LMFDB - Embedded newform 930.2.bg.h.391.3

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			391.3
Character	$\chi$	$=$	930.391
Dual form			930.2.bg.h.421.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.56932 - 2.85352i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.56932 - 2.85352i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(-1.87860 - 0.399310i) q^{11} +(0.104528 - 0.994522i) q^{12} +(0.00217483 + 0.0206921i) q^{13} +(3.75588 - 0.798336i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(7.11058 - 1.51140i) q^{17} +(0.104528 + 0.994522i) q^{18} +(0.814090 - 7.74555i) q^{19} +(-0.978148 - 0.207912i) q^{20} +(-3.50782 + 1.56178i) q^{21} +(-1.28511 - 1.42726i) q^{22} +(-1.30949 + 4.03021i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0104030 + 0.0180186i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.50782 + 1.56178i) q^{28} +(3.86725 + 2.80972i) q^{29} +1.00000 q^{30} +(1.01097 + 5.47521i) q^{31} -1.00000 q^{32} +(1.55378 + 1.12888i) q^{33} +(6.64096 + 2.95675i) q^{34} +(1.18656 + 3.65185i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.186156 - 0.322432i) q^{37} +(5.21133 - 5.78777i) q^{38} +(0.00642943 - 0.0197877i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(10.7111 - 4.76889i) q^{41} +(-3.75588 - 0.798336i) q^{42} +(0.832376 - 7.91953i) q^{43} +(-0.200755 - 1.91005i) q^{44} +(-0.978148 + 0.207912i) q^{45} +(-3.42830 + 2.49080i) q^{46} +(1.38957 - 1.00958i) q^{47} +(0.978148 - 0.207912i) q^{48} +(-0.809464 - 7.70154i) q^{49} +(0.104528 - 0.994522i) q^{50} +(-7.11058 - 1.51140i) q^{51} +(-0.0190073 + 0.00846259i) q^{52} +(8.49564 + 9.43536i) q^{53} +(0.309017 - 0.951057i) q^{54} +(1.28511 - 1.42726i) q^{55} +(1.91989 + 3.32535i) q^{56} +(-3.89411 + 6.74479i) q^{57} +(1.47716 + 4.54623i) q^{58} +(-7.66795 - 3.41399i) q^{59} +(0.809017 + 0.587785i) q^{60} -1.40266 q^{61} +(-2.40036 + 5.02377i) q^{62} +3.83979 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.0190073 - 0.00846259i) q^{65} +(0.593490 + 1.82657i) q^{66} +(-2.58708 + 4.48095i) q^{67} +(3.63472 + 6.29552i) q^{68} +(2.83551 - 3.14916i) q^{69} +(-1.18656 + 3.65185i) q^{70} +(-1.51775 - 1.68563i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(2.79773 + 0.594675i) q^{73} +(0.0389172 - 0.370273i) q^{74} +(0.104528 + 0.994522i) q^{75} +(7.61802 - 1.61926i) q^{76} +(-5.96617 + 4.33468i) q^{77} +(0.0168325 - 0.0122295i) q^{78} +(14.0815 - 2.99310i) q^{79} +(-0.104528 - 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(11.4686 + 2.43772i) q^{82} +(-0.768941 + 0.342354i) q^{83} +(-2.56932 - 2.85352i) q^{84} +(-2.24638 + 6.91365i) q^{85} +(5.32839 - 5.91778i) q^{86} +(-2.39009 - 4.13976i) q^{87} +(0.960287 - 1.66327i) q^{88} +(-0.939554 - 2.89165i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(0.0646330 + 0.0469586i) q^{91} -4.23761 q^{92} +(1.30340 - 5.41305i) q^{93} +1.71760 q^{94} +(6.30080 + 4.57780i) q^{95} +(0.913545 + 0.406737i) q^{96} +(1.22242 + 3.76222i) q^{97} +(3.87198 - 6.70647i) q^{98} +(-0.960287 - 1.66327i) 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} - 11 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 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−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
$7$	2.56932	−	2.85352i	0.971111	−	1.07853i	−0.0257745	−	0.999668i	$-0.508205\pi$
$7$	2.56932	−	2.85352i	0.971111	−	1.07853i	0.996886	−	0.0788604i	$-0.0251281\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.913545	+	0.406737i	−0.288888	+	0.128621i
$11$	−1.87860	−	0.399310i	−0.566421	−	0.120396i	−0.0842042	−	0.996449i	$-0.526835\pi$
$11$	−1.87860	−	0.399310i	−0.566421	−	0.120396i	−0.482216	+	0.876052i	$0.660168\pi$
$12$	0.104528	−	0.994522i	0.0301748	−	0.287094i
$13$	0.00217483	+	0.0206921i	0.000603188	+	0.00573895i	0.994819	−	0.101659i	$-0.0324149\pi$
$13$	0.00217483	+	0.0206921i	0.000603188	+	0.00573895i	−0.994216	+	0.107398i	$0.965748\pi$
$14$	3.75588	−	0.798336i	1.00380	−	0.213364i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	7.11058	−	1.51140i	1.72457	−	0.366569i	0.764131	−	0.645061i	$-0.223168\pi$
$17$	7.11058	−	1.51140i	1.72457	−	0.366569i	0.960438	+	0.278492i	$0.0898347\pi$
$18$	0.104528	+	0.994522i	0.0246376	+	0.234411i
$19$	0.814090	−	7.74555i	0.186765	−	1.77695i	−0.353479	−	0.935442i	$-0.615002\pi$
$19$	0.814090	−	7.74555i	0.186765	−	1.77695i	0.540244	−	0.841508i	$-0.318332\pi$
$20$	−0.978148	−	0.207912i	−0.218720	−	0.0464905i
$21$	−3.50782	+	1.56178i	−0.765469	+	0.340809i
$22$	−1.28511	−	1.42726i	−0.273987	−	0.304294i
$23$	−1.30949	+	4.03021i	−0.273048	+	0.840356i	0.716681	+	0.697401i	$0.245660\pi$
$23$	−1.30949	+	4.03021i	−0.273048	+	0.840356i	−0.989729	+	0.142955i	$0.954340\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.0104030	+	0.0180186i	−0.00204020	+	0.00353373i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	3.50782	+	1.56178i	0.662916	+	0.295149i
$29$	3.86725	+	2.80972i	0.718131	+	0.521752i	0.885786	−	0.464093i	$-0.153620\pi$
$29$	3.86725	+	2.80972i	0.718131	+	0.521752i	−0.167656	+	0.985846i	$0.553620\pi$
$30$	1.00000			0.182574
$31$	1.01097	+	5.47521i	0.181576	+	0.983377i
$31$	1.01097	+	5.47521i	0.181576	+	0.983377i
$32$	−1.00000			−0.176777
$33$	1.55378	+	1.12888i	0.270478	+	0.196514i
$34$	6.64096	+	2.95675i	1.13892	+	0.507078i
$35$	1.18656	+	3.65185i	0.200565	+	0.617276i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.186156	−	0.322432i	−0.0306039	−	0.0530075i	0.850318	−	0.526270i	$-0.176410\pi$
$37$	−0.186156	−	0.322432i	−0.0306039	−	0.0530075i	−0.880922	+	0.473262i	$0.843076\pi$
$38$	5.21133	−	5.78777i	0.845390	−	0.938900i
$39$	0.00642943	−	0.0197877i	0.00102953	−	0.00316857i
$40$	−0.669131	−	0.743145i	−0.105799	−	0.117502i
$41$	10.7111	−	4.76889i	1.67279	−	0.744776i	0.672807	−	0.739818i	$-0.265089\pi$
$41$	10.7111	−	4.76889i	1.67279	−	0.744776i	0.999988	−	0.00495775i	$-0.00157811\pi$
$42$	−3.75588	−	0.798336i	−0.579545	−	0.123186i
$43$	0.832376	−	7.91953i	0.126936	−	1.20772i	−0.726740	−	0.686913i	$-0.758965\pi$
$43$	0.832376	−	7.91953i	0.126936	−	1.20772i	0.853676	−	0.520804i	$-0.174368\pi$
$44$	−0.200755	−	1.91005i	−0.0302649	−	0.287951i
$45$	−0.978148	+	0.207912i	−0.145814	+	0.0309936i
$46$	−3.42830	+	2.49080i	−0.505475	+	0.367249i
$47$	1.38957	−	1.00958i	0.202689	−	0.147262i	−0.481811	−	0.876275i	$-0.660021\pi$
$47$	1.38957	−	1.00958i	0.202689	−	0.147262i	0.684500	+	0.729013i	$0.260021\pi$
$48$	0.978148	−	0.207912i	0.141183	−	0.0300095i
$49$	−0.809464	−	7.70154i	−0.115638	−	1.10022i
$50$	0.104528	−	0.994522i	0.0147826	−	0.140647i
$51$	−7.11058	−	1.51140i	−0.995681	−	0.211638i
$52$	−0.0190073	+	0.00846259i	−0.00263584	+	0.00117355i
$53$	8.49564	+	9.43536i	1.16697	+	1.29605i	0.947255	+	0.320481i	$0.103845\pi$
$53$	8.49564	+	9.43536i	1.16697	+	1.29605i	0.219710	+	0.975565i	$0.429489\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	1.28511	−	1.42726i	0.173285	−	0.192452i
$56$	1.91989	+	3.32535i	0.256557	+	0.444369i
$57$	−3.89411	+	6.74479i	−0.515787	+	0.893369i
$58$	1.47716	+	4.54623i	0.193960	+	0.596949i
$59$	−7.66795	−	3.41399i	−0.998282	−	0.444464i	−0.158483	−	0.987362i	$-0.550660\pi$
$59$	−7.66795	−	3.41399i	−0.998282	−	0.444464i	−0.839799	+	0.542898i	$0.817327\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−1.40266			−0.179592			−0.0897958	−	0.995960i	$-0.528621\pi$
$61$	−1.40266			−0.179592			−0.0897958	+	0.995960i	$0.528621\pi$
$62$	−2.40036	+	5.02377i	−0.304845	+	0.638020i
$63$	3.83979			0.483768
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.0190073	−	0.00846259i	−0.00235756	−	0.00104965i
$66$	0.593490	+	1.82657i	0.0730536	+	0.224836i
$67$	−2.58708	+	4.48095i	−0.316062	+	0.547435i	−0.979663	−	0.200652i	$-0.935694\pi$
$67$	−2.58708	+	4.48095i	−0.316062	+	0.547435i	0.663601	+	0.748087i	$0.269027\pi$
$68$	3.63472	+	6.29552i	0.440774	+	0.763444i
$69$	2.83551	−	3.14916i	0.341356	−	0.379114i
$70$	−1.18656	+	3.65185i	−0.141821	+	0.436480i
$71$	−1.51775	−	1.68563i	−0.180124	−	0.200047i	0.646321	−	0.763066i	$-0.276307\pi$
$71$	−1.51775	−	1.68563i	−0.180124	−	0.200047i	−0.826444	+	0.563018i	$0.809640\pi$
$72$	−0.913545	+	0.406737i	−0.107662	+	0.0479344i
$73$	2.79773	+	0.594675i	0.327449	+	0.0696015i	0.368703	−	0.929547i	$-0.379802\pi$
$73$	2.79773	+	0.594675i	0.327449	+	0.0696015i	−0.0412539	+	0.999149i	$0.513135\pi$
$74$	0.0389172	−	0.370273i	0.00452403	−	0.0430433i
$75$	0.104528	+	0.994522i	0.0120699	+	0.114837i
$76$	7.61802	−	1.61926i	0.873847	−	0.185742i
$77$	−5.96617	+	4.33468i	−0.679908	+	0.493982i
$78$	0.0168325	−	0.0122295i	0.00190590	−	0.00138472i
$79$	14.0815	−	2.99310i	1.58429	−	0.336751i	0.670172	−	0.742206i	$-0.266220\pi$
$79$	14.0815	−	2.99310i	1.58429	−	0.336751i	0.914115	+	0.405455i	$0.132887\pi$
$80$	−0.104528	−	0.994522i	−0.0116866	−	0.111191i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	11.4686	+	2.43772i	1.26649	+	0.269201i
$83$	−0.768941	+	0.342354i	−0.0844022	+	0.0375783i	−0.448504	−	0.893781i	$-0.648043\pi$
$83$	−0.768941	+	0.342354i	−0.0844022	+	0.0375783i	0.364101	+	0.931359i	$0.381376\pi$
$84$	−2.56932	−	2.85352i	−0.280336	−	0.311344i
$85$	−2.24638	+	6.91365i	−0.243654	+	0.749890i
