LMFDB - Embedded newform 728.2.h.a.27.15

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			27.15
Character	$\chi$	$=$	728.27
Dual form			728.2.h.a.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} +(1.62043 + 3.37257i) 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} +(3.23114 - 4.19044i) 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} +(4.73375 - 2.27444i) 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} +(-7.34750 - 1.41926i) 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} +(-5.04752 - 10.5053i) 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} +(-5.88172 - 4.53524i) 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} +(-4.12473 - 8.99926i) 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} + 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 $

$2$	−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	$-0.867207\pi$
$3$		−	1.40360i		−	0.810371i	0.914234	−	0.405186i	$-0.132793\pi$
$4$	−1.19233	+	1.60572i	−0.596166	+	0.802862i
$5$	−3.11493			−1.39304			−0.696520	−	0.717537i	$-0.745269\pi$
$5$	−3.11493			−1.39304			−0.696520	+	0.717537i	$0.745269\pi$
$6$	−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
$14$	1.62043	+	3.37257i	0.433077	+	0.901357i
$15$			4.37213i			1.12888i
$16$	−1.15669	−	3.82911i	−0.289173	−	0.957277i
$17$			0.128191i			0.0310908i	0.999879	+	0.0155454i	$0.00494846\pi$
$17$			0.128191i			0.0310908i	−0.999879	+	0.0155454i	$0.995052\pi$
$18$	−0.654477	−	1.30116i	−0.154262	−	0.306687i
$19$			5.49116i			1.25976i	0.776693	+	0.629879i	$0.216896\pi$
$19$			5.49116i			1.25976i	−0.776693	+	0.629879i	$0.783104\pi$
$20$	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
$28$	3.23114	−	4.19044i	0.610627	−	0.791918i
$29$		−	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	$-0.123709\pi$
$31$	10.3051			1.85085			0.925424	+	0.378934i	$0.123709\pi$
$32$	−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	$0.00250652\pi$
$41$			0.100841i			0.0157488i	−0.999969	+	0.00787439i	$0.997493\pi$
$42$	4.73375	−	2.27444i	0.730434	−	0.350954i
$43$	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	$-0.434235\pi$
$47$	2.81273			0.410278			0.205139	+	0.978733i	$0.434235\pi$
$48$	−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
$56$	−7.34750	−	1.41926i	−0.981850	−	0.189657i
$57$	7.70742			1.02087
$58$	−8.93608	+	4.49479i	−1.17336	+	0.590195i
$59$			7.38024i			0.960825i	0.877043	+	0.480413i	$0.159513\pi$
$59$			7.38024i			0.960825i	−0.877043	+	0.480413i	$0.840487\pi$
$60$	−7.02043	−	5.21303i	−0.906334	−	0.672999i
$61$	−11.3324			−1.45097			−0.725485	−	0.688238i	$-0.758384\pi$
$61$	−11.3324			−1.45097			−0.725485	+	0.688238i	$0.758384\pi$
$62$	−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
$70$	−5.04752	−	10.5053i	−0.603294	−	1.25563i
$71$			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	$0.168497\pi$
$73$			8.62895i			1.00994i	−0.863136	+	0.504971i	$0.831503\pi$
$74$	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	$0.0716720\pi$
$83$			4.06811i			0.446533i	−0.974757	+	0.223266i	$0.928328\pi$
$84$	−5.88172	−	4.53524i	−0.641748	−	0.494835i
$85$		−	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	$-0.961836\pi$
$89$		−	2.25678i		−	0.239218i	0.992821	−	0.119609i	$-0.0381641\pi$
$90$	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	$-0.916109\pi$
$97$		−	5.13148i		−	0.521023i	0.965471	−	0.260511i	$-0.0838912\pi$
$98$	−4.12473	−	8.99926i	−0.416660	−	0.909062i
$99$	−0.732821			−0.0736513
$100$	−5.60730	+	7.55140i	−0.560730	+	0.755140i
$101$	16.0644			1.59846			0.799231	−	0.601023i	$-0.205240\pi$
$101$	16.0644			1.59846			0.799231	+	0.601023i	$0.205240\pi$
$102$	−0.114341	−	0.227321i	−0.0113215	−	0.0225082i
