LMFDB - Embedded newform 4970.2.a.z.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4970,2,Mod(1,4970)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4970, 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("4970.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4970 = 2 \cdot 5 \cdot 7 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4970.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:	$39.6856498046$
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} - 4x^{8} - 9x^{7} + 47x^{6} + 6x^{5} - 151x^{4} + 80x^{3} + 79x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 47x^6 + 6x^5 - 151x^4 + 80x^3 + 79x^2 - 54x + 8
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			1.8
Root			$2.41697$ of defining polynomial
Character	$\chi$	$=$	4970.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.41697 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.41697 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.84175 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.41697 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.41697 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.84175 q^{9} -1.00000 q^{10} -0.708327 q^{11} +2.41697 q^{12} -4.14929 q^{13} +1.00000 q^{14} -2.41697 q^{15} +1.00000 q^{16} +6.83769 q^{17} +2.84175 q^{18} -1.61345 q^{19} -1.00000 q^{20} +2.41697 q^{21} -0.708327 q^{22} +3.07317 q^{23} +2.41697 q^{24} +1.00000 q^{25} -4.14929 q^{26} -0.382492 q^{27} +1.00000 q^{28} +10.4139 q^{29} -2.41697 q^{30} +5.25709 q^{31} +1.00000 q^{32} -1.71201 q^{33} +6.83769 q^{34} -1.00000 q^{35} +2.84175 q^{36} -0.789620 q^{37} -1.61345 q^{38} -10.0287 q^{39} -1.00000 q^{40} +9.45204 q^{41} +2.41697 q^{42} -2.61933 q^{43} -0.708327 q^{44} -2.84175 q^{45} +3.07317 q^{46} -4.28491 q^{47} +2.41697 q^{48} +1.00000 q^{49} +1.00000 q^{50} +16.5265 q^{51} -4.14929 q^{52} +1.25845 q^{53} -0.382492 q^{54} +0.708327 q^{55} +1.00000 q^{56} -3.89967 q^{57} +10.4139 q^{58} +1.90106 q^{59} -2.41697 q^{60} +2.54028 q^{61} +5.25709 q^{62} +2.84175 q^{63} +1.00000 q^{64} +4.14929 q^{65} -1.71201 q^{66} -13.6271 q^{67} +6.83769 q^{68} +7.42776 q^{69} -1.00000 q^{70} +1.00000 q^{71} +2.84175 q^{72} +14.1262 q^{73} -0.789620 q^{74} +2.41697 q^{75} -1.61345 q^{76} -0.708327 q^{77} -10.0287 q^{78} +5.07317 q^{79} -1.00000 q^{80} -9.44971 q^{81} +9.45204 q^{82} -9.10891 q^{83} +2.41697 q^{84} -6.83769 q^{85} -2.61933 q^{86} +25.1701 q^{87} -0.708327 q^{88} -0.706127 q^{89} -2.84175 q^{90} -4.14929 q^{91} +3.07317 q^{92} +12.7062 q^{93} -4.28491 q^{94} +1.61345 q^{95} +2.41697 q^{96} +1.35933 q^{97} +1.00000 q^{98} -2.01289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * 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
$3$	2.41697	1.39544	0.697719	−	0.716371i	$-0.254198\pi$
$3$	2.41697	1.39544	0.697719	+	0.716371i	$0.254198\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.41697	0.986724
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	2.84175	0.947249
$10$	−1.00000	−0.316228
$11$	−0.708327	−0.213569	−0.106784	−	0.994282i	$-0.534055\pi$
$11$	−0.708327	−0.213569	−0.106784	+	0.994282i	$0.534055\pi$
$12$	2.41697	0.697719
$13$	−4.14929	−1.15081	−0.575404	−	0.817870i	$-0.695155\pi$
$13$	−4.14929	−1.15081	−0.575404	+	0.817870i	$0.695155\pi$
$14$	1.00000	0.267261
$15$	−2.41697	−0.624059
$16$	1.00000	0.250000
$17$	6.83769	1.65838	0.829192	−	0.558964i	$-0.188801\pi$
$17$	6.83769	1.65838	0.829192	+	0.558964i	$0.188801\pi$
$18$	2.84175	0.669806
$19$	−1.61345	−0.370152	−0.185076	−	0.982724i	$-0.559253\pi$
$19$	−1.61345	−0.370152	−0.185076	+	0.982724i	$0.559253\pi$
$20$	−1.00000	−0.223607
$21$	2.41697	0.527426
$22$	−0.708327	−0.151016
$23$	3.07317	0.640800	0.320400	−	0.947282i	$-0.396183\pi$
$23$	3.07317	0.640800	0.320400	+	0.947282i	$0.396183\pi$
$24$	2.41697	0.493362
$25$	1.00000	0.200000
$26$	−4.14929	−0.813744
$27$	−0.382492	−0.0736106
$28$	1.00000	0.188982
$29$	10.4139	1.93381	0.966905	−	0.255135i	$-0.0821199\pi$
$29$	10.4139	1.93381	0.966905	+	0.255135i	$0.0821199\pi$
$30$	−2.41697	−0.441276
$31$	5.25709	0.944200	0.472100	−	0.881545i	$-0.343496\pi$
$31$	5.25709	0.944200	0.472100	+	0.881545i	$0.343496\pi$
$32$	1.00000	0.176777
$33$	−1.71201	−0.298022
$34$	6.83769	1.17265
$35$	−1.00000	−0.169031
$36$	2.84175	0.473625
$37$	−0.789620	−0.129813	−0.0649064	−	0.997891i	$-0.520675\pi$
$37$	−0.789620	−0.129813	−0.0649064	+	0.997891i	$0.520675\pi$
$38$	−1.61345	−0.261737
$39$	−10.0287	−1.60588
$40$	−1.00000	−0.158114
$41$	9.45204	1.47616	0.738081	−	0.674712i	$-0.235732\pi$
$41$	9.45204	1.47616	0.738081	+	0.674712i	$0.235732\pi$
$42$	2.41697	0.372947
$43$	−2.61933	−0.399444	−0.199722	−	0.979853i	$-0.564004\pi$
$43$	−2.61933	−0.399444	−0.199722	+	0.979853i	$0.564004\pi$
$44$	−0.708327	−0.106784
$45$	−2.84175	−0.423623
$46$	3.07317	0.453114
$47$	−4.28491	−0.625019	−0.312510	−	0.949915i	$-0.601170\pi$
$47$	−4.28491	−0.625019	−0.312510	+	0.949915i	$0.601170\pi$
$48$	2.41697	0.348860
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	16.5265	2.31417
$52$	−4.14929	−0.575404
$53$	1.25845	0.172862	0.0864309	−	0.996258i	$-0.472454\pi$
$53$	1.25845	0.172862	0.0864309	+	0.996258i	$0.472454\pi$
$54$	−0.382492	−0.0520505
$55$	0.708327	0.0955108
$56$	1.00000	0.133631
$57$	−3.89967	−0.516524
$58$	10.4139	1.36741
$59$	1.90106	0.247497	0.123748	−	0.992314i	$-0.460508\pi$
$59$	1.90106	0.247497	0.123748	+	0.992314i	$0.460508\pi$
$60$	−2.41697	−0.312030
$61$	2.54028	0.325250	0.162625	−	0.986688i	$-0.448004\pi$
$61$	2.54028	0.325250	0.162625	+	0.986688i	$0.448004\pi$
$62$	5.25709	0.667650
$63$	2.84175	0.358027
$64$	1.00000	0.125000
$65$	4.14929	0.514657
