LMFDB - Embedded newform 64.2.i.a.5.3

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			5.3
Character	$\chi$	$=$	64.5
Dual form			64.2.i.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599818 - 1.28071i) q^{2} +(-2.03902 - 1.36243i) q^{3} +(-1.28044 + 1.53639i) q^{4} +(-1.53851 - 0.306028i) q^{5} +(-0.521836 + 3.42860i) q^{6} +(1.01301 - 2.44562i) q^{7} +(2.73569 + 0.718315i) q^{8} +(1.15334 + 2.78440i) q^{9} +O(q^{10})$	\(q+(-0.599818 - 1.28071i) q^{2} +(-2.03902 - 1.36243i) q^{3} +(-1.28044 + 1.53639i) q^{4} +(-1.53851 - 0.306028i) q^{5} +(-0.521836 + 3.42860i) q^{6} +(1.01301 - 2.44562i) q^{7} +(2.73569 + 0.718315i) q^{8} +(1.15334 + 2.78440i) q^{9} +(0.530891 + 2.15394i) q^{10} +(-2.71620 - 4.06508i) q^{11} +(4.70405 - 1.38822i) q^{12} +(4.23055 - 0.841509i) q^{13} +(-3.73976 + 0.169557i) q^{14} +(2.72010 + 2.72010i) q^{15} +(-0.720966 - 3.93449i) q^{16} +(0.228271 - 0.228271i) q^{17} +(2.87422 - 3.14722i) q^{18} +(1.30758 + 6.57364i) q^{19} +(2.44014 - 1.97189i) q^{20} +(-5.39754 + 3.60652i) q^{21} +(-3.57696 + 5.91698i) q^{22} +(2.81320 - 1.16527i) q^{23} +(-4.59948 - 5.19185i) q^{24} +(-2.34605 - 0.971766i) q^{25} +(-3.61529 - 4.91336i) q^{26} +(0.00660900 - 0.0332257i) q^{27} +(2.46033 + 4.68784i) q^{28} +(1.67490 - 2.50666i) q^{29} +(1.85210 - 5.11523i) q^{30} +1.06551i q^{31} +(-4.60649 + 3.28333i) q^{32} +11.9894i q^{33} +(-0.429271 - 0.155428i) q^{34} +(-2.30695 + 3.45260i) q^{35} +(-5.75469 - 1.79328i) q^{36} +(2.13514 - 10.7341i) q^{37} +(7.63461 - 5.61762i) q^{38} +(-9.77267 - 4.04797i) q^{39} +(-3.98906 - 1.94233i) q^{40} +(-2.57626 + 1.06712i) q^{41} +(7.85644 + 4.74942i) q^{42} +(0.575838 - 0.384763i) q^{43} +(9.72346 + 1.03194i) q^{44} +(-0.922311 - 4.63677i) q^{45} +(-3.17978 - 2.90395i) q^{46} +(2.61525 - 2.61525i) q^{47} +(-3.89040 + 9.00477i) q^{48} +(-0.00513508 - 0.00513508i) q^{49} +(0.162653 + 3.58749i) q^{50} +(-0.776454 + 0.154446i) q^{51} +(-4.12407 + 7.57726i) q^{52} +(2.60438 + 3.89774i) q^{53} +(-0.0465166 + 0.0114652i) q^{54} +(2.93486 + 7.08539i) q^{55} +(4.52801 - 5.96282i) q^{56} +(6.28994 - 15.1853i) q^{57} +(-4.21494 - 0.641518i) q^{58} +(8.66346 + 1.72327i) q^{59} +(-7.66205 + 0.696210i) q^{60} +(6.23588 + 4.16668i) q^{61} +(1.36462 - 0.639115i) q^{62} +7.97794 q^{63} +(6.96805 + 3.93018i) q^{64} -6.76625 q^{65} +(15.3550 - 7.19147i) q^{66} +(-6.91594 - 4.62108i) q^{67} +(0.0584261 + 0.643000i) q^{68} +(-7.32376 - 1.45679i) q^{69} +(5.80553 + 0.883605i) q^{70} +(-0.606236 + 1.46358i) q^{71} +(1.15510 + 8.44573i) q^{72} +(-1.36883 - 3.30465i) q^{73} +(-15.0279 + 3.70399i) q^{74} +(3.45968 + 5.17778i) q^{75} +(-11.7739 - 6.40818i) q^{76} +(-12.6932 + 2.52483i) q^{77} +(0.677547 + 14.9440i) q^{78} +(4.69681 + 4.69681i) q^{79} +(-0.0948532 + 6.27387i) q^{80} +(6.33452 - 6.33452i) q^{81} +(2.91196 + 2.65936i) q^{82} +(0.803913 + 4.04154i) q^{83} +(1.37020 - 12.9106i) q^{84} +(-0.421054 + 0.281340i) q^{85} +(-0.838168 - 0.506694i) q^{86} +(-6.83030 + 2.82920i) q^{87} +(-4.51069 - 13.0719i) q^{88} +(-10.3334 - 4.28021i) q^{89} +(-5.38514 + 3.96243i) q^{90} +(2.22758 - 11.1988i) q^{91} +(-1.81182 + 5.81421i) q^{92} +(1.45169 - 2.17261i) q^{93} +(-4.91805 - 1.78070i) q^{94} -10.5137i q^{95} +(13.8660 - 0.418748i) q^{96} -7.30754i q^{97} +(-0.00349643 + 0.00965666i) q^{98} +(8.18612 - 12.2514i) 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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.599818	−	1.28071i	−0.424136	−	0.905599i
$2$	−0.599818	−	1.28071i	−0.424136	−	0.905599i
$3$	−2.03902	−	1.36243i	−1.17723	−	0.786599i	−0.196219	−	0.980560i	$-0.562866\pi$
$3$	−2.03902	−	1.36243i	−1.17723	−	0.786599i	−0.981009	+	0.193961i	$0.937866\pi$
$4$	−1.28044	+	1.53639i	−0.640218	+	0.768193i
$5$	−1.53851	−	0.306028i	−0.688041	−	0.136860i	−0.161325	−	0.986901i	$-0.551577\pi$
$5$	−1.53851	−	0.306028i	−0.688041	−	0.136860i	−0.526716	+	0.850041i	$0.676577\pi$
$6$	−0.521836	+	3.42860i	−0.213039	+	1.39972i
$7$	1.01301	−	2.44562i	0.382882	−	0.924359i	−0.608524	−	0.793536i	$-0.708238\pi$
$7$	1.01301	−	2.44562i	0.382882	−	0.924359i	0.991406	−	0.130823i	$-0.0417620\pi$
$8$	2.73569	+	0.718315i	0.967214	+	0.253963i
$9$	1.15334	+	2.78440i	0.384446	+	0.928134i
$10$	0.530891	+	2.15394i	0.167882	+	0.681136i
$11$	−2.71620	−	4.06508i	−0.818965	−	1.22567i	−0.971422	−	0.237358i	$-0.923719\pi$
$11$	−2.71620	−	4.06508i	−0.818965	−	1.22567i	0.152457	−	0.988310i	$-0.451281\pi$
$12$	4.70405	−	1.38822i	1.35794	−	0.400744i
$13$	4.23055	−	0.841509i	1.17334	−	0.233393i	0.430332	−	0.902671i	$-0.358397\pi$
$13$	4.23055	−	0.841509i	1.17334	−	0.233393i	0.743012	+	0.669278i	$0.233397\pi$
$14$	−3.73976	+	0.169557i	−0.999492	+	0.0453160i
$15$	2.72010	+	2.72010i	0.702327	+	0.702327i
$16$	−0.720966	−	3.93449i	−0.180241	−	0.983622i
$17$	0.228271	−	0.228271i	0.0553640	−	0.0553640i	−0.678883	−	0.734247i	$-0.737536\pi$
$17$	0.228271	−	0.228271i	0.0553640	−	0.0553640i	0.734247	+	0.678883i	$0.237536\pi$
$18$	2.87422	−	3.14722i	0.677460	−	0.741808i
$19$	1.30758	+	6.57364i	0.299979	+	1.50810i	0.777167	+	0.629295i	$0.216656\pi$
$19$	1.30758	+	6.57364i	0.299979	+	1.50810i	−0.477188	+	0.878801i	$0.658344\pi$
$20$	2.44014	−	1.97189i	0.545631	−	0.440928i
$21$	−5.39754	+	3.60652i	−1.17784	+	0.787007i
$22$	−3.57696	+	5.91698i	−0.762611	+	1.26150i
$23$	2.81320	−	1.16527i	0.586593	−	0.242975i	−0.0695913	−	0.997576i	$-0.522170\pi$
$23$	2.81320	−	1.16527i	0.586593	−	0.242975i	0.656184	+	0.754601i	$0.272170\pi$
$24$	−4.59948	−	5.19185i	−0.938865	−	1.05978i
$25$	−2.34605	−	0.971766i	−0.469210	−	0.194353i
$26$	−3.61529	−	4.91336i	−0.709017	−	0.963589i
$27$	0.00660900	−	0.0332257i	0.00127190	−	0.00639428i
$28$	2.46033	+	4.68784i	0.464958	+	0.885918i
$29$	1.67490	−	2.50666i	0.311021	−	0.465476i	−0.642722	−	0.766100i	$-0.722195\pi$
$29$	1.67490	−	2.50666i	0.311021	−	0.465476i	0.953743	+	0.300624i	$0.0971949\pi$
$30$	1.85210	−	5.11523i	0.338145	−	0.933909i
$31$			1.06551i			0.191372i	0.995412	+	0.0956860i	$0.0305045\pi$
$31$			1.06551i			0.191372i	−0.995412	+	0.0956860i	$0.969496\pi$
$32$	−4.60649	+	3.28333i	−0.814320	+	0.580416i
$33$			11.9894i			2.08709i
$34$	−0.429271	−	0.155428i	−0.0736193	−	0.0266557i
$35$	−2.30695	+	3.45260i	−0.389946	+	0.583595i
$36$	−5.75469	−	1.79328i	−0.959115	−	0.298880i
$37$	2.13514	−	10.7341i	0.351014	−	1.76467i	−0.252775	−	0.967525i	$-0.581343\pi$
$37$	2.13514	−	10.7341i	0.351014	−	1.76467i	0.603790	−	0.797144i	$-0.293657\pi$
$38$	7.63461	−	5.61762i	1.23850	−	0.911297i
$39$	−9.77267	−	4.04797i	−1.56488	−	0.648195i
$40$	−3.98906	−	1.94233i	−0.630725	−	0.307109i
$41$	−2.57626	+	1.06712i	−0.402344	+	0.166657i	−0.574673	−	0.818383i	$-0.694871\pi$
$41$	−2.57626	+	1.06712i	−0.402344	+	0.166657i	0.172329	+	0.985039i	$0.444871\pi$
$42$	7.85644	+	4.74942i	1.21228	+	0.732852i
$43$	0.575838	−	0.384763i	0.0878145	−	0.0586758i	−0.510888	−	0.859647i	$-0.670683\pi$
$43$	0.575838	−	0.384763i	0.0878145	−	0.0586758i	0.598702	+	0.800972i	$0.295683\pi$
$44$	9.72346	+	1.03194i	1.46587	+	0.155571i
$45$	−0.922311	−	4.63677i	−0.137490	−	0.691209i
$46$	−3.17978	−	2.90395i	−0.468832	−	0.428163i
$47$	2.61525	−	2.61525i	0.381474	−	0.381474i	−0.490159	−	0.871633i	$-0.663061\pi$
$47$	2.61525	−	2.61525i	0.381474	−	0.381474i	0.871633	+	0.490159i	$0.163061\pi$
$48$	−3.89040	+	9.00477i	−0.561531	+	1.29973i
$49$	−0.00513508	−	0.00513508i	−0.000733583	−	0.000733583i
$50$	0.162653	+	3.58749i	0.0230027	+	0.507348i
$51$	−0.776454	+	0.154446i	−0.108725	+	0.0216268i
$52$	−4.12407	+	7.57726i	−0.571905	+	1.05078i
$53$	2.60438	+	3.89774i	0.357740	+	0.535395i	0.966067	−	0.258291i	$-0.0831593\pi$
$53$	2.60438	+	3.89774i	0.357740	+	0.535395i	−0.608327	+	0.793686i	$0.708159\pi$
$54$	−0.0465166	+	0.0114652i	−0.00633011	+	0.00156021i
$55$	2.93486	+	7.08539i	0.395737	+	0.955393i
$56$	4.52801	−	5.96282i	0.605081	−	0.796815i
$57$	6.28994	−	15.1853i	0.833123	−	2.01134i
$58$	−4.21494	−	0.641518i	−0.553449	−	0.0842354i
$59$	8.66346	+	1.72327i	1.12789	+	0.224351i	0.723558	−	0.690263i	$-0.242505\pi$
$59$	8.66346	+	1.72327i	1.12789	+	0.224351i	0.404328	+	0.914614i	$0.367505\pi$
$60$	−7.66205	+	0.696210i	−0.989166	+	0.0898804i
$61$	6.23588	+	4.16668i	0.798422	+	0.533489i	0.886557	−	0.462620i	$-0.153091\pi$
$61$	6.23588	+	4.16668i	0.798422	+	0.533489i	−0.0881344	+	0.996109i	$0.528091\pi$
$62$	1.36462	−	0.639115i	0.173306	−	0.0811677i
$63$	7.97794			1.00513
$64$	6.96805	+	3.93018i	0.871006	+	0.491273i
$65$	−6.76625			−0.839251
$66$	15.3550	−	7.19147i	1.89006	−	0.885208i
$67$	−6.91594	−	4.62108i	−0.844917	−	0.564555i	0.0560578	−	0.998428i	$-0.482147\pi$
$67$	−6.91594	−	4.62108i	−0.844917	−	0.564555i	−0.900974	+	0.433872i	$0.857147\pi$
$68$	0.0584261	+	0.643000i	0.00708520	+	0.0779752i
$69$	−7.32376	−	1.45679i	−0.881677	−	0.175376i
$70$	5.80553	+	0.883605i	0.693893	+	0.105611i
$71$	−0.606236	+	1.46358i	−0.0719470	+	0.173695i	−0.955762	−	0.294141i	$-0.904966\pi$
$71$	−0.606236	+	1.46358i	−0.0719470	+	0.173695i	0.883815	+	0.467837i	$0.154966\pi$
$72$	1.15510	+	8.44573i	0.136130	+	0.995339i
$73$	−1.36883	−	3.30465i	−0.160210	−	0.386780i	0.823307	−	0.567596i	$-0.192126\pi$
$73$	−1.36883	−	3.30465i	−0.160210	−	0.386780i	−0.983517	+	0.180816i	$0.942126\pi$
$74$	−15.0279	+	3.70399i	−1.74696	+	0.430580i
$75$	3.45968	+	5.17778i	0.399489	+	0.597878i
