LMFDB - Embedded newform 4002.2.a.bh.1.2

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			1.2
Root			$0.586166$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65866 q^{5} +1.00000 q^{6} -1.05824 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65866 q^{5} +1.00000 q^{6} -1.05824 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.65866 q^{10} -2.77476 q^{11} +1.00000 q^{12} +5.36531 q^{13} -1.05824 q^{14} -1.65866 q^{15} +1.00000 q^{16} +5.11610 q^{17} +1.00000 q^{18} -0.230571 q^{19} -1.65866 q^{20} -1.05824 q^{21} -2.77476 q^{22} +1.00000 q^{23} +1.00000 q^{24} -2.24883 q^{25} +5.36531 q^{26} +1.00000 q^{27} -1.05824 q^{28} -1.00000 q^{29} -1.65866 q^{30} +3.97596 q^{31} +1.00000 q^{32} -2.77476 q^{33} +5.11610 q^{34} +1.75526 q^{35} +1.00000 q^{36} -4.94821 q^{37} -0.230571 q^{38} +5.36531 q^{39} -1.65866 q^{40} +5.80251 q^{41} -1.05824 q^{42} +2.66851 q^{43} -2.77476 q^{44} -1.65866 q^{45} +1.00000 q^{46} +4.87939 q^{47} +1.00000 q^{48} -5.88013 q^{49} -2.24883 q^{50} +5.11610 q^{51} +5.36531 q^{52} +5.26109 q^{53} +1.00000 q^{54} +4.60240 q^{55} -1.05824 q^{56} -0.230571 q^{57} -1.00000 q^{58} +6.68264 q^{59} -1.65866 q^{60} +1.45744 q^{61} +3.97596 q^{62} -1.05824 q^{63} +1.00000 q^{64} -8.89925 q^{65} -2.77476 q^{66} -7.07196 q^{67} +5.11610 q^{68} +1.00000 q^{69} +1.75526 q^{70} +3.51482 q^{71} +1.00000 q^{72} +13.2850 q^{73} -4.94821 q^{74} -2.24883 q^{75} -0.230571 q^{76} +2.93636 q^{77} +5.36531 q^{78} -2.10845 q^{79} -1.65866 q^{80} +1.00000 q^{81} +5.80251 q^{82} -1.00201 q^{83} -1.05824 q^{84} -8.48589 q^{85} +2.66851 q^{86} -1.00000 q^{87} -2.77476 q^{88} +11.2121 q^{89} -1.65866 q^{90} -5.67778 q^{91} +1.00000 q^{92} +3.97596 q^{93} +4.87939 q^{94} +0.382440 q^{95} +1.00000 q^{96} +0.785722 q^{97} -5.88013 q^{98} -2.77476 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.65866	−0.741777	−0.370889	−	0.928677i	$-0.620947\pi$
$5$	−1.65866	−0.741777	−0.370889	+	0.928677i	$0.620947\pi$
$6$	1.00000	0.408248
$7$	−1.05824	−0.399977	−0.199988	−	0.979798i	$-0.564090\pi$
$7$	−1.05824	−0.399977	−0.199988	+	0.979798i	$0.564090\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.65866	−0.524516
$11$	−2.77476	−0.836622	−0.418311	−	0.908304i	$-0.637378\pi$
$11$	−2.77476	−0.836622	−0.418311	+	0.908304i	$0.637378\pi$
$12$	1.00000	0.288675
$13$	5.36531	1.48807	0.744035	−	0.668141i	$-0.232910\pi$
$13$	5.36531	1.48807	0.744035	+	0.668141i	$0.232910\pi$
$14$	−1.05824	−0.282826
$15$	−1.65866	−0.428265
$16$	1.00000	0.250000
$17$	5.11610	1.24084	0.620418	−	0.784271i	$-0.286963\pi$
$17$	5.11610	1.24084	0.620418	+	0.784271i	$0.286963\pi$
$18$	1.00000	0.235702
$19$	−0.230571	−0.0528966	−0.0264483	−	0.999650i	$-0.508420\pi$
$19$	−0.230571	−0.0528966	−0.0264483	+	0.999650i	$0.508420\pi$
$20$	−1.65866	−0.370889
$21$	−1.05824	−0.230927
$22$	−2.77476	−0.591581
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−2.24883	−0.449767
$26$	5.36531	1.05222
$27$	1.00000	0.192450
$28$	−1.05824	−0.199988
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−1.65866	−0.302829
$31$	3.97596	0.714103	0.357052	−	0.934085i	$-0.383782\pi$
$31$	3.97596	0.714103	0.357052	+	0.934085i	$0.383782\pi$
$32$	1.00000	0.176777
$33$	−2.77476	−0.483024
$34$	5.11610	0.877404
$35$	1.75526	0.296694
$36$	1.00000	0.166667
$37$	−4.94821	−0.813481	−0.406740	−	0.913544i	$-0.633335\pi$
$37$	−4.94821	−0.813481	−0.406740	+	0.913544i	$0.633335\pi$
$38$	−0.230571	−0.0374036
$39$	5.36531	0.859138
$40$	−1.65866	−0.262258
$41$	5.80251	0.906200	0.453100	−	0.891460i	$-0.350318\pi$
$41$	5.80251	0.906200	0.453100	+	0.891460i	$0.350318\pi$
$42$	−1.05824	−0.163290
$43$	2.66851	0.406943	0.203472	−	0.979081i	$-0.434778\pi$
$43$	2.66851	0.406943	0.203472	+	0.979081i	$0.434778\pi$
$44$	−2.77476	−0.418311
$45$	−1.65866	−0.247259
$46$	1.00000	0.147442
$47$	4.87939	0.711733	0.355866	−	0.934537i	$-0.384186\pi$
$47$	4.87939	0.711733	0.355866	+	0.934537i	$0.384186\pi$
$48$	1.00000	0.144338
$49$	−5.88013	−0.840019
$50$	−2.24883	−0.318033
$51$	5.11610	0.716397
$52$	5.36531	0.744035
$53$	5.26109	0.722667	0.361333	−	0.932437i	$-0.382322\pi$
$53$	5.26109	0.722667	0.361333	+	0.932437i	$0.382322\pi$
$54$	1.00000	0.136083
$55$	4.60240	0.620587
$56$	−1.05824	−0.141413
$57$	−0.230571	−0.0305399
$58$	−1.00000	−0.131306
$59$	6.68264	0.870006	0.435003	−	0.900429i	$-0.356747\pi$
$59$	6.68264	0.870006	0.435003	+	0.900429i	$0.356747\pi$
$60$	−1.65866	−0.214133
$61$	1.45744	0.186605	0.0933027	−	0.995638i	$-0.470258\pi$
$61$	1.45744	0.186605	0.0933027	+	0.995638i	$0.470258\pi$
$62$	3.97596	0.504947
$63$	−1.05824	−0.133326
$64$	1.00000	0.125000
$65$	−8.89925	−1.10382
$66$	−2.77476	−0.341550
$67$	−7.07196	−0.863978	−0.431989	−	0.901879i	$-0.642188\pi$
$67$	−7.07196	−0.863978	−0.431989	+	0.901879i	$0.642188\pi$
$68$	5.11610	0.620418
$69$	1.00000	0.120386
$70$	1.75526	0.209794
$71$	3.51482	0.417132	0.208566	−	0.978008i	$-0.433120\pi$
$71$	3.51482	0.417132	0.208566	+	0.978008i	$0.433120\pi$
$72$	1.00000	0.117851
$73$	13.2850	1.55490	0.777448	−	0.628947i	$-0.216514\pi$
$73$	13.2850	1.55490	0.777448	+	0.628947i	$0.216514\pi$
$74$	−4.94821	−0.575218
$75$	−2.24883	−0.259673
$76$	−0.230571	−0.0264483
$77$	2.93636	0.334630
$78$	5.36531	0.607502
$79$	−2.10845	−0.237219	−0.118609	−	0.992941i	$-0.537844\pi$
$79$	−2.10845	−0.237219	−0.118609	+	0.992941i	$0.537844\pi$
$80$	−1.65866	−0.185444
$81$	1.00000	0.111111
$82$	5.80251	0.640780
$83$	−1.00201	−0.109984	−0.0549922	−	0.998487i	$-0.517513\pi$
