LMFDB - Embedded newform 64.2.i.a.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	64.53
Dual form			64.2.i.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.182356 + 1.40241i) q^{2} +(1.93660 - 0.385213i) q^{3} +(-1.93349 + 0.511475i) q^{4} +(-0.787711 - 1.17889i) q^{5} +(0.893376 + 2.64565i) q^{6} +(-2.16489 - 0.896725i) q^{7} +(-1.06988 - 2.61827i) q^{8} +(0.830380 - 0.343954i) q^{9} +O(q^{10})$	\(q+(0.182356 + 1.40241i) q^{2} +(1.93660 - 0.385213i) q^{3} +(-1.93349 + 0.511475i) q^{4} +(-0.787711 - 1.17889i) q^{5} +(0.893376 + 2.64565i) q^{6} +(-2.16489 - 0.896725i) q^{7} +(-1.06988 - 2.61827i) q^{8} +(0.830380 - 0.343954i) q^{9} +(1.50964 - 1.31967i) q^{10} +(-1.08337 + 5.44648i) q^{11} +(-3.54737 + 1.73533i) q^{12} +(1.49710 - 2.24057i) q^{13} +(0.862794 - 3.19957i) q^{14} +(-1.97960 - 1.97960i) q^{15} +(3.47679 - 1.97787i) q^{16} +(3.43875 - 3.43875i) q^{17} +(0.633789 + 1.10181i) q^{18} +(-1.24019 - 0.828669i) q^{19} +(2.12601 + 1.87649i) q^{20} +(-4.53794 - 0.902653i) q^{21} +(-7.83575 - 0.526131i) q^{22} +(2.14281 + 5.17319i) q^{23} +(-3.08052 - 4.65841i) q^{24} +(1.14412 - 2.76214i) q^{25} +(3.41520 + 1.69096i) q^{26} +(-3.44969 + 2.30501i) q^{27} +(4.64444 + 0.626526i) q^{28} +(1.63164 + 8.20281i) q^{29} +(2.41522 - 3.13720i) q^{30} -5.17816i q^{31} +(3.40779 + 4.51520i) q^{32} +10.9650i q^{33} +(5.44961 + 4.19545i) q^{34} +(0.648162 + 3.25853i) q^{35} +(-1.42961 + 1.08975i) q^{36} +(-6.79044 + 4.53723i) q^{37} +(0.935975 - 1.89037i) q^{38} +(2.03618 - 4.91578i) q^{39} +(-2.24391 + 3.32372i) q^{40} +(-2.24634 - 5.42314i) q^{41} +(0.438366 - 6.52865i) q^{42} +(4.16031 + 0.827538i) q^{43} +(-0.691046 - 11.0849i) q^{44} +(-1.05958 - 0.707992i) q^{45} +(-6.86417 + 3.94845i) q^{46} +(-0.733603 + 0.733603i) q^{47} +(5.97123 - 5.16963i) q^{48} +(-1.06713 - 1.06713i) q^{49} +(4.08229 + 1.10082i) q^{50} +(5.33482 - 7.98413i) q^{51} +(-1.74864 + 5.09785i) q^{52} +(0.575078 - 2.89111i) q^{53} +(-3.86163 - 4.41754i) q^{54} +(7.27421 - 3.01307i) q^{55} +(-0.0317030 + 6.62765i) q^{56} +(-2.72096 - 1.12706i) q^{57} +(-11.2061 + 3.78406i) q^{58} +(-3.31738 - 4.96481i) q^{59} +(4.84007 + 2.81503i) q^{60} +(0.382794 - 0.0761424i) q^{61} +(7.26190 - 0.944270i) q^{62} -2.10611 q^{63} +(-5.71071 + 5.60248i) q^{64} -3.82067 q^{65} +(-15.3774 + 1.99953i) q^{66} +(1.67538 - 0.333253i) q^{67} +(-4.88996 + 8.40763i) q^{68} +(6.14253 + 9.19295i) q^{69} +(-4.45159 + 1.50320i) q^{70} +(-0.843458 - 0.349372i) q^{71} +(-1.78897 - 1.80617i) q^{72} +(11.9774 - 4.96122i) q^{73} +(-7.60132 - 8.69558i) q^{74} +(1.15168 - 5.78989i) q^{75} +(2.82174 + 0.967899i) q^{76} +(7.22938 - 10.8195i) q^{77} +(7.26524 + 1.95914i) q^{78} +(-5.30583 - 5.30583i) q^{79} +(-5.07040 - 2.54077i) q^{80} +(-7.69937 + 7.69937i) q^{81} +(7.19581 - 4.13922i) q^{82} +(-1.28800 - 0.860615i) q^{83} +(9.23576 - 0.575771i) q^{84} +(-6.76266 - 1.34518i) q^{85} +(-0.401887 + 5.98536i) q^{86} +(6.31966 + 15.2570i) q^{87} +(15.4195 - 2.99052i) q^{88} +(-3.98900 + 9.63030i) q^{89} +(0.799671 - 1.61508i) q^{90} +(-5.25023 + 3.50809i) q^{91} +(-6.78906 - 8.90634i) q^{92} +(-1.99470 - 10.0280i) q^{93} +(-1.16259 - 0.895033i) q^{94} +2.11480i q^{95} +(8.33882 + 7.43139i) q^{96} +4.23236i q^{97} +(1.30196 - 1.69115i) q^{98} +(0.973732 + 4.89528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$1$

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 $

$2$	0.182356	+	1.40241i	0.128945	+	0.991652i
$2$	0.182356	+	1.40241i	0.128945	+	0.991652i
$3$	1.93660	−	0.385213i	1.11809	−	0.222403i	0.398752	−	0.917059i	$-0.369443\pi$
$3$	1.93660	−	0.385213i	1.11809	−	0.222403i	0.719342	+	0.694656i	$0.244443\pi$
$4$	−1.93349	+	0.511475i	−0.966746	+	0.255737i
$5$	−0.787711	−	1.17889i	−0.352275	−	0.527217i	0.612439	−	0.790518i	$-0.290189\pi$
$5$	−0.787711	−	1.17889i	−0.352275	−	0.527217i	−0.964714	+	0.263301i	$0.915189\pi$
$6$	0.893376	+	2.64565i	0.364719	+	1.08008i
$7$	−2.16489	−	0.896725i	−0.818250	−	0.338930i	−0.0660095	−	0.997819i	$-0.521027\pi$
$7$	−2.16489	−	0.896725i	−0.818250	−	0.338930i	−0.752240	+	0.658889i	$0.771027\pi$
$8$	−1.06988	−	2.61827i	−0.378260	−	0.925699i
$9$	0.830380	−	0.343954i	0.276793	−	0.114651i
$10$	1.50964	−	1.31967i	0.477391	−	0.417316i
$11$	−1.08337	+	5.44648i	−0.326649	+	1.64218i	0.373102	+	0.927790i	$0.378294\pi$
$11$	−1.08337	+	5.44648i	−0.326649	+	1.64218i	−0.699752	+	0.714386i	$0.746706\pi$
$12$	−3.54737	+	1.73533i	−1.02404	+	0.500946i
$13$	1.49710	−	2.24057i	0.415221	−	0.621422i	−0.563623	−	0.826032i	$-0.690593\pi$
$13$	1.49710	−	2.24057i	0.415221	−	0.621422i	0.978843	+	0.204610i	$0.0655927\pi$
$14$	0.862794	−	3.19957i	0.230591	−	0.855122i
$15$	−1.97960	−	1.97960i	−0.511132	−	0.511132i
$16$	3.47679	−	1.97787i	0.869197	−	0.494466i
$17$	3.43875	−	3.43875i	0.834020	−	0.834020i	−0.154044	−	0.988064i	$-0.549230\pi$
$17$	3.43875	−	3.43875i	0.834020	−	0.834020i	0.988064	+	0.154044i	$0.0492299\pi$
$18$	0.633789	+	1.10181i	0.149386	+	0.259699i
$19$	−1.24019	−	0.828669i	−0.284519	−	0.190110i	0.405118	−	0.914264i	$-0.367230\pi$
$19$	−1.24019	−	0.828669i	−0.284519	−	0.190110i	−0.689638	+	0.724154i	$0.742230\pi$
$20$	2.12601	+	1.87649i	0.475390	+	0.419595i
$21$	−4.53794	−	0.902653i	−0.990260	−	0.196975i
$22$	−7.83575	−	0.526131i	−1.67059	−	0.112171i
$23$	2.14281	+	5.17319i	0.446806	+	1.07868i	0.973512	+	0.228637i	$0.0734270\pi$
$23$	2.14281	+	5.17319i	0.446806	+	1.07868i	−0.526706	+	0.850048i	$0.676573\pi$
$24$	−3.08052	−	4.65841i	−0.628808	−	0.950894i
$25$	1.14412	−	2.76214i	0.228823	−	0.552429i
$26$	3.41520	+	1.69096i	0.669775	+	0.331625i
$27$	−3.44969	+	2.30501i	−0.663893	+	0.443599i
$28$	4.64444	+	0.626526i	0.877717	+	0.118402i
$29$	1.63164	+	8.20281i	0.302988	+	1.52322i	0.769464	+	0.638690i	$0.220524\pi$
$29$	1.63164	+	8.20281i	0.302988	+	1.52322i	−0.466476	+	0.884534i	$0.654476\pi$
$30$	2.41522	−	3.13720i	0.440957	−	0.572772i
$31$		−	5.17816i		−	0.930026i	−0.885304	−	0.465013i	$-0.846050\pi$
$31$		−	5.17816i		−	0.930026i	0.885304	−	0.465013i	$-0.153950\pi$
$32$	3.40779	+	4.51520i	0.602417	+	0.798181i
$33$			10.9650i			1.90876i
$34$	5.44961	+	4.19545i	0.934600	+	0.719514i
$35$	0.648162	+	3.25853i	0.109559	+	0.550792i
$36$	−1.42961	+	1.08975i	−0.238268	+	0.181625i
$37$	−6.79044	+	4.53723i	−1.11634	+	0.745916i	−0.969948	−	0.243310i	$-0.921767\pi$
$37$	−6.79044	+	4.53723i	−1.11634	+	0.745916i	−0.146394	+	0.989226i	$0.546767\pi$
$38$	0.935975	−	1.89037i	0.151835	−	0.306658i
$39$	2.03618	−	4.91578i	0.326050	−	0.787155i
$40$	−2.24391	+	3.32372i	−0.354793	+	0.525526i
$41$	−2.24634	−	5.42314i	−0.350819	−	0.846952i	−0.996519	−	0.0833609i	$-0.973435\pi$
$41$	−2.24634	−	5.42314i	−0.350819	−	0.846952i	0.645701	−	0.763591i	$-0.276565\pi$
$42$	0.438366	−	6.52865i	0.0676413	−	1.00739i
$43$	4.16031	+	0.827538i	0.634442	+	0.126198i	0.501825	−	0.864969i	$-0.332662\pi$
$43$	4.16031	+	0.827538i	0.634442	+	0.126198i	0.132617	+	0.991167i	$0.457662\pi$
$44$	−0.691046	−	11.0849i	−0.104179	−	1.67110i
$45$	−1.05958	−	0.707992i	−0.157954	−	0.105541i
$46$	−6.86417	+	3.94845i	−1.01207	+	0.582167i
$47$	−0.733603	+	0.733603i	−0.107007	+	0.107007i	−0.758583	−	0.651576i	$-0.774108\pi$
$47$	−0.733603	+	0.733603i	−0.107007	+	0.107007i	0.651576	+	0.758583i	$0.274108\pi$
$48$	5.97123	−	5.16963i	0.861873	−	0.746172i
$49$	−1.06713	−	1.06713i	−0.152448	−	0.152448i
$50$	4.08229	+	1.10082i	0.577322	+	0.155680i
$51$	5.33482	−	7.98413i	0.747025	−	1.11800i
$52$	−1.74864	+	5.09785i	−0.242492	+	0.706945i
$53$	0.575078	−	2.89111i	0.0789930	−	0.397125i	−0.920979	−	0.389613i	$-0.872609\pi$
$53$	0.575078	−	2.89111i	0.0789930	−	0.397125i	0.999972	−	0.00751192i	$-0.00239114\pi$
$54$	−3.86163	−	4.41754i	−0.525501	−	0.601150i
$55$	7.27421	−	3.01307i	0.980854	−	0.406283i
$56$	−0.0317030	+	6.62765i	−0.00423649	+	0.885657i
$57$	−2.72096	−	1.12706i	−0.360401	−	0.149283i
$58$	−11.2061	+	3.78406i	−1.47144	+	0.496871i
$59$	−3.31738	−	4.96481i	−0.431886	−	0.646363i	0.550148	−	0.835067i	$-0.314571\pi$
$59$	−3.31738	−	4.96481i	−0.431886	−	0.646363i	−0.982034	+	0.188704i	$0.939571\pi$
$60$	4.84007	+	2.81503i	0.624850	+	0.363419i
$61$	0.382794	−	0.0761424i	0.0490117	−	0.00974904i	−0.170524	−	0.985354i	$-0.554546\pi$
$61$	0.382794	−	0.0761424i	0.0490117	−	0.00974904i	0.219535	+	0.975605i	$0.429546\pi$
$62$	7.26190	−	0.944270i	0.922262	−	0.119922i
$63$	−2.10611			−0.265345
$64$	−5.71071	+	5.60248i	−0.713839	+	0.700310i
$65$	−3.82067			−0.473896
$66$	−15.3774	+	1.99953i	−1.89282	+	0.246125i
$67$	1.67538	−	0.333253i	0.204680	−	0.0407133i	−0.0916855	−	0.995788i	$-0.529225\pi$
$67$	1.67538	−	0.333253i	0.204680	−	0.0407133i	0.296365	+	0.955075i	$0.404225\pi$
$68$	−4.88996	+	8.40763i	−0.592995	+	1.01958i
$69$	6.14253	+	9.19295i	0.739474	+	1.10670i
$70$	−4.45159	+	1.50320i	−0.532067	+	0.179667i
$71$	−0.843458	−	0.349372i	−0.100100	−	0.0414628i	0.332071	−	0.943254i	$-0.392252\pi$
$71$	−0.843458	−	0.349372i	−0.100100	−	0.0414628i	−0.432172	+	0.901791i	$0.642252\pi$
$72$	−1.78897	−	1.80617i	−0.210833	−	0.212859i
$73$	11.9774	−	4.96122i	1.40185	−	0.580667i	0.451622	−	0.892210i	$-0.350846\pi$
$73$	11.9774	−	4.96122i	1.40185	−	0.580667i	0.950232	+	0.311543i	$0.100846\pi$
$74$	−7.60132	−	8.69558i	−0.883636	−	1.01084i
$75$	1.15168	−	5.78989i	0.132985	−	0.668559i
