LMFDB - Embedded newform 930.2.bt.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(13,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 45, 22]))

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

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

chi := DirichletCharacter("930.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bt (of order $60$, degree $16$, 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:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	930.13
Dual form			930.2.bt.a.787.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(0.358368 - 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.57500 - 1.58726i) q^{5} +(0.866025 + 0.500000i) q^{6} +(4.42218 + 0.231757i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(0.358368 - 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.57500 - 1.58726i) q^{5} +(0.866025 + 0.500000i) q^{6} +(4.42218 + 0.231757i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +(1.32133 + 1.80391i) q^{10} +(0.116689 + 0.548981i) q^{11} +(-0.629320 + 0.777146i) q^{12} +(-0.0686210 - 0.0847399i) q^{13} +(-0.920684 + 4.33148i) q^{14} +(-0.917402 - 2.03921i) q^{15} +(0.809017 + 0.587785i) q^{16} +(2.80411 + 4.31795i) q^{17} +(0.777146 - 0.629320i) q^{18} +(-1.20194 + 0.126329i) q^{19} +(-1.98840 + 1.02287i) q^{20} +(1.80113 - 4.04540i) q^{21} +(-0.560476 + 0.0293733i) q^{22} +(0.770176 + 0.392424i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.0387630 - 4.99985i) q^{25} +(0.0944313 - 0.0545199i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(-4.13412 - 1.58694i) q^{28} +(-0.416655 + 0.302718i) q^{29} +(2.15762 - 0.587105i) q^{30} +(-0.488292 - 5.54631i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.554336 + 0.0877981i) q^{33} +(-4.70345 + 2.09411i) q^{34} +(7.33278 - 6.65411i) q^{35} +(0.500000 + 0.866025i) q^{36} +(3.76068 - 1.00767i) q^{37} +(0.0632512 - 1.20691i) q^{38} +(-0.103703 + 0.0336952i) q^{39} +(-0.699221 - 2.12393i) q^{40} +(-7.12348 - 3.17158i) q^{41} +(3.71384 + 2.41180i) q^{42} +(-0.743720 - 0.602252i) q^{43} +(0.0586661 - 0.558171i) q^{44} +(-2.23253 + 0.125682i) q^{45} +(-0.508075 + 0.699305i) q^{46} +(-7.84804 + 1.24301i) q^{47} +(0.838671 - 0.544639i) q^{48} +(12.5403 + 1.31804i) q^{49} +(4.94436 + 0.743863i) q^{50} +(5.03605 - 1.07045i) q^{51} +(0.0390764 + 0.101797i) q^{52} +(-0.0641301 - 1.22367i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(1.05516 + 0.679428i) q^{55} +(2.21412 - 3.83497i) q^{56} +(-0.312799 + 1.16738i) q^{57} +(-0.233812 - 0.458881i) q^{58} +(2.13980 + 4.80607i) q^{59} +(0.242351 + 2.22290i) q^{60} +5.26418i q^{61} +(5.55441 + 0.385354i) q^{62} +(-3.13124 - 3.13124i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.242582 - 0.0245460i) q^{65} +(-0.173434 + 0.533776i) q^{66} +(10.2991 + 2.75965i) q^{67} +(-1.33255 - 4.97313i) q^{68} +(0.642366 - 0.578389i) q^{69} +(5.42509 + 8.28343i) q^{70} +(0.960794 - 1.06707i) q^{71} +(-0.933580 + 0.358368i) q^{72} +(4.60918 - 7.09751i) q^{73} +(0.406966 + 3.87202i) q^{74} +(-4.68165 - 1.75560i) q^{75} +(1.18215 + 0.251274i) q^{76} +(0.388792 + 2.45473i) q^{77} +(-0.0170576 - 0.107697i) q^{78} +(9.37289 + 1.99227i) q^{79} +(2.20717 - 0.358356i) q^{80} +(0.104528 + 0.994522i) q^{81} +(4.24689 - 6.53964i) q^{82} +(-0.618623 + 0.237467i) q^{83} +(-2.96308 + 3.29083i) q^{84} +(11.2702 + 2.34992i) q^{85} +(0.711181 - 0.640350i) q^{86} +(0.133295 + 0.497465i) q^{87} +(0.542121 + 0.145261i) q^{88} +(-1.63107 + 5.01991i) q^{89} +(0.225111 - 2.22471i) q^{90} +(-0.283815 - 0.390638i) q^{91} +(-0.611215 - 0.611215i) q^{92} +(-5.35292 - 1.53176i) q^{93} -7.94587i q^{94} +(-1.69254 + 2.10676i) q^{95} +(0.406737 + 0.913545i) q^{96} +(0.448684 + 0.880592i) q^{97} +(-3.26354 + 12.1797i) q^{98} +(0.280623 - 0.486053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{7}+O(q^{10}) $ 256 * q + 8 * q^7	$ 256 q + 8 q^{7} + 4 q^{10} - 24 q^{14} - 8 q^{15} + 64 q^{16} + 36 q^{17} - 40 q^{19} + 12 q^{20} - 16 q^{21} + 8 q^{22} - 32 q^{24} + 20 q^{25} + 4 q^{28} - 16 q^{29} - 8 q^{31} - 4 q^{33} - 24 q^{35} + 128 q^{36} + 4 q^{37} + 4 q^{38} + 48 q^{41} + 32 q^{42} - 24 q^{43} + 4 q^{44} - 12 q^{45} - 20 q^{46} - 168 q^{47} - 40 q^{49} + 48 q^{50} - 64 q^{53} + 64 q^{54} + 64 q^{55} + 28 q^{57} + 68 q^{58} - 24 q^{59} + 4 q^{62} + 4 q^{63} - 60 q^{65} + 12 q^{66} - 76 q^{67} - 4 q^{68} + 12 q^{69} - 16 q^{70} - 48 q^{71} + 52 q^{73} + 68 q^{74} + 48 q^{75} + 48 q^{76} + 84 q^{77} - 56 q^{79} - 32 q^{81} - 32 q^{82} + 136 q^{83} + 68 q^{85} + 24 q^{86} + 20 q^{87} + 56 q^{88} - 224 q^{89} + 40 q^{91} - 48 q^{93} - 4 q^{95} + 8 q^{97} + 64 q^{98} + 4 q^{99}+O(q^{100}) $ 256 * q + 8 * q^7 + 4 * q^10 - 24 * q^14 - 8 * q^15 + 64 * q^16 + 36 * q^17 - 40 * q^19 + 12 * q^20 - 16 * q^21 + 8 * q^22 - 32 * q^24 + 20 * q^25 + 4 * q^28 - 16 * q^29 - 8 * q^31 - 4 * q^33 - 24 * q^35 + 128 * q^36 + 4 * q^37 + 4 * q^38 + 48 * q^41 + 32 * q^42 - 24 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^46 - 168 * q^47 - 40 * q^49 + 48 * q^50 - 64 * q^53 + 64 * q^54 + 64 * q^55 + 28 * q^57 + 68 * q^58 - 24 * q^59 + 4 * q^62 + 4 * q^63 - 60 * q^65 + 12 * q^66 - 76 * q^67 - 4 * q^68 + 12 * q^69 - 16 * q^70 - 48 * q^71 + 52 * q^73 + 68 * q^74 + 48 * q^75 + 48 * q^76 + 84 * q^77 - 56 * q^79 - 32 * q^81 - 32 * q^82 + 136 * q^83 + 68 * q^85 + 24 * q^86 + 20 * q^87 + 56 * q^88 - 224 * q^89 + 40 * q^91 - 48 * q^93 - 4 * q^95 + 8 * q^97 + 64 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{11}{30}\right)$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	0.358368	−	0.933580i	0.206904	−	0.539003i
$3$	0.358368	−	0.933580i	0.206904	−	0.539003i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	1.57500	−	1.58726i	0.704360	−	0.709842i
$5$	1.57500	−	1.58726i	0.704360	−	0.709842i
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	4.42218	+	0.231757i	1.67143	+	0.0875957i	0.864363	−	0.502869i	$-0.167722\pi$
$7$	4.42218	+	0.231757i	1.67143	+	0.0875957i	0.807064	+	0.590465i	$0.201055\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	−0.743145	−	0.669131i	−0.247715	−	0.223044i
$10$	1.32133	+	1.80391i	0.417841	+	0.570446i
$11$	0.116689	+	0.548981i	0.0351832	+	0.165524i	0.992232	−	0.124404i	$-0.0397019\pi$
$11$	0.116689	+	0.548981i	0.0351832	+	0.165524i	−0.957048	+	0.289928i	$0.906369\pi$
$12$	−0.629320	+	0.777146i	−0.181669	+	0.224343i
$13$	−0.0686210	−	0.0847399i	−0.0190320	−	0.0235026i	0.767541	−	0.641000i	$-0.221480\pi$
$13$	−0.0686210	−	0.0847399i	−0.0190320	−	0.0235026i	−0.786573	+	0.617497i	$0.788147\pi$
$14$	−0.920684	+	4.33148i	−0.246063	+	1.15764i
$15$	−0.917402	−	2.03921i	−0.236872	−	0.526521i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	2.80411	+	4.31795i	0.680096	+	1.04726i	0.995168	+	0.0981882i	$0.0313047\pi$
$17$	2.80411	+	4.31795i	0.680096	+	1.04726i	−0.315072	+	0.949068i	$0.602029\pi$
$18$	0.777146	−	0.629320i	0.183175	−	0.148332i
$19$	−1.20194	+	0.126329i	−0.275744	+	0.0289819i	−0.241391	−	0.970428i	$-0.577604\pi$
$19$	−1.20194	+	0.126329i	−0.275744	+	0.0289819i	−0.0343529	+	0.999410i	$0.510937\pi$
$20$	−1.98840	+	1.02287i	−0.444620	+	0.228720i
$21$	1.80113	−	4.04540i	0.393039	−	0.882780i
$22$	−0.560476	+	0.0293733i	−0.119494	+	0.00626241i
$23$	0.770176	+	0.392424i	0.160593	+	0.0818261i	0.532440	−	0.846468i	$-0.321275\pi$
$23$	0.770176	+	0.392424i	0.160593	+	0.0818261i	−0.371847	+	0.928294i	$0.621275\pi$
$24$	−0.669131	−	0.743145i	−0.136586	−	0.151694i
$25$	−0.0387630	−	4.99985i	−0.00775260	−	0.999970i
$26$	0.0944313	−	0.0545199i	0.0185195	−	0.0106922i
$27$	−0.891007	+	0.453990i	−0.171474	+	0.0873705i
$28$	−4.13412	−	1.58694i	−0.781276	−	0.299904i
$29$	−0.416655	+	0.302718i	−0.0773709	+	0.0562133i	−0.625798	−	0.779985i	$-0.715227\pi$
$29$	−0.416655	+	0.302718i	−0.0773709	+	0.0562133i	0.548427	+	0.836198i	$0.315227\pi$
$30$	2.15762	−	0.587105i	0.393925	−	0.107190i
$31$	−0.488292	−	5.54631i	−0.0876998	−	0.996147i
$31$	−0.488292	−	5.54631i	−0.0876998	−	0.996147i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.554336	+	0.0877981i	0.0964974	+	0.0152837i
$34$	−4.70345	+	2.09411i	−0.806634	+	0.359137i
$35$	7.33278	−	6.65411i	1.23947	−	1.12475i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	3.76068	−	1.00767i	0.618253	−	0.165660i	0.0639193	−	0.997955i	$-0.479640\pi$
$37$	3.76068	−	1.00767i	0.618253	−	0.165660i	0.554333	+	0.832295i	$0.312973\pi$
$38$	0.0632512	−	1.20691i	0.0102607	−	0.195786i
$39$	−0.103703	+	0.0336952i	−0.0166058	+	0.00539554i
$40$	−0.699221	−	2.12393i	−0.110557	−	0.335823i
$41$	−7.12348	−	3.17158i	−1.11250	−	0.495317i	−0.233606	−	0.972331i	$-0.575052\pi$
$41$	−7.12348	−	3.17158i	−1.11250	−	0.495317i	−0.878896	+	0.477014i	$0.841719\pi$
$42$	3.71384	+	2.41180i	0.573058	+	0.372148i
$43$	−0.743720	−	0.602252i	−0.113416	−	0.0918426i	0.570935	−	0.820996i	$-0.306581\pi$
$43$	−0.743720	−	0.602252i	−0.113416	−	0.0918426i	−0.684351	+	0.729153i	$0.739914\pi$
$44$	0.0586661	−	0.558171i	0.00884425	−	0.0841474i
$45$	−2.23253	+	0.125682i	−0.332806	+	0.0187355i
$46$	−0.508075	+	0.699305i	−0.0749116	+	0.103107i
$47$	−7.84804	+	1.24301i	−1.14475	+	0.181311i	−0.699866	−	0.714275i	$-0.746757\pi$
$47$	−7.84804	+	1.24301i	−1.14475	+	0.181311i	−0.444889	+	0.895586i	$0.646757\pi$
$48$	0.838671	−	0.544639i	0.121052	−	0.0786119i
$49$	12.5403	+	1.31804i	1.79147	+	0.188291i
$50$	4.94436	+	0.743863i	0.699238	+	0.105198i
$51$	5.03605	−	1.07045i	0.705189	−	0.149892i
$52$	0.0390764	+	0.101797i	0.00541892	+	0.0141168i
$53$	−0.0641301	−	1.22367i	−0.00880894	−	0.168085i	−0.999491	−	0.0318920i	$-0.989847\pi$
$53$	−0.0641301	−	1.22367i	−0.00880894	−	0.168085i	0.990682	−	0.136193i	$-0.0434866\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	1.05516	+	0.679428i	0.142278	+	0.0916140i
$56$	2.21412	−	3.83497i	0.295875	−	0.512470i
$57$	−0.312799	+	1.16738i	−0.0414312	+	0.154623i
$58$	−0.233812	−	0.458881i	−0.0307010	−	0.0602540i
