LMFDB - Embedded newform 930.2.bg.i.361.3

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			361.3
Character	$\chi$	$=$	930.361
Dual form			930.2.bg.i.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.375052 + 3.56838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(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} +(0.375052 + 3.56838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.669131 - 0.743145i) q^{10} +(2.46539 + 1.09766i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(3.21645 - 0.683678i) q^{13} +(3.27784 - 1.45939i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.03306 + 2.68609i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-4.82043 - 1.02461i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-2.40087 + 2.66643i) q^{21} +(0.282091 - 2.68392i) q^{22} +(-5.88315 - 4.27436i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.64416 - 2.84776i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.40087 - 2.66643i) q^{28} +(0.732685 + 2.25497i) q^{29} +1.00000 q^{30} +(3.38195 + 4.42294i) q^{31} -1.00000 q^{32} +(0.833945 + 2.56662i) q^{33} +(4.41894 + 4.90773i) q^{34} +(-2.90278 + 2.10900i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.37534 + 7.57832i) q^{37} +(0.515128 + 4.90112i) q^{38} +(2.66030 + 1.93282i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(2.52273 - 2.80177i) q^{41} +(3.27784 + 1.45939i) q^{42} +(11.0650 + 2.35194i) q^{43} +(-2.63973 + 0.561092i) q^{44} +(-0.913545 + 0.406737i) q^{45} +(-2.24716 + 6.91606i) q^{46} +(0.373373 - 1.14913i) q^{47} +(0.913545 - 0.406737i) q^{48} +(-5.74566 + 1.22128i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-6.03306 - 2.68609i) q^{51} +(-2.20031 + 2.44369i) q^{52} +(0.683413 - 6.50224i) q^{53} +(0.809017 + 0.587785i) q^{54} +(0.282091 + 2.68392i) q^{55} +(-1.79402 + 3.10733i) q^{56} +(-2.46406 - 4.26787i) q^{57} +(1.91819 - 1.39365i) q^{58} +(6.68937 + 7.42930i) q^{59} +(-0.309017 - 0.951057i) q^{60} -8.69801 q^{61} +(3.16139 - 4.58319i) q^{62} -3.58804 q^{63} +(0.309017 + 0.951057i) q^{64} +(2.20031 + 2.44369i) q^{65} +(2.18330 - 1.58626i) q^{66} +(2.52065 + 4.36589i) q^{67} +(3.30200 - 5.71924i) q^{68} +(-0.760128 - 7.23214i) q^{69} +(2.90278 + 2.10900i) q^{70} +(0.818543 - 7.78792i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(1.24852 + 0.555877i) q^{73} +(8.55946 + 1.81937i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(4.50206 - 2.00445i) q^{76} +(-2.99223 + 9.20912i) q^{77} +(1.01614 - 3.12737i) q^{78} +(11.6334 - 5.17954i) q^{79} +(0.978148 - 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.44421 - 1.53346i) q^{82} +(-6.51668 + 7.23751i) q^{83} +(0.375052 - 3.56838i) q^{84} +(-5.34275 - 3.88174i) q^{85} +(-1.18245 - 11.2502i) q^{86} +(-1.18551 + 2.05336i) q^{87} +(1.34935 + 2.33714i) q^{88} +(10.7738 - 7.82765i) q^{89} +(0.669131 + 0.743145i) q^{90} +(3.64596 + 11.2211i) q^{91} +7.27197 q^{92} +(-1.02392 + 5.47280i) q^{93} -1.20826 q^{94} +(-1.52287 - 4.68692i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-6.58245 + 4.78243i) q^{97} +(2.93701 + 5.08705i) q^{98} +(-1.34935 + 2.33714i) 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} - 7 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 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{15}\right)$

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
$7$	0.375052	+	3.56838i	0.141756	+	1.34872i	0.801844	+	0.597533i	$0.203852\pi$
$7$	0.375052	+	3.56838i	0.141756	+	1.34872i	−0.660088	+	0.751189i	$0.729481\pi$
$8$	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
$11$	2.46539	+	1.09766i	0.743342	+	0.330957i	0.743224	−	0.669043i	$-0.233296\pi$
$11$	2.46539	+	1.09766i	0.743342	+	0.330957i	0.000118087		1.00000i	$0.499962\pi$
$12$	−0.978148	−	0.207912i	−0.282367	−	0.0600189i
$13$	3.21645	−	0.683678i	0.892084	−	0.189618i	0.261005	−	0.965337i	$-0.415946\pi$
$13$	3.21645	−	0.683678i	0.892084	−	0.189618i	0.631078	+	0.775719i	$0.282613\pi$
$14$	3.27784	−	1.45939i	0.876039	−	0.390038i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−6.03306	+	2.68609i	−1.46323	+	0.651473i	−0.975195	−	0.221349i	$-0.928954\pi$
$17$	−6.03306	+	2.68609i	−1.46323	+	0.651473i	−0.488038	+	0.872822i	$0.662287\pi$
$18$	0.978148	−	0.207912i	0.230552	−	0.0490053i
$19$	−4.82043	−	1.02461i	−1.10588	−	0.235062i	−0.381437	−	0.924395i	$-0.624571\pi$
$19$	−4.82043	−	1.02461i	−1.10588	−	0.235062i	−0.724445	+	0.689333i	$0.757904\pi$
$20$	−0.913545	−	0.406737i	−0.204275	−	0.0909491i
$21$	−2.40087	+	2.66643i	−0.523912	+	0.581863i
$22$	0.282091	−	2.68392i	0.0601420	−	0.572213i
$23$	−5.88315	−	4.27436i	−1.22672	−	0.891266i	−0.230082	−	0.973171i	$-0.573899\pi$
$23$	−5.88315	−	4.27436i	−1.22672	−	0.891266i	−0.996640	+	0.0819058i	$0.973899\pi$
$24$	0.104528	+	0.994522i	0.0213368	+	0.203006i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.64416	−	2.84776i	−0.322445	−	0.558492i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−2.40087	−	2.66643i	−0.453721	−	0.503908i
$29$	0.732685	+	2.25497i	0.136056	+	0.418738i	0.995753	−	0.0920671i	$-0.0293474\pi$
$29$	0.732685	+	2.25497i	0.136056	+	0.418738i	−0.859697	+	0.510805i	$0.829347\pi$
$30$	1.00000			0.182574
$31$	3.38195	+	4.42294i	0.607416	+	0.794384i
$31$	3.38195	+	4.42294i	0.607416	+	0.794384i
$32$	−1.00000			−0.176777
$33$	0.833945	+	2.56662i	0.145171	+	0.446791i
$34$	4.41894	+	4.90773i	0.757843	+	0.841670i
$35$	−2.90278	+	2.10900i	−0.490660	+	0.356485i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.37534	+	7.57832i	−0.719302	+	1.24587i	0.241975	+	0.970283i	$0.422205\pi$
$37$	−4.37534	+	7.57832i	−0.719302	+	1.24587i	−0.961277	+	0.275585i	$0.911128\pi$
$38$	0.515128	+	4.90112i	0.0835649	+	0.795067i
$39$	2.66030	+	1.93282i	0.425989	+	0.309499i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	2.52273	−	2.80177i	0.393984	−	0.437563i	−0.513219	−	0.858258i	$-0.671547\pi$
$41$	2.52273	−	2.80177i	0.393984	−	0.437563i	0.907202	+	0.420695i	$0.138214\pi$
$42$	3.27784	+	1.45939i	0.505781	+	0.225188i
$43$	11.0650	+	2.35194i	1.68740	+	0.358668i	0.948897	−	0.315585i	$-0.102201\pi$
$43$	11.0650	+	2.35194i	1.68740	+	0.358668i	0.738501	+	0.674253i	$0.235534\pi$
$44$	−2.63973	+	0.561092i	−0.397954	+	0.0845877i
$45$	−0.913545	+	0.406737i	−0.136183	+	0.0606327i
$46$	−2.24716	+	6.91606i	−0.331326	+	1.01972i
$47$	0.373373	−	1.14913i	0.0544621	−	0.167617i	−0.920126	−	0.391623i	$-0.871914\pi$
$47$	0.373373	−	1.14913i	0.0544621	−	0.167617i	0.974588	+	0.224006i	$0.0719136\pi$
$48$	0.913545	−	0.406737i	0.131859	−	0.0587074i
$49$	−5.74566	+	1.22128i	−0.820808	+	0.174468i
$50$	0.978148	+	0.207912i	0.138331	+	0.0294032i
$51$	−6.03306	−	2.68609i	−0.844798	−	0.376128i
$52$	−2.20031	+	2.44369i	−0.305128	+	0.338879i
$53$	0.683413	−	6.50224i	0.0938740	−	0.893151i	−0.841682	−	0.539973i	$-0.818434\pi$
$53$	0.683413	−	6.50224i	0.0938740	−	0.893151i	0.935556	−	0.353178i	$-0.114899\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	0.282091	+	2.68392i	0.0380372	+	0.361899i
$56$	−1.79402	+	3.10733i	−0.239736	+	0.415235i
$57$	−2.46406	−	4.26787i	−0.326372	−	0.565294i
$58$	1.91819	−	1.39365i	0.251871	−	0.182995i
$59$	6.68937	+	7.42930i	0.870882	+	0.967213i	0.999701	−	0.0244553i	$-0.00778514\pi$
$59$	6.68937	+	7.42930i	0.870882	+	0.967213i	−0.128819	+	0.991668i	$0.541118\pi$
$60$	−0.309017	−	0.951057i	−0.0398939	−	0.122781i
$61$	−8.69801			−1.11367			−0.556833	−	0.830624i	$-0.687984\pi$
$61$	−8.69801			−1.11367			−0.556833	+	0.830624i	$0.687984\pi$
$62$	3.16139	−	4.58319i	0.401497	−	0.582065i
$63$	−3.58804			−0.452050
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.20031	+	2.44369i	0.272915	+	0.303103i
$66$	2.18330	−	1.58626i	0.268745	−	0.195255i
$67$	2.52065	+	4.36589i	0.307946	+	0.533378i	0.977913	−	0.209013i	$-0.0670251\pi$
$67$	2.52065	+	4.36589i	0.307946	+	0.533378i	−0.669967	+	0.742391i	$0.733692\pi$
$68$	3.30200	−	5.71924i	0.400427	−	0.693560i
$69$	−0.760128	−	7.23214i	−0.0915087	−	0.870647i
$70$	2.90278	+	2.10900i	0.346949	+	0.252073i
$71$	0.818543	−	7.78792i	0.0971432	−	0.924256i	−0.832060	−	0.554686i	$-0.812838\pi$
$71$	0.818543	−	7.78792i	0.0971432	−	0.924256i	0.929203	−	0.369570i	$-0.120495\pi$
$72$	−0.669131	+	0.743145i	−0.0788578	+	0.0875805i
$73$	1.24852	+	0.555877i	0.146128	+	0.0650604i	0.478498	−	0.878089i	$-0.341181\pi$
$73$	1.24852	+	0.555877i	0.146128	+	0.0650604i	−0.332370	+	0.943149i	$0.607848\pi$
$74$	8.55946	+	1.81937i	0.995017	+	0.211497i
$75$	−0.978148	+	0.207912i	−0.112947	+	0.0240076i
$76$	4.50206	−	2.00445i	0.516422	−	0.229926i
$77$	−2.99223	+	9.20912i	−0.340996	+	1.04948i
$78$	1.01614	−	3.12737i	0.115056	−	0.354105i
$79$	11.6334	−	5.17954i	1.30886	−	0.582743i	0.370641	−	0.928776i	$-0.379138\pi$
$79$	11.6334	−	5.17954i	1.30886	−	0.582743i	0.938222	+	0.346033i	$0.112471\pi$
$80$	0.978148	−	0.207912i	0.109360	−	0.0232452i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−3.44421	−	1.53346i	−0.380349	−	0.169342i
$83$	−6.51668	+	7.23751i	−0.715298	+	0.794419i	−0.985733	−	0.168319i	$-0.946166\pi$
$83$	−6.51668	+	7.23751i	−0.715298	+	0.794419i	0.270434	+	0.962738i	$0.412833\pi$
