LMFDB - Embedded newform 728.2.h.a.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(27,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("728.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.h (of order $2$, degree $1$, 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:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.2
Character	$\chi$	$=$	728.27
Dual form			728.2.h.a.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40591 + 0.153058i) q^{2} +1.61368i q^{3} +(1.95315 - 0.430370i) q^{4} -3.74465 q^{5} +(-0.246987 - 2.26868i) q^{6} +(0.220320 - 2.63656i) q^{7} +(-2.68007 + 0.904005i) q^{8} +0.396033 q^{9} +(5.26463 - 0.573149i) q^{10} +3.49137 q^{11} +(0.694480 + 3.15176i) q^{12} -1.00000 q^{13} +(0.0937970 + 3.74048i) q^{14} -6.04268i q^{15} +(3.62956 - 1.68115i) q^{16} +2.76774i q^{17} +(-0.556786 + 0.0606160i) q^{18} -1.95616i q^{19} +(-7.31386 + 1.61159i) q^{20} +(4.25457 + 0.355526i) q^{21} +(-4.90853 + 0.534381i) q^{22} +3.57617i q^{23} +(-1.45878 - 4.32478i) q^{24} +9.02242 q^{25} +(1.40591 - 0.153058i) q^{26} +5.48011i q^{27} +(-0.704380 - 5.24441i) q^{28} +7.44638i q^{29} +(0.924879 + 8.49544i) q^{30} +2.83757 q^{31} +(-4.84551 + 2.91908i) q^{32} +5.63395i q^{33} +(-0.423625 - 3.89119i) q^{34} +(-0.825022 + 9.87301i) q^{35} +(0.773511 - 0.170441i) q^{36} +7.85432i q^{37} +(0.299406 + 2.75018i) q^{38} -1.61368i q^{39} +(10.0359 - 3.38518i) q^{40} -9.79226i q^{41} +(-6.03594 + 0.151358i) q^{42} -9.67807 q^{43} +(6.81915 - 1.50258i) q^{44} -1.48301 q^{45} +(-0.547360 - 5.02776i) q^{46} -0.142720 q^{47} +(2.71284 + 5.85696i) q^{48} +(-6.90292 - 1.16178i) q^{49} +(-12.6847 + 1.38095i) q^{50} -4.46625 q^{51} +(-1.95315 + 0.430370i) q^{52} -4.92001i q^{53} +(-0.838775 - 7.70453i) q^{54} -13.0740 q^{55} +(1.79299 + 7.26534i) q^{56} +3.15663 q^{57} +(-1.13973 - 10.4689i) q^{58} +14.9529i q^{59} +(-2.60059 - 11.8022i) q^{60} +6.42304 q^{61} +(-3.98936 + 0.434313i) q^{62} +(0.0872541 - 1.04417i) q^{63} +(6.36555 - 4.84559i) q^{64} +3.74465 q^{65} +(-0.862320 - 7.92081i) q^{66} +6.64374 q^{67} +(1.19115 + 5.40581i) q^{68} -5.77079 q^{69} +(-0.351237 - 14.0068i) q^{70} +2.19770i q^{71} +(-1.06140 + 0.358016i) q^{72} +7.29238i q^{73} +(-1.20217 - 11.0424i) q^{74} +14.5593i q^{75} +(-0.841875 - 3.82068i) q^{76} +(0.769218 - 9.20520i) q^{77} +(0.246987 + 2.26868i) q^{78} +7.84555i q^{79} +(-13.5915 + 6.29533i) q^{80} -7.65506 q^{81} +(1.49878 + 13.7670i) q^{82} +10.8229i q^{83} +(8.46281 - 1.13664i) q^{84} -10.3642i q^{85} +(13.6065 - 1.48130i) q^{86} -12.0161 q^{87} +(-9.35710 + 3.15621i) q^{88} +8.96702i q^{89} +(2.08497 - 0.226986i) q^{90} +(-0.220320 + 2.63656i) q^{91} +(1.53908 + 6.98478i) q^{92} +4.57894i q^{93} +(0.200651 - 0.0218444i) q^{94} +7.32516i q^{95} +(-4.71046 - 7.81911i) q^{96} -4.53127i q^{97} +(9.88268 + 0.576802i) q^{98} +1.38270 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) $ 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.40591	+	0.153058i	−0.994126	+	0.108228i
$2$	−1.40591	+	0.153058i	−0.994126	+	0.108228i
$3$			1.61368i			0.931659i	0.884874	+	0.465830i	$0.154244\pi$
$3$			1.61368i			0.931659i	−0.884874	+	0.465830i	$0.845756\pi$
$4$	1.95315	−	0.430370i	0.976573	−	0.215185i
$5$	−3.74465			−1.67466			−0.837330	−	0.546698i	$-0.815885\pi$
$5$	−3.74465			−1.67466			−0.837330	+	0.546698i	$0.815885\pi$
$6$	−0.246987	−	2.26868i	−0.100832	−	0.926187i
$7$	0.220320	−	2.63656i	0.0832732	−	0.996527i
$7$	0.220320	−	2.63656i	0.0832732	−	0.996527i
$8$	−2.68007	+	0.904005i	−0.947548	+	0.319614i
$9$	0.396033			0.132011
$10$	5.26463	−	0.573149i	1.66482	−	0.181245i
$11$	3.49137			1.05269			0.526343	−	0.850272i	$-0.323563\pi$
$11$	3.49137			1.05269			0.526343	+	0.850272i	$0.323563\pi$
$12$	0.694480	+	3.15176i	0.200479	+	0.909833i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	0.0937970	+	3.74048i	0.0250683	+	0.999686i
$15$		−	6.04268i		−	1.56021i
$16$	3.62956	−	1.68115i	0.907391	−	0.420288i
$17$			2.76774i			0.671276i	0.941991	+	0.335638i	$0.108952\pi$
$17$			2.76774i			0.671276i	−0.941991	+	0.335638i	$0.891048\pi$
$18$	−0.556786	+	0.0606160i	−0.131236	+	0.0142873i
$19$		−	1.95616i		−	0.448775i	−0.974500	−	0.224387i	$-0.927962\pi$
$19$		−	1.95616i		−	0.448775i	0.974500	−	0.224387i	$-0.0720381\pi$
$20$	−7.31386	+	1.61159i	−1.63543	+	0.360362i
$21$	4.25457	+	0.355526i	0.928423	+	0.0775822i
$22$	−4.90853	+	0.534381i	−1.04650	+	0.113930i
$23$			3.57617i			0.745682i	0.927895	+	0.372841i	$0.121616\pi$
$23$			3.57617i			0.745682i	−0.927895	+	0.372841i	$0.878384\pi$
$24$	−1.45878	−	4.32478i	−0.297771	−	0.882792i
$25$	9.02242			1.80448
$26$	1.40591	−	0.153058i	0.275721	−	0.0300171i
$27$			5.48011i			1.05465i
$28$	−0.704380	−	5.24441i	−0.133115	−	0.991101i
$29$			7.44638i			1.38276i	0.722493	+	0.691379i	$0.242996\pi$
$29$			7.44638i			1.38276i	−0.722493	+	0.691379i	$0.757004\pi$
$30$	0.924879	+	8.49544i	0.168859	+	1.55105i
$31$	2.83757			0.509643			0.254822	−	0.966988i	$-0.417983\pi$
$31$	2.83757			0.509643			0.254822	+	0.966988i	$0.417983\pi$
$32$	−4.84551	+	2.91908i	−0.856574	+	0.516025i
$33$			5.63395i			0.980745i
$34$	−0.423625	−	3.89119i	−0.0726511	−	0.667333i
$35$	−0.825022	+	9.87301i	−0.139454	+	1.66884i
$36$	0.773511	−	0.170441i	0.128919	−	0.0284068i
$37$			7.85432i			1.29124i	0.763658	+	0.645621i	$0.223402\pi$
$37$			7.85432i			1.29124i	−0.763658	+	0.645621i	$0.776598\pi$
$38$	0.299406	+	2.75018i	0.0485701	+	0.446139i
$39$		−	1.61368i		−	0.258396i
$40$	10.0359	−	3.38518i	1.58682	−	0.535244i
$41$		−	9.79226i		−	1.52929i	−0.644450	−	0.764647i	$-0.722914\pi$
$41$		−	9.79226i		−	1.52929i	0.644450	−	0.764647i	$-0.277086\pi$
$42$	−6.03594	+	0.151358i	−0.931366	+	0.0233551i
$43$	−9.67807			−1.47589			−0.737946	−	0.674860i	$-0.764204\pi$
$43$	−9.67807			−1.47589			−0.737946	+	0.674860i	$0.764204\pi$
$44$	6.81915	−	1.50258i	1.02803	−	0.226522i
$45$	−1.48301			−0.221074
$46$	−0.547360	−	5.02776i	−0.0807039	−	0.741302i
$47$	−0.142720			−0.0208178			−0.0104089	−	0.999946i	$-0.503313\pi$
$47$	−0.142720			−0.0208178			−0.0104089	+	0.999946i	$0.503313\pi$
$48$	2.71284	+	5.85696i	0.391565	+	0.845379i
$49$	−6.90292	−	1.16178i	−0.986131	−	0.165968i
$50$	−12.6847	+	1.38095i	−1.79389	+	0.195296i
$51$	−4.46625			−0.625401
$52$	−1.95315	+	0.430370i	−0.270853	+	0.0596816i
$53$		−	4.92001i		−	0.675815i	−0.941179	−	0.337907i	$-0.890281\pi$
$53$		−	4.92001i		−	0.675815i	0.941179	−	0.337907i	$-0.109719\pi$
$54$	−0.838775	−	7.70453i	−0.114143	−	1.04845i
$55$	−13.0740			−1.76289
$56$	1.79299	+	7.26534i	0.239598	+	0.970872i
$57$	3.15663			0.418105
$58$	−1.13973	−	10.4689i	−0.149653	−	1.37463i
$59$			14.9529i			1.94671i	0.229310	+	0.973354i	$0.426353\pi$
$59$			14.9529i			1.94671i	−0.229310	+	0.973354i	$0.573647\pi$
$60$	−2.60059	−	11.8022i	−0.335734	−	1.52366i
$61$	6.42304			0.822386			0.411193	−	0.911548i	$-0.365112\pi$
$61$	6.42304			0.822386			0.411193	+	0.911548i	$0.365112\pi$
$62$	−3.98936	+	0.434313i	−0.506650	+	0.0551578i
$63$	0.0872541	−	1.04417i	0.0109930	−	0.131553i
$64$	6.36555	−	4.84559i	0.795694	−	0.605699i
$65$	3.74465			0.464467
$66$	−0.862320	−	7.92081i	−0.106144	−	0.974984i
$67$	6.64374			0.811662			0.405831	−	0.913948i	$-0.366982\pi$
$67$	6.64374			0.811662			0.405831	+	0.913948i	$0.366982\pi$
$68$	1.19115	+	5.40581i	0.144449	+	0.655550i
$69$	−5.77079			−0.694722
$70$	−0.351237	−	14.0068i	−0.0419809	−	1.67413i
$71$			2.19770i			0.260819i	0.991460	+	0.130409i	$0.0416292\pi$
$71$			2.19770i			0.260819i	−0.991460	+	0.130409i	$0.958371\pi$
$72$	−1.06140	+	0.358016i	−0.125087	+	0.0421926i
$73$			7.29238i			0.853508i	0.904368	+	0.426754i	$0.140343\pi$
$73$			7.29238i			0.853508i	−0.904368	+	0.426754i	$0.859657\pi$
$74$	−1.20217	−	11.0424i	−0.139749	−	1.28366i
$75$			14.5593i			1.68116i
$76$	−0.841875	−	3.82068i	−0.0965697	−	0.438262i
$77$	0.769218	−	9.20520i	0.0876606	−	1.04903i
$78$	0.246987	+	2.26868i	0.0279657	+	0.256878i
