LMFDB - Embedded newform 4002.2.a.bh.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 16x^{5} + 51x^{4} + 45x^{3} - 152x^{2} - 54x + 70 $ x^7 - 3x^6 - 16x^5 + 51x^4 + 45x^3 - 152x^2 - 54x + 70
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.924948$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.09187 q^{5} +1.00000 q^{6} -2.85370 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.09187 q^{5} +1.00000 q^{6} -2.85370 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.09187 q^{10} +0.493452 q^{11} +1.00000 q^{12} -5.03601 q^{13} -2.85370 q^{14} -4.09187 q^{15} +1.00000 q^{16} -0.585323 q^{17} +1.00000 q^{18} +0.996199 q^{19} -4.09187 q^{20} -2.85370 q^{21} +0.493452 q^{22} +1.00000 q^{23} +1.00000 q^{24} +11.7434 q^{25} -5.03601 q^{26} +1.00000 q^{27} -2.85370 q^{28} -1.00000 q^{29} -4.09187 q^{30} +4.90003 q^{31} +1.00000 q^{32} +0.493452 q^{33} -0.585323 q^{34} +11.6770 q^{35} +1.00000 q^{36} -1.11526 q^{37} +0.996199 q^{38} -5.03601 q^{39} -4.09187 q^{40} +7.29132 q^{41} -2.85370 q^{42} +6.49702 q^{43} +0.493452 q^{44} -4.09187 q^{45} +1.00000 q^{46} +4.69052 q^{47} +1.00000 q^{48} +1.14359 q^{49} +11.7434 q^{50} -0.585323 q^{51} -5.03601 q^{52} +7.44832 q^{53} +1.00000 q^{54} -2.01914 q^{55} -2.85370 q^{56} +0.996199 q^{57} -1.00000 q^{58} +1.14773 q^{59} -4.09187 q^{60} -6.67719 q^{61} +4.90003 q^{62} -2.85370 q^{63} +1.00000 q^{64} +20.6067 q^{65} +0.493452 q^{66} +16.1639 q^{67} -0.585323 q^{68} +1.00000 q^{69} +11.6770 q^{70} +6.89243 q^{71} +1.00000 q^{72} +1.12859 q^{73} -1.11526 q^{74} +11.7434 q^{75} +0.996199 q^{76} -1.40816 q^{77} -5.03601 q^{78} -10.1085 q^{79} -4.09187 q^{80} +1.00000 q^{81} +7.29132 q^{82} -0.118271 q^{83} -2.85370 q^{84} +2.39507 q^{85} +6.49702 q^{86} -1.00000 q^{87} +0.493452 q^{88} -12.2737 q^{89} -4.09187 q^{90} +14.3713 q^{91} +1.00000 q^{92} +4.90003 q^{93} +4.69052 q^{94} -4.07632 q^{95} +1.00000 q^{96} +1.37030 q^{97} +1.14359 q^{98} +0.493452 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 + 11 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−4.09187	−1.82994	−0.914970	−	0.403521i	$-0.867786\pi$
$5$	−4.09187	−1.82994	−0.914970	+	0.403521i	$0.867786\pi$
$6$	1.00000	0.408248
$7$	−2.85370	−1.07860	−0.539298	−	0.842115i	$-0.681310\pi$
$7$	−2.85370	−1.07860	−0.539298	+	0.842115i	$0.681310\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.09187	−1.29396
$11$	0.493452	0.148781	0.0743907	−	0.997229i	$-0.476299\pi$
$11$	0.493452	0.148781	0.0743907	+	0.997229i	$0.476299\pi$
$12$	1.00000	0.288675
$13$	−5.03601	−1.39674	−0.698370	−	0.715737i	$-0.746091\pi$
$13$	−5.03601	−1.39674	−0.698370	+	0.715737i	$0.746091\pi$
$14$	−2.85370	−0.762683
$15$	−4.09187	−1.05652
$16$	1.00000	0.250000
$17$	−0.585323	−0.141962	−0.0709808	−	0.997478i	$-0.522613\pi$
$17$	−0.585323	−0.141962	−0.0709808	+	0.997478i	$0.522613\pi$
$18$	1.00000	0.235702
$19$	0.996199	0.228544	0.114272	−	0.993450i	$-0.463547\pi$
$19$	0.996199	0.228544	0.114272	+	0.993450i	$0.463547\pi$
$20$	−4.09187	−0.914970
$21$	−2.85370	−0.622728
$22$	0.493452	0.105204
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	11.7434	2.34868
$26$	−5.03601	−0.987644
$27$	1.00000	0.192450
$28$	−2.85370	−0.539298
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−4.09187	−0.747070
$31$	4.90003	0.880071	0.440035	−	0.897980i	$-0.354966\pi$
$31$	4.90003	0.880071	0.440035	+	0.897980i	$0.354966\pi$
$32$	1.00000	0.176777
$33$	0.493452	0.0858990
$34$	−0.585323	−0.100382
$35$	11.6770	1.97377
$36$	1.00000	0.166667
$37$	−1.11526	−0.183347	−0.0916737	−	0.995789i	$-0.529222\pi$
$37$	−1.11526	−0.183347	−0.0916737	+	0.995789i	$0.529222\pi$
$38$	0.996199	0.161605
$39$	−5.03601	−0.806408
$40$	−4.09187	−0.646982
$41$	7.29132	1.13871	0.569356	−	0.822091i	$-0.307193\pi$
$41$	7.29132	1.13871	0.569356	+	0.822091i	$0.307193\pi$
$42$	−2.85370	−0.440335
$43$	6.49702	0.990786	0.495393	−	0.868669i	$-0.335024\pi$
$43$	6.49702	0.990786	0.495393	+	0.868669i	$0.335024\pi$
$44$	0.493452	0.0743907
$45$	−4.09187	−0.609980
$46$	1.00000	0.147442
$47$	4.69052	0.684183	0.342092	−	0.939667i	$-0.388865\pi$
$47$	4.69052	0.684183	0.342092	+	0.939667i	$0.388865\pi$
$48$	1.00000	0.144338
$49$	1.14359	0.163370
$50$	11.7434	1.66077
$51$	−0.585323	−0.0819616
$52$	−5.03601	−0.698370
$53$	7.44832	1.02310	0.511552	−	0.859252i	$-0.329071\pi$
$53$	7.44832	1.02310	0.511552	+	0.859252i	$0.329071\pi$
$54$	1.00000	0.136083
$55$	−2.01914	−0.272261
$56$	−2.85370	−0.381341
$57$	0.996199	0.131950
$58$	−1.00000	−0.131306
$59$	1.14773	0.149421	0.0747107	−	0.997205i	$-0.476197\pi$
$59$	1.14773	0.149421	0.0747107	+	0.997205i	$0.476197\pi$
$60$	−4.09187	−0.528258
$61$	−6.67719	−0.854927	−0.427464	−	0.904033i	$-0.640593\pi$
$61$	−6.67719	−0.854927	−0.427464	+	0.904033i	$0.640593\pi$
$62$	4.90003	0.622304
$63$	−2.85370	−0.359532
$64$	1.00000	0.125000
$65$	20.6067	2.55595
$66$	0.493452	0.0607397
$67$	16.1639	1.97473	0.987367	−	0.158448i	$-0.0506491\pi$
$67$	16.1639	1.97473	0.987367	+	0.158448i	$0.0506491\pi$
$68$	−0.585323	−0.0709808
$69$	1.00000	0.120386
$70$	11.6770	1.39566
$71$	6.89243	0.817980	0.408990	−	0.912539i	$-0.365881\pi$
$71$	6.89243	0.817980	0.408990	+	0.912539i	$0.365881\pi$
$72$	1.00000	0.117851
$73$	1.12859	0.132091	0.0660455	−	0.997817i	$-0.478962\pi$
$73$	1.12859	0.132091	0.0660455	+	0.997817i	$0.478962\pi$
$74$	−1.11526	−0.129646
$75$	11.7434	1.35601
$76$	0.996199	0.114272
$77$	−1.40816	−0.160475
$78$	−5.03601	−0.570216
$79$	−10.1085	−1.13730	−0.568648	−	0.822581i	$-0.692533\pi$
