LMFDB - Embedded newform 4730.2.a.bb.1.8

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 $ x^11 - x^10 - 22x^9 + 21x^8 + 165x^7 - 130x^6 - 535x^5 + 323x^4 + 710x^3 - 343x^2 - 261*x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.56687$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.56687 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56687 q^{6} -4.55535 q^{7} -1.00000 q^{8} -0.544925 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.56687 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56687 q^{6} -4.55535 q^{7} -1.00000 q^{8} -0.544925 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.56687 q^{12} -4.63459 q^{13} +4.55535 q^{14} -1.56687 q^{15} +1.00000 q^{16} +2.48393 q^{17} +0.544925 q^{18} +0.136634 q^{19} -1.00000 q^{20} -7.13763 q^{21} +1.00000 q^{22} -6.63459 q^{23} -1.56687 q^{24} +1.00000 q^{25} +4.63459 q^{26} -5.55443 q^{27} -4.55535 q^{28} +7.05863 q^{29} +1.56687 q^{30} +0.167486 q^{31} -1.00000 q^{32} -1.56687 q^{33} -2.48393 q^{34} +4.55535 q^{35} -0.544925 q^{36} -8.45462 q^{37} -0.136634 q^{38} -7.26179 q^{39} +1.00000 q^{40} +12.1033 q^{41} +7.13763 q^{42} +1.00000 q^{43} -1.00000 q^{44} +0.544925 q^{45} +6.63459 q^{46} +2.16006 q^{47} +1.56687 q^{48} +13.7512 q^{49} -1.00000 q^{50} +3.89199 q^{51} -4.63459 q^{52} -11.2172 q^{53} +5.55443 q^{54} +1.00000 q^{55} +4.55535 q^{56} +0.214088 q^{57} -7.05863 q^{58} -0.387846 q^{59} -1.56687 q^{60} -6.33683 q^{61} -0.167486 q^{62} +2.48232 q^{63} +1.00000 q^{64} +4.63459 q^{65} +1.56687 q^{66} +14.1600 q^{67} +2.48393 q^{68} -10.3955 q^{69} -4.55535 q^{70} -3.26125 q^{71} +0.544925 q^{72} -7.40941 q^{73} +8.45462 q^{74} +1.56687 q^{75} +0.136634 q^{76} +4.55535 q^{77} +7.26179 q^{78} -2.22847 q^{79} -1.00000 q^{80} -7.06828 q^{81} -12.1033 q^{82} +12.1489 q^{83} -7.13763 q^{84} -2.48393 q^{85} -1.00000 q^{86} +11.0599 q^{87} +1.00000 q^{88} -2.62277 q^{89} -0.544925 q^{90} +21.1122 q^{91} -6.63459 q^{92} +0.262428 q^{93} -2.16006 q^{94} -0.136634 q^{95} -1.56687 q^{96} -6.95468 q^{97} -13.7512 q^{98} +0.544925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * 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
$3$	1.56687	0.904632	0.452316	−	0.891858i	$-0.350598\pi$
$3$	1.56687	0.904632	0.452316	+	0.891858i	$0.350598\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.56687	−0.639671
$7$	−4.55535	−1.72176	−0.860880	−	0.508808i	$-0.830086\pi$
$7$	−4.55535	−1.72176	−0.860880	+	0.508808i	$0.830086\pi$
$8$	−1.00000	−0.353553
$9$	−0.544925	−0.181642
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.56687	0.452316
$13$	−4.63459	−1.28540	−0.642702	−	0.766117i	$-0.722186\pi$
$13$	−4.63459	−1.28540	−0.642702	+	0.766117i	$0.722186\pi$
$14$	4.55535	1.21747
$15$	−1.56687	−0.404564
$16$	1.00000	0.250000
$17$	2.48393	0.602441	0.301221	−	0.953555i	$-0.402606\pi$
$17$	2.48393	0.602441	0.301221	+	0.953555i	$0.402606\pi$
$18$	0.544925	0.128440
$19$	0.136634	0.0313460	0.0156730	−	0.999877i	$-0.495011\pi$
$19$	0.136634	0.0313460	0.0156730	+	0.999877i	$0.495011\pi$
$20$	−1.00000	−0.223607
$21$	−7.13763	−1.55756
$22$	1.00000	0.213201
$23$	−6.63459	−1.38341	−0.691703	−	0.722182i	$-0.743139\pi$
$23$	−6.63459	−1.38341	−0.691703	+	0.722182i	$0.743139\pi$
$24$	−1.56687	−0.319836
$25$	1.00000	0.200000
$26$	4.63459	0.908917
$27$	−5.55443	−1.06895
$28$	−4.55535	−0.860880
$29$	7.05863	1.31076	0.655378	−	0.755301i	$-0.272509\pi$
$29$	7.05863	1.31076	0.655378	+	0.755301i	$0.272509\pi$
$30$	1.56687	0.286070
$31$	0.167486	0.0300814	0.0150407	−	0.999887i	$-0.495212\pi$
$31$	0.167486	0.0300814	0.0150407	+	0.999887i	$0.495212\pi$
$32$	−1.00000	−0.176777
$33$	−1.56687	−0.272757
$34$	−2.48393	−0.425990
$35$	4.55535	0.769995
$36$	−0.544925	−0.0908208
$37$	−8.45462	−1.38993	−0.694965	−	0.719043i	$-0.744580\pi$
$37$	−8.45462	−1.38993	−0.694965	+	0.719043i	$0.744580\pi$
$38$	−0.136634	−0.0221650
$39$	−7.26179	−1.16282
$40$	1.00000	0.158114
$41$	12.1033	1.89022	0.945110	−	0.326753i	$-0.105954\pi$
$41$	12.1033	1.89022	0.945110	+	0.326753i	$0.105954\pi$
$42$	7.13763	1.10136
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	0.544925	0.0812326
$46$	6.63459	0.978216
$47$	2.16006	0.315078	0.157539	−	0.987513i	$-0.449644\pi$
$47$	2.16006	0.315078	0.157539	+	0.987513i	$0.449644\pi$
$48$	1.56687	0.226158
$49$	13.7512	1.96446
$50$	−1.00000	−0.141421
$51$	3.89199	0.544987
$52$	−4.63459	−0.642702
$53$	−11.2172	−1.54080	−0.770399	−	0.637562i	$-0.779943\pi$
$53$	−11.2172	−1.54080	−0.770399	+	0.637562i	$0.779943\pi$
$54$	5.55443	0.755862
$55$	1.00000	0.134840
$56$	4.55535	0.608734
$57$	0.214088	0.0283566
$58$	−7.05863	−0.926844
$59$	−0.387846	−0.0504933	−0.0252466	−	0.999681i	$-0.508037\pi$
$59$	−0.387846	−0.0504933	−0.0252466	+	0.999681i	$0.508037\pi$
$60$	−1.56687	−0.202282
$61$	−6.33683	−0.811348	−0.405674	−	0.914018i	$-0.632963\pi$
$61$	−6.33683	−0.811348	−0.405674	+	0.914018i	$0.632963\pi$
$62$	−0.167486	−0.0212707
$63$	2.48232	0.312743
$64$	1.00000	0.125000
$65$	4.63459	0.574850
$66$	1.56687	0.192868
$67$	14.1600	1.72992	0.864961	−	0.501838i	$-0.167343\pi$
$67$	14.1600	1.72992	0.864961	+	0.501838i	$0.167343\pi$
$68$	2.48393	0.301221
$69$	−10.3955	−1.25147
$70$	−4.55535	−0.544468
$71$	−3.26125	−0.387039	−0.193520	−	0.981096i	$-0.561990\pi$
$71$	−3.26125	−0.387039	−0.193520	+	0.981096i	$0.561990\pi$
$72$	0.544925	0.0642200
$73$	−7.40941	−0.867206	−0.433603	−	0.901104i	$-0.642758\pi$
$73$	−7.40941	−0.867206	−0.433603	+	0.901104i	$0.642758\pi$
$74$	8.45462	0.982830
$75$	1.56687	0.180926
$76$	0.136634	0.0156730
$77$	4.55535	0.519130
