LMFDB - Embedded newform 930.2.bg.g.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.2
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.g.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.258263 + 2.45720i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.258263 + 2.45720i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(2.63149 - 1.17162i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(1.33391 + 0.283532i) q^{13} +(2.25713 + 1.00494i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.71130 + 2.09761i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(1.78066 - 0.378492i) q^{19} +(0.913545 - 0.406737i) q^{20} +(1.65325 + 1.83612i) q^{21} +(-0.301097 - 2.86475i) q^{22} +(1.86971 - 1.35842i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.681858 - 1.18101i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.65325 - 1.83612i) q^{28} +(1.38611 - 4.26599i) q^{29} +1.00000 q^{30} +(1.22678 - 5.43093i) q^{31} +1.00000 q^{32} +(0.890132 - 2.73955i) q^{33} +(3.45081 - 3.83252i) q^{34} +(-1.99887 - 1.45226i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.161663 - 0.280008i) q^{37} +(0.190288 - 1.81047i) q^{38} +(1.10327 - 0.801572i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(5.77308 + 6.41165i) q^{41} +(2.25713 - 1.00494i) q^{42} +(0.643552 - 0.136791i) q^{43} +(-2.81758 - 0.598896i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-0.714165 - 2.19797i) q^{46} +(3.34689 + 10.3007i) q^{47} +(0.913545 + 0.406737i) q^{48} +(0.875880 + 0.186174i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(4.71130 - 2.09761i) q^{51} +(-0.912504 - 1.01344i) q^{52} +(-0.899300 - 8.55627i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.301097 + 2.86475i) q^{55} +(-1.23537 - 2.13972i) q^{56} +(0.910223 - 1.57655i) q^{57} +(-3.62887 - 2.63653i) q^{58} +(-3.56168 + 3.95565i) q^{59} +(0.309017 - 0.951057i) q^{60} -6.43804 q^{61} +(-4.78603 - 2.84498i) q^{62} +2.47074 q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.912504 + 1.01344i) q^{65} +(-2.33040 - 1.69313i) q^{66} +(2.04761 - 3.54656i) q^{67} +(-2.57858 - 4.46623i) q^{68} +(0.241574 - 2.29843i) q^{69} +(-1.99887 + 1.45226i) q^{70} +(0.0859794 + 0.818040i) q^{71} +(0.669131 + 0.743145i) q^{72} +(-6.63757 + 2.95524i) q^{73} +(-0.316260 + 0.0672231i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(-1.66306 - 0.740442i) q^{76} +(2.19928 + 6.76870i) q^{77} +(-0.421411 - 1.29697i) q^{78} +(-7.67793 - 3.41844i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(7.88182 - 3.50921i) q^{82} +(1.86285 + 2.06890i) q^{83} +(-0.258263 - 2.45720i) q^{84} +(-4.17223 + 3.03130i) q^{85} +(0.0687723 - 0.654325i) q^{86} +(-2.24277 - 3.88459i) q^{87} +(-1.44026 + 2.49461i) q^{88} +(-3.13631 - 2.27866i) q^{89} +(0.669131 - 0.743145i) q^{90} +(-1.04120 + 3.20448i) q^{91} -2.31109 q^{92} +(-3.21510 - 4.54567i) q^{93} +10.8308 q^{94} +(-0.562549 + 1.73135i) q^{95} +(0.669131 - 0.743145i) q^{96} +(6.53627 + 4.74888i) q^{97} +(0.447724 - 0.775481i) q^{98} +(-1.44026 - 2.49461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.258263	+	2.45720i	−0.0976141	+	0.928736i	0.830645	+	0.556802i	$0.187972\pi$
$7$	−0.258263	+	2.45720i	−0.0976141	+	0.928736i	−0.928259	+	0.371934i	$0.878695\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	2.63149	−	1.17162i	0.793425	−	0.353256i	0.0303286	−	0.999540i	$-0.490345\pi$
$11$	2.63149	−	1.17162i	0.793425	−	0.353256i	0.763097	+	0.646284i	$0.223678\pi$
$12$	−0.978148	+	0.207912i	−0.282367	+	0.0600189i
$13$	1.33391	+	0.283532i	0.369961	+	0.0786377i	0.389141	−	0.921178i	$-0.372772\pi$
$13$	1.33391	+	0.283532i	0.369961	+	0.0786377i	−0.0191793	+	0.999816i	$0.506105\pi$
$14$	2.25713	+	1.00494i	0.603244	+	0.268582i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.71130	+	2.09761i	1.14266	+	0.508744i	0.888708	−	0.458473i	$-0.151603\pi$
$17$	4.71130	+	2.09761i	1.14266	+	0.508744i	0.253950	+	0.967217i	$0.418270\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	1.78066	−	0.378492i	0.408512	−	0.0868320i	0.000928126	−	1.00000i	$-0.499705\pi$
$19$	1.78066	−	0.378492i	0.408512	−	0.0868320i	0.407584	+	0.913168i	$0.366371\pi$
$20$	0.913545	−	0.406737i	0.204275	−	0.0909491i
$21$	1.65325	+	1.83612i	0.360768	+	0.400674i
$22$	−0.301097	−	2.86475i	−0.0641941	−	0.610767i
$23$	1.86971	−	1.35842i	0.389861	−	0.283251i	−0.375537	−	0.926807i	$-0.622542\pi$
$23$	1.86971	−	1.35842i	0.389861	−	0.283251i	0.765399	+	0.643557i	$0.222542\pi$
$24$	−0.104528	+	0.994522i	−0.0213368	+	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.681858	−	1.18101i	0.133723	−	0.231616i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	1.65325	−	1.83612i	0.312434	−	0.346993i
$29$	1.38611	−	4.26599i	0.257393	−	0.792175i	−0.735955	−	0.677030i	$-0.763267\pi$
$29$	1.38611	−	4.26599i	0.257393	−	0.792175i	0.993349	−	0.115145i	$-0.0367333\pi$
$30$	1.00000			0.182574
$31$	1.22678	−	5.43093i	0.220335	−	0.975424i
$31$	1.22678	−	5.43093i	0.220335	−	0.975424i
$32$	1.00000			0.176777
$33$	0.890132	−	2.73955i	0.154952	−	0.476894i
$34$	3.45081	−	3.83252i	0.591810	−	0.657271i
$35$	−1.99887	−	1.45226i	−0.337871	−	0.245477i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.161663	−	0.280008i	−0.0265772	−	0.0460330i	0.852431	−	0.522840i	$-0.175127\pi$
$37$	−0.161663	−	0.280008i	−0.0265772	−	0.0460330i	−0.879008	+	0.476807i	$0.841794\pi$
$38$	0.190288	−	1.81047i	0.0308689	−	0.293698i
$39$	1.10327	−	0.801572i	0.176664	−	0.128354i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	5.77308	+	6.41165i	0.901603	+	1.00133i	0.999981	+	0.00618234i	$0.00196791\pi$
$41$	5.77308	+	6.41165i	0.901603	+	1.00133i	−0.0983780	+	0.995149i	$0.531365\pi$
$42$	2.25713	−	1.00494i	0.348283	−	0.155066i
$43$	0.643552	−	0.136791i	0.0981407	−	0.0208605i	−0.158580	−	0.987346i	$-0.550691\pi$
$43$	0.643552	−	0.136791i	0.0981407	−	0.0208605i	0.256720	+	0.966486i	$0.417358\pi$
$44$	−2.81758	−	0.598896i	−0.424767	−	0.0902869i
$45$	0.913545	+	0.406737i	0.136183	+	0.0606327i
$46$	−0.714165	−	2.19797i	−0.105298	−	0.324074i
$47$	3.34689	+	10.3007i	0.488194	+	1.50251i	0.827300	+	0.561760i	$0.189875\pi$
$47$	3.34689	+	10.3007i	0.488194	+	1.50251i	−0.339106	+	0.940748i	$0.610125\pi$
$48$	0.913545	+	0.406737i	0.131859	+	0.0587074i
$49$	0.875880	+	0.186174i	0.125126	+	0.0265963i
$50$	−0.978148	+	0.207912i	−0.138331	+	0.0294032i
$51$	4.71130	−	2.09761i	0.659714	−	0.293724i
$52$	−0.912504	−	1.01344i	−0.126541	−	0.140539i
$53$	−0.899300	−	8.55627i	−0.123528	−	1.17529i	−0.864101	−	0.503318i	$-0.832113\pi$
$53$	−0.899300	−	8.55627i	−0.123528	−	1.17529i	0.740573	−	0.671976i	$-0.234554\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	−0.301097	+	2.86475i	−0.0405999	+	0.386283i
$56$	−1.23537	−	2.13972i	−0.165083	−	0.285932i
$57$	0.910223	−	1.57655i	0.120562	−	0.208819i
$58$	−3.62887	−	2.63653i	−0.476494	−	0.346193i
$59$	−3.56168	+	3.95565i	−0.463691	+	0.514981i	−0.928956	−	0.370190i	$-0.879292\pi$
$59$	−3.56168	+	3.95565i	−0.463691	+	0.514981i	0.465265	+	0.885172i	$0.345959\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	−6.43804			−0.824306			−0.412153	−	0.911115i	$-0.635223\pi$
$61$	−6.43804			−0.824306			−0.412153	+	0.911115i	$0.635223\pi$
$62$	−4.78603	−	2.84498i	−0.607826	−	0.361313i
$63$	2.47074			0.311284
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.912504	+	1.01344i	−0.113182	+	0.125702i
$66$	−2.33040	−	1.69313i	−0.286852	−	0.208410i
$67$	2.04761	−	3.54656i	0.250155	−	0.433281i	−0.713413	−	0.700743i	$-0.752852\pi$
$67$	2.04761	−	3.54656i	0.250155	−	0.433281i	0.963568	+	0.267462i	$0.0861851\pi$
$68$	−2.57858	−	4.46623i	−0.312699	−	0.541610i
$69$	0.241574	−	2.29843i	0.0290821	−	0.276698i
$70$	−1.99887	+	1.45226i	−0.238911	+	0.173579i
$71$	0.0859794	+	0.818040i	0.0102039	+	0.0970834i	0.998438	−	0.0558622i	$-0.0177907\pi$
$71$	0.0859794	+	0.818040i	0.0102039	+	0.0970834i	−0.988235	+	0.152946i	$0.951124\pi$
$72$	0.669131	+	0.743145i	0.0788578	+	0.0875805i
$73$	−6.63757	+	2.95524i	−0.776869	+	0.345884i	−0.756573	−	0.653910i	$-0.773128\pi$
$73$	−6.63757	+	2.95524i	−0.776869	+	0.345884i	−0.0202965	+	0.999794i	$0.506461\pi$
$74$	−0.316260	+	0.0672231i	−0.0367645	+	0.00781453i
$75$	−0.978148	−	0.207912i	−0.112947	−	0.0240076i
$76$	−1.66306	−	0.740442i	−0.190766	−	0.0849345i
$77$	2.19928	+	6.76870i	0.250632	+	0.771365i
$78$	−0.421411	−	1.29697i	−0.0477154	−	0.146853i
$79$	−7.67793	−	3.41844i	−0.863835	−	0.384604i	−0.0735119	−	0.997294i	$-0.523421\pi$
$79$	−7.67793	−	3.41844i	−0.863835	−	0.384604i	−0.790323	+	0.612690i	$0.790087\pi$
$80$	−0.978148	−	0.207912i	−0.109360	−	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	7.88182	−	3.50921i	0.870401	−	0.387528i
$83$	1.86285	+	2.06890i	0.204474	+	0.227091i	0.836656	−	0.547728i	$-0.184507\pi$
$83$	1.86285	+	2.06890i	0.204474	+	0.227091i	−0.632182	+	0.774820i	$0.717841\pi$
$84$	−0.258263	−	2.45720i	−0.0281788	−	0.268103i
$85$	−4.17223	+	3.03130i	−0.452542	+	0.328791i
$86$	0.0687723	−	0.654325i	0.00741591	−	0.0705577i
$87$	−2.24277	−	3.88459i	−0.240450	−	0.416471i
$88$	−1.44026	+	2.49461i	−0.153533	+	0.265926i
