LMFDB - Embedded newform 930.2.y.b.29.16

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			29.16
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.0933927 + 1.72953i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.13834 + 1.92463i) q^{5} +(-1.09215 + 1.34433i) q^{6} +(-3.43231 + 1.11523i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.98256 - 0.323051i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0933927 + 1.72953i) 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} +(-2.98256 - 0.323051i) q^{9} +(-0.210331 + 2.22615i) q^{10} +(1.53458 + 4.72295i) q^{11} +(-1.67374 + 0.445633i) q^{12} +(4.78611 - 3.47731i) q^{13} +(-3.43231 - 1.11523i) q^{14} +(-3.43501 + 1.78905i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.96229 + 1.61235i) q^{17} +(-2.22305 - 2.01446i) q^{18} +(-5.10320 - 3.70769i) q^{19} +(-1.47866 + 1.67737i) q^{20} +(-1.60826 - 6.04044i) q^{21} +(-1.53458 + 4.72295i) q^{22} +(0.0893747 + 0.0290396i) q^{23} +(-1.61602 - 0.623276i) q^{24} +(-2.40837 + 4.38175i) q^{25} +5.91596 q^{26} +(0.837276 - 5.12825i) q^{27} +(-2.12129 - 2.91970i) q^{28} +(-5.21829 - 3.79131i) q^{29} +(-3.83056 - 0.571680i) q^{30} +(-4.95361 + 2.54200i) q^{31} -1.00000 q^{32} +(-8.31182 + 2.21302i) 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} +(5.56713 + 8.60249i) q^{39} +(-2.18219 + 0.487883i) q^{40} +(2.84249 - 3.91236i) q^{41} +(2.24937 - 5.83214i) q^{42} +(2.90637 + 2.11160i) q^{43} +(-4.01759 + 2.91895i) q^{44} +(-2.77341 - 6.10804i) q^{45} +(0.0552366 + 0.0760267i) q^{46} +(-1.61393 + 1.17259i) q^{47} +(-0.941037 - 1.45411i) q^{48} +(4.87392 - 3.54111i) q^{49} +(-4.52394 + 2.12931i) q^{50} +(-3.25205 + 8.43186i) q^{51} +(4.78611 + 3.47731i) q^{52} +(4.60787 + 1.49719i) q^{53} +(3.69168 - 3.65670i) 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} +(-2.76296 - 2.71405i) 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} +(-8.02518 - 3.09520i) q^{66} -8.70224i q^{67} +5.21766i q^{68} +(-0.0585719 + 0.151864i) q^{69} +(-1.76074 - 7.87542i) q^{70} +(0.774655 + 0.251701i) q^{71} +(1.22890 - 2.73675i) q^{72} +(0.739534 + 2.27605i) q^{73} +(4.47560 + 3.25171i) q^{74} +(-7.35345 - 4.57457i) q^{75} +(1.94925 - 5.99917i) q^{76} +(-10.5343 - 14.4993i) q^{77} +(-0.552507 + 10.2318i) q^{78} +(16.3701 + 5.31895i) q^{79} +(-2.05220 - 0.887956i) q^{80} +(8.79128 + 1.92704i) q^{81} +(4.59925 - 1.49439i) q^{82} +(-2.68287 + 3.69265i) q^{83} +(5.24782 - 3.39615i) 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} +(1.34649 - 6.57168i) q^{90} +(-12.5494 + 17.2728i) q^{91} +0.0939742i q^{92} +(-3.93384 - 8.80482i) q^{93} -1.99493 q^{94} +(1.32675 - 14.0424i) q^{95} +(0.0933927 - 1.72953i) 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} - 35 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} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 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} - 5 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 - 35 * 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 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * 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 - 5 * 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
$3$	−0.0933927	+	1.72953i	−0.0539203	+	0.998545i
$3$	−0.0933927	+	1.72953i	−0.0539203	+	0.998545i
$4$	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
$9$	−2.98256	−	0.323051i	−0.994185	−	0.107684i
$10$	−0.210331	+	2.22615i	−0.0665125	+	0.703972i
$11$	1.53458	+	4.72295i	0.462694	+	1.42402i	0.861860	+	0.507146i	$0.169300\pi$
$11$	1.53458	+	4.72295i	0.462694	+	1.42402i	−0.399167	+	0.916878i	$0.630700\pi$
$12$	−1.67374	+	0.445633i	−0.483168	+	0.128643i
$13$	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
$15$	−3.43501	+	1.78905i	−0.886916	+	0.461930i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.96229	+	1.61235i	1.20353	+	0.391052i	0.841060	−	0.540942i	$-0.181932\pi$
$17$	4.96229	+	1.61235i	1.20353	+	0.391052i	0.362474	+	0.931994i	$0.381932\pi$
$18$	−2.22305	−	2.01446i	−0.523979	−	0.474812i
$19$	−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
$21$	−1.60826	−	6.04044i	−0.350952	−	1.31813i
$22$	−1.53458	+	4.72295i	−0.327174	+	1.00694i
$23$	0.0893747	+	0.0290396i	0.0186359	+	0.00605518i	0.318320	−	0.947983i	$-0.396881\pi$
$23$	0.0893747	+	0.0290396i	0.0186359	+	0.00605518i	−0.299684	+	0.954038i	$0.596881\pi$
$24$	−1.61602	−	0.623276i	−0.329869	−	0.127226i
$25$	−2.40837	+	4.38175i	−0.481674	+	0.876351i
$26$	5.91596			1.16022
$27$	0.837276	−	5.12825i	0.161134	−	0.986933i
$28$	−2.12129	−	2.91970i	−0.400885	−	0.551771i
$29$	−5.21829	−	3.79131i	−0.969012	−	0.704029i	−0.0137859	−	0.999905i	$-0.504388\pi$
$29$	−5.21829	−	3.79131i	−0.969012	−	0.704029i	−0.955226	+	0.295876i	$0.904388\pi$
$30$	−3.83056	−	0.571680i	−0.699361	−	0.104374i
$31$	−4.95361	+	2.54200i	−0.889694	+	0.456557i
$31$	−4.95361	+	2.54200i	−0.889694	+	0.456557i
$32$	−1.00000			−0.176777
$33$	−8.31182	+	2.21302i	−1.44690	+	0.385237i
$34$	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
$39$	5.56713	+	8.60249i	0.891455	+	1.37750i
$40$	−2.18219	+	0.487883i	−0.345035	+	0.0771410i
$41$	2.84249	−	3.91236i	0.443923	−	0.611007i	−0.527155	−	0.849769i	$-0.676741\pi$
$41$	2.84249	−	3.91236i	0.443923	−	0.611007i	0.971078	+	0.238762i	$0.0767414\pi$
$42$	2.24937	−	5.83214i	0.347085	−	0.899918i
$43$	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
$45$	−2.77341	−	6.10804i	−0.413435	−	0.910534i
$46$	0.0552366	+	0.0760267i	0.00814420	+	0.0112095i
$47$	−1.61393	+	1.17259i	−0.235416	+	0.171040i	−0.699239	−	0.714888i	$-0.746477\pi$
$47$	−1.61393	+	1.17259i	−0.235416	+	0.171040i	0.463823	+	0.885928i	$0.346477\pi$
$48$	−0.941037	−	1.45411i	−0.135827	−	0.209883i
$49$	4.87392	−	3.54111i	0.696274	−	0.505873i
$50$	−4.52394	+	2.12931i	−0.639782	+	0.301130i
$51$	−3.25205	+	8.43186i	−0.455378	+	1.18070i
$52$	4.78611	+	3.47731i	0.663714	+	0.482217i
$53$	4.60787	+	1.49719i	0.632940	+	0.205655i	0.607877	−	0.794031i	$-0.292021\pi$
$53$	4.60787	+	1.49719i	0.632940	+	0.205655i	0.0250631	+	0.999686i	$0.492021\pi$
$54$	3.69168	−	3.65670i	0.502374	−	0.497614i
$55$	−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	0.699984	−	0.714158i	$-0.253190\pi$
$59$	−1.50188	−	2.06716i	−0.195528	−	0.269121i	−0.895512	+	0.445037i	$0.853190\pi$
$60$	−2.76296	−	2.71405i	−0.356697	−	0.350382i
$61$			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
$66$	−8.02518	−	3.09520i	−0.987831	−	0.380992i
$67$		−	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
$69$	−0.0585719	+	0.151864i	−0.00705122	+	0.0182823i
