LMFDB - Embedded newform 930.2.y.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	930.29
Dual form			930.2.y.a.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.67374 - 0.445633i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.13834 - 1.92463i) q^{5} +(1.09215 + 1.34433i) q^{6} +(-3.43231 + 1.11523i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.60282 + 1.49175i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.67374 - 0.445633i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.13834 - 1.92463i) q^{5} +(1.09215 + 1.34433i) q^{6} +(-3.43231 + 1.11523i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.60282 + 1.49175i) q^{9} +(-0.210331 + 2.22615i) q^{10} +(-1.53458 - 4.72295i) q^{11} +(-0.0933927 - 1.72953i) q^{12} +(4.78611 - 3.47731i) q^{13} +(3.43231 + 1.11523i) q^{14} +(1.04761 + 3.72861i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.96229 - 1.61235i) q^{17} +(-1.22890 - 2.73675i) q^{18} +(-5.10320 - 3.70769i) q^{19} +(1.47866 - 1.67737i) q^{20} +(6.24179 - 0.337049i) q^{21} +(-1.53458 + 4.72295i) q^{22} +(-0.0893747 - 0.0290396i) q^{23} +(-0.941037 + 1.45411i) q^{24} +(-2.40837 + 4.38175i) q^{25} -5.91596 q^{26} +(-3.69168 - 3.65670i) q^{27} +(-2.12129 - 2.91970i) q^{28} +(5.21829 + 3.79131i) q^{29} +(1.34409 - 3.63228i) q^{30} +(-4.95361 + 2.54200i) q^{31} +1.00000 q^{32} +(0.463789 + 8.58887i) q^{33} +(3.06687 + 4.22118i) q^{34} +(6.05353 + 5.33641i) q^{35} +(-0.614421 + 2.93641i) q^{36} +5.53215 q^{37} +(1.94925 + 5.99917i) q^{38} +(-9.56032 + 3.68728i) q^{39} +(-2.18219 + 0.487883i) q^{40} +(-2.84249 + 3.91236i) q^{41} +(-5.24782 - 3.39615i) q^{42} +(2.90637 + 2.11160i) q^{43} +(4.01759 - 2.91895i) q^{44} +(-0.0918378 - 6.70758i) q^{45} +(0.0552366 + 0.0760267i) q^{46} +(1.61393 - 1.17259i) q^{47} +(1.61602 - 0.623276i) q^{48} +(4.87392 - 3.54111i) q^{49} +(4.52394 - 2.12931i) q^{50} +(7.58708 + 4.91001i) q^{51} +(4.78611 + 3.47731i) q^{52} +(-4.60787 - 1.49719i) q^{53} +(0.837276 + 5.12825i) q^{54} +(-7.34305 + 8.32982i) q^{55} +3.60895i q^{56} +(6.88917 + 8.47988i) q^{57} +(-1.99321 - 6.13447i) q^{58} +(1.50188 + 2.06716i) q^{59} +(-3.22239 + 2.14854i) q^{60} +12.0548i q^{61} +(5.50170 + 0.855136i) q^{62} +(-10.5973 - 2.21741i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-12.1407 - 5.25311i) q^{65} +(4.67320 - 7.22115i) q^{66} -8.70224i q^{67} -5.21766i q^{68} +(0.136649 + 0.0884331i) q^{69} +(-1.76074 - 7.87542i) q^{70} +(-0.774655 - 0.251701i) q^{71} +(2.22305 - 2.01446i) q^{72} +(0.739534 + 2.27605i) q^{73} +(-4.47560 - 3.25171i) q^{74} +(5.98364 - 6.26068i) q^{75} +(1.94925 - 5.99917i) q^{76} +(10.5343 + 14.4993i) q^{77} +(9.90179 + 2.63635i) q^{78} +(16.3701 + 5.31895i) q^{79} +(2.05220 + 0.887956i) q^{80} +(4.54937 + 7.76551i) q^{81} +(4.59925 - 1.49439i) q^{82} +(2.68287 - 3.69265i) q^{83} +(2.24937 + 5.83214i) q^{84} +(2.54561 + 11.3860i) q^{85} +(-1.11013 - 3.41664i) q^{86} +(-7.04454 - 8.67111i) q^{87} -4.96601 q^{88} +(-0.973495 - 2.99611i) q^{89} +(-3.86832 + 5.48052i) q^{90} +(-12.5494 + 17.2728i) q^{91} -0.0939742i q^{92} +(9.42386 - 2.04716i) q^{93} -1.99493 q^{94} +(-1.32675 + 14.0424i) q^{95} +(-1.67374 - 0.445633i) q^{96} +(1.22421 - 0.397770i) q^{97} -6.02449 q^{98} +(3.05122 - 14.5822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.67374	−	0.445633i	−0.966335	−	0.257286i
$3$	−1.67374	−	0.445633i	−0.966335	−	0.257286i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.13834	−	1.92463i	−0.509081	−	0.860719i
$5$	−1.13834	−	1.92463i	−0.509081	−	0.860719i
$6$	1.09215	+	1.34433i	0.445868	+	0.548818i
$7$	−3.43231	+	1.11523i	−1.29729	+	0.421516i	−0.874639	−	0.484776i	$-0.838901\pi$
$7$	−3.43231	+	1.11523i	−1.29729	+	0.421516i	−0.422653	+	0.906291i	$0.638901\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.60282	+	1.49175i	0.867608	+	0.497249i
$10$	−0.210331	+	2.22615i	−0.0665125	+	0.703972i
$11$	−1.53458	−	4.72295i	−0.462694	−	1.42402i	−0.861860	−	0.507146i	$-0.830700\pi$
$11$	−1.53458	−	4.72295i	−0.462694	−	1.42402i	0.399167	−	0.916878i	$-0.369300\pi$
$12$	−0.0933927	−	1.72953i	−0.0269601	−	0.499273i
$13$	4.78611	−	3.47731i	1.32743	−	0.964433i	0.327621	−	0.944809i	$-0.393753\pi$
$13$	4.78611	−	3.47731i	1.32743	−	0.964433i	0.999807	−	0.0196242i	$-0.00624698\pi$
$14$	3.43231	+	1.11523i	0.917324	+	0.298057i
$15$	1.04761	+	3.72861i	0.270492	+	0.962722i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.96229	−	1.61235i	−1.20353	−	0.391052i	−0.362474	−	0.931994i	$-0.618068\pi$
$17$	−4.96229	−	1.61235i	−1.20353	−	0.391052i	−0.841060	+	0.540942i	$0.818068\pi$
$18$	−1.22890	−	2.73675i	−0.289655	−	0.645058i
$19$	−5.10320	−	3.70769i	−1.17075	−	0.850603i	−0.179656	−	0.983730i	$-0.557498\pi$
$19$	−5.10320	−	3.70769i	−1.17075	−	0.850603i	−0.991099	+	0.133126i	$0.957498\pi$
$20$	1.47866	−	1.67737i	0.330639	−	0.375071i
$21$	6.24179	−	0.337049i	1.36207	−	0.0735502i
$22$	−1.53458	+	4.72295i	−0.327174	+	1.00694i
$23$	−0.0893747	−	0.0290396i	−0.0186359	−	0.00605518i	0.299684	−	0.954038i	$-0.403119\pi$
$23$	−0.0893747	−	0.0290396i	−0.0186359	−	0.00605518i	−0.318320	+	0.947983i	$0.603119\pi$
$24$	−0.941037	+	1.45411i	−0.192088	+	0.296820i
$25$	−2.40837	+	4.38175i	−0.481674	+	0.876351i
$26$	−5.91596			−1.16022
$27$	−3.69168	−	3.65670i	−0.710464	−	0.703733i
$28$	−2.12129	−	2.91970i	−0.400885	−	0.551771i
$29$	5.21829	+	3.79131i	0.969012	+	0.704029i	0.955226	−	0.295876i	$-0.0956117\pi$
$29$	5.21829	+	3.79131i	0.969012	+	0.704029i	0.0137859	+	0.999905i	$0.495612\pi$
$30$	1.34409	−	3.63228i	0.245396	−	0.663160i
$31$	−4.95361	+	2.54200i	−0.889694	+	0.456557i
$31$	−4.95361	+	2.54200i	−0.889694	+	0.456557i
$32$	1.00000			0.176777
$33$	0.463789	+	8.58887i	0.0807353	+	1.49513i
$34$	3.06687	+	4.22118i	0.525963	+	0.723926i
$35$	6.05353	+	5.33641i	1.02323	+	0.902018i
$36$	−0.614421	+	2.93641i	−0.102403	+	0.489401i
$37$	5.53215			0.909479			0.454740	−	0.890624i	$-0.349732\pi$
$37$	5.53215			0.909479			0.454740	+	0.890624i	$0.349732\pi$
$38$	1.94925	+	5.99917i	0.316210	+	0.973195i
$39$	−9.56032	+	3.68728i	−1.53088	+	0.590437i
$40$	−2.18219	+	0.487883i	−0.345035	+	0.0771410i
$41$	−2.84249	+	3.91236i	−0.443923	+	0.611007i	−0.971078	−	0.238762i	$-0.923259\pi$
$41$	−2.84249	+	3.91236i	−0.443923	+	0.611007i	0.527155	+	0.849769i	$0.323259\pi$
$42$	−5.24782	−	3.39615i	−0.809757	−	0.524037i
$43$	2.90637	+	2.11160i	0.443217	+	0.322016i	0.786912	−	0.617066i	$-0.211679\pi$
$43$	2.90637	+	2.11160i	0.443217	+	0.322016i	−0.343695	+	0.939081i	$0.611679\pi$
$44$	4.01759	−	2.91895i	0.605674	−	0.440048i
$45$	−0.0918378	−	6.70758i	−0.0136904	−	0.999906i
$46$	0.0552366	+	0.0760267i	0.00814420	+	0.0112095i
$47$	1.61393	−	1.17259i	0.235416	−	0.171040i	−0.463823	−	0.885928i	$-0.653523\pi$
$47$	1.61393	−	1.17259i	0.235416	−	0.171040i	0.699239	+	0.714888i	$0.253523\pi$
$48$	1.61602	−	0.623276i	0.233253	−	0.0899622i
$49$	4.87392	−	3.54111i	0.696274	−	0.505873i
$50$	4.52394	−	2.12931i	0.639782	−	0.301130i
$51$	7.58708	+	4.91001i	1.06240	+	0.687539i
$52$	4.78611	+	3.47731i	0.663714	+	0.482217i
$53$	−4.60787	−	1.49719i	−0.632940	−	0.205655i	−0.0250631	−	0.999686i	$-0.507979\pi$
$53$	−4.60787	−	1.49719i	−0.632940	−	0.205655i	−0.607877	+	0.794031i	$0.707979\pi$
$54$	0.837276	+	5.12825i	0.113939	+	0.697867i
$55$	−7.34305	+	8.32982i	−0.990136	+	1.12319i
$56$			3.60895i			0.482266i
$57$	6.88917	+	8.47988i	0.912493	+	1.12319i
$58$	−1.99321	−	6.13447i	−0.261721	−	0.805495i
$59$	1.50188	+	2.06716i	0.195528	+	0.269121i	0.895512	−	0.445037i	$-0.146810\pi$
$59$	1.50188	+	2.06716i	0.195528	+	0.269121i	−0.699984	+	0.714158i	$0.746810\pi$
$60$	−3.22239	+	2.14854i	−0.416008	+	0.277375i
$61$			12.0548i			1.54346i	0.635953	+	0.771728i	$0.280607\pi$
$61$			12.0548i			1.54346i	−0.635953	+	0.771728i	$0.719393\pi$
$62$	5.50170	+	0.855136i	0.698717	+	0.108602i
$63$	−10.5973	−	2.21741i	−1.33514	−	0.279368i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−12.1407	−	5.25311i	−1.50587	−	0.651568i
$66$	4.67320	−	7.22115i	0.575231	−	0.888862i
$67$		−	8.70224i		−	1.06315i	−0.847012	−	0.531574i	$-0.821601\pi$
$67$		−	8.70224i		−	1.06315i	0.847012	−	0.531574i	$-0.178399\pi$
$68$		−	5.21766i		−	0.632735i
$69$	0.136649	+	0.0884331i	0.0164506	+	0.0106461i
$70$	−1.76074	−	7.87542i	−0.210449	−	0.941293i
$71$	−0.774655	−	0.251701i	−0.0919346	−	0.0298714i	0.262689	−	0.964881i	$-0.415391\pi$
$71$	−0.774655	−	0.251701i	−0.0919346	−	0.0298714i	−0.354623	+	0.935009i	$0.615391\pi$
$72$	2.22305	−	2.01446i	0.261989	−	0.237406i
$73$	0.739534	+	2.27605i	0.0865559	+	0.266392i	0.984961	−	0.172776i	$-0.0552735\pi$
$73$	0.739534	+	2.27605i	0.0865559	+	0.266392i	−0.898405	+	0.439167i	$0.855274\pi$
$74$	−4.47560	−	3.25171i	−0.520278	−	0.378004i
$75$	5.98364	−	6.26068i	0.690931	−	0.722921i
$76$	1.94925	−	5.99917i	0.223594	−	0.688153i
$77$	10.5343	+	14.4993i	1.20050	+	1.65234i
$78$	9.90179	+	2.63635i	1.12116	+	0.298507i
$79$	16.3701	+	5.31895i	1.84178	+	0.598429i	0.998103	+	0.0615710i	$0.0196110\pi$
$79$	16.3701	+	5.31895i	1.84178	+	0.598429i	0.843673	+	0.536858i	$0.180389\pi$
$80$	2.05220	+	0.887956i	0.229443	+	0.0992765i
