LMFDB - Embedded newform 605.2.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

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:	yes
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.09529$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09529 q^{2} +1.91300 q^{3} +2.39026 q^{4} -1.00000 q^{5} +4.00829 q^{6} +3.06719 q^{7} +0.817703 q^{8} +0.659557 q^{9} +O(q^{10})$	\(q+2.09529 q^{2} +1.91300 q^{3} +2.39026 q^{4} -1.00000 q^{5} +4.00829 q^{6} +3.06719 q^{7} +0.817703 q^{8} +0.659557 q^{9} -2.09529 q^{10} +4.57255 q^{12} -3.04981 q^{13} +6.42666 q^{14} -1.91300 q^{15} -3.06719 q^{16} +0.463845 q^{17} +1.38197 q^{18} +7.89563 q^{19} -2.39026 q^{20} +5.86752 q^{21} -1.39026 q^{23} +1.56426 q^{24} +1.00000 q^{25} -6.39026 q^{26} -4.47726 q^{27} +7.33136 q^{28} -3.72162 q^{29} -4.00829 q^{30} -10.4765 q^{31} -8.06206 q^{32} +0.971892 q^{34} -3.06719 q^{35} +1.57651 q^{36} +1.84453 q^{37} +16.5437 q^{38} -5.83428 q^{39} -0.817703 q^{40} +4.40763 q^{41} +12.2942 q^{42} +1.31478 q^{43} -0.659557 q^{45} -2.91300 q^{46} -2.98018 q^{47} -5.86752 q^{48} +2.40763 q^{49} +2.09529 q^{50} +0.887334 q^{51} -7.28984 q^{52} +4.18814 q^{53} -9.38118 q^{54} +2.50805 q^{56} +15.1043 q^{57} -7.79789 q^{58} +2.81502 q^{59} -4.57255 q^{60} +2.01737 q^{61} -21.9513 q^{62} +2.02298 q^{63} -10.7580 q^{64} +3.04981 q^{65} -6.75753 q^{67} +1.10871 q^{68} -2.65956 q^{69} -6.42666 q^{70} -6.52195 q^{71} +0.539322 q^{72} +9.87581 q^{73} +3.86484 q^{74} +1.91300 q^{75} +18.8726 q^{76} -12.2245 q^{78} +11.5579 q^{79} +3.06719 q^{80} -10.5437 q^{81} +9.23528 q^{82} -8.91861 q^{83} +14.0249 q^{84} -0.463845 q^{85} +2.75485 q^{86} -7.11945 q^{87} -6.76978 q^{89} -1.38197 q^{90} -9.35435 q^{91} -3.32307 q^{92} -20.0415 q^{93} -6.24436 q^{94} -7.89563 q^{95} -15.4227 q^{96} +15.3543 q^{97} +5.04469 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8	$ 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} - q^{10} + 8 q^{12} + q^{13} + 2 q^{14} - 3 q^{16} - q^{17} + 10 q^{18} + 20 q^{19} + q^{20} + 10 q^{21} + 5 q^{23} + 11 q^{24} + 4 q^{25} - 15 q^{26} - 15 q^{27} + 13 q^{28} + 12 q^{29} - q^{30} - 5 q^{31} - 8 q^{32} + 2 q^{34} - 3 q^{35} + 7 q^{37} + 20 q^{38} + 7 q^{39} - 3 q^{40} + 11 q^{41} + 12 q^{42} + 19 q^{43} - 4 q^{46} + 5 q^{47} - 10 q^{48} + 3 q^{49} + q^{50} + 7 q^{51} - 11 q^{52} - 11 q^{53} - 8 q^{54} + 11 q^{56} - 5 q^{57} - 14 q^{58} + 9 q^{59} - 8 q^{60} + 12 q^{61} - 35 q^{62} - 5 q^{63} - 3 q^{64} - q^{65} - 19 q^{67} - 3 q^{68} - 8 q^{69} - 2 q^{70} + 5 q^{71} - 25 q^{72} + 11 q^{73} - 8 q^{78} + 34 q^{79} + 3 q^{80} + 4 q^{81} - 6 q^{82} - 11 q^{83} + 11 q^{84} + q^{85} + q^{86} - 19 q^{87} - 8 q^{89} - 10 q^{90} - 8 q^{91} - 12 q^{92} - 5 q^{93} - q^{94} - 20 q^{95} - 34 q^{96} + 32 q^{97} - 8 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8 - q^10 + 8 * q^12 + q^13 + 2 * q^14 - 3 * q^16 - q^17 + 10 * q^18 + 20 * q^19 + q^20 + 10 * q^21 + 5 * q^23 + 11 * q^24 + 4 * q^25 - 15 * q^26 - 15 * q^27 + 13 * q^28 + 12 * q^29 - q^30 - 5 * q^31 - 8 * q^32 + 2 * q^34 - 3 * q^35 + 7 * q^37 + 20 * q^38 + 7 * q^39 - 3 * q^40 + 11 * q^41 + 12 * q^42 + 19 * q^43 - 4 * q^46 + 5 * q^47 - 10 * q^48 + 3 * q^49 + q^50 + 7 * q^51 - 11 * q^52 - 11 * q^53 - 8 * q^54 + 11 * q^56 - 5 * q^57 - 14 * q^58 + 9 * q^59 - 8 * q^60 + 12 * q^61 - 35 * q^62 - 5 * q^63 - 3 * q^64 - q^65 - 19 * q^67 - 3 * q^68 - 8 * q^69 - 2 * q^70 + 5 * q^71 - 25 * q^72 + 11 * q^73 - 8 * q^78 + 34 * q^79 + 3 * q^80 + 4 * q^81 - 6 * q^82 - 11 * q^83 + 11 * q^84 + q^85 + q^86 - 19 * q^87 - 8 * q^89 - 10 * q^90 - 8 * q^91 - 12 * q^92 - 5 * q^93 - q^94 - 20 * q^95 - 34 * q^96 + 32 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	2.09529	1.48160	0.740798	−	0.671728i	$-0.234447\pi$
$2$	2.09529	1.48160	0.740798	+	0.671728i	$0.234447\pi$
$3$	1.91300	1.10447	0.552235	−	0.833689i	$-0.313775\pi$
$3$	1.91300	1.10447	0.552235	+	0.833689i	$0.313775\pi$
$4$	2.39026	1.19513
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.00829	1.63638
$7$	3.06719	1.15929	0.579644	−	0.814870i	$-0.303192\pi$
$7$	3.06719	1.15929	0.579644	+	0.814870i	$0.303192\pi$
$8$	0.817703	0.289102
$9$	0.659557	0.219852
$10$	−2.09529	−0.662590
$11$	0	0
$11$	0	0
$12$	4.57255	1.31998
$13$	−3.04981	−0.845866	−0.422933	−	0.906161i	$-0.638999\pi$
$13$	−3.04981	−0.845866	−0.422933	+	0.906161i	$0.638999\pi$
$14$	6.42666	1.71760
$15$	−1.91300	−0.493934
$16$	−3.06719	−0.766796
$17$	0.463845	0.112499	0.0562495	−	0.998417i	$-0.482086\pi$
$17$	0.463845	0.112499	0.0562495	+	0.998417i	$0.482086\pi$
$18$	1.38197	0.325733
$19$	7.89563	1.81138	0.905690	−	0.423940i	$-0.139353\pi$
$19$	7.89563	1.81138	0.905690	+	0.423940i	$0.139353\pi$
$20$	−2.39026	−0.534478
$21$	5.86752	1.28040
$22$	0	0
$23$	−1.39026	−0.289889	−0.144944	−	0.989440i	$-0.546300\pi$
$23$	−1.39026	−0.289889	−0.144944	+	0.989440i	$0.546300\pi$
$24$	1.56426	0.319304
$25$	1.00000	0.200000
$26$	−6.39026	−1.25323
$27$	−4.47726	−0.861649
$28$	7.33136	1.38550
$29$	−3.72162	−0.691087	−0.345544	−	0.938403i	$-0.612305\pi$
$29$	−3.72162	−0.691087	−0.345544	+	0.938403i	$0.612305\pi$
$30$	−4.00829	−0.731810
$31$	−10.4765	−1.88163	−0.940815	−	0.338921i	$-0.889938\pi$
$31$	−10.4765	−1.88163	−0.940815	+	0.338921i	$0.889938\pi$
$32$	−8.06206	−1.42518
$33$	0	0
$34$	0.971892	0.166678
$35$	−3.06719	−0.518449
$36$	1.57651	0.262752
$37$	1.84453	0.303239	0.151620	−	0.988439i	$-0.451551\pi$
$37$	1.84453	0.303239	0.151620	+	0.988439i	$0.451551\pi$
$38$	16.5437	2.68374
$39$	−5.83428	−0.934233
$40$	−0.817703	−0.129290
$41$	4.40763	0.688356	0.344178	−	0.938904i	$-0.388158\pi$
$41$	4.40763	0.688356	0.344178	+	0.938904i	$0.388158\pi$
$42$	12.2942	1.89703
$43$	1.31478	0.200502	0.100251	−	0.994962i	$-0.468035\pi$
$43$	1.31478	0.200502	0.100251	+	0.994962i	$0.468035\pi$
$44$	0	0
$45$	−0.659557	−0.0983210
$46$	−2.91300	−0.429498
$47$	−2.98018	−0.434704	−0.217352	−	0.976093i	$-0.569742\pi$
$47$	−2.98018	−0.434704	−0.217352	+	0.976093i	$0.569742\pi$
$48$	−5.86752	−0.846903
