LMFDB - Embedded newform 8030.2.a.bl.1.15

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			1.15
Root			$-1.49380$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.49380 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.49380 q^{6} +2.61865 q^{7} +1.00000 q^{8} +3.21904 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.49380 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.49380 q^{6} +2.61865 q^{7} +1.00000 q^{8} +3.21904 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.49380 q^{12} -1.45413 q^{13} +2.61865 q^{14} +2.49380 q^{15} +1.00000 q^{16} +2.28241 q^{17} +3.21904 q^{18} +7.37603 q^{19} +1.00000 q^{20} +6.53039 q^{21} +1.00000 q^{22} +1.38225 q^{23} +2.49380 q^{24} +1.00000 q^{25} -1.45413 q^{26} +0.546253 q^{27} +2.61865 q^{28} -6.59264 q^{29} +2.49380 q^{30} +0.701515 q^{31} +1.00000 q^{32} +2.49380 q^{33} +2.28241 q^{34} +2.61865 q^{35} +3.21904 q^{36} -4.99108 q^{37} +7.37603 q^{38} -3.62632 q^{39} +1.00000 q^{40} -2.35037 q^{41} +6.53039 q^{42} +7.04979 q^{43} +1.00000 q^{44} +3.21904 q^{45} +1.38225 q^{46} -2.52495 q^{47} +2.49380 q^{48} -0.142681 q^{49} +1.00000 q^{50} +5.69188 q^{51} -1.45413 q^{52} -9.09974 q^{53} +0.546253 q^{54} +1.00000 q^{55} +2.61865 q^{56} +18.3944 q^{57} -6.59264 q^{58} -9.20833 q^{59} +2.49380 q^{60} +9.89307 q^{61} +0.701515 q^{62} +8.42954 q^{63} +1.00000 q^{64} -1.45413 q^{65} +2.49380 q^{66} +7.41564 q^{67} +2.28241 q^{68} +3.44707 q^{69} +2.61865 q^{70} -1.62279 q^{71} +3.21904 q^{72} -1.00000 q^{73} -4.99108 q^{74} +2.49380 q^{75} +7.37603 q^{76} +2.61865 q^{77} -3.62632 q^{78} +8.69804 q^{79} +1.00000 q^{80} -8.29489 q^{81} -2.35037 q^{82} -13.8252 q^{83} +6.53039 q^{84} +2.28241 q^{85} +7.04979 q^{86} -16.4407 q^{87} +1.00000 q^{88} -7.40823 q^{89} +3.21904 q^{90} -3.80786 q^{91} +1.38225 q^{92} +1.74944 q^{93} -2.52495 q^{94} +7.37603 q^{95} +2.49380 q^{96} +10.4431 q^{97} -0.142681 q^{98} +3.21904 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.49380	1.43980	0.719898	−	0.694079i	$-0.244188\pi$
$3$	2.49380	1.43980	0.719898	+	0.694079i	$0.244188\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.49380	1.01809
$7$	2.61865	0.989756	0.494878	−	0.868962i	$-0.335213\pi$
$7$	2.61865	0.989756	0.494878	+	0.868962i	$0.335213\pi$
$8$	1.00000	0.353553
$9$	3.21904	1.07301
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.49380	0.719898
$13$	−1.45413	−0.403304	−0.201652	−	0.979457i	$-0.564631\pi$
$13$	−1.45413	−0.403304	−0.201652	+	0.979457i	$0.564631\pi$
$14$	2.61865	0.699863
$15$	2.49380	0.643897
$16$	1.00000	0.250000
$17$	2.28241	0.553566	0.276783	−	0.960932i	$-0.410732\pi$
$17$	2.28241	0.553566	0.276783	+	0.960932i	$0.410732\pi$
$18$	3.21904	0.758736
$19$	7.37603	1.69218	0.846089	−	0.533042i	$-0.178951\pi$
$19$	7.37603	1.69218	0.846089	+	0.533042i	$0.178951\pi$
$20$	1.00000	0.223607
$21$	6.53039	1.42505
$22$	1.00000	0.213201
$23$	1.38225	0.288220	0.144110	−	0.989562i	$-0.453968\pi$
$23$	1.38225	0.288220	0.144110	+	0.989562i	$0.453968\pi$
$24$	2.49380	0.509045
$25$	1.00000	0.200000
$26$	−1.45413	−0.285179
$27$	0.546253	0.105126
$28$	2.61865	0.494878
$29$	−6.59264	−1.22422	−0.612112	−	0.790771i	$-0.709680\pi$
$29$	−6.59264	−1.22422	−0.612112	+	0.790771i	$0.709680\pi$
$30$	2.49380	0.455304
$31$	0.701515	0.125996	0.0629979	−	0.998014i	$-0.479934\pi$
$31$	0.701515	0.125996	0.0629979	+	0.998014i	$0.479934\pi$
$32$	1.00000	0.176777
$33$	2.49380	0.434115
$34$	2.28241	0.391430
$35$	2.61865	0.442632
$36$	3.21904	0.536507
$37$	−4.99108	−0.820529	−0.410264	−	0.911967i	$-0.634564\pi$
$37$	−4.99108	−0.820529	−0.410264	+	0.911967i	$0.634564\pi$
$38$	7.37603	1.19655
$39$	−3.62632	−0.580676
$40$	1.00000	0.158114
$41$	−2.35037	−0.367066	−0.183533	−	0.983014i	$-0.558753\pi$
$41$	−2.35037	−0.367066	−0.183533	+	0.983014i	$0.558753\pi$
$42$	6.53039	1.00766
$43$	7.04979	1.07508	0.537541	−	0.843238i	$-0.319353\pi$
$43$	7.04979	1.07508	0.537541	+	0.843238i	$0.319353\pi$
$44$	1.00000	0.150756
$45$	3.21904	0.479867
$46$	1.38225	0.203802
$47$	−2.52495	−0.368301	−0.184151	−	0.982898i	$-0.558953\pi$
$47$	−2.52495	−0.368301	−0.184151	+	0.982898i	$0.558953\pi$
$48$	2.49380	0.359949
$49$	−0.142681	−0.0203830
$50$	1.00000	0.141421
$51$	5.69188	0.797023
$52$	−1.45413	−0.201652
$53$	−9.09974	−1.24995	−0.624973	−	0.780646i	$-0.714890\pi$
$53$	−9.09974	−1.24995	−0.624973	+	0.780646i	$0.714890\pi$
$54$	0.546253	0.0743356
$55$	1.00000	0.134840
$56$	2.61865	0.349932
$57$	18.3944	2.43639
$58$	−6.59264	−0.865657
$59$	−9.20833	−1.19882	−0.599411	−	0.800441i	$-0.704599\pi$
$59$	−9.20833	−1.19882	−0.599411	+	0.800441i	$0.704599\pi$
$60$	2.49380	0.321948
$61$	9.89307	1.26668	0.633339	−	0.773875i	$-0.281684\pi$
$61$	9.89307	1.26668	0.633339	+	0.773875i	$0.281684\pi$
$62$	0.701515	0.0890924
$63$	8.42954	1.06202
$64$	1.00000	0.125000
$65$	−1.45413	−0.180363
$66$	2.49380	0.306966
$67$	7.41564	0.905965	0.452982	−	0.891519i	$-0.350360\pi$
$67$	7.41564	0.905965	0.452982	+	0.891519i	$0.350360\pi$
$68$	2.28241	0.276783
$69$	3.44707	0.414978
$70$	2.61865	0.312988
$71$	−1.62279	−0.192590	−0.0962948	−	0.995353i	$-0.530699\pi$
$71$	−1.62279	−0.192590	−0.0962948	+	0.995353i	$0.530699\pi$
$72$	3.21904	0.379368
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−4.99108	−0.580201
$75$	2.49380	0.287959
$76$	7.37603	0.846089
$77$	2.61865	0.298423
$78$	−3.62632	−0.410600
$79$	8.69804	0.978606	0.489303	−	0.872114i	$-0.337251\pi$
$79$	8.69804	0.978606	0.489303	+	0.872114i	$0.337251\pi$
$80$	1.00000	0.111803
$81$	−8.29489	−0.921654
