LMFDB - Embedded newform 770.2.bv.a.3.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.13
Character	$\chi$	$=$	770.3
Dual form			770.2.bv.a.257.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 + 0.358368i) q^{2} +(-0.0326591 + 0.0212091i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.11379 - 0.729310i) q^{5} +(0.0228892 - 0.0315043i) q^{6} +(0.772445 + 2.53048i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-1.21959 + 2.73925i) q^{9} +O(q^{10})$	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.0326591 + 0.0212091i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.11379 - 0.729310i) q^{5} +(0.0228892 - 0.0315043i) q^{6} +(0.772445 + 2.53048i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-1.21959 + 2.73925i) q^{9} +(-1.71203 + 1.43838i) q^{10} +(-3.30987 + 0.211506i) q^{11} +(-0.0100788 + 0.0376146i) q^{12} +(-0.486774 + 3.07337i) q^{13} +(-1.62798 - 2.08559i) q^{14} +(-0.0535665 + 0.0686501i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-4.26228 - 1.63614i) q^{17} +(0.156929 - 2.99437i) q^{18} +(-2.47586 + 2.74972i) q^{19} +(1.08285 - 1.95638i) q^{20} +(-0.0788964 - 0.0662603i) q^{21} +(3.01424 - 1.38361i) q^{22} +(-1.46541 + 5.46899i) q^{23} +(-0.00407049 - 0.0387282i) q^{24} +(3.93621 - 3.08322i) q^{25} +(-0.646954 - 3.04368i) q^{26} +(-0.0365415 - 0.230714i) q^{27} +(2.26726 + 1.36365i) q^{28} +(-7.19949 - 2.33926i) q^{29} +(0.0254066 - 0.0832869i) q^{30} +(1.66563 - 0.175065i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.103612 - 0.0771069i) q^{33} +4.56552 q^{34} +(3.47829 + 4.78555i) q^{35} +(0.926582 + 2.85173i) q^{36} +(2.45496 - 3.78031i) q^{37} +(1.32600 - 3.45436i) q^{38} +(-0.0492857 - 0.110697i) q^{39} +(-0.309821 + 2.21450i) q^{40} +(3.04390 - 0.989024i) q^{41} +(0.0974018 + 0.0335854i) q^{42} +(2.39196 + 2.39196i) q^{43} +(-2.31819 + 2.37192i) q^{44} +(-0.580200 + 6.67966i) q^{45} +(-0.591831 - 5.63090i) q^{46} +(11.2878 - 0.591569i) q^{47} +(0.0176791 + 0.0346971i) q^{48} +(-5.80666 + 3.90931i) q^{49} +(-2.56985 + 4.28904i) q^{50} +(0.173903 - 0.0369642i) q^{51} +(1.69474 + 2.60967i) q^{52} +(-3.20206 + 3.95422i) q^{53} +(0.116795 + 0.202295i) q^{54} +(-6.84212 + 2.86100i) q^{55} +(-2.60536 - 0.460560i) q^{56} +(0.0225403 - 0.142314i) q^{57} +(7.55962 - 0.396183i) q^{58} +(3.20752 + 3.56231i) q^{59} +(0.00612823 + 0.0868599i) q^{60} +(-8.52258 - 0.895759i) q^{61} +(-1.49226 + 0.760345i) q^{62} +(-7.87369 - 0.970235i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(1.21250 + 6.85146i) q^{65} +(-0.0690971 + 0.109117i) q^{66} +(1.00037 + 3.73345i) q^{67} +(-4.26228 + 1.63614i) q^{68} +(-0.0681331 - 0.209692i) q^{69} +(-4.96225 - 3.22119i) q^{70} +(-7.32844 - 5.32442i) q^{71} +(-1.88701 - 2.33026i) q^{72} +(5.88438 + 0.308388i) q^{73} +(-0.937164 + 4.40901i) q^{74} +(-0.0631610 + 0.184178i) q^{75} +3.70012i q^{76} +(-3.09191 - 8.21219i) q^{77} +(0.0856825 + 0.0856825i) q^{78} +(-4.60389 + 10.3405i) q^{79} +(-0.504364 - 2.17844i) q^{80} +(-6.01304 - 6.67816i) q^{81} +(-2.48729 + 2.01417i) q^{82} +(9.17374 - 1.45298i) q^{83} +(-0.102968 + 0.00355100i) q^{84} +(-10.2028 - 0.349924i) q^{85} +(-3.09029 - 1.37589i) q^{86} +(0.284742 - 0.0762965i) q^{87} +(1.31420 - 3.04514i) q^{88} +(1.85842 + 3.21887i) q^{89} +(-1.85211 - 6.44393i) q^{90} +(-8.15310 + 1.14224i) q^{91} +(2.57046 + 5.04480i) q^{92} +(-0.0506850 + 0.0410439i) q^{93} +(-10.3261 + 4.59747i) q^{94} +(-3.22805 + 7.61801i) q^{95} +(-0.0289392 - 0.0260569i) q^{96} +(12.4639 + 1.97409i) q^{97} +(4.02001 - 5.73058i) q^{98} +(3.45733 - 9.32453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$3$	−0.0326591	+	0.0212091i	−0.0188557	+	0.0122451i	−0.554032	−	0.832495i	$-0.686912\pi$
$3$	−0.0326591	+	0.0212091i	−0.0188557	+	0.0122451i	0.535177	+	0.844740i	$0.320245\pi$
$4$	0.743145	−	0.669131i	0.371572	−	0.334565i
$5$	2.11379	−	0.729310i	0.945316	−	0.326157i
$5$	2.11379	−	0.729310i	0.945316	−	0.326157i
$6$	0.0228892	−	0.0315043i	0.00934449	−	0.0128616i
$7$	0.772445	+	2.53048i	0.291957	+	0.956432i
$7$	0.772445	+	2.53048i	0.291957	+	0.956432i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−1.21959	+	2.73925i	−0.406531	+	0.913084i
$10$	−1.71203	+	1.43838i	−0.541392	+	0.454857i
$11$	−3.30987	+	0.211506i	−0.997965	+	0.0637714i
$11$	−3.30987	+	0.211506i	−0.997965	+	0.0637714i
$12$	−0.0100788	+	0.0376146i	−0.00290950	+	0.0108584i
$13$	−0.486774	+	3.07337i	−0.135007	+	0.852399i	0.823497	+	0.567320i	$0.192020\pi$
$13$	−0.486774	+	3.07337i	−0.135007	+	0.852399i	−0.958504	+	0.285079i	$0.907980\pi$
$14$	−1.62798	−	2.08559i	−0.435097	−	0.557397i
$15$	−0.0535665	+	0.0686501i	−0.0138308	+	0.0177254i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−4.26228	−	1.63614i	−1.03375	−	0.396821i	−0.218447	−	0.975849i	$-0.570099\pi$
$17$	−4.26228	−	1.63614i	−1.03375	−	0.396821i	−0.815308	+	0.579028i	$0.803432\pi$
$18$	0.156929	−	2.99437i	0.0369884	−	0.705781i
$19$	−2.47586	+	2.74972i	−0.568002	+	0.630830i	−0.956888	−	0.290456i	$-0.906193\pi$
$19$	−2.47586	+	2.74972i	−0.568002	+	0.630830i	0.388887	+	0.921286i	$0.372860\pi$
$20$	1.08285	−	1.95638i	0.242132	−	0.437461i
$21$	−0.0788964	−	0.0662603i	−0.0172166	−	0.0144592i
$22$	3.01424	−	1.38361i	0.642637	−	0.294987i
$23$	−1.46541	+	5.46899i	−0.305559	+	1.14036i	0.626903	+	0.779097i	$0.284322\pi$
$23$	−1.46541	+	5.46899i	−0.305559	+	1.14036i	−0.932463	+	0.361266i	$0.882345\pi$
$24$	−0.00407049	−	0.0387282i	−0.000830886	−	0.00790535i
$25$	3.93621	−	3.08322i	0.787243	−	0.616643i
$26$	−0.646954	−	3.04368i	−0.126878	−	0.596915i
$27$	−0.0365415	−	0.230714i	−0.00703242	−	0.0444009i
$28$	2.26726	+	1.36365i	0.428472	+	0.257705i
$29$	−7.19949	−	2.33926i	−1.33691	−	0.434389i	−0.448643	−	0.893711i	$-0.648092\pi$
$29$	−7.19949	−	2.33926i	−1.33691	−	0.434389i	−0.888270	+	0.459322i	$0.848092\pi$
$30$	0.0254066	−	0.0832869i	0.00463859	−	0.0152060i
$31$	1.66563	−	0.175065i	0.299156	−	0.0314425i	0.0462385	−	0.998930i	$-0.485277\pi$
$31$	1.66563	−	0.175065i	0.299156	−	0.0314425i	0.252917	+	0.967488i	$0.418610\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.103612	−	0.0771069i	0.0180365	−	0.0134226i
$34$	4.56552			0.782980
$35$	3.47829	+	4.78555i	0.587938	+	0.808906i
$36$	0.926582	+	2.85173i	0.154430	+	0.475288i
$37$	2.45496	−	3.78031i	0.403594	−	0.621480i	−0.577183	−	0.816615i	$-0.695848\pi$
$37$	2.45496	−	3.78031i	0.403594	−	0.621480i	0.980776	+	0.195135i	$0.0625146\pi$
$38$	1.32600	−	3.45436i	0.215106	−	0.560371i
$39$	−0.0492857	−	0.110697i	−0.00789202	−	0.0177258i
$40$	−0.309821	+	2.21450i	−0.0489869	+	0.350143i
$41$	3.04390	−	0.989024i	0.475378	−	0.154460i	−0.0615218	−	0.998106i	$-0.519595\pi$
$41$	3.04390	−	0.989024i	0.475378	−	0.154460i	0.536900	+	0.843646i	$0.319595\pi$
$42$	0.0974018	+	0.0335854i	0.0150294	+	0.00518234i
$43$	2.39196	+	2.39196i	0.364771	+	0.364771i	0.865566	−	0.500795i	$-0.166959\pi$
$43$	2.39196	+	2.39196i	0.364771	+	0.364771i	−0.500795	+	0.865566i	$0.666959\pi$
$44$	−2.31819	+	2.37192i	−0.349480	+	0.357580i
$45$	−0.580200	+	6.67966i	−0.0864912	+	0.995745i
$46$	−0.591831	−	5.63090i	−0.0872608	−	0.830231i
$47$	11.2878	−	0.591569i	1.64650	−	0.0862893i	0.793625	−	0.608408i	$-0.208192\pi$
$47$	11.2878	−	0.591569i	1.64650	−	0.0862893i	0.852873	+	0.522119i	$0.174858\pi$
$48$	0.0176791	+	0.0346971i	0.00255175	+	0.00500810i
$49$	−5.80666	+	3.90931i	−0.829523	+	0.558473i
$50$	−2.56985	+	4.28904i	−0.363431	+	0.606562i
$51$	0.173903	−	0.0369642i	0.0243513	−	0.00517603i
$52$	1.69474	+	2.60967i	0.235018	+	0.361897i
$53$	−3.20206	+	3.95422i	−0.439837	+	0.543154i	−0.948068	−	0.318067i	$-0.896966\pi$
$53$	−3.20206	+	3.95422i	−0.439837	+	0.543154i	0.508231	+	0.861221i	$0.330300\pi$
$54$	0.116795	+	0.202295i	0.0158938	+	0.0275288i
$55$	−6.84212	+	2.86100i	−0.922592	+	0.385778i
$56$	−2.60536	−	0.460560i	−0.348155	−	0.0615450i
$57$	0.0225403	−	0.142314i	0.00298554	−	0.0188500i
$58$	7.55962	−	0.396183i	0.992627	−	0.0520214i
$59$	3.20752	+	3.56231i	0.417584	+	0.463774i	0.914832	−	0.403835i	$-0.132323\pi$
$59$	3.20752	+	3.56231i	0.417584	+	0.463774i	−0.497248	+	0.867608i	$0.665656\pi$
$60$	0.00612823	+	0.0868599i	0.000791152	+	0.0112136i
$61$	−8.52258	−	0.895759i	−1.09120	−	0.114690i	−0.458208	−	0.888845i	$-0.651508\pi$
$61$	−8.52258	−	0.895759i	−1.09120	−	0.114690i	−0.632996	+	0.774155i	$0.718175\pi$
$62$	−1.49226	+	0.760345i	−0.189517	+	0.0965639i
$63$	−7.87369	−	0.970235i	−0.991991	−	0.122238i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	1.21250	+	6.85146i	0.150392	+	0.849820i
$66$	−0.0690971	+	0.109117i	−0.00850527	+	0.0134313i
$67$	1.00037	+	3.73345i	0.122215	+	0.456113i	0.999725	−	0.0234451i	$-0.00746350\pi$
$67$	1.00037	+	3.73345i	0.122215	+	0.456113i	−0.877510	+	0.479558i	$0.840797\pi$
$68$	−4.26228	+	1.63614i	−0.516877	+	0.198411i
$69$	−0.0681331	−	0.209692i	−0.00820227	−	0.0252440i
$70$	−4.96225	−	3.22119i	−0.593103	−	0.385006i
$71$	−7.32844	−	5.32442i	−0.869725	−	0.631893i	0.0607878	−	0.998151i	$-0.480639\pi$
$71$	−7.32844	−	5.32442i	−0.869725	−	0.631893i	−0.930513	+	0.366258i	$0.880639\pi$
$72$	−1.88701	−	2.33026i	−0.222386	−	0.274624i
$73$	5.88438	+	0.308388i	0.688715	+	0.0360940i	0.393484	−	0.919332i	$-0.371270\pi$
$73$	5.88438	+	0.308388i	0.688715	+	0.0360940i	0.295232	+	0.955426i	$0.404603\pi$
$74$	−0.937164	+	4.40901i	−0.108943	+	0.512537i
$75$	−0.0631610	+	0.184178i	−0.00729321	+	0.0212671i
$76$			3.70012i			0.424433i
$77$	−3.09191	−	8.21219i	−0.352355	−	0.935866i
$78$	0.0856825	+	0.0856825i	0.00970164	+	0.00970164i
$79$	−4.60389	+	10.3405i	−0.517978	+	1.16340i	0.445420	+	0.895322i	$0.353054\pi$