$81$	4.54937	+	7.76551i	0.505486	+	0.862835i
$82$	4.59925	−	1.49439i	0.507902	−	0.165027i
$83$	2.68287	−	3.69265i	0.294483	−	0.405321i	−0.635981	−	0.771705i	$-0.719404\pi$
$83$	2.68287	−	3.69265i	0.294483	−	0.405321i	0.930464	+	0.366384i	$0.119404\pi$
$84$	2.24937	+	5.83214i	0.245426	+	0.636338i
$85$	2.54561	+	11.3860i	0.276110	+	1.23498i
$86$	−1.11013	−	3.41664i	−0.119709	−	0.368426i
$87$	−7.04454	−	8.67111i	−0.755254	−	0.929641i
$88$	−4.96601			−0.529378
$89$	−0.973495	−	2.99611i	−0.103190	−	0.317587i	0.886111	−	0.463473i	$-0.153397\pi$
$89$	−0.973495	−	2.99611i	−0.103190	−	0.317587i	−0.989301	+	0.145886i	$0.953397\pi$
$90$	−3.86832	+	5.48052i	−0.407756	+	0.577698i
$91$	−12.5494	+	17.2728i	−1.31554	+	1.81068i
$92$		−	0.0939742i		−	0.00979748i
$93$	9.42386	−	2.04716i	0.977209	−	0.212281i
$94$	−1.99493			−0.205761
$95$	−1.32675	+	14.0424i	−0.136121	+	1.44072i
$96$	−1.67374	−	0.445633i	−0.170826	−	0.0454822i
$97$	1.22421	−	0.397770i	0.124300	−	0.0403874i	−0.246207	−	0.969217i	$-0.579184\pi$
$97$	1.22421	−	0.397770i	0.124300	−	0.0403874i	0.370506	+	0.928830i	$0.379184\pi$
$98$	−6.02449			−0.608566
$99$	3.05122	−	14.5822i	0.306659	−	1.46557i
$100$	−4.91152	−	0.936458i	−0.491152	−	0.0936458i
$101$	−5.39353	−	1.75247i	−0.536677	−	0.174377i	0.0281236	−	0.999604i	$-0.491047\pi$
$101$	−5.39353	−	1.75247i	−0.536677	−	0.174377i	−0.564800	+	0.825228i	$0.691047\pi$
$102$	−3.25205	−	8.43186i	−0.322001	−	0.834879i
$103$	−11.0752	+	15.2437i	−1.09127	+	1.50200i	−0.244792	+	0.969576i	$0.578720\pi$
$103$	−11.0752	+	15.2437i	−1.09127	+	1.50200i	−0.846477	+	0.532426i	$0.821280\pi$
$104$	−1.82813	−	5.62641i	−0.179263	−	0.551715i
$105$	−7.75396	−	11.6294i	−0.756709	−	1.13492i
$106$	2.84782	+	3.91969i	0.276605	+	0.380714i
$107$	−0.903930	+	2.78201i	−0.0873862	+	0.268947i	−0.985195	−	0.171439i	$-0.945158\pi$
$107$	−0.903930	+	2.78201i	−0.0873862	+	0.268947i	0.897809	+	0.440386i	$0.145158\pi$
$108$	2.33694	−	4.64098i	0.224872	−	0.446579i
$109$	−12.2772	+	8.91994i	−1.17595	+	0.854375i	−0.991709	−	0.128506i	$-0.958982\pi$
$109$	−12.2772	+	8.91994i	−1.17595	+	0.854375i	−0.184238	+	0.982882i	$0.558982\pi$
$110$	10.8368	−	2.42283i	1.03325	−	0.231008i
$111$	−9.25938	−	2.46531i	−0.878862	−	0.233996i
$112$	2.12129	−	2.91970i	0.200443	−	0.275886i
$113$	3.37442	+	10.3854i	0.317439	+	0.976977i	0.974739	+	0.223348i	$0.0716986\pi$
$113$	3.37442	+	10.3854i	0.317439	+	0.976977i	−0.657300	+	0.753629i	$0.728301\pi$
$114$	−0.589112	−	10.9097i	−0.0551754	−	1.02179i
$115$	0.0458484	+	0.205070i	0.00427538	+	0.0191229i
$116$	−1.99321	+	6.13447i	−0.185065	+	0.569571i
$117$	17.6447	−	1.91116i	1.63125	−	0.176687i
$118$		−	2.55515i		−	0.235220i
$119$	18.8303			1.72617
$120$	3.86985	+	0.155867i	0.353267	+	0.0142287i
$121$	−11.0522	+	8.02988i	−1.00474	+	0.729989i
$122$	7.08562	−	9.75251i	0.641502	−	0.882951i
$123$	6.50107	−	5.28156i	0.586182	−	0.476223i
$124$	−3.94834	−	3.92564i	−0.354571	−	0.352533i
$125$	11.1748	−	0.352714i	0.999502	−	0.0315477i
$126$	7.27006	+	8.02288i	0.647669	+	0.714735i
$127$	1.53607	−	1.11602i	0.136304	−	0.0990309i	−0.517544	−	0.855657i	$-0.673154\pi$
$127$	1.53607	−	1.11602i	0.136304	−	0.0990309i	0.653848	+	0.756626i	$0.273154\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−3.92351	−	4.82944i	−0.345446	−	0.425209i
$130$	6.73437	+	11.3860i	0.590643	+	0.998619i
$131$	−14.5110	+	4.71491i	−1.26783	+	0.411944i	−0.864279	−	0.503012i	$-0.832225\pi$
$131$	−14.5110	+	4.71491i	−1.26783	+	0.411944i	−0.403554	+	0.914956i	$0.632225\pi$
$132$	−8.02518	+	3.09520i	−0.698502	+	0.269402i
$133$	21.6507	+	7.03474i	1.87735	+	0.609989i
$134$	−5.11505	+	7.04026i	−0.441873	+	0.608186i
$135$	−2.83540	+	11.2677i	−0.244033	+	0.969767i
$136$	−3.06687	+	4.22118i	−0.262982	+	0.361963i
$137$	−7.33902	−	10.1013i	−0.627015	−	0.863012i	0.370825	−	0.928703i	$-0.379075\pi$
$137$	−7.33902	−	10.1013i	−0.627015	−	0.863012i	−0.997840	+	0.0656907i	$0.979075\pi$
$138$	−0.0585719	−	0.151864i	−0.00498597	−	0.0129275i
$139$	−3.75633	−	5.17015i	−0.318608	−	0.438526i	0.619433	−	0.785049i	$-0.287362\pi$
$139$	−3.75633	−	5.17015i	−0.318608	−	0.438526i	−0.938042	+	0.346523i	$0.887362\pi$
$140$	−3.20459	+	7.40629i	−0.270837	+	0.625946i
$141$	−3.22385	+	1.24339i	−0.271497	+	0.104712i
$142$	0.478763	+	0.658961i	0.0401769	+	0.0552988i
$143$	−23.7679	−	17.2684i	−1.98757	−	1.44405i
$144$	−2.98256	+	0.323051i	−0.248546	+	0.0269209i
$145$	1.35667	−	14.3591i	0.112665	−	1.19245i
$146$	0.739534	−	2.27605i	0.0612043	−	0.188367i
$147$	−9.73571	+	3.75492i	−0.802988	+	0.309701i
$148$	1.70953	+	5.26138i	0.140522	+	0.432483i
$149$		−	17.2308i		−	1.41160i	−0.708412	−	0.705800i	$-0.750588\pi$
$149$		−	17.2308i		−	1.41160i	0.708412	−	0.705800i	$-0.249412\pi$
$150$	−8.52080	+	1.54790i	−0.695720	+	0.126385i
$151$	11.2981	−	3.67096i	0.919423	−	0.298739i	0.189193	−	0.981940i	$-0.439413\pi$
$151$	11.2981	−	3.67096i	0.919423	−	0.298739i	0.730230	+	0.683201i	$0.239413\pi$
$152$	−5.10320	+	3.70769i	−0.413924	+	0.300734i
$153$	−10.5108	−	11.5991i	−0.849744	−	0.937736i
$154$		−	17.9221i		−	1.44420i
$155$	10.5313	+	6.64018i	0.845893	+	0.533352i
$156$	−6.46111	−	7.95297i	−0.517303	−	0.636748i
$157$	−2.26721	+	3.12055i	−0.180943	+	0.249047i	−0.889848	−	0.456258i	$-0.849190\pi$
$157$	−2.26721	+	3.12055i	−0.180943	+	0.249047i	0.708905	+	0.705304i	$0.249190\pi$
$158$	−10.1173	−	13.9252i	−0.804885	−	1.10783i
$159$	7.04520	+	4.55933i	0.558720	+	0.361578i
$160$	−1.13834	−	1.92463i	−0.0899936	−	0.152155i
$161$	0.339148			0.0267286
$162$	0.883934	−	8.95649i	0.0694484	−	0.703688i
$163$	14.0952	+	4.57981i	1.10402	+	0.358719i	0.803649	−	0.595103i	$-0.202889\pi$
$163$	14.0952	+	4.57981i	1.10402	+	0.358719i	0.300373	+	0.953822i	$0.402889\pi$
$164$	−4.59925	−	1.49439i	−0.359141	−	0.116692i
$165$	16.0024	−	10.6697i	1.24579	−	0.830632i
$166$	−4.34097	+	1.41047i	−0.336925	+	0.109473i
$167$	−12.3171	+	16.9530i	−0.953125	+	1.31186i	−0.00299945	+	0.999996i	$0.500955\pi$
$167$	−12.3171	+	16.9530i	−0.953125	+	1.31186i	−0.950125	+	0.311868i	$0.899045\pi$
$168$	1.60826	−	6.04044i	0.124080	−	0.466030i
$169$	6.79794	−	20.9219i	0.522918	−	1.60938i
$170$	4.63306	−	10.7077i	0.355339	−	0.821243i
$171$	−7.75179	−	17.2632i	−0.592794	−	1.32015i
$172$	−1.11013	+	3.41664i	−0.0846468	+	0.260516i
$173$	−0.902895	+	0.655992i	−0.0686459	+	0.0498741i	−0.621579	−	0.783352i	$-0.713509\pi$
$173$	−0.902895	+	0.655992i	−0.0686459	+	0.0498741i	0.552933	+	0.833226i	$0.313509\pi$
$174$	0.602398	+	11.1558i	0.0456677	+	0.845716i
$175$	3.37963	−	17.7254i	0.255476	−	1.33992i
$176$	4.01759	+	2.91895i	0.302837	+	0.220024i
$177$	−1.59256	−	4.12917i	−0.119704	−	0.310368i
$178$	−0.973495	+	2.99611i	−0.0729665	+	0.224568i
$179$	2.59135	+	7.97536i	0.193687	+	0.596106i	0.999989	+	0.00460314i	$0.00146523\pi$
$179$	2.59135	+	7.97536i	0.193687	+	0.596106i	−0.806303	+	0.591503i	$0.798535\pi$
$180$	6.35090	−	2.16010i	0.473368	−	0.161004i
$181$		−	14.7770i		−	1.09837i	−0.835702	−	0.549183i	$-0.814939\pi$
$181$		−	14.7770i		−	1.09837i	0.835702	−	0.549183i	$-0.185061\pi$
$182$	20.3054	−	6.59763i	1.50514	−	0.489049i
$183$	5.37200	−	20.1766i	0.397110	−	1.49150i
$184$	−0.0552366	+	0.0760267i	−0.00407210	+	0.00560476i
$185$	−6.29746	−	10.6473i	−0.462998	−	0.782806i
$186$	−8.82735	−	3.88302i	−0.647253	−	0.284717i
$187$			25.9110i			1.89480i
$188$	1.61393	+	1.17259i	0.117708	+	0.0855198i
$189$	16.7491	+	8.43389i	1.21831	+	0.613475i
$190$	9.32726	−	10.5807i	0.676670	−	0.767603i
$191$		−	26.5140i		−	1.91849i	−0.282580	−	0.959244i	$-0.591190\pi$
$191$		−	26.5140i		−	1.91849i	0.282580	−	0.959244i	$-0.408810\pi$
$192$	1.09215	+	1.34433i	0.0788191	+	0.0970183i
$193$	0.431359	−	0.140157i	0.0310499	−	0.0100887i	−0.293451	−	0.955974i	$-0.594804\pi$
$193$	0.431359	−	0.140157i	0.0310499	−	0.0100887i	0.324501	+	0.945885i	$0.394804\pi$
$194$	−1.22421	−	0.397770i	−0.0878931	−	0.0285582i
$195$	17.9795	+	14.2027i	1.28754	+	1.01707i
$196$	4.87392	+	3.54111i	0.348137	+	0.252936i
$197$	−13.3435	+	4.33557i	−0.950685	+	0.308896i	−0.742994	−	0.669298i	$-0.766595\pi$
$197$	−13.3435	+	4.33557i	−0.950685	+	0.308896i	−0.207691	+	0.978194i	$0.566595\pi$
$198$	−11.0397	+	10.0038i	−0.784558	+	0.710940i
$199$	−7.65203	−	10.5321i	−0.542438	−	0.746602i	0.446524	−	0.894772i	$-0.352662\pi$
$199$	−7.65203	−	10.5321i	−0.542438	−	0.746602i	−0.988962	+	0.148170i	$0.952662\pi$
$200$	3.42307	+	3.64453i	0.242047	+	0.257707i
$201$	−3.87800	+	14.5653i	−0.273533	+	1.02736i
$202$	3.33339	+	4.58801i	0.234536	+	0.322812i
$203$	−22.1390	−	7.19339i	−1.55385	−	0.504877i
$204$	−2.32516	+	8.73302i	−0.162794	+	0.611434i
$205$	10.7655	+	1.01715i	0.751898	+	0.0710406i
$206$	17.9200	−	5.82256i	1.24854	−	0.405677i
$207$	−0.189307	−	0.208910i	−0.0131577	−	0.0145202i
$208$	−1.82813	+	5.62641i	−0.126758	+	0.390121i
$209$	−9.67999	+	29.7920i	−0.669579	+	2.06075i
$210$	−0.562517	+	13.9661i	−0.0388174	+	0.963750i
$211$	1.64266			0.113086			0.0565428	−	0.998400i	$-0.481992\pi$
$211$	1.64266			0.113086			0.0565428	+	0.998400i	$0.481992\pi$
$212$		−	4.84501i		−	0.332756i
