LMFDB - Embedded newform 4026.2.a.bc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 $ x^9 - x^8 - 30x^7 + 7x^6 + 284x^5 + 100x^4 - 777x^3 - 250x^2 + 574*x - 68
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			1.1
Root			$4.23292$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.23292 q^{5} +1.00000 q^{6} +4.29240 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.23292 q^{5} +1.00000 q^{6} +4.29240 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.23292 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.88047 q^{13} +4.29240 q^{14} -3.23292 q^{15} +1.00000 q^{16} -1.40871 q^{17} +1.00000 q^{18} +3.85835 q^{19} -3.23292 q^{20} +4.29240 q^{21} +1.00000 q^{22} +2.00280 q^{23} +1.00000 q^{24} +5.45180 q^{25} +2.88047 q^{26} +1.00000 q^{27} +4.29240 q^{28} -1.66491 q^{29} -3.23292 q^{30} +0.769881 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.40871 q^{34} -13.8770 q^{35} +1.00000 q^{36} +6.59775 q^{37} +3.85835 q^{38} +2.88047 q^{39} -3.23292 q^{40} -7.18702 q^{41} +4.29240 q^{42} -11.7343 q^{43} +1.00000 q^{44} -3.23292 q^{45} +2.00280 q^{46} +0.896639 q^{47} +1.00000 q^{48} +11.4247 q^{49} +5.45180 q^{50} -1.40871 q^{51} +2.88047 q^{52} -12.1997 q^{53} +1.00000 q^{54} -3.23292 q^{55} +4.29240 q^{56} +3.85835 q^{57} -1.66491 q^{58} +8.74700 q^{59} -3.23292 q^{60} -1.00000 q^{61} +0.769881 q^{62} +4.29240 q^{63} +1.00000 q^{64} -9.31234 q^{65} +1.00000 q^{66} +6.74484 q^{67} -1.40871 q^{68} +2.00280 q^{69} -13.8770 q^{70} +3.73137 q^{71} +1.00000 q^{72} +0.751328 q^{73} +6.59775 q^{74} +5.45180 q^{75} +3.85835 q^{76} +4.29240 q^{77} +2.88047 q^{78} +0.132373 q^{79} -3.23292 q^{80} +1.00000 q^{81} -7.18702 q^{82} +15.9513 q^{83} +4.29240 q^{84} +4.55426 q^{85} -11.7343 q^{86} -1.66491 q^{87} +1.00000 q^{88} +2.50051 q^{89} -3.23292 q^{90} +12.3641 q^{91} +2.00280 q^{92} +0.769881 q^{93} +0.896639 q^{94} -12.4737 q^{95} +1.00000 q^{96} +13.2106 q^{97} +11.4247 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * 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
$5$	−3.23292	−1.44581	−0.722904	−	0.690949i	$-0.757193\pi$
$5$	−3.23292	−1.44581	−0.722904	+	0.690949i	$0.757193\pi$
$6$	1.00000	0.408248
$7$	4.29240	1.62237	0.811187	−	0.584787i	$-0.198822\pi$
$7$	4.29240	1.62237	0.811187	+	0.584787i	$0.198822\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.23292	−1.02234
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	2.88047	0.798898	0.399449	−	0.916755i	$-0.369201\pi$
$13$	2.88047	0.798898	0.399449	+	0.916755i	$0.369201\pi$
$14$	4.29240	1.14719
$15$	−3.23292	−0.834737
$16$	1.00000	0.250000
$17$	−1.40871	−0.341663	−0.170831	−	0.985300i	$-0.554645\pi$
$17$	−1.40871	−0.341663	−0.170831	+	0.985300i	$0.554645\pi$
$18$	1.00000	0.235702
$19$	3.85835	0.885165	0.442583	−	0.896728i	$-0.354062\pi$
$19$	3.85835	0.885165	0.442583	+	0.896728i	$0.354062\pi$
$20$	−3.23292	−0.722904
$21$	4.29240	0.936678
$22$	1.00000	0.213201
$23$	2.00280	0.417614	0.208807	−	0.977957i	$-0.433042\pi$
$23$	2.00280	0.417614	0.208807	+	0.977957i	$0.433042\pi$
$24$	1.00000	0.204124
$25$	5.45180	1.09036
$26$	2.88047	0.564906
$27$	1.00000	0.192450
$28$	4.29240	0.811187
$29$	−1.66491	−0.309167	−0.154583	−	0.987980i	$-0.549403\pi$
$29$	−1.66491	−0.309167	−0.154583	+	0.987980i	$0.549403\pi$
$30$	−3.23292	−0.590248
$31$	0.769881	0.138275	0.0691373	−	0.997607i	$-0.477975\pi$
$31$	0.769881	0.138275	0.0691373	+	0.997607i	$0.477975\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−1.40871	−0.241592
$35$	−13.8770	−2.34564
$36$	1.00000	0.166667
$37$	6.59775	1.08466	0.542332	−	0.840164i	$-0.317542\pi$
$37$	6.59775	1.08466	0.542332	+	0.840164i	$0.317542\pi$
$38$	3.85835	0.625906
$39$	2.88047	0.461244
$40$	−3.23292	−0.511170
$41$	−7.18702	−1.12242	−0.561212	−	0.827672i	$-0.689665\pi$
$41$	−7.18702	−1.12242	−0.561212	+	0.827672i	$0.689665\pi$
$42$	4.29240	0.662332
$43$	−11.7343	−1.78946	−0.894729	−	0.446609i	$-0.852632\pi$
$43$	−11.7343	−1.78946	−0.894729	+	0.446609i	$0.852632\pi$
$44$	1.00000	0.150756
$45$	−3.23292	−0.481936
$46$	2.00280	0.295297
$47$	0.896639	0.130788	0.0653941	−	0.997860i	$-0.479170\pi$
$47$	0.896639	0.130788	0.0653941	+	0.997860i	$0.479170\pi$
$48$	1.00000	0.144338
$49$	11.4247	1.63210
$50$	5.45180	0.771001
$51$	−1.40871	−0.197259
$52$	2.88047	0.399449
$53$	−12.1997	−1.67576	−0.837881	−	0.545854i	$-0.816205\pi$
$53$	−12.1997	−1.67576	−0.837881	+	0.545854i	$0.816205\pi$
$54$	1.00000	0.136083
$55$	−3.23292	−0.435927
$56$	4.29240	0.573596
$57$	3.85835	0.511050
$58$	−1.66491	−0.218614
$59$	8.74700	1.13876	0.569381	−	0.822074i	$-0.307183\pi$
$59$	8.74700	1.13876	0.569381	+	0.822074i	$0.307183\pi$
$60$	−3.23292	−0.417369
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	0.769881	0.0977749
$63$	4.29240	0.540791
$64$	1.00000	0.125000
$65$	−9.31234	−1.15505
$66$	1.00000	0.123091
$67$	6.74484	0.824013	0.412007	−	0.911181i	$-0.364828\pi$
$67$	6.74484	0.824013	0.412007	+	0.911181i	$0.364828\pi$
$68$	−1.40871	−0.170831
$69$	2.00280	0.241109
$70$	−13.8770	−1.65862
$71$	3.73137	0.442832	0.221416	−	0.975179i	$-0.428932\pi$
$71$	3.73137	0.442832	0.221416	+	0.975179i	$0.428932\pi$
$72$	1.00000	0.117851
$73$	0.751328	0.0879362	0.0439681	−	0.999033i	$-0.486000\pi$
$73$	0.751328	0.0879362	0.0439681	+	0.999033i	$0.486000\pi$
$74$	6.59775	0.766973
$75$	5.45180	0.629519
$76$	3.85835	0.442583
$77$	4.29240	0.489164
$78$	2.88047	0.326149
$79$	0.132373	0.0148932	0.00744659	−	0.999972i	$-0.497630\pi$
$79$	0.132373	0.0148932	0.00744659	+	0.999972i	$0.497630\pi$