$70$	−1.76074	−	7.87542i	−0.210449	−	0.941293i
$71$	0.774655	+	0.251701i	0.0919346	+	0.0298714i	0.354623	−	0.935009i	$-0.384609\pi$
$71$	0.774655	+	0.251701i	0.0919346	+	0.0298714i	−0.262689	+	0.964881i	$0.584609\pi$
$72$	1.22890	−	2.73675i	0.144827	−	0.322529i
$73$	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
$75$	−7.35345	−	4.57457i	−0.849104	−	0.528226i
$76$	1.94925	−	5.99917i	0.223594	−	0.688153i
$77$	−10.5343	−	14.4993i	−1.20050	−	1.65234i
$78$	−0.552507	+	10.2318i	−0.0625591	+	1.15853i
$79$	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
$81$	8.79128	+	1.92704i	0.976808	+	0.214115i
$82$	4.59925	−	1.49439i	0.507902	−	0.165027i
$83$	−2.68287	+	3.69265i	−0.294483	+	0.405321i	−0.930464	−	0.366384i	$-0.880596\pi$
$83$	−2.68287	+	3.69265i	−0.294483	+	0.405321i	0.635981	+	0.771705i	$0.280596\pi$
$84$	5.24782	−	3.39615i	0.572584	−	0.370550i
$85$	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	0.989301	−	0.145886i	$-0.0466032\pi$
$89$	0.973495	+	2.99611i	0.103190	+	0.317587i	−0.886111	+	0.463473i	$0.846603\pi$
$90$	1.34649	−	6.57168i	0.141932	−	0.692716i
$91$	−12.5494	+	17.2728i	−1.31554	+	1.81068i
$92$			0.0939742i			0.00979748i
$93$	−3.93384	−	8.80482i	−0.407920	−	0.913018i
$94$	−1.99493			−0.205761
$95$	1.32675	−	14.0424i	0.136121	−	1.44072i
$96$	0.0933927	−	1.72953i	0.00953185	−	0.176520i
$97$	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	0.564800	−	0.825228i	$-0.308953\pi$
$101$	5.39353	+	1.75247i	0.536677	+	0.174377i	−0.0281236	+	0.999604i	$0.508953\pi$
$102$	−7.58708	+	4.91001i	−0.751233	+	0.486164i
$103$	−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
$105$	9.79484	−	9.97138i	0.955879	−	0.973107i
$106$	2.84782	+	3.91969i	0.276605	+	0.380714i
$107$	0.903930	−	2.78201i	0.0873862	−	0.268947i	−0.897809	−	0.440386i	$-0.854842\pi$
$107$	0.903930	−	2.78201i	0.0873862	−	0.268947i	0.985195	+	0.171439i	$0.0548416\pi$
$108$	5.13599	−	0.788420i	0.494211	−	0.0758658i
$109$	−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
$111$	−0.516662	+	9.56802i	−0.0490394	+	0.908156i
$112$	2.12129	−	2.91970i	0.200443	−	0.275886i
$113$	−3.37442	−	10.3854i	−0.317439	−	0.976977i	−0.974739	−	0.223348i	$-0.928301\pi$
$113$	−3.37442	−	10.3854i	−0.317439	−	0.976977i	0.657300	−	0.753629i	$-0.271699\pi$
$114$	10.5578	−	2.81101i	0.988829	−	0.263275i
$115$	0.0458484	+	0.205070i	0.00427538	+	0.0191229i
$116$	1.99321	−	6.13447i	0.185065	−	0.569571i
$117$	−15.3982	+	8.82512i	−1.42356	+	0.815883i
$118$		−	2.55515i		−	0.235220i
$119$	−18.8303			−1.72617
$120$	−0.640008	−	3.81974i	−0.0584244	−	0.348693i
$121$	−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
$126$	9.87679	+	4.43504i	0.879894	+	0.395104i
$127$	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	0.403554	−	0.914956i	$-0.367775\pi$
$131$	14.5110	−	4.71491i	1.26783	−	0.411944i	0.864279	+	0.503012i	$0.167775\pi$
$132$	−4.67320	−	7.22115i	−0.406749	−	0.628520i
$133$	21.6507	+	7.03474i	1.87735	+	0.609989i
$134$	5.11505	−	7.04026i	0.441873	−	0.608186i
$135$	10.8231	−	4.22625i	0.931502	−	0.363737i
$136$	−3.06687	+	4.22118i	−0.262982	+	0.361963i
$137$	7.33902	+	10.1013i	0.627015	+	0.863012i	0.997840	−	0.0656907i	$-0.0209251\pi$
$137$	7.33902	+	10.1013i	0.627015	+	0.863012i	−0.370825	+	0.928703i	$0.620925\pi$
$138$	−0.136649	+	0.0884331i	−0.0116324	+	0.00752793i
$139$	−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
$141$	−1.87730	−	2.90085i	−0.158097	−	0.244296i
$142$	0.478763	+	0.658961i	0.0401769	+	0.0552988i
$143$	23.7679	+	17.2684i	1.98757	+	1.44405i
$144$	2.60282	−	1.49175i	0.216902	−	0.124312i
$145$	1.35667	−	14.3591i	0.112665	−	1.19245i
$146$	−0.739534	+	2.27605i	−0.0612043	+	0.188367i
$147$	5.66927	+	8.76031i	0.467593	+	0.722538i
$148$	1.70953	+	5.26138i	0.140522	+	0.432483i
$149$			17.2308i			1.41160i	0.708412	+	0.705800i	$0.249412\pi$
$149$			17.2308i			1.41160i	−0.708412	+	0.705800i	$0.750588\pi$
$150$	−3.26020	−	8.02316i	−0.266195	−	0.655088i
$151$	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
$153$	−14.2794	−	6.41199i	−1.15442	−	0.518379i
$154$		−	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
$159$	−3.01978	+	7.82964i	−0.239484	+	0.620931i
$160$	−1.13834	−	1.92463i	−0.0899936	−	0.152155i
$161$	−0.339148			−0.0267286
$162$	5.97961	+	6.72639i	0.469802	+	0.528475i
$163$	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
$165$	−13.7209	−	13.4780i	−1.06817	−	1.04926i
$166$	−4.34097	+	1.41047i	−0.336925	+	0.109473i
$167$	12.3171	−	16.9530i	0.953125	−	1.31186i	0.00299945	−	0.999996i	$-0.499045\pi$
$167$	12.3171	−	16.9530i	0.953125	−	1.31186i	0.950125	−	0.311868i	$-0.100955\pi$
$168$	6.24179	+	0.337049i	0.481564	+	0.0260039i
$169$	6.79794	−	20.9219i	0.522918	−	1.60938i
$170$	−4.63306	+	10.7077i	−0.355339	+	0.821243i
$171$	14.0228	+	12.7070i	1.07235	+	0.971728i
$172$	−1.11013	+	3.41664i	−0.0846468	+	0.260516i
$173$	0.902895	−	0.655992i	0.0686459	−	0.0498741i	−0.552933	−	0.833226i	$-0.686491\pi$
$173$	0.902895	−	0.655992i	0.0686459	−	0.0498741i	0.621579	+	0.783352i	$0.286491\pi$
$174$	10.7959	−	2.87440i	0.818435	−	0.217908i
$175$	3.37963	−	17.7254i	0.255476	−	1.33992i
$176$	−4.01759	−	2.91895i	−0.302837	−	0.220024i
$177$	3.71548	−	2.40449i	0.279272	−	0.180732i
$178$	−0.973495	+	2.99611i	−0.0729665	+	0.224568i
$179$	−2.59135	−	7.97536i	−0.193687	−	0.596106i	−0.999989	−	0.00460314i	$-0.998535\pi$
$179$	−2.59135	−	7.97536i	−0.193687	−	0.596106i	0.806303	−	0.591503i	$-0.201465\pi$
$180$	4.95207	−	4.52516i	0.369105	−	0.337285i
$181$		−	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
$183$	−20.8491	−	1.12583i	−1.54121	−	0.0832235i
$184$	−0.0552366	+	0.0760267i	−0.00407210	+	0.00560476i
$185$	6.29746	+	10.6473i	0.462998	+	0.782806i
$186$	1.99280	−	9.43550i	0.146119	−	0.691845i
$187$			25.9110i			1.89480i
$188$	−1.61393	−	1.17259i	−0.117708	−	0.0855198i
$189$	2.84537	+	18.5355i	0.206970	+	1.34826i
$190$	9.32726	−	10.5807i	0.676670	−	0.767603i
$191$			26.5140i			1.91849i	0.282580	+	0.959244i	$0.408810\pi$
$191$			26.5140i			1.91849i	−0.282580	+	0.959244i	$0.591190\pi$
$192$	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
$195$	−10.2193	+	20.5072i	−0.731818	+	1.46855i
$196$	4.87392	+	3.54111i	0.348137	+	0.252936i
$197$	13.3435	−	4.33557i	0.950685	−	0.308896i	0.207691	−	0.978194i	$-0.433405\pi$
$197$	13.3435	−	4.33557i	0.950685	−	0.308896i	0.742994	+	0.669298i	$0.233405\pi$
$198$	6.10273	−	13.5907i	0.433702	−	0.965851i
$199$	−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
$201$	15.0508	+	0.812725i	1.06160	+	0.0573252i
$202$	3.33339	+	4.58801i	0.234536	+	0.322812i
$203$	22.1390	+	7.19339i	1.55385	+	0.504877i
