LMFDB - Embedded newform 841.2.e.c.267.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(63,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,4,-16,6,16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			267.1
Root			$0.781831 + 0.623490i$ of defining polynomial
Character	$\chi$	$=$	841.267
Dual form			841.2.e.c.63.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.347948 - 0.277479i) q^{2} +(1.21572 + 0.277479i) q^{3} +(-0.400969 - 1.75676i) q^{4} +(-0.431468 + 0.541044i) q^{5} +(-0.346011 - 0.433884i) q^{6} +(-0.0794168 + 0.347948i) q^{7} +(-0.734141 + 1.52446i) q^{8} +(-1.30194 - 0.626980i) q^{9} +(0.300257 - 0.0685317i) q^{10} +(-2.14295 - 4.44989i) q^{11} -2.24698i q^{12} +(-5.09299 + 2.45265i) q^{13} +(0.124181 - 0.0990311i) q^{14} +(-0.674671 + 0.538032i) q^{15} +(-2.56853 + 1.23694i) q^{16} +4.49396i q^{17} +(0.279032 + 0.579417i) q^{18} +(-2.29780 + 0.524459i) q^{19} +(1.12349 + 0.541044i) q^{20} +(-0.193096 + 0.400969i) q^{21} +(-0.489115 + 2.14295i) q^{22} +(1.43147 + 1.79500i) q^{23} +(-1.31551 + 1.64960i) q^{24} +(1.00604 + 4.40775i) q^{25} +(2.45265 + 0.559802i) q^{26} +(-4.33360 - 3.45593i) q^{27} +0.643104 q^{28} +0.384043 q^{30} +(-5.23203 - 4.17241i) q^{31} +(4.53614 + 1.03534i) q^{32} +(-1.37047 - 6.00442i) q^{33} +(1.24698 - 1.56366i) q^{34} +(-0.153989 - 0.193096i) q^{35} +(-0.579417 + 2.53859i) q^{36} +(2.14295 - 4.44989i) q^{37} +(0.945042 + 0.455108i) q^{38} +(-6.87219 + 1.56853i) q^{39} +(-0.508041 - 1.05496i) q^{40} -3.10992i q^{41} +(0.178448 - 0.0859360i) q^{42} +(2.66277 - 2.12349i) q^{43} +(-6.95812 + 5.54892i) q^{44} +(0.900969 - 0.433884i) q^{45} -1.02177i q^{46} +(-2.79640 - 5.80678i) q^{47} +(-3.46583 + 0.791053i) q^{48} +(6.19202 + 2.98192i) q^{49} +(0.873009 - 1.81282i) q^{50} +(-1.24698 + 5.46337i) q^{51} +(6.35086 + 7.96372i) q^{52} +(-2.92543 + 3.66837i) q^{53} +(0.548917 + 2.40496i) q^{54} +(3.33220 + 0.760553i) q^{55} +(-0.472129 - 0.376510i) q^{56} -2.93900 q^{57} -12.4940 q^{59} +(1.21572 + 0.969501i) q^{60} +(1.60191 + 0.365625i) q^{61} +(0.662718 + 2.90356i) q^{62} +(0.321552 - 0.403214i) q^{63} +(2.26391 + 2.83885i) q^{64} +(0.870469 - 3.81378i) q^{65} +(-1.18925 + 2.46950i) q^{66} +(-2.09299 - 1.00793i) q^{67} +(7.89481 - 1.80194i) q^{68} +(1.24218 + 2.57942i) q^{69} +0.109916i q^{70} +(-6.60872 + 3.18259i) q^{71} +(1.91161 - 1.52446i) q^{72} +(4.39831 - 3.50753i) q^{73} +(-1.98039 + 0.953703i) q^{74} +5.63773i q^{75} +(1.84270 + 3.82640i) q^{76} +(1.71851 - 0.392240i) q^{77} +(2.82640 + 1.36112i) q^{78} +(-2.02401 + 4.20291i) q^{79} +(0.439001 - 1.92339i) q^{80} +(-1.60656 - 2.01457i) q^{81} +(-0.862937 + 1.08209i) q^{82} +(-0.991271 - 4.34304i) q^{83} +(0.781831 + 0.178448i) q^{84} +(-2.43143 - 1.93900i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-4.44076 - 3.54138i) q^{89} +(-0.433884 - 0.0990311i) q^{90} +(-0.448927 - 1.96688i) q^{91} +(2.57942 - 3.23449i) q^{92} +(-5.20291 - 6.52424i) q^{93} +(-0.638260 + 2.79640i) q^{94} +(0.707674 - 1.46950i) q^{95} +(5.22737 + 2.51737i) q^{96} +(0.176076 - 0.0401881i) q^{97} +(-1.32708 - 2.75571i) q^{98} +7.13706i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 16 q^{5} + 6 q^{6} + 16 q^{7} + 2 q^{9} - 32 q^{13} - 20 q^{16} + 4 q^{20} - 12 q^{22} + 28 q^{23} + 14 q^{24} + 50 q^{25} + 24 q^{28} - 36 q^{30} + 12 q^{33} - 4 q^{34} - 12 q^{35} + 10 q^{36}+ \cdots + 18 q^{96}+O(q^{100}) $ 12 * q + 4 * q^4 - 16 * q^5 + 6 * q^6 + 16 * q^7 + 2 * q^9 - 32 * q^13 - 20 * q^16 + 4 * q^20 - 12 * q^22 + 28 * q^23 + 14 * q^24 + 50 * q^25 + 24 * q^28 - 36 * q^30 + 12 * q^33 - 4 * q^34 - 12 * q^35 + 10 * q^36 + 10 * q^38 - 6 * q^42 + 2 * q^45 + 54 * q^49 + 4 * q^51 + 22 * q^52 - 8 * q^53 - 30 * q^54 + 4 * q^57 - 112 * q^59 + 50 * q^62 + 12 * q^63 + 40 * q^64 - 18 * q^65 + 4 * q^67 + 2 * q^74 - 2 * q^78 - 34 * q^80 + 22 * q^81 - 32 * q^82 + 20 * q^83 + 32 * q^86 + 84 * q^88 - 80 * q^91 + 14 * q^92 - 36 * q^93 - 68 * q^94 + 18 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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 $

$2$	−0.347948	−	0.277479i	−0.246036	−	0.196207i	0.492705	−	0.870196i	$-0.336008\pi$
$2$	−0.347948	−	0.277479i	−0.246036	−	0.196207i	−0.738741	+	0.673989i	$0.764580\pi$
$3$	1.21572	+	0.277479i	0.701894	+	0.160203i	0.558551	−	0.829470i	$-0.311358\pi$
$3$	1.21572	+	0.277479i	0.701894	+	0.160203i	0.143343	+	0.989673i	$0.454215\pi$
$4$	−0.400969	−	1.75676i	−0.200484	−	0.878380i
$5$	−0.431468	+	0.541044i	−0.192959	+	0.241962i	−0.868894	−	0.494999i	$-0.835168\pi$
$5$	−0.431468	+	0.541044i	−0.192959	+	0.241962i	0.675935	+	0.736961i	$0.263740\pi$
$6$	−0.346011	−	0.433884i	−0.141258	−	0.177132i
$7$	−0.0794168	+	0.347948i	−0.0300167	+	0.131512i	−0.987716	−	0.156258i	$-0.950057\pi$
$7$	−0.0794168	+	0.347948i	−0.0300167	+	0.131512i	0.957699	+	0.287770i	$0.0929139\pi$
$8$	−0.734141	+	1.52446i	−0.259558	+	0.538978i
$9$	−1.30194	−	0.626980i	−0.433979	−	0.208993i
$10$	0.300257	−	0.0685317i	0.0949496	−	0.0216716i
$11$	−2.14295	−	4.44989i	−0.646124	−	1.34169i	−0.924486	−	0.381215i	$-0.875506\pi$
$11$	−2.14295	−	4.44989i	−0.646124	−	1.34169i	0.278362	−	0.960476i	$-0.410209\pi$
$12$		−	2.24698i		−	0.648647i
$13$	−5.09299	+	2.45265i	−1.41254	+	0.680244i	−0.975663	−	0.219276i	$-0.929630\pi$
$13$	−5.09299	+	2.45265i	−1.41254	+	0.680244i	−0.436879	+	0.899520i	$0.643916\pi$
$14$	0.124181	−	0.0990311i	0.0331888	−	0.0264672i
$15$	−0.674671	+	0.538032i	−0.174199	+	0.138919i
$16$	−2.56853	+	1.23694i	−0.642133	+	0.309235i
$17$			4.49396i			1.08995i	0.838454	+	0.544973i	$0.183460\pi$
$17$			4.49396i			1.08995i	−0.838454	+	0.544973i	$0.816540\pi$
$18$	0.279032	+	0.579417i	0.0657686	+	0.136570i
$19$	−2.29780	+	0.524459i	−0.527152	+	0.120319i	−0.477811	−	0.878463i	$-0.658569\pi$
$19$	−2.29780	+	0.524459i	−0.527152	+	0.120319i	−0.0493417	+	0.998782i	$0.515712\pi$
$20$	1.12349	+	0.541044i	0.251220	+	0.120981i
$21$	−0.193096	+	0.400969i	−0.0421371	+	0.0874986i
$22$	−0.489115	+	2.14295i	−0.104280	+	0.456879i
$23$	1.43147	+	1.79500i	0.298482	+	0.374284i	0.908344	−	0.418223i	$-0.137347\pi$
$23$	1.43147	+	1.79500i	0.298482	+	0.374284i	−0.609863	+	0.792507i	$0.708775\pi$
$24$	−1.31551	+	1.64960i	−0.268528	+	0.336723i
$25$	1.00604	+	4.40775i	0.201208	+	0.881551i
$26$	2.45265	+	0.559802i	0.481005	+	0.109786i
$27$	−4.33360	−	3.45593i	−0.834001	−	0.665093i
$28$	0.643104			0.121535
$29$		0			0
$29$		0			0
$30$	0.384043			0.0701163
$31$	−5.23203	−	4.17241i	−0.939701	−	0.749386i	0.0284913	−	0.999594i	$-0.490930\pi$
$31$	−5.23203	−	4.17241i	−0.939701	−	0.749386i	−0.968192	+	0.250208i	$0.919501\pi$
$32$	4.53614	+	1.03534i	0.801883	+	0.183025i
$33$	−1.37047	−	6.00442i	−0.238568	−	1.04524i
$34$	1.24698	−	1.56366i	0.213855	−	0.268166i
$35$	−0.153989	−	0.193096i	−0.0260289	−	0.0326393i
$36$	−0.579417	+	2.53859i	−0.0965695	+	0.423098i
$37$	2.14295	−	4.44989i	0.352299	−	0.731557i	−0.647228	−	0.762296i	$-0.724072\pi$
$37$	2.14295	−	4.44989i	0.352299	−	0.731557i	0.999527	+	0.0307395i	$0.00978622\pi$
$38$	0.945042	+	0.455108i	0.153306	+	0.0738283i
$39$	−6.87219	+	1.56853i	−1.10043	+	0.251166i
$40$	−0.508041	−	1.05496i	−0.0803283	−	0.166804i
$41$		−	3.10992i		−	0.485687i	−0.970065	−	0.242844i	$-0.921920\pi$
$41$		−	3.10992i		−	0.485687i	0.970065	−	0.242844i	$-0.0780802\pi$
$42$	0.178448	−	0.0859360i	0.0275351	−	0.0132602i
$43$	2.66277	−	2.12349i	0.406069	−	0.323829i	−0.399065	−	0.916923i	$-0.630665\pi$
$43$	2.66277	−	2.12349i	0.406069	−	0.323829i	0.805133	+	0.593094i	$0.202094\pi$
$44$	−6.95812	+	5.54892i	−1.04898	+	0.836531i
$45$	0.900969	−	0.433884i	0.134309	−	0.0646796i
$46$		−	1.02177i		−	0.150652i
$47$	−2.79640	−	5.80678i	−0.407897	−	0.847006i	−0.999178	−	0.0405407i	$-0.987092\pi$
$47$	−2.79640	−	5.80678i	−0.407897	−	0.847006i	0.591281	−	0.806465i	$-0.298622\pi$
$48$	−3.46583	+	0.791053i	−0.500249	+	0.114179i
$49$	6.19202	+	2.98192i	0.884574	+	0.425989i
$50$	0.873009	−	1.81282i	0.123462	−	0.256372i
$51$	−1.24698	+	5.46337i	−0.174612	+	0.765025i
$52$	6.35086	+	7.96372i	0.880705	+	1.10437i
$53$	−2.92543	+	3.66837i	−0.401838	+	0.503889i	−0.941044	−	0.338285i	$-0.890153\pi$
$53$	−2.92543	+	3.66837i	−0.401838	+	0.503889i	0.539205	+	0.842174i	$0.318725\pi$
$54$	0.548917	+	2.40496i	0.0746982	+	0.327274i
$55$	3.33220	+	0.760553i	0.449314	+	0.102553i
$56$	−0.472129	−	0.376510i	−0.0630909	−	0.0503133i
$57$	−2.93900			−0.389280
$58$		0			0
$59$	−12.4940			−1.62657			−0.813287	−	0.581862i	$-0.802324\pi$
$59$	−12.4940			−1.62657			−0.813287	+	0.581862i	$0.802324\pi$
$60$	1.21572	+	0.969501i	0.156948	+	0.125162i
$61$	1.60191	+	0.365625i	0.205103	+	0.0468135i	0.323838	−	0.946113i	$-0.395027\pi$
$61$	1.60191	+	0.365625i	0.205103	+	0.0468135i	−0.118735	+	0.992926i	$0.537884\pi$
$62$	0.662718	+	2.90356i	0.0841653	+	0.368752i
$63$	0.321552	−	0.403214i	0.0405118	−	0.0508001i
$64$	2.26391	+	2.83885i	0.282988	+	0.354856i
$65$	0.870469	−	3.81378i	0.107968	−	0.473041i
$66$	−1.18925	+	2.46950i	−0.146386	+	0.303975i
$67$	−2.09299	−	1.00793i	−0.255699	−	0.123138i	0.301643	−	0.953421i	$-0.402465\pi$
$67$	−2.09299	−	1.00793i	−0.255699	−	0.123138i	−0.557343	+	0.830282i	$0.688179\pi$
$68$	7.89481	−	1.80194i	0.957386	−	0.218517i
$69$	1.24218	+	2.57942i	0.149541	+	0.310525i
$70$			0.109916i			0.0131375i
$71$	−6.60872	+	3.18259i	−0.784311	+	0.377704i	−0.782783	−	0.622295i	$-0.786201\pi$