$103$	4.38089			0.431662			0.215831	−	0.976431i	$-0.430754\pi$
$103$	4.38089			0.431662			0.215831	+	0.976431i	$0.430754\pi$
$104$	−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
$112$	2.87610	+	10.1847i	0.271766	+	0.962363i
$113$	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
$126$	1.66887	+	3.47339i	0.148675	+	0.309434i
$127$			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	$0.133569\pi$
$131$			9.32611i			0.814826i	−0.913244	+	0.407413i	$0.866431\pi$
$132$	−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	$0.198019\pi$
$139$			13.7408i			1.16548i	−0.812659	+	0.582740i	$0.801981\pi$
$140$	−10.0648	+	13.0529i	−0.850628	+	1.10317i
$141$		−	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
$154$	−1.15301	−	2.39975i	−0.0929125	−	0.193377i
$155$	−32.0996			−2.57831
$156$	−2.25380	−	1.67356i	−0.180448	−	0.133992i
$157$	−7.52175			−0.600301			−0.300151	−	0.953892i	$-0.597037\pi$
$157$	−7.52175			−0.600301			−0.300151	+	0.953892i	$0.597037\pi$
$158$	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	$-0.623159\pi$
$167$	−9.75242			−0.754665			−0.377332	+	0.926078i	$0.623159\pi$
$168$	−1.99208	+	10.3130i	−0.153692	+	0.795663i
$169$	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	$-0.530896\pi$
$173$	−2.54932			−0.193821			−0.0969106	+	0.995293i	$0.530896\pi$
$174$	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	$-0.474418\pi$
$181$	2.16014			0.160562			0.0802810	+	0.996772i	$0.474418\pi$
$182$	−1.62043	−	3.37257i	−0.120114	−	0.249991i
$183$			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
$196$	−8.74843	+	10.9300i	−0.624888	+	0.780714i
$197$		−	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	$-0.307360\pi$
$199$	16.0513			1.13785			0.568924	+	0.822390i	$0.307360\pi$
$200$	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
$210$	−14.7453	+	7.08472i	−1.01752	+	0.488892i
$211$	−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	$-0.621001\pi$
$223$	−11.0819			−0.742096			−0.371048	+	0.928614i	$0.621001\pi$
$224$	11.0396	−	10.1058i	0.737613	−	0.675223i
$225$	4.84339			0.322893
$226$	−6.12084	−	12.1688i	−0.407152	−	0.809458i
$227$		−	13.0912i		−	0.868896i	−0.900697	−	0.434448i	$-0.856944\pi$
$227$		−	13.0912i		−	0.868896i	0.900697	−	0.434448i	$-0.143056\pi$
$228$	−9.18979	+	12.3760i	−0.608609	+	0.819619i
$229$	26.7429			1.76722			0.883610	−	0.468224i	$-0.155106\pi$
$229$	26.7429			1.76722			0.883610	+	0.468224i	$0.155106\pi$
$230$	−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
$238$	−0.432332	+	0.207724i	−0.0280239	+	0.0134647i
$239$		−	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	$0.134642\pi$
$241$			12.7451i			0.820981i	−0.911865	+	0.410490i	$0.865358\pi$
$242$	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	$0.250886\pi$
$251$			22.4676i			1.41814i	−0.705137	+	0.709071i	$0.749114\pi$
$252$	3.32773	−	4.31571i	0.209627	−	0.271864i
$253$		−	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	$0.147431\pi$
$257$			14.3250i			0.893568i	−0.894642	+	0.446784i	$0.852569\pi$
$258$	−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
$266$	−18.5193	+	8.89803i	−1.13549	+	0.545573i
$267$	−3.16762			−0.193855
$268$	17.2956	−	23.2921i	1.05650	−	1.42279i
$269$	−13.2650			−0.808782			−0.404391	−	0.914586i	$-0.632517\pi$
$269$	−13.2650			−0.808782			−0.404391	+	0.914586i	$0.632517\pi$
$270$	22.2600	−	11.1967i	1.35470	−	0.681407i
$271$	14.9368			0.907348			0.453674	−	0.891168i	$-0.350113\pi$
$271$	14.9368			0.907348			0.453674	+	0.891168i	$0.350113\pi$
$272$	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
$280$	22.8870	+	4.42090i	1.36776	+	0.264199i
$281$	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	$0.0451318\pi$
$283$			4.75444i			0.282622i	−0.989965	+	0.141311i	$0.954868\pi$