$204$	−9.02411	−	0.487292i	−0.631814	−	0.0341172i
$205$	10.7655	+	1.01715i	0.751898	+	0.0710406i
$206$	−17.9200	+	5.82256i	−1.24854	+	0.405677i
$207$	−0.257184	−	0.115485i	−0.0178755	−	0.00802675i
$208$	−1.82813	+	5.62641i	−0.126758	+	0.390121i
$209$	9.67999	−	29.7920i	0.669579	−	2.06075i
$210$	13.7852	−	2.30975i	0.951271	−	0.159388i
$211$	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
$213$	−0.507671	+	1.31628i	−0.0347851	+	0.0901902i
$214$	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
$219$	−4.00557	+	1.06648i	−0.270671	+	0.0720661i
$220$	−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
$225$	8.59862	−	12.2908i	0.573241	−	0.819386i
$226$	3.37442	−	10.3854i	0.224463	−	0.690827i
$227$	0.173417	+	0.125995i	0.0115101	+	0.00836258i	0.593525	−	0.804815i	$-0.297736\pi$
$227$	0.173417	+	0.125995i	0.0115101	+	0.00836258i	−0.582015	+	0.813178i	$0.697736\pi$
$228$	10.1937	+	3.93157i	0.675095	+	0.260374i
$229$	−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
$231$	26.0607	−	16.8653i	1.71467	−	1.10966i
$232$	5.21829	−	3.79131i	0.342598	−	0.248912i
$233$	−2.11696	+	1.53806i	−0.138687	+	0.100762i	−0.654966	−	0.755659i	$-0.727317\pi$
$233$	−2.11696	+	1.53806i	−0.138687	+	0.100762i	0.516279	+	0.856421i	$0.327317\pi$
$234$	−17.6447	−	1.91116i	−1.15347	−	0.124936i
$235$	−4.09399	−	1.77141i	−0.267063	−	0.115554i
$236$	1.50188	−	2.06716i	0.0977639	−	0.134560i
$237$	−10.7281	+	27.8158i	−0.696868	+	1.80683i
$238$	−15.2340	−	11.0682i	−0.987474	−	0.717442i
$239$	−3.74441	+	11.5241i	−0.242205	+	0.745432i	0.753878	+	0.657014i	$0.228181\pi$
$239$	−3.74441	+	11.5241i	−0.242205	+	0.745432i	−0.996084	+	0.0884174i	$0.971819\pi$
$240$	1.72741	−	3.46642i	0.111504	−	0.223756i
$241$	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
$246$	2.15505	+	8.09411i	0.137401	+	0.516062i
$247$	−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	−0.418867	−	0.908047i	$-0.637573\pi$
$251$	4.99529	−	3.62929i	0.315300	−	0.229079i	0.734167	+	0.678969i	$0.237573\pi$
$252$	5.38364	+	9.39345i	0.339137	+	0.591732i
$253$			0.466677i			0.0293397i
$254$	1.89869			0.119134
$255$	−19.9301	+	3.33934i	−1.24807	+	0.209118i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.27238	−	10.0713i	0.204125	−	0.628234i	−0.795623	−	0.605792i	$-0.792856\pi$
$257$	3.27238	−	10.0713i	0.204125	−	0.628234i	0.999748	−	0.0224411i	$-0.00714382\pi$
$258$	−6.01286	+	1.60092i	−0.374344	+	0.0996690i
$259$	−18.9880	+	6.16959i	−1.17986	+	0.383360i
$260$	−1.24431	+	13.1698i	−0.0771688	+	0.816759i
$261$	14.3391	+	12.9936i	0.887565	+	0.804282i
$262$	14.5110	+	4.71491i	0.896493	+	0.291288i
$263$	−11.9232	−	16.4108i	−0.735214	−	1.01193i	−0.998880	−	0.0473208i	$-0.984932\pi$
$263$	−11.9232	−	16.4108i	−0.735214	−	1.01193i	0.263666	−	0.964614i	$-0.415068\pi$
$264$	0.463789	−	8.58887i	0.0285442	−	0.528608i
$265$	2.36380	+	10.5727i	0.145207	+	0.649478i
$266$	13.3809	+	18.4172i	0.820434	+	1.12923i
$267$	−5.27278	+	1.40388i	−0.322689	+	0.0859158i
$268$	8.27632	−	2.68914i	0.505557	−	0.164265i
$269$	−2.17982	−	1.58373i	−0.132906	−	0.0965619i	0.519346	−	0.854564i	$-0.326176\pi$
$269$	−2.17982	−	1.58373i	−0.132906	−	0.0965619i	−0.652252	+	0.758002i	$0.726176\pi$
$270$	11.2402	+	2.94253i	0.684055	+	0.179077i
$271$	−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
$276$	−0.162531	−	0.00877650i	−0.00978323	−	0.000528283i
$277$	−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
$279$	15.5956	−	5.98139i	0.933685	−	0.358096i
$280$	6.94587	−	4.10820i	0.415095	−	0.245512i
$281$	−4.08990	+	5.62927i	−0.243983	+	0.335814i	−0.913393	−	0.407080i	$-0.866547\pi$
$281$	−4.08990	+	5.62927i	−0.243983	+	0.335814i	0.669409	+	0.742894i	$0.266547\pi$
$282$	0.186312	−	3.45029i	0.0110947	−	0.205462i
$283$	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
$285$	24.1628	+	3.60611i	1.43128	+	0.213607i
$286$	9.07852	+	27.9408i	0.536824	+	1.65217i
$287$	−5.39316	+	16.5984i	−0.318348	+	0.979775i
$288$	2.98256	+	0.323051i	0.175749	+	0.0190360i
$289$	8.27141	+	6.00953i	0.486554	+	0.353502i
$290$	9.53761	−	10.8193i	0.560068	−	0.635330i
$291$	0.573623	+	2.15446i	0.0336264	+	0.126296i
$292$	−1.93613	+	1.40668i	−0.113303	+	0.0823196i
$293$	−7.02650	+	21.6253i	−0.410493	+	1.26337i	0.505728	+	0.862693i	$0.331224\pi$
$293$	−7.02650	+	21.6253i	−0.410493	+	1.26337i	−0.916221	+	0.400673i	$0.868776\pi$
$294$	−0.562644	+	10.4196i	−0.0328140	+	0.607681i
$295$	2.26886	−	5.24368i	0.132098	−	0.305299i
$296$	−1.70953	+	5.26138i	−0.0993642	+	0.305812i
$297$	25.5054	−	3.91530i	1.47997	−	0.227189i
$298$	−10.1280	+	13.9400i	−0.586699	+	0.807521i
$299$	0.528737	−	0.171797i	0.0305777	−	0.00993529i
$300$	2.07833	−	8.40717i	0.119993	−	0.485388i
$301$	−12.3305	−	4.00641i	−0.710716	−	0.230926i
$302$	11.2981	+	3.67096i	0.650130	+	0.211240i
$303$	−3.53466	+	9.16462i	−0.203061	+	0.526494i
$304$	6.30791			0.361783
$305$	−23.2009	+	13.7224i	−1.32848	+	0.785743i
$306$	−7.78344	−	13.5807i	−0.444950	−	0.776355i
$307$	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	$-0.686213\pi$
$311$		−	29.4053i		−	1.66742i	0.552203	−	0.833710i	$-0.313787\pi$
$312$	−9.90179	+	2.63635i	−0.560578	+	0.149254i
$313$	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
$315$	16.3310	+	17.8717i	0.920150	+	1.00696i
$316$			17.2125i			0.968279i
$317$	−3.38445	−	10.4163i	−0.190090	−	0.585035i	0.809909	−	0.586555i	$-0.199516\pi$
$317$	−3.38445	−	10.4163i	−0.190090	−	0.585035i	−0.999999	+	0.00151971i	$0.999516\pi$
$318$	−7.04520	+	4.55933i	−0.395075	+	0.255674i
$319$	9.89829	−	30.4638i	0.554198	−	1.70565i
$320$	0.210331	−	2.22615i	0.0117579	−	0.124446i
$321$	4.72715	+	1.82319i	0.263844	+	0.101761i
$322$	−0.274376	−	0.199346i	−0.0152904	−	0.0111091i
$323$	−19.3455	−	26.6268i	−1.07641	−	1.48155i
$324$	0.883934	+	8.95649i	0.0491074	+	0.497583i
$325$	3.71001	+	29.3462i	0.205794	+	1.62784i
$326$	8.71132	+	11.9901i	0.482475	+	0.664070i
$327$	−14.2807	−	22.0669i	−0.789725	−	1.22030i
$328$	2.84249	+	3.91236i	0.156950	+	0.216024i
$329$	4.23181	−	5.82459i	0.233307	−	0.321120i
$330$	−3.17828	−	18.9688i	−0.174959	−	1.04420i
$331$	−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
$333$	−16.4999	−	1.78717i	−0.904191	−	0.0979361i
$334$	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
$339$	18.2770	−	4.86625i	0.992672	−	0.264298i
$340$	−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
$345$	−0.358957	+	0.0601442i	−0.0193256	+	0.00323805i
$346$	1.11604			0.0599987
$347$		−	5.39078i		−	0.289392i	−0.989476	−	0.144696i	$-0.953780\pi$
$347$		−	5.39078i		−	0.289392i	0.989476	−	0.144696i	$-0.0462205\pi$