$71$	−6.60872	+	3.18259i	−0.784311	+	0.377704i	−0.00152768	+	0.999999i	$0.500486\pi$
$72$	1.91161	−	1.52446i	0.225285	−	0.179659i
$73$	4.39831	−	3.50753i	0.514783	−	0.410526i	−0.331342	−	0.943511i	$-0.607501\pi$
$73$	4.39831	−	3.50753i	0.514783	−	0.410526i	0.846125	+	0.532985i	$0.178930\pi$
$74$	−1.98039	+	0.953703i	−0.230215	+	0.110866i
$75$			5.63773i			0.650989i
$76$	1.84270	+	3.82640i	0.211372	+	0.438918i
$77$	1.71851	−	0.392240i	0.195843	−	0.0446999i
$78$	2.82640	+	1.36112i	0.320026	+	0.154117i
$79$	−2.02401	+	4.20291i	−0.227719	+	0.472864i	−0.983253	−	0.182246i	$-0.941663\pi$
$79$	−2.02401	+	4.20291i	−0.227719	+	0.472864i	0.755534	+	0.655110i	$0.227378\pi$
$80$	0.439001	−	1.92339i	0.0490818	−	0.215041i
$81$	−1.60656	−	2.01457i	−0.178507	−	0.223841i
$82$	−0.862937	+	1.08209i	−0.0952954	+	0.119497i
$83$	−0.991271	−	4.34304i	−0.108806	−	0.476711i	−0.999745	−	0.0225872i	$-0.992810\pi$
$83$	−0.991271	−	4.34304i	−0.108806	−	0.476711i	0.890939	−	0.454123i	$-0.150047\pi$
$84$	0.781831	+	0.178448i	0.0853048	+	0.0194703i
$85$	−2.43143	−	1.93900i	−0.263726	−	0.210314i
$86$	−1.51573			−0.163445
$87$		0			0
$88$	8.35690			0.890848
$89$	−4.44076	−	3.54138i	−0.470719	−	0.375386i	0.359208	−	0.933257i	$-0.383047\pi$
$89$	−4.44076	−	3.54138i	−0.470719	−	0.375386i	−0.829927	+	0.557871i	$0.811618\pi$
$90$	−0.433884	−	0.0990311i	−0.0457354	−	0.0104388i
$91$	−0.448927	−	1.96688i	−0.0470603	−	0.206185i
$92$	2.57942	−	3.23449i	0.268923	−	0.337219i
$93$	−5.20291	−	6.52424i	−0.539516	−	0.676532i
$94$	−0.638260	+	2.79640i	−0.0658315	+	0.288427i
$95$	0.707674	−	1.46950i	0.0726058	−	0.150768i
$96$	5.22737	+	2.51737i	0.533516	+	0.256928i
$97$	0.176076	−	0.0401881i	0.0178778	−	0.00408049i	−0.213573	−	0.976927i	$-0.568510\pi$
$97$	0.176076	−	0.0401881i	0.0178778	−	0.00408049i	0.231450	+	0.972847i	$0.425653\pi$
$98$	−1.32708	−	2.75571i	−0.134055	−	0.278369i
$99$			7.13706i			0.717302i
$100$	7.33997	−	3.53474i	0.733997	−	0.353474i
$101$	−2.52494	+	2.01357i	−0.251241	+	0.200358i	−0.741010	−	0.671494i	$-0.765653\pi$
$101$	−2.52494	+	2.01357i	−0.251241	+	0.200358i	0.489769	+	0.871853i	$0.337081\pi$
$102$	1.94986	−	1.55496i	0.193064	−	0.153964i
$103$	12.3007	−	5.92372i	1.21203	−	0.583682i	0.284947	−	0.958543i	$-0.408024\pi$
$103$	12.3007	−	5.92372i	1.21203	−	0.583682i	0.927081	+	0.374861i	$0.122310\pi$
$104$		−	9.56465i		−	0.937891i
$105$	−0.133627	−	0.277479i	−0.0130406	−	0.0270792i
$106$	2.03579	−	0.464656i	0.197734	−	0.0451314i
$107$	−14.6359	−	7.04826i	−1.41490	−	0.681381i	−0.438779	−	0.898595i	$-0.644589\pi$
$107$	−14.6359	−	7.04826i	−1.41490	−	0.681381i	−0.976124	+	0.217214i	$0.930303\pi$
$108$	−4.33360	+	8.99880i	−0.417000	+	0.865910i
$109$	1.21648	−	5.32975i	0.116518	−	0.510497i	−0.882662	−	0.470008i	$-0.844251\pi$
$109$	1.21648	−	5.32975i	0.116518	−	0.510497i	0.999180	−	0.0404895i	$-0.0128917\pi$
$110$	−0.948394	−	1.18925i	−0.0904258	−	0.113390i
$111$	3.83997	−	4.81517i	0.364474	−	0.457036i
$112$	−0.226406	−	0.991949i	−0.0213933	−	0.0937303i
$113$	−10.4069	−	2.37531i	−0.979002	−	0.223451i	−0.297061	−	0.954858i	$-0.596007\pi$
$113$	−10.4069	−	2.37531i	−0.979002	−	0.223451i	−0.681940	+	0.731408i	$0.738864\pi$
$114$	1.02262	+	0.815511i	0.0957770	+	0.0763796i
$115$	−1.58881			−0.148157
$116$		0			0
$117$	8.16852			0.755180
$118$	4.34724	+	3.46681i	0.400196	+	0.319146i
$119$	−1.56366	−	0.356896i	−0.143341	−	0.0327166i
$120$	−0.324904	−	1.42350i	−0.0296596	−	0.129947i
$121$	−8.35086	+	10.4716i	−0.759169	+	0.951967i
$122$	−0.455927	−	0.571714i	−0.0412777	−	0.0517606i
$123$	0.862937	−	3.78077i	0.0778084	−	0.340901i
$124$	−5.23203	+	10.8644i	−0.469850	+	0.975654i
$125$	−5.93631	−	2.85878i	−0.530960	−	0.255697i
$126$	−0.223767	+	0.0510733i	−0.0199347	+	0.00454997i
$127$	0.449866	+	0.934157i	0.0399192	+	0.0828930i	0.919975	−	0.391978i	$-0.128209\pi$
$127$	0.449866	+	0.934157i	0.0399192	+	0.0828930i	−0.880055	+	0.474871i	$0.842495\pi$
$128$		−	10.9215i		−	0.965337i
$129$	3.82640	−	1.84270i	0.336895	−	0.162240i
$130$	−1.36112	+	1.08546i	−0.119378	+	0.0952009i
$131$	6.27167	−	5.00149i	0.547959	−	0.436982i	−0.309974	−	0.950745i	$-0.600320\pi$
$131$	6.27167	−	5.00149i	0.547959	−	0.436982i	0.857932	+	0.513763i	$0.171749\pi$
$132$	−9.99880	+	4.81517i	−0.870284	+	0.419107i
$133$		−	0.841166i		−	0.0729384i
$134$	0.448572	+	0.931468i	0.0387507	+	0.0804666i
$135$	3.73962	−	0.853543i	0.321855	−	0.0734613i
$136$	−6.85086	−	3.29920i	−0.587456	−	0.282904i
$137$	7.47690	−	15.5260i	0.638795	−	1.32647i	−0.290408	−	0.956903i	$-0.593791\pi$
$137$	7.47690	−	15.5260i	0.638795	−	1.32647i	0.929203	−	0.369569i	$-0.120495\pi$
$138$	0.283520	−	1.24218i	0.0241348	−	0.105742i
$139$	−10.3922	−	13.0315i	−0.881458	−	1.10531i	−0.993749	−	0.111638i	$-0.964390\pi$
$139$	−10.3922	−	13.0315i	−0.881458	−	1.10531i	0.112291	−	0.993675i	$-0.464181\pi$
$140$	−0.277479	+	0.347948i	−0.0234513	+	0.0294070i
$141$	−1.78836	−	7.83534i	−0.150607	−	0.659854i
$142$	3.18259	+	0.726406i	0.267077	+	0.0609586i
$143$	21.8281	+	17.4073i	1.82535	+	1.45567i
$144$	4.11960			0.343300
$145$		0			0
$146$	−2.50365			−0.207203
$147$	6.70031	+	5.34332i	0.552633	+	0.440710i
$148$	−8.67664	−	1.98039i	−0.713215	−	0.162787i
$149$	4.14042	+	18.1403i	0.339196	+	1.48612i	0.800748	+	0.599002i	$0.204436\pi$
$149$	4.14042	+	18.1403i	0.339196	+	1.48612i	−0.461552	+	0.887113i	$0.652707\pi$
$150$	1.56435	−	1.96163i	0.127729	−	0.160167i
$151$	4.69351	+	5.88548i	0.381953	+	0.478954i	0.935229	−	0.354045i	$-0.115194\pi$
$151$	4.69351	+	5.88548i	0.381953	+	0.478954i	−0.553276	+	0.832998i	$0.686622\pi$
$152$	0.887395	−	3.88793i	0.0719773	−	0.315353i
$153$	2.81762	−	5.85086i	0.227791	−	0.473014i
$154$	−0.706791	−	0.340373i	−0.0569549	−	0.0274280i
$155$	4.51491	−	1.03050i	0.362647	−	0.0827717i
$156$	5.51107	+	11.4438i	0.441238	+	0.916241i
$157$			18.2392i			1.45565i	0.685764	+	0.727824i	$0.259468\pi$
$157$			18.2392i			1.45565i	−0.685764	+	0.727824i	$0.740532\pi$
$158$	1.87047	−	0.900771i	0.148807	−	0.0716615i
$159$	−4.57438	+	3.64795i	−0.362772	+	0.289301i
$160$	−2.51737	+	2.00753i	−0.199015	+	0.158709i
$161$	−0.738250	+	0.355523i	−0.0581823	+	0.0280191i
$162$			1.14675i			0.0900973i
$163$	5.48460	+	11.3889i	0.429587	+	0.892046i	0.997614	+	0.0690367i	$0.0219926\pi$
$163$	5.48460	+	11.3889i	0.429587	+	0.892046i	−0.568027	+	0.823010i	$0.692293\pi$
$164$	−5.46337	+	1.24698i	−0.426618	+	0.0973727i
$165$	3.83997	+	1.84923i	0.298941	+	0.143963i
$166$	−0.860193	+	1.78621i	−0.0667639	+	0.138637i
$167$	−0.177251	+	0.776589i	−0.0137161	+	0.0600943i	−0.981323	−	0.192368i	$-0.938383\pi$
$167$	−0.177251	+	0.776589i	−0.0137161	+	0.0600943i	0.967607	+	0.252462i	$0.0812404\pi$
$168$	−0.469501	−	0.588735i	−0.0362228	−	0.0454219i
$169$	11.8177	−	14.8189i	0.909051	−	1.13991i
$170$	0.307979	+	1.34934i	0.0236209	+	0.103490i
$171$	3.32042	+	0.757865i	0.253919	+	0.0579554i
$172$	−4.79815	−	3.82640i	−0.365855	−	0.291760i
$173$	9.15346			0.695924			0.347962	−	0.937509i	$-0.386874\pi$
$173$	9.15346			0.695924			0.347962	+	0.937509i	$0.386874\pi$
$174$		0			0
$175$	−1.61356			−0.121974
$176$	11.0085	+	8.77897i	0.829796	+	0.661740i
$177$	−15.1891	−	3.46681i	−1.14168	−	0.260582i
$178$	0.562491	+	2.46443i	0.0421605	+	0.184717i
$179$	−2.12349	+	2.66277i	−0.158717	+	0.199025i	−0.854831	−	0.518906i	$-0.826339\pi$
$179$	−2.12349	+	2.66277i	−0.158717	+	0.199025i	0.696114	+	0.717931i	$0.254911\pi$
$180$	−1.12349	−	1.40881i	−0.0837400	−	0.105007i
$181$	−2.82036	+	12.3568i	−0.209635	+	0.918473i	0.755174	+	0.655524i	$0.227552\pi$
$181$	−2.82036	+	12.3568i	−0.209635	+	0.918473i	−0.964810	+	0.262949i	$0.915305\pi$
$182$	−0.389564	+	0.808938i	−0.0288764	+	0.0599625i
$183$	1.84601	+	0.888992i	0.136461	+	0.0657162i
$184$	−3.78731	+	0.864429i	−0.279204	+	0.0637265i
$185$	1.48297	+	3.07942i	0.109030	+	0.226403i
$186$			3.71379i			0.272308i
$187$	19.9976	−	9.63034i	1.46237	−	0.704240i
$188$	−9.07985	+	7.24094i	−0.662216	+	0.528100i
$189$	1.54664	−	1.23341i	0.112502	−	0.0897171i
$190$	−0.653989	+	0.314945i	−0.0474454	+	0.0228485i
$191$		−	10.6703i		−	0.772072i	−0.922484	−	0.386036i	$-0.873844\pi$
$191$		−	10.6703i		−	0.772072i	0.922484	−	0.386036i	$-0.126156\pi$
$192$	1.96454	+	4.07942i	0.141779	+	0.294407i
$193$	22.1590	−	5.05765i	1.59504	−	0.364057i	0.669531	−	0.742784i	$-0.266495\pi$
$193$	22.1590	−	5.05765i	1.59504	−	0.364057i	0.925509	+	0.378727i	$0.123638\pi$
$194$	−0.0724165	−	0.0348740i	−0.00519920	−	0.00250380i
$195$	2.11649	−	4.39493i	0.151565	−	0.314727i
$196$	2.75571	−	12.0735i	0.196836	−	0.862396i
$197$	−12.1942	−	15.2910i	−0.868799	−	1.08944i	−0.995239	−	0.0974654i	$-0.968926\pi$
$197$	−12.1942	−	15.2910i	−0.868799	−	1.08944i	0.126440	−	0.991974i	$-0.459645\pi$
$198$	1.98039	−	2.48333i	0.140740	−	0.176482i
$199$	0.194710	+	0.853080i	0.0138026	+	0.0604732i	0.981360	−	0.192177i	$-0.0615549\pi$
$199$	0.194710	+	0.853080i	0.0138026	+	0.0604732i	−0.967558	+	0.252650i	$0.918698\pi$
$200$	−7.45801	−	1.70224i	−0.527361	−	0.120367i
$201$	−2.26480	−	1.80612i	−0.159747	−	0.127394i
$202$	1.43727			0.101126
$203$		0			0
$204$	10.0978			0.706990
$205$	1.68260	+	1.34183i	0.117518	+	0.0937175i
$206$	−5.92372	−	1.35205i	−0.412725	−	0.0942019i
$207$	−0.738250	−	3.23449i	−0.0513120	−	0.224812i
$208$	10.0477	−	12.5994i	0.696684	−	0.873614i
$209$	7.25786	+	9.10107i	0.502037	+	0.629534i
$210$	−0.0304995	+	0.133627i	−0.00210466	+	0.00922113i