$213$	1.18441	+	0.766493i	0.0811542	+	0.0525193i
$214$	2.36652	−	1.71938i	0.161772	−	0.117534i
$215$	0.755607	−	7.99738i	0.0515319	−	0.545417i
$216$	−4.61853	+	2.38101i	−0.314251	+	0.162007i
$217$	14.1674	−	14.2493i	0.961747	−	0.967308i
$218$	15.1755			1.02782
$219$	−0.223506	−	4.13908i	−0.0151031	−	0.279693i
$220$	−10.1913	−	4.40960i	−0.687094	−	0.297295i
$221$	−29.3567	+	9.53858i	−1.97475	+	0.641634i
$222$	6.04193	+	7.43700i	0.405508	+	0.499139i
$223$	−0.917076			−0.0614119			−0.0307060	−	0.999528i	$-0.509776\pi$
$223$	−0.917076			−0.0614119			−0.0307060	+	0.999528i	$0.509776\pi$
$224$	−3.43231	+	1.11523i	−0.229331	+	0.0745142i
$225$	−12.8050	+	7.81225i	−0.853669	+	0.520817i
$226$	3.37442	−	10.3854i	0.224463	−	0.690827i
$227$	−0.173417	−	0.125995i	−0.0115101	−	0.00836258i	0.582015	−	0.813178i	$-0.302264\pi$
$227$	−0.173417	−	0.125995i	−0.0115101	−	0.00836258i	−0.593525	+	0.804815i	$0.702264\pi$
$228$	−5.93597	+	9.17242i	−0.393119	+	0.607458i
$229$	−0.457332	+	0.629463i	−0.0302213	+	0.0415961i	−0.823860	−	0.566793i	$-0.808184\pi$
$229$	−0.457332	+	0.629463i	−0.0302213	+	0.0415961i	0.793639	+	0.608389i	$0.208184\pi$
$230$	0.0834449	−	0.192854i	0.00550220	−	0.0127164i
$231$	−11.1704	−	28.9624i	−0.734958	−	1.90559i
$232$	5.21829	−	3.79131i	0.342598	−	0.248912i
$233$	2.11696	−	1.53806i	0.138687	−	0.100762i	−0.516279	−	0.856421i	$-0.672683\pi$
$233$	2.11696	−	1.53806i	0.138687	−	0.100762i	0.654966	+	0.755659i	$0.272683\pi$
$234$	−15.3982	−	8.82512i	−1.00661	−	0.576916i
$235$	−4.09399	−	1.77141i	−0.267063	−	0.115554i
$236$	−1.50188	+	2.06716i	−0.0977639	+	0.134560i
$237$	−25.0289	−	16.1976i	−1.62580	−	1.05215i
$238$	−15.2340	−	11.0682i	−0.987474	−	0.717442i
$239$	3.74441	−	11.5241i	0.242205	−	0.745432i	−0.753878	−	0.657014i	$-0.771819\pi$
$239$	3.74441	−	11.5241i	0.242205	−	0.745432i	0.996084	−	0.0884174i	$-0.0281809\pi$
$240$	−3.03915	−	2.40074i	−0.196177	−	0.154967i
$241$	2.57354	−	0.836195i	0.165776	−	0.0538640i	−0.224953	−	0.974370i	$-0.572223\pi$
$241$	2.57354	−	0.836195i	0.165776	−	0.0538640i	0.390729	+	0.920506i	$0.372223\pi$
$242$	13.6612			0.878178
$243$	−4.15391	−	15.0248i	−0.266473	−	0.963842i
$244$	−11.4648	+	3.72513i	−0.733957	+	0.238477i
$245$	−12.3635	−	5.34949i	−0.789874	−	0.341766i
$246$	−8.36390	+	0.451641i	−0.533263	+	0.0287956i
$247$	−37.3173			−2.37444
$248$	0.886837	+	5.49668i	0.0563142	+	0.349040i
$249$	−6.13599	+	4.98497i	−0.388853	+	0.315910i
$250$	−9.24790	−	6.28302i	−0.584889	−	0.397373i
$251$	−4.99529	+	3.62929i	−0.315300	+	0.229079i	−0.734167	−	0.678969i	$-0.762427\pi$
$251$	−4.99529	+	3.62929i	−0.315300	+	0.229079i	0.418867	+	0.908047i	$0.362427\pi$
$252$	−1.16587	−	10.7639i	−0.0734432	−	0.678061i
$253$			0.466677i			0.0293397i
$254$	−1.89869			−0.119134
$255$	0.813264	−	20.1916i	0.0509285	−	1.26444i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−3.27238	+	10.0713i	−0.204125	+	0.628234i	0.795623	+	0.605792i	$0.207144\pi$
$257$	−3.27238	+	10.0713i	−0.204125	+	0.628234i	−0.999748	+	0.0224411i	$0.992856\pi$
$258$	0.335510	+	6.21328i	0.0208879	+	0.386822i
$259$	−18.9880	+	6.16959i	−1.17986	+	0.383360i
$260$	1.24431	−	13.1698i	0.0771688	−	0.816759i
$261$	7.92660	+	17.6525i	0.490644	+	1.09266i
$262$	14.5110	+	4.71491i	0.896493	+	0.291288i
$263$	11.9232	+	16.4108i	0.735214	+	1.01193i	0.998880	+	0.0473208i	$0.0150683\pi$
$263$	11.9232	+	16.4108i	0.735214	+	1.01193i	−0.263666	+	0.964614i	$0.584932\pi$
$264$	8.31182	+	2.21302i	0.511557	+	0.136202i
$265$	2.36380	+	10.5727i	0.145207	+	0.649478i
$266$	−13.3809	−	18.4172i	−0.820434	−	1.12923i
$267$	0.294215	+	5.44853i	0.0180056	+	0.333445i
$268$	8.27632	−	2.68914i	0.505557	−	0.164265i
$269$	2.17982	+	1.58373i	0.132906	+	0.0965619i	0.652252	−	0.758002i	$-0.273824\pi$
$269$	2.17982	+	1.58373i	0.132906	+	0.0965619i	−0.519346	+	0.854564i	$0.673824\pi$
$270$	8.91686	−	7.44913i	0.542663	−	0.453340i
$271$	−5.14614	−	1.67208i	−0.312606	−	0.101572i	0.148512	−	0.988911i	$-0.452552\pi$
$271$	−5.14614	−	1.67208i	−0.312606	−	0.101572i	−0.461118	+	0.887339i	$0.652552\pi$
$272$	4.96229	−	1.61235i	0.300883	−	0.0977629i
$273$	28.7019	−	23.3178i	1.73712	−	1.41126i
$274$			12.4859i			0.754300i
$275$	24.3907	+	4.65046i	1.47081	+	0.280433i
$276$	−0.0418780	+	0.157288i	−0.00252076	+	0.00946765i
$277$	−20.1450	−	14.6362i	−1.21039	−	0.879403i	−0.215127	−	0.976586i	$-0.569017\pi$
$277$	−20.1450	−	14.6362i	−1.21039	−	0.879403i	−0.995266	+	0.0971835i	$0.969017\pi$
$278$			6.39066i			0.383286i
$279$	−16.6854	−	0.773161i	−0.998928	−	0.0462879i
$280$	6.94587	−	4.10820i	0.415095	−	0.245512i
$281$	4.08990	−	5.62927i	0.243983	−	0.335814i	−0.669409	−	0.742894i	$-0.733453\pi$
$281$	4.08990	−	5.62927i	0.243983	−	0.335814i	0.913393	+	0.407080i	$0.133453\pi$
$282$	3.33899	+	0.889005i	0.198834	+	0.0529395i
$283$	0.282524	−	0.0917976i	0.0167943	−	0.00545680i	−0.300608	−	0.953748i	$-0.597190\pi$
$283$	0.282524	−	0.0917976i	0.0167943	−	0.00545680i	0.317402	+	0.948291i	$0.397190\pi$
$284$		−	0.814520i		−	0.0483329i
$285$	8.47837	−	22.9121i	0.502215	−	1.35719i
$286$	9.07852	+	27.9408i	0.536824	+	1.65217i
$287$	5.39316	−	16.5984i	0.318348	−	0.979775i
$288$	2.60282	+	1.49175i	0.153373	+	0.0879021i
$289$	8.27141	+	6.00953i	0.486554	+	0.353502i
$290$	−9.53761	+	10.8193i	−0.560068	+	0.635330i
$291$	−2.22627	+	0.120216i	−0.130506	+	0.00704718i
$292$	−1.93613	+	1.40668i	−0.113303	+	0.0823196i
$293$	7.02650	−	21.6253i	0.410493	−	1.26337i	−0.505728	−	0.862693i	$-0.668776\pi$
$293$	7.02650	−	21.6253i	0.410493	−	1.26337i	0.916221	−	0.400673i	$-0.131224\pi$
$294$	10.0834	+	2.68471i	0.588079	+	0.156576i
$295$	2.26886	−	5.24368i	0.132098	−	0.305299i
$296$	1.70953	−	5.26138i	0.0993642	−	0.305812i
$297$	−11.6053	+	23.0472i	−0.673406	+	1.33733i
$298$	−10.1280	+	13.9400i	−0.586699	+	0.807521i
$299$	−0.528737	+	0.171797i	−0.0305777	+	0.00993529i
$300$	7.80330	+	3.75612i	0.450524	+	0.216860i
$301$	−12.3305	−	4.00641i	−0.710716	−	0.230926i
$302$	−11.2981	−	3.67096i	−0.650130	−	0.211240i
$303$	8.24643	+	5.33671i	0.473745	+	0.306586i
$304$	6.30791			0.361783
$305$	23.2009	−	13.7224i	1.32848	−	0.785743i
$306$	1.68557	+	15.5620i	0.0963578	+	0.889619i
$307$	15.4870	+	21.3160i	0.883888	+	1.21657i	0.975329	+	0.220756i	$0.0708526\pi$
$307$	15.4870	+	21.3160i	0.883888	+	1.21657i	−0.0914415	+	0.995810i	$0.529147\pi$
$308$	−10.5343	+	14.4993i	−0.600249	+	0.826171i
$309$	25.3300	−	20.5785i	1.44098	−	1.17067i
$310$	−4.61699	−	11.5622i	−0.262227	−	0.656686i
$311$			29.4053i			1.66742i	0.552203	+	0.833710i	$0.313787\pi$
$311$			29.4053i			1.66742i	−0.552203	+	0.833710i	$0.686213\pi$
$312$	0.552507	+	10.2318i	0.0312796	+	0.579264i
$313$	19.6207	−	14.2553i	1.10903	−	0.805755i	0.126516	−	0.991965i	$-0.459620\pi$
$313$	19.6207	−	14.2553i	1.10903	−	0.805755i	0.982510	+	0.186210i	$0.0596204\pi$
$314$	3.66842	−	1.19194i	0.207021	−	0.0672652i
$315$	7.79568	+	22.9201i	0.439237	+	1.29140i
$316$			17.2125i			0.968279i
$317$	3.38445	+	10.4163i	0.190090	+	0.585035i	0.999999	−	0.00151971i	$-0.000483739\pi$
$317$	3.38445	+	10.4163i	0.190090	+	0.585035i	−0.809909	+	0.586555i	$0.800484\pi$
$318$	−3.01978	−	7.82964i	−0.169341	−	0.439064i
$319$	9.89829	−	30.4638i	0.554198	−	1.70565i
$320$	−0.210331	+	2.22615i	−0.0117579	+	0.124446i
$321$	2.75270	−	4.25354i	0.153641	−	0.237410i
$322$	−0.274376	−	0.199346i	−0.0152904	−	0.0111091i
$323$	19.3455	+	26.6268i	1.07641	+	1.48155i
$324$	−5.97961	+	6.72639i	−0.332200	+	0.373688i
$325$	3.71001	+	29.3462i	0.205794	+	1.62784i
$326$	−8.71132	−	11.9901i	−0.482475	−	0.664070i
$327$	24.5240	−	9.45854i	1.35618	−	0.523058i
$328$	2.84249	+	3.91236i	0.156950	+	0.216024i
$329$	−4.23181	+	5.82459i	−0.233307	+	0.321120i
$330$	−19.2177	−	0.774039i	−1.05790	−	0.0426094i
$331$	−19.5733	+	26.9404i	−1.07585	+	1.48078i	−0.211836	+	0.977305i	$0.567944\pi$
$331$	−19.5733	+	26.9404i	−1.07585	+	1.48078i	−0.864011	+	0.503472i	$0.832056\pi$
$332$	4.34097	+	1.41047i	0.238242	+	0.0774094i
$333$	14.3992	+	8.25257i	0.789071	+	0.452238i
$334$	19.9295	−	6.47548i	1.09049	−	0.354322i
$335$	−16.7485	+	9.90610i	−0.915071	+	0.541228i
$336$	−4.85160	+	3.94151i	−0.264676	+	0.215027i
$337$	2.49129	+	7.66740i	0.135709	+	0.417670i	0.995700	−	0.0926401i	$-0.0295306\pi$
$337$	2.49129	+	7.66740i	0.135709	+	0.417670i	−0.859990	+	0.510310i	$0.829531\pi$
$338$	−17.7972	+	12.9304i	−0.968041	+	0.703323i
$339$	−1.01984	−	18.8862i	−0.0553899	−	1.02576i
$340$	−10.0421	+	5.93947i	−0.544607	+	0.322113i
$341$	19.6075	+	19.4948i	1.06180	+	1.05570i
$342$	−3.87571	+	18.5226i	−0.209574	+	1.00159i
$343$	2.06933	−	2.84818i	0.111733	−	0.153787i
$344$	2.90637	−	2.11160i	0.156701	−	0.113850i
$345$	0.0146475	−	0.363666i	0.000788595	−	0.0195791i
$346$	1.11604			0.0599987
$347$			5.39078i			0.289392i	0.989476	+	0.144696i	$0.0462205\pi$
$347$			5.39078i			0.289392i	−0.989476	+	0.144696i	$0.953780\pi$
$348$	6.06984	−	9.37928i	0.325377	−	0.502782i
$349$	9.39068	−	28.9016i	0.502672	−	1.54706i	−0.301978	−	0.953315i	$-0.597647\pi$
$349$	9.39068	−	28.9016i	0.502672	−	1.54706i	0.804650	−	0.593750i	$-0.202353\pi$
$350$	−13.1529	+	12.3537i	−0.703053	+	0.660331i