$348$	10.4236	+	4.02023i	0.558764	+	0.215507i
$349$	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
$351$	−13.8252	−	27.4559i	−0.737937	−	1.46549i
$352$	−1.53458	−	4.72295i	−0.0817934	−	0.251734i
$353$	10.1043	−	13.9073i	0.537796	−	0.740213i	−0.450497	−	0.892778i	$-0.648753\pi$
$353$	10.1043	−	13.9073i	0.537796	−	0.740213i	0.988293	+	0.152565i	$0.0487532\pi$
$354$	4.41921	+	0.238632i	0.234878	+	0.0126831i
$355$	0.397390	+	1.77744i	0.0210913	+	0.0943368i
$356$	−2.54864	+	1.85170i	−0.135078	+	0.0981398i
$357$	1.75861	−	32.5675i	0.0930755	−	1.72366i
$358$	2.59135	−	7.97536i	0.136957	−	0.421511i
$359$	−2.33260	−	3.21054i	−0.123110	−	0.169446i	0.743014	−	0.669276i	$-0.233396\pi$
$359$	−2.33260	−	3.21054i	−0.123110	−	0.169446i	−0.866123	+	0.499830i	$0.833396\pi$
$360$	6.66613	−	0.750177i	0.351336	−	0.0395378i
$361$	6.42436	+	19.7722i	0.338124	+	1.04064i
$362$	8.68570	−	11.9548i	0.456510	−	0.628332i
$363$	−12.8557	−	19.8650i	−0.674751	−	1.04264i
$364$	−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
$369$	−9.74178	+	10.7505i	−0.507137	+	0.559651i
$370$	−1.16358	+	12.3154i	−0.0604917	+	0.640248i
$371$	−17.4854			−0.907795
$372$	7.15826	−	6.46214i	0.371139	−	0.335046i
$373$		−	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
$375$	0.433612	−	19.3601i	0.0223916	−	0.999749i
$376$	−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
$381$	1.78674	+	2.76091i	0.0915373	+	0.141446i
$382$	−15.5846	+	21.4503i	−0.797375	+	1.09749i
$383$	30.6454	−	9.95728i	1.56590	−	0.508793i	0.607527	−	0.794299i	$-0.292161\pi$
$383$	30.6454	−	9.95728i	1.56590	−	0.508793i	0.958377	+	0.285505i	$0.0921615\pi$
$384$	1.67374	−	0.445633i	0.0854128	−	0.0227411i
$385$	15.9140	−	36.7797i	0.811052	−	1.87447i
$386$	0.431359	+	0.140157i	0.0219556	+	0.00713380i
$387$	−7.98624	−	7.23686i	−0.405964	−	0.367870i
$388$	0.756603	+	1.04137i	0.0384107	+	0.0528678i
$389$	−6.10415	+	18.7867i	−0.309493	+	0.952521i	0.668469	+	0.743740i	$0.266950\pi$
$389$	−6.10415	+	18.7867i	−0.309493	+	0.952521i	−0.977962	+	0.208781i	$0.933050\pi$
$390$	−20.3214	+	10.5839i	−1.02901	+	0.535938i
$391$	0.396682	+	0.288206i	0.0200611	+	0.0145752i
$392$	1.86167	+	5.72963i	0.0940286	+	0.289390i
$393$	6.79937	+	25.5376i	0.342983	+	1.28820i
$394$	13.3435	+	4.33557i	0.672236	+	0.218423i
$395$	8.39768	+	37.5610i	0.422533	+	1.88990i
$396$	12.9256	−	7.40804i	0.649538	−	0.372268i
$397$		−	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
$399$	−14.1888	+	36.7886i	−0.710329	+	1.84173i
$400$	−0.627119	−	4.96052i	−0.0313560	−	0.248026i
$401$	−7.35458	−	5.34342i	−0.367270	−	0.266838i	0.388808	−	0.921319i	$-0.372887\pi$
$401$	−7.35458	−	5.34342i	−0.367270	−	0.266838i	−0.756078	+	0.654481i	$0.772887\pi$
$402$	11.6986	+	9.50414i	0.583475	+	0.474023i
$403$	−14.8692	+	29.3915i	−0.740687	+	1.46410i
$404$			5.67110i			0.282148i
$405$	6.29863	+	19.1135i	0.312981	+	0.949759i
$406$	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
$411$	−18.1559	+	11.7497i	−0.895565	+	0.579569i
$412$	−17.9200	−	5.82256i	−0.882854	−	0.286857i
$413$	7.46026	+	5.42020i	0.367095	+	0.266710i
$414$	−0.140186	−	0.244598i	−0.00688976	−	0.0120213i
$415$	−10.1610	−	0.960027i	−0.498783	−	0.0471259i
$416$	−4.78611	+	3.47731i	−0.234658	+	0.170489i
$417$	9.29275	−	6.01384i	0.455068	−	0.294499i
$418$	25.3425	−	18.4124i	1.23954	−	0.900582i
$419$	−4.96693	−	6.83640i	−0.242651	−	0.333980i	0.670270	−	0.742117i	$-0.266178\pi$
$419$	−4.96693	−	6.83640i	−0.242651	−	0.333980i	−0.912920	+	0.408138i	$0.866178\pi$
$420$	12.5101	+	6.23412i	0.610431	+	0.304194i
$421$	−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
$423$	5.19244	−	2.97593i	0.252465	−	0.144695i
$424$	−2.84782	+	3.91969i	−0.138303	+	0.190357i
$425$	−19.0159	+	17.8604i	−0.922409	+	0.866358i
$426$	−1.18441	+	0.766493i	−0.0573847	+	0.0371367i
$427$	−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	0.706150	−	0.708062i	$-0.250430\pi$
$431$	−3.85046	−	5.29970i	−0.185470	−	0.255277i	−0.891620	+	0.452785i	$0.850430\pi$
$432$	2.33694	+	4.64098i	0.112436	+	0.223289i
$433$	−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
$435$	24.7077	+	3.68743i	1.18464	+	0.176799i
$436$	−12.2772	−	8.91994i	−0.587973	−	0.427188i
$437$	−0.348427	−	0.479569i	−0.0166675	−	0.0229409i
$438$	−3.86744	−	1.49161i	−0.184793	−	0.0712721i
$439$	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
$441$	−15.6807	+	8.98703i	−0.746700	+	0.427954i
$442$	29.3567	+	9.53858i	1.39636	+	0.453704i
$443$	7.94982	−	24.4670i	0.377707	−	1.16246i	−0.563926	−	0.825825i	$-0.690710\pi$
$443$	7.94982	−	24.4670i	0.377707	−	1.16246i	0.941634	−	0.336639i	$-0.109290\pi$
$444$	−9.25938	+	2.46531i	−0.439431	+	0.116998i
$445$	−4.65822	+	5.28420i	−0.220821	+	0.250495i
$446$	−0.741930	−	0.539044i	−0.0351314	−	0.0255245i
$447$	−29.8011	−	1.60923i	−1.40955	−	0.0761138i
$448$	3.43231	+	1.11523i	0.162162	+	0.0526895i
$449$	11.8837	−	8.63400i	0.560825	−	0.407463i	−0.270936	−	0.962597i	$-0.587333\pi$
$449$	11.8837	−	8.63400i	0.560825	−	0.407463i	0.831761	+	0.555134i	$0.187333\pi$
$450$	14.1808	−	4.88932i	0.668488	−	0.230485i
$451$	22.8399	+	7.42114i	1.07549	+	0.349448i
$452$	8.83436	−	6.41854i	0.415533	−	0.301903i
$453$	5.29388	+	19.8832i	0.248728	+	0.934193i
$454$	0.0662395	+	0.203864i	0.00310877	+	0.00956782i
$455$	−47.5292	−	4.49065i	−2.22820	−	0.210525i
$456$	5.93597	+	9.17242i	0.277977	+	0.429538i
$457$	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	0.866335	−	0.499463i	$-0.166469\pi$
$461$	−2.75089	−	8.46638i	−0.128122	−	0.394319i	−0.994457	+	0.105145i	$0.966469\pi$
$462$	30.9968	+	1.67379i	1.44210	+	0.0778717i
$463$	−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
$465$	12.4679	−	17.5940i	0.578187	−	0.815904i
$466$	−2.61671			−0.121217
$467$	17.7952	+	12.9290i	0.823463	+	0.598281i	0.917702	−	0.397268i	$-0.130042\pi$
$467$	17.7952	+	12.9290i	0.823463	+	0.598281i	−0.0942390	+	0.995550i	$0.530042\pi$
$468$	−13.1515	−	11.9174i	−0.607928	−	0.550884i
$469$	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
$474$	−25.0289	+	16.1976i	−1.14962	+	0.743980i
$475$	28.5366	−	13.4315i	1.30935	−	0.616279i
$476$	−5.81887	−	17.9087i	−0.266708	−	0.820842i
$477$	−13.2596	−	5.95403i	−0.607114	−	0.272616i
$478$	−9.80298	+	7.12228i	−0.448378	+	0.325766i
$479$	−16.1831	−	5.25822i	−0.739427	−	0.240254i	−0.0850014	−	0.996381i	$-0.527089\pi$
$479$	−16.1831	−	5.25822i	−0.739427	−	0.240254i	−0.654426	+	0.756126i	$0.727089\pi$
$480$	3.43501	−	1.78905i	0.156786	−	0.0816584i
$481$	26.4775	−	19.2370i	1.20727	−	0.877132i
$482$	2.57354	+	0.836195i	0.117222	+	0.0380876i
$483$	0.0316739	−	0.586567i	0.00144121	−	0.0266897i