$211$	7.92651	−	16.4596i	0.545684	−	1.13312i	−0.427695	−	0.903923i	$-0.640674\pi$
$211$	7.92651	−	16.4596i	0.545684	−	1.13312i	0.973379	−	0.229201i	$-0.0736113\pi$
$212$	7.61745	+	3.66837i	0.523169	+	0.251945i
$213$	−8.91742	+	2.03534i	−0.611012	+	0.139459i
$214$	3.13677	+	6.51357i	0.214425	+	0.445259i
$215$			2.35690i			0.160739i
$216$	8.44989	−	4.06925i	0.574942	−	0.276877i
$217$	1.86729	−	1.48911i	0.126760	−	0.101088i
$218$	−1.90216	+	1.51693i	−0.128831	+	0.102739i
$219$	6.32036	−	3.04372i	0.427090	−	0.205676i
$220$		−	6.15883i		−	0.415228i
$221$	−11.0221	−	22.8877i	−0.741429	−	1.53959i
$222$	−2.67222	+	0.609916i	−0.179348	+	0.0409349i
$223$	1.63826	+	0.788944i	0.109706	+	0.0528316i	0.487932	−	0.872882i	$-0.337751\pi$
$223$	1.63826	+	0.788944i	0.109706	+	0.0528316i	−0.378226	+	0.925713i	$0.623466\pi$
$224$	−0.720491	+	1.49612i	−0.0481398	+	0.0999634i
$225$	1.45377	−	6.36939i	0.0969181	−	0.424626i
$226$	2.96197	+	3.71419i	0.197027	+	0.247064i
$227$	−8.63922	+	10.8332i	−0.573405	+	0.719027i	−0.980972	−	0.194148i	$-0.937806\pi$
$227$	−8.63922	+	10.8332i	−0.573405	+	0.719027i	0.407567	+	0.913175i	$0.366377\pi$
$228$	1.17845	+	5.16312i	0.0780446	+	0.341936i
$229$	−12.4522	−	2.84213i	−0.822862	−	0.187813i	−0.209696	−	0.977767i	$-0.567247\pi$
$229$	−12.4522	−	2.84213i	−0.822862	−	0.187813i	−0.613166	+	0.789954i	$0.710105\pi$
$230$	0.552823	+	0.440862i	0.0364521	+	0.0290695i
$231$	2.19806			0.144622
$232$		0			0
$233$	−8.86592			−0.580826			−0.290413	−	0.956901i	$-0.593793\pi$
$233$	−8.86592			−0.580826			−0.290413	+	0.956901i	$0.593793\pi$
$234$	−2.84222	−	2.26659i	−0.185802	−	0.148172i
$235$	4.34828	+	0.992467i	0.283651	+	0.0647414i
$236$	5.00969	+	21.9489i	0.326103	+	1.42875i
$237$	−3.62684	+	4.54792i	−0.235589	+	0.295419i
$238$	0.445042	+	0.558065i	0.0288478	+	0.0361740i
$239$	5.68867	−	24.9237i	0.367969	−	1.61218i	−0.364380	−	0.931250i	$-0.618719\pi$
$239$	5.68867	−	24.9237i	0.367969	−	1.61218i	0.732349	−	0.680929i	$-0.238424\pi$
$240$	1.06740	−	2.21648i	0.0689004	−	0.143073i
$241$	8.76755	+	4.22223i	0.564768	+	0.271978i	0.694406	−	0.719584i	$-0.255667\pi$
$241$	8.76755	+	4.22223i	0.564768	+	0.271978i	−0.129638	+	0.991561i	$0.541382\pi$
$242$	5.81132	−	1.32640i	0.373566	−	0.0852640i
$243$	5.82077	+	12.0869i	0.373402	+	0.775378i
$244$		−	2.96077i		−	0.189544i
$245$	−4.28501	+	2.06355i	−0.273759	+	0.131836i
$246$	−1.34934	+	1.07606i	−0.0860309	+	0.0686074i
$247$	10.4164	−	8.30678i	0.662778	−	0.528548i
$248$	10.2017	−	4.91288i	0.647809	−	0.311968i
$249$		−	5.55496i		−	0.352031i
$250$	1.27228	+	2.64191i	0.0804658	+	0.167089i
$251$	−9.51560	+	2.17187i	−0.600620	+	0.137088i	−0.512011	−	0.858979i	$-0.671099\pi$
$251$	−9.51560	+	2.17187i	−0.600620	+	0.137088i	−0.0886088	+	0.996067i	$0.528242\pi$
$252$	−0.837282	−	0.403214i	−0.0527438	−	0.0254001i
$253$	4.92000	−	10.2165i	0.309318	−	0.642305i
$254$	0.102679	−	0.449866i	0.00644265	−	0.0282271i
$255$	−2.41789	−	3.03194i	−0.151414	−	0.189868i
$256$	1.49731	−	1.87757i	0.0935820	−	0.117348i
$257$	−3.63975	−	15.9468i	−0.227041	−	0.994734i	−0.952038	−	0.305981i	$-0.901016\pi$
$257$	−3.63975	−	15.9468i	−0.227041	−	0.994734i	0.724996	−	0.688753i	$-0.241841\pi$
$258$	−1.84270	−	0.420583i	−0.114721	−	0.0261844i
$259$	1.37814	+	1.09903i	0.0856335	+	0.0682905i
$260$	−7.04892			−0.437155
$261$		0			0
$262$	−3.57002			−0.220557
$263$	18.5478	+	14.7913i	1.14370	+	0.912074i	0.997023	−	0.0771102i	$-0.0245693\pi$
$263$	18.5478	+	14.7913i	1.14370	+	0.912074i	0.146682	+	0.989184i	$0.453141\pi$
$264$	10.1596	+	2.31886i	0.625280	+	0.142716i
$265$	−0.722521	−	3.16557i	−0.0443841	−	0.194459i
$266$	−0.233406	+	0.292682i	−0.0143110	+	0.0179455i
$267$	−4.41603	−	5.53753i	−0.270257	−	0.338891i
$268$	−0.931468	+	4.08103i	−0.0568985	+	0.249289i
$269$	−11.0009	+	22.8436i	−0.670737	+	1.39280i	0.236271	+	0.971687i	$0.424075\pi$
$269$	−11.0009	+	22.8436i	−0.670737	+	1.39280i	−0.907008	+	0.421113i	$0.861640\pi$
$270$	−1.53803	−	0.740677i	−0.0936017	−	0.0450762i
$271$	1.17327	−	0.267790i	0.0712709	−	0.0162671i	−0.186737	−	0.982410i	$-0.559791\pi$
$271$	1.17327	−	0.267790i	0.0712709	−	0.0162671i	0.258008	+	0.966143i	$0.416934\pi$
$272$	−5.55876	−	11.5429i	−0.337049	−	0.699890i
$273$		−	2.51573i		−	0.152259i
$274$	−6.90970	+	3.32754i	−0.417430	+	0.201024i
$275$	17.4581	−	13.9224i	1.05276	−	0.839551i
$276$	4.03334	−	3.21648i	0.242778	−	0.193609i
$277$	−9.60872	+	4.62732i	−0.577332	+	0.278028i	−0.699677	−	0.714459i	$-0.746673\pi$
$277$	−9.60872	+	4.62732i	−0.577332	+	0.278028i	0.122345	+	0.992488i	$0.460959\pi$
$278$			7.41789i			0.444896i
$279$	4.19576	+	8.71260i	0.251194	+	0.521609i
$280$	0.407417	−	0.0929903i	0.0243478	−	0.00555724i
$281$	14.6673	+	7.06341i	0.874979	+	0.421368i	0.816788	−	0.576938i	$-0.195752\pi$
$281$	14.6673	+	7.06341i	0.874979	+	0.421368i	0.0581911	+	0.998305i	$0.481467\pi$
$282$	−1.55188	+	3.22252i	−0.0924134	+	0.191898i
$283$	−1.16756	+	5.11543i	−0.0694044	+	0.304081i	−0.997702	−	0.0677581i	$-0.978415\pi$
$283$	−1.16756	+	5.11543i	−0.0694044	+	0.304081i	0.928297	+	0.371839i	$0.121273\pi$
$284$	8.24094	+	10.3338i	0.489010	+	0.613199i
$285$	1.26809	−	1.59013i	0.0751149	−	0.0941911i
$286$	−2.76487	−	12.1137i	−0.163490	−	0.716296i
$287$	1.08209	+	0.246980i	0.0638737	+	0.0145787i
$288$	−5.25663	−	4.19202i	−0.309750	−	0.247017i
$289$	−3.19567			−0.187981
$290$		0			0
$291$	0.225209			0.0132020
$292$	−7.92548	−	6.32036i	−0.463803	−	0.369871i
$293$	−6.59419	−	1.50508i	−0.385237	−	0.0879278i	0.0255163	−	0.999674i	$-0.491877\pi$
$293$	−6.59419	−	1.50508i	−0.385237	−	0.0879278i	−0.410753	+	0.911747i	$0.634734\pi$
$294$	−0.848699	−	3.71839i	−0.0494971	−	0.216861i
$295$	5.39075	−	6.75978i	0.313861	−	0.393570i
$296$	5.21044	+	6.53368i	0.302851	+	0.379763i
$297$	−6.09179	+	26.6899i	−0.353482	+	1.54870i
$298$	3.59292	−	7.46077i	0.208132	−	0.432191i
$299$	−11.6930	−	5.63104i	−0.676223	−	0.325652i
$300$	9.90413	−	2.26055i	0.571815	−	0.130513i
$301$	0.527395	+	1.09515i	0.0303985	+	0.0631232i
$302$		−	3.35019i		−	0.192782i
$303$	−3.62833	+	1.74731i	−0.208442	+	0.100381i
$304$	5.25326	−	4.18933i	0.301295	−	0.240275i
$305$	−0.888992	+	0.708947i	−0.0509035	+	0.0405942i
$306$	−2.60388	+	1.25396i	−0.148854	+	0.0716841i
$307$			4.51812i			0.257863i	0.991654	+	0.128931i	$0.0411547\pi$
$307$			4.51812i			0.257863i	−0.991654	+	0.128931i	$0.958845\pi$
$308$	−1.37814	−	2.86174i	−0.0785269	−	0.163063i
$309$	16.5979	−	3.78836i	0.944222	−	0.215513i
$310$	−1.85690	−	0.894234i	−0.105465	−	0.0507891i
$311$	−5.47412	+	11.3671i	−0.310409	+	0.644570i	−0.996559	−	0.0828899i	$-0.973585\pi$
$311$	−5.47412	+	11.3671i	−0.310409	+	0.644570i	0.686150	+	0.727460i	$0.259299\pi$
$312$	2.65399	−	11.6279i	0.150253	−	0.658299i
$313$	11.9961	+	15.0427i	0.678061	+	0.850261i	0.995174	−	0.0981266i	$-0.0312850\pi$
$313$	11.9961	+	15.0427i	0.678061	+	0.850261i	−0.317113	+	0.948388i	$0.602714\pi$
$314$	5.06100	−	6.34629i	0.285609	−	0.358142i
$315$	0.0794168	+	0.347948i	0.00447463	+	0.0196046i
$316$	8.19506	+	1.87047i	0.461008	+	0.105222i
$317$	−2.24254	−	1.78836i	−0.125953	−	0.100445i	0.558487	−	0.829513i	$-0.311382\pi$
$317$	−2.24254	−	1.78836i	−0.125953	−	0.100445i	−0.684441	+	0.729069i	$0.739953\pi$
$318$	2.60388			0.146018
$319$		0			0
$320$	−2.51275			−0.140467
$321$	−15.8373	−	12.6298i	−0.883952	−	0.704928i
$322$	0.355523	+	0.0811457i	0.0198125	+	0.00452207i
$323$	−2.35690	−	10.3262i	−0.131141	−	0.574567i
$324$	−2.89493	+	3.63012i	−0.160829	+	0.201674i
$325$	−15.9345	−	19.9812i	−0.883884	−	1.10836i
$326$	1.25182	−	5.48460i	0.0693321	−	0.303764i
$327$	2.95779	−	6.14191i	0.163566	−	0.339648i
$328$	4.74094	+	2.28312i	0.261775	+	0.126064i
$329$	2.24254	−	0.511845i	0.123635	−	0.0282189i
$330$	−0.822986	−	1.70895i	−0.0453039	−	0.0940745i
$331$		−	3.13408i		−	0.172265i	−0.996284	−	0.0861323i	$-0.972549\pi$
$331$		−	3.13408i		−	0.172265i	0.996284	−	0.0861323i	$-0.0274508\pi$
$332$	−7.23221	+	3.48285i	−0.396919	+	0.191146i
$333$	−5.57998	+	4.44989i	−0.305781	+	0.243852i
$334$	0.277162	−	0.221029i	0.0151656	−	0.0120942i
$335$	1.44839	−	0.697510i	0.0791342	−	0.0381090i
$336$		−	1.26875i		−	0.0692160i
$337$	2.16184	+	4.48911i	0.117763	+	0.244538i	0.951515	−	0.307601i	$-0.0995262\pi$
$337$	2.16184	+	4.48911i	0.117763	+	0.244538i	−0.833752	+	0.552139i	$0.813812\pi$
$338$	−8.22386	+	1.87704i	−0.447319	+	0.102098i
$339$	−11.9928	−	5.77541i	−0.651357	−	0.313677i
$340$	−2.43143	+	5.04892i	−0.131863	+	0.273816i
$341$	−7.35474	+	32.2232i	−0.398281	+	1.74499i
$342$	−0.945042	−	1.18505i	−0.0511020	−	0.0640799i
$343$	−3.08695	+	3.87091i	−0.166680	+	0.209010i
$344$	1.28232	+	5.61823i	0.0691382	+	0.302914i
$345$	−1.93154	−	0.440862i	−0.103991	−	0.0237352i
$346$	−3.18492	−	2.53989i	−0.171223	−	0.136545i
$347$	−20.1172			−1.07995			−0.539974	−	0.841682i	$-0.681566\pi$
$347$	−20.1172			−1.07995			−0.539974	+	0.841682i	$0.681566\pi$
$348$		0			0
$349$	20.4892			1.09676			0.548380	−	0.836229i	$-0.315245\pi$
$349$	20.4892			1.09676			0.548380	+	0.836229i	$0.315245\pi$
$350$	0.561436	+	0.447730i	0.0300100	+	0.0239322i
$351$	30.5472	+	6.97219i	1.63049	+	0.372148i
$352$	−5.11356	−	22.4040i	−0.272554	−	1.19414i
$353$	−11.2213	+	14.0711i	−0.597251	+	0.748929i	−0.984947	−	0.172859i	$-0.944700\pi$
$353$	−11.2213	+	14.0711i	−0.597251	+	0.748929i	0.387696	+	0.921787i	$0.373271\pi$
$354$	4.32304	+	5.42093i	0.229767	+	0.288119i