$78$	7.26179	0.822235
$79$	−2.22847	−0.250722	−0.125361	−	0.992111i	$-0.540009\pi$
$79$	−2.22847	−0.250722	−0.125361	+	0.992111i	$0.540009\pi$
$80$	−1.00000	−0.111803
$81$	−7.06828	−0.785365
$82$	−12.1033	−1.33659
$83$	12.1489	1.33351	0.666757	−	0.745275i	$-0.267682\pi$
$83$	12.1489	1.33351	0.666757	+	0.745275i	$0.267682\pi$
$84$	−7.13763	−0.778780
$85$	−2.48393	−0.269420
$86$	−1.00000	−0.107833
$87$	11.0599	1.18575
$88$	1.00000	0.106600
$89$	−2.62277	−0.278013	−0.139006	−	0.990291i	$-0.544391\pi$
$89$	−2.62277	−0.278013	−0.139006	+	0.990291i	$0.544391\pi$
$90$	−0.544925	−0.0574401
$91$	21.1122	2.21316
$92$	−6.63459	−0.691703
$93$	0.262428	0.0272126
$94$	−2.16006	−0.222794
$95$	−0.136634	−0.0140184
$96$	−1.56687	−0.159918
$97$	−6.95468	−0.706141	−0.353070	−	0.935597i	$-0.614862\pi$
$97$	−6.95468	−0.706141	−0.353070	+	0.935597i	$0.614862\pi$
$98$	−13.7512	−1.38908
$99$	0.544925	0.0547670
$100$	1.00000	0.100000
$101$	−1.34577	−0.133909	−0.0669547	−	0.997756i	$-0.521328\pi$
$101$	−1.34577	−0.133909	−0.0669547	+	0.997756i	$0.521328\pi$
$102$	−3.89199	−0.385364
$103$	3.13126	0.308532	0.154266	−	0.988029i	$-0.450699\pi$
$103$	3.13126	0.308532	0.154266	+	0.988029i	$0.450699\pi$
$104$	4.63459	0.454459
$105$	7.13763	0.696562
$106$	11.2172	1.08951
$107$	3.50573	0.338912	0.169456	−	0.985538i	$-0.445799\pi$
$107$	3.50573	0.338912	0.169456	+	0.985538i	$0.445799\pi$
$108$	−5.55443	−0.534475
$109$	1.90563	0.182526	0.0912630	−	0.995827i	$-0.470910\pi$
$109$	1.90563	0.182526	0.0912630	+	0.995827i	$0.470910\pi$
$110$	−1.00000	−0.0953463
$111$	−13.2473	−1.25738
$112$	−4.55535	−0.430440
$113$	4.10386	0.386059	0.193030	−	0.981193i	$-0.438169\pi$
$113$	4.10386	0.386059	0.193030	+	0.981193i	$0.438169\pi$
$114$	−0.214088	−0.0200512
$115$	6.63459	0.618678
$116$	7.05863	0.655378
$117$	2.52550	0.233483
$118$	0.387846	0.0357041
$119$	−11.3152	−1.03726
$120$	1.56687	0.143035
$121$	1.00000	0.0909091
$122$	6.33683	0.573710
$123$	18.9643	1.70995
$124$	0.167486	0.0150407
$125$	−1.00000	−0.0894427
$126$	−2.48232	−0.221143
$127$	22.4116	1.98871	0.994354	−	0.106114i	$-0.0338409\pi$
$127$	22.4116	1.98871	0.994354	+	0.106114i	$0.0338409\pi$
$128$	−1.00000	−0.0883883
$129$	1.56687	0.137955
$130$	−4.63459	−0.406480
$131$	8.01674	0.700426	0.350213	−	0.936670i	$-0.386109\pi$
$131$	8.01674	0.700426	0.350213	+	0.936670i	$0.386109\pi$
$132$	−1.56687	−0.136378
$133$	−0.622417	−0.0539704
$134$	−14.1600	−1.22324
$135$	5.55443	0.478049
$136$	−2.48393	−0.212995
$137$	3.04840	0.260442	0.130221	−	0.991485i	$-0.458431\pi$
$137$	3.04840	0.260442	0.130221	+	0.991485i	$0.458431\pi$
$138$	10.3955	0.884926
$139$	−9.08154	−0.770286	−0.385143	−	0.922857i	$-0.625848\pi$
$139$	−9.08154	−0.770286	−0.385143	+	0.922857i	$0.625848\pi$
$140$	4.55535	0.384997
$141$	3.38454	0.285029
$142$	3.26125	0.273678
$143$	4.63459	0.387564
$144$	−0.544925	−0.0454104
$145$	−7.05863	−0.586188
$146$	7.40941	0.613207
$147$	21.5463	1.77711
$148$	−8.45462	−0.694965
$149$	13.2198	1.08301	0.541504	−	0.840698i	$-0.317855\pi$
$149$	13.2198	1.08301	0.541504	+	0.840698i	$0.317855\pi$
$150$	−1.56687	−0.127934
$151$	22.2579	1.81132	0.905660	−	0.424004i	$-0.139376\pi$
$151$	22.2579	1.81132	0.905660	+	0.424004i	$0.139376\pi$
$152$	−0.136634	−0.0110825
$153$	−1.35355	−0.109428
$154$	−4.55535	−0.367081
$155$	−0.167486	−0.0134528
$156$	−7.26179	−0.581408
$157$	−9.63117	−0.768651	−0.384326	−	0.923198i	$-0.625566\pi$
$157$	−9.63117	−0.768651	−0.384326	+	0.923198i	$0.625566\pi$
$158$	2.22847	0.177287
$159$	−17.5758	−1.39386
$160$	1.00000	0.0790569
$161$	30.2229	2.38190
$162$	7.06828	0.555337
$163$	4.86103	0.380745	0.190373	−	0.981712i	$-0.439030\pi$
$163$	4.86103	0.380745	0.190373	+	0.981712i	$0.439030\pi$
$164$	12.1033	0.945110
$165$	1.56687	0.121981
$166$	−12.1489	−0.942937
$167$	−9.15528	−0.708457	−0.354228	−	0.935159i	$-0.615256\pi$
$167$	−9.15528	−0.708457	−0.354228	+	0.935159i	$0.615256\pi$
$168$	7.13763	0.550680
$169$	8.47939	0.652261
$170$	2.48393	0.190509
$171$	−0.0744554	−0.00569374
$172$	1.00000	0.0762493
$173$	9.46132	0.719331	0.359665	−	0.933081i	$-0.382891\pi$
$173$	9.46132	0.719331	0.359665	+	0.933081i	$0.382891\pi$
$174$	−11.0599	−0.838452
$175$	−4.55535	−0.344352
$176$	−1.00000	−0.0753778
$177$	−0.607704	−0.0456778
$178$	2.62277	0.196585
$179$	22.2884	1.66591	0.832955	−	0.553341i	$-0.186647\pi$
$179$	22.2884	1.66591	0.832955	+	0.553341i	$0.186647\pi$
$180$	0.544925	0.0406163
$181$	11.9906	0.891256	0.445628	−	0.895218i	$-0.352980\pi$
$181$	11.9906	0.891256	0.445628	+	0.895218i	$0.352980\pi$
$182$	−21.1122	−1.56494
$183$	−9.92898	−0.733971
$184$	6.63459	0.489108
$185$	8.45462	0.621596
$186$	−0.262428	−0.0192422
$187$	−2.48393	−0.181643
$188$	2.16006	0.157539
$189$	25.3024	1.84048
$190$	0.136634	0.00991249
$191$	−4.33732	−0.313837	−0.156919	−	0.987612i	$-0.550156\pi$
$191$	−4.33732	−0.313837	−0.156919	+	0.987612i	$0.550156\pi$
$192$	1.56687	0.113079
$193$	20.9353	1.50696	0.753479	−	0.657472i	$-0.228374\pi$
$193$	20.9353	1.50696	0.753479	+	0.657472i	$0.228374\pi$
$194$	6.95468	0.499317
$195$	7.26179	0.520027
$196$	13.7512	0.982230
$197$	22.1154	1.57566	0.787830	−	0.615893i	$-0.211205\pi$
$197$	22.1154	1.57566	0.787830	+	0.615893i	$0.211205\pi$
$198$	−0.544925	−0.0387261
$199$	−25.6167	−1.81592	−0.907961	−	0.419054i	$-0.862362\pi$
$199$	−25.6167	−1.81592	−0.907961	+	0.419054i	$0.862362\pi$
$200$	−1.00000	−0.0707107
$201$	22.1869	1.56494
$202$	1.34577	0.0946883
$203$	−32.1545	−2.25681
$204$	3.89199	0.272494
$205$	−12.1033	−0.845332
$206$	−3.13126	−0.218165
