LMFDB - Embedded newform 4730.2.a.be.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 $ x^12 - 3x^11 - 26x^10 + 79x^9 + 247x^8 - 766x^7 - 1023x^6 + 3281x^5 + 1634x^4 - 5557x^3 - 483x^2 + 1648*x + 392
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$3.12850$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.12850 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.12850 q^{6} -0.193657 q^{7} +1.00000 q^{8} +6.78751 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.12850 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.12850 q^{6} -0.193657 q^{7} +1.00000 q^{8} +6.78751 q^{9} +1.00000 q^{10} -1.00000 q^{11} +3.12850 q^{12} +6.24972 q^{13} -0.193657 q^{14} +3.12850 q^{15} +1.00000 q^{16} +4.69491 q^{17} +6.78751 q^{18} -3.31827 q^{19} +1.00000 q^{20} -0.605855 q^{21} -1.00000 q^{22} -4.24972 q^{23} +3.12850 q^{24} +1.00000 q^{25} +6.24972 q^{26} +11.8492 q^{27} -0.193657 q^{28} -3.16019 q^{29} +3.12850 q^{30} -4.43189 q^{31} +1.00000 q^{32} -3.12850 q^{33} +4.69491 q^{34} -0.193657 q^{35} +6.78751 q^{36} -9.89168 q^{37} -3.31827 q^{38} +19.5522 q^{39} +1.00000 q^{40} -6.26146 q^{41} -0.605855 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.78751 q^{45} -4.24972 q^{46} +5.29078 q^{47} +3.12850 q^{48} -6.96250 q^{49} +1.00000 q^{50} +14.6880 q^{51} +6.24972 q^{52} +9.92110 q^{53} +11.8492 q^{54} -1.00000 q^{55} -0.193657 q^{56} -10.3812 q^{57} -3.16019 q^{58} +13.1950 q^{59} +3.12850 q^{60} -11.8849 q^{61} -4.43189 q^{62} -1.31445 q^{63} +1.00000 q^{64} +6.24972 q^{65} -3.12850 q^{66} -12.5688 q^{67} +4.69491 q^{68} -13.2952 q^{69} -0.193657 q^{70} +7.75245 q^{71} +6.78751 q^{72} -5.20439 q^{73} -9.89168 q^{74} +3.12850 q^{75} -3.31827 q^{76} +0.193657 q^{77} +19.5522 q^{78} -4.61249 q^{79} +1.00000 q^{80} +16.7077 q^{81} -6.26146 q^{82} -1.70199 q^{83} -0.605855 q^{84} +4.69491 q^{85} +1.00000 q^{86} -9.88665 q^{87} -1.00000 q^{88} -5.37533 q^{89} +6.78751 q^{90} -1.21030 q^{91} -4.24972 q^{92} -13.8652 q^{93} +5.29078 q^{94} -3.31827 q^{95} +3.12850 q^{96} -2.37063 q^{97} -6.96250 q^{98} -6.78751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * 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
$3$	3.12850	1.80624	0.903120	−	0.429388i	$-0.141271\pi$
$3$	3.12850	1.80624	0.903120	+	0.429388i	$0.141271\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.12850	1.27720
$7$	−0.193657	−0.0731954	−0.0365977	−	0.999330i	$-0.511652\pi$
$7$	−0.193657	−0.0731954	−0.0365977	+	0.999330i	$0.511652\pi$
$8$	1.00000	0.353553
$9$	6.78751	2.26250
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.12850	0.903120
$13$	6.24972	1.73336	0.866680	−	0.498865i	$-0.166250\pi$
$13$	6.24972	1.73336	0.866680	+	0.498865i	$0.166250\pi$
$14$	−0.193657	−0.0517569
$15$	3.12850	0.807775
$16$	1.00000	0.250000
$17$	4.69491	1.13868	0.569341	−	0.822101i	$-0.307198\pi$
$17$	4.69491	1.13868	0.569341	+	0.822101i	$0.307198\pi$
$18$	6.78751	1.59983
$19$	−3.31827	−0.761262	−0.380631	−	0.924727i	$-0.624293\pi$
$19$	−3.31827	−0.761262	−0.380631	+	0.924727i	$0.624293\pi$
$20$	1.00000	0.223607
$21$	−0.605855	−0.132208
$22$	−1.00000	−0.213201
$23$	−4.24972	−0.886127	−0.443064	−	0.896490i	$-0.646108\pi$
$23$	−4.24972	−0.886127	−0.443064	+	0.896490i	$0.646108\pi$
$24$	3.12850	0.638602
$25$	1.00000	0.200000
$26$	6.24972	1.22567
$27$	11.8492	2.28038
$28$	−0.193657	−0.0365977
$29$	−3.16019	−0.586832	−0.293416	−	0.955985i	$-0.594792\pi$
$29$	−3.16019	−0.586832	−0.293416	+	0.955985i	$0.594792\pi$
$30$	3.12850	0.571183
$31$	−4.43189	−0.795991	−0.397995	−	0.917387i	$-0.630294\pi$
$31$	−4.43189	−0.795991	−0.397995	+	0.917387i	$0.630294\pi$
$32$	1.00000	0.176777
$33$	−3.12850	−0.544602
$34$	4.69491	0.805170
$35$	−0.193657	−0.0327340
$36$	6.78751	1.13125
$37$	−9.89168	−1.62618	−0.813091	−	0.582137i	$-0.802217\pi$
$37$	−9.89168	−1.62618	−0.813091	+	0.582137i	$0.802217\pi$
$38$	−3.31827	−0.538294
$39$	19.5522	3.13086
$40$	1.00000	0.158114
$41$	−6.26146	−0.977875	−0.488938	−	0.872319i	$-0.662615\pi$
$41$	−6.26146	−0.977875	−0.488938	+	0.872319i	$0.662615\pi$
$42$	−0.605855	−0.0934855
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	6.78751	1.01182
$46$	−4.24972	−0.626587
$47$	5.29078	0.771739	0.385869	−	0.922553i	$-0.373902\pi$
$47$	5.29078	0.771739	0.385869	+	0.922553i	$0.373902\pi$
$48$	3.12850	0.451560
$49$	−6.96250	−0.994642
$50$	1.00000	0.141421
$51$	14.6880	2.05673
$52$	6.24972	0.866680
$53$	9.92110	1.36277	0.681384	−	0.731926i	$-0.261379\pi$
$53$	9.92110	1.36277	0.681384	+	0.731926i	$0.261379\pi$
$54$	11.8492	1.61247
$55$	−1.00000	−0.134840
$56$	−0.193657	−0.0258785
$57$	−10.3812	−1.37502
$58$	−3.16019	−0.414953
$59$	13.1950	1.71784	0.858921	−	0.512108i	$-0.171135\pi$
$59$	13.1950	1.71784	0.858921	+	0.512108i	$0.171135\pi$
$60$	3.12850	0.403888
$61$	−11.8849	−1.52170	−0.760850	−	0.648927i	$-0.775218\pi$
$61$	−11.8849	−1.52170	−0.760850	+	0.648927i	$0.775218\pi$
$62$	−4.43189	−0.562851
$63$	−1.31445	−0.165605
$64$	1.00000	0.125000
$65$	6.24972	0.775182
$66$	−3.12850	−0.385092
$67$	−12.5688	−1.53552	−0.767762	−	0.640735i	$-0.778630\pi$
$67$	−12.5688	−1.53552	−0.767762	+	0.640735i	$0.778630\pi$
$68$	4.69491	0.569341
$69$	−13.2952	−1.60056
$70$	−0.193657	−0.0231464
$71$	7.75245	0.920047	0.460023	−	0.887907i	$-0.347841\pi$
$71$	7.75245	0.920047	0.460023	+	0.887907i	$0.347841\pi$
$72$	6.78751	0.799915
$73$	−5.20439	−0.609128	−0.304564	−	0.952492i	$-0.598511\pi$
$73$	−5.20439	−0.609128	−0.304564	+	0.952492i	$0.598511\pi$
$74$	−9.89168	−1.14988
$75$	3.12850	0.361248
$76$	−3.31827	−0.380631
