LMFDB - Embedded newform 8030.2.a.bl.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} - x^{17} + 200 x^{16} - 263 x^{15} - 1900 x^{14} + 3165 x^{13} + 10217 x^{12} + \cdots + 1388 $ x^19 - 9x^18 - x^17 + 200x^16 - 263x^15 - 1900x^14 + 3165x^13 + 10217x^12 - 16393x^11 - 33875x^10 + 44043x^9 + 68537x^8 - 63620x^7 - 79890x^6 + 48388x^5 + 49353x^4 - 17806x^3 - 14287x^2 + 2436*x + 1388
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.78636$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.78636 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.78636 q^{6} +4.72864 q^{7} +1.00000 q^{8} +4.76382 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.78636 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.78636 q^{6} +4.72864 q^{7} +1.00000 q^{8} +4.76382 q^{9} +1.00000 q^{10} +1.00000 q^{11} -2.78636 q^{12} +3.49861 q^{13} +4.72864 q^{14} -2.78636 q^{15} +1.00000 q^{16} -0.663795 q^{17} +4.76382 q^{18} +5.48849 q^{19} +1.00000 q^{20} -13.1757 q^{21} +1.00000 q^{22} +3.11362 q^{23} -2.78636 q^{24} +1.00000 q^{25} +3.49861 q^{26} -4.91465 q^{27} +4.72864 q^{28} +4.43117 q^{29} -2.78636 q^{30} -0.225536 q^{31} +1.00000 q^{32} -2.78636 q^{33} -0.663795 q^{34} +4.72864 q^{35} +4.76382 q^{36} +8.08617 q^{37} +5.48849 q^{38} -9.74841 q^{39} +1.00000 q^{40} +0.265487 q^{41} -13.1757 q^{42} -5.63759 q^{43} +1.00000 q^{44} +4.76382 q^{45} +3.11362 q^{46} +10.4223 q^{47} -2.78636 q^{48} +15.3600 q^{49} +1.00000 q^{50} +1.84957 q^{51} +3.49861 q^{52} -6.63414 q^{53} -4.91465 q^{54} +1.00000 q^{55} +4.72864 q^{56} -15.2929 q^{57} +4.43117 q^{58} +2.16535 q^{59} -2.78636 q^{60} +1.01969 q^{61} -0.225536 q^{62} +22.5264 q^{63} +1.00000 q^{64} +3.49861 q^{65} -2.78636 q^{66} -5.83444 q^{67} -0.663795 q^{68} -8.67568 q^{69} +4.72864 q^{70} -14.7619 q^{71} +4.76382 q^{72} -1.00000 q^{73} +8.08617 q^{74} -2.78636 q^{75} +5.48849 q^{76} +4.72864 q^{77} -9.74841 q^{78} +13.3851 q^{79} +1.00000 q^{80} -0.597459 q^{81} +0.265487 q^{82} +4.84198 q^{83} -13.1757 q^{84} -0.663795 q^{85} -5.63759 q^{86} -12.3469 q^{87} +1.00000 q^{88} -15.0882 q^{89} +4.76382 q^{90} +16.5437 q^{91} +3.11362 q^{92} +0.628426 q^{93} +10.4223 q^{94} +5.48849 q^{95} -2.78636 q^{96} -10.4858 q^{97} +15.3600 q^{98} +4.76382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) $ 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.78636	−1.60871	−0.804354	−	0.594150i	$-0.797488\pi$
$3$	−2.78636	−1.60871	−0.804354	+	0.594150i	$0.797488\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.78636	−1.13753
$7$	4.72864	1.78726	0.893628	−	0.448808i	$-0.148151\pi$
$7$	4.72864	1.78726	0.893628	+	0.448808i	$0.148151\pi$
$8$	1.00000	0.353553
$9$	4.76382	1.58794
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.78636	−0.804354
$13$	3.49861	0.970341	0.485170	−	0.874420i	$-0.338758\pi$
$13$	3.49861	0.970341	0.485170	+	0.874420i	$0.338758\pi$
$14$	4.72864	1.26378
$15$	−2.78636	−0.719436
$16$	1.00000	0.250000
$17$	−0.663795	−0.160994	−0.0804969	−	0.996755i	$-0.525651\pi$
$17$	−0.663795	−0.160994	−0.0804969	+	0.996755i	$0.525651\pi$
$18$	4.76382	1.12284
$19$	5.48849	1.25914	0.629572	−	0.776942i	$-0.283230\pi$
$19$	5.48849	1.25914	0.629572	+	0.776942i	$0.283230\pi$
$20$	1.00000	0.223607
$21$	−13.1757	−2.87517
$22$	1.00000	0.213201
$23$	3.11362	0.649235	0.324617	−	0.945845i	$-0.394764\pi$
$23$	3.11362	0.649235	0.324617	+	0.945845i	$0.394764\pi$
$24$	−2.78636	−0.568764
$25$	1.00000	0.200000
$26$	3.49861	0.686134
$27$	−4.91465	−0.945825
$28$	4.72864	0.893628
$29$	4.43117	0.822848	0.411424	−	0.911444i	$-0.365032\pi$
$29$	4.43117	0.822848	0.411424	+	0.911444i	$0.365032\pi$
$30$	−2.78636	−0.508718
$31$	−0.225536	−0.0405075	−0.0202538	−	0.999795i	$-0.506447\pi$
$31$	−0.225536	−0.0405075	−0.0202538	+	0.999795i	$0.506447\pi$
$32$	1.00000	0.176777
$33$	−2.78636	−0.485044
$34$	−0.663795	−0.113840
$35$	4.72864	0.799286
$36$	4.76382	0.793971
$37$	8.08617	1.32936	0.664679	−	0.747129i	$-0.268568\pi$
$37$	8.08617	1.32936	0.664679	+	0.747129i	$0.268568\pi$
$38$	5.48849	0.890350
$39$	−9.74841	−1.56099
$40$	1.00000	0.158114
$41$	0.265487	0.0414622	0.0207311	−	0.999785i	$-0.493401\pi$
$41$	0.265487	0.0414622	0.0207311	+	0.999785i	$0.493401\pi$
$42$	−13.1757	−2.03306
$43$	−5.63759	−0.859724	−0.429862	−	0.902895i	$-0.641438\pi$
$43$	−5.63759	−0.859724	−0.429862	+	0.902895i	$0.641438\pi$
$44$	1.00000	0.150756
$45$	4.76382	0.710149
$46$	3.11362	0.459078
$47$	10.4223	1.52025	0.760127	−	0.649774i	$-0.225137\pi$
$47$	10.4223	1.52025	0.760127	+	0.649774i	$0.225137\pi$
$48$	−2.78636	−0.402177
$49$	15.3600	2.19429
$50$	1.00000	0.141421
$51$	1.84957	0.258992
$52$	3.49861	0.485170
$53$	−6.63414	−0.911269	−0.455634	−	0.890167i	$-0.650588\pi$
$53$	−6.63414	−0.911269	−0.455634	+	0.890167i	$0.650588\pi$
$54$	−4.91465	−0.668800
$55$	1.00000	0.134840
$56$	4.72864	0.631891
$57$	−15.2929	−2.02560
$58$	4.43117	0.581842
$59$	2.16535	0.281904	0.140952	−	0.990016i	$-0.454984\pi$
$59$	2.16535	0.281904	0.140952	+	0.990016i	$0.454984\pi$
$60$	−2.78636	−0.359718
$61$	1.01969	0.130558	0.0652791	−	0.997867i	$-0.479206\pi$
$61$	1.01969	0.130558	0.0652791	+	0.997867i	$0.479206\pi$
$62$	−0.225536	−0.0286432
$63$	22.5264	2.83806
$64$	1.00000	0.125000
$65$	3.49861	0.433950
$66$	−2.78636	−0.342978
$67$	−5.83444	−0.712790	−0.356395	−	0.934335i	$-0.615994\pi$
$67$	−5.83444	−0.712790	−0.356395	+	0.934335i	$0.615994\pi$
$68$	−0.663795	−0.0804969
$69$	−8.67568	−1.04443
$70$	4.72864	0.565180
$71$	−14.7619	−1.75191	−0.875956	−	0.482390i	$-0.839769\pi$
$71$	−14.7619	−1.75191	−0.875956	+	0.482390i	$0.839769\pi$