$83$	−1.00201	−0.109984	−0.0549922	+	0.998487i	$0.517513\pi$
$84$	−1.05824	−0.115463
$85$	−8.48589	−0.920424
$86$	2.66851	0.287752
$87$	−1.00000	−0.107211
$88$	−2.77476	−0.295791
$89$	11.2121	1.18848	0.594242	−	0.804286i	$-0.297452\pi$
$89$	11.2121	1.18848	0.594242	+	0.804286i	$0.297452\pi$
$90$	−1.65866	−0.174839
$91$	−5.67778	−0.595194
$92$	1.00000	0.104257
$93$	3.97596	0.412288
$94$	4.87939	0.503271
$95$	0.382440	0.0392375
$96$	1.00000	0.102062
$97$	0.785722	0.0797780	0.0398890	−	0.999204i	$-0.487300\pi$
$97$	0.785722	0.0797780	0.0398890	+	0.999204i	$0.487300\pi$
$98$	−5.88013	−0.593983
$99$	−2.77476	−0.278874
$100$	−2.24883	−0.224883
$101$	19.1478	1.90528	0.952638	−	0.304105i	$-0.0983575\pi$
$101$	19.1478	1.90528	0.952638	+	0.304105i	$0.0983575\pi$
$102$	5.11610	0.506569
$103$	−14.0574	−1.38512	−0.692559	−	0.721361i	$-0.743517\pi$
$103$	−14.0574	−1.38512	−0.692559	+	0.721361i	$0.743517\pi$
$104$	5.36531	0.526112
$105$	1.75526	0.171296
$106$	5.26109	0.511003
$107$	10.6798	1.03245	0.516227	−	0.856452i	$-0.327336\pi$
$107$	10.6798	1.03245	0.516227	+	0.856452i	$0.327336\pi$
$108$	1.00000	0.0962250
$109$	12.7250	1.21883	0.609416	−	0.792851i	$-0.291404\pi$
$109$	12.7250	1.21883	0.609416	+	0.792851i	$0.291404\pi$
$110$	4.60240	0.438822
$111$	−4.94821	−0.469663
$112$	−1.05824	−0.0999942
$113$	−2.85161	−0.268257	−0.134129	−	0.990964i	$-0.542824\pi$
$113$	−2.85161	−0.268257	−0.134129	+	0.990964i	$0.542824\pi$
$114$	−0.230571	−0.0215950
$115$	−1.65866	−0.154671
$116$	−1.00000	−0.0928477
$117$	5.36531	0.496023
$118$	6.68264	0.615187
$119$	−5.41406	−0.496306
$120$	−1.65866	−0.151415
$121$	−3.30069	−0.300063
$122$	1.45744	0.131950
$123$	5.80251	0.523195
$124$	3.97596	0.357052
$125$	12.0234	1.07540
$126$	−1.05824	−0.0942754
$127$	11.5778	1.02737	0.513683	−	0.857980i	$-0.328281\pi$
$127$	11.5778	1.02737	0.513683	+	0.857980i	$0.328281\pi$
$128$	1.00000	0.0883883
$129$	2.66851	0.234949
$130$	−8.89925	−0.780516
$131$	13.7792	1.20389	0.601947	−	0.798536i	$-0.294392\pi$
$131$	13.7792	1.20389	0.601947	+	0.798536i	$0.294392\pi$
$132$	−2.77476	−0.241512
$133$	0.243999	0.0211574
$134$	−7.07196	−0.610924
$135$	−1.65866	−0.142755
$136$	5.11610	0.438702
$137$	6.47065	0.552825	0.276412	−	0.961039i	$-0.410854\pi$
$137$	6.47065	0.552825	0.276412	+	0.961039i	$0.410854\pi$
$138$	1.00000	0.0851257
$139$	−13.2123	−1.12065	−0.560324	−	0.828273i	$-0.689324\pi$
$139$	−13.2123	−1.12065	−0.560324	+	0.828273i	$0.689324\pi$
$140$	1.75526	0.148347
$141$	4.87939	0.410919
$142$	3.51482	0.294957
$143$	−14.8875	−1.24495
$144$	1.00000	0.0833333
$145$	1.65866	0.137745
$146$	13.2850	1.09948
$147$	−5.88013	−0.484985
$148$	−4.94821	−0.406740
$149$	−15.7224	−1.28803	−0.644015	−	0.765013i	$-0.722733\pi$
$149$	−15.7224	−1.28803	−0.644015	+	0.765013i	$0.722733\pi$
$150$	−2.24883	−0.183617
$151$	−4.23296	−0.344473	−0.172237	−	0.985056i	$-0.555099\pi$
$151$	−4.23296	−0.344473	−0.172237	+	0.985056i	$0.555099\pi$
$152$	−0.230571	−0.0187018
$153$	5.11610	0.413612
$154$	2.93636	0.236619
$155$	−6.59478	−0.529705
$156$	5.36531	0.429569
$157$	12.2854	0.980481	0.490241	−	0.871587i	$-0.336909\pi$
$157$	12.2854	0.980481	0.490241	+	0.871587i	$0.336909\pi$
$158$	−2.10845	−0.167739
$159$	5.26109	0.417232
$160$	−1.65866	−0.131129
$161$	−1.05824	−0.0834009
$162$	1.00000	0.0785674
$163$	7.95202	0.622850	0.311425	−	0.950271i	$-0.399194\pi$
$163$	7.95202	0.622850	0.311425	+	0.950271i	$0.399194\pi$
$164$	5.80251	0.453100
$165$	4.60240	0.358296
$166$	−1.00201	−0.0777708
$167$	0.657958	0.0509144	0.0254572	−	0.999676i	$-0.491896\pi$
$167$	0.657958	0.0509144	0.0254572	+	0.999676i	$0.491896\pi$
$168$	−1.05824	−0.0816449
$169$	15.7866	1.21435
$170$	−8.48589	−0.650838
$171$	−0.230571	−0.0176322
$172$	2.66851	0.203472
$173$	20.7183	1.57519	0.787593	−	0.616196i	$-0.211327\pi$
$173$	20.7183	1.57519	0.787593	+	0.616196i	$0.211327\pi$
$174$	−1.00000	−0.0758098
$175$	2.37980	0.179896
$176$	−2.77476	−0.209156
$177$	6.68264	0.502298
$178$	11.2121	0.840385
$179$	−5.52978	−0.413315	−0.206657	−	0.978413i	$-0.566259\pi$
$179$	−5.52978	−0.413315	−0.206657	+	0.978413i	$0.566259\pi$
$180$	−1.65866	−0.123630
$181$	1.53987	0.114458	0.0572288	−	0.998361i	$-0.481774\pi$
$181$	1.53987	0.114458	0.0572288	+	0.998361i	$0.481774\pi$
$182$	−5.67778	−0.420865
$183$	1.45744	0.107737
$184$	1.00000	0.0737210
$185$	8.20742	0.603422
$186$	3.97596	0.291531
$187$	−14.1960	−1.03811
$188$	4.87939	0.355866
$189$	−1.05824	−0.0769756
$190$	0.382440	0.0277451
$191$	−0.643260	−0.0465446	−0.0232723	−	0.999729i	$-0.507408\pi$
$191$	−0.643260	−0.0465446	−0.0232723	+	0.999729i	$0.507408\pi$
$192$	1.00000	0.0721688
$193$	−2.09993	−0.151156	−0.0755780	−	0.997140i	$-0.524080\pi$
$193$	−2.09993	−0.151156	−0.0755780	+	0.997140i	$0.524080\pi$
$194$	0.785722	0.0564116
$195$	−8.89925	−0.637289
$196$	−5.88013	−0.420009
$197$	−21.1713	−1.50839	−0.754197	−	0.656648i	$-0.771974\pi$
$197$	−21.1713	−1.50839	−0.754197	+	0.656648i	$0.771974\pi$
$198$	−2.77476	−0.197194
$199$	−5.72431	−0.405785	−0.202893	−	0.979201i	$-0.565034\pi$
$199$	−5.72431	−0.405785	−0.202893	+	0.979201i	$0.565034\pi$
$200$	−2.24883	−0.159017
$201$	−7.07196	−0.498818
$202$	19.1478	1.34723
$203$	1.05824	0.0742738
$204$	5.11610	0.358199
$205$	−9.62441	−0.672198
$206$	−14.0574	−0.979427
$207$	1.00000	0.0695048
$208$	5.36531	0.372017
$209$	0.639780	0.0442545
$210$	1.75526	0.121125
$211$	−14.7625	−1.01630	−0.508148	−	0.861270i	$-0.669670\pi$
$211$	−14.7625	−1.01630	−0.508148	+	0.861270i	$0.669670\pi$
$212$	5.26109	0.361333
