LMFDB - Embedded newform 8030.2.a.bl.1.14

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			1.14
Root			$-1.34302$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.34302 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.34302 q^{6} +2.12832 q^{7} +1.00000 q^{8} +2.48975 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.34302 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.34302 q^{6} +2.12832 q^{7} +1.00000 q^{8} +2.48975 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.34302 q^{12} -2.91503 q^{13} +2.12832 q^{14} +2.34302 q^{15} +1.00000 q^{16} +0.717368 q^{17} +2.48975 q^{18} +3.90206 q^{19} +1.00000 q^{20} +4.98669 q^{21} +1.00000 q^{22} +3.66693 q^{23} +2.34302 q^{24} +1.00000 q^{25} -2.91503 q^{26} -1.19552 q^{27} +2.12832 q^{28} +8.49265 q^{29} +2.34302 q^{30} +1.73527 q^{31} +1.00000 q^{32} +2.34302 q^{33} +0.717368 q^{34} +2.12832 q^{35} +2.48975 q^{36} -2.79824 q^{37} +3.90206 q^{38} -6.82999 q^{39} +1.00000 q^{40} +7.67046 q^{41} +4.98669 q^{42} -10.2024 q^{43} +1.00000 q^{44} +2.48975 q^{45} +3.66693 q^{46} +0.439238 q^{47} +2.34302 q^{48} -2.47027 q^{49} +1.00000 q^{50} +1.68081 q^{51} -2.91503 q^{52} +3.99308 q^{53} -1.19552 q^{54} +1.00000 q^{55} +2.12832 q^{56} +9.14261 q^{57} +8.49265 q^{58} -4.43115 q^{59} +2.34302 q^{60} -15.2018 q^{61} +1.73527 q^{62} +5.29898 q^{63} +1.00000 q^{64} -2.91503 q^{65} +2.34302 q^{66} -7.62212 q^{67} +0.717368 q^{68} +8.59170 q^{69} +2.12832 q^{70} +9.77501 q^{71} +2.48975 q^{72} -1.00000 q^{73} -2.79824 q^{74} +2.34302 q^{75} +3.90206 q^{76} +2.12832 q^{77} -6.82999 q^{78} -4.63557 q^{79} +1.00000 q^{80} -10.2704 q^{81} +7.67046 q^{82} +7.03300 q^{83} +4.98669 q^{84} +0.717368 q^{85} -10.2024 q^{86} +19.8985 q^{87} +1.00000 q^{88} +1.63889 q^{89} +2.48975 q^{90} -6.20411 q^{91} +3.66693 q^{92} +4.06578 q^{93} +0.439238 q^{94} +3.90206 q^{95} +2.34302 q^{96} -8.04281 q^{97} -2.47027 q^{98} +2.48975 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.34302	1.35274	0.676372	−	0.736560i	$-0.263551\pi$
$3$	2.34302	1.35274	0.676372	+	0.736560i	$0.263551\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.34302	0.956535
$7$	2.12832	0.804428	0.402214	−	0.915546i	$-0.368241\pi$
$7$	2.12832	0.804428	0.402214	+	0.915546i	$0.368241\pi$
$8$	1.00000	0.353553
$9$	2.48975	0.829918
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.34302	0.676372
$13$	−2.91503	−0.808485	−0.404242	−	0.914652i	$-0.632465\pi$
$13$	−2.91503	−0.808485	−0.404242	+	0.914652i	$0.632465\pi$
$14$	2.12832	0.568817
$15$	2.34302	0.604966
$16$	1.00000	0.250000
$17$	0.717368	0.173987	0.0869937	−	0.996209i	$-0.472274\pi$
$17$	0.717368	0.173987	0.0869937	+	0.996209i	$0.472274\pi$
$18$	2.48975	0.586840
$19$	3.90206	0.895194	0.447597	−	0.894235i	$-0.352280\pi$
$19$	3.90206	0.895194	0.447597	+	0.894235i	$0.352280\pi$
$20$	1.00000	0.223607
$21$	4.98669	1.08819
$22$	1.00000	0.213201
$23$	3.66693	0.764608	0.382304	−	0.924037i	$-0.375131\pi$
$23$	3.66693	0.764608	0.382304	+	0.924037i	$0.375131\pi$
$24$	2.34302	0.478267
$25$	1.00000	0.200000
$26$	−2.91503	−0.571685
$27$	−1.19552	−0.230078
$28$	2.12832	0.402214
$29$	8.49265	1.57705	0.788523	−	0.615006i	$-0.210846\pi$
$29$	8.49265	1.57705	0.788523	+	0.615006i	$0.210846\pi$
$30$	2.34302	0.427775
$31$	1.73527	0.311664	0.155832	−	0.987784i	$-0.450194\pi$
$31$	1.73527	0.311664	0.155832	+	0.987784i	$0.450194\pi$
$32$	1.00000	0.176777
$33$	2.34302	0.407868
$34$	0.717368	0.123028
$35$	2.12832	0.359751
$36$	2.48975	0.414959
$37$	−2.79824	−0.460028	−0.230014	−	0.973187i	$-0.573877\pi$
$37$	−2.79824	−0.460028	−0.230014	+	0.973187i	$0.573877\pi$
$38$	3.90206	0.632998
$39$	−6.82999	−1.09367
$40$	1.00000	0.158114
$41$	7.67046	1.19792	0.598962	−	0.800777i	$-0.295580\pi$
$41$	7.67046	1.19792	0.598962	+	0.800777i	$0.295580\pi$
$42$	4.98669	0.769463
$43$	−10.2024	−1.55585	−0.777926	−	0.628356i	$-0.783728\pi$
$43$	−10.2024	−1.55585	−0.777926	+	0.628356i	$0.783728\pi$
$44$	1.00000	0.150756
$45$	2.48975	0.371150
$46$	3.66693	0.540660
$47$	0.439238	0.0640694	0.0320347	−	0.999487i	$-0.489801\pi$
$47$	0.439238	0.0640694	0.0320347	+	0.999487i	$0.489801\pi$
$48$	2.34302	0.338186
$49$	−2.47027	−0.352895
$50$	1.00000	0.141421
$51$	1.68081	0.235360
$52$	−2.91503	−0.404242
$53$	3.99308	0.548492	0.274246	−	0.961660i	$-0.411572\pi$
$53$	3.99308	0.548492	0.274246	+	0.961660i	$0.411572\pi$
$54$	−1.19552	−0.162690
$55$	1.00000	0.134840
$56$	2.12832	0.284408
$57$	9.14261	1.21097
$58$	8.49265	1.11514
$59$	−4.43115	−0.576887	−0.288444	−	0.957497i	$-0.593138\pi$
$59$	−4.43115	−0.576887	−0.288444	+	0.957497i	$0.593138\pi$
$60$	2.34302	0.302483
$61$	−15.2018	−1.94639	−0.973193	−	0.229989i	$-0.926131\pi$
$61$	−15.2018	−1.94639	−0.973193	+	0.229989i	$0.926131\pi$
$62$	1.73527	0.220379
$63$	5.29898	0.667609
$64$	1.00000	0.125000
$65$	−2.91503	−0.361565
$66$	2.34302	0.288406
$67$	−7.62212	−0.931191	−0.465595	−	0.884998i	$-0.654160\pi$
$67$	−7.62212	−0.931191	−0.465595	+	0.884998i	$0.654160\pi$
$68$	0.717368	0.0869937
$69$	8.59170	1.03432
$70$	2.12832	0.254382
$71$	9.77501	1.16008	0.580040	−	0.814588i	$-0.303037\pi$
$71$	9.77501	1.16008	0.580040	+	0.814588i	$0.303037\pi$
$72$	2.48975	0.293420
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−2.79824	−0.325289
$75$	2.34302	0.270549
$76$	3.90206	0.447597
$77$	2.12832	0.242544
$78$	−6.82999	−0.773344
$79$	−4.63557	−0.521543	−0.260771	−	0.965401i	$-0.583977\pi$
$79$	−4.63557	−0.521543	−0.260771	+	0.965401i	$0.583977\pi$
$80$	1.00000	0.111803