$82$	−2.35037	−0.259555
$83$	−13.8252	−1.51751	−0.758755	−	0.651377i	$-0.774192\pi$
$83$	−13.8252	−1.51751	−0.758755	+	0.651377i	$0.774192\pi$
$84$	6.53039	0.712524
$85$	2.28241	0.247562
$86$	7.04979	0.760198
$87$	−16.4407	−1.76263
$88$	1.00000	0.106600
$89$	−7.40823	−0.785271	−0.392636	−	0.919694i	$-0.628437\pi$
$89$	−7.40823	−0.785271	−0.392636	+	0.919694i	$0.628437\pi$
$90$	3.21904	0.339317
$91$	−3.80786	−0.399173
$92$	1.38225	0.144110
$93$	1.74944	0.181408
$94$	−2.52495	−0.260428
$95$	7.37603	0.756765
$96$	2.49380	0.254523
$97$	10.4431	1.06034	0.530168	−	0.847892i	$-0.322129\pi$
$97$	10.4431	1.06034	0.530168	+	0.847892i	$0.322129\pi$
$98$	−0.142681	−0.0144130
$99$	3.21904	0.323526
$100$	1.00000	0.100000
$101$	3.30052	0.328414	0.164207	−	0.986426i	$-0.447493\pi$
$101$	3.30052	0.328414	0.164207	+	0.986426i	$0.447493\pi$
$102$	5.69188	0.563580
$103$	−8.59106	−0.846502	−0.423251	−	0.906012i	$-0.639111\pi$
$103$	−8.59106	−0.846502	−0.423251	+	0.906012i	$0.639111\pi$
$104$	−1.45413	−0.142590
$105$	6.53039	0.637301
$106$	−9.09974	−0.883845
$107$	−9.80520	−0.947905	−0.473952	−	0.880551i	$-0.657173\pi$
$107$	−9.80520	−0.947905	−0.473952	+	0.880551i	$0.657173\pi$
$108$	0.546253	0.0525632
$109$	17.0694	1.63495	0.817477	−	0.575961i	$-0.195372\pi$
$109$	17.0694	1.63495	0.817477	+	0.575961i	$0.195372\pi$
$110$	1.00000	0.0953463
$111$	−12.4468	−1.18139
$112$	2.61865	0.247439
$113$	1.26558	0.119056	0.0595279	−	0.998227i	$-0.481040\pi$
$113$	1.26558	0.119056	0.0595279	+	0.998227i	$0.481040\pi$
$114$	18.3944	1.72279
$115$	1.38225	0.128896
$116$	−6.59264	−0.612112
$117$	−4.68092	−0.432751
$118$	−9.20833	−0.847696
$119$	5.97683	0.547895
$120$	2.49380	0.227652
$121$	1.00000	0.0909091
$122$	9.89307	0.895676
$123$	−5.86135	−0.528500
$124$	0.701515	0.0629979
$125$	1.00000	0.0894427
$126$	8.42954	0.750964
$127$	−14.0467	−1.24644	−0.623222	−	0.782045i	$-0.714177\pi$
$127$	−14.0467	−1.24644	−0.623222	+	0.782045i	$0.714177\pi$
$128$	1.00000	0.0883883
$129$	17.5808	1.54790
$130$	−1.45413	−0.127536
$131$	−19.4959	−1.70337	−0.851683	−	0.524057i	$-0.824418\pi$
$131$	−19.4959	−1.70337	−0.851683	+	0.524057i	$0.824418\pi$
$132$	2.49380	0.217058
$133$	19.3152	1.67484
$134$	7.41564	0.640614
$135$	0.546253	0.0470139
$136$	2.28241	0.195715
$137$	−0.989430	−0.0845327	−0.0422664	−	0.999106i	$-0.513458\pi$
$137$	−0.989430	−0.0845327	−0.0422664	+	0.999106i	$0.513458\pi$
$138$	3.44707	0.293434
$139$	−8.42637	−0.714716	−0.357358	−	0.933968i	$-0.616322\pi$
$139$	−8.42637	−0.714716	−0.357358	+	0.933968i	$0.616322\pi$
$140$	2.61865	0.221316
$141$	−6.29671	−0.530279
$142$	−1.62279	−0.136181
$143$	−1.45413	−0.121601
$144$	3.21904	0.268254
$145$	−6.59264	−0.547489
$146$	−1.00000	−0.0827606
$147$	−0.355818	−0.0293474
$148$	−4.99108	−0.410264
$149$	−13.5062	−1.10647	−0.553234	−	0.833026i	$-0.686606\pi$
$149$	−13.5062	−1.10647	−0.553234	+	0.833026i	$0.686606\pi$
$150$	2.49380	0.203618
$151$	−11.0112	−0.896080	−0.448040	−	0.894013i	$-0.647878\pi$
$151$	−11.0112	−0.896080	−0.448040	+	0.894013i	$0.647878\pi$
$152$	7.37603	0.598275
$153$	7.34718	0.593985
$154$	2.61865	0.211017
$155$	0.701515	0.0563470
$156$	−3.62632	−0.290338
$157$	−13.3879	−1.06847	−0.534236	−	0.845335i	$-0.679401\pi$
$157$	−13.3879	−1.06847	−0.534236	+	0.845335i	$0.679401\pi$
$158$	8.69804	0.691979
$159$	−22.6930	−1.79967
$160$	1.00000	0.0790569
$161$	3.61964	0.285267
$162$	−8.29489	−0.651708
$163$	15.1279	1.18491	0.592456	−	0.805603i	$-0.298158\pi$
$163$	15.1279	1.18491	0.592456	+	0.805603i	$0.298158\pi$
$164$	−2.35037	−0.183533
$165$	2.49380	0.194142
$166$	−13.8252	−1.07304
$167$	15.1301	1.17080	0.585400	−	0.810745i	$-0.300937\pi$
$167$	15.1301	1.17080	0.585400	+	0.810745i	$0.300937\pi$
$168$	6.53039	0.503830
$169$	−10.8855	−0.837346
$170$	2.28241	0.175053
$171$	23.7438	1.81573
$172$	7.04979	0.537541
$173$	24.3796	1.85355	0.926774	−	0.375618i	$-0.122570\pi$
$173$	24.3796	1.85355	0.926774	+	0.375618i	$0.122570\pi$
$174$	−16.4407	−1.24637
$175$	2.61865	0.197951
$176$	1.00000	0.0753778
$177$	−22.9637	−1.72606
$178$	−7.40823	−0.555271
$179$	−6.34194	−0.474019	−0.237010	−	0.971507i	$-0.576167\pi$
$179$	−6.34194	−0.474019	−0.237010	+	0.971507i	$0.576167\pi$
$180$	3.21904	0.239933
$181$	13.6387	1.01375	0.506877	−	0.862018i	$-0.330800\pi$
$181$	13.6387	1.01375	0.506877	+	0.862018i	$0.330800\pi$
$182$	−3.80786	−0.282258
$183$	24.6713	1.82376
$184$	1.38225	0.101901
$185$	−4.99108	−0.366952
$186$	1.74944	0.128275
$187$	2.28241	0.166906
$188$	−2.52495	−0.184151
$189$	1.43044	0.104049
$190$	7.37603	0.535114
$191$	14.8694	1.07591	0.537957	−	0.842972i	$-0.319196\pi$
$191$	14.8694	1.07591	0.537957	+	0.842972i	$0.319196\pi$
$192$	2.49380	0.179975
$193$	9.59599	0.690735	0.345367	−	0.938468i	$-0.387754\pi$
$193$	9.59599	0.690735	0.345367	+	0.938468i	$0.387754\pi$
$194$	10.4431	0.749771
$195$	−3.62632	−0.259686
$196$	−0.142681	−0.0101915
$197$	7.84684	0.559064	0.279532	−	0.960136i	$-0.409821\pi$
$197$	7.84684	0.559064	0.279532	+	0.960136i	$0.409821\pi$
$198$	3.21904	0.228768
$199$	8.73315	0.619076	0.309538	−	0.950887i	$-0.399826\pi$
$199$	8.73315	0.619076	0.309538	+	0.950887i	$0.399826\pi$
$200$	1.00000	0.0707107
$201$	18.4931	1.30441
$202$	3.30052	0.232224
$203$	−17.2638	−1.21168
$204$	5.69188	0.398511
$205$	−2.35037	−0.164157
$206$	−8.59106	−0.598567
$207$	4.44954	0.309264
$208$	−1.45413	−0.100826
$209$	7.37603	0.510211
$210$	6.53039	0.450640
$211$	−7.75485	−0.533866	−0.266933	−	0.963715i	$-0.586010\pi$
$211$	−7.75485	−0.533866	−0.266933	+	0.963715i	$0.586010\pi$