$484$	−11.0522	−	8.02988i	−0.502372	−	0.364994i
$485$	2.15912	+	1.90335i	0.0980407	+	0.0864265i
$486$	−12.1919	+	9.71372i	−0.553038	+	0.440623i
$487$	−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
$489$	−9.23732	+	23.9504i	−0.417726	+	1.08307i
$490$	6.85792	+	11.5949i	0.309809	+	0.523804i
$491$	5.24795			0.236837			0.118418	−	0.992964i	$-0.462218\pi$
$491$	5.24795			0.236837			0.118418	+	0.992964i	$0.462218\pi$
$492$	−3.01412	+	7.81498i	−0.135887	+	0.352327i
$493$	−19.7818	−	27.2273i	−0.890927	−	1.22626i
$494$	−30.1903	−	21.9346i	−1.35833	−	0.986883i
$495$	24.5920	−	22.4720i	1.10533	−	1.01004i
$496$	2.51340	−	4.96818i	0.112855	−	0.223078i
$497$	−2.93956			−0.131857
$498$	−2.03403	−	7.63957i	−0.0911471	−	0.342337i
$499$	−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	$0.0984152\pi$
$503$	8.09139	+	24.9027i	0.360777	+	1.11036i	−0.591806	+	0.806080i	$0.701585\pi$
$504$	−1.16587	+	10.7639i	−0.0519322	+	0.479461i
$505$	2.76683	+	12.3754i	0.123122	+	0.550700i
$506$	−0.274306	+	0.377549i	−0.0121944	+	0.0167841i
$507$	35.5502	+	13.7112i	1.57884	+	0.608935i
$508$	1.53607	+	1.11602i	0.0681522	+	0.0495155i
$509$	27.6898	−	20.1178i	1.22733	−	0.891705i	0.230640	−	0.973039i	$-0.425918\pi$
$509$	27.6898	−	20.1178i	1.22733	−	0.891705i	0.996687	+	0.0813340i	$0.0259180\pi$
$510$	−18.0866	−	9.01304i	−0.800889	−	0.399104i
$511$	−5.07662	−	6.98737i	−0.224577	−	0.309103i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−23.2868	+	23.0661i	−1.02814	+	1.01840i
$514$	8.56720	−	6.22444i	0.377883	−	0.274548i
$515$	−41.9456	−	3.96309i	−1.84834	−	0.174635i
$516$	−5.80550	−	2.23910i	−0.255573	−	0.0985708i
$517$	−8.01479	−	5.82309i	−0.352490	−	0.256099i
$518$	−18.9880	−	6.16959i	−0.834287	−	0.271076i
$519$	1.05023	+	1.62285i	0.0461002	+	0.0712352i
$520$	−8.74770	+	9.92324i	−0.383612	+	0.435163i
$521$		−	25.3801i		−	1.11192i	−0.831208	−	0.555962i	$-0.812350\pi$
$521$		−	25.3801i		−	1.11192i	0.831208	−	0.555962i	$-0.187650\pi$
$522$	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
$525$	30.3410	+	7.50059i	1.32419	+	0.327353i
$526$		−	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
$531$	3.81164	+	6.65059i	0.165411	+	0.288611i
$532$			22.7649i			0.986983i
$533$		−	28.6092i		−	1.23920i
$534$	−5.09095	−	1.96350i	−0.220307	−	0.0849692i
$535$	6.38330	−	1.42714i	0.275974	−	0.0617008i
$536$	8.27632	+	2.68914i	0.357483	+	0.116153i
$537$	14.0356	−	3.73698i	0.605683	−	0.161263i
$538$	−0.832617	−	2.56253i	−0.0358967	−	0.110479i
$539$	24.2039	+	17.5852i	1.04254	+	0.757447i
$540$	7.36391	+	8.98737i	0.316892	+	0.386755i
$541$	−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
$543$	25.5573	+	1.38006i	1.09677	+	0.0592242i
$544$	−4.96229	−	1.61235i	−0.212757	−	0.0691288i
$545$	−31.1432	−	13.4752i	−1.33403	−	0.577214i
$546$	−9.51443	−	35.7350i	−0.407180	−	1.52932i
$547$	−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
$549$	3.89431	−	35.9540i	0.166205	−	1.53448i
$550$	−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
$555$	−19.0030	+	9.89727i	−0.806632	+	0.420116i
$556$	3.75633	−	5.17015i	0.159304	−	0.219263i
$557$			22.8740i			0.969201i	0.874736	+	0.484601i	$0.161035\pi$
$557$			22.8740i			0.969201i	−0.874736	+	0.484601i	$0.838965\pi$
$558$	16.1329	+	4.32782i	0.682959	+	0.183211i
$559$	21.2529			0.898901
$560$	8.03407	+	0.759073i	0.339501	+	0.0320767i
$561$	−44.8138	−	2.41989i	−1.89204	−	0.102168i
$562$	−6.61760	+	2.15019i	−0.279147	+	0.0907003i
$563$	30.8623			1.30069			0.650346	−	0.759638i	$-0.274624\pi$
$563$	30.8623			1.30069			0.650346	+	0.759638i	$0.274624\pi$
$564$	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
$567$	−32.3235	+	3.19007i	−1.35746	+	0.133970i
$568$	−0.478763	+	0.658961i	−0.0200884	+	0.0276494i
$569$	−9.10885	−	28.0342i	−0.381863	−	1.17525i	−0.938731	−	0.344652i	$-0.887997\pi$
$569$	−9.10885	−	28.0342i	−0.381863	−	1.17525i	0.556868	−	0.830601i	$-0.312003\pi$
$570$	17.4285	+	17.1199i	0.730000	+	0.717075i
$571$	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
$573$	−45.8568	−	2.47622i	−1.91570	−	0.103445i
$574$	−14.1195	+	10.2584i	−0.589336	+	0.428177i
$575$	−0.342492	+	0.321680i	−0.0142829	+	0.0134150i
$576$	2.22305	+	2.01446i	0.0926272	+	0.0839357i
$577$	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
$579$	0.202120	+	0.759138i	0.00839982	+	0.0315487i
$580$	14.0755	−	3.14692i	0.584453	−	0.130669i
$581$	5.09030	−	15.6663i	0.211181	−	0.649949i
$582$	−0.802287	+	2.08016i	−0.0332559	+	0.0862253i
$583$			24.0603i			0.996478i
$584$	−2.39318			−0.0990306
$585$	−34.5134	−	19.5898i	−1.42695	−	0.809938i
$586$	−18.3956	+	13.3652i	−0.759916	+	0.552111i
$587$	22.3605	−	30.7765i	0.922915	−	1.27028i	−0.0396449	−	0.999214i	$-0.512623\pi$
$587$	22.3605	−	30.7765i	0.922915	−	1.27028i	0.962560	−	0.271070i	$-0.0873773\pi$
$588$	−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
$591$	6.25231	+	23.4829i	0.257186	+	0.965958i
$592$	−4.47560	+	3.25171i	−0.183946	+	0.133645i
$593$	−8.07128	−	24.8409i	−0.331448	−	1.02009i	−0.968445	−	0.249226i	$-0.919824\pi$
$593$	−8.07128	−	24.8409i	−0.331448	−	1.02009i	0.636998	−	0.770866i	$-0.280176\pi$
$594$	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
$597$	18.9303	−	12.2508i	0.774764	−	0.501392i
$598$	0.528737	+	0.171797i	0.0216217	+	0.00702531i
$599$	−11.1209	+	15.3066i	−0.454388	+	0.625412i	−0.973333	−	0.229396i	$-0.926325\pi$
$599$	−11.1209	+	15.3066i	−0.454388	+	0.625412i	0.518945	+	0.854808i	$0.326325\pi$
$600$	6.62302	−	5.57993i	0.270384	−	0.227800i
$601$	−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
$603$	−2.81127	+	25.9549i	−0.114484	+	1.05697i
$604$	6.98258	+	9.61070i	0.284117	+	0.391054i
$605$	−28.0356	−	12.1306i	−1.13981	−	0.493178i
$606$	−8.24643	+	5.33671i	−0.334988	+	0.216789i
$607$	−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
$609$	−14.5088	+	37.6182i	−0.587926	+	1.52437i
$610$	−26.8358	−	2.53549i	−1.08655	−	0.102659i
$611$	−3.64699	+	11.2243i	−0.147541	+	0.454086i
$612$	1.68557	−	15.5620i	0.0681352	−	0.629056i
$613$	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
$615$	−2.76461	+	18.5243i	−0.111480	+	0.746974i
$616$	17.0449	−	5.53822i	0.686758	−	0.223141i
$617$	14.1457	−	10.2775i	0.569485	−	0.413755i	−0.265433	−	0.964129i	$-0.585515\pi$
$617$	14.1457	−	10.2775i	0.569485	−	0.413755i	0.834918	+	0.550374i	$0.185515\pi$
$618$	−8.39670	−	31.5370i	−0.337765	−	1.26860i
$619$			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
$624$	−9.56032	−	3.68728i	−0.382719	−	0.147609i
$625$	−13.3995	−	21.1058i	−0.535981	−	0.844230i
$626$	24.2525			0.969324