$66$	−1.71201	−0.210733
$67$	−13.6271	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$67$	−13.6271	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$68$	6.83769	0.829192
$69$	7.42776	0.894198
$70$	−1.00000	−0.119523
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	2.84175	0.334903
$73$	14.1262	1.65334	0.826671	−	0.562686i	$-0.190232\pi$
$73$	14.1262	1.65334	0.826671	+	0.562686i	$0.190232\pi$
$74$	−0.789620	−0.0917915
$75$	2.41697	0.279088
$76$	−1.61345	−0.185076
$77$	−0.708327	−0.0807213
$78$	−10.0287	−1.13553
$79$	5.07317	0.570776	0.285388	−	0.958412i	$-0.407878\pi$
$79$	5.07317	0.570776	0.285388	+	0.958412i	$0.407878\pi$
$80$	−1.00000	−0.111803
$81$	−9.44971	−1.04997
$82$	9.45204	1.04380
$83$	−9.10891	−0.999832	−0.499916	−	0.866074i	$-0.666636\pi$
$83$	−9.10891	−0.999832	−0.499916	+	0.866074i	$0.666636\pi$
$84$	2.41697	0.263713
$85$	−6.83769	−0.741652
$86$	−2.61933	−0.282450
$87$	25.1701	2.69851
$88$	−0.708327	−0.0755079
$89$	−0.706127	−0.0748493	−0.0374247	−	0.999299i	$-0.511915\pi$
$89$	−0.706127	−0.0748493	−0.0374247	+	0.999299i	$0.511915\pi$
$90$	−2.84175	−0.299546
$91$	−4.14929	−0.434964
$92$	3.07317	0.320400
$93$	12.7062	1.31757
$94$	−4.28491	−0.441955
$95$	1.61345	0.165537
$96$	2.41697	0.246681
$97$	1.35933	0.138019	0.0690094	−	0.997616i	$-0.478016\pi$
$97$	1.35933	0.138019	0.0690094	+	0.997616i	$0.478016\pi$
$98$	1.00000	0.101015
$99$	−2.01289	−0.202303
$100$	1.00000	0.100000
$101$	9.62731	0.957954	0.478977	−	0.877828i	$-0.341008\pi$
$101$	9.62731	0.957954	0.478977	+	0.877828i	$0.341008\pi$
$102$	16.5265	1.63637
$103$	4.02242	0.396341	0.198170	−	0.980168i	$-0.436500\pi$
$103$	4.02242	0.396341	0.198170	+	0.980168i	$0.436500\pi$
$104$	−4.14929	−0.406872
$105$	−2.41697	−0.235872
$106$	1.25845	0.122232
$107$	−12.8845	−1.24559	−0.622797	−	0.782384i	$-0.714004\pi$
$107$	−12.8845	−1.24559	−0.622797	+	0.782384i	$0.714004\pi$
$108$	−0.382492	−0.0368053
$109$	7.93578	0.760110	0.380055	−	0.924964i	$-0.375905\pi$
$109$	7.93578	0.760110	0.380055	+	0.924964i	$0.375905\pi$
$110$	0.708327	0.0675363
$111$	−1.90849	−0.181146
$112$	1.00000	0.0944911
$113$	10.1831	0.957949	0.478974	−	0.877829i	$-0.341009\pi$
$113$	10.1831	0.957949	0.478974	+	0.877829i	$0.341009\pi$
$114$	−3.89967	−0.365238
$115$	−3.07317	−0.286575
$116$	10.4139	0.966905
$117$	−11.7912	−1.09010
$118$	1.90106	0.175007
$119$	6.83769	0.626810
$120$	−2.41697	−0.220638
$121$	−10.4983	−0.954388
$122$	2.54028	0.229987
$123$	22.8453	2.05989
$124$	5.25709	0.472100
$125$	−1.00000	−0.0894427
$126$	2.84175	0.253163
$127$	1.14060	0.101212	0.0506061	−	0.998719i	$-0.483885\pi$
$127$	1.14060	0.101212	0.0506061	+	0.998719i	$0.483885\pi$
$128$	1.00000	0.0883883
$129$	−6.33085	−0.557400
$130$	4.14929	0.363917
$131$	13.5656	1.18523	0.592615	−	0.805486i	$-0.298096\pi$
$131$	13.5656	1.18523	0.592615	+	0.805486i	$0.298096\pi$
$132$	−1.71201	−0.149011
$133$	−1.61345	−0.139904
$134$	−13.6271	−1.17720
$135$	0.382492	0.0329196
$136$	6.83769	0.586327
$137$	19.9824	1.70721	0.853607	−	0.520917i	$-0.174410\pi$
$137$	19.9824	1.70721	0.853607	+	0.520917i	$0.174410\pi$
$138$	7.42776	0.632293
$139$	−20.4134	−1.73144	−0.865720	−	0.500529i	$-0.833139\pi$
$139$	−20.4134	−1.73144	−0.865720	+	0.500529i	$0.833139\pi$
$140$	−1.00000	−0.0845154
$141$	−10.3565	−0.872176
$142$	1.00000	0.0839181
$143$	2.93906	0.245776
$144$	2.84175	0.236812
$145$	−10.4139	−0.864827
$146$	14.1262	1.16909
$147$	2.41697	0.199348
$148$	−0.789620	−0.0649064
$149$	−12.4952	−1.02365	−0.511823	−	0.859091i	$-0.671030\pi$
$149$	−12.4952	−1.02365	−0.511823	+	0.859091i	$0.671030\pi$
$150$	2.41697	0.197345
$151$	−1.29314	−0.105234	−0.0526170	−	0.998615i	$-0.516756\pi$
$151$	−1.29314	−0.105234	−0.0526170	+	0.998615i	$0.516756\pi$
$152$	−1.61345	−0.130868
$153$	19.4310	1.57090
$154$	−0.708327	−0.0570786
$155$	−5.25709	−0.422259
$156$	−10.0287	−0.802940
$157$	8.71672	0.695670	0.347835	−	0.937556i	$-0.386917\pi$
$157$	8.71672	0.695670	0.347835	+	0.937556i	$0.386917\pi$
$158$	5.07317	0.403600
$159$	3.04164	0.241218
$160$	−1.00000	−0.0790569
$161$	3.07317	0.242200
$162$	−9.44971	−0.742440
$163$	−16.6888	−1.30717	−0.653584	−	0.756854i	$-0.726735\pi$
$163$	−16.6888	−1.30717	−0.653584	+	0.756854i	$0.726735\pi$
$164$	9.45204	0.738081
$165$	1.71201	0.133279
$166$	−9.10891	−0.706988
$167$	−18.8740	−1.46052	−0.730258	−	0.683171i	$-0.760600\pi$
$167$	−18.8740	−1.46052	−0.730258	+	0.683171i	$0.760600\pi$
$168$	2.41697	0.186473
$169$	4.21664	0.324357
$170$	−6.83769	−0.524427
$171$	−4.58503	−0.350626
$172$	−2.61933	−0.199722
$173$	−17.4529	−1.32692	−0.663460	−	0.748212i	$-0.730913\pi$
$173$	−17.4529	−1.32692	−0.663460	+	0.748212i	$0.730913\pi$
$174$	25.1701	1.90814
$175$	1.00000	0.0755929
$176$	−0.708327	−0.0533921
$177$	4.59480	0.345367
$178$	−0.706127	−0.0529265
$179$	−4.49679	−0.336106	−0.168053	−	0.985778i	$-0.553748\pi$
$179$	−4.49679	−0.336106	−0.168053	+	0.985778i	$0.553748\pi$
$180$	−2.84175	−0.211811
$181$	4.96765	0.369243	0.184621	−	0.982810i	$-0.440894\pi$
$181$	4.96765	0.369243	0.184621	+	0.982810i	$0.440894\pi$
$182$	−4.14929	−0.307566
$183$	6.13979	0.453867
$184$	3.07317	0.226557
$185$	0.789620	0.0580540
$186$	12.7062	0.931665
$187$	−4.84332	−0.354179
$188$	−4.28491	−0.312510
$189$	−0.382492	−0.0278222
$190$	1.61345	0.117052
$191$	−2.91352	−0.210815	−0.105407	−	0.994429i	$-0.533615\pi$
$191$	−2.91352	−0.210815	−0.105407	+	0.994429i	$0.533615\pi$
$192$	2.41697	0.174430
$193$	−9.47010	−0.681673	−0.340837	−	0.940123i	$-0.610710\pi$
$193$	−9.47010	−0.681673	−0.340837	+	0.940123i	$0.610710\pi$
$194$	1.35933	0.0975940
$195$	10.0287	0.718172
$196$	1.00000	0.0714286
