LMFDB - Embedded newform 6005.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09533 q^{2} -3.35381 q^{3} +2.39043 q^{4} -1.00000 q^{5} +7.02736 q^{6} +3.72693 q^{7} -0.818074 q^{8} +8.24805 q^{9} +O(q^{10})$	\(q-2.09533 q^{2} -3.35381 q^{3} +2.39043 q^{4} -1.00000 q^{5} +7.02736 q^{6} +3.72693 q^{7} -0.818074 q^{8} +8.24805 q^{9} +2.09533 q^{10} +3.89308 q^{11} -8.01704 q^{12} -2.10581 q^{13} -7.80916 q^{14} +3.35381 q^{15} -3.06671 q^{16} -1.56274 q^{17} -17.2824 q^{18} +0.817488 q^{19} -2.39043 q^{20} -12.4994 q^{21} -8.15731 q^{22} -5.50845 q^{23} +2.74367 q^{24} +1.00000 q^{25} +4.41239 q^{26} -17.6010 q^{27} +8.90895 q^{28} +7.10406 q^{29} -7.02736 q^{30} -6.08175 q^{31} +8.06194 q^{32} -13.0567 q^{33} +3.27446 q^{34} -3.72693 q^{35} +19.7164 q^{36} +6.67848 q^{37} -1.71291 q^{38} +7.06250 q^{39} +0.818074 q^{40} +0.872610 q^{41} +26.1904 q^{42} +12.5927 q^{43} +9.30612 q^{44} -8.24805 q^{45} +11.5420 q^{46} -4.75479 q^{47} +10.2852 q^{48} +6.88999 q^{49} -2.09533 q^{50} +5.24113 q^{51} -5.03379 q^{52} -14.3164 q^{53} +36.8799 q^{54} -3.89308 q^{55} -3.04890 q^{56} -2.74170 q^{57} -14.8854 q^{58} +1.26660 q^{59} +8.01704 q^{60} -0.800568 q^{61} +12.7433 q^{62} +30.7399 q^{63} -10.7590 q^{64} +2.10581 q^{65} +27.3581 q^{66} +6.97866 q^{67} -3.73561 q^{68} +18.4743 q^{69} +7.80916 q^{70} +12.7637 q^{71} -6.74751 q^{72} -1.12771 q^{73} -13.9937 q^{74} -3.35381 q^{75} +1.95414 q^{76} +14.5092 q^{77} -14.7983 q^{78} +9.12317 q^{79} +3.06671 q^{80} +34.2862 q^{81} -1.82841 q^{82} -15.3155 q^{83} -29.8789 q^{84} +1.56274 q^{85} -26.3859 q^{86} -23.8257 q^{87} -3.18483 q^{88} +6.32546 q^{89} +17.2824 q^{90} -7.84822 q^{91} -13.1675 q^{92} +20.3971 q^{93} +9.96288 q^{94} -0.817488 q^{95} -27.0382 q^{96} -0.984318 q^{97} -14.4368 q^{98} +32.1103 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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 $

$2$	−2.09533	−1.48163	−0.740813	−	0.671712i	$-0.765559\pi$
$2$	−2.09533	−1.48163	−0.740813	+	0.671712i	$0.765559\pi$
$3$	−3.35381	−1.93632	−0.968162	−	0.250325i	$-0.919463\pi$
$3$	−3.35381	−1.93632	−0.968162	+	0.250325i	$0.919463\pi$
$4$	2.39043	1.19521
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	7.02736	2.86891
$7$	3.72693	1.40865	0.704323	−	0.709880i	$-0.251251\pi$
$7$	3.72693	1.40865	0.704323	+	0.709880i	$0.251251\pi$
$8$	−0.818074	−0.289233
$9$	8.24805	2.74935
$10$	2.09533	0.662603
$11$	3.89308	1.17381	0.586904	−	0.809656i	$-0.300347\pi$
$11$	3.89308	1.17381	0.586904	+	0.809656i	$0.300347\pi$
$12$	−8.01704	−2.31432
$13$	−2.10581	−0.584048	−0.292024	−	0.956411i	$-0.594329\pi$
$13$	−2.10581	−0.584048	−0.292024	+	0.956411i	$0.594329\pi$
$14$	−7.80916	−2.08709
$15$	3.35381	0.865950
$16$	−3.06671	−0.766679
$17$	−1.56274	−0.379020	−0.189510	−	0.981879i	$-0.560690\pi$
$17$	−1.56274	−0.379020	−0.189510	+	0.981879i	$0.560690\pi$
$18$	−17.2824	−4.07351
$19$	0.817488	0.187544	0.0937722	−	0.995594i	$-0.470107\pi$
$19$	0.817488	0.187544	0.0937722	+	0.995594i	$0.470107\pi$
$20$	−2.39043	−0.534516
$21$	−12.4994	−2.72760
$22$	−8.15731	−1.73914
$23$	−5.50845	−1.14859	−0.574295	−	0.818648i	$-0.694724\pi$
$23$	−5.50845	−1.14859	−0.574295	+	0.818648i	$0.694724\pi$
$24$	2.74367	0.560048
$25$	1.00000	0.200000
$26$	4.41239	0.865340
$27$	−17.6010	−3.38731
$28$	8.90895	1.68363
$29$	7.10406	1.31919	0.659595	−	0.751621i	$-0.270728\pi$
$29$	7.10406	1.31919	0.659595	+	0.751621i	$0.270728\pi$
$30$	−7.02736	−1.28301
$31$	−6.08175	−1.09232	−0.546158	−	0.837682i	$-0.683910\pi$
$31$	−6.08175	−1.09232	−0.546158	+	0.837682i	$0.683910\pi$
$32$	8.06194	1.42516
$33$	−13.0567	−2.27287
$34$	3.27446	0.561565
$35$	−3.72693	−0.629966
$36$	19.7164	3.28606
$37$	6.67848	1.09794	0.548968	−	0.835843i	$-0.315021\pi$
$37$	6.67848	1.09794	0.548968	+	0.835843i	$0.315021\pi$
$38$	−1.71291	−0.277871
$39$	7.06250	1.13091
$40$	0.818074	0.129349
$41$	0.872610	0.136279	0.0681394	−	0.997676i	$-0.478294\pi$
$41$	0.872610	0.136279	0.0681394	+	0.997676i	$0.478294\pi$
$42$	26.1904	4.04127
$43$	12.5927	1.92037	0.960184	−	0.279369i	$-0.0901254\pi$
$43$	12.5927	1.92037	0.960184	+	0.279369i	$0.0901254\pi$
$44$	9.30612	1.40295
$45$	−8.24805	−1.22955
$46$	11.5420	1.70178
$47$	−4.75479	−0.693558	−0.346779	−	0.937947i	$-0.612725\pi$
$47$	−4.75479	−0.693558	−0.346779	+	0.937947i	$0.612725\pi$
$48$	10.2852	1.48454
$49$	6.88999	0.984284
$50$	−2.09533	−0.296325
$51$	5.24113	0.733905
$52$	−5.03379	−0.698062
$53$	−14.3164	−1.96650	−0.983251	−	0.182254i	$-0.941661\pi$
$53$	−14.3164	−1.96650	−0.983251	+	0.182254i	$0.941661\pi$
$54$	36.8799	5.01872
$55$	−3.89308	−0.524943
$56$	−3.04890	−0.407427
$57$	−2.74170	−0.363147
$58$	−14.8854	−1.95455
$59$	1.26660	0.164897	0.0824486	−	0.996595i	$-0.473726\pi$
$59$	1.26660	0.164897	0.0824486	+	0.996595i	$0.473726\pi$
$60$	8.01704	1.03500
$61$	−0.800568	−0.102502	−0.0512511	−	0.998686i	$-0.516321\pi$
$61$	−0.800568	−0.102502	−0.0512511	+	0.998686i	$0.516321\pi$
$62$	12.7433	1.61840
$63$	30.7399	3.87286
$64$	−10.7590	−1.34488
$65$	2.10581	0.261194
$66$	27.3581	3.36755
$67$	6.97866	0.852579	0.426290	−	0.904587i	$-0.359820\pi$
$67$	6.97866	0.852579	0.426290	+	0.904587i	$0.359820\pi$
$68$	−3.73561	−0.453009
$69$	18.4743	2.22404
$70$	7.80916	0.933373
$71$	12.7637	1.51478	0.757388	−	0.652965i	$-0.226475\pi$
$71$	12.7637	1.51478	0.757388	+	0.652965i	$0.226475\pi$
$72$	−6.74751	−0.795202
$73$	−1.12771	−0.131988	−0.0659940	−	0.997820i	$-0.521022\pi$
$73$	−1.12771	−0.131988	−0.0659940	+	0.997820i	$0.521022\pi$