$86$	5.32839	−	5.91778i	0.574575	−	0.638130i
$87$	−2.39009	−	4.13976i	−0.256245	−	0.443829i
$88$	0.960287	−	1.66327i	0.102367	−	0.177305i
$89$	−0.939554	−	2.89165i	−0.0995925	−	0.306514i	0.888831	−	0.458236i	$-0.151518\pi$
$89$	−0.939554	−	2.89165i	−0.0995925	−	0.306514i	−0.988423	+	0.151721i	$0.951518\pi$
$90$	−0.913545	−	0.406737i	−0.0962961	−	0.0428738i
$91$	0.0646330	+	0.0469586i	0.00677538	+	0.00492260i
$92$	−4.23761			−0.441801
$93$	1.30340	−	5.41305i	0.135156	−	0.561307i
$94$	1.71760			0.177157
$95$	6.30080	+	4.57780i	0.646448	+	0.469672i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	1.22242	+	3.76222i	0.124118	+	0.381996i	0.993739	−	0.111724i	$-0.0356371\pi$
$97$	1.22242	+	3.76222i	0.124118	+	0.381996i	−0.869621	+	0.493719i	$0.835637\pi$
$98$	3.87198	−	6.70647i	0.391129	−	0.677455i
$99$	−0.960287	−	1.66327i	−0.0965125	−	0.167164i
$100$	0.669131	−	0.743145i	0.0669131	−	0.0743145i
$101$	−1.57615	+	4.85088i	−0.156832	+	0.482680i	−0.998342	−	0.0575619i	$-0.981667\pi$
$101$	−1.57615	+	4.85088i	−0.156832	+	0.482680i	0.841510	+	0.540242i	$0.181667\pi$
$102$	−4.86420	−	5.40224i	−0.481628	−	0.534902i
$103$	−12.9159	+	5.75052i	−1.27264	+	0.566615i	−0.928161	−	0.372179i	$-0.878611\pi$
$103$	−12.9159	+	5.75052i	−1.27264	+	0.566615i	−0.344478	+	0.938794i	$0.611944\pi$
$104$	−0.0203514	−	0.00432582i	−0.00199562	−	0.000424182i
$105$	0.401367	−	3.81875i	0.0391694	−	0.372672i
$106$	1.32715	+	12.6270i	0.128904	+	1.22644i
$107$	−8.55226	+	1.81784i	−0.826779	+	0.175737i	−0.601821	−	0.798631i	$-0.705558\pi$
$107$	−8.55226	+	1.81784i	−0.826779	+	0.175737i	−0.224958	+	0.974368i	$0.572224\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−5.32009	+	3.86527i	−0.509572	+	0.370226i	−0.812661	−	0.582737i	$-0.801982\pi$
$109$	−5.32009	+	3.86527i	−0.509572	+	0.370226i	0.303089	+	0.952962i	$0.401982\pi$
$110$	1.87860	−	0.399310i	0.179118	−	0.0380727i
$111$	0.0389172	+	0.370273i	0.00369386	+	0.0351447i
$112$	−0.401367	+	3.81875i	−0.0379256	+	0.360838i
$113$	−14.5255	−	3.08748i	−1.36644	−	0.290446i	−0.534434	−	0.845210i	$-0.679475\pi$
$113$	−14.5255	−	3.08748i	−1.36644	−	0.290446i	−0.832008	+	0.554764i	$0.812809\pi$
$114$	−7.11489	+	3.16775i	−0.666370	+	0.296687i
$115$	−2.83551	−	3.14916i	−0.264413	−	0.293660i
$116$	−1.47716	+	4.54623i	−0.137151	+	0.422107i
$117$	−0.0139220	+	0.0154619i	−0.00128709	+	0.00142945i
$118$	−4.19681	−	7.26908i	−0.386347	−	0.669173i
$119$	13.9565	−	24.1734i	1.27939	−	2.21598i
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	−6.67929	−	2.97381i	−0.607208	−	0.270347i
$122$	−1.13477	−	0.824460i	−0.102737	−	0.0746431i
$123$	−11.7248			−1.05719
$124$	−4.89483	+	2.65342i	−0.439569	+	0.238285i
$125$	1.00000			0.0894427
$126$	3.10645	+	2.25697i	0.276745	+	0.201067i
$127$	−7.16697	−	3.19094i	−0.635966	−	0.283150i	0.0633190	−	0.997993i	$-0.479831\pi$
$127$	−7.16697	−	3.19094i	−0.635966	−	0.283150i	−0.699285	+	0.714843i	$0.746498\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−3.98158	+	6.89629i	−0.350558	+	0.607185i
$130$	−0.0104030	−	0.0180186i	−0.000912406	−	0.00158033i
$131$	0.970788	−	1.07817i	0.0848182	−	0.0942001i	−0.699242	−	0.714885i	$-0.746479\pi$
$131$	0.970788	−	1.07817i	0.0848182	−	0.0942001i	0.784060	+	0.620685i	$0.213146\pi$
$132$	−0.593490	+	1.82657i	−0.0516567	+	0.158983i
$133$	−20.0104	−	22.2238i	−1.73512	−	1.92705i
$134$	−4.72682	+	2.10452i	−0.408335	+	0.181803i
$135$	0.978148	+	0.207912i	0.0841855	+	0.0178942i
$136$	−0.759863	+	7.22961i	−0.0651577	+	0.619934i
$137$	−0.0251624	−	0.239404i	−0.00214977	−	0.0204537i	0.993394	−	0.114750i	$-0.0366066\pi$
$137$	−0.0251624	−	0.239404i	−0.00214977	−	0.0204537i	−0.995544	+	0.0942961i	$0.969940\pi$
$138$	4.14501	−	0.881049i	0.352846	−	0.0749998i
$139$	1.19471	−	0.868011i	0.101334	−	0.0736237i	−0.535964	−	0.844241i	$-0.680052\pi$
$139$	1.19471	−	0.868011i	0.101334	−	0.0736237i	0.637299	+	0.770617i	$0.280052\pi$
$140$	−3.10645	+	2.25697i	−0.262543	+	0.190749i
$141$	−1.68007	+	0.357109i	−0.141487	+	0.0300740i
$142$	−0.237095	−	2.25581i	−0.0198966	−	0.189304i
$143$	0.00417691	−	0.0397407i	0.000349291	−	0.00332328i
$144$	−0.978148	−	0.207912i	−0.0815123	−	0.0173260i
$145$	−4.36692	+	1.94428i	−0.362653	+	0.161463i
$146$	1.91387	+	2.12557i	0.158393	+	0.175913i
$147$	−2.39302	+	7.36494i	−0.197373	+	0.607450i
$148$	0.249125	−	0.276682i	0.0204780	−	0.0227431i
$149$	−8.63481	−	14.9559i	−0.707391	−	1.22524i	−0.965822	−	0.259208i	$-0.916539\pi$
$149$	−8.63481	−	14.9559i	−0.707391	−	1.22524i	0.258430	−	0.966030i	$-0.416795\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	0.727961	+	2.24043i	0.0592406	+	0.182324i	0.976298	−	0.216432i	$-0.0694420\pi$
$151$	0.727961	+	2.24043i	0.0592406	+	0.182324i	−0.917057	+	0.398756i	$0.869442\pi$
$152$	7.11489	+	3.16775i	0.577093	+	0.256939i
$153$	5.88110	+	4.27287i	0.475459	+	0.345441i
$154$	−7.37459			−0.594262
$155$	−5.24716	−	1.86208i	−0.421462	−	0.149566i
$156$	0.0208061			0.00166582
$157$	−14.9542	−	10.8649i	−1.19348	−	0.867112i	−0.199849	−	0.979827i	$-0.564045\pi$
$157$	−14.9542	−	10.8649i	−1.19348	−	0.867112i	−0.993627	+	0.112715i	$0.964045\pi$
$158$	13.1514	+	5.85540i	1.04627	+	0.465830i
$159$	−3.92344	−	12.0751i	−0.311149	−	0.957619i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	8.13576	+	14.0915i	0.641188	+	1.11057i
$162$	−0.669131	+	0.743145i	−0.0525719	+	0.0583870i
$163$	2.49734	−	7.68602i	0.195607	−	0.602015i	−0.804362	−	0.594139i	$-0.797493\pi$
$163$	2.49734	−	7.68602i	0.195607	−	0.602015i	0.999969	−	0.00787626i	$-0.00250712\pi$
$164$	7.84540	+	8.71320i	0.612623	+	0.680387i
$165$	−1.75453	+	0.781168i	−0.136590	+	0.0608138i
$166$	−0.823317	−	0.175001i	−0.0639018	−	0.0135827i
$167$	−1.76621	+	16.8044i	−0.136673	+	1.30036i	0.684219	+	0.729277i	$0.260143\pi$
$167$	−1.76621	+	16.8044i	−0.136673	+	1.30036i	−0.820892	+	0.571084i	$0.806523\pi$
$168$	−0.401367	−	3.81875i	−0.0309661	−	0.294623i
$169$	12.7155	−	2.70276i	0.978115	−	0.207905i
$170$	−5.88110	+	4.27287i	−0.451060	+	0.327714i
$171$	6.30080	−	4.57780i	0.481834	−	0.350073i
$172$	7.78914	−	1.65563i	0.593916	−	0.126241i
$173$	2.53943	+	24.1611i	0.193069	+	1.83693i	0.477972	+	0.878375i	$0.341372\pi$
$173$	2.53943	+	24.1611i	0.193069	+	1.83693i	−0.284902	+	0.958557i	$0.591961\pi$
$174$	0.499666	−	4.75400i	0.0378795	−	0.360400i
$175$	−3.75588	−	0.798336i	−0.283918	−	0.0603486i
$176$	1.75453	−	0.781168i	0.132253	−	0.0588827i
$177$	5.61642	+	6.23767i	0.422156	+	0.468852i
$178$	0.939554	−	2.89165i	0.0704226	−	0.216738i
$179$	5.18623	−	5.75989i	0.387637	−	0.430515i	−0.517468	−	0.855703i	$-0.673125\pi$
$179$	5.18623	−	5.75989i	0.387637	−	0.430515i	0.905105	+	0.425188i	$0.139792\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	3.53503	−	6.12285i	0.262757	−	0.455108i	−0.704217	−	0.709985i	$-0.748702\pi$
$181$	3.53503	−	6.12285i	0.262757	−	0.455108i	0.966973	+	0.254877i	$0.0820350\pi$
$182$	0.0246876	+	0.0759807i	0.00182997	+	0.00563206i
$183$	1.28139	+	0.570511i	0.0947230	+	0.0421734i
$184$	−3.42830	−	2.49080i	−0.252737	−	0.183625i
$185$	0.372312			0.0273729
$186$	4.23619	−	3.61313i	0.310612	−	0.264928i
$187$	−13.9615			−1.02097
$188$	1.38957	+	1.00958i	0.101345	+	0.0736311i
$189$	−3.50782	−	1.56178i	−0.255156	−	0.113603i
$190$	2.40669	+	7.40703i	0.174600	+	0.537362i
$191$	−1.94565	+	3.36996i	−0.140782	+	0.243842i	−0.927791	−	0.373099i	$-0.878295\pi$
$191$	−1.94565	+	3.36996i	−0.140782	+	0.243842i	0.787009	+	0.616941i	$0.211628\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−11.5936	+	12.8760i	−0.834524	+	0.926832i	−0.998218	−	0.0596788i	$-0.980992\pi$
$193$	−11.5936	+	12.8760i	−0.834524	+	0.926832i	0.163694	+	0.986511i	$0.447659\pi$
$194$	−1.22242	+	3.76222i	−0.0877646	+	0.270112i
$195$	0.0139220	+	0.0154619i	0.000996973	+	0.00110725i
$196$	7.07446	−	3.14975i	0.505319	−	0.224982i
$197$	−16.8941	−	3.59095i	−1.20365	−	0.255844i	−0.437927	−	0.899011i	$-0.644287\pi$
$197$	−16.8941	−	3.59095i	−1.20365	−	0.255844i	−0.765727	+	0.643166i	$0.777620\pi$
$198$	0.200755	−	1.91005i	0.0142670	−	0.135742i
$199$	−1.81521	−	17.2706i	−0.128677	−	1.22428i	−0.848149	−	0.529758i	$-0.822283\pi$
$199$	−1.81521	−	17.2706i	−0.128677	−	1.22428i	0.719472	−	0.694522i	$-0.244384\pi$
$200$	0.978148	−	0.207912i	0.0691655	−	0.0147016i
$201$	4.18598	−	3.04129i	0.295256	−	0.214516i
$202$	−4.12640	+	2.99801i	−0.290333	+	0.210939i
$203$	17.9538	−	3.81620i	1.26011	−	0.267845i
$204$	−0.759863	−	7.22961i	−0.0532011	−	0.506174i
$205$	−1.22557	+	11.6605i	−0.0855977	+	0.814407i
$206$	−13.8292	−	2.93949i	−0.963528	−	0.204804i
$207$	−3.87125	+	1.72359i	−0.269070	+	0.119798i
$208$	−0.0139220	−	0.0154619i	−0.000965315	−	0.00107209i
$209$	−4.62223	+	14.2257i	−0.319726	+	0.984016i
$210$	2.56932	−	2.85352i	0.177300	−	0.196911i
$211$	−4.68458	−	8.11393i	−0.322500	−	0.558586i	0.658503	−	0.752578i	$-0.271190\pi$
$211$	−4.68458	−	8.11393i	−0.322500	−	0.558586i	−0.981003	+	0.193992i	$0.937856\pi$
$212$	−6.34826	+	10.9955i	−0.436001	+	0.755175i
$213$	0.700924	+	2.15722i	0.0480265	+	0.147810i
$214$	−7.98743	−	3.55623i	−0.546009	−	0.243099i
$215$	6.44233	+	4.68062i	0.439363	+	0.319216i
$216$	1.00000			0.0680414
$217$	18.2211	+	11.1827i	1.23693	+	0.759134i