$81$	−10.2704	−1.14115
$82$	7.67046	0.847060
$83$	7.03300	0.771972	0.385986	−	0.922505i	$-0.373861\pi$
$83$	7.03300	0.771972	0.385986	+	0.922505i	$0.373861\pi$
$84$	4.98669	0.544093
$85$	0.717368	0.0778095
$86$	−10.2024	−1.10015
$87$	19.8985	2.13334
$88$	1.00000	0.106600
$89$	1.63889	0.173722	0.0868611	−	0.996220i	$-0.472316\pi$
$89$	1.63889	0.173722	0.0868611	+	0.996220i	$0.472316\pi$
$90$	2.48975	0.262443
$91$	−6.20411	−0.650368
$92$	3.66693	0.382304
$93$	4.06578	0.421601
$94$	0.439238	0.0453039
$95$	3.90206	0.400343
$96$	2.34302	0.239134
$97$	−8.04281	−0.816624	−0.408312	−	0.912842i	$-0.633882\pi$
$97$	−8.04281	−0.816624	−0.408312	+	0.912842i	$0.633882\pi$
$98$	−2.47027	−0.249535
$99$	2.48975	0.250230
$100$	1.00000	0.100000
$101$	−9.61417	−0.956645	−0.478323	−	0.878184i	$-0.658755\pi$
$101$	−9.61417	−0.956645	−0.478323	+	0.878184i	$0.658755\pi$
$102$	1.68081	0.166425
$103$	−3.58842	−0.353577	−0.176789	−	0.984249i	$-0.556571\pi$
$103$	−3.58842	−0.353577	−0.176789	+	0.984249i	$0.556571\pi$
$104$	−2.91503	−0.285843
$105$	4.98669	0.486651
$106$	3.99308	0.387842
$107$	14.2834	1.38083	0.690415	−	0.723413i	$-0.257428\pi$
$107$	14.2834	1.38083	0.690415	+	0.723413i	$0.257428\pi$
$108$	−1.19552	−0.115039
$109$	−15.1018	−1.44649	−0.723247	−	0.690589i	$-0.757351\pi$
$109$	−15.1018	−1.44649	−0.723247	+	0.690589i	$0.757351\pi$
$110$	1.00000	0.0953463
$111$	−6.55634	−0.622300
$112$	2.12832	0.201107
$113$	9.88955	0.930331	0.465165	−	0.885224i	$-0.345995\pi$
$113$	9.88955	0.930331	0.465165	+	0.885224i	$0.345995\pi$
$114$	9.14261	0.856284
$115$	3.66693	0.341943
$116$	8.49265	0.788523
$117$	−7.25771	−0.670976
$118$	−4.43115	−0.407921
$119$	1.52679	0.139960
$120$	2.34302	0.213888
$121$	1.00000	0.0909091
$122$	−15.2018	−1.37630
$123$	17.9721	1.62049
$124$	1.73527	0.155832
$125$	1.00000	0.0894427
$126$	5.29898	0.472071
$127$	5.99264	0.531761	0.265880	−	0.964006i	$-0.414337\pi$
$127$	5.99264	0.531761	0.265880	+	0.964006i	$0.414337\pi$
$128$	1.00000	0.0883883
$129$	−23.9045	−2.10467
$130$	−2.91503	−0.255665
$131$	−3.43267	−0.299914	−0.149957	−	0.988693i	$-0.547914\pi$
$131$	−3.43267	−0.299914	−0.149957	+	0.988693i	$0.547914\pi$
$132$	2.34302	0.203934
$133$	8.30482	0.720119
$134$	−7.62212	−0.658451
$135$	−1.19552	−0.102894
$136$	0.717368	0.0615138
$137$	8.30968	0.709944	0.354972	−	0.934877i	$-0.384490\pi$
$137$	8.30968	0.709944	0.354972	+	0.934877i	$0.384490\pi$
$138$	8.59170	0.731374
$139$	12.0383	1.02108	0.510538	−	0.859855i	$-0.329446\pi$
$139$	12.0383	1.02108	0.510538	+	0.859855i	$0.329446\pi$
$140$	2.12832	0.179876
$141$	1.02914	0.0866696
$142$	9.77501	0.820300
$143$	−2.91503	−0.243767
$144$	2.48975	0.207479
$145$	8.49265	0.705276
$146$	−1.00000	−0.0827606
$147$	−5.78789	−0.477377
$148$	−2.79824	−0.230014
$149$	3.18693	0.261083	0.130542	−	0.991443i	$-0.458328\pi$
$149$	3.18693	0.261083	0.130542	+	0.991443i	$0.458328\pi$
$150$	2.34302	0.191307
$151$	−4.15252	−0.337927	−0.168964	−	0.985622i	$-0.554042\pi$
$151$	−4.15252	−0.337927	−0.168964	+	0.985622i	$0.554042\pi$
$152$	3.90206	0.316499
$153$	1.78607	0.144395
$154$	2.12832	0.171505
$155$	1.73527	0.139380
$156$	−6.82999	−0.546837
$157$	4.87099	0.388747	0.194374	−	0.980928i	$-0.437733\pi$
$157$	4.87099	0.388747	0.194374	+	0.980928i	$0.437733\pi$
$158$	−4.63557	−0.368786
$159$	9.35588	0.741969
$160$	1.00000	0.0790569
$161$	7.80439	0.615072
$162$	−10.2704	−0.806918
$163$	2.82808	0.221513	0.110756	−	0.993848i	$-0.464673\pi$
$163$	2.82808	0.221513	0.110756	+	0.993848i	$0.464673\pi$
$164$	7.67046	0.598962
$165$	2.34302	0.182404
$166$	7.03300	0.545867
$167$	12.0558	0.932905	0.466452	−	0.884546i	$-0.345532\pi$
$167$	12.0558	0.932905	0.466452	+	0.884546i	$0.345532\pi$
$168$	4.98669	0.384732
$169$	−4.50258	−0.346352
$170$	0.717368	0.0550196
$171$	9.71516	0.742937
$172$	−10.2024	−0.777926
$173$	9.18842	0.698583	0.349292	−	0.937014i	$-0.386422\pi$
$173$	9.18842	0.698583	0.349292	+	0.937014i	$0.386422\pi$
$174$	19.8985	1.50850
$175$	2.12832	0.160886
$176$	1.00000	0.0753778
$177$	−10.3823	−0.780381
$178$	1.63889	0.122840
$179$	13.1788	0.985033	0.492516	−	0.870303i	$-0.336077\pi$
$179$	13.1788	0.985033	0.492516	+	0.870303i	$0.336077\pi$
$180$	2.48975	0.185575
$181$	22.6008	1.67990	0.839952	−	0.542660i	$-0.182583\pi$
$181$	22.6008	1.67990	0.839952	+	0.542660i	$0.182583\pi$
$182$	−6.20411	−0.459880
$183$	−35.6181	−2.63296
$184$	3.66693	0.270330
$185$	−2.79824	−0.205731
$186$	4.06578	0.298117
$187$	0.717368	0.0524592
$188$	0.439238	0.0320347
$189$	−2.54445	−0.185081
$190$	3.90206	0.283085
$191$	−9.05396	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$191$	−9.05396	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$192$	2.34302	0.169093
$193$	−1.44260	−0.103841	−0.0519204	−	0.998651i	$-0.516534\pi$
$193$	−1.44260	−0.103841	−0.0519204	+	0.998651i	$0.516534\pi$
$194$	−8.04281	−0.577440
$195$	−6.82999	−0.489106
$196$	−2.47027	−0.176448
$197$	−14.8394	−1.05726	−0.528631	−	0.848852i	$-0.677295\pi$
$197$	−14.8394	−1.05726	−0.528631	+	0.848852i	$0.677295\pi$
$198$	2.48975	0.176939
$199$	−20.7941	−1.47406	−0.737028	−	0.675862i	$-0.763772\pi$
$199$	−20.7941	−1.47406	−0.737028	+	0.675862i	$0.763772\pi$
$200$	1.00000	0.0707107
$201$	−17.8588	−1.25966
$202$	−9.61417	−0.676450
$203$	18.0750	1.26862
$204$	1.68081	0.117680
$205$	7.67046	0.535728
$206$	−3.58842	−0.250017
$207$	9.12975	0.634562
$208$	−2.91503	−0.202121
$209$	3.90206	0.269911
$210$	4.98669	0.344115
$211$	9.69127	0.667175	0.333587	−	0.942719i	$-0.391741\pi$