$84$	0.375052	−	3.56838i	0.0409215	−	0.389342i
$85$	−5.34275	−	3.88174i	−0.579503	−	0.421034i
$86$	−1.18245	−	11.2502i	−0.127507	−	1.21314i
$87$	−1.18551	+	2.05336i	−0.127100	+	0.220144i
$88$	1.34935	+	2.33714i	0.143841	+	0.249140i
$89$	10.7738	−	7.82765i	1.14202	−	0.829729i	0.154624	−	0.987973i	$-0.450583\pi$
$89$	10.7738	−	7.82765i	1.14202	−	0.829729i	0.987400	+	0.158244i	$0.0505834\pi$
$90$	0.669131	+	0.743145i	0.0705326	+	0.0783343i
$91$	3.64596	+	11.2211i	0.382201	+	1.17629i
$92$	7.27197			0.758156
$93$	−1.02392	+	5.47280i	−0.106176	+	0.567503i
$94$	−1.20826			−0.124623
$95$	−1.52287	−	4.68692i	−0.156243	−	0.480868i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	−6.58245	+	4.78243i	−0.668347	+	0.485582i	−0.869471	−	0.493983i	$-0.835540\pi$
$97$	−6.58245	+	4.78243i	−0.668347	+	0.485582i	0.201125	+	0.979566i	$0.435540\pi$
$98$	2.93701	+	5.08705i	0.296683	+	0.513870i
$99$	−1.34935	+	2.33714i	−0.135615	+	0.234892i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	0.327905	+	0.238237i	0.0326278	+	0.0237055i	0.603980	−	0.797000i	$-0.293581\pi$
$101$	0.327905	+	0.238237i	0.0326278	+	0.0237055i	−0.571352	+	0.820705i	$0.693581\pi$
$102$	−0.690307	+	6.56783i	−0.0683506	+	0.650312i
$103$	−4.04724	+	4.49492i	−0.398787	+	0.442898i	−0.908777	−	0.417283i	$-0.862982\pi$
$103$	−4.04724	+	4.49492i	−0.398787	+	0.442898i	0.509990	+	0.860180i	$0.329649\pi$
$104$	3.00402	+	1.33748i	0.294569	+	0.131150i
$105$	−3.50963	−	0.745995i	−0.342505	−	0.0728017i
$106$	−6.39518	+	1.35934i	−0.621155	+	0.132031i
$107$	6.46221	−	2.87716i	0.624725	−	0.278146i	−0.0698590	−	0.997557i	$-0.522255\pi$
$107$	6.46221	−	2.87716i	0.624725	−	0.278146i	0.694584	+	0.719411i	$0.255588\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−3.40564	+	10.4815i	−0.326201	+	1.00394i	0.644695	+	0.764440i	$0.276984\pi$
$109$	−3.40564	+	10.4815i	−0.326201	+	1.00394i	−0.970896	+	0.239503i	$0.923016\pi$
$110$	2.46539	−	1.09766i	0.235065	−	0.104658i
$111$	−8.55946	+	1.81937i	−0.812428	+	0.172687i
$112$	3.50963	+	0.745995i	0.331629	+	0.0704899i
$113$	6.70246	+	2.98413i	0.630514	+	0.280723i	0.697008	−	0.717064i	$-0.254514\pi$
$113$	6.70246	+	2.98413i	0.630514	+	0.280723i	−0.0664931	+	0.997787i	$0.521181\pi$
$114$	−3.29755	+	3.66230i	−0.308844	+	0.343006i
$115$	0.760128	−	7.23214i	0.0708823	−	0.674400i
$116$	−1.91819	−	1.39365i	−0.178100	−	0.129397i
$117$	0.343722	+	3.27030i	0.0317771	+	0.302339i
$118$	4.99856	−	8.65775i	0.460154	−	0.797011i
$119$	−11.8477	−	20.5208i	−1.08608	−	1.88114i
$120$	−0.809017	+	0.587785i	−0.0738528	+	0.0536572i
$121$	−2.48717	−	2.76228i	−0.226106	−	0.251116i
$122$	2.68783	+	8.27230i	0.243345	+	0.748939i
$123$	3.77015			0.339943
$124$	−5.33579	−	1.59038i	−0.479168	−	0.142820i
$125$	−1.00000			−0.0894427
$126$	1.10876	+	3.41243i	0.0987766	+	0.304003i
$127$	10.9193	+	12.1271i	0.968928	+	1.07610i	0.997070	+	0.0764993i	$0.0243743\pi$
$127$	10.9193	+	12.1271i	0.968928	+	1.07610i	−0.0281420	+	0.999604i	$0.508959\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	5.65610	+	9.79666i	0.497992	+	0.862548i
$130$	1.64416	−	2.84776i	0.144202	−	0.249765i
$131$	−1.87187	−	17.8097i	−0.163546	−	1.55604i	−0.701256	−	0.712909i	$-0.747377\pi$
$131$	−1.87187	−	17.8097i	−0.163546	−	1.55604i	0.537710	−	0.843130i	$-0.319290\pi$
$132$	−2.18330	−	1.58626i	−0.190031	−	0.138066i
$133$	1.84830	−	17.5854i	0.160268	−	1.52485i
$134$	3.37328	−	3.74641i	0.291407	−	0.323641i
$135$	−0.913545	−	0.406737i	−0.0786255	−	0.0350063i
$136$	−6.45969	−	1.37305i	−0.553914	−	0.117738i
$137$	4.52876	−	0.962618i	0.386918	−	0.0822420i	−0.0103456	−	0.999946i	$-0.503293\pi$
$137$	4.52876	−	0.962618i	0.386918	−	0.0822420i	0.397264	+	0.917704i	$0.369960\pi$
$138$	−6.64328	+	2.95778i	−0.565513	+	0.251783i
$139$	2.54297	−	7.82646i	0.215692	−	0.663832i	−0.783412	−	0.621503i	$-0.786522\pi$
$139$	2.54297	−	7.82646i	0.215692	−	0.663832i	0.999104	−	0.0423287i	$-0.0134777\pi$
$140$	1.10876	−	3.41243i	0.0937077	−	0.288403i
$141$	1.10380	−	0.491444i	0.0929569	−	0.0413871i
$142$	−7.65970	+	1.62812i	−0.642787	+	0.136629i
$143$	8.68025	+	1.84504i	0.725879	+	0.154290i
$144$	0.913545	+	0.406737i	0.0761288	+	0.0338947i
$145$	−1.58652	+	1.76201i	−0.131753	+	0.146327i
$146$	0.142856	−	1.35919i	0.0118229	−	0.112487i
$147$	−4.75218	−	3.45266i	−0.391953	−	0.284771i
$148$	−0.914696	−	8.70275i	−0.0751875	−	0.715362i
$149$	−5.53984	+	9.59528i	−0.453841	+	0.786076i	−0.998621	−	0.0525035i	$-0.983280\pi$
$149$	−5.53984	+	9.59528i	−0.453841	+	0.786076i	0.544780	+	0.838579i	$0.316613\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	12.0720	−	8.77080i	0.982403	−	0.713758i	0.0241590	−	0.999708i	$-0.492309\pi$
$151$	12.0720	−	8.77080i	0.982403	−	0.713758i	0.958244	+	0.285950i	$0.0923092\pi$
$152$	−3.29755	−	3.66230i	−0.267467	−	0.297052i
$153$	−2.04075	−	6.28078i	−0.164985	−	0.507771i
$154$	9.68304			0.780282
$155$	−2.13941	+	5.14032i	−0.171841	+	0.412881i
$156$	−3.28831			−0.263276
$157$	4.59930	+	14.1552i	0.367064	+	1.12971i	0.948678	+	0.316242i	$0.102421\pi$
$157$	4.59930	+	14.1552i	0.367064	+	1.12971i	−0.581614	+	0.813465i	$0.697579\pi$
$158$	−8.52096	−	9.46348i	−0.677891	−	0.752874i
$159$	5.28940	−	3.84297i	0.419476	−	0.304768i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	13.0461	−	22.5964i	1.02817	−	1.78085i
$162$	0.104528	+	0.994522i	0.00821253	+	0.0781370i
$163$	−3.14466	−	2.28473i	−0.246308	−	0.178954i	0.457781	−	0.889065i	$-0.348644\pi$
$163$	−3.14466	−	2.28473i	−0.246308	−	0.178954i	−0.704089	+	0.710112i	$0.748644\pi$
$164$	−0.394088	+	3.74950i	−0.0307731	+	0.292787i
$165$	−1.80578	+	2.00553i	−0.140580	+	0.156130i
$166$	8.89704	+	3.96122i	0.690544	+	0.307450i
$167$	−2.38819	−	0.507625i	−0.184804	−	0.0392812i	0.114580	−	0.993414i	$-0.463448\pi$
$167$	−2.38819	−	0.507625i	−0.184804	−	0.0392812i	−0.299384	+	0.954133i	$0.596781\pi$
$168$	−3.50963	+	0.745995i	−0.270774	+	0.0575548i
$169$	−1.99793	+	0.889537i	−0.153687	+	0.0684259i
$170$	−2.04075	+	6.28078i	−0.156518	+	0.481714i
$171$	1.52287	−	4.68692i	0.116457	−	0.358418i
$172$	−10.3342	+	4.60109i	−0.787977	+	0.350830i
$173$	17.0202	−	3.61777i	1.29403	−	0.275054i	0.491084	−	0.871112i	$-0.336601\pi$
$173$	17.0202	−	3.61777i	1.29403	−	0.275054i	0.802941	+	0.596058i	$0.203267\pi$
$174$	2.31921	+	0.492962i	0.175819	+	0.0373714i
$175$	−3.27784	−	1.45939i	−0.247781	−	0.110319i
$176$	1.80578	−	2.00553i	0.136116	−	0.151172i
$177$	−1.04498	+	9.94235i	−0.0785457	+	0.747313i
$178$	−10.7738	−	7.82765i	−0.807533	−	0.586707i
$179$	−0.297065	−	2.82638i	−0.0222036	−	0.211254i	−0.999999	−	0.00168954i	$-0.999462\pi$
$179$	−0.297065	−	2.82638i	−0.0222036	−	0.211254i	0.977795	−	0.209564i	$-0.0672045\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	8.29135	+	14.3610i	0.616291	+	1.06745i	0.990157	+	0.139964i	$0.0446988\pi$
$181$	8.29135	+	14.3610i	0.616291	+	1.06745i	−0.373865	+	0.927483i	$0.621968\pi$
$182$	9.54526	−	6.93504i	0.707542	−	0.514059i
$183$	−5.82010	−	6.46388i	−0.430234	−	0.477824i
$184$	−2.24716	−	6.91606i	−0.165663	−	0.509859i
$185$	−8.75069			−0.643363
$186$	5.52136	−	0.717380i	0.404845	−	0.0526009i
$187$	−17.8222			−1.30329
$188$	0.373373	+	1.14913i	0.0272311	+	0.0838086i
$189$	−2.40087	−	2.66643i	−0.174637	−	0.193954i
$190$	−3.98693	+	2.89667i	−0.289242	+	0.210147i
$191$	−10.7748	−	18.6626i	−0.779640	−	1.35038i	−0.932150	−	0.362074i	$-0.882069\pi$
$191$	−10.7748	−	18.6626i	−0.779640	−	1.35038i	0.152510	−	0.988302i	$-0.451264\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	0.611026	+	5.81352i	0.0439826	+	0.418466i	0.994254	+	0.107044i	$0.0341386\pi$
$193$	0.611026	+	5.81352i	0.0439826	+	0.418466i	−0.950272	+	0.311422i	$0.899195\pi$
$194$	6.58245	+	4.78243i	0.472592	+	0.343358i
$195$	−0.343722	+	3.27030i	−0.0246145	+	0.234191i
$196$	3.93049	−	4.36525i	0.280749	−	0.311803i
$197$	−14.1244	−	6.28860i	−1.00632	−	0.448044i	−0.163678	−	0.986514i	$-0.552336\pi$
$197$	−14.1244	−	6.28860i	−1.00632	−	0.448044i	−0.842645	+	0.538470i	$0.819003\pi$
$198$	2.63973	+	0.561092i	0.187597	+	0.0398750i
$199$	9.55526	−	2.03103i	0.677354	−	0.143976i	0.143626	−	0.989632i	$-0.454124\pi$
$199$	9.55526	−	2.03103i	0.677354	−	0.143976i	0.533728	+	0.845656i	$0.320790\pi$
$200$	−0.913545	+	0.406737i	−0.0645974	+	0.0287606i
$201$	−1.55785	+	4.79455i	−0.109882	+	0.338182i
$202$	0.125249	−	0.385476i	0.00881246	−	0.0271220i
$203$	−7.77181	+	3.46023i	−0.545474	+	0.242861i
$204$	6.45969	−	1.37305i	0.452269	−	0.0961328i
$205$	3.68777	+	0.783859i	0.257565	+	0.0547471i
$206$	5.52559	+	2.46015i	0.384986	+	0.171407i
$207$	4.86590	−	5.40413i	0.338203	−	0.375613i
$208$	0.343722	−	3.27030i	0.0238328	−	0.226754i
$209$	−10.7595	−	7.81726i	−0.744252	−	0.540731i
$210$	0.375052	+	3.56838i	0.0258811	+	0.246242i
$211$	7.19404	−	12.4604i	0.495258	−	0.857813i	−0.504727	−	0.863279i	$-0.668407\pi$
$211$	7.19404	−	12.4604i	0.495258	−	0.857813i	0.999985	+	0.00546648i	$0.00174004\pi$
$212$	3.26903	+	5.66212i	0.224518	+	0.388876i
$213$	6.33526	−	4.60284i	0.434085	−	0.315381i
$214$	−4.73328	−	5.25684i	−0.323560	−	0.359350i
$215$	3.49566	+	10.7585i	0.238402	+	0.733727i
