LMFDB - Embedded newform 224.2.be.a.19.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (of order $24$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			19.21
Character	$\chi$	$=$	224.19
Dual form			224.2.be.a.59.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.740565 + 1.20481i) q^{2} +(1.28344 - 0.168969i) q^{3} +(-0.903128 + 1.78448i) q^{4} +(1.88828 + 0.248596i) q^{5} +(1.15405 + 1.42117i) q^{6} +(-2.57099 + 0.624522i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(-1.27910 + 0.342734i) q^{9} +O(q^{10})$	\(q+(0.740565 + 1.20481i) q^{2} +(1.28344 - 0.168969i) q^{3} +(-0.903128 + 1.78448i) q^{4} +(1.88828 + 0.248596i) q^{5} +(1.15405 + 1.42117i) q^{6} +(-2.57099 + 0.624522i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(-1.27910 + 0.342734i) q^{9} +(1.09888 + 2.45911i) q^{10} +(4.04052 + 3.10040i) q^{11} +(-0.857592 + 2.44288i) q^{12} +(2.64057 - 6.37490i) q^{13} +(-2.65641 - 2.63505i) q^{14} +2.46550 q^{15} +(-2.36872 - 3.22322i) q^{16} +(-0.520718 - 0.901911i) q^{17} +(-1.36019 - 1.28726i) q^{18} +(1.12978 - 0.866913i) q^{19} +(-2.14897 + 3.14507i) q^{20} +(-3.19419 + 1.23595i) q^{21} +(-0.743121 + 7.16409i) q^{22} +(-0.846936 - 3.16081i) q^{23} +(-3.57830 + 0.775873i) q^{24} +(-1.32584 - 0.355257i) q^{25} +(9.63604 - 1.53964i) q^{26} +(-5.17168 + 2.14218i) q^{27} +(1.20748 - 5.15189i) q^{28} +(-1.14636 + 2.76757i) q^{29} +(1.82586 + 2.97046i) q^{30} +(1.53764 + 2.66328i) q^{31} +(2.12917 - 5.24086i) q^{32} +(5.70964 + 3.29646i) q^{33} +(0.701004 - 1.29529i) q^{34} +(-5.00999 + 0.540132i) q^{35} +(0.543590 - 2.59206i) q^{36} +(1.30043 - 9.87772i) q^{37} +(1.88114 + 0.719167i) q^{38} +(2.31186 - 8.62799i) q^{39} +(-5.38066 - 0.259966i) q^{40} +(-0.859509 + 0.859509i) q^{41} +(-3.85459 - 2.93309i) q^{42} +(-5.93649 + 2.45898i) q^{43} +(-9.18169 + 4.41016i) q^{44} +(-2.50050 + 0.329197i) q^{45} +(3.18096 - 3.36118i) q^{46} +(-1.27846 - 0.738121i) q^{47} +(-3.58474 - 3.73658i) q^{48} +(6.21995 - 3.21127i) q^{49} +(-0.553852 - 1.86047i) q^{50} +(-0.820707 - 1.06957i) q^{51} +(8.99109 + 10.4694i) q^{52} +(5.21196 - 6.79235i) q^{53} +(-6.41088 - 4.64446i) q^{54} +(6.85887 + 6.85887i) q^{55} +(7.10126 - 2.36052i) q^{56} +(1.30353 - 1.30353i) q^{57} +(-4.18335 + 0.668414i) q^{58} +(8.93385 + 6.85519i) q^{59} +(-2.22666 + 4.39963i) q^{60} +(-10.2555 + 7.86934i) q^{61} +(-2.07001 + 3.82489i) q^{62} +(3.07451 - 1.67999i) q^{63} +(7.89102 - 1.31595i) q^{64} +(6.57090 - 11.3811i) q^{65} +(0.256753 + 9.32027i) q^{66} +(1.23985 + 9.41758i) q^{67} +(2.07971 - 0.114670i) q^{68} +(-1.62107 - 3.91361i) q^{69} +(-4.36098 - 5.63608i) q^{70} +(-8.22460 - 8.22460i) q^{71} +(3.52550 - 1.26467i) q^{72} +(1.74751 + 0.468243i) q^{73} +(12.8638 - 5.74833i) q^{74} +(-1.76166 - 0.231928i) q^{75} +(0.526649 + 2.79901i) q^{76} +(-12.3244 - 5.44769i) q^{77} +(12.1072 - 3.60423i) q^{78} +(-6.23642 + 10.8018i) q^{79} +(-3.67152 - 6.67519i) q^{80} +(-2.83516 + 1.63688i) q^{81} +(-1.67207 - 0.399021i) q^{82} +(-5.52119 - 2.28695i) q^{83} +(0.679230 - 6.81619i) q^{84} +(-0.759049 - 1.83251i) q^{85} +(-7.35895 - 5.33131i) q^{86} +(-1.00366 + 3.74571i) q^{87} +(-12.1130 - 7.79617i) q^{88} +(9.66427 - 2.58953i) q^{89} +(-2.24840 - 2.76883i) q^{90} +(-2.80761 + 18.0389i) q^{91} +(6.40528 + 1.34327i) q^{92} +(2.42349 + 3.15835i) q^{93} +(-0.0574902 - 2.08693i) q^{94} +(2.34886 - 1.35611i) q^{95} +(1.84713 - 7.08611i) q^{96} +8.78032i q^{97} +(8.47524 + 5.11569i) q^{98} +(-6.23084 - 2.58090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.740565	+	1.20481i	0.523658	+	0.851928i
$2$	0.740565	+	1.20481i	0.523658	+	0.851928i
$3$	1.28344	−	0.168969i	0.740996	−	0.0975540i	0.249428	−	0.968393i	$-0.419757\pi$
$3$	1.28344	−	0.168969i	0.740996	−	0.0975540i	0.491568	+	0.870839i	$0.336424\pi$
$4$	−0.903128	+	1.78448i	−0.451564	+	0.892239i
$5$	1.88828	+	0.248596i	0.844463	+	0.111176i	0.540329	−	0.841454i	$-0.318300\pi$
$5$	1.88828	+	0.248596i	0.844463	+	0.111176i	0.304134	+	0.952629i	$0.401633\pi$
$6$	1.15405	+	1.42117i	0.471138	+	0.580191i
$7$	−2.57099	+	0.624522i	−0.971742	+	0.236047i
$7$	−2.57099	+	0.624522i	−0.971742	+	0.236047i
$8$	−2.81878	+	0.233426i	−0.996589	+	0.0825284i
$9$	−1.27910	+	0.342734i	−0.426367	+	0.114245i
$10$	1.09888	+	2.45911i	0.347497	+	0.777640i
$11$	4.04052	+	3.10040i	1.21826	+	0.934805i	0.999163	−	0.0408980i	$-0.0130219\pi$
$11$	4.04052	+	3.10040i	1.21826	+	0.934805i	0.219098	+	0.975703i	$0.429689\pi$
$12$	−0.857592	+	2.44288i	−0.247566	+	0.705198i
$13$	2.64057	−	6.37490i	0.732362	−	1.76808i	0.0978003	−	0.995206i	$-0.468819\pi$
$13$	2.64057	−	6.37490i	0.732362	−	1.76808i	0.634562	−	0.772872i	$-0.281181\pi$
$14$	−2.65641	−	2.63505i	−0.709956	−	0.704246i
$15$	2.46550			0.636590
$16$	−2.36872	−	3.22322i	−0.592180	−	0.805805i
$17$	−0.520718	−	0.901911i	−0.126293	−	0.218745i	0.795945	−	0.605369i	$-0.206975\pi$
$17$	−0.520718	−	0.901911i	−0.126293	−	0.218745i	−0.922238	+	0.386624i	$0.873641\pi$
$18$	−1.36019	−	1.28726i	−0.320599	−	0.303409i
$19$	1.12978	−	0.866913i	0.259190	−	0.198884i	−0.470990	−	0.882139i	$-0.656103\pi$
$19$	1.12978	−	0.866913i	0.259190	−	0.198884i	0.730180	+	0.683255i	$0.239436\pi$
$20$	−2.14897	+	3.14507i	−0.480524	+	0.703260i
$21$	−3.19419	+	1.23595i	−0.697030	+	0.269707i
$22$	−0.743121	+	7.16409i	−0.158434	+	1.52739i
$23$	−0.846936	−	3.16081i	−0.176598	−	0.659074i	−0.996274	−	0.0862461i	$-0.972513\pi$
$23$	−0.846936	−	3.16081i	−0.176598	−	0.659074i	0.819675	−	0.572828i	$-0.194154\pi$
$24$	−3.57830	+	0.775873i	−0.730418	+	0.158374i
$25$	−1.32584	−	0.355257i	−0.265168	−	0.0710514i
$26$	9.63604	−	1.53964i	1.88978	−	0.301949i
$27$	−5.17168	+	2.14218i	−0.995290	+	0.412263i
$28$	1.20748	−	5.15189i	0.228193	−	0.973616i
$29$	−1.14636	+	2.76757i	−0.212874	+	0.513924i	−0.993863	−	0.110621i	$-0.964716\pi$
$29$	−1.14636	+	2.76757i	−0.212874	+	0.513924i	0.780988	+	0.624546i	$0.214716\pi$
$30$	1.82586	+	2.97046i	0.333356	+	0.542329i
$31$	1.53764	+	2.66328i	0.276169	+	0.478339i	0.970429	−	0.241385i	$-0.0776018\pi$
$31$	1.53764	+	2.66328i	0.276169	+	0.478339i	−0.694260	+	0.719724i	$0.744268\pi$
$32$	2.12917	−	5.24086i	0.376388	−	0.926462i
$33$	5.70964	+	3.29646i	0.993921	+	0.573841i
$34$	0.701004	−	1.29529i	0.120221	−	0.222140i
$35$	−5.00999	+	0.540132i	−0.846843	+	0.0912989i
$36$	0.543590	−	2.59206i	0.0905983	−	0.432010i
$37$	1.30043	−	9.87772i	0.213789	−	1.62389i	−0.462062	−	0.886848i	$-0.652890\pi$
$37$	1.30043	−	9.87772i	0.213789	−	1.62389i	0.675850	−	0.737039i	$-0.263777\pi$
$38$	1.88114	+	0.719167i	0.305162	+	0.116664i
$39$	2.31186	−	8.62799i	0.370194	−	1.38158i
$40$	−5.38066	−	0.259966i	−0.850758	−	0.0411042i
$41$	−0.859509	+	0.859509i	−0.134233	+	0.134233i	−0.771031	−	0.636798i	$-0.780259\pi$
$41$	−0.859509	+	0.859509i	−0.134233	+	0.134233i	0.636798	+	0.771031i	$0.280259\pi$
$42$	−3.85459	−	2.93309i	−0.594777	−	0.452585i
$43$	−5.93649	+	2.45898i	−0.905307	+	0.374990i	−0.786258	−	0.617898i	$-0.787984\pi$
$43$	−5.93649	+	2.45898i	−0.905307	+	0.374990i	−0.119049	+	0.992888i	$0.537984\pi$
$44$	−9.18169	+	4.41016i	−1.38419	+	0.664856i
$45$	−2.50050	+	0.329197i	−0.372753	+	0.0490738i
$46$	3.18096	−	3.36118i	0.469007	−	0.495579i
$47$	−1.27846	−	0.738121i	−0.186483	−	0.107666i	0.403852	−	0.914824i	$-0.367671\pi$
$47$	−1.27846	−	0.738121i	−0.186483	−	0.107666i	−0.590335	+	0.807158i	$0.701004\pi$
$48$	−3.58474	−	3.73658i	−0.517413	−	0.539329i
$49$	6.21995	−	3.21127i	0.888564	−	0.458753i
$50$	−0.553852	−	1.86047i	−0.0783265	−	0.263110i
$51$	−0.820707	−	1.06957i	−0.114922	−	0.149769i
$52$	8.99109	+	10.4694i	1.24684	+	1.45184i
$53$	5.21196	−	6.79235i	0.715917	−	0.933001i	−0.283747	−	0.958899i	$-0.591578\pi$
$53$	5.21196	−	6.79235i	0.715917	−	0.933001i	0.999665	+	0.0258976i	$0.00824438\pi$
$54$	−6.41088	−	4.64446i	−0.872410	−	0.632031i
$55$	6.85887	+	6.85887i	0.924849	+	0.924849i
$56$	7.10126	−	2.36052i	0.948946	−	0.315438i
$57$	1.30353	−	1.30353i	0.172657	−	0.172657i
$58$	−4.18335	+	0.668414i	−0.549300	+	0.0877670i
$59$	8.93385	+	6.85519i	1.16309	+	0.892469i	0.995628	−	0.0934094i	$-0.0297765\pi$
$59$	8.93385	+	6.85519i	1.16309	+	0.892469i	0.167461	+	0.985879i	$0.446443\pi$
$60$	−2.22666	+	4.39963i	−0.287461	+	0.567990i
$61$	−10.2555	+	7.86934i	−1.31309	+	1.00757i	−0.314793	+	0.949160i	$0.601935\pi$
$61$	−10.2555	+	7.86934i	−1.31309	+	1.00757i	−0.998293	+	0.0584061i	$0.981398\pi$
$62$	−2.07001	+	3.82489i	−0.262892	+	0.485762i
$63$	3.07451	−	1.67999i	0.387352	−	0.211659i
$64$	7.89102	−	1.31595i	0.986378	−	0.164494i
$65$	6.57090	−	11.3811i	0.815020	−	1.41166i
$66$	0.256753	+	9.32027i	0.0316041	+	1.14725i
$67$	1.23985	+	9.41758i	0.151472	+	1.15054i	0.883218	+	0.468963i	$0.155372\pi$
$67$	1.23985	+	9.41758i	0.151472	+	1.15054i	−0.731746	+	0.681577i	$0.761294\pi$
$68$	2.07971	−	0.114670i	0.252202	−	0.0139058i
$69$	−1.62107	−	3.91361i	−0.195154	−	0.471144i
$70$	−4.36098	−	5.63608i	−0.521237	−	0.673640i
$71$	−8.22460	−	8.22460i	−0.976081	−	0.976081i	0.0236400	−	0.999721i	$-0.492474\pi$
$71$	−8.22460	−	8.22460i	−0.976081	−	0.976081i	−0.999721	+	0.0236400i	$0.992474\pi$
$72$	3.52550	−	1.26467i	0.415484	−	0.149042i
$73$	1.74751	+	0.468243i	0.204530	+	0.0548037i	0.359629	−	0.933095i	$-0.382903\pi$
$73$	1.74751	+	0.468243i	0.204530	+	0.0548037i	−0.155099	+	0.987899i	$0.549570\pi$
$74$	12.8638	−	5.74833i	1.49539	−	0.668229i
