LMFDB - Embedded newform 5290.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 12 $ x^3 - x^2 - 9*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.11903$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.11903 q^{6} -4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.11903 q^{6} -4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} +1.00000 q^{10} -4.33763 q^{11} -3.11903 q^{12} -3.72833 q^{13} -4.50973 q^{14} -3.11903 q^{15} +1.00000 q^{16} -1.11903 q^{17} +6.72833 q^{18} -4.50973 q^{19} +1.00000 q^{20} +14.0660 q^{21} -4.33763 q^{22} -3.11903 q^{24} +1.00000 q^{25} -3.72833 q^{26} -11.6288 q^{27} -4.50973 q^{28} -8.23805 q^{29} -3.11903 q^{30} +1.72833 q^{31} +1.00000 q^{32} +13.5292 q^{33} -1.11903 q^{34} -4.50973 q^{35} +6.72833 q^{36} +0.781399 q^{37} -4.50973 q^{38} +11.6288 q^{39} +1.00000 q^{40} +3.90043 q^{41} +14.0660 q^{42} -8.00000 q^{43} -4.33763 q^{44} +6.72833 q^{45} -11.4567 q^{47} -3.11903 q^{48} +13.3376 q^{49} +1.00000 q^{50} +3.49027 q^{51} -3.72833 q^{52} +6.00000 q^{53} -11.6288 q^{54} -4.33763 q^{55} -4.50973 q^{56} +14.0660 q^{57} -8.23805 q^{58} -2.23805 q^{59} -3.11903 q^{60} -3.55623 q^{61} +1.72833 q^{62} -30.3429 q^{63} +1.00000 q^{64} -3.72833 q^{65} +13.5292 q^{66} -2.43720 q^{67} -1.11903 q^{68} -4.50973 q^{70} +7.11903 q^{71} +6.72833 q^{72} -9.45665 q^{73} +0.781399 q^{74} -3.11903 q^{75} -4.50973 q^{76} +19.5615 q^{77} +11.6288 q^{78} +14.9133 q^{79} +1.00000 q^{80} +16.0854 q^{81} +3.90043 q^{82} -2.78140 q^{83} +14.0660 q^{84} -1.11903 q^{85} -8.00000 q^{86} +25.6947 q^{87} -4.33763 q^{88} +7.69471 q^{89} +6.72833 q^{90} +16.8137 q^{91} -5.39070 q^{93} -11.4567 q^{94} -4.50973 q^{95} -3.11903 q^{96} +0.642920 q^{97} +13.3376 q^{98} -29.1850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - q^{13} - 3 q^{14} + q^{15} + 3 q^{16} + 7 q^{17} + 10 q^{18} - 3 q^{19} + 3 q^{20} + 22 q^{21} - 3 q^{22} + q^{24} + 3 q^{25} - q^{26} - 14 q^{27} - 3 q^{28} - 4 q^{29} + q^{30} - 5 q^{31} + 3 q^{32} + 9 q^{33} + 7 q^{34} - 3 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 14 q^{39} + 3 q^{40} + q^{41} + 22 q^{42} - 24 q^{43} - 3 q^{44} + 10 q^{45} - 14 q^{47} + q^{48} + 30 q^{49} + 3 q^{50} + 21 q^{51} - q^{52} + 18 q^{53} - 14 q^{54} - 3 q^{55} - 3 q^{56} + 22 q^{57} - 4 q^{58} + 14 q^{59} + q^{60} - q^{61} - 5 q^{62} - 8 q^{63} + 3 q^{64} - q^{65} + 9 q^{66} - 8 q^{67} + 7 q^{68} - 3 q^{70} + 11 q^{71} + 10 q^{72} - 8 q^{73} + 2 q^{74} + q^{75} - 3 q^{76} - 24 q^{77} + 14 q^{78} + 4 q^{79} + 3 q^{80} + 7 q^{81} + q^{82} - 8 q^{83} + 22 q^{84} + 7 q^{85} - 24 q^{86} + 36 q^{87} - 3 q^{88} - 18 q^{89} + 10 q^{90} - q^{91} - 16 q^{93} - 14 q^{94} - 3 q^{95} + q^{96} + 33 q^{97} + 30 q^{98} - 57 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9 + 3 * q^10 - 3 * q^11 + q^12 - q^13 - 3 * q^14 + q^15 + 3 * q^16 + 7 * q^17 + 10 * q^18 - 3 * q^19 + 3 * q^20 + 22 * q^21 - 3 * q^22 + q^24 + 3 * q^25 - q^26 - 14 * q^27 - 3 * q^28 - 4 * q^29 + q^30 - 5 * q^31 + 3 * q^32 + 9 * q^33 + 7 * q^34 - 3 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + 3 * q^40 + q^41 + 22 * q^42 - 24 * q^43 - 3 * q^44 + 10 * q^45 - 14 * q^47 + q^48 + 30 * q^49 + 3 * q^50 + 21 * q^51 - q^52 + 18 * q^53 - 14 * q^54 - 3 * q^55 - 3 * q^56 + 22 * q^57 - 4 * q^58 + 14 * q^59 + q^60 - q^61 - 5 * q^62 - 8 * q^63 + 3 * q^64 - q^65 + 9 * q^66 - 8 * q^67 + 7 * q^68 - 3 * q^70 + 11 * q^71 + 10 * q^72 - 8 * q^73 + 2 * q^74 + q^75 - 3 * q^76 - 24 * q^77 + 14 * q^78 + 4 * q^79 + 3 * q^80 + 7 * q^81 + q^82 - 8 * q^83 + 22 * q^84 + 7 * q^85 - 24 * q^86 + 36 * q^87 - 3 * q^88 - 18 * q^89 + 10 * q^90 - q^91 - 16 * q^93 - 14 * q^94 - 3 * q^95 + q^96 + 33 * q^97 + 30 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.11903	−1.80077	−0.900385	−	0.435093i	$-0.856715\pi$
$3$	−3.11903	−1.80077	−0.900385	+	0.435093i	$0.856715\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.11903	−1.27334
$7$	−4.50973	−1.70452	−0.852258	−	0.523122i	$-0.824767\pi$
$7$	−4.50973	−1.70452	−0.852258	+	0.523122i	$0.824767\pi$
$8$	1.00000	0.353553
$9$	6.72833	2.24278
$10$	1.00000	0.316228
$11$	−4.33763	−1.30784	−0.653922	−	0.756562i	$-0.726878\pi$
$11$	−4.33763	−1.30784	−0.653922	+	0.756562i	$0.726878\pi$
$12$	−3.11903	−0.900385
$13$	−3.72833	−1.03405	−0.517026	−	0.855970i	$-0.672961\pi$
$13$	−3.72833	−1.03405	−0.517026	+	0.855970i	$0.672961\pi$
$14$	−4.50973	−1.20527
$15$	−3.11903	−0.805329
$16$	1.00000	0.250000
$17$	−1.11903	−0.271404	−0.135702	−	0.990750i	$-0.543329\pi$
$17$	−1.11903	−0.271404	−0.135702	+	0.990750i	$0.543329\pi$
$18$	6.72833	1.58588
$19$	−4.50973	−1.03460	−0.517301	−	0.855803i	$-0.673063\pi$
$19$	−4.50973	−1.03460	−0.517301	+	0.855803i	$0.673063\pi$
$20$	1.00000	0.223607
$21$	14.0660	3.06944
$22$	−4.33763	−0.924785
$23$	0	0
$23$	0	0
$24$	−3.11903	−0.636669
$25$	1.00000	0.200000
$26$	−3.72833	−0.731185
$27$	−11.6288	−2.23795
$28$	−4.50973	−0.852258
$29$	−8.23805	−1.52977	−0.764884	−	0.644168i	$-0.777204\pi$
$29$	−8.23805	−1.52977	−0.764884	+	0.644168i	$0.777204\pi$
$30$	−3.11903	−0.569454
$31$	1.72833	0.310417	0.155208	−	0.987882i	$-0.450395\pi$
$31$	1.72833	0.310417	0.155208	+	0.987882i	$0.450395\pi$
$32$	1.00000	0.176777
$33$	13.5292	2.35513
$34$	−1.11903	−0.191911
$35$	−4.50973	−0.762283
$36$	6.72833	1.12139
$37$	0.781399	0.128461	0.0642306	−	0.997935i	$-0.479541\pi$
$37$	0.781399	0.128461	0.0642306	+	0.997935i	$0.479541\pi$
$38$	−4.50973	−0.731574
$39$	11.6288	1.86209
$40$	1.00000	0.158114
$41$	3.90043	0.609144	0.304572	−	0.952489i	$-0.401487\pi$
$41$	3.90043	0.609144	0.304572	+	0.952489i	$0.401487\pi$
$42$	14.0660	2.17042
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−4.33763	−0.653922
$45$	6.72833	1.00300
$46$	0	0
$47$	−11.4567	−1.67112	−0.835562	−	0.549396i	$-0.814858\pi$
$47$	−11.4567	−1.67112	−0.835562	+	0.549396i	$0.814858\pi$
$48$	−3.11903	−0.450193
$49$	13.3376	1.90538