$212$	−9.09974	−0.624973
$213$	−4.04691	−0.277290
$214$	−9.80520	−0.670270
$215$	7.04979	0.480791
$216$	0.546253	0.0371678
$217$	1.83702	0.124705
$218$	17.0694	1.15609
$219$	−2.49380	−0.168515
$220$	1.00000	0.0674200
$221$	−3.31893	−0.223255
$222$	−12.4468	−0.835372
$223$	21.5223	1.44124	0.720619	−	0.693331i	$-0.243858\pi$
$223$	21.5223	1.44124	0.720619	+	0.693331i	$0.243858\pi$
$224$	2.61865	0.174966
$225$	3.21904	0.214603
$226$	1.26558	0.0841852
$227$	11.0051	0.730435	0.365217	−	0.930922i	$-0.380995\pi$
$227$	11.0051	0.730435	0.365217	+	0.930922i	$0.380995\pi$
$228$	18.3944	1.21820
$229$	24.5929	1.62514	0.812572	−	0.582861i	$-0.198067\pi$
$229$	24.5929	1.62514	0.812572	+	0.582861i	$0.198067\pi$
$230$	1.38225	0.0911432
$231$	6.53039	0.429668
$232$	−6.59264	−0.432828
$233$	−17.7343	−1.16181	−0.580907	−	0.813970i	$-0.697302\pi$
$233$	−17.7343	−1.16181	−0.580907	+	0.813970i	$0.697302\pi$
$234$	−4.68092	−0.306001
$235$	−2.52495	−0.164709
$236$	−9.20833	−0.599411
$237$	21.6912	1.40899
$238$	5.97683	0.387421
$239$	−9.06722	−0.586510	−0.293255	−	0.956034i	$-0.594738\pi$
$239$	−9.06722	−0.586510	−0.293255	+	0.956034i	$0.594738\pi$
$240$	2.49380	0.160974
$241$	−23.9756	−1.54440	−0.772202	−	0.635378i	$-0.780844\pi$
$241$	−23.9756	−1.54440	−0.772202	+	0.635378i	$0.780844\pi$
$242$	1.00000	0.0642824
$243$	−22.3246	−1.43212
$244$	9.89307	0.633339
$245$	−0.142681	−0.00911556
$246$	−5.86135	−0.373706
$247$	−10.7257	−0.682462
$248$	0.701515	0.0445462
$249$	−34.4772	−2.18490
$250$	1.00000	0.0632456
$251$	−5.25831	−0.331902	−0.165951	−	0.986134i	$-0.553069\pi$
$251$	−5.25831	−0.331902	−0.165951	+	0.986134i	$0.553069\pi$
$252$	8.42954	0.531011
$253$	1.38225	0.0869016
$254$	−14.0467	−0.881369
$255$	5.69188	0.356439
$256$	1.00000	0.0625000
$257$	22.9131	1.42928	0.714639	−	0.699493i	$-0.246591\pi$
$257$	22.9131	1.42928	0.714639	+	0.699493i	$0.246591\pi$
$258$	17.5808	1.09453
$259$	−13.0699	−0.812123
$260$	−1.45413	−0.0901815
$261$	−21.2220	−1.31361
$262$	−19.4959	−1.20446
$263$	25.1897	1.55327	0.776633	−	0.629954i	$-0.216926\pi$
$263$	25.1897	1.55327	0.776633	+	0.629954i	$0.216926\pi$
$264$	2.49380	0.153483
$265$	−9.09974	−0.558993
$266$	19.3152	1.18429
$267$	−18.4747	−1.13063
$268$	7.41564	0.452982
$269$	15.3013	0.932938	0.466469	−	0.884538i	$-0.345526\pi$
$269$	15.3013	0.932938	0.466469	+	0.884538i	$0.345526\pi$
$270$	0.546253	0.0332439
$271$	14.1112	0.857195	0.428597	−	0.903496i	$-0.359008\pi$
$271$	14.1112	0.857195	0.428597	+	0.903496i	$0.359008\pi$
$272$	2.28241	0.138392
$273$	−9.49606	−0.574727
$274$	−0.989430	−0.0597737
$275$	1.00000	0.0603023
$276$	3.44707	0.207489
$277$	7.85182	0.471770	0.235885	−	0.971781i	$-0.424201\pi$
$277$	7.85182	0.471770	0.235885	+	0.971781i	$0.424201\pi$
$278$	−8.42637	−0.505380
$279$	2.25821	0.135195
$280$	2.61865	0.156494
$281$	−2.05665	−0.122689	−0.0613447	−	0.998117i	$-0.519539\pi$
$281$	−2.05665	−0.122689	−0.0613447	+	0.998117i	$0.519539\pi$
$282$	−6.29671	−0.374964
$283$	−18.5326	−1.10165	−0.550825	−	0.834621i	$-0.685687\pi$
$283$	−18.5326	−1.10165	−0.550825	+	0.834621i	$0.685687\pi$
$284$	−1.62279	−0.0962948
$285$	18.3944	1.08959
$286$	−1.45413	−0.0859847
$287$	−6.15479	−0.363306
$288$	3.21904	0.189684
$289$	−11.7906	−0.693565
$290$	−6.59264	−0.387133
$291$	26.0430	1.52667
$292$	−1.00000	−0.0585206
$293$	−11.1394	−0.650772	−0.325386	−	0.945581i	$-0.605494\pi$
$293$	−11.1394	−0.650772	−0.325386	+	0.945581i	$0.605494\pi$
$294$	−0.355818	−0.0207517
$295$	−9.20833	−0.536130
$296$	−4.99108	−0.290101
$297$	0.546253	0.0316968
$298$	−13.5062	−0.782391
$299$	−2.00998	−0.116240
$300$	2.49380	0.143980
$301$	18.4609	1.06407
$302$	−11.0112	−0.633624
$303$	8.23085	0.472850
$304$	7.37603	0.423044
$305$	9.89307	0.566475
$306$	7.34718	0.420011
$307$	−8.43194	−0.481236	−0.240618	−	0.970620i	$-0.577350\pi$
$307$	−8.43194	−0.481236	−0.240618	+	0.970620i	$0.577350\pi$
$308$	2.61865	0.149211
$309$	−21.4244	−1.21879
$310$	0.701515	0.0398433
$311$	22.9011	1.29860	0.649302	−	0.760531i	$-0.275061\pi$
$311$	22.9011	1.29860	0.649302	+	0.760531i	$0.275061\pi$
$312$	−3.62632	−0.205300
$313$	4.51919	0.255440	0.127720	−	0.991810i	$-0.459234\pi$
$313$	4.51919	0.255440	0.127720	+	0.991810i	$0.459234\pi$
$314$	−13.3879	−0.755524
$315$	8.42954	0.474951
$316$	8.69804	0.489303
$317$	22.1293	1.24291	0.621453	−	0.783451i	$-0.286543\pi$
$317$	22.1293	1.24291	0.621453	+	0.783451i	$0.286543\pi$
$318$	−22.6930	−1.27256
$319$	−6.59264	−0.369117
$320$	1.00000	0.0559017
$321$	−24.4522	−1.36479
$322$	3.61964	0.201715
$323$	16.8351	0.936732
$324$	−8.29489	−0.460827
$325$	−1.45413	−0.0806608
$326$	15.1279	0.837859
$327$	42.5677	2.35400
$328$	−2.35037	−0.129777
$329$	−6.61194	−0.364528
$330$	2.49380	0.137279
$331$	−1.61487	−0.0887611	−0.0443805	−	0.999015i	$-0.514131\pi$
$331$	−1.61487	−0.0887611	−0.0443805	+	0.999015i	$0.514131\pi$
$332$	−13.8252	−0.758755
$333$	−16.0665	−0.880439
$334$	15.1301	0.827881
$335$	7.41564	0.405160
$336$	6.53039	0.356262
$337$	−17.7580	−0.967341	−0.483671	−	0.875250i	$-0.660697\pi$
$337$	−17.7580	−0.967341	−0.483671	+	0.875250i	$0.660697\pi$
$338$	−10.8855	−0.592093
$339$	3.15611	0.171416
$340$	2.28241	0.123781
$341$	0.701515	0.0379891
$342$	23.7438	1.28392
$343$	−18.7042	−1.00993
$344$	7.04979	0.380099
$345$	3.44707	0.185584
$346$	24.3796	1.31066
$347$	−25.7953	−1.38476	−0.692382	−	0.721531i	$-0.743439\pi$
$347$	−25.7953	−1.38476	−0.692382	+	0.721531i	$0.743439\pi$
$348$	−16.4407	−0.881316
$349$	−15.3997	−0.824326	−0.412163	−	0.911110i	$-0.635227\pi$
