LMFDB - Embedded newform 735.2.s.k.656.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(521,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("735.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.s (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.3
Root			$-0.385731i$ of defining polynomial
Character	$\chi$	$=$	735.656
Dual form			735.2.s.k.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.334053 - 0.192865i) q^{2} +(-1.42561 - 0.983691i) q^{3} +(-0.925606 - 1.60320i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.286507 + 0.603555i) q^{6} +1.48553i q^{8} +(1.06470 + 2.80471i) q^{9} +O(q^{10})$	\(q+(-0.334053 - 0.192865i) q^{2} +(-1.42561 - 0.983691i) q^{3} +(-0.925606 - 1.60320i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.286507 + 0.603555i) q^{6} +1.48553i q^{8} +(1.06470 + 2.80471i) q^{9} +(0.334053 - 0.192865i) q^{10} +(-2.20164 + 1.27112i) q^{11} +(-0.257501 + 3.19604i) q^{12} -3.06718i q^{13} +(1.56470 - 0.742765i) q^{15} +(-1.56470 + 2.71015i) q^{16} +(3.23065 + 5.59565i) q^{17} +(0.185264 - 1.14227i) q^{18} +(1.03570 + 0.597960i) q^{19} +1.85121 q^{20} +0.980620 q^{22} +(-2.64657 - 1.52800i) q^{23} +(1.46130 - 2.11778i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.591553 + 1.02460i) q^{26} +(1.24112 - 5.04575i) q^{27} +7.77029i q^{29} +(-0.665947 - 0.0536545i) q^{30} +(5.95299 - 3.43696i) q^{31} +(3.61840 - 2.08909i) q^{32} +(4.38907 + 0.353622i) q^{33} -2.49232i q^{34} +(3.51101 - 4.30299i) q^{36} +(1.77604 - 3.07619i) q^{37} +(-0.230652 - 0.399500i) q^{38} +(-3.01716 + 4.37259i) q^{39} +(-1.28651 - 0.742765i) q^{40} -2.31252 q^{41} +5.46130 q^{43} +(4.07571 + 2.35311i) q^{44} +(-2.96130 - 0.480295i) q^{45} +(0.589395 + 1.02086i) q^{46} +(1.61009 - 2.78876i) q^{47} +(4.89660 - 2.32442i) q^{48} +0.385731i q^{50} +(0.898757 - 11.1552i) q^{51} +(-4.91730 + 2.83900i) q^{52} +(11.4790 - 6.62740i) q^{53} +(-1.38775 + 1.44618i) q^{54} -2.54224i q^{55} +(-0.888288 - 1.87126i) q^{57} +(1.49862 - 2.59569i) q^{58} +(1.98146 + 3.43199i) q^{59} +(-2.63910 - 1.82102i) q^{60} +(8.08933 + 4.67038i) q^{61} -2.65148 q^{62} +4.64717 q^{64} +(2.65626 + 1.53359i) q^{65} +(-1.39798 - 0.964627i) q^{66} +(1.75966 + 3.04782i) q^{67} +(5.98062 - 10.3587i) q^{68} +(2.26989 + 4.78173i) q^{69} +0.921861i q^{71} +(-4.16649 + 1.58165i) q^{72} +(-0.256722 + 0.148218i) q^{73} +(-1.18658 + 0.685073i) q^{74} +(-0.139098 + 1.72646i) q^{75} -2.21390i q^{76} +(1.85121 - 0.878771i) q^{78} +(-4.14741 + 7.18352i) q^{79} +(-1.56470 - 2.71015i) q^{80} +(-6.73281 + 5.97238i) q^{81} +(0.772502 + 0.446004i) q^{82} -2.11171 q^{83} -6.46130 q^{85} +(-1.82436 - 1.05330i) q^{86} +(7.64357 - 11.0774i) q^{87} +(-1.88829 - 3.27061i) q^{88} +(-9.41507 + 16.3074i) q^{89} +(0.896599 + 0.731577i) q^{90} +5.65729i q^{92} +(-11.8675 - 0.956152i) q^{93} +(-1.07571 + 0.621062i) q^{94} +(-1.03570 + 0.597960i) q^{95} +(-7.21343 - 0.581177i) q^{96} +12.3692i q^{97} +(-5.90923 - 4.82161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.334053	−	0.192865i	−0.236211	−	0.136376i	0.377223	−	0.926122i	$-0.376879\pi$
$2$	−0.334053	−	0.192865i	−0.236211	−	0.136376i	−0.613434	+	0.789746i	$0.710212\pi$
$3$	−1.42561	−	0.983691i	−0.823074	−	0.567934i
$3$	−1.42561	−	0.983691i	−0.823074	−	0.567934i
$4$	−0.925606	−	1.60320i	−0.462803	−	0.801598i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.286507	+	0.603555i	0.116966	+	0.246400i
$7$		0			0
$7$		0			0
$8$			1.48553i			0.525214i
$9$	1.06470	+	2.80471i	0.354901	+	0.934904i
$10$	0.334053	−	0.192865i	0.105637	−	0.0609894i
$11$	−2.20164	+	1.27112i	−0.663821	+	0.383257i	−0.793731	−	0.608269i	$-0.791864\pi$
$11$	−2.20164	+	1.27112i	−0.663821	+	0.383257i	0.129910	+	0.991526i	$0.458531\pi$
$12$	−0.257501	+	3.19604i	−0.0743340	+	0.922616i
$13$		−	3.06718i		−	0.850683i	−0.905033	−	0.425342i	$-0.860154\pi$
$13$		−	3.06718i		−	0.850683i	0.905033	−	0.425342i	$-0.139846\pi$
$14$		0			0
$15$	1.56470	−	0.742765i	0.404005	−	0.191781i
$16$	−1.56470	+	2.71015i	−0.391176	+	0.677537i
$17$	3.23065	+	5.59565i	0.783548	+	1.35715i	0.929863	+	0.367907i	$0.119926\pi$
$17$	3.23065	+	5.59565i	0.783548	+	1.35715i	−0.146314	+	0.989238i	$0.546741\pi$
$18$	0.185264	−	1.14227i	0.0436672	−	0.269235i
$19$	1.03570	+	0.597960i	0.237605	+	0.137181i	0.614076	−	0.789247i	$-0.289529\pi$
$19$	1.03570	+	0.597960i	0.237605	+	0.137181i	−0.376470	+	0.926429i	$0.622862\pi$
$20$	1.85121			0.413944
$21$		0			0
$22$	0.980620			0.209069
$23$	−2.64657	−	1.52800i	−0.551848	−	0.318609i	0.198019	−	0.980198i	$-0.436549\pi$
$23$	−2.64657	−	1.52800i	−0.551848	−	0.318609i	−0.749867	+	0.661589i	$0.769882\pi$
$24$	1.46130	−	2.11778i	0.298287	−	0.432290i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.591553	+	1.02460i	−0.116013	+	0.200941i
$27$	1.24112	−	5.04575i	0.238854	−	0.971056i
$28$		0			0
$29$			7.77029i			1.44291i	0.692463	+	0.721454i	$0.256526\pi$
$29$			7.77029i			1.44291i	−0.692463	+	0.721454i	$0.743474\pi$
$30$	−0.665947	−	0.0536545i	−0.121585	−	0.00979593i
$31$	5.95299	−	3.43696i	1.06919	−	0.617297i	0.141229	−	0.989977i	$-0.454895\pi$
$31$	5.95299	−	3.43696i	1.06919	−	0.617297i	0.927960	+	0.372680i	$0.121561\pi$
$32$	3.61840	−	2.08909i	0.639649	−	0.369302i
$33$	4.38907	+	0.353622i	0.764039	+	0.0615576i
$34$		−	2.49232i		−	0.427430i
$35$		0			0
$36$	3.51101	−	4.30299i	0.585168	−	0.717165i
$37$	1.77604	−	3.07619i	0.291979	−	0.505722i	−0.682299	−	0.731074i	$-0.739020\pi$
$37$	1.77604	−	3.07619i	0.291979	−	0.505722i	0.974278	+	0.225351i	$0.0723529\pi$
$38$	−0.230652	−	0.399500i	−0.0374166	−	0.0648075i
$39$	−3.01716	+	4.37259i	−0.483132	+	0.700175i
$40$	−1.28651	−	0.742765i	−0.203415	−	0.117442i
$41$	−2.31252			−0.361154			−0.180577	−	0.983561i	$-0.557797\pi$
$41$	−2.31252			−0.361154			−0.180577	+	0.983561i	$0.557797\pi$
$42$		0			0
$43$	5.46130			0.832841			0.416420	−	0.909172i	$-0.363284\pi$
$43$	5.46130			0.832841			0.416420	+	0.909172i	$0.363284\pi$
$44$	4.07571	+	2.35311i	0.614437	+	0.354745i
$45$	−2.96130	−	0.480295i	−0.441445	−	0.0715981i
$46$	0.589395	+	1.02086i	0.0869016	+	0.150518i
$47$	1.61009	−	2.78876i	0.234856	−	0.406782i	−0.724375	−	0.689406i	$-0.757871\pi$
$47$	1.61009	−	2.78876i	0.234856	−	0.406782i	0.959231	+	0.282624i	$0.0912048\pi$
$48$	4.89660	−	2.32442i	0.706763	−	0.335501i
$49$		0			0
$50$			0.385731i			0.0545506i
$51$	0.898757	−	11.1552i	0.125851	−	1.56203i
$52$	−4.91730	+	2.83900i	−0.681906	+	0.393699i
$53$	11.4790	−	6.62740i	1.57676	−	0.910344i	0.581455	−	0.813579i	$-0.302484\pi$
$53$	11.4790	−	6.62740i	1.57676	−	0.910344i	0.995307	−	0.0967651i	$-0.0308496\pi$
$54$	−1.38775	+	1.44618i	−0.188849	+	0.196800i
$55$		−	2.54224i		−	0.342796i
$56$		0			0
$57$	−0.888288	−	1.87126i	−0.117657	−	0.247855i
$58$	1.49862	−	2.59569i	0.196779	−	0.340830i
$59$	1.98146	+	3.43199i	0.257964	+	0.446807i	0.965696	−	0.259674i	$-0.0836150\pi$
$59$	1.98146	+	3.43199i	0.257964	+	0.446807i	−0.707732	+	0.706481i	$0.750282\pi$
$60$	−2.63910	−	1.82102i	−0.340706	−	0.235093i
$61$	8.08933	+	4.67038i	1.03573	+	0.597981i	0.918622	−	0.395138i	$-0.129303\pi$
$61$	8.08933	+	4.67038i	1.03573	+	0.597981i	0.117111	+	0.993119i	$0.462637\pi$
$62$	−2.65148			−0.336739
$63$		0			0
$64$	4.64717			0.580896
$65$	2.65626	+	1.53359i	0.329468	+	0.190219i
$66$	−1.39798	−	0.964627i	−0.172079	−	0.118737i
$67$	1.75966	+	3.04782i	0.214977	+	0.372350i	0.953265	−	0.302134i	$-0.0976992\pi$
$67$	1.75966	+	3.04782i	0.214977	+	0.372350i	−0.738289	+	0.674485i	$0.764366\pi$
$68$	5.98062	−	10.3587i	0.725257	−	1.25618i
$69$	2.26989	+	4.78173i	0.273262	+	0.575652i
$70$		0			0
$71$			0.921861i			0.109405i	0.998503	+	0.0547024i	$0.0174210\pi$
$71$			0.921861i			0.109405i	−0.998503	+	0.0547024i	$0.982579\pi$
$72$	−4.16649	+	1.58165i	−0.491025	+	0.186399i
$73$	−0.256722	+	0.148218i	−0.0300470	+	0.0173477i	−0.514948	−	0.857221i	$-0.672189\pi$
$73$	−0.256722	+	0.148218i	−0.0300470	+	0.0173477i	0.484901	+	0.874569i	$0.338856\pi$
$74$	−1.18658	+	0.685073i	−0.137937	+	0.0796381i
$75$	−0.139098	+	1.72646i	−0.0160617	+	0.199354i
$76$		−	2.21390i		−	0.253952i
$77$		0			0
$78$	1.85121	−	0.878771i	0.209608	−	0.0995012i
$79$	−4.14741	+	7.18352i	−0.466620	+	0.808210i	−0.999273	−	0.0381242i	$-0.987862\pi$