$79$	−4.60389	+	10.3405i	−0.517978	+	1.16340i	−0.963398	+	0.268075i	$0.913612\pi$
$80$	−0.504364	−	2.17844i	−0.0563896	−	0.243557i
$81$	−6.01304	−	6.67816i	−0.668116	−	0.742018i
$82$	−2.48729	+	2.01417i	−0.274676	+	0.222428i
$83$	9.17374	−	1.45298i	1.00695	−	0.159485i	0.368890	−	0.929473i	$-0.379738\pi$
$83$	9.17374	−	1.45298i	1.00695	−	0.159485i	0.638059	+	0.769988i	$0.279738\pi$
$84$	−0.102968	+	0.00355100i	−0.0112348	+	0.000387446i
$85$	−10.2028	−	0.349924i	−1.10665	−	0.0379546i
$86$	−3.09029	−	1.37589i	−0.333235	−	0.148366i
$87$	0.284742	−	0.0762965i	0.0305276	−	0.00817984i
$88$	1.31420	−	3.04514i	0.140094	−	0.324613i
$89$	1.85842	+	3.21887i	0.196992	+	0.341200i	0.947552	−	0.319603i	$-0.103549\pi$
$89$	1.85842	+	3.21887i	0.196992	+	0.341200i	−0.750560	+	0.660802i	$0.770216\pi$
$90$	−1.85211	−	6.44393i	−0.195230	−	0.679250i
$91$	−8.15310	+	1.14224i	−0.854678	+	0.119739i
$92$	2.57046	+	5.04480i	0.267989	+	0.525957i
$93$	−0.0506850	+	0.0410439i	−0.00525579	+	0.00425605i
$94$	−10.3261	+	4.59747i	−1.06505	+	0.474193i
$95$	−3.22805	+	7.61801i	−0.331191	+	0.781591i
$96$	−0.0289392	−	0.0260569i	−0.00295359	−	0.00265943i
$97$	12.4639	+	1.97409i	1.26552	+	0.200439i	0.752876	−	0.658163i	$-0.228666\pi$
$97$	12.4639	+	1.97409i	1.26552	+	0.200439i	0.512644	+	0.858601i	$0.328666\pi$
$98$	4.02001	−	5.73058i	0.406082	−	0.578876i
$99$	3.45733	−	9.32453i	0.347475	−	0.937150i
$100$	0.862103	−	4.92512i	0.0862103	−	0.492512i
$101$	−7.16479	+	0.753049i	−0.712923	+	0.0749312i	−0.454045	−	0.890979i	$-0.650019\pi$
$101$	−7.16479	+	0.753049i	−0.712923	+	0.0749312i	−0.258878	+	0.965910i	$0.583353\pi$
$102$	−0.149106	+	0.0968303i	−0.0147637	+	0.00958763i
$103$	−7.42167	+	11.4284i	−0.731279	+	1.12607i	0.255939	+	0.966693i	$0.417615\pi$
$103$	−7.42167	+	11.4284i	−0.731279	+	1.12607i	−0.987218	+	0.159378i	$0.949051\pi$
$104$	−2.51740	−	1.82900i	−0.246851	−	0.179348i
$105$	−0.215095	−	0.0825205i	−0.0209911	−	0.00805317i
$106$	1.57232	−	4.83910i	0.152717	−	0.470015i
$107$	0.328707	+	6.27210i	0.0317773	+	0.606347i	0.967386	+	0.253308i	$0.0815185\pi$
$107$	0.328707	+	6.27210i	0.0317773	+	0.606347i	−0.935608	+	0.353039i	$0.885148\pi$
$108$	−0.181533	−	0.147003i	−0.0174681	−	0.0141454i
$109$	13.5451	+	7.82027i	1.29739	+	0.749046i	0.979952	−	0.199235i	$-0.0638456\pi$
$109$	13.5451	+	7.82027i	1.29739	+	0.749046i	0.317434	+	0.948280i	$0.397179\pi$
$110$	5.36238	−	5.12297i	0.511283	−	0.488456i
$111$			0.175529i			0.0166605i
$112$	2.59736	−	0.503706i	0.245427	−	0.0475958i
$113$	7.51055	−	14.7403i	0.706533	−	1.38665i	−0.206371	−	0.978474i	$-0.566165\pi$
$113$	7.51055	−	14.7403i	0.706533	−	1.38665i	0.912904	−	0.408175i	$-0.133835\pi$
$114$	0.0299576	+	0.140939i	0.00280579	+	0.0132002i
$115$	0.891017	+	12.6290i	0.0830878	+	1.17766i
$116$	−6.91553	+	3.07899i	−0.642091	+	0.285877i
$117$	−7.82506	−	5.08166i	−0.723427	−	0.469799i
$118$	−4.27110	−	2.17623i	−0.393186	−	0.200338i
$119$	0.847832	−	12.0494i	0.0777207	−	1.10457i
$120$	−0.0368490	−	0.0788946i	−0.00336384	−	0.00720205i
$121$	10.9105	−	1.40012i	0.991866	−	0.127283i
$122$	8.27752	−	2.21795i	0.749411	−	0.200804i
$123$	−0.0784348	+	0.0968590i	−0.00707223	+	0.00873348i
$124$	1.12066	−	1.24462i	0.100638	−	0.111770i
$125$	6.07171	−	9.38799i	0.543070	−	0.839687i
$126$	7.69842	−	1.91588i	0.685830	−	0.170681i
$127$	17.6958	−	2.80274i	1.57025	−	0.248703i	0.690211	−	0.723608i	$-0.257518\pi$
$127$	17.6958	−	2.80274i	1.57025	−	0.248703i	0.880037	+	0.474906i	$0.157518\pi$
$128$	0.838671	+	0.544639i	0.0741287	+	0.0481397i
$129$	−0.128851	−	0.0273880i	−0.0113447	−	0.00241138i
$130$	−3.58731	−	5.96187i	−0.314628	−	0.522891i
$131$	−7.97088	+	4.60199i	−0.696419	+	0.402077i	−0.806012	−	0.591899i	$-0.798378\pi$
$131$	−7.97088	+	4.60199i	−0.696419	+	0.402077i	0.109594	+	0.993976i	$0.465045\pi$
$132$	0.0254038	−	0.126631i	0.00221112	−	0.0110218i
$133$	−8.87059	−	4.14111i	−0.769177	−	0.359080i
$134$	−2.27188	−	3.12697i	−0.196260	−	0.270129i
$135$	−0.245503	−	0.461031i	−0.0211295	−	0.0396792i
$136$	3.39284	−	3.05493i	0.290934	−	0.261958i
$137$	5.52157	−	14.3842i	0.471739	−	1.22892i	−0.466989	−	0.884263i	$-0.654661\pi$
$137$	5.52157	−	14.3842i	0.471739	−	1.22892i	0.938728	−	0.344659i	$-0.112006\pi$
$138$	0.138755	+	0.171348i	0.0118116	+	0.0145861i
$139$	−1.52934	+	4.70683i	−0.129717	+	0.399228i	−0.994731	−	0.102520i	$-0.967309\pi$
$139$	−1.52934	+	4.70683i	−0.129717	+	0.399228i	0.865014	+	0.501748i	$0.167309\pi$
$140$	5.78703	+	1.22893i	0.489093	+	0.103863i
$141$	−0.356103	+	0.258724i	−0.0299893	+	0.0217885i
$142$	8.74979	+	2.34450i	0.734266	+	0.196746i
$143$	0.961124	−	10.2754i	0.0803732	−	0.859274i
$144$	2.59676	+	1.49924i	0.216397	+	0.124937i
$145$	−16.9243	+	0.305964i	−1.40548	+	0.0254090i
$146$	−5.60406	+	1.82087i	−0.463796	+	0.150696i
$147$	0.106727	−	0.250828i	0.00880272	−	0.0206880i
$148$	−0.705130	−	4.45201i	−0.0579613	−	0.365953i
$149$	13.7432	+	1.44447i	1.12589	+	0.118336i	0.649115	−	0.760690i	$-0.275139\pi$
$149$	13.7432	+	1.44447i	1.12589	+	0.118336i	0.476774	+	0.879026i	$0.341806\pi$
$150$	−0.00703772	−	0.194580i	−0.000574627	−	0.0158874i
$151$	7.10740	+	1.51073i	0.578392	+	0.122941i	0.487813	−	0.872948i	$-0.337795\pi$
$151$	7.10740	+	1.51073i	0.578392	+	0.122941i	0.0905793	+	0.995889i	$0.471128\pi$
$152$	−1.32600	−	3.45436i	−0.107553	−	0.280185i
$153$	9.68003	−	9.68003i	0.782584	−	0.782584i
$154$	5.82953	+	6.55870i	0.469757	+	0.528515i
$155$	3.39311	−	1.58481i	0.272541	−	0.127295i
$156$	−0.110697	−	0.0492857i	−0.00886289	−	0.00394601i
$157$	4.70352	+	7.24278i	0.375381	+	0.578037i	0.974988	−	0.222258i	$-0.0713428\pi$
$157$	4.70352	+	7.24278i	0.375381	+	0.578037i	−0.599606	+	0.800295i	$0.704676\pi$
$158$	0.592395	−	11.3036i	0.0471284	−	0.899264i
$159$	0.0207112	−	0.197054i	0.00164251	−	0.0156274i
$160$	1.25155	+	1.85300i	0.0989436	+	0.146493i
$161$	−14.9711	+	0.516299i	−1.17989	+	0.0406901i
$162$	8.00690	+	4.07972i	0.629082	+	0.320533i
$163$	8.06836	+	21.0188i	0.631963	+	1.64632i	0.756414	+	0.654094i	$0.226950\pi$
$163$	8.06836	+	21.0188i	0.631963	+	1.64632i	−0.124451	+	0.992226i	$0.539717\pi$
$164$	1.60027	−	2.77176i	0.124960	−	0.216438i
$165$	0.162778	−	0.238553i	0.0126723	−	0.0185713i
$166$	−8.04373	+	4.64405i	−0.624314	+	0.360448i
$167$	−7.59872	−	1.20352i	−0.588006	−	0.0931310i	−0.144660	−	0.989481i	$-0.546209\pi$
$167$	−7.59872	−	1.20352i	−0.588006	−	0.0931310i	−0.443346	+	0.896350i	$0.646209\pi$
$168$	0.0948566	−	0.0402157i	0.00731835	−	0.00310271i
$169$	3.15509	+	1.02515i	0.242699	+	0.0788577i
$170$	9.65054	−	3.32968i	0.740163	−	0.255375i
$171$	−4.51264	−	10.1355i	−0.345090	−	0.775085i
$172$	3.37811	+	0.177039i	0.257578	+	0.0134991i
$173$	0.528079	+	10.0764i	0.0401491	+	0.766091i	0.942320	+	0.334713i	$0.108639\pi$
$173$	0.528079	+	10.0764i	0.0401491	+	0.766091i	−0.902171	+	0.431378i	$0.858027\pi$
$174$	−0.238488	+	0.173271i	−0.0180797	+	0.0131357i
$175$	10.8425	+	7.57890i	0.819618	+	0.572911i
$176$	−0.135629	+	3.31385i	−0.0102234	+	0.249791i
$177$	−0.180308	−	0.0483134i	−0.0135528	−	0.00363146i
$178$	−2.88852	−	2.33908i	−0.216504	−	0.175321i
$179$	1.15326	−	5.42567i	0.0861988	−	0.405534i	−0.913801	−	0.406162i	$-0.866867\pi$
$179$	1.15326	−	5.42567i	0.0861988	−	0.405534i	1.00000		0.000628640i	$0.000200102\pi$
$180$	4.03839	+	5.35219i	0.301004	+	0.398928i
$181$	2.37185	−	3.26457i	0.176298	−	0.242653i	−0.711719	−	0.702465i	$-0.752083\pi$
$181$	2.37185	−	3.26457i	0.176298	−	0.242653i	0.888017	+	0.459811i	$0.152083\pi$
$182$	7.20224	−	3.98818i	0.533865	−	0.295624i
$183$	0.297338	−	0.151501i	0.0219798	−	0.0111993i
$184$	−4.20762	−	3.78856i	−0.310190	−	0.279296i
$185$	2.43226	−	9.78122i	0.178823	−	0.719130i
$186$	0.0326097	−	0.0564816i	0.00239106	−	0.00414143i
$187$	14.4537	+	4.51390i	1.05696	+	0.330089i
$188$	7.99265	−	7.99265i	0.582924	−	0.582924i
$189$	0.555591	−	0.270681i	0.0404133	−	0.0196892i
$190$	0.283595	−	8.26885i	0.0205742	−	0.599886i
$191$	9.74022	−	2.07035i	0.704778	−	0.149805i	0.158438	−	0.987369i	$-0.449354\pi$
$191$	9.74022	−	2.07035i	0.704778	−	0.149805i	0.546340	+	0.837564i	$0.316021\pi$
$192$	0.0363550	+	0.0139554i	0.00262370	+	0.00100714i
$193$	−20.2317	−	7.76622i	−1.45631	−	0.559025i	−0.503877	−	0.863776i	$-0.668093\pi$
$193$	−20.2317	−	7.76622i	−1.45631	−	0.559025i	−0.952432	+	0.304751i	$0.901427\pi$
$194$	−12.3435	+	2.62370i	−0.886213	+	0.188370i
$195$	−0.184912	−	0.198047i	−0.0132418	−	0.0141824i
$196$	−1.69935	+	6.79060i	−0.121382	+	0.485043i
$197$	−5.91984	+	5.91984i	−0.421771	+	0.421771i	−0.885813	−	0.464042i	$-0.846399\pi$
$197$	−5.91984	+	5.91984i	−0.421771	+	0.421771i	0.464042	+	0.885813i	$0.346399\pi$
$198$	0.113914	+	9.94419i	0.00809554	+	0.706703i
$199$	9.61425	−	16.6524i	0.681536	−	1.18046i	−0.292976	−	0.956120i	$-0.594645\pi$
$199$	9.61425	−	16.6524i	0.681536	−	1.18046i	0.974512	−	0.224336i	$-0.0720212\pi$
$200$	0.960162	+	4.90694i	0.0678937	+	0.346973i
$201$	−0.111854	−	0.100714i	−0.00788959	−	0.00710382i
$202$	6.41904	−	3.27066i	0.451642	−	0.230123i
$203$	0.358231	−	20.0251i	0.0251429	−	1.40549i
$204$	0.104501	−	0.143834i	0.00731655	−	0.0100704i
$205$	5.71287	−	4.31054i	0.399004	−	0.301061i
$206$	2.83316	−	13.3290i	0.197396	−	0.928675i
$207$	−13.1937	−	10.6841i	−0.917028	−	0.742594i
$208$	3.00565	+	0.805362i	0.208404	+	0.0558418i
$209$	7.61321	−	9.62490i	0.526617	−	0.665768i
$210$	0.230381		4.36098e-5i	0.0158978		3.00936e-6i
$211$	9.89685	−	7.19049i	0.681328	−	0.495013i	−0.192470	−	0.981303i	$-0.561650\pi$
$211$	9.89685	−	7.19049i	0.681328	−	0.495013i	0.873798	+	0.486289i	$0.161650\pi$
$212$	0.266292	+	5.08116i	0.0182890	+	0.348975i