$211$	9.69127	0.667175	0.333587	+	0.942719i	$0.391741\pi$
$212$	3.99308	0.274246
$213$	22.9031	1.56929
$214$	14.2834	0.976394
$215$	−10.2024	−0.695798
$216$	−1.19552	−0.0813449
$217$	3.69320	0.250711
$218$	−15.1018	−1.02283
$219$	−2.34302	−0.158327
$220$	1.00000	0.0674200
$221$	−2.09115	−0.140666
$222$	−6.55634	−0.440033
$223$	14.8819	0.996569	0.498285	−	0.867014i	$-0.333964\pi$
$223$	14.8819	0.996569	0.498285	+	0.867014i	$0.333964\pi$
$224$	2.12832	0.142204
$225$	2.48975	0.165984
$226$	9.88955	0.657843
$227$	−23.8012	−1.57974	−0.789872	−	0.613272i	$-0.789853\pi$
$227$	−23.8012	−1.57974	−0.789872	+	0.613272i	$0.789853\pi$
$228$	9.14261	0.605484
$229$	3.75189	0.247932	0.123966	−	0.992286i	$-0.460439\pi$
$229$	3.75189	0.247932	0.123966	+	0.992286i	$0.460439\pi$
$230$	3.66693	0.241790
$231$	4.98669	0.328100
$232$	8.49265	0.557570
$233$	−5.28906	−0.346498	−0.173249	−	0.984878i	$-0.555426\pi$
$233$	−5.28906	−0.346498	−0.173249	+	0.984878i	$0.555426\pi$
$234$	−7.25771	−0.474452
$235$	0.439238	0.0286527
$236$	−4.43115	−0.288444
$237$	−10.8612	−0.705514
$238$	1.52679	0.0989669
$239$	−10.4023	−0.672868	−0.336434	−	0.941707i	$-0.609221\pi$
$239$	−10.4023	−0.672868	−0.336434	+	0.941707i	$0.609221\pi$
$240$	2.34302	0.151241
$241$	19.8139	1.27633	0.638163	−	0.769902i	$-0.279695\pi$
$241$	19.8139	1.27633	0.638163	+	0.769902i	$0.279695\pi$
$242$	1.00000	0.0642824
$243$	−20.4772	−1.31361
$244$	−15.2018	−0.973193
$245$	−2.47027	−0.157820
$246$	17.9721	1.14586
$247$	−11.3746	−0.723751
$248$	1.73527	0.110190
$249$	16.4785	1.04428
$250$	1.00000	0.0632456
$251$	13.1020	0.826992	0.413496	−	0.910506i	$-0.364308\pi$
$251$	13.1020	0.826992	0.413496	+	0.910506i	$0.364308\pi$
$252$	5.29898	0.333804
$253$	3.66693	0.230538
$254$	5.99264	0.376012
$255$	1.68081	0.105256
$256$	1.00000	0.0625000
$257$	19.6863	1.22800	0.613999	−	0.789307i	$-0.289560\pi$
$257$	19.6863	1.22800	0.613999	+	0.789307i	$0.289560\pi$
$258$	−23.9045	−1.48823
$259$	−5.95554	−0.370059
$260$	−2.91503	−0.180783
$261$	21.1446	1.30882
$262$	−3.43267	−0.212071
$263$	−21.0443	−1.29765	−0.648823	−	0.760939i	$-0.724738\pi$
$263$	−21.0443	−1.29765	−0.648823	+	0.760939i	$0.724738\pi$
$264$	2.34302	0.144203
$265$	3.99308	0.245293
$266$	8.30482	0.509201
$267$	3.83996	0.235002
$268$	−7.62212	−0.465595
$269$	−25.8880	−1.57842	−0.789209	−	0.614124i	$-0.789509\pi$
$269$	−25.8880	−1.57842	−0.789209	+	0.614124i	$0.789509\pi$
$270$	−1.19552	−0.0727571
$271$	−4.81804	−0.292675	−0.146338	−	0.989235i	$-0.546749\pi$
$271$	−4.81804	−0.292675	−0.146338	+	0.989235i	$0.546749\pi$
$272$	0.717368	0.0434968
$273$	−14.5364	−0.879782
$274$	8.30968	0.502006
$275$	1.00000	0.0603023
$276$	8.59170	0.517160
$277$	−4.57206	−0.274709	−0.137354	−	0.990522i	$-0.543860\pi$
$277$	−4.57206	−0.274709	−0.137354	+	0.990522i	$0.543860\pi$
$278$	12.0383	0.722009
$279$	4.32039	0.258655
$280$	2.12832	0.127191
$281$	−15.4915	−0.924143	−0.462072	−	0.886843i	$-0.652894\pi$
$281$	−15.4915	−0.924143	−0.462072	+	0.886843i	$0.652894\pi$
$282$	1.02914	0.0612846
$283$	8.24112	0.489884	0.244942	−	0.969538i	$-0.421231\pi$
$283$	8.24112	0.489884	0.244942	+	0.969538i	$0.421231\pi$
$284$	9.77501	0.580040
$285$	9.14261	0.541562
$286$	−2.91503	−0.172370
$287$	16.3252	0.963644
$288$	2.48975	0.146710
$289$	−16.4854	−0.969728
$290$	8.49265	0.498706
$291$	−18.8445	−1.10468
$292$	−1.00000	−0.0585206
$293$	29.1562	1.70332	0.851661	−	0.524093i	$-0.175596\pi$
$293$	29.1562	1.70332	0.851661	+	0.524093i	$0.175596\pi$
$294$	−5.78789	−0.337557
$295$	−4.43115	−0.257992
$296$	−2.79824	−0.162644
$297$	−1.19552	−0.0693712
$298$	3.18693	0.184614
$299$	−10.6892	−0.618174
$300$	2.34302	0.135274
$301$	−21.7139	−1.25157
$302$	−4.15252	−0.238951
$303$	−22.5262	−1.29410
$304$	3.90206	0.223798
$305$	−15.2018	−0.870451
$306$	1.78607	0.102103
$307$	−18.4206	−1.05132	−0.525660	−	0.850694i	$-0.676182\pi$
$307$	−18.4206	−1.05132	−0.525660	+	0.850694i	$0.676182\pi$
$308$	2.12832	0.121272
$309$	−8.40774	−0.478299
$310$	1.73527	0.0985567
$311$	−32.8576	−1.86318	−0.931591	−	0.363507i	$-0.881579\pi$
$311$	−32.8576	−1.86318	−0.931591	+	0.363507i	$0.881579\pi$
$312$	−6.82999	−0.386672
$313$	4.56160	0.257837	0.128919	−	0.991655i	$-0.458849\pi$
$313$	4.56160	0.257837	0.128919	+	0.991655i	$0.458849\pi$
$314$	4.87099	0.274886
$315$	5.29898	0.298564
$316$	−4.63557	−0.260771
$317$	24.2735	1.36334	0.681668	−	0.731662i	$-0.261255\pi$
$317$	24.2735	1.36334	0.681668	+	0.731662i	$0.261255\pi$
$318$	9.35588	0.524652
$319$	8.49265	0.475497
$320$	1.00000	0.0559017
$321$	33.4664	1.86791
$322$	7.80439	0.434922
$323$	2.79921	0.155752
$324$	−10.2704	−0.570577
$325$	−2.91503	−0.161697
$326$	2.82808	0.156633
$327$	−35.3840	−1.95674
$328$	7.67046	0.423530
$329$	0.934837	0.0515393
$330$	2.34302	0.128979
$331$	−27.3387	−1.50267	−0.751336	−	0.659920i	$-0.770590\pi$
$331$	−27.3387	−1.50267	−0.751336	+	0.659920i	$0.770590\pi$
$332$	7.03300	0.385986
$333$	−6.96692	−0.381785
$334$	12.0558	0.659663
$335$	−7.62212	−0.416441
$336$	4.98669	0.272046
$337$	15.5280	0.845866	0.422933	−	0.906161i	$-0.361001\pi$
$337$	15.5280	0.845866	0.422933	+	0.906161i	$0.361001\pi$
$338$	−4.50258	−0.244908
$339$	23.1714	1.25850
$340$	0.717368	0.0389048
$341$	1.73527	0.0939701
$342$	9.71516	0.525336
$343$	−20.1557	−1.08831
$344$	−10.2024	−0.550077
$345$	8.59170	0.462562
$346$	9.18842	0.493973
$347$	−22.0413	−1.18324	−0.591620	−	0.806217i	$-0.701511\pi$
$347$	−22.0413	−1.18324	−0.591620	+	0.806217i	$0.701511\pi$
$348$	19.8985	1.06667