$75$	−1.76166	−	0.231928i	−0.203420	−	0.0267807i
$76$	0.526649	+	2.79901i	0.0604108	+	0.321068i
$77$	−12.3244	−	5.44769i	−1.40449	−	0.620822i
$78$	12.1072	−	3.60423i	1.37087	−	0.408099i
$79$	−6.23642	+	10.8018i	−0.701652	+	1.21530i	0.266234	+	0.963909i	$0.414221\pi$
$79$	−6.23642	+	10.8018i	−0.701652	+	1.21530i	−0.967886	+	0.251389i	$0.919113\pi$
$80$	−3.67152	−	6.67519i	−0.410489	−	0.746309i
$81$	−2.83516	+	1.63688i	−0.315018	+	0.181876i
$82$	−1.67207	−	0.399021i	−0.184649	−	0.0440646i
$83$	−5.52119	−	2.28695i	−0.606030	−	0.251026i	0.0585001	−	0.998287i	$-0.481368\pi$
$83$	−5.52119	−	2.28695i	−0.606030	−	0.251026i	−0.664530	+	0.747262i	$0.731368\pi$
$84$	0.679230	−	6.81619i	0.0741101	−	0.743707i
$85$	−0.759049	−	1.83251i	−0.0823304	−	0.198763i
$86$	−7.35895	−	5.33131i	−0.793536	−	0.574890i
$87$	−1.00366	+	3.74571i	−0.107604	+	0.401583i
$88$	−12.1130	−	7.79617i	−1.29125	−	0.831075i
$89$	9.66427	−	2.58953i	1.02441	−	0.274490i	0.292772	−	0.956182i	$-0.405422\pi$
$89$	9.66427	−	2.58953i	1.02441	−	0.274490i	0.731639	+	0.681692i	$0.238756\pi$
$90$	−2.24840	−	2.76883i	−0.237002	−	0.291861i
$91$	−2.80761	+	18.0389i	−0.294317	+	1.89099i
$92$	6.40528	+	1.34327i	0.667797	+	0.140046i
$93$	2.42349	+	3.15835i	0.251304	+	0.327506i
$94$	−0.0574902	−	2.08693i	−0.00592967	−	0.215250i
$95$	2.34886	−	1.35611i	0.240988	−	0.139134i
$96$	1.84713	−	7.08611i	0.188522	−	0.723223i
$97$			8.78032i			0.891506i	0.895156	+	0.445753i	$0.147064\pi$
$97$			8.78032i			0.891506i	−0.895156	+	0.445753i	$0.852936\pi$
$98$	8.47524	+	5.11569i	0.856129	+	0.516763i
$99$	−6.23084	−	2.58090i	−0.626223	−	0.259390i
$100$	1.83135	−	2.04509i	0.183135	−	0.204509i
$101$	1.10407	−	1.43885i	0.109859	−	0.143171i	−0.735188	−	0.677864i	$-0.762906\pi$
$101$	1.10407	−	1.43885i	0.109859	−	0.143171i	0.845047	+	0.534693i	$0.179573\pi$
$102$	0.680836	−	1.78088i	0.0674128	−	0.176333i
$103$	0.893268	+	3.33372i	0.0880163	+	0.328481i	0.995868	−	0.0908095i	$-0.0289454\pi$
$103$	0.893268	+	3.33372i	0.0880163	+	0.328481i	−0.907852	+	0.419291i	$0.862279\pi$
$104$	−5.95511	+	18.5858i	−0.583947	+	1.82249i
$105$	−6.33877	+	1.53976i	−0.618601	+	0.150265i
$106$	12.0433	+	1.24923i	1.16975	+	0.121336i
$107$	−0.550312	+	4.18003i	−0.0532007	+	0.404099i	0.944038	+	0.329837i	$0.106994\pi$
$107$	−0.550312	+	4.18003i	−0.0532007	+	0.404099i	−0.997239	+	0.0742626i	$0.976340\pi$
$108$	0.848014	−	11.1634i	0.0816002	−	1.07420i
$109$	0.475990	+	3.61550i	0.0455916	+	0.346302i	0.999004	+	0.0446310i	$0.0142112\pi$
$109$	0.475990	+	3.61550i	0.0455916	+	0.346302i	−0.953412	+	0.301671i	$0.902455\pi$
$110$	−3.18419	+	13.3431i	−0.303600	+	1.27221i
$111$		−	12.8972i		−	1.22415i
$112$	8.10292	+	6.80754i	0.765654	+	0.643252i
$113$			12.3773i			1.16436i	0.813061	+	0.582178i	$0.197800\pi$
$113$			12.3773i			1.16436i	−0.813061	+	0.582178i	$0.802200\pi$
$114$	2.53586	+	0.605156i	0.237505	+	0.0566781i
$115$	−0.813485	−	6.17903i	−0.0758578	−	0.576197i
$116$	−3.90335	−	4.54513i	−0.362417	−	0.422004i
$117$	−1.19266	+	9.05915i	−0.110261	+	0.837519i
$118$	−1.64309	+	15.8403i	−0.151259	+	1.45822i
$119$	1.90202	+	1.99360i	0.174358	+	0.182753i
$120$	−6.94970	+	0.575511i	−0.634418	+	0.0525367i
$121$	3.86630	+	14.4292i	0.351482	+	1.31175i
$122$	−17.0759	−	6.52819i	−1.54598	−	0.591035i
$123$	−0.957901	+	1.24836i	−0.0863710	+	0.112561i
$124$	−6.14124	+	0.338612i	−0.551500	+	0.0304083i
$125$	−11.2132	−	4.64466i	−1.00294	−	0.415431i
$126$	4.30094	+	2.46005i	0.383158	+	0.219159i
$127$			2.70749i			0.240251i	0.992759	+	0.120126i	$0.0383297\pi$
$127$			2.70749i			0.240251i	−0.992759	+	0.120126i	$0.961670\pi$
$128$	7.42928	+	8.53263i	0.656662	+	0.754185i
$129$	−7.20366	+	4.15904i	−0.634247	+	0.366183i
$130$	18.5783	−	0.511790i	1.62942	−	0.0448869i
$131$	−2.86798	−	3.73762i	−0.250577	−	0.326558i	0.651081	−	0.759008i	$-0.274316\pi$
$131$	−2.86798	−	3.73762i	−0.250577	−	0.326558i	−0.901658	+	0.432450i	$0.857649\pi$
$132$	−11.0390	+	7.21160i	−0.960822	+	0.627689i
$133$	−2.36325	+	2.93440i	−0.204920	+	0.254444i
$134$	−10.4282	+	8.46811i	−0.900859	+	0.731533i
$135$	−10.2981	+	2.75937i	−0.886320	+	0.237489i
$136$	1.67832	+	2.42074i	0.143915	+	0.207577i
$137$	0.744450	−	2.77832i	0.0636026	−	0.237368i	−0.926805	−	0.375542i	$-0.877457\pi$
$137$	0.744450	−	2.77832i	0.0636026	−	0.237368i	0.990408	+	0.138174i	$0.0441233\pi$
$138$	3.51465	−	4.85137i	0.299187	−	0.412976i
$139$	−4.39928	−	10.6208i	−0.373142	−	0.900844i	−0.993214	−	0.116300i	$-0.962897\pi$
$139$	−4.39928	−	10.6208i	−0.373142	−	0.900844i	0.620072	−	0.784545i	$-0.287103\pi$
$140$	3.56081	−	9.42802i	0.300943	−	0.796813i
$141$	−1.76555	−	0.731316i	−0.148686	−	0.0615880i
$142$	3.81822	−	15.9999i	0.320418	−	1.34268i
$143$	30.4340	−	17.5711i	2.54502	−	1.46937i
$144$	4.13454	+	3.31099i	0.344545	+	0.275915i
$145$	−2.85266	+	4.94095i	−0.236901	+	0.410324i
$146$	0.729999	+	2.45217i	0.0604151	+	0.202943i
$147$	7.44034	−	5.17246i	0.613669	−	0.426617i
$148$	16.4521	+	11.2414i	1.35236	+	0.924039i
$149$	−2.61976	−	0.344898i	−0.214619	−	0.0282551i	0.0224499	−	0.999748i	$-0.492853\pi$
$149$	−2.61976	−	0.344898i	−0.214619	−	0.0282551i	−0.237069	+	0.971493i	$0.576187\pi$
$150$	−1.02520	−	2.29423i	−0.0837071	−	0.187323i
$151$	−1.27553	−	0.341777i	−0.103801	−	0.0278134i	0.206545	−	0.978437i	$-0.433778\pi$
$151$	−1.27553	−	0.341777i	−0.103801	−	0.0278134i	−0.310346	+	0.950624i	$0.600445\pi$
$152$	−2.98225	+	2.70736i	−0.241892	+	0.219596i
$153$	0.975167	+	0.975167i	0.0788376	+	0.0788376i
$154$	−2.56358	−	18.8829i	−0.206579	−	1.52163i
$155$	2.24142	+	5.41126i	0.180035	+	0.434643i
$156$	13.3086	+	11.9176i	1.06554	+	0.954175i
$157$	3.12087	+	23.7053i	0.249072	+	1.89189i	0.421434	+	0.906859i	$0.361527\pi$
$157$	3.12087	+	23.7053i	0.249072	+	1.89189i	−0.172362	+	0.985034i	$0.555140\pi$
$158$	−17.6326	+	0.485738i	−1.40277	+	0.0386432i
$159$	5.54156	−	9.59826i	0.439474	−	0.761191i
$160$	5.32333	−	9.36689i	0.420846	−	0.740518i
$161$	4.15146	+	7.59747i	0.327181	+	0.598764i
$162$	−4.07175	−	2.20361i	−0.319907	−	0.173132i
$163$	4.45255	−	3.41656i	0.348751	−	0.267606i	−0.419499	−	0.907756i	$-0.637794\pi$
$163$	4.45255	−	3.41656i	0.348751	−	0.267606i	0.768250	+	0.640150i	$0.221128\pi$
$164$	−0.757528	−	2.31002i	−0.0591530	−	0.180382i
$165$	9.96190	+	7.64403i	0.775533	+	0.595087i
$166$	−1.33346	−	8.34562i	−0.103497	−	0.647746i
$167$	8.02123	−	8.02123i	0.620702	−	0.620702i	−0.325009	−	0.945711i	$-0.605367\pi$
$167$	8.02123	−	8.02123i	0.620702	−	0.620702i	0.945711	+	0.325009i	$0.105367\pi$
$168$	8.71521	−	4.22949i	0.672393	−	0.326312i
$169$	−24.4743	−	24.4743i	−1.88264	−	1.88264i
$170$	1.64569	−	2.27160i	0.126219	−	0.174224i
$171$	−1.14799	+	1.49608i	−0.0877887	+	0.114408i
$172$	0.973423	−	12.8143i	0.0742228	−	0.977082i
$173$	1.47489	+	1.92212i	0.112134	+	0.146136i	0.846048	−	0.533106i	$-0.178975\pi$
$173$	1.47489	+	1.92212i	0.112134	+	0.146136i	−0.733914	+	0.679242i	$0.762309\pi$
$174$	−5.25615	+	1.56472i	−0.398467	+	0.118621i
$175$	3.63058	+	0.0853472i	0.274446	+	0.00645164i
$176$	0.422411	−	20.3675i	0.0318404	−	1.53525i
$177$	12.6244	+	7.28870i	0.948908	+	0.547853i
$178$	10.2769	+	9.72588i	0.770287	+	0.728986i
$179$	−10.9532	+	1.44202i	−0.818681	+	0.107781i	−0.528222	−	0.849106i	$-0.677141\pi$
$179$	−10.9532	+	1.44202i	−0.818681	+	0.107781i	−0.290459	+	0.956888i	$0.593808\pi$
$180$	1.67083	−	4.75939i	0.124536	−	0.354744i
$181$	−2.76075	+	1.14354i	−0.205205	+	0.0849987i	−0.482919	−	0.875665i	$-0.660423\pi$
$181$	−2.76075	+	1.14354i	−0.205205	+	0.0849987i	0.277714	+	0.960664i	$0.410423\pi$
$182$	−23.8126	+	9.97632i	−1.76511	+	0.739494i
$183$	−11.8327	+	11.8327i	−0.874700	+	0.874700i
$184$	3.12514	+	8.71192i	0.230388	+	0.642252i
$185$	4.91113	−	18.3286i	0.361074	−	1.34754i
$186$	−2.01046	+	5.25880i	−0.147414	+	0.385594i
$187$	0.692310	−	5.25862i	0.0506267	−	0.384548i
$188$	2.47178	−	1.61477i	0.180273	−	0.117769i
$189$	11.9585	−	8.73734i	0.869851	−	0.635548i
$190$	3.37334	+	1.82563i	0.244727	+	0.132445i
$191$	−5.51336	−	3.18314i	−0.398933	−	0.230324i	0.287090	−	0.957903i	$-0.407312\pi$
$191$	−5.51336	−	3.18314i	−0.398933	−	0.230324i	−0.686023	+	0.727579i	$0.740645\pi$
$192$	9.90533	−	3.02228i	0.714856	−	0.218114i
$193$	−0.647141	−	1.12088i	−0.0465823	−	0.0806828i	0.841794	−	0.539799i	$-0.181500\pi$
$193$	−0.647141	−	1.12088i	−0.0465823	−	0.0806828i	−0.888376	+	0.459116i	$0.848166\pi$
$194$	−10.5786	+	6.50239i	−0.759499	+	0.466845i
$195$	6.51033	−	15.7173i	0.466214	−	1.12554i
$196$	0.113042	+	13.9995i	0.00807441	+	0.999967i
$197$	−1.64133	+	0.679859i	−0.116940	+	0.0484380i	−0.440386	−	0.897808i	$-0.645158\pi$
$197$	−1.64133	+	0.679859i	−0.116940	+	0.0484380i	0.323446	+	0.946246i	$0.395158\pi$
$198$	−1.50485	−	9.41829i	−0.106945	−	0.669329i
$199$	8.92924	+	2.39258i	0.632977	+	0.169606i	0.561020	−	0.827802i	$-0.310409\pi$
$199$	8.92924	+	2.39258i	0.632977	+	0.169606i	0.0719569	+	0.997408i	$0.477076\pi$
$200$	3.82017	+	0.691907i	0.270127	+	0.0489252i
$201$	3.18255	+	11.8774i	0.224480	+	0.837770i
$202$	2.55118	+	0.264630i	0.179500	+	0.0186193i
$203$	1.21888	−	7.83131i	0.0855487	−	0.549650i
$204$	2.64982	−	0.498579i	0.185525	−	0.0349075i
$205$	−1.83666	+	1.40932i	−0.128278	+	0.0984312i
$206$	−3.35497	+	3.54505i	−0.233752	+	0.246996i
$207$	2.16663	+	3.75272i	0.150592	+	0.260832i
$208$	−26.8025	+	6.58922i	−1.85842	+	0.456880i
$209$	7.25268			0.501678