$213$	0.352266	+	0.0184615i	0.0241369	+	0.00126496i
$214$	−2.55460	−	5.73772i	−0.174629	−	0.392222i
$215$	6.80059	+	3.31162i	0.463796	+	0.225851i
$216$	0.222157	+	0.0721833i	0.0151159	+	0.00491145i
$217$	1.72960	+	4.07961i	0.117413	+	0.276942i
$218$	−15.4480	−	2.44672i	−1.04627	−	0.165713i
$219$	−0.198719	+	0.114731i	−0.0134282	+	0.00775278i
$220$	−3.17030	+	6.70441i	−0.213742	+	0.452012i
$221$	7.10321	−	12.3031i	0.477814	−	0.827598i
$222$	−0.0629040	−	0.163871i	−0.00422184	−	0.0109983i
$223$	−23.4524	−	11.9496i	−1.57049	−	0.800203i	−0.570705	−	0.821155i	$-0.693330\pi$
$223$	−23.4524	−	11.9496i	−1.57049	−	0.800203i	−0.999780	+	0.0209524i	$0.993330\pi$
$224$	−2.24433	+	1.40106i	−0.149956	+	0.0936123i
$225$	3.64512	+	14.5425i	0.243008	+	0.969503i
$226$	−1.72926	+	16.4528i	−0.115028	+	1.09442i
$227$	−1.29715	+	24.7510i	−0.0860946	+	1.64278i	0.524912	+	0.851157i	$0.324098\pi$
$227$	−1.29715	+	24.7510i	−0.0860946	+	1.64278i	−0.611006	+	0.791626i	$0.709235\pi$
$228$	−0.0784760	−	0.120842i	−0.00519720	−	0.00800299i
$229$	−21.9171	−	9.75814i	−1.44833	−	0.644836i	−0.476208	−	0.879332i	$-0.657989\pi$
$229$	−21.9171	−	9.75814i	−1.44833	−	0.644836i	−0.972117	+	0.234497i	$0.924656\pi$
$230$	−5.35768	−	11.4709i	−0.353275	−	0.756369i
$231$	0.275152	+	0.202626i	0.0181037	+	0.0133318i
$232$	5.35280	−	5.35280i	0.351428	−	0.351428i
$233$	−2.56952	−	6.69383i	−0.168335	−	0.438527i	0.823299	−	0.567607i	$-0.192131\pi$
$233$	−2.56952	−	6.69383i	−0.168335	−	0.438527i	−0.991634	+	0.129080i	$0.958798\pi$
$234$	9.12643	+	1.93988i	0.596613	+	0.126814i
$235$	23.4286	−	9.48277i	1.52832	−	0.618588i
$236$	4.76730	+	0.501064i	0.310325	+	0.0326165i
$237$	−0.0689535	−	0.435355i	−0.00447901	−	0.0282794i
$238$	3.52661	+	11.5530i	0.228596	+	0.748867i
$239$	1.88350	−	0.611986i	0.121833	−	0.0395861i	−0.247466	−	0.968897i	$-0.579598\pi$
$239$	1.88350	−	0.611986i	0.121833	−	0.0395861i	0.369299	+	0.929311i	$0.379598\pi$
$240$	0.0626748	+	0.0604489i	0.00404564	+	0.00390196i
$241$	5.66639	+	3.27149i	0.365004	+	0.210735i	0.671274	−	0.741210i	$-0.265748\pi$
$241$	5.66639	+	3.27149i	0.365004	+	0.210735i	−0.306270	+	0.951945i	$0.599081\pi$
$242$	−9.68410	+	5.21711i	−0.622518	+	0.335368i
$243$	1.01491	+	0.271944i	0.0651065	+	0.0174452i
$244$	−6.93289	+	5.03704i	−0.443833	+	0.322463i
$245$	−9.42295	+	12.4983i	−0.602010	+	0.798488i
$246$	0.0385141	−	0.118534i	0.00245557	−	0.00755746i
$247$	−7.24573	−	8.94773i	−0.461035	−	0.569330i
$248$	−0.600196	+	1.56356i	−0.0381125	+	0.0992864i
$249$	−0.268790	+	0.242019i	−0.0170339	+	0.0153374i
$250$	−2.30407	+	10.9403i	−0.145722	+	0.691928i
$251$	−7.32051	−	10.0758i	−0.462066	−	0.635980i	0.512869	−	0.858467i	$-0.328583\pi$
$251$	−7.32051	−	10.0758i	−0.462066	−	0.635980i	−0.974936	+	0.222487i	$0.928583\pi$
$252$	−6.50050	+	4.54750i	−0.409493	+	0.286466i
$253$	3.69360	−	18.4116i	0.232215	−	1.15753i
$254$	−15.5160	+	8.95818i	−0.973562	+	0.562086i
$255$	0.340636	−	0.204964i	0.0213315	−	0.0128353i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	3.23662	+	2.10189i	0.201895	+	0.131112i	0.641627	−	0.767017i	$-0.278260\pi$
$257$	3.23662	+	2.10189i	0.201895	+	0.131112i	−0.439732	+	0.898129i	$0.644926\pi$
$258$	0.130107	−	0.0206070i	0.00810013	−	0.00128293i
$259$	11.4623	+	3.29215i	0.712235	+	0.204565i
$260$	5.48559	+	4.28031i	0.340202	+	0.265453i
$261$	15.1883	−	16.8683i	0.940130	−	1.04412i
$262$	5.79225	−	7.15283i	0.357846	−	0.441903i
$263$	26.9074	−	7.20983i	1.65918	−	0.444577i	0.697020	−	0.717051i	$-0.254509\pi$
$263$	26.9074	−	7.20983i	1.65918	−	0.444577i	0.962163	+	0.272474i	$0.0878420\pi$
$264$	0.0216641	+	0.127324i	0.00133333	+	0.00783628i
$265$	−3.88464	+	10.6937i	−0.238631	+	0.656908i
$266$	9.76545	+	0.687124i	0.598758	+	0.0421303i
$267$	−0.128963	−	0.0657101i	−0.00789243	−	0.00402139i
$268$	3.24159	+	2.10511i	0.198012	+	0.128590i
$269$	−15.1247	+	6.73396i	−0.922170	+	0.410577i	−0.812214	−	0.583360i	$-0.801738\pi$
$269$	−15.1247	+	6.73396i	−0.922170	+	0.410577i	−0.109956	+	0.993936i	$0.535071\pi$
$270$	0.394416	+	0.342429i	0.0240034	+	0.0208396i
$271$	1.48499	+	6.98633i	0.0902068	+	0.424389i	0.999957	+	0.00923427i	$0.00293940\pi$
$271$	1.48499	+	6.98633i	0.0902068	+	0.424389i	−0.909751	+	0.415155i	$0.863727\pi$
$272$	−2.07270	+	4.06791i	−0.125676	+	0.246653i
$273$	0.242047	−	0.210224i	0.0146494	−	0.0127233i
$274$			15.4075i			0.930803i
$275$	−12.3763	+	11.0376i	−0.746316	+	0.665592i
$276$	−0.190944	−	0.110242i	−0.0114935	−	0.00663577i
$277$	−6.56827	−	5.31888i	−0.394649	−	0.319581i	0.411372	−	0.911468i	$-0.365050\pi$
$277$	−6.56827	−	5.31888i	−0.394649	−	0.319581i	−0.806021	+	0.591887i	$0.798383\pi$
$278$	−0.259013	−	4.94227i	−0.0155346	−	0.296418i
$279$	−1.55184	+	4.77608i	−0.0929065	+	0.285937i
$280$	−5.84307	+	0.926585i	−0.349190	+	0.0553740i
$281$	−16.5509	−	12.0250i	−0.987345	−	0.717348i	−0.0280073	−	0.999608i	$-0.508916\pi$
$281$	−16.5509	−	12.0250i	−0.987345	−	0.717348i	−0.959338	+	0.282259i	$0.908916\pi$
$282$	0.239733	−	0.369156i	0.0142759	−	0.0219829i
$283$	−8.19059	+	5.31903i	−0.486880	+	0.316184i	−0.764630	−	0.644470i	$-0.777078\pi$
$283$	−8.19059	+	5.31903i	−0.486880	+	0.316184i	0.277750	+	0.960654i	$0.410411\pi$
$284$	−9.00882	+	0.946865i	−0.534575	+	0.0561861i
$285$	−0.0561456	−	0.317261i	−0.00332578	−	0.0187929i
$286$	2.78509	+	9.93737i	0.164686	+	0.587609i
$287$	4.85395	+	6.93857i	0.286520	+	0.409571i
$288$	−2.96157	−	0.469066i	−0.174512	−	0.0276400i
$289$	2.85661	+	2.57211i	0.168036	+	0.151300i
$290$	15.6905	−	6.35075i	0.921378	−	0.372929i
$291$	−0.448929	+	0.199876i	−0.0263167	+	0.0117169i
$292$	4.57930	−	3.70825i	0.267983	−	0.217009i
$293$	−10.5408	−	20.6874i	−0.615799	−	1.20857i	−0.962674	−	0.270662i	$-0.912757\pi$
$293$	−10.5408	−	20.6874i	−0.615799	−	1.20857i	0.346876	−	0.937911i	$-0.387243\pi$
$294$	−0.00974967	+	0.272416i	−0.000568613	+	0.0158876i
$295$	9.37805	+	5.19070i	0.546011	+	0.302214i
$296$	2.25375	+	3.90362i	0.130997	+	0.226893i
$297$	0.169745	+	0.755906i	0.00984962	+	0.0438621i
$298$	−13.3481	+	3.57660i	−0.773233	+	0.207187i
$299$	−16.0949	−	7.16591i	−0.930792	−	0.414415i
$300$	0.0763016	+	0.179134i	0.00440527	+	0.0103423i
$301$	−4.20515	+	7.90047i	−0.242381	+	0.455376i
$302$	−7.17673	+	1.13668i	−0.412974	+	0.0654087i
$303$	0.218024	−	0.176552i	0.0125251	−	0.0101427i
$304$	2.47586	+	2.74972i	0.142000	+	0.157707i
$305$	−18.6682	+	4.32215i	−1.06894	+	0.247486i
$306$	−5.56807	+	12.5061i	−0.318306	+	0.714926i
$307$	19.2422	+	19.2422i	1.09821	+	1.09821i	0.994620	+	0.103589i	$0.0330326\pi$
$307$	19.2422	+	19.2422i	1.09821	+	1.09821i	0.103589	+	0.994620i	$0.466967\pi$
$308$	−7.79276	−	4.03396i	−0.444034	−	0.229856i
$309$		−	0.530647i		−	0.0301874i
$310$	−2.59980	+	2.69553i	−0.147659	+	0.153096i
$311$	1.37345	−	6.46156i	0.0778810	−	0.366401i	−0.921898	−	0.387433i	$-0.873362\pi$
$311$	1.37345	−	6.46156i	0.0778810	−	0.366401i	0.999779	+	0.0210319i	$0.00669515\pi$
$312$	0.121007	+	0.00634173i	0.00685069	+	0.000359030i
$313$	10.6577	+	13.1611i	0.602406	+	0.743910i	0.983556	−	0.180603i	$-0.0578051\pi$
$313$	10.6577	+	13.1611i	0.602406	+	0.743910i	−0.381150	+	0.924513i	$0.624472\pi$
$314$	−6.98669	−	5.07613i	−0.394282	−	0.286462i
$315$	−17.3509	+	3.69149i	−0.977614	+	0.207992i
$316$	3.49779	+	10.7651i	0.196766	+	0.605584i
$317$	−4.85454	+	1.86348i	−0.272658	+	0.104664i	−0.490855	−	0.871241i	$-0.663316\pi$
$317$	−4.85454	+	1.86348i	−0.272658	+	0.104664i	0.218197	+	0.975905i	$0.429982\pi$
$318$	0.0512822	+	0.191388i	0.00287576	+	0.0107325i
$319$	24.3242	+	6.21991i	1.36189	+	0.348248i
$320$	−1.83248	−	1.28141i	−0.102439	−	0.0716332i
$321$	−0.143761	−	0.197870i	−0.00802394	−	0.0110440i
$322$	13.7917	−	5.84718i	0.768582	−	0.325850i
$323$	15.0517	−	7.66924i	0.837501	−	0.426728i
$324$	−8.93713	−	0.939330i	−0.496507	−	0.0521850i
$325$	7.55981	+	13.5983i	0.419343	+	0.754296i
$326$	−15.0649	−	16.7313i	−0.834369	−	0.926661i
$327$	−0.608231	+	0.0318760i	−0.0336353	+	0.00176275i
$328$	−0.500676	+	3.16115i	−0.0276452	+	0.174545i
$329$	10.2162	+	28.1066i	0.563236	+	1.54957i
$330$	−0.0664770	+	0.281043i	−0.00365944	+	0.0154709i
$331$	−2.65779	−	4.60343i	−0.146085	−	0.253027i	0.783692	−	0.621150i	$-0.213334\pi$
$331$	−2.65779	−	4.60343i	−0.146085	−	0.253027i	−0.929777	+	0.368122i	$0.880001\pi$
$332$	5.84519	−	7.21820i	0.320796	−	0.396150i
$333$	7.36117	+	11.3352i	0.403390	+	0.621166i
$334$	7.52531	−	1.59956i	0.411767	−	0.0875238i
$335$	4.83742	+	7.16214i	0.264297	+	0.391310i
$336$	−0.0741443	+	0.0715381i	−0.00404490	+	0.00390273i
$337$	−13.3513	−	26.2035i	−0.727293	−	1.42739i	−0.897060	−	0.441909i	$-0.854301\pi$
$337$	−13.3513	−	26.2035i	−0.727293	−	1.42739i	0.169767	−	0.985484i	$-0.445699\pi$
$338$	−3.31291	+	0.173622i	−0.180199	+	0.00944380i
$339$	0.0673398	+	0.640696i	0.00365740	+	0.0347978i
$340$	−7.81631	+	6.56697i	−0.423899	+	0.356144i
$341$	−5.47600	+	0.931732i	−0.296542	+	0.0504561i
$342$	7.84517	+	7.84517i	0.424218	+	0.424218i
$343$	−14.3778	−	11.6739i	−0.776326	−	0.630331i
$344$	−3.21718	+	1.04533i	−0.173459	+	0.0563602i
$345$	−0.296950	−	0.393555i	−0.0159872	−	0.0211883i
$346$	−4.10405	−	9.21784i	−0.220635	−	0.495554i
$347$	6.37945	−	16.6190i	0.342467	−	0.892157i	−0.648880	−	0.760890i	$-0.724762\pi$
$347$	6.37945	−	16.6190i	0.342467	−	0.892157i	0.991347	−	0.131266i	$-0.0419042\pi$
$348$	0.160552	−	0.247229i	0.00860652	−	0.0132529i
$349$	0.624555	+	1.92218i	0.0334317	+	0.102892i	0.966380	−	0.257119i	$-0.0827731\pi$
$349$	0.624555	+	1.92218i	0.0334317	+	0.102892i	−0.932948	+	0.360011i	$0.882773\pi$
$350$	−12.8384	−	3.18990i	−0.686241	−	0.170507i