$89$	−3.13631	−	2.27866i	−0.332448	−	0.241538i	0.409021	−	0.912525i	$-0.365870\pi$
$89$	−3.13631	−	2.27866i	−0.332448	−	0.241538i	−0.741469	+	0.670988i	$0.765870\pi$
$90$	0.669131	−	0.743145i	0.0705326	−	0.0783343i
$91$	−1.04120	+	3.20448i	−0.109147	+	0.335920i
$92$	−2.31109			−0.240947
$93$	−3.21510	−	4.54567i	−0.333390	−	0.471365i
$94$	10.8308			1.11711
$95$	−0.562549	+	1.73135i	−0.0577163	+	0.177632i
$96$	0.669131	−	0.743145i	0.0682929	−	0.0758469i
$97$	6.53627	+	4.74888i	0.663658	+	0.482176i	0.867896	−	0.496746i	$-0.165472\pi$
$97$	6.53627	+	4.74888i	0.663658	+	0.482176i	−0.204238	+	0.978921i	$0.565472\pi$
$98$	0.447724	−	0.775481i	0.0452270	−	0.0783354i
$99$	−1.44026	−	2.49461i	−0.144752	−	0.250718i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−11.5201	+	8.36983i	−1.14629	+	0.832829i	−0.987983	−	0.154561i	$-0.950604\pi$
$101$	−11.5201	+	8.36983i	−1.14629	+	0.832829i	−0.158308	+	0.987390i	$0.550604\pi$
$102$	−0.539070	−	5.12891i	−0.0533759	−	0.507838i
$103$	−8.21733	−	9.12627i	−0.809678	−	0.899238i	0.186859	−	0.982387i	$-0.440169\pi$
$103$	−8.21733	−	9.12627i	−0.809678	−	0.899238i	−0.996537	+	0.0831483i	$0.973502\pi$
$104$	−1.24582	+	0.554673i	−0.122162	+	0.0543902i
$105$	−2.41675	+	0.513696i	−0.235850	+	0.0501316i
$106$	−8.41539	−	1.78875i	−0.817375	−	0.173738i
$107$	6.58514	+	2.93189i	0.636610	+	0.283437i	0.699554	−	0.714580i	$-0.253382\pi$
$107$	6.58514	+	2.93189i	0.636610	+	0.283437i	−0.0629439	+	0.998017i	$0.520049\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	0.872326	+	2.68474i	0.0835537	+	0.257152i	0.984102	−	0.177604i	$-0.0568346\pi$
$109$	0.872326	+	2.68474i	0.0835537	+	0.257152i	−0.900548	+	0.434756i	$0.856835\pi$
$110$	2.63149	+	1.17162i	0.250903	+	0.111709i
$111$	−0.316260	−	0.0672231i	−0.0300181	−	0.00638054i
$112$	−2.41675	+	0.513696i	−0.228361	+	0.0485397i
$113$	14.2349	−	6.33779i	1.33911	−	0.596209i	0.392844	−	0.919605i	$-0.371491\pi$
$113$	14.2349	−	6.33779i	1.33911	−	0.596209i	0.946264	+	0.323396i	$0.104825\pi$
$114$	−1.21812	−	1.35285i	−0.114087	−	0.126706i
$115$	0.241574	+	2.29843i	0.0225269	+	0.214329i
$116$	−3.62887	+	2.63653i	−0.336932	+	0.244796i
$117$	0.142547	−	1.35624i	0.0131785	−	0.125385i
$118$	2.66142	+	4.60972i	0.245004	+	0.424359i
$119$	−6.37100	+	11.0349i	−0.584029	+	1.01157i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−1.80836	+	2.00839i	−0.164397	+	0.182581i
$122$	−1.98946	+	6.12294i	−0.180117	+	0.554345i
$123$	8.62773			0.777936
$124$	−4.18470	+	3.67264i	−0.375798	+	0.329812i
$125$	1.00000			0.0894427
$126$	0.763500	−	2.34981i	0.0680180	−	0.209338i
$127$	2.25144	−	2.50048i	0.199783	−	0.221882i	−0.634926	−	0.772573i	$-0.718969\pi$
$127$	2.25144	−	2.50048i	0.199783	−	0.221882i	0.834709	+	0.550692i	$0.185636\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	0.328965	−	0.569783i	0.0289637	−	0.0501666i
$130$	0.681858	+	1.18101i	0.0598029	+	0.103582i
$131$	−1.03754	+	9.87155i	−0.0906504	+	0.862481i	0.850836	+	0.525431i	$0.176096\pi$
$131$	−1.03754	+	9.87155i	−0.0906504	+	0.862481i	−0.941487	+	0.337050i	$0.890571\pi$
$132$	−2.33040	+	1.69313i	−0.202835	+	0.147368i
$133$	0.470153	+	4.47321i	0.0407674	+	0.387876i
$134$	−2.74023	−	3.04334i	−0.236720	−	0.262904i
$135$	0.913545	−	0.406737i	0.0786255	−	0.0350063i
$136$	−5.04447	+	1.07223i	−0.432559	+	0.0919433i
$137$	20.4180	+	4.33999i	1.74443	+	0.370790i	0.966321	−	0.257339i	$-0.0828456\pi$
$137$	20.4180	+	4.33999i	1.74443	+	0.370790i	0.778109	+	0.628129i	$0.216179\pi$
$138$	−2.11128	−	0.940004i	−0.179724	−	0.0800184i
$139$	−6.30003	−	19.3895i	−0.534361	−	1.64460i	−0.745025	−	0.667037i	$-0.767562\pi$
$139$	−6.30003	−	19.3895i	−0.534361	−	1.64460i	0.210664	−	0.977559i	$-0.432438\pi$
$140$	0.763500	+	2.34981i	0.0645276	+	0.198595i
$141$	9.89440	+	4.40527i	0.833259	+	0.370991i
$142$	0.804571	+	0.171017i	0.0675181	+	0.0143514i
$143$	3.84238	−	0.816723i	0.321316	−	0.0682978i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	3.00141	+	3.33340i	0.249253	+	0.276824i
$146$	0.759475	+	7.22593i	0.0628546	+	0.598022i
$147$	0.724433	−	0.526331i	0.0597502	−	0.0434111i
$148$	−0.0337967	+	0.321554i	−0.00277807	+	0.0264316i
$149$	2.94998	+	5.10951i	0.241672	+	0.418588i	0.961191	−	0.275885i	$-0.0889710\pi$
$149$	2.94998	+	5.10951i	0.241672	+	0.418588i	−0.719519	+	0.694473i	$0.755638\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−13.7662	−	10.0018i	−1.12028	−	0.813932i	−0.136029	−	0.990705i	$-0.543434\pi$
$151$	−13.7662	−	10.0018i	−1.12028	−	0.813932i	−0.984252	+	0.176773i	$0.943434\pi$
$152$	−1.21812	+	1.35285i	−0.0988023	+	0.109731i
$153$	1.59365	−	4.90475i	0.128839	−	0.396526i
$154$	7.11704			0.573507
$155$	4.08994	+	3.77788i	0.328512	+	0.303447i
$156$	−1.36372			−0.109185
$157$	−2.79214	+	8.59333i	−0.222837	+	0.685823i	0.775667	+	0.631143i	$0.217414\pi$
$157$	−2.79214	+	8.59333i	−0.222837	+	0.685823i	−0.998504	+	0.0546798i	$0.982586\pi$
$158$	−5.62374	+	6.24579i	−0.447401	+	0.496889i
$159$	−6.96029	−	5.05695i	−0.551987	−	0.401042i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.85505	+	4.94509i	0.225009	+	0.389727i
$162$	−0.104528	+	0.994522i	−0.00821253	+	0.0781370i
$163$	−3.95520	+	2.87362i	−0.309795	+	0.225079i	−0.731809	−	0.681510i	$-0.761324\pi$
$163$	−3.95520	+	2.87362i	−0.309795	+	0.225079i	0.422013	+	0.906590i	$0.361324\pi$
$164$	−0.901843	−	8.58046i	−0.0704221	−	0.670022i
$165$	1.92745	+	2.14065i	0.150052	+	0.166649i
$166$	2.54329	−	1.13235i	0.197398	−	0.0878872i
$167$	2.63461	−	0.560004i	0.203872	−	0.0433344i	−0.104843	−	0.994489i	$-0.533434\pi$
$167$	2.63461	−	0.560004i	0.203872	−	0.0433344i	0.308716	+	0.951154i	$0.400101\pi$
$168$	−2.41675	−	0.513696i	−0.186456	−	0.0396325i
$169$	−10.1772	−	4.53116i	−0.782858	−	0.348551i
$170$	1.59365	+	4.90475i	0.122227	+	0.376177i
$171$	−0.562549	−	1.73135i	−0.0430192	−	0.132399i
$172$	−0.601048	−	0.267604i	−0.0458295	−	0.0204046i
$173$	−12.0488	−	2.56105i	−0.916053	−	0.194713i	−0.274317	−	0.961639i	$-0.588452\pi$
$173$	−12.0488	−	2.56105i	−0.916053	−	0.194713i	−0.641735	+	0.766926i	$0.721785\pi$
$174$	−4.38751	+	0.932595i	−0.332616	+	0.0706998i
$175$	2.25713	−	1.00494i	0.170623	−	0.0759663i
$176$	1.92745	+	2.14065i	0.145287	+	0.161358i
$177$	0.556389	+	5.29369i	0.0418208	+	0.397898i
$178$	−3.13631	+	2.27866i	−0.235076	+	0.170793i
$179$	0.187539	−	1.78431i	0.0140173	−	0.133366i	−0.985275	−	0.170976i	$-0.945308\pi$
$179$	0.187539	−	1.78431i	0.0140173	−	0.133366i	0.999292	+	0.0376103i	$0.0119746\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	2.23973	−	3.87933i	0.166478	−	0.288349i	−0.770701	−	0.637197i	$-0.780094\pi$
$181$	2.23973	−	3.87933i	0.166478	−	0.288349i	0.937179	+	0.348848i	$0.113427\pi$
$182$	2.72589	+	1.98047i	0.202056	+	0.146803i
$183$	−4.30789	+	4.78439i	−0.318448	+	0.353673i
$184$	−0.714165	+	2.19797i	−0.0526490	+	0.162037i
$185$	0.323325			0.0237714
$186$	−5.31671	+	1.65305i	−0.389840	+	0.121207i
$187$	14.8554			1.08633
$188$	3.34689	−	10.3007i	0.244097	−	0.751254i
$189$	1.65325	−	1.83612i	0.120256	−	0.133558i
$190$	1.47277	+	1.07003i	0.106846	+	0.0776282i
$191$	−6.44038	+	11.1551i	−0.466010	+	0.807153i	−0.999246	−	0.0388135i	$-0.987642\pi$
$191$	−6.44038	+	11.1551i	−0.466010	+	0.807153i	0.533237	+	0.845966i	$0.320976\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−0.261144	+	2.48462i	−0.0187975	+	0.178847i	−0.999892	−	0.0146817i	$-0.995326\pi$
$193$	−0.261144	+	2.48462i	−0.0187975	+	0.178847i	0.981095	+	0.193528i	$0.0619932\pi$
$194$	6.53627	−	4.74888i	0.469277	−	0.340950i
$195$	0.142547	+	1.35624i	0.0102080	+	0.0971227i
$196$	−0.599172	−	0.665448i	−0.0427980	−	0.0475320i
$197$	−18.9032	+	8.41627i	−1.34680	+	0.599634i	−0.948254	−	0.317514i	$-0.897152\pi$
$197$	−18.9032	+	8.41627i	−1.34680	+	0.599634i	−0.398547	+	0.917148i	$0.630485\pi$
$198$	−2.81758	+	0.598896i	−0.200237	+	0.0425617i
$199$	3.62410	+	0.770327i	0.256906	+	0.0546070i	0.334564	−	0.942373i	$-0.391411\pi$
$199$	3.62410	+	0.770327i	0.256906	+	0.0546070i	−0.0776582	+	0.996980i	$0.524744\pi$
$200$	0.913545	+	0.406737i	0.0645974	+	0.0287606i
$201$	−1.26549	−	3.89478i	−0.0892608	−	0.274716i
$202$	4.40028	+	13.5427i	0.309603	+	0.952859i
$203$	10.1244	+	4.50769i	0.710596	+	0.316378i
$204$	−5.04447	−	1.07223i	−0.353183	−	0.0750714i
$205$	−8.43919	+	1.79381i	−0.589419	+	0.125285i
$206$	−11.2189	+	4.99497i	−0.781658	+	0.348016i
$207$	−1.54642	−	1.71747i	−0.107484	−	0.119373i
$208$	0.142547	+	1.35624i	0.00988386	+	0.0940386i
$209$	4.24236	−	3.08226i	0.293450	−	0.213204i
$210$	−0.258263	+	2.45720i	−0.0178218	+	0.169563i
$211$	−10.8047	−	18.7144i	−0.743830	−	1.28835i	−0.950740	−	0.309991i	$-0.899674\pi$
$211$	−10.8047	−	18.7144i	−0.743830	−	1.28835i	0.206910	−	0.978360i	$-0.433659\pi$
$212$	−4.30170	+	7.45076i	−0.295442	+	0.511720i
$213$	0.665453	+	0.483480i	0.0455961	+	0.0331275i
$214$	4.82332	−	5.35684i	0.329715	−	0.366186i
$215$	−0.203311	+	0.625728i	−0.0138657	+	0.0426743i
$216$	1.00000			0.0680414
$217$	13.0281	+	4.41704i	0.884404	+	0.299849i
$218$	2.82291			0.191191
$219$	−2.24523	+	6.91012i	−0.151719	+	0.466943i
$220$	1.92745	−	2.14065i	0.129949	−	0.144323i
$221$	5.68974	+	4.13383i	0.382733	+	0.278072i