$72$	4.76382	0.561422
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	8.08617	0.939998
$75$	−2.78636	−0.321742
$76$	5.48849	0.629572
$77$	4.72864	0.538878
$78$	−9.74841	−1.10379
$79$	13.3851	1.50595	0.752973	−	0.658051i	$-0.228619\pi$
$79$	13.3851	1.50595	0.752973	+	0.658051i	$0.228619\pi$
$80$	1.00000	0.111803
$81$	−0.597459	−0.0663843
$82$	0.265487	0.0293182
$83$	4.84198	0.531477	0.265738	−	0.964045i	$-0.414384\pi$
$83$	4.84198	0.531477	0.265738	+	0.964045i	$0.414384\pi$
$84$	−13.1757	−1.43759
$85$	−0.663795	−0.0719986
$86$	−5.63759	−0.607917
$87$	−12.3469	−1.32372
$88$	1.00000	0.106600
$89$	−15.0882	−1.59935	−0.799675	−	0.600433i	$-0.794995\pi$
$89$	−15.0882	−1.59935	−0.799675	+	0.600433i	$0.794995\pi$
$90$	4.76382	0.502151
$91$	16.5437	1.73425
$92$	3.11362	0.324617
$93$	0.628426	0.0651648
$94$	10.4223	1.07498
$95$	5.48849	0.563107
$96$	−2.78636	−0.284382
$97$	−10.4858	−1.06467	−0.532335	−	0.846534i	$-0.678685\pi$
$97$	−10.4858	−1.06467	−0.532335	+	0.846534i	$0.678685\pi$
$98$	15.3600	1.55160
$99$	4.76382	0.478782
$100$	1.00000	0.100000
$101$	4.48906	0.446678	0.223339	−	0.974741i	$-0.428304\pi$
$101$	4.48906	0.446678	0.223339	+	0.974741i	$0.428304\pi$
$102$	1.84957	0.183135
$103$	−3.02566	−0.298127	−0.149063	−	0.988828i	$-0.547626\pi$
$103$	−3.02566	−0.298127	−0.149063	+	0.988828i	$0.547626\pi$
$104$	3.49861	0.343067
$105$	−13.1757	−1.28582
$106$	−6.63414	−0.644364
$107$	−8.35178	−0.807397	−0.403698	−	0.914892i	$-0.632275\pi$
$107$	−8.35178	−0.807397	−0.403698	+	0.914892i	$0.632275\pi$
$108$	−4.91465	−0.472913
$109$	14.7415	1.41198	0.705990	−	0.708222i	$-0.250502\pi$
$109$	14.7415	1.41198	0.705990	+	0.708222i	$0.250502\pi$
$110$	1.00000	0.0953463
$111$	−22.5310	−2.13855
$112$	4.72864	0.446814
$113$	0.445666	0.0419247	0.0209624	−	0.999780i	$-0.493327\pi$
$113$	0.445666	0.0419247	0.0209624	+	0.999780i	$0.493327\pi$
$114$	−15.2929	−1.43231
$115$	3.11362	0.290347
$116$	4.43117	0.411424
$117$	16.6668	1.54084
$118$	2.16535	0.199336
$119$	−3.13884	−0.287737
$120$	−2.78636	−0.254359
$121$	1.00000	0.0909091
$122$	1.01969	0.0923186
$123$	−0.739745	−0.0667005
$124$	−0.225536	−0.0202538
$125$	1.00000	0.0894427
$126$	22.5264	2.00681
$127$	−11.1886	−0.992825	−0.496413	−	0.868087i	$-0.665350\pi$
$127$	−11.1886	−0.992825	−0.496413	+	0.868087i	$0.665350\pi$
$128$	1.00000	0.0883883
$129$	15.7084	1.38305
$130$	3.49861	0.306849
$131$	−17.7034	−1.54675	−0.773377	−	0.633946i	$-0.781434\pi$
$131$	−17.7034	−1.54675	−0.773377	+	0.633946i	$0.781434\pi$
$132$	−2.78636	−0.242522
$133$	25.9531	2.25042
$134$	−5.83444	−0.504019
$135$	−4.91465	−0.422986
$136$	−0.663795	−0.0569199
$137$	13.1212	1.12102	0.560509	−	0.828149i	$-0.310606\pi$
$137$	13.1212	1.12102	0.560509	+	0.828149i	$0.310606\pi$
$138$	−8.67568	−0.738523
$139$	−13.4895	−1.14416	−0.572082	−	0.820196i	$-0.693864\pi$
$139$	−13.4895	−1.14416	−0.572082	+	0.820196i	$0.693864\pi$
$140$	4.72864	0.399643
$141$	−29.0404	−2.44564
$142$	−14.7619	−1.23879
$143$	3.49861	0.292569
$144$	4.76382	0.396985
$145$	4.43117	0.367989
$146$	−1.00000	−0.0827606
$147$	−42.7986	−3.52997
$148$	8.08617	0.664679
$149$	−11.6046	−0.950690	−0.475345	−	0.879800i	$-0.657677\pi$
$149$	−11.6046	−0.950690	−0.475345	+	0.879800i	$0.657677\pi$
$150$	−2.78636	−0.227506
$151$	−4.20372	−0.342094	−0.171047	−	0.985263i	$-0.554715\pi$
$151$	−4.20372	−0.342094	−0.171047	+	0.985263i	$0.554715\pi$
$152$	5.48849	0.445175
$153$	−3.16220	−0.255649
$154$	4.72864	0.381044
$155$	−0.225536	−0.0181155
$156$	−9.74841	−0.780497
$157$	−18.9525	−1.51258	−0.756288	−	0.654239i	$-0.772989\pi$
$157$	−18.9525	−1.51258	−0.756288	+	0.654239i	$0.772989\pi$
$158$	13.3851	1.06486
$159$	18.4851	1.46597
$160$	1.00000	0.0790569
$161$	14.7232	1.16035
$162$	−0.597459	−0.0469408
$163$	3.82536	0.299625	0.149813	−	0.988714i	$-0.452133\pi$
$163$	3.82536	0.299625	0.149813	+	0.988714i	$0.452133\pi$
$164$	0.265487	0.0207311
$165$	−2.78636	−0.216918
$166$	4.84198	0.375811
$167$	−9.50880	−0.735813	−0.367906	−	0.929863i	$-0.619925\pi$
$167$	−9.50880	−0.735813	−0.367906	+	0.929863i	$0.619925\pi$
$168$	−13.1757	−1.01653
$169$	−0.759708	−0.0584391
$170$	−0.663795	−0.0509107
$171$	26.1462	1.99945
$172$	−5.63759	−0.429862
$173$	−14.1484	−1.07568	−0.537840	−	0.843047i	$-0.680760\pi$
$173$	−14.1484	−1.07568	−0.537840	+	0.843047i	$0.680760\pi$
$174$	−12.3469	−0.936013
$175$	4.72864	0.357451
$176$	1.00000	0.0753778
$177$	−6.03344	−0.453501
$178$	−15.0882	−1.13091
$179$	22.6675	1.69425	0.847125	−	0.531393i	$-0.178331\pi$
$179$	22.6675	1.69425	0.847125	+	0.531393i	$0.178331\pi$
$180$	4.76382	0.355074
$181$	−11.9363	−0.887217	−0.443608	−	0.896221i	$-0.646302\pi$
$181$	−11.9363	−0.887217	−0.443608	+	0.896221i	$0.646302\pi$
$182$	16.5437	1.22630
$183$	−2.84123	−0.210030
$184$	3.11362	0.229539
$185$	8.08617	0.594507
$186$	0.628426	0.0460785
$187$	−0.663795	−0.0485415
$188$	10.4223	0.760127
$189$	−23.2396	−1.69043
$190$	5.48849	0.398177
$191$	−16.7724	−1.21361	−0.606806	−	0.794850i	$-0.707549\pi$
$191$	−16.7724	−1.21361	−0.606806	+	0.794850i	$0.707549\pi$
$192$	−2.78636	−0.201088
$193$	−19.0646	−1.37230	−0.686150	−	0.727460i	$-0.740701\pi$
$193$	−19.0646	−1.37230	−0.686150	+	0.727460i	$0.740701\pi$
$194$	−10.4858	−0.752835
$195$	−9.74841	−0.698098
$196$	15.3600	1.09714
$197$	−13.3218	−0.949136	−0.474568	−	0.880219i	$-0.657396\pi$
$197$	−13.3218	−0.949136	−0.474568	+	0.880219i	$0.657396\pi$
$198$	4.76382	0.338550
$199$	5.85299	0.414907	0.207454	−	0.978245i	$-0.433482\pi$
$199$	5.85299	0.414907	0.207454	+	0.978245i	$0.433482\pi$