$79$			7.84555i			0.882694i	0.897337	+	0.441347i	$0.145499\pi$
$79$			7.84555i			0.882694i	−0.897337	+	0.441347i	$0.854501\pi$
$80$	−13.5915	+	6.29533i	−1.51957	+	0.703839i
$81$	−7.65506			−0.850562
$82$	1.49878	+	13.7670i	0.165513	+	1.52031i
$83$			10.8229i			1.18797i	0.804478	+	0.593983i	$0.202445\pi$
$83$			10.8229i			1.18797i	−0.804478	+	0.593983i	$0.797555\pi$
$84$	8.46281	−	1.13664i	0.923368	−	0.124018i
$85$		−	10.3642i		−	1.12416i
$86$	13.6065	−	1.48130i	1.46722	−	0.159733i
$87$	−12.0161			−1.28826
$88$	−9.35710	+	3.15621i	−0.997471	+	0.336453i
$89$			8.96702i			0.950502i	0.879850	+	0.475251i	$0.157643\pi$
$89$			8.96702i			0.950502i	−0.879850	+	0.475251i	$0.842357\pi$
$90$	2.08497	−	0.226986i	0.219775	−	0.0239264i
$91$	−0.220320	+	2.63656i	−0.0230958	+	0.276387i
$92$	1.53908	+	6.98478i	0.160460	+	0.728213i
$93$			4.57894i			0.474814i
$94$	0.200651	−	0.0218444i	0.0206955	−	0.00225307i
$95$			7.32516i			0.751545i
$96$	−4.71046	−	7.81911i	−0.480759	−	0.798035i
$97$		−	4.53127i		−	0.460080i	−0.973181	−	0.230040i	$-0.926114\pi$
$97$		−	4.53127i		−	0.460080i	0.973181	−	0.230040i	$-0.0738858\pi$
$98$	9.88268	+	0.576802i	0.998301	+	0.0582658i
$99$	1.38270			0.138966
$100$	17.6221	−	3.88298i	1.76221	−	0.388298i
$101$	4.60810			0.458523			0.229262	−	0.973365i	$-0.426369\pi$
$101$	4.60810			0.458523			0.229262	+	0.973365i	$0.426369\pi$
$102$	6.27914	−	0.683595i	0.621727	−	0.0676860i
$103$	19.7394			1.94498			0.972491	−	0.232940i	$-0.0748345\pi$
$103$	19.7394			1.94498			0.972491	+	0.232940i	$0.0748345\pi$
$104$	2.68007	−	0.904005i	0.262802	−	0.0886449i
$105$	−15.9319	−	1.33132i	−1.55479	−	0.129924i
$106$	0.753046	+	6.91707i	0.0731423	+	0.671845i
$107$	−12.6613			−1.22402			−0.612008	−	0.790851i	$-0.709638\pi$
$107$	−12.6613			−1.22402			−0.612008	+	0.790851i	$0.709638\pi$
$108$	2.35848	+	10.7035i	0.226945	+	1.02994i
$109$			5.65221i			0.541383i	0.962666	+	0.270692i	$0.0872523\pi$
$109$			5.65221i			0.541383i	−0.962666	+	0.270692i	$0.912748\pi$
$110$	18.3808	−	2.00107i	1.75254	−	0.190795i
$111$	−12.6744			−1.20300
$112$	−3.63279	−	9.93996i	−0.343267	−	0.939238i
$113$	17.5275			1.64885			0.824423	−	0.565973i	$-0.191500\pi$
$113$	17.5275			1.64885			0.824423	+	0.565973i	$0.191500\pi$
$114$	−4.43792	+	0.483146i	−0.415649	+	0.0452508i
$115$		−	13.3915i		−	1.24876i
$116$	3.20470	+	14.5439i	0.297549	+	1.35036i
$117$	−0.396033			−0.0366133
$118$	−2.28867	−	21.0224i	−0.210689	−	1.93527i
$119$	7.29733	+	0.609790i	0.668945	+	0.0558993i
$120$	5.46261	+	16.1948i	0.498665	+	1.47838i
$121$	1.18963			0.108149
$122$	−9.03019	+	0.983096i	−0.817555	+	0.0890054i
$123$	15.8016			1.42478
$124$	5.54220	−	1.22121i	0.497704	−	0.109668i
$125$	−15.0626			−1.34724
$126$	0.0371467	+	1.48136i	0.00330929	+	0.131970i
$127$			13.5718i			1.20431i	0.798381	+	0.602153i	$0.205690\pi$
$127$			13.5718i			1.20431i	−0.798381	+	0.602153i	$0.794310\pi$
$128$	−8.20771	+	7.78675i	−0.725466	+	0.688258i
$129$		−	15.6173i		−	1.37503i
$130$	−5.26463	+	0.573149i	−0.461739	+	0.0502685i
$131$			5.15777i			0.450637i	0.974285	+	0.225318i	$0.0723422\pi$
$131$			5.15777i			0.450637i	−0.974285	+	0.225318i	$0.927658\pi$
$132$	2.42468	+	11.0039i	0.211042	+	0.957769i
$133$	−5.15755	−	0.430983i	−0.447216	−	0.0373709i
$134$	−9.34047	+	1.01688i	−0.806894	+	0.0878447i
$135$		−	20.5211i		−	1.76618i
$136$	−2.50205	−	7.41774i	−0.214549	−	0.636066i
$137$	−5.20015			−0.444279			−0.222139	−	0.975015i	$-0.571304\pi$
$137$	−5.20015			−0.444279			−0.222139	+	0.975015i	$0.571304\pi$
$138$	8.11319	−	0.883265i	0.690641	−	0.0751885i
$139$		−	8.31677i		−	0.705419i	−0.935733	−	0.352710i	$-0.885260\pi$
$139$		−	8.31677i		−	0.705419i	0.935733	−	0.352710i	$-0.114740\pi$
$140$	2.63766	+	19.6385i	0.222923	+	1.65976i
$141$		−	0.230304i		−	0.0193951i
$142$	−0.336375	−	3.08976i	−0.0282280	−	0.259287i
$143$	−3.49137			−0.291963
$144$	1.43743	−	0.665792i	0.119786	−	0.0554827i
$145$		−	27.8841i		−	2.31565i
$146$	−1.11616	−	10.2524i	−0.0923737	−	0.848495i
$147$	1.87474	−	11.1391i	0.154626	−	0.918738i
$148$	3.38027	+	15.3406i	0.277856	+	1.26099i
$149$		−	15.9705i		−	1.30836i	−0.756340	−	0.654179i	$-0.773014\pi$
$149$		−	15.9705i		−	1.30836i	0.756340	−	0.654179i	$-0.226986\pi$
$150$	−2.22842	−	20.4690i	−0.181950	−	1.67129i
$151$			15.5186i			1.26288i	0.775424	+	0.631441i	$0.217536\pi$
$151$			15.5186i			1.26288i	−0.775424	+	0.631441i	$0.782464\pi$
$152$	1.76838	+	5.24266i	0.143435	+	0.425236i
$153$			1.09612i			0.0886159i
$154$	0.327480	+	13.0594i	0.0263891	+	1.05236i
$155$	−10.6257			−0.853479
$156$	−0.694480	−	3.15176i	−0.0556029	−	0.252342i
$157$	12.2216			0.975391			0.487695	−	0.873014i	$-0.337838\pi$
$157$	12.2216			0.975391			0.487695	+	0.873014i	$0.337838\pi$
$158$	−1.20082	−	11.0301i	−0.0955324	−	0.877509i
$159$	7.93932			0.629629
$160$	18.1448	−	10.9309i	1.43447	−	0.864165i
$161$	9.42878	+	0.787902i	0.743092	+	0.0620953i
$162$	10.7623	−	1.17167i	0.845566	−	0.0920548i
$163$	3.28510			0.257309			0.128655	−	0.991689i	$-0.458934\pi$
$163$	3.28510			0.257309			0.128655	+	0.991689i	$0.458934\pi$
$164$	−4.21429	−	19.1257i	−0.329081	−	1.49347i
$165$		−	21.0972i		−	1.64241i
$166$	−1.65653	−	15.2160i	−0.128571	−	1.18099i
$167$	−5.77822			−0.447132			−0.223566	−	0.974689i	$-0.571770\pi$
$167$	−5.77822			−0.447132			−0.223566	+	0.974689i	$0.571770\pi$
$168$	−11.7239	+	2.89332i	−0.904522	+	0.223224i
$169$	1.00000			0.0769231
$170$	1.58633	+	14.5711i	0.121666	+	1.11756i
$171$		−	0.774707i		−	0.0592433i
$172$	−18.9027	+	4.16515i	−1.44132	+	0.317590i
$173$	4.09736			0.311516			0.155758	−	0.987795i	$-0.450218\pi$
$173$	4.09736			0.311516			0.155758	+	0.987795i	$0.450218\pi$
$174$	16.8935	−	1.83915i	1.28069	−	0.139426i
$175$	1.98782	−	23.7882i	0.150265	−	1.79822i
$176$	12.6721	−	5.86952i	0.955198	−	0.442431i
$177$	−24.1293			−1.81367
$178$	−1.37247	−	12.6068i	−0.102871	−	0.944919i
$179$	4.61280			0.344777			0.172388	−	0.985029i	$-0.444852\pi$
$179$	4.61280			0.344777			0.172388	+	0.985029i	$0.444852\pi$
$180$	−2.89653	+	0.638242i	−0.215895	+	0.0475718i
$181$	17.7102			1.31639			0.658194	−	0.752848i	$-0.271321\pi$
$181$	17.7102			1.31639			0.658194	+	0.752848i	$0.271321\pi$
$182$	−0.0937970	−	3.74048i	−0.00695269	−	0.277263i
$183$			10.3647i			0.766183i
$184$	−3.23287	−	9.58438i	−0.238330	−	0.706570i
$185$		−	29.4117i		−	2.16239i
$186$	−0.700842	−	6.43756i	−0.0513883	−	0.472025i
$187$			9.66320i			0.706643i
$188$	−0.278752	+	0.0614223i	−0.0203301	+	0.00447968i
$189$	14.4487	+	1.20738i	1.05099	+	0.0878240i
$190$	−1.12117	−	10.2985i	−0.0813384	−	0.747131i
$191$		−	0.534042i		−	0.0386419i	−0.999813	−	0.0193210i	$-0.993850\pi$
$191$		−	0.534042i		−	0.0386419i	0.999813	−	0.0193210i	$-0.00615044\pi$
$192$	7.81924	+	10.2720i	0.564305	+	0.741316i
$193$	−0.442965			−0.0318853			−0.0159427	−	0.999873i	$-0.505075\pi$
$193$	−0.442965			−0.0318853			−0.0159427	+	0.999873i	$0.505075\pi$
$194$	0.693546	+	6.37054i	0.0497937	+	0.457378i
$195$			6.04268i			0.432725i
$196$	−13.9824	+	0.701692i	−0.998743	+	0.0501208i
$197$		−	24.5014i		−	1.74565i	−0.488031	−	0.872827i	$-0.662285\pi$
$197$		−	24.5014i		−	1.74565i	0.488031	−	0.872827i	$-0.337715\pi$
$198$	−1.94394	+	0.211633i	−0.138150	+	0.0150401i
$199$	−7.15645			−0.507308			−0.253654	−	0.967295i	$-0.581632\pi$
$199$	−7.15645			−0.507308			−0.253654	+	0.967295i	$0.581632\pi$
$200$	−24.1807	+	8.15631i	−1.70984	+	0.576738i
$201$			10.7209i			0.756192i
$202$	−6.47856	+	0.705306i	−0.455830	+	0.0496252i
$203$	19.6328	+	1.64059i	1.37795	+	0.115147i
$204$	−8.72325	+	1.92214i	−0.610750	+	0.134577i
$205$			36.6686i			2.56105i
$206$	−27.7518	+	3.02127i	−1.93356	+	0.210502i
$207$			1.41628i			0.0984384i
$208$	−3.62956	+	1.68115i	−0.251665	+	0.116567i
$209$		−	6.82969i		−	0.472419i
$210$	22.6025	−	0.566785i	1.55972	−	0.0391119i
$211$	6.55482			0.451252			0.225626	−	0.974214i	$-0.427557\pi$
$211$	6.55482			0.451252			0.225626	+	0.974214i	$0.427557\pi$
$212$	−2.11742	−	9.60950i	−0.145425	−	0.659983i
