LMFDB - Embedded newform 728.2.h.a.27.5

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			27.5
Character	$\chi$	$=$	728.27
Dual form			728.2.h.a.27.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32721 - 0.488382i) q^{2} +0.610846i q^{3} +(1.52297 + 1.29637i) q^{4} +0.780706 q^{5} +(0.298326 - 0.810720i) q^{6} +(2.18555 - 1.49110i) q^{7} +(-1.38817 - 2.46434i) q^{8} +2.62687 q^{9} +(-1.03616 - 0.381283i) q^{10} +3.13678 q^{11} +(-0.791882 + 0.930297i) q^{12} -1.00000 q^{13} +(-3.62891 + 0.911614i) q^{14} +0.476891i q^{15} +(0.638848 + 3.94865i) q^{16} -4.47267i q^{17} +(-3.48640 - 1.28292i) q^{18} +1.92835i q^{19} +(1.18899 + 1.01208i) q^{20} +(0.910831 + 1.33503i) q^{21} +(-4.16316 - 1.53195i) q^{22} -5.54704i q^{23} +(1.50533 - 0.847957i) q^{24} -4.39050 q^{25} +(1.32721 + 0.488382i) q^{26} +3.43715i q^{27} +(5.26153 + 0.562392i) q^{28} -2.44239i q^{29} +(0.232905 - 0.632934i) q^{30} -5.76655 q^{31} +(1.08057 - 5.55269i) q^{32} +1.91609i q^{33} +(-2.18437 + 5.93617i) q^{34} +(1.70627 - 1.16411i) q^{35} +(4.00063 + 3.40539i) q^{36} +0.0497032i q^{37} +(0.941771 - 2.55932i) q^{38} -0.610846i q^{39} +(-1.08375 - 1.92393i) q^{40} +9.71318i q^{41} +(-0.556855 - 2.21670i) q^{42} +9.34658 q^{43} +(4.77721 + 4.06643i) q^{44} +2.05081 q^{45} +(-2.70907 + 7.36208i) q^{46} +12.2688 q^{47} +(-2.41202 + 0.390238i) q^{48} +(2.55326 - 6.51774i) q^{49} +(5.82711 + 2.14424i) q^{50} +2.73211 q^{51} +(-1.52297 - 1.29637i) q^{52} -7.60088i q^{53} +(1.67864 - 4.56181i) q^{54} +2.44890 q^{55} +(-6.70849 - 3.31605i) q^{56} -1.17792 q^{57} +(-1.19282 + 3.24157i) q^{58} +13.2723i q^{59} +(-0.618227 + 0.726288i) q^{60} -8.35048 q^{61} +(7.65342 + 2.81628i) q^{62} +(5.74115 - 3.91692i) q^{63} +(-4.14597 + 6.84185i) q^{64} -0.780706 q^{65} +(0.935784 - 2.54305i) q^{66} +0.937154 q^{67} +(5.79824 - 6.81173i) q^{68} +3.38838 q^{69} +(-2.83311 + 0.711702i) q^{70} -13.0139i q^{71} +(-3.64654 - 6.47350i) q^{72} +0.406509i q^{73} +(0.0242741 - 0.0659665i) q^{74} -2.68192i q^{75} +(-2.49985 + 2.93681i) q^{76} +(6.85559 - 4.67725i) q^{77} +(-0.298326 + 0.810720i) q^{78} +4.03568i q^{79} +(0.498752 + 3.08274i) q^{80} +5.78103 q^{81} +(4.74374 - 12.8914i) q^{82} +11.9237i q^{83} +(-0.343535 + 3.21398i) q^{84} -3.49184i q^{85} +(-12.4049 - 4.56470i) q^{86} +1.49193 q^{87} +(-4.35438 - 7.73011i) q^{88} -15.7622i q^{89} +(-2.72185 - 1.00158i) q^{90} +(-2.18555 + 1.49110i) q^{91} +(7.19102 - 8.44795i) q^{92} -3.52247i q^{93} +(-16.2833 - 5.99186i) q^{94} +1.50547i q^{95} +(3.39184 + 0.660061i) q^{96} +7.10470i q^{97} +(-6.57185 + 7.40343i) q^{98} +8.23991 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 $

$2$	−1.32721	−	0.488382i	−0.938478	−	0.345338i
$2$	−1.32721	−	0.488382i	−0.938478	−	0.345338i
$3$			0.610846i			0.352672i	0.984330	+	0.176336i	$0.0564245\pi$
$3$			0.610846i			0.352672i	−0.984330	+	0.176336i	$0.943575\pi$
$4$	1.52297	+	1.29637i	0.761483	+	0.648185i
$5$	0.780706			0.349142			0.174571	−	0.984645i	$-0.444146\pi$
$5$	0.780706			0.349142			0.174571	+	0.984645i	$0.444146\pi$
$6$	0.298326	−	0.810720i	0.121791	−	0.330975i
$7$	2.18555	−	1.49110i	0.826060	−	0.563582i
$7$	2.18555	−	1.49110i	0.826060	−	0.563582i
$8$	−1.38817	−	2.46434i	−0.490792	−	0.871277i
$9$	2.62687			0.875622
$10$	−1.03616	−	0.381283i	−0.327662	−	0.120572i
$11$	3.13678			0.945775			0.472888	−	0.881123i	$-0.343212\pi$
$11$	3.13678			0.945775			0.472888	+	0.881123i	$0.343212\pi$
$12$	−0.791882	+	0.930297i	−0.228597	+	0.268554i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−3.62891	+	0.911614i	−0.969866	+	0.243639i
$15$			0.476891i			0.123133i
$16$	0.638848	+	3.94865i	0.159712	+	0.987164i
$17$		−	4.47267i		−	1.08478i	−0.840126	−	0.542391i	$-0.817519\pi$
$17$		−	4.47267i		−	1.08478i	0.840126	−	0.542391i	$-0.182481\pi$
$18$	−3.48640	−	1.28292i	−0.821753	−	0.302386i
$19$			1.92835i			0.442393i	0.975229	+	0.221197i	$0.0709962\pi$
$19$			1.92835i			0.442393i	−0.975229	+	0.221197i	$0.929004\pi$
$20$	1.18899	+	1.01208i	0.265866	+	0.226309i
$21$	0.910831	+	1.33503i	0.198760	+	0.291328i
$22$	−4.16316	−	1.53195i	−0.887590	−	0.326613i
$23$		−	5.54704i		−	1.15664i	−0.815811	−	0.578319i	$-0.803709\pi$
$23$		−	5.54704i		−	1.15664i	0.815811	−	0.578319i	$-0.196291\pi$
$24$	1.50533	−	0.847957i	0.307275	−	0.173089i
$25$	−4.39050			−0.878100
$26$	1.32721	+	0.488382i	0.260287	+	0.0957796i
$27$			3.43715i			0.661480i
$28$	5.26153	+	0.562392i	0.994336	+	0.106282i
$29$		−	2.44239i		−	0.453541i	−0.973948	−	0.226771i	$-0.927183\pi$
$29$		−	2.44239i		−	0.453541i	0.973948	−	0.226771i	$-0.0728167\pi$
$30$	0.232905	−	0.632934i	0.0425225	−	0.115557i
$31$	−5.76655			−1.03570			−0.517851	−	0.855471i	$-0.673268\pi$
$31$	−5.76655			−1.03570			−0.517851	+	0.855471i	$0.673268\pi$
$32$	1.08057	−	5.55269i	0.191019	−	0.981586i
$33$			1.91609i			0.333548i
$34$	−2.18437	+	5.93617i	−0.374617	+	1.01804i
$35$	1.70627	−	1.16411i	0.288413	−	0.196770i
$36$	4.00063	+	3.40539i	0.666771	+	0.567565i
$37$			0.0497032i			0.00817115i	0.999992	+	0.00408557i	$0.00130048\pi$
$37$			0.0497032i			0.00817115i	−0.999992	+	0.00408557i	$0.998700\pi$
$38$	0.941771	−	2.55932i	0.152775	−	0.415176i
$39$		−	0.610846i		−	0.0978136i
$40$	−1.08375	−	1.92393i	−0.171356	−	0.304200i
$41$			9.71318i			1.51694i	0.651706	+	0.758472i	$0.274054\pi$
$41$			9.71318i			1.51694i	−0.651706	+	0.758472i	$0.725946\pi$
$42$	−0.556855	−	2.21670i	−0.0859247	−	0.342045i
$43$	9.34658			1.42534			0.712670	−	0.701499i	$-0.247486\pi$
$43$	9.34658			1.42534			0.712670	+	0.701499i	$0.247486\pi$
$44$	4.77721	+	4.06643i	0.720192	+	0.613038i
$45$	2.05081			0.305717
$46$	−2.70907	+	7.36208i	−0.399431	+	1.08548i
$47$	12.2688			1.78959			0.894794	−	0.446479i	$-0.147322\pi$
$47$	12.2688			1.78959			0.894794	+	0.446479i	$0.147322\pi$
$48$	−2.41202	+	0.390238i	−0.348145	+	0.0563260i
$49$	2.55326	−	6.51774i	0.364751	−	0.931105i
$50$	5.82711	+	2.14424i	0.824077	+	0.303242i
$51$	2.73211			0.382572
$52$	−1.52297	−	1.29637i	−0.211197	−	0.179774i
$53$		−	7.60088i		−	1.04406i	−0.852927	−	0.522031i	$-0.825175\pi$
$53$		−	7.60088i		−	1.04406i	0.852927	−	0.522031i	$-0.174825\pi$
$54$	1.67864	−	4.56181i	0.228434	−	0.620784i
$55$	2.44890			0.330210
$56$	−6.70849	−	3.31605i	−0.896459	−	0.443126i
$57$	−1.17792			−0.156020
$58$	−1.19282	+	3.24157i	−0.156625	+	0.425638i
$59$			13.2723i			1.72791i	0.503568	+	0.863955i	$0.332020\pi$
$59$			13.2723i			1.72791i	−0.503568	+	0.863955i	$0.667980\pi$
$60$	−0.618227	+	0.726288i	−0.0798128	+	0.0937634i
$61$	−8.35048			−1.06917			−0.534585	−	0.845115i	$-0.679532\pi$
$61$	−8.35048			−1.06917			−0.534585	+	0.845115i	$0.679532\pi$
$62$	7.65342	+	2.81628i	0.971985	+	0.357668i
$63$	5.74115	−	3.91692i	0.723317	−	0.493485i
$64$	−4.14597	+	6.84185i	−0.518247	+	0.855231i
$65$	−0.780706			−0.0968346
$66$	0.935784	−	2.54305i	0.115187	−	0.313028i
$67$	0.937154			0.114492			0.0572458	−	0.998360i	$-0.481768\pi$
$67$	0.937154			0.114492			0.0572458	+	0.998360i	$0.481768\pi$
$68$	5.79824	−	6.81173i	0.703140	−	0.826043i
$69$	3.38838			0.407914
$70$	−2.83311	+	0.711702i	−0.338621	+	0.0850647i
$71$		−	13.0139i		−	1.54446i	−0.635341	−	0.772232i	$-0.719141\pi$
$71$		−	13.0139i		−	1.54446i	0.635341	−	0.772232i	$-0.280859\pi$
$72$	−3.64654	−	6.47350i	−0.429748	−	0.762910i
$73$			0.406509i			0.0475783i	0.999717	+	0.0237891i	$0.00757304\pi$
$73$			0.406509i			0.0475783i	−0.999717	+	0.0237891i	$0.992427\pi$
$74$	0.0242741	−	0.0659665i	0.00282181	−	0.00766844i
$75$		−	2.68192i		−	0.309681i
$76$	−2.49985	+	2.93681i	−0.286753	+	0.336875i
$77$	6.85559	−	4.67725i	0.781267	−	0.533022i
$78$	−0.298326	+	0.810720i	−0.0337788	+	0.0917959i
$79$			4.03568i			0.454049i	0.973889	+	0.227025i	$0.0728998\pi$
$79$			4.03568i			0.454049i	−0.973889	+	0.227025i	$0.927100\pi$
$80$	0.498752	+	3.08274i	0.0557622	+	0.344661i
$81$	5.78103			0.642337