$284$	−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	$-0.296006\pi$
$293$	20.4685			1.19578			0.597890	+	0.801578i	$0.296006\pi$
$294$	−12.6314	+	5.78948i	−0.736678	+	0.337650i
$295$		−	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	$-0.993670\pi$
$307$		−	0.696807i		−	0.0397689i	0.999802	−	0.0198844i	$-0.00632983\pi$
$308$	−2.29911	+	2.98170i	−0.131004	+	0.169898i
$309$		−	6.14903i		−	0.349806i
$310$	20.3987	+	40.5545i	1.15857	+	2.30334i
$311$	−21.4020			−1.21360			−0.606798	−	0.794856i	$-0.707546\pi$
$311$	−21.4020			−1.21360			−0.606798	+	0.794856i	$0.707546\pi$
$312$	−0.682124	+	3.91095i	−0.0386176	+	0.221414i
$313$			3.05480i			0.172667i	0.996266	+	0.0863337i	$0.0275151\pi$
$313$			3.05480i			0.172667i	−0.996266	+	0.0863337i	$0.972485\pi$
$314$	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
$322$	−17.2695	+	8.29753i	−0.962392	+	0.462403i
$323$	−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
$336$	14.2953	−	4.03691i	0.779872	−	0.220231i
$337$	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	$-0.512793\pi$
$349$	−1.50124			−0.0803598			−0.0401799	+	0.999192i	$0.512793\pi$
$350$	7.62055	+	15.8605i	0.407336	+	0.847781i
$351$			5.65638i			0.301915i
$352$	2.91921	−	2.77126i	0.155595	−	0.147708i
$353$		−	2.52907i		−	0.134609i	−0.997732	−	0.0673043i	$-0.978560\pi$
$353$		−	2.52907i		−	0.134609i	0.997732	−	0.0673043i	$-0.0214398\pi$
$354$	−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
$364$	−3.23114	+	4.19044i	−0.169358	+	0.219639i
$365$		−	26.8786i		−	1.40689i
$366$	20.0959	−	10.1081i	1.05043	−	0.528359i
$367$	13.6580			0.712944			0.356472	−	0.934306i	$-0.383980\pi$
$367$	13.6580			0.712944			0.356472	+	0.934306i	$0.383980\pi$
$368$	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
$378$	19.0765	−	9.16575i	0.981190	−	0.471435i
$379$	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	$-0.564746\pi$
$383$	−7.90669			−0.404013			−0.202007	+	0.979384i	$0.564746\pi$
$384$	−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
$392$	19.3684	+	4.10692i	0.978250	+	0.207431i
$393$	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	$-0.706557\pi$
$397$	−24.0822			−1.20865			−0.604325	+	0.796738i	$0.706557\pi$
$398$	−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
$406$	23.8544	−	11.4614i	1.18387	−	0.568820i
$407$		−	5.80480i		−	0.287733i
$408$	0.501348	+	0.0874419i	0.0248204	+	0.00432902i
$409$		−	17.5653i		−	0.868550i	−0.900780	−	0.434275i	$-0.857005\pi$
$409$		−	17.5653i		−	0.868550i	0.900780	−	0.434275i	$-0.142995\pi$
$410$	−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	$0.265033\pi$
$419$			30.2826i			1.47940i	−0.672935	+	0.739702i	$0.734967\pi$
$420$	18.3211	+	14.1270i	0.893981	+	0.689325i
$421$			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	$-0.818621\pi$
$433$		−	22.4517i		−	1.07896i	0.841998	−	0.539481i	$-0.181379\pi$
$434$	16.6986	+	34.7546i	0.801560	+	1.66827i
$435$	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	$-0.320972\pi$
$439$	22.3455			1.06649			0.533245	+	0.845961i	$0.320972\pi$
$440$	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
$448$	−19.7831	−	7.52531i	−0.934662	−	0.355538i
$449$	−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	$-0.613405\pi$
$461$	−14.9774			−0.697566			−0.348783	+	0.937203i	$0.613405\pi$
$462$	−3.36830	+	1.61837i	−0.156707	+	0.0752936i
$463$		−	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	$-0.854791\pi$
$467$		−	19.0398i		−	0.881058i	0.897738	−	0.440529i	$-0.145209\pi$
$468$	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
$476$	0.537175	+	0.414202i	0.0246214	+	0.0189849i
$477$		−	8.78716i		−	0.402336i
$478$	−17.4135	+	8.75887i	−0.796474	+	0.400622i
$479$	6.93161			0.316713			0.158357	−	0.987382i	$-0.449380\pi$