$213$	−3.54638			−0.242994
$214$	17.8006	−	1.93792i	1.21683	−	0.132473i
$215$	36.2410			2.47162
$216$	−4.95405	−	14.6871i	−0.337080	−	0.999330i
$217$	0.625174	−	7.48144i	0.0424396	−	0.507873i
$218$	−0.865114	−	7.94647i	−0.0585929	−	0.538203i
$219$	−11.7676			−0.795179
$220$	−25.5353	+	5.62664i	−1.72159	+	0.379348i
$221$		−	2.76774i		−	0.186179i
$222$	17.8190	−	1.93991i	1.19593	−	0.130198i
$223$	−18.5332			−1.24108			−0.620539	−	0.784176i	$-0.713086\pi$
$223$	−18.5332			−1.24108			−0.620539	+	0.784176i	$0.713086\pi$
$224$	6.62876	+	13.4186i	0.442903	+	0.896570i
$225$	3.57318			0.238212
$226$	−24.6420	+	2.68272i	−1.63916	+	0.178452i
$227$		−	3.50929i		−	0.232920i	−0.993195	−	0.116460i	$-0.962845\pi$
$227$		−	3.50929i		−	0.232920i	0.993195	−	0.116460i	$-0.0371547\pi$
$228$	6.16535	−	1.35852i	0.408311	−	0.0899700i
$229$	−17.2678			−1.14109			−0.570543	−	0.821268i	$-0.693267\pi$
$229$	−17.2678			−1.14109			−0.570543	+	0.821268i	$0.693267\pi$
$230$	2.04967	+	18.8272i	0.135152	+	1.24143i
$231$	14.8543	+	1.24127i	0.977339	+	0.0816698i
$232$	−6.73156	−	19.9568i	−0.441948	−	1.31023i
$233$	−12.4546			−0.815928			−0.407964	−	0.912998i	$-0.633761\pi$
$233$	−12.4546			−0.815928			−0.407964	+	0.912998i	$0.633761\pi$
$234$	0.556786	−	0.0606160i	0.0363982	−	0.00396259i
$235$	0.534436			0.0348627
$236$	6.43530	+	29.2053i	0.418902	+	1.90110i
$237$	−12.6602			−0.822370
$238$	−10.3527	+	0.259606i	−0.671065	+	0.0168278i
$239$		−	4.94110i		−	0.319613i	−0.987148	−	0.159807i	$-0.948913\pi$
$239$		−	4.94110i		−	0.319613i	0.987148	−	0.159807i	$-0.0510870\pi$
$240$	−10.1587	−	21.9323i	−0.655738	−	1.41572i
$241$		−	7.42809i		−	0.478486i	−0.970960	−	0.239243i	$-0.923101\pi$
$241$		−	7.42809i		−	0.478486i	0.970960	−	0.239243i	$-0.0768992\pi$
$242$	−1.67252	+	0.182083i	−0.107513	+	0.0117047i
$243$			4.08752i			0.262215i
$244$	12.5451	−	2.76428i	0.803120	−	0.176965i
$245$	25.8490	+	4.35045i	1.65143	+	0.277940i
$246$	−22.2155	+	2.41856i	−1.41641	+	0.154201i
$247$			1.95616i			0.124468i
$248$	−7.60489	+	2.56518i	−0.482911	+	0.162889i
$249$	−17.4647			−1.10678
$250$	21.1766	−	2.30545i	1.33932	−	0.145809i
$251$		−	31.0214i		−	1.95805i	−0.203734	−	0.979026i	$-0.565308\pi$
$251$		−	31.0214i		−	1.95805i	0.203734	−	0.979026i	$-0.434692\pi$
$252$	−0.278958	−	2.07696i	−0.0175727	−	0.130836i
$253$			12.4857i			0.784970i
$254$	−2.07728	−	19.0807i	−0.130340	−	1.19723i
$255$	16.7246			1.04733
$256$	10.3475	−	12.2037i	0.646716	−	0.762731i
$257$		−	29.8634i		−	1.86283i	−0.363961	−	0.931414i	$-0.618576\pi$
$257$		−	29.8634i		−	1.86283i	0.363961	−	0.931414i	$-0.381424\pi$
$258$	2.39035	+	21.9565i	0.148817	+	1.36695i
$259$	20.7084	+	1.73047i	1.28676	+	0.107526i
$260$	7.31386	−	1.61159i	0.453586	−	0.0999464i
$261$			2.94901i			0.182539i
$262$	−0.789437	−	7.25134i	−0.0487716	−	0.447990i
$263$			14.1934i			0.875204i	0.899169	+	0.437602i	$0.144172\pi$
$263$			14.1934i			0.875204i	−0.899169	+	0.437602i	$0.855828\pi$
$264$	−5.09312	−	15.0994i	−0.313460	−	0.929303i
$265$			18.4237i			1.13176i
$266$	7.31700	−	0.183482i	0.448634	−	0.0112500i
$267$	−14.4699			−0.885544
$268$	12.9762	−	2.85927i	0.792647	−	0.174657i
$269$	−12.5568			−0.765601			−0.382800	−	0.923831i	$-0.625040\pi$
$269$	−12.5568			−0.765601			−0.382800	+	0.923831i	$0.625040\pi$
$270$	3.14092	+	28.8508i	0.191150	+	1.75580i
$271$	−6.45697			−0.392233			−0.196117	−	0.980581i	$-0.562833\pi$
$271$	−6.45697			−0.392233			−0.196117	+	0.980581i	$0.562833\pi$
$272$	4.65300	+	10.0457i	0.282129	+	0.609110i
$273$	−4.25457	−	0.355526i	−0.257498	−	0.0215174i
$274$	7.31092	−	0.795924i	0.441669	−	0.0480835i
$275$	31.5006			1.89956
$276$	−11.2712	+	2.48358i	−0.678447	+	0.149494i
$277$			5.85021i			0.351505i	0.984434	+	0.175753i	$0.0562359\pi$
$277$			5.85021i			0.351505i	−0.984434	+	0.175753i	$0.943764\pi$
$278$	1.27295	+	11.6926i	0.0763463	+	0.701276i
$279$	1.12377			0.0672786
$280$	−6.71413	−	27.2062i	−0.401246	−	1.62588i
$281$	24.9322			1.48733			0.743666	−	0.668551i	$-0.233085\pi$
$281$	24.9322			1.48733			0.743666	+	0.668551i	$0.233085\pi$
$282$	0.0352498	+	0.323786i	0.00209910	+	0.0192812i
$283$			15.1831i			0.902543i	0.892387	+	0.451271i	$0.149029\pi$
$283$			15.1831i			0.902543i	−0.892387	+	0.451271i	$0.850971\pi$
$284$	0.945824	+	4.29243i	0.0561243	+	0.254709i
$285$	−11.8205			−0.700184
$286$	4.90853	−	0.534381i	0.290248	−	0.0315986i
$287$	−25.8179	−	2.15743i	−1.52398	−	0.127349i
$288$	−1.91899	+	1.15605i	−0.113077	+	0.0681210i
$289$	9.33960			0.549388
$290$	4.26788	+	39.2024i	0.250618	+	2.30205i
$291$	7.31202			0.428638
$292$	3.13842	+	14.2431i	0.183662	+	0.833513i
$293$	−25.1676			−1.47031			−0.735154	−	0.677900i	$-0.762890\pi$
$293$	−25.1676			−1.47031			−0.735154	+	0.677900i	$0.762890\pi$
$294$	−0.930774	+	15.9475i	−0.0542839	+	0.930076i
$295$		−	55.9936i		−	3.26007i
$296$	−7.10034	−	21.0501i	−0.412699	−	1.22351i
$297$			19.1331i			1.11021i
$298$	2.44442	+	22.4531i	0.141601	+	1.30067i
$299$		−	3.57617i		−	0.206815i
$300$	6.26589	+	28.4365i	0.361762	+	1.64178i
$301$	−2.13227	+	25.5168i	−0.122902	+	1.47077i
$302$	−2.37524	−	21.8176i	−0.136679	−	1.25546i
$303$			7.43601i			0.427187i
$304$	−3.28861	−	7.10002i	−0.188615	−	0.407214i
$305$	−24.0520			−1.37722
$306$	−0.167770	−	1.54104i	−0.00959075	−	0.0880954i
$307$		−	15.6955i		−	0.895788i	−0.894087	−	0.447894i	$-0.852174\pi$
$307$		−	15.6955i		−	0.895788i	0.894087	−	0.447894i	$-0.147826\pi$
$308$	−2.45925	−	18.3102i	−0.140129	−	1.04332i
$309$			31.8531i			1.81206i
$310$	14.9388	−	1.62635i	0.848465	−	0.0923705i
$311$	17.1019			0.969757			0.484879	−	0.874581i	$-0.338864\pi$
$311$	17.1019			0.969757			0.484879	+	0.874581i	$0.338864\pi$
$312$	1.45878	+	4.32478i	0.0825869	+	0.244842i
$313$			5.01251i			0.283324i	0.989915	+	0.141662i	$0.0452445\pi$
$313$			5.01251i			0.283324i	−0.989915	+	0.141662i	$0.954755\pi$
$314$	−17.1824	+	1.87061i	−0.969662	+	0.105565i
$315$	−0.326736	+	3.91004i	−0.0184095	+	0.220306i
$316$	3.37649	+	15.3235i	0.189943	+	0.862015i
$317$			26.3510i			1.48002i	0.672597	+	0.740009i	$0.265179\pi$
$317$			26.3510i			1.48002i	−0.672597	+	0.740009i	$0.734821\pi$
$318$	−11.1619	+	1.21518i	−0.625931	+	0.0681437i
$319$			25.9980i			1.45561i
$320$	−23.8368	+	18.1451i	−1.33252	+	1.01434i
$321$		−	20.4313i		−	1.14037i
$322$	−13.3766	+	0.335434i	−0.745448	+	0.0186930i
$323$	5.41416			0.301252
$324$	−14.9514	+	3.29451i	−0.830636	+	0.183028i
$325$	−9.02242			−0.500474
$326$	−4.61855	+	0.502811i	−0.255798	+	0.0278481i
$327$	−9.12086			−0.504385
$328$	8.85224	+	26.2439i	0.488783	+	1.44908i
$329$	−0.0314440	+	0.376289i	−0.00173356	+	0.0207455i
$330$	3.22909	+	29.6607i	0.177756	+	1.63277i
$331$	−20.3918			−1.12084			−0.560418	−	0.828210i	$-0.689359\pi$
$331$	−20.3918			−1.12084			−0.560418	+	0.828210i	$0.689359\pi$
$332$	4.65784	+	21.1387i	0.255632	+	1.16014i
$333$			3.11057i			0.170458i
$334$	8.12364	−	0.884403i	0.444506	−	0.0483924i
$335$	−24.8785			−1.35926
$336$	16.0399	−	5.86217i	0.875050	−	0.319808i
$337$	−7.26359			−0.395673			−0.197837	−	0.980235i	$-0.563392\pi$
$337$	−7.26359			−0.395673			−0.197837	+	0.980235i	$0.563392\pi$
$338$	−1.40591	+	0.153058i	−0.0764712	+	0.00832525i
$339$			28.2838i			1.53616i
$340$	−4.46046	−	20.2429i	−0.241902	−	1.09782i
$341$	9.90700			0.536494
$342$	0.118575	+	1.08917i	0.00641180	+	0.0588953i
$343$	−4.58395	+	17.9440i	−0.247510	+	0.968885i
$344$	25.9379	−	8.74902i	1.39848	−	0.471715i
$345$	21.6096			1.16342
$346$	−5.76050	+	0.627133i	−0.309687	+	0.0337149i
$347$	−20.2064			−1.08474			−0.542368	−	0.840141i	$-0.682472\pi$
$347$	−20.2064			−1.08474			−0.542368	+	0.840141i	$0.682472\pi$
$348$	−23.4692	+	5.17136i	−1.25808	+	0.277214i
$349$	28.4007			1.52026			0.760129	−	0.649773i	$-0.225136\pi$
$349$	28.4007			1.52026			0.760129	+	0.649773i	$0.225136\pi$
$350$	0.846276	+	33.7482i	0.0452354	+	1.80392i
$351$		−	5.48011i		−	0.292507i
$352$	−16.9175	+	10.1916i	−0.901704	+	0.543212i