$80$	−3.23292	−0.361452
$81$	1.00000	0.111111
$82$	−7.18702	−0.793673
$83$	15.9513	1.75088	0.875440	−	0.483327i	$-0.160572\pi$
$83$	15.9513	1.75088	0.875440	+	0.483327i	$0.160572\pi$
$84$	4.29240	0.468339
$85$	4.55426	0.493979
$86$	−11.7343	−1.26534
$87$	−1.66491	−0.178497
$88$	1.00000	0.106600
$89$	2.50051	0.265053	0.132527	−	0.991179i	$-0.457691\pi$
$89$	2.50051	0.265053	0.132527	+	0.991179i	$0.457691\pi$
$90$	−3.23292	−0.340780
$91$	12.3641	1.29611
$92$	2.00280	0.208807
$93$	0.769881	0.0798329
$94$	0.896639	0.0924813
$95$	−12.4737	−1.27978
$96$	1.00000	0.102062
$97$	13.2106	1.34133	0.670664	−	0.741761i	$-0.266009\pi$
$97$	13.2106	1.34133	0.670664	+	0.741761i	$0.266009\pi$
$98$	11.4247	1.15407
$99$	1.00000	0.100504
$100$	5.45180	0.545180
$101$	12.3663	1.23049	0.615246	−	0.788335i	$-0.289057\pi$
$101$	12.3663	1.23049	0.615246	+	0.788335i	$0.289057\pi$
$102$	−1.40871	−0.139483
$103$	−8.44990	−0.832594	−0.416297	−	0.909229i	$-0.636672\pi$
$103$	−8.44990	−0.832594	−0.416297	+	0.909229i	$0.636672\pi$
$104$	2.88047	0.282453
$105$	−13.8770	−1.35426
$106$	−12.1997	−1.18494
$107$	12.8377	1.24107	0.620533	−	0.784180i	$-0.286916\pi$
$107$	12.8377	1.24107	0.620533	+	0.784180i	$0.286916\pi$
$108$	1.00000	0.0962250
$109$	7.85123	0.752011	0.376006	−	0.926617i	$-0.377297\pi$
$109$	7.85123	0.752011	0.376006	+	0.926617i	$0.377297\pi$
$110$	−3.23292	−0.308247
$111$	6.59775	0.626231
$112$	4.29240	0.405594
$113$	−3.68244	−0.346415	−0.173208	−	0.984885i	$-0.555413\pi$
$113$	−3.68244	−0.346415	−0.173208	+	0.984885i	$0.555413\pi$
$114$	3.85835	0.361367
$115$	−6.47491	−0.603789
$116$	−1.66491	−0.154583
$117$	2.88047	0.266299
$118$	8.74700	0.805227
$119$	−6.04675	−0.554305
$120$	−3.23292	−0.295124
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−7.18702	−0.648032
$124$	0.769881	0.0691373
$125$	−1.46063	−0.130642
$126$	4.29240	0.382397
$127$	20.5720	1.82547	0.912733	−	0.408557i	$-0.133968\pi$
$127$	20.5720	1.82547	0.912733	+	0.408557i	$0.133968\pi$
$128$	1.00000	0.0883883
$129$	−11.7343	−1.03314
$130$	−9.31234	−0.816746
$131$	−0.892502	−0.0779783	−0.0389891	−	0.999240i	$-0.512414\pi$
$131$	−0.892502	−0.0779783	−0.0389891	+	0.999240i	$0.512414\pi$
$132$	1.00000	0.0870388
$133$	16.5616	1.43607
$134$	6.74484	0.582665
$135$	−3.23292	−0.278246
$136$	−1.40871	−0.120796
$137$	−6.13837	−0.524436	−0.262218	−	0.965009i	$-0.584454\pi$
$137$	−6.13837	−0.524436	−0.262218	+	0.965009i	$0.584454\pi$
$138$	2.00280	0.170490
$139$	−3.56248	−0.302166	−0.151083	−	0.988521i	$-0.548276\pi$
$139$	−3.56248	−0.302166	−0.151083	+	0.988521i	$0.548276\pi$
$140$	−13.8770	−1.17282
$141$	0.896639	0.0755106
$142$	3.73137	0.313129
$143$	2.88047	0.240877
$144$	1.00000	0.0833333
$145$	5.38254	0.446995
$146$	0.751328	0.0621803
$147$	11.4247	0.942293
$148$	6.59775	0.542332
$149$	−5.57250	−0.456517	−0.228258	−	0.973601i	$-0.573303\pi$
$149$	−5.57250	−0.456517	−0.228258	+	0.973601i	$0.573303\pi$
$150$	5.45180	0.445137
$151$	9.29629	0.756521	0.378261	−	0.925699i	$-0.376522\pi$
$151$	9.29629	0.756521	0.378261	+	0.925699i	$0.376522\pi$
$152$	3.85835	0.312953
$153$	−1.40871	−0.113888
$154$	4.29240	0.345891
$155$	−2.48897	−0.199919
$156$	2.88047	0.230622
$157$	−21.7347	−1.73462	−0.867308	−	0.497771i	$-0.834152\pi$
$157$	−21.7347	−1.73462	−0.867308	+	0.497771i	$0.834152\pi$
$158$	0.132373	0.0105311
$159$	−12.1997	−0.967501
$160$	−3.23292	−0.255585
$161$	8.59684	0.677526
$162$	1.00000	0.0785674
$163$	−9.29178	−0.727788	−0.363894	−	0.931440i	$-0.618553\pi$
$163$	−9.29178	−0.727788	−0.363894	+	0.931440i	$0.618553\pi$
$164$	−7.18702	−0.561212
$165$	−3.23292	−0.251683
$166$	15.9513	1.23806
$167$	−12.9130	−0.999239	−0.499620	−	0.866245i	$-0.666527\pi$
$167$	−12.9130	−0.999239	−0.499620	+	0.866245i	$0.666527\pi$
$168$	4.29240	0.331166
$169$	−4.70290	−0.361762
$170$	4.55426	0.349296
$171$	3.85835	0.295055
$172$	−11.7343	−0.894729
$173$	−23.3606	−1.77607	−0.888037	−	0.459771i	$-0.847931\pi$
$173$	−23.3606	−1.77607	−0.888037	+	0.459771i	$0.847931\pi$
$174$	−1.66491	−0.126217
$175$	23.4013	1.76897
$176$	1.00000	0.0753778
$177$	8.74700	0.657465
$178$	2.50051	0.187421
$179$	−4.01612	−0.300179	−0.150090	−	0.988672i	$-0.547956\pi$
$179$	−4.01612	−0.300179	−0.150090	+	0.988672i	$0.547956\pi$
$180$	−3.23292	−0.240968
$181$	−16.5937	−1.23340	−0.616699	−	0.787199i	$-0.711530\pi$
$181$	−16.5937	−1.23340	−0.616699	+	0.787199i	$0.711530\pi$
$182$	12.3641	0.916490
$183$	−1.00000	−0.0739221
$184$	2.00280	0.147649
$185$	−21.3300	−1.56821
$186$	0.769881	0.0564504
$187$	−1.40871	−0.103015
$188$	0.896639	0.0653941
$189$	4.29240	0.312226
$190$	−12.4737	−0.904940
$191$	7.04645	0.509863	0.254932	−	0.966959i	$-0.417947\pi$
$191$	7.04645	0.509863	0.254932	+	0.966959i	$0.417947\pi$
$192$	1.00000	0.0721688
$193$	−4.26409	−0.306936	−0.153468	−	0.988154i	$-0.549044\pi$
$193$	−4.26409	−0.306936	−0.153468	+	0.988154i	$0.549044\pi$
$194$	13.2106	0.948463
$195$	−9.31234	−0.666870
$196$	11.4247	0.816049
$197$	−3.05152	−0.217412	−0.108706	−	0.994074i	$-0.534671\pi$
$197$	−3.05152	−0.217412	−0.108706	+	0.994074i	$0.534671\pi$
$198$	1.00000	0.0710669
$199$	22.6750	1.60739	0.803696	−	0.595041i	$-0.202864\pi$
$199$	22.6750	1.60739	0.803696	+	0.595041i	$0.202864\pi$
$200$	5.45180	0.385500
$201$	6.74484	0.475744
$202$	12.3663	0.870089
$203$	−7.14647	−0.501584
$204$	−1.40871	−0.0986296
$205$	23.2351	1.62281
$206$	−8.44990	−0.588733
$207$	2.00280	0.139205
$208$	2.88047	0.199725
$209$	3.85835	0.266887