$79$	−10.1085	−1.13730	−0.568648	+	0.822581i	$0.692533\pi$
$80$	−4.09187	−0.457485
$81$	1.00000	0.111111
$82$	7.29132	0.805191
$83$	−0.118271	−0.0129819	−0.00649096	−	0.999979i	$-0.502066\pi$
$83$	−0.118271	−0.0129819	−0.00649096	+	0.999979i	$0.502066\pi$
$84$	−2.85370	−0.311364
$85$	2.39507	0.259781
$86$	6.49702	0.700592
$87$	−1.00000	−0.107211
$88$	0.493452	0.0526022
$89$	−12.2737	−1.30101	−0.650503	−	0.759504i	$-0.725442\pi$
$89$	−12.2737	−1.30101	−0.650503	+	0.759504i	$0.725442\pi$
$90$	−4.09187	−0.431321
$91$	14.3713	1.50652
$92$	1.00000	0.104257
$93$	4.90003	0.508109
$94$	4.69052	0.483790
$95$	−4.07632	−0.418221
$96$	1.00000	0.102062
$97$	1.37030	0.139133	0.0695667	−	0.997577i	$-0.477838\pi$
$97$	1.37030	0.139133	0.0695667	+	0.997577i	$0.477838\pi$
$98$	1.14359	0.115520
$99$	0.493452	0.0495938
$100$	11.7434	1.17434
$101$	9.39187	0.934526	0.467263	−	0.884118i	$-0.345240\pi$
$101$	9.39187	0.934526	0.467263	+	0.884118i	$0.345240\pi$
$102$	−0.585323	−0.0579556
$103$	9.77585	0.963244	0.481622	−	0.876379i	$-0.340048\pi$
$103$	9.77585	0.963244	0.481622	+	0.876379i	$0.340048\pi$
$104$	−5.03601	−0.493822
$105$	11.6770	1.13955
$106$	7.44832	0.723444
$107$	−10.2530	−0.991194	−0.495597	−	0.868553i	$-0.665051\pi$
$107$	−10.2530	−0.991194	−0.495597	+	0.868553i	$0.665051\pi$
$108$	1.00000	0.0962250
$109$	4.74008	0.454017	0.227009	−	0.973893i	$-0.427105\pi$
$109$	4.74008	0.454017	0.227009	+	0.973893i	$0.427105\pi$
$110$	−2.01914	−0.192518
$111$	−1.11526	−0.105856
$112$	−2.85370	−0.269649
$113$	8.46983	0.796775	0.398387	−	0.917217i	$-0.369570\pi$
$113$	8.46983	0.796775	0.398387	+	0.917217i	$0.369570\pi$
$114$	0.996199	0.0933026
$115$	−4.09187	−0.381569
$116$	−1.00000	−0.0928477
$117$	−5.03601	−0.465580
$118$	1.14773	0.105657
$119$	1.67033	0.153119
$120$	−4.09187	−0.373535
$121$	−10.7565	−0.977864
$122$	−6.67719	−0.604525
$123$	7.29132	0.657436
$124$	4.90003	0.440035
$125$	−27.5932	−2.46801
$126$	−2.85370	−0.254228
$127$	−13.0170	−1.15507	−0.577534	−	0.816366i	$-0.695985\pi$
$127$	−13.0170	−1.15507	−0.577534	+	0.816366i	$0.695985\pi$
$128$	1.00000	0.0883883
$129$	6.49702	0.572031
$130$	20.6067	1.80733
$131$	9.35723	0.817545	0.408773	−	0.912636i	$-0.365957\pi$
$131$	9.35723	0.817545	0.408773	+	0.912636i	$0.365957\pi$
$132$	0.493452	0.0429495
$133$	−2.84285	−0.246506
$134$	16.1639	1.39635
$135$	−4.09187	−0.352172
$136$	−0.585323	−0.0501910
$137$	−14.0617	−1.20138	−0.600688	−	0.799484i	$-0.705106\pi$
$137$	−14.0617	−1.20138	−0.600688	+	0.799484i	$0.705106\pi$
$138$	1.00000	0.0851257
$139$	1.33707	0.113408	0.0567042	−	0.998391i	$-0.481941\pi$
$139$	1.33707	0.113408	0.0567042	+	0.998391i	$0.481941\pi$
$140$	11.6770	0.986883
$141$	4.69052	0.395013
$142$	6.89243	0.578399
$143$	−2.48503	−0.207809
$144$	1.00000	0.0833333
$145$	4.09187	0.339811
$146$	1.12859	0.0934025
$147$	1.14359	0.0943216
$148$	−1.11526	−0.0916737
$149$	16.6516	1.36415	0.682077	−	0.731280i	$-0.261077\pi$
$149$	16.6516	1.36415	0.682077	+	0.731280i	$0.261077\pi$
$150$	11.7434	0.958845
$151$	−11.4148	−0.928922	−0.464461	−	0.885593i	$-0.653752\pi$
$151$	−11.4148	−0.928922	−0.464461	+	0.885593i	$0.653752\pi$
$152$	0.996199	0.0808024
$153$	−0.585323	−0.0473206
$154$	−1.40816	−0.113473
$155$	−20.0503	−1.61048
$156$	−5.03601	−0.403204
$157$	−15.9982	−1.27680	−0.638399	−	0.769705i	$-0.720403\pi$
$157$	−15.9982	−1.27680	−0.638399	+	0.769705i	$0.720403\pi$
$158$	−10.1085	−0.804190
$159$	7.44832	0.590690
$160$	−4.09187	−0.323491
$161$	−2.85370	−0.224903
$162$	1.00000	0.0785674
$163$	23.2198	1.81871	0.909356	−	0.416019i	$-0.136575\pi$
$163$	23.2198	1.81871	0.909356	+	0.416019i	$0.136575\pi$
$164$	7.29132	0.569356
$165$	−2.01914	−0.157190
$166$	−0.118271	−0.00917960
$167$	16.3016	1.26145	0.630727	−	0.776005i	$-0.282757\pi$
$167$	16.3016	1.26145	0.630727	+	0.776005i	$0.282757\pi$
$168$	−2.85370	−0.220168
$169$	12.3614	0.950880
$170$	2.39507	0.183693
$171$	0.996199	0.0761812
$172$	6.49702	0.495393
$173$	−16.9323	−1.28734	−0.643669	−	0.765304i	$-0.722589\pi$
$173$	−16.9323	−1.28734	−0.643669	+	0.765304i	$0.722589\pi$
$174$	−1.00000	−0.0758098
$175$	−33.5121	−2.53328
$176$	0.493452	0.0371953
$177$	1.14773	0.0862685
$178$	−12.2737	−0.919950
$179$	16.5484	1.23688	0.618442	−	0.785831i	$-0.287764\pi$
$179$	16.5484	1.23688	0.618442	+	0.785831i	$0.287764\pi$
$180$	−4.09187	−0.304990
$181$	9.58866	0.712719	0.356360	−	0.934349i	$-0.384018\pi$
$181$	9.58866	0.712719	0.356360	+	0.934349i	$0.384018\pi$
$182$	14.3713	1.06527
$183$	−6.67719	−0.493592
$184$	1.00000	0.0737210
$185$	4.56349	0.335515
$186$	4.90003	0.359287
$187$	−0.288829	−0.0211213
$188$	4.69052	0.342092
$189$	−2.85370	−0.207576
$190$	−4.07632	−0.295727
$191$	−0.377430	−0.0273099	−0.0136549	−	0.999907i	$-0.504347\pi$
$191$	−0.377430	−0.0273099	−0.0136549	+	0.999907i	$0.504347\pi$
$192$	1.00000	0.0721688
$193$	−5.97717	−0.430246	−0.215123	−	0.976587i	$-0.569015\pi$
$193$	−5.97717	−0.430246	−0.215123	+	0.976587i	$0.569015\pi$
$194$	1.37030	0.0983821
$195$	20.6067	1.47568
$196$	1.14359	0.0816849
$197$	23.4602	1.67147	0.835734	−	0.549135i	$-0.185043\pi$
$197$	23.4602	1.67147	0.835734	+	0.549135i	$0.185043\pi$
$198$	0.493452	0.0350681
$199$	−11.6183	−0.823600	−0.411800	−	0.911274i	$-0.635100\pi$
$199$	−11.6183	−0.823600	−0.411800	+	0.911274i	$0.635100\pi$
$200$	11.7434	0.830384
$201$	16.1639	1.14011
$202$	9.39187	0.660810
$203$	2.85370	0.200290
$204$	−0.585323	−0.0409808
$205$	−29.8351	−2.08378
$206$	9.77585	0.681116
$207$	1.00000	0.0695048
$208$	−5.03601	−0.349185
$209$	0.491576	0.0340030
