LMFDB - Embedded newform 728.2.h.b.27.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(27,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [48,1,0,1,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			27.15
Character	$\chi$	$=$	728.27
Dual form			728.2.h.b.27.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.635480 - 1.26339i) q^{2} +1.40360i q^{3} +(-1.19233 + 1.60572i) q^{4} +3.11493 q^{5} +(1.77331 - 0.891962i) q^{6} +(2.64532 - 0.0479799i) q^{7} +(2.78636 + 0.485980i) q^{8} +1.02989 q^{9} +(-1.97948 - 3.93539i) q^{10} -0.711549 q^{11} +(-2.25380 - 1.67356i) q^{12} +1.00000 q^{13} +(-1.74166 - 3.31159i) q^{14} +4.37213i q^{15} +(-1.15669 - 3.82911i) q^{16} -0.128191i q^{17} +(-0.654477 - 1.30116i) q^{18} -5.49116i q^{19} +(-3.71403 + 5.00172i) q^{20} +(0.0673448 + 3.71298i) q^{21} +(0.452175 + 0.898967i) q^{22} +5.12058i q^{23} +(-0.682124 + 3.91095i) q^{24} +4.70280 q^{25} +(-0.635480 - 1.26339i) q^{26} +5.65638i q^{27} +(-3.07705 + 4.30485i) q^{28} -7.07307i q^{29} +(5.52373 - 2.77840i) q^{30} -10.3051 q^{31} +(-4.10262 + 3.89468i) q^{32} -0.998733i q^{33} +(-0.161955 + 0.0814626i) q^{34} +(8.23998 - 0.149454i) q^{35} +(-1.22798 + 1.65373i) q^{36} +8.15798i q^{37} +(-6.93750 + 3.48952i) q^{38} +1.40360i q^{39} +(8.67934 + 1.51379i) q^{40} -0.100841i q^{41} +(4.64816 - 2.44460i) q^{42} +8.73959 q^{43} +(0.848402 - 1.14255i) q^{44} +3.20805 q^{45} +(6.46931 - 3.25403i) q^{46} -2.81273 q^{47} +(5.37455 - 1.62354i) q^{48} +(6.99540 - 0.253844i) q^{49} +(-2.98854 - 5.94150i) q^{50} +0.179929 q^{51} +(-1.19233 + 1.60572i) q^{52} -8.53210i q^{53} +(7.14624 - 3.59451i) q^{54} -2.21643 q^{55} +(7.39413 + 1.15188i) q^{56} +7.70742 q^{57} +(-8.93608 + 4.49479i) q^{58} -7.38024i q^{59} +(-7.02043 - 5.21303i) q^{60} +11.3324 q^{61} +(6.54867 + 13.0194i) q^{62} +(2.72440 - 0.0494143i) q^{63} +(7.52765 + 2.70823i) q^{64} +3.11493 q^{65} +(-1.26179 + 0.634675i) q^{66} -14.5057 q^{67} +(0.205839 + 0.152846i) q^{68} -7.18727 q^{69} +(-5.42516 - 10.3154i) q^{70} +8.43273i q^{71} +(2.86966 + 0.500508i) q^{72} -8.62895i q^{73} +(10.3067 - 5.18423i) q^{74} +6.60088i q^{75} +(8.81728 + 6.54728i) q^{76} +(-1.88227 + 0.0341401i) q^{77} +(1.77331 - 0.891962i) q^{78} +16.3766i q^{79} +(-3.60302 - 11.9274i) q^{80} -4.84963 q^{81} +(-0.127402 + 0.0640826i) q^{82} -4.06811i q^{83} +(-6.04231 - 4.31896i) q^{84} -0.399306i q^{85} +(-5.55383 - 11.0416i) q^{86} +9.92780 q^{87} +(-1.98263 - 0.345799i) q^{88} +2.25678i q^{89} +(-2.03865 - 4.05304i) q^{90} +(2.64532 - 0.0479799i) q^{91} +(-8.22223 - 6.10543i) q^{92} -14.4643i q^{93} +(1.78743 + 3.55358i) q^{94} -17.1046i q^{95} +(-5.46659 - 5.75845i) q^{96} +5.13148i q^{97} +(-4.76614 - 8.67663i) q^{98} -0.732821 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} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 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 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * 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 - 14 * 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 - 37 * 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 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * 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 $

$2$	−0.635480	−	1.26339i	−0.449352	−	0.893355i
$2$	−0.635480	−	1.26339i	−0.449352	−	0.893355i
$3$			1.40360i			0.810371i	0.914234	+	0.405186i	$0.132793\pi$
$3$			1.40360i			0.810371i	−0.914234	+	0.405186i	$0.867207\pi$
$4$	−1.19233	+	1.60572i	−0.596166	+	0.802862i
$5$	3.11493			1.39304			0.696520	−	0.717537i	$-0.254731\pi$
$5$	3.11493			1.39304			0.696520	+	0.717537i	$0.254731\pi$
$6$	1.77331	−	0.891962i	0.723949	−	0.364142i
$7$	2.64532	−	0.0479799i	0.999836	−	0.0181347i
$7$	2.64532	−	0.0479799i	0.999836	−	0.0181347i
$8$	2.78636	+	0.485980i	0.985128	+	0.171820i
$9$	1.02989			0.343298
$10$	−1.97948	−	3.93539i	−0.625965	−	1.24448i
$11$	−0.711549			−0.214540			−0.107270	−	0.994230i	$-0.534211\pi$
$11$	−0.711549			−0.214540			−0.107270	+	0.994230i	$0.534211\pi$
$12$	−2.25380	−	1.67356i	−0.650616	−	0.483115i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−1.74166	−	3.31159i	−0.465479	−	0.885059i
$15$			4.37213i			1.12888i
$16$	−1.15669	−	3.82911i	−0.289173	−	0.957277i
$17$		−	0.128191i		−	0.0310908i	−0.999879	−	0.0155454i	$-0.995052\pi$
$17$		−	0.128191i		−	0.0310908i	0.999879	−	0.0155454i	$-0.00494846\pi$
$18$	−0.654477	−	1.30116i	−0.154262	−	0.306687i
$19$		−	5.49116i		−	1.25976i	−0.776693	−	0.629879i	$-0.783104\pi$
$19$		−	5.49116i		−	1.25976i	0.776693	−	0.629879i	$-0.216896\pi$
$20$	−3.71403	+	5.00172i	−0.830483	+	1.11842i
$21$	0.0673448	+	3.71298i	0.0146958	+	0.810238i
$22$	0.452175	+	0.898967i	0.0964040	+	0.191660i
$23$			5.12058i			1.06771i	0.845574	+	0.533857i	$0.179258\pi$
$23$			5.12058i			1.06771i	−0.845574	+	0.533857i	$0.820742\pi$
$24$	−0.682124	+	3.91095i	−0.139238	+	0.798320i
$25$	4.70280			0.940561
$26$	−0.635480	−	1.26339i	−0.124628	−	0.247772i
$27$			5.65638i			1.08857i
$28$	−3.07705	+	4.30485i	−0.581508	+	0.813541i
$29$		−	7.07307i		−	1.31344i	−0.754136	−	0.656718i	$-0.771944\pi$
$29$		−	7.07307i		−	1.31344i	0.754136	−	0.656718i	$-0.228056\pi$
$30$	5.52373	−	2.77840i	1.00849	−	0.507264i
$31$	−10.3051			−1.85085			−0.925424	−	0.378934i	$-0.876291\pi$
$31$	−10.3051			−1.85085			−0.925424	+	0.378934i	$0.876291\pi$
$32$	−4.10262	+	3.89468i	−0.725247	+	0.688489i
$33$		−	0.998733i		−	0.173857i
$34$	−0.161955	+	0.0814626i	−0.0277751	+	0.0139707i
$35$	8.23998	−	0.149454i	1.39281	−	0.0252624i
$36$	−1.22798	+	1.65373i	−0.204663	+	0.275621i
$37$			8.15798i			1.34116i	0.741836	+	0.670582i	$0.233955\pi$
$37$			8.15798i			1.34116i	−0.741836	+	0.670582i	$0.766045\pi$
$38$	−6.93750	+	3.48952i	−1.12541	+	0.566075i
$39$			1.40360i			0.224757i
$40$	8.67934	+	1.51379i	1.37232	+	0.239352i
$41$		−	0.100841i		−	0.0157488i	−0.999969	−	0.00787439i	$-0.997493\pi$
$41$		−	0.100841i		−	0.0157488i	0.999969	−	0.00787439i	$-0.00250652\pi$
$42$	4.64816	−	2.44460i	0.717226	−	0.377211i
$43$	8.73959			1.33278			0.666388	−	0.745605i	$-0.267840\pi$
$43$	8.73959			1.33278			0.666388	+	0.745605i	$0.267840\pi$
$44$	0.848402	−	1.14255i	0.127901	−	0.172246i
$45$	3.20805			0.478228
$46$	6.46931	−	3.25403i	0.953848	−	0.479780i
$47$	−2.81273			−0.410278			−0.205139	−	0.978733i	$-0.565765\pi$
$47$	−2.81273			−0.410278			−0.205139	+	0.978733i	$0.565765\pi$
$48$	5.37455	−	1.62354i	0.775750	−	0.234338i
$49$	6.99540	−	0.253844i	0.999342	−	0.0362635i
$50$	−2.98854	−	5.94150i	−0.422643	−	0.840255i
$51$	0.179929			0.0251951
$52$	−1.19233	+	1.60572i	−0.165347	+	0.222674i
$53$		−	8.53210i		−	1.17197i	−0.810321	−	0.585987i	$-0.800707\pi$
$53$		−	8.53210i		−	1.17197i	0.810321	−	0.585987i	$-0.199293\pi$
$54$	7.14624	−	3.59451i	0.972480	−	0.489151i
$55$	−2.21643			−0.298863
$56$	7.39413	+	1.15188i	0.988082	+	0.153927i
$57$	7.70742			1.02087
$58$	−8.93608	+	4.49479i	−1.17336	+	0.590195i
$59$		−	7.38024i		−	0.960825i	−0.877043	−	0.480413i	$-0.840487\pi$
$59$		−	7.38024i		−	0.960825i	0.877043	−	0.480413i	$-0.159513\pi$
$60$	−7.02043	−	5.21303i	−0.906334	−	0.672999i
$61$	11.3324			1.45097			0.725485	−	0.688238i	$-0.241616\pi$
$61$	11.3324			1.45097			0.725485	+	0.688238i	$0.241616\pi$
$62$	6.54867	+	13.0194i	0.831682	+	1.65346i
$63$	2.72440	−	0.0494143i	0.343242	−	0.00622562i
$64$	7.52765	+	2.70823i	0.940956	+	0.338529i
$65$	3.11493			0.386360
$66$	−1.26179	+	0.634675i	−0.155316	+	0.0781231i
$67$	−14.5057			−1.77215			−0.886077	−	0.463539i	$-0.846580\pi$
$67$	−14.5057			−1.77215			−0.886077	+	0.463539i	$0.846580\pi$
$68$	0.205839	+	0.152846i	0.0249616	+	0.0185353i
$69$	−7.18727			−0.865246
$70$	−5.42516	−	10.3154i	−0.648431	−	1.23292i
$71$			8.43273i			1.00078i	0.865800	+	0.500390i	$0.166810\pi$
$71$			8.43273i			1.00078i	−0.865800	+	0.500390i	$0.833190\pi$
$72$	2.86966	+	0.500508i	0.338193	+	0.0589855i
$73$		−	8.62895i		−	1.00994i	−0.863136	−	0.504971i	$-0.831503\pi$
$73$		−	8.62895i		−	1.00994i	0.863136	−	0.504971i	$-0.168497\pi$
