LMFDB - Embedded newform 864.2.bt.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(11,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(72))

chi = DirichletCharacter(H, H._module([36, 45, 52]))

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

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

chi := DirichletCharacter("864.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bt (of order $72$, degree $24$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$3408$
Relative dimension:	$142$ over $\Q(\zeta_{72})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{72}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	864.11
Dual form			864.2.bt.a.707.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40429 - 0.167206i) q^{2} +(-0.631256 - 1.61292i) q^{3} +(1.94408 + 0.469613i) q^{4} +(-2.68720 - 2.46236i) q^{5} +(0.616779 + 2.37057i) q^{6} +(-2.07740 - 2.96684i) q^{7} +(-2.65154 - 0.984538i) q^{8} +(-2.20303 + 2.03633i) q^{9} +O(q^{10})$	\(q+(-1.40429 - 0.167206i) q^{2} +(-0.631256 - 1.61292i) q^{3} +(1.94408 + 0.469613i) q^{4} +(-2.68720 - 2.46236i) q^{5} +(0.616779 + 2.37057i) q^{6} +(-2.07740 - 2.96684i) q^{7} +(-2.65154 - 0.984538i) q^{8} +(-2.20303 + 2.03633i) q^{9} +(3.36189 + 3.90719i) q^{10} +(-1.11634 - 0.0487404i) q^{11} +(-0.469766 - 3.43210i) q^{12} +(-2.34204 - 1.21919i) q^{13} +(2.42121 + 4.51367i) q^{14} +(-2.27529 + 5.88861i) q^{15} +(3.55893 + 1.82593i) q^{16} +(-2.45692 - 4.25551i) q^{17} +(3.43419 - 2.49125i) q^{18} +(-0.231073 + 1.75517i) q^{19} +(-4.06778 - 6.04898i) q^{20} +(-3.47390 + 5.22352i) q^{21} +(1.55952 + 0.255104i) q^{22} +(-1.17952 - 0.825910i) q^{23} +(0.0858207 + 4.89823i) q^{24} +(0.722019 + 8.25271i) q^{25} +(3.08506 + 2.10370i) q^{26} +(4.67512 + 2.26787i) q^{27} +(-2.64538 - 6.74335i) q^{28} +(1.98249 - 6.28765i) q^{29} +(4.17978 - 7.88891i) q^{30} +(2.32454 - 0.409878i) q^{31} +(-4.69247 - 3.15922i) q^{32} +(0.626081 + 1.83133i) q^{33} +(2.73869 + 6.38680i) q^{34} +(-1.72304 + 13.0878i) q^{35} +(-5.23917 + 2.92423i) q^{36} +(8.99744 - 1.18453i) q^{37} +(0.617969 - 2.42614i) q^{38} +(-0.488029 + 4.54715i) q^{39} +(4.70093 + 9.17470i) q^{40} +(2.79184 + 0.244254i) q^{41} +(5.75179 - 6.75450i) q^{42} +(0.262891 - 6.02120i) q^{43} +(-2.14737 - 0.619003i) q^{44} +(10.9342 - 0.0473637i) q^{45} +(1.51830 + 1.35704i) q^{46} +(-11.6546 - 2.05502i) q^{47} +(0.698496 - 6.89290i) q^{48} +(-2.09238 + 5.74877i) q^{49} +(0.365977 - 11.7100i) q^{50} +(-5.31286 + 6.64913i) q^{51} +(-3.98058 - 3.47006i) q^{52} +(1.38293 - 3.33868i) q^{53} +(-6.18604 - 3.96647i) q^{54} +(2.87980 + 2.87980i) q^{55} +(2.58736 + 9.91198i) q^{56} +(2.97682 - 0.735260i) q^{57} +(-3.83533 + 8.49823i) q^{58} +(6.97604 - 7.61301i) q^{59} +(-7.18872 + 10.3795i) q^{60} +(-2.38616 - 10.7633i) q^{61} +(-3.33287 + 0.186913i) q^{62} +(10.6180 + 2.30576i) q^{63} +(6.06137 + 5.22109i) q^{64} +(3.29144 + 9.04315i) q^{65} +(-0.572992 - 2.67642i) q^{66} +(3.94211 + 2.05213i) q^{67} +(-2.77802 - 9.42687i) q^{68} +(-0.587548 + 2.42384i) q^{69} +(4.60801 - 18.0910i) q^{70} +(-4.22813 + 15.7796i) q^{71} +(7.84628 - 3.23046i) q^{72} +(0.149766 + 0.558935i) q^{73} +(-12.8331 + 0.159009i) q^{74} +(12.8552 - 6.37413i) q^{75} +(-1.27348 + 3.30369i) q^{76} +(2.17448 + 3.41325i) q^{77} +(1.44565 - 6.30393i) q^{78} +(0.376406 + 0.315842i) q^{79} +(-5.06742 - 13.6700i) q^{80} +(0.706699 - 8.97221i) q^{81} +(-3.87972 - 0.809817i) q^{82} +(-2.38579 + 7.56676i) q^{83} +(-9.20659 + 8.52357i) q^{84} +(-3.87638 + 17.4852i) q^{85} +(-1.37596 + 8.41158i) q^{86} +(-11.3929 + 0.771518i) q^{87} +(2.91203 + 1.22831i) q^{88} +(4.61035 + 17.2061i) q^{89} +(-15.3627 - 1.76175i) q^{90} +(1.24822 + 9.48120i) q^{91} +(-1.90523 - 2.15956i) q^{92} +(-2.12848 - 3.49055i) q^{93} +(16.0229 + 4.83458i) q^{94} +(4.94280 - 4.14750i) q^{95} +(-2.13343 + 9.56287i) q^{96} +(-1.41533 + 0.515136i) q^{97} +(3.89955 - 7.72311i) q^{98} +(2.55858 - 2.16586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 36 q^{8} - 24 q^{9}+O(q^{10}) $ 3408 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 36 * q^8 - 24 * q^9	\( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 36 q^{8} - 24 q^{9} - 12 q^{10} - 24 q^{11} - 24 q^{12} - 24 q^{13} - 24 q^{14} - 48 q^{15} - 24 q^{16} - 24 q^{18} - 12 q^{19} - 24 q^{20} - 24 q^{21} - 24 q^{22} - 24 q^{23} - 84 q^{24} - 24 q^{25} - 24 q^{27} - 48 q^{28} - 24 q^{29} - 24 q^{30} - 24 q^{32} - 48 q^{33} - 36 q^{35} - 24 q^{36} - 12 q^{37} - 24 q^{38} - 24 q^{39} - 24 q^{40} - 24 q^{41} + 96 q^{42} - 24 q^{43} - 36 q^{44} - 24 q^{45} - 12 q^{46} - 48 q^{47} - 24 q^{48} - 336 q^{50} + 12 q^{51} - 24 q^{52} - 24 q^{54} - 48 q^{55} - 24 q^{56} - 24 q^{57} - 132 q^{58} - 24 q^{59} - 24 q^{60} - 24 q^{61} - 36 q^{62} - 12 q^{64} - 48 q^{65} - 216 q^{66} - 24 q^{67} + 24 q^{68} - 24 q^{69} - 24 q^{70} - 36 q^{71} - 24 q^{72} - 12 q^{73} - 24 q^{74} - 24 q^{75} - 24 q^{76} - 24 q^{77} - 24 q^{78} - 48 q^{79} - 48 q^{82} + 96 q^{83} + 204 q^{84} + 36 q^{85} - 24 q^{86} - 24 q^{87} - 24 q^{88} - 36 q^{89} - 24 q^{90} - 12 q^{91} - 252 q^{92} - 24 q^{93} - 24 q^{94} - 24 q^{96} - 48 q^{97} - 36 q^{98} - 24 q^{99}+O(q^{100}) \) 3408 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 36 * q^8 - 24 * q^9 - 12 * q^10 - 24 * q^11 - 24 * q^12 - 24 * q^13 - 24 * q^14 - 48 * q^15 - 24 * q^16 - 24 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^21 - 24 * q^22 - 24 * q^23 - 84 * q^24 - 24 * q^25 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^30 - 24 * q^32 - 48 * q^33 - 36 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^38 - 24 * q^39 - 24 * q^40 - 24 * q^41 + 96 * q^42 - 24 * q^43 - 36 * q^44 - 24 * q^45 - 12 * q^46 - 48 * q^47 - 24 * q^48 - 336 * q^50 + 12 * q^51 - 24 * q^52 - 24 * q^54 - 48 * q^55 - 24 * q^56 - 24 * q^57 - 132 * q^58 - 24 * q^59 - 24 * q^60 - 24 * q^61 - 36 * q^62 - 12 * q^64 - 48 * q^65 - 216 * q^66 - 24 * q^67 + 24 * q^68 - 24 * q^69 - 24 * q^70 - 36 * q^71 - 24 * q^72 - 12 * q^73 - 24 * q^74 - 24 * q^75 - 24 * q^76 - 24 * q^77 - 24 * q^78 - 48 * q^79 - 48 * q^82 + 96 * q^83 + 204 * q^84 + 36 * q^85 - 24 * q^86 - 24 * q^87 - 24 * q^88 - 36 * q^89 - 24 * q^90 - 12 * q^91 - 252 * q^92 - 24 * q^93 - 24 * q^94 - 24 * q^96 - 48 * q^97 - 36 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−1.40429	−	0.167206i	−0.992986	−	0.118233i
$2$	−1.40429	−	0.167206i	−0.992986	−	0.118233i
$3$	−0.631256	−	1.61292i	−0.364456	−	0.931221i
$3$	−0.631256	−	1.61292i	−0.364456	−	0.931221i
$4$	1.94408	+	0.469613i	0.972042	+	0.234807i
$5$	−2.68720	−	2.46236i	−1.20175	−	1.10120i	−0.992361	−	0.123369i	$-0.960630\pi$
$5$	−2.68720	−	2.46236i	−1.20175	−	1.10120i	−0.209389	−	0.977832i	$-0.567148\pi$
$6$	0.616779	+	2.37057i	0.251799	+	0.967780i
$7$	−2.07740	−	2.96684i	−0.785184	−	1.12136i	−0.989793	−	0.142515i	$-0.954481\pi$
$7$	−2.07740	−	2.96684i	−0.785184	−	1.12136i	0.204609	−	0.978844i	$-0.434408\pi$
$8$	−2.65154	−	0.984538i	−0.937462	−	0.348087i
$9$	−2.20303	+	2.03633i	−0.734344	+	0.678778i
$10$	3.36189	+	3.90719i	1.06312	+	1.23556i
$11$	−1.11634	−	0.0487404i	−0.336589	−	0.0146958i	−0.125298	−	0.992119i	$-0.539989\pi$
$11$	−1.11634	−	0.0487404i	−0.336589	−	0.0146958i	−0.211290	+	0.977423i	$0.567767\pi$
$12$	−0.469766	−	3.43210i	−0.135610	−	0.990762i
$13$	−2.34204	−	1.21919i	−0.649565	−	0.338142i	0.104900	−	0.994483i	$-0.466548\pi$
$13$	−2.34204	−	1.21919i	−0.649565	−	0.338142i	−0.754465	+	0.656341i	$0.772103\pi$
$14$	2.42121	+	4.51367i	0.647095	+	1.20633i
$15$	−2.27529	+	5.88861i	−0.587477	+	1.52043i
$16$	3.55893	+	1.82593i	0.889732	+	0.456484i
$17$	−2.45692	−	4.25551i	−0.595890	−	1.03211i	−0.993421	−	0.114523i	$-0.963466\pi$
$17$	−2.45692	−	4.25551i	−0.595890	−	1.03211i	0.397530	−	0.917589i	$-0.369867\pi$
$18$	3.43419	−	2.49125i	0.809447	−	0.587193i
$19$	−0.231073	+	1.75517i	−0.0530117	+	0.402664i	0.944282	+	0.329138i	$0.106758\pi$
$19$	−0.231073	+	1.75517i	−0.0530117	+	0.402664i	−0.997293	+	0.0735253i	$0.976575\pi$
$20$	−4.06778	−	6.04898i	−0.909583	−	1.35259i
$21$	−3.47390	+	5.22352i	−0.758068	+	1.13987i
$22$	1.55952	+	0.255104i	0.332490	+	0.0543885i
$23$	−1.17952	−	0.825910i	−0.245947	−	0.172214i	0.444103	−	0.895976i	$-0.353523\pi$
$23$	−1.17952	−	0.825910i	−0.245947	−	0.172214i	−0.690050	+	0.723762i	$0.742411\pi$
$24$	0.0858207	+	4.89823i	0.0175181	+	0.999847i
$25$	0.722019	+	8.25271i	0.144404	+	1.65054i
$26$	3.08506	+	2.10370i	0.605030	+	0.412570i
$27$	4.67512	+	2.26787i	0.899728	+	0.436452i
$28$	−2.64538	−	6.74335i	−0.499929	−	1.27437i
$29$	1.98249	−	6.28765i	0.368139	−	1.16759i	−0.570093	−	0.821580i	$-0.693093\pi$
$29$	1.98249	−	6.28765i	0.368139	−	1.16759i	0.938232	−	0.346007i	$-0.112463\pi$
$30$	4.17978	−	7.88891i	0.763121	−	1.44031i
$31$	2.32454	−	0.409878i	0.417499	−	0.0736163i	0.0390472	−	0.999237i	$-0.487568\pi$
$31$	2.32454	−	0.409878i	0.417499	−	0.0736163i	0.378452	+	0.925621i	$0.376457\pi$
$32$	−4.69247	−	3.15922i	−0.829520	−	0.558477i
$33$	0.626081	+	1.83133i	0.108987	+	0.318794i
$34$	2.73869	+	6.38680i	0.469682	+	1.09533i
$35$	−1.72304	+	13.0878i	−0.291247	+	2.21224i
$36$	−5.23917	+	2.92423i	−0.873195	+	0.487372i
$37$	8.99744	−	1.18453i	1.47917	−	0.194736i	0.652656	−	0.757654i	$-0.273655\pi$
$37$	8.99744	−	1.18453i	1.47917	−	0.194736i	0.826513	+	0.562918i	$0.190321\pi$
$38$	0.617969	−	2.42614i	0.100248	−	0.393572i
$39$	−0.488029	+	4.54715i	−0.0781473	+	0.728126i
$40$	4.70093	+	9.17470i	0.743282	+	1.45065i
$41$	2.79184	+	0.244254i	0.436012	+	0.0381461i	0.303049	−	0.952975i	$-0.401995\pi$
$41$	2.79184	+	0.244254i	0.436012	+	0.0381461i	0.132963	+	0.991121i	$0.457551\pi$
$42$	5.75179	−	6.75450i	0.887520	−	1.04224i
$43$	0.262891	−	6.02120i	0.0400905	−	0.918224i	−0.867262	−	0.497853i	$-0.834122\pi$
$43$	0.262891	−	6.02120i	0.0400905	−	0.918224i	0.907352	−	0.420372i	$-0.138100\pi$
$44$	−2.14737	−	0.619003i	−0.323728	−	0.0933182i
$45$	10.9342	−	0.0473637i	1.62997	−	0.00706057i
$46$	1.51830	+	1.35704i	0.223861	+	0.200085i
$47$	−11.6546	−	2.05502i	−1.70000	−	0.299756i	−0.762306	−	0.647216i	$-0.775933\pi$