$77$	0.193657	0.0220692
$78$	19.5522	2.21385
$79$	−4.61249	−0.518946	−0.259473	−	0.965750i	$-0.583549\pi$
$79$	−4.61249	−0.518946	−0.259473	+	0.965750i	$0.583549\pi$
$80$	1.00000	0.111803
$81$	16.7077	1.85641
$82$	−6.26146	−0.691462
$83$	−1.70199	−0.186818	−0.0934089	−	0.995628i	$-0.529776\pi$
$83$	−1.70199	−0.186818	−0.0934089	+	0.995628i	$0.529776\pi$
$84$	−0.605855	−0.0661042
$85$	4.69491	0.509234
$86$	1.00000	0.107833
$87$	−9.88665	−1.05996
$88$	−1.00000	−0.106600
$89$	−5.37533	−0.569784	−0.284892	−	0.958560i	$-0.591958\pi$
$89$	−5.37533	−0.569784	−0.284892	+	0.958560i	$0.591958\pi$
$90$	6.78751	0.715466
$91$	−1.21030	−0.126874
$92$	−4.24972	−0.443064
$93$	−13.8652	−1.43775
$94$	5.29078	0.545702
$95$	−3.31827	−0.340447
$96$	3.12850	0.319301
$97$	−2.37063	−0.240701	−0.120350	−	0.992731i	$-0.538402\pi$
$97$	−2.37063	−0.240701	−0.120350	+	0.992731i	$0.538402\pi$
$98$	−6.96250	−0.703318
$99$	−6.78751	−0.682170
$100$	1.00000	0.100000
$101$	17.5532	1.74661	0.873305	−	0.487174i	$-0.161972\pi$
$101$	17.5532	1.74661	0.873305	+	0.487174i	$0.161972\pi$
$102$	14.6880	1.45433
$103$	−9.75744	−0.961429	−0.480714	−	0.876877i	$-0.659623\pi$
$103$	−9.75744	−0.961429	−0.480714	+	0.876877i	$0.659623\pi$
$104$	6.24972	0.612835
$105$	−0.605855	−0.0591254
$106$	9.92110	0.963622
$107$	−11.3919	−1.10130	−0.550648	−	0.834737i	$-0.685619\pi$
$107$	−11.3919	−1.10130	−0.550648	+	0.834737i	$0.685619\pi$
$108$	11.8492	1.14019
$109$	19.5074	1.86847	0.934236	−	0.356657i	$-0.116083\pi$
$109$	19.5074	1.86847	0.934236	+	0.356657i	$0.116083\pi$
$110$	−1.00000	−0.0953463
$111$	−30.9461	−2.93727
$112$	−0.193657	−0.0182988
$113$	−16.1060	−1.51513	−0.757564	−	0.652761i	$-0.773611\pi$
$113$	−16.1060	−1.51513	−0.757564	+	0.652761i	$0.773611\pi$
$114$	−10.3812	−0.972287
$115$	−4.24972	−0.396288
$116$	−3.16019	−0.293416
$117$	42.4200	3.92173
$118$	13.1950	1.21470
$119$	−0.909200	−0.0833463
$120$	3.12850	0.285592
$121$	1.00000	0.0909091
$122$	−11.8849	−1.07600
$123$	−19.5890	−1.76628
$124$	−4.43189	−0.397995
$125$	1.00000	0.0894427
$126$	−1.31445	−0.117100
$127$	16.6647	1.47876	0.739378	−	0.673290i	$-0.235120\pi$
$127$	16.6647	1.47876	0.739378	+	0.673290i	$0.235120\pi$
$128$	1.00000	0.0883883
$129$	3.12850	0.275449
$130$	6.24972	0.548137
$131$	−10.7205	−0.936651	−0.468326	−	0.883556i	$-0.655143\pi$
$131$	−10.7205	−0.936651	−0.468326	+	0.883556i	$0.655143\pi$
$132$	−3.12850	−0.272301
$133$	0.642604	0.0557209
$134$	−12.5688	−1.08578
$135$	11.8492	1.01982
$136$	4.69491	0.402585
$137$	1.88001	0.160620	0.0803102	−	0.996770i	$-0.474409\pi$
$137$	1.88001	0.160620	0.0803102	+	0.996770i	$0.474409\pi$
$138$	−13.2952	−1.13177
$139$	20.1904	1.71253	0.856266	−	0.516536i	$-0.172779\pi$
$139$	20.1904	1.71253	0.856266	+	0.516536i	$0.172779\pi$
$140$	−0.193657	−0.0163670
$141$	16.5522	1.39395
$142$	7.75245	0.650571
$143$	−6.24972	−0.522628
$144$	6.78751	0.565626
$145$	−3.16019	−0.262439
$146$	−5.20439	−0.430718
$147$	−21.7822	−1.79656
$148$	−9.89168	−0.813091
$149$	9.04828	0.741264	0.370632	−	0.928780i	$-0.379141\pi$
$149$	9.04828	0.741264	0.370632	+	0.928780i	$0.379141\pi$
$150$	3.12850	0.255441
$151$	−5.17559	−0.421183	−0.210592	−	0.977574i	$-0.567539\pi$
$151$	−5.17559	−0.421183	−0.210592	+	0.977574i	$0.567539\pi$
$152$	−3.31827	−0.269147
$153$	31.8667	2.57627
$154$	0.193657	0.0156053
$155$	−4.43189	−0.355978
$156$	19.5522	1.56543
$157$	8.79226	0.701699	0.350850	−	0.936432i	$-0.385893\pi$
$157$	8.79226	0.701699	0.350850	+	0.936432i	$0.385893\pi$
$158$	−4.61249	−0.366950
$159$	31.0381	2.46148
$160$	1.00000	0.0790569
$161$	0.822986	0.0648604
$162$	16.7077	1.31268
$163$	−0.776503	−0.0608204	−0.0304102	−	0.999538i	$-0.509681\pi$
$163$	−0.776503	−0.0608204	−0.0304102	+	0.999538i	$0.509681\pi$
$164$	−6.26146	−0.488938
$165$	−3.12850	−0.243553
$166$	−1.70199	−0.132100
$167$	−6.07340	−0.469974	−0.234987	−	0.971999i	$-0.575505\pi$
$167$	−6.07340	−0.469974	−0.234987	+	0.971999i	$0.575505\pi$
$168$	−0.605855	−0.0467427
$169$	26.0590	2.00454
$170$	4.69491	0.360083
$171$	−22.5227	−1.72236
$172$	1.00000	0.0762493
$173$	−17.3693	−1.32056	−0.660282	−	0.751017i	$-0.729563\pi$
$173$	−17.3693	−1.32056	−0.660282	+	0.751017i	$0.729563\pi$
$174$	−9.88665	−0.749505
$175$	−0.193657	−0.0146391
$176$	−1.00000	−0.0753778
$177$	41.2805	3.10284
$178$	−5.37533	−0.402898
$179$	−8.69359	−0.649790	−0.324895	−	0.945750i	$-0.605329\pi$
$179$	−8.69359	−0.649790	−0.324895	+	0.945750i	$0.605329\pi$
$180$	6.78751	0.505911
$181$	−9.10022	−0.676414	−0.338207	−	0.941072i	$-0.609820\pi$
$181$	−9.10022	−0.676414	−0.338207	+	0.941072i	$0.609820\pi$
$182$	−1.21030	−0.0897134
$183$	−37.1818	−2.74856
$184$	−4.24972	−0.313293
$185$	−9.89168	−0.727250
$186$	−13.8652	−1.01664
$187$	−4.69491	−0.343326
$188$	5.29078	0.385869
$189$	−2.29468	−0.166913
$190$	−3.31827	−0.240732
$191$	−15.7633	−1.14060	−0.570298	−	0.821438i	$-0.693172\pi$
$191$	−15.7633	−1.14060	−0.570298	+	0.821438i	$0.693172\pi$
$192$	3.12850	0.225780
$193$	27.7551	1.99786	0.998930	−	0.0462583i	$-0.0147297\pi$
$193$	27.7551	1.99786	0.998930	+	0.0462583i	$0.0147297\pi$
$194$	−2.37063	−0.170201
$195$	19.5522	1.40016
$196$	−6.96250	−0.497321
$197$	−3.09129	−0.220246	−0.110123	−	0.993918i	$-0.535124\pi$
$197$	−3.09129	−0.220246	−0.110123	+	0.993918i	$0.535124\pi$
$198$	−6.78751	−0.482367
$199$	5.65969	0.401205	0.200603	−	0.979673i	$-0.435710\pi$
$199$	5.65969	0.401205	0.200603	+	0.979673i	$0.435710\pi$
$200$	1.00000	0.0707107
$201$	−39.3215	−2.77353
$202$	17.5532	1.23504
$203$	0.611992	0.0429534
$204$	14.6880	1.02837