$197$	−13.6756	−0.974347	−0.487173	−	0.873305i	$-0.661972\pi$
$197$	−13.6756	−0.974347	−0.487173	+	0.873305i	$0.661972\pi$
$198$	−2.01289	−0.143050
$199$	−16.0019	−1.13435	−0.567173	−	0.823599i	$-0.691963\pi$
$199$	−16.0019	−1.13435	−0.567173	+	0.823599i	$0.691963\pi$
$200$	1.00000	0.0707107
$201$	−32.9362	−2.32314
$202$	9.62731	0.677375
$203$	10.4139	0.730912
$204$	16.5265	1.15709
$205$	−9.45204	−0.660159
$206$	4.02242	0.280255
$207$	8.73317	0.606998
$208$	−4.14929	−0.287702
$209$	1.14285	0.0790528
$210$	−2.41697	−0.166787
$211$	−13.5305	−0.931476	−0.465738	−	0.884923i	$-0.654211\pi$
$211$	−13.5305	−0.931476	−0.465738	+	0.884923i	$0.654211\pi$
$212$	1.25845	0.0864309
$213$	2.41697	0.165608
$214$	−12.8845	−0.880768
$215$	2.61933	0.178637
$216$	−0.382492	−0.0260253
$217$	5.25709	0.356874
$218$	7.93578	0.537479
$219$	34.1425	2.30714
$220$	0.708327	0.0477554
$221$	−28.3716	−1.90848
$222$	−1.90849	−0.128089
$223$	−11.7970	−0.789983	−0.394992	−	0.918685i	$-0.629252\pi$
$223$	−11.7970	−0.789983	−0.394992	+	0.918685i	$0.629252\pi$
$224$	1.00000	0.0668153
$225$	2.84175	0.189450
$226$	10.1831	0.677372
$227$	17.7436	1.17768	0.588841	−	0.808249i	$-0.299584\pi$
$227$	17.7436	1.17768	0.588841	+	0.808249i	$0.299584\pi$
$228$	−3.89967	−0.258262
$229$	8.22274	0.543374	0.271687	−	0.962386i	$-0.412418\pi$
$229$	8.22274	0.543374	0.271687	+	0.962386i	$0.412418\pi$
$230$	−3.07317	−0.202639
$231$	−1.71201	−0.112642
$232$	10.4139	0.683705
$233$	−13.6951	−0.897194	−0.448597	−	0.893734i	$-0.648076\pi$
$233$	−13.6951	−0.897194	−0.448597	+	0.893734i	$0.648076\pi$
$234$	−11.7912	−0.770818
$235$	4.28491	0.279517
$236$	1.90106	0.123748
$237$	12.2617	0.796483
$238$	6.83769	0.443222
$239$	4.63382	0.299737	0.149868	−	0.988706i	$-0.452115\pi$
$239$	4.63382	0.299737	0.149868	+	0.988706i	$0.452115\pi$
$240$	−2.41697	−0.156015
$241$	−5.25556	−0.338540	−0.169270	−	0.985570i	$-0.554141\pi$
$241$	−5.25556	−0.338540	−0.169270	+	0.985570i	$0.554141\pi$
$242$	−10.4983	−0.674855
$243$	−21.6922	−1.39156
$244$	2.54028	0.162625
$245$	−1.00000	−0.0638877
$246$	22.8453	1.45656
$247$	6.69470	0.425973
$248$	5.25709	0.333825
$249$	−22.0160	−1.39520
$250$	−1.00000	−0.0632456
$251$	26.1251	1.64900	0.824502	−	0.565859i	$-0.191455\pi$
$251$	26.1251	1.64900	0.824502	+	0.565859i	$0.191455\pi$
$252$	2.84175	0.179013
$253$	−2.17681	−0.136855
$254$	1.14060	0.0715679
$255$	−16.5265	−1.03493
$256$	1.00000	0.0625000
$257$	0.524738	0.0327323	0.0163661	−	0.999866i	$-0.494790\pi$
$257$	0.524738	0.0327323	0.0163661	+	0.999866i	$0.494790\pi$
$258$	−6.33085	−0.394142
$259$	−0.789620	−0.0490646
$260$	4.14929	0.257328
$261$	29.5936	1.83180
$262$	13.5656	0.838084
$263$	−10.1112	−0.623484	−0.311742	−	0.950167i	$-0.600912\pi$
$263$	−10.1112	−0.623484	−0.311742	+	0.950167i	$0.600912\pi$
$264$	−1.71201	−0.105367
$265$	−1.25845	−0.0773062
$266$	−1.61345	−0.0989272
$267$	−1.70669	−0.104448
$268$	−13.6271	−0.832405
$269$	0.355909	0.0217002	0.0108501	−	0.999941i	$-0.496546\pi$
$269$	0.355909	0.0217002	0.0108501	+	0.999941i	$0.496546\pi$
$270$	0.382492	0.0232777
$271$	2.70432	0.164276	0.0821378	−	0.996621i	$-0.473825\pi$
$271$	2.70432	0.164276	0.0821378	+	0.996621i	$0.473825\pi$
$272$	6.83769	0.414596
$273$	−10.0287	−0.606966
$274$	19.9824	1.20718
$275$	−0.708327	−0.0427137
$276$	7.42776	0.447099
$277$	20.5363	1.23391	0.616953	−	0.787000i	$-0.288367\pi$
$277$	20.5363	1.23391	0.616953	+	0.787000i	$0.288367\pi$
$278$	−20.4134	−1.22431
$279$	14.9393	0.894393
$280$	−1.00000	−0.0597614
$281$	−13.8687	−0.827336	−0.413668	−	0.910428i	$-0.635753\pi$
$281$	−13.8687	−0.827336	−0.413668	+	0.910428i	$0.635753\pi$
$282$	−10.3565	−0.616721
$283$	−24.4626	−1.45415	−0.727076	−	0.686557i	$-0.759121\pi$
$283$	−24.4626	−1.45415	−0.727076	+	0.686557i	$0.759121\pi$
$284$	1.00000	0.0593391
$285$	3.89967	0.230997
$286$	2.93906	0.173790
$287$	9.45204	0.557937
$288$	2.84175	0.167452
$289$	29.7541	1.75024
$290$	−10.4139	−0.611525
$291$	3.28545	0.192597
$292$	14.1262	0.826671
$293$	−28.5225	−1.66630	−0.833151	−	0.553046i	$-0.813466\pi$
$293$	−28.5225	−1.66630	−0.833151	+	0.553046i	$0.813466\pi$
$294$	2.41697	0.140961
$295$	−1.90106	−0.110684
$296$	−0.789620	−0.0458957
$297$	0.270929	0.0157209
$298$	−12.4952	−0.723827
$299$	−12.7515	−0.737438
$300$	2.41697	0.139544
$301$	−2.61933	−0.150976
$302$	−1.29314	−0.0744116
$303$	23.2689	1.33677
$304$	−1.61345	−0.0925380
$305$	−2.54028	−0.145456
$306$	19.4310	1.11080
$307$	−1.84030	−0.105031	−0.0525156	−	0.998620i	$-0.516724\pi$
$307$	−1.84030	−0.105031	−0.0525156	+	0.998620i	$0.516724\pi$
$308$	−0.708327	−0.0403607
$309$	9.72207	0.553069
$310$	−5.25709	−0.298582
$311$	15.9292	0.903262	0.451631	−	0.892205i	$-0.350842\pi$
$311$	15.9292	0.903262	0.451631	+	0.892205i	$0.350842\pi$
$312$	−10.0287	−0.567765
$313$	−31.2891	−1.76856	−0.884281	−	0.466954i	$-0.845351\pi$
$313$	−31.2891	−1.76856	−0.884281	+	0.466954i	$0.845351\pi$
$314$	8.71672	0.491913
$315$	−2.84175	−0.160114
$316$	5.07317	0.285388
$317$	5.31549	0.298548	0.149274	−	0.988796i	$-0.452306\pi$
$317$	5.31549	0.298548	0.149274	+	0.988796i	$0.452306\pi$
$318$	3.04164	0.170567
$319$	−7.37644	−0.413001
$320$	−1.00000	−0.0559017
$321$	−31.1415	−1.73815
$322$	3.07317	0.171261
$323$	−11.0323	−0.613854
$324$	−9.44971	−0.524984
$325$	−4.14929	−0.230161
$326$	−16.6888	−0.924307
$327$	19.1806	1.06069
$328$	9.45204	0.521902
$329$	−4.28491	−0.236235
$330$	1.71201	0.0942428
$331$	−4.26897	−0.234644	−0.117322	−	0.993094i	$-0.537431\pi$
$331$	−4.26897	−0.234644	−0.117322	+	0.993094i	$0.537431\pi$
$332$	−9.10891	−0.499916
$333$	−2.24390	−0.122965
$334$	−18.8740	−1.03274
$335$	13.6271	0.744526