$200$	1.00000	0.0707107
$201$	16.2569	1.14667
$202$	4.48906	0.315849
$203$	20.9534	1.47064
$204$	1.84957	0.129496
$205$	0.265487	0.0185424
$206$	−3.02566	−0.210807
$207$	14.8327	1.03095
$208$	3.49861	0.242585
$209$	5.48849	0.379646
$210$	−13.1757	−0.909210
$211$	−21.2153	−1.46052	−0.730261	−	0.683168i	$-0.760602\pi$
$211$	−21.2153	−1.46052	−0.730261	+	0.683168i	$0.760602\pi$
$212$	−6.63414	−0.455634
$213$	41.1320	2.81832
$214$	−8.35178	−0.570916
$215$	−5.63759	−0.384480
$216$	−4.91465	−0.334400
$217$	−1.06648	−0.0723974
$218$	14.7415	0.998420
$219$	2.78636	0.188285
$220$	1.00000	0.0674200
$221$	−2.32236	−0.156219
$222$	−22.5310	−1.51218
$223$	16.8210	1.12642	0.563209	−	0.826315i	$-0.309567\pi$
$223$	16.8210	1.12642	0.563209	+	0.826315i	$0.309567\pi$
$224$	4.72864	0.315945
$225$	4.76382	0.317588
$226$	0.445666	0.0296452
$227$	0.456956	0.0303292	0.0151646	−	0.999885i	$-0.495173\pi$
$227$	0.456956	0.0303292	0.0151646	+	0.999885i	$0.495173\pi$
$228$	−15.2929	−1.01280
$229$	−27.2392	−1.80001	−0.900007	−	0.435875i	$-0.856439\pi$
$229$	−27.2392	−1.80001	−0.900007	+	0.435875i	$0.856439\pi$
$230$	3.11362	0.205306
$231$	−13.1757	−0.866898
$232$	4.43117	0.290921
$233$	−9.87083	−0.646660	−0.323330	−	0.946286i	$-0.604802\pi$
$233$	−9.87083	−0.646660	−0.323330	+	0.946286i	$0.604802\pi$
$234$	16.6668	1.08954
$235$	10.4223	0.679878
$236$	2.16535	0.140952
$237$	−37.2959	−2.42263
$238$	−3.13884	−0.203461
$239$	−15.2319	−0.985267	−0.492633	−	0.870237i	$-0.663966\pi$
$239$	−15.2319	−0.985267	−0.492633	+	0.870237i	$0.663966\pi$
$240$	−2.78636	−0.179859
$241$	8.96792	0.577675	0.288837	−	0.957378i	$-0.406731\pi$
$241$	8.96792	0.577675	0.288837	+	0.957378i	$0.406731\pi$
$242$	1.00000	0.0642824
$243$	16.4087	1.05262
$244$	1.01969	0.0652791
$245$	15.3600	0.981315
$246$	−0.739745	−0.0471644
$247$	19.2021	1.22180
$248$	−0.225536	−0.0143216
$249$	−13.4915	−0.854991
$250$	1.00000	0.0632456
$251$	14.2977	0.902464	0.451232	−	0.892407i	$-0.350985\pi$
$251$	14.2977	0.902464	0.451232	+	0.892407i	$0.350985\pi$
$252$	22.5264	1.41903
$253$	3.11362	0.195752
$254$	−11.1886	−0.702034
$255$	1.84957	0.115825
$256$	1.00000	0.0625000
$257$	−13.5825	−0.847253	−0.423626	−	0.905837i	$-0.639243\pi$
$257$	−13.5825	−0.847253	−0.423626	+	0.905837i	$0.639243\pi$
$258$	15.7084	0.977961
$259$	38.2366	2.37590
$260$	3.49861	0.216975
$261$	21.1093	1.30663
$262$	−17.7034	−1.09372
$263$	5.00448	0.308590	0.154295	−	0.988025i	$-0.450689\pi$
$263$	5.00448	0.308590	0.154295	+	0.988025i	$0.450689\pi$
$264$	−2.78636	−0.171489
$265$	−6.63414	−0.407532
$266$	25.9531	1.59128
$267$	42.0413	2.57289
$268$	−5.83444	−0.356395
$269$	−18.3907	−1.12130	−0.560651	−	0.828052i	$-0.689449\pi$
$269$	−18.3907	−1.12130	−0.560651	+	0.828052i	$0.689449\pi$
$270$	−4.91465	−0.299096
$271$	6.25055	0.379694	0.189847	−	0.981814i	$-0.439201\pi$
$271$	6.25055	0.379694	0.189847	+	0.981814i	$0.439201\pi$
$272$	−0.663795	−0.0402485
$273$	−46.0967	−2.78990
$274$	13.1212	0.792679
$275$	1.00000	0.0603023
$276$	−8.67568	−0.522215
$277$	17.2459	1.03620	0.518102	−	0.855319i	$-0.326639\pi$
$277$	17.2459	1.03620	0.518102	+	0.855319i	$0.326639\pi$
$278$	−13.4895	−0.809046
$279$	−1.07442	−0.0643236
$280$	4.72864	0.282590
$281$	−22.5792	−1.34696	−0.673482	−	0.739204i	$-0.735202\pi$
$281$	−22.5792	−1.34696	−0.673482	+	0.739204i	$0.735202\pi$
$282$	−29.0404	−1.72933
$283$	−10.4357	−0.620336	−0.310168	−	0.950682i	$-0.600385\pi$
$283$	−10.4357	−0.620336	−0.310168	+	0.950682i	$0.600385\pi$
$284$	−14.7619	−0.875956
$285$	−15.2929	−0.905874
$286$	3.49861	0.206877
$287$	1.25539	0.0741036
$288$	4.76382	0.280711
$289$	−16.5594	−0.974081
$290$	4.43117	0.260207
$291$	29.2172	1.71274
$292$	−1.00000	−0.0585206
$293$	29.5590	1.72686	0.863428	−	0.504472i	$-0.168313\pi$
$293$	29.5590	1.72686	0.863428	+	0.504472i	$0.168313\pi$
$294$	−42.7986	−2.49606
$295$	2.16535	0.126071
$296$	8.08617	0.469999
$297$	−4.91465	−0.285177
$298$	−11.6046	−0.672239
$299$	10.8934	0.629979
$300$	−2.78636	−0.160871
$301$	−26.6581	−1.53655
$302$	−4.20372	−0.241897
$303$	−12.5082	−0.718575
$304$	5.48849	0.314786
$305$	1.01969	0.0583874
$306$	−3.16220	−0.180771
$307$	20.0800	1.14602	0.573012	−	0.819547i	$-0.305775\pi$
$307$	20.0800	1.14602	0.573012	+	0.819547i	$0.305775\pi$
$308$	4.72864	0.269439
$309$	8.43058	0.479599
$310$	−0.225536	−0.0128096
$311$	29.4152	1.66798	0.833991	−	0.551778i	$-0.186050\pi$
$311$	29.4152	1.66798	0.833991	+	0.551778i	$0.186050\pi$
$312$	−9.74841	−0.551895
$313$	26.5329	1.49973	0.749863	−	0.661593i	$-0.230119\pi$
$313$	26.5329	1.49973	0.749863	+	0.661593i	$0.230119\pi$
$314$	−18.9525	−1.06955
$315$	22.5264	1.26922
$316$	13.3851	0.752973
$317$	4.15823	0.233550	0.116775	−	0.993158i	$-0.462744\pi$
$317$	4.15823	0.233550	0.116775	+	0.993158i	$0.462744\pi$
$318$	18.4851	1.03659
$319$	4.43117	0.248098
$320$	1.00000	0.0559017
$321$	23.2711	1.29887
$322$	14.7232	0.820491
$323$	−3.64323	−0.202715
$324$	−0.597459	−0.0331922
$325$	3.49861	0.194068
$326$	3.82536	0.211867
$327$	−41.0752	−2.27146
$328$	0.265487	0.0146591
$329$	49.2835	2.71708
$330$	−2.78636	−0.153384
$331$	22.2717	1.22416	0.612082	−	0.790794i	$-0.290332\pi$
$331$	22.2717	1.22416	0.612082	+	0.790794i	$0.290332\pi$
$332$	4.84198	0.265738
$333$	38.5211	2.11094
$334$	−9.50880	−0.520298
$335$	−5.83444	−0.318769
$336$	−13.1757	−0.718794
$337$	−11.8330	−0.644584	−0.322292	−	0.946640i	$-0.604453\pi$
$337$	−11.8330	−0.644584	−0.322292	+	0.946640i	$0.604453\pi$
$338$	−0.759708	−0.0413227
$339$	−1.24179	−0.0674446
$340$	−0.663795	−0.0359993
$341$	−0.225536	−0.0122135