$79$	−4.14741	+	7.18352i	−0.466620	+	0.808210i	0.532653	+	0.846334i	$0.321195\pi$
$80$	−1.56470	−	2.71015i	−0.174939	−	0.303004i
$81$	−6.73281	+	5.97238i	−0.748090	+	0.663597i
$82$	0.772502	+	0.446004i	0.0853085	+	0.0492529i
$83$	−2.11171			−0.231790			−0.115895	−	0.993261i	$-0.536974\pi$
$83$	−2.11171			−0.231790			−0.115895	+	0.993261i	$0.536974\pi$
$84$		0			0
$85$	−6.46130			−0.700827
$86$	−1.82436	−	1.05330i	−0.196726	−	0.113580i
$87$	7.64357	−	11.0774i	0.819477	−	1.18762i
$88$	−1.88829	−	3.27061i	−0.201292	−	0.348648i
$89$	−9.41507	+	16.3074i	−0.997996	+	1.72858i	−0.444197	+	0.895929i	$0.646511\pi$
$89$	−9.41507	+	16.3074i	−0.997996	+	1.72858i	−0.553799	+	0.832651i	$0.686822\pi$
$90$	0.896599	+	0.731577i	0.0945098	+	0.0771149i
$91$		0			0
$92$			5.65729i			0.589813i
$93$	−11.8675	−	0.956152i	−1.23061	−	0.0991483i
$94$	−1.07571	+	0.621062i	−0.110951	+	0.0640576i
$95$	−1.03570	+	0.597960i	−0.106260	+	0.0613494i
$96$	−7.21343	−	0.581177i	−0.736218	−	0.0593161i
$97$			12.3692i			1.25590i	0.778252	+	0.627952i	$0.216106\pi$
$97$			12.3692i			1.25590i	−0.778252	+	0.627952i	$0.783894\pi$
$98$		0			0
$99$	−5.90923	−	4.82161i	−0.593900	−	0.484590i
$100$	−0.925606	+	1.60320i	−0.0925606	+	0.160320i
$101$	3.48815	+	6.04166i	0.347084	+	0.601167i	0.985730	−	0.168333i	$-0.0538385\pi$
$101$	3.48815	+	6.04166i	0.347084	+	0.601167i	−0.638646	+	0.769501i	$0.720505\pi$
$102$	−2.45168	+	3.55307i	−0.242752	+	0.351806i
$103$	−3.26767	−	1.88659i	−0.321973	−	0.185891i	0.330299	−	0.943876i	$-0.392850\pi$
$103$	−3.26767	−	1.88659i	−0.321973	−	0.185891i	−0.652272	+	0.757985i	$0.726184\pi$
$104$	4.55639			0.446791
$105$		0			0
$106$	−5.11279			−0.496598
$107$	11.4607	+	6.61684i	1.10795	+	0.639674i	0.938297	−	0.345830i	$-0.112403\pi$
$107$	11.4607	+	6.61684i	1.10795	+	0.639674i	0.169651	+	0.985504i	$0.445736\pi$
$108$	−9.23812	+	2.68062i	−0.888939	+	0.257943i
$109$	−1.25081	−	2.16647i	−0.119806	−	0.207510i	0.799885	−	0.600154i	$-0.204894\pi$
$109$	−1.25081	−	2.16647i	−0.119806	−	0.207510i	−0.919691	+	0.392644i	$0.871561\pi$
$110$	−0.490310	+	0.849242i	−0.0467492	+	0.0809721i
$111$	−5.55795	+	2.63836i	−0.527537	+	0.250422i
$112$		0			0
$113$		−	7.18425i		−	0.675837i	−0.941175	−	0.337919i	$-0.890277\pi$
$113$		−	7.18425i		−	0.675837i	0.941175	−	0.337919i	$-0.109723\pi$
$114$	−0.0641665	+	0.796420i	−0.00600975	+	0.0745916i
$115$	2.64657	−	1.52800i	0.246794	−	0.142486i
$116$	12.4573	−	7.19223i	1.15663	−	0.667782i
$117$	8.60256	−	3.26564i	0.795307	−	0.301909i
$118$		−	1.52862i		−	0.140721i
$119$		0			0
$120$	1.10340	+	2.32442i	0.100726	+	0.212189i
$121$	−2.26851	+	3.92917i	−0.206228	+	0.357197i
$122$	−1.80151	−	3.12030i	−0.163101	−	0.282499i
$123$	3.29674	+	2.27480i	0.297257	+	0.205112i
$124$	−11.0202	−	6.36254i	−0.989648	−	0.571373i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.1965			−0.993528			−0.496764	−	0.867886i	$-0.665478\pi$
$127$	−11.1965			−0.993528			−0.496764	+	0.867886i	$0.665478\pi$
$128$	−8.78920	−	5.07445i	−0.776863	−	0.448522i
$129$	−7.78567	−	5.37223i	−0.685490	−	0.472999i
$130$	−0.591553	−	1.02460i	−0.0518827	−	0.0898634i
$131$	7.83183	−	13.5651i	0.684270	−	1.18519i	−0.289395	−	0.957210i	$-0.593454\pi$
$131$	7.83183	−	13.5651i	0.684270	−	1.18519i	0.973666	−	0.227981i	$-0.0732125\pi$
$132$	−3.49562	−	7.36385i	−0.304255	−	0.640941i
$133$		0			0
$134$		−	1.35751i		−	0.117271i
$135$	3.74919	+	3.59772i	0.322679	+	0.309642i
$136$	−8.31252	+	4.79923i	−0.712792	+	0.411531i
$137$	−5.04755	+	2.91420i	−0.431241	+	0.248977i	−0.699875	−	0.714265i	$-0.746761\pi$
$137$	−5.04755	+	2.91420i	−0.431241	+	0.248977i	0.268634	+	0.963242i	$0.413428\pi$
$138$	0.163968	−	2.03513i	0.0139579	−	0.173242i
$139$			12.0365i			1.02092i	0.859900	+	0.510462i	$0.170525\pi$
$139$			12.0365i			1.02092i	−0.859900	+	0.510462i	$0.829475\pi$
$140$		0			0
$141$	−5.03863	+	2.39184i	−0.424330	+	0.201429i
$142$	0.177795	−	0.307950i	0.0149202	−	0.0258426i
$143$	3.89876	+	6.75285i	0.326030	+	0.564701i
$144$	−9.26713	−	1.50304i	−0.772261	−	0.125253i
$145$	−6.72927	−	3.88515i	−0.558836	−	0.322644i
$146$	0.114345			0.00946324
$147$		0			0
$148$	−6.57565			−0.540515
$149$	16.1925	+	9.34874i	1.32654	+	0.765879i	0.984763	−	0.173902i	$-0.0556377\pi$
$149$	16.1925	+	9.34874i	1.32654	+	0.765879i	0.341778	+	0.939781i	$0.388971\pi$
$150$	0.379440	−	0.549900i	0.0309811	−	0.0448992i
$151$	2.97531	+	5.15339i	0.242127	+	0.419377i	0.961320	−	0.275434i	$-0.0888215\pi$
$151$	2.97531	+	5.15339i	0.242127	+	0.419377i	−0.719193	+	0.694811i	$0.755488\pi$
$152$	−0.888288	+	1.53856i	−0.0720497	+	0.124794i
$153$	−12.2545	+	15.0188i	−0.990718	+	1.21419i
$154$		0			0
$155$			6.87392i			0.552127i
$156$	9.80283	+	0.789801i	0.784854	+	0.0632347i
$157$	−5.55364	+	3.20639i	−0.443228	+	0.255898i	−0.704966	−	0.709241i	$-0.749038\pi$
$157$	−5.55364	+	3.20639i	−0.443228	+	0.255898i	0.261738	+	0.965139i	$0.415704\pi$
$158$	2.77091	−	1.59978i	0.220441	−	0.127272i
$159$	−22.8838	−	1.84372i	−1.81481	−	0.146217i
$160$			4.17817i			0.330313i
$161$		0			0
$162$	3.40098	−	0.696562i	0.267206	−	0.0547271i
$163$	8.22174	−	14.2405i	0.643976	−	1.11540i	−0.340560	−	0.940223i	$-0.610617\pi$
$163$	8.22174	−	14.2405i	0.643976	−	1.11540i	0.984537	−	0.175177i	$-0.0560499\pi$
$164$	2.14048	+	3.70742i	0.167143	+	0.289501i
$165$	−2.50078	+	3.62423i	−0.194685	+	0.282146i
$166$	0.705423	+	0.407276i	0.0547514	+	0.0316108i
$167$	4.81089			0.372278			0.186139	−	0.982523i	$-0.440402\pi$
$167$	4.81089			0.372278			0.186139	+	0.982523i	$0.440402\pi$
$168$		0			0
$169$	3.59239			0.276338
$170$	2.15842	+	1.24616i	0.165543	+	0.0955762i
$171$	−0.574394	+	3.54148i	−0.0439250	+	0.270824i
$172$	−5.05501	−	8.75554i	−0.385441	−	0.667604i
$173$	3.40761	−	5.90215i	0.259075	−	0.448732i	−0.706919	−	0.707294i	$-0.749916\pi$
$173$	3.40761	−	5.90215i	0.259075	−	0.448732i	0.965994	+	0.258563i	$0.0832488\pi$
$174$	−4.68980	+	2.22625i	−0.355533	+	0.168771i
$175$		0			0
$176$		−	7.95571i		−	0.599684i
$177$	0.551236	−	6.84181i	0.0414335	−	0.514262i
$178$	6.29026	−	3.63168i	0.471475	−	0.272206i
$179$	−17.2931	+	9.98420i	−1.29255	+	0.746254i	−0.979106	−	0.203353i	$-0.934816\pi$
$179$	−17.2931	+	9.98420i	−1.29255	+	0.746254i	−0.313444	+	0.949607i	$0.601483\pi$
$180$	1.97099	+	5.19211i	0.146909	+	0.386997i
$181$			5.18808i			0.385627i	0.981235	+	0.192813i	$0.0617612\pi$
$181$			5.18808i			0.385627i	−0.981235	+	0.192813i	$0.938239\pi$
$182$		0			0
$183$	−6.93799	−	14.6155i	−0.512871	−	1.08041i
$184$	2.26989	−	3.93156i	0.167338	−	0.289838i
$185$	1.77604	+	3.07619i	0.130577	+	0.226166i
$186$	3.77997	+	2.60824i	0.277161	+	0.191245i
$187$	−14.2255	−	8.21309i	−1.04027	−	0.600601i
$188$	−5.96124			−0.434768
$189$		0			0
$190$	0.461303			0.0334665
$191$	−7.48332	−	4.32049i	−0.541474	−	0.312620i	0.204202	−	0.978929i	$-0.434540\pi$
$191$	−7.48332	−	4.32049i	−0.541474	−	0.312620i	−0.745676	+	0.666309i	$0.767873\pi$
$192$	−6.62503	−	4.57138i	−0.478120	−	0.329911i
$193$	11.8861	+	20.5873i	0.855578	+	1.48190i	0.876108	+	0.482115i	$0.160131\pi$
$193$	11.8861	+	20.5873i	0.855578	+	1.48190i	−0.0205300	+	0.999789i	$0.506535\pi$
$194$	2.38559	−	4.13197i	0.171276	−	0.296658i
$195$	−2.27820	−	4.79923i	−0.163145	−	0.343680i
$196$		0			0
$197$		−	11.6843i		−	0.832475i	−0.909256	−	0.416238i	$-0.863348\pi$
$197$		−	11.6843i		−	0.832475i	0.909256	−	0.416238i	$-0.136652\pi$
$198$	1.04407	+	2.75036i	0.0741989	+	0.195459i
$199$	12.2341	−	7.06338i	0.867254	−	0.500709i	0.000819396	−	1.00000i	$-0.499739\pi$
$199$	12.2341	−	7.06338i	0.867254	−	0.500709i	0.866435	+	0.499290i	$0.166406\pi$
$200$	1.28651	−	0.742765i	0.0909698	−	0.0525214i
$201$	0.489531	−	6.07595i	0.0345289	−	0.428564i
$202$		−	2.69098i		−	0.189336i
$203$		0			0
$204$	−18.7158	+	8.88440i	−1.31037	+	0.622032i
$205$	1.15626	−	2.00270i	0.0807565	−	0.139874i
$206$	0.727715	+	1.26044i	0.0507023	+	0.0878190i
$207$	1.46778	−	9.04972i	0.102018	−	0.628999i
$208$	8.31252	+	4.79923i	0.576369	+	0.332767i
$209$	−3.04032			−0.210303
$210$		0			0
$211$	4.49838			0.309681			0.154841	−	0.987939i	$-0.450514\pi$
$211$	4.49838			0.309681			0.154841	+	0.987939i	$0.450514\pi$
$212$	−21.2501	−	12.2687i	−1.45946	−	0.842620i
$213$	0.906827	−	1.31421i	0.0621347	−	0.0900482i
$214$	−2.55232	−	4.42075i	−0.174473	−	0.302196i