$82$	4.74374	−	12.8914i	0.523859	−	1.42362i
$83$			11.9237i			1.30879i	0.756151	+	0.654397i	$0.227078\pi$
$83$			11.9237i			1.30879i	−0.756151	+	0.654397i	$0.772922\pi$
$84$	−0.343535	+	3.21398i	−0.0374827	+	0.350674i
$85$		−	3.49184i		−	0.378743i
$86$	−12.4049	−	4.56470i	−1.33765	−	0.492225i
$87$	1.49193			0.159951
$88$	−4.35438	−	7.73011i	−0.464179	−	0.824032i
$89$		−	15.7622i		−	1.67079i	−0.549646	−	0.835397i	$-0.685238\pi$
$89$		−	15.7622i		−	1.67079i	0.549646	−	0.835397i	$-0.314762\pi$
$90$	−2.72185	−	1.00158i	−0.286909	−	0.105576i
$91$	−2.18555	+	1.49110i	−0.229108	+	0.156309i
$92$	7.19102	−	8.44795i	0.749715	−	0.880759i
$93$		−	3.52247i		−	0.365263i
$94$	−16.2833	−	5.99186i	−1.67949	−	0.618014i
$95$			1.50547i			0.154458i
$96$	3.39184	+	0.660061i	0.346178	+	0.0673671i
$97$			7.10470i			0.721373i	0.932687	+	0.360687i	$0.117458\pi$
$97$			7.10470i			0.721373i	−0.932687	+	0.360687i	$0.882542\pi$
$98$	−6.57185	+	7.40343i	−0.663857	+	0.747859i
$99$	8.23991			0.828142
$100$	−6.68658	−	5.69171i	−0.668658	−	0.569171i
$101$	7.67995			0.764184			0.382092	−	0.924124i	$-0.375204\pi$
$101$	7.67995			0.764184			0.382092	+	0.924124i	$0.375204\pi$
$102$	−3.62609	−	1.33432i	−0.359036	−	0.132117i
$103$	4.33561			0.427201			0.213600	−	0.976921i	$-0.431481\pi$
$103$	4.33561			0.427201			0.213600	+	0.976921i	$0.431481\pi$
$104$	1.38817	+	2.46434i	0.136121	+	0.241649i
$105$	0.711091	+	1.04227i	0.0693954	+	0.101715i
$106$	−3.71214	+	10.0880i	−0.360554	+	0.979829i
$107$	16.2564			1.57157			0.785784	−	0.618501i	$-0.212260\pi$
$107$	16.2564			1.57157			0.785784	+	0.618501i	$0.212260\pi$
$108$	−4.45582	+	5.23466i	−0.428761	+	0.503705i
$109$			3.71293i			0.355634i	0.984064	+	0.177817i	$0.0569035\pi$
$109$			3.71293i			0.355634i	−0.984064	+	0.177817i	$0.943097\pi$
$110$	−3.25021	−	1.19600i	−0.309895	−	0.114034i
$111$	−0.0303610			−0.00288174
$112$	7.28406	+	7.67740i	0.688279	+	0.725446i
$113$	−15.6349			−1.47081			−0.735403	−	0.677630i	$-0.763007\pi$
$113$	−15.6349			−1.47081			−0.735403	+	0.677630i	$0.763007\pi$
$114$	1.56335	+	0.575277i	0.146421	+	0.0538796i
$115$		−	4.33060i		−	0.403831i
$116$	3.16625	−	3.71968i	0.293979	−	0.345364i
$117$	−2.62687			−0.242854
$118$	6.48197	−	17.6152i	0.596714	−	1.62161i
$119$	−6.66919	−	9.77525i	−0.611364	−	0.896096i
$120$	1.17522	−	0.662005i	0.107283	−	0.0604325i
$121$	−1.16060			−0.105509
$122$	11.0828	+	4.07823i	1.00339	+	0.369225i
$123$	−5.93325			−0.534983
$124$	−8.78226	−	7.47558i	−0.788670	−	0.671327i
$125$	−7.33122			−0.655724
$126$	−9.53266	+	2.39469i	−0.849236	+	0.213336i
$127$			15.3966i			1.36623i	0.730313	+	0.683113i	$0.239374\pi$
$127$			15.3966i			1.36623i	−0.730313	+	0.683113i	$0.760626\pi$
$128$	8.84401	−	7.05574i	0.781708	−	0.623645i
$129$			5.70932i			0.502678i
$130$	1.03616	+	0.381283i	0.0908772	+	0.0334407i
$131$		−	17.2379i		−	1.50608i	−0.657972	−	0.753042i	$-0.728585\pi$
$131$		−	17.2379i		−	1.50608i	0.657972	−	0.753042i	$-0.271415\pi$
$132$	−2.48396	+	2.91814i	−0.216201	+	0.253991i
$133$	2.87535	+	4.21450i	0.249325	+	0.365443i
$134$	−1.24380	−	0.457689i	−0.107448	−	0.0395383i
$135$			2.68340i			0.230950i
$136$	−11.0222	+	6.20883i	−0.945146	+	0.532402i
$137$	−10.9864			−0.938628			−0.469314	−	0.883031i	$-0.655499\pi$
$137$	−10.9864			−0.938628			−0.469314	+	0.883031i	$0.655499\pi$
$138$	−4.49709	−	1.65483i	−0.382818	−	0.140868i
$139$			18.0704i			1.53271i	0.642419	+	0.766354i	$0.277931\pi$
$139$			18.0704i			1.53271i	−0.642419	+	0.766354i	$0.722069\pi$
$140$	4.10771	+	0.439062i	0.347165	+	0.0371076i
$141$			7.49434i			0.631138i
$142$	−6.35575	+	17.2721i	−0.533362	+	1.44944i
$143$	−3.13678			−0.262311
$144$	1.67817	+	10.3726i	0.139847	+	0.864383i
$145$		−	1.90679i		−	0.158350i
$146$	0.198532	−	0.539522i	0.0164306	−	0.0446512i
$147$	3.98133	+	1.55965i	0.328375	+	0.128637i
$148$	−0.0644337	+	0.0756962i	−0.00529642	+	0.00622219i
$149$			20.7169i			1.69720i	0.529038	+	0.848598i	$0.322553\pi$
$149$			20.7169i			1.69720i	−0.529038	+	0.848598i	$0.677447\pi$
$150$	−1.30980	+	3.55946i	−0.106945	+	0.290629i
$151$			12.7907i			1.04089i	0.853895	+	0.520446i	$0.174234\pi$
$151$			12.7907i			1.04089i	−0.853895	+	0.520446i	$0.825766\pi$
$152$	4.75211	−	2.67687i	0.385447	−	0.217123i
$153$		−	11.7491i		−	0.949860i
$154$	−11.3831	+	2.85953i	−0.917275	+	0.230428i
$155$	−4.50198			−0.361608
$156$	0.791882	−	0.930297i	0.0634013	−	0.0744834i
$157$	−5.52377			−0.440845			−0.220423	−	0.975404i	$-0.570744\pi$
$157$	−5.52377			−0.440845			−0.220423	+	0.975404i	$0.570744\pi$
$158$	1.97095	−	5.35619i	0.156801	−	0.426116i
$159$	4.64297			0.368211
$160$	0.843606	−	4.33502i	0.0666929	−	0.342713i
$161$	−8.27117	−	12.1233i	−0.651860	−	0.955452i
$162$	−7.67264	−	2.82335i	−0.602819	−	0.221824i
$163$	−0.876767			−0.0686737			−0.0343368	−	0.999410i	$-0.510932\pi$
$163$	−0.876767			−0.0686737			−0.0343368	+	0.999410i	$0.510932\pi$
$164$	−12.5919	+	14.7928i	−0.983260	+	1.15513i
$165$			1.49590i			0.116456i
$166$	5.82332	−	15.8252i	0.451977	−	1.22828i
$167$	−22.5988			−1.74875			−0.874373	−	0.485254i	$-0.838727\pi$
$167$	−22.5988			−1.74875			−0.874373	+	0.485254i	$0.838727\pi$
$168$	2.02560	−	4.09785i	0.156278	−	0.316156i
$169$	1.00000			0.0769231
$170$	−1.70535	+	4.63440i	−0.130795	+	0.355443i
$171$			5.06551i			0.387369i
$172$	14.2345	+	12.1166i	1.08537	+	0.923884i
$173$	−1.41995			−0.107956			−0.0539782	−	0.998542i	$-0.517190\pi$
$173$	−1.41995			−0.107956			−0.0539782	+	0.998542i	$0.517190\pi$
$174$	−1.98010	−	0.728630i	−0.150111	−	0.0552373i
$175$	−9.59565	+	6.54666i	−0.725363	+	0.494881i
$176$	2.00393	+	12.3861i	0.151052	+	0.933635i
$177$	−8.10735			−0.609386
$178$	−7.69800	+	20.9198i	−0.576990	+	1.56800i
$179$	12.0505			0.900698			0.450349	−	0.892852i	$-0.351299\pi$
$179$	12.0505			0.900698			0.450349	+	0.892852i	$0.351299\pi$
$180$	3.12331	+	2.65861i	0.232798	+	0.198161i
$181$	−23.9696			−1.78164			−0.890822	−	0.454352i	$-0.849871\pi$
$181$	−23.9696			−1.78164			−0.890822	+	0.454352i	$0.849871\pi$
$182$	3.62891	−	0.911614i	0.268992	−	0.0675733i
$183$		−	5.10086i		−	0.377066i
$184$	−13.6698	+	7.70022i	−1.00775	+	0.567668i
$185$			0.0388035i			0.00285289i
$186$	−1.72031	+	4.67506i	−0.126139	+	0.342792i
$187$		−	14.0298i		−	1.02596i
$188$	18.6850	+	15.9049i	1.36274	+	1.15998i
$189$	5.12512	+	7.51206i	0.372798	+	0.546422i
$190$	0.735246	−	1.99808i	0.0533403	−	0.144956i
$191$		−	12.0391i		−	0.871119i	−0.900160	−	0.435559i	$-0.856551\pi$
$191$		−	12.0391i		−	0.871119i	0.900160	−	0.435559i	$-0.143449\pi$
$192$	−4.17931	−	2.53255i	−0.301616	−	0.182771i
$193$	3.94730			0.284133			0.142066	−	0.989857i	$-0.454625\pi$
$193$	3.94730			0.284133			0.142066	+	0.989857i	$0.454625\pi$
$194$	3.46981	−	9.42942i	0.249118	−	0.676993i
$195$		−	0.476891i		−	0.0341509i
$196$	12.3379	−	6.61632i	0.881280	−	0.472594i
$197$			16.8982i			1.20394i	0.798517	+	0.601972i	$0.205618\pi$
$197$			16.8982i			1.20394i	−0.798517	+	0.601972i	$0.794382\pi$
$198$	−10.9361	−	4.02423i	−0.777193	−	0.285989i
$199$	11.8887			0.842767			0.421383	−	0.906883i	$-0.361545\pi$
$199$	11.8887			0.842767			0.421383	+	0.906883i	$0.361545\pi$
$200$	6.09475	+	10.8197i	0.430964	+	0.765068i
$201$			0.572456i			0.0403780i
$202$	−10.1929	−	3.75075i	−0.717170	−	0.263902i
$203$	−3.64185	−	5.33797i	−0.255608	−	0.374652i
$204$	4.16092	+	3.54183i	0.291322	+	0.247978i
$205$			7.58313i			0.529629i
$206$	−5.75426	−	2.11744i	−0.400919	−	0.147529i
$207$		−	14.5713i		−	1.01278i
$208$	−0.638848	−	3.94865i	−0.0442961	−	0.273790i
$209$			6.04880i			0.418405i
$210$	−0.434740	−	1.73059i	−0.0299999	−	0.119422i
$211$	−11.2892			−0.777182			−0.388591	−	0.921410i	$-0.627038\pi$
$211$	−11.2892			−0.777182			−0.388591	+	0.921410i	$0.627038\pi$
$212$	9.85356	−	11.5759i	0.676745	−	0.795035i
$213$	7.94947			0.544689
$214$	−21.5757	−	7.93935i	−1.47488	−	0.542723i