$222$	−0.161663	+	0.280008i	−0.0108501	+	0.0187929i
$223$	−2.66678	−	4.61900i	−0.178581	−	0.309311i	0.762814	−	0.646618i	$-0.223817\pi$
$223$	−2.66678	−	4.61900i	−0.178581	−	0.309311i	−0.941395	+	0.337307i	$0.890484\pi$
$224$	−0.258263	+	2.45720i	−0.0172559	+	0.164179i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−1.62877	−	15.4967i	−0.108344	−	1.03082i
$227$	−2.66648	−	2.96142i	−0.176980	−	0.196557i	0.648128	−	0.761532i	$-0.275552\pi$
$227$	−2.66648	−	2.96142i	−0.176980	−	0.196557i	−0.825108	+	0.564975i	$0.808886\pi$
$228$	−1.66306	+	0.740442i	−0.110139	+	0.0490370i
$229$	2.78633	−	0.592252i	0.184126	−	0.0391371i	−0.114926	−	0.993374i	$-0.536663\pi$
$229$	2.78633	−	0.592252i	0.184126	−	0.0391371i	0.299052	+	0.954237i	$0.403330\pi$
$230$	2.26058	+	0.480502i	0.149058	+	0.0316834i
$231$	6.50174	+	2.89476i	0.427783	+	0.190461i
$232$	1.38611	+	4.26599i	0.0910023	+	0.280076i
$233$	6.52899	+	20.0942i	0.427728	+	1.31641i	0.900357	+	0.435151i	$0.143305\pi$
$233$	6.52899	+	20.0942i	0.427728	+	1.31641i	−0.472629	+	0.881261i	$0.656695\pi$
$234$	−1.24582	−	0.554673i	−0.0814415	−	0.0362601i
$235$	−10.5941	−	2.25184i	−0.691082	−	0.146894i
$236$	5.20653	−	1.10668i	0.338916	−	0.0720389i
$237$	−7.67793	+	3.41844i	−0.498735	+	0.222051i
$238$	8.52606	+	9.46915i	0.552663	+	0.613794i
$239$	−0.698422	−	6.64504i	−0.0451771	−	0.429832i	−0.993611	−	0.112857i	$-0.964000\pi$
$239$	−0.698422	−	6.64504i	−0.0451771	−	0.429832i	0.948434	−	0.316974i	$-0.102667\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	−0.474055	+	4.51033i	−0.0305366	+	0.290536i	0.968587	+	0.248675i	$0.0799952\pi$
$241$	−0.474055	+	4.51033i	−0.0305366	+	0.290536i	−0.999123	+	0.0418607i	$0.986671\pi$
$242$	1.35128	+	2.34048i	0.0868634	+	0.150452i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.20848	+	3.78418i	0.333439	+	0.242257i
$245$	−0.599172	+	0.665448i	−0.0382797	+	0.0425139i
$246$	2.66611	−	8.20545i	0.169985	−	0.523161i
$247$	2.48257			0.157962
$248$	2.19974	+	5.11480i	0.139684	+	0.324790i
$249$	2.78398			0.176428
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−0.160631	+	0.178399i	−0.0101390	+	0.0112605i	−0.748193	−	0.663481i	$-0.769078\pi$
$251$	−0.160631	+	0.178399i	−0.0101390	+	0.0112605i	0.738054	+	0.674742i	$0.235745\pi$
$252$	−1.99887	−	1.45226i	−0.125917	−	0.0914840i
$253$	3.32858	−	5.76526i	0.209266	−	0.362459i
$254$	−1.68236	−	2.91394i	−0.105561	−	0.182837i
$255$	−0.539070	+	5.12891i	−0.0337579	+	0.321185i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	2.08563	+	19.8434i	0.130098	+	1.23780i	0.843533	+	0.537078i	$0.180472\pi$
$257$	2.08563	+	19.8434i	0.130098	+	1.23780i	−0.713435	+	0.700722i	$0.752862\pi$
$258$	−0.440241	−	0.488937i	−0.0274082	−	0.0304399i
$259$	0.729788	−	0.324923i	0.0453468	−	0.0201897i
$260$	1.33391	−	0.283532i	0.0827259	−	0.0175839i
$261$	−4.38751	−	0.932595i	−0.271580	−	0.0577262i
$262$	9.06778	+	4.03724i	0.560210	+	0.249421i
$263$	−9.16062	−	28.1935i	−0.564868	−	1.73848i	−0.668344	−	0.743852i	$-0.732997\pi$
$263$	−9.16062	−	28.1935i	−0.564868	−	1.73848i	0.103476	−	0.994632i	$-0.467003\pi$
$264$	0.890132	+	2.73955i	0.0547839	+	0.168607i
$265$	7.85959	+	3.49932i	0.482811	+	0.214961i
$266$	4.39956	+	0.935155i	0.269754	+	0.0573380i
$267$	−3.79197	+	0.806009i	−0.232065	+	0.0493270i
$268$	−3.74116	+	1.66567i	−0.228528	+	0.101747i
$269$	−11.1024	−	12.3304i	−0.676924	−	0.751801i	0.302602	−	0.953117i	$-0.402145\pi$
$269$	−11.1024	−	12.3304i	−0.676924	−	0.751801i	−0.979526	+	0.201316i	$0.935478\pi$
$270$	−0.104528	−	0.994522i	−0.00636140	−	0.0605247i
$271$	−5.59127	+	4.06229i	−0.339645	+	0.246767i	−0.744512	−	0.667609i	$-0.767318\pi$
$271$	−5.59127	+	4.06229i	−0.339645	+	0.246767i	0.404867	+	0.914376i	$0.367318\pi$
$272$	−0.539070	+	5.12891i	−0.0326859	+	0.310986i
$273$	1.68469	+	2.91797i	0.101962	+	0.176604i
$274$	10.4371	−	18.0776i	0.630528	−	1.09211i
$275$	−2.33040	−	1.69313i	−0.140528	−	0.102100i
$276$	−1.54642	+	1.71747i	−0.0930835	+	0.103380i
$277$	−9.69227	+	29.8297i	−0.582352	+	1.79229i	0.0273019	+	0.999627i	$0.491308\pi$
$277$	−9.69227	+	29.8297i	−0.582352	+	1.79229i	−0.609654	+	0.792668i	$0.708692\pi$
$278$	−20.3873			−1.22275
$279$	−5.52941	−	0.652368i	−0.331037	−	0.0390563i
$280$	2.47074			0.147655
$281$	−2.86657	+	8.82239i	−0.171005	+	0.526299i	−0.999429	−	0.0338028i	$-0.989238\pi$
$281$	−2.86657	+	8.82239i	−0.171005	+	0.526299i	0.828423	+	0.560102i	$0.189238\pi$
$282$	7.24720	−	8.04883i	0.431564	−	0.479301i
$283$	−5.18230	−	3.76516i	−0.308056	−	0.223816i	0.423006	−	0.906127i	$-0.360975\pi$
$283$	−5.18230	−	3.76516i	−0.308056	−	0.223816i	−0.731062	+	0.682311i	$0.760975\pi$
$284$	0.411273	−	0.712345i	0.0244046	−	0.0422699i
$285$	0.910223	+	1.57655i	0.0539169	+	0.0933869i
$286$	0.410611	−	3.90670i	0.0242799	−	0.231008i
$287$	−17.2457	+	12.5297i	−1.01798	+	0.739607i
$288$	−0.104528	−	0.994522i	−0.00615940	−	0.0586028i
$289$	6.42119	+	7.13145i	0.377717	+	0.419497i
$290$	4.09774	−	1.82443i	0.240627	−	0.107134i
$291$	7.90272	−	1.67978i	0.463266	−	0.0984702i
$292$	7.10695	+	1.51063i	0.415903	+	0.0884029i
$293$	2.50147	+	1.11373i	0.146137	+	0.0650646i	0.478502	−	0.878086i	$-0.341180\pi$
$293$	2.50147	+	1.11373i	0.146137	+	0.0650646i	−0.332365	+	0.943151i	$0.607847\pi$
$294$	−0.276709	−	0.851622i	−0.0161380	−	0.0496676i
$295$	−1.64485	−	5.06233i	−0.0957669	−	0.294740i
$296$	0.295372	+	0.131508i	0.0171682	+	0.00764376i
$297$	−2.81758	−	0.598896i	−0.163493	−	0.0347514i
$298$	5.77103	−	1.22667i	0.334307	−	0.0710591i
$299$	2.87919	−	1.28190i	0.166508	−	0.0741340i
$300$	0.669131	+	0.743145i	0.0386323	+	0.0429055i
$301$	0.169918	+	1.61667i	0.00979394	+	0.0931831i
$302$	−13.7662	+	10.0018i	−0.792158	+	0.575537i
$303$	−1.48844	+	14.1616i	−0.0855089	+	0.813563i
$304$	0.910223	+	1.57655i	0.0522049	+	0.0904215i
$305$	3.21902	−	5.57550i	0.184320	−	0.319252i
$306$	−4.17223	−	3.03130i	−0.238511	−	0.173288i
$307$	1.18967	−	1.32126i	0.0678981	−	0.0754085i	−0.708239	−	0.705973i	$-0.750510\pi$
$307$	1.18967	−	1.32126i	0.0678981	−	0.0754085i	0.776137	+	0.630565i	$0.217177\pi$
$308$	2.19928	−	6.76870i	0.125316	−	0.385683i
$309$	−12.2806			−0.698620
$310$	4.85684	−	2.72233i	0.275850	−	0.154618i
$311$	20.1530			1.14277			0.571386	−	0.820681i	$-0.306406\pi$
$311$	20.1530			1.14277			0.571386	+	0.820681i	$0.306406\pi$
$312$	−0.421411	+	1.29697i	−0.0238577	+	0.0734265i
$313$	6.56331	−	7.28930i	0.370980	−	0.412015i	−0.528530	−	0.848915i	$-0.677257\pi$
$313$	6.56331	−	7.28930i	0.370980	−	0.412015i	0.899511	+	0.436899i	$0.143923\pi$
$314$	7.30992	+	5.31097i	0.412523	+	0.299715i
$315$	−1.23537	+	2.13972i	−0.0696052	+	0.120560i
$316$	4.20227	+	7.27855i	0.236396	+	0.409450i
$317$	1.44550	−	13.7530i	0.0811876	−	0.772448i	−0.875869	−	0.482548i	$-0.839711\pi$
$317$	1.44550	−	13.7530i	0.0811876	−	0.772448i	0.957057	−	0.289900i	$-0.0936220\pi$
$318$	−6.96029	+	5.05695i	−0.390314	+	0.283580i
$319$	−1.35058	−	12.8499i	−0.0756180	−	0.719458i
$320$	0.669131	+	0.743145i	0.0374055	+	0.0415431i
$321$	6.58514	−	2.93189i	0.367547	−	0.163642i
$322$	5.58531	−	1.18720i	0.311257	−	0.0661598i
$323$	9.18317	+	1.95194i	0.510966	+	0.108609i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−0.421411	−	1.29697i	−0.0233757	−	0.0719430i
$326$	1.51075	+	4.64962i	0.0836728	+	0.257519i
$327$	2.57885	+	1.14818i	0.142611	+	0.0634945i
$328$	−8.43919	−	1.79381i	−0.465976	−	0.0990463i
$329$	−26.1752	+	5.56372i	−1.44309	+	0.306738i
$330$	2.63149	−	1.17162i	0.144859	−	0.0644954i
$331$	−4.92280	−	5.46732i	−0.270582	−	0.300511i	0.592505	−	0.805566i	$-0.298139\pi$
$331$	−4.92280	−	5.46732i	−0.270582	−	0.300511i	−0.863087	+	0.505055i	$0.831472\pi$
$332$	−0.291005	−	2.76873i	−0.0159710	−	0.151954i
$333$	−0.261576	+	0.190046i	−0.0143343	+	0.0104145i
$334$	0.281544	−	2.67871i	0.0154054	−	0.146573i
$335$	2.04761	+	3.54656i	0.111873	+	0.193769i
$336$	−1.23537	+	2.13972i	−0.0673949	+	0.116731i
$337$	11.6827	+	8.48794i	0.636395	+	0.462368i	0.858610	−	0.512630i	$-0.171329\pi$
$337$	11.6827	+	8.48794i	0.636395	+	0.462368i	−0.222215	+	0.974998i	$0.571329\pi$
$338$	−7.45430	+	8.27884i	−0.405461	+	0.450310i
$339$	4.81512	−	14.8194i	0.261521	−	0.804880i
$340$	5.15716			0.279686
$341$	−3.13472	−	15.7288i	−0.169754	−	0.851761i
$342$	−1.82045			−0.0984384
$343$	−6.02818	+	18.5528i	−0.325491	+	1.00176i
$344$	−0.440241	+	0.488937i	−0.0237362	+	0.0263617i
$345$	1.86971	+	1.35842i	0.100662	+	0.0731350i
$346$	−6.15899	+	10.6677i	−0.331109	+	0.573498i
$347$	−18.5216	−	32.0804i	−0.994292	−	1.72216i	−0.589547	−	0.807734i	$-0.700694\pi$
$347$	−18.5216	−	32.0804i	−0.994292	−	1.72216i	−0.404745	−	0.914430i	$-0.632640\pi$
$348$	−0.468866	+	4.46096i	−0.0251338	+	0.239133i
$349$	−14.4818	+	10.5217i	−0.775194	+	0.563211i	−0.903533	−	0.428519i	$-0.859035\pi$
$349$	−14.4818	+	10.5217i	−0.775194	+	0.563211i	0.128339	+	0.991730i	$0.459035\pi$
$350$	−0.258263	−	2.45720i	−0.0138047	−	0.131343i
$351$	−0.912504	−	1.01344i	−0.0487058	−	0.0540933i
$352$	2.63149	−	1.17162i	0.140259	−	0.0624474i
$353$	−19.9590	+	4.24242i	−1.06231	+	0.225801i	−0.705743	−	0.708468i	$-0.749387\pi$