$218$	−6.57599			−0.445382
$219$	−2.31397	−	1.68120i	−0.156364	−	0.113605i
$220$	1.75453	+	0.781168i	0.118290	+	0.0526663i
$221$	0.0467383	+	0.143846i	0.00314396	+	0.00967611i
$222$	−0.186156	+	0.322432i	−0.0124940	+	0.0216402i
$223$	−7.19354	−	12.4596i	−0.481715	−	0.834354i	0.518065	−	0.855341i	$-0.326653\pi$
$223$	−7.19354	−	12.4596i	−0.481715	−	0.834354i	−0.999780	+	0.0209868i	$0.993319\pi$
$224$	−2.56932	+	2.85352i	−0.171670	+	0.190659i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−9.93658	−	11.0357i	−0.660971	−	0.734083i
$227$	−4.91692	+	2.18915i	−0.326347	+	0.145299i	−0.563370	−	0.826205i	$-0.690495\pi$
$227$	−4.91692	+	2.18915i	−0.326347	+	0.145299i	0.237022	+	0.971504i	$0.423829\pi$
$228$	−7.61802	−	1.61926i	−0.504516	−	0.107238i
$229$	−2.63055	+	25.0280i	−0.173832	+	1.65390i	0.465558	+	0.885017i	$0.345854\pi$
$229$	−2.63055	+	25.0280i	−0.173832	+	1.65390i	−0.639390	+	0.768883i	$0.720813\pi$
$230$	−0.442951	−	4.21440i	−0.0292073	−	0.277889i
$231$	7.21344	−	1.53326i	0.474610	−	0.100881i
$232$	−3.86725	+	2.80972i	−0.253898	+	0.184467i
$233$	−6.11686	+	4.44416i	−0.400729	+	0.291147i	−0.769838	−	0.638240i	$-0.779663\pi$
$233$	−6.11686	+	4.44416i	−0.400729	+	0.291147i	0.369109	+	0.929386i	$0.379663\pi$
$234$	−0.0203514	+	0.00432582i	−0.00133041	+	0.000282788i
$235$	0.179538	+	1.70819i	0.0117118	+	0.111430i
$236$	0.877372	−	8.34763i	0.0571120	−	0.543385i
$237$	−14.0815	−	2.99310i	−0.914688	−	0.194423i
$238$	25.4999	−	11.3533i	1.65291	−	0.735924i
$239$	14.4335	+	16.0300i	0.933627	+	1.03690i	0.999237	+	0.0390523i	$0.0124339\pi$
$239$	14.4335	+	16.0300i	0.933627	+	1.03690i	−0.0656103	+	0.997845i	$0.520899\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	−16.6420	+	18.4828i	−1.07200	+	1.19058i	−0.0911499	+	0.995837i	$0.529054\pi$
$241$	−16.6420	+	18.4828i	−1.07200	+	1.19058i	−0.980854	+	0.194744i	$0.937612\pi$
$242$	−3.65570	−	6.33185i	−0.234997	−	0.407027i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.433444	−	1.33400i	−0.0277484	−	0.0854009i
$245$	7.07446	+	3.14975i	0.451971	+	0.201230i
$246$	−9.48554	−	6.89165i	−0.604776	−	0.439395i
$247$	0.162042			0.0103105
$248$	−5.51964	−	0.730442i	−0.350498	−	0.0463831i
$249$	0.841710			0.0533412
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	14.8619	+	6.61696i	0.938077	+	0.417659i	0.818073	−	0.575115i	$-0.195043\pi$
$251$	14.8619	+	6.61696i	0.938077	+	0.417659i	0.120004	+	0.992773i	$0.461709\pi$
$252$	1.18656	+	3.65185i	0.0747462	+	0.230045i
$253$	4.06932	−	7.04827i	0.255836	−	0.443121i
$254$	−3.92261	−	6.79417i	−0.246127	−	0.426304i
$255$	4.86420	−	5.40224i	0.304608	−	0.338302i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	17.9713	+	19.9591i	1.12102	+	1.24502i	0.966400	+	0.257043i	$0.0827482\pi$
$257$	17.9713	+	19.9591i	1.12102	+	1.24502i	0.154619	+	0.987974i	$0.450585\pi$
$258$	−7.27470	+	3.23891i	−0.452903	+	0.201646i
$259$	−1.39836	−	0.297230i	−0.0868898	−	0.0184690i
$260$	0.00217483	−	0.0206921i	0.000134877	−	0.00128327i
$261$	0.499666	+	4.75400i	0.0309285	+	0.294265i
$262$	1.41912	−	0.301642i	0.0876733	−	0.0186355i
$263$	4.71418	−	3.42505i	0.290689	−	0.211198i	−0.432877	−	0.901453i	$-0.642502\pi$
$263$	4.71418	−	3.42505i	0.290689	−	0.211198i	0.723566	+	0.690255i	$0.242502\pi$
$264$	−1.55378	+	1.12888i	−0.0956284	+	0.0694781i
$265$	−12.4191	+	2.63976i	−0.762898	+	0.162159i
$266$	−3.12593	−	29.7412i	−0.191663	−	1.82355i
$267$	−0.317815	+	3.02381i	−0.0194499	+	0.185054i
$268$	−5.06108	−	1.07577i	−0.309155	−	0.0657129i
$269$	17.4562	−	7.77200i	1.06432	−	0.473867i	0.201560	−	0.979476i	$-0.435399\pi$
$269$	17.4562	−	7.77200i	1.06432	−	0.473867i	0.862763	+	0.505609i	$0.168732\pi$
$270$	0.669131	+	0.743145i	0.0407220	+	0.0452264i
$271$	−4.36020	+	13.4193i	−0.264863	+	0.815166i	0.726861	+	0.686784i	$0.240978\pi$
$271$	−4.36020	+	13.4193i	−0.264863	+	0.815166i	−0.991725	+	0.128382i	$0.959022\pi$
$272$	−4.86420	+	5.40224i	−0.294936	+	0.327559i
$273$	−0.0399454	−	0.0691875i	−0.00241761	−	0.00418742i
$274$	0.120362	−	0.208472i	0.00727131	−	0.0125943i
$275$	0.593490	+	1.82657i	0.0357888	+	0.110147i
$276$	3.87125	+	1.72359i	0.233022	+	0.103748i
$277$	−17.3062	−	12.5737i	−1.03983	−	0.755481i	−0.0695776	−	0.997577i	$-0.522165\pi$
$277$	−17.3062	−	12.5737i	−1.03983	−	0.755481i	−0.970252	+	0.242096i	$0.922165\pi$
$278$	1.47675			0.0885695
$279$	−3.39240	+	4.41493i	−0.203098	+	0.264315i
$280$	−3.83979			−0.229471
$281$	−16.9336	−	12.3030i	−1.01018	−	0.733936i	−0.0459301	−	0.998945i	$-0.514625\pi$
$281$	−16.9336	−	12.3030i	−1.01018	−	0.733936i	−0.964246	+	0.265009i	$0.914625\pi$
$282$	−1.56910	−	0.698610i	−0.0934388	−	0.0416016i
$283$	−3.03256	−	9.33327i	−0.180267	−	0.554805i	0.819568	−	0.572982i	$-0.194214\pi$
$283$	−3.03256	−	9.33327i	−0.180267	−	0.554805i	−0.999835	+	0.0181772i	$0.994214\pi$
$284$	1.13412	−	1.96435i	0.0672976	−	0.116563i
$285$	−3.89411	−	6.74479i	−0.230667	−	0.399527i
$286$	0.0267382	−	0.0296957i	0.00158106	−	0.00175595i
$287$	13.9121	−	42.8171i	0.821207	−	2.52742i
$288$	−0.669131	−	0.743145i	−0.0394289	−	0.0437902i
$289$	32.7458	−	14.5794i	1.92622	−	0.857609i
$290$	−4.67573	−	0.993857i	−0.274568	−	0.0583613i
$291$	0.413497	−	3.93416i	0.0242396	−	0.230625i
$292$	0.298975	+	2.84456i	0.0174962	+	0.166465i
$293$	−22.3706	+	4.75501i	−1.30690	+	0.277791i	−0.808162	−	0.588960i	$-0.799537\pi$
$293$	−22.3706	+	4.75501i	−1.30690	+	0.277791i	−0.498741	+	0.866751i	$0.666204\pi$
$294$	−6.26500	+	4.55179i	−0.365382	+	0.265466i
$295$	6.79058	−	4.93364i	0.395363	−	0.287248i
$296$	0.364176	−	0.0774081i	0.0211673	−	0.00449925i
$297$	0.200755	+	1.91005i	0.0116490	+	0.110832i
$298$	1.80517	−	17.1750i	0.104571	−	0.994922i
$299$	−0.0862413	−	0.0183311i	−0.00498746	−	0.00106012i
$300$	−0.913545	+	0.406737i	−0.0527436	+	0.0234830i
$301$	−20.4599	−	22.7230i	−1.17929	−	1.30973i
$302$	−0.727961	+	2.24043i	−0.0418895	+	0.128922i
$303$	3.41291	−	3.79042i	0.196067	−	0.217754i
$304$	3.89411	+	6.74479i	0.223342	+	0.386840i
$305$	0.701328	−	1.21474i	0.0401579	−	0.0695555i
$306$	2.24638	+	6.91365i	0.128417	+	0.395227i
$307$	19.2166	+	8.55577i	1.09675	+	0.488303i	0.873681	−	0.486500i	$-0.161727\pi$
$307$	19.2166	+	8.55577i	1.09675	+	0.488303i	0.223067	+	0.974803i	$0.428393\pi$
$308$	−5.96617	−	4.33468i	−0.339954	−	0.246991i
$309$	14.1382			0.804293
$310$	−3.15054	−	4.59066i	−0.178939	−	0.260732i
$311$	24.7569			1.40384			0.701919	−	0.712257i	$-0.252327\pi$
$311$	24.7569			1.40384			0.701919	+	0.712257i	$0.252327\pi$
$312$	0.0168325	+	0.0122295i	0.000952950	+	0.000692359i
$313$	18.8129	+	8.37604i	1.06337	+	0.473442i	0.862437	−	0.506164i	$-0.168937\pi$
$313$	18.8129	+	8.37604i	1.06337	+	0.473442i	0.200930	+	0.979606i	$0.435603\pi$
$314$	−5.71200	−	17.5797i	−0.322347	−	0.992082i
$315$	−1.91989	+	3.32535i	−0.108174	+	0.187362i
$316$	7.19802	+	12.4673i	0.404920	+	0.701342i
$317$	−12.2500	+	13.6050i	−0.688030	+	0.764135i	−0.981423	−	0.191857i	$-0.938549\pi$
$317$	−12.2500	+	13.6050i	−0.688030	+	0.764135i	0.293392	+	0.955992i	$0.405216\pi$
$318$	3.92344	−	12.0751i	0.220016	−	0.677139i
$319$	−6.14309	−	6.82259i	−0.343947	−	0.381992i
$320$	0.913545	−	0.406737i	0.0510687	−	0.0227373i
$321$	8.55226	+	1.81784i	0.477341	+	0.101462i
$322$	−1.70084	+	16.1824i	−0.0947839	+	0.901809i
$323$	−5.91798	−	56.3058i	−0.329285	−	3.13294i
$324$	−0.978148	+	0.207912i	−0.0543415	+	0.0115506i
$325$	0.0168325	−	0.0122295i	0.000933697	−	0.000678370i
$326$	6.53812	−	4.75022i	0.362113	−	0.263090i
$327$	6.43229	−	1.36722i	0.355706	−	0.0756077i
$328$	1.22557	+	11.6605i	0.0676709	+	0.643846i
$329$	0.689388	−	6.55908i	0.0380072	−	0.361614i
$330$	−1.87860	−	0.399310i	−0.103414	−	0.0219813i
$331$	−16.5912	+	7.38686i	−0.911932	+	0.406018i	−0.808418	−	0.588609i	$-0.799676\pi$
$331$	−16.5912	+	7.38686i	−0.911932	+	0.406018i	−0.103515	+	0.994628i	$0.533009\pi$
$332$	−0.563214	−	0.625513i	−0.0309104	−	0.0343295i
$333$	0.115051	−	0.354090i	0.00630474	−	0.0194040i
$334$	−11.3062	+	12.5569i	−0.618650	+	0.687081i
$335$	−2.58708	−	4.48095i	−0.141347	−	0.244820i
$336$	1.91989	−	3.32535i	0.104739	−	0.181413i
$337$	1.36987	+	4.21602i	0.0746215	+	0.229661i	0.981409	−	0.191926i	$-0.0614732\pi$
$337$	1.36987	+	4.21602i	0.0746215	+	0.229661i	−0.906788	+	0.421587i	$0.861473\pi$
$338$	11.8757	+	5.28740i	0.645953	+	0.287597i
$339$	12.0139	+	8.72860i	0.652505	+	0.474073i
$340$	−7.26944			−0.394241
$341$	0.287089	−	10.6894i	0.0155468	−	0.578866i
$342$	7.78821			0.421138
$343$	−2.31108	−	1.67909i	−0.124786	−	0.0906626i
$344$	7.27470	+	3.23891i	0.392226	+	0.174630i
$345$	1.30949	+	4.03021i	0.0705008	+	0.216979i
$346$	−12.1471	+	21.0394i	−0.653031	+	1.13108i
$347$	5.75638	+	9.97035i	0.309019	+	0.535236i	0.978148	−	0.207910i	$-0.0666661\pi$
$347$	5.75638	+	9.97035i	0.309019	+	0.535236i	−0.669129	+	0.743146i	$0.733333\pi$
$348$	3.19857	−	3.55237i	0.171461	−	0.190427i
$349$	6.40798	−	19.7217i	0.343011	−	1.05568i	−0.619629	−	0.784895i	$-0.712717\pi$
$349$	6.40798	−	19.7217i	0.343011	−	1.05568i	0.962640	−	0.270785i	$-0.0872831\pi$
$350$	−2.56932	−	2.85352i	−0.137336	−	0.152527i
$351$	0.0190073	−	0.00846259i	0.00101453	−	0.000451699i