$627$	50.6221	+	19.5242i	2.02165	+	0.779721i
$628$	−3.66842	−	1.19194i	−0.146386	−	0.0475637i
$629$	27.4521	+	8.91974i	1.09459	+	0.355653i
$630$	2.70735	+	24.0577i	0.107863	+	0.958481i
$631$	−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
$633$	−0.153413	+	2.84104i	−0.00609761	+	0.112921i
$634$	3.38445	−	10.4163i	0.134414	−	0.413682i
$635$	3.89650	+	1.68595i	0.154628	+	0.0669050i
$636$	−8.37959	−	0.452488i	−0.332272	−	0.0179423i
$637$	11.0136	−	33.8963i	0.436374	−	1.34302i
$638$	25.9141	−	18.8277i	1.02595	−	0.745395i
$639$	−2.22914	−	1.00096i	−0.0881834	−	0.0395975i
$640$	1.47866	−	1.67737i	0.0584492	−	0.0663037i
$641$	17.6620	+	12.8322i	0.697606	+	0.506841i	0.879152	−	0.476542i	$-0.158110\pi$
$641$	17.6620	+	12.8322i	0.697606	+	0.506841i	−0.181545	+	0.983383i	$0.558110\pi$
$642$	2.75270	+	4.25354i	0.108640	+	0.167874i
$643$	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
$645$	−13.7612	−	2.05374i	−0.541845	−	0.0808660i
$646$		−	32.9125i		−	1.29493i
$647$	−3.15820	+	1.02616i	−0.124162	+	0.0403426i	−0.370439	−	0.928857i	$-0.620793\pi$
$647$	−3.15820	+	1.02616i	−0.124162	+	0.0403426i	0.246277	+	0.969199i	$0.420793\pi$
$648$	−4.54937	+	7.76551i	−0.178716	+	0.305058i
$649$	7.45834	−	10.2655i	0.292765	−	0.402957i
$650$	−14.2478	+	25.9223i	−0.558845	+	1.01676i
$651$	23.3215	+	25.8338i	0.914043	+	1.01251i
$652$			14.8206i			0.580419i
$653$	−26.7343	−	19.4236i	−1.04619	−	0.760104i	−0.0747082	−	0.997205i	$-0.523803\pi$
$653$	−26.7343	−	19.4236i	−1.04619	−	0.760104i	−0.971485	+	0.237102i	$0.923803\pi$
$654$	1.41728	−	26.2465i	0.0554201	−	1.02632i
$655$	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	0.429595	−	0.903022i	$-0.358656\pi$
$659$	6.32434	+	2.05490i	0.246361	+	0.0800477i	−0.183233	+	0.983069i	$0.558656\pi$
$660$	8.57832	−	17.2143i	0.333911	−	0.670064i
$661$	−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
$663$	13.7556	+	51.6642i	0.534222	+	2.00647i
$664$	−2.68287	−	3.69265i	−0.104115	−	0.143303i
$665$	11.1066	+	49.6774i	0.430695	+	1.92641i
$666$	−12.2983	−	11.1443i	−0.476548	−	0.431831i
$667$	−0.356285	−	0.490384i	−0.0137954	−	0.0189878i
$668$	19.9295	+	6.47548i	0.771094	+	0.250544i
$669$	0.0856482	−	1.58611i	0.00331135	−	0.0613226i
$670$	19.3725	+	1.83035i	0.748426	+	0.0707126i
$671$	−56.9341	+	18.4990i	−2.19792	+	0.714147i
$672$	1.60826	+	6.04044i	0.0620402	+	0.233015i
$673$	−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
$675$	20.4543	+	16.0195i	0.787285	+	0.616589i
$676$	21.9986			0.846099
$677$		−	12.4014i		−	0.476623i	−0.971189	−	0.238312i	$-0.923406\pi$
$677$		−	12.4014i		−	0.476623i	0.971189	−	0.238312i	$-0.0765940\pi$
$678$	17.6467	+	6.80609i	0.677719	+	0.261386i
$679$	−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	$-0.335644\pi$
$683$	25.8050			0.987402			0.493701	+	0.869632i	$0.335644\pi$
$684$	−7.75179	+	17.2632i	−0.296397	+	0.660074i
$685$	−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
$690$	−0.325754	−	0.162332i	−0.0124012	−	0.00617986i
$691$	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
$693$	26.7352	+	46.6479i	1.01559	+	1.77201i
$694$	3.16862	−	4.36123i	0.120279	−	0.165550i
$695$	5.67462	−	13.1149i	0.215251	−	0.497477i
$696$	6.06984	+	9.37928i	0.230077	+	0.355521i
$697$	20.4134	−	14.8312i	0.773211	−	0.561771i
$698$	24.5851	−	17.8621i	0.930561	−	0.676092i
$699$	−2.46242	−	3.80500i	−0.0931373	−	0.143918i
$700$	17.9022	−	2.26324i	0.676641	−	0.0855424i
$701$	24.1216	−	33.2005i	0.911059	−	1.25397i	−0.0557446	−	0.998445i	$-0.517753\pi$
$701$	24.1216	−	33.2005i	0.911059	−	1.25397i	0.966804	−	0.255520i	$-0.0822468\pi$
$702$	4.95329	−	30.3385i	0.186950	−	1.14505i
$703$	−28.2317	−	20.5115i	−1.06478	−	0.773606i
$704$	1.53458	−	4.72295i	0.0578367	−	0.178003i
$705$	3.44605	−	6.91525i	0.129786	−	0.260443i
$706$	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
$711$	−47.1063	−	21.1524i	−1.76662	−	0.793278i
$712$	−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
$717$	−19.5816	−	7.55233i	−0.731288	−	0.282047i
$718$		−	3.96845i		−	0.148101i
$719$	−9.57189			−0.356971			−0.178486	−	0.983943i	$-0.557120\pi$
$719$	−9.57189			−0.356971			−0.178486	+	0.983943i	$0.557120\pi$
$720$	5.83395	+	3.31134i	0.217419	+	0.123407i
$721$	21.0133	−	64.6723i	0.782576	−	2.40852i
$722$	−6.42436	+	19.7722i	−0.239090	+	0.735843i
$723$	1.20587	+	4.52912i	0.0448470	+	0.168440i
$724$	14.0538	−	4.56634i	0.522304	−	0.169707i
$725$	29.1801	−	13.7344i	1.08372	−	0.510082i
$726$	1.27586	−	23.6275i	0.0473516	−	0.876900i
$727$	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
$729$	−25.5979	−	8.58752i	−0.948072	−	0.318056i
$730$	−5.22239	+	1.16759i	−0.193289	+	0.0432145i
$731$	11.0176	+	15.1644i	0.407501	+	0.560877i
$732$	−5.37200	−	20.1766i	−0.198555	−	0.745748i
$733$	−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
$735$	−10.4068	+	20.8834i	−0.383859	+	0.770297i
$736$	−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
$741$	3.48516	−	64.5415i	0.128031	−	2.37099i
$742$	−14.1460	−	10.2776i	−0.519315	−	0.377304i
$743$			7.78833i			0.285726i	0.989742	+	0.142863i	$0.0456308\pi$
$743$			7.78833i			0.285726i	−0.989742	+	0.142863i	$0.954369\pi$
$744$	9.58951	−	1.02046i	0.351568	−	0.0374119i
$745$	−33.1628	+	19.6145i	−1.21499	+	0.718618i
$746$	3.55646	−	4.89504i	0.130211	−	0.179220i
$747$	9.19472	−	10.1468i	0.336417	−	0.371253i
$748$	−24.6428	+	8.00693i	−0.901030	+	0.292762i
$749$			10.5568i			0.385737i
$750$	11.7304	−	15.4077i	0.428332	−	0.562611i
$751$	−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
$753$	5.81045	+	8.97847i	0.211745	+	0.327194i
$754$	−30.8712	−	22.4292i	−1.12426	−	0.816825i
$755$	19.9262	+	17.5657i	0.725190	+	0.639282i
$756$	−16.7491	+	8.43389i	−0.609157	+	0.306738i
$757$	−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
$759$	−0.807132	−	0.0435842i	−0.0292970	−	0.00158201i
$760$	12.9451	+	5.60114i	0.469568	+	0.203175i
$761$	−14.5643	+	44.8243i	−0.527955	+	1.62488i	0.230442	+	0.973086i	$0.425983\pi$
$761$	−14.5643	+	44.8243i	−0.527955	+	1.62488i	−0.758397	+	0.651793i	$0.774017\pi$
$762$	−0.177324	+	3.28384i	−0.00642376	+	0.118961i
$763$	32.1916	−	44.3079i	1.16541	−	1.60405i
$764$	−25.2163	+	8.19329i	−0.912295	+	0.296423i
$765$	−3.91417	−	34.7816i	−0.141517	−	1.25753i
$766$	30.6454	+	9.95728i	1.10726	+	0.359771i
$767$	−14.3763	−	4.67115i	−0.519098	−	0.168665i
$768$	1.61602	+	0.623276i	0.0583132	+	0.0224905i
$769$	−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
$771$	17.1131	+	6.60027i	0.616313	+	0.237703i
$772$	0.266594	+	0.366936i	0.00959494	+	0.0132063i
$773$	−25.6432	+	35.2948i	−0.922320	+	1.26947i	0.0404602	+	0.999181i	$0.487118\pi$