$49$	2.40763	0.343947
$50$	2.09529	0.296319
$51$	0.887334	0.124252
$52$	−7.28984	−1.01092
$53$	4.18814	0.575286	0.287643	−	0.957738i	$-0.407128\pi$
$53$	4.18814	0.575286	0.287643	+	0.957738i	$0.407128\pi$
$54$	−9.38118	−1.27662
$55$	0	0
$56$	2.50805	0.335152
$57$	15.1043	2.00061
$58$	−7.79789	−1.02391
$59$	2.81502	0.366485	0.183242	−	0.983068i	$-0.441341\pi$
$59$	2.81502	0.366485	0.183242	+	0.983068i	$0.441341\pi$
$60$	−4.57255	−0.590314
$61$	2.01737	0.258298	0.129149	−	0.991625i	$-0.458775\pi$
$61$	2.01737	0.258298	0.129149	+	0.991625i	$0.458775\pi$
$62$	−21.9513	−2.78782
$63$	2.02298	0.254872
$64$	−10.7580	−1.34475
$65$	3.04981	0.378283
$66$	0	0
$67$	−6.75753	−0.825564	−0.412782	−	0.910830i	$-0.635443\pi$
$67$	−6.75753	−0.825564	−0.412782	+	0.910830i	$0.635443\pi$
$68$	1.10871	0.134451
$69$	−2.65956	−0.320173
$70$	−6.42666	−0.768132
$71$	−6.52195	−0.774013	−0.387007	−	0.922077i	$-0.626491\pi$
$71$	−6.52195	−0.774013	−0.387007	+	0.922077i	$0.626491\pi$
$72$	0.539322	0.0635597
$73$	9.87581	1.15588	0.577938	−	0.816081i	$-0.303858\pi$
$73$	9.87581	1.15588	0.577938	+	0.816081i	$0.303858\pi$
$74$	3.86484	0.449278
$75$	1.91300	0.220894
$76$	18.8726	2.16483
$77$	0	0
$78$	−12.2245	−1.38416
$79$	11.5579	1.30036	0.650180	−	0.759780i	$-0.274693\pi$
$79$	11.5579	1.30036	0.650180	+	0.759780i	$0.274693\pi$
$80$	3.06719	0.342922
$81$	−10.5437	−1.17152
$82$	9.23528	1.01987
$83$	−8.91861	−0.978945	−0.489472	−	0.872019i	$-0.662811\pi$
$83$	−8.91861	−0.978945	−0.489472	+	0.872019i	$0.662811\pi$
$84$	14.0249	1.53024
$85$	−0.463845	−0.0503111
$86$	2.75485	0.297063
$87$	−7.11945	−0.763285
$88$	0	0
$89$	−6.76978	−0.717595	−0.358797	−	0.933415i	$-0.616813\pi$
$89$	−6.76978	−0.717595	−0.358797	+	0.933415i	$0.616813\pi$
$90$	−1.38197	−0.145672
$91$	−9.35435	−0.980602
$92$	−3.32307	−0.346454
$93$	−20.0415	−2.07820
$94$	−6.24436	−0.644056
$95$	−7.89563	−0.810074
$96$	−15.4227	−1.57407
$97$	15.3543	1.55900	0.779499	−	0.626404i	$-0.215474\pi$
$97$	15.3543	1.55900	0.779499	+	0.626404i	$0.215474\pi$
$98$	5.04469	0.509591
$99$	0	0
$100$	2.39026	0.239026
$101$	−11.7326	−1.16744	−0.583718	−	0.811956i	$-0.698403\pi$
$101$	−11.7326	−1.16744	−0.583718	+	0.811956i	$0.698403\pi$
$102$	1.85923	0.184091
$103$	13.8881	1.36843	0.684215	−	0.729280i	$-0.260145\pi$
$103$	13.8881	1.36843	0.684215	+	0.729280i	$0.260145\pi$
$104$	−2.49384	−0.244541
$105$	−5.86752	−0.572611
$106$	8.77539	0.852341
$107$	7.32100	0.707748	0.353874	−	0.935293i	$-0.384864\pi$
$107$	7.32100	0.707748	0.353874	+	0.935293i	$0.384864\pi$
$108$	−10.7018	−1.02978
$109$	7.43306	0.711958	0.355979	−	0.934494i	$-0.384147\pi$
$109$	7.43306	0.711958	0.355979	+	0.934494i	$0.384147\pi$
$110$	0	0
$111$	3.52859	0.334919
$112$	−9.40763	−0.888937
$113$	−3.03640	−0.285640	−0.142820	−	0.989749i	$-0.545617\pi$
$113$	−3.03640	−0.285640	−0.142820	+	0.989749i	$0.545617\pi$
$114$	31.6480	2.96410
$115$	1.39026	0.129642
$116$	−8.89563	−0.825938
$117$	−2.01153	−0.185966
$118$	5.89830	0.542983
$119$	1.42270	0.130419
$120$	−1.56426	−0.142797
$121$	0	0
$122$	4.22699	0.382693
$123$	8.43178	0.760268
$124$	−25.0415	−2.24879
$125$	−1.00000	−0.0894427
$126$	4.23875	0.377618
$127$	0.451597	0.0400728	0.0200364	−	0.999799i	$-0.493622\pi$
$127$	0.451597	0.0400728	0.0200364	+	0.999799i	$0.493622\pi$
$128$	−6.41709	−0.567196
$129$	2.51517	0.221448
$130$	6.39026	0.560463
$131$	−0.629003	−0.0549563	−0.0274781	−	0.999622i	$-0.508748\pi$
$131$	−0.629003	−0.0549563	−0.0274781	+	0.999622i	$0.508748\pi$
$132$	0	0
$133$	24.2173	2.09991
$134$	−14.1590	−1.22315
$135$	4.47726	0.385341
$136$	0.379287	0.0325236
$137$	11.1834	0.955462	0.477731	−	0.878506i	$-0.341459\pi$
$137$	11.1834	0.955462	0.477731	+	0.878506i	$0.341459\pi$
$138$	−5.57255	−0.474367
$139$	2.37495	0.201441	0.100720	−	0.994915i	$-0.467885\pi$
$139$	2.37495	0.201441	0.100720	+	0.994915i	$0.467885\pi$
$140$	−7.33136	−0.619613
$141$	−5.70108	−0.480118
$142$	−13.6654	−1.14678
$143$	0	0
$144$	−2.02298	−0.168582
$145$	3.72162	0.309064
$146$	20.6927	1.71254
$147$	4.60579	0.379879
$148$	4.40891	0.362410
$149$	8.72034	0.714398	0.357199	−	0.934028i	$-0.383732\pi$
$149$	8.72034	0.714398	0.357199	+	0.934028i	$0.383732\pi$
$150$	4.00829	0.327276
$151$	−11.9354	−0.971291	−0.485646	−	0.874156i	$-0.661415\pi$
$151$	−11.9354	−0.971291	−0.485646	+	0.874156i	$0.661415\pi$
$152$	6.45628	0.523673
$153$	0.305932	0.0247332
$154$	0	0
$155$	10.4765	0.841490
$156$	−13.9454	−1.11653
$157$	3.87532	0.309284	0.154642	−	0.987971i	$-0.450578\pi$
$157$	3.87532	0.309284	0.154642	+	0.987971i	$0.450578\pi$
$158$	24.2171	1.92661
$159$	8.01190	0.635385
$160$	8.06206	0.637362
$161$	−4.26418	−0.336064
$162$	−22.0921	−1.73572
$163$	−9.93621	−0.778264	−0.389132	−	0.921182i	$-0.627225\pi$
$163$	−9.93621	−0.778264	−0.389132	+	0.921182i	$0.627225\pi$
$164$	10.5354	0.822674
$165$	0	0
$166$	−18.6871	−1.45040
$167$	−13.9200	−1.07716	−0.538581	−	0.842574i	$-0.681040\pi$
$167$	−13.9200	−1.07716	−0.538581	+	0.842574i	$0.681040\pi$
$168$	4.79789	0.370165
$169$	−3.69863	−0.284510
$170$	−0.971892	−0.0745407
$171$	5.20762	0.398236
$172$	3.14266	0.239626
$173$	−10.8311	−0.823475	−0.411737	−	0.911303i	$-0.635078\pi$
$173$	−10.8311	−0.823475	−0.411737	+	0.911303i	$0.635078\pi$
$174$	−14.9173	−1.13088
$175$	3.06719	0.231857
$176$	0	0
$177$	5.38513	0.404771
$178$	−14.1847	−1.06319
$179$	22.7335	1.69918	0.849589	−	0.527445i	$-0.176850\pi$
$179$	22.7335	1.69918	0.849589	+	0.527445i	$0.176850\pi$
$180$	−1.57651	−0.117506
$181$	2.39831	0.178265	0.0891327	−	0.996020i	$-0.471590\pi$
$181$	2.39831	0.178265	0.0891327	+	0.996020i	$0.471590\pi$
$182$	−19.6001	−1.45286
$183$	3.85923	0.285282
$184$	−1.13682	−0.0838073
$185$	−1.84453	−0.135613
$186$	−41.9927	−3.07906
$187$	0	0
$188$	−7.12340	−0.519527
$189$	−13.7326	−0.998899
$190$	−16.5437	−1.20020
$191$	17.2462	1.24789	0.623947	−	0.781466i	$-0.285528\pi$
$191$	17.2462	1.24789	0.623947	+	0.781466i	$0.285528\pi$
$192$	−20.5801	−1.48524
$193$	2.58574	0.186125	0.0930627	−	0.995660i	$-0.470334\pi$
