LMFDB - Embedded newform 576.2.bm.a.205.75

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(13,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 45, 16]))

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

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

chi := DirichletCharacter("576.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bm (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$1504$
Relative dimension:	$94$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			205.75
Character	$\chi$	$=$	576.205
Dual form			576.2.bm.a.517.75

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08644 + 0.905346i) q^{2} +(0.0543260 - 1.73120i) q^{3} +(0.360696 + 1.96721i) q^{4} +(-2.37549 - 2.70873i) q^{5} +(1.62636 - 1.83166i) q^{6} +(0.599302 + 0.0788996i) q^{7} +(-1.38913 + 2.46380i) q^{8} +(-2.99410 - 0.188098i) q^{9} +O(q^{10})$	\(q+(1.08644 + 0.905346i) q^{2} +(0.0543260 - 1.73120i) q^{3} +(0.360696 + 1.96721i) q^{4} +(-2.37549 - 2.70873i) q^{5} +(1.62636 - 1.83166i) q^{6} +(0.599302 + 0.0788996i) q^{7} +(-1.38913 + 2.46380i) q^{8} +(-2.99410 - 0.188098i) q^{9} +(-0.128487 - 5.09351i) q^{10} +(-2.82339 - 5.72527i) q^{11} +(3.42522 - 0.517566i) q^{12} +(0.527748 + 1.55469i) q^{13} +(0.579673 + 0.628295i) q^{14} +(-4.81840 + 3.96529i) q^{15} +(-3.73980 + 1.41913i) q^{16} +(-2.48259 - 2.48259i) q^{17} +(-3.08261 - 2.91505i) q^{18} +(-0.360105 + 1.81037i) q^{19} +(4.47179 - 5.65010i) q^{20} +(0.169149 - 1.03322i) q^{21} +(2.11591 - 8.77629i) q^{22} +(-0.431997 - 3.28134i) q^{23} +(4.18987 + 2.53871i) q^{24} +(-1.04162 + 7.91188i) q^{25} +(-0.834172 + 2.16687i) q^{26} +(-0.488293 + 5.17316i) q^{27} +(0.0609541 + 1.20741i) q^{28} +(7.89106 - 0.517207i) q^{29} +(-8.82485 - 0.0542735i) q^{30} +(2.49879 - 1.44268i) q^{31} +(-5.34786 - 1.84402i) q^{32} +(-10.0650 + 4.57682i) q^{33} +(-0.449578 - 4.94479i) q^{34} +(-1.20992 - 1.81077i) q^{35} +(-0.709931 - 5.95785i) q^{36} +(-1.97845 - 9.94633i) q^{37} +(-2.03024 + 1.64083i) q^{38} +(2.72016 - 0.829176i) q^{39} +(9.97363 - 2.08997i) q^{40} +(0.516405 + 3.92249i) q^{41} +(1.11920 - 0.969396i) q^{42} +(6.04673 - 2.98192i) q^{43} +(10.2444 - 7.61927i) q^{44} +(6.60294 + 8.55702i) q^{45} +(2.50141 - 3.95608i) q^{46} +(1.06439 - 0.285202i) q^{47} +(2.25362 + 6.55143i) q^{48} +(-6.40854 - 1.71716i) q^{49} +(-8.29465 + 7.65274i) q^{50} +(-4.43273 + 4.16299i) q^{51} +(-2.86805 + 1.59896i) q^{52} +(0.409002 - 0.612115i) q^{53} +(-5.21400 + 5.17824i) q^{54} +(-8.80125 + 21.2481i) q^{55} +(-1.02690 + 1.36696i) q^{56} +(3.11454 + 0.721763i) q^{57} +(9.04140 + 6.58222i) q^{58} +(6.59875 + 7.52443i) q^{59} +(-9.53852 - 8.04851i) q^{60} +(-0.876809 - 13.3775i) q^{61} +(4.02090 + 0.694891i) q^{62} +(-1.77953 - 0.348961i) q^{63} +(-4.14064 - 6.84508i) q^{64} +(2.95758 - 5.12269i) q^{65} +(-15.0786 - 4.13984i) q^{66} +(8.66852 + 4.27484i) q^{67} +(3.98831 - 5.77924i) q^{68} +(-5.70412 + 0.569610i) q^{69} +(0.324873 - 3.06268i) q^{70} +(0.0723646 + 0.174704i) q^{71} +(4.62262 - 7.11557i) q^{72} +(-2.42727 + 5.85995i) q^{73} +(6.85541 - 12.5973i) q^{74} +(13.6405 + 2.23307i) q^{75} +(-3.69125 - 0.0554071i) q^{76} +(-1.24034 - 3.65393i) q^{77} +(3.70597 + 1.56183i) q^{78} +(1.21604 + 4.53833i) q^{79} +(12.7279 + 6.75897i) q^{80} +(8.92924 + 1.12637i) q^{81} +(-2.99017 + 4.72907i) q^{82} +(7.35100 + 6.44666i) q^{83} +(2.09358 - 0.0399300i) q^{84} +(-0.827293 + 12.6220i) q^{85} +(9.26907 + 2.23472i) q^{86} +(-0.466698 - 13.6891i) q^{87} +(18.0280 + 0.996858i) q^{88} +(-4.84513 + 2.00692i) q^{89} +(-0.573377 + 15.2746i) q^{90} +(0.193615 + 0.973370i) q^{91} +(6.29925 - 2.03339i) q^{92} +(-2.36181 - 4.40428i) q^{93} +(1.41460 + 0.653786i) q^{94} +(5.75922 - 3.32509i) q^{95} +(-3.48289 + 9.15803i) q^{96} +(-10.5978 - 6.11862i) q^{97} +(-5.40786 - 7.66754i) q^{98} +(7.37659 + 17.6731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{15}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.08644	+	0.905346i	0.768228	+	0.640177i
$2$	1.08644	+	0.905346i	0.768228	+	0.640177i
$3$	0.0543260	−	1.73120i	0.0313652	−	0.999508i
$3$	0.0543260	−	1.73120i	0.0313652	−	0.999508i
$4$	0.360696	+	1.96721i	0.180348	+	0.983603i
$5$	−2.37549	−	2.70873i	−1.06235	−	1.21138i	−0.976600	−	0.215063i	$-0.931004\pi$
$5$	−2.37549	−	2.70873i	−1.06235	−	1.21138i	−0.0857511	−	0.996317i	$-0.527329\pi$
$6$	1.62636	−	1.83166i	0.663957	−	0.747771i
$7$	0.599302	+	0.0788996i	0.226515	+	0.0298212i	0.242929	−	0.970044i	$-0.421892\pi$
$7$	0.599302	+	0.0788996i	0.226515	+	0.0298212i	−0.0164144	+	0.999865i	$0.505225\pi$
$8$	−1.38913	+	2.46380i	−0.491131	+	0.871086i
$9$	−2.99410	−	0.188098i	−0.998032	−	0.0626994i
$10$	−0.128487	−	5.09351i	−0.0406312	−	1.61071i
$11$	−2.82339	−	5.72527i	−0.851284	−	1.72623i	−0.669385	−	0.742916i	$-0.733442\pi$
$11$	−2.82339	−	5.72527i	−0.851284	−	1.72623i	−0.181899	−	0.983317i	$-0.558224\pi$
$12$	3.42522	−	0.517566i	0.988776	−	0.149408i
$13$	0.527748	+	1.55469i	0.146371	+	0.431195i	0.995245	−	0.0973998i	$-0.0310526\pi$
$13$	0.527748	+	1.55469i	0.146371	+	0.431195i	−0.848874	+	0.528595i	$0.822719\pi$
$14$	0.579673	+	0.628295i	0.154924	+	0.167919i
$15$	−4.81840	+	3.96529i	−1.24410	+	1.02383i
$16$	−3.73980	+	1.41913i	−0.934949	+	0.354782i
$17$	−2.48259	−	2.48259i	−0.602118	−	0.602118i	0.338756	−	0.940874i	$-0.389994\pi$
$17$	−2.48259	−	2.48259i	−0.602118	−	0.602118i	−0.940874	+	0.338756i	$0.889994\pi$
$18$	−3.08261	−	2.91505i	−0.726578	−	0.687084i
$19$	−0.360105	+	1.81037i	−0.0826137	+	0.415327i	0.917242	+	0.398331i	$0.130410\pi$
$19$	−0.360105	+	1.81037i	−0.0826137	+	0.415327i	−0.999856	+	0.0169963i	$0.994590\pi$
$20$	4.47179	−	5.65010i	0.999923	−	1.26340i
$21$	0.169149	−	1.03322i	0.0369112	−	0.225468i
$22$	2.11591	−	8.77629i	0.451114	−	1.87111i
$23$	−0.431997	−	3.28134i	−0.0900775	−	0.684207i	−0.975591	−	0.219594i	$-0.929527\pi$
$23$	−0.431997	−	3.28134i	−0.0900775	−	0.684207i	0.885514	−	0.464613i	$-0.153807\pi$
$24$	4.18987	+	2.53871i	0.855253	+	0.518211i
$25$	−1.04162	+	7.91188i	−0.208324	+	1.58238i
$26$	−0.834172	+	2.16687i	−0.163595	+	0.424959i
$27$	−0.488293	+	5.17316i	−0.0939720	+	0.995575i
$28$	0.0609541	+	1.20741i	0.0115192	+	0.228179i
$29$	7.89106	−	0.517207i	1.46533	−	0.0960430i	0.688264	−	0.725460i	$-0.258373\pi$
$29$	7.89106	−	0.517207i	1.46533	−	0.0960430i	0.777068	+	0.629417i	$0.216706\pi$
$30$	−8.82485	−	0.0542735i	−1.61119	−	0.00990893i
$31$	2.49879	−	1.44268i	0.448796	−	0.259112i	−0.258526	−	0.966004i	$-0.583237\pi$
$31$	2.49879	−	1.44268i	0.448796	−	0.259112i	0.707322	+	0.706892i	$0.249903\pi$
$32$	−5.34786	−	1.84402i	−0.945377	−	0.325979i
$33$	−10.0650	+	4.57682i	−1.75208	+	0.796722i
$34$	−0.449578	−	4.94479i	−0.0771020	−	0.848025i
$35$	−1.20992	−	1.81077i	−0.204513	−	0.306076i
$36$	−0.709931	−	5.95785i	−0.118322	−	0.992975i
$37$	−1.97845	−	9.94633i	−0.325255	−	1.63517i	−0.704382	−	0.709822i	$-0.748776\pi$
$37$	−1.97845	−	9.94633i	−0.325255	−	1.63517i	0.379127	−	0.925345i	$-0.376224\pi$
$38$	−2.03024	+	1.64083i	−0.329349	+	0.266178i
$39$	2.72016	−	0.829176i	0.435573	−	0.132774i
$40$	9.97363	−	2.08997i	1.57697	−	0.330453i
$41$	0.516405	+	3.92249i	0.0806490	+	0.612590i	0.983270	+	0.182154i	$0.0583069\pi$
$41$	0.516405	+	3.92249i	0.0806490	+	0.612590i	−0.902621	+	0.430436i	$0.858360\pi$
$42$	1.11920	−	0.969396i	0.172696	−	0.149581i
$43$	6.04673	−	2.98192i	0.922118	−	0.454738i	0.0816875	−	0.996658i	$-0.473969\pi$
$43$	6.04673	−	2.98192i	0.922118	−	0.454738i	0.840430	+	0.541920i	$0.182302\pi$
$44$	10.2444	−	7.61927i	1.54440	−	1.14865i
$45$	6.60294	+	8.55702i	0.984308	+	1.27560i
$46$	2.50141	−	3.95608i	0.368813	−	0.583292i
$47$	1.06439	−	0.285202i	0.155257	−	0.0416010i	−0.180353	−	0.983602i	$-0.557724\pi$
$47$	1.06439	−	0.285202i	0.155257	−	0.0416010i	0.335610	+	0.942001i	$0.391057\pi$
$48$	2.25362	+	6.55143i	0.325282	+	0.945617i
$49$	−6.40854	−	1.71716i	−0.915506	−	0.245309i
$50$	−8.29465	+	7.65274i	−1.17304	+	1.08226i
$51$	−4.43273	+	4.16299i	−0.620707	+	0.582936i
$52$	−2.86805	+	1.59896i	−0.397727	+	0.221736i
$53$	0.409002	−	0.612115i	0.0561807	−	0.0840804i	−0.802316	−	0.596900i	$-0.796399\pi$
$53$	0.409002	−	0.612115i	0.0561807	−	0.0840804i	0.858496	+	0.512819i	$0.171399\pi$
$54$	−5.21400	+	5.17824i	−0.709536	+	0.704670i
$55$	−8.80125	+	21.2481i	−1.18676	+	2.86509i
$56$	−1.02690	+	1.36696i	−0.137225	+	0.182668i
$57$	3.11454	+	0.721763i	0.412531	+	0.0955998i
$58$	9.04140	+	6.58222i	1.18719	+	0.864288i
$59$	6.59875	+	7.52443i	0.859084	+	0.979597i	0.999946	−	0.0104319i	$-0.00332065\pi$
$59$	6.59875	+	7.52443i	0.859084	+	0.979597i	−0.140862	+	0.990029i	$0.544987\pi$
$60$	−9.53852	−	8.04851i	−1.23142	−	1.03906i
$61$	−0.876809	−	13.3775i	−0.112264	−	1.71282i	−0.568272	−	0.822841i	$-0.692388\pi$
$61$	−0.876809	−	13.3775i	−0.112264	−	1.71282i	0.456008	−	0.889975i	$-0.349279\pi$
$62$	4.02090	+	0.694891i	0.510655	+	0.0882512i
$63$	−1.77953	−	0.348961i	−0.224199	−	0.0439649i
$64$	−4.14064	−	6.84508i	−0.517581	−	0.855634i
$65$	2.95758	−	5.12269i	0.366843	−	0.635391i
$66$	−15.0786	−	4.13984i	−1.85604	−	0.509580i
$67$	8.66852	+	4.27484i	1.05903	+	0.522255i	0.886490	−	0.462748i	$-0.153136\pi$
$67$	8.66852	+	4.27484i	1.05903	+	0.522255i	0.172538	+	0.985003i	$0.444803\pi$
$68$	3.98831	−	5.77924i	0.483654	−	0.700835i
$69$	−5.70412	+	0.569610i	−0.686695	+	0.0685730i
$70$	0.324873	−	3.06268i	0.0388297	−	0.366061i
$71$	0.0723646	+	0.174704i	0.00858810	+	0.0207335i	0.928115	−	0.372293i	$-0.121428\pi$