$50$	1.00000	0.141421
$51$	3.49027	0.488736
$52$	−3.72833	−0.517026
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−11.6288	−1.58247
$55$	−4.33763	−0.584886
$56$	−4.50973	−0.602637
$57$	14.0660	1.86308
$58$	−8.23805	−1.08171
$59$	−2.23805	−0.291370	−0.145685	−	0.989331i	$-0.546539\pi$
$59$	−2.23805	−0.291370	−0.145685	+	0.989331i	$0.546539\pi$
$60$	−3.11903	−0.402665
$61$	−3.55623	−0.455329	−0.227664	−	0.973740i	$-0.573109\pi$
$61$	−3.55623	−0.455329	−0.227664	+	0.973740i	$0.573109\pi$
$62$	1.72833	0.219498
$63$	−30.3429	−3.82285
$64$	1.00000	0.125000
$65$	−3.72833	−0.462442
$66$	13.5292	1.66533
$67$	−2.43720	−0.297752	−0.148876	−	0.988856i	$-0.547565\pi$
$67$	−2.43720	−0.297752	−0.148876	+	0.988856i	$0.547565\pi$
$68$	−1.11903	−0.135702
$69$	0	0
$70$	−4.50973	−0.539015
$71$	7.11903	0.844873	0.422437	−	0.906393i	$-0.361175\pi$
$71$	7.11903	0.844873	0.422437	+	0.906393i	$0.361175\pi$
$72$	6.72833	0.792941
$73$	−9.45665	−1.10682	−0.553409	−	0.832910i	$-0.686673\pi$
$73$	−9.45665	−1.10682	−0.553409	+	0.832910i	$0.686673\pi$
$74$	0.781399	0.0908357
$75$	−3.11903	−0.360154
$76$	−4.50973	−0.517301
$77$	19.5615	2.22924
$78$	11.6288	1.31670
$79$	14.9133	1.67788	0.838939	−	0.544225i	$-0.183176\pi$
$79$	14.9133	1.67788	0.838939	+	0.544225i	$0.183176\pi$
$80$	1.00000	0.111803
$81$	16.0854	1.78727
$82$	3.90043	0.430730
$83$	−2.78140	−0.305298	−0.152649	−	0.988280i	$-0.548780\pi$
$83$	−2.78140	−0.305298	−0.152649	+	0.988280i	$0.548780\pi$
$84$	14.0660	1.53472
$85$	−1.11903	−0.121375
$86$	−8.00000	−0.862662
$87$	25.6947	2.75476
$88$	−4.33763	−0.462393
$89$	7.69471	0.815637	0.407819	−	0.913063i	$-0.366290\pi$
$89$	7.69471	0.815637	0.407819	+	0.913063i	$0.366290\pi$
$90$	6.72833	0.709228
$91$	16.8137	1.76256
$92$	0	0
$93$	−5.39070	−0.558989
$94$	−11.4567	−1.18166
$95$	−4.50973	−0.462688
$96$	−3.11903	−0.318334
$97$	0.642920	0.0652786	0.0326393	−	0.999467i	$-0.489609\pi$
$97$	0.642920	0.0652786	0.0326393	+	0.999467i	$0.489609\pi$
$98$	13.3376	1.34730
$99$	−29.1850	−2.93320
$100$	1.00000	0.100000
$101$	−8.23805	−0.819717	−0.409858	−	0.912149i	$-0.634422\pi$
$101$	−8.23805	−0.819717	−0.409858	+	0.912149i	$0.634422\pi$
$102$	3.49027	0.345589
$103$	−12.3376	−1.21566	−0.607831	−	0.794066i	$-0.707960\pi$
$103$	−12.3376	−1.21566	−0.607831	+	0.794066i	$0.707960\pi$
$104$	−3.72833	−0.365593
$105$	14.0660	1.37270
$106$	6.00000	0.582772
$107$	15.9328	1.54028	0.770139	−	0.637876i	$-0.220187\pi$
$107$	15.9328	1.54028	0.770139	+	0.637876i	$0.220187\pi$
$108$	−11.6288	−1.11898
$109$	1.49027	0.142742	0.0713712	−	0.997450i	$-0.477263\pi$
$109$	1.49027	0.142742	0.0713712	+	0.997450i	$0.477263\pi$
$110$	−4.33763	−0.413577
$111$	−2.43720	−0.231329
$112$	−4.50973	−0.426129
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	14.0660	1.31740
$115$	0	0
$116$	−8.23805	−0.764884
$117$	−25.0854	−2.31915
$118$	−2.23805	−0.206030
$119$	5.04650	0.462612
$120$	−3.11903	−0.284727
$121$	7.81502	0.710456
$122$	−3.55623	−0.321966
$123$	−12.1655	−1.09693
$124$	1.72833	0.155208
$125$	1.00000	0.0894427
$126$	−30.3429	−2.70316
$127$	−0.675256	−0.0599193	−0.0299597	−	0.999551i	$-0.509538\pi$
$127$	−0.675256	−0.0599193	−0.0299597	+	0.999551i	$0.509538\pi$
$128$	1.00000	0.0883883
$129$	24.9522	2.19692
$130$	−3.72833	−0.326996
$131$	−13.6947	−1.19651	−0.598256	−	0.801305i	$-0.704139\pi$
$131$	−13.6947	−1.19651	−0.598256	+	0.801305i	$0.704139\pi$
$132$	13.5292	1.17756
$133$	20.3376	1.76350
$134$	−2.43720	−0.210542
$135$	−11.6288	−1.00084
$136$	−1.11903	−0.0959557
$137$	−7.52918	−0.643261	−0.321631	−	0.946865i	$-0.604231\pi$
$137$	−7.52918	−0.643261	−0.321631	+	0.946865i	$0.604231\pi$
$138$	0	0
$139$	4.67526	0.396550	0.198275	−	0.980146i	$-0.436466\pi$
$139$	4.67526	0.396550	0.198275	+	0.980146i	$0.436466\pi$
$140$	−4.50973	−0.381141
$141$	35.7336	3.00931
$142$	7.11903	0.597415
$143$	16.1721	1.35238
$144$	6.72833	0.560694
$145$	−8.23805	−0.684133
$146$	−9.45665	−0.782638
$147$	−41.6004	−3.43114
$148$	0.781399	0.0642306
$149$	−7.52918	−0.616814	−0.308407	−	0.951254i	$-0.599796\pi$
$149$	−7.52918	−0.616814	−0.308407	+	0.951254i	$0.599796\pi$
$150$	−3.11903	−0.254667
$151$	−13.3571	−1.08698	−0.543492	−	0.839414i	$-0.682898\pi$
$151$	−13.3571	−1.08698	−0.543492	+	0.839414i	$0.682898\pi$
$152$	−4.50973	−0.365787
$153$	−7.52918	−0.608698
$154$	19.5615	1.57631
$155$	1.72833	0.138823
$156$	11.6288	0.931045
$157$	−16.2381	−1.29594	−0.647969	−	0.761667i	$-0.724381\pi$
$157$	−16.2381	−1.29594	−0.647969	+	0.761667i	$0.724381\pi$
$158$	14.9133	1.18644
$159$	−18.7142	−1.48413
$160$	1.00000	0.0790569
$161$	0	0
$162$	16.0854	1.26379
$163$	−3.29112	−0.257781	−0.128890	−	0.991659i	$-0.541142\pi$
$163$	−3.29112	−0.257781	−0.128890	+	0.991659i	$0.541142\pi$
$164$	3.90043	0.304572
$165$	13.5292	1.05325
$166$	−2.78140	−0.215878
$167$	22.9133	1.77309	0.886543	−	0.462647i	$-0.153100\pi$
$167$	22.9133	1.77309	0.886543	+	0.462647i	$0.153100\pi$
$168$	14.0660	1.08521
$169$	0.900425	0.0692635
$170$	−1.11903	−0.0858254
$171$	−30.3429	−2.32038
$172$	−8.00000	−0.609994
$173$	0.575681	0.0437683	0.0218841	−	0.999761i	$-0.493034\pi$
$173$	0.575681	0.0437683	0.0218841	+	0.999761i	$0.493034\pi$
$174$	25.6947	1.94791
$175$	−4.50973	−0.340903
$176$	−4.33763	−0.326961
$177$	6.98055	0.524690
$178$	7.69471	0.576743
$179$	5.01945	0.375171	0.187586	−	0.982248i	$-0.439934\pi$
$179$	5.01945	0.375171	0.187586	+	0.982248i	$0.439934\pi$
$180$	6.72833	0.501500
$181$	11.5292	0.856957	0.428479	−	0.903552i	$-0.359050\pi$
$181$	11.5292	0.856957	0.428479	+	0.903552i	$0.359050\pi$
$182$	16.8137	1.24632
$183$	11.0920	0.819942
$184$	0	0
$185$	0.781399	0.0574496
$186$	−5.39070	−0.395265
$187$	4.85392	0.354954
$188$	−11.4567	−0.835562
$189$	52.4425	3.81463
$190$	−4.50973	−0.327170
$191$	18.7142	1.35411	0.677055	−	0.735933i	$-0.263256\pi$
$191$	18.7142	1.35411	0.677055	+	0.735933i	$0.263256\pi$
$192$	−3.11903	−0.225096