$47$	−11.6546	−	2.05502i	−1.70000	−	0.299756i	−0.937695	+	0.347460i	$0.887044\pi$
$48$	0.698496	−	6.89290i	0.100819	−	0.994905i
$49$	−2.09238	+	5.74877i	−0.298912	+	0.821253i
$50$	0.365977	−	11.7100i	0.0517570	−	1.65604i
$51$	−5.31286	+	6.64913i	−0.743949	+	0.931065i
$52$	−3.98058	−	3.47006i	−0.552007	−	0.481211i
$53$	1.38293	−	3.33868i	0.189960	−	0.458604i	−0.799992	−	0.600011i	$-0.795163\pi$
$53$	1.38293	−	3.33868i	0.189960	−	0.458604i	0.989951	+	0.141408i	$0.0451628\pi$
$54$	−6.18604	−	3.96647i	−0.841814	−	0.539768i
$55$	2.87980	+	2.87980i	0.388313	+	0.388313i
$56$	2.58736	+	9.91198i	0.345750	+	1.32454i
$57$	2.97682	−	0.735260i	0.394289	−	0.0973876i
$58$	−3.83533	+	8.49823i	−0.503604	+	1.11587i
$59$	6.97604	−	7.61301i	0.908203	−	0.991130i	−0.0917860	−	0.995779i	$-0.529258\pi$
$59$	6.97604	−	7.61301i	0.908203	−	0.991130i	0.999989	+	0.00464888i	$0.00147979\pi$
$60$	−7.18872	+	10.3795i	−0.928060	+	1.33998i
$61$	−2.38616	−	10.7633i	−0.305517	−	1.37810i	−0.844398	−	0.535716i	$-0.820042\pi$
$61$	−2.38616	−	10.7633i	−0.305517	−	1.37810i	0.538881	−	0.842382i	$-0.318847\pi$
$62$	−3.33287	+	0.186913i	−0.423274	+	0.0237380i
$63$	10.6180	+	2.30576i	1.33775	+	0.290498i
$64$	6.06137	+	5.22109i	0.757671	+	0.652636i
$65$	3.29144	+	9.04315i	0.408252	+	1.12166i
$66$	−0.572992	−	2.67642i	−0.0705304	−	0.329444i
$67$	3.94211	+	2.05213i	0.481606	+	0.250708i	0.685210	−	0.728345i	$-0.259710\pi$
$67$	3.94211	+	2.05213i	0.481606	+	0.250708i	−0.203605	+	0.979053i	$0.565266\pi$
$68$	−2.77802	−	9.42687i	−0.336884	−	1.14318i
$69$	−0.587548	+	2.42384i	−0.0707325	+	0.291796i
$70$	4.60801	−	18.0910i	0.550763	−	2.16229i
$71$	−4.22813	+	15.7796i	−0.501787	+	1.87269i	−0.0136844	+	0.999906i	$0.504356\pi$
$71$	−4.22813	+	15.7796i	−0.501787	+	1.87269i	−0.488102	+	0.872787i	$0.662311\pi$
$72$	7.84628	−	3.23046i	0.924693	−	0.380713i
$73$	0.149766	+	0.558935i	0.0175288	+	0.0654184i	0.974136	−	0.225961i	$-0.0725523\pi$
$73$	0.149766	+	0.558935i	0.0175288	+	0.0654184i	−0.956607	+	0.291380i	$0.905886\pi$
$74$	−12.8331	+	0.159009i	−1.49182	+	0.0184845i
$75$	12.8552	−	6.37413i	1.48439	−	0.736022i
$76$	−1.27348	+	3.30369i	−0.146078	+	0.378959i
$77$	2.17448	+	3.41325i	0.247805	+	0.388976i
$78$	1.44565	−	6.30393i	0.163687	−	0.713780i
$79$	0.376406	+	0.315842i	0.0423490	+	0.0355350i	0.663716	−	0.747984i	$-0.268978\pi$
$79$	0.376406	+	0.315842i	0.0423490	+	0.0355350i	−0.621368	+	0.783519i	$0.713423\pi$
$80$	−5.06742	−	13.6700i	−0.566555	−	1.52835i
$81$	0.706699	−	8.97221i	0.0785222	−	0.996912i
$82$	−3.87972	−	0.809817i	−0.428443	−	0.0894293i
$83$	−2.38579	+	7.56676i	−0.261875	+	0.830560i	0.727619	+	0.685982i	$0.240627\pi$
$83$	−2.38579	+	7.56676i	−0.261875	+	0.830560i	−0.989493	+	0.144578i	$0.953817\pi$
$84$	−9.20659	+	8.52357i	−1.00452	+	0.929998i
$85$	−3.87638	+	17.4852i	−0.420452	+	1.89654i
$86$	−1.37596	+	8.41158i	−0.148373	+	0.907044i
$87$	−11.3929	+	0.771518i	−1.22145	+	0.0827154i
$88$	2.91203	+	1.22831i	0.310424	+	0.130939i
$89$	4.61035	+	17.2061i	0.488696	+	1.82384i	0.562806	+	0.826589i	$0.309722\pi$
$89$	4.61035	+	17.2061i	0.488696	+	1.82384i	−0.0741104	+	0.997250i	$0.523612\pi$
$90$	−15.3627	−	1.76175i	−1.61937	−	0.185704i
$91$	1.24822	+	9.48120i	0.130849	+	0.993899i
$92$	−1.90523	−	2.15956i	−0.198634	−	0.225150i
$93$	−2.12848	−	3.49055i	−0.220713	−	0.361954i
$94$	16.0229	+	4.83458i	1.65264	+	0.498649i
$95$	4.94280	−	4.14750i	0.507121	−	0.425525i
$96$	−2.13343	+	9.56287i	−0.217742	+	0.976006i
$97$	−1.41533	+	0.515136i	−0.143705	+	0.0523042i	−0.412871	−	0.910789i	$-0.635474\pi$
$97$	−1.41533	+	0.515136i	−0.143705	+	0.0523042i	0.269167	+	0.963094i	$0.413252\pi$
$98$	3.89955	−	7.72311i	0.393914	−	0.780151i
$99$	2.55858	−	2.16586i	0.257147	−	0.217677i
$100$	−2.47192	+	16.3830i	−0.247192	+	1.63830i
$101$	9.44379	−	14.8238i	0.939692	−	1.47502i	0.0607161	−	0.998155i	$-0.480662\pi$
$101$	9.44379	−	14.8238i	0.939692	−	1.47502i	0.878976	−	0.476866i	$-0.158227\pi$
$102$	8.57259	−	8.44900i	0.848813	−	0.836575i
$103$	−3.36581	+	1.56950i	−0.331643	+	0.154648i	−0.581306	−	0.813685i	$-0.697458\pi$
$103$	−3.36581	+	1.56950i	−0.331643	+	0.154648i	0.249663	+	0.968333i	$0.419680\pi$
$104$	5.00969	+	5.53856i	0.491240	+	0.543101i
$105$	22.1972	−	5.48261i	2.16623	−	0.535048i
$106$	−2.50029	+	4.45726i	−0.242849	+	0.432927i
$107$	−0.392475	−	0.162568i	−0.0379420	−	0.0157161i	0.363632	−	0.931543i	$-0.381537\pi$
$107$	−0.392475	−	0.162568i	−0.0379420	−	0.0157161i	−0.401574	+	0.915827i	$0.631537\pi$
$108$	8.02381	+	6.60443i	0.772091	+	0.635512i
$109$	6.32243	+	15.2637i	0.605579	+	1.46200i	0.867763	+	0.496979i	$0.165557\pi$
$109$	6.32243	+	15.2637i	0.605579	+	1.46200i	−0.262184	+	0.965018i	$0.584443\pi$
$110$	−3.56257	−	4.52561i	−0.339678	−	0.431500i
$111$	−7.59025	−	13.7644i	−0.720434	−	1.30646i
$112$	−1.97607	−	14.3520i	−0.186721	−	1.35613i
$113$	8.04620	+	2.92858i	0.756923	+	0.275497i	0.691516	−	0.722361i	$-0.256943\pi$
$113$	8.04620	+	2.92858i	0.756923	+	0.275497i	0.0654072	+	0.997859i	$0.479165\pi$
$114$	−4.30327	+	0.534779i	−0.403038	+	0.0500866i
$115$	1.13592	+	5.12379i	0.105925	+	0.477796i
$116$	6.80689	−	11.2927i	0.632004	−	1.04850i
$117$	7.64226	−	2.08326i	0.706528	−	0.192598i
$118$	−11.0694	+	9.52447i	−1.01902	+	0.876799i
$119$	−7.52139	+	16.1297i	−0.689485	+	1.47861i
$120$	11.8306	−	13.3738i	1.07998	−	1.22086i
$121$	−9.71431	−	0.849892i	−0.883119	−	0.0772629i
$122$	1.55119	+	15.5138i	0.140438	+	1.40455i
$123$	−1.36840	−	4.65720i	−0.123385	−	0.419926i
$124$	4.71158	+	0.294794i	0.423112	+	0.0264733i
$125$	7.28702	−	9.49663i	0.651771	−	0.849405i
$126$	−14.5253	−	5.01336i	−1.29402	−	0.446626i
$127$	−7.58818	−	4.38104i	−0.673342	−	0.388754i	0.124000	−	0.992282i	$-0.460428\pi$
$127$	−7.58818	−	4.38104i	−0.673342	−	0.388754i	−0.797342	+	0.603528i	$0.793761\pi$
$128$	−7.63895	−	8.34544i	−0.675194	−	0.737640i
$129$	−9.87768	+	3.37690i	−0.869681	+	0.297319i
$130$	−3.11008	−	13.2496i	−0.272772	−	1.16207i
$131$	2.96643	+	4.65636i	0.259178	+	0.406828i	0.948083	−	0.318024i	$-0.103019\pi$
$131$	2.96643	+	4.65636i	0.259178	+	0.406828i	−0.688905	+	0.724852i	$0.741908\pi$
$132$	0.357135	+	3.85428i	0.0310847	+	0.335472i
$133$	5.68734	−	2.96064i	0.493154	−	0.256720i
$134$	−5.19276	−	3.54094i	−0.448586	−	0.305891i
$135$	−6.97865	−	17.6060i	−0.600626	−	1.51529i
$136$	2.32492	+	13.7026i	0.199360	+	1.17499i
$137$	0.609910	+	6.97130i	0.0521081	+	0.595599i	0.976696	+	0.214629i	$0.0688542\pi$
$137$	0.609910	+	6.97130i	0.0521081	+	0.595599i	−0.924588	+	0.380970i	$0.875590\pi$
$138$	1.23037	−	3.30554i	0.104736	−	0.281386i
$139$	−21.7411	−	4.81989i	−1.84406	−	0.408818i	−0.850873	−	0.525372i	$-0.823926\pi$
$139$	−21.7411	−	4.81989i	−1.84406	−	0.408818i	−0.993184	+	0.116554i	$0.962815\pi$
$140$	−9.49593	+	24.6346i	−0.802552	+	2.08200i
$141$	4.04246	+	20.0952i	0.340436	+	1.69232i
$142$	8.57598	−	21.4522i	0.719680	−	1.80023i
$143$	2.55509	+	1.47518i	0.213667	+	0.123361i
$144$	−11.5586	+	3.22457i	−0.963220	+	0.268714i
$145$	−20.8098	+	12.0145i	−1.72816	+	0.997753i
$146$	−0.116858	−	0.809951i	−0.00967127	−	0.0670320i
$147$	10.5931	−	0.254098i	0.873708	−	0.0209577i
$148$	18.0480	+	1.92248i	1.48354	+	0.158027i
$149$	−4.56731	−	14.4857i	−0.374169	−	1.18671i	−0.933747	−	0.357935i	$-0.883481\pi$
$149$	−4.56731	−	14.4857i	−0.374169	−	1.18671i	0.559578	−	0.828778i	$-0.310963\pi$
$150$	−19.1183	+	6.80169i	−1.56100	+	0.555356i
$151$	−6.96756	−	3.24903i	−0.567012	−	0.264402i	0.117903	−	0.993025i	$-0.462383\pi$
$151$	−6.96756	−	3.24903i	−0.567012	−	0.264402i	−0.684915	+	0.728623i	$0.740161\pi$
$152$	2.34073	−	4.42641i	0.189858	−	0.359029i
$153$	14.0783	+	4.37192i	1.13816	+	0.353449i
$154$	−2.48289	−	5.15679i	−0.200077	−	0.415546i
$155$	−7.25575	−	4.62242i	−0.582796	−	0.371282i
$156$	−3.08417	+	8.61085i	−0.246931	+	0.689420i
$157$	1.99437	−	0.0870759i	0.159168	−	0.00694941i	0.0361031	−	0.999348i	$-0.488506\pi$
$157$	1.99437	−	0.0870759i	0.159168	−	0.00694941i	0.123065	+	0.992399i	$0.460728\pi$
$158$	−0.475774	−	0.506472i	−0.0378505	−	0.0402928i
$159$	−6.25802	−	0.122991i	−0.496293	−	0.00975380i
$160$	4.83044	+	20.0440i	0.381880	+	1.58462i
$161$			5.21520i			0.411015i
$162$	−2.49262	+	12.4815i	−0.195839	+	0.980636i
$163$	−2.16261	−	5.22101i	−0.169389	−	0.408941i	0.816275	−	0.577664i	$-0.196036\pi$
$163$	−2.16261	−	5.22101i	−0.169389	−	0.408941i	−0.985664	+	0.168723i	$0.946036\pi$
$164$	5.31286	+	1.78593i	0.414865	+	0.139458i
$165$	2.82700	−	6.46279i	0.220082	−	0.503128i
$166$	4.61556	−	10.2270i	0.358237	−	0.793772i
$167$	1.85964	+	3.98802i	0.143904	+	0.308602i	0.965028	−	0.262147i	$-0.0844306\pi$
$167$	1.85964	+	3.98802i	0.143904	+	0.308602i	−0.821124	+	0.570749i	$0.806653\pi$
$168$	14.3540	−	10.4302i	1.10743	−	0.804707i
$169$	−3.45776	−	4.93820i	−0.265982	−	0.379861i
$170$	8.36721	−	23.9062i	0.641735	−	1.83352i
$171$	−3.06505	−	4.33724i	−0.234390	−	0.331677i
$172$	3.33872	−	11.5823i	0.254575	−	0.883139i
$173$	15.2208	−	13.9473i	1.15722	−	1.06039i	0.159903	−	0.987133i	$-0.448882\pi$
$173$	15.2208	−	13.9473i	1.15722	−	1.06039i	0.997313	−	0.0732606i	$-0.0233405\pi$
$174$	16.1280	+	0.821532i	1.22266	+	0.0622802i
$175$	22.9845	−	19.2863i	1.73747	−	1.45791i
$176$	−3.88397	−	2.21183i	−0.292765	−	0.166723i
$177$	−16.6829	−	6.44605i	−1.25396	−	0.484515i
$178$	−3.59733	−	24.9332i	−0.269631	−	1.86883i
$179$	−7.50075	+	9.77517i	−0.560633	+	0.730631i	−0.984556	−	0.175067i	$-0.943986\pi$
$179$	−7.50075	+	9.77517i	−0.560633	+	0.730631i	0.423924	+	0.905698i	$0.360652\pi$
$180$	21.2792	+	5.04275i	1.58606	+	0.375864i
$181$	9.62209	−	7.38329i	0.715205	−	0.548796i	−0.185809	−	0.982586i	$-0.559491\pi$
$181$	9.62209	−	7.38329i	0.715205	−	0.548796i	0.901014	+	0.433790i	$0.142824\pi$
$182$	−0.167559	−	13.5231i	−0.0124203	−	1.00240i
$183$	−15.8541	+	10.6431i	−1.17197	+	0.786759i
$184$	2.31441	+	3.35122i	0.170621	+	0.247055i
$185$	−27.0946	−	18.9719i	−1.99204	−	1.39484i
$186$	2.40537	+	5.25766i	0.176370	+	0.385510i
$187$	2.53534	+	4.87034i	0.185402	+	0.356155i