$207$	3.61535	0.251284
$208$	−4.63459	−0.321351
$209$	−0.136634	−0.00945119
$210$	−7.13763	−0.492543
$211$	−7.46025	−0.513585	−0.256793	−	0.966467i	$-0.582666\pi$
$211$	−7.46025	−0.513585	−0.256793	+	0.966467i	$0.582666\pi$
$212$	−11.2172	−0.770399
$213$	−5.10995	−0.350128
$214$	−3.50573	−0.239647
$215$	−1.00000	−0.0681994
$216$	5.55443	0.377931
$217$	−0.762957	−0.0517929
$218$	−1.90563	−0.129065
$219$	−11.6096	−0.784502
$220$	1.00000	0.0674200
$221$	−11.5120	−0.774380
$222$	13.2473	0.889099
$223$	26.7032	1.78818	0.894091	−	0.447886i	$-0.147823\pi$
$223$	26.7032	1.78818	0.894091	+	0.447886i	$0.147823\pi$
$224$	4.55535	0.304367
$225$	−0.544925	−0.0363283
$226$	−4.10386	−0.272985
$227$	−22.5070	−1.49384	−0.746921	−	0.664913i	$-0.768469\pi$
$227$	−22.5070	−1.49384	−0.746921	+	0.664913i	$0.768469\pi$
$228$	0.214088	0.0141783
$229$	−9.92266	−0.655708	−0.327854	−	0.944728i	$-0.606325\pi$
$229$	−9.92266	−0.655708	−0.327854	+	0.944728i	$0.606325\pi$
$230$	−6.63459	−0.437472
$231$	7.13763	0.469622
$232$	−7.05863	−0.463422
$233$	−16.4822	−1.07979	−0.539893	−	0.841733i	$-0.681535\pi$
$233$	−16.4822	−1.07979	−0.539893	+	0.841733i	$0.681535\pi$
$234$	−2.52550	−0.165097
$235$	−2.16006	−0.140907
$236$	−0.387846	−0.0252466
$237$	−3.49171	−0.226811
$238$	11.3152	0.733453
$239$	−14.2579	−0.922264	−0.461132	−	0.887331i	$-0.652557\pi$
$239$	−14.2579	−0.922264	−0.461132	+	0.887331i	$0.652557\pi$
$240$	−1.56687	−0.101141
$241$	18.4476	1.18831	0.594157	−	0.804349i	$-0.297486\pi$
$241$	18.4476	1.18831	0.594157	+	0.804349i	$0.297486\pi$
$242$	−1.00000	−0.0642824
$243$	5.58822	0.358484
$244$	−6.33683	−0.405674
$245$	−13.7512	−0.878533
$246$	−18.9643	−1.20912
$247$	−0.633243	−0.0402923
$248$	−0.167486	−0.0106354
$249$	19.0357	1.20634
$250$	1.00000	0.0632456
$251$	25.1833	1.58956	0.794779	−	0.606899i	$-0.207587\pi$
$251$	25.1833	1.58956	0.794779	+	0.606899i	$0.207587\pi$
$252$	2.48232	0.156372
$253$	6.63459	0.417113
$254$	−22.4116	−1.40623
$255$	−3.89199	−0.243726
$256$	1.00000	0.0625000
$257$	−13.8923	−0.866579	−0.433289	−	0.901255i	$-0.642647\pi$
$257$	−13.8923	−0.866579	−0.433289	+	0.901255i	$0.642647\pi$
$258$	−1.56687	−0.0975489
$259$	38.5138	2.39313
$260$	4.63459	0.287425
$261$	−3.84642	−0.238088
$262$	−8.01674	−0.495276
$263$	−14.0820	−0.868331	−0.434166	−	0.900833i	$-0.642957\pi$
$263$	−14.0820	−0.868331	−0.434166	+	0.900833i	$0.642957\pi$
$264$	1.56687	0.0964341
$265$	11.2172	0.689066
$266$	0.622417	0.0381628
$267$	−4.10953	−0.251499
$268$	14.1600	0.864961
$269$	−28.8850	−1.76115	−0.880575	−	0.473906i	$-0.842844\pi$
$269$	−28.8850	−1.76115	−0.880575	+	0.473906i	$0.842844\pi$
$270$	−5.55443	−0.338032
$271$	24.9881	1.51792	0.758958	−	0.651140i	$-0.225709\pi$
$271$	24.9881	1.51792	0.758958	+	0.651140i	$0.225709\pi$
$272$	2.48393	0.150610
$273$	33.0800	2.00209
$274$	−3.04840	−0.184161
$275$	−1.00000	−0.0603023
$276$	−10.3955	−0.625737
$277$	−1.83307	−0.110138	−0.0550692	−	0.998483i	$-0.517538\pi$
$277$	−1.83307	−0.110138	−0.0550692	+	0.998483i	$0.517538\pi$
$278$	9.08154	0.544674
$279$	−0.0912672	−0.00546403
$280$	−4.55535	−0.272234
$281$	−15.6372	−0.932839	−0.466420	−	0.884564i	$-0.654456\pi$
$281$	−15.6372	−0.932839	−0.466420	+	0.884564i	$0.654456\pi$
$282$	−3.38454	−0.201546
$283$	4.31430	0.256458	0.128229	−	0.991745i	$-0.459071\pi$
$283$	4.31430	0.256458	0.128229	+	0.991745i	$0.459071\pi$
$284$	−3.26125	−0.193520
$285$	−0.214088	−0.0126815
$286$	−4.63459	−0.274049
$287$	−55.1348	−3.25451
$288$	0.544925	0.0321100
$289$	−10.8301	−0.637065
$290$	7.05863	0.414497
$291$	−10.8971	−0.638797
$292$	−7.40941	−0.433603
$293$	9.31692	0.544300	0.272150	−	0.962255i	$-0.412265\pi$
$293$	9.31692	0.544300	0.272150	+	0.962255i	$0.412265\pi$
$294$	−21.5463	−1.25661
$295$	0.387846	0.0225813
$296$	8.45462	0.491415
$297$	5.55443	0.322301
$298$	−13.2198	−0.765802
$299$	30.7486	1.77824
$300$	1.56687	0.0904632
$301$	−4.55535	−0.262566
$302$	−22.2579	−1.28080
$303$	−2.10865	−0.121139
$304$	0.136634	0.00783651
$305$	6.33683	0.362846
$306$	1.35355	0.0773775
$307$	4.45026	0.253990	0.126995	−	0.991903i	$-0.459467\pi$
$307$	4.45026	0.253990	0.126995	+	0.991903i	$0.459467\pi$
$308$	4.55535	0.259565
$309$	4.90627	0.279108
$310$	0.167486	0.00951256
$311$	8.16298	0.462880	0.231440	−	0.972849i	$-0.425656\pi$
$311$	8.16298	0.462880	0.231440	+	0.972849i	$0.425656\pi$
$312$	7.26179	0.411118
$313$	−1.74945	−0.0988847	−0.0494423	−	0.998777i	$-0.515744\pi$
$313$	−1.74945	−0.0988847	−0.0494423	+	0.998777i	$0.515744\pi$
$314$	9.63117	0.543519
$315$	−2.48232	−0.139863
$316$	−2.22847	−0.125361
$317$	8.44435	0.474282	0.237141	−	0.971475i	$-0.423790\pi$
$317$	8.44435	0.474282	0.237141	+	0.971475i	$0.423790\pi$
$318$	17.5758	0.985605
$319$	−7.05863	−0.395208
$320$	−1.00000	−0.0559017
$321$	5.49302	0.306590
$322$	−30.2229	−1.68425
$323$	0.339390	0.0188841
$324$	−7.06828	−0.392682
$325$	−4.63459	−0.257081
$326$	−4.86103	−0.269228
$327$	2.98587	0.165119
$328$	−12.1033	−0.668294
$329$	−9.83985	−0.542488
$330$	−1.56687	−0.0862532
$331$	24.3392	1.33780	0.668901	−	0.743352i	$-0.266765\pi$
$331$	24.3392	1.33780	0.668901	+	0.743352i	$0.266765\pi$
$332$	12.1489	0.666757
$333$	4.60713	0.252469
$334$	9.15528	0.500954
$335$	−14.1600	−0.773645
$336$	−7.13763	−0.389390
$337$	−16.1419	−0.879308	−0.439654	−	0.898167i	$-0.644899\pi$
$337$	−16.1419	−0.879308	−0.439654	+	0.898167i	$0.644899\pi$
$338$	−8.47939	−0.461218
$339$	6.43021	0.349241
$340$	−2.48393	−0.134710
$341$	−0.167486	−0.00906987
$342$	0.0744554	0.00402608
$343$	−30.7541	−1.66057
$344$	−1.00000	−0.0539164