$205$	−6.26146	−0.437319
$206$	−9.75744	−0.679833
$207$	−28.8450	−2.00487
$208$	6.24972	0.433340
$209$	3.31827	0.229529
$210$	−0.605855	−0.0418080
$211$	19.6553	1.35313	0.676563	−	0.736385i	$-0.263469\pi$
$211$	19.6553	1.35313	0.676563	+	0.736385i	$0.263469\pi$
$212$	9.92110	0.681384
$213$	24.2535	1.66182
$214$	−11.3919	−0.778734
$215$	1.00000	0.0681994
$216$	11.8492	0.806237
$217$	0.858265	0.0582628
$218$	19.5074	1.32121
$219$	−16.2819	−1.10023
$220$	−1.00000	−0.0674200
$221$	29.3418	1.97375
$222$	−30.9461	−2.07697
$223$	0.836405	0.0560098	0.0280049	−	0.999608i	$-0.491085\pi$
$223$	0.836405	0.0560098	0.0280049	+	0.999608i	$0.491085\pi$
$224$	−0.193657	−0.0129392
$225$	6.78751	0.452500
$226$	−16.1060	−1.07136
$227$	22.7464	1.50973	0.754867	−	0.655878i	$-0.227701\pi$
$227$	22.7464	1.50973	0.754867	+	0.655878i	$0.227701\pi$
$228$	−10.3812	−0.687511
$229$	2.59628	0.171567	0.0857836	−	0.996314i	$-0.472661\pi$
$229$	2.59628	0.171567	0.0857836	+	0.996314i	$0.472661\pi$
$230$	−4.24972	−0.280218
$231$	0.605855	0.0398623
$232$	−3.16019	−0.207477
$233$	−25.8388	−1.69275	−0.846377	−	0.532585i	$-0.821221\pi$
$233$	−25.8388	−1.69275	−0.846377	+	0.532585i	$0.821221\pi$
$234$	42.4200	2.77308
$235$	5.29078	0.345132
$236$	13.1950	0.858921
$237$	−14.4302	−0.937340
$238$	−0.909200	−0.0589347
$239$	−18.2999	−1.18372	−0.591860	−	0.806041i	$-0.701606\pi$
$239$	−18.2999	−1.18372	−0.591860	+	0.806041i	$0.701606\pi$
$240$	3.12850	0.201944
$241$	21.1752	1.36401	0.682007	−	0.731346i	$-0.261107\pi$
$241$	21.1752	1.36401	0.682007	+	0.731346i	$0.261107\pi$
$242$	1.00000	0.0642824
$243$	16.7225	1.07275
$244$	−11.8849	−0.760850
$245$	−6.96250	−0.444818
$246$	−19.5890	−1.24895
$247$	−20.7382	−1.31954
$248$	−4.43189	−0.281425
$249$	−5.32468	−0.337438
$250$	1.00000	0.0632456
$251$	−22.4564	−1.41743	−0.708717	−	0.705492i	$-0.750726\pi$
$251$	−22.4564	−1.41743	−0.708717	+	0.705492i	$0.750726\pi$
$252$	−1.31445	−0.0828023
$253$	4.24972	0.267177
$254$	16.6647	1.04564
$255$	14.6880	0.919799
$256$	1.00000	0.0625000
$257$	20.9293	1.30553	0.652766	−	0.757560i	$-0.273609\pi$
$257$	20.9293	1.30553	0.652766	+	0.757560i	$0.273609\pi$
$258$	3.12850	0.194772
$259$	1.91559	0.119029
$260$	6.24972	0.387591
$261$	−21.4498	−1.32771
$262$	−10.7205	−0.662313
$263$	12.9753	0.800090	0.400045	−	0.916495i	$-0.368994\pi$
$263$	12.9753	0.800090	0.400045	+	0.916495i	$0.368994\pi$
$264$	−3.12850	−0.192546
$265$	9.92110	0.609448
$266$	0.642604	0.0394006
$267$	−16.8167	−1.02917
$268$	−12.5688	−0.767762
$269$	23.9968	1.46311	0.731555	−	0.681783i	$-0.238795\pi$
$269$	23.9968	1.46311	0.731555	+	0.681783i	$0.238795\pi$
$270$	11.8492	0.721120
$271$	−16.9027	−1.02677	−0.513383	−	0.858160i	$-0.671608\pi$
$271$	−16.9027	−1.02677	−0.513383	+	0.858160i	$0.671608\pi$
$272$	4.69491	0.284671
$273$	−3.78642	−0.229165
$274$	1.88001	0.113576
$275$	−1.00000	−0.0603023
$276$	−13.2952	−0.800279
$277$	7.18000	0.431405	0.215702	−	0.976459i	$-0.430796\pi$
$277$	7.18000	0.431405	0.215702	+	0.976459i	$0.430796\pi$
$278$	20.1904	1.21094
$279$	−30.0815	−1.80093
$280$	−0.193657	−0.0115732
$281$	15.7186	0.937692	0.468846	−	0.883280i	$-0.344670\pi$
$281$	15.7186	0.937692	0.468846	+	0.883280i	$0.344670\pi$
$282$	16.5522	0.985668
$283$	−6.09885	−0.362539	−0.181269	−	0.983433i	$-0.558021\pi$
$283$	−6.09885	−0.362539	−0.181269	+	0.983433i	$0.558021\pi$
$284$	7.75245	0.460023
$285$	−10.3812	−0.614929
$286$	−6.24972	−0.369554
$287$	1.21257	0.0715759
$288$	6.78751	0.399958
$289$	5.04215	0.296597
$290$	−3.16019	−0.185573
$291$	−7.41650	−0.434763
$292$	−5.20439	−0.304564
$293$	16.1455	0.943228	0.471614	−	0.881805i	$-0.343672\pi$
$293$	16.1455	0.943228	0.471614	+	0.881805i	$0.343672\pi$
$294$	−21.7822	−1.27036
$295$	13.1950	0.768242
$296$	−9.89168	−0.574942
$297$	−11.8492	−0.687561
$298$	9.04828	0.524153
$299$	−26.5595	−1.53598
$300$	3.12850	0.180624
$301$	−0.193657	−0.0111622
$302$	−5.17559	−0.297822
$303$	54.9152	3.15480
$304$	−3.31827	−0.190316
$305$	−11.8849	−0.680525
$306$	31.8667	1.82170
$307$	30.3281	1.73091	0.865457	−	0.500983i	$-0.167028\pi$
$307$	30.3281	1.73091	0.865457	+	0.500983i	$0.167028\pi$
$308$	0.193657	0.0110346
$309$	−30.5261	−1.73657
$310$	−4.43189	−0.251714
$311$	14.5883	0.827224	0.413612	−	0.910453i	$-0.364267\pi$
$311$	14.5883	0.827224	0.413612	+	0.910453i	$0.364267\pi$
$312$	19.5522	1.10693
$313$	−29.5597	−1.67081	−0.835407	−	0.549632i	$-0.814768\pi$
$313$	−29.5597	−1.67081	−0.835407	+	0.549632i	$0.814768\pi$
$314$	8.79226	0.496176
$315$	−1.31445	−0.0740607
$316$	−4.61249	−0.259473
$317$	−4.24315	−0.238319	−0.119160	−	0.992875i	$-0.538020\pi$
$317$	−4.24315	−0.238319	−0.119160	+	0.992875i	$0.538020\pi$
$318$	31.0381	1.74053
$319$	3.16019	0.176937
$320$	1.00000	0.0559017
$321$	−35.6396	−1.98921
$322$	0.822986	0.0458632
$323$	−15.5789	−0.866836
$324$	16.7077	0.928207
$325$	6.24972	0.346672
$326$	−0.776503	−0.0430065
$327$	61.0289	3.37491
$328$	−6.26146	−0.345731
$329$	−1.02459	−0.0564877
$330$	−3.12850	−0.172218
$331$	−27.2051	−1.49533	−0.747663	−	0.664079i	$-0.768824\pi$
$331$	−27.2051	−1.49533	−0.747663	+	0.664079i	$0.768824\pi$
$332$	−1.70199	−0.0934089
$333$	−67.1398	−3.67924
$334$	−6.07340	−0.332322
$335$	−12.5688	−0.686707
$336$	−0.605855	−0.0330521
$337$	−19.5564	−1.06530	−0.532651	−	0.846335i	$-0.678804\pi$
$337$	−19.5564	−1.06530	−0.532651	+	0.846335i	$0.678804\pi$
$338$	26.0590	1.41742
$339$	−50.3877	−2.73668
$340$	4.69491	0.254617
$341$	4.43189	0.240000
$342$	−22.5227	−1.21789
$343$	2.70393	0.145999
$344$	1.00000	0.0539164
