LMFDB - Embedded newform 418.2.n.d.159.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			159.3
Character	$\chi$	$=$	418.159
Dual form			418.2.n.d.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 + 0.743145i) q^{2} +(-0.0430092 + 0.409205i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.51671 + 0.322387i) q^{5} +(-0.275320 - 0.305774i) q^{6} +(-0.764726 + 0.555606i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.76884 + 0.588536i) q^{9} +O(q^{10})$	\(q+(-0.669131 + 0.743145i) q^{2} +(-0.0430092 + 0.409205i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.51671 + 0.322387i) q^{5} +(-0.275320 - 0.305774i) q^{6} +(-0.764726 + 0.555606i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.76884 + 0.588536i) q^{9} +(0.775298 - 1.34285i) q^{10} +(1.64225 + 2.88150i) q^{11} +0.411459 q^{12} +(-2.99167 - 0.635899i) q^{13} +(0.0988059 - 0.940075i) q^{14} +(-0.0666898 - 0.634511i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-3.37121 + 0.716573i) q^{17} +(-2.29009 + 1.66384i) q^{18} +(-3.70812 + 2.29125i) q^{19} +(0.479160 + 1.47470i) q^{20} +(-0.194466 - 0.336826i) q^{21} +(-3.24025 - 0.707667i) q^{22} +(-2.38600 + 4.13267i) q^{23} +(-0.275320 + 0.305774i) q^{24} +(-2.37125 + 1.05575i) q^{25} +(2.47438 - 1.79774i) q^{26} +(-0.741361 + 2.28167i) q^{27} +(0.632498 + 0.702460i) q^{28} +(0.318981 + 3.03490i) q^{29} +(0.516158 + 0.375011i) q^{30} +(-0.954812 - 2.93861i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.24975 + 0.548086i) q^{33} +(1.72326 - 2.98478i) q^{34} +(0.980749 - 1.08923i) q^{35} +(0.295889 - 2.81519i) q^{36} +(0.239812 - 0.174234i) q^{37} +(0.778484 - 4.28882i) q^{38} +(0.388882 - 1.19686i) q^{39} +(-1.41654 - 0.630684i) q^{40} +(-0.0562149 + 0.534849i) q^{41} +(0.380434 + 0.0808637i) q^{42} +(1.05510 + 1.82749i) q^{43} +(2.69405 - 1.93445i) q^{44} -4.38927 q^{45} +(-1.47463 - 4.53844i) q^{46} +(5.04626 - 2.24674i) q^{47} +(-0.0430092 - 0.409205i) q^{48} +(-1.88701 + 5.80762i) q^{49} +(0.802101 - 2.46861i) q^{50} +(-0.148232 - 1.41034i) q^{51} +(-0.319701 + 3.04175i) q^{52} +(-0.632107 - 0.134358i) q^{53} +(-1.19955 - 2.07768i) q^{54} +(-3.41977 - 3.84096i) q^{55} -0.945254 q^{56} +(-0.778109 - 1.61593i) q^{57} +(-2.46881 - 1.79369i) q^{58} +(9.21305 + 4.10191i) q^{59} +(-0.624064 + 0.132649i) q^{60} +(-3.34752 - 3.71780i) q^{61} +(2.82270 + 1.25675i) q^{62} +(-2.44440 + 1.08832i) q^{63} +(0.309017 + 0.951057i) q^{64} +4.74250 q^{65} +(0.428941 - 1.29549i) q^{66} +(-5.73095 + 9.92629i) q^{67} +(1.06504 + 3.27784i) q^{68} +(-1.58849 - 1.15410i) q^{69} +(0.153208 + 1.45768i) q^{70} +(9.03188 - 1.91979i) q^{71} +(1.89411 + 2.10362i) q^{72} +(-9.51539 - 4.23653i) q^{73} +(-0.0309848 + 0.294801i) q^{74} +(-0.330032 - 1.01573i) q^{75} +(2.66631 + 3.44831i) q^{76} +(-2.85685 - 1.29111i) q^{77} +(0.629224 + 1.08985i) q^{78} +(8.33921 - 9.26163i) q^{79} +(1.41654 - 0.630684i) q^{80} +(6.85614 + 3.05255i) q^{81} +(-0.359855 - 0.399660i) q^{82} +(-0.539433 + 1.66020i) q^{83} +(-0.314653 + 0.228609i) q^{84} +(4.88214 - 2.17367i) q^{85} +(-2.06410 - 0.438737i) q^{86} -1.25561 q^{87} +(-0.365093 + 3.29647i) q^{88} +(1.88631 - 3.26718i) q^{89} +(2.93700 - 3.26186i) q^{90} +(2.64112 - 1.17590i) q^{91} +(4.35944 + 1.94095i) q^{92} +(1.24356 - 0.264326i) q^{93} +(-1.70696 + 5.25347i) q^{94} +(4.88548 - 4.67062i) q^{95} +(0.332877 + 0.241849i) q^{96} +(9.25015 - 10.2733i) q^{97} +(-3.05325 - 5.28838i) q^{98} +(2.85127 + 8.94493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$3$	−0.0430092	+	0.409205i	−0.0248314	+	0.236255i	0.975066	+	0.221916i	$0.0712310\pi$
$3$	−0.0430092	+	0.409205i	−0.0248314	+	0.236255i	−0.999897	+	0.0143388i	$0.995436\pi$
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	−1.51671	+	0.322387i	−0.678294	+	0.144176i	−0.534161	−	0.845383i	$-0.679372\pi$
$5$	−1.51671	+	0.322387i	−0.678294	+	0.144176i	−0.144132	+	0.989558i	$0.546039\pi$
$6$	−0.275320	−	0.305774i	−0.112399	−	0.124832i
$7$	−0.764726	+	0.555606i	−0.289039	+	0.209999i	−0.722851	−	0.691004i	$-0.757168\pi$
$7$	−0.764726	+	0.555606i	−0.289039	+	0.209999i	0.433811	+	0.901004i	$0.357168\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.76884	+	0.588536i	0.922948	+	0.196179i
$10$	0.775298	−	1.34285i	0.245171	−	0.424648i
$11$	1.64225	+	2.88150i	0.495157	+	0.868804i
$11$	1.64225	+	2.88150i	0.495157	+	0.868804i
$12$	0.411459			0.118778
$13$	−2.99167	−	0.635899i	−0.829740	−	0.176367i	−0.226586	−	0.973991i	$-0.572756\pi$
$13$	−2.99167	−	0.635899i	−0.829740	−	0.176367i	−0.603154	+	0.797625i	$0.706090\pi$
$14$	0.0988059	−	0.940075i	0.0264070	−	0.251246i
$15$	−0.0666898	−	0.634511i	−0.0172192	−	0.163830i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	−3.37121	+	0.716573i	−0.817639	+	0.173795i	−0.597701	−	0.801719i	$-0.703919\pi$
$17$	−3.37121	+	0.716573i	−0.817639	+	0.173795i	−0.219938	+	0.975514i	$0.570586\pi$
$18$	−2.29009	+	1.66384i	−0.539778	+	0.392172i
$19$	−3.70812	+	2.29125i	−0.850701	+	0.525650i
$19$	−3.70812	+	2.29125i	−0.850701	+	0.525650i
$20$	0.479160	+	1.47470i	0.107143	+	0.329754i
$21$	−0.194466	−	0.336826i	−0.0424361	−	0.0735014i
$22$	−3.24025	−	0.707667i	−0.690823	−	0.150875i
$23$	−2.38600	+	4.13267i	−0.497515	+	0.861721i	−0.999996	−	0.00286703i	$-0.999087\pi$
$23$	−2.38600	+	4.13267i	−0.497515	+	0.861721i	0.502481	+	0.864588i	$0.332421\pi$
$24$	−0.275320	+	0.305774i	−0.0561994	+	0.0624158i
$25$	−2.37125	+	1.05575i	−0.474250	+	0.211150i
$26$	2.47438	−	1.79774i	0.485266	−	0.352567i
$27$	−0.741361	+	2.28167i	−0.142675	+	0.439108i
$28$	0.632498	+	0.702460i	0.119531	+	0.132753i
$29$	0.318981	+	3.03490i	0.0592332	+	0.563567i	0.983384	+	0.181538i	$0.0581076\pi$
$29$	0.318981	+	3.03490i	0.0592332	+	0.563567i	−0.924151	+	0.382028i	$0.875226\pi$
$30$	0.516158	+	0.375011i	0.0942371	+	0.0684672i
$31$	−0.954812	−	2.93861i	−0.171489	−	0.527790i	0.827967	−	0.560778i	$-0.189498\pi$
$31$	−0.954812	−	2.93861i	−0.171489	−	0.527790i	−0.999456	+	0.0329880i	$0.989498\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.24975	+	0.548086i	−0.217554	+	0.0954095i
$34$	1.72326	−	2.98478i	0.295537	−	0.511885i
$35$	0.980749	−	1.08923i	0.165777	−	0.184114i
$36$	0.295889	−	2.81519i	0.0493148	−	0.469199i
$37$	0.239812	−	0.174234i	0.0394249	−	0.0286439i	−0.567898	−	0.823099i	$-0.692243\pi$
$37$	0.239812	−	0.174234i	0.0394249	−	0.0286439i	0.607323	+	0.794455i	$0.292243\pi$
$38$	0.778484	−	4.28882i	0.126287	−	0.695738i
$39$	0.388882	−	1.19686i	0.0622710	−	0.191650i
$40$	−1.41654	−	0.630684i	−0.223975	−	0.0997199i
$41$	−0.0562149	+	0.534849i	−0.00877929	+	0.0835294i	−0.998034	−	0.0626716i	$-0.980038\pi$
$41$	−0.0562149	+	0.534849i	−0.00877929	+	0.0835294i	0.989255	+	0.146201i	$0.0467046\pi$
$42$	0.380434	+	0.0808637i	0.0587022	+	0.0124775i
$43$	1.05510	+	1.82749i	0.160902	+	0.278690i	0.935192	−	0.354140i	$-0.115226\pi$
$43$	1.05510	+	1.82749i	0.160902	+	0.278690i	−0.774291	+	0.632830i	$0.781893\pi$
$44$	2.69405	−	1.93445i	0.406143	−	0.291630i
$45$	−4.38927			−0.654314
$46$	−1.47463	−	4.53844i	−0.217422	−	0.669156i
$47$	5.04626	−	2.24674i	0.736073	−	0.327721i	−0.00423274	−	0.999991i	$-0.501347\pi$
$47$	5.04626	−	2.24674i	0.736073	−	0.327721i	0.740306	+	0.672270i	$0.234681\pi$
$48$	−0.0430092	−	0.409205i	−0.00620784	−	0.0590636i
$49$	−1.88701	+	5.80762i	−0.269573	+	0.829660i
$50$	0.802101	−	2.46861i	0.113434	−	0.349115i
$51$	−0.148232	−	1.41034i	−0.0207567	−	0.197486i
$52$	−0.319701	+	3.04175i	−0.0443345	+	0.421815i
$53$	−0.632107	−	0.134358i	−0.0868265	−	0.0184555i	0.164294	−	0.986411i	$-0.447466\pi$
$53$	−0.632107	−	0.134358i	−0.0868265	−	0.0184555i	−0.251120	+	0.967956i	$0.580799\pi$
$54$	−1.19955	−	2.07768i	−0.163238	−	0.282736i
$55$	−3.41977	−	3.84096i	−0.461122	−	0.517914i
$56$	−0.945254			−0.126315
$57$	−0.778109	−	1.61593i	−0.103063	−	0.214035i
$58$	−2.46881	−	1.79369i	−0.324171	−	0.235524i
$59$	9.21305	+	4.10191i	1.19944	+	0.534024i	0.906540	−	0.422120i	$-0.138714\pi$
$59$	9.21305	+	4.10191i	1.19944	+	0.534024i	0.292897	+	0.956144i	$0.405381\pi$
$60$	−0.624064	+	0.132649i	−0.0805663	+	0.0171249i
$61$	−3.34752	−	3.71780i	−0.428606	−	0.476015i	0.489698	−	0.871892i	$-0.337107\pi$
$61$	−3.34752	−	3.71780i	−0.428606	−	0.476015i	−0.918303	+	0.395877i	$0.870441\pi$
$62$	2.82270	+	1.25675i	0.358484	+	0.159607i
$63$	−2.44440	+	1.08832i	−0.307966	+	0.137115i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	4.74250			0.588235
$66$	0.428941	−	1.29549i	0.0527990	−	0.159464i
$67$	−5.73095	+	9.92629i	−0.700146	+	1.21269i	0.268268	+	0.963344i	$0.413549\pi$
$67$	−5.73095	+	9.92629i	−0.700146	+	1.21269i	−0.968415	+	0.249345i	$0.919785\pi$
$68$	1.06504	+	3.27784i	0.129154	+	0.397497i
$69$	−1.58849	−	1.15410i	−0.191232	−	0.138938i
$70$	0.153208	+	1.45768i	0.0183119	+	0.174226i
$71$	9.03188	−	1.91979i	1.07189	−	0.227837i	0.362019	−	0.932171i	$-0.382088\pi$
$71$	9.03188	−	1.91979i	1.07189	−	0.227837i	0.709869	+	0.704334i	$0.248754\pi$
$72$	1.89411	+	2.10362i	0.223223	+	0.247914i
$73$	−9.51539	−	4.23653i	−1.11369	−	0.495848i	−0.234405	−	0.972139i	$-0.575314\pi$
$73$	−9.51539	−	4.23653i	−1.11369	−	0.495848i	−0.879288	+	0.476291i	$0.841981\pi$
$74$	−0.0309848	+	0.294801i	−0.00360191	+	0.0342699i
$75$	−0.330032	−	1.01573i	−0.0381088	−	0.117287i
$76$	2.66631	+	3.44831i	0.305846	+	0.395548i
$77$	−2.85685	−	1.29111i	−0.325568	−	0.147136i