$74$	10.3067	−	5.18423i	1.19813	−	0.602654i
$75$			6.60088i			0.762204i
$76$	8.81728	+	6.54728i	1.01141	+	0.751025i
$77$	−1.88227	+	0.0341401i	−0.214505	+	0.00389062i
$78$	1.77331	−	0.891962i	0.200787	−	0.100995i
$79$			16.3766i			1.84251i	0.388957	+	0.921256i	$0.372835\pi$
$79$			16.3766i			1.84251i	−0.388957	+	0.921256i	$0.627165\pi$
$80$	−3.60302	−	11.9274i	−0.402830	−	1.33352i
$81$	−4.84963			−0.538848
$82$	−0.127402	+	0.0640826i	−0.0140692	+	0.00707674i
$83$		−	4.06811i		−	0.446533i	−0.974757	−	0.223266i	$-0.928328\pi$
$83$		−	4.06811i		−	0.446533i	0.974757	−	0.223266i	$-0.0716720\pi$
$84$	−6.04231	−	4.31896i	−0.659270	−	0.471237i
$85$		−	0.399306i		−	0.0433108i
$86$	−5.55383	−	11.0416i	−0.598885	−	1.19064i
$87$	9.92780			1.06437
$88$	−1.98263	−	0.345799i	−0.211350	−	0.0368623i
$89$			2.25678i			0.239218i	0.992821	+	0.119609i	$0.0381641\pi$
$89$			2.25678i			0.239218i	−0.992821	+	0.119609i	$0.961836\pi$
$90$	−2.03865	−	4.05304i	−0.214893	−	0.427228i
$91$	2.64532	−	0.0479799i	0.277304	−	0.00502966i
$92$	−8.22223	−	6.10543i	−0.857227	−	0.636535i
$93$		−	14.4643i		−	1.49987i
$94$	1.78743	+	3.55358i	0.184359	+	0.366524i
$95$		−	17.1046i		−	1.75489i
$96$	−5.46659	−	5.75845i	−0.557931	−	0.587720i
$97$			5.13148i			0.521023i	0.965471	+	0.260511i	$0.0838912\pi$
$97$			5.13148i			0.521023i	−0.965471	+	0.260511i	$0.916109\pi$
$98$	−4.76614	−	8.67663i	−0.481453	−	0.876472i
$99$	−0.732821			−0.0736513
$100$	−5.60730	+	7.55140i	−0.560730	+	0.755140i
$101$	−16.0644			−1.59846			−0.799231	−	0.601023i	$-0.794760\pi$
$101$	−16.0644			−1.59846			−0.799231	+	0.601023i	$0.794760\pi$
$102$	−0.114341	−	0.227321i	−0.0113215	−	0.0225082i
$103$	−4.38089			−0.431662			−0.215831	−	0.976431i	$-0.569246\pi$
$103$	−4.38089			−0.431662			−0.215831	+	0.976431i	$0.569246\pi$
$104$	2.78636	+	0.485980i	0.273225	+	0.0476543i
$105$	0.209775	+	11.5657i	0.0204719	+	1.12869i
$106$	−10.7794	+	5.42197i	−1.04699	+	0.526629i
$107$	−2.75910			−0.266732			−0.133366	−	0.991067i	$-0.542579\pi$
$107$	−2.75910			−0.266732			−0.133366	+	0.991067i	$0.542579\pi$
$108$	−9.08258	−	6.74428i	−0.873971	−	0.648968i
$109$			14.4976i			1.38861i	0.719679	+	0.694307i	$0.244289\pi$
$109$			14.4976i			1.38861i	−0.719679	+	0.694307i	$0.755711\pi$
$110$	1.40849	+	2.80022i	0.134295	+	0.266991i
$111$	−11.4506			−1.08684
$112$	−3.24354	−	10.0737i	−0.306486	−	0.951875i
$113$	9.63185			0.906088			0.453044	−	0.891488i	$-0.350338\pi$
$113$	9.63185			0.906088			0.453044	+	0.891488i	$0.350338\pi$
$114$	−4.89791	−	9.73751i	−0.458731	−	0.912001i
$115$			15.9503i			1.48737i
$116$	11.3574	+	8.43344i	1.05451	+	0.783026i
$117$	1.02989			0.0952138
$118$	−9.32415	+	4.68999i	−0.858358	+	0.431749i
$119$	−0.00615058	−	0.339105i	−0.000563823	−	0.0310857i
$120$	−2.12477	+	12.1824i	−0.193964	+	1.11209i
$121$	−10.4937			−0.953973
$122$	−7.20153	−	14.3173i	−0.651996	−	1.29623i
$123$	0.141541			0.0127624
$124$	12.2871	−	16.5471i	1.10341	−	1.48597i
$125$	−0.925743			−0.0828010
$126$	−1.79373	−	3.41059i	−0.159798	−	0.303839i
$127$			12.5244i			1.11136i	0.831396	+	0.555681i	$0.187542\pi$
$127$			12.5244i			1.11136i	−0.831396	+	0.555681i	$0.812458\pi$
$128$	−1.36210	−	11.2314i	−0.120394	−	0.992726i
$129$			12.2669i			1.08004i
$130$	−1.97948	−	3.93539i	−0.173612	−	0.345156i
$131$		−	9.32611i		−	0.814826i	−0.913244	−	0.407413i	$-0.866431\pi$
$131$		−	9.32611i		−	0.814826i	0.913244	−	0.407413i	$-0.133569\pi$
$132$	1.60369	+	1.19082i	0.139583	+	0.103648i
$133$	−0.263466	−	14.5259i	−0.0228454	−	1.25955i
$134$	9.21808	+	18.3264i	0.796321	+	1.58316i
$135$			17.6192i			1.51642i
$136$	0.0622981	−	0.357186i	0.00534202	−	0.0306284i
$137$	3.48572			0.297806			0.148903	−	0.988852i	$-0.452426\pi$
$137$	3.48572			0.297806			0.148903	+	0.988852i	$0.452426\pi$
$138$	4.56736	+	9.08036i	0.388800	+	0.772971i
$139$		−	13.7408i		−	1.16548i	−0.812659	−	0.582740i	$-0.801981\pi$
$139$		−	13.7408i		−	1.16548i	0.812659	−	0.582740i	$-0.198019\pi$
$140$	−9.58480	+	13.4093i	−0.810064	+	1.13330i
$141$		−	3.94795i		−	0.332478i
$142$	10.6539	−	5.35883i	0.894052	−	0.449703i
$143$	−0.711549			−0.0595027
$144$	−1.19127	−	3.94358i	−0.0992727	−	0.328631i
$145$		−	22.0321i		−	1.82967i
$146$	−10.9018	+	5.48353i	−0.902237	+	0.453820i
$147$	0.356297	+	9.81877i	0.0293869	+	0.809838i
$148$	−13.0995	−	9.72701i	−1.07677	−	0.799555i
$149$			0.0763024i			0.00625094i	0.999995	+	0.00312547i	$0.000994869\pi$
$149$			0.0763024i			0.00625094i	−0.999995	+	0.00312547i	$0.999005\pi$
$150$	8.33951	−	4.19472i	0.680918	−	0.342498i
$151$			1.78506i			0.145266i	0.997359	+	0.0726329i	$0.0231402\pi$
$151$			1.78506i			0.145266i	−0.997359	+	0.0726329i	$0.976860\pi$
$152$	2.66859	−	15.3004i	0.216452	−	1.24102i
$153$		−	0.132023i		−	0.0106734i
$154$	1.23928	+	2.35636i	0.0998639	+	0.189881i
$155$	−32.0996			−2.57831
$156$	−2.25380	−	1.67356i	−0.180448	−	0.133992i
$157$	7.52175			0.600301			0.300151	−	0.953892i	$-0.402963\pi$
$157$	7.52175			0.600301			0.300151	+	0.953892i	$0.402963\pi$
$158$	20.6901	−	10.4070i	1.64602	−	0.827936i
$159$	11.9757			0.949734
$160$	−12.7794	+	12.1317i	−1.01030	+	0.959092i
$161$	0.245685	+	13.5456i	0.0193627	+	1.06754i
$162$	3.08184	+	6.12700i	0.242132	+	0.481382i
$163$	−5.68209			−0.445056			−0.222528	−	0.974926i	$-0.571431\pi$
$163$	−5.68209			−0.445056			−0.222528	+	0.974926i	$0.571431\pi$
$164$	0.161923	+	0.120236i	0.0126441	+	0.00938888i
$165$		−	3.11099i		−	0.242190i
$166$	−5.13962	+	2.58520i	−0.398912	+	0.200650i
$167$	9.75242			0.754665			0.377332	−	0.926078i	$-0.376841\pi$
$167$	9.75242			0.754665			0.377332	+	0.926078i	$0.376841\pi$
$168$	−1.61679	+	10.3784i	−0.124738	+	0.800714i
$169$	1.00000			0.0769231
$170$	−0.504480	+	0.253751i	−0.0386919	+	0.0194618i
$171$		−	5.65532i		−	0.432473i
$172$	−10.4205	+	14.0334i	−0.794555	+	1.07003i
$173$	2.54932			0.193821			0.0969106	−	0.995293i	$-0.469104\pi$
$173$	2.54932			0.193821			0.0969106	+	0.995293i	$0.469104\pi$
$174$	−6.30891	−	12.5427i	−0.478277	−	0.950861i
$175$	12.4404	−	0.225640i	0.940406	−	0.0170568i
$176$	0.823044	+	2.72460i	0.0620393	+	0.205374i
$177$	10.3589			0.778625
$178$	2.85120	−	1.43414i	0.213706	−	0.107493i
$179$	6.78232			0.506934			0.253467	−	0.967344i	$-0.418429\pi$
$179$	6.78232			0.506934			0.253467	+	0.967344i	$0.418429\pi$
$180$	−3.82506	+	5.15125i	−0.285103	+	0.383951i
$181$	−2.16014			−0.160562			−0.0802810	−	0.996772i	$-0.525582\pi$
$181$	−2.16014			−0.160562			−0.0802810	+	0.996772i	$0.525582\pi$
$182$	−1.74166	−	3.31159i	−0.129101	−	0.245471i
$183$			15.9063i			1.17582i
$184$	−2.48850	+	14.2678i	−0.183455	+	1.05184i
$185$			25.4116i			1.86829i
$186$	−18.2741	+	9.19174i	−1.33992	+	0.673971i
$187$			0.0912140i			0.00667023i
$188$	3.35370	−	4.51646i	0.244594	−	0.329397i
$189$	0.271393	+	14.9629i	0.0197409	+	1.08839i
$190$	−21.6098	+	10.8696i	−1.56774	+	0.788565i
$191$			9.22106i			0.667212i	0.942713	+	0.333606i	$0.108266\pi$
$191$			9.22106i			0.667212i	−0.942713	+	0.333606i	$0.891734\pi$
$192$	−3.80129	+	10.5658i	−0.274334	+	0.762524i
$193$	−13.3511			−0.961036			−0.480518	−	0.876985i	$-0.659551\pi$
$193$	−13.3511			−0.961036			−0.480518	+	0.876985i	$0.659551\pi$
$194$	6.48308	−	3.26095i	0.465458	−	0.234123i
$195$			4.37213i			0.313095i
$196$	−7.93322	+	11.5353i	−0.566659	+	0.823952i
$197$		−	24.6758i		−	1.75808i	−0.476751	−	0.879038i	$-0.658186\pi$
$197$		−	24.6758i		−	1.75808i	0.476751	−	0.879038i	$-0.341814\pi$
$198$	0.465693	+	0.925842i	0.0330953	+	0.0657967i
$199$	−16.0513			−1.13785			−0.568924	−	0.822390i	$-0.692640\pi$
$199$	−16.0513			−1.13785			−0.568924	+	0.822390i	$0.692640\pi$
$200$	13.1037	+	2.28547i	0.926573	+	0.161607i
$201$		−	20.3603i		−	1.43610i
$202$	10.2086	+	20.2956i	0.718273	+	1.42799i
$203$	−0.339366	−	18.7105i	−0.0238188	−	1.31322i
$204$	−0.214535	+	0.288916i	−0.0150205	+	0.0202282i
$205$		−	0.314114i		−	0.0219387i
$206$	2.78397	+	5.53479i	0.193968	+	0.385627i
$207$			5.27366i			0.366545i
$208$	−1.15669	−	3.82911i	−0.0802022	−	0.265501i