$210$	−6.54939	−	6.49672i	−0.451951	−	0.448316i
$211$	7.65203	−	18.4736i	0.526788	−	1.27178i	−0.406829	−	0.913504i	$-0.633365\pi$
$211$	7.65203	−	18.4736i	0.526788	−	1.27178i	0.933617	−	0.358274i	$-0.116635\pi$
$212$	7.41374	+	15.4350i	0.509178	+	1.06008i
$213$	−11.9455	−	9.16611i	−0.818493	−	0.628052i
$214$	−5.44368	+	2.43257i	−0.372123	+	0.166287i
$215$	−11.8210	+	3.16744i	−0.806188	+	0.216017i
$216$	14.0778	−	7.24553i	0.957871	−	0.492996i
$217$	−5.61653	−	5.88696i	−0.381275	−	0.399633i
$218$	−4.00349	+	3.25099i	−0.271150	+	0.220185i
$219$	2.32194	+	0.305690i	0.156902	+	0.0206566i
$220$	−18.4339	+	6.04506i	−1.24282	+	0.407558i
$221$	−7.12458	+	0.937969i	−0.479251	+	0.0630946i
$222$	15.5387	−	9.55123i	1.04289	−	0.641036i
$223$	−5.44239			−0.364449			−0.182225	−	0.983257i	$-0.558330\pi$
$223$	−5.44239			−0.364449			−0.182225	+	0.983257i	$0.558330\pi$
$224$	−2.20105	+	14.8039i	−0.147064	+	0.989127i
$225$	1.81764			0.121176
$226$	−14.9123	+	9.16618i	−0.991949	+	0.609725i
$227$	0.212579	−	0.0279866i	0.0141094	−	0.00185754i	−0.123468	−	0.992349i	$-0.539402\pi$
$227$	0.212579	−	0.0279866i	0.0141094	−	0.00185754i	0.137578	+	0.990491i	$0.456068\pi$
$228$	1.14887	+	3.50338i	0.0760856	+	0.232017i
$229$	21.1667	+	2.78665i	1.39874	+	0.184147i	0.791885	−	0.610670i	$-0.209100\pi$
$229$	21.1667	+	2.78665i	1.39874	+	0.184147i	0.606850	+	0.794817i	$0.292433\pi$
$230$	6.84211	−	5.55607i	0.451155	−	0.366356i
$231$	−16.7381	−	4.90937i	−1.10129	−	0.323013i
$232$	2.58532	−	8.06875i	0.169735	−	0.529739i
$233$	3.90806	−	1.04716i	0.256025	−	0.0686017i	−0.128523	−	0.991706i	$-0.541024\pi$
$233$	3.90806	−	1.04716i	0.256025	−	0.0686017i	0.384549	+	0.923105i	$0.374357\pi$
$234$	−11.7978	+	5.27196i	−0.771245	+	0.344639i
$235$	−2.23060	−	1.71160i	−0.145508	−	0.111652i
$236$	−20.3013	+	9.75115i	−1.32150	+	0.634746i
$237$	−6.17893	+	14.9173i	−0.401365	+	0.968980i
$238$	−0.993336	+	3.76796i	−0.0643884	+	0.244241i
$239$	−2.73300			−0.176783			−0.0883915	−	0.996086i	$-0.528173\pi$
$239$	−2.73300			−0.176783			−0.0883915	+	0.996086i	$0.528173\pi$
$240$	−5.84009	−	7.94686i	−0.376976	−	0.512968i
$241$	−7.50863	−	13.0053i	−0.483673	−	0.837747i	0.516151	−	0.856498i	$-0.327364\pi$
$241$	−7.50863	−	13.0053i	−0.483673	−	0.837747i	−0.999824	+	0.0187508i	$0.994031\pi$
$242$	−14.5212	+	15.3439i	−0.933458	+	0.986345i
$243$	9.96087	−	7.64325i	0.638990	−	0.490315i
$244$	−4.78062	−	25.4078i	−0.306048	−	1.62657i
$245$	12.5433	−	4.51752i	0.801362	−	0.288614i
$246$	−2.21342	−	0.229595i	−0.141123	−	0.0146384i
$247$	−2.54321	−	9.49140i	−0.161821	−	0.603923i
$248$	−4.95595	−	7.14826i	−0.314703	−	0.453915i
$249$	−7.47256	−	2.00227i	−0.473554	−	0.126889i
$250$	−2.70818	−	16.9494i	−0.171280	−	1.07198i
$251$	22.8325	−	9.45753i	1.44117	−	0.596954i	0.481092	−	0.876670i	$-0.340240\pi$
$251$	22.8325	−	9.45753i	1.44117	−	0.596954i	0.960083	+	0.279716i	$0.0902404\pi$
$252$	0.221235	+	7.00364i	0.0139365	+	0.441188i
$253$	6.37770	−	15.3971i	0.400963	−	0.968010i
$254$	−3.26201	+	2.00507i	−0.204677	+	0.125810i
$255$	−1.28383	−	2.22366i	−0.0803967	−	0.139251i
$256$	−4.77832	+	15.2698i	−0.298645	+	0.954364i
$257$	11.9243	+	6.88450i	0.743818	+	0.429443i	0.823456	−	0.567380i	$-0.192043\pi$
$257$	11.9243	+	6.88450i	0.743818	+	0.429443i	−0.0796379	+	0.996824i	$0.525376\pi$
$258$	−10.3456	−	5.59900i	−0.644090	−	0.348578i
$259$	2.82547	+	26.2076i	0.175566	+	1.62846i
$260$	14.3750	+	22.0042i	0.891501	+	1.36465i
$261$	0.517776	−	3.93290i	0.0320495	−	0.243440i
$262$	2.37920	−	6.22332i	0.146987	−	0.384478i
$263$	3.40199	−	12.6964i	0.209776	−	0.782894i	−0.778165	−	0.628060i	$-0.783849\pi$
$263$	3.40199	−	12.6964i	0.209776	−	0.782894i	0.987941	−	0.154834i	$-0.0494843\pi$
$264$	−16.8637	−	7.95922i	−1.03789	−	0.489856i
$265$	11.5302	−	11.5302i	0.708293	−	0.708293i
$266$	−5.28553	−	0.674155i	−0.324076	−	0.0413351i
$267$	11.9660	−	4.95648i	0.732307	−	0.303332i
$268$	−17.9252	−	6.29280i	−1.09496	−	0.384394i
$269$	−6.56368	+	0.864124i	−0.400194	+	0.0526866i	−0.327937	−	0.944699i	$-0.606354\pi$
$269$	−6.56368	+	0.864124i	−0.400194	+	0.0526866i	−0.0722570	+	0.997386i	$0.523020\pi$
$270$	−10.9509	−	10.3638i	−0.666452	−	0.630718i
$271$	20.6375	+	11.9151i	1.25364	+	0.723789i	0.971830	−	0.235681i	$-0.0757320\pi$
$271$	20.6375	+	11.9151i	1.25364	+	0.723789i	0.281809	+	0.959470i	$0.409065\pi$
$272$	−1.67362	+	3.81477i	−0.101478	+	0.231304i
$273$	−0.555403	+	23.6263i	−0.0336145	+	1.42993i
$274$	3.89866	−	1.16061i	0.235527	−	0.0701150i
$275$	−4.25563	−	5.54605i	−0.256624	−	0.334439i
$276$	8.44779	+	0.641726i	0.508497	+	0.0386273i
$277$	6.06464	−	7.90359i	0.364389	−	0.474881i	−0.574794	−	0.818298i	$-0.694918\pi$
$277$	6.06464	−	7.90359i	0.364389	−	0.474881i	0.939183	+	0.343417i	$0.111585\pi$
$278$	9.53808	−	13.1657i	0.572056	−	0.789625i
$279$	−2.87960	−	2.87960i	−0.172397	−	0.172397i
$280$	13.9960	−	2.69197i	0.836419	−	0.160876i
$281$	−17.1617	+	17.1617i	−1.02378	+	1.02378i	−0.0240710	+	0.999710i	$0.507663\pi$
$281$	−17.1617	+	17.1617i	−1.02378	+	1.02378i	−0.999710	+	0.0240710i	$0.992337\pi$
$282$	−0.426411	−	2.66874i	−0.0253924	−	0.158921i
$283$	−11.7375	−	9.00651i	−0.697723	−	0.535382i	0.197885	−	0.980225i	$-0.436593\pi$
$283$	−11.7375	−	9.00651i	−0.697723	−	0.535382i	−0.895608	+	0.444844i	$0.853259\pi$
$284$	22.1045	−	7.24875i	1.31166	−	0.430134i
$285$	2.78548	−	2.13738i	0.164998	−	0.126607i
$286$	43.7081	+	23.6546i	2.58451	+	1.39873i
$287$	1.67300	−	2.74657i	0.0987543	−	0.162125i
$288$	−0.927207	+	7.43333i	−0.0546362	+	0.438013i
$289$	7.95770	−	13.7831i	0.468100	−	0.810773i
$290$	−8.06548	+	0.222186i	−0.473621	+	0.0130472i
$291$	1.48360	+	11.2690i	0.0869700	+	0.660603i
$292$	−2.41379	+	2.69550i	−0.141256	+	0.157742i
$293$	−10.4831	−	25.3085i	−0.612430	−	1.47854i	−0.860323	−	0.509750i	$-0.829738\pi$
$293$	−10.4831	−	25.3085i	−0.612430	−	1.47854i	0.247892	−	0.968788i	$-0.420262\pi$
$294$	11.7419	+	5.13365i	0.684801	+	0.299400i
$295$	15.1654	+	15.1654i	0.882965	+	0.882965i
$296$	−1.35990	+	28.1467i	−0.0790427	+	1.63599i
$297$	−27.5379	−	7.37875i	−1.59791	−	0.428158i
$298$	−1.52456	−	3.41173i	−0.0883157	−	0.197636i
$299$	−22.3862	−	2.94720i	−1.29463	−	0.170441i
$300$	2.00488	−	2.93419i	0.115752	−	0.169406i
$301$	13.7270	−	10.0295i	0.791209	−	0.578089i
$302$	−0.532836	−	1.78988i	−0.0306613	−	0.102996i
$303$	1.17389	−	2.03324i	0.0674382	−	0.116806i
$304$	−5.47040	−	1.58807i	−0.313749	−	0.0910818i
$305$	−21.3216	+	12.3100i	−1.22087	+	0.704870i
$306$	−0.452715	+	1.89706i	−0.0258800	+	0.108448i
$307$	1.05530	+	0.437118i	0.0602290	+	0.0249477i	0.412595	−	0.910915i	$-0.364623\pi$
$307$	1.05530	+	0.437118i	0.0602290	+	0.0249477i	−0.352366	+	0.935862i	$0.614623\pi$
$308$	20.8518	−	17.0726i	1.18814	−	0.972803i
$309$	1.70975	+	4.12771i	0.0972644	+	0.234817i
$310$	−4.85961	+	6.70786i	−0.276008	+	0.380981i
$311$	1.88802	−	7.04619i	0.107060	−	0.399553i	−0.891511	−	0.452999i	$-0.850354\pi$
$311$	1.88802	−	7.04619i	0.107060	−	0.399553i	0.998571	+	0.0534464i	$0.0170206\pi$
$312$	−4.50264	+	24.8600i	−0.254912	+	1.40742i
$313$	5.62674	−	1.50768i	0.318042	−	0.0852192i	−0.0962664	−	0.995356i	$-0.530690\pi$
$313$	5.62674	−	1.50768i	0.318042	−	0.0852192i	0.414309	+	0.910136i	$0.364023\pi$
$314$	−26.2492	+	21.3154i	−1.48133	+	1.20290i
$315$	6.22316	−	2.40798i	0.350635	−	0.135674i
$316$	−13.6433	−	20.8842i	−0.767495	−	1.17483i
$317$	12.4289	+	16.1977i	0.698078	+	0.909753i	0.999037	−	0.0438839i	$-0.0139732\pi$
$317$	12.4289	+	16.1977i	0.698078	+	0.909753i	−0.300958	+	0.953637i	$0.597307\pi$
$318$	15.6679	−	0.431617i	0.878615	−	0.0242039i
$319$	−13.2125	+	7.62822i	−0.739756	+	0.427098i
$320$	15.2276	−	0.523198i	0.851248	−	0.0292477i
$321$			5.45782i			0.304626i
$322$	−6.07907	+	10.6281i	−0.338774	+	0.592282i
$323$	−1.37018	−	0.567546i	−0.0762387	−	0.0315791i
$324$	−0.360466	−	6.53760i	−0.0200259	−	0.363200i
$325$	−5.76569	+	7.51400i	−0.319823	+	0.416802i
$326$	7.41371	+	2.83429i	0.410607	+	0.156977i
$327$	1.22181	+	4.55987i	0.0675664	+	0.252161i
$328$	2.22213	−	2.62340i	0.122697	−	0.144853i
$329$	3.74788	+	1.09927i	0.206628	+	0.0606048i
$330$	−1.83217	+	17.6631i	−0.100857	+	0.972321i
$331$	−3.57924	+	27.1870i	−0.196733	+	1.49433i	0.553328	+	0.832963i	$0.313358\pi$
$331$	−3.57924	+	27.1870i	−0.196733	+	1.49433i	−0.750061	+	0.661369i	$0.769976\pi$
$332$	9.06736	−	7.78704i	0.497636	−	0.427369i
$333$	1.72205	+	13.0803i	0.0943680	+	0.716796i
$334$	15.6043	+	3.72381i	0.853829	+	0.203758i
$335$			18.0912i			0.988429i
$336$	11.5499	+	7.36796i	0.630099	+	0.401955i
$337$		−	16.1002i		−	0.877036i	−0.898722	−	0.438518i	$-0.855503\pi$
$337$		−	16.1002i		−	0.877036i	0.898722	−	0.438518i	$-0.144497\pi$
$338$	11.3620	−	47.6117i	0.618014	−	2.58973i
$339$	2.09137	+	15.8855i	0.113588	+	0.862784i
$340$	3.95558	+	0.300481i	0.214522	+	0.0162959i
$341$	−2.04434	+	15.5283i	−0.110707	+	0.840905i
$342$	−2.65265	−	0.275156i	−0.143439	−	0.0148787i
$343$	−13.9859	+	12.1406i	−0.755167	+	0.655532i
$344$	16.1597	−	8.31704i	0.871271	−	0.448425i
$345$	−2.08812	−	7.79298i	−0.112421	−	0.419560i
$346$	−1.22353	+	3.20041i	−0.0657773	+	0.172055i
$347$	10.2210	−	13.3202i	0.548691	−	0.715068i	−0.433877	−	0.900972i	$-0.642855\pi$
$347$	10.2210	−	13.3202i	0.548691	−	0.715068i	0.982568	+	0.185904i	$0.0595214\pi$
$348$	−5.77771	−	5.17387i	−0.309718	−	0.277348i
$349$	15.7087	+	6.50674i	0.840865	+	0.348298i	0.761195	−	0.648523i	$-0.224613\pi$