$78$	0.629224	+	1.08985i	0.0712456	+	0.123401i
$79$	8.33921	−	9.26163i	0.938234	−	1.04201i	−0.0608033	−	0.998150i	$-0.519366\pi$
$79$	8.33921	−	9.26163i	0.938234	−	1.04201i	0.999037	−	0.0438648i	$-0.0139671\pi$
$80$	1.41654	−	0.630684i	0.158374	−	0.0705126i
$81$	6.85614	+	3.05255i	0.761793	+	0.339172i
$82$	−0.359855	−	0.399660i	−0.0397394	−	0.0441350i
$83$	−0.539433	+	1.66020i	−0.0592105	+	0.182231i	−0.976287	−	0.216480i	$-0.930542\pi$
$83$	−0.539433	+	1.66020i	−0.0592105	+	0.182231i	0.917077	+	0.398711i	$0.130542\pi$
$84$	−0.314653	+	0.228609i	−0.0343315	+	0.0249433i
$85$	4.88214	−	2.17367i	0.529542	−	0.235767i
$86$	−2.06410	−	0.438737i	−0.222577	−	0.0473102i
$87$	−1.25561			−0.134616
$88$	−0.365093	+	3.29647i	−0.0389190	+	0.351405i
$89$	1.88631	−	3.26718i	0.199948	−	0.346321i	−0.748563	−	0.663064i	$-0.769256\pi$
$89$	1.88631	−	3.26718i	0.199948	−	0.346321i	0.948511	+	0.316743i	$0.102589\pi$
$90$	2.93700	−	3.26186i	0.309587	−	0.343831i
$91$	2.64112	−	1.17590i	0.276864	−	0.123268i
$92$	4.35944	+	1.94095i	0.454503	+	0.202358i
$93$	1.24356	−	0.264326i	0.128951	−	0.0274094i
$94$	−1.70696	+	5.25347i	−0.176059	+	0.541854i
$95$	4.88548	−	4.67062i	0.501239	−	0.479195i
$96$	0.332877	+	0.241849i	0.0339741	+	0.0246837i
$97$	9.25015	−	10.2733i	0.939211	−	1.04310i	−0.0597814	−	0.998211i	$-0.519040\pi$
$97$	9.25015	−	10.2733i	0.939211	−	1.04310i	0.998992	−	0.0448876i	$-0.0142930\pi$
$98$	−3.05325	−	5.28838i	−0.308425	−	0.534207i
$99$	2.85127	+	8.94493i	0.286563	+	0.899000i
$100$	1.29783	+	2.24790i	0.129783	+	0.224790i
$101$	0.481076	+	0.102256i	0.0478689	+	0.0101748i	0.231784	−	0.972767i	$-0.425544\pi$
$101$	0.481076	+	0.102256i	0.0478689	+	0.0101748i	−0.183915	+	0.982942i	$0.558877\pi$
$102$	1.14727	+	0.833540i	0.113597	+	0.0825328i
$103$	4.67846	−	3.39910i	0.460982	−	0.334923i	−0.332934	−	0.942950i	$-0.608039\pi$
$103$	4.67846	−	3.39910i	0.460982	−	0.334923i	0.793917	+	0.608027i	$0.208039\pi$
$104$	−2.04654	−	2.27291i	−0.200680	−	0.222877i
$105$	0.403538	+	0.448174i	0.0393812	+	0.0437373i
$106$	0.522810	−	0.379843i	0.0507798	−	0.0368937i
$107$	11.6482	+	8.46292i	1.12607	+	0.818141i	0.985119	−	0.171875i	$-0.0549825\pi$
$107$	11.6482	+	8.46292i	1.12607	+	0.818141i	0.140956	+	0.990016i	$0.454982\pi$
$108$	2.34667	+	0.498800i	0.225808	+	0.0479970i
$109$	4.67557	+	8.09832i	0.447838	+	0.775678i	0.998245	−	0.0592182i	$-0.0188608\pi$
$109$	4.67557	+	8.09832i	0.447838	+	0.775678i	−0.550407	+	0.834896i	$0.685527\pi$
$110$	5.14266	+	0.0287136i	0.490334	+	0.00273774i
$111$	0.0609832	+	0.105626i	0.00578827	+	0.0100256i
$112$	0.632498	−	0.702460i	0.0597655	−	0.0663763i
$113$	2.98406	+	2.16804i	0.280716	+	0.203952i	0.719230	−	0.694772i	$-0.244495\pi$
$113$	2.98406	+	2.16804i	0.280716	+	0.203952i	−0.438513	+	0.898725i	$0.644495\pi$
$114$	1.72152	+	0.503018i	0.161235	+	0.0471119i
$115$	2.28655	−	7.03728i	0.213222	−	0.656230i
$116$	2.98493	−	0.634467i	0.277144	−	0.0589088i
$117$	−7.90921	−	3.52141i	−0.731207	−	0.325554i
$118$	−9.21305	+	4.10191i	−0.848130	+	0.377612i
$119$	2.17992	−	2.42105i	0.199833	−	0.221937i
$120$	0.319003	−	0.552529i	0.0291209	−	0.0504388i
$121$	−5.60603	+	9.46427i	−0.509639	+	0.860388i
$122$	5.00279			0.452931
$123$	−0.216445	−	0.0460068i	−0.0195162	−	0.00414830i
$124$	−2.82270	+	1.25675i	−0.253486	+	0.112859i
$125$	9.52843	−	6.92281i	0.852249	−	0.619195i
$126$	0.826846	−	2.54477i	0.0736613	−	0.226706i
$127$	−6.67531	−	7.41368i	−0.592338	−	0.657858i	0.370217	−	0.928945i	$-0.379283\pi$
$127$	−6.67531	−	7.41368i	−0.592338	−	0.657858i	−0.962555	+	0.271087i	$0.912617\pi$
$128$	−0.913545	−	0.406737i	−0.0807468	−	0.0359508i
$129$	−0.793199	+	0.353155i	−0.0698372	+	0.0310935i
$130$	−3.17335	+	3.52437i	−0.278321	+	0.309107i
$131$	2.48059	+	4.29650i	0.216730	+	0.375387i	0.953806	−	0.300422i	$-0.0971276\pi$
$131$	2.48059	+	4.29650i	0.216730	+	0.375387i	−0.737077	+	0.675809i	$0.763794\pi$
$132$	0.675718	+	1.18562i	0.0588137	+	0.103195i
$133$	1.56266	−	3.81244i	0.135500	−	0.330580i
$134$	−3.54192	−	10.9009i	−0.305975	−	0.941695i
$135$	0.388848	−	3.69964i	0.0334667	−	0.318415i
$136$	−3.14856	−	1.40183i	−0.269987	−	0.120206i
$137$	1.94294	+	2.15785i	0.165996	+	0.184358i	0.820404	−	0.571784i	$-0.193749\pi$
$137$	1.94294	+	2.15785i	0.165996	+	0.184358i	−0.654408	+	0.756142i	$0.727082\pi$
$138$	1.92057	−	0.408230i	0.163490	−	0.0347509i
$139$	0.972971	+	9.25720i	0.0825263	+	0.785186i	0.955016	+	0.296553i	$0.0958373\pi$
$139$	0.972971	+	9.25720i	0.0825263	+	0.785186i	−0.872490	+	0.488632i	$0.837496\pi$
$140$	−1.18578	−	0.861520i	−0.100217	−	0.0728117i
$141$	0.702342	+	2.16159i	0.0591479	+	0.182038i
$142$	−4.61683	+	7.99658i	−0.387436	+	0.671058i
$143$	−3.08073	−	9.66478i	−0.257623	−	0.808210i
$144$	−2.83070			−0.235892
$145$	−1.46221	−	4.50023i	−0.121430	−	0.373724i
$146$	9.51539	−	4.23653i	0.787500	−	0.350617i
$147$	−2.29535	−	1.02195i	−0.189317	−	0.0842894i
$148$	−0.198347	−	0.220286i	−0.0163040	−	0.0181074i
$149$	−21.6634	+	4.60470i	−1.77474	+	0.377232i	−0.974840	−	0.222907i	$-0.928445\pi$
$149$	−21.6634	+	4.60470i	−1.77474	+	0.377232i	−0.799896	+	0.600139i	$0.795112\pi$
$150$	0.975671	+	0.434397i	0.0796632	+	0.0354684i
$151$	6.83627	+	4.96684i	0.556328	+	0.404196i	0.830113	−	0.557595i	$-0.188276\pi$
$151$	6.83627	+	4.96684i	0.556328	+	0.404196i	−0.273785	+	0.961791i	$0.588276\pi$
$152$	−4.34670	−	0.325915i	−0.352564	−	0.0264352i
$153$	−9.75609			−0.788733
$154$	2.87109	−	1.25913i	0.231359	−	0.101464i
$155$	2.39554	+	4.14920i	0.192415	+	0.333272i
$156$	−1.23095	−	0.261646i	−0.0985548	−	0.0209485i
$157$	1.84671	−	17.5703i	0.147383	−	1.40226i	−0.631639	−	0.775263i	$-0.717617\pi$
$157$	1.84671	−	17.5703i	0.147383	−	1.40226i	0.779022	−	0.626996i	$-0.215716\pi$
$158$	1.30271	+	12.3945i	0.103638	+	0.986052i
$159$	0.0821665	−	0.252882i	0.00651623	−	0.0200549i
$160$	−0.479160	+	1.47470i	−0.0378809	+	0.116586i
$161$	−0.471501	−	4.48604i	−0.0371595	−	0.353549i
$162$	−6.85614	+	3.05255i	−0.538669	+	0.239831i
$163$	−1.30168	−	4.00615i	−0.101955	−	0.313786i	0.887049	−	0.461676i	$-0.152752\pi$
$163$	−1.30168	−	4.00615i	−0.101955	−	0.313786i	−0.989004	+	0.147890i	$0.952752\pi$
$164$	0.537795			0.0419948
$165$	1.71882	−	1.23419i	0.133810	−	0.0960817i
$166$	−0.872821	−	1.51177i	−0.0677440	−	0.117336i
$167$	2.75337	+	0.585246i	0.213062	+	0.0452877i	0.313206	−	0.949685i	$-0.398597\pi$
$167$	2.75337	+	0.585246i	0.213062	+	0.0452877i	−0.100144	+	0.994973i	$0.531930\pi$
$168$	0.0406546	−	0.386802i	0.00313657	−	0.0298424i
$169$	−3.33038	−	1.48278i	−0.256183	−	0.114060i
$170$	−1.65144	+	5.08260i	−0.126660	+	0.389818i
$171$	−11.6157	+	4.16176i	−0.888274	+	0.318258i
$172$	1.70719	−	1.24035i	0.130172	−	0.0945757i
$173$	−0.265530	+	2.52634i	−0.0201878	+	0.192074i	−0.999968	−	0.00800273i	$-0.997453\pi$
$173$	−0.265530	+	2.52634i	−0.0201878	+	0.192074i	0.979780	+	0.200077i	$0.0641193\pi$
$174$	0.840170	−	0.933103i	0.0636931	−	0.0707384i
$175$	1.22678	−	2.12484i	0.0927356	−	0.160623i
$176$	−2.20546	−	2.47708i	−0.166243	−	0.186717i
$177$	−2.07477	+	3.59361i	−0.155949	+	0.270112i
$178$	1.16580	+	3.58797i	0.0873806	+	0.268930i
$179$	12.7027	+	9.22904i	0.949443	+	0.689811i	0.950675	−	0.310188i	$-0.100392\pi$
$179$	12.7027	+	9.22904i	0.949443	+	0.689811i	−0.00123175	+	0.999999i	$0.500392\pi$
$180$	0.458804	+	4.36523i	0.0341972	+	0.325365i
$181$	−2.07874	−	2.30867i	−0.154512	−	0.171602i	0.660919	−	0.750457i	$-0.270167\pi$
$181$	−2.07874	−	2.30867i	−0.154512	−	0.171602i	−0.815431	+	0.578855i	$0.803500\pi$
$182$	−0.893387	+	2.74956i	−0.0662223	+	0.203811i
$183$	1.66531	−	1.20992i	0.123104	−	0.0894400i
$184$	−4.35944	+	1.94095i	−0.321382	+	0.143088i
$185$	−0.307555	+	0.341575i	−0.0226119	+	0.0251131i
$186$	−0.635670	+	1.10101i	−0.0466096	+	0.0807302i
$187$	−7.60117	−	8.53734i	−0.555853	−	0.624312i
$188$	−2.76191	−	4.78377i	−0.201433	−	0.348892i
$189$	−0.700774	−	2.15676i	−0.0509738	−	0.156881i
$190$	0.201924	+	6.75587i	0.0146491	+	0.490122i
$191$	19.3215	−	14.0379i	1.39805	−	1.01574i	0.403125	−	0.915145i	$-0.367924\pi$
$191$	19.3215	−	14.0379i	1.39805	−	1.01574i	0.994927	−	0.100599i	$-0.0320759\pi$
$192$	−0.402467	+	0.0855471i	−0.0290456	+	0.00617383i
$193$	−22.3492	+	4.75047i	−1.60873	+	0.341946i	−0.922668	−	0.385596i	$-0.873996\pi$
$193$	−22.3492	+	4.75047i	−1.60873	+	0.341946i	−0.686063	+	0.727542i	$0.740663\pi$
$194$	1.44502	+	13.7484i	0.103746	+	0.987078i
$195$	−0.203971	+	1.94065i	−0.0146067	+	0.138973i
$196$	5.97305	+	1.26961i	0.426647	+	0.0906866i
$197$	−23.2106			−1.65369			−0.826844	−	0.562431i	$-0.809866\pi$
$197$	−23.2106			−1.65369			−0.826844	+	0.562431i	$0.809866\pi$
$198$	−8.55525	−	3.86642i	−0.607995	−	0.274775i
$199$	−6.48219	+	11.2275i	−0.459510	+	0.795895i	−0.998935	−	0.0461385i	$-0.985308\pi$
$199$	−6.48219	+	11.2275i	−0.459510	+	0.795895i	0.539425	+	0.842034i	$0.318642\pi$
$200$	−2.53893	−	0.539667i	−0.179530	−	0.0381602i
$201$	−3.81540	−	2.77205i	−0.269118	−	0.195525i
$202$	−0.397894	+	0.289087i	−0.0279957	+	0.0203401i
$203$	−1.93014	−	2.14364i	−0.135469	−	0.150454i
$204$	−1.38711	+	0.294840i	−0.0971175	+	0.0206430i
$205$	−0.0871666	−	0.829334i	−0.00608798	−	0.0579232i
$206$	−0.604477	+	5.75122i	−0.0421159	+	0.400706i
$207$	−9.03868	+	10.0385i	−0.628232	+	0.697722i
$208$	3.05850			0.212069
$209$	−12.6919	−	6.92212i	−0.877917	−	0.478813i
$210$	−0.603078			−0.0416163