$345$	−13.2952	−0.715792
$346$	−17.3693	−0.933780
$347$	−12.1096	−0.650079	−0.325040	−	0.945700i	$-0.605378\pi$
$347$	−12.1096	−0.650079	−0.325040	+	0.945700i	$0.605378\pi$
$348$	−9.88665	−0.529980
$349$	−14.2454	−0.762536	−0.381268	−	0.924465i	$-0.624513\pi$
$349$	−14.2454	−0.762536	−0.381268	+	0.924465i	$0.624513\pi$
$350$	−0.193657	−0.0103514
$351$	74.0542	3.95272
$352$	−1.00000	−0.0533002
$353$	−19.8649	−1.05730	−0.528650	−	0.848840i	$-0.677302\pi$
$353$	−19.8649	−1.05730	−0.528650	+	0.848840i	$0.677302\pi$
$354$	41.2805	2.19404
$355$	7.75245	0.411457
$356$	−5.37533	−0.284892
$357$	−2.84443	−0.150543
$358$	−8.69359	−0.459471
$359$	−14.7650	−0.779267	−0.389633	−	0.920970i	$-0.627398\pi$
$359$	−14.7650	−0.779267	−0.389633	+	0.920970i	$0.627398\pi$
$360$	6.78751	0.357733
$361$	−7.98912	−0.420480
$362$	−9.10022	−0.478297
$363$	3.12850	0.164204
$364$	−1.21030	−0.0634370
$365$	−5.20439	−0.272410
$366$	−37.1818	−1.94352
$367$	−22.7348	−1.18675	−0.593373	−	0.804928i	$-0.702204\pi$
$367$	−22.7348	−1.18675	−0.593373	+	0.804928i	$0.702204\pi$
$368$	−4.24972	−0.221532
$369$	−42.4997	−2.21244
$370$	−9.89168	−0.514244
$371$	−1.92129	−0.0997483
$372$	−13.8652	−0.718875
$373$	−18.7567	−0.971183	−0.485592	−	0.874186i	$-0.661396\pi$
$373$	−18.7567	−0.971183	−0.485592	+	0.874186i	$0.661396\pi$
$374$	−4.69491	−0.242768
$375$	3.12850	0.161555
$376$	5.29078	0.272851
$377$	−19.7503	−1.01719
$378$	−2.29468	−0.118026
$379$	7.68533	0.394769	0.197384	−	0.980326i	$-0.436755\pi$
$379$	7.68533	0.394769	0.197384	+	0.980326i	$0.436755\pi$
$380$	−3.31827	−0.170223
$381$	52.1356	2.67099
$382$	−15.7633	−0.806523
$383$	38.7917	1.98217	0.991083	−	0.133248i	$-0.0425408\pi$
$383$	38.7917	1.98217	0.991083	+	0.133248i	$0.0425408\pi$
$384$	3.12850	0.159651
$385$	0.193657	0.00986966
$386$	27.7551	1.41270
$387$	6.78751	0.345028
$388$	−2.37063	−0.120350
$389$	−19.1490	−0.970895	−0.485447	−	0.874266i	$-0.661343\pi$
$389$	−19.1490	−0.970895	−0.485447	+	0.874266i	$0.661343\pi$
$390$	19.5522	0.990066
$391$	−19.9520	−1.00902
$392$	−6.96250	−0.351659
$393$	−33.5390	−1.69182
$394$	−3.09129	−0.155737
$395$	−4.61249	−0.232079
$396$	−6.78751	−0.341085
$397$	17.7274	0.889714	0.444857	−	0.895602i	$-0.353254\pi$
$397$	17.7274	0.889714	0.444857	+	0.895602i	$0.353254\pi$
$398$	5.65969	0.283695
$399$	2.01039	0.100645
$400$	1.00000	0.0500000
$401$	−19.4462	−0.971099	−0.485550	−	0.874209i	$-0.661380\pi$
$401$	−19.4462	−0.971099	−0.485550	+	0.874209i	$0.661380\pi$
$402$	−39.3215	−1.96118
$403$	−27.6981	−1.37974
$404$	17.5532	0.873305
$405$	16.7077	0.830214
$406$	0.611992	0.0303726
$407$	9.89168	0.490312
$408$	14.6880	0.727165
$409$	25.0290	1.23760	0.618802	−	0.785547i	$-0.287618\pi$
$409$	25.0290	1.23760	0.618802	+	0.785547i	$0.287618\pi$
$410$	−6.26146	−0.309231
$411$	5.88162	0.290119
$412$	−9.75744	−0.480714
$413$	−2.55530	−0.125738
$414$	−28.8450	−1.41765
$415$	−1.70199	−0.0835474
$416$	6.24972	0.306418
$417$	63.1658	3.09324
$418$	3.31827	0.162302
$419$	−27.0833	−1.32310	−0.661552	−	0.749899i	$-0.730102\pi$
$419$	−27.0833	−1.32310	−0.661552	+	0.749899i	$0.730102\pi$
$420$	−0.605855	−0.0295627
$421$	31.7825	1.54899	0.774493	−	0.632583i	$-0.218005\pi$
$421$	31.7825	1.54899	0.774493	+	0.632583i	$0.218005\pi$
$422$	19.6553	0.956804
$423$	35.9112	1.74606
$424$	9.92110	0.481811
$425$	4.69491	0.227736
$426$	24.2535	1.17509
$427$	2.30158	0.111381
$428$	−11.3919	−0.550648
$429$	−19.5522	−0.943991
$430$	1.00000	0.0482243
$431$	−7.44734	−0.358726	−0.179363	−	0.983783i	$-0.557404\pi$
$431$	−7.44734	−0.358726	−0.179363	+	0.983783i	$0.557404\pi$
$432$	11.8492	0.570096
$433$	−6.15585	−0.295831	−0.147916	−	0.989000i	$-0.547256\pi$
$433$	−6.15585	−0.295831	−0.147916	+	0.989000i	$0.547256\pi$
$434$	0.858265	0.0411981
$435$	−9.88665	−0.474028
$436$	19.5074	0.934236
$437$	14.1017	0.674575
$438$	−16.2819	−0.777980
$439$	−14.2070	−0.678062	−0.339031	−	0.940775i	$-0.610099\pi$
$439$	−14.2070	−0.678062	−0.339031	+	0.940775i	$0.610099\pi$
$440$	−1.00000	−0.0476731
$441$	−47.2580	−2.25038
$442$	29.3418	1.39565
$443$	−16.9314	−0.804434	−0.402217	−	0.915544i	$-0.631760\pi$
$443$	−16.9314	−0.804434	−0.402217	+	0.915544i	$0.631760\pi$
$444$	−30.9461	−1.46864
$445$	−5.37533	−0.254815
$446$	0.836405	0.0396049
$447$	28.3075	1.33890
$448$	−0.193657	−0.00914942
$449$	3.31895	0.156631	0.0783155	−	0.996929i	$-0.475046\pi$
$449$	3.31895	0.156631	0.0783155	+	0.996929i	$0.475046\pi$
$450$	6.78751	0.319966
$451$	6.26146	0.294840
$452$	−16.1060	−0.757564
$453$	−16.1918	−0.760758
$454$	22.7464	1.06754
$455$	−1.21030	−0.0567397
$456$	−10.3812	−0.486144
$457$	11.2382	0.525700	0.262850	−	0.964837i	$-0.415338\pi$
$457$	11.2382	0.525700	0.262850	+	0.964837i	$0.415338\pi$
$458$	2.59628	0.121316
$459$	55.6310	2.59663
$460$	−4.24972	−0.198144
$461$	33.5807	1.56401	0.782004	−	0.623274i	$-0.214198\pi$
$461$	33.5807	1.56401	0.782004	+	0.623274i	$0.214198\pi$
$462$	0.605855	0.0281869
$463$	−35.3657	−1.64359	−0.821793	−	0.569787i	$-0.807026\pi$
$463$	−35.3657	−1.64359	−0.821793	+	0.569787i	$0.807026\pi$
$464$	−3.16019	−0.146708
$465$	−13.8652	−0.642982
$466$	−25.8388	−1.19696
$467$	−41.6956	−1.92944	−0.964721	−	0.263273i	$-0.915198\pi$
$467$	−41.6956	−1.92944	−0.964721	+	0.263273i	$0.915198\pi$
$468$	42.4200	1.96087
$469$	2.43403	0.112393
$470$	5.29078	0.244045
$471$	27.5066	1.26744
$472$	13.1950	0.607349
$473$	−1.00000	−0.0459800
$474$	−14.4302	−0.662800
$475$	−3.31827	−0.152252
$476$	−0.909200	−0.0416731
$477$	67.3395	3.08326
$478$	−18.2999	−0.837017
$479$	10.6458	0.486420	0.243210	−	0.969974i	$-0.421800\pi$