$349$	15.7087	+	6.50674i	0.840865	+	0.348298i	0.0796707	+	0.996821i	$0.474613\pi$
$350$	2.58585	+	4.43736i	0.138220	+	0.237187i
$351$			38.6255i			2.06168i
$352$	24.8517	−	14.5745i	1.32460	−	0.776823i
$353$	12.0664	−	6.96653i	0.642229	−	0.370791i	−0.143244	−	0.989687i	$-0.545753\pi$
$353$	12.0664	−	6.96653i	0.642229	−	0.370791i	0.785473	+	0.618897i	$0.212420\pi$
$354$	0.567697	+	20.6077i	0.0301728	+	1.09529i
$355$	−13.4857	−	17.5749i	−0.715748	−	0.932781i
$356$	−4.10711	+	19.5844i	−0.217676	+	1.03797i
$357$	2.77799	+	2.23729i	0.147027	+	0.118410i
$358$	−9.84891	−	12.1286i	−0.520531	−	0.641017i
$359$	−28.3121	+	7.58620i	−1.49426	+	0.400384i	−0.911171	−	0.412028i	$-0.864821\pi$
$359$	−28.3121	+	7.58620i	−1.49426	+	0.400384i	−0.583084	+	0.812412i	$0.698154\pi$
$360$	6.97151	−	1.51161i	0.367431	−	0.0796691i
$361$	−4.39269	+	16.3937i	−0.231194	+	0.862829i
$362$	−3.42226	−	2.47931i	−0.179870	−	0.130310i
$363$	7.40026	+	17.8658i	0.388413	+	0.937711i
$364$	−29.6543	−	21.3015i	−1.55431	−	1.11650i
$365$	3.18337	+	1.31860i	0.166625	+	0.0690185i
$366$	−23.0191	−	5.49327i	−1.20323	−	0.287138i
$367$	−10.1024	+	5.83264i	−0.527343	+	0.304462i	−0.739934	−	0.672680i	$-0.765143\pi$
$367$	−10.1024	+	5.83264i	−0.527343	+	0.304462i	0.212591	+	0.977141i	$0.431810\pi$
$368$	−8.18183	+	10.2169i	−0.426508	+	0.532595i
$369$	0.804816	−	1.39398i	0.0418970	−	0.0725678i
$370$	25.7195	−	7.65654i	1.33709	−	0.398044i
$371$	−9.15790	+	20.7180i	−0.475454	+	1.07563i
$372$	−7.82472	+	1.47227i	−0.405693	+	0.0763335i
$373$	−2.57965	−	0.339617i	−0.133569	−	0.0175847i	0.0634451	−	0.997985i	$-0.479791\pi$
$373$	−2.57965	−	0.339617i	−0.133569	−	0.0175847i	−0.197014	+	0.980401i	$0.563125\pi$
$374$	6.84833	−	3.06025i	0.354119	−	0.158242i
$375$	−15.1763	−	4.06648i	−0.783702	−	0.209992i
$376$	3.77600	+	1.78217i	0.194732	+	0.0919086i
$377$	14.6159	+	14.6159i	0.752757	+	0.752757i
$378$	19.3829	+	7.93711i	0.996946	+	0.408241i
$379$	2.88601	+	6.96745i	0.148244	+	0.357894i	0.980506	−	0.196490i	$-0.0629542\pi$
$379$	2.88601	+	6.96745i	0.148244	+	0.357894i	−0.832262	+	0.554383i	$0.812954\pi$
$380$	0.298636	+	5.41622i	0.0153197	+	0.277846i
$381$	0.457481	+	3.47491i	0.0234375	+	0.178025i
$382$	−0.247926	−	8.99987i	−0.0126850	−	0.460473i
$383$	11.5792	−	20.0558i	0.591670	−	1.02480i	−0.402338	−	0.915491i	$-0.631802\pi$
$383$	11.5792	−	20.0558i	0.591670	−	1.02480i	0.994008	−	0.109311i	$-0.0348644\pi$
$384$	10.9768	+	9.69583i	0.560158	+	0.494788i
$385$	−21.9176	−	13.3505i	−1.11702	−	0.680407i
$386$	0.871198	−	1.60977i	0.0443428	−	0.0819350i
$387$	6.75060	−	5.17992i	0.343152	−	0.263310i
$388$	−15.6683	−	7.92975i	−0.795436	−	0.402572i
$389$	19.0847	+	14.6442i	0.967633	+	0.742491i	0.966276	−	0.257508i	$-0.0829015\pi$
$389$	19.0847	+	14.6442i	0.967633	+	0.742491i	0.00135666	+	0.999999i	$0.499568\pi$
$390$	23.7577	−	3.79600i	1.20302	−	0.192218i
$391$	−2.40975	+	2.40975i	−0.121866	+	0.121866i
$392$	−16.7831	+	10.5038i	−0.847672	+	0.530520i
$393$	−4.31243	−	4.31243i	−0.217533	−	0.217533i
$394$	−2.03461	−	1.47400i	−0.102502	−	0.0742592i
$395$	−14.4614	+	18.8464i	−0.727631	+	0.948268i
$396$	10.2328	−	8.78792i	0.514218	−	0.441609i
$397$	−8.19865	−	10.6847i	−0.411479	−	0.536249i	0.540932	−	0.841066i	$-0.318071\pi$
$397$	−8.19865	−	10.6847i	−0.411479	−	0.536249i	−0.952411	+	0.304817i	$0.901405\pi$
$398$	3.73008	+	12.5299i	0.186972	+	0.628067i
$399$	−2.53728	+	4.16545i	−0.127023	+	0.208533i
$400$	1.99547	+	5.11497i	0.0997734	+	0.255749i
$401$	−4.45802	−	2.57384i	−0.222623	−	0.128531i	0.384541	−	0.923108i	$-0.374360\pi$
$401$	−4.45802	−	2.57384i	−0.222623	−	0.128531i	−0.607164	+	0.794576i	$0.707693\pi$
$402$	−11.9532	+	12.6304i	−0.596169	+	0.629946i
$403$	21.0384	−	2.76975i	1.04800	−	0.137971i
$404$	1.57048	+	3.26965i	0.0781345	+	0.162671i
$405$	−5.76050	+	2.38608i	−0.286241	+	0.118565i
$406$	10.3379	−	4.33107i	0.513061	−	0.214948i
$407$	35.8792	−	35.8792i	1.77847	−	1.77847i
$408$	2.56306	+	2.82330i	0.126890	+	0.139774i
$409$	−0.296281	+	1.10573i	−0.0146501	+	0.0546751i	−0.972864	−	0.231378i	$-0.925677\pi$
$409$	−0.296281	+	1.10573i	−0.0146501	+	0.0546751i	0.958214	+	0.286053i	$0.0923433\pi$
$410$	−3.05813	−	1.16913i	−0.151030	−	0.0577393i
$411$	0.486010	−	3.69161i	0.0239731	−	0.182094i
$412$	−6.75569	−	1.41676i	−0.332829	−	0.0697987i
$413$	−27.2500	−	12.0452i	−1.34089	−	0.592706i
$414$	−2.91678	+	5.38951i	−0.143352	+	0.264880i
$415$	−9.85702	−	5.69095i	−0.483862	−	0.279358i
$416$	−27.7877	−	27.4121i	−1.36240	−	1.34399i
$417$	−7.44080	−	12.8879i	−0.364378	−	0.631121i
$418$	5.37108	+	8.73809i	0.262708	+	0.427394i
$419$	10.7109	−	25.8583i	0.523261	−	1.26326i	−0.412606	−	0.910909i	$-0.635382\pi$
$419$	10.7109	−	25.8583i	0.523261	−	1.26326i	0.935867	−	0.352353i	$-0.114618\pi$
$420$	2.97705	−	12.7020i	0.145265	−	0.619794i
$421$	−10.9194	+	4.52297i	−0.532179	+	0.220436i	−0.632557	−	0.774514i	$-0.717995\pi$
$421$	−10.9194	+	4.52297i	−0.532179	+	0.220436i	0.100378	+	0.994949i	$0.467995\pi$
$422$	27.9240	−	4.46169i	1.35932	−	0.217192i
$423$	1.88826	+	0.505959i	0.0918105	+	0.0246005i
$424$	−13.1058	+	20.3627i	−0.636476	+	0.988902i
$425$	0.369978	+	1.38078i	0.0179466	+	0.0669775i
$426$	2.19699	−	21.1801i	0.106444	−	1.02618i
$427$	21.4523	−	26.6368i	1.03815	−	1.28904i
$428$	−6.96218	−	4.75712i	−0.336530	−	0.229944i
$429$	36.0913	−	27.6938i	1.74251	−	1.33707i
$430$	−12.5704	−	11.8964i	−0.606199	−	0.573695i
$431$	−16.1978	−	28.0554i	−0.780219	−	1.35138i	−0.931814	−	0.362937i	$-0.881774\pi$
$431$	−16.1978	−	28.0554i	−0.780219	−	1.35138i	0.151595	−	0.988443i	$-0.451559\pi$
$432$	19.1550	+	11.5952i	0.921595	+	0.557876i
$433$	−23.2185			−1.11581			−0.557905	−	0.829905i	$-0.688395\pi$
$433$	−23.2185			−1.11581			−0.557905	+	0.829905i	$0.688395\pi$
$434$	2.93325	−	11.1265i	0.140800	−	0.534090i
$435$	−2.82636	+	6.82344i	−0.135514	+	0.327159i
$436$	−6.88166	−	2.41587i	−0.329572	−	0.115699i
$437$	−3.69700	−	2.83681i	−0.176852	−	0.135703i
$438$	1.35125	+	3.02388i	0.0645653	+	0.144487i
$439$	−19.8391	+	5.31588i	−0.946870	+	0.253713i	−0.699034	−	0.715089i	$-0.746386\pi$
$439$	−19.8391	+	5.31588i	−0.946870	+	0.253713i	−0.247836	+	0.968802i	$0.579720\pi$
$440$	−20.9347	−	17.7326i	−0.998021	−	0.845368i
$441$	−6.85533	+	6.23933i	−0.326444	+	0.297111i
$442$	−6.40629	−	7.88913i	−0.304716	−	0.375248i
$443$	−24.8805	−	3.27557i	−1.18211	−	0.155627i	−0.486258	−	0.873816i	$-0.661638\pi$
$443$	−24.8805	−	3.27557i	−1.18211	−	0.155627i	−0.695849	+	0.718188i	$0.744972\pi$
$444$	23.0148	+	11.6478i	1.09223	+	0.552782i
$445$	18.8926	−	2.48726i	0.895594	−	0.117907i
$446$	−4.03044	−	6.55704i	−0.190847	−	0.310485i
$447$	−3.42059			−0.161788
$448$	−19.4659	+	8.31141i	−0.919676	+	0.392677i
$449$	20.2136			0.953938			0.476969	−	0.878920i	$-0.341735\pi$
$449$	20.2136			0.953938			0.476969	+	0.878920i	$0.341735\pi$
$450$	1.34608	+	2.18991i	0.0634548	+	0.103233i
$451$	−6.13768	+	0.808040i	−0.289012	+	0.0380491i
$452$	−22.0870	−	11.1783i	−1.03888	−	0.525781i
$453$	−1.69482	−	0.223127i	−0.0796295	−	0.0104834i
$454$	0.191147	+	0.235392i	0.00897099	+	0.0110475i
$455$	−9.78594	+	33.3644i	−0.458772	+	1.56415i
$456$	−3.37009	+	3.97864i	−0.157819	+	0.186317i
$457$	21.4011	−	5.73442i	1.00110	−	0.268245i	0.279196	−	0.960234i	$-0.409932\pi$
$457$	21.4011	−	5.73442i	1.00110	−	0.268245i	0.721908	+	0.691989i	$0.243266\pi$
$458$	12.3179	+	27.5655i	0.575579	+	1.28805i
$459$	4.62504	+	3.54892i	0.215879	+	0.165649i
$460$	11.7610	+	4.12881i	0.548360	+	0.192507i
$461$	−9.74244	+	23.5203i	−0.453751	+	1.09545i	0.517134	+	0.855904i	$0.326999\pi$
$461$	−9.74244	+	23.5203i	−0.453751	+	1.09545i	−0.970885	+	0.239546i	$0.923001\pi$
$462$	−6.48082	−	23.8019i	−0.301515	−	1.10737i
$463$	−12.3133			−0.572248			−0.286124	−	0.958193i	$-0.592367\pi$
$463$	−12.3133			−0.572248			−0.286124	+	0.958193i	$0.592367\pi$
$464$	11.6359	−	2.86061i	0.540183	−	0.132801i
$465$	3.79106	+	6.56631i	0.175806	+	0.304505i
$466$	4.15580	+	3.93297i	0.192514	+	0.182191i
$467$	22.9315	−	17.5960i	1.06114	−	0.814245i	0.0779780	−	0.996955i	$-0.475154\pi$
$467$	22.9315	−	17.5960i	1.06114	−	0.814245i	0.983167	+	0.182710i	$0.0584869\pi$
$468$	−15.0887	−	10.3098i	−0.697477	−	0.476573i
$469$	−9.06912	−	23.4382i	−0.418773	−	1.08227i
$470$	0.410246	−	3.95499i	0.0189232	−	0.182430i
$471$	8.01092	+	29.8971i	0.369123	+	1.37759i
$472$	−26.7827	−	17.2379i	−1.23278	−	0.793437i
$473$	−31.6103	−	8.46995i	−1.45344	−	0.389449i
$474$	−22.5483	+	3.60277i	−1.03568	+	0.165481i
$475$	−1.80589	+	0.748023i	−0.0828598	+	0.0343216i
$476$	−5.27531	+	1.59364i	−0.241793	+	0.0730444i
$477$	−4.33865	+	10.4744i	−0.198653	+	0.479591i
$478$	−2.02396	−	3.29274i	−0.0925739	−	0.150606i
$479$	10.5049	+	18.1950i	0.479980	+	0.831350i	0.999736	−	0.0229647i	$-0.00731053\pi$
$479$	10.5049	+	18.1950i	0.479980	+	0.831350i	−0.519756	+	0.854315i	$0.673977\pi$
$480$	5.24948	−	12.9214i	0.239605	−	0.589776i
$481$	−59.5356	−	34.3729i	−2.71459	−	1.56727i
$482$	10.1083	−	18.6778i	0.460421	−	0.850748i
$483$	6.61189	+	9.04945i	0.300851	+	0.411764i
$484$	−29.2404	−	6.13210i	−1.32911	−	0.278732i
$485$	−2.18276	+	16.5797i	−0.0991138	+	0.752844i
$486$	16.5853	+	6.34063i	0.752326	+	0.287617i
$487$	−2.34437	+	8.74932i	−0.106234	+	0.396469i	−0.998482	−	0.0550752i	$-0.982460\pi$
$487$	−2.34437	+	8.74932i	−0.106234	+	0.396469i	0.892249	+	0.451545i	$0.149127\pi$