$479$	6.93161			0.316713			0.158357	+	0.987382i	$0.449380\pi$
$480$	−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
$490$	12.8482	+	28.0321i	0.580425	+	1.26636i
$491$	−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	$-0.614649\pi$
$503$	−15.8090			−0.704888			−0.352444	+	0.935833i	$0.614649\pi$
$504$	−7.56715	−	1.46169i	−0.337068	−	0.0651088i
$505$	−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	$-0.411931\pi$
$509$	12.3255			0.546320			0.273160	+	0.961969i	$0.411931\pi$
$510$	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
$518$	−27.5133	+	13.2194i	−1.20887	+	0.580828i
$519$			3.57824i			0.157067i
$520$	8.67934	+	1.51379i	0.380614	+	0.0663843i
$521$		−	32.9577i		−	1.44390i	−0.691945	−	0.721950i	$-0.743246\pi$
$521$		−	32.9577i		−	1.44390i	0.691945	−	0.721950i	$-0.256754\pi$
$522$	−9.20322	+	4.62917i	−0.402814	+	0.202613i
$523$			2.21195i			0.0967220i	0.998830	+	0.0483610i	$0.0153998\pi$
$523$			2.21195i			0.0967220i	−0.998830	+	0.0483610i	$0.984600\pi$
$524$	−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
$532$	23.0104	+	17.7427i	0.997626	+	0.769243i
$533$		−	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
$546$	−4.73375	+	2.27444i	−0.202586	+	0.0973370i
$547$	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
$560$	−8.95885	−	31.7246i	−0.378581	−	1.34061i
$561$	−0.128028			−0.00540536
$562$	−4.86798	−	9.67802i	−0.205343	−	0.408242i
$563$			21.2293i			0.894707i	0.894357	+	0.447354i	$0.147633\pi$
$563$			21.2293i			0.894707i	−0.894357	+	0.447354i	$0.852367\pi$
$564$	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
$574$	−0.340094	+	0.163406i	−0.0141953	+	0.00682044i
$575$			24.0811i			1.00425i
$576$	7.75269	+	2.78920i	0.323029	+	0.116217i
$577$		−	32.8326i		−	1.36684i	−0.730025	−	0.683420i	$-0.760492\pi$
$577$		−	32.8326i		−	1.36684i	0.730025	−	0.683420i	$-0.239508\pi$
$578$	−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	$0.253180\pi$
$587$			34.6043i			1.42827i	−0.700008	+	0.714135i	$0.746820\pi$
$588$	15.3414	+	12.2793i	0.632669	+	0.506391i
$589$			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	$0.217789\pi$
$593$			30.7831i			1.26411i	−0.774923	+	0.632056i	$0.782211\pi$
$594$	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	$-0.984091\pi$
$601$		−	2.44947i		−	0.0999158i	0.998751	−	0.0499579i	$-0.0159087\pi$
$602$	14.1619	+	29.4749i	0.577195	+	1.20131i
$603$	−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	$-0.615689\pi$
$607$	−17.5171			−0.710998			−0.355499	+	0.934677i	$0.615689\pi$
$608$	−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
$616$	5.22810	+	1.00987i	0.210646	+	0.0406890i
$617$	−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	$0.0958277\pi$
$619$			14.7549i			0.593049i	−0.955025	+	0.296525i	$0.904172\pi$
$620$	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
$630$	−5.19842	−	10.8194i	−0.207110	−	0.431054i
$631$		−	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	$0.229041\pi$
$643$			33.4236i			1.31810i	−0.752101	+	0.659048i	$0.770959\pi$
$644$	21.4575	+	16.5453i	0.845543	+	0.651976i
$645$			38.2107i			1.50454i
$646$	0.447324	+	0.889323i	0.0175997	+	0.0349900i
$647$	34.4335			1.35372			0.676861	−	0.736111i	$-0.263340\pi$
$647$	34.4335			1.35372			0.676861	+	0.736111i	$0.263340\pi$
$648$	−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
$658$	4.55782	+	9.48611i	0.177682	+	0.369807i
$659$	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	$-0.582849\pi$
$661$	−13.2329			−0.514701			−0.257350	+	0.966318i	$0.582849\pi$
$662$	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
$672$	−14.1846	−	15.4952i	−0.547182	−	0.597741i
$673$	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	$-0.534915\pi$