$59$	2.13980	+	4.80607i	0.278578	+	0.625697i	0.997596	−	0.0692944i	$-0.0220748\pi$
$59$	2.13980	+	4.80607i	0.278578	+	0.625697i	−0.719018	+	0.694991i	$0.755408\pi$
$60$	0.242351	+	2.22290i	0.0312874	+	0.286975i
$61$			5.26418i			0.674009i	0.941503	+	0.337005i	$0.109414\pi$
$61$			5.26418i			0.674009i	−0.941503	+	0.337005i	$0.890586\pi$
$62$	5.55441	+	0.385354i	0.705411	+	0.0489400i
$63$	−3.13124	−	3.13124i	−0.394500	−	0.394500i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−0.242582	−	0.0245460i	−0.0300886	−	0.00304456i
$66$	−0.173434	+	0.533776i	−0.0213483	+	0.0657033i
$67$	10.2991	+	2.75965i	1.25824	+	0.337145i	0.825515	−	0.564381i	$-0.190885\pi$
$67$	10.2991	+	2.75965i	1.25824	+	0.337145i	0.432726	+	0.901525i	$0.357552\pi$
$68$	−1.33255	−	4.97313i	−0.161595	−	0.603080i
$69$	0.642366	−	0.578389i	0.0773318	−	0.0696298i
$70$	5.42509	+	8.28343i	0.648422	+	0.990059i
$71$	0.960794	−	1.06707i	0.114025	−	0.126638i	−0.683430	−	0.730016i	$-0.739512\pi$
$71$	0.960794	−	1.06707i	0.114025	−	0.126638i	0.797455	+	0.603378i	$0.206179\pi$
$72$	−0.933580	+	0.358368i	−0.110024	+	0.0422341i
$73$	4.60918	−	7.09751i	0.539463	−	0.830701i	−0.458864	−	0.888506i	$-0.651744\pi$
$73$	4.60918	−	7.09751i	0.539463	−	0.830701i	0.998328	+	0.0578054i	$0.0184103\pi$
$74$	0.406966	+	3.87202i	0.0473088	+	0.450113i
$75$	−4.68165	−	1.75560i	−0.540591	−	0.202719i
$76$	1.18215	+	0.251274i	0.135602	+	0.0288231i
$77$	0.388792	+	2.45473i	0.0443069	+	0.279743i
$78$	−0.0170576	−	0.107697i	−0.00193139	−	0.0121943i
$79$	9.37289	+	1.99227i	1.05453	+	0.224148i	0.702385	−	0.711797i	$-0.252118\pi$
$79$	9.37289	+	1.99227i	1.05453	+	0.224148i	0.352147	+	0.935945i	$0.385452\pi$
$80$	2.20717	−	0.358356i	0.246769	−	0.0400655i
$81$	0.104528	+	0.994522i	0.0116143	+	0.110502i
$82$	4.24689	−	6.53964i	0.468991	−	0.722182i
$83$	−0.618623	+	0.237467i	−0.0679027	+	0.0260654i	−0.392082	−	0.919930i	$-0.628245\pi$
$83$	−0.618623	+	0.237467i	−0.0679027	+	0.0260654i	0.324180	+	0.945996i	$0.394912\pi$
$84$	−2.96308	+	3.29083i	−0.323298	+	0.359059i
$85$	11.2702	+	2.34992i	1.22242	+	0.254885i
$86$	0.711181	−	0.640350i	0.0766886	−	0.0690508i
$87$	0.133295	+	0.497465i	0.0142908	+	0.0533339i
$88$	0.542121	+	0.145261i	0.0577903	+	0.0154849i
$89$	−1.63107	+	5.01991i	−0.172893	+	0.532109i	−0.999531	−	0.0306247i	$-0.990250\pi$
$89$	−1.63107	+	5.01991i	−0.172893	+	0.532109i	0.826638	+	0.562734i	$0.190250\pi$
$90$	0.225111	−	2.22471i	0.0237288	−	0.234505i
$91$	−0.283815	−	0.390638i	−0.0297519	−	0.0409500i
$92$	−0.611215	−	0.611215i	−0.0637236	−	0.0637236i
$93$	−5.35292	−	1.53176i	−0.555072	−	0.158836i
$94$		−	7.94587i		−	0.819554i
$95$	−1.69254	+	2.10676i	−0.173651	+	0.216149i
$96$	0.406737	+	0.913545i	0.0415124	+	0.0932383i
$97$	0.448684	+	0.880592i	0.0455570	+	0.0894106i	0.912663	−	0.408713i	$-0.134022\pi$
$97$	0.448684	+	0.880592i	0.0455570	+	0.0894106i	−0.867106	+	0.498124i	$0.834022\pi$
$98$	−3.26354	+	12.1797i	−0.329668	+	1.23034i
$99$	0.280623	−	0.486053i	0.0282036	−	0.0488501i
$100$	−1.50817	+	4.76712i	−0.150817	+	0.476712i
$101$	−0.460646	−	1.41772i	−0.0458360	−	0.141069i	0.925519	−	0.378700i	$-0.123629\pi$
$101$	−0.460646	−	1.41772i	−0.0458360	−	0.141069i	−0.971355	+	0.237632i	$0.923629\pi$
$102$	0.269455	+	5.14151i	0.0266800	+	0.509085i
$103$	−5.31706	−	13.8514i	−0.523905	−	1.36482i	−0.899047	−	0.437852i	$-0.855739\pi$
$103$	−5.31706	−	13.8514i	−0.523905	−	1.36482i	0.375142	−	0.926967i	$-0.377594\pi$
$104$	−0.106657	+	0.0226707i	−0.0104586	+	0.00222304i
$105$	−3.58432	−	9.23036i	−0.349793	−	0.900791i
$106$	1.21864	+	0.128084i	0.118365	+	0.0124407i
$107$	−14.5642	+	9.45813i	−1.40798	+	0.914352i	−0.407979	+	0.912991i	$0.633766\pi$
$107$	−14.5642	+	9.45813i	−1.40798	+	0.914352i	−0.999999	+	0.00136012i	$0.999567\pi$
$108$	0.987688	−	0.156434i	0.0950404	−	0.0150529i
$109$	−10.8226	+	14.8961i	−1.03662	+	1.42679i	−0.136762	+	0.990604i	$0.543670\pi$
$109$	−10.8226	+	14.8961i	−1.03662	+	1.42679i	−0.899858	+	0.436182i	$0.856330\pi$
$110$	−0.836126	+	0.935882i	−0.0797215	+	0.0892329i
$111$	0.406966	−	3.87202i	0.0386275	−	0.367516i
$112$	3.44139	+	2.78679i	0.325181	+	0.263327i
$113$	−6.58375	−	4.27554i	−0.619347	−	0.402209i	0.196477	−	0.980508i	$-0.437050\pi$
$113$	−6.58375	−	4.27554i	−0.619347	−	0.402209i	−0.815824	+	0.578300i	$0.803716\pi$
$114$	−1.10408	−	0.491566i	−0.103406	−	0.0460394i
$115$	1.83590	−	0.604399i	0.171199	−	0.0563605i
$116$	0.489808	−	0.159148i	0.0454775	−	0.0147765i
$117$	−0.00570670	+	0.108890i	−0.000527585	+	0.0100669i
$118$	−5.08164	+	1.36162i	−0.467803	+	0.125347i
$119$	11.3996	+	19.7446i	1.04500	+	1.80998i
$120$	−2.23344	−	0.108370i	−0.203884	−	0.00989278i
$121$	9.76124	−	4.34598i	0.887385	−	0.395089i
$122$	−5.19937	−	0.823499i	−0.470729	−	0.0745561i
$123$	−5.51375	+	5.51375i	−0.497158	+	0.497158i
$124$	−1.24951	+	5.42575i	−0.112209	+	0.487246i
$125$	−7.99709	−	7.81323i	−0.715282	−	0.698836i
$126$	3.58253	−	2.60286i	0.319157	−	0.231881i
$127$	−18.0280	−	6.92031i	−1.59973	−	0.614078i	−0.615054	−	0.788485i	$-0.710866\pi$
$127$	−18.0280	−	6.92031i	−1.59973	−	0.614078i	−0.984674	+	0.174407i	$0.944199\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	−0.828776	+	0.478494i	−0.0729697	+	0.0421291i
$130$	0.0621920	−	0.235755i	0.00545460	−	0.0206771i
$131$	6.08608	+	6.75928i	0.531743	+	0.590561i	0.947835	−	0.318762i	$-0.103267\pi$
$131$	6.08608	+	6.75928i	0.531743	+	0.590561i	−0.416092	+	0.909323i	$0.636600\pi$
$132$	−0.500073	−	0.254800i	−0.0435258	−	0.0221775i
$133$	−5.34447	+	0.280092i	−0.463425	+	0.0242871i
$134$	−4.33681	+	9.74064i	−0.374644	+	0.841464i
$135$	−0.682734	+	2.12929i	−0.0587604	+	0.183260i
$136$	5.12036	−	0.538171i	0.439067	−	0.0461478i
$137$	6.11453	−	4.95145i	0.522399	−	0.423031i	−0.331511	−	0.943452i	$-0.607558\pi$
$137$	6.11453	−	4.95145i	0.522399	−	0.423031i	0.853910	+	0.520421i	$0.174225\pi$
$138$	0.470780	+	0.724937i	0.0400754	+	0.0617108i
$139$	10.9537	+	7.95830i	0.929077	+	0.675014i	0.945767	−	0.324847i	$-0.105313\pi$
$139$	10.9537	+	7.95830i	0.929077	+	0.675014i	−0.0166898	+	0.999861i	$0.505313\pi$
$140$	−9.03012	+	4.06248i	−0.763184	+	0.343343i
$141$	−1.65204	+	7.77223i	−0.139127	+	0.654540i
$142$	0.903631	+	1.11589i	0.0758310	+	0.0936435i
$143$	0.0385132	−	0.0475599i	0.00322064	−	0.00397716i
$144$	−0.207912	−	0.978148i	−0.0173260	−	0.0815123i
$145$	−0.175741	+	1.13812i	−0.0145945	+	0.0945156i
$146$	6.28910	+	5.66273i	0.520489	+	0.468651i
$147$	5.72453	−	11.2350i	0.472152	−	0.926650i
$148$	−3.88801	−	0.203762i	−0.319593	−	0.0167491i
$149$	−14.2381	−	8.22038i	−1.16643	−	0.673439i	−0.213595	−	0.976922i	$-0.568517\pi$
$149$	−14.2381	−	8.22038i	−1.16643	−	0.673439i	−0.952837	+	0.303483i	$0.901850\pi$
$150$	2.46636	−	4.34938i	0.201377	−	0.355125i
$151$	−20.2873	−	6.59174i	−1.65096	−	0.536428i	−0.672009	−	0.740543i	$-0.734568\pi$
$151$	−20.2873	−	6.59174i	−1.65096	−	0.536428i	−0.978947	+	0.204115i	$0.934568\pi$
$152$	−0.433110	+	1.12829i	−0.0351298	+	0.0915163i
$153$	0.805413	−	5.08517i	0.0651137	−	0.411112i
$154$	−2.48533			−0.200274
$155$	−9.57247	−	7.96038i	−0.768880	−	0.639393i
$156$	0.109040			0.00873018
$157$	1.68486	−	10.6378i	0.134466	−	0.848986i	−0.824582	−	0.565742i	$-0.808590\pi$
$157$	1.68486	−	10.6378i	0.134466	−	0.848986i	0.959048	−	0.283243i	$-0.0914103\pi$
$158$	−3.43398	+	8.94583i	−0.273193	+	0.711692i
$159$	−1.16538	−	0.378655i	−0.0924207	−	0.0300293i
$160$	0.00866774	+	2.23605i	0.000685245	+	0.176775i
$161$	3.31491	+	1.91386i	0.261251	+	0.150834i
$162$	−0.998630	−	0.0523360i	−0.0784597	−	0.00411190i
$163$	−5.15506	+	10.1174i	−0.403775	+	0.792454i	−0.999946	−	0.0104040i	$-0.996688\pi$
$163$	−5.15506	+	10.1174i	−0.403775	+	0.792454i	0.596170	+	0.802858i	$0.296688\pi$
$164$	5.79476	+	5.21763i	0.452495	+	0.407428i
$165$	1.01244	−	0.741591i	0.0788180	−	0.0577327i
$166$	−0.137770	−	0.648155i	−0.0106930	−	0.0503066i
$167$	−14.4516	+	17.8462i	−1.11830	+	1.38098i	−0.202527	+	0.979277i	$0.564915\pi$
$167$	−14.4516	+	17.8462i	−1.11830	+	1.38098i	−0.915770	+	0.401704i	$0.868418\pi$
$168$	−2.78679	−	3.44139i	−0.215005	−	0.265509i
$169$	2.70038	−	12.7043i	0.207722	−	0.977253i
$170$	−4.08403	+	10.7638i	−0.313231	+	0.825545i
$171$	0.977747	+	0.710375i	0.0747702	+	0.0543237i
$172$	0.521213	+	0.802598i	0.0397421	+	0.0611975i
$173$	−9.47045	+	7.66902i	−0.720025	+	0.583065i	−0.917734	−	0.397196i	$-0.869983\pi$
$173$	−9.47045	+	7.66902i	−0.720025	+	0.583065i	0.197709	+	0.980261i	$0.436650\pi$
$174$	−0.512193	+	0.0538336i	−0.0388292	+	0.00408112i
$175$	0.987331	−	22.1192i	0.0746352	−	1.67206i
$176$	−0.228279	+	0.512723i	−0.0172072	+	0.0386480i
$177$	5.25369	−	0.275334i	0.394891	−	0.0206954i
$178$	−4.70295	−	2.39627i	−0.352501	−	0.179608i
$179$	−0.178793	−	0.198570i	−0.0133636	−	0.0148418i	0.736426	−	0.676518i	$-0.236512\pi$
$179$	−0.178793	−	0.198570i	−0.0133636	−	0.0148418i	−0.749790	+	0.661676i	$0.769845\pi$
$180$	2.16210	+	0.570360i	0.161154	+	0.0425121i
$181$	13.5647	−	7.83160i	1.00826	−	0.582118i	0.0975769	−	0.995228i	$-0.468891\pi$
$181$	13.5647	−	7.83160i	1.00826	−	0.582118i	0.910681	+	0.413110i	$0.135557\pi$
$182$	0.430227	−	0.219212i	0.0318906	−	0.0162491i
$183$	4.91454	+	1.88651i	0.363293	+	0.139455i
$184$	0.699305	−	0.508075i	0.0515535	−	0.0374558i
$185$	4.32364	−	7.55625i	0.317880	−	0.555547i
$186$	2.35028	−	5.04739i	0.172331	−	0.370093i
$187$	−2.04326	+	2.04326i	−0.149418	+	0.149418i
$188$	7.84804	+	1.24301i	0.572377	+	0.0906556i
$189$	−4.04540	+	1.80113i	−0.294260	+	0.131013i
$190$	−1.81605	−	2.00127i	−0.131750	−	0.145187i
$191$	11.4091	+	19.7612i	0.825536	+	1.42987i	0.901509	+	0.432760i	$0.142460\pi$
$191$	11.4091	+	19.7612i	0.825536	+	1.42987i	−0.0759730	+	0.997110i	$0.524206\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	0.526480	−	10.0458i	0.0378968	−	0.723114i	−0.911931	−	0.410343i	$-0.865409\pi$
$193$	0.526480	−	10.0458i	0.0378968	−	0.723114i	0.949828	−	0.312772i	$-0.101258\pi$
$194$	−0.939941	+	0.305405i	−0.0674838	+	0.0219268i