$488$	27.0712	−	24.5758i	1.22545	−	1.11250i
$489$	5.13730	−	5.13730i	0.232317	−	0.232317i
$490$	14.7319	+	11.7668i	0.665518	+	0.531568i
$491$	−9.93228	+	4.11409i	−0.448238	+	0.185666i	−0.595372	−	0.803450i	$-0.702995\pi$
$491$	−9.93228	+	4.11409i	−0.448238	+	0.185666i	0.147134	+	0.989117i	$0.452995\pi$
$492$	−1.36256	−	2.83678i	−0.0614292	−	0.127892i
$493$	3.09303	−	0.407205i	0.139303	−	0.0183396i
$494$	9.55190	−	10.0931i	0.429760	−	0.454109i
$495$	−11.1240	−	6.42242i	−0.499985	−	0.288666i
$496$	4.94208	−	11.2647i	0.221906	−	0.505801i
$497$	26.2818	+	16.0089i	1.17890	+	0.718097i
$498$	−3.12157	−	10.4858i	−0.139881	−	0.469881i
$499$	5.95194	+	7.75672i	0.266445	+	0.347238i	0.907345	−	0.420386i	$-0.138105\pi$
$499$	5.95194	+	7.75672i	0.266445	+	0.347238i	−0.640900	+	0.767624i	$0.721439\pi$
$500$	18.4153	−	15.8150i	0.823555	−	0.707268i
$501$	8.93946	−	11.6501i	0.399386	−	0.520489i
$502$	28.3035	+	20.5049i	1.26325	+	0.915177i
$503$	21.5342	+	21.5342i	0.960163	+	0.960163i	0.999236	−	0.0390731i	$-0.0124405\pi$
$503$	21.5342	+	21.5342i	0.960163	+	0.960163i	−0.0390731	+	0.999236i	$0.512441\pi$
$504$	−8.27420	+	5.45319i	−0.368562	+	0.242904i
$505$	2.44248	−	2.44248i	0.108689	−	0.108689i
$506$	23.2737	−	3.71867i	1.03464	−	0.165315i
$507$	−35.5468	−	27.2760i	−1.57869	−	1.21137i
$508$	−4.83146	−	2.44521i	−0.214361	−	0.108489i
$509$	10.7003	−	8.21064i	0.474283	−	0.363930i	−0.343788	−	0.939047i	$-0.611710\pi$
$509$	10.7003	−	8.21064i	0.474283	−	0.363930i	0.818071	+	0.575117i	$0.195044\pi$
$510$	1.72833	−	3.19354i	0.0765316	−	0.141412i
$511$	−4.78524	−	0.112491i	−0.211687	−	0.00497630i
$512$	−21.9359	+	5.55134i	−0.969438	+	0.245337i
$513$	−3.98579	+	6.90359i	−0.175977	+	0.304801i
$514$	0.536215	+	19.4649i	0.0236514	+	0.858561i
$515$	0.857986	+	6.51705i	0.0378074	+	0.287176i
$516$	−0.915882	−	16.6109i	−0.0403195	−	0.731255i
$517$	−2.87718	−	6.94613i	−0.126538	−	0.305491i
$518$	−29.4827	+	22.8126i	−1.29540	+	1.00233i
$519$	2.21772	+	2.21772i	0.0973469	+	0.0973469i
$520$	−15.8653	+	33.6147i	−0.695738	+	1.47410i
$521$	29.1247	+	7.80395i	1.27598	+	0.341897i	0.832318	−	0.554298i	$-0.187013\pi$
$521$	29.1247	+	7.80395i	1.27598	+	0.341897i	0.443659	+	0.896195i	$0.353680\pi$
$522$	5.12183	−	2.28874i	0.224177	−	0.100176i
$523$	−0.0554101	−	0.00729487i	−0.00242291	−	0.000318982i	0.129315	−	0.991604i	$-0.458722\pi$
$523$	−0.0554101	−	0.00729487i	−0.00242291	−	0.000318982i	−0.131738	+	0.991285i	$0.542056\pi$
$524$	9.25986	−	1.74229i	0.404519	−	0.0761125i
$525$	4.67406	−	0.503915i	0.203993	−	0.0219927i
$526$	17.8161	−	5.30377i	0.776821	−	0.231255i
$527$	1.60136	−	2.77363i	0.0697563	−	0.120821i
$528$	−2.89932	−	26.2118i	−0.126177	−	1.14072i
$529$	10.6452	−	6.14599i	0.462834	−	0.267217i
$530$	22.4305	+	5.35281i	0.974318	+	0.232511i
$531$	−13.7768	−	5.70654i	−0.597863	−	0.247643i
$532$	−3.10205	−	6.86730i	−0.134491	−	0.297735i
$533$	3.20969	+	7.74887i	0.139027	+	0.335641i
$534$	14.8332	+	10.7461i	0.641896	+	0.465031i
$535$	−2.07828	+	7.75626i	−0.0898520	+	0.335332i
$536$	−5.69316	−	26.2567i	−0.245907	−	1.13412i
$537$	−13.8142	+	3.70149i	−0.596125	+	0.159731i
$538$	−5.90193	−	7.26803i	−0.254450	−	0.313347i
$539$	35.0880	+	6.30910i	1.51135	+	0.271752i
$540$	4.37647	−	20.8688i	0.188333	−	0.898050i
$541$	−18.9597	−	24.7087i	−0.815139	−	1.06231i	−0.996878	−	0.0789633i	$-0.974839\pi$
$541$	−18.9597	−	24.7087i	−0.815139	−	1.06231i	0.181738	−	0.983347i	$-0.441828\pi$
$542$	0.928033	+	33.6881i	0.0398624	+	1.44703i
$543$	−3.35005	+	1.93415i	−0.143764	+	0.0830023i
$544$	−5.83549	+	0.808688i	−0.250194	+	0.0346722i
$545$			6.94540i			0.297508i
$546$	−28.8764	+	16.8276i	−1.23580	+	0.720156i
$547$	−34.0676	−	14.1112i	−1.45662	−	0.603353i	−0.492860	−	0.870109i	$-0.664048\pi$
$547$	−34.0676	−	14.1112i	−1.45662	−	0.603353i	−0.963764	+	0.266755i	$0.914048\pi$
$548$	4.28552	+	3.83763i	0.183068	+	0.163936i
$549$	10.4208	−	13.5806i	0.444748	−	0.579606i
$550$	3.53035	−	9.23443i	0.150535	−	0.393757i
$551$	1.10410	+	4.12055i	0.0470361	+	0.175541i
$552$	5.48298	+	10.6532i	0.233371	+	0.453431i
$553$	9.28780	−	31.6661i	0.394958	−	1.34658i
$554$	14.0136	+	1.45361i	0.595379	+	0.0617578i
$555$	3.20620	−	24.3535i	0.136096	−	1.03375i
$556$	22.9257	+	1.74152i	0.972266	+	0.0738569i
$557$	1.46204	+	11.1053i	0.0619485	+	0.470545i	0.994099	+	0.108475i	$0.0345967\pi$
$557$	1.46204	+	11.1053i	0.0619485	+	0.470545i	−0.932151	+	0.362070i	$0.882070\pi$
$558$	1.33683	−	5.60189i	0.0565927	−	0.237147i
$559$			44.3376i			1.87528i
$560$	13.6082	+	14.8689i	0.575053	+	0.628325i
$561$		−	6.86612i		−	0.289888i
$562$	−33.3859	−	7.96721i	−1.40830	−	0.336077i
$563$	0.415711	+	3.15763i	0.0175201	+	0.133078i	0.997970	−	0.0636927i	$-0.0202877\pi$
$563$	0.415711	+	3.15763i	0.0175201	+	0.133078i	−0.980449	+	0.196771i	$0.936954\pi$
$564$	2.89954	−	2.49012i	0.122093	−	0.104853i
$565$	−3.07695	+	23.3717i	−0.129448	+	0.983257i
$566$	2.15873	−	20.8114i	0.0907383	−	0.874767i
$567$	6.26690	−	5.97902i	0.263185	−	0.251095i
$568$	25.1032	+	21.2635i	1.05331	+	0.892196i
$569$	−8.44569	−	31.5198i	−0.354062	−	1.32138i	−0.881661	−	0.471883i	$-0.843574\pi$
$569$	−8.44569	−	31.5198i	−0.354062	−	1.32138i	0.527599	−	0.849493i	$-0.323092\pi$
$570$	4.63796	+	1.77311i	0.194263	+	0.0742673i
$571$	−17.4697	+	22.7670i	−0.731084	+	0.952768i	−0.999946	−	0.0104112i	$-0.996686\pi$
$571$	−17.4697	+	22.7670i	−0.731084	+	0.952768i	0.268861	+	0.963179i	$0.413353\pi$
$572$	3.86941	+	70.1776i	0.161788	+	2.93427i
$573$	−7.61394	−	3.15380i	−0.318077	−	0.131752i
$574$	4.54805	−	0.0183617i	0.189832	−	0.000766403i
$575$			4.49160i			0.187313i
$576$	−9.64240	+	4.38776i	−0.401767	+	0.182823i
$577$	−8.18229	+	4.72405i	−0.340633	+	0.196665i	−0.660552	−	0.750780i	$-0.729678\pi$
$577$	−8.18229	+	4.72405i	−0.340633	+	0.196665i	0.319919	+	0.947445i	$0.396344\pi$
$578$	22.4993	−	0.619804i	0.935846	−	0.0257804i
$579$	−1.01996	−	1.32924i	−0.0423882	−	0.0552414i
$580$	−6.24070	−	9.55282i	−0.259131	−	0.396659i
$581$	15.6232	+	2.43162i	0.648158	+	0.100881i
$582$	−12.4783	+	10.1329i	−0.517244	+	0.420022i
$583$	42.1180	−	11.2855i	1.74435	−	0.467397i
$584$	−5.03513	−	0.911960i	−0.208355	−	0.0377372i
$585$	−4.50415	+	16.8097i	−0.186223	+	0.694996i
$586$	22.7285	−	31.3727i	0.938904	−	1.29600i
$587$	1.45514	+	3.51303i	0.0600602	+	0.144998i	0.951061	−	0.309004i	$-0.0999957\pi$
$587$	1.45514	+	3.51303i	0.0600602	+	0.144998i	−0.891000	+	0.454002i	$0.849996\pi$
$588$	2.51056	+	17.9485i	0.103534	+	0.740184i
$589$	4.04603	+	1.67592i	0.166714	+	0.0690551i
$590$	−7.04045	+	29.5024i	−0.289851	+	1.21459i
$591$	−1.99167	+	1.14989i	−0.0819265	+	0.0473003i
$592$	−34.9184	+	19.2060i	−1.43514	+	0.789362i
$593$	24.2502	−	42.0026i	0.995837	−	1.72484i	0.418976	−	0.907997i	$-0.362389\pi$
$593$	24.2502	−	42.0026i	0.995837	−	1.72484i	0.576860	−	0.816843i	$-0.304278\pi$
$594$	−11.5036	−	38.6423i	−0.471998	−	1.58551i
$595$	3.09594	+	4.23731i	0.126921	+	0.173713i
$596$	2.98144	−	4.36341i	0.122124	−	0.178732i
$597$	11.8644	+	1.56198i	0.485580	+	0.0639278i
$598$	−13.0276	−	29.1537i	−0.532740	−	1.19218i
$599$	15.6944	+	4.20531i	0.641257	+	0.171824i	0.564773	−	0.825246i	$-0.308964\pi$
$599$	15.6944	+	4.20531i	0.641257	+	0.171824i	0.0764845	+	0.997071i	$0.475630\pi$
$600$	5.01988	+	0.242535i	0.204936	+	0.00990144i
$601$	11.9648	+	11.9648i	0.488053	+	0.488053i	0.907691	−	0.419638i	$-0.137843\pi$
$601$	11.9648	+	11.9648i	0.488053	+	0.488053i	−0.419638	+	0.907691i	$0.637843\pi$
$602$	22.2493	+	9.11089i	0.906813	+	0.371332i
$603$	−4.81362	−	11.6211i	−0.196026	−	0.473248i
$604$	1.76186	−	1.96748i	0.0716890	−	0.0800558i
$605$	3.71359	+	28.2075i	0.150979	+	1.14680i
$606$	3.31900	−	0.0914311i	0.134825	−	0.00371414i
$607$	1.40684	−	2.43672i	0.0571020	−	0.0989035i	−0.836061	−	0.548636i	$-0.815147\pi$
$607$	1.40684	−	2.43672i	0.0571020	−	0.0989035i	0.893163	+	0.449732i	$0.148481\pi$
$608$	−2.13787	−	7.76685i	−0.0867019	−	0.314987i
$609$	0.241120	−	10.2570i	0.00977068	−	0.415634i
$610$	−30.6212	−	16.5721i	−1.23982	−	0.670983i
$611$	−8.08131	+	6.20101i	−0.326935	+	0.250866i
$612$	−2.62086	+	0.859464i	−0.105942	+	0.0347418i
$613$	4.06770	+	3.12126i	0.164293	+	0.126066i	0.687636	−	0.726056i	$-0.258649\pi$
$613$	4.06770	+	3.12126i	0.164293	+	0.126066i	−0.523343	+	0.852122i	$0.675315\pi$
$614$	0.254872	+	1.59514i	0.0102858	+	0.0643748i
$615$	−2.11912	+	2.11912i	−0.0854512	+	0.0854512i
$616$	36.0113	+	12.4790i	1.45094	+	0.502793i
$617$	6.91032	+	6.91032i	0.278199	+	0.278199i	0.832390	−	0.554191i	$-0.186972\pi$
$617$	6.91032	+	6.91032i	0.278199	+	0.278199i	−0.554191	+	0.832390i	$0.686972\pi$
$618$	−3.70692	+	5.11676i	−0.149114	+	0.205826i
$619$	9.94309	−	12.9581i	0.399647	−	0.520830i	−0.549572	−	0.835446i	$-0.685209\pi$
$619$	9.94309	−	12.9581i	0.399647	−	0.520830i	0.949219	+	0.314617i	$0.101876\pi$
$620$	−11.6806	−	0.887298i	−0.469102	−	0.0356347i
$621$	11.1511	+	14.5324i	0.447478	+	0.583165i
$622$	9.88752	−	2.94346i	0.396453	−	0.118022i
$623$	−23.2295	+	12.6932i	−0.930670	+	0.508543i
$624$	−33.2861	+	12.9857i	−1.33251	+	0.519842i
$625$	−14.0754	−	8.12645i	−0.563017	−	0.325058i
$626$	5.98343	+	5.66261i	0.239146	+	0.226324i
$627$	9.30841	−	1.22547i	0.371742	−	0.0489408i
$628$	−45.1202	−	15.8398i	−1.80049	−	0.632078i
$629$	−9.58598	+	3.97064i	−0.382218	+	0.158320i
$630$	7.50981	+	5.71446i	0.299198	+	0.227669i