$677$	−5.69662			−0.218939			−0.109470	+	0.993990i	$0.534915\pi$
$678$	−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
$686$	10.4794	+	24.0038i	0.400106	+	0.916469i
$687$		−	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	$-0.790738\pi$
$691$		−	32.1264i		−	1.22215i	0.791575	−	0.611073i	$-0.209262\pi$
$692$	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
$700$	15.1954	−	19.7068i	0.574332	−	0.744847i
$701$			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
$714$	0.291562	+	0.606823i	0.0109114	+	0.0227098i
$715$	−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	$-0.542322\pi$
$719$	−7.10932			−0.265133			−0.132566	+	0.991174i	$0.542322\pi$
$720$	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	$-0.700109\pi$
$727$	−31.7118			−1.17613			−0.588063	+	0.808815i	$0.700109\pi$
$728$	7.34750	+	1.41926i	0.272316	+	0.0526013i
$729$	−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	$-0.476725\pi$
$733$	3.95576			0.146109			0.0730546	+	0.997328i	$0.476725\pi$
$734$	−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
$742$	28.7751	−	13.8256i	1.05637	−	0.507555i
$743$			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
$756$	−23.7027	−	18.2765i	−0.862059	−	0.664711i
$757$			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	$-0.882196\pi$
$761$		−	19.9559i		−	0.723401i	0.932294	−	0.361700i	$-0.117804\pi$
$762$	−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	$-0.926591\pi$
$769$		−	12.6775i		−	0.457162i	0.973525	−	0.228581i	$-0.0734086\pi$
$770$	3.59156	+	7.47505i	0.129431	+	0.269382i
$771$	20.1066			0.724122
$772$	15.9190	−	21.4382i	0.572937	−	0.771579i
$773$	−7.32173			−0.263344			−0.131672	−	0.991293i	$-0.542035\pi$
$773$	−7.32173			−0.263344			−0.131672	+	0.991293i	$0.542035\pi$
$774$	−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
$784$	−7.11953	−	27.0797i	−0.254269	−	0.967134i
$785$	23.4297			0.836244
$786$	−8.31854	−	16.5381i	−0.296713	−	0.589893i
$787$			50.2628i			1.79168i	0.444381	+	0.895838i	$0.353424\pi$
$787$			50.2628i			1.79168i	−0.444381	+	0.895838i	$0.646576\pi$
$788$	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	$-0.153723\pi$
$797$	50.0051			1.77127			0.885636	+	0.464381i	$0.153723\pi$
$798$	12.4893	+	25.9938i	0.442117	+	0.920170i
$799$			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	$-0.661154\pi$
$811$		−	49.8112i		−	1.74911i	0.484929	−	0.874554i	$-0.338846\pi$
$812$	−29.6393	−	22.8541i	−1.04013	−	0.802020i
$813$		−	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
$826$	−24.8904	+	11.9591i	−0.866046	+	0.416112i
$827$	−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	$-0.491448\pi$
$829$	1.54700			0.0537296			0.0268648	+	0.999639i	$0.491448\pi$
$830$	−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	$-0.430705\pi$
$839$	12.5119			0.431959			0.215980	+	0.976398i	$0.430705\pi$
$840$	6.20519	−	32.1242i	0.214100	−	1.10839i
$841$	−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	$-0.516917\pi$
$853$	−3.10292			−0.106242			−0.0531210	+	0.998588i	$0.516917\pi$
$854$	−18.3634	−	38.2194i	−0.628382	−	1.30784i
$855$		−	17.6159i		−	0.602452i
$856$	−7.68784	−	1.34087i	−0.262765	−	0.0458298i
$857$			35.6654i			1.21831i	0.793052	+	0.609154i	$0.208491\pi$
$857$			35.6654i			1.21831i	−0.793052	+	0.609154i	$0.791509\pi$
$858$	−1.26179	+	0.634675i	−0.0430769	+	0.0216674i
$859$		−	0.510482i		−	0.0174174i	−0.999962	−	0.00870870i	$-0.997228\pi$
$859$		−	0.510482i		−	0.0174174i	0.999962	−	0.00870870i	$-0.00277210\pi$
$860$	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
$868$	33.2971	−	43.1828i	1.13018	−	1.46572i
$869$		−	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	$0.0943538\pi$