$210$	−13.8770	−0.957604
$211$	2.07496	0.142846	0.0714231	−	0.997446i	$-0.477246\pi$
$211$	2.07496	0.142846	0.0714231	+	0.997446i	$0.477246\pi$
$212$	−12.1997	−0.837881
$213$	3.73137	0.255669
$214$	12.8377	0.877566
$215$	37.9360	2.58721
$216$	1.00000	0.0680414
$217$	3.30464	0.224333
$218$	7.85123	0.531752
$219$	0.751328	0.0507700
$220$	−3.23292	−0.217964
$221$	−4.05775	−0.272954
$222$	6.59775	0.442812
$223$	−4.87062	−0.326161	−0.163080	−	0.986613i	$-0.552143\pi$
$223$	−4.87062	−0.326161	−0.163080	+	0.986613i	$0.552143\pi$
$224$	4.29240	0.286798
$225$	5.45180	0.363453
$226$	−3.68244	−0.244952
$227$	22.1378	1.46934	0.734670	−	0.678425i	$-0.237337\pi$
$227$	22.1378	1.46934	0.734670	+	0.678425i	$0.237337\pi$
$228$	3.85835	0.255525
$229$	−21.5095	−1.42139	−0.710695	−	0.703500i	$-0.751620\pi$
$229$	−21.5095	−1.42139	−0.710695	+	0.703500i	$0.751620\pi$
$230$	−6.47491	−0.426943
$231$	4.29240	0.282419
$232$	−1.66491	−0.109307
$233$	−13.9601	−0.914554	−0.457277	−	0.889324i	$-0.651175\pi$
$233$	−13.9601	−0.914554	−0.457277	+	0.889324i	$0.651175\pi$
$234$	2.88047	0.188302
$235$	−2.89877	−0.189095
$236$	8.74700	0.569381
$237$	0.132373	0.00859858
$238$	−6.04675	−0.391953
$239$	4.12106	0.266569	0.133284	−	0.991078i	$-0.457448\pi$
$239$	4.12106	0.266569	0.133284	+	0.991078i	$0.457448\pi$
$240$	−3.23292	−0.208684
$241$	6.60585	0.425520	0.212760	−	0.977104i	$-0.431755\pi$
$241$	6.60585	0.425520	0.212760	+	0.977104i	$0.431755\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−36.9352	−2.35970
$246$	−7.18702	−0.458227
$247$	11.1138	0.707157
$248$	0.769881	0.0488875
$249$	15.9513	1.01087
$250$	−1.46063	−0.0923781
$251$	−25.8066	−1.62890	−0.814449	−	0.580235i	$-0.802961\pi$
$251$	−25.8066	−1.62890	−0.814449	+	0.580235i	$0.802961\pi$
$252$	4.29240	0.270396
$253$	2.00280	0.125915
$254$	20.5720	1.29080
$255$	4.55426	0.285199
$256$	1.00000	0.0625000
$257$	−21.8807	−1.36488	−0.682441	−	0.730940i	$-0.739082\pi$
$257$	−21.8807	−1.36488	−0.682441	+	0.730940i	$0.739082\pi$
$258$	−11.7343	−0.730543
$259$	28.3202	1.75973
$260$	−9.31234	−0.577527
$261$	−1.66491	−0.103056
$262$	−0.892502	−0.0551390
$263$	21.7683	1.34229	0.671147	−	0.741325i	$-0.265802\pi$
$263$	21.7683	1.34229	0.671147	+	0.741325i	$0.265802\pi$
$264$	1.00000	0.0615457
$265$	39.4408	2.42283
$266$	16.5616	1.01545
$267$	2.50051	0.153029
$268$	6.74484	0.412007
$269$	4.86810	0.296813	0.148407	−	0.988926i	$-0.452586\pi$
$269$	4.86810	0.296813	0.148407	+	0.988926i	$0.452586\pi$
$270$	−3.23292	−0.196749
$271$	19.8242	1.20424	0.602118	−	0.798407i	$-0.294324\pi$
$271$	19.8242	1.20424	0.602118	+	0.798407i	$0.294324\pi$
$272$	−1.40871	−0.0854157
$273$	12.3641	0.748311
$274$	−6.13837	−0.370833
$275$	5.45180	0.328756
$276$	2.00280	0.120555
$277$	−6.99143	−0.420075	−0.210037	−	0.977693i	$-0.567359\pi$
$277$	−6.99143	−0.420075	−0.210037	+	0.977693i	$0.567359\pi$
$278$	−3.56248	−0.213663
$279$	0.769881	0.0460916
$280$	−13.8770	−0.829309
$281$	−13.9571	−0.832609	−0.416305	−	0.909225i	$-0.636675\pi$
$281$	−13.9571	−0.832609	−0.416305	+	0.909225i	$0.636675\pi$
$282$	0.896639	0.0533941
$283$	−7.59877	−0.451700	−0.225850	−	0.974162i	$-0.572516\pi$
$283$	−7.59877	−0.451700	−0.225850	+	0.974162i	$0.572516\pi$
$284$	3.73137	0.221416
$285$	−12.4737	−0.738880
$286$	2.88047	0.170326
$287$	−30.8495	−1.82099
$288$	1.00000	0.0589256
$289$	−15.0155	−0.883267
$290$	5.38254	0.316073
$291$	13.2106	0.774416
$292$	0.751328	0.0439681
$293$	18.0763	1.05603	0.528013	−	0.849236i	$-0.322937\pi$
$293$	18.0763	1.05603	0.528013	+	0.849236i	$0.322937\pi$
$294$	11.4247	0.666301
$295$	−28.2784	−1.64643
$296$	6.59775	0.383486
$297$	1.00000	0.0580259
$298$	−5.57250	−0.322806
$299$	5.76902	0.333631
$300$	5.45180	0.314760
$301$	−50.3681	−2.90317
$302$	9.29629	0.534941
$303$	12.3663	0.710424
$304$	3.85835	0.221291
$305$	3.23292	0.185117
$306$	−1.40871	−0.0805307
$307$	−10.1292	−0.578104	−0.289052	−	0.957313i	$-0.593340\pi$
$307$	−10.1292	−0.578104	−0.289052	+	0.957313i	$0.593340\pi$
$308$	4.29240	0.244582
$309$	−8.44990	−0.480698
$310$	−2.48897	−0.141364
$311$	9.70940	0.550570	0.275285	−	0.961363i	$-0.411228\pi$
$311$	9.70940	0.550570	0.275285	+	0.961363i	$0.411228\pi$
$312$	2.88047	0.163074
$313$	−3.60353	−0.203683	−0.101842	−	0.994801i	$-0.532474\pi$
$313$	−3.60353	−0.203683	−0.101842	+	0.994801i	$0.532474\pi$
$314$	−21.7347	−1.22656
$315$	−13.8770	−0.781880
$316$	0.132373	0.00744659
$317$	−24.8688	−1.39677	−0.698386	−	0.715722i	$-0.746098\pi$
$317$	−24.8688	−1.39677	−0.698386	+	0.715722i	$0.746098\pi$
$318$	−12.1997	−0.684127
$319$	−1.66491	−0.0932172
$320$	−3.23292	−0.180726
$321$	12.8377	0.716530
$322$	8.59684	0.479083
$323$	−5.43530	−0.302428
$324$	1.00000	0.0555556
$325$	15.7037	0.871086
$326$	−9.29178	−0.514624
$327$	7.85123	0.434174
$328$	−7.18702	−0.396837
$329$	3.84873	0.212188
$330$	−3.23292	−0.177967
$331$	34.3670	1.88898	0.944490	−	0.328541i	$-0.106557\pi$
$331$	34.3670	1.88898	0.944490	+	0.328541i	$0.106557\pi$
$332$	15.9513	0.875440
$333$	6.59775	0.361554
$334$	−12.9130	−0.706569
$335$	−21.8055	−1.19136
$336$	4.29240	0.234170
$337$	−19.8632	−1.08202	−0.541008	−	0.841018i	$-0.681957\pi$
$337$	−19.8632	−1.08202	−0.541008	+	0.841018i	$0.681957\pi$
$338$	−4.70290	−0.255804
$339$	−3.68244	−0.200003
$340$	4.55426	0.246989
$341$	0.769881	0.0416914
$342$	3.85835	0.208635
$343$	18.9925	1.02550
$344$	−11.7343	−0.632669
$345$	−6.47491	−0.348598
$346$	−23.3606	−1.25587
$347$	2.88427	0.154836	0.0774180	−	0.996999i	$-0.475332\pi$