$213$	3.51482	0.240831
$214$	10.6798	0.730055
$215$	−4.42616	−0.301861
$216$	1.00000	0.0680414
$217$	−4.20752	−0.285625
$218$	12.7250	0.861844
$219$	13.2850	0.897720
$220$	4.60240	0.310294
$221$	27.4495	1.84645
$222$	−4.94821	−0.332102
$223$	−15.7388	−1.05395	−0.526975	−	0.849881i	$-0.676674\pi$
$223$	−15.7388	−1.05395	−0.526975	+	0.849881i	$0.676674\pi$
$224$	−1.05824	−0.0707066
$225$	−2.24883	−0.149922
$226$	−2.85161	−0.189686
$227$	0.335007	0.0222352	0.0111176	−	0.999938i	$-0.496461\pi$
$227$	0.335007	0.0222352	0.0111176	+	0.999938i	$0.496461\pi$
$228$	−0.230571	−0.0152699
$229$	−14.6268	−0.966567	−0.483284	−	0.875464i	$-0.660556\pi$
$229$	−14.6268	−0.966567	−0.483284	+	0.875464i	$0.660556\pi$
$230$	−1.65866	−0.109369
$231$	2.93636	0.193198
$232$	−1.00000	−0.0656532
$233$	−21.8588	−1.43202	−0.716008	−	0.698092i	$-0.754032\pi$
$233$	−21.8588	−1.43202	−0.716008	+	0.698092i	$0.754032\pi$
$234$	5.36531	0.350741
$235$	−8.09327	−0.527947
$236$	6.68264	0.435003
$237$	−2.10845	−0.136958
$238$	−5.41406	−0.350941
$239$	−17.7587	−1.14871	−0.574356	−	0.818605i	$-0.694748\pi$
$239$	−17.7587	−1.14871	−0.574356	+	0.818605i	$0.694748\pi$
$240$	−1.65866	−0.107066
$241$	8.48990	0.546883	0.273441	−	0.961889i	$-0.411838\pi$
$241$	8.48990	0.546883	0.273441	+	0.961889i	$0.411838\pi$
$242$	−3.30069	−0.212176
$243$	1.00000	0.0641500
$244$	1.45744	0.0933027
$245$	9.75316	0.623106
$246$	5.80251	0.369955
$247$	−1.23709	−0.0787139
$248$	3.97596	0.252474
$249$	−1.00201	−0.0634996
$250$	12.0234	0.760425
$251$	10.1452	0.640357	0.320179	−	0.947357i	$-0.396257\pi$
$251$	10.1452	0.640357	0.320179	+	0.947357i	$0.396257\pi$
$252$	−1.05824	−0.0666628
$253$	−2.77476	−0.174448
$254$	11.5778	0.726457
$255$	−8.48589	−0.531407
$256$	1.00000	0.0625000
$257$	5.91982	0.369268	0.184634	−	0.982807i	$-0.440890\pi$
$257$	5.91982	0.369268	0.184634	+	0.982807i	$0.440890\pi$
$258$	2.66851	0.166134
$259$	5.23639	0.325374
$260$	−8.89925	−0.551908
$261$	−1.00000	−0.0618984
$262$	13.7792	0.851282
$263$	−21.7397	−1.34052	−0.670262	−	0.742124i	$-0.733818\pi$
$263$	−21.7397	−1.34052	−0.670262	+	0.742124i	$0.733818\pi$
$264$	−2.77476	−0.170775
$265$	−8.72639	−0.536058
$266$	0.243999	0.0149606
$267$	11.2121	0.686171
$268$	−7.07196	−0.431989
$269$	−7.21655	−0.440001	−0.220000	−	0.975500i	$-0.570606\pi$
$269$	−7.21655	−0.440001	−0.220000	+	0.975500i	$0.570606\pi$
$270$	−1.65866	−0.100943
$271$	−17.0883	−1.03804	−0.519020	−	0.854762i	$-0.673703\pi$
$271$	−17.0883	−1.03804	−0.519020	+	0.854762i	$0.673703\pi$
$272$	5.11610	0.310209
$273$	−5.67778	−0.343635
$274$	6.47065	0.390906
$275$	6.23998	0.376285
$276$	1.00000	0.0601929
$277$	−4.93916	−0.296765	−0.148383	−	0.988930i	$-0.547407\pi$
$277$	−4.93916	−0.296765	−0.148383	+	0.988930i	$0.547407\pi$
$278$	−13.2123	−0.792418
$279$	3.97596	0.238034
$280$	1.75526	0.104897
$281$	−18.0978	−1.07962	−0.539812	−	0.841786i	$-0.681505\pi$
$281$	−18.0978	−1.07962	−0.539812	+	0.841786i	$0.681505\pi$
$282$	4.87939	0.290564
$283$	4.12106	0.244971	0.122486	−	0.992470i	$-0.460913\pi$
$283$	4.12106	0.244971	0.122486	+	0.992470i	$0.460913\pi$
$284$	3.51482	0.208566
$285$	0.382440	0.0226538
$286$	−14.8875	−0.880315
$287$	−6.14044	−0.362459
$288$	1.00000	0.0589256
$289$	9.17447	0.539675
$290$	1.65866	0.0974001
$291$	0.785722	0.0460599
$292$	13.2850	0.777448
$293$	−25.3794	−1.48268	−0.741342	−	0.671128i	$-0.765810\pi$
$293$	−25.3794	−1.48268	−0.741342	+	0.671128i	$0.765810\pi$
$294$	−5.88013	−0.342936
$295$	−11.0843	−0.645350
$296$	−4.94821	−0.287609
$297$	−2.77476	−0.161008
$298$	−15.7224	−0.910775
$299$	5.36531	0.310284
$300$	−2.24883	−0.129837
$301$	−2.82392	−0.162768
$302$	−4.23296	−0.243579
$303$	19.1478	1.10001
$304$	−0.230571	−0.0132242
$305$	−2.41739	−0.138420
$306$	5.11610	0.292468
$307$	3.50230	0.199887	0.0999434	−	0.994993i	$-0.468134\pi$
$307$	3.50230	0.199887	0.0999434	+	0.994993i	$0.468134\pi$
$308$	2.93636	0.167315
$309$	−14.0574	−0.799698
$310$	−6.59478	−0.374558
$311$	−4.24875	−0.240924	−0.120462	−	0.992718i	$-0.538438\pi$
$311$	−4.24875	−0.240924	−0.120462	+	0.992718i	$0.538438\pi$
$312$	5.36531	0.303751
$313$	−25.2728	−1.42850	−0.714251	−	0.699890i	$-0.753232\pi$
$313$	−25.2728	−1.42850	−0.714251	+	0.699890i	$0.753232\pi$
$314$	12.2854	0.693305
$315$	1.75526	0.0988979
$316$	−2.10845	−0.118609
$317$	7.84844	0.440812	0.220406	−	0.975408i	$-0.429262\pi$
$317$	7.84844	0.440812	0.220406	+	0.975408i	$0.429262\pi$
$318$	5.26109	0.295028
$319$	2.77476	0.155357
$320$	−1.65866	−0.0927221
$321$	10.6798	0.596088
$322$	−1.05824	−0.0589734
$323$	−1.17962	−0.0656361
$324$	1.00000	0.0555556
$325$	−12.0657	−0.669285
$326$	7.95202	0.440421
$327$	12.7250	0.703693
$328$	5.80251	0.320390
$329$	−5.16356	−0.284677
$330$	4.60240	0.253354
$331$	25.8647	1.42165	0.710825	−	0.703369i	$-0.248322\pi$
$331$	25.8647	1.42165	0.710825	+	0.703369i	$0.248322\pi$
$332$	−1.00201	−0.0549922
$333$	−4.94821	−0.271160
$334$	0.657958	0.0360019
$335$	11.7300	0.640879
$336$	−1.05824	−0.0577317
$337$	−19.1062	−1.04078	−0.520392	−	0.853928i	$-0.674214\pi$
$337$	−19.1062	−1.04078	−0.520392	+	0.853928i	$0.674214\pi$
$338$	15.7866	0.858677
$339$	−2.85161	−0.154878
$340$	−8.48589	−0.460212
$341$	−11.0323	−0.597435
$342$	−0.230571	−0.0124679
$343$	13.6303	0.735965
$344$	2.66851	0.143876
$345$	−1.65866	−0.0892995
$346$	20.7183	1.11382
$347$	−34.6891	−1.86221	−0.931103	−	0.364757i	$-0.881152\pi$
$347$	−34.6891	−1.86221	−0.931103	+	0.364757i	$0.881152\pi$
$348$	−1.00000	−0.0536056