$211$	13.2023	−	14.6627i	0.908886	−	1.00942i	−0.0910223	−	0.995849i	$-0.529013\pi$
$211$	13.2023	−	14.6627i	0.908886	−	1.00942i	0.999908	−	0.0135709i	$-0.00431989\pi$
$212$	−0.0675493	+	0.642688i	−0.00463930	+	0.0441400i
$213$	0.397132	+	3.77846i	0.0272110	+	0.258896i
$214$	−14.0833	+	2.99351i	−0.962717	+	0.204632i
$215$	−2.18945	−	2.43163i	−0.149319	−	0.165836i
$216$	−1.94091	+	1.41015i	−0.132062	+	0.0959487i
$217$	2.36288	+	1.71673i	0.160403	+	0.116539i
$218$	−9.14679	−	1.94421i	−0.619499	−	0.131679i
$219$	2.14286	−	3.71154i	0.144801	−	0.250802i
$220$	−3.46245	+	3.80253i	−0.233438	+	0.256366i
$221$	10.5412			0.709079
$222$	−0.119301	−	0.0253582i	−0.00800697	−	0.00170193i
$223$	0.830748	−	7.90404i	0.0556310	−	0.529293i	−0.930848	−	0.365406i	$-0.880930\pi$
$223$	0.830748	−	7.90404i	0.0556310	−	0.529293i	0.986479	−	0.163887i	$-0.0524033\pi$
$224$	0.0988059	+	0.940075i	0.00660175	+	0.0628114i
$225$	−7.18696	+	1.52764i	−0.479131	+	0.101842i
$226$	−3.60789	+	0.766881i	−0.239993	+	0.0510122i
$227$	−19.6069	+	14.2453i	−1.30136	+	0.945491i	−0.999968	−	0.00800981i	$-0.997450\pi$
$227$	−19.6069	+	14.2453i	−1.30136	+	0.945491i	−0.301389	+	0.953501i	$0.597450\pi$
$228$	−1.52574	+	0.942757i	−0.101045	+	0.0624356i
$229$	2.45015	+	7.54077i	0.161910	+	0.498308i	0.998795	−	0.0490703i	$-0.0156258\pi$
$229$	2.45015	+	7.54077i	0.161910	+	0.498308i	−0.836885	+	0.547378i	$0.815626\pi$
$230$	3.69972	+	6.40810i	0.243952	+	0.422537i
$231$	0.651200	−	1.11351i	0.0428458	−	0.0732633i
$232$	−1.52581	+	2.64278i	−0.100174	+	0.173507i
$233$	1.25708	−	1.39613i	0.0823540	−	0.0914633i	−0.700559	−	0.713594i	$-0.747066\pi$
$233$	1.25708	−	1.39613i	0.0823540	−	0.0914633i	0.782913	+	0.622131i	$0.213733\pi$
$234$	7.90921	−	3.52141i	0.517042	−	0.230202i
$235$	−6.92940	+	5.03451i	−0.452024	+	0.328415i
$236$	3.11642	−	9.59135i	0.202862	−	0.624344i
$237$	3.43124	+	3.81078i	0.222883	+	0.247537i
$238$	0.340537	+	3.23999i	0.0220737	+	0.210018i
$239$	8.48793	+	6.16684i	0.549038	+	0.398900i	0.827431	−	0.561568i	$-0.189802\pi$
$239$	8.48793	+	6.16684i	0.549038	+	0.398900i	−0.278393	+	0.960467i	$0.589802\pi$
$240$	0.197155	+	0.606780i	0.0127263	+	0.0391675i
$241$	9.17677	−	15.8946i	0.591128	−	1.02386i	−0.402953	−	0.915221i	$-0.632016\pi$
$241$	9.17677	−	15.8946i	0.591128	−	1.02386i	0.994081	−	0.108643i	$-0.0346505\pi$
$242$	−3.28216	−	10.4989i	−0.210985	−	0.674897i
$243$	−5.14264	+	8.90731i	−0.329900	+	0.571404i
$244$	−3.34752	+	3.71780i	−0.214303	+	0.238007i
$245$	0.989749	−	9.41683i	0.0632327	−	0.601619i
$246$	0.179020	−	0.130065i	0.0114139	−	0.00829267i
$247$	12.5505	−	4.49668i	0.798567	−	0.286117i
$248$	0.954812	−	2.93861i	0.0606306	−	0.186602i
$249$	−0.656163	−	0.292143i	−0.0415826	−	0.0185138i
$250$	−1.23111	+	11.7133i	−0.0778625	+	0.740812i
$251$	19.1613	+	4.07286i	1.20945	+	0.257077i	0.768143	−	0.640279i	$-0.221181\pi$
$251$	19.1613	+	4.07286i	1.20945	+	0.257077i	0.441308	+	0.897356i	$0.354515\pi$
$252$	1.33787	+	2.31725i	0.0842776	+	0.145973i
$253$	−15.8267	−	0.0883669i	−0.995015	−	0.00555558i
$254$	9.97609			0.625956
$255$	0.679499	+	2.09128i	0.0425519	+	0.130961i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−0.959888	−	9.13273i	−0.0598762	−	0.569684i	−0.982796	−	0.184692i	$-0.940871\pi$
$257$	−0.959888	−	9.13273i	−0.0598762	−	0.569684i	0.922920	−	0.384991i	$-0.125796\pi$
$258$	0.268308	−	0.825768i	0.0167041	−	0.0514101i
$259$	−0.0865854	+	0.266482i	−0.00538016	+	0.0165584i
$260$	−0.495726	−	4.71652i	−0.0307436	−	0.292506i
$261$	−0.902939	+	8.59089i	−0.0558905	+	0.531763i
$262$	−4.85276	−	1.03149i	−0.299804	−	0.0637254i
$263$	8.28145	+	14.3439i	0.510656	+	0.884483i	0.999924	+	0.0123488i	$0.00393083\pi$
$263$	8.28145	+	14.3439i	0.510656	+	0.884483i	−0.489268	+	0.872134i	$0.662736\pi$
$264$	−1.33323	−	0.291176i	−0.0820546	−	0.0179206i
$265$	1.00204			0.0615547
$266$	1.78757	+	3.71230i	0.109603	+	0.227616i
$267$	1.25582	+	0.912405i	0.0768548	+	0.0558383i
$268$	10.4710	+	4.66197i	0.639616	+	0.284775i
$269$	−25.8560	+	5.49587i	−1.57647	+	0.335089i	−0.911345	−	0.411643i	$-0.864955\pi$
$269$	−25.8560	+	5.49587i	−1.57647	+	0.335089i	−0.665125	+	0.746732i	$0.731622\pi$
$270$	2.48918	+	2.76452i	0.151487	+	0.168243i
$271$	9.06023	+	4.03388i	0.550370	+	0.245041i	0.663030	−	0.748593i	$-0.269270\pi$
$271$	9.06023	+	4.03388i	0.550370	+	0.245041i	−0.112660	+	0.993634i	$0.535937\pi$
$272$	3.14856	−	1.40183i	0.190909	−	0.0849983i
$273$	0.367592	+	1.13133i	0.0222477	+	0.0684713i
$274$	−2.90367			−0.175417
$275$	−6.93632	−	5.09894i	−0.418276	−	0.307478i
$276$	−0.981740	+	1.70042i	−0.0590938	+	0.102353i
$277$	6.98884	+	21.5094i	0.419919	+	1.29238i	0.907777	+	0.419454i	$0.137778\pi$
$277$	6.98884	+	21.5094i	0.419919	+	1.29238i	−0.487858	+	0.872923i	$0.662222\pi$
$278$	−7.53049	−	5.47122i	−0.451649	−	0.328142i
$279$	−0.914248	−	8.69849i	−0.0547346	−	0.520765i
$280$	1.43368	−	0.304737i	0.0856786	−	0.0182115i
$281$	−7.21370	−	8.01162i	−0.430333	−	0.477933i	0.488509	−	0.872559i	$-0.337541\pi$
$281$	−7.21370	−	8.01162i	−0.430333	−	0.477933i	−0.918842	+	0.394626i	$0.870874\pi$
$282$	−2.07633	−	0.924442i	−0.123644	−	0.0550497i
$283$	0.0375756	−	0.357508i	0.00223364	−	0.0212516i	−0.993348	−	0.115148i	$-0.963266\pi$
$283$	0.0375756	−	0.357508i	0.00223364	−	0.0212516i	0.995582	+	0.0938967i	$0.0299323\pi$
$284$	−2.85336	−	8.78173i	−0.169316	−	0.521100i
$285$	1.70112	+	2.20004i	0.100766	+	0.130319i
$286$	9.24374	+	4.17758i	0.546594	+	0.247025i
$287$	−0.254176	−	0.440247i	−0.0150036	−	0.0259869i
$288$	1.89411	−	2.10362i	0.111611	−	0.123957i
$289$	−4.67868	+	2.08308i	−0.275217	+	0.122534i
$290$	4.32273	+	1.92461i	0.253840	+	0.113017i
$291$	3.80606	+	4.22705i	0.223115	+	0.247794i
$292$	−3.21869	+	9.90610i	−0.188359	+	0.579711i
$293$	13.3813	−	9.72212i	0.781747	−	0.567972i	−0.123756	−	0.992313i	$-0.539494\pi$
$293$	13.3813	−	9.72212i	0.781747	−	0.567972i	0.905503	+	0.424340i	$0.139494\pi$
$294$	2.29535	−	1.02195i	0.133867	−	0.0596016i
$295$	−15.2959	−	3.25125i	−0.890564	−	0.189295i
$296$	0.296424			0.0172293
$297$	−7.79213	+	1.61085i	−0.452145	+	0.0934710i
$298$	11.0737	−	19.1802i	0.641482	−	1.11108i
$299$	9.76608	−	10.8463i	0.564787	−	0.627259i
$300$	−0.975671	+	0.434397i	−0.0563304	+	0.0250799i
$301$	−1.82223	−	0.811310i	−0.105032	−	0.0467631i
$302$	−8.26545	+	1.75687i	−0.475623	+	0.101097i
$303$	−0.0625343	+	0.192461i	−0.00359250	+	0.0110566i
$304$	3.15071	−	3.01215i	0.180706	−	0.172758i
$305$	6.27579	+	4.55963i	0.359350	+	0.261083i
$306$	6.52810	−	7.25019i	0.373186	−	0.414466i
$307$	−13.1296	−	22.7411i	−0.749345	−	1.29790i	−0.948137	−	0.317862i	$-0.897035\pi$
$307$	−13.1296	−	22.7411i	−0.749345	−	1.29790i	0.198792	−	0.980042i	$-0.436298\pi$
$308$	−0.985416	+	2.97616i	−0.0561493	+	0.169582i
$309$	1.18971	+	2.06064i	0.0676803	+	0.117226i
$310$	−4.68639	−	0.996122i	−0.266169	−	0.0565759i
$311$	−13.6705	−	9.93219i	−0.775182	−	0.563203i	0.128347	−	0.991729i	$-0.459033\pi$
$311$	−13.6705	−	9.93219i	−0.775182	−	0.563203i	−0.903529	+	0.428527i	$0.859033\pi$
$312$	1.01811	−	0.739698i	0.0576389	−	0.0418771i
$313$	22.3382	+	24.8090i	1.26263	+	1.40229i	0.877606	+	0.479383i	$0.159139\pi$
$313$	22.3382	+	24.8090i	1.26263	+	1.40229i	0.385022	+	0.922907i	$0.374194\pi$
$314$	11.8216	+	13.1292i	0.667129	+	0.740922i
$315$	3.35659	−	2.43871i	0.189123	−	0.137406i
$316$	−10.0826	−	7.32542i	−0.567189	−	0.412087i
$317$	15.0973	+	3.20904i	0.847952	+	0.180238i	0.611341	−	0.791367i	$-0.290630\pi$
$317$	15.0973	+	3.20904i	0.847952	+	0.180238i	0.236610	+	0.971605i	$0.423964\pi$
$318$	0.132948	+	0.230273i	0.00745536	+	0.0129131i
$319$	−8.22120	+	5.90320i	−0.460299	+	0.330516i
$320$	−0.775298	−	1.34285i	−0.0433405	−	0.0750679i
$321$	−3.96405	+	4.40252i	−0.221251	+	0.245725i
$322$	3.64927	+	2.65135i	0.203366	+	0.147754i
$323$	10.8590	−	10.3814i	0.604211	−	0.577639i
$324$	2.31917	−	7.13766i	0.128843	−	0.396536i
$325$	7.76534	−	1.65057i	0.430744	−	0.0915574i
$326$	3.84814	+	1.71330i	0.213129	+	0.0948910i
$327$	−3.51496	+	1.56496i	−0.194378	+	0.0865426i
$328$	−0.359855	+	0.399660i	−0.0198697	+	0.0220675i
$329$	−2.61071	+	4.52188i	−0.143933	+	0.249299i
$330$	−0.232931	+	2.10317i	−0.0128224	+	0.115776i
$331$	11.2139			0.616373			0.308187	−	0.951326i	$-0.400278\pi$
$331$	11.2139			0.616373			0.308187	+	0.951326i	$0.400278\pi$
$332$	1.70750	+	0.362939i	0.0937110	+	0.0199189i
$333$	0.766546	−	0.341288i	0.0420065	−	0.0187025i
$334$	−2.27728	+	1.65454i	−0.124607	+	0.0905326i
$335$	5.49208	−	16.9029i	0.300064	−	0.923504i
$336$	0.260247	+	0.289034i	0.0141976	+	0.0157681i
$337$	12.7761	+	5.68828i	0.695958	+	0.309860i	0.724052	−	0.689745i	$-0.242277\pi$
$337$	12.7761	+	5.68828i	0.695958	+	0.309860i	−0.0280946	+	0.999605i	$0.508944\pi$
$338$	3.33038	−	1.48278i	0.181149	−	0.0806526i
$339$	−1.01552	+	1.12784i	−0.0551552	+	0.0612561i
$340$	−2.67208	−	4.62818i	−0.144914	−	0.250999i
$341$	6.89955	−	7.57721i	0.373631	−	0.410329i
$342$	4.67962	−	11.4169i	0.253045	−	0.617355i
$343$	−3.82840	−	11.7826i	−0.206714	−	0.636201i
$344$	−0.220577	+	2.09865i	−0.0118927	+	0.113152i
$345$	2.78135	+	1.23834i	0.149743	+	0.0666697i
$346$	−1.69977	−	1.88778i	−0.0913800	−	0.101488i
$347$	−6.70667	+	1.42555i	−0.360033	+	0.0765274i	−0.384377	−	0.923176i	$-0.625584\pi$
$347$	−6.70667	+	1.42555i	−0.360033	+	0.0765274i	0.0243438	+	0.999704i	$0.492250\pi$
