LMFDB - Embedded newform 4017.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66982 q^{2} -1.00000 q^{3} +5.12792 q^{4} -3.00815 q^{5} +2.66982 q^{6} +2.19544 q^{7} -8.35096 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.66982 q^{2} -1.00000 q^{3} +5.12792 q^{4} -3.00815 q^{5} +2.66982 q^{6} +2.19544 q^{7} -8.35096 q^{8} +1.00000 q^{9} +8.03119 q^{10} +2.63808 q^{11} -5.12792 q^{12} -1.00000 q^{13} -5.86143 q^{14} +3.00815 q^{15} +12.0397 q^{16} -2.18589 q^{17} -2.66982 q^{18} -0.544925 q^{19} -15.4255 q^{20} -2.19544 q^{21} -7.04319 q^{22} +0.887710 q^{23} +8.35096 q^{24} +4.04894 q^{25} +2.66982 q^{26} -1.00000 q^{27} +11.2580 q^{28} +0.808105 q^{29} -8.03119 q^{30} +6.03482 q^{31} -15.4418 q^{32} -2.63808 q^{33} +5.83593 q^{34} -6.60421 q^{35} +5.12792 q^{36} +5.66562 q^{37} +1.45485 q^{38} +1.00000 q^{39} +25.1209 q^{40} -9.88379 q^{41} +5.86143 q^{42} -11.9839 q^{43} +13.5279 q^{44} -3.00815 q^{45} -2.37002 q^{46} +0.388731 q^{47} -12.0397 q^{48} -2.18003 q^{49} -10.8099 q^{50} +2.18589 q^{51} -5.12792 q^{52} -6.21503 q^{53} +2.66982 q^{54} -7.93573 q^{55} -18.3341 q^{56} +0.544925 q^{57} -2.15749 q^{58} +7.45364 q^{59} +15.4255 q^{60} +8.25729 q^{61} -16.1119 q^{62} +2.19544 q^{63} +17.1475 q^{64} +3.00815 q^{65} +7.04319 q^{66} -6.64410 q^{67} -11.2091 q^{68} -0.887710 q^{69} +17.6320 q^{70} +4.39752 q^{71} -8.35096 q^{72} -1.83577 q^{73} -15.1262 q^{74} -4.04894 q^{75} -2.79433 q^{76} +5.79176 q^{77} -2.66982 q^{78} -3.56175 q^{79} -36.2171 q^{80} +1.00000 q^{81} +26.3879 q^{82} +15.8818 q^{83} -11.2580 q^{84} +6.57548 q^{85} +31.9949 q^{86} -0.808105 q^{87} -22.0305 q^{88} +4.30024 q^{89} +8.03119 q^{90} -2.19544 q^{91} +4.55210 q^{92} -6.03482 q^{93} -1.03784 q^{94} +1.63921 q^{95} +15.4418 q^{96} -6.55507 q^{97} +5.82028 q^{98} +2.63808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	−2.66982	−1.88784	−0.943922	−	0.330167i	$-0.892895\pi$
$2$	−2.66982	−1.88784	−0.943922	+	0.330167i	$0.892895\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.12792	2.56396
$5$	−3.00815	−1.34528	−0.672642	−	0.739968i	$-0.734840\pi$
$5$	−3.00815	−1.34528	−0.672642	+	0.739968i	$0.734840\pi$
$6$	2.66982	1.08995
$7$	2.19544	0.829799	0.414900	−	0.909867i	$-0.363817\pi$
$7$	2.19544	0.829799	0.414900	+	0.909867i	$0.363817\pi$
$8$	−8.35096	−2.95251
$9$	1.00000	0.333333
$10$	8.03119	2.53969
$11$	2.63808	0.795412	0.397706	−	0.917513i	$-0.369806\pi$
$11$	2.63808	0.795412	0.397706	+	0.917513i	$0.369806\pi$
$12$	−5.12792	−1.48030
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.86143	−1.56653
$15$	3.00815	0.776700
$16$	12.0397	3.00992
$17$	−2.18589	−0.530157	−0.265078	−	0.964227i	$-0.585398\pi$
$17$	−2.18589	−0.530157	−0.265078	+	0.964227i	$0.585398\pi$
$18$	−2.66982	−0.629282
$19$	−0.544925	−0.125014	−0.0625071	−	0.998045i	$-0.519910\pi$
$19$	−0.544925	−0.125014	−0.0625071	+	0.998045i	$0.519910\pi$
$20$	−15.4255	−3.44925
$21$	−2.19544	−0.479085
$22$	−7.04319	−1.50161
$23$	0.887710	0.185100	0.0925502	−	0.995708i	$-0.470498\pi$
$23$	0.887710	0.185100	0.0925502	+	0.995708i	$0.470498\pi$
$24$	8.35096	1.70463
$25$	4.04894	0.809787
$26$	2.66982	0.523594
$27$	−1.00000	−0.192450
$28$	11.2580	2.12757
$29$	0.808105	0.150061	0.0750307	−	0.997181i	$-0.476095\pi$
$29$	0.808105	0.150061	0.0750307	+	0.997181i	$0.476095\pi$
$30$	−8.03119	−1.46629
$31$	6.03482	1.08389	0.541943	−	0.840415i	$-0.317689\pi$
$31$	6.03482	1.08389	0.541943	+	0.840415i	$0.317689\pi$
$32$	−15.4418	−2.72976
$33$	−2.63808	−0.459231
$34$	5.83593	1.00085
$35$	−6.60421	−1.11632
$36$	5.12792	0.854653
$37$	5.66562	0.931423	0.465711	−	0.884937i	$-0.345799\pi$
$37$	5.66562	0.931423	0.465711	+	0.884937i	$0.345799\pi$
$38$	1.45485	0.236008
$39$	1.00000	0.160128
$40$	25.1209	3.97196
$41$	−9.88379	−1.54359	−0.771794	−	0.635872i	$-0.780641\pi$
$41$	−9.88379	−1.54359	−0.771794	+	0.635872i	$0.780641\pi$
$42$	5.86143	0.904438
$43$	−11.9839	−1.82753	−0.913767	−	0.406238i	$-0.866840\pi$
$43$	−11.9839	−1.82753	−0.913767	+	0.406238i	$0.866840\pi$
$44$	13.5279	2.03940
$45$	−3.00815	−0.448428
$46$	−2.37002	−0.349441
$47$	0.388731	0.0567022	0.0283511	−	0.999598i	$-0.490974\pi$
$47$	0.388731	0.0567022	0.0283511	+	0.999598i	$0.490974\pi$
$48$	−12.0397	−1.73778
$49$	−2.18003	−0.311433
$50$	−10.8099	−1.52875
$51$	2.18589	0.306086
$52$	−5.12792	−0.711114
$53$	−6.21503	−0.853700	−0.426850	−	0.904322i	$-0.640377\pi$
$53$	−6.21503	−0.853700	−0.426850	+	0.904322i	$0.640377\pi$
$54$	2.66982	0.363316
$55$	−7.93573	−1.07005
$56$	−18.3341	−2.44999
$57$	0.544925	0.0721770
$58$	−2.15749	−0.283293
$59$	7.45364	0.970381	0.485191	−	0.874408i	$-0.338750\pi$
$59$	7.45364	0.970381	0.485191	+	0.874408i	$0.338750\pi$
$60$	15.4255	1.99143
$61$	8.25729	1.05724	0.528619	−	0.848859i	$-0.322710\pi$
$61$	8.25729	1.05724	0.528619	+	0.848859i	$0.322710\pi$
$62$	−16.1119	−2.04621
$63$	2.19544	0.276600
$64$	17.1475	2.14344
$65$	3.00815	0.373114
$66$	7.04319	0.866957
$67$	−6.64410	−0.811707	−0.405853	−	0.913938i	$-0.633026\pi$
$67$	−6.64410	−0.811707	−0.405853	+	0.913938i	$0.633026\pi$
$68$	−11.2091	−1.35930
$69$	−0.887710	−0.106868
$70$	17.6320	2.10743
$71$	4.39752	0.521889	0.260945	−	0.965354i	$-0.415966\pi$
$71$	4.39752	0.521889	0.260945	+	0.965354i	$0.415966\pi$
$72$	−8.35096	−0.984170
$73$	−1.83577	−0.214861	−0.107430	−	0.994213i	$-0.534262\pi$
$73$	−1.83577	−0.214861	−0.107430	+	0.994213i	$0.534262\pi$
$74$	−15.1262	−1.75838
$75$	−4.04894	−0.467531
$76$	−2.79433	−0.320531
$77$	5.79176	0.660032