$347$	2.88427	0.154836	0.0774180	+	0.996999i	$0.475332\pi$
$348$	−1.66491	−0.0892487
$349$	−9.43788	−0.505198	−0.252599	−	0.967571i	$-0.581285\pi$
$349$	−9.43788	−0.505198	−0.252599	+	0.967571i	$0.581285\pi$
$350$	23.4013	1.25085
$351$	2.88047	0.153748
$352$	1.00000	0.0533002
$353$	32.1549	1.71143	0.855717	−	0.517445i	$-0.173117\pi$
$353$	32.1549	1.71143	0.855717	+	0.517445i	$0.173117\pi$
$354$	8.74700	0.464898
$355$	−12.0632	−0.640250
$356$	2.50051	0.132527
$357$	−6.04675	−0.320028
$358$	−4.01612	−0.212259
$359$	−27.2400	−1.43767	−0.718835	−	0.695180i	$-0.755325\pi$
$359$	−27.2400	−1.43767	−0.718835	+	0.695180i	$0.755325\pi$
$360$	−3.23292	−0.170390
$361$	−4.11317	−0.216483
$362$	−16.5937	−0.872144
$363$	1.00000	0.0524864
$364$	12.3641	0.648056
$365$	−2.42898	−0.127139
$366$	−1.00000	−0.0522708
$367$	21.4924	1.12189	0.560947	−	0.827852i	$-0.310437\pi$
$367$	21.4924	1.12189	0.560947	+	0.827852i	$0.310437\pi$
$368$	2.00280	0.104403
$369$	−7.18702	−0.374141
$370$	−21.3300	−1.10890
$371$	−52.3661	−2.71871
$372$	0.769881	0.0399165
$373$	5.71898	0.296118	0.148059	−	0.988979i	$-0.452698\pi$
$373$	5.71898	0.296118	0.148059	+	0.988979i	$0.452698\pi$
$374$	−1.40871	−0.0728428
$375$	−1.46063	−0.0754264
$376$	0.896639	0.0462406
$377$	−4.79573	−0.246993
$378$	4.29240	0.220777
$379$	−6.50559	−0.334169	−0.167085	−	0.985943i	$-0.553435\pi$
$379$	−6.50559	−0.334169	−0.167085	+	0.985943i	$0.553435\pi$
$380$	−12.4737	−0.639889
$381$	20.5720	1.05393
$382$	7.04645	0.360528
$383$	20.2446	1.03445	0.517226	−	0.855849i	$-0.326965\pi$
$383$	20.2446	1.03445	0.517226	+	0.855849i	$0.326965\pi$
$384$	1.00000	0.0510310
$385$	−13.8770	−0.707237
$386$	−4.26409	−0.217037
$387$	−11.7343	−0.596486
$388$	13.2106	0.670664
$389$	−29.9629	−1.51918	−0.759589	−	0.650403i	$-0.774600\pi$
$389$	−29.9629	−1.51918	−0.759589	+	0.650403i	$0.774600\pi$
$390$	−9.31234	−0.471548
$391$	−2.82137	−0.142683
$392$	11.4247	0.577034
$393$	−0.892502	−0.0450208
$394$	−3.05152	−0.153734
$395$	−0.427953	−0.0215327
$396$	1.00000	0.0502519
$397$	−9.15525	−0.459489	−0.229744	−	0.973251i	$-0.573789\pi$
$397$	−9.15525	−0.459489	−0.229744	+	0.973251i	$0.573789\pi$
$398$	22.6750	1.13660
$399$	16.5616	0.829115
$400$	5.45180	0.272590
$401$	37.5872	1.87701	0.938506	−	0.345262i	$-0.112210\pi$
$401$	37.5872	1.87701	0.938506	+	0.345262i	$0.112210\pi$
$402$	6.74484	0.336402
$403$	2.21762	0.110467
$404$	12.3663	0.615246
$405$	−3.23292	−0.160645
$406$	−7.14647	−0.354673
$407$	6.59775	0.327038
$408$	−1.40871	−0.0697416
$409$	−21.3450	−1.05544	−0.527722	−	0.849417i	$-0.676954\pi$
$409$	−21.3450	−1.05544	−0.527722	+	0.849417i	$0.676954\pi$
$410$	23.2351	1.14750
$411$	−6.13837	−0.302784
$412$	−8.44990	−0.416297
$413$	37.5456	1.84750
$414$	2.00280	0.0984325
$415$	−51.5693	−2.53144
$416$	2.88047	0.141227
$417$	−3.56248	−0.174455
$418$	3.85835	0.188718
$419$	−0.827299	−0.0404162	−0.0202081	−	0.999796i	$-0.506433\pi$
$419$	−0.827299	−0.0404162	−0.0202081	+	0.999796i	$0.506433\pi$
$420$	−13.8770	−0.677128
$421$	−24.3906	−1.18872	−0.594362	−	0.804198i	$-0.702595\pi$
$421$	−24.3906	−1.18872	−0.594362	+	0.804198i	$0.702595\pi$
$422$	2.07496	0.101007
$423$	0.896639	0.0435961
$424$	−12.1997	−0.592471
$425$	−7.68001	−0.372535
$426$	3.73137	0.180785
$427$	−4.29240	−0.207724
$428$	12.8377	0.620533
$429$	2.88047	0.139070
$430$	37.9360	1.82944
$431$	−15.7849	−0.760331	−0.380165	−	0.924919i	$-0.624133\pi$
$431$	−15.7849	−0.760331	−0.380165	+	0.924919i	$0.624133\pi$
$432$	1.00000	0.0481125
$433$	−29.7369	−1.42906	−0.714531	−	0.699604i	$-0.753360\pi$
$433$	−29.7369	−1.42906	−0.714531	+	0.699604i	$0.753360\pi$
$434$	3.30464	0.158628
$435$	5.38254	0.258073
$436$	7.85123	0.376006
$437$	7.72751	0.369657
$438$	0.751328	0.0358998
$439$	−20.5160	−0.979173	−0.489587	−	0.871955i	$-0.662852\pi$
$439$	−20.5160	−0.979173	−0.489587	+	0.871955i	$0.662852\pi$
$440$	−3.23292	−0.154124
$441$	11.4247	0.544033
$442$	−4.05775	−0.193008
$443$	−17.3896	−0.826204	−0.413102	−	0.910685i	$-0.635555\pi$
$443$	−17.3896	−0.826204	−0.413102	+	0.910685i	$0.635555\pi$
$444$	6.59775	0.313115
$445$	−8.08395	−0.383216
$446$	−4.87062	−0.230631
$447$	−5.57250	−0.263570
$448$	4.29240	0.202797
$449$	−4.56127	−0.215260	−0.107630	−	0.994191i	$-0.534326\pi$
$449$	−4.56127	−0.215260	−0.107630	+	0.994191i	$0.534326\pi$
$450$	5.45180	0.257000
$451$	−7.18702	−0.338423
$452$	−3.68244	−0.173208
$453$	9.29629	0.436778
$454$	22.1378	1.03898
$455$	−39.9723	−1.87393
$456$	3.85835	0.180684
$457$	28.9963	1.35639	0.678196	−	0.734881i	$-0.262762\pi$
$457$	28.9963	1.35639	0.678196	+	0.734881i	$0.262762\pi$
$458$	−21.5095	−1.00508
$459$	−1.40871	−0.0657530
$460$	−6.47491	−0.301894
$461$	−9.76692	−0.454891	−0.227445	−	0.973791i	$-0.573037\pi$
$461$	−9.76692	−0.454891	−0.227445	+	0.973791i	$0.573037\pi$
$462$	4.29240	0.199700
$463$	16.4463	0.764326	0.382163	−	0.924095i	$-0.375179\pi$
$463$	16.4463	0.764326	0.382163	+	0.924095i	$0.375179\pi$
$464$	−1.66491	−0.0772916
$465$	−2.48897	−0.115423
$466$	−13.9601	−0.646687
$467$	−16.9538	−0.784528	−0.392264	−	0.919853i	$-0.628308\pi$
$467$	−16.9538	−0.784528	−0.392264	+	0.919853i	$0.628308\pi$
$468$	2.88047	0.133150
$469$	28.9515	1.33686
$470$	−2.89877	−0.133710
$471$	−21.7347	−1.00148
$472$	8.74700	0.402613
$473$	−11.7343	−0.539542
$474$	0.132373	0.00608011
$475$	21.0349	0.965148
$476$	−6.04675	−0.277152
$477$	−12.1997	−0.558587
$478$	4.12106	0.188493
$479$	19.0297	0.869487	0.434744	−	0.900554i	$-0.356839\pi$
$479$	19.0297	0.869487	0.434744	+	0.900554i	$0.356839\pi$