$353$			8.93734i			0.475687i	0.971304	+	0.237843i	$0.0764405\pi$
$353$			8.93734i			0.475687i	−0.971304	+	0.237843i	$0.923560\pi$
$354$	33.9235	−	3.69318i	1.80301	−	0.196290i
$355$		−	8.22962i		−	0.436783i
$356$	3.85914	+	17.5139i	0.204534	+	0.928235i
$357$	−0.984006	+	11.7756i	−0.0520791	+	0.623228i
$358$	−6.48516	+	0.706025i	−0.342751	+	0.0373146i
$359$		−	1.50795i		−	0.0795866i	−0.999208	−	0.0397933i	$-0.987330\pi$
$359$		−	1.50795i		−	0.0795866i	0.999208	−	0.0397933i	$-0.0126699\pi$
$360$	3.97456	−	1.34065i	0.209478	−	0.0706582i
$361$	15.1734			0.798601
$362$	−24.8989	+	2.71068i	−1.30866	+	0.142470i
$363$			1.91969i			0.100758i
$364$	0.704380	+	5.24441i	0.0369195	+	0.274882i
$365$		−	27.3074i		−	1.42934i
$366$	−1.58640	−	14.5718i	−0.0829227	−	0.761683i
$367$	10.3046			0.537896			0.268948	−	0.963155i	$-0.413324\pi$
$367$	10.3046			0.537896			0.268948	+	0.963155i	$0.413324\pi$
$368$	6.01208	+	12.9799i	0.313401	+	0.676625i
$369$		−	3.87806i		−	0.201884i
$370$	4.50169	+	41.3501i	0.234032	+	2.14969i
$371$	−12.9719	−	1.08398i	−0.673468	−	0.0562773i
$372$	1.97064	+	8.94334i	0.102173	+	0.463690i
$373$		−	36.6619i		−	1.89828i	−0.314850	−	0.949141i	$-0.601954\pi$
$373$		−	36.6619i		−	1.89828i	0.314850	−	0.949141i	$-0.398046\pi$
$374$	−1.47903	−	13.5856i	−0.0764788	−	0.702493i
$375$		−	24.3062i		−	1.25517i
$376$	0.382499	−	0.129019i	0.0197259	−	0.00665366i
$377$		−	7.44638i		−	0.383508i
$378$	−20.4983	+	0.514018i	−1.05432	+	0.0264382i
$379$	−26.4144			−1.35682			−0.678409	−	0.734685i	$-0.737330\pi$
$379$	−26.4144			−1.35682			−0.678409	+	0.734685i	$0.737330\pi$
$380$	3.15253	+	14.3071i	0.161721	+	0.733939i
$381$	−21.9006			−1.12200
$382$	0.0817393	+	0.750813i	0.00418215	+	0.0384149i
$383$	−10.8952			−0.556719			−0.278359	−	0.960477i	$-0.589791\pi$
$383$	−10.8952			−0.556719			−0.278359	+	0.960477i	$0.589791\pi$
$384$	−12.5653	−	13.2446i	−0.641222	−	0.675887i
$385$	−2.88046	+	34.4703i	−0.146802	+	1.75677i
$386$	0.622767	−	0.0677992i	0.0316980	−	0.00345089i
$387$	−3.83284			−0.194834
$388$	−1.95012	−	8.85023i	−0.0990024	−	0.449302i
$389$		−	5.69554i		−	0.288775i	−0.989521	−	0.144388i	$-0.953879\pi$
$389$		−	5.69554i		−	0.288775i	0.989521	−	0.144388i	$-0.0461212\pi$
$390$	−0.924879	−	8.49544i	−0.0468331	−	0.430183i
$391$	−9.89791			−0.500559
$392$	19.5506	−	3.12663i	0.987452	−	0.157919i
$393$	−8.32300			−0.419840
$394$	3.75013	+	34.4467i	0.188929	+	1.73540i
$395$		−	29.3789i		−	1.47821i
$396$	2.70061	−	0.595072i	0.135711	−	0.0299035i
$397$	25.6458			1.28713			0.643564	−	0.765392i	$-0.277455\pi$
$397$	25.6458			1.28713			0.643564	+	0.765392i	$0.277455\pi$
$398$	10.0613	−	1.09535i	0.504328	−	0.0549050i
$399$	0.695468	−	8.32264i	0.0348170	−	0.416653i
$400$	32.7475	−	15.1681i	1.63737	−	0.758403i
$401$	14.3701			0.717609			0.358804	−	0.933413i	$-0.383185\pi$
$401$	14.3701			0.717609			0.358804	+	0.933413i	$0.383185\pi$
$402$	−1.64091	−	15.0725i	−0.0818413	−	0.751750i
$403$	−2.83757			−0.141350
$404$	9.00030	−	1.98319i	0.447782	−	0.0986674i
$405$	28.6655			1.42440
$406$	−27.8530	+	0.698447i	−1.38232	+	0.0346634i
$407$			27.4223i			1.35927i
$408$	11.9699	−	4.03751i	0.592597	−	0.199887i
$409$			22.9637i			1.13548i	0.823208	+	0.567740i	$0.192182\pi$
$409$			22.9637i			1.13548i	−0.823208	+	0.567740i	$0.807818\pi$
$410$	−5.61242	−	51.5526i	−0.277177	−	2.54600i
$411$		−	8.39138i		−	0.413916i
$412$	38.5540	−	8.49525i	1.89942	−	0.418531i
$413$	39.4244	+	3.29443i	1.93995	+	0.162109i
$414$	−0.216773	−	1.99116i	−0.0106538	−	0.0978601i
$415$		−	40.5279i		−	1.98944i
$416$	4.84551	−	2.91908i	0.237571	−	0.143119i
$417$	13.4206			0.657210
$418$	1.04534	+	9.60190i	0.0511291	+	0.469644i
$419$			16.8449i			0.822928i	0.911426	+	0.411464i	$0.134982\pi$
$419$			16.8449i			0.822928i	−0.911426	+	0.411464i	$0.865018\pi$
$420$	−31.6903	+	4.25634i	−1.54633	+	0.207688i
$421$		−	26.7581i		−	1.30411i	−0.758172	−	0.652055i	$-0.773907\pi$
$421$		−	26.7581i		−	1.30411i	0.758172	−	0.652055i	$-0.226093\pi$
$422$	−9.21546	+	1.00327i	−0.448602	+	0.0488382i
$423$	−0.0565218			−0.00274818
$424$	4.44771	+	13.1860i	0.216000	+	0.640367i
$425$			24.9717i			1.21131i
$426$	4.98589	−	0.542802i	0.241567	−	0.0262988i
$427$	1.41512	−	16.9347i	0.0684827	−	0.819529i
$428$	−24.7294	+	5.44906i	−1.19534	+	0.263390i
$429$		−	5.63395i		−	0.272010i
$430$	−50.9515	+	5.54697i	−2.45710	+	0.267499i
$431$		−	4.59304i		−	0.221239i	−0.993863	−	0.110620i	$-0.964716\pi$
$431$		−	4.59304i		−	0.221239i	0.993863	−	0.110620i	$-0.0352835\pi$
$432$	9.21290	+	19.8904i	0.443256	+	0.956978i
$433$			23.4278i			1.12587i	0.826501	+	0.562935i	$0.190328\pi$
$433$			23.4278i			1.12587i	−0.826501	+	0.562935i	$0.809672\pi$
$434$	0.266156	+	10.6139i	0.0127759	+	0.509483i
$435$	44.9960			2.15739
$436$	2.43254	+	11.0396i	0.116498	+	0.528700i
$437$	6.99557			0.334644
$438$	16.5441	−	1.80112i	0.790508	−	0.0860608i
$439$	−10.6934			−0.510370			−0.255185	−	0.966892i	$-0.582136\pi$
$439$	−10.6934			−0.510370			−0.255185	+	0.966892i	$0.582136\pi$
$440$	35.0391	−	11.8189i	1.67042	−	0.563445i
$441$	−2.73379	−	0.460102i	−0.130180	−	0.0219096i
$442$	0.423625	+	3.89119i	0.0201498	+	0.185085i
$443$	35.3297			1.67856			0.839282	−	0.543696i	$-0.182976\pi$
$443$	35.3297			1.67856			0.839282	+	0.543696i	$0.182976\pi$
$444$	−24.7549	+	5.45467i	−1.17482	+	0.258867i
$445$		−	33.5784i		−	1.59177i
$446$	26.0560	−	2.83666i	1.23379	−	0.134320i
$447$	25.7714			1.21894
$448$	−11.3732	−	17.8508i	−0.537335	−	0.843369i
$449$	7.09060			0.334626			0.167313	−	0.985904i	$-0.446491\pi$
$449$	7.09060			0.334626			0.167313	+	0.985904i	$0.446491\pi$
$450$	−5.02356	+	0.546903i	−0.236813	+	0.0257813i
$451$		−	34.1883i		−	1.60987i
$452$	34.2337	−	7.54330i	1.61022	−	0.354807i
$453$	−25.0420			−1.17658
$454$	0.537125	+	4.93374i	0.0252085	+	0.231552i
$455$	0.825022	−	9.87301i	0.0386776	−	0.462854i
$456$	−8.45998	+	2.85360i	−0.396175	+	0.133632i
$457$	13.3891			0.626314			0.313157	−	0.949701i	$-0.398613\pi$
$457$	13.3891			0.626314			0.313157	+	0.949701i	$0.398613\pi$
$458$	24.2768	−	2.64296i	1.13438	−	0.123498i
$459$	−15.1675			−0.707961
$460$	−5.76330	−	26.1556i	−0.268715	−	1.21951i
$461$	−26.9894			−1.25702			−0.628510	−	0.777802i	$-0.716335\pi$
$461$	−26.9894			−1.25702			−0.628510	+	0.777802i	$0.716335\pi$
$462$	−21.0737	+	0.528448i	−0.980437	+	0.0245856i
$463$			4.39205i			0.204116i	0.994778	+	0.102058i	$0.0325427\pi$
$463$			4.39205i			0.204116i	−0.994778	+	0.102058i	$0.967457\pi$
$464$	12.5185	+	27.0271i	0.581156	+	1.25470i
$465$		−	17.1465i		−	0.795151i
$466$	17.5100	−	1.90627i	0.811135	−	0.0883064i
$467$		−	16.7259i		−	0.773981i	−0.922084	−	0.386991i	$-0.873515\pi$
$467$		−	16.7259i		−	0.773981i	0.922084	−	0.386991i	$-0.126485\pi$
$468$	−0.773511	+	0.170441i	−0.0357556	+	0.00787864i
$469$	1.46375	−	17.5166i	0.0675897	−	0.808842i
$470$	−0.751366	+	0.0817996i	−0.0346579	+	0.00377313i
$471$			19.7218i			0.908732i
$472$	−13.5175	−	40.0749i	−0.622195	−	1.84460i
$473$	−33.7897			−1.55365
$474$	17.7991	−	1.93775i	0.817539	−	0.0890037i
$475$		−	17.6493i		−	0.809808i
$476$	14.5152	−	1.94954i	0.665302	−	0.0893571i
$477$		−	1.94849i		−	0.0892151i
$478$	0.756274	+	6.94672i	0.0345912	+	0.317736i
$479$	−9.09335			−0.415486			−0.207743	−	0.978183i	$-0.566612\pi$
$479$	−9.09335			−0.415486			−0.207743	+	0.978183i	$0.566612\pi$
$480$	17.6390	+	29.2799i	0.805108	+	1.33644i
$481$		−	7.85432i		−	0.358126i
$482$	1.13693	+	10.4432i	0.0517857	+	0.475675i
$483$	−1.27142	+	15.2151i	−0.0578517	+	0.692309i
$484$	2.32353	−	0.511983i	0.105615	−	0.0232720i
$485$			16.9680i			0.770478i
$486$	−0.625628	−	5.74668i	−0.0283790	−	0.260675i
$487$		−	4.59179i		−	0.208074i	−0.994573	−	0.104037i	$-0.966824\pi$
$487$		−	4.59179i		−	0.208074i	0.994573	−	0.104037i	$-0.0331760\pi$
$488$	−17.2142	+	5.80646i	−0.779250	+	0.262846i
$489$			5.30111i			0.239724i
$490$	−37.0072	−	2.15992i	−1.67181	−	0.0975754i
$491$	−39.6003			−1.78714			−0.893569	−	0.448926i	$-0.851807\pi$