$71$	0.0723646	+	0.174704i	0.00858810	+	0.0207335i	−0.919527	+	0.393026i	$0.871428\pi$
$72$	4.62262	−	7.11557i	0.544781	−	0.838578i
$73$	−2.42727	+	5.85995i	−0.284090	+	0.685855i	−0.999923	−	0.0124172i	$-0.996047\pi$
$73$	−2.42727	+	5.85995i	−0.284090	+	0.685855i	0.715833	+	0.698272i	$0.246047\pi$
$74$	6.85541	−	12.5973i	0.796925	−	1.46440i
$75$	13.6405	+	2.23307i	1.57506	+	0.257853i
$76$	−3.69125	−	0.0554071i	−0.423416	−	0.00635563i
$77$	−1.24034	−	3.65393i	−0.141350	−	0.416404i
$78$	3.70597	+	1.56183i	0.419619	+	0.176843i
$79$	1.21604	+	4.53833i	0.136815	+	0.510602i	0.999984	+	0.00568592i	$0.00180989\pi$
$79$	1.21604	+	4.53833i	0.136815	+	0.510602i	−0.863168	+	0.504916i	$0.831523\pi$
$80$	12.7279	+	6.75897i	1.42302	+	0.755675i
$81$	8.92924	+	1.12637i	0.992138	+	0.125152i
$82$	−2.99017	+	4.72907i	−0.330209	+	0.522238i
$83$	7.35100	+	6.44666i	0.806877	+	0.707612i	0.959818	−	0.280623i	$-0.0905411\pi$
$83$	7.35100	+	6.44666i	0.806877	+	0.707612i	−0.152941	+	0.988235i	$0.548874\pi$
$84$	2.09358	−	0.0399300i	0.228428	−	0.00435672i
$85$	−0.827293	+	12.6220i	−0.0897325	+	1.36905i
$86$	9.26907	+	2.23472i	0.999509	+	0.240976i
$87$	−0.466698	−	13.6891i	−0.0500353	−	1.46762i
$88$	18.0280	+	0.996858i	1.92179	+	0.106265i
$89$	−4.84513	+	2.00692i	−0.513583	+	0.212733i	−0.624396	−	0.781108i	$-0.714655\pi$
$89$	−4.84513	+	2.00692i	−0.513583	+	0.212733i	0.110813	+	0.993841i	$0.464655\pi$
$90$	−0.573377	+	15.2746i	−0.0604393	+	1.61009i
$91$	0.193615	+	0.973370i	0.0202964	+	0.102037i
$92$	6.29925	−	2.03339i	0.656742	−	0.211996i
$93$	−2.36181	−	4.40428i	−0.244908	−	0.456702i
$94$	1.41460	+	0.653786i	0.145905	+	0.0674329i
$95$	5.75922	−	3.32509i	0.590883	−	0.341147i
$96$	−3.48289	+	9.15803i	−0.355471	+	0.934687i
$97$	−10.5978	−	6.11862i	−1.07604	−	0.621251i	−0.146214	−	0.989253i	$-0.546709\pi$
$97$	−10.5978	−	6.11862i	−1.07604	−	0.621251i	−0.929825	+	0.368002i	$0.880042\pi$
$98$	−5.40786	−	7.66754i	−0.546276	−	0.774539i
$99$	7.37659	+	17.6731i	0.741375	+	1.77621i
$100$	−15.9400	+	0.804706i	−1.59400	+	0.0804706i
$101$	−7.71721	−	2.61964i	−0.767891	−	0.260664i	−0.0901142	−	0.995931i	$-0.528723\pi$
$101$	−7.71721	−	2.61964i	−0.767891	−	0.260664i	−0.677777	+	0.735267i	$0.737057\pi$
$102$	−8.58484	+	0.509678i	−0.850026	+	0.0504656i
$103$	7.87639	+	6.04377i	0.776084	+	0.595510i	0.919015	−	0.394222i	$-0.128986\pi$
$103$	7.87639	+	6.04377i	0.776084	+	0.595510i	−0.142931	+	0.989733i	$0.545653\pi$
$104$	−4.56357	−	0.859404i	−0.447495	−	0.0842715i
$105$	−3.20053	+	1.99624i	−0.312340	+	0.194813i
$106$	0.998531	−	0.294736i	0.0969859	−	0.0286273i
$107$	−1.26716	−	0.846692i	−0.122501	−	0.0818528i	0.492810	−	0.870137i	$-0.335970\pi$
$107$	−1.26716	−	0.846692i	−0.122501	−	0.0818528i	−0.615311	+	0.788284i	$0.710970\pi$
$108$	−10.3528	+	0.905365i	−0.996198	+	0.0871188i
$109$	2.07004	−	10.4068i	0.198274	−	0.996791i	−0.745577	−	0.666420i	$-0.767826\pi$
$109$	2.07004	−	10.4068i	0.198274	−	0.996791i	0.943851	−	0.330372i	$-0.107174\pi$
$110$	−28.7989	+	15.1166i	−2.74587	+	1.44131i
$111$	−17.3266	+	2.88474i	−1.64456	+	0.273808i
$112$	−2.35324	+	0.555417i	−0.222360	+	0.0524820i
$113$	17.9720	+	4.81557i	1.69066	+	0.453011i	0.970560	−	0.240859i	$-0.0774293\pi$
$113$	17.9720	+	4.81557i	1.69066	+	0.453011i	0.720100	+	0.693870i	$0.244096\pi$
$114$	2.73031	+	3.60389i	0.255717	+	0.337535i
$115$	−7.86205	+	8.96495i	−0.733140	+	0.835986i
$116$	3.86373	+	15.3368i	0.358738	+	1.42398i
$117$	−1.28769	−	4.75418i	−0.119047	−	0.439524i
$118$	0.356917	+	14.1490i	0.0328569	+	1.30252i
$119$	−1.29195	−	1.68370i	−0.118433	−	0.154344i
$120$	−3.07632	−	17.3799i	−0.280828	−	1.58656i
$121$	−18.1108	+	23.6024i	−1.64643	+	2.14568i
$122$	11.1587	−	15.3277i	1.01026	−	1.38770i
$123$	6.81866	−	0.680907i	0.614818	−	0.0613953i
$124$	3.73935	+	4.39527i	0.335803	+	0.394707i
$125$	8.92740	−	5.96510i	0.798491	−	0.533534i
$126$	−1.61742	−	1.99021i	−0.144091	−	0.177302i
$127$	10.7518			0.954068			0.477034	−	0.878885i	$-0.341712\pi$
$127$	10.7518			0.954068			0.477034	+	0.878885i	$0.341712\pi$
$128$	1.69861	−	11.1855i	0.150137	−	0.988665i
$129$	−4.83380	−	10.6301i	−0.425592	−	0.935927i
$130$	7.85104	−	2.88784i	0.688581	−	0.253281i
$131$	−8.54248	−	4.21269i	−0.746360	−	0.368064i	0.0290033	−	0.999579i	$-0.490767\pi$
$131$	−8.54248	−	4.21269i	−0.746360	−	0.368064i	−0.775363	+	0.631515i	$0.782433\pi$
$132$	−12.6339	−	18.1490i	−1.09964	−	1.57967i
$133$	−0.358649	+	1.05654i	−0.0310988	+	0.0916140i
$134$	5.54760	+	12.4924i	0.479240	+	1.07918i
$135$	15.1726	−	10.9661i	1.30585	−	0.943814i
$136$	9.56527	−	2.66798i	0.820215	−	0.228777i
$137$	−10.4784	−	13.6557i	−0.895232	−	1.16669i	−0.985314	−	0.170755i	$-0.945379\pi$
$137$	−10.4784	−	13.6557i	−0.895232	−	1.16669i	0.0900813	−	0.995934i	$-0.471287\pi$
$138$	−6.71287	−	4.54536i	−0.571437	−	0.386927i
$139$	2.09699	+	0.137444i	0.177864	+	0.0116578i	0.154075	−	0.988059i	$-0.450760\pi$
$139$	2.09699	+	0.137444i	0.177864	+	0.0116578i	0.0237892	+	0.999717i	$0.492427\pi$
$140$	3.12574	−	3.03329i	0.264174	−	0.256360i
$141$	−0.435918	−	1.85816i	−0.0367109	−	0.156486i
$142$	−0.0795476	+	0.255320i	−0.00667548	+	0.0214259i
$143$	7.41100	−	7.41100i	0.619739	−	0.619739i
$144$	11.4643	−	3.54555i	0.955354	−	0.295463i
$145$	−20.1461	−	20.1461i	−1.67304	−	1.67304i
$146$	−7.94236	+	4.16895i	−0.657314	+	0.345025i
$147$	−3.32090	+	11.0012i	−0.273903	+	0.907362i
$148$	18.8529	−	7.47962i	1.54970	−	0.614821i
$149$	0.119838	−	1.82837i	0.00981751	−	0.149786i	−0.990136	−	0.140112i	$-0.955254\pi$
$149$	0.119838	−	1.82837i	0.00981751	−	0.149786i	0.999953	−	0.00967445i	$-0.00307952\pi$
$150$	12.7978	+	14.7754i	1.04494	+	1.20641i
$151$	10.7442	−	8.24431i	0.874350	−	0.670913i	−0.0708204	−	0.997489i	$-0.522562\pi$
$151$	10.7442	−	8.24431i	0.874350	−	0.670913i	0.945171	+	0.326576i	$0.105895\pi$
$152$	−3.96016	−	3.40206i	−0.321211	−	0.275944i
$153$	6.96616	+	7.90010i	0.563181	+	0.638685i
$154$	1.96052	−	5.09270i	0.157983	−	0.410382i
$155$	−9.84367	−	3.34147i	−0.790662	−	0.268394i
$156$	2.61231	+	5.05203i	0.209152	+	0.404486i
$157$	−3.74719	+	7.59854i	−0.299058	+	0.606430i	−0.993592	−	0.113031i	$-0.963944\pi$
$157$	−3.74719	+	7.59854i	−0.299058	+	0.606430i	0.694533	+	0.719460i	$0.255611\pi$
$158$	−2.78761	+	6.03155i	−0.221770	+	0.479845i
$159$	−1.03747	−	0.741317i	−0.0822769	−	0.0587903i
$160$	7.70885	+	18.8663i	0.609438	+	1.49151i
$161$		−	2.00060i		−	0.157669i
$162$	8.68131	+	9.30778i	0.682068	+	0.731289i
$163$	−8.65144	−	12.9478i	−0.677633	−	1.01415i	−0.997768	−	0.0667774i	$-0.978728\pi$
$163$	−8.65144	−	12.9478i	−0.677633	−	1.01415i	0.320135	−	0.947372i	$-0.396272\pi$
$164$	−7.53008	+	2.43070i	−0.588000	+	0.189806i
$165$	36.3066	+	16.3910i	2.82646	+	1.27604i
$166$	2.14995	+	13.6591i	0.166869	+	1.06015i
$167$	−8.55581	−	6.56511i	−0.662069	−	0.508023i	0.222200	−	0.975001i	$-0.428676\pi$
$167$	−8.55581	−	6.56511i	−0.662069	−	0.508023i	−0.884269	+	0.466978i	$0.845343\pi$
$168$	2.31069	+	1.85203i	0.178274	+	0.142887i
$169$	8.17504	−	6.27293i	0.628849	−	0.482533i
$170$	−12.3261	+	12.9641i	−0.945371	+	0.994300i
$171$	1.41872	−	5.35268i	0.108492	−	0.409330i
$172$	8.04708	+	10.8196i	0.613584	+	0.824986i
$173$	−4.64462	−	4.07322i	−0.353124	−	0.309681i	0.464345	−	0.885655i	$-0.346290\pi$
$173$	−4.64462	−	4.07322i	−0.353124	−	0.309681i	−0.817469	+	0.575973i	$0.804623\pi$
$174$	11.8863	−	15.2949i	0.901100	−	1.15950i
$175$	−1.24849	+	4.65942i	−0.0943768	+	0.352219i
$176$	18.6838	+	17.4046i	1.40834	+	1.31192i
$177$	13.3848	−	11.0150i	1.00606	−	0.827936i
$178$	−7.08089	−	2.20613i	−0.530735	−	0.165356i
$179$	−23.0206	−	4.57909i	−1.72064	−	0.342257i	−0.766646	−	0.642070i	$-0.778076\pi$
$179$	−23.0206	−	4.57909i	−1.72064	−	0.342257i	−0.953998	+	0.299813i	$0.903076\pi$
$180$	−14.4518	+	16.0758i	−1.07717	+	1.19822i
$181$	12.6356	−	18.9105i	0.939196	−	1.40561i	0.0252895	−	0.999680i	$-0.491949\pi$
$181$	12.6356	−	18.9105i	0.939196	−	1.40561i	0.913906	−	0.405925i	$-0.133051\pi$
$182$	−0.670886	+	1.23280i	−0.0497294	+	0.0913809i
$183$	−23.2068	+	0.791183i	−1.71549	+	0.0584859i
$184$	8.68467	+	3.49385i	0.640243	+	0.257570i
$185$	−22.2421	+	28.9865i	−1.63527	+	2.13113i
$186$	1.42143	−	6.92323i	0.104225	−	0.507636i
$187$	−7.20419	+	21.2228i	−0.526822	+	1.55197i
$188$	0.944973	+	1.99100i	0.0689192	+	0.145209i
$189$	−0.700795	+	3.06176i	−0.0509753	+	0.222710i
$190$	9.26739	+	1.60159i	0.672327	+	0.116191i
$191$	−4.57425	+	7.92284i	−0.330981	+	0.573276i	−0.982705	−	0.185180i	$-0.940713\pi$
$191$	−4.57425	+	7.92284i	−0.330981	+	0.573276i	0.651723	+	0.758457i	$0.274046\pi$
$192$	−12.0751	+	6.79641i	−0.871447	+	0.490489i
$193$	7.48600	+	12.9661i	0.538854	+	0.933323i	0.998966	+	0.0454621i	$0.0144760\pi$
$193$	7.48600	+	12.9661i	0.538854	+	0.933323i	−0.460112	+	0.887861i	$0.652191\pi$
$194$	−5.97434	−	16.2421i	−0.428933	−	1.16612i
$195$	−8.70771	−	5.39846i	−0.623572	−	0.386592i
$196$	1.06648	−	13.2263i	0.0761770	−	0.944736i
$197$	−2.00507	+	0.398833i	−0.142855	+	0.0284157i	−0.266000	−	0.963973i	$-0.585702\pi$
$197$	−2.00507	+	0.398833i	−0.142855	+	0.0284157i	0.123145	+	0.992389i	$0.460702\pi$
$198$	−7.98605	+	25.8791i	−0.567544	+	1.83915i
$199$	10.0293	+	24.2130i	0.710961	+	1.71641i	0.697586	+	0.716501i	$0.254257\pi$
$199$	10.0293	+	24.2130i	0.710961	+	1.71641i	0.0133748	+	0.999911i	$0.495743\pi$
$200$	−18.0464	−	13.5570i	−1.27607	−	0.958622i
$201$	7.87152	−	14.7747i	0.555215	−	1.04213i
$202$	−6.01259	−	9.83283i	−0.423045	−	0.691835i