$215$	−2.73065	+	4.72963i	−0.186229	+	0.322558i
$216$	7.49562	+	1.84372i	0.510012	+	0.125449i
$217$		0			0
$218$			0.964952i			0.0653548i
$219$	0.511785	+	0.0412339i	0.0345832	+	0.00278633i
$220$	−4.07571	+	2.35311i	−0.274784	+	0.158647i
$221$	17.1629	−	9.90900i	1.15450	−	0.666551i
$222$	2.36550	+	0.190585i	0.158762	+	0.0127912i
$223$		−	7.20662i		−	0.482591i	−0.970452	−	0.241296i	$-0.922428\pi$
$223$		−	7.20662i		−	0.482591i	0.970452	−	0.241296i	$-0.0775724\pi$
$224$		0			0
$225$	1.89660	−	2.32442i	0.126440	−	0.154961i
$226$	−1.38559	+	2.39992i	−0.0921682	+	0.159640i
$227$	−0.931518	−	1.61344i	−0.0618270	−	0.107087i	0.833455	−	0.552587i	$-0.186359\pi$
$227$	−0.931518	−	1.61344i	−0.0618270	−	0.107087i	−0.895282	+	0.445500i	$0.853026\pi$
$228$	−2.17780	+	3.15615i	−0.144228	+	0.209021i
$229$	17.4126	+	10.0532i	1.15066	+	0.664333i	0.949047	−	0.315133i	$-0.102049\pi$
$229$	17.4126	+	10.0532i	1.15066	+	0.664333i	0.201610	+	0.979466i	$0.435383\pi$
$230$	−1.17879			−0.0777271
$231$		0			0
$232$	−11.5430			−0.757836
$233$	1.35559	+	0.782650i	0.0888077	+	0.0512731i	0.543746	−	0.839250i	$-0.317005\pi$
$233$	1.35559	+	0.782650i	0.0888077	+	0.0512731i	−0.454938	+	0.890523i	$0.650339\pi$
$234$	−3.50354	−	0.568240i	−0.229033	−	0.0371470i
$235$	1.61009	+	2.78876i	0.105031	+	0.181919i
$236$	3.66811	−	6.35334i	0.238773	−	0.413568i
$237$	12.9789	−	6.16110i	0.843073	−	0.400207i
$238$		0			0
$239$			5.69230i			0.368205i	0.982907	+	0.184102i	$0.0589378\pi$
$239$			5.69230i			0.368205i	−0.982907	+	0.184102i	$0.941062\pi$
$240$	−0.435296	+	5.40279i	−0.0280982	+	0.348748i
$241$	−11.5466	+	6.66646i	−0.743785	+	0.429424i	−0.823444	−	0.567398i	$-0.807950\pi$
$241$	−11.5466	+	6.66646i	−0.743785	+	0.429424i	0.0796592	+	0.996822i	$0.474617\pi$
$242$	1.51560	−	0.875033i	0.0974266	−	0.0562492i
$243$	15.4733	−	1.89125i	0.992613	−	0.121324i
$244$		−	17.2917i		−	1.10699i
$245$		0			0
$246$	−0.662553	−	1.39573i	−0.0422428	−	0.0889884i
$247$	1.83405	−	3.17667i	0.116698	−	0.202127i
$248$	5.10571	+	8.84335i	0.324213	+	0.561554i
$249$	3.01047	+	2.07727i	0.190781	+	0.131642i
$250$	−0.334053	−	0.192865i	−0.0211273	−	0.0121979i
$251$	−5.32590			−0.336168			−0.168084	−	0.985773i	$-0.553758\pi$
$251$	−5.32590			−0.336168			−0.168084	+	0.985773i	$0.553758\pi$
$252$		0			0
$253$	7.76907			0.488437
$254$	3.74022	+	2.15941i	0.234682	+	0.135494i
$255$	9.21127	+	6.35593i	0.576832	+	0.398023i
$256$	−2.68980	−	4.65887i	−0.168112	−	0.291179i
$257$	−3.25003	+	5.62922i	−0.202731	+	0.351141i	−0.949408	−	0.314047i	$-0.898315\pi$
$257$	−3.25003	+	5.62922i	−0.202731	+	0.351141i	0.746676	+	0.665188i	$0.231648\pi$
$258$	1.56470	+	3.29619i	0.0974142	+	0.205212i
$259$		0			0
$260$		−	5.67800i		−	0.352135i
$261$	−21.7934	+	8.27307i	−1.34898	+	0.512090i
$262$	−5.23249	+	3.02098i	−0.323264	+	0.186637i
$263$	−12.8401	+	7.41326i	−0.791757	+	0.457121i	−0.840581	−	0.541686i	$-0.817786\pi$
$263$	−12.8401	+	7.41326i	−0.791757	+	0.457121i	0.0488236	+	0.998807i	$0.484453\pi$
$264$	−0.525316	+	6.52009i	−0.0323309	+	0.401284i
$265$			13.2548i			0.814236i
$266$		0			0
$267$	29.4636	−	13.9864i	1.80314	−	0.855953i
$268$	3.25750	−	5.64216i	0.198984	−	0.344650i
$269$	−12.3042	−	21.3115i	−0.750201	−	1.29939i	−0.947725	−	0.319088i	$-0.896624\pi$
$269$	−12.3042	−	21.3115i	−0.750201	−	1.29939i	0.197525	−	0.980298i	$-0.436710\pi$
$270$	−0.558552	−	1.92492i	−0.0339924	−	0.117147i
$271$	−3.30121	−	1.90595i	−0.200534	−	0.115778i	0.396371	−	0.918091i	$-0.370270\pi$
$271$	−3.30121	−	1.90595i	−0.200534	−	0.115778i	−0.596905	+	0.802312i	$0.703603\pi$
$272$	−20.2201			−1.22602
$273$		0			0
$274$	2.24819			0.135818
$275$	2.20164	+	1.27112i	0.132764	+	0.0766514i
$276$	5.56503	−	8.06507i	0.334975	−	0.485460i
$277$	9.38769	+	16.2600i	0.564052	+	0.976966i	0.997137	+	0.0756131i	$0.0240914\pi$
$277$	9.38769	+	16.2600i	0.564052	+	0.976966i	−0.433086	+	0.901353i	$0.642575\pi$
$278$	2.32143	−	4.02083i	0.139230	−	0.241153i
$279$	15.9779	+	13.0371i	0.956570	+	0.780509i
$280$		0			0
$281$			23.6885i			1.41314i	0.707643	+	0.706570i	$0.249758\pi$
$281$			23.6885i			1.41314i	−0.707643	+	0.706570i	$0.750242\pi$
$282$	2.14447	+	0.172777i	0.127701	+	0.0102887i
$283$	4.36831	−	2.52204i	0.259669	−	0.149920i	−0.364515	−	0.931198i	$-0.618765\pi$
$283$	4.36831	−	2.52204i	0.259669	−	0.149920i	0.624184	+	0.781278i	$0.285432\pi$
$284$	1.47792	−	0.853280i	0.0876987	−	0.0506329i
$285$	2.06470	+	0.166351i	0.122303	+	0.00985376i
$286$		−	3.00774i		−	0.177851i
$287$		0			0
$288$	9.71181	+	7.92431i	0.572274	+	0.466945i
$289$	−12.3742	+	21.4328i	−0.727895	+	1.26075i
$290$	1.49862	+	2.59569i	0.0880020	+	0.152424i
$291$	12.1675	−	17.6336i	0.713270	−	1.03370i
$292$	0.475246	+	0.274384i	0.0278117	+	0.0160571i
$293$	−6.29421			−0.367712			−0.183856	−	0.982953i	$-0.558858\pi$
$293$	−6.29421			−0.367712			−0.183856	+	0.982953i	$0.558858\pi$
$294$		0			0
$295$	−3.96292			−0.230730
$296$	4.56977	+	2.63836i	0.265613	+	0.153352i
$297$	3.68125	+	12.6866i	0.213608	+	0.736149i
$298$	−3.60610	−	6.24594i	−0.208896	−	0.361818i
$299$	−4.68664	+	8.11750i	−0.271036	+	0.469447i
$300$	2.89660	−	1.37502i	0.167235	−	0.0793866i
$301$		0			0
$302$		−	2.29534i		−	0.132082i
$303$	0.970393	−	12.0443i	0.0557476	−	0.691926i
$304$	−3.24112	+	1.87126i	−0.185891	+	0.107324i
$305$	−8.08933	+	4.67038i	−0.463194	+	0.267425i
$306$	6.99025	−	2.65359i	0.399606	−	0.151696i
$307$			16.0397i			0.915432i	0.889099	+	0.457716i	$0.151332\pi$
$307$			16.0397i			0.915432i	−0.889099	+	0.457716i	$0.848668\pi$
$308$		0			0
$309$	2.80258	+	5.90390i	0.159433	+	0.335861i
$310$	1.32574	−	2.29625i	0.0752971	−	0.130418i
$311$	−9.03624	−	15.6512i	−0.512398	−	0.887499i	−0.999897	−	0.0143755i	$-0.995424\pi$
$311$	−9.03624	−	15.6512i	−0.512398	−	0.887499i	0.487499	−	0.873124i	$-0.337909\pi$
$312$	−6.49562	−	4.48208i	−0.367742	−	0.253748i
$313$	16.1272	+	9.31104i	0.911563	+	0.526291i	0.880934	−	0.473240i	$-0.156916\pi$
$313$	16.1272	+	9.31104i	0.911563	+	0.526291i	0.0306290	+	0.999531i	$0.490249\pi$
$314$	2.47361			0.139594
$315$		0			0
$316$	15.3555			0.863812
$317$	−2.28327	−	1.31825i	−0.128241	−	0.0740402i	0.434507	−	0.900669i	$-0.356923\pi$
$317$	−2.28327	−	1.31825i	−0.128241	−	0.0740402i	−0.562748	+	0.826628i	$0.690256\pi$
$318$	7.28882	+	5.02940i	0.408737	+	0.282035i
$319$	−9.87698	−	17.1074i	−0.553005	−	0.957832i
$320$	−2.32358	+	4.02457i	−0.129892	+	0.224980i
$321$	−9.82952	−	20.7068i	−0.548630	−	1.15574i
$322$		0			0
$323$			7.72720i			0.429953i
$324$	15.8068	+	5.26595i	0.878157	+	0.292553i
$325$	−2.65626	+	1.53359i	−0.147343	+	0.0850683i
$326$	−5.49299	+	3.17138i	−0.304228	+	0.175646i
$327$	−0.347971	+	4.31894i	−0.0192429	+	0.238838i
$328$		−	3.43531i		−	0.189683i
$329$		0			0
$330$	1.53438	−	0.728371i	0.0844649	−	0.0400955i
$331$	15.1704	−	26.2759i	0.833842	−	1.44426i	−0.0611286	−	0.998130i	$-0.519470\pi$
$331$	15.1704	−	26.2759i	0.833842	−	1.44426i	0.894970	−	0.446126i	$-0.147197\pi$
$332$	1.95461	+	3.38549i	0.107273	+	0.185803i
$333$	10.5188	+	1.70604i	0.576426	+	0.0934906i
$334$	−1.60709	−	0.927855i	−0.0879362	−	0.0507700i
$335$	−3.51932			−0.192281
$336$		0			0
$337$	−1.84215			−0.100348			−0.0501741	−	0.998740i	$-0.515978\pi$
$337$	−1.84215			−0.100348			−0.0501741	+	0.998740i	$0.515978\pi$
$338$	−1.20005	−	0.692849i	−0.0652741	−	0.0376860i
$339$	−7.06708	+	10.2419i	−0.383831	+	0.556264i
$340$	5.98062	+	10.3587i	0.324345	+	0.561781i
$341$	−8.73758	+	15.1339i	−0.473167	+	0.819549i
$342$	0.874907	−	1.07226i	0.0473096	−	0.0579812i
$343$		0			0
$344$			8.11293i			0.437420i
$345$	−5.27604	−	0.425084i	−0.284052	−	0.0228857i
$346$	−2.27664	+	1.31442i	−0.122393	+	0.0706636i
$347$	7.09309	−	4.09520i	0.380777	−	0.219842i	−0.297379	−	0.954759i	$-0.596113\pi$
$347$	7.09309	−	4.09520i	0.380777	−	0.219842i	0.678156	+	0.734918i	$0.262779\pi$
$348$	−24.8341	−	2.00086i	−1.33125	−	0.107257i
$349$		−	36.3291i		−	1.94465i	−0.233627	−	0.972326i	$-0.575059\pi$
$349$		−	36.3291i		−	1.94465i	0.233627	−	0.972326i	$-0.424941\pi$
$350$		0			0
$351$	−15.4762	−	3.80674i	−0.826061	−	0.203189i
$352$	−5.31096	+	9.19885i	−0.283075	+	0.490300i
$353$	−2.85736	−	4.94910i	−0.152082	−	0.263414i	0.779911	−	0.625891i	$-0.215265\pi$