$76$	−11.7739	−	6.40818i	−1.35056	−	0.735069i
$77$	−12.6932	+	2.52483i	−1.44652	+	0.287732i
$78$	0.677547	+	14.9440i	0.0767170	+	1.69208i
$79$	4.69681	+	4.69681i	0.528433	+	0.528433i	0.920105	−	0.391672i	$-0.128103\pi$
$79$	4.69681	+	4.69681i	0.528433	+	0.528433i	−0.391672	+	0.920105i	$0.628103\pi$
$80$	−0.0948532	+	6.27387i	−0.0106049	+	0.701440i
$81$	6.33452	−	6.33452i	0.703836	−	0.703836i
$82$	2.91196	+	2.65936i	0.321573	+	0.293678i
$83$	0.803913	+	4.04154i	0.0882409	+	0.443617i	0.999495	+	0.0317726i	$0.0101152\pi$
$83$	0.803913	+	4.04154i	0.0882409	+	0.443617i	−0.911254	+	0.411844i	$0.864885\pi$
$84$	1.37020	−	12.9106i	0.149501	−	1.40866i
$85$	−0.421054	+	0.281340i	−0.0456698	+	0.0305156i
$86$	−0.838168	−	0.506694i	−0.0903820	−	0.0546382i
$87$	−6.83030	+	2.82920i	−0.732286	+	0.303323i
$88$	−4.51069	−	13.0719i	−0.480841	−	1.39347i
$89$	−10.3334	−	4.28021i	−1.09533	−	0.453702i	−0.239470	−	0.970904i	$-0.576974\pi$
$89$	−10.3334	−	4.28021i	−1.09533	−	0.453702i	−0.855863	+	0.517202i	$0.826974\pi$
$90$	−5.38514	+	3.96243i	−0.567644	+	0.417677i
$91$	2.22758	−	11.1988i	0.233514	−	1.17395i
$92$	−1.81182	+	5.81421i	−0.188896	+	0.606173i
$93$	1.45169	−	2.17261i	0.150533	−	0.225289i
$94$	−4.91805	−	1.78070i	−0.507258	−	0.183665i
$95$		−	10.5137i		−	1.07869i
$96$	13.8660	−	0.418748i	1.41520	−	0.0427382i
$97$		−	7.30754i		−	0.741969i	−0.928639	−	0.370984i	$-0.879020\pi$
$97$		−	7.30754i		−	0.741969i	0.928639	−	0.370984i	$-0.120980\pi$
$98$	−0.00349643	+	0.00965666i	−0.000353193	+	0.000975470i
$99$	8.18612	−	12.2514i	0.822736	−	1.23131i
$100$	4.49698	−	2.36015i	0.449698	−	0.236015i
$101$	−2.69620	+	13.5547i	−0.268281	+	1.34874i	0.578013	+	0.816027i	$0.303828\pi$
$101$	−2.69620	+	13.5547i	−0.268281	+	1.34874i	−0.846295	+	0.532715i	$0.821172\pi$
$102$	0.663532	+	0.901772i	0.0656994	+	0.0892888i
$103$	−8.88954	−	3.68217i	−0.875913	−	0.362815i	−0.101002	−	0.994886i	$-0.532205\pi$
$103$	−8.88954	−	3.68217i	−0.875913	−	0.362815i	−0.774910	+	0.632071i	$0.782205\pi$
$104$	12.1780	+	0.736758i	1.19415	+	0.0722450i
$105$	9.40784	−	3.89685i	0.918111	−	0.380294i
$106$	3.42971	−	5.67340i	0.333123	−	0.551049i
$107$	−3.97920	+	2.65882i	−0.384684	+	0.257037i	−0.732843	−	0.680398i	$-0.761807\pi$
$107$	−3.97920	+	2.65882i	−0.384684	+	0.257037i	0.348159	+	0.937435i	$0.386807\pi$
$108$	0.0425851	+	0.0526973i	0.00409775	+	0.00507080i
$109$	1.26589	+	6.36406i	0.121250	+	0.609566i	0.992852	+	0.119352i	$0.0380816\pi$
$109$	1.26589	+	6.36406i	0.121250	+	0.609566i	−0.871602	+	0.490215i	$0.836918\pi$
$110$	7.31394	−	8.00865i	0.697357	−	0.763595i
$111$	−18.9780	+	18.9780i	−1.80131	+	1.80131i
$112$	−10.3526	−	2.22247i	−0.978231	−	0.210003i
$113$	10.3282	+	10.3282i	0.971595	+	0.971595i	0.999608	−	0.0280126i	$-0.00891785\pi$
$113$	10.3282	+	10.3282i	0.971595	+	0.971595i	−0.0280126	+	0.999608i	$0.508918\pi$
$114$	−23.2207	+	1.05280i	−2.17482	+	0.0986042i
$115$	−4.68473	+	0.931850i	−0.436853	+	0.0868955i
$116$	1.70660	+	5.78292i	0.158454	+	0.536930i
$117$	7.22235	+	10.8090i	0.667706	+	0.999293i
$118$	−2.98949	−	12.1290i	−0.275205	−	1.11657i
$119$	−0.327025	−	0.789507i	−0.0299783	−	0.0723740i
$120$	5.48748	+	9.39526i	0.500936	+	0.857666i
$121$	−4.93762	+	11.9205i	−0.448875	+	1.08368i
$122$	1.59592	−	10.4856i	0.144487	−	0.949322i
$123$	6.70693	+	1.33409i	0.604743	+	0.120291i
$124$	−1.63704	−	1.36432i	−0.147011	−	0.122520i
$125$	9.83344	+	6.57049i	0.879529	+	0.587683i
$126$	−4.78531	−	10.2174i	−0.426309	−	0.910241i
$127$	3.04637			0.270322			0.135161	−	0.990824i	$-0.456845\pi$
$127$	3.04637			0.270322			0.135161	+	0.990824i	$0.456845\pi$
$128$	0.853861	−	11.2814i	0.0754714	−	0.997148i
$129$	−1.69836			−0.149532
$130$	4.05852	+	8.66561i	0.355956	+	0.760024i
$131$	6.26153	+	4.18382i	0.547072	+	0.365542i	0.798182	−	0.602417i	$-0.205795\pi$
$131$	6.26153	+	4.18382i	0.547072	+	0.365542i	−0.251109	+	0.967959i	$0.580795\pi$
$132$	−18.4204	−	15.3517i	−1.60329	−	1.33619i
$133$	17.4012	+	3.46132i	1.50888	+	0.300134i
$134$	−1.76996	+	11.6291i	−0.152901	+	1.00460i
$135$	−0.0203360	+	0.0490953i	−0.00175024	+	0.00422545i
$136$	0.788452	−	0.460510i	0.0676092	−	0.0394884i
$137$	2.52012	+	6.08411i	0.215308	+	0.519800i	0.994224	−	0.107329i	$-0.0342298\pi$
$137$	2.52012	+	6.08411i	0.215308	+	0.519800i	−0.778915	+	0.627129i	$0.784230\pi$
$138$	2.52720	+	10.2534i	0.215130	+	0.872829i
$139$	−2.36467	−	3.53898i	−0.200569	−	0.300172i	0.717527	−	0.696530i	$-0.245274\pi$
$139$	−2.36467	−	3.53898i	−0.200569	−	0.300172i	−0.918096	+	0.396358i	$0.870274\pi$
$140$	−2.35062	−	7.96520i	−0.198663	−	0.673182i
$141$	−8.89564	+	1.76945i	−0.749148	+	0.149015i
$142$	2.23806	−	0.101471i	0.187814	−	0.00851528i
$143$	−14.9118	−	14.9118i	−1.24699	−	1.24699i
$144$	10.1237	−	6.54525i	0.843640	−	0.545437i
$145$	−3.34395	+	3.34395i	−0.277700	+	0.277700i
$146$	−3.41125	+	3.73526i	−0.282317	+	0.309133i
$147$	0.00347435	+	0.0174667i	0.000286559	+	0.00144063i
$148$	13.7578	+	17.0247i	1.13088	+	1.39942i
$149$	−2.62422	+	1.75345i	−0.214985	+	0.143648i	−0.658400	−	0.752668i	$-0.728767\pi$
$149$	−2.62422	+	1.75345i	−0.214985	+	0.143648i	0.443416	+	0.896316i	$0.353767\pi$
$150$	4.55605	−	7.53657i	0.372000	−	0.615358i
$151$	15.7824	−	6.53730i	1.28436	−	0.531998i	0.367058	−	0.930198i	$-0.380365\pi$
$151$	15.7824	−	6.53730i	1.28436	−	0.531998i	0.917298	+	0.398200i	$0.130365\pi$
$152$	−1.14481	+	18.9227i	−0.0928564	+	1.53483i
$153$	0.898873	+	0.372325i	0.0726696	+	0.0301007i
$154$	10.8472	+	14.7419i	0.874091	+	1.18793i
$155$	0.326077	−	1.63930i	0.0261912	−	0.131672i
$156$	18.7325	−	9.83143i	1.49980	−	0.787144i
$157$	1.83146	−	2.74098i	0.146167	−	0.218754i	−0.751161	−	0.660119i	$-0.770506\pi$
$157$	1.83146	−	2.74098i	0.146167	−	0.218754i	0.897328	+	0.441365i	$0.145506\pi$
$158$	3.19802	−	8.83249i	0.254421	−	0.702675i
$159$		−	11.4959i		−	0.911680i
$160$	8.09190	−	3.64170i	0.639721	−	0.287902i
$161$		−	8.06045i		−	0.635253i
$162$	−11.9122	−	4.31312i	−0.935915	−	0.338871i
$163$	−1.97712	+	2.95896i	−0.154860	+	0.231764i	−0.900785	−	0.434266i	$-0.857008\pi$
$163$	−1.97712	+	2.95896i	−0.154860	+	0.231764i	0.745925	+	0.666030i	$0.232008\pi$
$164$	1.65923	−	5.32452i	0.129564	−	0.415775i
$165$	3.66909	−	18.4458i	0.285639	−	1.43600i
$166$	4.69384	−	3.45377i	0.364313	−	0.268064i
$167$	11.7493	+	4.86672i	0.909189	+	0.376598i	0.787746	−	0.616000i	$-0.211248\pi$
$167$	11.7493	+	4.86672i	0.909189	+	0.376598i	0.121443	+	0.992598i	$0.461248\pi$
$168$	−17.3566	+	5.98920i	−1.33909	+	0.462077i
$169$	5.17899	−	2.14521i	0.398384	−	0.165016i
$170$	0.612870	+	0.370496i	0.0470050	+	0.0284157i
$171$	−16.7956	+	11.2224i	−1.28439	+	0.858201i
$172$	−0.146180	+	1.37737i	−0.0111461	+	0.105024i
$173$	0.119835	+	0.602450i	0.00911086	+	0.0458034i	0.985073	−	0.172135i	$-0.0550667\pi$
$173$	0.119835	+	0.602450i	0.00911086	+	0.0458034i	−0.975962	+	0.217939i	$0.930067\pi$
$174$	7.72033	+	7.05063i	0.585277	+	0.534507i
$175$	−4.75315	+	4.75315i	−0.359304	+	0.359304i
$176$	−14.0357	+	13.6176i	−1.05798	+	1.02647i
$177$	−15.3171	−	15.3171i	−1.15131	−	1.15131i
$178$	0.716419	+	15.8014i	0.0536979	+	1.18436i
$179$	17.8336	−	3.54732i	1.33294	−	0.265139i	0.523344	−	0.852122i	$-0.324684\pi$
$179$	17.8336	−	3.54732i	1.33294	−	0.265139i	0.809600	+	0.586983i	$0.199684\pi$
$180$	8.30483	+	4.52006i	0.619006	+	0.336906i
$181$	−13.1144	−	19.6270i	−0.974783	−	1.45887i	−0.886477	−	0.462772i	$-0.846855\pi$
$181$	−13.1144	−	19.6270i	−0.974783	−	1.45887i	−0.0883053	−	0.996093i	$-0.528145\pi$
$182$	−15.6785	+	3.86436i	−1.16217	+	0.286445i
$183$	−7.03827	−	16.9919i	−0.520284	−	1.25608i
$184$	8.53308	−	1.16705i	0.629067	−	0.0860358i
$185$	−6.56984	+	15.8610i	−0.483024	+	1.16612i
$186$	−3.65323	−	0.556024i	−0.267868	−	0.0407696i
$187$	−1.54797	−	0.307911i	−0.113199	−	0.0225167i
$188$	0.669374	+	7.36670i	0.0488191	+	0.537272i
$189$	−0.0745625	−	0.0498210i	−0.00542362	−	0.00362395i
$190$	−13.4650	+	6.30633i	−0.976857	+	0.457509i
$191$	−9.08320			−0.657237			−0.328619	−	0.944463i	$-0.606583\pi$
$191$	−9.08320			−0.657237			−0.328619	+	0.944463i	$0.606583\pi$
$192$	−8.85339	−	17.5072i	−0.638938	−	1.26347i
$193$	−23.8071			−1.71367			−0.856836	−	0.515589i	$-0.827573\pi$
$193$	−23.8071			−1.71367			−0.856836	+	0.515589i	$0.827573\pi$
$194$	−9.35885	+	4.38320i	−0.671926	+	0.314695i
$195$	13.7965	+	9.21854i	0.987990	+	0.660154i
$196$	0.0144646	−	0.00131432i	0.00103319	−	9.38803e-5i
$197$	−7.77466	−	1.54648i	−0.553922	−	0.110182i	−0.0898105	−	0.995959i	$-0.528626\pi$
$197$	−7.77466	−	1.54648i	−0.553922	−	0.110182i	−0.464111	+	0.885777i	$0.653626\pi$
$198$	−20.6007	−	3.13544i	−1.46403	−	0.222826i
$199$	−3.63779	+	8.78239i	−0.257876	+	0.622567i	−0.998798	−	0.0490240i	$-0.984389\pi$
$199$	−3.63779	+	8.78239i	−0.257876	+	0.622567i	0.740922	+	0.671591i	$0.234389\pi$
$200$	−5.72004	−	4.34366i	−0.404468	−	0.307143i
$201$	7.80584	+	18.8450i	0.550581	+	1.32922i
$202$	18.9769	−	4.67730i	1.33521	−	0.329094i
$203$	−4.43367	−	6.63545i	−0.311182	−	0.465717i
$204$	0.756910	−	1.39069i	0.0529943	−	0.0973679i
$205$	4.29016	−	0.853366i	0.299638	−	0.0596017i
$206$	0.616318	+	13.5936i	0.0429409	+	0.947108i
$207$	6.48913	+	6.48913i	0.451026	+	0.451026i
$208$	−6.36099	−	16.0384i	−0.441055	−	1.11206i
$209$	23.1707	−	23.1707i	1.60275	−	1.60275i
$210$	−10.6337	−	9.71131i	−0.733797	−	0.670144i