$203$	4.76993	+	0.312638i	0.334784	+	0.0219429i
$204$	−9.78834	−	7.21852i	−0.685321	−	0.505398i
$205$	9.39823	−	10.7166i	0.656401	−	0.748482i
$206$	3.08551	+	13.6970i	0.214978	+	0.954318i
$207$	0.676225	+	9.90591i	0.0470009	+	0.688508i
$208$	−4.17998	−	5.06530i	−0.289829	−	0.351215i
$209$	11.3816	−	3.04968i	0.787279	−	0.210951i
$210$	−5.28447	−	0.728803i	−0.364663	−	0.0502922i
$211$	−9.87157	+	3.35095i	−0.679587	+	0.230689i	−0.639825	−	0.768520i	$-0.720993\pi$
$211$	−9.87157	+	3.35095i	−0.679587	+	0.230689i	−0.0397619	+	0.999209i	$0.512660\pi$
$212$	1.35168	+	0.583804i	0.0928338	+	0.0400958i
$213$	0.306378	−	0.115787i	0.0209927	−	0.00793356i
$214$	−0.610146	−	2.06710i	−0.0417087	−	0.141304i
$215$	−22.4411	−	9.29543i	−1.53047	−	0.633943i
$216$	−12.0673	−	8.38924i	−0.821078	−	0.570815i
$217$	1.61136	−	0.667445i	0.109386	−	0.0453091i
$218$	11.6707	−	9.43225i	0.790442	−	0.638832i
$219$	10.0129	+	4.52043i	0.676607	+	0.305463i
$220$	−44.9740	−	9.64977i	−3.03214	−	0.650587i
$221$	2.54949	−	5.16986i	0.171497	−	0.347762i
$222$	−21.4359	−	12.5524i	−1.43868	−	0.842464i
$223$	−3.19269	−	1.84330i	−0.213799	−	0.123437i	0.389277	−	0.921121i	$-0.372725\pi$
$223$	−3.19269	−	1.84330i	−0.213799	−	0.123437i	−0.603076	+	0.797684i	$0.706058\pi$
$224$	−3.05949	−	1.52707i	−0.204421	−	0.102031i
$225$	4.60692	−	23.4930i	0.307128	−	1.56620i
$226$	15.1657	+	21.5027i	1.00881	+	1.43034i
$227$	−10.1575	+	0.665759i	−0.674179	+	0.0441880i	−0.398648	−	0.917104i	$-0.630520\pi$
$227$	−10.1575	+	0.665759i	−0.674179	+	0.0441880i	−0.275531	+	0.961292i	$0.588854\pi$
$228$	−0.296452	+	6.38729i	−0.0196330	+	0.423008i
$229$	2.54037	−	2.22785i	0.167872	−	0.147220i	−0.571288	−	0.820750i	$-0.693556\pi$
$229$	2.54037	−	2.22785i	0.167872	−	0.147220i	0.739160	+	0.673530i	$0.235223\pi$
$230$	−16.6580	+	2.62199i	−1.09840	+	0.172889i
$231$	−6.39306	+	1.94877i	−0.420632	+	0.128220i
$232$	−9.68739	+	20.1605i	−0.636009	+	1.32360i
$233$	−12.2699	−	5.08235i	−0.803826	−	0.332956i	−0.0573385	−	0.998355i	$-0.518261\pi$
$233$	−12.2699	−	5.08235i	−0.803826	−	0.332956i	−0.746488	+	0.665399i	$0.768261\pi$
$234$	2.90518	−	6.33093i	0.189917	−	0.413866i
$235$	−3.30098	−	2.20564i	−0.215332	−	0.143880i
$236$	−12.4220	+	15.6951i	−0.808601	+	1.02167i
$237$	7.92281	−	1.85866i	0.514642	−	0.120733i
$238$	0.120709	−	2.99890i	0.00782442	−	0.194390i
$239$	3.36085	−	12.5429i	0.217395	−	0.811331i	−0.767914	−	0.640553i	$-0.778705\pi$
$239$	3.36085	−	12.5429i	0.217395	−	0.811331i	0.985310	−	0.170778i	$-0.0546281\pi$
$240$	12.3926	−	21.6673i	0.799937	−	1.39862i
$241$	0.614982	+	2.29515i	0.0396145	+	0.147843i	0.982900	−	0.184138i	$-0.0589495\pi$
$241$	0.614982	+	2.29515i	0.0396145	+	0.147843i	−0.943286	+	0.331982i	$0.892283\pi$
$242$	−41.0446	+	9.24605i	−2.63845	+	0.594359i
$243$	2.43506	−	15.3971i	0.156209	−	0.987724i
$244$	26.0001	−	6.55008i	1.66448	−	0.419326i
$245$	10.5721	+	21.4381i	0.675427	+	1.36963i
$246$	8.02451	+	5.43349i	0.511624	+	0.346426i
$247$	−3.00461	+	0.395565i	−0.191179	+	0.0251692i
$248$	0.0833312	+	8.16059i	0.00529154	+	0.518198i
$249$	11.5598	−	12.3758i	0.732572	−	0.784286i
$250$	15.0995	+	1.60168i	0.954979	+	0.101299i
$251$	19.6782	−	3.91424i	1.24208	−	0.247064i	0.470042	−	0.882644i	$-0.344239\pi$
$251$	19.6782	−	3.91424i	1.24208	−	0.247064i	0.772035	+	0.635580i	$0.219239\pi$
$252$	0.0446090	−	3.62656i	0.00281010	−	0.228452i
$253$	−17.5669	+	11.7378i	−1.10442	+	0.737949i
$254$	11.6812	+	9.73410i	0.732942	+	0.610772i
$255$	21.8063	+	2.11791i	1.36557	+	0.132629i
$256$	11.9722	−	10.6145i	0.748260	−	0.663406i
$257$	−3.88692	−	6.73235i	−0.242460	−	0.419952i	0.718955	−	0.695057i	$-0.244621\pi$
$257$	−3.88692	−	6.73235i	−0.242460	−	0.419952i	−0.961414	+	0.275105i	$0.911287\pi$
$258$	4.37229	−	15.9252i	0.272207	−	0.991459i
$259$	−0.400926	−	6.11695i	−0.0249123	−	0.380089i
$260$	11.1442	+	3.97044i	0.691132	+	0.246236i
$261$	−23.7239	+	0.0642741i	−1.46847	+	0.00397846i
$262$	−5.46694	−	12.3107i	−0.337749	−	0.760559i
$263$	5.59293	+	0.736323i	0.344875	+	0.0454036i	0.300974	−	0.953632i	$-0.402688\pi$
$263$	5.59293	+	0.736323i	0.344875	+	0.0454036i	0.0439005	+	0.999036i	$0.486022\pi$
$264$	2.70515	−	31.1559i	0.166490	−	1.91751i
$265$	−2.62963	+	0.346198i	−0.161537	+	0.0212667i
$266$	−1.34619	+	0.823169i	−0.0825401	+	0.0504718i
$267$	3.21116	+	8.49691i	0.196520	+	0.520003i
$268$	−5.28279	+	18.5947i	−0.322698	+	1.13585i
$269$	14.1324	+	2.81110i	0.861666	+	0.171396i	0.606093	−	0.795394i	$-0.292736\pi$
$269$	14.1324	+	2.81110i	0.861666	+	0.171396i	0.255573	+	0.966790i	$0.417736\pi$
$270$	26.4123	+	1.82244i	1.60740	+	0.110910i
$271$	10.4145	−	10.4145i	0.632634	−	0.632634i	−0.316094	−	0.948728i	$-0.602372\pi$
$271$	10.4145	−	10.4145i	0.632634	−	0.632634i	0.948728	+	0.316094i	$0.102372\pi$
$272$	12.8075	+	5.76128i	0.776570	+	0.349329i
$273$	1.69562	−	0.282307i	0.102623	−	0.0170860i
$274$	0.979021	−	24.3227i	0.0591448	−	1.46939i
$275$	48.2385	−	16.3748i	2.90889	−	0.987436i
$276$	−3.17799	−	11.0157i	−0.191293	−	0.663069i
$277$	−0.934240	+	0.460716i	−0.0561331	+	0.0276818i	−0.470139	−	0.882593i	$-0.655796\pi$
$277$	−0.934240	+	0.460716i	−0.0561331	+	0.0276818i	0.414006	+	0.910274i	$0.364129\pi$
$278$	2.15381	+	2.04782i	0.129177	+	0.122820i
$279$	−7.75299	+	3.84950i	−0.464159	+	0.230463i
$280$	6.14211	−	0.465606i	0.367061	−	0.0278253i
$281$	1.65507	−	12.5715i	0.0987332	−	0.749953i	−0.868433	−	0.495807i	$-0.834872\pi$
$281$	1.65507	−	12.5715i	0.0987332	−	0.749953i	0.967166	−	0.254146i	$-0.0817943\pi$
$282$	1.20868	−	2.41344i	0.0719761	−	0.143718i
$283$	−10.9494	+	9.60236i	−0.650874	+	0.570801i	−0.919814	−	0.392356i	$-0.871660\pi$
$283$	−10.9494	+	9.60236i	−0.650874	+	0.570801i	0.268939	+	0.963157i	$0.413327\pi$
$284$	−0.317576	+	0.205371i	−0.0188447	+	0.0121865i
$285$	−5.44351	−	10.1510i	−0.322446	−	0.601293i
$286$	14.7611	−	1.34207i	0.872844	−	0.0793585i
$287$			2.39150i			0.141166i
$288$	15.6652	+	6.52709i	0.923078	+	0.384613i
$289$		−	4.67345i		−	0.274909i
$290$	−3.64830	−	40.1267i	−0.214235	−	2.35632i
$291$	−11.1683	+	18.0144i	−0.654696	+	1.05602i
$292$	−12.4032	−	2.66128i	−0.725844	−	0.155740i
$293$	−2.97196	+	2.60634i	−0.173624	+	0.152264i	−0.741748	−	0.670679i	$-0.766003\pi$
$293$	−2.97196	+	2.60634i	−0.173624	+	0.152264i	0.568124	+	0.822943i	$0.307669\pi$
$294$	−13.5678	+	8.94553i	−0.791292	+	0.521714i
$295$	4.70637	−	35.7484i	0.274015	−	2.08135i
$296$	27.2541	+	8.94222i	1.58411	+	0.519756i
$297$	30.9964	−	11.8102i	1.79859	−	0.685299i
$298$	1.78551	−	1.87792i	0.103432	−	0.108785i
$299$	4.87350	−	2.40334i	0.281842	−	0.138989i
$300$	0.527149	+	27.6390i	0.0304350	+	1.59574i
$301$	3.85909	−	1.30998i	0.222434	−	0.0755062i
$302$	19.1369	+	0.770283i	1.10120	+	0.0443248i
$303$	−4.95436	+	13.2177i	−0.284621	+	0.759338i
$304$	−1.22242	−	7.28144i	−0.0701108	−	0.417619i
$305$	−34.1532	+	34.1532i	−1.95561	+	1.95561i
$306$	0.415972	+	14.8898i	0.0237796	+	0.851191i
$307$	5.64307	+	1.12248i	0.322067	+	0.0640632i	0.353476	−	0.935443i	$-0.384999\pi$
$307$	5.64307	+	1.12248i	0.322067	+	0.0640632i	−0.0314091	+	0.999507i	$0.509999\pi$
$308$	6.74064	−	3.75796i	0.384084	−	0.214130i
$309$	10.8909	−	13.3073i	0.619559	−	0.757024i
$310$	−7.66934	−	12.5422i	−0.435590	−	0.712351i
$311$	12.0691	−	1.58892i	0.684374	−	0.0900996i	0.219682	−	0.975572i	$-0.429498\pi$
$311$	12.0691	−	1.58892i	0.684374	−	0.0900996i	0.464693	+	0.885472i	$0.346165\pi$
$312$	−1.73572	+	7.85376i	−0.0982658	+	0.444631i
$313$	−1.24059	−	0.163326i	−0.0701221	−	0.00923175i	0.0953835	−	0.995441i	$-0.469592\pi$
$313$	−1.24059	−	0.163326i	−0.0701221	−	0.00923175i	−0.165506	+	0.986209i	$0.552926\pi$
$314$	−10.9504	+	4.86285i	−0.617967	+	0.274426i
$315$	3.28201	+	5.64920i	0.184920	+	0.318297i
$316$	−8.48921	+	4.02916i	−0.477555	+	0.226658i
$317$	−0.214961	−	3.27967i	−0.0120734	−	0.184205i	−0.999636	−	0.0269783i	$-0.991411\pi$
$317$	−0.214961	−	3.27967i	−0.0120734	−	0.184205i	0.987563	−	0.157226i	$-0.0502552\pi$
$318$	−0.456001	−	1.74467i	−0.0255713	−	0.0978361i
$319$	−25.2407	−	43.7181i	−1.41321	−	2.44775i
$320$	−8.70538	+	27.4763i	−0.486646	+	1.53597i
$321$	−1.53463	+	2.14772i	−0.0856548	+	0.119874i
$322$	1.81123	−	2.17353i	0.100936	−	0.121126i
$323$	5.38840	−	3.60042i	0.299819	−	0.200333i
$324$	1.00494	+	17.9719i	0.0558301	+	0.998440i
$325$	−12.8503	+	2.55608i	−0.712805	+	0.141786i
$326$	2.32298	−	21.8995i	0.128658	−	1.21290i
$327$	−17.9038	−	4.14901i	−0.990082	−	0.229441i
$328$	−10.3816	−	4.17652i	−0.573227	−	0.230610i
$329$	0.660393	−	0.0869423i	0.0364086	−	0.00479329i
$330$	24.6053	+	50.6779i	1.35447	+	2.78972i
$331$	1.05441	+	2.13814i	0.0579558	+	0.117523i	0.923924	−	0.382577i	$-0.124963\pi$
$331$	1.05441	+	2.13814i	0.0579558	+	0.117523i	−0.865968	+	0.500100i	$0.833297\pi$
$332$	−10.0304	+	16.7862i	−0.550491	+	0.921263i
$333$	4.05278	+	30.1524i	0.222091	+	1.65234i
$334$	−3.35167	−	14.8786i	−0.183395	−	0.814119i
$335$	−9.01260	−	33.6355i	−0.492411	−	1.83770i
$336$	0.833695	+	4.10409i	0.0454818	+	0.223897i
$337$	4.05601	−	15.1372i	0.220945	−	0.824578i	−0.763044	−	0.646347i	$-0.776296\pi$
$337$	4.05601	−	15.1372i	0.220945	−	0.824578i	0.983989	−	0.178231i	$-0.0570374\pi$
$338$	14.5608	+	0.586092i	0.792005	+	0.0318792i
$339$	9.31306	−	30.8514i	0.505816	−	1.67562i
$340$	−25.1286	+	2.92527i	−1.36279	+	0.158645i
$341$	−15.3148	−	10.2330i	−0.829341	−	0.554148i
$342$	6.38738	−	4.53093i	0.345390	−	0.245005i
$343$	−7.61439	−	3.15398i	−0.411138	−	0.170299i
$344$	−1.05283	+	19.0402i	−0.0567648	+	1.02658i