$480$	−3.23292	−0.147562
$481$	19.0046	0.866536
$482$	6.60585	0.300888
$483$	8.59684	0.391170
$484$	1.00000	0.0454545
$485$	−42.7087	−1.93930
$486$	1.00000	0.0453609
$487$	−5.55083	−0.251532	−0.125766	−	0.992060i	$-0.540139\pi$
$487$	−5.55083	−0.251532	−0.125766	+	0.992060i	$0.540139\pi$
$488$	−1.00000	−0.0452679
$489$	−9.29178	−0.420189
$490$	−36.9352	−1.66856
$491$	−8.75305	−0.395020	−0.197510	−	0.980301i	$-0.563285\pi$
$491$	−8.75305	−0.395020	−0.197510	+	0.980301i	$0.563285\pi$
$492$	−7.18702	−0.324016
$493$	2.34538	0.105631
$494$	11.1138	0.500035
$495$	−3.23292	−0.145309
$496$	0.769881	0.0345687
$497$	16.0165	0.718439
$498$	15.9513	0.714794
$499$	−5.13148	−0.229716	−0.114858	−	0.993382i	$-0.536641\pi$
$499$	−5.13148	−0.229716	−0.114858	+	0.993382i	$0.536641\pi$
$500$	−1.46063	−0.0653211
$501$	−12.9130	−0.576911
$502$	−25.8066	−1.15181
$503$	20.5428	0.915957	0.457979	−	0.888963i	$-0.348574\pi$
$503$	20.5428	0.915957	0.457979	+	0.888963i	$0.348574\pi$
$504$	4.29240	0.191199
$505$	−39.9793	−1.77905
$506$	2.00280	0.0890355
$507$	−4.70290	−0.208863
$508$	20.5720	0.912733
$509$	30.3874	1.34690	0.673449	−	0.739233i	$-0.264812\pi$
$509$	30.3874	1.34690	0.673449	+	0.739233i	$0.264812\pi$
$510$	4.55426	0.201666
$511$	3.22500	0.142665
$512$	1.00000	0.0441942
$513$	3.85835	0.170350
$514$	−21.8807	−0.965118
$515$	27.3179	1.20377
$516$	−11.7343	−0.516572
$517$	0.896639	0.0394341
$518$	28.3202	1.24432
$519$	−23.3606	−1.02542
$520$	−9.31234	−0.408373
$521$	21.4870	0.941364	0.470682	−	0.882303i	$-0.344008\pi$
$521$	21.4870	0.941364	0.470682	+	0.882303i	$0.344008\pi$
$522$	−1.66491	−0.0728713
$523$	−41.4608	−1.81295	−0.906477	−	0.422256i	$-0.861238\pi$
$523$	−41.4608	−1.81295	−0.906477	+	0.422256i	$0.861238\pi$
$524$	−0.892502	−0.0389891
$525$	23.4013	1.02132
$526$	21.7683	0.949145
$527$	−1.08454	−0.0472433
$528$	1.00000	0.0435194
$529$	−18.9888	−0.825599
$530$	39.4408	1.71320
$531$	8.74700	0.379587
$532$	16.5616	0.718035
$533$	−20.7020	−0.896702
$534$	2.50051	0.108208
$535$	−41.5033	−1.79434
$536$	6.74484	0.291333
$537$	−4.01612	−0.173309
$538$	4.86810	0.209879
$539$	11.4247	0.492096
$540$	−3.23292	−0.139123
$541$	−7.56723	−0.325341	−0.162670	−	0.986680i	$-0.552011\pi$
$541$	−7.56723	−0.325341	−0.162670	+	0.986680i	$0.552011\pi$
$542$	19.8242	0.851523
$543$	−16.5937	−0.712103
$544$	−1.40871	−0.0603980
$545$	−25.3824	−1.08726
$546$	12.3641	0.529136
$547$	−11.8607	−0.507126	−0.253563	−	0.967319i	$-0.581603\pi$
$547$	−11.8607	−0.507126	−0.253563	+	0.967319i	$0.581603\pi$
$548$	−6.13837	−0.262218
$549$	−1.00000	−0.0426790
$550$	5.45180	0.232465
$551$	−6.42381	−0.273663
$552$	2.00280	0.0852450
$553$	0.568200	0.0241623
$554$	−6.99143	−0.297038
$555$	−21.3300	−0.905409
$556$	−3.56248	−0.151083
$557$	−40.6138	−1.72086	−0.860430	−	0.509569i	$-0.829805\pi$
$557$	−40.6138	−1.72086	−0.860430	+	0.509569i	$0.829805\pi$
$558$	0.769881	0.0325916
$559$	−33.8002	−1.42960
$560$	−13.8770	−0.586410
$561$	−1.40871	−0.0594759
$562$	−13.9571	−0.588744
$563$	13.7241	0.578401	0.289201	−	0.957269i	$-0.406611\pi$
$563$	13.7241	0.578401	0.289201	+	0.957269i	$0.406611\pi$
$564$	0.896639	0.0377553
$565$	11.9051	0.500850
$566$	−7.59877	−0.319400
$567$	4.29240	0.180264
$568$	3.73137	0.156565
$569$	−8.21441	−0.344366	−0.172183	−	0.985065i	$-0.555082\pi$
$569$	−8.21441	−0.344366	−0.172183	+	0.985065i	$0.555082\pi$
$570$	−12.4737	−0.522467
$571$	8.58722	0.359364	0.179682	−	0.983725i	$-0.442493\pi$
$571$	8.58722	0.359364	0.179682	+	0.983725i	$0.442493\pi$
$572$	2.88047	0.120438
$573$	7.04645	0.294370
$574$	−30.8495	−1.28764
$575$	10.9189	0.455349
$576$	1.00000	0.0416667
$577$	24.6285	1.02530	0.512650	−	0.858598i	$-0.328664\pi$
$577$	24.6285	1.02530	0.512650	+	0.858598i	$0.328664\pi$
$578$	−15.0155	−0.624564
$579$	−4.26409	−0.177210
$580$	5.38254	0.223498
$581$	68.4692	2.84058
$582$	13.2106	0.547595
$583$	−12.1997	−0.505261
$584$	0.751328	0.0310902
$585$	−9.31234	−0.385018
$586$	18.0763	0.746723
$587$	17.7655	0.733261	0.366631	−	0.930367i	$-0.380511\pi$
$587$	17.7655	0.733261	0.366631	+	0.930367i	$0.380511\pi$
$588$	11.4247	0.471146
$589$	2.97047	0.122396
$590$	−28.2784	−1.16420
$591$	−3.05152	−0.125523
$592$	6.59775	0.271166
$593$	−21.9965	−0.903289	−0.451644	−	0.892198i	$-0.649162\pi$
$593$	−21.9965	−0.903289	−0.451644	+	0.892198i	$0.649162\pi$
$594$	1.00000	0.0410305
$595$	19.5487	0.801418
$596$	−5.57250	−0.228258
$597$	22.6750	0.928028
$598$	5.76902	0.235913
$599$	7.42717	0.303466	0.151733	−	0.988422i	$-0.451515\pi$
$599$	7.42717	0.303466	0.151733	+	0.988422i	$0.451515\pi$
$600$	5.45180	0.222569
$601$	−12.1774	−0.496725	−0.248363	−	0.968667i	$-0.579892\pi$
$601$	−12.1774	−0.496725	−0.248363	+	0.968667i	$0.579892\pi$
$602$	−50.3681	−2.05285
$603$	6.74484	0.274671
$604$	9.29629	0.378261
$605$	−3.23292	−0.131437
$606$	12.3663	0.502346
$607$	−30.0402	−1.21930	−0.609648	−	0.792672i	$-0.708689\pi$
$607$	−30.0402	−1.21930	−0.609648	+	0.792672i	$0.708689\pi$
$608$	3.85835	0.156477
$609$	−7.14647	−0.289590
$610$	3.23292	0.130897
$611$	2.58274	0.104487
$612$	−1.40871	−0.0569438
$613$	−37.9027	−1.53088	−0.765438	−	0.643509i	$-0.777478\pi$
$613$	−37.9027	−1.53088	−0.765438	+	0.643509i	$0.777478\pi$
$614$	−10.1292	−0.408781
$615$	23.2351	0.936929
$616$	4.29240	0.172946
$617$	−4.14439	−0.166847	−0.0834234	−	0.996514i	$-0.526585\pi$
$617$	−4.14439	−0.166847	−0.0834234	+	0.996514i	$0.526585\pi$
$618$	−8.44990	−0.339905
$619$	5.59655	0.224945	0.112472	−	0.993655i	$-0.464123\pi$