$773$	−25.6432	+	35.2948i	−0.922320	+	1.26947i	−0.962781	+	0.270284i	$0.912882\pi$
$774$	−2.20728	−	10.5489i	−0.0793392	−	0.379174i
$775$	0.791693	−	27.8276i	0.0284385	−	0.999596i
$776$			1.28721i			0.0462081i
$777$	−8.89716	−	33.4166i	−0.319184	−	1.19881i
$778$	−15.9809	+	11.6108i	−0.572942	+	0.416267i
$779$	−29.0116	+	9.42645i	−1.03945	+	0.337738i
$780$	−22.6614	−	3.38204i	−0.811409	−	0.121096i
$781$			4.04491i			0.144738i
$782$	0.151519	+	0.466327i	0.00541831	+	0.0166758i
$783$	−23.8119	+	23.5863i	−0.850969	+	0.842907i
$784$	−1.86167	+	5.72963i	−0.0664883	+	0.204630i
$785$	−8.58674	−	0.811290i	−0.306474	−	0.0289562i
$786$	−9.50981	+	24.6569i	−0.339204	+	0.879483i
$787$	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
$789$	29.4966	−	19.0888i	1.05011	−	0.679580i
$790$	−15.2839	+	35.3235i	−0.543778	+	1.25675i
$791$	23.1642	+	31.8827i	0.823622	+	1.13362i
$792$	14.8114	+	1.60427i	0.526300	+	0.0570054i
$793$	41.9182	+	57.6955i	1.48856	+	2.04883i
$794$	14.9067	−	20.5173i	0.529019	−	0.728132i
$795$	−18.5066	+	3.10084i	−0.656363	+	0.109975i
$796$	7.65203	−	10.5321i	0.271219	−	0.373301i
$797$	16.8703	+	5.48148i	0.597575	+	0.194164i	0.592159	−	0.805821i	$-0.298276\pi$
$797$	16.8703	+	5.48148i	0.597575	+	0.194164i	0.00541659	+	0.999985i	$0.498276\pi$
$798$	−33.1028	+	21.4226i	−1.17183	+	0.758352i
$799$	−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
$804$	3.87800	+	14.5653i	0.136767	+	0.513678i
$805$	−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	0.182337	−	0.983236i	$-0.441634\pi$
$809$	33.3862	−	24.2565i	1.17380	−	0.852812i	0.991458	+	0.130424i	$0.0416338\pi$
$810$	−6.13895	+	19.1654i	−0.215701	+	0.673404i
$811$	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
$813$	3.37253	−	8.74425i	0.118280	−	0.306674i
$814$	−8.48953	+	26.1281i	−0.297558	+	0.915789i
$815$	7.23071	+	32.3414i	0.253281	+	1.13287i
$816$	−2.32516	−	8.73302i	−0.0813970	−	0.305717i
$817$	−7.00261	−	21.5518i	−0.244990	−	0.754003i
$818$	−4.82020	+	6.63443i	−0.168534	+	0.231967i
$819$	43.0094	−	47.4630i	1.50287	−	1.65849i
$820$	2.35937	+	10.5530i	0.0823928	+	0.368525i
$821$	−30.6936	+	22.3002i	−1.07121	+	0.778283i	−0.976130	−	0.217186i	$-0.930312\pi$
$821$	−30.6936	+	22.3002i	−1.07121	+	0.778283i	−0.0950845	+	0.995469i	$0.530312\pi$
$822$	−21.5947	−	1.16609i	−0.753203	−	0.0406721i
$823$	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
$825$	10.3210	−	41.7501i	0.359332	−	1.45355i
$826$	2.84957	+	8.77006i	0.0991491	+	0.305149i
$827$	28.8605	−	39.7231i	1.00358	−	1.38131i	0.0804734	−	0.996757i	$-0.474357\pi$
$827$	28.8605	−	39.7231i	1.00358	−	1.38131i	0.923104	−	0.384550i	$-0.125643\pi$
$828$	0.0303585	−	0.280283i	0.00105503	−	0.00974051i
$829$	−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
$834$	11.0528	+	0.596841i	0.382729	+	0.0206669i
$835$	46.6492	+	4.40750i	1.61436	+	0.152528i
$836$	31.3251			1.08340
$837$	8.88848	+	27.5317i	0.307231	+	0.951635i
$838$		−	8.45025i		−	0.291909i
$839$	3.89156	−	5.35627i	0.134351	−	0.184919i	−0.736541	−	0.676393i	$-0.763542\pi$
$839$	3.89156	−	5.35627i	0.134351	−	0.184919i	0.870892	+	0.491475i	$0.163542\pi$
$840$	6.45657	+	12.3968i	0.222773	+	0.427729i
$841$	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
$846$	5.94998	+	0.644463i	0.204565	+	0.0221571i
$847$	28.9794	−	39.8867i	0.995744	−	1.37052i
$848$	−4.60787	+	1.49719i	−0.158235	+	0.0514137i
$849$	0.132381	+	0.497207i	0.00454331	+	0.0170641i
$850$	−25.8823	+	3.27210i	−0.887756	+	0.112232i
$851$	0.494434	+	0.160651i	0.0169490	+	0.00550706i
$852$	−1.40874	−	0.0760702i	−0.0482626	−	0.00260612i
$853$	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
$855$	−8.49350	+	41.4535i	−0.290472	+	1.41768i
$856$	2.36652	+	1.71938i	0.0808859	+	0.0587671i
$857$	17.0215	+	52.3868i	0.581444	+	1.78950i	0.613105	+	0.790002i	$0.289920\pi$
$857$	17.0215	+	52.3868i	0.581444	+	1.78950i	−0.0316610	+	0.999499i	$0.510080\pi$
$858$	−49.1724	+	13.0921i	−1.67872	+	0.446957i
$859$	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
$861$	−28.2038	−	10.8778i	−0.961185	−	0.370715i
$862$		−	6.55079i		−	0.223121i
$863$			38.2177i			1.30095i	0.759529	+	0.650473i	$0.225429\pi$
$863$			38.2177i			1.30095i	−0.759529	+	0.650473i	$0.774571\pi$
$864$	−0.837276	+	5.12825i	−0.0284847	+	0.174467i
$865$	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
$870$	17.8215	+	17.5060i	0.604207	+	0.593510i
$871$	−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
$876$	−2.25207	−	3.47996i	−0.0760905	−	0.117577i
$877$	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
$879$	−36.7455	−	14.1722i	−1.23939	−	0.478016i
$880$	1.04451	−	11.0551i	0.0352103	−	0.372667i
$881$	4.89388	−	3.55561i	0.164879	−	0.119792i	−0.502286	−	0.864702i	$-0.667508\pi$
$881$	4.89388	−	3.55561i	0.164879	−	0.119792i	0.667165	+	0.744910i	$0.267508\pi$
$882$	−17.9684	−	1.94622i	−0.605027	−	0.0655326i
$883$	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
$885$	8.85721	+	4.41378i	0.297732	+	0.148368i
$886$	20.8129	−	15.1215i	0.699223	−	0.508015i
$887$	24.0597	+	17.4804i	0.807845	+	0.586934i	0.913205	−	0.407500i	$-0.133599\pi$
$887$	24.0597	+	17.4804i	0.807845	+	0.586934i	−0.105360	+	0.994434i	$0.533599\pi$
$888$	−8.94007	−	3.44805i	−0.300009	−	0.115709i
$889$	−4.02766	+	5.54360i	−0.135083	+	0.185926i
$890$	−6.87456	+	1.53698i	−0.230436	+	0.0515195i
$891$	4.38962	+	44.4780i	0.147058	+	1.49007i
$892$	−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
$897$	0.247748	+	0.930512i	0.00827208	+	0.0310689i
$898$	14.6890			0.490179
$899$	35.4869	+	5.51577i	1.18355	+	0.183961i
$900$	14.3464	+	4.37971i	0.478212	+	0.145990i
$901$	20.4516	+	14.8590i	0.681343	+	0.495025i
$902$	14.1158	+	19.4288i	0.470006	+	0.646908i
$903$	8.08079	−	20.9517i	0.268912	−	0.697231i
$904$	10.9199			0.363189
$905$	28.4402	−	16.8212i	0.945384	−	0.559157i
$906$	−7.40420	+	19.1975i	−0.245988	+	0.637794i
$907$	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
$909$	−15.5204	−	6.96921i	−0.514779	−	0.231154i
$910$	−35.8124	−	31.5700i	−1.18717	−	1.04654i
$911$	−20.3150	−	14.7597i	−0.673064	−	0.489010i	0.197985	−	0.980205i	$-0.436560\pi$
$911$	−20.3150	−	14.7597i	−0.673064	−	0.489010i	−0.871050	+	0.491195i	$0.836560\pi$
$912$	−0.589112	+	10.9097i	−0.0195075	+	0.361257i
$913$	−21.5573	−	7.00439i	−0.713442	−	0.231811i
$914$	9.86729	−	7.16900i	0.326381	−	0.237130i
$915$	−21.5665	−	41.4083i	−0.712968	−	1.36892i
$916$	−0.739978	−	0.240433i	−0.0244496	−	0.00794415i
$917$	−44.5481	+	32.3661i	−1.47111	+	1.06882i
$918$	24.2151	−	12.1934i	0.799217	−	0.402441i
$919$	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