$353$	−19.9590	+	4.24242i	−1.06231	+	0.225801i	−0.356569	+	0.934269i	$0.616053\pi$
$354$	5.20653	+	1.10668i	0.276724	+	0.0588195i
$355$	−0.751433	−	0.334559i	−0.0398819	−	0.0177566i
$356$	1.19796	+	3.68695i	0.0634919	+	0.195408i
$357$	3.93749	+	12.1184i	0.208394	+	0.641372i
$358$	−1.63903	−	0.729743i	−0.0866254	−	0.0385681i
$359$	−19.4229	−	4.12847i	−1.02510	−	0.217892i	−0.335469	−	0.942051i	$-0.608895\pi$
$359$	−19.4229	−	4.12847i	−1.02510	−	0.217892i	−0.689633	+	0.724159i	$0.742228\pi$
$360$	−0.978148	+	0.207912i	−0.0515529	+	0.0109579i
$361$	−14.3299	+	6.38006i	−0.754203	+	0.335793i
$362$	−2.99735	−	3.32889i	−0.157537	−	0.174963i
$363$	0.282494	+	2.68775i	0.0148271	+	0.141070i
$364$	2.72589	−	1.98047i	0.142875	−	0.103805i
$365$	0.759475	−	7.22593i	0.0397528	−	0.378222i
$366$	3.21902	+	5.57550i	0.168261	+	0.291436i
$367$	1.64473	−	2.84875i	0.0858539	−	0.148703i	−0.819901	−	0.572506i	$-0.805971\pi$
$367$	1.64473	−	2.84875i	0.0858539	−	0.148703i	0.905755	+	0.423802i	$0.139305\pi$
$368$	1.86971	+	1.35842i	0.0974653	+	0.0708127i
$369$	5.77308	−	6.41165i	0.300534	−	0.333777i
$370$	0.0999130	−	0.307501i	0.00519423	−	0.0159862i
$371$	21.2568			1.10360
$372$	−0.0708133	+	5.56731i	−0.00367150	+	0.288652i
$373$	27.7835			1.43857			0.719287	−	0.694713i	$-0.244469\pi$
$373$	27.7835			1.43857			0.719287	+	0.694713i	$0.244469\pi$
$374$	4.59056	−	14.1283i	0.237372	−	0.730556i
$375$	0.669131	−	0.743145i	0.0345538	−	0.0383758i
$376$	−8.76228	−	6.36617i	−0.451880	−	0.328310i
$377$	3.05849	−	5.29747i	0.157520	−	0.272833i
$378$	−1.23537	−	2.13972i	−0.0635406	−	0.110055i
$379$	1.86837	−	17.7764i	0.0959719	−	0.913111i	−0.835547	−	0.549419i	$-0.814849\pi$
$379$	1.86837	−	17.7764i	0.0959719	−	0.913111i	0.931519	−	0.363693i	$-0.118484\pi$
$380$	1.47277	−	1.07003i	0.0755516	−	0.0548914i
$381$	−0.351710	−	3.34630i	−0.0180186	−	0.171436i
$382$	8.61891	+	9.57227i	0.440982	+	0.489760i
$383$	−8.79093	+	3.91397i	−0.449195	+	0.199995i	−0.618850	−	0.785509i	$-0.712401\pi$
$383$	−8.79093	+	3.91397i	−0.449195	+	0.199995i	0.169655	+	0.985504i	$0.445735\pi$
$384$	−0.978148	+	0.207912i	−0.0499159	+	0.0106099i
$385$	−6.96151	−	1.47971i	−0.354791	−	0.0754132i
$386$	2.28231	+	1.01615i	0.116167	+	0.0517207i
$387$	−0.203311	−	0.625728i	−0.0103349	−	0.0318075i
$388$	−2.49663	−	7.68385i	−0.126747	−	0.390088i
$389$	−7.59752	−	3.38264i	−0.385210	−	0.171506i	0.204989	−	0.978764i	$-0.434284\pi$
$389$	−7.59752	−	3.38264i	−0.385210	−	0.171506i	−0.590199	+	0.807258i	$0.700951\pi$
$390$	1.33391	+	0.283532i	0.0675454	+	0.0143572i
$391$	11.6582	−	2.47803i	0.589580	−	0.125319i
$392$	−0.818033	+	0.364212i	−0.0413169	+	0.0183955i
$393$	6.64174	+	7.37640i	0.335032	+	0.372090i
$394$	2.16292	+	20.5788i	0.108966	+	1.03675i
$395$	6.79942	−	4.94007i	0.342116	−	0.248562i
$396$	−0.301097	+	2.86475i	−0.0151307	+	0.143959i
$397$	−12.9223	−	22.3821i	−0.648553	−	1.12333i	−0.983469	−	0.181079i	$-0.942041\pi$
$397$	−12.9223	−	22.3821i	−0.648553	−	1.12333i	0.334916	−	0.942248i	$-0.391292\pi$
$398$	1.85253	−	3.20868i	0.0928591	−	0.160837i
$399$	3.63883	+	2.64377i	0.182170	+	0.132354i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	1.34923	−	4.15251i	0.0673775	−	0.207367i	−0.911699	−	0.410858i	$-0.865229\pi$
$401$	1.34923	−	4.15251i	0.0673775	−	0.207367i	0.979077	+	0.203492i	$0.0652290\pi$
$402$	−4.09521			−0.204251
$403$	3.17626	−	6.89657i	0.158221	−	0.343543i
$404$	14.2396			0.708447
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	7.41569	−	8.23596i	0.368035	−	0.408744i
$407$	−0.753476	−	0.547433i	−0.0373484	−	0.0271352i
$408$	−2.57858	+	4.46623i	−0.127659	+	0.221111i
$409$	−7.13879	−	12.3648i	−0.352991	−	0.611398i	0.633781	−	0.773512i	$-0.281502\pi$
$409$	−7.13879	−	12.3648i	−0.352991	−	0.611398i	−0.986772	+	0.162115i	$0.948169\pi$
$410$	−0.901843	+	8.58046i	−0.0445388	+	0.423759i
$411$	16.8876	−	12.2695i	0.833002	−	0.605212i
$412$	1.28367	+	12.2133i	0.0632421	+	0.601708i
$413$	−8.79998	−	9.77337i	−0.433019	−	0.480916i
$414$	−2.11128	+	0.940004i	−0.103764	+	0.0461987i
$415$	−2.72314	+	0.578822i	−0.133674	+	0.0284133i
$416$	1.33391	+	0.283532i	0.0654006	+	0.0139013i
$417$	−18.6247	−	8.29227i	−0.912057	−	0.406074i
$418$	−1.62044	−	4.98719i	−0.0792582	−	0.243932i
$419$	8.72321	+	26.8473i	0.426157	+	1.31158i	0.901882	+	0.431982i	$0.142186\pi$
$419$	8.72321	+	26.8473i	0.426157	+	1.31158i	−0.475726	+	0.879594i	$0.657814\pi$
$420$	2.25713	+	1.00494i	0.110137	+	0.0490361i
$421$	−24.7262	−	5.25571i	−1.20508	−	0.256148i	−0.438759	−	0.898605i	$-0.644582\pi$
$421$	−24.7262	−	5.25571i	−1.20508	−	0.256148i	−0.766322	+	0.642457i	$0.777915\pi$
$422$	−21.1373	+	4.49287i	−1.02895	+	0.218709i
$423$	9.89440	−	4.40527i	0.481082	−	0.214192i
$424$	5.75680	+	6.39357i	0.279575	+	0.310499i
$425$	−0.539070	−	5.12891i	−0.0261487	−	0.248789i
$426$	0.665453	−	0.483480i	0.0322413	−	0.0234247i
$427$	1.66270	−	15.8196i	0.0804639	−	0.765563i
$428$	−3.60417	−	6.24260i	−0.174214	−	0.301747i
$429$	1.96411	−	3.40194i	0.0948281	−	0.164247i
$430$	0.532276	+	0.386721i	0.0256686	+	0.0186493i
$431$	23.4304	−	26.0221i	1.12860	−	1.25344i	0.164942	−	0.986303i	$-0.447256\pi$
$431$	23.4304	−	26.0221i	1.12860	−	1.25344i	0.963659	−	0.267135i	$-0.0860770\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	32.0809			1.54171			0.770855	−	0.637011i	$-0.219829\pi$
$433$	32.0809			1.54171			0.770855	+	0.637011i	$0.219829\pi$
$434$	8.22676	−	11.0255i	0.394897	−	0.529241i
$435$	4.48553			0.215065
$436$	0.872326	−	2.68474i	0.0417769	−	0.128576i
$437$	2.81517	−	3.12657i	0.134668	−	0.149564i
$438$	5.87810	+	4.27069i	0.280866	+	0.204061i
$439$	6.40520	−	11.0941i	0.305703	−	0.529494i	−0.671714	−	0.740810i	$-0.734442\pi$
$439$	6.40520	−	11.0941i	0.305703	−	0.529494i	0.977418	+	0.211316i	$0.0677751\pi$
$440$	−1.44026	−	2.49461i	−0.0686619	−	0.118926i
$441$	0.0935998	−	0.890543i	0.00445713	−	0.0424068i
$442$	5.68974	−	4.13383i	0.270633	−	0.196626i
$443$	−0.980639	−	9.33016i	−0.0465916	−	0.443289i	−0.992805	−	0.119745i	$-0.961792\pi$
$443$	−0.980639	−	9.33016i	−0.0465916	−	0.443289i	0.946213	−	0.323544i	$-0.104874\pi$
$444$	0.216347	+	0.240278i	0.0102674	+	0.0114031i
$445$	3.54153	−	1.57679i	0.167885	−	0.0747471i
$446$	−5.21701	+	1.10891i	−0.247033	+	0.0525084i
$447$	5.77103	+	1.22667i	0.272960	+	0.0580195i
$448$	2.25713	+	1.00494i	0.106639	+	0.0474790i
$449$	−7.92126	−	24.3791i	−0.373827	−	1.15052i	−0.944266	−	0.329182i	$-0.893227\pi$
$449$	−7.92126	−	24.3791i	−0.373827	−	1.15052i	0.570439	−	0.821340i	$-0.306773\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	22.7038	+	10.1084i	1.06908	+	0.475985i
$452$	−15.2415	−	3.23969i	−0.716902	−	0.152382i
$453$	−16.6442	+	3.53783i	−0.782011	+	0.166222i
$454$	−3.64047	+	1.62084i	−0.170856	+	0.0760698i
$455$	−2.25456	−	2.50394i	−0.105695	−	0.117387i
$456$	0.190288	+	1.81047i	0.00891107	+	0.0847832i
$457$	−22.4121	+	16.2833i	−1.04839	+	0.761702i	−0.971906	−	0.235369i	$-0.924370\pi$
$457$	−22.4121	+	16.2833i	−1.04839	+	0.761702i	−0.0764862	+	0.997071i	$0.524370\pi$
$458$	0.297757	−	2.83297i	0.0139133	−	0.132376i
$459$	−2.57858	−	4.46623i	−0.120358	−	0.208466i
$460$	1.15554	−	2.00146i	0.0538775	−	0.0933186i
$461$	22.2156	+	16.1406i	1.03469	+	0.751743i	0.969241	−	0.246114i	$-0.0791536\pi$
$461$	22.2156	+	16.1406i	1.03469	+	0.751743i	0.0654441	+	0.997856i	$0.479154\pi$
$462$	4.76223	−	5.28899i	0.221559	−	0.246066i
$463$	−6.30815	+	19.4145i	−0.293165	+	0.902268i	0.690667	+	0.723173i	$0.257317\pi$
$463$	−6.30815	+	19.4145i	−0.293165	+	0.902268i	−0.983832	+	0.179095i	$0.942683\pi$
$464$	4.48553			0.208236
$465$	5.54422	−	0.511517i	0.257107	−	0.0237211i
$466$	21.1283			0.978747
$467$	5.96978	−	18.3731i	0.276249	−	0.850206i	−0.712638	−	0.701532i	$-0.752500\pi$
$467$	5.96978	−	18.3731i	0.276249	−	0.850206i	0.988886	−	0.148674i	$-0.0475004\pi$
$468$	−0.912504	+	1.01344i	−0.0421805	+	0.0468462i
$469$	8.18580	+	5.94733i	0.377985	+	0.274622i
$470$	−5.41539	+	9.37972i	−0.249793	+	0.432654i
$471$	4.51778	+	7.82503i	0.208168	+	0.360558i
$472$	0.556389	−	5.29369i	0.0256099	−	0.243662i
$473$	1.53324	−	1.11396i	0.0704983	−	0.0512200i
$474$	0.878514	+	8.35850i	0.0403515	+	0.383919i
$475$	−1.21812	−	1.35285i	−0.0558910	−	0.0620732i
$476$	11.6404	−	5.18264i	0.533537	−	0.237546i
$477$	−8.41539	+	1.78875i	−0.385314	+	0.0819011i
$478$	−6.53563	−	1.38919i	−0.298933	−	0.0635401i
$479$	−23.7284	−	10.5646i	−1.08418	−	0.482707i	−0.214700	−	0.976680i	$-0.568877\pi$
$479$	−23.7284	−	10.5646i	−1.08418	−	0.482707i	−0.869477	+	0.493973i	$0.835544\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−0.136253	−	0.419343i	−0.00621260	−	0.0191204i
$482$	4.14309	+	1.84462i	0.188713	+	0.0840203i
$483$	5.58531	+	1.18720i	0.254141	+	0.0540192i
$484$	2.64350	−	0.561893i	0.120159	−	0.0255406i
$485$	−7.38078	+	3.28614i	−0.335144	+	0.149216i
$486$	0.669131	+	0.743145i	0.0303524	+	0.0337097i
$487$	0.671406	+	6.38800i	0.0304243	+	0.289468i	0.999146	+	0.0413183i	$0.0131558\pi$
$487$	0.671406	+	6.38800i	0.0304243	+	0.289468i	−0.968722	+	0.248150i	$0.920178\pi$
$488$	5.20848	−	3.78418i	0.235777	−	0.171302i
$489$	−0.511029	+	4.86212i	−0.0231095	+	0.219872i