$336$	2.41697	0.131857
$337$	21.7612	1.18541	0.592703	−	0.805421i	$-0.298061\pi$
$337$	21.7612	1.18541	0.592703	+	0.805421i	$0.298061\pi$
$338$	4.21664	0.229355
$339$	24.6123	1.33676
$340$	−6.83769	−0.370826
$341$	−3.72373	−0.201652
$342$	−4.58503	−0.247930
$343$	1.00000	0.0539949
$344$	−2.61933	−0.141225
$345$	−7.42776	−0.399897
$346$	−17.4529	−0.938274
$347$	−11.0412	−0.592725	−0.296362	−	0.955076i	$-0.595774\pi$
$347$	−11.0412	−0.592725	−0.296362	+	0.955076i	$0.595774\pi$
$348$	25.1701	1.34926
$349$	−19.7977	−1.05975	−0.529873	−	0.848077i	$-0.677760\pi$
$349$	−19.7977	−1.05975	−0.529873	+	0.848077i	$0.677760\pi$
$350$	1.00000	0.0534522
$351$	1.58707	0.0847115
$352$	−0.708327	−0.0377539
$353$	21.9601	1.16882	0.584410	−	0.811459i	$-0.301326\pi$
$353$	21.9601	1.16882	0.584410	+	0.811459i	$0.301326\pi$
$354$	4.59480	0.244211
$355$	−1.00000	−0.0530745
$356$	−0.706127	−0.0374247
$357$	16.5265	0.874675
$358$	−4.49679	−0.237663
$359$	−31.8916	−1.68318	−0.841588	−	0.540120i	$-0.818379\pi$
$359$	−31.8916	−1.68318	−0.841588	+	0.540120i	$0.818379\pi$
$360$	−2.84175	−0.149773
$361$	−16.3968	−0.862988
$362$	4.96765	0.261094
$363$	−25.3740	−1.33179
$364$	−4.14929	−0.217482
$365$	−14.1262	−0.739397
$366$	6.13979	0.320932
$367$	34.7861	1.81582	0.907911	−	0.419164i	$-0.137677\pi$
$367$	34.7861	1.81582	0.907911	+	0.419164i	$0.137677\pi$
$368$	3.07317	0.160200
$369$	26.8603	1.39829
$370$	0.789620	0.0410504
$371$	1.25845	0.0653356
$372$	12.7062	0.658787
$373$	32.7326	1.69483	0.847414	−	0.530933i	$-0.178158\pi$
$373$	32.7326	1.69483	0.847414	+	0.530933i	$0.178158\pi$
$374$	−4.84332	−0.250442
$375$	−2.41697	−0.124812
$376$	−4.28491	−0.220978
$377$	−43.2103	−2.22544
$378$	−0.382492	−0.0196732
$379$	−9.30602	−0.478018	−0.239009	−	0.971017i	$-0.576823\pi$
$379$	−9.30602	−0.478018	−0.239009	+	0.971017i	$0.576823\pi$
$380$	1.61345	0.0827685
$381$	2.75681	0.141236
$382$	−2.91352	−0.149068
$383$	9.89623	0.505673	0.252837	−	0.967509i	$-0.418636\pi$
$383$	9.89623	0.505673	0.252837	+	0.967509i	$0.418636\pi$
$384$	2.41697	0.123341
$385$	0.708327	0.0360997
$386$	−9.47010	−0.482016
$387$	−7.44348	−0.378373
$388$	1.35933	0.0690094
$389$	20.4397	1.03633	0.518167	−	0.855280i	$-0.326615\pi$
$389$	20.4397	1.03633	0.518167	+	0.855280i	$0.326615\pi$
$390$	10.0287	0.507824
$391$	21.0134	1.06269
$392$	1.00000	0.0505076
$393$	32.7876	1.65392
$394$	−13.6756	−0.688967
$395$	−5.07317	−0.255259
$396$	−2.01289	−0.101151
$397$	9.89545	0.496638	0.248319	−	0.968678i	$-0.420122\pi$
$397$	9.89545	0.496638	0.248319	+	0.968678i	$0.420122\pi$
$398$	−16.0019	−0.802103
$399$	−3.89967	−0.195228
$400$	1.00000	0.0500000
$401$	−6.71779	−0.335470	−0.167735	−	0.985832i	$-0.553645\pi$
$401$	−6.71779	−0.335470	−0.167735	+	0.985832i	$0.553645\pi$
$402$	−32.9362	−1.64271
$403$	−21.8132	−1.08659
$404$	9.62731	0.478977
$405$	9.44971	0.469560
$406$	10.4139	0.516833
$407$	0.559309	0.0277239
$408$	16.5265	0.818184
$409$	−20.8618	−1.03155	−0.515775	−	0.856724i	$-0.672496\pi$
$409$	−20.8618	−1.03155	−0.515775	+	0.856724i	$0.672496\pi$
$410$	−9.45204	−0.466803
$411$	48.2970	2.38231
$412$	4.02242	0.198170
$413$	1.90106	0.0935450
$414$	8.73317	0.429212
$415$	9.10891	0.447139
$416$	−4.14929	−0.203436
$417$	−49.3385	−2.41612
$418$	1.14285	0.0558988
$419$	33.0668	1.61542	0.807710	−	0.589581i	$-0.200707\pi$
$419$	33.0668	1.61542	0.807710	+	0.589581i	$0.200707\pi$
$420$	−2.41697	−0.117936
$421$	−5.03125	−0.245208	−0.122604	−	0.992456i	$-0.539125\pi$
$421$	−5.03125	−0.245208	−0.122604	+	0.992456i	$0.539125\pi$
$422$	−13.5305	−0.658653
$423$	−12.1766	−0.592049
$424$	1.25845	0.0611159
$425$	6.83769	0.331677
$426$	2.41697	0.117103
$427$	2.54028	0.122933
$428$	−12.8845	−0.622797
$429$	7.10361	0.342966
$430$	2.61933	0.126315
$431$	12.8461	0.618773	0.309386	−	0.950936i	$-0.399876\pi$
$431$	12.8461	0.618773	0.309386	+	0.950936i	$0.399876\pi$
$432$	−0.382492	−0.0184026
$433$	6.97329	0.335115	0.167557	−	0.985862i	$-0.446412\pi$
$433$	6.97329	0.335115	0.167557	+	0.985862i	$0.446412\pi$
$434$	5.25709	0.252348
$435$	−25.1701	−1.20681
$436$	7.93578	0.380055
$437$	−4.95842	−0.237193
$438$	34.1425	1.63139
$439$	9.99643	0.477103	0.238552	−	0.971130i	$-0.423327\pi$
$439$	9.99643	0.477103	0.238552	+	0.971130i	$0.423327\pi$
$440$	0.708327	0.0337682
$441$	2.84175	0.135321
$442$	−28.3716	−1.34950
$443$	−40.5503	−1.92660	−0.963302	−	0.268421i	$-0.913498\pi$
$443$	−40.5503	−1.92660	−0.963302	+	0.268421i	$0.913498\pi$
$444$	−1.90849	−0.0905729
$445$	0.706127	0.0334736
$446$	−11.7970	−0.558602
$447$	−30.2005	−1.42843
$448$	1.00000	0.0472456
$449$	1.05084	0.0495921	0.0247960	−	0.999693i	$-0.492106\pi$
$449$	1.05084	0.0495921	0.0247960	+	0.999693i	$0.492106\pi$
$450$	2.84175	0.133961
$451$	−6.69514	−0.315262
$452$	10.1831	0.478974
$453$	−3.12547	−0.146847
$454$	17.7436	0.832747
$455$	4.14929	0.194522
$456$	−3.89967	−0.182619
$457$	14.6852	0.686943	0.343472	−	0.939163i	$-0.388397\pi$
$457$	14.6852	0.686943	0.343472	+	0.939163i	$0.388397\pi$
$458$	8.22274	0.384223
$459$	−2.61536	−0.122075
$460$	−3.07317	−0.143287
$461$	−5.76957	−0.268716	−0.134358	−	0.990933i	$-0.542897\pi$
$461$	−5.76957	−0.268716	−0.134358	+	0.990933i	$0.542897\pi$
$462$	−1.71201	−0.0796497
$463$	−10.9556	−0.509150	−0.254575	−	0.967053i	$-0.581936\pi$
$463$	−10.9556	−0.509150	−0.254575	+	0.967053i	$0.581936\pi$
$464$	10.4139	0.483453
$465$	−12.7062	−0.589237
$466$	−13.6951	−0.634412
$467$	19.8924	0.920510	0.460255	−	0.887787i	$-0.347758\pi$
$467$	19.8924	0.920510	0.460255	+	0.887787i	$0.347758\pi$
$468$	−11.7912	−0.545051
$469$	−13.6271	−0.629239
$470$	4.28491	0.197648
$471$	21.0681	0.970765
$472$	1.90106	0.0875033