$76$	2.82174	+	0.967899i	0.323676	+	0.111026i
$77$	7.22938	−	10.8195i	0.823864	−	1.23300i
$78$	7.26524	+	1.95914i	0.822626	+	0.221828i
$79$	−5.30583	−	5.30583i	−0.596952	−	0.596952i	0.342548	−	0.939500i	$-0.388710\pi$
$79$	−5.30583	−	5.30583i	−0.596952	−	0.596952i	−0.939500	+	0.342548i	$0.888710\pi$
$80$	−5.07040	−	2.54077i	−0.566888	−	0.284067i
$81$	−7.69937	+	7.69937i	−0.855486	+	0.855486i
$82$	7.19581	−	4.13922i	0.794645	−	0.457100i
$83$	−1.28800	−	0.860615i	−0.141376	−	0.0944647i	0.482871	−	0.875692i	$-0.339594\pi$
$83$	−1.28800	−	0.860615i	−0.141376	−	0.0944647i	−0.624247	+	0.781227i	$0.714594\pi$
$84$	9.23576	−	0.575771i	1.00770	−	0.0628218i
$85$	−6.76266	−	1.34518i	−0.733514	−	0.145905i
$86$	−0.401887	+	5.98536i	−0.0433366	+	0.645418i
$87$	6.31966	+	15.2570i	0.677539	+	1.63572i
$88$	15.4195	−	2.99052i	1.64372	−	0.318790i
$89$	−3.98900	+	9.63030i	−0.422833	+	1.02081i	0.558675	+	0.829387i	$0.311310\pi$
$89$	−3.98900	+	9.63030i	−0.422833	+	1.02081i	−0.981508	+	0.191422i	$0.938690\pi$
$90$	0.799671	−	1.61508i	0.0842928	−	0.170244i
$91$	−5.25023	+	3.50809i	−0.550373	+	0.367748i
$92$	−6.78906	−	8.90634i	−0.707808	−	0.928550i
$93$	−1.99470	−	10.0280i	−0.206840	−	1.03986i
$94$	−1.16259	−	0.895033i	−0.119912	−	0.0923156i
$95$			2.11480i			0.216974i
$96$	8.33882	+	7.43139i	0.851077	+	0.758463i
$97$			4.23236i			0.429731i	0.976644	+	0.214866i	$0.0689313\pi$
$97$			4.23236i			0.429731i	−0.976644	+	0.214866i	$0.931069\pi$
$98$	1.30196	−	1.69115i	0.131518	−	0.170832i
$99$	0.973732	+	4.89528i	0.0978637	+	0.491994i
$100$	−0.799375	+	5.92577i	−0.0799375	+	0.592577i
$101$	12.6885	−	8.47818i	1.26255	−	0.843610i	0.269697	−	0.962945i	$-0.413076\pi$
$101$	12.6885	−	8.47818i	1.26255	−	0.843610i	0.992854	+	0.119335i	$0.0380763\pi$
$102$	12.1698	+	6.02564i	1.20499	+	0.596627i
$103$	−1.63698	+	3.95201i	−0.161296	+	0.389404i	−0.983779	−	0.179387i	$-0.942589\pi$
$103$	−1.63698	+	3.95201i	−0.161296	+	0.389404i	0.822482	+	0.568791i	$0.192589\pi$
$104$	−7.46814	−	1.52268i	−0.732311	−	0.149311i
$105$	2.51046	+	6.06078i	0.244995	+	0.591471i
$106$	4.15938	+	0.279282i	0.403995	+	0.0271262i
$107$	6.49362	+	1.29166i	0.627762	+	0.124870i	0.498711	−	0.866768i	$-0.333807\pi$
$107$	6.49362	+	1.29166i	0.627762	+	0.124870i	0.129051	+	0.991638i	$0.458807\pi$
$108$	5.49099	−	6.22114i	0.528371	−	0.598630i
$109$	9.55062	+	6.38152i	0.914783	+	0.611239i	0.921348	−	0.388740i	$-0.127089\pi$
$109$	9.55062	+	6.38152i	0.914783	+	0.611239i	−0.00656414	+	0.999978i	$0.502089\pi$
$110$	5.55205	+	9.65195i	0.529368	+	0.920277i
$111$	−11.4026	+	11.4026i	−1.08228	+	1.08228i
$112$	−9.30045	+	1.16413i	−0.878810	+	0.110000i
$113$	−5.02130	−	5.02130i	−0.472365	−	0.472365i	0.430314	−	0.902679i	$-0.358403\pi$
$113$	−5.02130	−	5.02130i	−0.472365	−	0.472365i	−0.902679	+	0.430314i	$0.858403\pi$
$114$	1.08441	−	4.02143i	0.101565	−	0.376641i
$115$	4.41073	−	6.60112i	0.411302	−	0.615558i
$116$	−7.35030	−	15.0255i	−0.682458	−	1.39509i
$117$	0.472508	−	2.37546i	0.0436834	−	0.219611i
$118$	6.35774	−	5.55768i	0.585277	−	0.511626i
$119$	−10.5281	+	4.36089i	−0.965111	+	0.399762i
$120$	−3.06521	+	7.30108i	−0.279814	+	0.666495i
$121$	−18.3278	−	7.59162i	−1.66616	−	0.690148i
$122$	0.176587	+	0.522948i	0.0159875	+	0.0473455i
$123$	−6.43931	−	9.63711i	−0.580613	−	0.868949i
$124$	2.64850	+	10.0119i	0.237842	+	0.899099i
$125$	−11.1105	+	2.21002i	−0.993753	+	0.197670i
$126$	−0.384062	−	2.95362i	−0.0342149	−	0.263130i
$127$	14.0495			1.24669			0.623345	−	0.781947i	$-0.285773\pi$
$127$	14.0495			1.24669			0.623345	+	0.781947i	$0.285773\pi$
$128$	−8.89834	−	6.98710i	−0.786510	−	0.617578i
$129$	8.37563			0.737433
$130$	−0.696723	−	5.35814i	−0.0611067	−	0.469940i
$131$	−15.6501	+	3.11300i	−1.36736	+	0.271984i	−0.823559	−	0.567231i	$-0.808015\pi$
$131$	−15.6501	+	3.11300i	−1.36736	+	0.271984i	−0.543799	+	0.839216i	$0.683015\pi$
$132$	−5.60831	−	21.2007i	−0.488141	−	1.84528i
$133$	1.94178	+	2.90608i	0.168374	+	0.251989i
$134$	0.772871	+	2.28879i	0.0667659	+	0.197721i
$135$	5.43472	+	2.25113i	0.467746	+	0.193747i
$136$	−12.6826	−	5.32454i	−1.08753	−	0.456575i
$137$	−5.39532	+	2.23482i	−0.460953	+	0.190933i	−0.601061	−	0.799203i	$-0.705255\pi$
$137$	−5.39532	+	2.23482i	−0.460953	+	0.190933i	0.140108	+	0.990136i	$0.455255\pi$
$138$	−11.7721	+	10.2907i	−1.00211	+	0.876004i
$139$	−0.198971	+	1.00029i	−0.0168765	+	0.0848438i	−0.988306	−	0.152486i	$-0.951272\pi$
$139$	−0.198971	+	1.00029i	−0.0168765	+	0.0848438i	0.971429	+	0.237330i	$0.0762721\pi$
$140$	−2.91987	−	5.96882i	−0.246774	−	0.504458i
$141$	−1.13810	+	1.70329i	−0.0958452	+	0.143443i
$142$	0.336152	−	1.24658i	0.0282092	−	0.104611i
$143$	10.5813	+	10.5813i	0.884853	+	0.884853i
$144$	2.20676	−	2.83824i	0.183896	−	0.236520i
$145$	8.38498	−	8.38498i	0.696335	−	0.696335i
$146$	9.14181	+	15.8925i	0.756582	+	1.31528i
$147$	−2.47768	−	1.65553i	−0.204356	−	0.136546i
$148$	10.8086	−	12.2458i	0.888461	−	1.00660i
$149$	0.0445180	+	0.00885518i	0.00364705	+	0.000725444i	0.196914	−	0.980421i	$-0.436908\pi$
$149$	0.0445180	+	0.00885518i	0.00364705	+	0.000725444i	−0.193266	+	0.981146i	$0.561908\pi$
$150$	8.32980	+	0.559304i	0.680125	+	0.0456670i
$151$	−7.79199	−	18.8115i	−0.634103	−	1.53086i	−0.834419	−	0.551130i	$-0.814197\pi$
$151$	−7.79199	−	18.8115i	−0.634103	−	1.53086i	0.200316	−	0.979731i	$-0.435803\pi$
$152$	−0.842827	+	4.13374i	−0.0683623	+	0.335290i
$153$	1.67269	−	4.03824i	0.135229	−	0.326473i
$154$	16.4917	+	8.16552i	1.32894	+	0.657997i
$155$	−6.10450	+	4.07890i	−0.490325	+	0.327625i
$156$	−1.42265	+	10.5461i	−0.113903	+	0.844362i
$157$	2.88193	+	14.4885i	0.230003	+	1.15631i	0.907264	+	0.420562i	$0.138167\pi$
$157$	2.88193	+	14.4885i	0.230003	+	1.15631i	−0.677260	+	0.735743i	$0.736833\pi$
$158$	6.47338	−	8.40848i	0.514995	−	0.668943i
$159$		−	5.82044i		−	0.461591i
$160$	2.63858	−	7.57409i	0.208598	−	0.598784i
$161$		−	13.1209i		−	1.03407i
$162$	−12.2017	−	9.39363i	−0.958655	−	0.738033i
$163$	0.0805216	+	0.404809i	0.00630694	+	0.0317071i	0.983811	−	0.179211i	$-0.0573546\pi$
$163$	0.0805216	+	0.404809i	0.00630694	+	0.0317071i	−0.977504	+	0.210918i	$0.932355\pi$
$164$	7.11707	+	9.33665i	0.555750	+	0.729070i
$165$	12.9265	−	8.63723i	1.00633	−	0.672407i
$166$	0.972058	−	1.96324i	0.0754463	−	0.152377i
$167$	−1.88280	+	4.54548i	−0.145695	+	0.351740i	−0.979833	−	0.199816i	$-0.935966\pi$
$167$	−1.88280	+	4.54548i	−0.145695	+	0.351740i	0.834138	+	0.551556i	$0.185966\pi$
$168$	2.49166	+	12.8473i	0.192236	+	0.991191i
$169$	2.19604	+	5.30172i	0.168926	+	0.407825i
$170$	0.653274	−	9.72931i	0.0501038	−	0.746204i
$171$	−1.31485	−	0.261541i	−0.100549	−	0.0200005i
$172$	−8.46720	+	0.527858i	−0.645618	+	0.0402488i
$173$	−2.58681	−	1.72845i	−0.196672	−	0.131412i	0.453335	−	0.891340i	$-0.350234\pi$
$173$	−2.58681	−	1.72845i	−0.196672	−	0.131412i	−0.650007	+	0.759928i	$0.725234\pi$
$174$	−20.2441	+	11.6450i	−1.53470	+	0.882801i
$175$	−4.95377	+	4.95377i	−0.374469	+	0.374469i
$176$	7.00576	+	21.0790i	0.528079	+	1.58889i
$177$	−8.33693	−	8.33693i	−0.626642	−	0.626642i
$178$	−14.2330	−	3.83806i	−1.06681	−	0.287675i
$179$	−2.10987	+	3.15764i	−0.157699	+	0.236013i	−0.901902	−	0.431940i	$-0.857829\pi$
$179$	−2.10987	+	3.15764i	−0.157699	+	0.236013i	0.744204	+	0.667953i	$0.232829\pi$
$180$	2.41082	+	0.826946i	0.179692	+	0.0616369i
$181$	−0.219878	+	1.10540i	−0.0163434	+	0.0821639i	−0.988096	−	0.153837i	$-0.950837\pi$
$181$	−0.219878	+	1.10540i	−0.0163434	+	0.0821639i	0.971753	+	0.236001i	$0.0758369\pi$
$182$	−5.87718	−	6.72323i	−0.435646	−	0.498359i
$183$	0.711986	−	0.294914i	0.0526315	−	0.0218007i
$184$	11.2523	−	11.1451i	0.829529	−	0.821631i
$185$	10.6978	+	4.43118i	0.786519	+	0.325787i
$186$	13.6996	−	4.62605i	1.00450	−	0.339198i
$187$	15.0036	+	22.4545i	1.09718	+	1.64204i
$188$	1.04320	−	1.79363i	0.0760829	−	0.130814i
$189$	9.53514	−	1.89666i	0.693579	−	0.137961i
$190$	−2.96582	+	0.385647i	−0.215163	+	0.0279778i
$191$	22.3207			1.61507			0.807533	−	0.589822i	$-0.200802\pi$
$191$	22.3207			1.61507			0.807533	+	0.589822i	$0.200802\pi$
$192$	−8.90120	+	13.0496i	−0.642389	+	0.941773i
$193$	2.10778			0.151721			0.0758605	−	0.997118i	$-0.475830\pi$
$193$	2.10778			0.151721			0.0758605	+	0.997118i	$0.475830\pi$
$194$	−5.93549	+	0.771796i	−0.426144	+	0.0554118i
$195$	−7.39911	+	1.47177i	−0.529861	+	0.105396i
$196$	2.60911	+	1.51748i	0.186365	+	0.108392i
$197$	−3.12154	−	4.67172i	−0.222401	−	0.332846i	0.703444	−	0.710751i	$-0.251645\pi$
$197$	−3.12154	−	4.67172i	−0.222401	−	0.332846i	−0.925845	+	0.377905i	$0.876645\pi$
$198$	−6.68761	+	2.25825i	−0.475268	+	0.160487i
$199$	−14.6371	−	6.06290i	−1.03760	−	0.429787i	−0.202149	−	0.979355i	$-0.564793\pi$
$199$	−14.6371	−	6.06290i	−1.03760	−	0.429787i	−0.835449	+	0.549567i	$0.814793\pi$
$200$	−8.45611	−	0.0404493i	−0.597938	−	0.00286020i
$201$	3.11615	−	1.29075i	0.219796	−	0.0910427i
$202$	14.2037	+	16.2484i	0.999367	+	1.14323i
$203$	3.82335	−	19.2213i	0.268347	−	1.34907i
$204$	−6.23116	+	18.1659i	−0.436268	+	1.27187i
$205$	−4.62383	+	6.92006i	−0.322943	+	0.483318i
$206$	−5.84085	−	1.57504i	−0.406951	−	0.109738i
$207$	3.55868	+	3.55868i	0.247346	+	0.247346i
$208$	0.773554	−	10.7510i	0.0536363	−	0.745451i
$209$	5.85692	−	5.85692i	0.405132	−	0.405132i
$210$	−8.04188	+	4.62590i	−0.554943	+	0.319218i