$209$			3.90723i			0.270269i
$210$	14.4787	−	7.61478i	0.999125	−	0.525470i
$211$	−8.24694			−0.567743			−0.283871	−	0.958862i	$-0.591619\pi$
$211$	−8.24694			−0.567743			−0.283871	+	0.958862i	$0.591619\pi$
$212$	13.7002	+	10.1731i	0.940932	+	0.698690i
$213$	−11.8362			−0.811004
$214$	1.75335	+	3.48583i	0.119856	+	0.238286i
$215$	27.2232			1.85661
$216$	−2.74889	+	15.7607i	−0.187038	+	1.07238i
$217$	−27.2602	+	0.494437i	−1.85054	+	0.0335646i
$218$	18.3161	−	9.21290i	1.24052	−	0.623977i
$219$	12.1116			0.818429
$220$	2.64271	−	3.55897i	0.178172	−	0.239946i
$221$		−	0.128191i		−	0.00862304i
$222$	7.27661	+	14.4666i	0.488374	+	0.970934i
$223$	11.0819			0.742096			0.371048	−	0.928614i	$-0.378999\pi$
$223$	11.0819			0.742096			0.371048	+	0.928614i	$0.378999\pi$
$224$	−10.6659	+	10.4995i	−0.712642	+	0.701528i
$225$	4.84339			0.322893
$226$	−6.12084	−	12.1688i	−0.407152	−	0.809458i
$227$			13.0912i			0.868896i	0.900697	+	0.434448i	$0.143056\pi$
$227$			13.0912i			0.868896i	−0.900697	+	0.434448i	$0.856944\pi$
$228$	−9.18979	+	12.3760i	−0.608609	+	0.819619i
$229$	−26.7429			−1.76722			−0.883610	−	0.468224i	$-0.844894\pi$
$229$	−26.7429			−1.76722			−0.883610	+	0.468224i	$0.844894\pi$
$230$	20.1515	−	10.1361i	1.32875	−	0.668353i
$231$	−0.0479192	−	2.64197i	−0.00315285	−	0.173829i
$232$	3.43737	−	19.7082i	0.225675	−	1.29390i
$233$	−20.2305			−1.32535			−0.662673	−	0.748909i	$-0.730578\pi$
$233$	−20.2305			−1.32535			−0.662673	+	0.748909i	$0.730578\pi$
$234$	−0.654477	−	1.30116i	−0.0427845	−	0.0850597i
$235$	−8.76145			−0.571534
$236$	11.8506	+	8.79969i	0.771410	+	0.572811i
$237$	−22.9863			−1.49312
$238$	−0.424515	+	0.223265i	−0.0275172	+	0.0144721i
$239$		−	13.7831i		−	0.891554i	−0.895144	−	0.445777i	$-0.852927\pi$
$239$		−	13.7831i		−	0.891554i	0.895144	−	0.445777i	$-0.147073\pi$
$240$	16.7414	−	5.05722i	1.08065	−	0.326442i
$241$		−	12.7451i		−	0.820981i	−0.911865	−	0.410490i	$-0.865358\pi$
$241$		−	12.7451i		−	0.820981i	0.911865	−	0.410490i	$-0.134642\pi$
$242$	6.66853	+	13.2577i	0.428669	+	0.852236i
$243$			10.1622i			0.651903i
$244$	−13.5120	+	18.1968i	−0.865018	+	1.16493i
$245$	21.7902	−	0.790708i	1.39212	−	0.0505165i
$246$	−0.0899467	−	0.178823i	−0.00573479	−	0.0114013i
$247$		−	5.49116i		−	0.349394i
$248$	−28.7137	−	5.00806i	−1.82332	−	0.318012i
$249$	5.71001			0.361857
$250$	0.588291	+	1.16958i	0.0372068	+	0.0739707i
$251$		−	22.4676i		−	1.41814i	−0.705137	−	0.709071i	$-0.749114\pi$
$251$		−	22.4676i		−	1.41814i	0.705137	−	0.709071i	$-0.250886\pi$
$252$	−3.16904	+	4.43355i	−0.199631	+	0.279287i
$253$		−	3.64354i		−	0.229068i
$254$	15.8233	−	7.95901i	0.992841	−	0.499393i
$255$	0.560467			0.0350978
$256$	−13.3241	+	8.85820i	−0.832758	+	0.553638i
$257$		−	14.3250i		−	0.893568i	−0.894642	−	0.446784i	$-0.852569\pi$
$257$		−	14.3250i		−	0.893568i	0.894642	−	0.446784i	$-0.147431\pi$
$258$	15.4980	−	7.79539i	0.964862	−	0.485320i
$259$	0.391419	+	21.5804i	0.0243216	+	1.34094i
$260$	−3.71403	+	5.00172i	−0.230334	+	0.310193i
$261$		−	7.28452i		−	0.450901i
$262$	−11.7826	+	5.92656i	−0.727929	+	0.366144i
$263$		−	13.3682i		−	0.824317i	−0.911112	−	0.412158i	$-0.864775\pi$
$263$		−	13.3682i		−	0.824317i	0.911112	−	0.412158i	$-0.135225\pi$
$264$	0.485364	−	2.78283i	0.0298721	−	0.171272i
$265$		−	26.5769i		−	1.63261i
$266$	−18.1845	+	9.56375i	−1.11496	+	0.586391i
$267$	−3.16762			−0.193855
$268$	17.2956	−	23.2921i	1.05650	−	1.42279i
$269$	13.2650			0.808782			0.404391	−	0.914586i	$-0.367483\pi$
$269$	13.2650			0.808782			0.404391	+	0.914586i	$0.367483\pi$
$270$	22.2600	−	11.1967i	1.35470	−	0.681407i
$271$	−14.9368			−0.907348			−0.453674	−	0.891168i	$-0.649887\pi$
$271$	−14.9368			−0.907348			−0.453674	+	0.891168i	$0.649887\pi$
$272$	−0.490856	+	0.148277i	−0.0297625	+	0.00899064i
$273$	0.0673448	+	3.71298i	0.00407590	+	0.224720i
$274$	−2.21511	−	4.40384i	−0.133820	−	0.266046i
$275$	−3.34628			−0.201788
$276$	8.56960	−	11.5408i	0.515830	−	0.694672i
$277$			2.07792i			0.124850i	0.998050	+	0.0624251i	$0.0198834\pi$
$277$			2.07792i			0.124850i	−0.998050	+	0.0624251i	$0.980117\pi$
$278$	−17.3601	+	8.73200i	−1.04119	+	0.523711i
$279$	−10.6132			−0.635393
$280$	23.0322	+	3.58803i	1.37644	+	0.214426i
$281$	7.66033			0.456977			0.228488	−	0.973547i	$-0.426622\pi$
$281$	7.66033			0.456977			0.228488	+	0.973547i	$0.426622\pi$
$282$	−4.98782	+	2.50884i	−0.297020	+	0.149399i
$283$		−	4.75444i		−	0.282622i	−0.989965	−	0.141311i	$-0.954868\pi$
$283$		−	4.75444i		−	0.282622i	0.989965	−	0.141311i	$-0.0451318\pi$
$284$	−13.5406	−	10.0546i	−0.803488	−	0.596631i
$285$	24.0081			1.42212
$286$	0.452175	+	0.898967i	0.0267377	+	0.0531570i
$287$	−0.00483836	−	0.266757i	−0.000285599	−	0.0157462i
$288$	−4.22526	+	4.01111i	−0.248976	+	0.236357i
$289$	16.9836			0.999033
$290$	−27.8353	+	14.0010i	−1.63454	+	0.822166i
$291$	−7.20257			−0.422222
$292$	13.8557	+	10.2886i	0.810844	+	0.602093i
$293$	−20.4685			−1.19578			−0.597890	−	0.801578i	$-0.703994\pi$
$293$	−20.4685			−1.19578			−0.597890	+	0.801578i	$0.703994\pi$
$294$	12.1786	−	6.68977i	0.710268	−	0.390155i
$295$		−	22.9889i		−	1.33847i
$296$	−3.96461	+	22.7311i	−0.230439	+	1.32122i
$297$		−	4.02479i		−	0.233542i
$298$	0.0964001	−	0.0484886i	0.00558431	−	0.00280887i
$299$			5.12058i			0.296131i
$300$	−10.5992	−	7.87043i	−0.611944	−	0.454400i
$301$	23.1190	−	0.419325i	1.33256	−	0.0241695i
$302$	2.25523	−	1.13437i	0.129774	−	0.0652755i
$303$		−	22.5480i		−	1.29535i
$304$	−21.0262	+	6.35159i	−1.20594	+	0.364289i
$305$	35.2998			2.02126
$306$	−0.166797	+	0.0838979i	−0.00953516	+	0.00479613i
$307$			0.696807i			0.0397689i	0.999802	+	0.0198844i	$0.00632983\pi$
$307$			0.696807i			0.0397689i	−0.999802	+	0.0198844i	$0.993670\pi$
$308$	2.18947	−	3.06311i	0.124757	−	0.174537i
$309$		−	6.14903i		−	0.349806i
$310$	20.3987	+	40.5545i	1.15857	+	2.30334i
$311$	21.4020			1.21360			0.606798	−	0.794856i	$-0.292454\pi$
$311$	21.4020			1.21360			0.606798	+	0.794856i	$0.292454\pi$
$312$	−0.682124	+	3.91095i	−0.0386176	+	0.221414i
$313$		−	3.05480i		−	0.172667i	−0.996266	−	0.0863337i	$-0.972485\pi$
$313$		−	3.05480i		−	0.172667i	0.996266	−	0.0863337i	$-0.0275151\pi$
$314$	−4.77992	−	9.50294i	−0.269746	−	0.536282i
$315$	8.48632	−	0.153922i	0.478150	−	0.00867253i
$316$	−26.2963	−	19.5263i	−1.47928	−	1.09844i
$317$		−	26.8368i		−	1.50730i	−0.657274	−	0.753652i	$-0.728291\pi$
$317$		−	26.8368i		−	1.50730i	0.657274	−	0.753652i	$-0.271709\pi$
$318$	−7.61031	−	15.1300i	−0.426765	−	0.848449i
$319$			5.03284i			0.281785i
$320$	23.4481	+	8.43597i	1.31079	+	0.471585i
$321$		−	3.87268i		−	0.216152i
$322$	16.9573	−	8.91832i	0.944991	−	0.496999i
$323$	−0.703916			−0.0391669
$324$	5.78237	−	7.78717i	0.321243	−	0.432620i
$325$	4.70280			0.260865
$326$	3.61085	+	7.17872i	0.199987	+	0.397592i
$327$	−20.3488			−1.12529
$328$	0.0490069	−	0.280981i	0.00270595	−	0.0155146i
$329$	−7.44055	+	0.134954i	−0.410211	+	0.00744028i
$330$	−3.93040	+	1.97697i	−0.216362	+	0.108829i
$331$	−17.6603			−0.970696			−0.485348	−	0.874321i	$-0.661307\pi$
$331$	−17.6603			−0.970696			−0.485348	+	0.874321i	$0.661307\pi$
$332$	6.53225	+	4.85053i	0.358504	+	0.266207i
$333$			8.40186i			0.460419i
$334$	−6.19746	−	12.3211i	−0.339110	−	0.674183i
$335$	−45.1843			−2.46868
$336$	14.1395	−	4.55265i	0.771372	−	0.248367i
$337$	1.87767			0.102283			0.0511416	−	0.998691i	$-0.483714\pi$
$337$	1.87767			0.102283			0.0511416	+	0.998691i	$0.483714\pi$
$338$	−0.635480	−	1.26339i	−0.0345655	−	0.0687196i
$339$			13.5193i			0.734268i
$340$	0.641174	+	0.476104i	0.0347725	+	0.0258204i
$341$	7.33257			0.397081
$342$	−7.14490	+	3.59384i	−0.386352	+	0.194333i
$343$	18.4929	−	1.00714i	0.998520	−	0.0543803i
$344$	24.3517	+	4.24727i	1.31295	+	0.228997i
$345$	−22.3879			−1.20532
$346$	−1.62004	−	3.22080i	−0.0870940	−	0.173151i
$347$	14.7147			0.789924			0.394962	−	0.918697i	$-0.370758\pi$
$347$	14.7147			0.789924			0.394962	+	0.918697i	$0.370758\pi$
$348$	−11.8372	+	15.9413i	−0.634542	+	0.854543i