$193$	2.58574	0.186125	0.0930627	+	0.995660i	$0.470334\pi$
$194$	32.1719	2.30981
$195$	5.83428	0.417802
$196$	5.75485	0.411061
$197$	−0.144731	−0.0103116	−0.00515582	−	0.999987i	$-0.501641\pi$
$197$	−0.144731	−0.0103116	−0.00515582	+	0.999987i	$0.501641\pi$
$198$	0	0
$199$	−7.54177	−0.534622	−0.267311	−	0.963610i	$-0.586135\pi$
$199$	−7.54177	−0.534622	−0.267311	+	0.963610i	$0.586135\pi$
$200$	0.817703	0.0578203
$201$	−12.9271	−0.911810
$202$	−24.5832	−1.72967
$203$	−11.4149	−0.801169
$204$	2.12096	0.148497
$205$	−4.40763	−0.307842
$206$	29.0996	2.02746
$207$	−0.916954	−0.0637327
$208$	9.35435	0.648607
$209$	0	0
$210$	−12.2942	−0.848379
$211$	2.26881	0.156191	0.0780957	−	0.996946i	$-0.475116\pi$
$211$	2.26881	0.156191	0.0780957	+	0.996946i	$0.475116\pi$
$212$	10.0107	0.687540
$213$	−12.4765	−0.854874
$214$	15.3397	1.04860
$215$	−1.31478	−0.0896673
$216$	−3.66107	−0.249104
$217$	−32.1333	−2.18135
$218$	15.5744	1.05483
$219$	18.8924	1.27663
$220$	0	0
$221$	−1.41464	−0.0951591
$222$	7.39342	0.496214
$223$	8.57968	0.574538	0.287269	−	0.957850i	$-0.407253\pi$
$223$	8.57968	0.574538	0.287269	+	0.957850i	$0.407253\pi$
$224$	−24.7278	−1.65220
$225$	0.659557	0.0439705
$226$	−6.36215	−0.423204
$227$	−6.20039	−0.411534	−0.205767	−	0.978601i	$-0.565969\pi$
$227$	−6.20039	−0.411534	−0.205767	+	0.978601i	$0.565969\pi$
$228$	36.1032	2.39099
$229$	23.1659	1.53084	0.765422	−	0.643528i	$-0.222530\pi$
$229$	23.1659	1.53084	0.765422	+	0.643528i	$0.222530\pi$
$230$	2.91300	0.192077
$231$	0	0
$232$	−3.04318	−0.199794
$233$	27.8627	1.82535	0.912673	−	0.408690i	$-0.134014\pi$
$233$	27.8627	1.82535	0.912673	+	0.408690i	$0.134014\pi$
$234$	−4.21474	−0.275526
$235$	2.98018	0.194406
$236$	6.72863	0.437997
$237$	22.1102	1.43621
$238$	2.98097	0.193228
$239$	16.2862	1.05347	0.526734	−	0.850030i	$-0.323416\pi$
$239$	16.2862	1.05347	0.526734	+	0.850030i	$0.323416\pi$
$240$	5.86752	0.378747
$241$	−4.39063	−0.282826	−0.141413	−	0.989951i	$-0.545164\pi$
$241$	−4.39063	−0.282826	−0.141413	+	0.989951i	$0.545164\pi$
$242$	0	0
$243$	−6.73820	−0.432256
$244$	4.82204	0.308699
$245$	−2.40763	−0.153818
$246$	17.6671	1.12641
$247$	−24.0802	−1.53219
$248$	−8.56664	−0.543982
$249$	−17.0613	−1.08121
$250$	−2.09529	−0.132518
$251$	−2.66668	−0.168319	−0.0841597	−	0.996452i	$-0.526821\pi$
$251$	−2.66668	−0.168319	−0.0841597	+	0.996452i	$0.526821\pi$
$252$	4.83545	0.304605
$253$	0	0
$254$	0.946229	0.0593717
$255$	−0.887334	−0.0555670
$256$	8.07035	0.504397
$257$	−21.6327	−1.34941	−0.674704	−	0.738088i	$-0.735729\pi$
$257$	−21.6327	−1.34941	−0.674704	+	0.738088i	$0.735729\pi$
$258$	5.27002	0.328097
$259$	5.65752	0.351541
$260$	7.28984	0.452097
$261$	−2.45462	−0.151937
$262$	−1.31795	−0.0814230
$263$	−22.1392	−1.36516	−0.682581	−	0.730810i	$-0.739142\pi$
$263$	−22.1392	−1.36516	−0.682581	+	0.730810i	$0.739142\pi$
$264$	0	0
$265$	−4.18814	−0.257276
$266$	50.7425	3.11122
$267$	−12.9506	−0.792562
$268$	−16.1522	−0.986655
$269$	20.7184	1.26322	0.631611	−	0.775285i	$-0.282394\pi$
$269$	20.7184	1.26322	0.631611	+	0.775285i	$0.282394\pi$
$270$	9.38118	0.570920
$271$	0.423112	0.0257022	0.0128511	−	0.999917i	$-0.495909\pi$
$271$	0.423112	0.0257022	0.0128511	+	0.999917i	$0.495909\pi$
$272$	−1.42270	−0.0862638
$273$	−17.8948	−1.08304
$274$	23.4325	1.41561
$275$	0	0
$276$	−6.35702	−0.382648
$277$	8.57255	0.515075	0.257537	−	0.966268i	$-0.417089\pi$
$277$	8.57255	0.515075	0.257537	+	0.966268i	$0.417089\pi$
$278$	4.97623	0.298454
$279$	−6.90983	−0.413681
$280$	−2.50805	−0.149884
$281$	7.01108	0.418246	0.209123	−	0.977889i	$-0.432939\pi$
$281$	7.01108	0.418246	0.209123	+	0.977889i	$0.432939\pi$
$282$	−11.9454	−0.711341
$283$	−9.95317	−0.591655	−0.295827	−	0.955241i	$-0.595595\pi$
$283$	−9.95317	−0.591655	−0.295827	+	0.955241i	$0.595595\pi$
$284$	−15.5891	−0.925045
$285$	−15.1043	−0.894702
$286$	0	0
$287$	13.5190	0.798002
$288$	−5.31739	−0.313330
$289$	−16.7848	−0.987344
$290$	7.79789	0.457908
$291$	29.3728	1.72186
$292$	23.6057	1.38142
$293$	−21.8209	−1.27479	−0.637394	−	0.770538i	$-0.719988\pi$
$293$	−21.8209	−1.27479	−0.637394	+	0.770538i	$0.719988\pi$
$294$	9.65048	0.562827
$295$	−2.81502	−0.163897
$296$	1.50828	0.0876670
$297$	0	0
$298$	18.2717	1.05845
$299$	4.24002	0.245207
$300$	4.57255	0.263997
$301$	4.03268	0.232440
$302$	−25.0082	−1.43906
$303$	−22.4444	−1.28940
$304$	−24.2173	−1.38896
$305$	−2.01737	−0.115514
$306$	0.641018	0.0366446
$307$	30.8674	1.76170	0.880849	−	0.473397i	$-0.156972\pi$
$307$	30.8674	1.76170	0.880849	+	0.473397i	$0.156972\pi$
$308$	0	0
$309$	26.5678	1.51139
$310$	21.9513	1.24675
$311$	−19.4150	−1.10092	−0.550462	−	0.834860i	$-0.685549\pi$
$311$	−19.4150	−1.10092	−0.550462	+	0.834860i	$0.685549\pi$
$312$	−4.77071	−0.270088
$313$	1.05147	0.0594326	0.0297163	−	0.999558i	$-0.490540\pi$
$313$	1.05147	0.0594326	0.0297163	+	0.999558i	$0.490540\pi$
$314$	8.11993	0.458234
$315$	−2.02298	−0.113982
$316$	27.6263	1.55410
$317$	−23.8314	−1.33851	−0.669253	−	0.743034i	$-0.733386\pi$
$317$	−23.8314	−1.33851	−0.669253	+	0.743034i	$0.733386\pi$
$318$	16.7873	0.941385
$319$	0	0
$320$	10.7580	0.601391
$321$	14.0051	0.781686
$322$	−8.93470	−0.497912
$323$	3.66235	0.203778
$324$	−25.2020	−1.40011
$325$	−3.04981	−0.169173
$326$	−20.8193	−1.15307
$327$	14.2194	0.786336
$328$	3.60413	0.199005
$329$	−9.14077	−0.503947
$330$	0	0
$331$	25.6693	1.41091	0.705457	−	0.708753i	$-0.250742\pi$
$331$	25.6693	1.41091	0.705457	+	0.708753i	$0.250742\pi$
$332$	−21.3178	−1.16996
$333$	1.21657	0.0666679
$334$	−29.1665	−1.59592
$335$	6.75753	0.369203
$336$	−17.9968	−0.981804
$337$	23.8922	1.30149	0.650744	−	0.759297i	$-0.274457\pi$
$337$	23.8922	1.30149	0.650744	+	0.759297i	$0.274457\pi$
$338$	−7.74973	−0.421530
$339$	−5.80862	−0.315481
$340$	−1.10871	−0.0601282
$341$	0	0
$342$	10.9115	0.590026
$343$	−14.0857	−0.760554
$344$	1.07510	0.0579655
$345$	2.65956	0.143186
$346$	−22.6944	−1.22006
$347$	0.332152	0.0178309	0.00891543	−	0.999960i	$-0.497162\pi$