$353$	−2.85736	−	4.94910i	−0.152082	−	0.263414i	−0.931993	+	0.362477i	$0.881931\pi$
$354$	−1.50369	+	2.17921i	−0.0799203	+	0.115824i
$355$	−0.798355	−	0.460931i	−0.0423723	−	0.0244637i
$356$	34.8586			1.84750
$357$		0			0
$358$	7.70242			0.407086
$359$	4.16181	+	2.40282i	0.219652	+	0.126816i	0.605789	−	0.795625i	$-0.292858\pi$
$359$	4.16181	+	2.40282i	0.219652	+	0.126816i	−0.386137	+	0.922441i	$0.626191\pi$
$360$	0.713493	−	4.39911i	0.0376044	−	0.231853i
$361$	−8.78489	−	15.2159i	−0.462362	−	0.800835i
$362$	1.00060	−	1.73309i	0.0525904	−	0.0910892i
$363$	7.09909	−	3.36994i	0.372605	−	0.176876i
$364$		0			0
$365$		−	0.296437i		−	0.0155162i
$366$	−0.501174	+	6.22045i	−0.0261968	+	0.325148i
$367$	21.2836	−	12.2881i	1.11099	−	0.641433i	0.171908	−	0.985113i	$-0.445007\pi$
$367$	21.2836	−	12.2881i	1.11099	−	0.641433i	0.939087	+	0.343680i	$0.111673\pi$
$368$	8.28219	−	4.78173i	0.431739	−	0.249265i
$369$	−2.46214	−	6.48594i	−0.128174	−	0.337644i
$370$		−	1.37015i		−	0.0712305i
$371$		0			0
$372$	9.45176	+	19.9110i	0.490051	+	1.03234i
$373$	−13.2513	+	22.9519i	−0.686126	+	1.18840i	0.286956	+	0.957944i	$0.407357\pi$
$373$	−13.2513	+	22.9519i	−0.686126	+	1.18840i	−0.973082	+	0.230461i	$0.925977\pi$
$374$	3.16804	+	5.48721i	0.163816	+	0.283737i
$375$	−1.42561	−	0.983691i	−0.0736180	−	0.0507976i
$376$	4.14279	+	2.39184i	0.213648	+	0.123350i
$377$	23.8329			1.22746
$378$		0			0
$379$	13.0939			0.672588			0.336294	−	0.941757i	$-0.390826\pi$
$379$	13.0939			0.672588			0.336294	+	0.941757i	$0.390826\pi$
$380$	1.91730	+	1.10695i	0.0983552	+	0.0567854i
$381$	15.9618	+	11.0139i	0.817747	+	0.564258i
$382$	1.66655	+	2.88655i	0.0852680	+	0.147689i
$383$	−8.48299	+	14.6930i	−0.433461	+	0.750776i	−0.997169	−	0.0751982i	$-0.976041\pi$
$383$	−8.48299	+	14.6930i	−0.433461	+	0.750776i	0.563708	+	0.825974i	$0.309374\pi$
$384$	7.53825	+	15.8800i	0.384685	+	0.810374i
$385$		0			0
$386$		−	9.16964i		−	0.466723i
$387$	5.81467	+	15.3174i	0.295576	+	0.778626i
$388$	19.8303	−	11.4490i	1.00673	−	0.581236i
$389$	−2.13457	+	1.23239i	−0.108227	+	0.0624848i	−0.553136	−	0.833091i	$-0.686569\pi$
$389$	−2.13457	+	1.23239i	−0.108227	+	0.0624848i	0.444910	+	0.895576i	$0.353236\pi$
$390$	−0.164568	+	2.04258i	−0.00833324	+	0.103430i
$391$		−	19.7457i		−	0.998583i
$392$		0			0
$393$	−24.5090	+	11.6344i	−1.23632	+	0.586879i
$394$	−2.25351	+	3.90319i	−0.113530	+	0.196640i
$395$	−4.14741	−	7.18352i	−0.208679	−	0.361442i
$396$	−2.26037	+	13.9366i	−0.113588	+	0.700339i
$397$	−2.90437	−	1.67684i	−0.145766	−	0.0841582i	0.425343	−	0.905032i	$-0.360153\pi$
$397$	−2.90437	−	1.67684i	−0.145766	−	0.0841582i	−0.571109	+	0.820874i	$0.693487\pi$
$398$	−5.44912			−0.273140
$399$		0			0
$400$	3.12941			0.156470
$401$	−5.40992	−	3.12342i	−0.270158	−	0.155976i	0.358801	−	0.933414i	$-0.383186\pi$
$401$	−5.40992	−	3.12342i	−0.270158	−	0.155976i	−0.628960	+	0.777438i	$0.716519\pi$
$402$	−1.33537	+	1.93527i	−0.0666022	+	0.0965226i
$403$	−10.5418	−	18.2589i	−0.525124	−	0.909541i
$404$	6.45731	−	11.1844i	0.321263	−	0.556444i
$405$	−1.80582	−	8.81697i	−0.0897321	−	0.438119i
$406$		0			0
$407$			9.03024i			0.447612i
$408$	16.5713	+	1.33513i	0.820403	+	0.0660988i
$409$	10.2147	−	5.89748i	0.505086	−	0.291611i	−0.225726	−	0.974191i	$-0.572475\pi$
$409$	10.2147	−	5.89748i	0.505086	−	0.291611i	0.730811	+	0.682579i	$0.239142\pi$
$410$	−0.772502	+	0.446004i	−0.0381511	+	0.0220266i
$411$	10.0625	+	0.810722i	0.496346	+	0.0399899i
$412$			6.98495i			0.344124i
$413$		0			0
$414$	−2.23569	+	2.74000i	−0.109878	+	0.134664i
$415$	1.05586	−	1.82880i	0.0518299	−	0.0897721i
$416$	−6.40761	−	11.0983i	−0.314159	−	0.544139i
$417$	11.8402	−	17.1593i	0.579817	−	0.840295i
$418$	1.01563	+	0.586372i	0.0496759	+	0.0286804i
$419$	12.0419			0.588284			0.294142	−	0.955762i	$-0.404966\pi$
$419$	12.0419			0.588284			0.294142	+	0.955762i	$0.404966\pi$
$420$		0			0
$421$	11.4264			0.556888			0.278444	−	0.960453i	$-0.410181\pi$
$421$	11.4264			0.556888			0.278444	+	0.960453i	$0.410181\pi$
$422$	−1.50270	−	0.867582i	−0.0731501	−	0.0422332i
$423$	9.53594	+	1.54664i	0.463653	+	0.0752000i
$424$	9.84521	+	17.0524i	0.478126	+	0.828138i
$425$	3.23065	−	5.59565i	0.156710	−	0.271429i
$426$	−0.556394	+	0.264120i	−0.0269574	+	0.0127967i
$427$		0			0
$428$		−	24.4983i		−	1.18417i
$429$	1.08462	−	13.4621i	0.0523660	−	0.649955i
$430$	1.82436	−	1.05330i	0.0879786	−	0.0507945i
$431$	−28.2346	+	16.3013i	−1.36001	+	0.785205i	−0.989625	−	0.143672i	$-0.954109\pi$
$431$	−28.2346	+	16.3013i	−1.36001	+	0.785205i	−0.370389	+	0.928877i	$0.620776\pi$
$432$	11.7327	+	11.2587i	0.564492	+	0.541686i
$433$		−	4.37644i		−	0.210318i	−0.994455	−	0.105159i	$-0.966465\pi$
$433$		−	4.37644i		−	0.210318i	0.994455	−	0.105159i	$-0.0335352\pi$
$434$		0			0
$435$	5.77151	+	12.1582i	0.276723	+	0.582942i
$436$	−2.31551	+	4.01059i	−0.110893	+	0.192072i
$437$	−1.82736	−	3.16508i	−0.0874146	−	0.151407i
$438$	−0.163011	−	0.112480i	−0.00778895	−	0.00537450i
$439$	12.8416	+	7.41409i	0.612895	+	0.353855i	0.774098	−	0.633066i	$-0.218204\pi$
$439$	12.8416	+	7.41409i	0.612895	+	0.353855i	−0.161202	+	0.986921i	$0.551537\pi$
$440$	3.77658			0.180041
$441$		0			0
$442$	−7.64441			−0.363607
$443$	−13.7806	−	7.95622i	−0.654735	−	0.378011i	0.135533	−	0.990773i	$-0.456725\pi$
$443$	−13.7806	−	7.95622i	−0.654735	−	0.378011i	−0.790268	+	0.612762i	$0.790059\pi$
$444$	9.37428	+	6.46841i	0.444884	+	0.306977i
$445$	−9.41507	−	16.3074i	−0.446317	−	0.773044i
$446$	−1.38991	+	2.40739i	−0.0658141	+	0.113993i
$447$	−13.8878	−	29.2560i	−0.656872	−	1.38376i
$448$		0			0
$449$		−	35.1881i		−	1.66063i	−0.557294	−	0.830315i	$-0.688161\pi$
$449$		−	35.1881i		−	1.66063i	0.557294	−	0.830315i	$-0.311839\pi$
$450$	−1.08186	+	0.410689i	−0.0509995	+	0.0193601i
$451$	5.09134	−	2.93948i	0.239742	−	0.138415i
$452$	−11.5178	+	6.64978i	−0.541750	+	0.312779i
$453$	0.827721	−	10.2735i	0.0388897	−	0.482690i
$454$			0.718630i			0.0337270i
$455$		0			0
$456$	2.77982	−	1.31958i	0.130177	−	0.0617950i
$457$	−7.02954	+	12.1755i	−0.328828	+	0.569547i	−0.982280	−	0.187421i	$-0.939987\pi$
$457$	−7.02954	+	12.1755i	−0.328828	+	0.569547i	0.653451	+	0.756968i	$0.273320\pi$
$458$	−3.87782	−	6.71658i	−0.181199	−	0.313845i
$459$	32.2439	−	9.35619i	1.50502	−	0.436710i
$460$	−4.89936	−	2.82865i	−0.228434	−	0.131886i
$461$	−13.5161			−0.629506			−0.314753	−	0.949174i	$-0.601922\pi$
$461$	−13.5161			−0.629506			−0.314753	+	0.949174i	$0.601922\pi$
$462$		0			0
$463$	17.8381			0.829009			0.414504	−	0.910047i	$-0.363955\pi$
$463$	17.8381			0.829009			0.414504	+	0.910047i	$0.363955\pi$
$464$	−21.0586	−	12.1582i	−0.977623	−	0.564431i
$465$	6.76182	−	9.79951i	0.313572	−	0.454441i
$466$	−0.301892	−	0.522893i	−0.0139849	−	0.0242225i
$467$	4.59471	−	7.95827i	0.212618	−	0.368265i	−0.739915	−	0.672700i	$-0.765134\pi$
$467$	4.59471	−	7.95827i	0.212618	−	0.368265i	0.952533	+	0.304435i	$0.0984678\pi$
$468$	−13.1980	−	10.7689i	−0.610080	−	0.497792i
$469$		0			0
$470$		−	1.24212i		−	0.0572949i
$471$	11.0714	+	0.892008i	0.510143	+	0.0411016i
$472$	−5.09833	+	2.94352i	−0.234670	+	0.135487i
$473$	−12.0238	+	6.94197i	−0.552857	+	0.319192i
$474$	−5.52391	−	0.445055i	−0.253722	−	0.0204420i
$475$		−	1.19592i		−	0.0548726i
$476$		0			0
$477$	30.8097	+	25.1391i	1.41068	+	1.15104i
$478$	1.09785	−	1.90153i	0.0502144	−	0.0869739i
$479$	9.44037	+	16.3512i	0.431341	+	0.747105i	0.996989	−	0.0775419i	$-0.0247071\pi$
$479$	9.44037	+	16.3512i	0.431341	+	0.747105i	−0.565648	+	0.824647i	$0.691374\pi$
$480$	4.11003	−	5.95643i	0.187596	−	0.271872i
$481$	−9.43523	−	5.44743i	−0.430210	−	0.248382i
$482$	5.14291			0.234253
$483$		0			0
$484$	8.39897			0.381772
$485$	−10.7121	−	6.18461i	−0.486409	−	0.280828i
$486$	−5.53366	−	2.35249i	−0.251012	−	0.106711i
$487$	2.61762	+	4.53386i	0.118616	+	0.205449i	0.919219	−	0.393746i	$-0.128821\pi$
$487$	2.61762	+	4.53386i	0.118616	+	0.205449i	−0.800604	+	0.599194i	$0.795488\pi$
$488$	−6.93799	+	12.0170i	−0.314068	+	0.543982i
$489$	−25.7292	+	12.2136i	−1.16351	+	0.552320i
$490$		0			0
$491$		−	19.5201i		−	0.880930i	−0.897770	−	0.440465i	$-0.854814\pi$
$491$		−	19.5201i		−	0.880930i	0.897770	−	0.440465i	$-0.145186\pi$
$492$	0.595474	−	7.39088i	0.0268460	−	0.333207i
$493$	−43.4799	+	25.1031i	−1.95823	+	1.13059i