$349$	1.50124			0.0803598			0.0401799	−	0.999192i	$-0.487207\pi$
$349$	1.50124			0.0803598			0.0401799	+	0.999192i	$0.487207\pi$
$350$	−8.19070	−	15.5737i	−0.437811	−	0.832452i
$351$			5.65638i			0.301915i
$352$	2.91921	−	2.77126i	0.155595	−	0.147708i
$353$			2.52907i			0.134609i	0.997732	+	0.0673043i	$0.0214398\pi$
$353$			2.52907i			0.134609i	−0.997732	+	0.0673043i	$0.978560\pi$
$354$	−6.58289	−	13.0874i	−0.349877	−	0.695589i
$355$			26.2674i			1.39413i
$356$	−3.62376	−	2.69083i	−0.192059	−	0.142613i
$357$	0.475969	−	0.00863299i	0.0251910	−	0.000456906i
$358$	−4.31002	−	8.56874i	−0.227792	−	0.452872i
$359$		−	27.9988i		−	1.47772i	−0.673858	−	0.738861i	$-0.735364\pi$
$359$		−	27.9988i		−	1.47772i	0.673858	−	0.738861i	$-0.264636\pi$
$360$	8.93880	+	1.55905i	0.471116	+	0.0821691i
$361$	−11.1528			−0.586992
$362$	1.37273	+	2.72911i	0.0721489	+	0.143439i
$363$		−	14.7290i		−	0.773072i
$364$	−3.07705	+	4.30485i	−0.161281	+	0.225636i
$365$		−	26.8786i		−	1.40689i
$366$	20.0959	−	10.1081i	1.05043	−	0.528359i
$367$	−13.6580			−0.712944			−0.356472	−	0.934306i	$-0.616020\pi$
$367$	−13.6580			−0.712944			−0.356472	+	0.934306i	$0.616020\pi$
$368$	19.6073	−	5.92294i	1.02210	−	0.308755i
$369$		−	0.103856i		−	0.00540653i
$370$	32.1048	−	16.1485i	1.66905	−	0.839522i
$371$	−0.409369	−	22.5701i	−0.0212534	−	1.17178i
$372$	23.2256	+	17.2462i	1.20419	+	0.894173i
$373$			12.4286i			0.643528i	0.946820	+	0.321764i	$0.104276\pi$
$373$			12.4286i			0.643528i	−0.946820	+	0.321764i	$0.895724\pi$
$374$	0.115239	−	0.0579646i	0.00595888	−	0.00299728i
$375$		−	1.29938i		−	0.0670995i
$376$	−7.83728	−	1.36693i	−0.404177	−	0.0704939i
$377$		−	7.07307i		−	0.364282i
$378$	18.7316	−	9.85150i	0.963449	−	0.506707i
$379$	10.5288			0.540826			0.270413	−	0.962744i	$-0.412840\pi$
$379$	10.5288			0.540826			0.270413	+	0.962744i	$0.412840\pi$
$380$	27.4652	+	20.3943i	1.40894	+	1.04621i
$381$	−17.5793			−0.900616
$382$	11.6498	−	5.85979i	0.596057	−	0.299813i
$383$	7.90669			0.404013			0.202007	−	0.979384i	$-0.435254\pi$
$383$	7.90669			0.404013			0.202007	+	0.979384i	$0.435254\pi$
$384$	15.7645	−	1.91185i	0.804477	−	0.0975636i
$385$	−5.86315	+	0.106344i	−0.298814	+	0.00541979i
$386$	8.48438	+	16.8678i	0.431844	+	0.858546i
$387$	9.00086			0.457540
$388$	−8.23974	−	6.11842i	−0.418309	−	0.310616i
$389$			9.18004i			0.465446i	0.972543	+	0.232723i	$0.0747636\pi$
$389$			9.18004i			0.465446i	−0.972543	+	0.232723i	$0.925236\pi$
$390$	5.52373	−	2.77840i	0.279705	−	0.140690i
$391$	0.656411			0.0331961
$392$	19.6151	+	2.69232i	0.990711	+	0.135983i
$393$	13.0902			0.660312
$394$	−31.1752	+	15.6810i	−1.57059	+	0.789995i
$395$			51.0120i			2.56669i
$396$	0.873765	−	1.17671i	0.0439083	−	0.0591318i
$397$	24.0822			1.20865			0.604325	−	0.796738i	$-0.293443\pi$
$397$	24.0822			1.20865			0.604325	+	0.796738i	$0.293443\pi$
$398$	10.2003	+	20.2792i	0.511295	+	1.01650i
$399$	20.3886	−	0.369801i	1.02070	−	0.0185132i
$400$	−5.43970	−	18.0075i	−0.271985	−	0.900377i
$401$	−28.7217			−1.43429			−0.717146	−	0.696923i	$-0.754552\pi$
$401$	−28.7217			−1.43429			−0.717146	+	0.696923i	$0.754552\pi$
$402$	−25.7230	+	12.9385i	−1.28295	+	0.645316i
$403$	−10.3051			−0.513333
$404$	19.1540	−	25.7949i	0.952949	−	1.28334i
$405$	−15.1063			−0.750637
$406$	−23.4231	+	12.3189i	−1.16247	+	0.611377i
$407$		−	5.80480i		−	0.287733i
$408$	0.501348	+	0.0874419i	0.0248204	+	0.00432902i
$409$			17.5653i			0.868550i	0.900780	+	0.434275i	$0.142995\pi$
$409$			17.5653i			0.868550i	−0.900780	+	0.434275i	$0.857005\pi$
$410$	−0.396850	+	0.199613i	−0.0195990	+	0.00985819i
$411$			4.89258i			0.241333i
$412$	5.22347	−	7.03449i	0.257342	−	0.346565i
$413$	−0.354103	−	19.5231i	−0.0174243	−	0.960667i
$414$	6.66271	−	3.35130i	0.327454	−	0.164708i
$415$		−	12.6719i		−	0.622038i
$416$	−4.10262	+	3.89468i	−0.201147	+	0.190952i
$417$	19.2867			0.944471
$418$	4.93637	−	2.48297i	0.241446	−	0.121446i
$419$		−	30.2826i		−	1.47940i	−0.672935	−	0.739702i	$-0.734967\pi$
$419$		−	30.2826i		−	1.47940i	0.672935	−	0.739702i	$-0.265033\pi$
$420$	−18.8214	−	13.4533i	−0.918390	−	0.656452i
$421$			29.1955i			1.42290i	0.702736	+	0.711450i	$0.251961\pi$
$421$			29.1955i			1.42290i	−0.702736	+	0.711450i	$0.748039\pi$
$422$	5.24076	+	10.4191i	0.255116	+	0.507196i
$423$	−2.89681			−0.140848
$424$	4.14643	−	23.7735i	0.201368	−	1.15454i
$425$		−	0.602856i		−	0.0292428i
$426$	7.52167	+	14.9538i	0.364426	+	0.724514i
$427$	29.9779	−	0.543730i	1.45073	−	0.0263129i
$428$	3.28976	−	4.43034i	0.159016	−	0.214149i
$429$		−	0.998733i		−	0.0482193i
$430$	−17.2998	−	34.3937i	−0.834271	−	1.65861i
$431$			25.5623i			1.23129i	0.788023	+	0.615645i	$0.211105\pi$
$431$			25.5623i			1.23129i	−0.788023	+	0.615645i	$0.788895\pi$
$432$	21.6589	−	6.54269i	1.04206	−	0.314786i
$433$			22.4517i			1.07896i	0.841998	+	0.539481i	$0.181379\pi$
$433$			22.4517i			1.07896i	−0.841998	+	0.539481i	$0.818621\pi$
$434$	17.9480	+	34.1262i	0.861530	+	1.63811i
$435$	30.9244			1.48271
$436$	−23.2791	−	17.2859i	−1.11486	−	0.827844i
$437$	28.1179			1.34506
$438$	−7.69670	−	15.3018i	−0.367763	−	0.731147i
$439$	−22.3455			−1.06649			−0.533245	−	0.845961i	$-0.679028\pi$
$439$	−22.3455			−1.06649			−0.533245	+	0.845961i	$0.679028\pi$
$440$	−6.17577	−	1.07714i	−0.294418	−	0.0513506i
$441$	7.20452	−	0.261433i	0.343073	−	0.0124492i
$442$	−0.161955	+	0.0814626i	−0.00770344	+	0.00387478i
$443$	21.6237			1.02737			0.513686	−	0.857978i	$-0.328279\pi$
$443$	21.6237			1.02737			0.513686	+	0.857978i	$0.328279\pi$
$444$	13.6529	−	18.3865i	0.647937	−	0.872582i
$445$			7.02971i			0.333240i
$446$	−7.04229	−	14.0008i	−0.333462	−	0.662955i
$447$	−0.107098			−0.00506558
$448$	20.0429	+	6.80296i	0.946940	+	0.321410i
$449$	−2.89960			−0.136840			−0.0684202	−	0.997657i	$-0.521796\pi$
$449$	−2.89960			−0.136840			−0.0684202	+	0.997657i	$0.521796\pi$
$450$	−3.07788	−	6.11912i	−0.145093	−	0.288458i
$451$			0.0717536i			0.00337874i
$452$	−11.4843	+	15.4661i	−0.540178	+	0.727463i
$453$	−2.50551			−0.117719
$454$	16.5394	−	8.31921i	0.776232	−	0.390440i
$455$	8.23998	−	0.149454i	0.386296	−	0.00700652i
$456$	21.4757	+	3.74565i	1.00569	+	0.175406i
$457$	10.5445			0.493253			0.246626	−	0.969111i	$-0.420678\pi$
$457$	10.5445			0.493253			0.246626	+	0.969111i	$0.420678\pi$
$458$	16.9946	+	33.7868i	0.794104	+	1.57875i
$459$	0.725095			0.0338445
$460$	−25.6117	−	19.0180i	−1.19415	−	0.886719i
$461$	14.9774			0.697566			0.348783	−	0.937203i	$-0.386595\pi$
$461$	14.9774			0.697566			0.348783	+	0.937203i	$0.386595\pi$
$462$	−3.30739	+	1.73946i	−0.153874	+	0.0809268i
$463$		−	7.38989i		−	0.343438i	−0.985146	−	0.171719i	$-0.945068\pi$
$463$		−	7.38989i		−	0.343438i	0.985146	−	0.171719i	$-0.0549320\pi$
$464$	−27.0836	+	8.18138i	−1.25732	+	0.379811i
$465$		−	45.0552i		−	2.08938i
$466$	12.8561	+	25.5591i	0.595547	+	1.18400i
$467$			19.0398i			0.881058i	0.897738	+	0.440529i	$0.145209\pi$
$467$			19.0398i			0.881058i	−0.897738	+	0.440529i	$0.854791\pi$
$468$	−1.22798	+	1.65373i	−0.0567632	+	0.0764435i
$469$	−38.3722	+	0.695983i	−1.77186	+	0.0321375i
$470$	5.56772	+	11.0692i	0.256820	+	0.510583i
$471$			10.5576i			0.486467i
$472$	3.58665	−	20.5640i	0.165089	−	0.946536i
$473$	−6.21865			−0.285934
$474$	14.6073	+	29.0407i	0.670936	+	1.33388i
$475$		−	25.8239i		−	1.18488i
$476$	0.551842	+	0.394449i	0.0252937	+	0.0180796i
$477$		−	8.78716i		−	0.402336i
$478$	−17.4135	+	8.75887i	−0.796474	+	0.400622i
$479$	−6.93161			−0.316713			−0.158357	−	0.987382i	$-0.550620\pi$
$479$	−6.93161			−0.316713			−0.158357	+	0.987382i	$0.550620\pi$
$480$	−17.0281	−	17.9372i	−0.777221	−	0.818717i
$481$			8.15798i			0.371972i
$482$	−16.1020	+	8.09922i	−0.733427	+	0.368909i
$483$	−19.0126	+	0.344845i	−0.865103	+	0.0156910i
$484$	12.5120	−	16.8500i	0.568726	−	0.765908i
$485$			15.9842i			0.725806i
$486$	12.8388	−	6.45785i	0.582381	−	0.292934i
$487$		−	36.0554i		−	1.63383i	−0.576760	−	0.816914i	$-0.695683\pi$
$487$		−	36.0554i		−	1.63383i	0.576760	−	0.816914i	$-0.304317\pi$