$351$	0.726857			0.0387967
$352$	−1.06096	−	3.14235i	−0.0565492	−	0.167488i
$353$	−0.967545	−	3.61093i	−0.0514972	−	0.192190i	0.935385	−	0.353630i	$-0.115053\pi$
$353$	−0.967545	−	3.61093i	−0.0514972	−	0.192190i	−0.986883	+	0.161440i	$0.948386\pi$
$354$	0.185646	−	0.0195122i	0.00986697	−	0.00103706i
$355$	−19.3739	−	5.91000i	−1.02826	−	0.313670i
$356$	3.53492	+	1.14856i	0.187350	+	0.0608738i
$357$	0.227868	+	0.411505i	0.0120600	+	0.0217792i
$358$	0.867724	+	5.47859i	0.0458606	+	0.289553i
$359$	0.204543	+	0.962299i	0.0107954	+	0.0507882i	0.983216	−	0.182448i	$-0.0584020\pi$
$359$	0.204543	+	0.962299i	0.0107954	+	0.0507882i	−0.972420	+	0.233236i	$0.925069\pi$
$360$	−5.68822	−	3.54947i	−0.299795	−	0.187073i
$361$	0.554956	+	5.28005i	0.0292082	+	0.277897i
$362$	−1.04439	+	3.89773i	−0.0548921	+	0.204860i
$363$	−0.326633	+	0.277129i	−0.0171438	+	0.0145455i
$364$	−5.29463	+	6.30434i	−0.277514	+	0.330437i
$365$	12.6633	−	3.63967i	0.662825	−	0.190509i
$366$	−0.223296	+	0.247995i	−0.0116718	+	0.0129629i
$367$	−1.31293	+	25.0522i	−0.0685343	+	1.30771i	0.720539	+	0.693414i	$0.243894\pi$
$367$	−1.31293	+	25.0522i	−0.0685343	+	1.30771i	−0.789074	+	0.614299i	$0.789439\pi$
$368$	5.28585	+	2.02905i	0.275544	+	0.105771i
$369$	−1.00314	+	9.54422i	−0.0522213	+	0.496852i
$370$	1.23457	+	10.0032i	0.0641821	+	0.520042i
$371$	−12.4795	−	5.04834i	−0.647903	−	0.262097i
$372$	−0.0102026	+	0.0644164i	−0.000528978	+	0.00333984i
$373$	−4.99087	+	18.6262i	−0.258418	+	0.964428i	0.707740	+	0.706473i	$0.249715\pi$
$373$	−4.99087	+	18.6262i	−0.258418	+	0.964428i	−0.966157	+	0.257954i	$0.916952\pi$
$374$	−15.1113	+	0.965634i	−0.781386	+	0.0499318i
$375$	0.000813970		0.435378i	4.20332e−5		0.0224828i
$376$	−4.59747	+	10.3261i	−0.237096	+	0.532527i
$377$	10.6939	−	20.9880i	0.550765	−	1.08094i
$378$	−0.421685	+	0.451809i	−0.0216892	+	0.0232385i
$379$	−7.99904	+	11.0097i	−0.410883	+	0.565532i	−0.963434	−	0.267947i	$-0.913655\pi$
$379$	−7.99904	+	11.0097i	−0.410883	+	0.565532i	0.552550	+	0.833479i	$0.313655\pi$
$380$	2.69853	+	7.82127i	0.138432	+	0.401223i
$381$	−0.518485	+	0.466846i	−0.0265628	+	0.0239172i
$382$	−8.35134	+	5.42342i	−0.427292	+	0.277486i
$383$	0.347393	−	0.133352i	0.0177510	−	0.00681396i	−0.349476	−	0.936945i	$-0.613640\pi$
$383$	0.347393	−	0.133352i	0.0177510	−	0.00681396i	0.367227	+	0.930131i	$0.380307\pi$
$384$	−0.0389415			−0.00198722
$385$	−12.5249	−	15.1039i	−0.638327	−	0.769766i
$386$	21.6711			1.10303
$387$	−9.46940	+	3.63496i	−0.481357	+	0.184776i
$388$	10.5834	−	6.87295i	0.537292	−	0.348921i
$389$	23.5969	−	21.2468i	1.19641	−	1.07725i	0.201195	−	0.979551i	$-0.435517\pi$
$389$	23.5969	−	21.2468i	1.19641	−	1.07725i	0.995216	−	0.0977020i	$-0.0311492\pi$
$390$	0.243604	+	0.118626i	0.0123354	+	0.00600685i
$391$	15.1940	−	20.9127i	0.768394	−	1.05760i
$392$	−0.847056	−	6.94856i	−0.0427828	−	0.350955i
$393$	0.162718	−	0.319351i	0.00820802	−	0.0161091i
$394$	3.40517	−	7.64813i	0.171550	−	0.385307i
$395$	−2.19022	+	25.2153i	−0.110202	+	1.26872i
$396$	−3.67003	−	9.24288i	−0.184426	−	0.464472i
$397$	−8.89052	+	33.1799i	−0.446202	+	1.66525i	0.266540	+	0.963824i	$0.414120\pi$
$397$	−8.89052	+	33.1799i	−0.446202	+	1.66525i	−0.712742	+	0.701426i	$0.752547\pi$
$398$	−3.00800	+	18.9918i	−0.150777	+	0.951972i
$399$	0.377534	−	0.0528919i	0.0189004	−	0.00264791i
$400$	−2.65488	−	4.23693i	−0.132744	−	0.211847i
$401$	0.242161	−	2.30401i	0.0120929	−	0.115057i	−0.986810	−	0.161882i	$-0.948244\pi$
$401$	0.242161	−	2.30401i	0.0120929	−	0.115057i	0.998903	+	0.0468251i	$0.0149104\pi$
$402$	0.140518	+	0.0539397i	0.00700838	+	0.00269027i
$403$	−0.272746	+	5.20431i	−0.0135865	+	0.259245i
$404$	−4.82059	+	5.35380i	−0.239833	+	0.266362i
$405$	−17.5808	−	9.73086i	−0.873595	−	0.483530i
$406$	6.84192	+	18.8234i	0.339559	+	0.934192i
$407$	−7.32607	+	13.0316i	−0.363140	+	0.645953i
$408$	−0.0460149	+	0.171730i	−0.00227808	+	0.00850191i
$409$	−3.48125	−	33.1219i	−0.172137	−	1.63777i	−0.650427	−	0.759569i	$-0.725410\pi$
$409$	−3.48125	−	33.1219i	−0.172137	−	1.63777i	0.478291	−	0.878202i	$-0.341257\pi$
$410$	−3.78866	+	6.07154i	−0.187109	+	0.299852i
$411$	0.124745	+	0.586881i	0.00615324	+	0.0289487i
$412$	2.13170	+	13.4590i	0.105021	+	0.663077i
$413$	−6.53673	+	10.8683i	−0.321651	+	0.534792i
$414$	16.1462	+	5.24623i	0.793544	+	0.257838i
$415$	18.3317	−	9.76179i	0.899867	−	0.479187i
$416$	−3.09463	+	0.325259i	−0.151727	+	0.0159471i
$417$	−0.0498805	−	0.186157i	−0.00244266	−	0.00911613i
$418$	−3.65829	+	11.7139i	−0.178933	+	0.572948i
$419$	−32.4719			−1.58636			−0.793178	−	0.608990i	$-0.791575\pi$
$419$	−32.4719			−1.58636			−0.793178	+	0.608990i	$0.791575\pi$
$420$	−0.215064	+	0.0826019i	−0.0104940	+	0.00403056i
$421$	−1.45241	−	4.47005i	−0.0707860	−	0.217857i	0.909405	−	0.415912i	$-0.136538\pi$
$421$	−1.45241	−	4.47005i	−0.0707860	−	0.217857i	−0.980191	+	0.198055i	$0.936538\pi$
$422$	−6.66267	+	10.2596i	−0.324334	+	0.499430i
$423$	−12.1461	+	31.6416i	−0.590563	+	1.53847i
$424$	−2.06953	−	4.64824i	−0.100505	−	0.225738i
$425$	−21.8218	+	6.70134i	−1.05851	+	0.325063i
$426$	−0.335485	+	0.109006i	−0.0162543	+	0.00528134i
$427$	−4.31652	−	22.2581i	−0.208891	−	1.07715i
$428$	4.44113	+	4.44113i	0.214670	+	0.214670i
$429$	0.186543	+	0.355970i	0.00900636	+	0.0171864i
$430$	−7.53567	−	0.654554i	−0.363402	−	0.0315654i
$431$	0.449119	+	4.27308i	0.0216333	+	0.205827i	0.999999	−	0.00105381i	$-0.000335438\pi$
$431$	0.449119	+	4.27308i	0.0216333	+	0.205827i	−0.978366	+	0.206881i	$0.933669\pi$
$432$	−0.233270	+	0.0122252i	−0.0112232	+	0.000588183i
$433$	5.82074	+	11.4239i	0.279727	+	0.548995i	0.987533	−	0.157412i	$-0.0503149\pi$
$433$	5.82074	+	11.4239i	0.279727	+	0.548995i	−0.707806	+	0.706407i	$0.750315\pi$
$434$	−3.07673	−	3.18881i	−0.147688	−	0.153068i
$435$	0.546242	−	0.368940i	0.0261903	−	0.0176893i
$436$	15.2988	−	3.25185i	0.732677	−	0.155735i
$437$	−11.4101	−	17.5699i	−0.545817	−	0.840484i
$438$	0.144405	−	0.178325i	0.00689992	−	0.00852069i
$439$	5.93307	+	10.2764i	0.283170	+	0.490465i	0.972164	−	0.234302i	$-0.0752805\pi$
$439$	5.93307	+	10.2764i	0.283170	+	0.490465i	−0.688994	+	0.724767i	$0.741947\pi$
$440$	0.557087	−	7.39525i	0.0265581	−	0.352554i
$441$	−3.62683	−	20.6737i	−0.172706	−	0.984460i
$442$	−2.22237	+	14.0315i	−0.105708	+	0.667411i
$443$	13.1158	−	0.687368i	0.623149	−	0.0326579i	0.261851	−	0.965108i	$-0.415667\pi$
$443$	13.1158	−	0.687368i	0.623149	−	0.0326579i	0.361298	+	0.932450i	$0.382334\pi$
$444$	0.117452	+	0.130444i	0.00557402	+	0.00619058i
$445$	6.27585	+	5.44865i	0.297504	+	0.258291i
$446$	26.1770	+	2.75131i	1.23952	+	0.130278i
$447$	−0.479477	+	0.244306i	−0.0226785	+	0.0115553i
$448$	1.59317	−	2.11230i	0.0752702	−	0.0997968i
$449$	12.2765	+	16.8972i	0.579365	+	0.797428i	0.993626	−	0.112731i	$-0.0359597\pi$
$449$	12.2765	+	16.8972i	0.579365	+	0.797428i	−0.414260	+	0.910158i	$0.635960\pi$
$450$	−8.61460	−	12.2703i	−0.406096	−	0.578429i
$451$	−9.86575	+	3.91735i	−0.464560	+	0.184461i
$452$	−4.28175	−	15.9797i	−0.201396	−	0.751622i
$453$	−0.264162	+	0.101402i	−0.0124114	+	0.00476430i
$454$	−7.65898	−	23.5719i	−0.359454	−	1.10629i
$455$	−16.4009	+	8.36059i	−0.768886	+	0.391950i
$456$	0.116570	+	0.0846929i	0.00545888	+	0.00396611i
$457$	−11.3914	−	14.0672i	−0.532867	−	0.658036i	0.437629	−	0.899156i	$-0.355818\pi$
$457$	−11.3914	−	14.0672i	−0.532867	−	0.658036i	−0.970495	+	0.241120i	$0.922485\pi$
$458$	23.9584	+	1.25561i	1.11950	+	0.0586707i
$459$	−0.221729	+	1.04315i	−0.0103494	+	0.0486903i
$460$	9.11263	+	8.78899i	0.424878	+	0.409789i
$461$			5.86940i			0.273365i	0.990615	+	0.136683i	$0.0436441\pi$
$461$			5.86940i			0.273365i	−0.990615	+	0.136683i	$0.956356\pi$
$462$	−0.329491	−	0.0905624i	−0.0153293	−	0.00421334i
$463$	12.6579	+	12.6579i	0.588260	+	0.588260i	0.937160	−	0.348900i	$-0.113445\pi$
$463$	12.6579	+	12.6579i	0.588260	+	0.588260i	−0.348900	+	0.937160i	$0.613445\pi$
$464$	−3.07899	+	6.91553i	−0.142939	+	0.321046i
$465$	−0.0772037	+	0.123723i	−0.00358023	+	0.00573752i
$466$	4.79771	+	5.32839i	0.222250	+	0.246833i
$467$	−15.3521	+	12.4319i	−0.710410	+	0.575278i	−0.914944	−	0.403581i	$-0.867765\pi$
$467$	−15.3521	+	12.4319i	−0.710410	+	0.575278i	0.204534	+	0.978859i	$0.434432\pi$
$468$	−9.21545	+	1.45958i	−0.425984	+	0.0674693i
$469$	−8.67468	+	5.41531i	−0.400560	+	0.250056i
$470$	−18.4742	+	17.2490i	−0.852151	+	0.795637i
$471$	−0.307225	−	0.136785i	−0.0141562	−	0.00630274i
$472$	−4.63023	+	1.24067i	−0.213124	+	0.0571063i
$473$	−8.42301	−	7.41118i	−0.387290	−	0.340766i
$474$	0.220391	+	0.381729i	0.0101229	+	0.0175334i
$475$	−1.26753	+	18.4571i	−0.0581584	+	0.846870i
$476$	−7.43258	−	9.52179i	−0.340672	−	0.436430i
$477$	−6.92638	−	13.5938i	−0.317137	−	0.622417i
$478$	−1.53908	+	1.24632i	−0.0703959	+	0.0570055i
$479$	1.56433	−	0.696486i	0.0714763	−	0.0318233i	−0.370687	−	0.928758i	$-0.620878\pi$
$479$	1.56433	−	0.696486i	0.0714763	−	0.0318233i	0.442163	+	0.896935i	$0.354211\pi$
$480$	−0.0801749	−	0.0339733i	−0.00365947	−	0.00155066i
$481$	10.4233	+	9.38517i	0.475261	+	0.427927i
$482$	−6.46243	−	1.02355i	−0.294355	−	0.0466213i
$483$	0.477993	−	0.334385i	0.0217494	−	0.0152151i
$484$	7.17124	−	8.34106i	0.325966	−	0.379139i
$485$	27.7858	−	4.91725i	1.26169	−	0.223281i
$486$	−1.04496	+	0.109829i	−0.0474002	+	0.00498196i
$487$	−0.0697665	+	0.0453069i	−0.00316142	+	0.00205305i	−0.546219	−	0.837643i	$-0.683933\pi$
$487$	−0.0697665	+	0.0453069i	−0.00316142	+	0.00205305i	0.543057	+	0.839696i	$0.317267\pi$
$488$	4.66730	−	7.18700i	0.211279	−	0.325340i
$489$	−0.709294	−	0.515332i	−0.0320754	−	0.0233041i