$473$	1.85534	0.0853088
$474$	12.2617	0.563199
$475$	−1.61345	−0.0740304
$476$	6.83769	0.313405
$477$	3.57621	0.163743
$478$	4.63382	0.211946
$479$	15.4205	0.704582	0.352291	−	0.935890i	$-0.385403\pi$
$479$	15.4205	0.704582	0.352291	+	0.935890i	$0.385403\pi$
$480$	−2.41697	−0.110319
$481$	3.27637	0.149389
$482$	−5.25556	−0.239384
$483$	7.42776	0.337975
$484$	−10.4983	−0.477194
$485$	−1.35933	−0.0617239
$486$	−21.6922	−0.983978
$487$	12.3224	0.558383	0.279191	−	0.960236i	$-0.409934\pi$
$487$	12.3224	0.558383	0.279191	+	0.960236i	$0.409934\pi$
$488$	2.54028	0.114993
$489$	−40.3363	−1.82407
$490$	−1.00000	−0.0451754
$491$	−15.0982	−0.681374	−0.340687	−	0.940177i	$-0.610660\pi$
$491$	−15.0982	−0.681374	−0.340687	+	0.940177i	$0.610660\pi$
$492$	22.8453	1.02995
$493$	71.2070	3.20700
$494$	6.69470	0.301209
$495$	2.01289	0.0904725
$496$	5.25709	0.236050
$497$	1.00000	0.0448561
$498$	−22.0160	−0.986559
$499$	−19.5311	−0.874330	−0.437165	−	0.899381i	$-0.644017\pi$
$499$	−19.5311	−0.874330	−0.437165	+	0.899381i	$0.644017\pi$
$500$	−1.00000	−0.0447214
$501$	−45.6180	−2.03806
$502$	26.1251	1.16602
$503$	21.2306	0.946627	0.473314	−	0.880894i	$-0.343058\pi$
$503$	21.2306	0.946627	0.473314	+	0.880894i	$0.343058\pi$
$504$	2.84175	0.126581
$505$	−9.62731	−0.428410
$506$	−2.17681	−0.0967710
$507$	10.1915	0.452620
$508$	1.14060	0.0506061
$509$	−40.0152	−1.77364	−0.886821	−	0.462113i	$-0.847092\pi$
$509$	−40.0152	−1.77364	−0.886821	+	0.462113i	$0.847092\pi$
$510$	−16.5265	−0.731806
$511$	14.1262	0.624904
$512$	1.00000	0.0441942
$513$	0.617133	0.0272471
$514$	0.524738	0.0231452
$515$	−4.02242	−0.177249
$516$	−6.33085	−0.278700
$517$	3.03512	0.133484
$518$	−0.789620	−0.0346939
$519$	−42.1832	−1.85164
$520$	4.14929	0.181959
$521$	−15.1609	−0.664210	−0.332105	−	0.943242i	$-0.607759\pi$
$521$	−15.1609	−0.664210	−0.332105	+	0.943242i	$0.607759\pi$
$522$	29.5936	1.29528
$523$	−4.19904	−0.183611	−0.0918055	−	0.995777i	$-0.529264\pi$
$523$	−4.19904	−0.183611	−0.0918055	+	0.995777i	$0.529264\pi$
$524$	13.5656	0.592615
$525$	2.41697	0.105485
$526$	−10.1112	−0.440869
$527$	35.9463	1.56585
$528$	−1.71201	−0.0745055
$529$	−13.5556	−0.589375
$530$	−1.25845	−0.0546637
$531$	5.40233	0.234441
$532$	−1.61345	−0.0699521
$533$	−39.2193	−1.69878
$534$	−1.70669	−0.0738556
$535$	12.8845	0.557046
$536$	−13.6271	−0.588599
$537$	−10.8686	−0.469015
$538$	0.355909	0.0153443
$539$	−0.708327	−0.0305098
$540$	0.382492	0.0164598
$541$	32.3276	1.38987	0.694935	−	0.719072i	$-0.255433\pi$
$541$	32.3276	1.38987	0.694935	+	0.719072i	$0.255433\pi$
$542$	2.70432	0.116160
$543$	12.0067	0.515256
$544$	6.83769	0.293164
$545$	−7.93578	−0.339932
$546$	−10.0287	−0.429190
$547$	−7.08606	−0.302978	−0.151489	−	0.988459i	$-0.548407\pi$
$547$	−7.08606	−0.302978	−0.151489	+	0.988459i	$0.548407\pi$
$548$	19.9824	0.853607
$549$	7.21885	0.308093
$550$	−0.708327	−0.0302032
$551$	−16.8023	−0.715804
$552$	7.42776	0.316147
$553$	5.07317	0.215733
$554$	20.5363	0.872504
$555$	1.90849	0.0810108
$556$	−20.4134	−0.865720
$557$	−15.5593	−0.659271	−0.329635	−	0.944108i	$-0.606926\pi$
$557$	−15.5593	−0.659271	−0.329635	+	0.944108i	$0.606926\pi$
$558$	14.9393	0.632431
$559$	10.8684	0.459684
$560$	−1.00000	−0.0422577
$561$	−11.7062	−0.494235
$562$	−13.8687	−0.585015
$563$	−42.9191	−1.80882	−0.904412	−	0.426660i	$-0.859690\pi$
$563$	−42.9191	−1.80882	−0.904412	+	0.426660i	$0.859690\pi$
$564$	−10.3565	−0.436088
$565$	−10.1831	−0.428408
$566$	−24.4626	−1.02824
$567$	−9.44971	−0.396851
$568$	1.00000	0.0419591
$569$	10.3989	0.435943	0.217972	−	0.975955i	$-0.430056\pi$
$569$	10.3989	0.435943	0.217972	+	0.975955i	$0.430056\pi$
$570$	3.89967	0.163339
$571$	−20.8836	−0.873950	−0.436975	−	0.899474i	$-0.643950\pi$
$571$	−20.8836	−0.873950	−0.436975	+	0.899474i	$0.643950\pi$
$572$	2.93906	0.122888
$573$	−7.04188	−0.294179
$574$	9.45204	0.394521
$575$	3.07317	0.128160
$576$	2.84175	0.118406
$577$	10.7760	0.448610	0.224305	−	0.974519i	$-0.427989\pi$
$577$	10.7760	0.448610	0.224305	+	0.974519i	$0.427989\pi$
$578$	29.7541	1.23761
$579$	−22.8890	−0.951233
$580$	−10.4139	−0.432413
$581$	−9.10891	−0.377901
$582$	3.28545	0.136186
$583$	−0.891396	−0.0369179
$584$	14.1262	0.584545
$585$	11.7912	0.487508
$586$	−28.5225	−1.17825
$587$	−18.3676	−0.758113	−0.379056	−	0.925374i	$-0.623751\pi$
$587$	−18.3676	−0.758113	−0.379056	+	0.925374i	$0.623751\pi$
$588$	2.41697	0.0996742
$589$	−8.48207	−0.349498
$590$	−1.90106	−0.0782653
$591$	−33.0535	−1.35964
$592$	−0.789620	−0.0324532
$593$	5.50254	0.225962	0.112981	−	0.993597i	$-0.463960\pi$
$593$	5.50254	0.225962	0.112981	+	0.993597i	$0.463960\pi$
$594$	0.270929	0.0111164
$595$	−6.83769	−0.280318
$596$	−12.4952	−0.511823
$597$	−38.6761	−1.58291
$598$	−12.7515	−0.521447
$599$	36.2973	1.48307	0.741534	−	0.670915i	$-0.234098\pi$
$599$	36.2973	1.48307	0.741534	+	0.670915i	$0.234098\pi$
$600$	2.41697	0.0986724
$601$	−44.7738	−1.82636	−0.913180	−	0.407556i	$-0.866381\pi$
$601$	−44.7738	−1.82636	−0.913180	+	0.407556i	$0.866381\pi$
$602$	−2.61933	−0.106756
$603$	−38.7247	−1.57699
$604$	−1.29314	−0.0526170
$605$	10.4983	0.426815
$606$	23.2689	0.945236
$607$	36.3378	1.47490	0.737452	−	0.675399i	$-0.236029\pi$
$607$	36.3378	1.47490	0.737452	+	0.675399i	$0.236029\pi$
$608$	−1.61345	−0.0654342
$609$	25.1701	1.01994
$610$	−2.54028	−0.102853
$611$	17.7794	0.719276
$612$	19.4310	0.785452
$613$	−25.4666	−1.02859	−0.514293	−	0.857615i	$-0.671946\pi$
$613$	−25.4666	−1.02859	−0.514293	+	0.857615i	$0.671946\pi$
$614$	−1.84030	−0.0742683
$615$	−22.8453	−0.921212
$616$	−0.708327	−0.0285393
$617$	−31.4694	−1.26691	−0.633455	−	0.773780i	$-0.718364\pi$
