LMFDB - Embedded newform 930.2.bg.b.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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 195x^{12} + 892x^{10} + 2229x^{8} + 2923x^{6} + 1685x^{4} + 213x^{2} + 1 $ x^16 + 22x^14 + 195x^12 + 892x^10 + 2229x^8 + 2923x^6 + 1685x^4 + 213*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.2
Root			$1.75349i$ of defining polynomial
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.422760 - 4.02229i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(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} +(0.422760 - 4.02229i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-1.16610 + 0.519183i) q^{11} +(0.978148 - 0.207912i) q^{12} +(5.28065 + 1.12244i) q^{13} +(-3.69479 - 1.64503i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.00899 - 2.67537i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(0.874218 - 0.185821i) q^{19} +(0.913545 - 0.406737i) q^{20} +(2.70627 + 3.00561i) q^{21} +(0.133426 + 1.26947i) q^{22} +(-4.90799 + 3.56587i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.69931 - 4.67534i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.70627 + 3.00561i) q^{28} +(2.19469 - 6.75456i) q^{29} -1.00000 q^{30} +(-5.05208 - 2.34019i) q^{31} +1.00000 q^{32} +(0.394448 - 1.21399i) q^{33} +(-4.40131 + 4.88815i) q^{34} +(3.27203 + 2.37727i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.57842 - 9.66211i) q^{37} +(0.0934222 - 0.888852i) q^{38} +(-4.36758 + 3.17323i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(0.459053 + 0.509830i) q^{41} +(3.69479 - 1.64503i) q^{42} +(-3.38889 + 0.720332i) q^{43} +(1.24857 + 0.265391i) q^{44} +(0.913545 + 0.406737i) q^{45} +(1.87469 + 5.76969i) q^{46} +(-2.77834 - 8.55086i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(-9.15309 - 1.94555i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(6.00899 - 2.67537i) q^{51} +(-3.61238 - 4.01196i) q^{52} +(-1.23880 - 11.7864i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.133426 - 1.26947i) q^{55} +(2.02222 + 3.50260i) q^{56} +(-0.446874 + 0.774009i) q^{57} +(-5.74577 - 4.17455i) q^{58} +(-5.64617 + 6.27070i) q^{59} +(-0.309017 + 0.951057i) q^{60} +5.01299 q^{61} +(-3.78684 + 4.08165i) q^{62} -4.04445 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.61238 + 4.01196i) q^{65} +(-1.03268 - 0.750284i) q^{66} +(1.65998 - 2.87518i) q^{67} +(3.28883 + 5.69642i) q^{68} +(0.634134 - 6.03338i) q^{69} +(3.27203 - 2.37727i) q^{70} +(0.153125 + 1.45689i) q^{71} +(0.669131 + 0.743145i) q^{72} +(9.14518 - 4.07170i) q^{73} +(-10.9130 + 2.31964i) q^{74} +(0.978148 + 0.207912i) q^{75} +(-0.816480 - 0.363520i) q^{76} +(1.59532 + 4.90990i) q^{77} +(1.66827 + 5.13439i) q^{78} +(-3.66811 - 1.63315i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.626733 - 0.279039i) q^{82} +(5.39883 + 5.99601i) q^{83} +(-0.422760 - 4.02229i) q^{84} +(5.32144 - 3.86625i) q^{85} +(-0.362150 + 3.44562i) q^{86} +(3.55108 + 6.15065i) q^{87} +(0.638230 - 1.10545i) q^{88} +(-2.91413 - 2.11724i) q^{89} +(0.669131 - 0.743145i) q^{90} +(6.74722 - 20.7658i) q^{91} +6.06661 q^{92} +(5.11960 - 2.18853i) q^{93} -8.99091 q^{94} +(-0.276183 + 0.850005i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(11.4329 + 8.30648i) q^{97} +(-4.67879 + 8.10390i) q^{98} +(0.638230 + 1.10545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * 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
$7$	0.422760	−	4.02229i	0.159788	−	1.52028i	−0.561400	−	0.827545i	$-0.689737\pi$
$7$	0.422760	−	4.02229i	0.159788	−	1.52028i	0.721188	−	0.692739i	$-0.243596\pi$
$8$	−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
$11$	−1.16610	+	0.519183i	−0.351594	+	0.156540i	−0.574932	−	0.818202i	$-0.694971\pi$
$11$	−1.16610	+	0.519183i	−0.351594	+	0.156540i	0.223338	+	0.974741i	$0.428305\pi$
$12$	0.978148	−	0.207912i	0.282367	−	0.0600189i
$13$	5.28065	+	1.12244i	1.46459	+	0.311308i	0.870131	−	0.492820i	$-0.164034\pi$
$13$	5.28065	+	1.12244i	1.46459	+	0.311308i	0.594457	+	0.804128i	$0.297367\pi$
$14$	−3.69479	−	1.64503i	−0.987474	−	0.439652i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−6.00899	−	2.67537i	−1.45739	−	0.648873i	−0.483390	−	0.875405i	$-0.660595\pi$
$17$	−6.00899	−	2.67537i	−1.45739	−	0.648873i	−0.974004	+	0.226532i	$0.927261\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	0.874218	−	0.185821i	0.200559	−	0.0426302i	−0.106537	−	0.994309i	$-0.533976\pi$
$19$	0.874218	−	0.185821i	0.200559	−	0.0426302i	0.307096	+	0.951679i	$0.400643\pi$
$20$	0.913545	−	0.406737i	0.204275	−	0.0909491i
$21$	2.70627	+	3.00561i	0.590555	+	0.655878i
$22$	0.133426	+	1.26947i	0.0284466	+	0.270651i
$23$	−4.90799	+	3.56587i	−1.02339	+	0.743534i	−0.966975	−	0.254873i	$-0.917966\pi$
$23$	−4.90799	+	3.56587i	−1.02339	+	0.743534i	−0.0564128	+	0.998408i	$0.517966\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.69931	−	4.67534i	0.529378	−	0.916910i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−2.70627	+	3.00561i	−0.511436	+	0.568007i
$29$	2.19469	−	6.75456i	0.407543	−	1.25429i	−0.511209	−	0.859456i	$-0.670802\pi$
$29$	2.19469	−	6.75456i	0.407543	−	1.25429i	0.918753	−	0.394833i	$-0.129198\pi$
$30$	−1.00000			−0.182574
$31$	−5.05208	−	2.34019i	−0.907380	−	0.420311i
$31$	−5.05208	−	2.34019i	−0.907380	−	0.420311i
$32$	1.00000			0.176777
$33$	0.394448	−	1.21399i	0.0686645	−	0.211328i
$34$	−4.40131	+	4.88815i	−0.754819	+	0.838311i
$35$	3.27203	+	2.37727i	0.553074	+	0.401832i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−5.57842	−	9.66211i	−0.917087	−	1.58844i	−0.803816	−	0.594878i	$-0.797200\pi$
$37$	−5.57842	−	9.66211i	−0.917087	−	1.58844i	−0.113271	−	0.993564i	$-0.536133\pi$
$38$	0.0934222	−	0.888852i	0.0151551	−	0.144191i
$39$	−4.36758	+	3.17323i	−0.699372	+	0.508123i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	0.459053	+	0.509830i	0.0716921	+	0.0796221i	0.777924	−	0.628359i	$-0.216273\pi$
$41$	0.459053	+	0.509830i	0.0716921	+	0.0796221i	−0.706232	+	0.707981i	$0.749606\pi$
$42$	3.69479	−	1.64503i	0.570118	−	0.253833i
$43$	−3.38889	+	0.720332i	−0.516802	+	0.109850i	−0.458926	−	0.888474i	$-0.651766\pi$
$43$	−3.38889	+	0.720332i	−0.516802	+	0.109850i	−0.0578751	+	0.998324i	$0.518433\pi$
$44$	1.24857	+	0.265391i	0.188228	+	0.0400092i
$45$	0.913545	+	0.406737i	0.136183	+	0.0606327i
$46$	1.87469	+	5.76969i	0.276407	+	0.850695i
$47$	−2.77834	−	8.55086i	−0.405263	−	1.24727i	−0.920675	−	0.390329i	$-0.872361\pi$
$47$	−2.77834	−	8.55086i	−0.405263	−	1.24727i	0.515412	−	0.856942i	$-0.327639\pi$
$48$	−0.913545	−	0.406737i	−0.131859	−	0.0587074i
$49$	−9.15309	−	1.94555i	−1.30758	−	0.277936i
$50$	−0.978148	+	0.207912i	−0.138331	+	0.0294032i
$51$	6.00899	−	2.67537i	0.841427	−	0.374627i
$52$	−3.61238	−	4.01196i	−0.500947	−	0.556358i
$53$	−1.23880	−	11.7864i	−0.170162	−	1.61898i	−0.662835	−	0.748766i	$-0.730647\pi$
$53$	−1.23880	−	11.7864i	−0.170162	−	1.61898i	0.492673	−	0.870214i	$-0.336020\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	0.133426	−	1.26947i	0.0179912	−	0.171175i
$56$	2.02222	+	3.50260i	0.270231	+	0.468054i
$57$	−0.446874	+	0.774009i	−0.0591899	+	0.102520i
$58$	−5.74577	−	4.17455i	−0.754456	−	0.548145i
$59$	−5.64617	+	6.27070i	−0.735068	+	0.816376i	−0.988539	−	0.150967i	$-0.951761\pi$
$59$	−5.64617	+	6.27070i	−0.735068	+	0.816376i	0.253470	+	0.967343i	$0.418428\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	5.01299			0.641848			0.320924	−	0.947105i	$-0.396007\pi$
$61$	5.01299			0.641848			0.320924	+	0.947105i	$0.396007\pi$
$62$	−3.78684	+	4.08165i	−0.480929	+	0.518370i
$63$	−4.04445			−0.509553
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−3.61238	+	4.01196i	−0.448061	+	0.497622i
$66$	−1.03268	−	0.750284i	−0.127114	−	0.0923536i
$67$	1.65998	−	2.87518i	0.202799	−	0.351259i	−0.746630	−	0.665239i	$-0.768329\pi$
$67$	1.65998	−	2.87518i	0.202799	−	0.351259i	0.949429	+	0.313981i	$0.101663\pi$
$68$	3.28883	+	5.69642i	0.398829	+	0.690792i
$69$	0.634134	−	6.03338i	0.0763407	−	0.726334i
$70$	3.27203	−	2.37727i	0.391082	−	0.284138i
$71$	0.153125	+	1.45689i	0.0181726	+	0.172901i	0.999844	−	0.0176822i	$-0.00562872\pi$
$71$	0.153125	+	1.45689i	0.0181726	+	0.172901i	−0.981671	+	0.190583i	$0.938962\pi$
$72$	0.669131	+	0.743145i	0.0788578	+	0.0875805i
$73$	9.14518	−	4.07170i	1.07036	−	0.476556i	0.205547	−	0.978647i	$-0.434103\pi$
$73$	9.14518	−	4.07170i	1.07036	−	0.476556i	0.864815	+	0.502091i	$0.167436\pi$
$74$	−10.9130	+	2.31964i	−1.26862	+	0.269653i
$75$	0.978148	+	0.207912i	0.112947	+	0.0240076i
$76$	−0.816480	−	0.363520i	−0.0936567	−	0.0416986i
$77$	1.59532	+	4.90990i	0.181804	+	0.559535i
$78$	1.66827	+	5.13439i	0.188894	+	0.581356i
$79$	−3.66811	−	1.63315i	−0.412695	−	0.183744i	0.189878	−	0.981808i	$-0.439191\pi$
$79$	−3.66811	−	1.63315i	−0.412695	−	0.183744i	−0.602572	+	0.798064i	$0.705858\pi$
$80$	−0.978148	−	0.207912i	−0.109360	−	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.626733	−	0.279039i	0.0692110	−	0.0308147i
$83$	5.39883	+	5.99601i	0.592599	+	0.658148i	0.962614	−	0.270878i	$-0.0873140\pi$
$83$	5.39883	+	5.99601i	0.592599	+	0.658148i	−0.370015	+	0.929026i	$0.620647\pi$