$479$	10.6458	0.486420	0.243210	+	0.969974i	$0.421800\pi$
$480$	3.12850	0.142796
$481$	−61.8202	−2.81876
$482$	21.1752	0.964503
$483$	2.57471	0.117153
$484$	1.00000	0.0454545
$485$	−2.37063	−0.107645
$486$	16.7225	0.758547
$487$	26.0432	1.18013	0.590064	−	0.807356i	$-0.299102\pi$
$487$	26.0432	1.18013	0.590064	+	0.807356i	$0.299102\pi$
$488$	−11.8849	−0.538002
$489$	−2.42929	−0.109856
$490$	−6.96250	−0.314534
$491$	−2.01820	−0.0910800	−0.0455400	−	0.998963i	$-0.514501\pi$
$491$	−2.01820	−0.0910800	−0.0455400	+	0.998963i	$0.514501\pi$
$492$	−19.5890	−0.883138
$493$	−14.8368	−0.668215
$494$	−20.7382	−0.933057
$495$	−6.78751	−0.305076
$496$	−4.43189	−0.198998
$497$	−1.50131	−0.0673432
$498$	−5.32468	−0.238604
$499$	41.1976	1.84426	0.922129	−	0.386881i	$-0.126448\pi$
$499$	41.1976	1.84426	0.922129	+	0.386881i	$0.126448\pi$
$500$	1.00000	0.0447214
$501$	−19.0006	−0.848885
$502$	−22.4564	−1.00228
$503$	13.7250	0.611966	0.305983	−	0.952037i	$-0.401015\pi$
$503$	13.7250	0.611966	0.305983	+	0.952037i	$0.401015\pi$
$504$	−1.31445	−0.0585501
$505$	17.5532	0.781108
$506$	4.24972	0.188923
$507$	81.5255	3.62067
$508$	16.6647	0.739378
$509$	6.02206	0.266923	0.133462	−	0.991054i	$-0.457391\pi$
$509$	6.02206	0.266923	0.133462	+	0.991054i	$0.457391\pi$
$510$	14.6880	0.650396
$511$	1.00786	0.0445853
$512$	1.00000	0.0441942
$513$	−39.3188	−1.73597
$514$	20.9293	0.923150
$515$	−9.75744	−0.429964
$516$	3.12850	0.137724
$517$	−5.29078	−0.232688
$518$	1.91559	0.0841662
$519$	−54.3399	−2.38526
$520$	6.24972	0.274068
$521$	10.1266	0.443655	0.221828	−	0.975086i	$-0.428798\pi$
$521$	10.1266	0.443655	0.221828	+	0.975086i	$0.428798\pi$
$522$	−21.4498	−0.938832
$523$	−22.7197	−0.993465	−0.496732	−	0.867904i	$-0.665467\pi$
$523$	−22.7197	−0.993465	−0.496732	+	0.867904i	$0.665467\pi$
$524$	−10.7205	−0.468326
$525$	−0.605855	−0.0264417
$526$	12.9753	0.565749
$527$	−20.8073	−0.906381
$528$	−3.12850	−0.136150
$529$	−4.93990	−0.214778
$530$	9.92110	0.430945
$531$	89.5611	3.88662
$532$	0.642604	0.0278604
$533$	−39.1323	−1.69501
$534$	−16.8167	−0.727730
$535$	−11.3919	−0.492515
$536$	−12.5688	−0.542890
$537$	−27.1979	−1.17368
$538$	23.9968	1.03457
$539$	6.96250	0.299896
$540$	11.8492	0.509909
$541$	13.8163	0.594010	0.297005	−	0.954876i	$-0.404012\pi$
$541$	13.8163	0.594010	0.297005	+	0.954876i	$0.404012\pi$
$542$	−16.9027	−0.726033
$543$	−28.4700	−1.22177
$544$	4.69491	0.201292
$545$	19.5074	0.835606
$546$	−3.78642	−0.162044
$547$	−17.3469	−0.741700	−0.370850	−	0.928693i	$-0.620934\pi$
$547$	−17.3469	−0.741700	−0.370850	+	0.928693i	$0.620934\pi$
$548$	1.88001	0.0803102
$549$	−80.6686	−3.44285
$550$	−1.00000	−0.0426401
$551$	10.4863	0.446733
$552$	−13.2952	−0.565883
$553$	0.893240	0.0379844
$554$	7.18000	0.305049
$555$	−30.9461	−1.31359
$556$	20.1904	0.856266
$557$	−34.7817	−1.47375	−0.736873	−	0.676031i	$-0.763698\pi$
$557$	−34.7817	−1.47375	−0.736873	+	0.676031i	$0.763698\pi$
$558$	−30.0815	−1.27345
$559$	6.24972	0.264335
$560$	−0.193657	−0.00818349
$561$	−14.6880	−0.620128
$562$	15.7186	0.663048
$563$	29.9031	1.26027	0.630134	−	0.776487i	$-0.283000\pi$
$563$	29.9031	1.26027	0.630134	+	0.776487i	$0.283000\pi$
$564$	16.5522	0.696973
$565$	−16.1060	−0.677586
$566$	−6.09885	−0.256354
$567$	−3.23556	−0.135881
$568$	7.75245	0.325286
$569$	37.5427	1.57387	0.786937	−	0.617034i	$-0.211666\pi$
$569$	37.5427	1.57387	0.786937	+	0.617034i	$0.211666\pi$
$570$	−10.3812	−0.434820
$571$	−6.33780	−0.265229	−0.132614	−	0.991168i	$-0.542337\pi$
$571$	−6.33780	−0.265229	−0.132614	+	0.991168i	$0.542337\pi$
$572$	−6.24972	−0.261314
$573$	−49.3156	−2.06019
$574$	1.21257	0.0506118
$575$	−4.24972	−0.177225
$576$	6.78751	0.282813
$577$	0.991396	0.0412724	0.0206362	−	0.999787i	$-0.493431\pi$
$577$	0.991396	0.0412724	0.0206362	+	0.999787i	$0.493431\pi$
$578$	5.04215	0.209726
$579$	86.8319	3.60861
$580$	−3.16019	−0.131220
$581$	0.329602	0.0136742
$582$	−7.41650	−0.307424
$583$	−9.92110	−0.410890
$584$	−5.20439	−0.215359
$585$	42.4200	1.75385
$586$	16.1455	0.666963
$587$	−35.4653	−1.46381	−0.731906	−	0.681406i	$-0.761369\pi$
$587$	−35.4653	−1.46381	−0.731906	+	0.681406i	$0.761369\pi$
$588$	−21.7822	−0.898281
$589$	14.7062	0.605958
$590$	13.1950	0.543229
$591$	−9.67111	−0.397816
$592$	−9.89168	−0.406545
$593$	−11.2684	−0.462739	−0.231370	−	0.972866i	$-0.574321\pi$
$593$	−11.2684	−0.462739	−0.231370	+	0.972866i	$0.574321\pi$
$594$	−11.8492	−0.486179
$595$	−0.909200	−0.0372736
$596$	9.04828	0.370632
$597$	17.7063	0.724673
$598$	−26.5595	−1.08610
$599$	−29.5386	−1.20692	−0.603458	−	0.797395i	$-0.706211\pi$
$599$	−29.5386	−1.20692	−0.603458	+	0.797395i	$0.706211\pi$
$600$	3.12850	0.127720
$601$	37.8682	1.54468	0.772338	−	0.635211i	$-0.219087\pi$
$601$	37.8682	1.54468	0.772338	+	0.635211i	$0.219087\pi$
$602$	−0.193657	−0.00789286
$603$	−85.3109	−3.47413
$604$	−5.17559	−0.210592
$605$	1.00000	0.0406558
$606$	54.9152	2.23078
$607$	18.0637	0.733182	0.366591	−	0.930382i	$-0.380525\pi$
$607$	18.0637	0.733182	0.366591	+	0.930382i	$0.380525\pi$
$608$	−3.31827	−0.134573
$609$	1.91462	0.0775841
$610$	−11.8849	−0.481204
$611$	33.0659	1.33770
$612$	31.8667	1.28814
$613$	24.6658	0.996244	0.498122	−	0.867107i	$-0.334023\pi$
$613$	24.6658	0.996244	0.498122	+	0.867107i	$0.334023\pi$
$614$	30.3281	1.22394
$615$	−19.5890	−0.789903
$616$	0.193657	0.00780265
$617$	−18.3689	−0.739503	−0.369751	−	0.929131i	$-0.620557\pi$
$617$	−18.3689	−0.739503	−0.369751	+	0.929131i	$0.620557\pi$
$618$	−30.5261	−1.22794
$619$	21.3251	0.857127	0.428564	−	0.903512i	$-0.359020\pi$