$78$	−2.66982	−0.302297
$79$	−3.56175	−0.400729	−0.200364	−	0.979721i	$-0.564213\pi$
$79$	−3.56175	−0.400729	−0.200364	+	0.979721i	$0.564213\pi$
$80$	−36.2171	−4.04920
$81$	1.00000	0.111111
$82$	26.3879	2.91406
$83$	15.8818	1.74325	0.871626	−	0.490171i	$-0.163066\pi$
$83$	15.8818	1.74325	0.871626	+	0.490171i	$0.163066\pi$
$84$	−11.2580	−1.22835
$85$	6.57548	0.713211
$86$	31.9949	3.45010
$87$	−0.808105	−0.0866380
$88$	−22.0305	−2.34846
$89$	4.30024	0.455825	0.227912	−	0.973682i	$-0.426810\pi$
$89$	4.30024	0.455825	0.227912	+	0.973682i	$0.426810\pi$
$90$	8.03119	0.846562
$91$	−2.19544	−0.230145
$92$	4.55210	0.474590
$93$	−6.03482	−0.625782
$94$	−1.03784	−0.107045
$95$	1.63921	0.168180
$96$	15.4418	1.57603
$97$	−6.55507	−0.665566	−0.332783	−	0.943003i	$-0.607988\pi$
$97$	−6.55507	−0.665566	−0.332783	+	0.943003i	$0.607988\pi$
$98$	5.82028	0.587937
$99$	2.63808	0.265137
$100$	20.7626	2.07626
$101$	−12.1615	−1.21012	−0.605059	−	0.796180i	$-0.706851\pi$
$101$	−12.1615	−1.21012	−0.605059	+	0.796180i	$0.706851\pi$
$102$	−5.83593	−0.577843
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	8.35096	0.818879
$105$	6.60421	0.644505
$106$	16.5930	1.61165
$107$	−3.13608	−0.303176	−0.151588	−	0.988444i	$-0.548439\pi$
$107$	−3.13608	−0.303176	−0.151588	+	0.988444i	$0.548439\pi$
$108$	−5.12792	−0.493434
$109$	12.5874	1.20565	0.602825	−	0.797873i	$-0.294042\pi$
$109$	12.5874	1.20565	0.602825	+	0.797873i	$0.294042\pi$
$110$	21.1869	2.02010
$111$	−5.66562	−0.537757
$112$	26.4325	2.49763
$113$	−12.4219	−1.16855	−0.584277	−	0.811554i	$-0.698622\pi$
$113$	−12.4219	−1.16855	−0.584277	+	0.811554i	$0.698622\pi$
$114$	−1.45485	−0.136259
$115$	−2.67036	−0.249012
$116$	4.14390	0.384751
$117$	−1.00000	−0.0924500
$118$	−19.8998	−1.83193
$119$	−4.79900	−0.439924
$120$	−25.1209	−2.29321
$121$	−4.04052	−0.367320
$122$	−22.0455	−1.99590
$123$	9.88379	0.891191
$124$	30.9460	2.77904
$125$	2.86094	0.255890
$126$	−5.86143	−0.522177
$127$	12.8322	1.13868	0.569338	−	0.822104i	$-0.307200\pi$
$127$	12.8322	1.13868	0.569338	+	0.822104i	$0.307200\pi$
$128$	−14.8969	−1.31672
$129$	11.9839	1.05513
$130$	−8.03119	−0.704382
$131$	3.12414	0.272958	0.136479	−	0.990643i	$-0.456421\pi$
$131$	3.12414	0.272958	0.136479	+	0.990643i	$0.456421\pi$
$132$	−13.5279	−1.17745
$133$	−1.19635	−0.103737
$134$	17.7385	1.53238
$135$	3.00815	0.258900
$136$	18.2543	1.56529
$137$	−12.1174	−1.03526	−0.517628	−	0.855606i	$-0.673185\pi$
$137$	−12.1174	−1.03526	−0.517628	+	0.855606i	$0.673185\pi$
$138$	2.37002	0.201750
$139$	7.77144	0.659165	0.329583	−	0.944127i	$-0.393092\pi$
$139$	7.77144	0.659165	0.329583	+	0.944127i	$0.393092\pi$
$140$	−33.8658	−2.86219
$141$	−0.388731	−0.0327371
$142$	−11.7406	−0.985246
$143$	−2.63808	−0.220607
$144$	12.0397	1.00331
$145$	−2.43090	−0.201875
$146$	4.90117	0.405624
$147$	2.18003	0.179806
$148$	29.0528	2.38813
$149$	−8.23875	−0.674944	−0.337472	−	0.941335i	$-0.609572\pi$
$149$	−8.23875	−0.674944	−0.337472	+	0.941335i	$0.609572\pi$
$150$	10.8099	0.882626
$151$	4.04877	0.329484	0.164742	−	0.986337i	$-0.447321\pi$
$151$	4.04877	0.329484	0.164742	+	0.986337i	$0.447321\pi$
$152$	4.55064	0.369106
$153$	−2.18589	−0.176719
$154$	−15.4629	−1.24604
$155$	−18.1536	−1.45813
$156$	5.12792	0.410562
$157$	−14.3491	−1.14518	−0.572592	−	0.819840i	$-0.694062\pi$
$157$	−14.3491	−1.14518	−0.572592	+	0.819840i	$0.694062\pi$
$158$	9.50923	0.756513
$159$	6.21503	0.492884
$160$	46.4513	3.67230
$161$	1.94892	0.153596
$162$	−2.66982	−0.209761
$163$	15.3371	1.20129	0.600645	−	0.799515i	$-0.294910\pi$
$163$	15.3371	1.20129	0.600645	+	0.799515i	$0.294910\pi$
$164$	−50.6833	−3.95770
$165$	7.93573	0.617796
$166$	−42.4014	−3.29099
$167$	13.5746	1.05043	0.525216	−	0.850969i	$-0.323984\pi$
$167$	13.5746	1.05043	0.525216	+	0.850969i	$0.323984\pi$
$168$	18.3341	1.41450
$169$	1.00000	0.0769231
$170$	−17.5553	−1.34643
$171$	−0.544925	−0.0416714
$172$	−61.4527	−4.68572
$173$	24.9047	1.89347	0.946736	−	0.322010i	$-0.104359\pi$
$173$	24.9047	1.89347	0.946736	+	0.322010i	$0.104359\pi$
$174$	2.15749	0.163559
$175$	8.88921	0.671961
$176$	31.7617	2.39413
$177$	−7.45364	−0.560250
$178$	−11.4809	−0.860526
$179$	3.71185	0.277437	0.138718	−	0.990332i	$-0.455702\pi$
$179$	3.71185	0.277437	0.138718	+	0.990332i	$0.455702\pi$
$180$	−15.4255	−1.14975
$181$	0.511766	0.0380393	0.0190196	−	0.999819i	$-0.493945\pi$
$181$	0.511766	0.0380393	0.0190196	+	0.999819i	$0.493945\pi$
$182$	5.86143	0.434478
$183$	−8.25729	−0.610397
$184$	−7.41323	−0.546511
$185$	−17.0430	−1.25303
$186$	16.1119	1.18138
$187$	−5.76656	−0.421693
$188$	1.99338	0.145382
$189$	−2.19544	−0.159695
$190$	−4.37639	−0.317497
$191$	−12.7597	−0.923261	−0.461631	−	0.887072i	$-0.652735\pi$
$191$	−12.7597	−0.923261	−0.461631	+	0.887072i	$0.652735\pi$
$192$	−17.1475	−1.23751
$193$	−12.5704	−0.904835	−0.452418	−	0.891806i	$-0.649438\pi$
$193$	−12.5704	−0.904835	−0.452418	+	0.891806i	$0.649438\pi$
$194$	17.5008	1.25649
$195$	−3.00815	−0.215418
$196$	−11.1790	−0.798501
$197$	−12.7601	−0.909117	−0.454559	−	0.890717i	$-0.650203\pi$
$197$	−12.7601	−0.909117	−0.454559	+	0.890717i	$0.650203\pi$
$198$	−7.04319	−0.500538
$199$	8.24032	0.584141	0.292070	−	0.956397i	$-0.405656\pi$
$199$	8.24032	0.584141	0.292070	+	0.956397i	$0.405656\pi$
$200$	−33.8125	−2.39091
$201$	6.64410	0.468639
$202$	32.4691	2.28452
$203$	1.77415	0.124521
$204$	11.2091	0.784792
$205$	29.7319	2.07656
$206$	2.66982	0.186015
$207$	0.887710	0.0617001
$208$	−12.0397	−0.834802
$209$	−1.43756	−0.0994378