$211$	2.41276	+	1.61216i	0.166102	+	0.110986i	0.635843	−	0.771819i	$-0.280653\pi$
$211$	2.41276	+	1.61216i	0.166102	+	0.110986i	−0.469741	+	0.882804i	$0.655653\pi$
$212$	0.366822	+	5.88408i	0.0251935	+	0.404120i
$213$	−1.76802	−	0.351681i	−0.121143	−	0.0240968i
$214$	−0.627284	+	9.34224i	−0.0428803	+	0.638623i
$215$	−2.30155	−	5.55642i	−0.156964	−	0.378945i
$216$	9.72589	+	6.56614i	0.661763	+	0.446770i
$217$	−4.64339	+	11.2101i	−0.315214	+	0.760993i
$218$	−7.20788	+	14.5576i	−0.488179	+	0.985963i
$219$	21.2844	−	14.2217i	1.43826	−	0.961017i
$220$	−12.5235	+	9.54633i	−0.844335	+	0.643614i
$221$	−2.55660	−	12.8529i	−0.171976	−	0.864581i
$222$	−18.0703	−	13.9117i	−1.21280	−	0.933692i
$223$		−	1.84279i		−	0.123403i	−0.998095	−	0.0617013i	$-0.980347\pi$
$223$		−	1.84279i		−	0.123403i	0.998095	−	0.0617013i	$-0.0196526\pi$
$224$	−3.32858	−	12.8307i	−0.222400	−	0.857289i
$225$		−	2.68715i		−	0.179143i
$226$	6.12625	−	7.95758i	0.407512	−	0.529330i
$227$	−0.293813	−	1.47710i	−0.0195011	−	0.0980385i	0.969809	−	0.243866i	$-0.0784156\pi$
$227$	−0.293813	−	1.47710i	−0.0195011	−	0.0980385i	−0.989310	+	0.145827i	$0.953416\pi$
$228$	5.83743	+	0.787458i	0.386593	+	0.0521507i
$229$	−16.7852	+	11.2155i	−1.10920	+	0.741142i	−0.968526	−	0.248914i	$-0.919926\pi$
$229$	−16.7852	+	11.2155i	−1.10920	+	0.741142i	−0.140672	+	0.990056i	$0.544926\pi$
$230$	10.0618	+	4.98188i	0.663454	+	0.328496i
$231$	9.83256	−	23.7379i	0.646935	−	1.56184i
$232$	19.7316	−	13.0481i	1.29544	−	0.856651i
$233$	9.18563	+	22.1761i	0.601771	+	1.45280i	0.871757	+	0.489939i	$0.162981\pi$
$233$	9.18563	+	22.1761i	0.601771	+	1.45280i	−0.269986	+	0.962864i	$0.587019\pi$
$234$	3.41752	+	0.229469i	0.223410	+	0.0150009i
$235$	1.44271	+	0.286972i	0.0941118	+	0.0187200i
$236$	8.95350	+	7.90266i	0.582823	+	0.514420i
$237$	−12.3191	−	8.23137i	−0.800213	−	0.534685i
$238$	−8.03561	−	13.9695i	−0.520871	−	0.905506i
$239$	6.58253	−	6.58253i	0.425788	−	0.425788i	−0.461403	−	0.887191i	$-0.652654\pi$
$239$	6.58253	−	6.58253i	0.425788	−	0.425788i	0.887191	+	0.461403i	$0.152654\pi$
$240$	−10.7981	−	2.96727i	−0.697011	−	0.191536i
$241$	13.5889	+	13.5889i	0.875335	+	0.875335i	0.993048	−	0.117712i	$-0.0375561\pi$
$241$	13.5889	+	13.5889i	0.875335	+	0.875335i	−0.117712	+	0.993048i	$0.537556\pi$
$242$	7.30436	−	27.0874i	0.469542	−	1.74125i
$243$	−5.02966	+	7.52741i	−0.322653	+	0.482884i
$244$	−0.701184	+	0.343010i	−0.0448887	+	0.0219590i
$245$	−0.417443	+	2.09863i	−0.0266695	+	0.134076i
$246$	12.3409	−	10.7879i	0.786827	−	0.687813i
$247$	−3.71338	+	1.53813i	−0.236277	+	0.0978691i
$248$	−13.5579	+	5.54002i	−0.860924	+	0.351791i
$249$	−2.82586	−	1.17051i	−0.179081	−	0.0741780i
$250$	−5.12541	−	15.1784i	−0.324159	−	0.959969i
$251$	−8.95890	−	13.4079i	−0.565481	−	0.846302i	0.433000	−	0.901394i	$-0.357455\pi$
$251$	−8.95890	−	13.4079i	−0.565481	−	0.846302i	−0.998481	+	0.0550918i	$0.982455\pi$
$252$	4.07215	−	1.07722i	0.256521	−	0.0678586i
$253$	−30.4972	+	6.06626i	−1.91734	+	0.381383i
$254$	2.56201	+	19.7031i	0.160755	+	1.23628i
$255$	−13.6147			−0.852587
$256$	8.17609	−	13.7532i	0.511006	−	0.859577i
$257$	−13.3833			−0.834824			−0.417412	−	0.908717i	$-0.637063\pi$
$257$	−13.3833			−0.834824			−0.417412	+	0.908717i	$0.637063\pi$
$258$	1.52735	+	11.7460i	0.0950884	+	0.731277i
$259$	18.7692	−	3.73342i	1.16626	−	0.231984i
$260$	7.38725	−	1.95418i	0.458137	−	0.121193i
$261$	4.17628	+	6.25024i	0.258505	+	0.386880i
$262$	−7.21959	−	21.3802i	−0.446028	−	1.32087i
$263$	−19.9818	−	8.27672i	−1.23213	−	0.510364i	−0.330883	−	0.943672i	$-0.607346\pi$
$263$	−19.9818	−	8.27672i	−1.23213	−	0.510364i	−0.901246	+	0.433308i	$0.857346\pi$
$264$	28.7093	−	11.7312i	1.76693	−	0.722006i
$265$	−3.86131	+	1.59941i	−0.237198	+	0.0982507i
$266$	−3.72142	+	3.25311i	−0.228175	+	0.199461i
$267$	−4.01537	+	20.1866i	−0.245737	+	1.23540i
$268$	−3.06888	+	1.50125i	−0.187461	+	0.0917037i
$269$	−10.3945	+	15.5564i	−0.633762	+	0.948493i	0.366077	+	0.930584i	$0.380701\pi$
$269$	−10.3945	+	15.5564i	−0.633762	+	0.948493i	−0.999840	+	0.0179081i	$0.994299\pi$
$270$	−2.16595	+	8.03219i	−0.131816	+	0.488824i
$271$	−6.71687	−	6.71687i	−0.408021	−	0.408021i	0.473027	−	0.881048i	$-0.343161\pi$
$271$	−6.71687	−	6.71687i	−0.408021	−	0.408021i	−0.881048	+	0.473027i	$0.843161\pi$
$272$	5.15442	−	18.7572i	0.312532	−	1.13732i
$273$	−8.81621	+	8.81621i	−0.533581	+	0.533581i
$274$	−4.11799	−	7.15891i	−0.248777	−	0.432485i
$275$	13.8045	+	9.22385i	0.832440	+	0.556219i
$276$	−16.5785	−	14.6327i	−0.997909	−	0.880788i
$277$	7.75914	+	1.54339i	0.466201	+	0.0927332i	0.422601	−	0.906316i	$-0.361117\pi$
$277$	7.75914	+	1.54339i	0.466201	+	0.0927332i	0.0436004	+	0.999049i	$0.486117\pi$
$278$	−1.43910	−	0.0966284i	−0.0863116	−	0.00579539i
$279$	−1.78105	−	4.29984i	−0.106629	−	0.257425i
$280$	7.83827	−	5.18330i	0.468426	−	0.309761i
$281$	−1.28145	+	3.09369i	−0.0764447	+	0.184554i	−0.957482	−	0.288493i	$-0.906846\pi$
$281$	−1.28145	+	3.09369i	−0.0764447	+	0.184554i	0.881037	+	0.473047i	$0.156846\pi$
$282$	−2.59624	−	1.28547i	−0.154604	−	0.0765489i
$283$	−5.54432	+	3.70460i	−0.329576	+	0.220216i	−0.709338	−	0.704869i	$-0.751006\pi$
$283$	−5.54432	+	3.70460i	−0.329576	+	0.220216i	0.379762	+	0.925084i	$0.376006\pi$
$284$	1.80951	+	0.244100i	0.107375	+	0.0144847i
$285$	0.814650	+	4.09552i	0.0482557	+	0.242598i
$286$	−12.9097	+	16.7689i	−0.763368	+	0.991564i
$287$			13.7548i			0.811921i
$288$	4.38278	+	2.57720i	0.258258	+	0.151863i
$289$		−	6.65002i		−	0.391177i
$290$	13.2882	+	10.2301i	0.780310	+	0.600732i
$291$	1.63036	+	8.19637i	0.0955734	+	0.480480i
$292$	−20.6208	+	15.7186i	−1.20674	+	0.919864i
$293$	9.61191	−	6.42248i	0.561534	−	0.375205i	−0.242170	−	0.970234i	$-0.577859\pi$
$293$	9.61191	−	6.42248i	0.561534	−	0.375205i	0.803704	+	0.595029i	$0.202859\pi$
$294$	1.86991	−	3.77661i	0.109055	−	0.220257i
$295$	−3.23984	+	7.82167i	−0.188631	+	0.455395i
$296$	19.1447	+	12.9249i	1.11276	+	0.751247i
$297$	−8.81689	−	21.2858i	−0.511608	−	1.23513i
$298$	−0.00430044	+	0.0640471i	−0.000249118	+	0.00371015i
$299$	14.7989	+	2.94368i	0.855842	+	0.170238i
$300$	0.734617	+	11.7838i	0.0424131	+	0.680336i
$301$	−8.26453	−	5.52218i	−0.476359	−	0.318293i
$302$	24.9605	−	14.3579i	1.43632	−	0.826207i
$303$	21.3066	−	21.3066i	1.22403	−	1.22403i
$304$	−5.95088	−	0.428174i	−0.341306	−	0.0245575i
$305$	−0.391295	−	0.391295i	−0.0224055	−	0.0224055i
$306$	5.96829	+	1.60940i	0.341184	+	0.0920034i
$307$	−17.9541	+	26.8702i	−1.02469	+	1.53356i	−0.190804	+	0.981628i	$0.561109\pi$
$307$	−17.9541	+	26.8702i	−1.02469	+	1.53356i	−0.833889	+	0.551933i	$0.813891\pi$
$308$	−8.44403	+	24.6171i	−0.481143	+	1.40269i
$309$	−1.64780	+	8.28404i	−0.0937400	+	0.471263i
$310$	−6.83347	−	7.81719i	−0.388115	−	0.443986i
$311$	17.5995	−	7.28996i	0.997978	−	0.413376i	0.176923	−	0.984225i	$-0.443386\pi$
$311$	17.5995	−	7.28996i	0.997978	−	0.413376i	0.821055	+	0.570849i	$0.193386\pi$
$312$	−15.0493	−	0.0719876i	−0.852001	−	0.00407549i
$313$	27.5944	+	11.4300i	1.55973	+	0.646060i	0.985042	−	0.172315i	$-0.0551246\pi$
$313$	27.5944	+	11.4300i	1.55973	+	0.646060i	0.574685	+	0.818375i	$0.305125\pi$
$314$	−19.7932	+	6.68371i	−1.11699	+	0.377183i
$315$	1.65901	+	2.48288i	0.0934744	+	0.139894i
$316$	12.9726	+	7.54498i	0.729764	+	0.424438i
$317$	13.5672	−	2.69867i	0.762007	−	0.151573i	0.201235	−	0.979543i	$-0.435504\pi$
$317$	13.5672	−	2.69867i	0.762007	−	0.151573i	0.560772	+	0.827970i	$0.310504\pi$
$318$	8.16263	−	1.06139i	0.457738	−	0.0595200i
$319$	−46.4442			−2.60037
$320$	11.1031	+	2.31918i	0.620683	+	0.129646i
$321$	13.0731			0.729669
$322$	18.4008	−	2.39267i	1.02544	−	0.133338i
$323$	−7.11430	+	1.41512i	−0.395850	+	0.0787395i
$324$	10.9486	−	18.8247i	0.608258	−	1.04582i
$325$	−4.47591	−	6.69868i	−0.248279	−	0.371576i
$326$	−0.553024	+	0.186744i	−0.0306292	+	0.0103428i
$327$	20.9539	+	8.67941i	1.15876	+	0.479972i
$328$	−11.7959	+	11.6836i	−0.651322	+	0.645121i
$329$	2.24601	−	0.930326i	0.123826	−	0.0512905i
$330$	14.4701	+	16.5532i	0.796555	+	0.911224i
$331$	1.95265	−	9.81665i	0.107328	−	0.539572i	−0.889287	−	0.457351i	$-0.848798\pi$
$331$	1.95265	−	9.81665i	0.107328	−	0.539572i	0.996614	−	0.0822216i	$-0.0262015\pi$
$332$	2.93052	+	1.00521i	0.160833	+	0.0551682i
$333$	−4.07805	+	6.10323i	−0.223476	+	0.334455i
$334$	−6.71796	−	1.81156i	−0.367590	−	0.0991239i
$335$	−1.71258	−	1.71258i	−0.0935683	−	0.0935683i
$336$	−17.5628	+	5.83711i	−0.958128	+	0.318440i
$337$	19.8896	−	19.8896i	1.08346	−	1.08346i	0.0872738	−	0.996184i	$-0.472184\pi$
$337$	19.8896	−	19.8896i	1.08346	−	1.08346i	0.996184	−	0.0872738i	$-0.0278155\pi$
$338$	−7.03471	+	4.04655i	−0.382638	+	0.220103i
$339$	−11.6585	−	7.78997i	−0.633204	−	0.423093i
$340$	13.7636	−	0.858042i	0.746435	−	0.0465339i
$341$	28.2028	+	5.60988i	1.52727	+	0.303792i
$342$	0.127015	−	1.89165i	0.00686819	−	0.102289i
$343$	7.63037	+	18.4213i	0.412001	+	0.994659i
$344$	−2.28432	−	11.7782i	−0.123162	−	0.635038i
$345$	5.99896	−	14.4828i	0.322973	−	0.779727i
$346$	1.95227	−	3.94296i	0.104955	−	0.211975i
$347$	20.0723	−	13.4119i	1.07754	−	0.719988i	0.115612	−	0.993294i	$-0.463117\pi$
$347$	20.0723	−	13.4119i	1.07754	−	0.719988i	0.961927	+	0.273306i	$0.0881171\pi$
$348$	−20.0226	−	26.2670i	−1.07332	−	1.40806i