$215$	7.29693			0.497646
$216$	8.47031	−	4.77134i	0.576332	−	0.324649i
$217$	−12.6031	+	8.59849i	−0.855553	+	0.583703i
$218$	1.81333	−	4.92783i	0.122814	−	0.333755i
$219$	−0.248314			−0.0167795
$220$	3.72960	+	3.17469i	0.251449	+	0.214037i
$221$			4.47267i			0.300865i
$222$	0.0402953	+	0.0148278i	0.00270445	+	0.000995174i
$223$	−6.21212			−0.415994			−0.207997	−	0.978129i	$-0.566694\pi$
$223$	−6.21212			−0.415994			−0.207997	+	0.978129i	$0.566694\pi$
$224$	−5.91797	−	13.7469i	−0.395411	−	0.918504i
$225$	−11.5333			−0.768884
$226$	20.7508	+	7.63580i	1.38032	+	0.507926i
$227$			2.41724i			0.160438i	0.996777	+	0.0802188i	$0.0255619\pi$
$227$			2.41724i			0.160438i	−0.996777	+	0.0802188i	$0.974438\pi$
$228$	−1.79394	−	1.52702i	−0.118806	−	0.101130i
$229$	−0.777226			−0.0513606			−0.0256803	−	0.999670i	$-0.508175\pi$
$229$	−0.777226			−0.0513606			−0.0256803	+	0.999670i	$0.508175\pi$
$230$	−2.11499	+	5.74762i	−0.139458	+	0.378987i
$231$	2.85708	+	4.18771i	0.187982	+	0.275531i
$232$	−6.01890	+	3.39045i	−0.395160	+	0.222594i
$233$	0.935862			0.0613104			0.0306552	−	0.999530i	$-0.490241\pi$
$233$	0.935862			0.0613104			0.0306552	+	0.999530i	$0.490241\pi$
$234$	3.48640	+	1.28292i	0.227913	+	0.0838668i
$235$	9.57832			0.624821
$236$	−17.2059	+	20.2133i	−1.12001	+	1.31577i
$237$	−2.46518			−0.160131
$238$	4.07735	+	16.2309i	0.264295	+	1.05209i
$239$		−	8.07542i		−	0.522356i	−0.965291	−	0.261178i	$-0.915889\pi$
$239$		−	8.07542i		−	0.522356i	0.965291	−	0.261178i	$-0.0841109\pi$
$240$	−1.88308	+	0.304661i	−0.121552	+	0.0196658i
$241$		−	13.0922i		−	0.843344i	−0.906748	−	0.421672i	$-0.861443\pi$
$241$		−	13.0922i		−	0.843344i	0.906748	−	0.421672i	$-0.138557\pi$
$242$	1.54036	+	0.566816i	0.0990179	+	0.0364363i
$243$			13.8428i			0.888014i
$244$	−12.7175	−	10.8253i	−0.814155	−	0.693020i
$245$	1.99334	−	5.08843i	0.127350	−	0.325088i
$246$	7.87466	+	2.89770i	0.502070	+	0.184750i
$247$		−	1.92835i		−	0.122698i
$248$	8.00494	+	14.2108i	0.508315	+	0.902384i
$249$	−7.28353			−0.461575
$250$	9.73005	+	3.58044i	0.615383	+	0.226447i
$251$			11.6794i			0.737199i	0.929588	+	0.368599i	$0.120163\pi$
$251$			11.6794i			0.737199i	−0.929588	+	0.368599i	$0.879837\pi$
$252$	13.8213	+	1.47733i	0.870663	+	0.0930629i
$253$		−	17.3998i		−	1.09392i
$254$	7.51942	−	20.4345i	0.471810	−	1.28217i
$255$	2.13298			0.133572
$256$	−15.1837	+	5.04518i	−0.948984	+	0.315324i
$257$		−	22.9812i		−	1.43353i	−0.697315	−	0.716765i	$-0.745622\pi$
$257$		−	22.9812i		−	1.43353i	0.697315	−	0.716765i	$-0.254378\pi$
$258$	2.78833	−	7.57746i	0.173594	−	0.471752i
$259$	0.0741123	+	0.108629i	0.00460511	+	0.00674986i
$260$	−1.18899	−	1.01208i	−0.0737379	−	0.0627668i
$261$		−	6.41584i		−	0.397131i
$262$	−8.41870	+	22.8783i	−0.520109	+	1.41343i
$263$			8.58073i			0.529111i	0.964371	+	0.264555i	$0.0852252\pi$
$263$			8.58073i			0.529111i	−0.964371	+	0.264555i	$0.914775\pi$
$264$	4.72190	−	2.65986i	0.290613	−	0.163703i
$265$		−	5.93405i		−	0.364526i
$266$	−1.75791	−	6.99779i	−0.107784	−	0.429062i
$267$	9.62830			0.589243
$268$	1.42725	+	1.21490i	0.0871833	+	0.0742117i
$269$	−20.5726			−1.25433			−0.627167	−	0.778885i	$-0.715786\pi$
$269$	−20.5726			−1.25433			−0.627167	+	0.778885i	$0.715786\pi$
$270$	1.31053	−	3.56143i	0.0797561	−	0.216742i
$271$	−7.63381			−0.463721			−0.231861	−	0.972749i	$-0.574481\pi$
$271$	−7.63381			−0.463721			−0.231861	+	0.972749i	$0.574481\pi$
$272$	17.6610	−	2.85736i	1.07086	−	0.173253i
$273$	−0.910831	−	1.33503i	−0.0551260	−	0.0807999i
$274$	14.5812	+	5.36554i	0.880882	+	0.324144i
$275$	−13.7720			−0.830485
$276$	5.16039	+	4.39260i	0.310619	+	0.264404i
$277$			11.3502i			0.681965i	0.940070	+	0.340982i	$0.110760\pi$
$277$			11.3502i			0.681965i	−0.940070	+	0.340982i	$0.889240\pi$
$278$	8.82524	−	23.9831i	0.529303	−	1.43841i
$279$	−15.1480			−0.906885
$280$	−5.23736	−	2.58886i	−0.312992	−	0.154714i
$281$	6.35231			0.378947			0.189474	−	0.981886i	$-0.439322\pi$
$281$	6.35231			0.378947			0.189474	+	0.981886i	$0.439322\pi$
$282$	3.66010	−	9.94656i	0.217956	−	0.592309i
$283$		−	23.3762i		−	1.38957i	−0.719217	−	0.694785i	$-0.755499\pi$
$283$		−	23.3762i		−	1.38957i	0.719217	−	0.694785i	$-0.244501\pi$
$284$	16.8708	−	19.8197i	1.00110	−	1.17608i
$285$	−0.919611			−0.0544731
$286$	4.16316	+	1.53195i	0.246173	+	0.0905860i
$287$	14.4833	+	21.2286i	0.854922	+	1.25309i
$288$	2.83851	−	14.5862i	0.167261	−	0.859499i
$289$	−3.00481			−0.176753
$290$	−0.931243	+	2.53071i	−0.0546845	+	0.148608i
$291$	−4.33988			−0.254408
$292$	−0.526986	+	0.619099i	−0.0308395	+	0.0362301i
$293$	−0.300712			−0.0175678			−0.00878389	−	0.999961i	$-0.502796\pi$
$293$	−0.300712			−0.0175678			−0.00878389	+	0.999961i	$0.502796\pi$
$294$	−4.52235	−	4.01439i	−0.263749	−	0.234124i
$295$			10.3618i			0.603287i
$296$	0.122486	−	0.0689964i	0.00711933	−	0.00401033i
$297$			10.7816i			0.625611i
$298$	10.1178	−	27.4957i	0.586107	−	1.59278i
$299$			5.54704i			0.320793i
$300$	3.47676	−	4.08447i	0.200731	−	0.235817i
$301$	20.4274	−	13.9367i	1.17742	−	0.803296i
$302$	6.24675	−	16.9759i	0.359460	−	0.976854i
$303$			4.69127i			0.269506i
$304$	−7.61438	+	1.23192i	−0.436714	+	0.0706555i
$305$	−6.51927			−0.373292
$306$	−5.73806	+	15.5935i	−0.328023	+	0.891423i
$307$		−	10.2092i		−	0.582671i	−0.956621	−	0.291336i	$-0.905900\pi$
$307$		−	10.2092i		−	0.582671i	0.956621	−	0.291336i	$-0.0940997\pi$
$308$	16.5043	+	1.76410i	0.940418	+	0.100519i
$309$			2.64839i			0.150662i
$310$	5.97507	+	2.19869i	0.339361	+	0.124877i
$311$	3.99969			0.226802			0.113401	−	0.993549i	$-0.463826\pi$
$311$	3.99969			0.226802			0.113401	+	0.993549i	$0.463826\pi$
$312$	−1.50533	+	0.847957i	−0.0852227	+	0.0480061i
$313$			14.2771i			0.806988i	0.914982	+	0.403494i	$0.132204\pi$
$313$			14.2771i			0.806988i	−0.914982	+	0.403494i	$0.867796\pi$
$314$	7.33120	+	2.69771i	0.413724	+	0.152241i
$315$	4.48215	−	3.05796i	0.252540	−	0.172296i
$316$	−5.23174	+	6.14620i	−0.294308	+	0.345751i
$317$			4.92436i			0.276580i	0.990392	+	0.138290i	$0.0441605\pi$
$317$			4.92436i			0.276580i	−0.990392	+	0.138290i	$0.955839\pi$
$318$	−6.16219	−	2.26754i	−0.345558	−	0.127157i
$319$		−	7.66126i		−	0.428948i
$320$	−3.23679	+	5.34147i	−0.180942	+	0.298597i
$321$			9.93017i			0.554248i
$322$	5.05676	+	20.1297i	0.281802	+	1.12178i
$323$	8.62487			0.479900
$324$	8.80432	+	7.49436i	0.489129	+	0.416353i
$325$	4.39050			0.243541
$326$	1.16365	+	0.428197i	0.0644488	+	0.0237157i
$327$	−2.26802			−0.125422
$328$	23.9366	−	13.4835i	1.32168	−	0.744503i
$329$	26.8141	−	18.2940i	1.47831	−	1.00858i
$330$	0.730572	−	1.98538i	0.0402167	−	0.109291i
$331$	−10.2132			−0.561368			−0.280684	−	0.959800i	$-0.590561\pi$
$331$	−10.2132			−0.561368			−0.280684	+	0.959800i	$0.590561\pi$
$332$	−15.4575	+	18.1594i	−0.848341	+	0.996625i
$333$			0.130564i			0.00715484i
$334$	29.9933	+	11.0368i	1.64116	+	0.603909i
$335$	0.731641			0.0399738
$336$	−4.68971	+	4.44944i	−0.255844	+	0.242737i
$337$	−5.87706			−0.320144			−0.160072	−	0.987105i	$-0.551173\pi$
$337$	−5.87706			−0.320144			−0.160072	+	0.987105i	$0.551173\pi$
$338$	−1.32721	−	0.488382i	−0.0721906	−	0.0265645i
$339$		−	9.55050i		−	0.518712i
$340$	4.52672	−	5.31796i	0.245496	−	0.288407i
$341$	−18.0884			−0.979542
$342$	2.47391	−	6.72299i	0.133774	−	0.363538i
$343$	−4.13831	−	18.0520i	−0.223448	−	0.974716i
$344$	−12.9746	−	23.0332i	−0.699545	−	1.24187i
$345$	2.64533			0.142420
$346$	1.88456	+	0.693476i	0.101315	+	0.0372815i
$347$	−26.0891			−1.40053			−0.700267	−	0.713881i	$-0.746936\pi$
$347$	−26.0891			−1.40053			−0.700267	+	0.713881i	$0.746936\pi$
$348$	2.27215	+	1.93409i	0.121800	+	0.103678i
$349$	24.8684			1.33118			0.665588	−	0.746319i	$-0.268181\pi$
$349$	24.8684			1.33118			0.665588	+	0.746319i	$0.268181\pi$
$350$	15.9327	−	4.00244i	0.851639	−	0.213939i