$74$	−13.9937	−1.62673
$75$	−3.35381	−0.387265
$76$	1.95414	0.224156
$77$	14.5092	1.65348
$78$	−14.7983	−1.67558
$79$	9.12317	1.02644	0.513219	−	0.858258i	$-0.328453\pi$
$79$	9.12317	1.02644	0.513219	+	0.858258i	$0.328453\pi$
$80$	3.06671	0.342869
$81$	34.2862	3.80958
$82$	−1.82841	−0.201914
$83$	−15.3155	−1.68109	−0.840545	−	0.541741i	$-0.817765\pi$
$83$	−15.3155	−1.68109	−0.840545	+	0.541741i	$0.817765\pi$
$84$	−29.8789	−3.26006
$85$	1.56274	0.169503
$86$	−26.3859	−2.84526
$87$	−23.8257	−2.55438
$88$	−3.18483	−0.339504
$89$	6.32546	0.670497	0.335249	−	0.942130i	$-0.391180\pi$
$89$	6.32546	0.670497	0.335249	+	0.942130i	$0.391180\pi$
$90$	17.2824	1.82173
$91$	−7.84822	−0.822717
$92$	−13.1675	−1.37281
$93$	20.3971	2.11508
$94$	9.96288	1.02759
$95$	−0.817488	−0.0838725
$96$	−27.0382	−2.75958
$97$	−0.984318	−0.0999424	−0.0499712	−	0.998751i	$-0.515913\pi$
$97$	−0.984318	−0.0999424	−0.0499712	+	0.998751i	$0.515913\pi$
$98$	−14.4368	−1.45834
$99$	32.1103	3.22721
$100$	2.39043	0.239043
$101$	−2.34464	−0.233301	−0.116650	−	0.993173i	$-0.537216\pi$
$101$	−2.34464	−0.233301	−0.116650	+	0.993173i	$0.537216\pi$
$102$	−10.9819	−1.08737
$103$	13.6666	1.34661	0.673304	−	0.739366i	$-0.264875\pi$
$103$	13.6666	1.34661	0.673304	+	0.739366i	$0.264875\pi$
$104$	1.72271	0.168926
$105$	12.4994	1.21982
$106$	29.9976	2.91362
$107$	16.0074	1.54750	0.773748	−	0.633493i	$-0.218380\pi$
$107$	16.0074	1.54750	0.773748	+	0.633493i	$0.218380\pi$
$108$	−42.0738	−4.04856
$109$	−0.997445	−0.0955379	−0.0477690	−	0.998858i	$-0.515211\pi$
$109$	−0.997445	−0.0955379	−0.0477690	+	0.998858i	$0.515211\pi$
$110$	8.15731	0.777769
$111$	−22.3984	−2.12596
$112$	−11.4294	−1.07998
$113$	−0.528511	−0.0497181	−0.0248591	−	0.999691i	$-0.507914\pi$
$113$	−0.528511	−0.0497181	−0.0248591	+	0.999691i	$0.507914\pi$
$114$	5.74478	0.538048
$115$	5.50845	0.513665
$116$	16.9817	1.57671
$117$	−17.3689	−1.60575
$118$	−2.65395	−0.244316
$119$	−5.82421	−0.533905
$120$	−2.74367	−0.250461
$121$	4.15608	0.377826
$122$	1.67746	0.151870
$123$	−2.92657	−0.263880
$124$	−14.5380	−1.30555
$125$	−1.00000	−0.0894427
$126$	−64.4103	−5.73813
$127$	−10.5553	−0.936630	−0.468315	−	0.883561i	$-0.655139\pi$
$127$	−10.5553	−0.936630	−0.468315	+	0.883561i	$0.655139\pi$
$128$	6.41989	0.567443
$129$	−42.2335	−3.71845
$130$	−4.41239	−0.386992
$131$	−9.82531	−0.858441	−0.429221	−	0.903200i	$-0.641212\pi$
$131$	−9.82531	−0.858441	−0.429221	+	0.903200i	$0.641212\pi$
$132$	−31.2110	−2.71657
$133$	3.04672	0.264184
$134$	−14.6226	−1.26320
$135$	17.6010	1.51485
$136$	1.27844	0.109625
$137$	−11.3021	−0.965605	−0.482802	−	0.875729i	$-0.660381\pi$
$137$	−11.3021	−0.965605	−0.482802	+	0.875729i	$0.660381\pi$
$138$	−38.7098	−3.29520
$139$	−12.5505	−1.06452	−0.532259	−	0.846581i	$-0.678657\pi$
$139$	−12.5505	−1.06452	−0.532259	+	0.846581i	$0.678657\pi$
$140$	−8.90895	−0.752943
$141$	15.9467	1.34295
$142$	−26.7443	−2.24433
$143$	−8.19811	−0.685560
$144$	−25.2944	−2.10787
$145$	−7.10406	−0.589960
$146$	2.36292	0.195557
$147$	−23.1077	−1.90589
$148$	15.9644	1.31227
$149$	20.2767	1.66114	0.830568	−	0.556917i	$-0.188016\pi$
$149$	20.2767	1.66114	0.830568	+	0.556917i	$0.188016\pi$
$150$	7.02736	0.573781
$151$	−6.70902	−0.545972	−0.272986	−	0.962018i	$-0.588011\pi$
$151$	−6.70902	−0.545972	−0.272986	+	0.962018i	$0.588011\pi$
$152$	−0.668765	−0.0542440
$153$	−12.8895	−1.04206
$154$	−30.4017	−2.44984
$155$	6.08175	0.488498
$156$	16.8824	1.35167
$157$	5.24957	0.418961	0.209481	−	0.977813i	$-0.432823\pi$
$157$	5.24957	0.418961	0.209481	+	0.977813i	$0.432823\pi$
$158$	−19.1161	−1.52080
$159$	48.0144	3.80779
$160$	−8.06194	−0.637352
$161$	−20.5296	−1.61796
$162$	−71.8410	−5.64436
$163$	−11.9669	−0.937319	−0.468660	−	0.883379i	$-0.655263\pi$
$163$	−11.9669	−0.937319	−0.468660	+	0.883379i	$0.655263\pi$
$164$	2.08591	0.162882
$165$	13.0567	1.01646
$166$	32.0910	2.49075
$167$	−0.403780	−0.0312455	−0.0156227	−	0.999878i	$-0.504973\pi$
$167$	−0.403780	−0.0312455	−0.0156227	+	0.999878i	$0.504973\pi$
$168$	10.2254	0.788910
$169$	−8.56555	−0.658888
$170$	−3.27446	−0.251140
$171$	6.74268	0.515625
$172$	30.1019	2.29525
$173$	11.1688	0.849148	0.424574	−	0.905393i	$-0.360424\pi$
$173$	11.1688	0.849148	0.424574	+	0.905393i	$0.360424\pi$
$174$	49.9228	3.78463
$175$	3.72693	0.281729
$176$	−11.9390	−0.899934
$177$	−4.24793	−0.319294
$178$	−13.2540	−0.993426
$179$	8.16208	0.610062	0.305031	−	0.952342i	$-0.401333\pi$
$179$	8.16208	0.610062	0.305031	+	0.952342i	$0.401333\pi$
$180$	−19.7164	−1.46957
$181$	15.7726	1.17236	0.586182	−	0.810179i	$-0.300630\pi$
$181$	15.7726	1.17236	0.586182	+	0.810179i	$0.300630\pi$
$182$	16.4446	1.21896
$183$	2.68496	0.198478
$184$	4.50632	0.332210
$185$	−6.67848	−0.491012
$186$	−42.7387	−3.13375
$187$	−6.08387	−0.444897
$188$	−11.3660	−0.828949
$189$	−65.5975	−4.77152
$190$	1.71291	0.124268
$191$	−6.83236	−0.494372	−0.247186	−	0.968968i	$-0.579506\pi$
$191$	−6.83236	−0.494372	−0.247186	+	0.968968i	$0.579506\pi$
$192$	36.0838	2.60412
$193$	15.0475	1.08314	0.541572	−	0.840655i	$-0.317829\pi$
$193$	15.0475	1.08314	0.541572	+	0.840655i	$0.317829\pi$
$194$	2.06248	0.148077
$195$	−7.06250	−0.505756
$196$	16.4700	1.17643
$197$	−11.6700	−0.831451	−0.415726	−	0.909490i	$-0.636472\pi$
$197$	−11.6700	−0.831451	−0.415726	+	0.909490i	$0.636472\pi$
$198$	−67.2819	−4.78151
$199$	22.1714	1.57169	0.785844	−	0.618425i	$-0.212229\pi$
$199$	22.1714	1.57169	0.785844	+	0.618425i	$0.212229\pi$
$200$	−0.818074	−0.0578466
$201$	−23.4051	−1.65087