$345$	10.3955	0.559676
$346$	−9.46132	−0.508644
$347$	−4.48209	−0.240611	−0.120306	−	0.992737i	$-0.538387\pi$
$347$	−4.48209	−0.240611	−0.120306	+	0.992737i	$0.538387\pi$
$348$	11.0599	0.592875
$349$	−4.14263	−0.221750	−0.110875	−	0.993834i	$-0.535365\pi$
$349$	−4.14263	−0.221750	−0.110875	+	0.993834i	$0.535365\pi$
$350$	4.55535	0.243494
$351$	25.7425	1.37403
$352$	1.00000	0.0533002
$353$	8.99637	0.478829	0.239414	−	0.970917i	$-0.423045\pi$
$353$	8.99637	0.478829	0.239414	+	0.970917i	$0.423045\pi$
$354$	0.607704	0.0322991
$355$	3.26125	0.173089
$356$	−2.62277	−0.139006
$357$	−17.7294	−0.938338
$358$	−22.2884	−1.17798
$359$	−16.4567	−0.868550	−0.434275	−	0.900780i	$-0.642995\pi$
$359$	−16.4567	−0.868550	−0.434275	+	0.900780i	$0.642995\pi$
$360$	−0.544925	−0.0287200
$361$	−18.9813	−0.999017
$362$	−11.9906	−0.630213
$363$	1.56687	0.0822392
$364$	21.1122	1.10658
$365$	7.40941	0.387826
$366$	9.92898	0.518996
$367$	−28.2260	−1.47338	−0.736692	−	0.676229i	$-0.763613\pi$
$367$	−28.2260	−1.47338	−0.736692	+	0.676229i	$0.763613\pi$
$368$	−6.63459	−0.345852
$369$	−6.59539	−0.343342
$370$	−8.45462	−0.439535
$371$	51.0982	2.65289
$372$	0.262428	0.0136063
$373$	21.7113	1.12417	0.562083	−	0.827081i	$-0.310000\pi$
$373$	21.7113	1.12417	0.562083	+	0.827081i	$0.310000\pi$
$374$	2.48393	0.128441
$375$	−1.56687	−0.0809127
$376$	−2.16006	−0.111397
$377$	−32.7138	−1.68485
$378$	−25.3024	−1.30141
$379$	−18.0417	−0.926738	−0.463369	−	0.886165i	$-0.653360\pi$
$379$	−18.0417	−0.926738	−0.463369	+	0.886165i	$0.653360\pi$
$380$	−0.136634	−0.00700919
$381$	35.1160	1.79905
$382$	4.33732	0.221916
$383$	12.4567	0.636509	0.318255	−	0.948005i	$-0.396903\pi$
$383$	12.4567	0.636509	0.318255	+	0.948005i	$0.396903\pi$
$384$	−1.56687	−0.0799589
$385$	−4.55535	−0.232162
$386$	−20.9353	−1.06558
$387$	−0.544925	−0.0277001
$388$	−6.95468	−0.353070
$389$	−33.0120	−1.67378	−0.836888	−	0.547375i	$-0.815627\pi$
$389$	−33.0120	−1.67378	−0.836888	+	0.547375i	$0.815627\pi$
$390$	−7.26179	−0.367715
$391$	−16.4798	−0.833421
$392$	−13.7512	−0.694541
$393$	12.5612	0.633627
$394$	−22.1154	−1.11416
$395$	2.22847	0.112126
$396$	0.544925	0.0273835
$397$	−2.61096	−0.131040	−0.0655202	−	0.997851i	$-0.520871\pi$
$397$	−2.61096	−0.131040	−0.0655202	+	0.997851i	$0.520871\pi$
$398$	25.6167	1.28405
$399$	−0.975245	−0.0488233
$400$	1.00000	0.0500000
$401$	−38.1218	−1.90371	−0.951857	−	0.306543i	$-0.900828\pi$
$401$	−38.1218	−1.90371	−0.951857	+	0.306543i	$0.900828\pi$
$402$	−22.1869	−1.10658
$403$	−0.776228	−0.0386667
$404$	−1.34577	−0.0669547
$405$	7.06828	0.351226
$406$	32.1545	1.59580
$407$	8.45462	0.419080
$408$	−3.89199	−0.192682
$409$	0.729537	0.0360733	0.0180366	−	0.999837i	$-0.494258\pi$
$409$	0.729537	0.0360733	0.0180366	+	0.999837i	$0.494258\pi$
$410$	12.1033	0.597740
$411$	4.77644	0.235604
$412$	3.13126	0.154266
$413$	1.76678	0.0869373
$414$	−3.61535	−0.177685
$415$	−12.1489	−0.596366
$416$	4.63459	0.227229
$417$	−14.2296	−0.696825
$418$	0.136634	0.00668300
$419$	−21.2265	−1.03698	−0.518492	−	0.855082i	$-0.673506\pi$
$419$	−21.2265	−1.03698	−0.518492	+	0.855082i	$0.673506\pi$
$420$	7.13763	0.348281
$421$	25.6241	1.24884	0.624422	−	0.781087i	$-0.285335\pi$
$421$	25.6241	1.24884	0.624422	+	0.781087i	$0.285335\pi$
$422$	7.46025	0.363159
$423$	−1.17707	−0.0572312
$424$	11.2172	0.544755
$425$	2.48393	0.120488
$426$	5.10995	0.247578
$427$	28.8665	1.39695
$428$	3.50573	0.169456
$429$	7.26179	0.350602
$430$	1.00000	0.0482243
$431$	22.3855	1.07827	0.539136	−	0.842219i	$-0.318751\pi$
$431$	22.3855	1.07827	0.539136	+	0.842219i	$0.318751\pi$
$432$	−5.55443	−0.267238
$433$	19.7044	0.946931	0.473466	−	0.880812i	$-0.343003\pi$
$433$	19.7044	0.946931	0.473466	+	0.880812i	$0.343003\pi$
$434$	0.762957	0.0366231
$435$	−11.0599	−0.530284
$436$	1.90563	0.0912630
$437$	−0.906512	−0.0433643
$438$	11.6096	0.554727
$439$	−0.128117	−0.00611469	−0.00305734	−	0.999995i	$-0.500973\pi$
$439$	−0.128117	−0.00611469	−0.00305734	+	0.999995i	$0.500973\pi$
$440$	−1.00000	−0.0476731
$441$	−7.49337	−0.356827
$442$	11.5120	0.547569
$443$	−39.6401	−1.88336	−0.941678	−	0.336515i	$-0.890752\pi$
$443$	−39.6401	−1.88336	−0.941678	+	0.336515i	$0.890752\pi$
$444$	−13.2473	−0.628688
$445$	2.62277	0.124331
$446$	−26.7032	−1.26444
$447$	20.7137	0.979723
$448$	−4.55535	−0.215220
$449$	35.6224	1.68113	0.840563	−	0.541714i	$-0.182224\pi$
$449$	35.6224	1.68113	0.840563	+	0.541714i	$0.182224\pi$
$450$	0.544925	0.0256880
$451$	−12.1033	−0.569923
$452$	4.10386	0.193030
$453$	34.8752	1.63858
$454$	22.5070	1.05631
$455$	−21.1122	−0.989753
$456$	−0.214088	−0.0100256
$457$	−39.3357	−1.84004	−0.920022	−	0.391866i	$-0.871830\pi$
$457$	−39.3357	−1.84004	−0.920022	+	0.391866i	$0.871830\pi$
$458$	9.92266	0.463655
$459$	−13.7968	−0.643980
$460$	6.63459	0.309339
$461$	−4.70061	−0.218929	−0.109465	−	0.993991i	$-0.534914\pi$
$461$	−4.70061	−0.218929	−0.109465	+	0.993991i	$0.534914\pi$
$462$	−7.13763	−0.332073
$463$	−5.58181	−0.259409	−0.129704	−	0.991553i	$-0.541403\pi$
$463$	−5.58181	−0.259409	−0.129704	+	0.991553i	$0.541403\pi$
$464$	7.05863	0.327689
$465$	−0.262428	−0.0121698
$466$	16.4822	0.763525
$467$	12.3359	0.570838	0.285419	−	0.958403i	$-0.407867\pi$
$467$	12.3359	0.570838	0.285419	+	0.958403i	$0.407867\pi$
$468$	2.52550	0.116741
$469$	−64.5039	−2.97851
$470$	2.16006	0.0996363
$471$	−15.0908	−0.695346
$472$	0.387846	0.0178521
$473$	−1.00000	−0.0459800
$474$	3.49171	0.160380
$475$	0.136634	0.00626921
$476$	−11.3152	−0.518630
$477$	6.11252	0.279873
$478$	14.2579	0.652139