$490$	0.447724	+	0.775481i	0.0202261	+	0.0350327i
$491$	11.1104	−	19.2438i	0.501407	−	0.868462i	−0.498592	−	0.866837i	$-0.666149\pi$
$491$	11.1104	−	19.2438i	0.501407	−	0.868462i	0.999999	−	0.00162529i	$-0.000517345\pi$
$492$	−6.97998	−	5.07125i	−0.314682	−	0.228630i
$493$	15.4787	−	17.1909i	0.697127	−	0.774238i
$494$	0.767156	−	2.36106i	0.0345160	−	0.106229i
$495$	2.88053			0.129470
$496$	5.54422	−	0.511517i	0.248943	−	0.0229678i
$497$	−2.03230			−0.0911609
$498$	0.860298	−	2.64772i	0.0385509	−	0.118647i
$499$	4.86085	−	5.39852i	0.217601	−	0.241671i	−0.624454	−	0.781061i	$-0.714679\pi$
$499$	4.86085	−	5.39852i	0.217601	−	0.241671i	0.842056	+	0.539390i	$0.181345\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	1.34673	−	2.33261i	0.0601677	−	0.104213i
$502$	0.120030	+	0.207898i	0.00535720	+	0.00927894i
$503$	0.696973	−	6.63125i	0.0310765	−	0.295673i	−0.967934	−	0.251204i	$-0.919174\pi$
$503$	0.696973	−	6.63125i	0.0310765	−	0.295673i	0.999011	−	0.0444693i	$-0.0141597\pi$
$504$	−1.99887	+	1.45226i	−0.0890367	+	0.0646890i
$505$	−1.48844	−	14.1616i	−0.0662349	−	0.630183i
$506$	−4.45450	−	4.94723i	−0.198027	−	0.219931i
$507$	−10.1772	+	4.53116i	−0.451983	+	0.201236i
$508$	−3.29120	+	0.699566i	−0.146023	+	0.0310382i
$509$	25.0556	+	5.32572i	1.11057	+	0.236059i	0.726446	−	0.687224i	$-0.241171\pi$
$509$	25.0556	+	5.32572i	1.11057	+	0.236059i	0.384122	+	0.923282i	$0.374504\pi$
$510$	4.71130	+	2.09761i	0.208620	+	0.0928836i
$511$	−5.54739	−	17.0731i	−0.245402	−	0.755269i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.66306	−	0.740442i	−0.0734259	−	0.0326913i
$514$	19.5167	+	4.14841i	0.860846	+	0.182978i
$515$	12.0123	−	2.55328i	0.529323	−	0.112511i
$516$	−0.601048	+	0.267604i	−0.0264597	+	0.0117806i
$517$	20.8758	+	23.1849i	0.918115	+	1.01967i
$518$	−0.0835028	−	0.794476i	−0.00366890	−	0.0349073i
$519$	−9.96545	+	7.24032i	−0.437435	+	0.317815i
$520$	0.142547	−	1.35624i	0.00625110	−	0.0594753i
$521$	−11.8436	−	20.5137i	−0.518876	−	0.898720i	−0.999759	−	0.0219352i	$-0.993017\pi$
$521$	−11.8436	−	20.5137i	−0.518876	−	0.898720i	0.480883	−	0.876785i	$-0.340316\pi$
$522$	−2.24277	+	3.88459i	−0.0981632	+	0.170024i
$523$	−3.60588	−	2.61982i	−0.157674	−	0.114557i	0.506151	−	0.862445i	$-0.331068\pi$
$523$	−3.60588	−	2.61982i	−0.157674	−	0.114557i	−0.663825	+	0.747888i	$0.731068\pi$
$524$	6.64174	−	7.37640i	0.290146	−	0.322240i
$525$	0.763500	−	2.34981i	0.0333219	−	0.102554i
$526$	−29.6444			−1.29256
$527$	17.1717	−	23.0135i	0.748010	−	1.00248i
$528$	2.88053			0.125359
$529$	−5.45689	+	16.7946i	−0.237256	+	0.730200i
$530$	5.75680	−	6.39357i	0.250059	−	0.277719i
$531$	4.30627	+	3.12869i	0.186876	+	0.135774i
$532$	2.24892	−	3.89525i	0.0975032	−	0.168880i
$533$	5.88288	+	10.1894i	0.254816	+	0.441354i
$534$	−0.405224	+	3.85545i	−0.0175358	+	0.166842i
$535$	−5.83166	+	4.23695i	−0.252125	+	0.183179i
$536$	0.428066	+	4.07278i	0.0184896	+	0.175917i
$537$	−1.20052	−	1.33331i	−0.0518061	−	0.0575365i
$538$	−15.1578	+	6.74868i	−0.653498	+	0.290956i
$539$	2.52300	−	0.536280i	0.108673	−	0.0230992i
$540$	−0.978148	−	0.207912i	−0.0420928	−	0.00894709i
$541$	−29.3886	−	13.0846i	−1.26351	−	0.562553i	−0.337957	−	0.941162i	$-0.609736\pi$
$541$	−29.3886	−	13.0846i	−1.26351	−	0.562553i	−0.925557	+	0.378609i	$0.876403\pi$
$542$	2.13567	+	6.57293i	0.0917351	+	0.282332i
$543$	−1.38423	−	4.26023i	−0.0594031	−	0.182824i
$544$	4.71130	+	2.09761i	0.201995	+	0.0899341i
$545$	−2.76122	−	0.586915i	−0.118278	−	0.0251407i
$546$	3.29576	−	0.700534i	0.141045	−	0.0299801i
$547$	−33.3588	+	14.8523i	−1.42632	+	0.635038i	−0.967357	−	0.253419i	$-0.918445\pi$
$547$	−33.3588	+	14.8523i	−1.42632	+	0.635038i	−0.458961	+	0.888456i	$0.651778\pi$
$548$	−13.9676	−	15.5125i	−0.596664	−	0.662663i
$549$	0.672958	+	6.40277i	0.0287212	+	0.273263i
$550$	−2.33040	+	1.69313i	−0.0993685	+	0.0721954i
$551$	0.853545	−	8.12094i	0.0363622	−	0.345964i
$552$	1.15554	+	2.00146i	0.0491832	+	0.0851878i
$553$	10.3827	−	17.9834i	0.441518	−	0.764732i
$554$	25.3747	+	18.4358i	1.07807	+	0.783262i
$555$	0.216347	−	0.240278i	0.00918341	−	0.0101992i
$556$	−6.30003	+	19.3895i	−0.267181	+	0.822298i
$557$	41.5881			1.76215			0.881073	−	0.472981i	$-0.156822\pi$
$557$	41.5881			1.76215			0.881073	+	0.472981i	$0.156822\pi$
$558$	−2.32912	+	5.05719i	−0.0985996	+	0.214088i
$559$	0.897228			0.0379487
$560$	0.763500	−	2.34981i	0.0322638	−	0.0992977i
$561$	9.94017	−	11.0397i	0.419674	−	0.466096i
$562$	7.50477	+	5.45254i	0.316570	+	0.230001i
$563$	18.7960	−	32.5556i	0.792157	−	1.37206i	−0.132472	−	0.991187i	$-0.542292\pi$
$563$	18.7960	−	32.5556i	0.792157	−	1.37206i	0.924629	−	0.380869i	$-0.124375\pi$
$564$	−5.41539	−	9.37972i	−0.228029	−	0.394958i
$565$	−1.62877	+	15.4967i	−0.0685228	+	0.651950i
$566$	−5.18230	+	3.76516i	−0.217828	+	0.158262i
$567$	−0.258263	−	2.45720i	−0.0108460	−	0.103193i
$568$	−0.550390	−	0.611271i	−0.0230939	−	0.0256483i
$569$	−35.7810	+	15.9307i	−1.50002	+	0.667850i	−0.982234	−	0.187662i	$-0.939909\pi$
$569$	−35.7810	+	15.9307i	−1.50002	+	0.667850i	−0.517783	+	0.855512i	$0.673243\pi$
$570$	1.78066	−	0.378492i	0.0745838	−	0.0158533i
$571$	−5.13480	−	1.09144i	−0.214885	−	0.0456752i	0.0992112	−	0.995066i	$-0.468368\pi$
$571$	−5.13480	−	1.09144i	−0.214885	−	0.0456752i	−0.314096	+	0.949391i	$0.601701\pi$
$572$	−3.58861	−	1.59775i	−0.150047	−	0.0668053i
$573$	3.98038	+	12.2503i	0.166283	+	0.511765i
$574$	6.58727	+	20.2735i	0.274947	+	0.846201i
$575$	−2.11128	−	0.940004i	−0.0880466	−	0.0392009i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	21.3327	−	4.53441i	0.888092	−	0.188770i	0.258793	−	0.965933i	$-0.416675\pi$
$577$	21.3327	−	4.53441i	0.888092	−	0.188770i	0.629299	+	0.777163i	$0.283342\pi$
$578$	8.76667	−	3.90317i	0.364645	−	0.162351i
$579$	1.67169	+	1.85660i	0.0694731	+	0.0771577i
$580$	−0.468866	−	4.46096i	−0.0194686	−	0.185231i
$581$	−5.56482	+	4.04308i	−0.230868	+	0.167735i
$582$	0.844514	−	8.03502i	0.0350062	−	0.333062i
$583$	−12.3912	−	21.4621i	−0.513190	−	0.888871i
$584$	3.63286	−	6.29231i	0.150329	−	0.260377i
$585$	1.10327	+	0.801572i	0.0456146	+	0.0331409i
$586$	1.83221	−	2.03488i	0.0756880	−	0.0840601i
$587$	0.952653	−	2.93196i	0.0393202	−	0.121015i	−0.929470	−	0.368899i	$-0.879735\pi$
$587$	0.952653	−	2.93196i	0.0393202	−	0.121015i	0.968790	+	0.247883i	$0.0797350\pi$
$588$	−0.895448			−0.0369277
$589$	0.128912	−	10.1350i	0.00531172	−	0.417605i
$590$	−5.32285			−0.219138
$591$	−6.39423	+	19.6794i	−0.263024	+	0.809504i
$592$	0.216347	−	0.240278i	0.00889180	−	0.00987535i
$593$	−1.70869	−	1.24144i	−0.0701676	−	0.0509798i	0.552148	−	0.833746i	$-0.313808\pi$
$593$	−1.70869	−	1.24144i	−0.0701676	−	0.0509798i	−0.622316	+	0.782766i	$0.713808\pi$
$594$	−1.44026	+	2.49461i	−0.0590948	+	0.102355i
$595$	−6.37100	−	11.0349i	−0.261186	−	0.452387i
$596$	0.616713	−	5.86764i	0.0252616	−	0.240348i
$597$	2.99746	−	2.17778i	0.122678	−	0.0891308i
$598$	−0.329439	−	3.13440i	−0.0134717	−	0.128175i
$599$	−8.48962	−	9.42868i	−0.346877	−	0.385245i	0.544309	−	0.838885i	$-0.316792\pi$
$599$	−8.48962	−	9.42868i	−0.346877	−	0.385245i	−0.891185	+	0.453640i	$0.850125\pi$
$600$	0.913545	−	0.406737i	0.0372953	−	0.0166050i
$601$	−29.4956	+	6.26948i	−1.20315	+	0.255737i	−0.765516	−	0.643416i	$-0.777516\pi$
$601$	−29.4956	+	6.26948i	−1.20315	+	0.255737i	−0.437633	+	0.899154i	$0.644183\pi$
$602$	1.59005	+	0.337975i	0.0648055	+	0.0137748i
$603$	−3.74116	−	1.66567i	−0.152352	−	0.0678314i
$604$	5.25824	+	16.1832i	0.213955	+	0.658484i
$605$	−0.835135	−	2.57028i	−0.0339531	−	0.104497i
$606$	13.0085	+	5.79177i	0.528435	+	0.235275i
$607$	24.1735	+	5.13823i	0.981171	+	0.208554i	0.670456	−	0.741949i	$-0.266098\pi$
$607$	24.1735	+	5.13823i	0.981171	+	0.208554i	0.310715	+	0.950503i	$0.399432\pi$
$608$	1.78066	−	0.378492i	0.0722155	−	0.0153499i
$609$	10.1244	−	4.50769i	0.410263	−	0.182661i
$610$	−4.30789	−	4.78439i	−0.174421	−	0.193714i
$611$	1.54389	+	14.6892i	0.0624593	+	0.594260i
$612$	−4.17223	+	3.03130i	−0.168652	+	0.122533i
$613$	−1.06027	+	10.0878i	−0.0428240	+	0.407443i	0.952021	+	0.306033i	$0.0990019\pi$
$613$	−1.06027	+	10.0878i	−0.0428240	+	0.407443i	−0.994845	+	0.101409i	$0.967665\pi$
$614$	−0.888968	−	1.53974i	−0.0358758	−	0.0621388i
$615$	−4.31386	+	7.47183i	−0.173952	+	0.301293i
$616$	−5.75780	−	4.18329i	−0.231988	−	0.168549i
$617$	−15.9964	+	17.7658i	−0.643989	+	0.715223i	−0.973438	−	0.228951i	$-0.926470\pi$
$617$	−15.9964	+	17.7658i	−0.643989	+	0.715223i	0.329449	+	0.944174i	$0.393137\pi$
$618$	−3.79492	+	11.6796i	−0.152654	+	0.469821i
$619$	−11.3279			−0.455305			−0.227652	−	0.973742i	$-0.573105\pi$
$619$	−11.3279			−0.455305			−0.227652	+	0.973742i	$0.573105\pi$
$620$	−1.08824	−	5.46038i	−0.0437049	−	0.219294i
$621$	−2.31109			−0.0927407
$622$	6.22762	−	19.1666i	0.249705	−	0.768512i
$623$	6.40913	−	7.11806i	0.256776	−	0.285179i
$624$	1.10327	+	0.801572i	0.0441661	+	0.0320885i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.90436	−	8.49460i	−0.196018	−	0.339512i
$627$	0.548131	−	5.21512i	0.0218903	−	0.208272i
$628$	7.30992	−	5.31097i	0.291698	−	0.211931i
