0.108110i	0.590696	+	0.806894i	$0.298853\pi$
$740$	2.95373	−	23.9824i	0.108581	−	0.881610i
$741$		−	6.78456i		−	0.249237i
$742$		0			0
$743$		−	13.6149i		−	0.499482i	−0.968313	−	0.249741i	$-0.919654\pi$
$743$		−	13.6149i		−	0.499482i	0.968313	−	0.249741i	$-0.0803455\pi$
$744$		0			0
$745$	−14.6890	+	8.48071i	−0.538164	+	0.310709i
$746$	14.1156	+	0.865986i	0.516809	+	0.0317060i
$747$	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	−0.0727548	−	0.997350i	$-0.523179\pi$
$751$	−26.6607	−	15.3926i	−0.972863	−	0.561682i	−0.900108	+	0.435667i	$0.856512\pi$
$752$	39.7600	+	9.94476i	1.44990	+	0.362648i
$753$	−11.1231	−	19.2658i	−0.405349	−	0.702084i
$754$	−15.2925	+	7.62099i	−0.556919	+	0.277540i
$755$	−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	$0.309616\pi$
$758$	23.6737	−	11.7977i	0.859866	−	0.428513i
$759$	−4.56155	−	7.90084i	−0.165574	−	0.286782i
$760$	−5.07996	+	1.79571i	−0.184269	+	0.0651374i
$761$	−29.2765	−	16.9028i	−1.06127	−	0.612725i	−0.135488	−	0.990779i	$-0.543260\pi$
$761$	−29.2765	−	16.9028i	−1.06127	−	0.612725i	−0.925784	+	0.378054i	$0.876593\pi$
$762$	−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
$766$	−37.0481	−	2.27288i	−1.33860	−	0.0821227i
$767$	20.9263	−	12.0818i	0.755604	−	0.436248i
$768$	14.1160	+	7.53259i	0.509366	+	0.271809i
$769$		−	44.5173i		−	1.60533i	−0.596427	−	0.802667i	$-0.703414\pi$
$769$		−	44.5173i		−	1.60533i	0.596427	−	0.802667i	$-0.296586\pi$
$770$		0			0
$771$		−	19.8188i		−	0.713758i
$772$	18.5981	+	2.29059i	0.669361	+	0.0824403i
$773$	1.46890	−	0.848071i	0.0528327	−	0.0305030i	−0.473351	−	0.880874i	$-0.656956\pi$
$773$	1.46890	−	0.848071i	0.0528327	−	0.0305030i	0.526184	+	0.850371i	$0.323622\pi$
$774$	−0.702217	+	11.4462i	−0.0252407	+	0.411424i
$775$		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
$780$	−12.3387	+	16.3614i	−0.441798	+	0.585831i
$781$	18.8078	+	32.5760i	0.672995	+	1.16566i
$782$	8.27784	+	16.6105i	0.296015	+	0.593991i
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	7.01515			0.250382
$786$	−14.0325	−	28.1580i	−0.500524	−	1.00436i
$787$	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	$0.711314\pi$
$788$	−0.296494	+	0.393156i	−0.0105622	+	0.0140056i
$789$	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
$794$	1.40443	−	22.8923i	0.0498415	−	0.812418i
$795$	−6.23726	+	3.60109i	−0.221213	+	0.127717i
$796$	−10.1694	−	1.25249i	−0.360444	−	0.0443932i
$797$			34.1316i			1.20900i	0.796604	+	0.604502i	$0.206628\pi$
$797$			34.1316i			1.20900i	−0.796604	+	0.604502i	$0.793372\pi$
$798$		0			0
$799$			44.5173i			1.57491i
$800$	−11.4509	−	3.62217i	−0.404849	−	0.128063i
$801$	6.70047	−	3.86852i	0.236749	−	0.136687i
$802$	11.6400	+	0.714110i	0.411023	+	0.0252161i
$803$	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
$808$	18.6494	−	6.59236i	0.656082	−	0.231918i
$809$	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	$0.774284\pi$
$810$	−2.14688	+	1.06990i	−0.0754338	+	0.0375924i
$811$	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
$814$	27.2325	−	13.5713i	0.954498	−	0.475673i
$815$	−9.75379	−	16.8941i	−0.341660	−	0.591773i
$816$	−4.21693	+	16.8597i	−0.147622	+	0.590206i
$817$	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	$0.311789\pi$
$822$	22.9325	+	1.40690i	0.799863	+	0.0490712i
$823$	−39.0559	+	22.5490i	−1.36140	+	0.786007i	−0.989811	−	0.142388i	$-0.954522\pi$
$823$	−39.0559	+	22.5490i	−1.36140	+	0.786007i	−0.371594	+	0.928396i	$0.621189\pi$