$352$	1.87860	+	0.399310i	0.100130	+	0.0212833i
$353$	−3.55781	+	33.8503i	−0.189363	+	1.80167i	0.326710	+	0.945125i	$0.394060\pi$
$353$	−3.55781	+	33.8503i	−0.189363	+	1.80167i	−0.516073	+	0.856545i	$0.672607\pi$
$354$	0.877372	+	8.34763i	0.0466318	+	0.443672i
$355$	2.21867	−	0.471593i	0.117755	−	0.0250296i
$356$	2.45978	−	1.78714i	0.130368	−	0.0947181i
$357$	−22.5822	+	16.4069i	−1.19517	+	0.868345i
$358$	7.58133	−	1.61146i	0.400686	−	0.0851684i
$359$	1.71258	+	16.2941i	0.0903864	+	0.859969i	0.941958	+	0.335731i	$0.108983\pi$
$359$	1.71258	+	16.2941i	0.0903864	+	0.859969i	−0.851572	+	0.524238i	$0.824350\pi$
$360$	0.104528	−	0.994522i	0.00550913	−	0.0524159i
$361$	−40.7460	−	8.66082i	−2.14452	−	0.455833i
$362$	6.45882	−	2.87565i	0.339468	−	0.151141i
$363$	4.89228	+	5.43343i	0.256778	+	0.285181i
$364$	−0.0246876	+	0.0759807i	−0.00129398	+	0.00398247i
$365$	−1.91387	+	2.12557i	−0.100176	+	0.111257i
$366$	0.701328	+	1.21474i	0.0366590	+	0.0634952i
$367$	7.38953	−	12.7990i	0.385730	−	0.668105i	−0.606140	−	0.795358i	$-0.707283\pi$
$367$	7.38953	−	12.7990i	0.385730	−	0.668105i	0.991870	+	0.127254i	$0.0406162\pi$
$368$	−1.30949	−	4.03021i	−0.0682621	−	0.210089i
$369$	10.7111	+	4.76889i	0.557598	+	0.248259i
$370$	0.301207	+	0.218840i	0.0156590	+	0.0113769i
$371$	48.7520			2.53108
$372$	5.55089	−	0.433118i	0.287800	−	0.0224561i
$373$	34.5412			1.78848			0.894238	−	0.447592i	$-0.147718\pi$
$373$	34.5412			1.78848			0.894238	+	0.447592i	$0.147718\pi$
$374$	−11.2951	−	8.20636i	−0.584055	−	0.424341i
$375$	−0.913545	−	0.406737i	−0.0471753	−	0.0210038i
$376$	0.530767	+	1.63353i	0.0273722	+	0.0842431i
$377$	−0.0497284	+	0.0861321i	−0.00256114	+	0.00443603i
$378$	−1.91989	−	3.32535i	−0.0987487	−	0.171038i
$379$	10.3671	−	11.5139i	0.532524	−	0.591428i	−0.415513	−	0.909587i	$-0.636398\pi$
$379$	10.3671	−	11.5139i	0.532524	−	0.591428i	0.948037	+	0.318159i	$0.103065\pi$
$380$	−2.40669	+	7.40703i	−0.123461	+	0.379973i
$381$	5.24948	+	5.83014i	0.268939	+	0.298687i
$382$	−3.55488	+	1.58273i	−0.181883	+	0.0809797i
$383$	−9.73674	−	2.06961i	−0.497524	−	0.105752i	−0.0476864	−	0.998862i	$-0.515185\pi$
$383$	−9.73674	−	2.06961i	−0.497524	−	0.105752i	−0.449838	+	0.893110i	$0.648518\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	−0.770855	−	7.33419i	−0.0392864	−	0.373785i
$386$	−16.9477	+	3.60234i	−0.862615	+	0.183355i
$387$	6.44233	−	4.68062i	0.327482	−	0.237930i
$388$	−3.20034	+	2.32518i	−0.162472	+	0.118043i
$389$	12.3593	−	2.62706i	0.626643	−	0.133197i	0.116365	−	0.993207i	$-0.462876\pi$
$389$	12.3593	−	2.62706i	0.626643	−	0.133197i	0.510278	+	0.860009i	$0.329542\pi$
$390$	0.00217483	+	0.0206921i	0.000110127	+	0.00104778i
$391$	−3.22000	+	30.6363i	−0.162843	+	1.54934i
$392$	7.57474	+	1.61006i	0.382582	+	0.0813203i
$393$	−1.32539	+	0.590102i	−0.0668571	+	0.0297667i
$394$	−11.5569	−	12.8352i	−0.582228	−	0.646630i
$395$	−4.44862	+	13.6914i	−0.223834	+	0.688891i
$396$	1.28511	−	1.42726i	0.0645794	−	0.0717227i
$397$	14.0009	+	24.2502i	0.702684	+	1.21708i	0.967521	+	0.252792i	$0.0813487\pi$
$397$	14.0009	+	24.2502i	0.702684	+	1.21708i	−0.264836	+	0.964293i	$0.585318\pi$
$398$	8.68286	−	15.0392i	0.435233	−	0.753845i
$399$	9.24118	+	28.4414i	0.462637	+	1.42385i
$400$	0.913545	+	0.406737i	0.0456773	+	0.0203368i
$401$	5.94698	+	4.32073i	0.296978	+	0.215767i	0.726289	−	0.687390i	$-0.241244\pi$
$401$	5.94698	+	4.32073i	0.296978	+	0.215767i	−0.429311	+	0.903157i	$0.641244\pi$
$402$	5.17415			0.258063
$403$	−0.111095	+	0.0328267i	−0.00553403	+	0.00163522i
$404$	−5.10051			−0.253760
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	16.7680	+	7.46561i	0.832183	+	0.370512i
$407$	0.220964	+	0.680056i	0.0109528	+	0.0337091i
$408$	3.63472	−	6.29552i	0.179945	−	0.311675i
$409$	13.1946	+	22.8537i	0.652429	+	1.13004i	0.982532	+	0.186095i	$0.0595834\pi$
$409$	13.1946	+	22.8537i	0.652429	+	1.13004i	−0.330102	+	0.943945i	$0.607083\pi$
$410$	−7.84540	+	8.71320i	−0.387457	+	0.430314i
$411$	−0.0743875	+	0.228941i	−0.00366927	+	0.0112928i
$412$	−9.46029	−	10.5067i	−0.466075	−	0.517629i
$413$	−29.4433	+	13.1090i	−1.44881	+	0.645051i
$414$	−4.14501	−	0.881049i	−0.203716	−	0.0433012i
$415$	0.0879827	−	0.837099i	0.00431890	−	0.0410916i
$416$	−0.00217483	−	0.0206921i	−0.000106630	−	0.00101451i
$417$	−1.44448	+	0.307033i	−0.0707364	+	0.0150355i
$418$	−12.1011	+	8.79200i	−0.591886	+	0.430031i
$419$	−6.24100	+	4.53435i	−0.304893	+	0.221518i	−0.729702	−	0.683765i	$-0.760341\pi$
$419$	−6.24100	+	4.53435i	−0.304893	+	0.221518i	0.424809	+	0.905283i	$0.360341\pi$
$420$	3.75588	−	0.798336i	0.183268	−	0.0389548i
$421$	−1.39099	−	13.2344i	−0.0677926	−	0.645004i	−0.974676	−	0.223622i	$-0.928212\pi$
$421$	−1.39099	−	13.2344i	−0.0677926	−	0.645004i	0.906883	−	0.421382i	$-0.138455\pi$
$422$	0.979344	−	9.31783i	0.0476737	−	0.453585i
$423$	1.68007	+	0.357109i	0.0816876	+	0.0173632i
$424$	−11.5989	+	5.16414i	−0.563290	+	0.250793i
$425$	−4.86420	−	5.40224i	−0.235949	−	0.262047i
$426$	−0.700924	+	2.15722i	−0.0339599	+	0.104518i
$427$	−3.60387	+	4.00250i	−0.174403	+	0.193695i
$428$	−4.37166	−	7.57194i	−0.211312	−	0.366004i
$429$	−0.0199798	+	0.0346060i	−0.000964633	+	0.00167079i
$430$	2.46075	+	7.57341i	0.118668	+	0.365222i
$431$	−26.7469	−	11.9085i	−1.28835	−	0.573612i	−0.355772	−	0.934573i	$-0.615782\pi$
$431$	−26.7469	−	11.9085i	−1.28835	−	0.573612i	−0.932581	+	0.360961i	$0.882449\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	3.38912			0.162870			0.0814352	−	0.996679i	$-0.474050\pi$
$433$	3.38912			0.162870			0.0814352	+	0.996679i	$0.474050\pi$
$434$	8.16815	+	19.7571i	0.392084	+	0.948373i
$435$	4.78019			0.229192
$436$	−5.32009	−	3.86527i	−0.254786	−	0.185113i
$437$	30.1501	+	13.4237i	1.44228	+	0.642142i
$438$	−0.883860	−	2.72024i	−0.0422324	−	0.129978i
$439$	5.41154	−	9.37306i	0.258279	−	0.447352i	−0.707502	−	0.706711i	$-0.750178\pi$
$439$	5.41154	−	9.37306i	0.258279	−	0.447352i	0.965781	+	0.259359i	$0.0835114\pi$
$440$	0.960287	+	1.66327i	0.0457799	+	0.0792931i
$441$	5.18172	−	5.75488i	0.246749	−	0.274042i
$442$	−0.0467383	+	0.143846i	−0.00222311	+	0.00684204i
$443$	−0.502361	−	0.557928i	−0.0238679	−	0.0265080i	0.731093	−	0.682278i	$-0.239011\pi$
$443$	−0.502361	−	0.557928i	−0.0238679	−	0.0265080i	−0.754961	+	0.655770i	$0.772344\pi$
$444$	−0.340124	+	0.151433i	−0.0161416	+	0.00718669i
$445$	2.97402	+	0.632147i	0.140982	+	0.0299667i
$446$	1.50386	−	14.3083i	0.0712098	−	0.677516i
$447$	1.80517	+	17.1750i	0.0853815	+	0.812350i
$448$	−3.75588	+	0.798336i	−0.177449	+	0.0377179i
$449$	17.6279	−	12.8074i	0.831913	−	0.604420i	−0.0881867	−	0.996104i	$-0.528107\pi$
$449$	17.6279	−	12.8074i	0.831913	−	0.604420i	0.920100	+	0.391684i	$0.128107\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	−22.0262	+	4.68181i	−1.03717	+	0.220458i
$452$	−1.55225	−	14.7686i	−0.0730115	−	0.694658i
$453$	0.246241	−	2.34283i	0.0115694	−	0.110076i
$454$	−5.26462	−	1.11903i	−0.247081	−	0.0525187i
$455$	−0.0729839	+	0.0324945i	−0.00342154	+	0.00152337i
$456$	−5.21133	−	5.78777i	−0.244043	−	0.271037i
$457$	7.19903	−	22.1563i	0.336756	−	1.03643i	−0.629094	−	0.777329i	$-0.716574\pi$
$457$	7.19903	−	22.1563i	0.336756	−	1.03643i	0.965850	−	0.259100i	$-0.0834260\pi$
$458$	−16.8393	+	18.7019i	−0.786848	+	0.873883i
$459$	−3.63472	−	6.29552i	−0.169654	−	0.293850i
$460$	2.11880	−	3.66988i	0.0987898	−	0.171109i
$461$	−6.16250	−	18.9662i	−0.287016	−	0.883346i	−0.985787	−	0.168000i	$-0.946269\pi$
$461$	−6.16250	−	18.9662i	−0.287016	−	0.883346i	0.698771	−	0.715346i	$-0.253731\pi$
$462$	6.73703	+	2.99952i	0.313435	+	0.139550i
$463$	15.3939	+	11.1844i	0.715417	+	0.519781i	0.884917	−	0.465749i	$-0.154215\pi$
$463$	15.3939	+	11.1844i	0.715417	+	0.519781i	−0.169500	+	0.985530i	$0.554215\pi$
$464$	−4.78019			−0.221915
$465$	4.03614	+	3.83530i	0.187172	+	0.177858i
$466$	−7.56086			−0.350250
$467$	−20.2743	−	14.7301i	−0.938182	−	0.681629i	0.00979999	−	0.999952i	$-0.496881\pi$
$467$	−20.2743	−	14.7301i	−0.938182	−	0.681629i	−0.947982	+	0.318323i	$0.896881\pi$
$468$	−0.0190073	−	0.00846259i	−0.000878612	−	0.000391183i
$469$	6.13944	+	18.8952i	0.283493	+	0.872501i
$470$	−0.858800	+	1.48748i	−0.0396135	+	0.0686125i
$471$	9.24222	+	16.0080i	0.425859	+	0.737609i
$472$	5.61642	−	6.23767i	0.258517	−	0.287112i
$473$	−4.72605	+	14.5453i	−0.217304	+	0.668793i
$474$	−9.63283	−	10.6983i	−0.442451	−	0.491391i
$475$	−7.11489	+	3.16775i	−0.326453	+	0.145346i
$476$	27.3031	+	5.80346i	1.25144	+	0.266001i
$477$	−1.32715	+	12.6270i	−0.0607660	+	0.578149i
$478$	2.25474	+	21.4524i	0.103129	+	0.981210i
$479$	−15.4875	+	3.29197i	−0.707643	+	0.150414i	−0.547654	−	0.836705i	$-0.684479\pi$
$479$	−15.4875	+	3.29197i	−0.707643	+	0.150414i	−0.159988	+	0.987119i	$0.551146\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	0.00626693	−	0.00455319i	0.000285747	−	0.000207608i
$482$	−24.3276	+	5.17098i	−1.10809	+	0.235532i
$483$	−1.70084	−	16.1824i	−0.0773907	−	0.736324i
$484$	0.764249	−	7.27134i	0.0347386	−	0.330516i
$485$	−3.86939	−	0.822464i	−0.175700	−	0.0373462i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	14.6667	+	16.2890i	0.664611	+	0.738126i	0.977330	−	0.211720i	$-0.0679065\pi$