$216$	−1.00000			−0.0680414
$217$	−14.5144	+	13.7269i	−0.985298	+	0.931844i
$218$	11.0209			0.746428
$219$	0.422326	+	1.29978i	0.0285381	+	0.0878313i
$220$	−1.80578	−	2.00553i	−0.121746	−	0.135213i
$221$	−17.5686	+	12.7644i	−1.18179	+	0.858624i
$222$	4.37534	+	7.57832i	0.293654	+	0.508623i
$223$	−9.91150	+	17.1672i	−0.663723	+	1.14960i	0.315907	+	0.948790i	$0.397691\pi$
$223$	−9.91150	+	17.1672i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$224$	−0.375052	−	3.56838i	−0.0250592	−	0.238423i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	0.766900	−	7.29656i	0.0510134	−	0.485360i
$227$	3.89853	−	4.32975i	0.258754	−	0.287376i	−0.599744	−	0.800192i	$-0.704731\pi$
$227$	3.89853	−	4.32975i	0.258754	−	0.287376i	0.858499	+	0.512816i	$0.171398\pi$
$228$	4.50206	+	2.00445i	0.298156	+	0.132748i
$229$	7.54622	+	1.60400i	0.498668	+	0.105995i	0.450378	−	0.892838i	$-0.351289\pi$
$229$	7.54622	+	1.60400i	0.498668	+	0.105995i	0.0482904	+	0.998833i	$0.484623\pi$
$230$	−7.11306	+	1.51193i	−0.469022	+	0.0996936i
$231$	−8.84590	+	3.93845i	−0.582018	+	0.259131i
$232$	−0.732685	+	2.25497i	−0.0481031	+	0.148046i
$233$	−4.72940	+	14.5556i	−0.309833	+	0.953569i	0.667996	+	0.744165i	$0.267152\pi$
$233$	−4.72940	+	14.5556i	−0.309833	+	0.953569i	−0.977829	+	0.209404i	$0.932848\pi$
$234$	3.00402	−	1.33748i	0.196379	−	0.0874336i
$235$	1.18186	−	0.251212i	0.0770960	−	0.0163873i
$236$	−9.77865	−	2.07852i	−0.636536	−	0.135300i
$237$	11.6334	+	5.17954i	0.755672	+	0.336447i
$238$	−15.8553	+	17.6091i	−1.02775	+	1.14143i
$239$	1.79893	−	17.1157i	0.116363	−	1.10712i	−0.768041	−	0.640400i	$-0.778768\pi$
$239$	1.79893	−	17.1157i	0.116363	−	1.10712i	0.884404	−	0.466721i	$-0.154565\pi$
$240$	0.809017	+	0.587785i	0.0522218	+	0.0379414i
$241$	−2.26528	−	21.5527i	−0.145919	−	1.38833i	−0.785146	−	0.619311i	$-0.787412\pi$
$241$	−2.26528	−	21.5527i	−0.145919	−	1.38833i	0.639226	−	0.769019i	$-0.279255\pi$
$242$	−1.85851	+	3.21903i	−0.119469	+	0.206927i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.03684	−	5.11256i	0.450487	−	0.327298i
$245$	−3.93049	−	4.36525i	−0.251110	−	0.278885i
$246$	−1.16504	−	3.58563i	−0.0742803	−	0.228611i
$247$	−16.2052			−1.03111
$248$	0.136311	+	5.56610i	0.00865577	+	0.353447i
$249$	−9.73902			−0.617186
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	0.594653	+	0.660430i	0.0375342	+	0.0416859i	0.761620	−	0.648024i	$-0.224405\pi$
$251$	0.594653	+	0.660430i	0.0375342	+	0.0416859i	−0.724085	+	0.689710i	$0.757738\pi$
$252$	2.90278	−	2.10900i	0.182858	−	0.132854i
$253$	−9.81244	−	16.9957i	−0.616903	−	1.06851i
$254$	8.15929	−	14.1323i	0.511959	−	0.886740i
$255$	−0.690307	−	6.56783i	−0.0432287	−	0.411294i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	1.81495	−	17.2681i	0.113214	−	1.07715i	−0.779460	−	0.626452i	$-0.784507\pi$
$257$	1.81495	−	17.2681i	0.113214	−	1.07715i	0.892674	−	0.450703i	$-0.148827\pi$
$258$	7.56934	−	8.40661i	0.471247	−	0.523373i
$259$	−28.6833	−	12.7706i	−1.78229	−	0.793529i
$260$	−3.21645	−	0.683678i	−0.199476	−	0.0423999i
$261$	−2.31921	+	0.492962i	−0.143555	+	0.0305136i
$262$	−16.3596	+	7.28375i	−1.01070	+	0.449992i
$263$	2.95711	−	9.10104i	0.182343	−	0.561194i	−0.817549	−	0.575858i	$-0.804668\pi$
$263$	2.95711	−	9.10104i	0.182343	−	0.561194i	0.999892	+	0.0146643i	$0.00466797\pi$
$264$	−0.833945	+	2.56662i	−0.0513257	+	0.157964i
$265$	5.97281	−	2.65927i	0.366907	−	0.163357i
$266$	−17.2959	+	3.67635i	−1.06048	+	0.225412i
$267$	13.0262	+	2.76880i	0.797189	+	0.169448i
$268$	−4.60545	−	2.05048i	−0.281323	−	0.125253i
$269$	14.8322	−	16.4728i	0.904336	−	1.00437i	−0.0956238	−	0.995418i	$-0.530485\pi$
$269$	14.8322	−	16.4728i	0.904336	−	1.00437i	0.999960	−	0.00894954i	$-0.00284876\pi$
$270$	−0.104528	+	0.994522i	−0.00636140	+	0.0605247i
$271$	11.8279	+	8.59349i	0.718495	+	0.522017i	0.885903	−	0.463871i	$-0.153540\pi$
$271$	11.8279	+	8.59349i	0.718495	+	0.522017i	−0.167408	+	0.985888i	$0.553540\pi$
$272$	0.690307	+	6.56783i	0.0418560	+	0.398233i
$273$	−5.89929	+	10.2179i	−0.357042	+	0.618414i
$274$	−2.31497	−	4.00964i	−0.139852	−	0.242231i
$275$	−2.18330	+	1.58626i	−0.131658	+	0.0956549i
$276$	4.86590	+	5.40413i	0.292893	+	0.325290i
$277$	−7.62178	−	23.4574i	−0.457948	−	1.40942i	−0.867639	−	0.497195i	$-0.834363\pi$
$277$	−7.62178	−	23.4574i	−0.457948	−	1.40942i	0.409691	−	0.912225i	$-0.365637\pi$
$278$	−8.22923			−0.493556
$279$	−4.75222	+	2.90110i	−0.284508	+	0.173684i
$280$	−3.58804			−0.214426
$281$	6.45992	+	19.8816i	0.385367	+	1.18604i	0.936214	+	0.351430i	$0.114305\pi$
$281$	6.45992	+	19.8816i	0.385367	+	1.18604i	−0.550847	+	0.834606i	$0.685695\pi$
$282$	−0.808485	−	0.897914i	−0.0481446	−	0.0534700i
$283$	20.6463	−	15.0004i	1.22729	−	0.891680i	0.230608	−	0.973047i	$-0.425928\pi$
$283$	20.6463	−	15.0004i	1.22729	−	0.891680i	0.996684	+	0.0813664i	$0.0259284\pi$
$284$	3.91541	+	6.78169i	0.232337	+	0.402419i
$285$	2.46406	−	4.26787i	0.145958	−	0.252807i
$286$	−0.927603	−	8.82556i	−0.0548503	−	0.521866i
$287$	10.9439	+	7.95124i	0.646001	+	0.469347i
$288$	0.104528	−	0.994522i	0.00615940	−	0.0586028i
$289$	17.8075	−	19.7773i	1.04750	−	1.16337i
$290$	2.16603	+	0.964380i	0.127194	+	0.0566304i
$291$	−7.95856	−	1.69164i	−0.466539	−	0.0991659i
$292$	−1.33681	+	0.284148i	−0.0782309	+	0.0166285i
$293$	−18.2582	+	8.12907i	−1.06665	+	0.474905i	−0.863556	−	0.504253i	$-0.831768\pi$
$293$	−18.2582	+	8.12907i	−1.06665	+	0.474905i	−0.203099	+	0.979158i	$0.565101\pi$
$294$	−1.81517	+	5.58653i	−0.105863	+	0.325813i
$295$	−3.08928	+	9.50782i	−0.179865	+	0.553567i
$296$	−7.99415	+	3.55923i	−0.464651	+	0.206876i
$297$	−2.63973	+	0.561092i	−0.153173	+	0.0325578i
$298$	10.8376	+	2.30359i	0.627803	+	0.133444i
$299$	−21.8452	−	9.72610i	−1.26334	−	0.562475i
$300$	0.669131	−	0.743145i	0.0386323	−	0.0429055i
$301$	−4.24267	+	40.3663i	−0.244543	+	2.32667i
$302$	−12.0720	−	8.77080i	−0.694664	−	0.504703i
$303$	0.0423668	+	0.403093i	0.00243391	+	0.0231571i
$304$	−2.46406	+	4.26787i	−0.141323	+	0.244779i
$305$	−4.34900	−	7.53270i	−0.249023	−	0.431321i
$306$	−5.34275	+	3.88174i	−0.305425	+	0.221904i
$307$	−12.4560	−	13.8338i	−0.710900	−	0.789535i	0.274171	−	0.961681i	$-0.411597\pi$
$307$	−12.4560	−	13.8338i	−0.710900	−	0.789535i	−0.985071	+	0.172146i	$0.944930\pi$
$308$	−2.99223	−	9.20912i	−0.170498	−	0.524738i
$309$	−6.04851			−0.344088
$310$	5.54985	+	0.446251i	0.315210	+	0.0253453i
$311$	7.35076			0.416823			0.208412	−	0.978041i	$-0.433171\pi$
$311$	7.35076			0.416823			0.208412	+	0.978041i	$0.433171\pi$
$312$	1.01614	+	3.12737i	0.0575278	+	0.177052i
$313$	11.4226	+	12.6861i	0.645646	+	0.717062i	0.973760	−	0.227576i	$-0.0730799\pi$
$313$	11.4226	+	12.6861i	0.645646	+	0.717062i	−0.328115	+	0.944638i	$0.606413\pi$
$314$	12.0411	−	8.74839i	0.679520	−	0.493700i
$315$	−1.79402	−	3.10733i	−0.101082	−	0.175078i
$316$	−6.36719	+	11.0283i	−0.358182	+	0.620390i
$317$	3.05945	+	29.1087i	0.171836	+	1.63491i	0.652347	+	0.757920i	$0.273784\pi$
$317$	3.05945	+	29.1087i	0.171836	+	1.63491i	−0.480511	+	0.876989i	$0.659549\pi$
$318$	−5.28940	−	3.84297i	−0.296615	−	0.215503i
$319$	−0.668843	+	6.36362i	−0.0374480	+	0.356294i
$320$	−0.669131	+	0.743145i	−0.0374055	+	0.0415431i
$321$	6.46221	+	2.87716i	0.360685	+	0.160587i
$322$	−25.5219	−	5.42486i	−1.42228	−	0.302316i
$323$	31.8341	−	6.76655i	1.77130	−	0.376501i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	−1.01614	+	3.12737i	−0.0563655	+	0.173475i
$326$	−1.20115	+	3.69676i	−0.0665256	+	0.204745i
$327$	−10.0681	+	4.48259i	−0.556766	+	0.247888i
$328$	3.68777	−	0.783859i	0.203623	−	0.0432814i
$329$	4.24055	+	0.901358i	0.233789	+	0.0496935i
$330$	2.46539	+	1.09766i	0.135715	+	0.0604242i
$331$	18.6766	−	20.7425i	1.02656	−	1.14011i	0.0365165	−	0.999333i	$-0.488374\pi$
$331$	18.6766	−	20.7425i	1.02656	−	1.14011i	0.990042	−	0.140775i	$-0.0449595\pi$
$332$	1.01801	−	9.68567i	0.0558703	−	0.531570i
$333$	−7.07945	−	5.14352i	−0.387952	−	0.281863i
$334$	0.255211	+	2.42817i	0.0139645	+	0.132863i
$335$	−2.52065	+	4.36589i	−0.137718	+	0.238534i
$336$	1.79402	+	3.10733i	0.0978718	+	0.169519i
$337$	28.3174	−	20.5738i	1.54255	−	1.12073i	0.593833	−	0.804589i	$-0.297614\pi$
$337$	28.3174	−	20.5738i	1.54255	−	1.12073i	0.948714	−	0.316137i	$-0.102386\pi$
$338$	1.46339	+	1.62526i	0.0795982	+	0.0884027i
$339$	2.26718	+	6.97767i	0.123136	+	0.378975i
$340$	6.60401			0.358153
$341$	3.48291	+	14.6165i	0.188610	+	0.791528i
$342$	−4.92812			−0.266482
$343$	1.24845	+	3.84232i	0.0674098	+	0.207466i
$344$	7.56934	+	8.40661i	0.408112	+	0.453254i
$345$	5.88315	−	4.27436i	0.316738	−	0.230124i
$346$	−8.70025	−	15.0693i	−0.467728	−	0.810129i
$347$	−12.5047	+	21.6587i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$347$	−12.5047	+	21.6587i	−0.671287	+	1.16270i	−0.977540	+	0.210752i	$0.932409\pi$
$348$	−0.247839	−	2.35803i	−0.0132856	−	0.126404i
$349$	−15.6100	−	11.3413i	−0.835583	−	0.607087i	0.0855503	−	0.996334i	$-0.472735\pi$
$349$	−15.6100	−	11.3413i	−0.835583	−	0.607087i	−0.921133	+	0.389247i	$0.872735\pi$
$350$	−0.375052	+	3.56838i	−0.0200474	+	0.190738i
$351$	−2.20031	+	2.44369i	−0.117444	+	0.130435i