$188$	−21.6925	−	9.46830i	−1.58209	−	0.690547i
$189$	−2.98370	−	18.5816i	−0.217032	−	1.35161i
$190$	−7.63463	+	4.99785i	−0.553875	+	0.362582i
$191$	4.59920	+	3.85919i	0.332787	+	0.279241i	0.793834	−	0.608134i	$-0.208082\pi$
$191$	4.59920	+	3.85919i	0.332787	+	0.279241i	−0.461047	+	0.887375i	$0.652526\pi$
$192$	4.59493	−	13.0724i	0.331611	−	0.943416i
$193$	0.452790	+	2.56790i	0.0325925	+	0.184841i	0.996758	−	0.0804611i	$-0.0256393\pi$
$193$	0.452790	+	2.56790i	0.0325925	+	0.184841i	−0.964165	+	0.265302i	$0.914528\pi$
$194$	2.07367	−	0.486752i	0.148881	−	0.0349467i
$195$	12.5081	−	11.0174i	0.895727	−	0.788970i
$196$	−6.76746	+	10.1935i	−0.483390	+	0.728106i
$197$	−6.70404	+	5.14419i	−0.477643	+	0.366508i	−0.819346	−	0.573300i	$-0.805663\pi$
$197$	−6.70404	+	5.14419i	−0.477643	+	0.366508i	0.341703	+	0.939808i	$0.388996\pi$
$198$	−3.95515	+	2.61369i	−0.281080	+	0.185747i
$199$	−3.10848	−	0.832915i	−0.220354	−	0.0590438i	0.146953	−	0.989144i	$-0.453054\pi$
$199$	−3.10848	−	0.832915i	−0.220354	−	0.0590438i	−0.367307	+	0.930100i	$0.619720\pi$
$200$	6.21064	−	22.5933i	0.439159	−	1.59759i
$201$	0.821449	−	7.65374i	0.0579405	−	0.539853i
$202$	−15.7405	+	19.2379i	−1.10750	+	1.35357i
$203$	−22.7729	+	7.18025i	−1.59834	+	0.503955i
$204$	−13.4512	+	10.4315i	−0.941770	+	0.730350i
$205$	−6.90077	−	7.53087i	−0.481971	−	0.525979i
$206$	4.98902	−	1.64126i	0.347602	−	0.114352i
$207$	4.28035	−	0.582393i	0.297505	−	0.0404791i
$208$	−6.10899	−	8.61542i	−0.423582	−	0.597372i
$209$	0.343503	−	1.94810i	0.0237606	−	0.134753i
$210$	−32.0882	+	3.98769i	−2.21429	+	0.275176i
$211$	−15.8147	+	0.690484i	−1.08873	+	0.0475349i	−0.580939	−	0.813947i	$-0.697315\pi$
$211$	−15.8147	+	0.690484i	−1.08873	+	0.0475349i	−0.507788	+	0.861482i	$0.669537\pi$
$212$	4.25642	−	5.84124i	0.292332	−	0.401178i
$213$	28.1203	−	3.14132i	1.92677	−	0.215240i
$214$	0.523968	+	0.293918i	0.0358177	+	0.0200918i
$215$	−15.5328	+	15.5328i	−1.05933	+	1.05933i
$216$	−10.1635	−	10.6162i	−0.691538	−	0.722340i
$217$	−6.04503	−	6.04503i	−0.410364	−	0.410364i
$218$	−6.32637	−	22.4919i	−0.428476	−	1.52334i
$219$	0.806977	−	0.594392i	0.0545305	−	0.0401653i
$220$	4.24619	+	6.95097i	0.286278	+	0.468635i
$221$	0.565934	+	12.9620i	0.0380689	+	0.871920i
$222$	8.35744	+	20.5984i	0.560915	+	1.38248i
$223$	−9.62633	−	1.69738i	−0.644627	−	0.113665i	−0.158229	−	0.987402i	$-0.550578\pi$
$223$	−9.62633	−	1.69738i	−0.644627	−	0.113665i	−0.486398	+	0.873737i	$0.661690\pi$
$224$	0.375248	+	20.4848i	0.0250723	+	1.36870i
$225$	−18.3959	−	16.7107i	−1.22639	−	1.11405i
$226$	−10.8096	−	5.45796i	−0.719041	−	0.363058i
$227$	−14.7187	+	13.4872i	−0.976911	+	0.895174i	−0.994507	−	0.104671i	$-0.966621\pi$
$227$	−14.7187	+	13.4872i	−0.976911	+	0.895174i	0.0175957	+	0.999845i	$0.494399\pi$
$228$	6.13247	−	0.0314541i	0.406133	−	0.00208310i
$229$	−6.80195	−	21.5730i	−0.449485	−	1.42559i	−0.858385	−	0.513006i	$-0.828532\pi$
$229$	−6.80195	−	21.5730i	−0.449485	−	1.42559i	0.408899	−	0.912579i	$-0.365913\pi$
$230$	−0.738433	−	7.38524i	−0.0486908	−	0.486968i
$231$	4.13265	−	5.66190i	0.271908	−	0.372525i
$232$	−11.4471	+	14.7201i	−0.751538	+	0.966425i
$233$	−2.40004	+	8.95706i	−0.157232	+	0.586797i	0.841672	+	0.539989i	$0.181572\pi$
$233$	−2.40004	+	8.95706i	−0.157232	+	0.586797i	−0.998904	+	0.0468080i	$0.985095\pi$
$234$	−11.0803	+	1.64768i	−0.724343	+	0.107712i
$235$	26.2580	+	34.2201i	1.71289	+	2.23228i
$236$	17.1372	−	11.5243i	1.11554	−	0.750168i
$237$	0.271820	−	0.806490i	0.0176566	−	0.0523872i
$238$	13.2592	−	21.3932i	0.859468	−	1.38671i
$239$	2.85519	−	0.503447i	0.184687	−	0.0325653i	−0.0805396	−	0.996751i	$-0.525664\pi$
$239$	2.85519	−	0.503447i	0.184687	−	0.0325653i	0.265227	+	0.964186i	$0.414553\pi$
$240$	−18.8498	+	16.8026i	−1.21675	+	1.08460i
$241$	16.0665	−	19.1473i	1.03494	−	1.23339i	0.0630320	−	0.998012i	$-0.479923\pi$
$241$	16.0665	−	19.1473i	1.03494	−	1.23339i	0.971904	−	0.235377i	$-0.0756326\pi$
$242$	13.4996	+	2.81779i	0.867789	+	0.181134i
$243$	−14.9176	+	4.52391i	−0.956963	+	0.290209i
$244$	0.415678	−	22.0453i	0.0266111	−	1.41131i
$245$	19.7782	−	10.2959i	1.26358	−	0.657779i
$246$	1.14293	+	6.76889i	0.0728703	+	0.431568i
$247$	2.68107	−	3.82896i	0.170592	−	0.243631i
$248$	−6.56715	−	1.20178i	−0.417014	−	0.0763132i
$249$	13.7106	−	0.928470i	0.868876	−	0.0588394i
$250$	−11.8210	+	12.1176i	−0.747627	+	0.766386i
$251$	−14.4810	−	18.8720i	−0.914030	−	1.19119i	−0.981112	−	0.193440i	$-0.938035\pi$
$251$	−14.4810	−	18.8720i	−0.914030	−	1.19119i	0.0670817	−	0.997747i	$-0.478631\pi$
$252$	19.5596	+	9.46896i	1.23214	+	0.596488i
$253$	1.27649	+	0.979486i	0.0802523	+	0.0615798i
$254$	9.92350	+	7.42105i	0.622656	+	0.465638i
$255$	30.6493	−	4.78535i	1.91933	−	0.299670i
$256$	9.33192	+	12.9967i	0.583245	+	0.812296i
$257$	−10.4478	−	12.4512i	−0.651714	−	0.776683i	0.334457	−	0.942411i	$-0.391447\pi$
$257$	−10.4478	−	12.4512i	−0.651714	−	0.776683i	−0.986171	+	0.165728i	$0.947003\pi$
$258$	14.4358	−	3.09055i	0.898734	−	0.192409i
$259$	−22.2056	−	24.2332i	−1.37979	−	1.50578i
$260$	2.15205	+	19.1263i	0.133464	+	1.18617i
$261$	8.43626	+	17.8889i	0.522191	+	1.10730i
$262$	−3.38717	−	7.03491i	−0.209260	−	0.434618i
$263$	23.4517	−	16.4211i	1.44610	−	1.01257i	0.453479	−	0.891267i	$-0.350183\pi$
$263$	23.4517	−	16.4211i	1.44610	−	1.01257i	0.992616	−	0.121300i	$-0.0387063\pi$
$264$	0.142937	−	5.47226i	0.00879714	−	0.336795i
$265$	−11.9372	+	5.56643i	−0.733299	+	0.341943i
$266$	−8.48173	+	3.20665i	−0.520048	+	0.196612i
$267$	24.8417	−	18.2976i	1.52029	−	1.11979i
$268$	6.70009	+	5.84079i	0.409273	+	0.356783i
$269$	24.3091	−	10.0692i	1.48215	−	0.613928i	0.512560	−	0.858651i	$-0.328697\pi$
$269$	24.3091	−	10.0692i	1.48215	−	0.613928i	0.969593	+	0.244723i	$0.0786971\pi$
$270$	6.85624	+	25.8909i	0.417257	+	1.57567i
$271$	30.7642			1.86879			0.934397	−	0.356234i	$-0.115939\pi$
$271$	30.7642			1.86879			0.934397	+	0.356234i	$0.115939\pi$
$272$	−0.973714	−	19.6312i	−0.0590401	−	1.19032i
$273$	14.5045	−	7.99835i	0.877851	−	0.484082i
$274$	0.309151	−	9.89174i	0.0186765	−	0.597582i
$275$	−0.403777	−	9.24802i	−0.0243487	−	0.557676i
$276$	−2.28051	+	4.43622i	−0.137271	+	0.267029i
$277$	−8.85362	+	13.8974i	−0.531963	+	0.835014i	−0.998782	−	0.0493387i	$-0.984289\pi$
$277$	−8.85362	+	13.8974i	−0.531963	+	0.835014i	0.466820	+	0.884353i	$0.345400\pi$
$278$	29.7250	+	10.4038i	1.78279	+	0.623978i
$279$	−4.28638	+	5.63650i	−0.256619	+	0.337449i
$280$	17.4541	−	33.0064i	1.04308	−	1.97251i
$281$	−4.22394	+	9.05827i	−0.251979	+	0.540371i	−0.991087	−	0.133216i	$-0.957470\pi$
$281$	−4.22394	+	9.05827i	−0.251979	+	0.540371i	0.739108	+	0.673587i	$0.235247\pi$
$282$	−2.31675	−	28.8955i	−0.137961	−	1.72070i
$283$	−2.06840	+	0.652166i	−0.122954	+	0.0387672i	−0.361557	−	0.932350i	$-0.617755\pi$
$283$	−2.06840	+	0.652166i	−0.122954	+	0.0387672i	0.238603	+	0.971117i	$0.423310\pi$
$284$	−15.6301	+	28.6913i	−0.927478	+	1.70251i
$285$	−9.80977	−	5.35421i	−0.581081	−	0.317156i
$286$	−3.34143	−	2.49881i	−0.197583	−	0.147758i
$287$	−5.07510	−	8.79034i	−0.299574	−	0.518877i
$288$	16.7709	−	2.59556i	0.988235	−	0.152945i
$289$	−3.57291	+	6.18845i	−0.210171	+	0.364027i
$290$	31.2320	−	13.3924i	1.83401	−	0.786430i
$291$	1.72431	+	1.95763i	0.101081	+	0.114758i
$292$	0.0286749	+	1.15695i	0.00167807	+	0.0677053i
$293$	−5.76804	+	26.0180i	−0.336973	+	1.51999i	0.444347	+	0.895855i	$0.353436\pi$
$293$	−5.76804	+	26.0180i	−0.336973	+	1.51999i	−0.781320	+	0.624131i	$0.785453\pi$
$294$	−14.9184	−	1.41441i	−0.870057	−	0.0824900i
$295$	−37.4920	+	3.28012i	−2.18287	+	0.190976i
$296$	−25.0233	−	5.71747i	−1.45445	−	0.332321i
$297$	−5.10848	−	2.75958i	−0.296424	−	0.160127i
$298$	3.99176	+	21.1058i	0.231237	+	1.22263i
$299$	1.75555	+	3.37238i	0.101526	+	0.195030i
$300$	27.9850	−	6.35488i	1.61571	−	0.366899i
$301$	−18.4100	+	11.7285i	−1.06114	+	0.676019i
$302$	9.24124	+	5.72761i	0.531774	+	0.329587i
$303$	−29.8710	−	5.87449i	−1.71605	−	0.337481i
$304$	−4.02720	+	5.82460i	−0.230976	+	0.334064i
$305$	−20.0910	+	34.7986i	−1.15041	+	1.99256i
$306$	−19.0391	−	8.49344i	−1.08839	−	0.485537i
$307$	3.90259	+	2.99456i	0.222733	+	0.170909i	0.714100	−	0.700044i	$-0.246836\pi$
$307$	3.90259	+	2.99456i	0.222733	+	0.170909i	−0.491367	+	0.870952i	$0.663503\pi$
$308$	2.62446	+	7.65680i	0.149543	+	0.436287i
$309$	4.65617	+	4.43803i	0.264881	+	0.252471i
$310$	9.41631	+	7.70444i	0.534810	+	0.437583i
$311$	0.107937	−	1.23373i	0.00612057	−	0.0699584i	−0.992520	−	0.122081i	$-0.961043\pi$
$311$	0.107937	−	1.23373i	0.00612057	−	0.0699584i	0.998641	+	0.0521228i	$0.0165987\pi$
$312$	5.77087	−	11.5765i	0.326711	−	0.655389i
$313$	2.42119	+	1.12902i	0.136854	+	0.0638160i	0.489839	−	0.871813i	$-0.337056\pi$
$313$	2.42119	+	1.12902i	0.136854	+	0.0638160i	−0.352985	+	0.935629i	$0.614833\pi$
$314$	−2.81524	−	0.211190i	−0.158873	−	0.0119181i
$315$	−22.8552	−	32.3415i	−1.28774	−	1.82224i
$316$	0.583441	+	0.790788i	0.0328211	+	0.0444853i
$317$	6.67932	−	1.48077i	0.375148	−	0.0831683i	−0.0248334	−	0.999692i	$-0.507906\pi$
$317$	6.67932	−	1.48077i	0.375148	−	0.0831683i	0.399981	+	0.916523i	$0.369017\pi$
$318$	8.76753	+	1.21909i	0.491659	+	0.0683634i
$319$	−2.51959	+	6.92252i	−0.141070	+	0.387587i
$320$	−3.43188	−	28.9554i	−0.191848	−	1.61865i
$321$	−0.0144580	+	0.735653i	−0.000806968	+	0.0410602i
$322$	0.872013	−	7.32367i	0.0485954	−	0.408132i
$323$	8.03687	−	3.32898i	0.447184	−	0.185229i
$324$	5.58735	−	17.1109i	0.310408	−	0.950603i
$325$	8.37062	−	20.2085i	0.464319	−	1.12096i
$326$	2.16396	+	7.69344i	0.119851	+	0.426100i
$327$	20.6281	−	19.8329i	1.14073	−	1.09676i
$328$	−7.16220	−	3.39632i	−0.395466	−	0.187530i
$329$	18.1144	+	38.8465i	0.998679	+	2.14167i
$330$	−5.05056	+	8.60297i	−0.278024	+	0.473578i
$331$	17.2178	+	10.9690i	0.946376	+	0.602908i	0.917954	−	0.396688i	$-0.129840\pi$
$331$	17.2178	+	10.9690i	0.946376	+	0.602908i	0.0284228	+	0.999596i	$0.490952\pi$
$332$	−8.19163	+	13.5900i	−0.449574	+	0.745850i
$333$	−17.4095	+	20.9313i	−0.954036	+	1.14703i
$334$	−1.94467	−	5.91130i	−0.106407	−	0.323452i