$355$	1.12953	−	4.94880i	0.0599493	−	0.262655i
$356$	−4.44076	+	9.22132i	−0.235360	+	0.488729i
$357$	−1.80194	−	0.867767i	−0.0953687	−	0.0459271i
$358$	1.47773	−	0.337282i	0.0781003	−	0.0178259i
$359$	−10.2521	−	21.2887i	−0.541084	−	1.12357i	−0.974915	−	0.222578i	$-0.928553\pi$
$359$	−10.2521	−	21.2887i	−0.541084	−	1.12357i	0.433831	−	0.900994i	$-0.357162\pi$
$360$			1.69202i			0.0891774i
$361$	−12.1136	+	5.83359i	−0.637556	+	0.307031i
$362$	4.41009	−	3.51693i	0.231789	−	0.184846i
$363$	−13.0579	+	10.4133i	−0.685363	+	0.546559i
$364$	−3.27532	+	1.57731i	−0.171674	+	0.0826736i
$365$			3.89307i			0.203772i
$366$	−0.395639	−	0.821552i	−0.0206804	−	0.0429432i
$367$	−28.8999	+	6.59621i	−1.50856	+	0.344319i	−0.895265	−	0.445533i	$-0.853014\pi$
$367$	−28.8999	+	6.59621i	−1.50856	+	0.344319i	−0.613297	+	0.789853i	$0.710157\pi$
$368$	−5.89708	−	2.83989i	−0.307407	−	0.148039i
$369$	−1.94986	+	4.04892i	−0.101505	+	0.210778i
$370$	0.338478	−	1.48297i	0.0175966	−	0.0770959i
$371$	−1.04407	−	1.30923i	−0.0542056	−	0.0679716i
$372$	−9.37531	+	11.7563i	−0.486087	+	0.609534i
$373$	5.60483	+	24.5564i	0.290207	+	1.27148i	0.884237	+	0.467038i	$0.154679\pi$
$373$	5.60483	+	24.5564i	0.290207	+	1.27148i	−0.594030	+	0.804443i	$0.702464\pi$
$374$	−9.63034	−	2.19806i	−0.497973	−	0.113659i
$375$	−6.42361	−	5.12266i	−0.331714	−	0.264533i
$376$	10.9051			0.562390
$377$		0			0
$378$	−0.880395			−0.0452826
$379$	−21.0368	−	16.7763i	−1.08059	−	0.861740i	−0.0896379	−	0.995974i	$-0.528571\pi$
$379$	−21.0368	−	16.7763i	−1.08059	−	0.861740i	−0.990950	+	0.134235i	$0.957142\pi$
$380$	−2.86531	−	0.653989i	−0.146988	−	0.0335489i
$381$	0.287700	+	1.26050i	0.0147393	+	0.0645772i
$382$	−2.96077	+	3.71269i	−0.151486	+	0.189958i
$383$	12.2635	+	15.3780i	0.626637	+	0.785779i	0.989261	−	0.146157i	$-0.0466905\pi$
$383$	12.2635	+	15.3780i	0.626637	+	0.785779i	−0.362624	+	0.931936i	$0.618119\pi$
$384$	3.03050	−	13.2775i	0.154650	−	0.677564i
$385$	−0.529265	+	1.09903i	−0.0269739	+	0.0560118i
$386$	−9.11356	−	4.38886i	−0.463868	−	0.223387i
$387$	−4.79815	+	1.09515i	−0.243904	+	0.0556694i
$388$	−0.141202	−	0.293209i	−0.00716843	−	0.0148854i
$389$		−	24.8552i		−	1.26021i	−0.776511	−	0.630103i	$-0.783012\pi$
$389$		−	24.8552i		−	1.26021i	0.776511	−	0.630103i	$-0.216988\pi$
$390$	−1.95593	+	0.941925i	−0.0990422	+	0.0476962i
$391$	−8.06668	+	6.43296i	−0.407949	+	0.325329i
$392$	−9.09163	+	7.25033i	−0.459197	+	0.366197i
$393$	9.01238	−	4.34013i	0.454614	−	0.218931i
$394$			8.70410i			0.438506i
$395$	−1.40066	−	2.90850i	−0.0704749	−	0.146343i
$396$	12.5381	−	2.86174i	0.630063	−	0.143808i
$397$	3.59903	+	1.73320i	0.180630	+	0.0869869i	0.522013	−	0.852937i	$-0.325181\pi$
$397$	3.59903	+	1.73320i	0.180630	+	0.0869869i	−0.341383	+	0.939924i	$0.610895\pi$
$398$	0.168963	−	0.350855i	0.00846934	−	0.0175868i
$399$	0.233406	−	1.02262i	0.0116849	−	0.0511950i
$400$	−8.03617	−	10.0770i	−0.401809	−	0.503852i
$401$	−15.5293	+	19.4731i	−0.775496	+	0.972442i	−0.999998	−	0.00203202i	$-0.999353\pi$
$401$	−15.5293	+	19.4731i	−0.775496	+	0.972442i	0.224502	+	0.974474i	$0.427925\pi$
$402$	0.286872	+	1.25687i	0.0143079	+	0.0626869i
$403$	36.8802	+	8.41766i	1.83713	+	0.419313i
$404$	4.54979	+	3.62833i	0.226360	+	0.180516i
$405$	1.78315			0.0886055
$406$		0			0
$407$	−24.3937			−1.20915
$408$	−7.41323	−	5.91185i	−0.367010	−	0.292680i
$409$	−0.276123	−	0.0630233i	−0.0136534	−	0.00311630i	0.215689	−	0.976462i	$-0.430800\pi$
$409$	−0.276123	−	0.0630233i	−0.0136534	−	0.00311630i	−0.229342	+	0.973346i	$0.573657\pi$
$410$	−0.213128	−	0.933774i	−0.0105256	−	0.0461158i
$411$	13.3979	−	16.8005i	0.660870	−	0.828705i
$412$	−15.3388	−	19.2342i	−0.755687	−	0.947602i
$413$	0.992230	−	4.34724i	0.0488245	−	0.213914i
$414$	−0.640630	+	1.33028i	−0.0314852	+	0.0653798i
$415$	2.77748	+	1.33756i	0.136341	+	0.0656584i
$416$	−25.6418	+	5.85258i	−1.25719	+	0.286947i
$417$	−9.01805	−	18.7262i	−0.441616	−	0.917024i
$418$		−	5.18060i		−	0.253392i
$419$	−23.8654	+	11.4930i	−1.16590	+	0.561468i	−0.913773	−	0.406226i	$-0.866845\pi$
$419$	−23.8654	+	11.4930i	−1.16590	+	0.561468i	−0.252128	+	0.967694i	$0.581130\pi$
$420$	−0.433884	+	0.346011i	−0.0211714	+	0.0168836i
$421$	−13.7462	+	10.9623i	−0.669951	+	0.534268i	−0.898339	−	0.439302i	$-0.855226\pi$
$421$	−13.7462	+	10.9623i	−0.669951	+	0.534268i	0.228389	+	0.973570i	$0.426654\pi$
$422$	−7.32520	+	3.52763i	−0.356585	+	0.171722i
$423$			9.31336i			0.452831i
$424$	−3.44460	−	7.15279i	−0.167285	−	0.347370i
$425$	−19.8083	+	4.52111i	−0.960842	+	0.219306i
$426$	3.66756	+	1.76621i	0.177694	+	0.0855729i
$427$	−0.254437	+	0.528344i	−0.0123131	+	0.0255683i
$428$	−6.51357	+	28.5378i	−0.314845	+	1.37943i
$429$	21.7066	+	27.2192i	1.04800	+	1.31415i
$430$	0.653989	−	0.820077i	0.0315382	−	0.0395476i
$431$	6.18502	+	27.0983i	0.297922	+	1.30528i	0.873215	+	0.487334i	$0.162031\pi$
$431$	6.18502	+	27.0983i	0.297922	+	1.30528i	−0.575293	+	0.817947i	$0.695112\pi$
$432$	15.4058	+	3.51626i	0.741210	+	0.169176i
$433$	−4.59374	−	3.66338i	−0.220761	−	0.176051i	0.506864	−	0.862026i	$-0.330805\pi$
$433$	−4.59374	−	3.66338i	−0.220761	−	0.176051i	−0.727625	+	0.685975i	$0.759376\pi$
$434$	−1.06292			−0.0510217
$435$		0			0
$436$	−9.85086			−0.471770
$437$	−4.23064	−	3.37382i	−0.202379	−	0.161392i
$438$	−3.04372	−	0.694710i	−0.145435	−	0.0331945i
$439$	−3.50269	−	15.3463i	−0.167174	−	0.732438i	−0.987118	−	0.159994i	$-0.948853\pi$
$439$	−3.50269	−	15.3463i	−0.167174	−	0.732438i	0.819944	−	0.572444i	$-0.194005\pi$
$440$	−3.60574	+	4.52145i	−0.171897	+	0.215552i
$441$	−6.19202	−	7.76455i	−0.294858	−	0.369740i
$442$	−2.51573	+	11.0221i	−0.119661	+	0.524269i
$443$	−2.92375	+	6.07122i	−0.138911	+	0.288452i	−0.958806	−	0.284062i	$-0.908318\pi$
$443$	−2.92375	+	6.07122i	−0.138911	+	0.288452i	0.819894	+	0.572515i	$0.194032\pi$
$444$	−9.99880	−	4.81517i	−0.474522	−	0.228518i
$445$	3.83209	−	0.874650i	0.181659	−	0.0414624i
$446$	−0.351113	−	0.729094i	−0.0166257	−	0.0345236i
$447$			23.2024i			1.09743i
$448$	−1.16756	+	0.562269i	−0.0551622	+	0.0265647i
$449$	−9.63221	+	7.68143i	−0.454572	+	0.362509i	−0.823848	−	0.566811i	$-0.808177\pi$
$449$	−9.63221	+	7.68143i	−0.454572	+	0.362509i	0.369276	+	0.929320i	$0.379606\pi$
$450$	−2.27321	+	1.81282i	−0.107160	+	0.0854573i
$451$	−13.8388	+	6.66440i	−0.651642	+	0.313814i
$452$			19.2349i			0.904733i
$453$	4.07288	+	8.45742i	0.191361	+	0.397364i
$454$	6.01199	−	1.37220i	0.282157	−	0.0644005i
$455$	1.25786	+	0.605756i	0.0589696	+	0.0283983i
$456$	2.15764	−	4.48039i	0.101041	−	0.209813i
$457$	3.04019	−	13.3199i	0.142214	−	0.623080i	−0.852704	−	0.522394i	$-0.825039\pi$
$457$	3.04019	−	13.3199i	0.142214	−	0.623080i	0.994918	−	0.100686i	$-0.0321038\pi$
$458$	3.54407	+	4.44413i	0.165604	+	0.207660i
$459$	15.5308	−	19.4750i	0.724915	−	0.909015i
$460$	0.637063	+	2.79116i	0.0297032	+	0.130138i
$461$	11.3171	+	2.58306i	0.527092	+	0.120305i	0.477782	−	0.878478i	$-0.341441\pi$
$461$	11.3171	+	2.58306i	0.527092	+	0.120305i	0.0493096	+	0.998784i	$0.484298\pi$
$462$	−0.764811	−	0.609916i	−0.0355822	−	0.0283759i
$463$	7.24267			0.336595			0.168298	−	0.985736i	$-0.446173\pi$
$463$	7.24267			0.336595			0.168298	+	0.985736i	$0.446173\pi$
$464$		0			0
$465$	5.77479			0.267800
$466$	3.08488	+	2.46011i	0.142904	+	0.113962i
$467$	2.01166	+	0.459148i	0.0930884	+	0.0212468i	0.268811	−	0.963193i	$-0.413369\pi$
$467$	2.01166	+	0.459148i	0.0930884	+	0.0212468i	−0.175723	+	0.984440i	$0.556226\pi$
$468$	−3.27532	−	14.3501i	−0.151402	−	0.663335i
$469$	0.516926	−	0.648205i	0.0238694	−	0.0299313i
$470$	−1.23759	−	1.55188i	−0.0570856	−	0.0715831i
$471$	−5.06100	+	22.1737i	−0.233199	+	1.02171i
$472$	9.17232	−	19.0465i	0.422190	−	0.876687i
$473$	−15.1555	−	7.29850i	−0.696850	−	0.335585i
$474$	2.52390	−	0.576064i	0.115927	−	0.0264595i
$475$	−4.62337	−	9.60052i	−0.212135	−	0.440502i
$476$			2.89008i			0.132467i
$477$	6.10872	−	2.94180i	0.279699	−	0.134696i
$478$	−8.89516	+	7.09365i	−0.406855	+	0.324456i
$479$	−3.04056	+	2.42476i	−0.138927	+	0.110790i	−0.690487	−	0.723344i	$-0.742604\pi$
$479$	−3.04056	+	2.42476i	−0.138927	+	0.110790i	0.551561	+	0.834135i	$0.314032\pi$
$480$	−3.61745	+	1.74207i	−0.165113	+	0.0795143i
$481$			27.9191i			1.27300i
$482$	−1.87907	−	3.90193i	−0.0855893	−	0.177728i
$483$	−0.996152	+	0.227365i	−0.0453265	+	0.0103455i
$484$	21.7446	+	10.4716i	0.988390	+	0.475984i
$485$	−0.0542276	+	0.112605i	−0.00246235	+	0.00511311i
$486$	1.32855	−	5.82077i	0.0602644	−	0.264035i
$487$	6.13856	+	7.69750i	0.278164	+	0.348807i	0.901213	−	0.433376i	$-0.142678\pi$
$487$	6.13856	+	7.69750i	0.278164	+	0.348807i	−0.623049	+	0.782183i	$0.714106\pi$
$488$	−1.73341	+	2.17362i	−0.0784676	+	0.0983953i
$489$	3.50753	+	15.3675i	0.158616	+	0.694943i
$490$	2.06355	+	0.470992i	0.0932218	+	0.0212773i
$491$	−6.09139	−	4.85772i	−0.274901	−	0.219226i	0.476329	−	0.879267i	$-0.341967\pi$
$491$	−6.09139	−	4.85772i	−0.274901	−	0.219226i	−0.751229	+	0.660041i	$0.770539\pi$
$492$	−6.98792			−0.315040
$493$		0			0
$494$	−5.92931			−0.266772
$495$	−3.86147	−	3.07942i	−0.173560	−	0.138409i
$496$	18.5997	+	4.24525i	0.835149	+	0.190617i
$497$	−0.582532	−	2.55224i	−0.0261301	−	0.114484i
$498$	−1.54138	+	1.93284i	−0.0690711	+	0.0866124i
$499$	12.8222	+	16.0786i	0.574001	+	0.719775i	0.981077	−	0.193620i	$-0.0620228\pi$
$499$	12.8222	+	16.0786i	0.574001	+	0.719775i	−0.407075	+	0.913395i	$0.633451\pi$