$491$	−39.6003			−1.78714			−0.893569	+	0.448926i	$0.851807\pi$
$492$	30.8628	−	6.80053i	1.39140	−	0.306591i
$493$	−20.6097			−0.928212
$494$	−0.299406	−	2.75018i	−0.0134709	−	0.123737i
$495$	−5.17772			−0.232721
$496$	10.2991	−	4.77039i	0.462445	−	0.214197i
$497$	5.79437	+	0.484197i	0.259913	+	0.0217192i
$498$	24.5537	−	2.67311i	1.10028	−	0.119785i
$499$	−15.9420			−0.713664			−0.356832	−	0.934169i	$-0.616143\pi$
$499$	−15.9420			−0.713664			−0.356832	+	0.934169i	$0.616143\pi$
$500$	−29.4194	+	6.48248i	−1.31568	+	0.289905i
$501$		−	9.32421i		−	0.416575i
$502$	4.74807	+	43.6132i	0.211917	+	1.94655i
$503$	−31.3987			−1.40000			−0.699999	−	0.714144i	$-0.746816\pi$
$503$	−31.3987			−1.40000			−0.699999	+	0.714144i	$0.746816\pi$
$504$	0.710084	+	2.87732i	0.0316297	+	0.128166i
$505$	−17.2557			−0.767870
$506$	−1.91104	−	17.5537i	−0.0849559	−	0.780359i
$507$			1.61368i			0.0716661i
$508$	5.84091	+	26.5078i	0.259149	+	1.17609i
$509$	−28.4145			−1.25945			−0.629725	−	0.776818i	$-0.716833\pi$
$509$	−28.4145			−1.25945			−0.629725	+	0.776818i	$0.716833\pi$
$510$	−23.5132	+	2.55983i	−1.04118	+	0.113351i
$511$	19.2268	+	1.60666i	0.850544	+	0.0710744i
$512$	−12.6797	+	18.7410i	−0.560368	+	0.828244i
$513$	10.7200			0.473300
$514$	4.57083	+	41.9852i	0.201611	+	1.85189i
$515$	−73.9173			−3.25718
$516$	−6.72122	−	30.5029i	−0.295885	−	1.34282i
$517$	−0.498287			−0.0219146
$518$	−29.3790	+	0.736712i	−1.29084	+	0.0323693i
$519$			6.61183i			0.290227i
$520$	−10.0359	+	3.38518i	−0.440105	+	0.148450i
$521$			2.48871i			0.109032i	0.998513	+	0.0545161i	$0.0173616\pi$
$521$			2.48871i			0.109032i	−0.998513	+	0.0545161i	$0.982638\pi$
$522$	−0.451370	−	4.14604i	−0.0197559	−	0.181467i
$523$			12.1431i			0.530979i	0.964114	+	0.265489i	$0.0855335\pi$
$523$			12.1431i			0.530979i	−0.964114	+	0.265489i	$0.914467\pi$
$524$	2.21975	+	10.0739i	0.0969702	+	0.440080i
$525$	38.3865	+	3.20771i	1.67533	+	0.139996i
$526$	−2.17242	−	19.9546i	−0.0947218	−	0.870063i
$527$			7.85367i			0.342111i
$528$	9.47153	+	20.4488i	0.412195	+	0.889919i
$529$	10.2110			0.443958
$530$	−2.81989	−	25.9020i	−0.122488	−	1.12511i
$531$			5.92186i			0.256987i
$532$	−10.2589	+	1.37788i	−0.444781	+	0.0597388i
$533$			9.79226i			0.424150i
$534$	20.3433	−	2.21473i	0.880343	−	0.0958409i
$535$	47.4123			2.04981
$536$	−17.8057	+	6.00597i	−0.769088	+	0.259418i
$537$			7.44358i			0.321214i
$538$	17.6537	−	1.92192i	0.761104	−	0.0828596i
$539$	−24.1006	−	4.05618i	−1.03809	−	0.174712i
$540$	−8.83168	−	40.0808i	−0.380055	−	1.72480i
$541$			14.1176i			0.606965i	0.952837	+	0.303482i	$0.0981494\pi$
$541$			14.1176i			0.606965i	−0.952837	+	0.303482i	$0.901851\pi$
$542$	9.07790	−	0.988291i	0.389929	−	0.0424507i
$543$			28.5786i			1.22643i
$544$	−8.07925	−	13.4111i	−0.346395	−	0.574998i
$545$		−	21.1655i		−	0.906632i
$546$	6.03594	−	0.151358i	0.258315	−	0.00647754i
$547$	−17.1309			−0.732465			−0.366233	−	0.930523i	$-0.619353\pi$
$547$	−17.1309			−0.732465			−0.366233	+	0.930523i	$0.619353\pi$
$548$	−10.1567	+	2.23799i	−0.433871	+	0.0956021i
$549$	2.54374			0.108564
$550$	−44.2869	+	4.82141i	−1.88840	+	0.205586i
$551$	14.5663			0.620547
$552$	15.4661	−	5.21682i	0.658282	−	0.222043i
$553$	20.6853	+	1.72853i	0.879628	+	0.0735047i
$554$	−0.895421	−	8.22485i	−0.0380428	−	0.349440i
$555$	47.4611			2.01461
$556$	−3.57929	−	16.2439i	−0.151796	−	0.688894i
$557$		−	18.5102i		−	0.784302i	−0.919901	−	0.392151i	$-0.871731\pi$
$557$		−	18.5102i		−	0.784302i	0.919901	−	0.392151i	$-0.128269\pi$
$558$	−1.57992	+	0.172002i	−0.0668834	+	0.00728144i
$559$	9.67807			0.409339
$560$	13.6036	+	37.2217i	0.574855	+	1.57290i
$561$	−15.5933			−0.658351
$562$	−35.0524	+	3.81607i	−1.47860	+	0.160971i
$563$		−	14.4408i		−	0.608609i	−0.952575	−	0.304304i	$-0.901576\pi$
$563$		−	14.4408i		−	0.608609i	0.952575	−	0.304304i	$-0.0984240\pi$
$564$	−0.0991160	−	0.449817i	−0.00417353	−	0.0189407i
$565$	−65.6343			−2.76126
$566$	−2.32390	−	21.3460i	−0.0976806	−	0.897241i
$567$	−1.68656	+	20.1830i	−0.0708290	+	0.847608i
$568$	−1.98673	−	5.88999i	−0.0833613	−	0.247138i
$569$	−12.4987			−0.523972			−0.261986	−	0.965072i	$-0.584378\pi$
$569$	−12.4987			−0.523972			−0.261986	+	0.965072i	$0.584378\pi$
$570$	16.6185	−	1.80922i	0.696071	−	0.0757797i
$571$	12.7662			0.534248			0.267124	−	0.963662i	$-0.413927\pi$
$571$	12.7662			0.534248			0.267124	+	0.963662i	$0.413927\pi$
$572$	−6.81915	+	1.50258i	−0.285123	+	0.0628260i
$573$	0.861774			0.0360011
$574$	36.6277	−	0.918484i	1.52881	−	0.0383368i
$575$			32.2657i			1.34557i
$576$	2.52097	−	1.91902i	0.105040	−	0.0799590i
$577$		−	9.54539i		−	0.397380i	−0.980062	−	0.198690i	$-0.936331\pi$
$577$		−	9.54539i		−	0.397380i	0.980062	−	0.198690i	$-0.0636687\pi$
$578$	−13.1306	+	1.42950i	−0.546161	+	0.0594593i
$579$		−	0.714804i		−	0.0297062i
$580$	−12.0005	−	54.4617i	−0.498293	−	2.26140i
$581$	28.5352	+	2.38450i	1.18384	+	0.0989257i
$582$	−10.2800	+	1.11916i	−0.426120	+	0.0463908i
$583$		−	17.1775i		−	0.711421i
$584$	−6.59234	−	19.5441i	−0.272793	−	0.808740i
$585$	1.48301			0.0613148
$586$	35.3833	−	3.85210i	1.46167	−	0.159129i
$587$			39.2674i			1.62074i	0.585919	+	0.810370i	$0.300734\pi$
$587$			39.2674i			1.62074i	−0.585919	+	0.810370i	$0.699266\pi$
$588$	−1.13231	−	22.5631i	−0.0466955	−	0.930488i
$589$		−	5.55076i		−	0.228715i
$590$	8.57026	+	78.7217i	0.352832	+	3.24092i
$591$	39.5375			1.62635
$592$	13.2043	+	28.5078i	0.542694	+	1.17166i
$593$		−	20.3965i		−	0.837584i	−0.908082	−	0.418792i	$-0.862454\pi$
$593$		−	20.3965i		−	0.837584i	0.908082	−	0.418792i	$-0.137546\pi$
$594$	−2.92847	−	26.8993i	−0.120157	−	1.10369i
$595$	−27.3259	−	2.28345i	−1.12025	−	0.0936123i
$596$	−6.87324	−	31.1928i	−0.281539	−	1.27771i
$597$		−	11.5482i		−	0.472638i
$598$	0.547360	+	5.02776i	0.0223832	+	0.205600i
$599$			2.31530i			0.0946007i	0.998881	+	0.0473004i	$0.0150618\pi$
$599$			2.31530i			0.0946007i	−0.998881	+	0.0473004i	$0.984938\pi$
$600$	−13.1617	−	39.0200i	−0.537324	−	1.59298i
$601$			10.9430i			0.446374i	0.974776	+	0.223187i	$0.0716460\pi$
$601$			10.9430i			0.446374i	−0.974776	+	0.223187i	$0.928354\pi$
$602$	−0.907773	−	36.2006i	−0.0369981	−	1.47543i
$603$	2.63114			0.107148
$604$	6.67872	+	30.3100i	0.271753	+	1.23330i
$605$	−4.45477			−0.181112
$606$	−1.13814	−	10.4543i	−0.0462337	−	0.424678i
$607$	1.43777			0.0583574			0.0291787	−	0.999574i	$-0.490711\pi$
$607$	1.43777			0.0583574			0.0291787	+	0.999574i	$0.490711\pi$
$608$	5.71019	+	9.47862i	0.231579	+	0.384409i
$609$	−2.64738	+	31.6811i	−0.107277	+	1.28378i
$610$	33.8149	−	3.68135i	1.36913	−	0.149054i
$611$	0.142720			0.00577382
$612$	0.471737	+	2.14088i	0.0190688	+	0.0865400i
$613$			25.8050i			1.04225i	0.853479	+	0.521127i	$0.174488\pi$
$613$			25.8050i			1.04225i	−0.853479	+	0.521127i	$0.825512\pi$
$614$	2.40232	+	22.0664i	0.0969496	+	0.890526i
$615$	−59.1714			−2.38602
$616$	6.25999	+	25.3660i	0.252222	+	1.02202i
$617$	29.9570			1.20602			0.603011	−	0.797733i	$-0.293967\pi$
$617$	29.9570			1.20602			0.603011	+	0.797733i	$0.293967\pi$
$618$	−4.87537	−	44.7825i	−0.196116	−	1.80142i
$619$		−	16.3586i		−	0.657507i	−0.944416	−	0.328754i	$-0.893371\pi$
$619$		−	16.3586i		−	0.657507i	0.944416	−	0.328754i	$-0.106629\pi$
$620$	−20.7536	+	4.57299i	−0.833485	+	0.183656i
$621$	−19.5978			−0.786433
$622$	−24.0436	+	2.61757i	−0.964061	+	0.104955i
$623$	23.6421	+	1.97562i	0.947201	+	0.0791514i
$624$	−2.71284	−	5.85696i	−0.108601	−	0.234466i
$625$	11.2920			0.451680
$626$	−0.767203	−	7.04711i	−0.0306636	−	0.281659i
$627$	11.0209			0.440134
$628$	23.8706	−	5.25982i	0.952541	−	0.209890i
$629$	−21.7387			−0.866781
$630$	−0.139102	−	5.54716i	−0.00554194	−	0.221004i
$631$			24.0956i			0.959232i	0.877479	+	0.479616i	$0.159224\pi$
$631$			24.0956i			0.959232i	−0.877479	+	0.479616i	$0.840776\pi$
$632$	−7.09242	−	21.0266i	−0.282121	−	0.836395i
$633$			10.5774i			0.420413i
$634$	−4.03322	−	37.0470i	−0.160180	−	1.47132i