$210$	−17.6320	−1.21673
$211$	4.97701	0.342632	0.171316	−	0.985216i	$-0.445198\pi$
$211$	4.97701	0.342632	0.171316	+	0.985216i	$0.445198\pi$
$212$	−31.8702	−2.18885
$213$	−4.39752	−0.301313
$214$	8.37275	0.572350
$215$	36.0494	2.45855
$216$	8.35096	0.568211
$217$	13.2491	0.899407
$218$	−33.6059	−2.27608
$219$	1.83577	0.124050
$220$	−40.6938	−2.74357
$221$	2.18589	0.147039
$222$	15.1262	1.01520
$223$	−21.8745	−1.46483	−0.732413	−	0.680860i	$-0.761606\pi$
$223$	−21.8745	−1.46483	−0.732413	+	0.680860i	$0.761606\pi$
$224$	−33.9017	−2.26515
$225$	4.04894	0.269929
$226$	33.1642	2.20605
$227$	23.7966	1.57944	0.789719	−	0.613468i	$-0.210226\pi$
$227$	23.7966	1.57944	0.789719	+	0.613468i	$0.210226\pi$
$228$	2.79433	0.185059
$229$	8.22470	0.543504	0.271752	−	0.962367i	$-0.412397\pi$
$229$	8.22470	0.543504	0.271752	+	0.962367i	$0.412397\pi$
$230$	7.12937	0.470097
$231$	−5.79176	−0.381070
$232$	−6.74846	−0.443058
$233$	6.55798	0.429628	0.214814	−	0.976655i	$-0.431086\pi$
$233$	6.55798	0.429628	0.214814	+	0.976655i	$0.431086\pi$
$234$	2.66982	0.174531
$235$	−1.16936	−0.0762806
$236$	38.2216	2.48802
$237$	3.56175	0.231361
$238$	12.8124	0.830508
$239$	26.0831	1.68718	0.843589	−	0.536989i	$-0.180438\pi$
$239$	26.0831	1.68718	0.843589	+	0.536989i	$0.180438\pi$
$240$	36.2171	2.33781
$241$	−1.47131	−0.0947751	−0.0473876	−	0.998877i	$-0.515090\pi$
$241$	−1.47131	−0.0947751	−0.0473876	+	0.998877i	$0.515090\pi$
$242$	10.7875	0.693444
$243$	−1.00000	−0.0641500
$244$	42.3427	2.71071
$245$	6.55785	0.418966
$246$	−26.3879	−1.68243
$247$	0.544925	0.0346727
$248$	−50.3965	−3.20018
$249$	−15.8818	−1.00647
$250$	−7.63817	−0.483081
$251$	10.3372	0.652481	0.326241	−	0.945287i	$-0.394218\pi$
$251$	10.3372	0.652481	0.326241	+	0.945287i	$0.394218\pi$
$252$	11.2580	0.709190
$253$	2.34185	0.147231
$254$	−34.2597	−2.14964
$255$	−6.57548	−0.411773
$256$	5.47712	0.342320
$257$	−5.41779	−0.337952	−0.168976	−	0.985620i	$-0.554046\pi$
$257$	−5.41779	−0.337952	−0.168976	+	0.985620i	$0.554046\pi$
$258$	−31.9949	−1.99192
$259$	12.4385	0.772894
$260$	15.4255	0.956650
$261$	0.808105	0.0500205
$262$	−8.34089	−0.515302
$263$	20.2050	1.24590	0.622948	−	0.782264i	$-0.285935\pi$
$263$	20.2050	1.24590	0.622948	+	0.782264i	$0.285935\pi$
$264$	22.0305	1.35588
$265$	18.6957	1.14847
$266$	3.19404	0.195839
$267$	−4.30024	−0.263170
$268$	−34.0704	−2.08118
$269$	−2.32454	−0.141730	−0.0708650	−	0.997486i	$-0.522576\pi$
$269$	−2.32454	−0.141730	−0.0708650	+	0.997486i	$0.522576\pi$
$270$	−8.03119	−0.488763
$271$	−6.88548	−0.418263	−0.209132	−	0.977888i	$-0.567064\pi$
$271$	−6.88548	−0.418263	−0.209132	+	0.977888i	$0.567064\pi$
$272$	−26.3175	−1.59573
$273$	2.19544	0.132874
$274$	32.3511	1.95440
$275$	10.6814	0.644114
$276$	−4.55210	−0.274004
$277$	−17.0634	−1.02524	−0.512621	−	0.858615i	$-0.671325\pi$
$277$	−17.0634	−1.02524	−0.512621	+	0.858615i	$0.671325\pi$
$278$	−20.7483	−1.24440
$279$	6.03482	0.361295
$280$	55.1515	3.29593
$281$	−3.17710	−0.189530	−0.0947648	−	0.995500i	$-0.530210\pi$
$281$	−3.17710	−0.189530	−0.0947648	+	0.995500i	$0.530210\pi$
$282$	1.03784	0.0618025
$283$	2.14891	0.127739	0.0638697	−	0.997958i	$-0.479656\pi$
$283$	2.14891	0.127739	0.0638697	+	0.997958i	$0.479656\pi$
$284$	22.5501	1.33810
$285$	−1.63921	−0.0970985
$286$	7.04319	0.416473
$287$	−21.6993	−1.28087
$288$	−15.4418	−0.909919
$289$	−12.2219	−0.718934
$290$	6.49005	0.381109
$291$	6.55507	0.384265
$292$	−9.41369	−0.550894
$293$	−13.7682	−0.804345	−0.402173	−	0.915564i	$-0.631745\pi$
$293$	−13.7682	−0.804345	−0.402173	+	0.915564i	$0.631745\pi$
$294$	−5.82028	−0.339446
$295$	−22.4216	−1.30544
$296$	−47.3134	−2.75003
$297$	−2.63808	−0.153077
$298$	21.9959	1.27419
$299$	−0.887710	−0.0513376
$300$	−20.7626	−1.19873
$301$	−26.3101	−1.51649
$302$	−10.8095	−0.622015
$303$	12.1615	0.698662
$304$	−6.56072	−0.376283
$305$	−24.8391	−1.42228
$306$	5.83593	0.333618
$307$	−19.3543	−1.10461	−0.552303	−	0.833643i	$-0.686251\pi$
$307$	−19.3543	−1.10461	−0.552303	+	0.833643i	$0.686251\pi$
$308$	29.6996	1.69229
$309$	1.00000	0.0568880
$310$	48.4668	2.75273
$311$	−8.80742	−0.499423	−0.249711	−	0.968320i	$-0.580336\pi$
$311$	−8.80742	−0.499423	−0.249711	+	0.968320i	$0.580336\pi$
$312$	−8.35096	−0.472780
$313$	−13.8110	−0.780646	−0.390323	−	0.920678i	$-0.627637\pi$
$313$	−13.8110	−0.780646	−0.390323	+	0.920678i	$0.627637\pi$
$314$	38.3095	2.16193
$315$	−6.60421	−0.372105
$316$	−18.2644	−1.02745
$317$	−9.14107	−0.513414	−0.256707	−	0.966489i	$-0.582637\pi$
$317$	−9.14107	−0.513414	−0.256707	+	0.966489i	$0.582637\pi$
$318$	−16.5930	−0.930489
$319$	2.13185	0.119361
$320$	−51.5821	−2.88353
$321$	3.13608	0.175039
$322$	−5.20325	−0.289966
$323$	1.19115	0.0662771
$324$	5.12792	0.284884
$325$	−4.04894	−0.224595
$326$	−40.9471	−2.26785
$327$	−12.5874	−0.696082
$328$	82.5391	4.55746
$329$	0.853437	0.0470515
$330$	−21.1869	−1.16630
$331$	−15.1282	−0.831520	−0.415760	−	0.909474i	$-0.636484\pi$
$331$	−15.1282	−0.831520	−0.415760	+	0.909474i	$0.636484\pi$
$332$	81.4405	4.46963
$333$	5.66562	0.310474
$334$	−36.2416	−1.98305
$335$	19.9864	1.09198
$336$	−26.4325	−1.44201
$337$	−16.8163	−0.916042	−0.458021	−	0.888941i	$-0.651442\pi$
$337$	−16.8163	−0.916042	−0.458021	+	0.888941i	$0.651442\pi$
$338$	−2.66982	−0.145219
$339$	12.4219	0.674665
$340$	33.7185	1.82864
$341$	15.9203	0.862135
$342$	1.45485	0.0786692
$343$	−20.1542	−1.08823
$344$	100.077	5.39581
$345$	2.67036	0.143767
$346$	−66.4911	−3.57458
$347$	−6.89244	−0.370005	−0.185003	−	0.982738i	$-0.559229\pi$