$335$	−5.54013	−	15.2214i	−0.302690	−	0.831633i
$336$	−21.9012	+	12.2470i	−1.19481	+	0.668129i
$337$	3.41576	+	4.07074i	0.186068	+	0.221747i	0.851012	−	0.525146i	$-0.175989\pi$
$337$	3.41576	+	4.07074i	0.186068	+	0.221747i	−0.664944	+	0.746893i	$0.731545\pi$
$338$	4.03002	+	7.51284i	0.219204	+	0.408645i
$339$	−0.355646	−	14.8266i	−0.0193160	−	0.805269i
$340$	−15.7473	+	32.1723i	−0.854016	+	1.74479i
$341$	−2.61495	+	0.344264i	−0.141607	+	0.0186429i
$342$	3.57902	+	6.60325i	0.193531	+	0.357063i
$343$	−3.08662	+	0.827056i	−0.166662	+	0.0446568i
$344$	−6.62517	+	15.7067i	−0.357205	+	0.846846i
$345$	7.54722	−	5.06657i	0.406329	−	0.272775i
$346$	−23.7066	+	17.0411i	−1.27447	+	0.916135i
$347$	15.9138	+	3.52801i	0.854300	+	0.189394i	0.621774	−	0.783197i	$-0.286412\pi$
$347$	15.9138	+	3.52801i	0.854300	+	0.189394i	0.232526	+	0.972590i	$0.425301\pi$
$348$	−22.5112	−	3.85038i	−1.20672	−	0.206402i
$349$	−28.3820	−	8.94881i	−1.51925	−	0.479019i	−0.577805	−	0.816175i	$-0.696090\pi$
$349$	−28.3820	−	8.94881i	−1.51925	−	0.479019i	−0.941449	+	0.337156i	$0.890535\pi$
$350$	−35.5018	+	23.2405i	−1.89765	+	1.24226i
$351$	−8.18436	−	11.0113i	−0.436849	−	0.587740i
$352$	5.08441	+	3.75548i	0.271000	+	0.200168i
$353$	11.5175	−	13.7260i	0.613016	−	0.730564i	−0.366837	−	0.930285i	$-0.619559\pi$
$353$	11.5175	−	13.7260i	0.613016	−	0.730564i	0.979853	+	0.199722i	$0.0640037\pi$
$354$	22.3498	+	11.8416i	1.18788	+	0.629375i
$355$	50.2169	−	31.9917i	2.66523	−	1.69794i
$356$	0.882717	+	35.6151i	0.0467839	+	1.88760i
$357$	30.7638	+	1.94946i	1.62819	+	0.103176i
$358$	12.1677	−	12.4730i	0.643085	−	0.659221i
$359$	−22.5213	+	6.03455i	−1.18863	+	0.318491i	−0.798343	−	0.602203i	$-0.794290\pi$
$359$	−22.5213	+	6.03455i	−1.18863	+	0.318491i	−0.390284	+	0.920695i	$0.627623\pi$
$360$	−29.0390	−	10.6395i	−1.53049	−	0.560751i
$361$	15.3254	+	4.10642i	0.806598	+	0.216127i
$362$	−14.7468	+	8.75944i	−0.775074	+	0.460386i
$363$	4.76140	+	16.2049i	0.249909	+	0.850537i
$364$	−2.02584	+	19.0184i	−0.106183	+	0.996836i
$365$	0.973848	−	1.87075i	0.0509736	−	0.0979193i
$366$	24.0433	−	12.2951i	1.25677	−	0.642676i
$367$	−21.5492	+	7.84327i	−1.12486	+	0.409415i	−0.836423	−	0.548084i	$-0.815357\pi$
$367$	−21.5492	+	7.84327i	−1.12486	+	0.409415i	−0.288436	+	0.957499i	$0.593135\pi$
$368$	−2.68977	−	5.09308i	−0.140214	−	0.265495i
$369$	−6.64789	+	5.14701i	−0.346075	+	0.267943i
$370$	34.8766	+	31.1725i	1.81315	+	1.62058i
$371$	−12.7782	+	2.83286i	−0.663412	+	0.147075i
$372$	−2.49873	−	7.78549i	−0.129553	−	0.403659i
$373$	14.0715	+	12.8942i	0.728594	+	0.667634i	0.951654	−	0.307171i	$-0.0993823\pi$
$373$	14.0715	+	12.8942i	0.728594	+	0.667634i	−0.223060	+	0.974805i	$0.571605\pi$
$374$	−2.74601	−	7.26332i	−0.141993	−	0.375577i
$375$	−19.9173	−	5.75859i	−1.02852	−	0.297372i
$376$	28.8795	+	16.9234i	1.48935	+	0.872758i
$377$	−12.3089	+	12.3089i	−0.633941	+	0.633941i
$378$	1.08304	+	26.5929i	0.0557055	+	1.36779i
$379$	5.58696	+	2.31419i	0.286983	+	0.118872i	0.521531	−	0.853232i	$-0.325361\pi$
$379$	5.58696	+	2.31419i	0.286983	+	0.118872i	−0.234548	+	0.972104i	$0.575361\pi$
$380$	11.5569	−	5.74189i	0.592859	−	0.294553i
$381$	−2.27619	+	15.0047i	−0.116613	+	0.768714i
$382$	−5.81335	−	6.18845i	−0.297437	−	0.316629i
$383$	18.5065	+	6.73581i	0.945638	+	0.344184i	0.768390	−	0.639982i	$-0.221058\pi$
$383$	18.5065	+	6.73581i	0.945638	+	0.344184i	0.177248	+	0.984166i	$0.443281\pi$
$384$	−8.63842	+	17.5891i	−0.440827	+	0.897592i
$385$	2.56140	−	14.5264i	0.130541	−	0.740335i
$386$	−0.206482	−	3.68179i	−0.0105096	−	0.187398i
$387$	11.6820	+	13.8002i	0.593830	+	0.701505i
$388$	−2.99343	+	0.336813i	−0.151968	+	0.0170991i
$389$	−38.5132	−	1.68152i	−1.95270	−	0.0852567i	−0.967104	−	0.254381i	$-0.918128\pi$
$389$	−38.5132	−	1.68152i	−1.95270	−	0.0852567i	−0.985595	+	0.169124i	$0.945906\pi$
$390$	−19.4073	+	13.3802i	−0.982726	+	0.677532i
$391$	−0.616678	+	7.04866i	−0.0311867	+	0.356466i
$392$	11.2079	−	13.1831i	0.566086	−	0.665847i
$393$	5.63777	−	7.72398i	0.284388	−	0.389623i
$394$	10.2746	−	6.10300i	0.517626	−	0.307465i
$395$	−0.233759	−	1.77558i	−0.0117617	−	0.0893389i
$396$	5.99121	−	3.00907i	0.301070	−	0.151212i
$397$	−21.8818	−	2.88080i	−1.09822	−	0.144583i	−0.440430	−	0.897787i	$-0.645174\pi$
$397$	−21.8818	−	2.88080i	−1.09822	−	0.144583i	−0.657787	+	0.753204i	$0.728507\pi$
$398$	4.22596	+	1.68942i	0.211828	+	0.0846827i
$399$	−8.36544	−	7.30430i	−0.418796	−	0.365673i
$400$	−12.4993	+	30.6892i	−0.624965	+	1.53446i
$401$	0.370854	+	2.10322i	0.0185196	+	0.105030i	0.992666	−	0.120886i	$-0.0385736\pi$
$401$	0.370854	+	2.10322i	0.0185196	+	0.105030i	−0.974147	+	0.225916i	$0.927463\pi$
$402$	−2.43331	+	10.6107i	−0.121362	+	0.529216i
$403$	−5.94387	−	1.87410i	−0.296085	−	0.0933554i
$404$	25.3210	−	24.3837i	1.25976	−	1.21314i
$405$	−23.9919	+	22.3699i	−1.19217	+	1.11157i
$406$	33.1804	−	6.27543i	1.64671	−	0.311444i
$407$	−10.1019	+	0.883803i	−0.500734	+	0.0438085i
$408$	20.6336	−	12.3998i	1.02152	−	0.613880i
$409$	6.82745	−	9.75060i	0.337595	−	0.482136i	−0.614079	−	0.789244i	$-0.710472\pi$
$409$	6.82745	−	9.75060i	0.337595	−	0.482136i	0.951675	+	0.307108i	$0.0993613\pi$
$410$	8.43150	+	11.7294i	0.416402	+	0.579274i
$411$	10.8592	−	5.38441i	0.535643	−	0.265594i
$412$	−7.28048	+	1.47062i	−0.358684	+	0.0724522i
$413$	−37.0786	−	4.88149i	−1.82452	−	0.240202i
$414$	−6.10825	+	0.102149i	−0.300204	+	0.00502037i
$415$	25.0432	−	14.4587i	1.22932	−	0.709749i
$416$	7.13827	+	13.1200i	0.349982	+	0.643263i
$417$	5.95010	+	38.1093i	0.291378	+	1.86622i
$418$	−0.808114	+	2.67827i	−0.0395261	+	0.130999i
$419$	−15.6000	+	29.9673i	−0.762110	+	1.46400i	0.119908	+	0.992785i	$0.461740\pi$
$419$	−15.6000	+	29.9673i	−0.762110	+	1.46400i	−0.882018	+	0.471215i	$0.843816\pi$
$420$	45.7280	−	0.234544i	2.23130	−	0.0114446i
$421$	−0.754153	+	17.2729i	−0.0367551	+	0.841831i	0.887673	+	0.460475i	$0.152321\pi$
$421$	−0.754153	+	17.2729i	−0.0367551	+	0.841831i	−0.924428	+	0.381357i	$0.875457\pi$
$422$	22.3239	+	1.67467i	1.08671	+	0.0815216i
$423$	29.8602	−	19.2054i	1.45185	−	0.933799i
$424$	−6.95396	+	7.49112i	−0.337714	+	0.363801i
$425$	33.3456	−	23.3488i	1.61750	−	1.13258i
$426$	−40.0144	−	0.290544i	−1.93870	−	0.0140769i
$427$	−26.9759	+	29.4390i	−1.30545	+	1.42465i
$428$	−0.686660	−	0.500358i	−0.0331910	−	0.0241857i
$429$	0.766436	−	5.05237i	0.0370039	−	0.243931i
$430$	24.4098	−	19.2154i	1.17715	−	0.926651i
$431$			15.8322i			0.762612i	0.924449	+	0.381306i	$0.124526\pi$
$431$			15.8322i			0.762612i	−0.924449	+	0.381306i	$0.875474\pi$
$432$	12.4974	+	16.6077i	0.601283	+	0.799036i
$433$		−	10.6941i		−	0.513924i	−0.966422	−	0.256962i	$-0.917278\pi$
$433$		−	10.6941i		−	0.513924i	0.966422	−	0.256962i	$-0.0827215\pi$
$434$	7.47824	+	9.49977i	0.358967	+	0.456004i
$435$	32.5148	+	25.9803i	1.55897	+	1.24566i
$436$	5.12330	+	32.6430i	0.245362	+	1.56332i
$437$	1.72217	−	1.87942i	0.0823825	−	0.0899047i
$438$	−1.23262	+	0.699770i	−0.0588968	+	0.0334363i
$439$	15.0637	−	10.5477i	0.718952	−	0.503416i	−0.155920	−	0.987770i	$-0.549834\pi$
$439$	15.0637	−	10.5477i	0.718952	−	0.503416i	0.874872	+	0.484354i	$0.160945\pi$
$440$	−4.80065	−	10.4712i	−0.228862	−	0.499195i
$441$	−7.09683	−	16.9255i	−0.337944	−	0.805977i
$442$	1.37259	−	18.2971i	0.0652875	−	0.870305i
$443$	−0.742404	+	17.0038i	−0.0352727	+	0.807877i	0.896109	+	0.443834i	$0.146382\pi$
$443$	−0.742404	+	17.0038i	−0.0352727	+	0.807877i	−0.931382	+	0.364044i	$0.881396\pi$
$444$	−8.29213	−	30.3237i	−0.393527	−	1.43910i
$445$	29.9786	−	57.5884i	1.42112	−	2.72995i
$446$	13.2344	+	3.99321i	0.626667	+	0.189084i
$447$	−20.4811	+	16.5109i	−0.968723	+	0.780938i
$448$	2.89822	−	28.8294i	0.136928	−	1.36206i
$449$	−7.31332	+	4.22235i	−0.345137	+	0.199265i	−0.662541	−	0.749025i	$-0.730522\pi$
$449$	−7.31332	+	4.22235i	−0.345137	+	0.199265i	0.317404	+	0.948290i	$0.397189\pi$
$450$	23.0391	+	26.5427i	1.08607	+	1.25123i
$451$	−3.10473	−	0.408746i	−0.146196	−	0.0192471i
$452$	14.2672	+	9.47201i	0.671073	+	0.445526i
$453$	−0.842111	+	13.2891i	−0.0395658	+	0.624376i
$454$	22.9245	−	16.4789i	1.07590	−	0.773393i
$455$	19.9919	−	28.5514i	0.937235	−	1.33851i
$456$	−8.61706	−	0.981216i	−0.403531	−	0.0459497i
$457$	−9.99516	+	0.874464i	−0.467554	+	0.0409057i	−0.318499	−	0.947923i	$-0.603179\pi$
$457$	−9.99516	+	0.874464i	−0.467554	+	0.0409057i	−0.149055	+	0.988829i	$0.547623\pi$
$458$	5.94480	+	31.4322i	0.277782	+	1.46873i
$459$	−1.83545	−	25.4670i	−0.0856716	−	1.18870i
$460$	−0.197881	+	10.4945i	−0.00922624	+	0.489310i
$461$	24.0111	+	7.57068i	1.11831	+	0.352602i	0.802757	−	0.596307i	$-0.203366\pi$
$461$	24.0111	+	7.57068i	1.11831	+	0.352602i	0.315552	+	0.948908i	$0.397810\pi$
$462$	−6.75016	+	7.25996i	−0.314046	+	0.337764i
$463$	0.378055	+	2.14406i	0.0175697	+	0.0996428i	0.992332	−	0.123604i	$-0.0394454\pi$
$463$	0.378055	+	2.14406i	0.0175697	+	0.0996428i	−0.974762	+	0.223247i	$0.928334\pi$
$464$	18.5364	−	18.7574i	0.860530	−	0.870790i
$465$	−2.87537	+	14.6209i	−0.133342	+	0.678027i
$466$	4.86804	−	12.1771i	0.225507	−	0.564091i
$467$	18.7832	+	2.47286i	0.869184	+	0.114430i	0.551910	−	0.833904i	$-0.313899\pi$
$467$	18.7832	+	2.47286i	0.869184	+	0.114430i	0.317274	+	0.948334i	$0.397232\pi$
$468$	15.8355	−	0.461127i	0.731998	−	0.0213156i
$469$	−2.10100	−	15.9587i	−0.0970153	−	0.736904i
$470$	−31.1522	−	52.4456i	−1.43694	−	2.41914i
$471$	−1.39940	−	3.16179i	−0.0644810	−	0.145688i
$472$	−25.9926	+	13.3181i	−1.19641	+	0.613014i
$473$	−0.586951	+	6.70888i	−0.0269881	+	0.308475i
$474$	−0.516565	+	1.08710i	−0.0237266	+	0.0499321i
$475$	−14.6518	−	0.639710i	−0.672269	−	0.0293519i
$476$	−22.1969	+	27.8253i	−1.01739	+	1.27537i
$477$	3.75204	+	10.1713i	0.171794	+	0.465713i
$478$	−4.09371	+	0.229583i	−0.187242	+	0.0105009i
$479$	5.29459	−	30.0271i	0.241916	−	1.37197i	−0.585632	−	0.810577i	$-0.699153\pi$
$479$	5.29459	−	30.0271i	0.241916	−	1.37197i	0.827547	−	0.561396i	$-0.189735\pi$
$480$	29.2802	−	20.4440i	1.33645	−	0.933138i
$481$	−22.5165	−	8.19535i	−1.02667	−	0.373676i
$482$	−25.7637	+	24.2021i	−1.17350	+	1.10237i