$349$	−2.58414	−	12.9913i	−0.138326	−	0.695410i	−0.986246	−	0.165286i	$-0.947145\pi$
$349$	−2.58414	−	12.9913i	−0.138326	−	0.695410i	0.847920	−	0.530124i	$-0.177855\pi$
$350$	−7.85055	−	6.04385i	−0.419629	−	0.323057i
$351$			11.1801i			0.596749i
$352$	−28.2838	+	13.6688i	−1.50753	+	0.728550i
$353$		−	6.93502i		−	0.369114i	−0.982822	−	0.184557i	$-0.940915\pi$
$353$		−	6.93502i		−	0.369114i	0.982822	−	0.184557i	$-0.0590850\pi$
$354$	10.1715	−	13.2121i	0.540608	−	0.702213i
$355$	0.252529	+	1.26955i	0.0134029	+	0.0673808i
$356$	2.78705	−	20.6604i	0.147713	−	1.09500i
$357$	−18.7088	+	12.5009i	−0.990177	+	0.661615i
$358$	−4.81304	−	2.38308i	−0.254377	−	0.125950i
$359$	−5.35824	+	12.9359i	−0.282797	+	0.682732i	−0.999899	−	0.0142363i	$-0.995468\pi$
$359$	−5.35824	+	12.9359i	−0.282797	+	0.682732i	0.717102	+	0.696969i	$0.245468\pi$
$360$	−0.720088	+	3.53175i	−0.0379520	+	0.186140i
$361$	−6.41960	−	15.4983i	−0.337874	−	0.815700i
$362$	−1.59032	−	0.106782i	−0.0835854	−	0.00561234i
$363$	−38.4180	−	7.64181i	−2.01642	−	0.401091i
$364$	8.35697	−	9.46822i	0.438024	−	0.496270i
$365$	−15.2835	−	10.2121i	−0.799976	−	0.534527i
$366$	0.543425	+	0.944715i	0.0284053	+	0.0493811i
$367$	9.38352	−	9.38352i	0.489816	−	0.489816i	−0.418432	−	0.908248i	$-0.637420\pi$
$367$	9.38352	−	9.38352i	0.489816	−	0.489816i	0.908248	+	0.418432i	$0.137420\pi$
$368$	17.6820	+	13.7479i	0.921736	+	0.716659i
$369$	−3.73062	−	3.73062i	−0.194209	−	0.194209i
$370$	−4.26351	+	15.8108i	−0.221649	+	0.821962i
$371$	−3.83751	+	5.74324i	−0.199234	+	0.298174i
$372$	8.98581	+	18.3689i	0.465893	+	0.952381i
$373$	1.64789	−	8.28453i	0.0853248	−	0.428956i	−0.914385	−	0.404847i	$-0.867325\pi$
$373$	1.64789	−	8.28453i	0.0853248	−	0.428956i	0.999709	−	0.0241098i	$-0.00767512\pi$
$374$	−28.7544	+	25.1359i	−1.48686	+	1.29975i
$375$	−20.6652	+	8.55982i	−1.06715	+	0.442027i
$376$	2.70564	+	1.13591i	0.139533	+	0.0585798i
$377$	20.8217	+	8.62463i	1.07237	+	0.444191i
$378$	4.39868	+	13.0263i	0.226243	+	0.670000i
$379$	2.04578	+	3.06172i	0.105085	+	0.157270i	0.880285	−	0.474445i	$-0.157351\pi$
$379$	2.04578	+	3.06172i	0.105085	+	0.157270i	−0.775201	+	0.631715i	$0.782351\pi$
$380$	−1.08167	−	4.08896i	−0.0554885	−	0.209759i
$381$	27.2082	−	5.41204i	1.39392	−	0.277267i
$382$	4.07031	+	31.3027i	0.208255	+	1.60158i
$383$	12.3567			0.631396			0.315698	−	0.948860i	$-0.397761\pi$
$383$	12.3567			0.631396			0.315698	+	0.948860i	$0.397761\pi$
$384$	−19.9240	−	10.1034i	−1.01674	−	0.515589i
$385$	−18.4497			−0.940285
$386$	0.384366	+	2.95596i	0.0195637	+	0.150454i
$387$	3.73927	−	0.743788i	0.190078	−	0.0378089i
$388$	−2.16475	−	8.18324i	−0.109898	−	0.415441i
$389$	−2.74278	−	4.10486i	−0.139065	−	0.208125i	0.755400	−	0.655264i	$-0.227443\pi$
$389$	−2.74278	−	4.10486i	−0.139065	−	0.208125i	−0.894464	+	0.447140i	$0.852443\pi$
$390$	−3.41330	−	10.1082i	−0.172839	−	0.511847i
$391$	25.1579	+	10.4207i	1.27229	+	0.526999i
$392$	−1.65234	+	3.93575i	−0.0834559	+	0.198785i
$393$	−29.1088	+	12.0573i	−1.46835	+	0.608208i
$394$	5.98242	−	5.22959i	0.301390	−	0.263463i
$395$	−2.07554	+	10.4345i	−0.104432	+	0.525015i
$396$	−4.38652	−	8.96695i	−0.220431	−	0.450606i
$397$	19.4770	−	29.1493i	0.977521	−	1.46296i	0.0934430	−	0.995625i	$-0.470213\pi$
$397$	19.4770	−	29.1493i	0.977521	−	1.46296i	0.884078	−	0.467339i	$-0.154787\pi$
$398$	5.83348	−	21.6328i	0.292406	−	1.08436i
$399$	4.87991	+	4.87991i	0.244301	+	0.244301i
$400$	−1.48530	−	11.8663i	−0.0742649	−	0.593315i
$401$	−23.0145	+	23.0145i	−1.14929	+	1.14929i	−0.162599	+	0.986692i	$0.551988\pi$
$401$	−23.0145	+	23.0145i	−1.14929	+	1.14929i	−0.986692	+	0.162599i	$0.948012\pi$
$402$	2.37841	+	4.13474i	0.118624	+	0.206222i
$403$	−11.6020	−	7.75223i	−0.577939	−	0.386166i
$404$	−20.1967	+	22.8823i	−1.00482	+	1.13844i
$405$	15.1416	+	3.01185i	0.752393	+	0.149660i
$406$	27.6533	+	1.85678i	1.37241	+	0.0921504i
$407$	−17.3554	−	41.8995i	−0.860273	−	2.07688i
$408$	−26.6122	−	5.42597i	−1.31750	−	0.268625i
$409$	13.4728	−	32.5262i	0.666187	−	1.60832i	−0.121749	−	0.992561i	$-0.538850\pi$
$409$	13.4728	−	32.5262i	0.666187	−	1.60832i	0.787936	−	0.615757i	$-0.211150\pi$
$410$	−10.5479	−	5.22258i	−0.520925	−	0.257925i
$411$	−9.58768	+	6.40628i	−0.472925	+	0.315999i
$412$	1.14373	−	8.47846i	0.0563475	−	0.417704i
$413$	2.72968	+	13.7230i	0.134319	+	0.675266i
$414$	−4.34178	+	5.63967i	−0.213387	+	0.277175i
$415$			2.19633i			0.107814i
$416$	15.2184	−	0.875681i	0.746144	−	0.0429338i
$417$			2.01381i			0.0986167i
$418$	9.28184	+	7.14574i	0.453989	+	0.349510i
$419$	−3.73506	−	18.7774i	−0.182470	−	0.917337i	−0.958162	−	0.286226i	$-0.907599\pi$
$419$	−3.73506	−	18.7774i	−0.182470	−	0.917337i	0.775692	−	0.631111i	$-0.217401\pi$
$420$	−7.95388	−	10.4344i	−0.388110	−	0.509148i
$421$	−15.5376	+	10.3819i	−0.757256	+	0.505982i	−0.873253	−	0.487267i	$-0.837994\pi$
$421$	−15.5376	+	10.3819i	−0.757256	+	0.505982i	0.115997	+	0.993250i	$0.462994\pi$
$422$	−1.82092	+	3.67767i	−0.0886410	+	0.179026i
$423$	−0.356843	+	0.861495i	−0.0173503	+	0.0418873i
$424$	−8.18498	+	1.58743i	−0.397498	+	0.0770925i
$425$	−5.56399	−	13.4327i	−0.269893	−	0.651580i
$426$	0.170791	−	2.54362i	0.00827485	−	0.123239i
$427$	−0.896984	−	0.178421i	−0.0434081	−	0.00863440i
$428$	−13.2160	+	0.823906i	−0.638820	+	0.0398250i
$429$	24.5678	+	16.4157i	1.18614	+	0.792556i
$430$	7.37267	−	4.24095i	0.355542	−	0.204517i
$431$	−10.1766	+	10.1766i	−0.490192	+	0.490192i	−0.908367	−	0.418175i	$-0.862670\pi$
$431$	−10.1766	+	10.1766i	−0.490192	+	0.490192i	0.418175	+	0.908367i	$0.362670\pi$
$432$	−7.43483	+	14.8370i	−0.357709	+	0.713847i
$433$	7.09854	+	7.09854i	0.341134	+	0.341134i	0.856794	−	0.515660i	$-0.172453\pi$
$433$	7.09854	+	7.09854i	0.341134	+	0.341134i	−0.515660	+	0.856794i	$0.672453\pi$
$434$	−16.5679	−	4.46769i	−0.795286	−	0.214456i
$435$	13.0083	−	19.4683i	0.623701	−	0.933435i
$436$	−21.7300	−	7.45372i	−1.04068	−	0.356968i
$437$	1.62938	−	8.19142i	0.0779436	−	0.391849i
$438$	23.8260	+	27.2559i	1.13845	+	1.30234i
$439$	21.2594	−	8.80592i	1.01465	−	0.420284i	0.187504	−	0.982264i	$-0.439960\pi$
$439$	21.2594	−	8.80592i	1.01465	−	0.420284i	0.827151	+	0.561980i	$0.189960\pi$
$440$	−15.6716	−	15.8222i	−0.747113	−	0.754295i
$441$	−1.25317	−	0.519080i	−0.0596748	−	0.0247181i
$442$	17.5588	−	5.92921i	0.835187	−	0.282024i
$443$	−1.49883	−	2.24316i	−0.0712115	−	0.106576i	0.794155	−	0.607716i	$-0.207914\pi$
$443$	−1.49883	−	2.24316i	−0.0712115	−	0.106576i	−0.865366	+	0.501140i	$0.832914\pi$
$444$	16.2146	−	27.8789i	0.769512	−	1.32307i
$445$	14.4953	−	2.88329i	0.687142	−	0.136681i
$446$	2.58435	−	0.336045i	0.122372	−	0.0159122i
$447$	0.0896245			0.00423909
$448$	17.3869	−	7.00779i	0.821455	−	0.331087i
$449$	8.51822			0.402000			0.201000	−	0.979591i	$-0.435581\pi$
$449$	8.51822			0.402000			0.201000	+	0.979591i	$0.435581\pi$
$450$	3.76848	−	0.490018i	0.177648	−	0.0230997i
$451$	31.9706	−	6.35936i	1.50544	−	0.299450i
$452$	12.2769	+	7.14038i	0.577458	+	0.335855i
$453$	−22.3364	−	33.4288i	−1.04946	−	1.57062i
$454$	2.01792	−	0.681404i	0.0947054	−	0.0319799i
$455$	8.27132	+	3.42609i	0.387766	+	0.160618i
$456$	−0.0398463	+	8.33005i	−0.00186597	+	0.390090i
$457$	−11.6115	+	4.80963i	−0.543162	+	0.224985i	−0.637357	−	0.770569i	$-0.719972\pi$
$457$	−11.6115	+	4.80963i	−0.543162	+	0.224985i	0.0941951	+	0.995554i	$0.469972\pi$
$458$	−18.7896	−	21.4945i	−0.877981	−	1.00437i
$459$	−3.93627	+	19.7890i	−0.183729	+	0.923670i
$460$	−5.15180	+	15.0192i	−0.240204	+	0.700273i
$461$	−11.2805	+	16.8825i	−0.525388	+	0.786298i	−0.995343	−	0.0963919i	$-0.969270\pi$
$461$	−11.2805	+	16.8825i	−0.525388	+	0.786298i	0.469956	+	0.882690i	$0.344270\pi$
$462$	35.0832	+	9.46051i	1.63222	+	0.440143i
$463$	12.9581	+	12.9581i	0.602214	+	0.602214i	0.940899	−	0.338686i	$-0.109982\pi$
$463$	12.9581	+	12.9581i	0.602214	+	0.602214i	−0.338686	+	0.940899i	$0.609982\pi$
$464$	21.8969	+	25.2923i	1.01654	+	1.17416i
$465$	−10.2507	+	10.2507i	−0.475366	+	0.475366i
$466$	−29.4248	+	16.9259i	−1.36308	+	0.784079i
$467$	9.64631	+	6.44546i	0.446378	+	0.298260i	0.758370	−	0.651824i	$-0.225996\pi$
$467$	9.64631	+	6.44546i	0.446378	+	0.298260i	−0.311992	+	0.950085i	$0.600996\pi$
$468$	0.301396	+	4.83460i	0.0139321	+	0.223480i
$469$	−3.92583	−	0.780897i	−0.181278	−	0.0360585i
$470$	−0.139366	+	2.07559i	−0.00642845	+	0.0957399i
$471$	11.1623	+	26.9482i	0.514331	+	1.24171i
$472$	−9.45003	+	13.9976i	−0.434973	+	0.644290i
$473$	−9.01434	+	21.7625i	−0.414480	+	1.00064i
$474$	9.29727	−	18.7775i	0.427038	−	0.862478i
$475$	−3.70783	+	2.47749i	−0.170127	+	0.113675i
$476$	18.1255	−	13.8166i	0.830783	−	0.633283i
$477$	−0.516878	−	2.59852i	−0.0236662	−	0.118978i
$478$	10.4317	+	8.03102i	0.477137	+	0.367330i
$479$			12.0889i			0.552355i	0.961107	+	0.276178i	$0.0890678\pi$
$479$			12.0889i			0.552355i	−0.961107	+	0.276178i	$0.910932\pi$
$480$	2.19223	−	15.6844i	0.100061	−	0.715890i
$481$			22.0071i			1.00344i
$482$	−16.5791	+	21.5351i	−0.755158	+	0.980898i
$483$	−5.05433	−	25.4098i	−0.229980	−	1.15619i
$484$	39.3196	+	5.30414i	1.78725	+	0.241097i
$485$	4.98950	−	3.33388i	0.226562	−	0.151384i
$486$	−11.4737	−	5.68096i	−0.520457	−	0.257693i
$487$	−13.3448	+	32.2172i	−0.604711	+	1.45990i	0.263971	+	0.964531i	$0.414968\pi$