$195$	−0.109849	+	0.217673i	−0.00786647	+	0.0155879i
$196$	−11.5192	−	5.12869i	−0.822802	−	0.366335i
$197$	8.34296	+	5.41798i	0.594412	+	0.386015i	0.806499	−	0.591235i	$-0.201360\pi$
$197$	8.34296	+	5.41798i	0.594412	+	0.386015i	−0.212088	+	0.977251i	$0.568026\pi$
$198$	0.436170	+	0.353203i	0.0309972	+	0.0251011i
$199$	−1.18658	+	11.2895i	−0.0841142	+	0.800294i	0.868413	+	0.495841i	$0.165140\pi$
$199$	−1.18658	+	11.2895i	−0.0841142	+	0.800294i	−0.952528	+	0.304452i	$0.901527\pi$
$200$	−4.47250	−	2.23535i	−0.316253	−	0.158063i
$201$	6.26724	−	8.62611i	0.442057	−	0.608439i
$202$	1.47233	−	0.233194i	0.103593	−	0.0164075i
$203$	−1.91268	+	1.24211i	−0.134244	+	0.0871790i
$204$	−5.12036	−	0.538171i	−0.358497	−	0.0376795i
$205$	−16.2536	+	6.31156i	−1.13520	+	0.440819i
$206$	14.5126	−	3.08476i	1.01114	−	0.214925i
$207$	−0.309769	−	0.806976i	−0.0215304	−	0.0560887i
$208$	−0.00570670	−	0.108890i	−0.000395689	−	0.00755019i
$209$	−0.209606	−	0.645101i	−0.0144988	−	0.0446226i
$210$	9.67743	−	2.09624i	0.667806	−	0.144654i
$211$	−1.50933	+	2.61423i	−0.103906	+	0.179971i	−0.913291	−	0.407308i	$-0.866468\pi$
$211$	−1.50933	+	2.61423i	−0.103906	+	0.179971i	0.809384	+	0.587279i	$0.199801\pi$
$212$	−0.317145	+	1.18360i	−0.0217816	+	0.0812901i
$213$	−0.651878	−	1.27938i	−0.0446659	−	0.0876618i
$214$	−7.06333	−	15.8645i	−0.482839	−	1.08448i
$215$	−2.12729	+	0.231927i	−0.145080	+	0.0158173i
$216$			1.00000i			0.0680414i
$217$	−0.873920	−	24.6399i	−0.0593256	−	1.67267i
$218$	−13.0197	−	13.0197i	−0.881802	−	0.881802i
$219$	−4.97432	−	6.84656i	−0.336133	−	0.462648i
$220$	−0.793561	−	0.972236i	−0.0535019	−	0.0655481i
$221$	0.173482	−	0.533922i	0.0116696	−	0.0359155i
$222$	3.76068	+	1.00767i	0.252401	+	0.0676305i
$223$	4.62459	+	17.2592i	0.309686	+	1.15576i	0.928836	+	0.370491i	$0.120810\pi$
$223$	4.62459	+	17.2592i	0.309686	+	1.15576i	−0.619151	+	0.785272i	$0.712523\pi$
$224$	−3.29083	+	2.96308i	−0.219878	+	0.197979i
$225$	−3.31675	+	3.74155i	−0.221116	+	0.249437i
$226$	5.25282	−	5.83385i	0.349413	−	0.388062i
$227$	−12.7276	+	4.88568i	−0.844763	+	0.324274i	−0.741974	−	0.670429i	$-0.766110\pi$
$227$	−12.7276	+	4.88568i	−0.844763	+	0.324274i	−0.102789	+	0.994703i	$0.532777\pi$
$228$	0.658230	−	1.01358i	0.0435923	−	0.0671263i
$229$	0.0653122	+	0.621404i	0.00431595	+	0.0410635i	0.996468	−	0.0839744i	$-0.0267614\pi$
$229$	0.0653122	+	0.621404i	0.00431595	+	0.0410635i	−0.992152	+	0.125038i	$0.960095\pi$
$230$	0.309759	+	1.90785i	0.0204249	+	0.125800i
$231$	2.43102	+	0.516730i	0.159950	+	0.0339983i
$232$	0.0805660	+	0.508673i	0.00528941	+	0.0333961i
$233$	−2.37344	−	14.9853i	−0.155489	−	0.981720i	−0.934824	−	0.355112i	$-0.884443\pi$
$233$	−2.37344	−	14.9853i	−0.155489	−	0.981720i	0.779334	−	0.626608i	$-0.215557\pi$
$234$	−0.106657	−	0.0226707i	−0.00697239	−	0.00148203i
$235$	−10.3877	+	14.4146i	−0.677617	+	0.940304i
$236$	−0.549914	−	5.23208i	−0.0357963	−	0.340579i
$237$	5.21888	−	8.03638i	0.339003	−	0.522019i
$238$	−21.2848	+	8.17047i	−1.37969	+	0.529613i
$239$	−4.26320	+	4.73476i	−0.275763	+	0.306266i	−0.865078	−	0.501637i	$-0.832731\pi$
$239$	−4.26320	+	4.73476i	−0.275763	+	0.306266i	0.589315	+	0.807904i	$0.299398\pi$
$240$	0.456423	−	2.18899i	0.0294620	−	0.141299i
$241$	−15.0196	+	13.5237i	−0.967496	+	0.871138i	−0.991701	−	0.128569i	$-0.958961\pi$
$241$	−15.0196	+	13.5237i	−0.967496	+	0.871138i	0.0242042	+	0.999707i	$0.492295\pi$
$242$	2.76548	+	10.3209i	0.177772	+	0.663454i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	1.62672	−	5.00653i	0.104140	−	0.320510i
$245$	21.8430	−	17.8287i	1.39550	−	1.13904i
$246$	−4.58333	−	6.30841i	−0.292222	−	0.402210i
$247$	0.0931835	+	0.0931835i	0.00592912	+	0.00592912i
$248$	−5.16348	−	2.08290i	−0.327881	−	0.132264i
$249$			0.662635i			0.0419928i
$250$	8.96805	−	6.67638i	0.567189	−	0.422251i
$251$	10.0242	+	22.5148i	0.632723	+	1.42112i	0.890531	+	0.454923i	$0.150333\pi$
$251$	10.0242	+	22.5148i	0.632723	+	1.42112i	−0.257808	+	0.966196i	$0.583000\pi$
$252$	2.01038	+	3.94560i	0.126642	+	0.248549i
$253$	−0.125562	+	0.468604i	−0.00789401	+	0.0294609i
$254$	9.65531	−	16.7235i	0.605828	−	1.04932i
$255$	6.23270	−	9.67946i	0.390307	−	0.606151i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.48632	−	28.3607i	−0.0927142	−	1.76909i	−0.509865	−	0.860254i	$-0.670305\pi$
$257$	−1.48632	−	28.3607i	−0.0927142	−	1.76909i	0.417151	−	0.908837i	$-0.363029\pi$
$258$	−0.342954	−	0.893426i	−0.0213514	−	0.0556223i
$259$	16.8639	−	3.58454i	1.04787	−	0.222733i
$260$	0.223124	+	0.0983066i	0.0138376	+	0.00609672i
$261$	0.512193	+	0.0538336i	0.0317039	+	0.00333222i
$262$	−7.62813	+	4.95377i	−0.471267	+	0.306045i
$263$	−6.68705	+	1.05913i	−0.412341	+	0.0653085i	−0.359159	−	0.933276i	$-0.616936\pi$
$263$	−6.68705	+	1.05913i	−0.412341	+	0.0653085i	−0.0531823	+	0.998585i	$0.516936\pi$
$264$	0.329892	−	0.454057i	0.0203034	−	0.0279453i
$265$	−2.04329	−	1.82549i	−0.125518	−	0.112139i
$266$	0.559416	−	5.32249i	0.0343000	−	0.326343i
$267$	4.10196	+	3.32170i	0.251036	+	0.203285i
$268$	−8.94229	−	5.80719i	−0.546238	−	0.354731i
$269$	5.61873	+	2.50162i	0.342580	+	0.152526i	0.570813	−	0.821080i	$-0.306628\pi$
$269$	5.61873	+	2.50162i	0.342580	+	0.152526i	−0.228233	+	0.973607i	$0.573295\pi$
$270$	−1.99627	−	1.00742i	−0.121489	−	0.0613098i
$271$	15.9804	−	5.19235i	0.970741	−	0.315413i	0.219626	−	0.975584i	$-0.429516\pi$
$271$	15.9804	−	5.19235i	0.970741	−	0.315413i	0.751115	+	0.660171i	$0.229516\pi$
$272$	−0.269455	+	5.14151i	−0.0163381	+	0.311750i
$273$	−0.466402	+	0.124972i	−0.0282280	+	0.00756366i
$274$	3.93396	+	6.81382i	0.237659	+	0.411638i
$275$	2.74030	−	0.604710i	0.165246	−	0.0364654i
$276$	−0.789658	+	0.351579i	−0.0475318	+	0.0211625i
$277$	−20.8771	−	3.30660i	−1.25438	−	0.198674i	−0.506344	−	0.862332i	$-0.669003\pi$
$277$	−20.8771	−	3.30660i	−1.25438	−	0.198674i	−0.748037	+	0.663657i	$0.769003\pi$
$278$	−9.57385	+	9.57385i	−0.574201	+	0.574201i
$279$	−3.34834	+	4.44844i	−0.200460	+	0.266321i
$280$	−2.59985	−	9.55446i	−0.155371	−	0.570988i
$281$	−14.6997	+	10.6799i	−0.876909	+	0.637112i	−0.932432	−	0.361346i	$-0.882317\pi$
$281$	−14.6997	+	10.6799i	−0.876909	+	0.637112i	0.0555230	+	0.998457i	$0.482317\pi$
$282$	−7.41811	−	2.84754i	−0.441742	−	0.169569i
$283$	5.48266	−	2.79356i	0.325911	−	0.166060i	−0.283378	−	0.959008i	$-0.591455\pi$
$283$	5.48266	−	2.79356i	0.325911	−	0.166060i	0.609289	+	0.792949i	$0.291455\pi$
$284$	−1.24351	+	0.717942i	−0.0737889	+	0.0426020i
$285$	1.36027	+	2.33511i	0.0805757	+	0.138320i
$286$	0.0409495	+	0.0454791i	0.00242140	+	0.00268923i
$287$	−30.7663	−	15.6762i	−1.81608	−	0.925337i
$288$	0.998630	−	0.0523360i	0.0588448	−	0.00308393i
$289$	−3.86713	+	8.68571i	−0.227478	+	0.510924i
$290$	−1.09661	−	0.351618i	−0.0643954	−	0.0206477i
$291$	0.982898	−	0.103307i	0.0576185	−	0.00605595i
$292$	−6.57684	+	5.32582i	−0.384880	+	0.311670i
$293$	−1.74696	−	2.69009i	−0.102059	−	0.157157i	0.783952	−	0.620822i	$-0.213201\pi$
$293$	−1.74696	−	2.69009i	−0.102059	−	0.157157i	−0.886011	+	0.463665i	$0.846534\pi$
$294$	10.2012	+	7.41160i	0.594946	+	0.432253i
$295$	10.9986	+	4.17314i	0.640366	+	0.242970i
$296$	0.809472	−	3.80827i	0.0470496	−	0.221351i
$297$	−0.353203	−	0.436170i	−0.0204949	−	0.0253091i
$298$	10.3465	−	12.7769i	0.599357	−	0.740144i
$299$	−0.0195963	−	0.0921932i	−0.00113328	−	0.00533167i
$300$	3.91001	+	3.11638i	0.225744	+	0.179924i
$301$	−3.14929	−	2.83563i	−0.181522	−	0.163443i
$302$	9.68421	−	19.0063i	0.557264	−	1.09369i
$303$	−1.48864	−	0.0780163i	−0.0855201	−	0.00448192i
$304$	−1.04664	−	0.604281i	−0.0600292	−	0.0346579i
$305$	8.35560	+	8.29107i	0.478440	+	0.474746i
$306$	4.89657	+	1.59099i	0.279918	+	0.0909510i
$307$	−10.7074	+	27.8937i	−0.611102	+	1.59198i	0.182277	+	0.983247i	$0.441653\pi$
$307$	−10.7074	+	27.8937i	−0.611102	+	1.59198i	−0.793379	+	0.608728i	$0.791680\pi$
$308$	0.388792	−	2.45473i	0.0221535	−	0.139871i
$309$	−14.8369			−0.844040
$310$	9.35984	−	8.20934i	0.531603	−	0.466259i
$311$	−19.8709			−1.12677			−0.563387	−	0.826193i	$-0.690502\pi$
$311$	−19.8709			−1.12677			−0.563387	+	0.826193i	$0.690502\pi$
$312$	−0.0170576	+	0.107697i	−0.000965696	+	0.00609716i
$313$	−5.94763	+	15.4941i	−0.336180	+	0.875779i	0.656425	+	0.754391i	$0.272068\pi$
$313$	−5.94763	+	15.4941i	−0.336180	+	0.875779i	−0.992605	+	0.121388i	$0.961266\pi$
$314$	10.2432	+	3.32822i	0.578058	+	0.187823i
$315$	−9.90179	+	0.0383829i	−0.557902	+	0.00216263i
$316$	−8.29850	−	4.79114i	−0.466827	−	0.269523i
$317$	25.2358	+	1.32255i	1.41738	+	0.0742820i	0.745565	−	0.666433i	$-0.232180\pi$
$317$	25.2358	+	1.32255i	1.41738	+	0.0742820i	0.671820	+	0.740715i	$0.265513\pi$
$318$	0.556299	−	1.09180i	0.0311957	−	0.0612250i
$319$	−0.214806	−	0.193412i	−0.0120268	−	0.0108290i
$320$	−2.20988	−	0.341234i	−0.123536	−	0.0190756i
$321$	3.61057	+	16.9864i	0.201522	+	0.948087i
$322$	−2.40887	+	2.97470i	−0.134241	+	0.165774i
$323$	−3.91585	−	4.83568i	−0.217884	−	0.269064i
$324$	0.207912	−	0.978148i	0.0115506	−	0.0543415i
$325$	−0.421027	+	0.346379i	−0.0233544	+	0.0192137i
$326$	−9.18638	−	6.67430i	−0.508787	−	0.369655i
$327$	10.0282	+	15.4421i	0.554561	+	0.853949i
$328$	−6.05989	+	4.90720i	−0.334602	+	0.270955i
$329$	−34.9935	+	3.67797i	−1.92925	+	0.202773i
$330$	0.574081	+	1.11598i	0.0316021	+	0.0614327i
$331$	−9.24166	+	20.7571i	−0.507968	+	1.14091i	0.459559	+	0.888147i	$0.348007\pi$
$331$	−9.24166	+	20.7571i	−0.507968	+	1.14091i	−0.967527	+	0.252767i	$0.918659\pi$
$332$	0.661727	−	0.0346797i	0.0363170	−	0.00190329i
$333$	−3.46900	−	1.76754i	−0.190100	−	0.0968607i
$334$	−15.3658	−	17.0654i	−0.840777	−	0.933778i
$335$	20.6014	−	12.0009i	1.12558	−	0.655682i
$336$	3.83497	−	2.21412i	0.209215	−	0.120790i
$337$	−5.73083	+	2.92000i	−0.312178	+	0.159063i	−0.603059	−	0.797697i	$-0.706052\pi$
$337$	−5.73083	+	2.92000i	−0.312178	+	0.159063i	0.290881	+	0.956759i	$0.406052\pi$
$338$	12.1254	+	4.65452i	0.659537	+	0.253173i