$347$	0.332152	0.0178309	0.00891543	+	0.999960i	$0.497162\pi$
$348$	−17.0173	−0.912223
$349$	−1.22149	−0.0653846	−0.0326923	−	0.999465i	$-0.510408\pi$
$349$	−1.22149	−0.0653846	−0.0326923	+	0.999465i	$0.510408\pi$
$350$	6.42666	0.343519
$351$	13.6548	0.728840
$352$	0	0
$353$	−25.7038	−1.36808	−0.684039	−	0.729446i	$-0.739778\pi$
$353$	−25.7038	−1.36808	−0.684039	+	0.729446i	$0.739778\pi$
$354$	11.2834	0.599708
$355$	6.52195	0.346149
$356$	−16.1815	−0.857618
$357$	2.72162	0.144043
$358$	47.6333	2.51750
$359$	17.9315	0.946387	0.473193	−	0.880959i	$-0.343101\pi$
$359$	17.9315	0.946387	0.473193	+	0.880959i	$0.343101\pi$
$360$	−0.539322	−0.0284248
$361$	43.3409	2.28110
$362$	5.02517	0.264117
$363$	0	0
$364$	−22.3593	−1.17195
$365$	−9.87581	−0.516923
$366$	8.08621	0.422673
$367$	−8.49091	−0.443222	−0.221611	−	0.975135i	$-0.571131\pi$
$367$	−8.49091	−0.443222	−0.221611	+	0.975135i	$0.571131\pi$
$368$	4.26418	0.222286
$369$	2.90708	0.151337
$370$	−3.86484	−0.200923
$371$	12.8458	0.666921
$372$	−47.9042	−2.48372
$373$	−35.8450	−1.85598	−0.927991	−	0.372604i	$-0.878465\pi$
$373$	−35.8450	−1.85598	−0.927991	+	0.372604i	$0.878465\pi$
$374$	0	0
$375$	−1.91300	−0.0987867
$376$	−2.43690	−0.125674
$377$	11.3502	0.584567
$378$	−28.7738	−1.47997
$379$	17.5516	0.901564	0.450782	−	0.892634i	$-0.351145\pi$
$379$	17.5516	0.901564	0.450782	+	0.892634i	$0.351145\pi$
$380$	−18.8726	−0.968143
$381$	0.863904	0.0442592
$382$	36.1360	1.84888
$383$	−21.6250	−1.10499	−0.552494	−	0.833517i	$-0.686324\pi$
$383$	−21.6250	−1.10499	−0.552494	+	0.833517i	$0.686324\pi$
$384$	−12.2759	−0.626450
$385$	0	0
$386$	5.41788	0.275763
$387$	0.867173	0.0440809
$388$	36.7008	1.86320
$389$	35.7416	1.81217	0.906086	−	0.423093i	$-0.139056\pi$
$389$	35.7416	1.81217	0.906086	+	0.423093i	$0.139056\pi$
$390$	12.2245	0.619014
$391$	−0.644864	−0.0326122
$392$	1.96872	0.0994356
$393$	−1.20328	−0.0606975
$394$	−0.303254	−0.0152777
$395$	−11.5579	−0.581539
$396$	0	0
$397$	−20.0447	−1.00601	−0.503007	−	0.864282i	$-0.667773\pi$
$397$	−20.0447	−1.00601	−0.503007	+	0.864282i	$0.667773\pi$
$398$	−15.8022	−0.792094
$399$	46.3277	2.31929
$400$	−3.06719	−0.153359
$401$	−20.8987	−1.04363	−0.521815	−	0.853059i	$-0.674745\pi$
$401$	−20.8987	−1.04363	−0.521815	+	0.853059i	$0.674745\pi$
$402$	−27.0861	−1.35093
$403$	31.9513	1.59161
$404$	−28.0439	−1.39524
$405$	10.5437	0.523918
$406$	−23.9176	−1.18701
$407$	0	0
$408$	0.725576	0.0359214
$409$	−23.4982	−1.16191	−0.580955	−	0.813936i	$-0.697321\pi$
$409$	−23.4982	−1.16191	−0.580955	+	0.813936i	$0.697321\pi$
$410$	−9.23528	−0.456098
$411$	21.3938	1.05528
$412$	33.1960	1.63545
$413$	8.63420	0.424861
$414$	−1.92129	−0.0944261
$415$	8.91861	0.437797
$416$	24.5878	1.20552
$417$	4.54328	0.222485
$418$	0	0
$419$	−10.1128	−0.494043	−0.247022	−	0.969010i	$-0.579452\pi$
$419$	−10.1128	−0.494043	−0.247022	+	0.969010i	$0.579452\pi$
$420$	−14.0249	−0.684344
$421$	8.92283	0.434872	0.217436	−	0.976075i	$-0.430231\pi$
$421$	8.92283	0.434872	0.217436	+	0.976075i	$0.430231\pi$
$422$	4.75383	0.231413
$423$	−1.96560	−0.0955708
$424$	3.42466	0.166316
$425$	0.463845	0.0224998
$426$	−26.1419	−1.26658
$427$	6.18765	0.299442
$428$	17.4991	0.845850
$429$	0	0
$430$	−2.75485	−0.132851
$431$	17.6122	0.848352	0.424176	−	0.905580i	$-0.360564\pi$
$431$	17.6122	0.848352	0.424176	+	0.905580i	$0.360564\pi$
$432$	13.7326	0.660709
$433$	9.14397	0.439431	0.219716	−	0.975564i	$-0.429487\pi$
$433$	9.14397	0.439431	0.219716	+	0.975564i	$0.429487\pi$
$434$	−67.3287	−3.23188
$435$	7.11945	0.341351
$436$	17.7669	0.850881
$437$	−10.9769	−0.525099
$438$	39.5851	1.89145
$439$	−6.46946	−0.308770	−0.154385	−	0.988011i	$-0.549340\pi$
$439$	−6.46946	−0.308770	−0.154385	+	0.988011i	$0.549340\pi$
$440$	0	0
$441$	1.58797	0.0756176
$442$	−2.96409	−0.140987
$443$	−40.8842	−1.94247	−0.971233	−	0.238132i	$-0.923465\pi$
$443$	−40.8842	−1.94247	−0.971233	+	0.238132i	$0.923465\pi$
$444$	8.43423	0.400271
$445$	6.76978	0.320918
$446$	17.9769	0.851233
$447$	16.6820	0.789031
$448$	−32.9968	−1.55895
$449$	−12.1608	−0.573902	−0.286951	−	0.957945i	$-0.592642\pi$
$449$	−12.1608	−0.573902	−0.286951	+	0.957945i	$0.592642\pi$
$450$	1.38197	0.0651465
$451$	0	0
$452$	−7.25777	−0.341377
$453$	−22.8324	−1.07276
$454$	−12.9916	−0.609728
$455$	9.35435	0.438539
$456$	12.3508	0.578381
$457$	9.90240	0.463215	0.231607	−	0.972809i	$-0.425602\pi$
$457$	9.90240	0.463215	0.231607	+	0.972809i	$0.425602\pi$
$458$	48.5393	2.26809
$459$	−2.07676	−0.0969346
$460$	3.32307	0.154939
$461$	3.12529	0.145559	0.0727796	−	0.997348i	$-0.476813\pi$
$461$	3.12529	0.145559	0.0727796	+	0.997348i	$0.476813\pi$
$462$	0	0
$463$	−24.3518	−1.13173	−0.565863	−	0.824499i	$-0.691457\pi$
$463$	−24.3518	−1.13173	−0.565863	+	0.824499i	$0.691457\pi$
$464$	11.4149	0.529923
$465$	20.0415	0.929400
$466$	58.3806	2.70443
$467$	33.1737	1.53510	0.767548	−	0.640991i	$-0.221477\pi$
$467$	33.1737	1.53510	0.767548	+	0.640991i	$0.221477\pi$
$468$	−4.80806	−0.222253
$469$	−20.7266	−0.957065
$470$	6.24436	0.288031
$471$	7.41347	0.341595
$472$	2.30185	0.105951
$473$	0	0
$474$	46.3273	2.12788
$475$	7.89563	0.362276
$476$	3.40062	0.155867
$477$	2.76232	0.126478
$478$	34.1244	1.56082
$479$	17.2977	0.790353	0.395176	−	0.918605i	$-0.370683\pi$
$479$	17.2977	0.790353	0.395176	+	0.918605i	$0.370683\pi$
$480$	15.4227	0.703947
$481$	−5.62548	−0.256500
$482$	−9.19967	−0.419033
$483$	−8.15736	−0.371173
$484$	0	0
$485$	−15.3543	−0.697205
$486$	−14.1185	−0.640429
$487$	7.64061	0.346229	0.173114	−	0.984902i	$-0.444617\pi$
$487$	7.64061	0.346229	0.173114	+	0.984902i	$0.444617\pi$
$488$	1.64961	0.0746744
$489$	−19.0079	−0.859569
$490$	−5.04469	−0.227896
$491$	30.6563	1.38350	0.691750	−	0.722137i	$-0.256840\pi$
$491$	30.6563	1.38350	0.691750	+	0.722137i	$0.256840\pi$
$492$	20.1541	0.908618
$493$	−1.72625	−0.0777466
$494$	−50.4551	−2.27008
$495$	0	0
$496$	32.1333	1.44283
$497$	−20.0040	−0.897303
$498$	−35.7484	−1.60192
$499$	−37.4783	−1.67776	−0.838879	−	0.544317i	$-0.816789\pi$