$483$	8.41170	−	3.29212i	0.382746	−	0.149797i
$484$	−18.4863	−	6.21423i	−0.840287	−	0.282465i
$485$	5.07171	+	2.10077i	0.230294	+	0.0953910i
$486$	21.7051	−	3.85859i	0.984563	−	0.175029i
$487$	−4.46195	+	4.46195i	−0.202190	+	0.202190i	−0.800938	−	0.598748i	$-0.795665\pi$
$487$	−4.46195	+	4.46195i	−0.202190	+	0.202190i	0.598748	+	0.800938i	$0.295665\pi$
$488$	−4.26984	+	30.8886i	−0.193287	+	1.39826i
$489$	−7.05592	+	6.78392i	−0.319080	+	0.306780i
$490$	−29.4959	+	11.1514i	−1.33249	+	0.503769i
$491$	−0.657224	−	0.602234i	−0.0296601	−	0.0271785i	0.660623	−	0.750717i	$-0.270292\pi$
$491$	−0.657224	−	0.602234i	−0.0296601	−	0.0271785i	−0.690284	+	0.723539i	$0.742514\pi$
$492$	−0.473204	−	9.69661i	−0.0213337	−	0.437157i
$493$	−31.6280	+	7.01175i	−1.42445	+	0.315793i
$494$	−4.40523	+	4.92870i	−0.198201	+	0.221752i
$495$	−12.2085	−	0.480061i	−0.548733	−	0.0215772i
$496$	9.02126	+	2.78572i	0.405067	+	0.125083i
$497$	55.5990	−	20.2364i	2.49396	−	0.907725i
$498$	−19.4090	−	0.988658i	−0.869739	−	0.0443028i
$499$	−3.34730	+	6.43009i	−0.149846	+	0.287851i	−0.950179	−	0.311704i	$-0.899100\pi$
$499$	−3.34730	+	6.43009i	−0.149846	+	0.287851i	0.800334	+	0.599555i	$0.204656\pi$
$500$	18.6263	−	15.0402i	0.832995	−	0.672617i
$501$	5.25845	−	5.51692i	0.234930	−	0.246478i
$502$	17.1800	+	28.9231i	0.766782	+	1.29090i
$503$	31.3950	+	8.41228i	1.39984	+	0.375085i	0.878286	−	0.478136i	$-0.158687\pi$
$503$	31.3950	+	8.41228i	1.39984	+	0.375085i	0.521550	+	0.853221i	$0.325354\pi$
$504$	−25.8841	−	16.5677i	−1.15297	−	0.737983i
$505$	−61.8788	+	16.5804i	−2.75357	+	0.737817i
$506$	−1.62879	−	1.58892i	−0.0724087	−	0.0706363i
$507$	−5.78219	+	8.69437i	−0.256796	+	0.386130i
$508$	−12.6947	−	12.0806i	−0.563235	−	0.535991i
$509$	−30.7377	+	19.5821i	−1.36242	+	0.867959i	−0.997996	−	0.0632728i	$-0.979846\pi$
$509$	−30.7377	+	19.5821i	−1.36242	+	0.867959i	−0.364427	+	0.931232i	$0.618735\pi$
$510$	−43.8407	+	1.59529i	−1.94130	+	0.0706408i
$511$	1.34714	−	1.60546i	0.0595941	−	0.0710215i
$512$	−10.9316	−	19.8116i	−0.483114	−	0.875557i
$513$	−5.06079	+	7.68159i	−0.223439	+	0.339151i
$514$	12.5898	+	19.2320i	0.555314	+	0.848289i
$515$	12.9093	+	4.07028i	0.568851	+	0.179358i
$516$	−20.7889	+	1.92628i	−0.915179	+	0.0847999i
$517$	12.9103	+	2.86215i	0.567796	+	0.125877i
$518$	27.1313	+	37.7434i	1.19208	+	1.65835i
$519$	−32.1041	−	15.7456i	−1.40921	−	0.691157i
$520$	0.175931	−	27.2188i	0.00771508	−	1.19363i
$521$	12.8501	−	3.44318i	0.562975	−	0.150849i	0.0339021	−	0.999425i	$-0.489207\pi$
$521$	12.8501	−	3.44318i	0.562975	−	0.150849i	0.529073	+	0.848577i	$0.322540\pi$
$522$	−8.85586	−	26.5319i	−0.387610	−	1.16127i
$523$	2.06942	−	0.272444i	0.0904893	−	0.0119131i	−0.0851456	−	0.996369i	$-0.527136\pi$
$523$	2.06942	−	0.272444i	0.0904893	−	0.0119131i	0.175635	+	0.984455i	$0.443802\pi$
$524$	3.58030	+	10.4454i	0.156406	+	0.456311i
$525$	−45.6164	−	24.8976i	−1.99086	−	1.08662i
$526$	−35.6788	+	19.1387i	−1.55567	+	0.834489i
$527$	−7.45544	−	8.88504i	−0.324764	−	0.387039i
$528$	−1.11572	+	7.66077i	−0.0485555	+	0.333392i
$529$	−7.15732	−	19.6646i	−0.311188	−	0.854981i
$530$	17.6941	−	5.82092i	0.768584	−	0.252845i
$531$	0.134185	+	30.9773i	0.00582312	+	1.34430i
$532$	12.4470	−	3.08488i	0.539646	−	0.133747i
$533$	−6.24080	−	3.97583i	−0.270319	−	0.172212i
$534$	−37.9445	+	21.5415i	−1.64202	+	0.932191i
$535$	0.654354	+	1.40327i	0.0282902	+	0.0606686i
$536$	−8.43228	−	9.32248i	−0.364219	−	0.402670i
$537$	20.5015	+	5.92749i	0.884704	+	0.255790i
$538$	−35.8208	+	10.0754i	−1.54434	+	0.434383i
$539$	2.61600	−	6.31559i	0.112679	−	0.272032i
$540$	−5.29905	−	37.5049i	−0.228035	−	1.61395i
$541$	11.6741	−	4.83558i	0.501909	−	0.207898i	−0.117340	−	0.993092i	$-0.537437\pi$
$541$	11.6741	−	4.83558i	0.501909	−	0.207898i	0.619250	+	0.785194i	$0.287437\pi$
$542$	−43.2020	−	5.14397i	−1.85569	−	0.220952i
$543$	−17.9827	−	10.8589i	−0.771711	−	0.466002i
$544$	−1.91508	+	27.7308i	−0.0821083	+	1.18895i
$545$	20.5951	−	56.5846i	0.882198	−	2.42382i
$546$	−21.7059	+	8.80679i	−0.928928	+	0.376896i
$547$	−6.03634	+	1.33822i	−0.258095	+	0.0572184i	−0.343588	−	0.939120i	$-0.611642\pi$
$547$	−6.03634	+	1.33822i	−0.258095	+	0.0572184i	0.0854928	+	0.996339i	$0.472754\pi$
$548$	−2.08810	+	13.8392i	−0.0891992	+	0.591182i
$549$	27.1744	+	18.8528i	1.15978	+	0.804620i
$550$	−0.979303	+	13.0544i	−0.0417576	+	0.556644i
$551$	10.5778	+	4.93251i	0.450630	+	0.210132i
$552$	3.94427	−	5.84845i	0.167879	−	0.248926i
$553$	0.155106	−	1.77286i	0.00659576	−	0.0753899i
$554$	14.7568	−	18.0357i	0.626957	−	0.766262i
$555$	−13.4965	+	55.6776i	−0.572894	+	2.36338i
$556$	−40.0031	−	19.5802i	−1.69651	−	0.830385i
$557$	−12.9171	−	9.91166i	−0.547316	−	0.419971i	0.297741	−	0.954647i	$-0.403767\pi$
$557$	−12.9171	−	9.91166i	−0.547316	−	0.419971i	−0.845057	+	0.534676i	$0.820434\pi$
$558$	6.96179	−	7.19860i	0.294716	−	0.304741i
$559$	−7.95668	+	13.7814i	−0.336532	+	0.582890i
$560$	−30.0296	+	43.4323i	−1.26898	+	1.83535i
$561$	6.25503	−	7.16373i	0.264088	−	0.302453i
$562$	7.44626	−	12.0142i	0.314101	−	0.506789i
$563$	36.1039	−	23.0007i	1.52160	−	0.969365i	0.528908	−	0.848679i	$-0.322602\pi$
$563$	36.1039	−	23.0007i	1.52160	−	0.969365i	0.992691	−	0.120686i	$-0.0385093\pi$
$564$	−1.57811	+	40.9652i	−0.0664505	+	1.72495i
$565$	−14.4105	−	27.6823i	−0.606254	−	1.16460i
$566$	3.01369	−	0.569982i	0.126675	−	0.0239581i
$567$	−28.0872	+	16.5422i	−1.17955	+	0.694708i
$568$	26.7467	−	37.6775i	1.12227	−	1.58091i
$569$	−22.0118	+	1.92579i	−0.922784	+	0.0807331i	−0.538636	−	0.842539i	$-0.681060\pi$
$569$	−22.0118	+	1.92579i	−0.922784	+	0.0807331i	−0.384148	+	0.923272i	$0.625505\pi$
$570$	12.8805	+	9.15915i	0.539507	+	0.383634i
$571$	6.48291	−	29.2425i	0.271301	−	1.22376i	−0.625110	−	0.780537i	$-0.714946\pi$
$571$	6.48291	−	29.2425i	0.271301	−	1.22376i	0.896411	−	0.443224i	$-0.146165\pi$
$572$	4.27454	+	4.06778i	0.178727	+	0.170082i
$573$	3.32130	−	9.85429i	0.138749	−	0.411669i
$574$	5.65714	+	13.1928i	0.236125	+	0.550657i
$575$	5.96436	−	10.3306i	0.248731	−	0.430815i
$576$	−23.9853	+	0.840739i	−0.999386	+	0.0350308i
$577$	−20.1114	−	34.8341i	−0.837251	−	1.45016i	−0.892185	−	0.451671i	$-0.850828\pi$
$577$	−20.1114	−	34.8341i	−0.837251	−	1.45016i	0.0549343	−	0.998490i	$-0.482505\pi$
$578$	6.05216	−	8.09300i	0.251737	−	0.336624i
$579$	3.85599	−	2.35132i	0.160250	−	0.0977173i
$580$	−46.0982	+	13.5847i	−1.91412	+	0.564075i
$581$	27.4056	−	8.64095i	1.13698	−	0.358487i
$582$	−2.09411	−	3.03740i	−0.0868035	−	0.125904i
$583$	−1.70655	+	3.65970i	−0.0706779	+	0.151569i
$584$	0.153181	−	1.62949i	0.00633867	−	0.0674288i
$585$	−25.6660	−	13.2199i	−1.06116	−	0.546575i
$586$	12.4504	−	35.5724i	0.514321	−	1.46948i
$587$	−15.2057	+	23.8681i	−0.627604	+	0.985142i	0.370802	+	0.928712i	$0.379083\pi$
$587$	−15.2057	+	23.8681i	−0.627604	+	0.985142i	−0.998407	+	0.0564298i	$0.982028\pi$
$588$	20.7133	+	4.48069i	0.854202	+	0.184781i
$589$	0.182270	+	4.17467i	0.00751030	+	0.172014i
$590$	53.1982	+	1.66263i	2.19014	+	0.0684494i
$591$	12.5291	+	7.56579i	0.515380	+	0.311215i
$592$	34.1841	+	12.2131i	1.40496	+	0.501954i
$593$	32.5152			1.33524			0.667620	−	0.744502i	$-0.267313\pi$
$593$	32.5152			1.33524			0.667620	+	0.744502i	$0.267313\pi$
$594$	6.71239	+	4.72943i	0.275413	+	0.194051i
$595$	59.9285	−	24.8232i	2.45683	−	1.01765i
$596$	−2.07658	−	30.3062i	−0.0850602	−	1.24139i
$597$	0.618821	+	5.53952i	0.0253266	+	0.226717i
$598$	−1.90142	−	5.02935i	−0.0777550	−	0.205665i
$599$	24.1731	−	11.2721i	0.987687	−	0.460566i	0.139477	−	0.990225i	$-0.455458\pi$
$599$	24.1731	−	11.2721i	0.987687	−	0.460566i	0.848211	+	0.529659i	$0.177680\pi$
$600$	−40.3617	+	4.24487i	−1.64776	+	0.173296i
$601$	−15.9222	+	11.1489i	−0.649481	+	0.454771i	−0.851320	−	0.524648i	$-0.824197\pi$
$601$	−15.9222	+	11.1489i	−0.649481	+	0.454771i	0.201839	+	0.979419i	$0.435308\pi$
$602$	27.8142	−	13.3920i	1.13362	−	0.545816i
$603$	−12.8634	+	3.50653i	−0.523839	+	0.142797i
$604$	−12.0197	−	9.58844i	−0.489076	−	0.390148i
$605$	24.0115	+	26.2039i	0.976206	+	1.06534i
$606$	40.9655	+	13.2441i	1.66411	+	0.538006i
$607$	5.15670	+	6.14552i	0.209304	+	0.249439i	0.860476	−	0.509492i	$-0.170167\pi$
$607$	5.15670	+	6.14552i	0.209304	+	0.249439i	−0.651171	+	0.758931i	$0.725722\pi$
$608$	6.62928	−	7.50608i	0.268853	−	0.304412i
$609$	25.9567	+	32.1983i	1.05182	+	1.30474i
$610$	34.0322	−	45.5082i	1.37792	−	1.84257i
$611$	24.7901	+	19.0221i	1.00290	+	0.769553i
$612$	25.3163	+	15.1107i	1.02335	+	0.610815i
$613$	14.8931	+	19.4091i	0.601528	+	0.783926i	0.990528	−	0.137311i	$-0.0438461\pi$
$613$	14.8931	+	19.4091i	0.601528	+	0.783926i	−0.389000	+	0.921238i	$0.627179\pi$
$614$	−4.97968	−	4.85779i	−0.200963	−	0.196044i
$615$	−7.79055	+	15.8843i	−0.314145	+	0.640517i
$616$	−2.40525	−	11.1912i	−0.0969105	−	0.450908i
$617$	4.56116	−	6.51401i	0.183625	−	0.262244i	−0.716777	−	0.697303i	$-0.754383\pi$
$617$	4.56116	−	6.51401i	0.183625	−	0.262244i	0.900402	+	0.435058i	$0.143272\pi$
$618$	−5.79657	−	7.01084i	−0.233172	−	0.282017i
$619$	−9.06445	+	4.71866i	−0.364331	+	0.189659i	−0.634072	−	0.773274i	$-0.718618\pi$
$619$	−9.06445	+	4.71866i	−0.364331	+	0.189659i	0.269741	+	0.962933i	$0.413062\pi$
$620$	−11.9350	−	12.3938i	−0.479323	−	0.497746i
$621$	−3.64135	−	6.53623i	−0.146122	−	0.262290i
$622$	−0.357863	+	1.71447i	−0.0143490	+	0.0687441i
$623$	41.4700	−	49.4220i	1.66146	−	1.98005i
$624$	−10.0397	+	15.2919i	−0.401908	+	0.612164i
$625$	−2.17387	+	0.383313i	−0.0869550	+	0.0153325i
$626$	−3.21129	−	1.99031i	−0.128349	−	0.0795490i
$627$	−3.35897	+	0.675708i	−0.134145	+	0.0269852i
$628$	3.91811	+	0.767298i	0.156350	+	0.0306185i
$629$	−27.1468	−	35.3784i	−1.08241	−	1.41063i
$630$	26.6877	+	49.2385i	1.06326	+	1.96171i
$631$	−3.80540	+	14.2019i	−0.151490	+	0.565370i	0.847890	+	0.530172i	$0.177873\pi$
$631$	−3.80540	+	14.2019i	−0.151490	+	0.565370i	−0.999380	+	0.0351976i	$0.988794\pi$
$632$	−0.687098	−	1.20805i	−0.0273313	−	0.0480538i
$633$	11.0968	+	25.0720i	0.441058	+	0.996521i
$634$	−9.62732	+	0.962613i	−0.382350	+	0.0382302i