$487$	14.6667	+	16.2890i	0.664611	+	0.738126i	−0.312719	+	0.949846i	$0.601240\pi$
$488$	0.433444	−	1.33400i	0.0196211	−	0.0603875i
$489$	−5.40762	+	6.00577i	−0.244541	+	0.271590i
$490$	3.87198	+	6.70647i	0.174918	+	0.302967i
$491$	−5.61632	+	9.72776i	−0.253461	+	0.439008i	−0.964476	−	0.264169i	$-0.914902\pi$
$491$	−5.61632	+	9.72776i	−0.253461	+	0.439008i	0.711015	+	0.703177i	$0.248236\pi$
$492$	−3.62315	−	11.1509i	−0.163344	−	0.502722i
$493$	31.7450	+	14.1338i	1.42972	+	0.636554i
$494$	0.131095	+	0.0952459i	0.00589823	+	0.00428532i
$495$	1.92057			0.0863234
$496$	−4.03614	−	3.83530i	−0.181228	−	0.172210i
$497$	−8.70955			−0.390677
$498$	0.680958	+	0.494745i	0.0305145	+	0.0221701i
$499$	−15.6970	−	6.98877i	−0.702696	−	0.312860i	0.0241044	−	0.999709i	$-0.492327\pi$
$499$	−15.6970	−	6.98877i	−0.702696	−	0.312860i	−0.726800	+	0.686849i	$0.758993\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	8.44846	−	14.6332i	0.377449	−	0.653762i
$502$	8.13420	+	14.0889i	0.363047	+	0.628816i
$503$	5.14274	−	5.71159i	0.229303	−	0.254667i	−0.617503	−	0.786569i	$-0.711856\pi$
$503$	5.14274	−	5.71159i	0.229303	−	0.254667i	0.846806	+	0.531901i	$0.178522\pi$
$504$	−1.18656	+	3.65185i	−0.0528536	+	0.162667i
$505$	−3.41291	−	3.79042i	−0.151872	−	0.168671i
$506$	7.43502	−	3.31028i	0.330527	−	0.147160i
$507$	−12.7155	−	2.70276i	−0.564715	−	0.120034i
$508$	0.820049	−	7.80225i	0.0363838	−	0.346169i
$509$	1.62739	+	15.4836i	0.0721327	+	0.686297i	0.969513	+	0.245039i	$0.0788009\pi$
$509$	1.62739	+	15.4836i	0.0721327	+	0.686297i	−0.897380	+	0.441258i	$0.854532\pi$
$510$	7.11058	−	1.51140i	0.314862	−	0.0669260i
$511$	8.88517	−	6.45545i	0.393057	−	0.285572i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−7.61802	+	1.61926i	−0.336344	+	0.0714921i
$514$	2.80739	+	26.7105i	0.123829	+	1.17815i
$515$	1.47784	−	14.0607i	0.0651215	−	0.619590i
$516$	−7.78914	−	1.65563i	−0.342898	−	0.0728852i
$517$	−3.01358	+	1.34173i	−0.132537	+	0.0590093i
$518$	−0.956589	−	1.06240i	−0.0420301	−	0.0466791i
$519$	7.50731	−	23.1051i	0.329534	−	1.01420i
$520$	0.0139220	−	0.0154619i	0.000610519	−	0.000678050i
$521$	−15.6746	−	27.1493i	−0.686719	−	1.18943i	−0.972893	−	0.231254i	$-0.925717\pi$
$521$	−15.6746	−	27.1493i	−0.686719	−	1.18943i	0.286175	−	0.958177i	$-0.407616\pi$
$522$	−2.39009	+	4.13976i	−0.104612	+	0.181192i
$523$	12.8734	+	39.6203i	0.562915	+	1.73248i	0.674065	+	0.738672i	$0.264547\pi$
$523$	12.8734	+	39.6203i	0.562915	+	1.73248i	−0.111150	+	0.993804i	$0.535453\pi$
$524$	1.32539	+	0.590102i	0.0578999	+	0.0257787i
$525$	3.10645	+	2.25697i	0.135577	+	0.0985022i
$526$	5.82704			0.254071
$527$	15.4638	+	37.4040i	0.673615	+	1.62934i
$528$	−1.92057			−0.0835822
$529$	4.07960	+	2.96400i	0.177374	+	0.128870i
$530$	−11.5989	−	5.16414i	−0.503822	−	0.224316i
$531$	−2.59377	−	7.98280i	−0.112560	−	0.346424i
$532$	14.9525	−	25.8986i	0.648275	−	1.12284i
$533$	0.121973	+	0.211264i	0.00528324	+	0.00915084i
$534$	−2.03447	+	2.25950i	−0.0880399	+	0.0977783i
$535$	2.70184	−	8.31540i	0.116811	−	0.359506i
$536$	−3.46218	−	3.84514i	−0.149544	−	0.166085i
$537$	−7.08062	+	3.15249i	−0.305551	+	0.136040i
$538$	18.6906	+	3.97281i	0.805810	+	0.171280i
$539$	−1.55464	+	14.7914i	−0.0669629	+	0.637109i
$540$	0.104528	+	0.994522i	0.00449819	+	0.0427974i
$541$	23.6322	−	5.02319i	1.01603	−	0.215964i	0.330343	−	0.943861i	$-0.392835\pi$
$541$	23.6322	−	5.02319i	1.01603	−	0.215964i	0.685686	+	0.727897i	$0.259502\pi$
$542$	−11.4152	+	8.29360i	−0.490323	+	0.356241i
$543$	−5.71980	+	4.15568i	−0.245460	+	0.178337i
$544$	−7.11058	+	1.51140i	−0.304864	+	0.0648008i
$545$	−0.687378	−	6.53996i	−0.0294440	−	0.280141i
$546$	0.00835086	−	0.0794532i	0.000357384	−	0.00340028i
$547$	−6.72953	−	1.43040i	−0.287734	−	0.0611597i	0.0617837	−	0.998090i	$-0.480321\pi$
$547$	−6.72953	−	1.43040i	−0.287734	−	0.0611597i	−0.349517	+	0.936930i	$0.613654\pi$
$548$	0.219912	−	0.0979109i	0.00939416	−	0.00418255i
$549$	−0.938560	−	1.04238i	−0.0400567	−	0.0444875i
$550$	−0.593490	+	1.82657i	−0.0253065	+	0.0778854i
$551$	24.9111	−	27.6666i	1.06125	−	1.17864i
$552$	2.11880	+	3.66988i	0.0901823	+	0.156200i
$553$	27.6389	−	47.8719i	1.17532	−	2.03572i
$554$	−6.61039	−	20.3447i	−0.280848	−	0.864363i
$555$	−0.340124	−	0.151433i	−0.0144375	−	0.00642797i
$556$	1.19471	+	0.868011i	0.0506672	+	0.0368119i
$557$	−30.1588			−1.27787			−0.638935	−	0.769260i	$-0.720625\pi$
$557$	−30.1588			−1.27787			−0.638935	+	0.769260i	$0.720625\pi$
$558$	−5.33954	+	1.57775i	−0.226041	+	0.0667914i
$559$	0.165682			0.00700760
$560$	−3.10645	−	2.25697i	−0.131272	−	0.0953744i
$561$	12.7545	+	5.67865i	0.538494	+	0.239753i
$562$	−6.46807	−	19.9067i	−0.272839	−	0.839713i
$563$	0.602266	−	1.04316i	0.0253825	−	0.0439638i	−0.853055	−	0.521821i	$-0.825253\pi$
$563$	0.602266	−	1.04316i	0.0253825	−	0.0439638i	0.878438	+	0.477857i	$0.158586\pi$
$564$	−0.858800	−	1.48748i	−0.0361620	−	0.0626344i
$565$	9.93658	−	11.0357i	0.418035	−	0.464275i
$566$	3.03256	−	9.33327i	0.127468	−	0.392307i
$567$	2.56932	+	2.85352i	0.107901	+	0.119836i
$568$	2.07214	−	0.922576i	0.0869450	−	0.0387104i
$569$	−32.3324	−	6.87246i	−1.35544	−	0.288109i	−0.527803	−	0.849367i	$-0.676984\pi$
$569$	−32.3324	−	6.87246i	−1.35544	−	0.288109i	−0.827641	+	0.561258i	$0.810318\pi$
$570$	0.814090	−	7.74555i	0.0340985	−	0.324425i
$571$	3.37493	+	32.1103i	0.141236	+	1.34377i	0.803859	+	0.594820i	$0.202777\pi$
$571$	3.37493	+	32.1103i	0.141236	+	1.34377i	−0.662622	+	0.748954i	$0.730557\pi$
$572$	0.0390864	−	0.00830806i	0.00163428	−	0.000347378i
$573$	3.14813	−	2.28725i	0.131515	−	0.0955512i
$574$	36.4224	−	26.4625i	1.52024	−	1.10452i
$575$	4.14501	−	0.881049i	0.172859	−	0.0367423i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−3.13292	+	29.8077i	−0.130425	+	1.24091i	0.712032	+	0.702147i	$0.247775\pi$
$577$	−3.13292	+	29.8077i	−0.130425	+	1.24091i	−0.842457	+	0.538764i	$0.818892\pi$
$578$	35.0614	+	7.45254i	1.45836	+	0.309985i
$579$	15.8284	−	7.04725i	0.657805	−	0.292874i
$580$	−3.19857	−	3.55237i	−0.132813	−	0.147504i
$581$	−0.998739	+	3.07380i	−0.0414347	+	0.127523i
$582$	2.64697	−	2.93976i	0.109720	−	0.121857i
$583$	−12.1923	−	21.1177i	−0.504954	−	0.874606i
$584$	−1.43011	+	2.47703i	−0.0591786	+	0.102500i
$585$	−0.00642943	−	0.0197877i	−0.000265824	−	0.000818122i
$586$	−20.8931	−	9.30221i	−0.863086	−	0.384271i
$587$	−29.3254	−	21.3061i	−1.21039	−	0.879398i	−0.215121	−	0.976587i	$-0.569015\pi$
$587$	−29.3254	−	21.3061i	−1.21039	−	0.879398i	−0.995266	+	0.0971899i	$0.969015\pi$
$588$	−7.74396			−0.319356
$589$	43.2315	−	3.37321i	1.78132	−	0.138991i
$590$	8.39361			0.345560
$591$	13.9729	+	10.1519i	0.574770	+	0.417595i
$592$	0.340124	+	0.151433i	0.0139790	+	0.00622386i
$593$	8.21268	+	25.2760i	0.337254	+	1.03796i	0.965601	+	0.260028i	$0.0837319\pi$
$593$	8.21268	+	25.2760i	0.337254	+	1.03796i	−0.628347	+	0.777933i	$0.716268\pi$
$594$	−0.960287	+	1.66327i	−0.0394010	+	0.0682446i
$595$	13.9565	+	24.1734i	0.572162	+	0.991015i
$596$	11.5556	−	12.8338i	0.473337	−	0.525694i
$597$	−5.36631	+	16.5158i	−0.219628	+	0.675946i
$598$	−0.0589959	−	0.0655216i	−0.00241252	−	0.00267938i
$599$	−29.4413	+	13.1081i	−1.20294	+	0.535584i	−0.907611	−	0.419812i	$-0.862096\pi$
$599$	−29.4413	+	13.1081i	−1.20294	+	0.535584i	−0.295329	+	0.955395i	$0.595429\pi$
$600$	−0.978148	−	0.207912i	−0.0399327	−	0.00848796i
$601$	2.53541	−	24.1228i	0.103421	−	0.983989i	−0.812590	−	0.582836i	$-0.801943\pi$
$601$	2.53541	−	24.1228i	0.103421	−	0.983989i	0.916011	−	0.401153i	$-0.131390\pi$
$602$	−3.19615	−	30.4093i	−0.130265	−	1.23939i
$603$	−5.06108	+	1.07577i	−0.206103	+	0.0438086i
$604$	−1.90583	+	1.38466i	−0.0775470	+	0.0563412i
$605$	5.91504	−	4.29753i	0.240481	−	0.174719i
$606$	4.98905	−	1.06046i	0.202666	−	0.0430781i
$607$	−3.43317	−	32.6644i	−0.139348	−	1.32581i	−0.811046	−	0.584983i	$-0.801101\pi$
$607$	−3.43317	−	32.6644i	−0.139348	−	1.32581i	0.671698	−	0.740825i	$-0.265565\pi$
$608$	−0.814090	+	7.74555i	−0.0330157	+	0.314123i
$609$	−17.9538	−	3.81620i	−0.727525	−	0.154640i
$610$	1.28139	−	0.570511i	0.0518819	−	0.0230993i
$611$	0.0239124	+	0.0265574i	0.000967391	+	0.00107440i
$612$	−2.24638	+	6.91365i	−0.0908045	+	0.279468i
$613$	−26.3208	+	29.2322i	−1.06309	+	1.18068i	−0.0801423	+	0.996783i	$0.525537\pi$
$613$	−26.3208	+	29.2322i	−1.06309	+	1.18068i	−0.982946	+	0.183896i	$0.941129\pi$
$614$	10.5176	+	18.2170i	0.424455	+	0.735177i
$615$	5.86239	−	10.1539i	0.236394	−	0.409447i
$616$	−2.27887	−	7.01365i	−0.0918185	−	0.282588i
$617$	8.56710	+	3.81432i	0.344898	+	0.153559i	0.571873	−	0.820342i	$-0.306217\pi$
$617$	8.56710	+	3.81432i	0.344898	+	0.153559i	−0.226975	+	0.973901i	$0.572884\pi$
$618$	11.4380	+	8.31022i	0.460105	+	0.334286i
$619$	−22.7775			−0.915507			−0.457753	−	0.889079i	$-0.651346\pi$
$619$	−22.7775			−0.915507			−0.457753	+	0.889079i	$0.651346\pi$
$620$	0.149481	−	5.56576i	0.00600330	−	0.223526i
$621$	4.23761			0.170049
$622$	20.0288	+	14.5518i	0.803081	+	0.583472i
$623$	−10.6654	−	4.74854i	−0.427300	−	0.190246i
$624$	0.00642943	+	0.0197877i	0.000257383	+	0.000792143i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.2966	+	17.8343i	0.411537	+	0.712802i