$494$	−1.22534	+	0.707451i	−0.0551307	+	0.0318297i
$495$	7.13025	−	2.70673i	0.320481	−	0.121659i
$496$			21.5113i			0.965887i
$497$		0			0
$498$	−0.605021	−	1.27453i	−0.0271116	−	0.0571132i
$499$	18.3175	−	31.7269i	0.820005	−	1.42029i	−0.0856728	−	0.996323i	$-0.527304\pi$
$499$	18.3175	−	31.7269i	0.820005	−	1.42029i	0.905678	−	0.423967i	$-0.139363\pi$
$500$	−0.925606	−	1.60320i	−0.0413944	−	0.0716971i
$501$	−6.85844	−	4.73243i	−0.306413	−	0.211430i
$502$	1.77913	+	1.02718i	0.0794064	+	0.0458453i
$503$	40.7156			1.81542			0.907708	−	0.419602i	$-0.137830\pi$
$503$	40.7156			1.81542			0.907708	+	0.419602i	$0.137830\pi$
$504$		0			0
$505$	−6.97630			−0.310441
$506$	−2.59528	−	1.49838i	−0.115374	−	0.0666113i
$507$	−5.12134	−	3.53381i	−0.227447	−	0.156942i
$508$	10.3635	+	17.9502i	0.459807	+	0.796410i
$509$	−8.86384	+	15.3526i	−0.392883	+	0.680493i	−0.992828	−	0.119548i	$-0.961856\pi$
$509$	−8.86384	+	15.3526i	−0.392883	+	0.680493i	0.599946	+	0.800041i	$0.295189\pi$
$510$	−1.85121	−	3.89975i	−0.0819730	−	0.172684i
$511$		0			0
$512$			22.3729i			0.988751i
$513$	4.30258	−	4.48373i	0.189964	−	0.197962i
$514$	2.17136	−	1.25364i	0.0957747	−	0.0552956i
$515$	3.26767	−	1.88659i	0.143991	−	0.0831330i
$516$	−1.40629	+	17.4545i	−0.0619084	+	0.768393i
$517$			8.18648i			0.360041i
$518$		0			0
$519$	−10.6638	+	5.06210i	−0.468088	+	0.222202i
$520$	−2.27820	+	3.94595i	−0.0999055	+	0.173041i
$521$	−1.75780	−	3.04461i	−0.0770108	−	0.133387i	0.824948	−	0.565208i	$-0.191204\pi$
$521$	−1.75780	−	3.04461i	−0.0770108	−	0.133387i	−0.901959	+	0.431822i	$0.857871\pi$
$522$	8.87574	+	1.43956i	0.388481	+	0.0630078i
$523$	−4.20527	−	2.42791i	−0.183884	−	0.106165i	0.405232	−	0.914214i	$-0.367191\pi$
$523$	−4.20527	−	2.42791i	−0.183884	−	0.106165i	−0.589116	+	0.808048i	$0.700524\pi$
$524$	−28.9968			−1.26673
$525$		0			0
$526$	5.71904			0.249362
$527$	38.4641	+	22.2073i	1.67552	+	0.967363i
$528$	−7.82596	+	11.3417i	−0.340581	+	0.493584i
$529$	−6.83045	−	11.8307i	−0.296976	−	0.514378i
$530$	2.55639	−	4.42780i	0.111043	−	0.192331i
$531$	−7.51608	+	9.21148i	−0.326170	+	0.399744i
$532$		0			0
$533$			7.09290i			0.307228i
$534$	−12.5399	−	1.01032i	−0.542654	−	0.0437209i
$535$	−11.4607	+	6.61684i	−0.495489	+	0.286071i
$536$	−4.52763	+	2.61403i	−0.195564	+	0.112909i
$537$	34.4746	+	2.77757i	1.48769	+	0.119861i
$538$			9.49222i			0.409239i
$539$		0			0
$540$	2.29758	−	9.34076i	0.0988719	−	0.401962i
$541$	0.0193171	−	0.0334581i	0.000830506	−	0.00143848i	−0.865610	−	0.500719i	$-0.833069\pi$
$541$	0.0193171	−	0.0334581i	0.000830506	−	0.00143848i	0.866440	+	0.499281i	$0.166402\pi$
$542$	0.735184	+	1.27338i	0.0315789	+	0.0546962i
$543$	5.10346	−	7.39615i	0.219011	−	0.317399i
$544$	23.3796	+	13.4982i	1.00239	+	0.578731i
$545$	2.50162			0.107158
$546$		0			0
$547$	−36.3881			−1.55584			−0.777921	−	0.628362i	$-0.783726\pi$
$547$	−36.3881			−1.55584			−0.777921	+	0.628362i	$0.783726\pi$
$548$	9.34408	+	5.39480i	0.399159	+	0.230455i
$549$	−4.48632	+	27.6608i	−0.191471	+	1.18053i
$550$	−0.490310	−	0.849242i	−0.0209069	−	0.0362118i
$551$	−4.64633	+	8.04767i	−0.197940	+	0.342842i
$552$	−7.10340	+	3.37199i	−0.302341	+	0.143521i
$553$		0			0
$554$		−	7.24224i		−	0.307693i
$555$	0.494088	−	6.13251i	0.0209729	−	0.260310i
$556$	19.2969	−	11.1411i	0.818370	−	0.472486i
$557$	−15.0477	+	8.68779i	−0.637591	+	0.368114i	−0.783686	−	0.621157i	$-0.786663\pi$
$557$	−15.0477	+	8.68779i	−0.637591	+	0.368114i	0.146095	+	0.989271i	$0.453330\pi$
$558$	−2.82305	−	7.43665i	−0.119509	−	0.314818i
$559$		−	16.7508i		−	0.708484i
$560$		0			0
$561$	12.2008	+	25.7021i	0.515118	+	1.08514i
$562$	4.56870	−	7.91322i	0.192719	−	0.333799i
$563$	−10.4546	−	18.1078i	−0.440607	−	0.763153i	0.557128	−	0.830427i	$-0.311903\pi$
$563$	−10.4546	−	18.1078i	−0.440607	−	0.763153i	−0.997735	+	0.0672735i	$0.978570\pi$
$564$	8.49838	+	5.86402i	0.357846	+	0.246920i
$565$	6.22174	+	3.59212i	0.261751	+	0.151122i
$566$	−1.94566			−0.0817822
$567$		0			0
$568$	−1.36945			−0.0574610
$569$	−24.8873	−	14.3687i	−1.04333	−	0.602367i	−0.122556	−	0.992462i	$-0.539109\pi$
$569$	−24.8873	−	14.3687i	−1.04333	−	0.602367i	−0.920775	+	0.390094i	$0.872442\pi$
$570$	−0.657637	−	0.453780i	−0.0275454	−	0.0190067i
$571$	15.2499	+	26.4136i	0.638188	+	1.10537i	0.985830	+	0.167746i	$0.0536490\pi$
$571$	15.2499	+	26.4136i	0.638188	+	1.10537i	−0.347643	+	0.937627i	$0.613018\pi$
$572$	7.21742	−	12.5009i	0.301776	−	0.522691i
$573$	6.41823	+	13.5206i	0.268125	+	0.564831i
$574$		0			0
$575$			3.05599i			0.127444i
$576$	4.94786	+	13.0340i	0.206161	+	0.543082i
$577$	−20.3570	+	11.7531i	−0.847473	+	0.489289i	−0.859797	−	0.510635i	$-0.829410\pi$
$577$	−20.3570	+	11.7531i	−0.847473	+	0.489289i	0.0123245	+	0.999924i	$0.496077\pi$
$578$	8.26728	−	4.77312i	0.343874	−	0.198536i
$579$	3.30667	−	41.0416i	0.137420	−	1.70563i
$580$			14.3845i			0.597282i
$581$		0			0
$582$	−7.46549	+	3.54387i	−0.309455	+	0.146898i
$583$	−16.8485	+	29.1824i	−0.697792	+	1.20861i
$584$	−0.220183	−	0.381368i	−0.00911124	−	0.0157811i
$585$	−1.47315	+	9.08286i	−0.0609073	+	0.375530i
$586$	2.10260	+	1.21394i	0.0868575	+	0.0501472i
$587$	−24.4613			−1.00963			−0.504813	−	0.863229i	$-0.668439\pi$
$587$	−24.4613			−1.00963			−0.504813	+	0.863229i	$0.668439\pi$
$588$		0			0
$589$	8.22067			0.338727
$590$	1.32383	+	0.764311i	0.0545010	+	0.0314662i
$591$	−11.4938	+	16.6573i	−0.472791	+	0.685189i
$592$	5.55795	+	9.62665i	0.228430	+	0.395653i
$593$	1.87506	−	3.24770i	0.0769995	−	0.133367i	−0.824955	−	0.565199i	$-0.808799\pi$
$593$	1.87506	−	3.24770i	0.0769995	−	0.133367i	0.901954	+	0.431832i	$0.142133\pi$
$594$	1.21707	−	4.94797i	0.0499369	−	0.203018i
$595$		0			0
$596$		−	34.6130i		−	1.41780i
$597$	−24.3892	−	1.96501i	−0.998184	−	0.0804224i
$598$	3.13117	−	1.80778i	0.128043	−	0.0739257i
$599$	28.6663	−	16.5505i	1.17127	−	0.676235i	0.217294	−	0.976106i	$-0.430277\pi$
$599$	28.6663	−	16.5505i	1.17127	−	0.676235i	0.953980	+	0.299871i	$0.0969438\pi$
$600$	−2.56470	−	0.206635i	−0.104704	−	0.00843584i
$601$			3.36032i			0.137070i	0.997649	+	0.0685352i	$0.0218325\pi$
$601$			3.36032i			0.137070i	−0.997649	+	0.0685352i	$0.978167\pi$
$602$		0			0
$603$	−6.67473	+	8.18036i	−0.271816	+	0.333130i
$604$	5.50793	−	9.54001i	0.224114	−	0.388177i
$605$	−2.26851	−	3.92917i	−0.0922279	−	0.159743i
$606$	−2.64709	+	3.83627i	−0.107531	+	0.155838i
$607$	−38.5420	−	22.2522i	−1.56437	−	0.903190i	−0.996806	−	0.0798612i	$-0.974552\pi$
$607$	−38.5420	−	22.2522i	−1.56437	−	0.903190i	−0.567565	−	0.823329i	$-0.692114\pi$
$608$	4.99676			0.202645
$609$		0			0
$610$	3.60302			0.145882
$611$	−8.55364	−	4.93844i	−0.346043	−	0.199788i
$612$	35.4209	+	5.74492i	1.43180	+	0.232225i
$613$	−20.1567	−	34.9125i	−0.814123	−	1.41010i	−0.909956	−	0.414705i	$-0.863885\pi$
$613$	−20.1567	−	34.9125i	−0.814123	−	1.41010i	0.0958333	−	0.995397i	$-0.469448\pi$
$614$	3.09349	−	5.35809i	0.124843	−	0.216235i
$615$	−3.61840	+	1.71766i	−0.145908	+	0.0692626i
$616$		0			0
$617$		−	37.7372i		−	1.51924i	−0.650366	−	0.759621i	$-0.725384\pi$
$617$		−	37.7372i		−	1.51924i	0.650366	−	0.759621i	$-0.274616\pi$
$618$	0.202448	−	2.51274i	0.00814365	−	0.101077i
$619$	−12.7122	+	7.33941i	−0.510948	+	0.294996i	−0.733223	−	0.679988i	$-0.761985\pi$
$619$	−12.7122	+	7.33941i	−0.510948	+	0.294996i	0.222275	+	0.974984i	$0.428652\pi$
$620$	11.0202	−	6.36254i	0.442584	−	0.255526i
$621$	−10.9946	+	11.4575i	−0.441198	+	0.459774i
$622$			6.97111i			0.279516i
$623$		0			0
$624$	−7.12941	−	15.0188i	−0.285405	−	0.601232i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.59155	−	6.22075i	−0.143547	−	0.248631i
$627$	4.33429	+	2.99073i	0.173095	+	0.119438i
$628$	10.2810	+	5.93571i	0.410255	+	0.236861i
$629$	22.9511			0.915118
$630$		0			0
$631$	−35.8363			−1.42662			−0.713311	−	0.700848i	$-0.752805\pi$
$631$	−35.8363			−1.42662			−0.713311	+	0.700848i	$0.752805\pi$
$632$	−10.6713	−	6.16110i	−0.424483	−	0.245076i
$633$	−6.41292	−	4.42502i	−0.254891	−	0.175879i
$634$	0.508489	+	0.880729i	0.0201947	+	0.0349782i
$635$	5.59824	−	9.69644i	0.222160	−	0.384792i
$636$	18.2256	+	38.3939i	0.722691	+	1.52242i
$637$		0			0
$638$			7.61971i			0.301667i
$639$	−2.58555	+	0.981510i	−0.102283	+	0.0388279i
$640$	8.78920	−	5.07445i	0.347424	−	0.200585i