$339$	−6.35096	+	4.61424i	−0.344937	+	0.250611i
$340$	−9.99239	−	5.71758i	−0.541913	−	0.310079i
$341$	2.98784	−	0.915259i	0.161801	−	0.0495641i
$342$	−0.854582	+	0.854582i	−0.0462105	+	0.0462105i
$343$	24.5339	+	3.88578i	1.32470	+	0.209812i
$344$	−0.874253	+	0.389242i	−0.0471365	+	0.0209865i
$345$	0.0936738	−	1.93056i	0.00504323	−	0.103938i
$346$	−6.09309	−	10.5535i	−0.327567	−	0.567362i
$347$	−2.33610	+	0.625957i	−0.125409	+	0.0336032i	−0.320977	−	0.947087i	$-0.604011\pi$
$347$	−2.33610	+	0.625957i	−0.125409	+	0.0336032i	0.195569	+	0.980690i	$0.437345\pi$
$348$	0.0269538	−	0.514308i	0.00144487	−	0.0275698i
$349$	4.07817	−	1.32508i	0.218299	−	0.0709298i	−0.197825	−	0.980237i	$-0.563388\pi$
$349$	4.07817	−	1.32508i	0.218299	−	0.0709298i	0.416125	+	0.909308i	$0.363388\pi$
$350$	21.6924	+	4.43538i	1.15951	+	0.237081i
$351$	0.0996129	+	0.0443505i	0.00531694	+	0.00236725i
$352$	−0.470700	−	0.305676i	−0.0250884	−	0.0162926i
$353$	−14.4031	−	11.6634i	−0.766601	−	0.620781i	0.164150	−	0.986435i	$-0.447512\pi$
$353$	−14.4031	−	11.6634i	−0.766601	−	0.620781i	−0.930751	+	0.365654i	$0.880845\pi$
$354$	−0.549914	+	5.23208i	−0.0292276	+	0.278082i
$355$	−0.180464	−	3.20566i	−0.00957805	−	0.170139i
$356$	3.10247	−	4.27019i	0.164431	−	0.226319i
$357$	22.5184	−	3.56657i	1.19180	−	0.188763i
$358$	0.224095	−	0.145529i	0.0118438	−	0.00769144i
$359$	6.11400	+	0.642608i	0.322685	+	0.0339155i	0.264486	−	0.964389i	$-0.414798\pi$
$359$	6.11400	+	0.642608i	0.322685	+	0.0339155i	0.0581986	+	0.998305i	$0.481464\pi$
$360$	−0.901566	+	2.04626i	−0.0475167	+	0.107847i
$361$	−17.1561	+	3.64664i	−0.902953	+	0.191929i
$362$	5.61319	+	14.6229i	0.295023	+	0.768560i
$363$	−0.559210	−	10.6704i	−0.0293509	−	0.560049i
$364$	0.149211	+	0.459223i	0.00782076	+	0.0240698i
$365$	−4.00612	−	18.4945i	−0.209690	−	0.968047i
$366$	−2.63209	+	4.55891i	−0.137582	+	0.238298i
$367$	−5.68699	+	21.2241i	−0.296858	+	1.10789i	0.642872	+	0.765974i	$0.277743\pi$
$367$	−5.68699	+	21.2241i	−0.296858	+	1.10789i	−0.939730	+	0.341917i	$0.888924\pi$
$368$	0.392424	+	0.770176i	0.0204565	+	0.0401482i
$369$	3.17158	+	7.12348i	0.165106	+	0.370834i
$370$	6.78685	+	5.45246i	0.352832	+	0.283460i
$371$		−	5.42617i		−	0.281713i
$372$	4.61759	+	3.11093i	0.239411	+	0.161294i
$373$	4.43781	+	4.43781i	0.229781	+	0.229781i	0.812601	−	0.582820i	$-0.198051\pi$
$373$	4.43781	+	4.43781i	0.229781	+	0.229781i	−0.582820	+	0.812601i	$0.698051\pi$
$374$	−1.69847	−	2.33774i	−0.0878257	−	0.120882i
$375$	−10.1602	+	4.66592i	−0.524669	+	0.240947i
$376$	−2.45541	+	7.55697i	−0.126628	+	0.389721i
$377$	0.0542436	+	0.0145345i	0.00279369	+	0.000748566i
$378$	−1.14611	−	4.27736i	−0.0589498	−	0.220004i
$379$	16.9366	−	15.2498i	0.869975	−	0.783329i	−0.107539	−	0.994201i	$-0.534297\pi$
$379$	16.9366	−	15.2498i	0.869975	−	0.783329i	0.977514	+	0.210872i	$0.0676302\pi$
$380$	2.26072	−	1.48062i	0.115973	−	0.0759542i
$381$	−12.9213	+	14.3506i	−0.661979	+	0.735203i
$382$	−21.3027	+	8.17734i	−1.08994	+	0.418389i
$383$	19.4243	−	29.9108i	0.992534	−	1.52837i	0.150738	−	0.988574i	$-0.451835\pi$
$383$	19.4243	−	29.9108i	0.992534	−	1.52837i	0.841796	−	0.539795i	$-0.181498\pi$
$384$	−0.104528	−	0.994522i	−0.00533420	−	0.0507515i
$385$	4.50864	+	3.24909i	0.229782	+	0.165589i
$386$	9.83979	+	2.09151i	0.500832	+	0.106455i
$387$	0.149706	+	0.945206i	0.00760998	+	0.0480475i
$388$	−0.154606	−	0.976144i	−0.00784893	−	0.0495562i
$389$	13.3592	+	2.83959i	0.677340	+	0.143973i	0.533722	−	0.845660i	$-0.320793\pi$
$389$	13.3592	+	2.83959i	0.677340	+	0.143973i	0.143618	+	0.989633i	$0.454126\pi$
$390$	−0.197809	−	0.142548i	−0.0100164	−	0.00721822i
$391$	0.465189	+	4.42598i	0.0235256	+	0.223831i
$392$	6.86755	−	10.5751i	0.346864	−	0.534124i
$393$	8.49138	−	3.25954i	0.428334	−	0.164422i
$394$	−6.65641	+	7.39269i	−0.335345	+	0.372438i
$395$	17.9245	−	11.7394i	0.901880	−	0.590671i
$396$	−0.417087	+	0.375546i	−0.0209594	+	0.0188719i
$397$	6.29337	+	23.4872i	0.315855	+	1.17879i	0.923191	+	0.384343i	$0.125572\pi$
$397$	6.29337	+	23.4872i	0.315855	+	1.17879i	−0.607335	+	0.794446i	$0.707761\pi$
$398$	−10.9649	−	2.93804i	−0.549622	−	0.147271i
$399$	−1.65380	+	5.08987i	−0.0827935	+	0.254812i
$400$	2.90748	−	4.06775i	0.145374	−	0.203387i
$401$	13.8832	+	19.1085i	0.693293	+	0.954235i	0.999997	+	0.00243060i	$0.000773686\pi$
$401$	13.8832	+	19.1085i	0.693293	+	0.954235i	−0.306704	+	0.951805i	$0.599226\pi$
$402$	7.53950	+	7.53950i	0.376036	+	0.376036i
$403$	−0.436487	+	0.421971i	−0.0217430	+	0.0210199i
$404$			1.49068i			0.0741642i
$405$	1.74319	+	1.40046i	0.0866200	+	0.0695892i
$406$	−0.927608	−	2.08344i	−0.0460364	−	0.103399i
$407$	0.992025	+	1.94696i	0.0491729	+	0.0965072i
$408$	1.33255	−	4.97313i	0.0659709	−	0.246207i
$409$	20.1681	−	34.9322i	0.997250	−	1.72729i	0.434442	−	0.900700i	$-0.356946\pi$
$409$	20.1681	−	34.9322i	0.997250	−	1.72729i	0.562808	−	0.826588i	$-0.309721\pi$
$410$	−3.69124	−	17.0408i	−0.182297	−	0.841586i
$411$	−2.43132	−	7.48284i	−0.119928	−	0.369101i
$412$	0.776501	+	14.8165i	0.0382555	+	0.729958i
$413$	8.34874	+	21.7492i	0.410815	+	1.07021i
$414$	0.845500	−	0.179717i	0.0415540	−	0.00883258i
$415$	−0.597409	+	1.35592i	−0.0293257	+	0.0665597i
$416$	0.108443	+	0.0113978i	0.00531683	+	0.000558822i
$417$	11.3551	−	7.37412i	0.556064	−	0.361112i
$418$	0.669949	−	0.106109i	0.0327683	−	0.00518998i
$419$	0.0669756	−	0.0921840i	0.00327197	−	0.00450348i	−0.807378	−	0.590035i	$-0.799114\pi$
$419$	0.0669756	−	0.0921840i	0.00327197	−	0.00450348i	0.810650	+	0.585531i	$0.199114\pi$
$420$	0.556550	+	9.88621i	0.0271568	+	0.482398i
$421$	0.683004	−	6.49835i	0.0332876	−	0.316710i	−0.965190	−	0.261550i	$-0.915766\pi$
$421$	0.683004	−	6.49835i	0.0332876	−	0.316710i	0.998478	−	0.0551601i	$-0.0175669\pi$
$422$	−2.34594	−	1.89970i	−0.114198	−	0.0924760i
$423$	6.66397	+	4.32763i	0.324013	+	0.210417i
$424$	−1.11942	−	0.498396i	−0.0543637	−	0.0242043i
$425$	21.4804	−	14.1875i	1.04195	−	0.688195i
$426$	1.36561	−	0.443713i	0.0661639	−	0.0214979i
$427$	−1.22001	+	23.2791i	−0.0590403	+	1.12656i
$428$	16.7741	−	4.49462i	0.810808	−	0.217255i
$429$	−0.0305991	−	0.0529991i	−0.00147734	−	0.00255882i
$430$	0.103709	−	2.13738i	0.00500129	−	0.103073i
$431$	8.97920	−	3.99780i	0.432513	−	0.192567i	−0.178920	−	0.983864i	$-0.557260\pi$
$431$	8.97920	−	3.99780i	0.432513	−	0.192567i	0.611433	+	0.791297i	$0.290594\pi$
$432$	−0.987688	−	0.156434i	−0.0475202	−	0.00752646i
$433$	26.1406	−	26.1406i	1.25624	−	1.25624i	0.303363	−	0.952875i	$-0.401891\pi$
$433$	26.1406	−	26.1406i	1.25624	−	1.25624i	0.952875	−	0.303363i	$-0.0981094\pi$
$434$	24.4733	+	2.99138i	1.17476	+	0.143591i
$435$	0.999545	+	0.571933i	0.0479245	+	0.0274221i
$436$	14.8961	−	10.8226i	0.713393	−	0.518310i
$437$	−0.975280	−	0.374375i	−0.0466540	−	0.0179088i
$438$	7.54042	−	3.84204i	0.360295	−	0.183580i
$439$	−10.2967	+	5.94478i	−0.491433	+	0.283729i	−0.725169	−	0.688571i	$-0.758238\pi$
$439$	−10.2967	+	5.94478i	−0.491433	+	0.283729i	0.233736	+	0.972300i	$0.424905\pi$
$440$	1.08441	−	0.631700i	0.0516971	−	0.0301151i
$441$	−8.43732	−	9.37059i	−0.401777	−	0.446218i
$442$	0.500210	+	0.254870i	0.0237925	+	0.0121229i
$443$	−12.1540	+	0.636966i	−0.577456	+	0.0302632i	−0.338829	−	0.940848i	$-0.610031\pi$
$443$	−12.1540	+	0.636966i	−0.577456	+	0.0302632i	−0.238627	+	0.971111i	$0.576697\pi$
$444$	−1.58357	+	3.55675i	−0.0751528	+	0.168796i
$445$	5.39895	+	10.4953i	0.255935	+	0.497523i
$446$	−17.7702	+	1.86772i	−0.841442	+	0.0884391i
$447$	−12.7769	+	10.3465i	−0.604325	+	0.489373i
$448$	−2.41180	−	3.71384i	−0.113947	−	0.175462i
$449$	18.4803	+	13.4267i	0.872139	+	0.633646i	0.931160	−	0.364611i	$-0.118798\pi$
$449$	18.4803	+	13.4267i	0.872139	+	0.633646i	−0.0590209	+	0.998257i	$0.518798\pi$
$450$	−3.17663	−	3.86122i	−0.149748	−	0.182020i
$451$	0.909901	−	4.28075i	0.0428455	−	0.201572i
$452$	4.94030	+	6.10077i	0.232372	+	0.286956i
$453$	−13.4242	+	16.5775i	−0.630725	+	0.778881i
$454$	−2.83449	−	13.3352i	−0.133029	−	0.625853i
$455$	−1.06705	−	0.164767i	−0.0500241	−	0.00772439i
$456$	0.898136	+	0.808685i	0.0420591	+	0.0378702i
$457$	−9.51792	+	18.6800i	−0.445229	+	0.873812i	0.553920	+	0.832570i	$0.313131\pi$
$457$	−9.51792	+	18.6800i	−0.445229	+	0.873812i	−0.999149	+	0.0412419i	$0.986869\pi$
$458$	−0.623971	−	0.0327009i	−0.0291562	−	0.00152801i
$459$	−4.45879	−	2.57428i	−0.208118	−	0.120157i
$460$	−1.93282	+	0.00749229i	−0.0901181	+	0.000349330i
$461$	22.1680	+	7.20281i	1.03246	+	0.335468i	0.775764	−	0.631023i	$-0.217365\pi$
$461$	22.1680	+	7.20281i	1.03246	+	0.335468i	0.256701	+	0.966491i	$0.417365\pi$
$462$	−0.890664	+	2.32026i	−0.0414374	+	0.107948i
$463$	−1.35170	+	8.53430i	−0.0628188	+	0.396622i	0.936165	+	0.351560i	$0.114349\pi$
$463$	−1.35170	+	8.53430i	−0.0628188	+	0.396622i	−0.998984	+	0.0450624i	$0.985651\pi$
$464$	−0.515014			−0.0239089
$465$	−10.8621	+	6.08393i	−0.503719	+	0.282135i
$466$	15.1721			0.702834
$467$	2.04735	−	12.9265i	0.0947402	−	0.598166i	−0.893947	−	0.448173i	$-0.852075\pi$
$467$	2.04735	−	12.9265i	0.0947402	−	0.598166i	0.988687	−	0.149993i	$-0.0479252\pi$
$468$	0.0390764	−	0.101797i	0.00180631	−	0.00470559i
$469$	44.9051	+	14.5906i	2.07352	+	0.673729i
$470$	−12.6121	−	12.5147i	−0.581754	−	0.577261i
$471$	−9.32740	−	5.38518i	−0.429784	−	0.248136i
$472$	5.25369	+	0.275334i	0.241821	+	0.0126733i
$473$	0.243841	−	0.478564i	0.0112118	−	0.0220044i
$474$	7.12102	+	6.41180i	0.327079	+	0.294504i
$475$	0.678217	+	6.00463i	0.0311187	+	0.275511i
$476$	−4.74020	−	22.3009i	−0.217267	−	1.02216i
$477$	−0.771140	+	0.952279i	−0.0353081	+	0.0436019i
$478$	−4.00956	−	4.95139i	−0.183393	−	0.226471i
$479$	−5.23086	+	24.6093i	−0.239004	+	1.12443i	0.680929	+	0.732350i	$0.261576\pi$
$479$	−5.23086	+	24.6093i	−0.239004	+	1.12443i	−0.919933	+	0.392076i	$0.871757\pi$
$480$	2.09064	+	0.793237i	0.0954242	+	0.0362062i
$481$	−0.343452	−	0.249532i	−0.0156601	−	0.0113777i
$482$	−11.0076	−	16.9502i	−0.501383	−	0.772062i