$210$	11.6770	0.805787
$211$	12.4896	0.859816	0.429908	−	0.902873i	$-0.358546\pi$
$211$	12.4896	0.859816	0.429908	+	0.902873i	$0.358546\pi$
$212$	7.44832	0.511552
$213$	6.89243	0.472261
$214$	−10.2530	−0.700880
$215$	−26.5850	−1.81308
$216$	1.00000	0.0680414
$217$	−13.9832	−0.949241
$218$	4.74008	0.321039
$219$	1.12859	0.0762628
$220$	−2.01914	−0.136131
$221$	2.94770	0.198283
$222$	−1.11526	−0.0748512
$223$	−2.51777	−0.168602	−0.0843011	−	0.996440i	$-0.526866\pi$
$223$	−2.51777	−0.168602	−0.0843011	+	0.996440i	$0.526866\pi$
$224$	−2.85370	−0.190671
$225$	11.7434	0.782894
$226$	8.46983	0.563405
$227$	8.87577	0.589106	0.294553	−	0.955635i	$-0.404829\pi$
$227$	8.87577	0.589106	0.294553	+	0.955635i	$0.404829\pi$
$228$	0.996199	0.0659749
$229$	−22.0806	−1.45913	−0.729564	−	0.683913i	$-0.760277\pi$
$229$	−22.0806	−1.45913	−0.729564	+	0.683913i	$0.760277\pi$
$230$	−4.09187	−0.269810
$231$	−1.40816	−0.0926503
$232$	−1.00000	−0.0656532
$233$	10.8219	0.708968	0.354484	−	0.935062i	$-0.384657\pi$
$233$	10.8219	0.708968	0.354484	+	0.935062i	$0.384657\pi$
$234$	−5.03601	−0.329215
$235$	−19.1930	−1.25201
$236$	1.14773	0.0747107
$237$	−10.1085	−0.656618
$238$	1.67033	0.108272
$239$	21.4582	1.38802	0.694008	−	0.719967i	$-0.255843\pi$
$239$	21.4582	1.38802	0.694008	+	0.719967i	$0.255843\pi$
$240$	−4.09187	−0.264129
$241$	−4.15852	−0.267874	−0.133937	−	0.990990i	$-0.542762\pi$
$241$	−4.15852	−0.267874	−0.133937	+	0.990990i	$0.542762\pi$
$242$	−10.7565	−0.691454
$243$	1.00000	0.0641500
$244$	−6.67719	−0.427464
$245$	−4.67942	−0.298957
$246$	7.29132	0.464877
$247$	−5.01687	−0.319216
$248$	4.90003	0.311152
$249$	−0.118271	−0.00749511
$250$	−27.5932	−1.74514
$251$	−14.0739	−0.888337	−0.444168	−	0.895943i	$-0.646501\pi$
$251$	−14.0739	−0.888337	−0.444168	+	0.895943i	$0.646501\pi$
$252$	−2.85370	−0.179766
$253$	0.493452	0.0310231
$254$	−13.0170	−0.816757
$255$	2.39507	0.149985
$256$	1.00000	0.0625000
$257$	17.5843	1.09688	0.548439	−	0.836190i	$-0.315222\pi$
$257$	17.5843	1.09688	0.548439	+	0.836190i	$0.315222\pi$
$258$	6.49702	0.404487
$259$	3.18261	0.197758
$260$	20.6067	1.27797
$261$	−1.00000	−0.0618984
$262$	9.35723	0.578092
$263$	7.57374	0.467017	0.233508	−	0.972355i	$-0.424979\pi$
$263$	7.57374	0.467017	0.233508	+	0.972355i	$0.424979\pi$
$264$	0.493452	0.0303699
$265$	−30.4775	−1.87222
$266$	−2.84285	−0.174306
$267$	−12.2737	−0.751136
$268$	16.1639	0.987367
$269$	23.7986	1.45102	0.725512	−	0.688209i	$-0.241603\pi$
$269$	23.7986	1.45102	0.725512	+	0.688209i	$0.241603\pi$
$270$	−4.09187	−0.249023
$271$	0.414208	0.0251613	0.0125807	−	0.999921i	$-0.495995\pi$
$271$	0.414208	0.0251613	0.0125807	+	0.999921i	$0.495995\pi$
$272$	−0.585323	−0.0354904
$273$	14.3713	0.869788
$274$	−14.0617	−0.849501
$275$	5.79481	0.349440
$276$	1.00000	0.0601929
$277$	27.6210	1.65958	0.829792	−	0.558073i	$-0.188459\pi$
$277$	27.6210	1.65958	0.829792	+	0.558073i	$0.188459\pi$
$278$	1.33707	0.0801919
$279$	4.90003	0.293357
$280$	11.6770	0.697832
$281$	0.926190	0.0552519	0.0276259	−	0.999618i	$-0.491205\pi$
$281$	0.926190	0.0552519	0.0276259	+	0.999618i	$0.491205\pi$
$282$	4.69052	0.279317
$283$	31.2174	1.85568	0.927840	−	0.372979i	$-0.121664\pi$
$283$	31.2174	1.85568	0.927840	+	0.372979i	$0.121664\pi$
$284$	6.89243	0.408990
$285$	−4.07632	−0.241460
$286$	−2.48503	−0.146943
$287$	−20.8072	−1.22821
$288$	1.00000	0.0589256
$289$	−16.6574	−0.979847
$290$	4.09187	0.240283
$291$	1.37030	0.0803287
$292$	1.12859	0.0660455
$293$	−5.61469	−0.328014	−0.164007	−	0.986459i	$-0.552442\pi$
$293$	−5.61469	−0.328014	−0.164007	+	0.986459i	$0.552442\pi$
$294$	1.14359	0.0666955
$295$	−4.69636	−0.273432
$296$	−1.11526	−0.0648231
$297$	0.493452	0.0286330
$298$	16.6516	0.964603
$299$	−5.03601	−0.291240
$300$	11.7434	0.678006
$301$	−18.5405	−1.06866
$302$	−11.4148	−0.656847
$303$	9.39187	0.539549
$304$	0.996199	0.0571359
$305$	27.3222	1.56447
$306$	−0.585323	−0.0334607
$307$	30.8183	1.75889	0.879446	−	0.475998i	$-0.157913\pi$
$307$	30.8183	1.75889	0.879446	+	0.475998i	$0.157913\pi$
$308$	−1.40816	−0.0802375
$309$	9.77585	0.556129
$310$	−20.0503	−1.13878
$311$	7.44042	0.421908	0.210954	−	0.977496i	$-0.432343\pi$
$311$	7.44042	0.421908	0.210954	+	0.977496i	$0.432343\pi$
$312$	−5.03601	−0.285108
$313$	−21.6879	−1.22587	−0.612936	−	0.790133i	$-0.710012\pi$
$313$	−21.6879	−1.22587	−0.612936	+	0.790133i	$0.710012\pi$
$314$	−15.9982	−0.902833
$315$	11.6770	0.657922
$316$	−10.1085	−0.568648
$317$	15.4503	0.867774	0.433887	−	0.900967i	$-0.357142\pi$
$317$	15.4503	0.867774	0.433887	+	0.900967i	$0.357142\pi$
$318$	7.44832	0.417681
$319$	−0.493452	−0.0276280
$320$	−4.09187	−0.228743
$321$	−10.2530	−0.572266
$322$	−2.85370	−0.159030
$323$	−0.583098	−0.0324445
$324$	1.00000	0.0555556
$325$	−59.1400	−3.28050
$326$	23.2198	1.28602
$327$	4.74008	0.262127
$328$	7.29132	0.402596
$329$	−13.3853	−0.737957
$330$	−2.01914	−0.111150
$331$	−32.6232	−1.79313	−0.896567	−	0.442909i	$-0.853947\pi$
$331$	−32.6232	−1.79313	−0.896567	+	0.442909i	$0.853947\pi$
$332$	−0.118271	−0.00649096
$333$	−1.11526	−0.0611158
$334$	16.3016	0.891982
$335$	−66.1406	−3.61365
$336$	−2.85370	−0.155682
$337$	2.83896	0.154648	0.0773241	−	0.997006i	$-0.475362\pi$
$337$	2.83896	0.154648	0.0773241	+	0.997006i	$0.475362\pi$
$338$	12.3614	0.672374
$339$	8.46983	0.460018
$340$	2.39507	0.129891
$341$	2.41793	0.130938
$342$	0.996199	0.0538683
$343$	16.7124	0.902386
$344$	6.49702	0.350296
$345$	−4.09187	−0.220299
$346$	−16.9323	−0.910285
$347$	24.9698	1.34045	0.670224	−	0.742159i	$-0.266198\pi$