$342$	26.1462	1.41382
$343$	39.5314	2.13450
$344$	−5.63759	−0.303958
$345$	−8.67568	−0.467083
$346$	−14.1484	−0.760621
$347$	22.3540	1.20003	0.600013	−	0.799990i	$-0.295162\pi$
$347$	22.3540	1.20003	0.600013	+	0.799990i	$0.295162\pi$
$348$	−12.3469	−0.661861
$349$	14.0327	0.751152	0.375576	−	0.926792i	$-0.377445\pi$
$349$	14.0327	0.751152	0.375576	+	0.926792i	$0.377445\pi$
$350$	4.72864	0.252756
$351$	−17.1945	−0.917773
$352$	1.00000	0.0533002
$353$	−2.74704	−0.146210	−0.0731051	−	0.997324i	$-0.523291\pi$
$353$	−2.74704	−0.146210	−0.0731051	+	0.997324i	$0.523291\pi$
$354$	−6.03344	−0.320674
$355$	−14.7619	−0.783479
$356$	−15.0882	−0.799675
$357$	8.74596	0.462885
$358$	22.6675	1.19802
$359$	−0.305857	−0.0161425	−0.00807126	−	0.999967i	$-0.502569\pi$
$359$	−0.305857	−0.0161425	−0.00807126	+	0.999967i	$0.502569\pi$
$360$	4.76382	0.251076
$361$	11.1235	0.585446
$362$	−11.9363	−0.627357
$363$	−2.78636	−0.146246
$364$	16.5437	0.867124
$365$	−1.00000	−0.0523424
$366$	−2.84123	−0.148514
$367$	9.38251	0.489763	0.244881	−	0.969553i	$-0.421251\pi$
$367$	9.38251	0.489763	0.244881	+	0.969553i	$0.421251\pi$
$368$	3.11362	0.162309
$369$	1.26474	0.0658395
$370$	8.08617	0.420380
$371$	−31.3704	−1.62867
$372$	0.628426	0.0325824
$373$	27.4884	1.42330	0.711648	−	0.702536i	$-0.247949\pi$
$373$	27.4884	1.42330	0.711648	+	0.702536i	$0.247949\pi$
$374$	−0.663795	−0.0343240
$375$	−2.78636	−0.143887
$376$	10.4223	0.537491
$377$	15.5030	0.798443
$378$	−23.2396	−1.19532
$379$	−8.14203	−0.418228	−0.209114	−	0.977891i	$-0.567058\pi$
$379$	−8.14203	−0.418228	−0.209114	+	0.977891i	$0.567058\pi$
$380$	5.48849	0.281553
$381$	31.1754	1.59717
$382$	−16.7724	−0.858153
$383$	−27.9650	−1.42895	−0.714473	−	0.699663i	$-0.753333\pi$
$383$	−27.9650	−1.42895	−0.714473	+	0.699663i	$0.753333\pi$
$384$	−2.78636	−0.142191
$385$	4.72864	0.240994
$386$	−19.0646	−0.970363
$387$	−26.8565	−1.36519
$388$	−10.4858	−0.532335
$389$	−31.0113	−1.57233	−0.786167	−	0.618014i	$-0.787938\pi$
$389$	−31.0113	−1.57233	−0.786167	+	0.618014i	$0.787938\pi$
$390$	−9.74841	−0.493630
$391$	−2.06680	−0.104523
$392$	15.3600	0.775798
$393$	49.3281	2.48828
$394$	−13.3218	−0.671140
$395$	13.3851	0.673479
$396$	4.76382	0.239391
$397$	37.6631	1.89026	0.945128	−	0.326700i	$-0.105937\pi$
$397$	37.6631	1.89026	0.945128	+	0.326700i	$0.105937\pi$
$398$	5.85299	0.293384
$399$	−72.3146	−3.62026
$400$	1.00000	0.0500000
$401$	−10.5860	−0.528637	−0.264319	−	0.964435i	$-0.585147\pi$
$401$	−10.5860	−0.528637	−0.264319	+	0.964435i	$0.585147\pi$
$402$	16.2569	0.810819
$403$	−0.789065	−0.0393061
$404$	4.48906	0.223339
$405$	−0.597459	−0.0296880
$406$	20.9534	1.03990
$407$	8.08617	0.400817
$408$	1.84957	0.0915675
$409$	−12.6401	−0.625012	−0.312506	−	0.949916i	$-0.601168\pi$
$409$	−12.6401	−0.625012	−0.312506	+	0.949916i	$0.601168\pi$
$410$	0.265487	0.0131115
$411$	−36.5604	−1.80339
$412$	−3.02566	−0.149063
$413$	10.2391	0.503835
$414$	14.8327	0.728989
$415$	4.84198	0.237684
$416$	3.49861	0.171534
$417$	37.5867	1.84063
$418$	5.48849	0.268451
$419$	25.5754	1.24944	0.624719	−	0.780850i	$-0.285213\pi$
$419$	25.5754	1.24944	0.624719	+	0.780850i	$0.285213\pi$
$420$	−13.1757	−0.642908
$421$	27.2532	1.32824	0.664119	−	0.747627i	$-0.268807\pi$
$421$	27.2532	1.32824	0.664119	+	0.747627i	$0.268807\pi$
$422$	−21.2153	−1.03275
$423$	49.6502	2.41407
$424$	−6.63414	−0.322182
$425$	−0.663795	−0.0321988
$426$	41.1320	1.99285
$427$	4.82176	0.233341
$428$	−8.35178	−0.403698
$429$	−9.74841	−0.470658
$430$	−5.63759	−0.271869
$431$	32.3564	1.55855	0.779276	−	0.626681i	$-0.215587\pi$
$431$	32.3564	1.55855	0.779276	+	0.626681i	$0.215587\pi$
$432$	−4.91465	−0.236456
$433$	1.42172	0.0683237	0.0341618	−	0.999416i	$-0.489124\pi$
$433$	1.42172	0.0683237	0.0341618	+	0.999416i	$0.489124\pi$
$434$	−1.06648	−0.0511927
$435$	−12.3469	−0.591987
$436$	14.7415	0.705990
$437$	17.0891	0.817481
$438$	2.78636	0.133138
$439$	−4.33583	−0.206938	−0.103469	−	0.994633i	$-0.532994\pi$
$439$	−4.33583	−0.206938	−0.103469	+	0.994633i	$0.532994\pi$
$440$	1.00000	0.0476731
$441$	73.1724	3.48440
$442$	−2.32236	−0.110463
$443$	−15.0082	−0.713060	−0.356530	−	0.934284i	$-0.616040\pi$
$443$	−15.0082	−0.713060	−0.356530	+	0.934284i	$0.616040\pi$
$444$	−22.5310	−1.06927
$445$	−15.0882	−0.715251
$446$	16.8210	0.796497
$447$	32.3348	1.52938
$448$	4.72864	0.223407
$449$	−25.1951	−1.18903	−0.594515	−	0.804084i	$-0.702656\pi$
$449$	−25.1951	−1.18903	−0.594515	+	0.804084i	$0.702656\pi$
$450$	4.76382	0.224569
$451$	0.265487	0.0125013
$452$	0.445666	0.0209624
$453$	11.7131	0.550329
$454$	0.456956	0.0214460
$455$	16.5437	0.775579
$456$	−15.2929	−0.716156
$457$	28.5622	1.33608	0.668042	−	0.744124i	$-0.267133\pi$
$457$	28.5622	1.33608	0.668042	+	0.744124i	$0.267133\pi$
$458$	−27.2392	−1.27280
$459$	3.26232	0.152272
$460$	3.11362	0.145173
$461$	−26.7005	−1.24357	−0.621784	−	0.783189i	$-0.713592\pi$
$461$	−26.7005	−1.24357	−0.621784	+	0.783189i	$0.713592\pi$
$462$	−13.1757	−0.612989
$463$	−9.83016	−0.456846	−0.228423	−	0.973562i	$-0.573357\pi$
$463$	−9.83016	−0.456846	−0.228423	+	0.973562i	$0.573357\pi$
$464$	4.43117	0.205712
$465$	0.628426	0.0291426
$466$	−9.87083	−0.457258
$467$	11.1542	0.516155	0.258077	−	0.966124i	$-0.416911\pi$
$467$	11.1542	0.516155	0.258077	+	0.966124i	$0.416911\pi$
$468$	16.6668	0.770422
$469$	−27.5889	−1.27394
$470$	10.4223	0.480747
$471$	52.8086	2.43329
$472$	2.16535	0.0996682
$473$	−5.63759	−0.259217
$474$	−37.2959	−1.71306
$475$	5.48849	0.251829
$476$	−3.13884	−0.143869
$477$	−31.6039	−1.44704
$478$	−15.2319	−0.696689