$84$	−0.422760	−	4.02229i	−0.0461269	−	0.438868i
$85$	5.32144	−	3.86625i	0.577191	−	0.419354i
$86$	−0.362150	+	3.44562i	−0.0390516	+	0.371551i
$87$	3.55108	+	6.15065i	0.380716	+	0.659419i
$88$	0.638230	−	1.10545i	0.0680355	−	0.117841i
$89$	−2.91413	−	2.11724i	−0.308897	−	0.224427i	0.422526	−	0.906351i	$-0.361143\pi$
$89$	−2.91413	−	2.11724i	−0.308897	−	0.224427i	−0.731423	+	0.681924i	$0.761143\pi$
$90$	0.669131	−	0.743145i	0.0705326	−	0.0783343i
$91$	6.74722	−	20.7658i	0.707300	−	2.17685i
$92$	6.06661			0.632488
$93$	5.11960	−	2.18853i	0.530878	−	0.226940i
$94$	−8.99091			−0.927341
$95$	−0.276183	+	0.850005i	−0.0283358	+	0.0872087i
$96$	−0.669131	+	0.743145i	−0.0682929	+	0.0758469i
$97$	11.4329	+	8.30648i	1.16083	+	0.843396i	0.989883	−	0.141884i	$-0.0453160\pi$
$97$	11.4329	+	8.30648i	1.16083	+	0.843396i	0.170951	+	0.985280i	$0.445316\pi$
$98$	−4.67879	+	8.10390i	−0.472629	+	0.818617i
$99$	0.638230	+	1.10545i	0.0641445	+	0.111102i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−9.93987	+	7.22174i	−0.989054	+	0.718590i	−0.959714	−	0.280980i	$-0.909341\pi$
$101$	−9.93987	+	7.22174i	−0.989054	+	0.718590i	−0.0293403	+	0.999569i	$0.509341\pi$
$102$	−0.687552	−	6.54162i	−0.0680778	−	0.647717i
$103$	−2.41104	−	2.67773i	−0.237566	−	0.263844i	0.612559	−	0.790425i	$-0.290140\pi$
$103$	−2.41104	−	2.67773i	−0.237566	−	0.263844i	−0.850125	+	0.526581i	$0.823474\pi$
$104$	−4.93188	+	2.19582i	−0.483611	+	0.215318i
$105$	−3.95607	+	0.840888i	−0.386073	+	0.0820623i
$106$	−11.5923	−	2.46402i	−1.12594	−	0.239327i
$107$	−1.24546	−	0.554514i	−0.120403	−	0.0536069i	0.345651	−	0.938363i	$-0.387658\pi$
$107$	−1.24546	−	0.554514i	−0.120403	−	0.0536069i	−0.466054	+	0.884756i	$0.654325\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	4.49866	+	13.8455i	0.430894	+	1.32615i	0.897237	+	0.441550i	$0.145571\pi$
$109$	4.49866	+	13.8455i	0.430894	+	1.32615i	−0.466343	+	0.884604i	$0.654429\pi$
$110$	−1.16610	−	0.519183i	−0.111184	−	0.0495021i
$111$	10.9130	+	2.31964i	1.03582	+	0.220170i
$112$	3.95607	−	0.840888i	0.373813	−	0.0794565i
$113$	2.19507	−	0.977307i	0.206494	−	0.0919373i	−0.300883	−	0.953661i	$-0.597282\pi$
$113$	2.19507	−	0.977307i	0.206494	−	0.0919373i	0.507378	+	0.861724i	$0.330615\pi$
$114$	0.598034	+	0.664185i	0.0560111	+	0.0622066i
$115$	−0.634134	−	6.03338i	−0.0591333	−	0.562616i
$116$	−5.74577	+	4.17455i	−0.533481	+	0.387597i
$117$	0.564309	−	5.36905i	0.0521704	−	0.496368i
$118$	4.21903	+	7.30758i	0.388393	+	0.672717i
$119$	−13.3015	+	23.0389i	−1.21935	+	2.11197i
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	−6.27019	+	6.96375i	−0.570017	+	0.633068i
$122$	1.54910	−	4.76764i	0.140249	−	0.431642i
$123$	−0.686044			−0.0618585
$124$	2.71168	+	4.86279i	0.243516	+	0.436692i
$125$	1.00000			0.0894427
$126$	−1.24980	+	3.84650i	−0.111341	+	0.342674i
$127$	0.199485	−	0.221550i	0.0177014	−	0.0196594i	−0.734229	−	0.678902i	$-0.762456\pi$
$127$	0.199485	−	0.221550i	0.0177014	−	0.0196594i	0.751931	+	0.659242i	$0.229123\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	1.73230	−	3.00044i	0.152521	−	0.264174i
$130$	2.69931	+	4.67534i	0.236745	+	0.410055i
$131$	−1.44855	+	13.7821i	−0.126561	+	1.20414i	0.728289	+	0.685270i	$0.240316\pi$
$131$	−1.44855	+	13.7821i	−0.126561	+	1.20414i	−0.854850	+	0.518875i	$0.826351\pi$
$132$	−1.03268	+	0.750284i	−0.0898830	+	0.0653039i
$133$	−0.377841	−	3.59492i	−0.0327630	−	0.311719i
$134$	−2.22149	−	2.46722i	−0.191908	−	0.213135i
$135$	−0.913545	+	0.406737i	−0.0786255	+	0.0350063i
$136$	6.43392	−	1.36757i	0.551704	−	0.117268i
$137$	22.2776	+	4.73526i	1.90331	+	0.404560i	0.999716	−	0.0238352i	$-0.00758768\pi$
$137$	22.2776	+	4.73526i	1.90331	+	0.404560i	0.903591	+	0.428396i	$0.140921\pi$
$138$	−5.54213	−	2.46751i	−0.471777	−	0.210049i
$139$	−0.212800	−	0.654930i	−0.0180494	−	0.0555504i	0.941626	−	0.336660i	$-0.109297\pi$
$139$	−0.212800	−	0.654930i	−0.0180494	−	0.0555504i	−0.959676	+	0.281110i	$0.909297\pi$
$140$	−1.24980	−	3.84650i	−0.105628	−	0.325089i
$141$	8.21360	+	3.65693i	0.691710	+	0.307969i
$142$	1.43290	+	0.304573i	0.120247	+	0.0255592i
$143$	−6.74053	+	1.43274i	−0.563672	+	0.119812i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	4.75227	+	5.27793i	0.394655	+	0.438309i
$146$	−1.04640	−	9.95580i	−0.0866004	−	0.823948i
$147$	7.57044	−	5.50024i	0.624399	−	0.453653i
$148$	−1.16621	+	11.0957i	−0.0958617	+	0.912063i
$149$	0.143138	+	0.247923i	0.0117264	+	0.0203106i	0.871829	−	0.489810i	$-0.162934\pi$
$149$	0.143138	+	0.247923i	0.0117264	+	0.0203106i	−0.860103	+	0.510121i	$0.829601\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−13.6245	−	9.89880i	−1.10875	−	0.805553i	−0.126283	−	0.991994i	$-0.540305\pi$
$151$	−13.6245	−	9.89880i	−1.10875	−	0.805553i	−0.982466	+	0.186441i	$0.940305\pi$
$152$	−0.598034	+	0.664185i	−0.0485070	+	0.0538725i
$153$	−2.03261	+	6.25572i	−0.164327	+	0.505745i
$154$	5.16258			0.416012
$155$	4.55271	−	3.20513i	0.365682	−	0.257442i
$156$	5.39862			0.432236
$157$	0.306175	−	0.942311i	0.0244354	−	0.0752046i	−0.938095	−	0.346378i	$-0.887412\pi$
$157$	0.306175	−	0.942311i	0.0244354	−	0.0752046i	0.962531	+	0.271173i	$0.0874116\pi$
$158$	−2.68672	+	2.98391i	−0.213744	+	0.237387i
$159$	9.58788	+	6.96600i	0.760369	+	0.552440i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	12.2681	+	21.2489i	0.966858	+	1.67465i
$162$	−0.104528	+	0.994522i	−0.00821253	+	0.0781370i
$163$	5.68451	−	4.13004i	0.445245	−	0.323489i	−0.342471	−	0.939529i	$-0.611264\pi$
$163$	5.68451	−	4.13004i	0.445245	−	0.323489i	0.787716	+	0.616039i	$0.211264\pi$
$164$	−0.0717112	−	0.682286i	−0.00559970	−	0.0532776i
$165$	0.854118	+	0.948594i	0.0664930	+	0.0738480i
$166$	7.37088	−	3.28173i	0.572091	−	0.254711i
$167$	12.3724	−	2.62984i	0.957409	−	0.203503i	0.297393	−	0.954755i	$-0.403883\pi$
$167$	12.3724	−	2.62984i	0.957409	−	0.203503i	0.660016	+	0.751252i	$0.270550\pi$
$168$	−3.95607	−	0.840888i	−0.305217	−	0.0648760i
$169$	14.7493	+	6.56680i	1.13456	+	0.505139i
$170$	−2.03261	−	6.25572i	−0.155894	−	0.479792i
$171$	−0.276183	−	0.850005i	−0.0211203	−	0.0650015i
$172$	3.16507	+	1.40918i	0.241335	+	0.107449i
$173$	6.26678	+	1.33204i	0.476454	+	0.101273i	0.439878	−	0.898057i	$-0.355022\pi$
$173$	6.26678	+	1.33204i	0.476454	+	0.101273i	0.0365759	+	0.999331i	$0.488355\pi$
$174$	6.94696	−	1.47662i	0.526648	−	0.111942i
$175$	−3.69479	+	1.64503i	−0.279300	+	0.124352i
$176$	−0.854118	−	0.948594i	−0.0643816	−	0.0715030i
$177$	−0.882018	−	8.39184i	−0.0662965	−	0.630769i
$178$	−2.91413	+	2.11724i	−0.218423	+	0.158694i
$179$	2.44895	−	23.3002i	0.183043	−	1.74154i	−0.388930	−	0.921267i	$-0.627155\pi$
$179$	2.44895	−	23.3002i	0.183043	−	1.74154i	0.571973	−	0.820272i	$-0.306178\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	8.01578	−	13.8837i	0.595808	−	1.03197i	−0.397624	−	0.917548i	$-0.630165\pi$
$181$	8.01578	−	13.8837i	0.595808	−	1.03197i	0.993432	−	0.114422i	$-0.0365015\pi$
$182$	−17.6644	−	12.8340i	−1.30938	−	0.951317i
$183$	−3.35435	+	3.72538i	−0.247960	+	0.275388i
$184$	1.87469	−	5.76969i	0.138204	−	0.425347i
$185$	11.1568			0.820268
$186$	−0.499371	−	5.54532i	−0.0366156	−	0.406603i
$187$	8.39611			0.613985
$188$	−2.77834	+	8.55086i	−0.202632	+	0.623636i
$189$	2.70627	−	3.00561i	0.196852	−	0.218626i
$190$	0.723058	+	0.525332i	0.0524561	+	0.0381116i
$191$	−7.65595	+	13.2605i	−0.553965	+	0.959495i	0.444018	+	0.896018i	$0.353552\pi$
$191$	−7.65595	+	13.2605i	−0.553965	+	0.959495i	−0.997983	+	0.0634775i	$0.979781\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	0.168231	−	1.60061i	0.0121096	−	0.115215i	−0.986797	−	0.161960i	$-0.948218\pi$
$193$	0.168231	−	1.60061i	0.0121096	−	0.115215i	0.998907	+	0.0467456i	$0.0148850\pi$
$194$	11.4329	−	8.30648i	0.820834	−	0.596371i
$195$	−0.564309	−	5.36905i	−0.0404110	−	0.384485i
$196$	6.26144	+	6.95403i	0.447246	+	0.496717i
$197$	5.36479	−	2.38856i	0.382225	−	0.170178i	−0.206624	−	0.978420i	$-0.566248\pi$
$197$	5.36479	−	2.38856i	0.382225	−	0.170178i	0.588849	+	0.808243i	$0.299581\pi$
$198$	1.24857	−	0.265391i	0.0887317	−	0.0188605i
$199$	9.07158	+	1.92822i	0.643067	+	0.136688i	0.517891	−	0.855446i	$-0.326717\pi$
$199$	9.07158	+	1.92822i	0.643067	+	0.136688i	0.125176	+	0.992135i	$0.460050\pi$
$200$	0.913545	+	0.406737i	0.0645974	+	0.0287606i
$201$	1.02593	+	3.15748i	0.0723633	+	0.222711i
$202$	3.79669	+	11.6850i	0.267134	+	0.822155i
$203$	−26.2410	−	11.6832i	−1.84176	−	0.820003i
$204$	−6.43392	−	1.36757i	−0.450464	−	0.0957492i
$205$	−0.671053	+	0.142637i	−0.0468683	+	0.00996217i
$206$	−3.29172	+	1.46557i	−0.229345	+	0.102111i
$207$	4.05936	+	4.50837i	0.282145	+	0.313354i
$208$	0.564309	+	5.36905i	0.0391278	+	0.372276i
$209$	−0.922954	+	0.670565i	−0.0638421	+	0.0463840i
$210$	−0.422760	+	4.02229i	−0.0291732	+	0.277565i
$211$	11.6487	+	20.1762i	0.801932	+	1.38899i	0.918343	+	0.395785i	$0.129528\pi$
$211$	11.6487	+	20.1762i	0.801932	+	1.38899i	−0.116412	+	0.993201i	$0.537139\pi$
$212$	−5.92564	+	10.2635i	−0.406974	+	0.704900i
$213$	−1.18514	−	0.861056i	−0.0812046	−	0.0589986i
$214$	−0.912243	+	1.01315i	−0.0623596	+	0.0692574i
$215$	1.07062	−	3.29503i	0.0730158	−	0.224719i