$824$	14.7049	−	17.1978i	0.512271	−	0.599114i
$825$			6.41273i			0.223263i
$826$		0			0
$827$			30.9939i			1.07776i	0.842381	+	0.538882i	$0.181153\pi$
$827$			30.9939i			1.07776i	−0.842381	+	0.538882i	$0.818847\pi$
$828$	0.738433	−	5.99559i	0.0256623	−	0.208361i
$829$	27.4459	−	15.8459i	0.953236	−	0.550351i	0.0591514	−	0.998249i	$-0.481161\pi$
$829$	27.4459	−	15.8459i	0.953236	−	0.550351i	0.894085	+	0.447898i	$0.147827\pi$
$830$	−0.917465	+	14.9547i	−0.0318457	+	0.519085i
$831$	−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
$836$	−5.41687	−	4.08507i	−0.187346	−	0.141285i
$837$		0			0
$838$	−10.4031	−	20.8752i	−0.359371	−	0.721122i
$839$	−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
$842$	12.0625	+	24.2050i	0.415702	+	0.834159i
$843$	0.123106	+	0.213225i	0.00423998	+	0.00734387i
$844$	−6.34405	−	4.78429i	−0.218371	−	0.164682i
$845$	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
$850$	0.798818	−	13.0208i	0.0273992	−	0.446608i
$851$	18.6325	−	10.7575i	0.638714	−	0.368762i
$852$	−3.04464	+	24.7205i	−0.104308	+	0.846909i
$853$		−	37.4067i		−	1.28078i	−0.768050	−	0.640390i	$-0.778773\pi$
$853$		−	37.4067i		−	1.28078i	0.768050	−	0.640390i	$-0.221227\pi$
$854$		0			0
$855$			1.90495i			0.0651478i
$856$	−12.1869	−	10.4204i	−0.416541	−	0.356162i
$857$	17.5253	−	10.1182i	0.598652	−	0.345632i	−0.169859	−	0.985468i	$-0.554331\pi$
$857$	17.5253	−	10.1182i	0.598652	−	0.345632i	0.768511	+	0.639837i	$0.220998\pi$
$858$	−25.7556	−	1.58010i	−0.879282	−	0.0539436i
$859$	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	0.786622	−	0.617434i	$-0.211828\pi$
$863$	18.9545	+	10.9434i	0.645220	+	0.372518i	−0.141403	+	0.989952i	$0.545161\pi$
$864$	4.17423	−	3.81783i	0.142010	−	0.129885i
$865$	−7.19224	−	12.4573i	−0.244543	−	0.423562i
$866$	8.58753	−	4.27959i	0.291816	−	0.145426i
$867$	−1.87689			−0.0637427
$868$		0			0
$869$	−14.2462			−0.483270
$870$	4.29377	−	2.13979i	0.145572	−	0.0725458i
$871$	−6.24621	−	10.8188i	−0.211645	−	0.366580i
$872$	7.77336	+	21.9903i	0.263239	+	0.744687i
$873$	−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	$0.274903\pi$
$878$	−44.2797	−	2.71654i	−1.49437	−	0.0916787i
$879$	−6.05643	+	3.49668i	−0.204278	+	0.117940i
$880$	5.63380	+	19.7028i	0.189915	+	0.664181i
$881$		−	39.1028i		−	1.31741i	−0.752403	−	0.658703i	$-0.771105\pi$
$881$		−	39.1028i		−	1.31741i	0.752403	−	0.658703i	$-0.228895\pi$
$882$		0			0
$883$		−	26.9752i		−	0.907789i	−0.891056	−	0.453894i	$-0.850034\pi$
$883$		−	26.9752i		−	0.907789i	0.891056	−	0.453894i	$-0.149966\pi$
$884$	52.0988	+	6.41662i	1.75227	+	0.215814i
$885$	−5.87560	+	3.39228i	−0.197506	+	0.114030i
$886$	3.10660	−	50.6376i	0.104368	−	1.70120i
$887$	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
$892$	22.7320	−	30.1431i	0.761125	−	1.00926i
$893$	−5.75379	−	9.96585i	−0.192543	−	0.333495i
$894$	−6.30783	−	12.6575i	−0.210965	−	0.423329i
$895$	3.86174			0.129084
$896$		0			0
$897$	−18.2462			−0.609223
$898$	17.8172	+	35.7525i	0.594569	+	1.19308i
$899$		0			0
$900$	−2.55670	+	3.39022i	−0.0852232	+	0.113007i
$901$	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
$906$	0.702217	−	11.4462i	0.0233296	−	0.380273i
$907$	−10.3220	+	5.95938i	−0.342735	+	0.197878i	−0.661481	−	0.749962i	$-0.730072\pi$
$907$	−10.3220	+	5.95938i	−0.342735	+	0.197878i	0.318746	+	0.947840i	$0.396738\pi$
$908$	−32.7375	−	4.03204i	−1.08643	−	0.133808i
$909$		−	6.99337i		−	0.231955i
$910$		0			0