$635$	9.60322	+	30.4575i	0.381092	+	1.20867i
$636$	−12.1084	−	3.17795i	−0.480127	−	0.126014i
$637$	11.9093	−	10.9128i	0.471863	−	0.432383i
$638$	4.69573	−	9.29996i	0.185906	−	0.368189i
$639$	−22.8178	−	43.3728i	−0.902658	−	1.71580i
$640$	−0.0221452	+	41.2357i	−0.000875364	+	1.62998i
$641$	−8.83009	−	1.55698i	−0.348767	−	0.0614971i	−0.00347963	−	0.999994i	$-0.501108\pi$
$641$	−8.83009	−	1.55698i	−0.348767	−	0.0614971i	−0.345288	+	0.938497i	$0.612219\pi$
$642$	0.143309	−	1.03066i	0.00565596	−	0.0406768i
$643$	−0.0218078	−	0.499480i	−0.000860015	−	0.0196976i	0.998570	−	0.0534661i	$-0.0170269\pi$
$643$	−0.0218078	−	0.499480i	−0.000860015	−	0.0196976i	−0.999430	+	0.0337685i	$0.989249\pi$
$644$	−2.44912	+	10.1388i	−0.0965090	+	0.399524i
$645$	34.8584	+	15.2480i	1.37255	+	0.600390i
$646$	−11.8428	+	3.33106i	−0.465947	+	0.131059i
$647$	−10.7672	−	10.7672i	−0.423303	−	0.423303i	0.463036	−	0.886339i	$-0.346760\pi$
$647$	−10.7672	−	10.7672i	−0.423303	−	0.423303i	−0.886339	+	0.463036i	$0.846760\pi$
$648$	−10.7073	+	23.0944i	−0.420623	+	0.907235i
$649$	−8.15869	+	8.15869i	−0.320256	+	0.320256i
$650$	−15.1338	+	26.9790i	−0.593596	+	1.05820i
$651$	−5.93420	+	13.5661i	−0.232580	+	0.531698i
$652$	−1.75245	−	11.1657i	−0.0686312	−	0.437282i
$653$	−24.8191	+	1.08362i	−0.971246	+	0.0424055i	−0.523742	−	0.851877i	$-0.675465\pi$
$653$	−24.8191	+	1.08362i	−0.971246	+	0.0424055i	−0.447504	+	0.894282i	$0.647687\pi$
$654$	−32.2841	+	24.4021i	−1.26241	+	0.954196i
$655$	3.49427	−	19.8170i	0.136532	−	0.774313i
$656$	9.48995	+	5.96700i	0.370520	+	0.232972i
$657$	−1.46812	−	0.926378i	−0.0572767	−	0.0361414i
$658$	−18.9426	−	57.5807i	−0.738459	−	2.24473i
$659$	27.1450	+	29.6236i	1.05742	+	1.15397i	0.987693	+	0.156404i	$0.0499902\pi$
$659$	27.1450	+	29.6236i	1.05742	+	1.15397i	0.0697258	+	0.997566i	$0.477788\pi$
$660$	8.53094	−	11.2366i	0.332067	−	0.437384i
$661$	−3.41554	+	1.07692i	−0.132849	+	0.0418872i	−0.366400	−	0.930457i	$-0.619410\pi$
$661$	−3.41554	+	1.07692i	−0.132849	+	0.0418872i	0.233551	+	0.972345i	$0.424965\pi$
$662$	−22.3448	−	18.2826i	−0.868455	−	0.710572i
$663$	20.5495	−	9.09516i	0.798076	−	0.353227i
$664$	13.7758	−	17.7147i	0.534604	−	0.687464i
$665$	−22.5731	−	6.04845i	−0.875349	−	0.234549i
$666$	27.9480	−	26.4828i	1.08296	−	1.02619i
$667$	−7.53142	+	5.77907i	−0.291618	+	0.223766i
$668$	1.74248	+	8.62636i	0.0674185	+	0.333764i
$669$	3.33894	+	16.5980i	0.129091	+	0.641716i
$670$	5.23486	+	22.3016i	0.202240	+	0.861588i
$671$	2.13916	+	12.1318i	0.0825813	+	0.468342i
$672$	32.8035	−	13.5364i	1.26542	−	0.522177i
$673$	25.0987	+	21.0603i	0.967485	+	0.811816i	0.982154	−	0.188076i	$-0.0602252\pi$
$673$	25.0987	+	21.0603i	0.967485	+	0.811816i	−0.0146695	+	0.999892i	$0.504670\pi$
$674$	−4.11607	−	6.28765i	−0.158545	−	0.242191i
$675$	−15.3406	+	40.2199i	−0.590459	+	1.54806i
$676$	−4.40314	−	11.2241i	−0.169352	−	0.431695i
$677$	−3.42532	−	6.57998i	−0.131646	−	0.252889i	0.812129	−	0.583478i	$-0.198308\pi$
$677$	−3.42532	−	6.57998i	−0.131646	−	0.252889i	−0.943775	+	0.330588i	$0.892753\pi$
$678$	−1.97966	+	20.8803i	−0.0760285	+	0.801905i
$679$	4.46852	+	3.12889i	0.171486	+	0.120076i
$680$	27.4932	−	42.5464i	1.05432	−	1.63158i
$681$	31.0450	+	15.2262i	1.18965	+	0.583469i
$682$	3.72972	−	0.0462132i	0.142818	−	0.00176960i
$683$	24.5714	−	18.8543i	0.940198	−	0.721439i	−0.0202803	−	0.999794i	$-0.506456\pi$
$683$	24.5714	−	18.8543i	0.940198	−	0.721439i	0.960478	+	0.278355i	$0.0897892\pi$
$684$	−3.92189	−	9.87134i	−0.149957	−	0.377440i
$685$	15.5269	−	20.2351i	0.593253	−	0.773142i
$686$	4.47280	−	0.645329i	0.170772	−	0.0246388i
$687$	−30.5018	+	24.5891i	−1.16372	+	0.938133i
$688$	11.9299	−	20.9490i	0.454824	−	0.798673i
$689$	−7.30936	+	6.13328i	−0.278464	+	0.233659i
$690$	−11.4457	+	5.85301i	−0.435729	+	0.222820i
$691$	21.2527	−	19.4745i	0.808492	−	0.740846i	−0.160740	−	0.986997i	$-0.551388\pi$
$691$	21.2527	−	19.4745i	0.808492	−	0.740846i	0.969232	+	0.246151i	$0.0791658\pi$
$692$	36.1404	−	19.9668i	1.37385	−	0.759025i
$693$	−11.7410	−	3.09153i	−0.446002	−	0.117438i
$694$	−21.7578	−	7.61526i	−0.825915	−	0.289071i
$695$	46.5543	+	66.4864i	1.76591	+	2.52197i
$696$	30.9685	+	9.17107i	1.17386	+	0.347629i
$697$	−5.81989	−	12.4808i	−0.220444	−	0.472744i
$698$	38.3604	+	17.3124i	1.45196	+	0.655284i
$699$	15.9621	−	1.78313i	0.603741	−	0.0674440i
$700$	53.7410	−	26.7004i	2.03122	−	1.00918i
$701$	−10.6287	−	25.6599i	−0.401440	−	0.969163i	−0.987317	−	0.158762i	$-0.949250\pi$
$701$	−10.6287	−	25.6599i	−0.401440	−	0.969163i	0.585877	−	0.810400i	$-0.300750\pi$
$702$	9.65209	+	16.8316i	0.364295	+	0.635267i
$703$			16.0657i			0.605931i
$704$	−6.51206	−	6.12394i	−0.245433	−	0.230805i
$705$	38.6189	−	63.9538i	1.45447	−	2.40864i
$706$	−18.4691	+	17.3496i	−0.695092	+	0.652961i
$707$	−63.5983	+	2.77676i	−2.39186	+	0.104431i
$708$	−29.4057	−	20.3661i	−1.10514	−	0.765407i
$709$	4.04677	+	2.57808i	0.151980	+	0.0968217i	0.611104	−	0.791550i	$-0.290726\pi$
$709$	4.04677	+	2.57808i	0.151980	+	0.0968217i	−0.459124	+	0.888372i	$0.651837\pi$
$710$	−75.8684	+	36.5291i	−2.84729	+	1.37091i
$711$	−1.47239	+	0.0706774i	−0.0552191	+	0.00265061i
$712$	4.71547	−	50.1617i	0.176720	−	1.87989i
$713$	−3.08036	−	1.43640i	−0.115361	−	0.0537935i
$714$	−42.8755	−	7.88152i	−1.60458	−	0.294958i
$715$	−3.23359	−	10.2556i	−0.120929	−	0.383539i
$716$	−19.1726	+	15.4813i	−0.716515	+	0.578563i
$717$	−2.61438	−	4.28739i	−0.0976357	−	0.160116i
$718$	32.6355	−	4.70859i	1.21795	−	0.175723i
$719$	−33.6886	+	19.4501i	−1.25637	+	0.725367i	−0.972367	−	0.233456i	$-0.924996\pi$
$719$	−33.6886	+	19.4501i	−1.25637	+	0.725367i	−0.284005	+	0.958823i	$0.591663\pi$
$720$	39.0004	+	19.7965i	1.45346	+	0.737772i
$721$	11.6486	+	6.72532i	0.433817	+	0.250464i
$722$	−20.8347	−	8.32911i	−0.775387	−	0.309977i
$723$	−41.0253	−	13.8272i	−1.52575	−	0.514238i
$724$	22.1735	−	9.83508i	0.824070	−	0.365518i
$725$	53.3216	+	11.8211i	1.98031	+	0.439025i
$726$	−3.97685	−	23.5526i	−0.147595	−	0.874119i
$727$	3.42491	+	39.1469i	0.127023	+	1.45188i	0.745726	+	0.666252i	$0.232103\pi$
$727$	3.42491	+	39.1469i	0.127023	+	1.45188i	−0.618704	+	0.785624i	$0.712342\pi$
$728$	6.02488	−	26.3687i	0.223297	−	0.977290i
$729$	16.7135	+	21.2051i	0.619019	+	0.785376i
$730$	−1.68037	+	2.46424i	−0.0621933	+	0.0912057i
$731$	−26.2692	+	13.6749i	−0.971601	+	0.505783i
$732$	−35.8198	+	13.2458i	−1.32394	+	0.489578i
$733$	−13.3329	−	20.9285i	−0.492463	−	0.773013i	0.503383	−	0.864063i	$-0.332089\pi$
$733$	−13.3329	−	20.9285i	−0.492463	−	0.773013i	−0.995846	+	0.0910509i	$0.970977\pi$
$734$	31.5729	−	7.41110i	1.16538	−	0.273549i
$735$	−29.0915	−	25.4013i	−1.07306	−	0.936942i
$736$	2.92564	+	7.60194i	0.107841	+	0.280211i
$737$	−4.30071	−	2.48302i	−0.158419	−	0.0914631i
$738$	10.1962	−	6.11635i	0.375327	−	0.225146i
$739$	27.5312	−	35.8793i	1.01275	−	1.31984i	0.0660182	−	0.997818i	$-0.478970\pi$
$739$	27.5312	−	35.8793i	1.01275	−	1.31984i	0.946732	−	0.322023i	$-0.104363\pi$
$740$	−43.7648	−	49.6069i	−1.60883	−	1.82358i
$741$	−7.86825	−	1.90730i	−0.289047	−	0.0700663i
$742$	18.4181	−	1.84158i	0.676148	−	0.0676064i
$743$	−47.5190	−	4.15738i	−1.74330	−	0.152519i	−0.829455	−	0.558574i	$-0.811349\pi$
$743$	−47.5190	−	4.15738i	−1.74330	−	0.152519i	−0.913849	+	0.406054i	$0.866904\pi$
$744$	2.20717	+	11.3509i	0.0809188	+	0.416145i
$745$	−23.3957	+	50.1722i	−0.857152	+	1.83817i
$746$	−17.6045	−	20.4600i	−0.644548	−	0.749095i
$747$	−10.1525	−	21.5281i	−0.371459	−	0.787671i
$748$	2.64174	+	10.6590i	0.0965915	+	0.389731i
$749$	0.333014	+	1.50213i	0.0121681	+	0.0548866i
$750$	27.0069	+	11.4170i	0.986152	+	0.416892i
$751$	32.8936	+	11.9723i	1.20031	+	0.436876i	0.863331	−	0.504638i	$-0.168374\pi$
$751$	32.8936	+	11.9723i	1.20031	+	0.436876i	0.336975	+	0.941514i	$0.390596\pi$
$752$	−37.7256	−	28.5943i	−1.37571	−	1.04273i
$753$	−21.2978	+	35.2697i	−0.776135	+	1.28530i
$754$	19.3434	−	15.2272i	0.704447	−	0.554542i
$755$	10.7229	+	25.8874i	0.390247	+	0.942139i
$756$	2.92559	−	37.5254i	0.106403	−	1.36478i
$757$	−10.5521	−	4.37083i	−0.383523	−	0.158860i	0.182588	−	0.983190i	$-0.441553\pi$
$757$	−10.5521	−	4.37083i	−0.383523	−	0.158860i	−0.566111	+	0.824329i	$0.691553\pi$
$758$	−7.45879	−	4.18398i	−0.270915	−	0.151969i
$759$	0.774042	−	2.67719i	0.0280959	−	0.0971757i
$760$	−17.1894	+	6.13091i	−0.623526	+	0.222392i
$761$	−4.18208	+	1.95013i	−0.151600	+	0.0706923i	−0.496938	−	0.867786i	$-0.665542\pi$
$761$	−4.18208	+	1.95013i	−0.151600	+	0.0706923i	0.345337	+	0.938479i	$0.387764\pi$
$762$	5.70531	−	20.6904i	0.206682	−	0.749534i
$763$	32.1507	−	50.4664i	1.16393	−	1.82701i
$764$	7.12891	+	9.66244i	0.257915	+	0.349575i
$765$	−27.0659	−	46.4141i	−0.978570	−	1.67810i
$766$	−24.8623	−	12.5535i	−0.898311	−	0.453575i
$767$	−25.6199	+	9.32487i	−0.925080	+	0.336702i
$768$	15.0719	−	23.2559i	0.543860	−	0.839176i
$769$	5.32131	−	4.46511i	0.191891	−	0.161016i	−0.541780	−	0.840520i	$-0.682249\pi$
$769$	5.32131	−	4.46511i	0.191891	−	0.161016i	0.733672	+	0.679504i	$0.237805\pi$
$770$	−6.02586	+	19.9711i	−0.217157	+	0.719708i
$771$	−13.4875	+	24.7113i	−0.485742	+	0.889956i
$772$	−0.325657	+	5.20485i	−0.0117207	+	0.187327i
$773$	−6.18162	−	46.9541i	−0.222337	−	1.68882i	−0.630721	−	0.776010i	$-0.717241\pi$
$773$	−6.18162	−	46.9541i	−0.222337	−	1.68882i	0.408383	−	0.912811i	$-0.366093\pi$
$774$	−14.0975	−	21.3329i	−0.506724	−	0.766795i
$775$	5.06097	+	18.8878i	0.181795	+	0.678469i
$776$	4.25997	+	0.0275346i	0.152924	+	0.000988434i
$777$	−25.0688	+	51.1132i	−0.899337	+	1.83368i
$778$	53.8028	+	8.80100i	1.92892	+	0.315531i
$779$	−1.07382	+	4.84371i	−0.0384738	+	0.173544i
$780$	29.4908	−	15.5447i	1.05594	−	0.556590i
$781$	5.48913	−	17.4093i	0.196416	−	0.622953i
$782$	2.04458	−	9.79528i	0.0731139	−	0.350279i
$783$	23.5280	−	24.8995i	0.840820	−	0.889836i
$784$	−17.9435	+	16.6389i	−0.640840	+	0.594246i
$785$	−5.57366	−	4.67686i	−0.198933	−	0.166924i
$786$	−9.20858	+	9.90406i	−0.328459	+	0.353266i
$787$	15.1811	+	23.8295i	0.541147	+	0.849431i	0.999220	−	0.0394833i	$-0.0125712\pi$