$347$	−6.89244	−0.370005	−0.185003	+	0.982738i	$0.559229\pi$
$348$	−4.14390	−0.222136
$349$	3.15338	0.168796	0.0843982	−	0.996432i	$-0.473103\pi$
$349$	3.15338	0.168796	0.0843982	+	0.996432i	$0.473103\pi$
$350$	−23.7325	−1.26856
$351$	1.00000	0.0533761
$352$	−40.7368	−2.17128
$353$	5.26988	0.280487	0.140244	−	0.990117i	$-0.455211\pi$
$353$	5.26988	0.280487	0.140244	+	0.990117i	$0.455211\pi$
$354$	19.8998	1.05766
$355$	−13.2284	−0.702089
$356$	22.0513	1.16872
$357$	4.79900	0.253990
$358$	−9.90995	−0.523757
$359$	6.09418	0.321638	0.160819	−	0.986984i	$-0.448586\pi$
$359$	6.09418	0.321638	0.160819	+	0.986984i	$0.448586\pi$
$360$	25.1209	1.32399
$361$	−18.7031	−0.984371
$362$	−1.36632	−0.0718122
$363$	4.04052	0.212073
$364$	−11.2580	−0.590082
$365$	5.52227	0.289049
$366$	22.0455	1.15233
$367$	−22.8059	−1.19046	−0.595230	−	0.803555i	$-0.702939\pi$
$367$	−22.8059	−1.19046	−0.595230	+	0.803555i	$0.702939\pi$
$368$	10.6878	0.557138
$369$	−9.88379	−0.514530
$370$	45.5017	2.36552
$371$	−13.6447	−0.708400
$372$	−30.9460	−1.60448
$373$	−27.3408	−1.41565	−0.707825	−	0.706387i	$-0.750324\pi$
$373$	−27.3408	−1.41565	−0.707825	+	0.706387i	$0.750324\pi$
$374$	15.3957	0.796091
$375$	−2.86094	−0.147738
$376$	−3.24628	−0.167414
$377$	−0.808105	−0.0416195
$378$	5.86143	0.301479
$379$	3.06342	0.157357	0.0786787	−	0.996900i	$-0.474930\pi$
$379$	3.06342	0.157357	0.0786787	+	0.996900i	$0.474930\pi$
$380$	8.40574	0.431205
$381$	−12.8322	−0.657414
$382$	34.0661	1.74297
$383$	−1.25435	−0.0640945	−0.0320473	−	0.999486i	$-0.510203\pi$
$383$	−1.25435	−0.0640945	−0.0320473	+	0.999486i	$0.510203\pi$
$384$	14.8969	0.760206
$385$	−17.4224	−0.887930
$386$	33.5606	1.70819
$387$	−11.9839	−0.609178
$388$	−33.6138	−1.70648
$389$	7.79867	0.395408	0.197704	−	0.980262i	$-0.436651\pi$
$389$	7.79867	0.395408	0.197704	+	0.980262i	$0.436651\pi$
$390$	8.03119	0.406675
$391$	−1.94044	−0.0981322
$392$	18.2054	0.919509
$393$	−3.12414	−0.157592
$394$	34.0670	1.71627
$395$	10.7143	0.539093
$396$	13.5279	0.679801
$397$	−8.10843	−0.406950	−0.203475	−	0.979080i	$-0.565224\pi$
$397$	−8.10843	−0.406950	−0.203475	+	0.979080i	$0.565224\pi$
$398$	−22.0001	−1.10277
$399$	1.19635	0.0598924
$400$	48.7479	2.43740
$401$	−19.4873	−0.973150	−0.486575	−	0.873639i	$-0.661754\pi$
$401$	−19.4873	−0.973150	−0.486575	+	0.873639i	$0.661754\pi$
$402$	−17.7385	−0.884718
$403$	−6.03482	−0.300616
$404$	−62.3634	−3.10269
$405$	−3.00815	−0.149476
$406$	−4.73665	−0.235076
$407$	14.9464	0.740864
$408$	−18.2543	−0.903722
$409$	−10.4450	−0.516473	−0.258236	−	0.966082i	$-0.583141\pi$
$409$	−10.4450	−0.516473	−0.258236	+	0.966082i	$0.583141\pi$
$410$	−79.3786	−3.92023
$411$	12.1174	0.597706
$412$	−5.12792	−0.252634
$413$	16.3640	0.805222
$414$	−2.37002	−0.116480
$415$	−47.7747	−2.34517
$416$	15.4418	0.757099
$417$	−7.77144	−0.380569
$418$	3.83801	0.187723
$419$	−3.14691	−0.153737	−0.0768683	−	0.997041i	$-0.524492\pi$
$419$	−3.14691	−0.153737	−0.0768683	+	0.997041i	$0.524492\pi$
$420$	33.8658	1.65248
$421$	7.98287	0.389061	0.194531	−	0.980896i	$-0.437682\pi$
$421$	7.98287	0.389061	0.194531	+	0.980896i	$0.437682\pi$
$422$	−13.2877	−0.646835
$423$	0.388731	0.0189007
$424$	51.9015	2.52056
$425$	−8.85054	−0.429314
$426$	11.7406	0.568832
$427$	18.1284	0.877296
$428$	−16.0816	−0.777331
$429$	2.63808	0.127368
$430$	−96.2454	−4.64136
$431$	−24.1730	−1.16437	−0.582187	−	0.813055i	$-0.697803\pi$
$431$	−24.1730	−1.16437	−0.582187	+	0.813055i	$0.697803\pi$
$432$	−12.0397	−0.579260
$433$	35.0014	1.68206	0.841029	−	0.540990i	$-0.181950\pi$
$433$	35.0014	1.68206	0.841029	+	0.540990i	$0.181950\pi$
$434$	−35.3727	−1.69794
$435$	2.43090	0.116553
$436$	64.5469	3.09124
$437$	−0.483735	−0.0231402
$438$	−4.90117	−0.234187
$439$	−7.99025	−0.381354	−0.190677	−	0.981653i	$-0.561068\pi$
$439$	−7.99025	−0.381354	−0.190677	+	0.981653i	$0.561068\pi$
$440$	66.2710	3.15935
$441$	−2.18003	−0.103811
$442$	−5.83593	−0.277587
$443$	−40.5185	−1.92509	−0.962545	−	0.271123i	$-0.912605\pi$
$443$	−40.5185	−1.92509	−0.962545	+	0.271123i	$0.912605\pi$
$444$	−29.0528	−1.37879
$445$	−12.9357	−0.613213
$446$	58.4009	2.76536
$447$	8.23875	0.389679
$448$	37.6463	1.77862
$449$	−36.7459	−1.73415	−0.867074	−	0.498180i	$-0.834002\pi$
$449$	−36.7459	−1.73415	−0.867074	+	0.498180i	$0.834002\pi$
$450$	−10.8099	−0.509584
$451$	−26.0743	−1.22779
$452$	−63.6985	−2.99612
$453$	−4.04877	−0.190228
$454$	−63.5326	−2.98173
$455$	6.60421	0.309610
$456$	−4.55064	−0.213103
$457$	−5.10938	−0.239007	−0.119503	−	0.992834i	$-0.538130\pi$
$457$	−5.10938	−0.239007	−0.119503	+	0.992834i	$0.538130\pi$
$458$	−21.9584	−1.02605
$459$	2.18589	0.102029
$460$	−13.6934	−0.638457
$461$	−20.3985	−0.950051	−0.475026	−	0.879972i	$-0.657561\pi$
$461$	−20.3985	−0.950051	−0.475026	+	0.879972i	$0.657561\pi$
$462$	15.4629	0.719400
$463$	−16.5373	−0.768553	−0.384277	−	0.923218i	$-0.625549\pi$
$463$	−16.5373	−0.768553	−0.384277	+	0.923218i	$0.625549\pi$
$464$	9.72934	0.451673
$465$	18.1536	0.841853
$466$	−17.5086	−0.811070
$467$	−25.6768	−1.18818	−0.594091	−	0.804398i	$-0.702488\pi$
$467$	−25.6768	−1.18818	−0.594091	+	0.804398i	$0.702488\pi$
$468$	−5.12792	−0.237038
$469$	−14.5867	−0.673554
$470$	3.12197	0.144006
$471$	14.3491	0.661172
$472$	−62.2451	−2.86506
$473$	−31.6146	−1.45364
$474$	−9.50923	−0.436773
$475$	−2.20636	−0.101235
$476$	−24.6089	−1.12795
$477$	−6.21503	−0.284567
$478$	−69.6372	−3.18513
$479$	−23.7078	−1.08324	−0.541619	−	0.840624i	$-0.682189\pi$