$349$	−6.02554	−0.322540	−0.161270	−	0.986910i	$-0.551559\pi$
$349$	−6.02554	−0.322540	−0.161270	+	0.986910i	$0.551559\pi$
$350$	2.37980	0.127206
$351$	5.36531	0.286379
$352$	−2.77476	−0.147895
$353$	30.5662	1.62687	0.813437	−	0.581653i	$-0.197594\pi$
$353$	30.5662	1.62687	0.813437	+	0.581653i	$0.197594\pi$
$354$	6.68264	0.355178
$355$	−5.82990	−0.309419
$356$	11.2121	0.594242
$357$	−5.41406	−0.286542
$358$	−5.52978	−0.292258
$359$	1.92390	0.101540	0.0507698	−	0.998710i	$-0.483833\pi$
$359$	1.92390	0.101540	0.0507698	+	0.998710i	$0.483833\pi$
$360$	−1.65866	−0.0874193
$361$	−18.9468	−0.997202
$362$	1.53987	0.0809337
$363$	−3.30069	−0.173241
$364$	−5.67778	−0.297597
$365$	−22.0354	−1.15339
$366$	1.45744	0.0761814
$367$	−4.46795	−0.233225	−0.116613	−	0.993177i	$-0.537204\pi$
$367$	−4.46795	−0.233225	−0.116613	+	0.993177i	$0.537204\pi$
$368$	1.00000	0.0521286
$369$	5.80251	0.302067
$370$	8.20742	0.426683
$371$	−5.56750	−0.289050
$372$	3.97596	0.206144
$373$	−1.91010	−0.0989013	−0.0494507	−	0.998777i	$-0.515747\pi$
$373$	−1.91010	−0.0989013	−0.0494507	+	0.998777i	$0.515747\pi$
$374$	−14.1960	−0.734056
$375$	12.0234	0.620885
$376$	4.87939	0.251635
$377$	−5.36531	−0.276328
$378$	−1.05824	−0.0544300
$379$	7.23365	0.371568	0.185784	−	0.982591i	$-0.440518\pi$
$379$	7.23365	0.371568	0.185784	+	0.982591i	$0.440518\pi$
$380$	0.382440	0.0196188
$381$	11.5778	0.593150
$382$	−0.643260	−0.0329120
$383$	−5.16043	−0.263686	−0.131843	−	0.991271i	$-0.542089\pi$
$383$	−5.16043	−0.263686	−0.131843	+	0.991271i	$0.542089\pi$
$384$	1.00000	0.0510310
$385$	−4.87044	−0.248221
$386$	−2.09993	−0.106883
$387$	2.66851	0.135648
$388$	0.785722	0.0398890
$389$	−21.2095	−1.07537	−0.537683	−	0.843147i	$-0.680700\pi$
$389$	−21.2095	−1.07537	−0.537683	+	0.843147i	$0.680700\pi$
$390$	−8.89925	−0.450631
$391$	5.11610	0.258732
$392$	−5.88013	−0.296991
$393$	13.7792	0.695069
$394$	−21.1713	−1.06660
$395$	3.49721	0.175964
$396$	−2.77476	−0.139437
$397$	37.6136	1.88777	0.943887	−	0.330268i	$-0.107139\pi$
$397$	37.6136	1.88777	0.943887	+	0.330268i	$0.107139\pi$
$398$	−5.72431	−0.286934
$399$	0.243999	0.0122152
$400$	−2.24883	−0.112442
$401$	16.0932	0.803657	0.401829	−	0.915715i	$-0.368375\pi$
$401$	16.0932	0.803657	0.401829	+	0.915715i	$0.368375\pi$
$402$	−7.07196	−0.352717
$403$	21.3323	1.06264
$404$	19.1478	0.952638
$405$	−1.65866	−0.0824197
$406$	1.05824	0.0525195
$407$	13.7301	0.680576
$408$	5.11610	0.253285
$409$	−0.982969	−0.0486047	−0.0243023	−	0.999705i	$-0.507736\pi$
$409$	−0.982969	−0.0486047	−0.0243023	+	0.999705i	$0.507736\pi$
$410$	−9.62441	−0.475316
$411$	6.47065	0.319174
$412$	−14.0574	−0.692559
$413$	−7.07183	−0.347982
$414$	1.00000	0.0491473
$415$	1.66199	0.0815840
$416$	5.36531	0.263056
$417$	−13.2123	−0.647007
$418$	0.639780	0.0312927
$419$	23.3826	1.14231	0.571157	−	0.820841i	$-0.306495\pi$
$419$	23.3826	1.14231	0.571157	+	0.820841i	$0.306495\pi$
$420$	1.75526	0.0856481
$421$	−0.883707	−0.0430693	−0.0215346	−	0.999768i	$-0.506855\pi$
$421$	−0.883707	−0.0430693	−0.0215346	+	0.999768i	$0.506855\pi$
$422$	−14.7625	−0.718630
$423$	4.87939	0.237244
$424$	5.26109	0.255501
$425$	−11.5053	−0.558087
$426$	3.51482	0.170293
$427$	−1.54231	−0.0746379
$428$	10.6798	0.516227
$429$	−14.8875	−0.718774
$430$	−4.42616	−0.213448
$431$	36.1666	1.74208	0.871041	−	0.491210i	$-0.163445\pi$
$431$	36.1666	1.74208	0.871041	+	0.491210i	$0.163445\pi$
$432$	1.00000	0.0481125
$433$	−17.2988	−0.831329	−0.415664	−	0.909518i	$-0.636451\pi$
$433$	−17.2988	−0.831329	−0.415664	+	0.909518i	$0.636451\pi$
$434$	−4.20752	−0.201967
$435$	1.65866	0.0795268
$436$	12.7250	0.609416
$437$	−0.230571	−0.0110297
$438$	13.2850	0.634784
$439$	−31.3801	−1.49769	−0.748845	−	0.662745i	$-0.769391\pi$
$439$	−31.3801	−1.49769	−0.748845	+	0.662745i	$0.769391\pi$
$440$	4.60240	0.219411
$441$	−5.88013	−0.280006
$442$	27.4495	1.30564
$443$	8.51738	0.404673	0.202336	−	0.979316i	$-0.435147\pi$
$443$	8.51738	0.404673	0.202336	+	0.979316i	$0.435147\pi$
$444$	−4.94821	−0.234832
$445$	−18.5972	−0.881590
$446$	−15.7388	−0.745255
$447$	−15.7224	−0.743644
$448$	−1.05824	−0.0499971
$449$	23.0308	1.08689	0.543445	−	0.839444i	$-0.317119\pi$
$449$	23.0308	1.08689	0.543445	+	0.839444i	$0.317119\pi$
$450$	−2.24883	−0.106011
$451$	−16.1006	−0.758147
$452$	−2.85161	−0.134129
$453$	−4.23296	−0.198882
$454$	0.335007	0.0157226
$455$	9.41754	0.441501
$456$	−0.230571	−0.0107975
$457$	−38.4332	−1.79783	−0.898914	−	0.438126i	$-0.855642\pi$
$457$	−38.4332	−1.79783	−0.898914	+	0.438126i	$0.855642\pi$
$458$	−14.6268	−0.683466
$459$	5.11610	0.238799
$460$	−1.65866	−0.0773356
$461$	20.1537	0.938652	0.469326	−	0.883025i	$-0.344497\pi$
$461$	20.1537	0.938652	0.469326	+	0.883025i	$0.344497\pi$
$462$	2.93636	0.136612
$463$	−36.7091	−1.70602	−0.853009	−	0.521896i	$-0.825225\pi$
$463$	−36.7091	−1.70602	−0.853009	+	0.521896i	$0.825225\pi$
$464$	−1.00000	−0.0464238
$465$	−6.59478	−0.305826
$466$	−21.8588	−1.01259
$467$	−26.7479	−1.23775	−0.618873	−	0.785491i	$-0.712410\pi$
$467$	−26.7479	−1.23775	−0.618873	+	0.785491i	$0.712410\pi$
$468$	5.36531	0.248012
$469$	7.48383	0.345571
$470$	−8.09327	−0.373315
$471$	12.2854	0.566081
$472$	6.68264	0.307593
$473$	−7.40447	−0.340458
$474$	−2.10845	−0.0968442
$475$	0.518516	0.0237912
$476$	−5.41406	−0.248153
$477$	5.26109	0.240889
$478$	−17.7587	−0.812263
$479$	−6.15789	−0.281361	−0.140681	−	0.990055i	$-0.544929\pi$
$479$	−6.15789	−0.281361	−0.140681	+	0.990055i	$0.544929\pi$
$480$	−1.65866	−0.0757073
$481$	−26.5487	−1.21052
$482$	8.48990	0.386704