$619$	5.59655	0.224945	0.112472	+	0.993655i	$0.464123\pi$
$620$	−2.48897	−0.0999593
$621$	2.00280	0.0803698
$622$	9.70940	0.389312
$623$	10.7332	0.430016
$624$	2.88047	0.115311
$625$	−22.5369	−0.901476
$626$	−3.60353	−0.144026
$627$	3.85835	0.154087
$628$	−21.7347	−0.867308
$629$	−9.29433	−0.370589
$630$	−13.8770	−0.552873
$631$	−11.5182	−0.458532	−0.229266	−	0.973364i	$-0.573633\pi$
$631$	−11.5182	−0.458532	−0.229266	+	0.973364i	$0.573633\pi$
$632$	0.132373	0.00526553
$633$	2.07496	0.0824723
$634$	−24.8688	−0.987667
$635$	−66.5076	−2.63927
$636$	−12.1997	−0.483751
$637$	32.9085	1.30388
$638$	−1.66491	−0.0659145
$639$	3.73137	0.147611
$640$	−3.23292	−0.127793
$641$	−25.8167	−1.01970	−0.509849	−	0.860264i	$-0.670299\pi$
$641$	−25.8167	−1.01970	−0.509849	+	0.860264i	$0.670299\pi$
$642$	12.8377	0.506663
$643$	−13.2625	−0.523021	−0.261511	−	0.965201i	$-0.584221\pi$
$643$	−13.2625	−0.523021	−0.261511	+	0.965201i	$0.584221\pi$
$644$	8.59684	0.338763
$645$	37.9360	1.49373
$646$	−5.43530	−0.213849
$647$	−0.908404	−0.0357130	−0.0178565	−	0.999841i	$-0.505684\pi$
$647$	−0.908404	−0.0357130	−0.0178565	+	0.999841i	$0.505684\pi$
$648$	1.00000	0.0392837
$649$	8.74700	0.343350
$650$	15.7037	0.615951
$651$	3.30464	0.129519
$652$	−9.29178	−0.363894
$653$	−18.4193	−0.720804	−0.360402	−	0.932797i	$-0.617360\pi$
$653$	−18.4193	−0.720804	−0.360402	+	0.932797i	$0.617360\pi$
$654$	7.85123	0.307007
$655$	2.88539	0.112742
$656$	−7.18702	−0.280606
$657$	0.751328	0.0293121
$658$	3.84873	0.150039
$659$	14.8161	0.577152	0.288576	−	0.957457i	$-0.406818\pi$
$659$	14.8161	0.577152	0.288576	+	0.957457i	$0.406818\pi$
$660$	−3.23292	−0.125841
$661$	−30.8685	−1.20065	−0.600323	−	0.799758i	$-0.704961\pi$
$661$	−30.8685	−1.20065	−0.600323	+	0.799758i	$0.704961\pi$
$662$	34.3670	1.33571
$663$	−4.05775	−0.157590
$664$	15.9513	0.619030
$665$	−53.5423	−2.07628
$666$	6.59775	0.255658
$667$	−3.33450	−0.129112
$668$	−12.9130	−0.499620
$669$	−4.87062	−0.188309
$670$	−21.8055	−0.842422
$671$	−1.00000	−0.0386046
$672$	4.29240	0.165583
$673$	−33.2381	−1.28124	−0.640618	−	0.767860i	$-0.721322\pi$
$673$	−33.2381	−1.28124	−0.640618	+	0.767860i	$0.721322\pi$
$674$	−19.8632	−0.765100
$675$	5.45180	0.209840
$676$	−4.70290	−0.180881
$677$	31.6218	1.21532	0.607662	−	0.794196i	$-0.292108\pi$
$677$	31.6218	1.21532	0.607662	+	0.794196i	$0.292108\pi$
$678$	−3.68244	−0.141423
$679$	56.7050	2.17614
$680$	4.55426	0.174648
$681$	22.1378	0.848324
$682$	0.769881	0.0294803
$683$	−38.2580	−1.46390	−0.731950	−	0.681358i	$-0.761390\pi$
$683$	−38.2580	−1.46390	−0.731950	+	0.681358i	$0.761390\pi$
$684$	3.85835	0.147528
$685$	19.8449	0.758234
$686$	18.9925	0.725138
$687$	−21.5095	−0.820640
$688$	−11.7343	−0.447365
$689$	−35.1409	−1.33876
$690$	−6.47491	−0.246496
$691$	8.49250	0.323070	0.161535	−	0.986867i	$-0.448356\pi$
$691$	8.49250	0.323070	0.161535	+	0.986867i	$0.448356\pi$
$692$	−23.3606	−0.888037
$693$	4.29240	0.163055
$694$	2.88427	0.109486
$695$	11.5172	0.436873
$696$	−1.66491	−0.0631084
$697$	10.1244	0.383490
$698$	−9.43788	−0.357229
$699$	−13.9601	−0.528018
$700$	23.4013	0.884486
$701$	−38.7814	−1.46475	−0.732376	−	0.680901i	$-0.761589\pi$
$701$	−38.7814	−1.46475	−0.732376	+	0.680901i	$0.761589\pi$
$702$	2.88047	0.108716
$703$	25.4564	0.960106
$704$	1.00000	0.0376889
$705$	−2.89877	−0.109174
$706$	32.1549	1.21017
$707$	53.0810	1.99632
$708$	8.74700	0.328732
$709$	45.2752	1.70034	0.850172	−	0.526505i	$-0.176498\pi$
$709$	45.2752	1.70034	0.850172	+	0.526505i	$0.176498\pi$
$710$	−12.0632	−0.452725
$711$	0.132373	0.00496439
$712$	2.50051	0.0937105
$713$	1.54192	0.0577454
$714$	−6.04675	−0.226294
$715$	−9.31234	−0.348262
$716$	−4.01612	−0.150090
$717$	4.12106	0.153904
$718$	−27.2400	−1.01659
$719$	29.6250	1.10483	0.552413	−	0.833570i	$-0.313707\pi$
$719$	29.6250	1.10483	0.552413	+	0.833570i	$0.313707\pi$
$720$	−3.23292	−0.120484
$721$	−36.2704	−1.35078
$722$	−4.11317	−0.153076
$723$	6.60585	0.245674
$724$	−16.5937	−0.616699
$725$	−9.07677	−0.337103
$726$	1.00000	0.0371135
$727$	26.9803	1.00064	0.500322	−	0.865839i	$-0.333215\pi$
$727$	26.9803	1.00064	0.500322	+	0.865839i	$0.333215\pi$
$728$	12.3641	0.458245
$729$	1.00000	0.0370370
$730$	−2.42898	−0.0899008
$731$	16.5302	0.611391
$732$	−1.00000	−0.0369611
$733$	21.5038	0.794261	0.397131	−	0.917762i	$-0.370006\pi$
$733$	21.5038	0.794261	0.397131	+	0.917762i	$0.370006\pi$
$734$	21.4924	0.793299
$735$	−36.9352	−1.36237
$736$	2.00280	0.0738244
$737$	6.74484	0.248449
$738$	−7.18702	−0.264558
$739$	0.737726	0.0271377	0.0135688	−	0.999908i	$-0.495681\pi$
$739$	0.737726	0.0271377	0.0135688	+	0.999908i	$0.495681\pi$
$740$	−21.3300	−0.784107
$741$	11.1138	0.408277
$742$	−52.3661	−1.92242
$743$	20.2496	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$743$	20.2496	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$744$	0.769881	0.0282252
$745$	18.0155	0.660036
$746$	5.71898	0.209387
$747$	15.9513	0.583627
$748$	−1.40871	−0.0515076
$749$	55.1045	2.01347
$750$	−1.46063	−0.0533345
$751$	−20.2016	−0.737167	−0.368584	−	0.929595i	$-0.620157\pi$
$751$	−20.2016	−0.737167	−0.368584	+	0.929595i	$0.620157\pi$
$752$	0.896639	0.0326971
$753$	−25.8066	−0.940445
$754$	−4.79573	−0.174650
$755$	−30.0542	−1.09378
$756$	4.29240	0.156113
$757$	11.2010	0.407108	0.203554	−	0.979064i	$-0.434751\pi$
$757$	11.2010	0.407108	0.203554	+	0.979064i	$0.434751\pi$
$758$	−6.50559	−0.236293
$759$	2.00280	0.0726972
$760$	−12.4737	−0.452470