$216$	−1.00000			−0.0680414
$217$	−11.5488	+	19.3316i	−0.783981	+	1.31231i
$218$	14.5580			0.985990
$219$	−3.09346	+	9.52069i	−0.209037	+	0.643348i
$220$	−0.854118	+	0.948594i	−0.0575846	+	0.0639542i
$221$	−28.7284	−	20.8724i	−1.93248	−	1.40403i
$222$	5.57842	−	9.66211i	0.374399	−	0.648479i
$223$	−10.8392	−	18.7741i	−0.725848	−	1.25720i	−0.958624	−	0.284675i	$-0.908114\pi$
$223$	−10.8392	−	18.7741i	−0.725848	−	1.25720i	0.232777	−	0.972530i	$-0.425219\pi$
$224$	0.422760	−	4.02229i	0.0282469	−	0.268751i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−0.251161	−	2.38964i	−0.0167070	−	0.158956i
$227$	−14.9211	−	16.5716i	−0.990351	−	1.09990i	−0.994997	−	0.0999071i	$-0.968145\pi$
$227$	−14.9211	−	16.5716i	−0.990351	−	1.09990i	0.00464567	−	0.999989i	$-0.498521\pi$
$228$	0.816480	−	0.363520i	0.0540727	−	0.0240747i
$229$	−10.2169	+	2.17167i	−0.675153	+	0.143508i	−0.532714	−	0.846295i	$-0.678828\pi$
$229$	−10.2169	+	2.17167i	−0.675153	+	0.143508i	−0.142439	+	0.989804i	$0.545494\pi$
$230$	−5.93404	−	1.26132i	−0.391279	−	0.0831690i
$231$	−4.71625	−	2.09981i	−0.310306	−	0.138157i
$232$	2.19469	+	6.75456i	0.144088	+	0.443458i
$233$	−4.39053	−	13.5127i	−0.287633	−	0.885245i	−0.985597	−	0.169111i	$-0.945910\pi$
$233$	−4.39053	−	13.5127i	−0.287633	−	0.885245i	0.697963	−	0.716133i	$-0.254090\pi$
$234$	−4.93188	−	2.19582i	−0.322407	−	0.143545i
$235$	8.79444	+	1.86931i	0.573686	+	0.121941i
$236$	8.25367	−	1.75437i	0.537268	−	0.114200i
$237$	3.66811	−	1.63315i	0.238269	−	0.106084i
$238$	17.8009	+	19.7699i	1.15386	+	1.28149i
$239$	0.0853280	+	0.811842i	0.00551941	+	0.0525137i	0.996935	−	0.0782352i	$-0.0249285\pi$
$239$	0.0853280	+	0.811842i	0.00551941	+	0.0525137i	−0.991416	+	0.130749i	$0.958262\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	3.02323	−	28.7641i	0.194743	−	1.85286i	−0.264292	−	0.964443i	$-0.585138\pi$
$241$	3.02323	−	28.7641i	0.194743	−	1.85286i	0.459036	−	0.888418i	$-0.348195\pi$
$242$	4.68533	+	8.11522i	0.301184	+	0.521666i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.05560	−	2.94656i	−0.259633	−	0.188634i
$245$	6.26144	−	6.95403i	0.400029	−	0.444277i
$246$	−0.211999	+	0.652467i	−0.0135166	+	0.0415998i
$247$	4.82501			0.307008
$248$	5.46275	−	1.07628i	0.346885	−	0.0683438i
$249$	−8.06843			−0.511316
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	12.0336	−	13.3647i	0.759555	−	0.843572i	−0.232073	−	0.972698i	$-0.574551\pi$
$251$	12.0336	−	13.3647i	0.759555	−	0.843572i	0.991628	+	0.129127i	$0.0412174\pi$
$252$	3.27203	+	2.37727i	0.206118	+	0.149754i
$253$	3.87189	−	6.70632i	0.243424	−	0.421622i
$254$	−0.149063	−	0.258184i	−0.00935302	−	0.0161999i
$255$	−0.687552	+	6.54162i	−0.0430562	+	0.409652i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.18135	+	11.2398i	0.0736904	+	0.701117i	0.967534	+	0.252739i	$0.0813315\pi$
$257$	1.18135	+	11.2398i	0.0736904	+	0.701117i	−0.893844	+	0.448378i	$0.852002\pi$
$258$	−2.31827	−	2.57470i	−0.144329	−	0.160294i
$259$	−41.2222	+	18.3533i	−2.56142	+	1.14042i
$260$	5.28065	−	1.12244i	0.327492	−	0.0696105i
$261$	−6.94696	−	1.47662i	−0.430006	−	0.0914006i
$262$	12.6599	+	5.63655i	0.782131	+	0.348227i
$263$	2.19632	+	6.75957i	0.135431	+	0.416813i	0.995657	−	0.0931000i	$-0.0296776\pi$
$263$	2.19632	+	6.75957i	0.135431	+	0.416813i	−0.860226	+	0.509913i	$0.829678\pi$
$264$	0.394448	+	1.21399i	0.0242766	+	0.0747156i
$265$	10.8267	+	4.82035i	0.665078	+	0.296112i
$266$	−3.53573	−	0.751543i	−0.216790	−	0.0460800i
$267$	3.52334	−	0.748910i	0.215625	−	0.0458325i
$268$	−3.03294	+	1.35035i	−0.185266	+	0.0824859i
$269$	14.0812	+	15.6388i	0.858547	+	0.953513i	0.999333	−	0.0365273i	$-0.0116296\pi$
$269$	14.0812	+	15.6388i	0.858547	+	0.953513i	−0.140786	+	0.990040i	$0.544963\pi$
$270$	0.104528	+	0.994522i	0.00636140	+	0.0605247i
$271$	17.7302	−	12.8818i	1.07703	−	0.782512i	0.0998712	−	0.995000i	$-0.468157\pi$
$271$	17.7302	−	12.8818i	1.07703	−	0.782512i	0.977163	+	0.212489i	$0.0681569\pi$
$272$	0.687552	−	6.54162i	0.0416890	−	0.396644i
$273$	10.9172	+	18.9092i	0.660740	+	1.14444i
$274$	11.3877	−	19.7240i	0.687954	−	1.19157i
$275$	1.03268	+	0.750284i	0.0622728	+	0.0452438i
$276$	−4.05936	+	4.50837i	−0.244345	+	0.271372i
$277$	6.15855	−	18.9541i	0.370032	−	1.13884i	−0.576738	−	0.816929i	$-0.695675\pi$
$277$	6.15855	−	18.9541i	0.370032	−	1.13884i	0.946770	−	0.321911i	$-0.104325\pi$
$278$	−0.688634			−0.0413015
$279$	−1.79929	+	5.26902i	−0.107721	+	0.315448i
$280$	−4.04445			−0.241702
$281$	−9.77193	+	30.0749i	−0.582945	+	1.79412i	0.0244276	+	0.999702i	$0.492224\pi$
$281$	−9.77193	+	30.0749i	−0.582945	+	1.79412i	−0.607372	+	0.794417i	$0.707776\pi$
$282$	6.01609	−	6.68155i	0.358253	−	0.397880i
$283$	−13.9665	−	10.1472i	−0.830220	−	0.603190i	0.0894017	−	0.995996i	$-0.471505\pi$
$283$	−13.9665	−	10.1472i	−0.830220	−	0.603190i	−0.919622	+	0.392806i	$0.871505\pi$
$284$	0.732458	−	1.26865i	0.0434634	−	0.0752808i
$285$	−0.446874	−	0.774009i	−0.0264705	−	0.0458483i
$286$	−0.720318	+	6.85337i	−0.0425933	+	0.405248i
$287$	2.24476	−	1.63091i	0.132504	−	0.0962696i
$288$	−0.104528	−	0.994522i	−0.00615940	−	0.0586028i
$289$	17.5751	+	19.5191i	1.03383	+	1.14818i
$290$	6.48815	−	2.88871i	0.380997	−	0.169631i
$291$	−13.8230	+	2.93817i	−0.810320	+	0.172239i
$292$	−9.79189	−	2.08133i	−0.573027	−	0.121801i
$293$	22.4753	+	10.0066i	1.31302	+	0.584595i	0.939348	−	0.342966i	$-0.111432\pi$
$293$	22.4753	+	10.0066i	1.31302	+	0.584595i	0.373673	+	0.927560i	$0.378098\pi$
$294$	−2.89165	−	8.89958i	−0.168644	−	0.519034i
$295$	−2.60751	−	8.02508i	−0.151815	−	0.467238i
$296$	10.1923	+	4.53790i	0.592415	+	0.263760i
$297$	−1.24857	−	0.265391i	−0.0724491	−	0.0153995i
$298$	0.280021	−	0.0595203i	0.0162212	−	0.00344792i
$299$	−29.9198	+	13.3212i	−1.73031	+	0.770383i
$300$	−0.669131	−	0.743145i	−0.0386323	−	0.0429055i
$301$	1.46470	+	13.9357i	0.0844237	+	0.803238i
$302$	−13.6245	+	9.89880i	−0.784004	+	0.569612i
$303$	1.28427	−	12.2190i	0.0737796	−	0.701966i
$304$	0.446874	+	0.774009i	0.0256300	+	0.0443925i
$305$	−2.50650	+	4.34138i	−0.143522	+	0.248587i
$306$	5.32144	+	3.86625i	0.304206	+	0.221019i
$307$	−3.19620	+	3.54974i	−0.182417	+	0.202594i	−0.827417	−	0.561588i	$-0.810191\pi$
$307$	−3.19620	+	3.54974i	−0.182417	+	0.202594i	0.645000	+	0.764182i	$0.276857\pi$
$308$	1.59532	−	4.90990i	0.0909020	−	0.279768i
$309$	3.60324			0.204981
$310$	−1.64140	−	5.32032i	−0.0932250	−	0.302174i
$311$	10.8901			0.617523			0.308762	−	0.951139i	$-0.400085\pi$
$311$	10.8901			0.617523			0.308762	+	0.951139i	$0.400085\pi$
$312$	1.66827	−	5.13439i	0.0944469	−	0.290678i
$313$	−2.73635	+	3.03903i	−0.154668	+	0.171776i	−0.815499	−	0.578759i	$-0.803537\pi$
$313$	−2.73635	+	3.03903i	−0.154668	+	0.171776i	0.660831	+	0.750535i	$0.270204\pi$
$314$	−0.801577	−	0.582380i	−0.0452356	−	0.0328656i
$315$	2.02222	−	3.50260i	0.113939	−	0.197349i
$316$	2.00762	+	3.47731i	0.112938	+	0.195614i
$317$	2.21880	−	21.1105i	0.124620	−	1.18568i	−0.736196	−	0.676769i	$-0.763380\pi$
$317$	2.21880	−	21.1105i	0.124620	−	1.18568i	0.860816	−	0.508916i	$-0.169954\pi$
$318$	9.58788	−	6.96600i	0.537662	−	0.390634i
$319$	0.947615	+	9.01596i	0.0530563	+	0.504797i
$320$	0.669131	+	0.743145i	0.0374055	+	0.0415431i
$321$	1.24546	−	0.554514i	0.0695148	−	0.0309500i
$322$	23.9999	−	5.10134i	1.33746	−	0.284287i
$323$	−5.75030	−	1.22226i	−0.319955	−	0.0680086i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−1.66827	−	5.13439i	−0.0925387	−	0.284805i
$326$	−2.17129	−	6.68254i	−0.120257	−	0.370112i
$327$	−13.2994	−	5.92126i	−0.735457	−	0.327447i
$328$	−0.671053	−	0.142637i	−0.0370527	−	0.00787579i
$329$	−35.5687	+	7.56035i	−1.96096	+	0.416816i
$330$	1.16610	−	0.519183i	0.0641919	−	0.0285801i
$331$	−2.20693	−	2.45104i	−0.121304	−	0.134721i	0.679434	−	0.733737i	$-0.262225\pi$
$331$	−2.20693	−	2.45104i	−0.121304	−	0.134721i	−0.800737	+	0.599015i	$0.795559\pi$
$332$	−0.843381	−	8.02423i	−0.0462865	−	0.440387i
$333$	−9.02608	+	6.55783i	−0.494626	+	0.359367i
$334$	1.32217	−	12.5796i	0.0723457	−	0.688323i
$335$	1.65998	+	2.87518i	0.0906946	+	0.157088i
$336$	−2.02222	+	3.50260i	−0.110321	+	0.191082i
$337$	15.3080	+	11.1219i	0.833880	+	0.605849i	0.920654	−	0.390379i	$-0.127656\pi$
$337$	15.3080	+	11.1219i	0.833880	+	0.605849i	−0.0867743	+	0.996228i	$0.527656\pi$
$338$	10.8032	−	11.9981i	0.587615	−	0.652613i
$339$	−0.742506	+	2.28520i	−0.0403274	+	0.124115i
$340$	−6.57766			−0.356723
$341$	7.10624	+	0.105958i	0.384824	+	0.00573793i
$342$	−0.893748			−0.0483284
$343$	−2.94651	+	9.06842i	−0.159096	+	0.489648i
$344$	2.31827	−	2.57470i	0.124993	−	0.138819i
$345$	4.90799	+	3.56587i	0.264237	+	0.191980i
$346$	3.20339	−	5.54843i	0.172215	−	0.298286i
$347$	−2.63429	−	4.56273i	−0.141416	−	0.244940i	0.786614	−	0.617445i	$-0.211832\pi$
$347$	−2.63429	−	4.56273i	−0.141416	−	0.244940i	−0.928030	+	0.372505i	$0.878499\pi$
$348$	0.742378	−	7.06325i	0.0397956	−	0.378630i
$349$	11.5066	−	8.36005i	0.615935	−	0.447503i	−0.235564	−	0.971859i	$-0.575694\pi$
$349$	11.5066	−	8.36005i	0.615935	−	0.447503i	0.851499	+	0.524356i	$0.175694\pi$
$350$	0.422760	+	4.02229i	0.0225975	+	0.215001i