$627$	10.0087	−	11.1158i	0.399711	−	0.443924i
$628$	5.71200	−	17.5797i	0.227934	−	0.701508i
$629$	−1.81100	−	2.01132i	−0.0722094	−	0.0801966i
$630$	−3.50782	+	1.56178i	−0.139755	+	0.0622229i
$631$	−32.4758	−	6.90294i	−1.29284	−	0.274802i	−0.490380	−	0.871509i	$-0.663142\pi$
$631$	−32.4758	−	6.90294i	−1.29284	−	0.274802i	−0.802459	+	0.596707i	$0.796475\pi$
$632$	−1.50480	+	14.3172i	−0.0598576	+	0.569507i
$633$	0.979344	+	9.31783i	0.0389254	+	0.370351i
$634$	−17.9073	+	3.80632i	−0.711191	+	0.151168i
$635$	6.34692	−	4.61131i	0.251870	−	0.182994i
$636$	10.2717	−	7.46283i	0.407300	−	0.295921i
$637$	0.157600	−	0.0334990i	0.00624436	−	0.00132728i
$638$	−0.959645	−	9.13041i	−0.0379927	−	0.361476i
$639$	0.237095	−	2.25581i	0.00937935	−	0.0892386i
$640$	0.978148	+	0.207912i	0.0386647	+	0.00821843i
$641$	17.3142	−	7.70879i	0.683871	−	0.304479i	−0.0352356	−	0.999379i	$-0.511218\pi$
$641$	17.3142	−	7.70879i	0.683871	−	0.304479i	0.719106	+	0.694900i	$0.244551\pi$
$642$	5.85043	+	6.49756i	0.230898	+	0.256438i
$643$	−3.92711	+	12.0864i	−0.154870	+	0.476641i	−0.998148	−	0.0608371i	$-0.980623\pi$
$643$	−3.92711	+	12.0864i	−0.154870	+	0.476641i	0.843278	+	0.537478i	$0.180623\pi$
$644$	−10.8878	+	12.0921i	−0.429038	+	0.476495i
$645$	−3.98158	−	6.89629i	−0.156774	−	0.271541i
$646$	28.3080	−	49.0308i	1.11376	−	1.92909i
$647$	11.7566	+	36.1830i	0.462198	+	1.42250i	0.862473	+	0.506104i	$0.168915\pi$
$647$	11.7566	+	36.1830i	0.462198	+	1.42250i	−0.400275	+	0.916395i	$0.631085\pi$
$648$	−0.913545	−	0.406737i	−0.0358875	−	0.0159781i
$649$	13.0418	+	9.47543i	0.511936	+	0.371943i
$650$	0.0208061			0.000816081
$651$	−12.0974	−	17.6271i	−0.474134	−	0.690862i
$652$	8.08156			0.316498
$653$	34.9996	+	25.4287i	1.36964	+	0.995100i	0.997765	+	0.0668169i	$0.0212843\pi$
$653$	34.9996	+	25.4287i	1.36964	+	0.995100i	0.371873	+	0.928284i	$0.378716\pi$
$654$	6.00746	+	2.67470i	0.234910	+	0.104589i
$655$	0.448328	+	1.37981i	0.0175176	+	0.0539137i
$656$	−5.86239	+	10.1539i	−0.228888	+	0.396445i
$657$	1.43011	+	2.47703i	0.0557941	+	0.0966382i
$658$	4.41306	−	4.90120i	0.172039	−	0.191069i
$659$	−5.81950	+	17.9106i	−0.226696	+	0.697697i	0.771420	+	0.636327i	$0.219547\pi$
$659$	−5.81950	+	17.9106i	−0.226696	+	0.697697i	−0.998115	+	0.0613702i	$0.980453\pi$
$660$	−1.28511	−	1.42726i	−0.0500230	−	0.0555562i
$661$	−0.768172	+	0.342012i	−0.0298784	+	0.0133027i	−0.421621	−	0.906772i	$-0.638539\pi$
$661$	−0.768172	+	0.342012i	−0.0298784	+	0.0133027i	0.391743	+	0.920075i	$0.371872\pi$
$662$	−17.7644	−	3.77594i	−0.690433	−	0.146756i
$663$	0.0158098	−	0.150420i	0.000614000	−	0.00584182i
$664$	−0.0879827	−	0.837099i	−0.00341439	−	0.0324858i
$665$	29.2516	−	6.21761i	1.13433	−	0.241109i
$666$	0.301207	−	0.218840i	0.0116715	−	0.00847986i
$667$	−16.3879	+	11.9065i	−0.634542	+	0.461022i
$668$	−16.5277	+	3.51307i	−0.639475	+	0.135925i
$669$	1.50386	+	14.3083i	0.0581425	+	0.553189i
$670$	0.540846	−	5.14581i	0.0208947	−	0.198800i
$671$	2.63503	+	0.560094i	0.101724	+	0.0216222i
$672$	3.50782	−	1.56178i	0.135317	−	0.0602470i
$673$	−23.9459	−	26.5946i	−0.923045	−	1.02515i	−0.999606	−	0.0280804i	$-0.991061\pi$
$673$	−23.9459	−	26.5946i	−0.923045	−	1.02515i	0.0765607	−	0.997065i	$-0.475606\pi$
$674$	−1.36987	+	4.21602i	−0.0527653	+	0.162395i
$675$	−0.669131	+	0.743145i	−0.0257548	+	0.0286037i
$676$	6.49978	+	11.2580i	0.249992	+	0.432998i
$677$	12.3925	−	21.4644i	0.476281	−	0.824942i	−0.523350	−	0.852118i	$-0.675318\pi$
$677$	12.3925	−	21.4644i	0.476281	−	0.824942i	0.999631	+	0.0271754i	$0.00865126\pi$
$678$	4.58890	+	14.1232i	0.176236	+	0.542397i
$679$	13.8763	+	6.17815i	0.532525	+	0.237096i
$680$	−5.88110	−	4.27287i	−0.225530	−	0.163857i
$681$	5.38224			0.206248
$682$	6.51536	−	8.47920i	0.249486	−	0.324685i
$683$	−44.5543			−1.70482			−0.852411	−	0.522873i	$-0.824860\pi$
$683$	−44.5543			−1.70482			−0.852411	+	0.522873i	$0.824860\pi$
$684$	6.30080	+	4.57780i	0.240917	+	0.175036i
$685$	0.219912	+	0.0979109i	0.00840239	+	0.00374098i
$686$	−0.882752	−	2.71683i	−0.0337036	−	0.103729i
$687$	12.5830	−	21.7943i	0.480070	−	0.831505i
$688$	3.98158	+	6.89629i	0.151796	+	0.262919i
$689$	−0.176761	+	0.196313i	−0.00673405	+	0.00747892i
$690$	−1.30949	+	4.03021i	−0.0498516	+	0.153427i
$691$	28.1454	+	31.2587i	1.07070	+	1.18914i	0.981169	+	0.193152i	$0.0618709\pi$
$691$	28.1454	+	31.2587i	1.07070	+	1.18914i	0.0895334	+	0.995984i	$0.471462\pi$
$692$	−22.1938	+	9.88132i	−0.843682	+	0.375632i
$693$	−7.21344	−	1.53326i	−0.274016	−	0.0582439i
$694$	−1.20341	+	11.4497i	−0.0456809	+	0.434625i
$695$	0.154362	+	1.46866i	0.00585529	+	0.0557094i
$696$	4.67573	−	0.993857i	0.177233	−	0.0376720i
$697$	68.9545	−	50.0984i	2.61184	−	1.89761i
$698$	16.7763	−	12.1887i	0.634992	−	0.461349i
$699$	7.39564	−	1.57199i	0.279729	−	0.0594582i
$700$	−0.401367	−	3.81875i	−0.0151702	−	0.144335i
$701$	−0.687616	+	6.54223i	−0.0259709	+	0.247097i	0.973832	+	0.227267i	$0.0729790\pi$
$701$	−0.687616	+	6.54223i	−0.0259709	+	0.247097i	−0.999803	+	0.0198295i	$0.993688\pi$
$702$	0.0203514	+	0.00432582i	0.000768114	+	0.000163268i
$703$	−2.64896	+	1.17939i	−0.0999074	+	0.0444816i
$704$	1.28511	+	1.42726i	0.0484346	+	0.0537921i
$705$	0.530767	−	1.63353i	0.0199899	−	0.0615224i
$706$	−22.7750	+	25.2942i	−0.857150	+	0.951961i
$707$	9.79244	+	16.9610i	0.368283	+	0.637884i
$708$	−4.19681	+	7.26908i	−0.157726	+	0.273189i
$709$	−5.29360	−	16.2920i	−0.198805	−	0.611860i	−0.999911	−	0.0133371i	$-0.995755\pi$
$709$	−5.29360	−	16.2920i	−0.198805	−	0.611860i	0.801106	−	0.598523i	$-0.204245\pi$
$710$	2.07214	+	0.922576i	0.0777660	+	0.0346236i
$711$	11.6466	+	8.46178i	0.436783	+	0.317342i
$712$	3.04046			0.113946
$713$	−23.3901	−	3.09533i	−0.875966	−	0.115921i
$714$	−27.9131			−1.04462
$715$	0.0323280	+	0.0234876i	0.00120900	+	0.000878388i
$716$	7.08062	+	3.15249i	0.264615	+	0.117814i
$717$	−6.66567	−	20.5148i	−0.248934	−	0.766140i
$718$	−8.19192	+	14.1888i	−0.305720	+	0.529522i
$719$	−0.517248	−	0.895900i	−0.0192901	−	0.0334114i	0.856219	−	0.516613i	$-0.172807\pi$
$719$	−0.517248	−	0.895900i	−0.0192901	−	0.0334114i	−0.875509	+	0.483201i	$0.839474\pi$
$720$	0.669131	−	0.743145i	0.0249370	−	0.0276954i
$721$	−16.7758	+	51.6306i	−0.624763	+	1.92282i
$722$	−27.8735	−	30.9566i	−1.03734	−	1.15209i
$723$	22.7208	−	10.1160i	0.844997	−	0.376217i
$724$	6.91556	+	1.46995i	0.257015	+	0.0546302i
$725$	0.499666	−	4.75400i	0.0185571	−	0.176559i
$726$	0.764249	+	7.27134i	0.0283639	+	0.269865i
$727$	45.8137	−	9.73800i	1.69914	−	0.361162i	0.746525	−	0.665357i	$-0.231721\pi$
$727$	45.8137	−	9.73800i	1.69914	−	0.361162i	0.952610	+	0.304195i	$0.0983873\pi$
$728$	−0.0646330	+	0.0469586i	−0.00239546	+	0.00174040i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.79773	+	0.594675i	−0.103549	+	0.0220099i
$731$	−6.05091	−	57.5705i	−0.223801	−	2.12932i
$732$	−0.146617	+	1.39497i	−0.00541914	+	0.0515596i
$733$	1.36498	+	0.290135i	0.0504166	+	0.0107164i	0.233051	−	0.972465i	$-0.425129\pi$
$733$	1.36498	+	0.290135i	0.0504166	+	0.0107164i	−0.182634	+	0.983181i	$0.558462\pi$
$734$	13.5013	−	6.01119i	0.498344	−	0.221877i
$735$	−5.18172	−	5.75488i	−0.191131	−	0.212272i
$736$	1.30949	−	4.03021i	0.0482686	−	0.148555i
$737$	6.64938	−	7.38488i	0.244933	−	0.272026i
$738$	5.86239	+	10.1539i	0.215797	+	0.373772i
$739$	10.3103	−	17.8579i	0.379269	−	0.656914i	−0.611687	−	0.791100i	$-0.709509\pi$
$739$	10.3103	−	17.8579i	0.379269	−	0.656914i	0.990956	+	0.134186i	$0.0428421\pi$
$740$	0.115051	+	0.354090i	0.00422935	+	0.0130166i
$741$	−0.148033	−	0.0659084i	−0.00543812	−	0.00242121i
$742$	39.4412	+	28.6557i	1.44793	+	1.05198i
$743$	7.82456			0.287055			0.143528	−	0.989646i	$-0.454155\pi$
$743$	7.82456			0.287055			0.143528	+	0.989646i	$0.454155\pi$
$744$	4.74535	+	2.91233i	0.173973	+	0.106771i
$745$	17.2696			0.632710
$746$	27.9444	+	20.3028i	1.02312	+	0.743339i
$747$	−0.768941	−	0.342354i	−0.0281341	−	0.0125261i
$748$	−4.31434	−	13.2782i	−0.157748	−	0.485498i
$749$	−16.7863	+	29.0746i	−0.613356	+	1.06236i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	18.0554	−	20.0525i	0.658850	−	0.731727i	−0.317420	−	0.948285i	$-0.602816\pi$
$751$	18.0554	−	20.0525i	0.658850	−	0.731727i	0.976270	+	0.216558i	$0.0694831\pi$
$752$	−0.530767	+	1.63353i	−0.0193551	+	0.0595688i
$753$	−10.8857	−	12.0898i	−0.396697	−	0.440576i
$754$	−0.0908583	+	0.0404527i	−0.00330887	+	0.00147320i
$755$	−2.30425	−	0.489784i	−0.0838604	−	0.0178251i
$756$	0.401367	−	3.81875i	0.0145976	−	0.138887i
$757$	−1.60331	−	15.2545i	−0.0582732	−	0.554433i	−0.984241	−	0.176831i	$-0.943415\pi$
$757$	−1.60331	−	15.2545i	−0.0582732	−	0.554433i	0.925968	−	0.377602i	$-0.123251\pi$
$758$	15.1549	−	3.22127i	0.550450	−	0.117002i
$759$	−6.58430	+	4.78377i	−0.238995	+	0.173640i
$760$	−6.30080	+	4.57780i	−0.228554	+	0.166054i
$761$	−38.1473	+	8.10847i	−1.38284	+	0.293932i	−0.838486	−	0.544924i	$-0.816559\pi$
$761$	−38.1473	+	8.10847i	−1.38284	+	0.293932i	−0.544354	+	0.838855i	$0.683225\pi$
$762$	0.820049	+	7.80225i	0.0297073	+	0.282646i
$763$	−2.63938	+	25.1121i	−0.0955521	+	0.909118i
$764$	−3.80626	−	0.809046i	−0.137706	−	0.0292703i
$765$	−6.64096	+	2.95675i	−0.240104	+	0.106901i