$479$	15.1615	0.692745	0.346373	−	0.938097i	$-0.387413\pi$
$479$	15.1615	0.692745	0.346373	+	0.938097i	$0.387413\pi$
$480$	1.56687	0.0715174
$481$	39.1837	1.78662
$482$	−18.4476	−0.840265
$483$	47.3552	2.15474
$484$	1.00000	0.0454545
$485$	6.95468	0.315796
$486$	−5.58822	−0.253487
$487$	20.0421	0.908195	0.454097	−	0.890952i	$-0.349962\pi$
$487$	20.0421	0.908195	0.454097	+	0.890952i	$0.349962\pi$
$488$	6.33683	0.286855
$489$	7.61660	0.344434
$490$	13.7512	0.621216
$491$	−11.6057	−0.523758	−0.261879	−	0.965101i	$-0.584342\pi$
$491$	−11.6057	−0.523758	−0.261879	+	0.965101i	$0.584342\pi$
$492$	18.9643	0.854976
$493$	17.5331	0.789653
$494$	0.633243	0.0284910
$495$	−0.544925	−0.0244925
$496$	0.167486	0.00752034
$497$	14.8561	0.666389
$498$	−19.0357	−0.853011
$499$	4.05151	0.181371	0.0906853	−	0.995880i	$-0.471094\pi$
$499$	4.05151	0.181371	0.0906853	+	0.995880i	$0.471094\pi$
$500$	−1.00000	−0.0447214
$501$	−14.3451	−0.640892
$502$	−25.1833	−1.12399
$503$	36.5398	1.62923	0.814615	−	0.580002i	$-0.196948\pi$
$503$	36.5398	1.62923	0.814615	+	0.580002i	$0.196948\pi$
$504$	−2.48232	−0.110571
$505$	1.34577	0.0598861
$506$	−6.63459	−0.294943
$507$	13.2861	0.590056
$508$	22.4116	0.994354
$509$	16.4353	0.728483	0.364241	−	0.931305i	$-0.381328\pi$
$509$	16.4353	0.728483	0.364241	+	0.931305i	$0.381328\pi$
$510$	3.89199	0.172340
$511$	33.7525	1.49312
$512$	−1.00000	−0.0441942
$513$	−0.758925	−0.0335074
$514$	13.8923	0.612764
$515$	−3.13126	−0.137980
$516$	1.56687	0.0689775
$517$	−2.16006	−0.0949995
$518$	−38.5138	−1.69220
$519$	14.8246	0.650729
$520$	−4.63459	−0.203240
$521$	−5.68635	−0.249123	−0.124562	−	0.992212i	$-0.539752\pi$
$521$	−5.68635	−0.249123	−0.124562	+	0.992212i	$0.539752\pi$
$522$	3.84642	0.168353
$523$	7.31355	0.319799	0.159900	−	0.987133i	$-0.448883\pi$
$523$	7.31355	0.319799	0.159900	+	0.987133i	$0.448883\pi$
$524$	8.01674	0.350213
$525$	−7.13763	−0.311512
$526$	14.0820	0.614003
$527$	0.416023	0.0181223
$528$	−1.56687	−0.0681892
$529$	21.0177	0.913815
$530$	−11.2172	−0.487243
$531$	0.211347	0.00917168
$532$	−0.622417	−0.0269852
$533$	−56.0938	−2.42969
$534$	4.10953	0.177837
$535$	−3.50573	−0.151566
$536$	−14.1600	−0.611620
$537$	34.9229	1.50703
$538$	28.8850	1.24532
$539$	−13.7512	−0.592307
$540$	5.55443	0.239025
$541$	8.62292	0.370728	0.185364	−	0.982670i	$-0.440654\pi$
$541$	8.62292	0.370728	0.185364	+	0.982670i	$0.440654\pi$
$542$	−24.9881	−1.07333
$543$	18.7877	0.806258
$544$	−2.48393	−0.106498
$545$	−1.90563	−0.0816281
$546$	−33.0800	−1.41569
$547$	30.7618	1.31528	0.657640	−	0.753332i	$-0.271555\pi$
$547$	30.7618	1.31528	0.657640	+	0.753332i	$0.271555\pi$
$548$	3.04840	0.130221
$549$	3.45309	0.147374
$550$	1.00000	0.0426401
$551$	0.964451	0.0410870
$552$	10.3955	0.442463
$553$	10.1514	0.431683
$554$	1.83307	0.0778796
$555$	13.2473	0.562315
$556$	−9.08154	−0.385143
$557$	38.7000	1.63977	0.819885	−	0.572528i	$-0.194037\pi$
$557$	38.7000	1.63977	0.819885	+	0.572528i	$0.194037\pi$
$558$	0.0912672	0.00386365
$559$	−4.63459	−0.196022
$560$	4.55535	0.192499
$561$	−3.89199	−0.164320
$562$	15.6372	0.659617
$563$	−39.5602	−1.66726	−0.833632	−	0.552321i	$-0.813742\pi$
$563$	−39.5602	−1.66726	−0.833632	+	0.552321i	$0.813742\pi$
$564$	3.38454	0.142515
$565$	−4.10386	−0.172651
$566$	−4.31430	−0.181344
$567$	32.1985	1.35221
$568$	3.26125	0.136839
$569$	−35.1116	−1.47195	−0.735977	−	0.677006i	$-0.763277\pi$
$569$	−35.1116	−1.47195	−0.735977	+	0.677006i	$0.763277\pi$
$570$	0.214088	0.00896715
$571$	−31.1494	−1.30356	−0.651782	−	0.758407i	$-0.725978\pi$
$571$	−31.1494	−1.30356	−0.651782	+	0.758407i	$0.725978\pi$
$572$	4.63459	0.193782
$573$	−6.79600	−0.283907
$574$	55.1348	2.30128
$575$	−6.63459	−0.276681
$576$	−0.544925	−0.0227052
$577$	27.5299	1.14608	0.573042	−	0.819526i	$-0.305763\pi$
$577$	27.5299	1.14608	0.573042	+	0.819526i	$0.305763\pi$
$578$	10.8301	0.450473
$579$	32.8029	1.36324
$580$	−7.05863	−0.293094
$581$	−55.3425	−2.29599
$582$	10.8971	0.451698
$583$	11.2172	0.464568
$584$	7.40941	0.306604
$585$	−2.52550	−0.104417
$586$	−9.31692	−0.384879
$587$	34.7330	1.43359	0.716793	−	0.697286i	$-0.245609\pi$
$587$	34.7330	1.43359	0.716793	+	0.697286i	$0.245609\pi$
$588$	21.5463	0.888556
$589$	0.0228843	0.000942932 0
$590$	−0.387846	−0.0159674
$591$	34.6520	1.42539
$592$	−8.45462	−0.347483
$593$	−14.0828	−0.578311	−0.289156	−	0.957282i	$-0.593375\pi$
$593$	−14.0828	−0.578311	−0.289156	+	0.957282i	$0.593375\pi$
$594$	−5.55443	−0.227901
$595$	11.3152	0.463876
$596$	13.2198	0.541504
$597$	−40.1380	−1.64274
$598$	−30.7486	−1.25740
$599$	−13.5175	−0.552311	−0.276155	−	0.961113i	$-0.589060\pi$
$599$	−13.5175	−0.552311	−0.276155	+	0.961113i	$0.589060\pi$
$600$	−1.56687	−0.0639671
$601$	6.78944	0.276947	0.138474	−	0.990366i	$-0.455780\pi$
$601$	6.78944	0.276947	0.138474	+	0.990366i	$0.455780\pi$
$602$	4.55535	0.185662
$603$	−7.71615	−0.314226
$604$	22.2579	0.905660
$605$	−1.00000	−0.0406558
$606$	2.10865	0.0856580
$607$	−29.1142	−1.18171	−0.590854	−	0.806779i	$-0.701209\pi$
$607$	−29.1142	−1.18171	−0.590854	+	0.806779i	$0.701209\pi$
$608$	−0.136634	−0.00554125
$609$	−50.3819	−2.04158
$610$	−6.33683	−0.256571
$611$	−10.0110	−0.405002
$612$	−1.35355	−0.0547142
$613$	−43.6222	−1.76189	−0.880943	−	0.473223i	$-0.843091\pi$
$613$	−43.6222	−1.76189	−0.880943	+	0.473223i	$0.843091\pi$
$614$	−4.45026	−0.179598
$615$	−18.9643	−0.764714
$616$	−4.55535	−0.183540
$617$	−22.4784	−0.904948	−0.452474	−	0.891778i	$-0.649458\pi$
$617$	−22.4784	−0.904948	−0.452474	+	0.891778i	$0.649458\pi$
$618$	−4.90627	−0.197359
$619$	6.11252	0.245683	0.122841	−	0.992426i	$-0.460799\pi$