$500$	−2.64191	+	11.5750i	−0.118150	+	0.517648i
$501$	−0.430975	+	0.894928i	−0.0192545	+	0.0399824i
$502$	3.91358	+	1.88468i	0.174672	+	0.0841175i
$503$	−8.02843	+	1.83244i	−0.357970	+	0.0817043i	−0.397724	−	0.917505i	$-0.630200\pi$
$503$	−8.02843	+	1.83244i	−0.357970	+	0.0817043i	0.0397538	+	0.999210i	$0.487343\pi$
$504$	0.378618	+	0.786208i	0.0168650	+	0.0350205i
$505$		−	2.23490i		−	0.0994517i
$506$	−4.54676	+	2.18960i	−0.202128	+	0.0973398i
$507$	18.4788	−	14.7364i	0.820674	−	0.654466i
$508$	1.46071	−	1.16487i	0.0648084	−	0.0516829i
$509$	−7.13222	+	3.43470i	−0.316130	+	0.152240i	−0.585219	−	0.810875i	$-0.698992\pi$
$509$	−7.13222	+	3.43470i	−0.316130	+	0.152240i	0.269089	+	0.963115i	$0.413277\pi$
$510$			1.72587i			0.0764230i
$511$	0.871139	+	1.80894i	0.0385369	+	0.0800227i
$512$	−22.3374	+	5.09837i	−0.987183	+	0.225318i
$513$	11.7702	+	5.66825i	0.519669	+	0.250259i
$514$	−3.15846	+	6.55861i	−0.139314	+	0.289288i
$515$	−2.10238	+	9.21114i	−0.0926421	+	0.405892i
$516$	−4.77144	−	5.98319i	−0.210051	−	0.263395i
$517$	−19.8470	+	24.8873i	−0.872869	+	1.09454i
$518$	−0.174563	−	0.764811i	−0.00766986	−	0.0336039i
$519$	11.1280	+	2.53989i	0.488465	+	0.111489i
$520$	5.17490	+	4.12684i	0.226934	+	0.180974i
$521$	3.52542			0.154451			0.0772257	−	0.997014i	$-0.475394\pi$
$521$	3.52542			0.154451			0.0772257	+	0.997014i	$0.475394\pi$
$522$		0			0
$523$	10.0301			0.438587			0.219294	−	0.975659i	$-0.429625\pi$
$523$	10.0301			0.438587			0.219294	+	0.975659i	$0.429625\pi$
$524$	−11.3012	−	9.01238i	−0.493694	−	0.393708i
$525$	−1.96163	−	0.447730i	−0.0856127	−	0.0195406i
$526$	−2.34936	−	10.2932i	−0.102437	−	0.448806i
$527$	18.7506	−	23.5125i	0.816790	−	1.02422i
$528$	10.9472	+	13.7274i	0.476416	+	0.597406i
$529$	3.94504	−	17.2844i	0.171524	−	0.751494i
$530$	−0.626980	+	1.30194i	−0.0272343	+	0.0565526i
$531$	16.2664	+	7.83346i	0.705900	+	0.339943i
$532$	−1.47773	+	0.337282i	−0.0640676	+	0.0146230i
$533$	7.62755	+	15.8388i	0.330386	+	0.686053i
$534$			3.15213i			0.136406i
$535$	10.1283	−	4.87755i	0.437886	−	0.210875i
$536$	3.07310	−	2.45071i	0.132738	−	0.105855i
$537$	−3.32042	+	2.64795i	−0.143287	+	0.114267i
$538$	10.1664	−	4.89586i	0.438303	−	0.211076i
$539$		−	33.9439i		−	1.46207i
$540$	−2.99894	−	6.22737i	−0.129054	−	0.267983i
$541$	8.01795	−	1.83004i	0.344719	−	0.0786797i	−0.0466566	−	0.998911i	$-0.514857\pi$
$541$	8.01795	−	1.83004i	0.344719	−	0.0786797i	0.391375	+	0.920231i	$0.372000\pi$
$542$	−0.482542	−	0.232380i	−0.0207269	−	0.00998157i
$543$	−6.85750	+	14.2397i	−0.294283	+	0.611086i
$544$	−4.65279	+	20.3852i	−0.199487	+	0.874009i
$545$	2.35876	+	2.95779i	0.101038	+	0.126698i
$546$	−0.698062	+	0.875342i	−0.0298743	+	0.0374612i
$547$	−5.75504	−	25.2145i	−0.246068	−	1.07809i	−0.935384	−	0.353633i	$-0.884946\pi$
$547$	−5.75504	−	25.2145i	−0.246068	−	1.07809i	0.689316	−	0.724461i	$-0.257911\pi$
$548$	−30.2734	−	6.90970i	−1.29321	−	0.295168i
$549$	−1.85634	−	1.48039i	−0.0792269	−	0.0631813i
$550$	−9.93767			−0.423744
$551$		0			0
$552$	−4.84415			−0.206181
$553$	−1.30165	−	1.03803i	−0.0553518	−	0.0441416i
$554$	4.62732	+	1.05615i	0.196596	+	0.0448717i
$555$	0.948394	+	4.15519i	0.0402571	+	0.176378i
$556$	−18.7262	+	23.4819i	−0.794166	+	0.995853i
$557$	−14.3463	−	17.9897i	−0.607873	−	0.762248i	0.378709	−	0.925516i	$-0.376368\pi$
$557$	−14.3463	−	17.9897i	−0.607873	−	0.762248i	−0.986582	+	0.163268i	$0.947797\pi$
$558$	0.957656	−	4.19576i	0.0405408	−	0.177621i
$559$	−8.35328	+	17.3458i	−0.353306	+	0.733648i
$560$	0.634375	+	0.305499i	0.0268072	+	0.0129097i
$561$	26.9836	−	6.15883i	1.13925	−	0.260026i
$562$	−3.14351	−	6.52757i	−0.132601	−	0.275349i
$563$		−	43.1159i		−	1.81712i	−0.417757	−	0.908559i	$-0.637184\pi$
$563$		−	43.1159i		−	1.81712i	0.417757	−	0.908559i	$-0.362816\pi$
$564$	−13.0477	+	6.28345i	−0.549408	+	0.264581i
$565$	5.77541	−	4.60574i	0.242973	−	0.193765i
$566$	1.82567	−	1.45593i	0.0767388	−	0.0611972i
$567$	0.828552	−	0.399010i	0.0347959	−	0.0167568i
$568$		−	12.4112i		−	0.520762i
$569$	−10.5487	−	21.9046i	−0.442225	−	0.918289i	−0.996310	−	0.0858292i	$-0.972646\pi$
$569$	−10.5487	−	21.9046i	−0.442225	−	0.918289i	0.554085	−	0.832460i	$-0.313068\pi$
$570$	−0.882455	+	0.201415i	−0.0369620	+	0.00843633i
$571$	−16.6576	−	8.02190i	−0.697100	−	0.335706i	0.0515504	−	0.998670i	$-0.483584\pi$
$571$	−16.6576	−	8.02190i	−0.697100	−	0.335706i	−0.748651	+	0.662965i	$0.769298\pi$
$572$	21.8281	−	45.3265i	0.912677	−	1.89519i
$573$	2.96077	−	12.9720i	0.123688	−	0.541913i
$574$	−0.307979	−	0.386193i	−0.0128548	−	0.0161194i
$575$	−6.47182	+	8.11541i	−0.269894	+	0.338436i
$576$	−1.16756	−	5.11543i	−0.0486485	−	0.213143i
$577$	−36.9090	−	8.42423i	−1.53654	−	0.350705i	−0.631277	−	0.775557i	$-0.717469\pi$
$577$	−36.9090	−	8.42423i	−1.53654	−	0.350705i	−0.905263	+	0.424852i	$0.860326\pi$
$578$	1.11193	+	0.886731i	0.0462500	+	0.0368832i
$579$	28.3424			1.17787
$580$		0			0
$581$	1.58987			0.0659591
$582$	−0.0783611	−	0.0624909i	−0.00324817	−	0.00259033i
$583$	22.5929	+	5.15668i	0.935702	+	0.213568i
$584$	2.11811	+	9.28006i	0.0876481	+	0.384012i
$585$	−3.52446	+	4.41953i	−0.145718	+	0.182725i
$586$	1.87681	+	2.35344i	0.0775301	+	0.0972197i
$587$	3.21217	−	14.0734i	0.132580	−	0.580873i	−0.864372	−	0.502854i	$-0.832283\pi$
$587$	3.21217	−	14.0734i	0.132580	−	0.580873i	0.996952	−	0.0780188i	$-0.0248594\pi$
$588$	6.70031	−	13.9133i	0.276316	−	0.573777i
$589$	14.2104	+	6.84339i	0.585531	+	0.281977i
$590$	−3.75140	+	0.856232i	−0.154443	+	0.0352505i
$591$	−10.5817	−	21.9731i	−0.435273	−	0.903855i
$592$			14.0804i			0.578700i
$593$	−11.7143	+	5.64132i	−0.481050	+	0.231661i	−0.658662	−	0.752439i	$-0.728877\pi$
$593$	−11.7143	+	5.64132i	−0.481050	+	0.231661i	0.177612	+	0.984101i	$0.443163\pi$
$594$	9.52551	−	7.59634i	0.390837	−	0.311682i
$595$	0.867767	−	0.692021i	0.0355750	−	0.0283701i
$596$	30.2080	−	14.5474i	1.23737	−	0.595886i
$597$			1.09113i			0.0446570i
$598$	2.50605	+	5.20387i	0.102480	+	0.212802i
$599$	11.7903	−	2.69106i	0.481739	−	0.109954i	0.0252470	−	0.999681i	$-0.491963\pi$
$599$	11.7903	−	2.69106i	0.481739	−	0.109954i	0.456492	+	0.889727i	$0.349106\pi$
$600$	−8.59448	−	4.13888i	−0.350868	−	0.168969i
$601$	−9.69609	+	20.1341i	−0.395512	+	0.821289i	0.604189	+	0.796841i	$0.293497\pi$
$601$	−9.69609	+	20.1341i	−0.395512	+	0.821289i	−0.999701	+	0.0244478i	$0.992217\pi$
$602$	0.120374	−	0.527395i	0.00490609	−	0.0214950i
$603$	2.09299	+	2.62453i	0.0852332	+	0.106879i
$604$	8.45742	−	10.6053i	0.344127	−	0.431522i
$605$	−2.06249	−	9.03636i	−0.0838522	−	0.367380i
$606$	1.74731	+	0.398813i	0.0709798	+	0.0162007i
$607$	−32.4216	−	25.8553i	−1.31595	−	1.04944i	−0.994740	−	0.102428i	$-0.967339\pi$
$607$	−32.4216	−	25.8553i	−1.31595	−	1.04944i	−0.321210	−	0.947008i	$-0.604090\pi$
$608$	−10.9661			−0.444736
$609$		0			0
$610$	0.506041			0.0204890
$611$	28.4841	+	22.7153i	1.15234	+	0.918962i
$612$	−11.4083	−	2.60388i	−0.461154	−	0.105255i
$613$	5.73759	+	25.1380i	0.231739	+	1.01531i	0.948197	+	0.317684i	$0.102905\pi$
$613$	5.73759	+	25.1380i	0.231739	+	1.01531i	−0.716458	+	0.697631i	$0.754238\pi$
$614$	1.25368	−	1.57207i	0.0505946	−	0.0634436i
$615$	1.67324	+	2.09817i	0.0674714	+	0.0846064i
$616$	−0.663678	+	2.90776i	−0.0267403	+	0.117157i
$617$	−3.84652	+	7.98739i	−0.154855	+	0.321560i	−0.963935	−	0.266139i	$-0.914252\pi$
$617$	−3.84652	+	7.98739i	−0.154855	+	0.321560i	0.809079	+	0.587699i	$0.199966\pi$
$618$	−6.82640	−	3.28742i	−0.274598	−	0.132239i
$619$	−28.7129	+	6.55352i	−1.15407	+	0.263408i	−0.756393	−	0.654118i	$-0.773040\pi$
$619$	−28.7129	+	6.55352i	−1.15407	+	0.263408i	−0.397675	+	0.917526i	$0.630183\pi$
$620$	−3.62068	−	7.51842i	−0.145410	−	0.301947i
$621$		−	12.7259i		−	0.510672i
$622$	5.05884	−	2.43621i	0.202841	−	0.0976831i
$623$	1.58489	−	1.26391i	0.0634972	−	0.0506373i
$624$	15.7112	−	12.5293i	0.628953	−	0.501574i
$625$	−16.2588	+	7.82984i	−0.650353	+	0.313193i
$626$		−	8.56273i		−	0.342235i
$627$	6.29814	+	13.0782i	0.251523	+	0.522294i
$628$	32.0419	−	7.31336i	1.27861	−	0.291835i
$629$	19.9976	+	9.63034i	0.797357	+	0.383987i
$630$	0.0689153	−	0.143104i	0.00274565	−	0.00570141i
$631$	5.28956	−	23.1751i	0.210574	−	0.922585i	−0.753604	−	0.657329i	$-0.771686\pi$
$631$	5.28956	−	23.1751i	0.210574	−	0.922585i	0.964178	−	0.265256i	$-0.0854566\pi$
$632$	−4.92125	−	6.17105i	−0.195757	−	0.245471i
$633$	14.2036	−	17.8107i	0.564541	−	0.707912i
$634$	0.284052	+	1.24451i	0.0112812	+	0.0494260i
$635$	−0.699523	−	0.159662i	−0.0277597	−	0.00633598i
$636$	8.24275	+	6.57338i	0.326846	+	0.260651i
$637$	−38.8495			−1.53927
$638$		0			0
$639$	10.5996			0.419312
$640$	5.90904	+	4.71230i	0.233575	+	0.186270i
$641$	−27.7518	−	6.33417i	−1.09613	−	0.250185i	−0.364034	−	0.931386i	$-0.618601\pi$
$641$	−27.7518	−	6.33417i	−1.09613	−	0.250185i	−0.732096	+	0.681201i	$0.761458\pi$
$642$	2.00604	+	8.78904i	0.0791721	+	0.346876i
$643$	12.0625	−	15.1259i	0.475698	−	0.596507i	−0.484858	−	0.874593i	$-0.661129\pi$
$643$	12.0625	−	15.1259i	0.475698	−	0.596507i	0.960556	+	0.278086i	$0.0897001\pi$
$644$	0.920583	+	1.15437i	0.0362761	+	0.0454887i
$645$	−0.653989	+	2.86531i	−0.0257508	+	0.112822i
$646$	−2.04524	+	4.24698i	−0.0804688	+	0.167095i
$647$	20.4650	+	9.85540i	0.804560	+	0.387456i	0.790513	−	0.612446i	$-0.209814\pi$
$647$	20.4650	+	9.85540i	0.804560	+	0.387456i	0.0140475	+	0.999901i	$0.495528\pi$