$351$	−30.3843	−	4.66426i	−1.62179	−	0.248960i
$352$	−1.53458	−	4.72295i	−0.0817934	−	0.251734i
$353$	−10.1043	+	13.9073i	−0.537796	+	0.740213i	−0.988293	−	0.152565i	$-0.951247\pi$
$353$	−10.1043	+	13.9073i	−0.537796	+	0.740213i	0.450497	+	0.892778i	$0.351247\pi$
$354$	−1.13866	+	4.27666i	−0.0605189	+	0.227302i
$355$	0.397390	+	1.77744i	0.0210913	+	0.0943368i
$356$	2.54864	−	1.85170i	0.135078	−	0.0981398i
$357$	−31.5170	−	8.39139i	−1.66806	−	0.444119i
$358$	2.59135	−	7.97536i	0.136957	−	0.421511i
$359$	2.33260	+	3.21054i	0.123110	+	0.169446i	0.866123	−	0.499830i	$-0.166604\pi$
$359$	2.33260	+	3.21054i	0.123110	+	0.169446i	−0.743014	+	0.669276i	$0.766604\pi$
$360$	−6.40766	−	1.98541i	−0.337713	−	0.104640i
$361$	6.42436	+	19.7722i	0.338124	+	1.04064i
$362$	−8.68570	+	11.9548i	−0.456510	+	0.628332i
$363$	22.0769	−	8.51473i	1.15873	−	0.446907i
$364$	−20.3054	−	6.59763i	−1.06429	−	0.345810i
$365$	3.53871	−	4.01425i	0.185224	−	0.210115i
$366$	−16.2055	+	13.1656i	−0.847077	+	0.688177i
$367$	−3.58149			−0.186952			−0.0934762	−	0.995622i	$-0.529798\pi$
$367$	−3.58149			−0.186952			−0.0934762	+	0.995622i	$0.529798\pi$
$368$	0.0893747	−	0.0290396i	0.00465898	−	0.00151379i
$369$	−13.2348	+	5.94288i	−0.688974	+	0.309374i
$370$	−1.16358	+	12.3154i	−0.0604917	+	0.640248i
$371$	17.4854			0.907795
$372$	4.85910	+	8.33002i	0.251933	+	0.431891i
$373$		−	6.05061i		−	0.313288i	−0.987655	−	0.156644i	$-0.949932\pi$
$373$		−	6.05061i		−	0.313288i	0.987655	−	0.156644i	$-0.0500676\pi$
$374$	15.2301	−	20.9624i	0.787529	−	1.08394i
$375$	−18.8609	−	4.38949i	−0.973971	−	0.226672i
$376$	−0.616466	−	1.89729i	−0.0317918	−	0.0978452i
$377$	38.1589			1.96528
$378$	−8.59295	−	16.6680i	−0.441974	−	0.857310i
$379$	3.47466	+	10.6939i	0.178481	+	0.549308i	0.999775	−	0.0211966i	$-0.00674759\pi$
$379$	3.47466	+	10.6939i	0.178481	+	0.549308i	−0.821294	+	0.570505i	$0.806748\pi$
$380$	−13.7651	+	3.07752i	−0.706133	+	0.157873i
$381$	−3.06832	+	1.18341i	−0.157195	+	0.0606278i
$382$	−15.5846	+	21.4503i	−0.797375	+	1.09749i
$383$	−30.6454	+	9.95728i	−1.56590	+	0.508793i	−0.958377	−	0.285505i	$-0.907839\pi$
$383$	−30.6454	+	9.95728i	−1.56590	+	0.508793i	−0.607527	+	0.794299i	$0.707839\pi$
$384$	−0.0933927	−	1.72953i	−0.00476593	−	0.0882598i
$385$	15.9140	−	36.7797i	0.811052	−	1.87447i
$386$	−0.431359	−	0.140157i	−0.0219556	−	0.00713380i
$387$	4.41478	+	9.83168i	0.224416	+	0.499773i
$388$	0.756603	+	1.04137i	0.0384107	+	0.0528678i
$389$	6.10415	−	18.7867i	0.309493	−	0.952521i	−0.668469	−	0.743740i	$-0.733050\pi$
$389$	6.10415	−	18.7867i	0.309493	−	0.952521i	0.977962	−	0.208781i	$-0.0669497\pi$
$390$	−6.19762	−	22.0583i	−0.313828	−	1.11697i
$391$	0.396682	+	0.288206i	0.0200611	+	0.0145752i
$392$	−1.86167	−	5.72963i	−0.0940286	−	0.289390i
$393$	26.3888	−	1.42496i	1.33114	−	0.0718800i
$394$	13.3435	+	4.33557i	0.672236	+	0.218423i
$395$	−8.39768	−	37.5610i	−0.422533	−	1.88990i
$396$	14.8114	−	1.60427i	0.744301	−	0.0806178i
$397$		−	25.3608i		−	1.27282i	−0.771350	−	0.636411i	$-0.780418\pi$
$397$		−	25.3608i		−	1.27282i	0.771350	−	0.636411i	$-0.219582\pi$
$398$			13.0184i			0.652554i
$399$	−33.1028	−	21.4226i	−1.65721	−	1.07247i
$400$	−0.627119	−	4.96052i	−0.0313560	−	0.248026i
$401$	7.35458	+	5.34342i	0.367270	+	0.266838i	0.756078	−	0.654481i	$-0.227113\pi$
$401$	7.35458	+	5.34342i	0.367270	+	0.266838i	−0.388808	+	0.921319i	$0.627113\pi$
$402$	11.6986	−	9.50414i	0.583475	−	0.474023i
$403$	−14.8692	+	29.3915i	−0.740687	+	1.46410i
$404$		−	5.67110i		−	0.282148i
$405$	9.76698	−	17.5956i	0.485325	−	0.874334i
$406$	13.6826	+	18.8325i	0.679058	+	0.934643i
$407$	−8.48953	−	26.1281i	−0.420810	−	1.29512i
$408$	7.01424	−	5.69847i	0.347257	−	0.282116i
$409$			8.20061i			0.405494i	0.979231	+	0.202747i	$0.0649869\pi$
$409$			8.20061i			0.405494i	−0.979231	+	0.202747i	$0.935013\pi$
$410$	−8.11164	−	7.15072i	−0.400605	−	0.353149i
$411$	7.78216	+	20.1775i	0.383866	+	0.995281i
$412$	−17.9200	−	5.82256i	−0.882854	−	0.286857i
$413$	−7.46026	−	5.42020i	−0.367095	−	0.266710i
$414$	0.0303585	+	0.280283i	0.00149204	+	0.0137752i
$415$	−10.1610	−	0.960027i	−0.498783	−	0.0471259i
$416$	4.78611	−	3.47731i	0.234658	−	0.170489i
$417$	3.98314	+	10.3274i	0.195055	+	0.505737i
$418$	25.3425	−	18.4124i	1.23954	−	0.900582i
$419$	4.96693	+	6.83640i	0.242651	+	0.333980i	0.912920	−	0.408138i	$-0.133822\pi$
$419$	4.96693	+	6.83640i	0.242651	+	0.333980i	−0.670270	+	0.742117i	$0.733822\pi$
$420$	8.66413	−	10.9681i	0.422766	−	0.535191i
$421$	−4.03613	+	2.93242i	−0.196709	+	0.142918i	−0.681780	−	0.731557i	$-0.738794\pi$
$421$	−4.03613	+	2.93242i	−0.196709	+	0.142918i	0.485071	+	0.874475i	$0.338794\pi$
$422$	−1.32894	−	0.965534i	−0.0646919	−	0.0470014i
$423$	5.94998	−	0.644463i	0.289298	−	0.0313349i
$424$	−2.84782	+	3.91969i	−0.138303	+	0.190357i
$425$	19.0159	−	17.8604i	0.922409	−	0.866358i
$426$	−0.507671	−	1.31628i	−0.0245967	−	0.0637741i
$427$	−13.4438	−	41.3757i	−0.650591	−	2.00231i
$428$	−2.92518			−0.141394
$429$	32.0859	+	39.4945i	1.54912	+	1.90681i
$430$	−5.31204	+	6.02588i	−0.256169	+	0.290594i
$431$	3.85046	+	5.29970i	0.185470	+	0.255277i	0.891620	−	0.452785i	$-0.149570\pi$
$431$	3.85046	+	5.29970i	0.185470	+	0.255277i	−0.706150	+	0.708062i	$0.749570\pi$
$432$	5.13599	+	0.788420i	0.247105	+	0.0379329i
$433$	−0.766502			−0.0368357			−0.0184179	−	0.999830i	$-0.505863\pi$
$433$	−0.766502			−0.0368357			−0.0184179	+	0.999830i	$0.505863\pi$
$434$	−19.8372	+	3.20055i	−0.952218	+	0.153631i
$435$	−8.66958	+	23.4288i	−0.415674	+	1.12332i
$436$	−12.2772	−	8.91994i	−0.587973	−	0.427188i
$437$	0.348427	+	0.479569i	0.0166675	+	0.0229409i
$438$	−2.25207	+	3.47996i	−0.107608	+	0.166279i
$439$	29.7316			1.41901			0.709506	−	0.704700i	$-0.248918\pi$
$439$	29.7316			1.41901			0.709506	+	0.704700i	$0.248918\pi$
$440$	5.65300	+	9.55771i	0.269496	+	0.455646i
$441$	17.9684	−	1.94622i	0.855638	−	0.0926771i
$442$	29.3567	+	9.53858i	1.39636	+	0.453704i
$443$	−7.94982	+	24.4670i	−0.377707	+	1.16246i	0.563926	+	0.825825i	$0.309290\pi$
$443$	−7.94982	+	24.4670i	−0.377707	+	1.16246i	−0.941634	+	0.336639i	$0.890710\pi$
$444$	−0.516662	−	9.56802i	−0.0245197	−	0.454078i
$445$	−4.65822	+	5.28420i	−0.220821	+	0.250495i
$446$	0.741930	+	0.539044i	0.0351314	+	0.0255245i
$447$	−7.67859	+	28.8398i	−0.363185	+	1.36408i
$448$	3.43231	+	1.11523i	0.162162	+	0.0526895i
$449$	−11.8837	+	8.63400i	−0.560825	+	0.407463i	−0.831761	−	0.555134i	$-0.812667\pi$
$449$	−11.8837	+	8.63400i	−0.560825	+	0.407463i	0.270936	+	0.962597i	$0.412667\pi$
$450$	14.9514	+	1.20637i	0.704816	+	0.0568686i
$451$	22.8399	+	7.42114i	1.07549	+	0.349448i
$452$	−8.83436	+	6.41854i	−0.415533	+	0.301903i
$453$	−20.5459	+	1.10946i	−0.965332	+	0.0521268i
$454$	0.0662395	+	0.203864i	0.00310877	+	0.00956782i
$455$	47.5292	+	4.49065i	2.22820	+	0.210525i
$456$	10.1937	−	3.93157i	0.477364	−	0.184113i
$457$	3.76897	−	11.5997i	0.176305	−	0.542611i	−0.823386	−	0.567482i	$-0.807918\pi$
$457$	3.76897	−	11.5997i	0.176305	−	0.542611i	0.999691	+	0.0248714i	$0.00791763\pi$
$458$	0.739978	−	0.240433i	0.0345769	−	0.0112347i
$459$	12.4233	+	24.0979i	0.579871	+	1.12479i
$460$	−0.180865	+	0.106974i	−0.00843288	+	0.00498771i
$461$	2.75089	+	8.46638i	0.128122	+	0.394319i	0.994457	−	0.105145i	$-0.0335306\pi$
$461$	2.75089	+	8.46638i	0.128122	+	0.394319i	−0.866335	+	0.499463i	$0.833531\pi$
$462$	−7.98666	+	29.9969i	−0.371573	+	1.39558i
$463$	−13.1538	−	9.55683i	−0.611311	−	0.444144i	0.238565	−	0.971127i	$-0.423323\pi$
$463$	−13.1538	−	9.55683i	−0.611311	−	0.444144i	−0.849876	+	0.526983i	$0.823323\pi$
$464$	−6.45016			−0.299441
$465$	−14.6676	−	15.8070i	−0.680192	−	0.733034i
$466$	−2.61671			−0.121217
$467$	−17.7952	−	12.9290i	−0.823463	−	0.598281i	0.0942390	−	0.995550i	$-0.469958\pi$
$467$	−17.7952	−	12.9290i	−0.823463	−	0.598281i	−0.917702	+	0.397268i	$0.869958\pi$
$468$	7.27012	+	16.1905i	0.336062	+	0.748406i
$469$	9.70496	+	29.8688i	0.448133	+	1.37921i
$470$	2.27090	+	3.83949i	0.104749	+	0.177102i
$471$	5.18534	−	4.21265i	0.238928	−	0.194108i
$472$	2.43009	−	0.789584i	0.111854	−	0.0363435i
$473$	5.51293	−	16.9671i	0.253485	−	0.780146i
$474$	10.7281	+	27.8158i	0.492760	+	1.27762i
$475$	28.5366	−	13.4315i	1.30935	−	0.616279i
$476$	5.81887	+	17.9087i	0.266708	+	0.820842i
$477$	−9.76005	−	10.7707i	−0.446882	−	0.493157i
$478$	−9.80298	+	7.12228i	−0.448378	+	0.325766i
$479$	16.1831	+	5.25822i	0.739427	+	0.240254i	0.654426	−	0.756126i	$-0.272911\pi$
$479$	16.1831	+	5.25822i	0.739427	+	0.240254i	0.0850014	+	0.996381i	$0.472911\pi$
$480$	1.04761	+	3.72861i	0.0478166	+	0.170187i
$481$	26.4775	−	19.2370i	1.20727	−	0.877132i
$482$	−2.57354	−	0.836195i	−0.117222	−	0.0380876i
$483$	−0.567646	−	0.151135i	−0.0258288	−	0.00687690i
$484$	−11.0522	−	8.02988i	−0.502372	−	0.364994i
$485$	−2.15912	−	1.90335i	−0.0980407	−	0.0864265i
$486$	−5.47078	+	14.5969i	−0.248160	+	0.662130i
$487$	−10.6303	+	32.7166i	−0.481703	+	1.48253i	0.354996	+	0.934868i	$0.384482\pi$
$487$	−10.6303	+	32.7166i	−0.481703	+	1.48253i	−0.836699	+	0.547662i	$0.815518\pi$