$483$	2.97470	−	2.40887i	0.135354	−	0.109607i
$484$	−10.6265	+	1.11689i	−0.483021	+	0.0507676i
$485$	2.10440	+	0.674755i	0.0955560	+	0.0306390i
$486$	−0.406737	+	0.913545i	−0.0184499	+	0.0414393i
$487$	−23.6541	+	1.23966i	−1.07187	+	0.0561743i	−0.580096	−	0.814548i	$-0.696985\pi$
$487$	−23.6541	+	1.23966i	−1.07187	+	0.0561743i	−0.491775	+	0.870723i	$0.663652\pi$
$488$	4.69042	+	2.38989i	0.212325	+	0.108185i
$489$	7.59797	+	8.43841i	0.343592	+	0.381598i
$490$	14.1922	+	24.3631i	0.641140	+	1.10061i
$491$	−18.7875	+	10.8469i	−0.847867	+	0.489516i	−0.859930	−	0.510411i	$-0.829493\pi$
$491$	−18.7875	+	10.8469i	−0.847867	+	0.489516i	0.0120639	+	0.999927i	$0.496160\pi$
$492$	6.94773	−	3.54005i	0.313228	−	0.159598i
$493$	−2.47547	−	0.950242i	−0.111489	−	0.0427968i
$494$	−0.106613	+	0.0774591i	−0.00479676	+	0.00348505i
$495$	−0.329510	−	1.21095i	−0.0148104	−	0.0544283i
$496$	2.86500	−	4.77407i	0.128642	−	0.214362i
$497$	4.49610	−	4.49610i	0.201678	−	0.201678i
$498$	−0.654477	−	0.103659i	−0.0293278	−	0.00464507i
$499$	12.7536	−	5.67829i	0.570931	−	0.254195i	−0.100903	−	0.994896i	$-0.532173\pi$
$499$	12.7536	−	5.67829i	0.570931	−	0.254195i	0.671835	+	0.740701i	$0.265507\pi$
$500$	5.19127	+	9.90206i	0.232161	+	0.442833i
$501$	11.4819	+	19.8872i	0.512973	+	0.888495i
$502$	−23.8057	+	6.37872i	−1.06250	+	0.284696i
$503$	0.864938	−	16.5040i	0.0385657	−	0.735877i	−0.909093	−	0.416593i	$-0.863224\pi$
$503$	0.864938	−	16.5040i	0.0385657	−	0.735877i	0.947659	−	0.319284i	$-0.103443\pi$
$504$	−4.21151	+	1.36840i	−0.187596	+	0.0609535i
$505$	−2.97581	−	1.50175i	−0.132422	−	0.0668269i
$506$	−0.443192	−	0.197322i	−0.0197023	−	0.00877203i
$507$	−10.8927	−	7.07383i	−0.483764	−	0.314160i
$508$	15.0072	+	12.1526i	0.665835	+	0.539183i
$509$	2.41764	−	23.0023i	0.107160	−	1.01956i	−0.800351	−	0.599532i	$-0.795353\pi$
$509$	2.41764	−	23.0023i	0.107160	−	1.01956i	0.907511	−	0.420029i	$-0.137980\pi$
$510$	8.58528	+	7.67017i	0.380162	+	0.339641i
$511$	22.0275	−	30.3183i	0.974439	−	1.34120i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	1.01358	−	0.658230i	0.0447509	−	0.0290616i
$514$	28.2440	+	2.96857i	1.24579	+	0.130938i
$515$	−30.3601	−	13.3764i	−1.33782	−	0.589435i
$516$	0.936076	−	0.198969i	0.0412085	−	0.00875913i
$517$	−1.59817	−	4.16338i	−0.0702875	−	0.183105i
$518$	0.902308	+	17.2171i	0.0396452	+	0.756475i
$519$	3.76574	+	11.5898i	0.165298	+	0.508734i
$520$	−0.132001	+	0.204998i	−0.00578861	+	0.00898977i
$521$	−15.0985	+	26.1513i	−0.661476	+	1.14571i	0.318751	+	0.947838i	$0.396737\pi$
$521$	−15.0985	+	26.1513i	−0.661476	+	1.14571i	−0.980228	+	0.197872i	$0.936597\pi$
$522$	−0.133295	+	0.497465i	−0.00583418	+	0.0217735i
$523$	16.0436	+	31.4874i	0.701539	+	1.37685i	0.916424	+	0.400209i	$0.131062\pi$
$523$	16.0436	+	31.4874i	0.701539	+	1.37685i	−0.214885	+	0.976639i	$0.568938\pi$
$524$	−3.69947	−	8.30915i	−0.161612	−	0.362987i
$525$	−20.2962	−	8.84857i	−0.885800	−	0.386183i
$526$		−	6.77041i		−	0.295204i
$527$	22.5795	−	17.6609i	0.983577	−	0.769320i
$528$	0.396860	+	0.396860i	0.0172711	+	0.0172711i
$529$	−13.0799	−	18.0029i	−0.568691	−	0.782736i
$530$	2.12266	−	1.73256i	0.0922025	−	0.0752577i
$531$	1.62571	−	5.00341i	0.0705497	−	0.217130i
$532$	5.16945	+	1.38515i	0.224124	+	0.0600539i
$533$	0.220061	+	0.821280i	0.00953191	+	0.0355736i
$534$	−3.92250	+	3.53183i	−0.169743	+	0.152837i
$535$	−7.92618	+	38.0137i	−0.342678	+	1.64348i
$536$	7.13458	−	7.92375i	0.308167	−	0.342254i
$537$	−0.249455	+	0.0957567i	−0.0107648	+	0.00413221i
$538$	−3.34978	+	5.15821i	−0.144419	+	0.222386i
$539$	0.739743	+	7.03818i	0.0318630	+	0.303156i
$540$	1.30731	−	1.81410i	0.0562575	−	0.0780664i
$541$	9.74192	+	2.07071i	0.418838	+	0.0890267i	0.412510	−	0.910953i	$-0.364652\pi$
$541$	9.74192	+	2.07071i	0.418838	+	0.0890267i	0.00632815	+	0.999980i	$0.497986\pi$
$542$	2.62854	+	16.5959i	0.112905	+	0.712856i
$543$	−2.45026	−	15.4704i	−0.105151	−	0.663897i
$544$	−5.03605	−	1.07045i	−0.215919	−	0.0458950i
$545$	6.59826	+	40.6396i	0.282639	+	1.74081i
$546$	−0.0504721	−	0.480210i	−0.00216001	−	0.0205511i
$547$	6.14375	−	9.46055i	0.262688	−	0.404504i	−0.682574	−	0.730816i	$-0.739140\pi$
$547$	6.14375	−	9.46055i	0.262688	−	0.404504i	0.945262	+	0.326313i	$0.105806\pi$
$548$	−7.34534	+	2.81961i	−0.313777	+	0.120448i
$549$	3.52242	−	3.91205i	0.150333	−	0.166962i
$550$	0.168588	+	2.80116i	0.00718861	+	0.119442i
$551$	0.462553	−	0.416484i	0.0197054	−	0.0177428i
$552$	−0.223720	−	0.834935i	−0.00952217	−	0.0355372i
$553$	40.9868	+	10.9824i	1.74294	+	0.467019i
$554$	6.53178	−	20.1028i	0.277509	−	0.854084i
$555$	−5.50491	−	6.74438i	−0.233671	−	0.286283i
$556$	−7.95830	−	10.9537i	−0.337507	−	0.464538i
$557$	12.6596	+	12.6596i	0.536403	+	0.536403i	0.922471	−	0.386067i	$-0.126167\pi$
$557$	12.6596	+	12.6596i	0.536403	+	0.536403i	−0.386067	+	0.922471i	$0.626167\pi$
$558$	−3.86988	−	4.00300i	−0.163825	−	0.169461i
$559$			0.104350i			0.00441353i
$560$	9.84353	−	1.07319i	0.415965	−	0.0453506i
$561$	1.17531	+	2.63979i	0.0496216	+	0.111452i
$562$	−8.24891	−	16.1894i	−0.347959	−	0.682909i
$563$	−6.97328	+	26.0246i	−0.293889	+	1.09681i	0.648207	+	0.761464i	$0.275519\pi$
$563$	−6.97328	+	26.0246i	−0.293889	+	1.09681i	−0.942096	+	0.335344i	$0.891147\pi$
$564$	3.97293	−	6.88132i	0.167291	−	0.289756i
$565$	−17.1558	+	3.71613i	−0.721748	+	0.156339i
$566$	1.90149	+	5.85217i	0.0799254	+	0.245985i
$567$	0.231757	+	4.42218i	0.00973286	+	0.185714i
$568$	−0.514575	−	1.34051i	−0.0215911	−	0.0562467i
$569$	−20.4314	+	4.34284i	−0.856530	+	0.182061i	−0.615189	−	0.788379i	$-0.710920\pi$
$569$	−20.4314	+	4.34284i	−0.856530	+	0.182061i	−0.241341	+	0.970440i	$0.577587\pi$
$570$	−2.51916	+	0.978235i	−0.105516	+	0.0409738i
$571$	−18.6812	−	1.96347i	−0.781783	−	0.0821687i	−0.294776	−	0.955566i	$-0.595245\pi$
$571$	−18.6812	−	1.96347i	−0.781783	−	0.0821687i	−0.487008	+	0.873398i	$0.661912\pi$
$572$	−0.0513251	+	0.0333309i	−0.00214601	+	0.00139363i
$573$	22.5373	−	3.56956i	0.941511	−	0.149121i
$574$	20.2961	−	27.9352i	0.847143	−	1.16599i
$575$	1.93221	−	3.86598i	0.0805786	−	0.161222i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−6.96938	−	5.64370i	−0.290139	−	0.234950i	0.473189	−	0.880961i	$-0.343103\pi$
$577$	−6.96938	−	5.64370i	−0.290139	−	0.234950i	−0.763328	+	0.646011i	$0.776436\pi$
$578$	−7.97382	−	5.17826i	−0.331667	−	0.215387i
$579$	−9.18991	−	4.09161i	−0.381920	−	0.170042i
$580$	0.518837	−	1.02811i	0.0215435	−	0.0426899i
$581$	−2.79070	+	0.906752i	−0.115778	+	0.0376184i
$582$	−0.0517243	+	0.986958i	−0.00214404	+	0.0409107i
$583$	0.664291	−	0.177996i	0.0275121	−	0.00737185i
$584$	−4.23141	−	7.32901i	−0.175097	−	0.303277i
$585$	0.163849	+	0.180560i	0.00677432	+	0.00746524i
$586$	2.93026	−	1.30463i	0.121048	−	0.0538939i
$587$	28.3048	+	4.48304i	1.16826	+	0.185035i	0.710275	−	0.703924i	$-0.248570\pi$
$587$	28.3048	+	4.48304i	1.16826	+	0.185035i	0.457988	+	0.888959i	$0.348570\pi$
$588$	−8.91617	+	8.91617i	−0.367697	+	0.367697i
$589$	1.28756	+	6.60465i	0.0530529	+	0.272140i
$590$	−5.84233	+	10.2104i	−0.240525	+	0.420356i
$591$	8.04797	−	5.84720i	0.331049	−	0.240521i
$592$	3.63475	+	1.39525i	0.149387	+	0.0573444i
$593$	1.01214	−	0.515709i	0.0415634	−	0.0211776i	−0.433085	−	0.901353i	$-0.642575\pi$
$593$	1.01214	−	0.515709i	0.0415634	−	0.0211776i	0.474649	+	0.880175i	$0.342575\pi$
$594$	0.486053	−	0.280623i	0.0199430	−	0.0115141i
$595$	49.2940	+	13.0037i	2.02086	+	0.533100i
$596$	11.0010	+	12.2179i	0.450619	+	0.500463i
$597$	10.1145	+	5.15357i	0.413957	+	0.210922i
$598$	0.0941236	−	0.00493281i	0.00384900	−	0.000201718i
$599$	9.24900	−	20.7736i	0.377904	−	0.848786i	−0.620032	−	0.784576i	$-0.712881\pi$
$599$	9.24900	−	20.7736i	0.377904	−	0.848786i	0.997936	−	0.0642100i	$-0.0204527\pi$
$600$	−3.68967	+	3.37436i	−0.150630	+	0.137758i
$601$	−7.97035	+	0.837717i	−0.325117	+	0.0341712i	−0.265681	−	0.964061i	$-0.585597\pi$
$601$	−7.97035	+	0.837717i	−0.325117	+	0.0341712i	−0.0594360	+	0.998232i	$0.518930\pi$
$602$	3.29337	−	2.66692i	0.134228	−	0.108696i
$603$	−5.80719	−	8.94229i	−0.236487	−	0.364158i
$604$	17.2574	+	12.5382i	0.702193	+	0.510173i
$605$	8.47574	−	22.3385i	0.344588	−	0.908189i
$606$	0.309930	−	1.45811i	0.0125901	−	0.0592316i
$607$	−8.60313	−	10.6240i	−0.349190	−	0.431214i	0.572044	−	0.820223i	$-0.306151\pi$
$607$	−8.60313	−	10.6240i	−0.349190	−	0.431214i	−0.921234	+	0.389009i	$0.872817\pi$
$608$	0.760572	−	0.939229i	0.0308453	−	0.0380907i
$609$	0.474165	+	2.23077i	0.0192142	+	0.0903955i
$610$	−9.49610	+	6.95572i	−0.384486	+	0.281629i
$611$	0.643873	+	0.579746i	0.0260483	+	0.0234540i
$612$	−2.33740	+	4.58740i	−0.0944837	+	0.185435i
$613$	−10.7226	−	0.561947i	−0.433082	−	0.0226968i	−0.165450	−	0.986218i	$-0.552908\pi$
$613$	−10.7226	−	0.561947i	−0.433082	−	0.0226968i	−0.267632	+	0.963521i	$0.586241\pi$
$614$	−25.8752	−	14.9391i	−1.04424	−	0.602892i
$615$	0.0675878	+	17.4359i	0.00272540	+	0.703083i
$616$	2.36369	+	0.768010i	0.0952359	+	0.0309440i
$617$	9.64364	−	25.1225i	0.388238	−	1.01140i	−0.590637	−	0.806937i	$-0.701123\pi$
$617$	9.64364	−	25.1225i	0.388238	−	1.01140i	0.978875	−	0.204458i	$-0.0655432\pi$
$618$	2.32100	−	14.6542i	0.0933642	−	0.589478i
$619$	37.5291			1.50842			0.754212	−	0.656631i	$-0.228019\pi$
$619$	37.5291			1.50842			0.754212	+	0.656631i	$0.228019\pi$
$620$	6.64407	+	10.5288i	0.266832	+	0.422848i
$621$	−0.864389			−0.0346867
$622$	3.10849	−	19.6262i	0.124639	−	0.786941i
$623$	−8.37626	+	21.8209i	−0.335588	+	0.874236i
$624$	−0.103703	−	0.0336952i	−0.00415144	−	0.00134889i
$625$	−24.9970	+	0.387618i	−0.999880	+	0.0155047i
$626$	−14.3729	−	8.29822i	−0.574458	−	0.331664i
$627$	−0.677370	−	0.0354995i	−0.0270516	−	0.00141771i
$628$	−4.88964	+	9.59646i	−0.195118	+	0.382940i
$629$	14.8964	+	13.4128i	0.593960	+	0.534804i
$630$	1.51107	−	9.78588i	0.0602025	−	0.389879i
$631$	−7.14961	−	33.6363i	−0.284622	−	1.33904i	−0.855414	−	0.517945i	$-0.826697\pi$
$631$	−7.14961	−	33.6363i	−0.284622	−	1.33904i	0.570793	−	0.821094i	$-0.306636\pi$