$347$	24.9698	1.34045	0.670224	+	0.742159i	$0.266198\pi$
$348$	−1.00000	−0.0536056
$349$	−16.8513	−0.902029	−0.451015	−	0.892517i	$-0.648938\pi$
$349$	−16.8513	−0.902029	−0.451015	+	0.892517i	$0.648938\pi$
$350$	−33.5121	−1.79130
$351$	−5.03601	−0.268803
$352$	0.493452	0.0263011
$353$	−15.4083	−0.820103	−0.410052	−	0.912062i	$-0.634489\pi$
$353$	−15.4083	−0.820103	−0.410052	+	0.912062i	$0.634489\pi$
$354$	1.14773	0.0610011
$355$	−28.2029	−1.49686
$356$	−12.2737	−0.650503
$357$	1.67033	0.0884035
$358$	16.5484	0.874609
$359$	−22.8561	−1.20630	−0.603149	−	0.797628i	$-0.706088\pi$
$359$	−22.8561	−1.20630	−0.603149	+	0.797628i	$0.706088\pi$
$360$	−4.09187	−0.215661
$361$	−18.0076	−0.947768
$362$	9.58866	0.503969
$363$	−10.7565	−0.564570
$364$	14.3713	0.753259
$365$	−4.61803	−0.241719
$366$	−6.67719	−0.349023
$367$	−25.5708	−1.33478	−0.667392	−	0.744706i	$-0.732589\pi$
$367$	−25.5708	−1.33478	−0.667392	+	0.744706i	$0.732589\pi$
$368$	1.00000	0.0521286
$369$	7.29132	0.379571
$370$	4.56349	0.237245
$371$	−21.2552	−1.10352
$372$	4.90003	0.254055
$373$	−15.4087	−0.797832	−0.398916	−	0.916987i	$-0.630613\pi$
$373$	−15.4087	−0.797832	−0.398916	+	0.916987i	$0.630613\pi$
$374$	−0.288829	−0.0149350
$375$	−27.5932	−1.42490
$376$	4.69052	0.241895
$377$	5.03601	0.259368
$378$	−2.85370	−0.146778
$379$	23.4695	1.20555	0.602774	−	0.797912i	$-0.294062\pi$
$379$	23.4695	1.20555	0.602774	+	0.797912i	$0.294062\pi$
$380$	−4.07632	−0.209111
$381$	−13.0170	−0.666879
$382$	−0.377430	−0.0193110
$383$	−10.3053	−0.526574	−0.263287	−	0.964718i	$-0.584807\pi$
$383$	−10.3053	−0.526574	−0.263287	+	0.964718i	$0.584807\pi$
$384$	1.00000	0.0510310
$385$	5.76202	0.293660
$386$	−5.97717	−0.304230
$387$	6.49702	0.330262
$388$	1.37030	0.0695667
$389$	8.28993	0.420316	0.210158	−	0.977667i	$-0.432602\pi$
$389$	8.28993	0.420316	0.210158	+	0.977667i	$0.432602\pi$
$390$	20.6067	1.04346
$391$	−0.585323	−0.0296011
$392$	1.14359	0.0577600
$393$	9.35723	0.472010
$394$	23.4602	1.18191
$395$	41.3627	2.08118
$396$	0.493452	0.0247969
$397$	−9.28617	−0.466060	−0.233030	−	0.972470i	$-0.574864\pi$
$397$	−9.28617	−0.466060	−0.233030	+	0.972470i	$0.574864\pi$
$398$	−11.6183	−0.582373
$399$	−2.84285	−0.142321
$400$	11.7434	0.587170
$401$	−1.01662	−0.0507674	−0.0253837	−	0.999678i	$-0.508081\pi$
$401$	−1.01662	−0.0507674	−0.0253837	+	0.999678i	$0.508081\pi$
$402$	16.1639	0.806182
$403$	−24.6766	−1.22923
$404$	9.39187	0.467263
$405$	−4.09187	−0.203327
$406$	2.85370	0.141627
$407$	−0.550326	−0.0272787
$408$	−0.585323	−0.0289778
$409$	−8.46001	−0.418320	−0.209160	−	0.977881i	$-0.567073\pi$
$409$	−8.46001	−0.418320	−0.209160	+	0.977881i	$0.567073\pi$
$410$	−29.8351	−1.47345
$411$	−14.0617	−0.693614
$412$	9.77585	0.481622
$413$	−3.27527	−0.161165
$414$	1.00000	0.0491473
$415$	0.483949	0.0237561
$416$	−5.03601	−0.246911
$417$	1.33707	0.0654764
$418$	0.491576	0.0240438
$419$	7.56897	0.369768	0.184884	−	0.982760i	$-0.440809\pi$
$419$	7.56897	0.369768	0.184884	+	0.982760i	$0.440809\pi$
$420$	11.6770	0.569777
$421$	−13.2733	−0.646902	−0.323451	−	0.946245i	$-0.604843\pi$
$421$	−13.2733	−0.646902	−0.323451	+	0.946245i	$0.604843\pi$
$422$	12.4896	0.607982
$423$	4.69052	0.228061
$424$	7.44832	0.361722
$425$	−6.87369	−0.333423
$426$	6.89243	0.333939
$427$	19.0547	0.922121
$428$	−10.2530	−0.495597
$429$	−2.48503	−0.119978
$430$	−26.5850	−1.28204
$431$	11.5827	0.557917	0.278959	−	0.960303i	$-0.410011\pi$
$431$	11.5827	0.557917	0.278959	+	0.960303i	$0.410011\pi$
$432$	1.00000	0.0481125
$433$	2.27384	0.109274	0.0546368	−	0.998506i	$-0.482600\pi$
$433$	2.27384	0.109274	0.0546368	+	0.998506i	$0.482600\pi$
$434$	−13.9832	−0.671215
$435$	4.09187	0.196190
$436$	4.74008	0.227009
$437$	0.996199	0.0476547
$438$	1.12859	0.0539259
$439$	−23.6409	−1.12832	−0.564160	−	0.825666i	$-0.690800\pi$
$439$	−23.6409	−1.12832	−0.564160	+	0.825666i	$0.690800\pi$
$440$	−2.01914	−0.0962588
$441$	1.14359	0.0544566
$442$	2.94770	0.140208
$443$	8.74303	0.415394	0.207697	−	0.978193i	$-0.433403\pi$
$443$	8.74303	0.415394	0.207697	+	0.978193i	$0.433403\pi$
$444$	−1.11526	−0.0529278
$445$	50.2222	2.38076
$446$	−2.51777	−0.119220
$447$	16.6516	0.787595
$448$	−2.85370	−0.134825
$449$	−24.2675	−1.14526	−0.572628	−	0.819815i	$-0.694076\pi$
$449$	−24.2675	−1.14526	−0.572628	+	0.819815i	$0.694076\pi$
$450$	11.7434	0.553590
$451$	3.59791	0.169419
$452$	8.46983	0.398387
$453$	−11.4148	−0.536314
$454$	8.87577	0.416561
$455$	−58.8053	−2.75684
$456$	0.996199	0.0466513
$457$	10.8460	0.507352	0.253676	−	0.967289i	$-0.418360\pi$
$457$	10.8460	0.507352	0.253676	+	0.967289i	$0.418360\pi$
$458$	−22.0806	−1.03176
$459$	−0.585323	−0.0273205
$460$	−4.09187	−0.190784
$461$	0.313283	0.0145911	0.00729553	−	0.999973i	$-0.497678\pi$
$461$	0.313283	0.0145911	0.00729553	+	0.999973i	$0.497678\pi$
$462$	−1.40816	−0.0655136
$463$	−15.3959	−0.715506	−0.357753	−	0.933816i	$-0.616457\pi$
$463$	−15.3959	−0.715506	−0.357753	+	0.933816i	$0.616457\pi$
$464$	−1.00000	−0.0464238
$465$	−20.0503	−0.929809
$466$	10.8219	0.501316
$467$	−27.1999	−1.25866	−0.629330	−	0.777139i	$-0.716670\pi$
$467$	−27.1999	−1.25866	−0.629330	+	0.777139i	$0.716670\pi$
$468$	−5.03601	−0.232790
$469$	−46.1269	−2.12994
$470$	−19.1930	−0.885308
$471$	−15.9982	−0.737160
$472$	1.14773	0.0528285
$473$	3.20597	0.147411
$474$	−10.1085	−0.464299
$475$	11.6988	0.536777
$476$	1.67033	0.0765597
$477$	7.44832	0.341035
$478$	21.4582	0.981475
$479$	42.3206	1.93368	0.966838	−	0.255390i	$-0.0822040\pi$
$479$	42.3206	1.93368	0.966838	+	0.255390i	$0.0822040\pi$