$629$	−0.174295	−	1.65831i	−0.00694960	−	0.0661210i
$630$	1.65325	+	1.83612i	0.0658669	+	0.0731527i
$631$	37.2030	−	16.5638i	1.48103	−	0.659396i	0.502324	−	0.864679i	$-0.332478\pi$
$631$	37.2030	−	16.5638i	1.48103	−	0.659396i	0.978703	+	0.205284i	$0.0658117\pi$
$632$	8.22089	−	1.74740i	0.327009	−	0.0695080i
$633$	−21.1373	−	4.49287i	−0.840131	−	0.178575i
$634$	−12.6332	−	5.62468i	−0.501730	−	0.223385i
$635$	1.03976	+	3.20005i	0.0412615	+	0.126990i
$636$	2.65860	+	8.18232i	0.105420	+	0.324450i
$637$	1.11556	+	0.496681i	0.0442002	+	0.0196792i
$638$	−12.6384	−	2.68637i	−0.500357	−	0.106354i
$639$	0.804571	−	0.171017i	0.0318283	−	0.00676532i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−8.66512	−	9.62359i	−0.342252	−	0.380109i	0.547305	−	0.836933i	$-0.315654\pi$
$641$	−8.66512	−	9.62359i	−0.342252	−	0.380109i	−0.889557	+	0.456824i	$0.848987\pi$
$642$	−0.753476	−	7.16885i	−0.0297373	−	0.282932i
$643$	−2.50524	+	1.82016i	−0.0987968	+	0.0717801i	−0.636087	−	0.771617i	$-0.719448\pi$
$643$	−2.50524	+	1.82016i	−0.0987968	+	0.0717801i	0.537290	+	0.843398i	$0.319448\pi$
$644$	0.596867	−	5.67881i	0.0235199	−	0.223777i
$645$	0.328965	+	0.569783i	0.0129530	+	0.0224352i
$646$	4.69417	−	8.13053i	0.184690	−	0.319892i
$647$	−1.31602	−	0.956143i	−0.0517380	−	0.0375899i	0.561616	−	0.827398i	$-0.310180\pi$
$647$	−1.31602	−	0.956143i	−0.0517380	−	0.0375899i	−0.613354	+	0.789808i	$0.710180\pi$
$648$	0.669131	−	0.743145i	0.0262859	−	0.0291935i
$649$	−4.73804	+	14.5822i	−0.185984	+	0.572401i
$650$	−1.36372			−0.0534893
$651$	12.0000	−	6.72617i	0.470317	−	0.263619i
$652$	4.88890			0.191464
$653$	5.75202	−	17.7029i	0.225094	−	0.692767i	−0.773188	−	0.634177i	$-0.781339\pi$
$653$	5.75202	−	17.7029i	0.225094	−	0.692767i	0.998282	−	0.0585909i	$-0.0186608\pi$
$654$	1.88889	−	2.09783i	0.0738616	−	0.0820316i
$655$	−8.03024	−	5.83431i	−0.313768	−	0.227965i
$656$	−4.31386	+	7.47183i	−0.168428	+	0.291726i
$657$	3.63286	+	6.29231i	0.141732	+	0.245486i
$658$	−2.79718	+	26.6134i	−0.109046	+	1.03750i
$659$	−10.4580	+	7.59820i	−0.407387	+	0.295984i	−0.772543	−	0.634962i	$-0.781016\pi$
$659$	−10.4580	+	7.59820i	−0.407387	+	0.295984i	0.365156	+	0.930946i	$0.381016\pi$
$660$	−0.301097	−	2.86475i	−0.0117202	−	0.111510i
$661$	−18.7754	−	20.8522i	−0.730279	−	0.811057i	0.257605	−	0.966250i	$-0.417067\pi$
$661$	−18.7754	−	20.8522i	−0.730279	−	0.811057i	−0.987884	+	0.155194i	$0.950400\pi$
$662$	−6.72096	+	2.99237i	−0.261218	+	0.116302i
$663$	6.87921	−	1.46222i	0.267167	−	0.0567880i
$664$	−2.72314	−	0.578822i	−0.105679	−	0.0224627i
$665$	−4.10899	−	1.82944i	−0.159340	−	0.0709426i
$666$	0.0999130	+	0.307501i	0.00387155	+	0.0119154i
$667$	−3.20341	−	9.85908i	−0.124037	−	0.381745i
$668$	−2.46061	−	1.09553i	−0.0952037	−	0.0423874i
$669$	−5.21701	−	1.10891i	−0.201701	−	0.0428729i
$670$	4.00572	−	0.851442i	0.154755	−	0.0328941i
$671$	−16.9417	+	7.54291i	−0.654025	+	0.291191i
$672$	1.65325	+	1.83612i	0.0637754	+	0.0708298i
$673$	4.01427	+	38.1932i	0.154739	+	1.47224i	0.746100	+	0.665834i	$0.231924\pi$
$673$	4.01427	+	38.1932i	0.154739	+	1.47224i	−0.591361	+	0.806407i	$0.701409\pi$
$674$	11.6827	−	8.48794i	0.449999	−	0.326943i
$675$	−0.104528	+	0.994522i	−0.00402330	+	0.0382792i
$676$	5.57014	+	9.64777i	0.214236	+	0.371068i
$677$	−3.80066	+	6.58294i	−0.146071	+	0.253003i	−0.929772	−	0.368136i	$-0.879996\pi$
$677$	−3.80066	+	6.58294i	−0.146071	+	0.253003i	0.783701	+	0.621138i	$0.213330\pi$
$678$	−12.6061	−	9.15890i	−0.484136	−	0.351745i
$679$	−13.3570	+	14.8345i	−0.512596	+	0.569296i
$680$	1.59365	−	4.90475i	0.0611137	−	0.188089i
$681$	−3.98499			−0.152705
$682$	−15.9276	−	1.87917i	−0.609901	−	0.0719570i
$683$	44.8434			1.71588			0.857942	−	0.513747i	$-0.171743\pi$
$683$	44.8434			1.71588			0.857942	+	0.513747i	$0.171743\pi$
$684$	−0.562549	+	1.73135i	−0.0215096	+	0.0661997i
$685$	−13.9676	+	15.5125i	−0.533673	+	0.592704i
$686$	15.7820	+	11.4663i	0.602559	+	0.437784i
$687$	1.42429	−	2.46694i	0.0543399	−	0.0941195i
$688$	0.328965	+	0.569783i	0.0125417	+	0.0217228i
$689$	1.22639	−	11.6683i	0.0467217	−	0.444527i
$690$	1.86971	−	1.35842i	0.0711786	−	0.0517143i
$691$	−0.981498	−	9.33833i	−0.0373379	−	0.355247i	−0.997200	−	0.0747755i	$-0.976176\pi$
$691$	−0.981498	−	9.33833i	−0.0373379	−	0.355247i	0.959862	−	0.280471i	$-0.0904907\pi$
$692$	8.24233	+	9.15404i	0.313326	+	0.347984i
$693$	6.50174	−	2.89476i	0.246980	−	0.109963i
$694$	−36.2337	+	7.70172i	−1.37541	+	0.292353i
$695$	19.9418	+	4.23876i	0.756436	+	0.160785i
$696$	4.09774	+	1.82443i	0.155324	+	0.0691549i
$697$	13.7496	+	42.3169i	0.520802	+	1.60287i
$698$	5.53156	+	17.0244i	0.209373	+	0.644383i
$699$	19.3016	+	8.59364i	0.730054	+	0.325041i
$700$	−2.41675	−	0.513696i	−0.0913445	−	0.0194159i
$701$	11.9247	−	2.53467i	0.450389	−	0.0957331i	0.0228678	−	0.999738i	$-0.492720\pi$
$701$	11.9247	−	2.53467i	0.450389	−	0.0957331i	0.427521	+	0.904005i	$0.359387\pi$
$702$	−1.24582	+	0.554673i	−0.0470203	+	0.0209348i
$703$	−0.393848	−	0.437412i	−0.0148543	−	0.0164973i
$704$	−0.301097	−	2.86475i	−0.0113480	−	0.107969i
$705$	−8.76228	+	6.36617i	−0.330006	+	0.239764i
$706$	−2.13290	+	20.2931i	−0.0802726	+	0.763742i
$707$	−17.5912	−	30.4688i	−0.661584	−	1.14590i
$708$	2.66142	−	4.60972i	0.100022	−	0.173244i
$709$	28.8118	+	20.9330i	1.08205	+	0.786154i	0.978039	−	0.208422i	$-0.0668329\pi$
$709$	28.8118	+	20.9330i	1.08205	+	0.786154i	0.104009	+	0.994576i	$0.466833\pi$
$710$	−0.550390	+	0.611271i	−0.0206558	+	0.0229406i
$711$	−2.59715	+	7.99320i	−0.0974006	+	0.299768i
$712$	3.87669			0.145285
$713$	−5.08379	−	11.8207i	−0.190389	−	0.442690i
$714$	12.7420			0.476857
$715$	−1.21389	+	3.73596i	−0.0453968	+	0.139717i
$716$	−1.20052	+	1.33331i	−0.0448654	+	0.0498280i
$717$	−5.40556	−	3.92737i	−0.201874	−	0.146670i
$718$	−9.92842	+	17.1965i	−0.370525	+	0.641769i
$719$	11.8006	+	20.4393i	0.440090	+	0.762258i	0.997696	−	0.0678480i	$-0.0216133\pi$
$719$	11.8006	+	20.4393i	0.440090	+	0.762258i	−0.557606	+	0.830106i	$0.688280\pi$
$720$	−0.104528	+	0.994522i	−0.00389555	+	0.0370636i
$721$	24.5473	−	17.8347i	0.914191	−	0.664199i
$722$	1.63963	+	15.6000i	0.0610208	+	0.580574i
$723$	3.03463	+	3.37029i	0.112859	+	0.125343i
$724$	−4.09220	+	1.82196i	−0.152085	+	0.0677127i
$725$	−4.38751	+	0.932595i	−0.162948	+	0.0346357i
$726$	2.64350	+	0.561893i	0.0981094	+	0.0208538i
$727$	−42.7314	−	19.0252i	−1.58482	−	0.705607i	−0.590014	−	0.807393i	$-0.700878\pi$
$727$	−42.7314	−	19.0252i	−1.58482	−	0.705607i	−0.994806	+	0.101786i	$0.967544\pi$
$728$	−1.04120	−	3.20448i	−0.0385893	−	0.118766i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−6.63757	−	2.95524i	−0.245668	−	0.109378i
$731$	3.31890	+	0.705454i	0.122754	+	0.0260922i
$732$	6.29735	−	1.33854i	0.232757	−	0.0494740i
$733$	−15.6507	+	6.96816i	−0.578074	+	0.257375i	−0.674879	−	0.737928i	$-0.735804\pi$
$733$	−15.6507	+	6.96816i	−0.578074	+	0.257375i	0.0968055	+	0.995303i	$0.469138\pi$
$734$	−2.20107	−	2.44454i	−0.0812430	−	0.0902295i
$735$	0.0935998	+	0.890543i	0.00345248	+	0.0328482i
$736$	1.86971	−	1.35842i	0.0689184	−	0.0500721i
$737$	1.23306	−	11.7318i	0.0454202	−	0.432145i
$738$	−4.31386	−	7.47183i	−0.158795	−	0.275042i
$739$	10.7204	−	18.5683i	0.394356	−	0.683044i	−0.598663	−	0.801001i	$-0.704301\pi$
$739$	10.7204	−	18.5683i	0.394356	−	0.683044i	0.993019	+	0.117957i	$0.0376344\pi$
$740$	−0.261576	−	0.190046i	−0.00961571	−	0.00698623i
$741$	1.66116	−	1.84491i	0.0610244	−	0.0677744i
$742$	6.56870	−	20.2164i	0.241144	−	0.742166i
$743$	−8.93165			−0.327670			−0.163835	−	0.986488i	$-0.552387\pi$
$743$	−8.93165			−0.327670			−0.163835	+	0.986488i	$0.552387\pi$
$744$	5.27295	+	1.78774i	0.193316	+	0.0655418i
$745$	−5.89996			−0.216158
$746$	8.58556	−	26.4237i	0.314340	−	0.967439i
$747$	1.86285	−	2.06890i	0.0681580	−	0.0756971i
$748$	−12.0182	−	8.73176i	−0.439430	−	0.319265i
$749$	−8.90496	+	15.4238i	−0.325380	+	0.563575i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−4.23169	+	40.2619i	−0.154417	+	1.46918i	0.593205	+	0.805051i	$0.297862\pi$
$751$	−4.23169	+	40.2619i	−0.154417	+	1.46918i	−0.747622	+	0.664125i	$0.768804\pi$
$752$	−8.76228	+	6.36617i	−0.319527	+	0.232150i
$753$	0.0250931	+	0.238745i	0.000914443	+	0.00870034i
$754$	−4.09306	−	4.54581i	−0.149061	−	0.165549i
$755$	15.5449	−	6.92103i	0.565737	−	0.251882i
$756$	−2.41675	+	0.513696i	−0.0878963	+	0.0186829i
$757$	39.2303	+	8.33866i	1.42585	+	0.303074i	0.855276	−	0.518173i	$-0.173388\pi$
$757$	39.2303	+	8.33866i	1.42585	+	0.303074i	0.570574	+	0.821246i	$0.306721\pi$
$758$	−16.3290	−	7.27013i	−0.593095	−	0.264063i
$759$	−2.05717	−	6.33133i	−0.0746707	−	0.229813i
$760$	−0.562549	−	1.73135i	−0.0204058	−	0.0628025i
$761$	33.6299	+	14.9730i	1.21908	+	0.542770i	0.912501	−	0.409074i	$-0.134148\pi$
$761$	33.6299	+	14.9730i	1.21908	+	0.542770i	0.306581	+	0.951845i	$0.400815\pi$
$762$	−3.29120	−	0.699566i	−0.119228	−	0.0253426i
$763$	−6.82225	+	1.45011i	−0.246982	+	0.0524977i
$764$	11.7672	−	5.23908i	0.425721	−	0.189543i
$765$	3.45081	+	3.83252i	0.124764	+	0.138565i
$766$	1.00586	+	9.57015i	0.0363433	+	0.345784i
$767$	−5.87253	+	4.26664i	−0.212045	+	0.154060i