$619$	21.3251	0.857127	0.428564	+	0.903512i	$0.359020\pi$
$620$	−4.43189	−0.177989
$621$	−50.3558	−2.02071
$622$	14.5883	0.584936
$623$	1.04097	0.0417055
$624$	19.5522	0.782716
$625$	1.00000	0.0400000
$626$	−29.5597	−1.18144
$627$	10.3812	0.414585
$628$	8.79226	0.350850
$629$	−46.4405	−1.85170
$630$	−1.31445	−0.0523688
$631$	1.17951	0.0469556	0.0234778	−	0.999724i	$-0.492526\pi$
$631$	1.17951	0.0469556	0.0234778	+	0.999724i	$0.492526\pi$
$632$	−4.61249	−0.183475
$633$	61.4916	2.44407
$634$	−4.24315	−0.168517
$635$	16.6647	0.661320
$636$	31.0381	1.23074
$637$	−43.5136	−1.72407
$638$	3.16019	0.125113
$639$	52.6198	2.08161
$640$	1.00000	0.0395285
$641$	25.6176	1.01184	0.505918	−	0.862582i	$-0.331154\pi$
$641$	25.6176	1.01184	0.505918	+	0.862582i	$0.331154\pi$
$642$	−35.6396	−1.40658
$643$	−14.0320	−0.553366	−0.276683	−	0.960961i	$-0.589235\pi$
$643$	−14.0320	−0.553366	−0.276683	+	0.960961i	$0.589235\pi$
$644$	0.822986	0.0324302
$645$	3.12850	0.123185
$646$	−15.5789	−0.612945
$647$	2.39495	0.0941551	0.0470775	−	0.998891i	$-0.485009\pi$
$647$	2.39495	0.0941551	0.0470775	+	0.998891i	$0.485009\pi$
$648$	16.7077	0.656342
$649$	−13.1950	−0.517949
$650$	6.24972	0.245134
$651$	2.68508	0.105237
$652$	−0.776503	−0.0304102
$653$	−6.55041	−0.256337	−0.128169	−	0.991752i	$-0.540910\pi$
$653$	−6.55041	−0.256337	−0.128169	+	0.991752i	$0.540910\pi$
$654$	61.0289	2.38642
$655$	−10.7205	−0.418883
$656$	−6.26146	−0.244469
$657$	−35.3248	−1.37815
$658$	−1.02459	−0.0399428
$659$	−42.3962	−1.65152	−0.825760	−	0.564021i	$-0.809254\pi$
$659$	−42.3962	−1.65152	−0.825760	+	0.564021i	$0.809254\pi$
$660$	−3.12850	−0.121777
$661$	25.8356	1.00489	0.502444	−	0.864610i	$-0.332434\pi$
$661$	25.8356	1.00489	0.502444	+	0.864610i	$0.332434\pi$
$662$	−27.2051	−1.05735
$663$	91.7959	3.56506
$664$	−1.70199	−0.0660500
$665$	0.642604	0.0249191
$666$	−67.1398	−2.60162
$667$	13.4299	0.520008
$668$	−6.07340	−0.234987
$669$	2.61669	0.101167
$670$	−12.5688	−0.485575
$671$	11.8849	0.458810
$672$	−0.605855	−0.0233714
$673$	−6.73500	−0.259615	−0.129808	−	0.991539i	$-0.541436\pi$
$673$	−6.73500	−0.259615	−0.129808	+	0.991539i	$0.541436\pi$
$674$	−19.5564	−0.753283
$675$	11.8492	0.456076
$676$	26.0590	1.00227
$677$	21.7097	0.834373	0.417186	−	0.908821i	$-0.363016\pi$
$677$	21.7097	0.834373	0.417186	+	0.908821i	$0.363016\pi$
$678$	−50.3877	−1.93513
$679$	0.459088	0.0176182
$680$	4.69491	0.180041
$681$	71.1622	2.72694
$682$	4.43189	0.169706
$683$	−49.9877	−1.91272	−0.956362	−	0.292184i	$-0.905618\pi$
$683$	−49.9877	−1.91272	−0.956362	+	0.292184i	$0.905618\pi$
$684$	−22.5227	−0.861179
$685$	1.88001	0.0718316
$686$	2.70393	0.103237
$687$	8.12247	0.309891
$688$	1.00000	0.0381246
$689$	62.0040	2.36217
$690$	−13.2952	−0.506141
$691$	−15.1962	−0.578091	−0.289046	−	0.957315i	$-0.593338\pi$
$691$	−15.1962	−0.578091	−0.289046	+	0.957315i	$0.593338\pi$
$692$	−17.3693	−0.660282
$693$	1.31445	0.0499317
$694$	−12.1096	−0.459675
$695$	20.1904	0.765867
$696$	−9.88665	−0.374752
$697$	−29.3970	−1.11349
$698$	−14.2454	−0.539194
$699$	−80.8365	−3.05752
$700$	−0.193657	−0.00731954
$701$	−11.7539	−0.443938	−0.221969	−	0.975054i	$-0.571248\pi$
$701$	−11.7539	−0.443938	−0.221969	+	0.975054i	$0.571248\pi$
$702$	74.0542	2.79500
$703$	32.8232	1.23795
$704$	−1.00000	−0.0376889
$705$	16.5522	0.623391
$706$	−19.8649	−0.747625
$707$	−3.39930	−0.127844
$708$	41.2805	1.55142
$709$	18.5238	0.695676	0.347838	−	0.937555i	$-0.386916\pi$
$709$	18.5238	0.695676	0.347838	+	0.937555i	$0.386916\pi$
$710$	7.75245	0.290944
$711$	−31.3073	−1.17412
$712$	−5.37533	−0.201449
$713$	18.8343	0.705349
$714$	−2.84443	−0.106450
$715$	−6.24972	−0.233726
$716$	−8.69359	−0.324895
$717$	−57.2512	−2.13808
$718$	−14.7650	−0.551025
$719$	−25.4450	−0.948939	−0.474469	−	0.880272i	$-0.657360\pi$
$719$	−25.4450	−0.948939	−0.474469	+	0.880272i	$0.657360\pi$
$720$	6.78751	0.252955
$721$	1.88959	0.0703721
$722$	−7.98912	−0.297324
$723$	66.2466	2.46374
$724$	−9.10022	−0.338207
$725$	−3.16019	−0.117366
$726$	3.12850	0.116109
$727$	−4.50040	−0.166911	−0.0834554	−	0.996512i	$-0.526596\pi$
$727$	−4.50040	−0.166911	−0.0834554	+	0.996512i	$0.526596\pi$
$728$	−1.21030	−0.0448567
$729$	2.19309	0.0812255
$730$	−5.20439	−0.192623
$731$	4.69491	0.173647
$732$	−37.1818	−1.37428
$733$	14.0557	0.519158	0.259579	−	0.965722i	$-0.416416\pi$
$733$	14.0557	0.519158	0.259579	+	0.965722i	$0.416416\pi$
$734$	−22.7348	−0.839155
$735$	−21.7822	−0.803447
$736$	−4.24972	−0.156647
$737$	12.5688	0.462978
$738$	−42.4997	−1.56443
$739$	−34.9736	−1.28652	−0.643262	−	0.765646i	$-0.722420\pi$
$739$	−34.9736	−1.28652	−0.643262	+	0.765646i	$0.722420\pi$
$740$	−9.89168	−0.363625
$741$	−64.8795	−2.38341
$742$	−1.92129	−0.0705327
$743$	−51.3368	−1.88336	−0.941682	−	0.336505i	$-0.890755\pi$
$743$	−51.3368	−1.88336	−0.941682	+	0.336505i	$0.890755\pi$
$744$	−13.8652	−0.508322
$745$	9.04828	0.331503
$746$	−18.7567	−0.686730
$747$	−11.5523	−0.422676
$748$	−4.69491	−0.171663
$749$	2.20612	0.0806098
$750$	3.12850	0.114237
$751$	−21.2244	−0.774488	−0.387244	−	0.921977i	$-0.626573\pi$
$751$	−21.2244	−0.774488	−0.387244	+	0.921977i	$0.626573\pi$
$752$	5.29078	0.192935
$753$	−70.2548	−2.56023
$754$	−19.7503	−0.719263
$755$	−5.17559	−0.188359
$756$	−2.29468	−0.0834567
$757$	−0.637315	−0.0231636	−0.0115818	−	0.999933i	$-0.503687\pi$
$757$	−0.637315	−0.0231636	−0.0115818	+	0.999933i	$0.503687\pi$
$758$	7.68533	0.279144
$759$	13.2952	0.482587
$760$	−3.31827	−0.120366
$761$	−6.81940	−0.247203	−0.123602	−	0.992332i	$-0.539444\pi$