$348$	0.131247	+	1.24874i	0.00703560	+	0.0669393i
$349$	−4.91293	−	3.56946i	−0.262983	−	0.191069i	0.448478	−	0.893794i	$-0.351966\pi$
$349$	−4.91293	−	3.56946i	−0.262983	−	0.191069i	−0.711461	+	0.702725i	$0.751966\pi$
$350$	0.758189	+	2.33347i	0.0405269	+	0.124729i
$351$	3.66882	−	6.35458i	0.195827	−	0.339182i
$352$	3.31657	+	0.0185178i	0.176774	+	0.000987003i
$353$	0.484296			0.0257765			0.0128882	−	0.999917i	$-0.495897\pi$
$353$	0.484296			0.0257765			0.0128882	+	0.999917i	$0.495897\pi$
$354$	−1.28228	−	3.94644i	−0.0681523	−	0.209751i
$355$	−13.0798	+	5.82352i	−0.694206	+	0.309080i
$356$	−3.44646	−	1.53446i	−0.182662	−	0.0813263i
$357$	0.896948	+	0.996162i	0.0474715	+	0.0527225i
$358$	−15.3583	+	3.26450i	−0.811710	+	0.172534i
$359$	−6.38427	−	2.84246i	−0.336949	−	0.150019i	0.231286	−	0.972886i	$-0.425707\pi$
$359$	−6.38427	−	2.84246i	−0.336949	−	0.150019i	−0.568235	+	0.822867i	$0.692373\pi$
$360$	−3.55100	−	2.57995i	−0.187154	−	0.135975i
$361$	8.50031	−	16.9925i	0.447385	−	0.894342i
$362$	3.10663			0.163281
$363$	−3.63171	−	2.70107i	−0.190616	−	0.141769i
$364$	−1.44553	−	2.50373i	−0.0757664	−	0.131231i
$365$	15.7979	+	3.35795i	0.826900	+	0.175763i
$366$	−0.215166	+	2.04716i	−0.0112469	+	0.107007i
$367$	3.62769	+	34.5152i	0.189364	+	1.80168i	0.516063	+	0.856551i	$0.327397\pi$
$367$	3.62769	+	34.5152i	0.189364	+	1.80168i	−0.326699	+	0.945128i	$0.605936\pi$
$368$	1.47463	−	4.53844i	0.0768703	−	0.236582i
$369$	−0.470428	+	1.44783i	−0.0244895	+	0.0753710i
$370$	−0.0480449	−	0.457116i	−0.00249773	−	0.0237643i
$371$	0.558039	−	0.248455i	0.0289719	−	0.0128991i
$372$	−0.392866	−	1.20912i	−0.0203691	−	0.0626898i
$373$	9.28945			0.480989			0.240495	−	0.970650i	$-0.422690\pi$
$373$	9.28945			0.480989			0.240495	+	0.970650i	$0.422690\pi$
$374$	11.4307	+	0.0638221i	0.591065	+	0.00330016i
$375$	2.42304	+	4.19682i	0.125125	+	0.216723i
$376$	5.40311	+	1.14847i	0.278644	+	0.0592277i
$377$	0.975604	−	9.28225i	0.0502462	−	0.478060i
$378$	2.07169	+	0.922378i	0.106556	+	0.0474420i
$379$	−6.69335	+	20.6000i	−0.343814	+	1.05815i	0.618401	+	0.785862i	$0.287781\pi$
$379$	−6.69335	+	20.6000i	−0.343814	+	1.05815i	−0.962216	+	0.272289i	$0.912219\pi$
$380$	−5.15570	−	4.37050i	−0.264482	−	0.224202i
$381$	3.32081	−	2.41271i	0.170130	−	0.123607i
$382$	−2.49642	+	23.7518i	−0.127728	+	1.21525i
$383$	−5.70486	+	6.33589i	−0.291505	+	0.323749i	−0.871053	−	0.491189i	$-0.836562\pi$
$383$	−5.70486	+	6.33589i	−0.291505	+	0.323749i	0.579548	+	0.814938i	$0.303229\pi$
$384$	0.205729	−	0.356334i	0.0104986	−	0.0181841i
$385$	4.74925	+	1.03723i	0.242044	+	0.0528622i
$386$	11.4243	−	19.7874i	0.581479	−	1.00715i
$387$	1.84587	+	5.68101i	0.0938310	+	0.288782i
$388$	−11.1840	−	8.12562i	−0.567780	−	0.412516i
$389$	2.72367	+	25.9139i	0.138095	+	1.31389i	0.815705	+	0.578468i	$0.196349\pi$
$389$	2.72367	+	25.9139i	0.138095	+	1.31389i	−0.677610	+	0.735421i	$0.736984\pi$
$390$	−1.30570	−	1.45013i	−0.0661169	−	0.0734303i
$391$	5.08234	−	15.6418i	0.257025	−	0.791042i
$392$	−4.94026	+	3.58931i	−0.249521	+	0.181287i
$393$	−1.86484	+	0.830279i	−0.0940686	+	0.0418820i
$394$	15.5309	−	17.2488i	0.782437	−	0.868984i
$395$	−9.66234	+	16.7357i	−0.486165	+	0.842063i
$396$	8.59789	−	3.77065i	0.432060	−	0.189482i
$397$	14.3686	+	24.8871i	0.721137	+	1.24905i	0.960544	+	0.278127i	$0.0897136\pi$
$397$	14.3686	+	24.8871i	0.721137	+	1.24905i	−0.239407	+	0.970919i	$0.576953\pi$
$398$	−4.00621	−	12.3299i	−0.200813	−	0.618040i
$399$	1.49286	+	0.803419i	0.0747364	+	0.0402212i
$400$	2.09993	−	1.52569i	0.104996	−	0.0762844i
$401$	11.7820	−	2.50435i	0.588367	−	0.125061i	0.0958980	−	0.995391i	$-0.469428\pi$
$401$	11.7820	−	2.50435i	0.588367	−	0.125061i	0.492469	+	0.870330i	$0.336094\pi$
$402$	4.61304	−	0.980532i	0.230077	−	0.0489045i
$403$	0.987823	+	9.39850i	0.0492069	+	0.468173i
$404$	0.0514096	−	0.489130i	0.00255772	−	0.0243351i
$405$	−11.3829	−	2.41951i	−0.565620	−	0.120226i
$406$	2.88455			0.143158
$407$	0.895886	+	0.404883i	0.0444074	+	0.0200693i
$408$	0.709052	−	1.22811i	0.0351033	−	0.0608007i
$409$	31.0963	+	6.60973i	1.53761	+	0.326830i	0.897348	−	0.441323i	$-0.145491\pi$
$409$	31.0963	+	6.60973i	1.53761	+	0.326830i	0.640266	+	0.768153i	$0.278824\pi$
$410$	0.674641	+	0.490156i	0.0333182	+	0.0242071i
$411$	−0.966567	+	0.702252i	−0.0476772	+	0.0346395i
$412$	−3.86951	−	4.29753i	−0.190637	−	0.211724i
$413$	−9.32451	+	1.98199i	−0.458829	+	0.0975272i
$414$	−1.41198	−	13.4341i	−0.0693951	−	0.660250i
$415$	0.282936	−	2.69196i	0.0138888	−	0.132143i
$416$	−2.04654	+	2.27291i	−0.100340	+	0.111439i
$417$	−3.82994			−0.187553
$418$	13.6367	−	4.80011i	0.666992	−	0.234781i
$419$	14.9880			0.732214			0.366107	−	0.930573i	$-0.380690\pi$
$419$	14.9880			0.732214			0.366107	+	0.930573i	$0.380690\pi$
$420$	0.403538	−	0.448174i	0.0196906	−	0.0218687i
$421$	3.48387	−	33.1468i	0.169794	−	1.61548i	−0.495303	−	0.868720i	$-0.664943\pi$
$421$	3.48387	−	33.1468i	0.169794	−	1.61548i	0.665097	−	0.746757i	$-0.268390\pi$
$422$	2.06241	+	19.6225i	0.100396	+	0.955207i
$423$	15.2946	−	3.25097i	0.743649	−	0.158067i
$424$	−0.432411	−	0.480241i	−0.0209997	−	0.0233226i
$425$	7.23746	−	5.25832i	0.351068	−	0.255066i
$426$	−3.07367	−	2.23316i	−0.148920	−	0.108197i
$427$	4.62557	+	0.983194i	0.223847	+	0.0475801i
$428$	7.19899	−	12.4690i	0.347976	−	0.602712i
$429$	4.08738	−	0.844974i	0.197340	−	0.0407957i
$430$	3.27208			0.157794
$431$	−29.1100	−	6.18753i	−1.40218	−	0.298043i	−0.556108	−	0.831110i	$-0.687706\pi$
$431$	−29.1100	−	6.18753i	−1.40218	−	0.298043i	−0.846073	+	0.533067i	$0.821039\pi$
$432$	0.250774	−	2.38595i	0.0120653	−	0.114794i
$433$	1.32845	+	12.6393i	0.0638411	+	0.607408i	0.978936	+	0.204169i	$0.0654491\pi$
$433$	1.32845	+	12.6393i	0.0638411	+	0.607408i	−0.915095	+	0.403239i	$0.867884\pi$
$434$	−2.85685	+	0.607243i	−0.137133	+	0.0291486i
$435$	1.90440	−	0.404794i	0.0913092	−	0.0194084i
$436$	7.56523	−	5.49646i	0.362309	−	0.263233i
$437$	−0.621427	−	20.7914i	−0.0297269	−	0.994586i
$438$	1.32436	+	4.07595i	0.0632803	+	0.194757i
$439$	1.96937	+	3.41106i	0.0939931	+	0.162801i	0.909188	−	0.416386i	$-0.136704\pi$
$439$	1.96937	+	3.41106i	0.0939931	+	0.162801i	−0.815195	+	0.579187i	$0.803370\pi$
$440$	−0.508998	−	5.11749i	−0.0242655	−	0.243967i
$441$	−8.64283	+	14.9698i	−0.411563	+	0.712849i
$442$	−7.05345	+	7.83365i	−0.335498	+	0.372609i
$443$	−5.33843	+	2.37682i	−0.253636	+	0.112926i	−0.529617	−	0.848237i	$-0.677664\pi$
$443$	−5.33843	+	2.37682i	−0.253636	+	0.112926i	0.275980	+	0.961163i	$0.410998\pi$
$444$	0.0986729	−	0.0716901i	0.00468281	−	0.00340226i
$445$	−1.80769	+	5.56349i	−0.0856926	+	0.263735i
$446$	5.31796	+	5.90620i	0.251813	+	0.279667i
$447$	−0.952540	−	9.06281i	−0.0450536	−	0.428656i
$448$	−0.764726	−	0.555606i	−0.0361299	−	0.0262499i
$449$	−8.92107	−	27.4562i	−0.421011	−	1.29574i	−0.906762	−	0.421643i	$-0.861454\pi$
$449$	−8.92107	−	27.4562i	−0.421011	−	1.29574i	0.485751	−	0.874097i	$-0.338546\pi$
$450$	3.67376	−	6.36314i	0.173183	−	0.299961i
$451$	−1.63348	+	0.716373i	−0.0769178	+	0.0337327i
$452$	1.84425	−	3.19433i	0.0867461	−	0.150249i
$453$	−2.32648	+	2.58382i	−0.109308	+	0.121398i
$454$	2.53330	−	24.1027i	0.118894	−	1.13120i
$455$	−3.62672	+	2.63496i	−0.170023	+	0.123529i
$456$	0.320314	−	1.76467i	0.0150001	−	0.0826384i
$457$	8.93966	−	27.5135i	0.418180	−	1.28703i	−0.491196	−	0.871049i	$-0.663440\pi$
$457$	8.93966	−	27.5135i	0.418180	−	1.28703i	0.909376	−	0.415976i	$-0.136560\pi$
$458$	−7.24335	−	3.22495i	−0.338460	−	0.150692i
$459$	0.864298	−	8.22324i	0.0403420	−	0.383828i
$460$	−7.23774	−	1.53843i	−0.337461	−	0.0717296i
$461$	11.4315	+	19.7999i	0.532416	+	0.922172i	0.999284	+	0.0378449i	$0.0120493\pi$
$461$	11.4315	+	19.7999i	0.532416	+	0.922172i	−0.466867	+	0.884327i	$0.654617\pi$
$462$	0.391759	+	1.22902i	0.0182263	+	0.0571790i
$463$	−21.1560			−0.983203			−0.491602	−	0.870820i	$-0.663588\pi$
$463$	−21.1560			−0.983203			−0.491602	+	0.870820i	$0.663588\pi$
$464$	−0.943001	−	2.90226i	−0.0437777	−	0.134734i
$465$	−1.80090	+	0.801814i	−0.0835149	+	0.0371832i
$466$	0.196375	+	1.86838i	0.00909689	+	0.0865512i
$467$	−10.0518	+	30.9362i	−0.465141	+	1.43156i	0.393664	+	0.919254i	$0.371207\pi$
$467$	−10.0518	+	30.9362i	−0.465141	+	1.43156i	−0.858805	+	0.512303i	$0.828793\pi$
$468$	−2.67538	+	8.23397i	−0.123670	+	0.380616i
$469$	−1.13250	−	10.7750i	−0.0522941	−	0.497545i
$470$	0.895309	−	8.51829i	0.0412975	−	0.392920i
$471$	7.11041	+	1.51136i	0.327630	+	0.0696400i
$472$	5.04247	+	8.73381i	0.232098	+	0.402006i
$473$	−3.53317	+	6.04148i	−0.162455	+	0.277788i
$474$	−5.12791			−0.235533
$475$	6.37389	−	9.34797i	0.292454	−	0.428914i
$476$	−2.63565	−	1.91491i	−0.120805	−	0.0877698i
$477$	−1.67113	−	0.744035i	−0.0765158	−	0.0340670i
$478$	−10.2624	+	2.18134i	−0.469391	+	0.0997720i
$479$	8.87286	+	9.85431i	0.405411	+	0.450255i	0.910930	−	0.412561i	$-0.135366\pi$
$479$	8.87286	+	9.85431i	0.405411	+	0.450255i	−0.505519	+	0.862816i	$0.668699\pi$
$480$	−0.582848	−	0.259500i	−0.0266032	−	0.0118445i
$481$	−0.828234	+	0.368754i	−0.0377642	+	0.0168137i
$482$	5.67156	+	17.4553i	0.258332	+	0.795065i
$483$	1.85599			0.0844503
$484$	9.99841	+	4.58604i	0.454473	+	0.208456i
$485$	−10.7178	+	18.5638i	−0.486671	+	0.842939i
$486$	−3.17832	−	9.78187i	−0.144172	−	0.443715i
$487$	−9.13371	−	6.63603i	−0.413888	−	0.300707i	0.361286	−	0.932455i	$-0.382338\pi$