$499$	−37.4783	−1.67776	−0.838879	+	0.544317i	$0.816789\pi$
$500$	−2.39026	−0.106896
$501$	−26.6289	−1.18969
$502$	−5.58748	−0.249381
$503$	−8.47695	−0.377969	−0.188984	−	0.981980i	$-0.560520\pi$
$503$	−8.47695	−0.377969	−0.188984	+	0.981980i	$0.560520\pi$
$504$	1.65420	0.0736839
$505$	11.7326	0.522093
$506$	0	0
$507$	−7.07548	−0.314233
$508$	1.07943	0.0478921
$509$	−1.69723	−0.0752286	−0.0376143	−	0.999292i	$-0.511976\pi$
$509$	−1.69723	−0.0752286	−0.0376143	+	0.999292i	$0.511976\pi$
$510$	−1.85923	−0.0823279
$511$	30.2909	1.33999
$512$	29.7439	1.31451
$513$	−35.3508	−1.56077
$514$	−45.3268	−1.99928
$515$	−13.8881	−0.611981
$516$	6.01190	0.264659
$517$	0	0
$518$	11.8542	0.520843
$519$	−20.7199	−0.909502
$520$	2.49384	0.109362
$521$	−37.0929	−1.62507	−0.812535	−	0.582912i	$-0.801913\pi$
$521$	−37.0929	−1.62507	−0.812535	+	0.582912i	$0.801913\pi$
$522$	−5.14315	−0.225110
$523$	18.0818	0.790662	0.395331	−	0.918539i	$-0.370630\pi$
$523$	18.0818	0.790662	0.395331	+	0.918539i	$0.370630\pi$
$524$	−1.50348	−0.0656798
$525$	5.86752	0.256079
$526$	−46.3881	−2.02262
$527$	−4.85946	−0.211681
$528$	0	0
$529$	−21.0672	−0.915965
$530$	−8.77539	−0.381179
$531$	1.85667	0.0805726
$532$	57.8857	2.50966
$533$	−13.4424	−0.582257
$534$	−27.1352	−1.17426
$535$	−7.32100	−0.316515
$536$	−5.52565	−0.238672
$537$	43.4890	1.87669
$538$	43.4111	1.87159
$539$	0	0
$540$	10.7018	0.460532
$541$	−11.7524	−0.505275	−0.252638	−	0.967561i	$-0.581298\pi$
$541$	−11.7524	−0.505275	−0.252638	+	0.967561i	$0.581298\pi$
$542$	0.886544	0.0380803
$543$	4.58797	0.196889
$544$	−3.73955	−0.160332
$545$	−7.43306	−0.318397
$546$	−37.4949	−1.60464
$547$	21.7569	0.930256	0.465128	−	0.885243i	$-0.346008\pi$
$547$	21.7569	0.930256	0.465128	+	0.885243i	$0.346008\pi$
$548$	26.7312	1.14190
$549$	1.33057	0.0567874
$550$	0	0
$551$	−29.3845	−1.25182
$552$	−2.17473	−0.0925626
$553$	35.4501	1.50749
$554$	17.9620	0.763133
$555$	−3.52859	−0.149780
$556$	5.67675	0.240748
$557$	−4.83432	−0.204837	−0.102418	−	0.994741i	$-0.532658\pi$
$557$	−4.83432	−0.204837	−0.102418	+	0.994741i	$0.532658\pi$
$558$	−14.4781	−0.612908
$559$	−4.00984	−0.169598
$560$	9.40763	0.397545
$561$	0	0
$562$	14.6903	0.619672
$563$	−4.77199	−0.201115	−0.100558	−	0.994931i	$-0.532063\pi$
$563$	−4.77199	−0.201115	−0.100558	+	0.994931i	$0.532063\pi$
$564$	−13.6270	−0.573802
$565$	3.03640	0.127742
$566$	−20.8548	−0.876594
$567$	−32.3394	−1.35813
$568$	−5.33302	−0.223768
$569$	−35.7187	−1.49741	−0.748703	−	0.662905i	$-0.769323\pi$
$569$	−35.7187	−1.49741	−0.748703	+	0.662905i	$0.769323\pi$
$570$	−31.6480	−1.32559
$571$	33.9838	1.42218	0.711090	−	0.703101i	$-0.248202\pi$
$571$	33.9838	1.42218	0.711090	+	0.703101i	$0.248202\pi$
$572$	0	0
$573$	32.9920	1.37826
$574$	28.3263	1.18232
$575$	−1.39026	−0.0579777
$576$	−7.09553	−0.295647
$577$	−20.6579	−0.860000	−0.430000	−	0.902829i	$-0.641486\pi$
$577$	−20.6579	−0.860000	−0.430000	+	0.902829i	$0.641486\pi$
$578$	−35.1692	−1.46285
$579$	4.94650	0.205570
$580$	8.89563	0.369371
$581$	−27.3550	−1.13488
$582$	61.5447	2.55111
$583$	0	0
$584$	8.07548	0.334166
$585$	2.01153	0.0831664
$586$	−45.7211	−1.88872
$587$	13.3600	0.551428	0.275714	−	0.961240i	$-0.411086\pi$
$587$	13.3600	0.551428	0.275714	+	0.961240i	$0.411086\pi$
$588$	11.0090	0.454004
$589$	−82.7183	−3.40835
$590$	−5.89830	−0.242829
$591$	−0.276870	−0.0113889
$592$	−5.65752	−0.232523
$593$	−20.8062	−0.854410	−0.427205	−	0.904155i	$-0.640502\pi$
$593$	−20.8062	−0.854410	−0.427205	+	0.904155i	$0.640502\pi$
$594$	0	0
$595$	−1.42270	−0.0583250
$596$	20.8439	0.853798
$597$	−14.4274	−0.590473
$598$	8.88410	0.363298
$599$	−14.2456	−0.582061	−0.291030	−	0.956714i	$-0.593998\pi$
$599$	−14.2456	−0.582061	−0.291030	+	0.956714i	$0.593998\pi$
$600$	1.56426	0.0638608
$601$	20.7462	0.846255	0.423127	−	0.906070i	$-0.360932\pi$
$601$	20.7462	0.846255	0.423127	+	0.906070i	$0.360932\pi$
$602$	8.44964	0.344382
$603$	−4.45698	−0.181502
$604$	−28.5287	−1.16082
$605$	0	0
$606$	−47.0276	−1.91037
$607$	−17.9219	−0.727428	−0.363714	−	0.931511i	$-0.618492\pi$
$607$	−17.9219	−0.727428	−0.363714	+	0.931511i	$0.618492\pi$
$608$	−63.6550	−2.58155
$609$	−21.8367	−0.884866
$610$	−4.22699	−0.171146
$611$	9.08900	0.367702
$612$	0.731257	0.0295593
$613$	28.2019	1.13906	0.569531	−	0.821970i	$-0.307125\pi$
$613$	28.2019	1.13906	0.569531	+	0.821970i	$0.307125\pi$
$614$	64.6764	2.61013
$615$	−8.43178	−0.340002
$616$	0	0
$617$	−4.72930	−0.190394	−0.0951972	−	0.995458i	$-0.530348\pi$
$617$	−4.72930	−0.190394	−0.0951972	+	0.995458i	$0.530348\pi$
$618$	55.6674	2.23927
$619$	−30.0575	−1.20811	−0.604056	−	0.796942i	$-0.706450\pi$
$619$	−30.0575	−1.20811	−0.604056	+	0.796942i	$0.706450\pi$
$620$	25.0415	1.00569
$621$	6.22454	0.249782
$622$	−40.6802	−1.63113
$623$	−20.7642	−0.831899
$624$	17.8948	0.716367
$625$	1.00000	0.0400000
$626$	2.20314	0.0880551
$627$	0	0
$628$	9.26301	0.369634
$629$	0.855577	0.0341141
$630$	−4.23875	−0.168876
$631$	−31.7036	−1.26210	−0.631050	−	0.775742i	$-0.717376\pi$
$631$	−31.7036	−1.26210	−0.631050	+	0.775742i	$0.717376\pi$
$632$	9.45090	0.375936
$633$	4.34023	0.172509
$634$	−49.9338	−1.98313
$635$	−0.451597	−0.0179211
$636$	19.1505	0.759367
$637$	−7.34282	−0.290933
$638$	0	0
$639$	−4.30160	−0.170169
$640$	6.41709	0.253658
$641$	−18.9573	−0.748770	−0.374385	−	0.927273i	$-0.622146\pi$
$641$	−18.9573	−0.748770	−0.374385	+	0.927273i	$0.622146\pi$
$642$	29.3447	1.15814
$643$	−36.2489	−1.42952	−0.714758	−	0.699372i	$-0.753463\pi$
$643$	−36.2489	−1.42952	−0.714758	+	0.699372i	$0.753463\pi$
$644$	−10.1925	−0.401640
$645$	−2.51517	−0.0990347
$646$	7.67369	0.301917
$647$	−34.9519	−1.37410	−0.687050	−	0.726610i	$-0.741095\pi$
$647$	−34.9519	−1.37410	−0.687050	+	0.726610i	$0.741095\pi$
$648$	−8.62158	−0.338688
$649$	0	0
$650$	−6.39026	−0.250646
$651$	−61.4709	−2.40923
$652$	−23.7501	−0.930126
$653$	−29.7893	−1.16574	−0.582872	−	0.812564i	$-0.698071\pi$
$653$	−29.7893	−1.16574	−0.582872	+	0.812564i	$0.698071\pi$
$654$	29.7939	1.16503