$211$	−1.94225	−	9.76436i	−0.133710	−	0.672206i	−0.988253	−	0.152825i	$-0.951163\pi$
$211$	−1.94225	−	9.76436i	−0.133710	−	0.672206i	0.854543	−	0.519380i	$-0.173837\pi$
$212$	−9.32318	−	0.989463i	−0.640319	−	0.0679566i
$213$	3.23016	−	2.15832i	0.221327	−	0.147886i
$214$	5.79197	+	3.50139i	0.395931	+	0.239350i
$215$	−1.00368	+	0.415738i	−0.0684503	+	0.0283531i
$216$	0.0419467	−	0.0861479i	0.00285411	−	0.00586162i
$217$	2.60585	+	1.07938i	0.176896	+	0.0732729i
$218$	7.39121	−	5.43852i	0.500596	−	0.368343i
$219$	−1.71128	+	8.60318i	−0.115638	+	0.581349i
$220$	−14.6438	−	4.56330i	−0.987284	−	0.307658i
$221$	0.773622	−	1.15781i	0.0520394	−	0.0778825i
$222$	35.6886	+	12.9220i	2.39526	+	0.867265i
$223$			12.2329i			0.819179i	0.912270	+	0.409589i	$0.134328\pi$
$223$			12.2329i			0.819179i	−0.912270	+	0.409589i	$0.865672\pi$
$224$	3.36336	+	14.5918i	0.224724	+	0.974955i
$225$		−	7.65312i		−	0.510208i
$226$	7.03238	−	19.4225i	0.467787	−	1.29196i
$227$	9.90466	−	14.8234i	0.657395	−	0.983861i	−0.341635	−	0.939833i	$-0.610981\pi$
$227$	9.90466	−	14.8234i	0.657395	−	0.983861i	0.999030	−	0.0440287i	$-0.0140193\pi$
$228$	15.2766	+	29.1075i	1.01171	+	1.92769i
$229$	−3.25861	+	16.3821i	−0.215335	+	1.08256i	0.710229	+	0.703971i	$0.248591\pi$
$229$	−3.25861	+	16.3821i	−0.215335	+	1.08256i	−0.925564	+	0.378591i	$0.876409\pi$
$230$	4.00342	+	5.44084i	0.263977	+	0.358758i
$231$	29.3216	+	12.1454i	1.92922	+	0.799108i
$232$	6.38259	−	5.65436i	0.419037	−	0.371227i
$233$	−9.60560	+	3.97877i	−0.629283	+	0.260658i	−0.674449	−	0.738322i	$-0.735619\pi$
$233$	−9.60560	+	3.97877i	−0.629283	+	0.260658i	0.0451652	+	0.998980i	$0.485619\pi$
$234$	9.51111	−	15.7332i	0.621761	−	1.02851i
$235$	−4.82392	+	3.22324i	−0.314678	+	0.210261i
$236$	−13.7406	+	11.1039i	−0.894438	+	0.722801i
$237$	−3.17782	−	15.9760i	−0.206421	−	1.03775i
$238$	−0.814974	+	0.892384i	−0.0528269	+	0.0578447i
$239$	14.7694	−	14.7694i	0.955353	−	0.955353i	−0.0436917	−	0.999045i	$-0.513912\pi$
$239$	14.7694	−	14.7694i	0.955353	−	0.955353i	0.999045	+	0.0436917i	$0.0139119\pi$
$240$	8.74111	−	12.6633i	0.564236	−	0.817414i
$241$	7.07909	+	7.07909i	0.456004	+	0.456004i	0.897341	−	0.441337i	$-0.145496\pi$
$241$	7.07909	+	7.07909i	0.456004	+	0.456004i	−0.441337	+	0.897341i	$0.645496\pi$
$242$	18.2284	−	0.826456i	1.17176	−	0.0531266i
$243$	−21.6462	+	4.30570i	−1.38861	+	0.276211i
$244$	−14.3863	+	4.24555i	−0.920987	+	0.271793i
$245$	0.00632887	+	0.00947183i	0.000404337	+	0.000605133i
$246$	−2.31435	−	9.38984i	−0.147558	−	0.598674i
$247$	11.0635	+	26.7098i	0.703957	+	1.69950i
$248$	−0.765375	+	2.91492i	−0.0486014	+	0.185098i
$249$	3.86712	−	9.33606i	0.245069	−	0.591649i
$250$	2.51662	−	16.5349i	0.159165	−	1.04576i
$251$	−17.5456	−	3.49003i	−1.10747	−	0.220289i	−0.392710	−	0.919662i	$-0.628462\pi$
$251$	−17.5456	−	3.49003i	−1.10747	−	0.220289i	−0.714756	+	0.699374i	$0.753462\pi$
$252$	−10.2152	+	12.2572i	−0.643500	+	0.772131i
$253$	−12.3781	−	8.27079i	−0.778205	−	0.519980i
$254$	−1.82727	−	3.90152i	−0.114653	−	0.244803i
$255$	1.24184			0.0777672
$256$	−14.9604	+	5.67327i	−0.935026	+	0.354579i
$257$	26.9095			1.67857			0.839284	−	0.543694i	$-0.182975\pi$
$257$	26.9095			1.67857			0.839284	+	0.543694i	$0.182975\pi$
$258$	1.01871	+	2.17510i	0.0634219	+	0.135416i
$259$	−24.0885	−	16.0955i	−1.49679	−	1.00012i
$260$	8.66376	−	10.3956i	0.537303	−	0.644707i
$261$	8.91128	+	1.77256i	0.551594	+	0.109719i
$262$	1.60248	−	10.5287i	0.0990016	−	0.650467i
$263$	1.36380	−	3.29251i	0.0840956	−	0.203025i	−0.876238	−	0.481879i	$-0.839955\pi$
$263$	1.36380	−	3.29251i	0.0840956	−	0.203025i	0.960334	+	0.278854i	$0.0899546\pi$
$264$	−8.61218	+	32.7994i	−0.530043	+	2.01866i
$265$	−2.81405	−	6.79371i	−0.172865	−	0.417334i
$266$	−6.00463	−	24.3621i	−0.368167	−	1.49374i
$267$	15.2384	+	22.8059i	0.932576	+	1.39570i
$268$	15.9552	−	4.70855i	0.974618	−	0.287621i
$269$	−19.9604	+	3.97036i	−1.21700	+	0.242077i	−0.761505	−	0.648159i	$-0.775539\pi$
$269$	−19.9604	+	3.97036i	−1.21700	+	0.242077i	−0.455499	+	0.890236i	$0.650539\pi$
$270$	0.0750748	−	0.00340382i	0.00456891	−	0.000207150i
$271$	−1.83438	−	1.83438i	−0.111431	−	0.111431i	0.649193	−	0.760624i	$-0.275107\pi$
$271$	−1.83438	−	1.83438i	−0.111431	−	0.111431i	−0.760624	+	0.649193i	$0.775107\pi$
$272$	−1.06271	−	0.733556i	−0.0644361	−	0.0444783i
$273$	−19.7996	+	19.7996i	−1.19833	+	1.19833i
$274$	6.28036	−	6.87690i	0.379411	−	0.415449i
$275$	2.42204	+	12.1764i	0.146054	+	0.734264i
$276$	11.6158	−	9.38680i	0.699189	−	0.565019i
$277$	20.9494	−	13.9979i	1.25873	−	0.841055i	0.266300	−	0.963890i	$-0.414199\pi$
$277$	20.9494	−	13.9979i	1.25873	−	0.841055i	0.992427	+	0.122835i	$0.0391987\pi$
$278$	−3.11403	+	5.15120i	−0.186767	+	0.308948i
$279$	−2.96682	+	1.22890i	−0.177619	+	0.0735722i
$280$	−8.79117	+	7.78813i	−0.525373	+	0.465430i
$281$	11.8565	+	4.91114i	0.707302	+	0.292974i	0.707188	−	0.707026i	$-0.249964\pi$
$281$	11.8565	+	4.91114i	0.707302	+	0.292974i	0.000114440		1.00000i	$0.499964\pi$
$282$	7.60192	+	10.3314i	0.452688	+	0.615225i
$283$	−2.20386	+	11.0795i	−0.131006	+	0.658610i	0.858347	+	0.513070i	$0.171492\pi$
$283$	−2.20386	+	11.0795i	−0.131006	+	0.658610i	−0.989352	+	0.145540i	$0.953508\pi$
$284$	−1.47238	−	2.80544i	−0.0873699	−	0.166472i
$285$	−14.3242	+	21.4377i	−0.848494	+	1.26986i
$286$	−10.1533	+	28.0421i	−0.600380	+	1.65817i
$287$			7.38157i			0.435720i
$288$	−14.4549	−	9.03954i	−0.851765	−	0.532660i
$289$			16.8958i			0.993870i
$290$	6.28840	+	2.27687i	0.369267	+	0.133702i
$291$	−9.95601	+	14.9002i	−0.583632	+	0.873467i
$292$	6.82992	+	2.12834i	0.399691	+	0.124552i
$293$	3.55830	−	17.8888i	0.207878	−	1.04507i	−0.726058	−	0.687633i	$-0.758650\pi$
$293$	3.55830	−	17.8888i	0.207878	−	1.04507i	0.933936	−	0.357440i	$-0.116350\pi$
$294$	0.0202858	−	0.0149265i	0.00118309	−	0.000870530i
$295$	−12.8014	−	5.30252i	−0.745327	−	0.308725i
$296$	13.5515	−	27.8314i	0.787666	−	1.61767i
$297$	−0.153016	+	0.0633815i	−0.00887891	+	0.00367777i
$298$	3.81972	+	2.30912i	0.221270	+	0.133764i
$299$	10.9208	−	7.29705i	0.631566	−	0.421999i
$300$	−12.3850	−	1.31441i	−0.715046	−	0.0758874i
$301$	−0.357655	−	1.79805i	−0.0206149	−	0.103638i
$302$	−17.8390	−	16.2915i	−1.02652	−	0.937472i
$303$	23.9649	−	23.9649i	1.37675	−	1.37675i
$304$	24.9212	−	9.88402i	1.42933	−	0.566887i
$305$	−8.31881	−	8.31881i	−0.476334	−	0.476334i
$306$	−0.0623195	−	1.37452i	−0.00356257	−	0.0785763i
$307$	6.20347	−	1.23395i	0.354051	−	0.0704251i	−0.0148607	−	0.999890i	$-0.504730\pi$
$307$	6.20347	−	1.23395i	0.354051	−	0.0704251i	0.368912	+	0.929464i	$0.379730\pi$
$308$	12.3737	−	22.7345i	0.705058	−	1.29542i
$309$	13.1093	+	19.6194i	0.745759	+	1.11611i
$310$	−2.29506	+	0.565672i	−0.130350	+	0.0321280i
$311$	6.82557	+	16.4784i	0.387042	+	0.934403i	0.990563	+	0.137056i	$0.0437640\pi$
$311$	6.82557	+	16.4784i	0.387042	+	0.934403i	−0.603521	+	0.797347i	$0.706236\pi$
$312$	−23.8273	−	18.0939i	−1.34896	−	1.02436i
$313$	−2.69923	+	6.51651i	−0.152569	+	0.368335i	−0.981622	−	0.190836i	$-0.938880\pi$
$313$	−2.69923	+	6.51651i	−0.152569	+	0.368335i	0.829053	+	0.559170i	$0.188880\pi$
$314$	−4.60895	−	0.701485i	−0.260098	−	0.0395871i
$315$	−12.2741	−	2.44147i	−0.691567	−	0.137561i
$316$	−13.2301	+	1.20215i	−0.744251	+	0.0676262i
$317$	−27.9024	−	18.6438i	−1.56716	−	1.04714i	−0.969408	−	0.245456i	$-0.921062\pi$
$317$	−27.9024	−	18.6438i	−1.56716	−	1.04714i	−0.597748	−	0.801684i	$-0.703938\pi$
$318$	−14.7229	+	6.89542i	−0.825617	+	0.386676i
$319$	−14.7392			−0.825234
$320$	−9.51764	−	8.17902i	−0.532052	−	0.457221i
$321$	11.7361			0.655046
$322$	−10.3231	+	4.83481i	−0.575284	+	0.269433i
$323$	1.79906	+	1.20209i	0.100102	+	0.0668861i
$324$	1.62132	+	17.8432i	0.0900734	+	0.991290i
$325$	−10.7428	−	2.13688i	−0.595905	−	0.118533i
$326$	4.97549	+	0.757273i	0.275567	+	0.0419415i
$327$	6.08941	−	14.7011i	0.336745	−	0.812974i
$328$	−7.81439	+	1.06875i	−0.431478	+	0.0590120i
$329$	−3.74664	−	9.04519i	−0.206559	−	0.498678i
$330$	−25.8245	+	6.36507i	−1.42159	+	0.350386i
$331$	−6.61521	−	9.90037i	−0.363605	−	0.544173i	0.603889	−	0.797069i	$-0.293617\pi$
$331$	−6.61521	−	9.90037i	−0.363605	−	0.544173i	−0.967494	+	0.252895i	$0.918617\pi$
$332$	−7.23873	−	3.93982i	−0.397277	−	0.216226i
$333$	32.3505	−	6.43491i	1.77279	−	0.352631i
$334$	−0.814588	−	17.9666i	−0.0445723	−	0.983089i
$335$	9.22604	+	9.22604i	0.504072	+	0.504072i
$336$	18.0812	+	18.6364i	0.986413	+	1.01670i
$337$	−21.7272	+	21.7272i	−1.18356	+	1.18356i	−0.204740	+	0.978816i	$0.565635\pi$
$337$	−21.7272	+	21.7272i	−1.18356	+	1.18356i	−0.978816	+	0.204740i	$0.934365\pi$
$338$	−5.85385	−	5.34605i	−0.318407	−	0.290787i
$339$	−6.98796	−	35.1308i	−0.379534	−	1.90804i
$340$	0.106887	−	1.00714i	0.00579677	−	0.0546198i
$341$	4.33140	−	2.89415i	0.234559	−	0.156727i
$342$	24.4470	+	14.7788i	1.32194	+	0.799147i
$343$	17.1016	−	7.08372i	0.923400	−	0.382485i
$344$	1.85170	−	0.638960i	0.0998369	−	0.0344504i
$345$	10.8218	+	4.48255i	0.582628	+	0.241332i
$346$	0.699684	−	0.514834i	0.0376153	−	0.0276776i
$347$	−6.17477	+	31.0427i	−0.331479	+	1.66646i	0.351628	+	0.936140i	$0.385628\pi$
$347$	−6.17477	+	31.0427i	−0.331479	+	1.66646i	−0.683107	+	0.730318i	$0.739372\pi$
$348$	4.39902	−	14.1166i	0.235812	−	0.756729i
$349$	−3.28116	+	4.91061i	−0.175637	+	0.262859i	−0.908835	−	0.417156i	$-0.863027\pi$