$479$	−5.91011	−0.270040	−0.135020	−	0.990843i	$-0.543110\pi$
$479$	−5.91011	−0.270040	−0.135020	+	0.990843i	$0.543110\pi$
$480$	−2.78636	−0.127180
$481$	28.2904	1.28993
$482$	8.96792	0.408478
$483$	−41.0241	−1.86666
$484$	1.00000	0.0454545
$485$	−10.4858	−0.476135
$486$	16.4087	0.744314
$487$	33.6171	1.52334	0.761669	−	0.647966i	$-0.224380\pi$
$487$	33.6171	1.52334	0.761669	+	0.647966i	$0.224380\pi$
$488$	1.01969	0.0461593
$489$	−10.6589	−0.482010
$490$	15.3600	0.693894
$491$	15.2031	0.686107	0.343054	−	0.939316i	$-0.388539\pi$
$491$	15.2031	0.686107	0.343054	+	0.939316i	$0.388539\pi$
$492$	−0.739745	−0.0333503
$493$	−2.94139	−0.132473
$494$	19.2021	0.863943
$495$	4.76382	0.214118
$496$	−0.225536	−0.0101269
$497$	−69.8036	−3.13112
$498$	−13.4915	−0.604570
$499$	−5.72685	−0.256369	−0.128184	−	0.991750i	$-0.540915\pi$
$499$	−5.72685	−0.256369	−0.128184	+	0.991750i	$0.540915\pi$
$500$	1.00000	0.0447214
$501$	26.4950	1.18371
$502$	14.2977	0.638139
$503$	34.3977	1.53372	0.766858	−	0.641817i	$-0.221819\pi$
$503$	34.3977	1.53372	0.766858	+	0.641817i	$0.221819\pi$
$504$	22.5264	1.00341
$505$	4.48906	0.199761
$506$	3.11362	0.138417
$507$	2.11682	0.0940114
$508$	−11.1886	−0.496413
$509$	−12.6247	−0.559579	−0.279790	−	0.960061i	$-0.590265\pi$
$509$	−12.6247	−0.559579	−0.279790	+	0.960061i	$0.590265\pi$
$510$	1.84957	0.0819005
$511$	−4.72864	−0.209183
$512$	1.00000	0.0441942
$513$	−26.9740	−1.19093
$514$	−13.5825	−0.599098
$515$	−3.02566	−0.133326
$516$	15.7084	0.691523
$517$	10.4223	0.458374
$518$	38.2366	1.68002
$519$	39.4225	1.73046
$520$	3.49861	0.153424
$521$	−42.6657	−1.86922	−0.934608	−	0.355679i	$-0.884250\pi$
$521$	−42.6657	−1.86922	−0.934608	+	0.355679i	$0.884250\pi$
$522$	21.1093	0.923930
$523$	10.8448	0.474211	0.237105	−	0.971484i	$-0.423801\pi$
$523$	10.8448	0.474211	0.237105	+	0.971484i	$0.423801\pi$
$524$	−17.7034	−0.773377
$525$	−13.1757	−0.575035
$526$	5.00448	0.218206
$527$	0.149710	0.00652146
$528$	−2.78636	−0.121261
$529$	−13.3054	−0.578494
$530$	−6.63414	−0.288169
$531$	10.3153	0.447647
$532$	25.9531	1.12521
$533$	0.928838	0.0402324
$534$	42.0413	1.81931
$535$	−8.35178	−0.361079
$536$	−5.83444	−0.252009
$537$	−63.1600	−2.72555
$538$	−18.3907	−0.792880
$539$	15.3600	0.661602
$540$	−4.91465	−0.211493
$541$	23.1739	0.996324	0.498162	−	0.867084i	$-0.334009\pi$
$541$	23.1739	0.996324	0.498162	+	0.867084i	$0.334009\pi$
$542$	6.25055	0.268484
$543$	33.2588	1.42727
$544$	−0.663795	−0.0284600
$545$	14.7415	0.631456
$546$	−46.0967	−1.97276
$547$	−7.15911	−0.306101	−0.153051	−	0.988218i	$-0.548910\pi$
$547$	−7.15911	−0.306101	−0.153051	+	0.988218i	$0.548910\pi$
$548$	13.1212	0.560509
$549$	4.85763	0.207319
$550$	1.00000	0.0426401
$551$	24.3204	1.03609
$552$	−8.67568	−0.369261
$553$	63.2935	2.69151
$554$	17.2459	0.732707
$555$	−22.5310	−0.956388
$556$	−13.4895	−0.572082
$557$	−8.20276	−0.347562	−0.173781	−	0.984784i	$-0.555599\pi$
$557$	−8.20276	−0.347562	−0.173781	+	0.984784i	$0.555599\pi$
$558$	−1.07442	−0.0454836
$559$	−19.7237	−0.834225
$560$	4.72864	0.199821
$561$	1.84957	0.0780890
$562$	−22.5792	−0.952447
$563$	−15.0130	−0.632724	−0.316362	−	0.948638i	$-0.602461\pi$
$563$	−15.0130	−0.632724	−0.316362	+	0.948638i	$0.602461\pi$
$564$	−29.0404	−1.22282
$565$	0.445666	0.0187493
$566$	−10.4357	−0.438643
$567$	−2.82517	−0.118646
$568$	−14.7619	−0.619395
$569$	−27.1608	−1.13864	−0.569320	−	0.822116i	$-0.692794\pi$
$569$	−27.1608	−1.13864	−0.569320	+	0.822116i	$0.692794\pi$
$570$	−15.2929	−0.640550
$571$	−35.6428	−1.49161	−0.745803	−	0.666167i	$-0.767934\pi$
$571$	−35.6428	−1.49161	−0.745803	+	0.666167i	$0.767934\pi$
$572$	3.49861	0.146284
$573$	46.7341	1.95235
$574$	1.25539	0.0523991
$575$	3.11362	0.129847
$576$	4.76382	0.198493
$577$	−12.9642	−0.539707	−0.269853	−	0.962901i	$-0.586975\pi$
$577$	−12.9642	−0.539707	−0.269853	+	0.962901i	$0.586975\pi$
$578$	−16.5594	−0.688779
$579$	53.1209	2.20763
$580$	4.43117	0.183994
$581$	22.8960	0.949885
$582$	29.2172	1.21109
$583$	−6.63414	−0.274758
$584$	−1.00000	−0.0413803
$585$	16.6668	0.689086
$586$	29.5590	1.22107
$587$	37.4135	1.54422	0.772110	−	0.635488i	$-0.219201\pi$
$587$	37.4135	1.54422	0.772110	+	0.635488i	$0.219201\pi$
$588$	−42.7986	−1.76498
$589$	−1.23785	−0.0510049
$590$	2.16535	0.0891459
$591$	37.1192	1.52688
$592$	8.08617	0.332340
$593$	−10.3783	−0.426185	−0.213093	−	0.977032i	$-0.568354\pi$
$593$	−10.3783	−0.426185	−0.213093	+	0.977032i	$0.568354\pi$
$594$	−4.91465	−0.201651
$595$	−3.13884	−0.128680
$596$	−11.6046	−0.475345
$597$	−16.3086	−0.667465
$598$	10.8934	0.445462
$599$	−27.2520	−1.11349	−0.556744	−	0.830684i	$-0.687950\pi$
$599$	−27.2520	−1.11349	−0.556744	+	0.830684i	$0.687950\pi$
$600$	−2.78636	−0.113753
$601$	24.7805	1.01082	0.505409	−	0.862880i	$-0.331342\pi$
$601$	24.7805	1.01082	0.505409	+	0.862880i	$0.331342\pi$
$602$	−26.6581	−1.08650
$603$	−27.7942	−1.13187
$604$	−4.20372	−0.171047
$605$	1.00000	0.0406558
$606$	−12.5082	−0.508109
$607$	−10.7165	−0.434971	−0.217485	−	0.976064i	$-0.569785\pi$
$607$	−10.7165	−0.434971	−0.217485	+	0.976064i	$0.569785\pi$
$608$	5.48849	0.222587
$609$	−58.3838	−2.36583
$610$	1.01969	0.0412861
$611$	36.4637	1.47516
$612$	−3.16220	−0.127824
$613$	−7.49529	−0.302732	−0.151366	−	0.988478i	$-0.548367\pi$
$613$	−7.49529	−0.302732	−0.151366	+	0.988478i	$0.548367\pi$
$614$	20.0800	0.810361
$615$	−0.739745	−0.0298294
$616$	4.72864	0.190522
$617$	−27.0437	−1.08874	−0.544370	−	0.838846i	$-0.683231\pi$
$617$	−27.0437	−1.08874	−0.544370	+	0.838846i	$0.683231\pi$
$618$	8.43058	0.339128