$351$	3.61238	+	4.01196i	0.192815	+	0.214142i
$352$	−1.16610	+	0.519183i	−0.0621535	+	0.0276725i
$353$	31.1849	−	6.62855i	1.65980	−	0.352802i	0.719856	−	0.694124i	$-0.244208\pi$
$353$	31.1849	−	6.62855i	1.65980	−	0.352802i	0.939946	+	0.341322i	$0.110875\pi$
$354$	−8.25367	−	1.75437i	−0.438678	−	0.0932438i
$355$	−1.33827	−	0.595835i	−0.0710278	−	0.0316236i
$356$	1.11310	+	3.42576i	0.0589940	+	0.181565i
$357$	−8.22078	−	25.3010i	−0.435090	−	1.33907i
$358$	−21.4030	−	9.52925i	−1.13119	−	0.503637i
$359$	8.25029	+	1.75365i	0.435434	+	0.0925543i	0.420413	−	0.907333i	$-0.361885\pi$
$359$	8.25029	+	1.75365i	0.435434	+	0.0925543i	0.0150208	+	0.999887i	$0.495219\pi$
$360$	−0.978148	+	0.207912i	−0.0515529	+	0.0109579i
$361$	−16.6276	+	7.40310i	−0.875139	+	0.389637i
$362$	−10.7272	−	11.9138i	−0.563809	−	0.626174i
$363$	−0.979500	−	9.31932i	−0.0514104	−	0.489137i
$364$	−17.6644	+	12.8340i	−0.925868	+	0.672683i
$365$	−1.04640	+	9.95580i	−0.0547709	+	0.521111i
$366$	2.50650	+	4.34138i	0.131017	+	0.226928i
$367$	−6.01523	+	10.4187i	−0.313993	+	0.543851i	−0.979223	−	0.202787i	$-0.935000\pi$
$367$	−6.01523	+	10.4187i	−0.313993	+	0.543851i	0.665230	+	0.746638i	$0.268333\pi$
$368$	−4.90799	−	3.56587i	−0.255847	−	0.185884i
$369$	0.459053	−	0.509830i	0.0238974	−	0.0265407i
$370$	3.44766	−	10.6108i	0.179235	−	0.551629i
$371$	−47.9319			−2.48850
$372$	−5.42823	−	1.23867i	−0.281441	−	0.0642220i
$373$	−9.86500			−0.510790			−0.255395	−	0.966837i	$-0.582206\pi$
$373$	−9.86500			−0.510790			−0.255395	+	0.966837i	$0.582206\pi$
$374$	2.59454	−	7.98518i	0.134161	−	0.412904i
$375$	−0.669131	+	0.743145i	−0.0345538	+	0.0383758i
$376$	7.27380	+	5.28472i	0.375117	+	0.272539i
$377$	19.1709	−	33.2050i	0.987353	−	1.71015i
$378$	−2.02222	−	3.50260i	−0.104012	−	0.180154i
$379$	−2.10026	+	19.9827i	−0.107883	+	1.02644i	0.797926	+	0.602756i	$0.205931\pi$
$379$	−2.10026	+	19.9827i	−0.107883	+	1.02644i	−0.905809	+	0.423686i	$0.860736\pi$
$380$	0.723058	−	0.525332i	0.0370921	−	0.0269490i
$381$	0.0311626	+	0.296492i	0.00159651	+	0.0151898i
$382$	10.2457	+	11.3790i	0.524213	+	0.582198i
$383$	−10.7059	+	4.76656i	−0.547044	+	0.243560i	−0.661600	−	0.749857i	$-0.730122\pi$
$383$	−10.7059	+	4.76656i	−0.547044	+	0.243560i	0.114556	+	0.993417i	$0.463456\pi$
$384$	0.978148	−	0.207912i	0.0499159	−	0.0106099i
$385$	−5.04976	−	1.07336i	−0.257360	−	0.0547035i
$386$	−1.47029	−	0.654614i	−0.0748357	−	0.0333190i
$387$	1.07062	+	3.29503i	0.0544228	+	0.167496i
$388$	−4.36698	−	13.4402i	−0.221700	−	0.682321i
$389$	5.40025	+	2.40434i	0.273803	+	0.121905i	0.539045	−	0.842277i	$-0.318785\pi$
$389$	5.40025	+	2.40434i	0.273803	+	0.121905i	−0.265242	+	0.964182i	$0.585452\pi$
$390$	−5.28065	−	1.12244i	−0.267396	−	0.0568368i
$391$	39.0321	−	8.29653i	1.97394	−	0.419573i
$392$	8.54857	−	3.80607i	0.431768	−	0.192236i
$393$	−9.27280	−	10.2985i	−0.467751	−	0.519490i
$394$	−0.613842	−	5.84032i	−0.0309249	−	0.294231i
$395$	3.24840	−	2.36010i	0.163445	−	0.118750i
$396$	0.133426	−	1.26947i	0.00670493	−	0.0637931i
$397$	−2.47610	−	4.28872i	−0.124272	−	0.215245i	0.797176	−	0.603747i	$-0.206326\pi$
$397$	−2.47610	−	4.28872i	−0.124272	−	0.215245i	−0.921448	+	0.388502i	$0.872993\pi$
$398$	4.63712	−	8.03173i	0.232438	−	0.402594i
$399$	2.92437	+	2.12468i	0.146402	+	0.106367i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	3.30394	−	10.1685i	0.164991	−	0.507789i	−0.834045	−	0.551697i	$-0.813981\pi$
$401$	3.30394	−	10.1685i	0.164991	−	0.507789i	0.999036	+	0.0439073i	$0.0139806\pi$
$402$	3.31997			0.165585
$403$	−24.0515	−	18.0284i	−1.19809	−	0.898057i
$404$	12.2864			0.611269
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	−19.2203	+	21.3463i	−0.953889	+	1.05940i
$407$	11.5214	+	8.37081i	0.571096	+	0.414925i
$408$	−3.28883	+	5.69642i	−0.162821	+	0.282015i
$409$	18.5125	+	32.0647i	0.915386	+	1.58550i	0.806335	+	0.591460i	$0.201448\pi$
$409$	18.5125	+	32.0647i	0.915386	+	1.58550i	0.109052	+	0.994036i	$0.465219\pi$
$410$	−0.0717112	+	0.682286i	−0.00354156	+	0.0336957i
$411$	−18.4256	+	13.3870i	−0.908869	+	0.660332i
$412$	0.376641	+	3.58350i	0.0185558	+	0.176546i
$413$	22.8356	+	25.3615i	1.12367	+	1.24796i
$414$	5.54213	−	2.46751i	0.272381	−	0.121272i
$415$	−7.89212	+	1.67752i	−0.387409	+	0.0823463i
$416$	5.28065	+	1.12244i	0.258905	+	0.0550320i
$417$	0.629098	+	0.280093i	0.0308071	+	0.0137162i
$418$	0.352537	+	1.08500i	0.0172431	+	0.0530690i
$419$	−4.16403	−	12.8156i	−0.203426	−	0.626082i	−0.999774	−	0.0212433i	$-0.993238\pi$
$419$	−4.16403	−	12.8156i	−0.203426	−	0.626082i	0.796348	−	0.604839i	$-0.206762\pi$
$420$	3.69479	+	1.64503i	0.180287	+	0.0802690i
$421$	3.18123	+	0.676191i	0.155044	+	0.0329555i	0.284779	−	0.958593i	$-0.408080\pi$
$421$	3.18123	+	0.676191i	0.155044	+	0.0329555i	−0.129736	+	0.991549i	$0.541413\pi$
$422$	22.7884	−	4.84381i	1.10932	−	0.235793i
$423$	−8.21360	+	3.65693i	−0.399359	+	0.177806i
$424$	7.93005	+	8.80721i	0.385117	+	0.427716i
$425$	0.687552	+	6.54162i	0.0333512	+	0.317315i
$426$	−1.18514	+	0.861056i	−0.0574203	+	0.0417183i
$427$	2.11929	−	20.1637i	0.102560	−	0.975791i
$428$	0.681663	+	1.18067i	0.0329494	+	0.0570700i
$429$	3.44556	−	5.96789i	0.166353	−	0.288132i
$430$	−2.80292	−	2.03644i	−0.135169	−	0.0982060i
$431$	−8.61740	+	9.57059i	−0.415085	+	0.460999i	−0.914037	−	0.405631i	$-0.867052\pi$
$431$	−8.61740	+	9.57059i	−0.415085	+	0.460999i	0.498952	+	0.866630i	$0.333719\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	−38.3897			−1.84489			−0.922446	−	0.386126i	$-0.873813\pi$
$433$	−38.3897			−1.84489			−0.922446	+	0.386126i	$0.873813\pi$
$434$	14.8167	+	16.9573i	0.711223	+	0.813978i
$435$	−7.10216			−0.340523
$436$	4.49866	−	13.8455i	0.215447	−	0.663077i
$437$	−3.62804	+	4.02935i	−0.173553	+	0.192750i
$438$	8.09878	+	5.88411i	0.386975	+	0.281154i
$439$	15.8596	−	27.4696i	0.756936	−	1.31105i	−0.187470	−	0.982270i	$-0.560029\pi$
$439$	15.8596	−	27.4696i	0.756936	−	1.31105i	0.944406	−	0.328781i	$-0.106638\pi$
$440$	0.638230	+	1.10545i	0.0304264	+	0.0527001i
$441$	−0.978133	+	9.30631i	−0.0465778	+	0.443158i
$442$	−28.7284	+	20.8724i	−1.36647	+	0.992799i
$443$	0.155236	+	1.47697i	0.00737549	+	0.0701731i	0.997591	−	0.0693768i	$-0.0221011\pi$
$443$	0.155236	+	1.47697i	0.00737549	+	0.0701731i	−0.990215	+	0.139550i	$0.955434\pi$
$444$	−7.46539	−	8.29115i	−0.354292	−	0.393481i
$445$	3.29064	−	1.46509i	0.155991	−	0.0694519i
$446$	−21.2047	+	4.50720i	−1.00407	+	0.213422i
$447$	−0.280021	−	0.0595203i	−0.0132445	−	0.00281521i
$448$	−3.69479	−	1.64503i	−0.174562	−	0.0777202i
$449$	−3.37576	−	10.3895i	−0.159312	−	0.490312i	0.839260	−	0.543730i	$-0.182988\pi$
$449$	−3.37576	−	10.3895i	−0.159312	−	0.490312i	−0.998572	+	0.0534182i	$0.982988\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	−0.799999	−	0.356182i	−0.0376705	−	0.0167720i
$452$	−2.35029	−	0.499570i	−0.110548	−	0.0234978i
$453$	16.4728	−	3.50141i	0.773961	−	0.164511i
$454$	−20.3714	+	9.06994i	−0.956078	+	0.425673i
$455$	14.6101	+	16.2262i	0.684932	+	0.760694i
$456$	−0.0934222	−	0.888852i	−0.00437489	−	0.0416243i
$457$	1.70307	−	1.23735i	0.0796663	−	0.0578809i	−0.547239	−	0.836976i	$-0.684321\pi$
$457$	1.70307	−	1.23735i	0.0796663	−	0.0578809i	0.626906	+	0.779095i	$0.284321\pi$
$458$	−1.09182	+	10.3879i	−0.0510173	+	0.485397i
$459$	−3.28883	−	5.69642i	−0.153509	−	0.265886i
$460$	−3.03331	+	5.25384i	−0.141429	+	0.244962i
$461$	−16.9904	−	12.3443i	−0.791323	−	0.574930i	0.117033	−	0.993128i	$-0.462662\pi$
$461$	−16.9904	−	12.3443i	−0.791323	−	0.574930i	−0.908356	+	0.418198i	$0.862662\pi$
$462$	−3.45444	+	3.83654i	−0.160715	+	0.178492i
$463$	−11.9467	+	36.7681i	−0.555209	+	1.70876i	0.140181	+	0.990126i	$0.455231\pi$
$463$	−11.9467	+	36.7681i	−0.555209	+	1.70876i	−0.695390	+	0.718632i	$0.744769\pi$
$464$	7.10216			0.329710
$465$	−0.664479	+	5.52797i	−0.0308145	+	0.256354i
$466$	−14.2081			−0.658176
$467$	−2.94026	+	9.04918i	−0.136059	+	0.418746i	−0.995753	−	0.0920628i	$-0.970654\pi$
$467$	−2.94026	+	9.04918i	−0.136059	+	0.418746i	0.859694	+	0.510809i	$0.170654\pi$
$468$	−3.61238	+	4.01196i	−0.166982	+	0.185453i
$469$	−10.8630	−	7.89245i	−0.501608	−	0.364440i
$470$	4.49545	−	7.78636i	0.207360	−	0.359158i
$471$	0.495402	+	0.858061i	0.0228269	+	0.0395374i
$472$	0.882018	−	8.39184i	0.0405982	−	0.386266i
$473$	3.57782	−	2.59944i	0.164508	−	0.119522i
$474$	−0.419708	−	3.99325i	−0.0192778	−	0.183416i
$475$	−0.598034	−	0.664185i	−0.0274397	−	0.0304749i
$476$	24.3030	−	10.8204i	1.11393	−	0.495953i
$477$	−11.5923	+	2.46402i	−0.530775	+	0.112820i
$478$	0.798475	+	0.169721i	0.0365214	+	0.00776287i
$479$	13.7080	+	6.10321i	0.626336	+	0.278863i	0.695259	−	0.718759i	$-0.255290\pi$
$479$	13.7080	+	6.10321i	0.626336	+	0.278863i	−0.0689229	+	0.997622i	$0.521956\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	−18.6126	−	57.2836i	−0.848661	−	2.61191i
$482$	−26.4221	−	11.7639i	−1.20349	−	0.535830i
$483$	−23.9999	−	5.10134i	−1.09204	−	0.232119i
$484$	9.16588	−	1.94827i	0.416631	−	0.0885576i
$485$	−12.9101	+	5.74793i	−0.586216	+	0.261000i
$486$	−0.669131	−	0.743145i	−0.0303524	−	0.0337097i
$487$	3.83355	+	36.4738i	0.173715	+	1.65279i	0.640164	+	0.768238i	$0.278866\pi$