$655$	0.629003	0.0245772
$656$	−13.5190	−0.527829
$657$	6.51366	0.254122
$658$	−19.1526	−0.746646
$659$	7.30532	0.284575	0.142287	−	0.989825i	$-0.454554\pi$
$659$	7.30532	0.284575	0.142287	+	0.989825i	$0.454554\pi$
$660$	0	0
$661$	−22.7352	−0.884296	−0.442148	−	0.896942i	$-0.645783\pi$
$661$	−22.7352	−0.884296	−0.442148	+	0.896942i	$0.645783\pi$
$662$	53.7848	2.09040
$663$	−2.70620	−0.105100
$664$	−7.29277	−0.283014
$665$	−24.2173	−0.939109
$666$	2.54908	0.0987749
$667$	5.17401	0.200338
$668$	−33.2724	−1.28735
$669$	16.4129	0.634559
$670$	14.1590	0.547010
$671$	0	0
$672$	−47.3043	−1.82480
$673$	17.7451	0.684024	0.342012	−	0.939696i	$-0.388892\pi$
$673$	17.7451	0.684024	0.342012	+	0.939696i	$0.388892\pi$
$674$	50.0611	1.92828
$675$	−4.47726	−0.172330
$676$	−8.84069	−0.340026
$677$	−8.16216	−0.313697	−0.156849	−	0.987623i	$-0.550133\pi$
$677$	−8.16216	−0.313697	−0.156849	+	0.987623i	$0.550133\pi$
$678$	−12.1708	−0.467416
$679$	47.0946	1.80733
$680$	−0.379287	−0.0145450
$681$	−11.8613	−0.454527
$682$	0	0
$683$	−6.19100	−0.236892	−0.118446	−	0.992960i	$-0.537791\pi$
$683$	−6.19100	−0.236892	−0.118446	+	0.992960i	$0.537791\pi$
$684$	12.4475	0.475944
$685$	−11.1834	−0.427296
$686$	−29.5136	−1.12683
$687$	44.3163	1.69077
$688$	−4.03268	−0.153744
$689$	−12.7731	−0.486615
$690$	5.57255	0.212144
$691$	23.6051	0.897981	0.448990	−	0.893537i	$-0.351784\pi$
$691$	23.6051	0.897981	0.448990	+	0.893537i	$0.351784\pi$
$692$	−25.8892	−0.984158
$693$	0	0
$694$	0.695956	0.0264181
$695$	−2.37495	−0.0900871
$696$	−5.82159	−0.220667
$697$	2.04446	0.0774393
$698$	−2.55937	−0.0968737
$699$	53.3013	2.01604
$700$	7.33136	0.277099
$701$	−37.2284	−1.40610	−0.703049	−	0.711142i	$-0.748178\pi$
$701$	−37.2284	−1.40610	−0.703049	+	0.711142i	$0.748178\pi$
$702$	28.6108	1.07985
$703$	14.5637	0.549282
$704$	0	0
$705$	5.70108	0.214715
$706$	−53.8571	−2.02694
$707$	−35.9860	−1.35339
$708$	12.8719	0.483754
$709$	18.2537	0.685534	0.342767	−	0.939420i	$-0.388636\pi$
$709$	18.2537	0.685534	0.342767	+	0.939420i	$0.388636\pi$
$710$	13.6654	0.512853
$711$	7.62307	0.285887
$712$	−5.53567	−0.207458
$713$	14.5650	0.545463
$714$	5.70259	0.213414
$715$	0	0
$716$	54.3388	2.03074
$717$	31.1555	1.16352
$718$	37.5717	1.40216
$719$	9.57389	0.357046	0.178523	−	0.983936i	$-0.442868\pi$
$719$	9.57389	0.357046	0.178523	+	0.983936i	$0.442868\pi$
$720$	2.02298	0.0753922
$721$	42.5972	1.58640
$722$	90.8119	3.37967
$723$	−8.39927	−0.312372
$724$	5.73259	0.213050
$725$	−3.72162	−0.138217
$726$	0	0
$727$	−14.0175	−0.519882	−0.259941	−	0.965625i	$-0.583703\pi$
$727$	−14.0175	−0.519882	−0.259941	+	0.965625i	$0.583703\pi$
$728$	−7.64908	−0.283494
$729$	18.7408	0.694104
$730$	−20.6927	−0.765872
$731$	0.609854	0.0225563
$732$	9.22454	0.340949
$733$	−9.28772	−0.343050	−0.171525	−	0.985180i	$-0.554869\pi$
$733$	−9.28772	−0.343050	−0.171525	+	0.985180i	$0.554869\pi$
$734$	−17.7909	−0.656676
$735$	−4.60579	−0.169887
$736$	11.2083	0.413145
$737$	0	0
$738$	6.09119	0.224220
$739$	38.9586	1.43312	0.716558	−	0.697527i	$-0.245716\pi$
$739$	38.9586	1.43312	0.716558	+	0.697527i	$0.245716\pi$
$740$	−4.40891	−0.162075
$741$	−46.0653	−1.69225
$742$	26.9158	0.988108
$743$	−45.9296	−1.68499	−0.842497	−	0.538701i	$-0.818915\pi$
$743$	−45.9296	−1.68499	−0.842497	+	0.538701i	$0.818915\pi$
$744$	−16.3880	−0.600812
$745$	−8.72034	−0.319489
$746$	−75.1057	−2.74982
$747$	−5.88233	−0.215223
$748$	0	0
$749$	22.4549	0.820483
$750$	−4.00829	−0.146362
$751$	23.1928	0.846318	0.423159	−	0.906055i	$-0.360921\pi$
$751$	23.1928	0.846318	0.423159	+	0.906055i	$0.360921\pi$
$752$	9.14077	0.333330
$753$	−5.10135	−0.185904
$754$	23.7821	0.866093
$755$	11.9354	0.434375
$756$	−32.8244	−1.19381
$757$	−6.52202	−0.237047	−0.118523	−	0.992951i	$-0.537816\pi$
$757$	−6.52202	−0.237047	−0.118523	+	0.992951i	$0.537816\pi$
$758$	36.7757	1.33575
$759$	0	0
$760$	−6.45628	−0.234194
$761$	6.56682	0.238047	0.119024	−	0.992891i	$-0.462024\pi$
$761$	6.56682	0.238047	0.119024	+	0.992891i	$0.462024\pi$
$762$	1.81013	0.0655742
$763$	22.7986	0.825364
$764$	41.2230	1.49139
$765$	−0.305932	−0.0110610
$766$	−45.3108	−1.63715
$767$	−8.58530	−0.309997
$768$	15.4386	0.557091
$769$	−12.5950	−0.454188	−0.227094	−	0.973873i	$-0.572922\pi$
$769$	−12.5950	−0.454188	−0.227094	+	0.973873i	$0.572922\pi$
$770$	0	0
$771$	−41.3832	−1.49038
$772$	6.18057	0.222444
$773$	21.9448	0.789299	0.394650	−	0.918832i	$-0.370866\pi$
$773$	21.9448	0.789299	0.394650	+	0.918832i	$0.370866\pi$
$774$	1.81698	0.0653101
$775$	−10.4765	−0.376326
$776$	12.5553	0.450709
$777$	10.8228	0.388267
$778$	74.8892	2.68491
$779$	34.8010	1.24687
$780$	13.9454	0.499327
$781$	0	0
$782$	−1.35118	−0.0483181
$783$	16.6627	0.595475
$784$	−7.38464	−0.263737
$785$	−3.87532	−0.138316
$786$	−2.52123	−0.0899292
$787$	−16.7298	−0.596354	−0.298177	−	0.954511i	$-0.596379\pi$
$787$	−16.7298	−0.596354	−0.298177	+	0.954511i	$0.596379\pi$
$788$	−0.345944	−0.0123237
$789$	−42.3522	−1.50778
$790$	−24.2171	−0.861606
$791$	−9.31320	−0.331139
$792$	0	0
$793$	−6.15261	−0.218486
$794$	−41.9995	−1.49051
$795$	−8.01190	−0.284153
$796$	−18.0268	−0.638942
$797$	−11.7707	−0.416940	−0.208470	−	0.978029i	$-0.566848\pi$
$797$	−11.7707	−0.416940	−0.208470	+	0.978029i	$0.566848\pi$
$798$	97.0702	3.43625
$799$	−1.38234	−0.0489038
$800$	−8.06206	−0.285037
$801$	−4.46505	−0.157765
$802$	−43.7889	−1.54624
$803$	0	0
$804$	−30.8992	−1.08973
$805$	4.26418	0.150292
$806$	66.9473	2.35812
$807$	39.6342	1.39519
$808$	−9.59377	−0.337508
$809$	−1.19595	−0.0420472	−0.0210236	−	0.999779i	$-0.506693\pi$
$809$	−1.19595	−0.0420472	−0.0210236	+	0.999779i	$0.506693\pi$
$810$	22.0921	0.776236
$811$	−35.8253	−1.25800	−0.628998	−	0.777407i	$-0.716535\pi$
$811$	−35.8253	−1.25800	−0.628998	+	0.777407i	$0.716535\pi$
$812$	−27.2845	−0.957499
$813$	0.809412	0.0283873
$814$	0	0
$815$	9.93621	0.348050
$816$	−2.72162	−0.0952757
$817$	10.3810	0.363186
$818$	−49.2356	−1.72148
$819$	−6.16973	−0.215588
$820$	−10.5354	−0.367911