$619$	6.11252	0.245683	0.122841	+	0.992426i	$0.460799\pi$
$620$	−0.167486	−0.00672640
$621$	36.8513	1.47879
$622$	−8.16298	−0.327306
$623$	11.9476	0.478671
$624$	−7.26179	−0.290704
$625$	1.00000	0.0400000
$626$	1.74945	0.0699220
$627$	−0.214088	−0.00854984
$628$	−9.63117	−0.384326
$629$	−21.0007	−0.837351
$630$	2.48232	0.0988981
$631$	25.7723	1.02598	0.512990	−	0.858394i	$-0.328538\pi$
$631$	25.7723	1.02598	0.512990	+	0.858394i	$0.328538\pi$
$632$	2.22847	0.0886436
$633$	−11.6892	−0.464605
$634$	−8.44435	−0.335368
$635$	−22.4116	−0.889377
$636$	−17.5758	−0.696928
$637$	−63.7312	−2.52512
$638$	7.05863	0.279454
$639$	1.77714	0.0703024
$640$	1.00000	0.0395285
$641$	11.6695	0.460916	0.230458	−	0.973082i	$-0.425978\pi$
$641$	11.6695	0.460916	0.230458	+	0.973082i	$0.425978\pi$
$642$	−5.49302	−0.216792
$643$	−20.0406	−0.790324	−0.395162	−	0.918612i	$-0.629311\pi$
$643$	−20.0406	−0.790324	−0.395162	+	0.918612i	$0.629311\pi$
$644$	30.2229	1.19095
$645$	−1.56687	−0.0616954
$646$	−0.339390	−0.0133531
$647$	35.6857	1.40295	0.701475	−	0.712694i	$-0.252525\pi$
$647$	35.6857	1.40295	0.701475	+	0.712694i	$0.252525\pi$
$648$	7.06828	0.277668
$649$	0.387846	0.0152243
$650$	4.63459	0.181783
$651$	−1.19545	−0.0468535
$652$	4.86103	0.190373
$653$	−21.1216	−0.826552	−0.413276	−	0.910606i	$-0.635615\pi$
$653$	−21.1216	−0.826552	−0.413276	+	0.910606i	$0.635615\pi$
$654$	−2.98587	−0.116757
$655$	−8.01674	−0.313240
$656$	12.1033	0.472555
$657$	4.03757	0.157521
$658$	9.83985	0.383597
$659$	−13.7850	−0.536986	−0.268493	−	0.963282i	$-0.586526\pi$
$659$	−13.7850	−0.536986	−0.268493	+	0.963282i	$0.586526\pi$
$660$	1.56687	0.0609903
$661$	29.9294	1.16412	0.582060	−	0.813146i	$-0.302247\pi$
$661$	29.9294	1.16412	0.582060	+	0.813146i	$0.302247\pi$
$662$	−24.3392	−0.945969
$663$	−18.0378	−0.700528
$664$	−12.1489	−0.471469
$665$	0.622417	0.0241363
$666$	−4.60713	−0.178523
$667$	−46.8311	−1.81331
$668$	−9.15528	−0.354228
$669$	41.8405	1.61765
$670$	14.1600	0.547050
$671$	6.33683	0.244631
$672$	7.13763	0.275340
$673$	42.6915	1.64564	0.822818	−	0.568305i	$-0.192401\pi$
$673$	42.6915	1.64564	0.822818	+	0.568305i	$0.192401\pi$
$674$	16.1419	0.621764
$675$	−5.55443	−0.213790
$676$	8.47939	0.326130
$677$	18.6769	0.717812	0.358906	−	0.933374i	$-0.383150\pi$
$677$	18.6769	0.717812	0.358906	+	0.933374i	$0.383150\pi$
$678$	−6.43021	−0.246951
$679$	31.6810	1.21580
$680$	2.48393	0.0952543
$681$	−35.2655	−1.35138
$682$	0.167486	0.00641337
$683$	−9.12820	−0.349281	−0.174640	−	0.984632i	$-0.555876\pi$
$683$	−9.12820	−0.349281	−0.174640	+	0.984632i	$0.555876\pi$
$684$	−0.0744554	−0.00284687
$685$	−3.04840	−0.116473
$686$	30.7541	1.17420
$687$	−15.5475	−0.593174
$688$	1.00000	0.0381246
$689$	51.9870	1.98055
$690$	−10.3955	−0.395751
$691$	−2.39772	−0.0912136	−0.0456068	−	0.998959i	$-0.514522\pi$
$691$	−2.39772	−0.0912136	−0.0456068	+	0.998959i	$0.514522\pi$
$692$	9.46132	0.359665
$693$	−2.48232	−0.0942956
$694$	4.48209	0.170138
$695$	9.08154	0.344482
$696$	−11.0599	−0.419226
$697$	30.0638	1.13875
$698$	4.14263	0.156801
$699$	−25.8255	−0.976810
$700$	−4.55535	−0.172176
$701$	43.4366	1.64058	0.820289	−	0.571950i	$-0.193813\pi$
$701$	43.4366	1.64058	0.820289	+	0.571950i	$0.193813\pi$
$702$	−25.7425	−0.971587
$703$	−1.15519	−0.0435688
$704$	−1.00000	−0.0376889
$705$	−3.38454	−0.127469
$706$	−8.99637	−0.338583
$707$	6.13047	0.230560
$708$	−0.607704	−0.0228389
$709$	−1.87234	−0.0703172	−0.0351586	−	0.999382i	$-0.511194\pi$
$709$	−1.87234	−0.0703172	−0.0351586	+	0.999382i	$0.511194\pi$
$710$	−3.26125	−0.122393
$711$	1.21435	0.0455415
$712$	2.62277	0.0982923
$713$	−1.11120	−0.0416148
$714$	17.7294	0.663505
$715$	−4.63459	−0.173324
$716$	22.2884	0.832955
$717$	−22.3402	−0.834310
$718$	16.4567	0.614157
$719$	−24.6780	−0.920332	−0.460166	−	0.887833i	$-0.652210\pi$
$719$	−24.6780	−0.920332	−0.460166	+	0.887833i	$0.652210\pi$
$720$	0.544925	0.0203081
$721$	−14.2640	−0.531218
$722$	18.9813	0.706412
$723$	28.9050	1.07499
$724$	11.9906	0.445628
$725$	7.05863	0.262151
$726$	−1.56687	−0.0581519
$727$	29.1544	1.08128	0.540639	−	0.841255i	$-0.318182\pi$
$727$	29.1544	1.08128	0.540639	+	0.841255i	$0.318182\pi$
$728$	−21.1122	−0.782469
$729$	29.9609	1.10966
$730$	−7.40941	−0.274235
$731$	2.48393	0.0918714
$732$	−9.92898	−0.366986
$733$	−19.4911	−0.719919	−0.359959	−	0.932968i	$-0.617209\pi$
$733$	−19.4911	−0.719919	−0.359959	+	0.932968i	$0.617209\pi$
$734$	28.2260	1.04184
$735$	−21.5463	−0.794749
$736$	6.63459	0.244554
$737$	−14.1600	−0.521591
$738$	6.59539	0.242780
$739$	24.6389	0.906356	0.453178	−	0.891420i	$-0.350290\pi$
$739$	24.6389	0.906356	0.453178	+	0.891420i	$0.350290\pi$
$740$	8.45462	0.310798
$741$	−0.992209	−0.0364497
$742$	−51.0982	−1.87587
$743$	−5.37030	−0.197017	−0.0985087	−	0.995136i	$-0.531407\pi$
$743$	−5.37030	−0.197017	−0.0985087	+	0.995136i	$0.531407\pi$
$744$	−0.262428	−0.00962109
$745$	−13.2198	−0.484336
$746$	−21.7113	−0.794906
$747$	−6.62023	−0.242222
$748$	−2.48393	−0.0908214
$749$	−15.9698	−0.583525
$750$	1.56687	0.0572139
$751$	24.7189	0.902005	0.451002	−	0.892523i	$-0.351067\pi$
$751$	24.7189	0.902005	0.451002	+	0.892523i	$0.351067\pi$
$752$	2.16006	0.0787694
$753$	39.4590	1.43797
$754$	32.7138	1.19137
$755$	−22.2579	−0.810047
$756$	25.3024	0.920238
$757$	14.3717	0.522348	0.261174	−	0.965292i	$-0.415890\pi$
$757$	14.3717	0.522348	0.261174	+	0.965292i	$0.415890\pi$
$758$	18.0417	0.655303
$759$	10.3955	0.377334
$760$	0.136634	0.00495625
$761$	−9.70053	−0.351644	−0.175822	−	0.984422i	$-0.556258\pi$