$619$	−29.2059	−1.17389	−0.586943	−	0.809628i	$-0.699669\pi$
$619$	−29.2059	−1.17389	−0.586943	+	0.809628i	$0.699669\pi$
$620$	−0.225536	−0.00905776
$621$	−15.3024	−0.614063
$622$	29.4152	1.17944
$623$	−71.3468	−2.85845
$624$	−9.74841	−0.390249
$625$	1.00000	0.0400000
$626$	26.5329	1.06047
$627$	−15.2929	−0.610740
$628$	−18.9525	−0.756288
$629$	−5.36755	−0.214018
$630$	22.5264	0.897473
$631$	−6.87117	−0.273537	−0.136768	−	0.990603i	$-0.543672\pi$
$631$	−6.87117	−0.273537	−0.136768	+	0.990603i	$0.543672\pi$
$632$	13.3851	0.532432
$633$	59.1136	2.34955
$634$	4.15823	0.165144
$635$	−11.1886	−0.444005
$636$	18.4851	0.732983
$637$	53.7387	2.12921
$638$	4.43117	0.175432
$639$	−70.3230	−2.78193
$640$	1.00000	0.0395285
$641$	3.56055	0.140633	0.0703167	−	0.997525i	$-0.477599\pi$
$641$	3.56055	0.140633	0.0703167	+	0.997525i	$0.477599\pi$
$642$	23.2711	0.918437
$643$	18.8962	0.745192	0.372596	−	0.927994i	$-0.378468\pi$
$643$	18.8962	0.745192	0.372596	+	0.927994i	$0.378468\pi$
$644$	14.7232	0.580175
$645$	15.7084	0.618517
$646$	−3.64323	−0.143341
$647$	21.4608	0.843713	0.421856	−	0.906663i	$-0.361379\pi$
$647$	21.4608	0.843713	0.421856	+	0.906663i	$0.361379\pi$
$648$	−0.597459	−0.0234704
$649$	2.16535	0.0849973
$650$	3.49861	0.137227
$651$	2.97160	0.116466
$652$	3.82536	0.149813
$653$	−20.4420	−0.799958	−0.399979	−	0.916524i	$-0.630983\pi$
$653$	−20.4420	−0.799958	−0.399979	+	0.916524i	$0.630983\pi$
$654$	−41.0752	−1.60617
$655$	−17.7034	−0.691730
$656$	0.265487	0.0103655
$657$	−4.76382	−0.185854
$658$	49.2835	1.92127
$659$	31.3654	1.22182	0.610912	−	0.791699i	$-0.290803\pi$
$659$	31.3654	1.22182	0.610912	+	0.791699i	$0.290803\pi$
$660$	−2.78636	−0.108459
$661$	26.0108	1.01170	0.505851	−	0.862621i	$-0.331179\pi$
$661$	26.0108	1.01170	0.505851	+	0.862621i	$0.331179\pi$
$662$	22.2717	0.865615
$663$	6.47094	0.251310
$664$	4.84198	0.187905
$665$	25.9531	1.00642
$666$	38.5211	1.49266
$667$	13.7970	0.534222
$668$	−9.50880	−0.367906
$669$	−46.8694	−1.81208
$670$	−5.83444	−0.225404
$671$	1.01969	0.0393648
$672$	−13.1757	−0.508264
$673$	−44.5153	−1.71594	−0.857969	−	0.513701i	$-0.828274\pi$
$673$	−44.5153	−1.71594	−0.857969	+	0.513701i	$0.828274\pi$
$674$	−11.8330	−0.455790
$675$	−4.91465	−0.189165
$676$	−0.759708	−0.0292196
$677$	22.5556	0.866882	0.433441	−	0.901182i	$-0.357299\pi$
$677$	22.5556	0.866882	0.433441	+	0.901182i	$0.357299\pi$
$678$	−1.24179	−0.0476905
$679$	−49.5834	−1.90284
$680$	−0.663795	−0.0254554
$681$	−1.27325	−0.0487909
$682$	−0.225536	−0.00863624
$683$	7.54727	0.288788	0.144394	−	0.989520i	$-0.453877\pi$
$683$	7.54727	0.288788	0.144394	+	0.989520i	$0.453877\pi$
$684$	26.1462	0.999724
$685$	13.1212	0.501334
$686$	39.5314	1.50932
$687$	75.8982	2.89570
$688$	−5.63759	−0.214931
$689$	−23.2103	−0.884241
$690$	−8.67568	−0.330278
$691$	6.15065	0.233982	0.116991	−	0.993133i	$-0.462675\pi$
$691$	6.15065	0.233982	0.116991	+	0.993133i	$0.462675\pi$
$692$	−14.1484	−0.537840
$693$	22.5264	0.855707
$694$	22.3540	0.848546
$695$	−13.4895	−0.511686
$696$	−12.3469	−0.468007
$697$	−0.176229	−0.00667515
$698$	14.0327	0.531145
$699$	27.5037	1.04029
$700$	4.72864	0.178726
$701$	−5.44484	−0.205649	−0.102824	−	0.994700i	$-0.532788\pi$
$701$	−5.44484	−0.205649	−0.102824	+	0.994700i	$0.532788\pi$
$702$	−17.1945	−0.648963
$703$	44.3808	1.67385
$704$	1.00000	0.0376889
$705$	−29.0404	−1.09373
$706$	−2.74704	−0.103386
$707$	21.2271	0.798328
$708$	−6.03344	−0.226751
$709$	−15.9029	−0.597245	−0.298622	−	0.954371i	$-0.596527\pi$
$709$	−15.9029	−0.597245	−0.298622	+	0.954371i	$0.596527\pi$
$710$	−14.7619	−0.554004
$711$	63.7644	2.39135
$712$	−15.0882	−0.565456
$713$	−0.702235	−0.0262989
$714$	8.74596	0.327309
$715$	3.49861	0.130841
$716$	22.6675	0.847125
$717$	42.4415	1.58501
$718$	−0.305857	−0.0114145
$719$	14.0769	0.524979	0.262489	−	0.964935i	$-0.415457\pi$
$719$	14.0769	0.524979	0.262489	+	0.964935i	$0.415457\pi$
$720$	4.76382	0.177537
$721$	−14.3072	−0.532829
$722$	11.1235	0.413973
$723$	−24.9879	−0.929310
$724$	−11.9363	−0.443608
$725$	4.43117	0.164570
$726$	−2.78636	−0.103412
$727$	20.0594	0.743963	0.371982	−	0.928240i	$-0.378678\pi$
$727$	20.0594	0.743963	0.371982	+	0.928240i	$0.378678\pi$
$728$	16.5437	0.613149
$729$	−43.9282	−1.62697
$730$	−1.00000	−0.0370117
$731$	3.74220	0.138410
$732$	−2.84123	−0.105015
$733$	16.2296	0.599454	0.299727	−	0.954025i	$-0.403104\pi$
$733$	16.2296	0.599454	0.299727	+	0.954025i	$0.403104\pi$
$734$	9.38251	0.346315
$735$	−42.7986	−1.57865
$736$	3.11362	0.114770
$737$	−5.83444	−0.214914
$738$	1.26474	0.0465556
$739$	15.9606	0.587120	0.293560	−	0.955941i	$-0.405160\pi$
$739$	15.9606	0.587120	0.293560	+	0.955941i	$0.405160\pi$
$740$	8.08617	0.297253
$741$	−53.5040	−1.96552
$742$	−31.3704	−1.15164
$743$	−9.19892	−0.337475	−0.168738	−	0.985661i	$-0.553969\pi$
$743$	−9.19892	−0.337475	−0.168738	+	0.985661i	$0.553969\pi$
$744$	0.628426	0.0230392
$745$	−11.6046	−0.425161
$746$	27.4884	1.00642
$747$	23.0664	0.843954
$748$	−0.663795	−0.0242707
$749$	−39.4925	−1.44303
$750$	−2.78636	−0.101744
$751$	−31.4265	−1.14677	−0.573385	−	0.819286i	$-0.694370\pi$
$751$	−31.4265	−1.14677	−0.573385	+	0.819286i	$0.694370\pi$
$752$	10.4223	0.380064
$753$	−39.8387	−1.45180
$754$	15.5030	0.564585
$755$	−4.20372	−0.152989
$756$	−23.2396	−0.845216
$757$	−38.9232	−1.41469	−0.707344	−	0.706869i	$-0.750107\pi$
$757$	−38.9232	−1.41469	−0.707344	+	0.706869i	$0.750107\pi$
$758$	−8.14203	−0.295732
$759$	−8.67568	−0.314907
$760$	5.48849	0.199088
$761$	−33.0544	−1.19822	−0.599110	−	0.800667i	$-0.704479\pi$