$351$		−	3.43715i		−	0.183461i
$352$	3.38951	−	17.4176i	0.180661	−	0.928360i
$353$		−	1.35013i		−	0.0718601i	−0.999354	−	0.0359300i	$-0.988561\pi$
$353$		−	1.35013i		−	0.0718601i	0.999354	−	0.0359300i	$-0.0114393\pi$
$354$	10.7601	+	3.95949i	0.571895	+	0.210444i
$355$		−	10.1600i		−	0.539237i
$356$	20.4337	−	24.0054i	1.08298	−	1.27228i
$357$	5.97117	−	4.07385i	0.316028	−	0.215611i
$358$	−15.9936	−	5.88526i	−0.845286	−	0.311046i
$359$			4.82833i			0.254829i	0.991850	+	0.127415i	$0.0406679\pi$
$359$			4.82833i			0.254829i	−0.991850	+	0.127415i	$0.959332\pi$
$360$	−2.84687	−	5.05390i	−0.150043	−	0.266364i
$361$	15.2815			0.804288
$362$	31.8126	+	11.7063i	1.67203	+	0.615270i
$363$		−	0.708947i		−	0.0372101i
$364$	−5.26153	−	0.562392i	−0.275779	−	0.0294773i
$365$			0.317364i			0.0166116i
$366$	−2.49117	+	6.76990i	−0.130215	+	0.353869i
$367$	8.89488			0.464309			0.232155	−	0.972679i	$-0.425422\pi$
$367$	8.89488			0.464309			0.232155	+	0.972679i	$0.425422\pi$
$368$	21.9033	−	3.54371i	1.14179	−	0.184729i
$369$			25.5152i			1.32827i
$370$	0.0189510	−	0.0515004i	0.000985214	−	0.00267738i
$371$	−11.3337	−	16.6121i	−0.588414	−	0.862458i
$372$	4.56643	−	5.36461i	0.236758	−	0.278142i
$373$		−	35.8127i		−	1.85431i	−0.374674	−	0.927157i	$-0.622245\pi$
$373$		−	35.8127i		−	1.85431i	0.374674	−	0.927157i	$-0.377755\pi$
$374$	−6.85191	+	18.6205i	−0.354304	+	0.962842i
$375$		−	4.47824i		−	0.231255i
$376$	−17.0312	−	30.2345i	−0.878315	−	1.55923i
$377$			2.44239i			0.125790i
$378$	−3.13335	−	12.4731i	−0.161162	−	0.641546i
$379$	−12.9413			−0.664748			−0.332374	−	0.943148i	$-0.607850\pi$
$379$	−12.9413			−0.664748			−0.332374	+	0.943148i	$0.607850\pi$
$380$	−1.95165	+	2.29278i	−0.100117	+	0.117617i
$381$	−9.40493			−0.481829
$382$	−5.87968	+	15.9784i	−0.300831	+	0.817526i
$383$	16.3984			0.837918			0.418959	−	0.908005i	$-0.362395\pi$
$383$	16.3984			0.837918			0.418959	+	0.908005i	$0.362395\pi$
$384$	4.30997	+	5.40233i	0.219942	+	0.275686i
$385$	5.35220	−	3.65155i	0.272773	−	0.186100i
$386$	−5.23889	−	1.92779i	−0.266652	−	0.0981220i
$387$	24.5522			1.24806
$388$	−9.21032	+	10.8202i	−0.467583	+	0.549313i
$389$		−	19.3191i		−	0.979516i	−0.871858	−	0.489758i	$-0.837085\pi$
$389$		−	19.3191i		−	0.979516i	0.871858	−	0.489758i	$-0.162915\pi$
$390$	−0.232905	+	0.632934i	−0.0117936	+	0.0320498i
$391$	−24.8101			−1.25470
$392$	−19.6063	+	2.75562i	−0.990267	+	0.139180i
$393$	10.5297			0.531154
$394$	8.25277	−	22.4274i	0.415768	−	1.12988i
$395$			3.15068i			0.158528i
$396$	12.5491	+	10.6820i	0.630616	+	0.536789i
$397$	−27.8169			−1.39609			−0.698044	−	0.716055i	$-0.745946\pi$
$397$	−27.8169			−1.39609			−0.698044	+	0.716055i	$0.745946\pi$
$398$	−15.7788	−	5.80622i	−0.790918	−	0.291040i
$399$	−2.57441	+	1.75640i	−0.128882	+	0.0879299i
$400$	−2.80486	−	17.3366i	−0.140243	−	0.866828i
$401$	−32.8827			−1.64208			−0.821041	−	0.570869i	$-0.806606\pi$
$401$	−32.8827			−1.64208			−0.821041	+	0.570869i	$0.806606\pi$
$402$	0.279578	−	0.759769i	0.0139441	−	0.0378938i
$403$	5.76655			0.287252
$404$	11.6963	+	9.95606i	0.581913	+	0.495333i
$405$	4.51329			0.224267
$406$	2.22652	+	8.86322i	0.110500	+	0.439874i
$407$			0.155908i			0.00772807i
$408$	−3.79264	−	6.73287i	−0.187763	−	0.333327i
$409$			22.6861i			1.12176i	0.827899	+	0.560878i	$0.189536\pi$
$409$			22.6861i			1.12176i	−0.827899	+	0.560878i	$0.810464\pi$
$410$	3.70347	−	10.0644i	0.182901	−	0.497045i
$411$		−	6.71097i		−	0.331028i
$412$	6.60299	+	5.62056i	0.325306	+	0.276905i
$413$	19.7903	+	29.0074i	0.973819	+	1.42736i
$414$	−7.11638	+	19.3392i	−0.349751	+	0.950470i
$415$			9.30889i			0.456956i
$416$	−1.08057	+	5.55269i	−0.0529792	+	0.272243i
$417$	−11.0382			−0.540543
$418$	2.95413	−	8.02803i	0.144491	−	0.392664i
$419$		−	7.03620i		−	0.343741i	−0.985120	−	0.171870i	$-0.945019\pi$
$419$		−	7.03620i		−	0.343741i	0.985120	−	0.171870i	$-0.0549810\pi$
$420$	−0.268199	+	2.50918i	−0.0130868	+	0.122435i
$421$			13.2449i			0.645515i	0.946482	+	0.322757i	$0.104610\pi$
$421$			13.2449i			0.645515i	−0.946482	+	0.322757i	$0.895390\pi$
$422$	14.9832	+	5.51346i	0.729369	+	0.268391i
$423$	32.2285			1.56700
$424$	−18.7312	+	10.5513i	−0.909667	+	0.512417i
$425$			19.6373i			0.952547i
$426$	−10.5506	−	3.88238i	−0.511179	−	0.188102i
$427$	−18.2504	+	12.4514i	−0.883199	+	0.602565i
$428$	24.7580	+	21.0743i	1.19672	+	1.01867i
$429$		−	1.91609i		−	0.0925097i
$430$	−9.68455	−	3.56369i	−0.467030	−	0.171856i
$431$			28.2469i			1.36060i	0.732932	+	0.680302i	$0.238151\pi$
$431$			28.2469i			1.36060i	−0.732932	+	0.680302i	$0.761849\pi$
$432$	−13.5721	+	2.19582i	−0.652989	+	0.105646i
$433$		−	13.3814i		−	0.643071i	−0.946898	−	0.321535i	$-0.895801\pi$
$433$		−	13.3814i		−	0.643071i	0.946898	−	0.321535i	$-0.104199\pi$
$434$	20.9263	−	5.25687i	1.00449	−	0.252338i
$435$	1.16476			0.0558457
$436$	−4.81333	+	5.65466i	−0.230516	+	0.270809i
$437$	10.6966			0.511688
$438$	0.329565	+	0.121272i	0.0157472	+	0.00579462i
$439$	15.9433			0.760933			0.380467	−	0.924795i	$-0.375763\pi$
$439$	15.9433			0.760933			0.380467	+	0.924795i	$0.375763\pi$
$440$	−3.39949	−	6.03494i	−0.162064	−	0.287704i
$441$	6.70707	−	17.1212i	0.319384	−	0.815297i
$442$	2.18437	−	5.93617i	0.103900	−	0.282355i
$443$	−15.4639			−0.734714			−0.367357	−	0.930080i	$-0.619737\pi$
$443$	−15.4639			−0.734714			−0.367357	+	0.930080i	$0.619737\pi$
$444$	−0.0462387	−	0.0393591i	−0.00219439	−	0.00186790i
$445$		−	12.3057i		−	0.583345i
$446$	8.24478	+	3.03389i	0.390402	+	0.143659i
$447$	−12.6548			−0.598553
$448$	1.14063	+	21.1353i	0.0538897	+	0.998547i
$449$	−6.57371			−0.310233			−0.155116	−	0.987896i	$-0.549575\pi$
$449$	−6.57371			−0.310233			−0.155116	+	0.987896i	$0.549575\pi$
$450$	15.3070	+	5.63264i	0.721581	+	0.265525i
$451$			30.4681i			1.43469i
$452$	−23.8114	−	20.2686i	−1.11999	−	0.953355i
$453$	−7.81314			−0.367093
$454$	1.18054	−	3.20818i	0.0554053	−	0.150567i
$455$	−1.70627	+	1.16411i	−0.0799912	+	0.0545743i
$456$	1.63516	+	2.90281i	0.0765732	+	0.135936i
$457$	34.8367			1.62959			0.814796	−	0.579748i	$-0.196849\pi$
$457$	34.8367			1.62959			0.814796	+	0.579748i	$0.196849\pi$
$458$	1.03154	+	0.379583i	0.0482008	+	0.0177368i
$459$	15.3732			0.717562
$460$	5.61407	−	6.59536i	0.261757	−	0.307510i
$461$	−10.9767			−0.511236			−0.255618	−	0.966778i	$-0.582279\pi$
$461$	−10.9767			−0.511236			−0.255618	+	0.966778i	$0.582279\pi$
$462$	−1.74673	−	6.95331i	−0.0812654	−	0.323497i
$463$		−	18.8055i		−	0.873963i	−0.899470	−	0.436982i	$-0.856047\pi$
$463$		−	18.8055i		−	0.873963i	0.899470	−	0.436982i	$-0.143953\pi$
$464$	9.64417	−	1.56032i	0.447719	−	0.0724360i
$465$		−	2.75002i		−	0.127529i
$466$	−1.24208	−	0.457059i	−0.0575385	−	0.0211728i
$467$			14.3383i			0.663497i	0.943368	+	0.331748i	$0.107638\pi$
$467$			14.3383i			0.663497i	−0.943368	+	0.331748i	$0.892362\pi$
$468$	−4.00063	−	3.40539i	−0.184929	−	0.157414i
$469$	2.04820	−	1.39739i	0.0945769	−	0.0645254i
$470$	−12.7124	−	4.67788i	−0.586381	−	0.215775i
$471$		−	3.37417i		−	0.155474i
$472$	32.7076	−	18.4242i	1.50549	−	0.848044i
$473$	29.3182			1.34805
$474$	3.27181	+	1.20395i	0.150279	+	0.0552992i
$475$		−	8.46640i		−	0.388465i
$476$	2.51539	−	23.5331i	0.115293	−	1.07864i
$477$		−	19.9665i		−	0.914204i
$478$	−3.94389	+	10.7178i	−0.180390	+	0.490220i
$479$	−5.36064			−0.244934			−0.122467	−	0.992473i	$-0.539081\pi$
$479$	−5.36064			−0.244934			−0.122467	+	0.992473i	$0.539081\pi$
$480$	2.64803	+	0.515313i	0.120865	+	0.0235207i
$481$		−	0.0497032i		−	0.00226627i
$482$	−6.39401	+	17.3761i	−0.291239	+	0.791460i
$483$	7.40548	−	5.05241i	0.336961	−	0.229893i
$484$	−1.76755	−	1.50457i	−0.0803433	−	0.0683894i
$485$			5.54668i			0.251862i
$486$	6.76056	−	18.3722i	0.306665	−	0.833382i
$487$			14.7792i			0.669708i	0.942270	+	0.334854i	$0.108687\pi$
$487$			14.7792i			0.669708i	−0.942270	+	0.334854i	$0.891313\pi$