$202$	4.91281	0.345664
$203$	26.4763	1.85827
$204$	12.5285	0.877173
$205$	−0.872610	−0.0609458
$206$	−28.6360	−1.99517
$207$	−45.4339	−3.15788
$208$	6.45793	0.447777
$209$	3.18255	0.220141
$210$	−26.1904	−1.80731
$211$	14.7553	1.01580	0.507900	−	0.861416i	$-0.330422\pi$
$211$	14.7553	1.01580	0.507900	+	0.861416i	$0.330422\pi$
$212$	−34.2222	−2.35039
$213$	−42.8071	−2.93310
$214$	−33.5409	−2.29281
$215$	−12.5927	−0.858814
$216$	14.3989	0.979721
$217$	−22.6663	−1.53869
$218$	2.08998	0.141551
$219$	3.78211	0.255571
$220$	−9.30612	−0.627419
$221$	3.29084	0.221366
$222$	46.9321	3.14987
$223$	25.5622	1.71177	0.855885	−	0.517166i	$-0.173013\pi$
$223$	25.5622	1.71177	0.855885	+	0.517166i	$0.173013\pi$
$224$	30.0463	2.00755
$225$	8.24805	0.549870
$226$	1.10741	0.0736636
$227$	15.6442	1.03834	0.519171	−	0.854670i	$-0.326241\pi$
$227$	15.6442	1.03834	0.519171	+	0.854670i	$0.326241\pi$
$228$	−6.55383	−0.434038
$229$	15.3149	1.01204	0.506019	−	0.862522i	$-0.331116\pi$
$229$	15.3149	1.01204	0.506019	+	0.862522i	$0.331116\pi$
$230$	−11.5420	−0.761059
$231$	−48.6612	−3.20167
$232$	−5.81164	−0.381553
$233$	25.1188	1.64558	0.822792	−	0.568342i	$-0.192415\pi$
$233$	25.1188	1.64558	0.822792	+	0.568342i	$0.192415\pi$
$234$	36.3936	2.37912
$235$	4.75479	0.310169
$236$	3.02771	0.197087
$237$	−30.5974	−1.98752
$238$	12.2037	0.791047
$239$	−15.4473	−0.999200	−0.499600	−	0.866256i	$-0.666520\pi$
$239$	−15.4473	−0.999200	−0.499600	+	0.866256i	$0.666520\pi$
$240$	−10.2852	−0.663906
$241$	7.40690	0.477120	0.238560	−	0.971128i	$-0.423325\pi$
$241$	7.40690	0.477120	0.238560	+	0.971128i	$0.423325\pi$
$242$	−8.70838	−0.559796
$243$	−62.1865	−3.98926
$244$	−1.91370	−0.122512
$245$	−6.88999	−0.440185
$246$	6.13214	0.390971
$247$	−1.72148	−0.109535
$248$	4.97532	0.315933
$249$	51.3652	3.25514
$250$	2.09533	0.132521
$251$	−2.49690	−0.157603	−0.0788015	−	0.996890i	$-0.525109\pi$
$251$	−2.49690	−0.157603	−0.0788015	+	0.996890i	$0.525109\pi$
$252$	73.4814	4.62890
$253$	−21.4448	−1.34822
$254$	22.1169	1.38774
$255$	−5.24113	−0.328212
$256$	8.06625	0.504141
$257$	−6.29703	−0.392798	−0.196399	−	0.980524i	$-0.562925\pi$
$257$	−6.29703	−0.392798	−0.196399	+	0.980524i	$0.562925\pi$
$258$	88.4933	5.50935
$259$	24.8902	1.54660
$260$	5.03379	0.312183
$261$	58.5946	3.62692
$262$	20.5873	1.27189
$263$	−15.5060	−0.956142	−0.478071	−	0.878321i	$-0.658664\pi$
$263$	−15.5060	−0.956142	−0.478071	+	0.878321i	$0.658664\pi$
$264$	10.6813	0.657389
$265$	14.3164	0.879447
$266$	−6.38389	−0.391421
$267$	−21.2144	−1.29830
$268$	16.6820	1.01901
$269$	5.81859	0.354766	0.177383	−	0.984142i	$-0.443237\pi$
$269$	5.81859	0.354766	0.177383	+	0.984142i	$0.443237\pi$
$270$	−36.8799	−2.24444
$271$	−16.7892	−1.01987	−0.509936	−	0.860212i	$-0.670331\pi$
$271$	−16.7892	−1.01987	−0.509936	+	0.860212i	$0.670331\pi$
$272$	4.79247	0.290586
$273$	26.3214	1.59305
$274$	23.6817	1.43066
$275$	3.89308	0.234762
$276$	44.1614	2.65821
$277$	20.4411	1.22819	0.614094	−	0.789233i	$-0.289522\pi$
$277$	20.4411	1.22819	0.614094	+	0.789233i	$0.289522\pi$
$278$	26.2975	1.57722
$279$	−50.1626	−3.00316
$280$	3.04890	0.182207
$281$	−18.6979	−1.11542	−0.557712	−	0.830035i	$-0.688321\pi$
$281$	−18.6979	−1.11542	−0.557712	+	0.830035i	$0.688321\pi$
$282$	−33.4136	−1.98975
$283$	−26.2570	−1.56082	−0.780409	−	0.625269i	$-0.784989\pi$
$283$	−26.2570	−1.56082	−0.780409	+	0.625269i	$0.784989\pi$
$284$	30.5108	1.81048
$285$	2.74170	0.162404
$286$	17.1778	1.01574
$287$	3.25216	0.191969
$288$	66.4953	3.91827
$289$	−14.5578	−0.856344
$290$	14.8854	0.874100
$291$	3.30122	0.193521
$292$	−2.69570	−0.157754
$293$	5.83013	0.340600	0.170300	−	0.985392i	$-0.445526\pi$
$293$	5.83013	0.340600	0.170300	+	0.985392i	$0.445526\pi$
$294$	48.4184	2.82382
$295$	−1.26660	−0.0737442
$296$	−5.46349	−0.317559
$297$	−68.5220	−3.97605
$298$	−42.4866	−2.46118
$299$	11.5998	0.670832
$300$	−8.01704	−0.462864
$301$	46.9320	2.70512
$302$	14.0576	0.808927
$303$	7.86350	0.451746
$304$	−2.50700	−0.143786
$305$	0.800568	0.0458404
$306$	27.0079	1.54394
$307$	−15.5762	−0.888979	−0.444489	−	0.895784i	$-0.646615\pi$
$307$	−15.5762	−0.888979	−0.444489	+	0.895784i	$0.646615\pi$
$308$	34.6832	1.97626
$309$	−45.8351	−2.60747
$310$	−12.7433	−0.723771
$311$	−3.98225	−0.225813	−0.112906	−	0.993606i	$-0.536016\pi$
$311$	−3.98225	−0.225813	−0.112906	+	0.993606i	$0.536016\pi$
$312$	−5.77765	−0.327095
$313$	6.49179	0.366938	0.183469	−	0.983026i	$-0.441267\pi$
$313$	6.49179	0.366938	0.183469	+	0.983026i	$0.441267\pi$
$314$	−10.9996	−0.620744
$315$	−30.7399	−1.73200
$316$	21.8083	1.22681
$317$	−30.3184	−1.70285	−0.851427	−	0.524473i	$-0.824262\pi$
$317$	−30.3184	−1.70285	−0.851427	+	0.524473i	$0.824262\pi$
$318$	−100.606	−5.64171
$319$	27.6567	1.54848
$320$	10.7590	0.601448
$321$	−53.6859	−2.99645
$322$	43.0163	2.39721
$323$	−1.27752	−0.0710831
$324$	81.9586	4.55326
$325$	−2.10581	−0.116810
$326$	25.0746	1.38876
$327$	3.34524	0.184992
$328$	−0.713860	−0.0394163
$329$	−17.7208	−0.976978
$330$	−27.3581	−1.50601
$331$	4.40173	0.241941	0.120970	−	0.992656i	$-0.461399\pi$
$331$	4.40173	0.241941	0.120970	+	0.992656i	$0.461399\pi$
$332$	−36.6105	−2.00926
$333$	55.0845	3.01861
$334$	0.846055	0.0462941
$335$	−6.97866	−0.381285
$336$	38.3321	2.09119
$337$	7.05522	0.384322	0.192161	−	0.981363i	$-0.438450\pi$
$337$	7.05522	0.384322	0.192161	+	0.981363i	$0.438450\pi$
$338$	17.9477	0.976225
$339$	1.77253	0.0962704
$340$	3.73561	0.202592
$341$	−23.6768	−1.28217
$342$	−14.1282	−0.763964