$483$	−1.05824	−0.0481516
$484$	−3.30069	−0.150031
$485$	−1.30325	−0.0591775
$486$	1.00000	0.0453609
$487$	24.2773	1.10011	0.550054	−	0.835129i	$-0.314607\pi$
$487$	24.2773	1.10011	0.550054	+	0.835129i	$0.314607\pi$
$488$	1.45744	0.0659750
$489$	7.95202	0.359603
$490$	9.75316	0.440603
$491$	−27.4076	−1.23689	−0.618443	−	0.785830i	$-0.712236\pi$
$491$	−27.4076	−1.23689	−0.618443	+	0.785830i	$0.712236\pi$
$492$	5.80251	0.261597
$493$	−5.11610	−0.230418
$494$	−1.23709	−0.0556591
$495$	4.60240	0.206862
$496$	3.97596	0.178526
$497$	−3.71952	−0.166843
$498$	−1.00201	−0.0449010
$499$	15.6677	0.701384	0.350692	−	0.936491i	$-0.385946\pi$
$499$	15.6677	0.701384	0.350692	+	0.936491i	$0.385946\pi$
$500$	12.0234	0.537702
$501$	0.657958	0.0293954
$502$	10.1452	0.452801
$503$	−35.2818	−1.57314	−0.786569	−	0.617503i	$-0.788144\pi$
$503$	−35.2818	−1.57314	−0.786569	+	0.617503i	$0.788144\pi$
$504$	−1.05824	−0.0471377
$505$	−31.7598	−1.41329
$506$	−2.77476	−0.123353
$507$	15.7866	0.701107
$508$	11.5778	0.513683
$509$	−18.7608	−0.831556	−0.415778	−	0.909466i	$-0.636491\pi$
$509$	−18.7608	−0.831556	−0.415778	+	0.909466i	$0.636491\pi$
$510$	−8.48589	−0.375761
$511$	−14.0587	−0.621922
$512$	1.00000	0.0441942
$513$	−0.230571	−0.0101800
$514$	5.91982	0.261112
$515$	23.3165	1.02745
$516$	2.66851	0.117474
$517$	−13.5392	−0.595451
$518$	5.23639	0.230074
$519$	20.7183	0.909434
$520$	−8.89925	−0.390258
$521$	44.2494	1.93860	0.969300	−	0.245880i	$-0.0790768\pi$
$521$	44.2494	1.93860	0.969300	+	0.245880i	$0.0790768\pi$
$522$	−1.00000	−0.0437688
$523$	−2.82364	−0.123469	−0.0617346	−	0.998093i	$-0.519663\pi$
$523$	−2.82364	−0.123469	−0.0617346	+	0.998093i	$0.519663\pi$
$524$	13.7792	0.601947
$525$	2.37980	0.103863
$526$	−21.7397	−0.947894
$527$	20.3414	0.886085
$528$	−2.77476	−0.120756
$529$	1.00000	0.0434783
$530$	−8.72639	−0.379050
$531$	6.68264	0.290002
$532$	0.243999	0.0105787
$533$	31.1323	1.34849
$534$	11.2121	0.485196
$535$	−17.7142	−0.765851
$536$	−7.07196	−0.305462
$537$	−5.52978	−0.238627
$538$	−7.21655	−0.311127
$539$	16.3160	0.702778
$540$	−1.65866	−0.0713775
$541$	−17.0152	−0.731539	−0.365770	−	0.930705i	$-0.619194\pi$
$541$	−17.0152	−0.731539	−0.365770	+	0.930705i	$0.619194\pi$
$542$	−17.0883	−0.734005
$543$	1.53987	0.0660821
$544$	5.11610	0.219351
$545$	−21.1065	−0.904102
$546$	−5.67778	−0.242987
$547$	12.8246	0.548342	0.274171	−	0.961681i	$-0.411597\pi$
$547$	12.8246	0.548342	0.274171	+	0.961681i	$0.411597\pi$
$548$	6.47065	0.276412
$549$	1.45744	0.0622018
$550$	6.23998	0.266074
$551$	0.230571	0.00982266
$552$	1.00000	0.0425628
$553$	2.23124	0.0948821
$554$	−4.93916	−0.209845
$555$	8.20742	0.348386
$556$	−13.2123	−0.560324
$557$	−31.7301	−1.34445	−0.672224	−	0.740348i	$-0.734661\pi$
$557$	−31.7301	−1.34445	−0.672224	+	0.740348i	$0.734661\pi$
$558$	3.97596	0.168316
$559$	14.3174	0.605560
$560$	1.75526	0.0741734
$561$	−14.1960	−0.599354
$562$	−18.0978	−0.763409
$563$	−5.00413	−0.210899	−0.105450	−	0.994425i	$-0.533628\pi$
$563$	−5.00413	−0.210899	−0.105450	+	0.994425i	$0.533628\pi$
$564$	4.87939	0.205459
$565$	4.72987	0.198987
$566$	4.12106	0.173221
$567$	−1.05824	−0.0444419
$568$	3.51482	0.147478
$569$	41.9076	1.75686	0.878429	−	0.477874i	$-0.158592\pi$
$569$	41.9076	1.75686	0.878429	+	0.477874i	$0.158592\pi$
$570$	0.382440	0.0160186
$571$	−16.3772	−0.685366	−0.342683	−	0.939451i	$-0.611336\pi$
$571$	−16.3772	−0.685366	−0.342683	+	0.939451i	$0.611336\pi$
$572$	−14.8875	−0.622476
$573$	−0.643260	−0.0268726
$574$	−6.14044	−0.256297
$575$	−2.24883	−0.0937829
$576$	1.00000	0.0416667
$577$	28.0685	1.16851	0.584254	−	0.811571i	$-0.301387\pi$
$577$	28.0685	1.16851	0.584254	+	0.811571i	$0.301387\pi$
$578$	9.17447	0.381608
$579$	−2.09993	−0.0872700
$580$	1.65866	0.0688723
$581$	1.06036	0.0439912
$582$	0.785722	0.0325692
$583$	−14.5983	−0.604599
$584$	13.2850	0.549739
$585$	−8.89925	−0.367939
$586$	−25.3794	−1.04842
$587$	−37.7741	−1.55910	−0.779551	−	0.626339i	$-0.784553\pi$
$587$	−37.7741	−1.55910	−0.779551	+	0.626339i	$0.784553\pi$
$588$	−5.88013	−0.242492
$589$	−0.916741	−0.0377737
$590$	−11.0843	−0.456332
$591$	−21.1713	−0.870872
$592$	−4.94821	−0.203370
$593$	18.8453	0.773885	0.386942	−	0.922104i	$-0.373531\pi$
$593$	18.8453	0.773885	0.386942	+	0.922104i	$0.373531\pi$
$594$	−2.77476	−0.113850
$595$	8.98010	0.368148
$596$	−15.7224	−0.644015
$597$	−5.72431	−0.234280
$598$	5.36531	0.219404
$599$	−24.1452	−0.986548	−0.493274	−	0.869874i	$-0.664200\pi$
$599$	−24.1452	−0.986548	−0.493274	+	0.869874i	$0.664200\pi$
$600$	−2.24883	−0.0918083
$601$	−8.78119	−0.358192	−0.179096	−	0.983832i	$-0.557317\pi$
$601$	−8.78119	−0.358192	−0.179096	+	0.983832i	$0.557317\pi$
$602$	−2.82392	−0.115094
$603$	−7.07196	−0.287993
$604$	−4.23296	−0.172237
$605$	5.47474	0.222580
$606$	19.1478	0.777826
$607$	14.6236	0.593554	0.296777	−	0.954947i	$-0.404088\pi$
$607$	14.6236	0.593554	0.296777	+	0.954947i	$0.404088\pi$
$608$	−0.230571	−0.00935089
$609$	1.05824	0.0428820
$610$	−2.41739	−0.0978775
$611$	26.1795	1.05911
$612$	5.11610	0.206806
$613$	19.3263	0.780582	0.390291	−	0.920692i	$-0.372374\pi$
$613$	19.3263	0.780582	0.390291	+	0.920692i	$0.372374\pi$
$614$	3.50230	0.141341
$615$	−9.62441	−0.388094
$616$	2.93636	0.118309
$617$	21.3271	0.858595	0.429298	−	0.903163i	$-0.358761\pi$
$617$	21.3271	0.858595	0.429298	+	0.903163i	$0.358761\pi$
$618$	−14.0574	−0.565472
$619$	32.5977	1.31021	0.655106	−	0.755537i	$-0.272624\pi$
$619$	32.5977	1.31021	0.655106	+	0.755537i	$0.272624\pi$