$352$	−2.46539	−	1.09766i	−0.131406	−	0.0585055i
$353$	−28.5345	−	6.06520i	−1.51874	−	0.322818i	−0.628318	−	0.777957i	$-0.716256\pi$
$353$	−28.5345	−	6.06520i	−1.51874	−	0.322818i	−0.890420	+	0.455139i	$0.849590\pi$
$354$	9.77865	−	2.07852i	0.519730	−	0.110472i
$355$	7.15381	−	3.18508i	0.379685	−	0.169047i
$356$	−4.11524	+	12.6654i	−0.218107	+	0.671265i
$357$	7.32229	−	22.5357i	0.387537	−	1.19272i
$358$	−2.59625	+	1.15592i	−0.137216	+	0.0610925i
$359$	28.9504	−	6.15359i	1.52794	−	0.324774i	0.634134	−	0.773223i	$-0.281357\pi$
$359$	28.9504	−	6.15359i	1.52794	−	0.324774i	0.893808	+	0.448449i	$0.148023\pi$
$360$	−0.978148	−	0.207912i	−0.0515529	−	0.0109579i
$361$	4.82931	+	2.15015i	0.254174	+	0.113166i
$362$	11.0960	−	12.3233i	0.583192	−	0.647701i
$363$	0.388534	−	3.69665i	0.0203927	−	0.194024i
$364$	−9.54526	−	6.93504i	−0.500307	−	0.363495i
$365$	0.142856	+	1.35919i	0.00747744	+	0.0711431i
$366$	−4.34900	+	7.53270i	−0.227326	+	0.393740i
$367$	−8.31912	−	14.4091i	−0.434254	−	0.752151i	0.562980	−	0.826471i	$-0.309655\pi$
$367$	−8.31912	−	14.4091i	−0.434254	−	0.752151i	−0.997234	+	0.0743197i	$0.976321\pi$
$368$	−5.88315	+	4.27436i	−0.306680	+	0.222816i
$369$	2.52273	+	2.80177i	0.131328	+	0.145854i
$370$	2.70411	+	8.32240i	0.140580	+	0.432661i
$371$	23.4588			1.21792
$372$	−2.38846	−	5.02944i	−0.123836	−	0.260764i
$373$	13.1311			0.679902			0.339951	−	0.940443i	$-0.389589\pi$
$373$	13.1311			0.679902			0.339951	+	0.940443i	$0.389589\pi$
$374$	5.50738	+	16.9500i	0.284780	+	0.876462i
$375$	−0.669131	−	0.743145i	−0.0345538	−	0.0383758i
$376$	0.977504	−	0.710199i	0.0504109	−	0.0366257i
$377$	3.89832	+	6.75209i	0.200774	+	0.347751i
$378$	−1.79402	+	3.10733i	−0.0922744	+	0.159824i
$379$	−2.07754	−	19.7665i	−0.106716	−	1.01534i	−0.908546	−	0.417784i	$-0.862807\pi$
$379$	−2.07754	−	19.7665i	−0.106716	−	1.01534i	0.801830	−	0.597552i	$-0.203860\pi$
$380$	3.98693	+	2.89667i	0.204525	+	0.148596i
$381$	−1.70576	+	16.2292i	−0.0873885	+	0.831446i
$382$	−14.4195	+	16.0145i	−0.737768	+	0.819374i
$383$	19.7448	+	8.79096i	1.00891	+	0.449197i	0.843559	−	0.537037i	$-0.180456\pi$
$383$	19.7448	+	8.79096i	1.00891	+	0.449197i	0.165355	+	0.986234i	$0.447123\pi$
$384$	0.978148	+	0.207912i	0.0499159	+	0.0106099i
$385$	−9.47145	+	2.01322i	−0.482710	+	0.102603i
$386$	5.34017	−	2.37760i	0.271807	−	0.121016i
$387$	−3.49566	+	10.7585i	−0.177695	+	0.546888i
$388$	2.51427	−	7.73813i	0.127643	−	0.392844i
$389$	−4.00982	+	1.78529i	−0.203306	+	0.0905177i	−0.505864	−	0.862613i	$-0.668826\pi$
$389$	−4.00982	+	1.78529i	−0.203306	+	0.0905177i	0.302558	+	0.953131i	$0.402160\pi$
$390$	3.21645	−	0.683678i	0.162871	−	0.0346194i
$391$	46.9747	+	9.98479i	2.37561	+	0.504952i
$392$	−5.36618	−	2.38918i	−0.271033	−	0.120672i
$393$	11.9826	−	13.3081i	0.604444	−	0.671304i
$394$	−1.61613	+	15.3764i	−0.0814192	+	0.774652i
$395$	10.3023	+	7.48508i	0.518366	+	0.376615i
$396$	−0.282091	−	2.68392i	−0.0141756	−	0.134872i
$397$	3.81855	−	6.61392i	0.191647	−	0.331943i	−0.754149	−	0.656703i	$-0.771950\pi$
$397$	3.81855	−	6.61392i	0.191647	−	0.331943i	0.945796	+	0.324760i	$0.105284\pi$
$398$	−4.88436	−	8.45997i	−0.244831	−	0.424060i
$399$	14.3053	−	10.3934i	0.716159	−	0.520320i
$400$	0.669131	+	0.743145i	0.0334565	+	0.0371572i
$401$	−1.46980	−	4.52359i	−0.0733984	−	0.225897i	0.907627	−	0.419779i	$-0.137892\pi$
$401$	−1.46980	−	4.52359i	−0.0733984	−	0.225897i	−0.981025	+	0.193882i	$0.937892\pi$
$402$	5.04129			0.251437
$403$	13.9017	+	11.9140i	0.692495	+	0.593480i
$404$	−0.405313			−0.0201651
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	5.69250	+	6.32216i	0.282514	+	0.313764i
$407$	−19.1053	+	13.8808i	−0.947016	+	0.688048i
$408$	−3.30200	−	5.71924i	−0.163474	−	0.283145i
$409$	−14.4381	+	25.0076i	−0.713919	+	1.23654i	0.249456	+	0.968386i	$0.419748\pi$
$409$	−14.4381	+	25.0076i	−0.713919	+	1.23654i	−0.963375	+	0.268158i	$0.913585\pi$
$410$	−0.394088	−	3.74950i	−0.0194626	−	0.185175i
$411$	3.74570	+	2.72141i	0.184762	+	0.134237i
$412$	0.632242	−	6.01538i	0.0311483	−	0.296356i
$413$	−24.0017	+	26.6566i	−1.18105	+	1.31169i
$414$	−6.64328	−	2.95778i	−0.326499	−	0.145367i
$415$	−9.52620	−	2.02486i	−0.467623	−	0.0993963i
$416$	−3.21645	+	0.683678i	−0.157700	+	0.0335201i
$417$	7.51777	−	3.34713i	0.368147	−	0.163910i
$418$	−4.10978	+	12.6486i	−0.201016	+	0.618663i
$419$	6.86542	−	21.1296i	0.335397	−	1.03225i	−0.631128	−	0.775678i	$-0.717408\pi$
$419$	6.86542	−	21.1296i	0.335397	−	1.03225i	0.966526	−	0.256569i	$-0.0825921\pi$
$420$	3.27784	−	1.45939i	0.159942	−	0.0712108i
$421$	15.4817	−	3.29073i	0.754531	−	0.160381i	0.185441	−	0.982655i	$-0.440629\pi$
$421$	15.4817	−	3.29073i	0.754531	−	0.160381i	0.569090	+	0.822275i	$0.307295\pi$
$422$	−14.0737	−	2.99145i	−0.685096	−	0.145622i
$423$	1.10380	+	0.491444i	0.0536687	+	0.0238948i
$424$	4.37481	−	4.85872i	0.212460	−	0.235960i
$425$	0.690307	−	6.56783i	0.0334848	−	0.318587i
$426$	−6.33526	−	4.60284i	−0.306945	−	0.223008i
$427$	−3.26221	−	31.0378i	−0.157869	−	1.50203i
$428$	−3.53688	+	6.12606i	−0.170962	+	0.296114i
$429$	4.43708	+	7.68526i	0.214224	+	0.371048i
$430$	9.15177	−	6.64915i	0.441337	−	0.320650i
$431$	6.57907	+	7.30680i	0.316903	+	0.351956i	0.880460	−	0.474121i	$-0.157234\pi$
$431$	6.57907	+	7.30680i	0.316903	+	0.351956i	−0.563557	+	0.826077i	$0.690567\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−0.724369			−0.0348109			−0.0174055	−	0.999849i	$-0.505541\pi$
$433$	−0.724369			−0.0348109			−0.0174055	+	0.999849i	$0.505541\pi$
$434$	17.5403	+	9.56212i	0.841959	+	0.458996i
$435$	−2.37102			−0.113682
$436$	−3.40564	−	10.4815i	−0.163100	−	0.501972i
$437$	23.9797	+	26.6322i	1.14711	+	1.27399i
$438$	1.10566	−	0.803311i	0.0528306	−	0.0383837i
$439$	−3.32352	−	5.75651i	−0.158623	−	0.274743i	0.775749	−	0.631041i	$-0.217372\pi$
$439$	−3.32352	−	5.75651i	−0.158623	−	0.274743i	−0.934372	+	0.356298i	$0.884039\pi$
$440$	−1.34935	+	2.33714i	−0.0643278	+	0.111419i
$441$	−0.614002	−	5.84184i	−0.0292382	−	0.278183i
$442$	17.5686	+	12.7644i	0.835655	+	0.607139i
$443$	0.550347	−	5.23620i	0.0261478	−	0.248779i	−0.973638	−	0.228097i	$-0.926750\pi$
$443$	0.550347	−	5.23620i	0.0261478	−	0.248779i	0.999786	−	0.0206820i	$-0.00658375\pi$
$444$	5.85535	−	6.50303i	0.277883	−	0.308620i
$445$	12.1659	+	5.41659i	0.576717	+	0.256771i
$446$	19.3898	+	4.12143i	0.918135	+	0.195156i
$447$	−10.8376	+	2.30359i	−0.512599	+	0.108956i
$448$	−3.27784	+	1.45939i	−0.154863	+	0.0689495i
$449$	−10.4205	+	32.0711i	−0.491775	+	1.51353i	0.330147	+	0.943930i	$0.392902\pi$
$449$	−10.4205	+	32.0711i	−0.491775	+	1.51353i	−0.821922	+	0.569599i	$0.807098\pi$
$450$	−0.309017	+	0.951057i	−0.0145672	+	0.0448332i
$451$	9.29489	−	4.13835i	0.437679	−	0.194867i
$452$	−7.17643	+	1.52540i	−0.337551	+	0.0717487i
$453$	14.5957	+	3.10241i	0.685766	+	0.145764i
$454$	−5.32255	−	2.36975i	−0.249800	−	0.111218i
$455$	−7.89480	+	8.76806i	−0.370114	+	0.411053i
$456$	0.515128	−	4.90112i	0.0241231	−	0.229516i
$457$	−16.8495	−	12.2419i	−0.788186	−	0.572651i	0.119239	−	0.992866i	$-0.461955\pi$
$457$	−16.8495	−	12.2419i	−0.788186	−	0.572651i	−0.907425	+	0.420215i	$0.861955\pi$
$458$	−0.806417	−	7.67254i	−0.0376814	−	0.358514i
$459$	3.30200	−	5.71924i	0.154124	−	0.266951i
$460$	3.63599	+	6.29771i	0.169529	+	0.293632i
$461$	−12.8341	+	9.32455i	−0.597746	+	0.434288i	−0.845078	−	0.534643i	$-0.820446\pi$
$461$	−12.8341	+	9.32455i	−0.597746	+	0.434288i	0.247332	+	0.968931i	$0.420446\pi$
$462$	6.47922	+	7.19590i	0.301441	+	0.334784i
$463$	8.31945	+	25.6046i	0.386638	+	1.18995i	0.935285	+	0.353894i	$0.115143\pi$
$463$	8.31945	+	25.6046i	0.386638	+	1.18995i	−0.548648	+	0.836054i	$0.684857\pi$
$464$	2.37102			0.110072
$465$	−5.25155	+	1.84966i	−0.243535	+	0.0857758i
$466$	15.3047			0.708975
$467$	−5.18686	−	15.9635i	−0.240019	−	0.738703i	−0.996416	−	0.0845896i	$-0.973042\pi$
$467$	−5.18686	−	15.9635i	−0.240019	−	0.738703i	0.756397	−	0.654113i	$-0.226958\pi$
$468$	−2.20031	−	2.44369i	−0.101709	−	0.112960i
$469$	−14.6338	+	10.6321i	−0.675725	+	0.490943i
$470$	−0.604131	−	1.04639i	−0.0278665	−	0.0482662i
$471$	−7.44182	+	12.8896i	−0.342901	+	0.593922i
$472$	1.04498	+	9.94235i	0.0480992	+	0.457634i
$473$	24.6979	+	17.9441i	1.13561	+	0.825069i
$474$	1.33110	−	12.6646i	0.0611397	−	0.581705i
$475$	3.29755	−	3.66230i	0.151302	−	0.168038i
$476$	21.6469	+	9.63780i	0.992182	+	0.441748i
$477$	6.39518	+	1.35934i	0.292815	+	0.0622398i
$478$	−16.8339	+	3.57815i	−0.769964	+	0.163661i
$479$	−33.0649	+	14.7214i	−1.51077	+	0.672640i	−0.984130	−	0.177447i	$-0.943216\pi$
$479$	−33.0649	+	14.7214i	−1.51077	+	0.672640i	−0.526643	+	0.850086i	$0.676550\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	−8.89196	+	27.3666i	−0.405438	+	1.24781i
$482$	−19.7978	+	8.81455i	−0.901765	+	0.401492i
$483$	25.5219	−	5.42486i	1.16129	−	0.246840i
$484$	3.63579	+	0.772810i	0.165263	+	0.0351277i
$485$	−7.43293	−	3.30935i	−0.337512	−	0.150270i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	−2.42443	+	23.0669i	−0.109862	+	1.04526i	0.791196	+	0.611563i	$0.209459\pi$