$487$	−13.3448	+	32.2172i	−0.604711	+	1.45990i	−0.868682	+	0.495370i	$0.835032\pi$
$488$	−0.608905	−	0.920796i	−0.0275638	−	0.0416825i
$489$	0.311876	+	0.752935i	0.0141035	+	0.0340489i
$490$	−3.01926	−	0.202728i	−0.136396	−	0.00915831i
$491$	−26.1410	−	5.19977i	−1.17973	−	0.234662i	−0.433999	−	0.900913i	$-0.642898\pi$
$491$	−26.1410	−	5.19977i	−1.17973	−	0.234662i	−0.745727	+	0.666251i	$0.767898\pi$
$492$	17.3795	+	15.3397i	0.783528	+	0.691569i
$493$	33.8182	+	22.5966i	1.52310	+	1.01770i
$494$	−2.83425	−	4.92719i	−0.127519	−	0.221685i
$495$	5.00399	−	5.00399i	0.224913	−	0.224913i
$496$	−10.2417	−	18.0034i	−0.459867	−	0.808375i
$497$	1.51270	+	1.51270i	0.0678539	+	0.0678539i
$498$	1.12622	−	4.17645i	0.0504670	−	0.187151i
$499$	1.56309	−	2.33933i	0.0699736	−	0.104723i	−0.794832	−	0.606829i	$-0.792441\pi$
$499$	1.56309	−	2.33933i	0.0699736	−	0.104723i	0.864806	+	0.502106i	$0.167441\pi$
$500$	20.3517	−	9.95579i	0.910156	−	0.445237i
$501$	−1.89525	+	9.52804i	−0.0846733	+	0.425682i
$502$	17.1697	−	15.0090i	0.766321	−	0.669887i
$503$	−36.9205	+	15.2930i	−1.64620	+	0.681880i	−0.996902	−	0.0786507i	$-0.974939\pi$
$503$	−36.9205	+	15.2930i	−1.64620	+	0.681880i	−0.649302	+	0.760531i	$0.724939\pi$
$504$	2.25328	+	5.51437i	0.100369	+	0.245630i
$505$	−19.9897	−	8.28001i	−0.889531	−	0.368456i
$506$	−14.0687	−	41.6632i	−0.625430	−	1.85216i
$507$	6.29514	+	9.42135i	0.279577	+	0.418417i
$508$	−27.1646	+	7.18595i	−1.20523	+	0.318825i
$509$	−3.51571	+	0.699318i	−0.155831	+	0.0309967i	−0.272389	−	0.962187i	$-0.587814\pi$
$509$	−3.51571	+	0.699318i	−0.155831	+	0.0309967i	0.116558	+	0.993184i	$0.462814\pi$
$510$	−2.48273	−	19.0934i	−0.109937	−	0.845470i
$511$	−30.3786			−1.34387
$512$	20.7786	+	8.95823i	0.918293	+	0.395901i
$513$	6.18836			0.273223
$514$	−2.44052	−	18.7688i	−0.107647	−	0.827855i
$515$	5.94847	−	1.18322i	0.262121	−	0.0521391i
$516$	−16.1942	+	4.28392i	−0.712910	+	0.188589i
$517$	−3.20079	−	4.79032i	−0.140771	−	0.210678i
$518$	8.65845	+	25.6412i	0.380431	+	1.12661i
$519$	−5.67543	−	2.35084i	−0.249124	−	0.103190i
$520$	4.08766	+	10.0036i	0.179256	+	0.438686i
$521$	−13.4480	+	5.57034i	−0.589168	+	0.244041i	−0.657292	−	0.753636i	$-0.728298\pi$
$521$	−13.4480	+	5.57034i	−0.589168	+	0.244041i	0.0681249	+	0.997677i	$0.478298\pi$
$522$	−8.00381	+	6.99661i	−0.350317	+	0.306233i
$523$	−0.274054	+	1.37776i	−0.0119835	+	0.0602453i	−0.986314	−	0.164876i	$-0.947278\pi$
$523$	−0.274054	+	1.37776i	−0.0119835	+	0.0602453i	0.974331	+	0.225121i	$0.0722777\pi$
$524$	28.6672	−	14.0236i	1.25233	−	0.612624i
$525$	−7.68519	+	11.5017i	−0.335409	+	0.501975i
$526$	7.96354	−	29.5319i	0.347227	−	1.28765i
$527$	−17.8064	−	17.8064i	−0.775660	−	0.775660i
$528$	21.6872	+	38.1229i	0.943816	+	1.65908i
$529$	−5.90683	+	5.90683i	−0.256819	+	0.256819i
$530$	−2.94715	−	5.12346i	−0.128016	−	0.222549i
$531$	−4.46235	−	2.98165i	−0.193650	−	0.129392i
$532$	−5.24081	−	4.62572i	−0.227218	−	0.200550i
$533$	−15.5139	−	3.08591i	−0.671982	−	0.133665i
$534$	−29.0421	−	1.95003i	−1.25677	−	0.0843860i
$535$	−3.59237	−	8.67274i	−0.155312	−	0.374955i
$536$	−2.66500	−	4.03005i	−0.115110	−	0.174072i
$537$	−2.86960	+	6.92782i	−0.123832	+	0.298958i
$538$	−23.7120	−	11.7405i	−1.02229	−	0.506168i
$539$	6.96822	−	4.65602i	0.300143	−	0.200549i
$540$	−11.6594	−	1.57283i	−0.501740	−	0.0676837i
$541$	−8.09775	−	40.7102i	−0.348150	−	1.75027i	−0.616886	−	0.787053i	$-0.711606\pi$
$541$	−8.09775	−	40.7102i	−0.348150	−	1.75027i	0.268736	−	0.963214i	$-0.413394\pi$
$542$	8.19493	−	10.6447i	0.352002	−	0.457227i
$543$			2.22542i			0.0955018i
$544$	27.2452	+	3.80810i	1.16813	+	0.163271i
$545$		−	16.2860i		−	0.697614i
$546$	−13.9716	−	10.7562i	−0.597929	−	0.460324i
$547$	−8.11081	−	40.7758i	−0.346793	−	1.74345i	−0.622883	−	0.782315i	$-0.714039\pi$
$547$	−8.11081	−	40.7758i	−0.346793	−	1.74345i	0.276090	−	0.961132i	$-0.410961\pi$
$548$	9.28876	−	7.08057i	0.396796	−	0.302467i
$549$	0.291675	−	0.194891i	0.0124484	−	0.00831773i
$550$	−10.4183	+	21.0415i	−0.444236	+	0.897213i
$551$	4.77387	−	11.5251i	0.203374	−	0.490988i
$552$	17.4979	−	25.9182i	0.744759	−	1.10315i
$553$	6.72864	+	16.2444i	0.286131	+	0.690781i
$554$	−0.749534	+	11.1629i	−0.0318446	+	0.474267i
$555$	22.4243	+	4.46047i	0.951859	+	0.189337i
$556$	−0.126917	−	2.03583i	−0.00538246	−	0.0863383i
$557$	−0.577961	−	0.386181i	−0.0244890	−	0.0163630i	0.543265	−	0.839561i	$-0.317188\pi$
$557$	−0.577961	−	0.386181i	−0.0244890	−	0.0163630i	−0.567754	+	0.823198i	$0.692188\pi$
$558$	5.70534	−	3.28186i	0.241526	−	0.138932i
$559$	8.08256	−	8.08256i	0.341856	−	0.341856i
$560$	8.69845	+	10.0472i	0.367577	+	0.424573i
$561$	37.7058	+	37.7058i	1.59194	+	1.59194i
$562$	−4.57229	−	1.23296i	−0.192870	−	0.0520092i
$563$	−1.19920	+	1.79474i	−0.0505404	+	0.0756391i	−0.855879	−	0.517176i	$-0.826983\pi$
$563$	−1.19920	+	1.79474i	−0.0505404	+	0.0756391i	0.805339	+	0.592815i	$0.201983\pi$
$564$	1.32932	−	3.87540i	0.0559744	−	0.163184i
$565$	−1.96424	+	9.87492i	−0.0826364	+	0.415441i
$566$	−6.20640	−	7.09984i	−0.260874	−	0.298429i
$567$	23.5725	−	9.76404i	0.989951	−	0.410051i
$568$	−0.0123518	+	2.58219i	−0.000518268	+	0.108346i
$569$	−17.7585	−	7.35583i	−0.744477	−	0.308372i	−0.0219910	−	0.999758i	$-0.507001\pi$
$569$	−17.7585	−	7.35583i	−0.744477	−	0.308372i	−0.722486	+	0.691386i	$0.757001\pi$
$570$	−5.59504	+	1.88932i	−0.234350	+	0.0791347i
$571$	15.2733	+	22.8580i	0.639166	+	0.956579i	0.999716	+	0.0238392i	$0.00758897\pi$
$571$	15.2733	+	22.8580i	0.639166	+	0.956579i	−0.360550	+	0.932740i	$0.617411\pi$
$572$	−25.8709	−	15.0468i	−1.08172	−	0.629138i
$573$	43.2261	−	8.59821i	1.80580	−	0.359195i
$574$	−19.2899	+	2.50827i	−0.805143	+	0.104693i
$575$	16.7407			0.698136
$576$	−2.81506	+	6.61641i	−0.117294	+	0.275684i
$577$	−33.2616			−1.38470			−0.692350	−	0.721562i	$-0.743425\pi$
$577$	−33.2616			−1.38470			−0.692350	+	0.721562i	$0.743425\pi$
$578$	9.32603	−	1.21267i	0.387912	−	0.0504404i
$579$	4.08191	−	0.811943i	0.169638	−	0.0337432i
$580$	−11.9236	+	20.5010i	−0.495100	+	0.851258i
$581$	2.01664	+	3.01811i	0.0836643	+	0.125213i
$582$	−11.1973	+	3.78109i	−0.464145	+	0.156731i
$583$	15.1234	+	6.26430i	0.626346	+	0.259441i
$584$	−25.8043	−	26.0523i	−1.06779	−	1.07805i
$585$	−3.17261	+	1.31414i	−0.131171	+	0.0543329i
$586$	10.7597	+	12.3086i	0.444480	+	0.508465i
$587$	7.71743	−	38.7981i	0.318532	−	1.60137i	−0.407164	−	0.913355i	$-0.633482\pi$
$587$	7.71743	−	38.7981i	0.318532	−	1.60137i	0.725697	−	0.688015i	$-0.241518\pi$
$588$	5.63734	+	1.93369i	0.232480	+	0.0797440i
$589$	−4.29099	+	6.42191i	−0.176807	+	0.264610i
$590$	−11.5600	−	3.11725i	−0.475916	−	0.128335i
$591$	−7.84478	−	7.84478i	−0.322691	−	0.322691i
$592$	−14.6349	+	29.2056i	−0.601490	+	1.20034i
$593$	−18.9653	+	18.9653i	−0.778811	+	0.778811i	−0.979629	−	0.200817i	$-0.935640\pi$
$593$	−18.9653	+	18.9653i	−0.778811	+	0.778811i	0.200817	+	0.979629i	$0.435640\pi$
$594$	28.2436	−	16.2465i	1.15885	−	0.666601i
$595$	13.4341	+	8.97640i	0.550746	+	0.367997i
$596$	−0.0906044	+	0.00564841i	−0.00371130	+	0.000231368i
$597$	−30.6817	−	6.10297i	−1.25572	−	0.249778i
$598$	−1.42957	+	21.2909i	−0.0584596	+	0.870648i
$599$	7.92904	+	19.1424i	0.323972	+	0.782137i	0.999016	+	0.0443592i	$0.0141246\pi$
$599$	7.92904	+	19.1424i	0.323972	+	0.782137i	−0.675044	+	0.737777i	$0.735875\pi$
$600$	−16.3917	+	3.17907i	−0.669187	+	0.129785i
$601$	9.15574	−	22.1039i	0.373471	−	0.901638i	−0.619686	−	0.784850i	$-0.712740\pi$
$601$	9.15574	−	22.1039i	0.373471	−	0.901638i	0.993157	−	0.116788i	$-0.0372598\pi$
$602$	6.23726	−	12.5972i	0.254212	−	0.513425i
$603$	1.27657	−	0.852979i	0.0519861	−	0.0347360i
$604$	24.6874	+	32.3866i	1.00452	+	1.31779i
$605$	5.48730	+	27.5865i	0.223091	+	1.12155i
$606$	33.7659	+	25.9951i	1.37165	+	1.05598i
$607$		−	47.2885i		−	1.91938i	−0.281061	−	0.959690i	$-0.590686\pi$
$607$		−	47.2885i		−	1.91938i	0.281061	−	0.959690i	$-0.409314\pi$
$608$	−0.484703	−	8.42363i	−0.0196573	−	0.341623i
$609$		−	38.6967i		−	1.56807i
$610$	0.477400	−	0.620110i	0.0193293	−	0.0251075i
$611$	0.545411	+	2.74196i	0.0220649	+	0.110928i
$612$	−1.16868	+	8.66345i	−0.0472412	+	0.350199i
$613$	26.9337	−	17.9965i	1.08784	−	0.726873i	0.123717	−	0.992318i	$-0.460519\pi$
$613$	26.9337	−	17.9965i	1.08784	−	0.726873i	0.964126	+	0.265444i	$0.0855186\pi$
$614$	−40.9569	−	20.2790i	−1.65289	−	0.818393i
$615$	−6.28881	+	15.1825i	−0.253589	+	0.612218i
$616$	−36.0630	−	7.35289i	−1.45302	−	0.296256i
$617$	−2.14483	−	5.17808i	−0.0863476	−	0.208462i	0.874807	−	0.484471i	$-0.160988\pi$
$617$	−2.14483	−	5.17808i	−0.0863476	−	0.208462i	−0.961155	+	0.276009i	$0.910988\pi$
$618$	−11.9181	−	0.800240i	−0.479416	−	0.0321904i
$619$	−42.0718	−	8.36860i	−1.69101	−	0.336363i	−0.746634	−	0.665235i	$-0.768331\pi$
$619$	−42.0718	−	8.36860i	−1.69101	−	0.336363i	−0.944374	+	0.328872i	$0.893331\pi$
$620$	9.71676	−	11.0088i	0.390234	−	0.442125i
$621$	−19.3163	−	12.9067i	−0.775135	−	0.517928i
$622$	13.4329	+	23.3523i	0.538609	+	0.936344i
$623$	17.2715	−	17.2715i	0.691966	−	0.691966i
$624$	−2.64338	−	21.1184i	−0.105820	−	0.845414i
$625$	0.786975	+	0.786975i	0.0314790	+	0.0314790i
$626$	−10.9975	+	40.7829i	−0.439547	+	1.63001i
$627$	9.08633	−	13.5987i	0.362873	−	0.543078i
$628$	−12.9827	−	26.5393i	−0.518066	−	1.05903i
$629$	−7.74824	+	38.9530i	−0.308943	+	1.55316i