$821$	−5.49200	−0.191672	−0.0958360	−	0.995397i	$-0.530552\pi$
$821$	−5.49200	−0.191672	−0.0958360	+	0.995397i	$0.530552\pi$
$822$	44.8263	1.56350
$823$	42.7252	1.48931	0.744654	−	0.667451i	$-0.232614\pi$
$823$	42.7252	1.48931	0.744654	+	0.667451i	$0.232614\pi$
$824$	11.3563	0.395616
$825$	0	0
$826$	18.0912	0.629473
$827$	−32.4208	−1.12738	−0.563691	−	0.825986i	$-0.690619\pi$
$827$	−32.4208	−1.12738	−0.563691	+	0.825986i	$0.690619\pi$
$828$	−2.19176	−0.0761688
$829$	−2.91149	−0.101120	−0.0505600	−	0.998721i	$-0.516101\pi$
$829$	−2.91149	−0.101120	−0.0505600	+	0.998721i	$0.516101\pi$
$830$	18.6871	0.648639
$831$	16.3993	0.568884
$832$	32.8100	1.13748
$833$	1.11677	0.0386937
$834$	9.51950	0.329633
$835$	13.9200	0.481722
$836$	0	0
$837$	46.9059	1.62130
$838$	−21.1893	−0.731973
$839$	−20.8465	−0.719701	−0.359850	−	0.933010i	$-0.617172\pi$
$839$	−20.8465	−0.719701	−0.359850	+	0.933010i	$0.617172\pi$
$840$	−4.79789	−0.165543
$841$	−15.1496	−0.522398
$842$	18.6960	0.644305
$843$	13.4122	0.461940
$844$	5.42304	0.186669
$845$	3.69863	0.127237
$846$	−4.11851	−0.141597
$847$	0	0
$848$	−12.8458	−0.441127
$849$	−19.0404	−0.653464
$850$	0.971892	0.0333356
$851$	−2.56437	−0.0879056
$852$	−29.8220	−1.02168
$853$	−34.5509	−1.18300	−0.591500	−	0.806305i	$-0.701464\pi$
$853$	−34.5509	−1.18300	−0.591500	+	0.806305i	$0.701464\pi$
$854$	12.9650	0.443652
$855$	−5.20762	−0.178097
$856$	5.98641	0.204611
$857$	−33.2969	−1.13740	−0.568699	−	0.822545i	$-0.692553\pi$
$857$	−33.2969	−1.13740	−0.568699	+	0.822545i	$0.692553\pi$
$858$	0	0
$859$	−16.7665	−0.572067	−0.286034	−	0.958220i	$-0.592337\pi$
$859$	−16.7665	−0.572067	−0.286034	+	0.958220i	$0.592337\pi$
$860$	−3.14266	−0.107164
$861$	25.8618	0.881369
$862$	36.9028	1.25692
$863$	−1.48415	−0.0505211	−0.0252605	−	0.999681i	$-0.508042\pi$
$863$	−1.48415	−0.0505211	−0.0252605	+	0.999681i	$0.508042\pi$
$864$	36.0959	1.22801
$865$	10.8311	0.368269
$866$	19.1593	0.651060
$867$	−32.1094	−1.09049
$868$	−76.8068	−2.60699
$869$	0	0
$870$	14.9173	0.505745
$871$	20.6092	0.698316
$872$	6.07803	0.205828
$873$	10.1271	0.342749
$874$	−22.9999	−0.777984
$875$	−3.06719	−0.103690
$876$	45.1577	1.52574
$877$	24.8615	0.839513	0.419756	−	0.907637i	$-0.362115\pi$
$877$	24.8615	0.839513	0.419756	+	0.907637i	$0.362115\pi$
$878$	−13.5554	−0.457473
$879$	−41.7433	−1.40797
$880$	0	0
$881$	32.6968	1.10158	0.550792	−	0.834643i	$-0.314326\pi$
$881$	32.6968	1.10158	0.550792	+	0.834643i	$0.314326\pi$
$882$	3.32726	0.112035
$883$	47.6218	1.60260	0.801300	−	0.598263i	$-0.204142\pi$
$883$	47.6218	1.60260	0.801300	+	0.598263i	$0.204142\pi$
$884$	−3.38136	−0.113727
$885$	−5.38513	−0.181019
$886$	−85.6644	−2.87795
$887$	−59.0960	−1.98425	−0.992125	−	0.125251i	$-0.960026\pi$
$887$	−59.0960	−1.98425	−0.992125	+	0.125251i	$0.960026\pi$
$888$	2.88533	0.0968255
$889$	1.38513	0.0464559
$890$	14.1847	0.475471
$891$	0	0
$892$	20.5076	0.686646
$893$	−23.5304	−0.787415
$894$	34.9537	1.16903
$895$	−22.7335	−0.759896
$896$	−19.6824	−0.657543
$897$	8.11115	0.270824
$898$	−25.4804	−0.850291
$899$	38.9894	1.30037
$900$	1.57651	0.0525504
$901$	1.94265	0.0647190
$902$	0	0
$903$	7.71450	0.256722
$904$	−2.48287	−0.0825791
$905$	−2.39831	−0.0797227
$906$	−47.8407	−1.58940
$907$	34.6576	1.15079	0.575393	−	0.817877i	$-0.304849\pi$
$907$	34.6576	1.15079	0.575393	+	0.817877i	$0.304849\pi$
$908$	−14.8205	−0.491836
$909$	−7.73831	−0.256664
$910$	19.6001	0.649737
$911$	−10.1883	−0.337552	−0.168776	−	0.985654i	$-0.553981\pi$
$911$	−10.1883	−0.337552	−0.168776	+	0.985654i	$0.553981\pi$
$912$	−46.3277	−1.53406
$913$	0	0
$914$	20.7484	0.686298
$915$	−3.85923	−0.127582
$916$	55.3724	1.82956
$917$	−1.92927	−0.0637101
$918$	−4.35141	−0.143618
$919$	36.1289	1.19178	0.595891	−	0.803065i	$-0.296799\pi$
$919$	36.1289	1.19178	0.595891	+	0.803065i	$0.296799\pi$
$920$	1.13682	0.0374797
$921$	59.0493	1.94574
$922$	6.54840	0.215660
$923$	19.8907	0.654711
$924$	0	0
$925$	1.84453	0.0606479
$926$	−51.0242	−1.67676
$927$	9.15997	0.300853
$928$	30.0039	0.984927
$929$	28.1240	0.922717	0.461359	−	0.887214i	$-0.347362\pi$
$929$	28.1240	0.922717	0.461359	+	0.887214i	$0.347362\pi$
$930$	41.9927	1.37700
$931$	19.0097	0.623019
$932$	66.5990	2.18152
$933$	−37.1409	−1.21594
$934$	69.5087	2.27439
$935$	0	0
$936$	−1.64483	−0.0537630
$937$	−0.0851677	−0.00278231	−0.00139115	−	0.999999i	$-0.500443\pi$
$937$	−0.0851677	−0.00278231	−0.00139115	+	0.999999i	$0.500443\pi$
$938$	−43.4283	−1.41798
$939$	2.01146	0.0656414
$940$	7.12340	0.232340
$941$	41.8154	1.36314	0.681572	−	0.731751i	$-0.261297\pi$
$941$	41.8154	1.36314	0.681572	+	0.731751i	$0.261297\pi$
$942$	15.5334	0.506106
$943$	−6.12774	−0.199547
$944$	−8.63420	−0.281019
$945$	13.7326	0.446721
$946$	0	0
$947$	8.92463	0.290012	0.145006	−	0.989431i	$-0.453680\pi$
$947$	8.92463	0.290012	0.145006	+	0.989431i	$0.453680\pi$
$948$	52.8489	1.71645
$949$	−30.1194	−0.977716
$950$	16.5437	0.536747
$951$	−45.5894	−1.47834
$952$	1.16335	0.0377042
$953$	−5.26383	−0.170512	−0.0852561	−	0.996359i	$-0.527171\pi$
$953$	−5.26383	−0.170512	−0.0852561	+	0.996359i	$0.527171\pi$
$954$	5.78787	0.187389
$955$	−17.2462	−0.558075
$956$	38.9283	1.25903
$957$	0	0
$958$	36.2438	1.17098
$959$	34.3016	1.10765
$960$	20.5801	0.664218
$961$	78.7564	2.54053
$962$	−11.7870	−0.380029
$963$	4.82862	0.155600
$964$	−10.4947	−0.338013
$965$	−2.58574	−0.0832378
$966$	−17.0921	−0.549928
$967$	18.5421	0.596275	0.298138	−	0.954523i	$-0.403635\pi$
$967$	18.5421	0.596275	0.298138	+	0.954523i	$0.403635\pi$
$968$	0	0
$969$	7.00606	0.225067
$970$	−32.1719	−1.03298
$971$	−24.2230	−0.777354	−0.388677	−	0.921374i	$-0.627068\pi$
$971$	−24.2230	−0.777354	−0.388677	+	0.921374i	$0.627068\pi$
$972$	−16.1060	−0.516601
$973$	7.28442	0.233528
$974$	16.0093	0.512972
$975$	−5.83428	−0.186847
$976$	−6.18765	−0.198062
$977$	49.0618	1.56963	0.784813	−	0.619732i	$-0.212759\pi$
$977$	49.0618	1.56963	0.784813	+	0.619732i	$0.212759\pi$
$978$	−39.8272	−1.27353
$979$	0	0
$980$	−5.75485	−0.183832