$641$	−13.5251	+	7.80872i	−0.534209	+	0.308426i	−0.742729	−	0.669592i	$-0.766469\pi$
$641$	−13.5251	+	7.80872i	−0.534209	+	0.308426i	0.208519	+	0.978018i	$0.433136\pi$
$642$	−0.710047	+	8.81293i	−0.0280233	+	0.347819i
$643$		−	29.3208i		−	1.15630i	−0.815931	−	0.578149i	$-0.803775\pi$
$643$		−	29.3208i		−	1.15630i	0.815931	−	0.578149i	$-0.196225\pi$
$644$		0			0
$645$	8.54532	−	4.05647i	0.336472	−	0.159723i
$646$	1.49031	−	2.58129i	0.0586355	−	0.101560i
$647$	−3.33405	−	5.77475i	−0.131075	−	0.227029i	0.793016	−	0.609201i	$-0.208510\pi$
$647$	−3.33405	−	5.77475i	−0.131075	−	0.227029i	−0.924091	+	0.382172i	$0.875176\pi$
$648$	−8.87215	−	10.0018i	−0.348531	−	0.392908i
$649$	−8.72495	−	5.03735i	−0.342484	−	0.197733i
$650$	1.18311			0.0464053
$651$		0			0
$652$	−30.4404			−1.19214
$653$	38.2165	+	22.0643i	1.49553	+	0.863444i	0.999987	−	0.00514013i	$-0.00163616\pi$
$653$	38.2165	+	22.0643i	1.49553	+	0.863444i	0.495542	+	0.868584i	$0.334969\pi$
$654$	0.949214	−	1.37564i	0.0371172	−	0.0537918i
$655$	7.83183	+	13.5651i	0.306015	+	0.530034i
$656$	3.61840	−	6.26726i	0.141275	−	0.244695i
$657$	−0.689043	−	0.562222i	−0.0268821	−	0.0219344i
$658$		0			0
$659$			7.10057i			0.276599i	0.990390	+	0.138299i	$0.0441636\pi$
$659$			7.10057i			0.276599i	−0.990390	+	0.138299i	$0.955836\pi$
$660$	8.12509	+	0.654628i	0.316269	+	0.0254814i
$661$	20.5558	−	11.8679i	0.799527	−	0.461607i	−0.0437789	−	0.999041i	$-0.513940\pi$
$661$	20.5558	−	11.8679i	0.799527	−	0.461607i	0.843306	+	0.537434i	$0.180606\pi$
$662$	−10.1354	+	5.85170i	−0.393925	+	0.227433i
$663$	−34.2149	−	2.75665i	−1.32880	−	0.107059i
$664$		−	3.13701i		−	0.121740i
$665$		0			0
$666$	−3.18479	−	2.59862i	−0.123408	−	0.100694i
$667$	11.8730	−	20.5646i	0.459724	−	0.796265i
$668$	−4.45299	−	7.71281i	−0.172291	−	0.298418i
$669$	−7.08909	+	10.2738i	−0.274080	+	0.397208i
$670$	1.17564	+	0.678754i	0.0454188	+	0.0262226i
$671$	−23.7464			−0.916721
$672$		0			0
$673$	−14.7915			−0.570171			−0.285086	−	0.958502i	$-0.592022\pi$
$673$	−14.7915			−0.570171			−0.285086	+	0.958502i	$0.592022\pi$
$674$	0.615374	+	0.355286i	0.0237033	+	0.0136851i
$675$	−4.99031	+	1.44803i	−0.192077	+	0.0557349i
$676$	−3.32514	−	5.75931i	−0.127890	−	0.221512i
$677$	−18.2590	+	31.6255i	−0.701749	+	1.21547i	0.266103	+	0.963945i	$0.414264\pi$
$677$	−18.2590	+	31.6255i	−0.701749	+	1.21547i	−0.967852	+	0.251521i	$0.919069\pi$
$678$	4.33609	−	2.05834i	0.166526	−	0.0790501i
$679$		0			0
$680$		−	9.59847i		−	0.368084i
$681$	−0.259145	+	3.21645i	−0.00993047	+	0.123255i
$682$	5.83763	−	3.37035i	0.223534	−	0.129058i
$683$	−18.9828	+	10.9597i	−0.726356	+	0.419362i	−0.817088	−	0.576514i	$-0.804413\pi$
$683$	−18.9828	+	10.9597i	−0.726356	+	0.419362i	0.0907317	+	0.995875i	$0.471079\pi$
$684$	6.20936	−	2.35715i	0.237421	−	0.0901279i
$685$		−	5.82840i		−	0.222692i
$686$		0			0
$687$	−14.9343	−	31.4605i	−0.569779	−	1.20029i
$688$	−8.54532	+	14.8009i	−0.325787	+	0.564280i
$689$	−20.3275	−	35.2082i	−0.774414	−	1.34132i
$690$	1.68049	+	1.15957i	0.0639752	+	0.0441439i
$691$	−27.2031	−	15.7057i	−1.03485	−	0.597473i	−0.116482	−	0.993193i	$-0.537162\pi$
$691$	−27.2031	−	15.7057i	−1.03485	−	0.597473i	−0.918371	+	0.395720i	$0.870495\pi$
$692$	−12.6164			−0.479604
$693$		0			0
$694$	−3.15929			−0.119925
$695$	−10.4239	−	6.01825i	−0.395402	−	0.228285i
$696$	16.4558	+	11.3548i	0.623755	+	0.430401i
$697$	−7.47093	−	12.9400i	−0.282982	−	0.490139i
$698$	−7.00663	+	12.1358i	−0.265205	+	0.459348i
$699$	−1.16265	−	2.44923i	−0.0439755	−	0.0926385i
$700$		0			0
$701$			29.6988i			1.12171i	0.827915	+	0.560854i	$0.189527\pi$
$701$			29.6988i			1.12171i	−0.827915	+	0.560854i	$0.810473\pi$
$702$	4.43569	+	4.25648i	0.167414	+	0.160651i
$703$	3.67888	−	2.12400i	0.138751	−	0.0801082i
$704$	−10.2314	+	5.90711i	−0.385611	+	0.222633i
$705$	0.447922	−	5.55951i	0.0168697	−	0.209383i
$706$			2.20435i			0.0829617i
$707$		0			0
$708$	−11.4790	+	5.44908i	−0.431407	+	0.204789i
$709$	−6.66342	+	11.5414i	−0.250250	+	0.433446i	−0.963595	−	0.267368i	$-0.913846\pi$
$709$	−6.66342	+	11.5414i	−0.250250	+	0.433446i	0.713344	+	0.700814i	$0.247180\pi$
$710$	0.177795	+	0.307950i	0.00667253	+	0.0115572i
$711$	−24.5635	−	3.98396i	−0.921202	−	0.149410i
$712$	−24.2251	−	13.9864i	−0.907875	−	0.524162i
$713$	−21.0067			−0.786706
$714$		0			0
$715$	−7.79751			−0.291610
$716$	32.0133	+	18.4829i	1.19639	+	0.690737i
$717$	5.59947	−	8.11498i	0.209116	−	0.303060i
$718$	−0.926842	−	1.60534i	−0.0345895	−	0.0599107i
$719$	25.5863	−	44.3167i	0.954207	−	1.65273i	0.218034	−	0.975941i	$-0.430036\pi$
$719$	25.5863	−	44.3167i	0.954207	−	1.65273i	0.736173	−	0.676794i	$-0.236631\pi$
$720$	5.93523	−	7.27405i	0.221193	−	0.271088i
$721$		0			0
$722$			6.77720i			0.252221i
$723$	23.0187	+	1.85459i	0.856074	+	0.0689728i
$724$	8.31751	−	4.80211i	0.309118	−	0.178469i
$725$	6.72927	−	3.88515i	0.249919	−	0.144291i
$726$	−3.02141	−	0.243431i	−0.112135	−	0.00903459i
$727$			51.6371i			1.91511i	0.288246	+	0.957556i	$0.406928\pi$
$727$			51.6371i			1.91511i	−0.288246	+	0.957556i	$0.593072\pi$
$728$		0			0
$729$	−23.9192	−	12.5248i	−0.885898	−	0.463880i
$730$	−0.0571724	+	0.0990255i	−0.00211605	+	0.00366510i
$731$	17.6436	+	30.5596i	0.652571	+	1.13029i
$732$	−17.0097	+	24.6512i	−0.628697	+	0.911134i
$733$	−19.0043	−	10.9721i	−0.701940	−	0.405265i	0.106130	−	0.994352i	$-0.466154\pi$
$733$	−19.0043	−	10.9721i	−0.701940	−	0.405265i	−0.808069	+	0.589087i	$0.799487\pi$
$734$	−9.47979			−0.349905
$735$		0			0
$736$	−12.7685			−0.470652
$737$	−7.74829	−	4.47347i	−0.285412	−	0.164783i
$738$	−0.428427	+	2.64151i	−0.0157706	+	0.0972352i
$739$	19.2874	+	33.4068i	0.709500	+	1.22889i	0.965043	+	0.262092i	$0.0844125\pi$
$739$	19.2874	+	33.4068i	0.709500	+	1.22889i	−0.255543	+	0.966798i	$0.582254\pi$
$740$	3.28782	−	5.69468i	0.120863	−	0.209341i
$741$	−5.73950	+	2.72454i	−0.210846	+	0.100089i
$742$		0			0
$743$			3.81873i			0.140096i	0.997544	+	0.0700478i	$0.0223152\pi$
$743$			3.81873i			0.140096i	−0.997544	+	0.0700478i	$0.977685\pi$
$744$	1.42039	−	17.6296i	0.0520741	−	0.646332i
$745$	−16.1925	+	9.34874i	−0.593247	+	0.342511i
$746$	8.85325	−	5.11143i	0.324141	−	0.187143i
$747$	−2.24835	−	5.92274i	−0.0822628	−	0.216702i
$748$			30.4083i			1.11184i
$749$		0			0
$750$	0.286507	+	0.603555i	0.0104618	+	0.0220387i
$751$	−10.5271	+	18.2334i	−0.384139	+	0.665348i	−0.991649	−	0.128964i	$-0.958835\pi$
$751$	−10.5271	+	18.2334i	−0.384139	+	0.665348i	0.607511	+	0.794312i	$0.292168\pi$
$752$	5.03863	+	8.72717i	0.183740	+	0.318247i
$753$	7.59263	+	5.23904i	0.276691	+	0.190921i
$754$	−7.96145	−	4.59654i	−0.289939	−	0.167396i
$755$	−5.95062			−0.216565
$756$		0			0
$757$	28.6903			1.04277			0.521383	−	0.853323i	$-0.325416\pi$
$757$	28.6903			1.04277			0.521383	+	0.853323i	$0.325416\pi$
$758$	−4.37405	−	2.52536i	−0.158873	−	0.0917251i
$759$	−11.0756	−	7.64236i	−0.402020	−	0.277400i
$760$	−0.888288	−	1.53856i	−0.0322216	−	0.0558095i
$761$	−5.34875	+	9.26431i	−0.193892	+	0.335831i	−0.946537	−	0.322596i	$-0.895444\pi$
$761$	−5.34875	+	9.26431i	−0.193892	+	0.335831i	0.752645	+	0.658427i	$0.228778\pi$
$762$	−3.20788	−	6.75769i	−0.116209	−	0.244805i
$763$		0			0
$764$			15.9963i			0.578726i
$765$	−6.87938	−	18.1221i	−0.248724	−	0.655206i
$766$	5.66753	−	3.27215i	0.204776	−	0.118228i
$767$	10.5265	−	6.07750i	0.380092	−	0.219446i
$768$	−0.748293	+	9.28763i	−0.0270017	+	0.335139i
$769$			38.6874i			1.39510i	0.716535	+	0.697551i	$0.245727\pi$
$769$			38.6874i			1.39510i	−0.716535	+	0.697551i	$0.754273\pi$
$770$		0			0
$771$	10.1707	−	4.82802i	0.366288	−	0.173877i
$772$	22.0036	−	38.1114i	0.791928	−	1.37166i
$773$	−11.4438	−	19.8212i	−0.411603	−	0.712918i	0.583462	−	0.812141i	$-0.301698\pi$
$773$	−11.4438	−	19.8212i	−0.411603	−	0.712918i	−0.995065	+	0.0992225i	$0.968364\pi$
$774$	1.01179	−	6.23826i	0.0363679	−	0.224230i
$775$	−5.95299	−	3.43696i	−0.213838	−	0.123459i
$776$	−18.3748			−0.659618
$777$		0			0
$778$	0.950743			0.0340858
$779$	−2.39507	−	1.38279i	−0.0858121	−	0.0495437i
$780$	−5.58540	+	8.09460i	−0.199989	+	0.289833i
$781$	−1.17180	−	2.02961i	−0.0419302	−	0.0726252i
$782$	−3.80826	+	6.59610i	−0.136183	+	0.235876i
$783$	39.2070	+	9.64387i	1.40114	+	0.344644i
$784$		0			0