$349$	−0.781341	−0.0418242	−0.0209121	−	0.999781i	$-0.506657\pi$
$349$	−0.781341	−0.0418242	−0.0209121	+	0.999781i	$0.506657\pi$
$350$	2.12832	0.113763
$351$	3.48498	0.186015
$352$	1.00000	0.0533002
$353$	−32.4113	−1.72508	−0.862539	−	0.505991i	$-0.831127\pi$
$353$	−32.4113	−1.72508	−0.862539	+	0.505991i	$0.831127\pi$
$354$	−10.3823	−0.551813
$355$	9.77501	0.518804
$356$	1.63889	0.0868611
$357$	3.57730	0.189331
$358$	13.1788	0.696523
$359$	−20.6298	−1.08880	−0.544400	−	0.838826i	$-0.683242\pi$
$359$	−20.6298	−1.08880	−0.544400	+	0.838826i	$0.683242\pi$
$360$	2.48975	0.131221
$361$	−3.77393	−0.198628
$362$	22.6008	1.18787
$363$	2.34302	0.122977
$364$	−6.20411	−0.325184
$365$	−1.00000	−0.0523424
$366$	−35.6181	−1.86179
$367$	26.3294	1.37438	0.687192	−	0.726475i	$-0.258843\pi$
$367$	26.3294	1.37438	0.687192	+	0.726475i	$0.258843\pi$
$368$	3.66693	0.191152
$369$	19.0975	0.994178
$370$	−2.79824	−0.145474
$371$	8.49854	0.441222
$372$	4.06578	0.210801
$373$	−2.32581	−0.120426	−0.0602128	−	0.998186i	$-0.519178\pi$
$373$	−2.32581	−0.120426	−0.0602128	+	0.998186i	$0.519178\pi$
$374$	0.717368	0.0370942
$375$	2.34302	0.120993
$376$	0.439238	0.0226520
$377$	−24.7564	−1.27502
$378$	−2.54445	−0.130872
$379$	14.7911	0.759766	0.379883	−	0.925034i	$-0.375964\pi$
$379$	14.7911	0.759766	0.379883	+	0.925034i	$0.375964\pi$
$380$	3.90206	0.200171
$381$	14.0409	0.719337
$382$	−9.05396	−0.463241
$383$	−8.20911	−0.419466	−0.209733	−	0.977759i	$-0.567259\pi$
$383$	−8.20911	−0.419466	−0.209733	+	0.977759i	$0.567259\pi$
$384$	2.34302	0.119567
$385$	2.12832	0.108469
$386$	−1.44260	−0.0734266
$387$	−25.4015	−1.29123
$388$	−8.04281	−0.408312
$389$	15.0565	0.763393	0.381697	−	0.924288i	$-0.375340\pi$
$389$	15.0565	0.763393	0.381697	+	0.924288i	$0.375340\pi$
$390$	−6.82999	−0.345850
$391$	2.63054	0.133032
$392$	−2.47027	−0.124767
$393$	−8.04282	−0.405707
$394$	−14.8394	−0.747597
$395$	−4.63557	−0.233241
$396$	2.48975	0.125115
$397$	6.89810	0.346206	0.173103	−	0.984904i	$-0.444621\pi$
$397$	6.89810	0.346206	0.173103	+	0.984904i	$0.444621\pi$
$398$	−20.7941	−1.04232
$399$	19.4584	0.974137
$400$	1.00000	0.0500000
$401$	14.8707	0.742605	0.371303	−	0.928512i	$-0.378911\pi$
$401$	14.8707	0.742605	0.371303	+	0.928512i	$0.378911\pi$
$402$	−17.8588	−0.890716
$403$	−5.05837	−0.251975
$404$	−9.61417	−0.478323
$405$	−10.2704	−0.510340
$406$	18.0750	0.897050
$407$	−2.79824	−0.138704
$408$	1.68081	0.0832125
$409$	−13.4042	−0.662794	−0.331397	−	0.943491i	$-0.607520\pi$
$409$	−13.4042	−0.662794	−0.331397	+	0.943491i	$0.607520\pi$
$410$	7.67046	0.378817
$411$	19.4698	0.960373
$412$	−3.58842	−0.176789
$413$	−9.43090	−0.464064
$414$	9.12975	0.448703
$415$	7.03300	0.345236
$416$	−2.91503	−0.142921
$417$	28.2060	1.38125
$418$	3.90206	0.190856
$419$	9.57927	0.467978	0.233989	−	0.972239i	$-0.424822\pi$
$419$	9.57927	0.467978	0.233989	+	0.972239i	$0.424822\pi$
$420$	4.98669	0.243326
$421$	16.0529	0.782373	0.391186	−	0.920311i	$-0.372065\pi$
$421$	16.0529	0.782373	0.391186	+	0.920311i	$0.372065\pi$
$422$	9.69127	0.471764
$423$	1.09359	0.0531724
$424$	3.99308	0.193921
$425$	0.717368	0.0347975
$426$	22.9031	1.10966
$427$	−32.3542	−1.56573
$428$	14.2834	0.690415
$429$	−6.82999	−0.329755
$430$	−10.2024	−0.492004
$431$	−29.5950	−1.42554	−0.712771	−	0.701396i	$-0.752560\pi$
$431$	−29.5950	−1.42554	−0.712771	+	0.701396i	$0.752560\pi$
$432$	−1.19552	−0.0575195
$433$	−17.9140	−0.860890	−0.430445	−	0.902617i	$-0.641643\pi$
$433$	−17.9140	−0.860890	−0.430445	+	0.902617i	$0.641643\pi$
$434$	3.69320	0.177279
$435$	19.8985	0.954058
$436$	−15.1018	−0.723247
$437$	14.3086	0.684473
$438$	−2.34302	−0.111954
$439$	−17.7633	−0.847798	−0.423899	−	0.905710i	$-0.639339\pi$
$439$	−17.7633	−0.847798	−0.423899	+	0.905710i	$0.639339\pi$
$440$	1.00000	0.0476731
$441$	−6.15036	−0.292874
$442$	−2.09115	−0.0994660
$443$	−40.6235	−1.93008	−0.965040	−	0.262102i	$-0.915584\pi$
$443$	−40.6235	−1.93008	−0.965040	+	0.262102i	$0.915584\pi$
$444$	−6.55634	−0.311150
$445$	1.63889	0.0776909
$446$	14.8819	0.704681
$447$	7.46704	0.353179
$448$	2.12832	0.100554
$449$	−12.2932	−0.580151	−0.290076	−	0.957004i	$-0.593680\pi$
$449$	−12.2932	−0.580151	−0.290076	+	0.957004i	$0.593680\pi$
$450$	2.48975	0.117368
$451$	7.67046	0.361188
$452$	9.88955	0.465165
$453$	−9.72944	−0.457129
$454$	−23.8012	−1.11705
$455$	−6.20411	−0.290853
$456$	9.14261	0.428142
$457$	34.7297	1.62459	0.812295	−	0.583247i	$-0.198218\pi$
$457$	34.7297	1.62459	0.812295	+	0.583247i	$0.198218\pi$
$458$	3.75189	0.175314
$459$	−0.857629	−0.0400307
$460$	3.66693	0.170972
$461$	−1.94521	−0.0905975	−0.0452987	−	0.998973i	$-0.514424\pi$
$461$	−1.94521	−0.0905975	−0.0452987	+	0.998973i	$0.514424\pi$
$462$	4.98669	0.232002
$463$	−10.1038	−0.469563	−0.234781	−	0.972048i	$-0.575437\pi$
$463$	−10.1038	−0.469563	−0.234781	+	0.972048i	$0.575437\pi$
$464$	8.49265	0.394261
$465$	4.06578	0.188546
$466$	−5.28906	−0.245011
$467$	10.5811	0.489633	0.244816	−	0.969569i	$-0.421272\pi$
$467$	10.5811	0.489633	0.244816	+	0.969569i	$0.421272\pi$
$468$	−7.25771	−0.335488
$469$	−16.2223	−0.749076
$470$	0.439238	0.0202605
$471$	11.4128	0.525876
$472$	−4.43115	−0.203960
$473$	−10.2024	−0.469107
$474$	−10.8612	−0.498874
$475$	3.90206	0.179039
$476$	1.52679	0.0699802
$477$	9.94178	0.455203
$478$	−10.4023	−0.475790
$479$	−11.1788	−0.510771	−0.255386	−	0.966839i	$-0.582202\pi$
$479$	−11.1788	−0.510771	−0.255386	+	0.966839i	$0.582202\pi$
$480$	2.34302	0.106944
$481$	8.15696	0.371926
$482$	19.8139	0.902498
$483$	18.2859	0.832036