$488$	11.4648	+	3.72513i	0.518986	+	0.168629i
$489$	−21.5508	−	13.9467i	−0.974562	−	0.630692i
$490$	6.85792	+	11.5949i	0.309809	+	0.523804i
$491$	−5.24795			−0.236837			−0.118418	−	0.992964i	$-0.537782\pi$
$491$	−5.24795			−0.236837			−0.118418	+	0.992964i	$0.537782\pi$
$492$	7.03201	+	4.55079i	0.317027	+	0.205166i
$493$	−19.7818	−	27.2273i	−0.890927	−	1.22626i
$494$	30.1903	+	21.9346i	1.35833	+	0.986883i
$495$	−31.5386	+	10.7271i	−1.41756	+	0.482146i
$496$	2.51340	−	4.96818i	0.112855	−	0.223078i
$497$	2.93956			0.131857
$498$	7.89421	−	0.426278i	0.353748	−	0.0191020i
$499$	−15.7335	−	21.6554i	−0.704330	−	0.969427i	−0.999901	−	0.0141060i	$-0.995510\pi$
$499$	−15.7335	−	21.6554i	−0.704330	−	0.969427i	0.295571	−	0.955321i	$-0.404490\pi$
$500$	3.78865	+	10.5188i	0.169433	+	0.470417i
$501$	28.1704	−	22.8861i	1.25856	−	1.02247i
$502$	6.17452			0.275582
$503$	−8.09139	−	24.9027i	−0.360777	−	1.11036i	−0.952583	−	0.304278i	$-0.901585\pi$
$503$	−8.09139	−	24.9027i	−0.360777	−	1.11036i	0.591806	−	0.806080i	$-0.298415\pi$
$504$	−5.38364	+	9.39345i	−0.239806	+	0.418417i
$505$	2.76683	+	12.3754i	0.123122	+	0.550700i
$506$	0.274306	−	0.377549i	0.0121944	−	0.0167841i
$507$	−20.7015	+	31.9885i	−0.919385	+	1.42066i
$508$	1.53607	+	1.11602i	0.0681522	+	0.0495155i
$509$	−27.6898	+	20.1178i	−1.22733	+	0.891705i	−0.996687	−	0.0813340i	$-0.974082\pi$
$509$	−27.6898	+	20.1178i	−1.22733	+	0.891705i	−0.230640	+	0.973039i	$0.574082\pi$
$510$	−12.5262	+	15.8573i	−0.554671	+	0.702173i
$511$	−5.07662	−	6.98737i	−0.224577	−	0.309103i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	5.28146	+	32.3485i	0.233182	+	1.42822i
$514$	8.56720	−	6.22444i	0.377883	−	0.274548i
$515$	41.9456	+	3.96309i	1.84834	+	0.174635i
$516$	3.38064	−	5.22386i	0.148824	−	0.229968i
$517$	−8.01479	−	5.82309i	−0.352490	−	0.256099i
$518$	18.9880	+	6.16959i	0.834287	+	0.271076i
$519$	1.80354	−	0.695601i	0.0791668	−	0.0305335i
$520$	−8.74770	+	9.92324i	−0.383612	+	0.435163i
$521$			25.3801i			1.11192i	0.831208	+	0.555962i	$0.187650\pi$
$521$			25.3801i			1.11192i	−0.831208	+	0.555962i	$0.812350\pi$
$522$	3.96311	−	18.9403i	0.173461	−	0.828994i
$523$	−7.07757	−	21.7825i	−0.309480	−	0.952483i	−0.977967	−	0.208759i	$-0.933058\pi$
$523$	−7.07757	−	21.7825i	−0.309480	−	0.952483i	0.668487	−	0.743724i	$-0.266942\pi$
$524$	−8.96830	−	12.3438i	−0.391782	−	0.539242i
$525$	−13.5556	+	28.1617i	−0.591617	+	1.22908i
$526$		−	20.2849i		−	0.884463i
$527$	28.6798	−	4.62722i	1.24931	−	0.201565i
$528$	−5.42362	−	6.67593i	−0.236033	−	0.290533i
$529$	−18.6002	−	13.5139i	−0.808706	−	0.587560i
$530$	4.30215	−	9.94293i	0.186874	−	0.431893i
$531$	0.825443	+	7.62087i	0.0358212	+	0.330717i
$532$			22.7649i			0.986983i
$533$			28.6092i			1.23920i
$534$	2.96454	−	4.58089i	0.128288	−	0.198235i
$535$	6.38330	−	1.42714i	0.275974	−	0.0617008i
$536$	−8.27632	−	2.68914i	−0.357483	−	0.116153i
$537$	−0.783171	−	14.5035i	−0.0337963	−	0.625871i
$538$	−0.832617	−	2.56253i	−0.0358967	−	0.110479i
$539$	−24.2039	−	17.5852i	−1.04254	−	0.757447i
$540$	−11.5924	+	0.785275i	−0.498857	+	0.0337928i
$541$	−1.53748	+	4.73187i	−0.0661014	+	0.203439i	−0.978652	−	0.205525i	$-0.934110\pi$
$541$	−1.53748	+	4.73187i	−0.0661014	+	0.203439i	0.912551	+	0.408964i	$0.134110\pi$
$542$	3.18049	+	4.37757i	0.136614	+	0.188033i
$543$	−6.58511	+	24.7329i	−0.282594	+	1.06139i
$544$	−4.96229	−	1.61235i	−0.212757	−	0.0691288i
$545$	31.1432	+	13.4752i	1.33403	+	0.577214i
$546$	−36.9261	+	1.99397i	−1.58029	+	0.0853340i
$547$	−26.9462	+	8.75534i	−1.15214	+	0.374351i	−0.821947	−	0.569564i	$-0.807112\pi$
$547$	−26.9462	+	8.75534i	−1.15214	+	0.374351i	−0.330188	+	0.943915i	$0.607112\pi$
$548$	7.33902	−	10.1013i	0.313507	−	0.431506i
$549$	−17.9827	+	31.3764i	−0.767482	+	1.33911i
$550$	−16.9990	−	18.0988i	−0.724839	−	0.771734i
$551$	−12.5730	−	38.6956i	−0.535627	−	1.64849i
$552$	0.126332	−	0.102634i	0.00537704	−	0.00436838i
$553$	−62.1190			−2.64157
$554$	7.69469	+	23.6818i	0.326916	+	1.00614i
$555$	5.79553	+	20.6272i	0.246006	+	0.875576i
$556$	3.75633	−	5.17015i	0.159304	−	0.219263i
$557$		−	22.8740i		−	0.969201i	−0.874736	−	0.484601i	$-0.838965\pi$
$557$		−	22.8740i		−	0.969201i	0.874736	−	0.484601i	$-0.161035\pi$
$558$	13.0443	+	10.4329i	0.552210	+	0.441661i
$559$	21.2529			0.898901
$560$	−8.03407	−	0.759073i	−0.339501	−	0.0320767i
$561$	11.5468	−	43.3683i	0.487505	−	1.83101i
$562$	−6.61760	+	2.15019i	−0.279147	+	0.0907003i
$563$	−30.8623			−1.30069			−0.650346	−	0.759638i	$-0.725376\pi$
$563$	−30.8623			−1.30069			−0.650346	+	0.759638i	$0.725376\pi$
$564$	−2.17876	−	2.68183i	−0.0917422	−	0.112925i
$565$	16.1468	−	18.3166i	0.679300	−	0.770586i
$566$	−0.282524	−	0.0917976i	−0.0118754	−	0.00385854i
$567$	−24.2752	−	21.5801i	−1.01946	−	0.906278i
$568$	−0.478763	+	0.658961i	−0.0200884	+	0.0276494i
$569$	9.10885	+	28.0342i	0.381863	+	1.17525i	0.938731	+	0.344652i	$0.112003\pi$
$569$	9.10885	+	28.0342i	0.381863	+	1.17525i	−0.556868	+	0.830601i	$0.687997\pi$
$570$	−20.3265	+	13.5528i	−0.851384	+	0.567663i
$571$	3.92386	+	5.40074i	0.164209	+	0.226014i	0.883190	−	0.469016i	$-0.155391\pi$
$571$	3.92386	+	5.40074i	0.164209	+	0.226014i	−0.718981	+	0.695030i	$0.755391\pi$
$572$	9.07852	−	27.9408i	0.379592	−	1.16826i
$573$	−11.8155	+	44.3776i	−0.493600	+	1.85390i
$574$	−14.1195	+	10.2584i	−0.589336	+	0.428177i
$575$	0.342492	−	0.321680i	0.0142829	−	0.0134150i
$576$	−1.22890	−	2.73675i	−0.0512042	−	0.114031i
$577$	2.03580	−	2.80204i	0.0847516	−	0.116651i	−0.764536	−	0.644581i	$-0.777032\pi$
$577$	2.03580	−	2.80204i	0.0847516	−	0.116651i	0.849288	+	0.527930i	$0.177032\pi$
$578$	−3.15940	−	9.72363i	−0.131414	−	0.404450i
$579$	−0.784441	+	0.0423589i	−0.0326003	+	0.00176038i
$580$	14.0755	−	3.14692i	0.584453	−	0.130669i
$581$	−5.09030	+	15.6663i	−0.211181	+	0.649949i
$582$	1.87175	+	1.21131i	0.0775865	+	0.0502105i
$583$			24.0603i			0.996478i
$584$	2.39318			0.0990306
$585$	−23.7639	−	31.7839i	−0.982516	−	1.31410i
$586$	−18.3956	+	13.3652i	−0.759916	+	0.552111i
$587$	−22.3605	+	30.7765i	−0.922915	+	1.27028i	0.0396449	+	0.999214i	$0.487377\pi$
$587$	−22.3605	+	30.7765i	−0.922915	+	1.27028i	−0.962560	+	0.271070i	$0.912623\pi$
$588$	−6.57965	−	8.09888i	−0.271340	−	0.333992i
$589$	34.7042	+	5.39412i	1.42996	+	0.222261i
$590$	−4.91770	+	2.90862i	−0.202459	+	0.119746i
$591$	24.2656	−	1.31032i	0.998155	−	0.0538992i
$592$	−4.47560	+	3.25171i	−0.183946	+	0.133645i
$593$	8.07128	+	24.8409i	0.331448	+	1.02009i	0.968445	+	0.249226i	$0.0801761\pi$
$593$	8.07128	+	24.8409i	0.331448	+	1.02009i	−0.636998	+	0.770866i	$0.719824\pi$
$594$	22.9356	−	11.8241i	0.941061	−	0.485150i
$595$	−21.4352	−	36.2412i	−0.878759	−	1.48575i
$596$	16.3874	−	5.32460i	0.671255	−	0.218104i
$597$	8.11406	+	21.0380i	0.332087	+	0.861029i
$598$	0.528737	+	0.171797i	0.0216217	+	0.00702531i
$599$	11.1209	−	15.3066i	0.454388	−	0.625412i	−0.518945	−	0.854808i	$-0.673675\pi$
$599$	11.1209	−	15.3066i	0.454388	−	0.625412i	0.973333	+	0.229396i	$0.0736751\pi$
$600$	−4.10521	−	7.62543i	−0.167595	−	0.311307i
$601$	−23.4018	+	32.2098i	−0.954579	+	1.31387i	−0.00511594	+	0.999987i	$0.501628\pi$
$601$	−23.4018	+	32.2098i	−0.954579	+	1.31387i	−0.949463	+	0.313879i	$0.898372\pi$
$602$	7.62065	+	10.4889i	0.310594	+	0.427496i
$603$	12.9815	−	22.6504i	0.528650	−	0.922395i
$604$	6.98258	+	9.61070i	0.284117	+	0.391054i
$605$	28.0356	+	12.1306i	1.13981	+	0.493178i
$606$	−3.53466	−	9.16462i	−0.143586	−	0.372287i
$607$	−1.59987	−	2.20203i	−0.0649366	−	0.0893775i	0.775314	−	0.631577i	$-0.217592\pi$
$607$	−1.59987	−	2.20203i	−0.0649366	−	0.0893775i	−0.840250	+	0.542199i	$0.817592\pi$
$608$	−5.10320	−	3.70769i	−0.206962	−	0.150367i
$609$	33.8493	+	21.9057i	1.37164	+	0.887665i
$610$	−26.8358	−	2.53549i	−1.08655	−	0.102659i
$611$	3.64699	−	11.2243i	0.147541	−	0.454086i
$612$	7.78344	−	13.5807i	0.314627	−	0.548966i
$613$	0.748541	+	2.30377i	0.0302333	+	0.0930485i	0.965035	−	0.262123i	$-0.0844225\pi$
$613$	0.748541	+	2.30377i	0.0302333	+	0.0930485i	−0.934801	+	0.355171i	$0.884423\pi$
$614$		−	26.3480i		−	1.06332i
$615$	−17.5655	−	6.49992i	−0.708308	−	0.262102i
$616$	17.0449	−	5.53822i	0.686758	−	0.223141i
$617$	−14.1457	+	10.2775i	−0.569485	+	0.413755i	−0.834918	−	0.550374i	$-0.814485\pi$
$617$	−14.1457	+	10.2775i	−0.569485	+	0.413755i	0.265433	+	0.964129i	$0.414485\pi$
$618$	−32.5882	+	1.75972i	−1.31089	+	0.0707864i
$619$			42.8496i			1.72227i	0.508376	+	0.861135i	$0.330246\pi$
$619$			42.8496i			1.72227i	−0.508376	+	0.861135i	$0.669754\pi$
$620$	−3.06084	+	12.0678i	−0.122926	+	0.484654i
$621$	0.223754	+	0.434022i	0.00897893	+	0.0174167i
$622$	17.2840	−	23.7894i	0.693024	−	0.953866i
$623$	6.68268	+	9.19792i	0.267736	+	0.368507i
$624$	5.56713	−	8.60249i	0.222864	−	0.344375i
$625$	−13.3995	−	21.1058i	−0.535981	−	0.844230i
$626$	−24.2525			−0.969324
$627$	29.4781	−	45.5503i	1.17724	−	1.81910i
$628$	−3.66842	−	1.19194i	−0.146386	−	0.0475637i
$629$	−27.4521	−	8.91974i	−1.09459	−	0.355653i
$630$	7.16524	−	23.1249i	0.285470	−	0.921319i
$631$	−37.5125	+	12.1885i	−1.49335	+	0.485218i	−0.938070	−	0.346446i	$-0.887388\pi$