$761$	−6.81940	−0.247203	−0.123602	+	0.992332i	$0.539444\pi$
$762$	52.1356	1.88867
$763$	−3.77774	−0.136763
$764$	−15.7633	−0.570298
$765$	31.8667	1.15214
$766$	38.7917	1.40160
$767$	82.4650	2.97764
$768$	3.12850	0.112890
$769$	42.2996	1.52536	0.762680	−	0.646775i	$-0.223883\pi$
$769$	42.2996	1.52536	0.762680	+	0.646775i	$0.223883\pi$
$770$	0.193657	0.00697890
$771$	65.4772	2.35810
$772$	27.7551	0.998930
$773$	33.6663	1.21089	0.605446	−	0.795886i	$-0.292995\pi$
$773$	33.6663	1.21089	0.605446	+	0.795886i	$0.292995\pi$
$774$	6.78751	0.243972
$775$	−4.43189	−0.159198
$776$	−2.37063	−0.0851005
$777$	5.99292	0.214995
$778$	−19.1490	−0.686526
$779$	20.7772	0.744419
$780$	19.5522	0.700082
$781$	−7.75245	−0.277405
$782$	−19.9520	−0.713483
$783$	−37.4457	−1.33820
$784$	−6.96250	−0.248661
$785$	8.79226	0.313809
$786$	−33.5390	−1.19630
$787$	36.0197	1.28396	0.641982	−	0.766720i	$-0.278112\pi$
$787$	36.0197	1.28396	0.641982	+	0.766720i	$0.278112\pi$
$788$	−3.09129	−0.110123
$789$	40.5932	1.44515
$790$	−4.61249	−0.164105
$791$	3.11904	0.110900
$792$	−6.78751	−0.241184
$793$	−74.2770	−2.63766
$794$	17.7274	0.629123
$795$	31.0381	1.10081
$796$	5.65969	0.200603
$797$	−2.98746	−0.105821	−0.0529107	−	0.998599i	$-0.516850\pi$
$797$	−2.98746	−0.105821	−0.0529107	+	0.998599i	$0.516850\pi$
$798$	2.01039	0.0711669
$799$	24.8397	0.878765
$800$	1.00000	0.0353553
$801$	−36.4851	−1.28914
$802$	−19.4462	−0.686671
$803$	5.20439	0.183659
$804$	−39.3215	−1.38676
$805$	0.822986	0.0290065
$806$	−27.6981	−0.975623
$807$	75.0739	2.64273
$808$	17.5532	0.617520
$809$	−38.1914	−1.34274	−0.671370	−	0.741123i	$-0.734294\pi$
$809$	−38.1914	−1.34274	−0.671370	+	0.741123i	$0.734294\pi$
$810$	16.7077	0.587050
$811$	4.18912	0.147100	0.0735499	−	0.997292i	$-0.476567\pi$
$811$	4.18912	0.147100	0.0735499	+	0.997292i	$0.476567\pi$
$812$	0.611992	0.0214767
$813$	−52.8801	−1.85459
$814$	9.89168	0.346703
$815$	−0.776503	−0.0271997
$816$	14.6880	0.514183
$817$	−3.31827	−0.116091
$818$	25.0290	0.875119
$819$	−8.21492	−0.287053
$820$	−6.26146	−0.218659
$821$	36.3985	1.27032	0.635158	−	0.772383i	$-0.280935\pi$
$821$	36.3985	1.27032	0.635158	+	0.772383i	$0.280935\pi$
$822$	5.88162	0.205145
$823$	33.1651	1.15606	0.578032	−	0.816014i	$-0.303821\pi$
$823$	33.1651	1.15606	0.578032	+	0.816014i	$0.303821\pi$
$824$	−9.75744	−0.339916
$825$	−3.12850	−0.108920
$826$	−2.55530	−0.0889103
$827$	38.0894	1.32450	0.662250	−	0.749283i	$-0.269602\pi$
$827$	38.0894	1.32450	0.662250	+	0.749283i	$0.269602\pi$
$828$	−28.8450	−1.00243
$829$	35.6095	1.23677	0.618384	−	0.785876i	$-0.287788\pi$
$829$	35.6095	1.23677	0.618384	+	0.785876i	$0.287788\pi$
$830$	−1.70199	−0.0590770
$831$	22.4626	0.779220
$832$	6.24972	0.216670
$833$	−32.6883	−1.13258
$834$	63.1658	2.18725
$835$	−6.07340	−0.210179
$836$	3.31827	0.114765
$837$	−52.5144	−1.81516
$838$	−27.0833	−0.935576
$839$	8.12212	0.280407	0.140203	−	0.990123i	$-0.455224\pi$
$839$	8.12212	0.280407	0.140203	+	0.990123i	$0.455224\pi$
$840$	−0.605855	−0.0209040
$841$	−19.0132	−0.655628
$842$	31.7825	1.09530
$843$	49.1756	1.69370
$844$	19.6553	0.676563
$845$	26.0590	0.896456
$846$	35.9112	1.23465
$847$	−0.193657	−0.00665412
$848$	9.92110	0.340692
$849$	−19.0802	−0.654832
$850$	4.69491	0.161034
$851$	42.0368	1.44100
$852$	24.2535	0.830912
$853$	38.9334	1.33306	0.666528	−	0.745480i	$-0.267780\pi$
$853$	38.9334	1.33306	0.666528	+	0.745480i	$0.267780\pi$
$854$	2.30158	0.0787586
$855$	−22.5227	−0.770262
$856$	−11.3919	−0.389367
$857$	10.7332	0.366640	0.183320	−	0.983053i	$-0.441316\pi$
$857$	10.7332	0.366640	0.183320	+	0.983053i	$0.441316\pi$
$858$	−19.5522	−0.667502
$859$	−29.2949	−0.999528	−0.499764	−	0.866162i	$-0.666580\pi$
$859$	−29.2949	−0.999528	−0.499764	+	0.866162i	$0.666580\pi$
$860$	1.00000	0.0340997
$861$	3.79353	0.129283
$862$	−7.44734	−0.253657
$863$	4.65550	0.158475	0.0792376	−	0.996856i	$-0.474751\pi$
$863$	4.65550	0.158475	0.0792376	+	0.996856i	$0.474751\pi$
$864$	11.8492	0.403118
$865$	−17.3693	−0.590575
$866$	−6.15585	−0.209184
$867$	15.7744	0.535726
$868$	0.858265	0.0291314
$869$	4.61249	0.156468
$870$	−9.88665	−0.335189
$871$	−78.5515	−2.66162
$872$	19.5074	0.660604
$873$	−16.0906	−0.544586
$874$	14.1017	0.476997
$875$	−0.193657	−0.00654679
$876$	−16.2819	−0.550115
$877$	8.36090	0.282327	0.141164	−	0.989986i	$-0.454916\pi$
$877$	8.36090	0.282327	0.141164	+	0.989986i	$0.454916\pi$
$878$	−14.2070	−0.479462
$879$	50.5111	1.70370
$880$	−1.00000	−0.0337100
$881$	8.74262	0.294546	0.147273	−	0.989096i	$-0.452950\pi$
$881$	8.74262	0.294546	0.147273	+	0.989096i	$0.452950\pi$
$882$	−47.2580	−1.59126
$883$	−5.98650	−0.201462	−0.100731	−	0.994914i	$-0.532118\pi$
$883$	−5.98650	−0.201462	−0.100731	+	0.994914i	$0.532118\pi$
$884$	29.3418	0.986873
$885$	41.2805	1.38763
$886$	−16.9314	−0.568821
$887$	13.1918	0.442937	0.221469	−	0.975167i	$-0.428915\pi$
$887$	13.1918	0.442937	0.221469	+	0.975167i	$0.428915\pi$
$888$	−30.9461	−1.03848
$889$	−3.22724	−0.108238
$890$	−5.37533	−0.180181
$891$	−16.7077	−0.559730
$892$	0.836405	0.0280049
$893$	−17.5562	−0.587496
$894$	28.3075	0.946746
$895$	−8.69359	−0.290595
$896$	−0.193657	−0.00646962
$897$	−83.0915	−2.77434
$898$	3.31895	0.110755
$899$	14.0056	0.467113
$900$	6.78751	0.226250
$901$	46.5786	1.55176
$902$	6.26146	0.208484
$903$	−0.605855	−0.0201616
$904$	−16.1060	−0.535679
$905$	−9.10022	−0.302501
$906$	−16.1918	−0.537937
$907$	5.91848	0.196520	0.0982600	−	0.995161i	$-0.468672\pi$
$907$	5.91848	0.196520	0.0982600	+	0.995161i	$0.468672\pi$
$908$	22.7464	0.754867