$620$	−6.59478	−0.264853
$621$	1.00000	0.0401286
$622$	−4.24875	−0.170359
$623$	−11.8651	−0.475366
$624$	5.36531	0.214784
$625$	−8.69857	−0.347943
$626$	−25.2728	−1.01010
$627$	0.639780	0.0255504
$628$	12.2854	0.490241
$629$	−25.3155	−1.00940
$630$	1.75526	0.0699314
$631$	9.71994	0.386945	0.193472	−	0.981106i	$-0.438025\pi$
$631$	9.71994	0.386945	0.193472	+	0.981106i	$0.438025\pi$
$632$	−2.10845	−0.0838696
$633$	−14.7625	−0.586759
$634$	7.84844	0.311701
$635$	−19.2037	−0.762076
$636$	5.26109	0.208616
$637$	−31.5487	−1.25001
$638$	2.77476	0.109854
$639$	3.51482	0.139044
$640$	−1.65866	−0.0655644
$641$	−16.9723	−0.670364	−0.335182	−	0.942153i	$-0.608798\pi$
$641$	−16.9723	−0.670364	−0.335182	+	0.942153i	$0.608798\pi$
$642$	10.6798	0.421498
$643$	−13.5548	−0.534548	−0.267274	−	0.963621i	$-0.586123\pi$
$643$	−13.5548	−0.534548	−0.267274	+	0.963621i	$0.586123\pi$
$644$	−1.05824	−0.0417005
$645$	−4.42616	−0.174280
$646$	−1.17962	−0.0464117
$647$	−8.77165	−0.344849	−0.172425	−	0.985023i	$-0.555160\pi$
$647$	−8.77165	−0.344849	−0.172425	+	0.985023i	$0.555160\pi$
$648$	1.00000	0.0392837
$649$	−18.5427	−0.727866
$650$	−12.0657	−0.473256
$651$	−4.20752	−0.164906
$652$	7.95202	0.311425
$653$	6.25780	0.244887	0.122443	−	0.992476i	$-0.460927\pi$
$653$	6.25780	0.244887	0.122443	+	0.992476i	$0.460927\pi$
$654$	12.7250	0.497586
$655$	−22.8551	−0.893022
$656$	5.80251	0.226550
$657$	13.2850	0.518299
$658$	−5.16356	−0.201297
$659$	3.22585	0.125661	0.0628305	−	0.998024i	$-0.479987\pi$
$659$	3.22585	0.125661	0.0628305	+	0.998024i	$0.479987\pi$
$660$	4.60240	0.179148
$661$	−19.7731	−0.769085	−0.384542	−	0.923107i	$-0.625641\pi$
$661$	−19.7731	−0.769085	−0.384542	+	0.923107i	$0.625641\pi$
$662$	25.8647	1.00526
$663$	27.4495	1.06605
$664$	−1.00201	−0.0388854
$665$	−0.404713	−0.0156941
$666$	−4.94821	−0.191739
$667$	−1.00000	−0.0387202
$668$	0.657958	0.0254572
$669$	−15.7388	−0.608498
$670$	11.7300	0.453170
$671$	−4.04404	−0.156118
$672$	−1.05824	−0.0408225
$673$	3.45573	0.133208	0.0666042	−	0.997779i	$-0.478784\pi$
$673$	3.45573	0.133208	0.0666042	+	0.997779i	$0.478784\pi$
$674$	−19.1062	−0.735945
$675$	−2.24883	−0.0865577
$676$	15.7866	0.607176
$677$	−15.5507	−0.597660	−0.298830	−	0.954306i	$-0.596596\pi$
$677$	−15.5507	−0.597660	−0.298830	+	0.954306i	$0.596596\pi$
$678$	−2.85161	−0.109516
$679$	−0.831482	−0.0319094
$680$	−8.48589	−0.325419
$681$	0.335007	0.0128375
$682$	−11.0323	−0.422450
$683$	−19.9638	−0.763893	−0.381947	−	0.924184i	$-0.624746\pi$
$683$	−19.9638	−0.763893	−0.381947	+	0.924184i	$0.624746\pi$
$684$	−0.230571	−0.00881611
$685$	−10.7326	−0.410073
$686$	13.6303	0.520406
$687$	−14.6268	−0.558048
$688$	2.66851	0.101736
$689$	28.2274	1.07538
$690$	−1.65866	−0.0631443
$691$	31.5337	1.19960	0.599800	−	0.800150i	$-0.295247\pi$
$691$	31.5337	1.19960	0.599800	+	0.800150i	$0.295247\pi$
$692$	20.7183	0.787593
$693$	2.93636	0.111543
$694$	−34.6891	−1.31678
$695$	21.9147	0.831272
$696$	−1.00000	−0.0379049
$697$	29.6862	1.12445
$698$	−6.02554	−0.228070
$699$	−21.8588	−0.826774
$700$	2.37980	0.0899482
$701$	39.1587	1.47900	0.739502	−	0.673155i	$-0.235061\pi$
$701$	39.1587	1.47900	0.739502	+	0.673155i	$0.235061\pi$
$702$	5.36531	0.202501
$703$	1.14091	0.0430304
$704$	−2.77476	−0.104578
$705$	−8.09327	−0.304810
$706$	30.5662	1.15037
$707$	−20.2629	−0.762067
$708$	6.68264	0.251149
$709$	23.5832	0.885685	0.442842	−	0.896600i	$-0.353970\pi$
$709$	23.5832	0.885685	0.442842	+	0.896600i	$0.353970\pi$
$710$	−5.82990	−0.218792
$711$	−2.10845	−0.0790730
$712$	11.2121	0.420192
$713$	3.97596	0.148901
$714$	−5.41406	−0.202616
$715$	24.6933	0.923477
$716$	−5.52978	−0.206657
$717$	−17.7587	−0.663210
$718$	1.92390	0.0717994
$719$	20.4535	0.762787	0.381393	−	0.924413i	$-0.375444\pi$
$719$	20.4535	0.762787	0.381393	+	0.924413i	$0.375444\pi$
$720$	−1.65866	−0.0618148
$721$	14.8761	0.554015
$722$	−18.9468	−0.705128
$723$	8.48990	0.315743
$724$	1.53987	0.0572288
$725$	2.24883	0.0835196
$726$	−3.30069	−0.122500
$727$	48.3025	1.79144	0.895721	−	0.444617i	$-0.146660\pi$
$727$	48.3025	1.79144	0.895721	+	0.444617i	$0.146660\pi$
$728$	−5.67778	−0.210433
$729$	1.00000	0.0370370
$730$	−22.0354	−0.815567
$731$	13.6523	0.504950
$732$	1.45744	0.0538684
$733$	−21.4173	−0.791065	−0.395532	−	0.918452i	$-0.629440\pi$
$733$	−21.4173	−0.791065	−0.395532	+	0.918452i	$0.629440\pi$
$734$	−4.46795	−0.164915
$735$	9.75316	0.359751
$736$	1.00000	0.0368605
$737$	19.6230	0.722823
$738$	5.80251	0.213593
$739$	16.1125	0.592708	0.296354	−	0.955078i	$-0.404229\pi$
$739$	16.1125	0.592708	0.296354	+	0.955078i	$0.404229\pi$
$740$	8.20742	0.301711
$741$	−1.23709	−0.0454455
$742$	−5.56750	−0.204389
$743$	−37.6074	−1.37968	−0.689840	−	0.723962i	$-0.742319\pi$
$743$	−37.6074	−1.37968	−0.689840	+	0.723962i	$0.742319\pi$
$744$	3.97596	0.145766
$745$	26.0782	0.955431
$746$	−1.91010	−0.0699338
$747$	−1.00201	−0.0366615
$748$	−14.1960	−0.519056
$749$	−11.3018	−0.412958
$750$	12.0234	0.439032
$751$	23.3856	0.853354	0.426677	−	0.904404i	$-0.359684\pi$
$751$	23.3856	0.853354	0.426677	+	0.904404i	$0.359684\pi$
$752$	4.87939	0.177933
$753$	10.1452	0.369710
$754$	−5.36531	−0.195393
$755$	7.02105	0.255522
$756$	−1.05824	−0.0384878
$757$	−8.74211	−0.317737	−0.158869	−	0.987300i	$-0.550785\pi$
$757$	−8.74211	−0.317737	−0.158869	+	0.987300i	$0.550785\pi$
$758$	7.23365	0.262738
$759$	−2.77476	−0.100718
$760$	0.382440	0.0138726
$761$	33.9207	1.22962	0.614812	−	0.788674i	$-0.289232\pi$
$761$	33.9207	1.22962	0.614812	+	0.788674i	$0.289232\pi$