$768$	−0.104528	+	0.994522i	−0.00377185	+	0.0358867i
$769$	15.3373	+	26.5650i	0.553077	+	0.957957i	0.998050	+	0.0624132i	$0.0198797\pi$
$769$	15.3373	+	26.5650i	0.553077	+	0.957957i	−0.444974	+	0.895544i	$0.646787\pi$
$770$	−3.55852	+	6.16353i	−0.128240	+	0.222118i
$771$	16.1421	+	11.7279i	0.581344	+	0.422371i
$772$	1.67169	−	1.85660i	0.0601655	−	0.0668205i
$773$	−13.2907	+	40.9045i	−0.478032	+	1.47123i	0.363792	+	0.931480i	$0.381482\pi$
$773$	−13.2907	+	40.9045i	−0.478032	+	1.47123i	−0.841824	+	0.539752i	$0.818518\pi$
$774$	−0.657929			−0.0236488
$775$	−5.31671	+	1.65305i	−0.190982	+	0.0593792i
$776$	−8.07927			−0.290029
$777$	0.246859	−	0.759754i	0.00885602	−	0.0272560i
$778$	−5.56484	+	6.18038i	−0.199509	+	0.221577i
$779$	12.7067	+	9.23194i	0.455264	+	0.330768i
$780$	0.681858	−	1.18101i	0.0244144	−	0.0422870i
$781$	1.18468	+	2.05193i	0.0423913	+	0.0734239i
$782$	1.24584	−	11.8534i	0.0445511	−	0.423875i
$783$	−3.62887	+	2.63653i	−0.129685	+	0.0942219i
$784$	0.0935998	+	0.890543i	0.00334285	+	0.0318051i
$785$	−6.04597	−	6.71473i	−0.215790	−	0.239659i
$786$	9.06778	−	4.03724i	0.323437	−	0.144004i
$787$	−2.72647	+	0.579529i	−0.0971881	+	0.0206580i	−0.256249	−	0.966611i	$-0.582487\pi$
$787$	−2.72647	+	0.579529i	−0.0971881	+	0.0206580i	0.159061	+	0.987269i	$0.449153\pi$
$788$	20.2400	+	4.30215i	0.721020	+	0.153258i
$789$	−27.0815	−	12.0575i	−0.964126	−	0.429257i
$790$	−2.59715	−	7.99320i	−0.0924024	−	0.284385i
$791$	11.8969	+	36.6149i	0.423005	+	1.30188i
$792$	2.63149	+	1.17162i	0.0935061	+	0.0416316i
$793$	−8.58779	−	1.82539i	−0.304961	−	0.0648216i
$794$	−25.2799	+	5.37341i	−0.897150	+	0.190695i
$795$	7.85959	−	3.49932i	0.278751	−	0.124108i
$796$	−2.47917	−	2.75340i	−0.0878720	−	0.0975917i
$797$	−0.874050	−	8.31603i	−0.0309604	−	0.294569i	−0.999036	−	0.0439086i	$-0.986019\pi$
$797$	−0.874050	−	8.31603i	−0.0309604	−	0.294569i	0.968075	−	0.250660i	$-0.0806477\pi$
$798$	3.63883	−	2.64377i	0.128813	−	0.0935884i
$799$	−5.83855	+	55.5500i	−0.206553	+	1.96522i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−1.93834	+	3.35731i	−0.0684880	+	0.118625i
$802$	−3.53234	−	2.56639i	−0.124731	−	0.0906225i
$803$	−14.0043	+	15.5534i	−0.494202	+	0.548867i
$804$	−1.26549	+	3.89478i	−0.0446304	+	0.137358i
$805$	−5.71009			−0.201254
$806$	−5.57751	−	5.15196i	−0.196459	−	0.181470i
$807$	−16.5923			−0.584075
$808$	4.40028	−	13.5427i	0.154801	−	0.476429i
$809$	5.03713	−	5.59430i	0.177096	−	0.196685i	−0.648061	−	0.761588i	$-0.724420\pi$
$809$	5.03713	−	5.59430i	0.177096	−	0.196685i	0.825157	+	0.564903i	$0.191087\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−17.0002	+	29.4452i	−0.596958	+	1.03396i	0.396309	+	0.918117i	$0.370291\pi$
$811$	−17.0002	+	29.4452i	−0.596958	+	1.03396i	−0.993267	+	0.115845i	$0.963042\pi$
$812$	−5.54129	−	9.59780i	−0.194461	−	0.336817i
$813$	−0.722416	+	6.87333i	−0.0253362	+	0.241058i
$814$	−0.753476	+	0.547433i	−0.0264093	+	0.0191875i
$815$	−0.511029	−	4.86212i	−0.0179006	−	0.170312i
$816$	3.45081	+	3.83252i	0.120803	+	0.134165i
$817$	1.09418	−	0.487158i	0.0382804	−	0.0170435i
$818$	−13.9656	+	2.96848i	−0.488295	+	0.103790i
$819$	3.29576	+	0.700534i	0.115163	+	0.0244787i
$820$	7.88182	+	3.50921i	0.275245	+	0.122547i
$821$	1.58108	+	4.86605i	0.0551800	+	0.169826i	0.974848	−	0.222870i	$-0.0715424\pi$
$821$	1.58108	+	4.86605i	0.0551800	+	0.169826i	−0.919668	+	0.392696i	$0.871542\pi$
$822$	−6.45048	−	19.8525i	−0.224986	−	0.692437i
$823$	36.2407	+	16.1354i	1.26327	+	0.562445i	0.925487	−	0.378779i	$-0.123656\pi$
$823$	36.2407	+	16.1354i	1.26327	+	0.562445i	0.337784	+	0.941224i	$0.390323\pi$
$824$	12.0123	+	2.55328i	0.418467	+	0.0889478i
$825$	−2.81758	+	0.598896i	−0.0980956	+	0.0208509i
$826$	−12.0144	+	5.34914i	−0.418033	+	0.186120i
$827$	−24.2815	−	26.9673i	−0.844349	−	0.937745i	0.154387	−	0.988010i	$-0.450660\pi$
$827$	−24.2815	−	26.9673i	−0.844349	−	0.937745i	−0.998736	+	0.0502659i	$0.983993\pi$
$828$	0.241574	+	2.29843i	0.00839529	+	0.0798758i
$829$	10.3646	−	7.53030i	0.359976	−	0.261538i	−0.393066	−	0.919510i	$-0.628586\pi$
$829$	10.3646	−	7.53030i	0.359976	−	0.261538i	0.753042	+	0.657972i	$0.228586\pi$
$830$	−0.291005	+	2.76873i	−0.0101009	+	0.0961040i
$831$	15.6824	+	27.1627i	0.544017	+	0.942265i
$832$	0.681858	−	1.18101i	0.0236392	−	0.0409442i
$833$	3.73602	+	2.71438i	0.129445	+	0.0940475i
$834$	−13.6418	+	15.1507i	−0.472376	+	0.524627i
$835$	−0.832328	+	2.56164i	−0.0288039	+	0.0886493i
$836$	−5.24385			−0.181362
$837$	−4.18470	+	3.67264i	−0.144645	+	0.126945i
$838$	28.2289			0.975151
$839$	−3.96576	+	12.2053i	−0.136913	+	0.421375i	−0.995883	−	0.0906515i	$-0.971105\pi$
$839$	−3.96576	+	12.2053i	−0.136913	+	0.421375i	0.858970	+	0.512027i	$0.171105\pi$
$840$	1.65325	−	1.83612i	0.0570424	−	0.0633521i
$841$	7.18407	+	5.21953i	0.247727	+	0.179984i
$842$	−12.6393	+	21.8919i	−0.435579	+	0.754444i
$843$	4.63820	+	8.03360i	0.159748	+	0.276692i
$844$	−2.25881	+	21.4911i	−0.0777514	+	0.739755i
$845$	9.01268	−	6.54809i	0.310045	−	0.225261i
$846$	−1.13212	−	10.7714i	−0.0389232	−	0.370330i
$847$	−4.46799	−	4.96221i	−0.153522	−	0.170503i
$848$	7.85959	−	3.49932i	0.269900	−	0.120167i
$849$	−6.26570	+	1.33182i	−0.215038	+	0.0457078i
$850$	−5.04447	−	1.07223i	−0.173024	−	0.0367773i
$851$	−0.682631	−	0.303927i	−0.0234003	−	0.0104185i
$852$	−0.254181	−	0.782287i	−0.00870808	−	0.0268007i
$853$	−0.525259	−	1.61658i	−0.0179845	−	0.0553507i	0.941661	−	0.336561i	$-0.109264\pi$
$853$	−0.525259	−	1.61658i	−0.0179845	−	0.0553507i	−0.959646	+	0.281211i	$0.909264\pi$
$854$	−14.5315	−	6.46984i	−0.497258	−	0.221393i
$855$	1.78066	+	0.378492i	0.0608974	+	0.0129442i
$856$	−7.05081	+	1.49870i	−0.240992	+	0.0512244i
$857$	27.5830	−	12.2807i	0.942216	−	0.419502i	0.122627	−	0.992453i	$-0.460868\pi$
$857$	27.5830	−	12.2807i	0.942216	−	0.419502i	0.819589	+	0.572951i	$0.194202\pi$
$858$	−2.62849	−	2.91924i	−0.0897353	−	0.0996611i
$859$	−0.0553088	−	0.526228i	−0.00188711	−	0.0179547i	0.993538	−	0.113502i	$-0.0362067\pi$
$859$	−0.0553088	−	0.526228i	−0.00188711	−	0.0179547i	−0.995425	+	0.0955469i	$0.969540\pi$
$860$	0.532276	−	0.386721i	0.0181505	−	0.0131871i
$861$	−2.22822	+	21.2001i	−0.0759375	+	0.722497i
$862$	−17.5081	−	30.3249i	−0.596327	−	1.03287i
$863$	−10.6113	+	18.3793i	−0.361213	+	0.625640i	−0.988161	−	0.153422i	$-0.950971\pi$
$863$	−10.6113	+	18.3793i	−0.361213	+	0.625640i	0.626947	+	0.779062i	$0.284304\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	8.24233	−	9.15404i	0.280248	−	0.311247i
$866$	9.91354	−	30.5107i	0.336876	−	1.03680i
$867$	9.59631			0.325908
$868$	−7.94366	−	11.2312i	−0.269626	−	0.381211i
$869$	−24.2095			−0.821252
$870$	1.38611	−	4.26599i	0.0469934	−	0.144631i
$871$	3.73690	−	4.15024i	0.126620	−	0.140626i
$872$	−2.28378	−	1.65926i	−0.0773385	−	0.0561897i
$873$	4.03964	−	6.99686i	0.136721	−	0.236808i
$874$	−2.10360	−	3.64355i	−0.0711555	−	0.123245i
$875$	−0.258263	+	2.45720i	−0.00873087	+	0.0830687i
$876$	5.87810	−	4.27069i	0.198603	−	0.144293i
$877$	2.31260	+	22.0029i	0.0780910	+	0.742986i	0.961578	+	0.274531i	$0.0885226\pi$
$877$	2.31260	+	22.0029i	0.0780910	+	0.742986i	−0.883487	+	0.468455i	$0.844811\pi$
$878$	−8.57183	−	9.51998i	−0.289285	−	0.321284i
$879$	2.50147	−	1.11373i	0.0843725	−	0.0375651i
$880$	−2.81758	+	0.598896i	−0.0949807	+	0.0201888i
$881$	−37.3817	−	7.94572i	−1.25942	−	0.267698i	−0.470614	−	0.882339i	$-0.655968\pi$
$881$	−37.3817	−	7.94572i	−1.25942	−	0.267698i	−0.788807	+	0.614641i	$0.789301\pi$
$882$	−0.818033	−	0.364212i	−0.0275446	−	0.0122636i
$883$	0.352727	+	1.08558i	0.0118702	+	0.0365327i	0.956816	−	0.290694i	$-0.0938860\pi$
$883$	0.352727	+	1.08558i	0.0118702	+	0.0365327i	−0.944946	+	0.327226i	$0.893886\pi$
$884$	−2.17329	−	6.68868i	−0.0730955	−	0.224965i
$885$	−4.86266	−	2.16500i	−0.163457	−	0.0727756i
$886$	−9.17654	−	1.95053i	−0.308292	−	0.0655295i
$887$	−20.6207	+	4.38307i	−0.692377	+	0.147169i	−0.540643	−	0.841252i	$-0.681819\pi$
$887$	−20.6207	+	4.38307i	−0.692377	+	0.147169i	−0.151734	+	0.988421i	$0.548486\pi$
$888$	0.295372	−	0.131508i	0.00991205	−	0.00441313i
$889$	5.56273	+	6.17803i	0.186568	+	0.207205i
$890$	−0.405224	−	3.85545i	−0.0135832	−	0.129235i
$891$	−2.33040	+	1.69313i	−0.0780712	+	0.0567221i
$892$	−0.557509	+	5.30434i	−0.0186668	+	0.177603i
$893$	9.85841	+	17.0753i	0.329899	+	0.571402i
$894$	2.94998	−	5.10951i	0.0986620	−	0.170888i
$895$	1.45149	+	1.05457i	0.0485180	+	0.0352504i
$896$	1.65325	−	1.83612i	0.0552311	−	0.0613404i
$897$	0.973918	−	2.99741i	0.0325182	−	0.100081i
$898$	−25.6337			−0.855409
$899$	−21.4679	−	12.7613i	−0.715994	−	0.425612i
$900$	1.00000			0.0333333
$901$	13.7108	−	42.1975i	0.456773	−	1.40580i
$902$	16.6295	−	18.4689i	0.553702	−	0.614948i
$903$	1.31511	+	0.955487i	0.0437643	+	0.0317966i
$904$	−7.79102	+	13.4944i	−0.259126	+	0.448819i
$905$	2.23973	+	3.87933i	0.0744513	+	0.128953i
$906$	−1.77866	+	16.9228i	−0.0590919	+	0.562222i
$907$	22.4654	−	16.3220i	0.745950	−	0.541965i	−0.148619	−	0.988895i	$-0.547483\pi$
$907$	22.4654	−	16.3220i	0.745950	−	0.541965i	0.894569	+	0.446930i	$0.147483\pi$
$908$	0.416545	+	3.96316i	0.0138235	+	0.131522i