$349$	−15.3997	−0.824326	−0.412163	+	0.911110i	$0.635227\pi$
$350$	2.61865	0.139973
$351$	−0.794324	−0.0423979
$352$	1.00000	0.0533002
$353$	−9.27200	−0.493499	−0.246749	−	0.969079i	$-0.579362\pi$
$353$	−9.27200	−0.493499	−0.246749	+	0.969079i	$0.579362\pi$
$354$	−22.9637	−1.22051
$355$	−1.62279	−0.0861287
$356$	−7.40823	−0.392636
$357$	14.9050	0.788858
$358$	−6.34194	−0.335182
$359$	−5.02431	−0.265173	−0.132587	−	0.991171i	$-0.542328\pi$
$359$	−5.02431	−0.265173	−0.132587	+	0.991171i	$0.542328\pi$
$360$	3.21904	0.169659
$361$	35.4058	1.86347
$362$	13.6387	0.716833
$363$	2.49380	0.130891
$364$	−3.80786	−0.199586
$365$	−1.00000	−0.0523424
$366$	24.6713	1.28959
$367$	−30.1034	−1.57138	−0.785692	−	0.618618i	$-0.787693\pi$
$367$	−30.1034	−1.57138	−0.785692	+	0.618618i	$0.787693\pi$
$368$	1.38225	0.0720550
$369$	−7.56594	−0.393867
$370$	−4.99108	−0.259474
$371$	−23.8290	−1.23714
$372$	1.74944	0.0907041
$373$	−36.4262	−1.88608	−0.943040	−	0.332680i	$-0.892047\pi$
$373$	−36.4262	−1.88608	−0.943040	+	0.332680i	$0.892047\pi$
$374$	2.28241	0.118021
$375$	2.49380	0.128779
$376$	−2.52495	−0.130214
$377$	9.58659	0.493734
$378$	1.43044	0.0735741
$379$	26.6894	1.37094	0.685470	−	0.728101i	$-0.259597\pi$
$379$	26.6894	1.37094	0.685470	+	0.728101i	$0.259597\pi$
$380$	7.37603	0.378382
$381$	−35.0297	−1.79463
$382$	14.8694	0.760786
$383$	−32.5853	−1.66503	−0.832516	−	0.554001i	$-0.813100\pi$
$383$	−32.5853	−1.66503	−0.832516	+	0.554001i	$0.813100\pi$
$384$	2.49380	0.127261
$385$	2.61865	0.133459
$386$	9.59599	0.488423
$387$	22.6936	1.15358
$388$	10.4431	0.530168
$389$	22.4786	1.13971	0.569855	−	0.821745i	$-0.306999\pi$
$389$	22.4786	1.13971	0.569855	+	0.821745i	$0.306999\pi$
$390$	−3.62632	−0.183626
$391$	3.15487	0.159549
$392$	−0.142681	−0.00720648
$393$	−48.6190	−2.45250
$394$	7.84684	0.395318
$395$	8.69804	0.437646
$396$	3.21904	0.161763
$397$	12.4223	0.623456	0.311728	−	0.950171i	$-0.399092\pi$
$397$	12.4223	0.623456	0.311728	+	0.950171i	$0.399092\pi$
$398$	8.73315	0.437753
$399$	48.1683	2.41143
$400$	1.00000	0.0500000
$401$	−38.8097	−1.93806	−0.969032	−	0.246934i	$-0.920577\pi$
$401$	−38.8097	−1.93806	−0.969032	+	0.246934i	$0.920577\pi$
$402$	18.4931	0.922354
$403$	−1.02010	−0.0508146
$404$	3.30052	0.164207
$405$	−8.29489	−0.412176
$406$	−17.2638	−0.856789
$407$	−4.99108	−0.247399
$408$	5.69188	0.281790
$409$	−18.6146	−0.920433	−0.460216	−	0.887807i	$-0.652228\pi$
$409$	−18.6146	−0.920433	−0.460216	+	0.887807i	$0.652228\pi$
$410$	−2.35037	−0.116076
$411$	−2.46744	−0.121710
$412$	−8.59106	−0.423251
$413$	−24.1134	−1.18654
$414$	4.44954	0.218683
$415$	−13.8252	−0.678651
$416$	−1.45413	−0.0712948
$417$	−21.0137	−1.02905
$418$	7.37603	0.360773
$419$	−30.4617	−1.48815	−0.744077	−	0.668094i	$-0.767110\pi$
$419$	−30.4617	−1.48815	−0.744077	+	0.668094i	$0.767110\pi$
$420$	6.53039	0.318650
$421$	−3.10832	−0.151490	−0.0757450	−	0.997127i	$-0.524134\pi$
$421$	−3.10832	−0.151490	−0.0757450	+	0.997127i	$0.524134\pi$
$422$	−7.75485	−0.377500
$423$	−8.12791	−0.395193
$424$	−9.09974	−0.441923
$425$	2.28241	0.110713
$426$	−4.04691	−0.196074
$427$	25.9065	1.25370
$428$	−9.80520	−0.473952
$429$	−3.62632	−0.175080
$430$	7.04979	0.339971
$431$	−10.2368	−0.493089	−0.246545	−	0.969131i	$-0.579295\pi$
$431$	−10.2368	−0.493089	−0.246545	+	0.969131i	$0.579295\pi$
$432$	0.546253	0.0262816
$433$	10.5222	0.505666	0.252833	−	0.967510i	$-0.418638\pi$
$433$	10.5222	0.505666	0.252833	+	0.967510i	$0.418638\pi$
$434$	1.83702	0.0881798
$435$	−16.4407	−0.788273
$436$	17.0694	0.817477
$437$	10.1956	0.487719
$438$	−2.49380	−0.119158
$439$	−25.5247	−1.21823	−0.609114	−	0.793083i	$-0.708475\pi$
$439$	−25.5247	−1.21823	−0.609114	+	0.793083i	$0.708475\pi$
$440$	1.00000	0.0476731
$441$	−0.459296	−0.0218713
$442$	−3.31893	−0.157865
$443$	−7.89242	−0.374980	−0.187490	−	0.982267i	$-0.560035\pi$
$443$	−7.89242	−0.374980	−0.187490	+	0.982267i	$0.560035\pi$
$444$	−12.4468	−0.590697
$445$	−7.40823	−0.351184
$446$	21.5223	1.01911
$447$	−33.6817	−1.59309
$448$	2.61865	0.123720
$449$	18.8944	0.891682	0.445841	−	0.895112i	$-0.352905\pi$
$449$	18.8944	0.891682	0.445841	+	0.895112i	$0.352905\pi$
$450$	3.21904	0.151747
$451$	−2.35037	−0.110675
$452$	1.26558	0.0595279
$453$	−27.4598	−1.29017
$454$	11.0051	0.516495
$455$	−3.80786	−0.178515
$456$	18.3944	0.861395
$457$	25.0309	1.17089	0.585447	−	0.810711i	$-0.300919\pi$
$457$	25.0309	1.17089	0.585447	+	0.810711i	$0.300919\pi$
$458$	24.5929	1.14915
$459$	1.24677	0.0581944
$460$	1.38225	0.0644479
$461$	19.4195	0.904457	0.452228	−	0.891902i	$-0.350629\pi$
$461$	19.4195	0.904457	0.452228	+	0.891902i	$0.350629\pi$
$462$	6.53039	0.303821
$463$	26.8029	1.24564	0.622818	−	0.782367i	$-0.285988\pi$
$463$	26.8029	1.24564	0.622818	+	0.782367i	$0.285988\pi$
$464$	−6.59264	−0.306056
$465$	1.74944	0.0811282
$466$	−17.7343	−0.821527
$467$	−18.3839	−0.850703	−0.425352	−	0.905028i	$-0.639850\pi$
$467$	−18.3839	−0.850703	−0.425352	+	0.905028i	$0.639850\pi$
$468$	−4.68092	−0.216376
$469$	19.4190	0.896684
$470$	−2.52495	−0.116467
$471$	−33.3868	−1.53838
$472$	−9.20833	−0.423848
$473$	7.04979	0.324150
$474$	21.6912	0.996309
$475$	7.37603	0.338436
$476$	5.97683	0.273948
$477$	−29.2925	−1.34121
$478$	−9.06722	−0.414725
$479$	−11.0274	−0.503853	−0.251927	−	0.967746i	$-0.581064\pi$
$479$	−11.0274	−0.503853	−0.251927	+	0.967746i	$0.581064\pi$
$480$	2.49380	0.113826
$481$	7.25770	0.330923
$482$	−23.9756	−1.09206
$483$	9.02666	0.410727
$484$	1.00000	0.0454545
$485$	10.4431	0.474197