$479$	−23.7078	−1.08324	−0.541619	+	0.840624i	$0.682189\pi$
$480$	−46.4513	−2.12020
$481$	−5.66562	−0.258330
$482$	3.92811	0.178921
$483$	−1.94892	−0.0886788
$484$	−20.7195	−0.941794
$485$	19.7186	0.895375
$486$	2.66982	0.121105
$487$	1.43925	0.0652187	0.0326093	−	0.999468i	$-0.489618\pi$
$487$	1.43925	0.0652187	0.0326093	+	0.999468i	$0.489618\pi$
$488$	−68.9563	−3.12151
$489$	−15.3371	−0.693566
$490$	−17.5083	−0.790942
$491$	−27.5768	−1.24453	−0.622263	−	0.782808i	$-0.713786\pi$
$491$	−27.5768	−1.24453	−0.622263	+	0.782808i	$0.713786\pi$
$492$	50.6833	2.28498
$493$	−1.76643	−0.0795561
$494$	−1.45485	−0.0654567
$495$	−7.93573	−0.356685
$496$	72.6574	3.26241
$497$	9.65449	0.433063
$498$	42.4014	1.90005
$499$	1.39463	0.0624321	0.0312160	−	0.999513i	$-0.490062\pi$
$499$	1.39463	0.0624321	0.0312160	+	0.999513i	$0.490062\pi$
$500$	14.6706	0.656091
$501$	−13.5746	−0.606467
$502$	−27.5985	−1.23178
$503$	−14.8444	−0.661877	−0.330939	−	0.943652i	$-0.607365\pi$
$503$	−14.8444	−0.661877	−0.330939	+	0.943652i	$0.607365\pi$
$504$	−18.3341	−0.816664
$505$	36.5837	1.62795
$506$	−6.25231	−0.277949
$507$	−1.00000	−0.0444116
$508$	65.8025	2.91952
$509$	21.2363	0.941284	0.470642	−	0.882324i	$-0.344022\pi$
$509$	21.2363	0.941284	0.470642	+	0.882324i	$0.344022\pi$
$510$	17.5553	0.777363
$511$	−4.03033	−0.178291
$512$	15.1710	0.670469
$513$	0.544925	0.0240590
$514$	14.4645	0.638002
$515$	3.00815	0.132555
$516$	61.4527	2.70530
$517$	1.02550	0.0451016
$518$	−33.2086	−1.45910
$519$	−24.9047	−1.09320
$520$	−25.1209	−1.10162
$521$	−43.4512	−1.90363	−0.951816	−	0.306670i	$-0.900785\pi$
$521$	−43.4512	−1.90363	−0.951816	+	0.306670i	$0.900785\pi$
$522$	−2.15749	−0.0944309
$523$	12.4338	0.543692	0.271846	−	0.962341i	$-0.412366\pi$
$523$	12.4338	0.543692	0.271846	+	0.962341i	$0.412366\pi$
$524$	16.0204	0.699852
$525$	−8.88921	−0.387957
$526$	−53.9437	−2.35206
$527$	−13.1915	−0.574629
$528$	−31.7617	−1.38225
$529$	−22.2120	−0.965738
$530$	−49.9141	−2.16813
$531$	7.45364	0.323460
$532$	−6.13479	−0.265977
$533$	9.88379	0.428115
$534$	11.4809	0.496825
$535$	9.43378	0.407858
$536$	55.4846	2.39657
$537$	−3.71185	−0.160178
$538$	6.20611	0.267564
$539$	−5.75110	−0.247717
$540$	15.4255	0.663809
$541$	30.4766	1.31029	0.655145	−	0.755503i	$-0.272608\pi$
$541$	30.4766	1.31029	0.655145	+	0.755503i	$0.272608\pi$
$542$	18.3830	0.789616
$543$	−0.511766	−0.0219620
$544$	33.7542	1.44720
$545$	−37.8646	−1.62194
$546$	−5.86143	−0.250846
$547$	25.6241	1.09561	0.547805	−	0.836606i	$-0.315464\pi$
$547$	25.6241	1.09561	0.547805	+	0.836606i	$0.315464\pi$
$548$	−62.1368	−2.65435
$549$	8.25729	0.352413
$550$	−28.5174	−1.21599
$551$	−0.440356	−0.0187598
$552$	7.41323	0.315528
$553$	−7.81963	−0.332524
$554$	45.5562	1.93550
$555$	17.0430	0.723436
$556$	39.8513	1.69007
$557$	4.30836	0.182551	0.0912755	−	0.995826i	$-0.470906\pi$
$557$	4.30836	0.182551	0.0912755	+	0.995826i	$0.470906\pi$
$558$	−16.1119	−0.682069
$559$	11.9839	0.506867
$560$	−79.5127	−3.36002
$561$	5.76656	0.243464
$562$	8.48226	0.357803
$563$	21.4645	0.904620	0.452310	−	0.891861i	$-0.350600\pi$
$563$	21.4645	0.904620	0.452310	+	0.891861i	$0.350600\pi$
$564$	−1.99338	−0.0839364
$565$	37.3669	1.57204
$566$	−5.73719	−0.241152
$567$	2.19544	0.0921999
$568$	−36.7235	−1.54088
$569$	45.0558	1.88884	0.944419	−	0.328745i	$-0.106626\pi$
$569$	45.0558	1.88884	0.944419	+	0.328745i	$0.106626\pi$
$570$	4.37639	0.183307
$571$	12.9270	0.540977	0.270488	−	0.962723i	$-0.412815\pi$
$571$	12.9270	0.540977	0.270488	+	0.962723i	$0.412815\pi$
$572$	−13.5279	−0.565628
$573$	12.7597	0.533045
$574$	57.9331	2.41808
$575$	3.59428	0.149892
$576$	17.1475	0.714478
$577$	−5.45041	−0.226904	−0.113452	−	0.993544i	$-0.536191\pi$
$577$	−5.45041	−0.226904	−0.113452	+	0.993544i	$0.536191\pi$
$578$	32.6302	1.35724
$579$	12.5704	0.522407
$580$	−12.4654	−0.517599
$581$	34.8676	1.44655
$582$	−17.5008	−0.725432
$583$	−16.3958	−0.679043
$584$	15.3305	0.634379
$585$	3.00815	0.124371
$586$	36.7585	1.51848
$587$	29.0650	1.19964	0.599821	−	0.800134i	$-0.295238\pi$
$587$	29.0650	1.19964	0.599821	+	0.800134i	$0.295238\pi$
$588$	11.1790	0.461015
$589$	−3.28852	−0.135501
$590$	59.8616	2.46446
$591$	12.7601	0.524879
$592$	68.2123	2.80351
$593$	−15.4447	−0.634239	−0.317119	−	0.948386i	$-0.602716\pi$
$593$	−15.4447	−0.634239	−0.317119	+	0.948386i	$0.602716\pi$
$594$	7.04319	0.288986
$595$	14.4361	0.591822
$596$	−42.2476	−1.73053
$597$	−8.24032	−0.337254
$598$	2.37002	0.0969174
$599$	10.8919	0.445032	0.222516	−	0.974929i	$-0.428573\pi$
$599$	10.8919	0.445032	0.222516	+	0.974929i	$0.428573\pi$
$600$	33.8125	1.38039
$601$	5.68220	0.231782	0.115891	−	0.993262i	$-0.463028\pi$
$601$	5.68220	0.231782	0.115891	+	0.993262i	$0.463028\pi$
$602$	70.2430	2.86289
$603$	−6.64410	−0.270569
$604$	20.7617	0.844784
$605$	12.1545	0.494150
$606$	−32.4691	−1.31897
$607$	−19.2034	−0.779441	−0.389720	−	0.920933i	$-0.627428\pi$
$607$	−19.2034	−0.779441	−0.389720	+	0.920933i	$0.627428\pi$
$608$	8.41464	0.341259
$609$	−1.77415	−0.0718922
$610$	66.3159	2.68505
$611$	−0.388731	−0.0157264
$612$	−11.2091	−0.453100
$613$	−34.6631	−1.40003	−0.700014	−	0.714129i	$-0.746823\pi$
$613$	−34.6631	−1.40003	−0.700014	+	0.714129i	$0.746823\pi$
$614$	51.6723	2.08533
$615$	−29.7319	−1.19891
$616$	−48.3667	−1.94875
$617$	−7.03924	−0.283389	−0.141695	−	0.989910i	$-0.545255\pi$
$617$	−7.03924	−0.283389	−0.141695	+	0.989910i	$0.545255\pi$
$618$	−2.66982	−0.107396
$619$	37.6132	1.51180	0.755901	−	0.654686i	$-0.227199\pi$