$488$	11.5919	+	20.5785i	0.524740	+	0.931543i
$489$		−	0.535569i		−	0.0242193i
$490$	−5.13068	+	5.77990i	−0.231781	+	0.261109i
$491$	−21.0065			−0.948011			−0.474006	−	0.880522i	$-0.657192\pi$
$491$	−21.0065			−0.948011			−0.474006	+	0.880522i	$0.657192\pi$
$492$	−9.03614	−	7.69169i	−0.407381	−	0.346768i
$493$	−10.9240			−0.491993
$494$	−0.941771	+	2.55932i	−0.0423723	+	0.115149i
$495$	6.43295			0.289139
$496$	−3.68395	−	22.7701i	−0.165414	−	1.02241i
$497$	−19.4050	−	28.4425i	−0.870431	−	1.27582i
$498$	9.66677	+	3.55715i	0.433178	+	0.159400i
$499$	−14.2078			−0.636030			−0.318015	−	0.948086i	$-0.603016\pi$
$499$	−14.2078			−0.636030			−0.318015	+	0.948086i	$0.603016\pi$
$500$	−11.1652	−	9.50397i	−0.499323	−	0.425031i
$501$		−	13.8044i		−	0.616734i
$502$	5.70402	−	15.5010i	0.254583	−	0.691845i
$503$	−38.2658			−1.70619			−0.853095	−	0.521756i	$-0.825277\pi$
$503$	−38.2658			−1.70619			−0.853095	+	0.521756i	$0.825277\pi$
$504$	−17.6223	−	8.71082i	−0.784960	−	0.388011i
$505$	5.99578			0.266809
$506$	−8.49778	+	23.0932i	−0.377772	+	1.02662i
$507$			0.610846i			0.0271286i
$508$	−19.9597	+	23.4485i	−0.885567	+	1.04036i
$509$	9.93667			0.440435			0.220217	−	0.975451i	$-0.429323\pi$
$509$	9.93667			0.440435			0.220217	+	0.975451i	$0.429323\pi$
$510$	−2.83091	−	1.04171i	−0.125355	−	0.0461276i
$511$	0.606145	+	0.888446i	0.0268143	+	0.0393025i
$512$	22.6160	+	0.719465i	0.999494	+	0.0317961i
$513$	−6.62802			−0.292634
$514$	−11.2236	+	30.5009i	−0.495053	+	1.34534i
$515$	3.38484			0.149154
$516$	−7.40139	+	8.69510i	−0.325828	+	0.382780i
$517$	38.4845			1.69255
$518$	−0.0453101	−	0.180368i	−0.00199081	−	0.00792492i
$519$		−	0.867368i		−	0.0380732i
$520$	1.08375	+	1.92393i	0.0475256	+	0.0843698i
$521$			10.2606i			0.449524i	0.974414	+	0.224762i	$0.0721605\pi$
$521$			10.2606i			0.449524i	−0.974414	+	0.224762i	$0.927840\pi$
$522$	−3.13338	+	8.51516i	−0.137144	+	0.372699i
$523$		−	10.2265i		−	0.447173i	−0.974684	−	0.223587i	$-0.928223\pi$
$523$		−	10.2265i		−	0.447173i	0.974684	−	0.223587i	$-0.0717765\pi$
$524$	22.3467	−	26.2528i	0.976222	−	1.14686i
$525$	−3.99900	−	5.86146i	−0.174531	−	0.255815i
$526$	4.19068	−	11.3884i	0.182722	−	0.496559i
$527$			25.7919i			1.12351i
$528$	−7.56598	+	1.22409i	−0.329267	+	0.0532717i
$529$	−7.76963			−0.337810
$530$	−2.89809	+	7.87573i	−0.125885	+	0.342100i
$531$			34.8647i			1.51300i
$532$	−1.08449	+	10.1461i	−0.0470184	+	0.439887i
$533$		−	9.71318i		−	0.420724i
$534$	−12.7788	−	4.70229i	−0.552991	−	0.203488i
$535$	12.6915			0.548701
$536$	−1.30093	−	2.30947i	−0.0561915	−	0.0997538i
$537$			7.36101i			0.317651i
$538$	27.3042	+	10.0473i	1.17717	+	0.433170i
$539$	8.00901	−	20.4447i	0.344972	−	0.880616i
$540$	−3.47868	+	4.08673i	−0.149699	+	0.175865i
$541$			46.1245i			1.98305i	0.129934	+	0.991523i	$0.458523\pi$
$541$			46.1245i			1.98305i	−0.129934	+	0.991523i	$0.541477\pi$
$542$	10.1317	+	3.72822i	0.435192	+	0.160141i
$543$		−	14.6417i		−	0.628336i
$544$	−24.8354	−	4.83303i	−1.06481	−	0.207214i
$545$			2.89870i			0.124167i
$546$	0.556855	+	2.21670i	0.0238312	+	0.0948661i
$547$	−13.4615			−0.575573			−0.287787	−	0.957695i	$-0.592919\pi$
$547$	−13.4615			−0.575573			−0.287787	+	0.957695i	$0.592919\pi$
$548$	−16.7318	−	14.2424i	−0.714749	−	0.608405i
$549$	−21.9356			−0.936189
$550$	18.2784	+	6.72602i	0.779392	+	0.286798i
$551$	4.70978			0.200643
$552$	−4.70365	−	8.35014i	−0.200201	−	0.355406i
$553$	6.01759	+	8.82018i	0.255894	+	0.375072i
$554$	5.54321	−	15.0640i	0.235509	−	0.640009i
$555$	−0.0237030			−0.00100614
$556$	−23.4259	+	27.5205i	−0.993479	+	1.16713i
$557$		−	18.6109i		−	0.788568i	−0.918989	−	0.394284i	$-0.870993\pi$
$557$		−	18.6109i		−	0.788568i	0.918989	−	0.394284i	$-0.129007\pi$
$558$	20.1045	+	7.39800i	0.851092	+	0.313182i
$559$	−9.34658			−0.395318
$560$	5.68671	+	5.99379i	0.240307	+	0.253284i
$561$	8.57005			0.361828
$562$	−8.43084	−	3.10236i	−0.355634	−	0.130865i
$563$		−	22.1148i		−	0.932026i	−0.884778	−	0.466013i	$-0.845690\pi$
$563$		−	22.1148i		−	0.932026i	0.884778	−	0.466013i	$-0.154310\pi$
$564$	−9.71545	+	11.4136i	−0.409094	+	0.480600i
$565$	−12.2062			−0.513521
$566$	−11.4165	+	31.0251i	−0.479872	+	1.30408i
$567$	12.6347	−	8.62009i	0.530609	−	0.362010i
$568$	−32.0707	+	18.0655i	−1.34566	+	0.758010i
$569$	25.8418			1.08335			0.541673	−	0.840590i	$-0.317791\pi$
$569$	25.8418			1.08335			0.541673	+	0.840590i	$0.317791\pi$
$570$	1.22052	+	0.449122i	0.0511218	+	0.0188116i
$571$	−25.7728			−1.07856			−0.539279	−	0.842127i	$-0.681303\pi$
$571$	−25.7728			−1.07856			−0.539279	+	0.842127i	$0.681303\pi$
$572$	−4.77721	−	4.06643i	−0.199745	−	0.170026i
$573$	7.35403			0.307219
$574$	−8.85466	−	35.2482i	−0.369587	−	1.47123i
$575$			24.3543i			1.01564i
$576$	−10.8909	+	17.9726i	−0.453789	+	0.748860i
$577$		−	22.8537i		−	0.951410i	−0.879605	−	0.475705i	$-0.842193\pi$
$577$		−	22.8537i		−	0.951410i	0.879605	−	0.475705i	$-0.157807\pi$
$578$	3.98801	+	1.46750i	0.165879	+	0.0610397i
$579$			2.41119i			0.100206i
$580$	2.47191	−	2.90398i	0.102640	−	0.120581i
$581$	17.7794	+	26.0598i	0.737613	+	1.08114i
$582$	5.75992	+	2.11952i	0.238756	+	0.0878569i
$583$		−	23.8423i		−	0.987447i
$584$	1.00178	−	0.564303i	0.0414539	−	0.0233510i
$585$	−2.05081			−0.0847906
$586$	0.399108	+	0.146862i	0.0164870	+	0.00606683i
$587$			5.51657i			0.227693i	0.993498	+	0.113847i	$0.0363172\pi$
$587$			5.51657i			0.227693i	−0.993498	+	0.113847i	$0.963683\pi$
$588$	4.04155	+	7.53657i	0.166671	+	0.310803i
$589$		−	11.1199i		−	0.458188i
$590$	5.06051	−	13.7523i	0.208338	−	0.566171i
$591$	−10.3222			−0.424598
$592$	−0.196261	+	0.0317528i	−0.00806626	+	0.00130503i
$593$		−	5.37304i		−	0.220644i	−0.993896	−	0.110322i	$-0.964812\pi$
$593$		−	5.37304i		−	0.220644i	0.993896	−	0.110322i	$-0.0351883\pi$
$594$	5.26553	−	14.3094i	0.216048	−	0.587122i
$595$	−5.20668	−	7.63160i	−0.213453	−	0.312865i
$596$	−26.8568	+	31.5511i	−1.10010	+	1.29239i
$597$			7.26216i			0.297220i
$598$	2.70907	−	7.36208i	0.110782	−	0.301058i
$599$			4.38259i			0.179068i	0.995984	+	0.0895338i	$0.0285377\pi$
$599$			4.38259i			0.179068i	−0.995984	+	0.0895338i	$0.971462\pi$
$600$	−6.60917	+	3.72295i	−0.269818	+	0.151989i
$601$			32.9212i			1.34288i	0.741057	+	0.671442i	$0.234325\pi$
$601$			32.9212i			1.34288i	−0.741057	+	0.671442i	$0.765675\pi$
$602$	−33.9179	+	8.52047i	−1.38239	+	0.347268i
$603$	2.46178			0.100251
$604$	−16.5815	+	19.4798i	−0.674690	+	0.792621i
$605$	−0.906087			−0.0368377
$606$	2.29113	−	6.22629i	0.0930709	−	0.252926i
$607$	−16.1526			−0.655615			−0.327807	−	0.944745i	$-0.606310\pi$
$607$	−16.1526			−0.655615			−0.327807	+	0.944745i	$0.606310\pi$
$608$	10.7075	+	2.08371i	0.434247	+	0.0845056i
$609$	3.26068	−	2.22461i	0.132129	−	0.0901456i
$610$	8.65243	+	3.18390i	0.350327	+	0.128912i
$611$	−12.2688			−0.496342
$612$	15.2312	−	17.8935i	0.615685	−	0.723302i
$613$			38.2321i			1.54418i	0.635514	+	0.772090i	$0.280788\pi$
$613$			38.2321i			1.54418i	−0.635514	+	0.772090i	$0.719212\pi$
$614$	−4.98601	+	13.5498i	−0.201219	+	0.546824i
$615$	−4.63212			−0.186785
$616$	−21.0431	−	10.4017i	−0.847849	−	0.419097i
$617$	13.4473			0.541370			0.270685	−	0.962668i	$-0.412750\pi$
$617$	13.4473			0.541370			0.270685	+	0.962668i	$0.412750\pi$
$618$	1.29343	−	3.51497i	0.0520293	−	0.141393i
$619$		−	3.01278i		−	0.121094i	−0.998165	−	0.0605468i	$-0.980716\pi$
$619$		−	3.01278i		−	0.121094i	0.998165	−	0.0605468i	$-0.0192845\pi$
$620$	−6.85636	−	5.83623i	−0.275358	−	0.234389i
$621$	19.0660			0.765092
$622$	−5.30843	−	1.95338i	−0.212848	−	0.0783233i
$623$	−23.5030	−	34.4492i	−0.941630	−	1.38018i
$624$	2.41202	−	0.390238i	0.0965580	−	0.0156220i
$625$	16.2290			0.649159
$626$	6.97267	−	18.9487i	0.278684	−	0.757341i
$627$	−3.69489			−0.147560
$628$	−8.41252	−	7.16086i	−0.335696	−	0.285749i
$629$	0.222306			0.00886392