$487$	−9.13371	−	6.63603i	−0.413888	−	0.300707i	−0.775174	+	0.631748i	$0.782338\pi$
$488$	−0.522934	−	4.97538i	−0.0236721	−	0.225225i
$489$	1.69532	−	0.360351i	0.0766650	−	0.0162956i
$490$	6.33580	+	7.03662i	0.286222	+	0.317882i
$491$	3.50188	+	1.55914i	0.158038	+	0.0703630i	0.484231	−	0.874940i	$-0.339099\pi$
$491$	3.50188	+	1.55914i	0.158038	+	0.0703630i	−0.326193	+	0.945303i	$0.605766\pi$
$492$	−0.0231301	+	0.220068i	−0.00104279	+	0.00992145i
$493$	−3.25008	−	10.0027i	−0.146376	−	0.450500i
$494$	−5.05622	+	12.3357i	−0.227490	+	0.555009i
$495$	−7.20828	−	12.6477i	−0.323988	−	0.568470i
$496$	1.54492	+	2.67588i	0.0693688	+	0.120150i
$497$	−5.84027	+	6.48628i	−0.261972	+	0.290949i
$498$	0.656163	−	0.292143i	0.0294034	−	0.0130912i
$499$	−35.7115	−	15.8998i	−1.59867	−	0.711773i	−0.602409	−	0.798188i	$-0.705792\pi$
$499$	−35.7115	−	15.8998i	−1.59867	−	0.711773i	−0.996259	+	0.0864146i	$0.972459\pi$
$500$	−7.88088	−	8.75260i	−0.352444	−	0.391428i
$501$	−0.357905	+	1.10152i	−0.0159900	+	0.0492123i
$502$	−15.8481	+	11.5143i	−0.707337	+	0.513910i
$503$	3.94774	−	1.75765i	0.176021	−	0.0783696i	−0.316834	−	0.948481i	$-0.602620\pi$
$503$	3.94774	−	1.75765i	0.176021	−	0.0783696i	0.492855	+	0.870111i	$0.335953\pi$
$504$	−2.61726	−	0.556316i	−0.116582	−	0.0247803i
$505$	−0.762620			−0.0339361
$506$	10.6558	−	11.7024i	0.473707	−	0.520234i
$507$	0.749997	−	1.29903i	0.0333085	−	0.0576921i
$508$	−6.67531	+	7.41368i	−0.296169	+	0.328929i
$509$	−25.4964	+	11.3517i	−1.13011	+	0.503157i	−0.884652	−	0.466251i	$-0.845604\pi$
$509$	−25.4964	+	11.3517i	−1.13011	+	0.503157i	−0.245456	+	0.969408i	$0.578938\pi$
$510$	−2.00880	−	0.894375i	−0.0889511	−	0.0396036i
$511$	9.63051	−	2.04703i	0.426029	−	0.0905552i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−2.47884	−	10.1594i	−0.109443	−	0.448547i
$514$	7.42923	+	5.39765i	0.327689	+	0.238080i
$515$	−6.00005	+	6.66373i	−0.264394	+	0.293639i
$516$	0.434132	+	0.751939i	0.0191116	+	0.0331022i
$517$	14.7612	+	10.8511i	0.649197	+	0.477230i
$518$	−0.140098	−	0.242657i	−0.00615556	−	0.0106617i
$519$	−1.02237	−	0.217312i	−0.0448772	−	0.00953894i
$520$	3.83676	+	2.78757i	0.168253	+	0.122243i
$521$	3.92549	−	2.85204i	0.171979	−	0.124950i	−0.498466	−	0.866909i	$-0.666103\pi$
$521$	3.92549	−	2.85204i	0.171979	−	0.124950i	0.670445	+	0.741959i	$0.266103\pi$
$522$	−5.78009	−	6.41944i	−0.252988	−	0.280971i
$523$	6.28942	+	6.98511i	0.275017	+	0.305437i	0.864792	−	0.502130i	$-0.167450\pi$
$523$	6.28942	+	6.98511i	0.275017	+	0.305437i	−0.589775	+	0.807568i	$0.700784\pi$
$524$	4.01367	−	2.91610i	0.175338	−	0.127391i
$525$	0.816732	+	0.593390i	0.0356451	+	0.0258977i
$526$	−16.2010	−	3.44362i	−0.706396	−	0.150149i
$527$	5.32460	+	9.22248i	0.231943	+	0.401737i
$528$	1.10849	−	0.795947i	0.0482408	−	0.0346392i
$529$	0.114025	+	0.197497i	0.00495761	+	0.00858682i
$530$	−0.670495	+	0.744660i	−0.0291244	+	0.0323459i
$531$	23.0954	+	16.7798i	1.00225	+	0.728180i
$532$	−3.95489	−	1.15559i	−0.171466	−	0.0501013i
$533$	0.508286	−	1.56434i	0.0220163	−	0.0677593i
$534$	−1.51836	+	0.322736i	−0.0657057	+	0.0139662i
$535$	−20.3953	−	9.08057i	−0.881765	−	0.392587i
$536$	−10.4710	+	4.66197i	−0.452276	+	0.201366i
$537$	−4.32290	+	4.80107i	−0.186547	+	0.207181i
$538$	13.2168	−	22.8922i	0.569818	−	0.986954i
$539$	−19.8336	+	4.10015i	−0.854293	+	0.176606i
$540$	−3.72002			−0.160084
$541$	−35.3162	−	7.50668i	−1.51836	−	0.322737i	−0.628079	−	0.778149i	$-0.716159\pi$
$541$	−35.3162	−	7.50668i	−1.51836	−	0.322737i	−0.890281	+	0.455412i	$0.849492\pi$
$542$	−9.06023	+	4.03388i	−0.389170	+	0.173270i
$543$	1.03413	−	0.751336i	0.0443786	−	0.0322429i
$544$	−1.06504	+	3.27784i	−0.0456630	+	0.140536i
$545$	−9.70227	−	10.7755i	−0.415600	−	0.461570i
$546$	−1.08671	−	0.483835i	−0.0465069	−	0.0207062i
$547$	17.6402	−	7.85392i	0.754240	−	0.335809i	0.00665718	−	0.999978i	$-0.497881\pi$
$547$	17.6402	−	7.85392i	0.754240	−	0.335809i	0.747583	+	0.664169i	$0.231214\pi$
$548$	1.94294	−	2.15785i	0.0829982	−	0.0921788i
$549$	−7.08070	−	12.2641i	−0.302197	−	0.523420i
$550$	8.43055	−	1.74283i	0.359480	−	0.0743145i
$551$	−8.13654	−	10.5229i	−0.346628	−	0.448291i
$552$	−0.606749	−	1.86738i	−0.0258249	−	0.0794810i
$553$	−1.23139	+	11.7159i	−0.0523642	+	0.498212i
$554$	−20.6611	−	9.19891i	−0.877805	−	0.390824i
$555$	−0.126546	−	0.140544i	−0.00537159	−	0.00596576i
$556$	9.10479	−	1.93528i	0.386129	−	0.0820742i
$557$	0.881679	+	8.38861i	0.0373579	+	0.355437i	0.997193	+	0.0748725i	$0.0238550\pi$
$557$	0.881679	+	8.38861i	0.0373579	+	0.355437i	−0.959835	+	0.280564i	$0.909478\pi$
$558$	7.07599	+	5.14101i	0.299550	+	0.217636i
$559$	−1.99442	−	6.13820i	−0.0843550	−	0.259618i
$560$	−0.732853	+	1.26934i	−0.0309687	+	0.0536393i
$561$	3.82044	−	2.74325i	0.161299	−	0.115820i
$562$	10.7807			0.454756
$563$	11.6138	+	35.7435i	0.489462	+	1.50641i	0.825413	+	0.564529i	$0.190942\pi$
$563$	11.6138	+	35.7435i	0.489462	+	1.50641i	−0.335951	+	0.941879i	$0.609058\pi$
$564$	2.07633	−	0.924442i	0.0874293	−	0.0389260i
$565$	−5.22490	−	2.32627i	−0.219813	−	0.0978671i
$566$	0.240537	+	0.267144i	0.0101105	+	0.0112289i
$567$	−6.93908	+	1.47495i	−0.291414	+	0.0619420i
$568$	8.43537	+	3.75567i	0.353940	+	0.157584i
$569$	11.3237	+	8.22712i	0.474712	+	0.344899i	0.799275	−	0.600965i	$-0.205217\pi$
$569$	11.3237	+	8.22712i	0.474712	+	0.344899i	−0.324563	+	0.945864i	$0.605217\pi$
$570$	−2.77322	−	0.207936i	−0.116157	−	0.00870948i
$571$	37.8285			1.58307			0.791537	−	0.611121i	$-0.209281\pi$
$571$	37.8285			1.58307			0.791537	+	0.611121i	$0.209281\pi$
$572$	−9.28982	+	4.07410i	−0.388427	+	0.170347i
$573$	4.91336	+	8.51019i	0.205259	+	0.355518i
$574$	0.497244	+	0.105693i	0.0207546	+	0.00441152i
$575$	1.29474	−	12.3186i	0.0539943	−	0.513721i
$576$	0.295889	+	2.81519i	0.0123287	+	0.117300i
$577$	−3.66512	+	11.2801i	−0.152581	+	0.469596i	−0.997908	−	0.0646535i	$-0.979406\pi$
$577$	−3.66512	+	11.2801i	−0.152581	+	0.469596i	0.845327	+	0.534250i	$0.179406\pi$
$578$	1.58262	−	4.87079i	0.0658282	−	0.202598i
$579$	−0.982695	−	9.34972i	−0.0408394	−	0.388561i
$580$	−4.32273	+	1.92461i	−0.179492	+	0.0799149i
$581$	−0.509901	−	1.56931i	−0.0211543	−	0.0651061i
$582$	−5.68806			−0.235778
$583$	−0.650924	−	2.04206i	−0.0269585	−	0.0845736i
$584$	−5.20795	−	9.02043i	−0.215506	−	0.373268i
$585$	13.1312	+	2.79113i	0.542910	+	0.115399i
$586$	−1.72893	+	16.4496i	−0.0714213	+	0.679529i
$587$	−29.2980	−	13.0443i	−1.20926	−	0.538397i	−0.299725	−	0.954026i	$-0.596895\pi$
$587$	−29.2980	−	13.0443i	−1.20926	−	0.538397i	−0.909534	+	0.415629i	$0.863561\pi$
$588$	−0.776427	+	2.38960i	−0.0320193	+	0.0985453i
$589$	10.2737	+	8.70900i	0.423318	+	0.358848i
$590$	12.6511	−	9.19158i	0.520839	−	0.378412i
$591$	0.998269	−	9.49790i	0.0410633	−	0.390691i
$592$	−0.198347	+	0.220286i	−0.00815200	+	0.00905371i
$593$	0.496923	−	0.860696i	0.0204062	−	0.0353445i	−0.855642	−	0.517568i	$-0.826837\pi$
$593$	0.496923	−	0.860696i	0.0204062	−	0.0353445i	0.876048	+	0.482224i	$0.160171\pi$
$594$	4.01686	−	6.86855i	0.164814	−	0.281820i
$595$	−2.52580	+	4.37481i	−0.103548	+	0.179350i
$596$	6.84392	+	21.0634i	0.280338	+	0.862791i
$597$	−4.31555	−	3.13543i	−0.176624	−	0.128325i
$598$	1.52561	+	14.5152i	0.0623869	+	0.593571i
$599$	5.32384	+	5.91273i	0.217526	+	0.241588i	0.842025	−	0.539438i	$-0.181363\pi$
$599$	5.32384	+	5.91273i	0.217526	+	0.241588i	−0.624499	+	0.781026i	$0.714697\pi$
$600$	0.330032	−	1.01573i	0.0134735	−	0.0414671i
$601$	20.8259	−	15.1309i	0.849506	−	0.617202i	−0.0755036	−	0.997146i	$-0.524056\pi$
$601$	20.8259	−	15.1309i	0.849506	−	0.617202i	0.925010	+	0.379943i	$0.124056\pi$
$602$	1.82223	−	0.811310i	0.0742687	−	0.0330665i
$603$	−21.7101	+	24.1115i	−0.884102	+	0.981895i
$604$	4.22505	−	7.31800i	0.171915	−	0.297765i
$605$	5.45157	−	16.1619i	0.221638	−	0.657074i
$606$	−0.101183	−	0.175254i	−0.00411027	−	0.00711919i
$607$	0.672704	+	2.07037i	0.0273042	+	0.0840338i	0.963780	−	0.266698i	$-0.0859328\pi$
$607$	0.672704	+	2.07037i	0.0273042	+	0.0840338i	−0.936476	+	0.350732i	$0.885933\pi$
$608$	0.130224	+	4.35695i	0.00528127	+	0.176698i
$609$	0.960201	−	0.697627i	0.0389093	−	0.0282693i
$610$	−7.58778	+	1.61283i	−0.307220	+	0.0653017i
$611$	−16.5254	+	3.51259i	−0.668548	+	0.142104i
$612$	1.01979	+	9.70264i	0.0412225	+	0.392206i
$613$	−1.88886	+	17.9713i	−0.0762902	+	0.725853i	0.887791	+	0.460246i	$0.152239\pi$
$613$	−1.88886	+	17.9713i	−0.0762902	+	0.725853i	−0.964081	+	0.265607i	$0.914428\pi$
$614$	25.6853	+	5.45959i	1.03658	+	0.220331i
$615$	0.343117			0.0138358
$616$	−1.55234	−	2.72374i	−0.0625457	−	0.109743i
$617$	−3.78367	+	6.55351i	−0.152325	+	0.263834i	−0.932082	−	0.362248i	$-0.882009\pi$
$617$	−3.78367	+	6.55351i	−0.152325	+	0.263834i	0.779757	+	0.626082i	$0.215343\pi$
$618$	−2.32743	−	0.494710i	−0.0936229	−	0.0199002i
$619$	−12.9253	−	9.39074i	−0.519510	−	0.377446i	0.296909	−	0.954906i	$-0.404044\pi$
$619$	−12.9253	−	9.39074i	−0.519510	−	0.377446i	−0.816419	+	0.577460i	$0.804044\pi$
$620$	3.87607	−	2.81613i	0.155667	−	0.113098i
$621$	−7.66052	−	8.50787i	−0.307406	−	0.341409i
$622$	16.5284	−	3.51322i	0.662728	−	0.140867i
$623$	0.372757	+	3.54654i	0.0149342	+	0.142089i
$624$	−0.131544	+	1.25155i	−0.00526596	+	0.0501023i
$625$	−3.53589	+	3.92700i	−0.141436	+	0.157080i
$626$	−33.3839			−1.33429
$627$	3.37843	−	4.89587i	0.134922	−	0.195522i