$193$	23.4956	1.69125	0.845624	−	0.533780i	$-0.179229\pi$
$193$	23.4956	1.69125	0.845624	+	0.533780i	$0.179229\pi$
$194$	0.642920	0.0461590
$195$	11.6288	0.832752
$196$	13.3376	0.952688
$197$	−18.1385	−1.29231	−0.646157	−	0.763205i	$-0.723625\pi$
$197$	−18.1385	−1.29231	−0.646157	+	0.763205i	$0.723625\pi$
$198$	−29.1850	−2.07409
$199$	23.2575	1.64868	0.824340	−	0.566094i	$-0.191546\pi$
$199$	23.2575	1.64868	0.824340	+	0.566094i	$0.191546\pi$
$200$	1.00000	0.0707107
$201$	7.60170	0.536183
$202$	−8.23805	−0.579627
$203$	37.1514	2.60751
$204$	3.49027	0.244368
$205$	3.90043	0.272418
$206$	−12.3376	−0.859603
$207$	0	0
$208$	−3.72833	−0.258513
$209$	19.5615	1.35310
$210$	14.0660	0.970643
$211$	4.34420	0.299067	0.149533	−	0.988757i	$-0.452223\pi$
$211$	4.34420	0.299067	0.149533	+	0.988757i	$0.452223\pi$
$212$	6.00000	0.412082
$213$	−22.2044	−1.52142
$214$	15.9328	1.08914
$215$	−8.00000	−0.545595
$216$	−11.6288	−0.791236
$217$	−7.79428	−0.529110
$218$	1.49027	0.100934
$219$	29.4956	1.99313
$220$	−4.33763	−0.292443
$221$	4.17210	0.280646
$222$	−2.43720	−0.163574
$223$	12.4761	0.835462	0.417731	−	0.908571i	$-0.362825\pi$
$223$	12.4761	0.835462	0.417731	+	0.908571i	$0.362825\pi$
$224$	−4.50973	−0.301319
$225$	6.72833	0.448555
$226$	6.00000	0.399114
$227$	−15.9328	−1.05749	−0.528747	−	0.848779i	$-0.677338\pi$
$227$	−15.9328	−1.05749	−0.528747	+	0.848779i	$0.677338\pi$
$228$	14.0660	0.931541
$229$	3.56280	0.235436	0.117718	−	0.993047i	$-0.462442\pi$
$229$	3.56280	0.235436	0.117718	+	0.993047i	$0.462442\pi$
$230$	0	0
$231$	−61.0129	−4.01435
$232$	−8.23805	−0.540855
$233$	−27.4956	−1.80129	−0.900647	−	0.434552i	$-0.856907\pi$
$233$	−27.4956	−1.80129	−0.900647	+	0.434552i	$0.856907\pi$
$234$	−25.0854	−1.63988
$235$	−11.4567	−0.747350
$236$	−2.23805	−0.145685
$237$	−46.5150	−3.02147
$238$	5.04650	0.327116
$239$	10.0389	0.649363	0.324681	−	0.945823i	$-0.394743\pi$
$239$	10.0389	0.649363	0.324681	+	0.945823i	$0.394743\pi$
$240$	−3.11903	−0.201332
$241$	23.6947	1.52631	0.763155	−	0.646215i	$-0.223649\pi$
$241$	23.6947	1.52631	0.763155	+	0.646215i	$0.223649\pi$
$242$	7.81502	0.502368
$243$	−15.2846	−0.980505
$244$	−3.55623	−0.227664
$245$	13.3376	0.852110
$246$	−12.1655	−0.775646
$247$	16.8137	1.06983
$248$	1.72833	0.109749
$249$	8.67526	0.549772
$250$	1.00000	0.0632456
$251$	−12.4425	−0.785363	−0.392681	−	0.919675i	$-0.628452\pi$
$251$	−12.4425	−0.785363	−0.392681	+	0.919675i	$0.628452\pi$
$252$	−30.3429	−1.91142
$253$	0	0
$254$	−0.675256	−0.0423693
$255$	3.49027	0.218569
$256$	1.00000	0.0625000
$257$	5.45665	0.340377	0.170188	−	0.985412i	$-0.445562\pi$
$257$	5.45665	0.340377	0.170188	+	0.985412i	$0.445562\pi$
$258$	24.9522	1.55346
$259$	−3.52389	−0.218964
$260$	−3.72833	−0.231221
$261$	−55.4283	−3.43093
$262$	−13.6947	−0.846062
$263$	−0.138479	−0.00853895	−0.00426948	−	0.999991i	$-0.501359\pi$
$263$	−0.138479	−0.00853895	−0.00426948	+	0.999991i	$0.501359\pi$
$264$	13.5292	0.832663
$265$	6.00000	0.368577
$266$	20.3376	1.24698
$267$	−24.0000	−1.46878
$268$	−2.43720	−0.148876
$269$	14.6753	0.894766	0.447383	−	0.894342i	$-0.352356\pi$
$269$	14.6753	0.894766	0.447383	+	0.894342i	$0.352356\pi$
$270$	−11.6288	−0.707703
$271$	−8.31058	−0.504832	−0.252416	−	0.967619i	$-0.581225\pi$
$271$	−8.31058	−0.504832	−0.252416	+	0.967619i	$0.581225\pi$
$272$	−1.11903	−0.0678510
$273$	−52.4425	−3.17396
$274$	−7.52918	−0.454854
$275$	−4.33763	−0.261569
$276$	0	0
$277$	12.9133	0.775886	0.387943	−	0.921683i	$-0.373186\pi$
$277$	12.9133	0.775886	0.387943	+	0.921683i	$0.373186\pi$
$278$	4.67526	0.280403
$279$	11.6288	0.696195
$280$	−4.50973	−0.269508
$281$	−2.67526	−0.159592	−0.0797962	−	0.996811i	$-0.525427\pi$
$281$	−2.67526	−0.159592	−0.0797962	+	0.996811i	$0.525427\pi$
$282$	35.7336	2.12791
$283$	−0.742495	−0.0441367	−0.0220684	−	0.999756i	$-0.507025\pi$
$283$	−0.742495	−0.0441367	−0.0220684	+	0.999756i	$0.507025\pi$
$284$	7.11903	0.422437
$285$	14.0660	0.833195
$286$	16.1721	0.956276
$287$	−17.5898	−1.03830
$288$	6.72833	0.396470
$289$	−15.7478	−0.926340
$290$	−8.23805	−0.483755
$291$	−2.00528	−0.117552
$292$	−9.45665	−0.553409
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−41.6004	−2.42619
$295$	−2.23805	−0.130305
$296$	0.781399	0.0454179
$297$	50.4412	2.92690
$298$	−7.52918	−0.436154
$299$	0	0
$300$	−3.11903	−0.180077
$301$	36.0778	2.07949
$302$	−13.3571	−0.768614
$303$	25.6947	1.47612
$304$	−4.50973	−0.258651
$305$	−3.55623	−0.203629
$306$	−7.52918	−0.430414
$307$	30.5084	1.74121	0.870604	−	0.491984i	$-0.163728\pi$
$307$	30.5084	1.74121	0.870604	+	0.491984i	$0.163728\pi$
$308$	19.5615	1.11462
$309$	38.4814	2.18913
$310$	1.72833	0.0981624
$311$	5.56280	0.315437	0.157719	−	0.987484i	$-0.449586\pi$
$311$	5.56280	0.315437	0.157719	+	0.987484i	$0.449586\pi$
$312$	11.6288	0.658348
$313$	−4.07252	−0.230193	−0.115096	−	0.993354i	$-0.536718\pi$
$313$	−4.07252	−0.230193	−0.115096	+	0.993354i	$0.536718\pi$
$314$	−16.2381	−0.916366
$315$	−30.3429	−1.70963
$316$	14.9133	0.838939
$317$	−6.16553	−0.346291	−0.173145	−	0.984896i	$-0.555393\pi$
$317$	−6.16553	−0.346291	−0.173145	+	0.984896i	$0.555393\pi$
$318$	−18.7142	−1.04944
$319$	35.7336	2.00070
$320$	1.00000	0.0559017
$321$	−49.6947	−2.77369
$322$	0	0
$323$	5.04650	0.280795
$324$	16.0854	0.893634
$325$	−3.72833	−0.206810
$326$	−3.29112	−0.182279
$327$	−4.64820	−0.257046
$328$	3.90043	0.215365
$329$	51.6664	2.84846
$330$	13.5292	0.744757
$331$	27.5886	1.51640	0.758202	−	0.652019i	$-0.226078\pi$
$331$	27.5886	1.51640	0.758202	+	0.652019i	$0.226078\pi$
$332$	−2.78140	−0.152649
$333$	5.25751	0.288110
$334$	22.9133	1.25376
$335$	−2.43720	−0.133159
$336$	14.0660	0.767361
$337$	17.4230	0.949093	0.474547	−	0.880230i	$-0.342612\pi$
$337$	17.4230	0.949093	0.474547	+	0.880230i	$0.342612\pi$
$338$	0.900425	0.0489767
$339$	−18.7142	−1.01641
$340$	−1.11903	−0.0606877
$341$	−7.49684	−0.405977
$342$	−30.3429	−1.64076