$486$	−22.3246	−1.01266
$487$	−35.7454	−1.61978	−0.809888	−	0.586584i	$-0.800472\pi$
$487$	−35.7454	−1.61978	−0.809888	+	0.586584i	$0.800472\pi$
$488$	9.89307	0.447838
$489$	37.7261	1.70603
$490$	−0.142681	−0.00644567
$491$	−1.78857	−0.0807170	−0.0403585	−	0.999185i	$-0.512850\pi$
$491$	−1.78857	−0.0807170	−0.0403585	+	0.999185i	$0.512850\pi$
$492$	−5.86135	−0.264250
$493$	−15.0471	−0.677689
$494$	−10.7257	−0.482574
$495$	3.21904	0.144685
$496$	0.701515	0.0314989
$497$	−4.24951	−0.190617
$498$	−34.4772	−1.54496
$499$	5.91331	0.264716	0.132358	−	0.991202i	$-0.457745\pi$
$499$	5.91331	0.264716	0.132358	+	0.991202i	$0.457745\pi$
$500$	1.00000	0.0447214
$501$	37.7314	1.68571
$502$	−5.25831	−0.234690
$503$	22.9401	1.02285	0.511425	−	0.859328i	$-0.329118\pi$
$503$	22.9401	1.02285	0.511425	+	0.859328i	$0.329118\pi$
$504$	8.42954	0.375482
$505$	3.30052	0.146871
$506$	1.38225	0.0614487
$507$	−27.1463	−1.20561
$508$	−14.0467	−0.623222
$509$	−5.82890	−0.258361	−0.129181	−	0.991621i	$-0.541235\pi$
$509$	−5.82890	−0.258361	−0.129181	+	0.991621i	$0.541235\pi$
$510$	5.69188	0.252041
$511$	−2.61865	−0.115842
$512$	1.00000	0.0441942
$513$	4.02918	0.177892
$514$	22.9131	1.01065
$515$	−8.59106	−0.378567
$516$	17.5808	0.773950
$517$	−2.52495	−0.111047
$518$	−13.0699	−0.574258
$519$	60.7979	2.66873
$520$	−1.45413	−0.0637680
$521$	−5.43706	−0.238202	−0.119101	−	0.992882i	$-0.538001\pi$
$521$	−5.43706	−0.238202	−0.119101	+	0.992882i	$0.538001\pi$
$522$	−21.2220	−0.928862
$523$	−11.0970	−0.485239	−0.242620	−	0.970121i	$-0.578007\pi$
$523$	−11.0970	−0.485239	−0.242620	+	0.970121i	$0.578007\pi$
$524$	−19.4959	−0.851683
$525$	6.53039	0.285010
$526$	25.1897	1.09832
$527$	1.60114	0.0697470
$528$	2.49380	0.108529
$529$	−21.0894	−0.916929
$530$	−9.09974	−0.395268
$531$	−29.6420	−1.28635
$532$	19.3152	0.837422
$533$	3.41775	0.148039
$534$	−18.4747	−0.799477
$535$	−9.80520	−0.423916
$536$	7.41564	0.320307
$537$	−15.8155	−0.682491
$538$	15.3013	0.659687
$539$	−0.142681	−0.00614571
$540$	0.546253	0.0235070
$541$	−0.399097	−0.0171585	−0.00857926	−	0.999963i	$-0.502731\pi$
$541$	−0.399097	−0.0171585	−0.00857926	+	0.999963i	$0.502731\pi$
$542$	14.1112	0.606128
$543$	34.0121	1.45960
$544$	2.28241	0.0978576
$545$	17.0694	0.731174
$546$	−9.49606	−0.406394
$547$	19.6299	0.839315	0.419658	−	0.907682i	$-0.362150\pi$
$547$	19.6299	0.839315	0.419658	+	0.907682i	$0.362150\pi$
$548$	−0.989430	−0.0422664
$549$	31.8462	1.35916
$550$	1.00000	0.0426401
$551$	−48.6276	−2.07160
$552$	3.44707	0.146717
$553$	22.7771	0.968581
$554$	7.85182	0.333592
$555$	−12.4468	−0.528336
$556$	−8.42637	−0.357358
$557$	13.6952	0.580284	0.290142	−	0.956984i	$-0.406298\pi$
$557$	13.6952	0.580284	0.290142	+	0.956984i	$0.406298\pi$
$558$	2.25821	0.0955975
$559$	−10.2513	−0.433585
$560$	2.61865	0.110658
$561$	5.69188	0.240311
$562$	−2.05665	−0.0867545
$563$	−1.50631	−0.0634834	−0.0317417	−	0.999496i	$-0.510105\pi$
$563$	−1.50631	−0.0634834	−0.0317417	+	0.999496i	$0.510105\pi$
$564$	−6.29671	−0.265139
$565$	1.26558	0.0532434
$566$	−18.5326	−0.778984
$567$	−21.7214	−0.912213
$568$	−1.62279	−0.0680907
$569$	−0.213790	−0.00896254	−0.00448127	−	0.999990i	$-0.501426\pi$
$569$	−0.213790	−0.00896254	−0.00448127	+	0.999990i	$0.501426\pi$
$570$	18.3944	0.770455
$571$	41.8176	1.75001	0.875006	−	0.484111i	$-0.160857\pi$
$571$	41.8176	1.75001	0.875006	+	0.484111i	$0.160857\pi$
$572$	−1.45413	−0.0608004
$573$	37.0814	1.54910
$574$	−6.15479	−0.256896
$575$	1.38225	0.0576440
$576$	3.21904	0.134127
$577$	43.5069	1.81122	0.905608	−	0.424116i	$-0.139415\pi$
$577$	43.5069	1.81122	0.905608	+	0.424116i	$0.139415\pi$
$578$	−11.7906	−0.490424
$579$	23.9305	0.994517
$580$	−6.59264	−0.273745
$581$	−36.2033	−1.50196
$582$	26.0430	1.07952
$583$	−9.09974	−0.376873
$584$	−1.00000	−0.0413803
$585$	−4.68092	−0.193532
$586$	−11.1394	−0.460165
$587$	18.1407	0.748745	0.374373	−	0.927278i	$-0.377858\pi$
$587$	18.1407	0.748745	0.374373	+	0.927278i	$0.377858\pi$
$588$	−0.355818	−0.0146737
$589$	5.17439	0.213207
$590$	−9.20833	−0.379101
$591$	19.5685	0.804939
$592$	−4.99108	−0.205132
$593$	−7.30512	−0.299985	−0.149993	−	0.988687i	$-0.547925\pi$
$593$	−7.30512	−0.299985	−0.149993	+	0.988687i	$0.547925\pi$
$594$	0.546253	0.0224130
$595$	5.97683	0.245026
$596$	−13.5062	−0.553234
$597$	21.7787	0.891344
$598$	−2.00998	−0.0821943
$599$	17.5767	0.718165	0.359082	−	0.933306i	$-0.383090\pi$
$599$	17.5767	0.718165	0.359082	+	0.933306i	$0.383090\pi$
$600$	2.49380	0.101809
$601$	−1.24214	−0.0506680	−0.0253340	−	0.999679i	$-0.508065\pi$
$601$	−1.24214	−0.0506680	−0.0253340	+	0.999679i	$0.508065\pi$
$602$	18.4609	0.752411
$603$	23.8713	0.972114
$604$	−11.0112	−0.448040
$605$	1.00000	0.0406558
$606$	8.23085	0.334355
$607$	−3.64152	−0.147805	−0.0739024	−	0.997265i	$-0.523545\pi$
$607$	−3.64152	−0.147805	−0.0739024	+	0.997265i	$0.523545\pi$
$608$	7.37603	0.299138
$609$	−43.0525	−1.74458
$610$	9.89307	0.400559
$611$	3.67161	0.148537
$612$	7.34718	0.296992
$613$	24.1302	0.974610	0.487305	−	0.873232i	$-0.337980\pi$
$613$	24.1302	0.974610	0.487305	+	0.873232i	$0.337980\pi$
$614$	−8.43194	−0.340286
$615$	−5.86135	−0.236353
$616$	2.61865	0.105508
$617$	37.7153	1.51836	0.759180	−	0.650881i	$-0.225600\pi$
$617$	37.7153	1.51836	0.759180	+	0.650881i	$0.225600\pi$
$618$	−21.4244	−0.861815
$619$	8.29292	0.333321	0.166660	−	0.986014i	$-0.446702\pi$
$619$	8.29292	0.333321	0.166660	+	0.986014i	$0.446702\pi$
$620$	0.701515	0.0281735
$621$	0.755060	0.0302995
$622$	22.9011	0.918251