$488$	31.5763	+	5.50734i	1.42939	+	0.249305i
$489$		−	7.97540i		−	0.360660i
$490$	−14.8462	−	27.0271i	−0.670683	−	1.22096i
$491$	−28.4173			−1.28245			−0.641227	−	0.767352i	$-0.721574\pi$
$491$	−28.4173			−1.28245			−0.641227	+	0.767352i	$0.721574\pi$
$492$	−0.168764	+	0.227276i	−0.00760848	+	0.0102464i
$493$	−0.906702			−0.0408358
$494$	−6.93750	+	3.48952i	−0.312133	+	0.157001i
$495$	−2.28269			−0.102599
$496$	11.9198	+	39.4593i	0.535216	+	1.77177i
$497$	0.404602	+	22.3072i	0.0181489	+	1.00062i
$498$	−3.62860	−	7.21400i	−0.162601	−	0.323267i
$499$	16.1378			0.722429			0.361214	−	0.932483i	$-0.382362\pi$
$499$	16.1378			0.722429			0.361214	+	0.932483i	$0.382362\pi$
$500$	1.10379	−	1.48649i	0.0493631	−	0.0664777i
$501$			13.6885i			0.611559i
$502$	−28.3855	+	14.2777i	−1.26690	+	0.637245i
$503$	15.8090			0.704888			0.352444	−	0.935833i	$-0.385351\pi$
$503$	15.8090			0.704888			0.352444	+	0.935833i	$0.385351\pi$
$504$	7.61518	+	1.18632i	0.339207	+	0.0528427i
$505$	−50.0394			−2.22672
$506$	−4.60323	+	2.31540i	−0.204639	+	0.102932i
$507$			1.40360i			0.0623363i
$508$	−20.1107	−	14.9332i	−0.892270	−	0.662556i
$509$	−12.3255			−0.546320			−0.273160	−	0.961969i	$-0.588069\pi$
$509$	−12.3255			−0.546320			−0.273160	+	0.961969i	$0.588069\pi$
$510$	−0.356165	−	0.708091i	−0.0157713	−	0.0313548i
$511$	−0.414017	−	22.8263i	−0.0183150	−	1.00978i
$512$	19.6586	+	11.2044i	0.868796	+	0.495170i
$513$	31.0601			1.37134
$514$	−18.0981	+	9.10324i	−0.798273	+	0.401527i
$515$	−13.6462			−0.601322
$516$	−19.6973	−	14.6262i	−0.867125	−	0.643884i
$517$	2.00139			0.0880211
$518$	27.0159	−	14.2084i	1.18701	−	0.624283i
$519$			3.57824i			0.157067i
$520$	8.67934	+	1.51379i	0.380614	+	0.0663843i
$521$			32.9577i			1.44390i	0.691945	+	0.721950i	$0.256754\pi$
$521$			32.9577i			1.44390i	−0.691945	+	0.721950i	$0.743246\pi$
$522$	−9.20322	+	4.62917i	−0.402814	+	0.202613i
$523$		−	2.21195i		−	0.0967220i	−0.998830	−	0.0483610i	$-0.984600\pi$
$523$		−	2.21195i		−	0.0967220i	0.998830	−	0.0483610i	$-0.0153998\pi$
$524$	14.9752	+	11.1198i	0.654193	+	0.485771i
$525$	0.316710	+	17.4614i	0.0138223	+	0.762078i
$526$	−16.8893	+	8.49520i	−0.736407	+	0.370408i
$527$			1.32102i			0.0575444i
$528$	−3.82426	+	1.15523i	−0.166429	+	0.0502748i
$529$	−3.22035			−0.140015
$530$	−33.5771	+	16.8891i	−1.45850	+	0.733615i
$531$		−	7.60087i		−	0.329850i
$532$	23.6386	+	16.8966i	1.02487	+	0.732560i
$533$		−	0.100841i		−	0.00436792i
$534$	2.01296	+	4.00196i	0.0871093	+	0.173182i
$535$	−8.59440			−0.371568
$536$	−40.4182	−	7.04948i	−1.74580	−	0.304491i
$537$			9.51969i			0.410805i
$538$	−8.42965	−	16.7589i	−0.363428	−	0.722529i
$539$	−4.97757	+	0.180623i	−0.214399	+	0.00777997i
$540$	−28.2916	−	21.0080i	−1.21748	−	0.904039i
$541$			11.3965i			0.489976i	0.969526	+	0.244988i	$0.0787840\pi$
$541$			11.3965i			0.489976i	−0.969526	+	0.244988i	$0.921216\pi$
$542$	9.49205	+	18.8711i	0.407719	+	0.810584i
$543$		−	3.03198i		−	0.130115i
$544$	0.499262	+	0.525918i	0.0214057	+	0.0225485i
$545$			45.1589i			1.93440i
$546$	4.64816	−	2.44460i	0.198923	−	0.104619i
$547$	20.8868			0.893053			0.446527	−	0.894770i	$-0.352661\pi$
$547$	20.8868			0.893053			0.446527	+	0.894770i	$0.352661\pi$
$548$	−4.15614	+	5.59711i	−0.177541	+	0.239097i
$549$	11.6712			0.498115
$550$	2.12649	+	4.22767i	0.0906739	+	0.180268i
$551$	−38.8394			−1.65461
$552$	−20.0263	−	3.49287i	−0.852378	−	0.148666i
$553$	0.785748	+	43.3213i	0.0334134	+	1.84221i
$554$	2.62523	−	1.32048i	0.111535	−	0.0561017i
$555$	−35.6678			−1.51401
$556$	22.0639	+	16.3836i	0.935719	+	0.694819i
$557$			36.5235i			1.54755i	0.633460	+	0.773776i	$0.281634\pi$
$557$			36.5235i			1.54755i	−0.633460	+	0.773776i	$0.718366\pi$
$558$	6.74444	+	13.4086i	0.285515	+	0.567631i
$559$	8.73959			0.369645
$560$	−10.1034	−	31.3789i	−0.426947	−	1.32600i
$561$	−0.128028			−0.00540536
$562$	−4.86798	−	9.67802i	−0.205343	−	0.408242i
$563$		−	21.2293i		−	0.894707i	−0.894357	−	0.447354i	$-0.852367\pi$
$563$		−	21.2293i		−	0.894707i	0.894357	−	0.447354i	$-0.147633\pi$
$564$	6.33932	+	4.70727i	0.266934	+	0.198212i
$565$	30.0025			1.26222
$566$	−6.00674	+	3.02135i	−0.252482	+	0.126997i
$567$	−12.8288	+	0.232685i	−0.538759	+	0.00977185i
$568$	−4.09814	+	23.4966i	−0.171954	+	0.985897i
$569$	−18.2538			−0.765239			−0.382619	−	0.923906i	$-0.624978\pi$
$569$	−18.2538			−0.765239			−0.382619	+	0.923906i	$0.624978\pi$
$570$	−15.2566	−	30.3317i	−0.639031	−	1.27045i
$571$	4.06655			0.170180			0.0850899	−	0.996373i	$-0.472882\pi$
$571$	4.06655			0.170180			0.0850899	+	0.996373i	$0.472882\pi$
$572$	0.848402	−	1.14255i	0.0354735	−	0.0477724i
$573$	−12.9427			−0.540690
$574$	−0.333945	+	0.175632i	−0.0139386	+	0.00733072i
$575$			24.0811i			1.00425i
$576$	7.75269	+	2.78920i	0.323029	+	0.116217i
$577$			32.8326i			1.36684i	0.730025	+	0.683420i	$0.239508\pi$
$577$			32.8326i			1.36684i	−0.730025	+	0.683420i	$0.760492\pi$
$578$	−10.7927	−	21.4569i	−0.448918	−	0.892491i
$579$		−	18.7397i		−	0.778796i
$580$	35.3775	+	26.2696i	1.46897	+	1.09079i
$581$	−0.195187	−	10.7614i	−0.00809774	−	0.446459i
$582$	4.57709	+	9.09968i	0.189726	+	0.377194i
$583$			6.07100i			0.251435i
$584$	4.19350	−	24.0434i	0.173528	−	0.994923i
$585$	3.20805			0.132637
$586$	13.0073	+	25.8597i	0.537326	+	1.06826i
$587$		−	34.6043i		−	1.42827i	−0.700008	−	0.714135i	$-0.746820\pi$
$587$		−	34.6043i		−	1.42827i	0.700008	−	0.714135i	$-0.253180\pi$
$588$	−16.1910	−	11.1351i	−0.667707	−	0.459204i
$589$			56.5869i			2.33162i
$590$	−29.0441	+	14.6090i	−1.19573	+	0.601443i
$591$	34.6350			1.42469
$592$	31.2378	−	9.43628i	1.28386	−	0.387829i
$593$		−	30.7831i		−	1.26411i	−0.774923	−	0.632056i	$-0.782211\pi$
$593$		−	30.7831i		−	1.26411i	0.774923	−	0.632056i	$-0.217789\pi$
$594$	−5.08490	+	2.55767i	−0.208636	+	0.104943i
$595$	−0.0191587	−	1.05629i	−0.000785428	−	0.0433036i
$596$	−0.122521	−	0.0909777i	−0.00501864	−	0.00372659i
$597$		−	22.5297i		−	0.922080i
$598$	6.46931	−	3.25403i	0.264550	−	0.133067i
$599$			18.1200i			0.740363i	0.928959	+	0.370181i	$0.120704\pi$
$599$			18.1200i			0.740363i	−0.928959	+	0.370181i	$0.879296\pi$
$600$	−3.20789	+	18.3924i	−0.130962	+	0.750868i
$601$			2.44947i			0.0999158i	0.998751	+	0.0499579i	$0.0159087\pi$
$601$			2.44947i			0.0999158i	−0.998751	+	0.0499579i	$0.984091\pi$
$602$	−15.2214	−	28.9419i	−0.620379	−	1.17958i
$603$	−14.9393			−0.608377
$604$	−2.86631	−	2.12838i	−0.116628	−	0.0866025i
$605$	−32.6872			−1.32892
$606$	−28.4870	+	14.3288i	−1.15721	+	0.582067i
$607$	17.5171			0.710998			0.355499	−	0.934677i	$-0.384311\pi$
$607$	17.5171			0.710998			0.355499	+	0.934677i	$0.384311\pi$
$608$	21.3863	+	22.5281i	0.867329	+	0.913636i
$609$	26.2622	−	0.476335i	1.06420	−	0.0193021i
$610$	−22.4323	−	44.5975i	−0.908257	−	1.80570i
$611$	−2.81273			−0.113791
$612$	0.211992	+	0.157415i	0.00856928	+	0.00636313i
$613$			12.6633i			0.511465i	0.966748	+	0.255732i	$0.0823166\pi$
$613$			12.6633i			0.511465i	−0.966748	+	0.255732i	$0.917683\pi$
$614$	0.880342	−	0.442806i	0.0355277	−	0.0178702i
$615$	0.440892			0.0177785
$616$	−5.26129	−	0.819620i	−0.211983	−	0.0330234i
$617$	−39.5883			−1.59376			−0.796882	−	0.604135i	$-0.793519\pi$
$617$	−39.5883			−1.59376			−0.796882	+	0.604135i	$0.793519\pi$
$618$	−7.76865	+	3.90759i	−0.312501	+	0.157186i
$619$		−	14.7549i		−	0.593049i	−0.955025	−	0.296525i	$-0.904172\pi$
$619$		−	14.7549i		−	0.593049i	0.955025	−	0.296525i	$-0.0958277\pi$
$620$	38.2734	−	51.5431i	1.53710	−	2.07002i
$621$	−28.9639			−1.16228
$622$	−13.6005	−	27.0392i	−0.545332	−	1.08417i
$623$	0.108280	+	5.96989i	0.00433815	+	0.239179i
$624$	5.37455	−	1.62354i	0.215154	−	0.0649936i
$625$	−26.3977			−1.05591
$626$	−3.85942	+	1.94126i	−0.154253	+	0.0775884i
$627$	−5.48420			−0.219018
$628$	−8.96842	+	12.0778i	−0.357879	+	0.481959i
$629$	1.04578			0.0416979
$630$	−5.58735	−	10.6237i	−0.222605	−	0.423260i
$631$		−	24.2732i		−	0.966303i	−0.875537	−	0.483151i	$-0.839492\pi$
$631$		−	24.2732i		−	0.966303i	0.875537	−	0.483151i	$-0.160508\pi$