$911$		−	6.41273i		−	0.212463i	−0.994341	−	0.106232i	$-0.966122\pi$
$911$		−	6.41273i		−	0.212463i	0.994341	−	0.106232i	$-0.0338785\pi$
$912$	−1.23506	−	4.31932i	−0.0408970	−	0.143027i
$913$	−16.3387	+	9.43318i	−0.540733	+	0.312193i
$914$	22.9325	+	1.40690i	0.758540	+	0.0465361i
$915$	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	0.379683	−	0.925117i	$-0.376033\pi$
$919$	−7.02249	−	4.05444i	−0.231651	−	0.133743i	−0.611333	+	0.791373i	$0.709366\pi$
$920$	4.82934	+	13.6619i	0.159219	+	0.450419i
$921$	−10.8078	−	18.7196i	−0.356128	−	0.616832i
$922$	21.7331	−	10.8307i	0.715742	−	0.356690i
$923$	75.2311			2.47626
$924$		0			0
$925$	−15.1231			−0.497245
$926$	−49.9648	+	24.8999i	−1.64195	+	0.818263i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	−8.34846	+	7.63566i	−0.274051	+	0.250653i
$929$	43.9655	+	25.3835i	1.44246	+	0.832805i	0.998014	−	0.0629997i	$-0.0200667\pi$
$929$	43.9655	+	25.3835i	1.44246	+	0.832805i	0.444447	+	0.895805i	$0.353400\pi$
$930$		0			0
$931$		0			0
$932$	8.19224	+	19.3197i	0.268346	+	0.632838i
$933$	4.00000	−	6.92820i	0.130954	−	0.226819i
$934$	25.0605	+	1.53745i	0.820006	+	0.0503070i
$935$	−19.2765	+	11.1293i	−0.630410	+	0.363968i
$936$	−12.9863	−	11.1039i	−0.424470	−	0.362942i
$937$			56.5991i			1.84901i	0.381169	+	0.924505i	$0.375522\pi$
$937$			56.5991i			1.84901i	−0.381169	+	0.924505i	$0.624478\pi$
$938$		0			0
$939$		−	25.6509i		−	0.837086i
$940$	−4.24879	+	34.4974i	−0.138580	+	1.12518i
$941$	−11.5704	+	6.68016i	−0.377184	+	0.217767i	−0.676592	−	0.736358i	$-0.736544\pi$
$941$	−11.5704	+	6.68016i	−0.377184	+	0.217767i	0.299409	+	0.954125i	$0.403211\pi$
$942$	−0.358167	+	5.83814i	−0.0116697	+	0.190217i
$943$	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	−0.230715	−	0.973021i	$-0.574107\pi$
$947$	−36.5813	−	21.1202i	−1.18873	−	0.686316i	−0.958019	+	0.286705i	$0.907440\pi$
$948$	−7.53156	−	5.67983i	−0.244614	−	0.184472i
$949$	−10.2462	−	17.7470i	−0.332606	−	0.576091i
$950$	1.50408	+	3.01814i	0.0487990	+	0.0979212i
$951$	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	$0.0409549\pi$
$954$	−2.67844	−	5.37462i	−0.0867177	−	0.174010i
$955$	7.68466	+	13.3102i	0.248670	+	0.430709i
$956$	−3.63561	−	2.74175i	−0.117584	−	0.0886747i
$957$	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
$962$	3.72633	−	60.7393i	0.120142	−	1.95831i
$963$	−4.90955	+	2.83453i	−0.158208	+	0.0913415i
$964$	0.465718	−	3.78132i	0.0149998	−	0.121788i
$965$			15.8917i			0.511571i
$966$		0			0
$967$			40.9620i			1.31725i	0.752472	+	0.658624i	$0.228861\pi$
$967$			40.9620i			1.31725i	−0.752472	+	0.658624i	$0.771139\pi$
$968$	3.44995	−	4.03481i	0.110886	−	0.129684i
$969$	4.22587	−	2.43981i	0.135755	−	0.0783780i
$970$	20.8045	+	1.27634i	0.667991	+	0.0409810i
$971$	−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
$976$	−9.15564	+	36.6051i	−0.293065	+	1.17170i
$977$	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	$0.409375\pi$
$978$	14.5575	−	7.25473i	0.465499	−	0.231981i
$979$	−23.3693			−0.746887
$980$		0			0
$981$	8.24621			0.263281
$982$	−14.8218	+	7.38645i	−0.472984	+	0.235711i
$983$	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	$0.495540\pi$
$984$	20.6325	−	7.29338i	0.657740	−	0.232505i
$985$	−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
$990$	7.23157	+	0.443654i	0.229834	+	0.0141002i
$991$	−9.31626	+	5.37874i	−0.295941	+	0.170861i	−0.640618	−	0.767860i	$-0.721322\pi$
$991$	−9.31626	+	5.37874i	−0.295941	+	0.170861i	0.344677	+	0.938721i	$0.387988\pi$