$343$	−28.5810	−1.54323
$344$	−8.00000	−0.431331
$345$	0	0
$346$	0.575681	0.0309488
$347$	4.88097	0.262024	0.131012	−	0.991381i	$-0.458177\pi$
$347$	4.88097	0.262024	0.131012	+	0.991381i	$0.458177\pi$
$348$	25.6947	1.37738
$349$	24.0389	1.28677	0.643387	−	0.765542i	$-0.277529\pi$
$349$	24.0389	1.28677	0.643387	+	0.765542i	$0.277529\pi$
$350$	−4.50973	−0.241055
$351$	43.3558	2.31416
$352$	−4.33763	−0.231196
$353$	−14.3442	−0.763464	−0.381732	−	0.924273i	$-0.624672\pi$
$353$	−14.3442	−0.763464	−0.381732	+	0.924273i	$0.624672\pi$
$354$	6.98055	0.371012
$355$	7.11903	0.377839
$356$	7.69471	0.407819
$357$	−15.7402	−0.833059
$358$	5.01945	0.265286
$359$	−26.7814	−1.41347	−0.706734	−	0.707479i	$-0.749832\pi$
$359$	−26.7814	−1.41347	−0.706734	+	0.707479i	$0.749832\pi$
$360$	6.72833	0.354614
$361$	1.33763	0.0704015
$362$	11.5292	0.605960
$363$	−24.3752	−1.27937
$364$	16.8137	0.881279
$365$	−9.45665	−0.494984
$366$	11.0920	0.579787
$367$	20.4761	1.06884	0.534422	−	0.845218i	$-0.320529\pi$
$367$	20.4761	1.06884	0.534422	+	0.845218i	$0.320529\pi$
$368$	0	0
$369$	26.2433	1.36617
$370$	0.781399	0.0406230
$371$	−27.0584	−1.40480
$372$	−5.39070	−0.279495
$373$	3.89386	0.201616	0.100808	−	0.994906i	$-0.467857\pi$
$373$	3.89386	0.201616	0.100808	+	0.994906i	$0.467857\pi$
$374$	4.85392	0.250990
$375$	−3.11903	−0.161066
$376$	−11.4567	−0.590832
$377$	30.7142	1.58186
$378$	52.4425	2.69735
$379$	30.3765	1.56034	0.780169	−	0.625569i	$-0.215133\pi$
$379$	30.3765	1.56034	0.780169	+	0.625569i	$0.215133\pi$
$380$	−4.50973	−0.231344
$381$	2.10614	0.107901
$382$	18.7142	0.957500
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−3.11903	−0.159167
$385$	19.5615	0.996947
$386$	23.4956	1.19589
$387$	−53.8266	−2.73616
$388$	0.642920	0.0326393
$389$	18.6818	0.947206	0.473603	−	0.880738i	$-0.342953\pi$
$389$	18.6818	0.947206	0.473603	+	0.880738i	$0.342953\pi$
$390$	11.6288	0.588845
$391$	0	0
$392$	13.3376	0.673652
$393$	42.7142	2.15464
$394$	−18.1385	−0.913803
$395$	14.9133	0.750370
$396$	−29.1850	−1.46660
$397$	−28.5757	−1.43417	−0.717086	−	0.696985i	$-0.754525\pi$
$397$	−28.5757	−1.43417	−0.717086	+	0.696985i	$0.754525\pi$
$398$	23.2575	1.16579
$399$	−63.4336	−3.17565
$400$	1.00000	0.0500000
$401$	−12.1061	−0.604552	−0.302276	−	0.953220i	$-0.597746\pi$
$401$	−12.1061	−0.604552	−0.302276	+	0.953220i	$0.597746\pi$
$402$	7.60170	0.379138
$403$	−6.44377	−0.320987
$404$	−8.23805	−0.409858
$405$	16.0854	0.799290
$406$	37.1514	1.84379
$407$	−3.38942	−0.168007
$408$	3.49027	0.172794
$409$	25.2911	1.25057	0.625283	−	0.780398i	$-0.284984\pi$
$409$	25.2911	1.25057	0.625283	+	0.780398i	$0.284984\pi$
$410$	3.90043	0.192628
$411$	23.4837	1.15837
$412$	−12.3376	−0.607831
$413$	10.0930	0.496644
$414$	0	0
$415$	−2.78140	−0.136533
$416$	−3.72833	−0.182796
$417$	−14.5822	−0.714096
$418$	19.5615	0.956785
$419$	17.3505	0.847628	0.423814	−	0.905749i	$-0.360691\pi$
$419$	17.3505	0.847628	0.423814	+	0.905749i	$0.360691\pi$
$420$	14.0660	0.686348
$421$	−21.4230	−1.04409	−0.522047	−	0.852916i	$-0.674832\pi$
$421$	−21.4230	−1.04409	−0.522047	+	0.852916i	$0.674832\pi$
$422$	4.34420	0.211472
$423$	−77.0841	−3.74796
$424$	6.00000	0.291386
$425$	−1.11903	−0.0542808
$426$	−22.2044	−1.07581
$427$	16.0376	0.776115
$428$	15.9328	0.770139
$429$	−50.4412	−2.43532
$430$	−8.00000	−0.385794
$431$	−22.5822	−1.08775	−0.543874	−	0.839167i	$-0.683043\pi$
$431$	−22.5822	−1.08775	−0.543874	+	0.839167i	$0.683043\pi$
$432$	−11.6288	−0.559489
$433$	−1.01417	−0.0487378	−0.0243689	−	0.999703i	$-0.507758\pi$
$433$	−1.01417	−0.0487378	−0.0243689	+	0.999703i	$0.507758\pi$
$434$	−7.79428	−0.374138
$435$	25.6947	1.23197
$436$	1.49027	0.0713712
$437$	0	0
$438$	29.4956	1.40935
$439$	−26.7478	−1.27660	−0.638301	−	0.769787i	$-0.720362\pi$
$439$	−26.7478	−1.27660	−0.638301	+	0.769787i	$0.720362\pi$
$440$	−4.33763	−0.206788
$441$	89.7399	4.27333
$442$	4.17210	0.198446
$443$	10.2044	0.484827	0.242414	−	0.970173i	$-0.422061\pi$
$443$	10.2044	0.484827	0.242414	+	0.970173i	$0.422061\pi$
$444$	−2.43720	−0.115665
$445$	7.69471	0.364764
$446$	12.4761	0.590761
$447$	23.4837	1.11074
$448$	−4.50973	−0.213065
$449$	38.7867	1.83046	0.915228	−	0.402936i	$-0.132010\pi$
$449$	38.7867	1.83046	0.915228	+	0.402936i	$0.132010\pi$
$450$	6.72833	0.317176
$451$	−16.9186	−0.796665
$452$	6.00000	0.282216
$453$	41.6611	1.95741
$454$	−15.9328	−0.747762
$455$	16.8137	0.788240
$456$	14.0660	0.658699
$457$	−34.9522	−1.63500	−0.817498	−	0.575932i	$-0.804639\pi$
$457$	−34.9522	−1.63500	−0.817498	+	0.575932i	$0.804639\pi$
$458$	3.56280	0.166479
$459$	13.0129	0.607389
$460$	0	0
$461$	16.3700	0.762425	0.381213	−	0.924487i	$-0.375507\pi$
$461$	16.3700	0.762425	0.381213	+	0.924487i	$0.375507\pi$
$462$	−61.0129	−2.83858
$463$	29.2186	1.35790	0.678952	−	0.734183i	$-0.262435\pi$
$463$	29.2186	1.35790	0.678952	+	0.734183i	$0.262435\pi$
$464$	−8.23805	−0.382442
$465$	−5.39070	−0.249988
$466$	−27.4956	−1.27371
$467$	−24.2770	−1.12340	−0.561702	−	0.827340i	$-0.689853\pi$
$467$	−24.2770	−1.12340	−0.561702	+	0.827340i	$0.689853\pi$
$468$	−25.0854	−1.15957
$469$	10.9911	0.507523
$470$	−11.4567	−0.528456
$471$	50.6469	2.33369
$472$	−2.23805	−0.103015
$473$	34.7010	1.59555
$474$	−46.5150	−2.13651
$475$	−4.50973	−0.206920
$476$	5.04650	0.231306
$477$	40.3700	1.84841
$478$	10.0389	0.459169
$479$	−24.6080	−1.12437	−0.562185	−	0.827012i	$-0.690039\pi$
$479$	−24.6080	−1.12437	−0.562185	+	0.827012i	$0.690039\pi$
$480$	−3.11903	−0.142363
$481$	−2.91331	−0.132835
$482$	23.6947	1.07926
$483$	0	0
$484$	7.81502	0.355228
$485$	0.642920	0.0291935
$486$	−15.2846	−0.693322
$487$	−30.2381	−1.37022	−0.685108	−	0.728441i	$-0.740245\pi$
$487$	−30.2381	−1.37022	−0.685108	+	0.728441i	$0.740245\pi$
$488$	−3.55623	−0.160983
$489$	10.2651	0.464204
$490$	13.3376	0.602533
$491$	12.3311	0.556493	0.278246	−	0.960510i	$-0.410247\pi$