$648$	4.25057	−	0.970165i	0.166978	−	0.0381117i
$649$	26.7740	+	55.5967i	1.05097	+	2.18236i
$650$			11.3739i			0.446120i
$651$	2.68329	−	1.29221i	0.105167	−	0.0506455i
$652$	17.8084	−	14.2017i	0.697430	−	0.556182i
$653$	17.9284	−	14.2974i	0.701591	−	0.559500i	−0.206411	−	0.978465i	$-0.566179\pi$
$653$	17.9284	−	14.2974i	0.701591	−	0.559500i	0.908002	+	0.418965i	$0.137607\pi$
$654$	−2.73341	+	1.31634i	−0.106885	+	0.0514729i
$655$			5.55124i			0.216905i
$656$	3.84678	+	7.98792i	0.150191	+	0.311876i
$657$	−7.92548	+	1.80894i	−0.309202	+	0.0705734i
$658$	−0.922312	−	0.444162i	−0.0359555	−	0.0173152i
$659$	−8.32111	+	17.2790i	−0.324145	+	0.673093i	−0.997824	−	0.0659303i	$-0.978998\pi$
$659$	−8.32111	+	17.2790i	−0.324145	+	0.673093i	0.673680	+	0.739023i	$0.264713\pi$
$660$	1.70895	−	7.48739i	0.0665207	−	0.291446i
$661$	−2.11141	−	2.64762i	−0.0821243	−	0.102981i	0.739072	−	0.673626i	$-0.235264\pi$
$661$	−2.11141	−	2.64762i	−0.0821243	−	0.102981i	−0.821196	+	0.570646i	$0.806693\pi$
$662$	−0.869641	+	1.09050i	−0.0337996	+	0.0423833i
$663$	−7.04892	−	30.8833i	−0.273757	−	1.19941i
$664$	7.34852	+	1.67725i	0.285178	+	0.0650900i
$665$	0.455108	+	0.362937i	0.0176483	+	0.0140741i
$666$	3.17629			0.123079
$667$		0			0
$668$	1.43535			0.0555355
$669$	1.77274	+	1.41371i	0.0685382	+	0.0546574i
$670$	−0.697510	−	0.159202i	−0.0269472	−	0.00615051i
$671$	−1.80582	−	7.91183i	−0.0697130	−	0.305433i
$672$	−1.29105	+	1.61893i	−0.0498034	+	0.0624515i
$673$	−2.97434	−	3.72971i	−0.114653	−	0.143770i	0.721193	−	0.692734i	$-0.243594\pi$
$673$	−2.97434	−	3.72971i	−0.114653	−	0.143770i	−0.835846	+	0.548964i	$0.815022\pi$
$674$	0.493427	−	2.16184i	0.0190061	−	0.0832711i
$675$	10.8731	−	22.5782i	0.418506	−	0.869036i
$676$	−30.7717	−	14.8189i	−1.18353	−	0.569957i
$677$	42.0097	−	9.58844i	1.61456	−	0.368514i	0.682522	−	0.730865i	$-0.260883\pi$
$677$	42.0097	−	9.58844i	1.61456	−	0.368514i	0.932042	+	0.362351i	$0.118026\pi$
$678$	2.57030	+	5.33728i	0.0987118	+	0.204977i
$679$			0.0644568i			0.00247362i
$680$	4.74094	−	2.28312i	0.181807	−	0.0875535i
$681$	−13.5088	+	10.7729i	−0.517659	+	0.412820i
$682$	11.5003	−	9.17121i	0.440371	−	0.351184i
$683$	−21.1124	+	10.1672i	−0.807842	+	0.389036i	−0.791758	−	0.610834i	$-0.790834\pi$
$683$	−21.1124	+	10.1672i	−0.807842	+	0.389036i	−0.0160838	+	0.999871i	$0.505120\pi$
$684$		−	6.13706i		−	0.234656i
$685$	5.17418	+	10.7443i	0.197695	+	0.410518i
$686$	2.14819	−	0.490311i	0.0820184	−	0.0187202i
$687$	−14.3497	−	6.91043i	−0.547474	−	0.263649i
$688$	−4.21279	+	8.74794i	−0.160611	+	0.333512i
$689$	5.90193	−	25.8580i	0.224846	−	0.985113i
$690$	0.549745	+	0.689359i	0.0209284	+	0.0262434i
$691$	26.8959	−	33.7264i	1.02317	−	1.28301i	0.0646716	−	0.997907i	$-0.479400\pi$
$691$	26.8959	−	33.7264i	1.02317	−	1.28301i	0.958496	−	0.285105i	$-0.0920285\pi$
$692$	−3.67025	−	16.0804i	−0.139522	−	0.611286i
$693$	−2.48333	−	0.566803i	−0.0943337	−	0.0215311i
$694$	6.99974	+	5.58211i	0.265706	+	0.211894i
$695$	11.5345			0.437529
$696$		0			0
$697$	13.9758			0.529373
$698$	−7.12916	−	5.68532i	−0.269843	−	0.215192i
$699$	−10.7784	−	2.46011i	−0.407678	−	0.0930498i
$700$	0.646989	+	2.83464i	0.0244539	+	0.107139i
$701$	−2.63789	+	3.30781i	−0.0996318	+	0.124934i	−0.829148	−	0.559029i	$-0.811174\pi$
$701$	−2.63789	+	3.30781i	−0.0996318	+	0.124934i	0.729516	+	0.683964i	$0.239745\pi$
$702$	−8.69418	−	10.9022i	−0.328141	−	0.411475i
$703$	−2.59030	+	11.3489i	−0.0976951	+	0.428030i
$704$	7.78111	−	16.1576i	0.293262	−	0.608964i
$705$	5.01089	+	2.41312i	0.188721	+	0.0908832i
$706$	7.80887	−	1.78232i	0.293891	−	0.0670786i
$707$	−0.500096	−	1.03846i	−0.0188080	−	0.0390553i
$708$			28.0737i			1.05507i
$709$	12.8872	−	6.20613i	0.483987	−	0.233076i	−0.175946	−	0.984400i	$-0.556299\pi$
$709$	12.8872	−	6.20613i	0.483987	−	0.233076i	0.659934	+	0.751324i	$0.270584\pi$
$710$	−1.76621	+	1.40850i	−0.0662845	+	0.0528601i
$711$	5.27028	−	4.20291i	0.197651	−	0.157621i
$712$	8.65883	−	4.16987i	0.324504	−	0.156273i
$713$		−	15.3642i		−	0.575393i
$714$	0.386193	+	0.801938i	0.0144529	+	0.0300118i
$715$	−18.8362	+	4.29925i	−0.704436	+	0.160783i
$716$	5.52930	+	2.66277i	0.206640	+	0.0995125i
$717$	13.8316	−	28.7216i	0.516551	−	1.07263i
$718$	−2.33997	+	10.2521i	−0.0873269	+	0.382604i
$719$	−14.6151	−	18.3267i	−0.545050	−	0.683471i	0.430666	−	0.902511i	$-0.358279\pi$
$719$	−14.6151	−	18.3267i	−0.545050	−	0.683471i	−0.975716	+	0.219041i	$0.929707\pi$
$720$	−1.77748	+	2.22889i	−0.0662427	+	0.0830658i
$721$	1.08426	+	4.75046i	0.0403800	+	0.176916i
$722$	5.83359	+	1.33148i	0.217104	+	0.0495525i
$723$	9.48727	+	7.56584i	0.352835	+	0.281377i
$724$	22.8388			0.848796
$725$		0			0
$726$	7.43296			0.275863
$727$	40.6534	+	32.4200i	1.50775	+	1.20239i	0.919114	+	0.393992i	$0.128906\pi$
$727$	40.6534	+	32.4200i	1.50775	+	1.20239i	0.588636	+	0.808398i	$0.299665\pi$
$728$	3.32800	+	0.759594i	0.123344	+	0.0281524i
$729$	5.44265	+	23.8458i	0.201580	+	0.883178i
$730$	1.08024	−	1.35458i	0.0399817	−	0.0501354i
$731$	9.54288	+	11.9664i	0.352956	+	0.442593i
$732$	0.821552	−	3.59945i	0.0303654	−	0.133040i
$733$	−14.8346	+	30.8044i	−0.547929	+	1.13779i	0.424681	+	0.905343i	$0.360386\pi$
$733$	−14.8346	+	30.8044i	−0.547929	+	1.13779i	−0.972610	+	0.232443i	$0.925328\pi$
$734$	11.8860	+	5.72398i	0.438719	+	0.211276i
$735$	−5.78195	+	1.31969i	−0.213270	+	0.0486776i
$736$	4.63489	+	9.62445i	0.170844	+	0.354762i
$737$			11.4735i			0.422632i
$738$	1.80194	−	0.867767i	0.0663302	−	0.0319430i
$739$	−31.0958	+	24.7981i	−1.14388	+	0.912211i	−0.997035	−	0.0769489i	$-0.975482\pi$
$739$	−31.0958	+	24.7981i	−1.14388	+	0.912211i	−0.146842	+	0.989160i	$0.546911\pi$
$740$	4.81517	−	3.83997i	0.177009	−	0.141160i
$741$	14.9683	−	7.20836i	0.549874	−	0.264806i
$742$			0.745251i			0.0273590i
$743$	3.11451	+	6.46734i	0.114260	+	0.237264i	0.950255	−	0.311474i	$-0.100823\pi$
$743$	3.11451	+	6.46734i	0.114260	+	0.237264i	−0.835994	+	0.548738i	$0.815108\pi$
$744$	13.7656	−	3.14191i	0.504671	−	0.115188i
$745$	−11.6012	−	5.58684i	−0.425035	−	0.204686i
$746$	4.86369	−	10.0996i	0.178072	−	0.369771i
$747$	−1.43243	+	6.27588i	−0.0524098	+	0.229622i
$748$	−24.9366	−	31.2695i	−0.911773	−	1.14333i
$749$	3.61476	−	4.53277i	0.132080	−	0.165624i
$750$	0.813651	+	3.56484i	0.0297103	+	0.130169i
$751$	−26.4874	−	6.04556i	−0.966537	−	0.220606i	−0.290010	−	0.957024i	$-0.593659\pi$
$751$	−26.4874	−	6.04556i	−0.966537	−	0.220606i	−0.676527	+	0.736418i	$0.736516\pi$
$752$	14.3653	+	11.4559i	0.523848	+	0.417755i
$753$	−12.1709			−0.443533
$754$		0			0
$755$	−5.20941			−0.189590
$756$	−2.78695	−	2.22252i	−0.101361	−	0.0808323i
$757$	−23.0986	−	5.27210i	−0.839533	−	0.191618i	−0.218927	−	0.975741i	$-0.570256\pi$
$757$	−23.0986	−	5.27210i	−0.839533	−	0.191618i	−0.620605	+	0.784123i	$0.713113\pi$
$758$	2.66464	+	11.6745i	0.0967840	+	0.424038i
$759$	8.81618	−	11.0551i	0.320007	−	0.401276i
$760$	1.72066	+	2.15764i	0.0624149	+	0.0782658i
$761$	3.17187	−	13.8969i	0.114980	−	0.503762i	−0.884338	−	0.466847i	$-0.845390\pi$
$761$	3.17187	−	13.8969i	0.114980	−	0.503762i	0.999318	−	0.0369148i	$-0.0117530\pi$
$762$	0.249657	−	0.518418i	0.00904411	−	0.0187803i
$763$	1.75786	+	0.846543i	0.0636390	+	0.0306469i
$764$	−18.7451	+	4.27844i	−0.678173	+	0.154788i
$765$	1.94986	+	4.04892i	0.0704972	+	0.146389i
$766$		−	8.75361i		−	0.316281i
$767$	63.6316	−	30.6434i	2.29760	−	1.10647i
$768$	2.34129	−	1.86712i	0.0844841	−	0.0673738i
$769$	−34.9530	+	27.8741i	−1.26044	+	1.00517i	−0.261235	+	0.965275i	$0.584130\pi$
$769$	−34.9530	+	27.8741i	−1.26044	+	1.00517i	−0.999204	+	0.0398911i	$0.987299\pi$
$770$	0.489115	−	0.235545i	0.0176265	−	0.00848846i
$771$		−	20.3967i		−	0.734570i
$772$	−17.7701	−	36.9001i	−0.639561	−	1.32806i
$773$	22.3733	−	5.10656i	0.804712	−	0.183670i	0.199670	−	0.979863i	$-0.436013\pi$
$773$	22.3733	−	5.10656i	0.804712	−	0.183670i	0.605043	+	0.796193i	$0.293156\pi$
$774$	1.97339	+	0.950332i	0.0709319	+	0.0341590i
$775$	13.1273	−	27.2591i	0.471547	−	0.979176i
$776$	−0.0679992	+	0.297924i	−0.00244103	+	0.0106948i
$777$	1.37047	+	1.71851i	0.0491653	+	0.0616514i
$778$	−6.89679	+	8.64830i	−0.247262	+	0.310057i
$779$	1.63102	+	7.14598i	0.0584374	+	0.256031i
$780$	−8.56948	−	1.95593i	−0.306836	−	0.0700334i
$781$	28.3243	+	22.5879i	1.01352	+	0.808259i
$782$	4.59179			0.164202
$783$		0			0
$784$	−19.5929			−0.699745
$785$	−9.86822	−	7.86964i	−0.352212	−	0.280880i
$786$	−4.34013	−	0.990607i	−0.154807	−	0.0353338i
$787$	3.18933	+	13.9734i	0.113687	+	0.498097i	0.999425	+	0.0339106i	$0.0107962\pi$
$787$	3.18933	+	13.9734i	0.113687	+	0.498097i	−0.885737	+	0.464187i	$0.846347\pi$
$788$	−21.9731	+	27.5535i	−0.782761	+	0.981551i
$789$	18.4445	+	23.1287i	0.656642	+	0.823403i
$790$	−0.319692	+	1.40066i	−0.0113741	+	0.0498333i
$791$	1.65297	−	3.43243i	0.0587729	−	0.122043i
$792$	−10.8802	−	5.23961i	−0.386610	−	0.186181i
$793$	−9.05525	+	2.06680i	−0.321562	+	0.0733943i
$794$	−0.771347	−	1.60172i	−0.0273741	−	0.0568429i
$795$		−	4.04892i		−	0.143600i
$796$	1.42058	−	0.684117i	0.0503512	−	0.0242479i
$797$	−7.96942	+	6.35540i	−0.282291	+	0.225120i	−0.754391	−	0.656425i	$-0.772068\pi$
$797$	−7.96942	+	6.35540i	−0.282291	+	0.225120i	0.472100	+	0.881545i	$0.343496\pi$
$798$	−0.364968	+	0.291053i	−0.0129197	+	0.0103032i
$799$	26.0954	−	12.5669i	0.923190	−	0.444585i
$800$			21.0358i			0.743727i
$801$	3.56121	+	7.39493i	0.125829	+	0.261287i