$761$	−33.0544	−1.19822	−0.599110	+	0.800667i	$0.704479\pi$
$762$	31.1754	1.12937
$763$	69.7072	2.52357
$764$	−16.7724	−0.606806
$765$	−3.16220	−0.114330
$766$	−27.9650	−1.01042
$767$	7.57571	0.273543
$768$	−2.78636	−0.100544
$769$	−0.936476	−0.0337702	−0.0168851	−	0.999857i	$-0.505375\pi$
$769$	−0.936476	−0.0337702	−0.0168851	+	0.999857i	$0.505375\pi$
$770$	4.72864	0.170408
$771$	37.8458	1.36298
$772$	−19.0646	−0.686150
$773$	−4.09722	−0.147367	−0.0736834	−	0.997282i	$-0.523475\pi$
$773$	−4.09722	−0.147367	−0.0736834	+	0.997282i	$0.523475\pi$
$774$	−26.8565	−0.965336
$775$	−0.225536	−0.00810151
$776$	−10.4858	−0.376418
$777$	−106.541	−3.82214
$778$	−31.0113	−1.11181
$779$	1.45712	0.0522069
$780$	−9.74841	−0.349049
$781$	−14.7619	−0.528222
$782$	−2.06680	−0.0739088
$783$	−21.7777	−0.778271
$784$	15.3600	0.548572
$785$	−18.9525	−0.676444
$786$	49.3281	1.75948
$787$	−27.2832	−0.972543	−0.486271	−	0.873808i	$-0.661643\pi$
$787$	−27.2832	−0.972543	−0.486271	+	0.873808i	$0.661643\pi$
$788$	−13.3218	−0.474568
$789$	−13.9443	−0.496431
$790$	13.3851	0.476222
$791$	2.10739	0.0749302
$792$	4.76382	0.169275
$793$	3.56751	0.126686
$794$	37.6631	1.33661
$795$	18.4851	0.655600
$796$	5.85299	0.207454
$797$	−42.1209	−1.49200	−0.746000	−	0.665946i	$-0.768028\pi$
$797$	−42.1209	−1.49200	−0.746000	+	0.665946i	$0.768028\pi$
$798$	−72.3146	−2.55991
$799$	−6.91829	−0.244752
$800$	1.00000	0.0353553
$801$	−71.8777	−2.53967
$802$	−10.5860	−0.373803
$803$	−1.00000	−0.0352892
$804$	16.2569	0.573336
$805$	14.7232	0.518924
$806$	−0.789065	−0.0277936
$807$	51.2432	1.80385
$808$	4.48906	0.157925
$809$	43.2339	1.52002	0.760012	−	0.649910i	$-0.225193\pi$
$809$	43.2339	1.52002	0.760012	+	0.649910i	$0.225193\pi$
$810$	−0.597459	−0.0209926
$811$	35.3032	1.23966	0.619831	−	0.784735i	$-0.287201\pi$
$811$	35.3032	1.23966	0.619831	+	0.784735i	$0.287201\pi$
$812$	20.9534	0.735321
$813$	−17.4163	−0.610817
$814$	8.08617	0.283420
$815$	3.82536	0.133997
$816$	1.84957	0.0647480
$817$	−30.9418	−1.08252
$818$	−12.6401	−0.441950
$819$	78.8111	2.75388
$820$	0.265487	0.00927122
$821$	8.14609	0.284300	0.142150	−	0.989845i	$-0.454598\pi$
$821$	8.14609	0.284300	0.142150	+	0.989845i	$0.454598\pi$
$822$	−36.5604	−1.27519
$823$	29.9273	1.04320	0.521601	−	0.853190i	$-0.325335\pi$
$823$	29.9273	1.04320	0.521601	+	0.853190i	$0.325335\pi$
$824$	−3.02566	−0.105404
$825$	−2.78636	−0.0970087
$826$	10.2391	0.356265
$827$	24.3271	0.845935	0.422968	−	0.906145i	$-0.360988\pi$
$827$	24.3271	0.845935	0.422968	+	0.906145i	$0.360988\pi$
$828$	14.8327	0.515473
$829$	33.6479	1.16864	0.584320	−	0.811523i	$-0.301361\pi$
$829$	33.6479	1.16864	0.584320	+	0.811523i	$0.301361\pi$
$830$	4.84198	0.168068
$831$	−48.0533	−1.66695
$832$	3.49861	0.121293
$833$	−10.1959	−0.353267
$834$	37.5867	1.30152
$835$	−9.50880	−0.329066
$836$	5.48849	0.189823
$837$	1.10843	0.0383131
$838$	25.5754	0.883486
$839$	−12.3016	−0.424699	−0.212349	−	0.977194i	$-0.568111\pi$
$839$	−12.3016	−0.424699	−0.212349	+	0.977194i	$0.568111\pi$
$840$	−13.1757	−0.454605
$841$	−9.36470	−0.322921
$842$	27.2532	0.939207
$843$	62.9139	2.16687
$844$	−21.2153	−0.730261
$845$	−0.759708	−0.0261348
$846$	49.6502	1.70701
$847$	4.72864	0.162478
$848$	−6.63414	−0.227817
$849$	29.0775	0.997939
$850$	−0.663795	−0.0227680
$851$	25.1773	0.863066
$852$	41.1320	1.40916
$853$	42.6451	1.46014	0.730070	−	0.683372i	$-0.239487\pi$
$853$	42.6451	1.46014	0.730070	+	0.683372i	$0.239487\pi$
$854$	4.82176	0.164997
$855$	26.1462	0.894180
$856$	−8.35178	−0.285458
$857$	−35.7231	−1.22028	−0.610139	−	0.792294i	$-0.708886\pi$
$857$	−35.7231	−1.22028	−0.610139	+	0.792294i	$0.708886\pi$
$858$	−9.74841	−0.332805
$859$	39.4807	1.34706	0.673532	−	0.739158i	$-0.264777\pi$
$859$	39.4807	1.34706	0.673532	+	0.739158i	$0.264777\pi$
$860$	−5.63759	−0.192240
$861$	−3.49798	−0.119211
$862$	32.3564	1.10206
$863$	−27.8664	−0.948582	−0.474291	−	0.880368i	$-0.657296\pi$
$863$	−27.8664	−0.948582	−0.474291	+	0.880368i	$0.657296\pi$
$864$	−4.91465	−0.167200
$865$	−14.1484	−0.481059
$866$	1.42172	0.0483121
$867$	46.1404	1.56701
$868$	−1.06648	−0.0361987
$869$	13.3851	0.454060
$870$	−12.3469	−0.418598
$871$	−20.4124	−0.691649
$872$	14.7415	0.499210
$873$	−49.9524	−1.69063
$874$	17.0891	0.578046
$875$	4.72864	0.159857
$876$	2.78636	0.0941425
$877$	−0.437517	−0.0147739	−0.00738695	−	0.999973i	$-0.502351\pi$
$877$	−0.437517	−0.0147739	−0.00738695	+	0.999973i	$0.502351\pi$
$878$	−4.33583	−0.146327
$879$	−82.3622	−2.77801
$880$	1.00000	0.0337100
$881$	−6.45959	−0.217629	−0.108815	−	0.994062i	$-0.534705\pi$
$881$	−6.45959	−0.217629	−0.108815	+	0.994062i	$0.534705\pi$
$882$	73.1724	2.46384
$883$	−11.4557	−0.385514	−0.192757	−	0.981247i	$-0.561743\pi$
$883$	−11.4557	−0.385514	−0.192757	+	0.981247i	$0.561743\pi$
$884$	−2.32236	−0.0781094
$885$	−6.03344	−0.202812
$886$	−15.0082	−0.504209
$887$	−52.0715	−1.74839	−0.874194	−	0.485576i	$-0.838610\pi$
$887$	−52.0715	−1.74839	−0.874194	+	0.485576i	$0.838610\pi$
$888$	−22.5310	−0.756091
$889$	−52.9067	−1.77443
$890$	−15.0882	−0.505759
$891$	−0.597459	−0.0200156
$892$	16.8210	0.563209
$893$	57.2028	1.91422
$894$	32.3348	1.08144
$895$	22.6675	0.757692
$896$	4.72864	0.157973
$897$	−30.3528	−1.01345
$898$	−25.1951	−0.840772
$899$	−0.999391	−0.0333316
$900$	4.76382	0.158794
$901$	4.40370	0.146709
$902$	0.265487	0.00883977
$903$	74.2792	2.47186
$904$	0.445666	0.0148226
$905$	−11.9363	−0.396775
$906$	11.7131	0.389141
$907$	−37.9532	−1.26022	−0.630108	−	0.776508i	$-0.716989\pi$
$907$	−37.9532	−1.26022	−0.630108	+	0.776508i	$0.716989\pi$