$632$	6.03033	−	7.44683i	0.239873	−	0.296219i
$633$	1.89970	+	2.34594i	0.0755063	+	0.0932426i
$634$	−5.25402	+	24.7182i	−0.208664	+	0.981687i
$635$	−39.3784	+	17.7156i	−1.56268	+	0.703022i
$636$	0.991332	+	0.720245i	0.0393089	+	0.0285596i
$637$	−0.748837	−	1.15311i	−0.0296700	−	0.0456878i
$638$	0.224634	−	0.181905i	0.00889333	−	0.00720167i
$639$	−1.42802	+	0.150091i	−0.0564915	+	0.00593750i
$640$	0.682734	−	2.12929i	0.0269874	−	0.0841676i
$641$	9.12371	−	20.4922i	0.360365	−	0.809393i	−0.638833	−	0.769345i	$-0.720583\pi$
$641$	9.12371	−	20.4922i	0.360365	−	0.809393i	0.999198	−	0.0400472i	$-0.0127508\pi$
$642$	−17.3421	+	0.908859i	−0.684437	+	0.0358698i
$643$	22.3280	+	11.3767i	0.880531	+	0.448653i	0.834962	−	0.550308i	$-0.185490\pi$
$643$	22.3280	+	11.3767i	0.880531	+	0.448653i	0.0455694	+	0.998961i	$0.485490\pi$
$644$	−2.56125	−	2.84456i	−0.100927	−	0.112091i
$645$	−0.545828	+	2.06911i	−0.0214920	+	0.0814710i
$646$	5.38872	−	3.11118i	0.212016	−	0.122408i
$647$	−18.3128	+	9.33083i	−0.719950	+	0.366833i	−0.775265	−	0.631636i	$-0.782384\pi$
$647$	−18.3128	+	9.33083i	−0.719950	+	0.366833i	0.0553152	+	0.998469i	$0.482384\pi$
$648$	0.933580	+	0.358368i	0.0366745	+	0.0140780i
$649$	−2.38875	+	1.73553i	−0.0937666	+	0.0681254i
$650$	−0.276252	−	0.470029i	−0.0108355	−	0.0184360i
$651$	−23.3166	−	8.01429i	−0.913848	−	0.314105i
$652$	8.02919	−	8.02919i	0.314447	−	0.314447i
$653$	−23.1798	−	3.67132i	−0.907097	−	0.143670i	−0.314583	−	0.949230i	$-0.601865\pi$
$653$	−23.1798	−	3.67132i	−0.907097	−	0.143670i	−0.592514	+	0.805560i	$0.701865\pi$
$654$	−16.8207	+	7.48907i	−0.657742	+	0.292846i
$655$	20.3143	+	0.985680i	0.793744	+	0.0385137i
$656$	−3.89881	−	6.75294i	−0.152223	−	0.263658i
$657$	−8.17445	+	2.19034i	−0.318916	+	0.0854532i
$658$	1.84151	−	35.1380i	0.0717894	−	1.36982i
$659$	11.5240	−	3.74437i	0.448911	−	0.145860i	−0.0758323	−	0.997121i	$-0.524161\pi$
$659$	11.5240	−	3.74437i	0.448911	−	0.145860i	0.524743	+	0.851261i	$0.324161\pi$
$660$	−1.19205	+	0.392435i	−0.0464004	+	0.0152755i
$661$	−27.4469	−	12.2201i	−1.06756	−	0.475308i	−0.203696	−	0.979034i	$-0.565295\pi$
$661$	−27.4469	−	12.2201i	−1.06756	−	0.475308i	−0.863863	+	0.503726i	$0.831962\pi$
$662$	−19.0558	−	12.3750i	−0.740627	−	0.480969i
$663$	−0.436289	−	0.353299i	−0.0169440	−	0.0137210i
$664$	−0.0692642	+	0.659005i	−0.00268797	+	0.0255744i
$665$	−7.97296	+	8.92419i	−0.309178	+	0.346065i
$666$	2.28845	−	3.14978i	0.0886757	−	0.122052i
$667$	−0.439692	+	0.0696403i	−0.0170249	+	0.00269648i
$668$	19.2590	−	12.5070i	0.745155	−	0.483909i
$669$	17.7702	+	1.86772i	0.687035	+	0.0722103i
$670$	8.63042	+	22.2251i	0.333422	+	0.858632i
$671$	−2.88993	+	0.614275i	−0.111565	+	0.0237138i
$672$	1.58694	+	4.13412i	0.0612176	+	0.159477i
$673$	−0.117114	−	2.23467i	−0.00451442	−	0.0861403i	0.995443	−	0.0953574i	$-0.0303994\pi$
$673$	−0.117114	−	2.23467i	−0.00451442	−	0.0861403i	−0.999958	+	0.00921709i	$0.997066\pi$
$674$	−1.98755	−	6.11706i	−0.0765577	−	0.235620i
$675$	2.30442	+	4.43730i	0.0886973	+	0.170792i
$676$	−6.49406	+	11.2480i	−0.249771	+	0.432617i
$677$	2.00200	−	7.47155i	0.0769429	−	0.287155i	−0.916724	−	0.399521i	$-0.869176\pi$
$677$	2.00200	−	7.47155i	0.0769429	−	0.287155i	0.993667	+	0.112366i	$0.0358430\pi$
$678$	−3.56393	−	6.99460i	−0.136872	−	0.268626i
$679$	1.78008	+	3.99812i	0.0683132	+	0.153434i
$680$	7.21034	−	8.97494i	0.276504	−	0.344173i
$681$			13.6331i			0.522423i
$682$	0.436590	+	3.09423i	0.0167179	+	0.118484i
$683$	−21.1480	−	21.1480i	−0.809207	−	0.809207i	0.175307	−	0.984514i	$-0.443908\pi$
$683$	−21.1480	−	21.1480i	−0.809207	−	0.809207i	−0.984514	+	0.175307i	$0.943908\pi$
$684$	−0.710375	−	0.977747i	−0.0271618	−	0.0373851i
$685$	1.77115	−	17.5038i	0.0676723	−	0.668787i
$686$	−7.67588	+	23.6239i	−0.293066	+	0.901966i
$687$	0.603536	+	0.161717i	0.0230263	+	0.00616989i
$688$	−0.247687	−	0.924380i	−0.00944297	−	0.0352417i
$689$	−0.0992934	+	0.0894042i	−0.00378278	+	0.00340603i
$690$	1.89214	+	0.394527i	0.0720325	+	0.0150194i
$691$	−27.4448	+	30.4805i	−1.04405	+	1.15953i	−0.0571215	+	0.998367i	$0.518192\pi$
$691$	−27.4448	+	30.4805i	−1.04405	+	1.15953i	−0.986927	+	0.161166i	$0.948474\pi$
$692$	11.3768	−	4.36714i	0.432481	−	0.166014i
$693$	1.35361	−	2.08438i	0.0514194	−	0.0791789i
$694$	−0.252804	−	2.40526i	−0.00959629	−	0.0913026i
$695$	29.8838	−	4.85195i	1.13356	−	0.184045i
$696$	0.503760	+	0.107077i	0.0190950	+	0.00405876i
$697$	−6.28030	−	39.6523i	−0.237883	−	1.50194i
$698$	0.670797	+	4.23525i	0.0253900	+	0.160306i
$699$	−14.8406	−	3.15446i	−0.561321	−	0.119313i
$700$	−7.77422	+	20.7315i	−0.293838	+	0.783578i
$701$	−5.17162	−	49.2046i	−0.195329	−	1.85843i	−0.452108	−	0.891963i	$-0.649328\pi$
$701$	−5.17162	−	49.2046i	−0.195329	−	1.85843i	0.256779	−	0.966470i	$-0.417339\pi$
$702$	−0.0593874	+	0.0914485i	−0.00224143	+	0.00345150i
$703$	−4.39282	+	1.68625i	−0.165678	+	0.0635980i
$704$	0.375546	−	0.417087i	0.0141539	−	0.0157195i
$705$	9.73456	+	14.8635i	0.366625	+	0.559790i
$706$	13.7730	−	12.4012i	0.518353	−	0.466727i
$707$	−1.70849	−	6.37618i	−0.0642545	−	0.239801i
$708$	−5.08164	−	1.36162i	−0.190980	−	0.0511728i
$709$	11.8917	−	36.5990i	0.446603	−	1.37450i	−0.434113	−	0.900859i	$-0.642938\pi$
$709$	11.8917	−	36.5990i	0.446603	−	1.37450i	0.880716	−	0.473645i	$-0.157062\pi$
$710$	3.19442	+	0.323233i	0.119885	+	0.0121307i
$711$	−5.63232	−	7.75223i	−0.211229	−	0.290731i
$712$	3.73228	+	3.73228i	0.139873	+	0.139873i
$713$	1.80044	−	4.46325i	0.0674269	−	0.167150i
$714$			22.7991i			0.853235i
$715$	−0.0148314	−	0.136037i	−0.000554664	−	0.00508750i
$716$	0.108681	+	0.244101i	0.00406160	+	0.00912250i
$717$	2.89249	+	5.67682i	0.108022	+	0.212005i
$718$	−1.59114	+	5.93820i	−0.0593807	+	0.221612i
$719$	21.4437	−	37.1416i	0.799716	−	1.38515i	−0.120085	−	0.992764i	$-0.538317\pi$
$719$	21.4437	−	37.1416i	0.799716	−	1.38515i	0.919801	−	0.392385i	$-0.128350\pi$
$720$	−1.88003	−	1.21057i	−0.0700646	−	0.0451153i
$721$	−20.3028	−	62.4856i	−0.756116	−	2.32709i
$722$	−0.917940	−	17.5153i	−0.0341622	−	0.651854i
$723$	7.24292	+	18.8684i	0.269367	+	0.701725i
$724$	−15.3209	+	3.25656i	−0.569397	+	0.121029i
$725$	1.52969	+	2.07148i	0.0568114	+	0.0769328i
$726$	10.6265	+	1.11689i	0.394385	+	0.0414516i
$727$	24.2023	−	15.7171i	0.897612	−	0.582916i	−0.0112850	−	0.999936i	$-0.503592\pi$
$727$	24.2023	−	15.7171i	0.897612	−	0.582916i	0.908897	+	0.417020i	$0.136926\pi$
$728$	−0.476911	+	0.0755352i	−0.0176755	+	0.00279952i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	18.8935	−	1.06362i	0.699280	−	0.0393664i
$731$	0.515024	−	4.90012i	0.0190488	−	0.181238i
$732$	−4.09104	−	3.31286i	−0.151209	−	0.122447i
$733$	−34.7377	−	22.5589i	−1.28307	−	0.833233i	−0.290731	−	0.956805i	$-0.593899\pi$
$733$	−34.7377	−	22.5589i	−1.28307	−	0.833233i	−0.992336	+	0.123571i	$0.960565\pi$
$734$	−20.0732	−	8.93716i	−0.740915	−	0.329877i
$735$	−8.81674	−	26.7815i	−0.325210	−	0.987849i
$736$	−0.822082	+	0.267111i	−0.0303024	+	0.00984583i
$737$	−0.313192	+	5.97606i	−0.0115366	+	0.220131i
$738$	−7.53193	+	2.01817i	−0.277254	+	0.0742900i
$739$	−11.5689	−	20.0379i	−0.425568	−	0.737105i	0.570906	−	0.821016i	$-0.306592\pi$
$739$	−11.5689	−	20.0379i	−0.425568	−	0.737105i	−0.996473	+	0.0839109i	$0.973259\pi$
$740$	−6.44703	+	5.85034i	−0.236998	+	0.215063i
$741$	0.120388	−	0.0536003i	0.00442257	−	0.00196906i
$742$	5.35937	+	0.848840i	0.196748	+	0.0311619i
$743$	34.9918	−	34.9918i	1.28372	−	1.28372i	0.345192	−	0.938532i	$-0.387814\pi$
$743$	34.9918	−	34.9918i	1.28372	−	1.28372i	0.938532	−	0.345192i	$-0.112186\pi$
$744$	−3.79498	+	4.07408i	−0.139131	+	0.149363i
$745$	−35.4728	+	9.65245i	−1.29962	+	0.353638i
$746$	−5.07740	+	3.68895i	−0.185897	+	0.135062i
$747$	0.618623	+	0.237467i	0.0226342	+	0.00868847i
$748$	2.57466	−	1.31185i	0.0941388	−	0.0479661i
$749$	−66.5976	+	38.4502i	−2.43342	+	1.40494i
$750$	−3.01907	−	10.7650i	−0.110241	−	0.393082i
$751$	22.7913	+	25.3123i	0.831665	+	0.923658i	0.998051	−	0.0624027i	$-0.0198763\pi$
$751$	22.7913	+	25.3123i	0.831665	+	0.923658i	−0.166386	+	0.986061i	$0.553210\pi$
$752$	−7.07982	−	3.60735i	−0.258174	−	0.131546i
$753$	24.6117	−	1.28984i	0.896900	−	0.0470045i
$754$	−0.0228411	+	0.0513020i	−0.000831825	+	0.00186831i
$755$	−42.4152	+	21.8191i	−1.54365	+	0.794080i
$756$	4.40399	−	0.462878i	0.160172	−	0.0168347i
$757$	9.60867	−	7.78095i	0.349233	−	0.282803i	−0.438612	−	0.898676i	$-0.644530\pi$
$757$	9.60867	−	7.78095i	0.349233	−	0.282803i	0.787845	+	0.615873i	$0.211197\pi$
$758$	12.4126	+	19.1137i	0.450845	+	0.694240i
$759$	0.392482	+	0.285155i	0.0142462	+	0.0103505i
$760$	1.10874	+	2.46451i	0.0402181	+	0.0893971i
$761$	−6.01818	+	28.3133i	−0.218159	+	1.02636i	0.723640	+	0.690178i	$0.242468\pi$
$761$	−6.01818	+	28.3133i	−0.218159	+	1.02636i	−0.941798	+	0.336178i	$0.890865\pi$
$762$	−12.1526	−	15.0072i	−0.440241	−	0.543652i
$763$	−51.3119	+	63.3649i	−1.85762	+	2.29396i
$764$	−4.74418	−	22.3196i	−0.171639	−	0.807496i
$765$	−6.80295	−	9.28754i	−0.245961	−	0.335792i
$766$	26.5039	+	23.8642i	0.957625	+	0.862249i
$767$	0.260431	−	0.511124i	0.00940360	−	0.0184556i
$768$	0.998630	+	0.0523360i	0.0360349	+	0.00188851i
$769$	−22.1524	−	12.7897i	−0.798835	−	0.461208i	0.0442287	−	0.999021i	$-0.485917\pi$
$769$	−22.1524	−	12.7897i	−0.798835	−	0.461208i	−0.843064	+	0.537814i	$0.819250\pi$
$770$	−3.91439	+	3.94486i	−0.141065	+	0.142163i
$771$	−27.0096	−	8.77596i	−0.972728	−	0.316059i
$772$	−3.60504	+	9.39146i	−0.129748	+	0.338006i
$773$	3.84757	−	24.2926i	0.138387	−	0.873744i	−0.816623	−	0.577172i	$-0.804156\pi$
$773$	3.84757	−	24.2926i	0.138387	−	0.873744i	0.955010	−	0.296572i	$-0.0958436\pi$
$774$	−0.956989			−0.0343982
$775$	−27.7118	+	2.65638i	−0.995437	+	0.0954199i
$776$	0.988312			0.0354783
$777$	2.69704	−	17.0284i	0.0967558	−	0.610892i
$778$	−4.89448	+	12.7505i	−0.175476	+	0.457129i
$779$	8.96267	+	2.91215i	0.321121	+	0.104339i