$345$	15.0930	+	14.0978i	0.812580	+	0.759000i
$346$	−1.35842	−	8.63029i	−0.0730289	−	0.463967i
$347$	18.4499	−	16.1801i	0.990442	−	0.868595i	−0.000886400	−	1.00000i	$-0.500282\pi$
$347$	18.4499	−	16.1801i	0.990442	−	0.868595i	0.991329	+	0.131405i	$0.0419488\pi$
$348$	26.7609	−	5.85569i	1.43454	−	0.313898i
$349$	−6.37180	+	0.417630i	−0.341075	+	0.0223552i	−0.234978	−	0.972001i	$-0.575502\pi$
$349$	−6.37180	+	0.417630i	−0.341075	+	0.0223552i	−0.106096	+	0.994356i	$0.533835\pi$
$350$	−5.57480	+	3.93186i	−0.297985	+	0.210167i
$351$	−8.30038	+	1.97098i	−0.443041	+	0.105203i
$352$	4.54160	+	35.8243i	0.242068	+	1.90944i
$353$	−8.93303	−	5.15749i	−0.475457	−	0.274505i	0.243064	−	0.970010i	$-0.421847\pi$
$353$	−8.93303	−	5.15749i	−0.475457	−	0.274505i	−0.718521	+	0.695505i	$0.755181\pi$
$354$	24.5141	+	0.150763i	1.30291	+	0.00801298i
$355$	0.301323	−	0.611022i	0.0159926	−	0.0324297i
$356$	−5.69564	−	8.80748i	−0.301868	−	0.466796i
$357$	−2.98500	+	2.14515i	−0.157983	+	0.113533i
$358$	−20.8648	−	25.8166i	−1.10274	−	1.36445i
$359$	31.7049	−	13.1326i	1.67332	−	0.693112i	0.674348	−	0.738414i	$-0.264425\pi$
$359$	31.7049	−	13.1326i	1.67332	−	0.693112i	0.998973	+	0.0453016i	$0.0144249\pi$
$360$	−30.2551	+	4.38154i	−1.59459	+	0.230928i
$361$	14.4060	+	5.96714i	0.758208	+	0.314060i
$362$	30.8483	−	9.10550i	1.62135	−	0.478574i
$363$	39.8766	+	32.6356i	2.09298	+	1.71292i
$364$	−1.84498	+	0.731972i	−0.0967034	+	0.0383658i
$365$	21.6389	−	7.34543i	1.13263	−	0.384477i
$366$	−25.9290	−	20.1506i	−1.35533	−	1.05329i
$367$	21.4613	−	5.75054i	1.12027	−	0.300176i	0.349278	−	0.937019i	$-0.386427\pi$
$367$	21.4613	−	5.75054i	1.12027	−	0.300176i	0.770993	+	0.636843i	$0.219760\pi$
$368$	6.27222	+	11.6585i	0.326962	+	0.607741i
$369$	−0.808355	−	11.8414i	−0.0420813	−	0.616441i
$370$	−50.4075	+	11.3552i	−2.62056	+	0.590329i
$371$	0.293411	−	0.334571i	0.0152331	−	0.0173701i
$372$	7.81222	−	6.23477i	0.405045	−	0.323258i
$373$	−12.8932	−	0.845067i	−0.667586	−	0.0437559i	−0.272158	−	0.962253i	$-0.587737\pi$
$373$	−12.8932	−	0.845067i	−0.667586	−	0.0437559i	−0.395428	+	0.918497i	$0.629404\pi$
$374$	−27.0409	+	16.5350i	−1.39825	+	0.855006i
$375$	−9.84177	−	15.7792i	−0.508227	−	0.814832i
$376$	−0.775891	+	3.01863i	−0.0400135	+	0.155674i
$377$	4.96859	+	11.9952i	0.255895	+	0.617786i
$378$	−3.53332	+	2.69195i	−0.181734	+	0.138459i
$379$	−10.1984	+	2.02858i	−0.523855	+	0.104201i	−0.449932	−	0.893063i	$-0.648552\pi$
$379$	−10.1984	+	2.02858i	−0.523855	+	0.104201i	−0.0739228	+	0.997264i	$0.523552\pi$
$380$	8.61846	+	10.1302i	0.442117	+	0.519669i
$381$	0.584103	−	18.6135i	0.0299245	−	0.953599i
$382$	−12.1426	+	4.46639i	−0.621267	+	0.228520i
$383$	−0.386027	−	0.668618i	−0.0197250	−	0.0341648i	0.855994	−	0.516985i	$-0.172946\pi$
$383$	−0.386027	−	0.668618i	−0.0197250	−	0.0341648i	−0.875719	+	0.482820i	$0.839612\pi$
$384$	−19.2720	−	3.54829i	−0.983470	−	0.181073i
$385$	−6.95107	+	12.0396i	−0.354259	+	0.613595i
$386$	−3.60577	+	20.8643i	−0.183529	+	1.06197i
$387$	−18.6654	+	7.79077i	−0.948815	+	0.396027i
$388$	8.21401	−	23.0549i	0.417003	−	1.17044i
$389$	−9.05378	+	26.6716i	−0.459045	+	1.35230i	0.433422	+	0.901191i	$0.357306\pi$
$389$	−9.05378	+	26.6716i	−0.459045	+	1.35230i	−0.892467	+	0.451112i	$0.851027\pi$
$390$	−4.57292	−	13.7486i	−0.231559	−	0.696187i
$391$	−7.07377	+	9.21871i	−0.357736	+	0.466210i
$392$	13.1330	−	13.4040i	0.663319	−	0.677005i
$393$	−7.75708	+	14.5599i	−0.391293	+	0.734449i
$394$	−2.53947	−	1.38197i	−0.127936	−	0.0696229i
$395$	9.40440	−	14.0747i	0.473187	−	0.708174i
$396$	−32.1059	+	20.8859i	−1.61338	+	1.04956i
$397$	0.191355	+	0.0380628i	0.00960382	+	0.00191032i	0.199890	−	0.979818i	$-0.435942\pi$
$397$	0.191355	+	0.0380628i	0.00960382	+	0.00191032i	−0.190286	+	0.981729i	$0.560942\pi$
$398$	−11.0249	+	35.3859i	−0.552626	+	1.77374i
$399$	1.80960	+	0.678290i	0.0905936	+	0.0339570i
$400$	−7.33252	−	31.0670i	−0.366626	−	1.55335i
$401$	−7.62600	+	28.4606i	−0.380824	+	1.42126i	0.463821	+	0.885929i	$0.346478\pi$
$401$	−7.62600	+	28.4606i	−0.380824	+	1.42126i	−0.844645	+	0.535326i	$0.820189\pi$
$402$	21.9281	−	8.92534i	1.09368	−	0.445155i
$403$	3.56165	+	3.12349i	0.177419	+	0.155592i
$404$	2.36980	−	16.1262i	0.117902	−	0.802310i
$405$	−18.1603	−	26.8625i	−0.902392	−	1.33481i
$406$	4.89919	+	4.65810i	0.243143	+	0.231178i
$407$	−51.3595	+	39.4095i	−2.54579	+	1.95346i
$408$	−4.09916	−	16.7043i	−0.202939	−	0.826987i
$409$	−7.15125	−	5.48735i	−0.353607	−	0.271332i	0.416649	−	0.909068i	$-0.363205\pi$
$409$	−7.15125	−	5.48735i	−0.353607	−	0.271332i	−0.770255	+	0.637736i	$0.779871\pi$
$410$	19.9129	−	3.13430i	0.983426	−	0.154792i
$411$	−24.2101	+	17.3984i	−1.19419	+	0.858198i
$412$	−9.04835	+	17.6744i	−0.445780	+	0.870758i
$413$	3.36097	+	5.03004i	0.165382	+	0.247512i
$414$	−8.23360	+	11.3744i	−0.404659	+	0.559020i
$415$		−	35.2258i		−	1.72917i
$416$	0.0445632	−	9.28746i	0.00218489	−	0.455355i
$417$	0.351863	−	3.62283i	0.0172308	−	0.177411i
$418$	15.1264	+	6.99096i	0.739855	+	0.341939i
$419$	9.82169	−	19.9164i	0.479821	−	0.972981i	−0.513553	−	0.858058i	$-0.671671\pi$
$419$	9.82169	−	19.9164i	0.479821	−	0.972981i	0.993374	−	0.114923i	$-0.0366622\pi$
$420$	−5.08143	−	5.57607i	−0.247948	−	0.272084i
$421$	26.9661	+	9.15376i	1.31425	+	0.446127i	0.888567	−	0.458746i	$-0.151701\pi$
$421$	26.9661	+	9.15376i	1.31425	+	0.446127i	0.425681	+	0.904873i	$0.360035\pi$
$422$	−13.7586	−	5.29660i	−0.669759	−	0.257834i
$423$	−3.24053	+	0.653713i	−0.157560	+	0.0317846i
$424$	0.939973	+	1.85801i	0.0456491	+	0.0902327i
$425$	22.2279	−	17.0561i	1.07821	−	0.827341i
$426$	0.437687	+	0.151583i	0.0212060	+	0.00734423i
$427$	0.530008	−	8.08635i	0.0256489	−	0.391326i
$428$	1.20856	−	2.79817i	0.0584178	−	0.135255i
$429$	−12.4273	−	13.2325i	−0.599996	−	0.638873i
$430$	−15.9653	−	30.4159i	−0.769917	−	1.46679i
$431$	−4.56530	−	4.56530i	−0.219903	−	0.219903i	0.588555	−	0.808458i	$-0.299697\pi$
$431$	−4.56530	−	4.56530i	−0.219903	−	0.219903i	−0.808458	+	0.588555i	$0.799697\pi$
$432$	−5.51525	−	20.0395i	−0.265353	−	0.964151i
$433$	−27.1907	+	27.1907i	−1.30670	+	1.30670i	−0.382924	+	0.923780i	$0.625083\pi$
$433$	−27.1907	+	27.1907i	−1.30670	+	1.30670i	−0.923780	+	0.382924i	$0.874917\pi$
$434$	2.35491	+	0.733697i	0.113039	+	0.0352186i
$435$	−35.9713	+	33.7824i	−1.72469	+	1.61974i
$436$	21.2190	+	0.318505i	1.01620	+	0.0152536i
$437$	6.09600	+	0.399553i	0.291611	+	0.0191132i
$438$	6.78580	+	13.9763i	0.324238	+	0.667813i
$439$	11.8005	+	15.3787i	0.563206	+	0.733985i	0.984971	−	0.172721i	$-0.0552557\pi$
$439$	11.8005	+	15.3787i	0.563206	+	0.733985i	−0.421764	+	0.906705i	$0.638589\pi$
$440$	−40.1251	−	51.2009i	−1.91289	−	2.44091i
$441$	18.8648	+	6.34679i	0.898324	+	0.302228i
$442$	7.45038	−	3.30856i	0.354378	−	0.157372i
$443$	−4.26885	+	12.5756i	−0.202819	+	0.597486i	−0.999980	−	0.00628053i	$-0.998001\pi$
$443$	−4.26885	+	12.5756i	−0.202819	+	0.597486i	0.797161	+	0.603767i	$0.206334\pi$
$444$	−11.9245	−	33.0444i	−0.565912	−	1.56822i
$445$	16.9458	+	8.35672i	0.803306	+	0.396147i
$446$	−1.79984	−	4.89313i	−0.0852248	−	0.231696i
$447$	−3.15877	−	0.306792i	−0.149405	−	0.0145107i
$448$	−1.94142	−	4.42896i	−0.0917236	−	0.209249i
$449$	15.6548			0.738798			0.369399	−	0.929271i	$-0.379564\pi$
$449$	15.6548			0.738798			0.369399	+	0.929271i	$0.379564\pi$
$450$	26.2744	−	21.3529i	1.23859	−	1.00658i
$451$	20.9993	−	14.0313i	0.988817	−	0.660707i
$452$	−2.99081	+	37.0915i	−0.140676	+	1.74464i
$453$	−13.6889	−	19.0482i	−0.643158	−	0.894963i
$454$	−11.6383	−	8.47277i	−0.546211	−	0.397647i
$455$	2.17666	−	2.83668i	0.102044	−	0.132986i
$456$	−6.10478	+	6.67100i	−0.285883	+	0.312398i
$457$	5.38820	+	7.02204i	0.252049	+	0.328477i	0.902192	−	0.431335i	$-0.141957\pi$
$457$	5.38820	+	7.02204i	0.252049	+	0.328477i	−0.650142	+	0.759812i	$0.725291\pi$
$458$	4.77693	−	0.120501i	0.223211	−	0.00563065i
$459$	14.0551	−	11.6306i	0.656035	−	0.542871i
$460$	−20.4717	−	12.2326i	−0.954499	−	0.570350i
$461$	−24.5666	+	28.0129i	−1.14418	+	1.30469i	−0.198314	+	0.980139i	$0.563546\pi$
$461$	−24.5666	+	28.0129i	−1.14418	+	1.30469i	−0.945868	+	0.324551i	$0.894787\pi$
$462$	−8.70998	−	3.67071i	−0.405225	−	0.170777i
$463$	32.9039	+	8.81657i	1.52917	+	0.409741i	0.922750	−	0.385400i	$-0.125937\pi$
$463$	32.9039	+	8.81657i	1.52917	+	0.409741i	0.606424	+	0.795141i	$0.292603\pi$
$464$	−28.7770	+	13.1327i	−1.33594	+	0.609668i
$465$	−6.31952	+	16.8598i	−0.293061	+	0.781855i
$466$	−8.72918	−	16.6301i	−0.404371	−	0.770377i
$467$	−6.35442	+	31.9458i	−0.294047	+	1.47828i	0.497658	+	0.867373i	$0.334193\pi$
$467$	−6.35442	+	31.9458i	−0.294047	+	1.47828i	−0.791705	+	0.610903i	$0.790807\pi$
$468$	8.88798	−	4.24797i	0.410847	−	0.196362i
$469$	4.85778	+	3.24586i	0.224311	+	0.149880i
$470$	−1.58944	−	5.38483i	−0.0733154	−	0.248384i
$471$	12.9510	+	6.89992i	0.596751	+	0.317932i
$472$	−27.7052	+	5.80561i	−1.27524	+	0.267225i
$473$	−34.1445	−	26.2000i	−1.56997	−	1.20468i
$474$	10.2904	+	5.15357i	0.472653	+	0.236711i
$475$	−13.9483	−	4.73482i	−0.639993	−	0.217248i
$476$	2.84618	−	3.14883i	0.130455	−	0.144326i
$477$	−1.33973	+	1.75580i	−0.0613420	+	0.0803925i
$478$	15.0070	−	10.5843i	0.686404	−	0.484115i
$479$	−2.35163	−	1.35772i	−0.107449	−	0.0620356i	0.445313	−	0.895375i	$-0.353093\pi$
$479$	−2.35163	−	1.35772i	−0.107449	−	0.0620356i	−0.552761	+	0.833340i	$0.686426\pi$
$480$	33.0802	−	12.3206i	1.50990	−	0.562356i
$481$	14.4194	−	8.32503i	0.657467	−	0.379589i