$630$	−3.17948	+	2.77937i	−0.126673	+	0.110733i
$631$	20.3573	−	8.43229i	0.810413	−	0.335684i	0.0612942	−	0.998120i	$-0.480477\pi$
$631$	20.3573	−	8.43229i	0.810413	−	0.335684i	0.749119	+	0.662436i	$0.230477\pi$
$632$	−8.21551	+	19.5687i	−0.326795	+	0.778401i
$633$	5.29358	+	2.19267i	0.210401	+	0.0871509i
$634$	6.25869	+	18.5346i	0.248564	+	0.736101i
$635$	−11.0669	−	16.5628i	−0.439178	−	0.657276i
$636$	2.97701	+	11.2538i	0.118046	+	0.446242i
$637$	−3.98859	+	0.793380i	−0.158034	+	0.0314349i
$638$	−8.46937	−	65.1336i	−0.335306	−	2.57867i
$639$	−0.820558			−0.0324608
$640$	−1.22772	+	15.9940i	−0.0485300	+	0.632219i
$641$	24.2418			0.957494			0.478747	−	0.877953i	$-0.341091\pi$
$641$	24.2418			0.957494			0.478747	+	0.877953i	$0.341091\pi$
$642$	2.38396	+	18.3338i	0.0940873	+	0.723577i
$643$	−9.42785	+	1.87532i	−0.371798	+	0.0739552i	−0.377453	−	0.926029i	$-0.623200\pi$
$643$	−9.42785	+	1.87532i	−0.371798	+	0.0739552i	0.00565492	+	0.999984i	$0.498200\pi$
$644$	6.71100	+	25.3691i	0.264450	+	0.999683i
$645$	−6.59758	−	9.87397i	−0.259779	−	0.388787i
$646$	−3.28191	−	9.71908i	−0.129125	−	0.382392i
$647$	31.3004	+	12.9650i	1.23055	+	0.509709i	0.900748	−	0.434343i	$-0.143019\pi$
$647$	31.3004	+	12.9650i	1.23055	+	0.509709i	0.329798	+	0.944052i	$0.393019\pi$
$648$	28.3965	+	11.9217i	1.11552	+	0.468327i
$649$	30.6347	−	12.6893i	1.20252	−	0.498099i
$650$	8.57807	−	7.49860i	0.336459	−	0.294119i
$651$	−4.67408	+	23.4982i	−0.183192	+	0.920967i
$652$	−0.362738	−	0.741511i	−0.0142059	−	0.0290398i
$653$	−9.43917	+	14.1267i	−0.369383	+	0.552821i	−0.968872	−	0.247562i	$-0.920371\pi$
$653$	−9.43917	+	14.1267i	−0.369383	+	0.552821i	0.599489	+	0.800383i	$0.295371\pi$
$654$	−8.35099	+	30.9687i	−0.326549	+	1.21097i
$655$	15.9977	+	15.9977i	0.625081	+	0.625081i
$656$	−18.5363	−	14.4121i	−0.723720	−	0.562699i
$657$	8.23939	−	8.23939i	0.321449	−	0.321449i
$658$	1.71427	+	2.98016i	0.0668291	+	0.116179i
$659$	15.6666	+	10.4681i	0.610286	+	0.407780i	0.821948	−	0.569563i	$-0.192888\pi$
$659$	15.6666	+	10.4681i	0.610286	+	0.407780i	−0.211662	+	0.977343i	$0.567888\pi$
$660$	−20.5756	+	23.3116i	−0.800905	+	0.907403i
$661$	8.02511	+	1.59629i	0.312140	+	0.0620886i	0.348675	−	0.937244i	$-0.386632\pi$
$661$	8.02511	+	1.59629i	0.312140	+	0.0620886i	−0.0365342	+	0.999332i	$0.511632\pi$
$662$	14.1230	+	0.948290i	0.548907	+	0.0368563i
$663$	−9.90222	−	23.9061i	−0.384570	−	0.928435i
$664$	−0.875318	+	4.29309i	−0.0339689	+	0.166604i
$665$	1.89640	−	4.57831i	0.0735392	−	0.177539i
$666$	−9.30287	−	4.60612i	−0.360479	−	0.178484i
$667$	−38.9384	+	26.0178i	−1.50770	+	1.00741i
$668$	1.31548	−	9.75166i	0.0508974	−	0.377303i
$669$	−0.709869	−	3.56875i	−0.0274451	−	0.137976i
$670$	2.08944	−	2.71404i	0.0807220	−	0.104852i
$671$			2.16737i			0.0836704i
$672$	−11.3887	−	23.5657i	−0.439328	−	0.909068i
$673$			15.1387i			0.583554i	0.956486	+	0.291777i	$0.0942465\pi$
$673$			15.1387i			0.583554i	−0.956486	+	0.291777i	$0.905753\pi$
$674$	31.5204	+	24.2664i	1.21412	+	0.934706i
$675$	2.41991	+	12.1657i	0.0931425	+	0.468259i
$676$	−6.95773	−	9.12761i	−0.267605	−	0.351062i
$677$	−17.6776	+	11.8118i	−0.679406	+	0.453964i	−0.846790	−	0.531927i	$-0.821468\pi$
$677$	−17.6776	+	11.8118i	−0.679406	+	0.453964i	0.167384	+	0.985892i	$0.446468\pi$
$678$	8.79871	−	17.7705i	0.337912	−	0.682473i
$679$	3.79526	−	9.16258i	0.145649	−	0.351627i
$680$	3.71320	+	19.1457i	0.142395	+	0.734203i
$681$	−1.13800	−	2.74736i	−0.0436081	−	0.105279i
$682$	−2.72439	+	40.5748i	−0.104322	+	1.55369i
$683$	3.48191	+	0.692594i	0.133231	+	0.0265014i	0.261256	−	0.965270i	$-0.415863\pi$
$683$	3.48191	+	0.692594i	0.133231	+	0.0265014i	−0.128024	+	0.991771i	$0.540863\pi$
$684$	2.67603	−	0.166828i	0.102321	−	0.00637882i
$685$	6.88456	+	4.60012i	0.263046	+	0.175761i
$686$	−24.4428	+	14.0601i	−0.933230	+	0.536818i
$687$	−28.1858	+	28.1858i	−1.07536	+	1.07536i
$688$	16.1013	−	5.35137i	0.613856	−	0.204019i
$689$	−5.61679	−	5.61679i	−0.213982	−	0.213982i
$690$	21.4047	+	5.77197i	0.814863	+	0.219735i
$691$	2.86419	−	4.28656i	0.108959	−	0.163069i	−0.772983	−	0.634427i	$-0.781236\pi$
$691$	2.86419	−	4.28656i	0.108959	−	0.163069i	0.881942	+	0.471358i	$0.156236\pi$
$692$	5.88564	+	2.01886i	0.223738	+	0.0767455i
$693$	2.28170	−	11.4709i	0.0866747	−	0.435743i
$694$	22.4693	+	25.7038i	0.852921	+	0.975704i
$695$	1.33597	−	0.553377i	0.0506762	−	0.0209908i
$696$	33.1858	−	32.8698i	1.25790	−	1.24593i
$697$	−26.3734	−	10.9242i	−0.998964	−	0.413784i
$698$	17.7479	−	5.99306i	0.671768	−	0.226841i
$699$	26.3314	+	39.4077i	0.995944	+	1.49054i
$700$	7.04434	−	12.1118i	0.266251	−	0.457783i
$701$	−24.9906	+	4.97093i	−0.943881	+	0.187750i	−0.642960	−	0.765900i	$-0.722294\pi$
$701$	−24.9906	+	4.97093i	−0.943881	+	0.187750i	−0.300920	+	0.953649i	$0.597294\pi$
$702$	−15.6790	+	2.03876i	−0.591767	+	0.0769479i
$703$	12.1813			0.459427
$704$	−24.3270	−	37.1729i	−0.916857	−	1.40101i
$705$	2.90449			0.109389
$706$	9.72572	−	1.26464i	0.366032	−	0.0475955i
$707$	−35.0717	+	6.97620i	−1.31901	+	0.262367i
$708$	20.3835	+	11.8553i	0.766060	+	0.445548i
$709$	27.8695	+	41.7097i	1.04666	+	1.56644i	0.802450	+	0.596720i	$0.203530\pi$
$709$	27.8695	+	41.7097i	1.04666	+	1.56644i	0.244213	+	0.969722i	$0.421470\pi$
$710$	−1.73438	+	0.585659i	−0.0650900	+	0.0219794i
$711$	−6.23081	−	2.58089i	−0.233674	−	0.0967908i
$712$	29.4825	+	0.141028i	1.10490	+	0.00528524i
$713$	26.7876	−	11.0958i	1.00320	−	0.415541i
$714$	−20.9430	−	23.9578i	−0.783770	−	0.896599i
$715$	4.13921	−	20.8092i	0.154798	−	0.778221i
$716$	2.46436	−	7.18442i	0.0920974	−	0.268494i
$717$	10.2120	−	15.2834i	0.381375	−	0.570768i
$718$	−19.1185	−	5.15549i	−0.713498	−	0.192401i
$719$	−17.1962	−	17.1962i	−0.641311	−	0.641311i	0.309567	−	0.950878i	$-0.399816\pi$
$719$	−17.1962	−	17.1962i	−0.641311	−	0.641311i	−0.950878	+	0.309567i	$0.899816\pi$
$720$	−5.08426	−	0.365820i	−0.189479	−	0.0136333i
$721$	7.08774	−	7.08774i	0.263961	−	0.263961i
$722$	20.5643	−	11.8291i	0.765323	−	0.440234i
$723$	31.5508	+	21.0815i	1.17339	+	0.784031i
$724$	−0.140253	−	2.24975i	−0.00521245	−	0.0836113i
$725$	24.5241	+	4.87815i	0.910804	+	0.181170i
$726$	3.71118	−	55.2712i	0.137735	−	2.05130i
$727$	−7.53130	−	18.1822i	−0.279320	−	0.674339i	0.720497	−	0.693458i	$-0.243914\pi$
$727$	−7.53130	−	18.1822i	−0.279320	−	0.674339i	−0.999817	+	0.0191193i	$0.993914\pi$
$728$	14.8022	+	9.99329i	0.548608	+	0.370376i
$729$	5.65985	−	13.6641i	0.209624	−	0.506077i
$730$	11.5345	−	23.2960i	0.426911	−	0.862222i
$731$	17.1520	−	11.4606i	0.634389	−	0.423885i
$732$	−1.22578	+	0.934378i	−0.0453061	+	0.0345356i
$733$	−2.30717	−	11.5989i	−0.0852174	−	0.428417i	−0.999716	−	0.0238279i	$-0.992415\pi$
$733$	−2.30717	−	11.5989i	−0.0852174	−	0.428417i	0.914499	−	0.404589i	$-0.132585\pi$
$734$	14.8707	+	11.4484i	0.548886	+	0.422567i
$735$			4.22500i			0.155842i
$736$	−16.0557	+	27.3043i	−0.591823	+	1.00645i
$737$			9.48594i			0.349419i
$738$	4.55155	−	5.91216i	0.167545	−	0.217629i
$739$	3.47244	+	17.4572i	0.127736	+	0.642172i	0.990606	+	0.136746i	$0.0436645\pi$
$739$	3.47244	+	17.4572i	0.127736	+	0.642172i	−0.862870	+	0.505426i	$0.831336\pi$
$740$	−22.9506	−	3.09599i	−0.843680	−	0.113811i
$741$	−6.59881	+	4.40919i	−0.242413	+	0.161976i
$742$	−8.75415	−	4.33444i	−0.321375	−	0.159122i
$743$	16.7416	−	40.4177i	0.614188	−	1.48278i	−0.244171	−	0.969732i	$-0.578516\pi$
$743$	16.7416	−	40.4177i	0.614188	−	1.48278i	0.858359	−	0.513049i	$-0.171484\pi$
$744$	−24.1220	+	15.9514i	−0.884356	+	0.584808i
$745$	−0.0246280	−	0.0594573i	−0.000902300	−	0.00217835i
$746$	11.9188	+	0.800286i	0.436378	+	0.0293006i
$747$	−1.36554	−	0.271623i	−0.0499626	−	0.00993817i
$748$	−40.4944	−	35.7417i	−1.48062	−	1.30685i
$749$	−12.8997	−	8.61929i	−0.471344	−	0.314942i
$750$	−15.7728	−	27.4201i	−0.575941	−	1.00124i
$751$	−33.9816	+	33.9816i	−1.24001	+	1.24001i	−0.280008	+	0.959998i	$0.590337\pi$
$751$	−33.9816	+	33.9816i	−1.24001	+	1.24001i	−0.959998	+	0.280008i	$0.909663\pi$
$752$	−1.09961	+	4.00155i	−0.0400987	+	0.145921i
$753$	−22.5147	−	22.5147i	−0.820481	−	0.820481i
$754$	−8.29828	+	30.7733i	−0.302206	+	1.12070i
$755$	−16.0390	+	24.0040i	−0.583717	+	0.873595i
$756$	−17.4660	+	8.54416i	−0.635233	+	0.310748i
$757$	7.87408	−	39.5857i	0.286188	−	1.43877i	−0.523560	−	0.851989i	$-0.675396\pi$
$757$	7.87408	−	39.5857i	0.286188	−	1.43877i	0.809749	−	0.586777i	$-0.199604\pi$
$758$	−3.92072	+	3.42734i	−0.142407	+	0.124487i
$759$	−56.7239	+	23.4958i	−2.05895	+	0.852844i
$760$	5.53714	−	2.26259i	0.200853	−	0.0820727i
$761$	40.6579	+	16.8410i	1.47385	+	0.610488i	0.967733	−	0.251979i	$-0.0810813\pi$
$761$	40.6579	+	16.8410i	1.47385	+	0.610488i	0.506114	+	0.862466i	$0.331081\pi$
$762$	12.5515	+	37.1700i	0.454691	+	1.34653i
$763$	−14.9535	−	22.3795i	−0.541354	−	0.810194i
$764$	−43.1568	+	11.4165i	−1.56136	+	0.413033i
$765$	−6.07826	+	1.20904i	−0.219760	+	0.0437129i
$766$	2.25331	+	17.3291i	0.0814155	+	0.626125i
$767$	−16.0904			−0.580992
$768$	10.5359	−	29.7840i	0.380180	−	1.07474i
$769$	9.57488			0.345279			0.172639	−	0.984985i	$-0.444770\pi$
$769$	9.57488			0.345279			0.172639	+	0.984985i	$0.444770\pi$
$770$	−3.36442	−	25.8740i	−0.121245	−	0.932435i
$771$	−25.9180	+	5.15540i	−0.933413	+	0.185667i