$623$	−19.3996	−0.777227
$624$	−3.62632	−0.145169
$625$	1.00000	0.0400000
$626$	4.51919	0.180623
$627$	18.3944	0.734600
$628$	−13.3879	−0.534236
$629$	−11.3917	−0.454217
$630$	8.42954	0.335841
$631$	2.45580	0.0977639	0.0488819	−	0.998805i	$-0.484434\pi$
$631$	2.45580	0.0977639	0.0488819	+	0.998805i	$0.484434\pi$
$632$	8.69804	0.345989
$633$	−19.3391	−0.768658
$634$	22.1293	0.878867
$635$	−14.0467	−0.557427
$636$	−22.6930	−0.899834
$637$	0.207477	0.00822055
$638$	−6.59264	−0.261005
$639$	−5.22383	−0.206651
$640$	1.00000	0.0395285
$641$	35.4132	1.39874	0.699369	−	0.714761i	$-0.253464\pi$
$641$	35.4132	1.39874	0.699369	+	0.714761i	$0.253464\pi$
$642$	−24.4522	−0.965052
$643$	−2.93407	−0.115708	−0.0578542	−	0.998325i	$-0.518426\pi$
$643$	−2.93407	−0.115708	−0.0578542	+	0.998325i	$0.518426\pi$
$644$	3.61964	0.142634
$645$	17.5808	0.692242
$646$	16.8351	0.662370
$647$	38.7865	1.52485	0.762427	−	0.647075i	$-0.224008\pi$
$647$	38.7865	1.52485	0.762427	+	0.647075i	$0.224008\pi$
$648$	−8.29489	−0.325854
$649$	−9.20833	−0.361459
$650$	−1.45413	−0.0570358
$651$	4.58116	0.179550
$652$	15.1279	0.592456
$653$	4.38496	0.171597	0.0857983	−	0.996313i	$-0.472656\pi$
$653$	4.38496	0.171597	0.0857983	+	0.996313i	$0.472656\pi$
$654$	42.5677	1.66453
$655$	−19.4959	−0.761769
$656$	−2.35037	−0.0917665
$657$	−3.21904	−0.125587
$658$	−6.61194	−0.257760
$659$	28.8936	1.12553	0.562767	−	0.826616i	$-0.309737\pi$
$659$	28.8936	1.12553	0.562767	+	0.826616i	$0.309737\pi$
$660$	2.49380	0.0970711
$661$	−29.8748	−1.16199	−0.580997	−	0.813906i	$-0.697337\pi$
$661$	−29.8748	−1.16199	−0.580997	+	0.813906i	$0.697337\pi$
$662$	−1.61487	−0.0627636
$663$	−8.27675	−0.321442
$664$	−13.8252	−0.536521
$665$	19.3152	0.749013
$666$	−16.0665	−0.622565
$667$	−9.11271	−0.352846
$668$	15.1301	0.585400
$669$	53.6723	2.07509
$670$	7.41564	0.286491
$671$	9.89307	0.381918
$672$	6.53039	0.251915
$673$	−49.7661	−1.91834	−0.959171	−	0.282828i	$-0.908727\pi$
$673$	−49.7661	−1.91834	−0.959171	+	0.282828i	$0.908727\pi$
$674$	−17.7580	−0.684013
$675$	0.546253	0.0210253
$676$	−10.8855	−0.418673
$677$	−46.9475	−1.80434	−0.902170	−	0.431381i	$-0.858026\pi$
$677$	−46.9475	−1.80434	−0.902170	+	0.431381i	$0.858026\pi$
$678$	3.15611	0.121210
$679$	27.3468	1.04947
$680$	2.28241	0.0875265
$681$	27.4446	1.05168
$682$	0.701515	0.0268624
$683$	−45.7065	−1.74891	−0.874455	−	0.485106i	$-0.838781\pi$
$683$	−45.7065	−1.74891	−0.874455	+	0.485106i	$0.838781\pi$
$684$	23.7438	0.907866
$685$	−0.989430	−0.0378042
$686$	−18.7042	−0.714129
$687$	61.3298	2.33988
$688$	7.04979	0.268771
$689$	13.2322	0.504108
$690$	3.44707	0.131228
$691$	19.2859	0.733671	0.366835	−	0.930286i	$-0.380441\pi$
$691$	19.2859	0.733671	0.366835	+	0.930286i	$0.380441\pi$
$692$	24.3796	0.926774
$693$	8.42954	0.320212
$694$	−25.7953	−0.979176
$695$	−8.42637	−0.319631
$696$	−16.4407	−0.623185
$697$	−5.36451	−0.203195
$698$	−15.3997	−0.582887
$699$	−44.2259	−1.67278
$700$	2.61865	0.0989756
$701$	14.8915	0.562445	0.281223	−	0.959643i	$-0.409260\pi$
$701$	14.8915	0.562445	0.281223	+	0.959643i	$0.409260\pi$
$702$	−0.794324	−0.0299798
$703$	−36.8144	−1.38848
$704$	1.00000	0.0376889
$705$	−6.29671	−0.237148
$706$	−9.27200	−0.348956
$707$	8.64291	0.325050
$708$	−22.9637	−0.863030
$709$	−1.60621	−0.0603223	−0.0301612	−	0.999545i	$-0.509602\pi$
$709$	−1.60621	−0.0603223	−0.0301612	+	0.999545i	$0.509602\pi$
$710$	−1.62279	−0.0609022
$711$	27.9994	1.05006
$712$	−7.40823	−0.277635
$713$	0.969672	0.0363145
$714$	14.9050	0.557807
$715$	−1.45413	−0.0543815
$716$	−6.34194	−0.237010
$717$	−22.6118	−0.844455
$718$	−5.02431	−0.187506
$719$	8.89675	0.331793	0.165896	−	0.986143i	$-0.446948\pi$
$719$	8.89675	0.331793	0.165896	+	0.986143i	$0.446948\pi$
$720$	3.21904	0.119967
$721$	−22.4970	−0.837830
$722$	35.4058	1.31767
$723$	−59.7903	−2.22363
$724$	13.6387	0.506877
$725$	−6.59264	−0.244845
$726$	2.49380	0.0925536
$727$	−7.81091	−0.289691	−0.144845	−	0.989454i	$-0.546268\pi$
$727$	−7.81091	−0.289691	−0.144845	+	0.989454i	$0.546268\pi$
$728$	−3.80786	−0.141129
$729$	−30.7883	−1.14031
$730$	−1.00000	−0.0370117
$731$	16.0905	0.595129
$732$	24.6713	0.911879
$733$	−37.2924	−1.37743	−0.688713	−	0.725034i	$-0.741824\pi$
$733$	−37.2924	−1.37743	−0.688713	+	0.725034i	$0.741824\pi$
$734$	−30.1034	−1.11114
$735$	−0.355818	−0.0131245
$736$	1.38225	0.0509506
$737$	7.41564	0.273159
$738$	−7.56594	−0.278506
$739$	29.8089	1.09654	0.548270	−	0.836301i	$-0.315287\pi$
$739$	29.8089	1.09654	0.548270	+	0.836301i	$0.315287\pi$
$740$	−4.99108	−0.183476
$741$	−26.7478	−0.982607
$742$	−23.8290	−0.874791
$743$	−51.0102	−1.87138	−0.935692	−	0.352818i	$-0.885224\pi$
$743$	−51.0102	−1.87138	−0.935692	+	0.352818i	$0.885224\pi$
$744$	1.74944	0.0641375
$745$	−13.5062	−0.494827
$746$	−36.4262	−1.33366
$747$	−44.5038	−1.62831
$748$	2.28241	0.0834532
$749$	−25.6764	−0.938194
$750$	2.49380	0.0910607
$751$	5.45774	0.199156	0.0995779	−	0.995030i	$-0.468251\pi$
$751$	5.45774	0.199156	0.0995779	+	0.995030i	$0.468251\pi$
$752$	−2.52495	−0.0920753
$753$	−13.1132	−0.477871
$754$	9.58659	0.349123
$755$	−11.0112	−0.400739
$756$	1.43044	0.0520247
$757$	−27.1033	−0.985085	−0.492543	−	0.870288i	$-0.663932\pi$
$757$	−27.1033	−0.985085	−0.492543	+	0.870288i	$0.663932\pi$
$758$	26.6894	0.969402
$759$	3.44707	0.125121
$760$	7.37603	0.267557
$761$	41.6463	1.50968	0.754838	−	0.655911i	$-0.227716\pi$
$761$	41.6463	1.50968	0.754838	+	0.655911i	$0.227716\pi$
$762$	−35.0297	−1.26899
$763$	44.6988	1.61821
$764$	14.8694	0.537957
$765$	7.34718	0.265638