$482$	−1.40976	+	3.05031i	−0.0642129	+	0.138938i
$483$	−3.46343	−	0.108685i	−0.157592	−	0.00494532i
$484$	−52.9633	−	27.1143i	−2.40742	−	1.23247i
$485$	8.60120	+	43.2411i	0.390560	+	1.96348i
$486$	16.5852	−	14.5234i	0.752322	−	0.658796i
$487$	−36.0842	+	14.9465i	−1.63513	+	0.677293i	−0.995793	−	0.0916345i	$-0.970791\pi$
$487$	−36.0842	+	14.9465i	−1.63513	+	0.677293i	−0.639336	+	0.768927i	$0.720791\pi$
$488$	34.1776	+	16.4228i	1.54715	+	0.743426i
$489$	−22.8852	+	14.2740i	−1.03490	+	0.645491i
$490$	−7.92297	+	32.8626i	−0.357923	+	1.48458i
$491$	0.466291	−	7.11422i	0.0210434	−	0.321060i	−0.974340	−	0.225081i	$-0.927735\pi$
$491$	0.466291	−	7.11422i	0.0210434	−	0.321060i	0.995383	−	0.0959789i	$-0.0305981\pi$
$492$	3.79895	+	13.1681i	0.171270	+	0.593664i
$493$	−20.8743	−	18.3063i	−0.940132	−	0.824473i
$494$	−3.62245	−	2.29046i	−0.162982	−	0.103053i
$495$	30.3485	−	61.9634i	1.36407	−	2.78505i
$496$	−7.29762	+	8.94142i	−0.327673	+	0.401482i
$497$	0.0295842	+	0.110410i	0.00132703	+	0.00495255i
$498$	23.7634	−	2.97995i	1.06486	−	0.133535i
$499$	8.64195	+	25.4584i	0.386867	+	1.13967i	0.949716	+	0.313113i	$0.101372\pi$
$499$	8.64195	+	25.4584i	0.386867	+	1.13967i	−0.562849	+	0.826560i	$0.690295\pi$
$500$	14.9546	+	15.4104i	0.668792	+	0.689176i
$501$	−11.8303	+	14.4552i	−0.528539	+	0.645809i
$502$	24.9229	+	13.5630i	1.11236	+	0.605347i
$503$	−11.2364	+	27.1270i	−0.501005	+	1.20953i	0.447933	+	0.894067i	$0.352160\pi$
$503$	−11.2364	+	27.1270i	−0.501005	+	1.20953i	−0.948937	+	0.315465i	$0.897840\pi$
$504$	3.33176	−	3.89965i	0.148408	−	0.173704i
$505$	11.2363	+	27.1267i	0.500007	+	1.20712i
$506$	−29.7121	−	3.15170i	−1.32086	−	0.140110i
$507$	−10.4156	−	14.4934i	−0.462571	−	0.643674i
$508$	3.87813	+	21.1510i	0.172064	+	0.938424i
$509$	25.9513	+	12.7978i	1.15027	+	0.567252i	0.914512	−	0.404559i	$-0.132575\pi$
$509$	25.9513	+	12.7978i	1.15027	+	0.567252i	0.235761	+	0.971811i	$0.424242\pi$
$510$	21.7738	+	22.0433i	0.964159	+	0.976092i
$511$	−1.91701	+	3.32037i	−0.0848037	+	0.146884i
$512$	22.6168	−	0.693042i	0.999531	−	0.0306284i
$513$	−9.18948	−	2.74687i	−0.405726	−	0.121277i
$514$	1.87220	−	10.8333i	0.0825794	−	0.477836i
$515$	−2.33937	−	35.6919i	−0.103085	−	1.57277i
$516$	19.1680	−	13.3433i	0.843826	−	0.587406i
$517$	−4.63804	−	5.28868i	−0.203981	−	0.232596i
$518$	5.10238	−	7.00867i	0.224186	−	0.307943i
$519$	−7.30388	+	7.81947i	−0.320605	+	0.343237i
$520$	8.51282	+	14.4030i	0.373312	+	0.631612i
$521$	−2.98459	+	7.20543i	−0.130757	+	0.315675i	−0.975676	−	0.219220i	$-0.929649\pi$
$521$	−2.98459	+	7.20543i	−0.130757	+	0.315675i	0.844918	+	0.534895i	$0.179649\pi$
$522$	−25.8327	−	21.4085i	−1.13067	−	0.937024i
$523$	−9.45030	+	14.1434i	−0.413233	+	0.618447i	−0.978447	−	0.206498i	$-0.933793\pi$
$523$	−9.45030	+	14.1434i	−0.413233	+	0.618447i	0.565214	+	0.824944i	$0.308793\pi$
$524$	5.20598	−	18.3243i	0.227424	−	0.800502i
$525$	7.99856	+	2.41451i	0.349086	+	0.105378i
$526$	5.40974	+	5.86351i	0.235876	+	0.255661i
$527$	−9.78506	−	2.62190i	−0.426244	−	0.114212i
$528$	31.1458	−	31.3998i	1.35545	−	1.36650i
$529$	11.6357	−	3.11778i	0.505901	−	0.135556i
$530$	−3.17036	−	2.00460i	−0.137712	−	0.0870745i
$531$	−18.3420	−	23.7701i	−0.795973	−	1.03153i
$532$	−2.20780	−	0.324444i	−0.0957204	−	0.0140664i
$533$	−5.82574	+	2.87294i	−0.252341	+	0.124441i
$534$	−4.20392	+	12.1386i	−0.181922	+	0.525288i
$535$	0.716678	+	5.44371i	0.0309847	+	0.235352i
$536$	−22.5740	+	15.4192i	−0.975050	+	0.666009i
$537$	−9.17794	+	39.6045i	−0.396057	+	1.70906i
$538$	12.8089	+	15.8488i	0.552232	+	0.683290i
$539$	8.26259	+	41.5388i	0.355895	+	1.78920i
$540$	27.0453	+	25.8922i	1.16385	+	1.11422i
$541$	−17.1245	−	25.6286i	−0.736239	−	1.10186i	−0.990870	−	0.134822i	$-0.956954\pi$
$541$	−17.1245	−	25.6286i	−0.736239	−	1.10186i	0.254631	−	0.967038i	$-0.418046\pi$
$542$	20.7434	−	1.88598i	0.891004	−	0.0810096i
$543$	−32.0514	−	22.9020i	−1.37546	−	0.982821i
$544$	8.69862	+	17.8545i	0.372950	+	0.765506i
$545$	−33.1066	+	19.1141i	−1.41813	+	0.818757i
$546$	2.09777	+	1.22841i	0.0897762	+	0.0525711i
$547$	27.5076	−	1.80294i	1.17614	−	0.0770883i	0.535232	−	0.844705i	$-0.320224\pi$
$547$	27.5076	−	1.80294i	1.17614	−	0.0770883i	0.640909	+	0.767617i	$0.278558\pi$
$548$	23.0841	−	25.5388i	0.986106	−	1.09096i
$549$	0.108962	+	40.2185i	0.00465040	+	1.71648i
$550$	67.2330	+	25.8824i	2.86683	+	1.10363i
$551$	−1.90527	+	14.4720i	−0.0811672	+	0.616526i
$552$	6.52035	−	14.8451i	0.277525	−	0.631849i
$553$	0.370704	+	2.81577i	0.0157639	+	0.119739i
$554$	−1.43210	−	0.345271i	−0.0608442	−	0.0146692i
$555$	48.9730	+	40.0802i	2.07879	+	1.70131i
$556$	0.485995	+	4.17478i	0.0206108	+	0.177050i
$557$	1.46802	−	7.38024i	0.0622020	−	0.312711i	−0.937141	−	0.348951i	$-0.886538\pi$
$557$	1.46802	−	7.38024i	0.0622020	−	0.312711i	0.999343	+	0.0362400i	$0.0115381\pi$
$558$	−11.9083	−	2.83690i	−0.504117	−	0.120095i
$559$	7.82712	+	7.82712i	0.331052	+	0.331052i
$560$	7.09456	+	5.05488i	0.299800	+	0.213608i
$561$	36.3496	+	13.6248i	1.53468	+	0.575241i
$562$	13.1797	−	12.1597i	0.555952	−	0.512928i
$563$	−6.67927	−	19.6765i	−0.281498	−	0.829265i	−0.992075	−	0.125646i	$-0.959900\pi$
$563$	−6.67927	−	19.6765i	−0.281498	−	0.829265i	0.710577	−	0.703619i	$-0.248434\pi$
$564$	3.49816	−	1.52777i	0.147299	−	0.0643308i
$565$	−29.6481	−	60.1205i	−1.24731	−	2.52929i
$566$	−20.5893	+	0.519379i	−0.865433	+	0.0218311i
$567$	5.26244	+	1.37955i	0.221002	+	0.0579356i
$568$	−0.530959	−	0.0643936i	−0.0222785	−	0.00270190i
$569$	28.4914	+	3.75097i	1.19442	+	0.157249i	0.701400	−	0.712768i	$-0.252559\pi$
$569$	28.4914	+	3.75097i	1.19442	+	0.157249i	0.493023	+	0.870017i	$0.335892\pi$
$570$	3.27612	−	15.9567i	0.137222	−	0.668352i
$571$	16.3804	+	18.6782i	0.685497	+	0.781660i	0.985022	−	0.172429i	$-0.0551615\pi$
$571$	16.3804	+	18.6782i	0.685497	+	0.781660i	−0.299525	+	0.954089i	$0.596828\pi$
$572$	17.2521	+	11.9059i	0.721346	+	0.497809i
$573$	13.4675	+	8.34935i	0.562613	+	0.348799i
$574$	−2.16513	+	2.59822i	−0.0903710	+	0.108447i
$575$	26.4116			1.10144
$576$	11.1099	+	21.2737i	0.462914	+	0.886403i
$577$	−11.6077			−0.483235			−0.241618	−	0.970372i	$-0.577678\pi$
$577$	−11.6077			−0.483235			−0.241618	+	0.970372i	$0.577678\pi$
$578$	4.23109	−	5.07741i	0.175990	−	0.211192i
$579$	22.8536	−	12.2554i	0.949765	−	0.509315i
$580$	32.3649	−	46.8981i	1.34388	−	1.94734i
$581$	3.89683	+	4.44348i	0.161668	+	0.184347i
$582$	−28.4429	+	9.46040i	−1.17900	+	0.392146i
$583$	−4.65929	−	0.613407i	−0.192968	−	0.0254047i
$584$	−11.0660	−	14.1205i	−0.457913	−	0.584312i
$585$	−9.81886	+	14.7815i	−0.405960	+	0.611140i
$586$	−5.58849	+	0.140973i	−0.230858	+	0.00582355i
$587$	0.0812292	+	0.164717i	0.00335269	+	0.00679858i	0.898543	−	0.438886i	$-0.144627\pi$
$587$	0.0812292	+	0.164717i	0.00335269	+	0.00679858i	−0.895190	+	0.445685i	$0.852960\pi$
$588$	−22.8394	−	2.56482i	−0.941881	−	0.105771i
$589$	1.71195	+	5.04324i	0.0705397	+	0.207803i
$590$	37.4779	−	34.5775i	1.54294	−	1.42354i
$591$	0.581532	+	3.49284i	0.0239210	+	0.143676i
$592$	21.5141	+	34.3896i	0.884224	+	1.41340i
$593$	−5.33755	−	5.33755i	−0.219187	−	0.219187i	0.588969	−	0.808156i	$-0.299534\pi$
$593$	−5.33755	−	5.33755i	−0.219187	−	0.219187i	−0.808156	+	0.588969i	$0.799534\pi$
$594$	44.3680	+	15.2313i	1.82044	+	0.624950i
$595$	−1.49167	+	7.49914i	−0.0611526	+	0.307435i
$596$	3.64001	−	0.423741i	0.149101	−	0.0173571i
$597$	42.4623	−	16.0474i	1.73787	−	0.656776i
$598$	7.47061	+	1.80112i	0.305496	+	0.0736532i
$599$	6.18006	+	46.9422i	0.252510	+	1.91801i	0.377801	+	0.925887i	$0.376680\pi$
$599$	6.18006	+	46.9422i	0.252510	+	1.91801i	−0.125290	+	0.992120i	$0.539986\pi$
$600$	−24.4502	+	30.5054i	−0.998174	+	1.24538i
$601$	−5.18418	+	39.3778i	−0.211467	+	1.60625i	0.475602	+	0.879661i	$0.342230\pi$
$601$	−5.18418	+	39.3778i	−0.211467	+	1.60625i	−0.687069	+	0.726592i	$0.741103\pi$
$602$	5.37865	+	2.07059i	0.219217	+	0.0843911i
$603$	−25.1503	−	14.4298i	−1.02420	−	0.587628i
$604$	20.0936	+	18.1624i	0.817599	+	0.739016i
$605$	106.955	−	7.01017i	4.34832	−	0.285004i
$606$	−17.3492	+	9.87481i	−0.704764	+	0.401137i
$607$	−1.40029	+	0.808456i	−0.0568359	+	0.0328142i	−0.528149	−	0.849152i	$-0.677114\pi$
$607$	−1.40029	+	0.808456i	−0.0568359	+	0.0328142i	0.471313	+	0.881966i	$0.343780\pi$
$608$	5.26414	−	9.01756i	0.213489	−	0.365710i
$609$	0.800370	−	8.24071i	0.0324326	−	0.333931i
$610$	−68.0258	+	6.18487i	−2.75428	+	0.250418i
$611$	1.00513	+	1.50429i	0.0406633	+	0.0608569i
$612$	−13.0285	+	16.5534i	−0.526644	+	0.669132i
$613$	−5.31886	−	26.7397i	−0.214827	−	1.08001i	−0.926154	−	0.377146i	$-0.876905\pi$
$613$	−5.31886	−	26.7397i	−0.214827	−	1.08001i	0.711327	−	0.702861i	$-0.248095\pi$
$614$	5.11462	+	6.32844i	0.206409	+	0.255395i
$615$	−18.0420	−	16.8524i	−0.727526	−	0.679554i
$616$	10.7255	+	2.01982i	0.432145	+	0.0813808i
$617$	−1.36547	−	10.3718i	−0.0549718	−	0.417552i	−0.996700	−	0.0811766i	$-0.974132\pi$
$617$	−1.36547	−	10.3718i	−0.0549718	−	0.417552i	0.941728	−	0.336375i	$-0.109201\pi$
$618$	23.8799	−	4.59753i	0.960592	−	0.184940i
$619$	16.2335	−	8.00549i	0.652480	−	0.321768i	−0.0857497	−	0.996317i	$-0.527329\pi$
$619$	16.2335	−	8.00549i	0.652480	−	0.321768i	0.738230	+	0.674549i	$0.235662\pi$
$620$	3.02280	−	20.5698i	0.121398	−	0.826102i
$621$	17.1858	−	0.632532i	0.689644	−	0.0253826i
$622$	14.5508	+	9.20042i	0.583435	+	0.368903i
$623$	−3.06204	+	0.820471i	−0.122678	+	0.0328715i
$624$	−8.99612	+	6.96119i	−0.360133	+	0.278671i