$617$	−31.4694	−1.26691	−0.633455	+	0.773780i	$0.718364\pi$
$618$	9.72207	0.391079
$619$	25.8522	1.03909	0.519544	−	0.854444i	$-0.326102\pi$
$619$	25.8522	1.03909	0.519544	+	0.854444i	$0.326102\pi$
$620$	−5.25709	−0.211130
$621$	−1.17546	−0.0471697
$622$	15.9292	0.638703
$623$	−0.706127	−0.0282904
$624$	−10.0287	−0.401470
$625$	1.00000	0.0400000
$626$	−31.2891	−1.25056
$627$	2.76224	0.110313
$628$	8.71672	0.347835
$629$	−5.39918	−0.215279
$630$	−2.84175	−0.113218
$631$	35.3070	1.40555	0.702774	−	0.711413i	$-0.251945\pi$
$631$	35.3070	1.40555	0.702774	+	0.711413i	$0.251945\pi$
$632$	5.07317	0.201800
$633$	−32.7027	−1.29982
$634$	5.31549	0.211105
$635$	−1.14060	−0.0452635
$636$	3.04164	0.120609
$637$	−4.14929	−0.164401
$638$	−7.37644	−0.292036
$639$	2.84175	0.112418
$640$	−1.00000	−0.0395285
$641$	−22.9169	−0.905163	−0.452581	−	0.891723i	$-0.649497\pi$
$641$	−22.9169	−0.905163	−0.452581	+	0.891723i	$0.649497\pi$
$642$	−31.1415	−1.22906
$643$	−13.9280	−0.549266	−0.274633	−	0.961549i	$-0.588556\pi$
$643$	−13.9280	−0.549266	−0.274633	+	0.961549i	$0.588556\pi$
$644$	3.07317	0.121100
$645$	6.33085	0.249277
$646$	−11.0323	−0.434060
$647$	−29.4433	−1.15753	−0.578767	−	0.815493i	$-0.696466\pi$
$647$	−29.4433	−1.15753	−0.578767	+	0.815493i	$0.696466\pi$
$648$	−9.44971	−0.371220
$649$	−1.34657	−0.0528575
$650$	−4.14929	−0.162749
$651$	12.7062	0.497996
$652$	−16.6888	−0.653584
$653$	−23.8278	−0.932454	−0.466227	−	0.884665i	$-0.654387\pi$
$653$	−23.8278	−0.932454	−0.466227	+	0.884665i	$0.654387\pi$
$654$	19.1806	0.750019
$655$	−13.5656	−0.530051
$656$	9.45204	0.369040
$657$	40.1430	1.56613
$658$	−4.28491	−0.167043
$659$	−47.9497	−1.86786	−0.933928	−	0.357461i	$-0.883643\pi$
$659$	−47.9497	−1.86786	−0.933928	+	0.357461i	$0.883643\pi$
$660$	1.71201	0.0666397
$661$	14.2795	0.555407	0.277704	−	0.960667i	$-0.410427\pi$
$661$	14.2795	0.555407	0.277704	+	0.960667i	$0.410427\pi$
$662$	−4.26897	−0.165918
$663$	−68.5733	−2.66317
$664$	−9.10891	−0.353494
$665$	1.61345	0.0625671
$666$	−2.24390	−0.0869494
$667$	32.0037	1.23919
$668$	−18.8740	−0.730258
$669$	−28.5129	−1.10237
$670$	13.6271	0.526459
$671$	−1.79935	−0.0694632
$672$	2.41697	0.0932367
$673$	4.90673	0.189141	0.0945703	−	0.995518i	$-0.469852\pi$
$673$	4.90673	0.189141	0.0945703	+	0.995518i	$0.469852\pi$
$674$	21.7612	0.838208
$675$	−0.382492	−0.0147221
$676$	4.21664	0.162178
$677$	7.69477	0.295734	0.147867	−	0.989007i	$-0.452759\pi$
$677$	7.69477	0.295734	0.147867	+	0.989007i	$0.452759\pi$
$678$	24.6123	0.945231
$679$	1.35933	0.0521662
$680$	−6.83769	−0.262214
$681$	42.8857	1.64338
$682$	−3.72373	−0.142589
$683$	11.4333	0.437483	0.218741	−	0.975783i	$-0.429805\pi$
$683$	11.4333	0.437483	0.218741	+	0.975783i	$0.429805\pi$
$684$	−4.58503	−0.175313
$685$	−19.9824	−0.763489
$686$	1.00000	0.0381802
$687$	19.8741	0.758245
$688$	−2.61933	−0.0998611
$689$	−5.22169	−0.198931
$690$	−7.42776	−0.282770
$691$	−30.6912	−1.16755	−0.583775	−	0.811916i	$-0.698425\pi$
$691$	−30.6912	−1.16755	−0.583775	+	0.811916i	$0.698425\pi$
$692$	−17.4529	−0.663460
$693$	−2.01289	−0.0764632
$694$	−11.0412	−0.419120
$695$	20.4134	0.774323
$696$	25.1701	0.954069
$697$	64.6302	2.44804
$698$	−19.7977	−0.749354
$699$	−33.1006	−1.25198
$700$	1.00000	0.0377964
$701$	5.37699	0.203086	0.101543	−	0.994831i	$-0.467622\pi$
$701$	5.37699	0.203086	0.101543	+	0.994831i	$0.467622\pi$
$702$	1.58707	0.0599001
$703$	1.27402	0.0480504
$704$	−0.708327	−0.0266961
$705$	10.3565	0.390049
$706$	21.9601	0.826480
$707$	9.62731	0.362072
$708$	4.59480	0.172683
$709$	30.1906	1.13383	0.566917	−	0.823775i	$-0.308136\pi$
$709$	30.1906	1.13383	0.566917	+	0.823775i	$0.308136\pi$
$710$	−1.00000	−0.0375293
$711$	14.4167	0.540667
$712$	−0.706127	−0.0264632
$713$	16.1559	0.605044
$714$	16.5265	0.618489
$715$	−2.93906	−0.109914
$716$	−4.49679	−0.168053
$717$	11.1998	0.418264
$718$	−31.8916	−1.19019
$719$	−33.9925	−1.26771	−0.633853	−	0.773453i	$-0.718528\pi$
$719$	−33.9925	−1.26771	−0.633853	+	0.773453i	$0.718528\pi$
$720$	−2.84175	−0.105906
$721$	4.02242	0.149803
$722$	−16.3968	−0.610224
$723$	−12.7025	−0.472412
$724$	4.96765	0.184621
$725$	10.4139	0.386762
$726$	−25.3740	−0.941718
$727$	42.0754	1.56049	0.780246	−	0.625473i	$-0.215094\pi$
$727$	42.0754	1.56049	0.780246	+	0.625473i	$0.215094\pi$
$728$	−4.14929	−0.153783
$729$	−24.0803	−0.891862
$730$	−14.1262	−0.522833
$731$	−17.9102	−0.662432
$732$	6.13979	0.226933
$733$	15.7724	0.582567	0.291284	−	0.956637i	$-0.405918\pi$
$733$	15.7724	0.582567	0.291284	+	0.956637i	$0.405918\pi$
$734$	34.7861	1.28398
$735$	−2.41697	−0.0891513
$736$	3.07317	0.113279
$737$	9.65241	0.355551
$738$	26.8603	0.988742
$739$	29.7001	1.09253	0.546267	−	0.837611i	$-0.316048\pi$
$739$	29.7001	1.09253	0.546267	+	0.837611i	$0.316048\pi$
$740$	0.789620	0.0290270
$741$	16.1809	0.594420
$742$	1.25845	0.0461993
$743$	15.3704	0.563885	0.281942	−	0.959431i	$-0.409021\pi$
$743$	15.3704	0.563885	0.281942	+	0.959431i	$0.409021\pi$
$744$	12.7062	0.465833
$745$	12.4952	0.457788
$746$	32.7326	1.19842
$747$	−25.8852	−0.947090
$748$	−4.84332	−0.177089
$749$	−12.8845	−0.470790
$750$	−2.41697	−0.0882553
$751$	9.49317	0.346411	0.173205	−	0.984886i	$-0.444588\pi$
$751$	9.49317	0.346411	0.173205	+	0.984886i	$0.444588\pi$
$752$	−4.28491	−0.156255
$753$	63.1437	2.30108
$754$	−43.2103	−1.57363
$755$	1.29314	0.0470620
$756$	−0.382492	−0.0139111
$757$	27.0758	0.984088	0.492044	−	0.870570i	$-0.336250\pi$
$757$	27.0758	0.984088	0.492044	+	0.870570i	$0.336250\pi$
$758$	−9.30602	−0.338010
$759$	−5.26128	−0.190972
$760$	1.61345	0.0585261
$761$	19.2705	0.698555	0.349277	−	0.937019i	$-0.386427\pi$