$490$	4.31809	−	15.0451i	0.195071	−	0.679667i
$491$	−10.4662	+	32.2117i	−0.472333	+	1.45369i	0.377188	+	0.926137i	$0.376891\pi$
$491$	−10.4662	+	32.2117i	−0.472333	+	1.45369i	−0.849521	+	0.527555i	$0.823109\pi$
$492$	0.00652285	+	0.124463i	0.000294073	+	0.00561124i
$493$	26.8589	+	21.7499i	1.20966	+	0.979567i
$494$	9.97105	+	5.75679i	0.448619	+	0.259010i
$495$	0.507602	−	22.2316i	0.0228150	−	0.999234i
$496$		−	1.67480i		−	0.0752009i
$497$	7.81253	−	22.6573i	0.350440	−	1.01632i
$498$	0.164205	−	0.322270i	0.00735820	−	0.0144413i
$499$	−4.58300	−	21.5613i	−0.205163	−	0.965218i	−0.953382	−	0.301766i	$-0.902424\pi$
$499$	−4.58300	−	21.5613i	−0.205163	−	0.965218i	0.748219	−	0.663452i	$-0.230909\pi$
$500$	−1.76963	−	11.0394i	−0.0791404	−	0.493697i
$501$	0.273693	−	0.121856i	0.0122277	−	0.00544412i
$502$	10.4451	+	6.78315i	0.466189	+	0.302747i
$503$	8.36426	+	4.26180i	0.372944	+	0.190024i	0.630409	−	0.776263i	$-0.282887\pi$
$503$	8.36426	+	4.26180i	0.372944	+	0.190024i	−0.257465	+	0.966288i	$0.582887\pi$
$504$	4.43907	−	6.57503i	0.197732	−	0.292875i
$505$	−14.5956	+	6.81714i	−0.649498	+	0.303359i
$506$	3.14986	+	18.5124i	0.140028	+	0.822976i
$507$	−0.124785	+	0.0334360i	−0.00554189	+	0.00148494i
$508$	11.2751	−	13.9236i	0.500253	−	0.617761i
$509$	29.6016	−	32.8759i	1.31207	−	1.45720i	0.509723	−	0.860339i	$-0.329748\pi$
$509$	29.6016	−	32.8759i	1.31207	−	1.45720i	0.802345	−	0.596860i	$-0.203585\pi$
$510$	−0.244559	+	0.313423i	−0.0108292	+	0.0138786i
$511$	3.76499	+	15.1285i	0.166554	+	0.669247i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	0.724871	+	0.470737i	0.0320039	+	0.0207835i
$514$	−3.77490	−	0.802379i	−0.166504	−	0.0353914i
$515$	−7.35302	+	29.5699i	−0.324013	+	1.30300i
$516$	−0.114081	+	0.0658646i	−0.00502213	+	0.00289953i
$517$	−37.2361	+	4.34546i	−1.63764	+	0.191113i
$518$	−11.8808	+	1.03424i	−0.522013	+	0.0454420i
$519$	−0.230957	−	0.317884i	−0.0101379	−	0.0139536i
$520$	−6.65516	−	2.03015i	−0.291848	−	0.0890281i
$521$	−28.5115	+	25.6719i	−1.24911	+	1.12471i	−0.261933	+	0.965086i	$0.584360\pi$
$521$	−28.5115	+	25.6719i	−1.24911	+	1.12471i	−0.987179	+	0.159619i	$0.948973\pi$
$522$	−8.13442	+	21.1909i	−0.356034	+	0.927500i
$523$	−23.8611	−	29.4660i	−1.04337	−	1.28846i	−0.956342	−	0.292251i	$-0.905596\pi$
$523$	−23.8611	−	29.4660i	−1.04337	−	1.28846i	−0.0870295	−	0.996206i	$-0.527737\pi$
$524$	−2.84418	+	8.75350i	−0.124249	+	0.382398i
$525$	−0.514848	−	0.0175601i	−0.0224698	−	0.000766385i
$526$	−22.5365	+	16.3737i	−0.982637	+	0.713928i
$527$	−7.38580	−	1.97902i	−0.321731	−	0.0862075i
$528$	−0.0658541	−	0.111104i	−0.00286593	−	0.00483518i
$529$	−7.84384	−	4.52864i	−0.341036	−	0.196897i
$530$	−0.205652	−	11.3755i	−0.00893296	−	0.494122i
$531$	−13.6699	+	4.44163i	−0.593225	+	0.192750i
$532$	−9.36307	+	2.85814i	−0.405941	+	0.123916i
$533$	1.55794	+	9.83647i	0.0674820	+	0.426065i
$534$	0.143946	+	0.0151293i	0.00622916	+	0.000654711i
$535$	5.26913	+	13.0182i	0.227804	+	0.562825i
$536$	−3.78069	−	0.803610i	−0.163301	−	0.0347107i
$537$	0.0774089	+	0.201657i	0.00334044	+	0.00870214i
$538$	11.7069	−	11.7069i	0.504720	−	0.504720i
$539$	18.3925	−	14.1675i	0.792219	−	0.610236i
$540$	−0.490934	−	0.178339i	−0.0211264	−	0.00767449i
$541$	29.6907	+	13.2192i	1.27650	+	0.568337i	0.929256	−	0.369437i	$-0.120449\pi$
$541$	29.6907	+	13.2192i	1.27650	+	0.568337i	0.347249	+	0.937773i	$0.387116\pi$
$542$	−3.89004	−	5.99013i	−0.167091	−	0.257298i
$543$	−0.00822396	+	0.156922i	−0.000352924	+	0.00673419i
$544$	0.477227	−	4.54051i	0.0204609	−	0.194673i
$545$	34.3349	+	6.65182i	1.47075	+	0.284933i
$546$	−0.150633	+	0.283003i	−0.00644649	+	0.0121114i
$547$	−20.8831	−	10.6405i	−0.892898	−	0.454954i	−0.0535606	−	0.998565i	$-0.517057\pi$
$547$	−20.8831	−	10.6405i	−0.892898	−	0.454954i	−0.839338	+	0.543610i	$0.817057\pi$
$548$	−5.52157	−	14.3842i	−0.235870	−	0.614461i
$549$	12.8478	−	22.2530i	0.548330	−	0.949735i
$550$	7.59871	−	14.7397i	0.324010	−	0.628504i
$551$	24.2573	−	14.0049i	1.03339	−	0.596630i
$552$	0.217769	+	0.0344912i	0.00926886	+	0.00146804i
$553$	−29.7227	−	3.66258i	−1.26394	−	0.155749i
$554$	8.03813	+	2.61175i	0.341507	+	0.110962i
$555$	0.128015	+	0.371032i	0.00543394	+	0.0157494i
$556$	2.01296	+	4.52119i	0.0853686	+	0.191741i
$557$	32.6586	+	1.71156i	1.38379	+	0.0725212i	0.729632	−	0.683840i	$-0.239691\pi$
$557$	32.6586	+	1.71156i	1.38379	+	0.0725212i	0.654155	+	0.756361i	$0.273024\pi$
$558$	−0.262824	−	5.01499i	−0.0111262	−	0.212301i
$559$	−8.51573	+	6.18704i	−0.360177	+	0.261684i
$560$	5.12292	−	2.95901i	0.216483	−	0.125041i
$561$	−0.567779	+	0.159128i	−0.0239716	+	0.00671841i
$562$	19.7610	+	5.29494i	0.833567	+	0.223353i
$563$	−25.0046	−	20.2484i	−1.05382	−	0.853367i	−0.0643243	−	0.997929i	$-0.520489\pi$
$563$	−25.0046	−	20.2484i	−1.05382	−	0.853367i	−0.989496	+	0.144562i	$0.953823\pi$
$564$	−0.0915160	+	0.430549i	−0.00385352	+	0.0181294i
$565$	5.12549	−	36.6354i	0.215631	−	1.54126i
$566$	5.74041	−	7.90099i	0.241287	−	0.332103i
$567$	12.2542	−	20.3744i	0.514628	−	0.855644i
$568$	8.07113	−	4.11245i	0.338657	−	0.172555i
$569$	9.30809	+	8.38104i	0.390215	+	0.351352i	0.840765	−	0.541400i	$-0.182105\pi$
$569$	9.30809	+	8.38104i	0.390215	+	0.351352i	−0.450550	+	0.892751i	$0.648772\pi$
$570$	0.166113	+	0.276068i	0.00695769	+	0.0115632i
$571$	11.1745	−	19.3548i	0.467639	−	0.809974i	−0.531678	−	0.846947i	$-0.678438\pi$
$571$	11.1745	−	19.3548i	0.467639	−	0.809974i	0.999316	+	0.0369728i	$0.0117715\pi$
$572$	−6.16134	−	8.27924i	−0.257619	−	0.346172i
$573$	−0.274197	+	0.274197i	−0.0114547	+	0.0114547i
$574$	−7.01812	−	4.73821i	−0.292931	−	0.197769i
$575$	11.0939	+	26.0453i	0.462648	+	1.08616i
$576$	2.93296	−	0.623420i	0.122207	−	0.0259758i
$577$	21.5587	+	8.27560i	0.897499	+	0.344518i	0.763002	−	0.646396i	$-0.223725\pi$
$577$	21.5587	+	8.27560i	0.897499	+	0.344518i	0.134497	+	0.990914i	$0.457058\pi$
$578$	−3.58864	−	1.37755i	−0.149268	−	0.0572985i
$579$	0.825463	−	0.175457i	0.0343051	−	0.00729176i
$580$	−12.3724	+	11.5519i	−0.513738	+	0.479667i
$581$	10.7629	+	22.0916i	0.446522	+	0.916515i
$582$	0.347482	−	0.347482i	0.0144036	−	0.0144036i
$583$	9.76208	−	13.7652i	0.404304	−	0.570097i
$584$	−2.94623	+	5.10302i	−0.121916	+	0.211164i
$585$	−20.2466	−	5.03465i	−0.837095	−	0.208157i
$586$	17.2544	+	15.5359i	0.712772	+	0.641783i
$587$	−0.430046	+	0.219119i	−0.0177499	+	0.00904402i	−0.462843	−	0.886440i	$-0.653171\pi$
$587$	−0.430046	+	0.219119i	−0.0177499	+	0.00904402i	0.445093	+	0.895484i	$0.353171\pi$
$588$	−0.0885231	−	0.257816i	−0.00365063	−	0.0106322i
$589$	−3.64249	+	5.01345i	−0.150086	+	0.206576i
$590$	−10.6153	−	1.48514i	−0.437027	−	0.0611424i
$591$	0.0677823	−	0.318891i	0.00278819	−	0.0131174i
$592$	−3.50299	−	2.83667i	−0.143972	−	0.116586i
$593$	25.6900	+	6.88362i	1.05496	+	0.282676i	0.744301	−	0.667844i	$-0.232783\pi$
$593$	25.6900	+	6.88362i	1.05496	+	0.282676i	0.310661	+	0.950521i	$0.399450\pi$
$594$	−0.429363	−	0.644867i	−0.0176170	−	0.0264592i
$595$	−6.99563	−	26.0883i	−0.286793	−	1.06952i
$596$	11.1798	−	8.12257i	0.457941	−	0.332713i
$597$	0.0391885	+	0.747761i	0.00160388	+	0.0306038i
$598$	17.5939	+	0.922058i	0.719469	+	0.0377058i
$599$	10.4852	+	23.5501i	0.428412	+	0.962230i	0.990797	+	0.135354i	$0.0432173\pi$
$599$	10.4852	+	23.5501i	0.428412	+	0.962230i	−0.562385	+	0.826876i	$0.690116\pi$
$600$	−0.135430	−	0.139892i	−0.00552889	−	0.00571107i
$601$	23.0016	+	7.47369i	0.938257	+	0.304858i	0.737935	−	0.674872i	$-0.235801\pi$
$601$	23.0016	+	7.47369i	0.938257	+	0.304858i	0.200322	+	0.979730i	$0.435801\pi$
$602$	1.09457	−	8.88272i	0.0446115	−	0.362032i
$603$	−11.4469	−	1.81301i	−0.466154	−	0.0738315i
$604$	6.29270	−	3.63309i	0.256046	−	0.147828i
$605$	22.0414	−	10.9167i	0.896112	−	0.443827i
$606$	−0.140272	+	0.242959i	−0.00569817	+	0.00986952i
$607$	1.19004	+	3.10015i	0.0483021	+	0.125831i	0.955609	−	0.294638i	$-0.0951989\pi$
$607$	1.19004	+	3.10015i	0.0483021	+	0.125831i	−0.907307	+	0.420469i	$0.861866\pi$
$608$	−3.29683	−	1.67982i	−0.133704	−	0.0681256i
$609$	0.413014	+	0.661600i	0.0167362	+	0.0268094i
$610$	15.8794	−	10.7252i	0.642937	−	0.434249i
$611$	−3.67650	+	34.9796i	−0.148735	+	1.41512i
$612$	0.716460	−	13.6709i	0.0289612	−	0.552612i
$613$	8.46199	+	13.0303i	0.341777	+	0.526290i	0.967207	−	0.253990i	$-0.0817432\pi$
$613$	8.46199	+	13.0303i	0.341777	+	0.526290i	−0.625430	+	0.780280i	$0.715076\pi$
$614$	−24.8599	−	11.0683i	−1.00326	−	0.446682i
$615$	−0.0951546	+	0.261943i	−0.00383700	+	0.0105626i
$616$	8.72081	+	0.973348i	0.351372	+	0.0392173i
$617$	−12.7262	+	12.7262i	−0.512338	+	0.512338i	−0.915242	−	0.402904i	$-0.868001\pi$
$617$	−12.7262	+	12.7262i	−0.512338	+	0.512338i	0.402904	+	0.915242i	$0.368001\pi$
$618$	0.190167	+	0.495401i	0.00764963	+	0.0199280i
$619$	31.2315	+	6.63846i	1.25530	+	0.266822i	0.787114	−	0.616808i	$-0.211574\pi$
$619$	31.2315	+	6.63846i	1.25530	+	0.266822i	0.468186	+	0.883630i	$0.344908\pi$
$620$	1.46113	−	3.44818i	0.0586804	−	0.138482i
$621$	1.31532	+	0.138246i	0.0527820	+	0.00554761i
$622$	1.03339	+	6.52458i	0.0414352	+	0.261612i
$623$	−6.70976	+	7.18908i	−0.268821	+	0.288025i
$624$	−0.115243	+	0.0374446i	−0.00461340	+	0.00149899i
$625$	5.98756	−	24.2724i	0.239502	−	0.970896i
$626$	−14.6663	−	8.46759i	−0.586183	−	0.338433i
$627$	−0.0445054	+	0.475809i	−0.00177737	+	0.0190020i
$628$	8.34176	+	2.23517i	0.332872	+	0.0891929i
$629$	−16.6488	+	12.0961i	−0.663833	+	0.482303i
$630$	14.8756	−	9.66431i	0.592657	−	0.385035i
$631$	9.28058	−	28.5627i	0.369454	−	1.13706i	−0.577691	−	0.816256i	$-0.696046\pi$