$631$	32.1040	−	32.1040i	1.27804	−	1.27804i	0.336278	−	0.941763i	$-0.390832\pi$
$631$	32.1040	−	32.1040i	1.27804	−	1.27804i	0.941763	−	0.336278i	$-0.109168\pi$
$632$	15.0577	−	31.9036i	0.598962	−	1.26906i
$633$	6.69949	−	25.0028i	0.266281	−	0.993773i
$634$	−10.3107	+	26.9699i	−0.409490	+	1.07111i
$635$	−0.673073	+	5.11250i	−0.0267101	+	0.202883i
$636$	12.1231	+	18.5572i	0.480714	+	0.735842i
$637$	−4.04734	−	48.1311i	−0.160362	−	1.90702i
$638$	−18.9752	−	10.2693i	−0.751236	−	0.406565i
$639$	13.3389	+	7.70125i	0.527681	+	0.304657i
$640$	11.9074	+	17.9589i	0.470680	+	0.709886i
$641$	4.77006	+	8.26198i	0.188406	+	0.326329i	0.944719	−	0.327881i	$-0.106335\pi$
$641$	4.77006	+	8.26198i	0.188406	+	0.326329i	−0.756313	+	0.654210i	$0.773001\pi$
$642$	−6.57563	+	4.04187i	−0.259519	+	0.159520i
$643$	1.30599	−	3.15294i	0.0515033	−	0.124340i	−0.896034	−	0.443986i	$-0.853564\pi$
$643$	1.30599	−	3.15294i	0.0515033	−	0.124340i	0.947537	+	0.319646i	$0.103564\pi$
$644$	−17.3068	+	0.546697i	−0.681984	+	0.0215429i
$645$	−14.6364	+	6.06261i	−0.576309	+	0.238715i
$646$	−0.330921	−	2.07111i	−0.0130199	−	0.0814866i
$647$	22.6575	+	6.07105i	0.890757	+	0.238678i	0.675043	−	0.737779i	$-0.264125\pi$
$647$	22.6575	+	6.07105i	0.890757	+	0.238678i	0.215715	+	0.976456i	$0.430792\pi$
$648$	7.60961	−	5.27581i	0.298934	−	0.207253i
$649$	14.8436	+	55.3970i	0.582661	+	2.17452i
$650$	−13.3228	−	1.38195i	−0.522563	−	0.0542047i
$651$	−8.20321	−	6.60656i	−0.321509	−	0.258931i
$652$	2.07556	+	11.0311i	0.0812851	+	0.432010i
$653$	−38.5094	+	29.5493i	−1.50699	+	1.15635i	−0.562963	+	0.826482i	$0.690339\pi$
$653$	−38.5094	+	29.5493i	−1.50699	+	1.15635i	−0.944026	+	0.329871i	$0.892995\pi$
$654$	−4.58893	+	4.84893i	−0.179442	+	0.189608i
$655$	−4.48638	−	7.77064i	−0.175297	−	0.303624i
$656$	4.80632	+	0.734450i	0.187655	+	0.0286755i
$657$	−2.39572			−0.0934659
$658$	1.45114	+	5.32956i	0.0565713	+	0.207768i
$659$	−12.9028	+	31.1501i	−0.502621	+	1.21343i	0.445430	+	0.895317i	$0.353051\pi$
$659$	−12.9028	+	31.1501i	−0.502621	+	1.21343i	−0.948051	+	0.318118i	$0.896949\pi$
$660$	−22.6375	+	10.8732i	−0.881162	+	0.423241i
$661$	24.6657	+	18.9267i	0.959386	+	0.736163i	0.964571	−	0.263824i	$-0.0849837\pi$
$661$	24.6657	+	18.9267i	0.959386	+	0.736163i	−0.00518466	+	0.999987i	$0.501650\pi$
$662$	−35.4058	+	15.8214i	−1.37608	+	0.614918i
$663$	−8.98551	+	2.40766i	−0.348968	+	0.0935057i
$664$	16.0969	+	5.15763i	0.624679	+	0.200155i
$665$	−5.19196	+	4.95346i	−0.201335	+	0.192087i
$666$	−14.4840	+	11.7616i	−0.561242	+	0.455751i
$667$	9.71865	+	1.27948i	0.376308	+	0.0495418i
$668$	7.06951	+	21.5579i	0.273528	+	0.834100i
$669$	−6.98500	+	0.919592i	−0.270056	+	0.0355535i
$670$	−21.7965	+	13.3977i	−0.842071	+	0.517599i
$671$	−65.8357			−2.54156
$672$	−0.323526	+	19.3719i	−0.0124803	+	0.747286i
$673$	40.9511			1.57855			0.789274	−	0.614041i	$-0.210457\pi$
$673$	40.9511			1.57855			0.789274	+	0.614041i	$0.210457\pi$
$674$	19.3977	−	11.9233i	0.747172	−	0.459267i
$675$	7.61783	−	1.00291i	0.293210	−	0.0386019i
$676$	65.7773	−	21.5704i	2.52990	−	0.829632i
$677$	−16.3601	−	2.15385i	−0.628772	−	0.0827793i	−0.190596	−	0.981669i	$-0.561042\pi$
$677$	−16.3601	−	2.15385i	−0.628772	−	0.0827793i	−0.438176	+	0.898889i	$0.644375\pi$
$678$	−17.5902	+	14.2840i	−0.675549	+	0.548573i
$679$	−5.48350	−	22.5741i	−0.210437	−	0.866314i
$680$	2.56734	+	4.98825i	0.0984532	+	0.191291i
$681$	0.268105	−	0.0718385i	0.0102738	−	0.00275286i
$682$	−20.2226	+	9.03668i	−0.774364	+	0.346032i
$683$	1.45485	+	1.11634i	0.0556682	+	0.0427157i	0.636221	−	0.771507i	$-0.280497\pi$
$683$	1.45485	+	1.11634i	0.0556682	+	0.0427157i	−0.580553	+	0.814223i	$0.697163\pi$
$684$	−1.63295	−	3.39971i	−0.0624375	−	0.129991i
$685$	2.09641	−	5.06118i	0.0800996	−	0.193378i
$686$	−24.9846	−	7.85939i	−0.953916	−	0.300073i
$687$	27.6371			1.05442
$688$	21.9877	+	13.3100i	0.838274	+	0.507439i
$689$	−29.5380	−	51.1614i	−1.12531	−	1.94909i
$690$	7.84266	−	8.28700i	0.298565	−	0.315481i
$691$	−34.9091	+	26.7867i	−1.32800	+	1.01901i	−0.330846	+	0.943685i	$0.607334\pi$
$691$	−34.9091	+	26.7867i	−1.32800	+	1.01901i	−0.997159	+	0.0753290i	$0.975999\pi$
$692$	−4.76199	+	0.895995i	−0.181024	+	0.0340606i
$693$	17.6312	+	2.74416i	0.669755	+	0.104242i
$694$	23.6176	+	2.44982i	0.896513	+	0.0929940i
$695$	−5.66676	−	21.1487i	−0.214953	−	0.802214i
$696$	1.95475	−	10.7926i	0.0740947	−	0.409093i
$697$	1.22276	+	0.327638i	0.0463154	+	0.0124102i
$698$	3.79391	+	23.7446i	0.143601	+	0.898746i
$699$	4.83883	−	2.00431i	0.183021	−	0.0758099i
$700$	−3.43117	+	6.40160i	−0.129686	+	0.241958i
$701$	17.7520	−	42.8570i	0.670483	−	1.61869i	−0.110309	−	0.993897i	$-0.535184\pi$
$701$	17.7520	−	42.8570i	0.670483	−	1.61869i	0.780792	−	0.624791i	$-0.214816\pi$
$702$	−46.5363	+	28.6047i	−1.75640	+	1.07961i
$703$	−7.09392	−	12.2870i	−0.267552	−	0.463414i
$704$	35.9638	+	19.1482i	1.35544	+	0.721675i
$705$	−3.15205	−	1.81984i	−0.118713	−	0.0685391i
$706$	17.3293	+	9.37851i	0.652196	+	0.352965i
$707$	−1.93996	+	4.38878i	−0.0729595	+	0.165057i
$708$	−24.4080	+	15.9453i	−0.917308	+	0.599263i
$709$	−0.156432	+	1.18822i	−0.00587492	+	0.0446245i	−0.994131	−	0.108181i	$-0.965497\pi$
$709$	−0.156432	+	1.18822i	−0.00587492	+	0.0446245i	0.988256	+	0.152805i	$0.0488308\pi$
$710$	11.1874	−	29.2631i	0.419855	−	1.09822i
$711$	4.27487	−	15.9540i	0.160320	−	0.598323i
$712$	−26.6370	+	9.55521i	−0.998263	+	0.358097i
$713$	7.11582	−	7.11582i	0.266490	−	0.266490i
$714$	−0.638223	+	5.00381i	−0.0238849	+	0.187263i
$715$	61.8359	−	25.6133i	2.31253	−	0.957882i
$716$	7.31889	−	20.8481i	0.273520	−	0.779129i
$717$	−3.50765	+	0.461791i	−0.130996	+	0.0172459i
$718$	−30.1069	−	28.4926i	−1.12358	−	1.06333i
$719$	−19.7501	−	11.4027i	−0.736554	−	0.425250i	0.0842609	−	0.996444i	$-0.473147\pi$
$719$	−19.7501	−	11.4027i	−0.736554	−	0.425250i	−0.820815	+	0.571194i	$0.806480\pi$
$720$	6.98406	+	7.27989i	0.260281	+	0.271306i
$721$	−4.37856	−	8.01309i	−0.163066	−	0.298423i
$722$	−23.0044	+	6.84828i	−0.856135	+	0.254867i
$723$	−11.8344	−	15.4229i	−0.440126	−	0.573583i
$724$	0.452688	−	5.95926i	0.0168240	−	0.221474i
$725$	2.50309	−	3.26209i	0.0929625	−	0.121151i
$726$	−16.0445	+	22.1467i	−0.595467	+	0.821940i
$727$	1.25193	+	1.25193i	0.0464316	+	0.0464316i	0.729941	−	0.683510i	$-0.239547\pi$
$727$	1.25193	+	1.25193i	0.0464316	+	0.0464316i	−0.683510	+	0.729941i	$0.739547\pi$
$728$	3.70329	−	51.5029i	0.137253	−	1.90883i
$729$	18.4375	−	18.4375i	0.682869	−	0.682869i
$730$	0.768838	+	4.81186i	0.0284560	+	0.178095i
$731$	5.30902	+	4.07375i	0.196361	+	0.150673i
$732$	−10.4288	−	31.8017i	−0.385458	−	1.17542i
$733$	−19.6153	+	15.0514i	−0.724508	+	0.555935i	−0.903849	−	0.427852i	$-0.859270\pi$
$733$	−19.6153	+	15.0514i	−0.724508	+	0.555935i	0.179340	+	0.983787i	$0.442604\pi$
$734$	−14.5087	−	7.85205i	−0.535527	−	0.289824i
$735$	15.3353	−	7.91740i	0.565651	−	0.292038i
$736$	−18.3686	−	2.29124i	−0.677077	−	0.0844561i
$737$	−24.1886	+	41.8959i	−0.890999	+	1.54326i
$738$	2.27550	−	0.0626849i	0.0837623	−	0.00230746i
$739$	3.92638	+	29.8238i	0.144434	+	1.09709i	0.898089	+	0.439815i	$0.144956\pi$
$739$	3.92638	+	29.8238i	0.144434	+	1.09709i	−0.753654	+	0.657271i	$0.771711\pi$
$740$	28.2716	+	25.3169i	1.03928	+	0.930666i
$741$	−4.86781	−	11.7519i	−0.178824	−	0.431718i
$742$	−31.7433	+	4.30953i	−1.16533	+	0.158208i
$743$	−4.91671	−	4.91671i	−0.180377	−	0.180377i	0.611143	−	0.791520i	$-0.290710\pi$
$743$	−4.91671	−	4.91671i	−0.180377	−	0.180377i	−0.791520	+	0.611143i	$0.790710\pi$
$744$	−7.56851	−	8.33699i	−0.277475	−	0.305649i
$745$	−4.86109	−	1.30252i	−0.178097	−	0.0477208i
$746$	−1.50122	−	3.35949i	−0.0549637	−	0.123000i
$747$	7.84598	+	1.03294i	0.287070	+	0.0377934i
$748$	8.75864	+	5.98461i	0.320248	+	0.218819i
$749$	−1.19568	−	11.0905i	−0.0436891	−	0.405238i
$750$	−6.33971	−	21.2960i	−0.231494	−	0.777622i
$751$	−7.80945	+	13.5264i	−0.284971	+	0.493584i	−0.972602	−	0.232476i	$-0.925317\pi$
$751$	−7.80945	+	13.5264i	−0.284971	+	0.493584i	0.687631	+	0.726060i	$0.258651\pi$
$752$	0.649195	+	5.86917i	0.0236737	+	0.214027i
$753$	27.7062	−	15.9962i	1.00967	−	0.582933i
$754$	−6.78534	+	28.4334i	−0.247108	+	1.03548i
$755$	−2.32359	−	0.962461i	−0.0845640	−	0.0350276i
$756$	4.79156	+	29.2306i	0.174267	+	1.06311i
$757$	6.69326	+	16.1590i	0.243271	+	0.587308i	0.997604	−	0.0691842i	$-0.0220396\pi$
$757$	6.69326	+	16.1590i	0.243271	+	0.587308i	−0.754333	+	0.656492i	$0.772040\pi$
$758$	−6.25716	+	8.63694i	−0.227270	+	0.313708i
$759$	5.58379	−	20.8390i	0.202679	−	0.756407i
$760$	−6.30435	+	4.37086i	−0.228683	+	0.158548i
$761$	19.3129	−	5.17487i	0.700092	−	0.187589i	0.108820	−	0.994061i	$-0.465293\pi$
$761$	19.3129	−	5.17487i	0.700092	−	0.187589i	0.591272	+	0.806472i	$0.298626\pi$
$762$	−3.84781	+	3.12458i	−0.139391	+	0.113191i
$763$	−3.48172	−	8.99814i	−0.126047	−	0.325755i
$764$	10.6595	−	6.96369i	0.385648	−	0.251938i
$765$	1.59896	+	2.08381i	0.0578106	+	0.0753403i
$766$	32.7385	−	0.901873i	1.18289	−	0.0325860i
$767$	67.2916	−	38.8508i	2.42976	−	1.40282i
$768$	−3.55258	+	20.4053i	−0.128193	+	0.736314i
$769$			46.5336i			1.67804i	0.544098	+	0.839022i	$0.316872\pi$
$769$			46.5336i			1.67804i	−0.544098	+	0.839022i	$0.683128\pi$
$770$	−0.146526	−	36.2934i	−0.00528044	−	1.30792i
$771$	16.4674	+	6.82104i	0.593060	+	0.245654i
$772$	2.58464	−	0.142510i	0.0930232	−	0.00512906i