$630$	−7.44220	+	1.86955i	−0.296504	+	0.0744845i
$631$			45.0426i			1.79312i	0.442923	+	0.896560i	$0.353941\pi$
$631$			45.0426i			1.79312i	−0.442923	+	0.896560i	$0.646059\pi$
$632$	9.94530	−	5.60220i	0.395603	−	0.222844i
$633$		−	6.89598i		−	0.274090i
$634$	2.40497	−	6.53565i	0.0955136	−	0.259564i
$635$			12.0202i			0.477007i
$636$	7.07108	+	6.01900i	0.280386	+	0.238669i
$637$	−2.55326	+	6.51774i	−0.101164	+	0.258242i
$638$	−3.74162	+	10.1681i	−0.148132	+	0.402558i
$639$		−	34.1857i		−	1.35237i
$640$	6.90457	−	5.50846i	0.272927	−	0.217741i
$641$	−13.9305			−0.550223			−0.275111	−	0.961412i	$-0.588715\pi$
$641$	−13.9305			−0.550223			−0.275111	+	0.961412i	$0.588715\pi$
$642$	4.84972	−	13.1794i	0.191403	−	0.520150i
$643$			12.4706i			0.491793i	0.969296	+	0.245896i	$0.0790823\pi$
$643$			12.4706i			0.491793i	−0.969296	+	0.245896i	$0.920918\pi$
$644$	3.11961	−	29.1859i	0.122930	−	1.15009i
$645$			4.45730i			0.175506i
$646$	−11.4470	−	4.21223i	−0.450376	−	0.165728i
$647$	15.0662			0.592315			0.296157	−	0.955139i	$-0.404295\pi$
$647$	15.0662			0.592315			0.296157	+	0.955139i	$0.404295\pi$
$648$	−8.02505	−	14.2465i	−0.315254	−	0.559654i
$649$			41.6324i			1.63422i
$650$	−5.82711	−	2.14424i	−0.228558	−	0.0841041i
$651$	−5.25235	−	7.69854i	−0.205856	−	0.301730i
$652$	−1.33529	−	1.13661i	−0.0522938	−	0.0445133i
$653$		−	4.21959i		−	0.165125i	−0.996586	−	0.0825627i	$-0.973690\pi$
$653$		−	4.21959i		−	0.165125i	0.996586	−	0.0825627i	$-0.0263105\pi$
$654$	3.01014	+	1.10766i	0.117706	+	0.0433131i
$655$		−	13.4578i		−	0.525838i
$656$	−38.3540	+	6.20524i	−1.49747	+	0.242274i
$657$			1.06785i			0.0416606i
$658$	−44.5223	+	11.1844i	−1.73566	+	0.436014i
$659$	3.00756			0.117158			0.0585790	−	0.998283i	$-0.481343\pi$
$659$	3.00756			0.117158			0.0585790	+	0.998283i	$0.481343\pi$
$660$	−1.93924	+	2.27821i	−0.0754850	+	0.0886791i
$661$	18.4307			0.716871			0.358436	−	0.933554i	$-0.383310\pi$
$661$	18.4307			0.716871			0.358436	+	0.933554i	$0.383310\pi$
$662$	13.5550	+	4.98794i	0.526831	+	0.193862i
$663$	−2.73211			−0.106107
$664$	29.3841	−	16.5521i	1.14032	−	0.642346i
$665$	2.24481	+	3.29028i	0.0870498	+	0.127592i
$666$	0.0637649	−	0.173285i	0.00247084	−	0.00671466i
$667$	−13.5480			−0.524583
$668$	−34.4172	−	29.2964i	−1.33164	−	1.13351i
$669$		−	3.79465i		−	0.146710i
$670$	−0.971041	−	0.357321i	−0.0375146	−	0.0138045i
$671$	−26.1936			−1.01119
$672$	8.39725	−	3.61497i	0.323931	−	0.139450i
$673$	34.6624			1.33614			0.668069	−	0.744099i	$-0.267121\pi$
$673$	34.6624			1.33614			0.668069	+	0.744099i	$0.267121\pi$
$674$	7.80008	+	2.87025i	0.300448	+	0.110558i
$675$		−	15.0908i		−	0.580845i
$676$	1.52297	+	1.29637i	0.0585756	+	0.0498604i
$677$	−46.5739			−1.78998			−0.894990	−	0.446087i	$-0.852817\pi$
$677$	−46.5739			−1.78998			−0.894990	+	0.446087i	$0.852817\pi$
$678$	−4.66430	+	12.6755i	−0.179131	+	0.486800i
$679$	10.5938	+	15.5277i	0.406553	+	0.595898i
$680$	−8.60510	+	4.84727i	−0.329990	+	0.185884i
$681$	−1.47656			−0.0565819
$682$	24.0071	+	8.83406i	0.919279	+	0.338274i
$683$	13.1703			0.503947			0.251974	−	0.967734i	$-0.418920\pi$
$683$	13.1703			0.503947			0.251974	+	0.967734i	$0.418920\pi$
$684$	−6.56678	+	7.71460i	−0.251087	+	0.294975i
$685$	−8.57711			−0.327715
$686$	−3.32387	+	25.9798i	−0.126906	+	0.991915i
$687$		−	0.474765i		−	0.0181134i
$688$	5.97104	+	36.9064i	0.227644	+	1.40704i
$689$			7.60088i			0.289571i
$690$	−3.51091	−	1.29193i	−0.133658	−	0.0491831i
$691$		−	37.3690i		−	1.42158i	−0.703402	−	0.710792i	$-0.748337\pi$
$691$		−	37.3690i		−	1.42158i	0.703402	−	0.710792i	$-0.251663\pi$
$692$	−2.16253	−	1.84077i	−0.0822070	−	0.0699758i
$693$	18.0087	−	12.2865i	0.684095	−	0.466726i
$694$	34.6256	+	12.7414i	1.31437	+	0.483658i
$695$			14.1076i			0.535133i
$696$	−2.07104	−	3.67662i	−0.0785027	−	0.139362i
$697$	43.4439			1.64555
$698$	−33.0056	−	12.1453i	−1.24928	−	0.459707i
$699$			0.571668i			0.0216225i
$700$	−23.1007	−	2.46918i	−0.873126	−	0.0933262i
$701$			19.9712i			0.754302i	0.926152	+	0.377151i	$0.123096\pi$
$701$			19.9712i			0.754302i	−0.926152	+	0.377151i	$0.876904\pi$
$702$	−1.67864	+	4.56181i	−0.0633563	+	0.172175i
$703$	−0.0958449			−0.00361486
$704$	−13.0050	+	21.4614i	−0.490145	+	0.808856i
$705$			5.85088i			0.220357i
$706$	−0.659379	+	1.79190i	−0.0248160	+	0.0674391i
$707$	16.7849	−	11.4516i	0.631262	−	0.430680i
$708$	−12.3472	−	10.5101i	−0.464037	−	0.394995i
$709$		−	16.5434i		−	0.621302i	−0.950524	−	0.310651i	$-0.899453\pi$
$709$		−	16.5434i		−	0.621302i	0.950524	−	0.310651i	$-0.100547\pi$
$710$	−4.96197	+	13.4845i	−0.186219	+	0.506063i
$711$			10.6012i			0.397576i
$712$	−38.8436	+	21.8807i	−1.45572	+	0.820012i
$713$			31.9873i			1.19793i
$714$	−9.91459	+	2.49063i	−0.371044	+	0.0932096i
$715$	−2.44890			−0.0915838
$716$	18.3525	+	15.6219i	0.685866	+	0.583819i
$717$	4.93284			0.184220
$718$	2.35807	−	6.40820i	0.0880024	−	0.239152i
$719$	11.5055			0.429084			0.214542	−	0.976715i	$-0.431174\pi$
$719$	11.5055			0.429084			0.214542	+	0.976715i	$0.431174\pi$
$720$	1.31016	+	8.09794i	0.0488267	+	0.301793i
$721$	9.47570	−	6.46482i	0.352894	−	0.240763i
$722$	−20.2817	−	7.46320i	−0.754807	−	0.277752i
$723$	7.99733			0.297424
$724$	−36.5048	−	31.0735i	−1.35669	−	1.15484i
$725$			10.7233i			0.398254i
$726$	−0.346237	+	0.940921i	−0.0128501	+	0.0349209i
$727$	−24.4779			−0.907835			−0.453918	−	0.891044i	$-0.649974\pi$
$727$	−24.4779			−0.907835			−0.453918	+	0.891044i	$0.649974\pi$
$728$	6.70849	+	3.31605i	0.248633	+	0.122901i
$729$	8.88731			0.329160
$730$	0.154995	−	0.421208i	0.00573662	−	0.0155896i
$731$		−	41.8042i		−	1.54618i
$732$	6.61260	−	7.76843i	0.244409	−	0.287130i
$733$	−6.67143			−0.246415			−0.123207	−	0.992381i	$-0.539318\pi$
$733$	−6.67143			−0.246415			−0.123207	+	0.992381i	$0.539318\pi$
$734$	−11.8054	−	4.34410i	−0.435744	−	0.160344i
$735$	3.10825	+	1.21762i	0.114649	+	0.0449128i
$736$	−30.8010	−	5.99395i	−1.13534	−	0.220940i
$737$	2.93965			0.108283
$738$	12.4612	−	33.8640i	0.458702	−	1.24655i
$739$	−29.0139			−1.06730			−0.533648	−	0.845707i	$-0.679179\pi$
$739$	−29.0139			−1.06730			−0.533648	+	0.845707i	$0.679179\pi$
$740$	−0.0503038	+	0.0590965i	−0.00184920	+	0.00217243i
$741$	1.17792			0.0432721
$742$	6.92907	+	27.5829i	0.254374	+	1.01260i
$743$			6.25450i			0.229455i	0.993397	+	0.114728i	$0.0365996\pi$
$743$			6.25450i			0.229455i	−0.993397	+	0.114728i	$0.963400\pi$
$744$	−8.68058	+	4.88979i	−0.318246	+	0.179268i
$745$			16.1738i			0.592563i
$746$	−17.4903	+	47.5310i	−0.640366	+	1.74023i
$747$			31.3219i			1.14601i
$748$	18.1878	−	21.3669i	0.665012	−	0.781251i
$749$	35.5292	−	24.2399i	1.29821	−	0.885707i
$750$	−2.18709	+	5.94356i	−0.0798614	+	0.217028i
$751$			13.3309i			0.486450i	0.969970	+	0.243225i	$0.0782053\pi$
$751$			13.3309i			0.486450i	−0.969970	+	0.243225i	$0.921795\pi$
$752$	7.83790	+	48.4452i	0.285819	+	1.76662i
$753$	−7.13433			−0.259989
$754$	1.19282	−	3.24157i	0.0434400	−	0.118051i
$755$			9.98577i			0.363419i
$756$	−1.93302	+	18.0847i	−0.0703034	+	0.657733i
$757$		−	42.5601i		−	1.54687i	−0.633875	−	0.773436i	$-0.718537\pi$
$757$		−	42.5601i		−	1.54687i	0.633875	−	0.773436i	$-0.281463\pi$
$758$	17.1758	+	6.32028i	0.623851	+	0.229563i
$759$	10.6286			0.385795
$760$	3.71000	−	2.08985i	0.134576	−	0.0758068i
$761$			16.7302i			0.606470i	0.952916	+	0.303235i	$0.0980668\pi$
$761$			16.7302i			0.606470i	−0.952916	+	0.303235i	$0.901933\pi$
$762$	12.4823	+	4.59320i	0.452186	+	0.166394i
$763$	5.53633	+	8.11478i	0.200429	+	0.293775i
$764$	15.6071	−	18.3351i	0.564646	−	0.663342i
$765$		−	9.17261i		−	0.331636i
$766$	−21.7641	−	8.00867i	−0.786368	−	0.289365i
$767$		−	13.2723i		−	0.479236i
$768$	−3.08183	−	9.27493i	−0.111206	−	0.334680i
$769$		−	20.9434i		−	0.755238i	−0.925961	−	0.377619i	$-0.876743\pi$
$769$		−	20.9434i		−	0.755238i	0.925961	−	0.377619i	$-0.123257\pi$