$766$	−32.5853	−1.17735
$767$	13.3901	0.483490
$768$	2.49380	0.0899873
$769$	−36.1223	−1.30260	−0.651301	−	0.758820i	$-0.725776\pi$
$769$	−36.1223	−1.30260	−0.651301	+	0.758820i	$0.725776\pi$
$770$	2.61865	0.0943695
$771$	57.1407	2.05787
$772$	9.59599	0.345367
$773$	−19.3705	−0.696709	−0.348355	−	0.937363i	$-0.613260\pi$
$773$	−19.3705	−0.696709	−0.348355	+	0.937363i	$0.613260\pi$
$774$	22.6936	0.815704
$775$	0.701515	0.0251991
$776$	10.4431	0.374886
$777$	−32.5937	−1.16929
$778$	22.4786	0.805897
$779$	−17.3364	−0.621141
$780$	−3.62632	−0.129843
$781$	−1.62279	−0.0580679
$782$	3.15487	0.112818
$783$	−3.60125	−0.128698
$784$	−0.142681	−0.00509575
$785$	−13.3879	−0.477835
$786$	−48.6190	−1.73418
$787$	−2.10694	−0.0751041	−0.0375521	−	0.999295i	$-0.511956\pi$
$787$	−2.10694	−0.0751041	−0.0375521	+	0.999295i	$0.511956\pi$
$788$	7.84684	0.279532
$789$	62.8182	2.23639
$790$	8.69804	0.309462
$791$	3.31411	0.117836
$792$	3.21904	0.114384
$793$	−14.3858	−0.510856
$794$	12.4223	0.440850
$795$	−22.6930	−0.804836
$796$	8.73315	0.309538
$797$	7.66837	0.271627	0.135814	−	0.990734i	$-0.456635\pi$
$797$	7.66837	0.271627	0.135814	+	0.990734i	$0.456635\pi$
$798$	48.1683	1.70514
$799$	−5.76296	−0.203879
$800$	1.00000	0.0353553
$801$	−23.8474	−0.842607
$802$	−38.8097	−1.37042
$803$	−1.00000	−0.0352892
$804$	18.4931	0.652203
$805$	3.61964	0.127575
$806$	−1.02010	−0.0359313
$807$	38.1585	1.34324
$808$	3.30052	0.116112
$809$	−7.57920	−0.266470	−0.133235	−	0.991084i	$-0.542537\pi$
$809$	−7.57920	−0.266470	−0.133235	+	0.991084i	$0.542537\pi$
$810$	−8.29489	−0.291453
$811$	−4.58155	−0.160880	−0.0804400	−	0.996759i	$-0.525633\pi$
$811$	−4.58155	−0.160880	−0.0804400	+	0.996759i	$0.525633\pi$
$812$	−17.2638	−0.605841
$813$	35.1905	1.23419
$814$	−4.99108	−0.174937
$815$	15.1279	0.529909
$816$	5.69188	0.199256
$817$	51.9994	1.81923
$818$	−18.6146	−0.650844
$819$	−12.2577	−0.428318
$820$	−2.35037	−0.0820784
$821$	25.7597	0.899021	0.449511	−	0.893275i	$-0.351598\pi$
$821$	25.7597	0.899021	0.449511	+	0.893275i	$0.351598\pi$
$822$	−2.46744	−0.0860619
$823$	−46.6869	−1.62740	−0.813701	−	0.581284i	$-0.802551\pi$
$823$	−46.6869	−1.62740	−0.813701	+	0.581284i	$0.802551\pi$
$824$	−8.59106	−0.299284
$825$	2.49380	0.0868230
$826$	−24.1134	−0.839012
$827$	3.56445	0.123948	0.0619741	−	0.998078i	$-0.480260\pi$
$827$	3.56445	0.123948	0.0619741	+	0.998078i	$0.480260\pi$
$828$	4.44954	0.154632
$829$	53.9440	1.87355	0.936777	−	0.349928i	$-0.113794\pi$
$829$	53.9440	1.87355	0.936777	+	0.349928i	$0.113794\pi$
$830$	−13.8252	−0.479879
$831$	19.5809	0.679253
$832$	−1.45413	−0.0504130
$833$	−0.325657	−0.0112833
$834$	−21.0137	−0.727645
$835$	15.1301	0.523598
$836$	7.37603	0.255105
$837$	0.383204	0.0132455
$838$	−30.4617	−1.05228
$839$	−52.8146	−1.82336	−0.911681	−	0.410899i	$-0.865215\pi$
$839$	−52.8146	−1.82336	−0.911681	+	0.410899i	$0.865215\pi$
$840$	6.53039	0.225320
$841$	14.4630	0.498723
$842$	−3.10832	−0.107120
$843$	−5.12887	−0.176648
$844$	−7.75485	−0.266933
$845$	−10.8855	−0.374472
$846$	−8.12791	−0.279443
$847$	2.61865	0.0899778
$848$	−9.09974	−0.312487
$849$	−46.2167	−1.58615
$850$	2.28241	0.0782861
$851$	−6.89894	−0.236493
$852$	−4.04691	−0.138645
$853$	−30.5722	−1.04677	−0.523387	−	0.852095i	$-0.675332\pi$
$853$	−30.5722	−1.04677	−0.523387	+	0.852095i	$0.675332\pi$
$854$	25.9065	0.886501
$855$	23.7438	0.812020
$856$	−9.80520	−0.335135
$857$	15.1622	0.517930	0.258965	−	0.965887i	$-0.416619\pi$
$857$	15.1622	0.517930	0.258965	+	0.965887i	$0.416619\pi$
$858$	−3.62632	−0.123801
$859$	12.8377	0.438016	0.219008	−	0.975723i	$-0.429718\pi$
$859$	12.8377	0.438016	0.219008	+	0.975723i	$0.429718\pi$
$860$	7.04979	0.240396
$861$	−15.3488	−0.523086
$862$	−10.2368	−0.348667
$863$	57.3502	1.95222	0.976112	−	0.217269i	$-0.0697148\pi$
$863$	57.3502	1.95222	0.976112	+	0.217269i	$0.0697148\pi$
$864$	0.546253	0.0185839
$865$	24.3796	0.828932
$866$	10.5222	0.357560
$867$	−29.4034	−0.998592
$868$	1.83702	0.0623525
$869$	8.69804	0.295061
$870$	−16.4407	−0.557393
$871$	−10.7833	−0.365379
$872$	17.0694	0.578044
$873$	33.6168	1.13776
$874$	10.1956	0.344870
$875$	2.61865	0.0885265
$876$	−2.49380	−0.0842577
$877$	−23.5959	−0.796777	−0.398388	−	0.917217i	$-0.630430\pi$
$877$	−23.5959	−0.796777	−0.398388	+	0.917217i	$0.630430\pi$
$878$	−25.5247	−0.861417
$879$	−27.7795	−0.936979
$880$	1.00000	0.0337100
$881$	−24.9440	−0.840385	−0.420193	−	0.907435i	$-0.638038\pi$
$881$	−24.9440	−0.840385	−0.420193	+	0.907435i	$0.638038\pi$
$882$	−0.459296	−0.0154653
$883$	−52.2271	−1.75758	−0.878791	−	0.477207i	$-0.841649\pi$
$883$	−52.2271	−1.75758	−0.878791	+	0.477207i	$0.841649\pi$
$884$	−3.31893	−0.111628
$885$	−22.9637	−0.771918
$886$	−7.89242	−0.265151
$887$	−7.65508	−0.257032	−0.128516	−	0.991707i	$-0.541021\pi$
$887$	−7.65508	−0.257032	−0.128516	+	0.991707i	$0.541021\pi$
$888$	−12.4468	−0.417686
$889$	−36.7834	−1.23368
$890$	−7.40823	−0.248325
$891$	−8.29489	−0.277889
$892$	21.5223	0.720619
$893$	−18.6241	−0.623231
$894$	−33.6817	−1.12648
$895$	−6.34194	−0.211988
$896$	2.61865	0.0874829
$897$	−5.01250	−0.167362
$898$	18.8944	0.630515
$899$	−4.62484	−0.154247
$900$	3.21904	0.107301
$901$	−20.7694	−0.691928
$902$	−2.35037	−0.0782587
$903$	46.0378	1.53204
$904$	1.26558	0.0420926
$905$	13.6387	0.453365
$906$	−27.4598	−0.912290
$907$	−0.217161	−0.00721072	−0.00360536	−	0.999994i	$-0.501148\pi$
$907$	−0.217161	−0.00721072	−0.00360536	+	0.999994i	$0.501148\pi$
$908$	11.0051	0.365217
$909$	10.6245	0.352393
$910$	−3.80786	−0.126229