$487$	3.83355	+	36.4738i	0.173715	+	1.65279i	−0.466450	+	0.884548i	$0.654467\pi$
$488$	−4.05560	+	2.94656i	−0.183588	+	0.133385i
$489$	−0.734463	+	6.98795i	−0.0332135	+	0.316006i
$490$	−4.67879	−	8.10390i	−0.211366	−	0.366097i
$491$	−18.0988	+	31.3481i	−0.816788	+	1.41472i	0.0912487	+	0.995828i	$0.470914\pi$
$491$	−18.0988	+	31.3481i	−0.816788	+	1.41472i	−0.908037	+	0.418890i	$0.862419\pi$
$492$	0.555022	+	0.403247i	0.0250223	+	0.0181798i
$493$	−31.2588	+	34.7164i	−1.40783	+	1.56355i
$494$	1.49101	−	4.58886i	0.0670837	−	0.206462i
$495$	−1.27646			−0.0573726
$496$	0.664479	−	5.52797i	0.0298360	−	0.248213i
$497$	5.92478			0.265763
$498$	−2.49328	+	7.67353i	−0.111727	+	0.343859i
$499$	−21.6443	+	24.0384i	−0.968931	+	1.07611i	0.0281386	+	0.999604i	$0.491042\pi$
$499$	−21.6443	+	24.0384i	−0.968931	+	1.07611i	−0.997069	+	0.0765027i	$0.975625\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−6.32443	+	10.9542i	−0.282555	+	0.489399i
$502$	−8.99198	−	15.5746i	−0.401332	−	0.695127i
$503$	2.75484	−	26.2106i	0.122832	−	1.16867i	−0.743335	−	0.668919i	$-0.766757\pi$
$503$	2.75484	−	26.2106i	0.122832	−	1.16867i	0.866168	−	0.499753i	$-0.166576\pi$
$504$	3.27203	−	2.37727i	0.145748	−	0.105892i
$505$	−1.28427	−	12.2190i	−0.0571494	−	0.543741i
$506$	−5.18160	−	5.75476i	−0.230350	−	0.255830i
$507$	−14.7493	+	6.56680i	−0.655039	+	0.291642i
$508$	−0.291611	+	0.0619838i	−0.0129381	+	0.00275008i
$509$	−25.0303	−	5.32036i	−1.10945	−	0.235821i	−0.383481	−	0.923549i	$-0.625275\pi$
$509$	−25.0303	−	5.32036i	−1.10945	−	0.235821i	−0.725968	+	0.687728i	$0.758608\pi$
$510$	6.00899	+	2.67537i	0.266082	+	0.118468i
$511$	−12.5113	−	38.5059i	−0.553469	−	1.70340i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	0.816480	+	0.363520i	0.0360485	+	0.0160498i
$514$	11.0547	+	2.34975i	0.487602	+	0.103643i
$515$	3.52450	−	0.749155i	0.155308	−	0.0330117i
$516$	−3.16507	+	1.40918i	−0.139335	+	0.0620358i
$517$	7.67930	+	8.52873i	0.337735	+	0.375093i
$518$	4.71667	+	44.8761i	0.207239	+	1.97174i
$519$	−5.18319	+	3.76581i	−0.227517	+	0.165301i
$520$	0.564309	−	5.36905i	0.0247466	−	0.235448i
$521$	−14.1076	−	24.4351i	−0.618066	−	1.07052i	−0.989838	−	0.142198i	$-0.954583\pi$
$521$	−14.1076	−	24.4351i	−0.618066	−	1.07052i	0.371772	−	0.928324i	$-0.378750\pi$
$522$	−3.55108	+	6.15065i	−0.155427	+	0.269207i
$523$	12.9152	+	9.38341i	0.564740	+	0.410308i	0.833191	−	0.552986i	$-0.186512\pi$
$523$	12.9152	+	9.38341i	0.564740	+	0.410308i	−0.268450	+	0.963294i	$0.586512\pi$
$524$	9.27280	−	10.2985i	0.405084	−	0.449892i
$525$	1.24980	−	3.84650i	0.0545459	−	0.167875i
$526$	7.10743			0.309899
$527$	24.0970	+	27.5784i	1.04968	+	1.20133i
$528$	1.27646			0.0555508
$529$	4.26561	−	13.1282i	0.185461	−	0.570791i
$530$	7.93005	−	8.80721i	0.344459	−	0.382561i
$531$	6.82654	+	4.95977i	0.296246	+	0.215236i
$532$	−1.80736	+	3.13044i	−0.0783590	+	0.135722i
$533$	1.85185	+	3.20749i	0.0802124	+	0.138932i
$534$	0.376517	−	3.58232i	0.0162935	−	0.155022i
$535$	1.10295	−	0.801342i	0.0476848	−	0.0346451i
$536$	0.347031	+	3.30178i	0.0149895	+	0.142615i
$537$	15.6768	+	17.4108i	0.676502	+	0.751332i
$538$	19.2247	−	8.55938i	0.828835	−	0.369021i
$539$	11.6835	−	2.48342i	0.503246	−	0.106968i
$540$	0.978148	+	0.207912i	0.0420928	+	0.00894709i
$541$	16.4685	+	7.33224i	0.708035	+	0.315238i	0.728972	−	0.684543i	$-0.239998\pi$
$541$	16.4685	+	7.33224i	0.708035	+	0.315238i	−0.0209371	+	0.999781i	$0.506665\pi$
$542$	−6.77234	−	20.8431i	−0.290897	−	0.895289i
$543$	4.95402	+	15.2469i	0.212597	+	0.654308i
$544$	−6.00899	−	2.67537i	−0.257633	−	0.114706i
$545$	−14.2398	−	3.02677i	−0.609968	−	0.129653i
$546$	21.3573	−	4.53964i	0.914009	−	0.194279i
$547$	−25.1526	+	11.1987i	−1.07545	+	0.478821i	−0.866537	−	0.499113i	$-0.833659\pi$
$547$	−25.1526	+	11.1987i	−1.07545	+	0.478821i	−0.208913	+	0.977934i	$0.566992\pi$
$548$	−15.2397	−	16.9254i	−0.651007	−	0.723016i
$549$	−0.524000	−	4.98553i	−0.0223638	−	0.212777i
$550$	1.03268	−	0.750284i	0.0440335	−	0.0319922i
$551$	0.663499	−	6.31277i	0.0282660	−	0.268933i
$552$	3.03331	+	5.25384i	0.129106	+	0.223618i
$553$	−8.11973	+	14.0638i	−0.345286	+	0.598053i
$554$	−16.1233	−	11.7143i	−0.685014	−	0.497692i
$555$	−7.46539	+	8.29115i	−0.316888	+	0.351940i
$556$	−0.212800	+	0.654930i	−0.00902471	+	0.0277752i
$557$	3.55167			0.150489			0.0752446	−	0.997165i	$-0.476026\pi$
$557$	3.55167			0.150489			0.0752446	+	0.997165i	$0.476026\pi$
$558$	4.45512	+	3.33944i	0.188600	+	0.141370i
$559$	−18.7041			−0.791098
$560$	−1.24980	+	3.84650i	−0.0528138	+	0.162544i
$561$	−5.61810	+	6.23953i	−0.237196	+	0.263433i
$562$	25.5833	+	18.5873i	1.07916	+	0.784059i
$563$	4.13822	−	7.16762i	0.174405	−	0.302079i	−0.765550	−	0.643376i	$-0.777533\pi$
$563$	4.13822	−	7.16762i	0.174405	−	0.302079i	0.939955	+	0.341297i	$0.110866\pi$
$564$	−4.49545	−	7.78636i	−0.189293	−	0.327865i
$565$	−0.251161	+	2.38964i	−0.0105664	+	0.100533i
$566$	−13.9665	+	10.1472i	−0.587054	+	0.426520i
$567$	0.422760	+	4.02229i	0.0177543	+	0.168920i
$568$	−0.980220	−	1.08864i	−0.0411291	−	0.0456785i
$569$	11.8898	−	5.29366i	0.498445	−	0.221922i	−0.142086	−	0.989854i	$-0.545381\pi$
$569$	11.8898	−	5.29366i	0.498445	−	0.221922i	0.640531	+	0.767932i	$0.278714\pi$
$570$	−0.874218	+	0.185821i	−0.0366170	+	0.00778317i
$571$	−23.9315	−	5.08680i	−1.00150	−	0.212876i	−0.322151	−	0.946688i	$-0.604406\pi$
$571$	−23.9315	−	5.08680i	−1.00150	−	0.212876i	−0.679352	+	0.733812i	$0.737739\pi$
$572$	6.29535	+	2.80287i	0.263222	+	0.117194i
$573$	−4.73163	−	14.5625i	−0.197667	−	0.608356i
$574$	−0.857421	−	2.63887i	−0.0357881	−	0.110144i
$575$	5.54213	+	2.46751i	0.231123	+	0.102902i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	−17.7332	+	3.76931i	−0.738243	+	0.156918i	−0.561661	−	0.827367i	$-0.689837\pi$
$577$	−17.7332	+	3.76931i	−0.738243	+	0.156918i	−0.176582	+	0.984286i	$0.556504\pi$
$578$	23.9948	−	10.6832i	0.998051	−	0.444361i
$579$	1.07692	+	1.19604i	0.0447552	+	0.0497057i
$580$	−0.742378	−	7.06325i	−0.0308256	−	0.293286i
$581$	26.4001	−	19.1808i	1.09526	−	0.795755i
$582$	−1.47718	+	14.0544i	−0.0612310	+	0.582574i
$583$	7.56384	+	13.1009i	0.313262	+	0.542586i
$584$	−5.00532	+	8.66947i	−0.207122	+	0.358745i
$585$	4.36758	+	3.17323i	0.180577	+	0.131197i
$586$	16.4621	−	18.2831i	0.680045	−	0.755266i
$587$	−1.74395	+	5.36731i	−0.0719804	+	0.221533i	−0.980574	−	0.196148i	$-0.937157\pi$
$587$	−1.74395	+	5.36731i	−0.0719804	+	0.221533i	0.908594	+	0.417680i	$0.137157\pi$
$588$	−9.35758			−0.385900
$589$	−4.85147	−	1.10706i	−0.199901	−	0.0456156i
$590$	−8.43806			−0.347390
$591$	−1.81470	+	5.58507i	−0.0746468	+	0.229739i
$592$	7.46539	−	8.29115i	0.306826	−	0.340764i
$593$	−38.8188	−	28.2035i	−1.59410	−	1.15818i	−0.897781	−	0.440442i	$-0.854822\pi$
$593$	−38.8188	−	28.2035i	−1.59410	−	1.15818i	−0.696315	−	0.717736i	$-0.745178\pi$
$594$	−0.638230	+	1.10545i	−0.0261869	+	0.0453570i
$595$	−13.3015	−	23.0389i	−0.545308	−	0.944502i
$596$	0.0299241	−	0.284709i	0.00122574	−	0.0116621i
$597$	−7.50302	+	5.45126i	−0.307078	+	0.223105i
$598$	3.42345	+	32.5719i	0.139995	+	1.33197i
$599$	16.2130	+	18.0063i	0.662444	+	0.735719i	0.976934	−	0.213542i	$-0.0685000\pi$
$599$	16.2130	+	18.0063i	0.662444	+	0.735719i	−0.314490	+	0.949261i	$0.601833\pi$
$600$	−0.913545	+	0.406737i	−0.0372953	+	0.0166050i
$601$	−27.8666	+	5.92322i	−1.13670	+	0.241613i	−0.737563	−	0.675278i	$-0.764024\pi$
$601$	−27.8666	+	5.92322i	−1.13670	+	0.241613i	−0.399138	+	0.916891i	$0.630690\pi$
$602$	13.7062	+	2.91335i	0.558624	+	0.118739i
$603$	−3.03294	−	1.35035i	−0.123511	−	0.0549906i
$604$	5.20411	+	16.0166i	0.211752	+	0.651706i
$605$	−2.89569	−	8.91202i	−0.117727	−	0.362325i
$606$	−11.2241	−	4.99731i	−0.455950	−	0.203002i
$607$	25.2435	+	5.36566i	1.02460	+	0.217786i	0.689415	−	0.724367i	$-0.257868\pi$
$607$	25.2435	+	5.36566i	1.02460	+	0.217786i	0.335185	+	0.942152i	$0.391201\pi$
$608$	0.874218	−	0.185821i	0.0354542	−	0.00753603i
$609$	26.2410	−	11.6832i	1.06334	−	0.473429i
$610$	3.35435	+	3.72538i	0.135814	+	0.150836i
$611$	−5.07365	−	48.2726i	−0.205258	−	1.95290i
$612$	5.32144	−	3.86625i	0.215106	−	0.156284i
$613$	2.54238	−	24.1891i	0.102686	−	0.976988i	−0.814941	−	0.579544i	$-0.803231\pi$
$613$	2.54238	−	24.1891i	0.102686	−	0.976988i	0.917626	−	0.397444i	$-0.130103\pi$
$614$	2.38832	+	4.13670i	0.0963848	+	0.166943i
$615$	0.343022	−	0.594132i	0.0138320	−	0.0239577i
$616$	−4.17661	−	3.03449i	−0.168281	−	0.122263i
$617$	−7.21402	+	8.01198i	−0.290426	+	0.322550i	−0.870647	−	0.491909i	$-0.836299\pi$
$617$	−7.21402	+	8.01198i	−0.290426	+	0.322550i	0.580221	+	0.814459i	$0.302966\pi$
$618$	1.11346	−	3.42688i	0.0447900	−	0.137849i
$619$	18.5697			0.746380			0.373190	−	0.927755i	$-0.378264\pi$
$619$	18.5697			0.746380			0.373190	+	0.927755i	$0.378264\pi$
$620$	−5.56715	−	0.0830090i	−0.223582	−	0.00333372i
$621$	−6.06661			−0.243445
$622$	3.36524	−	10.3571i	0.134934	−	0.415283i
$623$	−9.74812	+	10.8264i	−0.390550	+	0.433750i
$624$	−4.36758	−	3.17323i	−0.174843	−	0.127031i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.04471	+	3.54154i	0.0817230	+	0.141548i