$484$	1.00000	0.0454545
$485$	−8.04281	−0.365205
$486$	−20.4772	−0.928864
$487$	4.55855	0.206568	0.103284	−	0.994652i	$-0.467065\pi$
$487$	4.55855	0.206568	0.103284	+	0.994652i	$0.467065\pi$
$488$	−15.2018	−0.688152
$489$	6.62626	0.299650
$490$	−2.47027	−0.111595
$491$	10.5103	0.474325	0.237162	−	0.971470i	$-0.423783\pi$
$491$	10.5103	0.474325	0.237162	+	0.971470i	$0.423783\pi$
$492$	17.9721	0.810243
$493$	6.09236	0.274386
$494$	−11.3746	−0.511769
$495$	2.48975	0.111906
$496$	1.73527	0.0779159
$497$	20.8043	0.933201
$498$	16.4785	0.738418
$499$	17.2404	0.771788	0.385894	−	0.922543i	$-0.373893\pi$
$499$	17.2404	0.771788	0.385894	+	0.922543i	$0.373893\pi$
$500$	1.00000	0.0447214
$501$	28.2470	1.26198
$502$	13.1020	0.584772
$503$	−26.0641	−1.16214	−0.581071	−	0.813853i	$-0.697366\pi$
$503$	−26.0641	−1.16214	−0.581071	+	0.813853i	$0.697366\pi$
$504$	5.29898	0.236035
$505$	−9.61417	−0.427825
$506$	3.66693	0.163015
$507$	−10.5496	−0.468526
$508$	5.99264	0.265880
$509$	29.2505	1.29651	0.648253	−	0.761425i	$-0.275500\pi$
$509$	29.2505	1.29651	0.648253	+	0.761425i	$0.275500\pi$
$510$	1.68081	0.0744275
$511$	−2.12832	−0.0941512
$512$	1.00000	0.0441942
$513$	−4.66499	−0.205965
$514$	19.6863	0.868326
$515$	−3.58842	−0.158124
$516$	−23.9045	−1.05234
$517$	0.439238	0.0193177
$518$	−5.95554	−0.261671
$519$	21.5287	0.945004
$520$	−2.91503	−0.127833
$521$	−33.7828	−1.48005	−0.740026	−	0.672578i	$-0.765187\pi$
$521$	−33.7828	−1.48005	−0.740026	+	0.672578i	$0.765187\pi$
$522$	21.1446	0.925474
$523$	−32.2676	−1.41096	−0.705482	−	0.708728i	$-0.749269\pi$
$523$	−32.2676	−1.41096	−0.705482	+	0.708728i	$0.749269\pi$
$524$	−3.43267	−0.149957
$525$	4.98669	0.217637
$526$	−21.0443	−0.917574
$527$	1.24483	0.0542255
$528$	2.34302	0.101967
$529$	−9.55361	−0.415374
$530$	3.99308	0.173448
$531$	−11.0325	−0.478769
$532$	8.30482	0.360060
$533$	−22.3596	−0.968504
$534$	3.83996	0.166171
$535$	14.2834	0.617526
$536$	−7.62212	−0.329226
$537$	30.8783	1.33250
$538$	−25.8880	−1.11611
$539$	−2.47027	−0.106402
$540$	−1.19552	−0.0514470
$541$	4.99253	0.214646	0.107323	−	0.994224i	$-0.465772\pi$
$541$	4.99253	0.214646	0.107323	+	0.994224i	$0.465772\pi$
$542$	−4.81804	−0.206953
$543$	52.9542	2.27248
$544$	0.717368	0.0307569
$545$	−15.1018	−0.646892
$546$	−14.5364	−0.622100
$547$	37.7598	1.61449	0.807246	−	0.590215i	$-0.200957\pi$
$547$	37.7598	1.61449	0.807246	+	0.590215i	$0.200957\pi$
$548$	8.30968	0.354972
$549$	−37.8486	−1.61534
$550$	1.00000	0.0426401
$551$	33.1388	1.41176
$552$	8.59170	0.365687
$553$	−9.86596	−0.419543
$554$	−4.57206	−0.194248
$555$	−6.55634	−0.278301
$556$	12.0383	0.510538
$557$	−8.13385	−0.344642	−0.172321	−	0.985041i	$-0.555127\pi$
$557$	−8.13385	−0.344642	−0.172321	+	0.985041i	$0.555127\pi$
$558$	4.32039	0.182897
$559$	29.7404	1.25788
$560$	2.12832	0.0899378
$561$	1.68081	0.0709638
$562$	−15.4915	−0.653468
$563$	−5.61027	−0.236445	−0.118222	−	0.992987i	$-0.537720\pi$
$563$	−5.61027	−0.236445	−0.118222	+	0.992987i	$0.537720\pi$
$564$	1.02914	0.0433348
$565$	9.88955	0.416057
$566$	8.24112	0.346400
$567$	−21.8586	−0.917977
$568$	9.77501	0.410150
$569$	−11.4754	−0.481074	−0.240537	−	0.970640i	$-0.577324\pi$
$569$	−11.4754	−0.481074	−0.240537	+	0.970640i	$0.577324\pi$
$570$	9.14261	0.382942
$571$	−21.7983	−0.912230	−0.456115	−	0.889921i	$-0.650759\pi$
$571$	−21.7983	−0.912230	−0.456115	+	0.889921i	$0.650759\pi$
$572$	−2.91503	−0.121884
$573$	−21.2136	−0.886212
$574$	16.3252	0.681399
$575$	3.66693	0.152922
$576$	2.48975	0.103740
$577$	−41.9009	−1.74436	−0.872179	−	0.489186i	$-0.837294\pi$
$577$	−41.9009	−1.74436	−0.872179	+	0.489186i	$0.837294\pi$
$578$	−16.4854	−0.685702
$579$	−3.38005	−0.140470
$580$	8.49265	0.352638
$581$	14.9685	0.620996
$582$	−18.8445	−0.781129
$583$	3.99308	0.165377
$584$	−1.00000	−0.0413803
$585$	−7.25771	−0.300070
$586$	29.1562	1.20443
$587$	−27.3854	−1.13032	−0.565159	−	0.824982i	$-0.691185\pi$
$587$	−27.3854	−1.13032	−0.565159	+	0.824982i	$0.691185\pi$
$588$	−5.78789	−0.238689
$589$	6.77113	0.278999
$590$	−4.43115	−0.182428
$591$	−34.7690	−1.43021
$592$	−2.79824	−0.115007
$593$	20.3160	0.834277	0.417139	−	0.908843i	$-0.363033\pi$
$593$	20.3160	0.834277	0.417139	+	0.908843i	$0.363033\pi$
$594$	−1.19552	−0.0490528
$595$	1.52679	0.0625922
$596$	3.18693	0.130542
$597$	−48.7211	−1.99402
$598$	−10.6892	−0.437115
$599$	6.89107	0.281562	0.140781	−	0.990041i	$-0.455039\pi$
$599$	6.89107	0.281562	0.140781	+	0.990041i	$0.455039\pi$
$600$	2.34302	0.0956535
$601$	4.06549	0.165835	0.0829175	−	0.996556i	$-0.473576\pi$
$601$	4.06549	0.165835	0.0829175	+	0.996556i	$0.473576\pi$
$602$	−21.7139	−0.884994
$603$	−18.9772	−0.772811
$604$	−4.15252	−0.168964
$605$	1.00000	0.0406558
$606$	−22.5262	−0.915065
$607$	10.6749	0.433279	0.216640	−	0.976252i	$-0.430490\pi$
$607$	10.6749	0.433279	0.216640	+	0.976252i	$0.430490\pi$
$608$	3.90206	0.158249
$609$	42.3502	1.71612
$610$	−15.2018	−0.615501
$611$	−1.28039	−0.0517992
$612$	1.78607	0.0721976
$613$	1.42544	0.0575728	0.0287864	−	0.999586i	$-0.490836\pi$
$613$	1.42544	0.0575728	0.0287864	+	0.999586i	$0.490836\pi$
$614$	−18.4206	−0.743396
$615$	17.9721	0.724703
$616$	2.12832	0.0857523
$617$	24.0667	0.968889	0.484444	−	0.874822i	$-0.339022\pi$
$617$	24.0667	0.968889	0.484444	+	0.874822i	$0.339022\pi$
$618$	−8.40774	−0.338209
$619$	−0.715371	−0.0287532	−0.0143766	−	0.999897i	$-0.504576\pi$
$619$	−0.715371	−0.0287532	−0.0143766	+	0.999897i	$0.504576\pi$
$620$	1.73527	0.0696901
$621$	−4.38389	−0.175920