$631$	9.28058	−	28.5627i	0.369454	−	1.13706i	0.947145	−	0.320806i	$-0.103954\pi$
$632$	−7.12333	−	8.79658i	−0.283351	−	0.349909i
$633$	−0.170719	+	0.444738i	−0.00678546	+	0.0176767i
$634$	3.86429	−	3.47942i	0.153471	−	0.138186i
$635$	35.3611	−	18.8301i	1.40326	−	0.747250i
$636$	−0.116463	−	0.160298i	−0.00461807	−	0.00635623i
$637$	−9.18823	−	19.7490i	−0.364051	−	0.782482i
$638$	−24.9376	+	2.91022i	−0.987289	+	0.115217i
$639$	23.5226	−	13.5808i	0.930541	−	0.537248i
$640$	2.16998	+	0.539602i	0.0857761	+	0.0213296i
$641$	26.3035	+	5.59099i	1.03893	+	0.220831i	0.695633	−	0.718397i	$-0.255124\pi$
$641$	26.3035	+	5.59099i	1.03893	+	0.220831i	0.343294	+	0.939228i	$0.388457\pi$
$642$	0.205122	+	0.133208i	0.00809553	+	0.00525730i
$643$	−7.64284	+	1.21051i	−0.301404	+	0.0477377i	−0.305305	−	0.952255i	$-0.598758\pi$
$643$	−7.64284	+	1.21051i	−0.301404	+	0.0477377i	0.00390071	+	0.999992i	$0.498758\pi$
$644$	−10.7802	+	10.4013i	−0.424801	+	0.409869i
$645$	−0.292337	+	0.0360795i	−0.0115108	+	0.00142063i
$646$	−11.3036	+	12.5539i	−0.444734	+	0.493927i
$647$	−5.87979	+	7.26094i	−0.231159	+	0.285457i	−0.879506	−	0.475887i	$-0.842127\pi$
$647$	−5.87979	+	7.26094i	−0.231159	+	0.285457i	0.648348	+	0.761344i	$0.275460\pi$
$648$	8.68015	−	2.32584i	0.340989	−	0.0913676i
$649$	−11.3699	−	11.1124i	−0.446309	−	0.436200i
$650$	−11.9309	−	9.98588i	−0.467967	−	0.391678i
$651$	−0.143012	−	0.0965532i	−0.00560508	−	0.00378422i
$652$	20.0603	+	10.2212i	0.785621	+	0.400294i
$653$	−25.5553	−	16.5958i	−1.00006	−	0.649444i	−0.0627789	−	0.998027i	$-0.519996\pi$
$653$	−25.5553	−	16.5958i	−1.00006	−	0.649444i	−0.937278	+	0.348583i	$0.886663\pi$
$654$	0.556409	−	0.247729i	0.0217573	−	0.00968699i
$655$	−13.4925	+	15.5409i	−0.527195	+	0.607232i
$656$	−0.665432	−	3.13061i	−0.0259807	−	0.122230i
$657$	−8.02131	+	15.7427i	−0.312941	+	0.614181i
$658$	−19.6101	−	22.5787i	−0.764483	−	0.880208i
$659$		−	33.7200i		−	1.31354i	−0.754089	−	0.656772i	$-0.771921\pi$
$659$		−	33.7200i		−	1.31354i	0.754089	−	0.656772i	$-0.228079\pi$
$660$	−0.0386551	−	0.286199i	−0.00150465	−	0.0111403i
$661$	−39.6823	−	22.9106i	−1.54346	−	0.891118i	−0.998617	−	0.0525804i	$-0.983255\pi$
$661$	−39.6823	−	22.9106i	−1.54346	−	0.891118i	−0.544844	−	0.838537i	$-0.683411\pi$
$662$	4.13098	+	3.34520i	0.160555	+	0.130015i
$663$	0.0289533	+	0.552461i	0.00112445	+	0.0214558i
$664$	−2.87018	+	8.83350i	−0.111385	+	0.342806i
$665$	−21.7707	−	2.28403i	−0.844232	−	0.0885708i
$666$	−10.9344	−	7.94432i	−0.423700	−	0.307836i
$667$	23.3436	−	35.9460i	0.903868	−	1.39183i
$668$	−6.45226	+	4.19014i	−0.249645	+	0.162122i
$669$	1.01937	−	0.107140i	0.0394112	−	0.00414228i
$670$	−7.08281	−	4.95286i	−0.273633	−	0.191346i
$671$	28.3981	+	1.16227i	1.09630	+	0.0448691i
$672$	0.0435827	−	0.0933575i	0.00168124	−	0.00360135i
$673$	13.1618	+	2.08463i	0.507351	+	0.0803565i	0.404862	−	0.914378i	$-0.367319\pi$
$673$	13.1618	+	2.08463i	0.507351	+	0.0803565i	0.102489	+	0.994734i	$0.467319\pi$
$674$	21.8550	+	19.6783i	0.841824	+	0.757982i
$675$	−0.855176	−	0.795474i	−0.0329158	−	0.0306178i
$676$	3.03065	−	1.34933i	0.116563	−	0.0518973i
$677$	−23.4913	+	19.0229i	−0.902844	+	0.731109i	−0.963686	−	0.267038i	$-0.913955\pi$
$677$	−23.4913	+	19.0229i	−0.902844	+	0.731109i	0.0608415	+	0.998147i	$0.480622\pi$
$678$	−0.292472	−	0.574009i	−0.0112323	−	0.0220447i
$679$	4.63229	+	33.0646i	0.177771	+	1.26890i
$680$	4.94376	−	8.93191i	0.189585	−	0.342523i
$681$	−0.482582	−	0.835857i	−0.0184926	−	0.0320301i
$682$	4.77838	−	2.83227i	0.182974	−	0.108453i
$683$	−8.18004	+	2.19183i	−0.313000	+	0.0838682i	−0.411900	−	0.911229i	$-0.635135\pi$
$683$	−8.18004	+	2.19183i	−0.313000	+	0.0838682i	0.0988991	+	0.995097i	$0.468468\pi$
$684$	−10.1355	−	4.51264i	−0.387542	−	0.172545i
$685$	1.18091	−	34.4320i	0.0451203	−	1.31558i
$686$	17.6063	+	5.74600i	0.672214	+	0.219383i
$687$	0.922755	−	0.146150i	0.0352053	−	0.00557597i
$688$	2.62889	−	2.12883i	0.100225	−	0.0811609i
$689$	−10.5941	−	11.7659i	−0.403603	−	0.448246i
$690$	0.418264	+	0.260998i	0.0159230	+	0.00993603i
$691$	3.27310	−	7.35150i	0.124515	−	0.279664i	−0.840523	−	0.541776i	$-0.817752\pi$
$691$	3.27310	−	7.35150i	0.124515	−	0.279664i	0.965038	+	0.262112i	$0.0844189\pi$
$692$	7.13484	+	7.13484i	0.271226	+	0.271226i
$693$	26.2661	+	1.54602i	0.997768	+	0.0587286i
$694$			17.8014i			0.675732i
$695$	0.200031	+	11.0646i	0.00758761	+	0.419705i
$696$	−0.0612897	+	0.288345i	−0.00232318	+	0.0109297i
$697$	−14.5921	−	0.764742i	−0.552717	−	0.0289667i
$698$	−1.27192	−	1.57069i	−0.0481429	−	0.0594516i
$699$	0.225888	+	0.164117i	0.00854387	+	0.00620748i
$700$	13.1288	−	1.62285i	0.496223	−	0.0613379i
$701$	7.22861	+	22.2474i	0.273021	+	0.840271i	0.989736	+	0.142906i	$0.0456446\pi$
$701$	7.22861	+	22.2474i	0.273021	+	0.840271i	−0.716716	+	0.697366i	$0.754355\pi$
$702$	−0.678579	+	0.260482i	−0.0256113	+	0.00983127i
$703$	4.31666	+	16.1100i	0.162806	+	0.607600i
$704$	2.11661	+	2.55342i	0.0797726	+	0.0962358i
$705$	−0.564037	+	0.806598i	−0.0212429	+	0.0303782i
$706$	2.19732	+	3.02435i	0.0826973	+	0.113823i
$707$	−7.43998	−	17.5487i	−0.279809	−	0.659985i
$708$	−0.166323	+	0.0847458i	−0.00625080	+	0.00318494i
$709$	29.6067	+	3.11179i	1.11190	+	0.116866i	0.642623	−	0.766183i	$-0.277846\pi$
$709$	29.6067	+	3.11179i	1.11190	+	0.116866i	0.469281	+	0.883049i	$0.344513\pi$
$710$	20.2051	−	1.42553i	0.758283	−	0.0534992i
$711$	−22.7104	−	25.2224i	−0.851705	−	0.945914i
$712$	−3.71174	+	0.194524i	−0.139103	+	0.00729009i
$713$	−1.48341	+	9.36585i	−0.0555540	+	0.350754i
$714$	−0.360203	−	0.302513i	−0.0134803	−	0.0113213i
$715$	−5.46235	−	22.4210i	−0.204280	−	0.838499i
$716$	−2.77344	−	4.80374i	−0.103648	−	0.179524i
$717$	−0.0485337	+	0.0599341i	−0.00181252	+	0.00223828i
$718$	−0.535815	−	0.825082i	−0.0199964	−	0.0307918i
$719$	5.10653	−	1.08543i	0.190442	−	0.0404796i	−0.111703	−	0.993742i	$-0.535631\pi$
$719$	5.10653	−	1.08543i	0.190442	−	0.0404796i	0.302145	+	0.953262i	$0.402297\pi$
$720$	6.58242	+	1.27524i	0.245312	+	0.0475253i
$721$	−34.6521	−	9.95260i	−1.29051	−	0.370654i
$722$	−2.41030	−	4.73047i	−0.0897019	−	0.176050i
$723$	−0.254444	+	0.0133349i	−0.00946288	+	0.000495929i
$724$	−0.421796	−	4.01312i	−0.0156759	−	0.149146i
$725$	−35.5512	+	12.9898i	−1.32034	+	0.482428i
$726$	0.205624	−	0.375777i	0.00763142	−	0.0139464i
$727$	10.4774	+	10.4774i	0.388585	+	0.388585i	0.874183	−	0.485597i	$-0.161398\pi$
$727$	10.4774	+	10.4774i	0.388585	+	0.388585i	−0.485597	+	0.874183i	$0.661398\pi$
$728$	2.68369	−	7.78303i	0.0994642	−	0.288458i
$729$	25.6007	−	8.31816i	0.948173	−	0.308080i
$730$	−10.5178	+	7.93604i	−0.389282	+	0.293726i
$731$	−6.28163	−	14.1088i	−0.232335	−	0.521832i
$732$	0.119591	−	0.311545i	0.00442021	−	0.0115150i
$733$	6.71501	−	10.3402i	0.248024	−	0.381924i	−0.692628	−	0.721295i	$-0.743547\pi$
$733$	6.71501	−	10.3402i	0.248024	−	0.381924i	0.940653	+	0.339371i	$0.110214\pi$
$734$	−7.75217	−	23.8587i	−0.286138	−	0.880642i
$735$	0.0426674	−	0.608036i	0.00157381	−	0.0224277i
$736$	−5.66192			−0.208701
$737$	−4.10076	−	12.1457i	−0.151053	−	0.447391i
$738$	−2.48383	−	9.26979i	−0.0914312	−	0.341226i
$739$	38.5823	−	4.05516i	1.41927	−	0.149172i	0.636403	−	0.771357i	$-0.280422\pi$
$739$	38.5823	−	4.05516i	1.41927	−	0.149172i	0.782870	+	0.622185i	$0.213755\pi$
$740$	−4.73739	−	8.89636i	−0.174150	−	0.327037i
$741$	0.426412	+	0.138550i	0.0156646	+	0.00508975i
$742$	13.4598	+	0.240783i	0.494124	+	0.00883943i
$743$	1.53122	+	9.66771i	0.0561748	+	0.354674i	0.999725	+	0.0234447i	$0.00746337\pi$
$743$	1.53122	+	9.66771i	0.0561748	+	0.354674i	−0.943550	+	0.331229i	$0.892537\pi$
$744$	−0.0135599	−	0.0637942i	−0.000497129	−	0.00233881i
$745$	30.1038	−	6.96977i	1.10292	−	0.255352i
$746$	−2.01565	−	19.1776i	−0.0737981	−	0.702142i
$747$	−7.20816	+	26.9012i	−0.263733	+	0.984264i
$748$	13.7616	−	6.31690i	0.503172	−	0.230969i
$749$	−15.6175	+	5.67664i	−0.570652	+	0.207420i
$750$	−0.156786	−	0.406169i	−0.00572500	−	0.0148312i
$751$	−23.7412	+	26.3673i	−0.866330	+	0.962157i	−0.999582	−	0.0289255i	$-0.990791\pi$
$751$	−23.7412	+	26.3673i	−0.866330	+	0.962157i	0.133252	+	0.991082i	$0.457458\pi$
$752$	0.591569	−	11.2878i	0.0215723	−	0.411624i
$753$	0.452780	+	0.173806i	0.0165002	+	0.00633384i
$754$	−2.46221	+	23.4264i	−0.0896684	+	0.853138i
$755$	16.1253	−	1.99014i	0.586861	−	0.0724288i
$756$	0.231763	−	0.572918i	0.00842915	−	0.0208368i
$757$	2.97758	−	18.7997i	0.108222	−	0.683286i	−0.872608	−	0.488421i	$-0.837573\pi$
$757$	2.97758	−	18.7997i	0.108222	−	0.683286i	0.980830	−	0.194865i	$-0.0624269\pi$
$758$	3.52221	−	13.1451i	0.127932	−	0.477451i
$759$	0.269863	+	0.679644i	0.00979541	+	0.0246695i
$760$	−5.32219	−	6.33472i	−0.193056	−	0.229784i
$761$	7.51671	−	16.8828i	0.272480	−	0.612001i	−0.724532	−	0.689241i	$-0.757944\pi$
$761$	7.51671	−	16.8828i	0.272480	−	0.612001i	0.997013	+	0.0772400i	$0.0246108\pi$
$762$	0.316745	−	0.621647i	0.0114745	−	0.0225199i
$763$	−9.32619	+	40.3163i	−0.337631	+	1.45955i
$764$	5.85306	−	8.05605i	0.211756	−	0.291458i
$765$	13.4018	−	27.5213i	0.484543	−	0.995034i
$766$	−0.276530	+	0.248989i	−0.00999145	+	0.00899634i
$767$	−12.5096	+	8.12385i	−0.451697	+	0.293335i
$768$	0.0363550	−	0.0139554i	0.00131185	−	0.000503572i
$769$	−36.4961			−1.31608			−0.658042	−	0.752981i	$-0.728615\pi$
$769$	−36.4961			−1.31608			−0.658042	+	0.752981i	$0.728615\pi$
$770$	17.1057	+	9.61218i	0.616448	+	0.346399i
$771$	−0.150284			−0.00541236
$772$	−20.2317	+	7.76622i	−0.728154	+	0.279512i
$773$	11.0177	−	7.15499i	0.396280	−	0.257347i	−0.331081	−	0.943602i	$-0.607413\pi$
$773$	11.0177	−	7.15499i	0.396280	−	0.257347i	0.727361	+	0.686255i	$0.240747\pi$