$631$	−37.5125	+	12.1885i	−1.49335	+	0.485218i	−0.555278	+	0.831665i	$0.687388\pi$
$632$	10.1173	−	13.9252i	0.402443	−	0.553915i
$633$	−2.74939	−	0.732025i	−0.109279	−	0.0290954i
$634$	3.38445	−	10.4163i	0.134414	−	0.413682i
$635$	−3.89650	−	1.68595i	−0.154628	−	0.0669050i
$636$	−2.15909	+	8.10929i	−0.0856136	+	0.321554i
$637$	11.0136	−	33.8963i	0.436374	−	1.34302i
$638$	−25.9141	+	18.8277i	−1.02595	+	0.745395i
$639$	−1.64082	−	1.81072i	−0.0649096	−	0.0716311i
$640$	1.47866	−	1.67737i	0.0584492	−	0.0663037i
$641$	−17.6620	−	12.8322i	−0.697606	−	0.506841i	0.181545	−	0.983383i	$-0.441890\pi$
$641$	−17.6620	−	12.8322i	−0.697606	−	0.506841i	−0.879152	+	0.476542i	$0.841890\pi$
$642$	−4.72715	+	1.82319i	−0.186566	+	0.0719557i
$643$	8.37657	−	25.7804i	0.330340	−	1.01668i	−0.638633	−	0.769512i	$-0.720500\pi$
$643$	8.37657	−	25.7804i	0.330340	−	1.01668i	0.968972	−	0.247169i	$-0.0795004\pi$
$644$	0.104802	+	0.322549i	0.00412979	+	0.0127102i
$645$	−4.82859	+	13.0488i	−0.190125	+	0.513797i
$646$		−	32.9125i		−	1.29493i
$647$	3.15820	−	1.02616i	0.124162	−	0.0403426i	−0.246277	−	0.969199i	$-0.579207\pi$
$647$	3.15820	−	1.02616i	0.124162	−	0.0403426i	0.370439	+	0.928857i	$0.379207\pi$
$648$	8.79128	−	1.92704i	0.345354	−	0.0757011i
$649$	7.45834	−	10.2655i	0.292765	−	0.402957i
$650$	14.2478	−	25.9223i	0.558845	−	1.01676i
$651$	−30.0626	+	17.5362i	−1.17825	+	0.687299i
$652$			14.8206i			0.580419i
$653$	26.7343	+	19.4236i	1.04619	+	0.760104i	0.971485	−	0.237102i	$-0.0761975\pi$
$653$	26.7343	+	19.4236i	1.04619	+	0.760104i	0.0747082	+	0.997205i	$0.476197\pi$
$654$	−25.3999	−	6.76271i	−0.993214	−	0.264443i
$655$	25.5929	+	22.5611i	0.999997	+	0.881535i
$656$		−	4.83594i		−	0.188812i
$657$	−1.47042	+	7.02736i	−0.0573666	+	0.274163i
$658$	6.84721	−	2.22479i	0.266932	−	0.0867315i
$659$	−6.32434	−	2.05490i	−0.246361	−	0.0800477i	0.183233	−	0.983069i	$-0.441344\pi$
$659$	−6.32434	−	2.05490i	−0.246361	−	0.0800477i	−0.429595	+	0.903022i	$0.641344\pi$
$660$	15.0925	+	11.9221i	0.587473	+	0.464066i
$661$	−18.7970	−	13.6568i	−0.731120	−	0.531190i	0.158798	−	0.987311i	$-0.449238\pi$
$661$	−18.7970	−	13.6568i	−0.731120	−	0.531190i	−0.889918	+	0.456121i	$0.849238\pi$
$662$	31.6703	−	10.2903i	1.23090	−	0.399944i
$663$	53.3863	−	2.88280i	2.07335	−	0.111959i
$664$	−2.68287	−	3.69265i	−0.104115	−	0.143303i
$665$	−11.1066	−	49.6774i	−0.430695	−	1.92641i
$666$	−6.79845	−	15.1401i	−0.263435	−	0.586667i
$667$	−0.356285	−	0.490384i	−0.0137954	−	0.0189878i
$668$	−19.9295	−	6.47548i	−0.771094	−	0.250544i
$669$	1.53495	+	0.408679i	0.0593445	+	0.0158004i
$670$	19.3725	+	1.83035i	0.748426	+	0.0707126i
$671$	56.9341	−	18.4990i	2.19792	−	0.714147i
$672$	6.24179	−	0.337049i	0.240782	−	0.0130020i
$673$	−2.47106	+	7.60515i	−0.0952525	+	0.293157i	−0.987319	−	0.158746i	$-0.949255\pi$
$673$	−2.47106	+	7.60515i	−0.0952525	+	0.293157i	0.892067	+	0.451903i	$0.149255\pi$
$674$	2.49129	−	7.66740i	0.0959609	−	0.295337i
$675$	24.9137	−	7.36935i	0.958929	−	0.283646i
$676$	21.9986			0.846099
$677$			12.4014i			0.476623i	0.971189	+	0.238312i	$0.0765940\pi$
$677$			12.4014i			0.476623i	−0.971189	+	0.238312i	$0.923406\pi$
$678$	−10.2760	+	15.8787i	−0.394647	+	0.609819i
$679$	−3.75826	+	2.73054i	−0.144229	+	0.104788i
$680$	11.6153	+	1.09744i	0.445427	+	0.0420848i
$681$	0.234108	+	0.288163i	0.00897104	+	0.0110424i
$682$	−4.40404	−	27.2966i	−0.168639	−	1.04524i
$683$	−25.8050			−0.987402			−0.493701	−	0.869632i	$-0.664356\pi$
$683$	−25.8050			−0.987402			−0.493701	+	0.869632i	$0.664356\pi$
$684$	14.0228	−	12.7070i	0.536176	−	0.485864i
$685$	−11.0869	+	25.6236i	−0.423609	+	0.979026i
$686$	−3.34824	+	1.08791i	−0.127836	+	0.0415366i
$687$	1.04596	−	0.849757i	0.0399060	−	0.0324202i
$688$	−3.59247			−0.136961
$689$	−27.2600	+	8.85731i	−1.03852	+	0.337437i
$690$	−0.225607	+	0.285602i	−0.00858872	+	0.0108727i
$691$	12.4565	−	38.3373i	0.473869	−	1.45842i	−0.373607	−	0.927587i	$-0.621879\pi$
$691$	12.4565	−	38.3373i	0.473869	−	1.45842i	0.847476	−	0.530833i	$-0.178121\pi$
$692$	−0.902895	−	0.655992i	−0.0343229	−	0.0249371i
$693$	5.78974	+	53.4535i	0.219934	+	2.03053i
$694$	3.16862	−	4.36123i	0.120279	−	0.165550i
$695$	−5.67462	+	13.1149i	−0.215251	+	0.497477i
$696$	−10.4236	+	4.02023i	−0.395106	+	0.152386i
$697$	20.4134	−	14.8312i	0.773211	−	0.561771i
$698$	−24.5851	+	17.8621i	−0.930561	+	0.676092i
$699$	−4.22866	+	1.63093i	−0.159943	+	0.0616875i
$700$	17.9022	−	2.26324i	0.676641	−	0.0855424i
$701$	−24.1216	+	33.2005i	−0.911059	+	1.25397i	0.0557446	+	0.998445i	$0.482247\pi$
$701$	−24.1216	+	33.2005i	−0.911059	+	1.25397i	−0.966804	+	0.255520i	$0.917753\pi$
$702$	21.8398	+	21.6329i	0.824292	+	0.816482i
$703$	−28.2317	−	20.5115i	−1.06478	−	0.773606i
$704$	−1.53458	+	4.72295i	−0.0578367	+	0.178003i
$705$	6.06289	+	4.78930i	0.228342	+	0.180375i
$706$	16.3491	−	5.31213i	0.615305	−	0.199925i
$707$	20.4667			0.769729
$708$	3.43495	−	2.79060i	0.129093	−	0.104877i
$709$	7.61150	−	2.47313i	0.285856	−	0.0928803i	−0.162579	−	0.986695i	$-0.551981\pi$
$709$	7.61150	−	2.47313i	0.285856	−	0.0928803i	0.448435	+	0.893815i	$0.351981\pi$
$710$	0.723258	−	1.67156i	0.0271434	−	0.0627325i
$711$	34.6738	+	38.2643i	1.30037	+	1.43502i
$712$	−3.15030			−0.118062
$713$	0.516546	−	0.0833398i	0.0193448	−	0.00312110i
$714$	20.5655	+	25.3140i	0.769643	+	0.947353i
$715$	−6.17925	+	65.4015i	−0.231091	+	2.44588i
$716$	−6.78424	+	4.92904i	−0.253539	+	0.184207i
$717$	−11.4027	+	17.6197i	−0.425841	+	0.658021i
$718$		−	3.96845i		−	0.148101i
$719$	9.57189			0.356971			0.178486	−	0.983943i	$-0.442880\pi$
$719$	9.57189			0.356971			0.178486	+	0.983943i	$0.442880\pi$
$720$	4.01691	+	5.37256i	0.149701	+	0.200224i
$721$	21.0133	−	64.6723i	0.782576	−	2.40852i
$722$	6.42436	−	19.7722i	0.239090	−	0.735843i
$723$	−4.68008	+	0.252719i	−0.174054	+	0.00939872i
$724$	14.0538	−	4.56634i	0.522304	−	0.169707i
$725$	−29.1801	+	13.7344i	−1.08372	+	0.510082i
$726$	−22.8654	−	6.08790i	−0.848614	−	0.225943i
$727$	28.2446	+	9.17723i	1.04753	+	0.340365i	0.781700	−	0.623654i	$-0.214353\pi$
$727$	28.2446	+	9.17723i	1.04753	+	0.340365i	0.265834	+	0.964019i	$0.414353\pi$
$728$	12.5494	+	17.2728i	0.465113	+	0.640173i
$729$	0.257021	+	26.9988i	0.00951929	+	0.999955i
$730$	−5.22239	+	1.16759i	−0.193289	+	0.0432145i
$731$	−11.0176	−	15.1644i	−0.407501	−	0.560877i
$732$	20.8491	−	1.12583i	0.770605	−	0.0416118i
$733$	−27.6025	+	8.96861i	−1.01952	+	0.331263i	−0.770640	−	0.637271i	$-0.780063\pi$
$733$	−27.6025	+	8.96861i	−1.01952	+	0.331263i	−0.248883	+	0.968534i	$0.580063\pi$
$734$	2.89749	+	2.10515i	0.106948	+	0.0777024i
$735$	18.3094	+	14.4632i	0.675351	+	0.533484i
$736$	−0.0893747	−	0.0290396i	−0.00329440	−	0.00107041i
$737$	−41.1003	+	13.3543i	−1.51395	+	0.491912i
$738$	14.2003	+	2.97130i	0.522720	+	0.109375i
$739$		−	12.3700i		−	0.455037i	−0.973774	−	0.227519i	$-0.926939\pi$
$739$		−	12.3700i		−	0.455037i	0.973774	−	0.227519i	$-0.0730613\pi$
$740$	8.18017	−	9.27944i	0.300709	−	0.341119i
$741$	62.4595	+	16.6298i	2.29451	+	0.610912i
$742$	−14.1460	−	10.2776i	−0.519315	−	0.377304i
$743$		−	7.78833i		−	0.285726i	−0.989742	−	0.142863i	$-0.954369\pi$
$743$		−	7.78833i		−	0.285726i	0.989742	−	0.142863i	$-0.0456308\pi$
$744$	0.965166	−	9.59523i	0.0353847	−	0.351778i
$745$	−33.1628	+	19.6145i	−1.21499	+	0.718618i
$746$	−3.55646	+	4.89504i	−0.130211	+	0.179220i
$747$	12.4915	−	5.60915i	0.457041	−	0.205228i
$748$	−24.6428	+	8.00693i	−0.901030	+	0.292762i
$749$		−	10.5568i		−	0.385737i
$750$	12.6787	+	14.6373i	0.462960	+	0.534479i
$751$	−13.5726	−	41.7721i	−0.495271	−	1.52429i	−0.816535	−	0.577297i	$-0.804108\pi$
$751$	−13.5726	−	41.7721i	−0.495271	−	1.52429i	0.321264	−	0.946990i	$-0.395892\pi$
$752$	−0.616466	+	1.89729i	−0.0224802	+	0.0691870i
$753$	9.97816	−	3.84843i	0.363625	−	0.140245i
$754$	−30.8712	−	22.4292i	−1.12426	−	0.816825i
$755$	−19.9262	−	17.5657i	−0.725190	−	0.639282i
$756$	−2.84537	+	18.5355i	−0.103485	+	0.674130i
$757$	−18.4659	+	13.4162i	−0.671154	+	0.487622i	−0.870411	−	0.492325i	$-0.836147\pi$
$757$	−18.4659	+	13.4162i	−0.671154	+	0.487622i	0.199258	+	0.979947i	$0.436147\pi$
$758$	3.47466	−	10.6939i	0.126205	−	0.388420i
$759$	0.207966	−	0.781096i	0.00754870	−	0.0283520i
$760$	12.9451	+	5.60114i	0.469568	+	0.203175i
$761$	14.5643	−	44.8243i	0.527955	−	1.62488i	−0.230442	−	0.973086i	$-0.574017\pi$
$761$	14.5643	−	44.8243i	0.527955	−	1.62488i	0.758397	−	0.651793i	$-0.225983\pi$
$762$	3.17792	+	0.846119i	0.115124	+	0.0306516i
$763$	32.1916	−	44.3079i	1.16541	−	1.60405i
$764$	25.2163	−	8.19329i	0.912295	−	0.296423i
$765$	−10.3592	+	33.4330i	−0.374538	+	1.20877i
$766$	30.6454	+	9.95728i	1.10726	+	0.359771i
$767$	14.3763	+	4.67115i	0.519098	+	0.168665i
$768$	−0.941037	+	1.45411i	−0.0339567	+	0.0524709i
$769$	−21.3432			−0.769654			−0.384827	−	0.922989i	$-0.625739\pi$
$769$	−21.3432			−0.769654			−0.384827	+	0.922989i	$0.625739\pi$
$770$	−34.4933	+	20.4014i	−1.24305	+	0.735215i
$771$	9.96524	−	15.3986i	0.358889	−	0.554566i
$772$	0.266594	+	0.366936i	0.00959494	+	0.0132063i