$632$	−7.95870	+	45.6312i	−0.316580	+	1.81511i
$633$		−	11.5754i		−	0.460082i
$634$	−33.9054	+	17.0542i	−1.34656	+	0.677310i
$635$			39.0127i			1.54817i
$636$	−14.2790	+	19.2296i	−0.566198	+	0.762505i
$637$	6.99540	−	0.253844i	0.277168	−	0.0100577i
$638$	6.35846	−	3.19827i	0.251734	−	0.126621i
$639$			8.68482i			0.343566i
$640$	−4.24285	−	34.9851i	−0.167713	−	1.38291i
$641$	−7.40358			−0.292424			−0.146212	−	0.989253i	$-0.546708\pi$
$641$	−7.40358			−0.292424			−0.146212	+	0.989253i	$0.546708\pi$
$642$	−4.89272	+	2.46101i	−0.193100	+	0.0971283i
$643$		−	33.4236i		−	1.31810i	−0.752101	−	0.659048i	$-0.770959\pi$
$643$		−	33.4236i		−	1.31810i	0.752101	−	0.659048i	$-0.229041\pi$
$644$	−22.0433	−	15.7563i	−0.868630	−	0.620885i
$645$			38.2107i			1.50454i
$646$	0.447324	+	0.889323i	0.0175997	+	0.0349900i
$647$	−34.4335			−1.35372			−0.676861	−	0.736111i	$-0.736660\pi$
$647$	−34.4335			−1.35372			−0.676861	+	0.736111i	$0.736660\pi$
$648$	−13.5128	−	2.35682i	−0.530834	−	0.0925848i
$649$			5.25140i			0.206136i
$650$	−2.98854	−	5.94150i	−0.117220	−	0.233045i
$651$	−0.693994	−	38.2625i	−0.0271998	−	1.49963i
$652$	6.77493	−	9.12386i	0.265327	−	0.357318i
$653$		−	3.01244i		−	0.117886i	−0.998261	−	0.0589430i	$-0.981227\pi$
$653$		−	3.01244i		−	0.117886i	0.998261	−	0.0589430i	$-0.0187730\pi$
$654$	12.9313	+	25.7086i	0.505653	+	1.00529i
$655$		−	29.0502i		−	1.13509i
$656$	−0.386132	+	0.116643i	−0.0150759	+	0.00455413i
$657$		−	8.88692i		−	0.346712i
$658$	4.89882	+	9.31459i	0.190976	+	0.363120i
$659$	49.8643			1.94244			0.971218	−	0.238191i	$-0.0765544\pi$
$659$	49.8643			1.94244			0.971218	+	0.238191i	$0.0765544\pi$
$660$	4.99538	+	3.70933i	0.194445	+	0.144385i
$661$	13.2329			0.514701			0.257350	−	0.966318i	$-0.417151\pi$
$661$	13.2329			0.514701			0.257350	+	0.966318i	$0.417151\pi$
$662$	11.2227	+	22.3119i	0.436184	+	0.867176i
$663$	0.179929			0.00698787
$664$	1.97702	−	11.3352i	0.0767232	−	0.439892i
$665$	−0.820677	−	45.2471i	−0.0318245	−	1.75461i
$666$	10.6149	−	5.33921i	0.411318	−	0.206890i
$667$	36.2182			1.40238
$668$	−11.6281	+	15.6597i	−0.449905	+	0.605891i
$669$			15.5545i			0.601373i
$670$	28.7137	+	57.0856i	1.10931	+	2.20541i
$671$	−8.06358			−0.311291
$672$	−14.7371	−	14.9706i	−0.568498	−	0.577505i
$673$	44.0069			1.69634			0.848170	−	0.529724i	$-0.177704\pi$
$673$	44.0069			1.69634			0.848170	+	0.529724i	$0.177704\pi$
$674$	−1.19322	−	2.37224i	−0.0459612	−	0.0913752i
$675$			26.6008i			1.02387i
$676$	−1.19233	+	1.60572i	−0.0458589	+	0.0617586i
$677$	5.69662			0.218939			0.109470	−	0.993990i	$-0.465085\pi$
$677$	5.69662			0.218939			0.109470	+	0.993990i	$0.465085\pi$
$678$	17.0802	−	8.59124i	0.655961	−	0.329945i
$679$	0.246208	+	13.5744i	0.00944860	+	0.520937i
$680$	0.194054	−	1.11261i	0.00744165	−	0.0426667i
$681$	−18.3749			−0.704128
$682$	−4.65970	−	9.26393i	−0.178429	−	0.354734i
$683$	21.1458			0.809121			0.404560	−	0.914511i	$-0.367425\pi$
$683$	21.1458			0.809121			0.404560	+	0.914511i	$0.367425\pi$
$684$	9.08088	+	6.74301i	0.347216	+	0.257825i
$685$	10.8578			0.414855
$686$	−13.0242	−	22.7238i	−0.497268	−	0.867597i
$687$		−	37.5364i		−	1.43210i
$688$	−10.1090	−	33.4648i	−0.385403	−	1.27583i
$689$		−	8.53210i		−	0.325047i
$690$	14.2270	+	28.2847i	0.541614	+	1.07678i
$691$			32.1264i			1.22215i	0.791575	+	0.611073i	$0.209262\pi$
$691$			32.1264i			1.22215i	−0.791575	+	0.611073i	$0.790738\pi$
$692$	−3.03963	+	4.09350i	−0.115550	+	0.155612i
$693$	−1.93854	+	0.0351607i	−0.0736391	+	0.00133564i
$694$	−9.35087	−	18.5904i	−0.354954	−	0.705683i
$695$		−	42.8017i		−	1.62356i
$696$	27.6625	+	4.82471i	1.04854	+	0.182880i
$697$	−0.0129269			−0.000489642
$698$	−0.954010	−	1.89666i	−0.0361098	−	0.0717898i
$699$		−	28.3956i		−	1.07402i
$700$	−14.4708	+	20.2449i	−0.546944	+	0.765185i
$701$			27.9007i			1.05379i	0.849929	+	0.526897i	$0.176645\pi$
$701$			27.9007i			1.05379i	−0.849929	+	0.526897i	$0.823355\pi$
$702$	7.14624	−	3.59451i	0.269717	−	0.135666i
$703$	44.7968			1.68954
$704$	−5.35629	−	1.92704i	−0.201873	−	0.0726281i
$705$		−	12.2976i		−	0.463155i
$706$	3.19521	−	1.60717i	0.120253	−	0.0604867i
$707$	−42.4953	+	0.770767i	−1.59820	+	0.0289877i
$708$	−12.3513	+	16.6336i	−0.464190	+	0.625128i
$709$			9.64782i			0.362331i	0.983453	+	0.181166i	$0.0579870\pi$
$709$			9.64782i			0.362331i	−0.983453	+	0.181166i	$0.942013\pi$
$710$	33.1861	−	16.6924i	1.24545	−	0.626454i
$711$			16.8662i			0.632531i
$712$	−1.09675	+	6.28820i	−0.0411024	+	0.235660i
$713$		−	52.7680i		−	1.97618i
$714$	−0.313376	−	0.595851i	−0.0117278	−	0.0222992i
$715$	−2.21643			−0.0828897
$716$	−8.08677	+	10.8905i	−0.302217	+	0.406998i
$717$	19.3460			0.722490
$718$	−35.3736	+	17.7927i	−1.32013	+	0.664017i
$719$	7.10932			0.265133			0.132566	−	0.991174i	$-0.457678\pi$
$719$	7.10932			0.265133			0.132566	+	0.991174i	$0.457678\pi$
$720$	−3.71073	−	12.2840i	−0.138291	−	0.457797i
$721$	−11.5888	+	0.210195i	−0.431591	+	0.00782806i
$722$	7.08741	+	14.0904i	0.263766	+	0.524392i
$723$	17.8890			0.665299
$724$	2.57560	−	3.46859i	0.0957215	−	0.128909i
$725$		−	33.2633i		−	1.23537i
$726$	−18.6085	+	9.35998i	−0.690628	+	0.347381i
$727$	31.7118			1.17613			0.588063	−	0.808815i	$-0.299891\pi$
$727$	31.7118			1.17613			0.588063	+	0.808815i	$0.299891\pi$
$728$	7.39413	+	1.15188i	0.274045	+	0.0426916i
$729$	−28.8126			−1.06713
$730$	−33.9583	+	17.0808i	−1.25685	+	0.632189i
$731$		−	1.12033i		−	0.0414371i
$732$	−25.5410	−	18.9655i	−0.944024	−	0.700986i
$733$	−3.95576			−0.146109			−0.0730546	−	0.997328i	$-0.523275\pi$
$733$	−3.95576			−0.146109			−0.0730546	+	0.997328i	$0.523275\pi$
$734$	8.67940	+	17.2555i	0.320363	+	0.636912i
$735$	1.10984	+	30.5848i	0.0409371	+	1.12814i
$736$	−19.9430	−	21.0078i	−0.735110	−	0.774357i
$737$	10.3215			0.380198
$738$	−0.131211	+	0.0659984i	−0.00482995	+	0.00242943i
$739$	4.79871			0.176523			0.0882617	−	0.996097i	$-0.471869\pi$
$739$	4.79871			0.176523			0.0882617	+	0.996097i	$0.471869\pi$
$740$	−40.8039	−	30.2990i	−1.49998	−	1.11381i
$741$	7.70742			0.283139
$742$	−28.2548	+	14.8600i	−1.03727	+	0.545529i
$743$			11.6943i			0.429021i	0.976722	+	0.214511i	$0.0688157\pi$
$743$			11.6943i			0.429021i	−0.976722	+	0.214511i	$0.931184\pi$
$744$	7.02934	−	40.3027i	0.257708	−	1.47757i
$745$			0.237677i			0.00870781i
$746$	15.7022	−	7.89812i	0.574899	−	0.289171i
$747$		−	4.18972i		−	0.153294i
$748$	−0.146464	−	0.108757i	−0.00535527	−	0.00397656i
$749$	−7.29868	+	0.132381i	−0.266688	+	0.00483710i
$750$	−1.64163	+	0.825728i	−0.0599437	+	0.0301513i
$751$			4.77337i			0.174183i	0.996200	+	0.0870914i	$0.0277572\pi$
$751$			4.77337i			0.174183i	−0.996200	+	0.0870914i	$0.972243\pi$
$752$	3.25346	+	10.7702i	0.118641	+	0.392750i
$753$	31.5356			1.14922
$754$	−8.93608	+	4.49479i	−0.325433	+	0.163691i
$755$			5.56033i			0.202361i
$756$	−24.3499	−	17.4050i	−0.885596	−	0.633012i
$757$			44.2310i			1.60760i	0.594898	+	0.803801i	$0.297192\pi$
$757$			44.2310i			1.60760i	−0.594898	+	0.803801i	$0.702808\pi$
$758$	−6.69082	−	13.3020i	−0.243021	−	0.483150i
$759$	5.11409			0.185630
$760$	8.31249	−	47.6596i	0.301526	−	1.72880i
$761$			19.9559i			0.723401i	0.932294	+	0.361700i	$0.117804\pi$
$761$			19.9559i			0.723401i	−0.932294	+	0.361700i	$0.882196\pi$
$762$	11.1713	+	22.2096i	0.404694	+	0.804570i
$763$	0.695592	+	38.3506i	0.0251821	+	1.38839i
$764$	−14.8065	−	10.9946i	−0.535679	−	0.397769i
$765$		−	0.411243i		−	0.0148685i
$766$	−5.02454	−	9.98927i	−0.181544	−	0.360927i
$767$		−	7.38024i		−	0.266485i
$768$	−12.4334	−	18.7018i	−0.448652	−	0.674843i
$769$			12.6775i			0.457162i	0.973525	+	0.228581i	$0.0734086\pi$
$769$			12.6775i			0.457162i	−0.973525	+	0.228581i	$0.926591\pi$
$770$	3.86027	+	7.33989i	0.139114	+	0.264511i
$771$	20.1066			0.724122
$772$	15.9190	−	21.4382i	0.572937	−	0.771579i
$773$	7.32173			0.263344			0.131672	−	0.991293i	$-0.457965\pi$
$773$	7.32173			0.263344			0.131672	+	0.991293i	$0.457965\pi$
$774$	−5.71987	−	11.3716i	−0.205596	−	0.408745i