$785$		−	6.41279i		−	0.228882i
$786$	10.4312	+	0.840427i	0.372068	+	0.0299770i
$787$	−28.1627	+	16.2597i	−1.00389	+	0.579597i	−0.909397	−	0.415929i	$-0.863457\pi$
$787$	−28.1627	+	16.2597i	−1.00389	+	0.579597i	−0.0944937	+	0.995525i	$0.530123\pi$
$788$	−18.7323	+	10.8151i	−0.667311	+	0.385272i
$789$	25.5973	+	2.06235i	0.911289	+	0.0734214i
$790$			3.19957i			0.113835i
$791$		0			0
$792$	7.16265	−	8.77834i	0.254514	−	0.311925i
$793$	14.3249	−	24.8115i	0.508692	−	0.881081i
$794$	0.646809	+	1.12031i	0.0229544	+	0.0397582i
$795$	13.0386	−	18.8961i	0.462433	−	0.670177i
$796$	−22.6480	−	13.0758i	−0.802736	−	0.463460i
$797$	31.9080			1.13024			0.565120	−	0.825009i	$-0.308830\pi$
$797$	31.9080			1.13024			0.565120	+	0.825009i	$0.308830\pi$
$798$		0			0
$799$	20.8066			0.736084
$800$	−3.61840	−	2.08909i	−0.127930	−	0.0738603i
$801$	−55.7618	−	9.04402i	−1.97025	−	0.319555i
$802$	1.20480	+	2.08677i	0.0425429	+	0.0736865i
$803$	0.376807	−	0.652648i	0.0132972	−	0.0230315i
$804$	−10.1941	+	4.83912i	−0.359516	+	0.170663i
$805$		0			0
$806$			8.13258i			0.286458i
$807$	−3.42299	+	42.4853i	−0.120495	+	1.49555i
$808$	−8.97507	+	5.18176i	−0.315742	+	0.182294i
$809$	17.9862	−	10.3843i	0.632360	−	0.365093i	−0.149305	−	0.988791i	$-0.547704\pi$
$809$	17.9862	−	10.3843i	0.632360	−	0.365093i	0.781666	+	0.623698i	$0.214370\pi$
$810$	−1.09725	+	3.29361i	−0.0385534	+	0.115726i
$811$		−	5.77041i		−	0.202627i	−0.994855	−	0.101313i	$-0.967696\pi$
$811$		−	5.77041i		−	0.202627i	0.994855	−	0.101313i	$-0.0323044\pi$
$812$		0			0
$813$	2.83135	+	5.96450i	0.0992998	+	0.209184i
$814$	1.74162	−	3.01657i	0.0610437	−	0.105731i
$815$	8.22174	+	14.2405i	0.287995	+	0.498822i
$816$	28.8258	+	19.8903i	1.00911	+	0.696299i
$817$	5.65626	+	3.26564i	0.197887	+	0.114250i
$818$	−4.54968			−0.159076
$819$		0			0
$820$	−4.28096			−0.149497
$821$	12.7908	+	7.38477i	0.446402	+	0.257730i	0.706309	−	0.707903i	$-0.250359\pi$
$821$	12.7908	+	7.38477i	0.446402	+	0.257730i	−0.259907	+	0.965634i	$0.583692\pi$
$822$	−3.20504	−	2.21153i	−0.111789	−	0.0771359i
$823$	−13.7054	−	23.7385i	−0.477741	−	0.827472i	0.521933	−	0.852986i	$-0.325211\pi$
$823$	−13.7054	−	23.7385i	−0.477741	−	0.827472i	−0.999674	+	0.0255145i	$0.991878\pi$
$824$	2.80258	−	4.85422i	0.0976326	−	0.169105i
$825$	−1.88829	−	3.97785i	−0.0657418	−	0.138491i
$826$		0			0
$827$		−	27.6521i		−	0.961557i	−0.876842	−	0.480779i	$-0.840354\pi$
$827$		−	27.6521i		−	0.961557i	0.876842	−	0.480779i	$-0.159646\pi$
$828$	−15.8671	+	6.02334i	−0.551419	+	0.209326i
$829$	18.6252	−	10.7533i	0.646880	−	0.373476i	−0.140380	−	0.990098i	$-0.544832\pi$
$829$	18.6252	−	10.7533i	0.646880	−	0.373476i	0.787260	+	0.616621i	$0.211499\pi$
$830$	−0.705423	+	0.407276i	−0.0244856	+	0.0141368i
$831$	2.61162	−	32.4149i	0.0905963	−	1.12446i
$832$		−	14.2537i		−	0.494158i
$833$		0			0
$834$	−7.26469	+	3.44855i	−0.251556	+	0.119414i
$835$	−2.40545	+	4.16636i	−0.0832439	+	0.144183i
$836$	2.81414	+	4.87423i	0.0973289	+	0.168579i
$837$	−9.95368	−	34.3030i	−0.344050	−	1.18569i
$838$	−4.02262	−	2.32246i	−0.138959	−	0.0802281i
$839$	−26.4538			−0.913286			−0.456643	−	0.889650i	$-0.650948\pi$
$839$	−26.4538			−0.913286			−0.456643	+	0.889650i	$0.650948\pi$
$840$		0			0
$841$	−31.3775			−1.08198
$842$	−3.81701	−	2.20375i	−0.131543	−	0.0759463i
$843$	23.3022	−	33.7705i	0.802570	−	1.16312i
$844$	−4.16373	−	7.21179i	−0.143321	−	0.248240i
$845$	−1.79620	+	3.11111i	−0.0617911	+	0.107025i
$846$	−2.88721	−	2.35581i	−0.0992644	−	0.0809944i
$847$		0			0
$848$			41.4797i			1.42442i
$849$	−8.70840	−	0.701625i	−0.298871	−	0.0240797i
$850$	−2.15842	+	1.24616i	−0.0740330	+	0.0427430i
$851$	−9.40081	+	5.42756i	−0.322256	+	0.186054i
$852$	−2.94630	−	0.237380i	−0.100939	−	0.00813250i
$853$			6.05997i			0.207490i	0.994604	+	0.103745i	$0.0330825\pi$
$853$			6.05997i			0.207490i	−0.994604	+	0.103745i	$0.966917\pi$
$854$		0			0
$855$	−2.77982	−	2.26818i	−0.0950677	−	0.0775702i
$856$	−9.82952	+	17.0252i	−0.335966	+	0.581910i
$857$	−5.16988	−	8.95449i	−0.176600	−	0.305880i	0.764114	−	0.645081i	$-0.223176\pi$
$857$	−5.16988	−	8.95449i	−0.176600	−	0.305880i	−0.940714	+	0.339202i	$0.889843\pi$
$858$	−2.95869	+	4.28785i	−0.101008	+	0.146385i
$859$	30.7393	+	17.7473i	1.04881	+	0.605531i	0.922316	−	0.386436i	$-0.126294\pi$
$859$	30.7393	+	17.7473i	1.04881	+	0.605531i	0.126495	+	0.991967i	$0.459627\pi$
$860$	10.1100			0.344749
$861$		0			0
$862$	12.5758			0.428334
$863$	13.1125	+	7.57049i	0.446354	+	0.257702i	0.706289	−	0.707924i	$-0.250368\pi$
$863$	13.1125	+	7.57049i	0.446354	+	0.257702i	−0.259935	+	0.965626i	$0.583701\pi$
$864$	−6.05014	−	20.8504i	−0.205830	−	0.709344i
$865$	3.40761	+	5.90215i	0.115862	+	0.200679i
$866$	−0.844064	+	1.46196i	−0.0286824	+	0.0496795i
$867$	38.7240	−	18.3823i	1.31514	−	0.624295i
$868$		0			0
$869$		−	21.0874i		−	0.715342i
$870$	0.416912	−	5.17461i	0.0141346	−	0.175436i
$871$	9.34821	−	5.39719i	0.316752	−	0.182877i
$872$	3.21835	−	1.85812i	0.108987	−	0.0629238i
$873$	−34.6921	+	13.1696i	−1.17415	+	0.445722i
$874$			1.40974i			0.0476852i
$875$		0			0
$876$	−0.407605	−	0.858658i	−0.0137717	−	0.0290114i
$877$	−9.79476	+	16.9650i	−0.330745	+	0.572868i	−0.982658	−	0.185426i	$-0.940633\pi$
$877$	−9.79476	+	16.9650i	−0.330745	+	0.572868i	0.651913	+	0.758294i	$0.273967\pi$
$878$	−2.85984	−	4.95339i	−0.0965150	−	0.167169i
$879$	8.97306	+	6.19156i	0.302654	+	0.208836i
$880$	6.88985	+	3.97785i	0.232257	+	0.134093i
$881$	28.7481			0.968548			0.484274	−	0.874917i	$-0.339084\pi$
$881$	28.7481			0.968548			0.484274	+	0.874917i	$0.339084\pi$
$882$		0			0
$883$	5.77550			0.194361			0.0971805	−	0.995267i	$-0.469018\pi$
$883$	5.77550			0.194361			0.0971805	+	0.995267i	$0.469018\pi$
$884$	−31.7721	−	18.3437i	−1.06861	−	0.616964i
$885$	5.64957	+	3.89829i	0.189908	+	0.131040i
$886$	3.06896	+	5.31559i	0.103104	+	0.178581i
$887$	−6.56917	+	11.3781i	−0.220571	+	0.382041i	−0.954982	−	0.296665i	$-0.904125\pi$
$887$	−6.56917	+	11.3781i	−0.220571	+	0.382041i	0.734410	+	0.678706i	$0.237459\pi$
$888$	−3.91937	−	8.25651i	−0.131525	−	0.277070i
$889$		0			0
$890$			7.26337i			0.243469i
$891$	7.23165	−	21.7073i	0.242269	−	0.727221i
$892$	−11.5536	+	6.67049i	−0.386844	+	0.223345i
$893$	3.33514	−	1.92554i	0.111606	−	0.0644358i
$894$	−1.00320	+	12.4515i	−0.0335522	+	0.416442i
$895$		−	19.9684i		−	0.667470i
$896$		0			0
$897$	14.6664	−	6.96215i	0.489698	−	0.232460i
$898$	−6.78657	+	11.7547i	−0.226471	+	0.392259i
$899$	26.7062	+	46.2565i	0.890702	+	1.54274i
$900$	−5.48200	−	0.889127i	−0.182733	−	0.0296376i
$901$	74.1693	+	42.8217i	2.47094	+	1.42660i
$902$	−2.26770			−0.0755061
$903$		0			0
$904$	10.6724			0.354959
$905$	−4.49301	−	2.59404i	−0.149353	−	0.0862287i
$906$	−2.25790	+	3.27225i	−0.0750138	+	0.108713i
$907$	3.08504	+	5.34345i	0.102437	+	0.177426i	0.912688	−	0.408657i	$-0.134003\pi$
$907$	3.08504	+	5.34345i	0.102437	+	0.177426i	−0.810251	+	0.586083i	$0.800669\pi$
$908$	−1.72444	+	2.98681i	−0.0572274	+	0.0991208i
$909$	−13.2313	+	16.2158i	−0.438853	+	0.537845i
$910$		0			0
$911$			53.7961i			1.78234i	0.453665	+	0.891172i	$0.350116\pi$
$911$			53.7961i			1.78234i	−0.453665	+	0.891172i	$0.649884\pi$
$912$	6.46130	+	0.520579i	0.213955	+	0.0172381i
$913$	4.64924	−	2.68424i	0.153867	−	0.0888354i
$914$	4.69648	−	2.71151i	0.155346	−	0.0896888i
$915$	16.1264	+	1.29928i	0.533123	+	0.0429530i
$916$		−	37.2211i		−	1.22982i
$917$		0			0
$918$	−12.5756	−	3.09327i	−0.415058	−	0.102093i
$919$	0.310140	−	0.537179i	0.0102306	−	0.0177199i	−0.860865	−	0.508834i	$-0.830077\pi$
$919$	0.310140	−	0.537179i	0.0102306	−	0.0177199i	0.871095	+	0.491114i	$0.163410\pi$
$920$	2.26989	+	3.93156i	0.0748359	+	0.129620i
$921$	15.7781	−	22.8662i	0.519905	−	0.753468i
$922$	4.51508	+	2.60678i	0.148696	+	0.0858498i
$923$	2.82752			0.0930688
$924$		0			0
$925$	−3.55208			−0.116792
$926$	−5.95888	−	3.44036i	−0.195821	−	0.113057i
$927$	1.81224	−	11.1735i	0.0595216	−	0.366986i
$928$	16.2328	+	28.1161i	0.532868	+	0.922955i
$929$	26.4805	−	45.8655i	0.868796	−	1.50480i	0.00556817	−	0.999984i	$-0.498228\pi$
$929$	26.4805	−	45.8655i	0.868796	−	1.50480i	0.863228	−	0.504814i	$-0.168439\pi$
$930$	−4.14879	+	1.96943i	−0.136044	+	0.0645802i
$931$		0			0
$932$		−	2.89770i		−	0.0949174i