$761$	8.72882	0.316420	0.158210	−	0.987406i	$-0.449428\pi$
$761$	8.72882	0.316420	0.158210	+	0.987406i	$0.449428\pi$
$762$	20.5720	0.745243
$763$	33.7006	1.22004
$764$	7.04645	0.254932
$765$	4.55426	0.164660
$766$	20.2446	0.731468
$767$	25.1955	0.909755
$768$	1.00000	0.0360844
$769$	6.64734	0.239709	0.119855	−	0.992791i	$-0.461757\pi$
$769$	6.64734	0.239709	0.119855	+	0.992791i	$0.461757\pi$
$770$	−13.8770	−0.500092
$771$	−21.8807	−0.788016
$772$	−4.26409	−0.153468
$773$	51.9468	1.86840	0.934199	−	0.356753i	$-0.116116\pi$
$773$	51.9468	1.86840	0.934199	+	0.356753i	$0.116116\pi$
$774$	−11.7343	−0.421779
$775$	4.19723	0.150769
$776$	13.2106	0.474231
$777$	28.3202	1.01598
$778$	−29.9629	−1.07422
$779$	−27.7300	−0.993530
$780$	−9.31234	−0.333435
$781$	3.73137	0.133519
$782$	−2.82137	−0.100892
$783$	−1.66491	−0.0594991
$784$	11.4247	0.408025
$785$	70.2666	2.50792
$786$	−0.892502	−0.0318345
$787$	−46.3543	−1.65235	−0.826177	−	0.563411i	$-0.809489\pi$
$787$	−46.3543	−1.65235	−0.826177	+	0.563411i	$0.809489\pi$
$788$	−3.05152	−0.108706
$789$	21.7683	0.774973
$790$	−0.427953	−0.0152259
$791$	−15.8065	−0.562015
$792$	1.00000	0.0355335
$793$	−2.88047	−0.102288
$794$	−9.15525	−0.324908
$795$	39.4408	1.39882
$796$	22.6750	0.803696
$797$	27.4104	0.970926	0.485463	−	0.874257i	$-0.338651\pi$
$797$	27.4104	0.970926	0.485463	+	0.874257i	$0.338651\pi$
$798$	16.5616	0.586273
$799$	−1.26311	−0.0446855
$800$	5.45180	0.192750
$801$	2.50051	0.0883511
$802$	37.5872	1.32725
$803$	0.751328	0.0265138
$804$	6.74484	0.237872
$805$	−27.7929	−0.979572
$806$	2.21762	0.0781122
$807$	4.86810	0.171365
$808$	12.3663	0.435044
$809$	−54.3029	−1.90919	−0.954594	−	0.297909i	$-0.903711\pi$
$809$	−54.3029	−1.90919	−0.954594	+	0.297909i	$0.903711\pi$
$810$	−3.23292	−0.113593
$811$	6.19540	0.217550	0.108775	−	0.994066i	$-0.465307\pi$
$811$	6.19540	0.217550	0.108775	+	0.994066i	$0.465307\pi$
$812$	−7.14647	−0.250792
$813$	19.8242	0.695265
$814$	6.59775	0.231251
$815$	30.0396	1.05224
$816$	−1.40871	−0.0493148
$817$	−45.2749	−1.58397
$818$	−21.3450	−0.746311
$819$	12.3641	0.432037
$820$	23.2351	0.811404
$821$	−24.7144	−0.862540	−0.431270	−	0.902223i	$-0.641934\pi$
$821$	−24.7144	−0.862540	−0.431270	+	0.902223i	$0.641934\pi$
$822$	−6.13837	−0.214100
$823$	1.01775	0.0354766	0.0177383	−	0.999843i	$-0.494353\pi$
$823$	1.01775	0.0354766	0.0177383	+	0.999843i	$0.494353\pi$
$824$	−8.44990	−0.294366
$825$	5.45180	0.189807
$826$	37.5456	1.30638
$827$	−13.5282	−0.470423	−0.235211	−	0.971944i	$-0.575578\pi$
$827$	−13.5282	−0.470423	−0.235211	+	0.971944i	$0.575578\pi$
$828$	2.00280	0.0696023
$829$	4.89375	0.169967	0.0849834	−	0.996382i	$-0.472916\pi$
$829$	4.89375	0.169967	0.0849834	+	0.996382i	$0.472916\pi$
$830$	−51.5693	−1.79000
$831$	−6.99143	−0.242530
$832$	2.88047	0.0998623
$833$	−16.0941	−0.557627
$834$	−3.56248	−0.123359
$835$	41.7468	1.44471
$836$	3.85835	0.133444
$837$	0.769881	0.0266110
$838$	−0.827299	−0.0285786
$839$	30.9029	1.06689	0.533443	−	0.845836i	$-0.320898\pi$
$839$	30.9029	1.06689	0.533443	+	0.845836i	$0.320898\pi$
$840$	−13.8770	−0.478802
$841$	−26.2281	−0.904416
$842$	−24.3906	−0.840555
$843$	−13.9571	−0.480707
$844$	2.07496	0.0714231
$845$	15.2041	0.523038
$846$	0.896639	0.0308271
$847$	4.29240	0.147489
$848$	−12.1997	−0.418940
$849$	−7.59877	−0.260789
$850$	−7.68001	−0.263422
$851$	13.2140	0.452970
$852$	3.73137	0.127835
$853$	30.6601	1.04978	0.524891	−	0.851169i	$-0.324106\pi$
$853$	30.6601	1.04978	0.524891	+	0.851169i	$0.324106\pi$
$854$	−4.29240	−0.146883
$855$	−12.4737	−0.426593
$856$	12.8377	0.438783
$857$	−23.2917	−0.795628	−0.397814	−	0.917466i	$-0.630231\pi$
$857$	−23.2917	−0.795628	−0.397814	+	0.917466i	$0.630231\pi$
$858$	2.88047	0.0983376
$859$	1.00051	0.0341369	0.0170685	−	0.999854i	$-0.494567\pi$
$859$	1.00051	0.0341369	0.0170685	+	0.999854i	$0.494567\pi$
$860$	37.9360	1.29361
$861$	−30.8495	−1.05135
$862$	−15.7849	−0.537635
$863$	31.7341	1.08024	0.540121	−	0.841587i	$-0.318378\pi$
$863$	31.7341	1.08024	0.540121	+	0.841587i	$0.318378\pi$
$864$	1.00000	0.0340207
$865$	75.5231	2.56786
$866$	−29.7369	−1.01050
$867$	−15.0155	−0.509954
$868$	3.30464	0.112167
$869$	0.132373	0.00449046
$870$	5.38254	0.182485
$871$	19.4283	0.658303
$872$	7.85123	0.265876
$873$	13.2106	0.447110
$874$	7.72751	0.261387
$875$	−6.26959	−0.211951
$876$	0.751328	0.0253850
$877$	38.1898	1.28958	0.644790	−	0.764360i	$-0.276945\pi$
$877$	38.1898	1.28958	0.644790	+	0.764360i	$0.276945\pi$
$878$	−20.5160	−0.692380
$879$	18.0763	0.609697
$880$	−3.23292	−0.108982
$881$	17.4629	0.588339	0.294169	−	0.955753i	$-0.404957\pi$
$881$	17.4629	0.588339	0.294169	+	0.955753i	$0.404957\pi$
$882$	11.4247	0.384689
$883$	−6.75763	−0.227412	−0.113706	−	0.993514i	$-0.536272\pi$
$883$	−6.75763	−0.227412	−0.113706	+	0.993514i	$0.536272\pi$
$884$	−4.05775	−0.136477
$885$	−28.2784	−0.950568
$886$	−17.3896	−0.584214
$887$	14.6558	0.492092	0.246046	−	0.969258i	$-0.420869\pi$
$887$	14.6558	0.492092	0.246046	+	0.969258i	$0.420869\pi$
$888$	6.59775	0.221406
$889$	88.3030	2.96159
$890$	−8.08395	−0.270975
$891$	1.00000	0.0335013
$892$	−4.87062	−0.163080
$893$	3.45954	0.115769
$894$	−5.57250	−0.186372
$895$	12.9838	0.434001
$896$	4.29240	0.143399
$897$	5.76902	0.192622
$898$	−4.56127	−0.152212
$899$	−1.28178	−0.0427499
$900$	5.45180	0.181727
$901$	17.1859	0.572545
$902$	−7.18702	−0.239301
$903$	−50.3681	−1.67615
$904$	−3.68244	−0.122476
$905$	53.6461	1.78326
$906$	9.29629	0.308849
$907$	−49.0950	−1.63017	−0.815086	−	0.579340i	$-0.803311\pi$