$343$	−0.410005	−0.0221382
$344$	−10.3018	−0.555433
$345$	−18.4743	−0.994622
$346$	−23.4024	−1.25812
$347$	−3.50336	−0.188070	−0.0940351	−	0.995569i	$-0.529977\pi$
$347$	−3.50336	−0.188070	−0.0940351	+	0.995569i	$0.529977\pi$
$348$	−56.9535	−3.05303
$349$	17.6098	0.942632	0.471316	−	0.881964i	$-0.343779\pi$
$349$	17.6098	0.942632	0.471316	+	0.881964i	$0.343779\pi$
$350$	−7.80916	−0.417417
$351$	37.0644	1.97835
$352$	31.3858	1.67287
$353$	−6.87571	−0.365957	−0.182979	−	0.983117i	$-0.558574\pi$
$353$	−6.87571	−0.365957	−0.182979	+	0.983117i	$0.558574\pi$
$354$	8.90084	0.473074
$355$	−12.7637	−0.677429
$356$	15.1205	0.801387
$357$	19.5333	1.03381
$358$	−17.1023	−0.903884
$359$	−0.330209	−0.0174277	−0.00871387	−	0.999962i	$-0.502774\pi$
$359$	−0.330209	−0.0174277	−0.00871387	+	0.999962i	$0.502774\pi$
$360$	6.74751	0.355625
$361$	−18.3317	−0.964827
$362$	−33.0488	−1.73700
$363$	−13.9387	−0.731593
$364$	−18.7606	−0.983322
$365$	1.12771	0.0590268
$366$	−5.62588	−0.294069
$367$	8.08620	0.422096	0.211048	−	0.977476i	$-0.432312\pi$
$367$	8.08620	0.422096	0.211048	+	0.977476i	$0.432312\pi$
$368$	16.8928	0.880600
$369$	7.19733	0.374678
$370$	13.9937	0.727495
$371$	−53.3560	−2.77011
$372$	48.7577	2.52797
$373$	18.6992	0.968210	0.484105	−	0.875010i	$-0.339145\pi$
$373$	18.6992	0.968210	0.484105	+	0.875010i	$0.339145\pi$
$374$	12.7477	0.659170
$375$	3.35381	0.173190
$376$	3.88977	0.200600
$377$	−14.9598	−0.770470
$378$	137.449	7.06960
$379$	21.4523	1.10193	0.550965	−	0.834529i	$-0.314260\pi$
$379$	21.4523	1.10193	0.550965	+	0.834529i	$0.314260\pi$
$380$	−1.95414	−0.100245
$381$	35.4004	1.81362
$382$	14.3161	0.732474
$383$	−18.8588	−0.963638	−0.481819	−	0.876271i	$-0.660024\pi$
$383$	−18.8588	−0.963638	−0.481819	+	0.876271i	$0.660024\pi$
$384$	−21.5311	−1.09875
$385$	−14.5092	−0.739459
$386$	−31.5296	−1.60481
$387$	103.865	5.27976
$388$	−2.35294	−0.119452
$389$	−35.2833	−1.78893	−0.894467	−	0.447134i	$-0.852445\pi$
$389$	−35.2833	−1.78893	−0.894467	+	0.447134i	$0.852445\pi$
$390$	14.7983	0.749341
$391$	8.60826	0.435338
$392$	−5.63652	−0.284687
$393$	32.9522	1.66222
$394$	24.4525	1.23190
$395$	−9.12317	−0.459037
$396$	76.7574	3.85720
$397$	−21.1254	−1.06025	−0.530127	−	0.847918i	$-0.677856\pi$
$397$	−21.1254	−1.06025	−0.530127	+	0.847918i	$0.677856\pi$
$398$	−46.4565	−2.32865
$399$	−10.2181	−0.511545
$400$	−3.06671	−0.153336
$401$	−12.0009	−0.599295	−0.299648	−	0.954050i	$-0.596869\pi$
$401$	−12.0009	−0.599295	−0.299648	+	0.954050i	$0.596869\pi$
$402$	49.0416	2.44597
$403$	12.8070	0.637964
$404$	−5.60470	−0.278844
$405$	−34.2862	−1.70369
$406$	−55.4767	−2.75326
$407$	25.9999	1.28877
$408$	−4.28763	−0.212269
$409$	−17.6330	−0.871895	−0.435948	−	0.899972i	$-0.643587\pi$
$409$	−17.6330	−0.871895	−0.435948	+	0.899972i	$0.643587\pi$
$410$	1.82841	0.0902988
$411$	37.9052	1.86972
$412$	32.6689	1.60948
$413$	4.72052	0.232282
$414$	95.1993	4.67879
$415$	15.3155	0.751806
$416$	−16.9769	−0.832363
$417$	42.0920	2.06125
$418$	−6.66850	−0.326167
$419$	5.13252	0.250740	0.125370	−	0.992110i	$-0.459988\pi$
$419$	5.13252	0.250740	0.125370	+	0.992110i	$0.459988\pi$
$420$	29.8789	1.45794
$421$	26.9605	1.31398	0.656988	−	0.753901i	$-0.271830\pi$
$421$	26.9605	1.31398	0.656988	+	0.753901i	$0.271830\pi$
$422$	−30.9174	−1.50503
$423$	−39.2178	−1.90683
$424$	11.7118	0.568777
$425$	−1.56274	−0.0758040
$426$	89.6953	4.34575
$427$	−2.98366	−0.144389
$428$	38.2646	1.84959
$429$	27.4949	1.32747
$430$	26.3859	1.27244
$431$	−0.468111	−0.0225481	−0.0112741	−	0.999936i	$-0.503589\pi$
$431$	−0.468111	−0.0225481	−0.0112741	+	0.999936i	$0.503589\pi$
$432$	53.9771	2.59698
$433$	−12.4759	−0.599553	−0.299777	−	0.954009i	$-0.596912\pi$
$433$	−12.4759	−0.599553	−0.299777	+	0.954009i	$0.596912\pi$
$434$	47.4934	2.27976
$435$	23.8257	1.14235
$436$	−2.38432	−0.114188
$437$	−4.50309	−0.215412
$438$	−7.92479	−0.378661
$439$	35.8234	1.70976	0.854878	−	0.518829i	$-0.173632\pi$
$439$	35.8234	1.70976	0.854878	+	0.518829i	$0.173632\pi$
$440$	3.18483	0.151831
$441$	56.8290	2.70614
$442$	−6.89540	−0.327981
$443$	7.32444	0.347995	0.173997	−	0.984746i	$-0.444332\pi$
$443$	7.32444	0.347995	0.173997	+	0.984746i	$0.444332\pi$
$444$	−53.5417	−2.54097
$445$	−6.32546	−0.299856
$446$	−53.5613	−2.53620
$447$	−68.0044	−3.21650
$448$	−40.0981	−1.89446
$449$	−20.0426	−0.945869	−0.472934	−	0.881098i	$-0.656805\pi$
$449$	−20.0426	−0.945869	−0.472934	+	0.881098i	$0.656805\pi$
$450$	−17.2824	−0.814701
$451$	3.39714	0.159965
$452$	−1.26337	−0.0594238
$453$	22.5008	1.05718
$454$	−32.7798	−1.53843
$455$	7.84822	0.367930
$456$	2.24291	0.105034
$457$	14.8166	0.693093	0.346547	−	0.938033i	$-0.387354\pi$
$457$	14.8166	0.693093	0.346547	+	0.938033i	$0.387354\pi$
$458$	−32.0899	−1.49946
$459$	27.5057	1.28386
$460$	13.1675	0.613939
$461$	23.6524	1.10160	0.550801	−	0.834637i	$-0.314322\pi$
$461$	23.6524	1.10160	0.550801	+	0.834637i	$0.314322\pi$
$462$	101.962	4.74368
$463$	21.2862	0.989253	0.494626	−	0.869106i	$-0.335305\pi$
$463$	21.2862	0.989253	0.494626	+	0.869106i	$0.335305\pi$
$464$	−21.7861	−1.01140
$465$	−20.3971	−0.945891
$466$	−52.6322	−2.43814
$467$	−12.3878	−0.573240	−0.286620	−	0.958044i	$-0.592532\pi$
$467$	−12.3878	−0.573240	−0.286620	+	0.958044i	$0.592532\pi$
$468$	−41.5190	−1.91922
$469$	26.0090	1.20098
$470$	−9.96288	−0.459553
$471$	−17.6061	−0.811245
$472$	−1.03617	−0.0476937
$473$	49.0244	2.25414
$474$	64.1118	2.94475
$475$	0.817488	0.0375089
$476$	−13.9224	−0.638130
$477$	−118.082	−5.40660
$478$	32.3672	1.48044