$766$	−6.66070	−	7.39746i	−0.240661	−	0.267281i
$767$	0.0539661	−	0.166091i	0.00194860	−	0.00599719i
$768$	−0.669131	+	0.743145i	−0.0241452	+	0.0268159i
$769$	−23.0578	−	39.9372i	−0.831485	−	1.44017i	−0.896861	−	0.442313i	$-0.854158\pi$
$769$	−23.0578	−	39.9372i	−0.831485	−	1.44017i	0.0653760	−	0.997861i	$-0.479175\pi$
$770$	3.68730	−	6.38658i	0.132881	−	0.230157i
$771$	−8.29948	−	25.5432i	−0.298898	−	0.919915i
$772$	−15.8284	−	7.04725i	−0.569676	−	0.253636i
$773$	−2.02222	−	1.46923i	−0.0727340	−	0.0528444i	0.550824	−	0.834621i	$-0.314314\pi$
$773$	−2.02222	−	1.46923i	−0.0727340	−	0.0528444i	−0.623558	+	0.781777i	$0.714314\pi$
$774$	7.96315			0.286230
$775$	4.23619	−	3.61313i	0.152168	−	0.129788i
$776$	−3.95583			−0.142006
$777$	1.15657	+	0.840297i	0.0414917	+	0.0301455i
$778$	11.5431	+	5.13930i	0.413839	+	0.184253i
$779$	−28.2179	−	86.8457i	−1.01101	−	3.11157i
$780$	−0.0104030	+	0.0180186i	−0.000372488	+	0.000645168i
$781$	2.17816	+	3.77268i	0.0779407	+	0.134997i
$782$	−20.6126	+	22.8926i	−0.737105	+	0.818638i
$783$	1.47716	−	4.54623i	0.0527893	−	0.162469i
$784$	5.18172	+	5.75488i	0.185061	+	0.205532i
$785$	16.8864	−	7.51830i	0.602700	−	0.268339i
$786$	−1.41912	−	0.301642i	−0.0506182	−	0.0107592i
$787$	1.64941	−	15.6931i	0.0587951	−	0.559398i	−0.924983	−	0.380008i	$-0.875921\pi$
$787$	1.64941	−	15.6931i	0.0587951	−	0.559398i	0.983778	−	0.179389i	$-0.0574122\pi$
$788$	−1.80536	−	17.1769i	−0.0643134	−	0.611902i
$789$	−5.69971	+	1.21151i	−0.202915	+	0.0431309i
$790$	−11.6466	+	8.46178i	−0.414369	+	0.301057i
$791$	−46.1308	+	33.5160i	−1.64022	+	1.19169i
$792$	1.87860	−	0.399310i	0.0667533	−	0.0141889i
$793$	−0.00305053	−	0.0290239i	−0.000108328	−	0.00103067i
$794$	−2.92698	+	27.8484i	−0.103875	+	0.988302i
$795$	12.4191	+	2.63976i	0.440459	+	0.0936225i
$796$	15.8644	−	7.06328i	0.562298	−	0.250351i
$797$	−8.01671	−	8.90345i	−0.283966	−	0.315376i	0.584239	−	0.811582i	$-0.301393\pi$
$797$	−8.01671	−	8.90345i	−0.283966	−	0.315376i	−0.868205	+	0.496205i	$0.834726\pi$
$798$	−9.24118	+	28.4414i	−0.327134	+	1.00682i
$799$	8.35475	−	9.27889i	0.295570	−	0.328264i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	1.52023	−	2.63312i	0.0537147	−	0.0930366i
$802$	2.27154	+	6.99109i	0.0802110	+	0.246864i
$803$	−5.01836	−	2.23432i	−0.177094	−	0.0788474i
$804$	4.18598	+	3.04129i	0.147628	+	0.107258i
$805$	−16.2715			−0.573496
$806$	−0.109173	−	0.0387425i	−0.00384544	−	0.00136465i
$807$	−19.1082			−0.672640
$808$	−4.12640	−	2.99801i	−0.145166	−	0.105469i
$809$	−28.5316	−	12.7031i	−1.00312	−	0.446616i	−0.161605	−	0.986856i	$-0.551667\pi$
$809$	−28.5316	−	12.7031i	−1.00312	−	0.446616i	−0.841511	+	0.540239i	$0.818334\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−24.2119	+	41.9363i	−0.850196	+	1.47258i	0.0308345	+	0.999525i	$0.490184\pi$
$811$	−24.2119	+	41.9363i	−0.850196	+	1.47258i	−0.881031	+	0.473059i	$0.843150\pi$
$812$	9.17745	+	15.8958i	0.322065	+	0.557833i
$813$	9.44137	−	10.4857i	0.331123	−	0.367750i
$814$	−0.220964	+	0.680056i	−0.00774477	+	0.0238359i
$815$	5.40762	+	6.00577i	0.189421	+	0.210373i
$816$	6.64096	−	2.95675i	0.232480	−	0.103507i
$817$	−60.6635	−	12.8944i	−2.12235	−	0.451119i
$818$	−2.75842	+	26.2446i	−0.0964457	+	0.917620i
$819$	0.00835086	+	0.0794532i	0.000291803	+	0.00277632i
$820$	−11.4686	+	2.43772i	−0.400499	+	0.0851288i
$821$	−30.2096	+	21.9486i	−1.05432	+	0.766011i	−0.973030	−	0.230679i	$-0.925905\pi$
$821$	−30.2096	+	21.9486i	−1.05432	+	0.766011i	−0.0812940	+	0.996690i	$0.525905\pi$
$822$	−0.194749	+	0.141494i	−0.00679266	+	0.00493515i
$823$	−30.5277	+	6.48886i	−1.06413	+	0.226187i	−0.706526	−	0.707687i	$-0.749739\pi$
$823$	−30.5277	+	6.48886i	−1.06413	+	0.226187i	−0.357602	+	0.933874i	$0.616406\pi$
$824$	−1.47784	−	14.0607i	−0.0514831	−	0.489829i
$825$	0.200755	−	1.91005i	0.00698938	−	0.0664995i
$826$	−31.5254	−	6.70093i	−1.09691	−	0.233155i
$827$	20.7948	−	9.25843i	0.723105	−	0.321947i	−0.0119740	−	0.999928i	$-0.503812\pi$
$827$	20.7948	−	9.25843i	0.723105	−	0.321947i	0.735079	+	0.677981i	$0.237145\pi$
$828$	−2.83551	−	3.14916i	−0.0985409	−	0.109441i
$829$	−1.73097	+	5.32738i	−0.0601191	+	0.185028i	−0.976606	−	0.215038i	$-0.931013\pi$
$829$	−1.73097	+	5.32738i	−0.0601191	+	0.185028i	0.916487	+	0.400065i	$0.131013\pi$
$830$	0.563214	−	0.625513i	0.0195494	−	0.0217119i
$831$	10.6958	+	18.5257i	0.371034	+	0.642650i
$832$	0.0104030	−	0.0180186i	0.000360660	−	0.000624682i
$833$	−17.3959	−	53.5390i	−0.602731	−	1.85502i
$834$	−1.34908	−	0.600648i	−0.0467147	−	0.0207987i
$835$	−13.6699	−	9.93176i	−0.473066	−	0.343703i
$836$	−14.9578			−0.517328
$837$	4.89483	−	2.65342i	0.169190	−	0.0917158i
$838$	−7.71430			−0.266486
$839$	−17.3528	−	12.6076i	−0.599085	−	0.435261i	0.246469	−	0.969151i	$-0.420730\pi$
$839$	−17.3528	−	12.6076i	−0.599085	−	0.435261i	−0.845554	+	0.533890i	$0.820730\pi$
$840$	3.50782	+	1.56178i	0.121031	+	0.0538866i
$841$	−1.90040	−	5.84882i	−0.0655310	−	0.201684i
$842$	6.65364	−	11.5244i	0.229299	−	0.397158i
$843$	10.4656	+	18.1269i	0.360453	+	0.624323i
$844$	6.26919	−	6.96264i	0.215794	−	0.239664i
$845$	−4.01709	+	12.3633i	−0.138192	+	0.425311i
$846$	1.14930	+	1.27642i	0.0395137	+	0.0438844i
$847$	−25.6471	+	11.4188i	−0.881243	+	0.392355i
$848$	−12.4191	−	2.63976i	−0.426473	−	0.0906496i
$849$	−1.02580	+	9.75982i	−0.0352053	+	0.334956i
$850$	−0.759863	−	7.22961i	−0.0260631	−	0.247974i
$851$	1.54324	−	0.328025i	0.0529015	−	0.0112446i
$852$	−1.83504	+	1.33324i	−0.0628676	+	0.0456760i
$853$	2.39377	−	1.73918i	0.0819611	−	0.0595483i	−0.546050	−	0.837753i	$-0.683869\pi$
$853$	2.39377	−	1.73918i	0.0819611	−	0.0595483i	0.628011	+	0.778204i	$0.283869\pi$
$854$	−5.26820	+	1.11979i	−0.180274	+	0.0383185i
$855$	0.814090	+	7.74555i	0.0278413	+	0.264892i
$856$	0.913926	−	8.69543i	0.0312374	−	0.297204i
$857$	15.3130	+	3.25487i	0.523081	+	0.111184i	0.461882	−	0.886941i	$-0.347174\pi$
$857$	15.3130	+	3.25487i	0.523081	+	0.111184i	0.0611990	+	0.998126i	$0.480508\pi$
$858$	−0.0365049	+	0.0162530i	−0.00124626	+	0.000554869i
$859$	12.7722	+	14.1850i	0.435783	+	0.483986i	0.920532	−	0.390668i	$-0.127756\pi$
$859$	12.7722	+	14.1850i	0.435783	+	0.483986i	−0.484749	+	0.874653i	$0.661089\pi$
$860$	−2.46075	+	7.57341i	−0.0839109	+	0.258251i
$861$	−30.1247	+	33.4568i	−1.02665	+	1.14021i
$862$	−14.6391	−	25.3556i	−0.498609	−	0.863616i
$863$	4.41735	−	7.65107i	0.150368	−	0.260445i	−0.780995	−	0.624538i	$-0.785287\pi$
$863$	4.41735	−	7.65107i	0.150368	−	0.260445i	0.931363	+	0.364092i	$0.118621\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−22.1938	−	9.88132i	−0.754612	−	0.335975i
$866$	2.74185	+	1.99207i	0.0931719	+	0.0676934i
$867$	−35.8447			−1.21735
$868$	−5.00478	+	20.7850i	−0.169873	+	0.705488i
$869$	−27.6487			−0.937916
$870$	3.86725	+	2.80972i	0.131112	+	0.0952585i
$871$	−0.0983465	−	0.0437867i	−0.00333235	−	0.00148366i
$872$	−2.03209	−	6.25414i	−0.0688153	−	0.211792i
$873$	−1.97792	+	3.42585i	−0.0669423	+	0.115947i
$874$	16.5017	+	28.5818i	0.558178	+	0.966793i
$875$	2.56932	−	2.85352i	0.0868588	−	0.0964665i
$876$	0.883860	−	2.72024i	0.0298628	−	0.0919084i
$877$	26.0039	+	28.8803i	0.878090	+	0.975218i	0.999850	−	0.0173417i	$-0.00552031\pi$
$877$	26.0039	+	28.8803i	0.878090	+	0.975218i	−0.121759	+	0.992560i	$0.538854\pi$
$878$	9.88737	−	4.40214i	0.333683	−	0.148565i
$879$	22.3706	+	4.75501i	0.754541	+	0.160383i
$880$	−0.200755	+	1.91005i	−0.00676744	+	0.0643879i
$881$	−5.30666	−	50.4895i	−0.178786	−	1.70104i	−0.604847	−	0.796341i	$-0.706766\pi$
$881$	−5.30666	−	50.4895i	−0.178786	−	1.70104i	0.426061	−	0.904694i	$-0.359901\pi$
$882$	7.57474	−	1.61006i	0.255055	−	0.0542135i
$883$	−19.8383	+	14.4133i	−0.667611	+	0.485048i	−0.869225	−	0.494417i	$-0.835381\pi$
$883$	−19.8383	+	14.4133i	−0.667611	+	0.485048i	0.201614	+	0.979465i	$0.435381\pi$
$884$	−0.122362	+	0.0889015i	−0.00411550	+	0.00299008i
$885$	−8.21019	+	1.74513i	−0.275983	+	0.0586619i
$886$	−0.0784765	−	0.746654i	−0.00263647	−	0.0250843i
$887$	1.58671	−	15.0965i	0.0532764	−	0.506891i	−0.935047	−	0.354523i	$-0.884643\pi$
$887$	1.58671	−	15.0965i	0.0532764	−	0.506891i	0.988324	−	0.152368i	$-0.0486900\pi$
$888$	−0.364176	−	0.0774081i	−0.0122210	−	0.00259764i
$889$	−27.5196	+	12.2525i	−0.922979	+	0.410937i
$890$	2.03447	+	2.25950i	0.0681954	+	0.0757387i
$891$	0.593490	−	1.82657i	0.0198827	−	0.0611925i
$892$	9.62683	−	10.6917i	0.322330	−	0.357984i
$893$	−6.68851	−	11.5848i	−0.223823	−	0.387672i
$894$	−8.63481	+	14.9559i	−0.288791	+	0.500201i
$895$	2.39510	+	7.37135i	0.0800593	+	0.246397i
$896$	−3.50782	−	1.56178i	−0.117188	−	0.0521755i
$897$	0.0713294	+	0.0518238i	0.00238162	+	0.00173035i
$898$	21.7893			0.727119
$899$	−11.4741	+	24.0146i	−0.382684	+	0.800931i
$900$	1.00000			0.0333333
$901$	74.6695	+	54.2506i	2.48760	+	1.80735i
$902$	−20.5715	−	9.15901i	−0.684955	−	0.304962i
$903$	9.44875	+	29.0803i	0.314435	+	0.967731i
$904$	7.42499	−	12.8605i	0.246952	−	0.427733i
$905$	3.53503	+	6.12285i	0.117508	+	0.203530i
$906$	1.57629	−	1.75065i	0.0523688	−	0.0581614i
$907$	8.65909	−	26.6499i	0.287520	−	0.884897i	−0.698112	−	0.715989i	$-0.745976\pi$
$907$	8.65909	−	26.6499i	0.287520	−	0.884897i	0.985632	−	0.168908i	$-0.0540239\pi$