$491$	12.3311	0.556493	0.278246	+	0.960510i	$0.410247\pi$
$492$	−12.1655	−0.548464
$493$	9.21860	0.415185
$494$	16.8137	0.756486
$495$	−29.1850	−1.31177
$496$	1.72833	0.0776042
$497$	−32.1049	−1.44010
$498$	8.67526	0.388748
$499$	−26.9133	−1.20481	−0.602403	−	0.798192i	$-0.705790\pi$
$499$	−26.9133	−1.20481	−0.602403	+	0.798192i	$0.705790\pi$
$500$	1.00000	0.0447214
$501$	−71.4672	−3.19292
$502$	−12.4425	−0.555335
$503$	−20.5097	−0.914483	−0.457242	−	0.889342i	$-0.651163\pi$
$503$	−20.5097	−0.914483	−0.457242	+	0.889342i	$0.651163\pi$
$504$	−30.3429	−1.35158
$505$	−8.23805	−0.366589
$506$	0	0
$507$	−2.80845	−0.124728
$508$	−0.675256	−0.0299597
$509$	−36.7142	−1.62733	−0.813663	−	0.581336i	$-0.802530\pi$
$509$	−36.7142	−1.62733	−0.813663	+	0.581336i	$0.802530\pi$
$510$	3.49027	0.154552
$511$	42.6469	1.88659
$512$	1.00000	0.0441942
$513$	52.4425	2.31539
$514$	5.45665	0.240683
$515$	−12.3376	−0.543661
$516$	24.9522	1.09846
$517$	49.6947	2.18557
$518$	−3.52389	−0.154831
$519$	−1.79557	−0.0788166
$520$	−3.72833	−0.163498
$521$	4.91331	0.215256	0.107628	−	0.994191i	$-0.465674\pi$
$521$	4.91331	0.215256	0.107628	+	0.994191i	$0.465674\pi$
$522$	−55.4283	−2.42603
$523$	0.344196	0.0150506	0.00752531	−	0.999972i	$-0.497605\pi$
$523$	0.344196	0.0150506	0.00752531	+	0.999972i	$0.497605\pi$
$524$	−13.6947	−0.598256
$525$	14.0660	0.613889
$526$	−0.138479	−0.00603795
$527$	−1.93404	−0.0842483
$528$	13.5292	0.588782
$529$	0	0
$530$	6.00000	0.260623
$531$	−15.0584	−0.653477
$532$	20.3376	0.881748
$533$	−14.5421	−0.629887
$534$	−24.0000	−1.03858
$535$	15.9328	0.688833
$536$	−2.43720	−0.105271
$537$	−15.6558	−0.675598
$538$	14.6753	0.632695
$539$	−57.8537	−2.49193
$540$	−11.6288	−0.500422
$541$	−6.13191	−0.263631	−0.131816	−	0.991274i	$-0.542081\pi$
$541$	−6.13191	−0.263631	−0.131816	+	0.991274i	$0.542081\pi$
$542$	−8.31058	−0.356970
$543$	−35.9598	−1.54318
$544$	−1.11903	−0.0479779
$545$	1.49027	0.0638363
$546$	−52.4425	−2.24433
$547$	−9.18498	−0.392721	−0.196361	−	0.980532i	$-0.562912\pi$
$547$	−9.18498	−0.392721	−0.196361	+	0.980532i	$0.562912\pi$
$548$	−7.52918	−0.321631
$549$	−23.9275	−1.02120
$550$	−4.33763	−0.184957
$551$	37.1514	1.58270
$552$	0	0
$553$	−67.2549	−2.85997
$554$	12.9133	0.548634
$555$	−2.43720	−0.103454
$556$	4.67526	0.198275
$557$	4.30529	0.182421	0.0912105	−	0.995832i	$-0.470926\pi$
$557$	4.30529	0.182421	0.0912105	+	0.995832i	$0.470926\pi$
$558$	11.6288	0.492284
$559$	29.8266	1.26153
$560$	−4.50973	−0.190571
$561$	−15.1395	−0.639191
$562$	−2.67526	−0.112849
$563$	−11.1256	−0.468888	−0.234444	−	0.972130i	$-0.575327\pi$
$563$	−11.1256	−0.468888	−0.234444	+	0.972130i	$0.575327\pi$
$564$	35.7336	1.50466
$565$	6.00000	0.252422
$566$	−0.742495	−0.0312094
$567$	−72.5408	−3.04643
$568$	7.11903	0.298708
$569$	16.0389	0.672386	0.336193	−	0.941793i	$-0.390861\pi$
$569$	16.0389	0.672386	0.336193	+	0.941793i	$0.390861\pi$
$570$	14.0660	0.589158
$571$	−17.9004	−0.749109	−0.374555	−	0.927205i	$-0.622204\pi$
$571$	−17.9004	−0.749109	−0.374555	+	0.927205i	$0.622204\pi$
$572$	16.1721	0.676189
$573$	−58.3700	−2.43844
$574$	−17.5898	−0.734186
$575$	0	0
$576$	6.72833	0.280347
$577$	−9.12559	−0.379903	−0.189952	−	0.981793i	$-0.560833\pi$
$577$	−9.12559	−0.379903	−0.189952	+	0.981793i	$0.560833\pi$
$578$	−15.7478	−0.655021
$579$	−73.2833	−3.04555
$580$	−8.23805	−0.342067
$581$	12.5433	0.520386
$582$	−2.00528	−0.0831217
$583$	−26.0258	−1.07788
$584$	−9.45665	−0.391319
$585$	−25.0854	−1.03715
$586$	6.00000	0.247858
$587$	−33.6340	−1.38823	−0.694113	−	0.719866i	$-0.744203\pi$
$587$	−33.6340	−1.38823	−0.694113	+	0.719866i	$0.744203\pi$
$588$	−41.6004	−1.71557
$589$	−7.79428	−0.321158
$590$	−2.23805	−0.0921392
$591$	56.5744	2.32716
$592$	0.781399	0.0321153
$593$	−17.4567	−0.716859	−0.358429	−	0.933557i	$-0.616688\pi$
$593$	−17.4567	−0.716859	−0.358429	+	0.933557i	$0.616688\pi$
$594$	50.4412	2.06963
$595$	5.04650	0.206886
$596$	−7.52918	−0.308407
$597$	−72.5408	−2.96890
$598$	0	0
$599$	−11.5951	−0.473764	−0.236882	−	0.971538i	$-0.576126\pi$
$599$	−11.5951	−0.473764	−0.236882	+	0.971538i	$0.576126\pi$
$600$	−3.11903	−0.127334
$601$	−31.6611	−1.29148	−0.645741	−	0.763556i	$-0.723452\pi$
$601$	−31.6611	−1.29148	−0.645741	+	0.763556i	$0.723452\pi$
$602$	36.0778	1.47042
$603$	−16.3983	−0.667790
$604$	−13.3571	−0.543492
$605$	7.81502	0.317726
$606$	25.6947	1.04378
$607$	−36.0778	−1.46435	−0.732177	−	0.681115i	$-0.761495\pi$
$607$	−36.0778	−1.46435	−0.732177	+	0.681115i	$0.761495\pi$
$608$	−4.50973	−0.182894
$609$	−115.876	−4.69554
$610$	−3.55623	−0.143988
$611$	42.7142	1.72803
$612$	−7.52918	−0.304349
$613$	32.0389	1.29404	0.647020	−	0.762473i	$-0.276015\pi$
$613$	32.0389	1.29404	0.647020	+	0.762473i	$0.276015\pi$
$614$	30.5084	1.23122
$615$	−12.1655	−0.490562
$616$	19.5615	0.788156
$617$	13.3960	0.539302	0.269651	−	0.962958i	$-0.413092\pi$
$617$	13.3960	0.539302	0.269651	+	0.962958i	$0.413092\pi$
$618$	38.4814	1.54795
$619$	−37.1309	−1.49242	−0.746208	−	0.665713i	$-0.768128\pi$
$619$	−37.1309	−1.49242	−0.746208	+	0.665713i	$0.768128\pi$
$620$	1.72833	0.0694113
$621$	0	0
$622$	5.56280	0.223048
$623$	−34.7010	−1.39027
$624$	11.6288	0.465523
$625$	1.00000	0.0400000
$626$	−4.07252	−0.162771
$627$	−61.0129	−2.43662
$628$	−16.2381	−0.647969
$629$	−0.874406	−0.0348648
$630$	−30.3429	−1.20889
$631$	−11.1125	−0.442380	−0.221190	−	0.975231i	$-0.570994\pi$
$631$	−11.1125	−0.442380	−0.221190	+	0.975231i	$0.570994\pi$
$632$	14.9133	0.593220
$633$	−13.5497	−0.538551
$634$	−6.16553	−0.244864
$635$	−0.675256	−0.0267967
$636$	−18.7142	−0.742065
$637$	−49.7270	−1.97026
$638$	35.7336	1.41471
$639$	47.8991	1.89486
$640$	1.00000	0.0395285
$641$	−12.3831	−0.489103	−0.244552	−	0.969636i	$-0.578641\pi$
$641$	−12.3831	−0.489103	−0.244552	+	0.969636i	$0.578641\pi$
$642$	−49.6947	−1.96129
$643$	37.4956	1.47868	0.739340	−	0.673332i	$-0.235138\pi$
$643$	37.4956	1.47868	0.739340	+	0.673332i	$0.235138\pi$