$775$	−48.4628			−1.74084
$776$	−2.49380	+	14.2982i	−0.0895221	+	0.513274i
$777$	−30.2904	+	0.549398i	−1.08666	+	0.0197095i
$778$	11.5980	−	5.83373i	0.415809	−	0.209149i
$779$	−0.553736			−0.0198397
$780$	−7.02043	−	5.21303i	−0.251372	−	0.186656i
$781$		−	6.00030i		−	0.214708i
$782$	−0.417136	−	0.829306i	−0.0149167	−	0.0296559i
$783$	40.0080			1.42977
$784$	−9.06352	−	26.4925i	−0.323697	−	0.946161i
$785$	23.4297			0.836244
$786$	−8.31854	−	16.5381i	−0.296713	−	0.589893i
$787$		−	50.2628i		−	1.79168i	−0.444381	−	0.895838i	$-0.646576\pi$
$787$		−	50.2628i		−	1.79168i	0.444381	−	0.895838i	$-0.353424\pi$
$788$	39.6225	+	29.4217i	1.41149	+	1.04810i
$789$	18.7636			0.668003
$790$	64.4483	−	32.4171i	2.29297	−	1.15335i
$791$	25.4793	−	0.462135i	0.905939	−	0.0164316i
$792$	−2.04191	−	0.356136i	−0.0725559	−	0.0126547i
$793$	11.3324			0.402427
$794$	−15.3037	−	30.4253i	−0.543109	−	1.07975i
$795$	37.3035			1.32302
$796$	19.1385	−	25.7740i	0.678346	−	0.913535i
$797$	−50.0051			−1.77127			−0.885636	−	0.464381i	$-0.846277\pi$
$797$	−50.0051			−1.77127			−0.885636	+	0.464381i	$0.846277\pi$
$798$	−13.4237	−	25.5238i	−0.475194	−	0.903532i
$799$			0.360565i			0.0127559i
$800$	−19.2938	+	18.3159i	−0.682139	+	0.647565i
$801$			2.32424i			0.0821231i
$802$	18.2520	+	36.2868i	0.644502	+	1.28133i
$803$			6.13992i			0.216673i
$804$	32.6929	+	24.2762i	1.15299	+	0.856155i
$805$	0.765293	+	42.1935i	0.0269730	+	1.48713i
$806$	6.54867	+	13.0194i	0.230667	+	0.458588i
$807$			18.6188i			0.655414i
$808$	−44.7611	−	7.80695i	−1.57469	−	0.274648i
$809$	−18.2457			−0.641483			−0.320742	−	0.947167i	$-0.603932\pi$
$809$	−18.2457			−0.641483			−0.320742	+	0.947167i	$0.603932\pi$
$810$	9.59973	+	19.0852i	0.337300	+	0.670585i
$811$			49.8112i			1.74911i	0.484929	+	0.874554i	$0.338846\pi$
$811$			49.8112i			1.74911i	−0.484929	+	0.874554i	$0.661154\pi$
$812$	30.4485	+	21.7642i	1.06853	+	0.763774i
$813$		−	20.9654i		−	0.735289i
$814$	−7.33375	+	3.68883i	−0.257048	+	0.129294i
$815$	−17.6993			−0.619980
$816$	−0.208123	−	0.688968i	−0.00728575	−	0.0241187i
$817$		−	47.9905i		−	1.67898i
$818$	22.1919	−	11.1624i	0.775923	−	0.390285i
$819$	2.72440	−	0.0494143i	0.0951982	−	0.00172668i
$820$	0.504380	+	0.374528i	0.0176137	+	0.0130791i
$821$			23.2872i			0.812727i	0.913711	+	0.406364i	$0.133203\pi$
$821$			23.2872i			0.812727i	−0.913711	+	0.406364i	$0.866797\pi$
$822$	6.18126	−	3.10913i	0.215596	−	0.108443i
$823$			46.7989i			1.63131i	0.578540	+	0.815654i	$0.303623\pi$
$823$			46.7989i			1.63131i	−0.578540	+	0.815654i	$0.696377\pi$
$824$	−12.2067	−	2.12902i	−0.425242	−	0.0741681i
$825$		−	4.69685i		−	0.163523i
$826$	−24.4403	+	12.8539i	−0.850387	+	0.447244i
$827$	−33.8764			−1.17800			−0.588998	−	0.808134i	$-0.700478\pi$
$827$	−33.8764			−1.17800			−0.588998	+	0.808134i	$0.700478\pi$
$828$	−8.46804	−	6.28795i	−0.294285	−	0.218521i
$829$	−1.54700			−0.0537296			−0.0268648	−	0.999639i	$-0.508552\pi$
$829$	−1.54700			−0.0537296			−0.0268648	+	0.999639i	$0.508552\pi$
$830$	−16.0096	+	8.05272i	−0.555700	+	0.279514i
$831$	−2.91658			−0.101175
$832$	7.52765	+	2.70823i	0.260974	+	0.0938911i
$833$	−0.0325405	−	0.896745i	−0.00112746	−	0.0310704i
$834$	−12.2563	−	24.3666i	−0.424400	−	0.843748i
$835$	30.3781			1.05128
$836$	−6.27393	−	4.65871i	−0.216988	−	0.161125i
$837$		−	58.2895i		−	2.01478i
$838$	−38.2589	+	19.2440i	−1.32163	+	0.664773i
$839$	−12.5119			−0.431959			−0.215980	−	0.976398i	$-0.569295\pi$
$839$	−12.5119			−0.431959			−0.215980	+	0.976398i	$0.569295\pi$
$840$	−5.03618	+	32.3281i	−0.173765	+	1.11543i
$841$	−21.0284			−0.725116
$842$	36.8854	−	18.5531i	1.27116	−	0.639383i
$843$			10.7521i			0.370321i
$844$	9.83308	−	13.2423i	0.338469	−	0.455819i
$845$	3.11493			0.107157
$846$	1.84086	+	3.65982i	0.0632902	+	0.125827i
$847$	−27.7591	+	0.503487i	−0.953816	+	0.0173000i
$848$	−32.6703	+	9.86902i	−1.12190	+	0.338903i
$849$	6.67336			0.229029
$850$	−0.761645	+	0.383103i	−0.0261242	+	0.0131403i
$851$	−41.7736			−1.43198
$852$	14.1127	−	19.0057i	0.483493	−	0.651124i
$853$	3.10292			0.106242			0.0531210	−	0.998588i	$-0.483083\pi$
$853$	3.10292			0.106242			0.0531210	+	0.998588i	$0.483083\pi$
$854$	−19.7373	−	37.5284i	−0.675396	−	1.28419i
$855$		−	17.6159i		−	0.602452i
$856$	−7.68784	−	1.34087i	−0.262765	−	0.0458298i
$857$		−	35.6654i		−	1.21831i	−0.793052	−	0.609154i	$-0.791509\pi$
$857$		−	35.6654i		−	1.21831i	0.793052	−	0.609154i	$-0.208491\pi$
$858$	−1.26179	+	0.634675i	−0.0430769	+	0.0216674i
$859$			0.510482i			0.0174174i	0.999962	+	0.00870870i	$0.00277210\pi$
$859$			0.510482i			0.0174174i	−0.999962	+	0.00870870i	$0.997228\pi$
$860$	−32.4591	+	43.7130i	−1.10685	+	1.49060i
$861$	0.374422	−	0.00679115i	0.0127603	−	0.000231442i
$862$	32.2952	−	16.2443i	1.09998	−	0.553283i
$863$		−	36.6222i		−	1.24663i	−0.781969	−	0.623317i	$-0.785785\pi$
$863$		−	36.6222i		−	1.24663i	0.781969	−	0.623317i	$-0.214215\pi$
$864$	−22.0298	−	23.2060i	−0.749468	−	0.789483i
$865$	7.94096			0.270001
$866$	28.3654	−	14.2676i	0.963895	−	0.484834i
$867$			23.8382i			0.809588i
$868$	31.7093	−	44.3619i	1.07628	−	1.50574i
$869$		−	11.6528i		−	0.395293i
$870$	−19.6518	−	39.0697i	−0.666260	−	1.32459i
$871$	−14.5057			−0.491507
$872$	−7.04552	+	40.3955i	−0.238591	+	1.36796i
$873$			5.28489i			0.178866i
$874$	−17.8684	−	35.5240i	−0.604407	−	1.20162i
$875$	−2.44888	+	0.0444171i	−0.0827874	+	0.00150157i
$876$	−14.4411	+	19.4479i	−0.487919	+	0.657085i
$877$			1.65400i			0.0558515i	0.999610	+	0.0279257i	$0.00889020\pi$
$877$			1.65400i			0.0558515i	−0.999610	+	0.0279257i	$0.991110\pi$
$878$	14.2001	+	28.2311i	0.479230	+	0.952754i
$879$		−	28.7296i		−	0.969026i
$880$	2.56373	+	8.48694i	0.0864232	+	0.286095i
$881$		−	17.3400i		−	0.584199i	−0.956388	−	0.292099i	$-0.905646\pi$
$881$		−	17.3400i		−	0.584199i	0.956388	−	0.292099i	$-0.0943538\pi$
$882$	−4.90862	−	8.93602i	−0.165282	−	0.300891i
$883$	18.7952			0.632510			0.316255	−	0.948674i	$-0.397574\pi$
$883$	18.7952			0.632510			0.316255	+	0.948674i	$0.397574\pi$
$884$	0.205839	+	0.152846i	0.00692311	+	0.00514076i
$885$	32.2674			1.08466
$886$	−13.7414	−	27.3193i	−0.461652	−	0.917808i
$887$	−1.74179			−0.0584836			−0.0292418	−	0.999572i	$-0.509309\pi$
$887$	−1.74179			−0.0584836			−0.0292418	+	0.999572i	$0.509309\pi$
$888$	−31.9055	−	5.56475i	−1.07068	−	0.186741i
$889$	0.600921	+	33.1310i	0.0201542	+	1.11118i
$890$	8.88130	−	4.46724i	0.297702	−	0.149742i
$891$	3.45075			0.115604
$892$	−13.2132	+	17.7944i	−0.442412	+	0.595800i
$893$			15.4451i			0.516851i
$894$	0.0680589	+	0.135308i	0.00227623	+	0.00452536i
$895$	21.1265			0.706180
$896$	−4.14206	−	29.6453i	−0.138377	−	0.990380i
$897$	−7.18727			−0.239976
$898$	1.84264	+	3.66334i	0.0614896	+	0.122247i
$899$			72.8886i			2.43097i
$900$	−5.77493	+	7.77715i	−0.192498	+	0.259238i
$901$	−1.09374			−0.0364376
$902$	0.0906531	−	0.0455979i	0.00301842	−	0.00151825i
$903$	0.588567	+	32.4499i	0.0195863	+	1.07987i
$904$	26.8378	+	4.68088i	0.892613	+	0.155684i
$905$	−6.72869			−0.223669
$906$	1.59220	+	3.16545i	0.0528974	+	0.105165i
$907$	−6.46569			−0.214690			−0.107345	−	0.994222i	$-0.534235\pi$
$907$	−6.46569			−0.214690			−0.107345	+	0.994222i	$0.534235\pi$
$908$	−21.0209	−	15.6091i	−0.697603	−	0.518006i
$909$	−16.5446			−0.548750
$910$	−5.42516	−	10.3154i	−0.179842	−	0.341951i
$911$		−	39.3511i		−	1.30376i	−0.758321	−	0.651881i	$-0.773980\pi$
$911$		−	39.3511i		−	1.30376i	0.758321	−	0.651881i	$-0.226020\pi$
$912$	−8.91512	−	29.5125i	−0.295209	−	0.977257i
$913$			2.89466i			0.0957991i
$914$	−6.70084	−	13.3219i	−0.221644	−	0.440650i
$915$			49.5469i			1.63797i
$916$	31.8864	−	42.9417i	1.05356	−	1.41883i
$917$	−0.447466	−	24.6705i	−0.0147766	−	0.814692i
$918$	−0.460783	−	0.916081i	−0.0152081	−	0.0302352i
$919$		−	1.51489i		−	0.0499716i	−0.999688	−	0.0249858i	$-0.992046\pi$
$919$		−	1.51489i		−	0.0499716i	0.999688	−	0.0249858i	$-0.00795405\pi$
$920$	−7.75151	+	44.4432i	−0.255560	+	1.46525i
$921$	−0.978041			−0.0322275