$761$	−9.70053	−0.351644	−0.175822	+	0.984422i	$0.556258\pi$
$762$	−35.1160	−1.27212
$763$	−8.68080	−0.314266
$764$	−4.33732	−0.156919
$765$	1.35355	0.0489378
$766$	−12.4567	−0.450080
$767$	1.79751	0.0649042
$768$	1.56687	0.0565395
$769$	50.8773	1.83468	0.917342	−	0.398100i	$-0.130330\pi$
$769$	50.8773	1.83468	0.917342	+	0.398100i	$0.130330\pi$
$770$	4.55535	0.164163
$771$	−21.7674	−0.783934
$772$	20.9353	0.753479
$773$	−15.5794	−0.560351	−0.280175	−	0.959949i	$-0.590393\pi$
$773$	−15.5794	−0.560351	−0.280175	+	0.959949i	$0.590393\pi$
$774$	0.544925	0.0195869
$775$	0.167486	0.00601627
$776$	6.95468	0.249658
$777$	60.3460	2.16490
$778$	33.0120	1.18354
$779$	1.65373	0.0592509
$780$	7.26179	0.260014
$781$	3.26125	0.116697
$782$	16.4798	0.589318
$783$	−39.2067	−1.40113
$784$	13.7512	0.491115
$785$	9.63117	0.343751
$786$	−12.5612	−0.448042
$787$	11.4655	0.408702	0.204351	−	0.978898i	$-0.434492\pi$
$787$	11.4655	0.408702	0.204351	+	0.978898i	$0.434492\pi$
$788$	22.1154	0.787830
$789$	−22.0646	−0.785520
$790$	−2.22847	−0.0792852
$791$	−18.6945	−0.664701
$792$	−0.544925	−0.0193630
$793$	29.3686	1.04291
$794$	2.61096	0.0926596
$795$	17.5758	0.623351
$796$	−25.6167	−0.907961
$797$	21.3997	0.758016	0.379008	−	0.925393i	$-0.376265\pi$
$797$	21.3997	0.758016	0.379008	+	0.925393i	$0.376265\pi$
$798$	0.975245	0.0345233
$799$	5.36544	0.189816
$800$	−1.00000	−0.0353553
$801$	1.42921	0.0504986
$802$	38.1218	1.34613
$803$	7.40941	0.261472
$804$	22.1869	0.782472
$805$	−30.2229	−1.06522
$806$	0.776228	0.0273415
$807$	−45.2590	−1.59319
$808$	1.34577	0.0473441
$809$	11.9099	0.418729	0.209364	−	0.977838i	$-0.432861\pi$
$809$	11.9099	0.418729	0.209364	+	0.977838i	$0.432861\pi$
$810$	−7.06828	−0.248354
$811$	2.45594	0.0862398	0.0431199	−	0.999070i	$-0.486270\pi$
$811$	2.45594	0.0862398	0.0431199	+	0.999070i	$0.486270\pi$
$812$	−32.1545	−1.12840
$813$	39.1530	1.37316
$814$	−8.45462	−0.296334
$815$	−4.86103	−0.170275
$816$	3.89199	0.136247
$817$	0.136634	0.00478023
$818$	−0.729537	−0.0255076
$819$	−11.5045	−0.402001
$820$	−12.1033	−0.422666
$821$	5.50383	0.192085	0.0960425	−	0.995377i	$-0.469382\pi$
$821$	5.50383	0.192085	0.0960425	+	0.995377i	$0.469382\pi$
$822$	−4.77644	−0.166598
$823$	34.6626	1.20826	0.604130	−	0.796885i	$-0.293521\pi$
$823$	34.6626	1.20826	0.604130	+	0.796885i	$0.293521\pi$
$824$	−3.13126	−0.109083
$825$	−1.56687	−0.0545513
$826$	−1.76678	−0.0614740
$827$	−28.9433	−1.00646	−0.503228	−	0.864154i	$-0.667854\pi$
$827$	−28.9433	−1.00646	−0.503228	+	0.864154i	$0.667854\pi$
$828$	3.61535	0.125642
$829$	23.2824	0.808631	0.404316	−	0.914620i	$-0.367510\pi$
$829$	23.2824	0.808631	0.404316	+	0.914620i	$0.367510\pi$
$830$	12.1489	0.421694
$831$	−2.87217	−0.0996346
$832$	−4.63459	−0.160675
$833$	34.1570	1.18347
$834$	14.2296	0.492730
$835$	9.15528	0.316831
$836$	−0.136634	−0.00472559
$837$	−0.930289	−0.0321555
$838$	21.2265	0.733259
$839$	26.5871	0.917890	0.458945	−	0.888465i	$-0.348228\pi$
$839$	26.5871	0.917890	0.458945	+	0.888465i	$0.348228\pi$
$840$	−7.13763	−0.246272
$841$	20.8243	0.718080
$842$	−25.6241	−0.883066
$843$	−24.5015	−0.843876
$844$	−7.46025	−0.256793
$845$	−8.47939	−0.291700
$846$	1.17707	0.0404686
$847$	−4.55535	−0.156524
$848$	−11.2172	−0.385200
$849$	6.75994	0.232000
$850$	−2.48393	−0.0851980
$851$	56.0929	1.92284
$852$	−5.10995	−0.175064
$853$	57.0650	1.95387	0.976935	−	0.213538i	$-0.0684987\pi$
$853$	57.0650	1.95387	0.976935	+	0.213538i	$0.0684987\pi$
$854$	−28.8665	−0.987791
$855$	0.0744554	0.00254632
$856$	−3.50573	−0.119823
$857$	−31.0690	−1.06130	−0.530648	−	0.847592i	$-0.678051\pi$
$857$	−31.0690	−1.06130	−0.530648	+	0.847592i	$0.678051\pi$
$858$	−7.26179	−0.247913
$859$	−12.3154	−0.420197	−0.210099	−	0.977680i	$-0.567379\pi$
$859$	−12.3154	−0.420197	−0.210099	+	0.977680i	$0.567379\pi$
$860$	−1.00000	−0.0340997
$861$	−86.3890	−2.94413
$862$	−22.3855	−0.762454
$863$	1.13831	0.0387486	0.0193743	−	0.999812i	$-0.493833\pi$
$863$	1.13831	0.0387486	0.0193743	+	0.999812i	$0.493833\pi$
$864$	5.55443	0.188966
$865$	−9.46132	−0.321694
$866$	−19.7044	−0.669581
$867$	−16.9693	−0.576309
$868$	−0.762957	−0.0258965
$869$	2.22847	0.0755955
$870$	11.0599	0.374967
$871$	−65.6259	−2.22365
$872$	−1.90563	−0.0645327
$873$	3.78977	0.128264
$874$	0.906512	0.0306632
$875$	4.55535	0.153999
$876$	−11.6096	−0.392251
$877$	−33.5855	−1.13410	−0.567052	−	0.823682i	$-0.691916\pi$
$877$	−33.5855	−1.13410	−0.567052	+	0.823682i	$0.691916\pi$
$878$	0.128117	0.00432374
$879$	14.5984	0.492391
$880$	1.00000	0.0337100
$881$	8.25259	0.278037	0.139018	−	0.990290i	$-0.455605\pi$
$881$	8.25259	0.278037	0.139018	+	0.990290i	$0.455605\pi$
$882$	7.49337	0.252315
$883$	46.4481	1.56310	0.781551	−	0.623841i	$-0.214429\pi$
$883$	46.4481	1.56310	0.781551	+	0.623841i	$0.214429\pi$
$884$	−11.5120	−0.387190
$885$	0.607704	0.0204277
$886$	39.6401	1.33173
$887$	−2.73441	−0.0918124	−0.0459062	−	0.998946i	$-0.514618\pi$
$887$	−2.73441	−0.0918124	−0.0459062	+	0.998946i	$0.514618\pi$
$888$	13.2473	0.444549
$889$	−102.093	−3.42408
$890$	−2.62277	−0.0879153
$891$	7.06828	0.236796
$892$	26.7032	0.894091
$893$	0.295139	0.00987644
$894$	−20.7137	−0.692769
$895$	−22.2884	−0.745017
$896$	4.55535	0.152184
$897$	48.1789	1.60865
$898$	−35.6224	−1.18874
$899$	1.18222	0.0394293
$900$	−0.544925	−0.0181642
$901$	−27.8627	−0.928241
$902$	12.1033	0.402996
$903$	−7.13763	−0.237526
$904$	−4.10386	−0.136493
$905$	−11.9906	−0.398582
$906$	−34.8752	−1.15865
$907$	9.43115	0.313156	0.156578	−	0.987666i	$-0.449954\pi$
$907$	9.43115	0.313156	0.156578	+	0.987666i	$0.449954\pi$