$480$	−4.09187	−0.186768
$481$	5.61646	0.256088
$482$	−4.15852	−0.189416
$483$	−2.85370	−0.129848
$484$	−10.7565	−0.488932
$485$	−5.60711	−0.254606
$486$	1.00000	0.0453609
$487$	11.7342	0.531727	0.265863	−	0.964011i	$-0.414343\pi$
$487$	11.7342	0.531727	0.265863	+	0.964011i	$0.414343\pi$
$488$	−6.67719	−0.302262
$489$	23.2198	1.05003
$490$	−4.67942	−0.211395
$491$	4.97472	0.224506	0.112253	−	0.993680i	$-0.464193\pi$
$491$	4.97472	0.224506	0.112253	+	0.993680i	$0.464193\pi$
$492$	7.29132	0.328718
$493$	0.585323	0.0263616
$494$	−5.01687	−0.225720
$495$	−2.01914	−0.0907537
$496$	4.90003	0.220018
$497$	−19.6689	−0.882271
$498$	−0.118271	−0.00529985
$499$	−16.3143	−0.730328	−0.365164	−	0.930943i	$-0.618987\pi$
$499$	−16.3143	−0.730328	−0.365164	+	0.930943i	$0.618987\pi$
$500$	−27.5932	−1.23400
$501$	16.3016	0.728300
$502$	−14.0739	−0.628149
$503$	−7.46348	−0.332780	−0.166390	−	0.986060i	$-0.553211\pi$
$503$	−7.46348	−0.332780	−0.166390	+	0.986060i	$0.553211\pi$
$504$	−2.85370	−0.127114
$505$	−38.4303	−1.71013
$506$	0.493452	0.0219366
$507$	12.3614	0.548991
$508$	−13.0170	−0.577534
$509$	−22.9421	−1.01689	−0.508446	−	0.861094i	$-0.669780\pi$
$509$	−22.9421	−1.01689	−0.508446	+	0.861094i	$0.669780\pi$
$510$	2.39507	0.106055
$511$	−3.22064	−0.142473
$512$	1.00000	0.0441942
$513$	0.996199	0.0439833
$514$	17.5843	0.775610
$515$	−40.0015	−1.76268
$516$	6.49702	0.286015
$517$	2.31455	0.101794
$518$	3.18261	0.139836
$519$	−16.9323	−0.743245
$520$	20.6067	0.903664
$521$	39.4342	1.72764	0.863821	−	0.503798i	$-0.168064\pi$
$521$	39.4342	1.72764	0.863821	+	0.503798i	$0.168064\pi$
$522$	−1.00000	−0.0437688
$523$	12.9422	0.565923	0.282961	−	0.959131i	$-0.408683\pi$
$523$	12.9422	0.565923	0.282961	+	0.959131i	$0.408683\pi$
$524$	9.35723	0.408773
$525$	−33.5121	−1.46259
$526$	7.57374	0.330231
$527$	−2.86810	−0.124936
$528$	0.493452	0.0214747
$529$	1.00000	0.0434783
$530$	−30.4775	−1.32386
$531$	1.14773	0.0498072
$532$	−2.84285	−0.123253
$533$	−36.7192	−1.59048
$534$	−12.2737	−0.531133
$535$	41.9539	1.81383
$536$	16.1639	0.698174
$537$	16.5484	0.714115
$538$	23.7986	1.02603
$539$	0.564306	0.0243064
$540$	−4.09187	−0.176086
$541$	34.1728	1.46920	0.734601	−	0.678500i	$-0.237369\pi$
$541$	34.1728	1.46920	0.734601	+	0.678500i	$0.237369\pi$
$542$	0.414208	0.0177918
$543$	9.58866	0.411489
$544$	−0.585323	−0.0250955
$545$	−19.3958	−0.830824
$546$	14.3713	0.615033
$547$	−3.71313	−0.158762	−0.0793809	−	0.996844i	$-0.525294\pi$
$547$	−3.71313	−0.158762	−0.0793809	+	0.996844i	$0.525294\pi$
$548$	−14.0617	−0.600688
$549$	−6.67719	−0.284976
$550$	5.79481	0.247091
$551$	−0.996199	−0.0424395
$552$	1.00000	0.0425628
$553$	28.8466	1.22668
$554$	27.6210	1.17350
$555$	4.56349	0.193709
$556$	1.33707	0.0567042
$557$	17.3170	0.733744	0.366872	−	0.930271i	$-0.380429\pi$
$557$	17.3170	0.733744	0.366872	+	0.930271i	$0.380429\pi$
$558$	4.90003	0.207435
$559$	−32.7191	−1.38387
$560$	11.6770	0.493442
$561$	−0.288829	−0.0121944
$562$	0.926190	0.0390690
$563$	−6.46608	−0.272513	−0.136256	−	0.990674i	$-0.543507\pi$
$563$	−6.46608	−0.272513	−0.136256	+	0.990674i	$0.543507\pi$
$564$	4.69052	0.197507
$565$	−34.6575	−1.45805
$566$	31.2174	1.31216
$567$	−2.85370	−0.119844
$568$	6.89243	0.289200
$569$	−4.60773	−0.193166	−0.0965830	−	0.995325i	$-0.530791\pi$
$569$	−4.60773	−0.193166	−0.0965830	+	0.995325i	$0.530791\pi$
$570$	−4.07632	−0.170738
$571$	−5.05862	−0.211697	−0.105848	−	0.994382i	$-0.533756\pi$
$571$	−5.05862	−0.211697	−0.105848	+	0.994382i	$0.533756\pi$
$572$	−2.48503	−0.103904
$573$	−0.377430	−0.0157674
$574$	−20.8072	−0.868476
$575$	11.7434	0.489734
$576$	1.00000	0.0416667
$577$	10.0785	0.419573	0.209786	−	0.977747i	$-0.432723\pi$
$577$	10.0785	0.419573	0.209786	+	0.977747i	$0.432723\pi$
$578$	−16.6574	−0.692856
$579$	−5.97717	−0.248403
$580$	4.09187	0.169906
$581$	0.337509	0.0140022
$582$	1.37030	0.0568009
$583$	3.67539	0.152219
$584$	1.12859	0.0467012
$585$	20.6067	0.851983
$586$	−5.61469	−0.231941
$587$	19.7036	0.813255	0.406627	−	0.913594i	$-0.366705\pi$
$587$	19.7036	0.813255	0.406627	+	0.913594i	$0.366705\pi$
$588$	1.14359	0.0471608
$589$	4.88140	0.201135
$590$	−4.69636	−0.193346
$591$	23.4602	0.965022
$592$	−1.11526	−0.0458368
$593$	8.31604	0.341499	0.170749	−	0.985314i	$-0.445381\pi$
$593$	8.31604	0.341499	0.170749	+	0.985314i	$0.445381\pi$
$594$	0.493452	0.0202466
$595$	−6.83479	−0.280199
$596$	16.6516	0.682077
$597$	−11.6183	−0.475506
$598$	−5.03601	−0.205938
$599$	−17.5413	−0.716717	−0.358358	−	0.933584i	$-0.616663\pi$
$599$	−17.5413	−0.716717	−0.358358	+	0.933584i	$0.616663\pi$
$600$	11.7434	0.479423
$601$	−34.2128	−1.39557	−0.697785	−	0.716307i	$-0.745831\pi$
$601$	−34.2128	−1.39557	−0.697785	+	0.716307i	$0.745831\pi$
$602$	−18.5405	−0.755656
$603$	16.1639	0.658245
$604$	−11.4148	−0.464461
$605$	44.0142	1.78943
$606$	9.39187	0.381519
$607$	34.6251	1.40539	0.702695	−	0.711491i	$-0.251980\pi$
$607$	34.6251	1.40539	0.702695	+	0.711491i	$0.251980\pi$
$608$	0.996199	0.0404012
$609$	2.85370	0.115638
$610$	27.3222	1.10624
$611$	−23.6215	−0.955625
$612$	−0.585323	−0.0236603
$613$	3.77392	0.152427	0.0762135	−	0.997092i	$-0.475717\pi$
$613$	3.77392	0.152427	0.0762135	+	0.997092i	$0.475717\pi$
$614$	30.8183	1.24372
$615$	−29.8351	−1.20307
$616$	−1.40816	−0.0567365
$617$	−32.6717	−1.31531	−0.657657	−	0.753318i	$-0.728452\pi$
$617$	−32.6717	−1.31531	−0.657657	+	0.753318i	$0.728452\pi$
$618$	9.77585	0.393243
$619$	−38.2842	−1.53877	−0.769387	−	0.638783i	$-0.779438\pi$