$907$	−49.0950	−1.63017	−0.815086	+	0.579340i	$0.803311\pi$
$908$	22.1378	0.734670
$909$	12.3663	0.410164
$910$	−39.9723	−1.32507
$911$	−35.7518	−1.18451	−0.592255	−	0.805751i	$-0.701762\pi$
$911$	−35.7518	−1.18451	−0.592255	+	0.805751i	$0.701762\pi$
$912$	3.85835	0.127763
$913$	15.9513	0.527910
$914$	28.9963	0.959114
$915$	3.23292	0.106877
$916$	−21.5095	−0.710695
$917$	−3.83098	−0.126510
$918$	−1.40871	−0.0464944
$919$	53.5791	1.76741	0.883705	−	0.468043i	$-0.155041\pi$
$919$	53.5791	1.76741	0.883705	+	0.468043i	$0.155041\pi$
$920$	−6.47491	−0.213472
$921$	−10.1292	−0.333768
$922$	−9.76692	−0.321656
$923$	10.7481	0.353778
$924$	4.29240	0.141210
$925$	35.9696	1.18267
$926$	16.4463	0.540460
$927$	−8.44990	−0.277531
$928$	−1.66491	−0.0546534
$929$	11.8727	0.389532	0.194766	−	0.980850i	$-0.437605\pi$
$929$	11.8727	0.389532	0.194766	+	0.980850i	$0.437605\pi$
$930$	−2.48897	−0.0816164
$931$	44.0804	1.44468
$932$	−13.9601	−0.457277
$933$	9.70940	0.317872
$934$	−16.9538	−0.554745
$935$	4.55426	0.148940
$936$	2.88047	0.0941511
$937$	9.72156	0.317589	0.158795	−	0.987312i	$-0.449239\pi$
$937$	9.72156	0.317589	0.158795	+	0.987312i	$0.449239\pi$
$938$	28.9515	0.945301
$939$	−3.60353	−0.117597
$940$	−2.89877	−0.0945473
$941$	−52.7256	−1.71881	−0.859403	−	0.511299i	$-0.829164\pi$
$941$	−52.7256	−1.71881	−0.859403	+	0.511299i	$0.829164\pi$
$942$	−21.7347	−0.708154
$943$	−14.3942	−0.468739
$944$	8.74700	0.284691
$945$	−13.8770	−0.451419
$946$	−11.7343	−0.381514
$947$	18.1553	0.589968	0.294984	−	0.955502i	$-0.404686\pi$
$947$	18.1553	0.589968	0.294984	+	0.955502i	$0.404686\pi$
$948$	0.132373	0.00429929
$949$	2.16418	0.0702521
$950$	21.0349	0.682463
$951$	−24.8688	−0.806426
$952$	−6.04675	−0.195976
$953$	7.25700	0.235077	0.117539	−	0.993068i	$-0.462500\pi$
$953$	7.25700	0.235077	0.117539	+	0.993068i	$0.462500\pi$
$954$	−12.1997	−0.394981
$955$	−22.7806	−0.737164
$956$	4.12106	0.133284
$957$	−1.66491	−0.0538190
$958$	19.0297	0.614820
$959$	−26.3483	−0.850832
$960$	−3.23292	−0.104342
$961$	−30.4073	−0.980880
$962$	19.0046	0.612733
$963$	12.8377	0.413689
$964$	6.60585	0.212760
$965$	13.7855	0.443771
$966$	8.59684	0.276599
$967$	13.9900	0.449887	0.224944	−	0.974372i	$-0.427780\pi$
$967$	13.9900	0.449887	0.224944	+	0.974372i	$0.427780\pi$
$968$	1.00000	0.0321412
$969$	−5.43530	−0.174607
$970$	−42.7087	−1.37129
$971$	−61.8624	−1.98526	−0.992630	−	0.121183i	$-0.961331\pi$
$971$	−61.8624	−1.98526	−0.992630	+	0.121183i	$0.961331\pi$
$972$	1.00000	0.0320750
$973$	−15.2916	−0.490226
$974$	−5.55083	−0.177860
$975$	15.7037	0.502922
$976$	−1.00000	−0.0320092
$977$	−29.1513	−0.932634	−0.466317	−	0.884618i	$-0.654419\pi$
$977$	−29.1513	−0.932634	−0.466317	+	0.884618i	$0.654419\pi$
$978$	−9.29178	−0.297118
$979$	2.50051	0.0799166
$980$	−36.9352	−1.17985
$981$	7.85123	0.250670
$982$	−8.75305	−0.279321
$983$	−30.2008	−0.963255	−0.481628	−	0.876376i	$-0.659954\pi$
$983$	−30.2008	−0.963255	−0.481628	+	0.876376i	$0.659954\pi$
$984$	−7.18702	−0.229114
$985$	9.86535	0.314336
$986$	2.34538	0.0746922
$987$	3.84873	0.122507
$988$	11.1138	0.353578
$989$	−23.5014	−0.747302
$990$	−3.23292	−0.102749
$991$	2.64881	0.0841423	0.0420711	−	0.999115i	$-0.486604\pi$
$991$	2.64881	0.0841423	0.0420711	+	0.999115i	$0.486604\pi$
$992$	0.769881	0.0244437
$993$	34.3670	1.09060
$994$	16.0165	0.508013
$995$	−73.3067	−2.32398
$996$	15.9513	0.505435
$997$	48.7450	1.54377	0.771886	−	0.635762i	$-0.219314\pi$
$997$	48.7450	1.54377	0.771886	+	0.635762i	$0.219314\pi$
$998$	−5.13148	−0.162434
$999$	6.59775	0.208744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bc.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bc.1.1	✓	9	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.23292 q^{5} +1.00000 q^{6} +4.29240 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.23292 q^{5} +1.00000 q^{6} +4.29240 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.23292 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.88047 q^{13} +4.29240 q^{14} -3.23292 q^{15} +1.00000 q^{16} -1.40871 q^{17} +1.00000 q^{18} +3.85835 q^{19} -3.23292 q^{20} +4.29240 q^{21} +1.00000 q^{22} +2.00280 q^{23} +1.00000 q^{24} +5.45180 q^{25} +2.88047 q^{26} +1.00000 q^{27} +4.29240 q^{28} -1.66491 q^{29} -3.23292 q^{30} +0.769881 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.40871 q^{34} -13.8770 q^{35} +1.00000 q^{36} +6.59775 q^{37} +3.85835 q^{38} +2.88047 q^{39} -3.23292 q^{40} -7.18702 q^{41} +4.29240 q^{42} -11.7343 q^{43} +1.00000 q^{44} -3.23292 q^{45} +2.00280 q^{46} +0.896639 q^{47} +1.00000 q^{48} +11.4247 q^{49} +5.45180 q^{50} -1.40871 q^{51} +2.88047 q^{52} -12.1997 q^{53} +1.00000 q^{54} -3.23292 q^{55} +4.29240 q^{56} +3.85835 q^{57} -1.66491 q^{58} +8.74700 q^{59} -3.23292 q^{60} -1.00000 q^{61} +0.769881 q^{62} +4.29240 q^{63} +1.00000 q^{64} -9.31234 q^{65} +1.00000 q^{66} +6.74484 q^{67} -1.40871 q^{68} +2.00280 q^{69} -13.8770 q^{70} +3.73137 q^{71} +1.00000 q^{72} +0.751328 q^{73} +6.59775 q^{74} +5.45180 q^{75} +3.85835 q^{76} +4.29240 q^{77} +2.88047 q^{78} +0.132373 q^{79} -3.23292 q^{80} +1.00000 q^{81} -7.18702 q^{82} +15.9513 q^{83} +4.29240 q^{84} +4.55426 q^{85} -11.7343 q^{86} -1.66491 q^{87} +1.00000 q^{88} +2.50051 q^{89} -3.23292 q^{90} +12.3641 q^{91} +2.00280 q^{92} +0.769881 q^{93} +0.896639 q^{94} -12.4737 q^{95} +1.00000 q^{96} +13.2106 q^{97} +11.4247 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

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