$628$	−17.6670			−0.704992
$629$	−0.683607	+	0.759222i	−0.0272572	+	0.0302722i
$630$	−0.433686	+	4.12625i	−0.0172785	+	0.164394i
$631$	−2.70457	−	25.7322i	−0.107667	−	1.02438i	−0.906320	−	0.422592i	$-0.861120\pi$
$631$	−2.70457	−	25.7322i	−0.107667	−	1.02438i	0.798653	−	0.601792i	$-0.205546\pi$
$632$	12.1904	−	2.59115i	0.484908	−	0.103070i
$633$	5.43221	+	6.03308i	0.215911	+	0.239794i
$634$	−12.4869	+	9.07225i	−0.495917	+	0.360305i
$635$	12.5146	+	9.09238i	0.496626	+	0.360820i
$636$	−0.260086	−	0.0552830i	−0.0103131	−	0.00219211i
$637$	9.33837	−	16.1745i	0.370000	−	0.640858i
$638$	1.11412	−	10.0596i	0.0441085	−	0.398262i
$639$	26.1377			1.03399
$640$	1.51671	+	0.322387i	0.0599533	+	0.0127435i
$641$	−4.49991	+	42.8138i	−0.177736	+	1.69104i	0.434743	+	0.900555i	$0.356839\pi$
$641$	−4.49991	+	42.8138i	−0.177736	+	1.69104i	−0.612479	+	0.790487i	$0.709827\pi$
$642$	−0.619245	−	5.89172i	−0.0244396	−	0.232528i
$643$	3.81653	−	0.811229i	0.150509	−	0.0319917i	−0.132041	−	0.991244i	$-0.542153\pi$
$643$	3.81653	−	0.811229i	0.150509	−	0.0319917i	0.282550	+	0.959253i	$0.408820\pi$
$644$	−4.41218	+	0.937837i	−0.173864	+	0.0369560i
$645$	1.08920	−	0.791350i	0.0428872	−	0.0311594i
$646$	0.448819	+	15.0164i	0.0176586	+	0.590811i
$647$	5.80356	+	17.8615i	0.228162	+	0.702209i	0.997955	+	0.0639163i	$0.0203591\pi$
$647$	5.80356	+	17.8615i	0.228162	+	0.702209i	−0.769794	+	0.638293i	$0.779641\pi$
$648$	3.75249	+	6.49950i	0.147412	+	0.255324i
$649$	3.31048	+	33.2837i	0.129948	+	1.30650i
$650$	−3.96941	+	6.87522i	−0.155693	+	0.269668i
$651$	−0.804120	+	0.893066i	−0.0315160	+	0.0350020i
$652$	−3.84814	+	1.71330i	−0.150705	+	0.0670981i
$653$	1.02702	−	0.746175i	0.0401905	−	0.0292001i	−0.567509	−	0.823367i	$-0.692093\pi$
$653$	1.02702	−	0.746175i	0.0401905	−	0.0292001i	0.607699	+	0.794167i	$0.292093\pi$
$654$	1.18898	−	3.65929i	0.0464926	−	0.143090i
$655$	−5.14747	−	5.71684i	−0.201128	−	0.223375i
$656$	−0.0562149	−	0.534849i	−0.00219482	−	0.0208823i
$657$	−23.8533	−	17.3304i	−0.930606	−	0.676124i
$658$	−1.61351	−	4.96586i	−0.0629010	−	0.193589i
$659$	−19.0793	+	33.0462i	−0.743222	+	1.28730i	0.207798	+	0.978172i	$0.433370\pi$
$659$	−19.0793	+	33.0462i	−0.743222	+	1.28730i	−0.951021	+	0.309127i	$0.899963\pi$
$660$	−1.40710	−	1.58040i	−0.0547712	−	0.0615168i
$661$	10.9883	−	19.0323i	0.427395	−	0.740270i	−0.569246	−	0.822167i	$-0.692765\pi$
$661$	10.9883	−	19.0323i	0.427395	−	0.740270i	0.996641	+	0.0818976i	$0.0260980\pi$
$662$	−7.50359	+	8.33358i	−0.291635	+	0.323894i
$663$	−0.453369	+	4.31352i	−0.0176074	+	0.167523i
$664$	−1.41225	+	1.02606i	−0.0548061	+	0.0398189i
$665$	−1.14103	+	6.28615i	−0.0442472	+	0.243766i
$666$	−0.259293	+	0.798021i	−0.0100474	+	0.0309227i
$667$	−13.3033	−	5.92302i	−0.515107	−	0.229340i
$668$	0.294235	−	2.79946i	0.0113843	−	0.108314i
$669$	3.19864	+	0.679892i	0.123667	+	0.0262861i
$670$	8.88638	+	15.3917i	0.343311	+	0.594631i
$671$	5.21535	−	15.7514i	0.201336	−	0.608076i
$672$	−0.388933			−0.0150034
$673$	6.87122	+	21.1474i	0.264866	+	0.815174i	0.991724	+	0.128386i	$0.0409798\pi$
$673$	6.87122	+	21.1474i	0.264866	+	0.815174i	−0.726858	+	0.686788i	$0.759020\pi$
$674$	−12.7761	+	5.68828i	−0.492117	+	0.219104i
$675$	−0.650922	−	6.19311i	−0.0250540	−	0.238373i
$676$	−1.12654	+	3.46713i	−0.0433284	+	0.133351i
$677$	−8.35921	+	25.7270i	−0.321270	+	0.988768i	0.651826	+	0.758369i	$0.274003\pi$
$677$	−8.35921	+	25.7270i	−0.321270	+	0.988768i	−0.973096	+	0.230400i	$0.925997\pi$
$678$	−0.158639	−	1.50935i	−0.00609250	−	0.0579662i
$679$	−1.36591	+	12.9957i	−0.0524187	+	0.498730i
$680$	5.22738	+	1.11111i	0.200461	+	0.0426093i
$681$	−4.98595	−	8.63592i	−0.191062	−	0.330929i
$682$	1.01427	+	10.1975i	0.0388384	+	0.390483i
$683$	−23.2928			−0.891275			−0.445638	−	0.895213i	$-0.647023\pi$
$683$	−23.2928			−0.891275			−0.445638	+	0.895213i	$0.647023\pi$
$684$	5.35313	+	11.1170i	0.204682	+	0.425071i
$685$	−3.64254	−	2.64646i	−0.139174	−	0.101116i
$686$	11.3179	+	5.03905i	0.432119	+	0.192392i
$687$	−3.19110	+	0.678289i	−0.121748	+	0.0258783i
$688$	−1.41200	−	1.56819i	−0.0538322	−	0.0597867i
$689$	1.80562	+	0.803912i	0.0687885	+	0.0306266i
$690$	−2.78135	+	1.23834i	−0.105884	+	0.0471426i
$691$	10.6885	+	32.8958i	0.406610	+	1.25142i	0.919544	+	0.392988i	$0.128559\pi$
$691$	10.6885	+	32.8958i	0.406610	+	1.25142i	−0.512934	+	0.858428i	$0.671441\pi$
$692$	2.54026			0.0965662
$693$	−7.15030	−	5.25624i	−0.271617	−	0.199668i
$694$	3.42825	−	5.93791i	0.130135	−	0.225400i
$695$	−4.46012	−	13.7268i	−0.169182	−	0.520688i
$696$	−1.01581	−	0.738032i	−0.0385043	−	0.0279750i
$697$	−0.193746	−	1.84337i	−0.00733866	−	0.0698227i
$698$	5.94002	−	1.26259i	0.224833	−	0.0477897i
$699$	0.517236	+	0.574449i	0.0195637	+	0.0217277i
$700$	−2.24143	−	0.997950i	−0.0847181	−	0.0377189i
$701$	4.59894	−	43.7560i	0.173700	−	1.65264i	−0.466564	−	0.884487i	$-0.654508\pi$
$701$	4.59894	−	43.7560i	0.173700	−	1.65264i	0.640264	−	0.768155i	$-0.278825\pi$
$702$	2.26746	+	6.97851i	0.0855796	+	0.263387i
$703$	−0.490039	+	1.19555i	−0.0184822	+	0.0450911i
$704$	−2.23298	+	2.45230i	−0.0841587	+	0.0924247i
$705$	−1.76212	−	3.05208i	−0.0663651	−	0.114948i
$706$	−0.324057	+	0.359902i	−0.0121961	+	0.0135451i
$707$	−0.424706	+	0.189091i	−0.0159727	+	0.00711151i
$708$	3.79079	+	1.68777i	0.142467	+	0.0634302i
$709$	−2.34558	−	2.60503i	−0.0880900	−	0.0978338i	0.697488	−	0.716596i	$-0.254301\pi$
$709$	−2.34558	−	2.60503i	−0.0880900	−	0.0978338i	−0.785578	+	0.618763i	$0.787634\pi$
$710$	4.42440	−	13.6169i	0.166045	−	0.511034i
$711$	28.5408	−	20.7361i	1.07036	−	0.777664i
$712$	3.44646	−	1.53446i	0.129161	−	0.0575064i
$713$	14.4225	+	3.06559i	0.540126	+	0.114807i
$714$	−1.34047			−0.0501657
$715$	7.78837	+	13.6655i	0.291269	+	0.511061i
$716$	7.85069	−	13.5978i	0.293394	−	0.508174i
$717$	−2.88856	+	3.20807i	−0.107875	+	0.119808i
$718$	6.38427	−	2.84246i	0.238259	−	0.106080i
$719$	−41.6877	−	18.5606i	−1.55469	−	0.692193i	−0.563682	−	0.825992i	$-0.690616\pi$
$719$	−41.6877	−	18.5606i	−1.55469	−	0.692193i	−0.991008	+	0.133799i	$0.957282\pi$
$720$	4.29336	−	0.912581i	0.160004	−	0.0340099i
$721$	−1.68918	+	5.19876i	−0.0629084	+	0.193612i
$722$	6.94006	+	17.6872i	0.258282	+	0.658248i
$723$	6.10948	+	4.43879i	0.227214	+	0.165081i
$724$	−2.07874	+	2.30867i	−0.0772558	+	0.0858012i
$725$	−3.96047	−	6.85974i	−0.147088	−	0.254764i
$726$	4.43737	−	0.891524i	0.164686	−	0.0330876i
$727$	−19.8184	−	34.3266i	−0.735025	−	1.27310i	−0.954712	−	0.297531i	$-0.903837\pi$
$727$	−19.8184	−	34.3266i	−0.735025	−	1.27310i	0.219687	−	0.975570i	$-0.429496\pi$
$728$	2.82789	+	0.601086i	0.104808	+	0.0222777i
$729$	14.7912	+	10.7465i	0.547823	+	0.398017i
$730$	−13.0663	+	9.49322i	−0.483605	+	0.351360i
$731$	−4.86651	−	5.40481i	−0.179994	−	0.199904i
$732$	−1.37737	−	1.52972i	−0.0509089	−	0.0565401i
$733$	4.43899	−	3.22511i	0.163958	−	0.119122i	−0.502781	−	0.864414i	$-0.667690\pi$
$733$	4.43899	−	3.22511i	0.163958	−	0.119122i	0.666739	+	0.745292i	$0.267690\pi$
$734$	−28.0772	−	20.3993i	−1.03635	−	0.752951i
$735$	3.81084	+	0.810020i	0.140565	+	0.0298780i
$736$	2.38600	+	4.13267i	0.0879491	+	0.152332i
$737$	−38.0142	−	0.212249i	−1.40027	−	0.00781830i
$738$	−0.761169	−	1.31838i	−0.0280190	−	0.0485304i
$739$	−11.2191	+	12.4601i	−0.412702	+	0.458352i	−0.913276	−	0.407342i	$-0.866456\pi$
$739$	−11.2191	+	12.4601i	−0.412702	+	0.458352i	0.500574	+	0.865694i	$0.333122\pi$
$740$	0.371852	+	0.270166i	0.0136695	+	0.00993151i
$741$	1.30028	+	5.32911i	0.0477669	+	0.195770i
$742$	−0.188763	+	0.580953i	−0.00692970	+	0.0213274i
$743$	16.2757	−	3.45951i	0.597099	−	0.126917i	0.100559	−	0.994931i	$-0.467937\pi$
$743$	16.2757	−	3.45951i	0.597099	−	0.126917i	0.496540	+	0.868014i	$0.334604\pi$
$744$	1.16143	+	0.517101i	0.0425800	+	0.0189578i
$745$	31.3726	−	13.9680i	1.14940	−	0.511748i
$746$	−6.21585	+	6.90340i	−0.227579	+	0.252752i
$747$	−2.47070	+	4.27937i	−0.0903980	+	0.156574i
$748$	−7.69603	+	8.45193i	−0.281395	+	0.309033i
$749$	−13.6097			−0.497289
$750$	−4.74018	−	1.00756i	−0.173087	−	0.0367907i
$751$	−21.7189	+	9.66989i	−0.792535	+	0.352859i	−0.762747	−	0.646697i	$-0.776150\pi$
$751$	−21.7189	+	9.66989i	−0.792535	+	0.352859i	−0.0297881	+	0.999556i	$0.509483\pi$
$752$	−4.46887	+	3.24682i	−0.162963	+	0.118399i
$753$	−2.49075	+	7.66573i	−0.0907678	+	0.279355i
$754$	6.24525	+	6.93605i	0.227439	+	0.252596i
$755$	−11.9699	−	5.32934i	−0.435629	−	0.193955i
$756$	−2.07169	+	0.922378i	−0.0753468	+	0.0335466i
$757$	21.2297	−	23.5780i	0.771606	−	0.856955i	−0.221380	−	0.975188i	$-0.571056\pi$
$757$	21.2297	−	23.5780i	0.771606	−	0.856955i	0.992986	+	0.118232i	$0.0377228\pi$
$758$	−10.8301	−	18.7582i	−0.393366	−	0.681329i
$759$	0.716852	−	6.47255i	0.0260201	−	0.234939i
$760$	6.69775	−	0.906999i	0.242953	−	0.0329003i
$761$	−6.80160	−	20.9332i	−0.246558	−	0.758827i	−0.995376	−	0.0960520i	$-0.969378\pi$
$761$	−6.80160	−	20.9332i	−0.246558	−	0.758827i	0.748818	−	0.662775i	$-0.230622\pi$
$762$	−0.429063	+	4.08227i	−0.0155433	+	0.147885i
$763$	−8.07500	−	3.59522i	−0.292335	−	0.130156i
$764$	−15.9806	−	17.7483i	−0.578158	−	0.642109i
$765$	14.7972	−	3.14523i	0.534993	−	0.113716i
$766$	−0.891187	−	8.47908i	−0.0321999	−	0.306361i
$767$	−24.9540	−	18.1301i	−0.901036	−	0.654641i
$768$	0.127148	+	0.391321i	0.00458805	+	0.0141206i
$769$	20.6890	−	35.8344i	0.746064	−	1.29222i	−0.203631	−	0.979048i	$-0.565274\pi$