$772$	−4.07537	+	1.07807i	−0.146676	+	0.0388007i
$773$	−8.88263	−	13.2938i	−0.319486	−	0.478145i	0.636615	−	0.771182i	$-0.280334\pi$
$773$	−8.88263	−	13.2938i	−0.319486	−	0.478145i	−0.956101	+	0.293037i	$0.905334\pi$
$774$	1.72497	+	5.10835i	0.0620029	+	0.183616i
$775$	−14.3028	−	5.92443i	−0.513773	−	0.212812i
$776$	11.0815	−	4.52812i	0.397802	−	0.162550i
$777$	34.9102	−	14.4603i	1.25240	−	0.518759i
$778$	5.25653	−	4.59504i	0.188456	−	0.164740i
$779$	−1.70810	+	8.58720i	−0.0611990	+	0.307668i
$780$	13.5533	−	6.63012i	0.485287	−	0.237396i
$781$	2.81663	−	4.21538i	0.100787	−	0.150838i
$782$	−10.0264	+	37.1819i	−0.358544	+	1.32962i
$783$	−24.5362	−	24.5362i	−0.876852	−	0.876852i
$784$	−5.82084	−	1.59955i	−0.207887	−	0.0571267i
$785$	14.8102	−	14.8102i	0.528599	−	0.528599i
$786$	−22.2174	−	38.6237i	−0.792467	−	1.37766i
$787$	−12.1334	−	8.10728i	−0.432509	−	0.288993i	0.320196	−	0.947351i	$-0.396251\pi$
$787$	−12.1334	−	8.10728i	−0.432509	−	0.288993i	−0.752705	+	0.658358i	$0.771251\pi$
$788$	8.42495	+	7.43614i	0.300126	+	0.264902i
$789$	−41.8849	−	8.33143i	−1.49114	−	0.296607i
$790$	−15.0119	−	1.00797i	−0.534098	−	0.0358620i
$791$	6.36782	+	15.3733i	0.226414	+	0.546611i
$792$	11.7754	−	7.78686i	0.418421	−	0.276694i
$793$	0.402478	−	0.971669i	0.0142924	−	0.0345050i
$794$	44.4310	+	21.9991i	1.57680	+	0.780718i
$795$	−6.86168	+	4.58483i	−0.243359	+	0.162607i
$796$	31.4018	+	4.23604i	1.11301	+	0.150143i
$797$	−5.58966	−	28.1011i	−0.197996	−	0.995393i	−0.944124	−	0.329591i	$-0.893089\pi$
$797$	−5.58966	−	28.1011i	−0.197996	−	0.995393i	0.746128	−	0.665803i	$-0.231911\pi$
$798$	−5.95374	+	7.73351i	−0.210760	+	0.273763i
$799$			5.04535i			0.178492i
$800$	16.3705	−	4.24688i	0.578785	−	0.150150i
$801$			9.36884i			0.331032i
$802$	−36.4726	−	28.0789i	−1.28789	−	0.991501i
$803$	14.0452	+	70.6098i	0.495643	+	2.49177i
$804$	−5.36487	+	4.08950i	−0.189204	+	0.144225i
$805$	−15.4681	+	10.3355i	−0.545179	+	0.364277i
$806$	8.75609	−	17.6844i	0.308420	−	0.622908i
$807$	−14.1374	+	34.1306i	−0.497659	+	1.20146i
$808$	−35.7733	−	24.1513i	−1.25850	−	0.849640i
$809$	2.83209	+	6.83727i	0.0995710	+	0.240386i	0.965813	−	0.259238i	$-0.0834715\pi$
$809$	2.83209	+	6.83727i	0.0995710	+	0.240386i	−0.866242	+	0.499624i	$0.833472\pi$
$810$	−1.46268	+	21.7839i	−0.0513934	+	0.765410i
$811$	46.3896	+	9.22747i	1.62896	+	0.324020i	0.923167	−	0.384399i	$-0.125591\pi$
$811$	46.3896	+	9.22747i	1.62896	+	0.324020i	0.705792	+	0.708419i	$0.250591\pi$
$812$	2.43878	+	39.1198i	0.0855846	+	1.37283i
$813$	−15.5953	−	10.4204i	−0.546951	−	0.365461i
$814$	55.5954	−	31.9799i	1.94862	−	1.12090i
$815$	0.413799	−	0.413799i	0.0144948	−	0.0144948i
$816$	2.75651	−	38.3107i	0.0964971	−	1.34114i
$817$	−4.47383	−	4.47383i	−0.156519	−	0.156519i
$818$	48.0718	+	12.9630i	1.68079	+	0.453241i
$819$	−3.15306	+	4.71888i	−0.110177	+	0.164891i
$820$	5.40071	−	15.7449i	0.188601	−	0.549834i
$821$	−3.86909	+	19.4512i	−0.135032	+	0.678852i	0.852663	+	0.522461i	$0.174986\pi$
$821$	−3.86909	+	19.4512i	−0.135032	+	0.678852i	−0.987695	+	0.156391i	$0.950014\pi$
$822$	−10.7326	−	12.2776i	−0.374342	−	0.428231i
$823$	32.9693	−	13.6563i	1.14924	−	0.476030i	0.274960	−	0.961456i	$-0.411335\pi$
$823$	32.9693	−	13.6563i	1.14924	−	0.476030i	0.874278	+	0.485426i	$0.161335\pi$
$824$	12.0988	+	0.0578740i	0.421483	+	0.00201614i
$825$	30.2868	+	12.5452i	1.05445	+	0.436768i
$826$	−18.7475	+	6.33060i	−0.652308	+	0.220270i
$827$	10.8849	+	16.2904i	0.378505	+	0.566473i	0.970994	−	0.239106i	$-0.0768543\pi$
$827$	10.8849	+	16.2904i	0.378505	+	0.566473i	−0.592488	+	0.805579i	$0.701854\pi$
$828$	−8.70087	−	5.06051i	−0.302376	−	0.175865i
$829$	−39.3454	+	7.82628i	−1.36652	+	0.271818i	−0.823221	−	0.567721i	$-0.807825\pi$
$829$	−39.3454	+	7.82628i	−1.36652	+	0.271818i	−0.543300	+	0.839539i	$0.682825\pi$
$830$	−3.08015	+	0.400514i	−0.106914	+	0.0139021i
$831$	15.6209			0.541882
$832$	4.00323	+	21.1827i	0.138787	+	0.734379i
$833$	−7.33921			−0.254289
$834$	−2.82418	+	0.367231i	−0.0977934	+	0.0127162i
$835$	6.84174	−	1.36091i	0.236768	−	0.0470961i
$836$	−8.32865	+	14.3200i	−0.288052	+	0.495267i
$837$	11.9357	+	17.8630i	0.412558	+	0.617437i
$838$	25.6525	−	8.66225i	0.886150	−	0.299233i
$839$	−37.2927	−	15.4471i	−1.28749	−	0.533294i	−0.369251	−	0.929330i	$-0.620386\pi$
$839$	−37.2927	−	15.4471i	−1.28749	−	0.533294i	−0.918235	+	0.396035i	$0.870386\pi$
$840$	13.1829	−	13.0574i	0.454853	−	0.450522i
$841$	−37.8314	+	15.6703i	−1.30453	+	0.540355i
$842$	−17.3930	−	19.8968i	−0.599403	−	0.685690i
$843$	−1.28992	+	6.48485i	−0.0444271	+	0.223350i
$844$	−5.48964	−	1.88303i	−0.188961	−	0.0648164i
$845$	4.52031	−	6.76513i	0.155503	−	0.232727i
$846$	−1.27324	−	0.343340i	−0.0437748	−	0.0118043i
$847$	32.8700	+	32.8700i	1.12943	+	1.12943i
$848$	−3.71881	−	11.1892i	−0.127704	−	0.384239i
$849$	−9.31006	+	9.31006i	−0.319520	+	0.319520i
$850$	17.8234	−	10.2525i	0.611339	−	0.351658i
$851$	−38.0226	−	25.4059i	−1.30340	−	0.870902i
$852$	3.59833	−	0.224325i	0.123277	−	0.00768526i
$853$	−4.15795	−	0.827067i	−0.142365	−	0.0283182i	0.123393	−	0.992358i	$-0.460622\pi$
$853$	−4.15795	−	0.827067i	−0.142365	−	0.0283182i	−0.265759	+	0.964040i	$0.585622\pi$
$854$	0.0866487	−	1.29047i	0.00296506	−	0.0441591i
$855$	0.727397	+	1.75609i	0.0248764	+	0.0600570i
$856$	−3.56547	−	18.3840i	−0.121865	−	0.628352i
$857$	−3.06475	+	7.39897i	−0.104690	+	0.252744i	−0.967541	−	0.252715i	$-0.918677\pi$
$857$	−3.06475	+	7.39897i	−0.104690	+	0.252744i	0.862851	+	0.505459i	$0.168677\pi$
$858$	−18.5414	+	37.4475i	−0.632992	+	1.27844i
$859$	25.3340	−	16.9276i	0.864385	−	0.577564i	−0.0424267	−	0.999100i	$-0.513509\pi$
$859$	25.3340	−	16.9276i	0.864385	−	0.577564i	0.906812	+	0.421536i	$0.138509\pi$
$860$	7.29199	+	9.56612i	0.248655	+	0.326202i
$861$	5.29854	+	26.6375i	0.180574	+	0.907805i
$862$	−16.1276	−	12.4160i	−0.549307	−	0.422891i
$863$		−	19.0711i		−	0.649189i	−0.945853	−	0.324595i	$-0.894772\pi$
$863$		−	19.0711i		−	0.649189i	0.945853	−	0.324595i	$-0.105228\pi$
$864$	−22.1634	−	7.72104i	−0.754013	−	0.262675i
$865$			4.41109i			0.149982i
$866$	−8.66058	+	11.2495i	−0.294298	+	0.382274i
$867$	−2.56167	−	12.8784i	−0.0869990	−	0.437373i
$868$	3.24426	−	24.0497i	0.110117	−	0.816300i
$869$	34.6463	−	23.1499i	1.17529	−	0.785307i
$870$	29.6747	+	14.6928i	1.00607	+	0.498132i
$871$	1.76153	−	4.25271i	0.0596871	−	0.144097i
$872$	6.49055	−	31.8336i	0.219798	−	1.07802i
$873$	1.45574	+	3.51447i	0.0492693	+	0.118947i
$874$	11.7848	+	0.791292i	0.398628	+	0.0267659i
$875$	26.0347	+	5.17863i	0.880135	+	0.175070i
$876$	−33.8791	+	38.3841i	−1.14467	+	1.29688i
$877$	18.3071	+	12.2324i	0.618187	+	0.413060i	0.824849	−	0.565353i	$-0.191260\pi$
$877$	18.3071	+	12.2324i	0.618187	+	0.413060i	−0.206662	+	0.978412i	$0.566260\pi$
$878$	16.2263	+	28.2085i	0.547610	+	0.951990i
$879$	16.1404	−	16.1404i	0.544402	−	0.544402i
$880$	19.3314	−	24.8632i	0.651662	−	0.838139i
$881$	−5.72028	−	5.72028i	−0.192721	−	0.192721i	0.604150	−	0.796871i	$-0.293513\pi$
$881$	−5.72028	−	5.72028i	−0.192721	−	0.192721i	−0.796871	+	0.604150i	$0.793513\pi$
$882$	0.499439	−	1.85211i	0.0168170	−	0.0623639i
$883$	−14.0036	+	20.9579i	−0.471259	+	0.705289i	−0.988613	−	0.150483i	$-0.951917\pi$
$883$	−14.0036	+	20.9579i	−0.471259	+	0.705289i	0.517353	+	0.855772i	$0.326917\pi$
$884$	11.5171	+	23.5434i	0.387363	+	0.791849i
$885$	−3.26126	+	16.3954i	−0.109626	+	0.551127i
$886$	2.87250	−	2.51102i	0.0965035	−	0.0843594i
$887$	−1.34482	+	0.557044i	−0.0451548	+	0.0187037i	−0.405147	−	0.914252i	$-0.632779\pi$
$887$	−1.34482	+	0.557044i	−0.0451548	+	0.0187037i	0.359992	+	0.932955i	$0.382779\pi$
$888$	42.0544	+	17.6556i	1.41125	+	0.592484i
$889$	−30.4155	−	12.5985i	−1.02010	−	0.422541i
$890$	6.68684	+	19.8025i	0.224144	+	0.663781i
$891$	−33.5932	−	50.2758i	−1.12541	−	1.68430i
$892$	0.942543	+	3.56303i	0.0315587	+	0.119299i
$893$	1.51772	−	0.301894i	0.0507886	−	0.0101025i
$894$	0.0163436	+	0.125690i	0.000546611	+	0.00420370i
$895$	5.38449			0.179984
$896$	12.9984	+	23.1056i	0.434245	+	0.771905i
$897$	29.7934			0.994774
$898$	1.55335	+	11.9460i	0.0518360	+	0.398644i
$899$	42.4755	−	8.44891i	1.41664	−	0.281787i
$900$	1.37441	+	5.19559i	0.0458137	+	0.173186i
$901$	−7.96426	−	11.9194i	−0.265328	−	0.397091i
$902$	14.7484	+	43.6762i	0.491070	+	1.45426i
$903$	−18.1323	−	7.51063i	−0.603404	−	0.249938i
$904$	−7.77495	+	18.5193i	−0.258591	+	0.615944i
$905$	1.47635	−	0.611525i	0.0490756	−	0.0203278i
$906$	42.8076	−	37.4207i	1.42219	−	1.24322i
$907$	5.15594	−	25.9207i	0.171200	−	0.860681i	−0.795732	−	0.605648i	$-0.792914\pi$
$907$	5.15594	−	25.9207i	0.171200	−	0.860681i	0.966932	−	0.255033i	$-0.0820862\pi$
$908$	1.32358	+	2.70568i	0.0439247	+	0.0897912i
$909$	7.62015	−	11.4044i	0.252745	−	0.378259i
$910$	−3.29645	+	12.2245i	−0.109276	+	0.405239i
$911$	9.32241	+	9.32241i	0.308865	+	0.308865i	0.844469	−	0.535604i	$-0.179916\pi$
$911$	9.32241	+	9.32241i	0.308865	+	0.308865i	−0.535604	+	0.844469i	$0.679916\pi$
$912$	−11.6894	+	1.46315i	−0.387074	+	0.0484499i
$913$	6.08271	−	6.08271i	0.201308	−	0.201308i
$914$	−8.86248	−	15.4069i	−0.293145	−	0.509617i
$915$	−0.908512	−	0.607048i	−0.0300345	−	0.0200684i
$916$	26.7176	−	30.2703i	0.882775	−	1.00016i
$917$	36.6722	+	7.29456i	1.21102	+	0.240888i
$918$	−28.4700	−	1.91162i	−0.939650	−	0.0630927i