$644$	0	0
$645$	24.9522	0.982492
$646$	5.04650	0.198552
$647$	14.5691	0.572771	0.286385	−	0.958114i	$-0.407546\pi$
$647$	14.5691	0.572771	0.286385	+	0.958114i	$0.407546\pi$
$648$	16.0854	0.631894
$649$	9.70784	0.381066
$650$	−3.72833	−0.146237
$651$	24.3106	0.952807
$652$	−3.29112	−0.128890
$653$	−4.41672	−0.172840	−0.0864198	−	0.996259i	$-0.527543\pi$
$653$	−4.41672	−0.172840	−0.0864198	+	0.996259i	$0.527543\pi$
$654$	−4.64820	−0.181759
$655$	−13.6947	−0.535097
$656$	3.90043	0.152286
$657$	−63.6275	−2.48234
$658$	51.6664	2.01416
$659$	31.8655	1.24130	0.620652	−	0.784086i	$-0.286868\pi$
$659$	31.8655	1.24130	0.620652	+	0.784086i	$0.286868\pi$
$660$	13.5292	0.526623
$661$	−33.1190	−1.28818	−0.644090	−	0.764949i	$-0.722764\pi$
$661$	−33.1190	−1.28818	−0.644090	+	0.764949i	$0.722764\pi$
$662$	27.5886	1.07226
$663$	−13.0129	−0.505379
$664$	−2.78140	−0.107939
$665$	20.3376	0.788659
$666$	5.25751	0.203724
$667$	0	0
$668$	22.9133	0.886543
$669$	−38.9133	−1.50448
$670$	−2.43720	−0.0941574
$671$	15.4256	0.595499
$672$	14.0660	0.542606
$673$	19.3505	0.745907	0.372954	−	0.927850i	$-0.378345\pi$
$673$	19.3505	0.745907	0.372954	+	0.927850i	$0.378345\pi$
$674$	17.4230	0.671110
$675$	−11.6288	−0.447591
$676$	0.900425	0.0346317
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	−18.7142	−0.718713
$679$	−2.89939	−0.111268
$680$	−1.11903	−0.0429127
$681$	49.6947	1.90431
$682$	−7.49684	−0.287069
$683$	38.3495	1.46740	0.733701	−	0.679472i	$-0.237791\pi$
$683$	38.3495	1.46740	0.733701	+	0.679472i	$0.237791\pi$
$684$	−30.3429	−1.16019
$685$	−7.52918	−0.287675
$686$	−28.5810	−1.09123
$687$	−11.1125	−0.423967
$688$	−8.00000	−0.304997
$689$	−22.3700	−0.852228
$690$	0	0
$691$	−21.0195	−0.799618	−0.399809	−	0.916599i	$-0.630923\pi$
$691$	−21.0195	−0.799618	−0.399809	+	0.916599i	$0.630923\pi$
$692$	0.575681	0.0218841
$693$	131.616	4.99969
$694$	4.88097	0.185279
$695$	4.67526	0.177343
$696$	25.6947	0.973955
$697$	−4.36468	−0.165324
$698$	24.0389	0.909886
$699$	85.7594	3.24372
$700$	−4.50973	−0.170452
$701$	−19.3169	−0.729589	−0.364794	−	0.931088i	$-0.618861\pi$
$701$	−19.3169	−0.729589	−0.364794	+	0.931088i	$0.618861\pi$
$702$	43.3558	1.63636
$703$	−3.52389	−0.132906
$704$	−4.33763	−0.163481
$705$	35.7336	1.34581
$706$	−14.3442	−0.539851
$707$	37.1514	1.39722
$708$	6.98055	0.262345
$709$	−12.2315	−0.459363	−0.229682	−	0.973266i	$-0.573768\pi$
$709$	−12.2315	−0.459363	−0.229682	+	0.973266i	$0.573768\pi$
$710$	7.11903	0.267172
$711$	100.342	3.76311
$712$	7.69471	0.288371
$713$	0	0
$714$	−15.7402	−0.589061
$715$	16.1721	0.604802
$716$	5.01945	0.187586
$717$	−31.3116	−1.16935
$718$	−26.7814	−0.999473
$719$	−40.6416	−1.51568	−0.757839	−	0.652442i	$-0.773745\pi$
$719$	−40.6416	−1.51568	−0.757839	+	0.652442i	$0.773745\pi$
$720$	6.72833	0.250750
$721$	55.6393	2.07212
$722$	1.33763	0.0497814
$723$	−73.9044	−2.74854
$724$	11.5292	0.428479
$725$	−8.23805	−0.305954
$726$	−24.3752	−0.904650
$727$	23.4501	0.869716	0.434858	−	0.900499i	$-0.356799\pi$
$727$	23.4501	0.869716	0.434858	+	0.900499i	$0.356799\pi$
$728$	16.8137	0.623158
$729$	−0.583281	−0.0216030
$730$	−9.45665	−0.350006
$731$	8.95221	0.331110
$732$	11.0920	0.409971
$733$	12.5150	0.462252	0.231126	−	0.972924i	$-0.425759\pi$
$733$	12.5150	0.462252	0.231126	+	0.972924i	$0.425759\pi$
$734$	20.4761	0.755787
$735$	−41.6004	−1.53445
$736$	0	0
$737$	10.5717	0.389413
$738$	26.2433	0.966031
$739$	−21.3505	−0.785391	−0.392696	−	0.919668i	$-0.628457\pi$
$739$	−21.3505	−0.785391	−0.392696	+	0.919668i	$0.628457\pi$
$740$	0.781399	0.0287248
$741$	−52.4425	−1.92652
$742$	−27.0584	−0.993343
$743$	−24.9858	−0.916641	−0.458321	−	0.888787i	$-0.651549\pi$
$743$	−24.9858	−0.916641	−0.458321	+	0.888787i	$0.651549\pi$
$744$	−5.39070	−0.197633
$745$	−7.52918	−0.275848
$746$	3.89386	0.142564
$747$	−18.7142	−0.684715
$748$	4.85392	0.177477
$749$	−71.8524	−2.62543
$750$	−3.11903	−0.113891
$751$	33.6275	1.22708	0.613542	−	0.789662i	$-0.289744\pi$
$751$	33.6275	1.22708	0.613542	+	0.789662i	$0.289744\pi$
$752$	−11.4567	−0.417781
$753$	38.8085	1.41426
$754$	30.7142	1.11854
$755$	−13.3571	−0.486114
$756$	52.4425	1.90731
$757$	37.1230	1.34926	0.674630	−	0.738156i	$-0.264303\pi$
$757$	37.1230	1.34926	0.674630	+	0.738156i	$0.264303\pi$
$758$	30.3765	1.10333
$759$	0	0
$760$	−4.50973	−0.163585
$761$	−3.87337	−0.140410	−0.0702048	−	0.997533i	$-0.522365\pi$
$761$	−3.87337	−0.140410	−0.0702048	+	0.997533i	$0.522365\pi$
$762$	2.10614	0.0762975
$763$	−6.72073	−0.243307
$764$	18.7142	0.677055
$765$	−7.52918	−0.272218
$766$	0	0
$767$	8.34420	0.301291
$768$	−3.11903	−0.112548
$769$	−23.1645	−0.835333	−0.417667	−	0.908600i	$-0.637152\pi$
$769$	−23.1645	−0.835333	−0.417667	+	0.908600i	$0.637152\pi$
$770$	19.5615	0.704948
$771$	−17.0195	−0.612941
$772$	23.4956	0.845624
$773$	8.78140	0.315845	0.157922	−	0.987452i	$-0.449520\pi$
$773$	8.78140	0.315845	0.157922	+	0.987452i	$0.449520\pi$
$774$	−53.8266	−1.93476
$775$	1.72833	0.0620834
$776$	0.642920	0.0230795
$777$	10.9911	0.394304
$778$	18.6818	0.669776
$779$	−17.5898	−0.630222
$780$	11.6288	0.416376
$781$	−30.8797	−1.10496
$782$	0	0
$783$	95.7983	3.42355
$784$	13.3376	0.476344
$785$	−16.2381	−0.579561
$786$	42.7142	1.52356
$787$	−49.6275	−1.76903	−0.884514	−	0.466513i	$-0.845510\pi$
$787$	−49.6275	−1.76903	−0.884514	+	0.466513i	$0.845510\pi$
$788$	−18.1385	−0.646157
$789$	0.431918	0.0153767
$790$	14.9133	0.530592
$791$	−27.0584	−0.962084
$792$	−29.1850	−1.03704
$793$	13.2588	0.470833
$794$	−28.5757	−1.01411
$795$	−18.7142	−0.663723
$796$	23.2575	0.824340
$797$	−18.3311	−0.649319	−0.324660	−	0.945831i	$-0.605250\pi$
$797$	−18.3311	−0.649319	−0.324660	+	0.945831i	$0.605250\pi$
$798$	−63.4336	−2.24553
$799$	12.8203	0.453550
$800$	1.00000	0.0353553
$801$	51.7725	1.82929
$802$	−12.1061	−0.427483
$803$	41.0195	1.44755
$804$	7.60170	0.268091
$805$	0	0
$806$	−6.44377	−0.226972