$349$	−3.28116	+	4.91061i	−0.175637	+	0.262859i	0.733198	+	0.680015i	$0.238027\pi$
$350$	8.93842	+	3.23638i	0.477779	+	0.172992i
$351$		−	0.146124i		−	0.00779954i
$352$	25.8591	+	9.80759i	1.37830	+	0.522746i
$353$		−	0.529453i		−	0.0281800i	−0.999901	−	0.0140900i	$-0.995515\pi$
$353$		−	0.529453i		−	0.0281800i	0.999901	−	0.0140900i	$-0.00448513\pi$
$354$	−10.4293	+	28.8043i	−0.554312	+	1.53093i
$355$	1.38060	−	2.06621i	0.0732744	−	0.109663i
$356$	19.8073	−	10.3955i	1.04978	−	0.550959i
$357$	−0.408838	+	2.05537i	−0.0216380	+	0.108782i
$358$	−15.2400	−	20.7119i	−0.805458	−	1.09466i
$359$	−20.4053	−	8.45215i	−1.07695	−	0.446087i	−0.227512	−	0.973775i	$-0.573059\pi$
$359$	−20.4053	−	8.45215i	−1.07695	−	0.446087i	−0.849438	+	0.527688i	$0.823059\pi$
$360$	0.807502	−	13.3473i	0.0425591	−	0.703464i
$361$	−23.9492	+	9.92010i	−1.26049	+	0.522110i
$362$	−17.2703	+	28.5683i	−0.907707	+	1.50152i
$363$	26.3087	−	17.5789i	1.38085	−	0.922654i
$364$	14.3534	+	17.7618i	0.752322	+	0.930969i
$365$	1.09464	+	5.50312i	0.0572960	+	0.288047i
$366$	−17.5400	+	19.2060i	−0.916830	+	1.00391i
$367$	−14.5467	+	14.5467i	−0.759333	+	0.759333i	−0.976201	−	0.216868i	$-0.930416\pi$
$367$	−14.5467	+	14.5467i	−0.759333	+	0.759333i	0.216868	+	0.976201i	$0.430416\pi$
$368$	−6.61295	−	10.2284i	−0.344724	−	0.533192i
$369$	−5.94259	−	5.94259i	−0.309359	−	0.309359i
$370$	24.2541	−	1.09965i	1.26091	−	0.0571683i
$371$	12.1707	−	2.42090i	0.631869	−	0.125687i
$372$	1.47917	+	5.01224i	0.0766912	+	0.259872i
$373$	−10.8226	−	16.1972i	−0.560375	−	0.838660i	0.437799	−	0.899073i	$-0.355758\pi$
$373$	−10.8226	−	16.1972i	−0.560375	−	0.838660i	−0.998173	+	0.0604127i	$0.980758\pi$
$374$	0.534158	+	2.16720i	0.0276206	+	0.112063i
$375$	−11.0987	−	26.7947i	−0.573136	−	1.38367i
$376$	9.03310	−	5.27595i	0.465847	−	0.272086i
$377$	4.97637	−	12.0140i	0.256296	−	0.618753i
$378$	−0.0190824	+	0.125376i	−0.000981492	+	0.00644867i
$379$	21.0139	+	4.17992i	1.07941	+	0.214708i	0.702602	−	0.711583i	$-0.252022\pi$
$379$	21.0139	+	4.17992i	1.07941	+	0.214708i	0.376808	+	0.926291i	$0.377022\pi$
$380$	16.1532	+	13.4622i	0.828640	+	0.690595i
$381$	−6.21161	−	4.15047i	−0.318231	−	0.212635i
$382$	5.44827	+	11.6329i	0.278758	+	0.595193i
$383$	−6.11960			−0.312697			−0.156348	−	0.987702i	$-0.549972\pi$
$383$	−6.11960			−0.312697			−0.156348	+	0.987702i	$0.549972\pi$
$384$	−17.1112	+	21.8398i	−0.873203	+	1.11451i
$385$	20.3012			1.03465
$386$	14.2799	+	30.4900i	0.726829	+	1.55190i
$387$	1.73547	+	1.15960i	0.0882189	+	0.0589460i
$388$	11.2272	+	9.35685i	0.569975	+	0.475022i
$389$	30.1172	+	5.99068i	1.52700	+	0.303740i	0.885959	−	0.463764i	$-0.153502\pi$
$389$	30.1172	+	5.99068i	1.52700	+	0.303740i	0.641044	+	0.767504i	$0.278502\pi$
$390$	3.53087	−	23.1988i	0.178793	−	1.17472i
$391$	0.376176	−	0.908170i	0.0190241	−	0.0459281i
$392$	−0.0103594	−	0.0177366i	−0.000523229	−	0.000895834i
$393$	−7.06722	−	17.0618i	−0.356494	−	0.860653i
$394$	2.68280	+	10.8847i	0.135157	+	0.548363i
$395$	−5.78872	−	8.66343i	−0.291262	−	0.435905i
$396$	8.34107	+	28.2642i	0.419155	+	1.42033i
$397$	28.0202	−	5.57357i	1.40630	−	0.279730i	0.567140	−	0.823621i	$-0.308050\pi$
$397$	28.0202	−	5.57357i	1.40630	−	0.279730i	0.839155	+	0.543892i	$0.183050\pi$
$398$	13.4297	−	0.608890i	0.673171	−	0.0305209i
$399$	−30.7656	−	30.7656i	−1.54021	−	1.54021i
$400$	−2.13198	+	9.93112i	−0.106599	+	0.496556i
$401$	3.48263	−	3.48263i	0.173914	−	0.173914i	−0.614782	−	0.788697i	$-0.710756\pi$
$401$	3.48263	−	3.48263i	0.173914	−	0.173914i	0.788697	+	0.614782i	$0.210756\pi$
$402$	19.4528	−	21.3006i	0.970220	−	1.06238i
$403$	0.896640	+	4.50771i	0.0446648	+	0.224545i
$404$	−17.3729	−	21.4983i	−0.864336	−	1.06958i
$405$	−11.6842	+	7.80716i	−0.580595	+	0.387941i
$406$	−5.83869	+	9.65830i	−0.289769	+	0.479333i
$407$	−49.4343	+	20.4764i	−2.45037	+	1.01498i
$408$	−2.23508	−	0.135221i	−0.110653	−	0.00669442i
$409$	18.5077	+	7.66613i	0.915145	+	0.379065i	0.790024	−	0.613076i	$-0.210068\pi$
$409$	18.5077	+	7.66613i	0.915145	+	0.379065i	0.125121	+	0.992141i	$0.460068\pi$
$410$	−3.66623	−	4.98259i	−0.181062	−	0.246073i
$411$	3.15059	−	15.8391i	0.155407	−	0.781285i
$412$	17.0397	−	8.94299i	0.839487	−	0.440589i
$413$	12.9906	−	19.4419i	0.639228	−	0.956672i
$414$	4.41840	−	12.2030i	0.217152	−	0.599745i
$415$		−	6.46396i		−	0.317303i
$416$	−16.7251	+	17.7667i	−0.820013	+	0.871083i
$417$			10.4377i			0.511138i
$418$	−43.5732	−	15.7768i	−2.13124	−	0.771667i
$419$	−17.7369	+	26.5451i	−0.866503	+	1.29681i	0.0872386	+	0.996187i	$0.472196\pi$
$419$	−17.7369	+	26.5451i	−0.866503	+	1.29681i	−0.953742	+	0.300626i	$0.902804\pi$
$420$	−6.05906	+	19.4437i	−0.295652	+	0.948758i
$421$	−4.00504	+	20.1347i	−0.195194	+	0.981304i	0.751638	+	0.659576i	$0.229264\pi$
$421$	−4.00504	+	20.1347i	−0.195194	+	0.981304i	−0.946832	+	0.321729i	$0.895736\pi$
$422$	−11.3403	+	8.34430i	−0.552038	+	0.406194i
$423$	10.2982	+	4.26564i	0.500714	+	0.207403i
$424$	4.32500	+	12.5338i	0.210040	+	0.608694i
$425$	−0.757362	+	0.313710i	−0.0367375	+	0.0152172i
$426$	−4.70169	−	2.84229i	−0.227798	−	0.137710i
$427$	16.5071	−	11.0297i	0.798836	−	0.533765i
$428$	1.01014	−	9.51803i	0.0488271	−	0.460071i
$429$	10.0892	+	50.7218i	0.487111	+	2.44887i
$430$	1.13446	+	1.03605i	0.0547087	+	0.0499630i
$431$	27.4402	−	27.4402i	1.32175	−	1.32175i	0.409388	−	0.912360i	$-0.365742\pi$
$431$	27.4402	−	27.4402i	1.32175	−	1.32175i	0.912360	−	0.409388i	$-0.134258\pi$
$432$	−0.135491	−	0.00204846i	−0.00651881	−	9.85564e-5i
$433$	5.45442	+	5.45442i	0.262123	+	0.262123i	0.825916	−	0.563793i	$-0.190659\pi$
$433$	5.45442	+	5.45442i	0.262123	+	0.262123i	−0.563793	+	0.825916i	$0.690659\pi$
$434$	−0.180665	−	3.98476i	−0.00867221	−	0.191275i
$435$	11.3743	−	2.26249i	0.545355	−	0.108478i
$436$	−11.3985	−	6.20388i	−0.545891	−	0.297112i
$437$	11.3385	+	16.9693i	0.542394	+	0.811751i
$438$	12.0446	−	2.96869i	0.575515	−	0.141850i
$439$	−8.42495	−	20.3396i	−0.402101	−	0.970757i	−0.987155	−	0.159763i	$-0.948927\pi$
$439$	−8.42495	−	20.3396i	−0.402101	−	0.970757i	0.585055	−	0.810994i	$-0.301073\pi$
$440$	2.93935	+	21.4916i	0.140128	+	1.02457i
$441$	0.00837565	−	0.0202206i	0.000398840	−	0.000962886i
$442$	−1.94685	−	0.296311i	−0.0926020	−	0.0140941i
$443$	−28.7291	−	5.71458i	−1.36496	−	0.271508i	−0.542370	−	0.840139i	$-0.682473\pi$
$443$	−28.7291	−	5.71458i	−1.36496	−	0.271508i	−0.822592	+	0.568632i	$0.807473\pi$
$444$	−4.85742	−	53.4576i	−0.230523	−	2.53699i
$445$	14.5881	+	9.74743i	0.691540	+	0.462072i
$446$	15.6669	−	7.33754i	0.741847	−	0.347443i
$447$	7.73980			0.366080
$448$	16.6704	−	13.0599i	0.787604	−	0.617022i
$449$	−6.13112			−0.289345			−0.144673	−	0.989480i	$-0.546213\pi$
$449$	−6.13112			−0.289345			−0.144673	+	0.989480i	$0.546213\pi$
$450$	−9.80142	+	4.59048i	−0.462044	+	0.216397i
$451$	11.3356	+	7.57419i	0.533772	+	0.356655i
$452$	−29.0927	+	2.64350i	−1.36841	+	0.124340i
$453$	−41.0873	−	8.17277i	−1.93045	−	0.383990i
$454$	−24.9254	−	3.79367i	−1.16981	−	0.178046i
$455$	−6.85428	+	16.5477i	−0.321334	+	0.775768i
$456$	28.1152	−	37.0241i	1.31661	−	1.73381i
$457$	−6.01802	−	14.5288i	−0.281511	−	0.679628i	0.718360	−	0.695672i	$-0.244893\pi$
$457$	−6.01802	−	14.5288i	−0.281511	−	0.679628i	−0.999871	+	0.0160431i	$0.994893\pi$
$458$	22.9353	−	5.65297i	1.07170	−	0.264146i
$459$	−0.00607582	−	0.00909311i	−0.000283595	−	0.000424430i
$460$	4.56681	−	8.39073i	0.212929	−	0.391220i
$461$	8.71608	−	1.73374i	0.405949	−	0.0807482i	0.0121074	−	0.999927i	$-0.496146\pi$
$461$	8.71608	−	1.73374i	0.405949	−	0.0807482i	0.393841	+	0.919179i	$0.371146\pi$
$462$	−2.03289	−	44.8375i	−0.0945784	−	2.08603i
$463$	28.3923	+	28.3923i	1.31950	+	1.31950i	0.914171	+	0.405329i	$0.132843\pi$
$463$	28.3923	+	28.3923i	1.31950	+	1.31950i	0.405329	+	0.914171i	$0.367157\pi$
$464$	−11.0700	−	4.78265i	−0.513911	−	0.222029i
$465$	−2.89831	+	2.89831i	−0.134406	+	0.134406i
$466$	10.8573	+	9.91544i	0.502953	+	0.459324i
$467$	−1.97602	−	9.93412i	−0.0914392	−	0.459696i	−0.999192	−	0.0401906i	$-0.987204\pi$
$467$	−1.97602	−	9.93412i	−0.0914392	−	0.459696i	0.907753	−	0.419505i	$-0.137796\pi$
$468$	−25.8546	−	2.74393i	−1.19513	−	0.126838i
$469$	−18.3073	+	12.2326i	−0.845355	+	0.564848i
$470$	7.02151	+	4.24468i	0.323878	+	0.195793i
$471$	−7.46878	+	3.09367i	−0.344143	+	0.142549i
$472$	22.4627	+	10.9374i	1.03393	+	0.503436i
$473$	−3.12819	−	1.29574i	−0.143834	−	0.0595780i
$474$	−18.5545	+	13.6525i	−0.852235	+	0.627082i
$475$	3.32039	−	16.6927i	0.152350	−	0.765915i
$476$	1.63172	+	0.508478i	0.0747899	+	0.0233060i
$477$	−7.84913	+	11.7471i	−0.359387	+	0.537861i
$478$	−27.7743	−	10.0564i	−1.27037	−	0.459968i
$479$			35.2640i			1.61125i	0.592424	+	0.805627i	$0.298171\pi$
$479$			35.2640i			1.61125i	−0.592424	+	0.805627i	$0.701829\pi$
$480$	−21.4611	−	3.59915i	−0.979561	−	0.164278i
$481$		−	47.2077i		−	2.15249i
$482$	4.82009	−	13.3124i	0.219549	−	0.606365i
$483$	−10.9818	+	16.4354i	−0.499689	+	0.747837i
$484$	−11.9921	−	22.8495i	−0.545098	−	1.03861i
$485$	−2.23631	+	11.2427i	−0.101546	+	0.510505i
$486$	18.4982	+	25.1399i	0.839093	+	1.14037i
$487$	13.0372	+	5.40020i	0.590774	+	0.244707i	0.657984	−	0.753032i	$-0.271410\pi$
$487$	13.0372	+	5.40020i	0.590774	+	0.244707i	−0.0672097	+	0.997739i	$0.521410\pi$