$619$	37.6132	1.51180	0.755901	+	0.654686i	$0.227199\pi$
$620$	−93.0902	−3.73859
$621$	−0.887710	−0.0356226
$622$	23.5142	0.942833
$623$	9.44093	0.378243
$624$	12.0397	0.481973
$625$	−28.8508	−1.15403
$626$	36.8729	1.47374
$627$	1.43756	0.0574104
$628$	−73.5811	−2.93620
$629$	−12.3844	−0.493800
$630$	17.6320	0.702477
$631$	21.4818	0.855179	0.427589	−	0.903973i	$-0.359363\pi$
$631$	21.4818	0.855179	0.427589	+	0.903973i	$0.359363\pi$
$632$	29.7441	1.18316
$633$	−4.97701	−0.197818
$634$	24.4050	0.969245
$635$	−38.6012	−1.53184
$636$	31.8702	1.26373
$637$	2.18003	0.0863760
$638$	−5.69164	−0.225334
$639$	4.39752	0.173963
$640$	44.8122	1.77136
$641$	47.0316	1.85764	0.928818	−	0.370536i	$-0.120826\pi$
$641$	47.0316	1.85764	0.928818	+	0.370536i	$0.120826\pi$
$642$	−8.37275	−0.330446
$643$	−35.7049	−1.40807	−0.704033	−	0.710168i	$-0.748619\pi$
$643$	−35.7049	−1.40807	−0.704033	+	0.710168i	$0.748619\pi$
$644$	9.99388	0.393814
$645$	−36.0494	−1.41945
$646$	−3.18014	−0.125121
$647$	−34.3178	−1.34917	−0.674586	−	0.738196i	$-0.735678\pi$
$647$	−34.3178	−1.34917	−0.674586	+	0.738196i	$0.735678\pi$
$648$	−8.35096	−0.328057
$649$	19.6633	0.771853
$650$	10.8099	0.424000
$651$	−13.2491	−0.519273
$652$	78.6471	3.08006
$653$	−13.9153	−0.544547	−0.272273	−	0.962220i	$-0.587775\pi$
$653$	−13.9153	−0.544547	−0.272273	+	0.962220i	$0.587775\pi$
$654$	33.6059	1.31410
$655$	−9.39788	−0.367206
$656$	−118.998	−4.64608
$657$	−1.83577	−0.0716203
$658$	−2.27852	−0.0888259
$659$	−28.2374	−1.09997	−0.549987	−	0.835173i	$-0.685367\pi$
$659$	−28.2374	−1.09997	−0.549987	+	0.835173i	$0.685367\pi$
$660$	40.6938	1.58400
$661$	−50.6599	−1.97044	−0.985221	−	0.171286i	$-0.945208\pi$
$661$	−50.6599	−1.97044	−0.985221	+	0.171286i	$0.945208\pi$
$662$	40.3894	1.56978
$663$	−2.18589	−0.0848930
$664$	−132.628	−5.14697
$665$	3.59880	0.139555
$666$	−15.1262	−0.586127
$667$	0.717363	0.0277764
$668$	69.6093	2.69326
$669$	21.8745	0.845718
$670$	−53.3601	−2.06148
$671$	21.7834	0.840940
$672$	33.9017	1.30779
$673$	−44.5611	−1.71770	−0.858852	−	0.512224i	$-0.828822\pi$
$673$	−44.5611	−1.71770	−0.858852	+	0.512224i	$0.828822\pi$
$674$	44.8964	1.72935
$675$	−4.04894	−0.155844
$676$	5.12792	0.197228
$677$	−16.2847	−0.625873	−0.312936	−	0.949774i	$-0.601313\pi$
$677$	−16.2847	−0.625873	−0.312936	+	0.949774i	$0.601313\pi$
$678$	−33.1642	−1.27366
$679$	−14.3913	−0.552286
$680$	−54.9116	−2.10576
$681$	−23.7966	−0.911889
$682$	−42.5044	−1.62758
$683$	−35.5745	−1.36122	−0.680610	−	0.732646i	$-0.738285\pi$
$683$	−35.5745	−1.36122	−0.680610	+	0.732646i	$0.738285\pi$
$684$	−2.79433	−0.106844
$685$	36.4508	1.39271
$686$	53.8081	2.05440
$687$	−8.22470	−0.313792
$688$	−144.283	−5.50074
$689$	6.21503	0.236774
$690$	−7.12937	−0.271411
$691$	34.3071	1.30510	0.652551	−	0.757745i	$-0.273699\pi$
$691$	34.3071	1.30510	0.652551	+	0.757745i	$0.273699\pi$
$692$	127.709	4.85478
$693$	5.79176	0.220011
$694$	18.4015	0.698513
$695$	−23.3776	−0.886764
$696$	6.74846	0.255800
$697$	21.6049	0.818344
$698$	−8.41894	−0.318661
$699$	−6.55798	−0.248046
$700$	45.5831	1.72288
$701$	−12.7986	−0.483398	−0.241699	−	0.970351i	$-0.577705\pi$
$701$	−12.7986	−0.483398	−0.241699	+	0.970351i	$0.577705\pi$
$702$	−2.66982	−0.100766
$703$	−3.08734	−0.116441
$704$	45.2365	1.70491
$705$	1.16936	0.0440406
$706$	−14.0696	−0.529516
$707$	−26.7000	−1.00416
$708$	−38.2216	−1.43646
$709$	23.2037	0.871432	0.435716	−	0.900084i	$-0.356495\pi$
$709$	23.2037	0.871432	0.435716	+	0.900084i	$0.356495\pi$
$710$	35.3173	1.32543
$711$	−3.56175	−0.133576
$712$	−35.9111	−1.34583
$713$	5.35717	0.200628
$714$	−12.8124	−0.479494
$715$	7.93573	0.296780
$716$	19.0340	0.711336
$717$	−26.0831	−0.974093
$718$	−16.2703	−0.607203
$719$	−24.2873	−0.905765	−0.452883	−	0.891570i	$-0.649604\pi$
$719$	−24.2873	−0.905765	−0.452883	+	0.891570i	$0.649604\pi$
$720$	−36.2171	−1.34973
$721$	−2.19544	−0.0817626
$722$	49.9337	1.85834
$723$	1.47131	0.0547184
$724$	2.62429	0.0975311
$725$	3.27197	0.121518
$726$	−10.7875	−0.400360
$727$	19.5451	0.724886	0.362443	−	0.932006i	$-0.381943\pi$
$727$	19.5451	0.724886	0.362443	+	0.932006i	$0.381943\pi$
$728$	18.3341	0.679505
$729$	1.00000	0.0370370
$730$	−14.7434	−0.545679
$731$	26.1956	0.968880
$732$	−42.3427	−1.56503
$733$	−2.31108	−0.0853618	−0.0426809	−	0.999089i	$-0.513590\pi$
$733$	−2.31108	−0.0853618	−0.0426809	+	0.999089i	$0.513590\pi$
$734$	60.8877	2.24740
$735$	−6.55785	−0.241890
$736$	−13.7079	−0.505279
$737$	−17.5277	−0.645641
$738$	26.3879	0.971352
$739$	−50.0688	−1.84181	−0.920904	−	0.389788i	$-0.872548\pi$
$739$	−50.0688	−1.84181	−0.920904	+	0.389788i	$0.872548\pi$
$740$	−87.3951	−3.21271
$741$	−0.544925	−0.0200183
$742$	36.4290	1.33735
$743$	38.3892	1.40836	0.704181	−	0.710021i	$-0.251314\pi$
$743$	38.3892	1.40836	0.704181	+	0.710021i	$0.251314\pi$
$744$	50.3965	1.84763
$745$	24.7833	0.907992
$746$	72.9948	2.67253
$747$	15.8818	0.581084
$748$	−29.5704	−1.08120
$749$	−6.88508	−0.251575
$750$	7.63817	0.278907
$751$	−21.0923	−0.769668	−0.384834	−	0.922986i	$-0.625741\pi$
$751$	−21.0923	−0.769668	−0.384834	+	0.922986i	$0.625741\pi$
$752$	4.68020	0.170669
$753$	−10.3372	−0.376710
$754$	2.15749	0.0785712
$755$	−12.1793	−0.443250
$756$	−11.2580	−0.409451
$757$	−4.45711	−0.161996	−0.0809982	−	0.996714i	$-0.525811\pi$
$757$	−4.45711	−0.161996	−0.0809982	+	0.996714i	$0.525811\pi$
$758$	−8.17877	−0.297066
$759$	−2.34185	−0.0850038
$760$	−13.6890	−0.496552
$761$	−24.9077	−0.902902	−0.451451	−	0.892296i	$-0.649093\pi$