$622$	−32.8576	−1.31747
$623$	3.48808	0.139747
$624$	−6.82999	−0.273418
$625$	1.00000	0.0400000
$626$	4.56160	0.182318
$627$	9.14261	0.365121
$628$	4.87099	0.194374
$629$	−2.00737	−0.0800390
$630$	5.29898	0.211116
$631$	36.6311	1.45826	0.729132	−	0.684374i	$-0.239924\pi$
$631$	36.6311	1.45826	0.729132	+	0.684374i	$0.239924\pi$
$632$	−4.63557	−0.184393
$633$	22.7069	0.902517
$634$	24.2735	0.964024
$635$	5.99264	0.237811
$636$	9.35588	0.370985
$637$	7.20092	0.285311
$638$	8.49265	0.336227
$639$	24.3374	0.962771
$640$	1.00000	0.0395285
$641$	28.1470	1.11174	0.555869	−	0.831270i	$-0.312386\pi$
$641$	28.1470	1.11174	0.555869	+	0.831270i	$0.312386\pi$
$642$	33.4664	1.32081
$643$	17.4342	0.687537	0.343769	−	0.939054i	$-0.388296\pi$
$643$	17.4342	0.687537	0.343769	+	0.939054i	$0.388296\pi$
$644$	7.80439	0.307536
$645$	−23.9045	−0.941237
$646$	2.79921	0.110134
$647$	−7.59140	−0.298449	−0.149224	−	0.988803i	$-0.547678\pi$
$647$	−7.59140	−0.298449	−0.149224	+	0.988803i	$0.547678\pi$
$648$	−10.2704	−0.403459
$649$	−4.43115	−0.173938
$650$	−2.91503	−0.114337
$651$	8.65326	0.339148
$652$	2.82808	0.110756
$653$	5.13723	0.201035	0.100518	−	0.994935i	$-0.467950\pi$
$653$	5.13723	0.201035	0.100518	+	0.994935i	$0.467950\pi$
$654$	−35.3840	−1.38362
$655$	−3.43267	−0.134126
$656$	7.67046	0.299481
$657$	−2.48975	−0.0971345
$658$	0.934837	0.0364438
$659$	−27.7566	−1.08124	−0.540621	−	0.841266i	$-0.681811\pi$
$659$	−27.7566	−1.08124	−0.540621	+	0.841266i	$0.681811\pi$
$660$	2.34302	0.0912020
$661$	2.92109	0.113617	0.0568086	−	0.998385i	$-0.481908\pi$
$661$	2.92109	0.113617	0.0568086	+	0.998385i	$0.481908\pi$
$662$	−27.3387	−1.06255
$663$	−4.89962	−0.190285
$664$	7.03300	0.272933
$665$	8.30482	0.322047
$666$	−6.96692	−0.269963
$667$	31.1420	1.20582
$668$	12.0558	0.466452
$669$	34.8687	1.34810
$670$	−7.62212	−0.294468
$671$	−15.2018	−0.586858
$672$	4.98669	0.192366
$673$	−26.2282	−1.01102	−0.505511	−	0.862820i	$-0.668696\pi$
$673$	−26.2282	−1.01102	−0.505511	+	0.862820i	$0.668696\pi$
$674$	15.5280	0.598118
$675$	−1.19552	−0.0460156
$676$	−4.50258	−0.173176
$677$	44.2780	1.70174	0.850871	−	0.525375i	$-0.176075\pi$
$677$	44.2780	1.70174	0.850871	+	0.525375i	$0.176075\pi$
$678$	23.1714	0.889894
$679$	−17.1177	−0.656915
$680$	0.717368	0.0275098
$681$	−55.7668	−2.13699
$682$	1.73527	0.0664469
$683$	15.7826	0.603906	0.301953	−	0.953323i	$-0.402361\pi$
$683$	15.7826	0.603906	0.301953	+	0.953323i	$0.402361\pi$
$684$	9.71516	0.371469
$685$	8.30968	0.317497
$686$	−20.1557	−0.769549
$687$	8.79077	0.335389
$688$	−10.2024	−0.388963
$689$	−11.6400	−0.443447
$690$	8.59170	0.327081
$691$	22.7474	0.865352	0.432676	−	0.901550i	$-0.357569\pi$
$691$	22.7474	0.865352	0.432676	+	0.901550i	$0.357569\pi$
$692$	9.18842	0.349292
$693$	5.29898	0.201292
$694$	−22.0413	−0.836677
$695$	12.0383	0.456639
$696$	19.8985	0.754249
$697$	5.50254	0.208424
$698$	−0.781341	−0.0295742
$699$	−12.3924	−0.468723
$700$	2.12832	0.0804428
$701$	−23.1600	−0.874741	−0.437370	−	0.899281i	$-0.644090\pi$
$701$	−23.1600	−0.874741	−0.437370	+	0.899281i	$0.644090\pi$
$702$	3.48498	0.131532
$703$	−10.9189	−0.411814
$704$	1.00000	0.0376889
$705$	1.02914	0.0387598
$706$	−32.4113	−1.21981
$707$	−20.4620	−0.769552
$708$	−10.3823	−0.390190
$709$	−22.7951	−0.856087	−0.428043	−	0.903758i	$-0.640797\pi$
$709$	−22.7951	−0.856087	−0.428043	+	0.903758i	$0.640797\pi$
$710$	9.77501	0.366850
$711$	−11.5414	−0.432837
$712$	1.63889	0.0614201
$713$	6.36312	0.238301
$714$	3.57730	0.133877
$715$	−2.91503	−0.109016
$716$	13.1788	0.492516
$717$	−24.3728	−0.910218
$718$	−20.6298	−0.769897
$719$	6.74353	0.251491	0.125746	−	0.992063i	$-0.459868\pi$
$719$	6.74353	0.251491	0.125746	+	0.992063i	$0.459868\pi$
$720$	2.48975	0.0927876
$721$	−7.63728	−0.284427
$722$	−3.77393	−0.140451
$723$	46.4244	1.72654
$724$	22.6008	0.839952
$725$	8.49265	0.315409
$726$	2.34302	0.0869577
$727$	31.5407	1.16978	0.584890	−	0.811112i	$-0.301138\pi$
$727$	31.5407	1.16978	0.584890	+	0.811112i	$0.301138\pi$
$728$	−6.20411	−0.229940
$729$	−17.1673	−0.635827
$730$	−1.00000	−0.0370117
$731$	−7.31888	−0.270699
$732$	−35.6181	−1.31648
$733$	−32.3157	−1.19361	−0.596804	−	0.802387i	$-0.703563\pi$
$733$	−32.3157	−1.19361	−0.596804	+	0.802387i	$0.703563\pi$
$734$	26.3294	0.971837
$735$	−5.78789	−0.213490
$736$	3.66693	0.135165
$737$	−7.62212	−0.280765
$738$	19.0975	0.702990
$739$	16.9085	0.621988	0.310994	−	0.950412i	$-0.399338\pi$
$739$	16.9085	0.621988	0.310994	+	0.950412i	$0.399338\pi$
$740$	−2.79824	−0.102865
$741$	−26.6510	−0.979050
$742$	8.49854	0.311991
$743$	−27.6152	−1.01310	−0.506552	−	0.862210i	$-0.669080\pi$
$743$	−27.6152	−1.01310	−0.506552	+	0.862210i	$0.669080\pi$
$744$	4.06578	0.149059
$745$	3.18693	0.116760
$746$	−2.32581	−0.0851538
$747$	17.5104	0.640673
$748$	0.717368	0.0262296
$749$	30.3996	1.11078
$750$	2.34302	0.0855551
$751$	8.11764	0.296217	0.148108	−	0.988971i	$-0.452682\pi$
$751$	8.11764	0.296217	0.148108	+	0.988971i	$0.452682\pi$
$752$	0.439238	0.0160174
$753$	30.6983	1.11871
$754$	−24.7564	−0.901573
$755$	−4.15252	−0.151126
$756$	−2.54445	−0.0925406
$757$	−42.8963	−1.55909	−0.779546	−	0.626345i	$-0.784550\pi$
$757$	−42.8963	−1.55909	−0.779546	+	0.626345i	$0.784550\pi$
$758$	14.7911	0.537236
$759$	8.59170	0.311859
$760$	3.90206	0.141543
$761$	−26.8634	−0.973798	−0.486899	−	0.873458i	$-0.661872\pi$
$761$	−26.8634	−0.973798	−0.486899	+	0.873458i	$0.661872\pi$
$762$	14.0409	0.508648
$763$	−32.1415	−1.16360
$764$	−9.05396	−0.327561
$765$	1.78607	0.0645755