$619$	−38.2842	−1.53877	−0.769387	+	0.638783i	$0.779438\pi$
$620$	−20.0503	−0.805239
$621$	1.00000	0.0401286
$622$	7.44042	0.298334
$623$	35.0253	1.40326
$624$	−5.03601	−0.201602
$625$	54.1906	2.16762
$626$	−21.6879	−0.866822
$627$	0.491576	0.0196317
$628$	−15.9982	−0.638399
$629$	0.652786	0.0260283
$630$	11.6770	0.465221
$631$	44.0796	1.75478	0.877392	−	0.479775i	$-0.159282\pi$
$631$	44.0796	1.75478	0.877392	+	0.479775i	$0.159282\pi$
$632$	−10.1085	−0.402095
$633$	12.4896	0.496415
$634$	15.4503	0.613609
$635$	53.2637	2.11371
$636$	7.44832	0.295345
$637$	−5.75913	−0.228185
$638$	−0.493452	−0.0195359
$639$	6.89243	0.272660
$640$	−4.09187	−0.161745
$641$	−2.86813	−0.113284	−0.0566421	−	0.998395i	$-0.518039\pi$
$641$	−2.86813	−0.113284	−0.0566421	+	0.998395i	$0.518039\pi$
$642$	−10.2530	−0.404653
$643$	32.3176	1.27448	0.637241	−	0.770664i	$-0.280076\pi$
$643$	32.3176	1.27448	0.637241	+	0.770664i	$0.280076\pi$
$644$	−2.85370	−0.112451
$645$	−26.5850	−1.04678
$646$	−0.583098	−0.0229417
$647$	−31.4708	−1.23724	−0.618622	−	0.785689i	$-0.712309\pi$
$647$	−31.4708	−1.23724	−0.618622	+	0.785689i	$0.712309\pi$
$648$	1.00000	0.0392837
$649$	0.566349	0.0222311
$650$	−59.1400	−2.31966
$651$	−13.9832	−0.548045
$652$	23.2198	0.909356
$653$	18.4318	0.721293	0.360647	−	0.932703i	$-0.382556\pi$
$653$	18.4318	0.721293	0.360647	+	0.932703i	$0.382556\pi$
$654$	4.74008	0.185352
$655$	−38.2886	−1.49606
$656$	7.29132	0.284678
$657$	1.12859	0.0440303
$658$	−13.3853	−0.521815
$659$	19.0985	0.743972	0.371986	−	0.928238i	$-0.378677\pi$
$659$	19.0985	0.743972	0.371986	+	0.928238i	$0.378677\pi$
$660$	−2.01914	−0.0785950
$661$	41.9628	1.63216	0.816082	−	0.577936i	$-0.196142\pi$
$661$	41.9628	1.63216	0.816082	+	0.577936i	$0.196142\pi$
$662$	−32.6232	−1.26794
$663$	2.94770	0.114479
$664$	−0.118271	−0.00458980
$665$	11.6326	0.451092
$666$	−1.11526	−0.0432154
$667$	−1.00000	−0.0387202
$668$	16.3016	0.630727
$669$	−2.51777	−0.0973426
$670$	−66.1406	−2.55523
$671$	−3.29487	−0.127197
$672$	−2.85370	−0.110084
$673$	19.6186	0.756243	0.378122	−	0.925756i	$-0.376570\pi$
$673$	19.6186	0.756243	0.378122	+	0.925756i	$0.376570\pi$
$674$	2.83896	0.109353
$675$	11.7434	0.452004
$676$	12.3614	0.475440
$677$	9.69381	0.372563	0.186282	−	0.982496i	$-0.440356\pi$
$677$	9.69381	0.372563	0.186282	+	0.982496i	$0.440356\pi$
$678$	8.46983	0.325282
$679$	−3.91043	−0.150069
$680$	2.39507	0.0918466
$681$	8.87577	0.340120
$682$	2.41793	0.0925872
$683$	19.3892	0.741907	0.370953	−	0.928651i	$-0.379031\pi$
$683$	19.3892	0.741907	0.370953	+	0.928651i	$0.379031\pi$
$684$	0.996199	0.0380906
$685$	57.5388	2.19845
$686$	16.7124	0.638083
$687$	−22.0806	−0.842428
$688$	6.49702	0.247697
$689$	−37.5098	−1.42901
$690$	−4.09187	−0.155775
$691$	6.35111	0.241607	0.120804	−	0.992676i	$-0.461453\pi$
$691$	6.35111	0.241607	0.120804	+	0.992676i	$0.461453\pi$
$692$	−16.9323	−0.643669
$693$	−1.40816	−0.0534917
$694$	24.9698	0.947839
$695$	−5.47110	−0.207531
$696$	−1.00000	−0.0379049
$697$	−4.26778	−0.161654
$698$	−16.8513	−0.637831
$699$	10.8219	0.409323
$700$	−33.5121	−1.26664
$701$	38.0299	1.43637	0.718185	−	0.695852i	$-0.244973\pi$
$701$	38.0299	1.43637	0.718185	+	0.695852i	$0.244973\pi$
$702$	−5.03601	−0.190072
$703$	−1.11102	−0.0419029
$704$	0.493452	0.0185977
$705$	−19.1930	−0.722851
$706$	−15.4083	−0.579900
$707$	−26.8016	−1.00798
$708$	1.14773	0.0431343
$709$	−24.5506	−0.922016	−0.461008	−	0.887396i	$-0.652512\pi$
$709$	−24.5506	−0.922016	−0.461008	+	0.887396i	$0.652512\pi$
$710$	−28.2029	−1.05844
$711$	−10.1085	−0.379099
$712$	−12.2737	−0.459975
$713$	4.90003	0.183507
$714$	1.67033	0.0625107
$715$	10.1684	0.380278
$716$	16.5484	0.618442
$717$	21.4582	0.801371
$718$	−22.8561	−0.852982
$719$	−20.8699	−0.778317	−0.389158	−	0.921171i	$-0.627234\pi$
$719$	−20.8699	−0.778317	−0.389158	+	0.921171i	$0.627234\pi$
$720$	−4.09187	−0.152495
$721$	−27.8973	−1.03895
$722$	−18.0076	−0.670173
$723$	−4.15852	−0.154657
$724$	9.58866	0.356360
$725$	−11.7434	−0.436139
$726$	−10.7565	−0.399211
$727$	−5.59285	−0.207427	−0.103714	−	0.994607i	$-0.533073\pi$
$727$	−5.59285	−0.207427	−0.103714	+	0.994607i	$0.533073\pi$
$728$	14.3713	0.532634
$729$	1.00000	0.0370370
$730$	−4.61803	−0.170921
$731$	−3.80286	−0.140654
$732$	−6.67719	−0.246796
$733$	−35.0249	−1.29367	−0.646837	−	0.762628i	$-0.723909\pi$
$733$	−35.0249	−1.29367	−0.646837	+	0.762628i	$0.723909\pi$
$734$	−25.5708	−0.943835
$735$	−4.67942	−0.172603
$736$	1.00000	0.0368605
$737$	7.97611	0.293804
$738$	7.29132	0.268397
$739$	−15.3778	−0.565682	−0.282841	−	0.959167i	$-0.591277\pi$
$739$	−15.3778	−0.565682	−0.282841	+	0.959167i	$0.591277\pi$
$740$	4.56349	0.167757
$741$	−5.01687	−0.184299
$742$	−21.2552	−0.780304
$743$	35.3729	1.29770	0.648852	−	0.760914i	$-0.275249\pi$
$743$	35.3729	1.29770	0.648852	+	0.760914i	$0.275249\pi$
$744$	4.90003	0.179644
$745$	−68.1363	−2.49632
$746$	−15.4087	−0.564152
$747$	−0.118271	−0.00432731
$748$	−0.288829	−0.0105606
$749$	29.2589	1.06910
$750$	−27.5932	−1.00756
$751$	12.0862	0.441032	0.220516	−	0.975383i	$-0.429226\pi$
$751$	12.0862	0.441032	0.220516	+	0.975383i	$0.429226\pi$
$752$	4.69052	0.171046
$753$	−14.0739	−0.512882
$754$	5.03601	0.183401
$755$	46.7078	1.69987
$756$	−2.85370	−0.103788
$757$	5.99283	0.217813	0.108907	−	0.994052i	$-0.465265\pi$
$757$	5.99283	0.217813	0.108907	+	0.994052i	$0.465265\pi$
$758$	23.4695	0.852451
$759$	0.493452	0.0179112
$760$	−4.07632	−0.147864
$761$	9.29539	0.336958	0.168479	−	0.985705i	$-0.446115\pi$
$761$	9.29539	0.336958	0.168479	+	0.985705i	$0.446115\pi$