$770$	−8.88684	+	2.23245i	−0.320260	+	0.0804521i
$771$	14.0380			0.505566
$772$	6.01160	+	5.11716i	0.216362	+	0.184171i
$773$	−7.79043			−0.280202			−0.140101	−	0.990137i	$-0.544743\pi$
$773$	−7.79043			−0.280202			−0.140101	+	0.990137i	$0.544743\pi$
$774$	−32.5859	−	11.9909i	−1.17128	−	0.431003i
$775$	25.3180			0.909450
$776$	17.5084	−	9.86253i	0.628516	−	0.354044i
$777$	−0.0663554	+	0.0452712i	−0.00238049	+	0.00162409i
$778$	−9.43510	+	25.6405i	−0.338265	+	0.919255i
$779$	−18.7304			−0.671085
$780$	0.618227	−	0.726288i	0.0221361	−	0.0260053i
$781$		−	40.8217i		−	1.46072i
$782$	32.9282	+	12.1168i	1.17751	+	0.433296i
$783$	8.39487			0.300008
$784$	27.3674	+	5.91808i	0.977408	+	0.211360i
$785$	−4.31244			−0.153918
$786$	−13.9751	−	5.14253i	−0.498476	−	0.183428i
$787$		−	46.2745i		−	1.64951i	−0.565491	−	0.824755i	$-0.691313\pi$
$787$		−	46.2745i		−	1.64951i	0.565491	−	0.824755i	$-0.308687\pi$
$788$	−21.9063	+	25.7353i	−0.780379	+	0.916783i
$789$	−5.24150			−0.186602
$790$	1.53874	−	4.18161i	0.0547458	−	0.148775i
$791$	−34.1708	+	23.3131i	−1.21497	+	0.828920i
$792$	−11.4384	−	20.3060i	−0.406445	−	0.721541i
$793$	8.35048			0.296534
$794$	36.9188	+	13.5853i	1.31020	+	0.482123i
$795$	3.62479			0.128558
$796$	18.1061	+	15.4121i	0.641752	+	0.546269i
$797$	−37.9333			−1.34367			−0.671833	−	0.740703i	$-0.734493\pi$
$797$	−37.9333			−1.34367			−0.671833	+	0.740703i	$0.734493\pi$
$798$	4.27457	−	1.07381i	0.151318	−	0.0380125i
$799$		−	54.8743i		−	1.94131i
$800$	−4.74423	+	24.3791i	−0.167734	+	0.861931i
$801$		−	41.4053i		−	1.46299i
$802$	43.6422	+	16.0593i	1.54106	+	0.567074i
$803$			1.27513i			0.0449984i
$804$	−0.742115	+	0.871831i	−0.0261724	+	0.0307471i
$805$	−6.45735	−	9.46475i	−0.227592	−	0.333589i
$806$	−7.65342	−	2.81628i	−0.269580	−	0.0991993i
$807$		−	12.5667i		−	0.442369i
$808$	−10.6611	−	18.9260i	−0.375055	−	0.665816i
$809$	27.1364			0.954066			0.477033	−	0.878885i	$-0.341712\pi$
$809$	27.1364			0.954066			0.477033	+	0.878885i	$0.341712\pi$
$810$	−5.99007	−	2.20421i	−0.210470	−	0.0774480i
$811$			13.4314i			0.471639i	0.971797	+	0.235820i	$0.0757774\pi$
$811$			13.4314i			0.471639i	−0.971797	+	0.235820i	$0.924223\pi$
$812$	1.37358	−	12.8507i	0.0482033	−	0.450972i
$813$		−	4.66308i		−	0.163541i
$814$	0.0761427	−	0.206922i	0.00266880	−	0.00725263i
$815$	−0.684497			−0.0239769
$816$	1.74541	+	10.7882i	0.0611014	+	0.377662i
$817$			18.0234i			0.630561i
$818$	11.0795	−	30.1092i	0.387385	−	1.05274i
$819$	−5.74115	+	3.91692i	−0.200612	+	0.136868i
$820$	−9.83055	+	11.5488i	−0.343298	+	0.403303i
$821$		−	22.5402i		−	0.786659i	−0.919398	−	0.393330i	$-0.871323\pi$
$821$		−	22.5402i		−	0.786659i	0.919398	−	0.393330i	$-0.128677\pi$
$822$	−3.27752	+	8.90686i	−0.114317	+	0.310662i
$823$			7.78576i			0.271394i	0.990750	+	0.135697i	$0.0433274\pi$
$823$			7.78576i			0.271394i	−0.990750	+	0.135697i	$0.956673\pi$
$824$	−6.01856	−	10.6844i	−0.209667	−	0.372210i
$825$		−	8.41259i		−	0.292889i
$826$	−12.0992	−	48.1641i	−0.420987	−	1.67584i
$827$	0.985448			0.0342674			0.0171337	−	0.999853i	$-0.494546\pi$
$827$	0.985448			0.0342674			0.0171337	+	0.999853i	$0.494546\pi$
$828$	18.8898	−	22.1916i	0.656467	−	0.771213i
$829$	54.4732			1.89193			0.945967	−	0.324264i	$-0.105117\pi$
$829$	54.4732			1.89193			0.945967	+	0.324264i	$0.105117\pi$
$830$	4.54630	−	12.3548i	0.157804	−	0.428843i
$831$	−6.93319			−0.240510
$832$	4.14597	−	6.84185i	0.143736	−	0.237198i
$833$	−29.1517	−	11.4199i	−1.01005	−	0.395675i
$834$	14.6500	+	5.39086i	0.507288	+	0.186670i
$835$	−17.6430			−0.610561
$836$	−7.84149	+	9.21212i	−0.271204	+	0.318608i
$837$		−	19.8205i		−	0.685096i
$838$	−3.43635	+	9.33850i	−0.118707	+	0.322593i
$839$	18.5284			0.639672			0.319836	−	0.947473i	$-0.396372\pi$
$839$	18.5284			0.639672			0.319836	+	0.947473i	$0.396372\pi$
$840$	1.58139	−	3.19922i	0.0545633	−	0.110383i
$841$	23.0347			0.794301
$842$	6.46855	−	17.5787i	0.222921	−	0.605802i
$843$			3.88028i			0.133644i
$844$	−17.1931	−	14.6350i	−0.591811	−	0.503758i
$845$	0.780706			0.0268571
$846$	−42.7740	−	15.7398i	−1.47060	−	0.541147i
$847$	−2.53655	+	1.73057i	−0.0871568	+	0.0594630i
$848$	30.0133	−	4.85581i	1.03066	−	0.166749i
$849$	14.2792			0.490063
$850$	9.59049	−	26.0627i	0.328951	−	0.893945i
$851$	0.275705			0.00945105
$852$	12.1068	+	10.3055i	0.414771	+	0.353059i
$853$	54.5504			1.86777			0.933886	−	0.357571i	$-0.116395\pi$
$853$	54.5504			1.86777			0.933886	+	0.357571i	$0.116395\pi$
$854$	30.3031	−	7.61242i	1.03695	−	0.260492i
$855$			3.95467i			0.135247i
$856$	−22.5667	−	40.0614i	−0.771313	−	1.36927i
$857$			17.4890i			0.597413i	0.954345	+	0.298706i	$0.0965551\pi$
$857$			17.4890i			0.597413i	−0.954345	+	0.298706i	$0.903445\pi$
$858$	−0.935784	+	2.54305i	−0.0319472	+	0.0868183i
$859$			32.4405i			1.10686i	0.832897	+	0.553428i	$0.186681\pi$
$859$			32.4405i			1.10686i	−0.832897	+	0.553428i	$0.813319\pi$
$860$	11.1130	+	9.45952i	0.378949	+	0.322567i
$861$	−12.9674	+	8.84706i	−0.441928	+	0.301507i
$862$	13.7953	−	37.4895i	0.469869	−	1.27690i
$863$		−	2.87423i		−	0.0978400i	−0.998803	−	0.0489200i	$-0.984422\pi$
$863$		−	2.87423i		−	0.0978400i	0.998803	−	0.0489200i	$-0.0155779\pi$
$864$	19.0854	+	3.71407i	0.649299	+	0.126355i
$865$	−1.10856			−0.0376922
$866$	−6.53526	+	17.7600i	−0.222077	+	0.603508i
$867$		−	1.83547i		−	0.0623360i
$868$	−30.3409	−	3.24306i	−1.02984	−	0.110077i
$869$			12.6590i			0.429429i
$870$	−1.54587	−	0.568846i	−0.0524100	−	0.0192857i
$871$	−0.937154			−0.0317542
$872$	9.14992	−	5.15417i	0.309855	−	0.174542i
$873$			18.6631i			0.631651i
$874$	−14.1966	−	5.22404i	−0.480208	−	0.176706i
$875$	−16.0227	+	10.9316i	−0.541667	+	0.369554i
$876$	−0.378174	−	0.321907i	−0.0127773	−	0.0108762i
$877$		−	11.8009i		−	0.398489i	−0.979950	−	0.199244i	$-0.936151\pi$
$877$		−	11.8009i		−	0.398489i	0.979950	−	0.199244i	$-0.0638487\pi$
$878$	−21.1601	−	7.78644i	−0.714119	−	0.262780i
$879$		−	0.183689i		−	0.00619567i
$880$	1.56448	+	9.66988i	0.0527385	+	0.325971i
$881$		−	11.1084i		−	0.374252i	−0.982336	−	0.187126i	$-0.940083\pi$
$881$		−	11.1084i		−	0.374252i	0.982336	−	0.187126i	$-0.0599173\pi$
$882$	−17.2634	+	19.4478i	−0.581288	+	0.654843i
$883$	−2.08414			−0.0701370			−0.0350685	−	0.999385i	$-0.511165\pi$
$883$	−2.08414			−0.0701370			−0.0350685	+	0.999385i	$0.511165\pi$
$884$	−5.79824	+	6.81173i	−0.195016	+	0.229103i
$885$	−6.32946			−0.212762
$886$	20.5239	+	7.55231i	0.689513	+	0.253725i
$887$	40.7788			1.36922			0.684609	−	0.728911i	$-0.259973\pi$
$887$	40.7788			1.36922			0.684609	+	0.728911i	$0.259973\pi$
$888$	0.0421461	+	0.0748198i	0.00141433	+	0.00251079i
$889$	22.9578	+	33.6500i	0.769980	+	1.12858i
$890$	−6.00987	+	16.3322i	−0.201451	+	0.547457i
$891$	18.1338			0.607507
$892$	−9.46085	−	8.05321i	−0.316773	−	0.269641i
$893$			23.6585i			0.791702i
$894$	16.7956	+	6.18040i	0.561729	+	0.206703i
$895$	9.40791			0.314472
$896$	8.80823	−	28.6080i	0.294262	−	0.955725i
$897$	−3.38838			−0.113135
$898$	8.72469	+	3.21048i	0.291147	+	0.107135i
$899$			14.0842i			0.469734i
$900$	−17.5648	−	14.9514i	−0.585492	−	0.498379i
$901$	−33.9963			−1.13258
$902$	14.8801	−	40.4375i	0.495453	−	1.34642i
$903$	8.51315	+	12.4780i	0.283300	+	0.415242i
$904$	21.7039	+	38.5297i	0.721860	+	1.28148i
$905$	−18.7132			−0.622047
$906$	10.3697	+	3.81580i	0.344509	+	0.126771i
$907$	28.4897			0.945984			0.472992	−	0.881067i	$-0.343174\pi$
$907$	28.4897			0.945984			0.472992	+	0.881067i	$0.343174\pi$
$908$	−3.13363	+	3.68137i	−0.103993	+	0.122170i
$909$	20.1742			0.669137
$910$	2.83311	−	0.711702i	0.0939166	−	0.0235927i
$911$			25.7994i			0.854772i	0.904069	+	0.427386i	$0.140565\pi$
$911$			25.7994i			0.854772i	−0.904069	+	0.427386i	$0.859435\pi$
$912$	−0.752514	−	4.65121i	−0.0249182	−	0.154017i
$913$			37.4020i			1.23783i
$914$	−46.2355	−	17.0136i	−1.52934	−	0.562760i