$802$	10.8068	−	2.46658i	0.381600	−	0.0870978i
$803$	−25.0335	−	12.0555i	−0.883412	−	0.425429i
$804$	−2.26480	+	4.70291i	−0.0798734	+	0.165859i
$805$	0.126178	−	0.552823i	0.00444720	−	0.0194844i
$806$	−10.4966	−	13.1624i	−0.369729	−	0.463625i
$807$	−19.7126	+	24.7188i	−0.693916	+	0.870143i
$808$	−1.21595	−	5.32741i	−0.0427769	−	0.187418i
$809$	8.74788	+	1.99665i	0.307559	+	0.0701984i	0.373515	−	0.927624i	$-0.378152\pi$
$809$	8.74788	+	1.99665i	0.307559	+	0.0701984i	−0.0659557	+	0.997823i	$0.521010\pi$
$810$	−0.620443	−	0.494787i	−0.0218002	−	0.0173850i
$811$	28.5628			1.00298			0.501489	−	0.865164i	$-0.332786\pi$
$811$	28.5628			1.00298			0.501489	+	0.865164i	$0.332786\pi$
$812$		0			0
$813$	1.50066			0.0526306
$814$	8.48774	+	6.76875i	0.297495	+	0.237245i
$815$	−8.52832	−	1.94653i	−0.298734	−	0.0681841i
$816$	−3.55496	−	15.5753i	−0.124448	−	0.545244i
$817$	−5.00484	+	6.27588i	−0.175097	+	0.219565i
$818$	0.0785888	+	0.0985473i	0.00274779	+	0.00344562i
$819$	−0.648718	+	2.84222i	−0.0226680	+	0.0993152i
$820$	1.68260	−	3.49396i	0.0587590	−	0.122014i
$821$	10.2126	+	4.91813i	0.356422	+	0.171644i	0.603522	−	0.797346i	$-0.293763\pi$
$821$	10.2126	+	4.91813i	0.356422	+	0.171644i	−0.247100	+	0.968990i	$0.579478\pi$
$822$	−9.32355	+	2.12804i	−0.325196	+	0.0742239i
$823$	−2.46106	−	5.11045i	−0.0857872	−	0.178139i	0.853662	−	0.520828i	$-0.174377\pi$
$823$	−2.46106	−	5.11045i	−0.0857872	−	0.178139i	−0.939449	+	0.342689i	$0.888662\pi$
$824$			23.1008i			0.804755i
$825$	25.0872	−	12.0814i	0.873426	−	0.420620i
$826$	−1.55151	+	1.23729i	−0.0539841	+	0.0430509i
$827$	−2.26984	+	1.81013i	−0.0789300	+	0.0629445i	−0.662160	−	0.749363i	$-0.730360\pi$
$827$	−2.26984	+	1.81013i	−0.0789300	+	0.0629445i	0.583230	+	0.812307i	$0.301789\pi$
$828$	−5.38620	+	2.59386i	−0.187183	+	0.0901428i
$829$		−	45.2137i		−	1.57034i	−0.619282	−	0.785169i	$-0.712576\pi$
$829$		−	45.2137i		−	1.57034i	0.619282	−	0.785169i	$-0.287424\pi$
$830$	−0.595272	−	1.23609i	−0.0206622	−	0.0429055i
$831$	−12.9655	+	2.95928i	−0.449766	+	0.102656i
$832$	−18.4928	−	8.90565i	−0.641121	−	0.308748i
$833$	−13.4006	+	27.8267i	−0.464304	+	0.964138i
$834$	−2.05831	+	9.01805i	−0.0712735	+	0.312269i
$835$	−0.343691	−	0.430975i	−0.0118939	−	0.0149145i
$836$	13.0782	−	16.3996i	0.452320	−	0.567191i
$837$	8.25398	+	36.1630i	0.285299	+	1.24998i
$838$	11.4930	+	2.62319i	0.397018	+	0.0906167i
$839$	35.6716	+	28.4471i	1.23152	+	0.982104i	0.999957	+	0.00928374i	$0.00295515\pi$
$839$	35.6716	+	28.4471i	1.23152	+	0.982104i	0.231562	+	0.972820i	$0.425616\pi$
$840$	0.521106			0.0179799
$841$		0			0
$842$	7.82477			0.269659
$843$	15.8713	+	12.6570i	0.546638	+	0.435929i
$844$	−32.0938	−	7.32520i	−1.10471	−	0.252144i
$845$	2.91872	+	12.7878i	0.100407	+	0.439912i
$846$	2.58426	−	3.24056i	0.0888487	−	0.111413i
$847$	−2.98039	−	3.73729i	−0.102407	−	0.128415i
$848$	2.97650	−	13.0409i	0.102213	−	0.447826i
$849$	−2.83885	+	5.89493i	−0.0974290	+	0.202313i
$850$	8.14675	+	3.92327i	0.279431	+	0.134567i
$851$	11.0551	−	2.52326i	0.378965	−	0.0864963i
$852$	7.15122	+	14.8497i	0.244997	+	0.508741i
$853$			36.9288i			1.26442i	0.774797	+	0.632210i	$0.217852\pi$
$853$			36.9288i			1.26442i	−0.774797	+	0.632210i	$0.782148\pi$
$854$	0.235135	−	0.113235i	0.00804615	−	0.00387482i
$855$	−1.84270	+	1.46950i	−0.0630189	+	0.0502559i
$856$	21.4896	−	17.1374i	0.734498	−	0.585743i
$857$	−32.0296	+	15.4246i	−1.09411	+	0.526896i	−0.891802	−	0.452426i	$-0.850559\pi$
$857$	−32.0296	+	15.4246i	−1.09411	+	0.526896i	−0.202308	+	0.979322i	$0.564844\pi$
$858$		−	15.4940i		−	0.528955i
$859$	18.3885	+	38.1841i	0.627408	+	1.30283i	0.936124	+	0.351671i	$0.114386\pi$
$859$	18.3885	+	38.1841i	0.627408	+	1.30283i	−0.308716	+	0.951154i	$0.599899\pi$
$860$	4.14050	−	0.945042i	0.141190	−	0.0322257i
$861$	1.24698	+	0.600514i	0.0424970	+	0.0204655i
$862$	5.36716	−	11.1450i	0.182806	−	0.379601i
$863$	11.0770	−	48.5316i	0.377066	−	1.65204i	−0.329327	−	0.944216i	$-0.606822\pi$
$863$	11.0770	−	48.5316i	0.377066	−	1.65204i	0.706393	−	0.707819i	$-0.250321\pi$
$864$	−16.0797	−	20.1633i	−0.547043	−	0.685970i
$865$	−3.94943	+	4.95242i	−0.134285	+	0.168387i
$866$	0.581868	+	2.54933i	0.0197727	+	0.0866298i
$867$	−3.88502	−	0.886731i	−0.131942	−	0.0301150i
$868$	−3.36474	−	2.68329i	−0.114207	−	0.0910769i
$869$	23.0398			0.781572
$870$		0			0
$871$	13.1317			0.444950
$872$	7.23191	+	5.76726i	0.244903	+	0.195304i
$873$	−0.254437	−	0.0580735i	−0.00861138	−	0.00196549i
$874$	0.535876	+	2.34783i	0.0181263	+	0.0794164i
$875$	1.46615	−	1.83849i	0.0495649	−	0.0621524i
$876$	−7.88135	−	9.88291i	−0.266286	−	0.333912i
$877$	−4.87167	+	21.3442i	−0.164504	+	0.720741i	0.823627	+	0.567132i	$0.191947\pi$
$877$	−4.87167	+	21.3442i	−0.164504	+	0.720741i	−0.988132	+	0.153610i	$0.950910\pi$
$878$	−3.03952	+	6.31163i	−0.102579	+	0.213007i
$879$	−7.59903	−	3.65950i	−0.256309	−	0.123432i
$880$	−9.49962	+	2.16823i	−0.320232	+	0.0730909i
$881$	14.5485	+	30.2102i	0.490150	+	1.01781i	0.988555	+	0.150863i	$0.0482052\pi$
$881$	14.5485	+	30.2102i	0.490150	+	1.01781i	−0.498404	+	0.866945i	$0.666081\pi$
$882$			4.41981i			0.148823i
$883$	−14.5303	+	6.99741i	−0.488982	+	0.235481i	−0.662094	−	0.749421i	$-0.730332\pi$
$883$	−14.5303	+	6.99741i	−0.488982	+	0.235481i	0.173112	+	0.984902i	$0.444618\pi$
$884$	−35.7886	+	28.5405i	−1.20370	+	0.959920i
$885$	8.42931	−	6.72215i	0.283348	−	0.225963i
$886$	2.70195	−	1.30119i	0.0907737	−	0.0437143i
$887$			52.7391i			1.77081i	0.464823	+	0.885403i	$0.346118\pi$
$887$			52.7391i			1.77081i	−0.464823	+	0.885403i	$0.653882\pi$
$888$	4.52145	+	9.38889i	0.151730	+	0.315070i
$889$	−0.360765	+	0.0823422i	−0.0120997	+	0.00276167i
$890$	−1.57606	−	0.758993i	−0.0528298	−	0.0254415i
$891$	−5.52181	+	11.4661i	−0.184987	+	0.384130i
$892$	0.729094	−	3.19437i	0.0244119	−	0.106955i
$893$	9.47099	+	11.8762i	0.316935	+	0.397424i
$894$	6.43817	−	8.07321i	0.215325	−	0.270009i
$895$	−0.524459	−	2.29780i	−0.0175307	−	0.0768071i
$896$	3.80013	+	0.867354i	0.126953	+	0.0289763i
$897$	−12.6528	−	10.0903i	−0.422466	−	0.336905i
$898$	5.48294			0.182968
$899$		0			0
$900$	−11.7724			−0.392413
$901$	−16.4855	−	13.1468i	−0.549212	−	0.437982i
$902$	6.66440	+	1.52111i	0.221900	+	0.0506473i
$903$	0.337282	+	1.47773i	0.0112240	+	0.0491757i
$904$	11.2612	−	14.1211i	0.374543	−	0.469661i
$905$	−5.46867	−	6.85750i	−0.181785	−	0.227951i
$906$	0.929608	−	4.07288i	0.0308842	−	0.135312i
$907$	12.9487	−	26.8882i	0.429954	−	0.892809i	−0.567626	−	0.823286i	$-0.692138\pi$
$907$	12.9487	−	26.8882i	0.429954	−	0.892809i	0.997580	−	0.0695225i	$-0.0221476\pi$
$908$	22.4955	+	10.8332i	0.746538	+	0.359514i
$909$	4.54979	−	1.03846i	0.150907	−	0.0344435i
$910$	−0.269587	−	0.559802i	−0.00893671	−	0.0185573i
$911$			9.34050i			0.309465i	0.987956	+	0.154732i	$0.0494515\pi$
$911$			9.34050i			0.309465i	−0.987956	+	0.154732i	$0.950548\pi$
$912$	7.54892	−	3.63537i	0.249970	−	0.120379i
$913$	−17.2018	+	13.7180i	−0.569296	+	0.453999i
$914$	−4.75383	+	3.79105i	−0.157243	+	0.125397i
$915$	−1.27748	+	0.615201i	−0.0422322	+	0.0203379i
$916$			23.0151i			0.760439i
$917$	1.24218	+	2.57942i	0.0410205	+	0.0851798i
$918$	−10.8078	+	2.46681i	−0.356711	+	0.0814169i
$919$	16.5966	+	7.99252i	0.547473	+	0.263649i	0.687110	−	0.726554i	$-0.258879\pi$
$919$	16.5966	+	7.99252i	0.547473	+	0.263649i	−0.139637	+	0.990203i	$0.544594\pi$
$920$	1.16641	−	2.42208i	0.0384554	−	0.0798535i
$921$	−1.25368	+	5.49275i	−0.0413103	+	0.180992i
$922$	−3.22103	−	4.03904i	−0.106079	−	0.133019i
$923$	25.8523	−	32.4178i	0.850940	−	1.06705i
$924$	−0.881355	−	3.86147i	−0.0289944	−	0.127033i
$925$	21.7699	+	4.96884i	0.715790	+	0.163374i
$926$	−2.52007	−	2.00969i	−0.0828146	−	0.0660425i
$927$	−19.7289			−0.647981
$928$		0			0
$929$	−4.84654			−0.159010			−0.0795050	−	0.996834i	$-0.525334\pi$
$929$	−4.84654			−0.159010			−0.0795050	+	0.996834i	$0.525334\pi$
$930$	−2.00933	−	1.60238i	−0.0658884	−	0.0525442i
$931$	−15.7919	−	3.60441i	−0.517560	−	0.118130i
$932$	3.55496	+	15.5753i	0.116447	+	0.510186i
$933$	−9.80910	+	12.3002i	−0.321136	+	0.402691i
$934$	−0.572548	−	0.717953i	−0.0187343	−	0.0234921i
$935$	−3.41789	+	14.9748i	−0.111777	+	0.489728i
$936$	−5.99684	+	12.4526i	−0.196013	+	0.407025i
$937$	−40.2863	−	19.4008i	−1.31609	−	0.633798i	−0.361686	−	0.932300i	$-0.617799\pi$
$937$	−40.2863	−	19.4008i	−1.31609	−	0.633798i	−0.954409	+	0.298502i	$0.903513\pi$
$938$	−0.359726	+	0.0821052i	−0.0117455	+	0.00268083i
$939$	10.4098	+	21.6163i	0.339712	+	0.705420i
$940$		−	8.03684i		−	0.262133i
$941$	12.2397	−	5.89435i	0.399004	−	0.192150i	−0.223611	−	0.974678i	$-0.571785\pi$
$941$	12.2397	−	5.89435i	0.399004	−	0.192150i	0.622615	+	0.782528i	$0.286070\pi$
$942$	7.91370	−	6.31096i	0.257842	−	0.205622i
$943$	5.58231	−	4.45175i	0.181785	−	0.144969i
$944$	32.0911	−	15.4543i	1.04448	−	0.502994i
$945$			1.36898i			0.0445328i
$946$	3.24814	+	6.74482i	0.105606	+	0.219293i
$947$	14.6352	−	3.34040i	0.475581	−	0.108548i	0.0219901	−	0.999758i	$-0.493000\pi$
$947$	14.6352	−	3.34040i	0.475581	−	0.108548i	0.453591	+	0.891210i	$0.350143\pi$
$948$	9.44385	+	4.54792i	0.306722	+	0.147709i
$949$	−13.7978	+	28.6514i	−0.447894	+	0.930062i
$950$	−1.05525	+	4.62337i	−0.0342369	+	0.150002i
$951$	−2.23005	−	2.79640i	−0.0723144	−	0.0906794i
$952$	1.69202	−	2.12173i	0.0548387	−	0.0687656i