$625$	1.17643	+	0.315223i	0.0470571	+	0.0126089i
$626$	−1.19995	−	1.30060i	−0.0479598	−	0.0519826i
$627$	−4.66129	−	19.8694i	−0.186154	−	0.793508i
$628$	−16.2995	−	4.63072i	−0.650421	−	0.184786i
$629$	−19.7810	+	29.6044i	−0.788721	+	1.18040i
$630$	−1.54879	+	9.10887i	−0.0617051	+	0.362906i
$631$	−3.01843	+	7.28714i	−0.120162	+	0.290097i	−0.972503	−	0.232889i	$-0.925182\pi$
$631$	−3.01843	+	7.28714i	−0.120162	+	0.290097i	0.852341	+	0.522986i	$0.175182\pi$
$632$	−12.8708	−	3.30824i	−0.511972	−	0.131595i
$633$	5.26487	+	17.2717i	0.209260	+	0.686488i
$634$	2.73569	−	3.75777i	0.108648	−	0.149240i
$635$	−25.5408	−	29.1237i	−1.01356	−	1.15574i
$636$	1.08411	−	2.30831i	0.0429878	−	0.0915305i
$637$	−0.712428	−	10.8696i	−0.0282274	−	0.430668i
$638$	12.1576	−	70.3486i	0.481325	−	2.78513i
$639$	−0.183805	−	0.536691i	−0.00727122	−	0.0212312i
$640$	−34.3334	+	21.9699i	−1.35715	+	0.868437i
$641$	−8.57017	+	14.8440i	−0.338501	+	0.586301i	−0.984151	−	0.177332i	$-0.943253\pi$
$641$	−8.57017	+	14.8440i	−0.338501	+	0.586301i	0.645650	+	0.763634i	$0.276587\pi$
$642$	−3.61171	+	0.943987i	−0.142543	+	0.0372562i
$643$	−14.0263	−	6.91699i	−0.553142	−	0.272780i	0.144163	−	0.989554i	$-0.453951\pi$
$643$	−14.0263	−	6.91699i	−0.553142	−	0.272780i	−0.697305	+	0.716774i	$0.745618\pi$
$644$	3.93559	−	0.721608i	0.155084	−	0.0284353i
$645$	−17.3114	+	38.3451i	−0.681634	+	1.50984i
$646$	9.11379	+	0.966742i	0.358577	+	0.0380359i
$647$	13.1701	+	31.7954i	0.517769	+	1.25001i	0.939271	+	0.343177i	$0.111503\pi$
$647$	13.1701	+	31.7954i	0.517769	+	1.25001i	−0.421502	+	0.906828i	$0.638497\pi$
$648$	−15.1790	+	20.4352i	−0.596288	+	0.802771i
$649$	24.4485	−	59.0240i	0.959689	−	2.31689i
$650$	−16.2752	−	8.85692i	−0.638364	−	0.347397i
$651$	−1.06794	−	2.82584i	−0.0418559	−	0.110753i
$652$	22.3504	−	21.6894i	0.875310	−	0.849422i
$653$	4.01193	+	11.8188i	0.156999	+	0.462504i	0.996758	−	0.0804551i	$-0.0256374\pi$
$653$	4.01193	+	11.8188i	0.156999	+	0.462504i	−0.839759	+	0.542959i	$0.817304\pi$
$654$	−15.6951	−	20.7168i	−0.613726	−	0.810090i
$655$	8.88156	+	33.1464i	0.347031	+	1.29514i
$656$	−7.49776	−	13.9365i	−0.292738	−	0.544128i
$657$	8.36973	−	17.0887i	0.326534	−	0.666693i
$658$	0.796189	+	0.503427i	0.0310387	+	0.0196256i
$659$	−7.55623	−	6.62664i	−0.294349	−	0.258137i	0.499415	−	0.866363i	$-0.333548\pi$
$659$	−7.55623	−	6.62664i	−0.294349	−	0.258137i	−0.793764	+	0.608226i	$0.791882\pi$
$660$	−19.1489	+	77.3346i	−0.745371	+	3.01025i
$661$	2.84885	−	43.4650i	0.110807	−	1.69059i	−0.474876	−	0.880053i	$-0.657507\pi$
$661$	2.84885	−	43.4650i	0.110807	−	1.69059i	0.585683	−	0.810540i	$-0.300826\pi$
$662$	−0.790201	+	3.27756i	−0.0307120	+	0.127386i
$663$	−8.81155	−	4.69454i	−0.342212	−	0.182321i
$664$	−26.0948	+	9.15618i	−1.01267	+	0.355329i
$665$	3.71386	−	1.53833i	0.144017	−	0.0596539i
$666$	−22.8953	+	36.4279i	−0.887174	+	1.41155i
$667$	−5.10604	−	25.6698i	−0.197707	−	0.993939i
$668$	9.82887	−	19.1991i	0.380290	−	0.742834i
$669$	−3.36457	+	5.42705i	−0.130082	+	0.209822i
$670$	20.6601	−	44.7024i	0.798171	−	1.72700i
$671$	−74.1143	+	42.7899i	−2.86115	+	1.65189i
$672$	−2.80987	+	5.21362i	−0.108393	+	0.201120i
$673$	−4.08641	−	2.35929i	−0.157520	−	0.0909440i	0.419168	−	0.907909i	$-0.362322\pi$
$673$	−4.08641	−	2.35929i	−0.157520	−	0.0909440i	−0.576688	+	0.816965i	$0.695655\pi$
$674$	18.1110	−	12.7736i	0.697611	−	0.492020i
$675$	−40.4208	−	9.25178i	−1.55580	−	0.356101i
$676$	15.2888	+	13.8194i	0.588032	+	0.531514i
$677$	−29.3680	−	9.96909i	−1.12870	−	0.383143i	−0.306236	−	0.951956i	$-0.599070\pi$
$677$	−29.3680	−	9.96909i	−1.12870	−	0.383143i	−0.822467	+	0.568813i	$0.807403\pi$
$678$	38.0493	−	25.0866i	1.46127	−	0.963446i
$679$	−5.86850	−	4.50306i	−0.225212	−	0.172811i
$680$	−29.9490	−	19.5719i	−1.14849	−	0.750549i
$681$	0.600743	+	17.6209i	0.0230205	+	0.675233i
$682$	−7.37414	−	24.9827i	−0.282370	−	0.956637i
$683$	−13.4132	−	8.96240i	−0.513241	−	0.342937i	0.271827	−	0.962346i	$-0.412372\pi$
$683$	−13.4132	−	8.96240i	−0.513241	−	0.342937i	−0.785068	+	0.619409i	$0.787372\pi$
$684$	11.0416	+	0.860213i	0.422184	+	0.0328911i
$685$	−12.0983	+	60.8223i	−0.462252	+	2.32390i
$686$	−5.41712	−	10.3203i	−0.206826	−	0.394030i
$687$	−3.71884	−	4.51892i	−0.141882	−	0.172407i
$688$	−18.3818	+	19.7328i	−0.700800	+	0.752308i
$689$	1.16750	+	0.312831i	0.0444783	+	0.0119179i
$690$	3.63422	+	28.9808i	0.138352	+	1.10328i
$691$	13.8271	−	15.7668i	0.526007	−	0.599796i	−0.426434	−	0.904519i	$-0.640230\pi$
$691$	13.8271	−	15.7668i	0.526007	−	0.599796i	0.952441	+	0.304722i	$0.0985637\pi$
$692$	6.33757	−	10.6061i	0.240918	−	0.403184i
$693$	3.02640	+	11.1735i	0.114964	+	0.424447i
$694$	34.6933	−	0.875161i	1.31694	−	0.0332207i
$695$	−4.60907	−	6.00666i	−0.174832	−	0.227846i
$696$	34.3755	+	17.8660i	1.30300	+	0.677211i
$697$	8.45592	−	11.0200i	0.320291	−	0.417411i
$698$	−7.30066	−	5.31495i	−0.276334	−	0.201174i
$699$	−9.46513	+	20.9655i	−0.358004	+	0.792988i
$700$	−9.61636	−	0.775398i	−0.363464	−	0.0293073i
$701$	9.51404	−	6.35708i	0.359340	−	0.240103i	−0.362774	−	0.931877i	$-0.618170\pi$
$701$	9.51404	−	6.35708i	0.359340	−	0.240103i	0.722114	+	0.691774i	$0.243170\pi$
$702$	−10.8023	−	5.37337i	−0.407705	−	0.202805i
$703$	18.7190			0.705999
$704$	−27.4992	+	43.0326i	−1.03642	+	1.62185i
$705$	−3.99774	+	5.59483i	−0.150564	+	0.210713i
$706$	−5.03587	−	13.6908i	−0.189528	−	0.515259i
$707$	−4.41825	−	2.17884i	−0.166165	−	0.0819437i
$708$	26.4965	+	22.3575i	0.995801	+	0.840248i
$709$	−8.26559	+	24.3496i	−0.310421	+	0.914470i	0.674014	+	0.738719i	$0.264569\pi$
$709$	−8.26559	+	24.3496i	−0.310421	+	0.914470i	−0.984435	+	0.175751i	$0.943765\pi$
$710$	0.880556	−	0.391036i	0.0330467	−	0.0146753i
$711$	−2.78730	−	13.8169i	−0.104532	−	0.518176i
$712$	1.78586	−	14.7253i	0.0669278	−	0.551855i
$713$	−5.81338	−	7.57615i	−0.217713	−	0.283729i
$714$	−5.18513	−	0.371890i	−0.194048	−	0.0139176i
$715$	−37.6792	−	2.46962i	−1.40912	−	0.0923586i
$716$	0.704557	−	46.9380i	0.0263305	−	1.75416i
$717$	−21.5316	−	6.49971i	−0.804113	−	0.242736i
$718$	46.3350	+	14.4362i	1.72921	+	0.538753i
$719$	−7.18948	+	7.18948i	−0.268122	+	0.268122i	−0.828343	−	0.560221i	$-0.810716\pi$
$719$	−7.18948	+	7.18948i	−0.268122	+	0.268122i	0.560221	+	0.828343i	$0.310716\pi$
$720$	−36.8371	−	22.6311i	−1.37284	−	0.843411i
$721$	4.24349	+	4.24349i	0.158036	+	0.158036i
$722$	10.2488	+	19.5253i	0.381423	+	0.726657i
$723$	4.00676	−	0.939970i	0.149013	−	0.0349579i
$724$	41.7584	+	18.0359i	1.55194	+	0.670297i
$725$	−4.12739	+	62.9718i	−0.153287	+	2.33872i
$726$	13.7770	+	71.5587i	0.511311	+	2.65579i
$727$	24.2477	−	18.6060i	0.899299	−	0.690057i	−0.0518940	−	0.998653i	$-0.516526\pi$
$727$	24.2477	−	18.6060i	0.899299	−	0.690057i	0.951193	+	0.308596i	$0.0998591\pi$
$728$	−2.66715	−	0.875106i	−0.0988511	−	0.0324336i
$729$	−26.5231	−	5.05203i	−0.982339	−	0.187112i
$730$	30.1595	+	11.6104i	1.11625	+	0.429719i
$731$	−22.4145	−	7.60869i	−0.829029	−	0.281417i
$732$	−9.92702	−	45.3671i	−0.366913	−	1.67682i
$733$	−18.6289	+	37.7756i	−0.688072	+	1.39527i	0.219599	+	0.975590i	$0.429525\pi$
$733$	−18.6289	+	37.7756i	−0.688072	+	1.39527i	−0.907671	+	0.419683i	$0.862141\pi$
$734$	28.5226	+	13.1823i	1.05279	+	0.486568i
$735$	37.6879	−	17.1378i	1.39014	−	0.632136i
$736$	−3.74059	+	18.3448i	−0.137880	+	0.676197i
$737$		−	61.6991i		−	2.27272i
$738$	9.84238	−	13.5968i	0.362303	−	0.500507i
$739$	−11.4631	−	17.1558i	−0.421678	−	0.631086i	0.558430	−	0.829552i	$-0.311404\pi$
$739$	−11.4631	−	17.1558i	−0.421678	−	0.631086i	−0.980108	+	0.198466i	$0.936404\pi$
$740$	−65.0450	−	33.2995i	−2.39110	−	1.22411i
$741$	0.521573	+	5.22307i	0.0191605	+	0.191874i
$742$	0.621676	−	0.0978524i	0.0228224	−	0.00359227i
$743$	−12.4915	−	9.58504i	−0.458267	−	0.351641i	0.353685	−	0.935365i	$-0.384928\pi$
$743$	−12.4915	−	9.58504i	−0.458267	−	0.351641i	−0.811952	+	0.583724i	$0.801595\pi$
$744$	14.1321	+	0.299070i	0.518109	+	0.0109644i
$745$	−5.23724	+	4.01868i	−0.191878	+	0.147233i
$746$	−13.2426	−	12.5909i	−0.484847	−	0.460987i
$747$	−20.7970	−	20.6846i	−0.760923	−	0.756811i
$748$	−44.3482	−	6.51712i	−1.62153	−	0.238289i
$749$	−0.692610	−	0.607403i	−0.0253074	−	0.0221940i
$750$	3.59312	−	26.0533i	0.131202	−	0.951332i
$751$	11.6792	−	43.5874i	0.426180	−	1.59053i	−0.335153	−	0.942164i	$-0.608788\pi$
$751$	11.6792	−	43.5874i	0.426180	−	1.59053i	0.761333	−	0.648361i	$-0.224545\pi$
$752$	−3.57586	+	2.57710i	−0.130398	+	0.0939772i
$753$	−5.70728	−	34.2795i	−0.207985	−	1.24921i
$754$	−5.46177	+	17.5304i	−0.198906	+	0.638418i
$755$	−47.8543	−	9.51882i	−1.74160	−	0.346425i
$756$	−6.27588	−	0.274244i	−0.228252	−	0.00997415i
$757$	3.41871	−	5.11647i	0.124255	−	0.185961i	−0.764127	−	0.645066i	$-0.776830\pi$
$757$	3.41871	−	5.11647i	0.124255	−	0.185961i	0.888382	+	0.459105i	$0.151830\pi$
$758$	−12.9165	−	7.02913i	−0.469147	−	0.255309i
$759$	19.3661	+	31.0494i	0.702946	+	1.12702i
$760$	0.192062	+	18.8085i	0.00696682	+	0.682258i
$761$	31.4108	−	40.9354i	1.13864	−	1.48391i	0.288404	−	0.957509i	$-0.406876\pi$
$761$	31.4108	−	40.9354i	1.13864	−	1.48391i	0.850238	−	0.526398i	$-0.176458\pi$
$762$	17.4863	−	19.6936i	0.633460	−	0.713424i
$763$	2.06167	−	6.07349i	0.0746376	−	0.219875i
$764$	−17.2358	−	6.14076i	−0.623568	−	0.222165i
$765$	4.85118	−	37.6360i	0.175395	−	1.36073i
$766$	0.185936	−	1.07590i	0.00671816	−	0.0388738i
$767$	−8.21572	+	14.2300i	−0.296652	+	0.513817i
$768$	−17.7254	−	21.3028i	−0.639610	−	0.768700i