$761$	19.2705	0.698555	0.349277	+	0.937019i	$0.386427\pi$
$762$	2.75681	0.0998686
$763$	7.93578	0.287295
$764$	−2.91352	−0.105407
$765$	−19.4310	−0.702529
$766$	9.89623	0.357565
$767$	−7.88805	−0.284821
$768$	2.41697	0.0872149
$769$	23.2739	0.839278	0.419639	−	0.907691i	$-0.362157\pi$
$769$	23.2739	0.839278	0.419639	+	0.907691i	$0.362157\pi$
$770$	0.708327	0.0255263
$771$	1.26828	0.0456759
$772$	−9.47010	−0.340837
$773$	−30.2012	−1.08626	−0.543132	−	0.839648i	$-0.682762\pi$
$773$	−30.2012	−1.08626	−0.543132	+	0.839648i	$0.682762\pi$
$774$	−7.44348	−0.267550
$775$	5.25709	0.188840
$776$	1.35933	0.0487970
$777$	−1.90849	−0.0684667
$778$	20.4397	0.732798
$779$	−15.2504	−0.546404
$780$	10.0287	0.359086
$781$	−0.708327	−0.0253459
$782$	21.0134	0.751438
$783$	−3.98323	−0.142349
$784$	1.00000	0.0357143
$785$	−8.71672	−0.311113
$786$	32.7876	1.16950
$787$	13.4889	0.480829	0.240414	−	0.970670i	$-0.422717\pi$
$787$	13.4889	0.480829	0.240414	+	0.970670i	$0.422717\pi$
$788$	−13.6756	−0.487173
$789$	−24.4385	−0.870033
$790$	−5.07317	−0.180495
$791$	10.1831	0.362071
$792$	−2.01289	−0.0715248
$793$	−10.5404	−0.374300
$794$	9.89545	0.351176
$795$	−3.04164	−0.107876
$796$	−16.0019	−0.567173
$797$	31.4484	1.11396	0.556981	−	0.830526i	$-0.311960\pi$
$797$	31.4484	1.11396	0.556981	+	0.830526i	$0.311960\pi$
$798$	−3.89967	−0.138047
$799$	−29.2989	−1.03652
$800$	1.00000	0.0353553
$801$	−2.00663	−0.0709010
$802$	−6.71779	−0.237213
$803$	−10.0059	−0.353102
$804$	−32.9362	−1.16157
$805$	−3.07317	−0.108315
$806$	−21.8132	−0.768337
$807$	0.860222	0.0302812
$808$	9.62731	0.338688
$809$	−7.09080	−0.249299	−0.124650	−	0.992201i	$-0.539781\pi$
$809$	−7.09080	−0.249299	−0.124650	+	0.992201i	$0.539781\pi$
$810$	9.44971	0.332029
$811$	36.3421	1.27614	0.638072	−	0.769977i	$-0.279732\pi$
$811$	36.3421	1.27614	0.638072	+	0.769977i	$0.279732\pi$
$812$	10.4139	0.365456
$813$	6.53626	0.229237
$814$	0.559309	0.0196038
$815$	16.6888	0.584583
$816$	16.5265	0.578543
$817$	4.22617	0.147855
$818$	−20.8618	−0.729416
$819$	−11.7912	−0.412019
$820$	−9.45204	−0.330080
$821$	−33.4392	−1.16703	−0.583517	−	0.812101i	$-0.698324\pi$
$821$	−33.4392	−1.16703	−0.583517	+	0.812101i	$0.698324\pi$
$822$	48.2970	1.68455
$823$	−34.0680	−1.18753	−0.593767	−	0.804637i	$-0.702360\pi$
$823$	−34.0680	−1.18753	−0.593767	+	0.804637i	$0.702360\pi$
$824$	4.02242	0.140128
$825$	−1.71201	−0.0596044
$826$	1.90106	0.0661463
$827$	−54.0076	−1.87803	−0.939015	−	0.343877i	$-0.888260\pi$
$827$	−54.0076	−1.87803	−0.939015	+	0.343877i	$0.888260\pi$
$828$	8.73317	0.303499
$829$	−22.5426	−0.782937	−0.391468	−	0.920192i	$-0.628033\pi$
$829$	−22.5426	−0.782937	−0.391468	+	0.920192i	$0.628033\pi$
$830$	9.10891	0.316175
$831$	49.6356	1.72184
$832$	−4.14929	−0.143851
$833$	6.83769	0.236912
$834$	−49.3385	−1.70845
$835$	18.8740	0.653163
$836$	1.14285	0.0395264
$837$	−2.01079	−0.0695031
$838$	33.0668	1.14227
$839$	−15.7670	−0.544336	−0.272168	−	0.962250i	$-0.587741\pi$
$839$	−15.7670	−0.544336	−0.272168	+	0.962250i	$0.587741\pi$
$840$	−2.41697	−0.0833934
$841$	79.4491	2.73962
$842$	−5.03125	−0.173388
$843$	−33.5202	−1.15450
$844$	−13.5305	−0.465738
$845$	−4.21664	−0.145057
$846$	−12.1766	−0.418642
$847$	−10.4983	−0.360725
$848$	1.25845	0.0432155
$849$	−59.1255	−2.02918
$850$	6.83769	0.234531
$851$	−2.42664	−0.0831841
$852$	2.41697	0.0828041
$853$	19.8839	0.680811	0.340406	−	0.940279i	$-0.389436\pi$
$853$	19.8839	0.680811	0.340406	+	0.940279i	$0.389436\pi$
$854$	2.54028	0.0869267
$855$	4.58503	0.156805
$856$	−12.8845	−0.440384
$857$	13.6531	0.466379	0.233190	−	0.972431i	$-0.425084\pi$
$857$	13.6531	0.466379	0.233190	+	0.972431i	$0.425084\pi$
$858$	7.10361	0.242513
$859$	31.6300	1.07920	0.539601	−	0.841921i	$-0.318575\pi$
$859$	31.6300	1.07920	0.539601	+	0.841921i	$0.318575\pi$
$860$	2.61933	0.0893185
$861$	22.8453	0.778566
$862$	12.8461	0.437538
$863$	32.3289	1.10049	0.550245	−	0.835003i	$-0.314534\pi$
$863$	32.3289	1.10049	0.550245	+	0.835003i	$0.314534\pi$
$864$	−0.382492	−0.0130126
$865$	17.4529	0.593417
$866$	6.97329	0.236962
$867$	71.9147	2.44235
$868$	5.25709	0.178437
$869$	−3.59346	−0.121900
$870$	−25.1701	−0.853345
$871$	56.5427	1.91588
$872$	7.93578	0.268740
$873$	3.86286	0.130738
$874$	−4.95842	−0.167721
$875$	−1.00000	−0.0338062
$876$	34.1425	1.15357
$877$	−35.0769	−1.18446	−0.592232	−	0.805768i	$-0.701753\pi$
$877$	−35.0769	−1.18446	−0.592232	+	0.805768i	$0.701753\pi$
$878$	9.99643	0.337363
$879$	−68.9380	−2.32522
$880$	0.708327	0.0238777
$881$	−8.56424	−0.288537	−0.144268	−	0.989539i	$-0.546083\pi$
$881$	−8.56424	−0.288537	−0.144268	+	0.989539i	$0.546083\pi$
$882$	2.84175	0.0956866
$883$	22.0370	0.741605	0.370802	−	0.928712i	$-0.379083\pi$
$883$	22.0370	0.741605	0.370802	+	0.928712i	$0.379083\pi$
$884$	−28.3716	−0.954240
$885$	−4.59480	−0.154453
$886$	−40.5503	−1.36231
$887$	26.9324	0.904303	0.452151	−	0.891941i	$-0.350657\pi$
$887$	26.9324	0.904303	0.452151	+	0.891941i	$0.350657\pi$
$888$	−1.90849	−0.0640447
$889$	1.14060	0.0382546
$890$	0.706127	0.0236694
$891$	6.69349	0.224240
$892$	−11.7970	−0.394992
$893$	6.91351	0.231352
$894$	−30.2005	−1.01006
$895$	4.49679	0.150311
$896$	1.00000	0.0334077
$897$	−30.8200	−1.02905
$898$	1.05084	0.0350669
$899$	54.7467	1.82590
$900$	2.84175	0.0947249
$901$	8.60492	0.286671
$902$	−6.69514	−0.222924
$903$	−6.33085	−0.210678
$904$	10.1831	0.338686
$905$	−4.96765	−0.165130
$906$	−3.12547	−0.103837
$907$	33.6605	1.11768	0.558839	−	0.829276i	$-0.311247\pi$
$907$	33.6605	1.11768	0.558839	+	0.829276i	$0.311247\pi$
$908$	17.7436	0.588841
$909$	27.3584	0.907421
$910$	4.14929	0.137548
$911$	6.15899	0.204056	0.102028	−	0.994782i	$-0.467467\pi$