$761$	−24.9077	−0.902902	−0.451451	+	0.892296i	$0.649093\pi$
$762$	34.2597	1.24110
$763$	27.6348	1.00045
$764$	−65.4308	−2.36720
$765$	6.57548	0.237737
$766$	3.34890	0.121001
$767$	−7.45364	−0.269135
$768$	−5.47712	−0.197639
$769$	−18.0094	−0.649434	−0.324717	−	0.945811i	$-0.605269\pi$
$769$	−18.0094	−0.649434	−0.324717	+	0.945811i	$0.605269\pi$
$770$	46.5147	1.67627
$771$	5.41779	0.195117
$772$	−64.4598	−2.31996
$773$	1.30811	0.0470494	0.0235247	−	0.999723i	$-0.492511\pi$
$773$	1.30811	0.0470494	0.0235247	+	0.999723i	$0.492511\pi$
$774$	31.9949	1.15003
$775$	24.4346	0.877717
$776$	54.7411	1.96509
$777$	−12.4385	−0.446230
$778$	−20.8210	−0.746469
$779$	5.38592	0.192971
$780$	−15.4255	−0.552322
$781$	11.6010	0.415117
$782$	5.18061	0.185258
$783$	−0.808105	−0.0288793
$784$	−26.2469	−0.937390
$785$	43.1642	1.54060
$786$	8.34089	0.297510
$787$	0.710166	0.0253147	0.0126573	−	0.999920i	$-0.495971\pi$
$787$	0.710166	0.0253147	0.0126573	+	0.999920i	$0.495971\pi$
$788$	−65.4326	−2.33094
$789$	−20.2050	−0.719318
$790$	−28.6051	−1.01772
$791$	−27.2716	−0.969665
$792$	−22.0305	−0.782820
$793$	−8.25729	−0.293225
$794$	21.6480	0.768259
$795$	−18.6957	−0.663069
$796$	42.2557	1.49771
$797$	26.7813	0.948642	0.474321	−	0.880352i	$-0.342694\pi$
$797$	26.7813	0.948642	0.474321	+	0.880352i	$0.342694\pi$
$798$	−3.19404	−0.113068
$799$	−0.849724	−0.0300611
$800$	−62.5230	−2.21052
$801$	4.30024	0.151942
$802$	52.0276	1.83716
$803$	−4.84292	−0.170903
$804$	34.0704	1.20157
$805$	−5.86262	−0.206630
$806$	16.1119	0.567516
$807$	2.32454	0.0818279
$808$	101.561	3.57289
$809$	−12.8730	−0.452589	−0.226294	−	0.974059i	$-0.572661\pi$
$809$	−12.8730	−0.452589	−0.226294	+	0.974059i	$0.572661\pi$
$810$	8.03119	0.282187
$811$	52.4523	1.84185	0.920925	−	0.389739i	$-0.127435\pi$
$811$	52.4523	1.84185	0.920925	+	0.389739i	$0.127435\pi$
$812$	9.09769	0.319266
$813$	6.88548	0.241484
$814$	−39.9041	−1.39864
$815$	−46.1361	−1.61608
$816$	26.3175	0.921296
$817$	6.53035	0.228468
$818$	27.8863	0.975021
$819$	−2.19544	−0.0767150
$820$	152.463	5.32422
$821$	2.80246	0.0978064	0.0489032	−	0.998804i	$-0.484427\pi$
$821$	2.80246	0.0978064	0.0489032	+	0.998804i	$0.484427\pi$
$822$	−32.3511	−1.12838
$823$	51.1527	1.78307	0.891535	−	0.452951i	$-0.149629\pi$
$823$	51.1527	1.78307	0.891535	+	0.452951i	$0.149629\pi$
$824$	8.35096	0.290919
$825$	−10.6814	−0.371879
$826$	−43.6890	−1.52013
$827$	−31.9273	−1.11022	−0.555111	−	0.831776i	$-0.687324\pi$
$827$	−31.9273	−1.11022	−0.555111	+	0.831776i	$0.687324\pi$
$828$	4.55210	0.158197
$829$	−6.01539	−0.208923	−0.104462	−	0.994529i	$-0.533312\pi$
$829$	−6.01539	−0.208923	−0.104462	+	0.994529i	$0.533312\pi$
$830$	127.550	4.42731
$831$	17.0634	0.591923
$832$	−17.1475	−0.594482
$833$	4.76531	0.165108
$834$	20.7483	0.718455
$835$	−40.8343	−1.41313
$836$	−7.37166	−0.254954
$837$	−6.03482	−0.208594
$838$	8.40167	0.290231
$839$	−48.7260	−1.68221	−0.841104	−	0.540873i	$-0.818094\pi$
$839$	−48.7260	−1.68221	−0.841104	+	0.540873i	$0.818094\pi$
$840$	−55.1515	−1.90291
$841$	−28.3470	−0.977482
$842$	−21.3128	−0.734487
$843$	3.17710	0.109425
$844$	25.5217	0.878493
$845$	−3.00815	−0.103483
$846$	−1.03784	−0.0356817
$847$	−8.87074	−0.304802
$848$	−74.8271	−2.56957
$849$	−2.14891	−0.0737503
$850$	23.6293	0.810479
$851$	5.02943	0.172407
$852$	−22.5501	−0.772553
$853$	41.5096	1.42126	0.710630	−	0.703566i	$-0.248410\pi$
$853$	41.5096	1.42126	0.710630	+	0.703566i	$0.248410\pi$
$854$	−48.3995	−1.65620
$855$	1.63921	0.0560599
$856$	26.1893	0.895131
$857$	16.1533	0.551787	0.275893	−	0.961188i	$-0.411026\pi$
$857$	16.1533	0.551787	0.275893	+	0.961188i	$0.411026\pi$
$858$	−7.04319	−0.240451
$859$	−5.71465	−0.194981	−0.0974906	−	0.995236i	$-0.531082\pi$
$859$	−5.71465	−0.194981	−0.0974906	+	0.995236i	$0.531082\pi$
$860$	184.859	6.30362
$861$	21.6993	0.739510
$862$	64.5375	2.19816
$863$	38.0181	1.29415	0.647075	−	0.762426i	$-0.275992\pi$
$863$	38.0181	1.29415	0.647075	+	0.762426i	$0.275992\pi$
$864$	15.4418	0.525342
$865$	−74.9171	−2.54726
$866$	−93.4472	−3.17546
$867$	12.2219	0.415077
$868$	67.9403	2.30604
$869$	−9.39620	−0.318744
$870$	−6.49005	−0.220033
$871$	6.64410	0.225127
$872$	−105.116	−3.55969
$873$	−6.55507	−0.221855
$874$	1.29148	0.0436851
$875$	6.28102	0.212337
$876$	9.41369	0.318059
$877$	30.9284	1.04438	0.522189	−	0.852830i	$-0.325116\pi$
$877$	30.9284	1.04438	0.522189	+	0.852830i	$0.325116\pi$
$878$	21.3325	0.719936
$879$	13.7682	0.464389
$880$	−95.5438	−3.22078
$881$	11.4898	0.387100	0.193550	−	0.981090i	$-0.438000\pi$
$881$	11.4898	0.387100	0.193550	+	0.981090i	$0.438000\pi$
$882$	5.82028	0.195979
$883$	−38.9152	−1.30960	−0.654800	−	0.755802i	$-0.727247\pi$
$883$	−38.9152	−1.30960	−0.654800	+	0.755802i	$0.727247\pi$
$884$	11.2091	0.377002
$885$	22.4216	0.753695
$886$	108.177	3.63427
$887$	−32.9261	−1.10555	−0.552775	−	0.833330i	$-0.686431\pi$
$887$	−32.9261	−1.10555	−0.552775	+	0.833330i	$0.686431\pi$
$888$	47.3134	1.58773
$889$	28.1724	0.944872
$890$	34.5361	1.15765
$891$	2.63808	0.0883791
$892$	−112.171	−3.75575
$893$	−0.211829	−0.00708859
$894$	−21.9959	−0.735654
$895$	−11.1658	−0.373231
$896$	−32.7054	−1.09261
$897$	0.887710	0.0296398
$898$	98.1049	3.27380
$899$	4.87677	0.162649
$900$	20.7626	0.692087
$901$	13.5854	0.452595
$902$	69.6134	2.31787
$903$	26.3101	0.875544
$904$	103.735	3.45017
$905$	−1.53947	−0.0511736
$906$	10.8095	0.359120
$907$	−11.7119	−0.388888	−0.194444	−	0.980914i	$-0.562290\pi$
$907$	−11.7119	−0.388888	−0.194444	+	0.980914i	$0.562290\pi$