$769$	20.6890	−	35.8344i	0.746064	−	1.29222i	0.949696	−	0.313174i	$-0.101392\pi$
$770$	−3.94868	+	2.83534i	−0.142301	+	0.102178i
$771$	3.77844			0.136077
$772$	7.06058	+	21.7302i	0.254116	+	0.782088i
$773$	8.01705	−	3.56942i	0.288353	−	0.128383i	−0.257463	−	0.966288i	$-0.582886\pi$
$773$	8.01705	−	3.56942i	0.288353	−	0.128383i	0.545816	+	0.837905i	$0.316220\pi$
$774$	−5.45694	−	2.42959i	−0.196146	−	0.0873298i
$775$	5.36652	+	5.96013i	0.192771	+	0.214094i
$776$	13.5220	−	2.87420i	0.485413	−	0.103178i
$777$	−0.105322	−	0.0468924i	−0.00377840	−	0.00168225i
$778$	−21.0803	−	15.3157i	−0.755765	−	0.549096i
$779$	−1.01702	−	2.11209i	−0.0364386	−	0.0756734i
$780$	1.95134			0.0698693
$781$	20.3645	+	22.8726i	0.728698	+	0.818445i
$782$	8.22341	+	14.2434i	0.294068	+	0.509341i
$783$	−7.16113	−	1.52215i	−0.255918	−	0.0543970i
$784$	0.638303	−	6.07304i	0.0227965	−	0.216894i
$785$	2.86350	+	27.2444i	0.102203	+	0.972393i
$786$	0.630802	−	1.94141i	0.0225000	−	0.0692478i
$787$	10.1145	−	31.1293i	0.360544	−	1.10964i	−0.592181	−	0.805805i	$-0.701733\pi$
$787$	10.1145	−	31.1293i	0.360544	−	1.10964i	0.952725	−	0.303835i	$-0.0982672\pi$
$788$	2.42617	+	23.0835i	0.0864287	+	0.822314i
$789$	−6.22577	+	2.77189i	−0.221643	+	0.0986819i
$790$	−5.97165	−	18.3789i	−0.212462	−	0.653891i
$791$	−3.48656			−0.123968
$792$	−2.95098	+	8.91254i	−0.104858	+	0.316693i
$793$	7.65052	+	13.2511i	0.271678	+	0.470560i
$794$	−28.1091	−	5.97478i	−0.997556	−	0.212037i
$795$	−0.0430968	+	0.410039i	−0.00152849	+	0.0145426i
$796$	11.8436	+	5.27309i	0.419784	+	0.186900i
$797$	10.8086	−	33.2655i	0.382861	−	1.17833i	−0.555159	−	0.831745i	$-0.687342\pi$
$797$	10.8086	−	33.2655i	0.382861	−	1.17833i	0.938020	−	0.346581i	$-0.112658\pi$
$798$	−1.59597	+	0.571818i	−0.0564969	+	0.0202421i
$799$	−15.4021	+	11.1903i	−0.544886	+	0.395883i
$800$	−0.271320	+	2.58144i	−0.00959260	+	0.0912675i
$801$	7.14575	−	7.93616i	0.252483	−	0.280410i
$802$	−6.02263	+	10.4315i	−0.212667	+	0.368349i
$803$	−3.41912	−	34.3760i	−0.120658	−	1.21310i
$804$	−2.35805	+	4.08426i	−0.0831619	+	0.144041i
$805$	2.16137	+	6.65201i	0.0761783	+	0.234453i
$806$	−7.64543	−	5.55473i	−0.269299	−	0.195657i
$807$	−1.13689	−	10.8168i	−0.0400204	−	0.380769i
$808$	0.329095	+	0.365496i	0.0115775	+	0.0128581i
$809$	1.86024	−	5.72523i	0.0654025	−	0.201288i	−0.913015	−	0.407926i	$-0.866252\pi$
$809$	1.86024	−	5.72523i	0.0654025	−	0.201288i	0.978418	+	0.206638i	$0.0662521\pi$
$810$	9.41468	−	6.84016i	0.330798	−	0.240339i
$811$	−28.0093	+	12.4706i	−0.983540	+	0.437900i	−0.834546	−	0.550938i	$-0.814270\pi$
$811$	−28.0093	+	12.4706i	−0.983540	+	0.437900i	−0.148994	+	0.988838i	$0.547603\pi$
$812$	−1.93014	+	2.14364i	−0.0677347	+	0.0752270i
$813$	−2.04035	+	3.53400i	−0.0715584	+	0.123943i
$814$	−0.900351	+	0.394854i	−0.0315573	+	0.0138396i
$815$	3.26579	+	5.65652i	0.114396	+	0.198139i
$816$	0.438218	+	1.34870i	0.0153407	+	0.0472138i
$817$	−8.09971	−	4.35906i	−0.283373	−	0.152504i
$818$	−25.7195	+	18.6863i	−0.899261	+	0.653351i
$819$	8.00490	−	1.70149i	0.279714	−	0.0594550i
$820$	−0.815680	+	0.173378i	−0.0284848	+	0.00605463i
$821$	1.66436	+	15.8353i	0.0580866	+	0.552657i	0.984405	+	0.175916i	$0.0562887\pi$
$821$	1.66436	+	15.8353i	0.0580866	+	0.552657i	−0.926319	+	0.376741i	$0.877045\pi$
$822$	0.124885	−	1.18820i	0.00435585	−	0.0414432i
$823$	−14.1253	−	3.00242i	−0.492377	−	0.104658i	−0.0449697	−	0.998988i	$-0.514319\pi$
$823$	−14.1253	−	3.00242i	−0.492377	−	0.104658i	−0.447407	+	0.894330i	$0.647652\pi$
$824$	5.78290			0.201457
$825$	2.38484	−	2.61907i	0.0830293	−	0.0911844i
$826$	4.76641	−	8.25567i	0.165845	−	0.287251i
$827$	46.3337	+	9.84854i	1.61118	+	0.342467i	0.923516	−	0.383560i	$-0.125302\pi$
$827$	46.3337	+	9.84854i	1.61118	+	0.342467i	0.687666	+	0.726028i	$0.258636\pi$
$828$	10.9283	+	7.93986i	0.379784	+	0.275929i
$829$	19.9171	−	14.4707i	0.691751	−	0.502587i	−0.185484	−	0.982647i	$-0.559385\pi$
$829$	19.9171	−	14.4707i	0.691751	−	0.502587i	0.877235	+	0.480061i	$0.159385\pi$
$830$	1.81119	+	2.01153i	0.0628674	+	0.0698213i
$831$	−9.10235	+	1.93476i	−0.315757	+	0.0671162i
$832$	−0.319701	−	3.04175i	−0.0110836	−	0.105454i
$833$	2.19993	−	20.9309i	0.0762229	−	0.725213i
$834$	2.56273	−	2.84620i	0.0887400	−	0.0985558i
$835$	−4.36474			−0.151048
$836$	−5.55754	+	13.3459i	−0.192211	+	0.461579i
$837$	7.41280			0.256224
$838$	−10.0290	+	11.1383i	−0.346445	+	0.384766i
$839$	−3.81188	+	36.2676i	−0.131601	+	1.25210i	0.706947	+	0.707267i	$0.250072\pi$
$839$	−3.81188	+	36.2676i	−0.131601	+	1.25210i	−0.838547	+	0.544829i	$0.816595\pi$
$840$	0.0630388	+	0.599774i	0.00217504	+	0.0206942i
$841$	19.2574	−	4.09329i	0.664049	−	0.141148i
$842$	22.3017	+	24.7686i	0.768568	+	0.853582i
$843$	3.58865	−	2.60731i	0.123600	−	0.0898004i
$844$	−15.9624	−	11.5973i	−0.549447	−	0.399197i
$845$	5.52925	+	1.17528i	0.190212	+	0.0404308i
$846$	−7.81815	+	13.5414i	−0.268793	+	0.465564i
$847$	−0.971327	−	10.3523i	−0.0333752	−	0.355710i
$848$	0.646228			0.0221916
$849$	0.144678	+	0.0307522i	0.00496533	+	0.00105541i
$850$	−0.935111	+	8.89699i	−0.0320740	+	0.305164i
$851$	0.147859	+	1.40679i	0.00506855	+	0.0482240i
$852$	3.71625	−	0.789913i	0.127317	−	0.0270620i
$853$	39.2067	−	8.33365i	1.34241	−	0.285339i	0.519969	−	0.854185i	$-0.325943\pi$
$853$	39.2067	−	8.33365i	1.34241	−	0.285339i	0.822444	+	0.568846i	$0.192610\pi$
$854$	−3.82576	+	2.77958i	−0.130915	+	0.0951152i
$855$	16.2759	−	10.0569i	0.556626	−	0.343940i
$856$	4.44922	+	13.6933i	0.152071	+	0.468027i
$857$	−23.3264	−	40.4025i	−0.796814	−	1.38012i	−0.921681	−	0.387948i	$-0.873184\pi$
$857$	−23.3264	−	40.4025i	−0.796814	−	1.38012i	0.124867	−	0.992173i	$-0.460149\pi$
$858$	−2.10705	+	3.60291i	−0.0719335	+	0.123001i
$859$	3.69181	−	6.39440i	0.125963	−	0.218174i	−0.796146	−	0.605104i	$-0.793131\pi$
$859$	3.69181	−	6.39440i	0.125963	−	0.218174i	0.922109	+	0.386930i	$0.126465\pi$
$860$	−2.18945	+	2.43163i	−0.0746596	+	0.0829178i
$861$	0.191083	−	0.0850756i	0.00651209	−	0.00289937i
$862$	24.0766	−	17.4927i	0.820054	−	0.595804i
$863$	8.76749	−	26.9836i	0.298449	−	0.918531i	−0.683592	−	0.729864i	$-0.739583\pi$
$863$	8.76749	−	26.9836i	0.298449	−	0.918531i	0.982041	−	0.188667i	$-0.0604166\pi$
$864$	1.60531	+	1.78287i	0.0546137	+	0.0606546i
$865$	−0.411729	−	3.91734i	−0.0139992	−	0.133193i
$866$	−10.2818	−	7.47014i	−0.349389	−	0.253846i
$867$	−0.651182	−	2.00413i	−0.0221153	−	0.0680639i
$868$	1.46034	−	2.52938i	0.0495671	−	0.0858528i
$869$	40.3824	+	8.81948i	1.36988	+	0.299180i
$870$	−0.973475	+	1.68611i	−0.0330039	+	0.0571644i
$871$	23.4572	−	26.0519i	0.794817	−	0.882734i
$872$	−0.977460	+	9.29991i	−0.0331010	+	0.314935i
$873$	31.6585	−	23.0012i	1.07148	−	0.778473i
$874$	15.8668	+	13.4503i	0.536703	+	0.454964i
$875$	−3.44028	+	10.5881i	−0.116303	+	0.357943i
$876$	−3.91519	−	1.74316i	−0.132282	−	0.0588958i
$877$	0.637203	−	6.06258i	0.0215168	−	0.204719i	−0.978482	−	0.206333i	$-0.933847\pi$
$877$	0.637203	−	6.06258i	0.0215168	−	0.204719i	0.999999	+	0.00161391i	$0.000513725\pi$
$878$	−3.85268	−	0.818912i	−0.130022	−	0.0276369i
$879$	3.40282	+	5.89385i	0.114774	+	0.198795i
$880$	4.14362	+	3.04601i	0.139682	+	0.102681i
$881$	−49.2504			−1.65929			−0.829644	−	0.558293i	$-0.811456\pi$
$881$	−49.2504			−1.65929			−0.829644	+	0.558293i	$0.811456\pi$
$882$	−5.34156	−	16.4396i	−0.179860	−	0.553552i
$883$	15.0347	−	6.69386i	0.505957	−	0.225266i	−0.137852	−	0.990453i	$-0.544020\pi$
$883$	15.0347	−	6.69386i	0.505957	−	0.225266i	0.643809	+	0.765186i	$0.277353\pi$
$884$	−1.10186	−	10.4835i	−0.0370595	−	0.352597i
$885$	1.98829	−	6.11934i	0.0668358	−	0.205699i
$886$	1.80578	−	5.55763i	0.0606665	−	0.186712i
$887$	0.428592	+	4.07778i	0.0143907	+	0.136918i	0.999358	−	0.0358213i	$-0.0114047\pi$
$887$	0.428592	+	4.07778i	0.0143907	+	0.136918i	−0.984968	+	0.172740i	$0.944738\pi$
$888$	−0.0127490	+	0.121298i	−0.000427827	+	0.00407050i
$889$	9.22387	+	1.96059i	0.309359	+	0.0657562i
$890$	−2.92490	−	5.06608i	−0.0980429	−	0.169815i
$891$	2.46358	+	24.7690i	0.0825331	+	0.829792i
$892$	−7.94757			−0.266104
$893$	−13.5643	+	19.8935i	−0.453912	+	0.665709i
$894$	7.37236	+	5.35633i	0.246569	+	0.179143i
$895$	−22.2416	−	9.90261i	−0.743456	−	0.331008i
$896$	0.924598	−	0.196529i	0.0308886	−	0.00656558i
$897$	4.01834	+	4.46282i	0.134168	+	0.149009i
$898$	26.3733	+	11.7422i	0.880089	+	0.391841i
$899$	8.61381	−	3.83512i	0.287287	−	0.127908i
$900$	2.27051	+	6.98791i	0.0756837	+	0.232930i
$901$	2.22724			0.0742002
$902$	0.560646	−	1.69326i	0.0186675	−	0.0563795i
$903$	0.410365	−	0.710773i	0.0136561	−	0.0236530i
$904$	1.13981	+	3.50797i	0.0379094	+	0.116673i
$905$	3.89713	+	2.83143i	0.129545	+	0.0941200i
$906$	−0.363432	−	3.45782i	−0.0120742	−	0.114878i
$907$	15.6516	−	3.32686i	0.519704	−	0.110466i	0.0594111	−	0.998234i	$-0.481078\pi$
$907$	15.6516	−	3.32686i	0.519704	−	0.110466i	0.460293	+	0.887767i	$0.347744\pi$
$908$	16.2167	+	18.0105i	0.538170	+	0.597699i
$909$	1.27184	+	0.566262i	0.0421844	+	0.0187817i
$910$	0.468587	−	4.45831i	0.0155335	−	0.147792i
$911$	−4.06870	−	12.5222i	−0.134802	−	0.414878i	0.860757	−	0.509016i	$-0.169991\pi$
$911$	−4.06870	−	12.5222i	−0.134802	−	0.414878i	−0.995559	+	0.0941379i	$0.969991\pi$
$912$	1.09708	+	1.41884i	0.0363278	+	0.0469824i
$913$	−5.66975	+	1.17210i	−0.187641	+	0.0387907i
$914$	14.4647	+	25.0536i	0.478449	+	0.828698i