$915$		−	3.98227i		−	0.131650i
$916$	−1.18369	−	1.00757i	−0.0391102	−	0.0332911i
$917$	−25.7034	−	37.6744i	−0.848802	−	1.24412i
$918$	−20.4035	−	7.50802i	−0.673416	−	0.247802i
$919$		−	48.7196i		−	1.60711i	−0.595230	−	0.803556i	$-0.702939\pi$
$919$		−	48.7196i		−	1.60711i	0.595230	−	0.803556i	$-0.297061\pi$
$920$	−10.6721	+	6.01161i	−0.351849	+	0.198197i
$921$	6.23626			0.205492
$922$	14.5684	+	5.36083i	0.479784	+	0.176550i
$923$			13.0139i			0.428357i
$924$	−1.07759	+	10.0816i	−0.0354502	+	0.331659i
$925$		−	0.218222i		−	0.00717508i
$926$	−9.18425	+	24.9588i	−0.301813	+	0.820196i
$927$	11.3891			0.374067
$928$	−13.5619	−	2.63917i	−0.445190	−	0.0866351i
$929$			16.1335i			0.529322i	0.964341	+	0.264661i	$0.0852601\pi$
$929$			16.1335i			0.529322i	−0.964341	+	0.264661i	$0.914740\pi$
$930$	−1.34306	+	3.64984i	−0.0440406	+	0.119683i
$931$	12.5685	+	4.92356i	0.411915	+	0.161363i
$932$	1.42529	+	1.21322i	0.0466868	+	0.0397405i
$933$			2.44320i			0.0799866i
$934$	7.00256	−	19.0299i	0.229131	−	0.622677i
$935$		−	10.9531i		−	0.358206i
$936$	3.64654	+	6.47350i	0.119191	+	0.211593i
$937$		−	11.6153i		−	0.379454i	−0.981837	−	0.189727i	$-0.939240\pi$
$937$		−	11.6153i		−	0.379454i	0.981837	−	0.189727i	$-0.0607604\pi$
$938$	−3.40084	+	0.854322i	−0.111041	+	0.0278946i
$939$	−8.72109			−0.284602
$940$	14.5875	+	12.4171i	0.475790	+	0.405000i
$941$	−16.5828			−0.540584			−0.270292	−	0.962778i	$-0.587120\pi$
$941$	−16.5828			−0.540584			−0.270292	+	0.962778i	$0.587120\pi$
$942$	−1.64789	+	4.47823i	−0.0536911	+	0.145909i
$943$	53.8794			1.75455
$944$	−52.4079	+	8.47901i	−1.70573	+	0.275968i
$945$	4.00121	+	5.86471i	0.130159	+	0.190779i
$946$	−38.9113	−	14.3185i	−1.26512	−	0.465534i
$947$	−20.6272			−0.670295			−0.335147	−	0.942166i	$-0.608786\pi$
$947$	−20.6272			−0.670295			−0.335147	+	0.942166i	$0.608786\pi$
$948$	−3.75438	−	3.19578i	−0.121937	−	0.103794i
$949$		−	0.406509i		−	0.0131958i
$950$	−4.13484	+	11.2367i	−0.134152	+	0.364566i
$951$	−3.00803			−0.0975419
$952$	−14.8316	+	30.0049i	−0.480695	+	0.972464i
$953$	−44.3425			−1.43640			−0.718198	−	0.695839i	$-0.755033\pi$
$953$	−44.3425			−1.43640			−0.718198	+	0.695839i	$0.755033\pi$
$954$	−9.75129	+	26.4997i	−0.315710	+	0.857960i
$955$		−	9.39899i		−	0.304144i
$956$	10.4687	−	12.2986i	0.338583	−	0.397765i
$957$	4.67985			0.151278
$958$	7.11468	+	2.61804i	0.229865	+	0.0845850i
$959$	−24.0112	+	16.3817i	−0.775363	+	0.528994i
$960$	−3.26282	−	1.97718i	−0.105307	−	0.0638131i
$961$	2.25310			0.0726807
$962$	−0.0242741	+	0.0659665i	−0.000782630	+	0.00212684i
$963$	42.7035			1.37610
$964$	16.9724	−	19.9390i	0.546643	−	0.642192i
$965$	3.08168			0.0992028
$966$	−12.2961	+	3.08890i	−0.395622	+	0.0993837i
$967$			11.2213i			0.360852i	0.983589	+	0.180426i	$0.0577477\pi$
$967$			11.2213i			0.360852i	−0.983589	+	0.180426i	$0.942252\pi$
$968$	1.61111	+	2.86012i	0.0517830	+	0.0919276i
$969$			5.26846i			0.169247i
$970$	2.70890	−	7.36160i	0.0869776	−	0.236367i
$971$		−	53.3628i		−	1.71249i	−0.516566	−	0.856247i	$-0.672790\pi$
$971$		−	53.3628i		−	1.71249i	0.516566	−	0.856247i	$-0.327210\pi$
$972$	−17.9454	+	21.0821i	−0.575597	+	0.676207i
$973$	26.9447	+	39.4937i	0.863806	+	1.26611i
$974$	7.21788	−	19.6150i	0.231276	−	0.628506i
$975$			2.68192i			0.0858901i
$976$	−5.33469	−	32.9732i	−0.170759	−	1.05545i
$977$	−61.6226			−1.97148			−0.985741	−	0.168270i	$-0.946182\pi$
$977$	−61.6226			−1.97148			−0.985741	+	0.168270i	$0.946182\pi$
$978$	−0.261563	+	0.710812i	−0.00836385	+	0.0227293i
$979$		−	49.4427i		−	1.58020i
$980$	9.63229	−	5.16540i	0.307692	−	0.165003i
$981$			9.75336i			0.311401i
$982$	27.8800	+	10.2592i	0.889688	+	0.327385i
$983$	19.3693			0.617786			0.308893	−	0.951097i	$-0.400042\pi$
$983$	19.3693			0.617786			0.308893	+	0.951097i	$0.400042\pi$
$984$	8.23636	+	14.6216i	0.262565	+	0.466119i
$985$			13.1925i			0.420348i
$986$	14.4985	+	5.33510i	0.461725	+	0.169904i
$987$	11.1748	+	16.3793i	0.355698	+	0.521358i
$988$	2.49985	−	2.93681i	0.0795309	−	0.0934323i
$989$		−	51.8458i		−	1.64860i
$990$	−8.53786	−	3.14174i	−0.271351	−	0.0998509i
$991$			10.3242i			0.327958i	0.986464	+	0.163979i	$0.0524329\pi$
$991$			10.3242i			0.327958i	−0.986464	+	0.163979i	$0.947567\pi$
$992$	−6.23115	+	32.0199i	−0.197839	+	1.01663i
$993$		−	6.23869i		−	0.197979i
$994$	11.8636	+	47.2261i	0.376291	+	1.49792i
$995$	9.28157			0.294245
$996$	−11.0926	−	9.44216i	−0.351482	−	0.299186i
$997$	44.2145			1.40029			0.700143	−	0.714002i	$-0.253119\pi$
$997$	44.2145			1.40029			0.700143	+	0.714002i	$0.253119\pi$
$998$	18.8568	+	6.93886i	0.596901	+	0.219646i
$999$	−0.170837			−0.00540505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.a.27.5	✓	48
4.3	odd	2		2912.2.h.a.2575.21		48
7.6	odd	2		728.2.h.b.27.5	yes	48
8.3	odd	2		728.2.h.b.27.6	yes	48
8.5	even	2		2912.2.h.b.2575.21		48
28.27	even	2		2912.2.h.b.2575.28		48
56.13	odd	2		2912.2.h.a.2575.28		48
56.27	even	2	inner	728.2.h.a.27.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.5	✓	48	1.1	even	1	trivial
728.2.h.a.27.6	yes	48	56.27	even	2	inner
728.2.h.b.27.5	yes	48	7.6	odd	2
728.2.h.b.27.6	yes	48	8.3	odd	2
2912.2.h.a.2575.21		48	4.3	odd	2
2912.2.h.a.2575.28		48	56.13	odd	2
2912.2.h.b.2575.21		48	8.5	even	2
2912.2.h.b.2575.28		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+(-1.32721 - 0.488382i) q^{2} +0.610846i q^{3} +(1.52297 + 1.29637i) q^{4} +0.780706 q^{5} +(0.298326 - 0.810720i) q^{6} +(2.18555 - 1.49110i) q^{7} +(-1.38817 - 2.46434i) q^{8} +2.62687 q^{9} +(-1.03616 - 0.381283i) q^{10} +3.13678 q^{11} +(-0.791882 + 0.930297i) q^{12} -1.00000 q^{13} +(-3.62891 + 0.911614i) q^{14} +0.476891i q^{15} +(0.638848 + 3.94865i) q^{16} -4.47267i q^{17} +(-3.48640 - 1.28292i) q^{18} +1.92835i q^{19} +(1.18899 + 1.01208i) q^{20} +(0.910831 + 1.33503i) q^{21} +(-4.16316 - 1.53195i) q^{22} -5.54704i q^{23} +(1.50533 - 0.847957i) q^{24} -4.39050 q^{25} +(1.32721 + 0.488382i) q^{26} +3.43715i q^{27} +(5.26153 + 0.562392i) q^{28} -2.44239i q^{29} +(0.232905 - 0.632934i) q^{30} -5.76655 q^{31} +(1.08057 - 5.55269i) q^{32} +1.91609i q^{33} +(-2.18437 + 5.93617i) q^{34} +(1.70627 - 1.16411i) q^{35} +(4.00063 + 3.40539i) q^{36} +0.0497032i q^{37} +(0.941771 - 2.55932i) q^{38} -0.610846i q^{39} +(-1.08375 - 1.92393i) q^{40} +9.71318i q^{41} +(-0.556855 - 2.21670i) q^{42} +9.34658 q^{43} +(4.77721 + 4.06643i) q^{44} +2.05081 q^{45} +(-2.70907 + 7.36208i) q^{46} +12.2688 q^{47} +(-2.41202 + 0.390238i) q^{48} +(2.55326 - 6.51774i) q^{49} +(5.82711 + 2.14424i) q^{50} +2.73211 q^{51} +(-1.52297 - 1.29637i) q^{52} -7.60088i q^{53} +(1.67864 - 4.56181i) q^{54} +2.44890 q^{55} +(-6.70849 - 3.31605i) q^{56} -1.17792 q^{57} +(-1.19282 + 3.24157i) q^{58} +13.2723i q^{59} +(-0.618227 + 0.726288i) q^{60} -8.35048 q^{61} +(7.65342 + 2.81628i) q^{62} +(5.74115 - 3.91692i) q^{63} +(-4.14597 + 6.84185i) q^{64} -0.780706 q^{65} +(0.935784 - 2.54305i) q^{66} +0.937154 q^{67} +(5.79824 - 6.81173i) q^{68} +3.38838 q^{69} +(-2.83311 + 0.711702i) q^{70} -13.0139i q^{71} +(-3.64654 - 6.47350i) q^{72} +0.406509i q^{73} +(0.0242741 - 0.0659665i) q^{74} -2.68192i q^{75} +(-2.49985 + 2.93681i) q^{76} +(6.85559 - 4.67725i) q^{77} +(-0.298326 + 0.810720i) q^{78} +4.03568i q^{79} +(0.498752 + 3.08274i) q^{80} +5.78103 q^{81} +(4.74374 - 12.8914i) q^{82} +11.9237i q^{83} +(-0.343535 + 3.21398i) q^{84} -3.49184i q^{85} +(-12.4049 - 4.56470i) q^{86} +1.49193 q^{87} +(-4.35438 - 7.73011i) q^{88} -15.7622i q^{89} +(-2.72185 - 1.00158i) q^{90} +(-2.18555 + 1.49110i) q^{91} +(7.19102 - 8.44795i) q^{92} -3.52247i q^{93} +(-16.2833 - 5.99186i) q^{94} +1.50547i q^{95} +(3.39184 + 0.660061i) q^{96} +7.10470i q^{97} +(-6.57185 + 7.40343i) q^{98} +8.23991 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

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