$627$	0.119250	−	1.13458i	0.00476237	−	0.0453109i
$628$	−0.801577	+	0.582380i	−0.0319864	+	0.0232395i
$629$	7.67092	+	72.9839i	0.305859	+	2.91006i
$630$	−2.70627	−	3.00561i	−0.107820	−	0.119746i
$631$	41.3174	−	18.3957i	1.64482	−	0.732320i	0.645317	−	0.763915i	$-0.276725\pi$
$631$	41.3174	−	18.3957i	1.64482	−	0.732320i	0.999501	+	0.0315948i	$0.0100586\pi$
$632$	3.92750	−	0.834817i	0.156228	−	0.0332072i
$633$	−22.7884	−	4.84381i	−0.905756	−	0.192524i
$634$	−19.3916	−	8.63372i	−0.770141	−	0.342889i
$635$	0.0921258	+	0.283534i	0.00365590	+	0.0112517i
$636$	−3.66225	−	11.2712i	−0.145217	−	0.446933i
$637$	−46.1505	−	20.5475i	−1.82855	−	0.814122i
$638$	8.86752	+	1.88485i	0.351068	+	0.0746219i
$639$	1.43290	−	0.304573i	0.0566848	−	0.0120487i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	9.96213	+	11.0641i	0.393481	+	0.437005i	0.907037	−	0.421052i	$-0.138339\pi$
$641$	9.96213	+	11.0641i	0.393481	+	0.437005i	−0.513556	+	0.858056i	$0.671672\pi$
$642$	−0.142506	−	1.35586i	−0.00562427	−	0.0535114i
$643$	36.9849	−	26.8711i	1.45854	−	1.05969i	0.474803	−	0.880092i	$-0.342519\pi$
$643$	36.9849	−	26.8711i	1.45854	−	1.05969i	0.983740	−	0.179601i	$-0.0574806\pi$
$644$	2.56472	−	24.4017i	0.101064	−	0.961562i
$645$	1.73230	+	3.00044i	0.0682093	+	0.118142i
$646$	−2.93938	+	5.09116i	−0.115649	+	0.200309i
$647$	−13.9415	−	10.1291i	−0.548098	−	0.398216i	0.278986	−	0.960295i	$-0.410002\pi$
$647$	−13.9415	−	10.1291i	−0.548098	−	0.398216i	−0.827084	+	0.562079i	$0.810002\pi$
$648$	0.669131	−	0.743145i	0.0262859	−	0.0291935i
$649$	3.32838	−	10.2437i	0.130650	−	0.402100i
$650$	−5.39862			−0.211751
$651$	−6.63855	−	21.5178i	−0.260185	−	0.843348i
$652$	−7.02644			−0.275177
$653$	13.4698	−	41.4558i	0.527114	−	1.62229i	−0.232984	−	0.972481i	$-0.574849\pi$
$653$	13.4698	−	41.4558i	0.527114	−	1.62229i	0.760098	−	0.649809i	$-0.225151\pi$
$654$	−9.74119	+	10.8187i	−0.380911	+	0.423044i
$655$	−11.2113	−	8.14552i	−0.438063	−	0.318272i
$656$	−0.343022	+	0.594132i	−0.0133928	+	0.0231970i
$657$	−5.00532	−	8.66947i	−0.195276	−	0.338228i
$658$	−3.80100	+	36.1641i	−0.148178	+	1.40982i
$659$	29.5524	−	21.4711i	1.15120	−	0.836395i	0.162559	−	0.986699i	$-0.448025\pi$
$659$	29.5524	−	21.4711i	1.15120	−	0.836395i	0.988640	+	0.150304i	$0.0480253\pi$
$660$	−0.133426	−	1.26947i	−0.00519361	−	0.0494139i
$661$	15.0896	+	16.7587i	0.586917	+	0.651837i	0.961322	−	0.275428i	$-0.0888196\pi$
$661$	15.0896	+	16.7587i	0.586917	+	0.651837i	−0.374405	+	0.927265i	$0.622153\pi$
$662$	−3.01306	+	1.34150i	−0.117106	+	0.0521388i
$663$	34.7343	−	7.38300i	1.34897	−	0.286732i
$664$	−7.89212	−	1.67752i	−0.306273	−	0.0651004i
$665$	3.30221	+	1.47024i	0.128054	+	0.0570134i
$666$	3.44766	+	10.6108i	0.133594	+	0.411160i
$667$	13.3143	+	40.9773i	0.515533	+	1.58665i
$668$	−11.5553	−	5.14475i	−0.447088	−	0.199056i
$669$	21.2047	+	4.50720i	0.819821	+	0.174258i
$670$	3.24742	−	0.690260i	0.125459	−	0.0266671i
$671$	−5.84567	+	2.60266i	−0.225670	+	0.100475i
$672$	2.70627	+	3.00561i	0.104396	+	0.115944i
$673$	−1.88896	−	17.9722i	−0.0728139	−	0.692778i	−0.968656	−	0.248406i	$-0.920093\pi$
$673$	−1.88896	−	17.9722i	−0.0728139	−	0.692778i	0.895842	−	0.444372i	$-0.146573\pi$
$674$	15.3080	−	11.1219i	0.589642	−	0.428400i
$675$	0.104528	−	0.994522i	0.00402330	−	0.0382792i
$676$	−8.07255	−	13.9821i	−0.310483	−	0.537772i
$677$	21.2791	−	36.8565i	0.817823	−	1.41651i	−0.0894607	−	0.995990i	$-0.528514\pi$
$677$	21.2791	−	36.8565i	0.817823	−	1.41651i	0.907283	−	0.420520i	$-0.138152\pi$
$678$	1.94391	+	1.41233i	0.0746552	+	0.0542402i
$679$	38.2445	−	42.4748i	1.46769	−	1.63003i
$680$	−2.03261	+	6.25572i	−0.0779469	+	0.239896i
$681$	22.2993			0.854511
$682$	2.29672	−	6.72569i	0.0879459	−	0.257540i
$683$	−17.6763			−0.676364			−0.338182	−	0.941081i	$-0.609812\pi$
$683$	−17.6763			−0.676364			−0.338182	+	0.941081i	$0.609812\pi$
$684$	−0.276183	+	0.850005i	−0.0105601	+	0.0325008i
$685$	−15.2397	+	16.9254i	−0.582278	+	0.646685i
$686$	7.71406	+	5.60459i	0.294524	+	0.213984i
$687$	5.22258	−	9.04578i	0.199254	−	0.345118i
$688$	−1.73230	−	3.00044i	−0.0660434	−	0.114391i
$689$	6.68779	−	63.6300i	0.254784	−	2.42411i
$690$	4.90799	−	3.56587i	0.186844	−	0.135750i
$691$	−4.76041	−	45.2923i	−0.181095	−	1.72300i	−0.587429	−	0.809276i	$-0.699860\pi$
$691$	−4.76041	−	45.2923i	−0.181095	−	1.72300i	0.406334	−	0.913724i	$-0.366807\pi$
$692$	−4.28697	−	4.76116i	−0.162966	−	0.180992i
$693$	4.71625	−	2.09981i	0.179155	−	0.0797652i
$694$	−5.15345	+	1.09540i	−0.195622	+	0.0415808i
$695$	0.673585	+	0.143175i	0.0255506	+	0.00543094i
$696$	−6.48815	−	2.88871i	−0.245933	−	0.109496i
$697$	−1.39446	−	4.29170i	−0.0528189	−	0.162560i
$698$	−4.39514	−	13.5268i	−0.166358	−	0.511999i
$699$	12.9797	+	5.77894i	0.490938	+	0.218580i
$700$	3.95607	+	0.840888i	0.149525	+	0.0317826i
$701$	5.15473	−	1.09567i	0.194691	−	0.0413829i	−0.109534	−	0.993983i	$-0.534936\pi$
$701$	5.15473	−	1.09567i	0.194691	−	0.0413829i	0.304225	+	0.952600i	$0.401602\pi$
$702$	4.93188	−	2.19582i	0.186142	−	0.0828758i
$703$	−6.67218	−	7.41021i	−0.251646	−	0.279481i
$704$	0.133426	+	1.26947i	0.00502870	+	0.0478448i
$705$	−7.27380	+	5.28472i	−0.273947	+	0.199034i
$706$	3.33253	−	31.7069i	0.125421	−	1.19330i
$707$	24.8458	+	43.0341i	0.934421	+	1.61847i
$708$	−4.21903	+	7.30758i	−0.158561	+	0.274636i
$709$	−2.88668	−	2.09730i	−0.108412	−	0.0787657i	0.532259	−	0.846582i	$-0.321343\pi$
$709$	−2.88668	−	2.09730i	−0.108412	−	0.0787657i	−0.640670	+	0.767816i	$0.721343\pi$
$710$	−0.980220	+	1.08864i	−0.0367870	+	0.0408561i
$711$	−1.24078	+	3.81873i	−0.0465329	+	0.143213i
$712$	3.60206			0.134993
$713$	33.1404	−	6.52937i	1.24112	−	0.244527i
$714$	−26.6030			−0.995592
$715$	2.12947	−	6.55385i	0.0796378	−	0.245100i
$716$	−15.6768	+	17.4108i	−0.585868	+	0.650672i
$717$	−0.660412	−	0.479817i	−0.0246635	−	0.0179191i
$718$	4.21730	−	7.30458i	0.157388	−	0.272605i
$719$	−0.333883	−	0.578302i	−0.0124517	−	0.0215670i	0.859732	−	0.510745i	$-0.170630\pi$
$719$	−0.333883	−	0.578302i	−0.0124517	−	0.0215670i	−0.872184	+	0.489178i	$0.837297\pi$
$720$	−0.104528	+	0.994522i	−0.00389555	+	0.0370636i
$721$	−11.7899	+	8.56586i	−0.439079	+	0.319009i
$722$	1.90254	+	18.1015i	0.0708054	+	0.673668i
$723$	19.3530	+	21.4937i	0.719745	+	0.799358i
$724$	−14.6456	+	6.52062i	−0.544298	+	0.242337i
$725$	−6.94696	+	1.47662i	−0.258004	+	0.0548404i
$726$	−9.16588	−	1.94827i	−0.340178	−	0.0723070i
$727$	−20.3826	−	9.07492i	−0.755949	−	0.336570i	−0.00768410	−	0.999970i	$-0.502446\pi$
$727$	−20.3826	−	9.07492i	−0.755949	−	0.336570i	−0.748265	+	0.663400i	$0.769113\pi$
$728$	6.74722	+	20.7658i	0.250068	+	0.769632i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	9.14518	+	4.07170i	0.338478	+	0.150700i
$731$	22.2910	+	4.73809i	0.824462	+	0.175245i
$732$	4.90345	−	1.04226i	0.181237	−	0.0385230i
$733$	10.0116	−	4.45745i	0.369787	−	0.164640i	−0.213426	−	0.976959i	$-0.568462\pi$
$733$	10.0116	−	4.45745i	0.369787	−	0.164640i	0.583212	+	0.812320i	$0.301796\pi$
$734$	8.04995	+	8.94038i	0.297129	+	0.329995i
$735$	0.978133	+	9.30631i	0.0360790	+	0.343269i
$736$	−4.90799	+	3.56587i	−0.180911	+	0.131440i
$737$	−0.442971	+	4.21459i	−0.0163171	+	0.155246i
$738$	−0.343022	−	0.594132i	−0.0126268	−	0.0218703i
$739$	−19.7296	+	34.1727i	−0.725765	+	1.25706i	0.232894	+	0.972502i	$0.425181\pi$
$739$	−19.7296	+	34.1727i	−0.725765	+	1.25706i	−0.958658	+	0.284559i	$0.908153\pi$
$740$	−9.02608	−	6.55783i	−0.331805	−	0.241071i
$741$	−3.22856	+	3.58568i	−0.118604	+	0.131723i
$742$	−14.8118	+	45.5859i	−0.543757	+	1.67351i
$743$	7.81776			0.286806			0.143403	−	0.989664i	$-0.454196\pi$
$743$	7.81776			0.286806			0.143403	+	0.989664i	$0.454196\pi$
$744$	−2.85546	+	4.77978i	−0.104686	+	0.175235i
$745$	−0.286277			−0.0104884
$746$	−3.04845	+	9.38217i	−0.111612	+	0.343506i
$747$	5.39883	−	5.99601i	0.197533	−	0.219383i
$748$	−6.79260	−	4.93511i	−0.248362	−	0.180446i
$749$	−2.75695	+	4.77518i	−0.100737	+	0.174481i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	1.10602	−	10.5231i	0.0403592	−	0.383992i	−0.955634	−	0.294558i	$-0.904828\pi$
$751$	1.10602	−	10.5231i	0.0403592	−	0.383992i	0.995993	−	0.0894339i	$-0.0285058\pi$
$752$	7.27380	−	5.28472i	0.265248	−	0.192714i
$753$	1.87984	+	17.8854i	0.0685050	+	0.651782i
$754$	−25.6557	−	28.4936i	−0.934326	−	1.03767i
$755$	15.3849	−	6.84979i	0.559913	−	0.249289i
$756$	−3.95607	+	0.840888i	−0.143881	+	0.0305828i
$757$	−39.4893	−	8.39371i	−1.43526	−	0.305075i	−0.576353	−	0.817201i	$-0.695525\pi$
$757$	−39.4893	−	8.39371i	−1.43526	−	0.305075i	−0.858910	+	0.512126i	$0.828858\pi$
$758$	18.3556	+	8.17246i	0.666707	+	0.296837i
$759$	2.39296	+	7.36478i	0.0868590	+	0.267325i
$760$	−0.276183	−	0.850005i	−0.0100182	−	0.0308329i
$761$	17.0997	+	7.61327i	0.619863	+	0.275981i	0.692546	−	0.721374i	$-0.256489\pi$
$761$	17.0997	+	7.61327i	0.619863	+	0.275981i	−0.0726821	+	0.997355i	$0.523156\pi$
$762$	0.291611	+	0.0619838i	0.0105639	+	0.00224543i
$763$	57.5924	−	12.2416i	2.08498	−	0.443177i
$764$	13.9881	−	6.22791i	0.506072	−	0.225318i
$765$	−4.40131	−	4.88815i	−0.159130	−	0.176731i
$766$	1.22497	+	11.6548i	0.0442600	+	0.421106i