$881$			17.3400i			0.584199i	−0.956388	+	0.292099i	$0.905646\pi$
$882$	−4.24804	−	9.26829i	−0.143039	−	0.312080i
$883$	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	$-0.490691\pi$
$887$	1.74179			0.0584836			0.0292418	+	0.999572i	$0.490691\pi$
$888$	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
$896$	3.06430	+	29.7760i	0.102371	+	0.994746i
$897$	−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
$910$	5.04752	+	10.5053i	0.167324	+	0.348248i
$911$		−	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
$924$	4.18513	+	3.22704i	0.137681	+	0.106162i
$925$			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	$0.162999\pi$
$929$			29.8691i			0.979975i	−0.871729	+	0.489987i	$0.837001\pi$
$930$	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	$-0.804359\pi$
$937$		−	35.3032i		−	1.15330i	0.816990	−	0.576652i	$-0.195641\pi$
$938$	−23.5054	−	48.9215i	−0.767480	−	1.59734i
$939$	4.28773			0.139925
$940$	10.4465	−	14.0685i	0.340729	−	0.458863i
$941$	−40.5751			−1.32271			−0.661355	−	0.750073i	$-0.730018\pi$
$941$	−40.5751			−1.32271			−0.661355	+	0.750073i	$0.730018\pi$
$942$	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
$952$	0.181936	−	0.941881i	0.00589658	−	0.0305265i
$953$	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
$966$	11.6464	+	24.2396i	0.374718	+	0.779895i
$967$			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	$-0.883163\pi$
$971$		−	22.3652i		−	0.717733i	0.933389	−	0.358866i	$-0.116837\pi$
$972$	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
$980$	27.2508	−	34.0462i	0.870494	−	1.08757i
$981$			14.9310i			0.476709i
$982$	18.0586	+	35.9022i	0.576273	+	1.14569i
$983$	−9.87533			−0.314974			−0.157487	−	0.987521i	$-0.550339\pi$
$983$	−9.87533			−0.314974			−0.157487	+	0.987521i	$0.550339\pi$
$984$	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
$994$	−28.4399	+	13.6646i	−0.902060	+	0.433415i
$995$	−49.9988			−1.58507
$996$	−6.80822	+	9.16870i	−0.215727	+	0.290521i
$997$	−5.86468			−0.185736			−0.0928682	−	0.995678i	$-0.529604\pi$
$997$	−5.86468			−0.185736			−0.0928682	+	0.995678i	$0.529604\pi$
$998$	−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.a.27.15	✓	48
4.3	odd	2		2912.2.h.a.2575.34		48
7.6	odd	2		728.2.h.b.27.15	yes	48
8.3	odd	2		728.2.h.b.27.16	yes	48
8.5	even	2		2912.2.h.b.2575.34		48
28.27	even	2		2912.2.h.b.2575.15		48
56.13	odd	2		2912.2.h.a.2575.15		48
56.27	even	2	inner	728.2.h.a.27.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.15	✓	48	1.1	even	1	trivial
728.2.h.a.27.16	yes	48	56.27	even	2	inner
728.2.h.b.27.15	yes	48	7.6	odd	2
728.2.h.b.27.16	yes	48	8.3	odd	2
2912.2.h.a.2575.15		48	56.13	odd	2
2912.2.h.a.2575.34		48	4.3	odd	2
2912.2.h.b.2575.15		48	28.27	even	2
2912.2.h.b.2575.34		48	8.5	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+(-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} +(1.62043 + 3.37257i) 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} +(3.23114 - 4.19044i) 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} +(4.73375 - 2.27444i) 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} +(-7.34750 - 1.41926i) 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} +(-5.04752 - 10.5053i) 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} +(-5.88172 - 4.53524i) 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} +(-4.12473 - 8.99926i) q^{98} -0.732821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} - 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} + 10 q^{12} - 48 q^{13} + 10 q^{14} + 5 q^{16} - 15 q^{18} - 22 q^{20} - 6 q^{22} + 48 q^{25} - q^{26} + 4 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 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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