$487$	−2.42443	+	23.0669i	−0.109862	+	1.04526i	−0.901057	+	0.433700i	$0.857208\pi$
$488$	−7.03684	−	5.11256i	−0.318543	−	0.231435i
$489$	−0.406303	−	3.86572i	−0.0183737	−	0.174814i
$490$	−2.93701	+	5.08705i	−0.132681	+	0.229810i
$491$	8.40489	+	14.5577i	0.379307	+	0.656980i	0.990962	−	0.134146i	$-0.0428290\pi$
$491$	8.40489	+	14.5577i	0.379307	+	0.656980i	−0.611654	+	0.791125i	$0.709496\pi$
$492$	−3.05012	+	2.21604i	−0.137510	+	0.0999068i
$493$	−10.4774	−	11.6363i	−0.471878	−	0.524074i
$494$	5.00768	+	15.4120i	0.225306	+	0.693421i
$495$	−2.69870			−0.121298
$496$	5.25155	−	1.84966i	0.235802	−	0.0830521i
$497$	28.0973			1.26034
$498$	3.00952	+	9.26236i	0.134860	+	0.415056i
$499$	−12.1266	−	13.4680i	−0.542862	−	0.602909i	0.407826	−	0.913060i	$-0.366287\pi$
$499$	−12.1266	−	13.4680i	−0.542862	−	0.602909i	−0.950687	+	0.310151i	$0.899620\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−1.22077	−	2.11444i	−0.0545400	−	0.0944661i
$502$	0.444348	−	0.769633i	0.0198322	−	0.0343504i
$503$	−0.225978	−	2.15004i	−0.0100759	−	0.0958655i	0.988328	−	0.152340i	$-0.0486808\pi$
$503$	−0.225978	−	2.15004i	−0.0100759	−	0.0958655i	−0.998404	+	0.0564743i	$0.982014\pi$
$504$	−2.90278	−	2.10900i	−0.129300	−	0.0939422i
$505$	−0.0423668	+	0.403093i	−0.00188530	+	0.0179374i
$506$	−13.1316	+	14.5841i	−0.583771	+	0.648344i
$507$	−1.99793	−	0.889537i	−0.0887313	−	0.0395057i
$508$	−15.9620	−	3.39282i	−0.708198	−	0.150532i
$509$	37.9017	−	8.05625i	1.67996	−	0.357087i	0.733448	−	0.679746i	$-0.237910\pi$
$509$	37.9017	−	8.05625i	1.67996	−	0.357087i	0.946515	+	0.322659i	$0.104577\pi$
$510$	−6.03306	+	2.68609i	−0.267148	+	0.118942i
$511$	−1.51532	+	4.66368i	−0.0670338	+	0.206309i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	4.50206	−	2.00445i	0.198771	−	0.0884984i
$514$	−16.9838	+	3.61002i	−0.749123	+	0.159231i
$515$	−5.91634	−	1.25756i	−0.260705	−	0.0554146i
$516$	−10.3342	−	4.60109i	−0.454938	−	0.202552i
$517$	2.18186	−	2.42320i	0.0959581	−	0.106572i
$518$	−3.28196	+	31.2258i	−0.144201	+	1.37198i
$519$	14.0773	+	10.2278i	0.617925	+	0.448949i
$520$	0.343722	+	3.27030i	0.0150732	+	0.143412i
$521$	−12.0759	+	20.9161i	−0.529055	+	0.916350i	0.470371	+	0.882469i	$0.344120\pi$
$521$	−12.0759	+	20.9161i	−0.529055	+	0.916350i	−0.999426	+	0.0338811i	$0.989213\pi$
$522$	1.18551	+	2.05336i	0.0518883	+	0.0898732i
$523$	20.3914	−	14.8152i	0.891654	−	0.647825i	−0.0446546	−	0.999002i	$-0.514219\pi$
$523$	20.3914	−	14.8152i	0.891654	−	0.647825i	0.936309	+	0.351178i	$0.114219\pi$
$524$	11.9826	+	13.3081i	0.523464	+	0.581366i
$525$	−1.10876	−	3.41243i	−0.0483905	−	0.148931i
$526$	−9.56940			−0.417246
$527$	−32.2839	−	17.5997i	−1.40631	−	0.766654i
$528$	2.69870			0.117446
$529$	9.23393	+	28.4191i	0.401475	+	1.23561i
$530$	−4.37481	−	4.85872i	−0.190030	−	0.211049i
$531$	−8.08783	+	5.87616i	−0.350982	+	0.255003i
$532$	8.84114	+	15.3133i	0.383312	+	0.663916i
$533$	6.19872	−	10.7365i	0.268496	−	0.465049i
$534$	−1.39203	−	13.2442i	−0.0602388	−	0.573134i
$535$	5.72280	+	4.15786i	0.247418	+	0.179760i
$536$	−0.526959	+	5.01368i	−0.0227611	+	0.216558i
$537$	1.90163	−	2.11198i	0.0820616	−	0.0911386i
$538$	−20.2500	−	9.01589i	−0.873040	−	0.388702i
$539$	−15.5058	−	3.29586i	−0.667883	−	0.141963i
$540$	0.978148	−	0.207912i	0.0420928	−	0.00894709i
$541$	18.1779	−	8.09332i	0.781529	−	0.347959i	0.0231155	−	0.999733i	$-0.492641\pi$
$541$	18.1779	−	8.09332i	0.781529	−	0.347959i	0.758414	+	0.651774i	$0.225975\pi$
$542$	4.51786	−	13.9046i	0.194059	−	0.597252i
$543$	−5.12434	+	15.7711i	−0.219906	+	0.676802i
$544$	6.03306	−	2.68609i	0.258665	−	0.115165i
$545$	−10.7800	+	2.29137i	−0.461766	+	0.0981514i
$546$	11.5408	+	2.45306i	0.493899	+	0.104981i
$547$	23.2772	+	10.3637i	0.995263	+	0.443119i	0.838727	−	0.544553i	$-0.183301\pi$
$547$	23.2772	+	10.3637i	0.995263	+	0.443119i	0.156536	+	0.987672i	$0.449967\pi$
$548$	−3.09803	+	3.44071i	−0.132341	+	0.146980i
$549$	0.909190	−	8.65036i	0.0388033	−	0.369188i
$550$	2.18330	+	1.58626i	0.0930960	+	0.0676382i
$551$	−1.22138	−	11.6206i	−0.0520325	−	0.495056i
$552$	3.63599	−	6.29771i	0.154758	−	0.268049i
$553$	22.8457	+	39.5699i	0.971499	+	1.68268i
$554$	−19.9541	+	14.4975i	−0.847767	+	0.615939i
$555$	−5.85535	−	6.50303i	−0.248546	−	0.276038i
$556$	2.54297	+	7.82646i	0.107846	+	0.331916i
$557$	34.9418			1.48053			0.740266	−	0.672314i	$-0.234700\pi$
$557$	34.9418			1.48053			0.740266	+	0.672314i	$0.234700\pi$
$558$	4.22763	+	3.62315i	0.178970	+	0.153380i
$559$	37.1981			1.57331
$560$	1.10876	+	3.41243i	0.0468539	+	0.144201i
$561$	−11.9254	−	13.2445i	−0.503491	−	0.559184i
$562$	16.9123	−	12.2875i	0.713402	−	0.518317i
$563$	−16.6491	−	28.8371i	−0.701676	−	1.21534i	−0.967878	−	0.251421i	$-0.919102\pi$
$563$	−16.6491	−	28.8371i	−0.701676	−	1.21534i	0.266202	−	0.963917i	$-0.414231\pi$
$564$	−0.604131	+	1.04639i	−0.0254385	+	0.0440608i
$565$	0.766900	+	7.29656i	0.0322637	+	0.306969i
$566$	−20.6463	−	15.0004i	−0.867827	−	0.630513i
$567$	0.375052	−	3.56838i	0.0157507	−	0.149858i
$568$	5.23984	−	5.81943i	0.219859	−	0.244178i
$569$	−14.8150	−	6.59606i	−0.621077	−	0.276521i	0.0719778	−	0.997406i	$-0.477069\pi$
$569$	−14.8150	−	6.59606i	−0.621077	−	0.276521i	−0.693055	+	0.720885i	$0.743736\pi$
$570$	−4.82043	−	1.02461i	−0.201905	−	0.0429163i
$571$	2.60048	−	0.552748i	0.108827	−	0.0231318i	−0.153176	−	0.988199i	$-0.548950\pi$
$571$	2.60048	−	0.552748i	0.108827	−	0.0231318i	0.262003	+	0.965067i	$0.415617\pi$
$572$	−8.10696	+	3.60945i	−0.338969	+	0.150919i
$573$	6.65921	−	20.4950i	0.278193	−	0.856189i
$574$	4.18021	−	12.8654i	0.174479	−	0.536990i
$575$	6.64328	−	2.95778i	0.277044	−	0.123348i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	−4.51082	−	0.958805i	−0.187788	−	0.0399156i	0.113058	−	0.993588i	$-0.463936\pi$
$577$	−4.51082	−	0.958805i	−0.187788	−	0.0399156i	−0.300846	+	0.953673i	$0.597269\pi$
$578$	−24.3121	−	10.8245i	−1.01125	−	0.450238i
$579$	−3.91143	+	4.34408i	−0.162554	+	0.180534i
$580$	0.247839	−	2.35803i	0.0102910	−	0.0979119i
$581$	−28.2703	−	20.5396i	−1.17285	−	0.852125i
$582$	0.850481	+	8.09178i	0.0352536	+	0.335415i
$583$	8.82213	−	15.2804i	0.365375	−	0.632848i
$584$	0.683337	+	1.18357i	0.0282767	+	0.0489767i
$585$	−2.66030	+	1.93282i	−0.109990	+	0.0799123i
$586$	13.3733	+	14.8525i	0.552446	+	0.613553i
$587$	−1.42285	−	4.37909i	−0.0587274	−	0.180744i	0.917389	−	0.397991i	$-0.130292\pi$
$587$	−1.42285	−	4.37909i	−0.0587274	−	0.180744i	−0.976117	+	0.217247i	$0.930292\pi$
$588$	5.87402			0.242241
$589$	−11.7706	−	24.7857i	−0.485000	−	1.02128i
$590$	9.99711			0.411575
$591$	−4.77774	−	14.7044i	−0.196530	−	0.604857i
$592$	5.85535	+	6.50303i	0.240654	+	0.267273i
$593$	−22.0382	+	16.0117i	−0.904999	+	0.657521i	−0.939745	−	0.341876i	$-0.888938\pi$
$593$	−22.0382	+	16.0117i	−0.904999	+	0.657521i	0.0347457	+	0.999396i	$0.488938\pi$
$594$	1.34935	+	2.33714i	0.0553645	+	0.0958942i
$595$	11.8477	−	20.5208i	0.485709	−	0.841273i
$596$	−1.15814	−	11.0190i	−0.0474393	−	0.451355i
$597$	7.90307	+	5.74191i	0.323451	+	0.235001i
$598$	−2.49954	+	23.7815i	−0.102214	+	0.972499i
$599$	−24.8032	+	27.5467i	−1.01343	+	1.12553i	−0.0213683	+	0.999772i	$0.506802\pi$
$599$	−24.8032	+	27.5467i	−1.01343	+	1.12553i	−0.992061	+	0.125756i	$0.959864\pi$
$600$	−0.913545	−	0.406737i	−0.0372953	−	0.0166050i
$601$	−31.2303	−	6.63820i	−1.27391	−	0.270778i	−0.479167	−	0.877724i	$-0.659061\pi$
$601$	−31.2303	−	6.63820i	−1.27391	−	0.270778i	−0.794743	+	0.606946i	$0.792395\pi$
$602$	39.7017	−	8.43885i	1.61812	−	0.343942i
$603$	−4.60545	+	2.05048i	−0.187548	+	0.0835019i
$604$	−4.61108	+	14.1915i	−0.187622	+	0.577442i
$605$	1.14862	−	3.53509i	0.0466980	−	0.143722i
$606$	0.370272	−	0.164856i	0.0150413	−	0.00669681i
$607$	−21.8824	+	4.65126i	−0.888181	+	0.188789i	−0.629339	−	0.777131i	$-0.716674\pi$
$607$	−21.8824	+	4.65126i	−0.888181	+	0.188789i	−0.258842	+	0.965920i	$0.583341\pi$
$608$	4.82043	+	1.02461i	0.195494	+	0.0415535i
$609$	−7.77181	−	3.46023i	−0.314930	−	0.140216i
$610$	−5.82010	+	6.46388i	−0.235649	+	0.261715i
$611$	0.415306	−	3.95138i	0.0168015	−	0.159856i
$612$	5.34275	+	3.88174i	0.215968	+	0.156910i
$613$	4.01605	+	38.2102i	0.162207	+	1.54329i	0.708506	+	0.705704i	$0.249369\pi$
$613$	4.01605	+	38.2102i	0.162207	+	1.54329i	−0.546300	+	0.837590i	$0.683964\pi$
$614$	−9.30759	+	16.1212i	−0.375624	+	0.650599i
$615$	1.88508	+	3.26505i	0.0760136	+	0.131659i
$616$	−7.83375	+	5.69155i	−0.315631	+	0.229319i
$617$	−15.1013	−	16.7717i	−0.607957	−	0.675204i	0.358056	−	0.933700i	$-0.383440\pi$
$617$	−15.1013	−	16.7717i	−0.607957	−	0.675204i	−0.966012	+	0.258496i	$0.916773\pi$
$618$	1.86909	+	5.75248i	0.0751860	+	0.231399i
$619$	28.9127			1.16210			0.581049	−	0.813868i	$-0.302642\pi$
$619$	28.9127			1.16210			0.581049	+	0.813868i	$0.302642\pi$
$620$	−1.29059	−	5.41612i	−0.0518313	−	0.217517i
$621$	7.27197			0.291814
$622$	−2.27151	−	6.99099i	−0.0910792	−	0.280313i
$623$	31.9728	+	35.5094i	1.28096	+	1.42265i
$624$	2.66030	−	1.93282i	0.106497	−	0.0773748i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.53543	−	14.7838i	0.341144	−	0.590880i
$627$	−1.39018	−	13.2267i	−0.0555184	−	0.528222i