$911$	31.4311	1.04136	0.520680	−	0.853752i	$-0.325679\pi$
$911$	31.4311	1.04136	0.520680	+	0.853752i	$0.325679\pi$
$912$	18.3944	0.609098
$913$	−13.8252	−0.457546
$914$	25.0309	0.827947
$915$	24.6713	0.815609
$916$	24.5929	0.812572
$917$	−51.0530	−1.68592
$918$	1.24677	0.0411496
$919$	26.9304	0.888351	0.444176	−	0.895940i	$-0.353497\pi$
$919$	26.9304	0.888351	0.444176	+	0.895940i	$0.353497\pi$
$920$	1.38225	0.0455716
$921$	−21.0276	−0.692883
$922$	19.4195	0.639547
$923$	2.35975	0.0776722
$924$	6.53039	0.214834
$925$	−4.99108	−0.164106
$926$	26.8029	0.880797
$927$	−27.6550	−0.908309
$928$	−6.59264	−0.216414
$929$	−56.9834	−1.86956	−0.934782	−	0.355221i	$-0.884405\pi$
$929$	−56.9834	−1.86956	−0.934782	+	0.355221i	$0.884405\pi$
$930$	1.74944	0.0573663
$931$	−1.05242	−0.0344917
$932$	−17.7343	−0.580907
$933$	57.1108	1.86972
$934$	−18.3839	−0.601538
$935$	2.28241	0.0746428
$936$	−4.68092	−0.153001
$937$	49.4666	1.61600	0.808001	−	0.589181i	$-0.200550\pi$
$937$	49.4666	1.61600	0.808001	+	0.589181i	$0.200550\pi$
$938$	19.4190	0.634051
$939$	11.2700	0.367782
$940$	−2.52495	−0.0823546
$941$	−14.2398	−0.464205	−0.232103	−	0.972691i	$-0.574561\pi$
$941$	−14.2398	−0.464205	−0.232103	+	0.972691i	$0.574561\pi$
$942$	−33.3868	−1.08780
$943$	−3.24881	−0.105796
$944$	−9.20833	−0.299706
$945$	1.43044	0.0465323
$946$	7.04979	0.229208
$947$	15.2172	0.494494	0.247247	−	0.968953i	$-0.420474\pi$
$947$	15.2172	0.494494	0.247247	+	0.968953i	$0.420474\pi$
$948$	21.6912	0.704497
$949$	1.45413	0.0472032
$950$	7.37603	0.239310
$951$	55.1861	1.78953
$952$	5.97683	0.193710
$953$	−43.8579	−1.42070	−0.710348	−	0.703850i	$-0.751463\pi$
$953$	−43.8579	−1.42070	−0.710348	+	0.703850i	$0.751463\pi$
$954$	−29.2925	−0.948379
$955$	14.8694	0.481164
$956$	−9.06722	−0.293255
$957$	−16.4407	−0.531454
$958$	−11.0274	−0.356278
$959$	−2.59097	−0.0836668
$960$	2.49380	0.0804871
$961$	−30.5079	−0.984125
$962$	7.25770	0.233998
$963$	−31.5634	−1.01712
$964$	−23.9756	−0.772202
$965$	9.59599	0.308906
$966$	9.02666	0.290428
$967$	12.9825	0.417489	0.208744	−	0.977970i	$-0.433062\pi$
$967$	12.9825	0.417489	0.208744	+	0.977970i	$0.433062\pi$
$968$	1.00000	0.0321412
$969$	41.9835	1.34870
$970$	10.4431	0.335308
$971$	−62.1062	−1.99308	−0.996541	−	0.0830996i	$-0.973518\pi$
$971$	−62.1062	−1.99308	−0.996541	+	0.0830996i	$0.973518\pi$
$972$	−22.3246	−0.716060
$973$	−22.0657	−0.707394
$974$	−35.7454	−1.14536
$975$	−3.62632	−0.116135
$976$	9.89307	0.316669
$977$	−17.4541	−0.558407	−0.279203	−	0.960232i	$-0.590070\pi$
$977$	−17.4541	−0.558407	−0.279203	+	0.960232i	$0.590070\pi$
$978$	37.7261	1.20635
$979$	−7.40823	−0.236768
$980$	−0.142681	−0.00455778
$981$	54.9472	1.75433
$982$	−1.78857	−0.0570755
$983$	−60.1619	−1.91887	−0.959434	−	0.281933i	$-0.909024\pi$
$983$	−60.1619	−1.91887	−0.959434	+	0.281933i	$0.909024\pi$
$984$	−5.86135	−0.186853
$985$	7.84684	0.250021
$986$	−15.0471	−0.479198
$987$	−16.4889	−0.524847
$988$	−10.7257	−0.341231
$989$	9.74460	0.309860
$990$	3.21904	0.102308
$991$	46.8163	1.48717	0.743585	−	0.668641i	$-0.233124\pi$
$991$	46.8163	1.48717	0.743585	+	0.668641i	$0.233124\pi$
$992$	0.701515	0.0222731
$993$	−4.02716	−0.127798
$994$	−4.24951	−0.134786
$995$	8.73315	0.276859
$996$	−34.4772	−1.09245
$997$	54.0814	1.71277	0.856387	−	0.516335i	$-0.172704\pi$
$997$	54.0814	1.71277	0.856387	+	0.516335i	$0.172704\pi$
$998$	5.91331	0.187183
$999$	−2.72639	−0.0862592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bl.1.15	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bl.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.49380 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.49380 q^{6} +2.61865 q^{7} +1.00000 q^{8} +3.21904 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.49380 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.49380 q^{6} +2.61865 q^{7} +1.00000 q^{8} +3.21904 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.49380 q^{12} -1.45413 q^{13} +2.61865 q^{14} +2.49380 q^{15} +1.00000 q^{16} +2.28241 q^{17} +3.21904 q^{18} +7.37603 q^{19} +1.00000 q^{20} +6.53039 q^{21} +1.00000 q^{22} +1.38225 q^{23} +2.49380 q^{24} +1.00000 q^{25} -1.45413 q^{26} +0.546253 q^{27} +2.61865 q^{28} -6.59264 q^{29} +2.49380 q^{30} +0.701515 q^{31} +1.00000 q^{32} +2.49380 q^{33} +2.28241 q^{34} +2.61865 q^{35} +3.21904 q^{36} -4.99108 q^{37} +7.37603 q^{38} -3.62632 q^{39} +1.00000 q^{40} -2.35037 q^{41} +6.53039 q^{42} +7.04979 q^{43} +1.00000 q^{44} +3.21904 q^{45} +1.38225 q^{46} -2.52495 q^{47} +2.49380 q^{48} -0.142681 q^{49} +1.00000 q^{50} +5.69188 q^{51} -1.45413 q^{52} -9.09974 q^{53} +0.546253 q^{54} +1.00000 q^{55} +2.61865 q^{56} +18.3944 q^{57} -6.59264 q^{58} -9.20833 q^{59} +2.49380 q^{60} +9.89307 q^{61} +0.701515 q^{62} +8.42954 q^{63} +1.00000 q^{64} -1.45413 q^{65} +2.49380 q^{66} +7.41564 q^{67} +2.28241 q^{68} +3.44707 q^{69} +2.61865 q^{70} -1.62279 q^{71} +3.21904 q^{72} -1.00000 q^{73} -4.99108 q^{74} +2.49380 q^{75} +7.37603 q^{76} +2.61865 q^{77} -3.62632 q^{78} +8.69804 q^{79} +1.00000 q^{80} -8.29489 q^{81} -2.35037 q^{82} -13.8252 q^{83} +6.53039 q^{84} +2.28241 q^{85} +7.04979 q^{86} -16.4407 q^{87} +1.00000 q^{88} -7.40823 q^{89} +3.21904 q^{90} -3.80786 q^{91} +1.38225 q^{92} +1.74944 q^{93} -2.52495 q^{94} +7.37603 q^{95} +2.49380 q^{96} +10.4431 q^{97} -0.142681 q^{98} +3.21904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) \) 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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