$762$	−13.0170	−0.471555
$763$	−13.5267	−0.489701
$764$	−0.377430	−0.0136549
$765$	2.39507	0.0865938
$766$	−10.3053	−0.372344
$767$	−5.77997	−0.208703
$768$	1.00000	0.0360844
$769$	−0.328834	−0.0118581	−0.00592904	−	0.999982i	$-0.501887\pi$
$769$	−0.328834	−0.0118581	−0.00592904	+	0.999982i	$0.501887\pi$
$770$	5.76202	0.207649
$771$	17.5843	0.633283
$772$	−5.97717	−0.215123
$773$	36.6062	1.31663	0.658317	−	0.752740i	$-0.271268\pi$
$773$	36.6062	1.31663	0.658317	+	0.752740i	$0.271268\pi$
$774$	6.49702	0.233531
$775$	57.5430	2.06701
$776$	1.37030	0.0491911
$777$	3.18261	0.114175
$778$	8.28993	0.297209
$779$	7.26360	0.260246
$780$	20.6067	0.737839
$781$	3.40108	0.121700
$782$	−0.585323	−0.0209311
$783$	−1.00000	−0.0357371
$784$	1.14359	0.0408425
$785$	65.4627	2.33647
$786$	9.35723	0.333761
$787$	42.8008	1.52568	0.762842	−	0.646585i	$-0.223804\pi$
$787$	42.8008	1.52568	0.762842	+	0.646585i	$0.223804\pi$
$788$	23.4602	0.835734
$789$	7.57374	0.269632
$790$	41.3627	1.47162
$791$	−24.1703	−0.859398
$792$	0.493452	0.0175341
$793$	33.6264	1.19411
$794$	−9.28617	−0.329554
$795$	−30.4775	−1.08093
$796$	−11.6183	−0.411800
$797$	14.9886	0.530925	0.265463	−	0.964121i	$-0.414475\pi$
$797$	14.9886	0.530925	0.265463	+	0.964121i	$0.414475\pi$
$798$	−2.84285	−0.100636
$799$	−2.74547	−0.0971278
$800$	11.7434	0.415192
$801$	−12.2737	−0.433669
$802$	−1.01662	−0.0358980
$803$	0.556903	0.0196527
$804$	16.1639	0.570057
$805$	11.6770	0.411559
$806$	−24.6766	−0.869196
$807$	23.7986	0.837749
$808$	9.39187	0.330405
$809$	27.8747	0.980021	0.490010	−	0.871717i	$-0.336993\pi$
$809$	27.8747	0.980021	0.490010	+	0.871717i	$0.336993\pi$
$810$	−4.09187	−0.143774
$811$	−7.76453	−0.272649	−0.136325	−	0.990664i	$-0.543529\pi$
$811$	−7.76453	−0.272649	−0.136325	+	0.990664i	$0.543529\pi$
$812$	2.85370	0.100145
$813$	0.414208	0.0145269
$814$	−0.550326	−0.0192889
$815$	−95.0122	−3.32813
$816$	−0.585323	−0.0204904
$817$	6.47233	0.226438
$818$	−8.46001	−0.295797
$819$	14.3713	0.502172
$820$	−29.8351	−1.04189
$821$	2.32292	0.0810703	0.0405352	−	0.999178i	$-0.487094\pi$
$821$	2.32292	0.0810703	0.0405352	+	0.999178i	$0.487094\pi$
$822$	−14.0617	−0.490459
$823$	34.2563	1.19410	0.597049	−	0.802205i	$-0.296340\pi$
$823$	34.2563	1.19410	0.597049	+	0.802205i	$0.296340\pi$
$824$	9.77585	0.340558
$825$	5.79481	0.201749
$826$	−3.27527	−0.113961
$827$	−16.3020	−0.566875	−0.283437	−	0.958991i	$-0.591475\pi$
$827$	−16.3020	−0.566875	−0.283437	+	0.958991i	$0.591475\pi$
$828$	1.00000	0.0347524
$829$	−16.3511	−0.567897	−0.283948	−	0.958840i	$-0.591644\pi$
$829$	−16.3511	−0.567897	−0.283948	+	0.958840i	$0.591644\pi$
$830$	0.483949	0.0167981
$831$	27.6210	0.958161
$832$	−5.03601	−0.174592
$833$	−0.669369	−0.0231923
$834$	1.33707	0.0462988
$835$	−66.7039	−2.30838
$836$	0.491576	0.0170015
$837$	4.90003	0.169370
$838$	7.56897	0.261466
$839$	24.2649	0.837717	0.418858	−	0.908052i	$-0.362430\pi$
$839$	24.2649	0.837717	0.418858	+	0.908052i	$0.362430\pi$
$840$	11.6770	0.402893
$841$	1.00000	0.0344828
$842$	−13.2733	−0.457429
$843$	0.926190	0.0318997
$844$	12.4896	0.429908
$845$	−50.5814	−1.74005
$846$	4.69052	0.161263
$847$	30.6958	1.05472
$848$	7.44832	0.255776
$849$	31.2174	1.07138
$850$	−6.87369	−0.235766
$851$	−1.11526	−0.0382306
$852$	6.89243	0.236131
$853$	−0.639461	−0.0218947	−0.0109474	−	0.999940i	$-0.503485\pi$
$853$	−0.639461	−0.0218947	−0.0109474	+	0.999940i	$0.503485\pi$
$854$	19.0547	0.652038
$855$	−4.07632	−0.139407
$856$	−10.2530	−0.350440
$857$	21.6836	0.740699	0.370349	−	0.928892i	$-0.379238\pi$
$857$	21.6836	0.740699	0.370349	+	0.928892i	$0.379238\pi$
$858$	−2.48503	−0.0848376
$859$	−0.283814	−0.00968360	−0.00484180	−	0.999988i	$-0.501541\pi$
$859$	−0.283814	−0.00968360	−0.00484180	+	0.999988i	$0.501541\pi$
$860$	−26.5850	−0.906540
$861$	−20.8072	−0.709108
$862$	11.5827	0.394507
$863$	14.0262	0.477459	0.238729	−	0.971086i	$-0.423269\pi$
$863$	14.0262	0.477459	0.238729	+	0.971086i	$0.423269\pi$
$864$	1.00000	0.0340207
$865$	69.2847	2.35575
$866$	2.27384	0.0772682
$867$	−16.6574	−0.565715
$868$	−13.9832	−0.474621
$869$	−4.98806	−0.169208
$870$	4.09187	0.138727
$871$	−81.4016	−2.75819
$872$	4.74008	0.160519
$873$	1.37030	0.0463778
$874$	0.996199	0.0336969
$875$	78.7425	2.66198
$876$	1.12859	0.0381314
$877$	−14.3936	−0.486038	−0.243019	−	0.970021i	$-0.578138\pi$
$877$	−14.3936	−0.486038	−0.243019	+	0.970021i	$0.578138\pi$
$878$	−23.6409	−0.797843
$879$	−5.61469	−0.189379
$880$	−2.01914	−0.0680653
$881$	24.8558	0.837414	0.418707	−	0.908121i	$-0.362483\pi$
$881$	24.8558	0.837414	0.418707	+	0.908121i	$0.362483\pi$
$882$	1.14359	0.0385066
$883$	−18.2276	−0.613406	−0.306703	−	0.951805i	$-0.599226\pi$
$883$	−18.2276	−0.613406	−0.306703	+	0.951805i	$0.599226\pi$
$884$	2.94770	0.0991417
$885$	−4.69636	−0.157866
$886$	8.74303	0.293728
$887$	−27.9892	−0.939786	−0.469893	−	0.882723i	$-0.655708\pi$
$887$	−27.9892	−0.939786	−0.469893	+	0.882723i	$0.655708\pi$
$888$	−1.11526	−0.0374256
$889$	37.1465	1.24585
$890$	50.2222	1.68345
$891$	0.493452	0.0165313
$892$	−2.51777	−0.0843011
$893$	4.67269	0.156366
$894$	16.6516	0.556914
$895$	−67.7138	−2.26342
$896$	−2.85370	−0.0953353
$897$	−5.03601	−0.168148
$898$	−24.2675	−0.809818
$899$	−4.90003	−0.163425
$900$	11.7434	0.391447
$901$	−4.35967	−0.145242
$902$	3.59791	0.119797
$903$	−18.5405	−0.616990
$904$	8.46983	0.281702
$905$	−39.2356	−1.30423
$906$	−11.4148	−0.379231
$907$	−10.0737	−0.334491	−0.167246	−	0.985915i	$-0.553487\pi$