$992$		0			0
$993$			5.46026i			0.173276i
$994$		0			0
$995$		−	8.68951i		−	0.275476i
$996$	−12.3987	−	1.52706i	−0.392869	−	0.0483868i
$997$	33.6832	−	19.4470i	1.06676	−	0.615892i	0.139463	−	0.990227i	$-0.455462\pi$
$997$	33.6832	−	19.4470i	1.06676	−	0.615892i	0.927294	+	0.374335i	$0.122129\pi$
$998$	1.51912	−	24.7616i	0.0480868	−	0.783816i
$999$	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.19.3		8
4.3	odd	2		588.2.o.c.19.1		8
7.2	even	3		84.2.b.b.55.3	yes	4
7.3	odd	6		588.2.o.c.31.1		8
7.4	even	3	inner	588.2.o.a.31.1		8
7.5	odd	6		84.2.b.a.55.3	✓	4
7.6	odd	2		588.2.o.c.19.3		8
21.2	odd	6		252.2.b.d.55.2		4
21.5	even	6		252.2.b.e.55.2		4
28.3	even	6	inner	588.2.o.a.31.3		8
28.11	odd	6		588.2.o.c.31.3		8
28.19	even	6		84.2.b.b.55.4	yes	4
28.23	odd	6		84.2.b.a.55.4	yes	4
28.27	even	2	inner	588.2.o.a.19.1		8
56.5	odd	6		1344.2.b.f.895.3		4
56.19	even	6		1344.2.b.e.895.3		4
56.37	even	6		1344.2.b.e.895.2		4
56.51	odd	6		1344.2.b.f.895.2		4
84.23	even	6		252.2.b.e.55.1		4
84.47	odd	6		252.2.b.d.55.1		4
168.5	even	6		4032.2.b.n.3583.2		4
168.107	even	6		4032.2.b.n.3583.3		4
168.131	odd	6		4032.2.b.j.3583.2		4
168.149	odd	6		4032.2.b.j.3583.3		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.630783 + 1.26575i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.20422 + 1.59682i) q^{4} +(-1.46890 - 0.848071i) q^{5} +(0.780776 - 1.17915i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.630783 + 1.26575i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.20422 + 1.59682i) 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} +(0.146883 - 2.39420i) q^{10} +(2.61578 - 1.51022i) q^{11} +(1.98500 + 0.244478i) q^{12} -6.04090i q^{13} +1.69614i q^{15} +(-1.09968 - 3.84587i) q^{16} +(3.76267 - 2.17238i) q^{17} +(-1.41156 - 0.0865986i) 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} +(0.942658 + 2.66672i) q^{24} +(-1.06155 - 1.83866i) q^{25} +(7.64624 - 3.81050i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-2.14688 + 1.06990i) q^{30} +(4.17423 - 3.81783i) 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} +(-1.58533 - 0.0972594i) q^{38} +(-5.23157 + 3.02045i) q^{39} +(3.64624 + 3.11771i) q^{40} -7.73704i q^{41} -8.10887i q^{43} +(-0.738433 + 5.99559i) q^{44} +(1.46890 - 0.848071i) q^{45} +(-0.261567 + 4.26354i) 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} +(9.64624 + 7.27460i) q^{52} +(2.12311 + 3.67733i) q^{53} +(0.630783 + 1.26575i) q^{54} -5.12311 q^{55} +1.12311 q^{57} +(-1.26157 - 2.53149i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-2.70844 - 2.04254i) q^{60} +(-8.16937 - 4.71659i) q^{61} +(7.46543 + 2.87529i) q^{64} +(-5.12311 + 8.87348i) q^{65} +(0.261567 - 4.26354i) q^{66} +(1.79092 - 1.03399i) q^{67} +(-1.06220 + 8.62434i) q^{68} -3.02045i q^{69} +12.4536i q^{71} +(1.83812 - 2.14973i) q^{72} +(2.93780 - 1.69614i) q^{73} +(10.0547 + 0.616851i) 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} +(-1.64624 + 6.58181i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.79312 - 4.88039i) q^{82} -6.24621 q^{83} -7.36932 q^{85} +(10.2638 - 5.11494i) q^{86} +(1.00000 + 1.73205i) q^{87} +(-8.05469 + 2.84725i) q^{88} +(-6.70047 - 3.86852i) q^{89} +(2.00000 + 1.32431i) q^{90} +(-5.56155 + 2.35829i) q^{92} +(-14.4631 - 0.887307i) q^{94} +(1.64973 - 0.952473i) q^{95} +(-5.39345 - 1.70607i) 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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