$911$	6.15899	0.204056	0.102028	+	0.994782i	$0.467467\pi$
$912$	−3.89967	−0.129131
$913$	6.45208	0.213533
$914$	14.6852	0.485742
$915$	−6.13979	−0.202975
$916$	8.22274	0.271687
$917$	13.5656	0.447975
$918$	−2.61536	−0.0863198
$919$	−0.148127	−0.00488627	−0.00244313	−	0.999997i	$-0.500778\pi$
$919$	−0.148127	−0.00488627	−0.00244313	+	0.999997i	$0.500778\pi$
$920$	−3.07317	−0.101319
$921$	−4.44794	−0.146565
$922$	−5.76957	−0.190011
$923$	−4.14929	−0.136576
$924$	−1.71201	−0.0563208
$925$	−0.789620	−0.0259626
$926$	−10.9556	−0.360024
$927$	11.4307	0.375434
$928$	10.4139	0.341853
$929$	−9.97480	−0.327263	−0.163631	−	0.986522i	$-0.552321\pi$
$929$	−9.97480	−0.327263	−0.163631	+	0.986522i	$0.552321\pi$
$930$	−12.7062	−0.416653
$931$	−1.61345	−0.0528788
$932$	−13.6951	−0.448597
$933$	38.5004	1.26045
$934$	19.8924	0.650899
$935$	4.84332	0.158394
$936$	−11.7912	−0.385409
$937$	−49.4979	−1.61703	−0.808513	−	0.588478i	$-0.799727\pi$
$937$	−49.4979	−1.61703	−0.808513	+	0.588478i	$0.799727\pi$
$938$	−13.6271	−0.444939
$939$	−75.6248	−2.46792
$940$	4.28491	0.139759
$941$	−31.9006	−1.03993	−0.519966	−	0.854187i	$-0.674055\pi$
$941$	−31.9006	−1.03993	−0.519966	+	0.854187i	$0.674055\pi$
$942$	21.0681	0.686435
$943$	29.0477	0.945925
$944$	1.90106	0.0618742
$945$	0.382492	0.0124425
$946$	1.85534	0.0603224
$947$	5.49904	0.178695	0.0893474	−	0.996001i	$-0.471522\pi$
$947$	5.49904	0.178695	0.0893474	+	0.996001i	$0.471522\pi$
$948$	12.2617	0.398242
$949$	−58.6136	−1.90268
$950$	−1.61345	−0.0523474
$951$	12.8474	0.416605
$952$	6.83769	0.221611
$953$	20.1434	0.652509	0.326254	−	0.945282i	$-0.394213\pi$
$953$	20.1434	0.652509	0.326254	+	0.945282i	$0.394213\pi$
$954$	3.57621	0.115784
$955$	2.91352	0.0942792
$956$	4.63382	0.149868
$957$	−17.8286	−0.576318
$958$	15.4205	0.498215
$959$	19.9824	0.645266
$960$	−2.41697	−0.0780074
$961$	−3.36305	−0.108486
$962$	3.27637	0.105634
$963$	−36.6145	−1.17989
$964$	−5.25556	−0.169270
$965$	9.47010	0.304853
$966$	7.42776	0.238984
$967$	−25.4892	−0.819677	−0.409838	−	0.912158i	$-0.634415\pi$
$967$	−25.4892	−0.819677	−0.409838	+	0.912158i	$0.634415\pi$
$968$	−10.4983	−0.337427
$969$	−26.6648	−0.856596
$970$	−1.35933	−0.0436454
$971$	35.0740	1.12558	0.562790	−	0.826600i	$-0.309728\pi$
$971$	35.0740	1.12558	0.562790	+	0.826600i	$0.309728\pi$
$972$	−21.6922	−0.695778
$973$	−20.4134	−0.654423
$974$	12.3224	0.394836
$975$	−10.0287	−0.321176
$976$	2.54028	0.0813125
$977$	16.3102	0.521810	0.260905	−	0.965364i	$-0.415979\pi$
$977$	16.3102	0.521810	0.260905	+	0.965364i	$0.415979\pi$
$978$	−40.3363	−1.28981
$979$	0.500169	0.0159855
$980$	−1.00000	−0.0319438
$981$	22.5515	0.720014
$982$	−15.0982	−0.481804
$983$	−17.6519	−0.563007	−0.281503	−	0.959560i	$-0.590833\pi$
$983$	−17.6519	−0.563007	−0.281503	+	0.959560i	$0.590833\pi$
$984$	22.8453	0.728282
$985$	13.6756	0.435741
$986$	71.2070	2.26769
$987$	−10.3565	−0.329651
$988$	6.69470	0.212987
$989$	−8.04966	−0.255964
$990$	2.01289	0.0639737
$991$	6.50821	0.206740	0.103370	−	0.994643i	$-0.467037\pi$
$991$	6.50821	0.206740	0.103370	+	0.994643i	$0.467037\pi$
$992$	5.25709	0.166913
$993$	−10.3180	−0.327431
$994$	1.00000	0.0317181
$995$	16.0019	0.507295
$996$	−22.0160	−0.697602
$997$	18.3267	0.580411	0.290206	−	0.956964i	$-0.406276\pi$
$997$	18.3267	0.580411	0.290206	+	0.956964i	$0.406276\pi$
$998$	−19.5311	−0.618245
$999$	0.302023	0.00955559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4970.2.a.z.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4970.2.a.z.1.8	✓	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:	\( N \)	\(=\)	\( 4970 = 2 \cdot 5 \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4970.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.41697 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.41697 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.84175 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.41697 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.41697 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.84175 q^{9} -1.00000 q^{10} -0.708327 q^{11} +2.41697 q^{12} -4.14929 q^{13} +1.00000 q^{14} -2.41697 q^{15} +1.00000 q^{16} +6.83769 q^{17} +2.84175 q^{18} -1.61345 q^{19} -1.00000 q^{20} +2.41697 q^{21} -0.708327 q^{22} +3.07317 q^{23} +2.41697 q^{24} +1.00000 q^{25} -4.14929 q^{26} -0.382492 q^{27} +1.00000 q^{28} +10.4139 q^{29} -2.41697 q^{30} +5.25709 q^{31} +1.00000 q^{32} -1.71201 q^{33} +6.83769 q^{34} -1.00000 q^{35} +2.84175 q^{36} -0.789620 q^{37} -1.61345 q^{38} -10.0287 q^{39} -1.00000 q^{40} +9.45204 q^{41} +2.41697 q^{42} -2.61933 q^{43} -0.708327 q^{44} -2.84175 q^{45} +3.07317 q^{46} -4.28491 q^{47} +2.41697 q^{48} +1.00000 q^{49} +1.00000 q^{50} +16.5265 q^{51} -4.14929 q^{52} +1.25845 q^{53} -0.382492 q^{54} +0.708327 q^{55} +1.00000 q^{56} -3.89967 q^{57} +10.4139 q^{58} +1.90106 q^{59} -2.41697 q^{60} +2.54028 q^{61} +5.25709 q^{62} +2.84175 q^{63} +1.00000 q^{64} +4.14929 q^{65} -1.71201 q^{66} -13.6271 q^{67} +6.83769 q^{68} +7.42776 q^{69} -1.00000 q^{70} +1.00000 q^{71} +2.84175 q^{72} +14.1262 q^{73} -0.789620 q^{74} +2.41697 q^{75} -1.61345 q^{76} -0.708327 q^{77} -10.0287 q^{78} +5.07317 q^{79} -1.00000 q^{80} -9.44971 q^{81} +9.45204 q^{82} -9.10891 q^{83} +2.41697 q^{84} -6.83769 q^{85} -2.61933 q^{86} +25.1701 q^{87} -0.708327 q^{88} -0.706127 q^{89} -2.84175 q^{90} -4.14929 q^{91} +3.07317 q^{92} +12.7062 q^{93} -4.28491 q^{94} +1.61345 q^{95} +2.41697 q^{96} +1.35933 q^{97} +1.00000 q^{98} -2.01289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * q^99

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