$787$	15.1811	+	23.8295i	0.541147	+	0.849431i	−0.458073	+	0.888915i	$0.651460\pi$
$788$	−15.4490	+	6.85243i	−0.550347	+	0.244108i
$789$	−41.2899	−	27.4599i	−1.46996	−	0.977598i
$790$	0.0313793	+	2.53252i	0.00111642	+	0.0901029i
$791$	−8.02658	−	29.9556i	−0.285392	−	1.06510i
$792$	−8.91656	+	3.22385i	−0.316836	+	0.114555i
$793$	−7.53399	+	28.1172i	−0.267540	+	0.998472i
$794$	30.2468	+	7.70426i	1.07342	+	0.273414i
$795$	16.5137	+	15.7400i	0.585679	+	0.558240i
$796$	−5.65200	−	3.07904i	−0.200330	−	0.109134i
$797$	−21.7772	−	11.3365i	−0.771388	−	0.401559i	0.0301174	−	0.999546i	$-0.490412\pi$
$797$	−21.7772	−	11.3365i	−0.771388	−	0.401559i	−0.801506	+	0.597987i	$0.795967\pi$
$798$	10.5262	+	11.6561i	0.372624	+	0.412623i
$799$	19.8893	+	54.6454i	0.703633	+	1.93321i
$800$	22.6841	−	41.0067i	0.802005	−	1.44980i
$801$	−45.1940	−	28.5173i	−1.59685	−	1.00761i
$802$	−0.169117	−	3.01555i	−0.00597174	−	0.106483i
$803$	−0.139947	−	0.631260i	−0.00493862	−	0.0222767i
$804$	5.19126	−	14.4937i	0.183082	−	0.511155i
$805$	12.8417	−	14.0142i	0.452610	−	0.493937i
$806$	8.03359	+	3.62563i	0.282971	+	0.127708i
$807$	−31.5861	−	32.8525i	−1.11188	−	1.15646i
$808$	−39.6352	+	30.0081i	−1.39436	+	1.05568i
$809$	4.15945	+	4.15945i	0.146239	+	0.146239i	0.776435	−	0.630197i	$-0.217026\pi$
$809$	4.15945	+	4.15945i	0.146239	+	0.146239i	−0.630197	+	0.776435i	$0.717026\pi$
$810$	37.4320	−	27.4024i	1.31523	−	0.962822i
$811$	10.1262	−	24.4467i	0.355578	−	0.858440i	−0.640333	−	0.768097i	$-0.721204\pi$
$811$	10.1262	−	24.4467i	0.355578	−	0.858440i	0.995911	−	0.0903430i	$-0.0287963\pi$
$812$	−47.6443	+	3.26459i	−1.67199	+	0.114565i
$813$	−19.4201	−	49.6203i	−0.681093	−	1.74026i
$814$	14.3338	+	0.447983i	0.502401	+	0.0157018i
$815$	−7.04465	+	19.3550i	−0.246763	+	0.677977i
$816$	−31.0490	+	13.9628i	−1.08693	+	0.488798i
$817$	10.5075	+	1.85275i	0.367610	+	0.0648196i
$818$	−11.2181	+	12.5511i	−0.392232	+	0.438840i
$819$	−22.0567	−	18.3456i	−0.770725	−	0.641046i
$820$	−9.87908	−	17.8813i	−0.344993	−	0.624443i
$821$	−0.178642	+	4.09158i	−0.00623466	+	0.142797i	0.993376	+	0.114906i	$0.0366568\pi$
$821$	−0.178642	+	4.09158i	−0.00623466	+	0.142797i	−0.999611	+	0.0278907i	$0.991121\pi$
$822$	−16.1498	+	5.74558i	−0.563287	+	0.200400i
$823$	−29.8919	−	2.61520i	−1.04197	−	0.0911602i	−0.446696	−	0.894686i	$-0.647399\pi$
$823$	−29.8919	−	2.61520i	−1.04197	−	0.0911602i	−0.595270	+	0.803526i	$0.702955\pi$
$824$	10.4698	−	0.847840i	0.364734	−	0.0295359i
$825$	−14.6614	+	6.48913i	−0.510446	+	0.225922i
$826$	51.2530	+	13.0548i	1.78332	+	0.454235i
$827$	−6.27779	+	0.826487i	−0.218300	+	0.0287398i	−0.238883	−	0.971048i	$-0.576781\pi$
$827$	−6.27779	+	0.826487i	−0.218300	+	0.0287398i	0.0205827	+	0.999788i	$0.493448\pi$
$828$	8.59487	+	0.877890i	0.298692	+	0.0305088i
$829$	−5.52289	+	41.9505i	−0.191818	+	1.45700i	0.576587	+	0.817036i	$0.304384\pi$
$829$	−5.52289	+	41.9505i	−0.191818	+	1.45700i	−0.768404	+	0.639965i	$0.778949\pi$
$830$	−37.5856	+	16.1169i	−1.30461	+	0.559425i
$831$	28.0043	+	5.50738i	0.971459	+	0.191049i
$832$	−7.83048	−	19.6180i	−0.271473	−	0.680130i
$833$	29.6048	−	5.22012i	1.02574	−	0.180866i
$834$	−1.98359	−	54.5115i	−0.0686861	−	1.88758i
$835$	4.82272	−	15.2957i	0.166897	−	0.529329i
$836$	1.58265	−	3.62596i	0.0547372	−	0.125407i
$837$	11.7970	+	3.35551i	0.407765	+	0.115984i
$838$	26.9177	−	39.4745i	0.929857	−	1.36363i
$839$	0.900965	+	10.2981i	0.0311048	+	0.355529i	0.995758	+	0.0920077i	$0.0293285\pi$
$839$	0.900965	+	10.2981i	0.0311048	+	0.355529i	−0.964654	+	0.263522i	$0.915116\pi$
$840$	−64.2548	−	7.31663i	−2.21700	−	0.252448i
$841$	−11.8489	−	8.29667i	−0.408582	−	0.286092i
$842$	3.94719	−	24.1302i	0.136029	−	0.831581i
$843$	17.2767	+	1.09480i	0.595040	+	0.0377069i
$844$	−31.0693	−	6.08442i	−1.06945	−	0.209434i
$845$	−2.86794	+	21.7842i	−0.0986601	+	0.749398i
$846$	−45.1438	+	21.9772i	−1.55208	+	0.755592i
$847$	17.6590	+	30.5863i	0.606771	+	1.05096i
$848$	11.0180	−	9.35700i	0.378358	−	0.321321i
$849$	2.35758	+	2.92449i	0.0809121	+	0.100368i
$850$	−50.7310	+	27.2130i	−1.74006	+	0.933399i
$851$	−11.5910	−	6.03389i	−0.397334	−	0.206839i
$852$	56.1434	+	7.09866i	1.92344	+	0.243196i
$853$	47.7577	+	2.08514i	1.63519	+	0.0713940i	0.842663	−	0.538441i	$-0.180987\pi$
$853$	47.7577	+	2.08514i	1.63519	+	0.0713940i	0.792528	+	0.609835i	$0.208764\pi$
$854$	42.8045	−	36.8305i	1.46474	−	1.26031i
$855$	−2.44345	+	19.2023i	−0.0835644	+	0.656704i
$856$	0.880610	+	0.817464i	0.0300986	+	0.0279403i
$857$	−3.46401	−	4.94712i	−0.118328	−	0.168991i	0.755618	−	0.655012i	$-0.227337\pi$
$857$	−3.46401	−	4.94712i	−0.118328	−	0.168991i	−0.873947	+	0.486022i	$0.838448\pi$
$858$	−1.92109	+	6.96686i	−0.0655849	+	0.237845i
$859$	17.3857	+	15.9311i	0.593193	+	0.543562i	0.915109	−	0.403207i	$-0.132104\pi$
$859$	17.3857	+	15.9311i	0.593193	+	0.543562i	−0.321915	+	0.946768i	$0.604327\pi$
$860$	−37.4915	+	22.9027i	−1.27845	+	0.780975i
$861$	−10.9744	+	13.7347i	−0.374008	+	0.468077i
$862$	2.64725	−	22.2331i	0.0901656	−	0.757263i
$863$	−23.0232			−0.783719			−0.391860	−	0.920025i	$-0.628168\pi$
$863$	−23.0232			−0.783719			−0.391860	+	0.920025i	$0.628168\pi$
$864$	−14.7732	−	25.4117i	−0.502593	−	0.864523i
$865$	−75.2445			−2.55839
$866$	−1.78811	+	15.0176i	−0.0607625	+	0.510319i
$867$	12.2369	+	1.85632i	0.415587	+	0.0630439i
$868$	−8.91323	−	14.5909i	−0.302535	−	0.495247i
$869$	−0.404802	−	0.370933i	−0.0137320	−	0.0125830i
$870$	−41.3163	−	41.9207i	−1.40075	−	1.42124i
$871$	−6.73065	−	9.61236i	−0.228059	−	0.325702i
$872$	−1.73652	−	46.6970i	−0.0588059	−	1.58136i
$873$	2.06902	−	4.01693i	0.0700256	−	0.135953i
$874$	−2.73268	+	2.35130i	−0.0924343	+	0.0795338i
$875$	−43.3130	−	1.89109i	−1.46425	−	0.0639304i
$876$	1.84797	−	0.776581i	0.0624370	−	0.0262382i
$877$	3.76336	+	1.95908i	0.127080	+	0.0661534i	0.524102	−	0.851655i	$-0.324401\pi$
$877$	3.76336	+	1.95908i	0.127080	+	0.0661534i	−0.397023	+	0.917809i	$0.629957\pi$
$878$	−22.9175	+	12.2934i	−0.773430	+	0.414881i
$879$	45.6061	−	7.12059i	1.53825	−	0.240172i
$880$	4.99068	+	15.5073i	0.168236	+	0.522752i
$881$	−6.40101	−	11.0869i	−0.215656	−	0.373527i	0.737820	−	0.674998i	$-0.235856\pi$
$881$	−6.40101	−	11.0869i	−0.215656	−	0.373527i	−0.953475	+	0.301471i	$0.902522\pi$
$882$	7.13598	+	24.9550i	0.240281	+	0.840279i
$883$	−2.33252	+	17.7173i	−0.0784956	+	0.596233i	0.906315	+	0.422602i	$0.138883\pi$
$883$	−2.33252	+	17.7173i	−0.0784956	+	0.596233i	−0.984811	+	0.173631i	$0.944450\pi$
$884$	−4.98691	+	25.4650i	−0.167728	+	0.856482i
$885$	28.9576	+	58.4010i	0.973399	+	1.96313i
$886$	3.88570	−	23.7543i	0.130543	−	0.798040i
$887$	−23.9304	−	16.7562i	−0.803503	−	0.562619i	0.0981033	−	0.995176i	$-0.468722\pi$
$887$	−23.9304	−	16.7562i	−0.803503	−	0.562619i	−0.901606	+	0.432557i	$0.857611\pi$
$888$	6.57429	+	43.9698i	0.220619	+	1.47553i
$889$	2.76587	+	31.6141i	0.0927643	+	1.06030i
$890$	−51.7279	+	75.8584i	−1.73392	+	2.54278i
$891$	−1.22623	+	9.98158i	−0.0410801	+	0.334396i
$892$	−17.9173	−	7.82051i	−0.599915	−	0.261850i
$893$	6.29998	−	19.9810i	0.210821	−	0.668638i
$894$	31.5222	−	19.7616i	1.05426	−	0.660926i
$895$	44.2260	−	7.79823i	1.47831	−	0.260666i
$896$	−8.89040	+	40.0004i	−0.297008	+	1.33632i
$897$	4.33118	−	4.96039i	0.144614	−	0.165623i
$898$	10.9761	−	4.70659i	0.366276	−	0.157061i
$899$	2.03119	−	15.4284i	0.0677441	−	0.514567i
$900$	−27.9156	−	41.1260i	−0.930520	−	1.37087i
$901$	−17.6055	+	2.31781i	−0.586526	+	0.0772176i
$902$	4.29161	+	1.09313i	0.142895	+	0.0363972i
$903$	30.5386	+	22.2903i	1.01626	+	0.741774i
$904$	−18.4516	−	15.6870i	−0.613690	−	0.521743i
$905$	−44.0368	−	3.85272i	−1.46383	−	0.128069i
$906$	3.40459	−	18.5210i	0.113110	−	0.615319i
$907$	1.98764	−	45.5245i	0.0659986	−	1.51162i	−0.620340	−	0.784333i	$-0.713005\pi$
$907$	1.98764	−	45.5245i	0.0659986	−	1.51162i	0.686338	−	0.727283i	$-0.259217\pi$
$908$	−34.9480	+	19.3081i	−1.15979	+	0.640762i
$909$	9.38118	+	51.8880i	0.311154	+	1.72101i
$910$	−32.8485	+	36.7518i	−1.08892	+	1.21831i
$911$	−19.5638	−	3.44963i	−0.648178	−	0.114291i	−0.160113	−	0.987099i	$-0.551186\pi$
$911$	−19.5638	−	3.44963i	−0.648178	−	0.114291i	−0.488065	+	0.872807i	$0.662297\pi$
$912$	11.9368	+	2.81874i	0.395268	+	0.0933378i
$913$	3.03216	−	8.33078i	0.100350	−	0.275709i
$914$	14.1824	+	0.443248i	0.469111	+	0.0146614i
$915$	68.8101	+	10.4384i	2.27479	+	0.345082i
$916$	−3.09259	−	45.1341i	−0.102182	−	1.49127i
$917$	7.65220	−	18.4740i	0.252698	−	0.610067i
$918$	−1.68072	+	36.0701i	−0.0554721	+	1.19049i
$919$	−37.8217	−	37.8217i	−1.24762	−	1.24762i	−0.956766	−	0.290858i	$-0.906059\pi$
$919$	−37.8217	−	37.8217i	−1.24762	−	1.24762i	−0.290858	−	0.956766i	$-0.593941\pi$
$920$	2.03263	−	14.7043i	0.0670139	−	0.484787i
$921$	2.36646	−	8.18491i	0.0779776	−	0.269702i
$922$	−32.4528	−	14.6463i	−1.06878	−	0.482349i
$923$	29.1408	−	31.8016i	0.959180	−	1.04676i
$924$	10.6931	−	9.06646i	0.351778	−	0.298265i
$925$	16.2719	+	73.3980i	0.535018	+	2.41331i
$926$	−0.172401	−	3.07410i	−0.00566545	−	0.101021i
$927$	4.21896	−	10.3116i	0.138569	−	0.338677i
$928$	−29.1669	+	23.2415i	−0.957449	+	0.762940i
$929$	4.64352	+	12.7580i	0.152349	+	0.418576i	0.992265	−	0.124142i	$-0.0396177\pi$
$929$	4.64352	+	12.7580i	0.152349	+	0.418576i	−0.839915	+	0.542717i	$0.817395\pi$
$930$	6.48256	−	20.0512i	0.212572	−	0.657506i
$931$	−9.60658	−	5.00087i	−0.314843	−	0.163897i
$932$	−8.87223	+	16.2862i	−0.290620	+	0.533472i
$933$	−2.05805	+	0.604705i	−0.0673774	+	0.0197971i
$934$	−25.9637	−	6.61329i	−0.849558	−	0.216394i
$935$	5.17959	−	19.3305i	0.169391	−	0.632174i
$936$	−22.3148	−	2.00024i	−0.729384	−	0.0653799i
$937$	−2.42840	−	9.06291i	−0.0793324	−	0.296072i	0.914848	−	0.403798i	$-0.132310\pi$
$937$	−2.42840	−	9.06291i	−0.0793324	−	0.296072i	−0.994181	+	0.107725i	$0.965643\pi$
$938$	0.282034	+	22.7620i	0.00920873	+	0.743206i
$939$	0.292629	−	4.61789i	0.00954960	−	0.150699i
$940$	34.9776	+	78.8579i	1.14084	+	2.57206i
$941$	−20.7113	−	32.5102i	−0.675168	−	1.05980i	−0.993720	−	0.111896i	$-0.964308\pi$