$780$	0.171738	−	0.173074i	0.00614919	−	0.00619705i
$781$	0.697915	+	0.402942i	0.0249734	+	0.0144184i
$782$	−4.44426	−	0.232914i	−0.158926	−	0.00832898i
$783$	0.233812	−	0.458881i	0.00835574	−	0.0163991i
$784$	9.37059	+	8.43732i	0.334664	+	0.301333i
$785$	−14.2312	−	19.4287i	−0.507933	−	0.693442i
$786$	1.89106	+	8.89674i	0.0674519	+	0.317336i
$787$	−20.0797	+	24.7964i	−0.715765	+	0.883896i	−0.997130	−	0.0757048i	$-0.975879\pi$
$787$	−20.0797	+	24.7964i	−0.715765	+	0.883896i	0.281366	+	0.959601i	$0.409213\pi$
$788$	−6.26038	−	7.73093i	−0.223017	−	0.275403i
$789$	−1.40765	+	6.62246i	−0.0501136	+	0.235766i
$790$	8.79081	+	19.5403i	0.312763	+	0.695212i
$791$	−28.1236	−	20.4330i	−0.999961	−	0.726514i
$792$	−0.305676	−	0.470700i	−0.0108617	−	0.0167256i
$793$	0.446086	−	0.361233i	0.0158410	−	0.0128278i
$794$	−24.1825	+	2.54169i	−0.858206	+	0.0902011i
$795$	−2.43650	+	1.25338i	−0.0864136	+	0.0444527i
$796$	4.61716	−	10.3703i	0.163651	−	0.367566i
$797$	50.7843	−	2.66149i	1.79887	−	0.0942749i	0.876696	−	0.481045i	$-0.159742\pi$
$797$	50.7843	−	2.66149i	1.79887	−	0.0942749i	0.922176	+	0.386770i	$0.126409\pi$
$798$	−4.76850	−	2.42967i	−0.168803	−	0.0860094i
$799$	−27.3740	−	30.4019i	−0.968422	−	1.07554i
$800$	3.56284	+	3.50802i	0.125965	+	0.124027i
$801$	4.57109	−	2.63912i	0.161512	−	0.0932487i
$802$	−21.0451	+	10.7230i	−0.743128	+	0.378643i
$803$	4.43424	+	1.70215i	0.156481	+	0.0600674i
$804$	−8.62611	+	6.26724i	−0.304220	+	0.221028i
$805$	8.25876	−	2.24728i	0.291083	−	0.0792061i
$806$	−0.348495	−	0.497124i	−0.0122752	−	0.0175104i
$807$	4.34903	−	4.34903i	0.153093	−	0.153093i
$808$	−1.47233	−	0.233194i	−0.0517964	−	0.00820374i
$809$	5.56803	−	2.47905i	0.195762	−	0.0871587i	−0.306514	−	0.951866i	$-0.599163\pi$
$809$	5.56803	−	2.47905i	0.195762	−	0.0871587i	0.502276	+	0.864707i	$0.332496\pi$
$810$	−1.65591	+	1.50265i	−0.0581827	+	0.0527978i
$811$	−3.05924	−	5.29875i	−0.107424	−	0.186064i	0.807302	−	0.590139i	$-0.200927\pi$
$811$	−3.05924	−	5.29875i	−0.107424	−	0.186064i	−0.914726	+	0.404074i	$0.867594\pi$
$812$	2.20290	−	0.590265i	0.0773066	−	0.0207143i
$813$	0.879391	−	16.7798i	0.0308416	−	0.588492i
$814$	−2.07818	+	0.675240i	−0.0728400	+	0.0236672i
$815$	7.93965	+	24.1172i	0.278114	+	0.844790i
$816$	4.70345	+	2.09411i	0.164654	+	0.0733085i
$817$	0.969989	+	0.629918i	0.0339356	+	0.0220381i
$818$	31.3472	+	25.3844i	1.09603	+	0.887546i
$819$	−0.0504721	+	0.480210i	−0.00176364	+	0.0167799i
$820$	17.4085	−	0.980019i	0.607930	−	0.0342237i
$821$	21.8016	−	30.0073i	0.760881	−	1.04726i	−0.236260	−	0.971690i	$-0.575922\pi$
$821$	21.8016	−	30.0073i	0.760881	−	1.04726i	0.997140	−	0.0755724i	$-0.0240784\pi$
$822$	7.77106	−	1.23081i	0.271047	−	0.0429296i
$823$	−36.1419	+	23.4708i	−1.25983	+	0.818141i	−0.989487	−	0.144624i	$-0.953803\pi$
$823$	−36.1419	+	23.4708i	−1.25983	+	0.818141i	−0.270340	+	0.962765i	$0.587136\pi$
$824$	−14.7556	−	1.55087i	−0.514035	−	0.0540273i
$825$	0.417490	−	2.77500i	0.0145351	−	0.0966130i
$826$	−22.7875	+	4.84363i	−0.792878	+	0.168531i
$827$	−19.4383	−	50.6385i	−0.675936	−	1.76087i	−0.648457	−	0.761251i	$-0.724586\pi$
$827$	−19.4383	−	50.6385i	−0.675936	−	1.76087i	−0.0274785	−	0.999622i	$-0.508748\pi$
$828$	0.0452386	+	0.863204i	0.00157215	+	0.0299984i
$829$	2.72848	+	8.39738i	0.0947639	+	0.291653i	0.987192	−	0.159536i	$-0.0509999\pi$
$829$	2.72848	+	8.39738i	0.0947639	+	0.291653i	−0.892428	+	0.451189i	$0.851000\pi$
$830$	−1.24577	−	0.802167i	−0.0432415	−	0.0278436i
$831$	−10.5686	+	18.3054i	−0.366622	+	0.635008i
$832$	−0.0282216	+	0.105324i	−0.000978408	+	0.00365147i
$833$	29.4731	+	57.8442i	1.02118	+	2.00418i
$834$	5.50700	+	12.3689i	0.190692	+	0.428300i
$835$	5.56530	+	51.0461i	0.192595	+	1.76652i
$836$			0.678300i			0.0234595i
$837$	2.95304	+	4.72012i	0.102072	+	0.163151i
$838$	0.0805717	+	0.0805717i	0.00278330	+	0.00278330i
$839$	−14.7776	−	20.3396i	−0.510178	−	0.702200i	0.473771	−	0.880648i	$-0.342892\pi$
$839$	−14.7776	−	20.3396i	−0.510178	−	0.702200i	−0.983949	+	0.178448i	$0.942892\pi$
$840$	−9.85156	−	0.996846i	−0.339911	−	0.0343945i
$841$	−8.87953	+	27.3284i	−0.306191	+	0.942358i
$842$	6.31149	+	1.69116i	0.217508	+	0.0582812i
$843$	4.70269	+	17.5507i	0.161969	+	0.604477i
$844$	2.24330	−	2.01987i	0.0772175	−	0.0695269i
$845$	−15.9119	−	24.2954i	−0.547385	−	0.835788i
$846$	−5.31682	+	5.90493i	−0.182796	+	0.203016i
$847$	44.1731	−	16.9565i	1.51781	−	0.582631i
$848$	0.667376	−	1.02767i	0.0229178	−	0.0352903i
$849$	−0.643199	−	6.11963i	−0.0220745	−	0.210025i
$850$	10.6525	+	23.4353i	0.365379	+	0.803826i
$851$	3.29182	+	0.699699i	0.112842	+	0.0239854i
$852$	0.224622	+	1.41821i	0.00769541	+	0.0485869i
$853$	0.229942	+	1.45179i	0.00787305	+	0.0497085i	0.991312	−	0.131531i	$-0.0419892\pi$
$853$	0.229942	+	1.45179i	0.00787305	+	0.0497085i	−0.983439	+	0.181239i	$0.941989\pi$
$854$	−22.8017	−	4.84665i	−0.780258	−	0.165849i
$855$	2.66750	−	0.433096i	0.0912264	−	0.0148116i
$856$	1.81523	+	17.2707i	0.0620432	+	0.590301i
$857$	−20.3959	+	31.4069i	−0.696709	+	1.07284i	0.296334	+	0.955085i	$0.404236\pi$
$857$	−20.3959	+	31.4069i	−0.696709	+	1.07284i	−0.993043	+	0.117754i	$0.962431\pi$
$858$	0.0571334	−	0.0219314i	0.00195050	−	0.000748727i
$859$	−17.6631	+	19.6169i	−0.602658	+	0.669320i	−0.964855	−	0.262782i	$-0.915360\pi$
$859$	−17.6631	+	19.6169i	−0.602658	+	0.669320i	0.362197	+	0.932102i	$0.382027\pi$
$860$	2.09484	+	0.436791i	0.0714334	+	0.0148945i
$861$	−25.6606	+	23.1049i	−0.874512	+	0.787414i
$862$	2.54392	+	9.49405i	0.0866463	+	0.323369i
$863$	5.27327	+	1.41297i	0.179504	+	0.0480980i	0.347451	−	0.937698i	$-0.387047\pi$
$863$	5.27327	+	1.41297i	0.179504	+	0.0480980i	−0.167947	+	0.985796i	$0.553714\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−2.74324	+	27.1107i	−0.0932730	+	0.921792i
$866$	21.7295	+	29.9081i	0.738398	+	1.01632i
$867$	6.72295	+	6.72295i	0.228323	+	0.228323i
$868$	−6.78301	+	23.7040i	−0.230230	+	0.804567i
$869$			5.37801i			0.182437i
$870$	−0.721255	+	0.897769i	−0.0244528	+	0.0304372i
$871$	−0.472886	−	1.06212i	−0.0160231	−	0.0359885i
$872$	8.35913	+	16.4057i	0.283076	+	0.555568i
$873$	0.255794	−	0.954636i	0.00865731	−	0.0323095i
$874$	0.522333	−	0.904708i	0.0176682	−	0.0306022i
$875$	−33.5538	−	36.4049i	−1.13433	−	1.23071i
$876$	2.61515	+	8.04861i	0.0883578	+	0.271937i
$877$	0.00685955	+	0.130888i	0.000231631	+	0.00441978i	0.998743	−	0.0501259i	$-0.0159623\pi$
$877$	0.00685955	+	0.130888i	0.000231631	+	0.00441978i	−0.998511	+	0.0545457i	$0.982629\pi$
$878$	−4.26083	−	11.0999i	−0.143796	−	0.374602i
$879$	−3.13747	+	0.666890i	−0.105824	+	0.0224936i
$880$	0.454284	+	1.16988i	0.0153139	+	0.0394365i
$881$	54.6033	+	5.73904i	1.83963	+	0.193353i	0.959564	−	0.281492i	$-0.0908292\pi$
$881$	54.6033	+	5.73904i	1.83963	+	0.193353i	0.880070	+	0.474845i	$0.157496\pi$
$882$	10.5751	−	6.86755i	0.356082	−	0.231243i
$883$	29.5196	−	4.67544i	0.993412	−	0.157341i	0.361493	−	0.932375i	$-0.382267\pi$
$883$	29.5196	−	4.67544i	0.993412	−	0.157341i	0.631920	+	0.775034i	$0.282267\pi$
$884$	−0.329982	+	0.454181i	−0.0110985	+	0.0152758i
$885$	7.83752	−	8.77260i	0.263455	−	0.294888i
$886$	1.27219	−	12.1040i	0.0427399	−	0.406643i
$887$	−32.9723	−	26.7004i	−1.10710	−	0.896513i	−0.111838	−	0.993726i	$-0.535674\pi$
$887$	−32.9723	−	26.7004i	−1.10710	−	0.896513i	−0.995264	+	0.0972131i	$0.969007\pi$
$888$	−3.26524	−	2.12047i	−0.109574	−	0.0711583i
$889$	−78.1193	−	34.7809i	−2.62004	−	1.16652i
$890$	−11.2106	+	3.69066i	−0.375781	+	0.123711i
$891$	−0.533776	+	0.173434i	−0.0178822	+	0.00581027i
$892$	0.935142	−	17.8436i	0.0313109	−	0.597447i
$893$	9.27585	−	2.48546i	0.310405	−	0.0831726i
$894$	−8.22038	−	14.2381i	−0.274931	−	0.476194i
$895$	−0.596780	−	0.0289567i	−0.0199482	−	0.000967916i
$896$	4.04540	−	1.80113i	0.135147	−	0.0601715i
$897$	−0.0930924	−	0.0147444i	−0.00310827	−	0.000492301i
$898$	−16.1524	+	16.1524i	−0.539012	+	0.539012i
$899$	1.88242	+	2.16308i	0.0627821	+	0.0721429i
$900$	4.31062	−	2.53349i	0.143687	−	0.0844498i
$901$	5.10394	−	3.70823i	0.170037	−	0.123539i
$902$	4.08570	+	1.56835i	0.136039	+	0.0522205i
$903$	−3.77589	+	1.92391i	−0.125654	+	0.0640238i
$904$	−6.79849	+	3.92511i	−0.226114	+	0.130547i
$905$	8.93366	−	33.8654i	0.296965	−	1.12573i
$906$	−14.2734	−	15.8523i	−0.474203	−	0.526656i
$907$	−10.3663	−	5.28190i	−0.344208	−	0.175382i	0.273337	−	0.961918i	$-0.411873\pi$
$907$	−10.3663	−	5.28190i	−0.344208	−	0.175382i	−0.617545	+	0.786536i	$0.711873\pi$
$908$	13.6145	−	0.713504i	0.451812	−	0.0236785i
$909$	−0.606315	+	1.36181i	−0.0201102	+	0.0451683i
$910$	0.329662	−	1.02814i	0.0109282	−	0.0340825i
$911$	−9.04636	+	0.950811i	−0.299719	+	0.0315018i	−0.253195	−	0.967415i	$-0.581481\pi$
$911$	−9.04636	+	0.950811i	−0.299719	+	0.0315018i	−0.0465247	+	0.998917i	$0.514815\pi$
$912$	−0.939229	+	0.760572i	−0.0311010	+	0.0251851i
$913$	−0.202552	−	0.311902i	−0.00670349	−	0.0103225i
$914$	−16.9611	−	12.3229i	−0.561022	−	0.407606i
$915$	10.7348	−	4.82937i	0.354880	−	0.159654i
$916$	0.129909	−	0.611173i	0.00429231	−	0.0201937i
$917$	25.3472	+	31.3012i	0.837039	+	1.03366i
$918$	3.24009	−	4.00118i	0.106939	−	0.132059i
$919$	−2.98086	−	14.0239i	−0.0983296	−	0.462604i	−0.999571	−	0.0292871i	$-0.990676\pi$
$919$	−2.98086	−	14.0239i	−0.0983296	−	0.462604i	0.901241	−	0.433317i	$-0.142657\pi$
$920$	0.294959	−	1.91019i	0.00972452	−	0.0629772i
$921$	22.2038	+	19.9924i	0.731640	+	0.658772i
$922$	−10.5820	+	20.7683i	−0.348498	+	0.683967i
$923$	−0.156354	−	0.00819417i	−0.00514645	−	0.000269714i
$924$	−2.15236	−	1.24267i	−0.0708075	−	0.0408807i
$925$	−5.18399	−	18.7638i	−0.170448	−	0.616950i
$926$	−8.21777	−	2.67012i	−0.270053	−	0.0877455i
$927$	−5.31706	+	13.8514i	−0.174635	+	0.454940i
$928$	0.0805660	−	0.508673i	0.00264471	−	0.0166980i
$929$	−12.3272			−0.404444			−0.202222	−	0.979340i	$-0.564816\pi$
$929$	−12.3272			−0.404444			−0.202222	+	0.979340i	$0.564816\pi$
$930$	−4.30981	−	11.6801i	−0.141324	−	0.383007i
$931$	−15.2392			−0.499445