$769$	10.7369	+	18.5969i	0.387182	+	0.670620i	0.992069	−	0.125692i	$-0.0401150\pi$
$769$	10.7369	+	18.5969i	0.387182	+	0.670620i	−0.604887	+	0.796311i	$0.706782\pi$
$770$	−18.4519	+	6.78717i	−0.664961	+	0.244592i
$771$	−11.8662	+	6.36329i	−0.427350	+	0.229168i
$772$	−22.8069	+	19.4033i	−0.820838	+	0.698342i
$773$	36.8106	−	7.32208i	1.32398	−	0.263357i	0.518044	−	0.855354i	$-0.326660\pi$
$773$	36.8106	−	7.32208i	1.32398	−	0.263357i	0.805940	+	0.591997i	$0.201660\pi$
$774$	−27.3321	−	8.43445i	−0.982434	−	0.303170i
$775$	8.81150	+	21.2728i	0.316519	+	0.764143i
$776$	29.7967	−	17.6112i	1.06964	−	0.632206i
$777$	−10.6114	+	0.361773i	−0.380683	+	0.0129785i
$778$	−33.9834	+	20.7802i	−1.21836	+	0.745007i
$779$	−7.28711	−	0.477622i	−0.261088	−	0.0171126i
$780$	7.47904	−	19.0771i	0.267793	−	0.683068i
$781$	0.795911	−	0.907563i	0.0284799	−	0.0324751i
$782$	−16.0313	+	3.61135i	−0.573279	+	0.129142i
$783$	−1.17755	+	41.0742i	−0.0420823	+	1.46787i
$784$	26.4035	−	2.67269i	0.942983	−	0.0954533i
$785$	29.4838	−	7.90016i	1.05232	−	0.281969i
$786$	−21.6093	+	8.79557i	−0.770779	+	0.313727i
$787$	−45.9341	+	15.5925i	−1.63738	+	0.555814i	−0.980215	−	0.197937i	$-0.936576\pi$
$787$	−45.9341	+	15.5925i	−1.63738	+	0.555814i	−0.657161	+	0.753751i	$0.728243\pi$
$788$	−1.50781	−	3.80053i	−0.0537134	−	0.135388i
$789$	1.57856	−	9.64247i	0.0561983	−	0.343281i
$790$	22.9598	−	6.77703i	0.816872	−	0.241116i
$791$	10.3907	+	4.30396i	0.369450	+	0.153031i
$792$	−53.7900	−	6.37572i	−1.91134	−	0.226551i
$793$	20.3352	−	8.42313i	0.722125	−	0.299114i
$794$	0.173435	+	0.214595i	0.00615498	+	0.00761570i
$795$	0.456479	+	4.57122i	0.0161896	+	0.162125i
$796$	−44.0143	+	28.4633i	−1.56005	+	1.00885i
$797$	−4.00309	+	8.11747i	−0.141797	+	0.287536i	−0.956173	−	0.292801i	$-0.905413\pi$
$797$	−4.00309	+	8.11747i	−0.141797	+	0.287536i	0.814376	+	0.580337i	$0.197079\pi$
$798$	1.35194	+	2.37524i	0.0478580	+	0.0840826i
$799$	−3.35049	−	1.93441i	−0.118532	−	0.0684343i
$800$	20.1601	−	40.3909i	0.712766	−	1.42803i
$801$	14.8843	−	5.09755i	0.525911	−	0.180113i
$802$	−34.0519	+	24.0165i	−1.20241	+	0.848053i
$803$	40.4029	−	2.64814i	1.42579	−	0.0934510i
$804$	31.9041	+	10.1557i	1.12517	+	0.358165i
$805$	−5.41907	+	4.75240i	−0.190997	+	0.167500i
$806$	1.04168	+	6.61800i	0.0366916	+	0.233109i
$807$	5.63434	−	24.3132i	0.198338	−	0.855866i
$808$	17.1745	−	15.3747i	0.604196	−	0.540879i
$809$	27.0877	+	11.2201i	0.952351	+	0.394477i	0.804114	−	0.594475i	$-0.202640\pi$
$809$	27.0877	+	11.2201i	0.952351	+	0.394477i	0.148237	+	0.988952i	$0.452640\pi$
$810$	4.58988	−	45.6258i	0.161272	−	1.60313i
$811$	−16.1062	−	10.7618i	−0.565565	−	0.377899i	0.239670	−	0.970855i	$-0.422961\pi$
$811$	−16.1062	−	10.7618i	−0.565565	−	0.377899i	−0.805235	+	0.592956i	$0.797961\pi$
$812$	1.10547	+	9.49620i	0.0387945	+	0.333251i
$813$	−17.4637	−	18.5953i	−0.612480	−	0.652165i
$814$	−91.4781	−	3.68211i	−3.20631	−	0.129058i
$815$	−14.5206	+	54.1917i	−0.508635	+	1.89825i
$816$	10.6697	−	21.8594i	0.373514	−	0.765231i
$817$	3.22091	+	12.0206i	0.112685	+	0.420548i
$818$	−2.80144	−	12.4360i	−0.0979502	−	0.434815i
$819$	−0.396614	−	2.95078i	−0.0138588	−	0.103109i
$820$	24.4717	+	14.6228i	0.854590	+	0.510651i
$821$	−1.95417	−	3.96266i	−0.0682010	−	0.138298i	0.860103	−	0.510121i	$-0.170399\pi$
$821$	−1.95417	−	3.96266i	−0.0682010	−	0.138298i	−0.928304	+	0.371823i	$0.878733\pi$
$822$	−42.0543	−	3.01624i	−1.46681	−	0.105203i
$823$	40.1204	−	5.28196i	1.39851	−	0.184117i	0.606723	−	0.794914i	$-0.292484\pi$
$823$	40.1204	−	5.28196i	1.39851	−	0.184117i	0.791788	+	0.610796i	$0.209150\pi$
$824$	−25.8320	+	11.0103i	−0.899899	+	0.383562i
$825$	−25.7274	−	84.4001i	−0.895712	−	2.93843i
$826$	−0.902447	+	8.50767i	−0.0314002	+	0.296020i
$827$	14.8458	−	2.95301i	0.516238	−	0.102686i	0.0699061	−	0.997554i	$-0.477730\pi$
$827$	14.8458	−	2.95301i	0.516238	−	0.102686i	0.446332	+	0.894867i	$0.352730\pi$
$828$	−19.2431	+	4.90330i	−0.668742	+	0.170401i
$829$	42.8724	−	28.6464i	1.48902	−	0.994932i	0.497153	−	0.867663i	$-0.334379\pi$
$829$	42.8724	−	28.6464i	1.48902	−	0.994932i	0.991868	−	0.127270i	$-0.0406213\pi$
$830$	31.8916	−	38.2707i	1.10697	−	1.32839i
$831$	0.746838	+	1.64238i	0.0259075	+	0.0569737i
$832$	8.45679	−	10.0499i	0.293186	−	0.348418i
$833$	11.6468	+	20.1728i	0.403537	+	0.698947i
$834$	3.66220	−	3.61743i	0.126811	−	0.125261i
$835$	2.54117	+	38.7707i	0.0879407	+	1.34172i
$836$	10.1046	+	21.2899i	0.349476	+	0.736325i
$837$	6.24306	+	13.6311i	0.215792	+	0.471159i
$838$	28.7019	−	12.7459i	0.991492	−	0.440301i
$839$	21.2630	+	2.79933i	0.734081	+	0.0966436i	0.488293	−	0.872680i	$-0.337620\pi$
$839$	21.2630	+	2.79933i	0.734081	+	0.0966436i	0.245788	+	0.969324i	$0.420953\pi$
$840$	−0.472381	−	10.6585i	−0.0162987	−	0.367753i
$841$	33.2494	−	4.37736i	1.14653	−	0.150943i
$842$	21.0097	+	34.3587i	0.724042	+	1.18408i
$843$	−21.6738	−	3.54821i	−0.746487	−	0.122207i
$844$	−10.1526	−	18.2107i	−0.349468	−	0.626840i
$845$	−36.4114	−	7.24267i	−1.25259	−	0.249155i
$846$	−4.11247	−	2.22358i	−0.141390	−	0.0764484i
$847$	−12.7160	+	12.7160i	−0.436928	+	0.436928i
$848$	−0.660916	+	2.86961i	−0.0226959	+	0.0985428i
$849$	16.0288	+	19.4772i	0.550106	+	0.668457i
$850$	39.5909	+	1.59358i	1.35796	+	0.0546595i
$851$	−31.7826	+	10.7887i	−1.08949	+	0.369833i
$852$	0.338285	+	0.560944i	0.0115895	+	0.0192176i
$853$	−6.55510	+	3.23262i	−0.224443	+	0.110683i	−0.551034	−	0.834483i	$-0.685767\pi$
$853$	−6.55510	+	3.23262i	−0.224443	+	0.110683i	0.326591	+	0.945166i	$0.394100\pi$
$854$	7.89677	−	8.30548i	0.270222	−	0.284208i
$855$	−17.8691	+	8.87233i	−0.611110	+	0.303427i
$856$	3.84634	−	1.94588i	0.131465	−	0.0665088i
$857$	−5.98689	+	45.4750i	−0.204508	+	1.55340i	0.513947	+	0.857822i	$0.328183\pi$
$857$	−5.98689	+	45.4750i	−0.204508	+	1.55340i	−0.718455	+	0.695573i	$0.755150\pi$
$858$	−1.52148	−	25.6273i	−0.0519425	−	0.874903i
$859$	13.4477	−	11.7933i	0.458828	−	0.402381i	−0.398487	−	0.917174i	$-0.630464\pi$
$859$	13.4477	−	11.7933i	0.458828	−	0.402381i	0.857315	+	0.514793i	$0.172131\pi$
$860$	10.1916	−	47.4992i	0.347530	−	1.61971i
$861$	4.14016	+	0.129921i	0.141096	+	0.00442768i
$862$	−0.826740	−	9.09310i	−0.0281589	−	0.309712i
$863$		−	36.6324i		−	1.24698i	−0.781831	−	0.623491i	$-0.785714\pi$
$863$		−	36.6324i		−	1.24698i	0.781831	−	0.623491i	$-0.214286\pi$
$864$	12.1507	−	26.7649i	0.413376	−	0.910561i
$865$			22.2569i			0.756757i
$866$	−54.1581	+	4.92403i	−1.84037	+	0.167325i
$867$	−8.09067	−	0.253890i	−0.274773	−	0.00862255i
$868$	1.89421	+	2.92912i	0.0642938	+	0.0994209i
$869$	22.5498	−	19.7756i	0.764949	−	0.670843i
$870$	−69.6655	+	4.13600i	−2.36188	+	0.140224i
$871$	−2.07128	+	15.7329i	−0.0701827	+	0.533090i
$872$	22.7648	+	19.5566i	0.770912	+	0.662269i
$873$	30.5798	+	20.3132i	1.03497	+	0.687496i
$874$	6.26119	+	5.95308i	0.211788	+	0.201366i
$875$	5.82085	−	2.87052i	0.196781	−	0.0970414i
$876$	−5.28102	+	21.3279i	−0.178429	+	0.720602i
$877$	−22.1892	+	7.53222i	−0.749276	+	0.254345i	−0.669851	−	0.742496i	$-0.733642\pi$
$877$	−22.1892	+	7.53222i	−0.749276	+	0.254345i	−0.0794253	+	0.996841i	$0.525309\pi$
$878$	−1.10254	+	27.3915i	−0.0372090	+	0.924419i
$879$	4.35063	+	5.28664i	0.146743	+	0.178314i
$880$	2.76114	−	91.9537i	0.0930780	−	3.09976i
$881$	10.0915	−	10.0915i	0.339991	−	0.339991i	−0.516373	−	0.856364i	$-0.672718\pi$
$881$	10.0915	−	10.0915i	0.339991	−	0.339991i	0.856364	+	0.516373i	$0.172718\pi$
$882$	14.7494	+	23.9746i	0.496638	+	0.807266i
$883$	−16.9081	−	3.36323i	−0.569003	−	0.113182i	−0.0977995	−	0.995206i	$-0.531180\pi$
$883$	−16.9081	−	3.36323i	−0.569003	−	0.113182i	−0.471204	+	0.882024i	$0.656180\pi$
$884$	11.0898	+	3.15063i	0.372989	+	0.105967i
$885$	−61.6319	−	10.0897i	−2.07173	−	0.339162i
$886$	−16.0231	+	9.79786i	−0.538308	+	0.329165i
$887$	44.2431	−	5.82472i	1.48554	−	0.195575i	0.656313	−	0.754489i	$-0.272115\pi$
$887$	44.2431	−	5.82472i	1.48554	−	0.195575i	0.829226	+	0.558914i	$0.188782\pi$
$888$	16.9614	−	46.6965i	0.569186	−	1.56703i
$889$	6.44357	+	0.848313i	0.216111	+	0.0284515i
$890$	10.8448	+	24.4208i	0.363518	+	0.818588i
$891$	−18.7619	−	54.3025i	−0.628549	−	1.81920i
$892$	2.47456	−	6.94556i	0.0828545	−	0.232554i
$893$	0.133030	+	2.02964i	0.00445166	+	0.0679193i
$894$	−3.15405	−	3.19309i	−0.105487	−	0.106793i
$895$	42.2818	+	73.2342i	1.41332	+	2.44795i
$896$	1.90051	−	6.56945i	0.0634915	−	0.219470i
$897$	−3.89591	−	8.56756i	−0.130081	−	0.286062i
$898$	17.0080	+	14.1731i	0.567565	+	0.472961i
$899$	18.9719	−	12.6766i	0.632749	−	0.422790i
$900$	47.8773	+	0.588920i	1.59591	+	0.0196307i
$901$	−2.53502	+	0.504247i	−0.0844537	+	0.0167989i
$902$	35.5176	+	3.76751i	1.18261	+	0.125444i
$903$	−2.05819	−	6.75201i	−0.0684924	−	0.224693i
$904$	−36.8300	+	37.5899i	−1.22495	+	1.25022i
$905$	−81.2391	+	10.6953i	−2.70048	+	0.355525i
$906$	2.37314	−	33.0879i	0.0788424	−	1.09927i
$907$	3.50336	+	7.10411i	0.116327	+	0.235888i	0.947247	−	0.320504i	$-0.103852\pi$
$907$	3.50336	+	7.10411i	0.116327	+	0.235888i	−0.830920	+	0.556392i	$0.812185\pi$
$908$	−4.97346	−	19.7418i	−0.165050	−	0.655155i
$909$	22.6133	+	9.29505i	0.750037	+	0.308297i
$910$	4.93299	−	1.11125i	0.163527	−	0.0368375i
$911$	−0.525641	−	1.96172i	−0.0174153	−	0.0649947i	0.956671	−	0.291170i	$-0.0940445\pi$
$911$	−0.525641	−	1.96172i	−0.0174153	−	0.0649947i	−0.974087	+	0.226175i	$0.927378\pi$
$912$	−12.6720	+	1.72069i	−0.419613	+	0.0569776i
$913$	16.1541	−	60.2879i	0.534622	−	1.99524i
$914$	−0.503430	+	12.5072i	−0.0166520	+	0.413701i