$479$	2.24855	0.102739	0.0513694	−	0.998680i	$-0.483641\pi$
$479$	2.24855	0.102739	0.0513694	+	0.998680i	$0.483641\pi$
$480$	27.0382	1.23412
$481$	−14.0636	−0.641247
$482$	−15.5199	−0.706913
$483$	68.8523	3.13289
$484$	9.93481	0.451582
$485$	0.984318	0.0446956
$486$	130.301	5.91059
$487$	1.56236	0.0707974	0.0353987	−	0.999373i	$-0.488730\pi$
$487$	1.56236	0.0707974	0.0353987	+	0.999373i	$0.488730\pi$
$488$	0.654924	0.0296470
$489$	40.1347	1.81495
$490$	14.4368	0.652189
$491$	43.1689	1.94819	0.974094	−	0.226145i	$-0.0726125\pi$
$491$	43.1689	1.94819	0.974094	+	0.226145i	$0.0726125\pi$
$492$	−6.99575	−0.315393
$493$	−11.1018	−0.499999
$494$	3.60707	0.162290
$495$	−32.1103	−1.44325
$496$	18.6510	0.837455
$497$	47.5695	2.13378
$498$	−107.627	−4.82289
$499$	8.18286	0.366315	0.183158	−	0.983084i	$-0.441368\pi$
$499$	8.18286	0.366315	0.183158	+	0.983084i	$0.441368\pi$
$500$	−2.39043	−0.106903
$501$	1.35420	0.0605013
$502$	5.23184	0.233509
$503$	14.1732	0.631951	0.315976	−	0.948767i	$-0.397668\pi$
$503$	14.1732	0.631951	0.315976	+	0.948767i	$0.397668\pi$
$504$	−25.1475	−1.12016
$505$	2.34464	0.104335
$506$	44.9341	1.99756
$507$	28.7272	1.27582
$508$	−25.2316	−1.11947
$509$	−41.5496	−1.84165	−0.920827	−	0.389971i	$-0.872485\pi$
$509$	−41.5496	−1.84165	−0.920827	+	0.389971i	$0.872485\pi$
$510$	10.9819	0.486288
$511$	−4.20288	−0.185924
$512$	−29.7413	−1.31439
$513$	−14.3886	−0.635271
$514$	13.1944	0.581980
$515$	−13.6666	−0.602221
$516$	−100.956	−4.44434
$517$	−18.5108	−0.814104
$518$	−52.1533	−2.29149
$519$	−37.4581	−1.64423
$520$	−1.72271	−0.0755459
$521$	−34.7825	−1.52385	−0.761925	−	0.647665i	$-0.775745\pi$
$521$	−34.7825	−1.52385	−0.761925	+	0.647665i	$0.775745\pi$
$522$	−122.775	−5.37373
$523$	31.5391	1.37911	0.689554	−	0.724234i	$-0.257807\pi$
$523$	31.5391	1.37911	0.689554	+	0.724234i	$0.257807\pi$
$524$	−23.4867	−1.02602
$525$	−12.4994	−0.545519
$526$	32.4903	1.41664
$527$	9.50419	0.414009
$528$	40.0410	1.74256
$529$	7.34298	0.319260
$530$	−29.9976	−1.30301
$531$	10.4470	0.453360
$532$	7.28295	0.315756
$533$	−1.83756	−0.0795934
$534$	44.4513	1.92359
$535$	−16.0074	−0.692061
$536$	−5.70906	−0.246594
$537$	−27.3741	−1.18128
$538$	−12.1919	−0.525630
$539$	26.8233	1.15536
$540$	42.0738	1.81057
$541$	17.0187	0.731692	0.365846	−	0.930675i	$-0.380780\pi$
$541$	17.0187	0.731692	0.365846	+	0.930675i	$0.380780\pi$
$542$	35.1790	1.51107
$543$	−52.8982	−2.27008
$544$	−12.5987	−0.540165
$545$	0.997445	0.0427259
$546$	−55.1522	−2.36030
$547$	−26.1695	−1.11893	−0.559463	−	0.828856i	$-0.688992\pi$
$547$	−26.1695	−1.11893	−0.559463	+	0.828856i	$0.688992\pi$
$548$	−27.0169	−1.15410
$549$	−6.60313	−0.281815
$550$	−8.15731	−0.347829
$551$	5.80748	0.247407
$552$	−15.1133	−0.643266
$553$	34.0014	1.44589
$554$	−42.8310	−1.81971
$555$	22.3984	0.950758
$556$	−30.0010	−1.27233
$557$	−14.4825	−0.613644	−0.306822	−	0.951767i	$-0.599266\pi$
$557$	−14.4825	−0.613644	−0.306822	+	0.951767i	$0.599266\pi$
$558$	105.107	4.44955
$559$	−26.5179	−1.12159
$560$	11.4294	0.482981
$561$	20.4041	0.861464
$562$	39.1784	1.65264
$563$	21.2476	0.895480	0.447740	−	0.894164i	$-0.352229\pi$
$563$	21.2476	0.895480	0.447740	+	0.894164i	$0.352229\pi$
$564$	38.1194	1.60511
$565$	0.528511	0.0222346
$566$	55.0172	2.31255
$567$	127.782	5.36634
$568$	−10.4417	−0.438123
$569$	−4.46422	−0.187150	−0.0935749	−	0.995612i	$-0.529829\pi$
$569$	−4.46422	−0.187150	−0.0935749	+	0.995612i	$0.529829\pi$
$570$	−5.74478	−0.240622
$571$	32.4818	1.35932	0.679661	−	0.733526i	$-0.262127\pi$
$571$	32.4818	1.35932	0.679661	+	0.733526i	$0.262127\pi$
$572$	−19.5970	−0.819390
$573$	22.9144	0.957264
$574$	−6.81435	−0.284426
$575$	−5.50845	−0.229718
$576$	−88.7410	−3.69754
$577$	−36.3442	−1.51303	−0.756513	−	0.653978i	$-0.773099\pi$
$577$	−36.3442	−1.51303	−0.756513	+	0.653978i	$0.773099\pi$
$578$	30.5036	1.26878
$579$	−50.4665	−2.09732
$580$	−16.9817	−0.705128
$581$	−57.0796	−2.36806
$582$	−6.91716	−0.286725
$583$	−55.7347	−2.30830
$584$	0.922546	0.0381752
$585$	17.3689	0.718114
$586$	−12.2161	−0.504641
$587$	41.1383	1.69796	0.848979	−	0.528427i	$-0.177218\pi$
$587$	41.1383	1.69796	0.848979	+	0.528427i	$0.177218\pi$
$588$	−55.2373	−2.27795
$589$	−4.97176	−0.204858
$590$	2.65395	0.109261
$591$	39.1389	1.60996
$592$	−20.4810	−0.841764
$593$	0.862479	0.0354178	0.0177089	−	0.999843i	$-0.494363\pi$
$593$	0.862479	0.0354178	0.0177089	+	0.999843i	$0.494363\pi$
$594$	143.577	5.89102
$595$	5.82421	0.238769
$596$	48.4701	1.98541
$597$	−74.3586	−3.04330
$598$	−24.3054	−0.993921
$599$	−33.7598	−1.37939	−0.689694	−	0.724101i	$-0.742255\pi$
$599$	−33.7598	−1.37939	−0.689694	+	0.724101i	$0.742255\pi$
$600$	2.74367	0.112010
$601$	−38.6012	−1.57458	−0.787288	−	0.616586i	$-0.788515\pi$
$601$	−38.6012	−1.57458	−0.787288	+	0.616586i	$0.788515\pi$
$602$	−98.3383	−4.00797
$603$	57.5604	2.34404
$604$	−16.0374	−0.652554
$605$	−4.15608	−0.168969
$606$	−16.4767	−0.669318
$607$	33.8077	1.37221	0.686106	−	0.727501i	$-0.259318\pi$
$607$	33.8077	1.37221	0.686106	+	0.727501i	$0.259318\pi$
$608$	6.59054	0.267282
$609$	−88.7966	−3.59822
$610$	−1.67746	−0.0679183
$611$	10.0127	0.405071
$612$	−30.8115	−1.24548
$613$	15.5341	0.627417	0.313708	−	0.949519i	$-0.398429\pi$
$613$	15.5341	0.627417	0.313708	+	0.949519i	$0.398429\pi$
$614$	32.6373	1.31713
$615$	2.92657	0.118011
$616$	−11.8696	−0.478241
$617$	32.7137	1.31701	0.658503	−	0.752579i	$-0.271190\pi$
$617$	32.7137	1.31701	0.658503	+	0.752579i	$0.271190\pi$
$618$	96.0399	3.86329