$773$	25.6432	−	35.2948i	0.922320	−	1.26947i	−0.0404602	−	0.999181i	$-0.512882\pi$
$773$	25.6432	−	35.2948i	0.922320	−	1.26947i	0.962781	−	0.270284i	$-0.0871176\pi$
$774$	2.20728	−	10.5489i	0.0793392	−	0.379174i
$775$	0.791693	−	27.8276i	0.0284385	−	0.999596i
$776$		−	1.28721i		−	0.0462081i
$777$	34.5305	−	1.86461i	1.23877	−	0.0668923i
$778$	−15.9809	+	11.6108i	−0.572942	+	0.416267i
$779$	29.0116	−	9.42645i	1.03945	−	0.337738i
$780$	−7.95156	+	21.4884i	−0.284712	+	0.769408i
$781$			4.04491i			0.144738i
$782$	−0.151519	−	0.466327i	−0.00541831	−	0.0166758i
$783$	−5.40056	−	33.0781i	−0.193000	−	1.18211i
$784$	−1.86167	+	5.72963i	−0.0664883	+	0.204630i
$785$	8.58674	+	0.811290i	0.306474	+	0.0289562i
$786$	−22.1866	−	14.3581i	−0.791369	−	0.512138i
$787$	35.8934	+	26.0781i	1.27946	+	0.929584i	0.999537	−	0.0304371i	$-0.00968993\pi$
$787$	35.8934	+	26.0781i	1.27946	+	0.929584i	0.279926	+	0.960021i	$0.409690\pi$
$788$	−8.24674	−	11.3507i	−0.293778	−	0.404351i
$789$	−12.6431	−	32.7808i	−0.450106	−	1.16703i
$790$	−15.2839	+	35.3235i	−0.543778	+	1.25675i
$791$	−23.1642	−	31.8827i	−0.823622	−	1.13362i
$792$	−12.9256	−	7.40804i	−0.459293	−	0.263233i
$793$	41.9182	+	57.6955i	1.48856	+	2.04883i
$794$	−14.9067	+	20.5173i	−0.529019	+	0.728132i
$795$	0.755178	−	18.7494i	0.0267834	−	0.664974i
$796$	7.65203	−	10.5321i	0.271219	−	0.373301i
$797$	−16.8703	−	5.48148i	−0.597575	−	0.194164i	−0.00541659	−	0.999985i	$-0.501724\pi$
$797$	−16.8703	−	5.48148i	−0.597575	−	0.194164i	−0.592159	+	0.805821i	$0.701724\pi$
$798$	14.1888	+	36.7886i	0.502279	+	1.30230i
$799$	−9.89941	+	3.21651i	−0.350216	+	0.113792i
$800$	−2.40837	+	4.38175i	−0.0851487	+	0.154918i
$801$	1.93561	−	9.25055i	0.0683913	−	0.326852i
$802$	−2.80920	−	8.64583i	−0.0991963	−	0.305295i
$803$	9.61482	−	6.98557i	0.339299	−	0.246515i
$804$	−15.0508	+	0.812725i	−0.530800	+	0.0286626i
$805$	−0.386065	−	0.652732i	−0.0136070	−	0.0230058i
$806$	29.3053	−	15.0384i	1.03224	−	0.529704i
$807$	−2.94269	−	3.62216i	−0.103588	−	0.127506i
$808$	−3.33339	+	4.58801i	−0.117268	+	0.161406i
$809$	−33.3862	+	24.2565i	−1.17380	+	0.852812i	−0.991458	−	0.130424i	$-0.958366\pi$
$809$	−33.3862	+	24.2565i	−1.17380	+	0.852812i	−0.182337	+	0.983236i	$0.558366\pi$
$810$	−18.2441	+	8.49428i	−0.641032	+	0.298458i
$811$	4.94631			0.173689			0.0868443	−	0.996222i	$-0.472322\pi$
$811$	4.94631			0.173689			0.0868443	+	0.996222i	$0.472322\pi$
$812$		−	23.2783i		−	0.816908i
$813$	7.86818	+	5.09192i	0.275949	+	0.178582i
$814$	−8.48953	+	26.1281i	−0.297558	+	0.915789i
$815$	−7.23071	−	32.3414i	−0.253281	−	1.13287i
$816$	−9.02411	+	0.487292i	−0.315907	+	0.0170586i
$817$	−7.00261	−	21.5518i	−0.244990	−	0.754003i
$818$	4.82020	−	6.63443i	0.168534	−	0.231967i
$819$	−58.4307	+	26.2375i	−2.04173	+	0.916812i
$820$	2.35937	+	10.5530i	0.0823928	+	0.368525i
$821$	30.6936	−	22.3002i	1.07121	−	0.778283i	0.0950845	−	0.995469i	$-0.469688\pi$
$821$	30.6936	−	22.3002i	1.07121	−	0.778283i	0.976130	+	0.217186i	$0.0696879\pi$
$822$	5.56412	−	20.8982i	0.194071	−	0.728907i
$823$	0.0296148	−	0.0911450i	0.00103231	−	0.00317711i	−0.950539	−	0.310605i	$-0.899468\pi$
$823$	0.0296148	−	0.0911450i	0.00103231	−	0.00317711i	0.951571	+	0.307428i	$0.0994683\pi$
$824$	11.0752	+	15.2437i	0.385822	+	0.531038i
$825$	−38.7513	−	18.6529i	−1.34915	−	0.649412i
$826$	2.84957	+	8.77006i	0.0991491	+	0.305149i
$827$	−28.8605	+	39.7231i	−1.00358	+	1.38131i	−0.0804734	+	0.996757i	$0.525643\pi$
$827$	−28.8605	+	39.7231i	−1.00358	+	1.38131i	−0.923104	+	0.384550i	$0.874357\pi$
$828$	0.140186	−	0.244598i	0.00487179	−	0.00850037i
$829$	−22.4757	−	7.30279i	−0.780612	−	0.253636i	−0.108511	−	0.994095i	$-0.534608\pi$
$829$	−22.4757	−	7.30279i	−0.780612	−	0.253636i	−0.672102	+	0.740459i	$0.734608\pi$
$830$	7.65612	+	6.74915i	0.265748	+	0.234267i
$831$	27.1951	+	33.4744i	0.943388	+	1.16122i
$832$	−5.91596			−0.205099
$833$	−29.8953	+	9.71358i	−1.03581	+	0.336555i
$834$	2.84789	−	10.6963i	0.0986142	−	0.370383i
$835$	46.6492	+	4.40750i	1.61436	+	0.152528i
$836$	−31.3251			−1.08340
$837$	27.5825	+	8.72963i	0.953390	+	0.301740i
$838$		−	8.45025i		−	0.291909i
$839$	−3.89156	+	5.35627i	−0.134351	+	0.184919i	−0.870892	−	0.491475i	$-0.836458\pi$
$839$	−3.89156	+	5.35627i	−0.134351	+	0.184919i	0.736541	+	0.676393i	$0.236458\pi$
$840$	−13.4563	+	3.78077i	−0.464288	+	0.130449i
$841$	3.89503	+	11.9877i	0.134311	+	0.413368i
$842$	4.98894			0.171930
$843$	−9.35403	+	7.59935i	−0.322170	+	0.261735i
$844$	0.507611	+	1.56227i	0.0174727	+	0.0537754i
$845$	−48.0052	+	10.7327i	−1.65143	+	0.369217i
$846$	−5.19244	−	2.97593i	−0.178520	−	0.102315i
$847$	28.9794	−	39.8867i	0.995744	−	1.37052i
$848$	4.60787	−	1.49719i	0.158235	−	0.0514137i
$849$	−0.513780	+	0.0277435i	−0.0176329	+	0.000952155i
$850$	−25.8823	+	3.27210i	−0.887756	+	0.112232i
$851$	−0.494434	−	0.160651i	−0.0169490	−	0.00550706i
$852$	−0.362977	+	1.36330i	−0.0124354	+	0.0467058i
$853$	8.20871	+	11.2983i	0.281061	+	0.386847i	0.926085	−	0.377315i	$-0.123153\pi$
$853$	8.20871	+	11.2983i	0.281061	+	0.386847i	−0.645024	+	0.764162i	$0.723153\pi$
$854$	−13.4438	+	41.3757i	−0.460037	+	1.41585i
$855$	−24.4010	+	34.5706i	−0.834496	+	1.18229i
$856$	2.36652	+	1.71938i	0.0808859	+	0.0587671i
$857$	−17.0215	−	52.3868i	−0.581444	−	1.78950i	−0.613105	−	0.790002i	$-0.710080\pi$
$857$	−17.0215	−	52.3868i	−0.581444	−	1.78950i	0.0316610	−	0.999499i	$-0.489920\pi$
$858$	−2.74376	−	50.8114i	−0.0936703	−	1.73467i
$859$	23.3734	+	7.59448i	0.797491	+	0.259120i	0.679291	−	0.733869i	$-0.262288\pi$
$859$	23.3734	+	7.59448i	0.797491	+	0.259120i	0.118200	+	0.992990i	$0.462288\pi$
$860$	7.83946	−	1.75270i	0.267323	−	0.0597666i
$861$	−16.4236	+	25.3781i	−0.559714	+	0.864885i
$862$		−	6.55079i		−	0.223121i
$863$		−	38.2177i		−	1.30095i	−0.759529	−	0.650473i	$-0.774571\pi$
$863$		−	38.2177i		−	1.30095i	0.759529	−	0.650473i	$-0.225429\pi$
$864$	−3.69168	−	3.65670i	−0.125594	−	0.124404i
$865$	2.29034	+	0.990994i	0.0778739	+	0.0336948i
$866$	0.620113	+	0.450539i	0.0210723	+	0.0153099i
$867$	−11.1662	−	13.7444i	−0.379223	−	0.466785i
$868$	17.9299	+	9.07074i	0.608580	+	0.307881i
$869$		−	85.4774i		−	2.89962i
$870$	20.7849	−	13.8584i	0.704675	−	0.469844i
$871$	−30.2604	−	41.6499i	−1.02533	−	1.41125i
$872$	4.68949	+	14.4328i	0.158806	+	0.488755i
$873$	3.77977	+	0.790888i	0.127926	+	0.0267675i
$874$		−	0.592780i		−	0.0200511i
$875$	−37.9620	+	13.6730i	−1.28335	+	0.462233i
$876$	3.86744	−	1.49161i	0.130669	−	0.0503970i
$877$	1.40554	+	0.456688i	0.0474618	+	0.0154213i	0.332652	−	0.943050i	$-0.392057\pi$
$877$	1.40554	+	0.456688i	0.0474618	+	0.0154213i	−0.285190	+	0.958471i	$0.592057\pi$
$878$	−24.0534	−	17.4758i	−0.811762	−	0.589779i
$879$	−21.3975	+	33.0640i	−0.721720	+	1.11522i
$880$	1.04451	−	11.0551i	0.0352103	−	0.372667i
$881$	−4.89388	+	3.55561i	−0.164879	+	0.119792i	−0.667165	−	0.744910i	$-0.732492\pi$
$881$	−4.89388	+	3.55561i	−0.164879	+	0.119792i	0.502286	+	0.864702i	$0.332492\pi$
$882$	−15.6807	−	8.98703i	−0.527996	−	0.302609i
$883$	36.6776	−	26.6478i	1.23430	−	0.896771i	0.237094	−	0.971487i	$-0.423805\pi$
$883$	36.6776	−	26.6478i	1.23430	−	0.896771i	0.997205	+	0.0747159i	$0.0238050\pi$
$884$	−18.1435	−	24.9723i	−0.610231	−	0.839910i
$885$	−6.13424	+	7.76549i	−0.206200	+	0.261034i
$886$	20.8129	−	15.1215i	0.699223	−	0.508015i
$887$	−24.0597	−	17.4804i	−0.807845	−	0.586934i	0.105360	−	0.994434i	$-0.466401\pi$
$887$	−24.0597	−	17.4804i	−0.807845	−	0.586934i	−0.913205	+	0.407500i	$0.866401\pi$
$888$	−5.20595	+	8.04438i	−0.174700	+	0.269952i
$889$	−4.02766	+	5.54360i	−0.135083	+	0.185926i
$890$	6.87456	−	1.53698i	0.230436	−	0.0515195i
$891$	29.6948	−	33.4033i	0.994813	−	1.11905i
$892$	−0.283392	−	0.872191i	−0.00948867	−	0.0292031i
$893$	−12.5838			−0.421101
$894$	23.1637	−	18.8186i	0.774712	−	0.629387i
$895$	12.3997	−	14.0660i	0.414478	−	0.470176i
$896$	−2.12129	−	2.91970i	−0.0708672	−	0.0975403i
$897$	0.961528	−	0.0519214i	0.0321045	−	0.00173361i
$898$	14.6890			0.490179
$899$	−35.4869	−	5.51577i	−1.18355	−	0.183961i
$900$	−11.3869	−	9.76419i	−0.379562	−	0.325473i
$901$	20.4516	+	14.8590i	0.681343	+	0.495025i
$902$	−14.1158	−	19.4288i	−0.470006	−	0.646908i
$903$	18.8526	+	12.2006i	0.627376	+	0.406009i
$904$	10.9199			0.363189
$905$	−28.4402	+	16.8212i	−0.945384	+	0.559157i
$906$	17.2741	+	11.1790i	0.573894	+	0.371398i
$907$	13.0706	+	4.24690i	0.434003	+	0.141016i	0.517867	−	0.855461i	$-0.326726\pi$
$907$	13.0706	+	4.24690i	0.434003	+	0.141016i	−0.0838643	+	0.996477i	$0.526726\pi$
$908$	0.0662395	−	0.203864i	0.00219823	−	0.00676547i
$909$	−11.4242	−	12.6072i	−0.378916	−	0.418153i
$910$	−35.8124	−	31.5700i	−1.18717	−	1.04654i
$911$	20.3150	+	14.7597i	0.673064	+	0.489010i	0.871050	−	0.491195i	$-0.163440\pi$
$911$	20.3150	+	14.7597i	0.673064	+	0.489010i	−0.197985	+	0.980205i	$0.563440\pi$
$912$	−10.5578	−	2.81101i	−0.349604	−	0.0930818i
$913$	−21.5573	−	7.00439i	−0.713442	−	0.231811i
$914$	−9.86729	+	7.16900i	−0.326381	+	0.237130i
$915$	−44.9475	+	12.6287i	−1.48592	+	0.417492i
$916$	−0.739978	−	0.240433i	−0.0244496	−	0.00794415i
$917$	44.5481	−	32.3661i	1.47111	−	1.06882i