$921$	−38.3130	+	24.7944i	−1.26246	+	0.817004i
$922$	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
$927$	37.9568	−	41.8872i	1.24666	−	1.37576i
$928$	5.21829	+	3.79131i	0.171299	+	0.124456i
$929$	8.01004			0.262801			0.131400	−	0.991329i	$-0.458053\pi$
$929$	8.01004			0.262801			0.131400	+	0.991329i	$0.458053\pi$
$930$	20.4283	−	6.90540i	0.669870	−	0.226437i
$931$	−38.0019			−1.24546
$932$	−2.11696	−	1.53806i	−0.0693434	−	0.0503809i
$933$	50.8573	+	2.74624i	1.66499	+	0.0899077i
$934$	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
$939$	22.8225	+	35.2659i	0.744783	+	1.15086i
$940$	0.419595	−	4.44101i	0.0136857	−	0.144850i
$941$	−1.51008	−	4.64756i	−0.0492273	−	0.151506i	0.923421	−	0.383788i	$-0.125381\pi$
$941$	−1.51008	−	4.64756i	−0.0492273	−	0.151506i	−0.972648	+	0.232282i	$0.925381\pi$
$942$	−1.71890	−	6.45597i	−0.0560047	−	0.210347i
$943$	0.367660	−	0.267121i	0.0119727	−	0.00869865i
$944$	2.43009	+	0.789584i	0.0790927	+	0.0256988i
$945$	−32.4349	+	26.5760i	−1.05511	+	0.864516i
$946$	−14.4330	+	10.4862i	−0.469259	+	0.340936i
$947$	−34.3662	−	11.1663i	−1.11675	−	0.362855i	−0.308225	−	0.951313i	$-0.599735\pi$
$947$	−34.3662	−	11.1663i	−1.11675	−	0.362855i	−0.808527	+	0.588459i	$0.799735\pi$
$948$	−29.7695	−	1.60752i	−0.966870	−	0.0522099i
$949$	11.4540	+	8.32185i	0.371814	+	0.270139i
$950$	30.9814	+	5.90709i	1.00517	+	0.191651i
$951$	18.3313	−	4.88071i	0.594434	−	0.158268i
$952$	5.81887	−	17.9087i	0.188591	−	0.580423i
$953$	28.0584	+	9.11673i	0.908901	+	0.295320i	0.725906	−	0.687794i	$-0.241421\pi$
$953$	28.0584	+	9.11673i	0.908901	+	0.295320i	0.182995	+	0.983114i	$0.441421\pi$
$954$	−7.22753	−	12.6107i	−0.234000	−	0.408286i
$955$	−51.0296	+	30.1820i	−1.65128	+	0.976665i
$956$	−12.1172			−0.391897
$957$	51.7637	+	19.9645i	1.67328	+	0.645361i
$958$	−10.0017	−	13.7662i	−0.323141	−	0.444766i
$959$	−36.4550	−	26.4861i	−1.17719	−	0.855282i
$960$	3.83056	+	0.571680i	0.123631	+	0.0184509i
$961$	18.0765	−	25.1841i	0.583112	−	0.812392i
$962$	32.7280			1.05519
$963$	−3.59475	+	8.00548i	−0.115839	+	0.257973i
$964$	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
$969$	47.8586	−	30.9719i	1.53744	−	0.994961i
$970$	0.628007	+	2.80894i	0.0201641	+	0.0901896i
$971$	20.7062	−	28.4996i	0.664493	−	0.914597i	−0.335126	−	0.942173i	$-0.608779\pi$
$971$	20.7062	−	28.4996i	0.664493	−	0.914597i	0.999620	+	0.0275765i	$0.00877898\pi$
$972$	−15.5731	+	0.692321i	−0.499507	+	0.0222062i
$973$	18.6588	+	13.5564i	0.598174	+	0.434599i
$974$	−27.8304	+	20.2200i	−0.891743	+	0.647889i
$975$	−51.1017	+	3.67586i	−1.63656	+	0.117722i
$976$	−7.08562	−	9.75251i	−0.226805	−	0.312170i
$977$	−24.8731	+	18.0714i	−0.795762	+	0.578155i	−0.909668	−	0.415336i	$-0.863664\pi$
$977$	−24.8731	+	18.0714i	−0.795762	+	0.578155i	0.113905	+	0.993492i	$0.463664\pi$
$978$	−21.5508	+	13.9467i	−0.689119	+	0.445967i
$979$	−12.6566	+	9.19555i	−0.404506	+	0.293891i
$980$	−1.26714	+	13.4115i	−0.0404772	+	0.428413i
$981$	39.4992	−	22.6380i	1.26111	−	0.722777i
$982$	4.24568	+	3.08467i	0.135485	+	0.0984358i
$983$	7.22044	+	2.34606i	0.230296	+	0.0748277i	0.421892	−	0.906646i	$-0.361366\pi$
$983$	7.22044	+	2.34606i	0.230296	+	0.0748277i	−0.191596	+	0.981474i	$0.561366\pi$
$984$	−7.03201	+	4.55079i	−0.224172	+	0.145074i
$985$	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
$990$	33.1040	−	3.72539i	1.05212	−	0.118401i
$991$		−	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
$996$	2.84486	−	7.37612i	0.0901429	−	0.233721i
$997$			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
$999$	4.63193	−	28.3702i	0.146548	−	0.897595i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0933927 + 1.72953i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.13834 + 1.92463i) q^{5} +(-1.09215 + 1.34433i) q^{6} +(-3.43231 + 1.11523i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.98256 - 0.323051i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0933927 + 1.72953i) 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} +(-2.98256 - 0.323051i) q^{9} +(-0.210331 + 2.22615i) q^{10} +(1.53458 + 4.72295i) q^{11} +(-1.67374 + 0.445633i) q^{12} +(4.78611 - 3.47731i) q^{13} +(-3.43231 - 1.11523i) q^{14} +(-3.43501 + 1.78905i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.96229 + 1.61235i) q^{17} +(-2.22305 - 2.01446i) q^{18} +(-5.10320 - 3.70769i) q^{19} +(-1.47866 + 1.67737i) q^{20} +(-1.60826 - 6.04044i) q^{21} +(-1.53458 + 4.72295i) q^{22} +(0.0893747 + 0.0290396i) q^{23} +(-1.61602 - 0.623276i) q^{24} +(-2.40837 + 4.38175i) q^{25} +5.91596 q^{26} +(0.837276 - 5.12825i) q^{27} +(-2.12129 - 2.91970i) q^{28} +(-5.21829 - 3.79131i) q^{29} +(-3.83056 - 0.571680i) q^{30} +(-4.95361 + 2.54200i) q^{31} -1.00000 q^{32} +(-8.31182 + 2.21302i) 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} +(5.56713 + 8.60249i) q^{39} +(-2.18219 + 0.487883i) q^{40} +(2.84249 - 3.91236i) q^{41} +(2.24937 - 5.83214i) q^{42} +(2.90637 + 2.11160i) q^{43} +(-4.01759 + 2.91895i) q^{44} +(-2.77341 - 6.10804i) q^{45} +(0.0552366 + 0.0760267i) q^{46} +(-1.61393 + 1.17259i) q^{47} +(-0.941037 - 1.45411i) q^{48} +(4.87392 - 3.54111i) q^{49} +(-4.52394 + 2.12931i) q^{50} +(-3.25205 + 8.43186i) q^{51} +(4.78611 + 3.47731i) q^{52} +(4.60787 + 1.49719i) q^{53} +(3.69168 - 3.65670i) 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} +(-2.76296 - 2.71405i) 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} +(-8.02518 - 3.09520i) q^{66} -8.70224i q^{67} +5.21766i q^{68} +(-0.0585719 + 0.151864i) q^{69} +(-1.76074 - 7.87542i) q^{70} +(0.774655 + 0.251701i) q^{71} +(1.22890 - 2.73675i) q^{72} +(0.739534 + 2.27605i) q^{73} +(4.47560 + 3.25171i) q^{74} +(-7.35345 - 4.57457i) q^{75} +(1.94925 - 5.99917i) q^{76} +(-10.5343 - 14.4993i) q^{77} +(-0.552507 + 10.2318i) q^{78} +(16.3701 + 5.31895i) q^{79} +(-2.05220 - 0.887956i) q^{80} +(8.79128 + 1.92704i) q^{81} +(4.59925 - 1.49439i) q^{82} +(-2.68287 + 3.69265i) q^{83} +(5.24782 - 3.39615i) 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} +(1.34649 - 6.57168i) q^{90} +(-12.5494 + 17.2728i) q^{91} +0.0939742i q^{92} +(-3.93384 - 8.80482i) q^{93} -1.99493 q^{94} +(1.32675 - 14.0424i) q^{95} +(0.0933927 - 1.72953i) 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	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * 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 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * 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 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

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