$773$	−17.7040	+	23.0723i	−0.636769	+	0.829853i	−0.994584	−	0.103939i	$-0.966855\pi$
$773$	−17.7040	+	23.0723i	−0.636769	+	0.829853i	0.357815	+	0.933792i	$0.383522\pi$
$774$	11.2401	+	4.29712i	0.404016	+	0.154457i
$775$	−1.09252	−	4.07733i	−0.0392444	−	0.146462i
$776$	−2.04955	−	24.7498i	−0.0735746	−	0.888465i
$777$	8.05459	+	33.1586i	0.288957	+	1.18956i
$778$	−3.51001	+	33.8384i	−0.125840	+	1.21317i
$779$	−0.225939	+	1.71618i	−0.00809511	+	0.0614884i
$780$	22.1676	+	25.8123i	0.793726	+	0.924228i
$781$	−7.73210	−	58.7312i	−0.276676	−	2.10157i
$782$	−4.68787	−	1.11871i	−0.167638	−	0.0400051i
$783$		−	16.7687i		−	0.599264i
$784$	−25.0840	−	12.4417i	−0.895856	−	0.444345i
$785$			45.5381i			1.62532i
$786$	2.00202	−	8.38929i	0.0714097	−	0.299236i
$787$	1.32966	+	10.0997i	0.0473971	+	0.360017i	0.998665	+	0.0516516i	$0.0164485\pi$
$787$	1.32966	+	10.0997i	0.0473971	+	0.360017i	−0.951268	+	0.308365i	$0.900218\pi$
$788$	0.269132	−	3.54291i	0.00958745	−	0.126211i
$789$	2.22097	−	16.8700i	0.0790687	−	0.600586i
$790$	−33.4160	−	3.46619i	−1.18889	−	0.123321i
$791$	−7.72988	−	31.8218i	−0.274843	−	1.13145i
$792$	18.1658	+	5.82054i	0.645494	+	0.206824i
$793$	23.0858	+	86.1575i	0.819802	+	3.05954i
$794$	6.80138	−	17.7905i	0.241372	−	0.631362i
$795$	12.8501	−	16.7466i	0.455746	−	0.593939i
$796$	−12.3338	+	13.7732i	−0.437158	+	0.488179i
$797$	29.1949	+	12.0929i	1.03414	+	0.428353i	0.834204	−	0.551457i	$-0.185928\pi$
$797$	29.1949	+	12.0929i	1.03414	+	0.428353i	0.199932	+	0.979810i	$0.435928\pi$
$798$	−6.89758	+	0.0278474i	−0.244172	+	0.000985787i
$799$			1.53741i			0.0543898i
$800$	−4.68479	+	6.19213i	−0.165632	+	0.218925i
$801$	−11.4741	+	6.62455i	−0.405416	+	0.234067i
$802$	−0.200469	−	7.27716i	−0.00707882	−	0.256965i
$803$	5.60909	+	7.30990i	0.197940	+	0.257961i
$804$	−24.0693	−	5.04765i	−0.848858	−	0.178017i
$805$	5.95040	+	15.3782i	0.209724	+	0.542009i
$806$	18.9173	+	23.2960i	0.666333	+	0.820567i
$807$	−8.27810	+	2.21811i	−0.291403	+	0.0780811i
$808$	−2.77626	+	4.31352i	−0.0976686	+	0.151749i
$809$	−4.66300	+	17.4026i	−0.163942	+	0.611841i	0.834230	+	0.551416i	$0.185912\pi$
$809$	−4.66300	+	17.4026i	−0.163942	+	0.611841i	−0.998173	+	0.0604253i	$0.980754\pi$
$810$	−7.14079	−	5.17325i	−0.250902	−	0.181770i
$811$	3.00766	+	7.26114i	0.105613	+	0.254973i	0.967848	−	0.251536i	$-0.0809357\pi$
$811$	3.00766	+	7.26114i	0.105613	+	0.254973i	−0.862235	+	0.506509i	$0.830936\pi$
$812$	12.8740	+	9.24773i	0.451788	+	0.324532i
$813$	28.5004	+	11.8052i	0.999551	+	0.414028i
$814$	69.7985	+	16.6567i	2.44644	+	0.583817i
$815$	9.25699	−	5.34453i	0.324258	−	0.187211i
$816$	−1.50342	+	5.17883i	−0.0526303	+	0.181295i
$817$	−4.57523	+	7.92453i	−0.160067	+	0.277244i
$818$	−1.55161	+	0.461907i	−0.0542509	+	0.0161502i
$819$	−2.59132	−	24.0358i	−0.0905481	−	0.839879i
$820$	−0.856160	−	4.55028i	−0.0298984	−	0.158903i
$821$	−44.2969	−	5.83180i	−1.54597	−	0.203531i	−0.691250	−	0.722616i	$-0.742940\pi$
$821$	−44.2969	−	5.83180i	−1.54597	−	0.203531i	−0.854723	+	0.519085i	$0.826273\pi$
$822$	4.80760	−	2.14833i	0.167684	−	0.0749315i
$823$	−21.3457	−	5.71956i	−0.744064	−	0.199371i	−0.133180	−	0.991092i	$-0.542519\pi$
$823$	−21.3457	−	5.71956i	−0.744064	−	0.199371i	−0.610884	+	0.791720i	$0.709186\pi$
$824$	−3.29610	−	9.18851i	−0.114825	−	0.320097i
$825$	−6.39897	−	6.39897i	−0.222783	−	0.222783i
$826$	−5.66824	−	41.7513i	−0.197223	−	1.45271i
$827$	10.4914	+	25.3284i	0.364821	+	0.880755i	0.994581	+	0.103965i	$0.0331532\pi$
$827$	10.4914	+	25.3284i	0.364821	+	0.880755i	−0.629760	+	0.776790i	$0.716847\pi$
$828$	−8.65339	+	0.477125i	−0.300726	+	0.0165813i
$829$	−2.50401	−	19.0198i	−0.0869678	−	0.660586i	−0.978294	−	0.207223i	$-0.933557\pi$
$829$	−2.50401	−	19.0198i	−0.0869678	−	0.660586i	0.891326	−	0.453363i	$-0.149776\pi$
$830$	−0.443253	−	16.0903i	−0.0153855	−	0.558504i
$831$	6.44816	−	11.1685i	0.223684	−	0.387432i
$832$	12.4477	−	53.7793i	0.431548	−	1.86446i
$833$	−6.13512	−	3.93767i	−0.212569	−	0.136432i
$834$	10.0170	−	18.5090i	0.346860	−	0.640915i
$835$	17.1404	−	13.1523i	0.593167	−	0.455153i
$836$	−6.55010	+	12.9422i	−0.226540	+	0.447617i
$837$	−13.6574	−	10.4797i	−0.472069	−	0.362231i
$838$	39.0865	−	6.24522i	1.35022	−	0.215738i
$839$	−6.91976	+	6.91976i	−0.238897	+	0.238897i	−0.816393	−	0.577497i	$-0.804030\pi$
$839$	−6.91976	+	6.91976i	−0.238897	+	0.238897i	0.577497	+	0.816393i	$0.304030\pi$
$840$	17.5082	−	5.81987i	0.604089	−	0.200805i
$841$	14.1608	+	14.1608i	0.488304	+	0.488304i
$842$	−13.5358	−	9.80624i	−0.466476	−	0.337945i
$843$	−19.1263	+	24.9259i	−0.658744	+	0.858492i
$844$	26.0550	+	30.3389i	0.896852	+	1.04431i
$845$	−40.1301	−	52.2985i	−1.38052	−	1.79912i
$846$	0.788798	+	2.64969i	0.0271194	+	0.0910982i
$847$	−18.9516	−	34.6827i	−0.651183	−	1.19171i
$848$	−34.2389	−	0.710098i	−1.17577	−	0.0243849i
$849$	−16.5863	−	9.57608i	−0.569239	−	0.328650i
$850$	−1.38958	+	1.46831i	−0.0476622	+	0.0503625i
$851$	−32.3230	+	4.25540i	−1.10802	+	0.145873i
$852$	27.1450	−	13.0383i	0.929974	−	0.446686i
$853$	−33.0362	+	13.6840i	−1.13114	+	0.468532i	−0.868167	−	0.496271i	$-0.834702\pi$
$853$	−33.0362	+	13.6840i	−1.13114	+	0.468532i	−0.262970	+	0.964804i	$0.584702\pi$
$854$	47.9790	+	6.11960i	1.64181	+	0.209408i
$855$	−2.53964	+	2.53964i	−0.0868538	+	0.0868538i
$856$	0.575481	−	11.9110i	0.0196695	−	0.407111i
$857$	−12.0838	+	45.0972i	−0.412774	+	1.54049i	0.376480	+	0.926425i	$0.377134\pi$
$857$	−12.0838	+	45.0972i	−0.412774	+	1.54049i	−0.789253	+	0.614068i	$0.789532\pi$
$858$	60.0937	+	22.9740i	2.05157	+	0.784321i
$859$	5.09660	−	38.7125i	0.173894	−	1.32085i	−0.652512	−	0.757778i	$-0.726285\pi$
$859$	5.09660	−	38.7125i	0.173894	−	1.32085i	0.826406	−	0.563075i	$-0.190382\pi$
$860$	5.02368	−	23.9550i	0.171306	−	0.816858i
$861$	1.68312	−	3.80775i	0.0573606	−	0.129768i
$862$	21.8058	−	40.2920i	0.742710	−	1.37235i
$863$	14.2685	+	8.23794i	0.485706	+	0.280423i	0.722792	−	0.691066i	$-0.242859\pi$
$863$	14.2685	+	8.23794i	0.485706	+	0.280423i	−0.237085	+	0.971489i	$0.576192\pi$
$864$	0.215462	+	31.6651i	0.00733015	+	1.07727i
$865$	2.30717	+	3.99614i	0.0784462	+	0.135873i
$866$	−17.1948	−	27.9739i	−0.584304	−	0.950591i
$867$	7.88434	−	19.0345i	0.267766	−	0.646445i
$868$	15.5776	−	4.70591i	0.528738	−	0.159729i
$869$	−58.6882	+	24.3095i	−1.99086	+	0.824642i
$870$	−10.3140	+	1.64798i	−0.349679	+	0.0558716i
$871$	63.3100	+	16.9639i	2.14518	+	0.574799i
$872$	−2.18566	−	10.0802i	−0.0740158	−	0.341358i
$873$	−3.00931	−	11.2309i	−0.101850	−	0.380109i
$874$	0.679943	−	6.55502i	0.0229994	−	0.221727i
$875$	31.7297	+	4.93848i	1.07266	+	0.166951i
$876$	−2.64251	+	3.86738i	−0.0892820	+	0.130667i
$877$	18.0190	−	13.8265i	0.608460	−	0.466888i	−0.257993	−	0.966147i	$-0.583061\pi$
$877$	18.0190	−	13.8265i	0.608460	−	0.466888i	0.866453	+	0.499259i	$0.166394\pi$
$878$	−21.0968	−	19.9656i	−0.711982	−	0.673806i
$879$	−17.7308	−	30.7107i	−0.598046	−	1.03585i
$880$	5.86091	−	38.3544i	0.197571	−	1.29293i
$881$	22.7253			0.765636			0.382818	−	0.923824i	$-0.374954\pi$
$881$	22.7253			0.765636			0.382818	+	0.923824i	$0.374954\pi$
$882$	−12.5940	−	3.63873i	−0.424063	−	0.122522i
$883$	−17.4587	+	42.1489i	−0.587530	+	1.41842i	0.298326	+	0.954464i	$0.403572\pi$
$883$	−17.4587	+	42.1489i	−0.587530	+	1.41842i	−0.885856	+	0.463960i	$0.846428\pi$
$884$	4.76062	−	13.5608i	0.160117	−	0.456098i
$885$	22.0264	+	16.9015i	0.740410	+	0.568137i
$886$	−14.4792	−	32.4020i	−0.486437	−	1.08857i
$887$	2.84834	−	0.763209i	0.0956377	−	0.0256261i	−0.210683	−	0.977554i	$-0.567569\pi$
$887$	2.84834	−	0.763209i	0.0956377	−	0.0256261i	0.306321	+	0.951928i	$0.400902\pi$
$888$	3.01054	+	36.3544i	0.101027	+	1.21997i
$889$	−1.69089	−	6.96093i	−0.0567106	−	0.233462i
$890$	16.9878	+	20.9200i	0.569434	+	0.701239i
$891$	−16.5305	−	2.17628i	−0.553793	−	0.0729082i
$892$	4.91517	−	9.71182i	0.164572	−	0.325176i
$893$	−2.08427	+	0.274400i	−0.0697475	+	0.00918244i
$894$	−2.53317	−	4.12115i	−0.0847218	−	0.137832i
$895$	−21.0412			−0.703329
$896$	−24.4294	−	17.2975i	−0.816129	−	0.577870i
$897$	−29.2294			−0.975942
$898$	14.9695	+	24.3535i	0.499537	+	0.812686i
$899$	−9.13349	+	1.20245i	−0.304619	+	0.0401039i
$900$	−1.64156	+	3.24354i	−0.0547187	+	0.108118i
$901$	−8.84006	−	1.16382i	−0.294505	−	0.0387723i
$902$	−5.51888	−	6.79632i	−0.183759	−	0.226293i
$903$	15.9231	−	15.1917i	0.529888	−	0.505547i
$904$	−2.88918	−	34.8888i	−0.0960925	−	1.16039i
$905$	−5.49735	+	1.47301i	−0.182738	+	0.0489645i
$906$	−0.986297	−	2.20717i	−0.0327675	−	0.0733283i
$907$	−33.7878	−	25.9263i	−1.12191	−	0.860868i	−0.130468	−	0.991452i	$-0.541648\pi$
$907$	−33.7878	−	25.9263i	−1.12191	−	0.860868i	−0.991437	+	0.130584i	$0.958315\pi$
$908$	−0.142045	+	0.404619i	−0.00471392	+	0.0134277i
$909$	−0.919074	+	2.21884i	−0.0304837	+	0.0735943i
$910$	−47.4449	+	12.9183i	−1.57278	+	0.428239i
$911$	−22.9192			−0.759346			−0.379673	−	0.925121i	$-0.623964\pi$
$911$	−22.9192			−0.759346			−0.379673	+	0.925121i	$0.623964\pi$
$912$	−7.28927	−	1.11387i	−0.241372	−	0.0368839i
$913$	−15.2180	−	26.3584i	−0.503643	−	0.872335i
$914$	22.7578	+	21.5376i	0.752761	+	0.712400i
$915$	−25.2850	+	19.4019i	−0.835897	+	0.641407i
$916$	−24.0889	+	35.2548i	−0.795921	+	1.16485i
$917$	9.70777	+	7.81827i	0.320579	+	0.258182i
$918$	−0.850626	+	8.20050i	−0.0280748	+	0.270657i
$919$	1.75789	+	6.56055i	0.0579876	+	0.216413i	0.988840	−	0.148984i	$-0.0476002\pi$