$619$	−5.16866	−0.207746	−0.103873	−	0.994591i	$-0.533124\pi$
$619$	−5.16866	−0.207746	−0.103873	+	0.994591i	$0.533124\pi$
$620$	14.5380	0.583860
$621$	96.9540	3.89063
$622$	8.34415	0.334570
$623$	23.5745	0.944494
$624$	−21.6587	−0.867041
$625$	1.00000	0.0400000
$626$	−13.6025	−0.543664
$627$	−10.6737	−0.426265
$628$	12.5487	0.500748
$629$	−10.4367	−0.416139
$630$	64.4103	2.56617
$631$	−5.67411	−0.225883	−0.112941	−	0.993602i	$-0.536027\pi$
$631$	−5.67411	−0.225883	−0.112941	+	0.993602i	$0.536027\pi$
$632$	−7.46343	−0.296879
$633$	−49.4866	−1.96692
$634$	63.5273	2.52299
$635$	10.5553	0.418874
$636$	114.775	4.55112
$637$	−14.5090	−0.574869
$638$	−57.9500	−2.29426
$639$	105.276	4.16465
$640$	−6.41989	−0.253768
$641$	−37.6938	−1.48882	−0.744408	−	0.667725i	$-0.767268\pi$
$641$	−37.6938	−1.48882	−0.744408	+	0.667725i	$0.767268\pi$
$642$	112.490	4.43962
$643$	−18.5987	−0.733463	−0.366732	−	0.930327i	$-0.619523\pi$
$643$	−18.5987	−0.733463	−0.366732	+	0.930327i	$0.619523\pi$
$644$	−49.0744	−1.93380
$645$	42.2335	1.66294
$646$	2.67683	0.105318
$647$	−36.5816	−1.43817	−0.719086	−	0.694921i	$-0.755439\pi$
$647$	−36.5816	−1.43817	−0.719086	+	0.694921i	$0.755439\pi$
$648$	−28.0486	−1.10185
$649$	4.93097	0.193558
$650$	4.41239	0.173068
$651$	76.0184	2.97939
$652$	−28.6060	−1.12030
$653$	23.5995	0.923519	0.461759	−	0.887005i	$-0.347218\pi$
$653$	23.5995	0.923519	0.461759	+	0.887005i	$0.347218\pi$
$654$	−7.00940	−0.274089
$655$	9.82531	0.383907
$656$	−2.67605	−0.104482
$657$	−9.30137	−0.362881
$658$	37.1309	1.44751
$659$	34.4976	1.34384	0.671918	−	0.740626i	$-0.265471\pi$
$659$	34.4976	1.34384	0.671918	+	0.740626i	$0.265471\pi$
$660$	31.2110	1.21489
$661$	10.5401	0.409963	0.204981	−	0.978766i	$-0.434287\pi$
$661$	10.5401	0.409963	0.204981	+	0.978766i	$0.434287\pi$
$662$	−9.22310	−0.358466
$663$	−11.0368	−0.428636
$664$	12.5292	0.486226
$665$	−3.04672	−0.118147
$666$	−115.420	−4.47245
$667$	−39.1323	−1.51521
$668$	−0.965207	−0.0373450
$669$	−85.7307	−3.31454
$670$	14.6226	0.564922
$671$	−3.11668	−0.120318
$672$	−100.770	−3.88727
$673$	−17.2919	−0.666555	−0.333278	−	0.942829i	$-0.608155\pi$
$673$	−17.2919	−0.666555	−0.333278	+	0.942829i	$0.608155\pi$
$674$	−14.7830	−0.569422
$675$	−17.6010	−0.677462
$676$	−20.4753	−0.787512
$677$	10.3684	0.398490	0.199245	−	0.979950i	$-0.436151\pi$
$677$	10.3684	0.398490	0.199245	+	0.979950i	$0.436151\pi$
$678$	−3.71403	−0.142637
$679$	−3.66848	−0.140783
$680$	−1.27844	−0.0490258
$681$	−52.4677	−2.01057
$682$	49.6107	1.89969
$683$	−31.1243	−1.19094	−0.595468	−	0.803379i	$-0.703034\pi$
$683$	−31.1243	−1.19094	−0.595468	+	0.803379i	$0.703034\pi$
$684$	16.1179	0.616282
$685$	11.3021	0.431832
$686$	0.859098	0.0328005
$687$	−51.3634	−1.95963
$688$	−38.6182	−1.47230
$689$	30.1476	1.14853
$690$	38.7098	1.47366
$691$	31.1502	1.18501	0.592505	−	0.805567i	$-0.298139\pi$
$691$	31.1502	1.18501	0.592505	+	0.805567i	$0.298139\pi$
$692$	26.6982	1.01491
$693$	119.673	4.54600
$694$	7.34071	0.278650
$695$	12.5505	0.476067
$696$	19.4912	0.738811
$697$	−1.36366	−0.0516524
$698$	−36.8985	−1.39663
$699$	−84.2436	−3.18639
$700$	8.90895	0.336726
$701$	−38.5488	−1.45597	−0.727984	−	0.685594i	$-0.759542\pi$
$701$	−38.5488	−1.45597	−0.727984	+	0.685594i	$0.759542\pi$
$702$	−77.6623	−2.93117
$703$	5.45958	0.205912
$704$	−41.8858	−1.57863
$705$	−15.9467	−0.600587
$706$	14.4069	0.542211
$707$	−8.73832	−0.328638
$708$	−10.1544	−0.381625
$709$	−15.4656	−0.580822	−0.290411	−	0.956902i	$-0.593792\pi$
$709$	−15.4656	−0.580822	−0.290411	+	0.956902i	$0.593792\pi$
$710$	26.7443	1.00370
$711$	75.2484	2.82204
$712$	−5.17469	−0.193930
$713$	33.5010	1.25462
$714$	−40.9288	−1.53172
$715$	8.19811	0.306592
$716$	19.5108	0.729155
$717$	51.8072	1.93477
$718$	0.691898	0.0258214
$719$	−12.8973	−0.480987	−0.240494	−	0.970651i	$-0.577309\pi$
$719$	−12.8973	−0.480987	−0.240494	+	0.970651i	$0.577309\pi$
$720$	25.2944	0.942667
$721$	50.9343	1.89689
$722$	38.4111	1.42951
$723$	−24.8413	−0.923859
$724$	37.7031	1.40123
$725$	7.10406	0.263838
$726$	29.2063	1.08395
$727$	40.0511	1.48541	0.742706	−	0.669617i	$-0.233542\pi$
$727$	40.0511	1.48541	0.742706	+	0.669617i	$0.233542\pi$
$728$	6.42042	0.237957
$729$	105.703	3.91493
$730$	−2.36292	−0.0874556
$731$	−19.6791	−0.727857
$732$	6.41819	0.237223
$733$	26.1204	0.964780	0.482390	−	0.875956i	$-0.339769\pi$
$733$	26.1204	0.964780	0.482390	+	0.875956i	$0.339769\pi$
$734$	−16.9433	−0.625388
$735$	23.1077	0.852341
$736$	−44.4088	−1.63693
$737$	27.1685	1.00076
$738$	−15.0808	−0.555133
$739$	13.9656	0.513734	0.256867	−	0.966447i	$-0.417310\pi$
$739$	13.9656	0.513734	0.256867	+	0.966447i	$0.417310\pi$
$740$	−15.9644	−0.586864
$741$	5.77351	0.212095
$742$	111.799	4.10426
$743$	27.8610	1.02212	0.511061	−	0.859545i	$-0.329253\pi$
$743$	27.8610	1.02212	0.511061	+	0.859545i	$0.329253\pi$
$744$	−16.6863	−0.611749
$745$	−20.2767	−0.742883
$746$	−39.1812	−1.43452
$747$	−126.323	−4.62191
$748$	−14.5430	−0.531746
$749$	59.6585	2.17987
$750$	−7.02736	−0.256603
$751$	26.1754	0.955154	0.477577	−	0.878590i	$-0.341515\pi$
$751$	26.1754	0.955154	0.477577	+	0.878590i	$0.341515\pi$
$752$	14.5816	0.531736
$753$	8.37413	0.305170
$754$	31.3458	1.14155
$755$	6.70902	0.244166
$756$	−156.806	−5.70298
$757$	38.7337	1.40780	0.703900	−	0.710299i	$-0.251440\pi$
$757$	38.7337	1.40780	0.703900	+	0.710299i	$0.251440\pi$
$758$	−44.9497	−1.63265
$759$	71.9219	2.61060
$760$	0.668765	0.0242587
$761$	−9.37460	−0.339829	−0.169914	−	0.985459i	$-0.554349\pi$