$488$	14.0665	+	15.8781i	0.636759	+	0.718767i
$489$	8.06276	−	3.33970i	0.364611	−	0.151027i
$490$	0.00833449	−	0.0137868i	0.000376514	−	0.000622825i
$491$	1.51681	−	1.01350i	0.0684528	−	0.0457387i	−0.520873	−	0.853634i	$-0.674393\pi$
$491$	1.51681	−	1.01350i	0.0684528	−	0.0457387i	0.589326	+	0.807896i	$0.299393\pi$
$492$	−10.6375	+	8.59621i	−0.479574	+	0.387547i
$493$	−0.189868	−	0.954531i	−0.00855123	−	0.0429899i
$494$	27.5714	−	30.1902i	1.24049	−	1.35832i
$495$	−16.3437	+	16.3437i	−0.734593	+	0.734593i
$496$	4.19226	−	0.768200i	0.188238	−	0.0344932i
$497$	2.96525	+	2.96525i	0.133010	+	0.133010i
$498$	−14.2764	+	0.647276i	−0.639739	+	0.0290051i
$499$	6.00903	−	1.19527i	0.269001	−	0.0535076i	−0.0587467	−	0.998273i	$-0.518710\pi$
$499$	6.00903	−	1.19527i	0.269001	−	0.0535076i	0.327748	+	0.944765i	$0.393710\pi$
$500$	−22.6859	+	6.69486i	−1.01454	+	0.299403i
$501$	−17.3265	−	25.9309i	−0.774091	−	1.15851i
$502$	6.05443	+	24.5642i	0.270223	+	1.09635i
$503$	0.252675	+	0.610011i	0.0112662	+	0.0271990i	0.929413	−	0.369042i	$-0.120314\pi$
$503$	0.252675	+	0.610011i	0.0112662	+	0.0271990i	−0.918146	+	0.396241i	$0.870314\pi$
$504$	21.8252	+	5.73067i	0.972172	+	0.255264i
$505$	8.29623	−	20.0289i	0.369177	−	0.891273i
$506$	−3.16787	+	20.8137i	−0.140829	+	0.925284i
$507$	−13.4828	−	2.68189i	−0.598791	−	0.119107i
$508$	−3.90069	+	4.68040i	−0.173065	+	0.207659i
$509$	0.523675	+	0.349909i	0.0232115	+	0.0155094i	0.567122	−	0.823634i	$-0.308057\pi$
$509$	0.523675	+	0.349909i	0.0232115	+	0.0155094i	−0.543910	+	0.839143i	$0.683057\pi$
$510$	−0.744880	−	1.59044i	−0.0329838	−	0.0704259i
$511$	−9.46857			−0.418865
$512$	16.2393	+	15.7570i	0.717684	+	0.696369i
$513$	0.227055			0.0100247
$514$	−16.1408	−	34.4632i	−0.711940	−	1.52011i
$515$	12.5498	+	8.38549i	0.553009	+	0.369509i
$516$	2.17464	−	2.60933i	0.0957332	−	0.114870i
$517$	−17.7348	−	3.52766i	−0.779974	−	0.155146i
$518$	−6.16486	+	40.5048i	−0.270868	+	1.77968i
$519$	0.576450	−	1.39167i	0.0253033	−	0.0610877i
$520$	−18.5104	−	4.86030i	−0.811735	−	0.213138i
$521$	0.0504944	+	0.121904i	0.00221220	+	0.00534072i	0.924982	−	0.380011i	$-0.124080\pi$
$521$	0.0504944	+	0.121904i	0.00221220	+	0.00534072i	−0.922770	+	0.385352i	$0.874080\pi$
$522$	−3.07501	−	12.4760i	−0.134589	−	0.546059i
$523$	2.15403	+	3.22374i	0.0941892	+	0.140964i	0.875572	−	0.483088i	$-0.160485\pi$
$523$	2.15403	+	3.22374i	0.0941892	+	0.140964i	−0.781382	+	0.624053i	$0.785485\pi$
$524$	−14.4455	+	4.26301i	−0.631053	+	0.186231i
$525$	16.1676	−	3.21593i	0.705611	−	0.140355i
$526$	−5.03478	+	0.228272i	−0.219527	+	0.00995313i
$527$	0.243227	+	0.243227i	0.0105951	+	0.0105951i
$528$	47.1722	−	8.64396i	2.05291	−	0.376180i
$529$	−9.70721	+	9.70721i	−0.422053	+	0.422053i
$530$	−7.01285	+	7.67896i	−0.304619	+	0.333553i
$531$	5.19361	+	26.1101i	0.225384	+	1.13308i
$532$	−27.5991	+	22.3030i	−1.19657	+	0.966958i
$533$	−10.0010	+	6.68246i	−0.433192	+	0.289450i
$534$	20.0675	−	33.1954i	0.868404	−	1.43650i
$535$	6.93569	−	2.87286i	0.299856	−	0.124204i
$536$	−15.6005	−	17.6097i	−0.673839	−	0.760623i
$537$	−41.1960	−	17.0639i	−1.77774	−	0.736363i
$538$	17.0575	+	23.1819i	0.735400	+	0.999444i
$539$	−0.00692661	+	0.0348224i	−0.000298350	+	0.00149991i
$540$	−0.0493905	−	0.0941074i	−0.00212543	−	0.00404974i
$541$	−6.56680	+	9.82791i	−0.282329	+	0.422535i	−0.945346	−	0.326070i	$-0.894276\pi$
$541$	−6.56680	+	9.82791i	−0.282329	+	0.422535i	0.663017	+	0.748604i	$0.269276\pi$
$542$	−1.24902	+	3.44961i	−0.0536498	+	0.148173i
$543$			57.8873i			2.48418i
$544$	−0.302041	+	1.80102i	−0.0129499	+	0.0772181i
$545$		−	10.1785i		−	0.436001i
$546$	37.2338	+	13.4814i	1.59346	+	0.576951i
$547$	3.90437	−	5.84330i	0.166939	−	0.249841i	−0.738563	−	0.674185i	$-0.764495\pi$
$547$	3.90437	−	5.84330i	0.166939	−	0.249841i	0.905501	+	0.424343i	$0.139495\pi$
$548$	−12.5744	−	3.91843i	−0.537151	−	0.167387i
$549$	−4.40964	+	22.1688i	−0.188199	+	0.946140i
$550$	14.1417	−	10.4055i	0.603002	−	0.443694i
$551$	18.6680	+	7.73252i	0.795282	+	0.329417i
$552$	−18.9891	−	9.24609i	−0.808231	−	0.393540i
$553$	16.2446	−	6.72872i	0.690789	−	0.286134i
$554$	−30.4931	−	18.4339i	−1.29553	−	0.783181i
$555$	35.0055	−	23.3900i	1.48590	−	0.992848i
$556$	8.46504	+	0.898390i	0.358998	+	0.0381002i
$557$	−8.38778	−	42.1682i	−0.355402	−	1.78672i	−0.582477	−	0.812847i	$-0.697916\pi$
$557$	−8.38778	−	42.1682i	−0.355402	−	1.78672i	0.227076	−	0.973877i	$-0.427084\pi$
$558$	3.35341	+	3.06252i	0.141961	+	0.129647i
$559$	2.11233	−	2.11233i	0.0893422	−	0.0893422i
$560$	15.2474	+	6.58747i	0.644322	+	0.278371i
$561$	2.73684	+	2.73684i	0.115549	+	0.115549i
$562$	−0.822023	−	18.1306i	−0.0346749	−	0.764793i
$563$	−10.4779	+	2.08419i	−0.441592	+	0.0878381i	−0.410879	−	0.911690i	$-0.634778\pi$
$563$	−10.4779	+	2.08419i	−0.441592	+	0.0878381i	−0.0307136	+	0.999528i	$0.509778\pi$
$564$	8.67174	−	15.9328i	0.365146	−	0.670893i
$565$	−12.7293	−	19.0507i	−0.535525	−	0.801469i
$566$	15.5116	−	3.82321i	0.652001	−	0.160701i
$567$	−9.07492	−	21.9088i	−0.381111	−	0.920083i
$568$	−2.70979	+	3.56845i	−0.113700	+	0.149729i
$569$	−9.56257	+	23.0861i	−0.400884	+	0.967819i	0.586568	+	0.809900i	$0.300479\pi$
$569$	−9.56257	+	23.0861i	−0.400884	+	0.967819i	−0.987452	+	0.157919i	$0.949521\pi$
$570$	36.0474	+	5.48644i	1.50986	+	0.229802i
$571$	20.9430	+	4.16583i	0.876439	+	0.174335i	0.612753	−	0.790274i	$-0.290062\pi$
$571$	20.9430	+	4.16583i	0.876439	+	0.174335i	0.263685	+	0.964609i	$0.415062\pi$
$572$	42.0040	−	3.81668i	1.75627	−	0.159584i
$573$	18.5208	+	12.3752i	0.773718	+	0.516982i
$574$	9.45365	−	4.42760i	0.394588	−	0.184804i
$575$	−7.73227			−0.322458
$576$	−2.90670	+	23.9347i	−0.121112	+	0.997278i
$577$	13.5096			0.562413			0.281207	−	0.959647i	$-0.409265\pi$
$577$	13.5096			0.562413			0.281207	+	0.959647i	$0.409265\pi$
$578$	21.6386	−	10.1344i	0.900047	−	0.421535i
$579$	48.5431	+	32.4355i	2.01738	+	1.34797i
$580$	−0.855885	−	9.41932i	−0.0355387	−	0.391116i
$581$	10.6985	+	2.12806i	0.443847	+	0.0882866i
$582$	25.0547	+	3.81334i	1.03855	+	0.158068i
$583$	8.77059	−	21.1741i	0.363241	−	0.876941i
$584$	−1.37092	−	10.0238i	−0.0567292	−	0.414786i
$585$	−7.80377	−	18.8400i	−0.322646	−	0.778937i
$586$	−25.0447	+	6.17286i	−1.03459	+	0.254999i
$587$	7.71852	+	11.5516i	0.318577	+	0.476785i	0.955851	−	0.293853i	$-0.0949377\pi$
$587$	7.71852	+	11.5516i	0.318577	+	0.476785i	−0.637273	+	0.770638i	$0.719938\pi$
$588$	−0.0312843	−	0.0170271i	−0.00129014	−	0.000702185i
$589$	−7.00431	+	1.39324i	−0.288607	+	0.0574076i
$590$	0.887532	+	19.5755i	0.0365391	+	0.805909i
$591$	13.7457	+	13.7457i	0.565423	+	0.565423i
$592$	−43.7724	−	0.661785i	−1.79903	−	0.0271992i
$593$	3.80843	−	3.80843i	0.156393	−	0.156393i	−0.624573	−	0.780966i	$-0.714727\pi$
$593$	3.80843	−	3.80843i	0.156393	−	0.156393i	0.780966	+	0.624573i	$0.214727\pi$
$594$	0.172955	+	0.157952i	0.00709644	+	0.00648086i
$595$	0.261518	+	1.31474i	0.0107212	+	0.0538991i
$596$	0.666174	−	6.27700i	0.0272876	−	0.257116i
$597$	19.3829	−	12.9512i	0.793290	−	0.530059i
$598$	−15.8959	−	9.60948i	−0.650032	−	0.392961i
$599$	9.18975	−	3.80652i	0.375483	−	0.155530i	−0.186957	−	0.982368i	$-0.559863\pi$
$599$	9.18975	−	3.80652i	0.375483	−	0.155530i	0.562440	+	0.826838i	$0.309863\pi$
$600$	5.74535	+	16.6500i	0.234553	+	0.679732i
$601$	28.7287	+	11.8998i	1.17187	+	0.485404i	0.881810	−	0.471605i	$-0.156325\pi$
$601$	28.7287	+	11.8998i	1.17187	+	0.485404i	0.290059	+	0.957009i	$0.406325\pi$
$602$	−2.08826	+	1.53656i	−0.0851110	+	0.0626254i
$603$	4.89054	−	24.5864i	0.199158	−	1.00124i
$604$	−10.1646	+	32.6185i	−0.413591	+	1.32723i
$605$	11.2446	−	16.8287i	0.457157	−	0.684183i
$606$	−45.0667	−	16.3175i	−1.83071	−	0.662853i
$607$		−	38.5851i		−	1.56612i	−0.621946	−	0.783060i	$-0.713657\pi$
$607$		−	38.5851i		−	1.56612i	0.621946	−	0.783060i	$-0.286343\pi$
$608$	−27.6067	−	25.9882i	−1.11960	−	1.05396i
$609$			19.5704i			0.793031i
$610$	−5.66421	+	15.6438i	−0.229337	+	0.633398i
$611$	8.86320	−	13.2647i	0.358567	−	0.536633i
$612$	−1.72299	+	0.904277i	−0.0696476	+	0.0365532i
$613$	−6.11185	+	30.7263i	−0.246855	+	1.24102i	0.636114	+	0.771595i	$0.280541\pi$
$613$	−6.11185	+	30.7263i	−0.246855	+	1.24102i	−0.882970	+	0.469430i	$0.844459\pi$
$614$	−5.30129	−	7.20471i	−0.213942	−	0.290758i
$615$	−9.91038	−	4.10501i	−0.399625	−	0.165530i
$616$	−36.5383	−	2.21054i	−1.47217	−	0.0890653i
$617$	29.6969	−	12.3009i	1.19555	−	0.495214i	0.305992	−	0.952034i	$-0.401012\pi$
$617$	29.6969	−	12.3009i	1.19555	−	0.495214i	0.889559	+	0.456820i	$0.151012\pi$
$618$	17.2636	−	28.5572i	0.694443	−	1.14874i
$619$	−29.9290	+	19.9979i	−1.20295	+	0.803784i	−0.985064	−	0.172191i	$-0.944915\pi$
$619$	−29.9290	+	19.9979i	−1.20295	+	0.803784i	−0.217884	+	0.975975i	$0.569915\pi$
$620$	2.10108	+	2.60000i	0.0843813	+	0.104419i
$621$	−0.0201243	−	0.101172i	−0.000807560	−	0.00405988i
$622$	17.0099	−	18.6256i	0.682036	−	0.746819i
$623$	−20.9356	+	20.9356i	−0.838766	+	0.838766i
$624$	−8.88095	+	41.3689i	−0.355522	+	1.65608i
$625$	−4.14010	−	4.14010i	−0.165604	−	0.165604i
$626$	9.96480	−	0.451794i	0.398274	−	0.0180573i
$627$	−78.8140	+	15.6771i	−3.14753	+	0.626083i
$628$	1.86613	+	6.32349i	0.0744667	+	0.252335i
$629$	−1.96289	−	2.93767i	−0.0782655	−	0.117133i
$630$	4.23541	+	17.1840i	0.168743	+	0.684627i