$807$	−45.7725	−1.61127
$808$	−8.23805	−0.289814
$809$	−1.93933	−0.0681832	−0.0340916	−	0.999419i	$-0.510854\pi$
$809$	−1.93933	−0.0681832	−0.0340916	+	0.999419i	$0.510854\pi$
$810$	16.0854	0.565184
$811$	−5.41775	−0.190243	−0.0951215	−	0.995466i	$-0.530324\pi$
$811$	−5.41775	−0.190243	−0.0951215	+	0.995466i	$0.530324\pi$
$812$	37.1514	1.30376
$813$	25.9209	0.909086
$814$	−3.38942	−0.118799
$815$	−3.29112	−0.115283
$816$	3.49027	0.122184
$817$	36.0778	1.26220
$818$	25.2911	0.884283
$819$	113.128	3.95302
$820$	3.90043	0.136209
$821$	37.8655	1.32152	0.660758	−	0.750599i	$-0.270235\pi$
$821$	37.8655	1.32152	0.660758	+	0.750599i	$0.270235\pi$
$822$	23.4837	0.819088
$823$	43.7336	1.52446	0.762229	−	0.647308i	$-0.224105\pi$
$823$	43.7336	1.52446	0.762229	+	0.647308i	$0.224105\pi$
$824$	−12.3376	−0.429802
$825$	13.5292	0.471026
$826$	10.0930	0.351181
$827$	−28.1991	−0.980581	−0.490290	−	0.871559i	$-0.663109\pi$
$827$	−28.1991	−0.980581	−0.490290	+	0.871559i	$0.663109\pi$
$828$	0	0
$829$	1.12559	0.0390935	0.0195468	−	0.999809i	$-0.493778\pi$
$829$	1.12559	0.0390935	0.0195468	+	0.999809i	$0.493778\pi$
$830$	−2.78140	−0.0965438
$831$	−40.2770	−1.39719
$832$	−3.72833	−0.129256
$833$	−14.9252	−0.517126
$834$	−14.5822	−0.504942
$835$	22.9133	0.792948
$836$	19.5615	0.676549
$837$	−20.0983	−0.694699
$838$	17.3505	0.599364
$839$	−39.9328	−1.37863	−0.689316	−	0.724461i	$-0.742089\pi$
$839$	−39.9328	−1.37863	−0.689316	+	0.724461i	$0.742089\pi$
$840$	14.0660	0.485322
$841$	38.8655	1.34019
$842$	−21.4230	−0.738287
$843$	8.34420	0.287389
$844$	4.34420	0.149533
$845$	0.900425	0.0309756
$846$	−77.0841	−2.65021
$847$	−35.2436	−1.21098
$848$	6.00000	0.206041
$849$	2.31586	0.0794801
$850$	−1.11903	−0.0383823
$851$	0	0
$852$	−22.2044	−0.760711
$853$	47.9921	1.64322	0.821610	−	0.570050i	$-0.193076\pi$
$853$	47.9921	1.64322	0.821610	+	0.570050i	$0.193076\pi$
$854$	16.0376	0.548796
$855$	−30.3429	−1.03771
$856$	15.9328	0.544571
$857$	−43.4283	−1.48348	−0.741742	−	0.670686i	$-0.766000\pi$
$857$	−43.4283	−1.48348	−0.741742	+	0.670686i	$0.766000\pi$
$858$	−50.4412	−1.72203
$859$	32.5433	1.11036	0.555182	−	0.831729i	$-0.312648\pi$
$859$	32.5433	1.11036	0.555182	+	0.831729i	$0.312648\pi$
$860$	−8.00000	−0.272798
$861$	54.8632	1.86973
$862$	−22.5822	−0.769154
$863$	46.1036	1.56938	0.784692	−	0.619886i	$-0.212821\pi$
$863$	46.1036	1.56938	0.784692	+	0.619886i	$0.212821\pi$
$864$	−11.6288	−0.395618
$865$	0.575681	0.0195738
$866$	−1.01417	−0.0344628
$867$	49.1177	1.66813
$868$	−7.79428	−0.264555
$869$	−64.6884	−2.19440
$870$	25.6947	0.871132
$871$	9.08669	0.307891
$872$	1.49027	0.0504670
$873$	4.32578	0.146405
$874$	0	0
$875$	−4.50973	−0.152457
$876$	29.4956	0.996563
$877$	−24.0996	−0.813785	−0.406892	−	0.913476i	$-0.633388\pi$
$877$	−24.0996	−0.813785	−0.406892	+	0.913476i	$0.633388\pi$
$878$	−26.7478	−0.902694
$879$	−18.7142	−0.631213
$880$	−4.33763	−0.146221
$881$	−2.34420	−0.0789780	−0.0394890	−	0.999220i	$-0.512573\pi$
$881$	−2.34420	−0.0789780	−0.0394890	+	0.999220i	$0.512573\pi$
$882$	89.7399	3.02170
$883$	−41.0505	−1.38146	−0.690730	−	0.723113i	$-0.742711\pi$
$883$	−41.0505	−1.38146	−0.690730	+	0.723113i	$0.742711\pi$
$884$	4.17210	0.140323
$885$	6.98055	0.234649
$886$	10.2044	0.342825
$887$	54.7788	1.83929	0.919647	−	0.392747i	$-0.128475\pi$
$887$	54.7788	1.83929	0.919647	+	0.392747i	$0.128475\pi$
$888$	−2.43720	−0.0817872
$889$	3.04522	0.102133
$890$	7.69471	0.257927
$891$	−69.7725	−2.33747
$892$	12.4761	0.417731
$893$	51.6664	1.72895
$894$	23.4837	0.785413
$895$	5.01945	0.167782
$896$	−4.50973	−0.150659
$897$	0	0
$898$	38.7867	1.29433
$899$	−14.2381	−0.474866
$900$	6.72833	0.224278
$901$	−6.71416	−0.223681
$902$	−16.9186	−0.563328
$903$	−112.528	−3.74469
$904$	6.00000	0.199557
$905$	11.5292	0.383243
$906$	41.6611	1.38410
$907$	10.1061	0.335569	0.167784	−	0.985824i	$-0.446339\pi$
$907$	10.1061	0.335569	0.167784	+	0.985824i	$0.446339\pi$
$908$	−15.9328	−0.528747
$909$	−55.4283	−1.83844
$910$	16.8137	0.557370
$911$	25.4178	0.842128	0.421064	−	0.907031i	$-0.361657\pi$
$911$	25.4178	0.842128	0.421064	+	0.907031i	$0.361657\pi$
$912$	14.0660	0.465770
$913$	12.0647	0.399282
$914$	−34.9522	−1.15612
$915$	11.0920	0.366689
$916$	3.56280	0.117718
$917$	61.7594	2.03947
$918$	13.0129	0.429489
$919$	−23.6017	−0.778548	−0.389274	−	0.921122i	$-0.627274\pi$
$919$	−23.6017	−0.778548	−0.389274	+	0.921122i	$0.627274\pi$
$920$	0	0
$921$	−95.1566	−3.13552
$922$	16.3700	0.539116
$923$	−26.5421	−0.873643
$924$	−61.0129	−2.00718
$925$	0.781399	0.0256922
$926$	29.2186	0.960183
$927$	−83.0116	−2.72646
$928$	−8.23805	−0.270427
$929$	−7.08669	−0.232507	−0.116253	−	0.993220i	$-0.537088\pi$
$929$	−7.08669	−0.232507	−0.116253	+	0.993220i	$0.537088\pi$
$930$	−5.39070	−0.176768
$931$	−60.1490	−1.97131
$932$	−27.4956	−0.900647
$933$	−17.3505	−0.568030
$934$	−24.2770	−0.794366
$935$	4.85392	0.158740
$936$	−25.0854	−0.819942
$937$	−27.3169	−0.892404	−0.446202	−	0.894932i	$-0.647224\pi$
$937$	−27.3169	−0.892404	−0.446202	+	0.894932i	$0.647224\pi$
$938$	10.9911	0.358873
$939$	12.7023	0.414524
$940$	−11.4567	−0.373675
$941$	−55.8979	−1.82222	−0.911109	−	0.412165i	$-0.864773\pi$
$941$	−55.8979	−1.82222	−0.911109	+	0.412165i	$0.864773\pi$
$942$	50.6469	1.65017
$943$	0	0
$944$	−2.23805	−0.0728424
$945$	52.4425	1.70595
$946$	34.7010	1.12823
$947$	37.5939	1.22164	0.610818	−	0.791771i	$-0.290841\pi$
$947$	37.5939	1.22164	0.610818	+	0.791771i	$0.290841\pi$
$948$	−46.5150	−1.51074
$949$	35.2575	1.14451
$950$	−4.50973	−0.146315
$951$	19.2305	0.623590
$952$	5.04650	0.163558
$953$	29.3828	0.951804	0.475902	−	0.879498i	$-0.342122\pi$
$953$	29.3828	0.951804	0.475902	+	0.879498i	$0.342122\pi$
$954$	40.3700	1.30703
$955$	18.7142	0.605576
$956$	10.0389	0.324681
$957$	−111.454	−3.60280
$958$	−24.6080	−0.795049
$959$	33.9545	1.09645
$960$	−3.11903	−0.100666
$961$	−28.0129	−0.903641