$908$	−3.60142	−	3.99978i	−0.119517	−	0.132737i
$909$	−4.65955	+	2.07457i	−0.154548	+	0.0688090i
$910$	−0.0781450	−	0.0166102i	−0.00259048	−	0.000550624i
$911$	1.69662	−	16.1423i	0.0562116	−	0.534818i	−0.929791	−	0.368088i	$-0.880013\pi$
$911$	1.69662	−	16.1423i	0.0562116	−	0.534818i	0.986003	−	0.166730i	$-0.0533208\pi$
$912$	−0.814090	−	7.74555i	−0.0269572	−	0.256481i
$913$	1.58124	−	0.336103i	0.0523314	−	0.0111234i
$914$	18.8473	−	13.6934i	0.623413	−	0.452936i
$915$	−1.13477	+	0.824460i	−0.0375144	+	0.0272558i
$916$	−24.6160	+	5.23229i	−0.813335	+	0.172880i
$917$	−0.582311	−	5.54032i	−0.0192296	−	0.182958i
$918$	0.759863	−	7.22961i	0.0250792	−	0.238613i
$919$	26.0055	+	5.52763i	0.857841	+	0.182340i	0.615777	−	0.787921i	$-0.288842\pi$
$919$	26.0055	+	5.52763i	0.857841	+	0.182340i	0.242064	+	0.970260i	$0.422176\pi$
$920$	3.87125	−	1.72359i	0.127631	−	0.0568251i
$921$	−14.0753	−	15.6322i	−0.463796	−	0.515097i
$922$	6.16250	−	18.9662i	0.202951	−	0.624620i
$923$	0.0315783	−	0.0350713i	0.00103941	−	0.00115439i
$924$	3.68730	+	6.38658i	0.121303	+	0.210103i
$925$	−0.186156	+	0.322432i	−0.00612077	+	0.0106015i
$926$	5.87996	+	18.0967i	0.193228	+	0.594693i
$927$	−12.9159	−	5.75052i	−0.424213	−	0.188872i
$928$	−3.86725	−	2.80972i	−0.126949	−	0.0922337i
$929$	4.15327			0.136264			0.0681322	−	0.997676i	$-0.478296\pi$
$929$	4.15327			0.136264			0.0681322	+	0.997676i	$0.478296\pi$
$930$	1.01097	+	5.47521i	0.0331511	+	0.179539i
$931$	−60.3116			−1.97663
$932$	−6.11686	−	4.44416i	−0.200364	−	0.145573i
$933$	−22.6166	−	10.0696i	−0.740434	−	0.329662i
$934$	−7.74409	−	23.8339i	−0.253394	−	0.779868i
$935$	6.98075	−	12.0910i	0.228295	−	0.395418i
$936$	−0.0104030	−	0.0180186i	−0.000340034	−	0.000588956i
$937$	30.8272	−	34.2370i	1.00708	−	1.11847i	0.0141340	−	0.999900i	$-0.495501\pi$
$937$	30.8272	−	34.2370i	1.00708	−	1.11847i	0.992945	−	0.118575i	$-0.0378325\pi$
$938$	−6.13944	+	18.8952i	−0.200460	+	0.616952i
$939$	−13.7796	−	15.3038i	−0.449680	−	0.499420i
$940$	−1.56910	+	0.698610i	−0.0511786	+	0.0227862i
$941$	−52.0719	−	11.0682i	−1.69750	−	0.360814i	−0.745400	−	0.666617i	$-0.767742\pi$
$941$	−52.0719	−	11.0682i	−1.69750	−	0.360814i	−0.952095	+	0.305803i	$0.901075\pi$
$942$	−1.93215	+	18.3832i	−0.0629528	+	0.598956i
$943$	5.19350	+	49.4128i	0.169124	+	1.60910i
$944$	8.21019	−	1.74513i	0.267219	−	0.0567992i
$945$	3.10645	−	2.25697i	0.101053	−	0.0734192i
$946$	−12.3730	+	8.98948i	−0.402280	+	0.292273i
$947$	−26.6549	+	5.66567i	−0.866167	+	0.184110i	−0.619506	−	0.784992i	$-0.712667\pi$
$947$	−26.6549	+	5.66567i	−0.866167	+	0.184110i	−0.246662	+	0.969102i	$0.579334\pi$
$948$	−1.50480	−	14.3172i	−0.0488735	−	0.465000i
$949$	−0.00622050	+	0.0591841i	−0.000201926	+	0.00192120i
$950$	−7.61802	−	1.61926i	−0.247161	−	0.0525357i
$951$	16.7246	−	7.44629i	0.542333	−	0.241462i
$952$	18.6775	+	20.7435i	0.605341	+	0.672300i
$953$	−6.33101	+	19.4848i	−0.205081	+	0.631176i	0.794629	+	0.607096i	$0.207666\pi$
$953$	−6.33101	+	19.4848i	−0.205081	+	0.631176i	−0.999710	+	0.0240798i	$0.992334\pi$
$954$	−8.49564	+	9.43536i	−0.275056	+	0.305481i
$955$	−1.94565	−	3.36996i	−0.0629597	−	0.109049i
$956$	−10.7853	+	18.6807i	−0.348821	+	0.604175i
$957$	2.83699	+	8.73137i	0.0917069	+	0.282245i
$958$	−14.4646	−	6.44007i	−0.467331	−	0.208069i
$959$	−0.747795	−	0.543305i	−0.0241476	−	0.0175442i
$960$	−1.00000			−0.0322749
$961$	−28.9559	+	11.0706i	−0.934060	+	0.357115i
$962$	0.00774635			0.000249752
$963$	−7.07350	−	5.13920i	−0.227940	−	0.165608i
$964$	−22.7208	−	10.1160i	−0.731789	−	0.325813i
$965$	−5.35413	−	16.4783i	−0.172355	−	0.530456i
$966$	8.13576	−	14.0915i	0.261764	−	0.453388i
$967$	8.12626	+	14.0751i	0.261323	+	0.452624i	0.966594	−	0.256314i	$-0.0825080\pi$
$967$	8.12626	+	14.0751i	0.261323	+	0.452624i	−0.705271	+	0.708938i	$0.749175\pi$
$968$	4.89228	−	5.43343i	0.157244	−	0.174637i
$969$	−17.4953	+	53.8449i	−0.562029	+	1.72975i
$970$	−2.64697	−	2.93976i	−0.0849890	−	0.0943899i
$971$	−43.0743	+	19.1779i	−1.38232	+	0.615448i	−0.957131	−	0.289656i	$-0.906459\pi$
$971$	−43.0743	+	19.1779i	−1.38232	+	0.615448i	−0.425189	+	0.905105i	$0.639792\pi$
$972$	0.978148	+	0.207912i	0.0313741	+	0.00666877i
$973$	0.592718	−	5.63933i	0.0190017	−	0.180789i
$974$	2.29116	+	21.7990i	0.0734136	+	0.698484i
$975$	−0.0203514	+	0.00432582i	−0.000651766	+	0.000138537i
$976$	1.13477	−	0.824460i	0.0363232	−	0.0263903i
$977$	6.11622	−	4.44370i	0.195675	−	0.142166i	−0.485634	−	0.874162i	$-0.661411\pi$
$977$	6.11622	−	4.44370i	0.195675	−	0.142166i	0.681309	+	0.731996i	$0.261411\pi$
$978$	−7.90496	+	1.68025i	−0.252773	+	0.0537285i
$979$	0.610387	+	5.80744i	0.0195080	+	0.185607i
$980$	−0.809464	+	7.70154i	−0.0258574	+	0.246017i
$981$	−6.43229	−	1.36722i	−0.205367	−	0.0436521i
$982$	−10.2615	+	4.56873i	−0.327459	+	0.145794i
$983$	28.2416	+	31.3655i	0.900767	+	1.00040i	0.999986	+	0.00533796i	$0.00169913\pi$
$983$	28.2416	+	31.3655i	0.900767	+	1.00040i	−0.0992183	+	0.995066i	$0.531634\pi$
$984$	3.62315	−	11.1509i	0.115502	−	0.355478i
$985$	11.5569	−	12.8352i	0.368233	−	0.408965i
$986$	17.3746	+	30.0937i	0.553321	+	0.958380i
$987$	−3.29761	+	5.71162i	−0.104964	+	0.181803i
$988$	0.0500737	+	0.154111i	0.00159306	+	0.00490293i
$989$	30.8274	+	13.7252i	0.980253	+	0.436437i
$990$	1.55378	+	1.12888i	0.0493823	+	0.0358783i
$991$	8.37229			0.265955			0.132977	−	0.991119i	$-0.457546\pi$
$991$	8.37229			0.265955			0.132977	+	0.991119i	$0.457546\pi$
$992$	−1.01097	−	5.47521i	−0.0320984	−	0.173838i
$993$	18.1613			0.576331
$994$	−7.04617	−	5.11935i	−0.223491	−	0.162376i
$995$	15.8644	+	7.06328i	0.502935	+	0.223921i
$996$	0.260103	+	0.800514i	0.00824167	+	0.0253653i
$997$	8.24117	−	14.2741i	0.261001	−	0.452066i	−0.705507	−	0.708702i	$-0.749281\pi$
$997$	8.24117	−	14.2741i	0.261001	−	0.452066i	0.966508	+	0.256636i	$0.0826142\pi$
$998$	−8.59127	−	14.8805i	−0.271952	−	0.471034i
$999$	−0.249125	+	0.276682i	−0.00788198	+	0.00875383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.h.391.3	✓	24
31.18	even	15	inner	930.2.bg.h.421.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.h.391.3	✓	24	1.1	even	1	trivial
930.2.bg.h.421.3	yes	24	31.18	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.56932 - 2.85352i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.56932 - 2.85352i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(-1.87860 - 0.399310i) q^{11} +(0.104528 - 0.994522i) q^{12} +(0.00217483 + 0.0206921i) q^{13} +(3.75588 - 0.798336i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(7.11058 - 1.51140i) q^{17} +(0.104528 + 0.994522i) q^{18} +(0.814090 - 7.74555i) q^{19} +(-0.978148 - 0.207912i) q^{20} +(-3.50782 + 1.56178i) q^{21} +(-1.28511 - 1.42726i) q^{22} +(-1.30949 + 4.03021i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0104030 + 0.0180186i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.50782 + 1.56178i) q^{28} +(3.86725 + 2.80972i) q^{29} +1.00000 q^{30} +(1.01097 + 5.47521i) q^{31} -1.00000 q^{32} +(1.55378 + 1.12888i) q^{33} +(6.64096 + 2.95675i) q^{34} +(1.18656 + 3.65185i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.186156 - 0.322432i) q^{37} +(5.21133 - 5.78777i) q^{38} +(0.00642943 - 0.0197877i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(10.7111 - 4.76889i) q^{41} +(-3.75588 - 0.798336i) q^{42} +(0.832376 - 7.91953i) q^{43} +(-0.200755 - 1.91005i) q^{44} +(-0.978148 + 0.207912i) q^{45} +(-3.42830 + 2.49080i) q^{46} +(1.38957 - 1.00958i) q^{47} +(0.978148 - 0.207912i) q^{48} +(-0.809464 - 7.70154i) q^{49} +(0.104528 - 0.994522i) q^{50} +(-7.11058 - 1.51140i) q^{51} +(-0.0190073 + 0.00846259i) q^{52} +(8.49564 + 9.43536i) q^{53} +(0.309017 - 0.951057i) q^{54} +(1.28511 - 1.42726i) q^{55} +(1.91989 + 3.32535i) q^{56} +(-3.89411 + 6.74479i) q^{57} +(1.47716 + 4.54623i) q^{58} +(-7.66795 - 3.41399i) q^{59} +(0.809017 + 0.587785i) q^{60} -1.40266 q^{61} +(-2.40036 + 5.02377i) q^{62} +3.83979 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.0190073 - 0.00846259i) q^{65} +(0.593490 + 1.82657i) q^{66} +(-2.58708 + 4.48095i) q^{67} +(3.63472 + 6.29552i) q^{68} +(2.83551 - 3.14916i) q^{69} +(-1.18656 + 3.65185i) q^{70} +(-1.51775 - 1.68563i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(2.79773 + 0.594675i) q^{73} +(0.0389172 - 0.370273i) q^{74} +(0.104528 + 0.994522i) q^{75} +(7.61802 - 1.61926i) q^{76} +(-5.96617 + 4.33468i) q^{77} +(0.0168325 - 0.0122295i) q^{78} +(14.0815 - 2.99310i) q^{79} +(-0.104528 - 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(11.4686 + 2.43772i) q^{82} +(-0.768941 + 0.342354i) q^{83} +(-2.56932 - 2.85352i) q^{84} +(-2.24638 + 6.91365i) q^{85} +(5.32839 - 5.91778i) q^{86} +(-2.39009 - 4.13976i) q^{87} +(0.960287 - 1.66327i) q^{88} +(-0.939554 - 2.89165i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(0.0646330 + 0.0469586i) q^{91} -4.23761 q^{92} +(1.30340 - 5.41305i) q^{93} +1.71760 q^{94} +(6.30080 + 4.57780i) q^{95} +(0.913545 + 0.406737i) q^{96} +(1.22242 + 3.76222i) q^{97} +(3.87198 - 6.70647i) q^{98} +(-0.960287 - 1.66327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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