$919$	1.75789	+	6.56055i	0.0579876	+	0.216413i	−0.930852	+	0.365396i	$0.880933\pi$
$920$	3.73538	+	17.2274i	0.123152	+	0.567971i
$921$	1.42827	+	0.382705i	0.0470632	+	0.0126105i
$922$	−35.5524	+	5.68055i	−1.17086	+	0.187079i
$923$	−74.1486	+	30.7134i	−2.44063	+	1.01094i
$924$	23.8773	−	25.4350i	0.785506	−	0.836751i
$925$	−5.23328	+	12.6343i	−0.172069	+	0.415412i
$926$	−9.11881	−	14.8352i	−0.299663	−	0.487515i
$927$	−2.28516	−	3.95801i	−0.0750545	−	0.129998i
$928$	12.0636	+	11.9006i	0.396008	+	0.390655i
$929$	2.88857	+	1.66772i	0.0947709	+	0.0547160i	0.546636	−	0.837370i	$-0.315908\pi$
$929$	2.88857	+	1.66772i	0.0947709	+	0.0547160i	−0.451866	+	0.892086i	$0.649241\pi$
$930$	−5.10362	+	9.43028i	−0.167354	+	0.309231i
$931$	4.24330	−	9.02020i	0.139068	−	0.295625i
$932$	−1.66084	+	7.91956i	−0.0544026	+	0.259414i
$933$	1.23258	−	9.36241i	0.0403530	−	0.306511i
$934$	38.1821	+	14.5971i	1.24936	+	0.477633i
$935$	2.61455	−	9.75762i	0.0855048	−	0.319108i
$936$	1.24721	−	25.8141i	0.0407662	−	0.843762i
$937$	30.7306	−	30.7306i	1.00392	−	1.00392i	0.00393267	−	0.999992i	$-0.498748\pi$
$937$	30.7306	−	30.7306i	1.00392	−	1.00392i	0.999992	−	0.00393267i	$-0.00125181\pi$
$938$	21.5222	−	28.2840i	0.702726	−	0.923506i
$939$	6.96685	−	2.88577i	0.227355	−	0.0941734i
$940$	5.06882	−	2.43466i	0.165327	−	0.0794099i
$941$	0.0279542	−	0.00368024i	0.000911282	−	0.000119973i	−0.130071	−	0.991505i	$-0.541520\pi$
$941$	0.0279542	−	0.00368024i	0.000911282	−	0.000119973i	0.130982	+	0.991385i	$0.458187\pi$
$942$	−30.0877	+	31.7924i	−0.980311	+	1.03585i
$943$	3.44469	+	1.98879i	0.112175	+	0.0647640i
$944$	0.933979	−	45.0338i	0.0303984	−	1.46573i
$945$	24.7530	−	13.5257i	0.805215	−	0.439991i
$946$	−13.2048	−	44.3569i	−0.429325	−	1.44217i
$947$	9.52398	+	12.4119i	0.309488	+	0.403332i	0.922038	−	0.387099i	$-0.126523\pi$
$947$	9.52398	+	12.4119i	0.309488	+	0.403332i	−0.612550	+	0.790432i	$0.709856\pi$
$948$	−21.0392	−	24.4984i	−0.683320	−	0.795669i
$949$	7.59941	−	9.90374i	0.246687	−	0.321489i
$950$	−2.23860	−	1.62179i	−0.0726298	−	0.0526178i
$951$	18.6887	+	18.6887i	0.606024	+	0.606024i
$952$	−5.82674	−	5.17554i	−0.188846	−	0.167740i
$953$	41.4334	−	41.4334i	1.34216	−	1.34216i	0.448251	−	0.893908i	$-0.352047\pi$
$953$	41.4334	−	41.4334i	1.34216	−	1.34216i	0.893908	−	0.448251i	$-0.147953\pi$
$954$	−15.8327	+	2.52975i	−0.512603	+	0.0819036i
$955$	−9.61944	−	7.38126i	−0.311278	−	0.238852i
$956$	2.46825	−	4.87698i	0.0798288	−	0.157733i
$957$	−15.6685	+	12.0229i	−0.506491	+	0.388644i
$958$	−14.1419	+	26.1309i	−0.456905	+	0.844252i
$959$	−0.178847	+	7.60796i	−0.00577527	+	0.245674i
$960$	19.4553	−	3.24448i	0.627918	−	0.104715i
$961$	10.7713	−	18.6565i	0.347462	−	0.601821i
$962$	−2.67721	−	97.1843i	−0.0863167	−	3.13335i
$963$	−0.728736	−	5.53530i	−0.0234832	−	0.178373i
$964$	29.9890	−	1.65351i	0.965880	−	0.0532561i
$965$	−0.943335	−	2.27741i	−0.0303670	−	0.0733125i
$966$	−6.00633	+	14.6678i	−0.193250	+	0.471928i
$967$	−42.0180	−	42.0180i	−1.35121	−	1.35121i	−0.884311	−	0.466898i	$-0.845372\pi$
$967$	−42.0180	−	42.0180i	−1.35121	−	1.35121i	−0.466898	−	0.884311i	$-0.654628\pi$
$968$	−14.2664	−	39.7703i	−0.458539	−	1.27827i
$969$	−1.85444	−	0.496896i	−0.0595733	−	0.0159626i
$970$	−21.5918	+	9.64852i	−0.693271	+	0.309795i
$971$	−28.1383	−	3.70447i	−0.902999	−	0.118882i	−0.335294	−	0.942114i	$-0.608836\pi$
$971$	−28.1383	−	3.70447i	−0.902999	−	0.118882i	−0.567706	+	0.823232i	$0.692169\pi$
$972$	4.64327	+	24.6778i	0.148933	+	0.791540i
$973$	17.9434	+	24.5585i	0.575239	+	0.787309i
$974$	−12.2774	+	3.65492i	−0.393394	+	0.117111i
$975$	−6.13031	+	10.6180i	−0.196327	+	0.340049i
$976$	49.6571	+	14.4156i	1.58949	+	0.461431i
$977$	−22.2372	+	12.8387i	−0.711431	+	0.410745i	−0.811591	−	0.584226i	$-0.801398\pi$
$977$	−22.2372	+	12.8387i	−0.711431	+	0.410745i	0.100159	+	0.994971i	$0.468065\pi$
$978$	9.99397	+	2.38496i	0.319572	+	0.0762627i
$979$	47.0772	+	19.5000i	1.50460	+	0.623224i
$980$	−3.26678	+	26.4631i	−0.104354	+	0.845333i
$981$	−1.84800	−	4.46146i	−0.0590020	−	0.142443i
$982$	−12.3122	−	8.91975i	−0.392898	−	0.284641i
$983$	1.53877	−	5.74279i	0.0490793	−	0.183166i	−0.937035	−	0.349236i	$-0.886441\pi$
$983$	1.53877	−	5.74279i	0.0490793	−	0.183166i	0.986114	+	0.166070i	$0.0531077\pi$
$984$	2.40871	−	3.74245i	0.0767869	−	0.119305i
$985$	−3.26829	+	0.875735i	−0.104136	+	0.0279032i
$986$	2.78119	+	3.42495i	0.0885713	+	0.109073i
$987$	4.99594	+	0.777578i	0.159022	+	0.0247506i
$988$	19.2340	+	4.03364i	0.611916	+	0.128327i
$989$	12.8002	+	16.6815i	0.407022	+	0.530442i
$990$	−0.500225	−	18.1585i	−0.0158982	−	0.577113i
$991$	−17.8271	+	10.2925i	−0.566296	+	0.326951i	−0.755669	−	0.654954i	$-0.772688\pi$
$991$	−17.8271	+	10.2925i	−0.566296	+	0.326951i	0.189373	+	0.981905i	$0.439355\pi$
$992$	17.2318	−	2.38800i	0.547109	−	0.0758189i
$993$			35.4977i			1.12649i
$994$	0.175703	+	43.5201i	0.00557295	+	1.38038i
$995$	16.2661	+	6.73764i	0.515670	+	0.213598i
$996$	10.3217	−	11.5263i	0.327055	−	0.365225i
$997$	−32.4961	+	42.3498i	−1.02916	+	1.34123i	−0.0906883	+	0.995879i	$0.528907\pi$
$997$	−32.4961	+	42.3498i	−1.02916	+	1.34123i	−0.938474	+	0.345351i	$0.887760\pi$
$998$	−4.93756	+	12.9153i	−0.156296	+	0.408827i
$999$	14.4345	+	53.8701i	0.456686	+	1.70438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.19.21	✓	240
4.3	odd	2		896.2.bi.a.495.9		240
7.3	odd	6	inner	224.2.be.a.115.2	yes	240
28.3	even	6		896.2.bi.a.367.9		240
32.5	even	8		896.2.bi.a.271.9		240
32.27	odd	8	inner	224.2.be.a.187.2	yes	240
224.59	even	24	inner	224.2.be.a.59.21	yes	240
224.101	odd	24		896.2.bi.a.143.9		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.21	✓	240	1.1	even	1	trivial
224.2.be.a.59.21	yes	240	224.59	even	24	inner
224.2.be.a.115.2	yes	240	7.3	odd	6	inner
224.2.be.a.187.2	yes	240	32.27	odd	8	inner
896.2.bi.a.143.9		240	224.101	odd	24
896.2.bi.a.271.9		240	32.5	even	8
896.2.bi.a.367.9		240	28.3	even	6
896.2.bi.a.495.9		240	4.3	odd	2

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.740565 + 1.20481i) q^{2} +(1.28344 - 0.168969i) q^{3} +(-0.903128 + 1.78448i) q^{4} +(1.88828 + 0.248596i) q^{5} +(1.15405 + 1.42117i) q^{6} +(-2.57099 + 0.624522i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(-1.27910 + 0.342734i) q^{9} +O(q^{10})\)	\(q+(0.740565 + 1.20481i) q^{2} +(1.28344 - 0.168969i) q^{3} +(-0.903128 + 1.78448i) q^{4} +(1.88828 + 0.248596i) q^{5} +(1.15405 + 1.42117i) q^{6} +(-2.57099 + 0.624522i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(-1.27910 + 0.342734i) q^{9} +(1.09888 + 2.45911i) q^{10} +(4.04052 + 3.10040i) q^{11} +(-0.857592 + 2.44288i) q^{12} +(2.64057 - 6.37490i) q^{13} +(-2.65641 - 2.63505i) q^{14} +2.46550 q^{15} +(-2.36872 - 3.22322i) q^{16} +(-0.520718 - 0.901911i) q^{17} +(-1.36019 - 1.28726i) q^{18} +(1.12978 - 0.866913i) q^{19} +(-2.14897 + 3.14507i) q^{20} +(-3.19419 + 1.23595i) q^{21} +(-0.743121 + 7.16409i) q^{22} +(-0.846936 - 3.16081i) q^{23} +(-3.57830 + 0.775873i) q^{24} +(-1.32584 - 0.355257i) q^{25} +(9.63604 - 1.53964i) q^{26} +(-5.17168 + 2.14218i) q^{27} +(1.20748 - 5.15189i) q^{28} +(-1.14636 + 2.76757i) q^{29} +(1.82586 + 2.97046i) q^{30} +(1.53764 + 2.66328i) q^{31} +(2.12917 - 5.24086i) q^{32} +(5.70964 + 3.29646i) q^{33} +(0.701004 - 1.29529i) q^{34} +(-5.00999 + 0.540132i) q^{35} +(0.543590 - 2.59206i) q^{36} +(1.30043 - 9.87772i) q^{37} +(1.88114 + 0.719167i) q^{38} +(2.31186 - 8.62799i) q^{39} +(-5.38066 - 0.259966i) q^{40} +(-0.859509 + 0.859509i) q^{41} +(-3.85459 - 2.93309i) q^{42} +(-5.93649 + 2.45898i) q^{43} +(-9.18169 + 4.41016i) q^{44} +(-2.50050 + 0.329197i) q^{45} +(3.18096 - 3.36118i) q^{46} +(-1.27846 - 0.738121i) q^{47} +(-3.58474 - 3.73658i) q^{48} +(6.21995 - 3.21127i) q^{49} +(-0.553852 - 1.86047i) q^{50} +(-0.820707 - 1.06957i) q^{51} +(8.99109 + 10.4694i) q^{52} +(5.21196 - 6.79235i) q^{53} +(-6.41088 - 4.64446i) q^{54} +(6.85887 + 6.85887i) q^{55} +(7.10126 - 2.36052i) q^{56} +(1.30353 - 1.30353i) q^{57} +(-4.18335 + 0.668414i) q^{58} +(8.93385 + 6.85519i) q^{59} +(-2.22666 + 4.39963i) q^{60} +(-10.2555 + 7.86934i) q^{61} +(-2.07001 + 3.82489i) q^{62} +(3.07451 - 1.67999i) q^{63} +(7.89102 - 1.31595i) q^{64} +(6.57090 - 11.3811i) q^{65} +(0.256753 + 9.32027i) q^{66} +(1.23985 + 9.41758i) q^{67} +(2.07971 - 0.114670i) q^{68} +(-1.62107 - 3.91361i) q^{69} +(-4.36098 - 5.63608i) q^{70} +(-8.22460 - 8.22460i) q^{71} +(3.52550 - 1.26467i) q^{72} +(1.74751 + 0.468243i) q^{73} +(12.8638 - 5.74833i) q^{74} +(-1.76166 - 0.231928i) q^{75} +(0.526649 + 2.79901i) q^{76} +(-12.3244 - 5.44769i) q^{77} +(12.1072 - 3.60423i) q^{78} +(-6.23642 + 10.8018i) q^{79} +(-3.67152 - 6.67519i) q^{80} +(-2.83516 + 1.63688i) q^{81} +(-1.67207 - 0.399021i) q^{82} +(-5.52119 - 2.28695i) q^{83} +(0.679230 - 6.81619i) q^{84} +(-0.759049 - 1.83251i) q^{85} +(-7.35895 - 5.33131i) q^{86} +(-1.00366 + 3.74571i) q^{87} +(-12.1130 - 7.79617i) q^{88} +(9.66427 - 2.58953i) q^{89} +(-2.24840 - 2.76883i) q^{90} +(-2.80761 + 18.0389i) q^{91} +(6.40528 + 1.34327i) q^{92} +(2.42349 + 3.15835i) q^{93} +(-0.0574902 - 2.08693i) q^{94} +(2.34886 - 1.35611i) q^{95} +(1.84713 - 7.08611i) q^{96} +8.78032i q^{97} +(8.47524 + 5.11569i) q^{98} +(-6.23084 - 2.58090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

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