$908$	0.456956	0.0151646
$909$	21.3851	0.709298
$910$	16.5437	0.548417
$911$	−47.9262	−1.58786	−0.793932	−	0.608006i	$-0.791969\pi$
$911$	−47.9262	−1.58786	−0.793932	+	0.608006i	$0.791969\pi$
$912$	−15.2929	−0.506399
$913$	4.84198	0.160246
$914$	28.5622	0.944754
$915$	−2.84123	−0.0939283
$916$	−27.2392	−0.900007
$917$	−83.7130	−2.76445
$918$	3.26232	0.107673
$919$	14.2914	0.471430	0.235715	−	0.971822i	$-0.424257\pi$
$919$	14.2914	0.471430	0.235715	+	0.971822i	$0.424257\pi$
$920$	3.11362	0.102653
$921$	−55.9501	−1.84362
$922$	−26.7005	−0.879336
$923$	−51.6461	−1.69995
$924$	−13.1757	−0.433449
$925$	8.08617	0.265872
$926$	−9.83016	−0.323039
$927$	−14.4137	−0.473408
$928$	4.43117	0.145460
$929$	34.0659	1.11766	0.558832	−	0.829281i	$-0.311250\pi$
$929$	34.0659	1.11766	0.558832	+	0.829281i	$0.311250\pi$
$930$	0.628426	0.0206069
$931$	84.3032	2.76292
$932$	−9.87083	−0.323330
$933$	−81.9614	−2.68330
$934$	11.1542	0.364977
$935$	−0.663795	−0.0217084
$936$	16.6668	0.544771
$937$	−23.9168	−0.781327	−0.390664	−	0.920534i	$-0.627754\pi$
$937$	−23.9168	−0.781327	−0.390664	+	0.920534i	$0.627754\pi$
$938$	−27.5889	−0.900811
$939$	−73.9302	−2.41262
$940$	10.4223	0.339939
$941$	−10.9947	−0.358417	−0.179209	−	0.983811i	$-0.557354\pi$
$941$	−10.9947	−0.358417	−0.179209	+	0.983811i	$0.557354\pi$
$942$	52.8086	1.72060
$943$	0.826627	0.0269187
$944$	2.16535	0.0704760
$945$	−23.2396	−0.755985
$946$	−5.63759	−0.183294
$947$	−33.4816	−1.08801	−0.544003	−	0.839083i	$-0.683092\pi$
$947$	−33.4816	−1.08801	−0.544003	+	0.839083i	$0.683092\pi$
$948$	−37.2959	−1.21131
$949$	−3.49861	−0.113570
$950$	5.48849	0.178070
$951$	−11.5863	−0.375713
$952$	−3.13884	−0.101730
$953$	56.1570	1.81910	0.909552	−	0.415589i	$-0.136425\pi$
$953$	56.1570	1.81910	0.909552	+	0.415589i	$0.136425\pi$
$954$	−31.6039	−1.02321
$955$	−16.7724	−0.542744
$956$	−15.2319	−0.492633
$957$	−12.3469	−0.399117
$958$	−5.91011	−0.190947
$959$	62.0453	2.00355
$960$	−2.78636	−0.0899295
$961$	−30.9491	−0.998359
$962$	28.2904	0.912118
$963$	−39.7864	−1.28210
$964$	8.96792	0.288837
$965$	−19.0646	−0.613711
$966$	−41.0241	−1.31993
$967$	50.4845	1.62347	0.811736	−	0.584024i	$-0.198523\pi$
$967$	50.4845	1.62347	0.811736	+	0.584024i	$0.198523\pi$
$968$	1.00000	0.0321412
$969$	10.1514	0.326108
$970$	−10.4858	−0.336678
$971$	−55.6941	−1.78731	−0.893654	−	0.448757i	$-0.851867\pi$
$971$	−55.6941	−1.78731	−0.893654	+	0.448757i	$0.851867\pi$
$972$	16.4087	0.526309
$973$	−63.7870	−2.04492
$974$	33.6171	1.07716
$975$	−9.74841	−0.312199
$976$	1.01969	0.0326396
$977$	−1.90500	−0.0609463	−0.0304732	−	0.999536i	$-0.509701\pi$
$977$	−1.90500	−0.0609463	−0.0304732	+	0.999536i	$0.509701\pi$
$978$	−10.6589	−0.340832
$979$	−15.0882	−0.482222
$980$	15.3600	0.490657
$981$	70.2259	2.24214
$982$	15.2031	0.485151
$983$	−29.1156	−0.928645	−0.464322	−	0.885666i	$-0.653702\pi$
$983$	−29.1156	−0.928645	−0.464322	+	0.885666i	$0.653702\pi$
$984$	−0.739745	−0.0235822
$985$	−13.3218	−0.424466
$986$	−2.94139	−0.0936729
$987$	−137.322	−4.37100
$988$	19.2021	0.610900
$989$	−17.5533	−0.558163
$990$	4.76382	0.151404
$991$	−55.1465	−1.75179	−0.875894	−	0.482504i	$-0.839727\pi$
$991$	−55.1465	−1.75179	−0.875894	+	0.482504i	$0.839727\pi$
$992$	−0.225536	−0.00716079
$993$	−62.0571	−1.96932
$994$	−69.8036	−2.21403
$995$	5.85299	0.185552
$996$	−13.4915	−0.427495
$997$	11.6106	0.367710	0.183855	−	0.982953i	$-0.441142\pi$
$997$	11.6106	0.367710	0.183855	+	0.982953i	$0.441142\pi$
$998$	−5.72685	−0.181280
$999$	−39.7407	−1.25734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bl.1.1	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bl.1.1	✓	19	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.78636 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.78636 q^{6} +4.72864 q^{7} +1.00000 q^{8} +4.76382 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.78636 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.78636 q^{6} +4.72864 q^{7} +1.00000 q^{8} +4.76382 q^{9} +1.00000 q^{10} +1.00000 q^{11} -2.78636 q^{12} +3.49861 q^{13} +4.72864 q^{14} -2.78636 q^{15} +1.00000 q^{16} -0.663795 q^{17} +4.76382 q^{18} +5.48849 q^{19} +1.00000 q^{20} -13.1757 q^{21} +1.00000 q^{22} +3.11362 q^{23} -2.78636 q^{24} +1.00000 q^{25} +3.49861 q^{26} -4.91465 q^{27} +4.72864 q^{28} +4.43117 q^{29} -2.78636 q^{30} -0.225536 q^{31} +1.00000 q^{32} -2.78636 q^{33} -0.663795 q^{34} +4.72864 q^{35} +4.76382 q^{36} +8.08617 q^{37} +5.48849 q^{38} -9.74841 q^{39} +1.00000 q^{40} +0.265487 q^{41} -13.1757 q^{42} -5.63759 q^{43} +1.00000 q^{44} +4.76382 q^{45} +3.11362 q^{46} +10.4223 q^{47} -2.78636 q^{48} +15.3600 q^{49} +1.00000 q^{50} +1.84957 q^{51} +3.49861 q^{52} -6.63414 q^{53} -4.91465 q^{54} +1.00000 q^{55} +4.72864 q^{56} -15.2929 q^{57} +4.43117 q^{58} +2.16535 q^{59} -2.78636 q^{60} +1.01969 q^{61} -0.225536 q^{62} +22.5264 q^{63} +1.00000 q^{64} +3.49861 q^{65} -2.78636 q^{66} -5.83444 q^{67} -0.663795 q^{68} -8.67568 q^{69} +4.72864 q^{70} -14.7619 q^{71} +4.76382 q^{72} -1.00000 q^{73} +8.08617 q^{74} -2.78636 q^{75} +5.48849 q^{76} +4.72864 q^{77} -9.74841 q^{78} +13.3851 q^{79} +1.00000 q^{80} -0.597459 q^{81} +0.265487 q^{82} +4.84198 q^{83} -13.1757 q^{84} -0.663795 q^{85} -5.63759 q^{86} -12.3469 q^{87} +1.00000 q^{88} -15.0882 q^{89} +4.76382 q^{90} +16.5437 q^{91} +3.11362 q^{92} +0.628426 q^{93} +10.4223 q^{94} +5.48849 q^{95} -2.78636 q^{96} -10.4858 q^{97} +15.3600 q^{98} +4.76382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * q^99

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