$628$	−12.0411	−	8.74839i	−0.480493	−	0.349099i
$629$	6.04066	−	57.4730i	0.240857	−	2.29160i
$630$	−2.40087	+	2.66643i	−0.0956528	+	0.106233i
$631$	41.6709	+	18.5531i	1.65889	+	0.738586i	0.999908	−	0.0135707i	$-0.00431981\pi$
$631$	41.6709	+	18.5531i	1.65889	+	0.738586i	0.658984	+	0.752157i	$0.270986\pi$
$632$	12.4561	+	2.64763i	0.495477	+	0.105317i
$633$	14.0737	−	2.99145i	0.559378	−	0.118900i
$634$	26.7386	−	11.9048i	1.06193	−	0.472800i
$635$	−5.04272	+	15.5199i	−0.200114	+	0.615888i
$636$	−2.02037	+	6.21806i	−0.0801129	+	0.246562i
$637$	−17.6457	+	7.85637i	−0.699148	+	0.311281i
$638$	6.25884	−	1.33036i	0.247790	−	0.0526694i
$639$	7.65970	+	1.62812i	0.303013	+	0.0644074i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	2.90813	−	3.22981i	0.114864	−	0.127570i	−0.682970	−	0.730446i	$-0.739312\pi$
$641$	2.90813	−	3.22981i	0.114864	−	0.127570i	0.797835	+	0.602876i	$0.205979\pi$
$642$	0.739410	−	7.03502i	0.0291822	−	0.277650i
$643$	−33.0078	−	23.9816i	−1.30170	−	0.945741i	−0.301730	−	0.953393i	$-0.597564\pi$
$643$	−33.0078	−	23.9816i	−1.30170	−	0.945741i	−0.999971	+	0.00765232i	$0.997564\pi$
$644$	2.72737	+	25.9492i	0.107473	+	1.02254i
$645$	−5.65610	+	9.79666i	−0.222709	+	0.385743i
$646$	−16.2727	−	28.1851i	−0.640239	−	1.10893i
$647$	3.51137	−	2.55116i	0.138046	−	0.100296i	−0.516619	−	0.856215i	$-0.672810\pi$
$647$	3.51137	−	2.55116i	0.138046	−	0.100296i	0.654665	+	0.755919i	$0.272810\pi$
$648$	−0.669131	−	0.743145i	−0.0262859	−	0.0291935i
$649$	8.33704	+	25.6588i	0.327257	+	1.00719i
$650$	3.28831			0.128978
$651$	−19.9131	−	1.60117i	−0.780455	−	0.0627546i
$652$	3.88701			0.152227
$653$	1.03357	+	3.18101i	0.0404469	+	0.124483i	0.969241	−	0.246113i	$-0.0791535\pi$
$653$	1.03357	+	3.18101i	0.0404469	+	0.124483i	−0.928794	+	0.370596i	$0.879153\pi$
$654$	7.37440	+	8.19011i	0.288362	+	0.320258i
$655$	14.4877	−	10.5259i	0.566081	−	0.411282i
$656$	−1.88508	−	3.26505i	−0.0735999	−	0.127479i
$657$	−0.683337	+	1.18357i	−0.0266595	+	0.0461757i
$658$	−0.453161	−	4.31154i	−0.0176661	−	0.168081i
$659$	−12.5526	−	9.11996i	−0.488978	−	0.355263i	0.315813	−	0.948821i	$-0.397723\pi$
$659$	−12.5526	−	9.11996i	−0.488978	−	0.355263i	−0.804791	+	0.593558i	$0.797723\pi$
$660$	0.282091	−	2.68392i	0.0109804	−	0.104471i
$661$	−3.31724	+	3.68416i	−0.129026	+	0.143297i	−0.804196	−	0.594365i	$-0.797404\pi$
$661$	−3.31724	+	3.68416i	−0.129026	+	0.143297i	0.675170	+	0.737662i	$0.264070\pi$
$662$	−25.4986	−	11.3527i	−0.991032	−	0.441236i
$663$	−21.2415	−	4.51502i	−0.824951	−	0.175349i
$664$	−9.52620	+	2.02486i	−0.369688	+	0.0785797i
$665$	16.1536	−	7.19203i	0.626408	−	0.278895i
$666$	−2.70411	+	8.32240i	−0.104782	+	0.322486i
$667$	5.32807	−	16.3981i	0.206304	−	0.634937i
$668$	2.23046	−	0.993065i	0.0862991	−	0.0384228i
$669$	−19.3898	+	4.12143i	−0.749654	+	0.159344i
$670$	4.93113	+	1.04814i	0.190506	+	0.0404933i
$671$	−21.4440	−	9.54746i	−0.827835	−	0.368576i
$672$	2.40087	−	2.66643i	0.0926154	−	0.102860i
$673$	2.50263	−	23.8109i	0.0964691	−	0.917843i	−0.834072	−	0.551655i	$-0.813996\pi$
$673$	2.50263	−	23.8109i	0.0964691	−	0.917843i	0.930541	−	0.366187i	$-0.119337\pi$
$674$	−28.3174	−	20.5738i	−1.09074	−	0.792473i
$675$	−0.104528	−	0.994522i	−0.00402330	−	0.0382792i
$676$	1.09350	−	1.89401i	0.0420579	−	0.0728464i
$677$	23.6538	+	40.9695i	0.909088	+	1.57459i	0.815334	+	0.578991i	$0.196553\pi$
$677$	23.6538	+	40.9695i	0.909088	+	1.57459i	0.0937537	+	0.995595i	$0.470113\pi$
$678$	5.93556	−	4.31244i	0.227954	−	0.165618i
$679$	−19.5343	−	21.6950i	−0.749658	−	0.832579i
$680$	−2.04075	−	6.28078i	−0.0782592	−	0.240857i
$681$	5.82626			0.223263
$682$	12.8248	−	7.82919i	0.491088	−	0.299795i
$683$	18.3160			0.700843			0.350421	−	0.936592i	$-0.386038\pi$
$683$	18.3160			0.700843			0.350421	+	0.936592i	$0.386038\pi$
$684$	1.52287	+	4.68692i	0.0582285	+	0.179209i
$685$	3.09803	+	3.44071i	0.118370	+	0.131463i
$686$	3.26847	−	2.37469i	0.124791	−	0.0906659i
$687$	3.85740	+	6.68122i	0.147169	+	0.254904i
$688$	5.65610	−	9.79666i	0.215637	−	0.373494i
$689$	−2.24727	−	21.3814i	−0.0856143	−	0.814566i
$690$	−5.88315	−	4.27436i	−0.223968	−	0.162722i
$691$	−2.48895	+	23.6807i	−0.0946839	+	0.900858i	0.839330	+	0.543622i	$0.182947\pi$
$691$	−2.48895	+	23.6807i	−0.0946839	+	0.900858i	−0.934014	+	0.357236i	$0.883719\pi$
$692$	−11.6432	+	12.9311i	−0.442608	+	0.491566i
$693$	−8.84590	−	3.93845i	−0.336028	−	0.149609i
$694$	24.4628	+	5.19974i	0.928597	+	0.197379i
$695$	8.04940	−	1.71095i	0.305331	−	0.0649001i
$696$	−2.16603	+	0.964380i	−0.0821033	+	0.0365547i
$697$	−7.69394	+	23.6795i	−0.291429	+	0.896926i
$698$	−5.96248	+	18.3506i	−0.225683	+	0.694582i
$699$	−13.9815	+	6.22497i	−0.528829	+	0.235450i
$700$	3.50963	−	0.745995i	0.132652	−	0.0281960i
$701$	−21.3600	−	4.54020i	−0.806755	−	0.171481i	−0.213968	−	0.976841i	$-0.568639\pi$
$701$	−21.3600	−	4.54020i	−0.806755	−	0.171481i	−0.592787	+	0.805360i	$0.701972\pi$
$702$	3.00402	+	1.33748i	0.113379	+	0.0504798i
$703$	28.8559	−	32.0477i	1.08832	−	1.20870i
$704$	−0.282091	+	2.68392i	−0.0106317	+	0.101154i
$705$	0.977504	+	0.710199i	0.0368149	+	0.0267476i
$706$	3.04930	+	29.0122i	0.114762	+	1.09189i
$707$	−0.727140	+	1.25944i	−0.0273469	+	0.0473662i
$708$	−4.99856	−	8.65775i	−0.187857	−	0.325378i
$709$	−26.4300	+	19.2025i	−0.992599	+	0.721165i	−0.960489	−	0.278319i	$-0.910223\pi$
$709$	−26.4300	+	19.2025i	−0.992599	+	0.721165i	−0.0321100	+	0.999484i	$0.510223\pi$
$710$	−5.23984	−	5.81943i	−0.196648	−	0.218399i
$711$	3.93514	+	12.1111i	0.147579	+	0.454202i
$712$	13.3172			0.499083
$713$	−0.991252	−	40.4765i	−0.0371227	−	1.51586i
$714$	−23.6954			−0.886779
$715$	2.74227	+	8.43984i	0.102555	+	0.315632i
$716$	1.90163	+	2.11198i	0.0710674	+	0.0789284i
$717$	13.9232	−	10.1158i	0.519970	−	0.377780i
$718$	−14.7986	−	25.6319i	−0.552278	−	0.956573i
$719$	−9.61434	+	16.6525i	−0.358554	+	0.621035i	−0.987720	−	0.156237i	$-0.950064\pi$
$719$	−9.61434	+	16.6525i	−0.358554	+	0.621035i	0.629165	+	0.777272i	$0.283397\pi$
$720$	0.104528	+	0.994522i	0.00389555	+	0.0370636i
$721$	−17.5575	−	12.7563i	−0.653876	−	0.475069i
$722$	0.552572	−	5.25737i	0.0205646	−	0.195659i
$723$	14.5010	−	16.1050i	0.539298	−	0.598951i
$724$	−15.1490	−	6.74479i	−0.563010	−	0.250668i
$725$	−2.31921	−	0.492962i	−0.0861332	−	0.0183082i
$726$	−3.63579	+	0.772810i	−0.134937	+	0.0286817i
$727$	−38.4057	+	17.0993i	−1.42439	+	0.634178i	−0.966927	−	0.255052i	$-0.917908\pi$
$727$	−38.4057	+	17.0993i	−1.42439	+	0.634178i	−0.457460	+	0.889230i	$0.651241\pi$
$728$	−3.64596	+	11.2211i	−0.135128	+	0.415883i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	1.24852	−	0.555877i	0.0462098	−	0.0205739i
$731$	−73.0734	+	15.5322i	−2.70272	+	0.574480i
$732$	8.50794	+	1.80842i	0.314462	+	0.0668410i
$733$	−8.11363	−	3.61242i	−0.299684	−	0.133428i	0.251386	−	0.967887i	$-0.419114\pi$
$733$	−8.11363	−	3.61242i	−0.299684	−	0.133428i	−0.551070	+	0.834459i	$0.685780\pi$
$734$	−11.1332	+	12.3646i	−0.410932	+	0.456386i
$735$	0.614002	−	5.84184i	0.0226478	−	0.215480i
$736$	5.88315	+	4.27436i	0.216856	+	0.157555i
$737$	1.42210	+	13.5304i	0.0523839	+	0.498399i
$738$	1.88508	−	3.26505i	0.0693906	−	0.120188i
$739$	−9.44215	−	16.3543i	−0.347335	−	0.601602i	0.638440	−	0.769672i	$-0.279580\pi$
$739$	−9.44215	−	16.3543i	−0.347335	−	0.601602i	−0.985775	+	0.168070i	$0.946247\pi$
$740$	7.07945	−	5.14352i	0.260246	−	0.189080i
$741$	−10.8434	−	12.0428i	−0.398342	−	0.442403i
$742$	−7.24917	−	22.3106i	−0.266125	−	0.819049i
$743$	−7.55537			−0.277180			−0.138590	−	0.990350i	$-0.544257\pi$
$743$	−7.55537			−0.277180			−0.138590	+	0.990350i	$0.544257\pi$
$744$	−4.04521	+	3.82574i	−0.148304	+	0.140259i
$745$	−11.0797			−0.405928
$746$	−4.05773	−	12.4884i	−0.148564	−	0.457233i
$747$	−6.51668	−	7.23751i	−0.238433	−	0.264806i
$748$	14.4185	−	10.4757i	0.527193	−	0.383028i
$749$	12.6905	+	21.9806i	0.463700	+	0.803152i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−5.38558	−	51.2403i	−0.196523	−	1.86979i	−0.437449	−	0.899243i	$-0.644118\pi$
$751$	−5.38558	−	51.2403i	−0.196523	−	1.86979i	0.240926	−	0.970543i	$-0.422549\pi$
$752$	−0.977504	−	0.710199i	−0.0356459	−	0.0258983i
$753$	−0.0928940	+	0.883827i	−0.00338525	+	0.0322085i
$754$	5.21698	−	5.79404i	0.189991	−	0.211006i
$755$	13.6317	+	6.06924i	0.496109	+	0.220882i
$756$	3.50963	+	0.745995i	0.127644	+	0.0271316i
$757$	13.2206	−	2.81012i	0.480510	−	0.102136i	0.0387127	−	0.999250i	$-0.487674\pi$
$757$	13.2206	−	2.81012i	0.480510	−	0.102136i	0.441798	+	0.897115i	$0.354341\pi$
$758$	−18.1570	+	8.08404i	−0.659494	+	0.293625i
$759$	6.06442	−	18.6644i	0.220125	−	0.677474i
$760$	1.52287	−	4.68692i	0.0552404	−	0.170012i
$761$	−9.81444	+	4.36967i	−0.355773	+	0.158400i	−0.576838	−	0.816859i	$-0.695714\pi$
$761$	−9.81444	+	4.36967i	−0.355773	+	0.158400i	0.221065	+	0.975259i	$0.429047\pi$
$762$	15.9620	−	3.39282i	0.578241	−	0.122909i
$763$	−38.6792	−	8.22152i	−1.40028	−	0.297639i
$764$	19.6866	+	8.76504i	0.712236	+	0.317108i
$765$	4.41894	−	4.90773i	0.159767	−	0.177440i
$766$	2.25922	−	21.4950i	0.0816288	−	0.776646i
$767$	26.5953	+	19.3226i	0.960301	+	0.697700i