$631$	−15.0722	−	36.3874i	−0.600013	−	1.44856i	−0.873567	−	0.486703i	$-0.838199\pi$
$631$	−15.0722	−	36.3874i	−0.600013	−	1.44856i	0.273554	−	0.961857i	$-0.411801\pi$
$632$	9.47525	+	16.2228i	0.376905	+	0.645310i
$633$	−9.34296	+	22.5559i	−0.371349	+	0.896516i
$634$	−7.14092	+	46.9178i	−0.283602	+	1.86334i
$635$	−4.68686	−	0.932275i	−0.185992	−	0.0369962i
$636$	17.6621	+	14.7197i	0.700347	+	0.583674i
$637$	−0.0260454	−	0.0174030i	−0.00103196	−	0.000689532i
$638$	8.84081	+	18.8766i	0.350011	+	0.747331i
$639$	−4.77440			−0.188872
$640$	−4.76611	+	17.0953i	−0.188397	+	0.675749i
$641$	−26.2384			−1.03636			−0.518178	−	0.855273i	$-0.673390\pi$
$641$	−26.2384			−1.03636			−0.518178	+	0.855273i	$0.673390\pi$
$642$	−7.03953	−	15.0306i	−0.277828	−	0.593209i
$643$	−38.6415	−	25.8194i	−1.52387	−	1.01822i	−0.984345	−	0.176251i	$-0.943603\pi$
$643$	−38.6415	−	25.8194i	−1.52387	−	1.01822i	−0.539527	−	0.841968i	$-0.681397\pi$
$644$	12.3840	+	10.3209i	0.487997	+	0.406700i
$645$	2.61293	+	0.519745i	0.102884	+	0.0204649i
$646$	0.460423	−	3.02511i	0.0181151	−	0.119021i
$647$	−12.2347	+	29.5371i	−0.480994	+	1.16122i	0.478143	+	0.878282i	$0.341310\pi$
$647$	−12.2347	+	29.5371i	−0.480994	+	1.16122i	−0.959137	+	0.282941i	$0.908690\pi$
$648$	21.8795	−	12.7791i	0.859508	−	0.502012i
$649$	−16.5265	−	39.8984i	−0.648721	−	1.56615i
$650$	3.70702	+	15.0402i	0.145401	+	0.589925i
$651$	−3.84280	−	5.75115i	−0.150611	−	0.225406i
$652$	−2.01454	−	6.82638i	−0.0788955	−	0.267342i
$653$	7.27084	−	1.44626i	0.284530	−	0.0565965i	−0.0507621	−	0.998711i	$-0.516165\pi$
$653$	7.27084	−	1.44626i	0.284530	−	0.0565965i	0.335292	+	0.942114i	$0.391165\pi$
$654$	−22.4804	+	1.01924i	−0.879054	+	0.0398554i
$655$	−8.35304	−	8.35304i	−0.326380	−	0.326380i
$656$	6.05598	+	9.36692i	0.236446	+	0.365717i
$657$	7.62275	−	7.62275i	0.297392	−	0.297392i
$658$	−9.33697	+	10.2238i	−0.363993	+	0.398567i
$659$	−3.26994	−	16.4391i	−0.127379	−	0.640376i	−0.990738	−	0.135786i	$-0.956644\pi$
$659$	−3.26994	−	16.4391i	−0.127379	−	0.640376i	0.863359	−	0.504589i	$-0.168356\pi$
$660$	23.6418	+	29.2558i	0.920256	+	1.13878i
$661$	33.5942	−	22.4469i	1.30666	−	0.873084i	0.309690	−	0.950838i	$-0.399775\pi$
$661$	33.5942	−	22.4469i	1.30666	−	0.873084i	0.996973	+	0.0777539i	$0.0247748\pi$
$662$	−8.71157	+	14.4106i	−0.338585	+	0.560083i
$663$	−3.15486	+	1.30679i	−0.122525	+	0.0507513i
$664$	−0.703841	+	11.6339i	−0.0273143	+	0.451482i
$665$	−25.7126	−	10.6505i	−0.997093	−	0.413010i
$666$	−27.6456	−	37.5718i	−1.07125	−	1.45588i
$667$	1.79090	−	9.00345i	0.0693438	−	0.348615i
$668$	−22.5214	+	11.8199i	−0.871379	+	0.457327i
$669$	16.6665	−	24.9432i	0.644365	−	0.964360i
$670$	6.28193	−	17.3498i	0.242692	−	0.670282i
$671$		−	36.6669i		−	1.41551i
$672$	13.0223	−	34.3353i	0.502347	−	1.32451i
$673$			23.6438i			0.911401i	0.890133	+	0.455701i	$0.150611\pi$
$673$			23.6438i			0.911401i	−0.890133	+	0.455701i	$0.849389\pi$
$674$	40.8586	+	14.7939i	1.57382	+	0.569839i
$675$	−0.0477926	+	0.0715267i	−0.00183954	+	0.00275306i
$676$	−3.33550	+	10.7037i	−0.128289	+	0.411682i
$677$	−4.38350	+	22.0374i	−0.168472	+	0.846964i	0.800412	+	0.599450i	$0.204614\pi$
$677$	−4.38350	+	22.0374i	−0.168472	+	0.846964i	−0.968884	+	0.247515i	$0.920386\pi$
$678$	−40.8009	+	30.0217i	−1.56695	+	1.15297i
$679$	−17.8715	−	7.40262i	−0.685845	−	0.284086i
$680$	−1.35397	+	0.467209i	−0.0519222	+	0.0179167i
$681$	−40.3916	+	16.7307i	−1.54781	+	0.641123i
$682$	−6.30462	−	3.81131i	−0.241417	−	0.145943i
$683$	−18.4573	+	12.3328i	−0.706251	+	0.471902i	−0.856102	−	0.516807i	$-0.827121\pi$
$683$	−18.4573	+	12.3328i	−0.706251	+	0.471902i	0.149851	+	0.988709i	$0.452121\pi$
$684$	4.26365	−	40.1741i	0.163025	−	1.53609i
$685$	−2.01531	−	10.1317i	−0.0770011	−	0.387111i
$686$	−19.3300	−	17.6533i	−0.738024	−	0.674004i
$687$	28.9639	−	28.9639i	1.10504	−	1.10504i
$688$	−1.92901	−	1.98823i	−0.0735427	−	0.0758005i
$689$	14.2980	+	14.2980i	0.544709	+	0.544709i
$690$	−0.750285	−	16.5483i	−0.0285629	−	0.629985i
$691$	31.1924	−	6.20456i	1.18662	−	0.236033i	0.437962	−	0.898993i	$-0.355700\pi$
$691$	31.1924	−	6.20456i	1.18662	−	0.236033i	0.748654	+	0.662961i	$0.230700\pi$
$692$	−1.07904	−	0.587286i	−0.0410188	−	0.0223253i
$693$	−21.6697	−	32.4310i	−0.823163	−	1.23195i
$694$	43.4604	−	10.7119i	1.64973	−	0.406617i
$695$	2.55503	+	6.16839i	0.0969179	+	0.233980i
$696$	−20.7179	+	2.83353i	−0.785309	+	0.107405i
$697$	−0.344493	+	0.831680i	−0.0130486	+	0.0315021i
$698$	8.25717	+	1.25675i	0.312538	+	0.0475686i
$699$	25.0068	+	4.97416i	0.945844	+	0.188140i
$700$	−1.21657	−	13.3888i	−0.0459819	−	0.506048i
$701$	−0.645283	−	0.431165i	−0.0243720	−	0.0162849i	0.543325	−	0.839523i	$-0.317165\pi$
$701$	−0.645283	−	0.431165i	−0.0243720	−	0.0162849i	−0.567697	+	0.823238i	$0.692165\pi$
$702$	−0.187143	+	0.0876481i	−0.00706326	+	0.00330806i
$703$	73.3537			2.76659
$704$	−2.95011	−	39.0008i	−0.111186	−	1.46990i
$705$	14.2275			0.535839
$706$	−0.678076	+	0.317576i	−0.0255197	+	0.0119521i
$707$	30.4184	+	20.3249i	1.14400	+	0.764397i
$708$	43.1456	−	3.92042i	1.62151	−	0.147338i
$709$	37.8179	+	7.52244i	1.42028	+	0.282511i	0.844703	−	0.535236i	$-0.179777\pi$
$709$	37.8179	+	7.52244i	1.42028	+	0.282511i	0.575578	+	0.817747i	$0.304777\pi$
$710$	−3.47432	−	0.528794i	−0.130389	−	0.0198453i
$711$	−7.66081	+	18.4948i	−0.287303	+	0.693610i
$712$	−25.1943	−	19.1320i	−0.944198	−	0.717001i
$713$	1.24161	+	2.99751i	0.0464986	+	0.112257i
$714$	2.87756	−	0.709244i	0.107690	−	0.0265428i
$715$	18.3785	+	27.5054i	0.687317	+	1.02864i
$716$	−17.3847	+	31.9414i	−0.649697	+	1.19370i
$717$	−50.2374	+	9.99283i	−1.87615	+	0.373189i
$718$	1.41471	+	31.2030i	0.0527966	+	1.16449i
$719$	−23.5486	−	23.5486i	−0.878215	−	0.878215i	0.115135	−	0.993350i	$-0.463270\pi$
$719$	−23.5486	−	23.5486i	−0.878215	−	0.878215i	−0.993350	+	0.115135i	$0.963270\pi$
$720$	−17.5784	+	6.97178i	−0.655107	+	0.259823i
$721$	−18.0104	+	18.0104i	−0.670742	+	0.670742i
$722$	27.0700	+	24.7218i	1.00744	+	0.920049i
$723$	−4.78964	−	24.0792i	−0.178129	−	0.895514i
$724$	46.9468	+	4.98243i	1.74476	+	0.185171i
$725$	−6.36529	+	4.25315i	−0.236401	+	0.157958i
$726$	−38.2940	−	23.1497i	−1.42122	−	0.859165i
$727$	−30.1679	+	12.4960i	−1.11887	+	0.463449i	−0.863982	−	0.503522i	$-0.832037\pi$
$727$	−30.1679	+	12.4960i	−1.11887	+	0.463449i	−0.254884	+	0.966972i	$0.582037\pi$
$728$	14.1382	−	29.0364i	0.523998	−	1.07616i
$729$	25.1739	+	10.4274i	0.932368	+	0.386200i
$730$	6.39132	−	4.70279i	0.236553	−	0.174058i
$731$	0.0436171	−	0.219278i	0.00161324	−	0.00811028i
$732$	35.1182	+	10.9435i	1.29800	+	0.404484i
$733$	−8.07259	+	12.0815i	−0.298168	+	0.446240i	−0.950058	−	0.312074i	$-0.898976\pi$
$733$	−8.07259	+	12.0815i	−0.298168	+	0.446240i	0.651890	+	0.758313i	$0.273976\pi$
$734$	27.3555	+	9.90475i	1.00971	+	0.365591i
$735$		−	0.0279359i		−	0.00103043i
$736$	−9.13303	+	14.6044i	−0.336648	+	0.538327i
$737$			40.6657i			1.49794i
$738$	−4.04626	+	11.1752i	−0.148945	+	0.411365i
$739$	−0.511163	+	0.765010i	−0.0188034	+	0.0281414i	−0.840752	−	0.541420i	$-0.817887\pi$
$739$	−0.511163	+	0.765010i	−0.0188034	+	0.0281414i	0.821949	+	0.569561i	$0.192887\pi$
$740$	−15.9564	−	30.4028i	−0.586568	−	1.11763i
$741$	13.8314	−	69.5351i	0.508109	−	2.55443i
$742$	−10.4007	−	14.1350i	−0.381820	−	0.518912i
$743$	1.25045	+	0.517953i	0.0458745	+	0.0190019i	0.405503	−	0.914094i	$-0.367096\pi$
$743$	1.25045	+	0.517953i	0.0458745	+	0.0190019i	−0.359628	+	0.933096i	$0.617096\pi$
$744$	5.53199	−	4.90081i	0.202813	−	0.179673i
$745$	4.57399	−	1.89461i	0.167578	−	0.0694131i
$746$	−14.2523	+	23.5760i	−0.521815	+	0.863180i
$747$	−10.3261	+	6.89967i	−0.377812	+	0.252446i
$748$	2.45515	−	1.98402i	0.0897692	−	0.0725431i
$749$	2.47149	+	12.4250i	0.0903063	+	0.454001i
$750$	−27.6590	+	30.2862i	−1.00997	+	1.10590i
$751$	−0.132681	+	0.132681i	−0.00484161	+	0.00484161i	−0.709523	−	0.704682i	$-0.751090\pi$
$751$	−0.132681	+	0.132681i	−0.00484161	+	0.00484161i	0.704682	+	0.709523i	$0.251090\pi$
$752$	−12.1752	−	8.40417i	−0.443983	−	0.306469i
$753$	31.0208	+	31.0208i	1.13046	+	1.13046i
$754$	−18.3714	+	0.832940i	−0.669046	+	0.0303339i
$755$	−26.2820	+	5.22781i	−0.956499	+	0.190259i
$756$	0.172017	−	0.0507641i	0.00625619	−	0.00184627i
$757$	13.3592	+	19.9934i	0.485547	+	0.726673i	0.990656	−	0.136383i	$-0.0435476\pi$
$757$	13.3592	+	19.9934i	0.485547	+	0.726673i	−0.505109	+	0.863056i	$0.668548\pi$
$758$	−7.25124	−	29.4199i	−0.263377	−	1.06858i
$759$	13.9708	+	33.7286i	0.507110	+	1.22427i
$760$	7.55218	−	28.7624i	0.273946	−	1.04332i
$761$	−5.79279	+	13.9850i	−0.209988	+	0.506957i	−0.993421	−	0.114520i	$-0.963467\pi$
$761$	−5.79279	+	13.9850i	−0.209988	+	0.506957i	0.783433	+	0.621477i	$0.213467\pi$
$762$	−1.58971	+	10.4448i	−0.0575890	+	0.378375i
$763$	16.8464	+	3.35097i	0.609882	+	0.121313i
$764$	11.6305	−	13.9553i	0.420775	−	0.504885i
$765$	−1.26898	−	0.847905i	−0.0458801	−	0.0306561i
$766$	3.67065	+	7.83743i	0.132626	+	0.283178i
$767$	38.1014			1.37576
$768$	38.2340	+	8.81461i	1.37965	+	0.318070i
$769$	−19.9780			−0.720424			−0.360212	−	0.932870i	$-0.617296\pi$
$769$	−19.9780			−0.720424			−0.360212	+	0.932870i	$0.617296\pi$
$770$	−12.1770	−	26.0000i	−0.438830	−	0.936974i
$771$	−54.8690	−	36.6623i	−1.97606	−	1.32036i
$772$	30.4835	−	36.5769i	1.09712	−	1.31643i
$773$	−22.0912	−	4.39422i	−0.794566	−	0.158049i	−0.218914	−	0.975744i	$-0.570252\pi$