$981$	4.90253	0.156526
$982$	64.2340	2.04979
$983$	49.1394	1.56731	0.783653	−	0.621199i	$-0.213354\pi$
$983$	49.1394	1.56731	0.783653	+	0.621199i	$0.213354\pi$
$984$	6.89469	0.219795
$985$	0.144731	0.00461151
$986$	−3.61701	−0.115189
$987$	−17.4863	−0.556594
$988$	−57.5578	−1.83116
$989$	−1.82788	−0.0581233
$990$	0	0
$991$	30.9620	0.983541	0.491771	−	0.870725i	$-0.336350\pi$
$991$	30.9620	0.983541	0.491771	+	0.870725i	$0.336350\pi$
$992$	84.4619	2.68167
$993$	49.1053	1.55831
$994$	−41.9143	−1.32944
$995$	7.54177	0.239090
$996$	−40.7808	−1.29219
$997$	−22.8939	−0.725058	−0.362529	−	0.931972i	$-0.618087\pi$
$997$	−22.8939	−0.725058	−0.362529	+	0.931972i	$0.618087\pi$
$998$	−78.5280	−2.48576
$999$	−8.25845	−0.261286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.k.1.4		4
3.2	odd	2		5445.2.a.bi.1.1		4
4.3	odd	2		9680.2.a.cm.1.1		4
5.4	even	2		3025.2.a.w.1.1		4
11.2	odd	10		605.2.g.m.81.2		8
11.3	even	5		605.2.g.k.251.2		8
11.4	even	5		605.2.g.k.511.2		8
11.5	even	5		605.2.g.e.366.1		8
11.6	odd	10		605.2.g.m.366.2		8
11.7	odd	10		55.2.g.b.16.1	✓	8
11.8	odd	10		55.2.g.b.31.1	yes	8
11.9	even	5		605.2.g.e.81.1		8
11.10	odd	2		605.2.a.j.1.1		4
33.8	even	10		495.2.n.e.361.2		8
33.29	even	10		495.2.n.e.181.2		8
33.32	even	2		5445.2.a.bp.1.4		4
44.7	even	10		880.2.bo.h.401.2		8
44.19	even	10		880.2.bo.h.801.2		8
44.43	even	2		9680.2.a.cn.1.1		4
55.7	even	20		275.2.z.a.49.4		16
55.8	even	20		275.2.z.a.174.4		16
55.18	even	20		275.2.z.a.49.1		16
55.19	odd	10		275.2.h.a.251.2		8
55.29	odd	10		275.2.h.a.126.2		8
55.52	even	20		275.2.z.a.174.1		16
55.54	odd	2		3025.2.a.bd.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.1	✓	8	11.7	odd	10
55.2.g.b.31.1	yes	8	11.8	odd	10
275.2.h.a.126.2		8	55.29	odd	10
275.2.h.a.251.2		8	55.19	odd	10
275.2.z.a.49.1		16	55.18	even	20
275.2.z.a.49.4		16	55.7	even	20
275.2.z.a.174.1		16	55.52	even	20
275.2.z.a.174.4		16	55.8	even	20
495.2.n.e.181.2		8	33.29	even	10
495.2.n.e.361.2		8	33.8	even	10
605.2.a.j.1.1		4	11.10	odd	2
605.2.a.k.1.4		4	1.1	even	1	trivial
605.2.g.e.81.1		8	11.9	even	5
605.2.g.e.366.1		8	11.5	even	5
605.2.g.k.251.2		8	11.3	even	5
605.2.g.k.511.2		8	11.4	even	5
605.2.g.m.81.2		8	11.2	odd	10
605.2.g.m.366.2		8	11.6	odd	10
880.2.bo.h.401.2		8	44.7	even	10
880.2.bo.h.801.2		8	44.19	even	10
3025.2.a.w.1.1		4	5.4	even	2
3025.2.a.bd.1.4		4	55.54	odd	2
5445.2.a.bi.1.1		4	3.2	odd	2
5445.2.a.bp.1.4		4	33.32	even	2
9680.2.a.cm.1.1		4	4.3	odd	2
9680.2.a.cn.1.1		4	44.43	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09529 q^{2} +1.91300 q^{3} +2.39026 q^{4} -1.00000 q^{5} +4.00829 q^{6} +3.06719 q^{7} +0.817703 q^{8} +0.659557 q^{9} +O(q^{10})\)	\(q+2.09529 q^{2} +1.91300 q^{3} +2.39026 q^{4} -1.00000 q^{5} +4.00829 q^{6} +3.06719 q^{7} +0.817703 q^{8} +0.659557 q^{9} -2.09529 q^{10} +4.57255 q^{12} -3.04981 q^{13} +6.42666 q^{14} -1.91300 q^{15} -3.06719 q^{16} +0.463845 q^{17} +1.38197 q^{18} +7.89563 q^{19} -2.39026 q^{20} +5.86752 q^{21} -1.39026 q^{23} +1.56426 q^{24} +1.00000 q^{25} -6.39026 q^{26} -4.47726 q^{27} +7.33136 q^{28} -3.72162 q^{29} -4.00829 q^{30} -10.4765 q^{31} -8.06206 q^{32} +0.971892 q^{34} -3.06719 q^{35} +1.57651 q^{36} +1.84453 q^{37} +16.5437 q^{38} -5.83428 q^{39} -0.817703 q^{40} +4.40763 q^{41} +12.2942 q^{42} +1.31478 q^{43} -0.659557 q^{45} -2.91300 q^{46} -2.98018 q^{47} -5.86752 q^{48} +2.40763 q^{49} +2.09529 q^{50} +0.887334 q^{51} -7.28984 q^{52} +4.18814 q^{53} -9.38118 q^{54} +2.50805 q^{56} +15.1043 q^{57} -7.79789 q^{58} +2.81502 q^{59} -4.57255 q^{60} +2.01737 q^{61} -21.9513 q^{62} +2.02298 q^{63} -10.7580 q^{64} +3.04981 q^{65} -6.75753 q^{67} +1.10871 q^{68} -2.65956 q^{69} -6.42666 q^{70} -6.52195 q^{71} +0.539322 q^{72} +9.87581 q^{73} +3.86484 q^{74} +1.91300 q^{75} +18.8726 q^{76} -12.2245 q^{78} +11.5579 q^{79} +3.06719 q^{80} -10.5437 q^{81} +9.23528 q^{82} -8.91861 q^{83} +14.0249 q^{84} -0.463845 q^{85} +2.75485 q^{86} -7.11945 q^{87} -6.76978 q^{89} -1.38197 q^{90} -9.35435 q^{91} -3.32307 q^{92} -20.0415 q^{93} -6.24436 q^{94} -7.89563 q^{95} -15.4227 q^{96} +15.3543 q^{97} +5.04469 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8	\( 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} - q^{10} + 8 q^{12} + q^{13} + 2 q^{14} - 3 q^{16} - q^{17} + 10 q^{18} + 20 q^{19} + q^{20} + 10 q^{21} + 5 q^{23} + 11 q^{24} + 4 q^{25} - 15 q^{26} - 15 q^{27} + 13 q^{28} + 12 q^{29} - q^{30} - 5 q^{31} - 8 q^{32} + 2 q^{34} - 3 q^{35} + 7 q^{37} + 20 q^{38} + 7 q^{39} - 3 q^{40} + 11 q^{41} + 12 q^{42} + 19 q^{43} - 4 q^{46} + 5 q^{47} - 10 q^{48} + 3 q^{49} + q^{50} + 7 q^{51} - 11 q^{52} - 11 q^{53} - 8 q^{54} + 11 q^{56} - 5 q^{57} - 14 q^{58} + 9 q^{59} - 8 q^{60} + 12 q^{61} - 35 q^{62} - 5 q^{63} - 3 q^{64} - q^{65} - 19 q^{67} - 3 q^{68} - 8 q^{69} - 2 q^{70} + 5 q^{71} - 25 q^{72} + 11 q^{73} - 8 q^{78} + 34 q^{79} + 3 q^{80} + 4 q^{81} - 6 q^{82} - 11 q^{83} + 11 q^{84} + q^{85} + q^{86} - 19 q^{87} - 8 q^{89} - 10 q^{90} - 8 q^{91} - 12 q^{92} - 5 q^{93} - q^{94} - 20 q^{95} - 34 q^{96} + 32 q^{97} - 8 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8 - q^10 + 8 * q^12 + q^13 + 2 * q^14 - 3 * q^16 - q^17 + 10 * q^18 + 20 * q^19 + q^20 + 10 * q^21 + 5 * q^23 + 11 * q^24 + 4 * q^25 - 15 * q^26 - 15 * q^27 + 13 * q^28 + 12 * q^29 - q^30 - 5 * q^31 - 8 * q^32 + 2 * q^34 - 3 * q^35 + 7 * q^37 + 20 * q^38 + 7 * q^39 - 3 * q^40 + 11 * q^41 + 12 * q^42 + 19 * q^43 - 4 * q^46 + 5 * q^47 - 10 * q^48 + 3 * q^49 + q^50 + 7 * q^51 - 11 * q^52 - 11 * q^53 - 8 * q^54 + 11 * q^56 - 5 * q^57 - 14 * q^58 + 9 * q^59 - 8 * q^60 + 12 * q^61 - 35 * q^62 - 5 * q^63 - 3 * q^64 - q^65 - 19 * q^67 - 3 * q^68 - 8 * q^69 - 2 * q^70 + 5 * q^71 - 25 * q^72 + 11 * q^73 - 8 * q^78 + 34 * q^79 + 3 * q^80 + 4 * q^81 - 6 * q^82 - 11 * q^83 + 11 * q^84 + q^85 + q^86 - 19 * q^87 - 8 * q^89 - 10 * q^90 - 8 * q^91 - 12 * q^92 - 5 * q^93 - q^94 - 20 * q^95 - 34 * q^96 + 32 * q^97 - 8 * q^98

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