$908$	122.027	4.04961
$909$	−12.1615	−0.403373
$910$	−17.6320	−0.584496
$911$	28.7756	0.953379	0.476689	−	0.879072i	$-0.341837\pi$
$911$	28.7756	0.953379	0.476689	+	0.879072i	$0.341837\pi$
$912$	6.56072	0.217247
$913$	41.8975	1.38660
$914$	13.6411	0.451207
$915$	24.8391	0.821157
$916$	42.1756	1.39352
$917$	6.85888	0.226500
$918$	−5.83593	−0.192614
$919$	−46.1667	−1.52290	−0.761450	−	0.648223i	$-0.775512\pi$
$919$	−46.1667	−1.52290	−0.761450	+	0.648223i	$0.775512\pi$
$920$	22.3001	0.735212
$921$	19.3543	0.637745
$922$	54.4601	1.79355
$923$	−4.39752	−0.144746
$924$	−29.6996	−0.977047
$925$	22.9397	0.754254
$926$	44.1515	1.45091
$927$	−1.00000	−0.0328443
$928$	−12.4786	−0.409631
$929$	45.3564	1.48810	0.744048	−	0.668126i	$-0.232903\pi$
$929$	45.3564	1.48810	0.744048	+	0.668126i	$0.232903\pi$
$930$	−48.4668	−1.58929
$931$	1.18795	0.0389336
$932$	33.6288	1.10155
$933$	8.80742	0.288342
$934$	68.5524	2.24310
$935$	17.3467	0.567296
$936$	8.35096	0.272960
$937$	−23.9131	−0.781207	−0.390604	−	0.920559i	$-0.627734\pi$
$937$	−23.9131	−0.781207	−0.390604	+	0.920559i	$0.627734\pi$
$938$	38.9439	1.27156
$939$	13.8110	0.450706
$940$	−5.99638	−0.195580
$941$	−7.72842	−0.251939	−0.125970	−	0.992034i	$-0.540204\pi$
$941$	−7.72842	−0.251939	−0.125970	+	0.992034i	$0.540204\pi$
$942$	−38.3095	−1.24819
$943$	−8.77394	−0.285719
$944$	89.7395	2.92077
$945$	6.60421	0.214835
$946$	84.4052	2.74425
$947$	31.7738	1.03251	0.516255	−	0.856435i	$-0.327326\pi$
$947$	31.7738	1.03251	0.516255	+	0.856435i	$0.327326\pi$
$948$	18.2644	0.593199
$949$	1.83577	0.0595917
$950$	5.89059	0.191116
$951$	9.14107	0.296420
$952$	40.0763	1.29888
$953$	6.61135	0.214163	0.107081	−	0.994250i	$-0.465849\pi$
$953$	6.61135	0.214163	0.107081	+	0.994250i	$0.465849\pi$
$954$	16.5930	0.537218
$955$	38.3831	1.24205
$956$	133.752	4.32586
$957$	−2.13185	−0.0689129
$958$	63.2955	2.04499
$959$	−26.6030	−0.859055
$960$	51.5821	1.66481
$961$	5.41903	0.174808
$962$	15.1262	0.487687
$963$	−3.13608	−0.101059
$964$	−7.54473	−0.242999
$965$	37.8135	1.21726
$966$	5.20325	0.167412
$967$	−53.5502	−1.72206	−0.861029	−	0.508556i	$-0.830179\pi$
$967$	−53.5502	−1.72206	−0.861029	+	0.508556i	$0.830179\pi$
$968$	33.7423	1.08452
$969$	−1.19115	−0.0382651
$970$	−52.6450	−1.69033
$971$	−30.6755	−0.984424	−0.492212	−	0.870475i	$-0.663812\pi$
$971$	−30.6755	−0.984424	−0.492212	+	0.870475i	$0.663812\pi$
$972$	−5.12792	−0.164478
$973$	17.0618	0.546975
$974$	−3.84253	−0.123123
$975$	4.04894	0.129670
$976$	99.4153	3.18221
$977$	2.02044	0.0646397	0.0323199	−	0.999478i	$-0.489710\pi$
$977$	2.02044	0.0646397	0.0323199	+	0.999478i	$0.489710\pi$
$978$	40.9471	1.30934
$979$	11.3444	0.362568
$980$	33.6281	1.07421
$981$	12.5874	0.401883
$982$	73.6251	2.34947
$983$	−19.2258	−0.613207	−0.306603	−	0.951837i	$-0.599193\pi$
$983$	−19.2258	−0.613207	−0.306603	+	0.951837i	$0.599193\pi$
$984$	−82.5391	−2.63125
$985$	38.3841	1.22302
$986$	4.71605	0.150190
$987$	−0.853437	−0.0271652
$988$	2.79433	0.0888994
$989$	−10.6383	−0.338277
$990$	21.1869	0.673365
$991$	−30.4162	−0.966202	−0.483101	−	0.875565i	$-0.660490\pi$
$991$	−30.4162	−0.966202	−0.483101	+	0.875565i	$0.660490\pi$
$992$	−93.1887	−2.95874
$993$	15.1282	0.480078
$994$	−25.7757	−0.817556
$995$	−24.7881	−0.785835
$996$	−81.4405	−2.58054
$997$	−6.48879	−0.205502	−0.102751	−	0.994707i	$-0.532764\pi$
$997$	−6.48879	−0.205502	−0.102751	+	0.994707i	$0.532764\pi$
$998$	−3.72340	−0.117862
$999$	−5.66562	−0.179252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.2	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.2	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66982 q^{2} -1.00000 q^{3} +5.12792 q^{4} -3.00815 q^{5} +2.66982 q^{6} +2.19544 q^{7} -8.35096 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.66982 q^{2} -1.00000 q^{3} +5.12792 q^{4} -3.00815 q^{5} +2.66982 q^{6} +2.19544 q^{7} -8.35096 q^{8} +1.00000 q^{9} +8.03119 q^{10} +2.63808 q^{11} -5.12792 q^{12} -1.00000 q^{13} -5.86143 q^{14} +3.00815 q^{15} +12.0397 q^{16} -2.18589 q^{17} -2.66982 q^{18} -0.544925 q^{19} -15.4255 q^{20} -2.19544 q^{21} -7.04319 q^{22} +0.887710 q^{23} +8.35096 q^{24} +4.04894 q^{25} +2.66982 q^{26} -1.00000 q^{27} +11.2580 q^{28} +0.808105 q^{29} -8.03119 q^{30} +6.03482 q^{31} -15.4418 q^{32} -2.63808 q^{33} +5.83593 q^{34} -6.60421 q^{35} +5.12792 q^{36} +5.66562 q^{37} +1.45485 q^{38} +1.00000 q^{39} +25.1209 q^{40} -9.88379 q^{41} +5.86143 q^{42} -11.9839 q^{43} +13.5279 q^{44} -3.00815 q^{45} -2.37002 q^{46} +0.388731 q^{47} -12.0397 q^{48} -2.18003 q^{49} -10.8099 q^{50} +2.18589 q^{51} -5.12792 q^{52} -6.21503 q^{53} +2.66982 q^{54} -7.93573 q^{55} -18.3341 q^{56} +0.544925 q^{57} -2.15749 q^{58} +7.45364 q^{59} +15.4255 q^{60} +8.25729 q^{61} -16.1119 q^{62} +2.19544 q^{63} +17.1475 q^{64} +3.00815 q^{65} +7.04319 q^{66} -6.64410 q^{67} -11.2091 q^{68} -0.887710 q^{69} +17.6320 q^{70} +4.39752 q^{71} -8.35096 q^{72} -1.83577 q^{73} -15.1262 q^{74} -4.04894 q^{75} -2.79433 q^{76} +5.79176 q^{77} -2.66982 q^{78} -3.56175 q^{79} -36.2171 q^{80} +1.00000 q^{81} +26.3879 q^{82} +15.8818 q^{83} -11.2580 q^{84} +6.57548 q^{85} +31.9949 q^{86} -0.808105 q^{87} -22.0305 q^{88} +4.30024 q^{89} +8.03119 q^{90} -2.19544 q^{91} +4.55210 q^{92} -6.03482 q^{93} -1.03784 q^{94} +1.63921 q^{95} +15.4418 q^{96} -6.55507 q^{97} +5.82028 q^{98} +2.63808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

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