$773$	−22.0912	−	4.39422i	−0.794566	−	0.158049i	−0.575652	+	0.817695i	$0.695252\pi$
$774$	0.444150	−	2.91819i	0.0159646	−	0.104892i
$775$	1.03543	−	2.49975i	0.0371938	−	0.0897937i
$776$	5.24912	−	19.9912i	0.188432	−	0.717643i
$777$	27.1881	+	65.6379i	0.975368	+	2.35475i
$778$	−10.3925	−	42.1647i	−0.372590	−	1.51168i
$779$	−10.3835	−	15.5401i	−0.372029	−	0.556781i
$780$	−31.8288	+	9.39303i	−1.13965	+	0.336325i
$781$	7.59625	−	1.51099i	0.271815	−	0.0540674i
$782$	−1.38874	+	0.0629641i	−0.0496612	+	0.00225159i
$783$	−0.0722162	−	0.0722162i	−0.00258080	−	0.00258080i
$784$	−0.0165017	+	0.0239061i	−0.000589347	+	0.000853791i
$785$	−3.65654	+	3.65654i	−0.130507	+	0.130507i
$786$	−17.6121	+	19.2850i	−0.628205	+	0.687874i
$787$	4.09490	+	20.5865i	0.145968	+	0.733828i	0.982552	+	0.185990i	$0.0595491\pi$
$787$	4.09490	+	20.5865i	0.145968	+	0.733828i	−0.836584	+	0.547838i	$0.815451\pi$
$788$	12.3309	−	9.96472i	0.439272	−	0.354978i
$789$	−7.26663	+	4.85541i	−0.258699	+	0.172857i
$790$	−7.62317	+	12.6102i	−0.271220	+	0.448649i
$791$	35.7214	−	14.7963i	1.27011	−	0.526096i
$792$	31.1951	−	27.6359i	1.10847	−	0.981998i
$793$	29.8875	+	12.3798i	1.06134	+	0.439620i
$794$	−23.9452	−	32.5427i	−0.849782	−	1.15490i
$795$	−3.51805	+	17.6864i	−0.124772	+	0.627273i
$796$	−8.83520	−	16.8343i	−0.313155	−	0.596677i
$797$	−8.04761	+	12.0441i	−0.285061	+	0.426624i	−0.946172	−	0.323664i	$-0.895085\pi$
$797$	−8.04761	+	12.0441i	−0.285061	+	0.426624i	0.661111	+	0.750288i	$0.270085\pi$
$798$	−20.9481	+	57.8557i	−0.741554	+	2.04807i
$799$		−	1.19397i		−	0.0422398i
$800$	13.9977	−	3.22642i	0.494893	−	0.114071i
$801$		−	33.7087i		−	1.19104i
$802$	−6.54919	−	2.37129i	−0.231260	−	0.0837333i
$803$	−9.71565	+	14.5405i	−0.342858	+	0.513123i
$804$	−38.9480	−	12.1370i	−1.37359	−	0.428039i
$805$	−2.46672	+	12.4011i	−0.0869406	+	0.437080i
$806$	5.23525	−	3.85215i	0.184404	−	0.135686i
$807$	46.1089	+	19.0989i	1.62311	+	0.672314i
$808$	−17.1125	+	35.1448i	−0.602016	+	1.23639i
$809$	22.9681	−	9.51370i	0.807516	−	0.334484i	0.0595534	−	0.998225i	$-0.481032\pi$
$809$	22.9681	−	9.51370i	0.807516	−	0.334484i	0.747962	+	0.663741i	$0.231032\pi$
$810$	17.0071	+	10.2812i	0.597570	+	0.361246i
$811$	−42.7853	+	28.5882i	−1.50240	+	1.00387i	−0.513037	+	0.858366i	$0.671480\pi$
$811$	−42.7853	+	28.5882i	−1.50240	+	1.00387i	−0.989358	+	0.145502i	$0.953520\pi$
$812$	15.8716	+	1.68445i	0.556985	+	0.0591125i
$813$	1.24112	+	6.23955i	0.0435281	+	0.218831i
$814$	55.8759	+	51.0289i	1.95845	+	1.78856i
$815$	3.94733	−	3.94733i	0.138269	−	0.138269i
$816$	1.16746	+	2.94360i	0.0408694	+	0.103047i
$817$	3.28225	+	3.28225i	0.114831	+	0.114831i
$818$	−1.28315	−	28.3012i	−0.0448643	−	0.989529i
$819$	33.7511	−	6.71351i	1.17936	−	0.234589i
$820$	−4.18218	+	7.68403i	−0.146048	+	0.268338i
$821$	23.3191	+	34.8995i	0.813842	+	1.21800i	0.973013	+	0.230750i	$0.0741178\pi$
$821$	23.3191	+	34.8995i	0.813842	+	1.21800i	−0.159171	+	0.987251i	$0.550882\pi$
$822$	−22.1751	+	5.46558i	−0.773444	+	0.190634i
$823$	9.73452	+	23.5012i	0.339324	+	0.819201i	0.997781	+	0.0665823i	$0.0212095\pi$
$823$	9.73452	+	23.5012i	0.339324	+	0.819201i	−0.658457	+	0.752618i	$0.728791\pi$
$824$	−21.6741	−	16.4588i	−0.755053	−	0.573369i
$825$	11.6509	−	28.1278i	0.405632	−	0.979283i
$826$	−32.6914	−	4.97566i	−1.13748	−	0.173125i
$827$	−32.4157	−	6.44788i	−1.12720	−	0.224215i	−0.403939	−	0.914786i	$-0.632359\pi$
$827$	−32.4157	−	6.44788i	−1.12720	−	0.224215i	−0.723265	+	0.690571i	$0.757359\pi$
$828$	−18.2787	+	1.66089i	−0.635230	+	0.0577200i
$829$	−35.9504	−	24.0213i	−1.24861	−	0.834295i	−0.257363	−	0.966315i	$-0.582854\pi$
$829$	−35.9504	−	24.0213i	−1.24861	−	0.834295i	−0.991247	+	0.132020i	$0.957854\pi$
$830$	−8.27845	+	3.87720i	−0.287349	+	0.134580i
$831$	−61.7874			−2.14338
$832$	32.7860	+	10.7632i	1.13665	+	0.373145i
$833$	−0.00234438			−8.12281e−5
$834$	13.3677	−	6.26074i	0.462886	−	0.216792i
$835$	−16.5870	−	11.0831i	−0.574018	−	0.383546i
$836$	5.93055	+	65.2678i	0.205112	+	2.25734i
$837$	0.0354024	+	0.00704198i	0.00122369	+	0.000243406i
$838$	44.6355	+	6.79356i	1.54191	+	0.234680i
$839$	10.8934	−	26.2990i	0.376083	−	0.907943i	−0.616610	−	0.787269i	$-0.711494\pi$
$839$	10.8934	−	26.2990i	0.376083	−	0.907943i	0.992692	−	0.120674i	$-0.0385057\pi$
$840$	28.5361	−	3.90281i	0.984590	−	0.134660i
$841$	7.61974	+	18.3957i	0.262750	+	0.634334i
$842$	28.1890	−	6.94786i	0.971457	−	0.239439i
$843$	−17.4846	−	26.1676i	−0.602203	−	0.901261i
$844$	17.4888	+	9.51859i	0.601988	+	0.327643i
$845$	−8.62441	+	1.71550i	−0.296689	+	0.0590150i
$846$	−0.713980	−	15.7476i	−0.0245471	−	0.541413i
$847$	24.1511	+	24.1511i	0.829843	+	0.829843i
$848$	13.4579	−	13.0571i	0.462147	−	0.448381i
$849$	19.5888	−	19.5888i	0.672286	−	0.672286i
$850$	0.856051	+	0.781793i	0.0293623	+	0.0268153i
$851$	−6.50146	−	32.6851i	−0.222867	−	1.12043i
$852$	−0.819994	+	7.72636i	−0.0280925	+	0.264701i
$853$	−17.6610	+	11.8007i	−0.604702	+	0.404049i	−0.819888	−	0.572524i	$-0.805964\pi$
$853$	−17.6610	+	11.8007i	−0.604702	+	0.404049i	0.215186	+	0.976573i	$0.430964\pi$
$854$	−24.0271	−	14.5250i	−0.822192	−	0.497036i
$855$	29.2745	−	12.1259i	1.00117	−	0.414696i
$856$	−12.7957	+	4.41539i	−0.437349	+	0.150915i
$857$	−49.6011	−	20.5455i	−1.69434	−	0.701820i	−0.694498	−	0.719494i	$-0.744374\pi$
$857$	−49.6011	−	20.5455i	−1.69434	−	0.701820i	−0.999844	+	0.0176747i	$0.994374\pi$
$858$	58.9083	−	43.3452i	2.01110	−	1.47978i
$859$	−2.87816	+	14.4695i	−0.0982015	+	0.493693i	0.900113	+	0.435657i	$0.143484\pi$
$859$	−2.87816	+	14.4695i	−0.0982015	+	0.493693i	−0.998314	+	0.0580359i	$0.981516\pi$
$860$	0.646414	−	2.07436i	0.0220425	−	0.0707352i
$861$	10.0569	−	15.0512i	0.342737	−	0.512942i
$862$	−51.6021	−	18.6838i	−1.75757	−	0.636373i
$863$		−	8.61085i		−	0.293117i	−0.989202	−	0.146558i	$-0.953180\pi$
$863$		−	8.61085i		−	0.293117i	0.989202	−	0.146558i	$-0.0468196\pi$
$864$	0.0786464	+	0.174753i	0.00267561	+	0.00594523i
$865$		−	0.963545i		−	0.0327615i
$866$	3.71387	−	10.2572i	0.126202	−	0.348554i
$867$	23.0193	−	34.4508i	0.781777	−	1.17001i
$868$	−4.99496	+	2.62151i	−0.169540	+	0.0889800i
$869$	6.33544	−	31.8504i	0.214915	−	1.08045i
$870$	−9.72009	−	13.2101i	−0.329542	−	0.447863i
$871$	−33.1469	−	13.7299i	−1.12314	−	0.465220i
$872$	−1.10831	+	18.3194i	−0.0375322	+	0.620374i
$873$	20.3471	−	8.42806i	0.688646	−	0.285247i
$874$	14.9317	−	24.6998i	0.505072	−	0.835484i
$875$	26.0303	−	17.3929i	0.879985	−	0.587987i
$876$	−11.0266	−	13.6450i	−0.372555	−	0.461022i
$877$	5.30612	+	26.6757i	0.179175	+	0.900774i	0.960846	+	0.277083i	$0.0893677\pi$
$877$	5.30612	+	26.6757i	0.179175	+	0.900774i	−0.781671	+	0.623691i	$0.785632\pi$
$878$	−20.9957	+	22.9900i	−0.708571	+	0.775874i
$879$	−31.6276	+	31.6276i	−1.06677	+	1.06677i
$880$	25.7614	−	16.6555i	0.868418	−	0.561457i
$881$	−29.5442	−	29.5442i	−0.995371	−	0.995371i	0.00461881	−	0.999989i	$-0.498530\pi$
$881$	−29.5442	−	29.5442i	−0.995371	−	0.995371i	−0.999989	+	0.00461881i	$0.998530\pi$
$882$	−0.0309206	+	0.00140191i	−0.00104115	+	4.72047e-5i
$883$	7.22231	−	1.43661i	0.243050	−	0.0483457i	−0.0720619	−	0.997400i	$-0.522958\pi$
$883$	7.22231	−	1.43661i	0.243050	−	0.0483457i	0.315112	+	0.949054i	$0.397958\pi$
$884$	0.788265	+	2.67108i	0.0265122	+	0.0898381i
$885$	18.8780	+	28.2530i	0.634578	+	0.949713i
$886$	9.91354	+	40.2214i	0.333052	+	1.35126i
$887$	−7.30913	−	17.6458i	−0.245417	−	0.592488i	0.752388	−	0.658721i	$-0.228902\pi$
$887$	−7.30913	−	17.6458i	−0.245417	−	0.592488i	−0.997804	+	0.0662325i	$0.978902\pi$
$888$	−65.5501	+	38.2858i	−2.19972	+	1.28479i
$889$	3.08601	−	7.45028i	0.103501	−	0.249874i
$890$	3.73345	−	24.5298i	0.125145	−	0.822239i
$891$	−42.9562	−	8.54452i	−1.43909	−	0.286252i
$892$	−18.7945	−	15.6635i	−0.629287	−	0.524453i
$893$	20.6114	+	13.7721i	0.689733	+	0.460865i
$894$	−4.64247	−	9.91244i	−0.155267	−	0.331521i
$895$	−28.5226			−0.953406
$896$	−26.7252	−	13.5164i	−0.892826	−	0.451553i
$897$	−32.2094			−1.07544
$898$	3.67755	+	7.85218i	0.122722	+	0.262031i
$899$	2.67089	+	1.78463i	0.0890791	+	0.0595207i
$900$	11.7581	+	9.79933i	0.391938	+	0.326644i
$901$	1.48425	+	0.295235i	0.0494475	+	0.00983572i
$902$	2.90106	−	19.0607i	0.0965947	−	0.634653i
$903$	−1.72045	+	4.15354i	−0.0572531	+	0.138221i
$904$	20.8359	+	35.6737i	0.692991	+	1.18649i
$905$	14.1701	+	34.2097i	0.471030	+	1.13717i
$906$	14.1780	+	57.5231i	0.471031	+	1.91108i
$907$	−0.812920	−	1.21662i	−0.0269926	−	0.0403973i	0.817728	−	0.575605i	$-0.195233\pi$
$907$	−0.812920	−	1.21662i	−0.0269926	−	0.0403973i	−0.844721	+	0.535208i	$0.820233\pi$
$908$	10.0921	+	34.1978i	0.334919	+	1.13489i
$909$	−40.8513	+	8.12583i	−1.35495	+	0.269517i
$910$	25.3041	−	1.14726i	0.838824	−	0.0380315i
$911$	−14.4917	−	14.4917i	−0.480130	−	0.480130i	0.425043	−	0.905173i	$-0.360259\pi$
$911$	−14.4917	−	14.4917i	−0.480130	−	0.480130i	−0.905173	+	0.425043i	$0.860259\pi$
$912$	−64.2811	−	13.7996i	−2.12856	−	0.456952i
$913$	14.2456	−	14.2456i	0.471461	−	0.471461i
$914$	−14.9975	+	16.4220i	−0.496072	+	0.543191i
$915$	5.62843	+	28.2960i	0.186070	+	0.935438i
$916$	−20.9969	−	25.9828i	−0.693755	−	0.858495i
$917$	16.5750	−	11.0751i	0.547356	−	0.365732i
$918$	−0.00800125	+	0.0132356i	−0.000264081	+	0.000436839i
$919$	5.31718	−	2.20245i	0.175397	−	0.0726520i	−0.293257	−	0.956034i	$-0.594739\pi$