$774$	7.53780	−	6.78706i	0.270940	−	0.243956i
$775$	6.01651	−	5.82459i	0.216119	−	0.209225i
$776$	−7.41743	+	10.2092i	−0.266270	+	0.366489i
$777$	−0.444173	+	0.135587i	−0.0159346	+	0.00486414i
$778$	−14.4155	+	28.2919i	−0.516819	+	1.01431i
$779$	−4.81674	+	10.8186i	−0.172578	+	0.387616i
$780$	−0.269936	−	0.0234468i	−0.00966525	−	0.000839530i
$781$	25.3823	+	16.0732i	0.908252	+	0.575143i
$782$	−6.69036	+	24.9688i	−0.239247	+	0.892881i
$783$	−0.276619	+	1.74650i	−0.00988556	+	0.0624150i
$784$	3.28094	+	6.18348i	0.117176	+	0.220839i
$785$	15.2245	+	11.8794i	0.543385	+	0.423994i
$786$	−0.0374647	+	0.356453i	−0.00133632	+	0.0127143i
$787$	13.1284	+	5.03951i	0.467976	+	0.179639i	0.580917	−	0.813963i	$-0.302694\pi$
$787$	13.1284	+	5.03951i	0.467976	+	0.179639i	−0.112942	+	0.993602i	$0.536027\pi$
$788$	−0.438152	+	8.36044i	−0.0156085	+	0.297828i
$789$	−0.725859	+	0.806148i	−0.0258413	+	0.0286996i
$790$	−6.99161	−	24.3254i	−0.248750	−	0.865459i
$791$	43.1015	+	7.61924i	1.53251	+	0.270909i
$792$	6.73862	+	7.31375i	0.239446	+	0.259883i
$793$	6.90156	−	25.7570i	0.245082	−	0.914657i
$794$	−3.59059	−	34.1622i	−0.127425	−	1.21237i
$795$	−0.0999343	−	0.431635i	−0.00354430	−	0.0153085i
$796$	−3.99783	−	18.8083i	−0.141699	−	0.666643i
$797$	3.32820	+	21.0134i	0.117891	+	0.744333i	0.973834	+	0.227262i	$0.0729775\pi$
$797$	3.32820	+	21.0134i	0.117891	+	0.744333i	−0.855943	+	0.517071i	$0.827022\pi$
$798$	−0.333504	+	0.184675i	−0.0118059	+	0.00653743i
$799$	−49.0797	−	15.9470i	−1.73632	−	0.564163i
$800$	3.99692	+	3.00410i	0.141313	+	0.106211i
$801$	−11.0838	+	1.16495i	−0.391627	+	0.0411617i
$802$	0.599605	+	2.23776i	0.0211728	+	0.0790180i
$803$	−19.5418	+	0.223858i	−0.689615	+	0.00789979i
$804$	−0.150515			−0.00530825
$805$	−31.2693	+	12.0099i	−1.10210	+	0.423295i
$806$	−1.61043	−	4.95638i	−0.0567249	−	0.174581i
$807$	0.351139	−	0.540706i	0.0123607	−	0.0190337i
$808$	2.58177	−	6.72575i	0.0908265	−	0.236611i
$809$	−5.72346	−	12.8551i	−0.201226	−	0.451961i	0.784541	−	0.620077i	$-0.212899\pi$
$809$	−5.72346	−	12.8551i	−0.201226	−	0.451961i	−0.985767	+	0.168115i	$0.946232\pi$
$810$	19.9003	+	2.78416i	0.699225	+	0.0978253i
$811$	−14.4127	+	4.68298i	−0.506099	+	0.164442i	−0.550928	−	0.834553i	$-0.685726\pi$
$811$	−14.4127	+	4.68298i	−0.506099	+	0.164442i	0.0448282	+	0.998995i	$0.485726\pi$
$812$	−13.1332	−	15.1213i	−0.460885	−	0.530653i
$813$	−0.196672	−	0.196672i	−0.00689759	−	0.00689759i
$814$	2.16936	−	14.7915i	0.0760361	−	0.518441i
$815$	32.3840	+	38.5450i	1.13436	+	1.35017i
$816$	−0.0185839	−	0.176814i	−0.000650567	−	0.00618973i
$817$	−12.4994	+	0.655066i	−0.437299	+	0.0229178i
$818$	15.1198	+	29.6743i	0.528653	+	1.03754i
$819$	6.81460	−	23.7265i	0.238121	−	0.829070i
$820$	1.36117	−	7.02601i	0.0475343	−	0.245359i
$821$	−45.3068	+	9.63027i	−1.58122	+	0.336099i	−0.913030	−	0.407892i	$-0.866264\pi$
$821$	−45.3068	+	9.63027i	−1.58122	+	0.336099i	−0.668190	+	0.743991i	$0.732931\pi$
$822$	−0.326779	−	0.503196i	−0.0113977	−	0.0175510i
$823$	−18.3804	+	22.6979i	−0.640699	+	0.791198i	−0.989272	−	0.146084i	$-0.953333\pi$
$823$	−18.3804	+	22.6979i	−0.640699	+	0.791198i	0.348573	+	0.937282i	$0.386666\pi$
$824$	−6.81338	−	11.8011i	−0.237355	−	0.411112i
$825$	0.170100	−	0.622966i	0.00592213	−	0.0216889i
$826$	2.20773	−	12.4889i	0.0768166	−	0.434546i
$827$	−2.34224	+	14.7883i	−0.0814477	+	0.514241i	0.912910	+	0.408161i	$0.133830\pi$
$827$	−2.34224	+	14.7883i	−0.0814477	+	0.514241i	−0.994358	+	0.106080i	$0.966170\pi$
$828$	−16.9539	+	0.888516i	−0.589189	+	0.0308781i
$829$	−10.8468	−	12.0466i	−0.376726	−	0.418397i	0.524729	−	0.851269i	$-0.324167\pi$
$829$	−10.8468	−	12.0466i	−0.376726	−	0.418397i	−0.901455	+	0.432872i	$0.857500\pi$
$830$	−13.6158	+	15.6829i	−0.472611	+	0.544362i
$831$	0.327322	+	0.0344030i	0.0113547	+	0.00119343i
$832$	2.77253	−	1.41267i	0.0961200	−	0.0489756i
$833$	31.1458	−	7.16210i	1.07914	−	0.248152i
$834$	0.113280	+	0.155917i	0.00392257	+	0.00539895i
$835$	−16.9398	+	2.99783i	−0.586227	+	0.103744i
$836$	−0.782597	−	12.2469i	−0.0270667	−	0.423569i
$837$	−0.101254	−	0.377887i	−0.00349987	−	0.0130617i
$838$	30.3151	−	11.6369i	1.04722	−	0.401990i
$839$	12.9179	+	39.7573i	0.445977	+	1.37258i	0.881409	+	0.472354i	$0.156596\pi$
$839$	12.9179	+	39.7573i	0.445977	+	1.37258i	−0.435432	+	0.900221i	$0.643404\pi$
$840$	0.171177	−	0.154187i	0.00590618	−	0.00531997i
$841$	22.8991	+	16.6372i	0.789624	+	0.573695i
$842$	2.95786	+	3.65265i	0.101935	+	0.125879i
$843$	0.795576	+	0.0416944i	0.0274011	+	0.00143603i
$844$	2.54342	−	11.9659i	0.0875482	−	0.411882i
$845$	7.41684	−	0.134085i	0.255147	−	0.00461267i
$846$		−	33.8928i		−	1.16526i
$847$	11.9707	+	26.5274i	0.411320	+	0.911491i
$848$	3.59785	+	3.59785i	0.123551	+	0.123551i
$849$	0.154686	−	0.347429i	0.00530880	−	0.0119237i
$850$	17.9709	−	14.0765i	0.616395	−	0.482819i
$851$	17.0770	+	18.9659i	0.585391	+	0.650142i
$852$	0.274138	−	0.221992i	0.00939181	−	0.00760533i
$853$	5.22487	−	0.827539i	0.178896	−	0.0283344i	−0.0663435	−	0.997797i	$-0.521133\pi$
$853$	5.22487	−	0.827539i	0.178896	−	0.0283344i	0.245240	+	0.969462i	$0.421133\pi$
$854$	12.0064	+	19.2329i	0.410851	+	0.658135i
$855$	−16.9307	−	18.1333i	−0.579019	−	0.620146i
$856$	−5.73772	−	2.55460i	−0.196111	−	0.0873143i
$857$	−23.9957	+	6.42964i	−0.819679	+	0.219632i	−0.644206	−	0.764852i	$-0.722812\pi$
$857$	−23.9957	+	6.42964i	−0.819679	+	0.219632i	−0.175473	+	0.984484i	$0.556145\pi$
$858$	−0.301721	−	0.265476i	−0.0103006	−	0.00906320i
$859$	−22.7541	−	39.4112i	−0.776358	−	1.34469i	−0.934028	−	0.357200i	$-0.883731\pi$
$859$	−22.7541	−	39.4112i	−0.776358	−	1.34469i	0.157670	−	0.987492i	$-0.449602\pi$
$860$	7.26973	−	2.08946i	0.247896	−	0.0712502i
$861$	−0.305686	−	0.123660i	−0.0104178	−	0.00421431i
$862$	−1.95062	−	3.82831i	−0.0664385	−	0.130393i
$863$	−4.43731	+	3.59326i	−0.151048	+	0.122316i	−0.701866	−	0.712309i	$-0.747649\pi$
$863$	−4.43731	+	3.59326i	−0.151048	+	0.122316i	0.550818	+	0.834626i	$0.314316\pi$
$864$	0.213395	−	0.0950096i	0.00725985	−	0.00323229i
$865$	8.46503	+	20.9142i	0.287820	+	0.711103i
$866$	−9.52807	−	8.57912i	−0.323777	−	0.291530i
$867$	−0.147846	−	0.0234166i	−0.00502113	−	0.000795268i
$868$	4.01514	+	1.87441i	0.136283	+	0.0636217i
$869$	13.0512	−	35.1995i	0.442732	−	1.19406i
$870$	−0.377744	+	0.540191i	−0.0128067	+	0.0183142i
$871$	−11.9612	+	1.25718i	−0.405291	+	0.0425978i
$872$	−13.1173	+	8.51845i	−0.444206	+	0.288471i
$873$	−20.6084	+	31.7342i	−0.697490	+	1.07404i
$874$	16.9487	+	12.3140i	0.573298	+	0.416526i
$875$	28.4462	+	8.11263i	0.961656	+	0.274257i
$876$	−0.0709074	+	0.218231i	−0.00239574	+	0.00737333i
$877$	−0.718294	−	13.7059i	−0.0242551	−	0.462814i	−0.983576	−	0.180496i	$-0.942230\pi$
$877$	−0.718294	−	13.7059i	−0.0242551	−	0.462814i	0.959321	−	0.282318i	$-0.0911035\pi$
$878$	−9.22173	−	7.46761i	−0.311218	−	0.252020i
$879$	0.783013	+	0.452073i	0.0264104	+	0.0152480i
$880$	2.13013	+	7.10370i	0.0718068	+	0.239466i
$881$			55.4025i			1.86656i	0.359154	+	0.933278i	$0.383065\pi$
$881$			55.4025i			1.86656i	−0.359154	+	0.933278i	$0.616935\pi$
$882$	10.7947	+	18.0008i	0.363477	+	0.606118i
$883$	−7.07947	+	13.8942i	−0.238243	+	0.467578i	−0.978909	−	0.204295i	$-0.934510\pi$
$883$	−7.07947	+	13.8942i	−0.238243	+	0.467578i	0.740666	+	0.671873i	$0.234510\pi$
$884$	−2.95368	−	13.8960i	−0.0993431	−	0.467372i
$885$	−0.416369	+	0.0293761i	−0.0139961	+	0.000987466i
$886$	−11.9983	+	5.34199i	−0.403091	+	0.179468i
$887$	11.9656	+	7.77054i	0.401765	+	0.260909i	0.729667	−	0.683802i	$-0.239675\pi$
$887$	11.9656	+	7.77054i	0.401765	+	0.260909i	−0.327902	+	0.944712i	$0.606342\pi$
$888$	−0.156398	−	0.0796885i	−0.00524836	−	0.00267417i
$889$	20.7613	+	42.6139i	0.696311	+	1.42922i
$890$	−7.81164	−	2.83769i	−0.261847	−	0.0951197i
$891$	21.3149	+	20.8321i	0.714076	+	0.697901i
$892$	−25.4243	+	6.81243i	−0.851269	+	0.228097i
$893$	−26.3204	+	32.5030i	−0.880779	+	1.08767i
$894$	0.360079	−	0.399908i	0.0120429	−	0.0133749i
$895$	−1.51924	−	12.3098i	−0.0507827	−	0.411472i
$896$	−0.730371	+	2.54294i	−0.0244000	+	0.0849538i
$897$	0.677627	−	0.107326i	0.0226253	−	0.00358350i
$898$	−17.5165	−	11.3754i	−0.584535	−	0.379601i
$899$	−12.4012	−	2.63596i	−0.413603	−	0.0879141i
$900$	12.4397	+	8.36816i	0.414657	+	0.278939i
$901$	20.1177	−	11.6150i	0.670218	−	0.386951i
$902$	7.80662	−	7.19273i	0.259932	−	0.239492i
$903$	−0.0302251	−	0.347209i	−0.00100583	−	0.0115544i
$904$	9.72397	+	13.3839i	0.323414	+	0.445142i
$905$	2.63270	−	8.63042i	0.0875141	−	0.286885i
$906$	0.210277	−	0.189335i	0.00698600	−	0.00629022i
$907$	−5.86045	+	15.2670i	−0.194593	+	0.506932i	−0.995810	−	0.0914410i	$-0.970853\pi$
$907$	−5.86045	+	15.2670i	−0.194593	+	0.506932i	0.801217	+	0.598373i	$0.204186\pi$
$908$	15.5977	+	19.2615i	0.517628	+	0.639217i
$909$	6.67533	−	20.5446i	0.221407	−	0.681420i
$910$	12.3154	−	13.6828i	0.408251	−	0.453582i
$911$	45.7498	−	33.2392i	1.51576	−	1.10126i	0.552217	−	0.833701i	$-0.313782\pi$
$911$	45.7498	−	33.2392i	1.51576	−	1.10126i	0.963541	−	0.267562i	$-0.0862179\pi$
$912$	−0.139178	−	0.0372927i	−0.00460866	−	0.00123489i
$913$	−30.0566	+	6.74947i	−0.994729	+	0.223375i
$914$	15.6760	+	9.05055i	0.518516	+	0.299366i
$915$	0.518018	−	0.537093i	0.0171252	−	0.0177557i
$916$	−22.8171	+	7.41372i	−0.753897	+	0.244956i
$917$	−17.8023	−	16.6154i	−0.587884	−	0.548687i
$918$	−0.166831	−	1.05333i	−0.00550624	−	0.0347650i
$919$	−35.3696	−	3.71749i	−1.16674	−	0.122629i	−0.498711	−	0.866768i	$-0.666193\pi$
$919$	−35.3696	−	3.71749i	−1.16674	−	0.122629i	−0.668024	+	0.744140i	$0.732860\pi$