$766$	−8.20911	−0.296607
$767$	12.9170	0.466405
$768$	2.34302	0.0845465
$769$	−31.9164	−1.15093	−0.575467	−	0.817825i	$-0.695180\pi$
$769$	−31.9164	−1.15093	−0.575467	+	0.817825i	$0.695180\pi$
$770$	2.12832	0.0766992
$771$	46.1255	1.66117
$772$	−1.44260	−0.0519204
$773$	39.6575	1.42638	0.713191	−	0.700970i	$-0.247249\pi$
$773$	39.6575	1.42638	0.713191	+	0.700970i	$0.247249\pi$
$774$	−25.4015	−0.913037
$775$	1.73527	0.0623327
$776$	−8.04281	−0.288720
$777$	−13.9540	−0.500596
$778$	15.0565	0.539801
$779$	29.9306	1.07237
$780$	−6.82999	−0.244553
$781$	9.77501	0.349777
$782$	2.63054	0.0940679
$783$	−10.1531	−0.362844
$784$	−2.47027	−0.0882239
$785$	4.87099	0.173853
$786$	−8.04282	−0.286878
$787$	−25.2764	−0.901006	−0.450503	−	0.892775i	$-0.648755\pi$
$787$	−25.2764	−0.901006	−0.450503	+	0.892775i	$0.648755\pi$
$788$	−14.8394	−0.528631
$789$	−49.3072	−1.75538
$790$	−4.63557	−0.164926
$791$	21.0481	0.748384
$792$	2.48975	0.0884695
$793$	44.3137	1.57362
$794$	6.89810	0.244804
$795$	9.35588	0.331819
$796$	−20.7941	−0.737028
$797$	47.7920	1.69288	0.846439	−	0.532485i	$-0.178742\pi$
$797$	47.7920	1.69288	0.846439	+	0.532485i	$0.178742\pi$
$798$	19.4584	0.688819
$799$	0.315095	0.0111473
$800$	1.00000	0.0353553
$801$	4.08044	0.144175
$802$	14.8707	0.525101
$803$	−1.00000	−0.0352892
$804$	−17.8588	−0.629832
$805$	7.80439	0.275069
$806$	−5.05837	−0.178173
$807$	−60.6561	−2.13520
$808$	−9.61417	−0.338225
$809$	−32.7042	−1.14982	−0.574909	−	0.818218i	$-0.694962\pi$
$809$	−32.7042	−1.14982	−0.574909	+	0.818218i	$0.694962\pi$
$810$	−10.2704	−0.360865
$811$	4.39911	0.154474	0.0772369	−	0.997013i	$-0.475390\pi$
$811$	4.39911	0.154474	0.0772369	+	0.997013i	$0.475390\pi$
$812$	18.0750	0.634310
$813$	−11.2888	−0.395915
$814$	−2.79824	−0.0980783
$815$	2.82808	0.0990634
$816$	1.68081	0.0588401
$817$	−39.8104	−1.39279
$818$	−13.4042	−0.468666
$819$	−15.4467	−0.539752
$820$	7.67046	0.267864
$821$	−37.1443	−1.29635	−0.648173	−	0.761493i	$-0.724467\pi$
$821$	−37.1443	−1.29635	−0.648173	+	0.761493i	$0.724467\pi$
$822$	19.4698	0.679086
$823$	5.76720	0.201032	0.100516	−	0.994935i	$-0.467951\pi$
$823$	5.76720	0.201032	0.100516	+	0.994935i	$0.467951\pi$
$824$	−3.58842	−0.125008
$825$	2.34302	0.0815736
$826$	−9.43090	−0.328143
$827$	−16.4930	−0.573517	−0.286758	−	0.958003i	$-0.592578\pi$
$827$	−16.4930	−0.573517	−0.286758	+	0.958003i	$0.592578\pi$
$828$	9.12975	0.317281
$829$	13.5166	0.469449	0.234725	−	0.972062i	$-0.424581\pi$
$829$	13.5166	0.469449	0.234725	+	0.972062i	$0.424581\pi$
$830$	7.03300	0.244119
$831$	−10.7124	−0.371610
$832$	−2.91503	−0.101061
$833$	−1.77209	−0.0613994
$834$	28.2060	0.976694
$835$	12.0558	0.417208
$836$	3.90206	0.134956
$837$	−2.07455	−0.0717070
$838$	9.57927	0.330910
$839$	40.1650	1.38665	0.693325	−	0.720625i	$-0.256145\pi$
$839$	40.1650	1.38665	0.693325	+	0.720625i	$0.256145\pi$
$840$	4.98669	0.172057
$841$	43.1251	1.48707
$842$	16.0529	0.553221
$843$	−36.2968	−1.25013
$844$	9.69127	0.333587
$845$	−4.50258	−0.154893
$846$	1.09359	0.0375985
$847$	2.12832	0.0731298
$848$	3.99308	0.137123
$849$	19.3091	0.662688
$850$	0.717368	0.0246055
$851$	−10.2610	−0.351741
$852$	22.9031	0.784646
$853$	−16.6085	−0.568663	−0.284332	−	0.958726i	$-0.591772\pi$
$853$	−16.6085	−0.568663	−0.284332	+	0.958726i	$0.591772\pi$
$854$	−32.3542	−1.10714
$855$	9.71516	0.332252
$856$	14.2834	0.488197
$857$	−12.9378	−0.441948	−0.220974	−	0.975280i	$-0.570924\pi$
$857$	−12.9378	−0.441948	−0.220974	+	0.975280i	$0.570924\pi$
$858$	−6.82999	−0.233172
$859$	−23.5370	−0.803074	−0.401537	−	0.915843i	$-0.631524\pi$
$859$	−23.5370	−0.803074	−0.401537	+	0.915843i	$0.631524\pi$
$860$	−10.2024	−0.347899
$861$	38.2502	1.30356
$862$	−29.5950	−1.00801
$863$	2.47055	0.0840987	0.0420493	−	0.999116i	$-0.486611\pi$
$863$	2.47055	0.0840987	0.0420493	+	0.999116i	$0.486611\pi$
$864$	−1.19552	−0.0406724
$865$	9.18842	0.312416
$866$	−17.9140	−0.608741
$867$	−38.6256	−1.31179
$868$	3.69320	0.125356
$869$	−4.63557	−0.157251
$870$	19.8985	0.674621
$871$	22.2187	0.752854
$872$	−15.1018	−0.511413
$873$	−20.0246	−0.677731
$874$	14.3086	0.483995
$875$	2.12832	0.0719502
$876$	−2.34302	−0.0791634
$877$	58.0001	1.95853	0.979263	−	0.202593i	$-0.0649370\pi$
$877$	58.0001	1.95853	0.979263	+	0.202593i	$0.0649370\pi$
$878$	−17.7633	−0.599483
$879$	68.3136	2.30416
$880$	1.00000	0.0337100
$881$	−54.5720	−1.83858	−0.919288	−	0.393585i	$-0.871235\pi$
$881$	−54.5720	−1.83858	−0.919288	+	0.393585i	$0.871235\pi$
$882$	−6.15036	−0.207093
$883$	−42.9461	−1.44525	−0.722626	−	0.691239i	$-0.757065\pi$
$883$	−42.9461	−1.44525	−0.722626	+	0.691239i	$0.757065\pi$
$884$	−2.09115	−0.0703331
$885$	−10.3823	−0.348997
$886$	−40.6235	−1.36477
$887$	2.34200	0.0786367	0.0393183	−	0.999227i	$-0.487481\pi$
$887$	2.34200	0.0786367	0.0393183	+	0.999227i	$0.487481\pi$
$888$	−6.55634	−0.220016
$889$	12.7542	0.427763
$890$	1.63889	0.0549358
$891$	−10.2704	−0.344071
$892$	14.8819	0.498285
$893$	1.71393	0.0573546
$894$	7.46704	0.249735
$895$	13.1788	0.440520
$896$	2.12832	0.0711021
$897$	−25.0451	−0.836232
$898$	−12.2932	−0.410229
$899$	14.7370	0.491508
$900$	2.48975	0.0829918
$901$	2.86451	0.0954307
$902$	7.67046	0.255398
$903$	−50.8763	−1.69306
$904$	9.88955	0.328922
$905$	22.6008	0.751276
$906$	−9.72944	−0.323239
$907$	−5.00284	−0.166117	−0.0830583	−	0.996545i	$-0.526469\pi$
$907$	−5.00284	−0.166117	−0.0830583	+	0.996545i	$0.526469\pi$
$908$	−23.8012	−0.789872
$909$	−23.9369	−0.793937
$910$	−6.20411	−0.205664