$762$	11.5778	0.419420
$763$	−13.4661	−0.487505
$764$	−0.643260	−0.0232723
$765$	−8.48589	−0.306808
$766$	−5.16043	−0.186454
$767$	35.8545	1.29463
$768$	1.00000	0.0360844
$769$	−28.3357	−1.02181	−0.510906	−	0.859637i	$-0.670690\pi$
$769$	−28.3357	−1.02181	−0.510906	+	0.859637i	$0.670690\pi$
$770$	−4.87044	−0.175518
$771$	5.91982	0.213197
$772$	−2.09993	−0.0755780
$773$	−49.2474	−1.77131	−0.885653	−	0.464347i	$-0.846289\pi$
$773$	−49.2474	−1.77131	−0.885653	+	0.464347i	$0.846289\pi$
$774$	2.66851	0.0959175
$775$	−8.94127	−0.321180
$776$	0.785722	0.0282058
$777$	5.23639	0.187855
$778$	−21.2095	−0.760398
$779$	−1.33789	−0.0479349
$780$	−8.89925	−0.318644
$781$	−9.75278	−0.348982
$782$	5.11610	0.182951
$783$	−1.00000	−0.0357371
$784$	−5.88013	−0.210005
$785$	−20.3773	−0.727299
$786$	13.7792	0.491488
$787$	−19.2819	−0.687325	−0.343662	−	0.939093i	$-0.611668\pi$
$787$	−19.2819	−0.687325	−0.343662	+	0.939093i	$0.611668\pi$
$788$	−21.1713	−0.754197
$789$	−21.7397	−0.773952
$790$	3.49721	0.124425
$791$	3.01769	0.107297
$792$	−2.77476	−0.0985969
$793$	7.81960	0.277682
$794$	37.6136	1.33486
$795$	−8.72639	−0.309493
$796$	−5.72431	−0.202893
$797$	34.3943	1.21831	0.609154	−	0.793052i	$-0.291509\pi$
$797$	34.3943	1.21831	0.609154	+	0.793052i	$0.291509\pi$
$798$	0.243999	0.00863748
$799$	24.9635	0.883144
$800$	−2.24883	−0.0795083
$801$	11.2121	0.396161
$802$	16.0932	0.568272
$803$	−36.8628	−1.30086
$804$	−7.07196	−0.249409
$805$	1.75526	0.0618649
$806$	21.3323	0.751397
$807$	−7.21655	−0.254034
$808$	19.1478	0.673617
$809$	4.95498	0.174208	0.0871039	−	0.996199i	$-0.472239\pi$
$809$	4.95498	0.174208	0.0871039	+	0.996199i	$0.472239\pi$
$810$	−1.65866	−0.0582795
$811$	25.5234	0.896248	0.448124	−	0.893971i	$-0.352092\pi$
$811$	25.5234	0.896248	0.448124	+	0.893971i	$0.352092\pi$
$812$	1.05824	0.0371369
$813$	−17.0883	−0.599312
$814$	13.7301	0.481240
$815$	−13.1897	−0.462016
$816$	5.11610	0.179099
$817$	−0.615281	−0.0215259
$818$	−0.982969	−0.0343687
$819$	−5.67778	−0.198398
$820$	−9.62441	−0.336099
$821$	38.8049	1.35430	0.677149	−	0.735846i	$-0.263215\pi$
$821$	38.8049	1.35430	0.677149	+	0.735846i	$0.263215\pi$
$822$	6.47065	0.225690
$823$	−31.7396	−1.10637	−0.553187	−	0.833057i	$-0.686588\pi$
$823$	−31.7396	−1.10637	−0.553187	+	0.833057i	$0.686588\pi$
$824$	−14.0574	−0.489713
$825$	6.23998	0.217248
$826$	−7.07183	−0.246061
$827$	31.9250	1.11014	0.555071	−	0.831803i	$-0.312691\pi$
$827$	31.9250	1.11014	0.555071	+	0.831803i	$0.312691\pi$
$828$	1.00000	0.0347524
$829$	22.6692	0.787335	0.393668	−	0.919253i	$-0.371206\pi$
$829$	22.6692	0.787335	0.393668	+	0.919253i	$0.371206\pi$
$830$	1.66199	0.0576886
$831$	−4.93916	−0.171337
$832$	5.36531	0.186009
$833$	−30.0833	−1.04233
$834$	−13.2123	−0.457503
$835$	−1.09133	−0.0377671
$836$	0.639780	0.0221273
$837$	3.97596	0.137429
$838$	23.3826	0.807738
$839$	2.79061	0.0963426	0.0481713	−	0.998839i	$-0.484661\pi$
$839$	2.79061	0.0963426	0.0481713	+	0.998839i	$0.484661\pi$
$840$	1.75526	0.0605623
$841$	1.00000	0.0344828
$842$	−0.883707	−0.0304546
$843$	−18.0978	−0.623321
$844$	−14.7625	−0.508148
$845$	−26.1846	−0.900779
$846$	4.87939	0.167757
$847$	3.49292	0.120018
$848$	5.26109	0.180667
$849$	4.12106	0.141434
$850$	−11.5053	−0.394627
$851$	−4.94821	−0.169623
$852$	3.51482	0.120416
$853$	3.10448	0.106295	0.0531477	−	0.998587i	$-0.483075\pi$
$853$	3.10448	0.106295	0.0531477	+	0.998587i	$0.483075\pi$
$854$	−1.54231	−0.0527769
$855$	0.382440	0.0130792
$856$	10.6798	0.365028
$857$	32.0106	1.09346	0.546731	−	0.837309i	$-0.315872\pi$
$857$	32.0106	1.09346	0.546731	+	0.837309i	$0.315872\pi$
$858$	−14.8875	−0.508250
$859$	47.9026	1.63442	0.817209	−	0.576342i	$-0.195520\pi$
$859$	47.9026	1.63442	0.817209	+	0.576342i	$0.195520\pi$
$860$	−4.42616	−0.150931
$861$	−6.14044	−0.209266
$862$	36.1666	1.23184
$863$	8.14152	0.277141	0.138570	−	0.990353i	$-0.455749\pi$
$863$	8.14152	0.277141	0.138570	+	0.990353i	$0.455749\pi$
$864$	1.00000	0.0340207
$865$	−34.3647	−1.16844
$866$	−17.2988	−0.587838
$867$	9.17447	0.311581
$868$	−4.20752	−0.142812
$869$	5.85044	0.198463
$870$	1.65866	0.0562340
$871$	−37.9433	−1.28566
$872$	12.7250	0.430922
$873$	0.785722	0.0265927
$874$	−0.230571	−0.00779918
$875$	−12.7236	−0.430137
$876$	13.2850	0.448860
$877$	5.35231	0.180735	0.0903674	−	0.995908i	$-0.471196\pi$
$877$	5.35231	0.180735	0.0903674	+	0.995908i	$0.471196\pi$
$878$	−31.3801	−1.05903
$879$	−25.3794	−0.856027
$880$	4.60240	0.155147
$881$	−5.18172	−0.174576	−0.0872882	−	0.996183i	$-0.527820\pi$
$881$	−5.18172	−0.174576	−0.0872882	+	0.996183i	$0.527820\pi$
$882$	−5.88013	−0.197994
$883$	−31.7625	−1.06889	−0.534446	−	0.845203i	$-0.679480\pi$
$883$	−31.7625	−1.06889	−0.534446	+	0.845203i	$0.679480\pi$
$884$	27.4495	0.923226
$885$	−11.0843	−0.372593
$886$	8.51738	0.286147
$887$	−38.9130	−1.30657	−0.653286	−	0.757111i	$-0.726610\pi$
$887$	−38.9130	−1.30657	−0.653286	+	0.757111i	$0.726610\pi$
$888$	−4.94821	−0.166051
$889$	−12.2521	−0.410923
$890$	−18.5972	−0.623378
$891$	−2.77476	−0.0929581
$892$	−15.7388	−0.526975
$893$	−1.12505	−0.0376483
$894$	−15.7224	−0.525836
$895$	9.17204	0.306587
$896$	−1.05824	−0.0353533
$897$	5.36531	0.179143
$898$	23.0308	0.768548
$899$	−3.97596	−0.132606
$900$	−2.24883	−0.0749611
$901$	26.9163	0.896711
$902$	−16.1006	−0.536091
$903$	−2.82392	−0.0939741
$904$	−2.85161	−0.0948432
$905$	−2.55412	−0.0849020
$906$	−4.23296	−0.140631
$907$	−33.2441	−1.10385	−0.551927	−	0.833893i	$-0.686107\pi$
$907$	−33.2441	−1.10385	−0.551927	+	0.833893i	$0.686107\pi$