$919$	5.31718	−	2.20245i	0.175397	−	0.0726520i	0.468654	+	0.883382i	$0.344739\pi$
$920$	−13.4853	−	0.815853i	−0.444599	−	0.0268979i
$921$	−14.3302	−	5.93575i	−0.472195	−	0.195590i
$922$	−7.44848	−	10.1228i	−0.245303	−	0.333378i
$923$	−1.33309	+	6.70192i	−0.0438793	+	0.220596i
$924$	−56.2044	+	29.4979i	−1.84899	+	0.970409i
$925$	−15.4401	+	23.1078i	−0.507668	+	0.759779i
$926$	19.3321	−	53.3924i	0.635291	−	1.75458i
$927$		−	28.9988i		−	0.952447i
$928$	0.514786	+	17.0462i	0.0168987	+	0.559568i
$929$		−	45.4656i		−	1.49168i	−0.666126	−	0.745839i	$-0.732049\pi$
$929$		−	45.4656i		−	1.49168i	0.666126	−	0.745839i	$-0.267951\pi$
$930$	5.45035	+	1.97343i	0.178724	+	0.0647115i
$931$	0.0270416	−	0.0404707i	0.000886254	−	0.00132637i
$932$	6.18643	−	19.8525i	0.202643	−	0.650289i
$933$	8.53316	−	42.8991i	0.279363	−	1.40445i
$934$	−11.5375	+	8.48937i	−0.377518	+	0.277781i
$935$	2.28734	+	0.947446i	0.0748039	+	0.0309848i
$936$	11.9939	+	34.7581i	0.392032	+	1.13610i
$937$	−23.3888	+	9.68796i	−0.764079	+	0.316492i	−0.730471	−	0.682943i	$-0.760700\pi$
$937$	−23.3888	+	9.68796i	−0.764079	+	0.316492i	−0.0336074	+	0.999435i	$0.510700\pi$
$938$	26.6475	+	16.1091i	0.870071	+	0.525980i
$939$	14.3821	−	9.60978i	0.469341	−	0.313603i
$940$	1.22458	−	11.5386i	0.0399414	−	0.376346i
$941$	−9.35177	−	47.0145i	−0.304859	−	1.53263i	−0.764558	−	0.644555i	$-0.777043\pi$
$941$	−9.35177	−	47.0145i	−0.304859	−	1.53263i	0.459698	−	0.888075i	$-0.347957\pi$
$942$	8.44201	+	7.70970i	0.275055	+	0.251196i
$943$	−6.00406	+	6.00406i	−0.195519	+	0.195519i
$944$	0.534127	−	35.3287i	0.0173843	−	1.14985i
$945$	0.0994682	+	0.0994682i	0.00323570	+	0.00323570i
$946$	0.216879	+	4.78351i	0.00705136	+	0.155525i
$947$	19.0706	−	3.79337i	0.619711	−	0.123268i	0.124757	−	0.992187i	$-0.460185\pi$
$947$	19.0706	−	3.79337i	0.619711	−	0.123268i	0.494954	+	0.868919i	$0.335185\pi$
$948$	28.6143	+	15.5739i	0.929348	+	0.505815i
$949$	−8.57180	−	12.8286i	−0.278252	−	0.416434i
$950$	−23.3702	+	5.76015i	−0.758229	+	0.186884i
$951$	31.4927	+	76.0301i	1.02122	+	2.46545i
$952$	−0.327524	−	2.39476i	−0.0106151	−	0.0776145i
$953$	11.3085	−	27.3010i	0.366317	−	0.884367i	−0.628030	−	0.778189i	$-0.716139\pi$
$953$	11.3085	−	27.3010i	0.366317	−	0.884367i	0.994347	−	0.106178i	$-0.0338614\pi$
$954$	19.7526	+	3.00636i	0.639515	+	0.0973346i
$955$	13.9746	+	2.77971i	0.452206	+	0.0899493i
$956$	3.78023	+	41.6028i	0.122261	+	1.34553i
$957$	30.0534	+	20.0811i	0.971489	+	0.649128i
$958$	45.1630	−	21.1520i	1.45915	−	0.683390i
$959$	17.4323			0.562920
$960$	8.26331	+	29.6443i	0.266697	+	0.956766i
$961$	29.8647			0.963377
$962$	−60.4594	+	28.3161i	−1.94929	+	0.912946i
$963$	−11.9926	−	8.01318i	−0.386455	−	0.258221i
$964$	−19.9405	+	1.81189i	−0.642242	+	0.0583572i
$965$	36.6274	+	7.28563i	1.17908	+	0.234533i
$966$	27.6361	+	4.20623i	0.889176	+	0.135333i
$967$	7.94230	−	19.1744i	0.255407	−	0.616607i	−0.743217	−	0.669051i	$-0.766701\pi$
$967$	7.94230	−	19.1744i	0.255407	−	0.616607i	0.998624	+	0.0524434i	$0.0167009\pi$
$968$	−22.0705	+	29.0640i	−0.709373	+	0.934153i
$969$	−2.03055	−	4.90217i	−0.0652306	−	0.157481i
$970$	15.7400	−	3.87951i	0.505382	−	0.124564i
$971$	13.5493	+	20.2780i	0.434819	+	0.650753i	0.982571	−	0.185888i	$-0.0595161\pi$
$971$	13.5493	+	20.2780i	0.434819	+	0.650753i	−0.547752	+	0.836641i	$0.684516\pi$
$972$	21.1014	−	38.7701i	0.676828	−	1.24355i
$973$	−11.0504	+	2.19807i	−0.354261	+	0.0704668i
$974$	−0.903881	−	19.9361i	−0.0289622	−	0.638793i
$975$	18.9935	+	18.9935i	0.608279	+	0.608279i
$976$	11.8979	−	27.5390i	0.380843	−	0.881503i
$977$	−2.62269	+	2.62269i	−0.0839073	+	0.0839073i	−0.747815	−	0.663907i	$-0.768897\pi$
$977$	−2.62269	+	2.62269i	−0.0839073	+	0.0839073i	0.663907	+	0.747815i	$0.268897\pi$
$978$	−9.11338	−	8.32284i	−0.291414	−	0.266135i
$979$	10.6680	+	53.6318i	0.340952	+	1.71408i
$980$	−0.0226561	−	0.00240448i	−0.000723723	−	7.68083e-5i
$981$	−16.2601	+	10.8646i	−0.519145	+	0.346882i
$982$	−2.20781	−	1.33468i	−0.0704541	−	0.0425913i
$983$	−15.6197	+	6.46990i	−0.498191	+	0.206358i	−0.617607	−	0.786487i	$-0.711898\pi$
$983$	−15.6197	+	6.46990i	−0.498191	+	0.206358i	0.119416	+	0.992844i	$0.461898\pi$
$984$	17.3898	+	8.46735i	0.554367	+	0.269929i
$985$	11.4881	+	4.75853i	0.366041	+	0.151619i
$986$	−1.10859	+	0.815711i	−0.0353047	+	0.0259775i
$987$	−4.68396	+	23.5479i	−0.149092	+	0.749537i
$988$	−55.2027	−	17.2023i	−1.75623	−	0.547277i
$989$	1.17160	−	1.75342i	0.0372546	−	0.0557555i
$990$	30.7347	+	11.1283i	0.976814	+	0.353680i
$991$		−	26.6890i		−	0.847803i	−0.905708	−	0.423902i	$-0.860660\pi$
$991$		−	26.6890i		−	0.847803i	0.905708	−	0.423902i	$-0.139340\pi$
$992$	−3.49843	−	4.90828i	−0.111075	−	0.155838i
$993$			29.1998i			0.926628i
$994$	2.01901	−	5.57624i	0.0640393	−	0.176867i
$995$	8.28441	−	12.3985i	0.262634	−	0.393059i
$996$	9.39219	+	17.8956i	0.297603	+	0.567044i
$997$	9.09171	−	45.7071i	0.287937	−	1.44756i	−0.517910	−	0.855435i	$-0.673290\pi$
$997$	9.09171	−	45.7071i	0.287937	−	1.44756i	0.805847	−	0.592124i	$-0.201710\pi$
$998$	−5.13512	−	6.97888i	−0.162549	−	0.220912i
$999$	−0.342535	−	0.141883i	−0.0108373	−	0.00448897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.5.3	✓	56
3.2	odd	2		576.2.bd.a.325.5		56
4.3	odd	2		256.2.i.a.113.7		56
8.3	odd	2		512.2.i.a.481.1		56
8.5	even	2		512.2.i.b.481.7		56
64.13	even	16	inner	64.2.i.a.13.3	yes	56
64.19	odd	16		512.2.i.a.33.1		56
64.45	even	16		512.2.i.b.33.7		56
64.51	odd	16		256.2.i.a.145.7		56
192.77	odd	16		576.2.bd.a.397.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.3	✓	56	1.1	even	1	trivial
64.2.i.a.13.3	yes	56	64.13	even	16	inner
256.2.i.a.113.7		56	4.3	odd	2
256.2.i.a.145.7		56	64.51	odd	16
512.2.i.a.33.1		56	64.19	odd	16
512.2.i.a.481.1		56	8.3	odd	2
512.2.i.b.33.7		56	64.45	even	16
512.2.i.b.481.7		56	8.5	even	2
576.2.bd.a.325.5		56	3.2	odd	2
576.2.bd.a.397.5		56	192.77	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)

\(f(q)\)	\(=\)	\(q+(-0.599818 - 1.28071i) q^{2} +(-2.03902 - 1.36243i) q^{3} +(-1.28044 + 1.53639i) q^{4} +(-1.53851 - 0.306028i) q^{5} +(-0.521836 + 3.42860i) q^{6} +(1.01301 - 2.44562i) q^{7} +(2.73569 + 0.718315i) q^{8} +(1.15334 + 2.78440i) q^{9} +O(q^{10})\)	\(q+(-0.599818 - 1.28071i) q^{2} +(-2.03902 - 1.36243i) q^{3} +(-1.28044 + 1.53639i) q^{4} +(-1.53851 - 0.306028i) q^{5} +(-0.521836 + 3.42860i) q^{6} +(1.01301 - 2.44562i) q^{7} +(2.73569 + 0.718315i) q^{8} +(1.15334 + 2.78440i) q^{9} +(0.530891 + 2.15394i) q^{10} +(-2.71620 - 4.06508i) q^{11} +(4.70405 - 1.38822i) q^{12} +(4.23055 - 0.841509i) q^{13} +(-3.73976 + 0.169557i) q^{14} +(2.72010 + 2.72010i) q^{15} +(-0.720966 - 3.93449i) q^{16} +(0.228271 - 0.228271i) q^{17} +(2.87422 - 3.14722i) q^{18} +(1.30758 + 6.57364i) q^{19} +(2.44014 - 1.97189i) q^{20} +(-5.39754 + 3.60652i) q^{21} +(-3.57696 + 5.91698i) q^{22} +(2.81320 - 1.16527i) q^{23} +(-4.59948 - 5.19185i) q^{24} +(-2.34605 - 0.971766i) q^{25} +(-3.61529 - 4.91336i) q^{26} +(0.00660900 - 0.0332257i) q^{27} +(2.46033 + 4.68784i) q^{28} +(1.67490 - 2.50666i) q^{29} +(1.85210 - 5.11523i) q^{30} +1.06551i q^{31} +(-4.60649 + 3.28333i) q^{32} +11.9894i q^{33} +(-0.429271 - 0.155428i) q^{34} +(-2.30695 + 3.45260i) q^{35} +(-5.75469 - 1.79328i) q^{36} +(2.13514 - 10.7341i) q^{37} +(7.63461 - 5.61762i) q^{38} +(-9.77267 - 4.04797i) q^{39} +(-3.98906 - 1.94233i) q^{40} +(-2.57626 + 1.06712i) q^{41} +(7.85644 + 4.74942i) q^{42} +(0.575838 - 0.384763i) q^{43} +(9.72346 + 1.03194i) q^{44} +(-0.922311 - 4.63677i) q^{45} +(-3.17978 - 2.90395i) q^{46} +(2.61525 - 2.61525i) q^{47} +(-3.89040 + 9.00477i) q^{48} +(-0.00513508 - 0.00513508i) q^{49} +(0.162653 + 3.58749i) q^{50} +(-0.776454 + 0.154446i) q^{51} +(-4.12407 + 7.57726i) q^{52} +(2.60438 + 3.89774i) q^{53} +(-0.0465166 + 0.0114652i) q^{54} +(2.93486 + 7.08539i) q^{55} +(4.52801 - 5.96282i) q^{56} +(6.28994 - 15.1853i) q^{57} +(-4.21494 - 0.641518i) q^{58} +(8.66346 + 1.72327i) q^{59} +(-7.66205 + 0.696210i) q^{60} +(6.23588 + 4.16668i) q^{61} +(1.36462 - 0.639115i) q^{62} +7.97794 q^{63} +(6.96805 + 3.93018i) q^{64} -6.76625 q^{65} +(15.3550 - 7.19147i) q^{66} +(-6.91594 - 4.62108i) q^{67} +(0.0584261 + 0.643000i) q^{68} +(-7.32376 - 1.45679i) q^{69} +(5.80553 + 0.883605i) q^{70} +(-0.606236 + 1.46358i) q^{71} +(1.15510 + 8.44573i) q^{72} +(-1.36883 - 3.30465i) q^{73} +(-15.0279 + 3.70399i) q^{74} +(3.45968 + 5.17778i) q^{75} +(-11.7739 - 6.40818i) q^{76} +(-12.6932 + 2.52483i) q^{77} +(0.677547 + 14.9440i) q^{78} +(4.69681 + 4.69681i) q^{79} +(-0.0948532 + 6.27387i) q^{80} +(6.33452 - 6.33452i) q^{81} +(2.91196 + 2.65936i) q^{82} +(0.803913 + 4.04154i) q^{83} +(1.37020 - 12.9106i) q^{84} +(-0.421054 + 0.281340i) q^{85} +(-0.838168 - 0.506694i) q^{86} +(-6.83030 + 2.82920i) q^{87} +(-4.51069 - 13.0719i) q^{88} +(-10.3334 - 4.28021i) q^{89} +(-5.38514 + 3.96243i) q^{90} +(2.22758 - 11.1988i) q^{91} +(-1.81182 + 5.81421i) q^{92} +(1.45169 - 2.17261i) q^{93} +(-4.91805 - 1.78070i) q^{94} -10.5137i q^{95} +(13.8660 - 0.418748i) q^{96} -7.30754i q^{97} +(-0.00349643 + 0.00965666i) q^{98} +(8.18612 - 12.2514i) 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

Fields

Representations

Groups

Database

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