$635$		−	50.8218i		−	2.01680i
$636$	15.5067	−	3.41685i	0.614879	−	0.135487i
$637$	6.90292	+	1.16178i	0.273504	+	0.0460312i
$638$	−3.97920	−	36.5508i	−0.157538	−	1.44706i
$639$			0.870362i			0.0344310i
$640$	30.7350	−	29.1587i	1.21491	−	1.15260i
$641$	−0.428772			−0.0169355			−0.00846774	−	0.999964i	$-0.502695\pi$
$641$	−0.428772			−0.0169355			−0.00846774	+	0.999964i	$0.502695\pi$
$642$	3.12718	+	28.7246i	0.123420	+	1.13367i
$643$		−	23.1417i		−	0.912619i	−0.889821	−	0.456309i	$-0.849171\pi$
$643$		−	23.1417i		−	0.912619i	0.889821	−	0.456309i	$-0.150829\pi$
$644$	18.7549	−	2.51898i	0.739046	−	0.0992617i
$645$			58.4814i			2.30270i
$646$	−7.61180	+	0.828680i	−0.299482	+	0.0326040i
$647$	−20.9849			−0.825002			−0.412501	−	0.910957i	$-0.635345\pi$
$647$	−20.9849			−0.825002			−0.412501	+	0.910957i	$0.635345\pi$
$648$	20.5161	−	6.92021i	0.805948	−	0.271851i
$649$			52.2062i			2.04927i
$650$	12.6847	−	1.38095i	0.497534	−	0.0541654i
$651$	12.0727	+	1.00883i	0.473165	+	0.0395393i
$652$	6.41628	−	1.41381i	0.251281	−	0.0553691i
$653$		−	13.3109i		−	0.520897i	−0.965488	−	0.260449i	$-0.916130\pi$
$653$		−	13.3109i		−	0.520897i	0.965488	−	0.260449i	$-0.0838705\pi$
$654$	12.8231	−	1.39602i	0.501422	−	0.0545887i
$655$		−	19.3141i		−	0.754663i
$656$	−16.4623	−	35.5416i	−0.642744	−	1.38767i
$657$			2.88803i			0.112673i
$658$	−0.0133867	−	0.533840i	−0.000521867	−	0.0208113i
$659$	15.6937			0.611338			0.305669	−	0.952138i	$-0.401120\pi$
$659$	15.6937			0.611338			0.305669	+	0.952138i	$0.401120\pi$
$660$	−9.07960	−	41.2059i	−0.353423	−	1.60394i
$661$	32.2192			1.25318			0.626591	−	0.779348i	$-0.284450\pi$
$661$	32.2192			1.25318			0.626591	+	0.779348i	$0.284450\pi$
$662$	28.6690	−	3.12113i	1.11425	−	0.121306i
$663$	4.46625			0.173455
$664$	−9.78393	−	29.0061i	−0.379690	−	1.12565i
$665$	19.3132	+	1.61388i	0.748935	+	0.0625836i
$666$	−0.476098	−	4.37318i	−0.0184484	−	0.169457i
$667$	−26.6295			−1.03110
$668$	−11.2857	+	2.48677i	−0.436658	+	0.0962162i
$669$		−	29.9067i		−	1.15626i
$670$	34.9768	−	3.80785i	1.35127	−	0.147110i
$671$	22.4252			0.865714
$672$	−21.6534	+	10.6967i	−0.835297	+	0.412634i
$673$	−31.6717			−1.22085			−0.610427	−	0.792072i	$-0.709002\pi$
$673$	−31.6717			−1.22085			−0.610427	+	0.792072i	$0.709002\pi$
$674$	10.2119	−	1.11175i	0.393349	−	0.0428230i
$675$			49.4439i			1.90310i
$676$	1.95315	−	0.430370i	0.0751210	−	0.0165527i
$677$	−2.73420			−0.105084			−0.0525419	−	0.998619i	$-0.516732\pi$
$677$	−2.73420			−0.105084			−0.0525419	+	0.998619i	$0.516732\pi$
$678$	−4.32905	−	39.7643i	−0.166256	−	1.52714i
$679$	−11.9470	−	0.998329i	−0.458483	−	0.0383124i
$680$	9.36932	+	27.7769i	0.359297	+	1.06519i
$681$	5.66288			0.217002
$682$	−13.9283	+	1.51634i	−0.533343	+	0.0580638i
$683$	25.4913			0.975398			0.487699	−	0.873012i	$-0.337836\pi$
$683$	25.4913			0.975398			0.487699	+	0.873012i	$0.337836\pi$
$684$	−0.333411	−	1.51312i	−0.0127483	−	0.0578554i
$685$	19.4728			0.744016
$686$	3.69813	−	25.9292i	0.141195	−	0.989982i
$687$		−	27.8646i		−	1.06310i
$688$	−35.1272	+	16.2703i	−1.33921	+	0.620299i
$689$			4.92001i			0.187437i
$690$	−30.3811	+	3.30752i	−1.15659	+	0.125915i
$691$		−	2.66422i		−	0.101352i	−0.998715	−	0.0506758i	$-0.983862\pi$
$691$		−	2.66422i		−	0.101352i	0.998715	−	0.0506758i	$-0.0161375\pi$
$692$	8.00274	−	1.76338i	0.304219	−	0.0670337i
$693$	0.304636	−	3.64557i	0.0115722	−	0.138484i
$694$	28.4083	−	3.09275i	1.07837	−	0.117399i
$695$			31.1434i			1.18134i
$696$	32.2039	−	10.8626i	1.22069	−	0.411745i
$697$	27.1024			1.02658
$698$	−39.9288	+	4.34696i	−1.51133	+	0.164535i
$699$		−	20.0977i		−	0.760167i
$700$	−6.35521	−	47.3173i	−0.240204	−	1.78843i
$701$		−	29.1497i		−	1.10097i	−0.834845	−	0.550485i	$-0.814443\pi$
$701$		−	29.1497i		−	1.10097i	0.834845	−	0.550485i	$-0.185557\pi$
$702$	0.838775	+	7.70453i	0.0316575	+	0.290789i
$703$	15.3644			0.579477
$704$	22.2245	−	16.9177i	0.837616	−	0.637611i
$705$			0.862409i			0.0324802i
$706$	−1.36793	−	12.5651i	−0.0514827	−	0.472893i
$707$	1.01526	−	12.1495i	0.0381827	−	0.456931i
$708$	−47.1280	+	10.3845i	−1.77118	+	0.390274i
$709$		−	26.8237i		−	1.00739i	−0.863883	−	0.503693i	$-0.831974\pi$
$709$		−	26.8237i		−	1.00739i	0.863883	−	0.503693i	$-0.168026\pi$
$710$	1.25961	+	11.5701i	0.0472722	+	0.434217i
$711$			3.10710i			0.116525i
$712$	−8.10623	−	24.0322i	−0.303794	−	0.900647i
$713$			10.1476i			0.380032i
$714$	−0.418921	−	16.7059i	−0.0156777	−	0.625204i
$715$	13.0740			0.488938
$716$	9.00947	−	1.98521i	0.336700	−	0.0741908i
$717$	7.97336			0.297770
$718$	0.230804	+	2.12004i	0.00861352	+	0.0791191i
$719$	42.5092			1.58532			0.792662	−	0.609661i	$-0.208694\pi$
$719$	42.5092			1.58532			0.792662	+	0.609661i	$0.208694\pi$
$720$	−5.38267	+	2.49316i	−0.200600	+	0.0929146i
$721$	4.34899	−	52.0442i	0.161965	−	1.93823i
$722$	−21.3324	+	2.32241i	−0.793910	+	0.0864312i
$723$	11.9866			0.445785
$724$	34.5906	−	7.62194i	1.28555	−	0.283267i
$725$			67.1843i			2.49516i
$726$	−0.293824	−	2.69891i	−0.0109048	−	0.100166i
$727$	−39.1500			−1.45199			−0.725997	−	0.687698i	$-0.758621\pi$
$727$	−39.1500			−1.45199			−0.725997	+	0.687698i	$0.758621\pi$
$728$	−1.79299	−	7.26534i	−0.0664527	−	0.269271i
$729$	−29.5611			−1.09486
$730$	4.17962	+	38.3917i	0.154695	+	1.42094i
$731$		−	26.7864i		−	0.990731i
$732$	4.46067	+	20.2438i	0.164871	+	0.748234i
$733$	−47.3188			−1.74776			−0.873881	−	0.486140i	$-0.838404\pi$
$733$	−47.3188			−1.74776			−0.873881	+	0.486140i	$0.838404\pi$
$734$	−14.4873	+	1.57720i	−0.534737	+	0.0582156i
$735$	−7.02023	+	41.7121i	−0.258945	+	1.53857i
$736$	−10.4391	−	17.3284i	−0.384790	−	0.638732i
$737$	23.1957			0.854425
$738$	0.593568	+	5.45219i	0.0218495	+	0.200698i
$739$	33.8702			1.24594			0.622968	−	0.782248i	$-0.285927\pi$
$739$	33.8702			1.24594			0.622968	+	0.782248i	$0.285927\pi$
$740$	−12.6579	−	57.4454i	−0.465314	−	2.11173i
$741$	−3.15663			−0.115962
$742$	18.4032	−	0.461482i	0.675603	−	0.0169415i
$743$		−	12.7354i		−	0.467216i	−0.972331	−	0.233608i	$-0.924947\pi$
$743$		−	12.7354i		−	0.467216i	0.972331	−	0.233608i	$-0.0750533\pi$
$744$	−4.13938	−	12.2719i	−0.151757	−	0.449909i
$745$			59.8041i			2.19105i
$746$	5.61140	+	51.5432i	0.205448	+	1.88713i
$747$			4.28622i			0.156825i
$748$	4.15875	+	18.8737i	0.152059	+	0.690089i
$749$	−2.78955	+	33.3824i	−0.101928	+	1.21977i
$750$	3.72025	+	34.1722i	0.135844	+	1.24779i
$751$		−	18.6960i		−	0.682227i	−0.940022	−	0.341114i	$-0.889196\pi$
$751$		−	18.6960i		−	0.682227i	0.940022	−	0.341114i	$-0.110804\pi$
$752$	−0.518010	+	0.239933i	−0.0188899	+	0.00874947i
$753$	50.0586			1.82424
$754$	1.13973	+	10.4689i	0.0415064	+	0.381255i
$755$		−	58.1116i		−	2.11490i
$756$	28.7400	−	3.86008i	1.04526	−	0.140390i
$757$		−	8.61922i		−	0.313271i	−0.987657	−	0.156635i	$-0.949935\pi$
$757$		−	8.61922i		−	0.313271i	0.987657	−	0.156635i	$-0.0500647\pi$
$758$	37.1362	−	4.04294i	1.34885	−	0.146846i
$759$	−20.1479			−0.731324
$760$	−6.62198	−	19.6319i	−0.240204	−	0.712125i
$761$		−	17.1945i		−	0.623300i	−0.950197	−	0.311650i	$-0.899118\pi$
$761$		−	17.1945i		−	0.623300i	0.950197	−	0.311650i	$-0.100882\pi$
$762$	30.7902	−	3.35206i	1.11541	−	0.121432i
$763$	14.9024	+	1.24529i	0.539503	+	0.0450827i
$764$	−0.229836	−	1.04306i	−0.00831517	−	0.0377367i
$765$		−	4.10458i		−	0.148402i
$766$	15.3176	−	1.66760i	0.553449	−	0.0602527i
$767$		−	14.9529i		−	0.539919i
$768$	19.6929	+	16.6975i	0.710605	+	0.602519i
$769$			50.8313i			1.83302i	0.400008	+	0.916511i	$0.369007\pi$
$769$			50.8313i			1.83302i	−0.400008	+	0.916511i	$0.630993\pi$
$770$	−1.22630	−	48.9029i	−0.0441927	−	1.76234i
$771$	48.1900			1.73552
$772$	−0.865175	+	0.190639i	−0.0311383	+	0.00686124i
$773$	43.5769			1.56735			0.783676	−	0.621170i	$-0.213343\pi$
$773$	43.5769			1.56735			0.783676	+	0.621170i	$0.213343\pi$
$774$	5.38861	−	0.586646i	0.193690	−	0.0210866i
$775$	25.6018			0.919643
$776$	4.09629	+	12.1441i	0.147048	+	0.435948i
$777$	−2.79242	+	33.4168i	−0.100178	+	1.19882i