$915$	57.2706	+	60.9814i	1.89331	+	2.01598i
$916$	5.29893	+	4.19386i	0.175082	+	0.138569i
$917$	−4.78715	−	3.19867i	−0.158085	−	0.105629i
$918$	25.7997	+	0.0887706i	0.851518	+	0.00292987i
$919$	3.50884	+	1.45341i	0.115746	+	0.0479435i	0.439805	−	0.898093i	$-0.355048\pi$
$919$	3.50884	+	1.45341i	0.115746	+	0.0479435i	−0.324059	+	0.946037i	$0.605048\pi$
$920$	−11.1665	−	31.8240i	−0.368148	−	1.04921i
$921$	2.24980	−	9.70830i	0.0741333	−	0.319899i
$922$	−52.0515	+	8.19295i	−1.71422	+	0.269820i
$923$	−0.233420	+	0.204704i	−0.00768313	+	0.00673792i
$924$	−6.13959	−	11.8735i	−0.201978	−	0.390611i
$925$	80.7550	−	5.29296i	2.65521	−	0.174031i
$926$	27.7660	+	39.3681i	0.912447	+	1.29372i
$927$	−22.4459	−	19.5772i	−0.737219	−	0.642999i
$928$	−43.1540	−	11.7853i	−1.41660	−	0.386871i
$929$	10.9451	+	6.31915i	0.359097	+	0.207324i	0.668684	−	0.743546i	$-0.266858\pi$
$929$	10.9451	+	6.31915i	0.359097	+	0.207324i	−0.309588	+	0.950871i	$0.600191\pi$
$930$	−22.1297	+	12.5958i	−0.725663	+	0.413032i
$931$	5.41644	−	10.9835i	0.177517	−	0.359968i
$932$	5.57233	−	25.9706i	0.182528	−	0.850694i
$933$	−2.09508	−	20.9803i	−0.0685897	−	0.686863i
$934$	−35.8257	+	28.9542i	−1.17225	+	0.947411i
$935$	74.6004	−	30.9005i	2.43969	−	1.01055i
$936$	13.5021	+	3.43154i	0.441331	+	0.112163i
$937$	10.7335	+	4.44595i	0.350648	+	0.145243i	0.551053	−	0.834470i	$-0.314226\pi$
$937$	10.7335	+	4.44595i	0.350648	+	0.145243i	−0.200406	+	0.979713i	$0.564226\pi$
$938$	2.33904	+	7.92440i	0.0763725	+	0.258741i
$939$	−0.350147	+	2.13883i	−0.0114266	+	0.0697981i
$940$	3.14831	−	7.28928i	0.102686	−	0.237750i
$941$	−18.5546	+	6.29844i	−0.604862	+	0.205323i	−0.607036	−	0.794674i	$-0.707642\pi$
$941$	−18.5546	+	6.29844i	−0.604862	+	0.205323i	0.00217331	+	0.999998i	$0.499308\pi$
$942$	7.82366	+	19.2215i	0.254909	+	0.626270i
$943$	12.6479	−	3.38900i	0.411873	−	0.110361i
$944$	−35.3561	−	18.7754i	−1.15074	−	0.611086i
$945$	9.95819	−	5.37491i	0.323940	−	0.174846i
$946$	−13.3758	−	59.3774i	−0.434886	−	1.93052i
$947$	−2.08722	+	2.38002i	−0.0678256	+	0.0773403i	−0.784757	−	0.619803i	$-0.787213\pi$
$947$	−2.08722	+	2.38002i	−0.0678256	+	0.0773403i	0.716932	+	0.697143i	$0.245546\pi$
$948$	6.51410	+	14.9154i	0.211568	+	0.484429i
$949$	−10.3914	−	0.681089i	−0.337320	−	0.0221091i
$950$	−10.8673	−	17.7722i	−0.352583	−	0.576605i
$951$	−5.68944	+	0.193968i	−0.184493	+	0.00628986i
$952$	5.94298	−	0.844230i	0.192613	−	0.0273616i
$953$	−14.1494	−	34.1598i	−0.458345	−	1.10654i	−0.969067	−	0.246797i	$-0.920622\pi$
$953$	−14.1494	−	34.1598i	−0.458345	−	1.10654i	0.510722	−	0.859746i	$-0.329378\pi$
$954$	−3.04514	+	0.694647i	−0.0985900	+	0.0224900i
$955$	32.3269	−	6.43022i	1.04607	−	0.208077i
$956$	25.8867	+	2.08732i	0.837234	+	0.0675088i
$957$	−77.0560	+	41.3216i	−2.49087	+	1.33574i
$958$	−1.32570	−	3.60412i	−0.0428314	−	0.116444i
$959$	−5.20231	−	9.01066i	−0.167991	−	0.290969i
$960$	47.0940	+	16.5634i	1.51995	+	0.534582i
$961$	−11.3374	+	19.6369i	−0.365721	+	0.633448i
$962$	23.2028	+	4.00990i	0.748089	+	0.129284i
$963$	3.63475	+	2.77343i	0.117128	+	0.0893725i
$964$	−4.29320	+	2.03765i	−0.138275	+	0.0656282i
$965$	17.3388	−	51.0785i	0.558156	−	1.64427i
$966$	−3.66441	−	3.25368i	−0.117900	−	0.104686i
$967$	18.2962	−	23.8441i	0.588367	−	0.766774i	−0.400384	−	0.916347i	$-0.631123\pi$
$967$	18.2962	−	23.8441i	0.588367	−	0.766774i	0.988751	+	0.149573i	$0.0477900\pi$
$968$	−32.9935	−	77.4082i	−1.06045	−	2.48799i
$969$	−5.94031	−	9.52399i	−0.190830	−	0.305955i
$970$	−29.8035	+	54.7659i	−0.956934	+	1.75843i
$971$	5.49509	−	8.22398i	0.176346	−	0.263920i	−0.732758	−	0.680489i	$-0.761767\pi$
$971$	5.49509	−	8.22398i	0.176346	−	0.263920i	0.909104	+	0.416569i	$0.136767\pi$
$972$	31.1676	−	0.763409i	0.999700	−	0.0244864i
$973$	1.24588	+	0.247822i	0.0399412	+	0.00794480i
$974$	−52.7350	−	16.4302i	−1.68974	−	0.526456i
$975$	3.72697	+	22.3852i	0.119359	+	0.716901i
$976$	22.2635	+	48.7849i	0.712637	+	1.56157i
$977$	2.27807	−	8.50188i	0.0728820	−	0.271999i	−0.919863	−	0.392240i	$-0.871700\pi$
$977$	2.27807	−	8.50188i	0.0728820	−	0.271999i	0.992745	+	0.120241i	$0.0383668\pi$
$978$	−37.7862	−	5.21126i	−1.20827	−	0.166638i
$979$	25.1698	+	22.0734i	0.804432	+	0.705468i
$980$	−38.3598	+	28.5301i	−1.22536	+	0.911362i
$981$	−8.15541	+	30.7696i	−0.260382	+	0.982398i
$982$	6.94743	−	7.30701i	0.221701	−	0.233176i
$983$	8.33375	−	6.39471i	0.265805	−	0.203960i	−0.467256	−	0.884122i	$-0.654757\pi$
$983$	8.33375	−	6.39471i	0.265805	−	0.203960i	0.733061	+	0.680162i	$0.238091\pi$
$984$	−7.79437	+	17.7457i	−0.248476	+	0.565712i
$985$	5.84335	+	4.48376i	0.186185	+	0.142864i
$986$	−6.10513	−	38.7871i	−0.194427	−	1.23523i
$987$	−0.114638	−	1.14799i	−0.00364897	−	0.0365411i
$988$	−1.86191	−	5.76801i	−0.0592353	−	0.183505i
$989$	−12.3969	−	18.5532i	−0.394197	−	0.589957i
$990$	89.0701	−	39.8435i	2.83083	−	1.26631i
$991$		−	32.9384i		−	1.04632i	−0.852234	−	0.523161i	$-0.824753\pi$
$991$		−	32.9384i		−	1.04632i	0.852234	−	0.523161i	$-0.175247\pi$
$992$	−16.0235	+	3.10742i	−0.508747	+	0.0986607i
$993$	3.75882	−	1.70924i	0.119283	−	0.0542412i
$994$	−0.0678176	+	0.146737i	−0.00215104	+	0.00465422i
$995$	41.7617	−	84.6844i	1.32394	−	2.68468i
$996$	28.5154	+	18.2766i	0.903544	+	0.579116i
$997$	−4.56219	−	1.54866i	−0.144486	−	0.0490464i	0.248260	−	0.968694i	$-0.420141\pi$
$997$	−4.56219	−	1.54866i	−0.144486	−	0.0490464i	−0.392746	+	0.919647i	$0.628475\pi$
$998$	−13.6597	+	35.4829i	−0.432390	+	1.12319i
$999$	52.4200	−	5.37810i	1.65850	−	0.170156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bm.a.205.75	yes	1504
9.4	even	3	inner	576.2.bm.a.13.11	✓	1504
64.5	even	16	inner	576.2.bm.a.133.11	yes	1504
576.517	even	48	inner	576.2.bm.a.517.75	yes	1504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.bm.a.13.11	✓	1504	9.4	even	3	inner
576.2.bm.a.133.11	yes	1504	64.5	even	16	inner
576.2.bm.a.205.75	yes	1504	1.1	even	1	trivial
576.2.bm.a.517.75	yes	1504	576.517	even	48	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bm (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08644 + 0.905346i) q^{2} +(0.0543260 - 1.73120i) q^{3} +(0.360696 + 1.96721i) q^{4} +(-2.37549 - 2.70873i) q^{5} +(1.62636 - 1.83166i) q^{6} +(0.599302 + 0.0788996i) q^{7} +(-1.38913 + 2.46380i) q^{8} +(-2.99410 - 0.188098i) q^{9} +O(q^{10})\)	\(q+(1.08644 + 0.905346i) q^{2} +(0.0543260 - 1.73120i) q^{3} +(0.360696 + 1.96721i) q^{4} +(-2.37549 - 2.70873i) q^{5} +(1.62636 - 1.83166i) q^{6} +(0.599302 + 0.0788996i) q^{7} +(-1.38913 + 2.46380i) q^{8} +(-2.99410 - 0.188098i) q^{9} +(-0.128487 - 5.09351i) q^{10} +(-2.82339 - 5.72527i) q^{11} +(3.42522 - 0.517566i) q^{12} +(0.527748 + 1.55469i) q^{13} +(0.579673 + 0.628295i) q^{14} +(-4.81840 + 3.96529i) q^{15} +(-3.73980 + 1.41913i) q^{16} +(-2.48259 - 2.48259i) q^{17} +(-3.08261 - 2.91505i) q^{18} +(-0.360105 + 1.81037i) q^{19} +(4.47179 - 5.65010i) q^{20} +(0.169149 - 1.03322i) q^{21} +(2.11591 - 8.77629i) q^{22} +(-0.431997 - 3.28134i) q^{23} +(4.18987 + 2.53871i) q^{24} +(-1.04162 + 7.91188i) q^{25} +(-0.834172 + 2.16687i) q^{26} +(-0.488293 + 5.17316i) q^{27} +(0.0609541 + 1.20741i) q^{28} +(7.89106 - 0.517207i) q^{29} +(-8.82485 - 0.0542735i) q^{30} +(2.49879 - 1.44268i) q^{31} +(-5.34786 - 1.84402i) q^{32} +(-10.0650 + 4.57682i) q^{33} +(-0.449578 - 4.94479i) q^{34} +(-1.20992 - 1.81077i) q^{35} +(-0.709931 - 5.95785i) q^{36} +(-1.97845 - 9.94633i) q^{37} +(-2.03024 + 1.64083i) q^{38} +(2.72016 - 0.829176i) q^{39} +(9.97363 - 2.08997i) q^{40} +(0.516405 + 3.92249i) q^{41} +(1.11920 - 0.969396i) q^{42} +(6.04673 - 2.98192i) q^{43} +(10.2444 - 7.61927i) q^{44} +(6.60294 + 8.55702i) q^{45} +(2.50141 - 3.95608i) q^{46} +(1.06439 - 0.285202i) q^{47} +(2.25362 + 6.55143i) q^{48} +(-6.40854 - 1.71716i) q^{49} +(-8.29465 + 7.65274i) q^{50} +(-4.43273 + 4.16299i) q^{51} +(-2.86805 + 1.59896i) q^{52} +(0.409002 - 0.612115i) q^{53} +(-5.21400 + 5.17824i) q^{54} +(-8.80125 + 21.2481i) q^{55} +(-1.02690 + 1.36696i) q^{56} +(3.11454 + 0.721763i) q^{57} +(9.04140 + 6.58222i) q^{58} +(6.59875 + 7.52443i) q^{59} +(-9.53852 - 8.04851i) q^{60} +(-0.876809 - 13.3775i) q^{61} +(4.02090 + 0.694891i) q^{62} +(-1.77953 - 0.348961i) q^{63} +(-4.14064 - 6.84508i) q^{64} +(2.95758 - 5.12269i) q^{65} +(-15.0786 - 4.13984i) q^{66} +(8.66852 + 4.27484i) q^{67} +(3.98831 - 5.77924i) q^{68} +(-5.70412 + 0.569610i) q^{69} +(0.324873 - 3.06268i) q^{70} +(0.0723646 + 0.174704i) q^{71} +(4.62262 - 7.11557i) q^{72} +(-2.42727 + 5.85995i) q^{73} +(6.85541 - 12.5973i) q^{74} +(13.6405 + 2.23307i) q^{75} +(-3.69125 - 0.0554071i) q^{76} +(-1.24034 - 3.65393i) q^{77} +(3.70597 + 1.56183i) q^{78} +(1.21604 + 4.53833i) q^{79} +(12.7279 + 6.75897i) q^{80} +(8.92924 + 1.12637i) q^{81} +(-2.99017 + 4.72907i) q^{82} +(7.35100 + 6.44666i) q^{83} +(2.09358 - 0.0399300i) q^{84} +(-0.827293 + 12.6220i) q^{85} +(9.26907 + 2.23472i) q^{86} +(-0.466698 - 13.6891i) q^{87} +(18.0280 + 0.996858i) q^{88} +(-4.84513 + 2.00692i) q^{89} +(-0.573377 + 15.2746i) q^{90} +(0.193615 + 0.973370i) q^{91} +(6.29925 - 2.03339i) q^{92} +(-2.36181 - 4.40428i) q^{93} +(1.41460 + 0.653786i) q^{94} +(5.75922 - 3.32509i) q^{95} +(-3.48289 + 9.15803i) q^{96} +(-10.5978 - 6.11862i) q^{97} +(-5.40786 - 7.66754i) q^{98} +(7.37659 + 17.6731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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Database

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