$761$	−9.37460	−0.339829	−0.169914	+	0.985459i	$0.554349\pi$
$762$	−74.1758	−2.68710
$763$	−3.71741	−0.134579
$764$	−16.3322	−0.590880
$765$	12.8895	0.466023
$766$	39.5154	1.42775
$767$	−2.66722	−0.0963078
$768$	−27.0527	−0.976179
$769$	−23.3696	−0.842730	−0.421365	−	0.906891i	$-0.638449\pi$
$769$	−23.3696	−0.842730	−0.421365	+	0.906891i	$0.638449\pi$
$770$	30.4017	1.09560
$771$	21.1191	0.760584
$772$	35.9700	1.29459
$773$	−22.7590	−0.818583	−0.409292	−	0.912404i	$-0.634224\pi$
$773$	−22.7590	−0.818583	−0.409292	+	0.912404i	$0.634224\pi$
$774$	−217.632	−7.82263
$775$	−6.08175	−0.218463
$776$	0.805245	0.0289066
$777$	−83.4771	−2.99472
$778$	73.9303	2.65053
$779$	0.713348	0.0255583
$780$	−16.8824	−0.604487
$781$	49.6902	1.77806
$782$	−18.0372	−0.645008
$783$	−125.038	−4.46851
$784$	−21.1296	−0.754630
$785$	−5.24957	−0.187365
$786$	−69.0460	−2.46279
$787$	42.1955	1.50411	0.752053	−	0.659103i	$-0.229064\pi$
$787$	42.1955	1.50411	0.752053	+	0.659103i	$0.229064\pi$
$788$	−27.8962	−0.993762
$789$	52.0043	1.85140
$790$	19.1161	0.680120
$791$	−1.96972	−0.0700352
$792$	−26.2686	−0.933415
$793$	1.68585	0.0598662
$794$	44.2648	1.57090
$795$	−48.0144	−1.70289
$796$	52.9991	1.87850
$797$	3.33663	0.118190	0.0590948	−	0.998252i	$-0.481179\pi$
$797$	3.33663	0.118190	0.0590948	+	0.998252i	$0.481179\pi$
$798$	21.4104	0.757919
$799$	7.43050	0.262872
$800$	8.06194	0.285033
$801$	52.1727	1.84343
$802$	25.1458	0.887931
$803$	−4.39025	−0.154928
$804$	−55.9482	−1.97314
$805$	20.5296	0.723573
$806$	−26.8350	−0.945224
$807$	−19.5145	−0.686942
$808$	1.91809	0.0674783
$809$	−28.0722	−0.986967	−0.493484	−	0.869755i	$-0.664277\pi$
$809$	−28.0722	−0.986967	−0.493484	+	0.869755i	$0.664277\pi$
$810$	71.8410	2.52424
$811$	−34.2898	−1.20408	−0.602039	−	0.798467i	$-0.705645\pi$
$811$	−34.2898	−1.20408	−0.602039	+	0.798467i	$0.705645\pi$
$812$	63.2897	2.22103
$813$	56.3079	1.97480
$814$	−54.4784	−1.90947
$815$	11.9669	0.419182
$816$	−16.0731	−0.562669
$817$	10.2944	0.360154
$818$	36.9470	1.29182
$819$	−64.7325	−2.26194
$820$	−2.08591	−0.0728432
$821$	−20.6375	−0.720253	−0.360126	−	0.932903i	$-0.617266\pi$
$821$	−20.6375	−0.720253	−0.360126	+	0.932903i	$0.617266\pi$
$822$	−79.4240	−2.77023
$823$	−24.9015	−0.868012	−0.434006	−	0.900910i	$-0.642900\pi$
$823$	−24.9015	−0.868012	−0.434006	+	0.900910i	$0.642900\pi$
$824$	−11.1803	−0.389483
$825$	−13.0567	−0.454575
$826$	−9.89107	−0.344154
$827$	46.9414	1.63231	0.816157	−	0.577830i	$-0.196100\pi$
$827$	46.9414	1.63231	0.816157	+	0.577830i	$0.196100\pi$
$828$	−108.606	−3.77434
$829$	17.6115	0.611672	0.305836	−	0.952084i	$-0.401064\pi$
$829$	17.6115	0.611672	0.305836	+	0.952084i	$0.401064\pi$
$830$	−32.0910	−1.11390
$831$	−68.5556	−2.37817
$832$	22.6565	0.785474
$833$	−10.7673	−0.373063
$834$	−88.1968	−3.05400
$835$	0.403780	0.0139734
$836$	7.60764	0.263116
$837$	107.045	3.70001
$838$	−10.7543	−0.371502
$839$	2.78652	0.0962014	0.0481007	−	0.998842i	$-0.484683\pi$
$839$	2.78652	0.0962014	0.0481007	+	0.998842i	$0.484683\pi$
$840$	−10.2254	−0.352811
$841$	21.4677	0.740264
$842$	−56.4913	−1.94682
$843$	62.7093	2.15982
$844$	35.2715	1.21410
$845$	8.56555	0.294664
$846$	82.1743	2.82521
$847$	15.4894	0.532223
$848$	43.9042	1.50768
$849$	88.0611	3.02225
$850$	3.27446	0.112313
$851$	−36.7881	−1.26108
$852$	−102.327	−3.50568
$853$	−12.8715	−0.440710	−0.220355	−	0.975420i	$-0.570722\pi$
$853$	−12.8715	−0.440710	−0.220355	+	0.975420i	$0.570722\pi$
$854$	6.25177	0.213931
$855$	−6.74268	−0.230595
$856$	−13.0953	−0.447587
$857$	−1.31828	−0.0450316	−0.0225158	−	0.999746i	$-0.507168\pi$
$857$	−1.31828	−0.0450316	−0.0225158	+	0.999746i	$0.507168\pi$
$858$	−57.6110	−1.96681
$859$	38.4110	1.31056	0.655282	−	0.755384i	$-0.272550\pi$
$859$	38.4110	1.31056	0.655282	+	0.755384i	$0.272550\pi$
$860$	−30.1019	−1.02647
$861$	−10.9071	−0.371714
$862$	0.980850	0.0334079
$863$	−34.0528	−1.15917	−0.579586	−	0.814911i	$-0.696786\pi$
$863$	−34.0528	−1.15917	−0.579586	+	0.814911i	$0.696786\pi$
$864$	−141.898	−4.82747
$865$	−11.1688	−0.379751
$866$	26.1412	0.888313
$867$	48.8243	1.65816
$868$	−54.1820	−1.83906
$869$	35.5173	1.20484
$870$	−49.9228	−1.69254
$871$	−14.6958	−0.497947
$872$	0.815984	0.0276327
$873$	−8.11871	−0.274777
$874$	9.43547	0.319160
$875$	−3.72693	−0.125993
$876$	9.04086	0.305462
$877$	−5.13258	−0.173315	−0.0866575	−	0.996238i	$-0.527619\pi$
$877$	−5.13258	−0.173315	−0.0866575	+	0.996238i	$0.527619\pi$
$878$	−75.0619	−2.53322
$879$	−19.5532	−0.659512
$880$	11.9390	0.402463
$881$	−22.5084	−0.758326	−0.379163	−	0.925330i	$-0.623788\pi$
$881$	−22.5084	−0.758326	−0.379163	+	0.925330i	$0.623788\pi$
$882$	−119.076	−4.00949
$883$	−16.5241	−0.556082	−0.278041	−	0.960569i	$-0.589685\pi$
$883$	−16.5241	−0.556082	−0.278041	+	0.960569i	$0.589685\pi$
$884$	7.86650	0.264579
$885$	4.24793	0.142793
$886$	−15.3472	−0.515598
$887$	45.4064	1.52460	0.762299	−	0.647225i	$-0.224071\pi$
$887$	45.4064	1.52460	0.762299	+	0.647225i	$0.224071\pi$
$888$	18.3235	0.614897
$889$	−39.3388	−1.31938
$890$	13.2540	0.444274
$891$	133.479	4.47171
$892$	61.1045	2.04593
$893$	−3.88698	−0.130073
$894$	142.492	4.76564
$895$	−8.16208	−0.272828
$896$	23.9265	0.799327
$897$	−38.9034	−1.29895
$898$	41.9960	1.40142
$899$	−43.2051	−1.44097
$900$	19.7164	0.657212
$901$	22.3727	0.745344
$902$	−7.11815	−0.237008
$903$	−157.401	−5.23798
$904$	0.432361	0.0143801
$905$	−15.7726	−0.524297
$906$	−47.1467	−1.56634
$907$	49.3114	1.63736	0.818679	−	0.574252i	$-0.194707\pi$