$778$	0.871747	+	8.00740i	0.0312536	+	0.287079i
$779$	−19.1553			−0.686309
$780$	2.60059	+	11.8022i	0.0931159	+	0.422588i
$781$			7.67297i			0.274560i
$782$	13.9155	−	1.51495i	0.497619	−	0.0541746i
$783$	−40.8070			−1.45832
$784$	−27.0077	+	7.38812i	−0.964561	+	0.263861i
$785$	−45.7657			−1.63345
$786$	11.7014	−	1.27390i	0.417374	−	0.0454385i
$787$		−	6.15291i		−	0.219328i	−0.993969	−	0.109664i	$-0.965023\pi$
$787$		−	6.15291i		−	0.219328i	0.993969	−	0.109664i	$-0.0349774\pi$
$788$	−10.5447	−	47.8548i	−0.375638	−	1.70476i
$789$	−22.9037			−0.815392
$790$	4.49667	+	41.3040i	0.159984	+	1.46953i
$791$	3.86166	−	46.2123i	0.137305	−	1.64312i
$792$	−3.70573	+	1.24996i	−0.131677	+	0.0444156i
$793$	−6.42304			−0.228089
$794$	−36.0556	+	3.92530i	−1.27957	+	0.139304i
$795$	−29.7300			−1.05441
$796$	−13.9776	+	3.07992i	−0.495423	+	0.109165i
$797$	38.1609			1.35173			0.675864	−	0.737027i	$-0.263771\pi$
$797$	38.1609			1.35173			0.675864	+	0.737027i	$0.263771\pi$
$798$	0.296082	+	11.8073i	0.0104812	+	0.417974i
$799$		−	0.395011i		−	0.0139745i
$800$	−43.7183	+	26.3371i	−1.54567	+	0.931158i
$801$			3.55124i			0.125477i
$802$	−20.2030	+	2.19946i	−0.713393	+	0.0776655i
$803$			25.4604i			0.898477i
$804$	4.61394	+	20.9394i	0.162721	+	0.738477i
$805$	−35.3075	−	2.95042i	−1.24443	−	0.103989i
$806$	3.98936	−	0.434313i	0.140519	−	0.0152980i
$807$		−	20.2627i		−	0.713279i
$808$	−12.3500	+	4.16575i	−0.434473	+	0.146550i
$809$	28.6279			1.00651			0.503253	−	0.864139i	$-0.332137\pi$
$809$	28.6279			1.00651			0.503253	+	0.864139i	$0.332137\pi$
$810$	−40.3011	+	4.38748i	−1.41603	+	0.154161i
$811$			18.4849i			0.649094i	0.945870	+	0.324547i	$0.105212\pi$
$811$			18.4849i			0.649094i	−0.945870	+	0.324547i	$0.894788\pi$
$812$	39.0519	−	5.24508i	1.37045	−	0.184066i
$813$		−	10.4195i		−	0.365428i
$814$	−4.19720	−	38.5532i	−0.147112	−	1.35129i
$815$	−12.3016			−0.430905
$816$	−16.2106	+	7.50845i	−0.567483	+	0.262848i
$817$			18.9319i			0.662343i
$818$	−3.51477	−	32.2848i	−0.122891	−	1.12881i
$819$	−0.0872541	+	1.04417i	−0.00304891	+	0.0364861i
$820$	15.7811	+	71.6191i	0.551099	+	2.50105i
$821$			13.5883i			0.474234i	0.971481	+	0.237117i	$0.0762024\pi$
$821$			13.5883i			0.474234i	−0.971481	+	0.237117i	$0.923798\pi$
$822$	1.28437	+	11.7975i	0.0447974	+	0.411485i
$823$		−	7.79884i		−	0.271850i	−0.990719	−	0.135925i	$-0.956599\pi$
$823$		−	7.79884i		−	0.271850i	0.990719	−	0.135925i	$-0.0434007\pi$
$824$	−52.9030	+	17.8445i	−1.84296	+	0.621643i
$825$			50.8319i			1.76974i
$826$	−55.9312	+	1.40254i	−1.94610	+	0.0488006i
$827$	13.7228			0.477187			0.238593	−	0.971120i	$-0.423314\pi$
$827$	13.7228			0.477187			0.238593	+	0.971120i	$0.423314\pi$
$828$	0.609525	+	2.76621i	0.0211825	+	0.0961323i
$829$	−31.6411			−1.09894			−0.549470	−	0.835513i	$-0.685170\pi$
$829$	−31.6411			−1.09894			−0.549470	+	0.835513i	$0.685170\pi$
$830$	6.20312	+	56.9785i	0.215313	+	1.97775i
$831$	−9.44037			−0.327483
$832$	−6.36555	+	4.84559i	−0.220686	+	0.167991i
$833$	3.21550	−	19.1055i	0.111410	−	0.661966i
$834$	−18.8681	+	2.05413i	−0.653350	+	0.0711287i
$835$	21.6374			0.748795
$836$	−2.93929	−	13.3394i	−0.101658	−	0.461352i
$837$			15.5502i			0.537494i
$838$	−2.57825	−	23.6824i	−0.0890641	−	0.818094i
$839$	2.34931			0.0811071			0.0405535	−	0.999177i	$-0.487088\pi$
$839$	2.34931			0.0811071			0.0405535	+	0.999177i	$0.487088\pi$
$840$	43.9021	−	10.8345i	1.51477	−	0.373824i
$841$	−26.4485			−0.912017
$842$	4.09554	+	37.6194i	0.141141	+	1.29645i
$843$			40.2327i			1.38569i
$844$	12.8025	−	2.82100i	0.440681	−	0.0971027i
$845$	−3.74465			−0.128820
$846$	0.0794643	−	0.00865110i	0.00273204	−	0.000297431i
$847$	0.262100	−	3.13655i	0.00900588	−	0.107773i
$848$	−8.27128	−	17.8575i	−0.284037	−	0.613228i
$849$	−24.5007			−0.840862
$850$	−3.82212	−	35.1079i	−0.131098	−	1.20419i
$851$	−28.0884			−0.962857
$852$	−6.92661	+	1.52626i	−0.237302	+	0.0522887i
$853$	8.75040			0.299608			0.149804	−	0.988716i	$-0.452136\pi$
$853$	8.75040			0.299608			0.149804	+	0.988716i	$0.452136\pi$
$854$	0.602462	+	24.0253i	0.0206158	+	0.822127i
$855$			2.90101i			0.0992124i
$856$	33.9332	−	11.4459i	1.15981	−	0.391213i
$857$			23.5240i			0.803565i	0.915735	+	0.401782i	$0.131609\pi$
$857$			23.5240i			0.803565i	−0.915735	+	0.401782i	$0.868391\pi$
$858$	0.862320	+	7.92081i	0.0294391	+	0.270412i
$859$		−	22.6120i		−	0.771512i	−0.922601	−	0.385756i	$-0.873941\pi$
$859$		−	22.6120i		−	0.771512i	0.922601	−	0.385756i	$-0.126059\pi$
$860$	70.7840	−	15.5970i	2.41371	−	0.531855i
$861$	3.48141	−	41.6618i	0.118646	−	1.41983i
$862$	0.703002	+	6.45739i	0.0239443	+	0.219940i
$863$		−	47.5417i		−	1.61834i	−0.587575	−	0.809170i	$-0.699917\pi$
$863$		−	47.5417i		−	1.61834i	0.587575	−	0.809170i	$-0.300083\pi$
$864$	−15.9969	−	26.5540i	−0.544225	−	0.903384i
$865$	−15.3432			−0.521684
$866$	−3.58582	−	32.9374i	−0.121851	−	1.11926i
$867$			15.0711i			0.511843i
$868$	−1.99873	−	14.8814i	−0.0678413	−	0.505108i
$869$			27.3917i			0.929200i
$870$	−63.2602	+	6.88700i	−2.14472	+	0.233491i
$871$	−6.64374			−0.225114
$872$	−5.10962	−	15.1483i	−0.173034	−	0.512986i
$873$		−	1.79453i		−	0.0607357i
$874$	−9.83512	+	1.07073i	−0.332678	+	0.0362179i
$875$	−3.31859	+	39.7134i	−0.112189	+	1.34256i
$876$	−22.9838	+	5.06441i	−0.776551	+	0.171111i
$877$		−	51.8073i		−	1.74941i	−0.484656	−	0.874705i	$-0.661055\pi$
$877$		−	51.8073i		−	1.74941i	0.484656	−	0.874705i	$-0.338945\pi$
$878$	15.0340	−	1.63672i	0.507372	−	0.0552365i
$879$		−	40.6125i		−	1.36983i
$880$	−47.4527	+	21.9793i	−1.59963	+	0.740922i
$881$		−	40.0432i		−	1.34909i	−0.738234	−	0.674545i	$-0.764340\pi$
$881$		−	40.0432i		−	1.34909i	0.738234	−	0.674545i	$-0.235660\pi$
$882$	3.91387	+	0.228433i	0.131787	+	0.00769173i
$883$	39.9810			1.34547			0.672733	−	0.739885i	$-0.265120\pi$
$883$	39.9810			1.34547			0.672733	+	0.739885i	$0.265120\pi$
$884$	−1.19115	−	5.40581i	−0.0400628	−	0.181817i
$885$	90.3558			3.03728
$886$	−49.6702	+	5.40749i	−1.66870	+	0.181668i
$887$	49.1208			1.64931			0.824657	−	0.565633i	$-0.191368\pi$
$887$	49.1208			1.64931			0.824657	+	0.565633i	$0.191368\pi$
$888$	33.9682	−	11.4577i	1.13990	−	0.384495i
$889$	35.7830	+	2.99015i	1.20012	+	0.100286i
$890$	5.13944	+	47.2081i	0.172274	+	1.58242i
$891$	−26.7266			−0.895375
$892$	−36.1981	+	7.97615i	−1.21200	+	0.267061i
$893$			0.279183i			0.00934251i
$894$	−36.2321	+	3.94451i	−1.21178	+	0.131924i
$895$	−17.2733			−0.577384
$896$	18.7219	+	23.3557i	0.625455	+	0.780260i
$897$	5.77079			0.192681
$898$	−9.96873	+	1.08527i	−0.332661	+	0.0362160i
$899$			21.1296i			0.704713i
$900$	6.97895	−	1.53779i	0.232632	−	0.0512597i
$901$	13.6173			0.453659
$902$	5.23279	+	48.0656i	0.174233	+	1.60041i
$903$	−41.1760	−	3.44081i	−1.37025	−	0.114503i
$904$	−46.9749	+	15.8449i	−1.56236	+	0.526994i
$905$	−66.3185			−2.20450
$906$	35.2067	−	3.83287i	1.16966	−	0.127339i
$907$	28.5979			0.949577			0.474788	−	0.880100i	$-0.342525\pi$
$907$	28.5979			0.949577			0.474788	+	0.880100i	$0.342525\pi$
$908$	−1.51030	−	6.85417i	−0.0501209	−	0.227464i
$909$	1.82496			0.0605302
$910$	0.351237	+	14.0068i	0.0116434	+	0.464321i
$911$			28.8950i			0.957335i	0.877996	+	0.478667i	$0.158880\pi$
$911$			28.8950i			0.957335i	−0.877996	+	0.478667i	$0.841120\pi$
$912$	11.4572	−	5.30677i	0.379385	−	0.175725i
$913$			37.7866i			1.25056i
$914$	−18.8238	+	2.04930i	−0.622635	+	0.0677849i
$915$		−	38.8123i		−	1.28310i
$916$	−33.7264	+	7.43152i	−1.11435	+	0.245544i
$917$	13.5988	+	1.13636i	0.449071	+	0.0375259i
$918$	21.3242	−	2.32151i	0.703802	−	0.0766213i
$919$			26.0590i			0.859607i	0.902923	+	0.429803i	$0.141417\pi$
$919$			26.0590i			0.859607i	−0.902923	+	0.429803i	$0.858583\pi$
$920$	12.1060	+	35.8902i	0.399122	+	1.18326i
$921$	25.3275			0.834569
$922$	37.9445	−	4.13093i	1.24964	−	0.136045i
$923$		−	2.19770i		−	0.0723381i
$924$	29.5468	−	3.96844i	0.972017	−	0.130552i
$925$			70.8650i			2.33003i
$926$	−0.672237	−	6.17481i	−0.0220911	−	0.202917i