$933$	−2.51385	+	31.2013i	−0.0822998	+	1.02149i
$934$	−3.06975	+	1.77232i	−0.100445	+	0.0579921i
$935$	14.2255	−	8.21309i	0.465223	−	0.268597i
$936$	4.85121	+	12.7794i	0.158567	+	0.417707i
$937$		−	0.667265i		−	0.0217986i	−0.999941	−	0.0108993i	$-0.996531\pi$
$937$		−	0.667265i		−	0.0217986i	0.999941	−	0.0108993i	$-0.00346942\pi$
$938$		0			0
$939$	−13.8318	−	29.1380i	−0.451385	−	0.950884i
$940$	2.98062	−	5.16259i	0.0972171	−	0.168385i
$941$	12.4842	+	21.6232i	0.406972	+	0.704896i	0.994549	−	0.104272i	$-0.0332514\pi$
$941$	12.4842	+	21.6232i	0.406972	+	0.704896i	−0.587577	+	0.809168i	$0.699918\pi$
$942$	−3.52639	−	2.43327i	−0.114896	−	0.0792801i
$943$	6.12023	+	3.53352i	0.199302	+	0.115067i
$944$	−12.4016			−0.403638
$945$		0			0
$946$	5.35547			0.174121
$947$	−47.6286	−	27.4984i	−1.54772	−	0.893577i	−0.998315	−	0.0580209i	$-0.981521\pi$
$947$	−47.6286	−	27.4984i	−1.54772	−	0.893577i	−0.549405	−	0.835556i	$-0.685146\pi$
$948$	−21.8908	−	15.1050i	−0.710981	−	0.490589i
$949$	0.454613	+	0.787412i	0.0147574	+	0.0255605i
$950$	−0.230652	+	0.399500i	−0.00748333	+	0.0129615i
$951$	1.95830	+	4.12534i	0.0635022	+	0.133773i
$952$		0			0
$953$		−	35.8657i		−	1.16180i	−0.813974	−	0.580902i	$-0.802700\pi$
$953$		−	35.8657i		−	1.16180i	0.813974	−	0.580902i	$-0.197300\pi$
$954$	−5.44361	−	14.3399i	−0.176243	−	0.464271i
$955$	7.48332	−	4.32049i	0.242154	−	0.139808i
$956$	9.12588	−	5.26883i	0.295152	−	0.170406i
$957$	−2.74774	+	34.1043i	−0.0888219	+	1.10244i
$958$		−	7.28288i		−	0.235299i
$959$		0			0
$960$	7.27144	−	3.45176i	0.234685	−	0.111405i
$961$	8.12541	−	14.0736i	0.262110	−	0.453988i
$962$	2.10124	+	3.63946i	0.0677468	+	0.117341i
$963$	−6.35607	+	39.1889i	−0.204821	+	1.26285i
$964$	21.3753	+	12.3410i	0.688451	+	0.397478i
$965$	−23.7721			−0.765252
$966$		0			0
$967$	11.8780			0.381971			0.190986	−	0.981593i	$-0.438832\pi$
$967$	11.8780			0.381971			0.190986	+	0.981593i	$0.438832\pi$
$968$	−5.83690	−	3.36994i	−0.187605	−	0.108314i
$969$	7.60118	−	11.0159i	0.244185	−	0.353883i
$970$	2.38559	+	4.13197i	0.0765968	+	0.132669i
$971$	−2.61333	+	4.52642i	−0.0838658	+	0.145260i	−0.904907	−	0.425609i	$-0.860060\pi$
$971$	−2.61333	+	4.52642i	−0.0838658	+	0.145260i	0.821042	+	0.570868i	$0.193393\pi$
$972$	−17.3542	−	23.0562i	−0.556637	−	0.739528i
$973$		0			0
$974$		−	2.01940i		−	0.0647056i
$975$	5.29536	+	0.426640i	0.169587	+	0.0136634i
$976$	−25.3148	+	14.6155i	−0.810308	+	0.467831i
$977$	15.5190	−	8.95992i	0.496498	−	0.286653i	−0.230768	−	0.973009i	$-0.574124\pi$
$977$	15.5190	−	8.95992i	0.496498	−	0.286653i	0.727266	+	0.686355i	$0.240791\pi$
$978$	10.9505	+	0.882267i	0.350158	+	0.0282118i
$979$		−	47.8708i		−	1.52996i
$980$		0			0
$981$	4.74457	−	5.81481i	0.151482	−	0.185653i
$982$	−3.76475	+	6.52074i	−0.120138	+	0.208085i
$983$	20.9414	+	36.2715i	0.667926	+	1.15688i	0.978483	+	0.206328i	$0.0661513\pi$
$983$	20.9414	+	36.2715i	0.667926	+	1.15688i	−0.310556	+	0.950555i	$0.600515\pi$
$984$	−3.37929	+	4.89740i	−0.107728	+	0.156123i
$985$	10.1189	+	5.84217i	0.322416	+	0.186147i
$986$	19.3661			0.616742
$987$		0			0
$988$	−6.79044			−0.216033
$989$	−14.4537	−	8.34485i	−0.459601	−	0.265351i
$990$	−2.90391	−	0.470987i	−0.0922925	−	0.0149689i
$991$	−4.88415	−	8.45960i	−0.155150	−	0.268728i	0.777964	−	0.628309i	$-0.216253\pi$
$991$	−4.88415	−	8.45960i	−0.155150	−	0.268728i	−0.933114	+	0.359581i	$0.882919\pi$
$992$	14.3602	−	24.8726i	0.455937	−	0.789706i
$993$	−47.4744	+	22.5361i	−1.50656	+	0.715162i
$994$		0			0
$995$			14.1268i			0.447848i
$996$	0.543767	−	6.74911i	0.0172299	−	0.213854i
$997$	30.4616	−	17.5870i	0.964728	−	0.556986i	0.0671032	−	0.997746i	$-0.478624\pi$
$997$	30.4616	−	17.5870i	0.964728	−	0.556986i	0.897625	+	0.440760i	$0.145291\pi$
$998$	−12.2380	+	7.06563i	−0.387388	+	0.223659i
$999$	−13.3174	−	12.7794i	−0.421344	−	0.404322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.k.656.3		8
3.2	odd	2		735.2.s.l.656.2		8
7.2	even	3		735.2.b.c.146.5		8
7.3	odd	6		735.2.s.l.521.2		8
7.4	even	3		105.2.s.d.101.2	yes	8
7.5	odd	6		735.2.b.d.146.5		8
7.6	odd	2		105.2.s.c.26.3	✓	8
21.2	odd	6		735.2.b.d.146.4		8
21.5	even	6		735.2.b.c.146.4		8
21.11	odd	6		105.2.s.c.101.3	yes	8
21.17	even	6	inner	735.2.s.k.521.3		8
21.20	even	2		105.2.s.d.26.2	yes	8
35.4	even	6		525.2.t.f.101.3		8
35.13	even	4		525.2.q.f.299.4		16
35.18	odd	12		525.2.q.e.374.4		16
35.27	even	4		525.2.q.f.299.5		16
35.32	odd	12		525.2.q.e.374.5		16
35.34	odd	2		525.2.t.g.26.2		8
105.32	even	12		525.2.q.f.374.4		16
105.53	even	12		525.2.q.f.374.5		16
105.62	odd	4		525.2.q.e.299.4		16
105.74	odd	6		525.2.t.g.101.2		8
105.83	odd	4		525.2.q.e.299.5		16
105.104	even	2		525.2.t.f.26.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.3	✓	8	7.6	odd	2
105.2.s.c.101.3	yes	8	21.11	odd	6
105.2.s.d.26.2	yes	8	21.20	even	2
105.2.s.d.101.2	yes	8	7.4	even	3
525.2.q.e.299.4		16	105.62	odd	4
525.2.q.e.299.5		16	105.83	odd	4
525.2.q.e.374.4		16	35.18	odd	12
525.2.q.e.374.5		16	35.32	odd	12
525.2.q.f.299.4		16	35.13	even	4
525.2.q.f.299.5		16	35.27	even	4
525.2.q.f.374.4		16	105.32	even	12
525.2.q.f.374.5		16	105.53	even	12
525.2.t.f.26.3		8	105.104	even	2
525.2.t.f.101.3		8	35.4	even	6
525.2.t.g.26.2		8	35.34	odd	2
525.2.t.g.101.2		8	105.74	odd	6
735.2.b.c.146.4		8	21.5	even	6
735.2.b.c.146.5		8	7.2	even	3
735.2.b.d.146.4		8	21.2	odd	6
735.2.b.d.146.5		8	7.5	odd	6
735.2.s.k.521.3		8	21.17	even	6	inner
735.2.s.k.656.3		8	1.1	even	1	trivial
735.2.s.l.521.2		8	7.3	odd	6
735.2.s.l.656.2		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.334053 - 0.192865i) q^{2} +(-1.42561 - 0.983691i) q^{3} +(-0.925606 - 1.60320i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.286507 + 0.603555i) q^{6} +1.48553i q^{8} +(1.06470 + 2.80471i) q^{9} +O(q^{10})\)	\(q+(-0.334053 - 0.192865i) q^{2} +(-1.42561 - 0.983691i) q^{3} +(-0.925606 - 1.60320i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.286507 + 0.603555i) q^{6} +1.48553i q^{8} +(1.06470 + 2.80471i) q^{9} +(0.334053 - 0.192865i) q^{10} +(-2.20164 + 1.27112i) q^{11} +(-0.257501 + 3.19604i) q^{12} -3.06718i q^{13} +(1.56470 - 0.742765i) q^{15} +(-1.56470 + 2.71015i) q^{16} +(3.23065 + 5.59565i) q^{17} +(0.185264 - 1.14227i) q^{18} +(1.03570 + 0.597960i) q^{19} +1.85121 q^{20} +0.980620 q^{22} +(-2.64657 - 1.52800i) q^{23} +(1.46130 - 2.11778i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.591553 + 1.02460i) q^{26} +(1.24112 - 5.04575i) q^{27} +7.77029i q^{29} +(-0.665947 - 0.0536545i) q^{30} +(5.95299 - 3.43696i) q^{31} +(3.61840 - 2.08909i) q^{32} +(4.38907 + 0.353622i) q^{33} -2.49232i q^{34} +(3.51101 - 4.30299i) q^{36} +(1.77604 - 3.07619i) q^{37} +(-0.230652 - 0.399500i) q^{38} +(-3.01716 + 4.37259i) q^{39} +(-1.28651 - 0.742765i) q^{40} -2.31252 q^{41} +5.46130 q^{43} +(4.07571 + 2.35311i) q^{44} +(-2.96130 - 0.480295i) q^{45} +(0.589395 + 1.02086i) q^{46} +(1.61009 - 2.78876i) q^{47} +(4.89660 - 2.32442i) q^{48} +0.385731i q^{50} +(0.898757 - 11.1552i) q^{51} +(-4.91730 + 2.83900i) q^{52} +(11.4790 - 6.62740i) q^{53} +(-1.38775 + 1.44618i) q^{54} -2.54224i q^{55} +(-0.888288 - 1.87126i) q^{57} +(1.49862 - 2.59569i) q^{58} +(1.98146 + 3.43199i) q^{59} +(-2.63910 - 1.82102i) q^{60} +(8.08933 + 4.67038i) q^{61} -2.65148 q^{62} +4.64717 q^{64} +(2.65626 + 1.53359i) q^{65} +(-1.39798 - 0.964627i) q^{66} +(1.75966 + 3.04782i) q^{67} +(5.98062 - 10.3587i) q^{68} +(2.26989 + 4.78173i) q^{69} +0.921861i q^{71} +(-4.16649 + 1.58165i) q^{72} +(-0.256722 + 0.148218i) q^{73} +(-1.18658 + 0.685073i) q^{74} +(-0.139098 + 1.72646i) q^{75} -2.21390i q^{76} +(1.85121 - 0.878771i) q^{78} +(-4.14741 + 7.18352i) q^{79} +(-1.56470 - 2.71015i) q^{80} +(-6.73281 + 5.97238i) q^{81} +(0.772502 + 0.446004i) q^{82} -2.11171 q^{83} -6.46130 q^{85} +(-1.82436 - 1.05330i) q^{86} +(7.64357 - 11.0774i) q^{87} +(-1.88829 - 3.27061i) q^{88} +(-9.41507 + 16.3074i) q^{89} +(0.896599 + 0.731577i) q^{90} +5.65729i q^{92} +(-11.8675 - 0.956152i) q^{93} +(-1.07571 + 0.621062i) q^{94} +(-1.03570 + 0.597960i) q^{95} +(-7.21343 - 0.581177i) q^{96} +12.3692i q^{97} +(-5.90923 - 4.82161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * q^96 - 34 * q^99

Introduction

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