$907$	49.3114	1.63736	0.818679	+	0.574252i	$0.194707\pi$
$908$	37.3963	1.24104
$909$	−19.3387	−0.641426
$910$	−16.4446	−0.545135
$911$	5.00051	0.165674	0.0828371	−	0.996563i	$-0.473602\pi$
$911$	5.00051	0.165674	0.0828371	+	0.996563i	$0.473602\pi$
$912$	8.40801	0.278417
$913$	−59.6243	−1.97328
$914$	−31.0458	−1.02690
$915$	−2.68496	−0.0887619
$916$	36.6092	1.20960
$917$	−36.6182	−1.20924
$918$	−57.6337	−1.90219
$919$	0.187099	0.00617183	0.00308592	−	0.999995i	$-0.499018\pi$
$919$	0.187099	0.00617183	0.00308592	+	0.999995i	$0.499018\pi$
$920$	−4.50632	−0.148569
$921$	52.2395	1.72135
$922$	−49.5597	−1.63216
$923$	−26.8780	−0.884702
$924$	−116.321	−3.82668
$925$	6.67848	0.219587
$926$	−44.6017	−1.46570
$927$	112.723	3.70229
$928$	57.2725	1.88006
$929$	12.8999	0.423231	0.211616	−	0.977353i	$-0.432127\pi$
$929$	12.8999	0.423231	0.211616	+	0.977353i	$0.432127\pi$
$930$	42.7387	1.40146
$931$	5.63248	0.184597
$932$	60.0446	1.96682
$933$	13.3557	0.437247
$934$	25.9566	0.849326
$935$	6.08387	0.198964
$936$	14.2090	0.464436
$937$	9.20330	0.300659	0.150329	−	0.988636i	$-0.451967\pi$
$937$	9.20330	0.300659	0.150329	+	0.988636i	$0.451967\pi$
$938$	−54.4975	−1.77941
$939$	−21.7722	−0.710510
$940$	11.3660	0.370717
$941$	58.8310	1.91783	0.958917	−	0.283686i	$-0.0915575\pi$
$941$	58.8310	1.91783	0.958917	+	0.283686i	$0.0915575\pi$
$942$	36.8906	1.20196
$943$	−4.80673	−0.156529
$944$	−3.88430	−0.126423
$945$	65.5975	2.13389
$946$	−102.722	−3.33979
$947$	50.0925	1.62779	0.813893	−	0.581014i	$-0.197344\pi$
$947$	50.0925	1.62779	0.813893	+	0.581014i	$0.197344\pi$
$948$	−73.1408	−2.37550
$949$	2.37474	0.0770872
$950$	−1.71291	−0.0555741
$951$	101.682	3.29728
$952$	4.76464	0.154423
$953$	57.9661	1.87771	0.938853	−	0.344319i	$-0.111890\pi$
$953$	57.9661	1.87771	0.938853	+	0.344319i	$0.111890\pi$
$954$	247.421	8.01056
$955$	6.83236	0.221090
$956$	−36.9255	−1.19426
$957$	−92.7553	−2.99835
$958$	−4.71146	−0.152220
$959$	−42.1222	−1.36020
$960$	−36.0838	−1.16460
$961$	5.98774	0.193153
$962$	29.4680	0.950088
$963$	132.030	4.25461
$964$	17.7056	0.570260
$965$	−15.0475	−0.484396
$966$	−144.269	−4.64177
$967$	−17.5930	−0.565752	−0.282876	−	0.959156i	$-0.591289\pi$
$967$	−17.5930	−0.565752	−0.282876	+	0.959156i	$0.591289\pi$
$968$	−3.39998	−0.109280
$969$	4.28456	0.137640
$970$	−2.06248	−0.0662221
$971$	26.2587	0.842683	0.421341	−	0.906902i	$-0.361559\pi$
$971$	26.2587	0.842683	0.421341	+	0.906902i	$0.361559\pi$
$972$	−148.652	−4.76802
$973$	−46.7748	−1.49953
$974$	−3.27367	−0.104895
$975$	7.06250	0.226181
$976$	2.45511	0.0785863
$977$	−38.5192	−1.23234	−0.616169	−	0.787614i	$-0.711316\pi$
$977$	−38.5192	−1.23234	−0.616169	+	0.787614i	$0.711316\pi$
$978$	−84.0956	−2.68908
$979$	24.6255	0.787035
$980$	−16.4700	−0.526115
$981$	−8.22698	−0.262667
$982$	−90.4534	−2.88648
$983$	25.8540	0.824613	0.412307	−	0.911045i	$-0.364723\pi$
$983$	25.8540	0.824613	0.412307	+	0.911045i	$0.364723\pi$
$984$	2.39415	0.0763227
$985$	11.6700	0.371836
$986$	23.2620	0.740812
$987$	59.4321	1.89175
$988$	−4.11506	−0.130918
$989$	−69.3662	−2.20572
$990$	67.2819	2.13836
$991$	−17.9437	−0.570002	−0.285001	−	0.958527i	$-0.591994\pi$
$991$	−17.9437	−0.570002	−0.285001	+	0.958527i	$0.591994\pi$
$992$	−49.0307	−1.55673
$993$	−14.7626	−0.468476
$994$	−99.6740	−3.16147
$995$	−22.1714	−0.702880
$996$	122.785	3.89058
$997$	21.0648	0.667129	0.333565	−	0.942727i	$-0.391748\pi$
$997$	21.0648	0.667129	0.333565	+	0.942727i	$0.391748\pi$
$998$	−17.1458	−0.542742
$999$	−117.548	−3.71905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.19	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.19	✓	113	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.09533 q^{2} -3.35381 q^{3} +2.39043 q^{4} -1.00000 q^{5} +7.02736 q^{6} +3.72693 q^{7} -0.818074 q^{8} +8.24805 q^{9} +O(q^{10})\)	\(q-2.09533 q^{2} -3.35381 q^{3} +2.39043 q^{4} -1.00000 q^{5} +7.02736 q^{6} +3.72693 q^{7} -0.818074 q^{8} +8.24805 q^{9} +2.09533 q^{10} +3.89308 q^{11} -8.01704 q^{12} -2.10581 q^{13} -7.80916 q^{14} +3.35381 q^{15} -3.06671 q^{16} -1.56274 q^{17} -17.2824 q^{18} +0.817488 q^{19} -2.39043 q^{20} -12.4994 q^{21} -8.15731 q^{22} -5.50845 q^{23} +2.74367 q^{24} +1.00000 q^{25} +4.41239 q^{26} -17.6010 q^{27} +8.90895 q^{28} +7.10406 q^{29} -7.02736 q^{30} -6.08175 q^{31} +8.06194 q^{32} -13.0567 q^{33} +3.27446 q^{34} -3.72693 q^{35} +19.7164 q^{36} +6.67848 q^{37} -1.71291 q^{38} +7.06250 q^{39} +0.818074 q^{40} +0.872610 q^{41} +26.1904 q^{42} +12.5927 q^{43} +9.30612 q^{44} -8.24805 q^{45} +11.5420 q^{46} -4.75479 q^{47} +10.2852 q^{48} +6.88999 q^{49} -2.09533 q^{50} +5.24113 q^{51} -5.03379 q^{52} -14.3164 q^{53} +36.8799 q^{54} -3.89308 q^{55} -3.04890 q^{56} -2.74170 q^{57} -14.8854 q^{58} +1.26660 q^{59} +8.01704 q^{60} -0.800568 q^{61} +12.7433 q^{62} +30.7399 q^{63} -10.7590 q^{64} +2.10581 q^{65} +27.3581 q^{66} +6.97866 q^{67} -3.73561 q^{68} +18.4743 q^{69} +7.80916 q^{70} +12.7637 q^{71} -6.74751 q^{72} -1.12771 q^{73} -13.9937 q^{74} -3.35381 q^{75} +1.95414 q^{76} +14.5092 q^{77} -14.7983 q^{78} +9.12317 q^{79} +3.06671 q^{80} +34.2862 q^{81} -1.82841 q^{82} -15.3155 q^{83} -29.8789 q^{84} +1.56274 q^{85} -26.3859 q^{86} -23.8257 q^{87} -3.18483 q^{88} +6.32546 q^{89} +17.2824 q^{90} -7.84822 q^{91} -13.1675 q^{92} +20.3971 q^{93} +9.96288 q^{94} -0.817488 q^{95} -27.0382 q^{96} -0.984318 q^{97} -14.4368 q^{98} +32.1103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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