$908$	0.335007	0.0111176
$909$	19.1478	0.635092
$910$	9.41754	0.312188
$911$	−47.5252	−1.57458	−0.787290	−	0.616583i	$-0.788517\pi$
$911$	−47.5252	−1.57458	−0.787290	+	0.616583i	$0.788517\pi$
$912$	−0.230571	−0.00763497
$913$	2.78033	0.0920155
$914$	−38.4332	−1.27126
$915$	−2.41739	−0.0799166
$916$	−14.6268	−0.483284
$917$	−14.5817	−0.481530
$918$	5.11610	0.168856
$919$	8.35007	0.275443	0.137722	−	0.990471i	$-0.456022\pi$
$919$	8.35007	0.275443	0.137722	+	0.990471i	$0.456022\pi$
$920$	−1.65866	−0.0546845
$921$	3.50230	0.115405
$922$	20.1537	0.663727
$923$	18.8581	0.620722
$924$	2.93636	0.0965992
$925$	11.1277	0.365877
$926$	−36.7091	−1.20634
$927$	−14.0574	−0.461706
$928$	−1.00000	−0.0328266
$929$	−23.1339	−0.758998	−0.379499	−	0.925192i	$-0.623904\pi$
$929$	−23.1339	−0.758998	−0.379499	+	0.925192i	$0.623904\pi$
$930$	−6.59478	−0.216251
$931$	1.35579	0.0444342
$932$	−21.8588	−0.716008
$933$	−4.24875	−0.139098
$934$	−26.7479	−0.875218
$935$	23.5463	0.770047
$936$	5.36531	0.175371
$937$	9.86115	0.322150	0.161075	−	0.986942i	$-0.448504\pi$
$937$	9.86115	0.322150	0.161075	+	0.986942i	$0.448504\pi$
$938$	7.48383	0.244356
$939$	−25.2728	−0.824746
$940$	−8.09327	−0.263973
$941$	48.1729	1.57039	0.785195	−	0.619248i	$-0.212562\pi$
$941$	48.1729	1.57039	0.785195	+	0.619248i	$0.212562\pi$
$942$	12.2854	0.400280
$943$	5.80251	0.188956
$944$	6.68264	0.217501
$945$	1.75526	0.0570987
$946$	−7.40447	−0.240740
$947$	0.110230	0.00358201	0.00179100	−	0.999998i	$-0.499430\pi$
$947$	0.110230	0.00358201	0.00179100	+	0.999998i	$0.499430\pi$
$948$	−2.10845	−0.0684792
$949$	71.2784	2.31379
$950$	0.518516	0.0168229
$951$	7.84844	0.254503
$952$	−5.41406	−0.175471
$953$	44.6029	1.44483	0.722415	−	0.691459i	$-0.243032\pi$
$953$	44.6029	1.44483	0.722415	+	0.691459i	$0.243032\pi$
$954$	5.26109	0.170334
$955$	1.06695	0.0345257
$956$	−17.7587	−0.574356
$957$	2.77476	0.0896953
$958$	−6.15789	−0.198953
$959$	−6.84749	−0.221117
$960$	−1.65866	−0.0535331
$961$	−15.1917	−0.490056
$962$	−26.5487	−0.855965
$963$	10.6798	0.344151
$964$	8.48990	0.273441
$965$	3.48307	0.112124
$966$	−1.05824	−0.0340483
$967$	−23.1412	−0.744171	−0.372086	−	0.928198i	$-0.621357\pi$
$967$	−23.1412	−0.744171	−0.372086	+	0.928198i	$0.621357\pi$
$968$	−3.30069	−0.106088
$969$	−1.17962	−0.0378950
$970$	−1.30325	−0.0418448
$971$	22.0716	0.708313	0.354156	−	0.935186i	$-0.384768\pi$
$971$	22.0716	0.708313	0.354156	+	0.935186i	$0.384768\pi$
$972$	1.00000	0.0320750
$973$	13.9817	0.448234
$974$	24.2773	0.777894
$975$	−12.0657	−0.386412
$976$	1.45744	0.0466514
$977$	8.77385	0.280700	0.140350	−	0.990102i	$-0.455177\pi$
$977$	8.77385	0.280700	0.140350	+	0.990102i	$0.455177\pi$
$978$	7.95202	0.254277
$979$	−31.1110	−0.994312
$980$	9.75316	0.311553
$981$	12.7250	0.406277
$982$	−27.4076	−0.874610
$983$	−40.0954	−1.27885	−0.639423	−	0.768855i	$-0.720827\pi$
$983$	−40.0954	−1.27885	−0.639423	+	0.768855i	$0.720827\pi$
$984$	5.80251	0.184977
$985$	35.1161	1.11889
$986$	−5.11610	−0.162930
$987$	−5.16356	−0.164358
$988$	−1.23709	−0.0393570
$989$	2.66851	0.0848536
$990$	4.60240	0.146274
$991$	−7.06614	−0.224463	−0.112232	−	0.993682i	$-0.535800\pi$
$991$	−7.06614	−0.224463	−0.112232	+	0.993682i	$0.535800\pi$
$992$	3.97596	0.126237
$993$	25.8647	0.820790
$994$	−3.71952	−0.117976
$995$	9.49470	0.301002
$996$	−1.00201	−0.0317498
$997$	−25.6909	−0.813640	−0.406820	−	0.913508i	$-0.633362\pi$
$997$	−25.6909	−0.813640	−0.406820	+	0.913508i	$0.633362\pi$
$998$	15.6677	0.495953
$999$	−4.94821	−0.156554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bh.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bh.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65866 q^{5} +1.00000 q^{6} -1.05824 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65866 q^{5} +1.00000 q^{6} -1.05824 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.65866 q^{10} -2.77476 q^{11} +1.00000 q^{12} +5.36531 q^{13} -1.05824 q^{14} -1.65866 q^{15} +1.00000 q^{16} +5.11610 q^{17} +1.00000 q^{18} -0.230571 q^{19} -1.65866 q^{20} -1.05824 q^{21} -2.77476 q^{22} +1.00000 q^{23} +1.00000 q^{24} -2.24883 q^{25} +5.36531 q^{26} +1.00000 q^{27} -1.05824 q^{28} -1.00000 q^{29} -1.65866 q^{30} +3.97596 q^{31} +1.00000 q^{32} -2.77476 q^{33} +5.11610 q^{34} +1.75526 q^{35} +1.00000 q^{36} -4.94821 q^{37} -0.230571 q^{38} +5.36531 q^{39} -1.65866 q^{40} +5.80251 q^{41} -1.05824 q^{42} +2.66851 q^{43} -2.77476 q^{44} -1.65866 q^{45} +1.00000 q^{46} +4.87939 q^{47} +1.00000 q^{48} -5.88013 q^{49} -2.24883 q^{50} +5.11610 q^{51} +5.36531 q^{52} +5.26109 q^{53} +1.00000 q^{54} +4.60240 q^{55} -1.05824 q^{56} -0.230571 q^{57} -1.00000 q^{58} +6.68264 q^{59} -1.65866 q^{60} +1.45744 q^{61} +3.97596 q^{62} -1.05824 q^{63} +1.00000 q^{64} -8.89925 q^{65} -2.77476 q^{66} -7.07196 q^{67} +5.11610 q^{68} +1.00000 q^{69} +1.75526 q^{70} +3.51482 q^{71} +1.00000 q^{72} +13.2850 q^{73} -4.94821 q^{74} -2.24883 q^{75} -0.230571 q^{76} +2.93636 q^{77} +5.36531 q^{78} -2.10845 q^{79} -1.65866 q^{80} +1.00000 q^{81} +5.80251 q^{82} -1.00201 q^{83} -1.05824 q^{84} -8.48589 q^{85} +2.66851 q^{86} -1.00000 q^{87} -2.77476 q^{88} +11.2121 q^{89} -1.65866 q^{90} -5.67778 q^{91} +1.00000 q^{92} +3.97596 q^{93} +4.87939 q^{94} +0.382440 q^{95} +1.00000 q^{96} +0.785722 q^{97} -5.88013 q^{98} -2.77476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 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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