$908$	−22.5070	−0.746921
$909$	0.733345	0.0243235
$910$	21.1122	0.699861
$911$	−10.9468	−0.362683	−0.181341	−	0.983420i	$-0.558044\pi$
$911$	−10.9468	−0.362683	−0.181341	+	0.983420i	$0.558044\pi$
$912$	0.214088	0.00708916
$913$	−12.1489	−0.402070
$914$	39.3357	1.30111
$915$	9.92898	0.328242
$916$	−9.92266	−0.327854
$917$	−36.5190	−1.20597
$918$	13.7968	0.455362
$919$	0.104303	0.00344064	0.00172032	−	0.999999i	$-0.499452\pi$
$919$	0.104303	0.00344064	0.00172032	+	0.999999i	$0.499452\pi$
$920$	−6.63459	−0.218736
$921$	6.97297	0.229767
$922$	4.70061	0.154806
$923$	15.1146	0.497502
$924$	7.13763	0.234811
$925$	−8.45462	−0.277986
$926$	5.58181	0.183430
$927$	−1.70630	−0.0560422
$928$	−7.05863	−0.231711
$929$	−26.6115	−0.873096	−0.436548	−	0.899681i	$-0.643799\pi$
$929$	−26.6115	−0.873096	−0.436548	+	0.899681i	$0.643799\pi$
$930$	0.262428	0.00860537
$931$	1.87889	0.0615780
$932$	−16.4822	−0.539893
$933$	12.7903	0.418736
$934$	−12.3359	−0.403644
$935$	2.48393	0.0812331
$936$	−2.52550	−0.0825485
$937$	18.8355	0.615330	0.307665	−	0.951495i	$-0.400452\pi$
$937$	18.8355	0.615330	0.307665	+	0.951495i	$0.400452\pi$
$938$	64.5039	2.10613
$939$	−2.74115	−0.0894542
$940$	−2.16006	−0.0704535
$941$	−4.80397	−0.156605	−0.0783025	−	0.996930i	$-0.524950\pi$
$941$	−4.80397	−0.156605	−0.0783025	+	0.996930i	$0.524950\pi$
$942$	15.0908	0.491684
$943$	−80.3005	−2.61494
$944$	−0.387846	−0.0126233
$945$	−25.3024	−0.823086
$946$	1.00000	0.0325128
$947$	−11.5046	−0.373848	−0.186924	−	0.982374i	$-0.559852\pi$
$947$	−11.5046	−0.373848	−0.186924	+	0.982374i	$0.559852\pi$
$948$	−3.49171	−0.113406
$949$	34.3396	1.11471
$950$	−0.136634	−0.00443300
$951$	13.2312	0.429051
$952$	11.3152	0.366727
$953$	−34.3746	−1.11350	−0.556752	−	0.830679i	$-0.687952\pi$
$953$	−34.3746	−1.11350	−0.556752	+	0.830679i	$0.687952\pi$
$954$	−6.11252	−0.197900
$955$	4.33732	0.140352
$956$	−14.2579	−0.461132
$957$	−11.0599	−0.357517
$958$	−15.1615	−0.489845
$959$	−13.8865	−0.448419
$960$	−1.56687	−0.0505704
$961$	−30.9719	−0.999095
$962$	−39.1837	−1.26333
$963$	−1.91036	−0.0615605
$964$	18.4476	0.594157
$965$	−20.9353	−0.673932
$966$	−47.3552	−1.52363
$967$	55.5424	1.78612	0.893061	−	0.449936i	$-0.148553\pi$
$967$	55.5424	1.78612	0.893061	+	0.449936i	$0.148553\pi$
$968$	−1.00000	−0.0321412
$969$	0.531779	0.0170832
$970$	−6.95468	−0.223301
$971$	56.0749	1.79953	0.899765	−	0.436375i	$-0.143738\pi$
$971$	56.0749	1.79953	0.899765	+	0.436375i	$0.143738\pi$
$972$	5.58822	0.179242
$973$	41.3696	1.32625
$974$	−20.0421	−0.642191
$975$	−7.26179	−0.232563
$976$	−6.33683	−0.202837
$977$	−24.4581	−0.782483	−0.391242	−	0.920288i	$-0.627954\pi$
$977$	−24.4581	−0.782483	−0.391242	+	0.920288i	$0.627954\pi$
$978$	−7.61660	−0.243552
$979$	2.62277	0.0838240
$980$	−13.7512	−0.439266
$981$	−1.03842	−0.0331543
$982$	11.6057	0.370353
$983$	−55.5078	−1.77042	−0.885212	−	0.465188i	$-0.845987\pi$
$983$	−55.5078	−1.77042	−0.885212	+	0.465188i	$0.845987\pi$
$984$	−18.9643	−0.604560
$985$	−22.1154	−0.704657
$986$	−17.5331	−0.558369
$987$	−15.4177	−0.490752
$988$	−0.633243	−0.0201462
$989$	−6.63459	−0.210968
$990$	0.544925	0.0173188
$991$	−12.2717	−0.389822	−0.194911	−	0.980821i	$-0.562442\pi$
$991$	−12.2717	−0.389822	−0.194911	+	0.980821i	$0.562442\pi$
$992$	−0.167486	−0.00531769
$993$	38.1363	1.21022
$994$	−14.8561	−0.471208
$995$	25.6167	0.812105
$996$	19.0357	0.603170
$997$	−62.4086	−1.97650	−0.988250	−	0.152844i	$-0.951157\pi$
$997$	−62.4086	−1.97650	−0.988250	+	0.152844i	$0.951157\pi$
$998$	−4.05151	−0.128248
$999$	46.9606	1.48577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.8	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.56687 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56687 q^{6} -4.55535 q^{7} -1.00000 q^{8} -0.544925 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.56687 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56687 q^{6} -4.55535 q^{7} -1.00000 q^{8} -0.544925 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.56687 q^{12} -4.63459 q^{13} +4.55535 q^{14} -1.56687 q^{15} +1.00000 q^{16} +2.48393 q^{17} +0.544925 q^{18} +0.136634 q^{19} -1.00000 q^{20} -7.13763 q^{21} +1.00000 q^{22} -6.63459 q^{23} -1.56687 q^{24} +1.00000 q^{25} +4.63459 q^{26} -5.55443 q^{27} -4.55535 q^{28} +7.05863 q^{29} +1.56687 q^{30} +0.167486 q^{31} -1.00000 q^{32} -1.56687 q^{33} -2.48393 q^{34} +4.55535 q^{35} -0.544925 q^{36} -8.45462 q^{37} -0.136634 q^{38} -7.26179 q^{39} +1.00000 q^{40} +12.1033 q^{41} +7.13763 q^{42} +1.00000 q^{43} -1.00000 q^{44} +0.544925 q^{45} +6.63459 q^{46} +2.16006 q^{47} +1.56687 q^{48} +13.7512 q^{49} -1.00000 q^{50} +3.89199 q^{51} -4.63459 q^{52} -11.2172 q^{53} +5.55443 q^{54} +1.00000 q^{55} +4.55535 q^{56} +0.214088 q^{57} -7.05863 q^{58} -0.387846 q^{59} -1.56687 q^{60} -6.33683 q^{61} -0.167486 q^{62} +2.48232 q^{63} +1.00000 q^{64} +4.63459 q^{65} +1.56687 q^{66} +14.1600 q^{67} +2.48393 q^{68} -10.3955 q^{69} -4.55535 q^{70} -3.26125 q^{71} +0.544925 q^{72} -7.40941 q^{73} +8.45462 q^{74} +1.56687 q^{75} +0.136634 q^{76} +4.55535 q^{77} +7.26179 q^{78} -2.22847 q^{79} -1.00000 q^{80} -7.06828 q^{81} -12.1033 q^{82} +12.1489 q^{83} -7.13763 q^{84} -2.48393 q^{85} -1.00000 q^{86} +11.0599 q^{87} +1.00000 q^{88} -2.62277 q^{89} -0.544925 q^{90} +21.1122 q^{91} -6.63459 q^{92} +0.262428 q^{93} -2.16006 q^{94} -0.136634 q^{95} -1.56687 q^{96} -6.95468 q^{97} -13.7512 q^{98} +0.544925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

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