$909$	119.143	3.95171
$910$	−1.21030	−0.0401211
$911$	19.1172	0.633381	0.316690	−	0.948529i	$-0.397428\pi$
$911$	19.1172	0.633381	0.316690	+	0.948529i	$0.397428\pi$
$912$	−10.3812	−0.343756
$913$	1.70199	0.0563277
$914$	11.2382	0.371726
$915$	−37.1818	−1.22919
$916$	2.59628	0.0857836
$917$	2.07609	0.0685585
$918$	55.6310	1.83610
$919$	−14.5898	−0.481274	−0.240637	−	0.970615i	$-0.577356\pi$
$919$	−14.5898	−0.481274	−0.240637	+	0.970615i	$0.577356\pi$
$920$	−4.24972	−0.140109
$921$	94.8813	3.12645
$922$	33.5807	1.10592
$923$	48.4506	1.59477
$924$	0.605855	0.0199312
$925$	−9.89168	−0.325236
$926$	−35.3657	−1.16219
$927$	−66.2287	−2.17523
$928$	−3.16019	−0.103738
$929$	−16.7769	−0.550433	−0.275216	−	0.961382i	$-0.588749\pi$
$929$	−16.7769	−0.550433	−0.275216	+	0.961382i	$0.588749\pi$
$930$	−13.8652	−0.454657
$931$	23.1034	0.757184
$932$	−25.8388	−0.846377
$933$	45.6394	1.49417
$934$	−41.6956	−1.36432
$935$	−4.69491	−0.153540
$936$	42.4200	1.38654
$937$	−34.4207	−1.12447	−0.562237	−	0.826976i	$-0.690059\pi$
$937$	−34.4207	−1.12447	−0.562237	+	0.826976i	$0.690059\pi$
$938$	2.43403	0.0794740
$939$	−92.4776	−3.01789
$940$	5.29078	0.172566
$941$	−29.7253	−0.969016	−0.484508	−	0.874787i	$-0.661001\pi$
$941$	−29.7253	−0.969016	−0.484508	+	0.874787i	$0.661001\pi$
$942$	27.5066	0.896213
$943$	26.6094	0.866522
$944$	13.1950	0.429461
$945$	−2.29468	−0.0746459
$946$	−1.00000	−0.0325128
$947$	27.0019	0.877443	0.438722	−	0.898623i	$-0.355431\pi$
$947$	27.0019	0.877443	0.438722	+	0.898623i	$0.355431\pi$
$948$	−14.4302	−0.468670
$949$	−32.5260	−1.05584
$950$	−3.31827	−0.107659
$951$	−13.2747	−0.430462
$952$	−0.909200	−0.0294674
$953$	48.2152	1.56184	0.780922	−	0.624629i	$-0.214750\pi$
$953$	48.2152	1.56184	0.780922	+	0.624629i	$0.214750\pi$
$954$	67.3395	2.18020
$955$	−15.7633	−0.510090
$956$	−18.2999	−0.591860
$957$	9.88665	0.319590
$958$	10.6458	0.343951
$959$	−0.364077	−0.0117567
$960$	3.12850	0.100972
$961$	−11.3584	−0.366398
$962$	−61.8202	−1.99316
$963$	−77.3226	−2.49169
$964$	21.1752	0.682007
$965$	27.7551	0.893470
$966$	2.57471	0.0828400
$967$	58.8840	1.89358	0.946791	−	0.321848i	$-0.104304\pi$
$967$	58.8840	1.89358	0.946791	+	0.321848i	$0.104304\pi$
$968$	1.00000	0.0321412
$969$	−48.7387	−1.56571
$970$	−2.37063	−0.0761162
$971$	8.42518	0.270377	0.135188	−	0.990820i	$-0.456836\pi$
$971$	8.42518	0.270377	0.135188	+	0.990820i	$0.456836\pi$
$972$	16.7225	0.536374
$973$	−3.91002	−0.125349
$974$	26.0432	0.834477
$975$	19.5522	0.626173
$976$	−11.8849	−0.380425
$977$	31.0307	0.992759	0.496380	−	0.868106i	$-0.334662\pi$
$977$	31.0307	0.992759	0.496380	+	0.868106i	$0.334662\pi$
$978$	−2.42929	−0.0776801
$979$	5.37533	0.171796
$980$	−6.96250	−0.222409
$981$	132.407	4.22742
$982$	−2.01820	−0.0644033
$983$	−41.0262	−1.30853	−0.654267	−	0.756264i	$-0.727023\pi$
$983$	−41.0262	−1.30853	−0.654267	+	0.756264i	$0.727023\pi$
$984$	−19.5890	−0.624473
$985$	−3.09129	−0.0984968
$986$	−14.8368	−0.472500
$987$	−3.20544	−0.102030
$988$	−20.7382	−0.659771
$989$	−4.24972	−0.135133
$990$	−6.78751	−0.215721
$991$	41.6398	1.32273	0.661366	−	0.750063i	$-0.269977\pi$
$991$	41.6398	1.32273	0.661366	+	0.750063i	$0.269977\pi$
$992$	−4.43189	−0.140713
$993$	−85.1110	−2.70092
$994$	−1.50131	−0.0476188
$995$	5.65969	0.179424
$996$	−5.32468	−0.168719
$997$	−25.0395	−0.793007	−0.396504	−	0.918033i	$-0.629777\pi$
$997$	−25.0395	−0.793007	−0.396504	+	0.918033i	$0.629777\pi$
$998$	41.1976	1.30409
$999$	−117.209	−3.70832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.be.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.be.1.12	✓	12	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.12850 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.12850 q^{6} -0.193657 q^{7} +1.00000 q^{8} +6.78751 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.12850 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.12850 q^{6} -0.193657 q^{7} +1.00000 q^{8} +6.78751 q^{9} +1.00000 q^{10} -1.00000 q^{11} +3.12850 q^{12} +6.24972 q^{13} -0.193657 q^{14} +3.12850 q^{15} +1.00000 q^{16} +4.69491 q^{17} +6.78751 q^{18} -3.31827 q^{19} +1.00000 q^{20} -0.605855 q^{21} -1.00000 q^{22} -4.24972 q^{23} +3.12850 q^{24} +1.00000 q^{25} +6.24972 q^{26} +11.8492 q^{27} -0.193657 q^{28} -3.16019 q^{29} +3.12850 q^{30} -4.43189 q^{31} +1.00000 q^{32} -3.12850 q^{33} +4.69491 q^{34} -0.193657 q^{35} +6.78751 q^{36} -9.89168 q^{37} -3.31827 q^{38} +19.5522 q^{39} +1.00000 q^{40} -6.26146 q^{41} -0.605855 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.78751 q^{45} -4.24972 q^{46} +5.29078 q^{47} +3.12850 q^{48} -6.96250 q^{49} +1.00000 q^{50} +14.6880 q^{51} +6.24972 q^{52} +9.92110 q^{53} +11.8492 q^{54} -1.00000 q^{55} -0.193657 q^{56} -10.3812 q^{57} -3.16019 q^{58} +13.1950 q^{59} +3.12850 q^{60} -11.8849 q^{61} -4.43189 q^{62} -1.31445 q^{63} +1.00000 q^{64} +6.24972 q^{65} -3.12850 q^{66} -12.5688 q^{67} +4.69491 q^{68} -13.2952 q^{69} -0.193657 q^{70} +7.75245 q^{71} +6.78751 q^{72} -5.20439 q^{73} -9.89168 q^{74} +3.12850 q^{75} -3.31827 q^{76} +0.193657 q^{77} +19.5522 q^{78} -4.61249 q^{79} +1.00000 q^{80} +16.7077 q^{81} -6.26146 q^{82} -1.70199 q^{83} -0.605855 q^{84} +4.69491 q^{85} +1.00000 q^{86} -9.88665 q^{87} -1.00000 q^{88} -5.37533 q^{89} +6.78751 q^{90} -1.21030 q^{91} -4.24972 q^{92} -13.8652 q^{93} +5.29078 q^{94} -3.31827 q^{95} +3.12850 q^{96} -2.37063 q^{97} -6.96250 q^{98} -6.78751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * q^99

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