$922$	−9.51782	−	18.9223i	−0.313453	−	0.623174i
$923$			8.43273i			0.277567i
$924$	4.29940	+	3.07315i	0.141440	+	0.101099i
$925$			38.3654i			1.26145i
$926$	−9.33635	+	4.69613i	−0.306812	+	0.154324i
$927$	−4.51185			−0.148189
$928$	27.5474	+	29.0181i	0.904286	+	0.952566i
$929$		−	29.8691i		−	0.979975i	−0.871729	−	0.489987i	$-0.837001\pi$
$929$		−	29.8691i		−	0.979975i	0.871729	−	0.489987i	$-0.162999\pi$
$930$	−56.9225	+	28.6317i	−1.86656	+	0.938869i
$931$	−1.39390	−	38.4128i	−0.0456832	−	1.25893i
$932$	24.1215	−	32.4846i	0.790125	−	1.06407i
$933$			30.0400i			0.983464i
$934$	24.0548	−	12.0994i	0.787098	−	0.395905i
$935$			0.284125i			0.00929190i
$936$	2.86966	+	0.500508i	0.0937978	+	0.0163596i
$937$			35.3032i			1.15330i	0.816990	+	0.576652i	$0.195641\pi$
$937$			35.3032i			1.15330i	−0.816990	+	0.576652i	$0.804359\pi$
$938$	25.2640	+	48.0369i	0.824900	+	1.56846i
$939$	4.28773			0.139925
$940$	10.4465	−	14.0685i	0.340729	−	0.458863i
$941$	40.5751			1.32271			0.661355	−	0.750073i	$-0.269982\pi$
$941$	40.5751			1.32271			0.661355	+	0.750073i	$0.269982\pi$
$942$	13.3384	−	6.70912i	0.434587	−	0.218595i
$943$	0.516366			0.0168152
$944$	−28.2597	+	8.53667i	−0.919776	+	0.277845i
$945$	0.845370	+	46.6084i	0.0274999	+	1.51617i
$946$	3.95183	+	7.85661i	0.128485	+	0.255440i
$947$	2.97693			0.0967373			0.0483687	−	0.998830i	$-0.484598\pi$
$947$	2.97693			0.0967373			0.0483687	+	0.998830i	$0.484598\pi$
$948$	27.4072	−	36.9096i	0.890146	−	1.19877i
$949$		−	8.62895i		−	0.280108i
$950$	−32.6257	+	16.4105i	−1.05852	+	0.532428i
$951$	37.6682			1.22148
$952$	0.147661	−	0.947859i	0.00478570	−	0.0307203i
$953$	31.5607			1.02235			0.511175	−	0.859477i	$-0.329210\pi$
$953$	31.5607			1.02235			0.511175	+	0.859477i	$0.329210\pi$
$954$	−11.1017	+	5.58406i	−0.359429	+	0.180791i
$955$			28.7230i			0.929453i
$956$	22.1318	+	16.4340i	0.715794	+	0.531514i
$957$	−7.06411			−0.228350
$958$	4.40490	+	8.75736i	0.142316	+	0.282937i
$959$	9.22084	−	0.167245i	0.297757	−	0.00540062i
$960$	−11.8408	+	32.9119i	−0.382159	+	1.06223i
$961$	75.1948			2.42564
$962$	10.3067	−	5.18423i	0.332303	−	0.167146i
$963$	−2.84158			−0.0915686
$964$	20.4650	+	15.1963i	0.659134	+	0.489441i
$965$	−41.5879			−1.33876
$966$	12.5178	+	23.8013i	0.402754	+	0.765793i
$967$			16.6169i			0.534365i	0.963646	+	0.267182i	$0.0860926\pi$
$967$			16.6169i			0.534365i	−0.963646	+	0.267182i	$0.913907\pi$
$968$	−29.2393	−	5.09973i	−0.939785	−	0.163911i
$969$		−	0.988019i		−	0.0317398i
$970$	20.1944	−	10.1576i	0.648402	−	0.326142i
$971$			22.3652i			0.717733i	0.933389	+	0.358866i	$0.116837\pi$
$971$			22.3652i			0.717733i	−0.933389	+	0.358866i	$0.883163\pi$
$972$	−16.3176	−	12.1167i	−0.523388	−	0.388642i
$973$	−0.659283	−	36.3488i	−0.0211356	−	1.16529i
$974$	−45.5522	+	22.9125i	−1.45959	+	0.734164i
$975$			6.60088i			0.211397i
$976$	−13.1082	−	43.3931i	−0.419582	−	1.38898i
$977$	46.7904			1.49696			0.748480	−	0.663158i	$-0.230784\pi$
$977$	46.7904			1.49696			0.748480	+	0.663158i	$0.230784\pi$
$978$	−10.0761	+	5.06821i	−0.322198	+	0.162063i
$979$		−	1.60581i		−	0.0513218i
$980$	−24.7115	+	35.9318i	−0.789379	+	1.14780i
$981$			14.9310i			0.476709i
$982$	18.0586	+	35.9022i	0.576273	+	1.14569i
$983$	9.87533			0.314974			0.157487	−	0.987521i	$-0.449661\pi$
$983$	9.87533			0.314974			0.157487	+	0.987521i	$0.449661\pi$
$984$	0.394386	+	0.0687863i	0.0125726	+	0.00219283i
$985$		−	76.8634i		−	2.44907i
$986$	0.576191	+	1.14552i	0.0183497	+	0.0364809i
$987$	−0.189423	−	10.4436i	−0.00602939	−	0.332423i
$988$	8.81728	+	6.54728i	0.280515	+	0.208297i
$989$			44.7518i			1.42302i
$990$	1.45060	+	2.88393i	0.0461031	+	0.0916574i
$991$			6.15361i			0.195476i	0.995212	+	0.0977379i	$0.0311607\pi$
$991$			6.15361i			0.195476i	−0.995212	+	0.0977379i	$0.968839\pi$
$992$	42.2778	−	40.1350i	1.34232	−	1.27429i
$993$		−	24.7880i		−	0.786624i
$994$	27.9257	−	14.6870i	0.885750	−	0.465842i
$995$	−49.9988			−1.58507
$996$	−6.80822	+	9.16870i	−0.215727	+	0.290521i
$997$	5.86468			0.185736			0.0928682	−	0.995678i	$-0.470396\pi$
$997$	5.86468			0.185736			0.0928682	+	0.995678i	$0.470396\pi$
$998$	−10.2553	−	20.3885i	−0.324625	−	0.645385i
$999$	−46.1446			−1.45995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.b.27.15	yes	48
4.3	odd	2		2912.2.h.b.2575.15		48
7.6	odd	2		728.2.h.a.27.15	✓	48
8.3	odd	2		728.2.h.a.27.16	yes	48
8.5	even	2		2912.2.h.a.2575.15		48
28.27	even	2		2912.2.h.a.2575.34		48
56.13	odd	2		2912.2.h.b.2575.34		48
56.27	even	2	inner	728.2.h.b.27.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.15	✓	48	7.6	odd	2
728.2.h.a.27.16	yes	48	8.3	odd	2
728.2.h.b.27.15	yes	48	1.1	even	1	trivial
728.2.h.b.27.16	yes	48	56.27	even	2	inner
2912.2.h.a.2575.15		48	8.5	even	2
2912.2.h.a.2575.34		48	28.27	even	2
2912.2.h.b.2575.15		48	4.3	odd	2
2912.2.h.b.2575.34		48	56.13	odd	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 $\F_{q}$
Belyi maps

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+(-0.635480 - 1.26339i) q^{2} +1.40360i q^{3} +(-1.19233 + 1.60572i) q^{4} +3.11493 q^{5} +(1.77331 - 0.891962i) q^{6} +(2.64532 - 0.0479799i) q^{7} +(2.78636 + 0.485980i) q^{8} +1.02989 q^{9} +(-1.97948 - 3.93539i) q^{10} -0.711549 q^{11} +(-2.25380 - 1.67356i) q^{12} +1.00000 q^{13} +(-1.74166 - 3.31159i) q^{14} +4.37213i q^{15} +(-1.15669 - 3.82911i) q^{16} -0.128191i q^{17} +(-0.654477 - 1.30116i) q^{18} -5.49116i q^{19} +(-3.71403 + 5.00172i) q^{20} +(0.0673448 + 3.71298i) q^{21} +(0.452175 + 0.898967i) q^{22} +5.12058i q^{23} +(-0.682124 + 3.91095i) q^{24} +4.70280 q^{25} +(-0.635480 - 1.26339i) q^{26} +5.65638i q^{27} +(-3.07705 + 4.30485i) q^{28} -7.07307i q^{29} +(5.52373 - 2.77840i) q^{30} -10.3051 q^{31} +(-4.10262 + 3.89468i) q^{32} -0.998733i q^{33} +(-0.161955 + 0.0814626i) q^{34} +(8.23998 - 0.149454i) q^{35} +(-1.22798 + 1.65373i) q^{36} +8.15798i q^{37} +(-6.93750 + 3.48952i) q^{38} +1.40360i q^{39} +(8.67934 + 1.51379i) q^{40} -0.100841i q^{41} +(4.64816 - 2.44460i) q^{42} +8.73959 q^{43} +(0.848402 - 1.14255i) q^{44} +3.20805 q^{45} +(6.46931 - 3.25403i) q^{46} -2.81273 q^{47} +(5.37455 - 1.62354i) q^{48} +(6.99540 - 0.253844i) q^{49} +(-2.98854 - 5.94150i) q^{50} +0.179929 q^{51} +(-1.19233 + 1.60572i) q^{52} -8.53210i q^{53} +(7.14624 - 3.59451i) q^{54} -2.21643 q^{55} +(7.39413 + 1.15188i) q^{56} +7.70742 q^{57} +(-8.93608 + 4.49479i) q^{58} -7.38024i q^{59} +(-7.02043 - 5.21303i) q^{60} +11.3324 q^{61} +(6.54867 + 13.0194i) q^{62} +(2.72440 - 0.0494143i) q^{63} +(7.52765 + 2.70823i) q^{64} +3.11493 q^{65} +(-1.26179 + 0.634675i) q^{66} -14.5057 q^{67} +(0.205839 + 0.152846i) q^{68} -7.18727 q^{69} +(-5.42516 - 10.3154i) q^{70} +8.43273i q^{71} +(2.86966 + 0.500508i) q^{72} -8.62895i q^{73} +(10.3067 - 5.18423i) q^{74} +6.60088i q^{75} +(8.81728 + 6.54728i) q^{76} +(-1.88227 + 0.0341401i) q^{77} +(1.77331 - 0.891962i) q^{78} +16.3766i q^{79} +(-3.60302 - 11.9274i) q^{80} -4.84963 q^{81} +(-0.127402 + 0.0640826i) q^{82} -4.06811i q^{83} +(-6.04231 - 4.31896i) q^{84} -0.399306i q^{85} +(-5.55383 - 11.0416i) q^{86} +9.92780 q^{87} +(-1.98263 - 0.345799i) q^{88} +2.25678i q^{89} +(-2.03865 - 4.05304i) q^{90} +(2.64532 - 0.0479799i) q^{91} +(-8.22223 - 6.10543i) q^{92} -14.4643i q^{93} +(1.78743 + 3.55358i) q^{94} -17.1046i q^{95} +(-5.46659 - 5.75845i) q^{96} +5.13148i q^{97} +(-4.76614 - 8.67663i) q^{98} -0.732821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} + 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} - 10 q^{12} + 48 q^{13} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 + 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 - 10 * q^12 + 48 * q^13 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * 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 - 14 * 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 - 37 * 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 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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