$907$	−10.0737	−0.334491	−0.167246	+	0.985915i	$0.553487\pi$
$908$	8.87577	0.294553
$909$	9.39187	0.311509
$910$	−58.8053	−1.94938
$911$	0.832587	0.0275848	0.0137924	−	0.999905i	$-0.495610\pi$
$911$	0.832587	0.0275848	0.0137924	+	0.999905i	$0.495610\pi$
$912$	0.996199	0.0329874
$913$	−0.0583610	−0.00193147
$914$	10.8460	0.358752
$915$	27.3222	0.903245
$916$	−22.0806	−0.729564
$917$	−26.7027	−0.881801
$918$	−0.585323	−0.0193185
$919$	0.989923	0.0326545	0.0163273	−	0.999867i	$-0.494803\pi$
$919$	0.989923	0.0326545	0.0163273	+	0.999867i	$0.494803\pi$
$920$	−4.09187	−0.134905
$921$	30.8183	1.01550
$922$	0.313283	0.0103174
$923$	−34.7104	−1.14251
$924$	−1.40816	−0.0463251
$925$	−13.0969	−0.430624
$926$	−15.3959	−0.505939
$927$	9.77585	0.321081
$928$	−1.00000	−0.0328266
$929$	−38.9861	−1.27909	−0.639546	−	0.768752i	$-0.720878\pi$
$929$	−38.9861	−1.27909	−0.639546	+	0.768752i	$0.720878\pi$
$930$	−20.0503	−0.657475
$931$	1.13924	0.0373372
$932$	10.8219	0.354484
$933$	7.44042	0.243588
$934$	−27.1999	−0.890006
$935$	1.18185	0.0386506
$936$	−5.03601	−0.164607
$937$	54.8428	1.79164	0.895819	−	0.444420i	$-0.146590\pi$
$937$	54.8428	1.79164	0.895819	+	0.444420i	$0.146590\pi$
$938$	−46.1269	−1.50610
$939$	−21.6879	−0.707757
$940$	−19.1930	−0.626007
$941$	−15.1819	−0.494916	−0.247458	−	0.968899i	$-0.579595\pi$
$941$	−15.1819	−0.494916	−0.247458	+	0.968899i	$0.579595\pi$
$942$	−15.9982	−0.521251
$943$	7.29132	0.237438
$944$	1.14773	0.0373554
$945$	11.6770	0.379852
$946$	3.20597	0.104235
$947$	−57.9806	−1.88412	−0.942059	−	0.335449i	$-0.891112\pi$
$947$	−57.9806	−1.88412	−0.942059	+	0.335449i	$0.891112\pi$
$948$	−10.1085	−0.328309
$949$	−5.68358	−0.184497
$950$	11.6988	0.379558
$951$	15.4503	0.501009
$952$	1.67033	0.0541359
$953$	21.7078	0.703183	0.351592	−	0.936153i	$-0.385641\pi$
$953$	21.7078	0.703183	0.351592	+	0.936153i	$0.385641\pi$
$954$	7.44832	0.241148
$955$	1.54440	0.0499755
$956$	21.4582	0.694008
$957$	−0.493452	−0.0159510
$958$	42.3206	1.36732
$959$	40.1279	1.29580
$960$	−4.09187	−0.132065
$961$	−6.98973	−0.225475
$962$	5.61646	0.181082
$963$	−10.2530	−0.330398
$964$	−4.15852	−0.133937
$965$	24.4578	0.787325
$966$	−2.85370	−0.0918162
$967$	−2.58204	−0.0830327	−0.0415163	−	0.999138i	$-0.513219\pi$
$967$	−2.58204	−0.0830327	−0.0415163	+	0.999138i	$0.513219\pi$
$968$	−10.7565	−0.345727
$969$	−0.583098	−0.0187318
$970$	−5.60711	−0.180033
$971$	−46.6368	−1.49664	−0.748322	−	0.663335i	$-0.769140\pi$
$971$	−46.6368	−1.49664	−0.748322	+	0.663335i	$0.769140\pi$
$972$	1.00000	0.0320750
$973$	−3.81558	−0.122322
$974$	11.7342	0.375988
$975$	−59.1400	−1.89399
$976$	−6.67719	−0.213732
$977$	−16.5727	−0.530206	−0.265103	−	0.964220i	$-0.585406\pi$
$977$	−16.5727	−0.530206	−0.265103	+	0.964220i	$0.585406\pi$
$978$	23.2198	0.742486
$979$	−6.05646	−0.193565
$980$	−4.67942	−0.149479
$981$	4.74008	0.151339
$982$	4.97472	0.158750
$983$	26.3074	0.839076	0.419538	−	0.907738i	$-0.362192\pi$
$983$	26.3074	0.839076	0.419538	+	0.907738i	$0.362192\pi$
$984$	7.29132	0.232439
$985$	−95.9960	−3.05869
$986$	0.585323	0.0186405
$987$	−13.3853	−0.426060
$988$	−5.01687	−0.159608
$989$	6.49702	0.206593
$990$	−2.01914	−0.0641725
$991$	−26.3784	−0.837936	−0.418968	−	0.908001i	$-0.637608\pi$
$991$	−26.3784	−0.837936	−0.418968	+	0.908001i	$0.637608\pi$
$992$	4.90003	0.155576
$993$	−32.6232	−1.03527
$994$	−19.6689	−0.623859
$995$	47.5406	1.50714
$996$	−0.118271	−0.00374756
$997$	−41.1572	−1.30346	−0.651731	−	0.758450i	$-0.725957\pi$
$997$	−41.1572	−1.30346	−0.651731	+	0.758450i	$0.725957\pi$
$998$	−16.3143	−0.516420
$999$	−1.11526	−0.0352852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bh.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bh.1.1	✓	7	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.09187 q^{5} +1.00000 q^{6} -2.85370 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.09187 q^{5} +1.00000 q^{6} -2.85370 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.09187 q^{10} +0.493452 q^{11} +1.00000 q^{12} -5.03601 q^{13} -2.85370 q^{14} -4.09187 q^{15} +1.00000 q^{16} -0.585323 q^{17} +1.00000 q^{18} +0.996199 q^{19} -4.09187 q^{20} -2.85370 q^{21} +0.493452 q^{22} +1.00000 q^{23} +1.00000 q^{24} +11.7434 q^{25} -5.03601 q^{26} +1.00000 q^{27} -2.85370 q^{28} -1.00000 q^{29} -4.09187 q^{30} +4.90003 q^{31} +1.00000 q^{32} +0.493452 q^{33} -0.585323 q^{34} +11.6770 q^{35} +1.00000 q^{36} -1.11526 q^{37} +0.996199 q^{38} -5.03601 q^{39} -4.09187 q^{40} +7.29132 q^{41} -2.85370 q^{42} +6.49702 q^{43} +0.493452 q^{44} -4.09187 q^{45} +1.00000 q^{46} +4.69052 q^{47} +1.00000 q^{48} +1.14359 q^{49} +11.7434 q^{50} -0.585323 q^{51} -5.03601 q^{52} +7.44832 q^{53} +1.00000 q^{54} -2.01914 q^{55} -2.85370 q^{56} +0.996199 q^{57} -1.00000 q^{58} +1.14773 q^{59} -4.09187 q^{60} -6.67719 q^{61} +4.90003 q^{62} -2.85370 q^{63} +1.00000 q^{64} +20.6067 q^{65} +0.493452 q^{66} +16.1639 q^{67} -0.585323 q^{68} +1.00000 q^{69} +11.6770 q^{70} +6.89243 q^{71} +1.00000 q^{72} +1.12859 q^{73} -1.11526 q^{74} +11.7434 q^{75} +0.996199 q^{76} -1.40816 q^{77} -5.03601 q^{78} -10.1085 q^{79} -4.09187 q^{80} +1.00000 q^{81} +7.29132 q^{82} -0.118271 q^{83} -2.85370 q^{84} +2.39507 q^{85} +6.49702 q^{86} -1.00000 q^{87} +0.493452 q^{88} -12.2737 q^{89} -4.09187 q^{90} +14.3713 q^{91} +1.00000 q^{92} +4.90003 q^{93} +4.69052 q^{94} -4.07632 q^{95} +1.00000 q^{96} +1.37030 q^{97} +1.14359 q^{98} +0.493452 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 + 11 * q^99

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