$941$	−20.7113	−	32.5102i	−0.675168	−	1.05980i	0.318552	−	0.947905i	$-0.396803\pi$
$942$	1.43650	+	4.67407i	0.0468038	+	0.152289i
$943$	−3.09130	−	2.59391i	−0.100667	−	0.0844693i
$944$	38.7281	−	14.3564i	1.26049	−	0.467260i
$945$	−37.7368	+	57.2793i	−1.22758	+	1.86330i
$946$	1.94602	−	9.32311i	0.0632705	−	0.303120i
$947$	−4.76256	+	15.1049i	−0.154762	+	0.490843i	−0.998980	−	0.0451574i	$-0.985621\pi$
$947$	−4.76256	+	15.1049i	−0.154762	+	0.490843i	0.844218	+	0.536001i	$0.180066\pi$
$948$	0.907179	−	1.44023i	0.0294638	−	0.0467766i
$949$	0.330689	−	1.49164i	0.0107346	−	0.0484207i
$950$	20.4684	+	3.34820i	0.664083	+	0.108630i
$951$	−6.60472	−	9.83847i	−0.214173	−	0.319034i
$952$	35.8236	−	35.3635i	1.16105	−	1.14614i
$953$	−4.05100	−	15.1185i	−0.131225	−	0.489737i	0.868760	−	0.495233i	$-0.164917\pi$
$953$	−4.05100	−	15.1185i	−0.131225	−	0.489737i	−0.999985	+	0.00549571i	$0.998251\pi$
$954$	−3.56825	−	14.9109i	−0.115526	−	0.482758i
$955$	−2.85624	−	21.6953i	−0.0924258	−	0.702043i
$956$	5.78716	+	0.362091i	0.187170	+	0.0117109i
$957$	12.7560	−	0.305979i	0.412343	−	0.00989089i
$958$	−12.4559	+	41.2816i	−0.402431	+	1.33375i
$959$	19.4157	−	16.2917i	0.626965	−	0.526086i
$960$	−44.5363	+	23.8136i	−1.43740	+	0.768581i
$961$	−23.8950	+	8.69707i	−0.770807	+	0.280551i
$962$	30.2495	+	15.2736i	0.975284	+	0.492440i
$963$	1.19568	−	0.441066i	0.0385302	−	0.0142132i
$964$	40.2265	−	29.6790i	1.29561	−	0.955896i
$965$	5.10636	−	8.01538i	0.164379	−	0.258024i
$966$	−12.3630	+	3.21662i	−0.397772	+	0.103493i
$967$	−20.3439	+	9.48651i	−0.654215	+	0.305065i	−0.721239	−	0.692686i	$-0.756427\pi$
$967$	−20.3439	+	9.48651i	−0.654215	+	0.305065i	0.0670244	+	0.997751i	$0.478649\pi$
$968$	24.9212	+	11.8176i	0.800996	+	0.379833i
$969$	−10.4427	−	10.8614i	−0.335468	−	0.348919i
$970$	−6.77091	−	3.79812i	−0.217401	−	0.121950i
$971$	−21.9957	−	9.11093i	−0.705876	−	0.292384i	0.000720659	−	1.00000i	$-0.499771\pi$
$971$	−21.9957	−	9.11093i	−0.705876	−	0.292384i	−0.706597	+	0.707616i	$0.749771\pi$
$972$	−31.1255	+	1.78937i	−0.998352	+	0.0573941i
$973$	30.8652	+	74.5152i	0.989493	+	2.38885i
$974$	7.01195	−	5.51982i	0.224677	−	0.176867i
$975$	−37.8787	−	0.744441i	−1.21309	−	0.0238412i
$976$	11.1609	−	42.6627i	0.357251	−	1.36560i
$977$	47.3733	+	17.2425i	1.51561	+	0.551636i	0.960047	−	0.279840i	$-0.0902815\pi$
$977$	47.3733	+	17.2425i	1.51561	+	0.551636i	0.555561	+	0.831476i	$0.312504\pi$
$978$	11.0429	−	8.34683i	0.353113	−	0.266902i
$979$	−4.30808	−	19.4325i	−0.137687	−	0.621065i
$980$	43.2855	−	10.7279i	1.38271	−	0.342692i
$981$	−45.0105	−	20.7518i	−1.43707	−	0.662555i
$982$	0.822238	+	0.955606i	0.0262387	+	0.0304946i
$983$	3.29989	−	7.07663i	0.105250	−	0.225710i	−0.846629	−	0.532184i	$-0.821372\pi$
$983$	3.29989	−	7.07663i	0.105250	−	0.225710i	0.951879	+	0.306474i	$0.0991493\pi$
$984$	−0.956815	+	13.6960i	−0.0305021	+	0.436613i
$985$	30.6819	+	2.68432i	0.977607	+	0.0855295i
$986$	45.5874	−	4.55817i	1.45180	−	0.145162i
$987$	51.2215	−	53.7392i	1.63040	−	1.71054i
$988$	7.01035	−	6.18476i	0.223029	−	0.196763i
$989$	−5.28306	+	6.88501i	−0.167991	+	0.218931i
$990$	17.0641	+	2.71549i	0.542333	+	0.0863039i
$991$	0.461237	+	0.266295i	0.0146517	+	0.00845914i	0.507308	−	0.861765i	$-0.330641\pi$
$991$	0.461237	+	0.266295i	0.0146517	+	0.00845914i	−0.492656	+	0.870224i	$0.663974\pi$
$992$	−12.2027	−	5.42038i	−0.387437	−	0.172097i
$993$	6.82322	−	34.6952i	0.216528	−	1.10102i
$994$	−81.4610	+	19.1213i	−2.58379	+	0.606492i
$995$	6.30216	+	9.89241i	0.199792	+	0.313610i
$996$	27.0907	+	4.63367i	0.858400	+	0.146824i
$997$	−48.8415	+	25.4253i	−1.54682	+	0.805226i	−0.999498	−	0.0316930i	$-0.989910\pi$
$997$	−48.8415	+	25.4253i	−1.54682	+	0.805226i	−0.547327	+	0.836919i	$0.684355\pi$
$998$	5.77574	−	8.47006i	0.182828	−	0.268115i
$999$	44.7505	+	14.8672i	1.41584	+	0.470377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bt.a.11.6	✓	3408
27.5	odd	18	inner	864.2.bt.a.491.85	yes	3408
32.3	odd	8	inner	864.2.bt.a.227.85	yes	3408
864.707	even	72	inner	864.2.bt.a.707.6	yes	3408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bt.a.11.6	✓	3408	1.1	even	1	trivial
864.2.bt.a.227.85	yes	3408	32.3	odd	8	inner
864.2.bt.a.491.85	yes	3408	27.5	odd	18	inner
864.2.bt.a.707.6	yes	3408	864.707	even	72	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bt (of order \(72\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40429 - 0.167206i) q^{2} +(-0.631256 - 1.61292i) q^{3} +(1.94408 + 0.469613i) q^{4} +(-2.68720 - 2.46236i) q^{5} +(0.616779 + 2.37057i) q^{6} +(-2.07740 - 2.96684i) q^{7} +(-2.65154 - 0.984538i) q^{8} +(-2.20303 + 2.03633i) q^{9} +O(q^{10})\)	\(q+(-1.40429 - 0.167206i) q^{2} +(-0.631256 - 1.61292i) q^{3} +(1.94408 + 0.469613i) q^{4} +(-2.68720 - 2.46236i) q^{5} +(0.616779 + 2.37057i) q^{6} +(-2.07740 - 2.96684i) q^{7} +(-2.65154 - 0.984538i) q^{8} +(-2.20303 + 2.03633i) q^{9} +(3.36189 + 3.90719i) q^{10} +(-1.11634 - 0.0487404i) q^{11} +(-0.469766 - 3.43210i) q^{12} +(-2.34204 - 1.21919i) q^{13} +(2.42121 + 4.51367i) q^{14} +(-2.27529 + 5.88861i) q^{15} +(3.55893 + 1.82593i) q^{16} +(-2.45692 - 4.25551i) q^{17} +(3.43419 - 2.49125i) q^{18} +(-0.231073 + 1.75517i) q^{19} +(-4.06778 - 6.04898i) q^{20} +(-3.47390 + 5.22352i) q^{21} +(1.55952 + 0.255104i) q^{22} +(-1.17952 - 0.825910i) q^{23} +(0.0858207 + 4.89823i) q^{24} +(0.722019 + 8.25271i) q^{25} +(3.08506 + 2.10370i) q^{26} +(4.67512 + 2.26787i) q^{27} +(-2.64538 - 6.74335i) q^{28} +(1.98249 - 6.28765i) q^{29} +(4.17978 - 7.88891i) q^{30} +(2.32454 - 0.409878i) q^{31} +(-4.69247 - 3.15922i) q^{32} +(0.626081 + 1.83133i) q^{33} +(2.73869 + 6.38680i) q^{34} +(-1.72304 + 13.0878i) q^{35} +(-5.23917 + 2.92423i) q^{36} +(8.99744 - 1.18453i) q^{37} +(0.617969 - 2.42614i) q^{38} +(-0.488029 + 4.54715i) q^{39} +(4.70093 + 9.17470i) q^{40} +(2.79184 + 0.244254i) q^{41} +(5.75179 - 6.75450i) q^{42} +(0.262891 - 6.02120i) q^{43} +(-2.14737 - 0.619003i) q^{44} +(10.9342 - 0.0473637i) q^{45} +(1.51830 + 1.35704i) q^{46} +(-11.6546 - 2.05502i) q^{47} +(0.698496 - 6.89290i) q^{48} +(-2.09238 + 5.74877i) q^{49} +(0.365977 - 11.7100i) q^{50} +(-5.31286 + 6.64913i) q^{51} +(-3.98058 - 3.47006i) q^{52} +(1.38293 - 3.33868i) q^{53} +(-6.18604 - 3.96647i) q^{54} +(2.87980 + 2.87980i) q^{55} +(2.58736 + 9.91198i) q^{56} +(2.97682 - 0.735260i) q^{57} +(-3.83533 + 8.49823i) q^{58} +(6.97604 - 7.61301i) q^{59} +(-7.18872 + 10.3795i) q^{60} +(-2.38616 - 10.7633i) q^{61} +(-3.33287 + 0.186913i) q^{62} +(10.6180 + 2.30576i) q^{63} +(6.06137 + 5.22109i) q^{64} +(3.29144 + 9.04315i) q^{65} +(-0.572992 - 2.67642i) q^{66} +(3.94211 + 2.05213i) q^{67} +(-2.77802 - 9.42687i) q^{68} +(-0.587548 + 2.42384i) q^{69} +(4.60801 - 18.0910i) q^{70} +(-4.22813 + 15.7796i) q^{71} +(7.84628 - 3.23046i) q^{72} +(0.149766 + 0.558935i) q^{73} +(-12.8331 + 0.159009i) q^{74} +(12.8552 - 6.37413i) q^{75} +(-1.27348 + 3.30369i) q^{76} +(2.17448 + 3.41325i) q^{77} +(1.44565 - 6.30393i) q^{78} +(0.376406 + 0.315842i) q^{79} +(-5.06742 - 13.6700i) q^{80} +(0.706699 - 8.97221i) q^{81} +(-3.87972 - 0.809817i) q^{82} +(-2.38579 + 7.56676i) q^{83} +(-9.20659 + 8.52357i) q^{84} +(-3.87638 + 17.4852i) q^{85} +(-1.37596 + 8.41158i) q^{86} +(-11.3929 + 0.771518i) q^{87} +(2.91203 + 1.22831i) q^{88} +(4.61035 + 17.2061i) q^{89} +(-15.3627 - 1.76175i) q^{90} +(1.24822 + 9.48120i) q^{91} +(-1.90523 - 2.15956i) q^{92} +(-2.12848 - 3.49055i) q^{93} +(16.0229 + 4.83458i) q^{94} +(4.94280 - 4.14750i) q^{95} +(-2.13343 + 9.56287i) q^{96} +(-1.41533 + 0.515136i) q^{97} +(3.89955 - 7.72311i) q^{98} +(2.55858 - 2.16586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 36 q^{8} - 24 q^{9}+O(q^{10}) \) 3408 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 36 * q^8 - 24 * q^9	\( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 36 q^{8} - 24 q^{9} - 12 q^{10} - 24 q^{11} - 24 q^{12} - 24 q^{13} - 24 q^{14} - 48 q^{15} - 24 q^{16} - 24 q^{18} - 12 q^{19} - 24 q^{20} - 24 q^{21} - 24 q^{22} - 24 q^{23} - 84 q^{24} - 24 q^{25} - 24 q^{27} - 48 q^{28} - 24 q^{29} - 24 q^{30} - 24 q^{32} - 48 q^{33} - 36 q^{35} - 24 q^{36} - 12 q^{37} - 24 q^{38} - 24 q^{39} - 24 q^{40} - 24 q^{41} + 96 q^{42} - 24 q^{43} - 36 q^{44} - 24 q^{45} - 12 q^{46} - 48 q^{47} - 24 q^{48} - 336 q^{50} + 12 q^{51} - 24 q^{52} - 24 q^{54} - 48 q^{55} - 24 q^{56} - 24 q^{57} - 132 q^{58} - 24 q^{59} - 24 q^{60} - 24 q^{61} - 36 q^{62} - 12 q^{64} - 48 q^{65} - 216 q^{66} - 24 q^{67} + 24 q^{68} - 24 q^{69} - 24 q^{70} - 36 q^{71} - 24 q^{72} - 12 q^{73} - 24 q^{74} - 24 q^{75} - 24 q^{76} - 24 q^{77} - 24 q^{78} - 48 q^{79} - 48 q^{82} + 96 q^{83} + 204 q^{84} + 36 q^{85} - 24 q^{86} - 24 q^{87} - 24 q^{88} - 36 q^{89} - 24 q^{90} - 12 q^{91} - 252 q^{92} - 24 q^{93} - 24 q^{94} - 24 q^{96} - 48 q^{97} - 36 q^{98} - 24 q^{99}+O(q^{100}) \) 3408 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 36 * q^8 - 24 * q^9 - 12 * q^10 - 24 * q^11 - 24 * q^12 - 24 * q^13 - 24 * q^14 - 48 * q^15 - 24 * q^16 - 24 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^21 - 24 * q^22 - 24 * q^23 - 84 * q^24 - 24 * q^25 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^30 - 24 * q^32 - 48 * q^33 - 36 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^38 - 24 * q^39 - 24 * q^40 - 24 * q^41 + 96 * q^42 - 24 * q^43 - 36 * q^44 - 24 * q^45 - 12 * q^46 - 48 * q^47 - 24 * q^48 - 336 * q^50 + 12 * q^51 - 24 * q^52 - 24 * q^54 - 48 * q^55 - 24 * q^56 - 24 * q^57 - 132 * q^58 - 24 * q^59 - 24 * q^60 - 24 * q^61 - 36 * q^62 - 12 * q^64 - 48 * q^65 - 216 * q^66 - 24 * q^67 + 24 * q^68 - 24 * q^69 - 24 * q^70 - 36 * q^71 - 24 * q^72 - 12 * q^73 - 24 * q^74 - 24 * q^75 - 24 * q^76 - 24 * q^77 - 24 * q^78 - 48 * q^79 - 48 * q^82 + 96 * q^83 + 204 * q^84 + 36 * q^85 - 24 * q^86 - 24 * q^87 - 24 * q^88 - 36 * q^89 - 24 * q^90 - 12 * q^91 - 252 * q^92 - 24 * q^93 - 24 * q^94 - 24 * q^96 - 48 * q^97 - 36 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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