$962$	−2.91331	−0.0939289
$963$	107.201	3.45450
$964$	23.6947	0.763155
$965$	23.4956	0.756349
$966$	0	0
$967$	−49.2292	−1.58310	−0.791552	−	0.611102i	$-0.790726\pi$
$967$	−49.2292	−1.58310	−0.791552	+	0.611102i	$0.790726\pi$
$968$	7.81502	0.251184
$969$	−15.7402	−0.505647
$970$	0.642920	0.0206429
$971$	−9.62347	−0.308832	−0.154416	−	0.988006i	$-0.549350\pi$
$971$	−9.62347	−0.308832	−0.154416	+	0.988006i	$0.549350\pi$
$972$	−15.2846	−0.490252
$973$	−21.0841	−0.675926
$974$	−30.2381	−0.968890
$975$	11.6288	0.372418
$976$	−3.55623	−0.113832
$977$	−18.9858	−0.607411	−0.303705	−	0.952766i	$-0.598224\pi$
$977$	−18.9858	−0.607411	−0.303705	+	0.952766i	$0.598224\pi$
$978$	10.2651	0.328242
$979$	−33.3768	−1.06673
$980$	13.3376	0.426055
$981$	10.0271	0.320139
$982$	12.3311	0.393500
$983$	−4.33763	−0.138349	−0.0691744	−	0.997605i	$-0.522037\pi$
$983$	−4.33763	−0.138349	−0.0691744	+	0.997605i	$0.522037\pi$
$984$	−12.1655	−0.387823
$985$	−18.1385	−0.577940
$986$	9.21860	0.293580
$987$	−161.149	−5.12942
$988$	16.8137	0.534916
$989$	0	0
$990$	−29.1850	−0.927560
$991$	1.96766	0.0625049	0.0312524	−	0.999512i	$-0.490050\pi$
$991$	1.96766	0.0625049	0.0312524	+	0.999512i	$0.490050\pi$
$992$	1.72833	0.0548744
$993$	−86.0495	−2.73070
$994$	−32.1049	−1.01830
$995$	23.2575	0.737312
$996$	8.67526	0.274886
$997$	3.96110	0.125449	0.0627246	−	0.998031i	$-0.480021\pi$
$997$	3.96110	0.125449	0.0627246	+	0.998031i	$0.480021\pi$
$998$	−26.9133	−0.851926
$999$	−9.08669	−0.287490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.r.1.1		3
23.22	odd	2		230.2.a.d.1.1	✓	3
69.68	even	2		2070.2.a.z.1.3		3
92.91	even	2		1840.2.a.r.1.3		3
115.22	even	4		1150.2.b.j.599.6		6
115.68	even	4		1150.2.b.j.599.1		6
115.114	odd	2		1150.2.a.q.1.3		3
184.45	odd	2		7360.2.a.bz.1.3		3
184.91	even	2		7360.2.a.ce.1.1		3
460.459	even	2		9200.2.a.cf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.d.1.1	✓	3	23.22	odd	2
1150.2.a.q.1.3		3	115.114	odd	2
1150.2.b.j.599.1		6	115.68	even	4
1150.2.b.j.599.6		6	115.22	even	4
1840.2.a.r.1.3		3	92.91	even	2
2070.2.a.z.1.3		3	69.68	even	2
5290.2.a.r.1.1		3	1.1	even	1	trivial
7360.2.a.bz.1.3		3	184.45	odd	2
7360.2.a.ce.1.1		3	184.91	even	2
9200.2.a.cf.1.1		3	460.459	even	2

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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.11903 q^{6} -4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.11903 q^{6} -4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} +1.00000 q^{10} -4.33763 q^{11} -3.11903 q^{12} -3.72833 q^{13} -4.50973 q^{14} -3.11903 q^{15} +1.00000 q^{16} -1.11903 q^{17} +6.72833 q^{18} -4.50973 q^{19} +1.00000 q^{20} +14.0660 q^{21} -4.33763 q^{22} -3.11903 q^{24} +1.00000 q^{25} -3.72833 q^{26} -11.6288 q^{27} -4.50973 q^{28} -8.23805 q^{29} -3.11903 q^{30} +1.72833 q^{31} +1.00000 q^{32} +13.5292 q^{33} -1.11903 q^{34} -4.50973 q^{35} +6.72833 q^{36} +0.781399 q^{37} -4.50973 q^{38} +11.6288 q^{39} +1.00000 q^{40} +3.90043 q^{41} +14.0660 q^{42} -8.00000 q^{43} -4.33763 q^{44} +6.72833 q^{45} -11.4567 q^{47} -3.11903 q^{48} +13.3376 q^{49} +1.00000 q^{50} +3.49027 q^{51} -3.72833 q^{52} +6.00000 q^{53} -11.6288 q^{54} -4.33763 q^{55} -4.50973 q^{56} +14.0660 q^{57} -8.23805 q^{58} -2.23805 q^{59} -3.11903 q^{60} -3.55623 q^{61} +1.72833 q^{62} -30.3429 q^{63} +1.00000 q^{64} -3.72833 q^{65} +13.5292 q^{66} -2.43720 q^{67} -1.11903 q^{68} -4.50973 q^{70} +7.11903 q^{71} +6.72833 q^{72} -9.45665 q^{73} +0.781399 q^{74} -3.11903 q^{75} -4.50973 q^{76} +19.5615 q^{77} +11.6288 q^{78} +14.9133 q^{79} +1.00000 q^{80} +16.0854 q^{81} +3.90043 q^{82} -2.78140 q^{83} +14.0660 q^{84} -1.11903 q^{85} -8.00000 q^{86} +25.6947 q^{87} -4.33763 q^{88} +7.69471 q^{89} +6.72833 q^{90} +16.8137 q^{91} -5.39070 q^{93} -11.4567 q^{94} -4.50973 q^{95} -3.11903 q^{96} +0.642920 q^{97} +13.3376 q^{98} -29.1850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - q^{13} - 3 q^{14} + q^{15} + 3 q^{16} + 7 q^{17} + 10 q^{18} - 3 q^{19} + 3 q^{20} + 22 q^{21} - 3 q^{22} + q^{24} + 3 q^{25} - q^{26} - 14 q^{27} - 3 q^{28} - 4 q^{29} + q^{30} - 5 q^{31} + 3 q^{32} + 9 q^{33} + 7 q^{34} - 3 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 14 q^{39} + 3 q^{40} + q^{41} + 22 q^{42} - 24 q^{43} - 3 q^{44} + 10 q^{45} - 14 q^{47} + q^{48} + 30 q^{49} + 3 q^{50} + 21 q^{51} - q^{52} + 18 q^{53} - 14 q^{54} - 3 q^{55} - 3 q^{56} + 22 q^{57} - 4 q^{58} + 14 q^{59} + q^{60} - q^{61} - 5 q^{62} - 8 q^{63} + 3 q^{64} - q^{65} + 9 q^{66} - 8 q^{67} + 7 q^{68} - 3 q^{70} + 11 q^{71} + 10 q^{72} - 8 q^{73} + 2 q^{74} + q^{75} - 3 q^{76} - 24 q^{77} + 14 q^{78} + 4 q^{79} + 3 q^{80} + 7 q^{81} + q^{82} - 8 q^{83} + 22 q^{84} + 7 q^{85} - 24 q^{86} + 36 q^{87} - 3 q^{88} - 18 q^{89} + 10 q^{90} - q^{91} - 16 q^{93} - 14 q^{94} - 3 q^{95} + q^{96} + 33 q^{97} + 30 q^{98} - 57 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9 + 3 * q^10 - 3 * q^11 + q^12 - q^13 - 3 * q^14 + q^15 + 3 * q^16 + 7 * q^17 + 10 * q^18 - 3 * q^19 + 3 * q^20 + 22 * q^21 - 3 * q^22 + q^24 + 3 * q^25 - q^26 - 14 * q^27 - 3 * q^28 - 4 * q^29 + q^30 - 5 * q^31 + 3 * q^32 + 9 * q^33 + 7 * q^34 - 3 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + 3 * q^40 + q^41 + 22 * q^42 - 24 * q^43 - 3 * q^44 + 10 * q^45 - 14 * q^47 + q^48 + 30 * q^49 + 3 * q^50 + 21 * q^51 - q^52 + 18 * q^53 - 14 * q^54 - 3 * q^55 - 3 * q^56 + 22 * q^57 - 4 * q^58 + 14 * q^59 + q^60 - q^61 - 5 * q^62 - 8 * q^63 + 3 * q^64 - q^65 + 9 * q^66 - 8 * q^67 + 7 * q^68 - 3 * q^70 + 11 * q^71 + 10 * q^72 - 8 * q^73 + 2 * q^74 + q^75 - 3 * q^76 - 24 * q^77 + 14 * q^78 + 4 * q^79 + 3 * q^80 + 7 * q^81 + q^82 - 8 * q^83 + 22 * q^84 + 7 * q^85 - 24 * q^86 + 36 * q^87 - 3 * q^88 - 18 * q^89 + 10 * q^90 - q^91 - 16 * q^93 - 14 * q^94 - 3 * q^95 + q^96 + 33 * q^97 + 30 * q^98 - 57 * q^99

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