$953$	−11.5365	−	50.5449i	−0.373705	−	1.63731i	−0.716276	−	0.697817i	$-0.754155\pi$
$953$	−11.5365	−	50.5449i	−0.373705	−	1.63731i	0.342571	−	0.939492i	$-0.388702\pi$
$954$	−2.94180	−	0.671448i	−0.0952444	−	0.0217389i
$955$	5.77308	+	4.60388i	0.186812	+	0.148978i
$956$	−46.0659			−1.48988
$957$		0			0
$958$	1.73078			0.0559188
$959$	4.80843	+	3.83459i	0.155272	+	0.123825i
$960$	−3.05478	−	0.697234i	−0.0985927	−	0.0225031i
$961$	3.06704	+	13.4376i	0.0989368	+	0.433470i
$962$	7.74698	−	9.71441i	0.249773	−	0.313205i
$963$	14.6359	+	18.3528i	0.471634	+	0.591411i
$964$	3.90193	−	17.0955i	0.125673	−	0.550608i
$965$	−6.82450	+	14.1712i	−0.219688	+	0.456187i
$966$	0.409698	+	0.197300i	0.0131818	+	0.00634803i
$967$	40.5813	−	9.26241i	1.30501	−	0.297859i	0.487168	−	0.873308i	$-0.338030\pi$
$967$	40.5813	−	9.26241i	1.30501	−	0.297859i	0.817838	+	0.575449i	$0.195173\pi$
$968$	−9.83288	−	20.4182i	−0.316041	−	0.656265i
$969$		−	13.2078i		−	0.424294i
$970$	0.0501138	−	0.0241335i	0.00160906	−	0.000774881i
$971$	43.6051	−	34.7739i	1.39935	−	1.11595i	0.421459	−	0.906847i	$-0.361518\pi$
$971$	43.6051	−	34.7739i	1.39935	−	1.11595i	0.977894	−	0.209100i	$-0.0670534\pi$
$972$	18.8999	−	15.0722i	0.606215	−	0.483440i
$973$	5.35958	−	2.58104i	0.171820	−	0.0827443i
$974$		−	4.38165i		−	0.140397i
$975$	−13.8274	−	28.7129i	−0.442831	−	0.919548i
$976$	−4.56681	+	1.04234i	−0.146180	+	0.0333646i
$977$	−44.1100	−	21.2422i	−1.41120	−	0.679600i	−0.435803	−	0.900042i	$-0.643536\pi$
$977$	−44.1100	−	21.2422i	−1.41120	−	0.679600i	−0.975400	+	0.220442i	$0.929250\pi$
$978$	3.04372	−	6.32036i	0.0973275	−	0.202103i
$979$	−6.24243	+	27.3499i	−0.199509	+	0.874106i
$980$	5.34332	+	6.70031i	0.170686	+	0.214034i
$981$	−4.92543	+	6.17629i	−0.157257	+	0.197194i
$982$	0.771570	+	3.38047i	0.0246218	+	0.107875i
$983$	5.04360	+	1.15117i	0.160866	+	0.0367166i	0.302195	−	0.953246i	$-0.402281\pi$
$983$	5.04360	+	1.15117i	0.160866	+	0.0367166i	−0.141329	+	0.989963i	$0.545138\pi$
$984$	5.13011	+	4.09113i	0.163542	+	0.130420i
$985$	13.5345			0.431246
$986$		0			0
$987$	2.86831			0.0912994
$988$	−18.7697	−	14.9683i	−0.597142	−	0.476205i
$989$	7.62335	+	1.73998i	0.242408	+	0.0553281i
$990$	0.489115	+	2.14295i	0.0155451	+	0.0681075i
$991$	10.5075	−	13.1760i	0.333783	−	0.418550i	−0.586411	−	0.810014i	$-0.699460\pi$
$991$	10.5075	−	13.1760i	0.333783	−	0.418550i	0.920194	+	0.391463i	$0.128031\pi$
$992$	−19.4133	−	24.3436i	−0.616374	−	0.772909i
$993$	0.869641	−	3.81015i	0.0275972	−	0.120911i
$994$	−0.505503	+	1.04969i	−0.0160336	+	0.0332940i
$995$	−0.545565	−	0.262730i	−0.0172956	−	0.00832911i
$996$	−9.75872	+	2.22737i	−0.309217	+	0.0705768i
$997$	−16.5786	−	34.4257i	−0.525048	−	1.09027i	−0.979860	−	0.199686i	$-0.936008\pi$
$997$	−16.5786	−	34.4257i	−0.525048	−	1.09027i	0.454812	−	0.890588i	$-0.349707\pi$
$998$		−	9.15239i		−	0.289714i
$999$	−24.6652	+	11.8781i	−0.780371	+	0.375807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.c.267.1		12
29.2	odd	28		841.2.d.b.778.1		6
29.3	odd	28		841.2.d.e.605.1		6
29.4	even	14		841.2.e.d.270.1		12
29.5	even	14	inner	841.2.e.c.63.1		12
29.6	even	14		841.2.e.d.651.2		12
29.7	even	7		841.2.e.b.236.2		12
29.8	odd	28		841.2.d.a.645.1		6
29.9	even	14		841.2.e.b.196.2		12
29.10	odd	28		841.2.d.d.571.1		6
29.11	odd	28		841.2.a.e.1.2		3
29.12	odd	4		841.2.d.c.574.1		6
29.13	even	14		841.2.b.c.840.4		6
29.14	odd	28		29.2.d.a.16.1	✓	6
29.15	odd	28		841.2.d.d.190.1		6
29.16	even	7		841.2.b.c.840.3		6
29.17	odd	4		841.2.d.b.574.1		6
29.18	odd	28		841.2.a.f.1.2		3
29.19	odd	28		29.2.d.a.20.1	yes	6
29.20	even	7		841.2.e.b.196.1		12
29.21	odd	28		841.2.d.e.645.1		6
29.22	even	14		841.2.e.b.236.1		12
29.23	even	7		841.2.e.d.651.1		12
29.24	even	7	inner	841.2.e.c.63.2		12
29.25	even	7		841.2.e.d.270.2		12
29.26	odd	28		841.2.d.a.605.1		6
29.27	odd	28		841.2.d.c.778.1		6
29.28	even	2	inner	841.2.e.c.267.2		12
87.11	even	28		7569.2.a.r.1.2		3
87.14	even	28		261.2.k.a.190.1		6
87.47	even	28		7569.2.a.p.1.2		3
87.77	even	28		261.2.k.a.136.1		6
116.19	even	28		464.2.u.f.49.1		6
116.43	even	28		464.2.u.f.161.1		6
145.14	odd	28		725.2.l.b.451.1		6
145.19	odd	28		725.2.l.b.426.1		6
145.43	even	28		725.2.r.b.74.2		12
145.48	even	28		725.2.r.b.49.1		12
145.72	even	28		725.2.r.b.74.1		12
145.77	even	28		725.2.r.b.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	29.14	odd	28
29.2.d.a.20.1	yes	6	29.19	odd	28
261.2.k.a.136.1		6	87.77	even	28
261.2.k.a.190.1		6	87.14	even	28
464.2.u.f.49.1		6	116.19	even	28
464.2.u.f.161.1		6	116.43	even	28
725.2.l.b.426.1		6	145.19	odd	28
725.2.l.b.451.1		6	145.14	odd	28
725.2.r.b.49.1		12	145.48	even	28
725.2.r.b.49.2		12	145.77	even	28
725.2.r.b.74.1		12	145.72	even	28
725.2.r.b.74.2		12	145.43	even	28
841.2.a.e.1.2		3	29.11	odd	28
841.2.a.f.1.2		3	29.18	odd	28
841.2.b.c.840.3		6	29.16	even	7
841.2.b.c.840.4		6	29.13	even	14
841.2.d.a.605.1		6	29.26	odd	28
841.2.d.a.645.1		6	29.8	odd	28
841.2.d.b.574.1		6	29.17	odd	4
841.2.d.b.778.1		6	29.2	odd	28
841.2.d.c.574.1		6	29.12	odd	4
841.2.d.c.778.1		6	29.27	odd	28
841.2.d.d.190.1		6	29.15	odd	28
841.2.d.d.571.1		6	29.10	odd	28
841.2.d.e.605.1		6	29.3	odd	28
841.2.d.e.645.1		6	29.21	odd	28
841.2.e.b.196.1		12	29.20	even	7
841.2.e.b.196.2		12	29.9	even	14
841.2.e.b.236.1		12	29.22	even	14
841.2.e.b.236.2		12	29.7	even	7
841.2.e.c.63.1		12	29.5	even	14	inner
841.2.e.c.63.2		12	29.24	even	7	inner
841.2.e.c.267.1		12	1.1	even	1	trivial
841.2.e.c.267.2		12	29.28	even	2	inner
841.2.e.d.270.1		12	29.4	even	14
841.2.e.d.270.2		12	29.25	even	7
841.2.e.d.651.1		12	29.23	even	7
841.2.e.d.651.2		12	29.6	even	14
7569.2.a.p.1.2		3	87.47	even	28
7569.2.a.r.1.2		3	87.11	even	28

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.347948 - 0.277479i) q^{2} +(1.21572 + 0.277479i) q^{3} +(-0.400969 - 1.75676i) q^{4} +(-0.431468 + 0.541044i) q^{5} +(-0.346011 - 0.433884i) q^{6} +(-0.0794168 + 0.347948i) q^{7} +(-0.734141 + 1.52446i) q^{8} +(-1.30194 - 0.626980i) q^{9} +(0.300257 - 0.0685317i) q^{10} +(-2.14295 - 4.44989i) q^{11} -2.24698i q^{12} +(-5.09299 + 2.45265i) q^{13} +(0.124181 - 0.0990311i) q^{14} +(-0.674671 + 0.538032i) q^{15} +(-2.56853 + 1.23694i) q^{16} +4.49396i q^{17} +(0.279032 + 0.579417i) q^{18} +(-2.29780 + 0.524459i) q^{19} +(1.12349 + 0.541044i) q^{20} +(-0.193096 + 0.400969i) q^{21} +(-0.489115 + 2.14295i) q^{22} +(1.43147 + 1.79500i) q^{23} +(-1.31551 + 1.64960i) q^{24} +(1.00604 + 4.40775i) q^{25} +(2.45265 + 0.559802i) q^{26} +(-4.33360 - 3.45593i) q^{27} +0.643104 q^{28} +0.384043 q^{30} +(-5.23203 - 4.17241i) q^{31} +(4.53614 + 1.03534i) q^{32} +(-1.37047 - 6.00442i) q^{33} +(1.24698 - 1.56366i) q^{34} +(-0.153989 - 0.193096i) q^{35} +(-0.579417 + 2.53859i) q^{36} +(2.14295 - 4.44989i) q^{37} +(0.945042 + 0.455108i) q^{38} +(-6.87219 + 1.56853i) q^{39} +(-0.508041 - 1.05496i) q^{40} -3.10992i q^{41} +(0.178448 - 0.0859360i) q^{42} +(2.66277 - 2.12349i) q^{43} +(-6.95812 + 5.54892i) q^{44} +(0.900969 - 0.433884i) q^{45} -1.02177i q^{46} +(-2.79640 - 5.80678i) q^{47} +(-3.46583 + 0.791053i) q^{48} +(6.19202 + 2.98192i) q^{49} +(0.873009 - 1.81282i) q^{50} +(-1.24698 + 5.46337i) q^{51} +(6.35086 + 7.96372i) q^{52} +(-2.92543 + 3.66837i) q^{53} +(0.548917 + 2.40496i) q^{54} +(3.33220 + 0.760553i) q^{55} +(-0.472129 - 0.376510i) q^{56} -2.93900 q^{57} -12.4940 q^{59} +(1.21572 + 0.969501i) q^{60} +(1.60191 + 0.365625i) q^{61} +(0.662718 + 2.90356i) q^{62} +(0.321552 - 0.403214i) q^{63} +(2.26391 + 2.83885i) q^{64} +(0.870469 - 3.81378i) q^{65} +(-1.18925 + 2.46950i) q^{66} +(-2.09299 - 1.00793i) q^{67} +(7.89481 - 1.80194i) q^{68} +(1.24218 + 2.57942i) q^{69} +0.109916i q^{70} +(-6.60872 + 3.18259i) q^{71} +(1.91161 - 1.52446i) q^{72} +(4.39831 - 3.50753i) q^{73} +(-1.98039 + 0.953703i) q^{74} +5.63773i q^{75} +(1.84270 + 3.82640i) q^{76} +(1.71851 - 0.392240i) q^{77} +(2.82640 + 1.36112i) q^{78} +(-2.02401 + 4.20291i) q^{79} +(0.439001 - 1.92339i) q^{80} +(-1.60656 - 2.01457i) q^{81} +(-0.862937 + 1.08209i) q^{82} +(-0.991271 - 4.34304i) q^{83} +(0.781831 + 0.178448i) q^{84} +(-2.43143 - 1.93900i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-4.44076 - 3.54138i) q^{89} +(-0.433884 - 0.0990311i) q^{90} +(-0.448927 - 1.96688i) q^{91} +(2.57942 - 3.23449i) q^{92} +(-5.20291 - 6.52424i) q^{93} +(-0.638260 + 2.79640i) q^{94} +(0.707674 - 1.46950i) q^{95} +(5.22737 + 2.51737i) q^{96} +(0.176076 - 0.0401881i) q^{97} +(-1.32708 - 2.75571i) q^{98} +7.13706i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 16 q^{5} + 6 q^{6} + 16 q^{7} + 2 q^{9} - 32 q^{13} - 20 q^{16} + 4 q^{20} - 12 q^{22} + 28 q^{23} + 14 q^{24} + 50 q^{25} + 24 q^{28} - 36 q^{30} + 12 q^{33} - 4 q^{34} - 12 q^{35} + 10 q^{36}+ \cdots + 18 q^{96}+O(q^{100}) \) 12 * q + 4 * q^4 - 16 * q^5 + 6 * q^6 + 16 * q^7 + 2 * q^9 - 32 * q^13 - 20 * q^16 + 4 * q^20 - 12 * q^22 + 28 * q^23 + 14 * q^24 + 50 * q^25 + 24 * q^28 - 36 * q^30 + 12 * q^33 - 4 * q^34 - 12 * q^35 + 10 * q^36 + 10 * q^38 - 6 * q^42 + 2 * q^45 + 54 * q^49 + 4 * q^51 + 22 * q^52 - 8 * q^53 - 30 * q^54 + 4 * q^57 - 112 * q^59 + 50 * q^62 + 12 * q^63 + 40 * q^64 - 18 * q^65 + 4 * q^67 + 2 * q^74 - 2 * q^78 - 34 * q^80 + 22 * q^81 - 32 * q^82 + 20 * q^83 + 32 * q^86 + 84 * q^88 - 80 * q^91 + 14 * q^92 - 36 * q^93 - 68 * q^94 + 18 * q^96

Introduction

L-functions

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