$767$	−36.8539	+	26.7759i	−1.33072	+	0.966822i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	4.12420	+	7.14332i	0.148722	+	0.257595i	0.930756	−	0.365642i	$-0.119151\pi$
$769$	4.12420	+	7.14332i	0.148722	+	0.257595i	−0.782033	+	0.623237i	$0.785817\pi$
$770$	−2.58129	+	4.47092i	−0.0930232	+	0.161121i
$771$	−9.14325	−	6.64296i	−0.329286	−	0.239240i
$772$	−1.07692	+	1.19604i	−0.0387592	+	0.0430464i
$773$	11.8168	−	36.3682i	0.425019	−	1.30807i	−0.477957	−	0.878383i	$-0.658622\pi$
$773$	11.8168	−	36.3682i	0.425019	−	1.30807i	0.902976	−	0.429691i	$-0.141378\pi$
$774$	3.46460			0.124533
$775$	0.499371	+	5.54532i	0.0179379	+	0.199194i
$776$	−14.1318			−0.507303
$777$	13.9439	−	42.9148i	0.500234	−	1.53956i
$778$	3.95544	−	4.39296i	0.141809	−	0.157495i
$779$	0.496050	+	0.360401i	0.0177728	+	0.0129127i
$780$	−2.69931	+	4.67534i	−0.0966508	+	0.167404i
$781$	−0.934953	−	1.61939i	−0.0334552	−	0.0579462i
$782$	4.17111	−	39.6855i	0.149159	−	1.41915i
$783$	5.74577	−	4.17455i	0.205337	−	0.149186i
$784$	−0.978133	−	9.30631i	−0.0349333	−	0.332368i
$785$	0.662977	+	0.736311i	0.0236627	+	0.0262801i
$786$	−12.6599	+	5.63655i	−0.451564	+	0.201049i
$787$	−14.9371	+	3.17498i	−0.532450	+	0.113176i	−0.466288	−	0.884633i	$-0.654409\pi$
$787$	−14.9371	+	3.17498i	−0.532450	+	0.113176i	−0.0661625	+	0.997809i	$0.521076\pi$
$788$	−5.74416	−	1.22096i	−0.204627	−	0.0434949i
$789$	−6.49296	−	2.89085i	−0.231156	−	0.102917i
$790$	−1.24078	−	3.81873i	−0.0441450	−	0.135864i
$791$	−3.00303	−	9.24237i	−0.106775	−	0.328621i
$792$	−1.16610	−	0.519183i	−0.0414357	−	0.0184484i
$793$	26.4718	+	5.62676i	0.940043	+	0.199812i
$794$	−4.84397	+	1.02962i	−0.171906	+	0.0365398i
$795$	−10.8267	+	4.82035i	−0.383983	+	0.170960i
$796$	−6.20568	−	6.89211i	−0.219955	−	0.244284i
$797$	4.07907	+	38.8098i	0.144488	+	1.37471i	0.791003	+	0.611812i	$0.209559\pi$
$797$	4.07907	+	38.8098i	0.144488	+	1.37471i	−0.646515	+	0.762901i	$0.723774\pi$
$798$	2.92437	−	2.12468i	0.103522	−	0.0752128i
$799$	−6.18172	+	58.8151i	−0.218694	+	2.08073i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−1.80103	+	3.11947i	−0.0636362	+	0.110221i
$802$	−8.64982	−	6.28446i	−0.305436	−	0.221912i
$803$	−8.55027	+	9.49604i	−0.301733	+	0.335108i
$804$	1.02593	−	3.15748i	0.0361816	−	0.111356i
$805$	−24.5361			−0.864784
$806$	−24.5783	+	17.3033i	−0.865735	+	0.609482i
$807$	−21.0440			−0.740785
$808$	3.79669	−	11.6850i	0.133567	−	0.411077i
$809$	3.92585	−	4.36009i	0.138025	−	0.153293i	−0.670169	−	0.742209i	$-0.733778\pi$
$809$	3.92585	−	4.36009i	0.138025	−	0.153293i	0.808194	+	0.588916i	$0.200445\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−5.39646	+	9.34695i	−0.189495	+	0.328216i	−0.945082	−	0.326833i	$-0.894019\pi$
$811$	−5.39646	+	9.34695i	−0.189495	+	0.328216i	0.755587	+	0.655049i	$0.227352\pi$
$812$	14.3622	+	24.8760i	0.504013	+	0.872977i
$813$	−2.29082	+	21.7957i	−0.0803426	+	0.764409i
$814$	11.5214	−	8.37081i	0.403826	−	0.293397i
$815$	0.734463	+	6.98795i	0.0257271	+	0.244777i
$816$	4.40131	+	4.88815i	0.154077	+	0.171120i
$817$	−2.82878	+	1.25945i	−0.0989665	+	0.0440627i
$818$	36.2160	−	7.69795i	1.26626	−	0.269152i
$819$	−21.3573	−	4.53964i	−0.746285	−	0.158628i
$820$	0.626733	+	0.279039i	0.0218865	+	0.00974448i
$821$	2.44428	+	7.52271i	0.0853059	+	0.262545i	0.984606	−	0.174787i	$-0.0559237\pi$
$821$	2.44428	+	7.52271i	0.0853059	+	0.262545i	−0.899300	+	0.437331i	$0.855924\pi$
$822$	7.03797	+	21.6606i	0.245477	+	0.755501i
$823$	−16.5918	−	7.38714i	−0.578353	−	0.257499i	0.0966450	−	0.995319i	$-0.469189\pi$
$823$	−16.5918	−	7.38714i	−0.578353	−	0.257499i	−0.674998	+	0.737820i	$0.735856\pi$
$824$	3.52450	+	0.749155i	0.122782	+	0.0260981i
$825$	−1.24857	+	0.265391i	−0.0434695	+	0.00923972i
$826$	31.1769	−	13.8808i	1.08478	−	0.482976i
$827$	−7.77340	−	8.63323i	−0.270308	−	0.300207i	0.592674	−	0.805442i	$-0.298072\pi$
$827$	−7.77340	−	8.63323i	−0.270308	−	0.300207i	−0.862981	+	0.505236i	$0.831406\pi$
$828$	−0.634134	−	6.03338i	−0.0220377	−	0.209674i
$829$	19.4801	−	14.1532i	0.676573	−	0.491559i	−0.195646	−	0.980675i	$-0.562680\pi$
$829$	19.4801	−	14.1532i	0.676573	−	0.491559i	0.872219	+	0.489115i	$0.162680\pi$
$830$	−0.843381	+	8.02423i	−0.0292742	+	0.278525i
$831$	9.96475	+	17.2595i	0.345673	+	0.598724i
$832$	2.69931	−	4.67534i	0.0935817	−	0.162088i
$833$	49.7957	+	36.1787i	1.72532	+	1.25352i
$834$	0.460786	−	0.511755i	0.0159557	−	0.0177206i
$835$	−3.90871	+	12.0298i	−0.135267	+	0.416308i
$836$	1.14083			0.0394566
$837$	−2.71168	−	4.86279i	−0.0937295	−	0.168083i
$838$	−13.4751			−0.465490
$839$	5.89305	−	18.1369i	0.203451	−	0.626157i	−0.796323	−	0.604872i	$-0.793224\pi$
$839$	5.89305	−	18.1369i	0.203451	−	0.626157i	0.999773	−	0.0212847i	$-0.00677565\pi$
$840$	2.70627	−	3.00561i	0.0933750	−	0.103703i
$841$	−17.3459	−	12.6025i	−0.598134	−	0.434570i
$842$	1.62615	−	2.81657i	0.0560408	−	0.0970655i
$843$	−15.8113	−	27.3860i	−0.544571	−	0.943224i
$844$	2.43525	−	23.1698i	0.0838247	−	0.797539i
$845$	−13.0617	+	9.48985i	−0.449335	+	0.326461i
$846$	0.939806	+	8.94166i	0.0323112	+	0.307420i
$847$	25.3595	+	28.1645i	0.871362	+	0.967745i
$848$	10.8267	−	4.82035i	0.371790	−	0.165531i
$849$	16.8862	−	3.58928i	0.579534	−	0.123184i
$850$	6.43392	+	1.36757i	0.220682	+	0.0469073i
$851$	61.8327	+	27.5297i	2.11960	+	0.943705i
$852$	0.452684	+	1.39322i	0.0155087	+	0.0477309i
$853$	7.56853	+	23.2936i	0.259142	+	0.797556i	0.992985	+	0.118238i	$0.0377245\pi$
$853$	7.56853	+	23.2936i	0.259142	+	0.797556i	−0.733844	+	0.679318i	$0.762276\pi$
$854$	−18.5219	−	8.24650i	−0.633808	−	0.282190i
$855$	0.874218	+	0.185821i	0.0298976	+	0.00635494i
$856$	1.33353	−	0.283451i	0.0455792	−	0.00968816i
$857$	3.95837	−	1.76238i	0.135215	−	0.0602018i	−0.338014	−	0.941141i	$-0.609755\pi$
$857$	3.95837	−	1.76238i	0.135215	−	0.0602018i	0.473229	+	0.880939i	$0.343088\pi$
$858$	−4.61106	−	5.12110i	−0.157419	−	0.174831i
$859$	−2.45320	−	23.3407i	−0.0837022	−	0.796373i	−0.953181	−	0.302402i	$-0.902212\pi$
$859$	−2.45320	−	23.3407i	−0.0837022	−	0.796373i	0.869478	−	0.493971i	$-0.164455\pi$
$860$	−2.80292	+	2.03644i	−0.0955789	+	0.0694421i
$861$	−0.290032	+	2.75947i	−0.00988427	+	0.0940426i
$862$	6.43925	+	11.1531i	0.219322	+	0.379876i
$863$	−12.1922	+	21.1175i	−0.415027	+	0.718847i	−0.995431	−	0.0954811i	$-0.969561\pi$
$863$	−12.1922	+	21.1175i	−0.415027	+	0.718847i	0.580405	+	0.814328i	$0.302894\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−4.28697	+	4.76116i	−0.145761	+	0.161884i
$866$	−11.8631	+	36.5108i	−0.403124	+	1.24069i
$867$	−26.2656			−0.892025
$868$	20.7060	−	8.85140i	0.702807	−	0.300436i
$869$	5.12530			0.173864
$870$	−2.19469	+	6.75456i	−0.0744069	+	0.229001i
$871$	11.9930	−	13.3196i	0.406367	−	0.451316i
$872$	−11.7776	−	8.55696i	−0.398842	−	0.289775i
$873$	7.06592	−	12.2385i	0.239145	−	0.414211i
$874$	2.71101	+	4.69561i	0.0917014	+	0.158831i
$875$	0.422760	−	4.02229i	0.0142919	−	0.135978i
$876$	8.09878	−	5.88411i	0.273632	−	0.198806i
$877$	4.07059	+	38.7291i	0.137454	+	1.30779i	0.818057	+	0.575137i	$0.195051\pi$
$877$	4.07059	+	38.7291i	0.137454	+	1.30779i	−0.680603	+	0.732652i	$0.738282\pi$
$878$	−21.2242	−	23.5719i	−0.716284	−	0.795514i
$879$	−22.4753	+	10.0066i	−0.758073	+	0.337516i
$880$	1.24857	−	0.265391i	0.0420891	−	0.00894632i
$881$	48.5430	+	10.3181i	1.63545	+	0.347627i	0.931816	−	0.362932i	$-0.118224\pi$
$881$	48.5430	+	10.3181i	1.63545	+	0.347627i	0.703638	+	0.710558i	$0.251558\pi$
$882$	8.54857	+	3.80607i	0.287845	+	0.128157i
$883$	16.5599	+	50.9663i	0.557286	+	1.71515i	0.689827	+	0.723974i	$0.257686\pi$
$883$	16.5599	+	50.9663i	0.557286	+	1.71515i	−0.132541	+	0.991178i	$0.542314\pi$
$884$	10.9733	+	33.7723i	0.369071	+	1.13588i
$885$	7.70856	+	3.43207i	0.259120	+	0.115368i
$886$	1.45266	+	0.308772i	0.0488029	+	0.0103734i
$887$	−23.2401	+	4.93984i	−0.780327	+	0.165864i	−0.580819	−	0.814033i	$-0.697268\pi$
$887$	−23.2401	+	4.93984i	−0.780327	+	0.165864i	−0.199508	+	0.979896i	$0.563934\pi$
$888$	−10.1923	+	4.53790i	−0.342031	+	0.152282i
$889$	−0.806806	−	0.896049i	−0.0270594	−	0.0300525i
$890$	−0.376517	−	3.58232i	−0.0126209	−	0.120080i
$891$	1.03268	−	0.750284i	0.0345960	−	0.0251355i
$892$	−2.26601	+	21.5597i	−0.0758717	+	0.721871i
$893$	−4.01781	−	6.95904i	−0.134451	−	0.232875i
$894$	−0.143138	+	0.247923i	−0.00478726	+	0.00829179i
$895$	18.9541	+	13.7710i	0.633566	+	0.460312i
$896$	−2.70627	+	3.00561i	−0.0904100	+	0.100410i
$897$	10.1207	−	31.1484i	0.337921	−	1.04001i
$898$	−10.9242			−0.364545
$899$	−26.8947	+	28.9885i	−0.896989	+	0.966822i
$900$	1.00000			0.0333333
$901$	−24.0890	+	74.1383i	−0.802521	+	2.46990i
$902$	−0.585963	+	0.650778i	−0.0195104	+	0.0216685i
$903$	−11.3363	−	8.23629i	−0.377248	−	0.274087i
$904$	−1.20140	+	2.08089i	−0.0399580	+	0.0692092i
$905$	8.01578	+	13.8837i	0.266453	+	0.461511i
$906$	1.76035	−	16.7486i	0.0584837	−	0.556435i
$907$	47.3992	−	34.4375i	1.57386	−	1.14348i	0.650531	−	0.759480i	$-0.274546\pi$
$907$	47.3992	−	34.4375i	1.57386	−	1.14348i	0.923333	−	0.384000i	$-0.125454\pi$
$908$	2.33091	+	22.1771i	0.0773540	+	0.735974i
$909$	8.22118	+	9.13054i	0.272679	+	0.302841i