$768$	−0.104528	−	0.994522i	−0.00377185	−	0.0358867i
$769$	−19.8732	+	34.4214i	−0.716646	+	1.24127i	0.245675	+	0.969352i	$0.420990\pi$
$769$	−19.8732	+	34.4214i	−0.716646	+	1.24127i	−0.962321	+	0.271915i	$0.912343\pi$
$770$	4.84152	+	8.38576i	0.174476	+	0.302202i
$771$	14.0471	−	10.2058i	0.505895	−	0.367555i
$772$	−3.91143	−	4.34408i	−0.140775	−	0.156347i
$773$	2.81795	+	8.67274i	0.101354	+	0.311937i	0.988858	−	0.148865i	$-0.0475619\pi$
$773$	2.81795	+	8.67274i	0.101354	+	0.311937i	−0.887503	+	0.460802i	$0.847562\pi$
$774$	11.3122			0.406609
$775$	−5.52136	+	0.717380i	−0.198333	+	0.0257690i
$776$	−8.13636			−0.292078
$777$	−9.70245	−	29.8611i	−0.348074	−	1.07126i
$778$	2.93701	+	3.26189i	0.105297	+	0.116944i
$779$	−15.0313	+	10.9209i	−0.538554	+	0.391282i
$780$	−1.64416	−	2.84776i	−0.0588702	−	0.101966i
$781$	10.5665	−	18.3017i	0.378100	−	0.654888i
$782$	−5.01989	−	47.7611i	−0.179511	−	1.70793i
$783$	−1.91819	−	1.39365i	−0.0685507	−	0.0498050i
$784$	−0.614002	+	5.84184i	−0.0219287	+	0.208637i
$785$	−9.95910	+	11.0607i	−0.355456	+	0.394774i
$786$	−16.3596	−	7.28375i	−0.583527	−	0.259803i
$787$	0.448226	+	0.0952735i	0.0159775	+	0.00339613i	0.215894	−	0.976417i	$-0.430734\pi$
$787$	0.448226	+	0.0952735i	0.0159775	+	0.00339613i	−0.199916	+	0.979813i	$0.564067\pi$
$788$	15.1232	−	3.21454i	0.538743	−	0.114513i
$789$	8.74208	−	3.89222i	0.311226	−	0.138567i
$790$	3.93514	−	12.1111i	0.140006	−	0.430894i
$791$	−8.13474	+	25.0361i	−0.289238	+	0.890183i
$792$	−2.46539	+	1.09766i	−0.0876037	+	0.0390037i
$793$	−27.9767	+	5.94664i	−0.993483	+	0.211171i
$794$	−7.47020	−	1.58784i	−0.265108	−	0.0563504i
$795$	5.97281	+	2.65927i	0.211834	+	0.0943145i
$796$	−6.53656	+	7.25958i	−0.231682	+	0.257309i
$797$	2.49978	−	23.7838i	0.0885466	−	0.842465i	−0.856636	−	0.515922i	$-0.827450\pi$
$797$	2.49978	−	23.7838i	0.0885466	−	0.842465i	0.945182	−	0.326543i	$-0.105884\pi$
$798$	−14.3053	−	10.3934i	−0.506401	−	0.367922i
$799$	0.834071	+	7.93566i	0.0295073	+	0.280743i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	6.65859	+	11.5330i	0.235270	+	0.407499i
$802$	−3.84799	+	2.79573i	−0.135877	+	0.0987206i
$803$	2.46792	+	2.74090i	0.0870909	+	0.0967243i
$804$	−1.55785	−	4.79455i	−0.0549410	−	0.169091i
$805$	26.0921			0.919627
$806$	7.03504	−	16.9030i	0.247799	−	0.595382i
$807$	22.1664			0.780294
$808$	0.125249	+	0.385476i	0.00440623	+	0.0135610i
$809$	−18.9795	−	21.0788i	−0.667282	−	0.741092i	0.310533	−	0.950563i	$-0.399493\pi$
$809$	−18.9795	−	21.0788i	−0.667282	−	0.741092i	−0.977815	+	0.209471i	$0.932826\pi$
$810$	−0.809017	+	0.587785i	−0.0284260	+	0.0206527i
$811$	−17.5909	−	30.4684i	−0.617702	−	1.06989i	−0.989904	−	0.141739i	$-0.954731\pi$
$811$	−17.5909	−	30.4684i	−0.617702	−	1.06989i	0.372202	−	0.928152i	$-0.378603\pi$
$812$	4.25365	−	7.36754i	0.149274	−	0.258550i
$813$	1.52822	+	14.5400i	0.0535969	+	0.509941i
$814$	19.1053	+	13.8808i	0.669642	+	0.486523i
$815$	0.406303	−	3.86572i	0.0142322	−	0.135410i
$816$	−4.41894	+	4.90773i	−0.154694	+	0.171805i
$817$	−50.9282	−	22.6747i	−1.78175	−	0.793287i
$818$	28.2452	+	6.00371i	0.987571	+	0.209915i
$819$	−11.5408	+	2.45306i	−0.403267	+	0.0857170i
$820$	−3.44421	+	1.53346i	−0.120277	+	0.0535507i
$821$	−11.2268	+	34.5525i	−0.391818	+	1.20589i	0.539595	+	0.841925i	$0.318577\pi$
$821$	−11.2268	+	34.5525i	−0.391818	+	1.20589i	−0.931412	+	0.363966i	$0.881423\pi$
$822$	1.43073	−	4.40333i	0.0499024	−	0.153584i
$823$	18.0607	−	8.04114i	0.629556	−	0.280297i	−0.0670505	−	0.997750i	$-0.521359\pi$
$823$	18.0607	−	8.04114i	0.629556	−	0.280297i	0.696607	+	0.717453i	$0.254692\pi$
$824$	−5.91634	+	1.25756i	−0.206105	+	0.0438091i
$825$	−2.63973	−	0.561092i	−0.0919035	−	0.0195347i
$826$	32.7689	+	14.5897i	1.14018	+	0.507639i
$827$	−9.41911	+	10.4610i	−0.327535	+	0.363764i	−0.884311	−	0.466898i	$-0.845371\pi$
$827$	−9.41911	+	10.4610i	−0.327535	+	0.363764i	0.556776	+	0.830662i	$0.312038\pi$
$828$	−0.760128	+	7.23214i	−0.0264163	+	0.251334i
$829$	−26.5684	−	19.3031i	−0.922760	−	0.670424i	0.0214498	−	0.999770i	$-0.493172\pi$
$829$	−26.5684	−	19.3031i	−0.922760	−	0.670424i	−0.944209	+	0.329346i	$0.893172\pi$
$830$	1.01801	+	9.68567i	0.0353355	+	0.336195i
$831$	12.3323	−	21.3602i	0.427803	−	0.740976i
$832$	1.64416	+	2.84776i	0.0570008	+	0.0987284i
$833$	31.3835	−	22.8014i	1.08737	−	0.790022i
$834$	−5.50643	−	6.11551i	−0.190672	−	0.211763i
$835$	−0.754478	−	2.32205i	−0.0261098	−	0.0803577i
$836$	13.2995			0.459973
$837$	−5.33579	−	1.59038i	−0.184432	−	0.0549715i
$838$	−22.2170			−0.767472
$839$	4.17692	+	12.8552i	0.144203	+	0.443812i	0.996908	−	0.0785816i	$-0.0250391\pi$
$839$	4.17692	+	12.8552i	0.144203	+	0.443812i	−0.852704	+	0.522394i	$0.825039\pi$
$840$	−2.40087	−	2.66643i	−0.0828378	−	0.0920007i
$841$	18.9134	−	13.7414i	0.652187	−	0.473841i
$842$	−7.91378	−	13.7071i	−0.272727	−	0.472377i
$843$	−10.4524	+	18.1040i	−0.359999	+	0.623536i
$844$	1.50396	+	14.3093i	0.0517686	+	0.492545i
$845$	−1.76933	−	1.28549i	−0.0608667	−	0.0442223i
$846$	0.126298	−	1.20164i	0.00434221	−	0.0413133i
$847$	8.92405	−	9.91116i	0.306634	−	0.340551i
$848$	−5.97281	−	2.65927i	−0.205107	−	0.0913196i
$849$	24.9625	+	5.30594i	0.856711	+	0.182099i
$850$	−6.45969	+	1.37305i	−0.221566	+	0.0470952i
$851$	58.1333	−	25.8826i	1.99278	−	0.887244i
$852$	−2.41986	+	7.44755i	−0.0829029	+	0.255149i
$853$	−2.70650	+	8.32976i	−0.0926690	+	0.285206i	−0.986639	−	0.162921i	$-0.947909\pi$
$853$	−2.70650	+	8.32976i	−0.0926690	+	0.285206i	0.893970	+	0.448126i	$0.147909\pi$
$854$	−28.5107	+	12.6938i	−0.975614	+	0.434372i
$855$	4.82043	−	1.02461i	0.164855	−	0.0350410i
$856$	6.91919	+	1.47072i	0.236493	+	0.0502682i
$857$	0.614605	+	0.273640i	0.0209945	+	0.00934736i	0.417207	−	0.908811i	$-0.363009\pi$
$857$	0.614605	+	0.273640i	0.0209945	+	0.00934736i	−0.396213	+	0.918159i	$0.629676\pi$
$858$	5.93798	−	6.59479i	0.202719	−	0.225143i
$859$	−5.62026	+	53.4732i	−0.191761	+	1.82448i	0.300212	+	0.953872i	$0.402942\pi$
$859$	−5.62026	+	53.4732i	−0.191761	+	1.82448i	−0.491973	+	0.870610i	$0.663724\pi$
$860$	−9.15177	−	6.64915i	−0.312073	−	0.226734i
$861$	1.41400	+	13.4534i	0.0481891	+	0.458489i
$862$	4.91613	−	8.51499i	0.167444	−	0.290022i
$863$	−12.4442	−	21.5539i	−0.423604	−	0.733704i	0.572685	−	0.819776i	$-0.305902\pi$
$863$	−12.4442	−	21.5539i	−0.423604	−	0.733704i	−0.996289	+	0.0860716i	$0.972569\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	11.6432	+	12.9311i	0.395881	+	0.439670i
$866$	0.223842	+	0.688915i	0.00760647	+	0.0234103i
$867$	26.6129			0.903822
$868$	3.67388	−	19.6366i	0.124700	−	0.666511i
$869$	34.3663			1.16580
$870$	0.732685	+	2.25497i	0.0248403	+	0.0764507i
$871$	11.0924	+	12.3194i	0.375852	+	0.417426i
$872$	−8.91607	+	6.47791i	−0.301936	+	0.219370i
$873$	−4.06818	−	7.04629i	−0.137687	−	0.238481i
$874$	17.9186	−	31.0359i	0.606105	−	1.04980i
$875$	−0.375052	−	3.56838i	−0.0126791	−	0.120633i
$876$	−1.10566	−	0.803311i	−0.0373569	−	0.0271414i
$877$	0.305854	−	2.91001i	0.0103280	−	0.0982640i	−0.988144	−	0.153533i	$-0.950935\pi$
$877$	0.305854	−	2.91001i	0.0103280	−	0.0982640i	0.998472	+	0.0552688i	$0.0176016\pi$
$878$	−4.44774	+	4.93971i	−0.150104	+	0.166707i
$879$	−18.2582	−	8.12907i	−0.615833	−	0.274187i
$880$	2.63973	+	0.561092i	0.0889852	+	0.0189144i
$881$	−0.520138	+	0.110559i	−0.0175239	+	0.00372482i	−0.216665	−	0.976246i	$-0.569518\pi$
$881$	−0.520138	+	0.110559i	−0.0175239	+	0.00372482i	0.199141	+	0.979971i	$0.436185\pi$
$882$	−5.36618	+	2.38918i	−0.180689	+	0.0804479i
$883$	−12.5692	+	38.6840i	−0.422988	+	1.30182i	0.481921	+	0.876215i	$0.339939\pi$
$883$	−12.5692	+	38.6840i	−0.422988	+	1.30182i	−0.904908	+	0.425607i	$0.860061\pi$
$884$	6.71062	−	20.6532i	0.225703	−	0.694641i
$885$	−9.13282	+	4.06619i	−0.306996	+	0.136684i
$886$	−5.14999	+	1.09466i	−0.173017	+	0.0367759i
$887$	−32.9095	−	6.99513i	−1.10499	−	0.234874i	−0.380928	−	0.924605i	$-0.624395\pi$
$887$	−32.9095	−	6.99513i	−1.10499	−	0.234874i	−0.724066	+	0.689731i	$0.757729\pi$
$888$	−7.99415	−	3.55923i	−0.268266	−	0.119440i
$889$	−39.1787	+	43.5124i	−1.31401	+	1.45936i
$890$	1.39203	−	13.2442i	0.0466608	−	0.443948i
$891$	−2.18330	−	1.58626i	−0.0731431	−	0.0531416i
$892$	−2.07207	−	19.7144i	−0.0693780	−	0.660087i
$893$	−2.97723	+	5.15671i	−0.0996291	+	0.172563i
$894$	5.53984	+	9.59528i	0.185280	+	0.320914i
$895$	2.29918	−	1.67046i	0.0768533	−	0.0558372i
$896$	2.40087	+	2.66643i	0.0802073	+	0.0890793i
$897$	−7.38937	−	22.7422i	−0.246724	−	0.759338i
$898$	33.7216			1.12530
$899$	−7.49572	+	10.8668i	−0.249996	+	0.362429i
$900$	1.00000			0.0333333
$901$	13.3425	+	41.0641i	0.444504	+	1.36804i
$902$	−6.80808	−	7.56114i	−0.226684	−	0.251758i
$903$	−32.8369	+	23.8574i	−1.09274	+	0.793925i
$904$	3.66838	+	6.35382i	0.122008	+	0.211325i
$905$	−8.29135	+	14.3610i	−0.275614	+	0.477377i
$906$	−1.55975	−	14.8400i	−0.0518193	−	0.493027i
$907$	−6.17995	−	4.48999i	−0.205202	−	0.149088i	0.480438	−	0.877029i	$-0.340478\pi$
$907$	−6.17995	−	4.48999i	−0.205202	−	0.149088i	−0.685640	+	0.727941i	$0.740478\pi$
$908$	−0.609010	+	5.79434i	−0.0202107	+	0.192292i