$911$	−27.9274	−0.925277	−0.462638	−	0.886547i	$-0.653097\pi$
$911$	−27.9274	−0.925277	−0.462638	+	0.886547i	$0.653097\pi$
$912$	9.14261	0.302742
$913$	7.03300	0.232758
$914$	34.7297	1.14876
$915$	−35.6181	−1.17750
$916$	3.75189	0.123966
$917$	−7.30581	−0.241259
$918$	−0.857629	−0.0283060
$919$	−56.5899	−1.86673	−0.933364	−	0.358930i	$-0.883142\pi$
$919$	−56.5899	−1.86673	−0.933364	+	0.358930i	$0.883142\pi$
$920$	3.66693	0.120895
$921$	−43.1599	−1.42217
$922$	−1.94521	−0.0640621
$923$	−28.4945	−0.937907
$924$	4.98669	0.164050
$925$	−2.79824	−0.0920056
$926$	−10.1038	−0.332031
$927$	−8.93427	−0.293440
$928$	8.49265	0.278785
$929$	30.3455	0.995605	0.497803	−	0.867290i	$-0.334140\pi$
$929$	30.3455	0.995605	0.497803	+	0.867290i	$0.334140\pi$
$930$	4.06578	0.133322
$931$	−9.63914	−0.315910
$932$	−5.28906	−0.173249
$933$	−76.9861	−2.52041
$934$	10.5811	0.346223
$935$	0.717368	0.0234605
$936$	−7.25771	−0.237226
$937$	13.9495	0.455711	0.227856	−	0.973695i	$-0.426829\pi$
$937$	13.9495	0.455711	0.227856	+	0.973695i	$0.426829\pi$
$938$	−16.2223	−0.529677
$939$	10.6879	0.348788
$940$	0.439238	0.0143264
$941$	1.07924	0.0351821	0.0175911	−	0.999845i	$-0.494400\pi$
$941$	1.07924	0.0351821	0.0175911	+	0.999845i	$0.494400\pi$
$942$	11.4128	0.371850
$943$	28.1270	0.915943
$944$	−4.43115	−0.144222
$945$	−2.54445	−0.0827709
$946$	−10.2024	−0.331709
$947$	−34.4104	−1.11819	−0.559093	−	0.829105i	$-0.688851\pi$
$947$	−34.4104	−1.11819	−0.559093	+	0.829105i	$0.688851\pi$
$948$	−10.8612	−0.352757
$949$	2.91503	0.0946260
$950$	3.90206	0.126600
$951$	56.8734	1.84424
$952$	1.52679	0.0494834
$953$	−22.9081	−0.742065	−0.371032	−	0.928620i	$-0.620996\pi$
$953$	−22.9081	−0.742065	−0.371032	+	0.928620i	$0.620996\pi$
$954$	9.94178	0.321877
$955$	−9.05396	−0.292979
$956$	−10.4023	−0.336434
$957$	19.8985	0.643226
$958$	−11.1788	−0.361170
$959$	17.6856	0.571099
$960$	2.34302	0.0756207
$961$	−27.9888	−0.902866
$962$	8.15696	0.262991
$963$	35.5622	1.14598
$964$	19.8139	0.638163
$965$	−1.44260	−0.0464390
$966$	18.2859	0.588338
$967$	−20.2272	−0.650464	−0.325232	−	0.945634i	$-0.605442\pi$
$967$	−20.2272	−0.650464	−0.325232	+	0.945634i	$0.605442\pi$
$968$	1.00000	0.0321412
$969$	6.55862	0.210693
$970$	−8.04281	−0.258239
$971$	−10.7269	−0.344244	−0.172122	−	0.985076i	$-0.555062\pi$
$971$	−10.7269	−0.344244	−0.172122	+	0.985076i	$0.555062\pi$
$972$	−20.4772	−0.656806
$973$	25.6213	0.821382
$974$	4.55855	0.146065
$975$	−6.82999	−0.218735
$976$	−15.2018	−0.486597
$977$	46.3901	1.48415	0.742076	−	0.670316i	$-0.233841\pi$
$977$	46.3901	1.48415	0.742076	+	0.670316i	$0.233841\pi$
$978$	6.62626	0.211884
$979$	1.63889	0.0523792
$980$	−2.47027	−0.0789098
$981$	−37.5999	−1.20047
$982$	10.5103	0.335398
$983$	31.6983	1.01102	0.505509	−	0.862821i	$-0.331305\pi$
$983$	31.6983	1.01102	0.505509	+	0.862821i	$0.331305\pi$
$984$	17.9721	0.572928
$985$	−14.8394	−0.472822
$986$	6.09236	0.194020
$987$	2.19034	0.0697194
$988$	−11.3746	−0.361875
$989$	−37.4115	−1.18962
$990$	2.48975	0.0791295
$991$	6.84588	0.217467	0.108733	−	0.994071i	$-0.465321\pi$
$991$	6.84588	0.217467	0.108733	+	0.994071i	$0.465321\pi$
$992$	1.73527	0.0550949
$993$	−64.0552	−2.03273
$994$	20.8043	0.659873
$995$	−20.7941	−0.659218
$996$	16.4785	0.522140
$997$	−16.0418	−0.508048	−0.254024	−	0.967198i	$-0.581754\pi$
$997$	−16.0418	−0.508048	−0.254024	+	0.967198i	$0.581754\pi$
$998$	17.2404	0.545736
$999$	3.34535	0.105842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bl.1.14	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bl.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.34302 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.34302 q^{6} +2.12832 q^{7} +1.00000 q^{8} +2.48975 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.34302 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.34302 q^{6} +2.12832 q^{7} +1.00000 q^{8} +2.48975 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.34302 q^{12} -2.91503 q^{13} +2.12832 q^{14} +2.34302 q^{15} +1.00000 q^{16} +0.717368 q^{17} +2.48975 q^{18} +3.90206 q^{19} +1.00000 q^{20} +4.98669 q^{21} +1.00000 q^{22} +3.66693 q^{23} +2.34302 q^{24} +1.00000 q^{25} -2.91503 q^{26} -1.19552 q^{27} +2.12832 q^{28} +8.49265 q^{29} +2.34302 q^{30} +1.73527 q^{31} +1.00000 q^{32} +2.34302 q^{33} +0.717368 q^{34} +2.12832 q^{35} +2.48975 q^{36} -2.79824 q^{37} +3.90206 q^{38} -6.82999 q^{39} +1.00000 q^{40} +7.67046 q^{41} +4.98669 q^{42} -10.2024 q^{43} +1.00000 q^{44} +2.48975 q^{45} +3.66693 q^{46} +0.439238 q^{47} +2.34302 q^{48} -2.47027 q^{49} +1.00000 q^{50} +1.68081 q^{51} -2.91503 q^{52} +3.99308 q^{53} -1.19552 q^{54} +1.00000 q^{55} +2.12832 q^{56} +9.14261 q^{57} +8.49265 q^{58} -4.43115 q^{59} +2.34302 q^{60} -15.2018 q^{61} +1.73527 q^{62} +5.29898 q^{63} +1.00000 q^{64} -2.91503 q^{65} +2.34302 q^{66} -7.62212 q^{67} +0.717368 q^{68} +8.59170 q^{69} +2.12832 q^{70} +9.77501 q^{71} +2.48975 q^{72} -1.00000 q^{73} -2.79824 q^{74} +2.34302 q^{75} +3.90206 q^{76} +2.12832 q^{77} -6.82999 q^{78} -4.63557 q^{79} +1.00000 q^{80} -10.2704 q^{81} +7.67046 q^{82} +7.03300 q^{83} +4.98669 q^{84} +0.717368 q^{85} -10.2024 q^{86} +19.8985 q^{87} +1.00000 q^{88} +1.63889 q^{89} +2.48975 q^{90} -6.20411 q^{91} +3.66693 q^{92} +4.06578 q^{93} +0.439238 q^{94} +3.90206 q^{95} +2.34302 q^{96} -8.04281 q^{97} -2.47027 q^{98} +2.48975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) \) 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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