$927$	7.81747			0.256759
$928$	−21.7365	−	36.0815i	−0.713537	−	1.18443i
$929$		−	15.2468i		−	0.500232i	−0.968216	−	0.250116i	$-0.919531\pi$
$929$		−	15.2468i		−	0.500232i	0.968216	−	0.250116i	$-0.0804688\pi$
$930$	2.62441	+	24.1064i	0.0860578	+	0.790481i
$931$	−2.27262	+	13.5032i	−0.0744823	+	0.442551i
$932$	−24.3257	+	5.36009i	−0.796813	+	0.175575i
$933$			27.5969i			0.903483i
$934$	2.56003	+	23.5150i	0.0837666	+	0.769435i
$935$		−	36.1853i		−	1.18339i
$936$	1.06140	−	0.358016i	0.0346929	−	0.0117021i
$937$		−	30.0544i		−	0.981835i	−0.871206	−	0.490917i	$-0.836662\pi$
$937$		−	30.0544i		−	0.981835i	0.871206	−	0.490917i	$-0.163338\pi$
$938$	0.623162	+	24.8508i	0.0203470	+	0.811407i
$939$	−8.08858			−0.263961
$940$	1.04383	−	0.230005i	0.0340460	−	0.00750194i
$941$	15.0095			0.489297			0.244649	−	0.969612i	$-0.421327\pi$
$941$	15.0095			0.489297			0.244649	+	0.969612i	$0.421327\pi$
$942$	−3.01857	−	27.7270i	−0.0983505	−	0.903394i
$943$	35.0187			1.14037
$944$	25.1382	+	54.2726i	0.818178	+	1.76642i
$945$	−54.1052	−	4.52122i	−1.76004	−	0.147075i
$946$	47.5051	−	5.17177i	1.54452	−	0.168149i
$947$	12.4781			0.405485			0.202743	−	0.979232i	$-0.435015\pi$
$947$	12.4781			0.405485			0.202743	+	0.979232i	$0.435015\pi$
$948$	−24.7273	+	5.44858i	−0.803104	+	0.176962i
$949$		−	7.29238i		−	0.236721i
$950$	2.70137	+	24.8133i	0.0876441	+	0.805051i
$951$	−42.5221			−1.37887
$952$	−20.1086	+	4.96254i	−0.651723	+	0.160837i
$953$	−3.80075			−0.123118			−0.0615592	−	0.998103i	$-0.519607\pi$
$953$	−3.80075			−0.123118			−0.0615592	+	0.998103i	$0.519607\pi$
$954$	0.298231	+	2.73939i	0.00965559	+	0.0886911i
$955$			1.99980i			0.0647121i
$956$	−2.12650	−	9.65069i	−0.0687759	−	0.312126i
$957$	−41.9525			−1.35613
$958$	12.7844	−	1.39181i	0.413045	−	0.0449673i
$959$	−1.14570	+	13.7105i	−0.0369965	+	0.442736i
$960$	−29.2803	−	38.4650i	−0.945019	−	1.24145i
$961$	−22.9482			−0.740264
$962$	1.20217	+	11.0424i	0.0387594	+	0.356023i
$963$	−5.01431			−0.161584
$964$	−3.19683	−	14.5082i	−0.102963	−	0.467276i
$965$	1.65875			0.0533970
$966$	−0.541283	−	21.5855i	−0.0174155	−	0.694503i
$967$			16.8661i			0.542378i	0.962526	+	0.271189i	$0.0874168\pi$
$967$			16.8661i			0.542378i	−0.962526	+	0.271189i	$0.912583\pi$
$968$	−3.18830	+	1.07544i	−0.102476	+	0.0345658i
$969$			8.73673i			0.280664i
$970$	−2.59709	−	23.8555i	−0.0833875	−	0.765952i
$971$			42.9001i			1.37673i	0.725365	+	0.688364i	$0.241671\pi$
$971$			42.9001i			1.37673i	−0.725365	+	0.688364i	$0.758329\pi$
$972$	1.75915	+	7.98353i	0.0564247	+	0.256072i
$973$	−21.9277	−	1.83235i	−0.702969	−	0.0587425i
$974$	0.702809	+	6.45562i	0.0225195	+	0.206852i
$975$		−	14.5593i		−	0.466271i
$976$	23.3128	−	10.7981i	0.746225	−	0.345639i
$977$	−35.4270			−1.13341			−0.566705	−	0.823921i	$-0.691782\pi$
$977$	−35.4270			−1.13341			−0.566705	+	0.823921i	$0.691782\pi$
$978$	−0.811376	−	7.45286i	−0.0259449	−	0.238316i
$979$			31.3072i			1.00058i
$980$	52.3592	−	2.62759i	1.67255	−	0.0839353i
$981$			2.23846i			0.0714686i
$982$	55.6744	−	6.06114i	1.77664	−	0.193419i
$983$	32.3803			1.03277			0.516385	−	0.856356i	$-0.327277\pi$
$983$	32.3803			1.03277			0.516385	+	0.856356i	$0.327277\pi$
$984$	−42.3493	+	14.2847i	−1.35005	+	0.455380i
$985$			91.7493i			2.92337i
$986$	28.9752	−	3.15447i	0.922760	−	0.100459i
$987$	−0.607211	−	0.0507406i	−0.0193277	−	0.00161509i
$988$	0.841875	+	3.82068i	0.0267836	+	0.121552i
$989$		−	34.6104i		−	1.10055i
$990$	7.27939	−	0.792491i	0.231354	−	0.0251870i
$991$			10.8930i			0.346027i	0.984919	+	0.173013i	$0.0553504\pi$
$991$			10.8930i			0.346027i	−0.984919	+	0.173013i	$0.944650\pi$
$992$	−13.7495	+	8.28309i	−0.436547	+	0.262988i
$993$		−	32.9059i		−	1.04424i
$994$	−8.22045	+	0.206137i	−0.260737	+	0.00653828i
$995$	26.7984			0.849567
$996$	−34.1111	+	7.51628i	−1.08085	+	0.238162i
$997$	−10.3344			−0.327294			−0.163647	−	0.986519i	$-0.552326\pi$
$997$	−10.3344			−0.327294			−0.163647	+	0.986519i	$0.552326\pi$
$998$	22.4130	−	2.44005i	0.709472	−	0.0772386i
$999$	−43.0426			−1.36181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.a.27.2	yes	48
4.3	odd	2		2912.2.h.a.2575.12		48
7.6	odd	2		728.2.h.b.27.2	yes	48
8.3	odd	2		728.2.h.b.27.1	yes	48
8.5	even	2		2912.2.h.b.2575.12		48
28.27	even	2		2912.2.h.b.2575.37		48
56.13	odd	2		2912.2.h.a.2575.37		48
56.27	even	2	inner	728.2.h.a.27.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.1	✓	48	56.27	even	2	inner
728.2.h.a.27.2	yes	48	1.1	even	1	trivial
728.2.h.b.27.1	yes	48	8.3	odd	2
728.2.h.b.27.2	yes	48	7.6	odd	2
2912.2.h.a.2575.12		48	4.3	odd	2
2912.2.h.a.2575.37		48	56.13	odd	2
2912.2.h.b.2575.12		48	8.5	even	2
2912.2.h.b.2575.37		48	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40591 + 0.153058i) q^{2} +1.61368i q^{3} +(1.95315 - 0.430370i) q^{4} -3.74465 q^{5} +(-0.246987 - 2.26868i) q^{6} +(0.220320 - 2.63656i) q^{7} +(-2.68007 + 0.904005i) q^{8} +0.396033 q^{9} +(5.26463 - 0.573149i) q^{10} +3.49137 q^{11} +(0.694480 + 3.15176i) q^{12} -1.00000 q^{13} +(0.0937970 + 3.74048i) q^{14} -6.04268i q^{15} +(3.62956 - 1.68115i) q^{16} +2.76774i q^{17} +(-0.556786 + 0.0606160i) q^{18} -1.95616i q^{19} +(-7.31386 + 1.61159i) q^{20} +(4.25457 + 0.355526i) q^{21} +(-4.90853 + 0.534381i) q^{22} +3.57617i q^{23} +(-1.45878 - 4.32478i) q^{24} +9.02242 q^{25} +(1.40591 - 0.153058i) q^{26} +5.48011i q^{27} +(-0.704380 - 5.24441i) q^{28} +7.44638i q^{29} +(0.924879 + 8.49544i) q^{30} +2.83757 q^{31} +(-4.84551 + 2.91908i) q^{32} +5.63395i q^{33} +(-0.423625 - 3.89119i) q^{34} +(-0.825022 + 9.87301i) q^{35} +(0.773511 - 0.170441i) q^{36} +7.85432i q^{37} +(0.299406 + 2.75018i) q^{38} -1.61368i q^{39} +(10.0359 - 3.38518i) q^{40} -9.79226i q^{41} +(-6.03594 + 0.151358i) q^{42} -9.67807 q^{43} +(6.81915 - 1.50258i) q^{44} -1.48301 q^{45} +(-0.547360 - 5.02776i) q^{46} -0.142720 q^{47} +(2.71284 + 5.85696i) q^{48} +(-6.90292 - 1.16178i) q^{49} +(-12.6847 + 1.38095i) q^{50} -4.46625 q^{51} +(-1.95315 + 0.430370i) q^{52} -4.92001i q^{53} +(-0.838775 - 7.70453i) q^{54} -13.0740 q^{55} +(1.79299 + 7.26534i) q^{56} +3.15663 q^{57} +(-1.13973 - 10.4689i) q^{58} +14.9529i q^{59} +(-2.60059 - 11.8022i) q^{60} +6.42304 q^{61} +(-3.98936 + 0.434313i) q^{62} +(0.0872541 - 1.04417i) q^{63} +(6.36555 - 4.84559i) q^{64} +3.74465 q^{65} +(-0.862320 - 7.92081i) q^{66} +6.64374 q^{67} +(1.19115 + 5.40581i) q^{68} -5.77079 q^{69} +(-0.351237 - 14.0068i) q^{70} +2.19770i q^{71} +(-1.06140 + 0.358016i) q^{72} +7.29238i q^{73} +(-1.20217 - 11.0424i) q^{74} +14.5593i q^{75} +(-0.841875 - 3.82068i) q^{76} +(0.769218 - 9.20520i) q^{77} +(0.246987 + 2.26868i) q^{78} +7.84555i q^{79} +(-13.5915 + 6.29533i) q^{80} -7.65506 q^{81} +(1.49878 + 13.7670i) q^{82} +10.8229i q^{83} +(8.46281 - 1.13664i) q^{84} -10.3642i q^{85} +(13.6065 - 1.48130i) q^{86} -12.0161 q^{87} +(-9.35710 + 3.15621i) q^{88} +8.96702i q^{89} +(2.08497 - 0.226986i) q^{90} +(-0.220320 + 2.63656i) q^{91} +(1.53908 + 6.98478i) q^{92} +4.57894i q^{93} +(0.200651 - 0.0218444i) q^{94} +7.32516i q^{95} +(-4.71046 - 7.81911i) q^{96} -4.53127i q^{97} +(9.88268 + 0.576802i) q^{98} +1.38270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 - 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 + 10 * q^12 - 48 * q^13 + 10 * q^14 + 5 * q^16 - 15 * q^18 - 22 * q^20 - 6 * q^22 + 48 * q^25 - q^26 + 4 * q^28 - 26 * q^30 - 19 * q^32 + 36 * q^34 + 12 * q^35 - 5 * q^36 - 10 * q^38 - 48 * q^40 + 3 * q^42 - 4 * q^43 - 30 * q^44 + 24 * q^45 + 2 * q^46 + 48 * q^48 + 11 * q^50 - 40 * q^51 - q^52 + 62 * q^54 + 10 * q^56 + 2 * q^58 + 18 * q^60 - 36 * q^62 + 20 * q^63 - 11 * q^64 + 32 * q^66 - 4 * q^67 + 62 * q^68 - 11 * q^70 + 13 * q^72 - 44 * q^74 - 48 * q^76 - 20 * q^77 + 10 * q^78 + 32 * q^80 + 64 * q^81 - 50 * q^82 + 21 * q^84 + 2 * q^86 - 40 * q^87 - 66 * q^88 + 74 * q^90 - 24 * q^92 - 26 * q^94 - 84 * q^96 - 6 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more