$909$	−0.271207	+	0.301206i	−0.00899538	+	0.00999038i
$910$	10.7785	+	4.79892i	0.357305	+	0.159083i
$911$	13.5929	+	2.88926i	0.450352	+	0.0957253i	0.427504	−	0.904014i	$-0.359393\pi$
$911$	13.5929	+	2.88926i	0.450352	+	0.0957253i	0.0228486	+	0.999739i	$0.492726\pi$
$912$	−4.82043	+	1.02461i	−0.159620	+	0.0339283i
$913$	−24.0105	+	10.6901i	−0.794630	+	0.353792i
$914$	−6.43593	+	19.8078i	−0.212882	+	0.655183i
$915$	2.68783	−	8.27230i	0.0888570	−	0.273474i
$916$	−7.04782	+	3.13789i	−0.232867	+	0.103679i
$917$	62.8497	−	13.3591i	2.07548	−	0.441157i
$918$	−6.45969	−	1.37305i	−0.213202	−	0.0453174i
$919$	−0.902685	−	0.401901i	−0.0297768	−	0.0132575i	0.391794	−	0.920053i	$-0.371855\pi$
$919$	−0.902685	−	0.401901i	−0.0297768	−	0.0132575i	−0.421571	+	0.906795i	$0.638521\pi$
$920$	4.86590	−	5.40413i	0.160424	−	0.178169i
$921$	1.94582	−	18.5132i	0.0641168	−	0.610031i
$922$	12.8341	+	9.32455i	0.422670	+	0.307088i
$923$	−2.69163	−	25.6091i	−0.0885959	−	0.842934i
$924$	4.84152	−	8.38576i	0.159274	−	0.275871i
$925$	−4.37534	−	7.57832i	−0.143860	−	0.249174i
$926$	21.7806	−	15.8245i	0.715755	−	0.520026i
$927$	−4.04724	−	4.49492i	−0.132929	−	0.147633i
$928$	−0.732685	−	2.25497i	−0.0240516	−	0.0740231i
$929$	20.2050			0.662904			0.331452	−	0.943472i	$-0.392462\pi$
$929$	20.2050			0.662904			0.331452	+	0.943472i	$0.392462\pi$
$930$	3.38195	+	4.42294i	0.110898	+	0.145034i
$931$	28.9479			0.948728
$932$	−4.72940	−	14.5556i	−0.154917	−	0.476785i
$933$	4.91862	+	5.46268i	0.161028	+	0.178840i
$934$	−13.5794	+	9.86598i	−0.444330	+	0.322825i
$935$	−8.91112	−	15.4345i	−0.291425	−	0.504763i
$936$	−1.64416	+	2.84776i	−0.0537409	+	0.0930820i
$937$	−3.99739	−	38.0326i	−0.130589	−	1.24247i	−0.841915	−	0.539610i	$-0.818572\pi$
$937$	−3.99739	−	38.0326i	−0.130589	−	1.24247i	0.711326	−	0.702862i	$-0.248095\pi$
$938$	14.6338	+	10.6321i	0.477810	+	0.347149i
$939$	−1.78439	+	16.9773i	−0.0582314	+	0.554035i
$940$	−0.808485	+	0.897914i	−0.0263699	+	0.0292867i
$941$	17.3210	+	7.71182i	0.564649	+	0.251398i	0.669151	−	0.743127i	$-0.266658\pi$
$941$	17.3210	+	7.71182i	0.564649	+	0.251398i	−0.104501	+	0.994525i	$0.533325\pi$
$942$	14.5584	+	3.09448i	0.474338	+	0.100824i
$943$	−26.8173	+	5.70020i	−0.873293	+	0.185624i
$944$	9.13282	−	4.06619i	0.297248	−	0.132343i
$945$	1.10876	−	3.41243i	0.0360681	−	0.111006i
$946$	9.43375	−	29.0341i	0.306718	−	0.943980i
$947$	14.4650	−	6.44023i	0.470049	−	0.209279i	−0.158022	−	0.987436i	$-0.550512\pi$
$947$	14.4650	−	6.44023i	0.470049	−	0.209279i	0.628071	+	0.778156i	$0.283845\pi$
$948$	−12.4561	+	2.64763i	−0.404555	+	0.0859909i
$949$	4.39585	+	0.934366i	0.142695	+	0.0303308i
$950$	−4.50206	−	2.00445i	−0.146066	−	0.0650328i
$951$	−19.5848	+	21.7512i	−0.635082	+	0.705329i
$952$	2.47685	−	23.5656i	0.0802751	−	0.763766i
$953$	4.82571	+	3.50608i	0.156320	+	0.113573i	0.663196	−	0.748446i	$-0.269200\pi$
$953$	4.82571	+	3.50608i	0.156320	+	0.113573i	−0.506876	+	0.862019i	$0.669200\pi$
$954$	−0.683413	−	6.50224i	−0.0221263	−	0.210518i
$955$	10.7748	−	18.6626i	0.348665	−	0.603906i
$956$	8.60498	+	14.9043i	0.278305	+	0.482039i
$957$	−5.17663	+	3.76104i	−0.167337	+	0.121577i
$958$	24.2185	+	26.8974i	0.782465	+	0.869016i
$959$	5.13351	+	15.7993i	0.165770	+	0.510187i
$960$	−1.00000			−0.0322749
$961$	−8.12487	+	29.9163i	−0.262093	+	0.965043i
$962$	28.7750			0.927743
$963$	2.18592	+	6.72755i	0.0704401	+	0.216792i
$964$	14.5010	+	16.1050i	0.467046	+	0.518707i
$965$	−4.72914	+	3.43592i	−0.152237	+	0.110606i
$966$	−13.0461	−	22.5964i	−0.419750	−	0.727029i
$967$	16.1356	−	27.9476i	0.518885	−	0.898735i	−0.480874	−	0.876790i	$-0.659681\pi$
$967$	16.1356	−	27.9476i	0.518885	−	0.898735i	0.999759	−	0.0219457i	$-0.00698610\pi$
$968$	−0.388534	−	3.69665i	−0.0124879	−	0.118815i
$969$	26.3297	+	19.1297i	0.845832	+	0.614533i
$970$	−0.850481	+	8.09178i	−0.0273073	+	0.259812i
$971$	14.0930	−	15.6519i	0.452267	−	0.502293i	−0.473287	−	0.880908i	$-0.656933\pi$
$971$	14.0930	−	15.6519i	0.452267	−	0.502293i	0.925554	+	0.378615i	$0.123599\pi$
$972$	0.913545	+	0.406737i	0.0293020	+	0.0130461i
$973$	28.8816	+	6.13896i	0.925900	+	0.196806i
$974$	22.6871	−	4.82230i	0.726943	−	0.154517i
$975$	−3.00402	+	1.33748i	−0.0962057	+	0.0428335i
$976$	−2.68783	+	8.27230i	−0.0860354	+	0.264790i
$977$	9.44605	−	29.0719i	0.302206	−	0.930094i	−0.678499	−	0.734601i	$-0.737369\pi$
$977$	9.44605	−	29.0719i	0.302206	−	0.930094i	0.980705	−	0.195493i	$-0.0626307\pi$
$978$	−3.55096	+	1.58099i	−0.113547	+	0.0505544i
$979$	35.1538	−	7.47216i	1.12352	−	0.238811i
$980$	5.74566	+	1.22128i	0.183538	+	0.0390123i
$981$	−10.0681	−	4.48259i	−0.321449	−	0.143118i
$982$	11.2479	−	12.4921i	0.358936	−	0.398639i
$983$	−5.86124	+	55.7660i	−0.186944	+	1.77866i	0.351688	+	0.936117i	$0.385608\pi$
$983$	−5.86124	+	55.7660i	−0.186944	+	1.77866i	−0.538633	+	0.842541i	$0.681059\pi$
$984$	3.05012	+	2.21604i	0.0972342	+	0.0706448i
$985$	−1.61613	−	15.3764i	−0.0514940	−	0.489933i
$986$	−7.82911	+	13.5604i	−0.249330	+	0.431852i
$987$	2.16765	+	3.75447i	0.0689969	+	0.119506i
$988$	13.1103	−	9.52517i	0.417093	−	0.303036i
$989$	−55.0441	−	61.1326i	−1.75030	−	1.94390i
$990$	0.833945	+	2.56662i	0.0265045	+	0.0815725i
$991$	39.1102			1.24238			0.621188	−	0.783662i	$-0.286650\pi$
$991$	39.1102			1.24238			0.621188	+	0.783662i	$0.286650\pi$
$992$	−3.38195	−	4.42294i	−0.107377	−	0.140429i
$993$	27.9117			0.885752
$994$	−8.68254	−	26.7221i	−0.275393	−	0.847574i
$995$	6.53656	+	7.25958i	0.207223	+	0.230144i
$996$	7.87904	−	5.72445i	0.249657	−	0.181386i
$997$	−5.52429	−	9.56835i	−0.174956	−	0.303033i	0.765190	−	0.643805i	$-0.222645\pi$
$997$	−5.52429	−	9.56835i	−0.174956	−	0.303033i	−0.940146	+	0.340772i	$0.889312\pi$
$998$	−9.06147	+	15.6949i	−0.286836	+	0.496814i
$999$	−0.914696	−	8.70275i	−0.0289397	−	0.275343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.i.361.3	✓	24
31.14	even	15	inner	930.2.bg.i.541.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.i.361.3	✓	24	1.1	even	1	trivial
930.2.bg.i.541.3	yes	24	31.14	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.375052 + 3.56838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(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} +(0.375052 + 3.56838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.669131 - 0.743145i) q^{10} +(2.46539 + 1.09766i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(3.21645 - 0.683678i) q^{13} +(3.27784 - 1.45939i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.03306 + 2.68609i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-4.82043 - 1.02461i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-2.40087 + 2.66643i) q^{21} +(0.282091 - 2.68392i) q^{22} +(-5.88315 - 4.27436i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.64416 - 2.84776i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.40087 - 2.66643i) q^{28} +(0.732685 + 2.25497i) q^{29} +1.00000 q^{30} +(3.38195 + 4.42294i) q^{31} -1.00000 q^{32} +(0.833945 + 2.56662i) q^{33} +(4.41894 + 4.90773i) q^{34} +(-2.90278 + 2.10900i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.37534 + 7.57832i) q^{37} +(0.515128 + 4.90112i) q^{38} +(2.66030 + 1.93282i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(2.52273 - 2.80177i) q^{41} +(3.27784 + 1.45939i) q^{42} +(11.0650 + 2.35194i) q^{43} +(-2.63973 + 0.561092i) q^{44} +(-0.913545 + 0.406737i) q^{45} +(-2.24716 + 6.91606i) q^{46} +(0.373373 - 1.14913i) q^{47} +(0.913545 - 0.406737i) q^{48} +(-5.74566 + 1.22128i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-6.03306 - 2.68609i) q^{51} +(-2.20031 + 2.44369i) q^{52} +(0.683413 - 6.50224i) q^{53} +(0.809017 + 0.587785i) q^{54} +(0.282091 + 2.68392i) q^{55} +(-1.79402 + 3.10733i) q^{56} +(-2.46406 - 4.26787i) q^{57} +(1.91819 - 1.39365i) q^{58} +(6.68937 + 7.42930i) q^{59} +(-0.309017 - 0.951057i) q^{60} -8.69801 q^{61} +(3.16139 - 4.58319i) q^{62} -3.58804 q^{63} +(0.309017 + 0.951057i) q^{64} +(2.20031 + 2.44369i) q^{65} +(2.18330 - 1.58626i) q^{66} +(2.52065 + 4.36589i) q^{67} +(3.30200 - 5.71924i) q^{68} +(-0.760128 - 7.23214i) q^{69} +(2.90278 + 2.10900i) q^{70} +(0.818543 - 7.78792i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(1.24852 + 0.555877i) q^{73} +(8.55946 + 1.81937i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(4.50206 - 2.00445i) q^{76} +(-2.99223 + 9.20912i) q^{77} +(1.01614 - 3.12737i) q^{78} +(11.6334 - 5.17954i) q^{79} +(0.978148 - 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.44421 - 1.53346i) q^{82} +(-6.51668 + 7.23751i) q^{83} +(0.375052 - 3.56838i) q^{84} +(-5.34275 - 3.88174i) q^{85} +(-1.18245 - 11.2502i) q^{86} +(-1.18551 + 2.05336i) q^{87} +(1.34935 + 2.33714i) q^{88} +(10.7738 - 7.82765i) q^{89} +(0.669131 + 0.743145i) q^{90} +(3.64596 + 11.2211i) q^{91} +7.27197 q^{92} +(-1.02392 + 5.47280i) q^{93} -1.20826 q^{94} +(-1.52287 - 4.68692i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-6.58245 + 4.78243i) q^{97} +(2.93701 + 5.08705i) q^{98} +(-1.34935 + 2.33714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

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