$919$	−10.1895	−	24.5995i	−0.336119	−	0.811464i	−0.998081	−	0.0619260i	$-0.980276\pi$
$919$	−10.1895	−	24.5995i	−0.336119	−	0.811464i	0.661961	−	0.749538i	$-0.269724\pi$
$920$	−22.0025	−	4.48608i	−0.725401	−	0.147902i
$921$	−24.4191	+	58.9528i	−0.804635	+	1.94256i
$922$	−25.7333	−	12.7413i	−0.847480	−	0.419612i
$923$	−2.04553	+	1.36678i	−0.0673295	+	0.0449882i
$924$	−6.86984	+	50.9262i	−0.226001	+	1.67535i
$925$	4.76341	+	23.9473i	0.156620	+	0.787382i
$926$	−15.8095	+	20.5355i	−0.519534	+	0.674839i
$927$			3.84472i			0.126277i
$928$	−31.4770	+	35.3206i	−1.03328	+	1.15946i
$929$			1.73073i			0.0567835i	0.999597	+	0.0283918i	$0.00903859\pi$
$929$			1.73073i			0.0567835i	−0.999597	+	0.0283918i	$0.990961\pi$
$930$	−16.2450	−	12.5064i	−0.532693	−	0.410101i
$931$	0.439149	+	2.20775i	0.0143925	+	0.0723561i
$932$	−29.1029	−	38.1791i	−0.953296	−	1.25060i
$933$	31.2750	−	20.8973i	1.02390	−	0.684147i
$934$	−7.28010	+	14.7034i	−0.238212	+	0.481111i
$935$	14.6530	−	35.3754i	0.479203	−	1.15690i
$936$	−6.72512	+	1.30430i	−0.219818	+	0.0426324i
$937$	18.3095	+	44.2031i	0.598146	+	1.44405i	0.875469	+	0.483275i	$0.160553\pi$
$937$	18.3095	+	44.2031i	0.598146	+	1.44405i	−0.277323	+	0.960777i	$0.589447\pi$
$938$	0.379236	−	5.64802i	0.0123825	−	0.184414i
$939$	57.8422	+	11.5055i	1.88761	+	0.375469i
$940$	−2.93624	+	0.183050i	−0.0957696	+	0.00597042i
$941$	−2.21555	−	1.48039i	−0.0722250	−	0.0482592i	0.518933	−	0.854815i	$-0.326329\pi$
$941$	−2.21555	−	1.48039i	−0.0722250	−	0.0482592i	−0.591158	+	0.806555i	$0.701329\pi$
$942$	−35.7568	+	20.5682i	−1.16502	+	0.670149i
$943$	23.2415	−	23.2415i	0.756846	−	0.756846i
$944$	−21.3535	−	10.7002i	−0.694999	−	0.348263i
$945$	−9.74689	−	9.74689i	−0.317066	−	0.317066i
$946$	−32.1638	−	8.67324i	−1.04573	−	0.281992i
$947$	14.3424	−	21.4649i	0.466065	−	0.697516i	−0.521759	−	0.853093i	$-0.674724\pi$
$947$	14.3424	−	21.4649i	0.466065	−	0.697516i	0.987824	+	0.155578i	$0.0497239\pi$
$948$	28.0291	+	9.61438i	0.910342	+	0.312261i
$949$	6.81548	−	34.2637i	0.221240	−	1.11225i
$950$	−4.15060	−	4.74810i	−0.134663	−	0.154049i
$951$	25.2345	−	10.4525i	0.818286	−	0.338945i
$952$	22.6818	+	22.8999i	0.735122	+	0.742189i
$953$	−24.3145	−	10.0714i	−0.787622	−	0.326244i	−0.0476352	−	0.998865i	$-0.515169\pi$
$953$	−24.3145	−	10.0714i	−0.787622	−	0.326244i	−0.739987	+	0.672621i	$0.765169\pi$
$954$	3.54993	−	1.19873i	0.114933	−	0.0388103i
$955$	−17.5822	−	26.3137i	−0.568948	−	0.851490i
$956$	−9.36047	+	16.0941i	−0.302739	+	0.520519i
$957$	−89.9436	+	17.8909i	−2.90746	+	0.578331i
$958$	−16.9535	+	2.20448i	−0.547744	+	0.0712236i
$959$	13.6843			0.441888
$960$	22.3956	+	0.214261i	0.722816	+	0.00691525i
$961$	4.18662			0.135052
$962$	−30.8630	+	4.01314i	−0.995063	+	0.129389i
$963$	5.83644	−	1.16094i	0.188077	−	0.0374108i
$964$	−33.2243	−	19.3236i	−1.07008	−	0.622371i
$965$	−1.66032	−	2.48484i	−0.0534475	−	0.0799899i
$966$	34.7133	−	11.7219i	1.11688	−	0.377145i
$967$	−8.02112	−	3.32246i	−0.257942	−	0.106843i	0.249965	−	0.968255i	$-0.419581\pi$
$967$	−8.02112	−	3.32246i	−0.257942	−	0.106843i	−0.507907	+	0.861412i	$0.669581\pi$
$968$	−0.268396	+	56.1093i	−0.00862656	+	1.80342i
$969$	−13.2324	+	5.48104i	−0.425086	+	0.176076i
$970$	5.58532	+	6.38936i	0.179334	+	0.205150i
$971$	−9.92238	+	49.8832i	−0.318424	+	1.60083i	0.407602	+	0.913160i	$0.366365\pi$
$971$	−9.92238	+	49.8832i	−0.318424	+	1.60083i	−0.726026	+	0.687667i	$0.758635\pi$
$972$	5.87472	−	17.1267i	0.188432	−	0.549340i
$973$	1.32774	−	1.98710i	0.0425653	−	0.0637034i
$974$	−47.6152	−	12.8398i	−1.52569	−	0.411415i
$975$	−11.2485	−	11.2485i	−0.360239	−	0.360239i
$976$	1.18029	−	1.02185i	0.0377803	−	0.0327085i
$977$	34.0542	−	34.0542i	1.08949	−	1.08949i	0.0939094	−	0.995581i	$-0.470064\pi$
$977$	34.0542	−	34.0542i	1.08949	−	1.08949i	0.995581	−	0.0939094i	$-0.0299364\pi$
$978$	−0.999049	+	0.574679i	−0.0319461	+	0.0183762i
$979$	−48.1297	−	32.1592i	−1.53823	−	1.02781i
$980$	−0.266273	−	4.27119i	−0.00850577	−	0.136438i
$981$	10.1256	+	2.01411i	0.323285	+	0.0643054i
$982$	2.52522	−	37.6085i	0.0805831	−	1.20014i
$983$	21.4849	+	51.8692i	0.685262	+	1.65437i	0.754114	+	0.656743i	$0.228066\pi$
$983$	21.4849	+	51.8692i	0.685262	+	1.65437i	−0.0688520	+	0.997627i	$0.521934\pi$
$984$	−18.3433	+	27.1704i	−0.584763	+	0.866162i
$985$	−3.04858	+	7.35993i	−0.0971360	+	0.234507i
$986$	−25.5227	+	51.5476i	−0.812809	+	1.64161i
$987$	3.99123	−	2.66686i	0.127042	−	0.0848870i
$988$	6.39308	−	4.87327i	0.203391	−	0.155039i
$989$	4.63373	+	23.2953i	0.147344	+	0.740749i
$990$	7.93014	+	6.10513i	0.252036	+	0.194034i
$991$			56.1598i			1.78397i	0.452061	+	0.891987i	$0.350689\pi$
$991$			56.1598i			1.78397i	−0.452061	+	0.891987i	$0.649311\pi$
$992$	23.3804	−	17.6461i	0.742329	−	0.560264i
$993$		−	19.7631i		−	0.627163i
$994$	−1.84557	+	2.39727i	−0.0585380	+	0.0760368i
$995$	4.38232	+	22.0314i	0.138929	+	0.698443i
$996$	6.06246	+	0.817814i	0.192096	+	0.0259134i
$997$	−19.4239	+	12.9787i	−0.615162	+	0.411038i	−0.823740	−	0.566968i	$-0.808116\pi$
$997$	−19.4239	+	12.9787i	−0.615162	+	0.411038i	0.208578	+	0.978006i	$0.433116\pi$
$998$	3.56573	+	1.76550i	0.112871	+	0.0558859i
$999$	12.9666	−	31.3041i	0.410244	−	0.990416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.53.4	yes	56
3.2	odd	2		576.2.bd.a.181.4		56
4.3	odd	2		256.2.i.a.49.2		56
8.3	odd	2		512.2.i.a.353.6		56
8.5	even	2		512.2.i.b.353.2		56
64.3	odd	16		512.2.i.a.161.6		56
64.29	even	16	inner	64.2.i.a.29.4	✓	56
64.35	odd	16		256.2.i.a.209.2		56
64.61	even	16		512.2.i.b.161.2		56
192.29	odd	16		576.2.bd.a.541.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.4	✓	56	64.29	even	16	inner
64.2.i.a.53.4	yes	56	1.1	even	1	trivial
256.2.i.a.49.2		56	4.3	odd	2
256.2.i.a.209.2		56	64.35	odd	16
512.2.i.a.161.6		56	64.3	odd	16
512.2.i.a.353.6		56	8.3	odd	2
512.2.i.b.161.2		56	64.61	even	16
512.2.i.b.353.2		56	8.5	even	2
576.2.bd.a.181.4		56	3.2	odd	2
576.2.bd.a.541.4		56	192.29	odd	16

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.182356 + 1.40241i) q^{2} +(1.93660 - 0.385213i) q^{3} +(-1.93349 + 0.511475i) q^{4} +(-0.787711 - 1.17889i) q^{5} +(0.893376 + 2.64565i) q^{6} +(-2.16489 - 0.896725i) q^{7} +(-1.06988 - 2.61827i) q^{8} +(0.830380 - 0.343954i) q^{9} +O(q^{10})\)	\(q+(0.182356 + 1.40241i) q^{2} +(1.93660 - 0.385213i) q^{3} +(-1.93349 + 0.511475i) q^{4} +(-0.787711 - 1.17889i) q^{5} +(0.893376 + 2.64565i) q^{6} +(-2.16489 - 0.896725i) q^{7} +(-1.06988 - 2.61827i) q^{8} +(0.830380 - 0.343954i) q^{9} +(1.50964 - 1.31967i) q^{10} +(-1.08337 + 5.44648i) q^{11} +(-3.54737 + 1.73533i) q^{12} +(1.49710 - 2.24057i) q^{13} +(0.862794 - 3.19957i) q^{14} +(-1.97960 - 1.97960i) q^{15} +(3.47679 - 1.97787i) q^{16} +(3.43875 - 3.43875i) q^{17} +(0.633789 + 1.10181i) q^{18} +(-1.24019 - 0.828669i) q^{19} +(2.12601 + 1.87649i) q^{20} +(-4.53794 - 0.902653i) q^{21} +(-7.83575 - 0.526131i) q^{22} +(2.14281 + 5.17319i) q^{23} +(-3.08052 - 4.65841i) q^{24} +(1.14412 - 2.76214i) q^{25} +(3.41520 + 1.69096i) q^{26} +(-3.44969 + 2.30501i) q^{27} +(4.64444 + 0.626526i) q^{28} +(1.63164 + 8.20281i) q^{29} +(2.41522 - 3.13720i) q^{30} -5.17816i q^{31} +(3.40779 + 4.51520i) q^{32} +10.9650i q^{33} +(5.44961 + 4.19545i) q^{34} +(0.648162 + 3.25853i) q^{35} +(-1.42961 + 1.08975i) q^{36} +(-6.79044 + 4.53723i) q^{37} +(0.935975 - 1.89037i) q^{38} +(2.03618 - 4.91578i) q^{39} +(-2.24391 + 3.32372i) q^{40} +(-2.24634 - 5.42314i) q^{41} +(0.438366 - 6.52865i) q^{42} +(4.16031 + 0.827538i) q^{43} +(-0.691046 - 11.0849i) q^{44} +(-1.05958 - 0.707992i) q^{45} +(-6.86417 + 3.94845i) q^{46} +(-0.733603 + 0.733603i) q^{47} +(5.97123 - 5.16963i) q^{48} +(-1.06713 - 1.06713i) q^{49} +(4.08229 + 1.10082i) q^{50} +(5.33482 - 7.98413i) q^{51} +(-1.74864 + 5.09785i) q^{52} +(0.575078 - 2.89111i) q^{53} +(-3.86163 - 4.41754i) q^{54} +(7.27421 - 3.01307i) q^{55} +(-0.0317030 + 6.62765i) q^{56} +(-2.72096 - 1.12706i) q^{57} +(-11.2061 + 3.78406i) q^{58} +(-3.31738 - 4.96481i) q^{59} +(4.84007 + 2.81503i) q^{60} +(0.382794 - 0.0761424i) q^{61} +(7.26190 - 0.944270i) q^{62} -2.10611 q^{63} +(-5.71071 + 5.60248i) q^{64} -3.82067 q^{65} +(-15.3774 + 1.99953i) q^{66} +(1.67538 - 0.333253i) q^{67} +(-4.88996 + 8.40763i) q^{68} +(6.14253 + 9.19295i) q^{69} +(-4.45159 + 1.50320i) q^{70} +(-0.843458 - 0.349372i) q^{71} +(-1.78897 - 1.80617i) q^{72} +(11.9774 - 4.96122i) q^{73} +(-7.60132 - 8.69558i) q^{74} +(1.15168 - 5.78989i) q^{75} +(2.82174 + 0.967899i) q^{76} +(7.22938 - 10.8195i) q^{77} +(7.26524 + 1.95914i) q^{78} +(-5.30583 - 5.30583i) q^{79} +(-5.07040 - 2.54077i) q^{80} +(-7.69937 + 7.69937i) q^{81} +(7.19581 - 4.13922i) q^{82} +(-1.28800 - 0.860615i) q^{83} +(9.23576 - 0.575771i) q^{84} +(-6.76266 - 1.34518i) q^{85} +(-0.401887 + 5.98536i) q^{86} +(6.31966 + 15.2570i) q^{87} +(15.4195 - 2.99052i) q^{88} +(-3.98900 + 9.63030i) q^{89} +(0.799671 - 1.61508i) q^{90} +(-5.25023 + 3.50809i) q^{91} +(-6.78906 - 8.90634i) q^{92} +(-1.99470 - 10.0280i) q^{93} +(-1.16259 - 0.895033i) q^{94} +2.11480i q^{95} +(8.33882 + 7.43139i) q^{96} +4.23236i q^{97} +(1.30196 - 1.69115i) q^{98} +(0.973732 + 4.89528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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