$932$	−2.37344	+	14.9853i	−0.0777446	+	0.490860i
$933$	−7.12109	+	18.5511i	−0.233134	+	0.607335i
$934$	12.4471	+	4.04429i	0.407280	+	0.132333i
$935$	0.0250464	+	6.46131i	0.000819103	+	0.211307i
$936$	0.0944313	+	0.0545199i	0.00308658	+	0.00178204i
$937$	41.8201	+	2.19170i	1.36620	+	0.0715997i	0.721278	−	0.692645i	$-0.243555\pi$
$937$	41.8201	+	2.19170i	1.36620	+	0.0715997i	0.644926	+	0.764245i	$0.276888\pi$
$938$	−21.4356	+	42.0698i	−0.699898	+	1.37363i
$939$	12.3336	+	11.1052i	0.402490	+	0.362404i
$940$	14.3336	−	10.4991i	0.467511	−	0.342443i
$941$	1.65362	+	7.77965i	0.0539063	+	0.253609i	0.996847	−	0.0793526i	$-0.0252853\pi$
$941$	1.65362	+	7.77965i	0.0539063	+	0.253609i	−0.942940	+	0.332962i	$0.891952\pi$
$942$	6.77801	−	8.37014i	0.220839	−	0.272714i
$943$	−4.24173	−	5.23810i	−0.138130	−	0.170576i
$944$	−1.09380	+	5.14594i	−0.0356002	+	0.167486i
$945$	−3.51265	+	9.25787i	−0.114266	+	0.301159i
$946$	0.434527	+	0.315703i	0.0141277	+	0.0102644i
$947$	−8.31021	−	12.7966i	−0.270046	−	0.415834i	0.677467	−	0.735554i	$-0.263078\pi$
$947$	−8.31021	−	12.7966i	−0.270046	−	0.415834i	−0.947512	+	0.319720i	$0.896411\pi$
$948$	−7.44683	+	6.03033i	−0.241862	+	0.195856i
$949$	−0.917729	+	0.0964572i	−0.0297907	+	0.00313113i
$950$	−6.03680	−	0.269463i	−0.195860	−	0.00874254i
$951$	10.2784	−	23.0857i	0.333301	−	0.748605i
$952$	22.7679	−	1.19321i	0.737910	−	0.0386722i
$953$	32.6753	+	16.6489i	1.05846	+	0.539311i	0.894459	−	0.447150i	$-0.147561\pi$
$953$	32.6753	+	16.6489i	1.05846	+	0.539311i	0.163998	+	0.986461i	$0.447561\pi$
$954$	−0.819922	−	0.910616i	−0.0265460	−	0.0294823i
$955$	49.3354	+	13.0146i	1.59646	+	0.421144i
$956$	5.51766	−	3.18562i	0.178454	−	0.103030i
$957$	−0.257545	+	0.131226i	−0.00832524	+	0.00424192i
$958$	−23.4880	−	9.01619i	−0.758862	−	0.291300i
$959$	28.1871	−	20.4791i	0.910208	−	0.661305i
$960$	−1.11052	+	1.94081i	−0.0358419	+	0.0626394i
$961$	−30.5231	+	5.41644i	−0.984617	+	0.174724i
$962$	0.300188	−	0.300188i	0.00967845	−	0.00967845i
$963$	17.1521	+	2.71662i	0.552717	+	0.0875418i
$964$	18.4635	−	8.22049i	0.594670	−	0.264764i
$965$	−15.1161	−	16.6578i	−0.486604	−	0.536234i
$966$	1.91386	+	3.31491i	0.0615775	+	0.106655i
$967$	45.3171	−	12.1427i	1.45730	−	0.390483i	0.558744	−	0.829340i	$-0.311283\pi$
$967$	45.3171	−	12.1427i	1.45730	−	0.390483i	0.898557	+	0.438857i	$0.144617\pi$
$968$	0.559210	−	10.6704i	0.0179737	−	0.342958i
$969$	−5.91781	+	1.92281i	−0.190107	+	0.0617696i
$970$	−0.995648	+	1.97294i	−0.0319683	+	0.0633473i
$971$	47.1901	+	21.0104i	1.51440	+	0.674255i	0.984753	−	0.173961i	$-0.0556566\pi$
$971$	47.1901	+	21.0104i	1.51440	+	0.674255i	0.529650	+	0.848216i	$0.322323\pi$
$972$	−0.838671	−	0.544639i	−0.0269004	−	0.0174693i
$973$	46.5946	+	37.7316i	1.49376	+	1.20962i
$974$	2.47592	−	23.5568i	0.0793337	−	0.754809i
$975$	0.172491	+	0.517194i	0.00552412	+	0.0165635i
$976$	−3.09421	+	4.25881i	−0.0990432	+	0.136321i
$977$	16.8719	−	2.67224i	0.539779	−	0.0854926i	0.119409	−	0.992845i	$-0.461900\pi$
$977$	16.8719	−	2.67224i	0.539779	−	0.0854926i	0.420370	+	0.907353i	$0.361900\pi$
$978$	−9.52310	+	6.18437i	−0.304515	+	0.197754i
$979$	−2.94616	−	0.309654i	−0.0941597	−	0.00989658i
$980$	−26.2833	+	10.2063i	−0.839590	+	0.326028i
$981$	18.0102	−	3.82819i	0.575022	−	0.122225i
$982$	−7.77440	−	20.2530i	−0.248091	−	0.646299i
$983$	−2.51439	−	47.9774i	−0.0801966	−	1.53024i	−0.681854	−	0.731488i	$-0.738826\pi$
$983$	−2.51439	−	47.9774i	−0.0801966	−	1.53024i	0.601658	−	0.798754i	$-0.294507\pi$
$984$	2.40960	+	7.41598i	0.0768152	+	0.236413i
$985$	21.7399	−	4.70911i	0.692690	−	0.150045i
$986$	1.32579	−	2.29634i	0.0422218	−	0.0731303i
$987$	−9.10687	+	33.9873i	−0.289875	+	1.08183i
$988$	−0.0598275	−	0.117418i	−0.00190337	−	0.00373557i
$989$	−0.336457	−	0.755694i	−0.0106987	−	0.0240297i
$990$	1.24759	−	0.136019i	0.0396510	−	0.00432295i
$991$		−	23.5432i		−	0.747873i	−0.927454	−	0.373937i	$-0.878008\pi$
$991$		−	23.5432i		−	0.747873i	0.927454	−	0.373937i	$-0.121992\pi$
$992$	4.26711	+	3.57656i	0.135481	+	0.113556i
$993$	16.0665	+	16.0665i	0.509856	+	0.509856i
$994$	3.73740	+	5.14409i	0.118543	+	0.163161i
$995$	16.0505	+	19.6644i	0.508836	+	0.623403i
$996$	0.204766	−	0.630204i	0.00648824	−	0.0199688i
$997$	7.38930	+	1.97996i	0.234021	+	0.0627058i	0.373924	−	0.927459i	$-0.378012\pi$
$997$	7.38930	+	1.97996i	0.234021	+	0.0627058i	−0.139902	+	0.990165i	$0.544679\pi$
$998$	3.61327	+	13.4849i	0.114376	+	0.426857i
$999$	−2.89332	+	2.60516i	−0.0915406	+	0.0824235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bt.a.13.5	✓	256
5.2	odd	4		930.2.bt.b.757.1	yes	256
31.12	odd	30		930.2.bt.b.43.1	yes	256
155.12	even	60	inner	930.2.bt.a.787.5	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bt.a.13.5	✓	256	1.1	even	1	trivial
930.2.bt.a.787.5	yes	256	155.12	even	60	inner
930.2.bt.b.43.1	yes	256	31.12	odd	30
930.2.bt.b.757.1	yes	256	5.2	odd	4

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.bt (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(0.358368 - 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.57500 - 1.58726i) q^{5} +(0.866025 + 0.500000i) q^{6} +(4.42218 + 0.231757i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(0.358368 - 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.57500 - 1.58726i) q^{5} +(0.866025 + 0.500000i) q^{6} +(4.42218 + 0.231757i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +(1.32133 + 1.80391i) q^{10} +(0.116689 + 0.548981i) q^{11} +(-0.629320 + 0.777146i) q^{12} +(-0.0686210 - 0.0847399i) q^{13} +(-0.920684 + 4.33148i) q^{14} +(-0.917402 - 2.03921i) q^{15} +(0.809017 + 0.587785i) q^{16} +(2.80411 + 4.31795i) q^{17} +(0.777146 - 0.629320i) q^{18} +(-1.20194 + 0.126329i) q^{19} +(-1.98840 + 1.02287i) q^{20} +(1.80113 - 4.04540i) q^{21} +(-0.560476 + 0.0293733i) q^{22} +(0.770176 + 0.392424i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.0387630 - 4.99985i) q^{25} +(0.0944313 - 0.0545199i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(-4.13412 - 1.58694i) q^{28} +(-0.416655 + 0.302718i) q^{29} +(2.15762 - 0.587105i) q^{30} +(-0.488292 - 5.54631i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.554336 + 0.0877981i) q^{33} +(-4.70345 + 2.09411i) q^{34} +(7.33278 - 6.65411i) q^{35} +(0.500000 + 0.866025i) q^{36} +(3.76068 - 1.00767i) q^{37} +(0.0632512 - 1.20691i) q^{38} +(-0.103703 + 0.0336952i) q^{39} +(-0.699221 - 2.12393i) q^{40} +(-7.12348 - 3.17158i) q^{41} +(3.71384 + 2.41180i) q^{42} +(-0.743720 - 0.602252i) q^{43} +(0.0586661 - 0.558171i) q^{44} +(-2.23253 + 0.125682i) q^{45} +(-0.508075 + 0.699305i) q^{46} +(-7.84804 + 1.24301i) q^{47} +(0.838671 - 0.544639i) q^{48} +(12.5403 + 1.31804i) q^{49} +(4.94436 + 0.743863i) q^{50} +(5.03605 - 1.07045i) q^{51} +(0.0390764 + 0.101797i) q^{52} +(-0.0641301 - 1.22367i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(1.05516 + 0.679428i) q^{55} +(2.21412 - 3.83497i) q^{56} +(-0.312799 + 1.16738i) q^{57} +(-0.233812 - 0.458881i) q^{58} +(2.13980 + 4.80607i) q^{59} +(0.242351 + 2.22290i) q^{60} +5.26418i q^{61} +(5.55441 + 0.385354i) q^{62} +(-3.13124 - 3.13124i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.242582 - 0.0245460i) q^{65} +(-0.173434 + 0.533776i) q^{66} +(10.2991 + 2.75965i) q^{67} +(-1.33255 - 4.97313i) q^{68} +(0.642366 - 0.578389i) q^{69} +(5.42509 + 8.28343i) q^{70} +(0.960794 - 1.06707i) q^{71} +(-0.933580 + 0.358368i) q^{72} +(4.60918 - 7.09751i) q^{73} +(0.406966 + 3.87202i) q^{74} +(-4.68165 - 1.75560i) q^{75} +(1.18215 + 0.251274i) q^{76} +(0.388792 + 2.45473i) q^{77} +(-0.0170576 - 0.107697i) q^{78} +(9.37289 + 1.99227i) q^{79} +(2.20717 - 0.358356i) q^{80} +(0.104528 + 0.994522i) q^{81} +(4.24689 - 6.53964i) q^{82} +(-0.618623 + 0.237467i) q^{83} +(-2.96308 + 3.29083i) q^{84} +(11.2702 + 2.34992i) q^{85} +(0.711181 - 0.640350i) q^{86} +(0.133295 + 0.497465i) q^{87} +(0.542121 + 0.145261i) q^{88} +(-1.63107 + 5.01991i) q^{89} +(0.225111 - 2.22471i) q^{90} +(-0.283815 - 0.390638i) q^{91} +(-0.611215 - 0.611215i) q^{92} +(-5.35292 - 1.53176i) q^{93} -7.94587i q^{94} +(-1.69254 + 2.10676i) q^{95} +(0.406737 + 0.913545i) q^{96} +(0.448684 + 0.880592i) q^{97} +(-3.26354 + 12.1797i) q^{98} +(0.280623 - 0.486053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{7}+O(q^{10}) \) 256 * q + 8 * q^7	\( 256 q + 8 q^{7} + 4 q^{10} - 24 q^{14} - 8 q^{15} + 64 q^{16} + 36 q^{17} - 40 q^{19} + 12 q^{20} - 16 q^{21} + 8 q^{22} - 32 q^{24} + 20 q^{25} + 4 q^{28} - 16 q^{29} - 8 q^{31} - 4 q^{33} - 24 q^{35} + 128 q^{36} + 4 q^{37} + 4 q^{38} + 48 q^{41} + 32 q^{42} - 24 q^{43} + 4 q^{44} - 12 q^{45} - 20 q^{46} - 168 q^{47} - 40 q^{49} + 48 q^{50} - 64 q^{53} + 64 q^{54} + 64 q^{55} + 28 q^{57} + 68 q^{58} - 24 q^{59} + 4 q^{62} + 4 q^{63} - 60 q^{65} + 12 q^{66} - 76 q^{67} - 4 q^{68} + 12 q^{69} - 16 q^{70} - 48 q^{71} + 52 q^{73} + 68 q^{74} + 48 q^{75} + 48 q^{76} + 84 q^{77} - 56 q^{79} - 32 q^{81} - 32 q^{82} + 136 q^{83} + 68 q^{85} + 24 q^{86} + 20 q^{87} + 56 q^{88} - 224 q^{89} + 40 q^{91} - 48 q^{93} - 4 q^{95} + 8 q^{97} + 64 q^{98} + 4 q^{99}+O(q^{100}) \) 256 * q + 8 * q^7 + 4 * q^10 - 24 * q^14 - 8 * q^15 + 64 * q^16 + 36 * q^17 - 40 * q^19 + 12 * q^20 - 16 * q^21 + 8 * q^22 - 32 * q^24 + 20 * q^25 + 4 * q^28 - 16 * q^29 - 8 * q^31 - 4 * q^33 - 24 * q^35 + 128 * q^36 + 4 * q^37 + 4 * q^38 + 48 * q^41 + 32 * q^42 - 24 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^46 - 168 * q^47 - 40 * q^49 + 48 * q^50 - 64 * q^53 + 64 * q^54 + 64 * q^55 + 28 * q^57 + 68 * q^58 - 24 * q^59 + 4 * q^62 + 4 * q^63 - 60 * q^65 + 12 * q^66 - 76 * q^67 - 4 * q^68 + 12 * q^69 - 16 * q^70 - 48 * q^71 + 52 * q^73 + 68 * q^74 + 48 * q^75 + 48 * q^76 + 84 * q^77 - 56 * q^79 - 32 * q^81 - 32 * q^82 + 136 * q^83 + 68 * q^85 + 24 * q^86 + 20 * q^87 + 56 * q^88 - 224 * q^89 + 40 * q^91 - 48 * q^93 - 4 * q^95 + 8 * q^97 + 64 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more