$918$	4.11371	−	26.7979i	0.135773	−	0.884462i
$919$	9.44663	+	29.0737i	0.311616	+	0.959054i	0.977125	+	0.212665i	$0.0682143\pi$
$919$	9.44663	+	29.0737i	0.311616	+	0.959054i	−0.665509	+	0.746389i	$0.731786\pi$
$920$	0.209201	+	0.0197657i	0.00689715	+	0.000651655i
$921$	−16.4221	−	42.5789i	−0.541126	−	1.40302i
$922$	2.75089	−	8.46638i	0.0905959	−	0.278825i
$923$	−4.58283	+	1.48905i	−0.150846	+	0.0490127i
$924$	24.0931	−	19.5736i	0.792604	−	0.643923i
$925$	−13.3234	+	24.2405i	−0.438072	+	0.797023i
$926$	5.02432	+	15.4633i	0.165109	+	0.508155i
$927$	−51.5664	+	23.1552i	−1.69366	+	0.760516i
$928$	5.21829	+	3.79131i	0.171299	+	0.124456i
$929$	−8.01004			−0.262801			−0.131400	−	0.991329i	$-0.541947\pi$
$929$	−8.01004			−0.262801			−0.131400	+	0.991329i	$0.541947\pi$
$930$	2.57517	+	21.4095i	0.0844431	+	0.702047i
$931$	−38.0019			−1.24546
$932$	2.11696	+	1.53806i	0.0693434	+	0.0503809i
$933$	13.1039	−	49.2168i	0.429004	−	1.61129i
$934$	6.79716	+	20.9195i	0.222410	+	0.684507i
$935$	49.8689	−	29.4955i	1.63089	−	0.964605i
$936$	3.63489	−	17.3717i	0.118810	−	0.567811i
$937$	4.20833	−	1.36737i	0.137480	−	0.0446700i	−0.239469	−	0.970904i	$-0.576973\pi$
$937$	4.20833	−	1.36737i	0.137480	−	0.0446700i	0.376949	+	0.926234i	$0.376973\pi$
$938$	9.70496	−	29.8688i	0.316878	−	0.975251i
$939$	−39.1926	+	15.1160i	−1.27900	+	0.493292i
$940$	0.419595	−	4.44101i	0.0136857	−	0.144850i
$941$	1.51008	+	4.64756i	0.0492273	+	0.151506i	0.972648	−	0.232282i	$-0.0746192\pi$
$941$	1.51008	+	4.64756i	0.0492273	+	0.151506i	−0.923421	+	0.383788i	$0.874619\pi$
$942$	−6.67116	+	0.360235i	−0.217358	+	0.0117371i
$943$	0.367660	−	0.267121i	0.0119727	−	0.00869865i
$944$	−2.43009	−	0.789584i	−0.0790927	−	0.0256988i
$945$	−2.83401	−	41.8363i	−0.0921905	−	1.36093i
$946$	−14.4330	+	10.4862i	−0.469259	+	0.340936i
$947$	34.3662	+	11.1663i	1.11675	+	0.362855i	0.808527	−	0.588459i	$-0.200265\pi$
$947$	34.3662	+	11.1663i	1.11675	+	0.362855i	0.308225	+	0.951313i	$0.400265\pi$
$948$	7.67045	−	28.8093i	0.249125	−	0.935682i
$949$	11.4540	+	8.32185i	0.371814	+	0.270139i
$950$	−30.9814	−	5.90709i	−1.00517	−	0.191651i
$951$	−1.02286	−	18.9423i	−0.0331687	−	0.614248i
$952$	5.81887	−	17.9087i	0.188591	−	0.580423i
$953$	−28.0584	−	9.11673i	−0.908901	−	0.295320i	−0.182995	−	0.983114i	$-0.558579\pi$
$953$	−28.0584	−	9.11673i	−0.908901	−	0.295320i	−0.725906	+	0.687794i	$0.758579\pi$
$954$	1.56518	+	14.4505i	0.0506747	+	0.467852i
$955$	−51.0296	+	30.1820i	−1.65128	+	0.976665i
$956$	12.1172			0.391897
$957$	−30.1429	+	46.5776i	−0.974380	+	1.50564i
$958$	−10.0017	−	13.7662i	−0.323141	−	0.444766i
$959$	36.4550	+	26.4861i	1.17719	+	0.855282i
$960$	1.34409	−	3.63228i	0.0433802	−	0.117231i
$961$	18.0765	−	25.1841i	0.583112	−	0.812392i
$962$	−32.7280			−1.05519
$963$	−6.50283	+	5.89264i	−0.209551	+	0.189888i
$964$	1.59054	+	2.18919i	0.0512277	+	0.0705089i
$965$	−0.760782	−	0.670658i	−0.0244904	−	0.0215892i
$966$	0.370400	+	0.455925i	0.0119174	+	0.0146691i
$967$	−48.4989			−1.55962			−0.779810	−	0.626017i	$-0.784684\pi$
$967$	−48.4989			−1.55962			−0.779810	+	0.626017i	$0.784684\pi$
$968$	4.22156	+	12.9926i	0.135686	+	0.417598i
$969$	−20.5136	−	53.1874i	−0.658992	−	1.70862i
$970$	0.628007	+	2.80894i	0.0201641	+	0.0901896i
$971$	−20.7062	+	28.4996i	−0.664493	+	0.914597i	−0.999620	−	0.0275765i	$-0.991221\pi$
$971$	−20.7062	+	28.4996i	−0.664493	+	0.914597i	0.335126	+	0.942173i	$0.391221\pi$
$972$	13.0058	−	8.59352i	0.417162	−	0.275637i
$973$	18.6588	+	13.5564i	0.598174	+	0.434599i
$974$	27.8304	−	20.2200i	0.891743	−	0.647889i
$975$	6.86803	−	50.7713i	0.219953	−	1.62598i
$976$	−7.08562	−	9.75251i	−0.226805	−	0.312170i
$977$	24.8731	−	18.0714i	0.795762	−	0.578155i	−0.113905	−	0.993492i	$-0.536336\pi$
$977$	24.8731	−	18.0714i	0.795762	−	0.578155i	0.909668	+	0.415336i	$0.136336\pi$
$978$	9.23732	+	23.9504i	0.295377	+	0.765849i
$979$	−12.6566	+	9.19555i	−0.404506	+	0.293891i
$980$	1.26714	−	13.4115i	0.0404772	−	0.428413i
$981$	−45.2618	+	4.90247i	−1.44510	+	0.156524i
$982$	4.24568	+	3.08467i	0.135485	+	0.0984358i
$983$	−7.22044	−	2.34606i	−0.230296	−	0.0748277i	0.191596	−	0.981474i	$-0.438634\pi$
$983$	−7.22044	−	2.34606i	−0.230296	−	0.0748277i	−0.421892	+	0.906646i	$0.638634\pi$
$984$	−3.01412	−	7.81498i	−0.0960868	−	0.249132i
$985$	23.5338	+	20.7459i	0.749848	+	0.661019i
$986$			33.6548i			1.07179i
$987$	9.67858	−	7.86302i	0.308073	−	0.250283i
$988$	−11.5317	−	35.4909i	−0.366872	−	1.12912i
$989$	−0.198436	−	0.273123i	−0.00630989	−	0.00868482i
$990$	31.8205	+	9.85957i	1.01132	+	0.313358i
$991$		−	12.0576i		−	0.383022i	−0.981490	−	0.191511i	$-0.938661\pi$
$991$		−	12.0576i		−	0.383022i	0.981490	−	0.191511i	$-0.0613388\pi$
$992$	−4.95361	+	2.54200i	−0.157277	+	0.0807086i
$993$	44.7662	−	36.3687i	1.42061	−	1.15413i
$994$	−2.37815	−	1.72783i	−0.0754305	−	0.0548034i
$995$	−11.5598	+	26.7164i	−0.366469	+	0.846967i
$996$	−6.63711	−	4.29524i	−0.210305	−	0.136100i
$997$			8.81522i			0.279181i	0.990209	+	0.139590i	$0.0445786\pi$
$997$			8.81522i			0.279181i	−0.990209	+	0.139590i	$0.955421\pi$
$998$			26.7675i			0.847310i
$999$	−20.4229	−	20.2294i	−0.646153	−	0.640031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.a.29.2	✓	128
3.2	odd	2		930.2.y.b.29.16	yes	128
5.4	even	2		930.2.y.b.29.31	yes	128
15.14	odd	2	inner	930.2.y.a.29.17	yes	128
31.15	odd	10	inner	930.2.y.a.449.17	yes	128
93.77	even	10		930.2.y.b.449.31	yes	128
155.139	odd	10		930.2.y.b.449.16	yes	128
465.449	even	10	inner	930.2.y.a.449.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.2	✓	128	1.1	even	1	trivial
930.2.y.a.29.17	yes	128	15.14	odd	2	inner
930.2.y.a.449.2	yes	128	465.449	even	10	inner
930.2.y.a.449.17	yes	128	31.15	odd	10	inner
930.2.y.b.29.16	yes	128	3.2	odd	2
930.2.y.b.29.31	yes	128	5.4	even	2
930.2.y.b.449.16	yes	128	155.139	odd	10
930.2.y.b.449.31	yes	128	93.77	even	10

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.67374 - 0.445633i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.13834 - 1.92463i) q^{5} +(1.09215 + 1.34433i) q^{6} +(-3.43231 + 1.11523i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.60282 + 1.49175i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.67374 - 0.445633i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.13834 - 1.92463i) q^{5} +(1.09215 + 1.34433i) q^{6} +(-3.43231 + 1.11523i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.60282 + 1.49175i) q^{9} +(-0.210331 + 2.22615i) q^{10} +(-1.53458 - 4.72295i) q^{11} +(-0.0933927 - 1.72953i) q^{12} +(4.78611 - 3.47731i) q^{13} +(3.43231 + 1.11523i) q^{14} +(1.04761 + 3.72861i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.96229 - 1.61235i) q^{17} +(-1.22890 - 2.73675i) q^{18} +(-5.10320 - 3.70769i) q^{19} +(1.47866 - 1.67737i) q^{20} +(6.24179 - 0.337049i) q^{21} +(-1.53458 + 4.72295i) q^{22} +(-0.0893747 - 0.0290396i) q^{23} +(-0.941037 + 1.45411i) q^{24} +(-2.40837 + 4.38175i) q^{25} -5.91596 q^{26} +(-3.69168 - 3.65670i) q^{27} +(-2.12129 - 2.91970i) q^{28} +(5.21829 + 3.79131i) q^{29} +(1.34409 - 3.63228i) q^{30} +(-4.95361 + 2.54200i) q^{31} +1.00000 q^{32} +(0.463789 + 8.58887i) q^{33} +(3.06687 + 4.22118i) q^{34} +(6.05353 + 5.33641i) q^{35} +(-0.614421 + 2.93641i) q^{36} +5.53215 q^{37} +(1.94925 + 5.99917i) q^{38} +(-9.56032 + 3.68728i) q^{39} +(-2.18219 + 0.487883i) q^{40} +(-2.84249 + 3.91236i) q^{41} +(-5.24782 - 3.39615i) q^{42} +(2.90637 + 2.11160i) q^{43} +(4.01759 - 2.91895i) q^{44} +(-0.0918378 - 6.70758i) q^{45} +(0.0552366 + 0.0760267i) q^{46} +(1.61393 - 1.17259i) q^{47} +(1.61602 - 0.623276i) q^{48} +(4.87392 - 3.54111i) q^{49} +(4.52394 - 2.12931i) q^{50} +(7.58708 + 4.91001i) q^{51} +(4.78611 + 3.47731i) q^{52} +(-4.60787 - 1.49719i) q^{53} +(0.837276 + 5.12825i) q^{54} +(-7.34305 + 8.32982i) q^{55} +3.60895i q^{56} +(6.88917 + 8.47988i) q^{57} +(-1.99321 - 6.13447i) q^{58} +(1.50188 + 2.06716i) q^{59} +(-3.22239 + 2.14854i) q^{60} +12.0548i q^{61} +(5.50170 + 0.855136i) q^{62} +(-10.5973 - 2.21741i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-12.1407 - 5.25311i) q^{65} +(4.67320 - 7.22115i) q^{66} -8.70224i q^{67} -5.21766i q^{68} +(0.136649 + 0.0884331i) q^{69} +(-1.76074 - 7.87542i) q^{70} +(-0.774655 - 0.251701i) q^{71} +(2.22305 - 2.01446i) q^{72} +(0.739534 + 2.27605i) q^{73} +(-4.47560 - 3.25171i) q^{74} +(5.98364 - 6.26068i) q^{75} +(1.94925 - 5.99917i) q^{76} +(10.5343 + 14.4993i) q^{77} +(9.90179 + 2.63635i) q^{78} +(16.3701 + 5.31895i) q^{79} +(2.05220 + 0.887956i) q^{80} +(4.54937 + 7.76551i) q^{81} +(4.59925 - 1.49439i) q^{82} +(2.68287 - 3.69265i) q^{83} +(2.24937 + 5.83214i) q^{84} +(2.54561 + 11.3860i) q^{85} +(-1.11013 - 3.41664i) q^{86} +(-7.04454 - 8.67111i) q^{87} -4.96601 q^{88} +(-0.973495 - 2.99611i) q^{89} +(-3.86832 + 5.48052i) q^{90} +(-12.5494 + 17.2728i) q^{91} -0.0939742i q^{92} +(9.42386 - 2.04716i) q^{93} -1.99493 q^{94} +(-1.32675 + 14.0424i) q^{95} +(-1.67374 - 0.445633i) q^{96} +(1.22421 - 0.397770i) q^{97} -6.02449 q^{98} +(3.05122 - 14.5822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more