$915$	−2.13574	+	2.37198i	−0.0706053	+	0.0784151i
$916$	7.24335	−	3.22495i	0.239327	−	0.106555i
$917$	−4.28413	−	1.90742i	−0.141474	−	0.0629885i
$918$	5.53273	+	6.14472i	0.182607	+	0.202806i
$919$	16.0152	−	49.2898i	0.528293	−	1.62592i	−0.229417	−	0.973328i	$-0.573682\pi$
$919$	16.0152	−	49.2898i	0.528293	−	1.62592i	0.757710	−	0.652591i	$-0.226318\pi$
$920$	5.98627	−	4.34928i	0.197361	−	0.143391i
$921$	9.87046	−	4.39461i	0.325243	−	0.144807i
$922$	−22.3633	−	4.75347i	−0.736497	−	0.156547i
$923$	−28.2412			−0.929570
$924$	−1.17548	−	0.531239i	−0.0386703	−	0.0174765i
$925$	−0.384708	+	0.666333i	−0.0126491	+	0.0219089i
$926$	14.1561	−	15.7220i	0.465199	−	0.516656i
$927$	14.9544	−	6.65814i	0.491168	−	0.218682i
$928$	2.78779	+	1.24120i	0.0915137	+	0.0407445i
$929$	−22.3035	+	4.74076i	−0.731754	+	0.155539i	−0.558696	−	0.829372i	$-0.688698\pi$
$929$	−22.3035	+	4.74076i	−0.731754	+	0.155539i	−0.173058	+	0.984912i	$0.555365\pi$
$930$	0.609176	−	1.87485i	0.0199757	−	0.0614787i
$931$	−6.30947	−	25.8590i	−0.206785	−	0.847494i
$932$	−1.51988	−	1.10426i	−0.0497853	−	0.0361711i
$933$	4.65226	−	5.16685i	0.152308	−	0.169155i
$934$	−16.2641	−	28.1703i	−0.532179	−	0.921760i
$935$	14.2811	+	10.4982i	0.467042	+	0.343326i
$936$	−4.32886	−	7.49780i	−0.141493	−	0.245073i
$937$	−19.8774	−	4.22508i	−0.649368	−	0.138027i	−0.128560	−	0.991702i	$-0.541036\pi$
$937$	−19.8774	−	4.22508i	−0.649368	−	0.138027i	−0.520807	+	0.853674i	$0.674369\pi$
$938$	8.76521	+	6.36830i	0.286194	+	0.207932i
$939$	−11.1127	+	8.07387i	−0.362650	+	0.263481i
$940$	5.73125	+	6.36519i	0.186933	+	0.207610i
$941$	4.82424	+	5.35786i	0.157266	+	0.174661i	0.816628	−	0.577164i	$-0.195841\pi$
$941$	4.82424	+	5.35786i	0.157266	+	0.174661i	−0.659363	+	0.751825i	$0.729174\pi$
$942$	−5.88095	+	4.27276i	−0.191612	+	0.139214i
$943$	−2.07623	−	1.50847i	−0.0676112	−	0.0491224i
$944$	−9.86456	−	2.09678i	−0.321064	−	0.0682443i
$945$	1.75818	+	3.04526i	0.0571937	+	0.0990624i
$946$	−2.12554	−	6.66820i	−0.0691073	−	0.216802i
$947$	−12.6135	−	21.8472i	−0.409883	−	0.709938i	0.584994	−	0.811038i	$-0.301097\pi$
$947$	−12.6135	−	21.8472i	−0.409883	−	0.709938i	−0.994876	+	0.101100i	$0.967764\pi$
$948$	3.43124	−	3.81078i	0.111442	−	0.123768i
$949$	25.7729	+	18.7251i	0.836624	+	0.607843i
$950$	2.68193	+	10.9917i	0.0870134	+	0.356619i
$951$	−1.96248	+	6.03989i	−0.0636378	+	0.195857i
$952$	3.18665	−	0.677343i	0.103280	−	0.0219528i
$953$	28.6794	+	12.7689i	0.929016	+	0.413624i	0.814741	−	0.579825i	$-0.196879\pi$
$953$	28.6794	+	12.7689i	0.929016	+	0.413624i	0.114274	+	0.993449i	$0.463546\pi$
$954$	1.67113	−	0.744035i	0.0541048	−	0.0240890i
$955$	−24.7794	+	27.5204i	−0.801844	+	0.890538i
$956$	5.24583	−	9.08604i	0.169662	−	0.293863i
$957$	−2.06203	−	3.61805i	−0.0666560	−	0.116955i
$958$	−13.2603			−0.428420
$959$	−2.68473	−	0.570657i	−0.0866945	−	0.0184275i
$960$	0.582848	−	0.259500i	0.0188113	−	0.00837534i
$961$	17.3558	−	12.6097i	0.559864	−	0.406765i
$962$	0.280160	−	0.862242i	0.00903271	−	0.0277998i
$963$	27.2713	+	30.2879i	0.878806	+	0.976013i
$964$	−16.7668	−	7.46506i	−0.540022	−	0.240433i
$965$	32.3658	−	14.4102i	1.04189	−	0.463880i
$966$	−1.24190	+	1.37927i	−0.0399574	+	0.0443772i
$967$	14.4188	+	24.9741i	0.463678	+	0.803114i	0.999141	−	0.0414446i	$-0.0131960\pi$
$967$	14.4188	+	24.9741i	0.463678	+	0.803114i	−0.535463	+	0.844559i	$0.679863\pi$
$968$	−10.0983	+	4.36161i	−0.324573	+	0.140188i
$969$	3.78110	+	4.89006i	0.121466	+	0.157091i
$970$	−6.62398	−	20.3865i	−0.212683	−	0.654571i
$971$	−1.59634	+	15.1882i	−0.0512291	+	0.487413i	0.938585	+	0.345048i	$0.112137\pi$
$971$	−1.59634	+	15.1882i	−0.0512291	+	0.487413i	−0.989814	+	0.142365i	$0.954529\pi$
$972$	9.39606	+	4.18340i	0.301379	+	0.134182i
$973$	−5.88741	−	6.53864i	−0.188742	−	0.209619i
$974$	11.0432	−	2.34730i	0.353846	−	0.0752123i
$975$	0.341442	+	3.24860i	0.0109349	+	0.104039i
$976$	4.04734	+	2.94056i	0.129552	+	0.0941252i
$977$	0.0334384	+	0.102913i	0.00106979	+	0.00329247i	0.951590	−	0.307370i	$-0.0994490\pi$
$977$	0.0334384	+	0.102913i	0.00106979	+	0.00329247i	−0.950520	+	0.310663i	$0.899449\pi$
$978$	−0.866596	+	1.50099i	−0.0277107	+	0.0479963i
$979$	12.5122	+	0.0698606i	0.399890	+	0.00223275i
$980$	−9.46870			−0.302467
$981$	8.17976	+	25.1747i	0.261160	+	0.803767i
$982$	−3.50188	+	1.55914i	−0.111750	+	0.0497541i
$983$	−44.7051	−	19.9040i	−1.42587	−	0.634839i	−0.458613	−	0.888636i	$-0.651654\pi$
$983$	−44.7051	−	19.9040i	−1.42587	−	0.634839i	−0.967257	+	0.253797i	$0.918320\pi$
$984$	−0.148066	−	0.164444i	−0.00472016	−	0.00524227i
$985$	35.2038	−	7.48280i	1.12169	−	0.238422i
$986$	9.60819	+	4.27784i	0.305987	+	0.136234i
$987$	−1.73809	−	1.26280i	−0.0553240	−	0.0401952i
$988$	−5.78393	−	12.0117i	−0.184011	−	0.382143i
$989$	−10.0699			−0.320204
$990$	14.2223	+	3.10615i	0.452015	+	0.0987198i
$991$	2.29613	+	3.97702i	0.0729391	+	0.126334i	0.900188	−	0.435501i	$-0.143429\pi$
$991$	2.29613	+	3.97702i	0.0729391	+	0.126334i	−0.827249	+	0.561835i	$0.810095\pi$
$992$	−3.02231	−	0.642413i	−0.0959586	−	0.0203966i
$993$	−0.482302	+	4.58880i	−0.0153054	+	0.145621i
$994$	−0.912340	−	8.68034i	−0.0289377	−	0.275324i
$995$	6.21202	−	19.1186i	0.196934	−	0.606101i
$996$	−0.221954	+	0.683106i	−0.00703290	+	0.0216450i
$997$	4.64038	+	44.1502i	0.146962	+	1.39825i	0.780798	+	0.624784i	$0.214813\pi$
$997$	4.64038	+	44.1502i	0.146962	+	1.39825i	−0.633835	+	0.773468i	$0.718520\pi$
$998$	35.7115	−	15.8998i	1.13043	−	0.503300i
$999$	0.219757	+	0.676344i	0.00695282	+	0.0213986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.159.3	yes	64
11.9	even	5	inner	418.2.n.d.273.6	yes	64
19.11	even	3	inner	418.2.n.d.49.6	✓	64
209.163	even	15	inner	418.2.n.d.163.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.49.6	✓	64	19.11	even	3	inner
418.2.n.d.159.3	yes	64	1.1	even	1	trivial
418.2.n.d.163.3	yes	64	209.163	even	15	inner
418.2.n.d.273.6	yes	64	11.9	even	5	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 0.743145i) q^{2} +(-0.0430092 + 0.409205i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.51671 + 0.322387i) q^{5} +(-0.275320 - 0.305774i) q^{6} +(-0.764726 + 0.555606i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.76884 + 0.588536i) q^{9} +O(q^{10})\)	\(q+(-0.669131 + 0.743145i) q^{2} +(-0.0430092 + 0.409205i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.51671 + 0.322387i) q^{5} +(-0.275320 - 0.305774i) q^{6} +(-0.764726 + 0.555606i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.76884 + 0.588536i) q^{9} +(0.775298 - 1.34285i) q^{10} +(1.64225 + 2.88150i) q^{11} +0.411459 q^{12} +(-2.99167 - 0.635899i) q^{13} +(0.0988059 - 0.940075i) q^{14} +(-0.0666898 - 0.634511i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-3.37121 + 0.716573i) q^{17} +(-2.29009 + 1.66384i) q^{18} +(-3.70812 + 2.29125i) q^{19} +(0.479160 + 1.47470i) q^{20} +(-0.194466 - 0.336826i) q^{21} +(-3.24025 - 0.707667i) q^{22} +(-2.38600 + 4.13267i) q^{23} +(-0.275320 + 0.305774i) q^{24} +(-2.37125 + 1.05575i) q^{25} +(2.47438 - 1.79774i) q^{26} +(-0.741361 + 2.28167i) q^{27} +(0.632498 + 0.702460i) q^{28} +(0.318981 + 3.03490i) q^{29} +(0.516158 + 0.375011i) q^{30} +(-0.954812 - 2.93861i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.24975 + 0.548086i) q^{33} +(1.72326 - 2.98478i) q^{34} +(0.980749 - 1.08923i) q^{35} +(0.295889 - 2.81519i) q^{36} +(0.239812 - 0.174234i) q^{37} +(0.778484 - 4.28882i) q^{38} +(0.388882 - 1.19686i) q^{39} +(-1.41654 - 0.630684i) q^{40} +(-0.0562149 + 0.534849i) q^{41} +(0.380434 + 0.0808637i) q^{42} +(1.05510 + 1.82749i) q^{43} +(2.69405 - 1.93445i) q^{44} -4.38927 q^{45} +(-1.47463 - 4.53844i) q^{46} +(5.04626 - 2.24674i) q^{47} +(-0.0430092 - 0.409205i) q^{48} +(-1.88701 + 5.80762i) q^{49} +(0.802101 - 2.46861i) q^{50} +(-0.148232 - 1.41034i) q^{51} +(-0.319701 + 3.04175i) q^{52} +(-0.632107 - 0.134358i) q^{53} +(-1.19955 - 2.07768i) q^{54} +(-3.41977 - 3.84096i) q^{55} -0.945254 q^{56} +(-0.778109 - 1.61593i) q^{57} +(-2.46881 - 1.79369i) q^{58} +(9.21305 + 4.10191i) q^{59} +(-0.624064 + 0.132649i) q^{60} +(-3.34752 - 3.71780i) q^{61} +(2.82270 + 1.25675i) q^{62} +(-2.44440 + 1.08832i) q^{63} +(0.309017 + 0.951057i) q^{64} +4.74250 q^{65} +(0.428941 - 1.29549i) q^{66} +(-5.73095 + 9.92629i) q^{67} +(1.06504 + 3.27784i) q^{68} +(-1.58849 - 1.15410i) q^{69} +(0.153208 + 1.45768i) q^{70} +(9.03188 - 1.91979i) q^{71} +(1.89411 + 2.10362i) q^{72} +(-9.51539 - 4.23653i) q^{73} +(-0.0309848 + 0.294801i) q^{74} +(-0.330032 - 1.01573i) q^{75} +(2.66631 + 3.44831i) q^{76} +(-2.85685 - 1.29111i) q^{77} +(0.629224 + 1.08985i) q^{78} +(8.33921 - 9.26163i) q^{79} +(1.41654 - 0.630684i) q^{80} +(6.85614 + 3.05255i) q^{81} +(-0.359855 - 0.399660i) q^{82} +(-0.539433 + 1.66020i) q^{83} +(-0.314653 + 0.228609i) q^{84} +(4.88214 - 2.17367i) q^{85} +(-2.06410 - 0.438737i) q^{86} -1.25561 q^{87} +(-0.365093 + 3.29647i) q^{88} +(1.88631 - 3.26718i) q^{89} +(2.93700 - 3.26186i) q^{90} +(2.64112 - 1.17590i) q^{91} +(4.35944 + 1.94095i) q^{92} +(1.24356 - 0.264326i) q^{93} +(-1.70696 + 5.25347i) q^{94} +(4.88548 - 4.67062i) q^{95} +(0.332877 + 0.241849i) q^{96} +(9.25015 - 10.2733i) q^{97} +(-3.05325 - 5.28838i) q^{98} +(2.85127 + 8.94493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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