$910$	19.9468	−	8.88087i	0.661229	−	0.294398i
$911$	−3.97094	+	0.844048i	−0.131563	+	0.0279646i	−0.273222	−	0.961951i	$-0.588090\pi$
$911$	−3.97094	+	0.844048i	−0.131563	+	0.0279646i	0.141660	+	0.989915i	$0.454756\pi$
$912$	−0.874218	−	0.185821i	−0.0289482	−	0.00615314i
$913$	−9.40863	−	4.18899i	−0.311380	−	0.138635i
$914$	−0.650515	−	2.00208i	−0.0215171	−	0.0662229i
$915$	−1.54910	−	4.76764i	−0.0512117	−	0.157613i
$916$	9.54214	+	4.24843i	0.315281	+	0.140372i
$917$	54.8231	+	11.6530i	1.81042	+	0.384817i
$918$	−6.43392	+	1.36757i	−0.212351	+	0.0451366i
$919$	2.68652	−	1.19612i	0.0886202	−	0.0394562i	−0.361948	−	0.932198i	$-0.617888\pi$
$919$	2.68652	−	1.19612i	0.0886202	−	0.0394562i	0.450568	+	0.892742i	$0.351221\pi$
$920$	4.05936	+	4.50837i	0.133833	+	0.148637i
$921$	−0.499295	−	4.75048i	−0.0164523	−	0.156534i
$922$	−16.9904	+	12.3443i	−0.559550	+	0.406537i
$923$	−0.826666	+	7.86520i	−0.0272100	+	0.258886i
$924$	2.58129	+	4.47092i	0.0849182	+	0.147083i
$925$	−5.57842	+	9.66211i	−0.183417	+	0.317688i
$926$	31.2768	+	22.7239i	1.02782	+	0.746755i
$927$	−2.41104	+	2.67773i	−0.0791888	+	0.0879481i
$928$	2.19469	−	6.75456i	0.0720442	−	0.221729i
$929$	−11.2512			−0.369139			−0.184570	−	0.982819i	$-0.559089\pi$
$929$	−11.2512			−0.369139			−0.184570	+	0.982819i	$0.559089\pi$
$930$	5.05208	+	2.34019i	0.165664	+	0.0767380i
$931$	−8.36332			−0.274097
$932$	−4.39053	+	13.5127i	−0.143817	+	0.442622i
$933$	−7.28692	+	8.09295i	−0.238563	+	0.264951i
$934$	7.69769	+	5.59270i	0.251876	+	0.182999i
$935$	−4.19806	+	7.27125i	−0.137291	+	0.237795i
$936$	2.69931	+	4.67534i	0.0882297	+	0.152818i
$937$	−2.39034	+	22.7426i	−0.0780890	+	0.742967i	0.883492	+	0.468446i	$0.155186\pi$
$937$	−2.39034	+	22.7426i	−0.0780890	+	0.742967i	−0.961581	+	0.274521i	$0.911481\pi$
$938$	−10.8630	+	7.89245i	−0.354690	+	0.257698i
$939$	−0.427460	−	4.06701i	−0.0139496	−	0.132722i
$940$	−6.01609	−	6.68155i	−0.196223	−	0.217928i
$941$	47.5925	−	21.1895i	1.55147	−	0.690759i	0.560916	−	0.827873i	$-0.310449\pi$
$941$	47.5925	−	21.1895i	1.55147	−	0.690759i	0.990555	+	0.137114i	$0.0437825\pi$
$942$	0.969153	−	0.206000i	0.0315767	−	0.00671183i
$943$	−4.07102	−	0.865321i	−0.132571	−	0.0281787i
$944$	−7.70856	−	3.43207i	−0.250892	−	0.111704i
$945$	1.24980	+	3.84650i	0.0406561	+	0.125127i
$946$	−1.36661	−	4.20598i	−0.0444322	−	0.136748i
$947$	−3.62090	−	1.61213i	−0.117664	−	0.0523872i	0.347061	−	0.937843i	$-0.387180\pi$
$947$	−3.62090	−	1.61213i	−0.117664	−	0.0523872i	−0.464724	+	0.885456i	$0.653846\pi$
$948$	−3.92750	−	0.834817i	−0.127559	−	0.0271136i
$949$	52.8627	−	11.2363i	1.71599	−	0.364746i
$950$	−0.816480	+	0.363520i	−0.0264901	+	0.0117942i
$951$	14.2035	+	15.7746i	0.460580	+	0.511526i
$952$	−2.78077	−	26.4573i	−0.0901253	−	0.857485i
$953$	6.10375	−	4.43463i	0.197720	−	0.143652i	−0.484520	−	0.874780i	$-0.661006\pi$
$953$	6.10375	−	4.43463i	0.197720	−	0.143652i	0.682240	+	0.731128i	$0.261006\pi$
$954$	−1.23880	+	11.7864i	−0.0401075	+	0.381597i
$955$	−7.65595	−	13.2605i	−0.247741	−	0.429099i
$956$	0.408157	−	0.706949i	0.0132007	−	0.0228644i
$957$	−7.33424	−	5.32864i	−0.237082	−	0.172250i
$958$	10.0405	−	11.1511i	0.324394	−	0.360276i
$959$	28.4647	−	87.6053i	0.919173	−	2.82892i
$960$	−1.00000			−0.0322749
$961$	20.0470	+	23.6457i	0.646677	+	0.762764i
$962$	−60.2316			−1.94194
$963$	−0.421291	+	1.29660i	−0.0135759	+	0.0417823i
$964$	−19.3530	+	21.4937i	−0.623317	+	0.692264i
$965$	1.30206	+	0.946000i	0.0419147	+	0.0304528i
$966$	−12.2681	+	21.2489i	−0.394718	+	0.683672i
$967$	−27.4790	−	47.5950i	−0.883665	−	1.53055i	−0.847237	−	0.531216i	$-0.821735\pi$
$967$	−27.4790	−	47.5950i	−0.883665	−	1.53055i	−0.0364280	−	0.999336i	$-0.511598\pi$
$968$	0.979500	−	9.31932i	0.0314823	−	0.299534i
$969$	4.75602	−	3.45545i	0.152786	−	0.111005i
$970$	1.47718	+	14.0544i	0.0474293	+	0.451260i
$971$	−11.2345	−	12.4772i	−0.360532	−	0.400411i	0.535403	−	0.844597i	$-0.320160\pi$
$971$	−11.2345	−	12.4772i	−0.360532	−	0.400411i	−0.895935	+	0.444186i	$0.853493\pi$
$972$	−0.913545	+	0.406737i	−0.0293020	+	0.0130461i
$973$	−2.72428	+	0.579064i	−0.0873365	+	0.0185639i
$974$	35.8733	+	7.62510i	1.14945	+	0.244324i
$975$	4.93188	+	2.19582i	0.157947	+	0.0703224i
$976$	1.54910	+	4.76764i	0.0495855	+	0.152608i
$977$	−7.36583	−	22.6697i	−0.235654	−	0.725267i	−0.997034	−	0.0769619i	$-0.975478\pi$
$977$	−7.36583	−	22.6697i	−0.235654	−	0.725267i	0.761380	−	0.648305i	$-0.224522\pi$
$978$	6.41897	+	2.85791i	0.205256	+	0.0913859i
$979$	4.49741	+	0.955953i	0.143738	+	0.0305524i
$980$	−9.15309	+	1.94555i	−0.292385	+	0.0621483i
$981$	13.2994	−	5.92126i	0.424616	−	0.189051i
$982$	24.2209	+	26.9001i	0.772921	+	0.858416i
$983$	3.91344	+	37.2339i	0.124819	+	1.18758i	0.860212	+	0.509936i	$0.170331\pi$
$983$	3.91344	+	37.2339i	0.124819	+	1.18758i	−0.735393	+	0.677641i	$0.763002\pi$
$984$	0.555022	−	0.403247i	0.0176934	−	0.0128550i
$985$	−0.613842	+	5.84032i	−0.0195586	+	0.186088i
$986$	23.3578	+	40.4569i	0.743863	+	1.28841i
$987$	18.1816	−	31.4915i	0.578728	−	1.00239i
$988$	−3.90351	−	2.83607i	−0.124187	−	0.0902274i
$989$	14.0641	−	15.6197i	0.447211	−	0.496678i
$990$	−0.394448	+	1.21399i	−0.0125364	+	0.0385830i
$991$	−37.2217			−1.18238			−0.591192	−	0.806531i	$-0.701343\pi$
$991$	−37.2217			−1.18238			−0.591192	+	0.806531i	$0.701343\pi$
$992$	−5.05208	−	2.34019i	−0.160404	−	0.0743013i
$993$	3.29820			0.104665
$994$	1.83086	−	5.63480i	0.0580713	−	0.178725i
$995$	−6.20568	+	6.89211i	−0.196733	+	0.218494i
$996$	6.52750	+	4.74250i	0.206832	+	0.150272i
$997$	2.02306	−	3.50405i	0.0640710	−	0.110974i	−0.832211	−	0.554460i	$-0.812925\pi$
$997$	2.02306	−	3.50405i	0.0640710	−	0.110974i	0.896282	+	0.443486i	$0.146258\pi$
$998$	16.1734	+	28.0132i	0.511961	+	0.886742i
$999$	1.16621	−	11.0957i	0.0368972	−	0.351053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.b.541.2	yes	16
31.20	even	15	inner	930.2.bg.b.361.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.b.361.2	✓	16	31.20	even	15	inner
930.2.bg.b.541.2	yes	16	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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.422760 - 4.02229i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(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} +(0.422760 - 4.02229i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-1.16610 + 0.519183i) q^{11} +(0.978148 - 0.207912i) q^{12} +(5.28065 + 1.12244i) q^{13} +(-3.69479 - 1.64503i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.00899 - 2.67537i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(0.874218 - 0.185821i) q^{19} +(0.913545 - 0.406737i) q^{20} +(2.70627 + 3.00561i) q^{21} +(0.133426 + 1.26947i) q^{22} +(-4.90799 + 3.56587i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.69931 - 4.67534i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.70627 + 3.00561i) q^{28} +(2.19469 - 6.75456i) q^{29} -1.00000 q^{30} +(-5.05208 - 2.34019i) q^{31} +1.00000 q^{32} +(0.394448 - 1.21399i) q^{33} +(-4.40131 + 4.88815i) q^{34} +(3.27203 + 2.37727i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.57842 - 9.66211i) q^{37} +(0.0934222 - 0.888852i) q^{38} +(-4.36758 + 3.17323i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(0.459053 + 0.509830i) q^{41} +(3.69479 - 1.64503i) q^{42} +(-3.38889 + 0.720332i) q^{43} +(1.24857 + 0.265391i) q^{44} +(0.913545 + 0.406737i) q^{45} +(1.87469 + 5.76969i) q^{46} +(-2.77834 - 8.55086i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(-9.15309 - 1.94555i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(6.00899 - 2.67537i) q^{51} +(-3.61238 - 4.01196i) q^{52} +(-1.23880 - 11.7864i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.133426 - 1.26947i) q^{55} +(2.02222 + 3.50260i) q^{56} +(-0.446874 + 0.774009i) q^{57} +(-5.74577 - 4.17455i) q^{58} +(-5.64617 + 6.27070i) q^{59} +(-0.309017 + 0.951057i) q^{60} +5.01299 q^{61} +(-3.78684 + 4.08165i) q^{62} -4.04445 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.61238 + 4.01196i) q^{65} +(-1.03268 - 0.750284i) q^{66} +(1.65998 - 2.87518i) q^{67} +(3.28883 + 5.69642i) q^{68} +(0.634134 - 6.03338i) q^{69} +(3.27203 - 2.37727i) q^{70} +(0.153125 + 1.45689i) q^{71} +(0.669131 + 0.743145i) q^{72} +(9.14518 - 4.07170i) q^{73} +(-10.9130 + 2.31964i) q^{74} +(0.978148 + 0.207912i) q^{75} +(-0.816480 - 0.363520i) q^{76} +(1.59532 + 4.90990i) q^{77} +(1.66827 + 5.13439i) q^{78} +(-3.66811 - 1.63315i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.626733 - 0.279039i) q^{82} +(5.39883 + 5.99601i) q^{83} +(-0.422760 - 4.02229i) q^{84} +(5.32144 - 3.86625i) q^{85} +(-0.362150 + 3.44562i) q^{86} +(3.55108 + 6.15065i) q^{87} +(0.638230 - 1.10545i) q^{88} +(-2.91413 - 2.11724i) q^{89} +(0.669131 - 0.743145i) q^{90} +(6.74722 - 20.7658i) q^{91} +6.06661 q^{92} +(5.11960 - 2.18853i) q^{93} -8.99091 q^{94} +(-0.276183 + 0.850005i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(11.4329 + 8.30648i) q^{97} +(-4.67879 + 8.10390i) q^{98} +(0.638230 + 1.10545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Introduction

L-functions

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