$920$	−11.6571	−	4.93956i	−0.384322	−	0.162852i
$921$	−1.03654	−	0.220323i	−0.0341552	−	0.00725990i
$922$	−2.10341	−	5.47956i	−0.0692720	−	0.180460i
$923$	19.9312	−	19.9312i	0.656043	−	0.656043i
$924$	0.340061	−	0.0335318i	0.0111872	−	0.00110311i
$925$	−1.99226	−	22.4493i	−0.0655050	−	0.738129i
$926$	−16.3533	−	7.28096i	−0.537403	−	0.239267i
$927$	−22.2538	−	34.2678i	−0.730909	−	1.12550i
$928$	0.396183	−	7.55962i	0.0130053	−	0.248157i
$929$	−1.08810	+	10.3526i	−0.0356995	+	0.339658i	0.962065	+	0.272822i	$0.0879570\pi$
$929$	−1.08810	+	10.3526i	−0.0356995	+	0.339658i	−0.997764	+	0.0668358i	$0.978710\pi$
$930$	0.0277374	−	0.143173i	0.000909545	−	0.00469482i
$931$	3.62695	−	25.6456i	0.118869	−	0.840501i
$932$	−6.38857	−	3.25514i	−0.209265	−	0.106626i
$933$	0.0921880	+	0.240158i	0.00301810	+	0.00786242i
$934$	9.87722	−	17.1078i	0.323193	−	0.559786i
$935$	33.8440	−	0.999750i	1.10682	−	0.0326953i
$936$	8.08029	−	4.66516i	0.264113	−	0.152485i
$937$	27.0343	+	4.28182i	0.883173	+	0.139881i	0.581515	−	0.813535i	$-0.302460\pi$
$937$	27.0343	+	4.28182i	0.883173	+	0.139881i	0.301658	+	0.953416i	$0.402460\pi$
$938$	6.15784	−	8.16436i	0.201061	−	0.266576i
$939$	−0.627204	−	0.203791i	−0.0204680	−	0.00665047i
$940$	11.0657	−	22.7239i	0.360922	−	0.741172i
$941$	3.34770	+	7.51905i	0.109132	+	0.245114i	0.959853	−	0.280503i	$-0.0905012\pi$
$941$	3.34770	+	7.51905i	0.109132	+	0.245114i	−0.850721	+	0.525617i	$0.823835\pi$
$942$	0.335839	+	0.0176006i	0.0109422	+	0.000573458i
$943$	0.948393	+	18.0964i	0.0308839	+	0.589300i
$944$	3.87808	−	2.81759i	0.126221	−	0.0917046i
$945$	0.976992	−	0.977362i	0.0317815	−	0.0317936i
$946$	10.5195	+	3.90040i	0.342018	+	0.126813i
$947$	−31.5815	−	8.46224i	−1.02626	−	0.274986i	−0.293852	−	0.955851i	$-0.594937\pi$
$947$	−31.5815	−	8.46224i	−1.02626	−	0.274986i	−0.732409	+	0.680865i	$0.761604\pi$
$948$	−0.342552	−	0.277393i	−0.0111256	−	0.00900931i
$949$	−3.81215	+	17.9348i	−0.123748	+	0.582187i
$950$	−5.43109	−	17.6854i	−0.176208	−	0.573792i
$951$	0.119022	−	0.163820i	0.00385956	−	0.00531222i
$952$	10.3512	+	6.22575i	0.335485	+	0.201778i
$953$	6.97463	−	3.55375i	0.225930	−	0.115117i	−0.337362	−	0.941375i	$-0.609535\pi$
$953$	6.97463	−	3.55375i	0.225930	−	0.115117i	0.563292	+	0.826258i	$0.309535\pi$
$954$	11.3379	+	10.2087i	0.367079	+	0.330519i
$955$	19.0789	−	11.4799i	0.617377	−	0.371482i
$956$	0.990213	−	1.71510i	0.0320258	−	0.0554703i
$957$	−0.926324	+	0.312756i	−0.0299438	+	0.0101100i
$958$	−1.21083	+	1.21083i	−0.0391203	+	0.0391203i
$959$	40.6640	+	2.86123i	1.31311	+	0.0923940i
$960$	0.0870247	+	0.00298467i	0.00280871	+	9.63298e-5i
$961$	−27.5789	+	5.86208i	−0.889642	+	0.189099i
$962$	−13.0943	−	5.02644i	−0.422178	−	0.162059i
$963$	−17.5818	−	6.74900i	−0.566564	−	0.217484i
$964$	6.40000	−	1.36036i	0.206130	−	0.0438143i
$965$	−48.4295	−	1.66098i	−1.55900	−	0.0534688i
$966$	−0.326412	+	0.483473i	−0.0105021	+	0.0155555i
$967$	−18.8868	+	18.8868i	−0.607359	+	0.607359i	−0.942255	−	0.334896i	$-0.891299\pi$
$967$	−18.8868	+	18.8868i	−0.607359	+	0.607359i	0.334896	+	0.942255i	$0.391299\pi$
$968$	−3.70576	+	10.3570i	−0.119108	+	0.332886i
$969$	−0.328918	+	0.569703i	−0.0105664	+	0.0183015i
$970$	−24.1781	+	14.5482i	−0.776313	+	0.467114i
$971$	−33.8825	−	30.5079i	−1.08734	−	0.979045i	−0.0874862	−	0.996166i	$-0.527883\pi$
$971$	−33.8825	−	30.5079i	−1.08734	−	0.979045i	−0.999853	+	0.0171207i	$0.994550\pi$
$972$	0.936191	−	0.477013i	0.0300283	−	0.0153002i
$973$	−13.0919	−	0.234202i	−0.419706	−	0.00750816i
$974$	0.0488961	−	0.0672997i	0.00156673	−	0.00215642i
$975$	−0.535303	−	0.283770i	−0.0171434	−	0.00908793i
$976$	−1.78170	+	8.38226i	−0.0570309	+	0.268309i
$977$	−2.32598	−	1.88354i	−0.0744147	−	0.0602599i	0.591391	−	0.806385i	$-0.298579\pi$
$977$	−2.32598	−	1.88354i	−0.0744147	−	0.0602599i	−0.665806	+	0.746125i	$0.731912\pi$
$978$	0.846862	+	0.226916i	0.0270797	+	0.00725597i
$979$	−6.83193	−	10.2610i	−0.218350	−	0.327943i
$980$	1.36039	+	15.5932i	0.0434560	+	0.498108i
$981$	−37.9412	+	27.5659i	−1.21137	+	0.880111i
$982$	−1.77258	−	33.8229i	−0.0565655	−	1.07933i
$983$	−27.7328	−	1.45342i	−0.884540	−	0.0463568i	−0.395346	−	0.918532i	$-0.629375\pi$
$983$	−27.7328	−	1.45342i	−0.884540	−	0.0463568i	−0.489193	+	0.872175i	$0.662709\pi$
$984$	−0.0506933	−	0.113859i	−0.00161604	−	0.00362969i
$985$	−8.19590	+	16.8307i	−0.261143	+	0.536270i
$986$	−32.8694	−	10.6799i	−1.04678	−	0.340118i
$987$	−0.929766	−	0.701262i	−0.0295948	−	0.0223214i
$988$	−11.3718	−	1.80112i	−0.361786	−	0.0573013i
$989$	−16.5868	+	9.57641i	−0.527430	+	0.304512i
$990$	7.49319	+	20.9369i	0.238149	+	0.665417i
$991$	23.2629	−	40.2925i	0.738971	−	1.27993i	−0.213989	−	0.976836i	$-0.568646\pi$
$991$	23.2629	−	40.2925i	0.738971	−	1.27993i	0.952959	−	0.303098i	$-0.0980211\pi$
$992$	0.600196	+	1.56356i	0.0190562	+	0.0496432i
$993$	0.184435	+	0.0939745i	0.00585288	+	0.00298219i
$994$	0.826023	+	23.9522i	0.0261998	+	0.759716i
$995$	8.17777	−	42.2114i	0.259253	−	1.33819i
$996$	−0.0378071	+	0.359711i	−0.00119796	+	0.0113979i
$997$	−1.45891	+	27.8376i	−0.0462040	+	0.881625i	0.872970	+	0.487774i	$0.162191\pi$
$997$	−1.45891	+	27.8376i	−0.0462040	+	0.881625i	−0.919174	+	0.393851i	$0.871142\pi$
$998$	12.0055	+	18.4868i	0.380027	+	0.585191i
$999$	−0.961880	−	0.428256i	−0.0304325	−	0.0135494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.3.13	✓	768
5.2	odd	4	inner	770.2.bv.a.157.12	yes	768
7.5	odd	6	inner	770.2.bv.a.663.36	yes	768
11.4	even	5	inner	770.2.bv.a.213.12	yes	768
35.12	even	12	inner	770.2.bv.a.47.12	yes	768
55.37	odd	20	inner	770.2.bv.a.367.36	yes	768
77.26	odd	30	inner	770.2.bv.a.103.12	yes	768
385.257	even	60	inner	770.2.bv.a.257.13	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.13	✓	768	1.1	even	1	trivial
770.2.bv.a.47.12	yes	768	35.12	even	12	inner
770.2.bv.a.103.12	yes	768	77.26	odd	30	inner
770.2.bv.a.157.12	yes	768	5.2	odd	4	inner
770.2.bv.a.213.12	yes	768	11.4	even	5	inner
770.2.bv.a.257.13	yes	768	385.257	even	60	inner
770.2.bv.a.367.36	yes	768	55.37	odd	20	inner
770.2.bv.a.663.36	yes	768	7.5	odd	6	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.0326591 + 0.0212091i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.11379 - 0.729310i) q^{5} +(0.0228892 - 0.0315043i) q^{6} +(0.772445 + 2.53048i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-1.21959 + 2.73925i) q^{9} +O(q^{10})\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.0326591 + 0.0212091i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.11379 - 0.729310i) q^{5} +(0.0228892 - 0.0315043i) q^{6} +(0.772445 + 2.53048i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-1.21959 + 2.73925i) q^{9} +(-1.71203 + 1.43838i) q^{10} +(-3.30987 + 0.211506i) q^{11} +(-0.0100788 + 0.0376146i) q^{12} +(-0.486774 + 3.07337i) q^{13} +(-1.62798 - 2.08559i) q^{14} +(-0.0535665 + 0.0686501i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-4.26228 - 1.63614i) q^{17} +(0.156929 - 2.99437i) q^{18} +(-2.47586 + 2.74972i) q^{19} +(1.08285 - 1.95638i) q^{20} +(-0.0788964 - 0.0662603i) q^{21} +(3.01424 - 1.38361i) q^{22} +(-1.46541 + 5.46899i) q^{23} +(-0.00407049 - 0.0387282i) q^{24} +(3.93621 - 3.08322i) q^{25} +(-0.646954 - 3.04368i) q^{26} +(-0.0365415 - 0.230714i) q^{27} +(2.26726 + 1.36365i) q^{28} +(-7.19949 - 2.33926i) q^{29} +(0.0254066 - 0.0832869i) q^{30} +(1.66563 - 0.175065i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.103612 - 0.0771069i) q^{33} +4.56552 q^{34} +(3.47829 + 4.78555i) q^{35} +(0.926582 + 2.85173i) q^{36} +(2.45496 - 3.78031i) q^{37} +(1.32600 - 3.45436i) q^{38} +(-0.0492857 - 0.110697i) q^{39} +(-0.309821 + 2.21450i) q^{40} +(3.04390 - 0.989024i) q^{41} +(0.0974018 + 0.0335854i) q^{42} +(2.39196 + 2.39196i) q^{43} +(-2.31819 + 2.37192i) q^{44} +(-0.580200 + 6.67966i) q^{45} +(-0.591831 - 5.63090i) q^{46} +(11.2878 - 0.591569i) q^{47} +(0.0176791 + 0.0346971i) q^{48} +(-5.80666 + 3.90931i) q^{49} +(-2.56985 + 4.28904i) q^{50} +(0.173903 - 0.0369642i) q^{51} +(1.69474 + 2.60967i) q^{52} +(-3.20206 + 3.95422i) q^{53} +(0.116795 + 0.202295i) q^{54} +(-6.84212 + 2.86100i) q^{55} +(-2.60536 - 0.460560i) q^{56} +(0.0225403 - 0.142314i) q^{57} +(7.55962 - 0.396183i) q^{58} +(3.20752 + 3.56231i) q^{59} +(0.00612823 + 0.0868599i) q^{60} +(-8.52258 - 0.895759i) q^{61} +(-1.49226 + 0.760345i) q^{62} +(-7.87369 - 0.970235i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(1.21250 + 6.85146i) q^{65} +(-0.0690971 + 0.109117i) q^{66} +(1.00037 + 3.73345i) q^{67} +(-4.26228 + 1.63614i) q^{68} +(-0.0681331 - 0.209692i) q^{69} +(-4.96225 - 3.22119i) q^{70} +(-7.32844 - 5.32442i) q^{71} +(-1.88701 - 2.33026i) q^{72} +(5.88438 + 0.308388i) q^{73} +(-0.937164 + 4.40901i) q^{74} +(-0.0631610 + 0.184178i) q^{75} +3.70012i q^{76} +(-3.09191 - 8.21219i) q^{77} +(0.0856825 + 0.0856825i) q^{78} +(-4.60389 + 10.3405i) q^{79} +(-0.504364 - 2.17844i) q^{80} +(-6.01304 - 6.67816i) q^{81} +(-2.48729 + 2.01417i) q^{82} +(9.17374 - 1.45298i) q^{83} +(-0.102968 + 0.00355100i) q^{84} +(-10.2028 - 0.349924i) q^{85} +(-3.09029 - 1.37589i) q^{86} +(0.284742 - 0.0762965i) q^{87} +(1.31420 - 3.04514i) q^{88} +(1.85842 + 3.21887i) q^{89} +(-1.85211 - 6.44393i) q^{90} +(-8.15310 + 1.14224i) q^{91} +(2.57046 + 5.04480i) q^{92} +(-0.0506850 + 0.0410439i) q^{93} +(-10.3261 + 4.59747i) q^{94} +(-3.22805 + 7.61801i) q^{95} +(-0.0289392 - 0.0260569i) q^{96} +(12.4639 + 1.97409i) q^{97} +(4.02001 - 5.73058i) q^{98} +(3.45733 - 9.32453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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