$909$	9.52816	+	10.5821i	0.316029	+	0.350986i
$910$	−3.07809	+	1.37045i	−0.102038	+	0.0454300i
$911$	−28.2979	+	6.01490i	−0.937551	+	0.199283i	−0.651255	−	0.758859i	$-0.725757\pi$
$911$	−28.2979	+	6.01490i	−0.937551	+	0.199283i	−0.286296	+	0.958141i	$0.592424\pi$
$912$	1.78066	+	0.378492i	0.0589637	+	0.0125331i
$913$	7.32603	+	3.26176i	0.242456	+	0.107948i
$914$	8.56065	+	26.3470i	0.283161	+	0.871480i
$915$	−1.98946	−	6.12294i	−0.0657696	−	0.202418i
$916$	−2.60230	−	1.15862i	−0.0859825	−	0.0382819i
$917$	−23.9885	−	5.09890i	−0.792169	−	0.168381i
$918$	−5.04447	+	1.07223i	−0.166492	+	0.0353890i
$919$	−15.3284	+	6.82463i	−0.505636	+	0.225124i	−0.643669	−	0.765304i	$-0.722589\pi$
$919$	−15.3284	+	6.82463i	−0.505636	+	0.225124i	0.138033	+	0.990428i	$0.455922\pi$
$920$	−1.54642	−	1.71747i	−0.0509839	−	0.0566234i
$921$	−0.185845	−	1.76820i	−0.00612380	−	0.0582641i
$922$	22.2156	−	16.1406i	0.731633	−	0.531562i
$923$	−0.117251	+	1.11557i	−0.00385938	+	0.0367195i
$924$	−3.55852	−	6.16353i	−0.117067	−	0.202765i
$925$	−0.161663	+	0.280008i	−0.00531544	+	0.00920661i
$926$	16.5150	+	11.9988i	0.542715	+	0.394306i
$927$	−8.21733	+	9.12627i	−0.269893	+	0.299746i
$928$	1.38611	−	4.26599i	0.0455012	−	0.140038i
$929$	40.9615			1.34390			0.671952	−	0.740595i	$-0.265456\pi$
$929$	40.9615			1.34390			0.671952	+	0.740595i	$0.265456\pi$
$930$	1.22678	−	5.43093i	0.0402276	−	0.178087i
$931$	1.63011			0.0534249
$932$	6.52899	−	20.0942i	0.213864	−	0.658206i
$933$	13.4850	−	14.9766i	0.441479	−	0.490312i
$934$	−15.6291	−	11.3552i	−0.511400	−	0.371554i
$935$	−7.42768	+	12.8651i	−0.242911	+	0.420734i
$936$	0.681858	+	1.18101i	0.0222872	+	0.0386026i
$937$	−2.70141	+	25.7022i	−0.0882511	+	0.839654i	0.857439	+	0.514585i	$0.172054\pi$
$937$	−2.70141	+	25.7022i	−0.0882511	+	0.839654i	−0.945690	+	0.325068i	$0.894613\pi$
$938$	8.18580	−	5.94733i	0.267276	−	0.194187i
$939$	−1.02529	−	9.75498i	−0.0334591	−	0.318342i
$940$	7.24720	+	8.04883i	0.236378	+	0.262524i
$941$	6.72083	−	2.99231i	0.219093	−	0.0975464i	−0.294255	−	0.955727i	$-0.595072\pi$
$941$	6.72083	−	2.99231i	0.219093	−	0.0975464i	0.513348	+	0.858180i	$0.328405\pi$
$942$	8.83811	−	1.87860i	0.287961	−	0.0612081i
$943$	19.5037	+	4.14564i	0.635128	+	0.135001i
$944$	−4.86266	−	2.16500i	−0.158266	−	0.0704646i
$945$	0.763500	+	2.34981i	0.0248367	+	0.0764394i
$946$	−0.585644	−	1.80243i	−0.0190409	−	0.0586020i
$947$	−25.5247	−	11.3643i	−0.829441	−	0.369291i	−0.0523111	−	0.998631i	$-0.516659\pi$
$947$	−25.5247	−	11.3643i	−0.829441	−	0.369291i	−0.777130	+	0.629340i	$0.783325\pi$
$948$	8.22089	+	1.74740i	0.267002	+	0.0567530i
$949$	−9.69186	+	2.06007i	−0.314611	+	0.0668727i
$950$	−1.66306	+	0.740442i	−0.0539568	+	0.0240231i
$951$	−9.25327	−	10.2768i	−0.300058	−	0.333248i
$952$	−1.33190	−	12.6722i	−0.0431672	−	0.410708i
$953$	−34.8356	+	25.3096i	−1.12844	+	0.819857i	−0.985467	−	0.169870i	$-0.945665\pi$
$953$	−34.8356	+	25.3096i	−1.12844	+	0.819857i	−0.142970	+	0.989727i	$0.545665\pi$
$954$	−0.899300	+	8.55627i	−0.0291159	+	0.277019i
$955$	−6.44038	−	11.1551i	−0.208406	−	0.360970i
$956$	−3.34082	+	5.78647i	−0.108050	+	0.187148i
$957$	−10.4531	−	7.59460i	−0.337900	−	0.245499i
$958$	−17.3800	+	19.3024i	−0.561521	+	0.623632i
$959$	−15.9374	+	49.0504i	−0.514647	+	1.58392i
$960$	1.00000			0.0322749
$961$	−27.9900	−	13.3251i	−0.902905	−	0.429841i
$962$	−0.440924			−0.0142160
$963$	2.22750	−	6.85553i	0.0717801	−	0.220916i
$964$	3.03463	−	3.37029i	0.0977387	−	0.108550i
$965$	−2.02117	−	1.46847i	−0.0650637	−	0.0472716i
$966$	2.85505	−	4.94509i	0.0918596	−	0.159106i
$967$	−14.6509	−	25.3761i	−0.471140	−	0.816039i	0.528315	−	0.849049i	$-0.322824\pi$
$967$	−14.6509	−	25.3761i	−0.471140	−	0.816039i	−0.999455	+	0.0330098i	$0.989491\pi$
$968$	0.282494	−	2.68775i	0.00907970	−	0.0863875i
$969$	7.59532	−	5.51832i	0.243997	−	0.177274i
$970$	0.844514	+	8.03502i	0.0271157	+	0.257989i
$971$	−6.96290	−	7.73309i	−0.223450	−	0.248167i	0.620987	−	0.783821i	$-0.286732\pi$
$971$	−6.96290	−	7.73309i	−0.223450	−	0.248167i	−0.844438	+	0.535654i	$0.820065\pi$
$972$	0.913545	−	0.406737i	0.0293020	−	0.0130461i
$973$	49.2710	−	10.4729i	1.57956	−	0.335745i
$974$	6.28282	+	1.33546i	0.201315	+	0.0427907i
$975$	−1.24582	−	0.554673i	−0.0398980	−	0.0177638i
$976$	−1.98946	−	6.12294i	−0.0636811	−	0.195990i
$977$	−15.0738	−	46.3923i	−0.482252	−	1.48422i	−0.835921	−	0.548850i	$-0.815066\pi$
$977$	−15.0738	−	46.3923i	−0.482252	−	1.48422i	0.353669	−	0.935371i	$-0.384934\pi$
$978$	4.46623	+	1.98849i	0.142814	+	0.0635850i
$979$	−10.9229	−	2.32173i	−0.349097	−	0.0742029i
$980$	0.875880	−	0.186174i	0.0279790	−	0.00594711i
$981$	2.57885	−	1.14818i	0.0823365	−	0.0366586i
$982$	−14.8687	−	16.5133i	−0.474478	−	0.526961i
$983$	0.660879	+	6.28784i	0.0210788	+	0.200551i	0.999993	−	0.00372022i	$-0.00118419\pi$
$983$	0.660879	+	6.28784i	0.0210788	+	0.200551i	−0.978914	+	0.204271i	$0.934518\pi$
$984$	−6.97998	+	5.07125i	−0.222514	+	0.161666i
$985$	2.16292	−	20.5788i	0.0689164	−	0.655696i
$986$	−11.5663	−	20.0334i	−0.368346	−	0.637994i
$987$	−13.3800	+	23.1748i	−0.425890	+	0.737664i
$988$	−2.00844	−	1.45922i	−0.0638970	−	0.0464239i
$989$	1.01743	−	1.12998i	0.0323525	−	0.0359311i
$990$	0.890132	−	2.73955i	0.0282903	−	0.0870685i
$991$	−43.2890			−1.37512			−0.687560	−	0.726128i	$-0.741318\pi$
$991$	−43.2890			−1.37512			−0.687560	+	0.726128i	$0.741318\pi$
$992$	1.22678	−	5.43093i	0.0389502	−	0.172432i
$993$	−7.35701			−0.233468
$994$	−0.628014	+	1.93283i	−0.0199194	+	0.0613056i
$995$	−2.47917	+	2.75340i	−0.0785951	+	0.0872887i
$996$	−2.25229	−	1.63638i	−0.0713665	−	0.0518508i
$997$	5.42603	−	9.39816i	0.171844	−	0.297643i	−0.767220	−	0.641383i	$-0.778361\pi$
$997$	5.42603	−	9.39816i	0.171844	−	0.297643i	0.939065	+	0.343741i	$0.111694\pi$
$998$	−3.63221	−	6.29117i	−0.114976	−	0.199144i
$999$	−0.0337967	+	0.321554i	−0.00106928	+	0.0101735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.g.541.2	yes	24
31.20	even	15	inner	930.2.bg.g.361.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.g.361.2	✓	24	31.20	even	15	inner
930.2.bg.g.541.2	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.258263 + 2.45720i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.258263 + 2.45720i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(2.63149 - 1.17162i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(1.33391 + 0.283532i) q^{13} +(2.25713 + 1.00494i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.71130 + 2.09761i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(1.78066 - 0.378492i) q^{19} +(0.913545 - 0.406737i) q^{20} +(1.65325 + 1.83612i) q^{21} +(-0.301097 - 2.86475i) q^{22} +(1.86971 - 1.35842i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.681858 - 1.18101i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.65325 - 1.83612i) q^{28} +(1.38611 - 4.26599i) q^{29} +1.00000 q^{30} +(1.22678 - 5.43093i) q^{31} +1.00000 q^{32} +(0.890132 - 2.73955i) q^{33} +(3.45081 - 3.83252i) q^{34} +(-1.99887 - 1.45226i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.161663 - 0.280008i) q^{37} +(0.190288 - 1.81047i) q^{38} +(1.10327 - 0.801572i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(5.77308 + 6.41165i) q^{41} +(2.25713 - 1.00494i) q^{42} +(0.643552 - 0.136791i) q^{43} +(-2.81758 - 0.598896i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-0.714165 - 2.19797i) q^{46} +(3.34689 + 10.3007i) q^{47} +(0.913545 + 0.406737i) q^{48} +(0.875880 + 0.186174i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(4.71130 - 2.09761i) q^{51} +(-0.912504 - 1.01344i) q^{52} +(-0.899300 - 8.55627i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.301097 + 2.86475i) q^{55} +(-1.23537 - 2.13972i) q^{56} +(0.910223 - 1.57655i) q^{57} +(-3.62887 - 2.63653i) q^{58} +(-3.56168 + 3.95565i) q^{59} +(0.309017 - 0.951057i) q^{60} -6.43804 q^{61} +(-4.78603 - 2.84498i) q^{62} +2.47074 q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.912504 + 1.01344i) q^{65} +(-2.33040 - 1.69313i) q^{66} +(2.04761 - 3.54656i) q^{67} +(-2.57858 - 4.46623i) q^{68} +(0.241574 - 2.29843i) q^{69} +(-1.99887 + 1.45226i) q^{70} +(0.0859794 + 0.818040i) q^{71} +(0.669131 + 0.743145i) q^{72} +(-6.63757 + 2.95524i) q^{73} +(-0.316260 + 0.0672231i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(-1.66306 - 0.740442i) q^{76} +(2.19928 + 6.76870i) q^{77} +(-0.421411 - 1.29697i) q^{78} +(-7.67793 - 3.41844i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(7.88182 - 3.50921i) q^{82} +(1.86285 + 2.06890i) q^{83} +(-0.258263 - 2.45720i) q^{84} +(-4.17223 + 3.03130i) q^{85} +(0.0687723 - 0.654325i) q^{86} +(-2.24277 - 3.88459i) q^{87} +(-1.44026 + 2.49461i) q^{88} +(-3.13631 - 2.27866i) q^{89} +(0.669131 - 0.743145i) q^{90} +(-1.04120 + 3.20448i) q^{91} -2.31109 q^{92} +(-3.21510 - 4.54567i) q^{93} +10.8308 q^{94} +(-0.562549 + 1.73135i) q^{95} +(0.669131 - 0.743145i) q^{96} +(6.53627 + 4.74888i) q^{97} +(0.447724 - 0.775481i) q^{98} +(-1.44026 - 2.49461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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